LMFDB - Embedded newform 882.2.f.q.589.3

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)

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);

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")

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			589.3
Root			$-0.965926 - 0.258819i$ of defining polynomial
Character	$\chi$	$=$	882.589
Dual form			882.2.f.q.295.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.500000 - 0.866025i) q^{2} +(0.448288 - 1.67303i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(1.93185 - 3.34607i) q^{5} +(-1.67303 + 0.448288i) q^{6} +1.00000 q^{8} +(-2.59808 - 1.50000i) q^{9} -3.86370 q^{10} +(1.86603 + 3.23205i) q^{11} +(1.22474 + 1.22474i) q^{12} +(3.34607 - 5.79555i) q^{13} +(-4.73205 - 4.73205i) q^{15} +(-0.500000 - 0.866025i) q^{16} -5.41662 q^{17} +3.00000i q^{18} +2.96713 q^{19} +(1.93185 + 3.34607i) q^{20} +(1.86603 - 3.23205i) q^{22} +(0.732051 - 1.26795i) q^{23} +(0.448288 - 1.67303i) q^{24} +(-4.96410 - 8.59808i) q^{25} -6.69213 q^{26} +(-3.67423 + 3.67423i) q^{27} +(2.00000 + 3.46410i) q^{29} +(-1.73205 + 6.46410i) q^{30} +(0.896575 - 1.55291i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(6.24384 - 1.67303i) q^{33} +(2.70831 + 4.69093i) q^{34} +(2.59808 - 1.50000i) q^{36} +0.535898 q^{37} +(-1.48356 - 2.56961i) q^{38} +(-8.19615 - 8.19615i) q^{39} +(1.93185 - 3.34607i) q^{40} +(-0.637756 + 1.10463i) q^{41} +(-1.86603 - 3.23205i) q^{43} -3.73205 q^{44} +(-10.0382 + 5.79555i) q^{45} -1.46410 q^{46} +(5.27792 + 9.14162i) q^{47} +(-1.67303 + 0.448288i) q^{48} +(-4.96410 + 8.59808i) q^{50} +(-2.42820 + 9.06218i) q^{51} +(3.34607 + 5.79555i) q^{52} -2.92820 q^{53} +(5.01910 + 1.34486i) q^{54} +14.4195 q^{55} +(1.33013 - 4.96410i) q^{57} +(2.00000 - 3.46410i) q^{58} +(-4.31199 + 7.46859i) q^{59} +(6.46410 - 1.73205i) q^{60} +(3.48477 + 6.03579i) q^{61} -1.79315 q^{62} +1.00000 q^{64} +(-12.9282 - 22.3923i) q^{65} +(-4.57081 - 4.57081i) q^{66} +(-2.76795 + 4.79423i) q^{67} +(2.70831 - 4.69093i) q^{68} +(-1.79315 - 1.79315i) q^{69} +2.53590 q^{71} +(-2.59808 - 1.50000i) q^{72} +6.83083 q^{73} +(-0.267949 - 0.464102i) q^{74} +(-16.6102 + 4.45069i) q^{75} +(-1.48356 + 2.56961i) q^{76} +(-3.00000 + 11.1962i) q^{78} +(2.46410 + 4.26795i) q^{79} -3.86370 q^{80} +(4.50000 + 7.79423i) q^{81} +1.27551 q^{82} +(-8.95215 - 15.5056i) q^{83} +(-10.4641 + 18.1244i) q^{85} +(-1.86603 + 3.23205i) q^{86} +(6.69213 - 1.79315i) q^{87} +(1.86603 + 3.23205i) q^{88} -7.07107 q^{89} +(10.0382 + 5.79555i) q^{90} +(0.732051 + 1.26795i) q^{92} +(-2.19615 - 2.19615i) q^{93} +(5.27792 - 9.14162i) q^{94} +(5.73205 - 9.92820i) q^{95} +(1.22474 + 1.22474i) q^{96} +(-2.94855 - 5.10703i) q^{97} -11.1962i 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
$3$	0.448288	−	1.67303i	0.258819	−	0.965926i
$3$	0.448288	−	1.67303i	0.258819	−	0.965926i
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	1.93185	−	3.34607i	0.863950	−	1.49641i	−0.00413535	−	0.999991i	$-0.501316\pi$
$5$	1.93185	−	3.34607i	0.863950	−	1.49641i	0.868086	−	0.496414i	$-0.165350\pi$
$6$	−1.67303	+	0.448288i	−0.683013	+	0.183013i
$7$		0			0
$7$		0			0
$8$	1.00000			0.353553
$9$	−2.59808	−	1.50000i	−0.866025	−	0.500000i
$10$	−3.86370			−1.22181
$11$	1.86603	+	3.23205i	0.562628	+	0.974500i	0.997266	+	0.0738948i	$0.0235429\pi$
$11$	1.86603	+	3.23205i	0.562628	+	0.974500i	−0.434638	+	0.900605i	$0.643124\pi$
$12$	1.22474	+	1.22474i	0.353553	+	0.353553i
$13$	3.34607	−	5.79555i	0.928032	−	1.60740i	0.141420	−	0.989950i	$-0.454833\pi$
$13$	3.34607	−	5.79555i	0.928032	−	1.60740i	0.786612	−	0.617448i	$-0.211833\pi$
$14$		0			0
$15$	−4.73205	−	4.73205i	−1.22181	−	1.22181i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−5.41662			−1.31372			−0.656861	−	0.754011i	$-0.728116\pi$
$17$	−5.41662			−1.31372			−0.656861	+	0.754011i	$0.728116\pi$
$18$			3.00000i			0.707107i
$19$	2.96713			0.680706			0.340353	−	0.940298i	$-0.389453\pi$
$19$	2.96713			0.680706			0.340353	+	0.940298i	$0.389453\pi$
$20$	1.93185	+	3.34607i	0.431975	+	0.748203i
$21$		0			0
$22$	1.86603	−	3.23205i	0.397838	−	0.689076i
$23$	0.732051	−	1.26795i	0.152643	−	0.264386i	−0.779555	−	0.626334i	$-0.784555\pi$
$23$	0.732051	−	1.26795i	0.152643	−	0.264386i	0.932198	+	0.361948i	$0.117888\pi$
$24$	0.448288	−	1.67303i	0.0915064	−	0.341506i
$25$	−4.96410	−	8.59808i	−0.992820	−	1.71962i
$26$	−6.69213			−1.31243
$27$	−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	+	6.46410i	−0.316228	+	1.18018i
$31$	0.896575	−	1.55291i	0.161030	−	0.278912i	−0.774209	−	0.632931i	$-0.781852\pi$
$31$	0.896575	−	1.55291i	0.161030	−	0.278912i	0.935238	+	0.354019i	$0.115185\pi$
$32$	−0.500000	+	0.866025i	−0.0883883	+	0.153093i
$33$	6.24384	−	1.67303i	1.08691	−	0.291238i
$34$	2.70831	+	4.69093i	0.464471	+	0.804488i
$35$		0			0
$36$	2.59808	−	1.50000i	0.433013	−	0.250000i
$37$	0.535898			0.0881012			0.0440506	−	0.999029i	$-0.485974\pi$
$37$	0.535898			0.0881012			0.0440506	+	0.999029i	$0.485974\pi$
$38$	−1.48356	−	2.56961i	−0.240666	−	0.416845i
$39$	−8.19615	−	8.19615i	−1.31243	−	1.31243i
$40$	1.93185	−	3.34607i	0.305453	−	0.529059i
$41$	−0.637756	+	1.10463i	−0.0996008	+	0.172514i	−0.911519	−	0.411257i	$-0.865090\pi$
$41$	−0.637756	+	1.10463i	−0.0996008	+	0.172514i	0.811919	+	0.583771i	$0.198423\pi$
$42$		0			0
$43$	−1.86603	−	3.23205i	−0.284566	−	0.492883i	0.687938	−	0.725770i	$-0.258516\pi$
$43$	−1.86603	−	3.23205i	−0.284566	−	0.492883i	−0.972504	+	0.232887i	$0.925183\pi$
$44$	−3.73205			−0.562628
$45$	−10.0382	+	5.79555i	−1.49641	+	0.863950i
$46$	−1.46410			−0.215870
$47$	5.27792	+	9.14162i	0.769863	+	1.33344i	0.937637	+	0.347617i	$0.113009\pi$
$47$	5.27792	+	9.14162i	0.769863	+	1.33344i	−0.167773	+	0.985826i	$0.553658\pi$
$48$	−1.67303	+	0.448288i	−0.241481	+	0.0647048i
$49$		0			0
$50$	−4.96410	+	8.59808i	−0.702030	+	1.21595i
$51$	−2.42820	+	9.06218i	−0.340016	+	1.26896i
$52$	3.34607	+	5.79555i	0.464016	+	0.803699i
$53$	−2.92820			−0.402220			−0.201110	−	0.979569i	$-0.564455\pi$
$53$	−2.92820			−0.402220			−0.201110	+	0.979569i	$0.564455\pi$
$54$	5.01910	+	1.34486i	0.683013	+	0.183013i
$55$	14.4195			1.94433
$56$		0			0
$57$	1.33013	−	4.96410i	0.176180	−	0.657511i
$58$	2.00000	−	3.46410i	0.262613	−	0.454859i
$59$	−4.31199	+	7.46859i	−0.561373	+	0.972327i	0.436004	+	0.899945i	$0.356394\pi$
$59$	−4.31199	+	7.46859i	−0.561373	+	0.972327i	−0.997377	+	0.0723823i	$0.976940\pi$
$60$	6.46410	−	1.73205i	0.834512	−	0.223607i
$61$	3.48477	+	6.03579i	0.446179	+	0.772804i	0.998133	−	0.0610700i	$-0.0194513\pi$
$61$	3.48477	+	6.03579i	0.446179	+	0.772804i	−0.551955	+	0.833874i	$0.686118\pi$
$62$	−1.79315			−0.227730
$63$		0			0
$64$	1.00000			0.125000
$65$	−12.9282	−	22.3923i	−1.60355	−	2.77742i
$66$	−4.57081	−	4.57081i	−0.562628	−	0.562628i
$67$	−2.76795	+	4.79423i	−0.338159	+	0.585708i	−0.984086	−	0.177690i	$-0.943137\pi$
$67$	−2.76795	+	4.79423i	−0.338159	+	0.585708i	0.645928	+	0.763399i	$0.276471\pi$
$68$	2.70831	−	4.69093i	0.328431	−	0.568859i
$69$	−1.79315	−	1.79315i	−0.215870	−	0.215870i
$70$		0			0
$71$	2.53590			0.300956			0.150478	−	0.988613i	$-0.451919\pi$
$71$	2.53590			0.300956			0.150478	+	0.988613i	$0.451919\pi$
$72$	−2.59808	−	1.50000i	−0.306186	−	0.176777i
$73$	6.83083			0.799488			0.399744	−	0.916627i	$-0.369099\pi$
$73$	6.83083			0.799488			0.399744	+	0.916627i	$0.369099\pi$
$74$	−0.267949	−	0.464102i	−0.0311485	−	0.0539507i
$75$	−16.6102	+	4.45069i	−1.91798	+	0.513922i
$76$	−1.48356	+	2.56961i	−0.170176	+	0.294754i
$77$		0			0
$78$	−3.00000	+	11.1962i	−0.339683	+	1.26771i
$79$	2.46410	+	4.26795i	0.277233	+	0.480182i	0.970696	−	0.240310i	$-0.0772492\pi$
$79$	2.46410	+	4.26795i	0.277233	+	0.480182i	−0.693463	+	0.720492i	$0.743916\pi$
$80$	−3.86370			−0.431975
$81$	4.50000	+	7.79423i	0.500000	+	0.866025i
$82$	1.27551			0.140857
$83$	−8.95215	−	15.5056i	−0.982626	−	1.70196i	−0.652043	−	0.758182i	$-0.726088\pi$
$83$	−8.95215	−	15.5056i	−0.982626	−	1.70196i	−0.330583	−	0.943777i	$-0.607245\pi$
$84$		0			0
$85$	−10.4641	+	18.1244i	−1.13499	+	1.96586i
$86$	−1.86603	+	3.23205i	−0.201219	+	0.348521i
$87$	6.69213	−	1.79315i	0.717472	−	0.192246i
$88$	1.86603	+	3.23205i	0.198919	+	0.344538i
$89$	−7.07107			−0.749532			−0.374766	−	0.927119i	$-0.622277\pi$
$89$	−7.07107			−0.749532			−0.374766	+	0.927119i	$0.622277\pi$
$90$	10.0382	+	5.79555i	1.05812	+	0.610905i
$91$		0			0
$92$	0.732051	+	1.26795i	0.0763216	+	0.132193i
$93$	−2.19615	−	2.19615i	−0.227730	−	0.227730i
$94$	5.27792	−	9.14162i	0.544376	−	0.942886i
$95$	5.73205	−	9.92820i	0.588096	−	1.01861i
$96$	1.22474	+	1.22474i	0.125000	+	0.125000i
$97$	−2.94855	−	5.10703i	−0.299379	−	0.518540i	0.676615	−	0.736337i	$-0.263446\pi$
$97$	−2.94855	−	5.10703i	−0.299379	−	0.518540i	−0.975994	+	0.217797i	$0.930113\pi$
$98$		0			0
$99$		−	11.1962i		−	1.12526i
$100$	9.92820			0.992820
$101$	2.44949	+	4.24264i	0.243733	+	0.422159i	0.961775	−	0.273842i	$-0.0882945\pi$
$101$	2.44949	+	4.24264i	0.243733	+	0.422159i	−0.718041	+	0.696000i	$0.754961\pi$
$102$	9.06218	−	2.42820i	0.897289	−	0.240428i
$103$	3.72500	−	6.45189i	0.367035	−	0.635724i	−0.622065	−	0.782965i	$-0.713706\pi$
$103$	3.72500	−	6.45189i	0.367035	−	0.635724i	0.989101	+	0.147241i	$0.0470394\pi$
$104$	3.34607	−	5.79555i	0.328109	−	0.568301i
$105$		0			0
$106$	1.46410	+	2.53590i	0.142206	+	0.246308i
$107$	3.39230			0.327946			0.163973	−	0.986465i	$-0.447569\pi$
$107$	3.39230			0.327946			0.163973	+	0.986465i	$0.447569\pi$
$108$	−1.34486	−	5.01910i	−0.129410	−	0.482963i
$109$	−8.92820			−0.855167			−0.427583	−	0.903976i	$-0.640635\pi$
$109$	−8.92820			−0.855167			−0.427583	+	0.903976i	$0.640635\pi$
$110$	−7.20977	−	12.4877i	−0.687424	−	1.19065i
$111$	0.240237	−	0.896575i	0.0228023	−	0.0850992i
$112$		0			0
$113$	−3.46410	+	6.00000i	−0.325875	+	0.564433i	−0.981689	−	0.190490i	$-0.938992\pi$
$113$	−3.46410	+	6.00000i	−0.325875	+	0.564433i	0.655814	+	0.754923i	$0.272326\pi$
$114$	−4.96410	+	1.33013i	−0.464931	+	0.124578i
$115$	−2.82843	−	4.89898i	−0.263752	−	0.456832i
$116$	−4.00000			−0.371391
$117$	−17.3867	+	10.0382i	−1.60740	+	0.928032i
$118$	8.62398			0.793902
$119$		0			0
$120$	−4.73205	−	4.73205i	−0.431975	−	0.431975i
$121$	−1.46410	+	2.53590i	−0.133100	+	0.230536i
$122$	3.48477	−	6.03579i	0.315496	−	0.546455i
$123$	1.56218	+	1.56218i	0.140857	+	0.140857i
$124$	0.896575	+	1.55291i	0.0805149	+	0.139456i
$125$	−19.0411			−1.70309
$126$		0			0
$127$	6.53590			0.579967			0.289984	−	0.957032i	$-0.406350\pi$
$127$	6.53590			0.579967			0.289984	+	0.957032i	$0.406350\pi$
$128$	−0.500000	−	0.866025i	−0.0441942	−	0.0765466i
$129$	−6.24384	+	1.67303i	−0.549740	+	0.147302i
$130$	−12.9282	+	22.3923i	−1.13388	+	1.96394i
$131$	3.01790	−	5.22715i	0.263675	−	0.456698i	−0.703541	−	0.710655i	$-0.748399\pi$
$131$	3.01790	−	5.22715i	0.263675	−	0.456698i	0.967216	+	0.253957i	$0.0817321\pi$
$132$	−1.67303	+	6.24384i	−0.145619	+	0.543457i
$133$		0			0
$134$	5.53590			0.478229
$135$	5.19615	+	19.3923i	0.447214	+	1.66902i
$136$	−5.41662			−0.464471
$137$	4.33013	+	7.50000i	0.369948	+	0.640768i	0.989557	−	0.144142i	$-0.0460423\pi$
$137$	4.33013	+	7.50000i	0.369948	+	0.640768i	−0.619609	+	0.784910i	$0.712709\pi$
$138$	−0.656339	+	2.44949i	−0.0558713	+	0.208514i
$139$	−8.17569	+	14.1607i	−0.693453	+	1.20110i	0.277246	+	0.960799i	$0.410578\pi$
$139$	−8.17569	+	14.1607i	−0.693453	+	1.20110i	−0.970699	+	0.240297i	$0.922755\pi$
$140$		0			0
$141$	17.6603	−	4.73205i	1.48726	−	0.398511i
$142$	−1.26795	−	2.19615i	−0.106404	−	0.184297i
$143$	24.9754			2.08855
$144$			3.00000i			0.250000i
$145$	15.4548			1.28345
$146$	−3.41542	−	5.91567i	−0.282662	−	0.489585i
$147$		0			0
$148$	−0.267949	+	0.464102i	−0.0220253	+	0.0381489i
$149$	−4.53590	+	7.85641i	−0.371595	+	0.643622i	−0.989811	−	0.142386i	$-0.954522\pi$
$149$	−4.53590	+	7.85641i	−0.371595	+	0.643622i	0.618216	+	0.786008i	$0.287856\pi$
$150$	12.1595	+	12.1595i	0.992820	+	0.992820i
$151$	1.19615	+	2.07180i	0.0973415	+	0.168600i	0.910583	−	0.413325i	$-0.135633\pi$
$151$	1.19615	+	2.07180i	0.0973415	+	0.168600i	−0.813242	+	0.581926i	$0.802299\pi$
$152$	2.96713			0.240666
$153$	14.0728	+	8.12493i	1.13772	+	0.656861i
$154$		0			0
$155$	−3.46410	−	6.00000i	−0.278243	−	0.481932i
$156$	11.1962	−	3.00000i	0.896410	−	0.240192i
$157$	2.31079	−	4.00240i	0.184421	−	0.319427i	−0.758960	−	0.651137i	$-0.774292\pi$
$157$	2.31079	−	4.00240i	0.184421	−	0.319427i	0.943381	+	0.331710i	$0.107626\pi$
$158$	2.46410	−	4.26795i	0.196033	−	0.339540i
$159$	−1.31268	+	4.89898i	−0.104102	+	0.388514i
$160$	1.93185	+	3.34607i	0.152726	+	0.264530i
$161$		0			0
$162$	4.50000	−	7.79423i	0.353553	−	0.612372i
$163$	21.3205			1.66995			0.834976	−	0.550287i	$-0.185482\pi$
$163$	21.3205			1.66995			0.834976	+	0.550287i	$0.185482\pi$
$164$	−0.637756	−	1.10463i	−0.0498004	−	0.0862568i
$165$	6.46410	−	24.1244i	0.503230	−	1.87808i
$166$	−8.95215	+	15.5056i	−0.694822	+	1.20347i
$167$	10.5558	−	18.2832i	0.816835	−	1.41480i	−0.0911679	−	0.995836i	$-0.529060\pi$
$167$	10.5558	−	18.2832i	0.816835	−	1.41480i	0.908003	−	0.418964i	$-0.137607\pi$
$168$		0			0
$169$	−15.8923	−	27.5263i	−1.22248	−	2.11741i
$170$	20.9282			1.60512
$171$	−7.70882	−	4.45069i	−0.589509	−	0.340353i
$172$	3.73205			0.284566
$173$	0.896575	+	1.55291i	0.0681654	+	0.118066i	0.898094	−	0.439804i	$-0.144952\pi$
$173$	0.896575	+	1.55291i	0.0681654	+	0.118066i	−0.829928	+	0.557870i	$0.811619\pi$
$174$	−4.89898	−	4.89898i	−0.371391	−	0.371391i
$175$		0			0
$176$	1.86603	−	3.23205i	0.140657	−	0.243625i
$177$	10.5622	+	10.5622i	0.793902	+	0.793902i
$178$	3.53553	+	6.12372i	0.264999	+	0.458993i
$179$	18.9282			1.41476			0.707380	−	0.706833i	$-0.249877\pi$
$179$	18.9282			1.41476			0.707380	+	0.706833i	$0.249877\pi$
$180$		−	11.5911i		−	0.863950i
$181$	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
$183$	11.6603	−	3.12436i	0.861951	−	0.230959i
$184$	0.732051	−	1.26795i	0.0539675	−	0.0934745i
$185$	1.03528	−	1.79315i	0.0761150	−	0.131835i
$186$	−0.803848	+	3.00000i	−0.0589410	+	0.219971i
$187$	−10.1075	−	17.5068i	−0.739137	−	1.28022i
$188$	−10.5558			−0.769863
$189$		0			0
$190$	−11.4641			−0.831693
$191$	−0.535898	−	0.928203i	−0.0387762	−	0.0671624i	0.845986	−	0.533205i	$-0.179013\pi$
$191$	−0.535898	−	0.928203i	−0.0387762	−	0.0671624i	−0.884762	+	0.466043i	$0.845679\pi$
$192$	0.448288	−	1.67303i	0.0323524	−	0.120741i
$193$	11.5263	−	19.9641i	0.829680	−	1.43705i	−0.0686098	−	0.997644i	$-0.521856\pi$
$193$	11.5263	−	19.9641i	0.829680	−	1.43705i	0.898290	−	0.439404i	$-0.144810\pi$
$194$	−2.94855	+	5.10703i	−0.211693	+	0.366663i
$195$	−43.2586	+	11.5911i	−3.09781	+	0.830057i
$196$		0			0
$197$	−3.07180			−0.218856			−0.109428	−	0.993995i	$-0.534902\pi$
$197$	−3.07180			−0.218856			−0.109428	+	0.993995i	$0.534902\pi$
$198$	−9.69615	+	5.59808i	−0.689076	+	0.397838i
$199$	17.8028			1.26200			0.631002	−	0.775781i	$-0.282644\pi$
$199$	17.8028			1.26200			0.631002	+	0.775781i	$0.282644\pi$
$200$	−4.96410	−	8.59808i	−0.351015	−	0.607976i
$201$	6.78006	+	6.78006i	0.478229	+	0.478229i
$202$	2.44949	−	4.24264i	0.172345	−	0.298511i
$203$		0			0
$204$	−6.63397	−	6.63397i	−0.464471	−	0.464471i
$205$	2.46410	+	4.26795i	0.172100	+	0.298087i
$206$	−7.45001			−0.519066
$207$	−3.80385	+	2.19615i	−0.264386	+	0.152643i
$208$	−6.69213			−0.464016
$209$	5.53674	+	9.58991i	0.382984	+	0.663348i
$210$		0			0
$211$	−2.53590	+	4.39230i	−0.174578	+	0.302379i	−0.940015	−	0.341132i	$-0.889190\pi$
$211$	−2.53590	+	4.39230i	−0.174578	+	0.302379i	0.765437	+	0.643511i	$0.222523\pi$
$212$	1.46410	−	2.53590i	0.100555	−	0.174166i
$213$	1.13681	−	4.24264i	0.0778931	−	0.290701i
$214$	−1.69615	−	2.93782i	−0.115947	−	0.200825i
$215$	−14.4195			−0.983404
$216$	−3.67423	+	3.67423i	−0.250000	+	0.250000i
$217$		0			0
$218$	4.46410	+	7.73205i	0.302347	+	0.523681i
$219$	3.06218	−	11.4282i	0.206923	−	0.772246i
$220$	−7.20977	+	12.4877i	−0.486082	+	0.841920i
$221$	−18.1244	+	31.3923i	−1.21918	+	2.11167i
$222$	−0.896575	+	0.240237i	−0.0601742	+	0.0161236i
$223$	−13.3843	−	23.1822i	−0.896276	−	1.55240i	−0.832217	−	0.554450i	$-0.812929\pi$
$223$	−13.3843	−	23.1822i	−0.896276	−	1.55240i	−0.0640595	−	0.997946i	$-0.520405\pi$
$224$		0			0
$225$			29.7846i			1.98564i
$226$	6.92820			0.460857
$227$	−5.25933	−	9.10943i	−0.349074	−	0.604614i	0.637011	−	0.770855i	$-0.280171\pi$
$227$	−5.25933	−	9.10943i	−0.349074	−	0.604614i	−0.986085	+	0.166240i	$0.946837\pi$
$228$	3.63397	+	3.63397i	0.240666	+	0.240666i
$229$	12.4877	−	21.6293i	0.825209	−	1.42930i	−0.0765496	−	0.997066i	$-0.524390\pi$
$229$	12.4877	−	21.6293i	0.825209	−	1.42930i	0.901759	−	0.432239i	$-0.142276\pi$
$230$	−2.82843	+	4.89898i	−0.186501	+	0.323029i
$231$		0			0
$232$	2.00000	+	3.46410i	0.131306	+	0.227429i
$233$	−24.1244			−1.58044			−0.790220	−	0.612824i	$-0.790034\pi$
$233$	−24.1244			−1.58044			−0.790220	+	0.612824i	$0.790034\pi$
$234$	17.3867	+	10.0382i	1.13660	+	0.656217i
$235$	40.7846			2.66049
$236$	−4.31199	−	7.46859i	−0.280687	−	0.486164i
$237$	8.24504	−	2.20925i	0.535573	−	0.143506i
$238$		0			0
$239$	6.46410	−	11.1962i	0.418128	−	0.724219i	−0.577623	−	0.816304i	$-0.696020\pi$
$239$	6.46410	−	11.1962i	0.418128	−	0.724219i	0.995751	+	0.0920846i	$0.0293530\pi$
$240$	−1.73205	+	6.46410i	−0.111803	+	0.417256i
$241$	11.7112	+	20.2844i	0.754387	+	1.30664i	0.945679	+	0.325103i	$0.105399\pi$
$241$	11.7112	+	20.2844i	0.754387	+	1.30664i	−0.191292	+	0.981533i	$0.561268\pi$
$242$	2.92820			0.188232
$243$	15.0573	−	4.03459i	0.965926	−	0.258819i
$244$	−6.96953			−0.446179
$245$		0			0
$246$	0.571797	−	2.13397i	0.0364564	−	0.136057i
$247$	9.92820	−	17.1962i	0.631716	−	1.09416i
$248$	0.896575	−	1.55291i	0.0569326	−	0.0986102i
$249$	−29.9545	+	8.02628i	−1.89829	+	0.508645i
$250$	9.52056	+	16.4901i	0.602133	+	1.04292i
$251$	16.3514			1.03209			0.516045	−	0.856561i	$-0.327404\pi$
$251$	16.3514			1.03209			0.516045	+	0.856561i	$0.327404\pi$
$252$		0			0
$253$	5.46410			0.343525
$254$	−3.26795	−	5.66025i	−0.205049	−	0.355156i
$255$	25.6317	+	25.6317i	1.60512	+	1.60512i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	1.34486	−	2.32937i	0.0838903	−	0.145302i	−0.821028	−	0.570889i	$-0.806599\pi$
$257$	1.34486	−	2.32937i	0.0838903	−	0.145302i	0.904918	+	0.425586i	$0.139932\pi$
$258$	4.57081	+	4.57081i	0.284566	+	0.284566i
$259$		0			0
$260$	25.8564			1.60355
$261$		−	12.0000i		−	0.742781i
$262$	−6.03579			−0.372892
$263$	7.73205	+	13.3923i	0.476779	+	0.825805i	0.999646	−	0.0266092i	$-0.00847098\pi$
$263$	7.73205	+	13.3923i	0.476779	+	0.825805i	−0.522867	+	0.852414i	$0.675138\pi$
$264$	6.24384	−	1.67303i	0.384282	−	0.102968i
$265$	−5.65685	+	9.79796i	−0.347498	+	0.601884i
$266$		0			0
$267$	−3.16987	+	11.8301i	−0.193993	+	0.723992i
$268$	−2.76795	−	4.79423i	−0.169079	−	0.292854i
$269$	5.65685			0.344904			0.172452	−	0.985018i	$-0.444831\pi$
$269$	5.65685			0.344904			0.172452	+	0.985018i	$0.444831\pi$
$270$	14.1962	−	14.1962i	0.863950	−	0.863950i
$271$	−18.0058			−1.09378			−0.546888	−	0.837206i	$-0.684188\pi$
$271$	−18.0058			−1.09378			−0.546888	+	0.837206i	$0.684188\pi$
$272$	2.70831	+	4.69093i	0.164215	+	0.284429i
$273$		0			0
$274$	4.33013	−	7.50000i	0.261593	−	0.453092i
$275$	18.5263	−	32.0885i	1.11718	−	1.93501i
$276$	2.44949	−	0.656339i	0.147442	−	0.0395070i
$277$	−12.2679	−	21.2487i	−0.737110	−	1.27671i	−0.953792	−	0.300469i	$-0.902857\pi$
$277$	−12.2679	−	21.2487i	−0.737110	−	1.27671i	0.216682	−	0.976242i	$-0.430477\pi$
$278$	16.3514			0.980691
$279$	−4.65874	+	2.68973i	−0.278912	+	0.161030i
$280$		0			0
$281$	4.92820	+	8.53590i	0.293992	+	0.509209i	0.974750	−	0.223299i	$-0.0716828\pi$
$281$	4.92820	+	8.53590i	0.293992	+	0.509209i	−0.680758	+	0.732508i	$0.738349\pi$
$282$	−12.9282	−	12.9282i	−0.769863	−	0.769863i
$283$	4.70951	−	8.15711i	0.279951	−	0.484890i	−0.691421	−	0.722452i	$-0.743015\pi$
$283$	4.70951	−	8.15711i	0.279951	−	0.484890i	0.971372	+	0.237562i	$0.0763483\pi$
$284$	−1.26795	+	2.19615i	−0.0752389	+	0.130318i
$285$	−14.0406	−	14.0406i	−0.831693	−	0.831693i
$286$	−12.4877	−	21.6293i	−0.738412	−	1.27897i
$287$		0			0
$288$	2.59808	−	1.50000i	0.153093	−	0.0883883i
$289$	12.3397			0.725867
$290$	−7.72741	−	13.3843i	−0.453769	−	0.785951i
$291$	−9.86603	+	2.64359i	−0.578357	+	0.154970i
$292$	−3.41542	+	5.91567i	−0.199872	+	0.346189i
$293$	−9.52056	+	16.4901i	−0.556197	+	0.963361i	0.441612	+	0.897206i	$0.354407\pi$
$293$	−9.52056	+	16.4901i	−0.556197	+	0.963361i	−0.997809	+	0.0661554i	$0.978927\pi$
$294$		0			0
$295$	16.6603	+	28.8564i	0.969997	+	1.68008i
$296$	0.535898			0.0311485
$297$	−18.7315	−	5.01910i	−1.08691	−	0.291238i
$298$	9.07180			0.525515
$299$	−4.89898	−	8.48528i	−0.283315	−	0.490716i
$300$	4.45069	−	16.6102i	0.256961	−	0.958991i
$301$		0			0
$302$	1.19615	−	2.07180i	0.0688308	−	0.119219i
$303$	8.19615	−	2.19615i	0.470857	−	0.126166i
$304$	−1.48356	−	2.56961i	−0.0850882	−	0.147377i
$305$	26.9282			1.54190
$306$		−	16.2499i		−	0.928942i
$307$	11.0735			0.631996			0.315998	−	0.948760i	$-0.397661\pi$
$307$	11.0735			0.631996			0.315998	+	0.948760i	$0.397661\pi$
$308$		0			0
$309$	−9.12436	−	9.12436i	−0.519066	−	0.519066i
$310$	−3.46410	+	6.00000i	−0.196748	+	0.340777i
$311$	−6.17449	+	10.6945i	−0.350123	+	0.606431i	−0.986271	−	0.165136i	$-0.947194\pi$
$311$	−6.17449	+	10.6945i	−0.350123	+	0.606431i	0.636147	+	0.771568i	$0.280527\pi$
$312$	−8.19615	−	8.19615i	−0.464016	−	0.464016i
$313$	11.7112	+	20.2844i	0.661958	+	1.14654i	0.980101	+	0.198502i	$0.0636075\pi$
$313$	11.7112	+	20.2844i	0.661958	+	1.14654i	−0.318143	+	0.948043i	$0.603059\pi$
$314$	−4.62158			−0.260811
$315$		0			0
$316$	−4.92820			−0.277233
$317$	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	−	1.31268i	0.274721	−	0.0736113i
$319$	−7.46410	+	12.9282i	−0.417909	+	0.723840i
$320$	1.93185	−	3.34607i	0.107994	−	0.187051i
$321$	1.52073	−	5.67544i	0.0848788	−	0.316772i
$322$		0			0
$323$	−16.0718			−0.894259
$324$	−9.00000			−0.500000
$325$	−66.4408			−3.68547
$326$	−10.6603	−	18.4641i	−0.590417	−	1.02263i
$327$	−4.00240	+	14.9372i	−0.221333	+	0.826028i
$328$	−0.637756	+	1.10463i	−0.0352142	+	0.0609928i
$329$		0			0
$330$	−24.1244	+	6.46410i	−1.32800	+	0.355837i
$331$	2.26795	+	3.92820i	0.124658	+	0.215914i	0.921599	−	0.388143i	$-0.126883\pi$
$331$	2.26795	+	3.92820i	0.124658	+	0.215914i	−0.796941	+	0.604057i	$0.793550\pi$
$332$	17.9043			0.982626
$333$	−1.39230	−	0.803848i	−0.0762978	−	0.0440506i
$334$	−21.1117			−1.15518
$335$	10.6945	+	18.5235i	0.584305	+	1.01205i
$336$		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	$0.105605\pi$
$338$	−15.8923	+	27.5263i	−0.864427	+	1.49723i
$339$	8.48528	+	8.48528i	0.460857	+	0.460857i
$340$	−10.4641	−	18.1244i	−0.567496	−	0.982931i
$341$	6.69213			0.362399
$342$			8.90138i			0.481332i
$343$		0			0
$344$	−1.86603	−	3.23205i	−0.100609	−	0.174261i
$345$	−9.46410	+	2.53590i	−0.509530	+	0.136528i
$346$	0.896575	−	1.55291i	0.0482002	−	0.0834852i
$347$	−10.7942	+	18.6962i	−0.579465	+	1.00366i	0.416076	+	0.909330i	$0.363405\pi$
$347$	−10.7942	+	18.6962i	−0.579465	+	1.00366i	−0.995541	+	0.0943323i	$0.969928\pi$
$348$	−1.79315	+	6.69213i	−0.0961230	+	0.358736i
$349$	8.24504	+	14.2808i	0.441347	+	0.764436i	0.997790	−	0.0664504i	$-0.0211674\pi$
$349$	8.24504	+	14.2808i	0.441347	+	0.764436i	−0.556443	+	0.830886i	$0.687834\pi$
$350$		0			0
$351$	9.00000	+	33.5885i	0.480384	+	1.79282i
$352$	−3.73205			−0.198919
$353$	−13.2134	−	22.8862i	−0.703277	−	1.21811i	−0.967310	−	0.253598i	$-0.918386\pi$
$353$	−13.2134	−	22.8862i	−0.703277	−	1.21811i	0.264033	−	0.964514i	$-0.414947\pi$
$354$	3.86603	−	14.4282i	0.205477	−	0.766850i
$355$	4.89898	−	8.48528i	0.260011	−	0.450352i
$356$	3.53553	−	6.12372i	0.187383	−	0.324557i
$357$		0			0
$358$	−9.46410	−	16.3923i	−0.500193	−	0.866360i
$359$	0.535898			0.0282836			0.0141418	−	0.999900i	$-0.495498\pi$
$359$	0.535898			0.0282836			0.0141418	+	0.999900i	$0.495498\pi$
$360$	−10.0382	+	5.79555i	−0.529059	+	0.305453i
$361$	−10.1962			−0.536640
$362$	−8.48528	−	14.6969i	−0.445976	−	0.772454i
$363$	3.58630	+	3.58630i	0.188232	+	0.188232i
$364$		0			0
$365$	13.1962	−	22.8564i	0.690718	−	1.19636i
$366$	−8.53590	−	8.53590i	−0.446179	−	0.446179i
$367$	−7.86611	−	13.6245i	−0.410607	−	0.711193i	0.584349	−	0.811503i	$-0.301350\pi$
$367$	−7.86611	−	13.6245i	−0.410607	−	0.711193i	−0.994956	+	0.100310i	$0.968017\pi$
$368$	−1.46410			−0.0763216
$369$	3.31388	−	1.91327i	0.172514	−	0.0996008i
$370$	−2.07055			−0.107643
$371$		0			0
$372$	3.00000	−	0.803848i	0.155543	−	0.0416776i
$373$	−15.3923	+	26.6603i	−0.796983	+	1.38042i	0.124589	+	0.992208i	$0.460239\pi$
$373$	−15.3923	+	26.6603i	−0.796983	+	1.38042i	−0.921572	+	0.388207i	$0.873095\pi$
$374$	−10.1075	+	17.5068i	−0.522649	+	0.905254i
$375$	−8.53590	+	31.8564i	−0.440792	+	1.64506i
$376$	5.27792	+	9.14162i	0.272188	+	0.471443i
$377$	26.7685			1.37865
$378$		0			0
$379$	−17.5885			−0.903458			−0.451729	−	0.892155i	$-0.649193\pi$
$379$	−17.5885			−0.903458			−0.451729	+	0.892155i	$0.649193\pi$
$380$	5.73205	+	9.92820i	0.294048	+	0.509306i
$381$	2.92996	−	10.9348i	0.150107	−	0.560205i
$382$	−0.535898	+	0.928203i	−0.0274189	+	0.0474910i
$383$	−10.8332	+	18.7637i	−0.553552	+	0.958781i	0.444462	+	0.895798i	$0.353395\pi$
$383$	−10.8332	+	18.7637i	−0.553552	+	0.958781i	−0.998015	+	0.0629833i	$0.979939\pi$
$384$	−1.67303	+	0.448288i	−0.0853766	+	0.0228766i
$385$		0			0
$386$	−23.0526			−1.17334
$387$			11.1962i			0.569132i
$388$	5.89709			0.299379
$389$	−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	$0.898340\pi$
$390$	31.6675	+	31.6675i	1.60355	+	1.60355i
$391$	−3.96524	+	6.86800i	−0.200531	+	0.347329i
$392$		0			0
$393$	−7.39230	−	7.39230i	−0.372892	−	0.372892i
$394$	1.53590	+	2.66025i	0.0773774	+	0.134022i
$395$	19.0411			0.958062
$396$	9.69615	+	5.59808i	0.487250	+	0.281314i
$397$	−18.0058			−0.903687			−0.451844	−	0.892097i	$-0.649233\pi$
$397$	−18.0058			−0.903687			−0.451844	+	0.892097i	$0.649233\pi$
$398$	−8.90138	−	15.4176i	−0.446186	−	0.772817i
$399$		0			0
$400$	−4.96410	+	8.59808i	−0.248205	+	0.429904i
$401$	−8.89230	+	15.4019i	−0.444061	+	0.769135i	−0.997986	−	0.0634307i	$-0.979796\pi$
$401$	−8.89230	+	15.4019i	−0.444061	+	0.769135i	0.553926	+	0.832566i	$0.313129\pi$
$402$	2.48168	−	9.26174i	0.123775	−	0.461934i
$403$	−6.00000	−	10.3923i	−0.298881	−	0.517678i
$404$	−4.89898			−0.243733
$405$	34.7733			1.72790
$406$		0			0
$407$	1.00000	+	1.73205i	0.0495682	+	0.0858546i
$408$	−2.42820	+	9.06218i	−0.120214	+	0.448645i
$409$	8.36516	−	14.4889i	0.413631	−	0.716429i	−0.581653	−	0.813437i	$-0.697594\pi$
$409$	8.36516	−	14.4889i	0.413631	−	0.716429i	0.995284	+	0.0970077i	$0.0309271\pi$
$410$	2.46410	−	4.26795i	0.121693	−	0.210779i
$411$	14.4889	−	3.88229i	0.714684	−	0.191499i
$412$	3.72500	+	6.45189i	0.183518	+	0.317862i
$413$		0			0
$414$	3.80385	+	2.19615i	0.186949	+	0.107935i
$415$	−69.1769			−3.39576
$416$	3.34607	+	5.79555i	0.164054	+	0.284150i
$417$	20.0263	+	20.0263i	0.980691	+	0.980691i
$418$	5.53674	−	9.58991i	0.270811	−	0.469058i
$419$	−3.95164	+	6.84443i	−0.193050	+	0.334373i	−0.946260	−	0.323408i	$-0.895171\pi$
$419$	−3.95164	+	6.84443i	−0.193050	+	0.334373i	0.753209	+	0.657781i	$0.228505\pi$
$420$		0			0
$421$	−14.1962	−	24.5885i	−0.691878	−	1.19837i	−0.971222	−	0.238177i	$-0.923450\pi$
$421$	−14.1962	−	24.5885i	−0.691878	−	1.19837i	0.279344	−	0.960191i	$-0.409883\pi$
$422$	5.07180			0.246891
$423$		−	31.6675i		−	1.53973i
$424$	−2.92820			−0.142206
$425$	26.8886	+	46.5725i	1.30429	+	2.25910i
$426$	−4.24264	+	1.13681i	−0.205557	+	0.0550787i
$427$		0			0
$428$	−1.69615	+	2.93782i	−0.0819866	+	0.142005i
$429$	11.1962	−	41.7846i	0.540555	−	2.01738i
$430$	7.20977	+	12.4877i	0.347686	+	0.602210i
$431$	−37.8564			−1.82348			−0.911739	−	0.410769i	$-0.865260\pi$
$431$	−37.8564			−1.82348			−0.911739	+	0.410769i	$0.865260\pi$
$432$	5.01910	+	1.34486i	0.241481	+	0.0647048i
$433$	−7.10823			−0.341600			−0.170800	−	0.985306i	$-0.554635\pi$
$433$	−7.10823			−0.341600			−0.170800	+	0.985306i	$0.554635\pi$
$434$		0			0
$435$	6.92820	−	25.8564i	0.332182	−	1.23972i
$436$	4.46410	−	7.73205i	0.213792	−	0.370298i
$437$	2.17209	−	3.76217i	0.103905	−	0.179969i
$438$	−11.4282	+	3.06218i	−0.546061	+	0.146317i
$439$	−9.79796	−	16.9706i	−0.467631	−	0.809961i	0.531685	−	0.846942i	$-0.321559\pi$
$439$	−9.79796	−	16.9706i	−0.467631	−	0.809961i	−0.999316	+	0.0369815i	$0.988226\pi$
$440$	14.4195			0.687424
$441$		0			0
$442$	36.2487			1.72418
$443$	9.16025	+	15.8660i	0.435217	+	0.753818i	0.997313	−	0.0732540i	$-0.0233384\pi$
$443$	9.16025	+	15.8660i	0.435217	+	0.753818i	−0.562097	+	0.827072i	$0.690005\pi$
$444$	0.656339	+	0.656339i	0.0311485	+	0.0311485i
$445$	−13.6603	+	23.6603i	−0.647558	+	1.12160i
$446$	−13.3843	+	23.1822i	−0.633763	+	1.09771i
$447$	11.1106	+	11.1106i	0.525515	+	0.525515i
$448$		0			0
$449$	−17.7846			−0.839308			−0.419654	−	0.907684i	$-0.637849\pi$
$449$	−17.7846			−0.839308			−0.419654	+	0.907684i	$0.637849\pi$
$450$	25.7942	−	14.8923i	1.21595	−	0.702030i
$451$	−4.76028			−0.224153
$452$	−3.46410	−	6.00000i	−0.162938	−	0.282216i
$453$	4.00240	−	1.07244i	0.188049	−	0.0503877i
$454$	−5.25933	+	9.10943i	−0.246833	+	0.427527i
$455$		0			0
$456$	1.33013	−	4.96410i	0.0622889	−	0.232465i
$457$	−3.52628	−	6.10770i	−0.164952	−	0.285706i	0.771686	−	0.636004i	$-0.219414\pi$
$457$	−3.52628	−	6.10770i	−0.164952	−	0.285706i	−0.936638	+	0.350298i	$0.886080\pi$
$458$	−24.9754			−1.16702
$459$	19.9019	−	19.9019i	0.928942	−	0.928942i
$460$	5.65685			0.263752
$461$	−12.8666	−	22.2856i	−0.599258	−	1.03795i	−0.992931	−	0.118695i	$-0.962129\pi$
$461$	−12.8666	−	22.2856i	−0.599258	−	1.03795i	0.393672	−	0.919251i	$-0.371204\pi$
$462$		0			0
$463$	−19.3205	+	33.4641i	−0.897900	+	1.55521i	−0.0677264	+	0.997704i	$0.521575\pi$
$463$	−19.3205	+	33.4641i	−0.897900	+	1.55521i	−0.830174	+	0.557505i	$0.811759\pi$
$464$	2.00000	−	3.46410i	0.0928477	−	0.160817i
$465$	−11.5911	+	3.10583i	−0.537525	+	0.144029i
$466$	12.0622	+	20.8923i	0.558770	+	0.967817i
$467$	27.5636			1.27549			0.637745	−	0.770248i	$-0.279867\pi$
$467$	27.5636			1.27549			0.637745	+	0.770248i	$0.279867\pi$
$468$		−	20.0764i		−	0.928032i
$469$		0			0
$470$	−20.3923	−	35.3205i	−0.940627	−	1.62921i
$471$	−5.66025	−	5.66025i	−0.260811	−	0.260811i
$472$	−4.31199	+	7.46859i	−0.198475	+	0.343770i
$473$	6.96410	−	12.0622i	0.320210	−	0.554620i
$474$	−6.03579	−	6.03579i	−0.277233	−	0.277233i
$475$	−14.7291	−	25.5116i	−0.675819	−	1.17055i
$476$		0			0
$477$	7.60770	+	4.39230i	0.348332	+	0.201110i
$478$	−12.9282			−0.591322
$479$	7.72741	+	13.3843i	0.353074	+	0.611542i	0.986786	−	0.162026i	$-0.0518030\pi$
$479$	7.72741	+	13.3843i	0.353074	+	0.611542i	−0.633712	+	0.773569i	$0.718470\pi$
$480$	6.46410	−	1.73205i	0.295045	−	0.0790569i
$481$	1.79315	−	3.10583i	0.0817606	−	0.141614i
$482$	11.7112	−	20.2844i	0.533432	−	0.923931i
$483$		0			0
$484$	−1.46410	−	2.53590i	−0.0665501	−	0.115268i
$485$	−22.7846			−1.03460
$486$	−11.0227	−	11.0227i	−0.500000	−	0.500000i
$487$	38.7846			1.75750			0.878749	−	0.477284i	$-0.158379\pi$
$487$	38.7846			1.75750			0.878749	+	0.477284i	$0.158379\pi$
$488$	3.48477	+	6.03579i	0.157748	+	0.273227i
$489$	9.55772	−	35.6699i	0.432215	−	1.61305i
$490$		0			0
$491$	0.696152	−	1.20577i	0.0314169	−	0.0544157i	−0.849889	−	0.526961i	$-0.823331\pi$
$491$	0.696152	−	1.20577i	0.0314169	−	0.0544157i	0.881306	+	0.472545i	$0.156665\pi$
$492$	−2.13397	+	0.571797i	−0.0962070	+	0.0257786i
$493$	−10.8332	−	18.7637i	−0.487904	−	0.845075i
$494$	−19.8564			−0.893382
$495$	−37.4631	−	21.6293i	−1.68384	−	0.972165i
$496$	−1.79315			−0.0805149
$497$		0			0
$498$	21.9282	+	21.9282i	0.982626	+	0.982626i
$499$	−6.30385	+	10.9186i	−0.282199	+	0.488783i	−0.971926	−	0.235286i	$-0.924397\pi$
$499$	−6.30385	+	10.9186i	−0.282199	+	0.488783i	0.689727	+	0.724069i	$0.257731\pi$
$500$	9.52056	−	16.4901i	0.425772	−	0.737459i
$501$	−25.8564	−	25.8564i	−1.15518	−	1.15518i
$502$	−8.17569	−	14.1607i	−0.364899	−	0.632024i
$503$	7.45001			0.332179			0.166090	−	0.986111i	$-0.446886\pi$
$503$	7.45001			0.332179			0.166090	+	0.986111i	$0.446886\pi$
$504$		0			0
$505$	18.9282			0.842294
$506$	−2.73205	−	4.73205i	−0.121454	−	0.210365i
$507$	−53.1767	+	14.2487i	−2.36166	+	0.632805i
$508$	−3.26795	+	5.66025i	−0.144992	+	0.251133i
$509$	13.2456	−	22.9420i	0.587099	−	1.01689i	−0.407511	−	0.913200i	$-0.633603\pi$
$509$	13.2456	−	22.9420i	0.587099	−	1.01689i	0.994610	−	0.103685i	$-0.0330635\pi$
$510$	9.38186	−	35.0136i	0.415436	−	1.55043i
$511$		0			0
$512$	1.00000			0.0441942
$513$	−10.9019	+	10.9019i	−0.481332	+	0.481332i
$514$	−2.68973			−0.118639
$515$	−14.3923	−	24.9282i	−0.634201	−	1.09847i
$516$	1.67303	−	6.24384i	0.0736512	−	0.274870i
$517$	−19.6975	+	34.1170i	−0.866293	+	1.50046i
$518$		0			0
$519$	3.00000	−	0.803848i	0.131685	−	0.0352850i
$520$	−12.9282	−	22.3923i	−0.566939	−	0.981968i
$521$	−32.3610			−1.41776			−0.708881	−	0.705328i	$-0.750800\pi$
$521$	−32.3610			−1.41776			−0.708881	+	0.705328i	$0.750800\pi$
$522$	−10.3923	+	6.00000i	−0.454859	+	0.262613i
$523$	3.76217			0.164508			0.0822540	−	0.996611i	$-0.473788\pi$
$523$	3.76217			0.164508			0.0822540	+	0.996611i	$0.473788\pi$
$524$	3.01790	+	5.22715i	0.131837	+	0.228349i
$525$		0			0
$526$	7.73205	−	13.3923i	0.337133	−	0.583932i
$527$	−4.85641	+	8.41154i	−0.211548	+	0.366413i
$528$	−4.57081	−	4.57081i	−0.198919	−	0.198919i
$529$	10.4282	+	18.0622i	0.453400	+	0.785312i
$530$	11.3137			0.491436
$531$	22.4058	−	12.9360i	0.972327	−	0.561373i
$532$		0			0
$533$	4.26795	+	7.39230i	0.184865	+	0.320196i
$534$	11.8301	−	3.16987i	0.511940	−	0.137174i
$535$	6.55343	−	11.3509i	0.283329	−	0.490741i
$536$	−2.76795	+	4.79423i	−0.119557	+	0.207079i
$537$	8.48528	−	31.6675i	0.366167	−	1.36655i
$538$	−2.82843	−	4.89898i	−0.121942	−	0.211210i
$539$		0			0
$540$	−19.3923	−	5.19615i	−0.834512	−	0.223607i
$541$	−19.3205			−0.830654			−0.415327	−	0.909672i	$-0.636333\pi$
$541$	−19.3205			−0.830654			−0.415327	+	0.909672i	$0.636333\pi$
$542$	9.00292	+	15.5935i	0.386709	+	0.669799i
$543$	7.60770	−	28.3923i	0.326477	−	1.21843i
$544$	2.70831	−	4.69093i	0.116118	−	0.201122i
$545$	−17.2480	+	29.8744i	−0.738822	+	1.27968i
$546$		0			0
$547$	19.1865	+	33.2321i	0.820357	+	1.42090i	0.905417	+	0.424524i	$0.139559\pi$
$547$	19.1865	+	33.2321i	0.820357	+	1.42090i	−0.0850597	+	0.996376i	$0.527108\pi$
$548$	−8.66025			−0.369948
$549$		−	20.9086i		−	0.892357i
$550$	−37.0526			−1.57993
$551$	5.93426	+	10.2784i	0.252808	+	0.437876i
$552$	−1.79315	−	1.79315i	−0.0763216	−	0.0763216i
$553$		0			0
$554$	−12.2679	+	21.2487i	−0.521215	+	0.902771i
$555$	−2.53590	−	2.53590i	−0.107643	−	0.107643i
$556$	−8.17569	−	14.1607i	−0.346727	−	0.600548i
$557$	6.92820			0.293557			0.146779	−	0.989169i	$-0.453109\pi$
$557$	6.92820			0.293557			0.146779	+	0.989169i	$0.453109\pi$
$558$	4.65874	+	2.68973i	0.197220	+	0.113865i
$559$	−24.9754			−1.05635
$560$		0			0
$561$	−33.8205	+	9.06218i	−1.42790	+	0.382605i
$562$	4.92820	−	8.53590i	0.207884	−	0.360065i
$563$	−12.7973	+	22.1655i	−0.539341	+	0.934166i	0.459599	+	0.888127i	$0.347993\pi$
$563$	−12.7973	+	22.1655i	−0.539341	+	0.934166i	−0.998940	+	0.0460390i	$0.985340\pi$
$564$	−4.73205	+	17.6603i	−0.199255	+	0.743631i
$565$	13.3843	+	23.1822i	0.563080	+	0.975283i
$566$	−9.41902			−0.395911
$567$		0			0
$568$	2.53590			0.106404
$569$	−7.89230	−	13.6699i	−0.330863	−	0.573071i	0.651819	−	0.758375i	$-0.274006\pi$
$569$	−7.89230	−	13.6699i	−0.330863	−	0.573071i	−0.982681	+	0.185304i	$0.940673\pi$
$570$	−5.13922	+	19.1798i	−0.215258	+	0.803354i
$571$	−2.52628	+	4.37564i	−0.105722	+	0.183115i	−0.914033	−	0.405640i	$-0.867049\pi$
$571$	−2.52628	+	4.37564i	−0.105722	+	0.183115i	0.808311	+	0.588755i	$0.200382\pi$
$572$	−12.4877	+	21.6293i	−0.522136	+	0.904367i
$573$	−1.79315	+	0.480473i	−0.0749100	+	0.0200721i
$574$		0			0
$575$	−14.5359			−0.606189
$576$	−2.59808	−	1.50000i	−0.108253	−	0.0625000i
$577$	44.6357			1.85821			0.929103	−	0.369820i	$-0.120581\pi$
$577$	44.6357			1.85821			0.929103	+	0.369820i	$0.120581\pi$
$578$	−6.16987	−	10.6865i	−0.256633	−	0.444501i
$579$	−28.2335	−	28.2335i	−1.17334	−	1.17334i
$580$	−7.72741	+	13.3843i	−0.320863	+	0.555751i
$581$		0			0
$582$	7.22243	+	7.22243i	0.299379	+	0.299379i
$583$	−5.46410	−	9.46410i	−0.226300	−	0.391963i
$584$	6.83083			0.282662
$585$			77.5692i			3.20709i
$586$	19.0411			0.786581
$587$	14.5768	+	25.2478i	0.601650	+	1.04209i	0.992571	+	0.121664i	$0.0388230\pi$
$587$	14.5768	+	25.2478i	0.601650	+	1.04209i	−0.390922	+	0.920424i	$0.627844\pi$
$588$		0			0
$589$	2.66025	−	4.60770i	0.109614	−	0.189857i
$590$	16.6603	−	28.8564i	0.685892	−	1.18800i
$591$	−1.37705	+	5.13922i	−0.0566442	+	0.211399i
$592$	−0.267949	−	0.464102i	−0.0110126	−	0.0190745i
$593$	2.72689			0.111980			0.0559900	−	0.998431i	$-0.482169\pi$
$593$	2.72689			0.111980			0.0559900	+	0.998431i	$0.482169\pi$
$594$	5.01910	+	18.7315i	0.205936	+	0.768564i
$595$		0			0
$596$	−4.53590	−	7.85641i	−0.185798	−	0.321811i
$597$	7.98076	−	29.7846i	0.326631	−	1.21900i
$598$	−4.89898	+	8.48528i	−0.200334	+	0.346989i
$599$	18.3923	−	31.8564i	0.751489	−	1.30162i	−0.195612	−	0.980681i	$-0.562669\pi$
$599$	18.3923	−	31.8564i	0.751489	−	1.30162i	0.947101	−	0.320936i	$-0.103997\pi$
$600$	−16.6102	+	4.45069i	−0.678109	+	0.181699i
$601$	−0.448288	−	0.776457i	−0.0182860	−	0.0316723i	0.856738	−	0.515753i	$-0.172488\pi$
$601$	−0.448288	−	0.776457i	−0.0182860	−	0.0316723i	−0.875024	+	0.484080i	$0.839154\pi$
$602$		0			0
$603$	14.3827	−	8.30385i	0.585708	−	0.338159i
$604$	−2.39230			−0.0973415
$605$	5.65685	+	9.79796i	0.229984	+	0.398344i
$606$	−6.00000	−	6.00000i	−0.243733	−	0.243733i
$607$	−15.8338	+	27.4249i	−0.642672	+	1.11314i	0.342162	+	0.939641i	$0.388841\pi$
$607$	−15.8338	+	27.4249i	−0.642672	+	1.11314i	−0.984834	+	0.173500i	$0.944492\pi$
$608$	−1.48356	+	2.56961i	−0.0601665	+	0.104211i
$609$		0			0
$610$	−13.4641	−	23.3205i	−0.545146	−	0.944220i
$611$	70.6410			2.85783
$612$	−14.0728	+	8.12493i	−0.568859	+	0.328431i
$613$	11.0718			0.447186			0.223593	−	0.974683i	$-0.428221\pi$
$613$	11.0718			0.447186			0.223593	+	0.974683i	$0.428221\pi$
$614$	−5.53674	−	9.58991i	−0.223444	−	0.387017i
$615$	8.24504	−	2.20925i	0.332472	−	0.0890857i
$616$		0			0
$617$	15.4282	−	26.7224i	0.621116	−	1.07580i	−0.368162	−	0.929762i	$-0.620013\pi$
$617$	15.4282	−	26.7224i	0.621116	−	1.07580i	0.989278	−	0.146043i	$-0.0466538\pi$
$618$	−3.33975	+	12.4641i	−0.134344	+	0.501380i
$619$	12.3168	+	21.3333i	0.495054	+	0.857459i	0.999984	−	0.00570182i	$-0.00181496\pi$
$619$	12.3168	+	21.3333i	0.495054	+	0.857459i	−0.504930	+	0.863160i	$0.668482\pi$
$620$	6.92820			0.278243
$621$	1.96902	+	7.34847i	0.0790139	+	0.294884i
$622$	12.3490			0.495149
$623$		0			0
$624$	−3.00000	+	11.1962i	−0.120096	+	0.448205i
$625$	−11.9641	+	20.7224i	−0.478564	+	0.828897i
$626$	11.7112	−	20.2844i	0.468075	−	0.810729i
$627$	18.5263	−	4.96410i	0.739868	−	0.198247i
$628$	2.31079	+	4.00240i	0.0922105	+	0.159713i
$629$	−2.90276			−0.115740
$630$		0			0
$631$	35.7128			1.42170			0.710852	−	0.703341i	$-0.248309\pi$
$631$	35.7128			1.42170			0.710852	+	0.703341i	$0.248309\pi$
$632$	2.46410	+	4.26795i	0.0980167	+	0.169770i
$633$	6.21166	+	6.21166i	0.246891	+	0.246891i
$634$	13.0000	−	22.5167i	0.516296	−	0.894251i
$635$	12.6264	−	21.8695i	0.501063	−	0.867866i
$636$	−3.58630	−	3.58630i	−0.142206	−	0.142206i
$637$		0			0
$638$	14.9282			0.591013
$639$	−6.58846	−	3.80385i	−0.260635	−	0.150478i
$640$	−3.86370			−0.152726
$641$	−8.96410	−	15.5263i	−0.354061	−	0.613251i	0.632896	−	0.774237i	$-0.281866\pi$
$641$	−8.96410	−	15.5263i	−0.354061	−	0.613251i	−0.986957	+	0.160986i	$0.948533\pi$
$642$	−5.67544	+	1.52073i	−0.223992	+	0.0600184i
$643$	−6.53485	+	11.3187i	−0.257709	+	0.446365i	−0.965628	−	0.259929i	$-0.916301\pi$
$643$	−6.53485	+	11.3187i	−0.257709	+	0.446365i	0.707919	+	0.706294i	$0.249634\pi$
$644$		0			0
$645$	−6.46410	+	24.1244i	−0.254524	+	0.949896i
$646$	8.03590	+	13.9186i	0.316168	+	0.547619i
$647$	−12.0716			−0.474583			−0.237291	−	0.971439i	$-0.576260\pi$
$647$	−12.0716			−0.474583			−0.237291	+	0.971439i	$0.576260\pi$
$648$	4.50000	+	7.79423i	0.176777	+	0.306186i
$649$	−32.1851			−1.26338
$650$	33.2204	+	57.5394i	1.30301	+	2.25688i
$651$		0			0
$652$	−10.6603	+	18.4641i	−0.417488	+	0.723110i
$653$	−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	$0.204122\pi$
$654$	14.9372	−	4.00240i	0.584090	−	0.156506i
$655$	−11.6603	−	20.1962i	−0.455604	−	0.789129i
$656$	1.27551			0.0498004
$657$	−17.7470	−	10.2462i	−0.692377	−	0.399744i
$658$		0			0
$659$	−0.124356	−	0.215390i	−0.00484421	−	0.00839042i	0.863593	−	0.504189i	$-0.168209\pi$
$659$	−0.124356	−	0.215390i	−0.00484421	−	0.00839042i	−0.868437	+	0.495799i	$0.834875\pi$
$660$	17.6603	+	17.6603i	0.687424	+	0.687424i
$661$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$661$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$662$	2.26795	−	3.92820i	0.0881463	−	0.152674i
$663$	44.3954	+	44.3954i	1.72418	+	1.72418i
$664$	−8.95215	−	15.5056i	−0.347411	−	0.601733i
$665$		0			0
$666$			1.60770i			0.0622969i
$667$	5.85641			0.226761
$668$	10.5558	+	18.2832i	0.408417	+	0.707400i
$669$	−44.7846	+	12.0000i	−1.73147	+	0.463947i
$670$	10.6945	−	18.5235i	0.413166	−	0.715624i
$671$	−13.0053	+	22.5259i	−0.502065	+	0.869602i
$672$		0			0
$673$	20.7846	+	36.0000i	0.801188	+	1.38770i	0.918835	+	0.394643i	$0.129132\pi$
$673$	20.7846	+	36.0000i	0.801188	+	1.38770i	−0.117647	+	0.993055i	$0.537535\pi$
$674$	−7.00000			−0.269630
$675$	49.8306	+	13.3521i	1.91798	+	0.513922i
$676$	31.7846			1.22248
$677$	−10.0382	−	17.3867i	−0.385799	−	0.668224i	0.606081	−	0.795403i	$-0.292741\pi$
$677$	−10.0382	−	17.3867i	−0.385799	−	0.668224i	−0.991880	+	0.127179i	$0.959408\pi$
$678$	3.10583	−	11.5911i	0.119279	−	0.445154i
$679$		0			0
$680$	−10.4641	+	18.1244i	−0.401280	+	0.695037i
$681$	−17.5981	+	4.71539i	−0.674360	+	0.180694i
$682$	−3.34607	−	5.79555i	−0.128127	−	0.221923i
$683$	−3.67949			−0.140792			−0.0703959	−	0.997519i	$-0.522426\pi$
$683$	−3.67949			−0.140792			−0.0703959	+	0.997519i	$0.522426\pi$
$684$	7.70882	−	4.45069i	0.294754	−	0.170176i
$685$	33.4607			1.27847
$686$		0			0
$687$	−30.5885	−	30.5885i	−1.16702	−	1.16702i
$688$	−1.86603	+	3.23205i	−0.0711416	+	0.123221i
$689$	−9.79796	+	16.9706i	−0.373273	+	0.646527i
$690$	6.92820	+	6.92820i	0.263752	+	0.263752i
$691$	4.81105	+	8.33298i	0.183021	+	0.317001i	0.942908	−	0.333054i	$-0.108079\pi$
$691$	4.81105	+	8.33298i	0.183021	+	0.317001i	−0.759887	+	0.650055i	$0.774746\pi$
$692$	−1.79315			−0.0681654
$693$		0			0
$694$	21.5885			0.819487
$695$	31.5885	+	54.7128i	1.19822	+	2.07538i
$696$	6.69213	−	1.79315i	0.253665	−	0.0679692i
$697$	3.45448	−	5.98334i	0.130848	−	0.226635i
$698$	8.24504	−	14.2808i	0.312080	−	0.540538i
$699$	−10.8147	+	40.3608i	−0.409048	+	1.52659i
$700$		0			0
$701$	20.7846			0.785024			0.392512	−	0.919747i	$-0.371606\pi$
$701$	20.7846			0.785024			0.392512	+	0.919747i	$0.371606\pi$
$702$	24.5885	−	24.5885i	0.928032	−	0.928032i
$703$	1.59008			0.0599710
$704$	1.86603	+	3.23205i	0.0703285	+	0.121812i
$705$	18.2832	−	68.2340i	0.688587	−	2.56984i
$706$	−13.2134	+	22.8862i	−0.497292	+	0.861335i
$707$		0			0
$708$	−14.4282	+	3.86603i	−0.542245	+	0.145294i
$709$	−4.19615	−	7.26795i	−0.157590	−	0.272954i	0.776409	−	0.630229i	$-0.217039\pi$
$709$	−4.19615	−	7.26795i	−0.157590	−	0.272954i	−0.933999	+	0.357276i	$0.883706\pi$
$710$	−9.79796			−0.367711
$711$		−	14.7846i		−	0.554466i
$712$	−7.07107			−0.264999
$713$	−1.31268	−	2.27362i	−0.0491602	−	0.0851479i
$714$		0			0
$715$	48.2487	−	83.5692i	1.80440	−	3.12531i
$716$	−9.46410	+	16.3923i	−0.353690	+	0.612609i
$717$	−15.8338	−	15.8338i	−0.591322	−	0.591322i
$718$	−0.267949	−	0.464102i	−0.00999978	−	0.0173201i
$719$	15.3805			0.573595			0.286798	−	0.957991i	$-0.407409\pi$
$719$	15.3805			0.573595			0.286798	+	0.957991i	$0.407409\pi$
$720$	10.0382	+	5.79555i	0.374101	+	0.215988i
$721$		0			0
$722$	5.09808	+	8.83013i	0.189731	+	0.328623i
$723$	39.1865	−	10.5000i	1.45736	−	0.390499i
$724$	−8.48528	+	14.6969i	−0.315353	+	0.546207i
$725$	19.8564	−	34.3923i	0.737448	−	1.27730i
$726$	1.31268	−	4.89898i	0.0487180	−	0.181818i
$727$	−0.795040	−	1.37705i	−0.0294864	−	0.0510719i	0.850906	−	0.525319i	$-0.176054\pi$
$727$	−0.795040	−	1.37705i	−0.0294864	−	0.0510719i	−0.880392	+	0.474247i	$0.842721\pi$
$728$		0			0
$729$		−	27.0000i		−	1.00000i
$730$	−26.3923			−0.976823
$731$	10.1075	+	17.5068i	0.373841	+	0.647512i
$732$	−3.12436	+	11.6603i	−0.115480	+	0.430975i
$733$	−8.24504	+	14.2808i	−0.304538	+	0.527475i	−0.977158	−	0.212513i	$-0.931835\pi$
$733$	−8.24504	+	14.2808i	−0.304538	+	0.527475i	0.672621	+	0.739988i	$0.265169\pi$
$734$	−7.86611	+	13.6245i	−0.290343	+	0.502889i
$735$		0			0
$736$	0.732051	+	1.26795i	0.0269838	+	0.0467372i
$737$	−20.6603			−0.761030
$738$	−3.31388	−	1.91327i	−0.121986	−	0.0704284i
$739$	−18.1244			−0.666715			−0.333358	−	0.942800i	$-0.608182\pi$
$739$	−18.1244			−0.666715			−0.333358	+	0.942800i	$0.608182\pi$
$740$	1.03528	+	1.79315i	0.0380575	+	0.0659175i
$741$	−24.3190	−	24.3190i	−0.893382	−	0.893382i
$742$		0			0
$743$	−25.7846	+	44.6603i	−0.945946	+	1.63843i	−0.192099	+	0.981376i	$0.561529\pi$
$743$	−25.7846	+	44.6603i	−0.945946	+	1.63843i	−0.753847	+	0.657050i	$0.771804\pi$
$744$	−2.19615	−	2.19615i	−0.0805149	−	0.0805149i
$745$	17.5254	+	30.3548i	0.642080	+	1.11211i
$746$	30.7846			1.12710
$747$			53.7129i			1.96525i
$748$	20.2151			0.739137
$749$		0			0
$750$	31.8564	−	8.53590i	1.16323	−	0.311687i
$751$	3.39230	−	5.87564i	0.123787	−	0.214405i	−0.797471	−	0.603357i	$-0.793829\pi$
$751$	3.39230	−	5.87564i	0.123787	−	0.214405i	0.921258	+	0.388952i	$0.127163\pi$
$752$	5.27792	−	9.14162i	0.192466	−	0.333361i
$753$	7.33013	−	27.3564i	0.267125	−	0.996923i
$754$	−13.3843	−	23.1822i	−0.487426	−	0.844247i
$755$	9.24316			0.336393
$756$		0			0
$757$	−15.3205			−0.556833			−0.278417	−	0.960460i	$-0.589810\pi$
$757$	−15.3205			−0.556833			−0.278417	+	0.960460i	$0.589810\pi$
$758$	8.79423	+	15.2321i	0.319421	+	0.553253i
$759$	2.44949	−	9.14162i	0.0889108	−	0.331820i
$760$	5.73205	−	9.92820i	0.207923	−	0.360134i
$761$	−15.2282	+	26.3760i	−0.552021	+	0.956129i	0.446108	+	0.894979i	$0.352810\pi$
$761$	−15.2282	+	26.3760i	−0.552021	+	0.956129i	−0.998129	+	0.0611492i	$0.980523\pi$
$762$	−10.9348	+	2.92996i	−0.396125	+	0.106141i
$763$		0			0
$764$	1.07180			0.0387762
$765$	54.3731	−	31.3923i	1.96586	−	1.13499i
$766$	21.6665			0.782841
$767$	28.8564	+	49.9808i	1.04194	+	1.80470i
$768$	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
$771$	−3.29423	−	3.29423i	−0.118639	−	0.118639i
$772$	11.5263	+	19.9641i	0.414840	+	0.718524i
$773$	−0.203072			−0.00730399			−0.00365199	−	0.999993i	$-0.501162\pi$
$773$	−0.203072			−0.00730399			−0.00365199	+	0.999993i	$0.501162\pi$
$774$	9.69615	−	5.59808i	0.348521	−	0.201219i
$775$	−17.8028			−0.639494
$776$	−2.94855	−	5.10703i	−0.105847	−	0.183332i
$777$		0			0
$778$	−4.00000	+	6.92820i	−0.143407	+	0.248388i
$779$	−1.89230	+	3.27757i	−0.0677989	+	0.117431i
$780$	11.5911	−	43.2586i	0.415028	−	1.54891i
$781$	4.73205	+	8.19615i	0.169326	+	0.293281i
$782$	7.93048			0.283593
$783$	−20.0764	−	5.37945i	−0.717472	−	0.192246i
$784$		0			0
$785$	−8.92820	−	15.4641i	−0.318661	−	0.551937i
$786$	−2.70577	+	10.0981i	−0.0965117	+	0.360186i
$787$	−23.3717	+	40.4810i	−0.833111	+	1.44299i	0.0624487	+	0.998048i	$0.480109\pi$
$787$	−23.3717	+	40.4810i	−0.833111	+	1.44299i	−0.895559	+	0.444942i	$0.853224\pi$
$788$	1.53590	−	2.66025i	0.0547141	−	0.0947676i
$789$	25.8719	−	6.93237i	0.921066	−	0.246799i
$790$	−9.52056	−	16.4901i	−0.338726	−	0.586691i
$791$		0			0
$792$		−	11.1962i		−	0.397838i
$793$	46.6410			1.65627
$794$	9.00292	+	15.5935i	0.319502	+	0.553393i
$795$	13.8564	+	13.8564i	0.491436	+	0.491436i
$796$	−8.90138	+	15.4176i	−0.315501	+	0.546464i
$797$	10.4543	−	18.1074i	0.370310	−	0.641396i	−0.619303	−	0.785152i	$-0.712585\pi$
$797$	10.4543	−	18.1074i	0.370310	−	0.641396i	0.989613	+	0.143756i	$0.0459181\pi$
$798$		0			0
$799$	−28.5885	−	49.5167i	−1.01139	−	1.75177i
$800$	9.92820			0.351015
$801$	18.3712	+	10.6066i	0.649113	+	0.374766i
$802$	17.7846			0.627996
$803$	12.7465	+	22.0776i	0.449814	+	0.779101i
$804$	−9.26174	+	2.48168i	−0.326636	+	0.0875219i
$805$		0			0
$806$	−6.00000	+	10.3923i	−0.211341	+	0.366053i
$807$	2.53590	−	9.46410i	0.0892679	−	0.333152i
$808$	2.44949	+	4.24264i	0.0861727	+	0.149256i
$809$	−26.2679			−0.923532			−0.461766	−	0.887002i	$-0.652784\pi$
$809$	−26.2679			−0.923532			−0.461766	+	0.887002i	$0.652784\pi$
$810$	−17.3867	−	30.1146i	−0.610905	−	1.05812i
$811$	−46.1242			−1.61964			−0.809820	−	0.586679i	$-0.800435\pi$
$811$	−46.1242			−1.61964			−0.809820	+	0.586679i	$0.800435\pi$
$812$		0			0
$813$	−8.07180	+	30.1244i	−0.283090	+	1.05651i
$814$	1.00000	−	1.73205i	0.0350500	−	0.0607083i
$815$	41.1881	−	71.3398i	1.44275	−	2.49892i
$816$	9.06218	−	2.42820i	0.317240	−	0.0850041i
$817$	−5.53674	−	9.58991i	−0.193706	−	0.335508i
$818$	−16.7303			−0.584962
$819$		0			0
$820$	−4.92820			−0.172100
$821$	5.19615	+	9.00000i	0.181347	+	0.314102i	0.942339	−	0.334659i	$-0.108621\pi$
$821$	5.19615	+	9.00000i	0.181347	+	0.314102i	−0.760993	+	0.648761i	$0.775288\pi$
$822$	−10.6066	−	10.6066i	−0.369948	−	0.369948i
$823$	−15.3923	+	26.6603i	−0.536542	+	0.929318i	0.462545	+	0.886596i	$0.346936\pi$
$823$	−15.3923	+	26.6603i	−0.536542	+	0.929318i	−0.999087	+	0.0427222i	$0.986397\pi$
$824$	3.72500	−	6.45189i	0.129767	−	0.224762i
$825$	−45.3799	−	45.3799i	−1.57993	−	1.57993i
$826$		0			0
$827$	−12.0000			−0.417281			−0.208640	−	0.977992i	$-0.566904\pi$
$827$	−12.0000			−0.417281			−0.208640	+	0.977992i	$0.566904\pi$
$828$		−	4.39230i		−	0.152643i
$829$	−37.3244			−1.29633			−0.648164	−	0.761501i	$-0.724463\pi$
$829$	−37.3244			−1.29633			−0.648164	+	0.761501i	$0.724463\pi$
$830$	34.5885	+	59.9090i	1.20058	+	2.07947i
$831$	−41.0494	+	10.9991i	−1.42399	+	0.381556i
$832$	3.34607	−	5.79555i	0.116004	−	0.200925i
$833$		0			0
$834$	7.33013	−	27.3564i	0.253822	−	0.947275i
$835$	−40.7846	−	70.6410i	−1.41141	−	2.44463i
$836$	−11.0735			−0.382984
$837$	2.41154	+	9.00000i	0.0833551	+	0.311086i
$838$	7.90327			0.273014
$839$	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
$842$	−14.1962	+	24.5885i	−0.489232	+	0.847374i
$843$	16.4901	−	4.41851i	0.567949	−	0.152181i
$844$	−2.53590	−	4.39230i	−0.0872892	−	0.151189i
$845$	−122.806			−4.22467
$846$	−27.4249	+	15.8338i	−0.942886	+	0.544376i
$847$		0			0
$848$	1.46410	+	2.53590i	0.0502775	+	0.0870831i
$849$	−11.5359	−	11.5359i	−0.395911	−	0.395911i
$850$	26.8886	−	46.5725i	0.922273	−	1.59742i
$851$	0.392305	−	0.679492i	0.0134480	−	0.0232927i
$852$	3.10583	+	3.10583i	0.106404	+	0.106404i
$853$	−8.00481	−	13.8647i	−0.274079	−	0.474719i	0.695823	−	0.718213i	$-0.255040\pi$
$853$	−8.00481	−	13.8647i	−0.274079	−	0.474719i	−0.969902	+	0.243494i	$0.921706\pi$
$854$		0			0
$855$	−29.7846	+	17.1962i	−1.01861	+	0.588096i
$856$	3.39230			0.115947
$857$	4.19187	+	7.26054i	0.143192	+	0.248015i	0.928697	−	0.370840i	$-0.120930\pi$
$857$	4.19187	+	7.26054i	0.143192	+	0.248015i	−0.785505	+	0.618855i	$0.787597\pi$
$858$	−41.7846	+	11.1962i	−1.42650	+	0.382230i
$859$	7.36705	−	12.7601i	0.251361	−	0.435369i	−0.712540	−	0.701631i	$-0.752455\pi$
$859$	7.36705	−	12.7601i	0.251361	−	0.435369i	0.963901	+	0.266262i	$0.0857887\pi$
$860$	7.20977	−	12.4877i	0.245851	−	0.425827i
$861$		0			0
$862$	18.9282	+	32.7846i	0.644697	+	1.11665i
$863$	22.1051			0.752467			0.376233	−	0.926525i	$-0.377219\pi$
$863$	22.1051			0.752467			0.376233	+	0.926525i	$0.377219\pi$
$864$	−1.34486	−	5.01910i	−0.0457532	−	0.170753i
$865$	6.92820			0.235566
$866$	3.55412	+	6.15591i	0.120774	+	0.209186i
$867$	5.53176	−	20.6448i	0.187868	−	0.701134i
$868$		0			0
$869$	−9.19615	+	15.9282i	−0.311958	+	0.540327i
$870$	−25.8564	+	6.92820i	−0.876614	+	0.234888i
$871$	18.5235	+	32.0836i	0.627644	+	1.08711i
$872$	−8.92820			−0.302347
$873$			17.6913i			0.598759i
$874$	−4.34418			−0.146944
$875$		0			0
$876$	8.36603	+	8.36603i	0.282662	+	0.282662i
$877$	−16.5885	+	28.7321i	−0.560152	+	0.970212i	0.437330	+	0.899301i	$0.355924\pi$
$877$	−16.5885	+	28.7321i	−0.560152	+	0.970212i	−0.997483	+	0.0709114i	$0.977409\pi$
$878$	−9.79796	+	16.9706i	−0.330665	+	0.572729i
$879$	23.3205	+	23.3205i	0.786581	+	0.786581i
$880$	−7.20977	−	12.4877i	−0.243041	−	0.420960i
$881$	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
$883$	7.53590			0.253603			0.126802	−	0.991928i	$-0.459529\pi$
$883$	7.53590			0.253603			0.126802	+	0.991928i	$0.459529\pi$
$884$	−18.1244	−	31.3923i	−0.609588	−	1.05584i
$885$	55.7463	−	14.9372i	1.87389	−	0.502108i
$886$	9.16025	−	15.8660i	0.307745	−	0.533030i
$887$	14.3824	−	24.9110i	0.482913	−	0.836430i	−0.516895	−	0.856049i	$-0.672912\pi$
$887$	14.3824	−	24.9110i	0.482913	−	0.836430i	0.999808	+	0.0196195i	$0.00624547\pi$
$888$	0.240237	−	0.896575i	0.00806181	−	0.0300871i
$889$		0			0
$890$	27.3205			0.915786
$891$	−16.7942	+	29.0885i	−0.562628	+	0.974500i
$892$	26.7685			0.896276
$893$	15.6603	+	27.1244i	0.524050	+	0.907682i
$894$	4.06678	−	15.1774i	0.136013	−	0.507609i
$895$	36.5665	−	63.3350i	1.22228	−	2.11706i
$896$		0			0
$897$	−16.3923	+	4.39230i	−0.547323	+	0.146655i
$898$	8.89230	+	15.4019i	0.296740	+	0.513969i
$899$	7.17260			0.239220
$900$	−25.7942	−	14.8923i	−0.859808	−	0.496410i
$901$	15.8610			0.528405
$902$	2.38014	+	4.12252i	0.0792500	+	0.137265i
$903$		0			0
$904$	−3.46410	+	6.00000i	−0.115214	+	0.199557i
$905$	32.7846	−	56.7846i	1.08980	−	1.88758i
$906$	−2.92996	−	2.92996i	−0.0973415	−	0.0973415i
$907$	−21.6244	−	37.4545i	−0.718025	−	1.24366i	−0.961781	−	0.273819i	$-0.911713\pi$
$907$	−21.6244	−	37.4545i	−0.718025	−	1.24366i	0.243756	−	0.969837i	$-0.421620\pi$
$908$	10.5187			0.349074
$909$		−	14.6969i		−	0.487467i
$910$		0			0
$911$	23.4641	+	40.6410i	0.777400	+	1.34650i	0.933435	+	0.358745i	$0.116795\pi$
$911$	23.4641	+	40.6410i	0.777400	+	1.34650i	−0.156035	+	0.987752i	$0.549871\pi$
$912$	−4.96410	+	1.33013i	−0.164378	+	0.0440449i
$913$	33.4099	−	57.8676i	1.10571	−	1.91514i
$914$	−3.52628	+	6.10770i	−0.116639	+	0.202025i
$915$	12.0716	−	45.0518i	0.399074	−	1.48937i
$916$	12.4877	+	21.6293i	0.412605	+	0.714652i
$917$		0			0
$918$	−27.1865	−	7.28461i	−0.897289	−	0.240428i
$919$	22.9282			0.756332			0.378166	−	0.925738i	$-0.376555\pi$
$919$	22.9282			0.756332			0.378166	+	0.925738i	$0.376555\pi$
$920$	−2.82843	−	4.89898i	−0.0932505	−	0.161515i
$921$	4.96410	−	18.5263i	0.163573	−	0.610462i
$922$	−12.8666	+	22.2856i	−0.423740	+	0.733939i
$923$	8.48528	−	14.6969i	0.279296	−	0.483756i
$924$		0			0
$925$	−2.66025	−	4.60770i	−0.0874686	−	0.151500i
$926$	38.6410			1.26982
$927$	−19.3557	+	11.1750i	−0.635724	+	0.367035i
$928$	−4.00000			−0.131306
$929$	−13.9898	−	24.2311i	−0.458991	−	0.794997i	0.539916	−	0.841719i	$-0.318456\pi$
$929$	−13.9898	−	24.2311i	−0.458991	−	0.794997i	−0.998908	+	0.0467220i	$0.985122\pi$
$930$	8.48528	+	8.48528i	0.278243	+	0.278243i
$931$		0			0
$932$	12.0622	−	20.8923i	0.395110	−	0.684350i
$933$	15.1244	+	15.1244i	0.495149	+	0.495149i
$934$	−13.7818	−	23.8707i	−0.450954	−	0.781075i
$935$	−78.1051			−2.55431
$936$	−17.3867	+	10.0382i	−0.568301	+	0.328109i
$937$	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
$939$	39.1865	−	10.5000i	1.27880	−	0.342655i
$940$	−20.3923	+	35.3205i	−0.665124	+	1.15203i
$941$	−4.34418	+	7.52433i	−0.141616	+	0.245286i	−0.928105	−	0.372318i	$-0.878563\pi$
$941$	−4.34418	+	7.52433i	−0.141616	+	0.245286i	0.786489	+	0.617604i	$0.211897\pi$
$942$	−2.07180	+	7.73205i	−0.0675028	+	0.251924i
$943$	0.933740	+	1.61729i	0.0304068	+	0.0526661i
$944$	8.62398			0.280687
$945$		0			0
$946$	−13.9282			−0.452845
$947$	−3.06218	−	5.30385i	−0.0995074	−	0.172352i	0.811973	−	0.583694i	$-0.198393\pi$
$947$	−3.06218	−	5.30385i	−0.0995074	−	0.172352i	−0.911481	+	0.411342i	$0.865060\pi$
$948$	−2.20925	+	8.24504i	−0.0717532	+	0.267787i
$949$	22.8564	−	39.5885i	0.741950	−	1.28510i
$950$	−14.7291	+	25.5116i	−0.477876	+	0.827705i
$951$	43.4988	−	11.6555i	1.41055	−	0.377955i
$952$		0			0
$953$	19.0000			0.615470			0.307735	−	0.951472i	$-0.400429\pi$
$953$	19.0000			0.615470			0.307735	+	0.951472i	$0.400429\pi$
$954$		−	8.78461i		−	0.284412i
$955$	−4.14110			−0.134003
$956$	6.46410	+	11.1962i	0.209064	+	0.362109i
$957$	18.2832	+	18.2832i	0.591013	+	0.591013i
$958$	7.72741	−	13.3843i	0.249661	−	0.432426i
$959$		0			0
$960$	−4.73205	−	4.73205i	−0.152726	−	0.152726i
$961$	13.8923	+	24.0622i	0.448139	+	0.776199i
$962$	−3.58630			−0.115627
$963$	−8.81347	−	5.08846i	−0.284010	−	0.163973i
$964$	−23.4225			−0.754387
$965$	−44.5341	−	77.1354i	−1.43360	−	2.48308i
$966$		0			0
$967$	−17.7846	+	30.8038i	−0.571914	+	0.990585i	0.424455	+	0.905449i	$0.360466\pi$
$967$	−17.7846	+	30.8038i	−0.571914	+	0.990585i	−0.996369	+	0.0851359i	$0.972868\pi$
$968$	−1.46410	+	2.53590i	−0.0470580	+	0.0815069i
$969$	−7.20479	+	26.8886i	−0.231451	+	0.863788i
$970$	11.3923	+	19.7321i	0.365785	+	0.633558i
$971$	3.00429			0.0964123			0.0482062	−	0.998837i	$-0.484650\pi$
$971$	3.00429			0.0964123			0.0482062	+	0.998837i	$0.484650\pi$
$972$	−4.03459	+	15.0573i	−0.129410	+	0.482963i
$973$		0			0
$974$	−19.3923	−	33.5885i	−0.621370	−	1.07624i
$975$	−29.7846	+	111.158i	−0.953871	+	3.55989i
$976$	3.48477	−	6.03579i	0.111545	−	0.193201i
$977$	24.9904	−	43.2846i	0.799513	−	1.38480i	−0.120420	−	0.992723i	$-0.538424\pi$
$977$	24.9904	−	43.2846i	0.799513	−	1.38480i	0.919934	−	0.392074i	$-0.128242\pi$
$978$	−35.6699	+	9.55772i	−1.14060	+	0.305622i
$979$	−13.1948	−	22.8541i	−0.421707	−	0.730419i
$980$		0			0
$981$	23.1962	+	13.3923i	0.740596	+	0.427583i
$982$	−1.39230			−0.0444302
$983$	−3.48477	−	6.03579i	−0.111147	−	0.192512i	0.805086	−	0.593158i	$-0.202119\pi$
$983$	−3.48477	−	6.03579i	−0.111147	−	0.192512i	−0.916233	+	0.400646i	$0.868786\pi$
$984$	1.56218	+	1.56218i	0.0498004	+	0.0498004i
$985$	−5.93426	+	10.2784i	−0.189081	+	0.327498i
$986$	−10.8332	+	18.7637i	−0.345000	+	0.597558i
$987$		0			0
$988$	9.92820	+	17.1962i	0.315858	+	0.547082i
$989$	−5.46410			−0.173748
$990$			43.2586i			1.37485i
$991$	1.75129			0.0556315			0.0278158	−	0.999613i	$-0.491145\pi$
$991$	1.75129			0.0556315			0.0278158	+	0.999613i	$0.491145\pi$
$992$	0.896575	+	1.55291i	0.0284663	+	0.0493051i
$993$	7.58871	−	2.03339i	0.240820	−	0.0645276i
$994$		0			0
$995$	34.3923	−	59.5692i	1.09031	−	1.88847i
$996$	8.02628	−	29.9545i	0.254322	−	0.949144i
$997$	3.24453	+	5.61969i	0.102755	+	0.177977i	0.912819	−	0.408365i	$-0.133901\pi$
$997$	3.24453	+	5.61969i	0.102755	+	0.177977i	−0.810064	+	0.586342i	$0.800567\pi$
$998$	12.6077			0.399090
$999$	−1.96902	+	1.96902i	−0.0622969	+	0.0622969i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	882.2.f.q.589.3	yes	8
3.2	odd	2		2646.2.f.r.1765.1		8
7.2	even	3		882.2.h.q.67.4		8
7.3	odd	6		882.2.e.s.373.4		8
7.4	even	3		882.2.e.s.373.1		8
7.5	odd	6		882.2.h.q.67.1		8
7.6	odd	2	inner	882.2.f.q.589.2	yes	8
9.2	odd	6		2646.2.f.r.883.1		8
9.4	even	3		7938.2.a.cp.1.1		4
9.5	odd	6		7938.2.a.ci.1.4		4
9.7	even	3	inner	882.2.f.q.295.3	yes	8
21.2	odd	6		2646.2.h.t.361.4		8
21.5	even	6		2646.2.h.t.361.1		8
21.11	odd	6		2646.2.e.q.1549.1		8
21.17	even	6		2646.2.e.q.1549.4		8
21.20	even	2		2646.2.f.r.1765.4		8
63.2	odd	6		2646.2.e.q.2125.1		8
63.11	odd	6		2646.2.h.t.667.4		8
63.13	odd	6		7938.2.a.cp.1.4		4
63.16	even	3		882.2.e.s.655.1		8
63.20	even	6		2646.2.f.r.883.4		8
63.25	even	3		882.2.h.q.79.3		8
63.34	odd	6	inner	882.2.f.q.295.2	✓	8
63.38	even	6		2646.2.h.t.667.1		8
63.41	even	6		7938.2.a.ci.1.1		4
63.47	even	6		2646.2.e.q.2125.4		8
63.52	odd	6		882.2.h.q.79.2		8
63.61	odd	6		882.2.e.s.655.4		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
882.2.e.s.373.1		8	7.4	even	3
882.2.e.s.373.4		8	7.3	odd	6
882.2.e.s.655.1		8	63.16	even	3
882.2.e.s.655.4		8	63.61	odd	6
882.2.f.q.295.2	✓	8	63.34	odd	6	inner
882.2.f.q.295.3	yes	8	9.7	even	3	inner
882.2.f.q.589.2	yes	8	7.6	odd	2	inner
882.2.f.q.589.3	yes	8	1.1	even	1	trivial
882.2.h.q.67.1		8	7.5	odd	6
882.2.h.q.67.4		8	7.2	even	3
882.2.h.q.79.2		8	63.52	odd	6
882.2.h.q.79.3		8	63.25	even	3
2646.2.e.q.1549.1		8	21.11	odd	6
2646.2.e.q.1549.4		8	21.17	even	6
2646.2.e.q.2125.1		8	63.2	odd	6
2646.2.e.q.2125.4		8	63.47	even	6
2646.2.f.r.883.1		8	9.2	odd	6
2646.2.f.r.883.4		8	63.20	even	6
2646.2.f.r.1765.1		8	3.2	odd	2
2646.2.f.r.1765.4		8	21.20	even	2
2646.2.h.t.361.1		8	21.5	even	6
2646.2.h.t.361.4		8	21.2	odd	6
2646.2.h.t.667.1		8	63.38	even	6
2646.2.h.t.667.4		8	63.11	odd	6
7938.2.a.ci.1.1		4	63.41	even	6
7938.2.a.ci.1.4		4	9.5	odd	6
7938.2.a.cp.1.1		4	9.4	even	3
7938.2.a.cp.1.4		4	63.13	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-0.500000 - 0.866025i) q^{2} +(0.448288 - 1.67303i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(1.93185 - 3.34607i) q^{5} +(-1.67303 + 0.448288i) q^{6} +1.00000 q^{8} +(-2.59808 - 1.50000i) q^{9} -3.86370 q^{10} +(1.86603 + 3.23205i) q^{11} +(1.22474 + 1.22474i) q^{12} +(3.34607 - 5.79555i) q^{13} +(-4.73205 - 4.73205i) q^{15} +(-0.500000 - 0.866025i) q^{16} -5.41662 q^{17} +3.00000i q^{18} +2.96713 q^{19} +(1.93185 + 3.34607i) q^{20} +(1.86603 - 3.23205i) q^{22} +(0.732051 - 1.26795i) q^{23} +(0.448288 - 1.67303i) q^{24} +(-4.96410 - 8.59808i) q^{25} -6.69213 q^{26} +(-3.67423 + 3.67423i) q^{27} +(2.00000 + 3.46410i) q^{29} +(-1.73205 + 6.46410i) q^{30} +(0.896575 - 1.55291i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(6.24384 - 1.67303i) q^{33} +(2.70831 + 4.69093i) q^{34} +(2.59808 - 1.50000i) q^{36} +0.535898 q^{37} +(-1.48356 - 2.56961i) q^{38} +(-8.19615 - 8.19615i) q^{39} +(1.93185 - 3.34607i) q^{40} +(-0.637756 + 1.10463i) q^{41} +(-1.86603 - 3.23205i) q^{43} -3.73205 q^{44} +(-10.0382 + 5.79555i) q^{45} -1.46410 q^{46} +(5.27792 + 9.14162i) q^{47} +(-1.67303 + 0.448288i) q^{48} +(-4.96410 + 8.59808i) q^{50} +(-2.42820 + 9.06218i) q^{51} +(3.34607 + 5.79555i) q^{52} -2.92820 q^{53} +(5.01910 + 1.34486i) q^{54} +14.4195 q^{55} +(1.33013 - 4.96410i) q^{57} +(2.00000 - 3.46410i) q^{58} +(-4.31199 + 7.46859i) q^{59} +(6.46410 - 1.73205i) q^{60} +(3.48477 + 6.03579i) q^{61} -1.79315 q^{62} +1.00000 q^{64} +(-12.9282 - 22.3923i) q^{65} +(-4.57081 - 4.57081i) q^{66} +(-2.76795 + 4.79423i) q^{67} +(2.70831 - 4.69093i) q^{68} +(-1.79315 - 1.79315i) q^{69} +2.53590 q^{71} +(-2.59808 - 1.50000i) q^{72} +6.83083 q^{73} +(-0.267949 - 0.464102i) q^{74} +(-16.6102 + 4.45069i) q^{75} +(-1.48356 + 2.56961i) q^{76} +(-3.00000 + 11.1962i) q^{78} +(2.46410 + 4.26795i) q^{79} -3.86370 q^{80} +(4.50000 + 7.79423i) q^{81} +1.27551 q^{82} +(-8.95215 - 15.5056i) q^{83} +(-10.4641 + 18.1244i) q^{85} +(-1.86603 + 3.23205i) q^{86} +(6.69213 - 1.79315i) q^{87} +(1.86603 + 3.23205i) q^{88} -7.07107 q^{89} +(10.0382 + 5.79555i) q^{90} +(0.732051 + 1.26795i) q^{92} +(-2.19615 - 2.19615i) q^{93} +(5.27792 - 9.14162i) q^{94} +(5.73205 - 9.92820i) q^{95} +(1.22474 + 1.22474i) q^{96} +(-2.94855 - 5.10703i) q^{97} -11.1962i 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

L-functions

Modular forms

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