LMFDB - Embedded newform 2646.2.e.q.1549.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [2646,2,Mod(1549,2646)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(2646, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([2, 2])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("2646.1549"); S:= CuspForms(chi, 2); N := Newforms(S);

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

Newform invariants

comment:select newform

sage:traces = [8,-8,0,8,0,0,0,-8,0,0,-8,0,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(13)] == traces)

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			1549.1
Root			$0.965926 - 0.258819i$ of defining polynomial
Character	$\chi$	$=$	2646.1549
Dual form			2646.2.e.q.2125.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-1.00000 q^{2} +1.00000 q^{4} +(-1.93185 - 3.34607i) q^{5} -1.00000 q^{8} +(1.93185 + 3.34607i) q^{10} +(-1.86603 + 3.23205i) q^{11} +(3.34607 - 5.79555i) q^{13} +1.00000 q^{16} +(-2.70831 - 4.69093i) q^{17} +(-1.48356 + 2.56961i) q^{19} +(-1.93185 - 3.34607i) q^{20} +(1.86603 - 3.23205i) q^{22} +(-0.732051 - 1.26795i) q^{23} +(-4.96410 + 8.59808i) q^{25} +(-3.34607 + 5.79555i) q^{26} +(-2.00000 - 3.46410i) q^{29} -1.79315 q^{31} -1.00000 q^{32} +(2.70831 + 4.69093i) q^{34} +(-0.267949 + 0.464102i) q^{37} +(1.48356 - 2.56961i) q^{38} +(1.93185 + 3.34607i) q^{40} +(0.637756 - 1.10463i) q^{41} +(-1.86603 - 3.23205i) q^{43} +(-1.86603 + 3.23205i) q^{44} +(0.732051 + 1.26795i) q^{46} +10.5558 q^{47} +(4.96410 - 8.59808i) q^{50} +(3.34607 - 5.79555i) q^{52} +(-1.46410 - 2.53590i) q^{53} +14.4195 q^{55} +(2.00000 + 3.46410i) q^{58} -8.62398 q^{59} -6.96953 q^{61} +1.79315 q^{62} +1.00000 q^{64} -25.8564 q^{65} +5.53590 q^{67} +(-2.70831 - 4.69093i) q^{68} -2.53590 q^{71} +(-3.41542 - 5.91567i) q^{73} +(0.267949 - 0.464102i) q^{74} +(-1.48356 + 2.56961i) q^{76} -4.92820 q^{79} +(-1.93185 - 3.34607i) q^{80} +(-0.637756 + 1.10463i) q^{82} +(8.95215 + 15.5056i) q^{83} +(-10.4641 + 18.1244i) q^{85} +(1.86603 + 3.23205i) q^{86} +(1.86603 - 3.23205i) q^{88} +(-3.53553 + 6.12372i) q^{89} +(-0.732051 - 1.26795i) q^{92} -10.5558 q^{94} +11.4641 q^{95} +(-2.94855 - 5.10703i) q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 8 q^{2} + 8 q^{4} - 8 q^{8} - 8 q^{11} + 8 q^{16} + 8 q^{22} + 8 q^{23} - 12 q^{25} - 16 q^{29} - 8 q^{32} - 16 q^{37} - 8 q^{43} - 8 q^{44} - 8 q^{46} + 12 q^{50} + 16 q^{53} + 16 q^{58} + 8 q^{64}+ \cdots + 64 q^{95}+O(q^{100}) $ 8 * q - 8 * q^2 + 8 * q^4 - 8 * q^8 - 8 * q^11 + 8 * q^16 + 8 * q^22 + 8 * q^23 - 12 * q^25 - 16 * q^29 - 8 * q^32 - 16 * q^37 - 8 * q^43 - 8 * q^44 - 8 * q^46 + 12 * q^50 + 16 * q^53 + 16 * q^58 + 8 * q^64 - 96 * q^65 + 72 * q^67 - 48 * q^71 + 16 * q^74 + 16 * q^79 - 56 * q^85 + 8 * q^86 + 8 * q^88 + 8 * q^92 + 64 * q^95

Character values

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

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

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 $

$2$	−1.00000			−0.707107
$2$	−1.00000			−0.707107
$3$		0			0
$3$		0			0
$4$	1.00000			0.500000
$5$	−1.93185	−	3.34607i	−0.863950	−	1.49641i	−0.868086	−	0.496414i	$-0.834650\pi$
$5$	−1.93185	−	3.34607i	−0.863950	−	1.49641i	0.00413535	−	0.999991i	$-0.498684\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$	−1.00000			−0.353553
$9$		0			0
$10$	1.93185	+	3.34607i	0.610905	+	1.05812i
$11$	−1.86603	+	3.23205i	−0.562628	+	0.974500i	0.434638	+	0.900605i	$0.356876\pi$
$11$	−1.86603	+	3.23205i	−0.562628	+	0.974500i	−0.997266	+	0.0738948i	$0.976457\pi$
$12$		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
$16$	1.00000			0.250000
$17$	−2.70831	−	4.69093i	−0.656861	−	1.13772i	−0.981424	−	0.191853i	$-0.938550\pi$
$17$	−2.70831	−	4.69093i	−0.656861	−	1.13772i	0.324562	−	0.945864i	$-0.394783\pi$
$18$		0			0
$19$	−1.48356	+	2.56961i	−0.340353	+	0.589509i	−0.984498	−	0.175395i	$-0.943880\pi$
$19$	−1.48356	+	2.56961i	−0.340353	+	0.589509i	0.644145	+	0.764903i	$0.277213\pi$
$20$	−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	$-0.215445\pi$
$23$	−0.732051	−	1.26795i	−0.152643	−	0.264386i	−0.932198	+	0.361948i	$0.882112\pi$
$24$		0			0
$25$	−4.96410	+	8.59808i	−0.992820	+	1.71962i
$26$	−3.34607	+	5.79555i	−0.656217	+	1.13660i
$27$		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
$31$	−1.79315			−0.322059			−0.161030	−	0.986950i	$-0.551481\pi$
$31$	−1.79315			−0.322059			−0.161030	+	0.986950i	$0.551481\pi$
$32$	−1.00000			−0.176777
$33$		0			0
$34$	2.70831	+	4.69093i	0.464471	+	0.804488i
$35$		0			0
$36$		0			0
$37$	−0.267949	+	0.464102i	−0.0440506	+	0.0762978i	−0.887210	−	0.461366i	$-0.847360\pi$
$37$	−0.267949	+	0.464102i	−0.0440506	+	0.0762978i	0.843159	+	0.537664i	$0.180693\pi$
$38$	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	$0.925183\pi$
$44$	−1.86603	+	3.23205i	−0.281314	+	0.487250i
$45$		0			0
$46$	0.732051	+	1.26795i	0.107935	+	0.186949i
$47$	10.5558			1.53973			0.769863	−	0.638209i	$-0.220324\pi$
$47$	10.5558			1.53973			0.769863	+	0.638209i	$0.220324\pi$
$48$		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
$53$	−1.46410	−	2.53590i	−0.201110	−	0.348332i	0.747776	−	0.663951i	$-0.231121\pi$
$53$	−1.46410	−	2.53590i	−0.201110	−	0.348332i	−0.948886	+	0.315618i	$0.897788\pi$
$54$		0			0
$55$	14.4195			1.94433
$56$		0			0
$57$		0			0
$58$	2.00000	+	3.46410i	0.262613	+	0.454859i
$59$	−8.62398			−1.12275			−0.561373	−	0.827563i	$-0.689727\pi$
$59$	−8.62398			−1.12275			−0.561373	+	0.827563i	$0.689727\pi$
$60$		0			0
$61$	−6.96953			−0.892357			−0.446179	−	0.894944i	$-0.647215\pi$
$61$	−6.96953			−0.892357			−0.446179	+	0.894944i	$0.647215\pi$
$62$	1.79315			0.227730
$63$		0			0
$64$	1.00000			0.125000
$65$	−25.8564			−3.20709
$66$		0			0
$67$	5.53590			0.676318			0.338159	−	0.941089i	$-0.390196\pi$
$67$	5.53590			0.676318			0.338159	+	0.941089i	$0.390196\pi$
$68$	−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
$73$	−3.41542	−	5.91567i	−0.399744	−	0.692377i	0.593950	−	0.804502i	$-0.297568\pi$
$73$	−3.41542	−	5.91567i	−0.399744	−	0.692377i	−0.993694	+	0.112125i	$0.964234\pi$
$74$	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
$79$	−4.92820			−0.554466			−0.277233	−	0.960803i	$-0.589417\pi$
$79$	−4.92820			−0.554466			−0.277233	+	0.960803i	$0.589417\pi$
$80$	−1.93185	−	3.34607i	−0.215988	−	0.374101i
$81$		0			0
$82$	−0.637756	+	1.10463i	−0.0704284	+	0.121986i
$83$	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
$89$	−3.53553	+	6.12372i	−0.374766	+	0.649113i	−0.990292	−	0.139003i	$-0.955610\pi$
$89$	−3.53553	+	6.12372i	−0.374766	+	0.649113i	0.615526	+	0.788116i	$0.288944\pi$
$90$		0			0
$91$		0			0
$92$	−0.732051	−	1.26795i	−0.0763216	−	0.132193i
$93$		0			0
$94$	−10.5558			−1.08875
$95$	11.4641			1.17619
$96$		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
$100$	−4.96410	+	8.59808i	−0.496410	+	0.859808i
$101$	−2.44949	+	4.24264i	−0.243733	+	0.422159i	−0.961775	−	0.273842i	$-0.911706\pi$
$101$	−2.44949	+	4.24264i	−0.243733	+	0.422159i	0.718041	+	0.696000i	$0.245039\pi$
$102$		0			0
$103$	3.72500	+	6.45189i	0.367035	+	0.635724i	0.989101	−	0.147241i	$-0.0470394\pi$
$103$	3.72500	+	6.45189i	0.367035	+	0.635724i	−0.622065	+	0.782965i	$0.713706\pi$
$104$	−3.34607	+	5.79555i	−0.328109	+	0.568301i
$105$		0			0
$106$	1.46410	+	2.53590i	0.142206	+	0.246308i
$107$	1.69615	−	2.93782i	0.163973	−	0.284010i	−0.772317	−	0.635237i	$-0.780902\pi$
$107$	1.69615	−	2.93782i	0.163973	−	0.284010i	0.936290	+	0.351227i	$0.114236\pi$
$108$		0			0
$109$	4.46410	+	7.73205i	0.427583	+	0.740596i	0.996658	−	0.0816899i	$-0.0260317\pi$
$109$	4.46410	+	7.73205i	0.427583	+	0.740596i	−0.569074	+	0.822286i	$0.692698\pi$
$110$	−14.4195			−1.37485
$111$		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
$116$	−2.00000	−	3.46410i	−0.185695	−	0.321634i
$117$		0			0
$118$	8.62398			0.793902
$119$		0			0
$120$		0			0
$121$	−1.46410	−	2.53590i	−0.133100	−	0.230536i
$122$	6.96953			0.630992
$123$		0			0
$124$	−1.79315			−0.161030
$125$	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	$0.406350\pi$
$128$	−1.00000			−0.0883883
$129$		0			0
$130$	25.8564			2.26776
$131$	−3.01790	−	5.22715i	−0.263675	−	0.456698i	0.703541	−	0.710655i	$-0.251601\pi$
$131$	−3.01790	−	5.22715i	−0.263675	−	0.456698i	−0.967216	+	0.253957i	$0.918268\pi$
$132$		0			0
$133$		0			0
$134$	−5.53590			−0.478229
$135$		0			0
$136$	2.70831	+	4.69093i	0.232236	+	0.402244i
$137$	−4.33013	+	7.50000i	−0.369948	+	0.640768i	−0.989557	−	0.144142i	$-0.953958\pi$
$137$	−4.33013	+	7.50000i	−0.369948	+	0.640768i	0.619609	+	0.784910i	$0.287291\pi$
$138$		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
$142$	2.53590			0.212808
$143$	12.4877	+	21.6293i	1.04427	+	1.80873i
$144$		0			0
$145$	−7.72741	+	13.3843i	−0.641726	+	1.11150i
$146$	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	$-0.0454776\pi$
$149$	4.53590	+	7.85641i	0.371595	+	0.643622i	−0.618216	+	0.786008i	$0.712144\pi$
$150$		0			0
$151$	1.19615	−	2.07180i	0.0973415	−	0.168600i	−0.813242	−	0.581926i	$-0.802299\pi$
$151$	1.19615	−	2.07180i	0.0973415	−	0.168600i	0.910583	+	0.413325i	$0.135633\pi$
$152$	1.48356	−	2.56961i	0.120333	−	0.208423i
$153$		0			0
$154$		0			0
$155$	3.46410	+	6.00000i	0.278243	+	0.481932i
$156$		0			0
$157$	−4.62158			−0.368842			−0.184421	−	0.982847i	$-0.559041\pi$
$157$	−4.62158			−0.368842			−0.184421	+	0.982847i	$0.559041\pi$
$158$	4.92820			0.392067
$159$		0			0
$160$	1.93185	+	3.34607i	0.152726	+	0.264530i
$161$		0			0
$162$		0			0
$163$	−10.6603	+	18.4641i	−0.834976	+	1.44622i	0.0590748	+	0.998254i	$0.481185\pi$
$163$	−10.6603	+	18.4641i	−0.834976	+	1.44622i	−0.894050	+	0.447966i	$0.852148\pi$
$164$	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
$170$	10.4641	−	18.1244i	0.802560	−	1.39007i
$171$		0			0
$172$	−1.86603	−	3.23205i	−0.142283	−	0.246442i
$173$	1.79315			0.136331			0.0681654	−	0.997674i	$-0.478285\pi$
$173$	1.79315			0.136331			0.0681654	+	0.997674i	$0.478285\pi$
$174$		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
$179$	9.46410	+	16.3923i	0.707380	+	1.22522i	0.965826	+	0.259193i	$0.0834564\pi$
$179$	9.46410	+	16.3923i	0.707380	+	1.22522i	−0.258446	+	0.966026i	$0.583210\pi$
$180$		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
$185$	2.07055			0.152230
$186$		0			0
$187$	20.2151			1.47827
$188$	10.5558			0.769863
$189$		0			0
$190$	−11.4641			−0.831693
$191$	−1.07180			−0.0775525			−0.0387762	−	0.999248i	$-0.512346\pi$
$191$	−1.07180			−0.0775525			−0.0387762	+	0.999248i	$0.512346\pi$
$192$		0			0
$193$	−23.0526			−1.65936			−0.829680	−	0.558240i	$-0.811477\pi$
$193$	−23.0526			−1.65936			−0.829680	+	0.558240i	$0.811477\pi$
$194$	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
$199$	−8.90138	−	15.4176i	−0.631002	−	1.09293i	−0.987347	−	0.158574i	$-0.949310\pi$
$199$	−8.90138	−	15.4176i	−0.631002	−	1.09293i	0.356345	−	0.934355i	$-0.384023\pi$
$200$	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
$205$	−4.92820			−0.344201
$206$	−3.72500	−	6.45189i	−0.259533	−	0.449525i
$207$		0			0
$208$	3.34607	−	5.79555i	0.232008	−	0.401849i
$209$	−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
$215$	−7.20977	+	12.4877i	−0.491702	+	0.851653i
$216$		0			0
$217$		0			0
$218$	−4.46410	−	7.73205i	−0.302347	−	0.523681i
$219$		0			0
$220$	14.4195			0.972165
$221$	−36.2487			−2.43835
$222$		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
$226$	−3.46410	+	6.00000i	−0.230429	+	0.399114i
$227$	5.25933	−	9.10943i	0.349074	−	0.604614i	−0.637011	−	0.770855i	$-0.719829\pi$
$227$	5.25933	−	9.10943i	0.349074	−	0.604614i	0.986085	+	0.166240i	$0.0531627\pi$
$228$		0			0
$229$	12.4877	+	21.6293i	0.825209	+	1.42930i	0.901759	+	0.432239i	$0.142276\pi$
$229$	12.4877	+	21.6293i	0.825209	+	1.42930i	−0.0765496	+	0.997066i	$0.524390\pi$
$230$	2.82843	−	4.89898i	0.186501	−	0.323029i
$231$		0			0
$232$	2.00000	+	3.46410i	0.131306	+	0.227429i
$233$	−12.0622	+	20.8923i	−0.790220	+	1.36870i	0.135611	+	0.990762i	$0.456700\pi$
$233$	−12.0622	+	20.8923i	−0.790220	+	1.36870i	−0.925831	+	0.377938i	$0.876633\pi$
$234$		0			0
$235$	−20.3923	−	35.3205i	−1.33025	−	2.30406i
$236$	−8.62398			−0.561373
$237$		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	−0.191292	−	0.981533i	$-0.561268\pi$
$241$	11.7112	−	20.2844i	0.754387	−	1.30664i	0.945679	−	0.325103i	$-0.105399\pi$
$242$	1.46410	+	2.53590i	0.0941160	+	0.163014i
$243$		0			0
$244$	−6.96953			−0.446179
$245$		0			0
$246$		0			0
$247$	9.92820	+	17.1962i	0.631716	+	1.09416i
$248$	1.79315			0.113865
$249$		0			0
$250$	−19.0411			−1.20427
$251$	−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
$254$	−6.53590			−0.410099
$255$		0			0
$256$	1.00000			0.0625000
$257$	−1.34486	−	2.32937i	−0.0838903	−	0.145302i	0.821028	−	0.570889i	$-0.193401\pi$
$257$	−1.34486	−	2.32937i	−0.0838903	−	0.145302i	−0.904918	+	0.425586i	$0.860068\pi$
$258$		0			0
$259$		0			0
$260$	−25.8564			−1.60355
$261$		0			0
$262$	3.01790	+	5.22715i	0.186446	+	0.322934i
$263$	−7.73205	+	13.3923i	−0.476779	+	0.825805i	−0.999646	−	0.0266092i	$-0.991529\pi$
$263$	−7.73205	+	13.3923i	−0.476779	+	0.825805i	0.522867	+	0.852414i	$0.324862\pi$
$264$		0			0
$265$	−5.65685	+	9.79796i	−0.347498	+	0.601884i
$266$		0			0
$267$		0			0
$268$	5.53590			0.338159
$269$	2.82843	+	4.89898i	0.172452	+	0.298696i	0.939277	−	0.343161i	$-0.111498\pi$
$269$	2.82843	+	4.89898i	0.172452	+	0.298696i	−0.766824	+	0.641857i	$0.778164\pi$
$270$		0			0
$271$	9.00292	−	15.5935i	0.546888	−	0.947239i	−0.451597	−	0.892222i	$-0.649146\pi$
$271$	9.00292	−	15.5935i	0.546888	−	0.947239i	0.998485	−	0.0550165i	$-0.0175211\pi$
$272$	−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	0.216682	+	0.976242i	$0.430477\pi$
$277$	−12.2679	+	21.2487i	−0.737110	+	1.27671i	−0.953792	+	0.300469i	$0.902857\pi$
$278$	8.17569	−	14.1607i	0.490346	−	0.849303i
$279$		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
$283$	−9.41902			−0.559903			−0.279951	−	0.960014i	$-0.590318\pi$
$283$	−9.41902			−0.559903			−0.279951	+	0.960014i	$0.590318\pi$
$284$	−2.53590			−0.150478
$285$		0			0
$286$	−12.4877	−	21.6293i	−0.738412	−	1.27897i
$287$		0			0
$288$		0			0
$289$	−6.16987	+	10.6865i	−0.362934	+	0.628620i
$290$	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
$296$	0.267949	−	0.464102i	0.0155742	−	0.0269754i
$297$		0			0
$298$	−4.53590	−	7.85641i	−0.262758	−	0.455109i
$299$	−9.79796			−0.566631
$300$		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
$305$	13.4641	+	23.3205i	0.770952	+	1.33533i
$306$		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
$311$	−12.3490			−0.700247			−0.350123	−	0.936704i	$-0.613860\pi$
$311$	−12.3490			−0.700247			−0.350123	+	0.936704i	$0.613860\pi$
$312$		0			0
$313$	−23.4225			−1.32392			−0.661958	−	0.749541i	$-0.730274\pi$
$313$	−23.4225			−1.32392			−0.661958	+	0.749541i	$0.730274\pi$
$314$	4.62158			0.260811
$315$		0			0
$316$	−4.92820			−0.277233
$317$	26.0000			1.46031			0.730153	−	0.683284i	$-0.239449\pi$
$317$	26.0000			1.46031			0.730153	+	0.683284i	$0.239449\pi$
$318$		0			0
$319$	14.9282			0.835819
$320$	−1.93185	−	3.34607i	−0.107994	−	0.187051i
$321$		0			0
$322$		0			0
$323$	16.0718			0.894259
$324$		0			0
$325$	33.2204	+	57.5394i	1.84274	+	3.19171i
$326$	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
$331$	−4.53590			−0.249316			−0.124658	−	0.992200i	$-0.539783\pi$
$331$	−4.53590			−0.249316			−0.124658	+	0.992200i	$0.539783\pi$
$332$	8.95215	+	15.5056i	0.491313	+	0.850979i
$333$		0			0
$334$	10.5558	−	18.2832i	0.577590	−	1.00041i
$335$	−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
$341$	3.34607	−	5.79555i	0.181200	−	0.313847i
$342$		0			0
$343$		0			0
$344$	1.86603	+	3.23205i	0.100609	+	0.174261i
$345$		0			0
$346$	−1.79315			−0.0964004
$347$	−21.5885			−1.15893			−0.579465	−	0.814997i	$-0.696738\pi$
$347$	−21.5885			−1.15893			−0.579465	+	0.814997i	$0.696738\pi$
$348$		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
$352$	1.86603	−	3.23205i	0.0994595	−	0.172269i
$353$	13.2134	−	22.8862i	0.703277	−	1.21811i	−0.264033	−	0.964514i	$-0.585053\pi$
$353$	13.2134	−	22.8862i	0.703277	−	1.21811i	0.967310	−	0.253598i	$-0.0816139\pi$
$354$		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
$359$	0.267949	−	0.464102i	0.0141418	−	0.0244943i	−0.858868	−	0.512197i	$-0.828832\pi$
$359$	0.267949	−	0.464102i	0.0141418	−	0.0244943i	0.873010	+	0.487703i	$0.162165\pi$
$360$		0			0
$361$	5.09808	+	8.83013i	0.268320	+	0.464744i
$362$	−16.9706			−0.891953
$363$		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	−0.994956	−	0.100310i	$-0.968017\pi$
$367$	−7.86611	+	13.6245i	−0.410607	+	0.711193i	0.584349	+	0.811503i	$0.301350\pi$
$368$	−0.732051	−	1.26795i	−0.0381608	−	0.0660964i
$369$		0			0
$370$	−2.07055			−0.107643
$371$		0			0
$372$		0			0
$373$	−15.3923	−	26.6603i	−0.796983	−	1.38042i	−0.921572	−	0.388207i	$-0.873095\pi$
$373$	−15.3923	−	26.6603i	−0.796983	−	1.38042i	0.124589	−	0.992208i	$-0.460239\pi$
$374$	−20.2151			−1.04530
$375$		0			0
$376$	−10.5558			−0.544376
$377$	−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	$0.649193\pi$
$380$	11.4641			0.588096
$381$		0			0
$382$	1.07180			0.0548379
$383$	10.8332	+	18.7637i	0.553552	+	0.958781i	0.998015	+	0.0629833i	$0.0200615\pi$
$383$	10.8332	+	18.7637i	0.553552	+	0.958781i	−0.444462	+	0.895798i	$0.646605\pi$
$384$		0			0
$385$		0			0
$386$	23.0526			1.17334
$387$		0			0
$388$	−2.94855	−	5.10703i	−0.149690	−	0.259270i
$389$	4.00000	−	6.92820i	0.202808	−	0.351274i	−0.746624	−	0.665246i	$-0.768327\pi$
$389$	4.00000	−	6.92820i	0.202808	−	0.351274i	0.949432	+	0.313972i	$0.101660\pi$
$390$		0			0
$391$	−3.96524	+	6.86800i	−0.200531	+	0.347329i
$392$		0			0
$393$		0			0
$394$	−3.07180			−0.154755
$395$	9.52056	+	16.4901i	0.479031	+	0.829706i
$396$		0			0
$397$	9.00292	−	15.5935i	0.451844	−	0.782616i	−0.546657	−	0.837357i	$-0.684100\pi$
$397$	9.00292	−	15.5935i	0.451844	−	0.782616i	0.998501	+	0.0547406i	$0.0174332\pi$
$398$	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	$-0.0202042\pi$
$401$	8.89230	+	15.4019i	0.444061	+	0.769135i	−0.553926	+	0.832566i	$0.686871\pi$
$402$		0			0
$403$	−6.00000	+	10.3923i	−0.298881	+	0.517678i
$404$	−2.44949	+	4.24264i	−0.121867	+	0.211079i
$405$		0			0
$406$		0			0
$407$	−1.00000	−	1.73205i	−0.0495682	−	0.0858546i
$408$		0			0
$409$	−16.7303			−0.827261			−0.413631	−	0.910445i	$-0.635740\pi$
$409$	−16.7303			−0.827261			−0.413631	+	0.910445i	$0.635740\pi$
$410$	4.92820			0.243387
$411$		0			0
$412$	3.72500	+	6.45189i	0.183518	+	0.317862i
$413$		0			0
$414$		0			0
$415$	34.5885	−	59.9090i	1.69788	−	2.94082i
$416$	−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	$-0.409883\pi$
$422$	2.53590	−	4.39230i	0.123446	−	0.213814i
$423$		0			0
$424$	1.46410	+	2.53590i	0.0711031	+	0.123154i
$425$	53.7773			2.60858
$426$		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
$431$	−18.9282	−	32.7846i	−0.911739	−	1.57918i	−0.811606	−	0.584205i	$-0.801406\pi$
$431$	−18.9282	−	32.7846i	−0.911739	−	1.57918i	−0.100133	−	0.994974i	$-0.531927\pi$
$432$		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
$437$	4.34418			0.207810
$438$		0			0
$439$	19.5959			0.935262			0.467631	−	0.883924i	$-0.345108\pi$
$439$	19.5959			0.935262			0.467631	+	0.883924i	$0.345108\pi$
$440$	−14.4195			−0.687424
$441$		0			0
$442$	36.2487			1.72418
$443$	18.3205			0.870434			0.435217	−	0.900326i	$-0.356672\pi$
$443$	18.3205			0.870434			0.435217	+	0.900326i	$0.356672\pi$
$444$		0			0
$445$	27.3205			1.29512
$446$	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
$451$	2.38014	+	4.12252i	0.112076	+	0.194122i
$452$	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
$457$	7.05256			0.329905			0.164952	−	0.986302i	$-0.447253\pi$
$457$	7.05256			0.329905			0.164952	+	0.986302i	$0.447253\pi$
$458$	−12.4877	−	21.6293i	−0.583511	−	1.01067i
$459$		0			0
$460$	−2.82843	+	4.89898i	−0.131876	+	0.228416i
$461$	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
$467$	13.7818	−	23.8707i	0.637745	−	1.10461i	−0.348182	−	0.937427i	$-0.613201\pi$
$467$	13.7818	−	23.8707i	0.637745	−	1.10461i	0.985927	−	0.167179i	$-0.0534659\pi$
$468$		0			0
$469$		0			0
$470$	20.3923	+	35.3205i	0.940627	+	1.62921i
$471$		0			0
$472$	8.62398			0.396951
$473$	13.9282			0.640419
$474$		0			0
$475$	−14.7291	−	25.5116i	−0.675819	−	1.17055i
$476$		0			0
$477$		0			0
$478$	6.46410	−	11.1962i	0.295661	−	0.512100i
$479$	−7.72741	+	13.3843i	−0.353074	+	0.611542i	−0.986786	−	0.162026i	$-0.948197\pi$
$479$	−7.72741	+	13.3843i	−0.353074	+	0.611542i	0.633712	+	0.773569i	$0.281530\pi$
$480$		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
$485$	−11.3923	+	19.7321i	−0.517298	+	0.895986i
$486$		0			0
$487$	−19.3923	−	33.5885i	−0.878749	−	1.52204i	−0.852714	−	0.522377i	$-0.825045\pi$
$487$	−19.3923	−	33.5885i	−0.878749	−	1.52204i	−0.0260347	−	0.999661i	$-0.508288\pi$
$488$	6.96953			0.315496
$489$		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
$494$	−9.92820	−	17.1962i	−0.446691	−	0.773691i
$495$		0			0
$496$	−1.79315			−0.0805149
$497$		0			0
$498$		0			0
$499$	−6.30385	−	10.9186i	−0.282199	−	0.488783i	0.689727	−	0.724069i	$-0.257731\pi$
$499$	−6.30385	−	10.9186i	−0.282199	−	0.488783i	−0.971926	+	0.235286i	$0.924397\pi$
$500$	19.0411			0.851545
$501$		0			0
$502$	16.3514			0.729798
$503$	−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
$506$	−5.46410			−0.242909
$507$		0			0
$508$	6.53590			0.289984
$509$	−13.2456	−	22.9420i	−0.587099	−	1.01689i	−0.994610	−	0.103685i	$-0.966937\pi$
$509$	−13.2456	−	22.9420i	−0.587099	−	1.01689i	0.407511	−	0.913200i	$-0.366397\pi$
$510$		0			0
$511$		0			0
$512$	−1.00000			−0.0441942
$513$		0			0
$514$	1.34486	+	2.32937i	0.0593194	+	0.102744i
$515$	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
$520$	25.8564			1.13388
$521$	−16.1805	−	28.0255i	−0.708881	−	1.22782i	−0.965273	−	0.261244i	$-0.915867\pi$
$521$	−16.1805	−	28.0255i	−0.708881	−	1.22782i	0.256392	−	0.966573i	$-0.417466\pi$
$522$		0			0
$523$	−1.88108	+	3.25813i	−0.0822540	+	0.142468i	−0.904218	−	0.427072i	$-0.859545\pi$
$523$	−1.88108	+	3.25813i	−0.0822540	+	0.142468i	0.821964	+	0.569540i	$0.192879\pi$
$524$	−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
$530$	5.65685	−	9.79796i	0.245718	−	0.425596i
$531$		0			0
$532$		0			0
$533$	−4.26795	−	7.39230i	−0.184865	−	0.320196i
$534$		0			0
$535$	−13.1069			−0.566659
$536$	−5.53590			−0.239114
$537$		0			0
$538$	−2.82843	−	4.89898i	−0.121942	−	0.211210i
$539$		0			0
$540$		0			0
$541$	9.66025	−	16.7321i	0.415327	−	0.719367i	−0.580136	−	0.814520i	$-0.697001\pi$
$541$	9.66025	−	16.7321i	0.415327	−	0.719367i	0.995463	+	0.0951526i	$0.0303339\pi$
$542$	−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	$0.527108\pi$
$548$	−4.33013	+	7.50000i	−0.184974	+	0.320384i
$549$		0			0
$550$	18.5263	+	32.0885i	0.789963	+	1.36826i
$551$	11.8685			0.505616
$552$		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
$557$	3.46410	+	6.00000i	0.146779	+	0.254228i	0.930035	−	0.367471i	$-0.119776\pi$
$557$	3.46410	+	6.00000i	0.146779	+	0.254228i	−0.783256	+	0.621699i	$0.786443\pi$
$558$		0			0
$559$	−24.9754			−1.05635
$560$		0			0
$561$		0			0
$562$	4.92820	+	8.53590i	0.207884	+	0.360065i
$563$	−25.5945			−1.07868			−0.539341	−	0.842088i	$-0.681327\pi$
$563$	−25.5945			−1.07868			−0.539341	+	0.842088i	$0.681327\pi$
$564$		0			0
$565$	−26.7685			−1.12616
$566$	9.41902			0.395911
$567$		0			0
$568$	2.53590			0.106404
$569$	−15.7846			−0.661725			−0.330863	−	0.943679i	$-0.607340\pi$
$569$	−15.7846			−0.661725			−0.330863	+	0.943679i	$0.607340\pi$
$570$		0			0
$571$	5.05256			0.211443			0.105722	−	0.994396i	$-0.466285\pi$
$571$	5.05256			0.211443			0.105722	+	0.994396i	$0.466285\pi$
$572$	12.4877	+	21.6293i	0.522136	+	0.904367i
$573$		0			0
$574$		0			0
$575$	14.5359			0.606189
$576$		0			0
$577$	−22.3178	−	38.6556i	−0.929103	−	1.60925i	−0.784825	−	0.619717i	$-0.787247\pi$
$577$	−22.3178	−	38.6556i	−0.929103	−	1.60925i	−0.144278	−	0.989537i	$-0.546086\pi$
$578$	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
$583$	10.9282			0.452600
$584$	3.41542	+	5.91567i	0.141331	+	0.244792i
$585$		0			0
$586$	−9.52056	+	16.4901i	−0.393291	+	0.681199i
$587$	−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
$593$	1.36345	−	2.36156i	0.0559900	−	0.0969775i	−0.836672	−	0.547704i	$-0.815502\pi$
$593$	1.36345	−	2.36156i	0.0559900	−	0.0969775i	0.892662	+	0.450727i	$0.148835\pi$
$594$		0			0
$595$		0			0
$596$	4.53590	+	7.85641i	0.185798	+	0.321811i
$597$		0			0
$598$	9.79796			0.400668
$599$	36.7846			1.50298			0.751489	−	0.659745i	$-0.229336\pi$
$599$	36.7846			1.50298			0.751489	+	0.659745i	$0.229336\pi$
$600$		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
$604$	1.19615	−	2.07180i	0.0486708	−	0.0843002i
$605$	−5.65685	+	9.79796i	−0.229984	+	0.398344i
$606$		0			0
$607$	−15.8338	−	27.4249i	−0.642672	−	1.11314i	−0.984834	−	0.173500i	$-0.944492\pi$
$607$	−15.8338	−	27.4249i	−0.642672	−	1.11314i	0.342162	−	0.939641i	$-0.388841\pi$
$608$	1.48356	−	2.56961i	0.0601665	−	0.104211i
$609$		0			0
$610$	−13.4641	−	23.3205i	−0.545146	−	0.944220i
$611$	35.3205	−	61.1769i	1.42891	−	2.47495i
$612$		0			0
$613$	−5.53590	−	9.58846i	−0.223593	−	0.387274i	0.732304	−	0.680978i	$-0.238445\pi$
$613$	−5.53590	−	9.58846i	−0.223593	−	0.387274i	−0.955896	+	0.293704i	$0.905112\pi$
$614$	−11.0735			−0.446889
$615$		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	−0.504930	−	0.863160i	$-0.668482\pi$
$619$	12.3168	−	21.3333i	0.495054	−	0.857459i	0.999984	+	0.00570182i	$0.00181496\pi$
$620$	3.46410	+	6.00000i	0.139122	+	0.240966i
$621$		0			0
$622$	12.3490			0.495149
$623$		0			0
$624$		0			0
$625$	−11.9641	−	20.7224i	−0.478564	−	0.828897i
$626$	23.4225			0.936150
$627$		0			0
$628$	−4.62158			−0.184421
$629$	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	$0.248309\pi$
$632$	4.92820			0.196033
$633$		0			0
$634$	−26.0000			−1.03259
$635$	−12.6264	−	21.8695i	−0.501063	−	0.867866i
$636$		0			0
$637$		0			0
$638$	−14.9282			−0.591013
$639$		0			0
$640$	1.93185	+	3.34607i	0.0763631	+	0.132265i
$641$	8.96410	−	15.5263i	0.354061	−	0.613251i	−0.632896	−	0.774237i	$-0.718134\pi$
$641$	8.96410	−	15.5263i	0.354061	−	0.613251i	0.986957	+	0.160986i	$0.0514673\pi$
$642$		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
$646$	−16.0718			−0.632336
$647$	−6.03579	−	10.4543i	−0.237291	−	0.411001i	0.722645	−	0.691220i	$-0.242926\pi$
$647$	−6.03579	−	10.4543i	−0.237291	−	0.411001i	−0.959936	+	0.280219i	$0.909593\pi$
$648$		0			0
$649$	16.0926	−	27.8731i	0.631689	−	1.09412i
$650$	−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	$-0.129211\pi$
$653$	3.00000	+	5.19615i	0.117399	+	0.203341i	−0.801337	+	0.598213i	$0.795878\pi$
$654$		0			0
$655$	−11.6603	+	20.1962i	−0.455604	+	0.789129i
$656$	0.637756	−	1.10463i	0.0249002	−	0.0431284i
$657$		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			−	1.00000i	$-0.5\pi$
$661$		0			0				1.00000i	$0.5\pi$
$662$	4.53590			0.176293
$663$		0			0
$664$	−8.95215	−	15.5056i	−0.347411	−	0.601733i
$665$		0			0
$666$		0			0
$667$	−2.92820	+	5.07180i	−0.113380	+	0.196381i
$668$	−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	$0.537535\pi$
$674$	−3.50000	+	6.06218i	−0.134815	+	0.233506i
$675$		0			0
$676$	−15.8923	−	27.5263i	−0.611242	−	1.05870i
$677$	−20.0764			−0.771598			−0.385799	−	0.922583i	$-0.626074\pi$
$677$	−20.0764			−0.771598			−0.385799	+	0.922583i	$0.626074\pi$
$678$		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
$683$	−1.83975	−	3.18653i	−0.0703959	−	0.121929i	0.828679	−	0.559724i	$-0.189093\pi$
$683$	−1.83975	−	3.18653i	−0.0703959	−	0.121929i	−0.899075	+	0.437795i	$0.855760\pi$
$684$		0			0
$685$	33.4607			1.27847
$686$		0			0
$687$		0			0
$688$	−1.86603	−	3.23205i	−0.0711416	−	0.123221i
$689$	−19.5959			−0.746545
$690$		0			0
$691$	−9.62209			−0.366042			−0.183021	−	0.983109i	$-0.558588\pi$
$691$	−9.62209			−0.366042			−0.183021	+	0.983109i	$0.558588\pi$
$692$	1.79315			0.0681654
$693$		0			0
$694$	21.5885			0.819487
$695$	63.1769			2.39644
$696$		0			0
$697$	−6.90897			−0.261696
$698$	−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
$703$	−0.795040	−	1.37705i	−0.0299855	−	0.0519364i
$704$	−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
$709$	8.39230			0.315180			0.157590	−	0.987505i	$-0.449628\pi$
$709$	8.39230			0.315180			0.157590	+	0.987505i	$0.449628\pi$
$710$	−4.89898	−	8.48528i	−0.183855	−	0.318447i
$711$		0			0
$712$	3.53553	−	6.12372i	0.132500	−	0.229496i
$713$	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
$719$	7.69024	−	13.3199i	0.286798	−	0.496748i	−0.686246	−	0.727370i	$-0.740743\pi$
$719$	7.69024	−	13.3199i	0.286798	−	0.496748i	0.973044	+	0.230622i	$0.0740759\pi$
$720$		0			0
$721$		0			0
$722$	−5.09808	−	8.83013i	−0.189731	−	0.328623i
$723$		0			0
$724$	16.9706			0.630706
$725$	39.7128			1.47490
$726$		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
$730$	13.1962	−	22.8564i	0.488412	−	0.845954i
$731$	−10.1075	+	17.5068i	−0.373841	+	0.647512i
$732$		0			0
$733$	−8.24504	−	14.2808i	−0.304538	−	0.527475i	0.672621	−	0.739988i	$-0.265169\pi$
$733$	−8.24504	−	14.2808i	−0.304538	−	0.527475i	−0.977158	+	0.212513i	$0.931835\pi$
$734$	7.86611	−	13.6245i	0.290343	−	0.502889i
$735$		0			0
$736$	0.732051	+	1.26795i	0.0269838	+	0.0467372i
$737$	−10.3301	+	17.8923i	−0.380515	+	0.659072i
$738$		0			0
$739$	9.06218	+	15.6962i	0.333358	+	0.577392i	0.983168	−	0.182704i	$-0.0584850\pi$
$739$	9.06218	+	15.6962i	0.333358	+	0.577392i	−0.649810	+	0.760096i	$0.725152\pi$
$740$	2.07055			0.0761150
$741$		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
$746$	15.3923	+	26.6603i	0.563552	+	0.976101i
$747$		0			0
$748$	20.2151			0.739137
$749$		0			0
$750$		0			0
$751$	3.39230	+	5.87564i	0.123787	+	0.214405i	0.921258	−	0.388952i	$-0.127163\pi$
$751$	3.39230	+	5.87564i	0.123787	+	0.214405i	−0.797471	+	0.603357i	$0.793829\pi$
$752$	10.5558			0.384932
$753$		0			0
$754$	26.7685			0.974852
$755$	−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	$0.589810\pi$
$758$	17.5885			0.638842
$759$		0			0
$760$	−11.4641			−0.415847
$761$	15.2282	+	26.3760i	0.552021	+	0.956129i	0.998129	+	0.0611492i	$0.0194765\pi$
$761$	15.2282	+	26.3760i	0.552021	+	0.956129i	−0.446108	+	0.894979i	$0.647190\pi$
$762$		0			0
$763$		0			0
$764$	−1.07180			−0.0387762
$765$		0			0
$766$	−10.8332	−	18.7637i	−0.391421	−	0.677961i
$767$	−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
$772$	−23.0526			−0.829680
$773$	−0.101536	−	0.175865i	−0.00365199	−	0.00632544i	0.864194	−	0.503159i	$-0.167829\pi$
$773$	−0.101536	−	0.175865i	−0.00365199	−	0.00632544i	−0.867846	+	0.496834i	$0.834496\pi$
$774$		0			0
$775$	8.90138	−	15.4176i	0.319747	−	0.553818i
$776$	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
$782$	3.96524	−	6.86800i	0.141797	−	0.245599i
$783$		0			0
$784$		0			0
$785$	8.92820	+	15.4641i	0.318661	+	0.551937i
$786$		0			0
$787$	46.7434			1.66622			0.833111	−	0.553106i	$-0.186558\pi$
$787$	46.7434			1.66622			0.833111	+	0.553106i	$0.186558\pi$
$788$	3.07180			0.109428
$789$		0			0
$790$	−9.52056	−	16.4901i	−0.338726	−	0.586691i
$791$		0			0
$792$		0			0
$793$	−23.3205	+	40.3923i	−0.828136	+	1.43437i
$794$	−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
$800$	4.96410	−	8.59808i	0.175507	−	0.303988i
$801$		0			0
$802$	−8.89230	−	15.4019i	−0.313998	−	0.543861i
$803$	25.4930			0.899629
$804$		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
$809$	−13.1340	−	22.7487i	−0.461766	−	0.799802i	0.537283	−	0.843402i	$-0.319451\pi$
$809$	−13.1340	−	22.7487i	−0.461766	−	0.799802i	−0.999049	+	0.0435999i	$0.986117\pi$
$810$		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
$815$	82.3761			2.88551
$816$		0			0
$817$	11.0735			0.387412
$818$	16.7303			0.584962
$819$		0			0
$820$	−4.92820			−0.172100
$821$	10.3923			0.362694			0.181347	−	0.983419i	$-0.441954\pi$
$821$	10.3923			0.362694			0.181347	+	0.983419i	$0.441954\pi$
$822$		0			0
$823$	30.7846			1.07308			0.536542	−	0.843874i	$-0.319730\pi$
$823$	30.7846			1.07308			0.536542	+	0.843874i	$0.319730\pi$
$824$	−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
$829$	18.6622	+	32.3238i	0.648164	+	1.12265i	0.983561	+	0.180576i	$0.0577963\pi$
$829$	18.6622	+	32.3238i	0.648164	+	1.12265i	−0.335397	+	0.942077i	$0.608870\pi$
$830$	−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
$835$	81.5692			2.82282
$836$	−5.53674	−	9.58991i	−0.191492	−	0.331674i
$837$		0			0
$838$	−3.95164	+	6.84443i	−0.136507	+	0.236437i
$839$	−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
$845$	−61.4032	+	106.353i	−2.11233	+	3.65867i
$846$		0			0
$847$		0			0
$848$	−1.46410	−	2.53590i	−0.0502775	−	0.0870831i
$849$		0			0
$850$	−53.7773			−1.84455
$851$	0.784610			0.0268961
$852$		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
$856$	−1.69615	+	2.93782i	−0.0579733	+	0.100413i
$857$	−4.19187	+	7.26054i	−0.143192	+	0.248015i	−0.928697	−	0.370840i	$-0.879070\pi$
$857$	−4.19187	+	7.26054i	−0.143192	+	0.248015i	0.785505	+	0.618855i	$0.212403\pi$
$858$		0			0
$859$	7.36705	+	12.7601i	0.251361	+	0.435369i	0.963901	−	0.266262i	$-0.0857887\pi$
$859$	7.36705	+	12.7601i	0.251361	+	0.435369i	−0.712540	+	0.701631i	$0.752455\pi$
$860$	−7.20977	+	12.4877i	−0.245851	+	0.425827i
$861$		0			0
$862$	18.9282	+	32.7846i	0.644697	+	1.11665i
$863$	11.0526	−	19.1436i	0.376233	−	0.651656i	−0.614277	−	0.789090i	$-0.710552\pi$
$863$	11.0526	−	19.1436i	0.376233	−	0.651656i	0.990511	+	0.137435i	$0.0438857\pi$
$864$		0			0
$865$	−3.46410	−	6.00000i	−0.117783	−	0.204006i
$866$	7.10823			0.241548
$867$		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
$872$	−4.46410	−	7.73205i	−0.151174	−	0.261840i
$873$		0			0
$874$	−4.34418			−0.146944
$875$		0			0
$876$		0			0
$877$	−16.5885	−	28.7321i	−0.560152	−	0.970212i	−0.997483	−	0.0709114i	$-0.977409\pi$
$877$	−16.5885	−	28.7321i	−0.560152	−	0.970212i	0.437330	−	0.899301i	$-0.355924\pi$
$878$	−19.5959			−0.661330
$879$		0			0
$880$	14.4195			0.486082
$881$	−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	$0.459529\pi$
$884$	−36.2487			−1.21918
$885$		0			0
$886$	−18.3205			−0.615490
$887$	−14.3824	−	24.9110i	−0.482913	−	0.836430i	0.516895	−	0.856049i	$-0.327088\pi$
$887$	−14.3824	−	24.9110i	−0.482913	−	0.836430i	−0.999808	+	0.0196195i	$0.993755\pi$
$888$		0			0
$889$		0			0
$890$	−27.3205			−0.915786
$891$		0			0
$892$	−13.3843	−	23.1822i	−0.448138	−	0.776198i
$893$	−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
$898$	−17.7846			−0.593480
$899$	3.58630	+	6.21166i	0.119610	+	0.207170i
$900$		0			0
$901$	−7.93048	+	13.7360i	−0.264203	+	0.457612i
$902$	−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	0.243756	+	0.969837i	$0.421620\pi$
$907$	−21.6244	+	37.4545i	−0.718025	+	1.24366i	−0.961781	+	0.273819i	$0.911713\pi$
$908$	5.25933	−	9.10943i	0.174537	−	0.302307i
$909$		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
$913$	−66.8198			−2.21141
$914$	−7.05256			−0.233278
$915$		0			0
$916$	12.4877	+	21.6293i	0.412605	+	0.714652i
$917$		0			0
$918$		0			0
$919$	−11.4641	+	19.8564i	−0.378166	+	0.655002i	−0.990795	−	0.135368i	$-0.956778\pi$
$919$	−11.4641	+	19.8564i	−0.378166	+	0.655002i	0.612630	+	0.790370i	$0.290112\pi$
$920$	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
$926$	19.3205	−	33.4641i	0.634911	−	1.09970i
$927$		0			0
$928$	2.00000	+	3.46410i	0.0656532	+	0.113715i
$929$	−27.9797			−0.917983			−0.458991	−	0.888441i	$-0.651789\pi$
$929$	−27.9797			−0.917983			−0.458991	+	0.888441i	$0.651789\pi$
$930$		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
$935$	−39.0526	−	67.6410i	−1.27716	−	2.21210i
$936$		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
$941$	−8.68835			−0.283232			−0.141616	−	0.989922i	$-0.545230\pi$
$941$	−8.68835			−0.283232			−0.141616	+	0.989922i	$0.545230\pi$
$942$		0			0
$943$	−1.86748			−0.0608135
$944$	−8.62398			−0.280687
$945$		0			0
$946$	−13.9282			−0.452845
$947$	−6.12436			−0.199015			−0.0995074	−	0.995037i	$-0.531727\pi$
$947$	−6.12436			−0.199015			−0.0995074	+	0.995037i	$0.531727\pi$
$948$		0			0
$949$	−45.7128			−1.48390
$950$	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
$955$	2.07055	+	3.58630i	0.0670015	+	0.116050i
$956$	−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
$961$	−27.7846			−0.896278
$962$	−1.79315	−	3.10583i	−0.0578135	−	0.100136i
$963$		0			0
$964$	11.7112	−	20.2844i	0.377193	−	0.653318i
$965$	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
$971$	1.50215	−	2.60179i	0.0482062	−	0.0834955i	−0.840915	−	0.541166i	$-0.817983\pi$
$971$	1.50215	−	2.60179i	0.0482062	−	0.0834955i	0.889122	+	0.457671i	$0.151316\pi$
$972$		0			0
$973$		0			0
$974$	19.3923	+	33.5885i	0.621370	+	1.07624i
$975$		0			0
$976$	−6.96953			−0.223089
$977$	49.9808			1.59903			0.799513	−	0.600649i	$-0.205091\pi$
$977$	49.9808			1.59903			0.799513	+	0.600649i	$0.205091\pi$
$978$		0			0
$979$	−13.1948	−	22.8541i	−0.421707	−	0.730419i
$980$		0			0
$981$		0			0
$982$	0.696152	−	1.20577i	0.0222151	−	0.0384777i
$983$	3.48477	−	6.03579i	0.111147	−	0.192512i	−0.805086	−	0.593158i	$-0.797881\pi$
$983$	3.48477	−	6.03579i	0.111147	−	0.192512i	0.916233	+	0.400646i	$0.131214\pi$
$984$		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
$989$	−2.73205	+	4.73205i	−0.0868742	+	0.150470i
$990$		0			0
$991$	−0.875644	−	1.51666i	−0.0278158	−	0.0481783i	0.851782	−	0.523896i	$-0.175522\pi$
$991$	−0.875644	−	1.51666i	−0.0278158	−	0.0481783i	−0.879598	+	0.475717i	$0.842189\pi$
$992$	1.79315			0.0569326
$993$		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	−0.810064	−	0.586342i	$-0.800567\pi$
$997$	3.24453	−	5.61969i	0.102755	−	0.177977i	0.912819	+	0.408365i	$0.133901\pi$
$998$	6.30385	+	10.9186i	0.199545	+	0.345622i
$999$		0			0

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
882.2.e.s.373.1		8	3.2	odd	2
882.2.e.s.373.4		8	21.20	even	2
882.2.e.s.655.1		8	63.11	odd	6
882.2.e.s.655.4		8	63.38	even	6
882.2.f.q.295.2	✓	8	63.47	even	6
882.2.f.q.295.3	yes	8	63.2	odd	6
882.2.f.q.589.2	yes	8	21.5	even	6
882.2.f.q.589.3	yes	8	21.2	odd	6
882.2.h.q.67.1		8	21.17	even	6
882.2.h.q.67.4		8	21.11	odd	6
882.2.h.q.79.2		8	63.20	even	6
882.2.h.q.79.3		8	9.2	odd	6
2646.2.e.q.1549.1		8	1.1	even	1	trivial
2646.2.e.q.1549.4		8	7.6	odd	2	inner
2646.2.e.q.2125.1		8	63.25	even	3	inner
2646.2.e.q.2125.4		8	63.52	odd	6	inner
2646.2.f.r.883.1		8	63.16	even	3
2646.2.f.r.883.4		8	63.61	odd	6
2646.2.f.r.1765.1		8	7.2	even	3
2646.2.f.r.1765.4		8	7.5	odd	6
2646.2.h.t.361.1		8	7.3	odd	6
2646.2.h.t.361.4		8	7.4	even	3
2646.2.h.t.667.1		8	63.34	odd	6
2646.2.h.t.667.4		8	9.7	even	3
7938.2.a.ci.1.1		4	63.40	odd	6
7938.2.a.ci.1.4		4	63.58	even	3
7938.2.a.cp.1.1		4	63.23	odd	6
7938.2.a.cp.1.4		4	63.5	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 $\F_{q}$
Belyi maps

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

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +1.00000 q^{4} +(-1.93185 - 3.34607i) q^{5} -1.00000 q^{8} +(1.93185 + 3.34607i) q^{10} +(-1.86603 + 3.23205i) q^{11} +(3.34607 - 5.79555i) q^{13} +1.00000 q^{16} +(-2.70831 - 4.69093i) q^{17} +(-1.48356 + 2.56961i) q^{19} +(-1.93185 - 3.34607i) q^{20} +(1.86603 - 3.23205i) q^{22} +(-0.732051 - 1.26795i) q^{23} +(-4.96410 + 8.59808i) q^{25} +(-3.34607 + 5.79555i) q^{26} +(-2.00000 - 3.46410i) q^{29} -1.79315 q^{31} -1.00000 q^{32} +(2.70831 + 4.69093i) q^{34} +(-0.267949 + 0.464102i) q^{37} +(1.48356 - 2.56961i) q^{38} +(1.93185 + 3.34607i) q^{40} +(0.637756 - 1.10463i) q^{41} +(-1.86603 - 3.23205i) q^{43} +(-1.86603 + 3.23205i) q^{44} +(0.732051 + 1.26795i) q^{46} +10.5558 q^{47} +(4.96410 - 8.59808i) q^{50} +(3.34607 - 5.79555i) q^{52} +(-1.46410 - 2.53590i) q^{53} +14.4195 q^{55} +(2.00000 + 3.46410i) q^{58} -8.62398 q^{59} -6.96953 q^{61} +1.79315 q^{62} +1.00000 q^{64} -25.8564 q^{65} +5.53590 q^{67} +(-2.70831 - 4.69093i) q^{68} -2.53590 q^{71} +(-3.41542 - 5.91567i) q^{73} +(0.267949 - 0.464102i) q^{74} +(-1.48356 + 2.56961i) q^{76} -4.92820 q^{79} +(-1.93185 - 3.34607i) q^{80} +(-0.637756 + 1.10463i) q^{82} +(8.95215 + 15.5056i) q^{83} +(-10.4641 + 18.1244i) q^{85} +(1.86603 + 3.23205i) q^{86} +(1.86603 - 3.23205i) q^{88} +(-3.53553 + 6.12372i) q^{89} +(-0.732051 - 1.26795i) q^{92} -10.5558 q^{94} +11.4641 q^{95} +(-2.94855 - 5.10703i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 8 q^{2} + 8 q^{4} - 8 q^{8} - 8 q^{11} + 8 q^{16} + 8 q^{22} + 8 q^{23} - 12 q^{25} - 16 q^{29} - 8 q^{32} - 16 q^{37} - 8 q^{43} - 8 q^{44} - 8 q^{46} + 12 q^{50} + 16 q^{53} + 16 q^{58} + 8 q^{64}+ \cdots + 64 q^{95}+O(q^{100}) \) 8 * q - 8 * q^2 + 8 * q^4 - 8 * q^8 - 8 * q^11 + 8 * q^16 + 8 * q^22 + 8 * q^23 - 12 * q^25 - 16 * q^29 - 8 * q^32 - 16 * q^37 - 8 * q^43 - 8 * q^44 - 8 * q^46 + 12 * q^50 + 16 * q^53 + 16 * q^58 + 8 * q^64 - 96 * q^65 + 72 * q^67 - 48 * q^71 + 16 * q^74 + 16 * q^79 - 56 * q^85 + 8 * q^86 + 8 * q^88 + 8 * q^92 + 64 * q^95

Introduction

L-functions

Modular forms

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Database

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