LMFDB - Embedded newform 882.2.f.q.589.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [882,2,Mod(295,882)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(882, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([4, 0])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("882.295"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 882 = 2 \cdot 3^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	882.f (of order $3$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [8,-4,0,-4,0,0,0,8,0] 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:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 3^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			589.4
Root			$0.258819 - 0.965926i$ of defining polynomial
Character	$\chi$	$=$	882.589
Dual form			882.2.f.q.295.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.500000 - 0.866025i) q^{2} +(1.67303 + 0.448288i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.517638 + 0.896575i) q^{5} +(-0.448288 - 1.67303i) q^{6} +1.00000 q^{8} +(2.59808 + 1.50000i) q^{9} +1.03528 q^{10} +(0.133975 + 0.232051i) q^{11} +(-1.22474 + 1.22474i) q^{12} +(0.896575 - 1.55291i) q^{13} +(-1.26795 + 1.26795i) q^{15} +(-0.500000 - 0.866025i) q^{16} +6.83083 q^{17} -3.00000i q^{18} -4.38134 q^{19} +(-0.517638 - 0.896575i) q^{20} +(0.133975 - 0.232051i) q^{22} +(-2.73205 + 4.73205i) q^{23} +(1.67303 + 0.448288i) q^{24} +(1.96410 + 3.40192i) q^{25} -1.79315 q^{26} +(3.67423 + 3.67423i) q^{27} +(2.00000 + 3.46410i) q^{29} +(1.73205 + 0.464102i) q^{30} +(3.34607 - 5.79555i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(0.120118 + 0.448288i) q^{33} +(-3.41542 - 5.91567i) q^{34} +(-2.59808 + 1.50000i) q^{36} +7.46410 q^{37} +(2.19067 + 3.79435i) q^{38} +(2.19615 - 2.19615i) q^{39} +(-0.517638 + 0.896575i) q^{40} +(-4.31199 + 7.46859i) q^{41} +(-0.133975 - 0.232051i) q^{43} -0.267949 q^{44} +(-2.68973 + 1.55291i) q^{45} +5.46410 q^{46} +(0.378937 + 0.656339i) q^{47} +(-0.448288 - 1.67303i) q^{48} +(1.96410 - 3.40192i) q^{50} +(11.4282 + 3.06218i) q^{51} +(0.896575 + 1.55291i) q^{52} +10.9282 q^{53} +(1.34486 - 5.01910i) q^{54} -0.277401 q^{55} +(-7.33013 - 1.96410i) q^{57} +(2.00000 - 3.46410i) q^{58} +(-0.637756 + 1.10463i) q^{59} +(-0.464102 - 1.73205i) q^{60} +(-6.31319 - 10.9348i) q^{61} -6.69213 q^{62} +1.00000 q^{64} +(0.928203 + 1.60770i) q^{65} +(0.328169 - 0.328169i) q^{66} +(-6.23205 + 10.7942i) q^{67} +(-3.41542 + 5.91567i) q^{68} +(-6.69213 + 6.69213i) q^{69} +9.46410 q^{71} +(2.59808 + 1.50000i) q^{72} -5.41662 q^{73} +(-3.73205 - 6.46410i) q^{74} +(1.76097 + 6.57201i) q^{75} +(2.19067 - 3.79435i) q^{76} +(-3.00000 - 0.803848i) q^{78} +(-4.46410 - 7.73205i) q^{79} +1.03528 q^{80} +(4.50000 + 7.79423i) q^{81} +8.62398 q^{82} +(3.29530 + 5.70762i) q^{83} +(-3.53590 + 6.12436i) q^{85} +(-0.133975 + 0.232051i) q^{86} +(1.79315 + 6.69213i) q^{87} +(0.133975 + 0.232051i) q^{88} -7.07107 q^{89} +(2.68973 + 1.55291i) q^{90} +(-2.73205 - 4.73205i) q^{92} +(8.19615 - 8.19615i) q^{93} +(0.378937 - 0.656339i) q^{94} +(2.26795 - 3.92820i) q^{95} +(-1.22474 + 1.22474i) q^{96} +(-9.07227 - 15.7136i) q^{97} +0.803848i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 4 q^{2} - 4 q^{4} + 8 q^{8} + 8 q^{11} - 24 q^{15} - 4 q^{16} + 8 q^{22} - 8 q^{23} - 12 q^{25} + 16 q^{29} - 4 q^{32} + 32 q^{37} - 24 q^{39} - 8 q^{43} - 16 q^{44} + 16 q^{46} - 12 q^{50} + 36 q^{51}+ \cdots + 32 q^{95}+O(q^{100}) $ 8 * q - 4 * q^2 - 4 * q^4 + 8 * q^8 + 8 * q^11 - 24 * q^15 - 4 * q^16 + 8 * q^22 - 8 * q^23 - 12 * q^25 + 16 * q^29 - 4 * q^32 + 32 * q^37 - 24 * q^39 - 8 * q^43 - 16 * q^44 + 16 * q^46 - 12 * q^50 + 36 * q^51 + 32 * q^53 - 24 * q^57 + 16 * q^58 + 24 * q^60 + 8 * q^64 - 48 * q^65 - 36 * q^67 + 48 * q^71 - 16 * q^74 - 24 * q^78 - 8 * q^79 + 36 * q^81 - 56 * q^85 - 8 * q^86 + 8 * q^88 - 8 * q^92 + 24 * q^93 + 32 * q^95

Character values

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

$n$	$199$	$785$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$

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 $

$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$3$	1.67303	+	0.448288i	0.965926	+	0.258819i
$3$	1.67303	+	0.448288i	0.965926	+	0.258819i
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	−0.517638	+	0.896575i	−0.231495	+	0.400961i	−0.958248	−	0.285938i	$-0.907695\pi$
$5$	−0.517638	+	0.896575i	−0.231495	+	0.400961i	0.726753	+	0.686898i	$0.241028\pi$
$6$	−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
$10$	1.03528			0.327383
$11$	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	$0.820472\pi$
$12$	−1.22474	+	1.22474i	−0.353553	+	0.353553i
$13$	0.896575	−	1.55291i	0.248665	−	0.430701i	−0.714490	−	0.699645i	$-0.753341\pi$
$13$	0.896575	−	1.55291i	0.248665	−	0.430701i	0.963156	+	0.268944i	$0.0866747\pi$
$14$		0			0
$15$	−1.26795	+	1.26795i	−0.327383	+	0.327383i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	6.83083			1.65672			0.828360	−	0.560196i	$-0.189274\pi$
$17$	6.83083			1.65672			0.828360	+	0.560196i	$0.189274\pi$
$18$		−	3.00000i		−	0.707107i
$19$	−4.38134			−1.00515			−0.502574	−	0.864534i	$-0.667614\pi$
$19$	−4.38134			−1.00515			−0.502574	+	0.864534i	$0.667614\pi$
$20$	−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	$0.973737\pi$
$24$	1.67303	+	0.448288i	0.341506	+	0.0915064i
$25$	1.96410	+	3.40192i	0.392820	+	0.680385i
$26$	−1.79315			−0.351666
$27$	3.67423	+	3.67423i	0.707107	+	0.707107i
$28$		0			0
$29$	2.00000	+	3.46410i	0.371391	+	0.643268i	0.989780	−	0.142605i	$-0.0455477\pi$
$29$	2.00000	+	3.46410i	0.371391	+	0.643268i	−0.618389	+	0.785872i	$0.712214\pi$
$30$	1.73205	+	0.464102i	0.316228	+	0.0847330i
$31$	3.34607	−	5.79555i	0.600971	−	1.04091i	−0.391703	−	0.920092i	$-0.628114\pi$
$31$	3.34607	−	5.79555i	0.600971	−	1.04091i	0.992674	−	0.120821i	$-0.0385526\pi$
$32$	−0.500000	+	0.866025i	−0.0883883	+	0.153093i
$33$	0.120118	+	0.448288i	0.0209099	+	0.0780369i
$34$	−3.41542	−	5.91567i	−0.585739	−	1.01453i
$35$		0			0
$36$	−2.59808	+	1.50000i	−0.433013	+	0.250000i
$37$	7.46410			1.22709			0.613545	−	0.789659i	$-0.289743\pi$
$37$	7.46410			1.22709			0.613545	+	0.789659i	$0.289743\pi$
$38$	2.19067	+	3.79435i	0.355374	+	0.615525i
$39$	2.19615	−	2.19615i	0.351666	−	0.351666i
$40$	−0.517638	+	0.896575i	−0.0818458	+	0.141761i
$41$	−4.31199	+	7.46859i	−0.673420	+	1.16640i	0.303508	+	0.952829i	$0.401842\pi$
$41$	−4.31199	+	7.46859i	−0.673420	+	1.16640i	−0.976928	+	0.213569i	$0.931491\pi$
$42$		0			0
$43$	−0.133975	−	0.232051i	−0.0204309	−	0.0353874i	0.855629	−	0.517589i	$-0.173170\pi$
$43$	−0.133975	−	0.232051i	−0.0204309	−	0.0353874i	−0.876060	+	0.482202i	$0.839837\pi$
$44$	−0.267949			−0.0403949
$45$	−2.68973	+	1.55291i	−0.400961	+	0.231495i
$46$	5.46410			0.805638
$47$	0.378937	+	0.656339i	0.0552737	+	0.0957369i	0.892338	−	0.451367i	$-0.149064\pi$
$47$	0.378937	+	0.656339i	0.0552737	+	0.0957369i	−0.837065	+	0.547104i	$0.815730\pi$
$48$	−0.448288	−	1.67303i	−0.0647048	−	0.241481i
$49$		0			0
$50$	1.96410	−	3.40192i	0.277766	−	0.481105i
$51$	11.4282	+	3.06218i	1.60027	+	0.428791i
$52$	0.896575	+	1.55291i	0.124333	+	0.215350i
$53$	10.9282			1.50110			0.750552	−	0.660811i	$-0.229788\pi$
$53$	10.9282			1.50110			0.750552	+	0.660811i	$0.229788\pi$
$54$	1.34486	−	5.01910i	0.183013	−	0.683013i
$55$	−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
$59$	−0.637756	+	1.10463i	−0.0830288	+	0.143810i	−0.904550	−	0.426369i	$-0.859793\pi$
$59$	−0.637756	+	1.10463i	−0.0830288	+	0.143810i	0.821521	+	0.570179i	$0.193126\pi$
$60$	−0.464102	−	1.73205i	−0.0599153	−	0.223607i
$61$	−6.31319	−	10.9348i	−0.808322	−	1.40005i	−0.914026	−	0.405656i	$-0.867043\pi$
$61$	−6.31319	−	10.9348i	−0.808322	−	1.40005i	0.105704	−	0.994398i	$-0.466290\pi$
$62$	−6.69213			−0.849901
$63$		0			0
$64$	1.00000			0.125000
$65$	0.928203	+	1.60770i	0.115129	+	0.199410i
$66$	0.328169	−	0.328169i	0.0403949	−	0.0403949i
$67$	−6.23205	+	10.7942i	−0.761366	+	1.31872i	0.180780	+	0.983524i	$0.442138\pi$
$67$	−6.23205	+	10.7942i	−0.761366	+	1.31872i	−0.942146	+	0.335201i	$0.891196\pi$
$68$	−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
$73$	−5.41662			−0.633967			−0.316984	−	0.948431i	$-0.602670\pi$
$73$	−5.41662			−0.633967			−0.316984	+	0.948431i	$0.602670\pi$
$74$	−3.73205	−	6.46410i	−0.433842	−	0.751437i
$75$	1.76097	+	6.57201i	0.203339	+	0.758871i
$76$	2.19067	−	3.79435i	0.251287	−	0.435242i
$77$		0			0
$78$	−3.00000	−	0.803848i	−0.339683	−	0.0910178i
$79$	−4.46410	−	7.73205i	−0.502251	−	0.869924i	−0.999997	−	0.00260080i	$-0.999172\pi$
$79$	−4.46410	−	7.73205i	−0.502251	−	0.869924i	0.497746	−	0.867323i	$-0.334161\pi$
$80$	1.03528			0.115747
$81$	4.50000	+	7.79423i	0.500000	+	0.866025i
$82$	8.62398			0.952360
$83$	3.29530	+	5.70762i	0.361706	+	0.626493i	0.988242	−	0.152900i	$-0.0488611\pi$
$83$	3.29530	+	5.70762i	0.361706	+	0.626493i	−0.626536	+	0.779393i	$0.715528\pi$
$84$		0			0
$85$	−3.53590	+	6.12436i	−0.383522	+	0.664280i
$86$	−0.133975	+	0.232051i	−0.0144469	+	0.0250227i
$87$	1.79315	+	6.69213i	0.192246	+	0.717472i
$88$	0.133975	+	0.232051i	0.0142817	+	0.0247367i
$89$	−7.07107			−0.749532			−0.374766	−	0.927119i	$-0.622277\pi$
$89$	−7.07107			−0.749532			−0.374766	+	0.927119i	$0.622277\pi$
$90$	2.68973	+	1.55291i	0.283522	+	0.163692i
$91$		0			0
$92$	−2.73205	−	4.73205i	−0.284836	−	0.493350i
$93$	8.19615	−	8.19615i	0.849901	−	0.849901i
$94$	0.378937	−	0.656339i	0.0390844	−	0.0676962i
$95$	2.26795	−	3.92820i	0.232687	−	0.403025i
$96$	−1.22474	+	1.22474i	−0.125000	+	0.125000i
$97$	−9.07227	−	15.7136i	−0.921149	−	1.59548i	−0.797640	−	0.603134i	$-0.793918\pi$
$97$	−9.07227	−	15.7136i	−0.921149	−	1.59548i	−0.123510	−	0.992343i	$-0.539415\pi$
$98$		0			0
$99$			0.803848i			0.0807897i
$100$	−3.92820			−0.392820
$101$	−2.44949	−	4.24264i	−0.243733	−	0.422159i	0.718041	−	0.696000i	$-0.245039\pi$
$101$	−2.44949	−	4.24264i	−0.243733	−	0.422159i	−0.961775	+	0.273842i	$0.911706\pi$
$102$	−3.06218	−	11.4282i	−0.303201	−	1.13156i
$103$	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
$107$	−17.3923			−1.68138			−0.840689	−	0.541519i	$-0.817850\pi$
$107$	−17.3923			−1.68138			−0.840689	+	0.541519i	$0.817850\pi$
$108$	−5.01910	+	1.34486i	−0.482963	+	0.129410i
$109$	4.92820			0.472036			0.236018	−	0.971749i	$-0.424158\pi$
$109$	4.92820			0.472036			0.236018	+	0.971749i	$0.424158\pi$
$110$	0.138701	+	0.240237i	0.0132246	+	0.0229057i
$111$	12.4877	+	3.34607i	1.18528	+	0.317594i
$112$		0			0
$113$	3.46410	−	6.00000i	0.325875	−	0.564433i	−0.655814	−	0.754923i	$-0.727674\pi$
$113$	3.46410	−	6.00000i	0.325875	−	0.564433i	0.981689	+	0.190490i	$0.0610077\pi$
$114$	1.96410	+	7.33013i	0.183955	+	0.686529i
$115$	−2.82843	−	4.89898i	−0.263752	−	0.456832i
$116$	−4.00000			−0.371391
$117$	4.65874	−	2.68973i	0.430701	−	0.248665i
$118$	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
$122$	−6.31319	+	10.9348i	−0.571570	+	0.989988i
$123$	−10.5622	+	10.5622i	−0.952360	+	0.952360i
$124$	3.34607	+	5.79555i	0.300486	+	0.520456i
$125$	−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	$0.296211\pi$
$128$	−0.500000	−	0.866025i	−0.0441942	−	0.0765466i
$129$	−0.120118	−	0.448288i	−0.0105758	−	0.0394695i
$130$	0.928203	−	1.60770i	0.0814088	−	0.141004i
$131$	5.46739	−	9.46979i	0.477688	−	0.827379i	−0.521985	−	0.852955i	$-0.674808\pi$
$131$	5.46739	−	9.46979i	0.477688	−	0.827379i	0.999673	+	0.0255752i	$0.00814172\pi$
$132$	−0.448288	−	0.120118i	−0.0390184	−	0.0104550i
$133$		0			0
$134$	12.4641			1.07673
$135$	−5.19615	+	1.39230i	−0.447214	+	0.119831i
$136$	6.83083			0.585739
$137$	−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	$0.953958\pi$
$138$	9.14162	+	2.44949i	0.778186	+	0.208514i
$139$	0.397520	−	0.688524i	0.0337172	−	0.0583999i	−0.848674	−	0.528916i	$-0.822599\pi$
$139$	0.397520	−	0.688524i	0.0337172	−	0.0583999i	0.882392	+	0.470516i	$0.155932\pi$
$140$		0			0
$141$	0.339746	+	1.26795i	0.0286118	+	0.106781i
$142$	−4.73205	−	8.19615i	−0.397105	−	0.687806i
$143$	0.480473			0.0401792
$144$		−	3.00000i		−	0.250000i
$145$	−4.14110			−0.343900
$146$	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	$0.778258\pi$
$150$	4.81105	−	4.81105i	0.392820	−	0.392820i
$151$	−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	$-0.435831\pi$
$152$	−4.38134			−0.355374
$153$	17.7470	+	10.2462i	1.43476	+	0.828360i
$154$		0			0
$155$	3.46410	+	6.00000i	0.278243	+	0.481932i
$156$	0.803848	+	3.00000i	0.0643593	+	0.240192i
$157$	4.76028	−	8.24504i	0.379912	−	0.658026i	−0.611137	−	0.791524i	$-0.709288\pi$
$157$	4.76028	−	8.24504i	0.379912	−	0.658026i	0.991049	+	0.133498i	$0.0426211\pi$
$158$	−4.46410	+	7.73205i	−0.355145	+	0.615129i
$159$	18.2832	+	4.89898i	1.44996	+	0.388514i
$160$	−0.517638	−	0.896575i	−0.0409229	−	0.0708805i
$161$		0			0
$162$	4.50000	−	7.79423i	0.353553	−	0.612372i
$163$	−13.3205			−1.04334			−0.521671	−	0.853147i	$-0.674691\pi$
$163$	−13.3205			−1.04334			−0.521671	+	0.853147i	$0.674691\pi$
$164$	−4.31199	−	7.46859i	−0.336710	−	0.583199i
$165$	−0.464102	−	0.124356i	−0.0361303	−	0.00968107i
$166$	3.29530	−	5.70762i	0.255765	−	0.442997i
$167$	0.757875	−	1.31268i	0.0586461	−	0.101578i	−0.835212	−	0.549928i	$-0.814655\pi$
$167$	0.757875	−	1.31268i	0.0586461	−	0.101578i	0.893858	+	0.448350i	$0.147988\pi$
$168$		0			0
$169$	4.89230	+	8.47372i	0.376331	+	0.651825i
$170$	7.07180			0.542382
$171$	−11.3831	−	6.57201i	−0.870484	−	0.502574i
$172$	0.267949			0.0204309
$173$	3.34607	+	5.79555i	0.254397	+	0.440628i	0.964731	−	0.263236i	$-0.0847898\pi$
$173$	3.34607	+	5.79555i	0.254397	+	0.440628i	−0.710335	+	0.703864i	$0.751456\pi$
$174$	4.89898	−	4.89898i	0.371391	−	0.371391i
$175$		0			0
$176$	0.133975	−	0.232051i	0.0100987	−	0.0174915i
$177$	−1.56218	+	1.56218i	−0.117420	+	0.117420i
$178$	3.53553	+	6.12372i	0.264999	+	0.458993i
$179$	5.07180			0.379084			0.189542	−	0.981873i	$-0.439300\pi$
$179$	5.07180			0.379084			0.189542	+	0.981873i	$0.439300\pi$
$180$		−	3.10583i		−	0.231495i
$181$	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
$183$	−5.66025	−	21.1244i	−0.418418	−	1.56156i
$184$	−2.73205	+	4.73205i	−0.201409	+	0.348851i
$185$	−3.86370	+	6.69213i	−0.284065	+	0.492015i
$186$	−11.1962	−	3.00000i	−0.820942	−	0.219971i
$187$	0.915158	+	1.58510i	0.0669230	+	0.115914i
$188$	−0.757875			−0.0552737
$189$		0			0
$190$	−4.53590			−0.329069
$191$	−7.46410	−	12.9282i	−0.540083	−	0.935452i	−0.998899	−	0.0469202i	$-0.985059\pi$
$191$	−7.46410	−	12.9282i	−0.540083	−	0.935452i	0.458815	−	0.888532i	$-0.348274\pi$
$192$	1.67303	+	0.448288i	0.120741	+	0.0323524i
$193$	−7.52628	+	13.0359i	−0.541753	+	0.938344i	0.457050	+	0.889441i	$0.348906\pi$
$193$	−7.52628	+	13.0359i	−0.541753	+	0.938344i	−0.998804	+	0.0489035i	$0.984427\pi$
$194$	−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	$0.706045\pi$
$198$	0.696152	−	0.401924i	0.0494734	−	0.0285635i
$199$	−26.2880			−1.86351			−0.931755	−	0.363087i	$-0.881723\pi$
$199$	−26.2880			−1.86351			−0.931755	+	0.363087i	$0.881723\pi$
$200$	1.96410	+	3.40192i	0.138883	+	0.240552i
$201$	−15.2653	+	15.2653i	−1.07673	+	1.07673i
$202$	−2.44949	+	4.24264i	−0.172345	+	0.298511i
$203$		0			0
$204$	−8.36603	+	8.36603i	−0.585739	+	0.585739i
$205$	−4.46410	−	7.73205i	−0.311786	−	0.540030i
$206$	−12.3490			−0.860395
$207$	−14.1962	+	8.19615i	−0.986701	+	0.569672i
$208$	−1.79315			−0.124333
$209$	−0.586988	−	1.01669i	−0.0406028	−	0.0703262i
$210$		0			0
$211$	−9.46410	+	16.3923i	−0.651536	+	1.12849i	0.331215	+	0.943555i	$0.392542\pi$
$211$	−9.46410	+	16.3923i	−0.651536	+	1.12849i	−0.982750	+	0.184937i	$0.940792\pi$
$212$	−5.46410	+	9.46410i	−0.375276	+	0.649997i
$213$	15.8338	+	4.24264i	1.08491	+	0.290701i
$214$	8.69615	+	15.0622i	0.594457	+	1.02963i
$215$	0.277401			0.0189186
$216$	3.67423	+	3.67423i	0.250000	+	0.250000i
$217$		0			0
$218$	−2.46410	−	4.26795i	−0.166890	−	0.289062i
$219$	−9.06218	−	2.42820i	−0.612365	−	0.164083i
$220$	0.138701	−	0.240237i	0.00935120	−	0.0161968i
$221$	6.12436	−	10.6077i	0.411969	−	0.713551i
$222$	−3.34607	−	12.4877i	−0.224573	−	0.838119i
$223$	−3.58630	−	6.21166i	−0.240157	−	0.415963i	0.720602	−	0.693349i	$-0.243865\pi$
$223$	−3.58630	−	6.21166i	−0.240157	−	0.415963i	−0.960759	+	0.277385i	$0.910532\pi$
$224$		0			0
$225$			11.7846i			0.785641i
$226$	−6.92820			−0.460857
$227$	−13.8325	−	23.9587i	−0.918098	−	1.59019i	−0.802300	−	0.596920i	$-0.796391\pi$
$227$	−13.8325	−	23.9587i	−0.918098	−	1.59019i	−0.115798	−	0.993273i	$-0.536943\pi$
$228$	5.36603	−	5.36603i	0.355374	−	0.355374i
$229$	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
$233$	0.124356			0.00814681			0.00407340	−	0.999992i	$-0.498703\pi$
$233$	0.124356			0.00814681			0.00407340	+	0.999992i	$0.498703\pi$
$234$	−4.65874	−	2.68973i	−0.304552	−	0.175833i
$235$	−0.784610			−0.0511823
$236$	−0.637756	−	1.10463i	−0.0415144	−	0.0719051i
$237$	−4.00240	−	14.9372i	−0.259984	−	0.970274i
$238$		0			0
$239$	−0.464102	+	0.803848i	−0.0300202	+	0.0519966i	−0.880645	−	0.473776i	$-0.842891\pi$
$239$	−0.464102	+	0.803848i	−0.0300202	+	0.0519966i	0.850625	+	0.525773i	$0.176224\pi$
$240$	1.73205	+	0.464102i	0.111803	+	0.0299576i
$241$	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	$0.768545\pi$
$242$	−10.9282			−0.702492
$243$	4.03459	+	15.0573i	0.258819	+	0.965926i
$244$	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
$248$	3.34607	−	5.79555i	0.212475	−	0.368018i
$249$	2.95448	+	11.0263i	0.187233	+	0.698762i
$250$	4.62158	+	8.00481i	0.292294	+	0.506269i
$251$	−0.795040			−0.0501824			−0.0250912	−	0.999685i	$-0.507988\pi$
$251$	−0.795040			−0.0501824			−0.0250912	+	0.999685i	$0.507988\pi$
$252$		0			0
$253$	−1.46410			−0.0920473
$254$	−6.73205	−	11.6603i	−0.422406	−	0.731629i
$255$	−8.66115	+	8.66115i	−0.542382	+	0.542382i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	5.01910	−	8.69333i	0.313083	−	0.542275i	−0.665945	−	0.746001i	$-0.731972\pi$
$257$	5.01910	−	8.69333i	0.313083	−	0.542275i	0.979028	+	0.203725i	$0.0653050\pi$
$258$	−0.328169	+	0.328169i	−0.0204309	+	0.0204309i
$259$		0			0
$260$	−1.85641			−0.115129
$261$			12.0000i			0.742781i
$262$	−10.9348			−0.675552
$263$	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	$0.748564\pi$
$264$	0.120118	+	0.448288i	0.00739277	+	0.0275902i
$265$	−5.65685	+	9.79796i	−0.347498	+	0.601884i
$266$		0			0
$267$	−11.8301	−	3.16987i	−0.723992	−	0.193993i
$268$	−6.23205	−	10.7942i	−0.380683	−	0.659362i
$269$	5.65685			0.344904			0.172452	−	0.985018i	$-0.444831\pi$
$269$	5.65685			0.344904			0.172452	+	0.985018i	$0.444831\pi$
$270$	3.80385	+	3.80385i	0.231495	+	0.231495i
$271$	−13.1069			−0.796185			−0.398093	−	0.917345i	$-0.630328\pi$
$271$	−13.1069			−0.796185			−0.398093	+	0.917345i	$0.630328\pi$
$272$	−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
$276$	−2.44949	−	9.14162i	−0.147442	−	0.550261i
$277$	−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	$-0.560846\pi$
$278$	−0.795040			−0.0476833
$279$	17.3867	−	10.0382i	1.04091	−	0.600971i
$280$		0			0
$281$	−8.92820	−	15.4641i	−0.532612	−	0.922511i	−0.999275	−	0.0380757i	$-0.987877\pi$
$281$	−8.92820	−	15.4641i	−0.532612	−	0.922511i	0.466663	−	0.884435i	$-0.345456\pi$
$282$	0.928203	−	0.928203i	0.0552737	−	0.0552737i
$283$	−7.53794	+	13.0561i	−0.448084	+	0.776104i	−0.998261	−	0.0589437i	$-0.981227\pi$
$283$	−7.53794	+	13.0561i	−0.448084	+	0.776104i	0.550177	+	0.835048i	$0.314560\pi$
$284$	−4.73205	+	8.19615i	−0.280796	+	0.486352i
$285$	5.55532	−	5.55532i	0.329069	−	0.329069i
$286$	−0.240237	−	0.416102i	−0.0142055	−	0.0246046i
$287$		0			0
$288$	−2.59808	+	1.50000i	−0.153093	+	0.0883883i
$289$	29.6603			1.74472
$290$	2.07055	+	3.58630i	0.121587	+	0.210595i
$291$	−8.13397	−	30.3564i	−0.476822	−	1.77952i
$292$	2.70831	−	4.69093i	0.158492	−	0.274516i
$293$	−4.62158	+	8.00481i	−0.269995	+	0.467646i	−0.968860	−	0.247608i	$-0.920356\pi$
$293$	−4.62158	+	8.00481i	−0.269995	+	0.467646i	0.698865	+	0.715254i	$0.253689\pi$
$294$		0			0
$295$	−0.660254	−	1.14359i	−0.0384415	−	0.0665826i
$296$	7.46410			0.433842
$297$	−0.360355	+	1.34486i	−0.0209099	+	0.0780369i
$298$	22.9282			1.32820
$299$	4.89898	+	8.48528i	0.283315	+	0.490716i
$300$	−6.57201	−	1.76097i	−0.379435	−	0.101669i
$301$		0			0
$302$	−9.19615	+	15.9282i	−0.529179	+	0.916565i
$303$	−2.19615	−	8.19615i	−0.126166	−	0.470857i
$304$	2.19067	+	3.79435i	0.125644	+	0.217621i
$305$	13.0718			0.748489
$306$		−	20.4925i		−	1.17148i
$307$	−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
$309$	15.1244	−	15.1244i	0.860395	−	0.860395i
$310$	3.46410	−	6.00000i	0.196748	−	0.340777i
$311$	−3.72500	+	6.45189i	−0.211226	+	0.365853i	−0.952098	−	0.305792i	$-0.901079\pi$
$311$	−3.72500	+	6.45189i	−0.211226	+	0.365853i	0.740873	+	0.671645i	$0.234412\pi$
$312$	2.19615	−	2.19615i	0.124333	−	0.124333i
$313$	3.13801	+	5.43520i	0.177371	+	0.307216i	0.940979	−	0.338464i	$-0.109907\pi$
$313$	3.13801	+	5.43520i	0.177371	+	0.307216i	−0.763608	+	0.645680i	$0.776574\pi$
$314$	−9.52056			−0.537276
$315$		0			0
$316$	8.92820			0.502251
$317$	13.0000	+	22.5167i	0.730153	+	1.26466i	0.956818	+	0.290689i	$0.0938844\pi$
$317$	13.0000	+	22.5167i	0.730153	+	1.26466i	−0.226665	+	0.973973i	$0.572782\pi$
$318$	−4.89898	−	18.2832i	−0.274721	−	1.02527i
$319$	−0.535898	+	0.928203i	−0.0300045	+	0.0519694i
$320$	−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
$324$	−9.00000			−0.500000
$325$	7.04386			0.390723
$326$	6.66025	+	11.5359i	0.368877	+	0.638914i
$327$	8.24504	+	2.20925i	0.455952	+	0.122172i
$328$	−4.31199	+	7.46859i	−0.238090	+	0.412384i
$329$		0			0
$330$	0.124356	+	0.464102i	0.00684555	+	0.0255480i
$331$	5.73205	+	9.92820i	0.315062	+	0.545703i	0.979451	−	0.201684i	$-0.0646413\pi$
$331$	5.73205	+	9.92820i	0.315062	+	0.545703i	−0.664389	+	0.747387i	$0.731308\pi$
$332$	−6.59059			−0.361706
$333$	19.3923	+	11.1962i	1.06269	+	0.613545i
$334$	−1.51575			−0.0829381
$335$	−6.45189	−	11.1750i	−0.352505	−	0.610556i
$336$		0			0
$337$	3.50000	−	6.06218i	0.190657	−	0.330228i	−0.754811	−	0.655942i	$-0.772271\pi$
$337$	3.50000	−	6.06218i	0.190657	−	0.330228i	0.945468	+	0.325714i	$0.105605\pi$
$338$	4.89230	−	8.47372i	0.266106	−	0.460910i
$339$	8.48528	−	8.48528i	0.460857	−	0.460857i
$340$	−3.53590	−	6.12436i	−0.191761	−	0.332140i
$341$	1.79315			0.0971046
$342$			13.1440i			0.710747i
$343$		0			0
$344$	−0.133975	−	0.232051i	−0.00722343	−	0.0125113i
$345$	−2.53590	−	9.46410i	−0.136528	−	0.509530i
$346$	3.34607	−	5.79555i	0.179886	−	0.311571i
$347$	4.79423	−	8.30385i	0.257368	−	0.445774i	−0.708168	−	0.706044i	$-0.750478\pi$
$347$	4.79423	−	8.30385i	0.257368	−	0.445774i	0.965536	+	0.260270i	$0.0838115\pi$
$348$	−6.69213	−	1.79315i	−0.358736	−	0.0961230i
$349$	−4.00240	−	6.93237i	−0.214244	−	0.371081i	0.738795	−	0.673931i	$-0.235395\pi$
$349$	−4.00240	−	6.93237i	−0.214244	−	0.371081i	−0.953038	+	0.302850i	$0.902062\pi$
$350$		0			0
$351$	9.00000	−	2.41154i	0.480384	−	0.128719i
$352$	−0.267949			−0.0142817
$353$	12.5063	+	21.6615i	0.665641	+	1.15292i	0.979111	+	0.203327i	$0.0651753\pi$
$353$	12.5063	+	21.6615i	0.665641	+	1.15292i	−0.313470	+	0.949598i	$0.601491\pi$
$354$	2.13397	+	0.571797i	0.113419	+	0.0303907i
$355$	−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
$359$	7.46410			0.393940			0.196970	−	0.980409i	$-0.436890\pi$
$359$	7.46410			0.393940			0.196970	+	0.980409i	$0.436890\pi$
$360$	−2.68973	+	1.55291i	−0.141761	+	0.0818458i
$361$	0.196152			0.0103238
$362$	−8.48528	−	14.6969i	−0.445976	−	0.772454i
$363$	13.3843	−	13.3843i	0.702492	−	0.702492i
$364$		0			0
$365$	2.80385	−	4.85641i	0.146760	−	0.254196i
$366$	−15.4641	+	15.4641i	−0.808322	+	0.808322i
$367$	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	$0.672361\pi$
$368$	5.46410			0.284836
$369$	−22.4058	+	12.9360i	−1.16640	+	0.673420i
$370$	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	$0.0765964\pi$
$374$	0.915158	−	1.58510i	0.0473217	−	0.0819636i
$375$	−15.4641	−	4.14359i	−0.798563	−	0.213974i
$376$	0.378937	+	0.656339i	0.0195422	+	0.0338481i
$377$	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	$0.386523\pi$
$380$	2.26795	+	3.92820i	0.116343	+	0.201513i
$381$	22.5259	+	6.03579i	1.15404	+	0.309223i
$382$	−7.46410	+	12.9282i	−0.381897	+	0.661464i
$383$	13.6617	−	23.6627i	0.698078	−	1.20911i	−0.271054	−	0.962564i	$-0.587372\pi$
$383$	13.6617	−	23.6627i	0.698078	−	1.20911i	0.969132	−	0.246543i	$-0.0792946\pi$
$384$	−0.448288	−	1.67303i	−0.0228766	−	0.0853766i
$385$		0			0
$386$	15.0526			0.766155
$387$		−	0.803848i		−	0.0408619i
$388$	18.1445			0.921149
$389$	−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	$0.898340\pi$
$390$	2.27362	−	2.27362i	0.115129	−	0.115129i
$391$	−18.6622	+	32.3238i	−0.943787	+	1.63469i
$392$		0			0
$393$	13.3923	−	13.3923i	0.675552	−	0.675552i
$394$	8.46410	+	14.6603i	0.426415	+	0.738573i
$395$	9.24316			0.465074
$396$	−0.696152	−	0.401924i	−0.0349830	−	0.0201974i
$397$	−13.1069			−0.657814			−0.328907	−	0.944362i	$-0.606680\pi$
$397$	−13.1069			−0.657814			−0.328907	+	0.944362i	$0.606680\pi$
$398$	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	$-0.0357353\pi$
$402$	20.8528	+	5.58750i	1.04005	+	0.278679i
$403$	−6.00000	−	10.3923i	−0.298881	−	0.517678i
$404$	4.89898			0.243733
$405$	−9.31749			−0.462990
$406$		0			0
$407$	1.00000	+	1.73205i	0.0495682	+	0.0858546i
$408$	11.4282	+	3.06218i	0.565780	+	0.151600i
$409$	2.24144	−	3.88229i	0.110832	−	0.191967i	−0.805274	−	0.592903i	$-0.797982\pi$
$409$	2.24144	−	3.88229i	0.110832	−	0.191967i	0.916106	+	0.400936i	$0.131315\pi$
$410$	−4.46410	+	7.73205i	−0.220466	+	0.381859i
$411$	−3.88229	−	14.4889i	−0.191499	−	0.714684i
$412$	6.17449	+	10.6945i	0.304195	+	0.526882i
$413$		0			0
$414$	14.1962	+	8.19615i	0.697703	+	0.402819i
$415$	−6.82309			−0.334932
$416$	0.896575	+	1.55291i	0.0439582	+	0.0761379i
$417$	0.973721	−	0.973721i	0.0476833	−	0.0476833i
$418$	−0.586988	+	1.01669i	−0.0287105	+	0.0497281i
$419$	18.0938	−	31.3393i	0.883939	−	1.53103i	0.0370132	−	0.999315i	$-0.488216\pi$
$419$	18.0938	−	31.3393i	0.883939	−	1.53103i	0.846925	−	0.531712i	$-0.178451\pi$
$420$		0			0
$421$	−3.80385	−	6.58846i	−0.185388	−	0.321102i	0.758319	−	0.651884i	$-0.226021\pi$
$421$	−3.80385	−	6.58846i	−0.185388	−	0.321102i	−0.943707	+	0.330782i	$0.892688\pi$
$422$	18.9282			0.921411
$423$			2.27362i			0.110547i
$424$	10.9282			0.530720
$425$	13.4164	+	23.2380i	0.650793	+	1.12721i
$426$	−4.24264	−	15.8338i	−0.205557	−	0.767148i
$427$		0			0
$428$	8.69615	−	15.0622i	0.420344	−	0.728058i
$429$	0.803848	+	0.215390i	0.0388101	+	0.0103991i
$430$	−0.138701	−	0.240237i	−0.00668874	−	0.0115852i
$431$	−10.1436			−0.488600			−0.244300	−	0.969700i	$-0.578558\pi$
$431$	−10.1436			−0.488600			−0.244300	+	0.969700i	$0.578558\pi$
$432$	1.34486	−	5.01910i	0.0647048	−	0.241481i
$433$	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
$435$	−6.92820	−	1.85641i	−0.332182	−	0.0890079i
$436$	−2.46410	+	4.26795i	−0.118009	+	0.204398i
$437$	11.9700	−	20.7327i	0.572605	−	0.991781i
$438$	2.42820	+	9.06218i	0.116024	+	0.433008i
$439$	9.79796	+	16.9706i	0.467631	+	0.809961i	0.999316	−	0.0369815i	$-0.0117743\pi$
$439$	9.79796	+	16.9706i	0.467631	+	0.809961i	−0.531685	+	0.846942i	$0.678441\pi$
$440$	−0.277401			−0.0132246
$441$		0			0
$442$	−12.2487			−0.582612
$443$	−8.16025	−	14.1340i	−0.387705	−	0.671525i	0.604435	−	0.796654i	$-0.293399\pi$
$443$	−8.16025	−	14.1340i	−0.387705	−	0.671525i	−0.992140	+	0.125129i	$0.960066\pi$
$444$	−9.14162	+	9.14162i	−0.433842	+	0.433842i
$445$	3.66025	−	6.33975i	0.173513	−	0.300533i
$446$	−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	$0.310327\pi$
$450$	10.2058	−	5.89230i	0.481105	−	0.277766i
$451$	−2.31079			−0.108811
$452$	3.46410	+	6.00000i	0.162938	+	0.282216i
$453$	−8.24504	−	30.7709i	−0.387386	−	1.44574i
$454$	−13.8325	+	23.9587i	−0.649194	+	1.12444i
$455$		0			0
$456$	−7.33013	−	1.96410i	−0.343265	−	0.0919775i
$457$	15.5263	+	26.8923i	0.726289	+	1.25797i	0.958441	+	0.285290i	$0.0920898\pi$
$457$	15.5263	+	26.8923i	0.726289	+	1.25797i	−0.232153	+	0.972679i	$0.574577\pi$
$458$	−0.480473			−0.0224510
$459$	25.0981	+	25.0981i	1.17148	+	1.17148i
$460$	5.65685			0.263752
$461$	−5.51815	−	9.55772i	−0.257006	−	0.445148i	0.708432	−	0.705779i	$-0.249403\pi$
$461$	−5.51815	−	9.55772i	−0.257006	−	0.445148i	−0.965438	+	0.260631i	$0.916069\pi$
$462$		0			0
$463$	15.3205	−	26.5359i	0.712004	−	1.23323i	−0.252099	−	0.967701i	$-0.581121\pi$
$463$	15.3205	−	26.5359i	0.712004	−	1.23323i	0.964104	−	0.265526i	$-0.0855457\pi$
$464$	2.00000	−	3.46410i	0.0928477	−	0.160817i
$465$	3.10583	+	11.5911i	0.144029	+	0.537525i
$466$	−0.0621778	−	0.107695i	−0.00288033	−	0.00498888i
$467$	−9.17878			−0.424744			−0.212372	−	0.977189i	$-0.568119\pi$
$467$	−9.17878			−0.424744			−0.212372	+	0.977189i	$0.568119\pi$
$468$			5.37945i			0.248665i
$469$		0			0
$470$	0.392305	+	0.679492i	0.0180957	+	0.0313426i
$471$	11.6603	−	11.6603i	0.537276	−	0.537276i
$472$	−0.637756	+	1.10463i	−0.0293551	+	0.0508446i
$473$	0.0358984	−	0.0621778i	0.00165061	−	0.00285894i
$474$	−10.9348	+	10.9348i	−0.502251	+	0.502251i
$475$	−8.60540	−	14.9050i	−0.394843	−	0.683888i
$476$		0			0
$477$	28.3923	+	16.3923i	1.29999	+	0.750552i
$478$	0.928203			0.0424550
$479$	−2.07055	−	3.58630i	−0.0946060	−	0.163862i	0.814838	−	0.579689i	$-0.196826\pi$
$479$	−2.07055	−	3.58630i	−0.0946060	−	0.163862i	−0.909444	+	0.415826i	$0.863492\pi$
$480$	−0.464102	−	1.73205i	−0.0211832	−	0.0790569i
$481$	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
$485$	18.7846			0.852965
$486$	11.0227	−	11.0227i	0.500000	−	0.500000i
$487$	−2.78461			−0.126183			−0.0630914	−	0.998008i	$-0.520096\pi$
$487$	−2.78461			−0.126183			−0.0630914	+	0.998008i	$0.520096\pi$
$488$	−6.31319	−	10.9348i	−0.285785	−	0.494994i
$489$	−22.2856	−	5.97142i	−1.00779	−	0.270037i
$490$		0			0
$491$	−9.69615	+	16.7942i	−0.437581	+	0.757913i	−0.997502	−	0.0706330i	$-0.977498\pi$
$491$	−9.69615	+	16.7942i	−0.437581	+	0.757913i	0.559921	+	0.828546i	$0.310831\pi$
$492$	−3.86603	−	14.4282i	−0.174294	−	0.650474i
$493$	13.6617	+	23.6627i	0.615290	+	1.06571i
$494$	7.85641			0.353476
$495$	−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	$0.897958\pi$
$500$	4.62158	−	8.00481i	0.206683	−	0.357986i
$501$	1.85641	−	1.85641i	0.0829381	−	0.0829381i
$502$	0.397520	+	0.688524i	0.0177422	+	0.0307303i
$503$	12.3490			0.550614			0.275307	−	0.961356i	$-0.411220\pi$
$503$	12.3490			0.550614			0.275307	+	0.961356i	$0.411220\pi$
$504$		0			0
$505$	5.07180			0.225692
$506$	0.732051	+	1.26795i	0.0325436	+	0.0563672i
$507$	4.38632	+	16.3700i	0.194803	+	0.727016i
$508$	−6.73205	+	11.6603i	−0.298686	+	0.517340i
$509$	10.7961	−	18.6993i	0.478527	−	0.828834i	−0.521169	−	0.853453i	$-0.674504\pi$
$509$	10.7961	−	18.6993i	0.478527	−	0.828834i	0.999697	+	0.0246194i	$0.00783740\pi$
$510$	11.8313	+	3.17020i	0.523901	+	0.140379i
$511$		0			0
$512$	1.00000			0.0441942
$513$	−16.0981	−	16.0981i	−0.710747	−	0.710747i
$514$	−10.0382			−0.442766
$515$	6.39230	+	11.0718i	0.281679	+	0.487882i
$516$	0.448288	+	0.120118i	0.0197348	+	0.00528791i
$517$	−0.101536	+	0.175865i	−0.00446555	+	0.00773455i
$518$		0			0
$519$	3.00000	+	11.1962i	0.131685	+	0.491457i
$520$	0.928203	+	1.60770i	0.0407044	+	0.0705021i
$521$	33.7752			1.47972			0.739860	−	0.672761i	$-0.234892\pi$
$521$	33.7752			1.47972			0.739860	+	0.672761i	$0.234892\pi$
$522$	10.3923	−	6.00000i	0.454859	−	0.262613i
$523$	−20.7327			−0.906579			−0.453289	−	0.891363i	$-0.649750\pi$
$523$	−20.7327			−0.906579			−0.453289	+	0.891363i	$0.649750\pi$
$524$	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
$528$	0.328169	−	0.328169i	0.0142817	−	0.0142817i
$529$	−3.42820	−	5.93782i	−0.149052	−	0.258166i
$530$	11.3137			0.491436
$531$	−3.31388	+	1.91327i	−0.143810	+	0.0830288i
$532$		0			0
$533$	7.73205	+	13.3923i	0.334912	+	0.580085i
$534$	3.16987	+	11.8301i	0.137174	+	0.511940i
$535$	9.00292	−	15.5935i	0.389230	−	0.674166i
$536$	−6.23205	+	10.7942i	−0.269184	+	0.466240i
$537$	8.48528	+	2.27362i	0.366167	+	0.0981141i
$538$	−2.82843	−	4.89898i	−0.121942	−	0.211210i
$539$		0			0
$540$	1.39230	−	5.19615i	0.0599153	−	0.223607i
$541$	15.3205			0.658680			0.329340	−	0.944211i	$-0.393174\pi$
$541$	15.3205			0.658680			0.329340	+	0.944211i	$0.393174\pi$
$542$	6.55343	+	11.3509i	0.281494	+	0.487562i
$543$	28.3923	+	7.60770i	1.21843	+	0.326477i
$544$	−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	−0.954792	−	0.297274i	$-0.903922\pi$
$547$	−17.1865	−	29.7679i	−0.734843	−	1.27279i	0.219949	−	0.975511i	$-0.429411\pi$
$548$	8.66025			0.369948
$549$		−	37.8792i		−	1.61664i
$550$	1.05256			0.0448813
$551$	−8.76268	−	15.1774i	−0.373303	−	0.646579i
$552$	−6.69213	+	6.69213i	−0.284836	+	0.284836i
$553$		0			0
$554$	−15.7321	+	27.2487i	−0.668391	+	1.15769i
$555$	−9.46410	+	9.46410i	−0.401729	+	0.401729i
$556$	0.397520	+	0.688524i	0.0168586	+	0.0291999i
$557$	−6.92820			−0.293557			−0.146779	−	0.989169i	$-0.546891\pi$
$557$	−6.92820			−0.293557			−0.146779	+	0.989169i	$0.546891\pi$
$558$	−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
$563$	−9.12304	+	15.8016i	−0.384490	+	0.665957i	−0.991698	−	0.128586i	$-0.958956\pi$
$563$	−9.12304	+	15.8016i	−0.384490	+	0.665957i	0.607208	+	0.794543i	$0.292289\pi$
$564$	−1.26795	−	0.339746i	−0.0533903	−	0.0143059i
$565$	3.58630	+	6.21166i	0.150877	+	0.261326i
$566$	15.0759			0.633686
$567$		0			0
$568$	9.46410			0.397105
$569$	12.8923	+	22.3301i	0.540474	+	0.936128i	0.998877	+	0.0473833i	$0.0150882\pi$
$569$	12.8923	+	22.3301i	0.540474	+	0.936128i	−0.458403	+	0.888744i	$0.651578\pi$
$570$	−7.58871	−	2.03339i	−0.317856	−	0.0851692i
$571$	16.5263	−	28.6244i	0.691603	−	1.19789i	−0.279709	−	0.960085i	$-0.590238\pi$
$571$	16.5263	−	28.6244i	0.691603	−	1.19789i	0.971312	−	0.237807i	$-0.0764286\pi$
$572$	−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
$577$	27.4892			1.14439			0.572196	−	0.820117i	$-0.306092\pi$
$577$	27.4892			1.14439			0.572196	+	0.820117i	$0.306092\pi$
$578$	−14.8301	−	25.6865i	−0.616852	−	1.06842i
$579$	−18.4355	+	18.4355i	−0.766155	+	0.766155i
$580$	2.07055	−	3.58630i	0.0859750	−	0.148913i
$581$		0			0
$582$	−22.2224	+	22.2224i	−0.921149	+	0.921149i
$583$	1.46410	+	2.53590i	0.0606369	+	0.105026i
$584$	−5.41662			−0.224141
$585$			5.56922i			0.230259i
$586$	9.24316			0.381831
$587$	−20.9408	−	36.2705i	−0.864319	−	1.49704i	−0.867722	−	0.497049i	$-0.834417\pi$
$587$	−20.9408	−	36.2705i	−0.864319	−	1.49704i	0.00340370	−	0.999994i	$-0.498917\pi$
$588$		0			0
$589$	−14.6603	+	25.3923i	−0.604065	+	1.04627i
$590$	−0.660254	+	1.14359i	−0.0271822	+	0.0470810i
$591$	−28.3214	−	7.58871i	−1.16499	−	0.312158i
$592$	−3.73205	−	6.46410i	−0.153386	−	0.265673i
$593$	−16.8690			−0.692728			−0.346364	−	0.938100i	$-0.612584\pi$
$593$	−16.8690			−0.692728			−0.346364	+	0.938100i	$0.612584\pi$
$594$	1.34486	−	0.360355i	0.0551804	−	0.0147855i
$595$		0			0
$596$	−11.4641	−	19.8564i	−0.469588	−	0.813350i
$597$	−43.9808	−	11.7846i	−1.80001	−	0.482312i
$598$	4.89898	−	8.48528i	0.200334	−	0.346989i
$599$	−2.39230	+	4.14359i	−0.0977469	+	0.169303i	−0.910752	−	0.412954i	$-0.864497\pi$
$599$	−2.39230	+	4.14359i	−0.0977469	+	0.169303i	0.813005	+	0.582257i	$0.197830\pi$
$600$	1.76097	+	6.57201i	0.0718911	+	0.268301i
$601$	−1.67303	−	2.89778i	−0.0682444	−	0.118203i	0.829884	−	0.557936i	$-0.188406\pi$
$601$	−1.67303	−	2.89778i	−0.0682444	−	0.118203i	−0.898129	+	0.439733i	$0.855073\pi$
$602$		0			0
$603$	−32.3827	+	18.6962i	−1.31872	+	0.761366i
$604$	18.3923			0.748372
$605$	5.65685	+	9.79796i	0.229984	+	0.398344i
$606$	−6.00000	+	6.00000i	−0.243733	+	0.243733i
$607$	−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
$611$	1.35898			0.0549786
$612$	−17.7470	+	10.2462i	−0.717381	+	0.414180i
$613$	24.9282			1.00684			0.503420	−	0.864042i	$-0.332075\pi$
$613$	24.9282			1.00684			0.503420	+	0.864042i	$0.332075\pi$
$614$	0.586988	+	1.01669i	0.0236889	+	0.0410304i
$615$	−4.00240	−	14.9372i	−0.161393	−	0.602325i
$616$		0			0
$617$	1.57180	−	2.72243i	0.0632782	−	0.109601i	−0.832651	−	0.553798i	$-0.813178\pi$
$617$	1.57180	−	2.72243i	0.0632782	−	0.109601i	0.895929	+	0.444197i	$0.146511\pi$
$618$	−20.6603	−	5.53590i	−0.831077	−	0.222686i
$619$	−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	$-0.386557\pi$
$620$	−6.92820			−0.278243
$621$	−27.4249	+	7.34847i	−1.10052	+	0.294884i
$622$	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
$626$	3.13801	−	5.43520i	0.125420	−	0.217234i
$627$	−0.526279	−	1.96410i	−0.0210176	−	0.0784387i
$628$	4.76028	+	8.24504i	0.189956	+	0.329013i
$629$	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	$0.628347\pi$
$632$	−4.46410	−	7.73205i	−0.177572	−	0.307564i
$633$	−23.1822	+	23.1822i	−0.921411	+	0.921411i
$634$	13.0000	−	22.5167i	0.516296	−	0.894251i
$635$	−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
$640$	1.03528			0.0409229
$641$	−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	$0.858957\pi$
$642$	7.79676	+	29.0979i	0.307713	+	1.14840i
$643$	−22.4565	+	38.8959i	−0.885599	+	1.53390i	−0.0405737	+	0.999177i	$0.512919\pi$
$643$	−22.4565	+	38.8959i	−0.885599	+	1.53390i	−0.845025	+	0.534726i	$0.820415\pi$
$644$		0			0
$645$	0.464102	+	0.124356i	0.0182740	+	0.00489650i
$646$	14.9641	+	25.9186i	0.588755	+	1.01975i
$647$	−21.8695			−0.859780			−0.429890	−	0.902881i	$-0.641448\pi$
$647$	−21.8695			−0.859780			−0.429890	+	0.902881i	$0.641448\pi$
$648$	4.50000	+	7.79423i	0.176777	+	0.306186i
$649$	−0.341773			−0.0134157
$650$	−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	$0.204122\pi$
$654$	−2.20925	−	8.24504i	−0.0863886	−	0.322407i
$655$	5.66025	+	9.80385i	0.221164	+	0.383068i
$656$	8.62398			0.336710
$657$	−14.0728	−	8.12493i	−0.549032	−	0.316984i
$658$		0			0
$659$	24.1244	+	41.7846i	0.939751	+	1.62770i	0.765934	+	0.642919i	$0.222277\pi$
$659$	24.1244	+	41.7846i	0.939751	+	1.62770i	0.173818	+	0.984778i	$0.444390\pi$
$660$	0.339746	−	0.339746i	0.0132246	−	0.0132246i
$661$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$661$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$662$	5.73205	−	9.92820i	0.222782	−	0.385871i
$663$	15.0015	−	15.0015i	0.582612	−	0.582612i
$664$	3.29530	+	5.70762i	0.127882	+	0.221499i
$665$		0			0
$666$		−	22.3923i		−	0.867684i
$667$	−21.8564			−0.846283
$668$	0.757875	+	1.31268i	0.0293231	+	0.0507890i
$669$	−3.21539	−	12.0000i	−0.124314	−	0.463947i
$670$	−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	−0.918835	−	0.394643i	$-0.870868\pi$
$673$	−20.7846	−	36.0000i	−0.801188	−	1.38770i	0.117647	−	0.993055i	$-0.462465\pi$
$674$	−7.00000			−0.269630
$675$	−5.28290	+	19.7160i	−0.203339	+	0.758871i
$676$	−9.78461			−0.376331
$677$	−2.68973	−	4.65874i	−0.103375	−	0.179050i	0.809698	−	0.586846i	$-0.199631\pi$
$677$	−2.68973	−	4.65874i	−0.103375	−	0.179050i	−0.913073	+	0.407796i	$0.866297\pi$
$678$	−11.5911	−	3.10583i	−0.445154	−	0.119279i
$679$		0			0
$680$	−3.53590	+	6.12436i	−0.135596	+	0.234858i
$681$	−12.4019	−	46.2846i	−0.475243	−	1.77363i
$682$	−0.896575	−	1.55291i	−0.0343316	−	0.0594642i
$683$	−38.3205			−1.46629			−0.733147	−	0.680070i	$-0.761949\pi$
$683$	−38.3205			−1.46629			−0.733147	+	0.680070i	$0.761949\pi$
$684$	11.3831	−	6.57201i	0.435242	−	0.251287i
$685$	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
$689$	9.79796	−	16.9706i	0.373273	−	0.646527i
$690$	−6.92820	+	6.92820i	−0.263752	+	0.263752i
$691$	12.1595	+	21.0609i	0.462570	+	0.801194i	0.999088	−	0.0426942i	$-0.0135941\pi$
$691$	12.1595	+	21.0609i	0.462570	+	0.801194i	−0.536518	+	0.843889i	$0.680261\pi$
$692$	−6.69213			−0.254397
$693$		0			0
$694$	−9.58846			−0.363973
$695$	0.411543	+	0.712813i	0.0156107	+	0.0270385i
$696$	1.79315	+	6.69213i	0.0679692	+	0.253665i
$697$	−29.4545	+	51.0167i	−1.11567	+	1.93239i
$698$	−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	$0.628394\pi$
$702$	−6.58846	−	6.58846i	−0.248665	−	0.248665i
$703$	−32.7028			−1.23341
$704$	0.133975	+	0.232051i	0.00504936	+	0.00874574i
$705$	−1.31268	−	0.351731i	−0.0494383	−	0.0132470i
$706$	12.5063	−	21.6615i	0.470680	−	0.815241i
$707$		0			0
$708$	−0.571797	−	2.13397i	−0.0214894	−	0.0801997i
$709$	6.19615	+	10.7321i	0.232701	+	0.403051i	0.958602	−	0.284749i	$-0.0919102\pi$
$709$	6.19615	+	10.7321i	0.232701	+	0.403051i	−0.725901	+	0.687799i	$0.758577\pi$
$710$	9.79796			0.367711
$711$		−	26.7846i		−	1.00450i
$712$	−7.07107			−0.264999
$713$	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
$717$	−1.13681	+	1.13681i	−0.0424550	+	0.0424550i
$718$	−3.73205	−	6.46410i	−0.139279	−	0.241238i
$719$	49.6733			1.85250			0.926251	−	0.376906i	$-0.123012\pi$
$719$	49.6733			1.85250			0.926251	+	0.376906i	$0.123012\pi$
$720$	2.68973	+	1.55291i	0.100240	+	0.0578737i
$721$		0			0
$722$	−0.0980762	−	0.169873i	−0.00365002	−	0.00632202i
$723$	2.81347	+	10.5000i	0.104634	+	0.390499i
$724$	−8.48528	+	14.6969i	−0.315353	+	0.546207i
$725$	−7.85641	+	13.6077i	−0.291780	+	0.505377i
$726$	−18.2832	−	4.89898i	−0.678555	−	0.181818i
$727$	16.3514	+	28.3214i	0.606439	+	1.05038i	0.991822	+	0.127627i	$0.0407361\pi$
$727$	16.3514	+	28.3214i	0.606439	+	1.05038i	−0.385383	+	0.922757i	$0.625931\pi$
$728$		0			0
$729$			27.0000i			1.00000i
$730$	−5.60770			−0.207550
$731$	−0.915158	−	1.58510i	−0.0338483	−	0.0586270i
$732$	21.1244	+	5.66025i	0.780779	+	0.209209i
$733$	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
$737$	−3.33975			−0.123021
$738$	22.4058	+	12.9360i	0.824768	+	0.476180i
$739$	6.12436			0.225288			0.112644	−	0.993635i	$-0.464068\pi$
$739$	6.12436			0.225288			0.112644	+	0.993635i	$0.464068\pi$
$740$	−3.86370	−	6.69213i	−0.142033	−	0.246008i
$741$	−9.62209	+	9.62209i	−0.353476	+	0.353476i
$742$		0			0
$743$	15.7846	−	27.3397i	0.579081	−	1.00300i	−0.416504	−	0.909134i	$-0.636745\pi$
$743$	15.7846	−	27.3397i	0.579081	−	1.00300i	0.995585	−	0.0938641i	$-0.0299219\pi$
$744$	8.19615	−	8.19615i	0.300486	−	0.300486i
$745$	−11.8685	−	20.5569i	−0.434829	−	0.753145i
$746$	−10.7846			−0.394853
$747$			19.7718i			0.723412i
$748$	−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	$0.947809\pi$
$752$	0.378937	−	0.656339i	0.0138184	−	0.0239342i
$753$	−1.33013	−	0.356406i	−0.0484725	−	0.0129882i
$754$	−3.58630	−	6.21166i	−0.130605	−	0.226215i
$755$	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	$0.385805\pi$
$758$	−6.79423	−	11.7679i	−0.246777	−	0.427431i
$759$	−2.44949	−	0.656339i	−0.0889108	−	0.0238236i
$760$	2.26795	−	3.92820i	0.0822672	−	0.142491i
$761$	−20.1272	+	34.8613i	−0.729609	+	1.26372i	0.227440	+	0.973792i	$0.426965\pi$
$761$	−20.1272	+	34.8613i	−0.729609	+	1.26372i	−0.957049	+	0.289928i	$0.906369\pi$
$762$	−6.03579	−	22.5259i	−0.218654	−	0.816027i
$763$		0			0
$764$	14.9282			0.540083
$765$	−18.3731	+	10.6077i	−0.664280	+	0.383522i
$766$	−27.3233			−0.987232
$767$	1.14359	+	1.98076i	0.0412928	+	0.0715212i
$768$	−1.22474	+	1.22474i	−0.0441942	+	0.0441942i
$769$	19.0919	−	33.0681i	0.688471	−	1.19247i	−0.283862	−	0.958865i	$-0.591616\pi$
$769$	19.0919	−	33.0681i	0.688471	−	1.19247i	0.972332	−	0.233601i	$-0.0750511\pi$
$770$		0			0
$771$	12.2942	−	12.2942i	0.442766	−	0.442766i
$772$	−7.52628	−	13.0359i	−0.270877	−	0.469172i
$773$	−39.3949			−1.41694			−0.708468	−	0.705743i	$-0.750613\pi$
$773$	−39.3949			−1.41694			−0.708468	+	0.705743i	$0.750613\pi$
$774$	−0.696152	+	0.401924i	−0.0250227	+	0.0144469i
$775$	26.2880			0.944295
$776$	−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
$780$	−3.10583	−	0.832204i	−0.111207	−	0.0297977i
$781$	1.26795	+	2.19615i	0.0453708	+	0.0785845i
$782$	37.3244			1.33472
$783$	−5.37945	+	20.0764i	−0.192246	+	0.717472i
$784$		0			0
$785$	4.92820	+	8.53590i	0.175895	+	0.304659i
$786$	−18.2942	−	4.90192i	−0.652534	−	0.174846i
$787$	3.57270	−	6.18810i	0.127353	−	0.220582i	−0.795297	−	0.606220i	$-0.792685\pi$
$787$	3.57270	−	6.18810i	0.127353	−	0.220582i	0.922650	+	0.385638i	$0.126019\pi$
$788$	8.46410	−	14.6603i	0.301521	−	0.522250i
$789$	3.82654	+	14.2808i	0.136228	+	0.508411i
$790$	−4.62158	−	8.00481i	−0.164428	−	0.284798i
$791$		0			0
$792$			0.803848i			0.0285635i
$793$	−22.6410			−0.804006
$794$	6.55343	+	11.3509i	0.232573	+	0.402827i
$795$	−13.8564	+	13.8564i	−0.491436	+	0.491436i
$796$	13.1440	−	22.7661i	0.465878	−	0.806924i
$797$	−18.9396	+	32.8043i	−0.670874	+	1.16199i	0.306782	+	0.951780i	$0.400748\pi$
$797$	−18.9396	+	32.8043i	−0.670874	+	1.16199i	−0.977657	+	0.210209i	$0.932586\pi$
$798$		0			0
$799$	2.58846	+	4.48334i	0.0915730	+	0.158609i
$800$	−3.92820			−0.138883
$801$	−18.3712	−	10.6066i	−0.649113	−	0.374766i
$802$	−23.7846			−0.839864
$803$	−0.725689	−	1.25693i	−0.0256090	−	0.0443561i
$804$	−5.58750	−	20.8528i	−0.197056	−	0.735423i
$805$		0			0
$806$	−6.00000	+	10.3923i	−0.211341	+	0.366053i
$807$	9.46410	+	2.53590i	0.333152	+	0.0892679i
$808$	−2.44949	−	4.24264i	−0.0861727	−	0.149256i
$809$	−29.7321			−1.04532			−0.522662	−	0.852540i	$-0.675061\pi$
$809$	−29.7321			−1.04532			−0.522662	+	0.852540i	$0.675061\pi$
$810$	4.65874	+	8.06918i	0.163692	+	0.283522i
$811$	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
$813$	−21.9282	−	5.87564i	−0.769056	−	0.206068i
$814$	1.00000	−	1.73205i	0.0350500	−	0.0607083i
$815$	6.89520	−	11.9428i	0.241528	−	0.418339i
$816$	−3.06218	−	11.4282i	−0.107198	−	0.400067i
$817$	0.586988	+	1.01669i	0.0205361	+	0.0355696i
$818$	−4.48288			−0.156740
$819$		0			0
$820$	8.92820			0.311786
$821$	−5.19615	−	9.00000i	−0.181347	−	0.314102i	0.760993	−	0.648761i	$-0.224712\pi$
$821$	−5.19615	−	9.00000i	−0.181347	−	0.314102i	−0.942339	+	0.334659i	$0.891379\pi$
$822$	−10.6066	+	10.6066i	−0.369948	+	0.369948i
$823$	5.39230	−	9.33975i	0.187964	−	0.325563i	−0.756607	−	0.653870i	$-0.773145\pi$
$823$	5.39230	−	9.33975i	0.187964	−	0.325563i	0.944571	+	0.328306i	$0.106478\pi$
$824$	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	$0.566904\pi$
$828$		−	16.3923i		−	0.569672i
$829$	−7.93048			−0.275437			−0.137718	−	0.990471i	$-0.543977\pi$
$829$	−7.93048			−0.275437			−0.137718	+	0.990471i	$0.543977\pi$
$830$	3.41154	+	5.90897i	0.118416	+	0.205103i
$831$	−14.1050	−	52.6405i	−0.489296	−	1.82608i
$832$	0.896575	−	1.55291i	0.0310832	−	0.0538376i
$833$		0			0
$834$	−1.33013	−	0.356406i	−0.0460585	−	0.0123413i
$835$	0.784610	+	1.35898i	0.0271525	+	0.0470296i
$836$	1.17398			0.0406028
$837$	33.5885	−	9.00000i	1.16099	−	0.311086i
$838$	−36.1875			−1.25008
$839$	11.3137	+	19.5959i	0.390593	+	0.676526i	0.992528	−	0.122019i	$-0.0389368\pi$
$839$	11.3137	+	19.5959i	0.390593	+	0.676526i	−0.601935	+	0.798545i	$0.705603\pi$
$840$		0			0
$841$	6.50000	−	11.2583i	0.224138	−	0.388218i
$842$	−3.80385	+	6.58846i	−0.131089	+	0.227053i
$843$	−8.00481	−	29.8744i	−0.275700	−	1.02893i
$844$	−9.46410	−	16.3923i	−0.325768	−	0.564246i
$845$	−10.1298			−0.348475
$846$	1.96902	−	1.13681i	0.0676962	−	0.0390844i
$847$		0			0
$848$	−5.46410	−	9.46410i	−0.187638	−	0.324999i
$849$	−18.4641	+	18.4641i	−0.633686	+	0.633686i
$850$	13.4164	−	23.2380i	0.460180	−	0.797056i
$851$	−20.3923	+	35.3205i	−0.699039	+	1.21077i
$852$	−11.5911	+	11.5911i	−0.397105	+	0.397105i
$853$	16.4901	+	28.5617i	0.564610	+	0.977933i	0.997086	+	0.0762876i	$0.0243067\pi$
$853$	16.4901	+	28.5617i	0.564610	+	0.977933i	−0.432476	+	0.901645i	$0.642360\pi$
$854$		0			0
$855$	11.7846	−	6.80385i	0.403025	−	0.232687i
$856$	−17.3923			−0.594457
$857$	−5.60609	−	9.71003i	−0.191500	−	0.331688i	0.754247	−	0.656590i	$-0.228002\pi$
$857$	−5.60609	−	9.71003i	−0.191500	−	0.331688i	−0.945748	+	0.324902i	$0.894669\pi$
$858$	−0.215390	−	0.803848i	−0.00735330	−	0.0274429i
$859$	−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
$863$	−54.1051			−1.84176			−0.920880	−	0.389847i	$-0.872528\pi$
$863$	−54.1051			−1.84176			−0.920880	+	0.389847i	$0.872528\pi$
$864$	−5.01910	+	1.34486i	−0.170753	+	0.0457532i
$865$	−6.92820			−0.235566
$866$	−9.91808	−	17.1786i	−0.337030	−	0.583753i
$867$	49.6226	+	13.2963i	1.68527	+	0.451567i
$868$		0			0
$869$	1.19615	−	2.07180i	0.0405767	−	0.0702809i
$870$	1.85641	+	6.92820i	0.0629381	+	0.234888i
$871$	11.1750	+	19.3557i	0.378651	+	0.655842i
$872$	4.92820			0.166890
$873$		−	54.4336i		−	1.84230i
$874$	−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	$0.00270695\pi$
$878$	9.79796	−	16.9706i	0.330665	−	0.572729i
$879$	−11.3205	+	11.3205i	−0.381831	+	0.381831i
$880$	0.138701	+	0.240237i	0.00467560	+	0.00809838i
$881$	12.7279			0.428815			0.214407	−	0.976744i	$-0.431218\pi$
$881$	12.7279			0.428815			0.214407	+	0.976744i	$0.431218\pi$
$882$		0			0
$883$	14.4641			0.486756			0.243378	−	0.969932i	$-0.421744\pi$
$883$	14.4641			0.486756			0.243378	+	0.969932i	$0.421744\pi$
$884$	6.12436	+	10.6077i	0.205984	+	0.356775i
$885$	−0.591968	−	2.20925i	−0.0198988	−	0.0742632i
$886$	−8.16025	+	14.1340i	−0.274149	+	0.474840i
$887$	26.6298	−	46.1242i	0.894142	−	1.54870i	0.0592788	−	0.998241i	$-0.481120\pi$
$887$	26.6298	−	46.1242i	0.894142	−	1.54870i	0.834863	−	0.550458i	$-0.185547\pi$
$888$	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
$892$	7.17260			0.240157
$893$	−1.66025	−	2.87564i	−0.0555583	−	0.0962298i
$894$	38.3596	+	10.2784i	1.28294	+	0.343762i
$895$	−2.62536	+	4.54725i	−0.0877559	+	0.151998i
$896$		0			0
$897$	4.39230	+	16.3923i	0.146655	+	0.547323i
$898$	−11.8923	−	20.5981i	−0.396851	−	0.687367i
$899$	26.7685			0.892780
$900$	−10.2058	−	5.89230i	−0.340192	−	0.196410i
$901$	74.6487			2.48691
$902$	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
$906$	−22.5259	+	22.5259i	−0.748372	+	0.748372i
$907$	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	$0.805560\pi$
$908$	27.6651			0.918098
$909$		−	14.6969i		−	0.487467i
$910$		0			0
$911$	16.5359	+	28.6410i	0.547859	+	0.948919i	0.998421	+	0.0561742i	$0.0178902\pi$
$911$	16.5359	+	28.6410i	0.547859	+	0.948919i	−0.450562	+	0.892745i	$0.648776\pi$
$912$	1.96410	+	7.33013i	0.0650379	+	0.242725i
$913$	−0.882972	+	1.52935i	−0.0292221	+	0.0506142i
$914$	15.5263	−	26.8923i	0.513564	−	0.889518i
$915$	21.8695	+	5.85993i	0.722985	+	0.193723i
$916$	0.240237	+	0.416102i	0.00793764	+	0.0137484i
$917$		0			0
$918$	9.18653	−	34.2846i	0.303201	−	1.13156i
$919$	9.07180			0.299251			0.149625	−	0.988743i	$-0.452193\pi$
$919$	9.07180			0.299251			0.149625	+	0.988743i	$0.452193\pi$
$920$	−2.82843	−	4.89898i	−0.0932505	−	0.161515i
$921$	−1.96410	−	0.526279i	−0.0647193	−	0.0173415i
$922$	−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
$926$	−30.6410			−1.00693
$927$	32.0836	−	18.5235i	1.05376	−	0.608391i
$928$	−4.00000			−0.131306
$929$	15.4040	+	26.6806i	0.505390	+	0.875362i	0.999981	+	0.00623544i	$0.00198482\pi$
$929$	15.4040	+	26.6806i	0.505390	+	0.875362i	−0.494590	+	0.869126i	$0.664682\pi$
$930$	8.48528	−	8.48528i	0.278243	−	0.278243i
$931$		0			0
$932$	−0.0621778	+	0.107695i	−0.00203670	+	0.00352767i
$933$	−9.12436	+	9.12436i	−0.298718	+	0.298718i
$934$	4.58939	+	7.94906i	0.150170	+	0.260101i
$935$	−1.89488			−0.0619693
$936$	4.65874	−	2.68973i	0.152276	−	0.0879165i
$937$	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
$939$	2.81347	+	10.5000i	0.0918140	+	0.342655i
$940$	0.392305	−	0.679492i	0.0127956	−	0.0221626i
$941$	−23.9401	+	41.4655i	−0.780425	+	1.35174i	0.151270	+	0.988493i	$0.451664\pi$
$941$	−23.9401	+	41.4655i	−0.780425	+	1.35174i	−0.931694	+	0.363243i	$0.881670\pi$
$942$	−15.9282	−	4.26795i	−0.518969	−	0.139057i
$943$	−23.5612	−	40.8091i	−0.767257	−	1.32893i
$944$	1.27551			0.0415144
$945$		0			0
$946$	−0.0717968			−0.00233431
$947$	9.06218	+	15.6962i	0.294481	+	0.510056i	0.974864	−	0.222800i	$-0.0715198\pi$
$947$	9.06218	+	15.6962i	0.294481	+	0.510056i	−0.680383	+	0.732857i	$0.738186\pi$
$948$	14.9372	+	4.00240i	0.485137	+	0.129992i
$949$	−4.85641	+	8.41154i	−0.157646	+	0.273050i
$950$	−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	$0.400429\pi$
$954$		−	32.7846i		−	1.06144i
$955$	15.4548			0.500106
$956$	−0.464102	−	0.803848i	−0.0150101	−	0.0259983i
$957$	−1.31268	+	1.31268i	−0.0424328	+	0.0424328i
$958$	−2.07055	+	3.58630i	−0.0668965	+	0.115868i
$959$		0			0
$960$	−1.26795	+	1.26795i	−0.0409229	+	0.0409229i
$961$	−6.89230	−	11.9378i	−0.222332	−	0.385091i
$962$	−13.3843			−0.431526
$963$	−45.1865	−	26.0885i	−1.45612	−	0.840689i
$964$	−6.27603			−0.202137
$965$	−7.79178	−	13.4958i	−0.250826	−	0.434444i
$966$		0			0
$967$	23.7846	−	41.1962i	0.764861	−	1.32478i	−0.175458	−	0.984487i	$-0.556141\pi$
$967$	23.7846	−	41.1962i	0.764861	−	1.32478i	0.940320	−	0.340292i	$-0.110526\pi$
$968$	5.46410	−	9.46410i	0.175623	−	0.304188i
$969$	−50.0709	−	13.4164i	−1.60851	−	0.430998i
$970$	−9.39230	−	16.2679i	−0.301569	−	0.522332i
$971$	−31.2886			−1.00410			−0.502049	−	0.864839i	$-0.667420\pi$
$971$	−31.2886			−1.00410			−0.502049	+	0.864839i	$0.667420\pi$
$972$	−15.0573	−	4.03459i	−0.482963	−	0.129410i
$973$		0			0
$974$	1.39230	+	2.41154i	0.0446123	+	0.0772708i
$975$	11.7846	+	3.15768i	0.377410	+	0.101127i
$976$	−6.31319	+	10.9348i	−0.202080	+	0.350013i
$977$	−0.990381	+	1.71539i	−0.0316851	+	0.0548802i	−0.881433	−	0.472309i	$-0.843421\pi$
$977$	−0.990381	+	1.71539i	−0.0316851	+	0.0548802i	0.849748	+	0.527189i	$0.176754\pi$
$978$	5.97142	+	22.2856i	0.190945	+	0.712616i
$979$	−0.947343	−	1.64085i	−0.0302772	−	0.0524417i
$980$		0			0
$981$	12.8038	+	7.39230i	0.408795	+	0.236018i
$982$	19.3923			0.618833
$983$	6.31319	+	10.9348i	0.201360	+	0.348765i	0.948967	−	0.315376i	$-0.102131\pi$
$983$	6.31319	+	10.9348i	0.201360	+	0.348765i	−0.747607	+	0.664141i	$0.768797\pi$
$984$	−10.5622	+	10.5622i	−0.336710	+	0.336710i
$985$	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
$989$	1.46410			0.0465557
$990$			0.832204i			0.0264492i
$991$	50.2487			1.59620			0.798101	−	0.602523i	$-0.205838\pi$
$991$	50.2487			1.59620			0.798101	+	0.602523i	$0.205838\pi$
$992$	3.34607	+	5.79555i	0.106238	+	0.184009i
$993$	5.13922	+	19.1798i	0.163088	+	0.608653i
$994$		0			0
$995$	13.6077	−	23.5692i	0.431393	−	0.747194i
$996$	−11.0263	−	2.95448i	−0.349381	−	0.0936164i
$997$	−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	$-0.369685\pi$
$998$	33.3923			1.05701
$999$	27.4249	+	27.4249i	0.867684	+	0.867684i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
882.2.e.s.373.2		8	7.4	even	3
882.2.e.s.373.3		8	7.3	odd	6
882.2.e.s.655.2		8	63.16	even	3
882.2.e.s.655.3		8	63.61	odd	6
882.2.f.q.295.1	✓	8	63.34	odd	6	inner
882.2.f.q.295.4	yes	8	9.7	even	3	inner
882.2.f.q.589.1	yes	8	7.6	odd	2	inner
882.2.f.q.589.4	yes	8	1.1	even	1	trivial
882.2.h.q.67.2		8	7.2	even	3
882.2.h.q.67.3		8	7.5	odd	6
882.2.h.q.79.1		8	63.25	even	3
882.2.h.q.79.4		8	63.52	odd	6
2646.2.e.q.1549.2		8	21.17	even	6
2646.2.e.q.1549.3		8	21.11	odd	6
2646.2.e.q.2125.2		8	63.47	even	6
2646.2.e.q.2125.3		8	63.2	odd	6
2646.2.f.r.883.2		8	63.20	even	6
2646.2.f.r.883.3		8	9.2	odd	6
2646.2.f.r.1765.2		8	21.20	even	2
2646.2.f.r.1765.3		8	3.2	odd	2
2646.2.h.t.361.2		8	21.2	odd	6
2646.2.h.t.361.3		8	21.5	even	6
2646.2.h.t.667.2		8	63.11	odd	6
2646.2.h.t.667.3		8	63.38	even	6
7938.2.a.ci.1.2		4	9.5	odd	6
7938.2.a.ci.1.3		4	63.41	even	6
7938.2.a.cp.1.2		4	63.13	odd	6
7938.2.a.cp.1.3		4	9.4	even	3

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 882 = 2 \cdot 3^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	882.f (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 - 0.866025i) q^{2} +(1.67303 + 0.448288i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.517638 + 0.896575i) q^{5} +(-0.448288 - 1.67303i) q^{6} +1.00000 q^{8} +(2.59808 + 1.50000i) q^{9} +1.03528 q^{10} +(0.133975 + 0.232051i) q^{11} +(-1.22474 + 1.22474i) q^{12} +(0.896575 - 1.55291i) q^{13} +(-1.26795 + 1.26795i) q^{15} +(-0.500000 - 0.866025i) q^{16} +6.83083 q^{17} -3.00000i q^{18} -4.38134 q^{19} +(-0.517638 - 0.896575i) q^{20} +(0.133975 - 0.232051i) q^{22} +(-2.73205 + 4.73205i) q^{23} +(1.67303 + 0.448288i) q^{24} +(1.96410 + 3.40192i) q^{25} -1.79315 q^{26} +(3.67423 + 3.67423i) q^{27} +(2.00000 + 3.46410i) q^{29} +(1.73205 + 0.464102i) q^{30} +(3.34607 - 5.79555i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(0.120118 + 0.448288i) q^{33} +(-3.41542 - 5.91567i) q^{34} +(-2.59808 + 1.50000i) q^{36} +7.46410 q^{37} +(2.19067 + 3.79435i) q^{38} +(2.19615 - 2.19615i) q^{39} +(-0.517638 + 0.896575i) q^{40} +(-4.31199 + 7.46859i) q^{41} +(-0.133975 - 0.232051i) q^{43} -0.267949 q^{44} +(-2.68973 + 1.55291i) q^{45} +5.46410 q^{46} +(0.378937 + 0.656339i) q^{47} +(-0.448288 - 1.67303i) q^{48} +(1.96410 - 3.40192i) q^{50} +(11.4282 + 3.06218i) q^{51} +(0.896575 + 1.55291i) q^{52} +10.9282 q^{53} +(1.34486 - 5.01910i) q^{54} -0.277401 q^{55} +(-7.33013 - 1.96410i) q^{57} +(2.00000 - 3.46410i) q^{58} +(-0.637756 + 1.10463i) q^{59} +(-0.464102 - 1.73205i) q^{60} +(-6.31319 - 10.9348i) q^{61} -6.69213 q^{62} +1.00000 q^{64} +(0.928203 + 1.60770i) q^{65} +(0.328169 - 0.328169i) q^{66} +(-6.23205 + 10.7942i) q^{67} +(-3.41542 + 5.91567i) q^{68} +(-6.69213 + 6.69213i) q^{69} +9.46410 q^{71} +(2.59808 + 1.50000i) q^{72} -5.41662 q^{73} +(-3.73205 - 6.46410i) q^{74} +(1.76097 + 6.57201i) q^{75} +(2.19067 - 3.79435i) q^{76} +(-3.00000 - 0.803848i) q^{78} +(-4.46410 - 7.73205i) q^{79} +1.03528 q^{80} +(4.50000 + 7.79423i) q^{81} +8.62398 q^{82} +(3.29530 + 5.70762i) q^{83} +(-3.53590 + 6.12436i) q^{85} +(-0.133975 + 0.232051i) q^{86} +(1.79315 + 6.69213i) q^{87} +(0.133975 + 0.232051i) q^{88} -7.07107 q^{89} +(2.68973 + 1.55291i) q^{90} +(-2.73205 - 4.73205i) q^{92} +(8.19615 - 8.19615i) q^{93} +(0.378937 - 0.656339i) q^{94} +(2.26795 - 3.92820i) q^{95} +(-1.22474 + 1.22474i) q^{96} +(-9.07227 - 15.7136i) q^{97} +0.803848i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 4 q^{2} - 4 q^{4} + 8 q^{8} + 8 q^{11} - 24 q^{15} - 4 q^{16} + 8 q^{22} - 8 q^{23} - 12 q^{25} + 16 q^{29} - 4 q^{32} + 32 q^{37} - 24 q^{39} - 8 q^{43} - 16 q^{44} + 16 q^{46} - 12 q^{50} + 36 q^{51}+ \cdots + 32 q^{95}+O(q^{100}) \) 8 * q - 4 * q^2 - 4 * q^4 + 8 * q^8 + 8 * q^11 - 24 * q^15 - 4 * q^16 + 8 * q^22 - 8 * q^23 - 12 * q^25 + 16 * q^29 - 4 * q^32 + 32 * q^37 - 24 * q^39 - 8 * q^43 - 16 * q^44 + 16 * q^46 - 12 * q^50 + 36 * q^51 + 32 * q^53 - 24 * q^57 + 16 * q^58 + 24 * q^60 + 8 * q^64 - 48 * q^65 - 36 * q^67 + 48 * q^71 - 16 * q^74 - 24 * q^78 - 8 * q^79 + 36 * q^81 - 56 * q^85 - 8 * q^86 + 8 * q^88 - 8 * q^92 + 24 * q^93 + 32 * q^95

Introduction

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