LMFDB - Embedded newform 580.2.j.a.17.5

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [580,2,Mod(17,580)] 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("580.17"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(580, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([0, 1, 3])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 580 = 2^{2} \cdot 5 \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	580.j (of order $4$, 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:	$4.63132331723$
Analytic rank:	$0$
Dimension:	$30$
Relative dimension:	$15$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			17.5
Character	$\chi$	$=$	580.17
Dual form			580.2.j.a.273.11

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-0.993874i q^{3} +(0.775222 - 2.09739i) q^{5} +(1.61651 + 1.61651i) q^{7} +2.01221 q^{9} +(-0.197513 + 0.197513i) q^{11} +(-1.05868 - 1.05868i) q^{13} +(-2.08454 - 0.770473i) q^{15} +6.74344 q^{17} +(-1.09587 - 1.09587i) q^{19} +(1.60661 - 1.60661i) q^{21} +(-1.08510 + 1.08510i) q^{23} +(-3.79806 - 3.25188i) q^{25} -4.98151i q^{27} +(-4.70835 + 2.61369i) q^{29} +(0.918384 - 0.918384i) q^{31} +(0.196303 + 0.196303i) q^{33} +(4.64359 - 2.13729i) q^{35} -4.58488i q^{37} +(-1.05219 + 1.05219i) q^{39} +(-2.22718 - 2.22718i) q^{41} -7.54441i q^{43} +(1.55991 - 4.22039i) q^{45} +8.00102i q^{47} -1.77380i q^{49} -6.70213i q^{51} +(8.28855 - 8.28855i) q^{53} +(0.261145 + 0.567377i) q^{55} +(-1.08916 + 1.08916i) q^{57} +14.3607i q^{59} +(-2.74633 + 2.74633i) q^{61} +(3.25276 + 3.25276i) q^{63} +(-3.04117 + 1.39975i) q^{65} +(-4.37476 + 4.37476i) q^{67} +(1.07845 + 1.07845i) q^{69} +8.12214i q^{71} +7.75512 q^{73} +(-3.23196 + 3.77480i) q^{75} -0.638562 q^{77} +(2.84324 + 2.84324i) q^{79} +1.08565 q^{81} +(-5.67373 + 5.67373i) q^{83} +(5.22766 - 14.1436i) q^{85} +(2.59768 + 4.67951i) q^{87} +(-3.53138 - 3.53138i) q^{89} -3.42272i q^{91} +(-0.912759 - 0.912759i) q^{93} +(-3.14801 + 1.44892i) q^{95} +8.15306i q^{97} +(-0.397438 + 0.397438i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 30 q - 38 q^{9} - 4 q^{11} + 6 q^{13} + 14 q^{15} + 12 q^{17} - 4 q^{21} - 2 q^{25} - 4 q^{31} - 4 q^{33} + 16 q^{35} + 12 q^{39} + 10 q^{41} - 20 q^{45} - 18 q^{53} - 2 q^{55} - 24 q^{57} - 22 q^{61} - 24 q^{63}+ \cdots - 60 q^{95}+O(q^{100}) $ 30 * q - 38 * q^9 - 4 * q^11 + 6 * q^13 + 14 * q^15 + 12 * q^17 - 4 * q^21 - 2 * q^25 - 4 * q^31 - 4 * q^33 + 16 * q^35 + 12 * q^39 + 10 * q^41 - 20 * q^45 - 18 * q^53 - 2 * q^55 - 24 * q^57 - 22 * q^61 - 24 * q^63 - 10 * q^65 - 16 * q^67 + 8 * q^69 - 20 * q^73 + 34 * q^75 + 20 * q^77 + 20 * q^79 + 70 * q^81 + 56 * q^83 + 12 * q^85 + 4 * q^87 + 6 * q^89 - 44 * q^93 - 60 * q^95

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/580\mathbb{Z}\right)^\times$.

$n$	$117$	$291$	$321$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$1$	$e\left(\frac{3}{4}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		0			0
$2$		0			0
$3$		−	0.993874i		−	0.573814i	−0.957959	−	0.286907i	$-0.907373\pi$
$3$		−	0.993874i		−	0.573814i	0.957959	−	0.286907i	$-0.0926270\pi$
$4$		0			0
$5$	0.775222	−	2.09739i	0.346690	−	0.937980i
$5$	0.775222	−	2.09739i	0.346690	−	0.937980i
$6$		0			0
$7$	1.61651	+	1.61651i	0.610983	+	0.610983i	0.943202	−	0.332220i	$-0.107797\pi$
$7$	1.61651	+	1.61651i	0.610983	+	0.610983i	−0.332220	+	0.943202i	$0.607797\pi$
$8$		0			0
$9$	2.01221			0.670738
$10$		0			0
$11$	−0.197513	+	0.197513i	−0.0595524	+	0.0595524i	−0.736256	−	0.676703i	$-0.763408\pi$
$11$	−0.197513	+	0.197513i	−0.0595524	+	0.0595524i	0.676703	+	0.736256i	$0.263408\pi$
$12$		0			0
$13$	−1.05868	−	1.05868i	−0.293625	−	0.293625i	0.544886	−	0.838510i	$-0.316573\pi$
$13$	−1.05868	−	1.05868i	−0.293625	−	0.293625i	−0.838510	+	0.544886i	$0.816573\pi$
$14$		0			0
$15$	−2.08454	−	0.770473i	−0.538226	−	0.198935i
$16$		0			0
$17$	6.74344			1.63552			0.817762	−	0.575556i	$-0.195214\pi$
$17$	6.74344			1.63552			0.817762	+	0.575556i	$0.195214\pi$
$18$		0			0
$19$	−1.09587	−	1.09587i	−0.251410	−	0.251410i	0.570138	−	0.821549i	$-0.306890\pi$
$19$	−1.09587	−	1.09587i	−0.251410	−	0.251410i	−0.821549	+	0.570138i	$0.806890\pi$
$20$		0			0
$21$	1.60661	−	1.60661i	0.350590	−	0.350590i
$22$		0			0
$23$	−1.08510	+	1.08510i	−0.226259	+	0.226259i	−0.811128	−	0.584869i	$-0.801146\pi$
$23$	−1.08510	+	1.08510i	−0.226259	+	0.226259i	0.584869	+	0.811128i	$0.301146\pi$
$24$		0			0
$25$	−3.79806	−	3.25188i	−0.759613	−	0.650376i
$26$		0			0
$27$		−	4.98151i		−	0.958692i
$28$		0			0
$29$	−4.70835	+	2.61369i	−0.874319	+	0.485351i
$29$	−4.70835	+	2.61369i	−0.874319	+	0.485351i
$30$		0			0
$31$	0.918384	−	0.918384i	0.164947	−	0.164947i	−0.619807	−	0.784754i	$-0.712789\pi$
$31$	0.918384	−	0.918384i	0.164947	−	0.164947i	0.784754	+	0.619807i	$0.212789\pi$
$32$		0			0
$33$	0.196303	+	0.196303i	0.0341720	+	0.0341720i
$34$		0			0
$35$	4.64359	−	2.13729i	0.784911	−	0.361268i
$36$		0			0
$37$		−	4.58488i		−	0.753749i	−0.926264	−	0.376875i	$-0.876999\pi$
$37$		−	4.58488i		−	0.753749i	0.926264	−	0.376875i	$-0.123001\pi$
$38$		0			0
$39$	−1.05219	+	1.05219i	−0.168486	+	0.168486i
$40$		0			0
$41$	−2.22718	−	2.22718i	−0.347826	−	0.347826i	0.511473	−	0.859299i	$-0.329100\pi$
$41$	−2.22718	−	2.22718i	−0.347826	−	0.347826i	−0.859299	+	0.511473i	$0.829100\pi$
$42$		0			0
$43$		−	7.54441i		−	1.15051i	−0.817973	−	0.575256i	$-0.804902\pi$
$43$		−	7.54441i		−	1.15051i	0.817973	−	0.575256i	$-0.195098\pi$
$44$		0			0
$45$	1.55991	−	4.22039i	0.232538	−	0.629139i
$46$		0			0
$47$			8.00102i			1.16707i	0.812089	+	0.583534i	$0.198331\pi$
$47$			8.00102i			1.16707i	−0.812089	+	0.583534i	$0.801669\pi$
$48$		0			0
$49$		−	1.77380i		−	0.253401i
$50$		0			0
$51$		−	6.70213i		−	0.938486i
$52$		0			0
$53$	8.28855	−	8.28855i	1.13852	−	1.13852i	0.149805	−	0.988716i	$-0.452135\pi$
$53$	8.28855	−	8.28855i	1.13852	−	1.13852i	0.988716	−	0.149805i	$-0.0478646\pi$
$54$		0			0
$55$	0.261145	+	0.567377i	0.0352127	+	0.0765051i
$56$		0			0
$57$	−1.08916	+	1.08916i	−0.144263	+	0.144263i
$58$		0			0
$59$			14.3607i			1.86960i	0.355168	+	0.934802i	$0.384424\pi$
$59$			14.3607i			1.86960i	−0.355168	+	0.934802i	$0.615576\pi$
$60$		0			0
$61$	−2.74633	+	2.74633i	−0.351631	+	0.351631i	−0.860716	−	0.509085i	$-0.829984\pi$
$61$	−2.74633	+	2.74633i	−0.351631	+	0.351631i	0.509085	+	0.860716i	$0.329984\pi$
$62$		0			0
$63$	3.25276	+	3.25276i	0.409809	+	0.409809i
$64$		0			0
$65$	−3.04117	+	1.39975i	−0.377210	+	0.173617i
$66$		0			0
$67$	−4.37476	+	4.37476i	−0.534461	+	0.534461i	−0.921897	−	0.387435i	$-0.873361\pi$
$67$	−4.37476	+	4.37476i	−0.534461	+	0.534461i	0.387435	+	0.921897i	$0.373361\pi$
$68$		0			0
$69$	1.07845	+	1.07845i	0.129830	+	0.129830i
$70$		0			0
$71$			8.12214i			0.963921i	0.876193	+	0.481961i	$0.160075\pi$
$71$			8.12214i			0.963921i	−0.876193	+	0.481961i	$0.839925\pi$
$72$		0			0
$73$	7.75512			0.907668			0.453834	−	0.891086i	$-0.350056\pi$
$73$	7.75512			0.907668			0.453834	+	0.891086i	$0.350056\pi$
$74$		0			0
$75$	−3.23196	+	3.77480i	−0.373194	+	0.435876i
$76$		0			0
$77$	−0.638562			−0.0727709
$78$		0			0
$79$	2.84324	+	2.84324i	0.319890	+	0.319890i	0.848725	−	0.528835i	$-0.177371\pi$
$79$	2.84324	+	2.84324i	0.319890	+	0.319890i	−0.528835	+	0.848725i	$0.677371\pi$
$80$		0			0
$81$	1.08565			0.120627
$82$		0			0
$83$	−5.67373	+	5.67373i	−0.622773	+	0.622773i	−0.946240	−	0.323467i	$-0.895152\pi$
$83$	−5.67373	+	5.67373i	−0.622773	+	0.622773i	0.323467	+	0.946240i	$0.395152\pi$
$84$		0			0
$85$	5.22766	−	14.1436i	0.567019	−	1.53409i
$86$		0			0
$87$	2.59768	+	4.67951i	0.278501	+	0.501696i
$88$		0			0
$89$	−3.53138	−	3.53138i	−0.374325	−	0.374325i	0.494725	−	0.869050i	$-0.335269\pi$
$89$	−3.53138	−	3.53138i	−0.374325	−	0.374325i	−0.869050	+	0.494725i	$0.835269\pi$
$90$		0			0
$91$		−	3.42272i		−	0.358799i
$92$		0			0
$93$	−0.912759	−	0.912759i	−0.0946487	−	0.0946487i
$94$		0			0
$95$	−3.14801	+	1.44892i	−0.322979	+	0.148656i
$96$		0			0
$97$			8.15306i			0.827818i	0.910318	+	0.413909i	$0.135837\pi$
$97$			8.15306i			0.827818i	−0.910318	+	0.413909i	$0.864163\pi$
$98$		0			0
$99$	−0.397438	+	0.397438i	−0.0399440	+	0.0399440i
$100$		0			0
$101$	−10.8451	+	10.8451i	−1.07913	+	1.07913i	−0.0825447	+	0.996587i	$0.526305\pi$
$101$	−10.8451	+	10.8451i	−1.07913	+	1.07913i	−0.996587	+	0.0825447i	$0.973695\pi$
$102$		0			0
$103$	4.54767	−	4.54767i	0.448095	−	0.448095i	−0.446626	−	0.894721i	$-0.647374\pi$
$103$	4.54767	−	4.54767i	0.448095	−	0.448095i	0.894721	+	0.446626i	$0.147374\pi$
$104$		0			0
$105$	−2.12420	−	4.61515i	−0.207301	−	0.450392i
$106$		0			0
$107$	0.904693	+	0.904693i	0.0874600	+	0.0874600i	0.749483	−	0.662023i	$-0.230302\pi$
$107$	0.904693	+	0.904693i	0.0874600	+	0.0874600i	−0.662023	+	0.749483i	$0.730302\pi$
$108$		0			0
$109$	−10.0100			−0.958788			−0.479394	−	0.877600i	$-0.659144\pi$
$109$	−10.0100			−0.958788			−0.479394	+	0.877600i	$0.659144\pi$
$110$		0			0
$111$	−4.55679			−0.432512
$112$		0			0
$113$	10.7606			1.01227			0.506134	−	0.862455i	$-0.331074\pi$
$113$	10.7606			1.01227			0.506134	+	0.862455i	$0.331074\pi$
$114$		0			0
$115$	1.43468	+	3.11706i	0.133784	+	0.290667i
$116$		0			0
$117$	−2.13029	−	2.13029i	−0.196945	−	0.196945i
$118$		0			0
$119$	10.9008	+	10.9008i	0.999277	+	0.999277i
$120$		0			0
$121$			10.9220i			0.992907i
$122$		0			0
$123$	−2.21353	+	2.21353i	−0.199587	+	0.199587i
$124$		0			0
$125$	−9.76479	+	5.44508i	−0.873389	+	0.487023i
$126$		0			0
$127$	−6.69204			−0.593823			−0.296911	−	0.954905i	$-0.595957\pi$
$127$	−6.69204			−0.593823			−0.296911	+	0.954905i	$0.595957\pi$
$128$		0			0
$129$	−7.49820			−0.660180
$130$		0			0
$131$	−14.0171	−	14.0171i	−1.22468	−	1.22468i	−0.965950	−	0.258729i	$-0.916696\pi$
$131$	−14.0171	−	14.0171i	−1.22468	−	1.22468i	−0.258729	−	0.965950i	$-0.583304\pi$
$132$		0			0
$133$		−	3.54297i		−	0.307215i
$134$		0			0
$135$	−10.4482	−	3.86177i	−0.899234	−	0.332369i
$136$		0			0
$137$	4.01363			0.342907			0.171454	−	0.985192i	$-0.445154\pi$
$137$	4.01363			0.342907			0.171454	+	0.985192i	$0.445154\pi$
$138$		0			0
$139$			19.4233i			1.64746i	0.566980	+	0.823731i	$0.308112\pi$
$139$			19.4233i			1.64746i	−0.566980	+	0.823731i	$0.691888\pi$
$140$		0			0
$141$	7.95200			0.669680
$142$		0			0
$143$	0.418205			0.0349721
$144$		0			0
$145$	1.83191	+	11.9014i	0.152132	+	0.988360i
$146$		0			0
$147$	−1.76294			−0.145405
$148$		0			0
$149$	−1.23860			−0.101470			−0.0507352	−	0.998712i	$-0.516156\pi$
$149$	−1.23860			−0.101470			−0.0507352	+	0.998712i	$0.516156\pi$
$150$		0			0
$151$			10.8036i			0.879186i	0.898197	+	0.439593i	$0.144877\pi$
$151$			10.8036i			0.879186i	−0.898197	+	0.439593i	$0.855123\pi$
$152$		0			0
$153$	13.5692			1.09701
$154$		0			0
$155$	−1.21426	−	2.63816i	−0.0975314	−	0.211902i
$156$		0			0
$157$		−	1.53851i		−	0.122786i	−0.998114	−	0.0613930i	$-0.980446\pi$
$157$		−	1.53851i		−	0.122786i	0.998114	−	0.0613930i	$-0.0195543\pi$
$158$		0			0
$159$	−8.23778	−	8.23778i	−0.653299	−	0.653299i
$160$		0			0
$161$	−3.50814			−0.276480
$162$		0			0
$163$	20.0047			1.56689			0.783444	−	0.621462i	$-0.213461\pi$
$163$	20.0047			1.56689			0.783444	+	0.621462i	$0.213461\pi$
$164$		0			0
$165$	0.563902	−	0.259545i	0.0438997	−	0.0202055i
$166$		0			0
$167$	−12.9208	+	12.9208i	−0.999843	+	0.999843i	−1.00000		0.000157414i	$-0.999950\pi$
$167$	−12.9208	+	12.9208i	−0.999843	+	0.999843i	0.000157414		1.00000i	$0.499950\pi$
$168$		0			0
$169$		−	10.7584i		−	0.827569i
$170$		0			0
$171$	−2.20513	−	2.20513i	−0.168630	−	0.168630i
$172$		0			0
$173$	7.97331	+	7.97331i	0.606199	+	0.606199i	0.941951	−	0.335751i	$-0.108990\pi$
$173$	7.97331	+	7.97331i	0.606199	+	0.606199i	−0.335751	+	0.941951i	$0.608990\pi$
$174$		0			0
$175$	−0.882911	−	11.3963i	−0.0667418	−	0.861478i
$176$		0			0
$177$	14.2727			1.07280
$178$		0			0
$179$	−6.43500			−0.480975			−0.240487	−	0.970652i	$-0.577307\pi$
$179$	−6.43500			−0.480975			−0.240487	+	0.970652i	$0.577307\pi$
$180$		0			0
$181$	−4.30876			−0.320267			−0.160134	−	0.987095i	$-0.551193\pi$
$181$	−4.30876			−0.320267			−0.160134	+	0.987095i	$0.551193\pi$
$182$		0			0
$183$	2.72950	+	2.72950i	0.201771	+	0.201771i
$184$		0			0
$185$	−9.61626	−	3.55430i	−0.707002	−	0.261317i
$186$		0			0
$187$	−1.33192	+	1.33192i	−0.0973994	+	0.0973994i
$188$		0			0
$189$	8.05265	−	8.05265i	0.585744	−	0.585744i
$190$		0			0
$191$	2.69621	−	2.69621i	0.195091	−	0.195091i	−0.602801	−	0.797892i	$-0.705949\pi$
$191$	2.69621	−	2.69621i	0.195091	−	0.195091i	0.797892	+	0.602801i	$0.205949\pi$
$192$		0			0
$193$		−	2.10697i		−	0.151663i	−0.997121	−	0.0758317i	$-0.975839\pi$
$193$		−	2.10697i		−	0.151663i	0.997121	−	0.0758317i	$-0.0241612\pi$
$194$		0			0
$195$	1.39117	+	3.02254i	0.0996240	+	0.216448i
$196$		0			0
$197$	8.82785	+	8.82785i	0.628958	+	0.628958i	0.947806	−	0.318848i	$-0.103296\pi$
$197$	8.82785	+	8.82785i	0.628958	+	0.628958i	−0.318848	+	0.947806i	$0.603296\pi$
$198$		0			0
$199$			10.2415i			0.726002i	0.931789	+	0.363001i	$0.118248\pi$
$199$			10.2415i			0.726002i	−0.931789	+	0.363001i	$0.881752\pi$
$200$		0			0
$201$	4.34796	+	4.34796i	0.306681	+	0.306681i
$202$		0			0
$203$	−11.8362	−	3.38603i	−0.830735	−	0.237653i
$204$		0			0
$205$	−6.39780	+	2.94469i	−0.446842	+	0.205666i
$206$		0			0
$207$	−2.18345	+	2.18345i	−0.151760	+	0.151760i
$208$		0			0
$209$	0.432898			0.0299442
$210$		0			0
$211$	−4.24331	−	4.24331i	−0.292122	−	0.292122i	0.545796	−	0.837918i	$-0.316227\pi$
$211$	−4.24331	−	4.24331i	−0.292122	−	0.292122i	−0.837918	+	0.545796i	$0.816227\pi$
$212$		0			0
$213$	8.07239			0.553111
$214$		0			0
$215$	−15.8236	−	5.84859i	−1.07916	−	0.398871i
$216$		0			0
$217$	2.96915			0.201559
$218$		0			0
$219$		−	7.70761i		−	0.520832i
$220$		0			0
$221$	−7.13913	−	7.13913i	−0.480230	−	0.480230i
$222$		0			0
$223$	2.92781	−	2.92781i	0.196061	−	0.196061i	−0.602248	−	0.798309i	$-0.705728\pi$
$223$	2.92781	−	2.92781i	0.196061	−	0.196061i	0.798309	+	0.602248i	$0.205728\pi$
$224$		0			0
$225$	−7.64252	−	6.54348i	−0.509501	−	0.436232i
$226$		0			0
$227$	4.70219	+	4.70219i	0.312095	+	0.312095i	0.845721	−	0.533626i	$-0.179171\pi$
$227$	4.70219	+	4.70219i	0.312095	+	0.312095i	−0.533626	+	0.845721i	$0.679171\pi$
$228$		0			0
$229$	15.4423	−	15.4423i	1.02045	−	1.02045i	0.0206674	−	0.999786i	$-0.493421\pi$
$229$	15.4423	−	15.4423i	1.02045	−	1.02045i	0.999786	−	0.0206674i	$-0.00657912\pi$
$230$		0			0
$231$			0.634651i			0.0417569i
$232$		0			0
$233$	−12.2426	+	12.2426i	−0.802038	+	0.802038i	−0.983414	−	0.181375i	$-0.941945\pi$
$233$	−12.2426	+	12.2426i	−0.802038	+	0.802038i	0.181375	+	0.983414i	$0.441945\pi$
$234$		0			0
$235$	16.7812	+	6.20256i	1.09469	+	0.404610i
$236$		0			0
$237$	2.82583	−	2.82583i	0.183557	−	0.183557i
$238$		0			0
$239$			11.6057i			0.750711i	0.926881	+	0.375355i	$0.122479\pi$
$239$			11.6057i			0.750711i	−0.926881	+	0.375355i	$0.877521\pi$
$240$		0			0
$241$		−	15.6504i		−	1.00813i	−0.863666	−	0.504065i	$-0.831837\pi$
$241$		−	15.6504i		−	1.00813i	0.863666	−	0.504065i	$-0.168163\pi$
$242$		0			0
$243$		−	16.0235i		−	1.02791i
$244$		0			0
$245$	−3.72035	−	1.37509i	−0.237685	−	0.0878513i
$246$		0			0
$247$			2.32035i			0.147640i
$248$		0			0
$249$	5.63898	+	5.63898i	0.357356	+	0.357356i
$250$		0			0
$251$	19.0827	−	19.0827i	1.20449	−	1.20449i	0.231701	−	0.972787i	$-0.425571\pi$
$251$	19.0827	−	19.0827i	1.20449	−	1.20449i	0.972787	−	0.231701i	$-0.0744291\pi$
$252$		0			0
$253$		−	0.428642i		−	0.0269485i
$254$		0			0
$255$	−14.0570	−	5.19564i	−0.880281	−	0.325363i
$256$		0			0
$257$	−0.528836	−	0.528836i	−0.0329879	−	0.0329879i	0.690420	−	0.723408i	$-0.257426\pi$
$257$	−0.528836	−	0.528836i	−0.0329879	−	0.0329879i	−0.723408	+	0.690420i	$0.757426\pi$
$258$		0			0
$259$	7.41149	−	7.41149i	0.460528	−	0.460528i
$260$		0			0
$261$	−9.47422	+	5.25931i	−0.586439	+	0.325543i
$262$		0			0
$263$		−	10.3389i		−	0.637524i	−0.947835	−	0.318762i	$-0.896733\pi$
$263$		−	10.3389i		−	0.637524i	0.947835	−	0.318762i	$-0.103267\pi$
$264$		0			0
$265$	−10.9588	−	23.8098i	−0.673196	−	1.46262i
$266$		0			0
$267$	−3.50974	+	3.50974i	−0.214793	+	0.214793i
$268$		0			0
$269$	−15.5320	+	15.5320i	−0.947005	+	0.947005i	−0.998665	−	0.0516599i	$-0.983549\pi$
$269$	−15.5320	+	15.5320i	−0.947005	+	0.947005i	0.0516599	+	0.998665i	$0.483549\pi$
$270$		0			0
$271$	−11.2924	−	11.2924i	−0.685965	−	0.685965i	0.275373	−	0.961338i	$-0.411199\pi$
$271$	−11.2924	−	11.2924i	−0.685965	−	0.685965i	−0.961338	+	0.275373i	$0.911199\pi$
$272$		0			0
$273$	−3.40176			−0.205884
$274$		0			0
$275$	1.39245	−	0.107878i	0.0839682	−	0.00650531i
$276$		0			0
$277$	7.10226	+	7.10226i	0.426733	+	0.426733i	0.887514	−	0.460781i	$-0.152431\pi$
$277$	7.10226	+	7.10226i	0.426733	+	0.426733i	−0.460781	+	0.887514i	$0.652431\pi$
$278$		0			0
$279$	1.84799	−	1.84799i	0.110636	−	0.110636i
$280$		0			0
$281$	17.9241			1.06926			0.534630	−	0.845086i	$-0.320451\pi$
$281$	17.9241			1.06926			0.534630	+	0.845086i	$0.320451\pi$
$282$		0			0
$283$	−21.3191	−	21.3191i	−1.26729	−	1.26729i	−0.947483	−	0.319805i	$-0.896383\pi$
$283$	−21.3191	−	21.3191i	−1.26729	−	1.26729i	−0.319805	−	0.947483i	$-0.603617\pi$
$284$		0			0
$285$	1.44005	+	3.12873i	0.0853011	+	0.185330i
$286$		0			0
$287$		−	7.20049i		−	0.425032i
$288$		0			0
$289$	28.4740			1.67494
$290$		0			0
$291$	8.10311			0.475013
$292$		0			0
$293$			20.7956i			1.21489i	0.794362	+	0.607445i	$0.207805\pi$
$293$			20.7956i			1.21489i	−0.794362	+	0.607445i	$0.792195\pi$
$294$		0			0
$295$	30.1200	+	11.1327i	1.75365	+	0.648173i
$296$		0			0
$297$	0.983913	+	0.983913i	0.0570924	+	0.0570924i
$298$		0			0
$299$	2.29754			0.132870
$300$		0			0
$301$	12.1956	−	12.1956i	0.702943	−	0.702943i
$302$		0			0
$303$	10.7787	+	10.7787i	0.619221	+	0.619221i
$304$		0			0
$305$	3.63110	+	7.88912i	0.207916	+	0.451730i
$306$		0			0
$307$	15.2567			0.870749			0.435374	−	0.900250i	$-0.356616\pi$
$307$	15.2567			0.870749			0.435374	+	0.900250i	$0.356616\pi$
$308$		0			0
$309$	−4.51981	−	4.51981i	−0.257123	−	0.257123i
$310$		0			0
$311$	−8.30645	+	8.30645i	−0.471016	+	0.471016i	−0.902243	−	0.431228i	$-0.858081\pi$
$311$	−8.30645	+	8.30645i	−0.471016	+	0.471016i	0.431228	+	0.902243i	$0.358081\pi$
$312$		0			0
$313$	1.75658	−	1.75658i	0.0992880	−	0.0992880i	−0.655718	−	0.755006i	$-0.727634\pi$
$313$	1.75658	−	1.75658i	0.0992880	−	0.0992880i	0.755006	+	0.655718i	$0.227634\pi$
$314$		0			0
$315$	9.34391	−	4.30069i	0.526469	−	0.242316i
$316$		0			0
$317$		−	12.3737i		−	0.694978i	−0.937684	−	0.347489i	$-0.887034\pi$
$317$		−	12.3737i		−	0.694978i	0.937684	−	0.347489i	$-0.112966\pi$
$318$		0			0
$319$	0.413722	−	1.44620i	0.0231640	−	0.0809716i
$320$		0			0
$321$	0.899151	−	0.899151i	0.0501857	−	0.0501857i
$322$		0			0
$323$	−7.38995	−	7.38995i	−0.411188	−	0.411188i
$324$		0			0
$325$	0.578233	+	7.46362i	0.0320746	+	0.414007i
$326$		0			0
$327$			9.94872i			0.550166i
$328$		0			0
$329$	−12.9337	+	12.9337i	−0.713058	+	0.713058i
$330$		0			0
$331$	−3.25994	−	3.25994i	−0.179182	−	0.179182i	0.611817	−	0.790999i	$-0.290439\pi$
$331$	−3.25994	−	3.25994i	−0.179182	−	0.179182i	−0.790999	+	0.611817i	$0.790439\pi$
$332$		0			0
$333$		−	9.22576i		−	0.505568i
$334$		0			0
$335$	5.78415	+	12.5670i	0.316022	+	0.686606i
$336$		0			0
$337$		−	15.2065i		−	0.828352i	−0.910197	−	0.414176i	$-0.864070\pi$
$337$		−	15.2065i		−	0.828352i	0.910197	−	0.414176i	$-0.135930\pi$
$338$		0			0
$339$		−	10.6946i		−	0.580853i
$340$		0			0
$341$			0.362785i			0.0196459i
$342$		0			0
$343$	14.1829	−	14.1829i	0.765806	−	0.765806i
$344$		0			0
$345$	3.09797	−	1.42589i	0.166789	−	0.0767673i
$346$		0			0
$347$	11.8556	−	11.8556i	0.636444	−	0.636444i	−0.313232	−	0.949676i	$-0.601412\pi$
$347$	11.8556	−	11.8556i	0.636444	−	0.636444i	0.949676	+	0.313232i	$0.101412\pi$
$348$		0			0
$349$			9.46482i			0.506640i	0.967383	+	0.253320i	$0.0815226\pi$
$349$			9.46482i			0.506640i	−0.967383	+	0.253320i	$0.918477\pi$
$350$		0			0
$351$	−5.27382	+	5.27382i	−0.281496	+	0.281496i
$352$		0			0
$353$	−6.01830	−	6.01830i	−0.320322	−	0.320322i	0.528569	−	0.848891i	$-0.322729\pi$
$353$	−6.01830	−	6.01830i	−0.320322	−	0.320322i	−0.848891	+	0.528569i	$0.822729\pi$
$354$		0			0
$355$	17.0353	+	6.29646i	0.904139	+	0.334181i
$356$		0			0
$357$	10.8340	−	10.8340i	0.573399	−	0.573399i
$358$		0			0
$359$	6.20789	+	6.20789i	0.327640	+	0.327640i	0.851688	−	0.524049i	$-0.175579\pi$
$359$	6.20789	+	6.20789i	0.327640	+	0.327640i	−0.524049	+	0.851688i	$0.675579\pi$
$360$		0			0
$361$		−	16.5981i		−	0.873586i
$362$		0			0
$363$	10.8551			0.569744
$364$		0			0
$365$	6.01193	−	16.2655i	0.314679	−	0.851374i
$366$		0			0
$367$	−36.0492			−1.88175			−0.940876	−	0.338751i	$-0.889996\pi$
$367$	−36.0492			−1.88175			−0.940876	+	0.338751i	$0.889996\pi$
$368$		0			0
$369$	−4.48155	−	4.48155i	−0.233300	−	0.233300i
$370$		0			0
$371$	26.7970			1.39123
$372$		0			0
$373$	4.91494	−	4.91494i	0.254486	−	0.254486i	−0.568321	−	0.822807i	$-0.692407\pi$
$373$	4.91494	−	4.91494i	0.254486	−	0.254486i	0.822807	+	0.568321i	$0.192407\pi$
$374$		0			0
$375$	5.41173	+	9.70497i	0.279460	+	0.501163i
$376$		0			0
$377$	7.75169	+	2.21757i	0.399233	+	0.114211i
$378$		0			0
$379$	−7.46638	−	7.46638i	−0.383522	−	0.383522i	0.488847	−	0.872369i	$-0.337418\pi$
$379$	−7.46638	−	7.46638i	−0.383522	−	0.383522i	−0.872369	+	0.488847i	$0.837418\pi$
$380$		0			0
$381$			6.65105i			0.340744i
$382$		0			0
$383$	−2.56732	−	2.56732i	−0.131184	−	0.131184i	0.638466	−	0.769650i	$-0.279569\pi$
$383$	−2.56732	−	2.56732i	−0.131184	−	0.131184i	−0.769650	+	0.638466i	$0.779569\pi$
$384$		0			0
$385$	−0.495027	+	1.33931i	−0.0252289	+	0.0682577i
$386$		0			0
$387$		−	15.1810i		−	0.771692i
$388$		0			0
$389$	−23.9192	+	23.9192i	−1.21275	+	1.21275i	−0.242632	+	0.970118i	$0.578011\pi$
$389$	−23.9192	+	23.9192i	−1.21275	+	1.21275i	−0.970118	+	0.242632i	$0.921989\pi$
$390$		0			0
$391$	−7.31729	+	7.31729i	−0.370051	+	0.370051i
$392$		0			0
$393$	−13.9312	+	13.9312i	−0.702738	+	0.702738i
$394$		0			0
$395$	8.16752	−	3.75924i	0.410953	−	0.189148i
$396$		0			0
$397$	−14.6638	−	14.6638i	−0.735956	−	0.735956i	0.235837	−	0.971793i	$-0.424217\pi$
$397$	−14.6638	−	14.6638i	−0.735956	−	0.735956i	−0.971793	+	0.235837i	$0.924217\pi$
$398$		0			0
$399$	−3.52127			−0.176284
$400$		0			0
$401$	−27.5628			−1.37642			−0.688209	−	0.725512i	$-0.741603\pi$
$401$	−27.5628			−1.37642			−0.688209	+	0.725512i	$0.741603\pi$
$402$		0			0
$403$	−1.94455			−0.0968648
$404$		0			0
$405$	0.841617	−	2.27702i	0.0418203	−	0.113146i
$406$		0			0
$407$	0.905573	+	0.905573i	0.0448876	+	0.0448876i
$408$		0			0
$409$	−15.5287	−	15.5287i	−0.767844	−	0.767844i	0.209883	−	0.977727i	$-0.432692\pi$
$409$	−15.5287	−	15.5287i	−0.767844	−	0.767844i	−0.977727	+	0.209883i	$0.932692\pi$
$410$		0			0
$411$		−	3.98904i		−	0.196765i
$412$		0			0
$413$	−23.2142	+	23.2142i	−1.14230	+	1.14230i
$414$		0			0
$415$	7.50161	+	16.2984i	0.368240	+	0.800057i
$416$		0			0
$417$	19.3043			0.945337
$418$		0			0
$419$	33.8996			1.65610			0.828052	−	0.560651i	$-0.189449\pi$
$419$	33.8996			1.65610			0.828052	+	0.560651i	$0.189449\pi$
$420$		0			0
$421$	9.15396	+	9.15396i	0.446137	+	0.446137i	0.894068	−	0.447931i	$-0.147839\pi$
$421$	9.15396	+	9.15396i	0.446137	+	0.446137i	−0.447931	+	0.894068i	$0.647839\pi$
$422$		0			0
$423$			16.0998i			0.782797i
$424$		0			0
$425$	−25.6120	−	21.9288i	−1.24236	−	1.06371i
$426$		0			0
$427$	−8.87892			−0.429681
$428$		0			0
$429$		−	0.415643i		−	0.0200675i
$430$		0			0
$431$	−18.7112			−0.901285			−0.450643	−	0.892705i	$-0.648805\pi$
$431$	−18.7112			−0.901285			−0.450643	+	0.892705i	$0.648805\pi$
$432$		0			0
$433$	−16.8981			−0.812070			−0.406035	−	0.913857i	$-0.633089\pi$
$433$	−16.8981			−0.812070			−0.406035	+	0.913857i	$0.633089\pi$
$434$		0			0
$435$	11.8285	−	1.82069i	0.567134	−	0.0872954i
$436$		0			0
$437$	2.37826			0.113767
$438$		0			0
$439$	−28.7266			−1.37104			−0.685522	−	0.728051i	$-0.740426\pi$
$439$	−28.7266			−1.37104			−0.685522	+	0.728051i	$0.740426\pi$
$440$		0			0
$441$		−	3.56927i		−	0.169965i
$442$		0			0
$443$	0.238897			0.0113503			0.00567516	−	0.999984i	$-0.498194\pi$
$443$	0.238897			0.0113503			0.00567516	+	0.999984i	$0.498194\pi$
$444$		0			0
$445$	−10.1443	+	4.66906i	−0.480884	+	0.221335i
$446$		0			0
$447$			1.23102i			0.0582251i
$448$		0			0
$449$	2.41413	+	2.41413i	0.113930	+	0.113930i	0.761773	−	0.647844i	$-0.224329\pi$
$449$	2.41413	+	2.41413i	0.113930	+	0.113930i	−0.647844	+	0.761773i	$0.724329\pi$
$450$		0			0
$451$	0.879792			0.0414278
$452$		0			0
$453$	10.7374			0.504489
$454$		0			0
$455$	−7.17878	−	2.65337i	−0.336546	−	0.124392i
$456$		0			0
$457$	−19.7132	+	19.7132i	−0.922143	+	0.922143i	−0.997181	−	0.0750375i	$-0.976092\pi$
$457$	−19.7132	+	19.7132i	−0.922143	+	0.922143i	0.0750375	+	0.997181i	$0.476092\pi$
$458$		0			0
$459$		−	33.5925i		−	1.56796i
$460$		0			0
$461$	16.2945	+	16.2945i	0.758911	+	0.758911i	0.976124	−	0.217213i	$-0.0696967\pi$
$461$	16.2945	+	16.2945i	0.758911	+	0.758911i	−0.217213	+	0.976124i	$0.569697\pi$
$462$		0			0
$463$	−5.65604	−	5.65604i	−0.262859	−	0.262859i	0.563356	−	0.826214i	$-0.309510\pi$
$463$	−5.65604	−	5.65604i	−0.262859	−	0.262859i	−0.826214	+	0.563356i	$0.809510\pi$
$464$		0			0
$465$	−2.62200	+	1.20682i	−0.121592	+	0.0559648i
$466$		0			0
$467$	−10.8150			−0.500461			−0.250230	−	0.968186i	$-0.580506\pi$
$467$	−10.8150			−0.500461			−0.250230	+	0.968186i	$0.580506\pi$
$468$		0			0
$469$	−14.1437			−0.653093
$470$		0			0
$471$	−1.52908			−0.0704563
$472$		0			0
$473$	1.49012	+	1.49012i	0.0685158	+	0.0685158i
$474$		0			0
$475$	0.598548	+	7.72583i	0.0274633	+	0.354486i
$476$		0			0
$477$	16.6783	−	16.6783i	0.763649	−	0.763649i
$478$		0			0
$479$	18.2586	−	18.2586i	0.834256	−	0.834256i	−0.153840	−	0.988096i	$-0.549164\pi$
$479$	18.2586	−	18.2586i	0.834256	−	0.834256i	0.988096	+	0.153840i	$0.0491640\pi$
$480$		0			0
$481$	−4.85391	+	4.85391i	−0.221319	+	0.221319i
$482$		0			0
$483$			3.48665i			0.158648i
$484$		0			0
$485$	17.1001	+	6.32043i	0.776476	+	0.286996i
$486$		0			0
$487$	−19.5462	−	19.5462i	−0.885724	−	0.885724i	0.108385	−	0.994109i	$-0.465432\pi$
$487$	−19.5462	−	19.5462i	−0.885724	−	0.885724i	−0.994109	+	0.108385i	$0.965432\pi$
$488$		0			0
$489$		−	19.8821i		−	0.899102i
$490$		0			0
$491$	9.31006	+	9.31006i	0.420157	+	0.420157i	0.885258	−	0.465101i	$-0.153982\pi$
$491$	9.31006	+	9.31006i	0.420157	+	0.420157i	−0.465101	+	0.885258i	$0.653982\pi$
$492$		0			0
$493$	−31.7505	+	17.6253i	−1.42997	+	0.793803i
$494$		0			0
$495$	0.525479	+	1.14168i	0.0236185	+	0.0513149i
$496$		0			0
$497$	−13.1295	+	13.1295i	−0.588939	+	0.588939i
$498$		0			0
$499$	34.7980			1.55777			0.778887	−	0.627164i	$-0.215784\pi$
$499$	34.7980			1.55777			0.778887	+	0.627164i	$0.215784\pi$
$500$		0			0
$501$	12.8417	+	12.8417i	0.573723	+	0.573723i
$502$		0			0
$503$	5.80557			0.258858			0.129429	−	0.991589i	$-0.458686\pi$
$503$	5.80557			0.258858			0.129429	+	0.991589i	$0.458686\pi$
$504$		0			0
$505$	14.3391	+	31.1538i	0.638080	+	1.38633i
$506$		0			0
$507$	−10.6925			−0.474870
$508$		0			0
$509$			19.5991i			0.868714i	0.900741	+	0.434357i	$0.143024\pi$
$509$			19.5991i			0.868714i	−0.900741	+	0.434357i	$0.856976\pi$
$510$		0			0
$511$	12.5362	+	12.5362i	0.554569	+	0.554569i
$512$		0			0
$513$	−5.45910	+	5.45910i	−0.241025	+	0.241025i
$514$		0			0
$515$	−6.01277	−	13.0637i	−0.264954	−	0.575654i
$516$		0			0
$517$	−1.58030	−	1.58030i	−0.0695017	−	0.0695017i
$518$		0			0
$519$	7.92446	−	7.92446i	0.347845	−	0.347845i
$520$		0			0
$521$			42.0368i			1.84166i	0.389959	+	0.920832i	$0.372489\pi$
$521$			42.0368i			1.84166i	−0.389959	+	0.920832i	$0.627511\pi$
$522$		0			0
$523$	−6.25373	+	6.25373i	−0.273457	+	0.273457i	−0.830490	−	0.557034i	$-0.811939\pi$
$523$	−6.25373	+	6.25373i	−0.273457	+	0.273457i	0.557034	+	0.830490i	$0.311939\pi$
$524$		0			0
$525$	−11.3265	+	0.877503i	−0.494328	+	0.0382974i
$526$		0			0
$527$	6.19307	−	6.19307i	0.269774	−	0.269774i
$528$		0			0
$529$			20.6451i			0.897614i
$530$		0			0
$531$			28.8968i			1.25402i
$532$		0			0
$533$			4.71572i			0.204261i
$534$		0			0
$535$	2.59883	−	1.19615i	0.112357	−	0.0517142i
$536$		0			0
$537$			6.39558i			0.275990i
$538$		0			0
$539$	0.350349	+	0.350349i	0.0150906	+	0.0150906i
$540$		0			0
$541$	−9.97405	+	9.97405i	−0.428818	+	0.428818i	−0.888226	−	0.459408i	$-0.848062\pi$
$541$	−9.97405	+	9.97405i	−0.428818	+	0.428818i	0.459408	+	0.888226i	$0.348062\pi$
$542$		0			0
$543$			4.28236i			0.183774i
$544$		0			0
$545$	−7.76000	+	20.9949i	−0.332402	+	0.899324i
$546$		0			0
$547$	−21.5172	−	21.5172i	−0.920009	−	0.920009i	0.0770203	−	0.997030i	$-0.475459\pi$
$547$	−21.5172	−	21.5172i	−0.920009	−	0.920009i	−0.997030	+	0.0770203i	$0.975459\pi$
$548$		0			0
$549$	−5.52620	+	5.52620i	−0.235852	+	0.235852i
$550$		0			0
$551$	8.02403	+	2.29548i	0.341835	+	0.0977907i
$552$		0			0
$553$			9.19225i			0.390894i
$554$		0			0
$555$	−3.53252	+	9.55736i	−0.149947	+	0.405687i
$556$		0			0
$557$	−9.68033	+	9.68033i	−0.410169	+	0.410169i	−0.881797	−	0.471628i	$-0.843666\pi$
$557$	−9.68033	+	9.68033i	−0.410169	+	0.410169i	0.471628	+	0.881797i	$0.343666\pi$
$558$		0			0
$559$	−7.98711	+	7.98711i	−0.337819	+	0.337819i
$560$		0			0
$561$	1.32376	+	1.32376i	0.0558891	+	0.0558891i
$562$		0			0
$563$	−38.2543			−1.61223			−0.806114	−	0.591761i	$-0.798433\pi$
$563$	−38.2543			−1.61223			−0.806114	+	0.591761i	$0.798433\pi$
$564$		0			0
$565$	8.34181	−	22.5690i	0.350943	−	0.949486i
$566$		0			0
$567$	1.75496	+	1.75496i	0.0737013	+	0.0737013i
$568$		0			0
$569$	21.1865	−	21.1865i	0.888186	−	0.888186i	−0.106163	−	0.994349i	$-0.533857\pi$
$569$	21.1865	−	21.1865i	0.888186	−	0.888186i	0.994349	+	0.106163i	$0.0338566\pi$
$570$		0			0
$571$	38.9000			1.62791			0.813957	−	0.580925i	$-0.197309\pi$
$571$	38.9000			1.62791			0.813957	+	0.580925i	$0.197309\pi$
$572$		0			0
$573$	−2.67970	−	2.67970i	−0.111946	−	0.111946i
$574$		0			0
$575$	7.64988	−	0.592663i	0.319022	−	0.0247158i
$576$		0			0
$577$			11.6709i			0.485866i	0.970043	+	0.242933i	$0.0781095\pi$
$577$			11.6709i			0.485866i	−0.970043	+	0.242933i	$0.921891\pi$
$578$		0			0
$579$	−2.09407			−0.0870265
$580$		0			0
$581$	−18.3433			−0.761007
$582$		0			0
$583$			3.27419i			0.135603i
$584$		0			0
$585$	−6.11948	+	2.81659i	−0.253009	+	0.116452i
$586$		0			0
$587$	14.8952	+	14.8952i	0.614792	+	0.614792i	0.944191	−	0.329399i	$-0.106846\pi$
$587$	14.8952	+	14.8952i	0.614792	+	0.614792i	−0.329399	+	0.944191i	$0.606846\pi$
$588$		0			0
$589$	−2.01286			−0.0829386
$590$		0			0
$591$	8.77378	−	8.77378i	0.360905	−	0.360905i
$592$		0			0
$593$	28.9594	+	28.9594i	1.18922	+	1.18922i	0.977284	+	0.211934i	$0.0679762\pi$
$593$	28.9594	+	28.9594i	1.18922	+	1.18922i	0.211934	+	0.977284i	$0.432024\pi$
$594$		0			0
$595$	31.3138	−	14.4127i	1.28374	−	0.590863i
$596$		0			0
$597$	10.1788			0.416590
$598$		0			0
$599$	−33.3651	−	33.3651i	−1.36326	−	1.36326i	−0.869725	−	0.493537i	$-0.835704\pi$
$599$	−33.3651	−	33.3651i	−1.36326	−	1.36326i	−0.493537	−	0.869725i	$-0.664296\pi$
$600$		0			0
$601$	6.29536	−	6.29536i	0.256793	−	0.256793i	−0.566955	−	0.823748i	$-0.691879\pi$
$601$	6.29536	−	6.29536i	0.256793	−	0.256793i	0.823748	+	0.566955i	$0.191879\pi$
$602$		0			0
$603$	−8.80294	+	8.80294i	−0.358484	+	0.358484i
$604$		0			0
$605$	22.9076	+	8.46695i	0.931327	+	0.344231i
$606$		0			0
$607$			46.9821i			1.90695i	0.301480	+	0.953473i	$0.402519\pi$
$607$			46.9821i			1.90695i	−0.301480	+	0.953473i	$0.597481\pi$
$608$		0			0
$609$	−3.36529	+	11.7636i	−0.136369	+	0.476687i
$610$		0			0
$611$	8.47050	−	8.47050i	0.342680	−	0.342680i
$612$		0			0
$613$	−18.5597	−	18.5597i	−0.749617	−	0.749617i	0.224790	−	0.974407i	$-0.427830\pi$
$613$	−18.5597	−	18.5597i	−0.749617	−	0.749617i	−0.974407	+	0.224790i	$0.927830\pi$
$614$		0			0
$615$	2.92666	+	6.35861i	0.118014	+	0.256404i
$616$		0			0
$617$		−	45.9054i		−	1.84808i	−0.382295	−	0.924041i	$-0.624866\pi$
$617$		−	45.9054i		−	1.84808i	0.382295	−	0.924041i	$-0.375134\pi$
$618$		0			0
$619$	25.3863	−	25.3863i	1.02036	−	1.02036i	0.0205731	−	0.999788i	$-0.493451\pi$
$619$	25.3863	−	25.3863i	1.02036	−	1.02036i	0.999788	−	0.0205731i	$-0.00654908\pi$
$620$		0			0
$621$	5.40543	+	5.40543i	0.216912	+	0.216912i
$622$		0			0
$623$		−	11.4170i		−	0.457412i
$624$		0			0
$625$	3.85057	+	24.7017i	0.154023	+	0.988067i
$626$		0			0
$627$		−	0.430246i		−	0.0171824i
$628$		0			0
$629$		−	30.9178i		−	1.23278i
$630$		0			0
$631$		−	14.2527i		−	0.567391i	−0.958914	−	0.283696i	$-0.908439\pi$
$631$		−	14.2527i		−	0.567391i	0.958914	−	0.283696i	$-0.0915606\pi$
$632$		0			0
$633$	−4.21732	+	4.21732i	−0.167623	+	0.167623i
$634$		0			0
$635$	−5.18782	+	14.0358i	−0.205872	+	0.556994i
$636$		0			0
$637$	−1.87789	+	1.87789i	−0.0744046	+	0.0744046i
$638$		0			0
$639$			16.3435i			0.646539i
$640$		0			0
$641$	−13.9898	+	13.9898i	−0.552563	+	0.552563i	−0.927180	−	0.374616i	$-0.877774\pi$
$641$	−13.9898	+	13.9898i	−0.552563	+	0.552563i	0.374616	+	0.927180i	$0.377774\pi$
$642$		0			0
$643$	−9.25182	−	9.25182i	−0.364856	−	0.364856i	0.500741	−	0.865597i	$-0.333061\pi$
$643$	−9.25182	−	9.25182i	−0.364856	−	0.364856i	−0.865597	+	0.500741i	$0.833061\pi$
$644$		0			0
$645$	−5.81277	+	15.7266i	−0.228877	+	0.619235i
$646$		0			0
$647$	13.9184	−	13.9184i	0.547190	−	0.547190i	−0.378437	−	0.925627i	$-0.623538\pi$
$647$	13.9184	−	13.9184i	0.547190	−	0.547190i	0.925627	+	0.378437i	$0.123538\pi$
$648$		0			0
$649$	−2.83642	−	2.83642i	−0.111339	−	0.111339i
$650$		0			0
$651$		−	2.95096i		−	0.115657i
$652$		0			0
$653$	11.9706			0.468446			0.234223	−	0.972183i	$-0.424745\pi$
$653$	11.9706			0.468446			0.234223	+	0.972183i	$0.424745\pi$
$654$		0			0
$655$	−40.2656	+	18.5329i	−1.57331	+	0.724141i
$656$		0			0
$657$	15.6050			0.608807
$658$		0			0
$659$	−25.9396	−	25.9396i	−1.01046	−	1.01046i	−0.999945	−	0.0105167i	$-0.996652\pi$
$659$	−25.9396	−	25.9396i	−1.01046	−	1.01046i	−0.0105167	−	0.999945i	$-0.503348\pi$
$660$		0			0
$661$	−18.4630			−0.718129			−0.359065	−	0.933313i	$-0.616904\pi$
$661$	−18.4630			−0.718129			−0.359065	+	0.933313i	$0.616904\pi$
$662$		0			0
$663$	−7.09540	+	7.09540i	−0.275562	+	0.275562i
$664$		0			0
$665$	−7.43098	−	2.74659i	−0.288161	−	0.106508i
$666$		0			0
$667$	2.27291	−	7.94514i	0.0880075	−	0.307637i
$668$		0			0
$669$	−2.90988	−	2.90988i	−0.112502	−	0.112502i
$670$		0			0
$671$		−	1.08487i		−	0.0418809i
$672$		0			0
$673$	11.9323	+	11.9323i	0.459958	+	0.459958i	0.898641	−	0.438684i	$-0.144555\pi$
$673$	11.9323	+	11.9323i	0.459958	+	0.459958i	−0.438684	+	0.898641i	$0.644555\pi$
$674$		0			0
$675$	−16.1993	+	18.9201i	−0.623510	+	0.728235i
$676$		0			0
$677$		−	10.0065i		−	0.384581i	−0.981338	−	0.192291i	$-0.938408\pi$
$677$		−	10.0065i		−	0.384581i	0.981338	−	0.192291i	$-0.0615916\pi$
$678$		0			0
$679$	−13.1795	+	13.1795i	−0.505782	+	0.505782i
$680$		0			0
$681$	4.67339	−	4.67339i	0.179085	−	0.179085i
$682$		0			0
$683$	−17.8873	+	17.8873i	−0.684439	+	0.684439i	−0.960997	−	0.276558i	$-0.910806\pi$
$683$	−17.8873	+	17.8873i	−0.684439	+	0.684439i	0.276558	+	0.960997i	$0.410806\pi$
$684$		0			0
$685$	3.11145	−	8.41813i	0.118882	−	0.321640i
$686$		0			0
$687$	−15.3477	−	15.3477i	−0.585550	−	0.585550i
$688$		0			0
$689$	−17.5498			−0.668595
$690$		0			0
$691$	9.76958			0.371653			0.185826	−	0.982583i	$-0.440504\pi$
$691$	9.76958			0.371653			0.185826	+	0.982583i	$0.440504\pi$
$692$		0			0
$693$	−1.28492			−0.0488102
$694$		0			0
$695$	40.7382	+	15.0574i	1.54529	+	0.571158i
$696$		0			0
$697$	−15.0188	−	15.0188i	−0.568878	−	0.568878i
$698$		0			0
$699$	12.1676	+	12.1676i	0.460221	+	0.460221i
$700$		0			0
$701$			14.6556i			0.553534i	0.960937	+	0.276767i	$0.0892631\pi$
$701$			14.6556i			0.553534i	−0.960937	+	0.276767i	$0.910737\pi$
$702$		0			0
$703$	−5.02444	+	5.02444i	−0.189500	+	0.189500i
$704$		0			0
$705$	6.16456	−	16.6784i	0.232171	−	0.628146i
$706$		0			0
$707$	−35.0625			−1.31866
$708$		0			0
$709$	46.1907			1.73473			0.867365	−	0.497673i	$-0.165812\pi$
$709$	46.1907			1.73473			0.867365	+	0.497673i	$0.165812\pi$
$710$		0			0
$711$	5.72121	+	5.72121i	0.214562	+	0.214562i
$712$		0			0
$713$			1.99307i			0.0746412i
$714$		0			0
$715$	0.324202	−	0.877138i	0.0121245	−	0.0328031i
$716$		0			0
$717$	11.5346			0.430768
$718$		0			0
$719$		−	23.0680i		−	0.860290i	−0.902760	−	0.430145i	$-0.858462\pi$
$719$		−	23.0680i		−	0.860290i	0.902760	−	0.430145i	$-0.141538\pi$
$720$		0			0
$721$	14.7027			0.547557
$722$		0			0
$723$	−15.5545			−0.578478
$724$		0			0
$725$	26.3820	+	5.38402i	0.979805	+	0.199958i
$726$		0			0
$727$	−47.9276			−1.77754			−0.888768	−	0.458357i	$-0.848438\pi$
$727$	−47.9276			−1.77754			−0.888768	+	0.458357i	$0.848438\pi$
$728$		0			0
$729$	−12.6684			−0.469201
$730$		0			0
$731$		−	50.8753i		−	1.88169i
$732$		0			0
$733$	−31.5656			−1.16590			−0.582952	−	0.812507i	$-0.698102\pi$
$733$	−31.5656			−1.16590			−0.582952	+	0.812507i	$0.698102\pi$
$734$		0			0
$735$	−1.36667	+	3.69756i	−0.0504103	+	0.136387i
$736$		0			0
$737$		−	1.72814i		−	0.0636569i
$738$		0			0
$739$	8.21639	+	8.21639i	0.302245	+	0.302245i	0.841892	−	0.539647i	$-0.181442\pi$
$739$	8.21639	+	8.21639i	0.302245	+	0.302245i	−0.539647	+	0.841892i	$0.681442\pi$
$740$		0			0
$741$	2.30614			0.0847181
$742$		0			0
$743$	16.4911			0.605001			0.302501	−	0.953149i	$-0.402179\pi$
$743$	16.4911			0.605001			0.302501	+	0.953149i	$0.402179\pi$
$744$		0			0
$745$	−0.960192	+	2.59783i	−0.0351787	+	0.0951772i
$746$		0			0
$747$	−11.4168	+	11.4168i	−0.417717	+	0.417717i
$748$		0			0
$749$			2.92489i			0.106873i
$750$		0			0
$751$	−14.2082	−	14.2082i	−0.518463	−	0.518463i	0.398643	−	0.917106i	$-0.369481\pi$
$751$	−14.2082	−	14.2082i	−0.518463	−	0.518463i	−0.917106	+	0.398643i	$0.869481\pi$
$752$		0			0
$753$	−18.9658	−	18.9658i	−0.691152	−	0.691152i
$754$		0			0
$755$	22.6594	+	8.37519i	0.824658	+	0.304805i
$756$		0			0
$757$	33.7032			1.22496			0.612482	−	0.790485i	$-0.290171\pi$
$757$	33.7032			1.22496			0.612482	+	0.790485i	$0.290171\pi$
$758$		0			0
$759$	−0.426016			−0.0154634
$760$		0			0
$761$	−14.3051			−0.518559			−0.259280	−	0.965802i	$-0.583485\pi$
$761$	−14.3051			−0.518559			−0.259280	+	0.965802i	$0.583485\pi$
$762$		0			0
$763$	−16.1813	−	16.1813i	−0.585803	−	0.585803i
$764$		0			0
$765$	10.5192	−	28.4599i	0.380321	−	1.02897i
$766$		0			0
$767$	15.2034	−	15.2034i	0.548962	−	0.548962i
$768$		0			0
$769$	23.7936	−	23.7936i	0.858019	−	0.858019i	−0.133085	−	0.991105i	$-0.542488\pi$
$769$	23.7936	−	23.7936i	0.858019	−	0.858019i	0.991105	+	0.133085i	$0.0424884\pi$
$770$		0			0
$771$	−0.525597	+	0.525597i	−0.0189289	+	0.0189289i
$772$		0			0
$773$		−	23.3108i		−	0.838431i	−0.907887	−	0.419215i	$-0.862305\pi$
$773$		−	23.3108i		−	0.838431i	0.907887	−	0.419215i	$-0.137695\pi$
$774$		0			0
$775$	−6.47456	+	0.501607i	−0.232573	+	0.0180183i
$776$		0			0
$777$	−7.36609	−	7.36609i	−0.264257	−	0.264257i
$778$		0			0
$779$			4.88140i			0.174894i
$780$		0			0
$781$	−1.60423	−	1.60423i	−0.0574038	−	0.0574038i
$782$		0			0
$783$	13.0201	+	23.4547i	0.465302	+	0.838203i
$784$		0			0
$785$	−3.22684	−	1.19268i	−0.115171	−	0.0425687i
$786$		0			0
$787$	−5.45485	+	5.45485i	−0.194444	+	0.194444i	−0.797613	−	0.603169i	$-0.793904\pi$
$787$	−5.45485	+	5.45485i	−0.194444	+	0.194444i	0.603169	+	0.797613i	$0.293904\pi$
$788$		0			0
$789$	−10.2756			−0.365820
$790$		0			0
$791$	17.3945	+	17.3945i	0.618478	+	0.618478i
$792$		0			0
$793$	5.81495			0.206495
$794$		0			0
$795$	−23.6639	+	10.8917i	−0.839273	+	0.386289i
$796$		0			0
$797$	4.14376			0.146779			0.0733897	−	0.997303i	$-0.476618\pi$
$797$	4.14376			0.146779			0.0733897	+	0.997303i	$0.476618\pi$
$798$		0			0
$799$			53.9544i			1.90877i
$800$		0			0
$801$	−7.10588	−	7.10588i	−0.251074	−	0.251074i
$802$		0			0
$803$	−1.53174	+	1.53174i	−0.0540538	+	0.0540538i
$804$		0			0
$805$	−2.71958	+	7.35792i	−0.0958528	+	0.259333i
$806$		0			0
$807$	15.4369	+	15.4369i	0.543404	+	0.543404i
$808$		0			0
$809$	27.7649	−	27.7649i	0.976161	−	0.976161i	−0.0235611	−	0.999722i	$-0.507500\pi$
$809$	27.7649	−	27.7649i	0.976161	−	0.976161i	0.999722	+	0.0235611i	$0.00750042\pi$
$810$		0			0
$811$		−	51.5829i		−	1.81132i	−0.424005	−	0.905660i	$-0.639376\pi$
$811$		−	51.5829i		−	1.81132i	0.424005	−	0.905660i	$-0.360624\pi$
$812$		0			0
$813$	−11.2232	+	11.2232i	−0.393616	+	0.393616i
$814$		0			0
$815$	15.5081	−	41.9576i	0.543224	−	1.46971i
$816$		0			0
$817$	−8.26771	+	8.26771i	−0.289251	+	0.289251i
$818$		0			0
$819$		−	6.88725i		−	0.240660i
$820$		0			0
$821$			16.7823i			0.585707i	0.956157	+	0.292854i	$0.0946048\pi$
$821$			16.7823i			0.585707i	−0.956157	+	0.292854i	$0.905395\pi$
$822$		0			0
$823$			5.42581i			0.189132i	0.995519	+	0.0945659i	$0.0301463\pi$
$823$			5.42581i			0.189132i	−0.995519	+	0.0945659i	$0.969854\pi$
$824$		0			0
$825$	−0.107218	−	1.38392i	−0.00373284	−	0.0481821i
$826$		0			0
$827$		−	38.5626i		−	1.34095i	−0.741931	−	0.670476i	$-0.766090\pi$
$827$		−	38.5626i		−	1.34095i	0.741931	−	0.670476i	$-0.233910\pi$
$828$		0			0
$829$	8.95068	+	8.95068i	0.310870	+	0.310870i	0.845247	−	0.534377i	$-0.179454\pi$
$829$	8.95068	+	8.95068i	0.310870	+	0.310870i	−0.534377	+	0.845247i	$0.679454\pi$
$830$		0			0
$831$	7.05875	−	7.05875i	0.244865	−	0.244865i
$832$		0			0
$833$		−	11.9615i		−	0.414443i
$834$		0			0
$835$	17.0835	+	37.1164i	0.591197	+	1.28447i
$836$		0			0
$837$	−4.57494	−	4.57494i	−0.158133	−	0.158133i
$838$		0			0
$839$	26.4724	−	26.4724i	0.913928	−	0.913928i	−0.0826509	−	0.996579i	$-0.526339\pi$
$839$	26.4724	−	26.4724i	0.913928	−	0.913928i	0.996579	+	0.0826509i	$0.0263386\pi$
$840$		0			0
$841$	15.3372	−	24.6124i	0.528869	−	0.848703i
$842$		0			0
$843$		−	17.8143i		−	0.613556i
$844$		0			0
$845$	−22.5645	−	8.34014i	−0.776243	−	0.286910i
$846$		0			0
$847$	−17.6555	+	17.6555i	−0.606649	+	0.606649i
$848$		0			0
$849$	−21.1885	+	21.1885i	−0.727187	+	0.727187i
$850$		0			0
$851$	4.97504	+	4.97504i	0.170542	+	0.170542i
$852$		0			0
$853$	36.6180			1.25378			0.626889	−	0.779109i	$-0.284328\pi$
$853$	36.6180			1.25378			0.626889	+	0.779109i	$0.284328\pi$
$854$		0			0
$855$	−6.33447	+	2.91555i	−0.216634	+	0.0997095i
$856$		0			0
$857$	16.1305	+	16.1305i	0.551009	+	0.551009i	0.926732	−	0.375723i	$-0.122606\pi$
$857$	16.1305	+	16.1305i	0.551009	+	0.551009i	−0.375723	+	0.926732i	$0.622606\pi$
$858$		0			0
$859$	32.1574	−	32.1574i	1.09720	−	1.09720i	0.102461	−	0.994737i	$-0.467328\pi$
$859$	32.1574	−	32.1574i	1.09720	−	1.09720i	0.994737	−	0.102461i	$-0.0326716\pi$
$860$		0			0
$861$	−7.15638			−0.243889
$862$		0			0
$863$	−16.3149	−	16.3149i	−0.555367	−	0.555367i	0.372618	−	0.927985i	$-0.378460\pi$
$863$	−16.3149	−	16.3149i	−0.555367	−	0.555367i	−0.927985	+	0.372618i	$0.878460\pi$
$864$		0			0
$865$	22.9042	−	10.5420i	0.778766	−	0.358440i
$866$		0			0
$867$		−	28.2995i		−	0.961103i
$868$		0			0
$869$	−1.12315			−0.0381004
$870$		0			0
$871$	9.26292			0.313862
$872$		0			0
$873$			16.4057i			0.555249i
$874$		0			0
$875$	−24.5869	−	6.98284i	−0.831188	−	0.236063i
$876$		0			0
$877$	29.4977	+	29.4977i	0.996067	+	0.996067i	0.999992	−	0.00392579i	$-0.00124962\pi$
$877$	29.4977	+	29.4977i	0.996067	+	0.996067i	−0.00392579	+	0.999992i	$0.501250\pi$
$878$		0			0
$879$	20.6682			0.697120
$880$		0			0
$881$	−22.8019	+	22.8019i	−0.768215	+	0.768215i	−0.977792	−	0.209577i	$-0.932791\pi$
$881$	−22.8019	+	22.8019i	−0.768215	+	0.768215i	0.209577	+	0.977792i	$0.432791\pi$
$882$		0			0
$883$	−5.09963	−	5.09963i	−0.171616	−	0.171616i	0.616073	−	0.787689i	$-0.288723\pi$
$883$	−5.09963	−	5.09963i	−0.171616	−	0.171616i	−0.787689	+	0.616073i	$0.788723\pi$
$884$		0			0
$885$	11.0645	−	29.9355i	0.371930	−	1.00627i
$886$		0			0
$887$	37.2601			1.25107			0.625536	−	0.780195i	$-0.284880\pi$
$887$	37.2601			1.25107			0.625536	+	0.780195i	$0.284880\pi$
$888$		0			0
$889$	−10.8177	−	10.8177i	−0.362815	−	0.362815i
$890$		0			0
$891$	−0.214429	+	0.214429i	−0.00718365	+	0.00718365i
$892$		0			0
$893$	8.76809	−	8.76809i	0.293413	−	0.293413i
$894$		0			0
$895$	−4.98855	+	13.4967i	−0.166749	+	0.451145i
$896$		0			0
$897$		−	2.28346i		−	0.0762427i
$898$		0			0
$899$	−1.92370	+	6.72445i	−0.0641591	+	0.224273i
$900$		0			0
$901$	55.8934	−	55.8934i	1.86208	−	1.86208i
$902$		0			0
$903$	−12.1209	−	12.1209i	−0.403358	−	0.403358i
$904$		0			0
$905$	−3.34024	+	9.03713i	−0.111033	+	0.300404i
$906$		0			0
$907$			6.72399i			0.223266i	0.993749	+	0.111633i	$0.0356082\pi$
$907$			6.72399i			0.223266i	−0.993749	+	0.111633i	$0.964392\pi$
$908$		0			0
$909$	−21.8227	+	21.8227i	−0.723815	+	0.723815i
$910$		0			0
$911$	−11.0913	−	11.0913i	−0.367470	−	0.367470i	0.499084	−	0.866554i	$-0.333670\pi$
$911$	−11.0913	−	11.0913i	−0.367470	−	0.367470i	−0.866554	+	0.499084i	$0.833670\pi$
$912$		0			0
$913$		−	2.24127i		−	0.0741752i
$914$		0			0
$915$	7.84079	−	3.60885i	0.259209	−	0.119305i
$916$		0			0
$917$		−	45.3175i		−	1.49652i
$918$		0			0
$919$		−	0.847466i		−	0.0279553i	−0.999902	−	0.0139777i	$-0.995551\pi$
$919$		−	0.847466i		−	0.0279553i	0.999902	−	0.0139777i	$-0.00444938\pi$
$920$		0			0
$921$		−	15.1633i		−	0.499647i
$922$		0			0
$923$	8.59874	−	8.59874i	0.283031	−	0.283031i
$924$		0			0
$925$	−14.9095	+	17.4137i	−0.490220	+	0.572558i
$926$		0			0
$927$	9.15088	−	9.15088i	0.300554	−	0.300554i
$928$		0			0
$929$		−	3.38451i		−	0.111042i	−0.998458	−	0.0555212i	$-0.982318\pi$
$929$		−	3.38451i		−	0.111042i	0.998458	−	0.0555212i	$-0.0176820\pi$
$930$		0			0
$931$	−1.94386	+	1.94386i	−0.0637075	+	0.0637075i
$932$		0			0
$933$	8.25557	+	8.25557i	0.270275	+	0.270275i
$934$		0			0
$935$	1.76101	+	3.82607i	0.0575913	+	0.125126i
$936$		0			0
$937$	26.5059	−	26.5059i	0.865910	−	0.865910i	−0.126107	−	0.992017i	$-0.540248\pi$
$937$	26.5059	−	26.5059i	0.865910	−	0.865910i	0.992017	+	0.126107i	$0.0402483\pi$
$938$		0			0
$939$	−1.74582	−	1.74582i	−0.0569728	−	0.0569728i
$940$		0			0
$941$			26.7334i			0.871483i	0.900072	+	0.435742i	$0.143514\pi$
$941$			26.7334i			0.871483i	−0.900072	+	0.435742i	$0.856486\pi$
$942$		0			0
$943$	4.83341			0.157397
$944$		0			0
$945$	−10.6469	−	23.1321i	−0.346345	−	0.752488i
$946$		0			0
$947$	49.3024			1.60211			0.801056	−	0.598589i	$-0.204272\pi$
$947$	49.3024			1.60211			0.801056	+	0.598589i	$0.204272\pi$
$948$		0			0
$949$	−8.21017	−	8.21017i	−0.266514	−	0.266514i
$950$		0			0
$951$	−12.2979			−0.398788
$952$		0			0
$953$	25.7578	−	25.7578i	0.834377	−	0.834377i	−0.153735	−	0.988112i	$-0.549130\pi$
$953$	25.7578	−	25.7578i	0.834377	−	0.834377i	0.988112	+	0.153735i	$0.0491302\pi$
$954$		0			0
$955$	−3.56484	−	7.74516i	−0.115355	−	0.250627i
$956$		0			0
$957$	−1.43734	−	0.411188i	−0.0464626	−	0.0132918i
$958$		0			0
$959$	6.48806	+	6.48806i	0.209510	+	0.209510i
$960$		0			0
$961$			29.3131i			0.945585i
$962$		0			0
$963$	1.82044	+	1.82044i	0.0586627	+	0.0586627i
$964$		0			0
$965$	−4.41914	−	1.63337i	−0.142257	−	0.0525801i
$966$		0			0
$967$			30.9377i			0.994888i	0.867496	+	0.497444i	$0.165728\pi$
$967$			30.9377i			0.994888i	−0.867496	+	0.497444i	$0.834272\pi$
$968$		0			0
$969$	−7.34468	+	7.34468i	−0.235945	+	0.235945i
$970$		0			0
$971$	2.46673	−	2.46673i	0.0791611	−	0.0791611i	−0.666418	−	0.745579i	$-0.732173\pi$
$971$	2.46673	−	2.46673i	0.0791611	−	0.0791611i	0.745579	+	0.666418i	$0.232173\pi$
$972$		0			0
$973$	−31.3979	+	31.3979i	−1.00657	+	1.00657i
$974$		0			0
$975$	7.41790	−	0.574691i	0.237563	−	0.0184048i
$976$		0			0
$977$	−17.0348	−	17.0348i	−0.544992	−	0.544992i	0.379996	−	0.924988i	$-0.375925\pi$
$977$	−17.0348	−	17.0348i	−0.544992	−	0.544992i	−0.924988	+	0.379996i	$0.875925\pi$
$978$		0			0
$979$	1.39498			0.0445839
$980$		0			0
$981$	−20.1423			−0.643096
$982$		0			0
$983$	31.8443			1.01568			0.507838	−	0.861453i	$-0.330445\pi$
$983$	31.8443			1.01568			0.507838	+	0.861453i	$0.330445\pi$
$984$		0			0
$985$	25.3590	−	11.6719i	0.808004	−	0.371897i
$986$		0			0
$987$	12.8545	+	12.8545i	0.409163	+	0.409163i
$988$		0			0
$989$	8.18643	+	8.18643i	0.260313	+	0.260313i
$990$		0			0
$991$		−	57.6960i		−	1.83278i	−0.400292	−	0.916388i	$-0.631091\pi$
$991$		−	57.6960i		−	1.83278i	0.400292	−	0.916388i	$-0.368909\pi$
$992$		0			0
$993$	−3.23997	+	3.23997i	−0.102817	+	0.102817i
$994$		0			0
$995$	21.4804	+	7.93945i	0.680976	+	0.251697i
$996$		0			0
$997$	−46.7293			−1.47993			−0.739966	−	0.672644i	$-0.765158\pi$
$997$	−46.7293			−1.47993			−0.739966	+	0.672644i	$0.765158\pi$
$998$		0			0
$999$	−22.8396			−0.722614

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	580.2.j.a.17.5	✓	30
5.2	odd	4		2900.2.s.d.1293.5		30
5.3	odd	4		580.2.s.a.133.11	yes	30
5.4	even	2		2900.2.j.d.1757.11		30
29.12	odd	4		580.2.s.a.157.11	yes	30
145.12	even	4		2900.2.j.d.2593.5		30
145.99	odd	4		2900.2.s.d.157.5		30
145.128	even	4	inner	580.2.j.a.273.11	yes	30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
580.2.j.a.17.5	✓	30	1.1	even	1	trivial
580.2.j.a.273.11	yes	30	145.128	even	4	inner
580.2.s.a.133.11	yes	30	5.3	odd	4
580.2.s.a.157.11	yes	30	29.12	odd	4
2900.2.j.d.1757.11		30	5.4	even	2
2900.2.j.d.2593.5		30	145.12	even	4
2900.2.s.d.157.5		30	145.99	odd	4
2900.2.s.d.1293.5		30	5.2	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:	\( N \)	\(=\)	\( 580 = 2^{2} \cdot 5 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	580.j (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-0.993874i q^{3} +(0.775222 - 2.09739i) q^{5} +(1.61651 + 1.61651i) q^{7} +2.01221 q^{9} +(-0.197513 + 0.197513i) q^{11} +(-1.05868 - 1.05868i) q^{13} +(-2.08454 - 0.770473i) q^{15} +6.74344 q^{17} +(-1.09587 - 1.09587i) q^{19} +(1.60661 - 1.60661i) q^{21} +(-1.08510 + 1.08510i) q^{23} +(-3.79806 - 3.25188i) q^{25} -4.98151i q^{27} +(-4.70835 + 2.61369i) q^{29} +(0.918384 - 0.918384i) q^{31} +(0.196303 + 0.196303i) q^{33} +(4.64359 - 2.13729i) q^{35} -4.58488i q^{37} +(-1.05219 + 1.05219i) q^{39} +(-2.22718 - 2.22718i) q^{41} -7.54441i q^{43} +(1.55991 - 4.22039i) q^{45} +8.00102i q^{47} -1.77380i q^{49} -6.70213i q^{51} +(8.28855 - 8.28855i) q^{53} +(0.261145 + 0.567377i) q^{55} +(-1.08916 + 1.08916i) q^{57} +14.3607i q^{59} +(-2.74633 + 2.74633i) q^{61} +(3.25276 + 3.25276i) q^{63} +(-3.04117 + 1.39975i) q^{65} +(-4.37476 + 4.37476i) q^{67} +(1.07845 + 1.07845i) q^{69} +8.12214i q^{71} +7.75512 q^{73} +(-3.23196 + 3.77480i) q^{75} -0.638562 q^{77} +(2.84324 + 2.84324i) q^{79} +1.08565 q^{81} +(-5.67373 + 5.67373i) q^{83} +(5.22766 - 14.1436i) q^{85} +(2.59768 + 4.67951i) q^{87} +(-3.53138 - 3.53138i) q^{89} -3.42272i q^{91} +(-0.912759 - 0.912759i) q^{93} +(-3.14801 + 1.44892i) q^{95} +8.15306i q^{97} +(-0.397438 + 0.397438i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q - 38 q^{9} - 4 q^{11} + 6 q^{13} + 14 q^{15} + 12 q^{17} - 4 q^{21} - 2 q^{25} - 4 q^{31} - 4 q^{33} + 16 q^{35} + 12 q^{39} + 10 q^{41} - 20 q^{45} - 18 q^{53} - 2 q^{55} - 24 q^{57} - 22 q^{61} - 24 q^{63}+ \cdots - 60 q^{95}+O(q^{100}) \) 30 * q - 38 * q^9 - 4 * q^11 + 6 * q^13 + 14 * q^15 + 12 * q^17 - 4 * q^21 - 2 * q^25 - 4 * q^31 - 4 * q^33 + 16 * q^35 + 12 * q^39 + 10 * q^41 - 20 * q^45 - 18 * q^53 - 2 * q^55 - 24 * q^57 - 22 * q^61 - 24 * q^63 - 10 * q^65 - 16 * q^67 + 8 * q^69 - 20 * q^73 + 34 * q^75 + 20 * q^77 + 20 * q^79 + 70 * q^81 + 56 * q^83 + 12 * q^85 + 4 * q^87 + 6 * q^89 - 44 * q^93 - 60 * q^95

Introduction

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