LMFDB - Embedded newform 2646.2.f.r.1765.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2646,2,Mod(883,2646)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2646, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("2646.883");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

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

Embedding invariants

Embedding label			1765.1
Root			$0.965926 + 0.258819i$ of defining polynomial
Character	$\chi$	$=$	2646.1765
Dual form			2646.2.f.r.883.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(-1.93185 + 3.34607i) q^{5} -1.00000 q^{8} -3.86370 q^{10} +(-1.86603 - 3.23205i) q^{11} +(3.34607 - 5.79555i) q^{13} +(-0.500000 - 0.866025i) q^{16} +5.41662 q^{17} +2.96713 q^{19} +(-1.93185 - 3.34607i) q^{20} +(1.86603 - 3.23205i) q^{22} +(-0.732051 + 1.26795i) q^{23} +(-4.96410 - 8.59808i) q^{25} +6.69213 q^{26} +(-2.00000 - 3.46410i) q^{29} +(0.896575 - 1.55291i) q^{31} +(0.500000 - 0.866025i) q^{32} +(2.70831 + 4.69093i) q^{34} +0.535898 q^{37} +(1.48356 + 2.56961i) q^{38} +(1.93185 - 3.34607i) q^{40} +(0.637756 - 1.10463i) q^{41} +(-1.86603 - 3.23205i) q^{43} +3.73205 q^{44} -1.46410 q^{46} +(-5.27792 - 9.14162i) q^{47} +(4.96410 - 8.59808i) q^{50} +(3.34607 + 5.79555i) q^{52} +2.92820 q^{53} +14.4195 q^{55} +(2.00000 - 3.46410i) q^{58} +(4.31199 - 7.46859i) q^{59} +(3.48477 + 6.03579i) q^{61} +1.79315 q^{62} +1.00000 q^{64} +(12.9282 + 22.3923i) q^{65} +(-2.76795 + 4.79423i) q^{67} +(-2.70831 + 4.69093i) q^{68} -2.53590 q^{71} +6.83083 q^{73} +(0.267949 + 0.464102i) q^{74} +(-1.48356 + 2.56961i) q^{76} +(2.46410 + 4.26795i) q^{79} +3.86370 q^{80} +1.27551 q^{82} +(8.95215 + 15.5056i) q^{83} +(-10.4641 + 18.1244i) q^{85} +(1.86603 - 3.23205i) q^{86} +(1.86603 + 3.23205i) q^{88} +7.07107 q^{89} +(-0.732051 - 1.26795i) q^{92} +(5.27792 - 9.14162i) q^{94} +(-5.73205 + 9.92820i) q^{95} +(-2.94855 - 5.10703i) q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 4 q^{2} - 4 q^{4} - 8 q^{8} - 8 q^{11} - 4 q^{16} + 8 q^{22} + 8 q^{23} - 12 q^{25} - 16 q^{29} + 4 q^{32} + 32 q^{37} - 8 q^{43} + 16 q^{44} + 16 q^{46} + 12 q^{50} - 32 q^{53} + 16 q^{58} + 8 q^{64}+ \cdots - 32 q^{95}+O(q^{100}) $ 8 * q + 4 * q^2 - 4 * q^4 - 8 * q^8 - 8 * q^11 - 4 * q^16 + 8 * q^22 + 8 * q^23 - 12 * q^25 - 16 * q^29 + 4 * q^32 + 32 * q^37 - 8 * q^43 + 16 * q^44 + 16 * q^46 + 12 * q^50 - 32 * q^53 + 16 * q^58 + 8 * q^64 + 48 * q^65 - 36 * q^67 - 48 * q^71 + 16 * q^74 - 8 * q^79 - 56 * q^85 + 8 * q^86 + 8 * q^88 + 8 * q^92 - 32 * q^95

Character values

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

$n$	$785$	$1081$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$

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			0
$3$		0			0
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	−1.93185	+	3.34607i	−0.863950	+	1.49641i	0.00413535	+	0.999991i	$0.498684\pi$
$5$	−1.93185	+	3.34607i	−0.863950	+	1.49641i	−0.868086	+	0.496414i	$0.834650\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$	−1.00000			−0.353553
$9$		0			0
$10$	−3.86370			−1.22181
$11$	−1.86603	−	3.23205i	−0.562628	−	0.974500i	−0.997266	−	0.0738948i	$-0.976457\pi$
$11$	−1.86603	−	3.23205i	−0.562628	−	0.974500i	0.434638	−	0.900605i	$-0.356876\pi$
$12$		0			0
$13$	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
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	5.41662			1.31372			0.656861	−	0.754011i	$-0.271884\pi$
$17$	5.41662			1.31372			0.656861	+	0.754011i	$0.271884\pi$
$18$		0			0
$19$	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	−0.932198	−	0.361948i	$-0.882112\pi$
$23$	−0.732051	+	1.26795i	−0.152643	+	0.264386i	0.779555	+	0.626334i	$0.215445\pi$
$24$		0			0
$25$	−4.96410	−	8.59808i	−0.992820	−	1.71962i
$26$	6.69213			1.31243
$27$		0			0
$28$		0			0
$29$	−2.00000	−	3.46410i	−0.371391	−	0.643268i	0.618389	−	0.785872i	$-0.287786\pi$
$29$	−2.00000	−	3.46410i	−0.371391	−	0.643268i	−0.989780	+	0.142605i	$0.954452\pi$
$30$		0			0
$31$	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
$33$		0			0
$34$	2.70831	+	4.69093i	0.464471	+	0.804488i
$35$		0			0
$36$		0			0
$37$	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
$39$		0			0
$40$	1.93185	−	3.34607i	0.305453	−	0.529059i
$41$	0.637756	−	1.10463i	0.0996008	−	0.172514i	−0.811919	−	0.583771i	$-0.801577\pi$
$41$	0.637756	−	1.10463i	0.0996008	−	0.172514i	0.911519	+	0.411257i	$0.134910\pi$
$42$		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
$45$		0			0
$46$	−1.46410			−0.215870
$47$	−5.27792	−	9.14162i	−0.769863	−	1.33344i	−0.937637	−	0.347617i	$-0.886991\pi$
$47$	−5.27792	−	9.14162i	−0.769863	−	1.33344i	0.167773	−	0.985826i	$-0.446342\pi$
$48$		0			0
$49$		0			0
$50$	4.96410	−	8.59808i	0.702030	−	1.21595i
$51$		0			0
$52$	3.34607	+	5.79555i	0.464016	+	0.803699i
$53$	2.92820			0.402220			0.201110	−	0.979569i	$-0.435545\pi$
$53$	2.92820			0.402220			0.201110	+	0.979569i	$0.435545\pi$
$54$		0			0
$55$	14.4195			1.94433
$56$		0			0
$57$		0			0
$58$	2.00000	−	3.46410i	0.262613	−	0.454859i
$59$	4.31199	−	7.46859i	0.561373	−	0.972327i	−0.436004	−	0.899945i	$-0.643606\pi$
$59$	4.31199	−	7.46859i	0.561373	−	0.972327i	0.997377	−	0.0723823i	$-0.0230602\pi$
$60$		0			0
$61$	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
$66$		0			0
$67$	−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
$69$		0			0
$70$		0			0
$71$	−2.53590			−0.300956			−0.150478	−	0.988613i	$-0.548081\pi$
$71$	−2.53590			−0.300956			−0.150478	+	0.988613i	$0.548081\pi$
$72$		0			0
$73$	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
$75$		0			0
$76$	−1.48356	+	2.56961i	−0.170176	+	0.294754i
$77$		0			0
$78$		0			0
$79$	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
$81$		0			0
$82$	1.27551			0.140857
$83$	8.95215	+	15.5056i	0.982626	+	1.70196i	0.652043	+	0.758182i	$0.273912\pi$
$83$	8.95215	+	15.5056i	0.982626	+	1.70196i	0.330583	+	0.943777i	$0.392755\pi$
$84$		0			0
$85$	−10.4641	+	18.1244i	−1.13499	+	1.96586i
$86$	1.86603	−	3.23205i	0.201219	−	0.348521i
$87$		0			0
$88$	1.86603	+	3.23205i	0.198919	+	0.344538i
$89$	7.07107			0.749532			0.374766	−	0.927119i	$-0.377723\pi$
$89$	7.07107			0.749532			0.374766	+	0.927119i	$0.377723\pi$
$90$		0			0
$91$		0			0
$92$	−0.732051	−	1.26795i	−0.0763216	−	0.132193i
$93$		0			0
$94$	5.27792	−	9.14162i	0.544376	−	0.942886i
$95$	−5.73205	+	9.92820i	−0.588096	+	1.01861i
$96$		0			0
$97$	−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
$99$		0			0
$100$	9.92820			0.992820
$101$	−2.44949	−	4.24264i	−0.243733	−	0.422159i	0.718041	−	0.696000i	$-0.245039\pi$
$101$	−2.44949	−	4.24264i	−0.243733	−	0.422159i	−0.961775	+	0.273842i	$0.911706\pi$
$102$		0			0
$103$	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	$-0.552431\pi$
$107$	−3.39230			−0.327946			−0.163973	+	0.986465i	$0.552431\pi$
$108$		0			0
$109$	−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			0
$112$		0			0
$113$	3.46410	−	6.00000i	0.325875	−	0.564433i	−0.655814	−	0.754923i	$-0.727674\pi$
$113$	3.46410	−	6.00000i	0.325875	−	0.564433i	0.981689	+	0.190490i	$0.0610077\pi$
$114$		0			0
$115$	−2.82843	−	4.89898i	−0.263752	−	0.456832i
$116$	4.00000			0.371391
$117$		0			0
$118$	8.62398			0.793902
$119$		0			0
$120$		0			0
$121$	−1.46410	+	2.53590i	−0.133100	+	0.230536i
$122$	−3.48477	+	6.03579i	−0.315496	+	0.546455i
$123$		0			0
$124$	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
$129$		0			0
$130$	−12.9282	+	22.3923i	−1.13388	+	1.96394i
$131$	−3.01790	+	5.22715i	−0.263675	+	0.456698i	−0.967216	−	0.253957i	$-0.918268\pi$
$131$	−3.01790	+	5.22715i	−0.263675	+	0.456698i	0.703541	+	0.710655i	$0.251601\pi$
$132$		0			0
$133$		0			0
$134$	−5.53590			−0.478229
$135$		0			0
$136$	−5.41662			−0.464471
$137$	−4.33013	−	7.50000i	−0.369948	−	0.640768i	0.619609	−	0.784910i	$-0.287291\pi$
$137$	−4.33013	−	7.50000i	−0.369948	−	0.640768i	−0.989557	+	0.144142i	$0.953958\pi$
$138$		0			0
$139$	−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
$141$		0			0
$142$	−1.26795	−	2.19615i	−0.106404	−	0.184297i
$143$	−24.9754			−2.08855
$144$		0			0
$145$	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	−0.618216	−	0.786008i	$-0.712144\pi$
$149$	4.53590	−	7.85641i	0.371595	−	0.643622i	0.989811	+	0.142386i	$0.0454776\pi$
$150$		0			0
$151$	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
$153$		0			0
$154$		0			0
$155$	3.46410	+	6.00000i	0.278243	+	0.481932i
$156$		0			0
$157$	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
$159$		0			0
$160$	1.93185	+	3.34607i	0.152726	+	0.264530i
$161$		0			0
$162$		0			0
$163$	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
$165$		0			0
$166$	−8.95215	+	15.5056i	−0.694822	+	1.20347i
$167$	−10.5558	+	18.2832i	−0.816835	+	1.41480i	0.0911679	+	0.995836i	$0.470940\pi$
$167$	−10.5558	+	18.2832i	−0.816835	+	1.41480i	−0.908003	+	0.418964i	$0.862393\pi$
$168$		0			0
$169$	−15.8923	−	27.5263i	−1.22248	−	2.11741i
$170$	−20.9282			−1.60512
$171$		0			0
$172$	3.73205			0.284566
$173$	−0.896575	−	1.55291i	−0.0681654	−	0.118066i	0.829928	−	0.557870i	$-0.188381\pi$
$173$	−0.896575	−	1.55291i	−0.0681654	−	0.118066i	−0.898094	+	0.439804i	$0.855048\pi$
$174$		0			0
$175$		0			0
$176$	−1.86603	+	3.23205i	−0.140657	+	0.243625i
$177$		0			0
$178$	3.53553	+	6.12372i	0.264999	+	0.458993i
$179$	−18.9282			−1.41476			−0.707380	−	0.706833i	$-0.750123\pi$
$179$	−18.9282			−1.41476			−0.707380	+	0.706833i	$0.750123\pi$
$180$		0			0
$181$	16.9706			1.26141			0.630706	−	0.776022i	$-0.282765\pi$
$181$	16.9706			1.26141			0.630706	+	0.776022i	$0.282765\pi$
$182$		0			0
$183$		0			0
$184$	0.732051	−	1.26795i	0.0539675	−	0.0934745i
$185$	−1.03528	+	1.79315i	−0.0761150	+	0.131835i
$186$		0			0
$187$	−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	0.884762	−	0.466043i	$-0.154321\pi$
$191$	0.535898	+	0.928203i	0.0387762	+	0.0671624i	−0.845986	+	0.533205i	$0.820987\pi$
$192$		0			0
$193$	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
$195$		0			0
$196$		0			0
$197$	3.07180			0.218856			0.109428	−	0.993995i	$-0.465098\pi$
$197$	3.07180			0.218856			0.109428	+	0.993995i	$0.465098\pi$
$198$		0			0
$199$	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
$201$		0			0
$202$	2.44949	−	4.24264i	0.172345	−	0.298511i
$203$		0			0
$204$		0			0
$205$	2.46410	+	4.26795i	0.172100	+	0.298087i
$206$	7.45001			0.519066
$207$		0			0
$208$	−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
$213$		0			0
$214$	−1.69615	−	2.93782i	−0.115947	−	0.200825i
$215$	14.4195			0.983404
$216$		0			0
$217$		0			0
$218$	−4.46410	−	7.73205i	−0.302347	−	0.523681i
$219$		0			0
$220$	−7.20977	+	12.4877i	−0.486082	+	0.841920i
$221$	18.1244	−	31.3923i	1.21918	−	2.11167i
$222$		0			0
$223$	−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
$225$		0			0
$226$	6.92820			0.460857
$227$	5.25933	+	9.10943i	0.349074	+	0.604614i	0.986085	−	0.166240i	$-0.0531627\pi$
$227$	5.25933	+	9.10943i	0.349074	+	0.604614i	−0.637011	+	0.770855i	$0.719829\pi$
$228$		0			0
$229$	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	$-0.209966\pi$
$233$	24.1244			1.58044			0.790220	+	0.612824i	$0.209966\pi$
$234$		0			0
$235$	40.7846			2.66049
$236$	4.31199	+	7.46859i	0.280687	+	0.486164i
$237$		0			0
$238$		0			0
$239$	−6.46410	+	11.1962i	−0.418128	+	0.724219i	−0.995751	−	0.0920846i	$-0.970647\pi$
$239$	−6.46410	+	11.1962i	−0.418128	+	0.724219i	0.577623	+	0.816304i	$0.303980\pi$
$240$		0			0
$241$	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
$243$		0			0
$244$	−6.96953			−0.446179
$245$		0			0
$246$		0			0
$247$	9.92820	−	17.1962i	0.631716	−	1.09416i
$248$	−0.896575	+	1.55291i	−0.0569326	+	0.0986102i
$249$		0			0
$250$	9.52056	+	16.4901i	0.602133	+	1.04292i
$251$	−16.3514			−1.03209			−0.516045	−	0.856561i	$-0.672596\pi$
$251$	−16.3514			−1.03209			−0.516045	+	0.856561i	$0.672596\pi$
$252$		0			0
$253$	5.46410			0.343525
$254$	3.26795	+	5.66025i	0.205049	+	0.355156i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−1.34486	+	2.32937i	−0.0838903	+	0.145302i	−0.904918	−	0.425586i	$-0.860068\pi$
$257$	−1.34486	+	2.32937i	−0.0838903	+	0.145302i	0.821028	+	0.570889i	$0.193401\pi$
$258$		0			0
$259$		0			0
$260$	−25.8564			−1.60355
$261$		0			0
$262$	−6.03579			−0.372892
$263$	−7.73205	−	13.3923i	−0.476779	−	0.825805i	0.522867	−	0.852414i	$-0.324862\pi$
$263$	−7.73205	−	13.3923i	−0.476779	−	0.825805i	−0.999646	+	0.0266092i	$0.991529\pi$
$264$		0			0
$265$	−5.65685	+	9.79796i	−0.347498	+	0.601884i
$266$		0			0
$267$		0			0
$268$	−2.76795	−	4.79423i	−0.169079	−	0.292854i
$269$	−5.65685			−0.344904			−0.172452	−	0.985018i	$-0.555169\pi$
$269$	−5.65685			−0.344904			−0.172452	+	0.985018i	$0.555169\pi$
$270$		0			0
$271$	−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
$276$		0			0
$277$	−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
$279$		0			0
$280$		0			0
$281$	−4.92820	−	8.53590i	−0.293992	−	0.509209i	0.680758	−	0.732508i	$-0.261651\pi$
$281$	−4.92820	−	8.53590i	−0.293992	−	0.509209i	−0.974750	+	0.223299i	$0.928317\pi$
$282$		0			0
$283$	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
$285$		0			0
$286$	−12.4877	−	21.6293i	−0.738412	−	1.27897i
$287$		0			0
$288$		0			0
$289$	12.3397			0.725867
$290$	7.72741	+	13.3843i	0.453769	+	0.785951i
$291$		0			0
$292$	−3.41542	+	5.91567i	−0.199872	+	0.346189i
$293$	9.52056	−	16.4901i	0.556197	−	0.963361i	−0.441612	−	0.897206i	$-0.645593\pi$
$293$	9.52056	−	16.4901i	0.556197	−	0.963361i	0.997809	−	0.0661554i	$-0.0210733\pi$
$294$		0			0
$295$	16.6603	+	28.8564i	0.969997	+	1.68008i
$296$	−0.535898			−0.0311485
$297$		0			0
$298$	9.07180			0.525515
$299$	4.89898	+	8.48528i	0.283315	+	0.490716i
$300$		0			0
$301$		0			0
$302$	−1.19615	+	2.07180i	−0.0688308	+	0.119219i
$303$		0			0
$304$	−1.48356	−	2.56961i	−0.0850882	−	0.147377i
$305$	−26.9282			−1.54190
$306$		0			0
$307$	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
$309$		0			0
$310$	−3.46410	+	6.00000i	−0.196748	+	0.340777i
$311$	6.17449	−	10.6945i	0.350123	−	0.606431i	−0.636147	−	0.771568i	$-0.719473\pi$
$311$	6.17449	−	10.6945i	0.350123	−	0.606431i	0.986271	+	0.165136i	$0.0528063\pi$
$312$		0			0
$313$	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	$-0.906116\pi$
$317$	−13.0000	−	22.5167i	−0.730153	−	1.26466i	0.226665	−	0.973973i	$-0.427218\pi$
$318$		0			0
$319$	−7.46410	+	12.9282i	−0.417909	+	0.723840i
$320$	−1.93185	+	3.34607i	−0.107994	+	0.187051i
$321$		0			0
$322$		0			0
$323$	16.0718			0.894259
$324$		0			0
$325$	−66.4408			−3.68547
$326$	10.6603	+	18.4641i	0.590417	+	1.02263i
$327$		0			0
$328$	−0.637756	+	1.10463i	−0.0352142	+	0.0609928i
$329$		0			0
$330$		0			0
$331$	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
$333$		0			0
$334$	−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
$339$		0			0
$340$	−10.4641	−	18.1244i	−0.567496	−	0.982931i
$341$	−6.69213			−0.362399
$342$		0			0
$343$		0			0
$344$	1.86603	+	3.23205i	0.100609	+	0.174261i
$345$		0			0
$346$	0.896575	−	1.55291i	0.0482002	−	0.0834852i
$347$	10.7942	−	18.6962i	0.579465	−	1.00366i	−0.416076	−	0.909330i	$-0.636595\pi$
$347$	10.7942	−	18.6962i	0.579465	−	1.00366i	0.995541	−	0.0943323i	$-0.0300716\pi$
$348$		0			0
$349$	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
$351$		0			0
$352$	−3.73205			−0.198919
$353$	13.2134	+	22.8862i	0.703277	+	1.21811i	0.967310	+	0.253598i	$0.0816139\pi$
$353$	13.2134	+	22.8862i	0.703277	+	1.21811i	−0.264033	+	0.964514i	$0.585053\pi$
$354$		0			0
$355$	4.89898	−	8.48528i	0.260011	−	0.450352i
$356$	−3.53553	+	6.12372i	−0.187383	+	0.324557i
$357$		0			0
$358$	−9.46410	−	16.3923i	−0.500193	−	0.866360i
$359$	−0.535898			−0.0282836			−0.0141418	−	0.999900i	$-0.504502\pi$
$359$	−0.535898			−0.0282836			−0.0141418	+	0.999900i	$0.504502\pi$
$360$		0			0
$361$	−10.1962			−0.536640
$362$	8.48528	+	14.6969i	0.445976	+	0.772454i
$363$		0			0
$364$		0			0
$365$	−13.1962	+	22.8564i	−0.690718	+	1.19636i
$366$		0			0
$367$	−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
$369$		0			0
$370$	−2.07055			−0.107643
$371$		0			0
$372$		0			0
$373$	−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
$375$		0			0
$376$	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
$381$		0			0
$382$	−0.535898	+	0.928203i	−0.0274189	+	0.0474910i
$383$	10.8332	−	18.7637i	0.553552	−	0.958781i	−0.444462	−	0.895798i	$-0.646605\pi$
$383$	10.8332	−	18.7637i	0.553552	−	0.958781i	0.998015	−	0.0629833i	$-0.0200615\pi$
$384$		0			0
$385$		0			0
$386$	23.0526			1.17334
$387$		0			0
$388$	5.89709			0.299379
$389$	4.00000	+	6.92820i	0.202808	+	0.351274i	0.949432	−	0.313972i	$-0.101660\pi$
$389$	4.00000	+	6.92820i	0.202808	+	0.351274i	−0.746624	+	0.665246i	$0.768327\pi$
$390$		0			0
$391$	−3.96524	+	6.86800i	−0.200531	+	0.347329i
$392$		0			0
$393$		0			0
$394$	1.53590	+	2.66025i	0.0773774	+	0.134022i
$395$	−19.0411			−0.958062
$396$		0			0
$397$	−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	−0.553926	−	0.832566i	$-0.686871\pi$
$401$	8.89230	−	15.4019i	0.444061	−	0.769135i	0.997986	+	0.0634307i	$0.0202042\pi$
$402$		0			0
$403$	−6.00000	−	10.3923i	−0.298881	−	0.517678i
$404$	4.89898			0.243733
$405$		0			0
$406$		0			0
$407$	−1.00000	−	1.73205i	−0.0495682	−	0.0858546i
$408$		0			0
$409$	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
$411$		0			0
$412$	3.72500	+	6.45189i	0.183518	+	0.317862i
$413$		0			0
$414$		0			0
$415$	−69.1769			−3.39576
$416$	−3.34607	−	5.79555i	−0.164054	−	0.284150i
$417$		0			0
$418$	5.53674	−	9.58991i	0.270811	−	0.469058i
$419$	3.95164	−	6.84443i	0.193050	−	0.334373i	−0.753209	−	0.657781i	$-0.771495\pi$
$419$	3.95164	−	6.84443i	0.193050	−	0.334373i	0.946260	+	0.323408i	$0.104829\pi$
$420$		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
$423$		0			0
$424$	−2.92820			−0.142206
$425$	−26.8886	−	46.5725i	−1.30429	−	2.25910i
$426$		0			0
$427$		0			0
$428$	1.69615	−	2.93782i	0.0819866	−	0.142005i
$429$		0			0
$430$	7.20977	+	12.4877i	0.347686	+	0.602210i
$431$	37.8564			1.82348			0.911739	−	0.410769i	$-0.134740\pi$
$431$	37.8564			1.82348			0.911739	+	0.410769i	$0.134740\pi$
$432$		0			0
$433$	−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
$435$		0			0
$436$	4.46410	−	7.73205i	0.213792	−	0.370298i
$437$	−2.17209	+	3.76217i	−0.103905	+	0.179969i
$438$		0			0
$439$	−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	0.562097	−	0.827072i	$-0.309995\pi$
$443$	−9.16025	−	15.8660i	−0.435217	−	0.753818i	−0.997313	+	0.0732540i	$0.976662\pi$
$444$		0			0
$445$	−13.6603	+	23.6603i	−0.647558	+	1.12160i
$446$	13.3843	−	23.1822i	0.633763	−	1.09771i
$447$		0			0
$448$		0			0
$449$	17.7846			0.839308			0.419654	−	0.907684i	$-0.362151\pi$
$449$	17.7846			0.839308			0.419654	+	0.907684i	$0.362151\pi$
$450$		0			0
$451$	−4.76028			−0.224153
$452$	3.46410	+	6.00000i	0.162938	+	0.282216i
$453$		0			0
$454$	−5.25933	+	9.10943i	−0.246833	+	0.427527i
$455$		0			0
$456$		0			0
$457$	−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
$459$		0			0
$460$	5.65685			0.263752
$461$	12.8666	+	22.2856i	0.599258	+	1.03795i	0.992931	+	0.118695i	$0.0378711\pi$
$461$	12.8666	+	22.2856i	0.599258	+	1.03795i	−0.393672	+	0.919251i	$0.628796\pi$
$462$		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
$465$		0			0
$466$	12.0622	+	20.8923i	0.558770	+	0.967817i
$467$	−27.5636			−1.27549			−0.637745	−	0.770248i	$-0.720133\pi$
$467$	−27.5636			−1.27549			−0.637745	+	0.770248i	$0.720133\pi$
$468$		0			0
$469$		0			0
$470$	20.3923	+	35.3205i	0.940627	+	1.62921i
$471$		0			0
$472$	−4.31199	+	7.46859i	−0.198475	+	0.343770i
$473$	−6.96410	+	12.0622i	−0.320210	+	0.554620i
$474$		0			0
$475$	−14.7291	−	25.5116i	−0.675819	−	1.17055i
$476$		0			0
$477$		0			0
$478$	−12.9282			−0.591322
$479$	−7.72741	−	13.3843i	−0.353074	−	0.611542i	0.633712	−	0.773569i	$-0.281530\pi$
$479$	−7.72741	−	13.3843i	−0.353074	−	0.611542i	−0.986786	+	0.162026i	$0.948197\pi$
$480$		0			0
$481$	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
$486$		0			0
$487$	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
$489$		0			0
$490$		0			0
$491$	−0.696152	+	1.20577i	−0.0314169	+	0.0544157i	−0.881306	−	0.472545i	$-0.843335\pi$
$491$	−0.696152	+	1.20577i	−0.0314169	+	0.0544157i	0.849889	+	0.526961i	$0.176669\pi$
$492$		0			0
$493$	−10.8332	−	18.7637i	−0.487904	−	0.845075i
$494$	19.8564			0.893382
$495$		0			0
$496$	−1.79315			−0.0805149
$497$		0			0
$498$		0			0
$499$	−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
$501$		0			0
$502$	−8.17569	−	14.1607i	−0.364899	−	0.632024i
$503$	−7.45001			−0.332179			−0.166090	−	0.986111i	$-0.553114\pi$
$503$	−7.45001			−0.332179			−0.166090	+	0.986111i	$0.553114\pi$
$504$		0			0
$505$	18.9282			0.842294
$506$	2.73205	+	4.73205i	0.121454	+	0.210365i
$507$		0			0
$508$	−3.26795	+	5.66025i	−0.144992	+	0.251133i
$509$	−13.2456	+	22.9420i	−0.587099	+	1.01689i	0.407511	+	0.913200i	$0.366397\pi$
$509$	−13.2456	+	22.9420i	−0.587099	+	1.01689i	−0.994610	+	0.103685i	$0.966937\pi$
$510$		0			0
$511$		0			0
$512$	−1.00000			−0.0441942
$513$		0			0
$514$	−2.68973			−0.118639
$515$	14.3923	+	24.9282i	0.634201	+	1.09847i
$516$		0			0
$517$	−19.6975	+	34.1170i	−0.866293	+	1.50046i
$518$		0			0
$519$		0			0
$520$	−12.9282	−	22.3923i	−0.566939	−	0.981968i
$521$	32.3610			1.41776			0.708881	−	0.705328i	$-0.249200\pi$
$521$	32.3610			1.41776			0.708881	+	0.705328i	$0.249200\pi$
$522$		0			0
$523$	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
$528$		0			0
$529$	10.4282	+	18.0622i	0.453400	+	0.785312i
$530$	−11.3137			−0.491436
$531$		0			0
$532$		0			0
$533$	−4.26795	−	7.39230i	−0.184865	−	0.320196i
$534$		0			0
$535$	6.55343	−	11.3509i	0.283329	−	0.490741i
$536$	2.76795	−	4.79423i	0.119557	−	0.207079i
$537$		0			0
$538$	−2.82843	−	4.89898i	−0.121942	−	0.211210i
$539$		0			0
$540$		0			0
$541$	−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
$543$		0			0
$544$	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
$549$		0			0
$550$	−37.0526			−1.57993
$551$	−5.93426	−	10.2784i	−0.252808	−	0.437876i
$552$		0			0
$553$		0			0
$554$	12.2679	−	21.2487i	0.521215	−	0.902771i
$555$		0			0
$556$	−8.17569	−	14.1607i	−0.346727	−	0.600548i
$557$	−6.92820			−0.293557			−0.146779	−	0.989169i	$-0.546891\pi$
$557$	−6.92820			−0.293557			−0.146779	+	0.989169i	$0.546891\pi$
$558$		0			0
$559$	−24.9754			−1.05635
$560$		0			0
$561$		0			0
$562$	4.92820	−	8.53590i	0.207884	−	0.360065i
$563$	12.7973	−	22.1655i	0.539341	−	0.934166i	−0.459599	−	0.888127i	$-0.652007\pi$
$563$	12.7973	−	22.1655i	0.539341	−	0.934166i	0.998940	−	0.0460390i	$-0.0146598\pi$
$564$		0			0
$565$	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	0.982681	−	0.185304i	$-0.0593270\pi$
$569$	7.89230	+	13.6699i	0.330863	+	0.573071i	−0.651819	+	0.758375i	$0.725994\pi$
$570$		0			0
$571$	−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
$573$		0			0
$574$		0			0
$575$	14.5359			0.606189
$576$		0			0
$577$	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
$579$		0			0
$580$	−7.72741	+	13.3843i	−0.320863	+	0.555751i
$581$		0			0
$582$		0			0
$583$	−5.46410	−	9.46410i	−0.226300	−	0.391963i
$584$	−6.83083			−0.282662
$585$		0			0
$586$	19.0411			0.786581
$587$	−14.5768	−	25.2478i	−0.601650	−	1.04209i	−0.992571	−	0.121664i	$-0.961177\pi$
$587$	−14.5768	−	25.2478i	−0.601650	−	1.04209i	0.390922	−	0.920424i	$-0.372156\pi$
$588$		0			0
$589$	2.66025	−	4.60770i	0.109614	−	0.189857i
$590$	−16.6603	+	28.8564i	−0.685892	+	1.18800i
$591$		0			0
$592$	−0.267949	−	0.464102i	−0.0110126	−	0.0190745i
$593$	−2.72689			−0.111980			−0.0559900	−	0.998431i	$-0.517831\pi$
$593$	−2.72689			−0.111980			−0.0559900	+	0.998431i	$0.517831\pi$
$594$		0			0
$595$		0			0
$596$	4.53590	+	7.85641i	0.185798	+	0.321811i
$597$		0			0
$598$	−4.89898	+	8.48528i	−0.200334	+	0.346989i
$599$	−18.3923	+	31.8564i	−0.751489	+	1.30162i	0.195612	+	0.980681i	$0.437331\pi$
$599$	−18.3923	+	31.8564i	−0.751489	+	1.30162i	−0.947101	+	0.320936i	$0.896003\pi$
$600$		0			0
$601$	−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
$603$		0			0
$604$	−2.39230			−0.0973415
$605$	−5.65685	−	9.79796i	−0.229984	−	0.398344i
$606$		0			0
$607$	−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
$612$		0			0
$613$	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
$615$		0			0
$616$		0			0
$617$	−15.4282	+	26.7224i	−0.621116	+	1.07580i	0.368162	+	0.929762i	$0.379987\pi$
$617$	−15.4282	+	26.7224i	−0.621116	+	1.07580i	−0.989278	+	0.146043i	$0.953346\pi$
$618$		0			0
$619$	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
$621$		0			0
$622$	12.3490			0.495149
$623$		0			0
$624$		0			0
$625$	−11.9641	+	20.7224i	−0.478564	+	0.828897i
$626$	−11.7112	+	20.2844i	−0.468075	+	0.810729i
$627$		0			0
$628$	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
$633$		0			0
$634$	13.0000	−	22.5167i	0.516296	−	0.894251i
$635$	−12.6264	+	21.8695i	−0.501063	+	0.867866i
$636$		0			0
$637$		0			0
$638$	−14.9282			−0.591013
$639$		0			0
$640$	−3.86370			−0.152726
$641$	8.96410	+	15.5263i	0.354061	+	0.613251i	0.986957	−	0.160986i	$-0.0514673\pi$
$641$	8.96410	+	15.5263i	0.354061	+	0.613251i	−0.632896	+	0.774237i	$0.718134\pi$
$642$		0			0
$643$	−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
$645$		0			0
$646$	8.03590	+	13.9186i	0.316168	+	0.547619i
$647$	12.0716			0.474583			0.237291	−	0.971439i	$-0.423740\pi$
$647$	12.0716			0.474583			0.237291	+	0.971439i	$0.423740\pi$
$648$		0			0
$649$	−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	−0.801337	−	0.598213i	$-0.795878\pi$
$653$	3.00000	−	5.19615i	0.117399	−	0.203341i	0.918736	+	0.394872i	$0.129211\pi$
$654$		0			0
$655$	−11.6603	−	20.1962i	−0.455604	−	0.789129i
$656$	−1.27551			−0.0498004
$657$		0			0
$658$		0			0
$659$	0.124356	+	0.215390i	0.00484421	+	0.00839042i	0.868437	−	0.495799i	$-0.165125\pi$
$659$	0.124356	+	0.215390i	0.00484421	+	0.00839042i	−0.863593	+	0.504189i	$0.831791\pi$
$660$		0			0
$661$		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
$663$		0			0
$664$	−8.95215	−	15.5056i	−0.347411	−	0.601733i
$665$		0			0
$666$		0			0
$667$	5.85641			0.226761
$668$	−10.5558	−	18.2832i	−0.408417	−	0.707400i
$669$		0			0
$670$	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
$675$		0			0
$676$	31.7846			1.22248
$677$	10.0382	+	17.3867i	0.385799	+	0.668224i	0.991880	−	0.127179i	$-0.0405924\pi$
$677$	10.0382	+	17.3867i	0.385799	+	0.668224i	−0.606081	+	0.795403i	$0.707259\pi$
$678$		0			0
$679$		0			0
$680$	10.4641	−	18.1244i	0.401280	−	0.695037i
$681$		0			0
$682$	−3.34607	−	5.79555i	−0.128127	−	0.221923i
$683$	3.67949			0.140792			0.0703959	−	0.997519i	$-0.477574\pi$
$683$	3.67949			0.140792			0.0703959	+	0.997519i	$0.477574\pi$
$684$		0			0
$685$	33.4607			1.27847
$686$		0			0
$687$		0			0
$688$	−1.86603	+	3.23205i	−0.0711416	+	0.123221i
$689$	9.79796	−	16.9706i	0.373273	−	0.646527i
$690$		0			0
$691$	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
$696$		0			0
$697$	3.45448	−	5.98334i	0.130848	−	0.226635i
$698$	−8.24504	+	14.2808i	−0.312080	+	0.540538i
$699$		0			0
$700$		0			0
$701$	−20.7846			−0.785024			−0.392512	−	0.919747i	$-0.628394\pi$
$701$	−20.7846			−0.785024			−0.392512	+	0.919747i	$0.628394\pi$
$702$		0			0
$703$	1.59008			0.0599710
$704$	−1.86603	−	3.23205i	−0.0703285	−	0.121812i
$705$		0			0
$706$	−13.2134	+	22.8862i	−0.497292	+	0.861335i
$707$		0			0
$708$		0			0
$709$	−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
$711$		0			0
$712$	−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
$717$		0			0
$718$	−0.267949	−	0.464102i	−0.00999978	−	0.0173201i
$719$	−15.3805			−0.573595			−0.286798	−	0.957991i	$-0.592591\pi$
$719$	−15.3805			−0.573595			−0.286798	+	0.957991i	$0.592591\pi$
$720$		0			0
$721$		0			0
$722$	−5.09808	−	8.83013i	−0.189731	−	0.328623i
$723$		0			0
$724$	−8.48528	+	14.6969i	−0.315353	+	0.546207i
$725$	−19.8564	+	34.3923i	−0.737448	+	1.27730i
$726$		0			0
$727$	−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
$729$		0			0
$730$	−26.3923			−0.976823
$731$	−10.1075	−	17.5068i	−0.373841	−	0.647512i
$732$		0			0
$733$	−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
$738$		0			0
$739$	−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
$741$		0			0
$742$		0			0
$743$	25.7846	−	44.6603i	0.945946	−	1.63843i	0.192099	−	0.981376i	$-0.438471\pi$
$743$	25.7846	−	44.6603i	0.945946	−	1.63843i	0.753847	−	0.657050i	$-0.228196\pi$
$744$		0			0
$745$	17.5254	+	30.3548i	0.642080	+	1.11211i
$746$	−30.7846			−1.12710
$747$		0			0
$748$	20.2151			0.739137
$749$		0			0
$750$		0			0
$751$	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
$753$		0			0
$754$	−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
$759$		0			0
$760$	5.73205	−	9.92820i	0.207923	−	0.360134i
$761$	15.2282	−	26.3760i	0.552021	−	0.956129i	−0.446108	−	0.894979i	$-0.647190\pi$
$761$	15.2282	−	26.3760i	0.552021	−	0.956129i	0.998129	−	0.0611492i	$-0.0194765\pi$
$762$		0			0
$763$		0			0
$764$	−1.07180			−0.0387762
$765$		0			0
$766$	21.6665			0.782841
$767$	−28.8564	−	49.9808i	−1.04194	−	1.80470i
$768$		0			0
$769$	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
$771$		0			0
$772$	11.5263	+	19.9641i	0.414840	+	0.718524i
$773$	0.203072			0.00730399			0.00365199	−	0.999993i	$-0.498838\pi$
$773$	0.203072			0.00730399			0.00365199	+	0.999993i	$0.498838\pi$
$774$		0			0
$775$	−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
$780$		0			0
$781$	4.73205	+	8.19615i	0.169326	+	0.293281i
$782$	−7.93048			−0.283593
$783$		0			0
$784$		0			0
$785$	8.92820	+	15.4641i	0.318661	+	0.551937i
$786$		0			0
$787$	−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
$789$		0			0
$790$	−9.52056	−	16.4901i	−0.338726	−	0.586691i
$791$		0			0
$792$		0			0
$793$	46.6410			1.65627
$794$	−9.00292	−	15.5935i	−0.319502	−	0.553393i
$795$		0			0
$796$	−8.90138	+	15.4176i	−0.315501	+	0.546464i
$797$	−10.4543	+	18.1074i	−0.370310	+	0.641396i	−0.989613	−	0.143756i	$-0.954082\pi$
$797$	−10.4543	+	18.1074i	−0.370310	+	0.641396i	0.619303	+	0.785152i	$0.287415\pi$
$798$		0			0
$799$	−28.5885	−	49.5167i	−1.01139	−	1.75177i
$800$	−9.92820			−0.351015
$801$		0			0
$802$	17.7846			0.627996
$803$	−12.7465	−	22.0776i	−0.449814	−	0.779101i
$804$		0			0
$805$		0			0
$806$	6.00000	−	10.3923i	0.211341	−	0.366053i
$807$		0			0
$808$	2.44949	+	4.24264i	0.0861727	+	0.149256i
$809$	26.2679			0.923532			0.461766	−	0.887002i	$-0.347216\pi$
$809$	26.2679			0.923532			0.461766	+	0.887002i	$0.347216\pi$
$810$		0			0
$811$	−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
$813$		0			0
$814$	1.00000	−	1.73205i	0.0350500	−	0.0607083i
$815$	−41.1881	+	71.3398i	−1.44275	+	2.49892i
$816$		0			0
$817$	−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	0.760993	−	0.648761i	$-0.224712\pi$
$821$	−5.19615	−	9.00000i	−0.181347	−	0.314102i	−0.942339	+	0.334659i	$0.891379\pi$
$822$		0			0
$823$	−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
$825$		0			0
$826$		0			0
$827$	12.0000			0.417281			0.208640	−	0.977992i	$-0.433096\pi$
$827$	12.0000			0.417281			0.208640	+	0.977992i	$0.433096\pi$
$828$		0			0
$829$	−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
$831$		0			0
$832$	3.34607	−	5.79555i	0.116004	−	0.200925i
$833$		0			0
$834$		0			0
$835$	−40.7846	−	70.6410i	−1.41141	−	2.44463i
$836$	11.0735			0.382984
$837$		0			0
$838$	7.90327			0.273014
$839$	−11.3137	−	19.5959i	−0.390593	−	0.676526i	0.601935	−	0.798545i	$-0.294397\pi$
$839$	−11.3137	−	19.5959i	−0.390593	−	0.676526i	−0.992528	+	0.122019i	$0.961063\pi$
$840$		0			0
$841$	6.50000	−	11.2583i	0.224138	−	0.388218i
$842$	14.1962	−	24.5885i	0.489232	−	0.847374i
$843$		0			0
$844$	−2.53590	−	4.39230i	−0.0872892	−	0.151189i
$845$	122.806			4.22467
$846$		0			0
$847$		0			0
$848$	−1.46410	−	2.53590i	−0.0502775	−	0.0870831i
$849$		0			0
$850$	26.8886	−	46.5725i	0.922273	−	1.59742i
$851$	−0.392305	+	0.679492i	−0.0134480	+	0.0232927i
$852$		0			0
$853$	−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
$855$		0			0
$856$	3.39230			0.115947
$857$	−4.19187	−	7.26054i	−0.143192	−	0.248015i	0.785505	−	0.618855i	$-0.212403\pi$
$857$	−4.19187	−	7.26054i	−0.143192	−	0.248015i	−0.928697	+	0.370840i	$0.879070\pi$
$858$		0			0
$859$	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	$-0.622781\pi$
$863$	−22.1051			−0.752467			−0.376233	+	0.926525i	$0.622781\pi$
$864$		0			0
$865$	6.92820			0.235566
$866$	−3.55412	−	6.15591i	−0.120774	−	0.209186i
$867$		0			0
$868$		0			0
$869$	9.19615	−	15.9282i	0.311958	−	0.540327i
$870$		0			0
$871$	18.5235	+	32.0836i	0.627644	+	1.08711i
$872$	8.92820			0.302347
$873$		0			0
$874$	−4.34418			−0.146944
$875$		0			0
$876$		0			0
$877$	−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
$879$		0			0
$880$	−7.20977	−	12.4877i	−0.243041	−	0.420960i
$881$	−12.7279			−0.428815			−0.214407	−	0.976744i	$-0.568782\pi$
$881$	−12.7279			−0.428815			−0.214407	+	0.976744i	$0.568782\pi$
$882$		0			0
$883$	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
$885$		0			0
$886$	9.16025	−	15.8660i	0.307745	−	0.533030i
$887$	−14.3824	+	24.9110i	−0.482913	+	0.836430i	−0.999808	−	0.0196195i	$-0.993755\pi$
$887$	−14.3824	+	24.9110i	−0.482913	+	0.836430i	0.516895	+	0.856049i	$0.327088\pi$
$888$		0			0
$889$		0			0
$890$	−27.3205			−0.915786
$891$		0			0
$892$	26.7685			0.896276
$893$	−15.6603	−	27.1244i	−0.524050	−	0.907682i
$894$		0			0
$895$	36.5665	−	63.3350i	1.22228	−	2.11706i
$896$		0			0
$897$		0			0
$898$	8.89230	+	15.4019i	0.296740	+	0.513969i
$899$	−7.17260			−0.239220
$900$		0			0
$901$	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
$906$		0			0
$907$	−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
$909$		0			0
$910$		0			0
$911$	−23.4641	−	40.6410i	−0.777400	−	1.34650i	−0.933435	−	0.358745i	$-0.883205\pi$
$911$	−23.4641	−	40.6410i	−0.777400	−	1.34650i	0.156035	−	0.987752i	$-0.450129\pi$
$912$		0			0
$913$	33.4099	−	57.8676i	1.10571	−	1.91514i
$914$	3.52628	−	6.10770i	0.116639	−	0.202025i
$915$		0			0
$916$	12.4877	+	21.6293i	0.412605	+	0.714652i
$917$		0			0
$918$		0			0
$919$	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
$921$		0			0
$922$	−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
$927$		0			0
$928$	−4.00000			−0.131306
$929$	13.9898	+	24.2311i	0.458991	+	0.794997i	0.998908	−	0.0467220i	$-0.0148775\pi$
$929$	13.9898	+	24.2311i	0.458991	+	0.794997i	−0.539916	+	0.841719i	$0.681544\pi$
$930$		0			0
$931$		0			0
$932$	−12.0622	+	20.8923i	−0.395110	+	0.684350i
$933$		0			0
$934$	−13.7818	−	23.8707i	−0.450954	−	0.781075i
$935$	78.1051			2.55431
$936$		0			0
$937$	9.89949			0.323402			0.161701	−	0.986840i	$-0.448302\pi$
$937$	9.89949			0.323402			0.161701	+	0.986840i	$0.448302\pi$
$938$		0			0
$939$		0			0
$940$	−20.3923	+	35.3205i	−0.665124	+	1.15203i
$941$	4.34418	−	7.52433i	0.141616	−	0.245286i	−0.786489	−	0.617604i	$-0.788103\pi$
$941$	4.34418	−	7.52433i	0.141616	−	0.245286i	0.928105	+	0.372318i	$0.121437\pi$
$942$		0			0
$943$	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	0.911481	−	0.411342i	$-0.134940\pi$
$947$	3.06218	+	5.30385i	0.0995074	+	0.172352i	−0.811973	+	0.583694i	$0.801607\pi$
$948$		0			0
$949$	22.8564	−	39.5885i	0.741950	−	1.28510i
$950$	14.7291	−	25.5116i	0.477876	−	0.827705i
$951$		0			0
$952$		0			0
$953$	−19.0000			−0.615470			−0.307735	−	0.951472i	$-0.599571\pi$
$953$	−19.0000			−0.615470			−0.307735	+	0.951472i	$0.599571\pi$
$954$		0			0
$955$	−4.14110			−0.134003
$956$	−6.46410	−	11.1962i	−0.209064	−	0.362109i
$957$		0			0
$958$	7.72741	−	13.3843i	0.249661	−	0.432426i
$959$		0			0
$960$		0			0
$961$	13.8923	+	24.0622i	0.448139	+	0.776199i
$962$	3.58630			0.115627
$963$		0			0
$964$	−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
$969$		0			0
$970$	11.3923	+	19.7321i	0.365785	+	0.633558i
$971$	−3.00429			−0.0964123			−0.0482062	−	0.998837i	$-0.515350\pi$
$971$	−3.00429			−0.0964123			−0.0482062	+	0.998837i	$0.515350\pi$
$972$		0			0
$973$		0			0
$974$	19.3923	+	33.5885i	0.621370	+	1.07624i
$975$		0			0
$976$	3.48477	−	6.03579i	0.111545	−	0.193201i
$977$	−24.9904	+	43.2846i	−0.799513	+	1.38480i	0.120420	+	0.992723i	$0.461576\pi$
$977$	−24.9904	+	43.2846i	−0.799513	+	1.38480i	−0.919934	+	0.392074i	$0.871758\pi$
$978$		0			0
$979$	−13.1948	−	22.8541i	−0.421707	−	0.730419i
$980$		0			0
$981$		0			0
$982$	−1.39230			−0.0444302
$983$	3.48477	+	6.03579i	0.111147	+	0.192512i	0.916233	−	0.400646i	$-0.131214\pi$
$983$	3.48477	+	6.03579i	0.111147	+	0.192512i	−0.805086	+	0.593158i	$0.797881\pi$
$984$		0			0
$985$	−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
$990$		0			0
$991$	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
$993$		0			0
$994$		0			0
$995$	−34.3923	+	59.5692i	−1.09031	+	1.88847i
$996$		0			0
$997$	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
$999$		0			0

Twists

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

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

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

\(f(q)\)	\(=\)	\(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(-1.93185 + 3.34607i) q^{5} -1.00000 q^{8} -3.86370 q^{10} +(-1.86603 - 3.23205i) q^{11} +(3.34607 - 5.79555i) q^{13} +(-0.500000 - 0.866025i) q^{16} +5.41662 q^{17} +2.96713 q^{19} +(-1.93185 - 3.34607i) q^{20} +(1.86603 - 3.23205i) q^{22} +(-0.732051 + 1.26795i) q^{23} +(-4.96410 - 8.59808i) q^{25} +6.69213 q^{26} +(-2.00000 - 3.46410i) q^{29} +(0.896575 - 1.55291i) q^{31} +(0.500000 - 0.866025i) q^{32} +(2.70831 + 4.69093i) q^{34} +0.535898 q^{37} +(1.48356 + 2.56961i) q^{38} +(1.93185 - 3.34607i) q^{40} +(0.637756 - 1.10463i) q^{41} +(-1.86603 - 3.23205i) q^{43} +3.73205 q^{44} -1.46410 q^{46} +(-5.27792 - 9.14162i) q^{47} +(4.96410 - 8.59808i) q^{50} +(3.34607 + 5.79555i) q^{52} +2.92820 q^{53} +14.4195 q^{55} +(2.00000 - 3.46410i) q^{58} +(4.31199 - 7.46859i) q^{59} +(3.48477 + 6.03579i) q^{61} +1.79315 q^{62} +1.00000 q^{64} +(12.9282 + 22.3923i) q^{65} +(-2.76795 + 4.79423i) q^{67} +(-2.70831 + 4.69093i) q^{68} -2.53590 q^{71} +6.83083 q^{73} +(0.267949 + 0.464102i) q^{74} +(-1.48356 + 2.56961i) q^{76} +(2.46410 + 4.26795i) q^{79} +3.86370 q^{80} +1.27551 q^{82} +(8.95215 + 15.5056i) q^{83} +(-10.4641 + 18.1244i) q^{85} +(1.86603 - 3.23205i) q^{86} +(1.86603 + 3.23205i) q^{88} +7.07107 q^{89} +(-0.732051 - 1.26795i) q^{92} +(5.27792 - 9.14162i) q^{94} +(-5.73205 + 9.92820i) q^{95} +(-2.94855 - 5.10703i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 4 q^{2} - 4 q^{4} - 8 q^{8} - 8 q^{11} - 4 q^{16} + 8 q^{22} + 8 q^{23} - 12 q^{25} - 16 q^{29} + 4 q^{32} + 32 q^{37} - 8 q^{43} + 16 q^{44} + 16 q^{46} + 12 q^{50} - 32 q^{53} + 16 q^{58} + 8 q^{64}+ \cdots - 32 q^{95}+O(q^{100}) \) 8 * q + 4 * q^2 - 4 * q^4 - 8 * q^8 - 8 * q^11 - 4 * q^16 + 8 * q^22 + 8 * q^23 - 12 * q^25 - 16 * q^29 + 4 * q^32 + 32 * q^37 - 8 * q^43 + 16 * q^44 + 16 * q^46 + 12 * q^50 - 32 * q^53 + 16 * q^58 + 8 * q^64 + 48 * q^65 - 36 * q^67 - 48 * q^71 + 16 * q^74 - 8 * q^79 - 56 * q^85 + 8 * q^86 + 8 * q^88 + 8 * q^92 - 32 * q^95

Introduction

L-functions

Modular forms

Varieties

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Database

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