LMFDB - Embedded newform 2646.2.t.a.2285.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2646,2,Mod(1979,2646)]

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([1, 5]))

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

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

chi := DirichletCharacter("2646.1979");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2646 = 2 \cdot 3^{3} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2646.t (of order $6$, 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:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 6x^{14} + 9x^{12} + 54x^{10} - 288x^{8} + 486x^{6} + 729x^{4} - 4374x^{2} + 6561 $ x^16 - 6x^14 + 9x^12 + 54x^10 - 288x^8 + 486x^6 + 729x^4 - 4374*x^2 + 6561
Coefficient ring:	$\Z[a_1, \ldots, a_{17}]$
Coefficient ring index:	$ 2^{2}\cdot 3^{4} $
Twist minimal:	no (minimal twist has level 126)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			2285.2
Root			$1.40917 - 1.00709i$ of defining polynomial
Character	$\chi$	$=$	2646.2285
Dual form			2646.2.t.a.1979.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 - 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} -2.34936 q^{5} -1.00000i q^{8} +O(q^{10})$	\(q+(-0.866025 - 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} -2.34936 q^{5} -1.00000i q^{8} +(2.03460 + 1.17468i) q^{10} +5.67667i q^{11} +(-1.48943 - 0.859925i) q^{13} +(-0.500000 + 0.866025i) q^{16} +(0.884414 - 1.53185i) q^{17} +(-0.986680 + 0.569660i) q^{19} +(-1.17468 - 2.03460i) q^{20} +(2.83834 - 4.91614i) q^{22} -3.67509i q^{23} +0.519482 q^{25} +(0.859925 + 1.48943i) q^{26} +(-3.59886 + 2.07781i) q^{29} +(-7.24879 + 4.18509i) q^{31} +(0.866025 - 0.500000i) q^{32} +(-1.53185 + 0.884414i) q^{34} +(4.59886 + 7.96547i) q^{37} +1.13932 q^{38} +2.34936i q^{40} +(3.99709 - 6.92317i) q^{41} +(1.76053 + 3.04933i) q^{43} +(-4.91614 + 2.83834i) q^{44} +(-1.83755 + 3.18272i) q^{46} +(5.90494 - 10.2277i) q^{47} +(-0.449885 - 0.259741i) q^{50} -1.71985i q^{52} -13.3365i q^{55} +4.15561 q^{58} +(1.11483 + 1.93094i) q^{59} +(7.79396 + 4.49985i) q^{61} +8.37019 q^{62} -1.00000 q^{64} +(3.49921 + 2.02027i) q^{65} +(-5.43562 - 9.41477i) q^{67} +1.76883 q^{68} +4.52106i q^{71} +(-4.62660 - 2.67117i) q^{73} -9.19773i q^{74} +(-0.986680 - 0.569660i) q^{76} +(6.51422 - 11.2830i) q^{79} +(1.17468 - 2.03460i) q^{80} +(-6.92317 + 3.99709i) q^{82} +(-6.27298 - 10.8651i) q^{83} +(-2.07781 + 3.59886i) q^{85} -3.52106i q^{86} +5.67667 q^{88} +(0.580529 + 1.00551i) q^{89} +(3.18272 - 1.83755i) q^{92} +(-10.2277 + 5.90494i) q^{94} +(2.31806 - 1.33834i) q^{95} +(3.97536 - 2.29517i) q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 8 q^{4}+O(q^{10}) $ 16 * q + 8 * q^4	$ 16 q + 8 q^{4} - 8 q^{16} + 16 q^{25} + 12 q^{29} + 4 q^{37} + 4 q^{43} - 12 q^{44} - 12 q^{46} - 60 q^{50} + 24 q^{58} - 16 q^{64} + 84 q^{65} - 28 q^{67} - 4 q^{79} - 12 q^{85} + 48 q^{92} + 12 q^{95}+O(q^{100}) $ 16 * q + 8 * q^4 - 8 * q^16 + 16 * q^25 + 12 * q^29 + 4 * q^37 + 4 * q^43 - 12 * q^44 - 12 * q^46 - 60 * q^50 + 24 * q^58 - 16 * q^64 + 84 * q^65 - 28 * q^67 - 4 * q^79 - 12 * q^85 + 48 * q^92 + 12 * q^95

Display 100 coefficients 10 coefficients

Character values

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

$n$	$785$	$1081$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{6}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.866025	−	0.500000i	−0.612372	−	0.353553i
$2$	−0.866025	−	0.500000i	−0.612372	−	0.353553i
$3$		0			0
$3$		0			0
$4$	0.500000	+	0.866025i	0.250000	+	0.433013i
$5$	−2.34936			−1.05066			−0.525332	−	0.850897i	$-0.676059\pi$
$5$	−2.34936			−1.05066			−0.525332	+	0.850897i	$0.676059\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$		−	1.00000i		−	0.353553i
$9$		0			0
$10$	2.03460	+	1.17468i	0.643398	+	0.371466i
$11$			5.67667i			1.71158i	0.517323	+	0.855790i	$0.326929\pi$
$11$			5.67667i			1.71158i	−0.517323	+	0.855790i	$0.673071\pi$
$12$		0			0
$13$	−1.48943	−	0.859925i	−0.413094	−	0.238500i	0.279024	−	0.960284i	$-0.409989\pi$
$13$	−1.48943	−	0.859925i	−0.413094	−	0.238500i	−0.692118	+	0.721784i	$0.743322\pi$
$14$		0			0
$15$		0			0
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	0.884414	−	1.53185i	0.214502	−	0.371528i	−0.738616	−	0.674126i	$-0.764520\pi$
$17$	0.884414	−	1.53185i	0.214502	−	0.371528i	0.953118	+	0.302598i	$0.0978538\pi$
$18$		0			0
$19$	−0.986680	+	0.569660i	−0.226360	+	0.130689i	−0.608892	−	0.793253i	$-0.708386\pi$
$19$	−0.986680	+	0.569660i	−0.226360	+	0.130689i	0.382532	+	0.923942i	$0.375052\pi$
$20$	−1.17468	−	2.03460i	−0.262666	−	0.454951i
$21$		0			0
$22$	2.83834	−	4.91614i	0.605135	−	1.04812i
$23$		−	3.67509i		−	0.766310i	−0.923684	−	0.383155i	$-0.874838\pi$
$23$		−	3.67509i		−	0.766310i	0.923684	−	0.383155i	$-0.125162\pi$
$24$		0			0
$25$	0.519482			0.103896
$26$	0.859925	+	1.48943i	0.168645	+	0.292102i
$27$		0			0
$28$		0			0
$29$	−3.59886	+	2.07781i	−0.668292	+	0.385839i	−0.795429	−	0.606046i	$-0.792755\pi$
$29$	−3.59886	+	2.07781i	−0.668292	+	0.385839i	0.127137	+	0.991885i	$0.459421\pi$
$30$		0			0
$31$	−7.24879	+	4.18509i	−1.30192	+	0.751665i	−0.980734	−	0.195350i	$-0.937416\pi$
$31$	−7.24879	+	4.18509i	−1.30192	+	0.751665i	−0.321188	+	0.947015i	$0.604082\pi$
$32$	0.866025	−	0.500000i	0.153093	−	0.0883883i
$33$		0			0
$34$	−1.53185	+	0.884414i	−0.262710	+	0.151676i
$35$		0			0
$36$		0			0
$37$	4.59886	+	7.96547i	0.756049	+	1.30951i	0.944851	+	0.327500i	$0.106206\pi$
$37$	4.59886	+	7.96547i	0.756049	+	1.30951i	−0.188803	+	0.982015i	$0.560461\pi$
$38$	1.13932			0.184822
$39$		0			0
$40$			2.34936i			0.371466i
$41$	3.99709	−	6.92317i	0.624241	−	1.08122i	−0.364446	−	0.931225i	$-0.618742\pi$
$41$	3.99709	−	6.92317i	0.624241	−	1.08122i	0.988687	−	0.149993i	$-0.0479251\pi$
$42$		0			0
$43$	1.76053	+	3.04933i	0.268478	+	0.465018i	0.968469	−	0.249134i	$-0.0801459\pi$
$43$	1.76053	+	3.04933i	0.268478	+	0.465018i	−0.699991	+	0.714152i	$0.746813\pi$
$44$	−4.91614	+	2.83834i	−0.741136	+	0.427895i
$45$		0			0
$46$	−1.83755	+	3.18272i	−0.270931	+	0.469267i
$47$	5.90494	−	10.2277i	0.861324	−	1.49186i	−0.00932669	−	0.999957i	$-0.502969\pi$
$47$	5.90494	−	10.2277i	0.861324	−	1.49186i	0.870651	−	0.491901i	$-0.163698\pi$
$48$		0			0
$49$		0			0
$50$	−0.449885	−	0.259741i	−0.0636233	−	0.0367329i
$51$		0			0
$52$		−	1.71985i		−	0.238500i
$53$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$53$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$54$		0			0
$55$		−	13.3365i		−	1.79830i
$56$		0			0
$57$		0			0
$58$	4.15561			0.545658
$59$	1.11483	+	1.93094i	0.145139	+	0.251387i	0.929425	−	0.369012i	$-0.120304\pi$
$59$	1.11483	+	1.93094i	0.145139	+	0.251387i	−0.784286	+	0.620399i	$0.786971\pi$
$60$		0			0
$61$	7.79396	+	4.49985i	0.997915	+	0.576146i	0.907631	−	0.419770i	$-0.137889\pi$
$61$	7.79396	+	4.49985i	0.997915	+	0.576146i	0.0902842	+	0.995916i	$0.471222\pi$
$62$	8.37019			1.06301
$63$		0			0
$64$	−1.00000			−0.125000
$65$	3.49921	+	2.02027i	0.434024	+	0.250584i
$66$		0			0
$67$	−5.43562	−	9.41477i	−0.664067	−	1.15020i	−0.979537	−	0.201262i	$-0.935496\pi$
$67$	−5.43562	−	9.41477i	−0.664067	−	1.15020i	0.315470	−	0.948935i	$-0.397838\pi$
$68$	1.76883			0.214502
$69$		0			0
$70$		0			0
$71$			4.52106i			0.536551i	0.963342	+	0.268276i	$0.0864538\pi$
$71$			4.52106i			0.536551i	−0.963342	+	0.268276i	$0.913546\pi$
$72$		0			0
$73$	−4.62660	−	2.67117i	−0.541503	−	0.312637i	0.204185	−	0.978932i	$-0.434546\pi$
$73$	−4.62660	−	2.67117i	−0.541503	−	0.312637i	−0.745688	+	0.666295i	$0.767879\pi$
$74$		−	9.19773i		−	1.06921i
$75$		0			0
$76$	−0.986680	−	0.569660i	−0.113180	−	0.0653445i
$77$		0			0
$78$		0			0
$79$	6.51422	−	11.2830i	0.732907	−	1.26943i	−0.222729	−	0.974880i	$-0.571497\pi$
$79$	6.51422	−	11.2830i	0.732907	−	1.26943i	0.955636	−	0.294551i	$-0.0951701\pi$
$80$	1.17468	−	2.03460i	0.131333	−	0.227476i
$81$		0			0
$82$	−6.92317	+	3.99709i	−0.764536	+	0.441405i
$83$	−6.27298	−	10.8651i	−0.688549	−	1.19260i	−0.972307	−	0.233707i	$-0.924915\pi$
$83$	−6.27298	−	10.8651i	−0.688549	−	1.19260i	0.283758	−	0.958896i	$-0.408419\pi$
$84$		0			0
$85$	−2.07781	+	3.59886i	−0.225370	+	0.390352i
$86$		−	3.52106i		−	0.379686i
$87$		0			0
$88$	5.67667			0.605135
$89$	0.580529	+	1.00551i	0.0615360	+	0.106583i	0.895152	−	0.445761i	$-0.147067\pi$
$89$	0.580529	+	1.00551i	0.0615360	+	0.106583i	−0.833616	+	0.552344i	$0.813733\pi$
$90$		0			0
$91$		0			0
$92$	3.18272	−	1.83755i	0.331822	−	0.191577i
$93$		0			0
$94$	−10.2277	+	5.90494i	−1.05490	+	0.609048i
$95$	2.31806	−	1.33834i	0.237828	−	0.137310i
$96$		0			0
$97$	3.97536	−	2.29517i	0.403636	−	0.233039i	−0.284416	−	0.958701i	$-0.591800\pi$
$97$	3.97536	−	2.29517i	0.403636	−	0.233039i	0.688052	+	0.725662i	$0.258466\pi$
$98$		0			0
$99$		0			0
$100$	0.259741	+	0.449885i	0.0259741	+	0.0449885i
$101$	−6.62310			−0.659023			−0.329511	−	0.944152i	$-0.606884\pi$
$101$	−6.62310			−0.659023			−0.329511	+	0.944152i	$0.606884\pi$
$102$		0			0
$103$		−	5.85977i		−	0.577381i	−0.957423	−	0.288690i	$-0.906780\pi$
$103$		−	5.85977i		−	0.577381i	0.957423	−	0.288690i	$-0.0932198\pi$
$104$	−0.859925	+	1.48943i	−0.0843225	+	0.146051i
$105$		0			0
$106$		0			0
$107$	−4.08386	+	2.35782i	−0.394802	+	0.227939i	−0.684239	−	0.729258i	$-0.739865\pi$
$107$	−4.08386	+	2.35782i	−0.394802	+	0.227939i	0.289437	+	0.957197i	$0.406532\pi$
$108$		0			0
$109$	−2.11835	+	3.66908i	−0.202901	+	0.351435i	−0.949462	−	0.313882i	$-0.898370\pi$
$109$	−2.11835	+	3.66908i	−0.202901	+	0.351435i	0.746561	+	0.665317i	$0.231704\pi$
$110$	−6.66826	+	11.5498i	−0.635794	+	1.10123i
$111$		0			0
$112$		0			0
$113$	−5.91693	−	3.41614i	−0.556618	−	0.321363i	0.195169	−	0.980770i	$-0.437474\pi$
$113$	−5.91693	−	3.41614i	−0.556618	−	0.321363i	−0.751787	+	0.659406i	$0.770808\pi$
$114$		0			0
$115$			8.63411i			0.805135i
$116$	−3.59886	−	2.07781i	−0.334146	−	0.192919i
$117$		0			0
$118$		−	2.22966i		−	0.205257i
$119$		0			0
$120$		0			0
$121$	−21.2246			−1.92951
$122$	−4.49985	−	7.79396i	−0.407397	−	0.705632i
$123$		0			0
$124$	−7.24879	−	4.18509i	−0.650961	−	0.375832i
$125$	10.5263			0.941504
$126$		0			0
$127$	−6.67667			−0.592459			−0.296229	−	0.955117i	$-0.595729\pi$
$127$	−6.67667			−0.592459			−0.296229	+	0.955117i	$0.595729\pi$
$128$	0.866025	+	0.500000i	0.0765466	+	0.0441942i
$129$		0			0
$130$	−2.02027	−	3.49921i	−0.177189	−	0.306901i
$131$	−7.47305			−0.652923			−0.326462	−	0.945210i	$-0.605856\pi$
$131$	−7.47305			−0.652923			−0.326462	+	0.945210i	$0.605856\pi$
$132$		0			0
$133$		0			0
$134$			10.8712i			0.939133i
$135$		0			0
$136$	−1.53185	−	0.884414i	−0.131355	−	0.0758379i
$137$		−	7.98789i		−	0.682452i	−0.939981	−	0.341226i	$-0.889158\pi$
$137$		−	7.98789i		−	0.682452i	0.939981	−	0.341226i	$-0.110842\pi$
$138$		0			0
$139$	−17.9792	−	10.3803i	−1.52498	−	0.880446i	−0.999562	−	0.0295993i	$-0.990577\pi$
$139$	−17.9792	−	10.3803i	−1.52498	−	0.880446i	−0.525415	−	0.850846i	$-0.676090\pi$
$140$		0			0
$141$		0			0
$142$	2.26053	−	3.91535i	0.189699	−	0.328569i
$143$	4.88151	−	8.45502i	0.408212	−	0.707044i
$144$		0			0
$145$	8.45502	−	4.88151i	0.702151	−	0.405387i
$146$	2.67117	+	4.62660i	0.221068	+	0.382900i
$147$		0			0
$148$	−4.59886	+	7.96547i	−0.378024	+	0.654757i
$149$		−	1.19773i		−	0.0981218i	−0.998796	−	0.0490609i	$-0.984377\pi$
$149$		−	1.19773i		−	0.0981218i	0.998796	−	0.0490609i	$-0.0156228\pi$
$150$		0			0
$151$	15.2246			1.23896			0.619480	−	0.785013i	$-0.287344\pi$
$151$	15.2246			1.23896			0.619480	+	0.785013i	$0.287344\pi$
$152$	0.569660	+	0.986680i	0.0462055	+	0.0800303i
$153$		0			0
$154$		0			0
$155$	17.0300	−	9.83228i	1.36788	−	0.789748i
$156$		0			0
$157$	8.68358	−	5.01347i	0.693025	−	0.400118i	−0.111719	−	0.993740i	$-0.535636\pi$
$157$	8.68358	−	5.01347i	0.693025	−	0.400118i	0.804744	+	0.593621i	$0.202302\pi$
$158$	−11.2830	+	6.51422i	−0.897624	+	0.518243i
$159$		0			0
$160$	−2.03460	+	1.17468i	−0.160850	+	0.0928665i
$161$		0			0
$162$		0			0
$163$	−6.00158	−	10.3950i	−0.470080	−	0.814202i	0.529335	−	0.848413i	$-0.322442\pi$
$163$	−6.00158	−	10.3950i	−0.470080	−	0.814202i	−0.999415	+	0.0342109i	$0.989108\pi$
$164$	7.99419			0.624241
$165$		0			0
$166$			12.5460i			0.973756i
$167$	8.57472	−	14.8518i	0.663532	−	1.14927i	−0.316150	−	0.948709i	$-0.602390\pi$
$167$	8.57472	−	14.8518i	0.663532	−	1.14927i	0.979681	−	0.200561i	$-0.0642765\pi$
$168$		0			0
$169$	−5.02106	−	8.69673i	−0.386235	−	0.668979i
$170$	3.59886	−	2.07781i	0.276020	−	0.159360i
$171$		0			0
$172$	−1.76053	+	3.04933i	−0.134239	+	0.232509i
$173$	0.993738	−	1.72121i	0.0755525	−	0.130861i	−0.825774	−	0.564001i	$-0.809261\pi$
$173$	0.993738	−	1.72121i	0.0755525	−	0.130861i	0.901326	+	0.433140i	$0.142595\pi$
$174$		0			0
$175$		0			0
$176$	−4.91614	−	2.83834i	−0.370568	−	0.213948i
$177$		0			0
$178$		−	1.16106i		−	0.0870250i
$179$	7.19773	+	4.15561i	0.537984	+	0.310605i	0.744261	−	0.667889i	$-0.232802\pi$
$179$	7.19773	+	4.15561i	0.537984	+	0.310605i	−0.206278	+	0.978493i	$0.566135\pi$
$180$		0			0
$181$		−	15.4541i		−	1.14870i	−0.818611	−	0.574348i	$-0.805256\pi$
$181$		−	15.4541i		−	1.14870i	0.818611	−	0.574348i	$-0.194744\pi$
$182$		0			0
$183$		0			0
$184$	−3.67509			−0.270931
$185$	−10.8044	−	18.7137i	−0.794354	−	1.37586i
$186$		0			0
$187$	8.69581	+	5.02053i	0.635901	+	0.367137i
$188$	11.8099			0.861324
$189$		0			0
$190$	−2.67667			−0.194186
$191$	10.6851	+	6.16904i	0.773146	+	0.446376i	0.833996	−	0.551771i	$-0.186048\pi$
$191$	10.6851	+	6.16904i	0.773146	+	0.446376i	−0.0608498	+	0.998147i	$0.519381\pi$
$192$		0			0
$193$	−2.19694	−	3.80521i	−0.158139	−	0.273905i	0.776058	−	0.630661i	$-0.217216\pi$
$193$	−2.19694	−	3.80521i	−0.158139	−	0.273905i	−0.934198	+	0.356756i	$0.883883\pi$
$194$	−4.59035			−0.329568
$195$		0			0
$196$		0			0
$197$		−	10.8865i		−	0.775632i	−0.921737	−	0.387816i	$-0.873230\pi$
$197$		−	10.8865i		−	0.775632i	0.921737	−	0.387816i	$-0.126770\pi$
$198$		0			0
$199$	−23.8733	−	13.7832i	−1.69233	−	0.977068i	−0.952629	−	0.304135i	$-0.901633\pi$
$199$	−23.8733	−	13.7832i	−1.69233	−	0.977068i	−0.739703	−	0.672933i	$-0.765034\pi$
$200$		−	0.519482i		−	0.0367329i
$201$		0			0
$202$	5.73577	+	3.31155i	0.403567	+	0.233000i
$203$		0			0
$204$		0			0
$205$	−9.39060	+	16.2650i	−0.655868	+	1.13600i
$206$	−2.92989	+	5.07471i	−0.204135	+	0.353572i
$207$		0			0
$208$	1.48943	−	0.859925i	0.103274	−	0.0596250i
$209$	−3.23377	−	5.60106i	−0.223685	−	0.387433i
$210$		0			0
$211$	5.15561	−	8.92978i	0.354927	−	0.614751i	−0.632179	−	0.774823i	$-0.717839\pi$
$211$	5.15561	−	8.92978i	0.354927	−	0.614751i	0.987105	+	0.160071i	$0.0511724\pi$
$212$		0			0
$213$		0			0
$214$	4.71563			0.322354
$215$	−4.13611	−	7.16396i	−0.282081	−	0.488578i
$216$		0			0
$217$		0			0
$218$	3.66908	−	2.11835i	0.248502	−	0.143473i
$219$		0			0
$220$	11.5498	−	6.66826i	0.778686	−	0.449574i
$221$	−2.63455	+	1.52106i	−0.177219	+	0.102318i
$222$		0			0
$223$	6.24329	−	3.60456i	0.418081	−	0.241379i	−0.276175	−	0.961107i	$-0.589067\pi$
$223$	6.24329	−	3.60456i	0.418081	−	0.241379i	0.694256	+	0.719728i	$0.255733\pi$
$224$		0			0
$225$		0			0
$226$	3.41614	+	5.91693i	0.227238	+	0.393588i
$227$	−12.7560			−0.846645			−0.423323	−	0.905979i	$-0.639136\pi$
$227$	−12.7560			−0.846645			−0.423323	+	0.905979i	$0.639136\pi$
$228$		0			0
$229$			4.49418i			0.296984i	0.988914	+	0.148492i	$0.0474419\pi$
$229$			4.49418i			0.296984i	−0.988914	+	0.148492i	$0.952558\pi$
$230$	4.31705	−	7.47736i	0.284658	−	0.493042i
$231$		0			0
$232$	2.07781	+	3.59886i	0.136415	+	0.236277i
$233$	−1.86545	+	1.07702i	−0.122210	+	0.0705577i	−0.559859	−	0.828588i	$-0.689145\pi$
$233$	−1.86545	+	1.07702i	−0.122210	+	0.0705577i	0.437649	+	0.899146i	$0.355811\pi$
$234$		0			0
$235$	−13.8728	+	24.0284i	−0.904963	+	1.56744i
$236$	−1.11483	+	1.93094i	−0.0725693	+	0.125694i
$237$		0			0
$238$		0			0
$239$	8.78317	+	5.07096i	0.568136	+	0.328013i	0.756404	−	0.654104i	$-0.226954\pi$
$239$	8.78317	+	5.07096i	0.568136	+	0.328013i	−0.188269	+	0.982118i	$0.560288\pi$
$240$		0			0
$241$		−	10.5481i		−	0.679461i	−0.940523	−	0.339731i	$-0.889664\pi$
$241$		−	10.5481i		−	0.679461i	0.940523	−	0.339731i	$-0.110336\pi$
$242$	18.3810	+	10.6123i	1.18158	+	0.682184i
$243$		0			0
$244$			8.99970i			0.576146i
$245$		0			0
$246$		0			0
$247$	1.95946			0.124677
$248$	4.18509	+	7.24879i	0.265754	+	0.460299i
$249$		0			0
$250$	−9.11608	−	5.26317i	−0.576551	−	0.332872i
$251$	−29.3005			−1.84943			−0.924714	−	0.380662i	$-0.875696\pi$
$251$	−29.3005			−1.84943			−0.924714	+	0.380662i	$0.875696\pi$
$252$		0			0
$253$	20.8623			1.31160
$254$	5.78217	+	3.33834i	0.362805	+	0.209466i
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	7.62860			0.475859			0.237930	−	0.971282i	$-0.423531\pi$
$257$	7.62860			0.475859			0.237930	+	0.971282i	$0.423531\pi$
$258$		0			0
$259$		0			0
$260$			4.04054i			0.250584i
$261$		0			0
$262$	6.47185	+	3.73653i	0.399832	+	0.230843i
$263$			12.1856i			0.751398i	0.926742	+	0.375699i	$0.122597\pi$
$263$			12.1856i			0.751398i	−0.926742	+	0.375699i	$0.877403\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$		0			0
$268$	5.43562	−	9.41477i	0.332034	−	0.575099i
$269$	−1.38717	+	2.40264i	−0.0845771	+	0.146492i	−0.905211	−	0.424963i	$-0.860287\pi$
$269$	−1.38717	+	2.40264i	−0.0845771	+	0.146492i	0.820634	+	0.571454i	$0.193621\pi$
$270$		0			0
$271$	−2.77815	+	1.60396i	−0.168760	+	0.0974338i	−0.582001	−	0.813188i	$-0.697730\pi$
$271$	−2.77815	+	1.60396i	−0.168760	+	0.0974338i	0.413241	+	0.910622i	$0.364397\pi$
$272$	0.884414	+	1.53185i	0.0536255	+	0.0928821i
$273$		0			0
$274$	−3.99395	+	6.91772i	−0.241283	+	0.417915i
$275$			2.94893i			0.177827i
$276$		0			0
$277$	10.0811			0.605714			0.302857	−	0.953036i	$-0.402060\pi$
$277$	10.0811			0.605714			0.302857	+	0.953036i	$0.402060\pi$
$278$	10.3803	+	17.9792i	0.622569	+	1.07832i
$279$		0			0
$280$		0			0
$281$	−4.21999	+	2.43641i	−0.251743	+	0.145344i	−0.620562	−	0.784157i	$-0.713096\pi$
$281$	−4.21999	+	2.43641i	−0.251743	+	0.145344i	0.368819	+	0.929501i	$0.379762\pi$
$282$		0			0
$283$	−2.44030	+	1.40891i	−0.145061	+	0.0837508i	−0.570774	−	0.821107i	$-0.693357\pi$
$283$	−2.44030	+	1.40891i	−0.145061	+	0.0837508i	0.425713	+	0.904858i	$0.360023\pi$
$284$	−3.91535	+	2.26053i	−0.232333	+	0.134138i
$285$		0			0
$286$	−8.45502	+	4.88151i	−0.499956	+	0.288650i
$287$		0			0
$288$		0			0
$289$	6.93562	+	12.0129i	0.407978	+	0.706638i
$290$	−9.76302			−0.573304
$291$		0			0
$292$		−	5.34234i		−	0.312637i
$293$	−4.05694	+	7.02683i	−0.237009	+	0.410512i	−0.959855	−	0.280498i	$-0.909500\pi$
$293$	−4.05694	+	7.02683i	−0.237009	+	0.410512i	0.722846	+	0.691010i	$0.242834\pi$
$294$		0			0
$295$	−2.61914	−	4.53648i	−0.152492	−	0.264124i
$296$	7.96547	−	4.59886i	0.462983	−	0.267304i
$297$		0			0
$298$	−0.598865	+	1.03726i	−0.0346913	+	0.0600871i
$299$	−3.16030	+	5.47381i	−0.182765	+	0.316558i
$300$		0			0
$301$		0			0
$302$	−13.1849	−	7.61229i	−0.758705	−	0.438038i
$303$		0			0
$304$		−	1.13932i		−	0.0653445i
$305$	−18.3108	−	10.5718i	−1.04847	−	0.605337i
$306$		0			0
$307$			10.8996i			0.622074i	0.950398	+	0.311037i	$0.100676\pi$
$307$			10.8996i			0.622074i	−0.950398	+	0.311037i	$0.899324\pi$
$308$		0			0
$309$		0			0
$310$	−19.6646			−1.11687
$311$	4.11819	+	7.13291i	0.233521	+	0.404470i	0.958842	−	0.283941i	$-0.0916419\pi$
$311$	4.11819	+	7.13291i	0.233521	+	0.404470i	−0.725321	+	0.688411i	$0.758309\pi$
$312$		0			0
$313$	−29.2736	−	16.9011i	−1.65464	−	0.955308i	−0.975127	−	0.221648i	$-0.928857\pi$
$313$	−29.2736	−	16.9011i	−1.65464	−	0.955308i	−0.679516	−	0.733661i	$-0.737810\pi$
$314$	−10.0269			−0.565853
$315$		0			0
$316$	13.0284			0.732907
$317$	5.82913	+	3.36545i	0.327396	+	0.189022i	0.654685	−	0.755902i	$-0.272801\pi$
$317$	5.82913	+	3.36545i	0.327396	+	0.189022i	−0.327288	+	0.944925i	$0.606135\pi$
$318$		0			0
$319$	−11.7950	−	20.4296i	−0.660394	−	1.14384i
$320$	2.34936			0.131333
$321$		0			0
$322$		0			0
$323$			2.01526i			0.112132i
$324$		0			0
$325$	−0.773734	−	0.446715i	−0.0429190	−	0.0247793i
$326$			12.0032i			0.664793i
$327$		0			0
$328$	−6.92317	−	3.99709i	−0.382268	−	0.220703i
$329$		0			0
$330$		0			0
$331$	16.0284	−	27.7621i	0.881002	−	1.52594i	0.0307744	−	0.999526i	$-0.490203\pi$
$331$	16.0284	−	27.7621i	0.881002	−	1.52594i	0.850228	−	0.526415i	$-0.176464\pi$
$332$	6.27298	−	10.8651i	0.344275	−	0.596301i
$333$		0			0
$334$	−14.8518	+	8.57472i	−0.812657	+	0.469188i
$335$	12.7702	+	22.1187i	0.697712	+	1.20847i
$336$		0			0
$337$	−12.1123	+	20.9791i	−0.659799	+	1.14280i	0.320869	+	0.947124i	$0.396025\pi$
$337$	−12.1123	+	20.9791i	−0.659799	+	1.14280i	−0.980668	+	0.195681i	$0.937308\pi$
$338$			10.0421i			0.546219i
$339$		0			0
$340$	−4.15561			−0.225370
$341$	−23.7574	−	41.1490i	−1.28654	−	2.22834i
$342$		0			0
$343$		0			0
$344$	3.04933	−	1.76053i	0.164409	−	0.0949214i
$345$		0			0
$346$	−1.72121	+	0.993738i	−0.0925326	+	0.0534237i
$347$	19.7453	−	11.3999i	1.05998	−	0.611981i	0.134554	−	0.990906i	$-0.457040\pi$
$347$	19.7453	−	11.3999i	1.05998	−	0.611981i	0.925427	+	0.378926i	$0.123706\pi$
$348$		0			0
$349$	2.46389	−	1.42253i	0.131889	−	0.0761461i	−0.432604	−	0.901584i	$-0.642405\pi$
$349$	2.46389	−	1.42253i	0.131889	−	0.0761461i	0.564493	+	0.825438i	$0.309072\pi$
$350$		0			0
$351$		0			0
$352$	2.83834	+	4.91614i	0.151284	+	0.262031i
$353$	7.14424			0.380249			0.190125	−	0.981760i	$-0.439111\pi$
$353$	7.14424			0.380249			0.190125	+	0.981760i	$0.439111\pi$
$354$		0			0
$355$		−	10.6216i		−	0.563735i
$356$	−0.580529	+	1.00551i	−0.0307680	+	0.0532917i
$357$		0			0
$358$	−4.15561	−	7.19773i	−0.219631	−	0.380412i
$359$	−10.0491	+	5.80186i	−0.530372	+	0.306210i	−0.741168	−	0.671320i	$-0.765728\pi$
$359$	−10.0491	+	5.80186i	−0.530372	+	0.306210i	0.210796	+	0.977530i	$0.432394\pi$
$360$		0			0
$361$	−8.85097	+	15.3303i	−0.465841	+	0.806860i
$362$	−7.72706	+	13.3837i	−0.406125	+	0.703429i
$363$		0			0
$364$		0			0
$365$	10.8695	+	6.27554i	0.568938	+	0.328477i
$366$		0			0
$367$		−	7.83493i		−	0.408980i	−0.978869	−	0.204490i	$-0.934446\pi$
$367$		−	7.83493i		−	0.408980i	0.978869	−	0.204490i	$-0.0655536\pi$
$368$	3.18272	+	1.83755i	0.165911	+	0.0957887i
$369$		0			0
$370$			21.6088i			1.12339i
$371$		0			0
$372$		0			0
$373$	25.6677			1.32902			0.664512	−	0.747278i	$-0.268639\pi$
$373$	25.6677			1.32902			0.664512	+	0.747278i	$0.268639\pi$
$374$	−5.02053	−	8.69581i	−0.259605	−	0.449650i
$375$		0			0
$376$	−10.2277	−	5.90494i	−0.527451	−	0.304524i
$377$	7.14702			0.368091
$378$		0			0
$379$	−15.1045			−0.775868			−0.387934	−	0.921687i	$-0.626811\pi$
$379$	−15.1045			−0.775868			−0.387934	+	0.921687i	$0.626811\pi$
$380$	2.31806	+	1.33834i	0.118914	+	0.0686551i
$381$		0			0
$382$	−6.16904	−	10.6851i	−0.315636	−	0.546697i
$383$	−1.52664			−0.0780079			−0.0390040	−	0.999239i	$-0.512418\pi$
$383$	−1.52664			−0.0780079			−0.0390040	+	0.999239i	$0.512418\pi$
$384$		0			0
$385$		0			0
$386$			4.39388i			0.223643i
$387$		0			0
$388$	3.97536	+	2.29517i	0.201818	+	0.116520i
$389$		−	14.8897i		−	0.754936i	−0.926023	−	0.377468i	$-0.876795\pi$
$389$		−	14.8897i		−	0.754936i	0.926023	−	0.377468i	$-0.123205\pi$
$390$		0			0
$391$	−5.62969	−	3.25030i	−0.284706	−	0.164375i
$392$		0			0
$393$		0			0
$394$	−5.44325	+	9.42799i	−0.274227	+	0.474975i
$395$	−15.3042	+	26.5077i	−0.770039	+	1.33375i
$396$		0			0
$397$	24.9302	−	14.3935i	1.25121	−	0.722388i	0.279862	−	0.960040i	$-0.409711\pi$
$397$	24.9302	−	14.3935i	1.25121	−	0.722388i	0.971350	+	0.237653i	$0.0763780\pi$
$398$	13.7832	+	23.8733i	0.690892	+	1.19666i
$399$		0			0
$400$	−0.259741	+	0.449885i	−0.0129871	+	0.0224942i
$401$		−	38.1735i		−	1.90629i	−0.302507	−	0.953147i	$-0.597824\pi$
$401$		−	38.1735i		−	1.90629i	0.302507	−	0.953147i	$-0.402176\pi$
$402$		0			0
$403$	14.3955			0.717089
$404$	−3.31155	−	5.73577i	−0.164756	−	0.285365i
$405$		0			0
$406$		0			0
$407$	−45.2173	+	26.1062i	−2.24134	+	1.29404i
$408$		0			0
$409$	6.03355	−	3.48347i	0.298340	−	0.172247i	−0.343357	−	0.939205i	$-0.611564\pi$
$409$	6.03355	−	3.48347i	0.298340	−	0.172247i	0.641697	+	0.766958i	$0.278231\pi$
$410$	16.2650	−	9.39060i	0.803271	−	0.463769i
$411$		0			0
$412$	5.07471	−	2.92989i	0.250013	−	0.144345i
$413$		0			0
$414$		0			0
$415$	14.7375	+	25.5261i	0.723435	+	1.25303i
$416$	−1.71985			−0.0843225
$417$		0			0
$418$			6.46754i			0.316338i
$419$	−17.4232	+	30.1778i	−0.851177	+	1.47428i	0.0289690	+	0.999580i	$0.490778\pi$
$419$	−17.4232	+	30.1778i	−0.851177	+	1.47428i	−0.880146	+	0.474702i	$0.842556\pi$
$420$		0			0
$421$	2.84597	+	4.92936i	0.138704	+	0.240242i	0.927006	−	0.375046i	$-0.122373\pi$
$421$	2.84597	+	4.92936i	0.138704	+	0.240242i	−0.788302	+	0.615288i	$0.789040\pi$
$422$	−8.92978	+	5.15561i	−0.434695	+	0.250971i
$423$		0			0
$424$		0			0
$425$	0.459437	−	0.795769i	0.0222860	−	0.0386005i
$426$		0			0
$427$		0			0
$428$	−4.08386	−	2.35782i	−0.197401	−	0.113969i
$429$		0			0
$430$			8.27223i			0.398922i
$431$	−26.2350	−	15.1468i	−1.26370	−	0.729595i	−0.289908	−	0.957055i	$-0.593625\pi$
$431$	−26.2350	−	15.1468i	−1.26370	−	0.729595i	−0.973787	+	0.227460i	$0.926958\pi$
$432$		0			0
$433$			23.6094i			1.13459i	0.823513	+	0.567297i	$0.192011\pi$
$433$			23.6094i			1.13459i	−0.823513	+	0.567297i	$0.807989\pi$
$434$		0			0
$435$		0			0
$436$	−4.23669			−0.202901
$437$	2.09355	+	3.62614i	0.100148	+	0.173462i
$438$		0			0
$439$	21.6681	+	12.5101i	1.03416	+	0.597075i	0.918175	−	0.396175i	$-0.129663\pi$
$439$	21.6681	+	12.5101i	1.03416	+	0.597075i	0.115989	+	0.993250i	$0.462996\pi$
$440$	−13.3365			−0.635794
$441$		0			0
$442$	3.04212			0.144699
$443$	−19.9446	−	11.5150i	−0.947595	−	0.547094i	−0.0552622	−	0.998472i	$-0.517599\pi$
$443$	−19.9446	−	11.5150i	−0.947595	−	0.547094i	−0.892333	+	0.451377i	$0.850933\pi$
$444$		0			0
$445$	−1.36387	−	2.36229i	−0.0646537	−	0.111983i
$446$	−7.20913			−0.341362
$447$		0			0
$448$		0			0
$449$		−	15.9028i		−	0.750501i	−0.926923	−	0.375251i	$-0.877557\pi$
$449$		−	15.9028i		−	0.750501i	0.926923	−	0.375251i	$-0.122443\pi$
$450$		0			0
$451$	39.3006	+	22.6902i	1.85059	+	1.06844i
$452$		−	6.83228i		−	0.321363i
$453$		0			0
$454$	11.0470	+	6.37800i	0.518462	+	0.299334i
$455$		0			0
$456$		0			0
$457$	2.83307	−	4.90702i	0.132525	−	0.229541i	−0.792124	−	0.610360i	$-0.791025\pi$
$457$	2.83307	−	4.90702i	0.132525	−	0.229541i	0.924649	+	0.380819i	$0.124358\pi$
$458$	2.24709	−	3.89208i	0.105000	−	0.181865i
$459$		0			0
$460$	−7.47736	+	4.31705i	−0.348634	+	0.201284i
$461$	−15.7292	−	27.2438i	−0.732582	−	1.26887i	−0.955776	−	0.294095i	$-0.904982\pi$
$461$	−15.7292	−	27.2438i	−0.732582	−	1.26887i	0.223194	−	0.974774i	$-0.428352\pi$
$462$		0			0
$463$	4.55148	−	7.88340i	0.211525	−	0.366373i	−0.740667	−	0.671873i	$-0.765490\pi$
$463$	4.55148	−	7.88340i	0.211525	−	0.366373i	0.952192	+	0.305500i	$0.0988236\pi$
$464$		−	4.15561i		−	0.192919i
$465$		0			0
$466$	2.15403			0.0997837
$467$	15.1516	+	26.2433i	0.701132	+	1.21440i	0.968069	+	0.250682i	$0.0806549\pi$
$467$	15.1516	+	26.2433i	0.701132	+	1.21440i	−0.266938	+	0.963714i	$0.586012\pi$
$468$		0			0
$469$		0			0
$470$	24.0284	−	13.8728i	1.10835	−	0.639906i
$471$		0			0
$472$	1.93094	−	1.11483i	0.0888788	−	0.0513142i
$473$	−17.3100	+	9.99395i	−0.795916	+	0.459522i
$474$		0			0
$475$	−0.512563	+	0.295928i	−0.0235180	+	0.0135781i
$476$		0			0
$477$		0			0
$478$	−5.07096	−	8.78317i	−0.231940	−	0.401733i
$479$	4.66286			0.213052			0.106526	−	0.994310i	$-0.466027\pi$
$479$	4.66286			0.213052			0.106526	+	0.994310i	$0.466027\pi$
$480$		0			0
$481$		−	15.8187i		−	0.721271i
$482$	−5.27404	+	9.13490i	−0.240226	+	0.416083i
$483$		0			0
$484$	−10.6123	−	18.3810i	−0.482377	−	0.835501i
$485$	−9.33953	+	5.39218i	−0.424086	+	0.244846i
$486$		0			0
$487$	9.74105	−	16.8720i	0.441409	−	0.764543i	−0.556385	−	0.830924i	$-0.687812\pi$
$487$	9.74105	−	16.8720i	0.441409	−	0.764543i	0.997794	+	0.0663816i	$0.0211455\pi$
$488$	4.49985	−	7.79396i	0.203699	−	0.352816i
$489$		0			0
$490$		0			0
$491$	17.7437	+	10.2443i	0.800762	+	0.462320i	0.843737	−	0.536756i	$-0.180351\pi$
$491$	17.7437	+	10.2443i	0.800762	+	0.462320i	−0.0429758	+	0.999076i	$0.513684\pi$
$492$		0			0
$493$			7.35056i			0.331053i
$494$	−1.69694	−	0.979729i	−0.0763490	−	0.0440801i
$495$		0			0
$496$		−	8.37019i		−	0.375832i
$497$		0			0
$498$		0			0
$499$	−10.2520			−0.458941			−0.229470	−	0.973316i	$-0.573699\pi$
$499$	−10.2520			−0.458941			−0.229470	+	0.973316i	$0.573699\pi$
$500$	5.26317	+	9.11608i	0.235376	+	0.407683i
$501$		0			0
$502$	25.3749	+	14.6502i	1.13254	+	0.653872i
$503$	−14.5521			−0.648845			−0.324422	−	0.945912i	$-0.605170\pi$
$503$	−14.5521			−0.648845			−0.324422	+	0.945912i	$0.605170\pi$
$504$		0			0
$505$	15.5600			0.692412
$506$	−18.0673	−	10.4311i	−0.803188	−	0.463721i
$507$		0			0
$508$	−3.33834	−	5.78217i	−0.148115	−	0.256542i
$509$	33.3234			1.47703			0.738517	−	0.674235i	$-0.235527\pi$
$509$	33.3234			1.47703			0.738517	+	0.674235i	$0.235527\pi$
$510$		0			0
$511$		0			0
$512$			1.00000i			0.0441942i
$513$		0			0
$514$	−6.60656	−	3.81430i	−0.291403	−	0.168242i
$515$			13.7667i			0.606634i
$516$		0			0
$517$	58.0591	+	33.5204i	2.55343	+	1.47423i
$518$		0			0
$519$		0			0
$520$	2.02027	−	3.49921i	0.0885947	−	0.153451i
$521$	3.26963	−	5.66316i	0.143245	−	0.248108i	−0.785472	−	0.618897i	$-0.787580\pi$
$521$	3.26963	−	5.66316i	0.143245	−	0.248108i	0.928717	+	0.370790i	$0.120913\pi$
$522$		0			0
$523$	−0.681439	+	0.393429i	−0.0297972	+	0.0172034i	−0.514825	−	0.857296i	$-0.672143\pi$
$523$	−0.681439	+	0.393429i	−0.0297972	+	0.0172034i	0.485027	+	0.874499i	$0.338810\pi$
$524$	−3.73653	−	6.47185i	−0.163231	−	0.282724i
$525$		0			0
$526$	6.09281	−	10.5531i	0.265659	−	0.460135i
$527$			14.8054i			0.644934i
$528$		0			0
$529$	9.49369			0.412769
$530$		0			0
$531$		0			0
$532$		0			0
$533$	−11.9068	+	6.87440i	−0.515741	+	0.297763i
$534$		0			0
$535$	9.59445	−	5.53936i	0.414804	−	0.239487i
$536$	−9.41477	+	5.43562i	−0.406656	+	0.234783i
$537$		0			0
$538$	2.40264	−	1.38717i	0.103585	−	0.0598050i
$539$		0			0
$540$		0			0
$541$	−2.80227	−	4.85367i	−0.120479	−	0.208676i	0.799478	−	0.600696i	$-0.205110\pi$
$541$	−2.80227	−	4.85367i	−0.120479	−	0.208676i	−0.919957	+	0.392020i	$0.871776\pi$
$542$	3.20793			0.137792
$543$		0			0
$544$		−	1.76883i		−	0.0758379i
$545$	4.97675	−	8.61999i	0.213181	−	0.369240i
$546$		0			0
$547$	−6.91456	−	11.9764i	−0.295645	−	0.512073i	0.679489	−	0.733685i	$-0.262201\pi$
$547$	−6.91456	−	11.9764i	−0.295645	−	0.512073i	−0.975135	+	0.221612i	$0.928868\pi$
$548$	6.91772	−	3.99395i	0.295510	−	0.170613i
$549$		0			0
$550$	1.47446	−	2.55385i	0.0628714	−	0.108896i
$551$	2.36729	−	4.10026i	0.100850	−	0.174677i
$552$		0			0
$553$		0			0
$554$	−8.73047	−	5.04054i	−0.370922	−	0.214152i
$555$		0			0
$556$		−	20.7606i		−	0.880446i
$557$	24.0957	+	13.9117i	1.02097	+	0.589456i	0.914384	−	0.404848i	$-0.132675\pi$
$557$	24.0957	+	13.9117i	1.02097	+	0.589456i	0.106584	+	0.994304i	$0.466009\pi$
$558$		0			0
$559$		−	6.05569i		−	0.256128i
$560$		0			0
$561$		0			0
$562$	4.87282			0.205548
$563$	12.2650	+	21.2436i	0.516909	+	0.895312i	0.999807	+	0.0196359i	$0.00625069\pi$
$563$	12.2650	+	21.2436i	0.516909	+	0.895312i	−0.482898	+	0.875676i	$0.660416\pi$
$564$		0			0
$565$	13.9010	+	8.02574i	0.584819	+	0.337645i
$566$	2.81781			0.118441
$567$		0			0
$568$	4.52106			0.189699
$569$	−23.4762	−	13.5540i	−0.984172	−	0.568212i	−0.0806449	−	0.996743i	$-0.525698\pi$
$569$	−23.4762	−	13.5540i	−0.984172	−	0.568212i	−0.903527	+	0.428531i	$0.859031\pi$
$570$		0			0
$571$	14.9177	+	25.8382i	0.624287	+	1.08130i	0.988678	+	0.150051i	$0.0479438\pi$
$571$	14.9177	+	25.8382i	0.624287	+	1.08130i	−0.364391	+	0.931246i	$0.618723\pi$
$572$	9.76302			0.408212
$573$		0			0
$574$		0			0
$575$		−	1.90915i		−	0.0796169i
$576$		0			0
$577$	24.3930	+	14.0833i	1.01549	+	0.586296i	0.912796	−	0.408416i	$-0.133919\pi$
$577$	24.3930	+	14.0833i	1.01549	+	0.586296i	0.102699	+	0.994712i	$0.467252\pi$
$578$		−	13.8712i		−	0.576968i
$579$		0			0
$580$	8.45502	+	4.88151i	0.351076	+	0.202694i
$581$		0			0
$582$		0			0
$583$		0			0
$584$	−2.67117	+	4.62660i	−0.110534	+	0.191450i
$585$		0			0
$586$	7.02683	−	4.05694i	0.290276	−	0.167591i
$587$	4.95928	+	8.58973i	0.204692	+	0.354536i	0.950034	−	0.312145i	$-0.101048\pi$
$587$	4.95928	+	8.58973i	0.204692	+	0.354536i	−0.745343	+	0.666681i	$0.767714\pi$
$588$		0			0
$589$	4.76816	−	8.25870i	0.196469	−	0.340294i
$590$			5.23827i			0.215656i
$591$		0			0
$592$	−9.19773			−0.378024
$593$	2.34936	+	4.06921i	0.0964766	+	0.167102i	0.910224	−	0.414116i	$-0.135909\pi$
$593$	2.34936	+	4.06921i	0.0964766	+	0.167102i	−0.813747	+	0.581219i	$0.802576\pi$
$594$		0			0
$595$		0			0
$596$	1.03726	−	0.598865i	0.0424880	−	0.0245305i
$597$		0			0
$598$	5.47381	−	3.16030i	0.223841	−	0.129234i
$599$	12.7309	−	7.35019i	0.520170	−	0.300320i	−0.216834	−	0.976208i	$-0.569573\pi$
$599$	12.7309	−	7.35019i	0.520170	−	0.300320i	0.737004	+	0.675888i	$0.236240\pi$
$600$		0			0
$601$	−16.2923	+	9.40634i	−0.664575	+	0.383693i	−0.794018	−	0.607894i	$-0.792014\pi$
$601$	−16.2923	+	9.40634i	−0.664575	+	0.383693i	0.129443	+	0.991587i	$0.458681\pi$
$602$		0			0
$603$		0			0
$604$	7.61229	+	13.1849i	0.309740	+	0.536485i
$605$	49.8641			2.02727
$606$		0			0
$607$			12.5922i			0.511100i	0.966796	+	0.255550i	$0.0822565\pi$
$607$			12.5922i			0.511100i	−0.966796	+	0.255550i	$0.917743\pi$
$608$	−0.569660	+	0.986680i	−0.0231028	+	0.0400152i
$609$		0			0
$610$	10.5718	+	18.3108i	0.428038	+	0.741383i
$611$	−17.5900	+	10.1556i	−0.711617	+	0.410852i
$612$		0			0
$613$	4.91009	−	8.50452i	0.198317	−	0.343494i	−0.749666	−	0.661816i	$-0.769786\pi$
$613$	4.91009	−	8.50452i	0.198317	−	0.343494i	0.947983	+	0.318322i	$0.103119\pi$
$614$	5.44981	−	9.43935i	0.219937	−	0.380941i
$615$		0			0
$616$		0			0
$617$	3.25158	+	1.87730i	0.130904	+	0.0755772i	0.564022	−	0.825760i	$-0.309253\pi$
$617$	3.25158	+	1.87730i	0.130904	+	0.0755772i	−0.433118	+	0.901337i	$0.642587\pi$
$618$		0			0
$619$		−	11.0494i		−	0.444111i	−0.975034	−	0.222055i	$-0.928723\pi$
$619$		−	11.0494i		−	0.444111i	0.975034	−	0.222055i	$-0.0712766\pi$
$620$	17.0300	+	9.83228i	0.683942	+	0.394874i
$621$		0			0
$622$		−	8.23637i		−	0.330248i
$623$		0			0
$624$		0			0
$625$	−27.3275			−1.09310
$626$	16.9011	+	29.2736i	0.675505	+	1.17001i
$627$		0			0
$628$	8.68358	+	5.01347i	0.346513	+	0.200059i
$629$	16.2692			0.648696
$630$		0			0
$631$	19.4921			0.775969			0.387984	−	0.921666i	$-0.373171\pi$
$631$	19.4921			0.775969			0.387984	+	0.921666i	$0.373171\pi$
$632$	−11.2830	−	6.51422i	−0.448812	−	0.259122i
$633$		0			0
$634$	−3.36545	−	5.82913i	−0.133659	−	0.231504i
$635$	15.6859			0.622475
$636$		0			0
$637$		0			0
$638$			23.5900i			0.933938i
$639$		0			0
$640$	−2.03460	−	1.17468i	−0.0804248	−	0.0464333i
$641$			26.1735i			1.03379i	0.856048	+	0.516896i	$0.172913\pi$
$641$			26.1735i			1.03379i	−0.856048	+	0.516896i	$0.827087\pi$
$642$		0			0
$643$	−9.50955	−	5.49034i	−0.375020	−	0.216518i	0.300629	−	0.953741i	$-0.402803\pi$
$643$	−9.50955	−	5.49034i	−0.375020	−	0.216518i	−0.675649	+	0.737223i	$0.736137\pi$
$644$		0			0
$645$		0			0
$646$	1.00763	−	1.74527i	0.0396447	−	0.0686666i
$647$	−16.0063	+	27.7237i	−0.629273	+	1.08993i	0.358425	+	0.933558i	$0.383314\pi$
$647$	−16.0063	+	27.7237i	−0.629273	+	1.08993i	−0.987698	+	0.156374i	$0.950019\pi$
$648$		0			0
$649$	−10.9613	+	6.32852i	−0.430270	+	0.248416i
$650$	0.446715	+	0.773734i	0.0175216	+	0.0303483i
$651$		0			0
$652$	6.00158	−	10.3950i	0.235040	−	0.407101i
$653$			22.3649i			0.875208i	0.899168	+	0.437604i	$0.144173\pi$
$653$			22.3649i			0.875208i	−0.899168	+	0.437604i	$0.855827\pi$
$654$		0			0
$655$	17.5569			0.686004
$656$	3.99709	+	6.92317i	0.156060	+	0.270304i
$657$		0			0
$658$		0			0
$659$	19.2546	−	11.1166i	0.750053	−	0.433043i	−0.0756603	−	0.997134i	$-0.524106\pi$
$659$	19.2546	−	11.1166i	0.750053	−	0.433043i	0.825713	+	0.564091i	$0.190773\pi$
$660$		0			0
$661$	−9.13646	+	5.27494i	−0.355367	+	0.205171i	−0.667047	−	0.745016i	$-0.732442\pi$
$661$	−9.13646	+	5.27494i	−0.355367	+	0.205171i	0.311679	+	0.950187i	$0.399108\pi$
$662$	−27.7621	+	16.0284i	−1.07900	+	0.622963i
$663$		0			0
$664$	−10.8651	+	6.27298i	−0.421649	+	0.243439i
$665$		0			0
$666$		0			0
$667$	7.63613	+	13.2262i	0.295672	+	0.512119i
$668$	17.1494			0.663532
$669$		0			0
$670$		−	25.5404i		−	0.986713i
$671$	−25.5442	+	44.2438i	−0.986121	+	1.70801i
$672$		0			0
$673$	9.93562	+	17.2090i	0.382990	+	0.663358i	0.991488	−	0.130197i	$-0.0415610\pi$
$673$	9.93562	+	17.2090i	0.382990	+	0.663358i	−0.608498	+	0.793555i	$0.708228\pi$
$674$	20.9791	−	12.1123i	0.808085	−	0.466548i
$675$		0			0
$676$	5.02106	−	8.69673i	0.193118	−	0.334490i
$677$	−7.96449	+	13.7949i	−0.306100	+	0.530181i	−0.977506	−	0.210909i	$-0.932358\pi$
$677$	−7.96449	+	13.7949i	−0.306100	+	0.530181i	0.671405	+	0.741090i	$0.265691\pi$
$678$		0			0
$679$		0			0
$680$	3.59886	+	2.07781i	0.138010	+	0.0796802i
$681$		0			0
$682$			47.5148i			1.81944i
$683$	−16.4777	−	9.51343i	−0.630503	−	0.364021i	0.150444	−	0.988619i	$-0.451930\pi$
$683$	−16.4777	−	9.51343i	−0.630503	−	0.364021i	−0.780947	+	0.624597i	$0.785263\pi$
$684$		0			0
$685$			18.7664i			0.717028i
$686$		0			0
$687$		0			0
$688$	−3.52106			−0.134239
$689$		0			0
$690$		0			0
$691$	0.139477	+	0.0805273i	0.00530597	+	0.00306340i	0.502651	−	0.864490i	$-0.332358\pi$
$691$	0.139477	+	0.0805273i	0.00530597	+	0.00306340i	−0.497345	+	0.867553i	$0.665692\pi$
$692$	1.98748			0.0755525
$693$		0			0
$694$	−22.7999			−0.865471
$695$	42.2396	+	24.3870i	1.60224	+	0.925053i
$696$		0			0
$697$	−7.07017	−	12.2459i	−0.267802	−	0.463847i
$698$	−2.84505			−0.107687
$699$		0			0
$700$		0			0
$701$		−	9.98234i		−	0.377028i	−0.982071	−	0.188514i	$-0.939633\pi$
$701$		−	9.98234i		−	0.377028i	0.982071	−	0.188514i	$-0.0603670\pi$
$702$		0			0
$703$	−9.07522	−	5.23958i	−0.342278	−	0.197614i
$704$		−	5.67667i		−	0.213948i
$705$		0			0
$706$	−6.18709	−	3.57212i	−0.232854	−	0.134438i
$707$		0			0
$708$		0			0
$709$	12.1962	−	21.1244i	0.458036	−	0.793342i	−0.540821	−	0.841138i	$-0.681886\pi$
$709$	12.1962	−	21.1244i	0.458036	−	0.793342i	0.998857	+	0.0477959i	$0.0152197\pi$
$710$	−5.31079	+	9.19856i	−0.199311	+	0.345216i
$711$		0			0
$712$	1.00551	−	0.580529i	0.0376829	−	0.0217563i
$713$	15.3806	+	26.6400i	0.576008	+	0.997676i
$714$		0			0
$715$	−11.4684	+	19.8639i	−0.428894	+	0.742867i
$716$			8.31122i			0.310605i
$717$		0			0
$718$	11.6037			0.433047
$719$	8.13460	+	14.0895i	0.303370	+	0.525451i	0.976897	−	0.213711i	$-0.0685550\pi$
$719$	8.13460	+	14.0895i	0.303370	+	0.525451i	−0.673527	+	0.739162i	$0.735222\pi$
$720$		0			0
$721$		0			0
$722$	15.3303	−	8.85097i	0.570536	−	0.329399i
$723$		0			0
$724$	13.3837	−	7.72706i	0.497400	−	0.287174i
$725$	−1.86955	+	1.07938i	−0.0694332	+	0.0400873i
$726$		0			0
$727$	−20.6626	+	11.9296i	−0.766335	+	0.442444i	−0.831566	−	0.555427i	$-0.812555\pi$
$727$	−20.6626	+	11.9296i	−0.766335	+	0.442444i	0.0652306	+	0.997870i	$0.479222\pi$
$728$		0			0
$729$		0			0
$730$	−6.27554	−	10.8695i	−0.232268	−	0.402300i
$731$	6.22815			0.230356
$732$		0			0
$733$			12.2697i			0.453193i	0.973989	+	0.226596i	$0.0727598\pi$
$733$			12.2697i			0.453193i	−0.973989	+	0.226596i	$0.927240\pi$
$734$	−3.91747	+	6.78525i	−0.144596	+	0.250448i
$735$		0			0
$736$	−1.83755	−	3.18272i	−0.0677329	−	0.117317i
$737$	53.4446	−	30.8562i	1.96866	−	1.13660i
$738$		0			0
$739$	−20.9446	+	36.2771i	−0.770459	+	1.33447i	0.166853	+	0.985982i	$0.446639\pi$
$739$	−20.9446	+	36.2771i	−0.770459	+	1.33447i	−0.937312	+	0.348492i	$0.886694\pi$
$740$	10.8044	−	18.7137i	0.397177	−	0.687931i
$741$		0			0
$742$		0			0
$743$	−43.9160	−	25.3549i	−1.61112	−	0.930182i	−0.989111	−	0.147173i	$-0.952982\pi$
$743$	−43.9160	−	25.3549i	−1.61112	−	0.930182i	−0.622011	−	0.783008i	$-0.713684\pi$
$744$		0			0
$745$			2.81390i			0.103093i
$746$	−22.2289	−	12.8339i	−0.813858	−	0.469881i
$747$		0			0
$748$			10.0411i			0.367137i
$749$		0			0
$750$		0			0
$751$	−32.7367			−1.19458			−0.597289	−	0.802026i	$-0.703756\pi$
$751$	−32.7367			−1.19458			−0.597289	+	0.802026i	$0.703756\pi$
$752$	5.90494	+	10.2277i	0.215331	+	0.372964i
$753$		0			0
$754$	−6.18951	−	3.57351i	−0.225408	−	0.130140i
$755$	−35.7680			−1.30173
$756$		0			0
$757$	−17.9255			−0.651512			−0.325756	−	0.945454i	$-0.605619\pi$
$757$	−17.9255			−0.651512			−0.325756	+	0.945454i	$0.605619\pi$
$758$	13.0809	+	7.55227i	0.475120	+	0.274311i
$759$		0			0
$760$	−1.33834	−	2.31806i	−0.0485465	−	0.0840850i
$761$	−43.7019			−1.58419			−0.792096	−	0.610397i	$-0.791010\pi$
$761$	−43.7019			−1.58419			−0.792096	+	0.610397i	$0.791010\pi$
$762$		0			0
$763$		0			0
$764$			12.3381i			0.446376i
$765$		0			0
$766$	1.32211	+	0.763322i	0.0477699	+	0.0275800i
$767$		−	3.83468i		−	0.138462i
$768$		0			0
$769$	37.0864	+	21.4118i	1.33737	+	0.772131i	0.986417	−	0.164262i	$-0.0525242\pi$
$769$	37.0864	+	21.4118i	1.33737	+	0.772131i	0.350953	+	0.936393i	$0.385858\pi$
$770$		0			0
$771$		0			0
$772$	2.19694	−	3.80521i	0.0790696	−	0.136953i
$773$	10.8025	−	18.7105i	0.388540	−	0.672971i	−0.603714	−	0.797201i	$-0.706313\pi$
$773$	10.8025	−	18.7105i	0.388540	−	0.672971i	0.992253	+	0.124231i	$0.0396462\pi$
$774$		0			0
$775$	−3.76562	+	2.17408i	−0.135265	+	0.0780953i
$776$	−2.29517	−	3.97536i	−0.0823919	−	0.142707i
$777$		0			0
$778$	−7.44483	+	12.8948i	−0.266910	+	0.462302i
$779$			9.10794i			0.326326i
$780$		0			0
$781$	−25.6646			−0.918350
$782$	3.25030	+	5.62969i	0.116231	+	0.201317i
$783$		0			0
$784$		0			0
$785$	−20.4008	+	11.7784i	−0.728137	+	0.420390i
$786$		0			0
$787$	−44.4307	+	25.6521i	−1.58378	+	0.914398i	−0.589484	+	0.807780i	$0.700669\pi$
$787$	−44.4307	+	25.6521i	−1.58378	+	0.914398i	−0.994300	+	0.106618i	$0.965998\pi$
$788$	9.42799	−	5.44325i	0.335858	−	0.193908i
$789$		0			0
$790$	26.5077	−	15.3042i	0.943102	−	0.544500i
$791$		0			0
$792$		0			0
$793$	−7.73906	−	13.4044i	−0.274822	−	0.476006i
$794$	−28.7869			−1.02161
$795$		0			0
$796$		−	27.5665i		−	0.977068i
$797$	−0.899094	+	1.55728i	−0.0318476	+	0.0551616i	−0.881510	−	0.472166i	$-0.843472\pi$
$797$	−0.899094	+	1.55728i	−0.0318476	+	0.0551616i	0.849662	+	0.527327i	$0.176806\pi$
$798$		0			0
$799$	−10.4448	−	18.0910i	−0.369512	−	0.640013i
$800$	0.449885	−	0.259741i	0.0159058	−	0.00918323i
$801$		0			0
$802$	−19.0868	+	33.0592i	−0.673977	+	1.16736i
$803$	15.1634	−	26.2637i	0.535103	−	0.926826i
$804$		0			0
$805$		0			0
$806$	−12.4668	−	7.19773i	−0.439125	−	0.253529i
$807$		0			0
$808$			6.62310i			0.233000i
$809$	35.2371	+	20.3441i	1.23887	+	0.715262i	0.968863	−	0.247597i	$-0.0796409\pi$
$809$	35.2371	+	20.3441i	1.23887	+	0.715262i	0.270006	+	0.962859i	$0.412974\pi$
$810$		0			0
$811$		−	0.378710i		−	0.0132983i	−0.999978	−	0.00664916i	$-0.997883\pi$
$811$		−	0.378710i		−	0.0132983i	0.999978	−	0.00664916i	$-0.00211651\pi$
$812$		0			0
$813$		0			0
$814$	52.2125			1.83005
$815$	14.0999	+	24.4217i	0.493896	+	0.855453i
$816$		0			0
$817$	−3.47416	−	2.00581i	−0.121545	−	0.0701743i
$818$	−6.96694			−0.243593
$819$		0			0
$820$	−18.7812			−0.655868
$821$	11.4968	+	6.63771i	0.401243	+	0.231658i	0.687020	−	0.726638i	$-0.258918\pi$
$821$	11.4968	+	6.63771i	0.401243	+	0.231658i	−0.285777	+	0.958296i	$0.592252\pi$
$822$		0			0
$823$	−13.8711	−	24.0255i	−0.483517	−	0.837476i	0.516304	−	0.856405i	$-0.327308\pi$
$823$	−13.8711	−	24.0255i	−0.483517	−	0.837476i	−0.999821	+	0.0189295i	$0.993974\pi$
$824$	−5.85977			−0.204135
$825$		0			0
$826$		0			0
$827$		−	27.7183i		−	0.963859i	−0.876210	−	0.481929i	$-0.839936\pi$
$827$		−	27.7183i		−	0.963859i	0.876210	−	0.481929i	$-0.160064\pi$
$828$		0			0
$829$	37.0105	+	21.3680i	1.28543	+	0.742143i	0.977835	−	0.209375i	$-0.0671431\pi$
$829$	37.0105	+	21.3680i	1.28543	+	0.742143i	0.307593	+	0.951518i	$0.400476\pi$
$830$		−	29.4750i		−	1.02309i
$831$		0			0
$832$	1.48943	+	0.859925i	0.0516368	+	0.0298125i
$833$		0			0
$834$		0			0
$835$	−20.1451	+	34.8923i	−0.697149	+	1.20750i
$836$	3.23377	−	5.60106i	0.111842	−	0.193717i
$837$		0			0
$838$	30.1778	−	17.4232i	1.04248	−	0.601873i
$839$	−1.92438	−	3.33313i	−0.0664370	−	0.115072i	0.830894	−	0.556431i	$-0.187830\pi$
$839$	−1.92438	−	3.33313i	−0.0664370	−	0.115072i	−0.897331	+	0.441359i	$0.854496\pi$
$840$		0			0
$841$	−5.86545	+	10.1593i	−0.202257	+	0.350319i
$842$		−	5.69193i		−	0.196157i
$843$		0			0
$844$	10.3112			0.354927
$845$	11.7963	+	20.4317i	0.405804	+	0.702873i
$846$		0			0
$847$		0			0
$848$		0			0
$849$		0			0
$850$	−0.795769	+	0.459437i	−0.0272946	+	0.0157586i
$851$	29.2738	−	16.9013i	1.00349	−	0.579368i
$852$		0			0
$853$	26.3470	−	15.2114i	0.902103	−	0.520830i	0.0242213	−	0.999707i	$-0.492289\pi$
$853$	26.3470	−	15.2114i	0.902103	−	0.520830i	0.877882	+	0.478877i	$0.158956\pi$
$854$		0			0
$855$		0			0
$856$	2.35782	+	4.08386i	0.0805885	+	0.139583i
$857$	−38.9315			−1.32987			−0.664937	−	0.746900i	$-0.731541\pi$
$857$	−38.9315			−1.32987			−0.664937	+	0.746900i	$0.731541\pi$
$858$		0			0
$859$			13.3855i			0.456708i	0.973578	+	0.228354i	$0.0733343\pi$
$859$			13.3855i			0.456708i	−0.973578	+	0.228354i	$0.926666\pi$
$860$	4.13611	−	7.16396i	0.141040	−	0.244289i
$861$		0			0
$862$	15.1468	+	26.2350i	0.515901	+	0.893567i
$863$	18.8118	−	10.8610i	0.640360	−	0.369712i	−0.144393	−	0.989520i	$-0.546123\pi$
$863$	18.8118	−	10.8610i	0.640360	−	0.369712i	0.784753	+	0.619809i	$0.212790\pi$
$864$		0			0
$865$	−2.33465	+	4.04373i	−0.0793804	+	0.137491i
$866$	11.8047	−	20.4463i	0.401139	−	0.694794i
$867$		0			0
$868$		0			0
$869$	64.0496	+	36.9791i	2.17273	+	1.25443i
$870$		0			0
$871$			18.6969i			0.633520i
$872$	3.66908	+	2.11835i	0.124251	+	0.0717363i
$873$		0			0
$874$		−	4.18711i		−	0.141631i
$875$		0			0
$876$		0			0
$877$	0.392305			0.0132472			0.00662360	−	0.999978i	$-0.497892\pi$
$877$	0.392305			0.0132472			0.00662360	+	0.999978i	$0.497892\pi$
$878$	−12.5101	−	21.6681i	−0.422196	−	0.731265i
$879$		0			0
$880$	11.5498	+	6.66826i	0.389343	+	0.224787i
$881$	43.3363			1.46004			0.730018	−	0.683427i	$-0.239511\pi$
$881$	43.3363			1.46004			0.730018	+	0.683427i	$0.239511\pi$
$882$		0			0
$883$	2.17403			0.0731618			0.0365809	−	0.999331i	$-0.488353\pi$
$883$	2.17403			0.0731618			0.0365809	+	0.999331i	$0.488353\pi$
$884$	−2.63455	−	1.52106i	−0.0886096	−	0.0511588i
$885$		0			0
$886$	11.5150	+	19.9446i	0.386854	+	0.670051i
$887$	11.4443			0.384262			0.192131	−	0.981369i	$-0.438460\pi$
$887$	11.4443			0.384262			0.192131	+	0.981369i	$0.438460\pi$
$888$		0			0
$889$		0			0
$890$			2.72774i			0.0914341i
$891$		0			0
$892$	6.24329	+	3.60456i	0.209041	+	0.120690i
$893$			13.4552i			0.450262i
$894$		0			0
$895$	−16.9100	−	9.76302i	−0.565240	−	0.326342i
$896$		0			0
$897$		0			0
$898$	−7.95142	+	13.7723i	−0.265342	+	0.459586i
$899$	17.3916	−	30.1232i	0.580043	−	1.00466i
$900$		0			0
$901$		0			0
$902$	−22.6902	−	39.3006i	−0.755501	−	1.30857i
$903$		0			0
$904$	−3.41614	+	5.91693i	−0.113619	+	0.196794i
$905$			36.3072i			1.20689i
$906$		0			0
$907$	−53.8891			−1.78936			−0.894680	−	0.446708i	$-0.852596\pi$
$907$	−53.8891			−1.78936			−0.894680	+	0.446708i	$0.852596\pi$
$908$	−6.37800	−	11.0470i	−0.211661	−	0.366608i
$909$		0			0
$910$		0			0
$911$	7.00460	−	4.04411i	0.232073	−	0.133987i	−0.379455	−	0.925210i	$-0.623889\pi$
$911$	7.00460	−	4.04411i	0.232073	−	0.133987i	0.611528	+	0.791223i	$0.290555\pi$
$912$		0			0
$913$	61.6777	−	35.6097i	2.04124	−	1.17851i
$914$	−4.90702	+	2.83307i	−0.162310	+	0.0937096i
$915$		0			0
$916$	−3.89208	+	2.24709i	−0.128598	+	0.0742460i
$917$		0			0
$918$		0			0
$919$	−12.8375	−	22.2353i	−0.423472	−	0.733474i	0.572805	−	0.819692i	$-0.305855\pi$
$919$	−12.8375	−	22.2353i	−0.423472	−	0.733474i	−0.996276	+	0.0862175i	$0.972522\pi$
$920$	8.63411			0.284658
$921$		0			0
$922$			31.4584i			1.03603i
$923$	3.88777	−	6.73382i	0.127968	−	0.221646i
$924$		0			0
$925$	2.38903	+	4.13792i	0.0785507	+	0.136054i
$926$	−7.88340	+	4.55148i	−0.259064	+	0.149571i
$927$		0			0
$928$	−2.07781	+	3.59886i	−0.0682073	+	0.118139i
$929$	5.42618	−	9.39842i	0.178027	−	0.308352i	−0.763177	−	0.646189i	$-0.776362\pi$
$929$	5.42618	−	9.39842i	0.178027	−	0.308352i	0.941205	+	0.337837i	$0.109695\pi$
$930$		0			0
$931$		0			0
$932$	−1.86545	−	1.07702i	−0.0611048	−	0.0352789i
$933$		0			0
$934$		−	30.3032i		−	0.991550i
$935$	−20.4296	−	11.7950i	−0.668118	−	0.385738i
$936$		0			0
$937$		−	0.458120i		−	0.0149661i	−0.999972	−	0.00748306i	$-0.997618\pi$
$937$		−	0.458120i		−	0.0149661i	0.999972	−	0.00748306i	$-0.00238195\pi$
$938$		0			0
$939$		0			0
$940$	−27.7456			−0.904963
$941$	−3.68890	−	6.38937i	−0.120255	−	0.208287i	0.799613	−	0.600515i	$-0.205038\pi$
$941$	−3.68890	−	6.38937i	−0.120255	−	0.208287i	−0.919868	+	0.392228i	$0.871704\pi$
$942$		0			0
$943$	−25.4433	−	14.6897i	−0.828548	−	0.478362i
$944$	−2.22966			−0.0725693
$945$		0			0
$946$	19.9879			0.649862
$947$	−10.3846	−	5.99552i	−0.337453	−	0.194828i	0.321692	−	0.946844i	$-0.395748\pi$
$947$	−10.3846	−	5.99552i	−0.337453	−	0.194828i	−0.659145	+	0.752016i	$0.729082\pi$
$948$		0			0
$949$	4.59401	+	7.95706i	0.149128	+	0.258297i
$950$	0.591856			0.0192024
$951$		0			0
$952$		0			0
$953$		−	58.6883i		−	1.90110i	−0.310572	−	0.950550i	$-0.600521\pi$
$953$		−	58.6883i		−	1.90110i	0.310572	−	0.950550i	$-0.399479\pi$
$954$		0			0
$955$	−25.1031	−	14.4933i	−0.812317	−	0.468992i
$956$			10.1419i			0.328013i
$957$		0			0
$958$	−4.03816	−	2.33143i	−0.130467	−	0.0753251i
$959$		0			0
$960$		0			0
$961$	19.5300	−	33.8270i	0.630000	−	1.09119i
$962$	−7.90935	+	13.6994i	−0.255008	+	0.441686i
$963$		0			0
$964$	9.13490	−	5.27404i	0.294215	−	0.169865i
$965$	5.16140	+	8.93981i	0.166151	+	0.287783i
$966$		0			0
$967$	−3.37560	+	5.84671i	−0.108552	+	0.188018i	−0.915184	−	0.403037i	$-0.867955\pi$
$967$	−3.37560	+	5.84671i	−0.108552	+	0.188018i	0.806632	+	0.591054i	$0.201288\pi$
$968$			21.2246i			0.682184i
$969$		0			0
$970$	10.7844			0.346265
$971$	3.20362	+	5.54883i	0.102809	+	0.178070i	0.912841	−	0.408315i	$-0.133884\pi$
$971$	3.20362	+	5.54883i	0.102809	+	0.178070i	−0.810032	+	0.586386i	$0.800550\pi$
$972$		0			0
$973$		0			0
$974$	−16.8720	+	9.74105i	−0.540613	+	0.312123i
$975$		0			0
$976$	−7.79396	+	4.49985i	−0.249479	+	0.144037i
$977$	11.7769	−	6.79937i	0.376775	−	0.217531i	−0.299639	−	0.954053i	$-0.596866\pi$
$977$	11.7769	−	6.79937i	0.376775	−	0.217531i	0.676414	+	0.736521i	$0.263533\pi$
$978$		0			0
$979$	−5.70793	+	3.29547i	−0.182426	+	0.105324i
$980$		0			0
$981$		0			0
$982$	−10.2443	−	17.7437i	−0.326910	−	0.566224i
$983$	−22.7698			−0.726244			−0.363122	−	0.931742i	$-0.618289\pi$
$983$	−22.7698			−0.726244			−0.363122	+	0.931742i	$0.618289\pi$
$984$		0			0
$985$			25.5763i			0.814929i
$986$	3.67528	−	6.36577i	0.117045	−	0.202728i
$987$		0			0
$988$	0.979729	+	1.69694i	0.0311693	+	0.0539869i
$989$	11.2066	−	6.47011i	0.356348	−	0.205738i
$990$		0			0
$991$	13.4953	−	23.3745i	0.428691	−	0.742515i	−0.568066	−	0.822983i	$-0.692308\pi$
$991$	13.4953	−	23.3745i	0.428691	−	0.742515i	0.996757	+	0.0804680i	$0.0256415\pi$
$992$	−4.18509	+	7.24879i	−0.132877	+	0.230149i
$993$		0			0
$994$		0			0
$995$	56.0869	+	32.3818i	1.77807	+	1.02657i
$996$		0			0
$997$			19.3139i			0.611677i	0.952083	+	0.305838i	$0.0989367\pi$
$997$			19.3139i			0.611677i	−0.952083	+	0.305838i	$0.901063\pi$
$998$	8.87845	+	5.12598i	0.281043	+	0.162260i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2646.2.t.a.2285.2		16
3.2	odd	2		882.2.t.b.815.8		16
7.2	even	3		2646.2.l.b.1097.7		16
7.3	odd	6		378.2.m.a.125.6		16
7.4	even	3		378.2.m.a.125.7		16
7.5	odd	6		2646.2.l.b.1097.6		16
7.6	odd	2	inner	2646.2.t.a.2285.3		16
9.2	odd	6		2646.2.l.b.521.2		16
9.7	even	3		882.2.l.a.227.7		16
21.2	odd	6		882.2.l.a.509.2		16
21.5	even	6		882.2.l.a.509.3		16
21.11	odd	6		126.2.m.a.41.2	✓	16
21.17	even	6		126.2.m.a.41.3	yes	16
21.20	even	2		882.2.t.b.815.5		16
28.3	even	6		3024.2.cc.b.881.2		16
28.11	odd	6		3024.2.cc.b.881.7		16
63.2	odd	6	inner	2646.2.t.a.1979.3		16
63.4	even	3		1134.2.d.a.1133.10		16
63.11	odd	6		378.2.m.a.251.6		16
63.16	even	3		882.2.t.b.803.5		16
63.20	even	6		2646.2.l.b.521.3		16
63.25	even	3		126.2.m.a.83.3	yes	16
63.31	odd	6		1134.2.d.a.1133.15		16
63.32	odd	6		1134.2.d.a.1133.7		16
63.34	odd	6		882.2.l.a.227.6		16
63.38	even	6		378.2.m.a.251.7		16
63.47	even	6	inner	2646.2.t.a.1979.2		16
63.52	odd	6		126.2.m.a.83.2	yes	16
63.59	even	6		1134.2.d.a.1133.2		16
63.61	odd	6		882.2.t.b.803.8		16
84.11	even	6		1008.2.cc.b.545.6		16
84.59	odd	6		1008.2.cc.b.545.3		16
252.11	even	6		3024.2.cc.b.2897.2		16
252.115	even	6		1008.2.cc.b.209.6		16
252.151	odd	6		1008.2.cc.b.209.3		16
252.227	odd	6		3024.2.cc.b.2897.7		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
126.2.m.a.41.2	✓	16	21.11	odd	6
126.2.m.a.41.3	yes	16	21.17	even	6
126.2.m.a.83.2	yes	16	63.52	odd	6
126.2.m.a.83.3	yes	16	63.25	even	3
378.2.m.a.125.6		16	7.3	odd	6
378.2.m.a.125.7		16	7.4	even	3
378.2.m.a.251.6		16	63.11	odd	6
378.2.m.a.251.7		16	63.38	even	6
882.2.l.a.227.6		16	63.34	odd	6
882.2.l.a.227.7		16	9.7	even	3
882.2.l.a.509.2		16	21.2	odd	6
882.2.l.a.509.3		16	21.5	even	6
882.2.t.b.803.5		16	63.16	even	3
882.2.t.b.803.8		16	63.61	odd	6
882.2.t.b.815.5		16	21.20	even	2
882.2.t.b.815.8		16	3.2	odd	2
1008.2.cc.b.209.3		16	252.151	odd	6
1008.2.cc.b.209.6		16	252.115	even	6
1008.2.cc.b.545.3		16	84.59	odd	6
1008.2.cc.b.545.6		16	84.11	even	6
1134.2.d.a.1133.2		16	63.59	even	6
1134.2.d.a.1133.7		16	63.32	odd	6
1134.2.d.a.1133.10		16	63.4	even	3
1134.2.d.a.1133.15		16	63.31	odd	6
2646.2.l.b.521.2		16	9.2	odd	6
2646.2.l.b.521.3		16	63.20	even	6
2646.2.l.b.1097.6		16	7.5	odd	6
2646.2.l.b.1097.7		16	7.2	even	3
2646.2.t.a.1979.2		16	63.47	even	6	inner
2646.2.t.a.1979.3		16	63.2	odd	6	inner
2646.2.t.a.2285.2		16	1.1	even	1	trivial
2646.2.t.a.2285.3		16	7.6	odd	2	inner
3024.2.cc.b.881.2		16	28.3	even	6
3024.2.cc.b.881.7		16	28.11	odd	6
3024.2.cc.b.2897.2		16	252.11	even	6
3024.2.cc.b.2897.7		16	252.227	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 2646 = 2 \cdot 3^{3} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2646.t (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 - 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} -2.34936 q^{5} -1.00000i q^{8} +O(q^{10})\)	\(q+(-0.866025 - 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} -2.34936 q^{5} -1.00000i q^{8} +(2.03460 + 1.17468i) q^{10} +5.67667i q^{11} +(-1.48943 - 0.859925i) q^{13} +(-0.500000 + 0.866025i) q^{16} +(0.884414 - 1.53185i) q^{17} +(-0.986680 + 0.569660i) q^{19} +(-1.17468 - 2.03460i) q^{20} +(2.83834 - 4.91614i) q^{22} -3.67509i q^{23} +0.519482 q^{25} +(0.859925 + 1.48943i) q^{26} +(-3.59886 + 2.07781i) q^{29} +(-7.24879 + 4.18509i) q^{31} +(0.866025 - 0.500000i) q^{32} +(-1.53185 + 0.884414i) q^{34} +(4.59886 + 7.96547i) q^{37} +1.13932 q^{38} +2.34936i q^{40} +(3.99709 - 6.92317i) q^{41} +(1.76053 + 3.04933i) q^{43} +(-4.91614 + 2.83834i) q^{44} +(-1.83755 + 3.18272i) q^{46} +(5.90494 - 10.2277i) q^{47} +(-0.449885 - 0.259741i) q^{50} -1.71985i q^{52} -13.3365i q^{55} +4.15561 q^{58} +(1.11483 + 1.93094i) q^{59} +(7.79396 + 4.49985i) q^{61} +8.37019 q^{62} -1.00000 q^{64} +(3.49921 + 2.02027i) q^{65} +(-5.43562 - 9.41477i) q^{67} +1.76883 q^{68} +4.52106i q^{71} +(-4.62660 - 2.67117i) q^{73} -9.19773i q^{74} +(-0.986680 - 0.569660i) q^{76} +(6.51422 - 11.2830i) q^{79} +(1.17468 - 2.03460i) q^{80} +(-6.92317 + 3.99709i) q^{82} +(-6.27298 - 10.8651i) q^{83} +(-2.07781 + 3.59886i) q^{85} -3.52106i q^{86} +5.67667 q^{88} +(0.580529 + 1.00551i) q^{89} +(3.18272 - 1.83755i) q^{92} +(-10.2277 + 5.90494i) q^{94} +(2.31806 - 1.33834i) q^{95} +(3.97536 - 2.29517i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 8 q^{4}+O(q^{10}) \) 16 * q + 8 * q^4	\( 16 q + 8 q^{4} - 8 q^{16} + 16 q^{25} + 12 q^{29} + 4 q^{37} + 4 q^{43} - 12 q^{44} - 12 q^{46} - 60 q^{50} + 24 q^{58} - 16 q^{64} + 84 q^{65} - 28 q^{67} - 4 q^{79} - 12 q^{85} + 48 q^{92} + 12 q^{95}+O(q^{100}) \) 16 * q + 8 * q^4 - 8 * q^16 + 16 * q^25 + 12 * q^29 + 4 * q^37 + 4 * q^43 - 12 * q^44 - 12 * q^46 - 60 * q^50 + 24 * q^58 - 16 * q^64 + 84 * q^65 - 28 * q^67 - 4 * q^79 - 12 * q^85 + 48 * q^92 + 12 * q^95

Introduction

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Database

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