LMFDB - Embedded newform 882.2.t.b.803.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [882,2,Mod(803,882)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(882, 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("882.803");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 882 = 2 \cdot 3^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	882.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:	$7.04280545828$
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:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{2}\cdot 3^{2} $
Twist minimal:	no (minimal twist has level 126)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			803.5
Root			$1.40917 + 1.00709i$ of defining polynomial
Character	$\chi$	$=$	882.803
Dual form			882.2.t.b.815.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.866025 - 0.500000i) q^{2} +(-1.57675 - 0.716830i) q^{3} +(0.500000 - 0.866025i) q^{4} -2.34936 q^{5} +(-1.72392 + 0.167584i) q^{6} -1.00000i q^{8} +(1.97231 + 2.26053i) q^{9} +O(q^{10})$	\(q+(0.866025 - 0.500000i) q^{2} +(-1.57675 - 0.716830i) q^{3} +(0.500000 - 0.866025i) q^{4} -2.34936 q^{5} +(-1.72392 + 0.167584i) q^{6} -1.00000i q^{8} +(1.97231 + 2.26053i) q^{9} +(-2.03460 + 1.17468i) q^{10} +5.67667i q^{11} +(-1.40917 + 1.00709i) q^{12} +(1.48943 - 0.859925i) q^{13} +(3.70436 + 1.68409i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(0.884414 + 1.53185i) q^{17} +(2.83834 + 0.971521i) q^{18} +(0.986680 + 0.569660i) q^{19} +(-1.17468 + 2.03460i) q^{20} +(2.83834 + 4.91614i) q^{22} -3.67509i q^{23} +(-0.716830 + 1.57675i) q^{24} +0.519482 q^{25} +(0.859925 - 1.48943i) q^{26} +(-1.48943 - 4.97811i) q^{27} +(3.59886 + 2.07781i) q^{29} +(4.05012 - 0.393716i) q^{30} +(7.24879 + 4.18509i) q^{31} +(-0.866025 - 0.500000i) q^{32} +(4.06921 - 8.95072i) q^{33} +(1.53185 + 0.884414i) q^{34} +(2.94383 - 0.577806i) q^{36} +(4.59886 - 7.96547i) q^{37} +1.13932 q^{38} +(-2.96489 + 0.288220i) q^{39} +2.34936i q^{40} +(3.99709 + 6.92317i) q^{41} +(1.76053 - 3.04933i) q^{43} +(4.91614 + 2.83834i) q^{44} +(-4.63366 - 5.31079i) q^{45} +(-1.83755 - 3.18272i) q^{46} +(5.90494 + 10.2277i) q^{47} +(0.167584 + 1.72392i) q^{48} +(0.449885 - 0.259741i) q^{50} +(-0.296428 - 3.04933i) q^{51} -1.71985i q^{52} +(-3.77894 - 3.56645i) q^{54} -13.3365i q^{55} +(-1.14740 - 1.60550i) q^{57} +4.15561 q^{58} +(1.11483 - 1.93094i) q^{59} +(3.31064 - 2.36603i) q^{60} +(-7.79396 + 4.49985i) q^{61} +8.37019 q^{62} -1.00000 q^{64} +(-3.49921 + 2.02027i) q^{65} +(-0.951321 - 9.78615i) q^{66} +(-5.43562 + 9.41477i) q^{67} +1.76883 q^{68} +(-2.63442 + 5.79472i) q^{69} +4.52106i q^{71} +(2.26053 - 1.97231i) q^{72} +(4.62660 - 2.67117i) q^{73} -9.19773i q^{74} +(-0.819096 - 0.372380i) q^{75} +(0.986680 - 0.569660i) q^{76} +(-2.42356 + 1.73205i) q^{78} +(6.51422 + 11.2830i) q^{79} +(1.17468 + 2.03460i) q^{80} +(-1.21999 + 8.91693i) q^{81} +(6.92317 + 3.99709i) q^{82} +(-6.27298 + 10.8651i) q^{83} +(-2.07781 - 3.59886i) q^{85} -3.52106i q^{86} +(-4.18509 - 5.85596i) q^{87} +5.67667 q^{88} +(0.580529 - 1.00551i) q^{89} +(-6.66826 - 2.28245i) q^{90} +(-3.18272 - 1.83755i) q^{92} +(-8.42957 - 11.7950i) q^{93} +(10.2277 + 5.90494i) q^{94} +(-2.31806 - 1.33834i) q^{95} +(1.00709 + 1.40917i) q^{96} +(-3.97536 - 2.29517i) q^{97} +(-12.8323 + 11.1962i) q^{99} +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} + 12 q^{30} + 12 q^{36} + 4 q^{37} + 36 q^{39} + 4 q^{43} + 12 q^{44} - 12 q^{46} + 60 q^{50} - 36 q^{51} + 48 q^{57} + 24 q^{58} - 24 q^{60} - 16 q^{64} - 84 q^{65} - 28 q^{67} + 12 q^{72} - 24 q^{78} - 4 q^{79} - 36 q^{81} - 12 q^{85} - 48 q^{92} + 12 q^{93} - 12 q^{95} - 72 q^{99}+O(q^{100}) $ 16 * q + 8 * q^4 - 8 * q^16 + 16 * q^25 - 12 * q^29 + 12 * q^30 + 12 * q^36 + 4 * q^37 + 36 * q^39 + 4 * q^43 + 12 * q^44 - 12 * q^46 + 60 * q^50 - 36 * q^51 + 48 * q^57 + 24 * q^58 - 24 * q^60 - 16 * q^64 - 84 * q^65 - 28 * q^67 + 12 * q^72 - 24 * q^78 - 4 * q^79 - 36 * q^81 - 12 * q^85 - 48 * q^92 + 12 * q^93 - 12 * q^95 - 72 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/882\mathbb{Z}\right)^\times$.

$n$	$199$	$785$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{6}\right)$

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
$3$	−1.57675	−	0.716830i	−0.910340	−	0.413862i
$3$	−1.57675	−	0.716830i	−0.910340	−	0.413862i
$4$	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	$0.676059\pi$
$6$	−1.72392	+	0.167584i	−0.703789	+	0.0684160i
$7$		0			0
$7$		0			0
$8$		−	1.00000i		−	0.353553i
$9$	1.97231	+	2.26053i	0.657437	+	0.753510i
$10$	−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	$0.673071\pi$
$12$	−1.40917	+	1.00709i	−0.406792	+	0.290723i
$13$	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
$15$	3.70436	+	1.68409i	0.956462	+	0.434830i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	0.884414	+	1.53185i	0.214502	+	0.371528i	0.953118	−	0.302598i	$-0.0978538\pi$
$17$	0.884414	+	1.53185i	0.214502	+	0.371528i	−0.738616	+	0.674126i	$0.764520\pi$
$18$	2.83834	+	0.971521i	0.669002	+	0.228990i
$19$	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	$-0.874838\pi$
$23$		−	3.67509i		−	0.766310i	0.923684	−	0.383155i	$-0.125162\pi$
$24$	−0.716830	+	1.57675i	−0.146322	+	0.321854i
$25$	0.519482			0.103896
$26$	0.859925	−	1.48943i	0.168645	−	0.292102i
$27$	−1.48943	−	4.97811i	−0.286642	−	0.958038i
$28$		0			0
$29$	3.59886	+	2.07781i	0.668292	+	0.385839i	0.795429	−	0.606046i	$-0.207245\pi$
$29$	3.59886	+	2.07781i	0.668292	+	0.385839i	−0.127137	+	0.991885i	$0.540579\pi$
$30$	4.05012	−	0.393716i	0.739447	−	0.0718823i
$31$	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
$33$	4.06921	−	8.95072i	0.708358	−	1.55812i
$34$	1.53185	+	0.884414i	0.262710	+	0.151676i
$35$		0			0
$36$	2.94383	−	0.577806i	0.490638	−	0.0963009i
$37$	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
$39$	−2.96489	+	0.288220i	−0.474762	+	0.0461521i
$40$			2.34936i			0.371466i
$41$	3.99709	+	6.92317i	0.624241	+	1.08122i	0.988687	+	0.149993i	$0.0479251\pi$
$41$	3.99709	+	6.92317i	0.624241	+	1.08122i	−0.364446	+	0.931225i	$0.618742\pi$
$42$		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
$45$	−4.63366	−	5.31079i	−0.690745	−	0.791686i
$46$	−1.83755	−	3.18272i	−0.270931	−	0.469267i
$47$	5.90494	+	10.2277i	0.861324	+	1.49186i	0.870651	+	0.491901i	$0.163698\pi$
$47$	5.90494	+	10.2277i	0.861324	+	1.49186i	−0.00932669	+	0.999957i	$0.502969\pi$
$48$	0.167584	+	1.72392i	0.0241887	+	0.248827i
$49$		0			0
$50$	0.449885	−	0.259741i	0.0636233	−	0.0367329i
$51$	−0.296428	−	3.04933i	−0.0415082	−	0.426991i
$52$		−	1.71985i		−	0.238500i
$53$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$53$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$54$	−3.77894	−	3.56645i	−0.514249	−	0.485333i
$55$		−	13.3365i		−	1.79830i
$56$		0			0
$57$	−1.14740	−	1.60550i	−0.151977	−	0.212653i
$58$	4.15561			0.545658
$59$	1.11483	−	1.93094i	0.145139	−	0.251387i	−0.784286	−	0.620399i	$-0.786971\pi$
$59$	1.11483	−	1.93094i	0.145139	−	0.251387i	0.929425	+	0.369012i	$0.120304\pi$
$60$	3.31064	−	2.36603i	0.427402	−	0.305453i
$61$	−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
$66$	−0.951321	−	9.78615i	−0.117100	−	1.20459i
$67$	−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
$69$	−2.63442	+	5.79472i	−0.317147	+	0.697602i
$70$		0			0
$71$			4.52106i			0.536551i	0.963342	+	0.268276i	$0.0864538\pi$
$71$			4.52106i			0.536551i	−0.963342	+	0.268276i	$0.913546\pi$
$72$	2.26053	−	1.97231i	0.266406	−	0.232439i
$73$	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
$75$	−0.819096	−	0.372380i	−0.0945810	−	0.0429988i
$76$	0.986680	−	0.569660i	0.113180	−	0.0653445i
$77$		0			0
$78$	−2.42356	+	1.73205i	−0.274414	+	0.196116i
$79$	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
$81$	−1.21999	+	8.91693i	−0.135554	+	0.990770i
$82$	6.92317	+	3.99709i	0.764536	+	0.441405i
$83$	−6.27298	+	10.8651i	−0.688549	+	1.19260i	0.283758	+	0.958896i	$0.408419\pi$
$83$	−6.27298	+	10.8651i	−0.688549	+	1.19260i	−0.972307	+	0.233707i	$0.924915\pi$
$84$		0			0
$85$	−2.07781	−	3.59886i	−0.225370	−	0.390352i
$86$		−	3.52106i		−	0.379686i
$87$	−4.18509	−	5.85596i	−0.448689	−	0.627825i
$88$	5.67667			0.605135
$89$	0.580529	−	1.00551i	0.0615360	−	0.106583i	−0.833616	−	0.552344i	$-0.813733\pi$
$89$	0.580529	−	1.00551i	0.0615360	−	0.106583i	0.895152	+	0.445761i	$0.147067\pi$
$90$	−6.66826	−	2.28245i	−0.702897	−	0.240591i
$91$		0			0
$92$	−3.18272	−	1.83755i	−0.331822	−	0.191577i
$93$	−8.42957	−	11.7950i	−0.874106	−	1.22309i
$94$	10.2277	+	5.90494i	1.05490	+	0.609048i
$95$	−2.31806	−	1.33834i	−0.237828	−	0.137310i
$96$	1.00709	+	1.40917i	0.102786	+	0.143823i
$97$	−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
$99$	−12.8323	+	11.1962i	−1.28969	+	1.12526i
$100$	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	$0.606884\pi$
$102$	−1.78138	−	2.49258i	−0.176383	−	0.246802i
$103$		−	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	$-0.260135\pi$
$107$	4.08386	+	2.35782i	0.394802	+	0.227939i	−0.289437	+	0.957197i	$0.593468\pi$
$108$	−5.05589	−	1.19917i	−0.486503	−	0.115390i
$109$	−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
$111$	−12.9612	+	9.26298i	−1.23022	+	0.879203i
$112$		0			0
$113$	5.91693	−	3.41614i	0.556618	−	0.321363i	−0.195169	−	0.980770i	$-0.562526\pi$
$113$	5.91693	−	3.41614i	0.556618	−	0.321363i	0.751787	+	0.659406i	$0.229192\pi$
$114$	−1.79643	−	0.816699i	−0.168251	−	0.0764908i
$115$			8.63411i			0.805135i
$116$	3.59886	−	2.07781i	0.334146	−	0.192919i
$117$	4.88151	+	1.67087i	0.451296	+	0.154472i
$118$		−	2.22966i		−	0.205257i
$119$		0			0
$120$	1.68409	−	3.70436i	0.153736	−	0.338160i
$121$	−21.2246			−1.92951
$122$	−4.49985	+	7.79396i	−0.407397	+	0.705632i
$123$	−1.33970	−	13.7814i	−0.120797	−	1.24262i
$124$	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
$129$	−4.96177	+	3.54604i	−0.436860	+	0.312211i
$130$	−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	$0.605856\pi$
$132$	−5.71694	−	7.99939i	−0.497596	−	0.696258i
$133$		0			0
$134$			10.8712i			0.939133i
$135$	3.49921	+	11.6954i	0.301164	+	1.00658i
$136$	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	$-0.110842\pi$
$138$	0.615888	+	6.33558i	0.0524279	+	0.539321i
$139$	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
$141$	−1.97915	−	20.3593i	−0.166675	−	1.71457i
$142$	2.26053	+	3.91535i	0.189699	+	0.328569i
$143$	4.88151	+	8.45502i	0.408212	+	0.707044i
$144$	0.971521	−	2.83834i	0.0809601	−	0.236528i
$145$	−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	$-0.0156228\pi$
$150$	−0.895548	+	0.0870571i	−0.0731212	+	0.00710818i
$151$	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
$153$	−1.71845	+	5.02053i	−0.138929	+	0.405886i
$154$		0			0
$155$	−17.0300	−	9.83228i	−1.36788	−	0.789748i
$156$	−1.23284	+	2.71178i	−0.0987061	+	0.217116i
$157$	−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
$162$	3.40192	+	8.33228i	0.267280	+	0.654646i
$163$	−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
$165$	−9.56002	+	21.0284i	−0.744247	+	1.63706i
$166$			12.5460i			0.973756i
$167$	8.57472	+	14.8518i	0.663532	+	1.14927i	0.979681	+	0.200561i	$0.0642765\pi$
$167$	8.57472	+	14.8518i	0.663532	+	1.14927i	−0.316150	+	0.948709i	$0.602390\pi$
$168$		0			0
$169$	−5.02106	+	8.69673i	−0.386235	+	0.668979i
$170$	−3.59886	−	2.07781i	−0.276020	−	0.159360i
$171$	0.658305	+	3.35397i	0.0503419	+	0.256484i
$172$	−1.76053	−	3.04933i	−0.134239	−	0.232509i
$173$	0.993738	+	1.72121i	0.0755525	+	0.130861i	0.901326	−	0.433140i	$-0.142595\pi$
$173$	0.993738	+	1.72121i	0.0755525	+	0.130861i	−0.825774	+	0.564001i	$0.809261\pi$
$174$	−6.55238	−	2.97887i	−0.496735	−	0.225827i
$175$		0			0
$176$	4.91614	−	2.83834i	0.370568	−	0.213948i
$177$	−3.14197	+	2.24548i	−0.236165	+	0.168781i
$178$		−	1.16106i		−	0.0870250i
$179$	−7.19773	+	4.15561i	−0.537984	+	0.310605i	−0.744261	−	0.667889i	$-0.767198\pi$
$179$	−7.19773	+	4.15561i	−0.537984	+	0.310605i	0.206278	+	0.978493i	$0.433865\pi$
$180$	−6.91611	+	1.35747i	−0.515497	+	0.101180i
$181$		−	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
$183$	15.5148	−	1.50821i	1.14689	−	0.111490i
$184$	−3.67509			−0.270931
$185$	−10.8044	+	18.7137i	−0.794354	+	1.37586i
$186$	−13.1977	−	6.00000i	−0.967704	−	0.439941i
$187$	−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	$-0.813952\pi$
$191$	−10.6851	+	6.16904i	−0.773146	+	0.446376i	0.0608498	+	0.998147i	$0.480619\pi$
$192$	1.57675	+	0.716830i	0.113792	+	0.0517327i
$193$	−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
$195$	6.96559	−	0.677132i	0.498816	−	0.0484904i
$196$		0			0
$197$		−	10.8865i		−	0.775632i	−0.921737	−	0.387816i	$-0.873230\pi$
$197$		−	10.8865i		−	0.775632i	0.921737	−	0.387816i	$-0.126770\pi$
$198$	−5.51501	+	16.1123i	−0.391934	+	1.14505i
$199$	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
$201$	15.3194	−	10.9484i	1.08055	−	0.772239i
$202$	−5.73577	+	3.31155i	−0.403567	+	0.233000i
$203$		0			0
$204$	−2.78901	−	1.26795i	−0.195270	−	0.0887742i
$205$	−9.39060	−	16.2650i	−0.655868	−	1.13600i
$206$	−2.92989	−	5.07471i	−0.204135	−	0.353572i
$207$	8.30766	−	7.24842i	0.577422	−	0.503800i
$208$	−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
$213$	3.24083	−	7.12860i	0.222058	−	0.488444i
$214$	4.71563			0.322354
$215$	−4.13611	+	7.16396i	−0.282081	+	0.488578i
$216$	−4.97811	+	1.48943i	−0.338718	+	0.101343i
$217$		0			0
$218$	−3.66908	−	2.11835i	−0.248502	−	0.143473i
$219$	−9.20979	+	0.895293i	−0.622340	+	0.0604983i
$220$	−11.5498	−	6.66826i	−0.778686	−	0.449574i
$221$	2.63455	+	1.52106i	0.177219	+	0.102318i
$222$	−6.59321	+	14.5026i	−0.442507	+	0.973348i
$223$	−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
$225$	1.02458	+	1.17430i	0.0683053	+	0.0782870i
$226$	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	$0.639136\pi$
$228$	−1.96410	+	0.190932i	−0.130076	+	0.0126448i
$229$			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	$-0.310855\pi$
$233$	1.86545	+	1.07702i	0.122210	+	0.0705577i	−0.437649	+	0.899146i	$0.644189\pi$
$234$	5.06295	−	0.993738i	0.330975	−	0.0649627i
$235$	−13.8728	−	24.0284i	−0.904963	−	1.56744i
$236$	−1.11483	−	1.93094i	−0.0725693	−	0.125694i
$237$	−2.18336	−	22.4600i	−0.141825	−	1.45894i
$238$		0			0
$239$	−8.78317	+	5.07096i	−0.568136	+	0.328013i	−0.756404	−	0.654104i	$-0.773046\pi$
$239$	−8.78317	+	5.07096i	−0.568136	+	0.328013i	0.188269	+	0.982118i	$0.439712\pi$
$240$	−0.393716	−	4.05012i	−0.0254142	−	0.261434i
$241$		−	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
$243$	8.31554	−	13.1853i	0.533442	−	0.845836i
$244$			8.99970i			0.576146i
$245$		0			0
$246$	−8.05090	−	11.2652i	−0.513307	−	0.718241i
$247$	1.95946			0.124677
$248$	4.18509	−	7.24879i	0.265754	−	0.460299i
$249$	17.6794	−	12.6350i	1.12039	−	0.800709i
$250$	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
$255$	0.696415	+	7.16396i	0.0436112	+	0.448625i
$256$	−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	$0.423531\pi$
$258$	−2.52400	+	5.55185i	−0.157137	+	0.345643i
$259$		0			0
$260$			4.04054i			0.250584i
$261$	2.40114	+	12.2334i	0.148627	+	0.757229i
$262$	−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	$0.877403\pi$
$264$	−8.95072	−	4.06921i	−0.550878	−	0.250442i
$265$		0			0
$266$		0			0
$267$	−1.63613	+	1.16930i	−0.100129	+	0.0715597i
$268$	5.43562	+	9.41477i	0.332034	+	0.575099i
$269$	−1.38717	−	2.40264i	−0.0845771	−	0.146492i	0.820634	−	0.571454i	$-0.193621\pi$
$269$	−1.38717	−	2.40264i	−0.0845771	−	0.146492i	−0.905211	+	0.424963i	$0.860287\pi$
$270$	8.87809	+	8.37888i	0.540303	+	0.509922i
$271$	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
$276$	3.70117	+	5.17883i	0.222784	+	0.311729i
$277$	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
$279$	4.83634	+	24.6404i	0.289544	+	1.47518i
$280$		0			0
$281$	4.21999	+	2.43641i	0.251743	+	0.145344i	0.620562	−	0.784157i	$-0.286904\pi$
$281$	4.21999	+	2.43641i	0.251743	+	0.145344i	−0.368819	+	0.929501i	$0.620238\pi$
$282$	−11.8937	−	16.6421i	−0.708258	−	0.991025i
$283$	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
$285$	2.69566	+	3.77188i	0.159677	+	0.223427i
$286$	8.45502	+	4.88151i	0.499956	+	0.288650i
$287$		0			0
$288$	−0.577806	−	2.94383i	−0.0340475	−	0.173467i
$289$	6.93562	−	12.0129i	0.407978	−	0.706638i
$290$	−9.76302			−0.573304
$291$	4.62291	+	6.46858i	0.271000	+	0.379195i
$292$		−	5.34234i		−	0.312637i
$293$	−4.05694	−	7.02683i	−0.237009	−	0.410512i	0.722846	−	0.691010i	$-0.242834\pi$
$293$	−4.05694	−	7.02683i	−0.237009	−	0.410512i	−0.959855	+	0.280498i	$0.909500\pi$
$294$		0			0
$295$	−2.61914	+	4.53648i	−0.152492	+	0.264124i
$296$	−7.96547	−	4.59886i	−0.462983	−	0.267304i
$297$	28.2591	−	8.45502i	1.63976	−	0.490610i
$298$	−0.598865	−	1.03726i	−0.0346913	−	0.0600871i
$299$	−3.16030	−	5.47381i	−0.182765	−	0.316558i
$300$	−0.732039	+	0.523168i	−0.0422643	+	0.0302051i
$301$		0			0
$302$	13.1849	−	7.61229i	0.758705	−	0.438038i
$303$	10.4430	+	4.74763i	0.599935	+	0.272744i
$304$		−	1.13932i		−	0.0653445i
$305$	18.3108	−	10.5718i	1.04847	−	0.605337i
$306$	1.02204	+	5.20713i	0.0584261	+	0.297672i
$307$			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
$309$	−4.20046	+	9.23943i	−0.238956	+	0.525613i
$310$	−19.6646			−1.11687
$311$	4.11819	−	7.13291i	0.233521	−	0.404470i	−0.725321	−	0.688411i	$-0.758309\pi$
$311$	4.11819	−	7.13291i	0.233521	−	0.404470i	0.958842	+	0.283941i	$0.0916419\pi$
$312$	0.288220	+	2.96489i	0.0163172	+	0.167854i
$313$	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	−0.654685	−	0.755902i	$-0.727199\pi$
$317$	−5.82913	+	3.36545i	−0.327396	+	0.189022i	0.327288	+	0.944925i	$0.393865\pi$
$318$		0			0
$319$	−11.7950	+	20.4296i	−0.660394	+	1.14384i
$320$	2.34936			0.131333
$321$	−4.74909	−	6.64513i	−0.265068	−	0.370895i
$322$		0			0
$323$			2.01526i			0.112132i
$324$	7.11229	+	5.51501i	0.395127	+	0.306389i
$325$	0.773734	−	0.446715i	0.0429190	−	0.0247793i
$326$			12.0032i			0.664793i
$327$	0.710004	+	7.30374i	0.0392633	+	0.403898i
$328$	6.92317	−	3.99709i	0.382268	−	0.220703i
$329$		0			0
$330$	2.23499	+	22.9912i	0.123032	+	1.26562i
$331$	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
$333$	27.0766	−	5.31450i	1.48379	−	0.291233i
$334$	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
$339$	−11.7783	+	1.14498i	−0.639711	+	0.0621870i
$340$	−4.15561			−0.225370
$341$	−23.7574	+	41.1490i	−1.28654	+	2.22834i
$342$	2.24709	+	2.57547i	0.121509	+	0.139265i
$343$		0			0
$344$	−3.04933	−	1.76053i	−0.164409	−	0.0949214i
$345$	6.18919	−	13.6139i	0.333215	−	0.732946i
$346$	1.72121	+	0.993738i	0.0925326	+	0.0534237i
$347$	−19.7453	−	11.3999i	−1.05998	−	0.611981i	−0.134554	−	0.990906i	$-0.542960\pi$
$347$	−19.7453	−	11.3999i	−1.05998	−	0.611981i	−0.925427	+	0.378926i	$0.876294\pi$
$348$	−7.16396	+	0.696415i	−0.384029	+	0.0373318i
$349$	−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
$351$	−6.49921	−	6.13376i	−0.346902	−	0.327396i
$352$	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	$0.439111\pi$
$354$	−1.59829	+	3.51563i	−0.0849480	+	0.186854i
$355$		−	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	$-0.234272\pi$
$359$	10.0491	+	5.80186i	0.530372	+	0.306210i	−0.210796	+	0.977530i	$0.567606\pi$
$360$	−5.31079	+	4.63366i	−0.279903	+	0.244215i
$361$	−8.85097	−	15.3303i	−0.465841	−	0.806860i
$362$	−7.72706	−	13.3837i	−0.406125	−	0.703429i
$363$	33.4660	+	15.2144i	1.75651	+	0.798550i
$364$		0			0
$365$	−10.8695	+	6.27554i	−0.568938	+	0.328477i
$366$	12.6821	−	9.06354i	0.662904	−	0.473759i
$367$		−	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
$369$	−7.76652	+	22.6902i	−0.404309	+	1.18120i
$370$			21.6088i			1.12339i
$371$		0			0
$372$	−14.4296	+	1.40271i	−0.748138	+	0.0727272i
$373$	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
$375$	−16.5975	−	7.54560i	−0.857089	−	0.389653i
$376$	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
$381$	10.5275	+	4.78604i	0.539339	+	0.245196i
$382$	−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	$0.512418\pi$
$384$	1.72392	−	0.167584i	0.0879737	−	0.00855200i
$385$		0			0
$386$			4.39388i			0.223643i
$387$	10.3654	−	2.03449i	0.526903	−	0.103419i
$388$	−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	$-0.123205\pi$
$390$	5.69381	−	4.06921i	0.288317	−	0.206052i
$391$	5.62969	−	3.25030i	0.284706	−	0.164375i
$392$		0			0
$393$	11.7832	+	5.35691i	0.594382	+	0.270220i
$394$	−5.44325	−	9.42799i	−0.274227	−	0.474975i
$395$	−15.3042	−	26.5077i	−0.770039	−	1.33375i
$396$	3.28001	+	16.7112i	0.164827	+	0.839767i
$397$	−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	$-0.597824\pi$
$401$		−	38.1735i		−	1.90629i	0.302507	−	0.953147i	$-0.402176\pi$
$402$	7.79283	−	17.1413i	0.388671	−	0.854930i
$403$	14.3955			0.717089
$404$	−3.31155	+	5.73577i	−0.164756	+	0.285365i
$405$	2.86619	−	20.9491i	0.142422	−	1.04097i
$406$		0			0
$407$	45.2173	+	26.1062i	2.24134	+	1.29404i
$408$	−3.04933	+	0.296428i	−0.150964	+	0.0146754i
$409$	−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
$411$	−5.72596	+	12.5949i	−0.282441	+	0.621263i
$412$	−5.07471	−	2.92989i	−0.250013	−	0.144345i
$413$		0			0
$414$	3.57043	−	10.4311i	0.175477	−	0.512663i
$415$	14.7375	−	25.5261i	0.723435	−	1.25303i
$416$	−1.71985			−0.0843225
$417$	−35.7897	+	3.47915i	−1.75263	+	0.170375i
$418$			6.46754i			0.316338i
$419$	−17.4232	−	30.1778i	−0.851177	−	1.47428i	−0.880146	−	0.474702i	$-0.842556\pi$
$419$	−17.4232	−	30.1778i	−0.851177	−	1.47428i	0.0289690	−	0.999580i	$-0.490778\pi$
$420$		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
$423$	−11.4736	+	33.5204i	−0.557863	+	1.62982i
$424$		0			0
$425$	0.459437	+	0.795769i	0.0222860	+	0.0386005i
$426$	−0.757659	−	7.79396i	−0.0367087	−	0.377619i
$427$		0			0
$428$	4.08386	−	2.35782i	0.197401	−	0.113969i
$429$	−1.63613	−	16.8307i	−0.0789931	−	0.812594i
$430$			8.27223i			0.398922i
$431$	26.2350	−	15.1468i	1.26370	−	0.729595i	0.289908	−	0.957055i	$-0.406375\pi$
$431$	26.2350	−	15.1468i	1.26370	−	0.729595i	0.973787	+	0.227460i	$0.0730420\pi$
$432$	−3.56645	+	3.77894i	−0.171591	+	0.181814i
$433$			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
$435$	9.83228	+	13.7578i	0.471422	+	0.659634i
$436$	−4.23669			−0.202901
$437$	2.09355	−	3.62614i	0.100148	−	0.173462i
$438$	−7.52827	+	5.38024i	−0.359715	+	0.257078i
$439$	−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	0.0552622	−	0.998472i	$-0.482401\pi$
$443$	19.9446	−	11.5150i	0.947595	−	0.547094i	0.892333	+	0.451377i	$0.149067\pi$
$444$	1.54140	+	15.8562i	0.0731514	+	0.752502i
$445$	−1.36387	+	2.36229i	−0.0646537	+	0.111983i
$446$	−7.20913			−0.341362
$447$	−0.858568	+	1.88853i	−0.0406089	+	0.0893242i
$448$		0			0
$449$		−	15.9028i		−	0.750501i	−0.926923	−	0.375251i	$-0.877557\pi$
$449$		−	15.9028i		−	0.750501i	0.926923	−	0.375251i	$-0.122443\pi$
$450$	1.47446	+	0.504688i	0.0695069	+	0.0237912i
$451$	−39.3006	+	22.6902i	−1.85059	+	1.06844i
$452$		−	6.83228i		−	0.321363i
$453$	−24.0054	−	10.9134i	−1.12787	−	0.512758i
$454$	−11.0470	+	6.37800i	−0.518462	+	0.299334i
$455$		0			0
$456$	−1.60550	+	1.14740i	−0.0751842	+	0.0537321i
$457$	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
$459$	6.30845	−	6.68430i	0.294453	−	0.311996i
$460$	7.47736	+	4.31705i	0.348634	+	0.201284i
$461$	−15.7292	+	27.2438i	−0.732582	+	1.26887i	0.223194	+	0.974774i	$0.428352\pi$
$461$	−15.7292	+	27.2438i	−0.732582	+	1.26887i	−0.955776	+	0.294095i	$0.904982\pi$
$462$		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
$465$	19.8041	+	27.7107i	0.918392	+	1.28505i
$466$	2.15403			0.0997837
$467$	15.1516	−	26.2433i	0.701132	−	1.21440i	−0.266938	−	0.963714i	$-0.586012\pi$
$467$	15.1516	−	26.2433i	0.701132	−	1.21440i	0.968069	−	0.250682i	$-0.0806549\pi$
$468$	3.88777	−	3.39208i	0.179712	−	0.156799i
$469$		0			0
$470$	−24.0284	−	13.8728i	−1.10835	−	0.639906i
$471$	10.0981	+	14.1297i	0.465295	+	0.651061i
$472$	−1.93094	−	1.11483i	−0.0888788	−	0.0513142i
$473$	17.3100	+	9.99395i	0.795916	+	0.459522i
$474$	−13.1209	−	18.3593i	−0.602661	−	0.843270i
$475$	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	$0.466027\pi$
$480$	−2.36603	−	3.31064i	−0.107994	−	0.151110i
$481$		−	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
$486$	0.608830	−	15.5766i	0.0276171	−	0.706567i
$487$	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
$489$	16.9145	−	12.0883i	0.764900	−	0.546652i
$490$		0			0
$491$	−17.7437	+	10.2443i	−0.800762	+	0.462320i	−0.843737	−	0.536756i	$-0.819649\pi$
$491$	−17.7437	+	10.2443i	−0.800762	+	0.462320i	0.0429758	+	0.999076i	$0.486316\pi$
$492$	−12.6049	−	5.73047i	−0.568272	−	0.258350i
$493$			7.35056i			0.331053i
$494$	1.69694	−	0.979729i	0.0763490	−	0.0440801i
$495$	30.1476	−	26.3038i	1.35503	−	1.18227i
$496$		−	8.37019i		−	0.375832i
$497$		0			0
$498$	8.99332	−	19.7819i	0.403000	−	0.886449i
$499$	−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
$501$	−2.87398	−	29.5643i	−0.128400	−	1.32084i
$502$	−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
$507$	14.1511	−	10.1134i	0.628470	−	0.449150i
$508$	−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	$0.235527\pi$
$510$	4.18509	+	5.85596i	0.185319	+	0.259306i
$511$		0			0
$512$			1.00000i			0.0441942i
$513$	1.36624	−	5.76027i	0.0603208	−	0.254322i
$514$	6.60656	−	3.81430i	0.291403	−	0.168242i
$515$			13.7667i			0.606634i
$516$	0.590074	+	6.07004i	0.0259766	+	0.267219i
$517$	−58.0591	+	33.5204i	−2.55343	+	1.47423i
$518$		0			0
$519$	−0.333070	−	3.42626i	−0.0146202	−	0.150396i
$520$	2.02027	+	3.49921i	0.0885947	+	0.153451i
$521$	3.26963	+	5.66316i	0.143245	+	0.248108i	0.928717	−	0.370790i	$-0.120913\pi$
$521$	3.26963	+	5.66316i	0.143245	+	0.248108i	−0.785472	+	0.618897i	$0.787580\pi$
$522$	8.19615	+	9.39388i	0.358736	+	0.411159i
$523$	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
$528$	−9.78615	+	0.951321i	−0.425888	+	0.0414009i
$529$	9.49369			0.412769
$530$		0			0
$531$	6.56374	−	1.28831i	0.284842	−	0.0559079i
$532$		0			0
$533$	11.9068	+	6.87440i	0.515741	+	0.297763i
$534$	−0.832281	+	1.83070i	−0.0360163	+	0.0792223i
$535$	−9.59445	−	5.53936i	−0.414804	−	0.239487i
$536$	9.41477	+	5.43562i	0.406656	+	0.234783i
$537$	14.3279	−	1.39283i	0.618295	−	0.0601051i
$538$	−2.40264	−	1.38717i	−0.103585	−	0.0598050i
$539$		0			0
$540$	11.8781	+	2.81728i	0.511152	+	0.121236i
$541$	−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
$543$	−11.0780	+	24.3673i	−0.475401	+	1.04570i
$544$		−	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
$549$	−25.5442	−	8.74339i	−1.09020	−	0.373159i
$550$	1.47446	+	2.55385i	0.0628714	+	0.108896i
$551$	2.36729	+	4.10026i	0.100850	+	0.174677i
$552$	5.79472	+	2.63442i	0.246640	+	0.112128i
$553$		0			0
$554$	8.73047	−	5.04054i	0.370922	−	0.214152i
$555$	30.4504	−	21.7621i	1.29255	−	0.923748i
$556$		−	20.7606i		−	0.880446i
$557$	−24.0957	+	13.9117i	−1.02097	+	0.589456i	−0.914384	−	0.404848i	$-0.867325\pi$
$557$	−24.0957	+	13.9117i	−1.02097	+	0.589456i	−0.106584	+	0.994304i	$0.533991\pi$
$558$	16.5086	+	18.9211i	0.698865	+	0.800992i
$559$		−	6.05569i		−	0.256128i
$560$		0			0
$561$	17.3100	−	1.68272i	0.730830	−	0.0710447i
$562$	4.87282			0.205548
$563$	12.2650	−	21.2436i	0.516909	−	0.895312i	−0.482898	−	0.875676i	$-0.660416\pi$
$563$	12.2650	−	21.2436i	0.516909	−	0.895312i	0.999807	−	0.0196359i	$-0.00625069\pi$
$564$	−18.6213	−	8.46568i	−0.784098	−	0.356469i
$565$	−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	$-0.474302\pi$
$569$	23.4762	−	13.5540i	0.984172	−	0.568212i	0.903527	+	0.428531i	$0.140969\pi$
$570$	4.22045	+	1.91872i	0.176775	+	0.0803662i
$571$	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
$573$	21.2699	−	2.06767i	0.888563	−	0.0863781i
$574$		0			0
$575$		−	1.90915i		−	0.0796169i
$576$	−1.97231	−	2.26053i	−0.0821796	−	0.0941887i
$577$	−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
$579$	6.19173	−	4.42505i	0.257319	−	0.183899i
$580$	−8.45502	+	4.88151i	−0.351076	+	0.202694i
$581$		0			0
$582$	7.23785	+	3.29050i	0.300018	+	0.136395i
$583$		0			0
$584$	−2.67117	−	4.62660i	−0.110534	−	0.191450i
$585$	−11.4684	−	3.92547i	−0.474160	−	0.162298i
$586$	−7.02683	−	4.05694i	−0.290276	−	0.167591i
$587$	4.95928	−	8.58973i	0.204692	−	0.354536i	−0.745343	−	0.666681i	$-0.767714\pi$
$587$	4.95928	−	8.58973i	0.204692	−	0.354536i	0.950034	+	0.312145i	$0.101048\pi$
$588$		0			0
$589$	4.76816	+	8.25870i	0.196469	+	0.340294i
$590$			5.23827i			0.215656i
$591$	−7.80377	+	17.1653i	−0.321004	+	0.706088i
$592$	−9.19773			−0.378024
$593$	2.34936	−	4.06921i	0.0964766	−	0.167102i	−0.813747	−	0.581219i	$-0.802576\pi$
$593$	2.34936	−	4.06921i	0.0964766	−	0.167102i	0.910224	+	0.414116i	$0.135909\pi$
$594$	20.2456	−	21.4518i	0.830686	−	0.880178i
$595$		0			0
$596$	−1.03726	−	0.598865i	−0.0424880	−	0.0245305i
$597$	−47.5225	+	4.61971i	−1.94497	+	0.189072i
$598$	−5.47381	−	3.16030i	−0.223841	−	0.129234i
$599$	−12.7309	−	7.35019i	−0.520170	−	0.300320i	0.216834	−	0.976208i	$-0.430427\pi$
$599$	−12.7309	−	7.35019i	−0.520170	−	0.300320i	−0.737004	+	0.675888i	$0.763760\pi$
$600$	−0.372380	+	0.819096i	−0.0152024	+	0.0334394i
$601$	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
$603$	−32.0031	+	6.28147i	−1.30327	+	0.255801i
$604$	7.61229	−	13.1849i	0.309740	−	0.536485i
$605$	49.8641			2.02727
$606$	11.4177	−	1.10993i	0.463813	−	0.0450877i
$607$			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
$612$	3.48868	+	3.99849i	0.141021	+	0.161629i
$613$	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
$615$	3.14744	+	32.3774i	0.126917	+	1.30558i
$616$		0			0
$617$	−3.25158	+	1.87730i	−0.130904	+	0.0755772i	−0.564022	−	0.825760i	$-0.690747\pi$
$617$	−3.25158	+	1.87730i	−0.130904	+	0.0755772i	0.433118	+	0.901337i	$0.357413\pi$
$618$	0.982007	+	10.1018i	0.0395021	+	0.406354i
$619$		−	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
$621$	−18.2950	+	5.47381i	−0.734154	+	0.219656i
$622$		−	8.23637i		−	0.330248i
$623$		0			0
$624$	1.73205	+	2.42356i	0.0693375	+	0.0970201i
$625$	−27.3275			−1.09310
$626$	16.9011	−	29.2736i	0.675505	−	1.17001i
$627$	9.11387	−	6.51343i	0.363973	−	0.260121i
$628$	−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
$633$	−1.72800	−	17.7758i	−0.0686818	−	0.706523i
$634$	−3.36545	+	5.82913i	−0.133659	+	0.231504i
$635$	15.6859			0.622475
$636$		0			0
$637$		0			0
$638$			23.5900i			0.933938i
$639$	−10.2200	+	8.91693i	−0.404296	+	0.352748i
$640$	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	$0.827087\pi$
$642$	−7.43540	−	3.38031i	−0.293452	−	0.133410i
$643$	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
$645$	11.6570	−	8.33092i	0.458993	−	0.328029i
$646$	1.00763	+	1.74527i	0.0396447	+	0.0686666i
$647$	−16.0063	−	27.7237i	−0.629273	−	1.08993i	−0.987698	−	0.156374i	$-0.950019\pi$
$647$	−16.0063	−	27.7237i	−0.629273	−	1.08993i	0.358425	−	0.933558i	$-0.383314\pi$
$648$	8.91693	+	1.21999i	0.350290	+	0.0479257i
$649$	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	$0.855827\pi$
$654$	4.26675	+	5.97022i	0.166843	+	0.233454i
$655$	17.5569			0.686004
$656$	3.99709	−	6.92317i	0.156060	−	0.270304i
$657$	15.1634	+	5.19020i	0.591579	+	0.202489i
$658$		0			0
$659$	−19.2546	−	11.1166i	−0.750053	−	0.433043i	0.0756603	−	0.997134i	$-0.475894\pi$
$659$	−19.2546	−	11.1166i	−0.750053	−	0.433043i	−0.825713	+	0.564091i	$0.809227\pi$
$660$	13.4311	+	18.7934i	0.522807	+	0.731534i
$661$	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
$663$	−3.06370	−	4.28686i	−0.118984	−	0.166488i
$664$	10.8651	+	6.27298i	0.421649	+	0.243439i
$665$		0			0
$666$	20.7917	−	18.1408i	0.805664	−	0.702941i
$667$	7.63613	−	13.2262i	0.295672	−	0.512119i
$668$	17.1494			0.663532
$669$	7.26027	+	10.1589i	0.280698	+	0.392765i
$670$		−	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
$675$	−0.773734	−	2.58604i	−0.0297810	−	0.0995367i
$676$	5.02106	+	8.69673i	0.193118	+	0.334490i
$677$	−7.96449	−	13.7949i	−0.306100	−	0.530181i	0.671405	−	0.741090i	$-0.265691\pi$
$677$	−7.96449	−	13.7949i	−0.306100	−	0.530181i	−0.977506	+	0.210909i	$0.932358\pi$
$678$	−9.62785	+	6.88075i	−0.369755	+	0.264254i
$679$		0			0
$680$	−3.59886	+	2.07781i	−0.138010	+	0.0796802i
$681$	20.1131	+	9.14388i	0.770735	+	0.350394i
$682$			47.5148i			1.81944i
$683$	16.4777	−	9.51343i	0.630503	−	0.364021i	−0.150444	−	0.988619i	$-0.548070\pi$
$683$	16.4777	−	9.51343i	0.630503	−	0.364021i	0.780947	+	0.624597i	$0.214737\pi$
$684$	3.23377	+	1.10687i	0.123646	+	0.0423224i
$685$			18.7664i			0.717028i
$686$		0			0
$687$	3.22157	−	7.08623i	0.122910	−	0.270356i
$688$	−3.52106			−0.134239
$689$		0			0
$690$	−1.44694	−	14.8846i	−0.0550841	−	0.566645i
$691$	−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
$696$	−5.85596	+	4.18509i	−0.221970	+	0.158636i
$697$	−7.07017	+	12.2459i	−0.267802	+	0.463847i
$698$	−2.84505			−0.107687
$699$	−2.16932	−	3.03540i	−0.0820511	−	0.114809i
$700$		0			0
$701$		−	9.98234i		−	0.377028i	−0.982071	−	0.188514i	$-0.939633\pi$
$701$		−	9.98234i		−	0.377028i	0.982071	−	0.188514i	$-0.0603670\pi$
$702$	−8.69536	−	2.06239i	−0.328185	−	0.0778399i
$703$	9.07522	−	5.23958i	0.342278	−	0.197614i
$704$		−	5.67667i		−	0.213948i
$705$	4.64974	+	47.8314i	0.175119	+	1.80143i
$706$	6.18709	−	3.57212i	0.232854	−	0.134438i
$707$		0			0
$708$	0.373656	+	3.84377i	0.0140429	+	0.144458i
$709$	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
$711$	−12.6574	+	36.9791i	−0.474690	+	1.38682i
$712$	−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
$717$	17.4839	−	1.69963i	0.652949	−	0.0634738i
$718$	11.6037			0.433047
$719$	8.13460	−	14.0895i	0.303370	−	0.525451i	−0.673527	−	0.739162i	$-0.735222\pi$
$719$	8.13460	−	14.0895i	0.303370	−	0.525451i	0.976897	+	0.213711i	$0.0685550\pi$
$720$	−2.28245	+	6.66826i	−0.0850619	+	0.248512i
$721$		0			0
$722$	−15.3303	−	8.85097i	−0.570536	−	0.329399i
$723$	−7.56118	+	16.6317i	−0.281203	+	0.618541i
$724$	−13.3837	−	7.72706i	−0.497400	−	0.287174i
$725$	1.86955	+	1.07938i	0.0694332	+	0.0400873i
$726$	36.5896	−	3.55691i	1.35797	−	0.132009i
$727$	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
$729$	−22.5632	+	14.8291i	−0.835673	+	0.549227i
$730$	−6.27554	+	10.8695i	−0.232268	+	0.402300i
$731$	6.22815			0.230356
$732$	6.45125	−	14.1903i	0.238445	−	0.524489i
$733$			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
$738$	4.61909	+	23.5335i	0.170031	+	0.866282i
$739$	−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
$741$	−3.08959	−	1.40460i	−0.113499	−	0.0515992i
$742$		0			0
$743$	43.9160	−	25.3549i	1.61112	−	0.930182i	0.622011	−	0.783008i	$-0.286316\pi$
$743$	43.9160	−	25.3549i	1.61112	−	0.930182i	0.989111	−	0.147173i	$-0.0470176\pi$
$744$	−11.7950	+	8.42957i	−0.432426	+	0.309043i
$745$			2.81390i			0.103093i
$746$	22.2289	−	12.8339i	0.813858	−	0.469881i
$747$	−36.9332	+	7.24913i	−1.35132	+	0.265232i
$748$			10.0411i			0.367137i
$749$		0			0
$750$	−18.1466	+	1.76405i	−0.662621	+	0.0644140i
$751$	−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
$753$	46.1996	+	21.0034i	1.68361	+	0.765408i
$754$	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
$759$	−32.8947	−	14.9547i	−1.19400	−	0.542822i
$760$	−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	$0.791010\pi$
$762$	11.5101	−	1.11891i	0.416966	−	0.0405337i
$763$		0			0
$764$			12.3381i			0.446376i
$765$	4.03726	−	11.7950i	0.145968	−	0.426450i
$766$	−1.32211	+	0.763322i	−0.0477699	+	0.0275800i
$767$		−	3.83468i		−	0.138462i
$768$	1.40917	−	1.00709i	0.0508490	−	0.0363404i
$769$	−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
$771$	−12.0284	−	5.46841i	−0.433193	−	0.196940i
$772$	2.19694	+	3.80521i	0.0790696	+	0.136953i
$773$	10.8025	+	18.7105i	0.388540	+	0.672971i	0.992253	−	0.124231i	$-0.0396462\pi$
$773$	10.8025	+	18.7105i	0.388540	+	0.672971i	−0.603714	+	0.797201i	$0.706313\pi$
$774$	7.95946	−	6.94462i	0.286097	−	0.249619i
$775$	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
$780$	2.89638	−	6.37094i	0.103707	−	0.228116i
$781$	−25.6646			−0.918350
$782$	3.25030	−	5.62969i	0.116231	−	0.201317i
$783$	4.98328	−	21.0103i	0.178088	−	0.750847i
$784$		0			0
$785$	20.4008	+	11.7784i	0.728137	+	0.420390i
$786$	12.8830	−	1.25237i	0.459520	−	0.0446704i
$787$	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
$789$	8.73502	−	19.2137i	0.310975	−	0.684027i
$790$	−26.5077	−	15.3042i	−0.943102	−	0.544500i
$791$		0			0
$792$	11.1962	+	12.8323i	0.397838	+	0.455975i
$793$	−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	0.849662	−	0.527327i	$-0.176806\pi$
$797$	−0.899094	−	1.55728i	−0.0318476	−	0.0551616i	−0.881510	+	0.472166i	$0.843472\pi$
$798$		0			0
$799$	−10.4448	+	18.0910i	−0.369512	+	0.640013i
$800$	−0.449885	−	0.259741i	−0.0159058	−	0.00918323i
$801$	3.41796	−	0.670866i	0.120768	−	0.0237039i
$802$	−19.0868	−	33.0592i	−0.673977	−	1.16736i
$803$	15.1634	+	26.2637i	0.535103	+	0.926826i
$804$	−1.82185	−	18.7412i	−0.0642517	−	0.660951i
$805$		0			0
$806$	12.4668	−	7.19773i	0.439125	−	0.253529i
$807$	0.464935	+	4.78274i	0.0163665	+	0.168361i
$808$			6.62310i			0.233000i
$809$	−35.2371	+	20.3441i	−1.23887	+	0.715262i	−0.968863	−	0.247597i	$-0.920359\pi$
$809$	−35.2371	+	20.3441i	−1.23887	+	0.715262i	−0.270006	+	0.962859i	$0.587026\pi$
$810$	−7.99234	−	19.5755i	−0.280822	−	0.687813i
$811$		−	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
$813$	−3.23068	−	4.52051i	−0.113305	−	0.158541i
$814$	52.2125			1.83005
$815$	14.0999	−	24.4217i	0.493896	−	0.855453i
$816$	−2.49258	+	1.78138i	−0.0872578	+	0.0623607i
$817$	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	$-0.741082\pi$
$821$	−11.4968	+	6.63771i	−0.401243	+	0.231658i	0.285777	+	0.958296i	$0.407748\pi$
$822$	1.33865	+	13.7705i	0.0466906	+	0.480302i
$823$	−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
$825$	2.11388	−	4.64974i	0.0735959	−	0.161883i
$826$		0			0
$827$		−	27.7183i		−	0.963859i	−0.876210	−	0.481929i	$-0.839936\pi$
$827$		−	27.7183i		−	0.963859i	0.876210	−	0.481929i	$-0.160064\pi$
$828$	−2.12349	−	10.8189i	−0.0737964	−	0.375981i
$829$	−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
$831$	−15.8954	−	7.22642i	−0.551405	−	0.250682i
$832$	−1.48943	+	0.859925i	−0.0516368	+	0.0298125i
$833$		0			0
$834$	−29.2552	+	20.9079i	−1.01303	+	0.723981i
$835$	−20.1451	−	34.8923i	−0.697149	−	1.20750i
$836$	3.23377	+	5.60106i	0.111842	+	0.193717i
$837$	10.0373	−	42.3187i	0.346939	−	1.46275i
$838$	−30.1778	−	17.4232i	−1.04248	−	0.601873i
$839$	−1.92438	+	3.33313i	−0.0664370	+	0.115072i	−0.897331	−	0.441359i	$-0.854496\pi$
$839$	−1.92438	+	3.33313i	−0.0664370	+	0.115072i	0.830894	+	0.556431i	$0.187830\pi$
$840$		0			0
$841$	−5.86545	−	10.1593i	−0.202257	−	0.350319i
$842$		−	5.69193i		−	0.196157i
$843$	−4.90739	−	6.86664i	−0.169020	−	0.236500i
$844$	10.3112			0.354927
$845$	11.7963	−	20.4317i	0.405804	−	0.702873i
$846$	6.82382	+	34.7663i	0.234608	+	1.19529i
$847$		0			0
$848$		0			0
$849$	−2.83780	−	3.97078i	−0.0973931	−	0.136277i
$850$	0.795769	+	0.459437i	0.0272946	+	0.0157586i
$851$	−29.2738	−	16.9013i	−1.00349	−	0.579368i
$852$	−4.55313	−	6.37094i	−0.155988	−	0.218265i
$853$	−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
$855$	−1.54660	−	7.87967i	−0.0528924	−	0.269479i
$856$	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	$0.731541\pi$
$858$	−9.83228	−	13.7578i	−0.335669	−	0.469682i
$859$			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	$-0.453877\pi$
$863$	−18.8118	−	10.8610i	−0.640360	−	0.369712i	−0.784753	+	0.619809i	$0.787210\pi$
$864$	−1.19917	+	5.05589i	−0.0407965	+	0.172005i
$865$	−2.33465	−	4.04373i	−0.0793804	−	0.137491i
$866$	11.8047	+	20.4463i	0.401139	+	0.694794i
$867$	−19.5469	+	13.9697i	−0.663849	+	0.474434i
$868$		0			0
$869$	−64.0496	+	36.9791i	−2.17273	+	1.25443i
$870$	15.3939	+	6.99842i	0.521901	+	0.237269i
$871$			18.6969i			0.633520i
$872$	−3.66908	+	2.11835i	−0.124251	+	0.0717363i
$873$	−2.65233	−	13.5132i	−0.0897677	−	0.457353i
$874$		−	4.18711i		−	0.141631i
$875$		0			0
$876$	−3.82955	+	8.42356i	−0.129388	+	0.284606i
$877$	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
$879$	1.35976	+	13.9877i	0.0458636	+	0.471794i
$880$	−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
$885$	7.38162	−	5.27543i	0.248130	−	0.177332i
$886$	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	$0.438460\pi$
$888$	9.26298	+	12.9612i	0.310845	+	0.434948i
$889$		0			0
$890$			2.72774i			0.0914341i
$891$	−50.6185	−	6.92547i	−1.69578	−	0.232012i
$892$	−6.24329	+	3.60456i	−0.209041	+	0.120690i
$893$			13.4552i			0.450262i
$894$	0.200721	+	2.06480i	0.00671311	+	0.0690571i
$895$	16.9100	−	9.76302i	0.565240	−	0.326342i
$896$		0			0
$897$	1.05923	+	10.8962i	0.0353668	+	0.363815i
$898$	−7.95142	−	13.7723i	−0.265342	−	0.459586i
$899$	17.3916	+	30.1232i	0.580043	+	1.00466i
$900$	1.52927	−	0.300160i	0.0509756	−	0.0100053i
$901$		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
$906$	−26.2460	+	2.55140i	−0.871966	+	0.0847647i
$907$	−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
$909$	−13.0628	−	14.9717i	−0.433266	−	0.496580i
$910$		0			0
$911$	−7.00460	−	4.04411i	−0.232073	−	0.133987i	0.379455	−	0.925210i	$-0.376111\pi$
$911$	−7.00460	−	4.04411i	−0.232073	−	0.133987i	−0.611528	+	0.791223i	$0.709445\pi$
$912$	−0.816699	+	1.79643i	−0.0270436	+	0.0594857i
$913$	−61.6777	−	35.6097i	−2.04124	−	1.17851i
$914$	4.90702	+	2.83307i	0.162310	+	0.0937096i
$915$	−36.4498	+	3.54332i	−1.20499	+	0.117139i
$916$	3.89208	+	2.24709i	0.128598	+	0.0742460i
$917$		0			0
$918$	2.12112	−	8.94300i	0.0700075	−	0.295163i
$919$	−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
$921$	7.81318	−	17.1860i	0.257453	−	0.566299i
$922$			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
$927$	13.2462	−	11.5573i	0.435062	−	0.379591i
$928$	−2.07781	−	3.59886i	−0.0682073	−	0.118139i
$929$	5.42618	+	9.39842i	0.178027	+	0.308352i	0.941205	−	0.337837i	$-0.109695\pi$
$929$	5.42618	+	9.39842i	0.178027	+	0.308352i	−0.763177	+	0.646189i	$0.776362\pi$
$930$	31.0062	+	14.0961i	1.01673	+	0.462231i
$931$		0			0
$932$	1.86545	−	1.07702i	0.0611048	−	0.0352789i
$933$	−11.6065	+	8.29481i	−0.379978	+	0.271560i
$934$		−	30.3032i		−	0.991550i
$935$	20.4296	−	11.7950i	0.668118	−	0.385738i
$936$	1.67087	−	4.88151i	0.0546141	−	0.159557i
$937$		−	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
$939$	−58.2725	+	5.66473i	−1.90165	+	0.184861i
$940$	−27.7456			−0.904963
$941$	−3.68890	+	6.38937i	−0.120255	+	0.208287i	−0.919868	−	0.392228i	$-0.871704\pi$
$941$	−3.68890	+	6.38937i	−0.120255	+	0.208287i	0.799613	+	0.600515i	$0.205038\pi$
$942$	15.8100	+	7.18761i	0.515118	+	0.234185i
$943$	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	$-0.604252\pi$
$947$	10.3846	−	5.99552i	0.337453	−	0.194828i	0.659145	+	0.752016i	$0.270918\pi$
$948$	−20.5426	−	9.33917i	−0.667194	−	0.303322i
$949$	4.59401	−	7.95706i	0.149128	−	0.258297i
$950$	0.591856			0.0192024
$951$	11.6036	−	1.12799i	0.376271	−	0.0365777i
$952$		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
$957$	33.2424	−	23.7574i	1.07457	−	0.767968i
$958$	4.03816	−	2.33143i	0.130467	−	0.0753251i
$959$		0			0
$960$	−3.70436	−	1.68409i	−0.119558	−	0.0543538i
$961$	19.5300	+	33.8270i	0.630000	+	1.09119i
$962$	−7.90935	−	13.6994i	−0.255008	−	0.441686i
$963$	2.72472	+	13.8820i	0.0878029	+	0.447342i
$964$	−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
$969$	1.44460	−	3.17757i	0.0464072	−	0.102078i
$970$	10.7844			0.346265
$971$	3.20362	−	5.54883i	0.102809	−	0.178070i	−0.810032	−	0.586386i	$-0.800550\pi$
$971$	3.20362	−	5.54883i	0.102809	−	0.178070i	0.912841	+	0.408315i	$0.133884\pi$
$972$	−7.26102	−	13.7941i	−0.232897	−	0.442446i
$973$		0			0
$974$	16.8720	+	9.74105i	0.540613	+	0.312123i
$975$	−1.54021	+	0.149725i	−0.0493261	+	0.00479504i
$976$	7.79396	+	4.49985i	0.249479	+	0.144037i
$977$	−11.7769	−	6.79937i	−0.376775	−	0.217531i	0.299639	−	0.954053i	$-0.403134\pi$
$977$	−11.7769	−	6.79937i	−0.376775	−	0.217531i	−0.676414	+	0.736521i	$0.736467\pi$
$978$	8.60422	−	18.9260i	0.275133	−	0.605188i
$979$	5.70793	+	3.29547i	0.182426	+	0.105324i
$980$		0			0
$981$	4.11604	−	12.0252i	0.131415	−	0.383934i
$982$	−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	$0.618289\pi$
$984$	−13.7814	+	1.33970i	−0.439334	+	0.0427081i
$985$			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
$990$	12.9567	−	37.8535i	0.411792	−	1.20306i
$991$	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
$993$	−5.37223	−	55.2636i	−0.170483	−	1.75374i
$994$		0			0
$995$	−56.0869	+	32.3818i	−1.77807	+	1.02657i
$996$	−2.10251	−	21.6283i	−0.0666205	−	0.685319i
$997$			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
$999$	−46.5027	−	11.0296i	−1.47128	−	0.348962i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
126.2.m.a.41.2	✓	16	63.23	odd	6
126.2.m.a.41.3	yes	16	63.5	even	6
126.2.m.a.83.2	yes	16	7.5	odd	6
126.2.m.a.83.3	yes	16	7.2	even	3
378.2.m.a.125.6		16	63.40	odd	6
378.2.m.a.125.7		16	63.58	even	3
378.2.m.a.251.6		16	21.2	odd	6
378.2.m.a.251.7		16	21.5	even	6
882.2.l.a.227.6		16	7.3	odd	6
882.2.l.a.227.7		16	7.4	even	3
882.2.l.a.509.2		16	9.5	odd	6
882.2.l.a.509.3		16	63.41	even	6
882.2.t.b.803.5		16	1.1	even	1	trivial
882.2.t.b.803.8		16	7.6	odd	2	inner
882.2.t.b.815.5		16	63.59	even	6	inner
882.2.t.b.815.8		16	63.32	odd	6	inner
1008.2.cc.b.209.3		16	28.23	odd	6
1008.2.cc.b.209.6		16	28.19	even	6
1008.2.cc.b.545.3		16	252.131	odd	6
1008.2.cc.b.545.6		16	252.23	even	6
1134.2.d.a.1133.2		16	63.47	even	6
1134.2.d.a.1133.7		16	63.2	odd	6
1134.2.d.a.1133.10		16	63.16	even	3
1134.2.d.a.1133.15		16	63.61	odd	6
2646.2.l.b.521.2		16	21.11	odd	6
2646.2.l.b.521.3		16	21.17	even	6
2646.2.l.b.1097.6		16	63.13	odd	6
2646.2.l.b.1097.7		16	9.4	even	3
2646.2.t.a.1979.2		16	21.20	even	2
2646.2.t.a.1979.3		16	3.2	odd	2
2646.2.t.a.2285.2		16	63.4	even	3
2646.2.t.a.2285.3		16	63.31	odd	6
3024.2.cc.b.881.2		16	252.103	even	6
3024.2.cc.b.881.7		16	252.247	odd	6
3024.2.cc.b.2897.2		16	84.23	even	6
3024.2.cc.b.2897.7		16	84.47	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:	\( N \)	\(=\)	\( 882 = 2 \cdot 3^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	882.t (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.866025 - 0.500000i) q^{2} +(-1.57675 - 0.716830i) q^{3} +(0.500000 - 0.866025i) q^{4} -2.34936 q^{5} +(-1.72392 + 0.167584i) q^{6} -1.00000i q^{8} +(1.97231 + 2.26053i) q^{9} +O(q^{10})\)	\(q+(0.866025 - 0.500000i) q^{2} +(-1.57675 - 0.716830i) q^{3} +(0.500000 - 0.866025i) q^{4} -2.34936 q^{5} +(-1.72392 + 0.167584i) q^{6} -1.00000i q^{8} +(1.97231 + 2.26053i) q^{9} +(-2.03460 + 1.17468i) q^{10} +5.67667i q^{11} +(-1.40917 + 1.00709i) q^{12} +(1.48943 - 0.859925i) q^{13} +(3.70436 + 1.68409i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(0.884414 + 1.53185i) q^{17} +(2.83834 + 0.971521i) q^{18} +(0.986680 + 0.569660i) q^{19} +(-1.17468 + 2.03460i) q^{20} +(2.83834 + 4.91614i) q^{22} -3.67509i q^{23} +(-0.716830 + 1.57675i) q^{24} +0.519482 q^{25} +(0.859925 - 1.48943i) q^{26} +(-1.48943 - 4.97811i) q^{27} +(3.59886 + 2.07781i) q^{29} +(4.05012 - 0.393716i) q^{30} +(7.24879 + 4.18509i) q^{31} +(-0.866025 - 0.500000i) q^{32} +(4.06921 - 8.95072i) q^{33} +(1.53185 + 0.884414i) q^{34} +(2.94383 - 0.577806i) q^{36} +(4.59886 - 7.96547i) q^{37} +1.13932 q^{38} +(-2.96489 + 0.288220i) q^{39} +2.34936i q^{40} +(3.99709 + 6.92317i) q^{41} +(1.76053 - 3.04933i) q^{43} +(4.91614 + 2.83834i) q^{44} +(-4.63366 - 5.31079i) q^{45} +(-1.83755 - 3.18272i) q^{46} +(5.90494 + 10.2277i) q^{47} +(0.167584 + 1.72392i) q^{48} +(0.449885 - 0.259741i) q^{50} +(-0.296428 - 3.04933i) q^{51} -1.71985i q^{52} +(-3.77894 - 3.56645i) q^{54} -13.3365i q^{55} +(-1.14740 - 1.60550i) q^{57} +4.15561 q^{58} +(1.11483 - 1.93094i) q^{59} +(3.31064 - 2.36603i) q^{60} +(-7.79396 + 4.49985i) q^{61} +8.37019 q^{62} -1.00000 q^{64} +(-3.49921 + 2.02027i) q^{65} +(-0.951321 - 9.78615i) q^{66} +(-5.43562 + 9.41477i) q^{67} +1.76883 q^{68} +(-2.63442 + 5.79472i) q^{69} +4.52106i q^{71} +(2.26053 - 1.97231i) q^{72} +(4.62660 - 2.67117i) q^{73} -9.19773i q^{74} +(-0.819096 - 0.372380i) q^{75} +(0.986680 - 0.569660i) q^{76} +(-2.42356 + 1.73205i) q^{78} +(6.51422 + 11.2830i) q^{79} +(1.17468 + 2.03460i) q^{80} +(-1.21999 + 8.91693i) q^{81} +(6.92317 + 3.99709i) q^{82} +(-6.27298 + 10.8651i) q^{83} +(-2.07781 - 3.59886i) q^{85} -3.52106i q^{86} +(-4.18509 - 5.85596i) q^{87} +5.67667 q^{88} +(0.580529 - 1.00551i) q^{89} +(-6.66826 - 2.28245i) q^{90} +(-3.18272 - 1.83755i) q^{92} +(-8.42957 - 11.7950i) q^{93} +(10.2277 + 5.90494i) q^{94} +(-2.31806 - 1.33834i) q^{95} +(1.00709 + 1.40917i) q^{96} +(-3.97536 - 2.29517i) q^{97} +(-12.8323 + 11.1962i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 8 q^{4}+O(q^{10}) \) 16 * q + 8 * q^4	\( 16 q + 8 q^{4} - 8 q^{16} + 16 q^{25} - 12 q^{29} + 12 q^{30} + 12 q^{36} + 4 q^{37} + 36 q^{39} + 4 q^{43} + 12 q^{44} - 12 q^{46} + 60 q^{50} - 36 q^{51} + 48 q^{57} + 24 q^{58} - 24 q^{60} - 16 q^{64} - 84 q^{65} - 28 q^{67} + 12 q^{72} - 24 q^{78} - 4 q^{79} - 36 q^{81} - 12 q^{85} - 48 q^{92} + 12 q^{93} - 12 q^{95} - 72 q^{99}+O(q^{100}) \) 16 * q + 8 * q^4 - 8 * q^16 + 16 * q^25 - 12 * q^29 + 12 * q^30 + 12 * q^36 + 4 * q^37 + 36 * q^39 + 4 * q^43 + 12 * q^44 - 12 * q^46 + 60 * q^50 - 36 * q^51 + 48 * q^57 + 24 * q^58 - 24 * q^60 - 16 * q^64 - 84 * q^65 - 28 * q^67 + 12 * q^72 - 24 * q^78 - 4 * q^79 - 36 * q^81 - 12 * q^85 - 48 * q^92 + 12 * q^93 - 12 * q^95 - 72 * q^99

Introduction

L-functions

Modular forms

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