LMFDB - Embedded newform 3584.2.m.bc.2689.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3584,2,Mod(897,3584)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3584, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 1, 0]))

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

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

chi := DirichletCharacter("3584.897");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 3584 = 2^{9} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	3584.m (of order $4$, degree $2$, 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:	$28.6183840844$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(i)$
Coefficient field:	$\Q(\zeta_{12})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{2} + 1 $ x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{3} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			2689.1
Root			$0.866025 + 0.500000i$ of defining polynomial
Character	$\chi$	$=$	3584.2689
Dual form			3584.2.m.bc.897.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.73205 - 1.73205i) q^{3} +(0.732051 - 0.732051i) q^{5} +1.00000i q^{7} +3.00000i q^{9} +O(q^{10})$	\(q+(-1.73205 - 1.73205i) q^{3} +(0.732051 - 0.732051i) q^{5} +1.00000i q^{7} +3.00000i q^{9} +(-2.00000 + 2.00000i) q^{11} +(1.26795 + 1.26795i) q^{13} -2.53590 q^{15} +3.46410 q^{17} +(-1.73205 - 1.73205i) q^{19} +(1.73205 - 1.73205i) q^{21} +2.53590i q^{23} +3.92820i q^{25} +(-4.46410 - 4.46410i) q^{29} +0.535898 q^{31} +6.92820 q^{33} +(0.732051 + 0.732051i) q^{35} +(6.46410 - 6.46410i) q^{37} -4.39230i q^{39} -3.46410i q^{41} +(0.535898 - 0.535898i) q^{43} +(2.19615 + 2.19615i) q^{45} -4.53590 q^{47} -1.00000 q^{49} +(-6.00000 - 6.00000i) q^{51} +(-1.00000 + 1.00000i) q^{53} +2.92820i q^{55} +6.00000i q^{57} +(5.73205 - 5.73205i) q^{59} +(-8.73205 - 8.73205i) q^{61} -3.00000 q^{63} +1.85641 q^{65} +(-10.9282 - 10.9282i) q^{67} +(4.39230 - 4.39230i) q^{69} -4.00000i q^{71} -6.00000i q^{73} +(6.80385 - 6.80385i) q^{75} +(-2.00000 - 2.00000i) q^{77} -4.00000 q^{79} +9.00000 q^{81} +(5.73205 + 5.73205i) q^{83} +(2.53590 - 2.53590i) q^{85} +15.4641i q^{87} +4.92820i q^{89} +(-1.26795 + 1.26795i) q^{91} +(-0.928203 - 0.928203i) q^{93} -2.53590 q^{95} +18.3923 q^{97} +(-6.00000 - 6.00000i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 4 q^{5}+O(q^{10}) $ 4 * q - 4 * q^5	$ 4 q - 4 q^{5} - 8 q^{11} + 12 q^{13} - 24 q^{15} - 4 q^{29} + 16 q^{31} - 4 q^{35} + 12 q^{37} + 16 q^{43} - 12 q^{45} - 32 q^{47} - 4 q^{49} - 24 q^{51} - 4 q^{53} + 16 q^{59} - 28 q^{61} - 12 q^{63} - 48 q^{65} - 16 q^{67} - 24 q^{69} + 48 q^{75} - 8 q^{77} - 16 q^{79} + 36 q^{81} + 16 q^{83} + 24 q^{85} - 12 q^{91} + 24 q^{93} - 24 q^{95} + 32 q^{97} - 24 q^{99}+O(q^{100}) $ 4 * q - 4 * q^5 - 8 * q^11 + 12 * q^13 - 24 * q^15 - 4 * q^29 + 16 * q^31 - 4 * q^35 + 12 * q^37 + 16 * q^43 - 12 * q^45 - 32 * q^47 - 4 * q^49 - 24 * q^51 - 4 * q^53 + 16 * q^59 - 28 * q^61 - 12 * q^63 - 48 * q^65 - 16 * q^67 - 24 * q^69 + 48 * q^75 - 8 * q^77 - 16 * q^79 + 36 * q^81 + 16 * q^83 + 24 * q^85 - 12 * q^91 + 24 * q^93 - 24 * q^95 + 32 * q^97 - 24 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/3584\mathbb{Z}\right)^\times$.

$n$	$1023$	$1025$	$1541$
$\chi(n)$	$1$	$1$	$e\left(\frac{3}{4}\right)$

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
$3$	−1.73205	−	1.73205i	−1.00000	−	1.00000i		−	1.00000i	$-0.5\pi$
$3$	−1.73205	−	1.73205i	−1.00000	−	1.00000i	−1.00000			$\pi$
$4$		0			0
$5$	0.732051	−	0.732051i	0.327383	−	0.327383i	−0.524207	−	0.851591i	$-0.675638\pi$
$5$	0.732051	−	0.732051i	0.327383	−	0.327383i	0.851591	+	0.524207i	$0.175638\pi$
$6$		0			0
$7$			1.00000i			0.377964i
$7$			1.00000i			0.377964i
$8$		0			0
$9$			3.00000i			1.00000i
$10$		0			0
$11$	−2.00000	+	2.00000i	−0.603023	+	0.603023i	−0.941113	−	0.338091i	$-0.890219\pi$
$11$	−2.00000	+	2.00000i	−0.603023	+	0.603023i	0.338091	+	0.941113i	$0.390219\pi$
$12$		0			0
$13$	1.26795	+	1.26795i	0.351666	+	0.351666i	0.860729	−	0.509063i	$-0.170008\pi$
$13$	1.26795	+	1.26795i	0.351666	+	0.351666i	−0.509063	+	0.860729i	$0.670008\pi$
$14$		0			0
$15$	−2.53590			−0.654766
$16$		0			0
$17$	3.46410			0.840168			0.420084	−	0.907485i	$-0.362001\pi$
$17$	3.46410			0.840168			0.420084	+	0.907485i	$0.362001\pi$
$18$		0			0
$19$	−1.73205	−	1.73205i	−0.397360	−	0.397360i	0.479941	−	0.877301i	$-0.340658\pi$
$19$	−1.73205	−	1.73205i	−0.397360	−	0.397360i	−0.877301	+	0.479941i	$0.840658\pi$
$20$		0			0
$21$	1.73205	−	1.73205i	0.377964	−	0.377964i
$22$		0			0
$23$			2.53590i			0.528771i	0.964417	+	0.264386i	$0.0851692\pi$
$23$			2.53590i			0.528771i	−0.964417	+	0.264386i	$0.914831\pi$
$24$		0			0
$25$			3.92820i			0.785641i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	−4.46410	−	4.46410i	−0.828963	−	0.828963i	0.158410	−	0.987373i	$-0.449363\pi$
$29$	−4.46410	−	4.46410i	−0.828963	−	0.828963i	−0.987373	+	0.158410i	$0.949363\pi$
$30$		0			0
$31$	0.535898			0.0962502			0.0481251	−	0.998841i	$-0.484675\pi$
$31$	0.535898			0.0962502			0.0481251	+	0.998841i	$0.484675\pi$
$32$		0			0
$33$	6.92820			1.20605
$34$		0			0
$35$	0.732051	+	0.732051i	0.123739	+	0.123739i
$36$		0			0
$37$	6.46410	−	6.46410i	1.06269	−	1.06269i	0.0647930	−	0.997899i	$-0.479361\pi$
$37$	6.46410	−	6.46410i	1.06269	−	1.06269i	0.997899	−	0.0647930i	$-0.0206387\pi$
$38$		0			0
$39$		−	4.39230i		−	0.703332i
$40$		0			0
$41$		−	3.46410i		−	0.541002i	−0.962720	−	0.270501i	$-0.912811\pi$
$41$		−	3.46410i		−	0.541002i	0.962720	−	0.270501i	$-0.0871893\pi$
$42$		0			0
$43$	0.535898	−	0.535898i	0.0817237	−	0.0817237i	−0.665063	−	0.746787i	$-0.731595\pi$
$43$	0.535898	−	0.535898i	0.0817237	−	0.0817237i	0.746787	+	0.665063i	$0.231595\pi$
$44$		0			0
$45$	2.19615	+	2.19615i	0.327383	+	0.327383i
$46$		0			0
$47$	−4.53590			−0.661629			−0.330814	−	0.943696i	$-0.607323\pi$
$47$	−4.53590			−0.661629			−0.330814	+	0.943696i	$0.607323\pi$
$48$		0			0
$49$	−1.00000			−0.142857
$50$		0			0
$51$	−6.00000	−	6.00000i	−0.840168	−	0.840168i
$52$		0			0
$53$	−1.00000	+	1.00000i	−0.137361	+	0.137361i	−0.772444	−	0.635083i	$-0.780966\pi$
$53$	−1.00000	+	1.00000i	−0.137361	+	0.137361i	0.635083	+	0.772444i	$0.280966\pi$
$54$		0			0
$55$			2.92820i			0.394839i
$56$		0			0
$57$			6.00000i			0.794719i
$58$		0			0
$59$	5.73205	−	5.73205i	0.746249	−	0.746249i	−0.227523	−	0.973773i	$-0.573063\pi$
$59$	5.73205	−	5.73205i	0.746249	−	0.746249i	0.973773	+	0.227523i	$0.0730628\pi$
$60$		0			0
$61$	−8.73205	−	8.73205i	−1.11802	−	1.11802i	−0.992031	−	0.125993i	$-0.959788\pi$
$61$	−8.73205	−	8.73205i	−1.11802	−	1.11802i	−0.125993	−	0.992031i	$-0.540212\pi$
$62$		0			0
$63$	−3.00000			−0.377964
$64$		0			0
$65$	1.85641			0.230259
$66$		0			0
$67$	−10.9282	−	10.9282i	−1.33509	−	1.33509i	−0.900746	−	0.434347i	$-0.856979\pi$
$67$	−10.9282	−	10.9282i	−1.33509	−	1.33509i	−0.434347	−	0.900746i	$-0.643021\pi$
$68$		0			0
$69$	4.39230	−	4.39230i	0.528771	−	0.528771i
$70$		0			0
$71$		−	4.00000i		−	0.474713i	−0.971423	−	0.237356i	$-0.923719\pi$
$71$		−	4.00000i		−	0.474713i	0.971423	−	0.237356i	$-0.0762809\pi$
$72$		0			0
$73$		−	6.00000i		−	0.702247i	−0.936329	−	0.351123i	$-0.885800\pi$
$73$		−	6.00000i		−	0.702247i	0.936329	−	0.351123i	$-0.114200\pi$
$74$		0			0
$75$	6.80385	−	6.80385i	0.785641	−	0.785641i
$76$		0			0
$77$	−2.00000	−	2.00000i	−0.227921	−	0.227921i
$78$		0			0
$79$	−4.00000			−0.450035			−0.225018	−	0.974355i	$-0.572244\pi$
$79$	−4.00000			−0.450035			−0.225018	+	0.974355i	$0.572244\pi$
$80$		0			0
$81$	9.00000			1.00000
$82$		0			0
$83$	5.73205	+	5.73205i	0.629174	+	0.629174i	0.947860	−	0.318686i	$-0.103242\pi$
$83$	5.73205	+	5.73205i	0.629174	+	0.629174i	−0.318686	+	0.947860i	$0.603242\pi$
$84$		0			0
$85$	2.53590	−	2.53590i	0.275057	−	0.275057i
$86$		0			0
$87$			15.4641i			1.65793i
$88$		0			0
$89$			4.92820i			0.522388i	0.965286	+	0.261194i	$0.0841163\pi$
$89$			4.92820i			0.522388i	−0.965286	+	0.261194i	$0.915884\pi$
$90$		0			0
$91$	−1.26795	+	1.26795i	−0.132917	+	0.132917i
$92$		0			0
$93$	−0.928203	−	0.928203i	−0.0962502	−	0.0962502i
$94$		0			0
$95$	−2.53590			−0.260178
$96$		0			0
$97$	18.3923			1.86746			0.933728	−	0.357984i	$-0.116536\pi$
$97$	18.3923			1.86746			0.933728	+	0.357984i	$0.116536\pi$
$98$		0			0
$99$	−6.00000	−	6.00000i	−0.603023	−	0.603023i
$100$		0			0
$101$	4.73205	−	4.73205i	0.470857	−	0.470857i	−0.431335	−	0.902192i	$-0.641957\pi$
$101$	4.73205	−	4.73205i	0.470857	−	0.470857i	0.902192	+	0.431335i	$0.141957\pi$
$102$		0			0
$103$		−	8.53590i		−	0.841067i	−0.907277	−	0.420534i	$-0.861843\pi$
$103$		−	8.53590i		−	0.841067i	0.907277	−	0.420534i	$-0.138157\pi$
$104$		0			0
$105$		−	2.53590i		−	0.247478i
$106$		0			0
$107$	5.46410	−	5.46410i	0.528235	−	0.528235i	−0.391811	−	0.920046i	$-0.628151\pi$
$107$	5.46410	−	5.46410i	0.528235	−	0.528235i	0.920046	+	0.391811i	$0.128151\pi$
$108$		0			0
$109$	1.53590	+	1.53590i	0.147112	+	0.147112i	0.776827	−	0.629714i	$-0.216828\pi$
$109$	1.53590	+	1.53590i	0.147112	+	0.147112i	−0.629714	+	0.776827i	$0.716828\pi$
$110$		0			0
$111$	−22.3923			−2.12538
$112$		0			0
$113$	−13.8564			−1.30350			−0.651751	−	0.758433i	$-0.725965\pi$
$113$	−13.8564			−1.30350			−0.651751	+	0.758433i	$0.725965\pi$
$114$		0			0
$115$	1.85641	+	1.85641i	0.173111	+	0.173111i
$116$		0			0
$117$	−3.80385	+	3.80385i	−0.351666	+	0.351666i
$118$		0			0
$119$			3.46410i			0.317554i
$120$		0			0
$121$			3.00000i			0.272727i
$122$		0			0
$123$	−6.00000	+	6.00000i	−0.541002	+	0.541002i
$124$		0			0
$125$	6.53590	+	6.53590i	0.584589	+	0.584589i
$126$		0			0
$127$	−20.3923			−1.80952			−0.904762	−	0.425917i	$-0.859952\pi$
$127$	−20.3923			−1.80952			−0.904762	+	0.425917i	$0.859952\pi$
$128$		0			0
$129$	−1.85641			−0.163447
$130$		0			0
$131$	−9.73205	−	9.73205i	−0.850293	−	0.850293i	0.139876	−	0.990169i	$-0.455330\pi$
$131$	−9.73205	−	9.73205i	−0.850293	−	0.850293i	−0.990169	+	0.139876i	$0.955330\pi$
$132$		0			0
$133$	1.73205	−	1.73205i	0.150188	−	0.150188i
$134$		0			0
$135$		0			0
$136$		0			0
$137$		−	14.9282i		−	1.27540i	−0.770284	−	0.637701i	$-0.779885\pi$
$137$		−	14.9282i		−	1.27540i	0.770284	−	0.637701i	$-0.220115\pi$
$138$		0			0
$139$	9.19615	−	9.19615i	0.780007	−	0.780007i	−0.199824	−	0.979832i	$-0.564037\pi$
$139$	9.19615	−	9.19615i	0.780007	−	0.780007i	0.979832	+	0.199824i	$0.0640371\pi$
$140$		0			0
$141$	7.85641	+	7.85641i	0.661629	+	0.661629i
$142$		0			0
$143$	−5.07180			−0.424125
$144$		0			0
$145$	−6.53590			−0.542777
$146$		0			0
$147$	1.73205	+	1.73205i	0.142857	+	0.142857i
$148$		0			0
$149$	−3.92820	+	3.92820i	−0.321811	+	0.321811i	−0.849462	−	0.527651i	$-0.823073\pi$
$149$	−3.92820	+	3.92820i	−0.321811	+	0.321811i	0.527651	+	0.849462i	$0.323073\pi$
$150$		0			0
$151$		−	12.3923i		−	1.00847i	−0.863566	−	0.504236i	$-0.831774\pi$
$151$		−	12.3923i		−	1.00847i	0.863566	−	0.504236i	$-0.168226\pi$
$152$		0			0
$153$			10.3923i			0.840168i
$154$		0			0
$155$	0.392305	−	0.392305i	0.0315107	−	0.0315107i
$156$		0			0
$157$	1.26795	+	1.26795i	0.101193	+	0.101193i	0.755891	−	0.654698i	$-0.227204\pi$
$157$	1.26795	+	1.26795i	0.101193	+	0.101193i	−0.654698	+	0.755891i	$0.727204\pi$
$158$		0			0
$159$	3.46410			0.274721
$160$		0			0
$161$	−2.53590			−0.199857
$162$		0			0
$163$	−6.00000	−	6.00000i	−0.469956	−	0.469956i	0.431944	−	0.901900i	$-0.357828\pi$
$163$	−6.00000	−	6.00000i	−0.469956	−	0.469956i	−0.901900	+	0.431944i	$0.857828\pi$
$164$		0			0
$165$	5.07180	−	5.07180i	0.394839	−	0.394839i
$166$		0			0
$167$			25.3205i			1.95936i	0.200568	+	0.979680i	$0.435721\pi$
$167$			25.3205i			1.95936i	−0.200568	+	0.979680i	$0.564279\pi$
$168$		0			0
$169$		−	9.78461i		−	0.752662i
$170$		0			0
$171$	5.19615	−	5.19615i	0.397360	−	0.397360i
$172$		0			0
$173$	1.26795	+	1.26795i	0.0964004	+	0.0964004i	0.753662	−	0.657262i	$-0.228285\pi$
$173$	1.26795	+	1.26795i	0.0964004	+	0.0964004i	−0.657262	+	0.753662i	$0.728285\pi$
$174$		0			0
$175$	−3.92820			−0.296944
$176$		0			0
$177$	−19.8564			−1.49250
$178$		0			0
$179$	−13.8564	−	13.8564i	−1.03568	−	1.03568i	−0.999340	−	0.0363368i	$-0.988431\pi$
$179$	−13.8564	−	13.8564i	−1.03568	−	1.03568i	−0.0363368	−	0.999340i	$-0.511569\pi$
$180$		0			0
$181$	−5.66025	+	5.66025i	−0.420723	+	0.420723i	−0.885453	−	0.464729i	$-0.846152\pi$
$181$	−5.66025	+	5.66025i	−0.420723	+	0.420723i	0.464729	+	0.885453i	$0.346152\pi$
$182$		0			0
$183$			30.2487i			2.23605i
$184$		0			0
$185$		−	9.46410i		−	0.695815i
$186$		0			0
$187$	−6.92820	+	6.92820i	−0.506640	+	0.506640i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	6.92820			0.501307			0.250654	−	0.968077i	$-0.419354\pi$
$191$	6.92820			0.501307			0.250654	+	0.968077i	$0.419354\pi$
$192$		0			0
$193$	−10.0000			−0.719816			−0.359908	−	0.932988i	$-0.617192\pi$
$193$	−10.0000			−0.719816			−0.359908	+	0.932988i	$0.617192\pi$
$194$		0			0
$195$	−3.21539	−	3.21539i	−0.230259	−	0.230259i
$196$		0			0
$197$	−16.8564	+	16.8564i	−1.20097	+	1.20097i	−0.227097	+	0.973872i	$0.572923\pi$
$197$	−16.8564	+	16.8564i	−1.20097	+	1.20097i	−0.973872	+	0.227097i	$0.927077\pi$
$198$		0			0
$199$			6.39230i			0.453138i	0.973995	+	0.226569i	$0.0727510\pi$
$199$			6.39230i			0.453138i	−0.973995	+	0.226569i	$0.927249\pi$
$200$		0			0
$201$			37.8564i			2.67019i
$202$		0			0
$203$	4.46410	−	4.46410i	0.313319	−	0.313319i
$204$		0			0
$205$	−2.53590	−	2.53590i	−0.177115	−	0.177115i
$206$		0			0
$207$	−7.60770			−0.528771
$208$		0			0
$209$	6.92820			0.479234
$210$		0			0
$211$	17.8564	+	17.8564i	1.22929	+	1.22929i	0.964234	+	0.265051i	$0.0853889\pi$
$211$	17.8564	+	17.8564i	1.22929	+	1.22929i	0.265051	+	0.964234i	$0.414611\pi$
$212$		0			0
$213$	−6.92820	+	6.92820i	−0.474713	+	0.474713i
$214$		0			0
$215$		−	0.784610i		−	0.0535099i
$216$		0			0
$217$			0.535898i			0.0363792i
$218$		0			0
$219$	−10.3923	+	10.3923i	−0.702247	+	0.702247i
$220$		0			0
$221$	4.39230	+	4.39230i	0.295458	+	0.295458i
$222$		0			0
$223$	2.92820			0.196087			0.0980435	−	0.995182i	$-0.468742\pi$
$223$	2.92820			0.196087			0.0980435	+	0.995182i	$0.468742\pi$
$224$		0			0
$225$	−11.7846			−0.785641
$226$		0			0
$227$	−2.80385	−	2.80385i	−0.186098	−	0.186098i	0.607909	−	0.794007i	$-0.292009\pi$
$227$	−2.80385	−	2.80385i	−0.186098	−	0.186098i	−0.794007	+	0.607909i	$0.792009\pi$
$228$		0			0
$229$	−13.2679	+	13.2679i	−0.876771	+	0.876771i	−0.993199	−	0.116428i	$-0.962855\pi$
$229$	−13.2679	+	13.2679i	−0.876771	+	0.876771i	0.116428	+	0.993199i	$0.462855\pi$
$230$		0			0
$231$			6.92820i			0.455842i
$232$		0			0
$233$		−	19.8564i		−	1.30084i	−0.759576	−	0.650418i	$-0.774594\pi$
$233$		−	19.8564i		−	1.30084i	0.759576	−	0.650418i	$-0.225406\pi$
$234$		0			0
$235$	−3.32051	+	3.32051i	−0.216606	+	0.216606i
$236$		0			0
$237$	6.92820	+	6.92820i	0.450035	+	0.450035i
$238$		0			0
$239$	2.53590			0.164034			0.0820168	−	0.996631i	$-0.473864\pi$
$239$	2.53590			0.164034			0.0820168	+	0.996631i	$0.473864\pi$
$240$		0			0
$241$	−21.3205			−1.37337			−0.686687	−	0.726953i	$-0.740936\pi$
$241$	−21.3205			−1.37337			−0.686687	+	0.726953i	$0.740936\pi$
$242$		0			0
$243$	−15.5885	−	15.5885i	−1.00000	−	1.00000i
$244$		0			0
$245$	−0.732051	+	0.732051i	−0.0467690	+	0.0467690i
$246$		0			0
$247$		−	4.39230i		−	0.279476i
$248$		0			0
$249$		−	19.8564i		−	1.25835i
$250$		0			0
$251$	−2.26795	+	2.26795i	−0.143152	+	0.143152i	−0.775051	−	0.631899i	$-0.782276\pi$
$251$	−2.26795	+	2.26795i	−0.143152	+	0.143152i	0.631899	+	0.775051i	$0.282276\pi$
$252$		0			0
$253$	−5.07180	−	5.07180i	−0.318861	−	0.318861i
$254$		0			0
$255$	−8.78461			−0.550114
$256$		0			0
$257$	7.07180			0.441127			0.220563	−	0.975373i	$-0.429210\pi$
$257$	7.07180			0.441127			0.220563	+	0.975373i	$0.429210\pi$
$258$		0			0
$259$	6.46410	+	6.46410i	0.401660	+	0.401660i
$260$		0			0
$261$	13.3923	−	13.3923i	0.828963	−	0.828963i
$262$		0			0
$263$		−	28.7846i		−	1.77494i	−0.460870	−	0.887468i	$-0.652463\pi$
$263$		−	28.7846i		−	1.77494i	0.460870	−	0.887468i	$-0.347537\pi$
$264$		0			0
$265$			1.46410i			0.0899390i
$266$		0			0
$267$	8.53590	−	8.53590i	0.522388	−	0.522388i
$268$		0			0
$269$	−11.1244	−	11.1244i	−0.678264	−	0.678264i	0.281343	−	0.959607i	$-0.409220\pi$
$269$	−11.1244	−	11.1244i	−0.678264	−	0.678264i	−0.959607	+	0.281343i	$0.909220\pi$
$270$		0			0
$271$	−10.9282			−0.663841			−0.331921	−	0.943307i	$-0.607697\pi$
$271$	−10.9282			−0.663841			−0.331921	+	0.943307i	$0.607697\pi$
$272$		0			0
$273$	4.39230			0.265834
$274$		0			0
$275$	−7.85641	−	7.85641i	−0.473759	−	0.473759i
$276$		0			0
$277$	−3.00000	+	3.00000i	−0.180253	+	0.180253i	−0.791466	−	0.611213i	$-0.790682\pi$
$277$	−3.00000	+	3.00000i	−0.180253	+	0.180253i	0.611213	+	0.791466i	$0.290682\pi$
$278$		0			0
$279$			1.60770i			0.0962502i
$280$		0			0
$281$			10.0000i			0.596550i	0.954480	+	0.298275i	$0.0964112\pi$
$281$			10.0000i			0.596550i	−0.954480	+	0.298275i	$0.903589\pi$
$282$		0			0
$283$	9.73205	−	9.73205i	0.578510	−	0.578510i	−0.355982	−	0.934493i	$-0.615854\pi$
$283$	9.73205	−	9.73205i	0.578510	−	0.578510i	0.934493	+	0.355982i	$0.115854\pi$
$284$		0			0
$285$	4.39230	+	4.39230i	0.260178	+	0.260178i
$286$		0			0
$287$	3.46410			0.204479
$288$		0			0
$289$	−5.00000			−0.294118
$290$		0			0
$291$	−31.8564	−	31.8564i	−1.86746	−	1.86746i
$292$		0			0
$293$	−20.7321	+	20.7321i	−1.21118	+	1.21118i	−0.240540	+	0.970639i	$0.577325\pi$
$293$	−20.7321	+	20.7321i	−1.21118	+	1.21118i	−0.970639	+	0.240540i	$0.922675\pi$
$294$		0			0
$295$		−	8.39230i		−	0.488619i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	−3.21539	+	3.21539i	−0.185951	+	0.185951i
$300$		0			0
$301$	0.535898	+	0.535898i	0.0308887	+	0.0308887i
$302$		0			0
$303$	−16.3923			−0.941713
$304$		0			0
$305$	−12.7846			−0.732045
$306$		0			0
$307$	1.73205	+	1.73205i	0.0988534	+	0.0988534i	0.754804	−	0.655951i	$-0.227732\pi$
$307$	1.73205	+	1.73205i	0.0988534	+	0.0988534i	−0.655951	+	0.754804i	$0.727732\pi$
$308$		0			0
$309$	−14.7846	+	14.7846i	−0.841067	+	0.841067i
$310$		0			0
$311$			27.7128i			1.57145i	0.618576	+	0.785725i	$0.287710\pi$
$311$			27.7128i			1.57145i	−0.618576	+	0.785725i	$0.712290\pi$
$312$		0			0
$313$		−	16.2487i		−	0.918431i	−0.888325	−	0.459216i	$-0.848130\pi$
$313$		−	16.2487i		−	0.918431i	0.888325	−	0.459216i	$-0.151870\pi$
$314$		0			0
$315$	−2.19615	+	2.19615i	−0.123739	+	0.123739i
$316$		0			0
$317$	−1.92820	−	1.92820i	−0.108299	−	0.108299i	0.650881	−	0.759180i	$-0.274400\pi$
$317$	−1.92820	−	1.92820i	−0.108299	−	0.108299i	−0.759180	+	0.650881i	$0.774400\pi$
$318$		0			0
$319$	17.8564			0.999767
$320$		0			0
$321$	−18.9282			−1.05647
$322$		0			0
$323$	−6.00000	−	6.00000i	−0.333849	−	0.333849i
$324$		0			0
$325$	−4.98076	+	4.98076i	−0.276283	+	0.276283i
$326$		0			0
$327$		−	5.32051i		−	0.294225i
$328$		0			0
$329$		−	4.53590i		−	0.250072i
$330$		0			0
$331$	15.4641	−	15.4641i	0.849984	−	0.849984i	−0.140147	−	0.990131i	$-0.544757\pi$
$331$	15.4641	−	15.4641i	0.849984	−	0.849984i	0.990131	+	0.140147i	$0.0447575\pi$
$332$		0			0
$333$	19.3923	+	19.3923i	1.06269	+	1.06269i
$334$		0			0
$335$	−16.0000			−0.874173
$336$		0			0
$337$	20.0000			1.08947			0.544735	−	0.838608i	$-0.316630\pi$
$337$	20.0000			1.08947			0.544735	+	0.838608i	$0.316630\pi$
$338$		0			0
$339$	24.0000	+	24.0000i	1.30350	+	1.30350i
$340$		0			0
$341$	−1.07180	+	1.07180i	−0.0580410	+	0.0580410i
$342$		0			0
$343$		−	1.00000i		−	0.0539949i
$344$		0			0
$345$		−	6.43078i		−	0.346222i
$346$		0			0
$347$	1.60770	−	1.60770i	0.0863056	−	0.0863056i	−0.662636	−	0.748942i	$-0.730562\pi$
$347$	1.60770	−	1.60770i	0.0863056	−	0.0863056i	0.748942	+	0.662636i	$0.230562\pi$
$348$		0			0
$349$	−21.6603	−	21.6603i	−1.15945	−	1.15945i	−0.984595	−	0.174852i	$-0.944055\pi$
$349$	−21.6603	−	21.6603i	−1.15945	−	1.15945i	−0.174852	−	0.984595i	$-0.555945\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−0.928203			−0.0494033			−0.0247016	−	0.999695i	$-0.507864\pi$
$353$	−0.928203			−0.0494033			−0.0247016	+	0.999695i	$0.507864\pi$
$354$		0			0
$355$	−2.92820	−	2.92820i	−0.155413	−	0.155413i
$356$		0			0
$357$	6.00000	−	6.00000i	0.317554	−	0.317554i
$358$		0			0
$359$		−	22.5359i		−	1.18940i	−0.803948	−	0.594700i	$-0.797271\pi$
$359$		−	22.5359i		−	1.18940i	0.803948	−	0.594700i	$-0.202729\pi$
$360$		0			0
$361$		−	13.0000i		−	0.684211i
$362$		0			0
$363$	5.19615	−	5.19615i	0.272727	−	0.272727i
$364$		0			0
$365$	−4.39230	−	4.39230i	−0.229904	−	0.229904i
$366$		0			0
$367$	−34.9282			−1.82324			−0.911619	−	0.411037i	$-0.865167\pi$
$367$	−34.9282			−1.82324			−0.911619	+	0.411037i	$0.865167\pi$
$368$		0			0
$369$	10.3923			0.541002
$370$		0			0
$371$	−1.00000	−	1.00000i	−0.0519174	−	0.0519174i
$372$		0			0
$373$	3.92820	−	3.92820i	0.203395	−	0.203395i	−0.598058	−	0.801453i	$-0.704061\pi$
$373$	3.92820	−	3.92820i	0.203395	−	0.203395i	0.801453	+	0.598058i	$0.204061\pi$
$374$		0			0
$375$		−	22.6410i		−	1.16918i
$376$		0			0
$377$		−	11.3205i		−	0.583036i
$378$		0			0
$379$	10.3923	−	10.3923i	0.533817	−	0.533817i	−0.387889	−	0.921706i	$-0.626796\pi$
$379$	10.3923	−	10.3923i	0.533817	−	0.533817i	0.921706	+	0.387889i	$0.126796\pi$
$380$		0			0
$381$	35.3205	+	35.3205i	1.80952	+	1.80952i
$382$		0			0
$383$	32.2487			1.64783			0.823916	−	0.566712i	$-0.191785\pi$
$383$	32.2487			1.64783			0.823916	+	0.566712i	$0.191785\pi$
$384$		0			0
$385$	−2.92820			−0.149235
$386$		0			0
$387$	1.60770	+	1.60770i	0.0817237	+	0.0817237i
$388$		0			0
$389$	11.5359	−	11.5359i	0.584893	−	0.584893i	−0.351351	−	0.936244i	$-0.614278\pi$
$389$	11.5359	−	11.5359i	0.584893	−	0.584893i	0.936244	+	0.351351i	$0.114278\pi$
$390$		0			0
$391$			8.78461i			0.444257i
$392$		0			0
$393$			33.7128i			1.70059i
$394$		0			0
$395$	−2.92820	+	2.92820i	−0.147334	+	0.147334i
$396$		0			0
$397$	−19.5167	−	19.5167i	−0.979513	−	0.979513i	0.0202812	−	0.999794i	$-0.493544\pi$
$397$	−19.5167	−	19.5167i	−0.979513	−	0.979513i	−0.999794	+	0.0202812i	$0.993544\pi$
$398$		0			0
$399$	−6.00000			−0.300376
$400$		0			0
$401$	24.9282			1.24486			0.622428	−	0.782677i	$-0.286147\pi$
$401$	24.9282			1.24486			0.622428	+	0.782677i	$0.286147\pi$
$402$		0			0
$403$	0.679492	+	0.679492i	0.0338479	+	0.0338479i
$404$		0			0
$405$	6.58846	−	6.58846i	0.327383	−	0.327383i
$406$		0			0
$407$			25.8564i			1.28165i
$408$		0			0
$409$		−	1.32051i		−	0.0652949i	−0.999467	−	0.0326475i	$-0.989606\pi$
$409$		−	1.32051i		−	0.0652949i	0.999467	−	0.0326475i	$-0.0103939\pi$
$410$		0			0
$411$	−25.8564	+	25.8564i	−1.27540	+	1.27540i
$412$		0			0
$413$	5.73205	+	5.73205i	0.282056	+	0.282056i
$414$		0			0
$415$	8.39230			0.411962
$416$		0			0
$417$	−31.8564			−1.56001
$418$		0			0
$419$	21.1962	+	21.1962i	1.03550	+	1.03550i	0.999346	+	0.0361536i	$0.0115105\pi$
$419$	21.1962	+	21.1962i	1.03550	+	1.03550i	0.0361536	+	0.999346i	$0.488489\pi$
$420$		0			0
$421$	−13.0000	+	13.0000i	−0.633581	+	0.633581i	−0.948964	−	0.315383i	$-0.897867\pi$
$421$	−13.0000	+	13.0000i	−0.633581	+	0.633581i	0.315383	+	0.948964i	$0.397867\pi$
$422$		0			0
$423$		−	13.6077i		−	0.661629i
$424$		0			0
$425$			13.6077i			0.660070i
$426$		0			0
$427$	8.73205	−	8.73205i	0.422574	−	0.422574i
$428$		0			0
$429$	8.78461	+	8.78461i	0.424125	+	0.424125i
$430$		0			0
$431$	30.2487			1.45703			0.728515	−	0.685030i	$-0.240211\pi$
$431$	30.2487			1.45703			0.728515	+	0.685030i	$0.240211\pi$
$432$		0			0
$433$	−6.39230			−0.307195			−0.153597	−	0.988134i	$-0.549086\pi$
$433$	−6.39230			−0.307195			−0.153597	+	0.988134i	$0.549086\pi$
$434$		0			0
$435$	11.3205	+	11.3205i	0.542777	+	0.542777i
$436$		0			0
$437$	4.39230	−	4.39230i	0.210112	−	0.210112i
$438$		0			0
$439$		−	30.6410i		−	1.46242i	−0.682155	−	0.731208i	$-0.738957\pi$
$439$		−	30.6410i		−	1.46242i	0.682155	−	0.731208i	$-0.261043\pi$
$440$		0			0
$441$		−	3.00000i		−	0.142857i
$442$		0			0
$443$	−14.9282	+	14.9282i	−0.709260	+	0.709260i	−0.966380	−	0.257119i	$-0.917227\pi$
$443$	−14.9282	+	14.9282i	−0.709260	+	0.709260i	0.257119	+	0.966380i	$0.417227\pi$
$444$		0			0
$445$	3.60770	+	3.60770i	0.171021	+	0.171021i
$446$		0			0
$447$	13.6077			0.643622
$448$		0			0
$449$		0			0			−	1.00000i	$-0.5\pi$
$449$		0			0				1.00000i	$0.5\pi$
$450$		0			0
$451$	6.92820	+	6.92820i	0.326236	+	0.326236i
$452$		0			0
$453$	−21.4641	+	21.4641i	−1.00847	+	1.00847i
$454$		0			0
$455$			1.85641i			0.0870297i
$456$		0			0
$457$		−	23.8564i		−	1.11596i	−0.829856	−	0.557978i	$-0.811577\pi$
$457$		−	23.8564i		−	1.11596i	0.829856	−	0.557978i	$-0.188423\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−7.80385	−	7.80385i	−0.363461	−	0.363461i	0.501624	−	0.865086i	$-0.332736\pi$
$461$	−7.80385	−	7.80385i	−0.363461	−	0.363461i	−0.865086	+	0.501624i	$0.832736\pi$
$462$		0			0
$463$	13.8564			0.643962			0.321981	−	0.946746i	$-0.395651\pi$
$463$	13.8564			0.643962			0.321981	+	0.946746i	$0.395651\pi$
$464$		0			0
$465$	−1.35898			−0.0630214
$466$		0			0
$467$	−17.1962	−	17.1962i	−0.795743	−	0.795743i	0.186678	−	0.982421i	$-0.440228\pi$
$467$	−17.1962	−	17.1962i	−0.795743	−	0.795743i	−0.982421	+	0.186678i	$0.940228\pi$
$468$		0			0
$469$	10.9282	−	10.9282i	0.504618	−	0.504618i
$470$		0			0
$471$		−	4.39230i		−	0.202387i
$472$		0			0
$473$			2.14359i			0.0985625i
$474$		0			0
$475$	6.80385	−	6.80385i	0.312182	−	0.312182i
$476$		0			0
$477$	−3.00000	−	3.00000i	−0.137361	−	0.137361i
$478$		0			0
$479$	−9.60770			−0.438987			−0.219493	−	0.975614i	$-0.570440\pi$
$479$	−9.60770			−0.438987			−0.219493	+	0.975614i	$0.570440\pi$
$480$		0			0
$481$	16.3923			0.747425
$482$		0			0
$483$	4.39230	+	4.39230i	0.199857	+	0.199857i
$484$		0			0
$485$	13.4641	−	13.4641i	0.611373	−	0.611373i
$486$		0			0
$487$		−	38.2487i		−	1.73321i	−0.498991	−	0.866607i	$-0.666296\pi$
$487$		−	38.2487i		−	1.73321i	0.498991	−	0.866607i	$-0.333704\pi$
$488$		0			0
$489$			20.7846i			0.939913i
$490$		0			0
$491$	−26.9282	+	26.9282i	−1.21525	+	1.21525i	−0.245977	+	0.969276i	$0.579109\pi$
$491$	−26.9282	+	26.9282i	−1.21525	+	1.21525i	−0.969276	+	0.245977i	$0.920891\pi$
$492$		0			0
$493$	−15.4641	−	15.4641i	−0.696468	−	0.696468i
$494$		0			0
$495$	−8.78461			−0.394839
$496$		0			0
$497$	4.00000			0.179425
$498$		0			0
$499$	−1.46410	−	1.46410i	−0.0655422	−	0.0655422i	0.673576	−	0.739118i	$-0.264757\pi$
$499$	−1.46410	−	1.46410i	−0.0655422	−	0.0655422i	−0.739118	+	0.673576i	$0.764757\pi$
$500$		0			0
$501$	43.8564	−	43.8564i	1.95936	−	1.95936i
$502$		0			0
$503$			32.7846i			1.46179i	0.682488	+	0.730897i	$0.260898\pi$
$503$			32.7846i			1.46179i	−0.682488	+	0.730897i	$0.739102\pi$
$504$		0			0
$505$		−	6.92820i		−	0.308301i
$506$		0			0
$507$	−16.9474	+	16.9474i	−0.752662	+	0.752662i
$508$		0			0
$509$	−5.26795	−	5.26795i	−0.233498	−	0.233498i	0.580653	−	0.814151i	$-0.302797\pi$
$509$	−5.26795	−	5.26795i	−0.233498	−	0.233498i	−0.814151	+	0.580653i	$0.802797\pi$
$510$		0			0
$511$	6.00000			0.265424
$512$		0			0
$513$		0			0
$514$		0			0
$515$	−6.24871	−	6.24871i	−0.275351	−	0.275351i
$516$		0			0
$517$	9.07180	−	9.07180i	0.398977	−	0.398977i
$518$		0			0
$519$		−	4.39230i		−	0.192801i
$520$		0			0
$521$			27.1769i			1.19064i	0.803488	+	0.595321i	$0.202975\pi$
$521$			27.1769i			1.19064i	−0.803488	+	0.595321i	$0.797025\pi$
$522$		0			0
$523$	22.2679	−	22.2679i	0.973709	−	0.973709i	−0.0259537	−	0.999663i	$-0.508262\pi$
$523$	22.2679	−	22.2679i	0.973709	−	0.973709i	0.999663	+	0.0259537i	$0.00826225\pi$
$524$		0			0
$525$	6.80385	+	6.80385i	0.296944	+	0.296944i
$526$		0			0
$527$	1.85641			0.0808663
$528$		0			0
$529$	16.5692			0.720401
$530$		0			0
$531$	17.1962	+	17.1962i	0.746249	+	0.746249i
$532$		0			0
$533$	4.39230	−	4.39230i	0.190252	−	0.190252i
$534$		0			0
$535$		−	8.00000i		−	0.345870i
$536$		0			0
$537$			48.0000i			2.07135i
$538$		0			0
$539$	2.00000	−	2.00000i	0.0861461	−	0.0861461i
$540$		0			0
$541$	26.8564	+	26.8564i	1.15465	+	1.15465i	0.985610	+	0.169037i	$0.0540659\pi$
$541$	26.8564	+	26.8564i	1.15465	+	1.15465i	0.169037	+	0.985610i	$0.445934\pi$
$542$		0			0
$543$	19.6077			0.841447
$544$		0			0
$545$	2.24871			0.0963242
$546$		0			0
$547$	−7.85641	−	7.85641i	−0.335916	−	0.335916i	0.518912	−	0.854828i	$-0.326337\pi$
$547$	−7.85641	−	7.85641i	−0.335916	−	0.335916i	−0.854828	+	0.518912i	$0.826337\pi$
$548$		0			0
$549$	26.1962	−	26.1962i	1.11802	−	1.11802i
$550$		0			0
$551$			15.4641i			0.658793i
$552$		0			0
$553$		−	4.00000i		−	0.170097i
$554$		0			0
$555$	−16.3923	+	16.3923i	−0.695815	+	0.695815i
$556$		0			0
$557$	−28.7128	−	28.7128i	−1.21660	−	1.21660i	−0.968815	−	0.247786i	$-0.920297\pi$
$557$	−28.7128	−	28.7128i	−1.21660	−	1.21660i	−0.247786	−	0.968815i	$-0.579703\pi$
$558$		0			0
$559$	1.35898			0.0574789
$560$		0			0
$561$	24.0000			1.01328
$562$		0			0
$563$	19.5885	+	19.5885i	0.825555	+	0.825555i	0.986898	−	0.161343i	$-0.0515826\pi$
$563$	19.5885	+	19.5885i	0.825555	+	0.825555i	−0.161343	+	0.986898i	$0.551583\pi$
$564$		0			0
$565$	−10.1436	+	10.1436i	−0.426744	+	0.426744i
$566$		0			0
$567$			9.00000i			0.377964i
$568$		0			0
$569$		−	26.7846i		−	1.12287i	−0.827521	−	0.561435i	$-0.810250\pi$
$569$		−	26.7846i		−	1.12287i	0.827521	−	0.561435i	$-0.189750\pi$
$570$		0			0
$571$	−12.5359	+	12.5359i	−0.524611	+	0.524611i	−0.918961	−	0.394350i	$-0.870970\pi$
$571$	−12.5359	+	12.5359i	−0.524611	+	0.524611i	0.394350	+	0.918961i	$0.370970\pi$
$572$		0			0
$573$	−12.0000	−	12.0000i	−0.501307	−	0.501307i
$574$		0			0
$575$	−9.96152			−0.415424
$576$		0			0
$577$	18.7846			0.782014			0.391007	−	0.920388i	$-0.372127\pi$
$577$	18.7846			0.782014			0.391007	+	0.920388i	$0.372127\pi$
$578$		0			0
$579$	17.3205	+	17.3205i	0.719816	+	0.719816i
$580$		0			0
$581$	−5.73205	+	5.73205i	−0.237806	+	0.237806i
$582$		0			0
$583$		−	4.00000i		−	0.165663i
$584$		0			0
$585$			5.56922i			0.230259i
$586$		0			0
$587$	18.5167	−	18.5167i	0.764264	−	0.764264i	−0.212826	−	0.977090i	$-0.568267\pi$
$587$	18.5167	−	18.5167i	0.764264	−	0.764264i	0.977090	+	0.212826i	$0.0682667\pi$
$588$		0			0
$589$	−0.928203	−	0.928203i	−0.0382459	−	0.0382459i
$590$		0			0
$591$	58.3923			2.40194
$592$		0			0
$593$	40.6410			1.66893			0.834463	−	0.551064i	$-0.185778\pi$
$593$	40.6410			1.66893			0.834463	+	0.551064i	$0.185778\pi$
$594$		0			0
$595$	2.53590	+	2.53590i	0.103962	+	0.103962i
$596$		0			0
$597$	11.0718	−	11.0718i	0.453138	−	0.453138i
$598$		0			0
$599$			24.7846i			1.01267i	0.862336	+	0.506336i	$0.169000\pi$
$599$			24.7846i			1.01267i	−0.862336	+	0.506336i	$0.831000\pi$
$600$		0			0
$601$			32.6410i			1.33145i	0.746195	+	0.665727i	$0.231879\pi$
$601$			32.6410i			1.33145i	−0.746195	+	0.665727i	$0.768121\pi$
$602$		0			0
$603$	32.7846	−	32.7846i	1.33509	−	1.33509i
$604$		0			0
$605$	2.19615	+	2.19615i	0.0892863	+	0.0892863i
$606$		0			0
$607$	5.85641			0.237704			0.118852	−	0.992912i	$-0.462079\pi$
$607$	5.85641			0.237704			0.118852	+	0.992912i	$0.462079\pi$
$608$		0			0
$609$	−15.4641			−0.626637
$610$		0			0
$611$	−5.75129	−	5.75129i	−0.232672	−	0.232672i
$612$		0			0
$613$	−5.53590	+	5.53590i	−0.223593	+	0.223593i	−0.810010	−	0.586417i	$-0.800538\pi$
$613$	−5.53590	+	5.53590i	−0.223593	+	0.223593i	0.586417	+	0.810010i	$0.300538\pi$
$614$		0			0
$615$			8.78461i			0.354230i
$616$		0			0
$617$		−	17.8564i		−	0.718872i	−0.933170	−	0.359436i	$-0.882969\pi$
$617$		−	17.8564i		−	0.718872i	0.933170	−	0.359436i	$-0.117031\pi$
$618$		0			0
$619$	−11.0526	+	11.0526i	−0.444240	+	0.444240i	−0.893434	−	0.449194i	$-0.851711\pi$
$619$	−11.0526	+	11.0526i	−0.444240	+	0.444240i	0.449194	+	0.893434i	$0.351711\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	−4.92820			−0.197444
$624$		0			0
$625$	−10.0718			−0.402872
$626$		0			0
$627$	−12.0000	−	12.0000i	−0.479234	−	0.479234i
$628$		0			0
$629$	22.3923	−	22.3923i	0.892840	−	0.892840i
$630$		0			0
$631$			23.7128i			0.943992i	0.881601	+	0.471996i	$0.156466\pi$
$631$			23.7128i			0.943992i	−0.881601	+	0.471996i	$0.843534\pi$
$632$		0			0
$633$		−	61.8564i		−	2.45857i
$634$		0			0
$635$	−14.9282	+	14.9282i	−0.592408	+	0.592408i
$636$		0			0
$637$	−1.26795	−	1.26795i	−0.0502380	−	0.0502380i
$638$		0			0
$639$	12.0000			0.474713
$640$		0			0
$641$	−4.92820			−0.194652			−0.0973262	−	0.995253i	$-0.531029\pi$
$641$	−4.92820			−0.194652			−0.0973262	+	0.995253i	$0.531029\pi$
$642$		0			0
$643$	21.1962	+	21.1962i	0.835895	+	0.835895i	0.988316	−	0.152421i	$-0.0487070\pi$
$643$	21.1962	+	21.1962i	0.835895	+	0.835895i	−0.152421	+	0.988316i	$0.548707\pi$
$644$		0			0
$645$	−1.35898	+	1.35898i	−0.0535099	+	0.0535099i
$646$		0			0
$647$			10.6795i			0.419854i	0.977717	+	0.209927i	$0.0673227\pi$
$647$			10.6795i			0.419854i	−0.977717	+	0.209927i	$0.932677\pi$
$648$		0			0
$649$			22.9282i			0.900011i
$650$		0			0
$651$	0.928203	−	0.928203i	0.0363792	−	0.0363792i
$652$		0			0
$653$	−6.32051	−	6.32051i	−0.247341	−	0.247341i	0.572538	−	0.819878i	$-0.305959\pi$
$653$	−6.32051	−	6.32051i	−0.247341	−	0.247341i	−0.819878	+	0.572538i	$0.805959\pi$
$654$		0			0
$655$	−14.2487			−0.556743
$656$		0			0
$657$	18.0000			0.702247
$658$		0			0
$659$	22.7846	+	22.7846i	0.887562	+	0.887562i	0.994288	−	0.106726i	$-0.0340368\pi$
$659$	22.7846	+	22.7846i	0.887562	+	0.887562i	−0.106726	+	0.994288i	$0.534037\pi$
$660$		0			0
$661$	20.0526	−	20.0526i	0.779954	−	0.779954i	−0.199869	−	0.979823i	$-0.564052\pi$
$661$	20.0526	−	20.0526i	0.779954	−	0.779954i	0.979823	+	0.199869i	$0.0640515\pi$
$662$		0			0
$663$		−	15.2154i		−	0.590917i
$664$		0			0
$665$		−	2.53590i		−	0.0983379i
$666$		0			0
$667$	11.3205	−	11.3205i	0.438332	−	0.438332i
$668$		0			0
$669$	−5.07180	−	5.07180i	−0.196087	−	0.196087i
$670$		0			0
$671$	34.9282			1.34839
$672$		0			0
$673$	22.9282			0.883817			0.441909	−	0.897060i	$-0.354302\pi$
$673$	22.9282			0.883817			0.441909	+	0.897060i	$0.354302\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−26.0526	+	26.0526i	−1.00128	+	1.00128i	−0.00128200	+	0.999999i	$0.500408\pi$
$677$	−26.0526	+	26.0526i	−1.00128	+	1.00128i	−0.999999	+	0.00128200i	$0.999592\pi$
$678$		0			0
$679$			18.3923i			0.705832i
$680$		0			0
$681$			9.71281i			0.372196i
$682$		0			0
$683$	−13.4641	+	13.4641i	−0.515190	+	0.515190i	−0.916112	−	0.400922i	$-0.868690\pi$
$683$	−13.4641	+	13.4641i	−0.515190	+	0.515190i	0.400922	+	0.916112i	$0.368690\pi$
$684$		0			0
$685$	−10.9282	−	10.9282i	−0.417545	−	0.417545i
$686$		0			0
$687$	45.9615			1.75354
$688$		0			0
$689$	−2.53590			−0.0966100
$690$		0			0
$691$	11.8756	+	11.8756i	0.451771	+	0.451771i	0.895942	−	0.444171i	$-0.146502\pi$
$691$	11.8756	+	11.8756i	0.451771	+	0.451771i	−0.444171	+	0.895942i	$0.646502\pi$
$692$		0			0
$693$	6.00000	−	6.00000i	0.227921	−	0.227921i
$694$		0			0
$695$		−	13.4641i		−	0.510722i
$696$		0			0
$697$		−	12.0000i		−	0.454532i
$698$		0			0
$699$	−34.3923	+	34.3923i	−1.30084	+	1.30084i
$700$		0			0
$701$	−10.4641	−	10.4641i	−0.395224	−	0.395224i	0.481321	−	0.876544i	$-0.340157\pi$
$701$	−10.4641	−	10.4641i	−0.395224	−	0.395224i	−0.876544	+	0.481321i	$0.840157\pi$
$702$		0			0
$703$	−22.3923			−0.844542
$704$		0			0
$705$	11.5026			0.433212
$706$		0			0
$707$	4.73205	+	4.73205i	0.177967	+	0.177967i
$708$		0			0
$709$	−9.53590	+	9.53590i	−0.358128	+	0.358128i	−0.863123	−	0.504994i	$-0.831495\pi$
$709$	−9.53590	+	9.53590i	−0.358128	+	0.358128i	0.504994	+	0.863123i	$0.331495\pi$
$710$		0			0
$711$		−	12.0000i		−	0.450035i
$712$		0			0
$713$			1.35898i			0.0508943i
$714$		0			0
$715$	−3.71281	+	3.71281i	−0.138851	+	0.138851i
$716$		0			0
$717$	−4.39230	−	4.39230i	−0.164034	−	0.164034i
$718$		0			0
$719$	4.53590			0.169160			0.0845802	−	0.996417i	$-0.473045\pi$
$719$	4.53590			0.169160			0.0845802	+	0.996417i	$0.473045\pi$
$720$		0			0
$721$	8.53590			0.317893
$722$		0			0
$723$	36.9282	+	36.9282i	1.37337	+	1.37337i
$724$		0			0
$725$	17.5359	−	17.5359i	0.651267	−	0.651267i
$726$		0			0
$727$		−	36.5359i		−	1.35504i	−0.735504	−	0.677521i	$-0.763054\pi$
$727$		−	36.5359i		−	1.35504i	0.735504	−	0.677521i	$-0.236946\pi$
$728$		0			0
$729$			27.0000i			1.00000i
$730$		0			0
$731$	1.85641	−	1.85641i	0.0686617	−	0.0686617i
$732$		0			0
$733$	5.80385	+	5.80385i	0.214370	+	0.214370i	0.806121	−	0.591751i	$-0.201563\pi$
$733$	5.80385	+	5.80385i	0.214370	+	0.214370i	−0.591751	+	0.806121i	$0.701563\pi$
$734$		0			0
$735$	2.53590			0.0935380
$736$		0			0
$737$	43.7128			1.61018
$738$		0			0
$739$	3.07180	+	3.07180i	0.112998	+	0.112998i	0.761345	−	0.648347i	$-0.224539\pi$
$739$	3.07180	+	3.07180i	0.112998	+	0.112998i	−0.648347	+	0.761345i	$0.724539\pi$
$740$		0			0
$741$	−7.60770	+	7.60770i	−0.279476	+	0.279476i
$742$		0			0
$743$		−	39.3205i		−	1.44253i	−0.692659	−	0.721265i	$-0.743561\pi$
$743$		−	39.3205i		−	1.44253i	0.692659	−	0.721265i	$-0.256439\pi$
$744$		0			0
$745$			5.75129i			0.210711i
$746$		0			0
$747$	−17.1962	+	17.1962i	−0.629174	+	0.629174i
$748$		0			0
$749$	5.46410	+	5.46410i	0.199654	+	0.199654i
$750$		0			0
$751$	8.39230			0.306240			0.153120	−	0.988208i	$-0.451068\pi$
$751$	8.39230			0.306240			0.153120	+	0.988208i	$0.451068\pi$
$752$		0			0
$753$	7.85641			0.286303
$754$		0			0
$755$	−9.07180	−	9.07180i	−0.330156	−	0.330156i
$756$		0			0
$757$	0.320508	−	0.320508i	0.0116491	−	0.0116491i	−0.701258	−	0.712907i	$-0.747378\pi$
$757$	0.320508	−	0.320508i	0.0116491	−	0.0116491i	0.712907	+	0.701258i	$0.247378\pi$
$758$		0			0
$759$			17.5692i			0.637722i
$760$		0			0
$761$			43.1769i			1.56516i	0.622549	+	0.782581i	$0.286097\pi$
$761$			43.1769i			1.56516i	−0.622549	+	0.782581i	$0.713903\pi$
$762$		0			0
$763$	−1.53590	+	1.53590i	−0.0556033	+	0.0556033i
$764$		0			0
$765$	7.60770	+	7.60770i	0.275057	+	0.275057i
$766$		0			0
$767$	14.5359			0.524861
$768$		0			0
$769$	−7.46410			−0.269162			−0.134581	−	0.990903i	$-0.542969\pi$
$769$	−7.46410			−0.269162			−0.134581	+	0.990903i	$0.542969\pi$
$770$		0			0
$771$	−12.2487	−	12.2487i	−0.441127	−	0.441127i
$772$		0			0
$773$	28.0526	−	28.0526i	1.00898	−	1.00898i	0.00902110	−	0.999959i	$-0.497128\pi$
$773$	28.0526	−	28.0526i	1.00898	−	1.00898i	0.999959	−	0.00902110i	$-0.00287155\pi$
$774$		0			0
$775$			2.10512i			0.0756181i
$776$		0			0
$777$		−	22.3923i		−	0.803319i
$778$		0			0
$779$	−6.00000	+	6.00000i	−0.214972	+	0.214972i
$780$		0			0
$781$	8.00000	+	8.00000i	0.286263	+	0.286263i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	1.85641			0.0662580
$786$		0			0
$787$	23.5885	+	23.5885i	0.840838	+	0.840838i	0.988968	−	0.148130i	$-0.0473255\pi$
$787$	23.5885	+	23.5885i	0.840838	+	0.840838i	−0.148130	+	0.988968i	$0.547325\pi$
$788$		0			0
$789$	−49.8564	+	49.8564i	−1.77494	+	1.77494i
$790$		0			0
$791$		−	13.8564i		−	0.492677i
$792$		0			0
$793$		−	22.1436i		−	0.786342i
$794$		0			0
$795$	2.53590	−	2.53590i	0.0899390	−	0.0899390i
$796$		0			0
$797$	−18.7321	−	18.7321i	−0.663523	−	0.663523i	0.292685	−	0.956209i	$-0.405451\pi$
$797$	−18.7321	−	18.7321i	−0.663523	−	0.663523i	−0.956209	+	0.292685i	$0.905451\pi$
$798$		0			0
$799$	−15.7128			−0.555879
$800$		0			0
$801$	−14.7846			−0.522388
$802$		0			0
$803$	12.0000	+	12.0000i	0.423471	+	0.423471i
$804$		0			0
$805$	−1.85641	+	1.85641i	−0.0654297	+	0.0654297i
$806$		0			0
$807$			38.5359i			1.35653i
$808$		0			0
$809$		−	30.0000i		−	1.05474i	−0.849635	−	0.527372i	$-0.823177\pi$
$809$		−	30.0000i		−	1.05474i	0.849635	−	0.527372i	$-0.176823\pi$
$810$		0			0
$811$	7.58846	−	7.58846i	0.266467	−	0.266467i	−0.561208	−	0.827675i	$-0.689663\pi$
$811$	7.58846	−	7.58846i	0.266467	−	0.266467i	0.827675	+	0.561208i	$0.189663\pi$
$812$		0			0
$813$	18.9282	+	18.9282i	0.663841	+	0.663841i
$814$		0			0
$815$	−8.78461			−0.307711
$816$		0			0
$817$	−1.85641			−0.0649474
$818$		0			0
$819$	−3.80385	−	3.80385i	−0.132917	−	0.132917i
$820$		0			0
$821$	−3.78461	+	3.78461i	−0.132084	+	0.132084i	−0.770058	−	0.637974i	$-0.779773\pi$
$821$	−3.78461	+	3.78461i	−0.132084	+	0.132084i	0.637974	+	0.770058i	$0.279773\pi$
$822$		0			0
$823$		−	46.6410i		−	1.62580i	−0.582401	−	0.812902i	$-0.697887\pi$
$823$		−	46.6410i		−	1.62580i	0.582401	−	0.812902i	$-0.302113\pi$
$824$		0			0
$825$			27.2154i			0.947518i
$826$		0			0
$827$	−1.46410	+	1.46410i	−0.0509118	+	0.0509118i	−0.732104	−	0.681193i	$-0.761462\pi$
$827$	−1.46410	+	1.46410i	−0.0509118	+	0.0509118i	0.681193	+	0.732104i	$0.261462\pi$
$828$		0			0
$829$	−11.6603	−	11.6603i	−0.404977	−	0.404977i	0.475005	−	0.879983i	$-0.342446\pi$
$829$	−11.6603	−	11.6603i	−0.404977	−	0.404977i	−0.879983	+	0.475005i	$0.842446\pi$
$830$		0			0
$831$	10.3923			0.360505
$832$		0			0
$833$	−3.46410			−0.120024
$834$		0			0
$835$	18.5359	+	18.5359i	0.641461	+	0.641461i
$836$		0			0
$837$		0			0
$838$		0			0
$839$			1.60770i			0.0555038i	0.999615	+	0.0277519i	$0.00883484\pi$
$839$			1.60770i			0.0555038i	−0.999615	+	0.0277519i	$0.991165\pi$
$840$		0			0
$841$			10.8564i			0.374359i
$842$		0			0
$843$	17.3205	−	17.3205i	0.596550	−	0.596550i
$844$		0			0
$845$	−7.16283	−	7.16283i	−0.246409	−	0.246409i
$846$		0			0
$847$	−3.00000			−0.103081
$848$		0			0
$849$	−33.7128			−1.15702
$850$		0			0
$851$	16.3923	+	16.3923i	0.561921	+	0.561921i
$852$		0			0
$853$	−20.5885	+	20.5885i	−0.704935	+	0.704935i	−0.965466	−	0.260530i	$-0.916103\pi$
$853$	−20.5885	+	20.5885i	−0.704935	+	0.704935i	0.260530	+	0.965466i	$0.416103\pi$
$854$		0			0
$855$		−	7.60770i		−	0.260178i
$856$		0			0
$857$		−	40.5359i		−	1.38468i	−0.721571	−	0.692340i	$-0.756580\pi$
$857$		−	40.5359i		−	1.38468i	0.721571	−	0.692340i	$-0.243420\pi$
$858$		0			0
$859$	33.1962	−	33.1962i	1.13264	−	1.13264i	0.142901	−	0.989737i	$-0.454357\pi$
$859$	33.1962	−	33.1962i	1.13264	−	1.13264i	0.989737	−	0.142901i	$-0.0456431\pi$
$860$		0			0
$861$	−6.00000	−	6.00000i	−0.204479	−	0.204479i
$862$		0			0
$863$	6.14359			0.209130			0.104565	−	0.994518i	$-0.466655\pi$
$863$	6.14359			0.209130			0.104565	+	0.994518i	$0.466655\pi$
$864$		0			0
$865$	1.85641			0.0631197
$866$		0			0
$867$	8.66025	+	8.66025i	0.294118	+	0.294118i
$868$		0			0
$869$	8.00000	−	8.00000i	0.271381	−	0.271381i
$870$		0			0
$871$		−	27.7128i		−	0.939013i
$872$		0			0
$873$			55.1769i			1.86746i
$874$		0			0
$875$	−6.53590	+	6.53590i	−0.220954	+	0.220954i
$876$		0			0
$877$	−13.3923	−	13.3923i	−0.452226	−	0.452226i	0.443867	−	0.896093i	$-0.353606\pi$
$877$	−13.3923	−	13.3923i	−0.452226	−	0.452226i	−0.896093	+	0.443867i	$0.853606\pi$
$878$		0			0
$879$	71.8179			2.42236
$880$		0			0
$881$	−16.9282			−0.570326			−0.285163	−	0.958479i	$-0.592048\pi$
$881$	−16.9282			−0.570326			−0.285163	+	0.958479i	$0.592048\pi$
$882$		0			0
$883$	28.3923	+	28.3923i	0.955477	+	0.955477i	0.999050	−	0.0435731i	$-0.0138741\pi$
$883$	28.3923	+	28.3923i	0.955477	+	0.955477i	−0.0435731	+	0.999050i	$0.513874\pi$
$884$		0			0
$885$	−14.5359	+	14.5359i	−0.488619	+	0.488619i
$886$		0			0
$887$		−	34.3923i		−	1.15478i	−0.816468	−	0.577390i	$-0.804071\pi$
$887$		−	34.3923i		−	1.15478i	0.816468	−	0.577390i	$-0.195929\pi$
$888$		0			0
$889$		−	20.3923i		−	0.683936i
$890$		0			0
$891$	−18.0000	+	18.0000i	−0.603023	+	0.603023i
$892$		0			0
$893$	7.85641	+	7.85641i	0.262905	+	0.262905i
$894$		0			0
$895$	−20.2872			−0.678126
$896$		0			0
$897$	11.1384			0.371902
$898$		0			0
$899$	−2.39230	−	2.39230i	−0.0797878	−	0.0797878i
$900$		0			0
$901$	−3.46410	+	3.46410i	−0.115406	+	0.115406i
$902$		0			0
$903$		−	1.85641i		−	0.0617773i
$904$		0			0
$905$			8.28719i			0.275475i
$906$		0			0
$907$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$907$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$908$		0			0
$909$	14.1962	+	14.1962i	0.470857	+	0.470857i
$910$		0			0
$911$	2.24871			0.0745031			0.0372516	−	0.999306i	$-0.488140\pi$
$911$	2.24871			0.0745031			0.0372516	+	0.999306i	$0.488140\pi$
$912$		0			0
$913$	−22.9282			−0.758813
$914$		0			0
$915$	22.1436	+	22.1436i	0.732045	+	0.732045i
$916$		0			0
$917$	9.73205	−	9.73205i	0.321381	−	0.321381i
$918$		0			0
$919$		−	10.1436i		−	0.334606i	−0.985906	−	0.167303i	$-0.946494\pi$
$919$		−	10.1436i		−	0.334606i	0.985906	−	0.167303i	$-0.0535059\pi$
$920$		0			0
$921$		−	6.00000i		−	0.197707i
$922$		0			0
$923$	5.07180	−	5.07180i	0.166940	−	0.166940i
$924$		0			0
$925$	25.3923	+	25.3923i	0.834894	+	0.834894i
$926$		0			0
$927$	25.6077			0.841067
$928$		0			0
$929$	−0.535898			−0.0175823			−0.00879113	−	0.999961i	$-0.502798\pi$
$929$	−0.535898			−0.0175823			−0.00879113	+	0.999961i	$0.502798\pi$
$930$		0			0
$931$	1.73205	+	1.73205i	0.0567657	+	0.0567657i
$932$		0			0
$933$	48.0000	−	48.0000i	1.57145	−	1.57145i
$934$		0			0
$935$			10.1436i			0.331731i
$936$		0			0
$937$		−	36.6410i		−	1.19701i	−0.801119	−	0.598505i	$-0.795762\pi$
$937$		−	36.6410i		−	1.19701i	0.801119	−	0.598505i	$-0.204238\pi$
$938$		0			0
$939$	−28.1436	+	28.1436i	−0.918431	+	0.918431i
$940$		0			0
$941$	6.19615	+	6.19615i	0.201989	+	0.201989i	0.800852	−	0.598863i	$-0.204381\pi$
$941$	6.19615	+	6.19615i	0.201989	+	0.201989i	−0.598863	+	0.800852i	$0.704381\pi$
$942$		0			0
$943$	8.78461			0.286066
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−34.7846	−	34.7846i	−1.13035	−	1.13035i	−0.990119	−	0.140229i	$-0.955216\pi$
$947$	−34.7846	−	34.7846i	−1.13035	−	1.13035i	−0.140229	−	0.990119i	$-0.544784\pi$
$948$		0			0
$949$	7.60770	−	7.60770i	0.246956	−	0.246956i
$950$		0			0
$951$			6.67949i			0.216597i
$952$		0			0
$953$			53.8564i			1.74458i	0.488989	+	0.872290i	$0.337366\pi$
$953$			53.8564i			1.74458i	−0.488989	+	0.872290i	$0.662634\pi$
$954$		0			0
$955$	5.07180	−	5.07180i	0.164119	−	0.164119i
$956$		0			0
$957$	−30.9282	−	30.9282i	−0.999767	−	0.999767i
$958$		0			0
$959$	14.9282			0.482057
$960$		0			0
$961$	−30.7128			−0.990736
$962$		0			0
$963$	16.3923	+	16.3923i	0.528235	+	0.528235i
$964$		0			0
$965$	−7.32051	+	7.32051i	−0.235655	+	0.235655i
$966$		0			0
$967$		−	53.4641i		−	1.71929i	−0.510892	−	0.859645i	$-0.670685\pi$
$967$		−	53.4641i		−	1.71929i	0.510892	−	0.859645i	$-0.329315\pi$
$968$		0			0
$969$			20.7846i			0.667698i
$970$		0			0
$971$	18.2679	−	18.2679i	0.586246	−	0.586246i	−0.350366	−	0.936613i	$-0.613943\pi$
$971$	18.2679	−	18.2679i	0.586246	−	0.586246i	0.936613	+	0.350366i	$0.113943\pi$
$972$		0			0
$973$	9.19615	+	9.19615i	0.294815	+	0.294815i
$974$		0			0
$975$	17.2539			0.552566
$976$		0			0
$977$	−22.9282			−0.733538			−0.366769	−	0.930312i	$-0.619536\pi$
$977$	−22.9282			−0.733538			−0.366769	+	0.930312i	$0.619536\pi$
$978$		0			0
$979$	−9.85641	−	9.85641i	−0.315012	−	0.315012i
$980$		0			0
$981$	−4.60770	+	4.60770i	−0.147112	+	0.147112i
$982$		0			0
$983$		−	5.32051i		−	0.169698i	−0.996394	−	0.0848489i	$-0.972959\pi$
$983$		−	5.32051i		−	0.169698i	0.996394	−	0.0848489i	$-0.0270408\pi$
$984$		0			0
$985$			24.6795i			0.786354i
$986$		0			0
$987$	−7.85641	+	7.85641i	−0.250072	+	0.250072i
$988$		0			0
$989$	1.35898	+	1.35898i	0.0432132	+	0.0432132i
$990$		0			0
$991$	−43.7128			−1.38858			−0.694292	−	0.719694i	$-0.744282\pi$
$991$	−43.7128			−1.38858			−0.694292	+	0.719694i	$0.744282\pi$
$992$		0			0
$993$	−53.5692			−1.69997
$994$		0			0
$995$	4.67949	+	4.67949i	0.148350	+	0.148350i
$996$		0			0
$997$	8.33975	−	8.33975i	0.264122	−	0.264122i	−0.562604	−	0.826726i	$-0.690200\pi$
$997$	8.33975	−	8.33975i	0.264122	−	0.264122i	0.826726	+	0.562604i	$0.190200\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3584.2.m.bc.2689.1	yes	4
4.3	odd	2		3584.2.m.bd.2689.2	yes	4
8.3	odd	2		3584.2.m.be.2689.1	yes	4
8.5	even	2		3584.2.m.bf.2689.2	yes	4
16.3	odd	4		3584.2.m.be.897.1	yes	4
16.5	even	4	inner	3584.2.m.bc.897.1	✓	4
16.11	odd	4		3584.2.m.bd.897.2	yes	4
16.13	even	4		3584.2.m.bf.897.2	yes	4
32.5	even	8		7168.2.a.u.1.3		4
32.11	odd	8		7168.2.a.v.1.4		4
32.21	even	8		7168.2.a.u.1.2		4
32.27	odd	8		7168.2.a.v.1.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3584.2.m.bc.897.1	✓	4	16.5	even	4	inner
3584.2.m.bc.2689.1	yes	4	1.1	even	1	trivial
3584.2.m.bd.897.2	yes	4	16.11	odd	4
3584.2.m.bd.2689.2	yes	4	4.3	odd	2
3584.2.m.be.897.1	yes	4	16.3	odd	4
3584.2.m.be.2689.1	yes	4	8.3	odd	2
3584.2.m.bf.897.2	yes	4	16.13	even	4
3584.2.m.bf.2689.2	yes	4	8.5	even	2
7168.2.a.u.1.2		4	32.21	even	8
7168.2.a.u.1.3		4	32.5	even	8
7168.2.a.v.1.1		4	32.27	odd	8
7168.2.a.v.1.4		4	32.11	odd	8

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:	\( N \)	\(=\)	\( 3584 = 2^{9} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3584.m (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.73205 - 1.73205i) q^{3} +(0.732051 - 0.732051i) q^{5} +1.00000i q^{7} +3.00000i q^{9} +O(q^{10})\)	\(q+(-1.73205 - 1.73205i) q^{3} +(0.732051 - 0.732051i) q^{5} +1.00000i q^{7} +3.00000i q^{9} +(-2.00000 + 2.00000i) q^{11} +(1.26795 + 1.26795i) q^{13} -2.53590 q^{15} +3.46410 q^{17} +(-1.73205 - 1.73205i) q^{19} +(1.73205 - 1.73205i) q^{21} +2.53590i q^{23} +3.92820i q^{25} +(-4.46410 - 4.46410i) q^{29} +0.535898 q^{31} +6.92820 q^{33} +(0.732051 + 0.732051i) q^{35} +(6.46410 - 6.46410i) q^{37} -4.39230i q^{39} -3.46410i q^{41} +(0.535898 - 0.535898i) q^{43} +(2.19615 + 2.19615i) q^{45} -4.53590 q^{47} -1.00000 q^{49} +(-6.00000 - 6.00000i) q^{51} +(-1.00000 + 1.00000i) q^{53} +2.92820i q^{55} +6.00000i q^{57} +(5.73205 - 5.73205i) q^{59} +(-8.73205 - 8.73205i) q^{61} -3.00000 q^{63} +1.85641 q^{65} +(-10.9282 - 10.9282i) q^{67} +(4.39230 - 4.39230i) q^{69} -4.00000i q^{71} -6.00000i q^{73} +(6.80385 - 6.80385i) q^{75} +(-2.00000 - 2.00000i) q^{77} -4.00000 q^{79} +9.00000 q^{81} +(5.73205 + 5.73205i) q^{83} +(2.53590 - 2.53590i) q^{85} +15.4641i q^{87} +4.92820i q^{89} +(-1.26795 + 1.26795i) q^{91} +(-0.928203 - 0.928203i) q^{93} -2.53590 q^{95} +18.3923 q^{97} +(-6.00000 - 6.00000i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 4 q^{5}+O(q^{10}) \) 4 * q - 4 * q^5	\( 4 q - 4 q^{5} - 8 q^{11} + 12 q^{13} - 24 q^{15} - 4 q^{29} + 16 q^{31} - 4 q^{35} + 12 q^{37} + 16 q^{43} - 12 q^{45} - 32 q^{47} - 4 q^{49} - 24 q^{51} - 4 q^{53} + 16 q^{59} - 28 q^{61} - 12 q^{63} - 48 q^{65} - 16 q^{67} - 24 q^{69} + 48 q^{75} - 8 q^{77} - 16 q^{79} + 36 q^{81} + 16 q^{83} + 24 q^{85} - 12 q^{91} + 24 q^{93} - 24 q^{95} + 32 q^{97} - 24 q^{99}+O(q^{100}) \) 4 * q - 4 * q^5 - 8 * q^11 + 12 * q^13 - 24 * q^15 - 4 * q^29 + 16 * q^31 - 4 * q^35 + 12 * q^37 + 16 * q^43 - 12 * q^45 - 32 * q^47 - 4 * q^49 - 24 * q^51 - 4 * q^53 + 16 * q^59 - 28 * q^61 - 12 * q^63 - 48 * q^65 - 16 * q^67 - 24 * q^69 + 48 * q^75 - 8 * q^77 - 16 * q^79 + 36 * q^81 + 16 * q^83 + 24 * q^85 - 12 * q^91 + 24 * q^93 - 24 * q^95 + 32 * q^97 - 24 * q^99

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