LMFDB - Embedded newform 882.2.h.q.79.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [882,2,Mod(67,882)] 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([2, 4])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("882.67"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 882 = 2 \cdot 3^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	882.h (of order $3$, degree $2$, not 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			79.1
Root			$-0.258819 - 0.965926i$ of defining polynomial
Character	$\chi$	$=$	882.79
Dual form			882.2.h.q.67.2

$q$-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} +(-1.22474 - 1.22474i) q^{3} +(-0.500000 + 0.866025i) q^{4} +1.03528 q^{5} +(-0.448288 + 1.67303i) q^{6} +1.00000 q^{8} +3.00000i q^{9} +(-0.517638 - 0.896575i) q^{10} -0.267949 q^{11} +(1.67303 - 0.448288i) q^{12} +(0.896575 + 1.55291i) q^{13} +(-1.26795 - 1.26795i) q^{15} +(-0.500000 - 0.866025i) 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} +5.46410 q^{23} +(-1.22474 - 1.22474i) q^{24} -3.92820 q^{25} +(0.896575 - 1.55291i) q^{26} +(3.67423 - 3.67423i) q^{27} +(2.00000 - 3.46410i) q^{29} +(-0.464102 + 1.73205i) q^{30} +(3.34607 - 5.79555i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(0.328169 + 0.328169i) q^{33} +(-3.41542 + 5.91567i) q^{34} +(-2.59808 - 1.50000i) q^{36} +(-3.73205 + 6.46410i) q^{37} -4.38134 q^{38} +(0.803848 - 3.00000i) q^{39} +1.03528 q^{40} +(-4.31199 - 7.46859i) q^{41} +(-0.133975 + 0.232051i) q^{43} +(0.133975 - 0.232051i) q^{44} +3.10583i q^{45} +(-2.73205 - 4.73205i) q^{46} +(0.378937 + 0.656339i) q^{47} +(-0.448288 + 1.67303i) q^{48} +(1.96410 + 3.40192i) q^{50} +(-3.06218 + 11.4282i) q^{51} -1.79315 q^{52} +(-5.46410 - 9.46410i) q^{53} +(-5.01910 - 1.34486i) q^{54} -0.277401 q^{55} +(-7.33013 + 1.96410i) q^{57} -4.00000 q^{58} +(-0.637756 + 1.10463i) q^{59} +(1.73205 - 0.464102i) q^{60} +(-6.31319 - 10.9348i) q^{61} -6.69213 q^{62} +1.00000 q^{64} +(0.928203 + 1.60770i) q^{65} +(0.120118 - 0.448288i) q^{66} +(-6.23205 + 10.7942i) q^{67} +6.83083 q^{68} +(-6.69213 - 6.69213i) q^{69} +9.46410 q^{71} +3.00000i q^{72} +(2.70831 + 4.69093i) q^{73} +7.46410 q^{74} +(4.81105 + 4.81105i) q^{75} +(2.19067 + 3.79435i) q^{76} +(-3.00000 + 0.803848i) q^{78} +(-4.46410 - 7.73205i) q^{79} +(-0.517638 - 0.896575i) q^{80} -9.00000 q^{81} +(-4.31199 + 7.46859i) q^{82} +(3.29530 - 5.70762i) q^{83} +(-3.53590 - 6.12436i) q^{85} +0.267949 q^{86} +(-6.69213 + 1.79315i) q^{87} -0.267949 q^{88} +(3.53553 - 6.12372i) q^{89} +(2.68973 - 1.55291i) q^{90} +(-2.73205 + 4.73205i) q^{92} +(-11.1962 + 3.00000i) q^{93} +(0.378937 - 0.656339i) q^{94} +(2.26795 - 3.92820i) q^{95} +(1.67303 - 0.448288i) 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} - 16 q^{11} - 24 q^{15} - 4 q^{16} + 8 q^{22} + 16 q^{23} + 24 q^{25} + 16 q^{29} + 24 q^{30} - 4 q^{32} - 16 q^{37} + 48 q^{39} - 8 q^{43} + 8 q^{44} - 8 q^{46} - 12 q^{50}+ \cdots + 32 q^{95}+O(q^{100}) $ 8 * q - 4 * q^2 - 4 * q^4 + 8 * q^8 - 16 * q^11 - 24 * q^15 - 4 * q^16 + 8 * q^22 + 16 * q^23 + 24 * q^25 + 16 * q^29 + 24 * q^30 - 4 * q^32 - 16 * q^37 + 48 * q^39 - 8 * q^43 + 8 * q^44 - 8 * q^46 - 12 * q^50 + 24 * q^51 - 16 * q^53 - 24 * q^57 - 32 * q^58 + 8 * q^64 - 48 * q^65 - 36 * q^67 + 48 * q^71 + 32 * q^74 - 24 * q^78 - 8 * q^79 - 72 * q^81 - 56 * q^85 + 16 * q^86 - 16 * q^88 - 8 * q^92 - 48 * q^93 + 32 * q^95

Character values

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

$n$	$199$	$785$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$

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 $

$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$3$	−1.22474	−	1.22474i	−0.707107	−	0.707107i
$3$	−1.22474	−	1.22474i	−0.707107	−	0.707107i
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	1.03528			0.462990			0.231495	−	0.972836i	$-0.425638\pi$
$5$	1.03528			0.462990			0.231495	+	0.972836i	$0.425638\pi$
$6$	−0.448288	+	1.67303i	−0.183013	+	0.683013i
$7$		0			0
$7$		0			0
$8$	1.00000			0.353553
$9$			3.00000i			1.00000i
$10$	−0.517638	−	0.896575i	−0.163692	−	0.283522i
$11$	−0.267949			−0.0807897			−0.0403949	−	0.999184i	$-0.512862\pi$
$11$	−0.267949			−0.0807897			−0.0403949	+	0.999184i	$0.512862\pi$
$12$	1.67303	−	0.448288i	0.482963	−	0.129410i
$13$	0.896575	+	1.55291i	0.248665	+	0.430701i	0.963156	−	0.268944i	$-0.0866747\pi$
$13$	0.896575	+	1.55291i	0.248665	+	0.430701i	−0.714490	+	0.699645i	$0.753341\pi$
$14$		0			0
$15$	−1.26795	−	1.26795i	−0.327383	−	0.327383i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−3.41542	−	5.91567i	−0.828360	−	1.43476i	−0.899324	−	0.437283i	$-0.855941\pi$
$17$	−3.41542	−	5.91567i	−0.828360	−	1.43476i	0.0709642	−	0.997479i	$-0.477392\pi$
$18$	2.59808	−	1.50000i	0.612372	−	0.353553i
$19$	2.19067	−	3.79435i	0.502574	−	0.870484i	−0.497421	−	0.867509i	$-0.665720\pi$
$19$	2.19067	−	3.79435i	0.502574	−	0.870484i	0.999996	−	0.00297513i	$-0.000947015\pi$
$20$	−0.517638	+	0.896575i	−0.115747	+	0.200480i
$21$		0			0
$22$	0.133975	+	0.232051i	0.0285635	+	0.0494734i
$23$	5.46410			1.13934			0.569672	−	0.821872i	$-0.307070\pi$
$23$	5.46410			1.13934			0.569672	+	0.821872i	$0.307070\pi$
$24$	−1.22474	−	1.22474i	−0.250000	−	0.250000i
$25$	−3.92820			−0.785641
$26$	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	$0.0455477\pi$
$30$	−0.464102	+	1.73205i	−0.0847330	+	0.316228i
$31$	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
$33$	0.328169	+	0.328169i	0.0571270	+	0.0571270i
$34$	−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	0.377092	+	0.926176i	$0.376924\pi$
$37$	−3.73205	+	6.46410i	−0.613545	+	1.06269i	−0.990638	+	0.136516i	$0.956409\pi$
$38$	−4.38134			−0.710747
$39$	0.803848	−	3.00000i	0.128719	−	0.480384i
$40$	1.03528			0.163692
$41$	−4.31199	−	7.46859i	−0.673420	−	1.16640i	−0.976928	−	0.213569i	$-0.931491\pi$
$41$	−4.31199	−	7.46859i	−0.673420	−	1.16640i	0.303508	−	0.952829i	$-0.401842\pi$
$42$		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
$45$			3.10583i			0.462990i
$46$	−2.73205	−	4.73205i	−0.402819	−	0.697703i
$47$	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
$51$	−3.06218	+	11.4282i	−0.428791	+	1.60027i
$52$	−1.79315			−0.248665
$53$	−5.46410	−	9.46410i	−0.750552	−	1.29999i	−0.947555	−	0.319592i	$-0.896454\pi$
$53$	−5.46410	−	9.46410i	−0.750552	−	1.29999i	0.197003	−	0.980403i	$-0.436879\pi$
$54$	−5.01910	−	1.34486i	−0.683013	−	0.183013i
$55$	−0.277401			−0.0374048
$56$		0			0
$57$	−7.33013	+	1.96410i	−0.970899	+	0.260152i
$58$	−4.00000			−0.525226
$59$	−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	$0.193126\pi$
$60$	1.73205	−	0.464102i	0.223607	−	0.0599153i
$61$	−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
$66$	0.120118	−	0.448288i	0.0147855	−	0.0551804i
$67$	−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	$0.891196\pi$
$68$	6.83083			0.828360
$69$	−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	$0.310189\pi$
$72$			3.00000i			0.353553i
$73$	2.70831	+	4.69093i	0.316984	+	0.549032i	0.979857	−	0.199700i	$-0.0639967\pi$
$73$	2.70831	+	4.69093i	0.316984	+	0.549032i	−0.662874	+	0.748731i	$0.730663\pi$
$74$	7.46410			0.867684
$75$	4.81105	+	4.81105i	0.555532	+	0.555532i
$76$	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	$-0.334161\pi$
$80$	−0.517638	−	0.896575i	−0.0578737	−	0.100240i
$81$	−9.00000			−1.00000
$82$	−4.31199	+	7.46859i	−0.476180	+	0.824768i
$83$	3.29530	−	5.70762i	0.361706	−	0.626493i	−0.626536	−	0.779393i	$-0.715528\pi$
$83$	3.29530	−	5.70762i	0.361706	−	0.626493i	0.988242	+	0.152900i	$0.0488611\pi$
$84$		0			0
$85$	−3.53590	−	6.12436i	−0.383522	−	0.664280i
$86$	0.267949			0.0288937
$87$	−6.69213	+	1.79315i	−0.717472	+	0.192246i
$88$	−0.267949			−0.0285635
$89$	3.53553	−	6.12372i	0.374766	−	0.649113i	−0.615526	−	0.788116i	$-0.711056\pi$
$89$	3.53553	−	6.12372i	0.374766	−	0.649113i	0.990292	+	0.139003i	$0.0443898\pi$
$90$	2.68973	−	1.55291i	0.283522	−	0.163692i
$91$		0			0
$92$	−2.73205	+	4.73205i	−0.284836	+	0.493350i
$93$	−11.1962	+	3.00000i	−1.16099	+	0.311086i
$94$	0.378937	−	0.656339i	0.0390844	−	0.0676962i
$95$	2.26795	−	3.92820i	0.232687	−	0.403025i
$96$	1.67303	−	0.448288i	0.170753	−	0.0457532i
$97$	−9.07227	+	15.7136i	−0.921149	+	1.59548i	−0.123510	+	0.992343i	$0.539415\pi$
$97$	−9.07227	+	15.7136i	−0.921149	+	1.59548i	−0.797640	+	0.603134i	$0.793918\pi$
$98$		0			0
$99$		−	0.803848i		−	0.0807897i
$100$	1.96410	−	3.40192i	0.196410	−	0.340192i
$101$	4.89898			0.487467			0.243733	−	0.969842i	$-0.421628\pi$
$101$	4.89898			0.487467			0.243733	+	0.969842i	$0.421628\pi$
$102$	11.4282	−	3.06218i	1.13156	−	0.303201i
$103$	−12.3490			−1.21678			−0.608391	−	0.793638i	$-0.708185\pi$
$103$	−12.3490			−1.21678			−0.608391	+	0.793638i	$0.708185\pi$
$104$	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	−0.0486244	−	0.998817i	$-0.515484\pi$
$107$	8.69615	−	15.0622i	0.840689	−	1.45612i	0.889313	−	0.457299i	$-0.151183\pi$
$108$	1.34486	+	5.01910i	0.129410	+	0.482963i
$109$	−2.46410	−	4.26795i	−0.236018	−	0.408795i	0.723550	−	0.690272i	$-0.242509\pi$
$109$	−2.46410	−	4.26795i	−0.236018	−	0.408795i	−0.959568	+	0.281477i	$0.909176\pi$
$110$	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	0.981689	−	0.190490i	$-0.0610077\pi$
$113$	3.46410	+	6.00000i	0.325875	+	0.564433i	−0.655814	+	0.754923i	$0.727674\pi$
$114$	5.36603	+	5.36603i	0.502574	+	0.502574i
$115$	5.65685			0.527504
$116$	2.00000	+	3.46410i	0.185695	+	0.321634i
$117$	−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
$121$	−10.9282			−0.993473
$122$	−6.31319	+	10.9348i	−0.571570	+	0.989988i
$123$	−3.86603	+	14.4282i	−0.348588	+	1.30095i
$124$	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
$129$	0.448288	−	0.120118i	0.0394695	−	0.0105758i
$130$	0.928203	−	1.60770i	0.0814088	−	0.141004i
$131$	−10.9348			−0.955375			−0.477688	−	0.878530i	$-0.658525\pi$
$131$	−10.9348			−0.955375			−0.477688	+	0.878530i	$0.658525\pi$
$132$	−0.448288	+	0.120118i	−0.0390184	+	0.0104550i
$133$		0			0
$134$	12.4641			1.07673
$135$	3.80385	−	3.80385i	0.327383	−	0.327383i
$136$	−3.41542	−	5.91567i	−0.292869	−	0.507265i
$137$	8.66025			0.739895			0.369948	−	0.929053i	$-0.379376\pi$
$137$	8.66025			0.739895			0.369948	+	0.929053i	$0.379376\pi$
$138$	−2.44949	+	9.14162i	−0.208514	+	0.778186i
$139$	0.397520	+	0.688524i	0.0337172	+	0.0583999i	0.882392	−	0.470516i	$-0.155932\pi$
$139$	0.397520	+	0.688524i	0.0337172	+	0.0583999i	−0.848674	+	0.528916i	$0.822599\pi$
$140$		0			0
$141$	0.339746	−	1.26795i	0.0286118	−	0.106781i
$142$	−4.73205	−	8.19615i	−0.397105	−	0.687806i
$143$	−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
$149$	22.9282			1.87835			0.939176	−	0.343437i	$-0.111591\pi$
$149$	22.9282			1.87835			0.939176	+	0.343437i	$0.111591\pi$
$150$	1.76097	−	6.57201i	0.143782	−	0.536603i
$151$	18.3923			1.49674			0.748372	−	0.663279i	$-0.230836\pi$
$151$	18.3923			1.49674			0.748372	+	0.663279i	$0.230836\pi$
$152$	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
$156$	2.19615	+	2.19615i	0.175833	+	0.175833i
$157$	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
$159$	−4.89898	+	18.2832i	−0.388514	+	1.44996i
$160$	−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	−0.478011	−	0.878354i	$-0.658642\pi$
$163$	6.66025	−	11.5359i	0.521671	−	0.903561i	0.999682	−	0.0252074i	$-0.00802461\pi$
$164$	8.62398			0.673420
$165$	0.339746	+	0.339746i	0.0264492	+	0.0264492i
$166$	−6.59059			−0.511529
$167$	0.757875	+	1.31268i	0.0586461	+	0.101578i	0.893858	−	0.448350i	$-0.147988\pi$
$167$	0.757875	+	1.31268i	0.0586461	+	0.101578i	−0.835212	+	0.549928i	$0.814655\pi$
$168$		0			0
$169$	4.89230	−	8.47372i	0.376331	−	0.651825i
$170$	−3.53590	+	6.12436i	−0.271191	+	0.469717i
$171$	11.3831	+	6.57201i	0.870484	+	0.502574i
$172$	−0.133975	−	0.232051i	−0.0102155	−	0.0176937i
$173$	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
$177$	2.13397	−	0.571797i	0.160399	−	0.0429789i
$178$	−7.07107			−0.529999
$179$	−2.53590	−	4.39230i	−0.189542	−	0.328296i	0.755556	−	0.655084i	$-0.227367\pi$
$179$	−2.53590	−	4.39230i	−0.189542	−	0.328296i	−0.945098	+	0.326788i	$0.894034\pi$
$180$	−2.68973	−	1.55291i	−0.200480	−	0.115747i
$181$	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
$184$	5.46410			0.402819
$185$	−3.86370	+	6.69213i	−0.284065	+	0.492015i
$186$	8.19615	+	8.19615i	0.600971	+	0.600971i
$187$	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	$-0.348274\pi$
$192$	−1.22474	−	1.22474i	−0.0883883	−	0.0883883i
$193$	−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	$0.984427\pi$
$194$	18.1445			1.30270
$195$	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
$199$	13.1440	+	22.7661i	0.931755	+	1.61385i	0.780320	+	0.625380i	$0.215056\pi$
$199$	13.1440	+	22.7661i	0.931755	+	1.61385i	0.151435	+	0.988467i	$0.451611\pi$
$200$	−3.92820			−0.277766
$201$	20.8528	−	5.58750i	1.47085	−	0.394112i
$202$	−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
$206$	6.17449	+	10.6945i	0.430197	+	0.745124i
$207$			16.3923i			1.13934i
$208$	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	$-0.392542\pi$
$212$	10.9282			0.750552
$213$	−11.5911	−	11.5911i	−0.794210	−	0.794210i
$214$	−17.3923			−1.18891
$215$	−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
$219$	2.42820	−	9.06218i	0.164083	−	0.612365i
$220$	0.138701	−	0.240237i	0.00935120	−	0.0161968i
$221$	6.12436	−	10.6077i	0.411969	−	0.713551i
$222$	−9.14162	−	9.14162i	−0.613545	−	0.613545i
$223$	−3.58630	+	6.21166i	−0.240157	+	0.415963i	−0.960759	−	0.277385i	$-0.910532\pi$
$223$	−3.58630	+	6.21166i	−0.240157	+	0.415963i	0.720602	+	0.693349i	$0.243865\pi$
$224$		0			0
$225$		−	11.7846i		−	0.785641i
$226$	3.46410	−	6.00000i	0.230429	−	0.399114i
$227$	27.6651			1.83620			0.918098	−	0.396352i	$-0.129724\pi$
$227$	27.6651			1.83620			0.918098	+	0.396352i	$0.129724\pi$
$228$	1.96410	−	7.33013i	0.130076	−	0.485450i
$229$	−0.480473			−0.0317506			−0.0158753	−	0.999874i	$-0.505053\pi$
$229$	−0.480473			−0.0317506			−0.0158753	+	0.999874i	$0.505053\pi$
$230$	−2.82843	−	4.89898i	−0.186501	−	0.323029i
$231$		0			0
$232$	2.00000	−	3.46410i	0.131306	−	0.227429i
$233$	−0.0621778	+	0.107695i	−0.00407340	+	0.00705534i	−0.868055	−	0.496468i	$-0.834630\pi$
$233$	−0.0621778	+	0.107695i	−0.00407340	+	0.00705534i	0.863982	+	0.503524i	$0.167963\pi$
$234$	4.65874	+	2.68973i	0.304552	+	0.175833i
$235$	0.392305	+	0.679492i	0.0255911	+	0.0443252i
$236$	−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	0.850625	−	0.525773i	$-0.176224\pi$
$239$	−0.464102	−	0.803848i	−0.0300202	−	0.0519966i	−0.880645	+	0.473776i	$0.842891\pi$
$240$	−0.464102	+	1.73205i	−0.0299576	+	0.111803i
$241$	−6.27603			−0.404275			−0.202137	−	0.979357i	$-0.564789\pi$
$241$	−6.27603			−0.404275			−0.202137	+	0.979357i	$0.564789\pi$
$242$	5.46410	+	9.46410i	0.351246	+	0.608375i
$243$	11.0227	+	11.0227i	0.707107	+	0.707107i
$244$	12.6264			0.808322
$245$		0			0
$246$	14.4282	−	3.86603i	0.919909	−	0.246489i
$247$	7.85641			0.499891
$248$	3.34607	−	5.79555i	0.212475	−	0.368018i
$249$	−11.0263	+	2.95448i	−0.698762	+	0.187233i
$250$	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
$255$	−3.17020	+	11.8313i	−0.198526	+	0.740908i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−10.0382			−0.626165			−0.313083	−	0.949726i	$-0.601362\pi$
$257$	−10.0382			−0.626165			−0.313083	+	0.949726i	$0.601362\pi$
$258$	−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
$263$	−8.53590			−0.526346			−0.263173	−	0.964749i	$-0.584769\pi$
$263$	−8.53590			−0.526346			−0.263173	+	0.964749i	$0.584769\pi$
$264$	0.328169	+	0.328169i	0.0201974	+	0.0201974i
$265$	−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
$269$	−2.82843	−	4.89898i	−0.172452	−	0.298696i	0.766824	−	0.641857i	$-0.221836\pi$
$269$	−2.82843	−	4.89898i	−0.172452	−	0.298696i	−0.939277	+	0.343161i	$0.888502\pi$
$270$	−5.19615	−	1.39230i	−0.316228	−	0.0847330i
$271$	6.55343	−	11.3509i	0.398093	−	0.689516i	−0.595398	−	0.803431i	$-0.703006\pi$
$271$	6.55343	−	11.3509i	0.398093	−	0.689516i	0.993491	+	0.113914i	$0.0363390\pi$
$272$	−3.41542	+	5.91567i	−0.207090	+	0.358690i
$273$		0			0
$274$	−4.33013	−	7.50000i	−0.261593	−	0.453092i
$275$	1.05256			0.0634717
$276$	9.14162	−	2.44949i	0.550261	−	0.147442i
$277$	31.4641			1.89049			0.945247	−	0.326355i	$-0.105820\pi$
$277$	31.4641			1.89049			0.945247	+	0.326355i	$0.105820\pi$
$278$	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	$0.987877\pi$
$282$	−1.26795	+	0.339746i	−0.0755053	+	0.0202316i
$283$	−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
$285$	−7.58871	+	2.03339i	−0.449516	+	0.120447i
$286$	−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
$290$	−4.14110			−0.243174
$291$	30.3564	−	8.13397i	1.77952	−	0.476822i
$292$	−5.41662			−0.316984
$293$	−4.62158	−	8.00481i	−0.269995	−	0.467646i	0.698865	−	0.715254i	$-0.253689\pi$
$293$	−4.62158	−	8.00481i	−0.269995	−	0.467646i	−0.968860	+	0.247608i	$0.920356\pi$
$294$		0			0
$295$	−0.660254	+	1.14359i	−0.0384415	+	0.0665826i
$296$	−3.73205	+	6.46410i	−0.216921	+	0.375718i
$297$	−0.984508	+	0.984508i	−0.0571270	+	0.0571270i
$298$	−11.4641	−	19.8564i	−0.664098	−	1.15025i
$299$	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
$303$	−6.00000	−	6.00000i	−0.344691	−	0.344691i
$304$	−4.38134			−0.251287
$305$	−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	$-0.510666\pi$
$307$	−1.17398			−0.0670024			−0.0335012	+	0.999439i	$0.510666\pi$
$308$		0			0
$309$	15.1244	+	15.1244i	0.860395	+	0.860395i
$310$	−6.92820			−0.393496
$311$	−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	$0.234412\pi$
$312$	0.803848	−	3.00000i	0.0455089	−	0.169842i
$313$	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	$0.572782\pi$
$318$	18.2832	−	4.89898i	1.02527	−	0.274721i
$319$	−0.535898	+	0.928203i	−0.0300045	+	0.0519694i
$320$	1.03528			0.0578737
$321$	−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
$326$	−13.3205			−0.737755
$327$	−2.20925	+	8.24504i	−0.122172	+	0.455952i
$328$	−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	$0.731308\pi$
$332$	3.29530	+	5.70762i	0.180853	+	0.313246i
$333$	−19.3923	−	11.1962i	−1.06269	−	0.613545i
$334$	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	$0.772271\pi$
$338$	−9.78461			−0.532213
$339$	3.10583	−	11.5911i	0.168685	−	0.629543i
$340$	7.07180			0.383522
$341$	−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
$345$	−6.92820	−	6.92820i	−0.373002	−	0.373002i
$346$	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	$0.0838115\pi$
$348$	1.79315	−	6.69213i	0.0961230	−	0.358736i
$349$	−4.00240	+	6.93237i	−0.214244	+	0.371081i	−0.953038	−	0.302850i	$-0.902062\pi$
$349$	−4.00240	+	6.93237i	−0.214244	+	0.371081i	0.738795	+	0.673931i	$0.235395\pi$
$350$		0			0
$351$	9.00000	+	2.41154i	0.480384	+	0.128719i
$352$	0.133975	−	0.232051i	0.00714087	−	0.0123683i
$353$	−25.0125			−1.33128			−0.665641	−	0.746272i	$-0.731842\pi$
$353$	−25.0125			−1.33128			−0.665641	+	0.746272i	$0.731842\pi$
$354$	−1.56218	−	1.56218i	−0.0830288	−	0.0830288i
$355$	9.79796			0.520022
$356$	3.53553	+	6.12372i	0.187383	+	0.324557i
$357$		0			0
$358$	−2.53590	+	4.39230i	−0.134026	+	0.232141i
$359$	−3.73205	+	6.46410i	−0.196970	+	0.341162i	−0.947545	−	0.319624i	$-0.896444\pi$
$359$	−3.73205	+	6.46410i	−0.196970	+	0.341162i	0.750574	+	0.660786i	$0.229777\pi$
$360$			3.10583i			0.163692i
$361$	−0.0980762	−	0.169873i	−0.00516191	−	0.00894068i
$362$	−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
$366$	21.1244	−	5.66025i	1.10419	−	0.295866i
$367$	−18.5606			−0.968858			−0.484429	−	0.874831i	$-0.660973\pi$
$367$	−18.5606			−0.968858			−0.484429	+	0.874831i	$0.660973\pi$
$368$	−2.73205	−	4.73205i	−0.142418	−	0.246675i
$369$	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
$373$	−10.7846			−0.558406			−0.279203	−	0.960232i	$-0.590070\pi$
$373$	−10.7846			−0.558406			−0.279203	+	0.960232i	$0.590070\pi$
$374$	0.915158	−	1.58510i	0.0473217	−	0.0819636i
$375$	11.3205	+	11.3205i	0.584589	+	0.584589i
$376$	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
$381$	−16.4901	−	16.4901i	−0.844813	−	0.844813i
$382$	−7.46410	+	12.9282i	−0.381897	+	0.661464i
$383$	−27.3233			−1.39616			−0.698078	−	0.716021i	$-0.745961\pi$
$383$	−27.3233			−1.39616			−0.698078	+	0.716021i	$0.745961\pi$
$384$	−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
$389$	8.00000			0.405616			0.202808	−	0.979219i	$-0.434993\pi$
$389$	8.00000			0.405616			0.202808	+	0.979219i	$0.434993\pi$
$390$	−3.10583	+	0.832204i	−0.157270	+	0.0421403i
$391$	−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
$395$	−4.62158	−	8.00481i	−0.232537	−	0.402766i
$396$	0.696152	+	0.401924i	0.0349830	+	0.0201974i
$397$	6.55343	−	11.3509i	0.328907	−	0.569684i	−0.653388	−	0.757023i	$-0.726653\pi$
$397$	6.55343	−	11.3509i	0.328907	−	0.569684i	0.982295	+	0.187339i	$0.0599863\pi$
$398$	13.1440	−	22.7661i	0.658850	−	1.14116i
$399$		0			0
$400$	1.96410	+	3.40192i	0.0982051	+	0.170096i
$401$	−23.7846			−1.18775			−0.593873	−	0.804559i	$-0.702402\pi$
$401$	−23.7846			−1.18775			−0.593873	+	0.804559i	$0.702402\pi$
$402$	−15.2653	−	15.2653i	−0.761366	−	0.761366i
$403$	12.0000			0.597763
$404$	−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
$408$	−3.06218	+	11.4282i	−0.151600	+	0.565780i
$409$	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
$411$	−10.6066	−	10.6066i	−0.523185	−	0.523185i
$412$	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
$416$	−1.79315			−0.0879165
$417$	0.356406	−	1.33013i	0.0174533	−	0.0651366i
$418$	1.17398			0.0574211
$419$	18.0938	+	31.3393i	0.883939	+	1.53103i	0.846925	+	0.531712i	$0.178451\pi$
$419$	18.0938	+	31.3393i	0.883939	+	1.53103i	0.0370132	+	0.999315i	$0.488216\pi$
$420$		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
$425$	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
$429$	−0.215390	+	0.803848i	−0.0103991	+	0.0388101i
$430$	0.277401			0.0133775
$431$	5.07180	+	8.78461i	0.244300	+	0.423140i	0.961935	−	0.273280i	$-0.0881085\pi$
$431$	5.07180	+	8.78461i	0.244300	+	0.423140i	−0.717635	+	0.696420i	$0.754775\pi$
$432$	−5.01910	−	1.34486i	−0.241481	−	0.0647048i
$433$	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
$436$	4.92820			0.236018
$437$	11.9700	−	20.7327i	0.572605	−	0.991781i
$438$	−9.06218	+	2.42820i	−0.433008	+	0.116024i
$439$	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	$0.960066\pi$
$444$	−3.34607	+	12.4877i	−0.158797	+	0.592639i
$445$	3.66025	−	6.33975i	0.173513	−	0.300533i
$446$	7.17260			0.339633
$447$	−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
$451$	1.15539	+	2.00120i	0.0544054	+	0.0942329i
$452$	−6.92820			−0.325875
$453$	−22.5259	−	22.5259i	−1.05836	−	1.05836i
$454$	−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	$0.574577\pi$
$458$	0.240237	+	0.416102i	0.0112255	+	0.0194432i
$459$	−34.2846	−	9.18653i	−1.60027	−	0.428791i
$460$	−2.82843	+	4.89898i	−0.131876	+	0.228416i
$461$	−5.51815	+	9.55772i	−0.257006	+	0.445148i	−0.965438	−	0.260631i	$-0.916069\pi$
$461$	−5.51815	+	9.55772i	−0.257006	+	0.445148i	0.708432	+	0.705779i	$0.249403\pi$
$462$		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	$0.581121\pi$
$464$	−4.00000			−0.185695
$465$	−11.5911	+	3.10583i	−0.537525	+	0.144029i
$466$	0.124356			0.00576066
$467$	4.58939	−	7.94906i	0.212372	−	0.367839i	−0.740085	−	0.672514i	$-0.765215\pi$
$467$	4.58939	−	7.94906i	0.212372	−	0.367839i	0.952456	+	0.304675i	$0.0985479\pi$
$468$		−	5.37945i		−	0.248665i
$469$		0			0
$470$	0.392305	−	0.679492i	0.0180957	−	0.0313426i
$471$	−15.9282	+	4.26795i	−0.733933	+	0.196657i
$472$	−0.637756	+	1.10463i	−0.0293551	+	0.0508446i
$473$	0.0358984	−	0.0621778i	0.00165061	−	0.00285894i
$474$	14.9372	−	4.00240i	0.686087	−	0.183837i
$475$	−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
$479$	4.14110			0.189212			0.0946060	−	0.995515i	$-0.469841\pi$
$479$	4.14110			0.189212			0.0946060	+	0.995515i	$0.469841\pi$
$480$	1.73205	−	0.464102i	0.0790569	−	0.0211832i
$481$	−13.3843			−0.610270
$482$	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
$486$	4.03459	−	15.0573i	0.183013	−	0.683013i
$487$	1.39230	+	2.41154i	0.0630914	+	0.109277i	0.895846	−	0.444365i	$-0.146571\pi$
$487$	1.39230	+	2.41154i	0.0630914	+	0.109277i	−0.832754	+	0.553643i	$0.813237\pi$
$488$	−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	0.559921	−	0.828546i	$-0.310831\pi$
$491$	−9.69615	−	16.7942i	−0.437581	−	0.757913i	−0.997502	+	0.0706330i	$0.977498\pi$
$492$	−10.5622	−	10.5622i	−0.476180	−	0.476180i
$493$	−27.3233			−1.23058
$494$	−3.92820	−	6.80385i	−0.176738	−	0.306120i
$495$		−	0.832204i		−	0.0374048i
$496$	−6.69213			−0.300486
$497$		0			0
$498$	8.07180	+	8.07180i	0.361706	+	0.361706i
$499$	33.3923			1.49484			0.747422	−	0.664349i	$-0.231291\pi$
$499$	33.3923			1.49484			0.747422	+	0.664349i	$0.231291\pi$
$500$	4.62158	−	8.00481i	0.206683	−	0.357986i
$501$	0.679492	−	2.53590i	0.0303575	−	0.113296i
$502$	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
$507$	−16.3700	+	4.38632i	−0.727016	+	0.194803i
$508$	−6.73205	+	11.6603i	−0.298686	+	0.517340i
$509$	−21.5921			−0.957055			−0.478527	−	0.878073i	$-0.658829\pi$
$509$	−21.5921			−0.957055			−0.478527	+	0.878073i	$0.658829\pi$
$510$	11.8313	−	3.17020i	0.523901	−	0.140379i
$511$		0			0
$512$	1.00000			0.0441942
$513$	−5.89230	−	21.9904i	−0.260152	−	0.970899i
$514$	5.01910	+	8.69333i	0.221383	+	0.383446i
$515$	−12.7846			−0.563357
$516$	−0.120118	+	0.448288i	−0.00528791	+	0.0197348i
$517$	−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
$521$	−16.8876	−	29.2502i	−0.739860	−	1.28147i	−0.952558	−	0.304357i	$-0.901559\pi$
$521$	−16.8876	−	29.2502i	−0.739860	−	1.28147i	0.212699	−	0.977118i	$-0.431775\pi$
$522$		−	12.0000i		−	0.525226i
$523$	10.3664	−	17.9551i	0.453289	−	0.785120i	−0.545299	−	0.838242i	$-0.683584\pi$
$523$	10.3664	−	17.9551i	0.453289	−	0.785120i	0.998588	+	0.0531215i	$0.0169170\pi$
$524$	5.46739	−	9.46979i	0.238844	−	0.413690i
$525$		0			0
$526$	4.26795	+	7.39230i	0.186091	+	0.322320i
$527$	−45.7128			−1.99128
$528$	0.120118	−	0.448288i	0.00522748	−	0.0195092i
$529$	6.85641			0.298105
$530$	−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
$534$	8.66025	+	8.66025i	0.374766	+	0.374766i
$535$	9.00292	−	15.5935i	0.389230	−	0.674166i
$536$	−6.23205	+	10.7942i	−0.269184	+	0.466240i
$537$	−2.27362	+	8.48528i	−0.0981141	+	0.366167i
$538$	−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	−0.982381	−	0.186889i	$-0.940160\pi$
$541$	−7.66025	+	13.2679i	−0.329340	+	0.570434i	0.653041	+	0.757323i	$0.273493\pi$
$542$	−13.1069			−0.562988
$543$	−20.7846	−	20.7846i	−0.891953	−	0.891953i
$544$	6.83083			0.292869
$545$	−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
$551$	−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
$555$	12.9282	−	3.46410i	0.548772	−	0.147043i
$556$	−0.795040			−0.0337172
$557$	3.46410	+	6.00000i	0.146779	+	0.254228i	0.930035	−	0.367471i	$-0.119776\pi$
$557$	3.46410	+	6.00000i	0.146779	+	0.254228i	−0.783256	+	0.621699i	$0.786443\pi$
$558$		−	20.0764i		−	0.849901i
$559$	−0.480473			−0.0203219
$560$		0			0
$561$	0.820508	−	3.06218i	0.0346419	−	0.129285i
$562$	17.8564			0.753227
$563$	−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	$0.292289\pi$
$564$	0.928203	+	0.928203i	0.0390844	+	0.0390844i
$565$	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	$0.651578\pi$
$570$	5.55532	+	5.55532i	0.232687	+	0.232687i
$571$	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	$-0.0764286\pi$
$572$	0.480473			0.0200896
$573$	−6.69213	+	24.9754i	−0.279568	+	1.04336i
$574$		0			0
$575$	−21.4641			−0.895115
$576$			3.00000i			0.125000i
$577$	−13.7446	−	23.8064i	−0.572196	−	0.991072i	−0.996340	−	0.0854776i	$-0.972758\pi$
$577$	−13.7446	−	23.8064i	−0.572196	−	0.991072i	0.424144	−	0.905595i	$-0.360575\pi$
$578$	29.6603			1.23370
$579$	25.1834	−	6.74788i	1.04659	−	0.280432i
$580$	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
$584$	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	$0.498917\pi$
$587$	−20.9408	+	36.2705i	−0.864319	+	1.49704i	−0.867722	+	0.497049i	$0.834417\pi$
$588$		0			0
$589$	−14.6603	−	25.3923i	−0.604065	−	1.04627i
$590$	1.32051			0.0543645
$591$	20.7327	+	20.7327i	0.852831	+	0.852831i
$592$	7.46410			0.306773
$593$	8.43451	−	14.6090i	0.346364	−	0.599920i	−0.639237	−	0.769010i	$-0.720750\pi$
$593$	8.43451	−	14.6090i	0.346364	−	0.599920i	0.985601	+	0.169090i	$0.0540829\pi$
$594$	1.34486	+	0.360355i	0.0551804	+	0.0147855i
$595$		0			0
$596$	−11.4641	+	19.8564i	−0.469588	+	0.813350i
$597$	11.7846	−	43.9808i	0.482312	−	1.80001i
$598$	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	$0.197830\pi$
$600$	4.81105	+	4.81105i	0.196410	+	0.196410i
$601$	−1.67303	+	2.89778i	−0.0682444	+	0.118203i	−0.898129	−	0.439733i	$-0.855073\pi$
$601$	−1.67303	+	2.89778i	−0.0682444	+	0.118203i	0.829884	+	0.557936i	$0.188406\pi$
$602$		0			0
$603$	−32.3827	−	18.6962i	−1.31872	−	0.761366i
$604$	−9.19615	+	15.9282i	−0.374186	+	0.648109i
$605$	−11.3137			−0.459968
$606$	−2.19615	+	8.19615i	−0.0892126	+	0.332946i
$607$	2.27362			0.0922836			0.0461418	−	0.998935i	$-0.485307\pi$
$607$	2.27362			0.0922836			0.0461418	+	0.998935i	$0.485307\pi$
$608$	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
$612$			20.4925i			0.828360i
$613$	−12.4641	−	21.5885i	−0.503420	−	0.871950i	−0.999992	−	0.00395396i	$-0.998741\pi$
$613$	−12.4641	−	21.5885i	−0.503420	−	0.871950i	0.496572	−	0.867996i	$-0.334592\pi$
$614$	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	0.895929	−	0.444197i	$-0.146511\pi$
$617$	1.57180	+	2.72243i	0.0632782	+	0.109601i	−0.832651	+	0.553798i	$0.813178\pi$
$618$	5.53590	−	20.6603i	0.222686	−	0.831077i
$619$	31.7047			1.27432			0.637159	−	0.770732i	$-0.280109\pi$
$619$	31.7047			1.27432			0.637159	+	0.770732i	$0.280109\pi$
$620$	3.46410	+	6.00000i	0.139122	+	0.240966i
$621$	20.0764	−	20.0764i	0.805638	−	0.805638i
$622$	7.45001			0.298718
$623$		0			0
$624$	−3.00000	+	0.803848i	−0.120096	+	0.0321797i
$625$	10.0718			0.402872
$626$	3.13801	−	5.43520i	0.125420	−	0.217234i
$627$	1.96410	−	0.526279i	0.0784387	−	0.0210176i
$628$	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
$633$	−8.48528	+	31.6675i	−0.337260	+	1.25867i
$634$	13.0000	−	22.5167i	0.516296	−	0.894251i
$635$	13.9391			0.553155
$636$	−13.3843	−	13.3843i	−0.530720	−	0.530720i
$637$		0			0
$638$	1.07180			0.0424328
$639$			28.3923i			1.12318i
$640$	−0.517638	−	0.896575i	−0.0204614	−	0.0354403i
$641$	4.07180			0.160826			0.0804132	−	0.996762i	$-0.474376\pi$
$641$	4.07180			0.160826			0.0804132	+	0.996762i	$0.474376\pi$
$642$	21.3011	+	21.3011i	0.840689	+	0.840689i
$643$	−22.4565	−	38.8959i	−0.885599	−	1.53390i	−0.845025	−	0.534726i	$-0.820415\pi$
$643$	−22.4565	−	38.8959i	−0.885599	−	1.53390i	−0.0405737	−	0.999177i	$-0.512919\pi$
$644$		0			0
$645$	0.464102	−	0.124356i	0.0182740	−	0.00489650i
$646$	14.9641	+	25.9186i	0.588755	+	1.01975i
$647$	10.9348	+	18.9396i	0.429890	+	0.744592i	0.996863	−	0.0791447i	$-0.0252189\pi$
$647$	10.9348	+	18.9396i	0.429890	+	0.744592i	−0.566973	+	0.823736i	$0.691886\pi$
$648$	−9.00000			−0.353553
$649$	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
$653$	6.00000			0.234798			0.117399	−	0.993085i	$-0.462544\pi$
$653$	6.00000			0.234798			0.117399	+	0.993085i	$0.462544\pi$
$654$	8.24504	−	2.20925i	0.322407	−	0.0863886i
$655$	−11.3205			−0.442329
$656$	−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	$-0.222277\pi$
$660$	−0.464102	+	0.124356i	−0.0180651	+	0.00484054i
$661$		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
$663$	−20.4925	+	5.49095i	−0.795862	+	0.213251i
$664$	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
$668$	−1.51575			−0.0586461
$669$	12.0000	−	3.21539i	0.463947	−	0.124314i
$670$	12.9038			0.498517
$671$	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
$675$	−14.4331	+	14.4331i	−0.555532	+	0.555532i
$676$	4.89230	+	8.47372i	0.188166	+	0.325912i
$677$	−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
$681$	−33.8827	−	33.8827i	−1.29839	−	1.29839i
$682$	1.79315			0.0686633
$683$	19.1603	+	33.1865i	0.733147	+	1.26985i	0.955532	+	0.294888i	$0.0952825\pi$
$683$	19.1603	+	33.1865i	0.733147	+	1.26985i	−0.222385	+	0.974959i	$0.571384\pi$
$684$	−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
$688$	0.267949			0.0102155
$689$	9.79796	−	16.9706i	0.373273	−	0.646527i
$690$	−2.53590	+	9.46410i	−0.0965400	+	0.360292i
$691$	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
$696$	−6.69213	+	1.79315i	−0.253665	+	0.0679692i
$697$	−29.4545	+	51.0167i	−1.11567	+	1.93239i
$698$	8.00481			0.302986
$699$	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	$0.628394\pi$
$702$	−2.41154	−	9.00000i	−0.0910178	−	0.339683i
$703$	16.3514	+	28.3214i	0.616704	+	1.06816i
$704$	−0.267949			−0.0100987
$705$	0.351731	−	1.31268i	0.0132470	−	0.0494383i
$706$	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	$0.758577\pi$
$710$	−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
$716$	5.07180			0.189542
$717$	−0.416102	+	1.55291i	−0.0155396	+	0.0579946i
$718$	7.46410			0.278558
$719$	−24.8367	+	43.0184i	−0.926251	+	1.60431i	−0.136716	+	0.990610i	$0.543655\pi$
$719$	−24.8367	+	43.0184i	−0.926251	+	1.60431i	−0.789536	+	0.613704i	$0.789679\pi$
$720$	2.68973	−	1.55291i	0.100240	−	0.0578737i
$721$		0			0
$722$	−0.0980762	+	0.169873i	−0.00365002	+	0.00632202i
$723$	7.68653	+	7.68653i	0.285865	+	0.285865i
$724$	−8.48528	+	14.6969i	−0.315353	+	0.546207i
$725$	−7.85641	+	13.6077i	−0.291780	+	0.505377i
$726$	4.89898	−	18.2832i	0.181818	−	0.678555i
$727$	16.3514	−	28.3214i	0.606439	−	1.05038i	−0.385383	−	0.922757i	$-0.625931\pi$
$727$	16.3514	−	28.3214i	0.606439	−	1.05038i	0.991822	−	0.127627i	$-0.0407361\pi$
$728$		0			0
$729$		−	27.0000i		−	1.00000i
$730$	2.80385	−	4.85641i	0.103775	−	0.179744i
$731$	1.83032			0.0676967
$732$	−15.4641	−	15.4641i	−0.571570	−	0.571570i
$733$	−8.00481			−0.295664			−0.147832	−	0.989012i	$-0.547230\pi$
$733$	−8.00481			−0.295664			−0.147832	+	0.989012i	$0.547230\pi$
$734$	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
$738$	−22.4058	−	12.9360i	−0.824768	−	0.476180i
$739$	−3.06218	−	5.30385i	−0.112644	−	0.195105i	0.804191	−	0.594370i	$-0.202599\pi$
$739$	−3.06218	−	5.30385i	−0.112644	−	0.195105i	−0.916836	+	0.399265i	$0.869265\pi$
$740$	−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	0.995585	+	0.0938641i	$0.0299219\pi$
$743$	15.7846	+	27.3397i	0.579081	+	1.00300i	−0.416504	+	0.909134i	$0.636745\pi$
$744$	−11.1962	+	3.00000i	−0.410471	+	0.109985i
$745$	23.7370			0.869657
$746$	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
$751$	34.7846			1.26931			0.634654	−	0.772796i	$-0.281143\pi$
$751$	34.7846			1.26931			0.634654	+	0.772796i	$0.281143\pi$
$752$	0.378937	−	0.656339i	0.0138184	−	0.0239342i
$753$	0.973721	+	0.973721i	0.0354843	+	0.0354843i
$754$	−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
$759$	1.79315	+	1.79315i	0.0650873	+	0.0650873i
$760$	2.26795	−	3.92820i	0.0822672	−	0.142491i
$761$	40.2543			1.45922			0.729609	−	0.683865i	$-0.239702\pi$
$761$	40.2543			1.45922			0.729609	+	0.683865i	$0.239702\pi$
$762$	−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
$766$	13.6617	+	23.6627i	0.493616	+	0.854968i
$767$	−2.28719			−0.0825855
$768$	1.67303	−	0.448288i	0.0603704	−	0.0161762i
$769$	19.0919	+	33.0681i	0.688471	+	1.19247i	0.972332	+	0.233601i	$0.0750511\pi$
$769$	19.0919	+	33.0681i	0.688471	+	1.19247i	−0.283862	+	0.958865i	$0.591616\pi$
$770$		0			0
$771$	12.2942	+	12.2942i	0.442766	+	0.442766i
$772$	−7.52628	−	13.0359i	−0.270877	−	0.469172i
$773$	19.6975	+	34.1170i	0.708468	+	1.22710i	0.965425	+	0.260680i	$0.0839468\pi$
$773$	19.6975	+	34.1170i	0.708468	+	1.22710i	−0.256957	+	0.966423i	$0.582720\pi$
$774$			0.803848i			0.0288937i
$775$	−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
$779$	−37.7846			−1.35377
$780$	2.27362	+	2.27362i	0.0814088	+	0.0814088i
$781$	−2.53590			−0.0907416
$782$	−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
$786$	4.90192	−	18.2942i	0.174846	−	0.652534i
$787$	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
$789$	10.4543	+	10.4543i	0.372183	+	0.372183i
$790$	−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
$794$	−13.1069			−0.465145
$795$	−5.07180	+	18.9282i	−0.179878	+	0.671314i
$796$	−26.2880			−0.931755
$797$	−18.9396	−	32.8043i	−0.670874	−	1.16199i	−0.977657	−	0.210209i	$-0.932586\pi$
$797$	−18.9396	−	32.8043i	−0.670874	−	1.16199i	0.306782	−	0.951780i	$-0.400748\pi$
$798$		0			0
$799$	2.58846	−	4.48334i	0.0915730	−	0.158609i
$800$	1.96410	−	3.40192i	0.0694415	−	0.120276i
$801$	18.3712	+	10.6066i	0.649113	+	0.374766i
$802$	11.8923	+	20.5981i	0.419932	+	0.727343i
$803$	−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
$807$	−2.53590	+	9.46410i	−0.0892679	+	0.333152i
$808$	4.89898			0.172345
$809$	14.8660	+	25.7487i	0.522662	+	0.905276i	0.999652	+	0.0263681i	$0.00839421\pi$
$809$	14.8660	+	25.7487i	0.522662	+	0.905276i	−0.476991	+	0.878908i	$0.658272\pi$
$810$	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
$814$	−2.00000			−0.0701000
$815$	6.89520	−	11.9428i	0.241528	−	0.418339i
$816$	11.4282	−	3.06218i	0.400067	−	0.107198i
$817$	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	$0.891379\pi$
$822$	−3.88229	+	14.4889i	−0.135410	+	0.505358i
$823$	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	$0.106478\pi$
$824$	−12.3490			−0.430197
$825$	−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	$-0.122690\pi$
$829$	3.96524	+	6.86800i	0.137718	+	0.238535i	−0.788914	+	0.614503i	$0.789356\pi$
$830$	−6.82309			−0.236833
$831$	−38.5355	−	38.5355i	−1.33678	−	1.33678i
$832$	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
$836$	−0.586988	−	1.01669i	−0.0203014	−	0.0351631i
$837$	−9.00000	−	33.5885i	−0.311086	−	1.16099i
$838$	18.0938	−	31.3393i	0.625039	−	1.08260i
$839$	11.3137	−	19.5959i	0.390593	−	0.676526i	−0.601935	−	0.798545i	$-0.705603\pi$
$839$	11.3137	−	19.5959i	0.390593	−	0.676526i	0.992528	+	0.122019i	$0.0389368\pi$
$840$		0			0
$841$	6.50000	+	11.2583i	0.224138	+	0.388218i
$842$	7.60770			0.262178
$843$	29.8744	−	8.00481i	1.02893	−	0.275700i
$844$	18.9282			0.651536
$845$	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
$849$	25.2224	−	6.75833i	0.865632	−	0.231945i
$850$	13.4164	−	23.2380i	0.460180	−	0.797056i
$851$	−20.3923	+	35.3205i	−0.699039	+	1.21077i
$852$	15.8338	−	4.24264i	0.542455	−	0.145350i
$853$	16.4901	−	28.5617i	0.564610	−	0.977933i	−0.432476	−	0.901645i	$-0.642360\pi$
$853$	16.4901	−	28.5617i	0.564610	−	0.977933i	0.997086	−	0.0762876i	$-0.0243067\pi$
$854$		0			0
$855$	11.7846	+	6.80385i	0.403025	+	0.232687i
$856$	8.69615	−	15.0622i	0.297228	−	0.514815i
$857$	11.2122			0.383001			0.191500	−	0.981493i	$-0.438665\pi$
$857$	11.2122			0.383001			0.191500	+	0.981493i	$0.438665\pi$
$858$	0.803848	−	0.215390i	0.0274429	−	0.00735330i
$859$	41.6042			1.41952			0.709758	−	0.704446i	$-0.248804\pi$
$859$	41.6042			1.41952			0.709758	+	0.704446i	$0.248804\pi$
$860$	−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	0.122823	−	0.992429i	$-0.460805\pi$
$863$	27.0526	−	46.8564i	0.920880	−	1.59501i	0.798057	−	0.602582i	$-0.205861\pi$
$864$	1.34486	+	5.01910i	0.0457532	+	0.170753i
$865$	3.46410	+	6.00000i	0.117783	+	0.204006i
$866$	−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
$870$	5.07180	+	5.07180i	0.171950	+	0.171950i
$871$	−22.3500			−0.757301
$872$	−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
$877$	−29.1769			−0.985234			−0.492617	−	0.870246i	$-0.663960\pi$
$877$	−29.1769			−0.985234			−0.492617	+	0.870246i	$0.663960\pi$
$878$	9.79796	−	16.9706i	0.330665	−	0.572729i
$879$	−4.14359	+	15.4641i	−0.139760	+	0.521591i
$880$	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
$885$	2.20925	−	0.591968i	0.0742632	−	0.0198988i
$886$	−8.16025	+	14.1340i	−0.274149	+	0.474840i
$887$	−53.2596			−1.78828			−0.894142	−	0.447784i	$-0.852213\pi$
$887$	−53.2596			−1.78828			−0.894142	+	0.447784i	$0.852213\pi$
$888$	12.4877	−	3.34607i	0.419059	−	0.112287i
$889$		0			0
$890$	−7.32051			−0.245384
$891$	2.41154			0.0807897
$892$	−3.58630	−	6.21166i	−0.120078	−	0.207982i
$893$	3.32051			0.111117
$894$	−10.2784	+	38.3596i	−0.343762	+	1.28294i
$895$	−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
$899$	−13.3843	−	23.1822i	−0.446390	−	0.773170i
$900$	10.2058	+	5.89230i	0.340192	+	0.196410i
$901$	−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
$905$	17.5692			0.584021
$906$	−8.24504	+	30.7709i	−0.273923	+	1.02230i
$907$	−5.24871			−0.174281			−0.0871403	−	0.996196i	$-0.527773\pi$
$907$	−5.24871			−0.174281			−0.0871403	+	0.996196i	$0.527773\pi$
$908$	−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	$-0.0178902\pi$
$912$	5.36603	+	5.36603i	0.177687	+	0.177687i
$913$	−0.882972	+	1.52935i	−0.0292221	+	0.0506142i
$914$	15.5263	−	26.8923i	0.513564	−	0.889518i
$915$	−5.85993	+	21.8695i	−0.193723	+	0.722985i
$916$	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	−0.931089	−	0.364792i	$-0.881140\pi$
$919$	−4.53590	+	7.85641i	−0.149625	+	0.259159i	0.781464	+	0.623951i	$0.214473\pi$
$920$	5.65685			0.186501
$921$	1.43782	+	1.43782i	0.0473779	+	0.0473779i
$922$	11.0363			0.363461
$923$	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
$927$		−	37.0470i		−	1.21678i
$928$	2.00000	+	3.46410i	0.0656532	+	0.113715i
$929$	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
$933$	12.4641	−	3.33975i	0.408056	−	0.109338i
$934$	−9.17878			−0.300339
$935$	0.947441	+	1.64102i	0.0309846	+	0.0536670i
$936$	−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
$940$	−0.784610			−0.0255911
$941$	−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	$0.881670\pi$
$942$	11.6603	+	11.6603i	0.379912	+	0.379912i
$943$	−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	$0.738186\pi$
$948$	−10.9348	−	10.9348i	−0.355145	−	0.355145i
$949$	−4.85641	+	8.41154i	−0.157646	+	0.273050i
$950$	17.2108			0.558392
$951$	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
$956$	0.928203			0.0300202
$957$	1.79315	−	0.480473i	0.0579643	−	0.0155315i
$958$	−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
$962$	6.69213	+	11.5911i	0.215763	+	0.373712i
$963$	45.1865	+	26.0885i	1.45612	+	0.840689i
$964$	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	$0.556141\pi$
$968$	−10.9282			−0.351246
$969$	36.6544	+	36.6544i	1.17751	+	1.17751i
$970$	18.7846			0.603137
$971$	15.6443	−	27.0967i	0.502049	−	0.869574i	−0.497948	−	0.867207i	$-0.665913\pi$
$971$	15.6443	−	27.0967i	0.502049	−	0.869574i	0.999997	−	0.00236748i	$-0.000753594\pi$
$972$	−15.0573	+	4.03459i	−0.482963	+	0.129410i
$973$		0			0
$974$	1.39230	−	2.41154i	0.0446123	−	0.0772708i
$975$	−3.15768	+	11.7846i	−0.101127	+	0.377410i
$976$	−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	$0.176754\pi$
$978$	16.3142	+	16.3142i	0.521671	+	0.521671i
$979$	−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
$983$	−12.6264			−0.402719			−0.201360	−	0.979517i	$-0.564536\pi$
$983$	−12.6264			−0.402719			−0.201360	+	0.979517i	$0.564536\pi$
$984$	−3.86603	+	14.4282i	−0.123244	+	0.459954i
$985$	−17.5254			−0.558405
$986$	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	−0.920851	−	0.389915i	$-0.872505\pi$
$991$	−25.1244	−	43.5167i	−0.798101	−	1.38235i	0.122750	−	0.992438i	$-0.460829\pi$
$992$	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
$996$	2.95448	−	11.0263i	0.0936164	−	0.349381i
$997$	37.6018			1.19086			0.595430	−	0.803407i	$-0.296982\pi$
$997$	37.6018			1.19086			0.595430	+	0.803407i	$0.296982\pi$
$998$	−16.6962	−	28.9186i	−0.528507	−	0.915402i
$999$	10.0382	+	37.4631i	0.317594	+	1.18528i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
882.2.e.s.373.2		8	9.4	even	3
882.2.e.s.373.3		8	63.13	odd	6
882.2.e.s.655.2		8	7.4	even	3
882.2.e.s.655.3		8	7.3	odd	6
882.2.f.q.295.1	✓	8	7.5	odd	6
882.2.f.q.295.4	yes	8	7.2	even	3
882.2.f.q.589.1	yes	8	63.40	odd	6
882.2.f.q.589.4	yes	8	63.58	even	3
882.2.h.q.67.2		8	63.4	even	3	inner
882.2.h.q.67.3		8	63.31	odd	6	inner
882.2.h.q.79.1		8	1.1	even	1	trivial
882.2.h.q.79.4		8	7.6	odd	2	inner
2646.2.e.q.1549.2		8	63.41	even	6
2646.2.e.q.1549.3		8	9.5	odd	6
2646.2.e.q.2125.2		8	21.17	even	6
2646.2.e.q.2125.3		8	21.11	odd	6
2646.2.f.r.883.2		8	21.5	even	6
2646.2.f.r.883.3		8	21.2	odd	6
2646.2.f.r.1765.2		8	63.5	even	6
2646.2.f.r.1765.3		8	63.23	odd	6
2646.2.h.t.361.2		8	63.32	odd	6
2646.2.h.t.361.3		8	63.59	even	6
2646.2.h.t.667.2		8	3.2	odd	2
2646.2.h.t.667.3		8	21.20	even	2
7938.2.a.ci.1.2		4	63.2	odd	6
7938.2.a.ci.1.3		4	63.47	even	6
7938.2.a.cp.1.2		4	63.61	odd	6
7938.2.a.cp.1.3		4	63.16	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.h (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 - 0.866025i) q^{2} +(-1.22474 - 1.22474i) q^{3} +(-0.500000 + 0.866025i) q^{4} +1.03528 q^{5} +(-0.448288 + 1.67303i) q^{6} +1.00000 q^{8} +3.00000i q^{9} +(-0.517638 - 0.896575i) q^{10} -0.267949 q^{11} +(1.67303 - 0.448288i) q^{12} +(0.896575 + 1.55291i) q^{13} +(-1.26795 - 1.26795i) q^{15} +(-0.500000 - 0.866025i) 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} +5.46410 q^{23} +(-1.22474 - 1.22474i) q^{24} -3.92820 q^{25} +(0.896575 - 1.55291i) q^{26} +(3.67423 - 3.67423i) q^{27} +(2.00000 - 3.46410i) q^{29} +(-0.464102 + 1.73205i) q^{30} +(3.34607 - 5.79555i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(0.328169 + 0.328169i) q^{33} +(-3.41542 + 5.91567i) q^{34} +(-2.59808 - 1.50000i) q^{36} +(-3.73205 + 6.46410i) q^{37} -4.38134 q^{38} +(0.803848 - 3.00000i) q^{39} +1.03528 q^{40} +(-4.31199 - 7.46859i) q^{41} +(-0.133975 + 0.232051i) q^{43} +(0.133975 - 0.232051i) q^{44} +3.10583i q^{45} +(-2.73205 - 4.73205i) q^{46} +(0.378937 + 0.656339i) q^{47} +(-0.448288 + 1.67303i) q^{48} +(1.96410 + 3.40192i) q^{50} +(-3.06218 + 11.4282i) q^{51} -1.79315 q^{52} +(-5.46410 - 9.46410i) q^{53} +(-5.01910 - 1.34486i) q^{54} -0.277401 q^{55} +(-7.33013 + 1.96410i) q^{57} -4.00000 q^{58} +(-0.637756 + 1.10463i) q^{59} +(1.73205 - 0.464102i) q^{60} +(-6.31319 - 10.9348i) q^{61} -6.69213 q^{62} +1.00000 q^{64} +(0.928203 + 1.60770i) q^{65} +(0.120118 - 0.448288i) q^{66} +(-6.23205 + 10.7942i) q^{67} +6.83083 q^{68} +(-6.69213 - 6.69213i) q^{69} +9.46410 q^{71} +3.00000i q^{72} +(2.70831 + 4.69093i) q^{73} +7.46410 q^{74} +(4.81105 + 4.81105i) q^{75} +(2.19067 + 3.79435i) q^{76} +(-3.00000 + 0.803848i) q^{78} +(-4.46410 - 7.73205i) q^{79} +(-0.517638 - 0.896575i) q^{80} -9.00000 q^{81} +(-4.31199 + 7.46859i) q^{82} +(3.29530 - 5.70762i) q^{83} +(-3.53590 - 6.12436i) q^{85} +0.267949 q^{86} +(-6.69213 + 1.79315i) q^{87} -0.267949 q^{88} +(3.53553 - 6.12372i) q^{89} +(2.68973 - 1.55291i) q^{90} +(-2.73205 + 4.73205i) q^{92} +(-11.1962 + 3.00000i) q^{93} +(0.378937 - 0.656339i) q^{94} +(2.26795 - 3.92820i) q^{95} +(1.67303 - 0.448288i) q^{96} +(-9.07227 + 15.7136i) q^{97} -0.803848i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 4 q^{2} - 4 q^{4} + 8 q^{8} - 16 q^{11} - 24 q^{15} - 4 q^{16} + 8 q^{22} + 16 q^{23} + 24 q^{25} + 16 q^{29} + 24 q^{30} - 4 q^{32} - 16 q^{37} + 48 q^{39} - 8 q^{43} + 8 q^{44} - 8 q^{46} - 12 q^{50}+ \cdots + 32 q^{95}+O(q^{100}) \) 8 * q - 4 * q^2 - 4 * q^4 + 8 * q^8 - 16 * q^11 - 24 * q^15 - 4 * q^16 + 8 * q^22 + 16 * q^23 + 24 * q^25 + 16 * q^29 + 24 * q^30 - 4 * q^32 - 16 * q^37 + 48 * q^39 - 8 * q^43 + 8 * q^44 - 8 * q^46 - 12 * q^50 + 24 * q^51 - 16 * q^53 - 24 * q^57 - 32 * q^58 + 8 * q^64 - 48 * q^65 - 36 * q^67 + 48 * q^71 + 32 * q^74 - 24 * q^78 - 8 * q^79 - 72 * q^81 - 56 * q^85 + 16 * q^86 - 16 * q^88 - 8 * q^92 - 48 * q^93 + 32 * q^95

Introduction

L-functions

Modular forms

Varieties

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Database

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