LMFDB - Embedded newform 168.2.u.a.89.6

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [168,2,Mod(17,168)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(168, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 0, 3, 1])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("168.17"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 168 = 2^{3} \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	168.u (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$1.34148675396$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 6 x^{15} + 19 x^{14} - 42 x^{13} + 65 x^{12} - 48 x^{11} - 94 x^{10} + 444 x^{9} - 962 x^{8} + \cdots + 6561 $ x^16 - 6x^15 + 19x^14 - 42x^13 + 65x^12 - 48x^11 - 94x^10 + 444x^9 - 962x^8 + 1332x^7 - 846x^6 - 1296x^5 + 5265x^4 - 10206x^3 + 13851x^2 - 13122*x + 6561
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{8} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			89.6
Root			$0.247636 - 1.71426i$ of defining polynomial
Character	$\chi$	$=$	168.89
Dual form			168.2.u.a.17.6

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.642670 - 1.60841i) q^{3} +(1.28955 - 2.23357i) q^{5} +(-0.203402 + 2.63792i) q^{7} +(-2.17395 - 2.06735i) q^{9} +(-1.43199 + 0.826762i) q^{11} -5.71177i q^{13} +(-2.76373 - 3.50957i) q^{15} +(3.79313 + 6.56990i) q^{17} +(2.58961 + 1.49511i) q^{19} +(4.11213 + 2.02247i) q^{21} +(-0.249340 - 0.143957i) q^{23} +(-0.825879 - 1.43046i) q^{25} +(-4.72227 + 2.16798i) q^{27} +2.05856i q^{29} +(-5.21209 + 3.00920i) q^{31} +(0.409472 + 2.83457i) q^{33} +(5.62967 + 3.85604i) q^{35} +(-0.877523 + 1.51991i) q^{37} +(-9.18685 - 3.67078i) q^{39} +4.28635 q^{41} +2.46537 q^{43} +(-7.42098 + 2.18971i) q^{45} +(-0.186586 + 0.323176i) q^{47} +(-6.91726 - 1.07312i) q^{49} +(13.0048 - 1.87863i) q^{51} +(-6.73264 + 3.88709i) q^{53} +4.26461i q^{55} +(4.06901 - 3.20429i) q^{57} +(4.89610 + 8.48029i) q^{59} +(0.889794 + 0.513723i) q^{61} +(5.89569 - 5.31421i) q^{63} +(-12.7576 - 7.36561i) q^{65} +(-1.18281 - 2.04868i) q^{67} +(-0.391784 + 0.308524i) q^{69} -15.6655i q^{71} +(-3.30170 + 1.90624i) q^{73} +(-2.83154 + 0.409034i) q^{75} +(-1.88966 - 3.94565i) q^{77} +(4.56033 - 7.89872i) q^{79} +(0.452128 + 8.98864i) q^{81} -6.65166 q^{83} +19.5657 q^{85} +(3.31101 + 1.32298i) q^{87} +(7.25723 - 12.5699i) q^{89} +(15.0672 + 1.16179i) q^{91} +(1.49037 + 10.3171i) q^{93} +(6.67886 - 3.85604i) q^{95} +4.43739i q^{97} +(4.82229 + 1.16309i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 4 q^{7} + 2 q^{9} + 8 q^{15} - 6 q^{19} + 14 q^{21} - 18 q^{25} - 48 q^{31} - 12 q^{33} - 2 q^{37} - 22 q^{39} + 20 q^{43} - 42 q^{45} - 28 q^{49} + 6 q^{51} - 8 q^{57} + 36 q^{61} - 32 q^{63} + 14 q^{67}+ \cdots + 20 q^{99}+O(q^{100}) $ 16 * q + 4 * q^7 + 2 * q^9 + 8 * q^15 - 6 * q^19 + 14 * q^21 - 18 * q^25 - 48 * q^31 - 12 * q^33 - 2 * q^37 - 22 * q^39 + 20 * q^43 - 42 * q^45 - 28 * q^49 + 6 * q^51 - 8 * q^57 + 36 * q^61 - 32 * q^63 + 14 * q^67 + 30 * q^73 + 54 * q^75 + 28 * q^79 + 30 * q^81 + 16 * q^85 + 78 * q^87 + 66 * q^91 + 16 * q^93 + 20 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/168\mathbb{Z}\right)^\times$.

$n$	$73$	$85$	$113$	$127$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$	$-1$	$1$

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
$3$	0.642670	−	1.60841i	0.371046	−	0.928615i
$3$	0.642670	−	1.60841i	0.371046	−	0.928615i
$4$		0			0
$5$	1.28955	−	2.23357i	0.576704	−	0.998881i	−0.419150	−	0.907917i	$-0.637672\pi$
$5$	1.28955	−	2.23357i	0.576704	−	0.998881i	0.995854	−	0.0909641i	$-0.0289949\pi$
$6$		0			0
$7$	−0.203402	+	2.63792i	−0.0768787	+	0.997040i
$7$	−0.203402	+	2.63792i	−0.0768787	+	0.997040i
$8$		0			0
$9$	−2.17395	−	2.06735i	−0.724650	−	0.689117i
$10$		0			0
$11$	−1.43199	+	0.826762i	−0.431763	+	0.249278i	−0.700097	−	0.714048i	$-0.746860\pi$
$11$	−1.43199	+	0.826762i	−0.431763	+	0.249278i	0.268335	+	0.963326i	$0.413527\pi$
$12$		0			0
$13$		−	5.71177i		−	1.58416i	−0.610418	−	0.792080i	$-0.708998\pi$
$13$		−	5.71177i		−	1.58416i	0.610418	−	0.792080i	$-0.291002\pi$
$14$		0			0
$15$	−2.76373	−	3.50957i	−0.713592	−	0.906167i
$16$		0			0
$17$	3.79313	+	6.56990i	0.919970	+	1.59343i	0.799458	+	0.600722i	$0.205120\pi$
$17$	3.79313	+	6.56990i	0.919970	+	1.59343i	0.120512	+	0.992712i	$0.461547\pi$
$18$		0			0
$19$	2.58961	+	1.49511i	0.594097	+	0.343002i	0.766716	−	0.641987i	$-0.221890\pi$
$19$	2.58961	+	1.49511i	0.594097	+	0.343002i	−0.172619	+	0.984989i	$0.555223\pi$
$20$		0			0
$21$	4.11213	+	2.02247i	0.897341	+	0.441338i
$22$		0			0
$23$	−0.249340	−	0.143957i	−0.0519910	−	0.0300170i	0.473779	−	0.880644i	$-0.342889\pi$
$23$	−0.249340	−	0.143957i	−0.0519910	−	0.0300170i	−0.525770	+	0.850627i	$0.676223\pi$
$24$		0			0
$25$	−0.825879	−	1.43046i	−0.165176	−	0.286093i
$26$		0			0
$27$	−4.72227	+	2.16798i	−0.908802	+	0.417227i
$28$		0			0
$29$			2.05856i			0.382265i	0.981564	+	0.191133i	$0.0612161\pi$
$29$			2.05856i			0.382265i	−0.981564	+	0.191133i	$0.938784\pi$
$30$		0			0
$31$	−5.21209	+	3.00920i	−0.936118	+	0.540468i	−0.888741	−	0.458409i	$-0.848420\pi$
$31$	−5.21209	+	3.00920i	−0.936118	+	0.540468i	−0.0473770	+	0.998877i	$0.515086\pi$
$32$		0			0
$33$	0.409472	+	2.83457i	0.0712798	+	0.493435i
$34$		0			0
$35$	5.62967	+	3.85604i	0.951589	+	0.651790i
$36$		0			0
$37$	−0.877523	+	1.51991i	−0.144264	+	0.249872i	−0.929098	−	0.369833i	$-0.879415\pi$
$37$	−0.877523	+	1.51991i	−0.144264	+	0.249872i	0.784834	+	0.619706i	$0.212748\pi$
$38$		0			0
$39$	−9.18685	−	3.67078i	−1.47107	−	0.587795i
$40$		0			0
$41$	4.28635			0.669415			0.334708	−	0.942322i	$-0.391362\pi$
$41$	4.28635			0.669415			0.334708	+	0.942322i	$0.391362\pi$
$42$		0			0
$43$	2.46537			0.375965			0.187982	−	0.982172i	$-0.439805\pi$
$43$	2.46537			0.375965			0.187982	+	0.982172i	$0.439805\pi$
$44$		0			0
$45$	−7.42098	+	2.18971i	−1.10625	+	0.326423i
$46$		0			0
$47$	−0.186586	+	0.323176i	−0.0272163	+	0.0471401i	−0.879313	−	0.476245i	$-0.841998\pi$
$47$	−0.186586	+	0.323176i	−0.0272163	+	0.0471401i	0.852096	+	0.523385i	$0.175331\pi$
$48$		0			0
$49$	−6.91726	−	1.07312i	−0.988179	−	0.153302i
$50$		0			0
$51$	13.0048	−	1.87863i	1.82104	−	0.263061i
$52$		0			0
$53$	−6.73264	+	3.88709i	−0.924799	+	0.533933i	−0.885163	−	0.465281i	$-0.845953\pi$
$53$	−6.73264	+	3.88709i	−0.924799	+	0.533933i	−0.0396361	+	0.999214i	$0.512620\pi$
$54$		0			0
$55$			4.26461i			0.575039i
$56$		0			0
$57$	4.06901	−	3.20429i	0.538954	−	0.424418i
$58$		0			0
$59$	4.89610	+	8.48029i	0.637417	+	1.10404i	0.985997	+	0.166760i	$0.0533306\pi$
$59$	4.89610	+	8.48029i	0.637417	+	1.10404i	−0.348580	+	0.937279i	$0.613336\pi$
$60$		0			0
$61$	0.889794	+	0.513723i	0.113926	+	0.0657755i	0.555880	−	0.831262i	$-0.312381\pi$
$61$	0.889794	+	0.513723i	0.113926	+	0.0657755i	−0.441954	+	0.897038i	$0.645715\pi$
$62$		0			0
$63$	5.89569	−	5.31421i	0.742787	−	0.669527i
$64$		0			0
$65$	−12.7576	−	7.36561i	−1.58239	−	0.913592i
$66$		0			0
$67$	−1.18281	−	2.04868i	−0.144503	−	0.250286i	0.784685	−	0.619895i	$-0.212825\pi$
$67$	−1.18281	−	2.04868i	−0.144503	−	0.250286i	−0.929187	+	0.369609i	$0.879492\pi$
$68$		0			0
$69$	−0.391784	+	0.308524i	−0.0471653	+	0.0371419i
$70$		0			0
$71$		−	15.6655i		−	1.85915i	−0.368631	−	0.929576i	$-0.620174\pi$
$71$		−	15.6655i		−	1.85915i	0.368631	−	0.929576i	$-0.379826\pi$
$72$		0			0
$73$	−3.30170	+	1.90624i	−0.386434	+	0.223108i	−0.680614	−	0.732642i	$-0.738287\pi$
$73$	−3.30170	+	1.90624i	−0.386434	+	0.223108i	0.294180	+	0.955750i	$0.404954\pi$
$74$		0			0
$75$	−2.83154	+	0.409034i	−0.326958	+	0.0472312i
$76$		0			0
$77$	−1.88966	−	3.94565i	−0.215347	−	0.449649i
$78$		0			0
$79$	4.56033	−	7.89872i	0.513077	−	0.888676i	−0.486808	−	0.873509i	$-0.661839\pi$
$79$	4.56033	−	7.89872i	0.513077	−	0.888676i	0.999885	−	0.0151665i	$-0.00482783\pi$
$80$		0			0
$81$	0.452128	+	8.98864i	0.0502364	+	0.998737i
$82$		0			0
$83$	−6.65166			−0.730114			−0.365057	−	0.930985i	$-0.618951\pi$
$83$	−6.65166			−0.730114			−0.365057	+	0.930985i	$0.618951\pi$
$84$		0			0
$85$	19.5657			2.12220
$86$		0			0
$87$	3.31101	+	1.32298i	0.354977	+	0.141838i
$88$		0			0
$89$	7.25723	−	12.5699i	0.769265	−	1.33241i	−0.168697	−	0.985668i	$-0.553956\pi$
$89$	7.25723	−	12.5699i	0.769265	−	1.33241i	0.937962	−	0.346738i	$-0.112711\pi$
$90$		0			0
$91$	15.0672	+	1.16179i	1.57947	+	0.121788i
$92$		0			0
$93$	1.49037	+	10.3171i	0.154544	+	1.06983i
$94$		0			0
$95$	6.67886	−	3.85604i	0.685237	−	0.395622i
$96$		0			0
$97$			4.43739i			0.450548i	0.974295	+	0.225274i	$0.0723278\pi$
$97$			4.43739i			0.450548i	−0.974295	+	0.225274i	$0.927672\pi$
$98$		0			0
$99$	4.82229	+	1.16309i	0.484659	+	0.116895i
$100$		0			0
$101$	−2.03628	−	3.52694i	−0.202617	−	0.350943i	0.746754	−	0.665101i	$-0.231611\pi$
$101$	−2.03628	−	3.52694i	−0.202617	−	0.350943i	−0.949371	+	0.314157i	$0.898278\pi$
$102$		0			0
$103$	−7.30346	−	4.21666i	−0.719632	−	0.415479i	0.0949855	−	0.995479i	$-0.469720\pi$
$103$	−7.30346	−	4.21666i	−0.719632	−	0.415479i	−0.814617	+	0.579999i	$0.803053\pi$
$104$		0			0
$105$	9.82011	−	6.57665i	0.958345	−	0.641815i
$106$		0			0
$107$	−12.6334	−	7.29389i	−1.22132	−	0.705127i	−0.256118	−	0.966646i	$-0.582444\pi$
$107$	−12.6334	−	7.29389i	−1.22132	−	0.705127i	−0.965199	+	0.261518i	$0.915777\pi$
$108$		0			0
$109$	−8.64994	−	14.9821i	−0.828514	−	1.43503i	−0.899204	−	0.437530i	$-0.855853\pi$
$109$	−8.64994	−	14.9821i	−0.828514	−	1.43503i	0.0706901	−	0.997498i	$-0.477480\pi$
$110$		0			0
$111$	1.88068	+	2.38822i	0.178507	+	0.226680i
$112$		0			0
$113$			4.00000i			0.376288i	0.982141	+	0.188144i	$0.0602472\pi$
$113$			4.00000i			0.376288i	−0.982141	+	0.188144i	$0.939753\pi$
$114$		0			0
$115$	−0.643073	+	0.371279i	−0.0599669	+	0.0346219i
$116$		0			0
$117$	−11.8082	+	12.4171i	−1.09167	+	1.14796i
$118$		0			0
$119$	−18.1024	+	8.66965i	−1.65944	+	0.794746i
$120$		0			0
$121$	−4.13293	+	7.15844i	−0.375721	+	0.650767i
$122$		0			0
$123$	2.75471	−	6.89420i	0.248384	−	0.621629i
$124$		0			0
$125$	8.63545			0.772378
$126$		0			0
$127$	−16.6481			−1.47728			−0.738641	−	0.674099i	$-0.764532\pi$
$127$	−16.6481			−1.47728			−0.738641	+	0.674099i	$0.764532\pi$
$128$		0			0
$129$	1.58442	−	3.96531i	0.139500	−	0.349126i
$130$		0			0
$131$	8.29744	−	14.3716i	0.724951	−	1.25565i	−0.234043	−	0.972226i	$-0.575196\pi$
$131$	8.29744	−	14.3716i	0.724951	−	1.25565i	0.958994	−	0.283426i	$-0.0914709\pi$
$132$		0			0
$133$	−4.47072	+	6.52708i	−0.387660	+	0.565969i
$134$		0			0
$135$	−1.24729	+	13.3432i	−0.107350	+	1.14840i
$136$		0			0
$137$	−8.61684	+	4.97493i	−0.736186	+	0.425037i	−0.820681	−	0.571387i	$-0.806406\pi$
$137$	−8.61684	+	4.97493i	−0.736186	+	0.425037i	0.0844948	+	0.996424i	$0.473072\pi$
$138$		0			0
$139$			3.11952i			0.264594i	0.991210	+	0.132297i	$0.0422353\pi$
$139$			3.11952i			0.264594i	−0.991210	+	0.132297i	$0.957765\pi$
$140$		0			0
$141$	0.399886	+	0.507801i	0.0336765	+	0.0427646i
$142$		0			0
$143$	4.72227	+	8.17922i	0.394896	+	0.683981i
$144$		0			0
$145$	4.59794	+	2.65462i	0.381838	+	0.220454i
$146$		0			0
$147$	−6.17152	+	10.4361i	−0.509018	+	0.860756i
$148$		0			0
$149$	0.987090	+	0.569897i	0.0808655	+	0.0466877i	0.539888	−	0.841737i	$-0.318467\pi$
$149$	0.987090	+	0.569897i	0.0808655	+	0.0466877i	−0.459022	+	0.888425i	$0.651800\pi$
$150$		0			0
$151$	6.38621	+	11.0612i	0.519702	+	0.900151i	0.999738	+	0.0229016i	$0.00729044\pi$
$151$	6.38621	+	11.0612i	0.519702	+	0.900151i	−0.480036	+	0.877249i	$0.659376\pi$
$152$		0			0
$153$	5.33619	−	22.1244i	0.431406	−	1.78865i
$154$		0			0
$155$			15.5221i			1.24676i
$156$		0			0
$157$	7.82053	−	4.51518i	0.624146	−	0.360351i	−0.154335	−	0.988019i	$-0.549324\pi$
$157$	7.82053	−	4.51518i	0.624146	−	0.360351i	0.778481	+	0.627668i	$0.215990\pi$
$158$		0			0
$159$	1.92516	+	13.3269i	0.152675	+	1.05690i
$160$		0			0
$161$	0.430463	−	0.628459i	0.0339252	−	0.0495295i
$162$		0			0
$163$	−0.0498774	+	0.0863903i	−0.00390670	+	0.00676661i	−0.867972	−	0.496613i	$-0.834577\pi$
$163$	−0.0498774	+	0.0863903i	−0.00390670	+	0.00676661i	0.864065	+	0.503379i	$0.167910\pi$
$164$		0			0
$165$	6.85922	+	2.74073i	0.533990	+	0.213366i
$166$		0			0
$167$	3.08612			0.238811			0.119406	−	0.992846i	$-0.461901\pi$
$167$	3.08612			0.238811			0.119406	+	0.992846i	$0.461901\pi$
$168$		0			0
$169$	−19.6243			−1.50956
$170$		0			0
$171$	−2.53877	−	8.60393i	−0.194144	−	0.657959i
$172$		0			0
$173$	−3.73038	+	6.46120i	−0.283615	+	0.491236i	−0.972272	−	0.233851i	$-0.924867\pi$
$173$	−3.73038	+	6.46120i	−0.283615	+	0.491236i	0.688657	+	0.725087i	$0.258201\pi$
$174$		0			0
$175$	3.94144	−	1.88764i	0.297945	−	0.142693i
$176$		0			0
$177$	16.7863	−	2.42490i	1.26174	−	0.182266i
$178$		0			0
$179$	2.61465	−	1.50957i	0.195428	−	0.112830i	−0.399093	−	0.916910i	$-0.630675\pi$
$179$	2.61465	−	1.50957i	0.195428	−	0.112830i	0.594521	+	0.804080i	$0.297342\pi$
$180$		0			0
$181$		−	0.762552i		−	0.0566801i	−0.999598	−	0.0283400i	$-0.990978\pi$
$181$		−	0.762552i		−	0.0566801i	0.999598	−	0.0283400i	$-0.00902212\pi$
$182$		0			0
$183$	1.39812	−	1.10100i	0.103352	−	0.0813881i
$184$		0			0
$185$	2.26322	+	3.92001i	0.166395	+	0.288205i
$186$		0			0
$187$	−10.8635	−	6.27204i	−0.794417	−	0.458657i
$188$		0			0
$189$	−4.75843	−	12.8980i	−0.346125	−	0.938188i
$190$		0			0
$191$	1.05844	+	0.611089i	0.0765859	+	0.0442169i	0.537804	−	0.843070i	$-0.319254\pi$
$191$	1.05844	+	0.611089i	0.0765859	+	0.0442169i	−0.461218	+	0.887287i	$0.652587\pi$
$192$		0			0
$193$	11.7587	+	20.3666i	0.846409	+	1.46602i	0.884392	+	0.466744i	$0.154573\pi$
$193$	11.7587	+	20.3666i	0.846409	+	1.46602i	−0.0379837	+	0.999278i	$0.512093\pi$
$194$		0			0
$195$	−20.0458	+	15.7858i	−1.43551	+	1.13044i
$196$		0			0
$197$			14.7312i			1.04956i	0.851239	+	0.524778i	$0.175852\pi$
$197$			14.7312i			1.04956i	−0.851239	+	0.524778i	$0.824148\pi$
$198$		0			0
$199$	5.96032	−	3.44119i	0.422516	−	0.243940i	−0.273637	−	0.961833i	$-0.588227\pi$
$199$	5.96032	−	3.44119i	0.422516	−	0.243940i	0.696153	+	0.717893i	$0.254893\pi$
$200$		0			0
$201$	−4.05527	+	0.585810i	−0.286036	+	0.0413198i
$202$		0			0
$203$	−5.43032	−	0.418716i	−0.381134	−	0.0293881i
$204$		0			0
$205$	5.52746	−	9.57384i	0.386055	−	0.668666i
$206$		0			0
$207$	0.244445	+	0.828428i	0.0169901	+	0.0575797i
$208$		0			0
$209$	−4.94441			−0.342012
$210$		0			0
$211$	−19.0897			−1.31419			−0.657093	−	0.753809i	$-0.728214\pi$
$211$	−19.0897			−1.31419			−0.657093	+	0.753809i	$0.728214\pi$
$212$		0			0
$213$	−25.1965	−	10.0677i	−1.72644	−	0.689830i
$214$		0			0
$215$	3.17921	−	5.50656i	0.216821	−	0.375544i
$216$		0			0
$217$	−6.87788	−	14.3612i	−0.466901	−	0.974898i
$218$		0			0
$219$	0.944103	+	6.53555i	0.0637966	+	0.441632i
$220$		0			0
$221$	37.5257	−	21.6655i	2.52425	−	1.45738i
$222$		0			0
$223$		−	10.9876i		−	0.735785i	−0.929868	−	0.367892i	$-0.880079\pi$
$223$		−	10.9876i		−	0.735785i	0.929868	−	0.367892i	$-0.119921\pi$
$224$		0			0
$225$	−1.16185	+	4.81714i	−0.0774567	+	0.321143i
$226$		0			0
$227$	−9.45418	−	16.3751i	−0.627496	−	1.08686i	−0.988052	−	0.154118i	$-0.950746\pi$
$227$	−9.45418	−	16.3751i	−0.627496	−	1.08686i	0.360556	−	0.932737i	$-0.382587\pi$
$228$		0			0
$229$	14.9744	+	8.64545i	0.989533	+	0.571307i	0.905135	−	0.425125i	$-0.139770\pi$
$229$	14.9744	+	8.64545i	0.989533	+	0.571307i	0.0843986	+	0.996432i	$0.473103\pi$
$230$		0			0
$231$	−7.56065	+	0.503597i	−0.497454	+	0.0331343i
$232$		0			0
$233$	4.45119	+	2.56990i	0.291607	+	0.168360i	0.638666	−	0.769484i	$-0.279486\pi$
$233$	4.45119	+	2.56990i	0.291607	+	0.168360i	−0.347059	+	0.937843i	$0.612820\pi$
$234$		0			0
$235$	0.481223	+	0.833503i	0.0313916	+	0.0543718i
$236$		0			0
$237$	−9.77358	−	12.4111i	−0.634862	−	0.806190i
$238$		0			0
$239$			5.67983i			0.367398i	0.982983	+	0.183699i	$0.0588071\pi$
$239$			5.67983i			0.367398i	−0.982983	+	0.183699i	$0.941193\pi$
$240$		0			0
$241$	20.1604	−	11.6396i	1.29864	−	0.749773i	0.318475	−	0.947931i	$-0.396829\pi$
$241$	20.1604	−	11.6396i	1.29864	−	0.749773i	0.980170	+	0.198158i	$0.0634960\pi$
$242$		0			0
$243$	14.7480	+	5.04952i	0.946082	+	0.323927i
$244$		0			0
$245$	−11.3170	+	14.0663i	−0.723018	+	0.898664i
$246$		0			0
$247$	8.53973	−	14.7913i	0.543370	−	0.941145i
$248$		0			0
$249$	−4.27482	+	10.6986i	−0.270906	+	0.677995i
$250$		0			0
$251$	21.3799			1.34949			0.674744	−	0.738052i	$-0.264254\pi$
$251$	21.3799			1.34949			0.674744	+	0.738052i	$0.264254\pi$
$252$		0			0
$253$	0.476072			0.0299304
$254$		0			0
$255$	12.5743	−	31.4697i	0.787433	−	1.97071i
$256$		0			0
$257$	−7.09305	+	12.2855i	−0.442452	+	0.766349i	−0.997871	−	0.0652214i	$-0.979225\pi$
$257$	−7.09305	+	12.2855i	−0.442452	+	0.766349i	0.555419	+	0.831571i	$0.312558\pi$
$258$		0			0
$259$	−3.83092	−	2.62399i	−0.238042	−	0.163047i
$260$		0			0
$261$	4.25577	−	4.47521i	0.263425	−	0.277009i
$262$		0			0
$263$	−1.90698	+	1.10100i	−0.117590	+	0.0678904i	−0.557641	−	0.830082i	$-0.688293\pi$
$263$	−1.90698	+	1.10100i	−0.117590	+	0.0678904i	0.440052	+	0.897973i	$0.354960\pi$
$264$		0			0
$265$			20.0504i			1.23169i
$266$		0			0
$267$	−15.5535	−	19.7509i	−0.951860	−	1.20873i
$268$		0			0
$269$	−7.33275	−	12.7007i	−0.447086	−	0.774375i	0.551109	−	0.834433i	$-0.314205\pi$
$269$	−7.33275	−	12.7007i	−0.447086	−	0.774375i	−0.998195	+	0.0600579i	$0.980871\pi$
$270$		0			0
$271$	17.6687	+	10.2010i	1.07330	+	0.619669i	0.929081	−	0.369877i	$-0.120600\pi$
$271$	17.6687	+	10.2010i	1.07330	+	0.619669i	0.144217	+	0.989546i	$0.453934\pi$
$272$		0			0
$273$	11.5519	−	23.4875i	0.699150	−	1.42153i
$274$		0			0
$275$	2.36531	+	1.36561i	0.142633	+	0.0823495i
$276$		0			0
$277$	−0.00535275	−	0.00927123i	−0.000321615	−	0.000557054i	0.865865	−	0.500279i	$-0.166769\pi$
$277$	−0.00535275	−	0.00927123i	−0.000321615	−	0.000557054i	−0.866186	+	0.499721i	$0.833436\pi$
$278$		0			0
$279$	17.5519	+	4.23335i	1.05080	+	0.253444i
$280$		0			0
$281$		−	8.11712i		−	0.484227i	−0.970248	−	0.242114i	$-0.922159\pi$
$281$		−	8.11712i		−	0.484227i	0.970248	−	0.242114i	$-0.0778406\pi$
$282$		0			0
$283$	−3.34466	+	1.93104i	−0.198819	+	0.114788i	−0.596105	−	0.802907i	$-0.703286\pi$
$283$	−3.34466	+	1.93104i	−0.198819	+	0.114788i	0.397285	+	0.917695i	$0.369952\pi$
$284$		0			0
$285$	−1.90979	−	13.2205i	−0.113126	−	0.783115i
$286$		0			0
$287$	−0.871852	+	11.3070i	−0.0514638	+	0.667434i
$288$		0			0
$289$	−20.2757	+	35.1185i	−1.19269	+	2.06580i
$290$		0			0
$291$	7.13713	+	2.85177i	0.418386	+	0.167174i
$292$		0			0
$293$	5.75351			0.336123			0.168062	−	0.985776i	$-0.446249\pi$
$293$	5.75351			0.336123			0.168062	+	0.985776i	$0.446249\pi$
$294$		0			0
$295$	25.2550			1.47041
$296$		0			0
$297$	4.96987	−	7.00873i	0.288381	−	0.406688i
$298$		0			0
$299$	−0.822247	+	1.42417i	−0.0475518	+	0.0823621i
$300$		0			0
$301$	−0.501460	+	6.50344i	−0.0289037	+	0.374852i
$302$		0			0
$303$	−6.98141	+	1.00851i	−0.401071	+	0.0579374i
$304$		0			0
$305$	2.29487	−	1.32494i	0.131404	−	0.0758660i
$306$		0			0
$307$		−	23.9041i		−	1.36428i	−0.731221	−	0.682140i	$-0.761049\pi$
$307$		−	23.9041i		−	1.36428i	0.731221	−	0.682140i	$-0.238951\pi$
$308$		0			0
$309$	−11.4758	+	9.03703i	−0.652836	+	0.514099i
$310$		0			0
$311$	10.5789	+	18.3232i	0.599874	+	1.03901i	0.992839	+	0.119459i	$0.0381159\pi$
$311$	10.5789	+	18.3232i	0.599874	+	1.03901i	−0.392965	+	0.919553i	$0.628551\pi$
$312$		0			0
$313$	−18.2861	−	10.5575i	−1.03359	−	0.596746i	−0.115582	−	0.993298i	$-0.536873\pi$
$313$	−18.2861	−	10.5575i	−1.03359	−	0.596746i	−0.918012	+	0.396552i	$0.870207\pi$
$314$		0			0
$315$	−4.26685	−	20.0214i	−0.240410	−	1.12808i
$316$		0			0
$317$	−13.8698	−	8.00775i	−0.779007	−	0.449760i	0.0570712	−	0.998370i	$-0.481824\pi$
$317$	−13.8698	−	8.00775i	−0.779007	−	0.449760i	−0.836078	+	0.548610i	$0.815157\pi$
$318$		0			0
$319$	−1.70194	−	2.94785i	−0.0952904	−	0.165048i
$320$		0			0
$321$	−19.8507	+	15.6321i	−1.10796	+	0.872498i
$322$		0			0
$323$			22.6846i			1.26221i
$324$		0			0
$325$	−8.17048	+	4.71723i	−0.453217	+	0.261665i
$326$		0			0
$327$	−29.6564	+	4.28406i	−1.64000	+	0.236909i
$328$		0			0
$329$	−0.814561	−	0.557933i	−0.0449082	−	0.0307599i
$330$		0			0
$331$	−9.48985	+	16.4369i	−0.521610	+	0.903454i	0.478074	+	0.878319i	$0.341335\pi$
$331$	−9.48985	+	16.4369i	−0.521610	+	0.903454i	−0.999684	+	0.0251350i	$0.991998\pi$
$332$		0			0
$333$	5.04989	−	1.49007i	0.276732	−	0.0816555i
$334$		0			0
$335$	−6.10115			−0.333341
$336$		0			0
$337$	0.151144			0.00823337			0.00411668	−	0.999992i	$-0.498690\pi$
$337$	0.151144			0.00823337			0.00411668	+	0.999992i	$0.498690\pi$
$338$		0			0
$339$	6.43363	+	2.57068i	0.349427	+	0.139620i
$340$		0			0
$341$	4.97579	−	8.61831i	0.269454	−	0.466708i
$342$		0			0
$343$	4.23778	−	18.0289i	0.228819	−	0.973469i
$344$		0			0
$345$	0.183884	+	1.27293i	0.00989996	+	0.0685325i
$346$		0			0
$347$	11.5977	−	6.69596i	0.622599	−	0.359458i	−0.155281	−	0.987870i	$-0.549628\pi$
$347$	11.5977	−	6.69596i	0.622599	−	0.359458i	0.777880	+	0.628412i	$0.216295\pi$
$348$		0			0
$349$			13.4025i			0.717421i	0.933449	+	0.358710i	$0.116783\pi$
$349$			13.4025i			0.717421i	−0.933449	+	0.358710i	$0.883217\pi$
$350$		0			0
$351$	12.3830	+	26.9725i	0.660955	+	1.43969i
$352$		0			0
$353$	10.7469	+	18.6141i	0.571998	+	0.990729i	0.996361	+	0.0852371i	$0.0271648\pi$
$353$	10.7469	+	18.6141i	0.571998	+	0.990729i	−0.424363	+	0.905492i	$0.639502\pi$
$354$		0			0
$355$	−34.9899	−	20.2014i	−1.85707	−	1.07218i
$356$		0			0
$357$	2.31047	+	34.6878i	0.122283	+	1.83587i
$358$		0			0
$359$	24.4173	+	14.0974i	1.28870	+	0.744030i	0.978422	−	0.206616i	$-0.0662452\pi$
$359$	24.4173	+	14.0974i	1.28870	+	0.744030i	0.310276	+	0.950647i	$0.399579\pi$
$360$		0			0
$361$	−5.02928	−	8.71097i	−0.264699	−	0.458472i
$362$		0			0
$363$	8.85759	+	11.2479i	0.464903	+	0.590364i
$364$		0			0
$365$			9.83274i			0.514669i
$366$		0			0
$367$	−19.6810	+	11.3628i	−1.02734	+	0.593135i	−0.916221	−	0.400673i	$-0.868776\pi$
$367$	−19.6810	+	11.3628i	−1.02734	+	0.593135i	−0.111118	+	0.993807i	$0.535443\pi$
$368$		0			0
$369$	−9.31831	−	8.86138i	−0.485092	−	0.461305i
$370$		0			0
$371$	−8.88441	−	18.5508i	−0.461255	−	0.963110i
$372$		0			0
$373$	6.95699	−	12.0499i	0.360219	−	0.623918i	−0.627778	−	0.778393i	$-0.716035\pi$
$373$	6.95699	−	12.0499i	0.360219	−	0.623918i	0.987997	+	0.154475i	$0.0493686\pi$
$374$		0			0
$375$	5.54974	−	13.8893i	0.286588	−	0.717242i
$376$		0			0
$377$	11.7580			0.605569
$378$		0			0
$379$	20.8656			1.07179			0.535897	−	0.844283i	$-0.319973\pi$
$379$	20.8656			1.07179			0.535897	+	0.844283i	$0.319973\pi$
$380$		0			0
$381$	−10.6992	+	26.7770i	−0.548139	+	1.37183i
$382$		0			0
$383$	−1.23577	+	2.14042i	−0.0631451	+	0.109371i	−0.895870	−	0.444317i	$-0.853446\pi$
$383$	−1.23577	+	2.14042i	−0.0631451	+	0.109371i	0.832725	+	0.553687i	$0.186780\pi$
$384$		0			0
$385$	−11.2497	−	0.867429i	−0.573337	−	0.0442083i
$386$		0			0
$387$	−5.35959	−	5.09677i	−0.272443	−	0.259084i
$388$		0			0
$389$	−20.4245	+	11.7921i	−1.03556	+	0.597882i	−0.918573	−	0.395251i	$-0.870658\pi$
$389$	−20.4245	+	11.7921i	−1.03556	+	0.597882i	−0.116989	+	0.993133i	$0.537324\pi$
$390$		0			0
$391$		−	2.18419i		−	0.110459i
$392$		0			0
$393$	−17.7829	−	22.5819i	−0.897027	−	1.13910i
$394$		0			0
$395$	−11.7615	−	20.3716i	−0.591788	−	1.02501i
$396$		0			0
$397$	−1.79160	−	1.03438i	−0.0899181	−	0.0519142i	0.454367	−	0.890815i	$-0.349866\pi$
$397$	−1.79160	−	1.03438i	−0.0899181	−	0.0519142i	−0.544285	+	0.838901i	$0.683199\pi$
$398$		0			0
$399$	7.62501	+	11.3855i	0.381728	+	0.569988i
$400$		0			0
$401$	−6.46052	−	3.72998i	−0.322623	−	0.186266i	0.329938	−	0.944003i	$-0.392972\pi$
$401$	−6.46052	−	3.72998i	−0.322623	−	0.186266i	−0.652561	+	0.757736i	$0.726305\pi$
$402$		0			0
$403$	17.1879	+	29.7702i	0.856188	+	1.48296i
$404$		0			0
$405$	20.6598	+	10.5814i	1.02659	+	0.525796i
$406$		0			0
$407$		−	2.90201i		−	0.143847i
$408$		0			0
$409$	29.2897	−	16.9104i	1.44828	−	0.836166i	0.449902	−	0.893078i	$-0.351459\pi$
$409$	29.2897	−	16.9104i	1.44828	−	0.836166i	0.998379	+	0.0569122i	$0.0181255\pi$
$410$		0			0
$411$	2.46394	+	17.0566i	0.121537	+	0.841342i
$412$		0			0
$413$	−23.3662	+	11.1906i	−1.14978	+	0.550654i
$414$		0			0
$415$	−8.57764	+	14.8569i	−0.421060	+	0.729297i
$416$		0			0
$417$	5.01746	+	2.00482i	0.245706	+	0.0981765i
$418$		0			0
$419$	−15.2980			−0.747358			−0.373679	−	0.927558i	$-0.621904\pi$
$419$	−15.2980			−0.747358			−0.373679	+	0.927558i	$0.621904\pi$
$420$		0			0
$421$	11.8931			0.579633			0.289816	−	0.957082i	$-0.406406\pi$
$421$	11.8931			0.579633			0.289816	+	0.957082i	$0.406406\pi$
$422$		0			0
$423$	1.07375	−	0.316831i	0.0522073	−	0.0154048i
$424$		0			0
$425$	6.26534	−	10.8519i	0.303913	−	0.526393i
$426$		0			0
$427$	−1.53615	+	2.24271i	−0.0743393	+	0.108533i
$428$		0			0
$429$	16.1904	−	2.33881i	0.781679	−	0.112919i
$430$		0			0
$431$	−14.9148	+	8.61109i	−0.718423	+	0.414782i	−0.814172	−	0.580624i	$-0.802809\pi$
$431$	−14.9148	+	8.61109i	−0.718423	+	0.414782i	0.0957491	+	0.995405i	$0.469475\pi$
$432$		0			0
$433$			1.55093i			0.0745329i	0.999305	+	0.0372664i	$0.0118650\pi$
$433$			1.55093i			0.0745329i	−0.999305	+	0.0372664i	$0.988135\pi$
$434$		0			0
$435$	7.22466	−	5.68931i	0.346396	−	0.272782i
$436$		0			0
$437$	−0.430463	−	0.745583i	−0.0205918	−	0.0356661i
$438$		0			0
$439$	16.8278	+	9.71551i	0.803145	+	0.463696i	0.844570	−	0.535446i	$-0.179856\pi$
$439$	16.8278	+	9.71551i	0.803145	+	0.463696i	−0.0414249	+	0.999142i	$0.513190\pi$
$440$		0			0
$441$	12.8193	+	16.6333i	0.610441	+	0.792062i
$442$		0			0
$443$	−3.08964	−	1.78380i	−0.146793	−	0.0847510i	0.424805	−	0.905285i	$-0.360343\pi$
$443$	−3.08964	−	1.78380i	−0.146793	−	0.0847510i	−0.571598	+	0.820534i	$0.693676\pi$
$444$		0			0
$445$	−18.7171	−	32.4190i	−0.887277	−	1.53681i
$446$		0			0
$447$	1.55100	−	1.22139i	0.0733597	−	0.0577697i
$448$		0			0
$449$		−	29.5796i		−	1.39595i	−0.716124	−	0.697973i	$-0.754085\pi$
$449$		−	29.5796i		−	1.39595i	0.716124	−	0.697973i	$-0.245915\pi$
$450$		0			0
$451$	−6.13803	+	3.54379i	−0.289028	+	0.166871i
$452$		0			0
$453$	21.8952	−	3.16290i	1.02873	−	0.148606i
$454$		0			0
$455$	22.0248	−	32.1554i	1.03254	−	1.50747i
$456$		0			0
$457$	11.2312	−	19.4530i	0.525374	−	0.909975i	−0.474189	−	0.880423i	$-0.657259\pi$
$457$	11.2312	−	19.4530i	0.525374	−	0.909975i	0.999563	−	0.0295520i	$-0.00940807\pi$
$458$		0			0
$459$	−32.1556	−	22.8014i	−1.50089	−	1.06428i
$460$		0			0
$461$	−9.31904			−0.434031			−0.217015	−	0.976168i	$-0.569632\pi$
$461$	−9.31904			−0.434031			−0.217015	+	0.976168i	$0.569632\pi$
$462$		0			0
$463$	−16.6243			−0.772597			−0.386298	−	0.922374i	$-0.626246\pi$
$463$	−16.6243			−0.772597			−0.386298	+	0.922374i	$0.626246\pi$
$464$		0			0
$465$	24.9658	+	9.97556i	1.15776	+	0.462605i
$466$		0			0
$467$	−6.06560	+	10.5059i	−0.280683	+	0.486156i	−0.971553	−	0.236822i	$-0.923894\pi$
$467$	−6.06560	+	10.5059i	−0.280683	+	0.486156i	0.690871	+	0.722979i	$0.257227\pi$
$468$		0			0
$469$	5.64484	−	2.70344i	0.260654	−	0.124833i
$470$		0			0
$471$	−2.23624	−	15.4804i	−0.103040	−	0.713298i
$472$		0			0
$473$	−3.53039	+	2.03827i	−0.162328	+	0.0937198i
$474$		0			0
$475$		−	4.93913i		−	0.226623i
$476$		0			0
$477$	22.6724	+	5.46838i	1.03810	+	0.250380i
$478$		0			0
$479$	−13.2594	−	22.9660i	−0.605839	−	1.04934i	−0.991918	−	0.126878i	$-0.959504\pi$
$479$	−13.2594	−	22.9660i	−0.605839	−	1.04934i	0.386080	−	0.922465i	$-0.373829\pi$
$480$		0			0
$481$	8.68140	+	5.01221i	0.395838	+	0.228537i
$482$		0			0
$483$	−0.734173	−	1.09625i	−0.0334060	−	0.0498811i
$484$		0			0
$485$	9.91120	+	5.72223i	0.450044	+	0.259833i
$486$		0			0
$487$	17.5986	+	30.4817i	0.797469	+	1.38126i	0.921260	+	0.388948i	$0.127161\pi$
$487$	17.5986	+	30.4817i	0.797469	+	1.38126i	−0.123791	+	0.992308i	$0.539505\pi$
$488$		0			0
$489$	0.106896	+	0.135744i	0.00483401	+	0.00613854i
$490$		0			0
$491$		−	32.5795i		−	1.47029i	−0.677910	−	0.735145i	$-0.737114\pi$
$491$		−	32.5795i		−	1.47029i	0.677910	−	0.735145i	$-0.262886\pi$
$492$		0			0
$493$	−13.5245	+	7.80840i	−0.609115	+	0.351673i
$494$		0			0
$495$	8.81643	−	9.27104i	0.396269	−	0.416702i
$496$		0			0
$497$	41.3243	+	3.18639i	1.85365	+	0.142929i
$498$		0			0
$499$	−2.46895	+	4.27635i	−0.110525	+	0.191436i	−0.915982	−	0.401219i	$-0.868587\pi$
$499$	−2.46895	+	4.27635i	−0.110525	+	0.191436i	0.805457	+	0.592655i	$0.201920\pi$
$500$		0			0
$501$	1.98336	−	4.96374i	0.0886099	−	0.221764i
$502$		0			0
$503$	−16.7907			−0.748661			−0.374331	−	0.927295i	$-0.622127\pi$
$503$	−16.7907			−0.748661			−0.374331	+	0.927295i	$0.622127\pi$
$504$		0			0
$505$	−10.5035			−0.467401
$506$		0			0
$507$	−12.6119	+	31.5639i	−0.560116	+	1.40180i
$508$		0			0
$509$	−0.631490	+	1.09377i	−0.0279903	+	0.0484806i	−0.879681	−	0.475564i	$-0.842244\pi$
$509$	−0.631490	+	1.09377i	−0.0279903	+	0.0484806i	0.851691	+	0.524044i	$0.175577\pi$
$510$		0			0
$511$	−4.35693	−	9.09735i	−0.192739	−	0.402443i
$512$		0			0
$513$	−15.4702	−	1.44611i	−0.683027	−	0.0638475i
$514$		0			0
$515$	−18.8364	+	10.8752i	−0.830029	+	0.479218i
$516$		0			0
$517$		−	0.617048i		−	0.0271378i
$518$		0			0
$519$	7.99485	+	10.1524i	0.350935	+	0.445640i
$520$		0			0
$521$	−14.9945	−	25.9713i	−0.656922	−	1.13782i	−0.981408	−	0.191932i	$-0.938525\pi$
$521$	−14.9945	−	25.9713i	−0.656922	−	1.13782i	0.324486	−	0.945891i	$-0.394809\pi$
$522$		0			0
$523$	30.7587	+	17.7586i	1.34499	+	0.776528i	0.987534	−	0.157404i	$-0.0503125\pi$
$523$	30.7587	+	17.7586i	1.34499	+	0.776528i	0.357451	+	0.933932i	$0.383646\pi$
$524$		0			0
$525$	−0.503059	−	7.55257i	−0.0219553	−	0.329621i
$526$		0			0
$527$	−39.5403	−	22.8286i	−1.72240	−	0.994429i
$528$		0			0
$529$	−11.4586	−	19.8468i	−0.498198	−	0.862904i
$530$		0			0
$531$	6.88785	−	28.5577i	0.298907	−	1.23930i
$532$		0			0
$533$		−	24.4826i		−	1.06046i
$534$		0			0
$535$	−32.5828	+	18.8117i	−1.40868	+	0.813300i
$536$		0			0
$537$	−0.747645	−	5.17557i	−0.0322633	−	0.223343i
$538$		0			0
$539$	10.7927	−	4.18223i	0.464874	−	0.180141i
$540$		0			0
$541$	11.9158	−	20.6388i	0.512300	−	0.887330i	−0.487598	−	0.873068i	$-0.662127\pi$
$541$	11.9158	−	20.6388i	0.512300	−	0.887330i	0.999898	−	0.0142616i	$-0.00453975\pi$
$542$		0			0
$543$	−1.22649	−	0.490069i	−0.0526339	−	0.0210309i
$544$		0			0
$545$	−44.6181			−1.91123
$546$		0			0
$547$	21.1040			0.902342			0.451171	−	0.892437i	$-0.351006\pi$
$547$	21.1040			0.902342			0.451171	+	0.892437i	$0.351006\pi$
$548$		0			0
$549$	−0.872324	−	2.95632i	−0.0372299	−	0.126173i
$550$		0			0
$551$	−3.07778	+	5.33087i	−0.131118	+	0.227103i
$552$		0			0
$553$	19.9086	+	13.6364i	0.846601	+	0.579879i
$554$		0			0
$555$	7.75948	−	1.12091i	0.329372	−	0.0475799i
$556$		0			0
$557$	19.3020	−	11.1440i	0.817852	−	0.472187i	−0.0318235	−	0.999494i	$-0.510131\pi$
$557$	19.3020	−	11.1440i	0.817852	−	0.472187i	0.849675	+	0.527307i	$0.176798\pi$
$558$		0			0
$559$		−	14.0816i		−	0.595588i
$560$		0			0
$561$	−17.0696	+	13.4421i	−0.720680	+	0.567525i
$562$		0			0
$563$	20.2197	+	35.0215i	0.852157	+	1.47598i	0.879258	+	0.476347i	$0.158039\pi$
$563$	20.2197	+	35.0215i	0.852157	+	1.47598i	−0.0271005	+	0.999633i	$0.508627\pi$
$564$		0			0
$565$	8.93427	+	5.15820i	0.375867	+	0.217007i
$566$		0			0
$567$	−23.8033	−	0.635629i	−0.999644	−	0.0266939i
$568$		0			0
$569$	21.7717	+	12.5699i	0.912717	+	0.526957i	0.881304	−	0.472549i	$-0.156666\pi$
$569$	21.7717	+	12.5699i	0.912717	+	0.526957i	0.0314127	+	0.999506i	$0.489999\pi$
$570$		0			0
$571$	−0.655344	−	1.13509i	−0.0274253	−	0.0475020i	0.851987	−	0.523563i	$-0.175398\pi$
$571$	−0.655344	−	1.13509i	−0.0274253	−	0.0475020i	−0.879412	+	0.476061i	$0.842064\pi$
$572$		0			0
$573$	1.66311	−	1.30967i	0.0694773	−	0.0547123i
$574$		0			0
$575$			0.475563i			0.0198324i
$576$		0			0
$577$	5.21739	−	3.01226i	0.217203	−	0.125402i	−0.387452	−	0.921890i	$-0.626645\pi$
$577$	5.21739	−	3.01226i	0.217203	−	0.125402i	0.604654	+	0.796488i	$0.293311\pi$
$578$		0			0
$579$	40.3148	−	5.82374i	1.67543	−	0.242026i
$580$		0			0
$581$	1.35296	−	17.5465i	0.0561303	−	0.727953i
$582$		0			0
$583$	6.42740	−	11.1326i	0.266196	−	0.461065i
$584$		0			0
$585$	12.5071	+	42.3869i	0.517106	+	1.75248i
$586$		0			0
$587$	39.5131			1.63088			0.815439	−	0.578843i	$-0.196496\pi$
$587$	39.5131			1.63088			0.815439	+	0.578843i	$0.196496\pi$
$588$		0			0
$589$	−17.9964			−0.741527
$590$		0			0
$591$	23.6938	+	9.46731i	0.974633	+	0.389433i
$592$		0			0
$593$	−6.75855	+	11.7062i	−0.277540	+	0.480714i	−0.970773	−	0.240000i	$-0.922853\pi$
$593$	−6.75855	+	11.7062i	−0.277540	+	0.480714i	0.693232	+	0.720714i	$0.256186\pi$
$594$		0			0
$595$	−3.97971	+	51.6129i	−0.163152	+	2.11592i
$596$		0			0
$597$	−1.70432	−	11.7982i	−0.0697533	−	0.482867i
$598$		0			0
$599$	−5.68762	+	3.28375i	−0.232390	+	0.134170i	−0.611674	−	0.791110i	$-0.709504\pi$
$599$	−5.68762	+	3.28375i	−0.232390	+	0.134170i	0.379284	+	0.925280i	$0.376170\pi$
$600$		0			0
$601$		−	10.0499i		−	0.409946i	−0.978768	−	0.204973i	$-0.934289\pi$
$601$		−	10.0499i		−	0.409946i	0.978768	−	0.204973i	$-0.0657106\pi$
$602$		0			0
$603$	−1.66398	+	6.89900i	−0.0677623	+	0.280949i
$604$		0			0
$605$	10.6592	+	18.4623i	0.433360	+	0.750601i
$606$		0			0
$607$	−0.673920	−	0.389088i	−0.0273536	−	0.0157926i	0.486261	−	0.873814i	$-0.338360\pi$
$607$	−0.673920	−	0.389088i	−0.0273536	−	0.0157926i	−0.513614	+	0.858021i	$0.671694\pi$
$608$		0			0
$609$	−4.16337	+	8.46508i	−0.168708	+	0.343022i
$610$		0			0
$611$	1.84591	+	1.06573i	0.0746774	+	0.0431150i
$612$		0			0
$613$	−19.3349	−	33.4890i	−0.780928	−	1.35261i	−0.931402	−	0.363993i	$-0.881413\pi$
$613$	−19.3349	−	33.4890i	−0.780928	−	1.35261i	0.150474	−	0.988614i	$-0.451920\pi$
$614$		0			0
$615$	−11.8463	−	15.0432i	−0.477689	−	0.606602i
$616$		0			0
$617$		−	7.83523i		−	0.315434i	−0.987484	−	0.157717i	$-0.949587\pi$
$617$		−	7.83523i		−	0.315434i	0.987484	−	0.157717i	$-0.0504134\pi$
$618$		0			0
$619$	17.9235	−	10.3481i	0.720407	−	0.415927i	−0.0944957	−	0.995525i	$-0.530124\pi$
$619$	17.9235	−	10.3481i	0.720407	−	0.415927i	0.814902	+	0.579598i	$0.196791\pi$
$620$		0			0
$621$	1.48955	+	0.139239i	0.0597735	+	0.00558747i
$622$		0			0
$623$	31.6823	+	21.7008i	1.26932	+	0.869422i
$624$		0			0
$625$	15.2652	−	26.4402i	0.610610	−	1.05761i
$626$		0			0
$627$	−3.17762	+	7.95263i	−0.126902	+	0.317597i
$628$		0			0
$629$	−13.3142			−0.530874
$630$		0			0
$631$	−7.21022			−0.287034			−0.143517	−	0.989648i	$-0.545841\pi$
$631$	−7.21022			−0.287034			−0.143517	+	0.989648i	$0.545841\pi$
$632$		0			0
$633$	−12.2683	+	30.7040i	−0.487623	+	1.22037i
$634$		0			0
$635$	−21.4686	+	37.1847i	−0.851955	+	1.47563i
$636$		0			0
$637$	−6.12940	+	39.5098i	−0.242855	+	1.56543i
$638$		0			0
$639$	−32.3860	+	34.0560i	−1.28117	+	1.34723i
$640$		0			0
$641$	−31.9156	+	18.4265i	−1.26059	+	0.727802i	−0.973189	−	0.230009i	$-0.926124\pi$
$641$	−31.9156	+	18.4265i	−1.26059	+	0.727802i	−0.287401	+	0.957810i	$0.592791\pi$
$642$		0			0
$643$		−	10.5183i		−	0.414801i	−0.978256	−	0.207400i	$-0.933500\pi$
$643$		−	10.5183i		−	0.414801i	0.978256	−	0.207400i	$-0.0665003\pi$
$644$		0			0
$645$	−6.81361	−	8.65237i	−0.268286	−	0.340687i
$646$		0			0
$647$	−10.2057	−	17.6768i	−0.401228	−	0.694948i	0.592646	−	0.805463i	$-0.298083\pi$
$647$	−10.2057	−	17.6768i	−0.401228	−	0.694948i	−0.993874	+	0.110515i	$0.964750\pi$
$648$		0			0
$649$	−14.0224	−	8.09581i	−0.550426	−	0.317789i
$650$		0			0
$651$	−27.5188	+	1.83296i	−1.07855	+	0.0718395i
$652$		0			0
$653$	28.7382	+	16.5920i	1.12461	+	0.649295i	0.942574	−	0.333996i	$-0.108397\pi$
$653$	28.7382	+	16.5920i	1.12461	+	0.649295i	0.182038	+	0.983291i	$0.441731\pi$
$654$		0			0
$655$	−21.3999	−	37.0658i	−0.836165	−	1.44828i
$656$		0			0
$657$	11.1186	+	2.68170i	0.433777	+	0.104623i
$658$		0			0
$659$			7.18286i			0.279804i	0.990165	+	0.139902i	$0.0446788\pi$
$659$			7.18286i			0.279804i	−0.990165	+	0.139902i	$0.955321\pi$
$660$		0			0
$661$	−18.2360	+	10.5285i	−0.709297	+	0.409513i	−0.810801	−	0.585323i	$-0.800968\pi$
$661$	−18.2360	+	10.5285i	−0.709297	+	0.409513i	0.101504	+	0.994835i	$0.467635\pi$
$662$		0			0
$663$	−10.7303	−	74.2804i	−0.416730	−	2.88481i
$664$		0			0
$665$	8.81344	+	18.4026i	0.341771	+	0.713624i
$666$		0			0
$667$	0.296344	−	0.513282i	0.0114745	−	0.0198744i
$668$		0			0
$669$	−17.6726	−	7.06140i	−0.683261	−	0.273010i
$670$		0			0
$671$	−1.69891			−0.0655856
$672$		0			0
$673$	−21.5441			−0.830464			−0.415232	−	0.909715i	$-0.636300\pi$
$673$	−21.5441			−0.830464			−0.415232	+	0.909715i	$0.636300\pi$
$674$		0			0
$675$	7.00124	+	4.96456i	0.269478	+	0.191086i
$676$		0			0
$677$	2.69876	−	4.67439i	0.103722	−	0.179651i	−0.809493	−	0.587129i	$-0.800258\pi$
$677$	2.69876	−	4.67439i	0.103722	−	0.179651i	0.913215	+	0.407477i	$0.133592\pi$
$678$		0			0
$679$	−11.7055	−	0.902573i	−0.449215	−	0.0346376i
$680$		0			0
$681$	−32.4138	+	4.68238i	−1.24210	+	0.179429i
$682$		0			0
$683$	−28.9007	+	16.6858i	−1.10585	+	0.638465i	−0.937752	−	0.347305i	$-0.887097\pi$
$683$	−28.9007	+	16.6858i	−1.10585	+	0.638465i	−0.168101	+	0.985770i	$0.553764\pi$
$684$		0			0
$685$			25.6617i			0.980483i
$686$		0			0
$687$	23.5290	−	18.5287i	0.897686	−	0.706914i
$688$		0			0
$689$	22.2022	+	38.4553i	0.845835	+	1.46503i
$690$		0			0
$691$	−34.4696	−	19.9010i	−1.31128	−	0.757070i	−0.328975	−	0.944339i	$-0.606703\pi$
$691$	−34.4696	−	19.9010i	−1.31128	−	0.757070i	−0.982309	+	0.187268i	$0.940037\pi$
$692$		0			0
$693$	−4.04901	+	12.4843i	−0.153809	+	0.474238i
$694$		0			0
$695$	6.96765	+	4.02278i	0.264298	+	0.152593i
$696$		0			0
$697$	16.2587	+	28.1609i	0.615842	+	1.06667i
$698$		0			0
$699$	6.99409	−	5.50774i	0.264541	−	0.208322i
$700$		0			0
$701$			10.6583i			0.402559i	0.979534	+	0.201280i	$0.0645100\pi$
$701$			10.6583i			0.402559i	−0.979534	+	0.201280i	$0.935490\pi$
$702$		0			0
$703$	−4.54488	+	2.62399i	−0.171414	+	0.0989657i
$704$		0			0
$705$	1.64988	−	0.238336i	0.0621381	−	0.00897626i
$706$		0			0
$707$	9.71797	−	4.65416i	0.365482	−	0.175038i
$708$		0			0
$709$	−17.5727	+	30.4367i	−0.659955	+	1.14308i	0.320672	+	0.947190i	$0.396091\pi$
$709$	−17.5727	+	30.4367i	−0.659955	+	1.14308i	−0.980627	+	0.195885i	$0.937242\pi$
$710$		0			0
$711$	−26.2434	+	7.74364i	−0.984203	+	0.290409i
$712$		0			0
$713$	1.73278			0.0648930
$714$		0			0
$715$	24.3584			0.910954
$716$		0			0
$717$	9.13549	+	3.65026i	0.341171	+	0.136321i
$718$		0			0
$719$	15.6309	−	27.0734i	0.582932	−	1.00967i	−0.412197	−	0.911095i	$-0.635239\pi$
$719$	15.6309	−	27.0734i	0.582932	−	1.00967i	0.995130	−	0.0985739i	$-0.0314281\pi$
$720$		0			0
$721$	12.6087	−	18.4083i	0.469574	−	0.685560i
$722$		0			0
$723$	−5.76476	−	39.9066i	−0.214394	−	1.48414i
$724$		0			0
$725$	2.94470	−	1.70012i	0.109363	−	0.0631410i
$726$		0			0
$727$			39.7975i			1.47601i	0.674797	+	0.738003i	$0.264231\pi$
$727$			39.7975i			1.47601i	−0.674797	+	0.738003i	$0.735769\pi$
$728$		0			0
$729$	17.5998	−	20.4756i	0.651843	−	0.758354i
$730$		0			0
$731$	9.35146	+	16.1972i	0.345876	+	0.599075i
$732$		0			0
$733$	10.5878	+	6.11289i	0.391071	+	0.225785i	0.682624	−	0.730770i	$-0.260839\pi$
$733$	10.5878	+	6.11289i	0.391071	+	0.225785i	−0.291553	+	0.956555i	$0.594172\pi$
$734$		0			0
$735$	15.3513	+	27.2424i	0.566240	+	1.00485i
$736$		0			0
$737$	3.38754	+	1.95580i	0.124782	+	0.0720428i
$738$		0			0
$739$	−14.5001	−	25.1148i	−0.533393	−	0.923864i	−0.999239	−	0.0389981i	$-0.987583\pi$
$739$	−14.5001	−	25.1148i	−0.533393	−	0.923864i	0.465846	−	0.884866i	$-0.345750\pi$
$740$		0			0
$741$	−18.3021	−	23.2413i	−0.672346	−	0.853789i
$742$		0			0
$743$			33.4864i			1.22850i	0.789113	+	0.614248i	$0.210541\pi$
$743$			33.4864i			1.22850i	−0.789113	+	0.614248i	$0.789459\pi$
$744$		0			0
$745$	2.54580	−	1.46982i	0.0932710	−	0.0538501i
$746$		0			0
$747$	14.4604	+	13.7513i	0.529078	+	0.503134i
$748$		0			0
$749$	21.8104	−	31.8423i	0.796934	−	1.16349i
$750$		0			0
$751$	−5.86021	+	10.1502i	−0.213842	+	0.370385i	−0.952914	−	0.303242i	$-0.901931\pi$
$751$	−5.86021	+	10.1502i	−0.213842	+	0.370385i	0.739072	+	0.673627i	$0.235264\pi$
$752$		0			0
$753$	13.7402	−	34.3876i	0.500722	−	1.25315i
$754$		0			0
$755$	32.9413			1.19886
$756$		0			0
$757$	11.2688			0.409571			0.204785	−	0.978807i	$-0.434350\pi$
$757$	11.2688			0.409571			0.204785	+	0.978807i	$0.434350\pi$
$758$		0			0
$759$	0.305957	−	0.765717i	0.0111055	−	0.0277938i
$760$		0			0
$761$	−10.0633	+	17.4301i	−0.364793	+	0.631841i	−0.988743	−	0.149624i	$-0.952194\pi$
$761$	−10.0633	+	17.4301i	−0.364793	+	0.631841i	0.623950	+	0.781465i	$0.285527\pi$
$762$		0			0
$763$	41.2811	−	19.7705i	1.49448	−	0.715739i
$764$		0			0
$765$	−42.5349	−	40.4492i	−1.53785	−	1.46244i
$766$		0			0
$767$	48.4374	−	27.9654i	1.74897	−	1.00977i
$768$		0			0
$769$			7.95157i			0.286741i	0.989669	+	0.143370i	$0.0457940\pi$
$769$			7.95157i			0.286741i	−0.989669	+	0.143370i	$0.954206\pi$
$770$		0			0
$771$	15.2016	+	19.3040i	0.547473	+	0.695218i
$772$		0			0
$773$	−15.8927	−	27.5269i	−0.571620	−	0.990075i	−0.996400	−	0.0847784i	$-0.972982\pi$
$773$	−15.8927	−	27.5269i	−0.571620	−	0.990075i	0.424780	−	0.905297i	$-0.360352\pi$
$774$		0			0
$775$	8.60911	+	4.97047i	0.309248	+	0.178545i
$776$		0			0
$777$	−6.68246	+	4.47533i	−0.239732	+	0.160552i
$778$		0			0
$779$	11.1000	+	6.40857i	0.397698	+	0.229611i
$780$		0			0
$781$	12.9516	+	22.4329i	0.463446	+	0.802712i
$782$		0			0
$783$	−4.46291	−	9.72110i	−0.159492	−	0.347404i
$784$		0			0
$785$		−	23.2902i		−	0.831264i
$786$		0			0
$787$	26.3569	−	15.2172i	0.939523	−	0.542434i	0.0497122	−	0.998764i	$-0.484170\pi$
$787$	26.3569	−	15.2172i	0.939523	−	0.542434i	0.889811	+	0.456330i	$0.150836\pi$
$788$		0			0
$789$	0.545292	+	3.77478i	0.0194129	+	0.134386i
$790$		0			0
$791$	−10.5517	−	0.813608i	−0.375175	−	0.0289286i
$792$		0			0
$793$	2.93427	−	5.08230i	0.104199	−	0.180478i
$794$		0			0
$795$	32.2492	+	12.8858i	1.14376	+	0.457012i
$796$		0			0
$797$	−40.0924			−1.42015			−0.710074	−	0.704127i	$-0.751338\pi$
$797$	−40.0924			−1.42015			−0.710074	+	0.704127i	$0.751338\pi$
$798$		0			0
$799$	−2.83098			−0.100153
$800$		0			0
$801$	−41.7632	+	12.3231i	−1.47563	+	0.435415i
$802$		0			0
$803$	3.15201	−	5.45944i	0.111232	−	0.192659i
$804$		0			0
$805$	−0.848601	−	1.77190i	−0.0299093	−	0.0624511i
$806$		0			0
$807$	−25.1404	+	3.63170i	−0.884985	+	0.127842i
$808$		0			0
$809$	−34.0306	+	19.6476i	−1.19645	+	0.690773i	−0.959763	−	0.280812i	$-0.909396\pi$
$809$	−34.0306	+	19.6476i	−1.19645	+	0.690773i	−0.236691	+	0.971585i	$0.576063\pi$
$810$		0			0
$811$		−	23.6789i		−	0.831480i	−0.909484	−	0.415740i	$-0.863523\pi$
$811$		−	23.6789i		−	0.831480i	0.909484	−	0.415740i	$-0.136477\pi$
$812$		0			0
$813$	27.7626	−	21.8626i	0.973676	−	0.766755i
$814$		0			0
$815$	0.128639	+	0.222809i	0.00450602	+	0.00780466i
$816$		0			0
$817$	6.38434	+	3.68600i	0.223360	+	0.128957i
$818$		0			0
$819$	−30.3535	−	33.6748i	−1.06064	−	1.17669i
$820$		0			0
$821$	37.4772	+	21.6374i	1.30796	+	0.755152i	0.981756	−	0.190146i	$-0.0608963\pi$
$821$	37.4772	+	21.6374i	1.30796	+	0.755152i	0.326206	+	0.945299i	$0.394230\pi$
$822$		0			0
$823$	0.484756	+	0.839623i	0.0168975	+	0.0292674i	0.874351	−	0.485295i	$-0.161288\pi$
$823$	0.484756	+	0.839623i	0.0168975	+	0.0292674i	−0.857453	+	0.514562i	$0.827954\pi$
$824$		0			0
$825$	3.71657	−	2.92674i	0.129394	−	0.101896i
$826$		0			0
$827$		−	43.9510i		−	1.52833i	−0.645023	−	0.764163i	$-0.723152\pi$
$827$		−	43.9510i		−	1.52833i	0.645023	−	0.764163i	$-0.276848\pi$
$828$		0			0
$829$	−6.57119	+	3.79388i	−0.228227	+	0.131767i	−0.609754	−	0.792591i	$-0.708732\pi$
$829$	−6.57119	+	3.79388i	−0.228227	+	0.131767i	0.381527	+	0.924358i	$0.375398\pi$
$830$		0			0
$831$	−0.0183520	+	0.00265106i	−0.000636622	+	9.19643e-5i
$832$		0			0
$833$	−19.1878	−	49.5161i	−0.664818	−	1.71563i
$834$		0			0
$835$	3.97971	−	6.89306i	0.137724	−	0.238544i
$836$		0			0
$837$	18.0890	−	25.5099i	0.625248	−	0.881753i
$838$		0			0
$839$	8.87477			0.306391			0.153196	−	0.988196i	$-0.451044\pi$
$839$	8.87477			0.306391			0.153196	+	0.988196i	$0.451044\pi$
$840$		0			0
$841$	24.7623			0.853873
$842$		0			0
$843$	−13.0556	−	5.21663i	−0.449660	−	0.179670i
$844$		0			0
$845$	−25.3065	+	43.8322i	−0.870570	+	1.50787i
$846$		0			0
$847$	−18.0428	−	12.3584i	−0.619957	−	0.424639i
$848$		0			0
$849$	0.956387	+	6.62059i	0.0328231	+	0.227218i
$850$		0			0
$851$	0.437604	−	0.252651i	0.0150009	−	0.00866075i
$852$		0			0
$853$		−	0.208510i		−	0.00713924i	−0.999994	−	0.00356962i	$-0.998864\pi$
$853$		−	0.208510i		−	0.00713924i	0.999994	−	0.00356962i	$-0.00113625\pi$
$854$		0			0
$855$	−22.4913	−	5.42470i	−0.769187	−	0.185521i
$856$		0			0
$857$	−14.9945	−	25.9713i	−0.512204	−	0.887163i	−0.999900	−	0.0141492i	$-0.995496\pi$
$857$	−14.9945	−	25.9713i	−0.512204	−	0.887163i	0.487696	−	0.873013i	$-0.337837\pi$
$858$		0			0
$859$	17.9227	+	10.3477i	0.611513	+	0.353057i	0.773557	−	0.633726i	$-0.218475\pi$
$859$	17.9227	+	10.3477i	0.611513	+	0.353057i	−0.162044	+	0.986783i	$0.551809\pi$
$860$		0			0
$861$	17.6260	+	8.66899i	0.600694	+	0.295438i
$862$		0			0
$863$	14.8134	+	8.55253i	0.504254	+	0.291131i	0.730469	−	0.682946i	$-0.239302\pi$
$863$	14.8134	+	8.55253i	0.504254	+	0.291131i	−0.226214	+	0.974078i	$0.572635\pi$
$864$		0			0
$865$	9.62102	+	16.6641i	0.327124	+	0.566596i
$866$		0			0
$867$	43.4543	+	55.1812i	1.47579	+	1.87405i
$868$		0			0
$869$			15.0812i			0.511596i
$870$		0			0
$871$	−11.7016	+	6.75591i	−0.396493	+	0.228915i
$872$		0			0
$873$	9.17363	−	9.64666i	0.310480	−	0.326490i
$874$		0			0
$875$	−1.75647	+	22.7796i	−0.0593795	+	0.770092i
$876$		0			0
$877$	−9.71713	+	16.8306i	−0.328124	+	0.568328i	−0.982140	−	0.188153i	$-0.939750\pi$
$877$	−9.71713	+	16.8306i	−0.328124	+	0.568328i	0.654015	+	0.756481i	$0.273083\pi$
$878$		0			0
$879$	3.69760	−	9.25398i	0.124717	−	0.312129i
$880$		0			0
$881$	30.0526			1.01250			0.506249	−	0.862387i	$-0.331032\pi$
$881$	30.0526			1.01250			0.506249	+	0.862387i	$0.331032\pi$
$882$		0			0
$883$	−16.8382			−0.566649			−0.283324	−	0.959024i	$-0.591437\pi$
$883$	−16.8382			−0.566649			−0.283324	+	0.959024i	$0.591437\pi$
$884$		0			0
$885$	16.2307	−	40.6204i	0.545587	−	1.36544i
$886$		0			0
$887$	−13.3283	+	23.0853i	−0.447520	+	0.775128i	−0.998224	−	0.0595728i	$-0.981026\pi$
$887$	−13.3283	+	23.0853i	−0.447520	+	0.775128i	0.550704	+	0.834701i	$0.314359\pi$
$888$		0			0
$889$	3.38626	−	43.9164i	0.113572	−	1.47291i
$890$		0			0
$891$	−8.07891	−	12.4979i	−0.270654	−	0.418695i
$892$		0			0
$893$	−0.966369	+	0.557933i	−0.0323383	+	0.0186705i
$894$		0			0
$895$		−	7.78665i		−	0.260279i
$896$		0			0
$897$	1.76222	+	2.23778i	0.0588388	+	0.0747174i
$898$		0			0
$899$	−6.19462	−	10.7294i	−0.206602	−	0.357846i
$900$		0			0
$901$	−51.0756	−	29.4885i	−1.70157	−	0.982404i
$902$		0			0
$903$	10.1379	+	4.98612i	0.337369	+	0.165928i
$904$		0			0
$905$	−1.70321	−	0.983349i	−0.0566166	−	0.0326876i
$906$		0			0
$907$	−4.22753	−	7.32230i	−0.140373	−	0.243133i	0.787264	−	0.616616i	$-0.211497\pi$
$907$	−4.22753	−	7.32230i	−0.140373	−	0.243133i	−0.927637	+	0.373483i	$0.878163\pi$
$908$		0			0
$909$	−2.86464	+	11.8771i	−0.0950143	+	0.393938i
$910$		0			0
$911$		−	15.4171i		−	0.510792i	−0.966837	−	0.255396i	$-0.917794\pi$
$911$		−	15.4171i		−	0.510792i	0.966837	−	0.255396i	$-0.0822058\pi$
$912$		0			0
$913$	9.52513	−	5.49934i	0.315236	−	0.182002i
$914$		0			0
$915$	−0.656206	−	4.54258i	−0.0216935	−	0.150173i
$916$		0			0
$917$	36.2234	+	24.8112i	1.19620	+	0.819338i
$918$		0			0
$919$	28.7933	−	49.8714i	0.949802	−	1.64511i	0.203964	−	0.978978i	$-0.434617\pi$
$919$	28.7933	−	49.8714i	0.949802	−	1.64511i	0.745838	−	0.666127i	$-0.232049\pi$
$920$		0			0
$921$	−38.4476	−	15.3625i	−1.26689	−	0.506210i
$922$		0			0
$923$	−89.4776			−2.94519
$924$		0			0
$925$	2.89891			0.0953156
$926$		0			0
$927$	7.16007	+	24.2656i	0.235167	+	0.796988i
$928$		0			0
$929$	23.6879	−	41.0287i	0.777176	−	1.34611i	−0.156388	−	0.987696i	$-0.549985\pi$
$929$	23.6879	−	41.0287i	0.777176	−	1.34611i	0.933563	−	0.358412i	$-0.116682\pi$
$930$		0			0
$931$	−16.3086	−	13.1210i	−0.534492	−	0.430024i
$932$		0			0
$933$	36.2699	−	5.23942i	1.18742	−	0.171531i
$934$		0			0
$935$	−28.0180	+	16.1762i	−0.916287	+	0.529019i
$936$		0			0
$937$			40.6136i			1.32679i	0.748270	+	0.663394i	$0.230885\pi$
$937$			40.6136i			1.32679i	−0.748270	+	0.663394i	$0.769115\pi$
$938$		0			0
$939$	−28.7327	+	22.6266i	−0.937657	+	0.738391i
$940$		0			0
$941$	−14.9142	−	25.8322i	−0.486189	−	0.842105i	0.513685	−	0.857979i	$-0.328280\pi$
$941$	−14.9142	−	25.8322i	−0.486189	−	0.842105i	−0.999874	+	0.0158745i	$0.994947\pi$
$942$		0			0
$943$	−1.06876	−	0.617048i	−0.0348036	−	0.0200939i
$944$		0			0
$945$	−34.9447	−	6.00429i	−1.13675	−	0.195320i
$946$		0			0
$947$	35.1139	+	20.2730i	1.14105	+	0.658785i	0.946690	−	0.322145i	$-0.104404\pi$
$947$	35.1139	+	20.2730i	1.14105	+	0.658785i	0.194359	+	0.980930i	$0.437737\pi$
$948$		0			0
$949$	10.8880	+	18.8585i	0.353439	+	0.612174i
$950$		0			0
$951$	−21.7934	+	17.1620i	−0.706701	+	0.556516i
$952$		0			0
$953$			36.7169i			1.18938i	0.803956	+	0.594688i	$0.202724\pi$
$953$			36.7169i			1.18938i	−0.803956	+	0.594688i	$0.797276\pi$
$954$		0			0
$955$	2.72982	−	1.57606i	0.0883348	−	0.0510001i
$956$		0			0
$957$	−5.83513	+	0.842923i	−0.188623	+	0.0272478i
$958$		0			0
$959$	−11.3708	−	23.7425i	−0.367182	−	0.766684i
$960$		0			0
$961$	2.61057	−	4.52163i	0.0842118	−	0.145859i
$962$		0			0
$963$	12.3854	+	41.9742i	0.399112	+	1.35260i
$964$		0			0
$965$	60.6536			1.95251
$966$		0			0
$967$	30.1106			0.968290			0.484145	−	0.874988i	$-0.339131\pi$
$967$	30.1106			0.968290			0.484145	+	0.874988i	$0.339131\pi$
$968$		0			0
$969$	36.4861	+	14.5787i	1.17210	+	0.468336i
$970$		0			0
$971$	−11.1290	+	19.2760i	−0.357147	+	0.618597i	−0.987483	−	0.157726i	$-0.949584\pi$
$971$	−11.1290	+	19.2760i	−0.357147	+	0.618597i	0.630336	+	0.776322i	$0.282917\pi$
$972$		0			0
$973$	−8.22904	−	0.634516i	−0.263811	−	0.0203417i
$974$		0			0
$975$	2.33631	+	16.1731i	0.0748217	+	0.517953i
$976$		0			0
$977$	48.3918	−	27.9390i	1.54819	−	0.893849i	0.549912	−	0.835223i	$-0.314661\pi$
$977$	48.3918	−	27.9390i	1.54819	−	0.893849i	0.998280	−	0.0586266i	$-0.0186721\pi$
$978$		0			0
$979$			24.0000i			0.767044i
$980$		0			0
$981$	−12.1688	+	50.4529i	−0.388519	+	1.61084i
$982$		0			0
$983$	−21.8878	−	37.9109i	−0.698114	−	1.20917i	−0.969120	−	0.246591i	$-0.920690\pi$
$983$	−21.8878	−	37.9109i	−0.698114	−	1.20917i	0.271006	−	0.962578i	$-0.412644\pi$
$984$		0			0
$985$	32.9032	+	18.9966i	1.04838	+	0.605284i
$986$		0			0
$987$	−1.42088	+	0.951579i	−0.0452270	+	0.0302891i
$988$		0			0
$989$	−0.614715	−	0.354906i	−0.0195468	−	0.0112853i
$990$		0			0
$991$	11.7736	+	20.3924i	0.374000	+	0.647787i	0.990177	−	0.139821i	$-0.0446528\pi$
$991$	11.7736	+	20.3924i	0.374000	+	0.647787i	−0.616177	+	0.787608i	$0.711319\pi$
$992$		0			0
$993$	20.3384	+	25.8271i	0.645420	+	0.819597i
$994$		0			0
$995$		−	17.7504i		−	0.562724i
$996$		0			0
$997$	−16.4923	+	9.52186i	−0.522318	+	0.301560i	−0.737882	−	0.674929i	$-0.764174\pi$
$997$	−16.4923	+	9.52186i	−0.522318	+	0.301560i	0.215565	+	0.976490i	$0.430841\pi$
$998$		0			0
$999$	0.848765	−	9.07990i	0.0268537	−	0.287275i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	168.2.u.a.89.6	yes	16
3.2	odd	2	inner	168.2.u.a.89.8	yes	16
4.3	odd	2		336.2.bc.f.257.3		16
7.2	even	3		1176.2.k.a.881.12		16
7.3	odd	6	inner	168.2.u.a.17.8	yes	16
7.4	even	3		1176.2.u.b.521.1		16
7.5	odd	6		1176.2.k.a.881.5		16
7.6	odd	2		1176.2.u.b.1097.3		16
12.11	even	2		336.2.bc.f.257.1		16
21.2	odd	6		1176.2.k.a.881.6		16
21.5	even	6		1176.2.k.a.881.11		16
21.11	odd	6		1176.2.u.b.521.3		16
21.17	even	6	inner	168.2.u.a.17.6	✓	16
21.20	even	2		1176.2.u.b.1097.1		16
28.3	even	6		336.2.bc.f.17.1		16
28.19	even	6		2352.2.k.i.881.12		16
28.23	odd	6		2352.2.k.i.881.5		16
84.23	even	6		2352.2.k.i.881.11		16
84.47	odd	6		2352.2.k.i.881.6		16
84.59	odd	6		336.2.bc.f.17.3		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
168.2.u.a.17.6	✓	16	21.17	even	6	inner
168.2.u.a.17.8	yes	16	7.3	odd	6	inner
168.2.u.a.89.6	yes	16	1.1	even	1	trivial
168.2.u.a.89.8	yes	16	3.2	odd	2	inner
336.2.bc.f.17.1		16	28.3	even	6
336.2.bc.f.17.3		16	84.59	odd	6
336.2.bc.f.257.1		16	12.11	even	2
336.2.bc.f.257.3		16	4.3	odd	2
1176.2.k.a.881.5		16	7.5	odd	6
1176.2.k.a.881.6		16	21.2	odd	6
1176.2.k.a.881.11		16	21.5	even	6
1176.2.k.a.881.12		16	7.2	even	3
1176.2.u.b.521.1		16	7.4	even	3
1176.2.u.b.521.3		16	21.11	odd	6
1176.2.u.b.1097.1		16	21.20	even	2
1176.2.u.b.1097.3		16	7.6	odd	2
2352.2.k.i.881.5		16	28.23	odd	6
2352.2.k.i.881.6		16	84.47	odd	6
2352.2.k.i.881.11		16	84.23	even	6
2352.2.k.i.881.12		16	28.19	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 168 = 2^{3} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	168.u (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.642670 - 1.60841i) q^{3} +(1.28955 - 2.23357i) q^{5} +(-0.203402 + 2.63792i) q^{7} +(-2.17395 - 2.06735i) q^{9} +(-1.43199 + 0.826762i) q^{11} -5.71177i q^{13} +(-2.76373 - 3.50957i) q^{15} +(3.79313 + 6.56990i) q^{17} +(2.58961 + 1.49511i) q^{19} +(4.11213 + 2.02247i) q^{21} +(-0.249340 - 0.143957i) q^{23} +(-0.825879 - 1.43046i) q^{25} +(-4.72227 + 2.16798i) q^{27} +2.05856i q^{29} +(-5.21209 + 3.00920i) q^{31} +(0.409472 + 2.83457i) q^{33} +(5.62967 + 3.85604i) q^{35} +(-0.877523 + 1.51991i) q^{37} +(-9.18685 - 3.67078i) q^{39} +4.28635 q^{41} +2.46537 q^{43} +(-7.42098 + 2.18971i) q^{45} +(-0.186586 + 0.323176i) q^{47} +(-6.91726 - 1.07312i) q^{49} +(13.0048 - 1.87863i) q^{51} +(-6.73264 + 3.88709i) q^{53} +4.26461i q^{55} +(4.06901 - 3.20429i) q^{57} +(4.89610 + 8.48029i) q^{59} +(0.889794 + 0.513723i) q^{61} +(5.89569 - 5.31421i) q^{63} +(-12.7576 - 7.36561i) q^{65} +(-1.18281 - 2.04868i) q^{67} +(-0.391784 + 0.308524i) q^{69} -15.6655i q^{71} +(-3.30170 + 1.90624i) q^{73} +(-2.83154 + 0.409034i) q^{75} +(-1.88966 - 3.94565i) q^{77} +(4.56033 - 7.89872i) q^{79} +(0.452128 + 8.98864i) q^{81} -6.65166 q^{83} +19.5657 q^{85} +(3.31101 + 1.32298i) q^{87} +(7.25723 - 12.5699i) q^{89} +(15.0672 + 1.16179i) q^{91} +(1.49037 + 10.3171i) q^{93} +(6.67886 - 3.85604i) q^{95} +4.43739i q^{97} +(4.82229 + 1.16309i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 4 q^{7} + 2 q^{9} + 8 q^{15} - 6 q^{19} + 14 q^{21} - 18 q^{25} - 48 q^{31} - 12 q^{33} - 2 q^{37} - 22 q^{39} + 20 q^{43} - 42 q^{45} - 28 q^{49} + 6 q^{51} - 8 q^{57} + 36 q^{61} - 32 q^{63} + 14 q^{67}+ \cdots + 20 q^{99}+O(q^{100}) \) 16 * q + 4 * q^7 + 2 * q^9 + 8 * q^15 - 6 * q^19 + 14 * q^21 - 18 * q^25 - 48 * q^31 - 12 * q^33 - 2 * q^37 - 22 * q^39 + 20 * q^43 - 42 * q^45 - 28 * q^49 + 6 * q^51 - 8 * q^57 + 36 * q^61 - 32 * q^63 + 14 * q^67 + 30 * q^73 + 54 * q^75 + 28 * q^79 + 30 * q^81 + 16 * q^85 + 78 * q^87 + 66 * q^91 + 16 * q^93 + 20 * q^99

Introduction

L-functions

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