LMFDB - Embedded newform 580.2.j.a.17.6

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			17.6
Character	$\chi$	$=$	580.17
Dual form			580.2.j.a.273.10

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-0.938623i q^{3} +(-2.12400 + 0.699017i) q^{5} +(0.222978 + 0.222978i) q^{7} +2.11899 q^{9} +(2.93604 - 2.93604i) q^{11} +(-2.74510 - 2.74510i) q^{13} +(0.656113 + 1.99364i) q^{15} -1.47784 q^{17} +(-1.36329 - 1.36329i) q^{19} +(0.209292 - 0.209292i) q^{21} +(2.25887 - 2.25887i) q^{23} +(4.02275 - 2.96942i) q^{25} -4.80480i q^{27} +(2.88756 - 4.54555i) q^{29} +(1.98193 - 1.98193i) q^{31} +(-2.75584 - 2.75584i) q^{33} +(-0.629470 - 0.317740i) q^{35} -5.75611i q^{37} +(-2.57661 + 2.57661i) q^{39} +(-2.97076 - 2.97076i) q^{41} -0.249211i q^{43} +(-4.50073 + 1.48121i) q^{45} +9.82124i q^{47} -6.90056i q^{49} +1.38714i q^{51} +(-7.72225 + 7.72225i) q^{53} +(-4.18381 + 8.28850i) q^{55} +(-1.27962 + 1.27962i) q^{57} -2.39231i q^{59} +(2.67445 - 2.67445i) q^{61} +(0.472487 + 0.472487i) q^{63} +(7.74946 + 3.91172i) q^{65} +(4.02141 - 4.02141i) q^{67} +(-2.12023 - 2.12023i) q^{69} +12.2153i q^{71} +4.55648 q^{73} +(-2.78717 - 3.77585i) q^{75} +1.30935 q^{77} +(2.74957 + 2.74957i) q^{79} +1.84706 q^{81} +(-3.42166 + 3.42166i) q^{83} +(3.13894 - 1.03304i) q^{85} +(-4.26656 - 2.71033i) q^{87} +(7.12209 + 7.12209i) q^{89} -1.22419i q^{91} +(-1.86028 - 1.86028i) q^{93} +(3.84859 + 1.94266i) q^{95} -14.0099i q^{97} +(6.22144 - 6.22144i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$		−	0.938623i		−	0.541915i	−0.962591	−	0.270957i	$-0.912660\pi$
$3$		−	0.938623i		−	0.541915i	0.962591	−	0.270957i	$-0.0873402\pi$
$4$		0			0
$5$	−2.12400	+	0.699017i	−0.949882	+	0.312610i
$5$	−2.12400	+	0.699017i	−0.949882	+	0.312610i
$6$		0			0
$7$	0.222978	+	0.222978i	0.0842777	+	0.0842777i	0.747989	−	0.663711i	$-0.231020\pi$
$7$	0.222978	+	0.222978i	0.0842777	+	0.0842777i	−0.663711	+	0.747989i	$0.731020\pi$
$8$		0			0
$9$	2.11899			0.706329
$10$		0			0
$11$	2.93604	−	2.93604i	0.885251	−	0.885251i	−0.108812	−	0.994062i	$-0.534705\pi$
$11$	2.93604	−	2.93604i	0.885251	−	0.885251i	0.994062	+	0.108812i	$0.0347045\pi$
$12$		0			0
$13$	−2.74510	−	2.74510i	−0.761353	−	0.761353i	0.215214	−	0.976567i	$-0.430955\pi$
$13$	−2.74510	−	2.74510i	−0.761353	−	0.761353i	−0.976567	+	0.215214i	$0.930955\pi$
$14$		0			0
$15$	0.656113	+	1.99364i	0.169408	+	0.514755i
$16$		0			0
$17$	−1.47784			−0.358430			−0.179215	−	0.983810i	$-0.557356\pi$
$17$	−1.47784			−0.358430			−0.179215	+	0.983810i	$0.557356\pi$
$18$		0			0
$19$	−1.36329	−	1.36329i	−0.312760	−	0.312760i	0.533218	−	0.845978i	$-0.320983\pi$
$19$	−1.36329	−	1.36329i	−0.312760	−	0.312760i	−0.845978	+	0.533218i	$0.820983\pi$
$20$		0			0
$21$	0.209292	−	0.209292i	0.0456713	−	0.0456713i
$22$		0			0
$23$	2.25887	−	2.25887i	0.471008	−	0.471008i	−0.431233	−	0.902241i	$-0.641921\pi$
$23$	2.25887	−	2.25887i	0.471008	−	0.471008i	0.902241	+	0.431233i	$0.141921\pi$
$24$		0			0
$25$	4.02275	−	2.96942i	0.804550	−	0.593884i
$26$		0			0
$27$		−	4.80480i		−	0.924684i
$28$		0			0
$29$	2.88756	−	4.54555i	0.536206	−	0.844087i
$29$	2.88756	−	4.54555i	0.536206	−	0.844087i
$30$		0			0
$31$	1.98193	−	1.98193i	0.355964	−	0.355964i	−0.506359	−	0.862323i	$-0.669009\pi$
$31$	1.98193	−	1.98193i	0.355964	−	0.355964i	0.862323	+	0.506359i	$0.169009\pi$
$32$		0			0
$33$	−2.75584	−	2.75584i	−0.479730	−	0.479730i
$34$		0			0
$35$	−0.629470	−	0.317740i	−0.106400	−	0.0537078i
$36$		0			0
$37$		−	5.75611i		−	0.946299i	−0.880982	−	0.473149i	$-0.843117\pi$
$37$		−	5.75611i		−	0.946299i	0.880982	−	0.473149i	$-0.156883\pi$
$38$		0			0
$39$	−2.57661	+	2.57661i	−0.412588	+	0.412588i
$40$		0			0
$41$	−2.97076	−	2.97076i	−0.463955	−	0.463955i	0.435995	−	0.899949i	$-0.356397\pi$
$41$	−2.97076	−	2.97076i	−0.463955	−	0.463955i	−0.899949	+	0.435995i	$0.856397\pi$
$42$		0			0
$43$		−	0.249211i		−	0.0380044i	−0.999819	−	0.0190022i	$-0.993951\pi$
$43$		−	0.249211i		−	0.0380044i	0.999819	−	0.0190022i	$-0.00604895\pi$
$44$		0			0
$45$	−4.50073	+	1.48121i	−0.670929	+	0.220805i
$46$		0			0
$47$			9.82124i			1.43258i	0.697805	+	0.716288i	$0.254160\pi$
$47$			9.82124i			1.43258i	−0.697805	+	0.716288i	$0.745840\pi$
$48$		0			0
$49$		−	6.90056i		−	0.985795i
$50$		0			0
$51$			1.38714i			0.194238i
$52$		0			0
$53$	−7.72225	+	7.72225i	−1.06073	+	1.06073i	−0.0627003	+	0.998032i	$0.519971\pi$
$53$	−7.72225	+	7.72225i	−1.06073	+	1.06073i	−0.998032	+	0.0627003i	$0.980029\pi$
$54$		0			0
$55$	−4.18381	+	8.28850i	−0.564145	+	1.11762i
$56$		0			0
$57$	−1.27962	+	1.27962i	−0.169489	+	0.169489i
$58$		0			0
$59$		−	2.39231i		−	0.311452i	−0.987800	−	0.155726i	$-0.950228\pi$
$59$		−	2.39231i		−	0.311452i	0.987800	−	0.155726i	$-0.0497717\pi$
$60$		0			0
$61$	2.67445	−	2.67445i	0.342428	−	0.342428i	−0.514851	−	0.857279i	$-0.672153\pi$
$61$	2.67445	−	2.67445i	0.342428	−	0.342428i	0.857279	+	0.514851i	$0.172153\pi$
$62$		0			0
$63$	0.472487	+	0.472487i	0.0595278	+	0.0595278i
$64$		0			0
$65$	7.74946	+	3.91172i	0.961202	+	0.485189i
$66$		0			0
$67$	4.02141	−	4.02141i	0.491293	−	0.491293i	−0.417421	−	0.908713i	$-0.637066\pi$
$67$	4.02141	−	4.02141i	0.491293	−	0.491293i	0.908713	+	0.417421i	$0.137066\pi$
$68$		0			0
$69$	−2.12023	−	2.12023i	−0.255246	−	0.255246i
$70$		0			0
$71$			12.2153i			1.44969i	0.688911	+	0.724846i	$0.258089\pi$
$71$			12.2153i			1.44969i	−0.688911	+	0.724846i	$0.741911\pi$
$72$		0			0
$73$	4.55648			0.533295			0.266648	−	0.963794i	$-0.414084\pi$
$73$	4.55648			0.533295			0.266648	+	0.963794i	$0.414084\pi$
$74$		0			0
$75$	−2.78717	−	3.77585i	−0.321835	−	0.435998i
$76$		0			0
$77$	1.30935			0.149214
$78$		0			0
$79$	2.74957	+	2.74957i	0.309351	+	0.309351i	0.844658	−	0.535307i	$-0.179804\pi$
$79$	2.74957	+	2.74957i	0.309351	+	0.309351i	−0.535307	+	0.844658i	$0.679804\pi$
$80$		0			0
$81$	1.84706			0.205229
$82$		0			0
$83$	−3.42166	+	3.42166i	−0.375575	+	0.375575i	−0.869503	−	0.493928i	$-0.835561\pi$
$83$	−3.42166	+	3.42166i	−0.375575	+	0.375575i	0.493928	+	0.869503i	$0.335561\pi$
$84$		0			0
$85$	3.13894	−	1.03304i	0.340466	−	0.112049i
$86$		0			0
$87$	−4.26656	−	2.71033i	−0.457423	−	0.290578i
$88$		0			0
$89$	7.12209	+	7.12209i	0.754940	+	0.754940i	0.975397	−	0.220457i	$-0.0707549\pi$
$89$	7.12209	+	7.12209i	0.754940	+	0.754940i	−0.220457	+	0.975397i	$0.570755\pi$
$90$		0			0
$91$		−	1.22419i		−	0.128330i
$92$		0			0
$93$	−1.86028	−	1.86028i	−0.192902	−	0.192902i
$94$		0			0
$95$	3.84859	+	1.94266i	0.394857	+	0.199313i
$96$		0			0
$97$		−	14.0099i		−	1.42249i	−0.702944	−	0.711246i	$-0.748131\pi$
$97$		−	14.0099i		−	1.42249i	0.702944	−	0.711246i	$-0.251869\pi$
$98$		0			0
$99$	6.22144	−	6.22144i	0.625278	−	0.625278i
$100$		0			0
$101$	−5.50418	+	5.50418i	−0.547686	+	0.547686i	−0.925771	−	0.378085i	$-0.876583\pi$
$101$	−5.50418	+	5.50418i	−0.547686	+	0.547686i	0.378085	+	0.925771i	$0.376583\pi$
$102$		0			0
$103$	−12.7862	+	12.7862i	−1.25986	+	1.25986i	−0.308707	+	0.951157i	$0.599896\pi$
$103$	−12.7862	+	12.7862i	−1.25986	+	1.25986i	−0.951157	+	0.308707i	$0.900104\pi$
$104$		0			0
$105$	−0.298238	+	0.590836i	−0.0291051	+	0.0576597i
$106$		0			0
$107$	7.36816	+	7.36816i	0.712307	+	0.712307i	0.967017	−	0.254710i	$-0.0819801\pi$
$107$	7.36816	+	7.36816i	0.712307	+	0.712307i	−0.254710	+	0.967017i	$0.581980\pi$
$108$		0			0
$109$	15.1584			1.45191			0.725957	−	0.687741i	$-0.241397\pi$
$109$	15.1584			1.45191			0.725957	+	0.687741i	$0.241397\pi$
$110$		0			0
$111$	−5.40282			−0.512813
$112$		0			0
$113$	−3.46580			−0.326036			−0.163018	−	0.986623i	$-0.552123\pi$
$113$	−3.46580			−0.326036			−0.163018	+	0.986623i	$0.552123\pi$
$114$		0			0
$115$	−3.21886	+	6.37684i	−0.300160	+	0.594643i
$116$		0			0
$117$	−5.81682	−	5.81682i	−0.537766	−	0.537766i
$118$		0			0
$119$	−0.329527	−	0.329527i	−0.0302076	−	0.0302076i
$120$		0			0
$121$		−	6.24072i		−	0.567338i
$122$		0			0
$123$	−2.78842	+	2.78842i	−0.251424	+	0.251424i
$124$		0			0
$125$	−6.46865	+	9.11902i	−0.578574	+	0.815630i
$126$		0			0
$127$	5.90337			0.523839			0.261920	−	0.965090i	$-0.415645\pi$
$127$	5.90337			0.523839			0.261920	+	0.965090i	$0.415645\pi$
$128$		0			0
$129$	−0.233916			−0.0205951
$130$		0			0
$131$	13.2842	+	13.2842i	1.16065	+	1.16065i	0.984335	+	0.176311i	$0.0564163\pi$
$131$	13.2842	+	13.2842i	1.16065	+	1.16065i	0.176311	+	0.984335i	$0.443584\pi$
$132$		0			0
$133$		−	0.607967i		−	0.0527174i
$134$		0			0
$135$	3.35863	+	10.2054i	0.289065	+	0.878341i
$136$		0			0
$137$	−4.66035			−0.398161			−0.199080	−	0.979983i	$-0.563795\pi$
$137$	−4.66035			−0.398161			−0.199080	+	0.979983i	$0.563795\pi$
$138$		0			0
$139$		−	2.37926i		−	0.201806i	−0.994896	−	0.100903i	$-0.967827\pi$
$139$		−	2.37926i		−	0.201806i	0.994896	−	0.100903i	$-0.0321732\pi$
$140$		0			0
$141$	9.21845			0.776334
$142$		0			0
$143$	−16.1195			−1.34798
$144$		0			0
$145$	−2.95577	+	11.6732i	−0.245463	+	0.969406i
$146$		0			0
$147$	−6.47703			−0.534216
$148$		0			0
$149$	10.3036			0.844100			0.422050	−	0.906572i	$-0.361311\pi$
$149$	10.3036			0.844100			0.422050	+	0.906572i	$0.361311\pi$
$150$		0			0
$151$			16.1315i			1.31276i	0.754431	+	0.656380i	$0.227913\pi$
$151$			16.1315i			1.31276i	−0.754431	+	0.656380i	$0.772087\pi$
$152$		0			0
$153$	−3.13153			−0.253169
$154$		0			0
$155$	−2.82421	+	5.59501i	−0.226846	+	0.449402i
$156$		0			0
$157$		−	14.9682i		−	1.19459i	−0.802021	−	0.597295i	$-0.796242\pi$
$157$		−	14.9682i		−	1.19459i	0.802021	−	0.597295i	$-0.203758\pi$
$158$		0			0
$159$	7.24829	+	7.24829i	0.574826	+	0.574826i
$160$		0			0
$161$	1.00736			0.0793909
$162$		0			0
$163$	0.434439			0.0340279			0.0170140	−	0.999855i	$-0.494584\pi$
$163$	0.434439			0.0340279			0.0170140	+	0.999855i	$0.494584\pi$
$164$		0			0
$165$	7.77978	+	3.92703i	0.605655	+	0.305719i
$166$		0			0
$167$	4.50274	−	4.50274i	0.348432	−	0.348432i	−0.511093	−	0.859525i	$-0.670759\pi$
$167$	4.50274	−	4.50274i	0.348432	−	0.348432i	0.859525	+	0.511093i	$0.170759\pi$
$168$		0			0
$169$			2.07113i			0.159318i
$170$		0			0
$171$	−2.88879	−	2.88879i	−0.220911	−	0.220911i
$172$		0			0
$173$	−11.0298	−	11.0298i	−0.838579	−	0.838579i	0.150093	−	0.988672i	$-0.452043\pi$
$173$	−11.0298	−	11.0298i	−0.838579	−	0.838579i	−0.988672	+	0.150093i	$0.952043\pi$
$174$		0			0
$175$	1.55910	+	0.234869i	0.117857	+	0.0177544i
$176$		0			0
$177$	−2.24548			−0.168780
$178$		0			0
$179$	−18.1776			−1.35865			−0.679327	−	0.733836i	$-0.737728\pi$
$179$	−18.1776			−1.35865			−0.679327	+	0.733836i	$0.737728\pi$
$180$		0			0
$181$	−15.1483			−1.12597			−0.562984	−	0.826468i	$-0.690347\pi$
$181$	−15.1483			−1.12597			−0.562984	+	0.826468i	$0.690347\pi$
$182$		0			0
$183$	−2.51030	−	2.51030i	−0.185567	−	0.185567i
$184$		0			0
$185$	4.02362	+	12.2260i	0.295822	+	0.898872i
$186$		0			0
$187$	−4.33901	+	4.33901i	−0.317300	+	0.317300i
$188$		0			0
$189$	1.07136	−	1.07136i	0.0779303	−	0.0779303i
$190$		0			0
$191$	−6.47669	+	6.47669i	−0.468637	+	0.468637i	−0.901473	−	0.432836i	$-0.857513\pi$
$191$	−6.47669	+	6.47669i	−0.468637	+	0.468637i	0.432836	+	0.901473i	$0.357513\pi$
$192$		0			0
$193$			2.72915i			0.196448i	0.995164	+	0.0982241i	$0.0313162\pi$
$193$			2.72915i			0.196448i	−0.995164	+	0.0982241i	$0.968684\pi$
$194$		0			0
$195$	3.67163	−	7.27382i	0.262931	−	0.520889i
$196$		0			0
$197$	−4.53810	−	4.53810i	−0.323326	−	0.323326i	0.526715	−	0.850042i	$-0.323423\pi$
$197$	−4.53810	−	4.53810i	−0.323326	−	0.323326i	−0.850042	+	0.526715i	$0.823423\pi$
$198$		0			0
$199$		−	8.50602i		−	0.602976i	−0.953470	−	0.301488i	$-0.902517\pi$
$199$		−	8.50602i		−	0.602976i	0.953470	−	0.301488i	$-0.0974833\pi$
$200$		0			0
$201$	−3.77459	−	3.77459i	−0.266239	−	0.266239i
$202$		0			0
$203$	1.65742	−	0.369694i	0.116328	−	0.0259475i
$204$		0			0
$205$	8.38650	+	4.23328i	0.585739	+	0.295665i
$206$		0			0
$207$	4.78652	−	4.78652i	0.332686	−	0.332686i
$208$		0			0
$209$	−8.00536			−0.553742
$210$		0			0
$211$	−3.38351	−	3.38351i	−0.232930	−	0.232930i	0.580984	−	0.813915i	$-0.302668\pi$
$211$	−3.38351	−	3.38351i	−0.232930	−	0.232930i	−0.813915	+	0.580984i	$0.802668\pi$
$212$		0			0
$213$	11.4656			0.785609
$214$		0			0
$215$	0.174203	+	0.529325i	0.0118805	+	0.0360997i
$216$		0			0
$217$	0.883851			0.0599997
$218$		0			0
$219$		−	4.27682i		−	0.289001i
$220$		0			0
$221$	4.05683	+	4.05683i	0.272892	+	0.272892i
$222$		0			0
$223$	−13.8509	+	13.8509i	−0.927525	+	0.927525i	−0.997546	−	0.0700206i	$-0.977694\pi$
$223$	−13.8509	+	13.8509i	−0.927525	+	0.927525i	0.0700206	+	0.997546i	$0.477694\pi$
$224$		0			0
$225$	8.52415	−	6.29216i	0.568277	−	0.419478i
$226$		0			0
$227$	13.9160	+	13.9160i	0.923635	+	0.923635i	0.997284	−	0.0736493i	$-0.0234645\pi$
$227$	13.9160	+	13.9160i	0.923635	+	0.923635i	−0.0736493	+	0.997284i	$0.523465\pi$
$228$		0			0
$229$	−0.819413	+	0.819413i	−0.0541483	+	0.0541483i	−0.733662	−	0.679514i	$-0.762191\pi$
$229$	−0.819413	+	0.819413i	−0.0541483	+	0.0541483i	0.679514	+	0.733662i	$0.262191\pi$
$230$		0			0
$231$		−	1.22898i		−	0.0808612i
$232$		0			0
$233$	4.47190	−	4.47190i	0.292964	−	0.292964i	−0.545286	−	0.838250i	$-0.683579\pi$
$233$	4.47190	−	4.47190i	0.292964	−	0.292964i	0.838250	+	0.545286i	$0.183579\pi$
$234$		0			0
$235$	−6.86521	−	20.8603i	−0.447837	−	1.36078i
$236$		0			0
$237$	2.58081	−	2.58081i	0.167642	−	0.167642i
$238$		0			0
$239$		−	28.4692i		−	1.84152i	−0.390132	−	0.920759i	$-0.627571\pi$
$239$		−	28.4692i		−	1.84152i	0.390132	−	0.920759i	$-0.372429\pi$
$240$		0			0
$241$			21.5356i			1.38723i	0.720347	+	0.693614i	$0.243983\pi$
$241$			21.5356i			1.38723i	−0.720347	+	0.693614i	$0.756017\pi$
$242$		0			0
$243$		−	16.1481i		−	1.03590i
$244$		0			0
$245$	4.82361	+	14.6568i	0.308169	+	0.936388i
$246$		0			0
$247$			7.48473i			0.476242i
$248$		0			0
$249$	3.21165	+	3.21165i	0.203530	+	0.203530i
$250$		0			0
$251$	17.0325	−	17.0325i	1.07508	−	1.07508i	0.0781409	−	0.996942i	$-0.475102\pi$
$251$	17.0325	−	17.0325i	1.07508	−	1.07508i	0.996942	−	0.0781409i	$-0.0248984\pi$
$252$		0			0
$253$		−	13.2643i		−	0.833920i
$254$		0			0
$255$	−0.969633	−	2.94628i	−0.0607208	−	0.184503i
$256$		0			0
$257$	−1.40755	−	1.40755i	−0.0878003	−	0.0878003i	0.661843	−	0.749643i	$-0.269775\pi$
$257$	−1.40755	−	1.40755i	−0.0878003	−	0.0878003i	−0.749643	+	0.661843i	$0.769775\pi$
$258$		0			0
$259$	1.28349	−	1.28349i	0.0797519	−	0.0797519i
$260$		0			0
$261$	6.11870	−	9.63195i	0.378738	−	0.596203i
$262$		0			0
$263$		−	8.92579i		−	0.550388i	−0.961389	−	0.275194i	$-0.911258\pi$
$263$		−	8.92579i		−	0.550388i	0.961389	−	0.275194i	$-0.0887421\pi$
$264$		0			0
$265$	11.0041	−	21.8000i	0.675975	−	1.33917i
$266$		0			0
$267$	6.68496	−	6.68496i	0.409113	−	0.409113i
$268$		0			0
$269$	−14.2650	+	14.2650i	−0.869751	+	0.869751i	−0.992445	−	0.122694i	$-0.960847\pi$
$269$	−14.2650	+	14.2650i	−0.869751	+	0.869751i	0.122694	+	0.992445i	$0.460847\pi$
$270$		0			0
$271$	4.72633	+	4.72633i	0.287104	+	0.287104i	0.835934	−	0.548830i	$-0.184927\pi$
$271$	4.72633	+	4.72633i	0.287104	+	0.287104i	−0.548830	+	0.835934i	$0.684927\pi$
$272$		0			0
$273$	−1.14906			−0.0695440
$274$		0			0
$275$	3.09262	−	20.5293i	0.186492	−	1.23797i
$276$		0			0
$277$	−19.2669	−	19.2669i	−1.15764	−	1.15764i	−0.984983	−	0.172653i	$-0.944766\pi$
$277$	−19.2669	−	19.2669i	−1.15764	−	1.15764i	−0.172653	−	0.984983i	$-0.555234\pi$
$278$		0			0
$279$	4.19967	−	4.19967i	0.251428	−	0.251428i
$280$		0			0
$281$	22.6252			1.34971			0.674854	−	0.737952i	$-0.264207\pi$
$281$	22.6252			1.34971			0.674854	+	0.737952i	$0.264207\pi$
$282$		0			0
$283$	4.61151	+	4.61151i	0.274126	+	0.274126i	0.830759	−	0.556633i	$-0.187907\pi$
$283$	4.61151	+	4.61151i	0.274126	+	0.274126i	−0.556633	+	0.830759i	$0.687907\pi$
$284$		0			0
$285$	1.82343	−	3.61238i	0.108011	−	0.213979i
$286$		0			0
$287$		−	1.32483i		−	0.0782021i
$288$		0			0
$289$	−14.8160			−0.871528
$290$		0			0
$291$	−13.1500			−0.770869
$292$		0			0
$293$		−	1.15065i		−	0.0672218i	−0.999435	−	0.0336109i	$-0.989299\pi$
$293$		−	1.15065i		−	0.0672218i	0.999435	−	0.0336109i	$-0.0107007\pi$
$294$		0			0
$295$	1.67226	+	5.08126i	0.0973629	+	0.295842i
$296$		0			0
$297$	−14.1071	−	14.1071i	−0.818577	−	0.818577i
$298$		0			0
$299$	−12.4017			−0.717207
$300$		0			0
$301$	0.0555686	−	0.0555686i	0.00320292	−	0.00320292i
$302$		0			0
$303$	5.16635	+	5.16635i	0.296799	+	0.296799i
$304$		0			0
$305$	−3.81104	+	7.55001i	−0.218220	+	0.432312i
$306$		0			0
$307$	30.4549			1.73816			0.869078	−	0.494675i	$-0.164713\pi$
$307$	30.4549			1.73816			0.869078	+	0.494675i	$0.164713\pi$
$308$		0			0
$309$	12.0015	+	12.0015i	0.682739	+	0.682739i
$310$		0			0
$311$	9.95976	−	9.95976i	0.564766	−	0.564766i	−0.365891	−	0.930658i	$-0.619236\pi$
$311$	9.95976	−	9.95976i	0.564766	−	0.564766i	0.930658	+	0.365891i	$0.119236\pi$
$312$		0			0
$313$	3.25532	−	3.25532i	0.184002	−	0.184002i	−0.609095	−	0.793097i	$-0.708467\pi$
$313$	3.25532	−	3.25532i	0.184002	−	0.184002i	0.793097	+	0.609095i	$0.208467\pi$
$314$		0			0
$315$	−1.33384	−	0.673286i	−0.0751533	−	0.0379354i
$316$		0			0
$317$			33.4859i			1.88075i	0.340133	+	0.940377i	$0.389528\pi$
$317$			33.4859i			1.88075i	−0.340133	+	0.940377i	$0.610472\pi$
$318$		0			0
$319$	−4.86792	−	21.8239i	−0.272551	−	1.22191i
$320$		0			0
$321$	6.91593	−	6.91593i	0.386010	−	0.386010i
$322$		0			0
$323$	2.01473	+	2.01473i	0.112102	+	0.112102i
$324$		0			0
$325$	−19.1942	−	2.89149i	−1.06470	−	0.160391i
$326$		0			0
$327$		−	14.2280i		−	0.786813i
$328$		0			0
$329$	−2.18992	+	2.18992i	−0.120734	+	0.120734i
$330$		0			0
$331$	−0.142386	−	0.142386i	−0.00782625	−	0.00782625i	0.703183	−	0.711009i	$-0.251762\pi$
$331$	−0.142386	−	0.142386i	−0.00782625	−	0.00782625i	−0.711009	+	0.703183i	$0.751762\pi$
$332$		0			0
$333$		−	12.1971i		−	0.668398i
$334$		0			0
$335$	−5.73044	+	11.3525i	−0.313087	+	0.620253i
$336$		0			0
$337$			34.2982i			1.86834i	0.356829	+	0.934170i	$0.383858\pi$
$337$			34.2982i			1.86834i	−0.356829	+	0.934170i	$0.616142\pi$
$338$		0			0
$339$			3.25309i			0.176683i
$340$		0			0
$341$		−	11.6380i		−	0.630235i
$342$		0			0
$343$	3.09952	−	3.09952i	0.167358	−	0.167358i
$344$		0			0
$345$	5.98545	+	3.02130i	0.322246	+	0.162661i
$346$		0			0
$347$	−3.30007	+	3.30007i	−0.177157	+	0.177157i	−0.790115	−	0.612958i	$-0.789979\pi$
$347$	−3.30007	+	3.30007i	−0.177157	+	0.177157i	0.612958	+	0.790115i	$0.289979\pi$
$348$		0			0
$349$		−	4.67146i		−	0.250058i	−0.992153	−	0.125029i	$-0.960098\pi$
$349$		−	4.67146i		−	0.250058i	0.992153	−	0.125029i	$-0.0399023\pi$
$350$		0			0
$351$	−13.1896	+	13.1896i	−0.704011	+	0.704011i
$352$		0			0
$353$	−6.31051	−	6.31051i	−0.335874	−	0.335874i	0.518938	−	0.854812i	$-0.326328\pi$
$353$	−6.31051	−	6.31051i	−0.335874	−	0.335874i	−0.854812	+	0.518938i	$0.826328\pi$
$354$		0			0
$355$	−8.53871	−	25.9453i	−0.453188	−	1.37704i
$356$		0			0
$357$	−0.309301	+	0.309301i	−0.0163700	+	0.0163700i
$358$		0			0
$359$	24.3848	+	24.3848i	1.28698	+	1.28698i	0.936611	+	0.350370i	$0.113944\pi$
$359$	24.3848	+	24.3848i	1.28698	+	1.28698i	0.350370	+	0.936611i	$0.386056\pi$
$360$		0			0
$361$		−	15.2829i		−	0.804362i
$362$		0			0
$363$	−5.85768			−0.307449
$364$		0			0
$365$	−9.67796	+	3.18505i	−0.506568	+	0.166713i
$366$		0			0
$367$	28.7993			1.50331			0.751655	−	0.659557i	$-0.229256\pi$
$367$	28.7993			1.50331			0.751655	+	0.659557i	$0.229256\pi$
$368$		0			0
$369$	−6.29500	−	6.29500i	−0.327704	−	0.327704i
$370$		0			0
$371$	−3.44378			−0.178792
$372$		0			0
$373$	−3.59627	+	3.59627i	−0.186208	+	0.186208i	−0.794055	−	0.607847i	$-0.792034\pi$
$373$	−3.59627	+	3.59627i	−0.186208	+	0.186208i	0.607847	+	0.794055i	$0.292034\pi$
$374$		0			0
$375$	8.55933	+	6.07163i	0.442002	+	0.313537i
$376$		0			0
$377$	−20.4046	+	4.55134i	−1.05089	+	0.234406i
$378$		0			0
$379$	−5.87606	−	5.87606i	−0.301833	−	0.301833i	0.539898	−	0.841731i	$-0.318463\pi$
$379$	−5.87606	−	5.87606i	−0.301833	−	0.301833i	−0.841731	+	0.539898i	$0.818463\pi$
$380$		0			0
$381$		−	5.54104i		−	0.283876i
$382$		0			0
$383$	5.49376	+	5.49376i	0.280718	+	0.280718i	0.833395	−	0.552677i	$-0.186394\pi$
$383$	5.49376	+	5.49376i	0.280718	+	0.280718i	−0.552677	+	0.833395i	$0.686394\pi$
$384$		0			0
$385$	−2.78105	+	0.915255i	−0.141736	+	0.0466457i
$386$		0			0
$387$		−	0.528075i		−	0.0268436i
$388$		0			0
$389$	2.77468	−	2.77468i	0.140682	−	0.140682i	−0.633258	−	0.773940i	$-0.718283\pi$
$389$	2.77468	−	2.77468i	0.140682	−	0.140682i	0.773940	+	0.633258i	$0.218283\pi$
$390$		0			0
$391$	−3.33826	+	3.33826i	−0.168823	+	0.168823i
$392$		0			0
$393$	12.4689	−	12.4689i	0.628970	−	0.628970i
$394$		0			0
$395$	−7.76209	−	3.91810i	−0.390553	−	0.197141i
$396$		0			0
$397$	8.86939	+	8.86939i	0.445142	+	0.445142i	0.893736	−	0.448594i	$-0.148075\pi$
$397$	8.86939	+	8.86939i	0.445142	+	0.445142i	−0.448594	+	0.893736i	$0.648075\pi$
$398$		0			0
$399$	−0.570652			−0.0285683
$400$		0			0
$401$	13.4693			0.672627			0.336313	−	0.941750i	$-0.390820\pi$
$401$	13.4693			0.672627			0.336313	+	0.941750i	$0.390820\pi$
$402$		0			0
$403$	−10.8812			−0.542029
$404$		0			0
$405$	−3.92315	+	1.29112i	−0.194943	+	0.0641565i
$406$		0			0
$407$	−16.9002	−	16.9002i	−0.837712	−	0.837712i
$408$		0			0
$409$	−19.1549	−	19.1549i	−0.947148	−	0.947148i	0.0515239	−	0.998672i	$-0.483592\pi$
$409$	−19.1549	−	19.1549i	−0.947148	−	0.947148i	−0.998672	+	0.0515239i	$0.983592\pi$
$410$		0			0
$411$			4.37431i			0.215769i
$412$		0			0
$413$	0.533432	−	0.533432i	0.0262485	−	0.0262485i
$414$		0			0
$415$	4.87580	−	9.65939i	0.239344	−	0.474161i
$416$		0			0
$417$	−2.23323			−0.109362
$418$		0			0
$419$	−13.8552			−0.676873			−0.338436	−	0.940989i	$-0.609898\pi$
$419$	−13.8552			−0.676873			−0.338436	+	0.940989i	$0.609898\pi$
$420$		0			0
$421$	−4.99170	−	4.99170i	−0.243281	−	0.243281i	0.574925	−	0.818206i	$-0.305031\pi$
$421$	−4.99170	−	4.99170i	−0.243281	−	0.243281i	−0.818206	+	0.574925i	$0.805031\pi$
$422$		0			0
$423$			20.8111i			1.01187i
$424$		0			0
$425$	−5.94500	+	4.38834i	−0.288375	+	0.212866i
$426$		0			0
$427$	1.19269			0.0577181
$428$		0			0
$429$			15.1301i			0.730488i
$430$		0			0
$431$	−21.1501			−1.01876			−0.509381	−	0.860541i	$-0.670126\pi$
$431$	−21.1501			−1.01876			−0.509381	+	0.860541i	$0.670126\pi$
$432$		0			0
$433$	7.38253			0.354782			0.177391	−	0.984140i	$-0.443234\pi$
$433$	7.38253			0.354782			0.177391	+	0.984140i	$0.443234\pi$
$434$		0			0
$435$	10.9567	+	2.77435i	0.525335	+	0.133020i
$436$		0			0
$437$	−6.15900			−0.294625
$438$		0			0
$439$	38.8380			1.85364			0.926819	−	0.375508i	$-0.122532\pi$
$439$	38.8380			1.85364			0.926819	+	0.375508i	$0.122532\pi$
$440$		0			0
$441$		−	14.6222i		−	0.696295i
$442$		0			0
$443$	14.9232			0.709022			0.354511	−	0.935052i	$-0.384647\pi$
$443$	14.9232			0.709022			0.354511	+	0.935052i	$0.384647\pi$
$444$		0			0
$445$	−20.1058	−	10.1489i	−0.953105	−	0.481102i
$446$		0			0
$447$		−	9.67116i		−	0.457430i
$448$		0			0
$449$	25.0464	+	25.0464i	1.18201	+	1.18201i	0.979222	+	0.202791i	$0.0650011\pi$
$449$	25.0464	+	25.0464i	1.18201	+	1.18201i	0.202791	+	0.979222i	$0.434999\pi$
$450$		0			0
$451$	−17.4446			−0.821432
$452$		0			0
$453$	15.1414			0.711403
$454$		0			0
$455$	0.855731	+	2.60019i	0.0401173	+	0.121899i
$456$		0			0
$457$	17.5600	−	17.5600i	0.821423	−	0.821423i	−0.164890	−	0.986312i	$-0.552727\pi$
$457$	17.5600	−	17.5600i	0.821423	−	0.821423i	0.986312	+	0.164890i	$0.0527268\pi$
$458$		0			0
$459$			7.10074i			0.331434i
$460$		0			0
$461$	13.8708	+	13.8708i	0.646026	+	0.646026i	0.952030	−	0.306004i	$-0.0989921\pi$
$461$	13.8708	+	13.8708i	0.646026	+	0.646026i	−0.306004	+	0.952030i	$0.598992\pi$
$462$		0			0
$463$	9.13946	+	9.13946i	0.424747	+	0.424747i	0.886834	−	0.462088i	$-0.152899\pi$
$463$	9.13946	+	9.13946i	0.424747	+	0.424747i	−0.462088	+	0.886834i	$0.652899\pi$
$464$		0			0
$465$	5.25161	+	2.65087i	0.243537	+	0.122931i
$466$		0			0
$467$	−17.6699			−0.817666			−0.408833	−	0.912609i	$-0.634064\pi$
$467$	−17.6699			−0.817666			−0.408833	+	0.912609i	$0.634064\pi$
$468$		0			0
$469$	1.79337			0.0828101
$470$		0			0
$471$	−14.0495			−0.647366
$472$		0			0
$473$	−0.731696	−	0.731696i	−0.0336434	−	0.0336434i
$474$		0			0
$475$	−9.53236	−	1.43599i	−0.437375	−	0.0658879i
$476$		0			0
$477$	−16.3633	+	16.3633i	−0.749226	+	0.749226i
$478$		0			0
$479$	−24.3123	+	24.3123i	−1.11086	+	1.11086i	−0.117825	+	0.993034i	$0.537592\pi$
$479$	−24.3123	+	24.3123i	−1.11086	+	1.11086i	−0.993034	+	0.117825i	$0.962408\pi$
$480$		0			0
$481$	−15.8011	+	15.8011i	−0.720468	+	0.720468i
$482$		0			0
$483$		−	0.945530i		−	0.0430231i
$484$		0			0
$485$	9.79316	+	29.7571i	0.444685	+	1.35120i
$486$		0			0
$487$	−17.4500	−	17.4500i	−0.790737	−	0.790737i	0.190877	−	0.981614i	$-0.438867\pi$
$487$	−17.4500	−	17.4500i	−0.790737	−	0.790737i	−0.981614	+	0.190877i	$0.938867\pi$
$488$		0			0
$489$		−	0.407775i		−	0.0184402i
$490$		0			0
$491$	−9.86833	−	9.86833i	−0.445352	−	0.445352i	0.448454	−	0.893806i	$-0.351975\pi$
$491$	−9.86833	−	9.86833i	−0.445352	−	0.445352i	−0.893806	+	0.448454i	$0.851975\pi$
$492$		0			0
$493$	−4.26736	+	6.71761i	−0.192192	+	0.302546i
$494$		0			0
$495$	−8.86544	+	17.5632i	−0.398472	+	0.789408i
$496$		0			0
$497$	−2.72375	+	2.72375i	−0.122177	+	0.122177i
$498$		0			0
$499$	15.4209			0.690333			0.345167	−	0.938541i	$-0.387822\pi$
$499$	15.4209			0.690333			0.345167	+	0.938541i	$0.387822\pi$
$500$		0			0
$501$	−4.22638	−	4.22638i	−0.188821	−	0.188821i
$502$		0			0
$503$	37.5060			1.67231			0.836156	−	0.548492i	$-0.184798\pi$
$503$	37.5060			1.67231			0.836156	+	0.548492i	$0.184798\pi$
$504$		0			0
$505$	7.84336	−	15.5384i	0.349025	−	0.691449i
$506$		0			0
$507$	1.94401			0.0863366
$508$		0			0
$509$		−	7.63901i		−	0.338593i	−0.985565	−	0.169297i	$-0.945850\pi$
$509$		−	7.63901i		−	0.338593i	0.985565	−	0.169297i	$-0.0541496\pi$
$510$		0			0
$511$	1.01599	+	1.01599i	0.0449449	+	0.0449449i
$512$		0			0
$513$	−6.55033	+	6.55033i	−0.289204	+	0.289204i
$514$		0			0
$515$	18.2202	−	36.0957i	0.802876	−	1.59057i
$516$		0			0
$517$	28.8356	+	28.8356i	1.26819	+	1.26819i
$518$		0			0
$519$	−10.3528	+	10.3528i	−0.454438	+	0.454438i
$520$		0			0
$521$			11.7721i			0.515744i	0.966179	+	0.257872i	$0.0830212\pi$
$521$			11.7721i			0.515744i	−0.966179	+	0.257872i	$0.916979\pi$
$522$		0			0
$523$	13.3897	−	13.3897i	0.585492	−	0.585492i	−0.350915	−	0.936407i	$-0.614130\pi$
$523$	13.3897	−	13.3897i	0.585492	−	0.585492i	0.936407	+	0.350915i	$0.114130\pi$
$524$		0			0
$525$	0.220454	−	1.46341i	0.00962139	−	0.0638684i
$526$		0			0
$527$	−2.92898	+	2.92898i	−0.127588	+	0.127588i
$528$		0			0
$529$			12.7950i			0.556303i
$530$		0			0
$531$		−	5.06926i		−	0.219987i
$532$		0			0
$533$			16.3101i			0.706467i
$534$		0			0
$535$	−20.8004	−	10.4995i	−0.899282	−	0.453933i
$536$		0			0
$537$			17.0619i			0.736274i
$538$		0			0
$539$	−20.2604	−	20.2604i	−0.872675	−	0.872675i
$540$		0			0
$541$	25.7779	−	25.7779i	1.10828	−	1.10828i	0.114900	−	0.993377i	$-0.463345\pi$
$541$	25.7779	−	25.7779i	1.10828	−	1.10828i	0.993377	−	0.114900i	$-0.0366547\pi$
$542$		0			0
$543$			14.2186i			0.610178i
$544$		0			0
$545$	−32.1965	+	10.5960i	−1.37915	+	0.453882i
$546$		0			0
$547$	17.3591	+	17.3591i	0.742224	+	0.742224i	0.973005	−	0.230782i	$-0.0741284\pi$
$547$	17.3591	+	17.3591i	0.742224	+	0.742224i	−0.230782	+	0.973005i	$0.574128\pi$
$548$		0			0
$549$	5.66712	−	5.66712i	0.241867	−	0.241867i
$550$		0			0
$551$	−10.1335	+	2.26032i	−0.431701	+	0.0962927i
$552$		0			0
$553$			1.22619i			0.0521428i
$554$		0			0
$555$	11.4756	−	3.77666i	0.487112	−	0.160310i
$556$		0			0
$557$	−28.9649	+	28.9649i	−1.22728	+	1.22728i	−0.262292	+	0.964989i	$0.584478\pi$
$557$	−28.9649	+	28.9649i	−1.22728	+	1.22728i	−0.964989	+	0.262292i	$0.915522\pi$
$558$		0			0
$559$	−0.684110	+	0.684110i	−0.0289348	+	0.0289348i
$560$		0			0
$561$	4.07270	+	4.07270i	0.171950	+	0.171950i
$562$		0			0
$563$	21.5921			0.909998			0.454999	−	0.890492i	$-0.349640\pi$
$563$	21.5921			0.909998			0.454999	+	0.890492i	$0.349640\pi$
$564$		0			0
$565$	7.36137	−	2.42265i	0.309695	−	0.101922i
$566$		0			0
$567$	0.411854	+	0.411854i	0.0172962	+	0.0172962i
$568$		0			0
$569$	−24.5938	+	24.5938i	−1.03103	+	1.03103i	−0.0315235	+	0.999503i	$0.510036\pi$
$569$	−24.5938	+	24.5938i	−1.03103	+	1.03103i	−0.999503	+	0.0315235i	$0.989964\pi$
$570$		0			0
$571$	−3.04961			−0.127622			−0.0638111	−	0.997962i	$-0.520326\pi$
$571$	−3.04961			−0.127622			−0.0638111	+	0.997962i	$0.520326\pi$
$572$		0			0
$573$	6.07917	+	6.07917i	0.253961	+	0.253961i
$574$		0			0
$575$	2.37934	−	15.7944i	0.0992253	−	0.658674i
$576$		0			0
$577$			41.0652i			1.70957i	0.518986	+	0.854783i	$0.326310\pi$
$577$			41.0652i			1.70957i	−0.518986	+	0.854783i	$0.673690\pi$
$578$		0			0
$579$	2.56164			0.106458
$580$		0			0
$581$	−1.52591			−0.0633053
$582$		0			0
$583$			45.3457i			1.87803i
$584$		0			0
$585$	16.4210	+	8.28888i	0.678924	+	0.342703i
$586$		0			0
$587$	2.01688	+	2.01688i	0.0832455	+	0.0832455i	0.747503	−	0.664258i	$-0.231252\pi$
$587$	2.01688	+	2.01688i	0.0832455	+	0.0832455i	−0.664258	+	0.747503i	$0.731252\pi$
$588$		0			0
$589$	−5.40388			−0.222663
$590$		0			0
$591$	−4.25957	+	4.25957i	−0.175215	+	0.175215i
$592$		0			0
$593$	10.2714	+	10.2714i	0.421797	+	0.421797i	0.885822	−	0.464025i	$-0.153595\pi$
$593$	10.2714	+	10.2714i	0.421797	+	0.421797i	−0.464025	+	0.885822i	$0.653595\pi$
$594$		0			0
$595$	0.930259	+	0.469570i	0.0381369	+	0.0192505i
$596$		0			0
$597$	−7.98395			−0.326761
$598$		0			0
$599$	8.05472	+	8.05472i	0.329107	+	0.329107i	0.852247	−	0.523140i	$-0.175240\pi$
$599$	8.05472	+	8.05472i	0.329107	+	0.329107i	−0.523140	+	0.852247i	$0.675240\pi$
$600$		0			0
$601$	−13.6509	+	13.6509i	−0.556832	+	0.556832i	−0.928404	−	0.371572i	$-0.878819\pi$
$601$	−13.6509	+	13.6509i	−0.556832	+	0.556832i	0.371572	+	0.928404i	$0.378819\pi$
$602$		0			0
$603$	8.52130	−	8.52130i	0.347014	−	0.347014i
$604$		0			0
$605$	4.36236	+	13.2553i	0.177355	+	0.538904i
$606$		0			0
$607$			7.86669i			0.319299i	0.987174	+	0.159650i	$0.0510364\pi$
$607$			7.86669i			0.319299i	−0.987174	+	0.159650i	$0.948964\pi$
$608$		0			0
$609$	−0.347004	−	1.55569i	−0.0140613	−	0.0630398i
$610$		0			0
$611$	26.9603	−	26.9603i	1.09070	−	1.09070i
$612$		0			0
$613$	12.5975	+	12.5975i	0.508807	+	0.508807i	0.914160	−	0.405353i	$-0.132851\pi$
$613$	12.5975	+	12.5975i	0.508807	+	0.508807i	−0.405353	+	0.914160i	$0.632851\pi$
$614$		0			0
$615$	3.97346	−	7.87177i	0.160225	−	0.317420i
$616$		0			0
$617$		−	27.6162i		−	1.11179i	−0.831254	−	0.555893i	$-0.812376\pi$
$617$		−	27.6162i		−	1.11179i	0.831254	−	0.555893i	$-0.187624\pi$
$618$		0			0
$619$	−19.3619	+	19.3619i	−0.778222	+	0.778222i	−0.979528	−	0.201306i	$-0.935481\pi$
$619$	−19.3619	+	19.3619i	−0.778222	+	0.778222i	0.201306	+	0.979528i	$0.435481\pi$
$620$		0			0
$621$	−10.8534	−	10.8534i	−0.435533	−	0.435533i
$622$		0			0
$623$			3.17614i			0.127249i
$624$		0			0
$625$	7.36506	−	23.8905i	0.294603	−	0.955620i
$626$		0			0
$627$			7.51402i			0.300081i
$628$		0			0
$629$			8.50663i			0.339182i
$630$		0			0
$631$		−	25.2646i		−	1.00577i	−0.864354	−	0.502884i	$-0.832272\pi$
$631$		−	25.2646i		−	1.00577i	0.864354	−	0.502884i	$-0.167728\pi$
$632$		0			0
$633$	−3.17584	+	3.17584i	−0.126228	+	0.126228i
$634$		0			0
$635$	−12.5387	+	4.12655i	−0.497585	+	0.163757i
$636$		0			0
$637$	−18.9427	+	18.9427i	−0.750538	+	0.750538i
$638$		0			0
$639$			25.8841i			1.02396i
$640$		0			0
$641$	−28.6799	+	28.6799i	−1.13279	+	1.13279i	−0.143075	+	0.989712i	$0.545699\pi$
$641$	−28.6799	+	28.6799i	−1.13279	+	1.13279i	−0.989712	+	0.143075i	$0.954301\pi$
$642$		0			0
$643$	21.1925	+	21.1925i	0.835749	+	0.835749i	0.988296	−	0.152547i	$-0.0487477\pi$
$643$	21.1925	+	21.1925i	0.835749	+	0.835749i	−0.152547	+	0.988296i	$0.548748\pi$
$644$		0			0
$645$	0.496837	−	0.163511i	0.0195629	−	0.00643824i
$646$		0			0
$647$	14.1553	−	14.1553i	0.556503	−	0.556503i	−0.371807	−	0.928310i	$-0.621262\pi$
$647$	14.1553	−	14.1553i	0.556503	−	0.556503i	0.928310	+	0.371807i	$0.121262\pi$
$648$		0			0
$649$	−7.02392	−	7.02392i	−0.275713	−	0.275713i
$650$		0			0
$651$		−	0.829604i		−	0.0325147i
$652$		0			0
$653$	10.3023			0.403158			0.201579	−	0.979472i	$-0.435393\pi$
$653$	10.3023			0.403158			0.201579	+	0.979472i	$0.435393\pi$
$654$		0			0
$655$	−37.5015	−	18.9298i	−1.46530	−	0.739647i
$656$		0			0
$657$	9.65511			0.376682
$658$		0			0
$659$	4.74515	+	4.74515i	0.184845	+	0.184845i	0.793463	−	0.608618i	$-0.208276\pi$
$659$	4.74515	+	4.74515i	0.184845	+	0.184845i	−0.608618	+	0.793463i	$0.708276\pi$
$660$		0			0
$661$	−8.62644			−0.335530			−0.167765	−	0.985827i	$-0.553655\pi$
$661$	−8.62644			−0.335530			−0.167765	+	0.985827i	$0.553655\pi$
$662$		0			0
$663$	3.80783	−	3.80783i	0.147884	−	0.147884i
$664$		0			0
$665$	0.424979	+	1.29132i	0.0164800	+	0.0500753i
$666$		0			0
$667$	−3.74518	−	16.7905i	−0.145014	−	0.650129i
$668$		0			0
$669$	13.0008	+	13.0008i	0.502639	+	0.502639i
$670$		0			0
$671$		−	15.7046i		−	0.606269i
$672$		0			0
$673$	−17.2085	−	17.2085i	−0.663339	−	0.663339i	0.292827	−	0.956165i	$-0.405404\pi$
$673$	−17.2085	−	17.2085i	−0.663339	−	0.663339i	−0.956165	+	0.292827i	$0.905404\pi$
$674$		0			0
$675$	−14.2675	−	19.3285i	−0.549156	−	0.743955i
$676$		0			0
$677$		−	22.6658i		−	0.871116i	−0.900161	−	0.435558i	$-0.856551\pi$
$677$		−	22.6658i		−	0.871116i	0.900161	−	0.435558i	$-0.143449\pi$
$678$		0			0
$679$	3.12390	−	3.12390i	0.119884	−	0.119884i
$680$		0			0
$681$	13.0618	−	13.0618i	0.500531	−	0.500531i
$682$		0			0
$683$	19.1113	−	19.1113i	0.731274	−	0.731274i	−0.239598	−	0.970872i	$-0.577016\pi$
$683$	19.1113	−	19.1113i	0.731274	−	0.731274i	0.970872	+	0.239598i	$0.0770157\pi$
$684$		0			0
$685$	9.89858	−	3.25766i	0.378205	−	0.124469i
$686$		0			0
$687$	0.769120	+	0.769120i	0.0293438	+	0.0293438i
$688$		0			0
$689$	42.3967			1.61518
$690$		0			0
$691$	−39.4653			−1.50133			−0.750665	−	0.660683i	$-0.770267\pi$
$691$	−39.4653			−1.50133			−0.750665	+	0.660683i	$0.770267\pi$
$692$		0			0
$693$	2.77449			0.105394
$694$		0			0
$695$	1.66314	+	5.05355i	0.0630866	+	0.191692i
$696$		0			0
$697$	4.39032	+	4.39032i	0.166295	+	0.166295i
$698$		0			0
$699$	−4.19743	−	4.19743i	−0.158761	−	0.158761i
$700$		0			0
$701$		−	18.7035i		−	0.706420i	−0.935544	−	0.353210i	$-0.885090\pi$
$701$		−	18.7035i		−	0.706420i	0.935544	−	0.353210i	$-0.114910\pi$
$702$		0			0
$703$	−7.84725	+	7.84725i	−0.295964	+	0.295964i
$704$		0			0
$705$	−19.5800	+	6.44385i	−0.737425	+	0.242689i
$706$		0			0
$707$	−2.45462			−0.0923155
$708$		0			0
$709$	−16.5658			−0.622142			−0.311071	−	0.950387i	$-0.600688\pi$
$709$	−16.5658			−0.622142			−0.311071	+	0.950387i	$0.600688\pi$
$710$		0			0
$711$	5.82631	+	5.82631i	0.218504	+	0.218504i
$712$		0			0
$713$		−	8.95384i		−	0.335324i
$714$		0			0
$715$	34.2377	−	11.2678i	1.28042	−	0.421391i
$716$		0			0
$717$	−26.7218			−0.997945
$718$		0			0
$719$		−	25.7451i		−	0.960128i	−0.877233	−	0.480064i	$-0.840613\pi$
$719$		−	25.7451i		−	0.960128i	0.877233	−	0.480064i	$-0.159387\pi$
$720$		0			0
$721$	−5.70209			−0.212357
$722$		0			0
$723$	20.2138			0.751759
$724$		0			0
$725$	−1.88171	−	26.8600i	−0.0698849	−	0.997555i
$726$		0			0
$727$	37.6949			1.39803			0.699013	−	0.715109i	$-0.253623\pi$
$727$	37.6949			1.39803			0.699013	+	0.715109i	$0.253623\pi$
$728$		0			0
$729$	−9.61580			−0.356141
$730$		0			0
$731$			0.368295i			0.0136219i
$732$		0			0
$733$	45.5602			1.68281			0.841403	−	0.540408i	$-0.181730\pi$
$733$	45.5602			1.68281			0.841403	+	0.540408i	$0.181730\pi$
$734$		0			0
$735$	13.7572	−	4.52755i	0.507442	−	0.167001i
$736$		0			0
$737$		−	23.6141i		−	0.869835i
$738$		0			0
$739$	−23.1855	−	23.1855i	−0.852894	−	0.852894i	0.137594	−	0.990489i	$-0.456063\pi$
$739$	−23.1855	−	23.1855i	−0.852894	−	0.852894i	−0.990489	+	0.137594i	$0.956063\pi$
$740$		0			0
$741$	7.02534			0.258082
$742$		0			0
$743$	−44.8804			−1.64650			−0.823252	−	0.567676i	$-0.807843\pi$
$743$	−44.8804			−1.64650			−0.823252	+	0.567676i	$0.807843\pi$
$744$		0			0
$745$	−21.8848	+	7.20236i	−0.801796	+	0.263874i
$746$		0			0
$747$	−7.25044	+	7.25044i	−0.265280	+	0.265280i
$748$		0			0
$749$			3.28588i			0.120063i
$750$		0			0
$751$	21.2222	+	21.2222i	0.774407	+	0.774407i	0.978874	−	0.204466i	$-0.0655459\pi$
$751$	21.2222	+	21.2222i	0.774407	+	0.774407i	−0.204466	+	0.978874i	$0.565546\pi$
$752$		0			0
$753$	−15.9871	−	15.9871i	−0.582603	−	0.582603i
$754$		0			0
$755$	−11.2762	−	34.2632i	−0.410381	−	1.24697i
$756$		0			0
$757$	19.9113			0.723688			0.361844	−	0.932239i	$-0.382147\pi$
$757$	19.9113			0.723688			0.361844	+	0.932239i	$0.382147\pi$
$758$		0			0
$759$	−12.4502			−0.451913
$760$		0			0
$761$	−3.88256			−0.140743			−0.0703714	−	0.997521i	$-0.522418\pi$
$761$	−3.88256			−0.140743			−0.0703714	+	0.997521i	$0.522418\pi$
$762$		0			0
$763$	3.37999	+	3.37999i	0.122364	+	0.122364i
$764$		0			0
$765$	6.65137	−	2.18899i	0.240481	−	0.0791431i
$766$		0			0
$767$	−6.56712	+	6.56712i	−0.237125	+	0.237125i
$768$		0			0
$769$	−20.5915	+	20.5915i	−0.742548	+	0.742548i	−0.973068	−	0.230519i	$-0.925958\pi$
$769$	−20.5915	+	20.5915i	−0.742548	+	0.742548i	0.230519	+	0.973068i	$0.425958\pi$
$770$		0			0
$771$	−1.32116	+	1.32116i	−0.0475803	+	0.0475803i
$772$		0			0
$773$		−	21.8949i		−	0.787505i	−0.919216	−	0.393753i	$-0.871177\pi$
$773$		−	21.8949i		−	0.787505i	0.919216	−	0.393753i	$-0.128823\pi$
$774$		0			0
$775$	2.08762	−	13.8580i	0.0749895	−	0.497793i
$776$		0			0
$777$	−1.20471	−	1.20471i	−0.0432187	−	0.0432187i
$778$		0			0
$779$			8.10001i			0.290213i
$780$		0			0
$781$	35.8647	+	35.8647i	1.28334	+	1.28334i
$782$		0			0
$783$	−21.8404	−	13.8742i	−0.780514	−	0.495822i
$784$		0			0
$785$	10.4630	+	31.7924i	0.373441	+	1.13472i
$786$		0			0
$787$	5.63978	−	5.63978i	0.201036	−	0.201036i	−0.599408	−	0.800444i	$-0.704597\pi$
$787$	5.63978	−	5.63978i	0.201036	−	0.201036i	0.800444	+	0.599408i	$0.204597\pi$
$788$		0			0
$789$	−8.37796			−0.298263
$790$		0			0
$791$	−0.772798	−	0.772798i	−0.0274775	−	0.0274775i
$792$		0			0
$793$	−14.6832			−0.521417
$794$		0			0
$795$	−20.4620	−	10.3287i	−0.725713	−	0.366321i
$796$		0			0
$797$	40.4892			1.43420			0.717101	−	0.696969i	$-0.245469\pi$
$797$	40.4892			1.43420			0.717101	+	0.696969i	$0.245469\pi$
$798$		0			0
$799$		−	14.5143i		−	0.513478i
$800$		0			0
$801$	15.0916	+	15.0916i	0.533235	+	0.533235i
$802$		0			0
$803$	13.3780	−	13.3780i	0.472100	−	0.472100i
$804$		0			0
$805$	−2.13963	+	0.704160i	−0.0754120	+	0.0248184i
$806$		0			0
$807$	13.3894	+	13.3894i	0.471330	+	0.471330i
$808$		0			0
$809$	9.98815	−	9.98815i	0.351165	−	0.351165i	−0.509378	−	0.860543i	$-0.670125\pi$
$809$	9.98815	−	9.98815i	0.351165	−	0.351165i	0.860543	+	0.509378i	$0.170125\pi$
$810$		0			0
$811$			48.2080i			1.69281i	0.532537	+	0.846407i	$0.321239\pi$
$811$			48.2080i			1.69281i	−0.532537	+	0.846407i	$0.678761\pi$
$812$		0			0
$813$	4.43624	−	4.43624i	0.155586	−	0.155586i
$814$		0			0
$815$	−0.922749	+	0.303680i	−0.0323225	+	0.0106375i
$816$		0			0
$817$	−0.339747	+	0.339747i	−0.0118862	+	0.0118862i
$818$		0			0
$819$		−	2.59405i		−	0.0906434i
$820$		0			0
$821$		−	46.8667i		−	1.63566i	−0.575462	−	0.817829i	$-0.695178\pi$
$821$		−	46.8667i		−	1.63566i	0.575462	−	0.817829i	$-0.304822\pi$
$822$		0			0
$823$		−	9.01038i		−	0.314082i	−0.987592	−	0.157041i	$-0.949804\pi$
$823$		−	9.01038i		−	0.314082i	0.987592	−	0.157041i	$-0.0501955\pi$
$824$		0			0
$825$	−19.2693	−	2.90281i	−0.670871	−	0.101063i
$826$		0			0
$827$			54.8553i			1.90750i	0.300595	+	0.953752i	$0.402815\pi$
$827$			54.8553i			1.90750i	−0.300595	+	0.953752i	$0.597185\pi$
$828$		0			0
$829$	−25.6050	−	25.6050i	−0.889298	−	0.889298i	0.105158	−	0.994456i	$-0.466465\pi$
$829$	−25.6050	−	25.6050i	−0.889298	−	0.889298i	−0.994456	+	0.105158i	$0.966465\pi$
$830$		0			0
$831$	−18.0844	+	18.0844i	−0.627340	+	0.627340i
$832$		0			0
$833$			10.1979i			0.353338i
$834$		0			0
$835$	−6.41633	+	12.7113i	−0.222046	+	0.439893i
$836$		0			0
$837$	−9.52276	−	9.52276i	−0.329155	−	0.329155i
$838$		0			0
$839$	9.00678	−	9.00678i	0.310949	−	0.310949i	−0.534328	−	0.845277i	$-0.679435\pi$
$839$	9.00678	−	9.00678i	0.310949	−	0.310949i	0.845277	+	0.534328i	$0.179435\pi$
$840$		0			0
$841$	−12.3240	−	26.2511i	−0.424965	−	0.905210i
$842$		0			0
$843$		−	21.2366i		−	0.731426i
$844$		0			0
$845$	−1.44775	−	4.39908i	−0.0498042	−	0.151333i
$846$		0			0
$847$	1.39154	−	1.39154i	0.0478139	−	0.0478139i
$848$		0			0
$849$	4.32847	−	4.32847i	0.148553	−	0.148553i
$850$		0			0
$851$	−13.0023	−	13.0023i	−0.445714	−	0.445714i
$852$		0			0
$853$	11.1368			0.381316			0.190658	−	0.981657i	$-0.438938\pi$
$853$	11.1368			0.381316			0.190658	+	0.981657i	$0.438938\pi$
$854$		0			0
$855$	8.15510	+	4.11648i	0.278899	+	0.140781i
$856$		0			0
$857$	−21.9212	−	21.9212i	−0.748814	−	0.748814i	0.225443	−	0.974256i	$-0.427617\pi$
$857$	−21.9212	−	21.9212i	−0.748814	−	0.748814i	−0.974256	+	0.225443i	$0.927617\pi$
$858$		0			0
$859$	−37.6528	+	37.6528i	−1.28470	+	1.28470i	−0.346735	+	0.937963i	$0.612710\pi$
$859$	−37.6528	+	37.6528i	−1.28470	+	1.28470i	−0.937963	+	0.346735i	$0.887290\pi$
$860$		0			0
$861$	−1.24351			−0.0423789
$862$		0			0
$863$	−19.4819	−	19.4819i	−0.663170	−	0.663170i	0.292956	−	0.956126i	$-0.405361\pi$
$863$	−19.4819	−	19.4819i	−0.663170	−	0.663170i	−0.956126	+	0.292956i	$0.905361\pi$
$864$		0			0
$865$	31.1373	+	15.7173i	1.05870	+	0.534403i
$866$		0			0
$867$			13.9066i			0.472294i
$868$		0			0
$869$	16.1457			0.547707
$870$		0			0
$871$	−22.0783			−0.748095
$872$		0			0
$873$		−	29.6868i		−	1.00475i
$874$		0			0
$875$	−3.47571	+	0.590975i	−0.117500	+	0.0199786i
$876$		0			0
$877$	−5.47516	−	5.47516i	−0.184883	−	0.184883i	0.608597	−	0.793480i	$-0.291733\pi$
$877$	−5.47516	−	5.47516i	−0.184883	−	0.184883i	−0.793480	+	0.608597i	$0.791733\pi$
$878$		0			0
$879$	−1.08003			−0.0364285
$880$		0			0
$881$	21.5029	−	21.5029i	0.724449	−	0.724449i	−0.245059	−	0.969508i	$-0.578807\pi$
$881$	21.5029	−	21.5029i	0.724449	−	0.724449i	0.969508	+	0.245059i	$0.0788073\pi$
$882$		0			0
$883$	−21.4012	−	21.4012i	−0.720207	−	0.720207i	0.248440	−	0.968647i	$-0.420082\pi$
$883$	−21.4012	−	21.4012i	−0.720207	−	0.720207i	−0.968647	+	0.248440i	$0.920082\pi$
$884$		0			0
$885$	4.76939	−	1.56962i	0.160321	−	0.0527623i
$886$		0			0
$887$	−19.3475			−0.649627			−0.324813	−	0.945778i	$-0.605302\pi$
$887$	−19.3475			−0.649627			−0.324813	+	0.945778i	$0.605302\pi$
$888$		0			0
$889$	1.31632	+	1.31632i	0.0441480	+	0.0441480i
$890$		0			0
$891$	5.42305	−	5.42305i	0.181679	−	0.181679i
$892$		0			0
$893$	13.3892	−	13.3892i	0.448052	−	0.448052i
$894$		0			0
$895$	38.6091	−	12.7064i	1.29056	−	0.424728i
$896$		0			0
$897$			11.6405i			0.388665i
$898$		0			0
$899$	−3.28601	−	14.7319i	−0.109594	−	0.491335i
$900$		0			0
$901$	11.4123	−	11.4123i	0.380198	−	0.380198i
$902$		0			0
$903$	−0.0521580	−	0.0521580i	−0.00173571	−	0.00173571i
$904$		0			0
$905$	32.1751	−	10.5889i	1.06954	−	0.351988i
$906$		0			0
$907$		−	25.4445i		−	0.844871i	−0.906393	−	0.422436i	$-0.861175\pi$
$907$		−	25.4445i		−	0.844871i	0.906393	−	0.422436i	$-0.138825\pi$
$908$		0			0
$909$	−11.6633	+	11.6633i	−0.386846	+	0.386846i
$910$		0			0
$911$	3.89736	+	3.89736i	0.129125	+	0.129125i	0.768716	−	0.639591i	$-0.220896\pi$
$911$	3.89736	+	3.89736i	0.129125	+	0.129125i	−0.639591	+	0.768716i	$0.720896\pi$
$912$		0			0
$913$			20.0923i			0.664957i
$914$		0			0
$915$	7.08662	+	3.57714i	0.234276	+	0.118256i
$916$		0			0
$917$			5.92416i			0.195633i
$918$		0			0
$919$			8.41705i			0.277653i	0.990317	+	0.138826i	$0.0443330\pi$
$919$			8.41705i			0.277653i	−0.990317	+	0.138826i	$0.955667\pi$
$920$		0			0
$921$		−	28.5857i		−	0.941932i
$922$		0			0
$923$	33.5322	−	33.5322i	1.10373	−	1.10373i
$924$		0			0
$925$	−17.0923	−	23.1554i	−0.561992	−	0.761345i
$926$		0			0
$927$	−27.0938	+	27.0938i	−0.889878	+	0.889878i
$928$		0			0
$929$		−	15.6189i		−	0.512439i	−0.966619	−	0.256220i	$-0.917523\pi$
$929$		−	15.6189i		−	0.512439i	0.966619	−	0.256220i	$-0.0824771\pi$
$930$		0			0
$931$	−9.40746	+	9.40746i	−0.308317	+	0.308317i
$932$		0			0
$933$	−9.34846	−	9.34846i	−0.306055	−	0.306055i
$934$		0			0
$935$	6.18302	−	12.2491i	0.202206	−	0.400589i
$936$		0			0
$937$	14.6933	−	14.6933i	0.480009	−	0.480009i	−0.425125	−	0.905134i	$-0.639770\pi$
$937$	14.6933	−	14.6933i	0.480009	−	0.480009i	0.905134	+	0.425125i	$0.139770\pi$
$938$		0			0
$939$	−3.05552	−	3.05552i	−0.0997133	−	0.0997133i
$940$		0			0
$941$			25.6971i			0.837701i	0.908055	+	0.418850i	$0.137567\pi$
$941$			25.6971i			0.837701i	−0.908055	+	0.418850i	$0.862433\pi$
$942$		0			0
$943$	−13.4211			−0.437053
$944$		0			0
$945$	−1.52668	+	3.02448i	−0.0496628	+	0.0983863i
$946$		0			0
$947$	56.9170			1.84955			0.924777	−	0.380510i	$-0.124252\pi$
$947$	56.9170			1.84955			0.924777	+	0.380510i	$0.124252\pi$
$948$		0			0
$949$	−12.5080	−	12.5080i	−0.406026	−	0.406026i
$950$		0			0
$951$	31.4306			1.01921
$952$		0			0
$953$	9.26193	−	9.26193i	0.300023	−	0.300023i	−0.540999	−	0.841023i	$-0.681954\pi$
$953$	9.26193	−	9.26193i	0.300023	−	0.300023i	0.841023	+	0.540999i	$0.181954\pi$
$954$		0			0
$955$	9.22917	−	18.2838i	0.298649	−	0.591650i
$956$		0			0
$957$	−20.4845	+	4.56915i	−0.662168	+	0.147700i
$958$		0			0
$959$	−1.03916	−	1.03916i	−0.0335561	−	0.0335561i
$960$		0			0
$961$			23.1439i			0.746579i
$962$		0			0
$963$	15.6130	+	15.6130i	0.503123	+	0.503123i
$964$		0			0
$965$	−1.90772	−	5.79671i	−0.0614116	−	0.186603i
$966$		0			0
$967$			15.7425i			0.506244i	0.967434	+	0.253122i	$0.0814574\pi$
$967$			15.7425i			0.506244i	−0.967434	+	0.253122i	$0.918543\pi$
$968$		0			0
$969$	1.89107	−	1.89107i	0.0607500	−	0.0607500i
$970$		0			0
$971$	7.94933	−	7.94933i	0.255106	−	0.255106i	−0.567954	−	0.823060i	$-0.692265\pi$
$971$	7.94933	−	7.94933i	0.255106	−	0.255106i	0.823060	+	0.567954i	$0.192265\pi$
$972$		0			0
$973$	0.530523	−	0.530523i	0.0170078	−	0.0170078i
$974$		0			0
$975$	−2.71402	+	18.0161i	−0.0869183	+	0.576978i
$976$		0			0
$977$	−6.98639	−	6.98639i	−0.223514	−	0.223514i	0.586462	−	0.809977i	$-0.300520\pi$
$977$	−6.98639	−	6.98639i	−0.223514	−	0.223514i	−0.809977	+	0.586462i	$0.800520\pi$
$978$		0			0
$979$	41.8215			1.33662
$980$		0			0
$981$	32.1205			1.02553
$982$		0			0
$983$	22.5588			0.719513			0.359757	−	0.933046i	$-0.382860\pi$
$983$	22.5588			0.719513			0.359757	+	0.933046i	$0.382860\pi$
$984$		0			0
$985$	12.8111	+	6.46672i	0.408197	+	0.206047i
$986$		0			0
$987$	2.05551	+	2.05551i	0.0654276	+	0.0654276i
$988$		0			0
$989$	−0.562937	−	0.562937i	−0.0179004	−	0.0179004i
$990$		0			0
$991$		−	0.0581784i		−	0.00184810i	−1.00000		0.000924048i	$-0.999706\pi$
$991$		−	0.0581784i		−	0.00184810i	1.00000		0.000924048i	$-0.000294134\pi$
$992$		0			0
$993$	−0.133647	+	0.133647i	−0.00424116	+	0.00424116i
$994$		0			0
$995$	5.94585	+	18.0668i	0.188496	+	0.572755i
$996$		0			0
$997$	−29.2987			−0.927899			−0.463949	−	0.885862i	$-0.653568\pi$
$997$	−29.2987			−0.927899			−0.463949	+	0.885862i	$0.653568\pi$
$998$		0			0
$999$	−27.6570			−0.875028

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	580.2.j.a.17.6	✓	30
5.2	odd	4		2900.2.s.d.1293.6		30
5.3	odd	4		580.2.s.a.133.10	yes	30
5.4	even	2		2900.2.j.d.1757.10		30
29.12	odd	4		580.2.s.a.157.10	yes	30
145.12	even	4		2900.2.j.d.2593.6		30
145.99	odd	4		2900.2.s.d.157.6		30
145.128	even	4	inner	580.2.j.a.273.10	yes	30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
580.2.j.a.17.6	✓	30	1.1	even	1	trivial
580.2.j.a.273.10	yes	30	145.128	even	4	inner
580.2.s.a.133.10	yes	30	5.3	odd	4
580.2.s.a.157.10	yes	30	29.12	odd	4
2900.2.j.d.1757.10		30	5.4	even	2
2900.2.j.d.2593.6		30	145.12	even	4
2900.2.s.d.157.6		30	145.99	odd	4
2900.2.s.d.1293.6		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)

\(f(q)\)	\(=\)	\(q-0.938623i q^{3} +(-2.12400 + 0.699017i) q^{5} +(0.222978 + 0.222978i) q^{7} +2.11899 q^{9} +(2.93604 - 2.93604i) q^{11} +(-2.74510 - 2.74510i) q^{13} +(0.656113 + 1.99364i) q^{15} -1.47784 q^{17} +(-1.36329 - 1.36329i) q^{19} +(0.209292 - 0.209292i) q^{21} +(2.25887 - 2.25887i) q^{23} +(4.02275 - 2.96942i) q^{25} -4.80480i q^{27} +(2.88756 - 4.54555i) q^{29} +(1.98193 - 1.98193i) q^{31} +(-2.75584 - 2.75584i) q^{33} +(-0.629470 - 0.317740i) q^{35} -5.75611i q^{37} +(-2.57661 + 2.57661i) q^{39} +(-2.97076 - 2.97076i) q^{41} -0.249211i q^{43} +(-4.50073 + 1.48121i) q^{45} +9.82124i q^{47} -6.90056i q^{49} +1.38714i q^{51} +(-7.72225 + 7.72225i) q^{53} +(-4.18381 + 8.28850i) q^{55} +(-1.27962 + 1.27962i) q^{57} -2.39231i q^{59} +(2.67445 - 2.67445i) q^{61} +(0.472487 + 0.472487i) q^{63} +(7.74946 + 3.91172i) q^{65} +(4.02141 - 4.02141i) q^{67} +(-2.12023 - 2.12023i) q^{69} +12.2153i q^{71} +4.55648 q^{73} +(-2.78717 - 3.77585i) q^{75} +1.30935 q^{77} +(2.74957 + 2.74957i) q^{79} +1.84706 q^{81} +(-3.42166 + 3.42166i) q^{83} +(3.13894 - 1.03304i) q^{85} +(-4.26656 - 2.71033i) q^{87} +(7.12209 + 7.12209i) q^{89} -1.22419i q^{91} +(-1.86028 - 1.86028i) q^{93} +(3.84859 + 1.94266i) q^{95} -14.0099i q^{97} +(6.22144 - 6.22144i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q - 38 q^{9} - 4 q^{11} + 6 q^{13} + 14 q^{15} + 12 q^{17} - 4 q^{21} - 2 q^{25} - 4 q^{31} - 4 q^{33} + 16 q^{35} + 12 q^{39} + 10 q^{41} - 20 q^{45} - 18 q^{53} - 2 q^{55} - 24 q^{57} - 22 q^{61} - 24 q^{63}+ \cdots - 60 q^{95}+O(q^{100}) \) 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

L-functions

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Database

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