LMFDB - Embedded newform 2646.2.t.a.1979.3

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			1979.3
Root			$-1.40917 - 1.00709i$ of defining polynomial
Character	$\chi$	$=$	2646.1979
Dual form			2646.2.t.a.2285.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 + 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +2.34936 q^{5} +1.00000i q^{8} +O(q^{10})$	\(q+(-0.866025 + 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +2.34936 q^{5} +1.00000i q^{8} +(-2.03460 + 1.17468i) q^{10} -5.67667i q^{11} +(1.48943 - 0.859925i) q^{13} +(-0.500000 - 0.866025i) q^{16} +(-0.884414 - 1.53185i) q^{17} +(0.986680 + 0.569660i) q^{19} +(1.17468 - 2.03460i) q^{20} +(2.83834 + 4.91614i) q^{22} +3.67509i q^{23} +0.519482 q^{25} +(-0.859925 + 1.48943i) q^{26} +(-3.59886 - 2.07781i) q^{29} +(7.24879 + 4.18509i) q^{31} +(0.866025 + 0.500000i) q^{32} +(1.53185 + 0.884414i) q^{34} +(4.59886 - 7.96547i) q^{37} -1.13932 q^{38} +2.34936i q^{40} +(-3.99709 - 6.92317i) q^{41} +(1.76053 - 3.04933i) q^{43} +(-4.91614 - 2.83834i) q^{44} +(-1.83755 - 3.18272i) q^{46} +(-5.90494 - 10.2277i) q^{47} +(-0.449885 + 0.259741i) q^{50} -1.71985i q^{52} -13.3365i q^{55} +4.15561 q^{58} +(-1.11483 + 1.93094i) q^{59} +(-7.79396 + 4.49985i) q^{61} -8.37019 q^{62} -1.00000 q^{64} +(3.49921 - 2.02027i) q^{65} +(-5.43562 + 9.41477i) q^{67} -1.76883 q^{68} -4.52106i q^{71} +(4.62660 - 2.67117i) q^{73} +9.19773i q^{74} +(0.986680 - 0.569660i) q^{76} +(6.51422 + 11.2830i) q^{79} +(-1.17468 - 2.03460i) q^{80} +(6.92317 + 3.99709i) q^{82} +(6.27298 - 10.8651i) q^{83} +(-2.07781 - 3.59886i) q^{85} +3.52106i q^{86} +5.67667 q^{88} +(-0.580529 + 1.00551i) q^{89} +(3.18272 + 1.83755i) q^{92} +(10.2277 + 5.90494i) q^{94} +(2.31806 + 1.33834i) q^{95} +(-3.97536 - 2.29517i) q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/2646\mathbb{Z}\right)^\times$.

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

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	$-0.323941\pi$
$5$	2.34936			1.05066			0.525332	+	0.850897i	$0.323941\pi$
$6$		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	$-0.673071\pi$
$11$		−	5.67667i		−	1.71158i	0.517323	−	0.855790i	$-0.326929\pi$
$12$		0			0
$13$	1.48943	−	0.859925i	0.413094	−	0.238500i	−0.279024	−	0.960284i	$-0.590011\pi$
$13$	1.48943	−	0.859925i	0.413094	−	0.238500i	0.692118	+	0.721784i	$0.256678\pi$
$14$		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	$-0.235480\pi$
$17$	−0.884414	−	1.53185i	−0.214502	−	0.371528i	−0.953118	+	0.302598i	$0.902146\pi$
$18$		0			0
$19$	0.986680	+	0.569660i	0.226360	+	0.130689i	0.608892	−	0.793253i	$-0.291614\pi$
$19$	0.986680	+	0.569660i	0.226360	+	0.130689i	−0.382532	+	0.923942i	$0.624948\pi$
$20$	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	$0.125162\pi$
$23$			3.67509i			0.766310i	−0.923684	+	0.383155i	$0.874838\pi$
$24$		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	0.127137	−	0.991885i	$-0.459421\pi$
$29$	−3.59886	−	2.07781i	−0.668292	−	0.385839i	−0.795429	+	0.606046i	$0.792755\pi$
$30$		0			0
$31$	7.24879	+	4.18509i	1.30192	+	0.751665i	0.980734	−	0.195350i	$-0.0625844\pi$
$31$	7.24879	+	4.18509i	1.30192	+	0.751665i	0.321188	+	0.947015i	$0.395918\pi$
$32$	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	−0.188803	−	0.982015i	$-0.560461\pi$
$37$	4.59886	−	7.96547i	0.756049	−	1.30951i	0.944851	−	0.327500i	$-0.106206\pi$
$38$	−1.13932			−0.184822
$39$		0			0
$40$			2.34936i			0.371466i
$41$	−3.99709	−	6.92317i	−0.624241	−	1.08122i	−0.988687	−	0.149993i	$-0.952075\pi$
$41$	−3.99709	−	6.92317i	−0.624241	−	1.08122i	0.364446	−	0.931225i	$-0.381258\pi$
$42$		0			0
$43$	1.76053	−	3.04933i	0.268478	−	0.465018i	−0.699991	−	0.714152i	$-0.746813\pi$
$43$	1.76053	−	3.04933i	0.268478	−	0.465018i	0.968469	+	0.249134i	$0.0801459\pi$
$44$	−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	−0.870651	−	0.491901i	$-0.836302\pi$
$47$	−5.90494	−	10.2277i	−0.861324	−	1.49186i	0.00932669	−	0.999957i	$-0.497031\pi$
$48$		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	$-0.666667\pi$
$53$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$54$		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	$-0.879696\pi$
$59$	−1.11483	+	1.93094i	−0.145139	+	0.251387i	0.784286	+	0.620399i	$0.213029\pi$
$60$		0			0
$61$	−7.79396	+	4.49985i	−0.997915	+	0.576146i	−0.907631	−	0.419770i	$-0.862111\pi$
$61$	−7.79396	+	4.49985i	−0.997915	+	0.576146i	−0.0902842	+	0.995916i	$0.528778\pi$
$62$	−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	0.315470	+	0.948935i	$0.397838\pi$
$67$	−5.43562	+	9.41477i	−0.664067	+	1.15020i	−0.979537	+	0.201262i	$0.935496\pi$
$68$	−1.76883			−0.214502
$69$		0			0
$70$		0			0
$71$		−	4.52106i		−	0.536551i	−0.963342	−	0.268276i	$-0.913546\pi$
$71$		−	4.52106i		−	0.536551i	0.963342	−	0.268276i	$-0.0864538\pi$
$72$		0			0
$73$	4.62660	−	2.67117i	0.541503	−	0.312637i	−0.204185	−	0.978932i	$-0.565454\pi$
$73$	4.62660	−	2.67117i	0.541503	−	0.312637i	0.745688	+	0.666295i	$0.232121\pi$
$74$			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	0.955636	+	0.294551i	$0.0951701\pi$
$79$	6.51422	+	11.2830i	0.732907	+	1.26943i	−0.222729	+	0.974880i	$0.571497\pi$
$80$	−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	−0.283758	−	0.958896i	$-0.591581\pi$
$83$	6.27298	−	10.8651i	0.688549	−	1.19260i	0.972307	−	0.233707i	$-0.0750855\pi$
$84$		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	$-0.852933\pi$
$89$	−0.580529	+	1.00551i	−0.0615360	+	0.106583i	0.833616	+	0.552344i	$0.186267\pi$
$90$		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	$-0.408200\pi$
$97$	−3.97536	−	2.29517i	−0.403636	−	0.233039i	−0.688052	+	0.725662i	$0.741534\pi$
$98$		0			0
$99$		0			0
$100$	0.259741	−	0.449885i	0.0259741	−	0.0449885i
$101$	6.62310			0.659023			0.329511	−	0.944152i	$-0.393116\pi$
$101$	6.62310			0.659023			0.329511	+	0.944152i	$0.393116\pi$
$102$		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	0.289437	−	0.957197i	$-0.406532\pi$
$107$	−4.08386	−	2.35782i	−0.394802	−	0.227939i	−0.684239	+	0.729258i	$0.739865\pi$
$108$		0			0
$109$	−2.11835	−	3.66908i	−0.202901	−	0.351435i	0.746561	−	0.665317i	$-0.231704\pi$
$109$	−2.11835	−	3.66908i	−0.202901	−	0.351435i	−0.949462	+	0.313882i	$0.898370\pi$
$110$	6.66826	+	11.5498i	0.635794	+	1.10123i
$111$		0			0
$112$		0			0
$113$	−5.91693	+	3.41614i	−0.556618	+	0.321363i	−0.751787	−	0.659406i	$-0.770808\pi$
$113$	−5.91693	+	3.41614i	−0.556618	+	0.321363i	0.195169	+	0.980770i	$0.437474\pi$
$114$		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	$-0.394144\pi$
$131$	7.47305			0.652923			0.326462	+	0.945210i	$0.394144\pi$
$132$		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	$0.110842\pi$
$137$			7.98789i			0.682452i	−0.939981	+	0.341226i	$0.889158\pi$
$138$		0			0
$139$	17.9792	−	10.3803i	1.52498	−	0.880446i	0.525415	−	0.850846i	$-0.323910\pi$
$139$	17.9792	−	10.3803i	1.52498	−	0.880446i	0.999562	−	0.0295993i	$-0.00942312\pi$
$140$		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	$0.0156228\pi$
$149$			1.19773i			0.0981218i	−0.998796	+	0.0490609i	$0.984377\pi$
$150$		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	$-0.464364\pi$
$157$	−8.68358	−	5.01347i	−0.693025	−	0.400118i	−0.804744	+	0.593621i	$0.797698\pi$
$158$	−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	−0.999415	−	0.0342109i	$-0.989108\pi$
$163$	−6.00158	+	10.3950i	−0.470080	+	0.814202i	0.529335	+	0.848413i	$0.322442\pi$
$164$	−7.99419			−0.624241
$165$		0			0
$166$			12.5460i			0.973756i
$167$	−8.57472	−	14.8518i	−0.663532	−	1.14927i	−0.979681	−	0.200561i	$-0.935723\pi$
$167$	−8.57472	−	14.8518i	−0.663532	−	1.14927i	0.316150	−	0.948709i	$-0.397610\pi$
$168$		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	$-0.190739\pi$
$173$	−0.993738	−	1.72121i	−0.0755525	−	0.130861i	−0.901326	+	0.433140i	$0.857405\pi$
$174$		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	−0.206278	−	0.978493i	$-0.566135\pi$
$179$	7.19773	−	4.15561i	0.537984	−	0.310605i	0.744261	+	0.667889i	$0.232802\pi$
$180$		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	−0.0608498	−	0.998147i	$-0.519381\pi$
$191$	10.6851	−	6.16904i	0.773146	−	0.446376i	0.833996	+	0.551771i	$0.186048\pi$
$192$		0			0
$193$	−2.19694	+	3.80521i	−0.158139	+	0.273905i	−0.934198	−	0.356756i	$-0.883883\pi$
$193$	−2.19694	+	3.80521i	−0.158139	+	0.273905i	0.776058	+	0.630661i	$0.217216\pi$
$194$	4.59035			0.329568
$195$		0			0
$196$		0			0
$197$			10.8865i			0.775632i	0.921737	+	0.387816i	$0.126770\pi$
$197$			10.8865i			0.775632i	−0.921737	+	0.387816i	$0.873230\pi$
$198$		0			0
$199$	23.8733	−	13.7832i	1.69233	−	0.977068i	0.739703	−	0.672933i	$-0.234966\pi$
$199$	23.8733	−	13.7832i	1.69233	−	0.977068i	0.952629	−	0.304135i	$-0.0983674\pi$
$200$			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	0.987105	−	0.160071i	$-0.0511724\pi$
$211$	5.15561	+	8.92978i	0.354927	+	0.614751i	−0.632179	+	0.774823i	$0.717839\pi$
$212$		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	$-0.410933\pi$
$223$	−6.24329	−	3.60456i	−0.418081	−	0.241379i	−0.694256	+	0.719728i	$0.744267\pi$
$224$		0			0
$225$		0			0
$226$	3.41614	−	5.91693i	0.227238	−	0.393588i
$227$	12.7560			0.846645			0.423323	−	0.905979i	$-0.360864\pi$
$227$	12.7560			0.846645			0.423323	+	0.905979i	$0.360864\pi$
$228$		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	0.437649	−	0.899146i	$-0.355811\pi$
$233$	−1.86545	−	1.07702i	−0.122210	−	0.0705577i	−0.559859	+	0.828588i	$0.689145\pi$
$234$		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	−0.188269	−	0.982118i	$-0.560288\pi$
$239$	8.78317	−	5.07096i	0.568136	−	0.328013i	0.756404	+	0.654104i	$0.226954\pi$
$240$		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	$-0.124304\pi$
$251$	29.3005			1.84943			0.924714	+	0.380662i	$0.124304\pi$
$252$		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	$-0.576469\pi$
$257$	−7.62860			−0.475859			−0.237930	+	0.971282i	$0.576469\pi$
$258$		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	$-0.877403\pi$
$263$		−	12.1856i		−	0.751398i	0.926742	−	0.375699i	$-0.122597\pi$
$264$		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	$-0.139713\pi$
$269$	1.38717	+	2.40264i	0.0845771	+	0.146492i	−0.820634	+	0.571454i	$0.806379\pi$
$270$		0			0
$271$	2.77815	+	1.60396i	0.168760	+	0.0974338i	0.582001	−	0.813188i	$-0.302270\pi$
$271$	2.77815	+	1.60396i	0.168760	+	0.0974338i	−0.413241	+	0.910622i	$0.635603\pi$
$272$	−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	0.368819	−	0.929501i	$-0.379762\pi$
$281$	−4.21999	−	2.43641i	−0.251743	−	0.145344i	−0.620562	+	0.784157i	$0.713096\pi$
$282$		0			0
$283$	2.44030	+	1.40891i	0.145061	+	0.0837508i	0.570774	−	0.821107i	$-0.306643\pi$
$283$	2.44030	+	1.40891i	0.145061	+	0.0837508i	−0.425713	+	0.904858i	$0.639977\pi$
$284$	−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	$-0.0904995\pi$
$293$	4.05694	+	7.02683i	0.237009	+	0.410512i	−0.722846	+	0.691010i	$0.757166\pi$
$294$		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	$-0.908358\pi$
$311$	−4.11819	+	7.13291i	−0.233521	+	0.404470i	0.725321	+	0.688411i	$0.241691\pi$
$312$		0			0
$313$	29.2736	−	16.9011i	1.65464	−	0.955308i	0.679516	−	0.733661i	$-0.262190\pi$
$313$	29.2736	−	16.9011i	1.65464	−	0.955308i	0.975127	−	0.221648i	$-0.0711435\pi$
$314$	10.0269			0.565853
$315$		0			0
$316$	13.0284			0.732907
$317$	5.82913	−	3.36545i	0.327396	−	0.189022i	−0.327288	−	0.944925i	$-0.606135\pi$
$317$	5.82913	−	3.36545i	0.327396	−	0.189022i	0.654685	+	0.755902i	$0.272801\pi$
$318$		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	0.850228	+	0.526415i	$0.176464\pi$
$331$	16.0284	+	27.7621i	0.881002	+	1.52594i	0.0307744	+	0.999526i	$0.490203\pi$
$332$	−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	−0.980668	−	0.195681i	$-0.937308\pi$
$337$	−12.1123	−	20.9791i	−0.659799	−	1.14280i	0.320869	−	0.947124i	$-0.396025\pi$
$338$		−	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	0.925427	−	0.378926i	$-0.123706\pi$
$347$	19.7453	+	11.3999i	1.05998	+	0.611981i	0.134554	+	0.990906i	$0.457040\pi$
$348$		0			0
$349$	−2.46389	−	1.42253i	−0.131889	−	0.0761461i	0.432604	−	0.901584i	$-0.357595\pi$
$349$	−2.46389	−	1.42253i	−0.131889	−	0.0761461i	−0.564493	+	0.825438i	$0.690928\pi$
$350$		0			0
$351$		0			0
$352$	2.83834	−	4.91614i	0.151284	−	0.262031i
$353$	−7.14424			−0.380249			−0.190125	−	0.981760i	$-0.560889\pi$
$353$	−7.14424			−0.380249			−0.190125	+	0.981760i	$0.560889\pi$
$354$		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	0.210796	−	0.977530i	$-0.432394\pi$
$359$	−10.0491	−	5.80186i	−0.530372	−	0.306210i	−0.741168	+	0.671320i	$0.765728\pi$
$360$		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	$-0.487582\pi$
$383$	1.52664			0.0780079			0.0390040	+	0.999239i	$0.487582\pi$
$384$		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	$0.123205\pi$
$389$			14.8897i			0.754936i	−0.926023	+	0.377468i	$0.876795\pi$
$390$		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	$-0.590289\pi$
$397$	−24.9302	−	14.3935i	−1.25121	−	0.722388i	−0.971350	+	0.237653i	$0.923622\pi$
$398$	−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	$0.402176\pi$
$401$			38.1735i			1.90629i	−0.302507	+	0.953147i	$0.597824\pi$
$402$		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	$-0.388436\pi$
$409$	−6.03355	−	3.48347i	−0.298340	−	0.172247i	−0.641697	+	0.766958i	$0.721769\pi$
$410$	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	0.880146	+	0.474702i	$0.157444\pi$
$419$	17.4232	+	30.1778i	0.851177	+	1.47428i	−0.0289690	+	0.999580i	$0.509222\pi$
$420$		0			0
$421$	2.84597	−	4.92936i	0.138704	−	0.240242i	−0.788302	−	0.615288i	$-0.789040\pi$
$421$	2.84597	−	4.92936i	0.138704	−	0.240242i	0.927006	+	0.375046i	$0.122373\pi$
$422$	−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	−0.973787	−	0.227460i	$-0.926958\pi$
$431$	−26.2350	+	15.1468i	−1.26370	+	0.729595i	−0.289908	+	0.957055i	$0.593625\pi$
$432$		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	$-0.870337\pi$
$439$	−21.6681	+	12.5101i	−1.03416	+	0.597075i	−0.115989	+	0.993250i	$0.537004\pi$
$440$	13.3365			0.635794
$441$		0			0
$442$	3.04212			0.144699
$443$	−19.9446	+	11.5150i	−0.947595	+	0.547094i	−0.892333	−	0.451377i	$-0.850933\pi$
$443$	−19.9446	+	11.5150i	−0.947595	+	0.547094i	−0.0552622	+	0.998472i	$0.517599\pi$
$444$		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	$0.122443\pi$
$449$			15.9028i			0.750501i	−0.926923	+	0.375251i	$0.877557\pi$
$450$		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	0.924649	−	0.380819i	$-0.124358\pi$
$457$	2.83307	+	4.90702i	0.132525	+	0.229541i	−0.792124	+	0.610360i	$0.791025\pi$
$458$	−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	−0.223194	−	0.974774i	$-0.571648\pi$
$461$	15.7292	−	27.2438i	0.732582	−	1.26887i	0.955776	−	0.294095i	$-0.0950183\pi$
$462$		0			0
$463$	4.55148	+	7.88340i	0.211525	+	0.366373i	0.952192	−	0.305500i	$-0.0988236\pi$
$463$	4.55148	+	7.88340i	0.211525	+	0.366373i	−0.740667	+	0.671873i	$0.765490\pi$
$464$			4.15561i			0.192919i
$465$		0			0
$466$	2.15403			0.0997837
$467$	−15.1516	+	26.2433i	−0.701132	+	1.21440i	0.266938	+	0.963714i	$0.413988\pi$
$467$	−15.1516	+	26.2433i	−0.701132	+	1.21440i	−0.968069	+	0.250682i	$0.919345\pi$
$468$		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	$-0.533973\pi$
$479$	−4.66286			−0.213052			−0.106526	+	0.994310i	$0.533973\pi$
$480$		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	0.997794	−	0.0663816i	$-0.0211455\pi$
$487$	9.74105	+	16.8720i	0.441409	+	0.764543i	−0.556385	+	0.830924i	$0.687812\pi$
$488$	−4.49985	−	7.79396i	−0.203699	−	0.352816i
$489$		0			0
$490$		0			0
$491$	17.7437	−	10.2443i	0.800762	−	0.462320i	−0.0429758	−	0.999076i	$-0.513684\pi$
$491$	17.7437	−	10.2443i	0.800762	−	0.462320i	0.843737	+	0.536756i	$0.180351\pi$
$492$		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	$-0.394830\pi$
$503$	14.5521			0.648845			0.324422	+	0.945912i	$0.394830\pi$
$504$		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	$-0.764473\pi$
$509$	−33.3234			−1.47703			−0.738517	+	0.674235i	$0.764473\pi$
$510$		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	$-0.212420\pi$
$521$	−3.26963	−	5.66316i	−0.143245	−	0.248108i	−0.928717	+	0.370790i	$0.879087\pi$
$522$		0			0
$523$	0.681439	+	0.393429i	0.0297972	+	0.0172034i	0.514825	−	0.857296i	$-0.327857\pi$
$523$	0.681439	+	0.393429i	0.0297972	+	0.0172034i	−0.485027	+	0.874499i	$0.661190\pi$
$524$	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	−0.919957	−	0.392020i	$-0.871776\pi$
$541$	−2.80227	+	4.85367i	−0.120479	+	0.208676i	0.799478	+	0.600696i	$0.205110\pi$
$542$	−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	−0.975135	−	0.221612i	$-0.928868\pi$
$547$	−6.91456	+	11.9764i	−0.295645	+	0.512073i	0.679489	+	0.733685i	$0.262201\pi$
$548$	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	0.106584	−	0.994304i	$-0.466009\pi$
$557$	24.0957	−	13.9117i	1.02097	−	0.589456i	0.914384	+	0.404848i	$0.132675\pi$
$558$		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	0.482898	+	0.875676i	$0.339584\pi$
$563$	−12.2650	+	21.2436i	−0.516909	+	0.895312i	−0.999807	+	0.0196359i	$0.993749\pi$
$564$		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	−0.903527	−	0.428531i	$-0.859031\pi$
$569$	−23.4762	+	13.5540i	−0.984172	+	0.568212i	−0.0806449	+	0.996743i	$0.525698\pi$
$570$		0			0
$571$	14.9177	−	25.8382i	0.624287	−	1.08130i	−0.364391	−	0.931246i	$-0.618723\pi$
$571$	14.9177	−	25.8382i	0.624287	−	1.08130i	0.988678	−	0.150051i	$-0.0479438\pi$
$572$	−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	$-0.866081\pi$
$577$	−24.3930	+	14.0833i	−1.01549	+	0.586296i	−0.102699	+	0.994712i	$0.532748\pi$
$578$			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	$-0.898952\pi$
$587$	−4.95928	+	8.58973i	−0.204692	+	0.354536i	0.745343	+	0.666681i	$0.232286\pi$
$588$		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	$-0.864091\pi$
$593$	−2.34936	+	4.06921i	−0.0964766	+	0.167102i	0.813747	+	0.581219i	$0.197424\pi$
$594$		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	0.737004	−	0.675888i	$-0.236240\pi$
$599$	12.7309	+	7.35019i	0.520170	+	0.300320i	−0.216834	+	0.976208i	$0.569573\pi$
$600$		0			0
$601$	16.2923	+	9.40634i	0.664575	+	0.383693i	0.794018	−	0.607894i	$-0.207986\pi$
$601$	16.2923	+	9.40634i	0.664575	+	0.383693i	−0.129443	+	0.991587i	$0.541319\pi$
$602$		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	0.947983	−	0.318322i	$-0.103119\pi$
$613$	4.91009	+	8.50452i	0.198317	+	0.343494i	−0.749666	+	0.661816i	$0.769786\pi$
$614$	−5.44981	−	9.43935i	−0.219937	−	0.380941i
$615$		0			0
$616$		0			0
$617$	3.25158	−	1.87730i	0.130904	−	0.0755772i	−0.433118	−	0.901337i	$-0.642587\pi$
$617$	3.25158	−	1.87730i	0.130904	−	0.0755772i	0.564022	+	0.825760i	$0.309253\pi$
$618$		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	$-0.827087\pi$
$641$		−	26.1735i		−	1.03379i	0.856048	−	0.516896i	$-0.172913\pi$
$642$		0			0
$643$	9.50955	−	5.49034i	0.375020	−	0.216518i	−0.300629	−	0.953741i	$-0.597197\pi$
$643$	9.50955	−	5.49034i	0.375020	−	0.216518i	0.675649	+	0.737223i	$0.263863\pi$
$644$		0			0
$645$		0			0
$646$	1.00763	+	1.74527i	0.0396447	+	0.0686666i
$647$	16.0063	+	27.7237i	0.629273	+	1.08993i	0.987698	+	0.156374i	$0.0499805\pi$
$647$	16.0063	+	27.7237i	0.629273	+	1.08993i	−0.358425	+	0.933558i	$0.616686\pi$
$648$		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	$-0.855827\pi$
$653$		−	22.3649i		−	0.875208i	0.899168	−	0.437604i	$-0.144173\pi$
$654$		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	0.825713	−	0.564091i	$-0.190773\pi$
$659$	19.2546	+	11.1166i	0.750053	+	0.433043i	−0.0756603	+	0.997134i	$0.524106\pi$
$660$		0			0
$661$	9.13646	+	5.27494i	0.355367	+	0.205171i	0.667047	−	0.745016i	$-0.267558\pi$
$661$	9.13646	+	5.27494i	0.355367	+	0.205171i	−0.311679	+	0.950187i	$0.600892\pi$
$662$	−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	−0.608498	−	0.793555i	$-0.708228\pi$
$673$	9.93562	−	17.2090i	0.382990	−	0.663358i	0.991488	+	0.130197i	$0.0415610\pi$
$674$	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	$-0.0676424\pi$
$677$	7.96449	+	13.7949i	0.306100	+	0.530181i	−0.671405	+	0.741090i	$0.734309\pi$
$678$		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	−0.780947	−	0.624597i	$-0.785263\pi$
$683$	−16.4777	+	9.51343i	−0.630503	+	0.364021i	0.150444	+	0.988619i	$0.451930\pi$
$684$		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	$-0.667642\pi$
$691$	−0.139477	+	0.0805273i	−0.00530597	+	0.00306340i	0.497345	+	0.867553i	$0.334308\pi$
$692$	−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	$0.0603670\pi$
$701$			9.98234i			0.377028i	−0.982071	+	0.188514i	$0.939633\pi$
$702$		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	0.998857	−	0.0477959i	$-0.0152197\pi$
$709$	12.1962	+	21.1244i	0.458036	+	0.793342i	−0.540821	+	0.841138i	$0.681886\pi$
$710$	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	$-0.931445\pi$
$719$	−8.13460	+	14.0895i	−0.303370	+	0.525451i	0.673527	+	0.739162i	$0.264778\pi$
$720$		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	$-0.187445\pi$
$727$	20.6626	+	11.9296i	0.766335	+	0.442444i	−0.0652306	+	0.997870i	$0.520778\pi$
$728$		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	−0.937312	−	0.348492i	$-0.886694\pi$
$739$	−20.9446	−	36.2771i	−0.770459	−	1.33447i	0.166853	−	0.985982i	$-0.446639\pi$
$740$	−10.8044	−	18.7137i	−0.397177	−	0.687931i
$741$		0			0
$742$		0			0
$743$	−43.9160	+	25.3549i	−1.61112	+	0.930182i	−0.622011	+	0.783008i	$0.713684\pi$
$743$	−43.9160	+	25.3549i	−1.61112	+	0.930182i	−0.989111	+	0.147173i	$0.952982\pi$
$744$		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	$-0.208990\pi$
$761$	43.7019			1.58419			0.792096	+	0.610397i	$0.208990\pi$
$762$		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	$-0.947476\pi$
$769$	−37.0864	+	21.4118i	−1.33737	+	0.772131i	−0.350953	+	0.936393i	$0.614142\pi$
$770$		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	$-0.293687\pi$
$773$	−10.8025	−	18.7105i	−0.388540	−	0.672971i	−0.992253	+	0.124231i	$0.960354\pi$
$774$		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	0.994300	+	0.106618i	$0.0340020\pi$
$787$	44.4307	+	25.6521i	1.58378	+	0.914398i	0.589484	+	0.807780i	$0.299331\pi$
$788$	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	$-0.156528\pi$
$797$	0.899094	+	1.55728i	0.0318476	+	0.0551616i	−0.849662	+	0.527327i	$0.823194\pi$
$798$		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	0.270006	−	0.962859i	$-0.412974\pi$
$809$	35.2371	−	20.3441i	1.23887	−	0.715262i	0.968863	+	0.247597i	$0.0796409\pi$
$810$		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	−0.285777	−	0.958296i	$-0.592252\pi$
$821$	11.4968	−	6.63771i	0.401243	−	0.231658i	0.687020	+	0.726638i	$0.258918\pi$
$822$		0			0
$823$	−13.8711	+	24.0255i	−0.483517	+	0.837476i	−0.999821	−	0.0189295i	$-0.993974\pi$
$823$	−13.8711	+	24.0255i	−0.483517	+	0.837476i	0.516304	+	0.856405i	$0.327308\pi$
$824$	5.85977			0.204135
$825$		0			0
$826$		0			0
$827$			27.7183i			0.963859i	0.876210	+	0.481929i	$0.160064\pi$
$827$			27.7183i			0.963859i	−0.876210	+	0.481929i	$0.839936\pi$
$828$		0			0
$829$	−37.0105	+	21.3680i	−1.28543	+	0.742143i	−0.977835	−	0.209375i	$-0.932857\pi$
$829$	−37.0105	+	21.3680i	−1.28543	+	0.742143i	−0.307593	+	0.951518i	$0.599524\pi$
$830$			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	$-0.812170\pi$
$839$	1.92438	−	3.33313i	0.0664370	−	0.115072i	0.897331	+	0.441359i	$0.145504\pi$
$840$		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	$-0.507711\pi$
$853$	−26.3470	−	15.2114i	−0.902103	−	0.520830i	−0.877882	+	0.478877i	$0.841044\pi$
$854$		0			0
$855$		0			0
$856$	2.35782	−	4.08386i	0.0805885	−	0.139583i
$857$	38.9315			1.32987			0.664937	−	0.746900i	$-0.268459\pi$
$857$	38.9315			1.32987			0.664937	+	0.746900i	$0.268459\pi$
$858$		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	0.784753	−	0.619809i	$-0.212790\pi$
$863$	18.8118	+	10.8610i	0.640360	+	0.369712i	−0.144393	+	0.989520i	$0.546123\pi$
$864$		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	$-0.760489\pi$
$881$	−43.3363			−1.46004			−0.730018	+	0.683427i	$0.760489\pi$
$882$		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	$-0.561540\pi$
$887$	−11.4443			−0.384262			−0.192131	+	0.981369i	$0.561540\pi$
$888$		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	0.611528	−	0.791223i	$-0.290555\pi$
$911$	7.00460	+	4.04411i	0.232073	+	0.133987i	−0.379455	+	0.925210i	$0.623889\pi$
$912$		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	−0.996276	−	0.0862175i	$-0.972522\pi$
$919$	−12.8375	+	22.2353i	−0.423472	+	0.733474i	0.572805	+	0.819692i	$0.305855\pi$
$920$	−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	$-0.223638\pi$
$929$	−5.42618	−	9.39842i	−0.178027	−	0.308352i	−0.941205	+	0.337837i	$0.890305\pi$
$930$		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	$-0.794962\pi$
$941$	3.68890	−	6.38937i	0.120255	−	0.208287i	0.919868	+	0.392228i	$0.128296\pi$
$942$		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	−0.659145	−	0.752016i	$-0.729082\pi$
$947$	−10.3846	+	5.99552i	−0.337453	+	0.194828i	0.321692	+	0.946844i	$0.395748\pi$
$948$		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	$0.399479\pi$
$953$			58.6883i			1.90110i	−0.310572	+	0.950550i	$0.600521\pi$
$954$		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	0.806632	−	0.591054i	$-0.201288\pi$
$967$	−3.37560	−	5.84671i	−0.108552	−	0.188018i	−0.915184	+	0.403037i	$0.867955\pi$
$968$		−	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	$-0.866116\pi$
$971$	−3.20362	+	5.54883i	−0.102809	+	0.178070i	0.810032	+	0.586386i	$0.199450\pi$
$972$		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	0.676414	−	0.736521i	$-0.263533\pi$
$977$	11.7769	+	6.79937i	0.376775	+	0.217531i	−0.299639	+	0.954053i	$0.596866\pi$
$978$		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	$-0.381711\pi$
$983$	22.7698			0.726244			0.363122	+	0.931742i	$0.381711\pi$
$984$		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	0.996757	−	0.0804680i	$-0.0256415\pi$
$991$	13.4953	+	23.3745i	0.428691	+	0.742515i	−0.568066	+	0.822983i	$0.692308\pi$
$992$	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.1979.3		16
3.2	odd	2		882.2.t.b.803.5		16
7.2	even	3		378.2.m.a.251.6		16
7.3	odd	6		2646.2.l.b.521.3		16
7.4	even	3		2646.2.l.b.521.2		16
7.5	odd	6		378.2.m.a.251.7		16
7.6	odd	2	inner	2646.2.t.a.1979.2		16
9.4	even	3		882.2.l.a.509.2		16
9.5	odd	6		2646.2.l.b.1097.7		16
21.2	odd	6		126.2.m.a.83.3	yes	16
21.5	even	6		126.2.m.a.83.2	yes	16
21.11	odd	6		882.2.l.a.227.7		16
21.17	even	6		882.2.l.a.227.6		16
21.20	even	2		882.2.t.b.803.8		16
28.19	even	6		3024.2.cc.b.2897.7		16
28.23	odd	6		3024.2.cc.b.2897.2		16
63.2	odd	6		1134.2.d.a.1133.10		16
63.4	even	3		882.2.t.b.815.8		16
63.5	even	6		378.2.m.a.125.6		16
63.13	odd	6		882.2.l.a.509.3		16
63.16	even	3		1134.2.d.a.1133.7		16
63.23	odd	6		378.2.m.a.125.7		16
63.31	odd	6		882.2.t.b.815.5		16
63.32	odd	6	inner	2646.2.t.a.2285.2		16
63.40	odd	6		126.2.m.a.41.3	yes	16
63.41	even	6		2646.2.l.b.1097.6		16
63.47	even	6		1134.2.d.a.1133.15		16
63.58	even	3		126.2.m.a.41.2	✓	16
63.59	even	6	inner	2646.2.t.a.2285.3		16
63.61	odd	6		1134.2.d.a.1133.2		16
84.23	even	6		1008.2.cc.b.209.3		16
84.47	odd	6		1008.2.cc.b.209.6		16
252.23	even	6		3024.2.cc.b.881.7		16
252.103	even	6		1008.2.cc.b.545.3		16
252.131	odd	6		3024.2.cc.b.881.2		16
252.247	odd	6		1008.2.cc.b.545.6		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
126.2.m.a.41.2	✓	16	63.58	even	3
126.2.m.a.41.3	yes	16	63.40	odd	6
126.2.m.a.83.2	yes	16	21.5	even	6
126.2.m.a.83.3	yes	16	21.2	odd	6
378.2.m.a.125.6		16	63.5	even	6
378.2.m.a.125.7		16	63.23	odd	6
378.2.m.a.251.6		16	7.2	even	3
378.2.m.a.251.7		16	7.5	odd	6
882.2.l.a.227.6		16	21.17	even	6
882.2.l.a.227.7		16	21.11	odd	6
882.2.l.a.509.2		16	9.4	even	3
882.2.l.a.509.3		16	63.13	odd	6
882.2.t.b.803.5		16	3.2	odd	2
882.2.t.b.803.8		16	21.20	even	2
882.2.t.b.815.5		16	63.31	odd	6
882.2.t.b.815.8		16	63.4	even	3
1008.2.cc.b.209.3		16	84.23	even	6
1008.2.cc.b.209.6		16	84.47	odd	6
1008.2.cc.b.545.3		16	252.103	even	6
1008.2.cc.b.545.6		16	252.247	odd	6
1134.2.d.a.1133.2		16	63.61	odd	6
1134.2.d.a.1133.7		16	63.16	even	3
1134.2.d.a.1133.10		16	63.2	odd	6
1134.2.d.a.1133.15		16	63.47	even	6
2646.2.l.b.521.2		16	7.4	even	3
2646.2.l.b.521.3		16	7.3	odd	6
2646.2.l.b.1097.6		16	63.41	even	6
2646.2.l.b.1097.7		16	9.5	odd	6
2646.2.t.a.1979.2		16	7.6	odd	2	inner
2646.2.t.a.1979.3		16	1.1	even	1	trivial
2646.2.t.a.2285.2		16	63.32	odd	6	inner
2646.2.t.a.2285.3		16	63.59	even	6	inner
3024.2.cc.b.881.2		16	252.131	odd	6
3024.2.cc.b.881.7		16	252.23	even	6
3024.2.cc.b.2897.2		16	28.23	odd	6
3024.2.cc.b.2897.7		16	28.19	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 2646 = 2 \cdot 3^{3} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2646.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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