LMFDB - Embedded newform 1920.2.bc.i.607.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1920,2,Mod(607,1920)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1920.607"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1920, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([2, 3, 0, 1])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 1920 = 2^{7} \cdot 3 \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1920.bc (of order $4$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [16,0,0,0,8,0,-4,0,-16,0,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(11)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$15.3312771881$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 6 x^{15} + 14 x^{14} - 10 x^{13} - 26 x^{12} + 78 x^{11} - 66 x^{10} - 74 x^{9} + 233 x^{8} + \cdots + 256 $ x^16 - 6x^15 + 14x^14 - 10x^13 - 26x^12 + 78x^11 - 66x^10 - 74x^9 + 233x^8 - 148x^7 - 264x^6 + 624x^5 - 416x^4 - 320x^3 + 896x^2 - 768*x + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{12} $
Twist minimal:	no (minimal twist has level 240)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			607.4
Root			$0.424183 + 1.34910i$ of defining polynomial
Character	$\chi$	$=$	1920.607
Dual form			1920.2.bc.i.1183.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+1.00000i q^{3} +(0.609492 - 2.15140i) q^{5} +(0.566689 + 0.566689i) q^{7} -1.00000 q^{9} +(-3.64458 - 3.64458i) q^{11} +2.74185 q^{13} +(2.15140 + 0.609492i) q^{15} +(2.08381 + 2.08381i) q^{17} +(-5.79168 - 5.79168i) q^{19} +(-0.566689 + 0.566689i) q^{21} +(-4.28027 + 4.28027i) q^{23} +(-4.25704 - 2.62252i) q^{25} -1.00000i q^{27} +(-2.63716 + 2.63716i) q^{29} -8.10909i q^{31} +(3.64458 - 3.64458i) q^{33} +(1.56457 - 0.873782i) q^{35} +2.28428 q^{37} +2.74185i q^{39} +2.27486i q^{41} -3.06480 q^{43} +(-0.609492 + 2.15140i) q^{45} +(-1.80573 + 1.80573i) q^{47} -6.35773i q^{49} +(-2.08381 + 2.08381i) q^{51} +6.32215i q^{53} +(-10.0623 + 5.61960i) q^{55} +(5.79168 - 5.79168i) q^{57} +(-5.56839 + 5.56839i) q^{59} +(-4.82071 - 4.82071i) q^{61} +(-0.566689 - 0.566689i) q^{63} +(1.67114 - 5.89881i) q^{65} -3.34296 q^{67} +(-4.28027 - 4.28027i) q^{69} -2.81803 q^{71} +(-10.7052 - 10.7052i) q^{73} +(2.62252 - 4.25704i) q^{75} -4.13068i q^{77} +12.1478 q^{79} +1.00000 q^{81} -1.97640i q^{83} +(5.75316 - 3.21304i) q^{85} +(-2.63716 - 2.63716i) q^{87} -10.0322 q^{89} +(1.55378 + 1.55378i) q^{91} +8.10909 q^{93} +(-15.9902 + 8.93024i) q^{95} +(-1.02135 - 1.02135i) q^{97} +(3.64458 + 3.64458i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 8 q^{5} - 4 q^{7} - 16 q^{9} + 8 q^{13} + 4 q^{15} - 8 q^{17} + 8 q^{19} + 4 q^{21} - 32 q^{25} + 12 q^{29} - 12 q^{35} + 24 q^{37} - 24 q^{43} - 8 q^{45} + 32 q^{47} + 8 q^{51} - 4 q^{55} - 8 q^{57}+ \cdots + 48 q^{97}+O(q^{100}) $ 16 * q + 8 * q^5 - 4 * q^7 - 16 * q^9 + 8 * q^13 + 4 * q^15 - 8 * q^17 + 8 * q^19 + 4 * q^21 - 32 * q^25 + 12 * q^29 - 12 * q^35 + 24 * q^37 - 24 * q^43 - 8 * q^45 + 32 * q^47 + 8 * q^51 - 4 * q^55 - 8 * q^57 - 24 * q^59 - 40 * q^61 + 4 * q^63 - 4 * q^65 - 16 * q^67 - 8 * q^73 - 24 * q^75 + 48 * q^79 + 16 * q^81 + 8 * q^85 + 12 * q^87 + 40 * q^91 + 32 * q^93 - 8 * q^95 + 48 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1920\mathbb{Z}\right)^\times$.

$n$	$511$	$641$	$901$	$1537$
$\chi(n)$	$-1$	$1$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{1}{4}\right)$

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
$3$			1.00000i			0.577350i
$3$			1.00000i			0.577350i
$4$		0			0
$5$	0.609492	−	2.15140i	0.272573	−	0.962135i
$5$	0.609492	−	2.15140i	0.272573	−	0.962135i
$6$		0			0
$7$	0.566689	+	0.566689i	0.214188	+	0.214188i	0.806044	−	0.591856i	$-0.201604\pi$
$7$	0.566689	+	0.566689i	0.214188	+	0.214188i	−0.591856	+	0.806044i	$0.701604\pi$
$8$		0			0
$9$	−1.00000			−0.333333
$10$		0			0
$11$	−3.64458	−	3.64458i	−1.09888	−	1.09888i	−0.994542	−	0.104339i	$-0.966727\pi$
$11$	−3.64458	−	3.64458i	−1.09888	−	1.09888i	−0.104339	−	0.994542i	$-0.533273\pi$
$12$		0			0
$13$	2.74185			0.760452			0.380226	−	0.924894i	$-0.375846\pi$
$13$	2.74185			0.760452			0.380226	+	0.924894i	$0.375846\pi$
$14$		0			0
$15$	2.15140	+	0.609492i	0.555489	+	0.157370i
$16$		0			0
$17$	2.08381	+	2.08381i	0.505397	+	0.505397i	0.913110	−	0.407713i	$-0.133674\pi$
$17$	2.08381	+	2.08381i	0.505397	+	0.505397i	−0.407713	+	0.913110i	$0.633674\pi$
$18$		0			0
$19$	−5.79168	−	5.79168i	−1.32870	−	1.32870i	−0.906502	−	0.422201i	$-0.861258\pi$
$19$	−5.79168	−	5.79168i	−1.32870	−	1.32870i	−0.422201	−	0.906502i	$-0.638742\pi$
$20$		0			0
$21$	−0.566689	+	0.566689i	−0.123662	+	0.123662i
$22$		0			0
$23$	−4.28027	+	4.28027i	−0.892499	+	0.892499i	−0.994758	−	0.102259i	$-0.967393\pi$
$23$	−4.28027	+	4.28027i	−0.892499	+	0.892499i	0.102259	+	0.994758i	$0.467393\pi$
$24$		0			0
$25$	−4.25704	−	2.62252i	−0.851408	−	0.524505i
$26$		0			0
$27$		−	1.00000i		−	0.192450i
$28$		0			0
$29$	−2.63716	+	2.63716i	−0.489709	+	0.489709i	−0.908214	−	0.418506i	$-0.862554\pi$
$29$	−2.63716	+	2.63716i	−0.489709	+	0.489709i	0.418506	+	0.908214i	$0.362554\pi$
$30$		0			0
$31$		−	8.10909i		−	1.45644i	−0.685346	−	0.728218i	$-0.740349\pi$
$31$		−	8.10909i		−	1.45644i	0.685346	−	0.728218i	$-0.259651\pi$
$32$		0			0
$33$	3.64458	−	3.64458i	0.634439	−	0.634439i
$34$		0			0
$35$	1.56457	−	0.873782i	0.264460	−	0.147696i
$36$		0			0
$37$	2.28428			0.375534			0.187767	−	0.982214i	$-0.439875\pi$
$37$	2.28428			0.375534			0.187767	+	0.982214i	$0.439875\pi$
$38$		0			0
$39$			2.74185i			0.439047i
$40$		0			0
$41$			2.27486i			0.355273i	0.984096	+	0.177637i	$0.0568452\pi$
$41$			2.27486i			0.355273i	−0.984096	+	0.177637i	$0.943155\pi$
$42$		0			0
$43$	−3.06480			−0.467378			−0.233689	−	0.972311i	$-0.575080\pi$
$43$	−3.06480			−0.467378			−0.233689	+	0.972311i	$0.575080\pi$
$44$		0			0
$45$	−0.609492	+	2.15140i	−0.0908578	+	0.320712i
$46$		0			0
$47$	−1.80573	+	1.80573i	−0.263392	+	0.263392i	−0.826431	−	0.563039i	$-0.809632\pi$
$47$	−1.80573	+	1.80573i	−0.263392	+	0.263392i	0.563039	+	0.826431i	$0.309632\pi$
$48$		0			0
$49$		−	6.35773i		−	0.908247i
$50$		0			0
$51$	−2.08381	+	2.08381i	−0.291791	+	0.291791i
$52$		0			0
$53$			6.32215i			0.868415i	0.900813	+	0.434207i	$0.142971\pi$
$53$			6.32215i			0.868415i	−0.900813	+	0.434207i	$0.857029\pi$
$54$		0			0
$55$	−10.0623	+	5.61960i	−1.35680	+	0.757746i
$56$		0			0
$57$	5.79168	−	5.79168i	0.767127	−	0.767127i
$58$		0			0
$59$	−5.56839	+	5.56839i	−0.724942	+	0.724942i	−0.969608	−	0.244665i	$-0.921322\pi$
$59$	−5.56839	+	5.56839i	−0.724942	+	0.724942i	0.244665	+	0.969608i	$0.421322\pi$
$60$		0			0
$61$	−4.82071	−	4.82071i	−0.617228	−	0.617228i	0.327591	−	0.944820i	$-0.393763\pi$
$61$	−4.82071	−	4.82071i	−0.617228	−	0.617228i	−0.944820	+	0.327591i	$0.893763\pi$
$62$		0			0
$63$	−0.566689	−	0.566689i	−0.0713961	−	0.0713961i
$64$		0			0
$65$	1.67114	−	5.89881i	0.207279	−	0.731658i
$66$		0			0
$67$	−3.34296			−0.408407			−0.204204	−	0.978928i	$-0.565461\pi$
$67$	−3.34296			−0.408407			−0.204204	+	0.978928i	$0.565461\pi$
$68$		0			0
$69$	−4.28027	−	4.28027i	−0.515284	−	0.515284i
$70$		0			0
$71$	−2.81803			−0.334439			−0.167219	−	0.985920i	$-0.553479\pi$
$71$	−2.81803			−0.334439			−0.167219	+	0.985920i	$0.553479\pi$
$72$		0			0
$73$	−10.7052	−	10.7052i	−1.25295	−	1.25295i	−0.954391	−	0.298559i	$-0.903494\pi$
$73$	−10.7052	−	10.7052i	−1.25295	−	1.25295i	−0.298559	−	0.954391i	$-0.596506\pi$
$74$		0			0
$75$	2.62252	−	4.25704i	0.302823	−	0.491560i
$76$		0			0
$77$		−	4.13068i		−	0.470735i
$78$		0			0
$79$	12.1478			1.36673			0.683367	−	0.730075i	$-0.260515\pi$
$79$	12.1478			1.36673			0.683367	+	0.730075i	$0.260515\pi$
$80$		0			0
$81$	1.00000			0.111111
$82$		0			0
$83$		−	1.97640i		−	0.216938i	−0.994100	−	0.108469i	$-0.965405\pi$
$83$		−	1.97640i		−	0.216938i	0.994100	−	0.108469i	$-0.0345948\pi$
$84$		0			0
$85$	5.75316	−	3.21304i	0.624018	−	0.348503i
$86$		0			0
$87$	−2.63716	−	2.63716i	−0.282733	−	0.282733i
$88$		0			0
$89$	−10.0322			−1.06341			−0.531706	−	0.846929i	$-0.678449\pi$
$89$	−10.0322			−1.06341			−0.531706	+	0.846929i	$0.678449\pi$
$90$		0			0
$91$	1.55378	+	1.55378i	0.162880	+	0.162880i
$92$		0			0
$93$	8.10909			0.840874
$94$		0			0
$95$	−15.9902	+	8.93024i	−1.64056	+	0.916223i
$96$		0			0
$97$	−1.02135	−	1.02135i	−0.103702	−	0.103702i	0.653352	−	0.757054i	$-0.273362\pi$
$97$	−1.02135	−	1.02135i	−0.103702	−	0.103702i	−0.757054	+	0.653352i	$0.773362\pi$
$98$		0			0
$99$	3.64458	+	3.64458i	0.366294	+	0.366294i
$100$		0			0
$101$	13.1932	−	13.1932i	1.31277	−	1.31277i	0.393412	−	0.919362i	$-0.371295\pi$
$101$	13.1932	−	13.1932i	1.31277	−	1.31277i	0.919362	−	0.393412i	$-0.128705\pi$
$102$		0			0
$103$	4.51726	−	4.51726i	0.445099	−	0.445099i	−0.448623	−	0.893721i	$-0.648085\pi$
$103$	4.51726	−	4.51726i	0.445099	−	0.445099i	0.893721	+	0.448623i	$0.148085\pi$
$104$		0			0
$105$	0.873782	+	1.56457i	0.0852723	+	0.152686i
$106$		0			0
$107$		−	3.88249i		−	0.375334i	−0.982233	−	0.187667i	$-0.939907\pi$
$107$		−	3.88249i		−	0.375334i	0.982233	−	0.187667i	$-0.0600926\pi$
$108$		0			0
$109$	−2.51614	+	2.51614i	−0.241003	+	0.241003i	−0.817265	−	0.576262i	$-0.804511\pi$
$109$	−2.51614	+	2.51614i	−0.241003	+	0.241003i	0.576262	+	0.817265i	$0.304511\pi$
$110$		0			0
$111$			2.28428i			0.216815i
$112$		0			0
$113$	−3.89520	+	3.89520i	−0.366429	+	0.366429i	−0.866173	−	0.499744i	$-0.833427\pi$
$113$	−3.89520	+	3.89520i	−0.366429	+	0.366429i	0.499744	+	0.866173i	$0.333427\pi$
$114$		0			0
$115$	6.59978	+	11.8174i	0.615433	+	1.10198i
$116$		0			0
$117$	−2.74185			−0.253484
$118$		0			0
$119$			2.36174i			0.216500i
$120$		0			0
$121$			15.5659i			1.41508i
$122$		0			0
$123$	−2.27486			−0.205117
$124$		0			0
$125$	−8.23673	+	7.56018i	−0.736715	+	0.676203i
$126$		0			0
$127$	3.11993	−	3.11993i	0.276849	−	0.276849i	−0.555001	−	0.831850i	$-0.687282\pi$
$127$	3.11993	−	3.11993i	0.276849	−	0.276849i	0.831850	+	0.555001i	$0.187282\pi$
$128$		0			0
$129$		−	3.06480i		−	0.269841i
$130$		0			0
$131$	8.69631	−	8.69631i	0.759800	−	0.759800i	−0.216486	−	0.976286i	$-0.569459\pi$
$131$	8.69631	−	8.69631i	0.759800	−	0.759800i	0.976286	+	0.216486i	$0.0694595\pi$
$132$		0			0
$133$		−	6.56416i		−	0.569185i
$134$		0			0
$135$	−2.15140	−	0.609492i	−0.185163	−	0.0524567i
$136$		0			0
$137$	16.1963	−	16.1963i	1.38375	−	1.38375i	0.545891	−	0.837856i	$-0.316191\pi$
$137$	16.1963	−	16.1963i	1.38375	−	1.38375i	0.837856	−	0.545891i	$-0.183809\pi$
$138$		0			0
$139$	−10.8859	+	10.8859i	−0.923329	+	0.923329i	−0.997263	−	0.0739337i	$-0.976445\pi$
$139$	−10.8859	+	10.8859i	−0.923329	+	0.923329i	0.0739337	+	0.997263i	$0.476445\pi$
$140$		0			0
$141$	−1.80573	−	1.80573i	−0.152070	−	0.152070i
$142$		0			0
$143$	−9.99288	−	9.99288i	−0.835646	−	0.835646i
$144$		0			0
$145$	4.06626	+	7.28092i	0.337684	+	0.604647i
$146$		0			0
$147$	6.35773			0.524377
$148$		0			0
$149$	8.06960	+	8.06960i	0.661088	+	0.661088i	0.955636	−	0.294549i	$-0.0951694\pi$
$149$	8.06960	+	8.06960i	0.661088	+	0.661088i	−0.294549	+	0.955636i	$0.595169\pi$
$150$		0			0
$151$	10.9071			0.887609			0.443804	−	0.896124i	$-0.353628\pi$
$151$	10.9071			0.887609			0.443804	+	0.896124i	$0.353628\pi$
$152$		0			0
$153$	−2.08381	−	2.08381i	−0.168466	−	0.168466i
$154$		0			0
$155$	−17.4459	−	4.94243i	−1.40129	−	0.396985i
$156$		0			0
$157$		−	14.0713i		−	1.12301i	−0.827472	−	0.561507i	$-0.810222\pi$
$157$		−	14.0713i		−	1.12301i	0.827472	−	0.561507i	$-0.189778\pi$
$158$		0			0
$159$	−6.32215			−0.501379
$160$		0			0
$161$	−4.85117			−0.382325
$162$		0			0
$163$			2.82750i			0.221467i	0.993850	+	0.110734i	$0.0353200\pi$
$163$			2.82750i			0.221467i	−0.993850	+	0.110734i	$0.964680\pi$
$164$		0			0
$165$	−5.61960	−	10.0623i	−0.437485	−	0.783347i
$166$		0			0
$167$	−5.12509	−	5.12509i	−0.396591	−	0.396591i	0.480438	−	0.877029i	$-0.340478\pi$
$167$	−5.12509	−	5.12509i	−0.396591	−	0.396591i	−0.877029	+	0.480438i	$0.840478\pi$
$168$		0			0
$169$	−5.48226			−0.421712
$170$		0			0
$171$	5.79168	+	5.79168i	0.442901	+	0.442901i
$172$		0			0
$173$	−4.60016			−0.349743			−0.174872	−	0.984591i	$-0.555951\pi$
$173$	−4.60016			−0.349743			−0.174872	+	0.984591i	$0.555951\pi$
$174$		0			0
$175$	−0.926262	−	3.89857i	−0.0700188	−	0.294704i
$176$		0			0
$177$	−5.56839	−	5.56839i	−0.418546	−	0.418546i
$178$		0			0
$179$	−3.06396	−	3.06396i	−0.229011	−	0.229011i	0.583268	−	0.812280i	$-0.301774\pi$
$179$	−3.06396	−	3.06396i	−0.229011	−	0.229011i	−0.812280	+	0.583268i	$0.801774\pi$
$180$		0			0
$181$	3.08559	−	3.08559i	0.229350	−	0.229350i	−0.583071	−	0.812421i	$-0.698149\pi$
$181$	3.08559	−	3.08559i	0.229350	−	0.229350i	0.812421	+	0.583071i	$0.198149\pi$
$182$		0			0
$183$	4.82071	−	4.82071i	0.356357	−	0.356357i
$184$		0			0
$185$	1.39225	−	4.91440i	0.102360	−	0.361314i
$186$		0			0
$187$		−	15.1892i		−	1.11074i
$188$		0			0
$189$	0.566689	−	0.566689i	0.0412205	−	0.0412205i
$190$		0			0
$191$		−	21.0908i		−	1.52608i	−0.646353	−	0.763038i	$-0.723707\pi$
$191$		−	21.0908i		−	1.52608i	0.646353	−	0.763038i	$-0.276293\pi$
$192$		0			0
$193$	15.2332	−	15.2332i	1.09651	−	1.09651i	0.101692	−	0.994816i	$-0.467574\pi$
$193$	15.2332	−	15.2332i	1.09651	−	1.09651i	0.994816	−	0.101692i	$-0.0324255\pi$
$194$		0			0
$195$	5.89881	+	1.67114i	0.422423	+	0.119673i
$196$		0			0
$197$	−14.0460			−1.00073			−0.500367	−	0.865814i	$-0.666801\pi$
$197$	−14.0460			−1.00073			−0.500367	+	0.865814i	$0.666801\pi$
$198$		0			0
$199$			2.42066i			0.171596i	0.996313	+	0.0857978i	$0.0273439\pi$
$199$			2.42066i			0.171596i	−0.996313	+	0.0857978i	$0.972656\pi$
$200$		0			0
$201$		−	3.34296i		−	0.235794i
$202$		0			0
$203$	−2.98890			−0.209780
$204$		0			0
$205$	4.89413	+	1.38651i	0.341821	+	0.0968380i
$206$		0			0
$207$	4.28027	−	4.28027i	0.297500	−	0.297500i
$208$		0			0
$209$			42.2164i			2.92017i
$210$		0			0
$211$	−5.18795	+	5.18795i	−0.357153	+	0.357153i	−0.862762	−	0.505609i	$-0.831268\pi$
$211$	−5.18795	+	5.18795i	−0.357153	+	0.357153i	0.505609	+	0.862762i	$0.331268\pi$
$212$		0			0
$213$		−	2.81803i		−	0.193088i
$214$		0			0
$215$	−1.86797	+	6.59361i	−0.127395	+	0.449681i
$216$		0			0
$217$	4.59533	−	4.59533i	0.311951	−	0.311951i
$218$		0			0
$219$	10.7052	−	10.7052i	0.723391	−	0.723391i
$220$		0			0
$221$	5.71348	+	5.71348i	0.384331	+	0.384331i
$222$		0			0
$223$	11.3379	+	11.3379i	0.759240	+	0.759240i	0.976184	−	0.216944i	$-0.0696089\pi$
$223$	11.3379	+	11.3379i	0.759240	+	0.759240i	−0.216944	+	0.976184i	$0.569609\pi$
$224$		0			0
$225$	4.25704	+	2.62252i	0.283803	+	0.174835i
$226$		0			0
$227$	−19.8951			−1.32049			−0.660243	−	0.751052i	$-0.729547\pi$
$227$	−19.8951			−1.32049			−0.660243	+	0.751052i	$0.729547\pi$
$228$		0			0
$229$	−14.1933	−	14.1933i	−0.937918	−	0.937918i	0.0602643	−	0.998182i	$-0.480806\pi$
$229$	−14.1933	−	14.1933i	−0.937918	−	0.937918i	−0.998182	+	0.0602643i	$0.980806\pi$
$230$		0			0
$231$	4.13068			0.271779
$232$		0			0
$233$	13.9475	+	13.9475i	0.913734	+	0.913734i	0.996564	−	0.0828295i	$-0.0263957\pi$
$233$	13.9475	+	13.9475i	0.913734	+	0.913734i	−0.0828295	+	0.996564i	$0.526396\pi$
$234$		0			0
$235$	2.78426	+	4.98541i	0.181625	+	0.325212i
$236$		0			0
$237$			12.1478i			0.789085i
$238$		0			0
$239$	−16.4452			−1.06375			−0.531876	−	0.846822i	$-0.678513\pi$
$239$	−16.4452			−1.06375			−0.531876	+	0.846822i	$0.678513\pi$
$240$		0			0
$241$	−4.70995			−0.303394			−0.151697	−	0.988427i	$-0.548474\pi$
$241$	−4.70995			−0.303394			−0.151697	+	0.988427i	$0.548474\pi$
$242$		0			0
$243$			1.00000i			0.0641500i
$244$		0			0
$245$	−13.6780	−	3.87499i	−0.873856	−	0.247564i
$246$		0			0
$247$	−15.8799	−	15.8799i	−1.01042	−	1.01042i
$248$		0			0
$249$	1.97640			0.125249
$250$		0			0
$251$	14.6935	+	14.6935i	0.927448	+	0.927448i	0.997541	−	0.0700924i	$-0.0223294\pi$
$251$	14.6935	+	14.6935i	0.927448	+	0.927448i	−0.0700924	+	0.997541i	$0.522329\pi$
$252$		0			0
$253$	31.1996			1.96150
$254$		0			0
$255$	3.21304	+	5.75316i	0.201208	+	0.360277i
$256$		0			0
$257$	5.02979	+	5.02979i	0.313750	+	0.313750i	0.846360	−	0.532611i	$-0.178789\pi$
$257$	5.02979	+	5.02979i	0.313750	+	0.313750i	−0.532611	+	0.846360i	$0.678789\pi$
$258$		0			0
$259$	1.29448	+	1.29448i	0.0804349	+	0.0804349i
$260$		0			0
$261$	2.63716	−	2.63716i	0.163236	−	0.163236i
$262$		0			0
$263$	8.84851	−	8.84851i	0.545622	−	0.545622i	−0.379549	−	0.925172i	$-0.623921\pi$
$263$	8.84851	−	8.84851i	0.545622	−	0.545622i	0.925172	+	0.379549i	$0.123921\pi$
$264$		0			0
$265$	13.6015	+	3.85330i	0.835532	+	0.236707i
$266$		0			0
$267$		−	10.0322i		−	0.613961i
$268$		0			0
$269$	−4.66057	+	4.66057i	−0.284160	+	0.284160i	−0.834766	−	0.550605i	$-0.814397\pi$
$269$	−4.66057	+	4.66057i	−0.284160	+	0.284160i	0.550605	+	0.834766i	$0.314397\pi$
$270$		0			0
$271$			3.87643i			0.235477i	0.993045	+	0.117738i	$0.0375644\pi$
$271$			3.87643i			0.235477i	−0.993045	+	0.117738i	$0.962436\pi$
$272$		0			0
$273$	−1.55378	+	1.55378i	−0.0940388	+	0.0940388i
$274$		0			0
$275$	5.95712	+	25.0731i	0.359228	+	1.51196i
$276$		0			0
$277$	14.6951			0.882941			0.441471	−	0.897276i	$-0.354457\pi$
$277$	14.6951			0.882941			0.441471	+	0.897276i	$0.354457\pi$
$278$		0			0
$279$			8.10909i			0.485479i
$280$		0			0
$281$			0.328587i			0.0196019i	0.999952	+	0.00980093i	$0.00311978\pi$
$281$			0.328587i			0.0196019i	−0.999952	+	0.00980093i	$0.996880\pi$
$282$		0			0
$283$	22.9890			1.36656			0.683278	−	0.730158i	$-0.260554\pi$
$283$	22.9890			1.36656			0.683278	+	0.730158i	$0.260554\pi$
$284$		0			0
$285$	−8.93024	−	15.9902i	−0.528981	−	0.947178i
$286$		0			0
$287$	−1.28914	+	1.28914i	−0.0760953	+	0.0760953i
$288$		0			0
$289$		−	8.31550i		−	0.489147i
$290$		0			0
$291$	1.02135	−	1.02135i	0.0598725	−	0.0598725i
$292$		0			0
$293$			22.0162i			1.28620i	0.765781	+	0.643101i	$0.222352\pi$
$293$			22.0162i			1.28620i	−0.765781	+	0.643101i	$0.777648\pi$
$294$		0			0
$295$	8.58594	+	15.3737i	0.499893	+	0.895092i
$296$		0			0
$297$	−3.64458	+	3.64458i	−0.211480	+	0.211480i
$298$		0			0
$299$	−11.7359	+	11.7359i	−0.678703	+	0.678703i
$300$		0			0
$301$	−1.73679	−	1.73679i	−0.100107	−	0.100107i
$302$		0			0
$303$	13.1932	+	13.1932i	0.757931	+	0.757931i
$304$		0			0
$305$	−13.3095	+	7.43308i	−0.762097	+	0.425617i
$306$		0			0
$307$	3.08698			0.176183			0.0880916	−	0.996112i	$-0.471923\pi$
$307$	3.08698			0.176183			0.0880916	+	0.996112i	$0.471923\pi$
$308$		0			0
$309$	4.51726	+	4.51726i	0.256978	+	0.256978i
$310$		0			0
$311$	24.3682			1.38179			0.690897	−	0.722953i	$-0.257216\pi$
$311$	24.3682			1.38179			0.690897	+	0.722953i	$0.257216\pi$
$312$		0			0
$313$	3.31911	+	3.31911i	0.187607	+	0.187607i	0.794661	−	0.607054i	$-0.207649\pi$
$313$	3.31911	+	3.31911i	0.187607	+	0.187607i	−0.607054	+	0.794661i	$0.707649\pi$
$314$		0			0
$315$	−1.56457	+	0.873782i	−0.0881533	+	0.0492320i
$316$		0			0
$317$		−	5.35749i		−	0.300907i	−0.988617	−	0.150453i	$-0.951927\pi$
$317$		−	5.35749i		−	0.300907i	0.988617	−	0.150453i	$-0.0480733\pi$
$318$		0			0
$319$	19.2227			1.07626
$320$		0			0
$321$	3.88249			0.216699
$322$		0			0
$323$		−	24.1375i		−	1.34305i
$324$		0			0
$325$	−11.6722	−	7.19056i	−0.647455	−	0.398861i
$326$		0			0
$327$	−2.51614	−	2.51614i	−0.139143	−	0.139143i
$328$		0			0
$329$	−2.04657			−0.112831
$330$		0			0
$331$	2.76903	+	2.76903i	0.152200	+	0.152200i	0.779100	−	0.626900i	$-0.215677\pi$
$331$	2.76903	+	2.76903i	0.152200	+	0.152200i	−0.626900	+	0.779100i	$0.715677\pi$
$332$		0			0
$333$	−2.28428			−0.125178
$334$		0			0
$335$	−2.03751	+	7.19204i	−0.111321	+	0.392943i
$336$		0			0
$337$	−7.30028	−	7.30028i	−0.397672	−	0.397672i	0.479739	−	0.877411i	$-0.340731\pi$
$337$	−7.30028	−	7.30028i	−0.397672	−	0.397672i	−0.877411	+	0.479739i	$0.840731\pi$
$338$		0			0
$339$	−3.89520	−	3.89520i	−0.211558	−	0.211558i
$340$		0			0
$341$	−29.5542	+	29.5542i	−1.60045	+	1.60045i
$342$		0			0
$343$	7.56968	−	7.56968i	0.408724	−	0.408724i
$344$		0			0
$345$	−11.8174	+	6.59978i	−0.636226	+	0.355320i
$346$		0			0
$347$			17.0824i			0.917032i	0.888686	+	0.458516i	$0.151619\pi$
$347$			17.0824i			0.917032i	−0.888686	+	0.458516i	$0.848381\pi$
$348$		0			0
$349$	1.38113	−	1.38113i	0.0739302	−	0.0739302i	−0.669175	−	0.743105i	$-0.733352\pi$
$349$	1.38113	−	1.38113i	0.0739302	−	0.0739302i	0.743105	+	0.669175i	$0.233352\pi$
$350$		0			0
$351$		−	2.74185i		−	0.146349i
$352$		0			0
$353$	−6.69565	+	6.69565i	−0.356373	+	0.356373i	−0.862474	−	0.506101i	$-0.831086\pi$
$353$	−6.69565	+	6.69565i	−0.356373	+	0.356373i	0.506101	+	0.862474i	$0.331086\pi$
$354$		0			0
$355$	−1.71757	+	6.06271i	−0.0911590	+	0.321775i
$356$		0			0
$357$	−2.36174			−0.124997
$358$		0			0
$359$		−	1.90946i		−	0.100777i	−0.998730	−	0.0503886i	$-0.983954\pi$
$359$		−	1.90946i		−	0.100777i	0.998730	−	0.0503886i	$-0.0160460\pi$
$360$		0			0
$361$			48.0872i			2.53090i
$362$		0			0
$363$	−15.5659			−0.816996
$364$		0			0
$365$	−29.5559	+	16.5064i	−1.54703	+	0.863986i
$366$		0			0
$367$	−20.2767	+	20.2767i	−1.05844	+	1.05844i	−0.0602537	+	0.998183i	$0.519191\pi$
$367$	−20.2767	+	20.2767i	−1.05844	+	1.05844i	−0.998183	+	0.0602537i	$0.980809\pi$
$368$		0			0
$369$		−	2.27486i		−	0.118424i
$370$		0			0
$371$	−3.58269	+	3.58269i	−0.186004	+	0.186004i
$372$		0			0
$373$			34.5736i			1.79015i	0.445914	+	0.895076i	$0.352879\pi$
$373$			34.5736i			1.79015i	−0.445914	+	0.895076i	$0.647121\pi$
$374$		0			0
$375$	−7.56018	−	8.23673i	−0.390406	−	0.425343i
$376$		0			0
$377$	−7.23070	+	7.23070i	−0.372400	+	0.372400i
$378$		0			0
$379$	21.2172	−	21.2172i	1.08986	−	1.08986i	0.0943133	−	0.995543i	$-0.469934\pi$
$379$	21.2172	−	21.2172i	1.08986	−	1.08986i	0.995543	−	0.0943133i	$-0.0300656\pi$
$380$		0			0
$381$	3.11993	+	3.11993i	0.159839	+	0.159839i
$382$		0			0
$383$	−3.13204	−	3.13204i	−0.160040	−	0.160040i	0.622544	−	0.782584i	$-0.286099\pi$
$383$	−3.13204	−	3.13204i	−0.160040	−	0.160040i	−0.782584	+	0.622544i	$0.786099\pi$
$384$		0			0
$385$	−8.88674	−	2.51762i	−0.452910	−	0.128310i
$386$		0			0
$387$	3.06480			0.155793
$388$		0			0
$389$	15.2777	+	15.2777i	0.774610	+	0.774610i	0.978909	−	0.204299i	$-0.0654913\pi$
$389$	15.2777	+	15.2777i	0.774610	+	0.774610i	−0.204299	+	0.978909i	$0.565491\pi$
$390$		0			0
$391$	−17.8385			−0.902133
$392$		0			0
$393$	8.69631	+	8.69631i	0.438671	+	0.438671i
$394$		0			0
$395$	7.40399	−	26.1348i	0.372535	−	1.31498i
$396$		0			0
$397$		−	9.39676i		−	0.471610i	−0.971800	−	0.235805i	$-0.924227\pi$
$397$		−	9.39676i		−	0.471610i	0.971800	−	0.235805i	$-0.0757726\pi$
$398$		0			0
$399$	6.56416			0.328619
$400$		0			0
$401$	0.722171			0.0360635			0.0180317	−	0.999837i	$-0.494260\pi$
$401$	0.722171			0.0360635			0.0180317	+	0.999837i	$0.494260\pi$
$402$		0			0
$403$		−	22.2339i		−	1.10755i
$404$		0			0
$405$	0.609492	−	2.15140i	0.0302859	−	0.106904i
$406$		0			0
$407$	−8.32524	−	8.32524i	−0.412667	−	0.412667i
$408$		0			0
$409$	−20.7860			−1.02780			−0.513900	−	0.857850i	$-0.671800\pi$
$409$	−20.7860			−1.02780			−0.513900	+	0.857850i	$0.671800\pi$
$410$		0			0
$411$	16.1963	+	16.1963i	0.798907	+	0.798907i
$412$		0			0
$413$	−6.31109			−0.310548
$414$		0			0
$415$	−4.25203	−	1.20460i	−0.208724	−	0.0591315i
$416$		0			0
$417$	−10.8859	−	10.8859i	−0.533085	−	0.533085i
$418$		0			0
$419$	−6.25484	−	6.25484i	−0.305569	−	0.305569i	0.537619	−	0.843188i	$-0.319324\pi$
$419$	−6.25484	−	6.25484i	−0.305569	−	0.305569i	−0.843188	+	0.537619i	$0.819324\pi$
$420$		0			0
$421$	−16.2076	+	16.2076i	−0.789909	+	0.789909i	−0.981479	−	0.191570i	$-0.938642\pi$
$421$	−16.2076	+	16.2076i	−0.789909	+	0.789909i	0.191570	+	0.981479i	$0.438642\pi$
$422$		0			0
$423$	1.80573	−	1.80573i	0.0877974	−	0.0877974i
$424$		0			0
$425$	−3.40601	−	14.3357i	−0.165216	−	0.695382i
$426$		0			0
$427$		−	5.46368i		−	0.264406i
$428$		0			0
$429$	9.99288	−	9.99288i	0.482461	−	0.482461i
$430$		0			0
$431$			16.1416i			0.777512i	0.921341	+	0.388756i	$0.127095\pi$
$431$			16.1416i			0.777512i	−0.921341	+	0.388756i	$0.872905\pi$
$432$		0			0
$433$	−23.9381	+	23.9381i	−1.15039	+	1.15039i	−0.163919	+	0.986474i	$0.552414\pi$
$433$	−23.9381	+	23.9381i	−1.15039	+	1.15039i	−0.986474	+	0.163919i	$0.947586\pi$
$434$		0			0
$435$	−7.28092	+	4.06626i	−0.349093	+	0.194962i
$436$		0			0
$437$	49.5800			2.37173
$438$		0			0
$439$		−	13.2194i		−	0.630927i	−0.948938	−	0.315464i	$-0.897840\pi$
$439$		−	13.2194i		−	0.630927i	0.948938	−	0.315464i	$-0.102160\pi$
$440$		0			0
$441$			6.35773i			0.302749i
$442$		0			0
$443$	7.03868			0.334418			0.167209	−	0.985921i	$-0.446525\pi$
$443$	7.03868			0.334418			0.167209	+	0.985921i	$0.446525\pi$
$444$		0			0
$445$	−6.11455	+	21.5833i	−0.289857	+	1.02315i
$446$		0			0
$447$	−8.06960	+	8.06960i	−0.381679	+	0.381679i
$448$		0			0
$449$		−	28.2211i		−	1.33184i	−0.746025	−	0.665918i	$-0.768040\pi$
$449$		−	28.2211i		−	1.33184i	0.746025	−	0.665918i	$-0.231960\pi$
$450$		0			0
$451$	8.29089	−	8.29089i	0.390403	−	0.390403i
$452$		0			0
$453$			10.9071i			0.512461i
$454$		0			0
$455$	4.28981	−	2.39578i	0.201109	−	0.112316i
$456$		0			0
$457$	27.6086	−	27.6086i	1.29148	−	1.29148i	0.357605	−	0.933873i	$-0.383594\pi$
$457$	27.6086	−	27.6086i	1.29148	−	1.29148i	0.933873	−	0.357605i	$-0.116406\pi$
$458$		0			0
$459$	2.08381	−	2.08381i	0.0972638	−	0.0972638i
$460$		0			0
$461$	16.4823	+	16.4823i	0.767657	+	0.767657i	0.977694	−	0.210036i	$-0.0673583\pi$
$461$	16.4823	+	16.4823i	0.767657	+	0.767657i	−0.210036	+	0.977694i	$0.567358\pi$
$462$		0			0
$463$	18.5827	+	18.5827i	0.863610	+	0.863610i	0.991755	−	0.128145i	$-0.0409024\pi$
$463$	18.5827	+	18.5827i	0.863610	+	0.863610i	−0.128145	+	0.991755i	$0.540902\pi$
$464$		0			0
$465$	4.94243	−	17.4459i	0.229200	−	0.809034i
$466$		0			0
$467$	−11.5112			−0.532676			−0.266338	−	0.963880i	$-0.585814\pi$
$467$	−11.5112			−0.532676			−0.266338	+	0.963880i	$0.585814\pi$
$468$		0			0
$469$	−1.89442	−	1.89442i	−0.0874761	−	0.0874761i
$470$		0			0
$471$	14.0713			0.648373
$472$		0			0
$473$	11.1699	+	11.1699i	0.513593	+	0.513593i
$474$		0			0
$475$	9.46659	+	39.8442i	0.434357	+	1.82818i
$476$		0			0
$477$		−	6.32215i		−	0.289472i
$478$		0			0
$479$	10.5991			0.484286			0.242143	−	0.970241i	$-0.422150\pi$
$479$	10.5991			0.484286			0.242143	+	0.970241i	$0.422150\pi$
$480$		0			0
$481$	6.26316			0.285575
$482$		0			0
$483$		−	4.85117i		−	0.220736i
$484$		0			0
$485$	−2.81983	+	1.57482i	−0.128042	+	0.0715091i
$486$		0			0
$487$	23.1871	+	23.1871i	1.05071	+	1.05071i	0.998644	+	0.0520644i	$0.0165801\pi$
$487$	23.1871	+	23.1871i	1.05071	+	1.05071i	0.0520644	+	0.998644i	$0.483420\pi$
$488$		0			0
$489$	−2.82750			−0.127864
$490$		0			0
$491$	17.0460	+	17.0460i	0.769277	+	0.769277i	0.977979	−	0.208702i	$-0.0669239\pi$
$491$	17.0460	+	17.0460i	0.769277	+	0.769277i	−0.208702	+	0.977979i	$0.566924\pi$
$492$		0			0
$493$	−10.9907			−0.494995
$494$		0			0
$495$	10.0623	−	5.61960i	0.452266	−	0.252582i
$496$		0			0
$497$	−1.59695	−	1.59695i	−0.0716328	−	0.0716328i
$498$		0			0
$499$	23.5253	+	23.5253i	1.05314	+	1.05314i	0.998507	+	0.0546291i	$0.0173976\pi$
$499$	23.5253	+	23.5253i	1.05314	+	1.05314i	0.0546291	+	0.998507i	$0.482602\pi$
$500$		0			0
$501$	5.12509	−	5.12509i	0.228972	−	0.228972i
$502$		0			0
$503$	−16.1405	+	16.1405i	−0.719669	+	0.719669i	−0.968537	−	0.248868i	$-0.919941\pi$
$503$	−16.1405	+	16.1405i	−0.719669	+	0.719669i	0.248868	+	0.968537i	$0.419941\pi$
$504$		0			0
$505$	−20.3427	−	36.4250i	−0.905239	−	1.62089i
$506$		0			0
$507$		−	5.48226i		−	0.243476i
$508$		0			0
$509$	29.4832	−	29.4832i	1.30682	−	1.30682i	0.383124	−	0.923697i	$-0.374848\pi$
$509$	29.4832	−	29.4832i	1.30682	−	1.30682i	0.923697	−	0.383124i	$-0.125152\pi$
$510$		0			0
$511$		−	12.1330i		−	0.536734i
$512$		0			0
$513$	−5.79168	+	5.79168i	−0.255709	+	0.255709i
$514$		0			0
$515$	−6.96519	−	12.4717i	−0.306923	−	0.549567i
$516$		0			0
$517$	13.1622			0.578873
$518$		0			0
$519$		−	4.60016i		−	0.201924i
$520$		0			0
$521$			18.6350i			0.816416i	0.912889	+	0.408208i	$0.133846\pi$
$521$			18.6350i			0.816416i	−0.912889	+	0.408208i	$0.866154\pi$
$522$		0			0
$523$	16.2282			0.709611			0.354805	−	0.934940i	$-0.384547\pi$
$523$	16.2282			0.709611			0.354805	+	0.934940i	$0.384547\pi$
$524$		0			0
$525$	3.89857	−	0.926262i	0.170148	−	0.0404254i
$526$		0			0
$527$	16.8978	−	16.8978i	0.736079	−	0.736079i
$528$		0			0
$529$		−	13.6415i		−	0.593108i
$530$		0			0
$531$	5.56839	−	5.56839i	0.241647	−	0.241647i
$532$		0			0
$533$			6.23732i			0.270168i
$534$		0			0
$535$	−8.35278	−	2.36635i	−0.361122	−	0.102306i
$536$		0			0
$537$	3.06396	−	3.06396i	0.132220	−	0.132220i
$538$		0			0
$539$	−23.1712	+	23.1712i	−0.998055	+	0.998055i
$540$		0			0
$541$	12.4579	+	12.4579i	0.535609	+	0.535609i	0.922236	−	0.386627i	$-0.126360\pi$
$541$	12.4579	+	12.4579i	0.535609	+	0.535609i	−0.386627	+	0.922236i	$0.626360\pi$
$542$		0			0
$543$	3.08559	+	3.08559i	0.132415	+	0.132415i
$544$		0			0
$545$	3.87966	+	6.94679i	0.166186	+	0.297568i
$546$		0			0
$547$	−1.52574			−0.0652358			−0.0326179	−	0.999468i	$-0.510384\pi$
$547$	−1.52574			−0.0652358			−0.0326179	+	0.999468i	$0.510384\pi$
$548$		0			0
$549$	4.82071	+	4.82071i	0.205743	+	0.205743i
$550$		0			0
$551$	30.5472			1.30135
$552$		0			0
$553$	6.88402	+	6.88402i	0.292738	+	0.292738i
$554$		0			0
$555$	4.91440	+	1.39225i	0.208605	+	0.0590978i
$556$		0			0
$557$		−	14.5277i		−	0.615560i	−0.951458	−	0.307780i	$-0.900414\pi$
$557$		−	14.5277i		−	0.615560i	0.951458	−	0.307780i	$-0.0995860\pi$
$558$		0			0
$559$	−8.40322			−0.355419
$560$		0			0
$561$	15.1892			0.641288
$562$		0			0
$563$		−	37.1864i		−	1.56722i	−0.621253	−	0.783610i	$-0.713376\pi$
$563$		−	37.1864i		−	1.56722i	0.621253	−	0.783610i	$-0.286624\pi$
$564$		0			0
$565$	6.00603	+	10.7542i	0.252676	+	0.452434i
$566$		0			0
$567$	0.566689	+	0.566689i	0.0237987	+	0.0237987i
$568$		0			0
$569$	−22.2439			−0.932513			−0.466256	−	0.884650i	$-0.654398\pi$
$569$	−22.2439			−0.932513			−0.466256	+	0.884650i	$0.654398\pi$
$570$		0			0
$571$	−32.0005	−	32.0005i	−1.33918	−	1.33918i	−0.896854	−	0.442327i	$-0.854153\pi$
$571$	−32.0005	−	32.0005i	−1.33918	−	1.33918i	−0.442327	−	0.896854i	$-0.645847\pi$
$572$		0			0
$573$	21.0908			0.881081
$574$		0			0
$575$	29.4464	−	6.99617i	1.22800	−	0.291761i
$576$		0			0
$577$	3.38284	+	3.38284i	0.140830	+	0.140830i	0.774007	−	0.633177i	$-0.218250\pi$
$577$	3.38284	+	3.38284i	0.140830	+	0.140830i	−0.633177	+	0.774007i	$0.718250\pi$
$578$		0			0
$579$	15.2332	+	15.2332i	0.633069	+	0.633069i
$580$		0			0
$581$	1.12000	−	1.12000i	0.0464656	−	0.0464656i
$582$		0			0
$583$	23.0416	−	23.0416i	0.954284	−	0.954284i
$584$		0			0
$585$	−1.67114	+	5.89881i	−0.0690930	+	0.243886i
$586$		0			0
$587$		−	5.27446i		−	0.217700i	−0.994058	−	0.108850i	$-0.965283\pi$
$587$		−	5.27446i		−	0.217700i	0.994058	−	0.108850i	$-0.0347168\pi$
$588$		0			0
$589$	−46.9653	+	46.9653i	−1.93517	+	1.93517i
$590$		0			0
$591$		−	14.0460i		−	0.577774i
$592$		0			0
$593$	20.6039	−	20.6039i	0.846101	−	0.846101i	−0.143543	−	0.989644i	$-0.545850\pi$
$593$	20.6039	−	20.6039i	0.846101	−	0.846101i	0.989644	+	0.143543i	$0.0458495\pi$
$594$		0			0
$595$	5.08105	+	1.43946i	0.208303	+	0.0590122i
$596$		0			0
$597$	−2.42066			−0.0990708
$598$		0			0
$599$			31.6423i			1.29287i	0.762969	+	0.646435i	$0.223741\pi$
$599$			31.6423i			1.29287i	−0.762969	+	0.646435i	$0.776259\pi$
$600$		0			0
$601$		−	12.1679i		−	0.496338i	−0.968717	−	0.248169i	$-0.920171\pi$
$601$		−	12.1679i		−	0.496338i	0.968717	−	0.248169i	$-0.0798289\pi$
$602$		0			0
$603$	3.34296			0.136136
$604$		0			0
$605$	33.4884	+	9.48727i	1.36150	+	0.385712i
$606$		0			0
$607$	−19.4977	+	19.4977i	−0.791387	+	0.791387i	−0.981720	−	0.190332i	$-0.939043\pi$
$607$	−19.4977	+	19.4977i	−0.791387	+	0.791387i	0.190332	+	0.981720i	$0.439043\pi$
$608$		0			0
$609$		−	2.98890i		−	0.121116i
$610$		0			0
$611$	−4.95103	+	4.95103i	−0.200297	+	0.200297i
$612$		0			0
$613$		−	40.9232i		−	1.65287i	−0.563029	−	0.826437i	$-0.690364\pi$
$613$		−	40.9232i		−	1.65287i	0.563029	−	0.826437i	$-0.309636\pi$
$614$		0			0
$615$	−1.38651	+	4.89413i	−0.0559094	+	0.197350i
$616$		0			0
$617$	−12.9650	+	12.9650i	−0.521952	+	0.521952i	−0.918160	−	0.396209i	$-0.870326\pi$
$617$	−12.9650	+	12.9650i	−0.521952	+	0.521952i	0.396209	+	0.918160i	$0.370326\pi$
$618$		0			0
$619$	12.2565	−	12.2565i	0.492632	−	0.492632i	−0.416503	−	0.909135i	$-0.636744\pi$
$619$	12.2565	−	12.2565i	0.492632	−	0.492632i	0.909135	+	0.416503i	$0.136744\pi$
$620$		0			0
$621$	4.28027	+	4.28027i	0.171761	+	0.171761i
$622$		0			0
$623$	−5.68514	−	5.68514i	−0.227770	−	0.227770i
$624$		0			0
$625$	11.2447	+	22.3284i	0.449790	+	0.893134i
$626$		0			0
$627$	−42.2164			−1.68596
$628$		0			0
$629$	4.76000	+	4.76000i	0.189794	+	0.189794i
$630$		0			0
$631$	7.42406			0.295547			0.147774	−	0.989021i	$-0.452789\pi$
$631$	7.42406			0.295547			0.147774	+	0.989021i	$0.452789\pi$
$632$		0			0
$633$	−5.18795	−	5.18795i	−0.206202	−	0.206202i
$634$		0			0
$635$	−4.81064	−	8.61379i	−0.190905	−	0.341828i
$636$		0			0
$637$		−	17.4319i		−	0.690678i
$638$		0			0
$639$	2.81803			0.111480
$640$		0			0
$641$	−28.7869			−1.13702			−0.568508	−	0.822678i	$-0.692479\pi$
$641$	−28.7869			−1.13702			−0.568508	+	0.822678i	$0.692479\pi$
$642$		0			0
$643$		−	5.25971i		−	0.207423i	−0.994607	−	0.103711i	$-0.966928\pi$
$643$		−	5.25971i		−	0.207423i	0.994607	−	0.103711i	$-0.0330718\pi$
$644$		0			0
$645$	−6.59361	−	1.86797i	−0.259623	−	0.0735514i
$646$		0			0
$647$	−32.0670	−	32.0670i	−1.26068	−	1.26068i	−0.950762	−	0.309923i	$-0.899697\pi$
$647$	−32.0670	−	32.0670i	−1.26068	−	1.26068i	−0.309923	−	0.950762i	$-0.600303\pi$
$648$		0			0
$649$	40.5888			1.59325
$650$		0			0
$651$	4.59533	+	4.59533i	0.180105	+	0.180105i
$652$		0			0
$653$	−31.6376			−1.23807			−0.619037	−	0.785362i	$-0.712477\pi$
$653$	−31.6376			−1.23807			−0.619037	+	0.785362i	$0.712477\pi$
$654$		0			0
$655$	−13.4089	−	24.0096i	−0.523929	−	0.938131i
$656$		0			0
$657$	10.7052	+	10.7052i	0.417650	+	0.417650i
$658$		0			0
$659$	12.8616	+	12.8616i	0.501015	+	0.501015i	0.911753	−	0.410738i	$-0.134729\pi$
$659$	12.8616	+	12.8616i	0.501015	+	0.501015i	−0.410738	+	0.911753i	$0.634729\pi$
$660$		0			0
$661$	−28.8603	+	28.8603i	−1.12254	+	1.12254i	−0.131178	+	0.991359i	$0.541876\pi$
$661$	−28.8603	+	28.8603i	−1.12254	+	1.12254i	−0.991359	+	0.131178i	$0.958124\pi$
$662$		0			0
$663$	−5.71348	+	5.71348i	−0.221893	+	0.221893i
$664$		0			0
$665$	−14.1221	−	4.00081i	−0.547633	−	0.155145i
$666$		0			0
$667$		−	22.5756i		−	0.874129i
$668$		0			0
$669$	−11.3379	+	11.3379i	−0.438347	+	0.438347i
$670$		0			0
$671$			35.1389i			1.35652i
$672$		0			0
$673$	8.69401	−	8.69401i	0.335130	−	0.335130i	−0.519401	−	0.854531i	$-0.673845\pi$
$673$	8.69401	−	8.69401i	0.335130	−	0.335130i	0.854531	+	0.519401i	$0.173845\pi$
$674$		0			0
$675$	−2.62252	+	4.25704i	−0.100941	+	0.163853i
$676$		0			0
$677$	−13.3965			−0.514871			−0.257435	−	0.966295i	$-0.582877\pi$
$677$	−13.3965			−0.514871			−0.257435	+	0.966295i	$0.582877\pi$
$678$		0			0
$679$		−	1.15757i		−	0.0444236i
$680$		0			0
$681$		−	19.8951i		−	0.762383i
$682$		0			0
$683$	20.0009			0.765312			0.382656	−	0.923891i	$-0.375009\pi$
$683$	20.0009			0.765312			0.382656	+	0.923891i	$0.375009\pi$
$684$		0			0
$685$	−24.9733	−	44.7164i	−0.954179	−	1.70852i
$686$		0			0
$687$	14.1933	−	14.1933i	0.541507	−	0.541507i
$688$		0			0
$689$			17.3344i			0.660388i
$690$		0			0
$691$	29.3786	−	29.3786i	1.11761	−	1.11761i	0.125524	−	0.992091i	$-0.459939\pi$
$691$	29.3786	−	29.3786i	1.11761	−	1.11761i	0.992091	−	0.125524i	$-0.0400613\pi$
$692$		0			0
$693$			4.13068i			0.156912i
$694$		0			0
$695$	16.7850	+	30.0548i	0.636693	+	1.14004i
$696$		0			0
$697$	−4.74036	+	4.74036i	−0.179554	+	0.179554i
$698$		0			0
$699$	−13.9475	+	13.9475i	−0.527545	+	0.527545i
$700$		0			0
$701$	−22.4862	−	22.4862i	−0.849291	−	0.849291i	0.140754	−	0.990045i	$-0.455047\pi$
$701$	−22.4862	−	22.4862i	−0.849291	−	0.849291i	−0.990045	+	0.140754i	$0.955047\pi$
$702$		0			0
$703$	−13.2298	−	13.2298i	−0.498973	−	0.498973i
$704$		0			0
$705$	−4.98541	+	2.78426i	−0.187762	+	0.104861i
$706$		0			0
$707$	14.9529			0.562362
$708$		0			0
$709$	−3.15802	−	3.15802i	−0.118602	−	0.118602i	0.645315	−	0.763917i	$-0.276726\pi$
$709$	−3.15802	−	3.15802i	−0.118602	−	0.118602i	−0.763917	+	0.645315i	$0.776726\pi$
$710$		0			0
$711$	−12.1478			−0.455578
$712$		0			0
$713$	34.7091	+	34.7091i	1.29987	+	1.29987i
$714$		0			0
$715$	−27.5893	+	15.4081i	−1.03178	+	0.576230i
$716$		0			0
$717$		−	16.4452i		−	0.614157i
$718$		0			0
$719$	1.88866			0.0704352			0.0352176	−	0.999380i	$-0.488788\pi$
$719$	1.88866			0.0704352			0.0352176	+	0.999380i	$0.488788\pi$
$720$		0			0
$721$	5.11976			0.190670
$722$		0			0
$723$		−	4.70995i		−	0.175165i
$724$		0			0
$725$	18.1425	−	4.31048i	0.673796	−	0.160087i
$726$		0			0
$727$	−0.978984	−	0.978984i	−0.0363085	−	0.0363085i	0.688719	−	0.725028i	$-0.258173\pi$
$727$	−0.978984	−	0.978984i	−0.0363085	−	0.0363085i	−0.725028	+	0.688719i	$0.758173\pi$
$728$		0			0
$729$	−1.00000			−0.0370370
$730$		0			0
$731$	−6.38645	−	6.38645i	−0.236211	−	0.236211i
$732$		0			0
$733$	18.1447			0.670189			0.335094	−	0.942185i	$-0.391232\pi$
$733$	18.1447			0.670189			0.335094	+	0.942185i	$0.391232\pi$
$734$		0			0
$735$	3.87499	−	13.6780i	0.142931	−	0.504521i
$736$		0			0
$737$	12.1837	+	12.1837i	0.448791	+	0.448791i
$738$		0			0
$739$	−18.8493	−	18.8493i	−0.693383	−	0.693383i	0.269592	−	0.962975i	$-0.413111\pi$
$739$	−18.8493	−	18.8493i	−0.693383	−	0.693383i	−0.962975	+	0.269592i	$0.913111\pi$
$740$		0			0
$741$	15.8799	−	15.8799i	0.583364	−	0.583364i
$742$		0			0
$743$	−6.80504	+	6.80504i	−0.249653	+	0.249653i	−0.820828	−	0.571175i	$-0.806488\pi$
$743$	−6.80504	+	6.80504i	−0.249653	+	0.249653i	0.571175	+	0.820828i	$0.306488\pi$
$744$		0			0
$745$	22.2793	−	12.4426i	0.816250	−	0.455861i
$746$		0			0
$747$			1.97640i			0.0723127i
$748$		0			0
$749$	2.20016	−	2.20016i	0.0803922	−	0.0803922i
$750$		0			0
$751$		−	1.26232i		−	0.0460627i	−0.999735	−	0.0230313i	$-0.992668\pi$
$751$		−	1.26232i		−	0.0460627i	0.999735	−	0.0230313i	$-0.00733175\pi$
$752$		0			0
$753$	−14.6935	+	14.6935i	−0.535462	+	0.535462i
$754$		0			0
$755$	6.64781	−	23.4656i	0.241938	−	0.854000i
$756$		0			0
$757$	−29.2534			−1.06323			−0.531617	−	0.846985i	$-0.678415\pi$
$757$	−29.2534			−1.06323			−0.531617	+	0.846985i	$0.678415\pi$
$758$		0			0
$759$			31.1996i			1.13247i
$760$		0			0
$761$		−	43.1952i		−	1.56583i	−0.622131	−	0.782913i	$-0.713733\pi$
$761$		−	43.1952i		−	1.56583i	0.622131	−	0.782913i	$-0.286267\pi$
$762$		0			0
$763$	−2.85174			−0.103240
$764$		0			0
$765$	−5.75316	+	3.21304i	−0.208006	+	0.116168i
$766$		0			0
$767$	−15.2677	+	15.2677i	−0.551284	+	0.551284i
$768$		0			0
$769$		−	22.3663i		−	0.806550i	−0.915079	−	0.403275i	$-0.867872\pi$
$769$		−	22.3663i		−	0.806550i	0.915079	−	0.403275i	$-0.132128\pi$
$770$		0			0
$771$	−5.02979	+	5.02979i	−0.181143	+	0.181143i
$772$		0			0
$773$		−	25.3081i		−	0.910270i	−0.890422	−	0.455135i	$-0.849591\pi$
$773$		−	25.3081i		−	0.910270i	0.890422	−	0.455135i	$-0.150409\pi$
$774$		0			0
$775$	−21.2663	+	34.5207i	−0.763907	+	1.24002i
$776$		0			0
$777$	−1.29448	+	1.29448i	−0.0464391	+	0.0464391i
$778$		0			0
$779$	13.1753	−	13.1753i	0.472053	−	0.472053i
$780$		0			0
$781$	10.2705	+	10.2705i	0.367508	+	0.367508i
$782$		0			0
$783$	2.63716	+	2.63716i	0.0942445	+	0.0942445i
$784$		0			0
$785$	−30.2731	−	8.57637i	−1.08049	−	0.306104i
$786$		0			0
$787$	−28.2019			−1.00529			−0.502645	−	0.864493i	$-0.667640\pi$
$787$	−28.2019			−1.00529			−0.502645	+	0.864493i	$0.667640\pi$
$788$		0			0
$789$	8.84851	+	8.84851i	0.315015	+	0.315015i
$790$		0			0
$791$	−4.41473			−0.156970
$792$		0			0
$793$	−13.2177	−	13.2177i	−0.469373	−	0.469373i
$794$		0			0
$795$	−3.85330	+	13.6015i	−0.136663	+	0.482395i
$796$		0			0
$797$		−	15.2969i		−	0.541846i	−0.962601	−	0.270923i	$-0.912671\pi$
$797$		−	15.2969i		−	0.541846i	0.962601	−	0.270923i	$-0.0873288\pi$
$798$		0			0
$799$	−7.52557			−0.266235
$800$		0			0
$801$	10.0322			0.354470
$802$		0			0
$803$			78.0319i			2.75369i
$804$		0			0
$805$	−2.95675	+	10.4368i	−0.104212	+	0.367849i
$806$		0			0
$807$	−4.66057	−	4.66057i	−0.164060	−	0.164060i
$808$		0			0
$809$	−6.74990			−0.237314			−0.118657	−	0.992935i	$-0.537859\pi$
$809$	−6.74990			−0.237314			−0.118657	+	0.992935i	$0.537859\pi$
$810$		0			0
$811$	4.99242	+	4.99242i	0.175307	+	0.175307i	0.789307	−	0.613999i	$-0.210440\pi$
$811$	4.99242	+	4.99242i	0.175307	+	0.175307i	−0.613999	+	0.789307i	$0.710440\pi$
$812$		0			0
$813$	−3.87643			−0.135952
$814$		0			0
$815$	6.08309	+	1.72334i	0.213081	+	0.0603660i
$816$		0			0
$817$	17.7504	+	17.7504i	0.621006	+	0.621006i
$818$		0			0
$819$	−1.55378	−	1.55378i	−0.0542933	−	0.0542933i
$820$		0			0
$821$	28.2761	−	28.2761i	0.986842	−	0.986842i	−0.0130724	−	0.999915i	$-0.504161\pi$
$821$	28.2761	−	28.2761i	0.986842	−	0.986842i	0.999915	+	0.0130724i	$0.00416120\pi$
$822$		0			0
$823$	20.7586	−	20.7586i	0.723599	−	0.723599i	−0.245738	−	0.969336i	$-0.579030\pi$
$823$	20.7586	−	20.7586i	0.723599	−	0.723599i	0.969336	+	0.245738i	$0.0790302\pi$
$824$		0			0
$825$	−25.0731	+	5.95712i	−0.872933	+	0.207400i
$826$		0			0
$827$		−	17.1914i		−	0.597804i	−0.954284	−	0.298902i	$-0.903380\pi$
$827$		−	17.1914i		−	0.597804i	0.954284	−	0.298902i	$-0.0966204\pi$
$828$		0			0
$829$	21.3409	−	21.3409i	0.741201	−	0.741201i	−0.231608	−	0.972809i	$-0.574399\pi$
$829$	21.3409	−	21.3409i	0.741201	−	0.741201i	0.972809	+	0.231608i	$0.0743987\pi$
$830$		0			0
$831$			14.6951i			0.509766i
$832$		0			0
$833$	13.2483	−	13.2483i	0.459025	−	0.459025i
$834$		0			0
$835$	−14.1498	+	7.90241i	−0.489674	+	0.273474i
$836$		0			0
$837$	−8.10909			−0.280291
$838$		0			0
$839$		−	24.3978i		−	0.842305i	−0.906990	−	0.421153i	$-0.861626\pi$
$839$		−	24.3978i		−	0.842305i	0.906990	−	0.421153i	$-0.138374\pi$
$840$		0			0
$841$			15.0907i			0.520371i
$842$		0			0
$843$	−0.328587			−0.0113171
$844$		0			0
$845$	−3.34140	+	11.7945i	−0.114947	+	0.405744i
$846$		0			0
$847$	−8.82100	+	8.82100i	−0.303093	+	0.303093i
$848$		0			0
$849$			22.9890i			0.788982i
$850$		0			0
$851$	−9.77735	+	9.77735i	−0.335163	+	0.335163i
$852$		0			0
$853$		−	57.1946i		−	1.95831i	−0.203124	−	0.979153i	$-0.565109\pi$
$853$		−	57.1946i		−	1.95831i	0.203124	−	0.979153i	$-0.434891\pi$
$854$		0			0
$855$	15.9902	−	8.93024i	0.546854	−	0.305408i
$856$		0			0
$857$	−13.4584	+	13.4584i	−0.459731	+	0.459731i	−0.898567	−	0.438836i	$-0.855391\pi$
$857$	−13.4584	+	13.4584i	−0.459731	+	0.459731i	0.438836	+	0.898567i	$0.355391\pi$
$858$		0			0
$859$	2.91627	−	2.91627i	0.0995019	−	0.0995019i	−0.655603	−	0.755105i	$-0.727586\pi$
$859$	2.91627	−	2.91627i	0.0995019	−	0.0995019i	0.755105	+	0.655603i	$0.227586\pi$
$860$		0			0
$861$	−1.28914	−	1.28914i	−0.0439337	−	0.0439337i
$862$		0			0
$863$	−25.5234	−	25.5234i	−0.868825	−	0.868825i	0.123517	−	0.992342i	$-0.460583\pi$
$863$	−25.5234	−	25.5234i	−0.868825	−	0.868825i	−0.992342	+	0.123517i	$0.960583\pi$
$864$		0			0
$865$	−2.80376	+	9.89677i	−0.0953307	+	0.336500i
$866$		0			0
$867$	8.31550			0.282409
$868$		0			0
$869$	−44.2736	−	44.2736i	−1.50188	−	1.50188i
$870$		0			0
$871$	−9.16589			−0.310574
$872$		0			0
$873$	1.02135	+	1.02135i	0.0345674	+	0.0345674i
$874$		0			0
$875$	−8.95193	−	0.383390i	−0.302631	−	0.0129609i
$876$		0			0
$877$			52.9978i			1.78961i	0.446460	+	0.894804i	$0.352685\pi$
$877$			52.9978i			1.78961i	−0.446460	+	0.894804i	$0.647315\pi$
$878$		0			0
$879$	−22.0162			−0.742589
$880$		0			0
$881$	42.2460			1.42331			0.711653	−	0.702531i	$-0.247947\pi$
$881$	42.2460			1.42331			0.711653	+	0.702531i	$0.247947\pi$
$882$		0			0
$883$			23.6484i			0.795830i	0.917422	+	0.397915i	$0.130266\pi$
$883$			23.6484i			0.795830i	−0.917422	+	0.397915i	$0.869734\pi$
$884$		0			0
$885$	−15.3737	+	8.58594i	−0.516782	+	0.288613i
$886$		0			0
$887$	−30.6018	−	30.6018i	−1.02751	−	1.02751i	−0.999611	−	0.0278982i	$-0.991119\pi$
$887$	−30.6018	−	30.6018i	−1.02751	−	1.02751i	−0.0278982	−	0.999611i	$-0.508881\pi$
$888$		0			0
$889$	3.53606			0.118596
$890$		0			0
$891$	−3.64458	−	3.64458i	−0.122098	−	0.122098i
$892$		0			0
$893$	20.9164			0.699940
$894$		0			0
$895$	−8.45927	+	4.72435i	−0.282762	+	0.157918i
$896$		0			0
$897$	−11.7359	−	11.7359i	−0.391849	−	0.391849i
$898$		0			0
$899$	21.3850	+	21.3850i	0.713229	+	0.713229i
$900$		0			0
$901$	−13.1741	+	13.1741i	−0.438894	+	0.438894i
$902$		0			0
$903$	1.73679	−	1.73679i	0.0577967	−	0.0577967i
$904$		0			0
$905$	−4.75770	−	8.51898i	−0.158151	−	0.283181i
$906$		0			0
$907$			34.6654i			1.15105i	0.817785	+	0.575523i	$0.195202\pi$
$907$			34.6654i			1.15105i	−0.817785	+	0.575523i	$0.804798\pi$
$908$		0			0
$909$	−13.1932	+	13.1932i	−0.437591	+	0.437591i
$910$		0			0
$911$			19.8125i			0.656418i	0.944605	+	0.328209i	$0.106445\pi$
$911$			19.8125i			0.656418i	−0.944605	+	0.328209i	$0.893555\pi$
$912$		0			0
$913$	−7.20314	+	7.20314i	−0.238389	+	0.238389i
$914$		0			0
$915$	−7.43308	−	13.3095i	−0.245730	−	0.439997i
$916$		0			0
$917$	9.85620			0.325480
$918$		0			0
$919$		−	16.7104i		−	0.551226i	−0.961269	−	0.275613i	$-0.911119\pi$
$919$		−	16.7104i		−	0.551226i	0.961269	−	0.275613i	$-0.0888808\pi$
$920$		0			0
$921$			3.08698i			0.101719i
$922$		0			0
$923$	−7.72661			−0.254325
$924$		0			0
$925$	−9.72428	−	5.99058i	−0.319732	−	0.196969i
$926$		0			0
$927$	−4.51726	+	4.51726i	−0.148366	+	0.148366i
$928$		0			0
$929$		−	9.62355i		−	0.315739i	−0.987460	−	0.157869i	$-0.949538\pi$
$929$		−	9.62355i		−	0.315739i	0.987460	−	0.157869i	$-0.0504625\pi$
$930$		0			0
$931$	−36.8219	+	36.8219i	−1.20679	+	1.20679i
$932$		0			0
$933$			24.3682i			0.797780i
$934$		0			0
$935$	−32.6780	−	9.25769i	−1.06868	−	0.302759i
$936$		0			0
$937$	19.6920	−	19.6920i	0.643310	−	0.643310i	−0.308057	−	0.951368i	$-0.599679\pi$
$937$	19.6920	−	19.6920i	0.643310	−	0.643310i	0.951368	+	0.308057i	$0.0996789\pi$
$938$		0			0
$939$	−3.31911	+	3.31911i	−0.108315	+	0.108315i
$940$		0			0
$941$	19.3709	+	19.3709i	0.631473	+	0.631473i	0.948437	−	0.316965i	$-0.102664\pi$
$941$	19.3709	+	19.3709i	0.631473	+	0.631473i	−0.316965	+	0.948437i	$0.602664\pi$
$942$		0			0
$943$	−9.73702	−	9.73702i	−0.317081	−	0.317081i
$944$		0			0
$945$	−0.873782	−	1.56457i	−0.0284241	−	0.0508954i
$946$		0			0
$947$	3.74620			0.121735			0.0608676	−	0.998146i	$-0.480613\pi$
$947$	3.74620			0.121735			0.0608676	+	0.998146i	$0.480613\pi$
$948$		0			0
$949$	−29.3521	−	29.3521i	−0.952809	−	0.952809i
$950$		0			0
$951$	5.35749			0.173728
$952$		0			0
$953$	−11.3723	−	11.3723i	−0.368385	−	0.368385i	0.498503	−	0.866888i	$-0.333883\pi$
$953$	−11.3723	−	11.3723i	−0.368385	−	0.368385i	−0.866888	+	0.498503i	$0.833883\pi$
$954$		0			0
$955$	−45.3747	−	12.8547i	−1.46829	−	0.415968i
$956$		0			0
$957$			19.2227i			0.621381i
$958$		0			0
$959$	18.3566			0.592765
$960$		0			0
$961$	−34.7574			−1.12121
$962$		0			0
$963$			3.88249i			0.125111i
$964$		0			0
$965$	−23.4881	−	42.0571i	−0.756110	−	1.35387i
$966$		0			0
$967$	−7.94580	−	7.94580i	−0.255520	−	0.255520i	0.567709	−	0.823229i	$-0.307830\pi$
$967$	−7.94580	−	7.94580i	−0.255520	−	0.255520i	−0.823229	+	0.567709i	$0.807830\pi$
$968$		0			0
$969$	24.1375			0.775408
$970$		0			0
$971$	−27.9413	−	27.9413i	−0.896679	−	0.896679i	0.0984615	−	0.995141i	$-0.468608\pi$
$971$	−27.9413	−	27.9413i	−0.896679	−	0.896679i	−0.995141	+	0.0984615i	$0.968608\pi$
$972$		0			0
$973$	−12.3378			−0.395533
$974$		0			0
$975$	7.19056	−	11.6722i	0.230282	−	0.373808i
$976$		0			0
$977$	−26.4111	−	26.4111i	−0.844968	−	0.844968i	0.144533	−	0.989500i	$-0.453832\pi$
$977$	−26.4111	−	26.4111i	−0.844968	−	0.844968i	−0.989500	+	0.144533i	$0.953832\pi$
$978$		0			0
$979$	36.5631	+	36.5631i	1.16856	+	1.16856i
$980$		0			0
$981$	2.51614	−	2.51614i	0.0803342	−	0.0803342i
$982$		0			0
$983$	25.4583	−	25.4583i	0.811993	−	0.811993i	−0.172940	−	0.984932i	$-0.555327\pi$
$983$	25.4583	−	25.4583i	0.811993	−	0.811993i	0.984932	+	0.172940i	$0.0553265\pi$
$984$		0			0
$985$	−8.56090	+	30.2185i	−0.272773	+	0.962840i
$986$		0			0
$987$		−	2.04657i		−	0.0651430i
$988$		0			0
$989$	13.1182	−	13.1182i	0.417134	−	0.417134i
$990$		0			0
$991$		−	29.0499i		−	0.922801i	−0.887192	−	0.461400i	$-0.847347\pi$
$991$		−	29.0499i		−	0.922801i	0.887192	−	0.461400i	$-0.152653\pi$
$992$		0			0
$993$	−2.76903	+	2.76903i	−0.0878726	+	0.0878726i
$994$		0			0
$995$	5.20780	+	1.47537i	0.165098	+	0.0467724i
$996$		0			0
$997$	40.4803			1.28202			0.641011	−	0.767531i	$-0.278515\pi$
$997$	40.4803			1.28202			0.641011	+	0.767531i	$0.278515\pi$
$998$		0			0
$999$		−	2.28428i		−	0.0722715i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1920.2.bc.i.607.4		16
4.3	odd	2		1920.2.bc.j.607.4		16
5.3	odd	4		1920.2.y.i.223.7		16
8.3	odd	2		960.2.bc.e.367.5		16
8.5	even	2		240.2.bc.e.67.3	yes	16
16.3	odd	4		240.2.y.e.187.8	yes	16
16.5	even	4		1920.2.y.j.1567.7		16
16.11	odd	4		1920.2.y.i.1567.7		16
16.13	even	4		960.2.y.e.847.2		16
20.3	even	4		1920.2.y.j.223.7		16
24.5	odd	2		720.2.bd.f.307.6		16
40.3	even	4		960.2.y.e.943.2		16
40.13	odd	4		240.2.y.e.163.8	✓	16
48.35	even	4		720.2.z.f.667.1		16
80.3	even	4		240.2.bc.e.43.3	yes	16
80.13	odd	4		960.2.bc.e.463.5		16
80.43	even	4	inner	1920.2.bc.i.1183.4		16
80.53	odd	4		1920.2.bc.j.1183.4		16
120.53	even	4		720.2.z.f.163.1		16
240.83	odd	4		720.2.bd.f.523.6		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
240.2.y.e.163.8	✓	16	40.13	odd	4
240.2.y.e.187.8	yes	16	16.3	odd	4
240.2.bc.e.43.3	yes	16	80.3	even	4
240.2.bc.e.67.3	yes	16	8.5	even	2
720.2.z.f.163.1		16	120.53	even	4
720.2.z.f.667.1		16	48.35	even	4
720.2.bd.f.307.6		16	24.5	odd	2
720.2.bd.f.523.6		16	240.83	odd	4
960.2.y.e.847.2		16	16.13	even	4
960.2.y.e.943.2		16	40.3	even	4
960.2.bc.e.367.5		16	8.3	odd	2
960.2.bc.e.463.5		16	80.13	odd	4
1920.2.y.i.223.7		16	5.3	odd	4
1920.2.y.i.1567.7		16	16.11	odd	4
1920.2.y.j.223.7		16	20.3	even	4
1920.2.y.j.1567.7		16	16.5	even	4
1920.2.bc.i.607.4		16	1.1	even	1	trivial
1920.2.bc.i.1183.4		16	80.43	even	4	inner
1920.2.bc.j.607.4		16	4.3	odd	2
1920.2.bc.j.1183.4		16	80.53	odd	4

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 1920 = 2^{7} \cdot 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1920.bc (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+1.00000i q^{3} +(0.609492 - 2.15140i) q^{5} +(0.566689 + 0.566689i) q^{7} -1.00000 q^{9} +(-3.64458 - 3.64458i) q^{11} +2.74185 q^{13} +(2.15140 + 0.609492i) q^{15} +(2.08381 + 2.08381i) q^{17} +(-5.79168 - 5.79168i) q^{19} +(-0.566689 + 0.566689i) q^{21} +(-4.28027 + 4.28027i) q^{23} +(-4.25704 - 2.62252i) q^{25} -1.00000i q^{27} +(-2.63716 + 2.63716i) q^{29} -8.10909i q^{31} +(3.64458 - 3.64458i) q^{33} +(1.56457 - 0.873782i) q^{35} +2.28428 q^{37} +2.74185i q^{39} +2.27486i q^{41} -3.06480 q^{43} +(-0.609492 + 2.15140i) q^{45} +(-1.80573 + 1.80573i) q^{47} -6.35773i q^{49} +(-2.08381 + 2.08381i) q^{51} +6.32215i q^{53} +(-10.0623 + 5.61960i) q^{55} +(5.79168 - 5.79168i) q^{57} +(-5.56839 + 5.56839i) q^{59} +(-4.82071 - 4.82071i) q^{61} +(-0.566689 - 0.566689i) q^{63} +(1.67114 - 5.89881i) q^{65} -3.34296 q^{67} +(-4.28027 - 4.28027i) q^{69} -2.81803 q^{71} +(-10.7052 - 10.7052i) q^{73} +(2.62252 - 4.25704i) q^{75} -4.13068i q^{77} +12.1478 q^{79} +1.00000 q^{81} -1.97640i q^{83} +(5.75316 - 3.21304i) q^{85} +(-2.63716 - 2.63716i) q^{87} -10.0322 q^{89} +(1.55378 + 1.55378i) q^{91} +8.10909 q^{93} +(-15.9902 + 8.93024i) q^{95} +(-1.02135 - 1.02135i) q^{97} +(3.64458 + 3.64458i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 8 q^{5} - 4 q^{7} - 16 q^{9} + 8 q^{13} + 4 q^{15} - 8 q^{17} + 8 q^{19} + 4 q^{21} - 32 q^{25} + 12 q^{29} - 12 q^{35} + 24 q^{37} - 24 q^{43} - 8 q^{45} + 32 q^{47} + 8 q^{51} - 4 q^{55} - 8 q^{57}+ \cdots + 48 q^{97}+O(q^{100}) \) 16 * q + 8 * q^5 - 4 * q^7 - 16 * q^9 + 8 * q^13 + 4 * q^15 - 8 * q^17 + 8 * q^19 + 4 * q^21 - 32 * q^25 + 12 * q^29 - 12 * q^35 + 24 * q^37 - 24 * q^43 - 8 * q^45 + 32 * q^47 + 8 * q^51 - 4 * q^55 - 8 * q^57 - 24 * q^59 - 40 * q^61 + 4 * q^63 - 4 * q^65 - 16 * q^67 - 8 * q^73 - 24 * q^75 + 48 * q^79 + 16 * q^81 + 8 * q^85 + 12 * q^87 + 40 * q^91 + 32 * q^93 - 8 * q^95 + 48 * q^97

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