LMFDB - Embedded newform 1344.2.s.d.239.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1344,2,Mod(239,1344)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1344, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 3, 2, 0]))

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

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

chi := DirichletCharacter("1344.239");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1344 = 2^{6} \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1344.s (of order $4$, 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:	$10.7318940317$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(i)$
Twist minimal:	no (minimal twist has level 336)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			239.2
Character	$\chi$	$=$	1344.239
Dual form			1344.2.s.d.911.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.66117 + 0.490427i) q^{3} +(2.27018 + 2.27018i) q^{5} -1.00000 q^{7} +(2.51896 - 1.62936i) q^{9} +O(q^{10})$	\(q+(-1.66117 + 0.490427i) q^{3} +(2.27018 + 2.27018i) q^{5} -1.00000 q^{7} +(2.51896 - 1.62936i) q^{9} +(1.28969 - 1.28969i) q^{11} +(-2.15412 - 2.15412i) q^{13} +(-4.88450 - 2.65779i) q^{15} -6.50745i q^{17} +(3.42567 - 3.42567i) q^{19} +(1.66117 - 0.490427i) q^{21} -5.60715i q^{23} +5.30740i q^{25} +(-3.38534 + 3.94202i) q^{27} +(-3.59282 + 3.59282i) q^{29} -0.730914i q^{31} +(-1.50989 + 2.77489i) q^{33} +(-2.27018 - 2.27018i) q^{35} +(7.94100 - 7.94100i) q^{37} +(4.63480 + 2.52192i) q^{39} -3.23899 q^{41} +(8.55003 + 8.55003i) q^{43} +(9.41743 + 2.01954i) q^{45} -7.39702 q^{47} +1.00000 q^{49} +(3.19143 + 10.8100i) q^{51} +(-0.785056 - 0.785056i) q^{53} +5.85564 q^{55} +(-4.01057 + 7.37066i) q^{57} +(4.42285 - 4.42285i) q^{59} +(-1.23526 - 1.23526i) q^{61} +(-2.51896 + 1.62936i) q^{63} -9.78048i q^{65} +(2.62374 - 2.62374i) q^{67} +(2.74990 + 9.31443i) q^{69} +1.31590i q^{71} -10.4065i q^{73} +(-2.60289 - 8.81649i) q^{75} +(-1.28969 + 1.28969i) q^{77} +9.74158i q^{79} +(3.69034 - 8.20862i) q^{81} +(-0.603062 - 0.603062i) q^{83} +(14.7731 - 14.7731i) q^{85} +(4.20627 - 7.73031i) q^{87} -0.657476 q^{89} +(2.15412 + 2.15412i) q^{91} +(0.358460 + 1.21417i) q^{93} +15.5538 q^{95} +8.66806 q^{97} +(1.14730 - 5.35005i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 48 q^{7}+O(q^{10}) $ 48 * q - 48 * q^7	$ 48 q - 48 q^{7} - 8 q^{19} + 12 q^{27} + 16 q^{37} + 24 q^{39} + 48 q^{43} + 20 q^{45} + 48 q^{49} + 32 q^{55} + 8 q^{61} + 16 q^{67} - 28 q^{69} + 12 q^{75} - 48 q^{85} - 56 q^{87} - 64 q^{93} - 32 q^{99}+O(q^{100}) $ 48 * q - 48 * q^7 - 8 * q^19 + 12 * q^27 + 16 * q^37 + 24 * q^39 + 48 * q^43 + 20 * q^45 + 48 * q^49 + 32 * q^55 + 8 * q^61 + 16 * q^67 - 28 * q^69 + 12 * q^75 - 48 * q^85 - 56 * q^87 - 64 * q^93 - 32 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1344\mathbb{Z}\right)^\times$.

$n$	$127$	$449$	$577$	$1093$
$\chi(n)$	$-1$	$-1$	$1$	$e\left(\frac{3}{4}\right)$

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			0
$2$		0			0
$3$	−1.66117	+	0.490427i	−0.959076	+	0.283148i
$3$	−1.66117	+	0.490427i	−0.959076	+	0.283148i
$4$		0			0
$5$	2.27018	+	2.27018i	1.01525	+	1.01525i	0.999882	+	0.0153719i	$0.00489322\pi$
$5$	2.27018	+	2.27018i	1.01525	+	1.01525i	0.0153719	+	0.999882i	$0.495107\pi$
$6$		0			0
$7$	−1.00000			−0.377964
$7$	−1.00000			−0.377964
$8$		0			0
$9$	2.51896	−	1.62936i	0.839654	−	0.543122i
$10$		0			0
$11$	1.28969	−	1.28969i	0.388855	−	0.388855i	−0.485424	−	0.874279i	$-0.661335\pi$
$11$	1.28969	−	1.28969i	0.388855	−	0.388855i	0.874279	+	0.485424i	$0.161335\pi$
$12$		0			0
$13$	−2.15412	−	2.15412i	−0.597446	−	0.597446i	0.342186	−	0.939632i	$-0.388833\pi$
$13$	−2.15412	−	2.15412i	−0.597446	−	0.597446i	−0.939632	+	0.342186i	$0.888833\pi$
$14$		0			0
$15$	−4.88450	−	2.65779i	−1.26117	−	0.686238i
$16$		0			0
$17$		−	6.50745i		−	1.57829i	−0.614208	−	0.789144i	$-0.710524\pi$
$17$		−	6.50745i		−	1.57829i	0.614208	−	0.789144i	$-0.289476\pi$
$18$		0			0
$19$	3.42567	−	3.42567i	0.785903	−	0.785903i	−0.194917	−	0.980820i	$-0.562444\pi$
$19$	3.42567	−	3.42567i	0.785903	−	0.785903i	0.980820	+	0.194917i	$0.0624437\pi$
$20$		0			0
$21$	1.66117	−	0.490427i	0.362497	−	0.107020i
$22$		0			0
$23$		−	5.60715i		−	1.16917i	−0.811332	−	0.584586i	$-0.801257\pi$
$23$		−	5.60715i		−	1.16917i	0.811332	−	0.584586i	$-0.198743\pi$
$24$		0			0
$25$			5.30740i			1.06148i
$26$		0			0
$27$	−3.38534	+	3.94202i	−0.651508	+	0.758642i
$28$		0			0
$29$	−3.59282	+	3.59282i	−0.667171	+	0.667171i	−0.957060	−	0.289889i	$-0.906381\pi$
$29$	−3.59282	+	3.59282i	−0.667171	+	0.667171i	0.289889	+	0.957060i	$0.406381\pi$
$30$		0			0
$31$		−	0.730914i		−	0.131276i	−0.997843	−	0.0656380i	$-0.979092\pi$
$31$		−	0.730914i		−	0.131276i	0.997843	−	0.0656380i	$-0.0209083\pi$
$32$		0			0
$33$	−1.50989	+	2.77489i	−0.262838	+	0.483046i
$34$		0			0
$35$	−2.27018	−	2.27018i	−0.383730	−	0.383730i
$36$		0			0
$37$	7.94100	−	7.94100i	1.30549	−	1.30549i	0.380859	−	0.924633i	$-0.375628\pi$
$37$	7.94100	−	7.94100i	1.30549	−	1.30549i	0.924633	−	0.380859i	$-0.124372\pi$
$38$		0			0
$39$	4.63480	+	2.52192i	0.742162	+	0.403830i
$40$		0			0
$41$	−3.23899			−0.505846			−0.252923	−	0.967486i	$-0.581392\pi$
$41$	−3.23899			−0.505846			−0.252923	+	0.967486i	$0.581392\pi$
$42$		0			0
$43$	8.55003	+	8.55003i	1.30387	+	1.30387i	0.925762	+	0.378106i	$0.123424\pi$
$43$	8.55003	+	8.55003i	1.30387	+	1.30387i	0.378106	+	0.925762i	$0.376576\pi$
$44$		0			0
$45$	9.41743	+	2.01954i	1.40387	+	0.301056i
$46$		0			0
$47$	−7.39702			−1.07897			−0.539483	−	0.841996i	$-0.681380\pi$
$47$	−7.39702			−1.07897			−0.539483	+	0.841996i	$0.681380\pi$
$48$		0			0
$49$	1.00000			0.142857
$50$		0			0
$51$	3.19143	+	10.8100i	0.446890	+	1.51370i
$52$		0			0
$53$	−0.785056	−	0.785056i	−0.107836	−	0.107836i	0.651130	−	0.758966i	$-0.274295\pi$
$53$	−0.785056	−	0.785056i	−0.107836	−	0.107836i	−0.758966	+	0.651130i	$0.774295\pi$
$54$		0			0
$55$	5.85564			0.789574
$56$		0			0
$57$	−4.01057	+	7.37066i	−0.531214	+	0.976268i
$58$		0			0
$59$	4.42285	−	4.42285i	0.575805	−	0.575805i	−0.357939	−	0.933745i	$-0.616521\pi$
$59$	4.42285	−	4.42285i	0.575805	−	0.575805i	0.933745	+	0.357939i	$0.116521\pi$
$60$		0			0
$61$	−1.23526	−	1.23526i	−0.158159	−	0.158159i	0.623591	−	0.781751i	$-0.285673\pi$
$61$	−1.23526	−	1.23526i	−0.158159	−	0.158159i	−0.781751	+	0.623591i	$0.785673\pi$
$62$		0			0
$63$	−2.51896	+	1.62936i	−0.317359	+	0.205281i
$64$		0			0
$65$		−	9.78048i		−	1.21312i
$66$		0			0
$67$	2.62374	−	2.62374i	0.320540	−	0.320540i	−0.528434	−	0.848974i	$-0.677221\pi$
$67$	2.62374	−	2.62374i	0.320540	−	0.320540i	0.848974	+	0.528434i	$0.177221\pi$
$68$		0			0
$69$	2.74990	+	9.31443i	0.331049	+	1.12133i
$70$		0			0
$71$			1.31590i			0.156169i	0.996947	+	0.0780843i	$0.0248803\pi$
$71$			1.31590i			0.156169i	−0.996947	+	0.0780843i	$0.975120\pi$
$72$		0			0
$73$		−	10.4065i		−	1.21799i	−0.793175	−	0.608993i	$-0.791574\pi$
$73$		−	10.4065i		−	1.21799i	0.793175	−	0.608993i	$-0.208426\pi$
$74$		0			0
$75$	−2.60289	−	8.81649i	−0.300556	−	1.01804i
$76$		0			0
$77$	−1.28969	+	1.28969i	−0.146974	+	0.146974i
$78$		0			0
$79$			9.74158i			1.09601i	0.836474	+	0.548006i	$0.184613\pi$
$79$			9.74158i			1.09601i	−0.836474	+	0.548006i	$0.815387\pi$
$80$		0			0
$81$	3.69034	−	8.20862i	0.410038	−	0.912068i
$82$		0			0
$83$	−0.603062	−	0.603062i	−0.0661946	−	0.0661946i	0.673234	−	0.739429i	$-0.264904\pi$
$83$	−0.603062	−	0.603062i	−0.0661946	−	0.0661946i	−0.739429	+	0.673234i	$0.764904\pi$
$84$		0			0
$85$	14.7731	−	14.7731i	1.60236	−	1.60236i
$86$		0			0
$87$	4.20627	−	7.73031i	0.450959	−	0.828776i
$88$		0			0
$89$	−0.657476			−0.0696923			−0.0348462	−	0.999393i	$-0.511094\pi$
$89$	−0.657476			−0.0696923			−0.0348462	+	0.999393i	$0.511094\pi$
$90$		0			0
$91$	2.15412	+	2.15412i	0.225813	+	0.225813i
$92$		0			0
$93$	0.358460	+	1.21417i	0.0371706	+	0.125904i
$94$		0			0
$95$	15.5538			1.59578
$96$		0			0
$97$	8.66806			0.880108			0.440054	−	0.897971i	$-0.354959\pi$
$97$	8.66806			0.880108			0.440054	+	0.897971i	$0.354959\pi$
$98$		0			0
$99$	1.14730	−	5.35005i	0.115308	−	0.537700i
$100$		0			0
$101$	6.86450	+	6.86450i	0.683044	+	0.683044i	0.960685	−	0.277641i	$-0.0895527\pi$
$101$	6.86450	+	6.86450i	0.683044	+	0.683044i	−0.277641	+	0.960685i	$0.589553\pi$
$102$		0			0
$103$	−8.38381			−0.826081			−0.413041	−	0.910713i	$-0.635533\pi$
$103$	−8.38381			−0.826081			−0.413041	+	0.910713i	$0.635533\pi$
$104$		0			0
$105$	4.88450	+	2.65779i	0.476679	+	0.259374i
$106$		0			0
$107$	10.4659	−	10.4659i	1.01178	−	1.01178i	0.0118454	−	0.999930i	$-0.496229\pi$
$107$	10.4659	−	10.4659i	1.01178	−	1.01178i	0.999930	−	0.0118454i	$-0.00377060\pi$
$108$		0			0
$109$	9.36493	+	9.36493i	0.896998	+	0.896998i	0.995169	−	0.0981718i	$-0.0312995\pi$
$109$	9.36493	+	9.36493i	0.896998	+	0.896998i	−0.0981718	+	0.995169i	$0.531299\pi$
$110$		0			0
$111$	−9.29685	+	17.0858i	−0.882418	+	1.62171i
$112$		0			0
$113$		−	3.62807i		−	0.341300i	−0.985332	−	0.170650i	$-0.945413\pi$
$113$		−	3.62807i		−	0.341300i	0.985332	−	0.170650i	$-0.0545868\pi$
$114$		0			0
$115$	12.7292	−	12.7292i	1.18701	−	1.18701i
$116$		0			0
$117$	−8.93600	−	1.91630i	−0.826134	−	0.177162i
$118$		0			0
$119$			6.50745i			0.596537i
$120$		0			0
$121$			7.67341i			0.697583i
$122$		0			0
$123$	5.38052	−	1.58849i	0.485145	−	0.143229i
$124$		0			0
$125$	−0.697856	+	0.697856i	−0.0624181	+	0.0624181i
$126$		0			0
$127$		−	3.31704i		−	0.294339i	−0.989111	−	0.147170i	$-0.952984\pi$
$127$		−	3.31704i		−	0.294339i	0.989111	−	0.147170i	$-0.0470163\pi$
$128$		0			0
$129$	−18.3962	−	10.0099i	−1.61970	−	0.881321i
$130$		0			0
$131$	1.98650	+	1.98650i	0.173562	+	0.173562i	0.788542	−	0.614981i	$-0.210836\pi$
$131$	1.98650	+	1.98650i	0.173562	+	0.173562i	−0.614981	+	0.788542i	$0.710836\pi$
$132$		0			0
$133$	−3.42567	+	3.42567i	−0.297043	+	0.297043i
$134$		0			0
$135$	−16.6344	+	1.26376i	−1.43166	+	0.108768i
$136$		0			0
$137$	−13.4203			−1.14657			−0.573286	−	0.819355i	$-0.694332\pi$
$137$	−13.4203			−1.14657			−0.573286	+	0.819355i	$0.694332\pi$
$138$		0			0
$139$	−14.1855	−	14.1855i	−1.20320	−	1.20320i	−0.973189	−	0.230008i	$-0.926125\pi$
$139$	−14.1855	−	14.1855i	−1.20320	−	1.20320i	−0.230008	−	0.973189i	$-0.573875\pi$
$140$		0			0
$141$	12.2877	−	3.62770i	1.03481	−	0.305507i
$142$		0			0
$143$	−5.55629			−0.464640
$144$		0			0
$145$	−16.3127			−1.35470
$146$		0			0
$147$	−1.66117	+	0.490427i	−0.137011	+	0.0404498i
$148$		0			0
$149$	−0.311090	−	0.311090i	−0.0254855	−	0.0254855i	0.694249	−	0.719735i	$-0.255737\pi$
$149$	−0.311090	−	0.311090i	−0.0254855	−	0.0254855i	−0.719735	+	0.694249i	$0.755737\pi$
$150$		0			0
$151$	20.1035			1.63600			0.817999	−	0.575220i	$-0.195084\pi$
$151$	20.1035			1.63600			0.817999	+	0.575220i	$0.195084\pi$
$152$		0			0
$153$	−10.6030	−	16.3920i	−0.857203	−	1.32522i
$154$		0			0
$155$	1.65930	−	1.65930i	0.133279	−	0.133279i
$156$		0			0
$157$	7.95586	+	7.95586i	0.634947	+	0.634947i	0.949305	−	0.314358i	$-0.101789\pi$
$157$	7.95586	+	7.95586i	0.634947	+	0.634947i	−0.314358	+	0.949305i	$0.601789\pi$
$158$		0			0
$159$	1.68912	+	0.919097i	0.133956	+	0.0728891i
$160$		0			0
$161$			5.60715i			0.441906i
$162$		0			0
$163$	12.2408	−	12.2408i	0.958775	−	0.958775i	−0.0404083	−	0.999183i	$-0.512866\pi$
$163$	12.2408	−	12.2408i	0.958775	−	0.958775i	0.999183	+	0.0404083i	$0.0128659\pi$
$164$		0			0
$165$	−9.72720	+	2.87176i	−0.757262	+	0.223567i
$166$		0			0
$167$		−	3.00323i		−	0.232397i	−0.993226	−	0.116198i	$-0.962929\pi$
$167$		−	3.00323i		−	0.232397i	0.993226	−	0.116198i	$-0.0370708\pi$
$168$		0			0
$169$		−	3.71951i		−	0.286116i
$170$		0			0
$171$	3.04747	−	14.2108i	0.233046	−	1.08673i
$172$		0			0
$173$	−16.3777	+	16.3777i	−1.24517	+	1.24517i	−0.287349	+	0.957826i	$0.592774\pi$
$173$	−16.3777	+	16.3777i	−1.24517	+	1.24517i	−0.957826	+	0.287349i	$0.907226\pi$
$174$		0			0
$175$		−	5.30740i		−	0.401202i
$176$		0			0
$177$	−5.17801	+	9.51618i	−0.389203	+	0.715280i
$178$		0			0
$179$	5.60043	+	5.60043i	0.418596	+	0.418596i	0.884720	−	0.466124i	$-0.154350\pi$
$179$	5.60043	+	5.60043i	0.418596	+	0.418596i	−0.466124	+	0.884720i	$0.654350\pi$
$180$		0			0
$181$	−11.8857	+	11.8857i	−0.883454	+	0.883454i	−0.993884	−	0.110430i	$-0.964777\pi$
$181$	−11.8857	+	11.8857i	−0.883454	+	0.883454i	0.110430	+	0.993884i	$0.464777\pi$
$182$		0			0
$183$	2.65779	+	1.44617i	0.196469	+	0.106904i
$184$		0			0
$185$	36.0549			2.65081
$186$		0			0
$187$	−8.39258	−	8.39258i	−0.613726	−	0.613726i
$188$		0			0
$189$	3.38534	−	3.94202i	0.246247	−	0.286740i
$190$		0			0
$191$	1.49917			0.108476			0.0542382	−	0.998528i	$-0.482727\pi$
$191$	1.49917			0.108476			0.0542382	+	0.998528i	$0.482727\pi$
$192$		0			0
$193$	2.29555			0.165237			0.0826186	−	0.996581i	$-0.473672\pi$
$193$	2.29555			0.165237			0.0826186	+	0.996581i	$0.473672\pi$
$194$		0			0
$195$	4.79661	+	16.2470i	0.343492	+	1.16347i
$196$		0			0
$197$	−4.21633	−	4.21633i	−0.300401	−	0.300401i	0.540770	−	0.841171i	$-0.318133\pi$
$197$	−4.21633	−	4.21633i	−0.300401	−	0.300401i	−0.841171	+	0.540770i	$0.818133\pi$
$198$		0			0
$199$	4.09403			0.290218			0.145109	−	0.989416i	$-0.453647\pi$
$199$	4.09403			0.290218			0.145109	+	0.989416i	$0.453647\pi$
$200$		0			0
$201$	−3.07172	+	5.64522i	−0.216662	+	0.398183i
$202$		0			0
$203$	3.59282	−	3.59282i	0.252167	−	0.252167i
$204$		0			0
$205$	−7.35309	−	7.35309i	−0.513562	−	0.513562i
$206$		0			0
$207$	−9.13610	−	14.1242i	−0.635003	−	0.981701i
$208$		0			0
$209$		−	8.83609i		−	0.611205i
$210$		0			0
$211$	−9.76923	+	9.76923i	−0.672541	+	0.672541i	−0.958301	−	0.285760i	$-0.907754\pi$
$211$	−9.76923	+	9.76923i	−0.672541	+	0.672541i	0.285760	+	0.958301i	$0.407754\pi$
$212$		0			0
$213$	−0.645353	−	2.18593i	−0.0442189	−	0.149778i
$214$		0			0
$215$			38.8202i			2.64751i
$216$		0			0
$217$			0.730914i			0.0496177i
$218$		0			0
$219$	5.10362	+	17.2869i	0.344871	+	1.16814i
$220$		0			0
$221$	−14.0178	+	14.0178i	−0.942942	+	0.942942i
$222$		0			0
$223$		−	5.84418i		−	0.391355i	−0.980668	−	0.195678i	$-0.937309\pi$
$223$		−	5.84418i		−	0.391355i	0.980668	−	0.195678i	$-0.0626906\pi$
$224$		0			0
$225$	8.64769	+	13.3691i	0.576513	+	0.891276i
$226$		0			0
$227$	−6.43042	−	6.43042i	−0.426802	−	0.426802i	0.460735	−	0.887538i	$-0.347586\pi$
$227$	−6.43042	−	6.43042i	−0.426802	−	0.426802i	−0.887538	+	0.460735i	$0.847586\pi$
$228$		0			0
$229$	0.741920	−	0.741920i	0.0490275	−	0.0490275i	−0.682168	−	0.731195i	$-0.738963\pi$
$229$	0.741920	−	0.741920i	0.0490275	−	0.0490275i	0.731195	+	0.682168i	$0.238963\pi$
$230$		0			0
$231$	1.50989	−	2.77489i	0.0993435	−	0.182574i
$232$		0			0
$233$	−20.8459			−1.36566			−0.682831	−	0.730576i	$-0.739251\pi$
$233$	−20.8459			−1.36566			−0.682831	+	0.730576i	$0.739251\pi$
$234$		0			0
$235$	−16.7925	−	16.7925i	−1.09542	−	1.09542i
$236$		0			0
$237$	−4.77753	−	16.1824i	−0.310334	−	1.05116i
$238$		0			0
$239$	−12.2887			−0.794892			−0.397446	−	0.917626i	$-0.630103\pi$
$239$	−12.2887			−0.794892			−0.397446	+	0.917626i	$0.630103\pi$
$240$		0			0
$241$	20.9833			1.35165			0.675826	−	0.737061i	$-0.263787\pi$
$241$	20.9833			1.35165			0.675826	+	0.737061i	$0.263787\pi$
$242$		0			0
$243$	−2.10455	+	15.4457i	−0.135007	+	0.990845i
$244$		0			0
$245$	2.27018	+	2.27018i	0.145036	+	0.145036i
$246$		0			0
$247$	−14.7586			−0.939069
$248$		0			0
$249$	1.29754	+	0.706029i	0.0822286	+	0.0447428i
$250$		0			0
$251$	−15.6696	+	15.6696i	−0.989056	+	0.989056i	−0.999941	−	0.0108844i	$-0.996535\pi$
$251$	−15.6696	+	15.6696i	−0.989056	+	0.989056i	0.0108844	+	0.999941i	$0.496535\pi$
$252$		0			0
$253$	−7.23148	−	7.23148i	−0.454639	−	0.454639i
$254$		0			0
$255$	−17.2954	+	31.7857i	−1.08308	+	1.99049i
$256$		0			0
$257$		−	2.87847i		−	0.179554i	−0.995962	−	0.0897771i	$-0.971385\pi$
$257$		−	2.87847i		−	0.179554i	0.995962	−	0.0897771i	$-0.0286155\pi$
$258$		0			0
$259$	−7.94100	+	7.94100i	−0.493430	+	0.493430i
$260$		0			0
$261$	−3.19617	+	14.9042i	−0.197838	+	0.922548i
$262$		0			0
$263$		−	3.38442i		−	0.208692i	−0.994541	−	0.104346i	$-0.966725\pi$
$263$		−	3.38442i		−	0.208692i	0.994541	−	0.104346i	$-0.0332750\pi$
$264$		0			0
$265$		−	3.56443i		−	0.218961i
$266$		0			0
$267$	1.09218	−	0.322444i	0.0668403	−	0.0197333i
$268$		0			0
$269$	−21.9081	+	21.9081i	−1.33576	+	1.33576i	−0.435634	+	0.900124i	$0.643476\pi$
$269$	−21.9081	+	21.9081i	−1.33576	+	1.33576i	−0.900124	+	0.435634i	$0.856524\pi$
$270$		0			0
$271$		−	15.2450i		−	0.926069i	−0.886340	−	0.463035i	$-0.846761\pi$
$271$		−	15.2450i		−	0.926069i	0.886340	−	0.463035i	$-0.153239\pi$
$272$		0			0
$273$	−4.63480	−	2.52192i	−0.280511	−	0.152634i
$274$		0			0
$275$	6.84489	+	6.84489i	0.412762	+	0.412762i
$276$		0			0
$277$	−9.03535	+	9.03535i	−0.542882	+	0.542882i	−0.924373	−	0.381491i	$-0.875411\pi$
$277$	−9.03535	+	9.03535i	−0.542882	+	0.542882i	0.381491	+	0.924373i	$0.375411\pi$
$278$		0			0
$279$	−1.19093	−	1.84115i	−0.0712989	−	0.110226i
$280$		0			0
$281$	6.55154			0.390832			0.195416	−	0.980720i	$-0.437394\pi$
$281$	6.55154			0.390832			0.195416	+	0.980720i	$0.437394\pi$
$282$		0			0
$283$	5.58014	+	5.58014i	0.331705	+	0.331705i	0.853234	−	0.521529i	$-0.174638\pi$
$283$	5.58014	+	5.58014i	0.331705	+	0.331705i	−0.521529	+	0.853234i	$0.674638\pi$
$284$		0			0
$285$	−25.8374	+	7.62799i	−1.53048	+	0.451843i
$286$		0			0
$287$	3.23899			0.191192
$288$		0			0
$289$	−25.3469			−1.49099
$290$		0			0
$291$	−14.3991	+	4.25105i	−0.844090	+	0.249201i
$292$		0			0
$293$	21.2015	+	21.2015i	1.23860	+	1.23860i	0.960572	+	0.278032i	$0.0896820\pi$
$293$	21.2015	+	21.2015i	1.23860	+	1.23860i	0.278032	+	0.960572i	$0.410318\pi$
$294$		0			0
$295$	20.0813			1.16918
$296$		0			0
$297$	0.717945	+	9.45000i	0.0416594	+	0.548344i
$298$		0			0
$299$	−12.0785	+	12.0785i	−0.698518	+	0.698518i
$300$		0			0
$301$	−8.55003	−	8.55003i	−0.492816	−	0.492816i
$302$		0			0
$303$	−14.7696	−	8.03656i	−0.848493	−	0.461688i
$304$		0			0
$305$		−	5.60854i		−	0.321144i
$306$		0			0
$307$	−18.6587	+	18.6587i	−1.06491	+	1.06491i	−0.0671654	+	0.997742i	$0.521396\pi$
$307$	−18.6587	+	18.6587i	−1.06491	+	1.06491i	−0.997742	+	0.0671654i	$0.978604\pi$
$308$		0			0
$309$	13.9269	−	4.11165i	0.792275	−	0.233903i
$310$		0			0
$311$			2.15121i			0.121984i	0.998138	+	0.0609919i	$0.0194264\pi$
$311$			2.15121i			0.121984i	−0.998138	+	0.0609919i	$0.980574\pi$
$312$		0			0
$313$		−	11.1212i		−	0.628606i	−0.949323	−	0.314303i	$-0.898229\pi$
$313$		−	11.1212i		−	0.628606i	0.949323	−	0.314303i	$-0.101771\pi$
$314$		0			0
$315$	−9.41743	−	2.01954i	−0.530612	−	0.113788i
$316$		0			0
$317$	13.7663	−	13.7663i	0.773192	−	0.773192i	−0.205471	−	0.978663i	$-0.565873\pi$
$317$	13.7663	−	13.7663i	0.773192	−	0.773192i	0.978663	+	0.205471i	$0.0658727\pi$
$318$		0			0
$319$			9.26724i			0.518866i
$320$		0			0
$321$	−12.2528	+	22.5184i	−0.683887	+	1.25685i
$322$		0			0
$323$	−22.2924	−	22.2924i	−1.24038	−	1.24038i
$324$		0			0
$325$	11.4328	−	11.4328i	0.634177	−	0.634177i
$326$		0			0
$327$	−20.1495	−	10.9639i	−1.11427	−	0.606306i
$328$		0			0
$329$	7.39702			0.407811
$330$		0			0
$331$	−1.82707	−	1.82707i	−0.100425	−	0.100425i	0.655109	−	0.755534i	$-0.272623\pi$
$331$	−1.82707	−	1.82707i	−0.100425	−	0.100425i	−0.755534	+	0.655109i	$0.772623\pi$
$332$		0			0
$333$	7.06429	−	32.9419i	0.387121	−	1.80520i
$334$		0			0
$335$	11.9127			0.650859
$336$		0			0
$337$	25.8200			1.40650			0.703252	−	0.710941i	$-0.251731\pi$
$337$	25.8200			1.40650			0.703252	+	0.710941i	$0.251731\pi$
$338$		0			0
$339$	1.77930	+	6.02684i	0.0966385	+	0.327333i
$340$		0			0
$341$	−0.942651	−	0.942651i	−0.0510474	−	0.0510474i
$342$		0			0
$343$	−1.00000			−0.0539949
$344$		0			0
$345$	−14.9026	+	27.3882i	−0.802331	+	1.47453i
$346$		0			0
$347$	11.7500	−	11.7500i	0.630770	−	0.630770i	−0.317491	−	0.948261i	$-0.602840\pi$
$347$	11.7500	−	11.7500i	0.630770	−	0.630770i	0.948261	+	0.317491i	$0.102840\pi$
$348$		0			0
$349$	−3.25078	−	3.25078i	−0.174010	−	0.174010i	0.614728	−	0.788739i	$-0.289266\pi$
$349$	−3.25078	−	3.25078i	−0.174010	−	0.174010i	−0.788739	+	0.614728i	$0.789266\pi$
$350$		0			0
$351$	15.7840	−	1.19916i	0.842488	−	0.0640064i
$352$		0			0
$353$		−	1.23082i		−	0.0655098i	−0.999463	−	0.0327549i	$-0.989572\pi$
$353$		−	1.23082i		−	0.0655098i	0.999463	−	0.0327549i	$-0.0104281\pi$
$354$		0			0
$355$	−2.98733	+	2.98733i	−0.158551	+	0.158551i
$356$		0			0
$357$	−3.19143	−	10.8100i	−0.168908	−	0.572124i
$358$		0			0
$359$		−	8.68746i		−	0.458507i	−0.973367	−	0.229253i	$-0.926372\pi$
$359$		−	8.68746i		−	0.458507i	0.973367	−	0.229253i	$-0.0736284\pi$
$360$		0			0
$361$		−	4.47044i		−	0.235286i
$362$		0			0
$363$	−3.76325	−	12.7468i	−0.197519	−	0.669035i
$364$		0			0
$365$	23.6246	−	23.6246i	1.23657	−	1.23657i
$366$		0			0
$367$			6.48836i			0.338689i	0.985557	+	0.169345i	$0.0541651\pi$
$367$			6.48836i			0.338689i	−0.985557	+	0.169345i	$0.945835\pi$
$368$		0			0
$369$	−8.15890	+	5.27750i	−0.424736	+	0.274736i
$370$		0			0
$371$	0.785056	+	0.785056i	0.0407581	+	0.0407581i
$372$		0			0
$373$	8.51133	−	8.51133i	0.440700	−	0.440700i	−0.451547	−	0.892247i	$-0.649128\pi$
$373$	8.51133	−	8.51133i	0.440700	−	0.440700i	0.892247	+	0.451547i	$0.149128\pi$
$374$		0			0
$375$	0.817009	−	1.50150i	0.0421901	−	0.0775373i
$376$		0			0
$377$	15.4788			0.797197
$378$		0			0
$379$	18.0451	+	18.0451i	0.926916	+	0.926916i	0.997505	−	0.0705899i	$-0.0224882\pi$
$379$	18.0451	+	18.0451i	0.926916	+	0.926916i	−0.0705899	+	0.997505i	$0.522488\pi$
$380$		0			0
$381$	1.62676	+	5.51016i	0.0833417	+	0.282294i
$382$		0			0
$383$	10.5037			0.536715			0.268357	−	0.963319i	$-0.413519\pi$
$383$	10.5037			0.536715			0.268357	+	0.963319i	$0.413519\pi$
$384$		0			0
$385$	−5.85564			−0.298431
$386$		0			0
$387$	35.4683	+	7.60609i	1.80296	+	0.386639i
$388$		0			0
$389$	−14.1412	−	14.1412i	−0.716989	−	0.716989i	0.250998	−	0.967987i	$-0.419241\pi$
$389$	−14.1412	−	14.1412i	−0.716989	−	0.716989i	−0.967987	+	0.250998i	$0.919241\pi$
$390$		0			0
$391$	−36.4883			−1.84529
$392$		0			0
$393$	−4.27415	−	2.32568i	−0.215603	−	0.117315i
$394$		0			0
$395$	−22.1151	+	22.1151i	−1.11273	+	1.11273i
$396$		0			0
$397$	12.4687	+	12.4687i	0.625787	+	0.625787i	0.947005	−	0.321218i	$-0.104092\pi$
$397$	12.4687	+	12.4687i	0.625787	+	0.625787i	−0.321218	+	0.947005i	$0.604092\pi$
$398$		0			0
$399$	4.01057	−	7.37066i	0.200780	−	0.368994i
$400$		0			0
$401$			7.28320i			0.363706i	0.983326	+	0.181853i	$0.0582094\pi$
$401$			7.28320i			0.363706i	−0.983326	+	0.181853i	$0.941791\pi$
$402$		0			0
$403$	−1.57448	+	1.57448i	−0.0784304	+	0.0784304i
$404$		0			0
$405$	27.0127	−	10.2573i	1.34227	−	0.509688i
$406$		0			0
$407$		−	20.4828i		−	1.01530i
$408$		0			0
$409$		−	33.5956i		−	1.66119i	−0.556873	−	0.830597i	$-0.687999\pi$
$409$		−	33.5956i		−	1.66119i	0.556873	−	0.830597i	$-0.312001\pi$
$410$		0			0
$411$	22.2934	−	6.58167i	1.09965	−	0.324650i
$412$		0			0
$413$	−4.42285	+	4.42285i	−0.217634	+	0.217634i
$414$		0			0
$415$		−	2.73811i		−	0.134409i
$416$		0			0
$417$	30.5214	+	16.6075i	1.49464	+	0.813274i
$418$		0			0
$419$	−15.3527	−	15.3527i	−0.750029	−	0.750029i	0.224456	−	0.974484i	$-0.427940\pi$
$419$	−15.3527	−	15.3527i	−0.750029	−	0.750029i	−0.974484	+	0.224456i	$0.927940\pi$
$420$		0			0
$421$	−19.1550	+	19.1550i	−0.933560	+	0.933560i	−0.997926	−	0.0643664i	$-0.979497\pi$
$421$	−19.1550	+	19.1550i	−0.933560	+	0.933560i	0.0643664	+	0.997926i	$0.479497\pi$
$422$		0			0
$423$	−18.6328	+	12.0524i	−0.905958	+	0.586010i
$424$		0			0
$425$	34.5377			1.67532
$426$		0			0
$427$	1.23526	+	1.23526i	0.0597786	+	0.0597786i
$428$		0			0
$429$	9.22993	−	2.72496i	0.445625	−	0.131562i
$430$		0			0
$431$	28.7862			1.38658			0.693292	−	0.720657i	$-0.256160\pi$
$431$	28.7862			1.38658			0.693292	+	0.720657i	$0.256160\pi$
$432$		0			0
$433$	−9.30076			−0.446966			−0.223483	−	0.974708i	$-0.571743\pi$
$433$	−9.30076			−0.446966			−0.223483	+	0.974708i	$0.571743\pi$
$434$		0			0
$435$	27.0981	−	8.00019i	1.29926	−	0.383580i
$436$		0			0
$437$	−19.2083	−	19.2083i	−0.918856	−	0.918856i
$438$		0			0
$439$	13.3333			0.636363			0.318182	−	0.948030i	$-0.396928\pi$
$439$	13.3333			0.636363			0.318182	+	0.948030i	$0.396928\pi$
$440$		0			0
$441$	2.51896	−	1.62936i	0.119951	−	0.0775888i
$442$		0			0
$443$	−16.3081	+	16.3081i	−0.774821	+	0.774821i	−0.978945	−	0.204124i	$-0.934565\pi$
$443$	−16.3081	+	16.3081i	−0.774821	+	0.774821i	0.204124	+	0.978945i	$0.434565\pi$
$444$		0			0
$445$	−1.49259	−	1.49259i	−0.0707554	−	0.0707554i
$446$		0			0
$447$	0.669341	+	0.364206i	0.0316587	+	0.0172264i
$448$		0			0
$449$		−	42.0919i		−	1.98644i	−0.116250	−	0.993220i	$-0.537087\pi$
$449$		−	42.0919i		−	1.98644i	0.116250	−	0.993220i	$-0.462913\pi$
$450$		0			0
$451$	−4.17729	+	4.17729i	−0.196701	+	0.196701i
$452$		0			0
$453$	−33.3953	+	9.85929i	−1.56905	+	0.463230i
$454$		0			0
$455$			9.78048i			0.458516i
$456$		0			0
$457$		−	7.09163i		−	0.331733i	−0.986148	−	0.165866i	$-0.946958\pi$
$457$		−	7.09163i		−	0.331733i	0.986148	−	0.165866i	$-0.0530420\pi$
$458$		0			0
$459$	25.6525	+	22.0299i	1.19736	+	1.02827i
$460$		0			0
$461$	21.5049	−	21.5049i	1.00158	−	1.00158i	0.00158208	−	0.999999i	$-0.499496\pi$
$461$	21.5049	−	21.5049i	1.00158	−	1.00158i	0.999999	−	0.00158208i	$-0.000503592\pi$
$462$		0			0
$463$		−	11.6751i		−	0.542590i	−0.962496	−	0.271295i	$-0.912548\pi$
$463$		−	11.6751i		−	0.542590i	0.962496	−	0.271295i	$-0.0874519\pi$
$464$		0			0
$465$	−1.94262	+	3.57015i	−0.0900867	+	0.165562i
$466$		0			0
$467$	−17.1941	−	17.1941i	−0.795649	−	0.795649i	0.186757	−	0.982406i	$-0.440202\pi$
$467$	−17.1941	−	17.1941i	−0.795649	−	0.795649i	−0.982406	+	0.186757i	$0.940202\pi$
$468$		0			0
$469$	−2.62374	+	2.62374i	−0.121153	+	0.121153i
$470$		0			0
$471$	−17.1178	−	9.31425i	−0.788746	−	0.429178i
$472$		0			0
$473$	22.0537			1.01403
$474$		0			0
$475$	18.1814	+	18.1814i	0.834220	+	0.834220i
$476$		0			0
$477$	−3.25667	−	0.698383i	−0.149113	−	0.0319768i
$478$		0			0
$479$	2.98046			0.136181			0.0680904	−	0.997679i	$-0.478309\pi$
$479$	2.98046			0.136181			0.0680904	+	0.997679i	$0.478309\pi$
$480$		0			0
$481$	−34.2118			−1.55992
$482$		0			0
$483$	−2.74990	−	9.31443i	−0.125125	−	0.423821i
$484$		0			0
$485$	19.6780	+	19.6780i	0.893533	+	0.893533i
$486$		0			0
$487$	−23.8458			−1.08056			−0.540279	−	0.841486i	$-0.681681\pi$
$487$	−23.8458			−1.08056			−0.540279	+	0.841486i	$0.681681\pi$
$488$		0			0
$489$	−14.3308	+	26.3373i	−0.648063	+	1.19101i
$490$		0			0
$491$	3.63955	−	3.63955i	0.164251	−	0.164251i	−0.620196	−	0.784447i	$-0.712947\pi$
$491$	3.63955	−	3.63955i	0.164251	−	0.164251i	0.784447	+	0.620196i	$0.212947\pi$
$492$		0			0
$493$	23.3801	+	23.3801i	1.05299	+	1.05299i
$494$		0			0
$495$	14.7501	−	9.54097i	0.662969	−	0.428835i
$496$		0			0
$497$		−	1.31590i		−	0.0590262i
$498$		0			0
$499$	4.83486	−	4.83486i	0.216438	−	0.216438i	−0.590558	−	0.806996i	$-0.701092\pi$
$499$	4.83486	−	4.83486i	0.216438	−	0.216438i	0.806996	+	0.590558i	$0.201092\pi$
$500$		0			0
$501$	1.47286	+	4.98887i	0.0658027	+	0.222886i
$502$		0			0
$503$		−	25.8257i		−	1.15151i	−0.817622	−	0.575755i	$-0.804708\pi$
$503$		−	25.8257i		−	1.15151i	0.817622	−	0.575755i	$-0.195292\pi$
$504$		0			0
$505$			31.1673i			1.38693i
$506$		0			0
$507$	1.82415	+	6.17874i	0.0810134	+	0.274407i
$508$		0			0
$509$	16.2497	−	16.2497i	0.720254	−	0.720254i	−0.248403	−	0.968657i	$-0.579906\pi$
$509$	16.2497	−	16.2497i	0.720254	−	0.720254i	0.968657	+	0.248403i	$0.0799058\pi$
$510$		0			0
$511$			10.4065i			0.460356i
$512$		0			0
$513$	1.90701	+	25.1011i	0.0841964	+	1.10824i
$514$		0			0
$515$	−19.0327	−	19.0327i	−0.838682	−	0.838682i
$516$		0			0
$517$	−9.53985	+	9.53985i	−0.419562	+	0.419562i
$518$		0			0
$519$	19.1741	−	35.2382i	0.841648	−	1.54679i
$520$		0			0
$521$	−31.9912			−1.40156			−0.700780	−	0.713377i	$-0.747165\pi$
$521$	−31.9912			−1.40156			−0.700780	+	0.713377i	$0.747165\pi$
$522$		0			0
$523$	3.23155	+	3.23155i	0.141306	+	0.141306i	0.774221	−	0.632915i	$-0.218142\pi$
$523$	3.23155	+	3.23155i	0.141306	+	0.141306i	−0.632915	+	0.774221i	$0.718142\pi$
$524$		0			0
$525$	2.60289	+	8.81649i	0.113600	+	0.384783i
$526$		0			0
$527$	−4.75639			−0.207192
$528$		0			0
$529$	−8.44018			−0.366964
$530$		0			0
$531$	3.93455	−	18.3474i	0.170745	−	0.796210i
$532$		0			0
$533$	6.97719	+	6.97719i	0.302216	+	0.302216i
$534$		0			0
$535$	47.5188			2.05442
$536$		0			0
$537$	−12.0499	−	6.55666i	−0.519990	−	0.282941i
$538$		0			0
$539$	1.28969	−	1.28969i	0.0555508	−	0.0555508i
$540$		0			0
$541$	−1.55521	−	1.55521i	−0.0668635	−	0.0668635i	0.672884	−	0.739748i	$-0.265055\pi$
$541$	−1.55521	−	1.55521i	−0.0668635	−	0.0668635i	−0.739748	+	0.672884i	$0.765055\pi$
$542$		0			0
$543$	13.9150	−	25.5731i	0.597151	−	1.09745i
$544$		0			0
$545$			42.5201i			1.82136i
$546$		0			0
$547$	28.9521	−	28.9521i	1.23790	−	1.23790i	0.277045	−	0.960857i	$-0.410645\pi$
$547$	28.9521	−	28.9521i	1.23790	−	1.23790i	0.960857	−	0.277045i	$-0.0893551\pi$
$548$		0			0
$549$	−5.12428	−	1.09889i	−0.218699	−	0.0468994i
$550$		0			0
$551$			24.6157i			1.04866i
$552$		0			0
$553$		−	9.74158i		−	0.414254i
$554$		0			0
$555$	−59.8933	+	17.6823i	−2.54233	+	0.750573i
$556$		0			0
$557$	−4.99540	+	4.99540i	−0.211662	+	0.211662i	−0.804973	−	0.593311i	$-0.797820\pi$
$557$	−4.99540	+	4.99540i	−0.211662	+	0.211662i	0.593311	+	0.804973i	$0.297820\pi$
$558$		0			0
$559$		−	36.8356i		−	1.55798i
$560$		0			0
$561$	18.0574	+	9.82554i	0.762386	+	0.414835i
$562$		0			0
$563$	−9.20717	−	9.20717i	−0.388036	−	0.388036i	0.485950	−	0.873986i	$-0.338474\pi$
$563$	−9.20717	−	9.20717i	−0.388036	−	0.388036i	−0.873986	+	0.485950i	$0.838474\pi$
$564$		0			0
$565$	8.23636	−	8.23636i	0.346506	−	0.346506i
$566$		0			0
$567$	−3.69034	+	8.20862i	−0.154980	+	0.344729i
$568$		0			0
$569$	−24.4833			−1.02639			−0.513196	−	0.858272i	$-0.671538\pi$
$569$	−24.4833			−1.02639			−0.513196	+	0.858272i	$0.671538\pi$
$570$		0			0
$571$	−3.81239	−	3.81239i	−0.159544	−	0.159544i	0.622821	−	0.782364i	$-0.285987\pi$
$571$	−3.81239	−	3.81239i	−0.159544	−	0.159544i	−0.782364	+	0.622821i	$0.785987\pi$
$572$		0			0
$573$	−2.49038	+	0.735236i	−0.104037	+	0.0307149i
$574$		0			0
$575$	29.7594			1.24105
$576$		0			0
$577$	12.7113			0.529177			0.264589	−	0.964361i	$-0.414764\pi$
$577$	12.7113			0.529177			0.264589	+	0.964361i	$0.414764\pi$
$578$		0			0
$579$	−3.81329	+	1.12580i	−0.158475	+	0.0467866i
$580$		0			0
$581$	0.603062	+	0.603062i	0.0250192	+	0.0250192i
$582$		0			0
$583$	−2.02495			−0.0838650
$584$		0			0
$585$	−15.9360	−	24.6366i	−0.658871	−	1.01860i
$586$		0			0
$587$	−24.1308	+	24.1308i	−0.995985	+	0.995985i	−0.999992	−	0.00400654i	$-0.998725\pi$
$587$	−24.1308	+	24.1308i	−0.995985	+	0.995985i	0.00400654	+	0.999992i	$0.498725\pi$
$588$		0			0
$589$	−2.50387	−	2.50387i	−0.103170	−	0.103170i
$590$		0			0
$591$	9.07183	+	4.93623i	0.373165	+	0.203049i
$592$		0			0
$593$		−	7.81607i		−	0.320968i	−0.987038	−	0.160484i	$-0.948695\pi$
$593$		−	7.81607i		−	0.320968i	0.987038	−	0.160484i	$-0.0513054\pi$
$594$		0			0
$595$	−14.7731	+	14.7731i	−0.605636	+	0.605636i
$596$		0			0
$597$	−6.80088	+	2.00783i	−0.278342	+	0.0821749i
$598$		0			0
$599$			36.8480i			1.50557i	0.658268	+	0.752784i	$0.271290\pi$
$599$			36.8480i			1.50557i	−0.658268	+	0.752784i	$0.728710\pi$
$600$		0			0
$601$			46.9927i			1.91687i	0.285306	+	0.958436i	$0.407905\pi$
$601$			46.9927i			1.91687i	−0.285306	+	0.958436i	$0.592095\pi$
$602$		0			0
$603$	2.33407	−	10.8841i	0.0950506	−	0.443235i
$604$		0			0
$605$	−17.4200	+	17.4200i	−0.708224	+	0.708224i
$606$		0			0
$607$			44.8233i			1.81932i	0.415353	+	0.909660i	$0.363658\pi$
$607$			44.8233i			1.81932i	−0.415353	+	0.909660i	$0.636342\pi$
$608$		0			0
$609$	−4.20627	+	7.73031i	−0.170447	+	0.313248i
$610$		0			0
$611$	15.9341	+	15.9341i	0.644624	+	0.644624i
$612$		0			0
$613$	32.0395	−	32.0395i	1.29406	−	1.29406i	0.361813	−	0.932251i	$-0.382158\pi$
$613$	32.0395	−	32.0395i	1.29406	−	1.29406i	0.932251	−	0.361813i	$-0.117842\pi$
$614$		0			0
$615$	15.8209	+	8.60856i	0.637959	+	0.347131i
$616$		0			0
$617$	−3.37809			−0.135997			−0.0679985	−	0.997685i	$-0.521661\pi$
$617$	−3.37809			−0.135997			−0.0679985	+	0.997685i	$0.521661\pi$
$618$		0			0
$619$	0.353620	+	0.353620i	0.0142132	+	0.0142132i	0.714178	−	0.699964i	$-0.246801\pi$
$619$	0.353620	+	0.353620i	0.0142132	+	0.0142132i	−0.699964	+	0.714178i	$0.746801\pi$
$620$		0			0
$621$	22.1035	+	18.9821i	0.886983	+	0.761726i
$622$		0			0
$623$	0.657476			0.0263412
$624$		0			0
$625$	23.3685			0.934740
$626$		0			0
$627$	4.33346	+	14.6782i	0.173062	+	0.586192i
$628$		0			0
$629$	−51.6756	−	51.6756i	−2.06044	−	2.06044i
$630$		0			0
$631$	5.49410			0.218717			0.109358	−	0.994002i	$-0.465120\pi$
$631$	5.49410			0.218717			0.109358	+	0.994002i	$0.465120\pi$
$632$		0			0
$633$	11.4372	−	21.0194i	0.454589	−	0.835447i
$634$		0			0
$635$	7.53026	−	7.53026i	0.298829	−	0.298829i
$636$		0			0
$637$	−2.15412	−	2.15412i	−0.0853494	−	0.0853494i
$638$		0			0
$639$	2.14408	+	3.31470i	0.0848185	+	0.131128i
$640$		0			0
$641$			12.3855i			0.489198i	0.969624	+	0.244599i	$0.0786563\pi$
$641$			12.3855i			0.489198i	−0.969624	+	0.244599i	$0.921344\pi$
$642$		0			0
$643$	8.45364	−	8.45364i	0.333379	−	0.333379i	−0.520489	−	0.853868i	$-0.674250\pi$
$643$	8.45364	−	8.45364i	0.333379	−	0.333379i	0.853868	+	0.520489i	$0.174250\pi$
$644$		0			0
$645$	−19.0385	−	64.4869i	−0.749639	−	2.53917i
$646$		0			0
$647$			31.5511i			1.24040i	0.784443	+	0.620200i	$0.212949\pi$
$647$			31.5511i			1.24040i	−0.784443	+	0.620200i	$0.787051\pi$
$648$		0			0
$649$		−	11.4082i		−	0.447810i
$650$		0			0
$651$	−0.358460	−	1.21417i	−0.0140492	−	0.0475871i
$652$		0			0
$653$	−24.3917	+	24.3917i	−0.954521	+	0.954521i	−0.999010	−	0.0444889i	$-0.985834\pi$
$653$	−24.3917	+	24.3917i	−0.954521	+	0.954521i	0.0444889	+	0.999010i	$0.485834\pi$
$654$		0			0
$655$			9.01943i			0.352418i
$656$		0			0
$657$	−16.9560	−	26.2135i	−0.661515	−	1.02269i
$658$		0			0
$659$	8.56243	+	8.56243i	0.333545	+	0.333545i	0.853931	−	0.520386i	$-0.174212\pi$
$659$	8.56243	+	8.56243i	0.333545	+	0.333545i	−0.520386	+	0.853931i	$0.674212\pi$
$660$		0			0
$661$	−8.35402	+	8.35402i	−0.324934	+	0.324934i	−0.850656	−	0.525722i	$-0.823795\pi$
$661$	−8.35402	+	8.35402i	−0.324934	+	0.324934i	0.525722	+	0.850656i	$0.323795\pi$
$662$		0			0
$663$	16.4113	−	30.1607i	0.637361	−	1.17135i
$664$		0			0
$665$	−15.5538			−0.603149
$666$		0			0
$667$	20.1455	+	20.1455i	0.780038	+	0.780038i
$668$		0			0
$669$	2.86615	+	9.70817i	0.110812	+	0.375340i
$670$		0			0
$671$	−3.18621			−0.123002
$672$		0			0
$673$	38.6443			1.48963			0.744813	−	0.667273i	$-0.232538\pi$
$673$	38.6443			1.48963			0.744813	+	0.667273i	$0.232538\pi$
$674$		0			0
$675$	−20.9219	−	17.9673i	−0.805283	−	0.691563i
$676$		0			0
$677$	14.6806	+	14.6806i	0.564223	+	0.564223i	0.930504	−	0.366281i	$-0.119369\pi$
$677$	14.6806	+	14.6806i	0.564223	+	0.564223i	−0.366281	+	0.930504i	$0.619369\pi$
$678$		0			0
$679$	−8.66806			−0.332649
$680$		0			0
$681$	13.8357	+	7.52836i	0.530184	+	0.288487i
$682$		0			0
$683$	−11.0844	+	11.0844i	−0.424132	+	0.424132i	−0.886624	−	0.462492i	$-0.846956\pi$
$683$	−11.0844	+	11.0844i	−0.424132	+	0.424132i	0.462492	+	0.886624i	$0.346956\pi$
$684$		0			0
$685$	−30.4664	−	30.4664i	−1.16406	−	1.16406i
$686$		0			0
$687$	−0.868597	+	1.59631i	−0.0331390	+	0.0609031i
$688$		0			0
$689$			3.38221i			0.128852i
$690$		0			0
$691$	−31.1872	+	31.1872i	−1.18642	+	1.18642i	−0.208364	+	0.978051i	$0.566814\pi$
$691$	−31.1872	+	31.1872i	−1.18642	+	1.18642i	−0.978051	+	0.208364i	$0.933186\pi$
$692$		0			0
$693$	−1.14730	+	5.35005i	−0.0435824	+	0.203231i
$694$		0			0
$695$		−	64.4071i		−	2.44310i
$696$		0			0
$697$			21.0776i			0.798371i
$698$		0			0
$699$	34.6286	−	10.2234i	1.30977	−	0.386685i
$700$		0			0
$701$	22.3603	−	22.3603i	0.844537	−	0.844537i	−0.144909	−	0.989445i	$-0.546289\pi$
$701$	22.3603	−	22.3603i	0.844537	−	0.844537i	0.989445	+	0.144909i	$0.0462888\pi$
$702$		0			0
$703$		−	54.4065i		−	2.05198i
$704$		0			0
$705$	36.1308	+	19.6597i	1.36076	+	0.740428i
$706$		0			0
$707$	−6.86450	−	6.86450i	−0.258166	−	0.258166i
$708$		0			0
$709$	−17.5606	+	17.5606i	−0.659501	+	0.659501i	−0.955262	−	0.295761i	$-0.904427\pi$
$709$	−17.5606	+	17.5606i	−0.659501	+	0.659501i	0.295761	+	0.955262i	$0.404427\pi$
$710$		0			0
$711$	15.8726	+	24.5387i	0.595268	+	0.920272i
$712$		0			0
$713$	−4.09835			−0.153484
$714$		0			0
$715$	−12.6138	−	12.6138i	−0.471728	−	0.471728i
$716$		0			0
$717$	20.4136	−	6.02673i	0.762361	−	0.225072i
$718$		0			0
$719$	6.22460			0.232138			0.116069	−	0.993241i	$-0.462971\pi$
$719$	6.22460			0.232138			0.116069	+	0.993241i	$0.462971\pi$
$720$		0			0
$721$	8.38381			0.312229
$722$		0			0
$723$	−34.8568	+	10.2908i	−1.29634	+	0.382718i
$724$		0			0
$725$	−19.0686	−	19.0686i	−0.708189	−	0.708189i
$726$		0			0
$727$	−32.0728			−1.18952			−0.594758	−	0.803905i	$-0.702752\pi$
$727$	−32.0728			−1.18952			−0.594758	+	0.803905i	$0.702752\pi$
$728$		0			0
$729$	−4.07900	−	26.6901i	−0.151074	−	0.988522i
$730$		0			0
$731$	55.6389	−	55.6389i	2.05788	−	2.05788i
$732$		0			0
$733$	−13.0287	−	13.0287i	−0.481226	−	0.481226i	0.424297	−	0.905523i	$-0.360521\pi$
$733$	−13.0287	−	13.0287i	−0.481226	−	0.481226i	−0.905523	+	0.424297i	$0.860521\pi$
$734$		0			0
$735$	−4.88450	−	2.65779i	−0.180168	−	0.0980340i
$736$		0			0
$737$		−	6.76760i		−	0.249288i
$738$		0			0
$739$	6.57440	−	6.57440i	0.241843	−	0.241843i	−0.575769	−	0.817612i	$-0.695297\pi$
$739$	6.57440	−	6.57440i	0.241843	−	0.241843i	0.817612	+	0.575769i	$0.195297\pi$
$740$		0			0
$741$	24.5166	−	7.23803i	0.900639	−	0.265896i
$742$		0			0
$743$			18.1728i			0.666694i	0.942804	+	0.333347i	$0.108178\pi$
$743$			18.1728i			0.666694i	−0.942804	+	0.333347i	$0.891822\pi$
$744$		0			0
$745$		−	1.41246i		−	0.0517485i
$746$		0			0
$747$	−2.50170	−	0.536482i	−0.0915323	−	0.0196289i
$748$		0			0
$749$	−10.4659	+	10.4659i	−0.382415	+	0.382415i
$750$		0			0
$751$		−	12.6900i		−	0.463065i	−0.972827	−	0.231532i	$-0.925626\pi$
$751$		−	12.6900i		−	0.463065i	0.972827	−	0.231532i	$-0.0743739\pi$
$752$		0			0
$753$	18.3450	−	33.7146i	0.668531	−	1.22863i
$754$		0			0
$755$	45.6384	+	45.6384i	1.66095	+	1.66095i
$756$		0			0
$757$	−20.3686	+	20.3686i	−0.740311	+	0.740311i	−0.972638	−	0.232327i	$-0.925366\pi$
$757$	−20.3686	+	20.3686i	−0.740311	+	0.740311i	0.232327	+	0.972638i	$0.425366\pi$
$758$		0			0
$759$	15.5592	+	8.46619i	0.564764	+	0.307303i
$760$		0			0
$761$	24.1751			0.876346			0.438173	−	0.898891i	$-0.355626\pi$
$761$	24.1751			0.876346			0.438173	+	0.898891i	$0.355626\pi$
$762$		0			0
$763$	−9.36493	−	9.36493i	−0.339033	−	0.339033i
$764$		0			0
$765$	13.1421	−	61.2835i	0.475153	−	2.21571i
$766$		0			0
$767$	−19.0547			−0.688025
$768$		0			0
$769$	21.7492			0.784298			0.392149	−	0.919902i	$-0.371732\pi$
$769$	21.7492			0.784298			0.392149	+	0.919902i	$0.371732\pi$
$770$		0			0
$771$	1.41168	+	4.78163i	0.0508404	+	0.172206i
$772$		0			0
$773$	−25.0813	−	25.0813i	−0.902112	−	0.902112i	0.0935069	−	0.995619i	$-0.470192\pi$
$773$	−25.0813	−	25.0813i	−0.902112	−	0.902112i	−0.995619	+	0.0935069i	$0.970192\pi$
$774$		0			0
$775$	3.87926			0.139347
$776$		0			0
$777$	9.29685	−	17.0858i	0.333523	−	0.612950i
$778$		0			0
$779$	−11.0957	+	11.0957i	−0.397546	+	0.397546i
$780$		0			0
$781$	1.69710	+	1.69710i	0.0607270	+	0.0607270i
$782$		0			0
$783$	−2.00006	−	26.3259i	−0.0714762	−	0.940811i
$784$		0			0
$785$			36.1224i			1.28926i
$786$		0			0
$787$	12.7875	−	12.7875i	0.455824	−	0.455824i	−0.441458	−	0.897282i	$-0.645538\pi$
$787$	12.7875	−	12.7875i	0.455824	−	0.455824i	0.897282	+	0.441458i	$0.145538\pi$
$788$		0			0
$789$	1.65981	+	5.62209i	0.0590909	+	0.200152i
$790$		0			0
$791$			3.62807i			0.128999i
$792$		0			0
$793$			5.32182i			0.188983i
$794$		0			0
$795$	1.74809	+	5.92112i	0.0619985	+	0.210000i
$796$		0			0
$797$	−15.0855	+	15.0855i	−0.534356	+	0.534356i	−0.921866	−	0.387510i	$-0.873335\pi$
$797$	−15.0855	+	15.0855i	−0.534356	+	0.534356i	0.387510	+	0.921866i	$0.373335\pi$
$798$		0			0
$799$			48.1357i			1.70292i
$800$		0			0
$801$	−1.65616	+	1.07127i	−0.0585175	+	0.0378514i
$802$		0			0
$803$	−13.4211	−	13.4211i	−0.473621	−	0.473621i
$804$		0			0
$805$	−12.7292	+	12.7292i	−0.448646	+	0.448646i
$806$		0			0
$807$	25.6487	−	47.1373i	0.902876	−	1.65931i
$808$		0			0
$809$	46.1180			1.62142			0.810712	−	0.585445i	$-0.199080\pi$
$809$	46.1180			1.62142			0.810712	+	0.585445i	$0.199080\pi$
$810$		0			0
$811$	33.5469	+	33.5469i	1.17799	+	1.17799i	0.980255	+	0.197737i	$0.0633592\pi$
$811$	33.5469	+	33.5469i	1.17799	+	1.17799i	0.197737	+	0.980255i	$0.436641\pi$
$812$		0			0
$813$	7.47658	+	25.3246i	0.262215	+	0.888171i
$814$		0			0
$815$	55.5776			1.94680
$816$		0			0
$817$	58.5792			2.04943
$818$		0			0
$819$	8.93600	+	1.91630i	0.312249	+	0.0669610i
$820$		0			0
$821$	32.2408	+	32.2408i	1.12521	+	1.12521i	0.990945	+	0.134265i	$0.0428674\pi$
$821$	32.2408	+	32.2408i	1.12521	+	1.12521i	0.134265	+	0.990945i	$0.457133\pi$
$822$		0			0
$823$	15.6995			0.547252			0.273626	−	0.961836i	$-0.411777\pi$
$823$	15.6995			0.547252			0.273626	+	0.961836i	$0.411777\pi$
$824$		0			0
$825$	−14.7274	−	8.01360i	−0.512744	−	0.278998i
$826$		0			0
$827$	−17.5343	+	17.5343i	−0.609728	+	0.609728i	−0.942875	−	0.333147i	$-0.891889\pi$
$827$	−17.5343	+	17.5343i	−0.609728	+	0.609728i	0.333147	+	0.942875i	$0.391889\pi$
$828$		0			0
$829$	−14.8343	−	14.8343i	−0.515216	−	0.515216i	0.400904	−	0.916120i	$-0.368696\pi$
$829$	−14.8343	−	14.8343i	−0.515216	−	0.515216i	−0.916120	+	0.400904i	$0.868696\pi$
$830$		0			0
$831$	10.5781	−	19.4404i	0.366949	−	0.674381i
$832$		0			0
$833$		−	6.50745i		−	0.225470i
$834$		0			0
$835$	6.81785	−	6.81785i	0.235942	−	0.235942i
$836$		0			0
$837$	2.88128	+	2.47439i	0.0995915	+	0.0855274i
$838$		0			0
$839$			1.23295i			0.0425661i	0.999773	+	0.0212830i	$0.00677511\pi$
$839$			1.23295i			0.0425661i	−0.999773	+	0.0212830i	$0.993225\pi$
$840$		0			0
$841$			3.18322i			0.109766i
$842$		0			0
$843$	−10.8832	+	3.21306i	−0.374838	+	0.110663i
$844$		0			0
$845$	8.44395	−	8.44395i	0.290481	−	0.290481i
$846$		0			0
$847$		−	7.67341i		−	0.263662i
$848$		0			0
$849$	−12.0062	−	6.53290i	−0.412052	−	0.224209i
$850$		0			0
$851$	−44.5264	−	44.5264i	−1.52635	−	1.52635i
$852$		0			0
$853$	−3.79105	+	3.79105i	−0.129803	+	0.129803i	−0.769024	−	0.639220i	$-0.779257\pi$
$853$	−3.79105	+	3.79105i	−0.129803	+	0.129803i	0.639220	+	0.769024i	$0.279257\pi$
$854$		0			0
$855$	39.1793	−	25.3427i	1.33990	−	0.866703i
$856$		0			0
$857$	27.4939			0.939175			0.469588	−	0.882886i	$-0.344403\pi$
$857$	27.4939			0.939175			0.469588	+	0.882886i	$0.344403\pi$
$858$		0			0
$859$	−21.1302	−	21.1302i	−0.720954	−	0.720954i	0.247846	−	0.968800i	$-0.420277\pi$
$859$	−21.1302	−	21.1302i	−0.720954	−	0.720954i	−0.968800	+	0.247846i	$0.920277\pi$
$860$		0			0
$861$	−5.38052	+	1.58849i	−0.183367	+	0.0541356i
$862$		0			0
$863$	−2.27110			−0.0773092			−0.0386546	−	0.999253i	$-0.512307\pi$
$863$	−2.27110			−0.0773092			−0.0386546	+	0.999253i	$0.512307\pi$
$864$		0			0
$865$	−74.3606			−2.52834
$866$		0			0
$867$	42.1055	−	12.4308i	1.42998	−	0.422173i
$868$		0			0
$869$	12.5636	+	12.5636i	0.426191	+	0.426191i
$870$		0			0
$871$	−11.3037			−0.383011
$872$		0			0
$873$	21.8345	−	14.1234i	0.738986	−	0.478006i
$874$		0			0
$875$	0.697856	−	0.697856i	0.0235918	−	0.0235918i
$876$		0			0
$877$	−22.9389	−	22.9389i	−0.774591	−	0.774591i	0.204314	−	0.978905i	$-0.434504\pi$
$877$	−22.9389	−	22.9389i	−0.774591	−	0.774591i	−0.978905	+	0.204314i	$0.934504\pi$
$878$		0			0
$879$	−45.6170	−	24.8214i	−1.53862	−	0.837207i
$880$		0			0
$881$		−	11.5927i		−	0.390569i	−0.980747	−	0.195284i	$-0.937437\pi$
$881$		−	11.5927i		−	0.390569i	0.980747	−	0.195284i	$-0.0625629\pi$
$882$		0			0
$883$	−34.7982	+	34.7982i	−1.17105	+	1.17105i	−0.189093	+	0.981959i	$0.560555\pi$
$883$	−34.7982	+	34.7982i	−1.17105	+	1.17105i	−0.981959	+	0.189093i	$0.939445\pi$
$884$		0			0
$885$	−33.3584	+	9.84841i	−1.12133	+	0.331051i
$886$		0			0
$887$		−	14.8054i		−	0.497115i	−0.968617	−	0.248558i	$-0.920043\pi$
$887$		−	14.8054i		−	0.497115i	0.968617	−	0.248558i	$-0.0799565\pi$
$888$		0			0
$889$			3.31704i			0.111250i
$890$		0			0
$891$	−5.82716	−	15.3459i	−0.195217	−	0.514108i
$892$		0			0
$893$	−25.3398	+	25.3398i	−0.847963	+	0.847963i
$894$		0			0
$895$			25.4279i			0.849962i
$896$		0			0
$897$	14.1408	−	25.9880i	0.472147	−	0.867716i
$898$		0			0
$899$	2.62605	+	2.62605i	0.0875836	+	0.0875836i
$900$		0			0
$901$	−5.10871	+	5.10871i	−0.170196	+	0.170196i
$902$		0			0
$903$	18.3962	+	10.0099i	0.612188	+	0.333108i
$904$		0			0
$905$	−53.9651			−1.79386
$906$		0			0
$907$	7.13712	+	7.13712i	0.236984	+	0.236984i	0.815600	−	0.578616i	$-0.196407\pi$
$907$	7.13712	+	7.13712i	0.236984	+	0.236984i	−0.578616	+	0.815600i	$0.696407\pi$
$908$		0			0
$909$	28.4762	+	6.10664i	0.944496	+	0.202545i
$910$		0			0
$911$	−16.9295			−0.560901			−0.280450	−	0.959869i	$-0.590484\pi$
$911$	−16.9295			−0.560901			−0.280450	+	0.959869i	$0.590484\pi$
$912$		0			0
$913$	−1.55552			−0.0514803
$914$		0			0
$915$	2.75058	+	9.31672i	0.0909313	+	0.308001i
$916$		0			0
$917$	−1.98650	−	1.98650i	−0.0656001	−	0.0656001i
$918$		0			0
$919$	−12.9874			−0.428414			−0.214207	−	0.976788i	$-0.568717\pi$
$919$	−12.9874			−0.428414			−0.214207	+	0.976788i	$0.568717\pi$
$920$		0			0
$921$	21.8445	−	40.1459i	0.719800	−	1.32285i
$922$		0			0
$923$	2.83461	−	2.83461i	0.0933023	−	0.0933023i
$924$		0			0
$925$	42.1461	+	42.1461i	1.38575	+	1.38575i
$926$		0			0
$927$	−21.1185	+	13.6603i	−0.693622	+	0.448662i
$928$		0			0
$929$		−	34.0965i		−	1.11867i	−0.828942	−	0.559335i	$-0.811057\pi$
$929$		−	34.0965i		−	1.11867i	0.828942	−	0.559335i	$-0.188943\pi$
$930$		0			0
$931$	3.42567	−	3.42567i	0.112272	−	0.112272i
$932$		0			0
$933$	−1.05501	−	3.57352i	−0.0345395	−	0.116992i
$934$		0			0
$935$		−	38.1053i		−	1.24618i
$936$		0			0
$937$			16.6312i			0.543317i	0.962394	+	0.271659i	$0.0875722\pi$
$937$			16.6312i			0.543317i	−0.962394	+	0.271659i	$0.912428\pi$
$938$		0			0
$939$	5.45413	+	18.4741i	0.177989	+	0.602881i
$940$		0			0
$941$	8.04851	−	8.04851i	0.262374	−	0.262374i	−0.563644	−	0.826018i	$-0.690601\pi$
$941$	8.04851	−	8.04851i	0.262374	−	0.262374i	0.826018	+	0.563644i	$0.190601\pi$
$942$		0			0
$943$			18.1615i			0.591421i
$944$		0			0
$945$	16.6344	−	1.26376i	0.541117	−	0.0411103i
$946$		0			0
$947$	6.31033	+	6.31033i	0.205058	+	0.205058i	0.802163	−	0.597105i	$-0.203682\pi$
$947$	6.31033	+	6.31033i	0.205058	+	0.205058i	−0.597105	+	0.802163i	$0.703682\pi$
$948$		0			0
$949$	−22.4168	+	22.4168i	−0.727681	+	0.727681i
$950$		0			0
$951$	−16.1168	+	29.6195i	−0.522622	+	0.960478i
$952$		0			0
$953$	−50.9888			−1.65169			−0.825845	−	0.563897i	$-0.809302\pi$
$953$	−50.9888			−1.65169			−0.825845	+	0.563897i	$0.809302\pi$
$954$		0			0
$955$	3.40339	+	3.40339i	0.110131	+	0.110131i
$956$		0			0
$957$	−4.54491	−	15.3945i	−0.146916	−	0.497632i
$958$		0			0
$959$	13.4203			0.433364
$960$		0			0
$961$	30.4658			0.982767
$962$		0			0
$963$	9.31042	−	43.4159i	0.300024	−	1.39906i
$964$		0			0
$965$	5.21130	+	5.21130i	0.167758	+	0.167758i
$966$		0			0
$967$	−26.3341			−0.846849			−0.423424	−	0.905931i	$-0.639172\pi$
$967$	−26.3341			−0.846849			−0.423424	+	0.905931i	$0.639172\pi$
$968$		0			0
$969$	47.9642	+	26.0986i	1.54083	+	0.838408i
$970$		0			0
$971$	10.1620	−	10.1620i	0.326114	−	0.326114i	−0.524993	−	0.851107i	$-0.675932\pi$
$971$	10.1620	−	10.1620i	0.326114	−	0.326114i	0.851107	+	0.524993i	$0.175932\pi$
$972$		0			0
$973$	14.1855	+	14.1855i	0.454766	+	0.454766i
$974$		0			0
$975$	−13.3848	+	24.5987i	−0.428658	+	0.787790i
$976$		0			0
$977$			40.0377i			1.28092i	0.767992	+	0.640460i	$0.221256\pi$
$977$			40.0377i			1.28092i	−0.767992	+	0.640460i	$0.778744\pi$
$978$		0			0
$979$	−0.847939	+	0.847939i	−0.0271002	+	0.0271002i
$980$		0			0
$981$	38.8488	+	8.33102i	1.24035	+	0.265989i
$982$		0			0
$983$		−	29.8253i		−	0.951280i	−0.879640	−	0.475640i	$-0.842217\pi$
$983$		−	29.8253i		−	0.951280i	0.879640	−	0.475640i	$-0.157783\pi$
$984$		0			0
$985$		−	19.1436i		−	0.609966i
$986$		0			0
$987$	−12.2877	+	3.62770i	−0.391122	+	0.115471i
$988$		0			0
$989$	47.9414	−	47.9414i	1.52445	−	1.52445i
$990$		0			0
$991$			47.9793i			1.52411i	0.647511	+	0.762056i	$0.275810\pi$
$991$			47.9793i			1.52411i	−0.647511	+	0.762056i	$0.724190\pi$
$992$		0			0
$993$	3.93112	+	2.13903i	0.124750	+	0.0678800i
$994$		0			0
$995$	9.29418	+	9.29418i	0.294645	+	0.294645i
$996$		0			0
$997$	24.4353	−	24.4353i	0.773873	−	0.773873i	−0.204908	−	0.978781i	$-0.565690\pi$
$997$	24.4353	−	24.4353i	0.773873	−	0.773873i	0.978781	+	0.204908i	$0.0656896\pi$
$998$		0			0
$999$	4.42060	+	58.1865i	0.139862	+	1.84094i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1344.2.s.d.239.2		48
3.2	odd	2	inner	1344.2.s.d.239.10		48
4.3	odd	2		336.2.s.d.323.14	yes	48
12.11	even	2		336.2.s.d.323.11	yes	48
16.5	even	4		336.2.s.d.155.11	✓	48
16.11	odd	4	inner	1344.2.s.d.911.10		48
48.5	odd	4		336.2.s.d.155.14	yes	48
48.11	even	4	inner	1344.2.s.d.911.2		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
336.2.s.d.155.11	✓	48	16.5	even	4
336.2.s.d.155.14	yes	48	48.5	odd	4
336.2.s.d.323.11	yes	48	12.11	even	2
336.2.s.d.323.14	yes	48	4.3	odd	2
1344.2.s.d.239.2		48	1.1	even	1	trivial
1344.2.s.d.239.10		48	3.2	odd	2	inner
1344.2.s.d.911.2		48	48.11	even	4	inner
1344.2.s.d.911.10		48	16.11	odd	4	inner

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:	\( N \)	\(=\)	\( 1344 = 2^{6} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1344.s (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.66117 + 0.490427i) q^{3} +(2.27018 + 2.27018i) q^{5} -1.00000 q^{7} +(2.51896 - 1.62936i) q^{9} +O(q^{10})\)	\(q+(-1.66117 + 0.490427i) q^{3} +(2.27018 + 2.27018i) q^{5} -1.00000 q^{7} +(2.51896 - 1.62936i) q^{9} +(1.28969 - 1.28969i) q^{11} +(-2.15412 - 2.15412i) q^{13} +(-4.88450 - 2.65779i) q^{15} -6.50745i q^{17} +(3.42567 - 3.42567i) q^{19} +(1.66117 - 0.490427i) q^{21} -5.60715i q^{23} +5.30740i q^{25} +(-3.38534 + 3.94202i) q^{27} +(-3.59282 + 3.59282i) q^{29} -0.730914i q^{31} +(-1.50989 + 2.77489i) q^{33} +(-2.27018 - 2.27018i) q^{35} +(7.94100 - 7.94100i) q^{37} +(4.63480 + 2.52192i) q^{39} -3.23899 q^{41} +(8.55003 + 8.55003i) q^{43} +(9.41743 + 2.01954i) q^{45} -7.39702 q^{47} +1.00000 q^{49} +(3.19143 + 10.8100i) q^{51} +(-0.785056 - 0.785056i) q^{53} +5.85564 q^{55} +(-4.01057 + 7.37066i) q^{57} +(4.42285 - 4.42285i) q^{59} +(-1.23526 - 1.23526i) q^{61} +(-2.51896 + 1.62936i) q^{63} -9.78048i q^{65} +(2.62374 - 2.62374i) q^{67} +(2.74990 + 9.31443i) q^{69} +1.31590i q^{71} -10.4065i q^{73} +(-2.60289 - 8.81649i) q^{75} +(-1.28969 + 1.28969i) q^{77} +9.74158i q^{79} +(3.69034 - 8.20862i) q^{81} +(-0.603062 - 0.603062i) q^{83} +(14.7731 - 14.7731i) q^{85} +(4.20627 - 7.73031i) q^{87} -0.657476 q^{89} +(2.15412 + 2.15412i) q^{91} +(0.358460 + 1.21417i) q^{93} +15.5538 q^{95} +8.66806 q^{97} +(1.14730 - 5.35005i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 48 q^{7}+O(q^{10}) \) 48 * q - 48 * q^7	\( 48 q - 48 q^{7} - 8 q^{19} + 12 q^{27} + 16 q^{37} + 24 q^{39} + 48 q^{43} + 20 q^{45} + 48 q^{49} + 32 q^{55} + 8 q^{61} + 16 q^{67} - 28 q^{69} + 12 q^{75} - 48 q^{85} - 56 q^{87} - 64 q^{93} - 32 q^{99}+O(q^{100}) \) 48 * q - 48 * q^7 - 8 * q^19 + 12 * q^27 + 16 * q^37 + 24 * q^39 + 48 * q^43 + 20 * q^45 + 48 * q^49 + 32 * q^55 + 8 * q^61 + 16 * q^67 - 28 * q^69 + 12 * q^75 - 48 * q^85 - 56 * q^87 - 64 * q^93 - 32 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more