LMFDB - Embedded newform 532.2.l.b.501.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [532,2,Mod(429,532)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(532, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 2, 4]))

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

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

chi := DirichletCharacter("532.429");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 532 = 2^{2} \cdot 7 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	532.l (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$4.24804138753$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			501.5
Character	$\chi$	$=$	532.501
Dual form			532.2.l.b.429.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q-1.07341 q^{3} +(-1.76093 + 3.05002i) q^{5} +(-1.25747 - 2.32783i) q^{7} -1.84780 q^{9} +(2.10632 - 3.64826i) q^{11} +(0.480174 - 0.831685i) q^{13} +(1.89019 - 3.27391i) q^{15} +4.91112 q^{17} +(2.82145 - 3.32256i) q^{19} +(1.34977 + 2.49870i) q^{21} +3.66925 q^{23} +(-3.70175 - 6.41162i) q^{25} +5.20366 q^{27} +(2.27123 - 3.93389i) q^{29} +(-3.20022 + 5.54294i) q^{31} +(-2.26094 + 3.91606i) q^{33} +(9.31423 + 0.263836i) q^{35} +(1.28136 + 2.21938i) q^{37} +(-0.515421 + 0.892735i) q^{39} +(-3.84650 - 6.66233i) q^{41} +(-5.27278 - 9.13272i) q^{43} +(3.25385 - 5.63583i) q^{45} -0.902080 q^{47} +(-3.83755 + 5.85433i) q^{49} -5.27162 q^{51} +(-6.91014 - 11.9687i) q^{53} +(7.41817 + 12.8486i) q^{55} +(-3.02856 + 3.56646i) q^{57} +7.62965 q^{59} -2.34374 q^{61} +(2.32355 + 4.30136i) q^{63} +(1.69110 + 2.92908i) q^{65} +(-5.49087 - 9.51046i) q^{67} -3.93859 q^{69} +(0.929896 + 1.61063i) q^{71} -9.95225 q^{73} +(3.97348 + 6.88227i) q^{75} +(-11.1411 - 0.315586i) q^{77} +(4.45483 - 7.71599i) q^{79} -0.0422331 q^{81} -0.481118 q^{83} +(-8.64814 + 14.9790i) q^{85} +(-2.43795 + 4.22265i) q^{87} +17.2609 q^{89} +(-2.53982 - 0.0719434i) q^{91} +(3.43513 - 5.94982i) q^{93} +(5.16550 + 14.4563i) q^{95} +(2.65545 + 4.59937i) q^{97} +(-3.89206 + 6.74125i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 2 q^{3} - 6 q^{5} - 6 q^{7} + 30 q^{9} + q^{11} - 7 q^{13} - 2 q^{15} - 6 q^{17} + 17 q^{19} - 18 q^{21} - 16 q^{23} - 8 q^{25} + 20 q^{27} - 22 q^{29} - 7 q^{31} + 7 q^{33} - 21 q^{35} + 9 q^{37}+ \cdots - 27 q^{99}+O(q^{100}) $ 24 * q + 2 * q^3 - 6 * q^5 - 6 * q^7 + 30 * q^9 + q^11 - 7 * q^13 - 2 * q^15 - 6 * q^17 + 17 * q^19 - 18 * q^21 - 16 * q^23 - 8 * q^25 + 20 * q^27 - 22 * q^29 - 7 * q^31 + 7 * q^33 - 21 * q^35 + 9 * q^37 + 12 * q^39 - 11 * q^41 - 9 * q^43 - 28 * q^45 - 22 * q^47 - 32 * q^49 - 16 * q^51 - 7 * q^53 - 11 * q^55 + 11 * q^57 + 16 * q^59 + 12 * q^61 + 20 * q^63 + 3 * q^65 - 27 * q^67 + 108 * q^69 - 13 * q^71 + 20 * q^73 + 25 * q^75 + 2 * q^77 - 14 * q^79 + 80 * q^81 - 12 * q^83 - 19 * q^85 + 19 * q^87 + 74 * q^89 - 21 * q^91 + 5 * q^93 + 47 * q^95 - 21 * q^97 - 27 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/532\mathbb{Z}\right)^\times$.

$n$	$267$	$381$	$477$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−1.07341			−0.619731			−0.309866	−	0.950780i	$-0.600284\pi$
$3$	−1.07341			−0.619731			−0.309866	+	0.950780i	$0.600284\pi$
$4$		0			0
$5$	−1.76093	+	3.05002i	−0.787512	+	1.36401i	0.139975	+	0.990155i	$0.455298\pi$
$5$	−1.76093	+	3.05002i	−0.787512	+	1.36401i	−0.927487	+	0.373855i	$0.878036\pi$
$6$		0			0
$7$	−1.25747	−	2.32783i	−0.475278	−	0.879836i
$7$	−1.25747	−	2.32783i	−0.475278	−	0.879836i
$8$		0			0
$9$	−1.84780			−0.615933
$10$		0			0
$11$	2.10632	−	3.64826i	0.635080	−	1.09999i	−0.351418	−	0.936218i	$-0.614301\pi$
$11$	2.10632	−	3.64826i	0.635080	−	1.09999i	0.986498	−	0.163772i	$-0.0523661\pi$
$12$		0			0
$13$	0.480174	−	0.831685i	0.133176	−	0.230668i	−0.791723	−	0.610880i	$-0.790816\pi$
$13$	0.480174	−	0.831685i	0.133176	−	0.230668i	0.924899	+	0.380212i	$0.124149\pi$
$14$		0			0
$15$	1.89019	−	3.27391i	0.488046	−	0.845320i
$16$		0			0
$17$	4.91112			1.19112			0.595561	−	0.803310i	$-0.296930\pi$
$17$	4.91112			1.19112			0.595561	+	0.803310i	$0.296930\pi$
$18$		0			0
$19$	2.82145	−	3.32256i	0.647285	−	0.762248i
$19$	2.82145	−	3.32256i	0.647285	−	0.762248i
$20$		0			0
$21$	1.34977	+	2.49870i	0.294545	+	0.545261i
$22$		0			0
$23$	3.66925			0.765091			0.382546	−	0.923937i	$-0.375047\pi$
$23$	3.66925			0.765091			0.382546	+	0.923937i	$0.375047\pi$
$24$		0			0
$25$	−3.70175	−	6.41162i	−0.740350	−	1.28232i
$26$		0			0
$27$	5.20366			1.00144
$28$		0			0
$29$	2.27123	−	3.93389i	0.421757	−	0.730504i	−0.574355	−	0.818607i	$-0.694747\pi$
$29$	2.27123	−	3.93389i	0.421757	−	0.730504i	0.996111	+	0.0881024i	$0.0280803\pi$
$30$		0			0
$31$	−3.20022	+	5.54294i	−0.574776	+	0.995541i	0.421290	+	0.906926i	$0.361577\pi$
$31$	−3.20022	+	5.54294i	−0.574776	+	0.995541i	−0.996066	+	0.0886152i	$0.971756\pi$
$32$		0			0
$33$	−2.26094	+	3.91606i	−0.393579	+	0.681698i
$34$		0			0
$35$	9.31423	+	0.263836i	1.57439	+	0.0445965i
$36$		0			0
$37$	1.28136	+	2.21938i	0.210654	+	0.364864i	0.951920	−	0.306348i	$-0.0991072\pi$
$37$	1.28136	+	2.21938i	0.210654	+	0.364864i	−0.741265	+	0.671212i	$0.765774\pi$
$38$		0			0
$39$	−0.515421	+	0.892735i	−0.0825334	+	0.142952i
$40$		0			0
$41$	−3.84650	−	6.66233i	−0.600722	−	1.04048i	−0.992712	−	0.120512i	$-0.961546\pi$
$41$	−3.84650	−	6.66233i	−0.600722	−	1.04048i	0.391990	−	0.919970i	$-0.371787\pi$
$42$		0			0
$43$	−5.27278	−	9.13272i	−0.804091	−	1.39273i	−0.916903	−	0.399110i	$-0.869319\pi$
$43$	−5.27278	−	9.13272i	−0.804091	−	1.39273i	0.112812	−	0.993616i	$-0.464014\pi$
$44$		0			0
$45$	3.25385	−	5.63583i	0.485055	−	0.840140i
$46$		0			0
$47$	−0.902080			−0.131582			−0.0657910	−	0.997833i	$-0.520957\pi$
$47$	−0.902080			−0.131582			−0.0657910	+	0.997833i	$0.520957\pi$
$48$		0			0
$49$	−3.83755	+	5.85433i	−0.548221	+	0.836333i
$50$		0			0
$51$	−5.27162			−0.738175
$52$		0			0
$53$	−6.91014	−	11.9687i	−0.949181	−	1.64403i	−0.747156	−	0.664649i	$-0.768581\pi$
$53$	−6.91014	−	11.9687i	−0.949181	−	1.64403i	−0.202025	−	0.979380i	$-0.564752\pi$
$54$		0			0
$55$	7.41817	+	12.8486i	1.00027	+	1.73251i
$56$		0			0
$57$	−3.02856	+	3.56646i	−0.401143	+	0.472389i
$58$		0			0
$59$	7.62965			0.993295			0.496648	−	0.867952i	$-0.334564\pi$
$59$	7.62965			0.993295			0.496648	+	0.867952i	$0.334564\pi$
$60$		0			0
$61$	−2.34374			−0.300086			−0.150043	−	0.988680i	$-0.547941\pi$
$61$	−2.34374			−0.300086			−0.150043	+	0.988680i	$0.547941\pi$
$62$		0			0
$63$	2.32355	+	4.30136i	0.292740	+	0.541920i
$64$		0			0
$65$	1.69110	+	2.92908i	0.209756	+	0.363307i
$66$		0			0
$67$	−5.49087	−	9.51046i	−0.670816	−	1.16189i	−0.977673	−	0.210132i	$-0.932611\pi$
$67$	−5.49087	−	9.51046i	−0.670816	−	1.16189i	0.306857	−	0.951756i	$-0.400723\pi$
$68$		0			0
$69$	−3.93859			−0.474151
$70$		0			0
$71$	0.929896	+	1.61063i	0.110358	+	0.191146i	0.915915	−	0.401373i	$-0.131467\pi$
$71$	0.929896	+	1.61063i	0.110358	+	0.191146i	−0.805556	+	0.592519i	$0.798133\pi$
$72$		0			0
$73$	−9.95225			−1.16482			−0.582411	−	0.812894i	$-0.697891\pi$
$73$	−9.95225			−1.16482			−0.582411	+	0.812894i	$0.697891\pi$
$74$		0			0
$75$	3.97348	+	6.88227i	0.458818	+	0.794696i
$76$		0			0
$77$	−11.1411	−	0.315586i	−1.26965	−	0.0359643i
$78$		0			0
$79$	4.45483	−	7.71599i	0.501207	−	0.868116i	−0.498792	−	0.866722i	$-0.666223\pi$
$79$	4.45483	−	7.71599i	0.501207	−	0.868116i	0.999999	−	0.00139443i	$-0.000443862\pi$
$80$		0			0
$81$	−0.0422331			−0.00469256
$82$		0			0
$83$	−0.481118			−0.0528096			−0.0264048	−	0.999651i	$-0.508406\pi$
$83$	−0.481118			−0.0528096			−0.0264048	+	0.999651i	$0.508406\pi$
$84$		0			0
$85$	−8.64814	+	14.9790i	−0.938022	+	1.62470i
$86$		0			0
$87$	−2.43795	+	4.22265i	−0.261376	+	0.452716i
$88$		0			0
$89$	17.2609			1.82965			0.914824	−	0.403852i	$-0.132329\pi$
$89$	17.2609			1.82965			0.914824	+	0.403852i	$0.132329\pi$
$90$		0			0
$91$	−2.53982	−	0.0719434i	−0.266246	−	0.00754171i
$92$		0			0
$93$	3.43513	−	5.94982i	0.356207	−	0.616968i
$94$		0			0
$95$	5.16550	+	14.4563i	0.529969	+	1.48318i
$96$		0			0
$97$	2.65545	+	4.59937i	0.269620	+	0.466995i	0.968764	−	0.247986i	$-0.0797686\pi$
$97$	2.65545	+	4.59937i	0.269620	+	0.466995i	−0.699144	+	0.714981i	$0.746435\pi$
$98$		0			0
$99$	−3.89206	+	6.74125i	−0.391167	+	0.677521i
$100$		0			0
$101$	−0.256882	−	0.444932i	−0.0255607	−	0.0442724i	0.852962	−	0.521973i	$-0.174804\pi$
$101$	−0.256882	−	0.444932i	−0.0255607	−	0.0442724i	−0.878523	+	0.477700i	$0.841470\pi$
$102$		0			0
$103$	1.97370	+	3.41855i	0.194474	+	0.336840i	0.946728	−	0.322034i	$-0.104367\pi$
$103$	1.97370	+	3.41855i	0.194474	+	0.336840i	−0.752254	+	0.658874i	$0.771033\pi$
$104$		0			0
$105$	−9.99795	−	0.283203i	−0.975700	−	0.0276378i
$106$		0			0
$107$	6.55897	+	11.3605i	0.634080	+	1.09826i	0.986709	+	0.162496i	$0.0519543\pi$
$107$	6.55897	+	11.3605i	0.634080	+	1.09826i	−0.352629	+	0.935763i	$0.614712\pi$
$108$		0			0
$109$	13.5930			1.30197			0.650986	−	0.759090i	$-0.274356\pi$
$109$	13.5930			1.30197			0.650986	+	0.759090i	$0.274356\pi$
$110$		0			0
$111$	−1.37542	−	2.38230i	−0.130549	−	0.226118i
$112$		0			0
$113$	−12.1668			−1.14456			−0.572278	−	0.820060i	$-0.693940\pi$
$113$	−12.1668			−1.14456			−0.572278	+	0.820060i	$0.693940\pi$
$114$		0			0
$115$	−6.46129	+	11.1913i	−0.602518	+	1.04359i
$116$		0			0
$117$	−0.887265	+	1.53679i	−0.0820277	+	0.142076i
$118$		0			0
$119$	−6.17557	−	11.4322i	−0.566114	−	1.04799i
$120$		0			0
$121$	−3.37318	−	5.84252i	−0.306653	−	0.531138i
$122$		0			0
$123$	4.12885	+	7.15138i	0.372286	+	0.644818i
$124$		0			0
$125$	8.46478			0.757113
$126$		0			0
$127$	−8.99904	+	15.5868i	−0.798536	+	1.38310i	0.122033	+	0.992526i	$0.461058\pi$
$127$	−8.99904	+	15.5868i	−0.798536	+	1.38310i	−0.920569	+	0.390579i	$0.872275\pi$
$128$		0			0
$129$	5.65983	+	9.80311i	0.498320	+	0.863116i
$130$		0			0
$131$	10.6005	−	18.3606i	0.926168	−	1.60417i	0.136497	−	0.990640i	$-0.456416\pi$
$131$	10.6005	−	18.3606i	0.926168	−	1.60417i	0.789671	−	0.613530i	$-0.210251\pi$
$132$		0			0
$133$	−11.2822	−	2.38983i	−0.978293	−	0.207225i
$134$		0			0
$135$	−9.16327	+	15.8713i	−0.788649	+	1.36598i
$136$		0			0
$137$	−4.16789	−	7.21901i	−0.356087	−	0.616761i	0.631216	−	0.775607i	$-0.282556\pi$
$137$	−4.16789	−	7.21901i	−0.356087	−	0.616761i	−0.987303	+	0.158846i	$0.949223\pi$
$138$		0			0
$139$	3.11485	−	5.39507i	0.264198	−	0.457604i	−0.703155	−	0.711036i	$-0.748226\pi$
$139$	3.11485	−	5.39507i	0.264198	−	0.457604i	0.967353	+	0.253432i	$0.0815595\pi$
$140$		0			0
$141$	0.968298			0.0815454
$142$		0			0
$143$	−2.02280	−	3.50359i	−0.169155	−	0.292985i
$144$		0			0
$145$	7.99895	+	13.8546i	0.664277	+	1.15056i
$146$		0			0
$147$	4.11925	−	6.28407i	0.339750	−	0.518302i
$148$		0			0
$149$	−4.77180	+	8.26501i	−0.390921	+	0.677096i	−0.992571	−	0.121664i	$-0.961177\pi$
$149$	−4.77180	+	8.26501i	−0.390921	+	0.677096i	0.601650	+	0.798760i	$0.294510\pi$
$150$		0			0
$151$	6.87274	−	11.9039i	0.559295	−	0.968728i	−0.438260	−	0.898848i	$-0.644405\pi$
$151$	6.87274	−	11.9039i	0.559295	−	0.968728i	0.997555	−	0.0698798i	$-0.0222616\pi$
$152$		0			0
$153$	−9.07477			−0.733651
$154$		0			0
$155$	−11.2707	−	19.5215i	−0.905286	−	1.56800i
$156$		0			0
$157$	1.71213			0.136643			0.0683216	−	0.997663i	$-0.478236\pi$
$157$	1.71213			0.136643			0.0683216	+	0.997663i	$0.478236\pi$
$158$		0			0
$159$	7.41738	+	12.8473i	0.588237	+	1.01886i
$160$		0			0
$161$	−4.61396	−	8.54137i	−0.363631	−	0.673155i
$162$		0			0
$163$	−6.98910	−	12.1055i	−0.547429	−	0.948174i	−0.998450	−	0.0556609i	$-0.982273\pi$
$163$	−6.98910	−	12.1055i	−0.547429	−	0.948174i	0.451021	−	0.892513i	$-0.351060\pi$
$164$		0			0
$165$	−7.96270	−	13.7918i	−0.619896	−	1.07369i
$166$		0			0
$167$	4.31099	−	7.46686i	0.333595	−	0.577803i	−0.649619	−	0.760260i	$-0.725072\pi$
$167$	4.31099	−	7.46686i	0.333595	−	0.577803i	0.983214	+	0.182457i	$0.0584050\pi$
$168$		0			0
$169$	6.03887	+	10.4596i	0.464528	+	0.804586i
$170$		0			0
$171$	−5.21348	+	6.13943i	−0.398685	+	0.469494i
$172$		0			0
$173$	−6.08442	+	10.5385i	−0.462590	+	0.801230i	−0.999089	−	0.0426712i	$-0.986413\pi$
$173$	−6.08442	+	10.5385i	−0.462590	+	0.801230i	0.536499	+	0.843901i	$0.319747\pi$
$174$		0			0
$175$	−10.2703	+	16.6794i	−0.776362	+	1.26085i
$176$		0			0
$177$	−8.18971			−0.615576
$178$		0			0
$179$	2.05077	−	3.55204i	0.153282	−	0.265492i	−0.779150	−	0.626837i	$-0.784349\pi$
$179$	2.05077	−	3.55204i	0.153282	−	0.265492i	0.932432	+	0.361345i	$0.117682\pi$
$180$		0			0
$181$	−7.33178	+	12.6990i	−0.544967	+	0.943910i	0.453642	+	0.891184i	$0.350124\pi$
$181$	−7.33178	+	12.6990i	−0.544967	+	0.943910i	−0.998609	+	0.0527261i	$0.983209\pi$
$182$		0			0
$183$	2.51579			0.185972
$184$		0			0
$185$	−9.02554			−0.663571
$186$		0			0
$187$	10.3444	−	17.9170i	0.756457	−	1.31022i
$188$		0			0
$189$	−6.54343	−	12.1132i	−0.475965	−	0.881106i
$190$		0			0
$191$	−0.614388	−	1.06415i	−0.0444556	−	0.0769993i	0.842941	−	0.538005i	$-0.180822\pi$
$191$	−0.614388	−	1.06415i	−0.0444556	−	0.0769993i	−0.887397	+	0.461006i	$0.847489\pi$
$192$		0			0
$193$	14.2993			1.02928			0.514641	−	0.857406i	$-0.327925\pi$
$193$	14.2993			1.02928			0.514641	+	0.857406i	$0.327925\pi$
$194$		0			0
$195$	−1.81524	−	3.14409i	−0.129992	−	0.225153i
$196$		0			0
$197$	4.74408			0.338002			0.169001	−	0.985616i	$-0.445946\pi$
$197$	4.74408			0.338002			0.169001	+	0.985616i	$0.445946\pi$
$198$		0			0
$199$	−7.30530	−	12.6532i	−0.517859	−	0.896958i	−0.999785	−	0.0207462i	$-0.993396\pi$
$199$	−7.30530	−	12.6532i	−0.517859	−	0.896958i	0.481926	−	0.876212i	$-0.339938\pi$
$200$		0			0
$201$	5.89393	+	10.2086i	0.415726	+	0.720058i
$202$		0			0
$203$	−12.0134	−	0.340293i	−0.843175	−	0.0238839i
$204$		0			0
$205$	27.0937			1.89230
$206$		0			0
$207$	−6.78004			−0.471245
$208$		0			0
$209$	−6.17867	−	17.2918i	−0.427388	−	1.19610i
$210$		0			0
$211$	5.21725	+	9.03653i	0.359170	+	0.622101i	0.987822	−	0.155586i	$-0.0497265\pi$
$211$	5.21725	+	9.03653i	0.359170	+	0.622101i	−0.628652	+	0.777686i	$0.716393\pi$
$212$		0			0
$213$	−0.998156	−	1.72886i	−0.0683925	−	0.118459i
$214$		0			0
$215$	37.1400			2.53292
$216$		0			0
$217$	16.9272	+	0.479482i	1.14909	+	0.0325493i
$218$		0			0
$219$	10.6828			0.721877
$220$		0			0
$221$	2.35819	−	4.08450i	0.158629	−	0.274753i
$222$		0			0
$223$	5.70940	+	9.88897i	0.382330	+	0.662214i	0.991395	−	0.130906i	$-0.0417885\pi$
$223$	5.70940	+	9.88897i	0.382330	+	0.662214i	−0.609065	+	0.793120i	$0.708455\pi$
$224$		0			0
$225$	6.84009	+	11.8474i	0.456006	+	0.789826i
$226$		0			0
$227$	−4.18733	+	7.25267i	−0.277923	+	0.481377i	−0.970868	−	0.239613i	$-0.922979\pi$
$227$	−4.18733	+	7.25267i	−0.277923	+	0.481377i	0.692945	+	0.720990i	$0.256313\pi$
$228$		0			0
$229$	−5.01465	−	8.68563i	−0.331377	−	0.573963i	0.651405	−	0.758730i	$-0.274180\pi$
$229$	−5.01465	−	8.68563i	−0.331377	−	0.573963i	−0.982782	+	0.184768i	$0.940847\pi$
$230$		0			0
$231$	11.9590	+	0.338751i	0.786842	+	0.0222882i
$232$		0			0
$233$	−0.174986	+	0.303084i	−0.0114637	+	0.0198557i	−0.871700	−	0.490039i	$-0.836982\pi$
$233$	−0.174986	+	0.303084i	−0.0114637	+	0.0198557i	0.860237	+	0.509895i	$0.170316\pi$
$234$		0			0
$235$	1.58850	−	2.75136i	0.103622	−	0.179479i
$236$		0			0
$237$	−4.78184	+	8.28238i	−0.310614	+	0.537999i
$238$		0			0
$239$	5.04052			0.326044			0.163022	−	0.986622i	$-0.447876\pi$
$239$	5.04052			0.326044			0.163022	+	0.986622i	$0.447876\pi$
$240$		0			0
$241$	9.00937	+	15.6047i	0.580344	+	1.00519i	0.995438	+	0.0954074i	$0.0304154\pi$
$241$	9.00937	+	15.6047i	0.580344	+	1.00519i	−0.415094	+	0.909779i	$0.636251\pi$
$242$		0			0
$243$	−15.5656			−0.998536
$244$		0			0
$245$	−11.0982	−	22.0137i	−0.709037	−	1.40640i
$246$		0			0
$247$	−1.40854	−	3.94196i	−0.0896232	−	0.250821i
$248$		0			0
$249$	0.516435			0.0327278
$250$		0			0
$251$	12.7890	−	22.1511i	0.807233	−	1.39817i	−0.107541	−	0.994201i	$-0.534298\pi$
$251$	12.7890	−	22.1511i	0.807233	−	1.39817i	0.914774	−	0.403967i	$-0.132369\pi$
$252$		0			0
$253$	7.72862	−	13.3864i	0.485894	−	0.841593i
$254$		0			0
$255$	9.28296	−	16.0786i	0.581321	−	1.00688i
$256$		0			0
$257$	−5.72264			−0.356969			−0.178484	−	0.983943i	$-0.557119\pi$
$257$	−5.72264			−0.356969			−0.178484	+	0.983943i	$0.557119\pi$
$258$		0			0
$259$	3.55506	−	5.77359i	0.220901	−	0.358753i
$260$		0			0
$261$	−4.19678	+	7.26903i	−0.259774	+	0.449942i
$262$		0			0
$263$	3.47486			0.214269			0.107135	−	0.994245i	$-0.465832\pi$
$263$	3.47486			0.214269			0.107135	+	0.994245i	$0.465832\pi$
$264$		0			0
$265$	48.6731			2.98996
$266$		0			0
$267$	−18.5279			−1.13389
$268$		0			0
$269$	16.5851			1.01121			0.505607	−	0.862764i	$-0.331269\pi$
$269$	16.5851			1.01121			0.505607	+	0.862764i	$0.331269\pi$
$270$		0			0
$271$	−9.80196	+	16.9775i	−0.595427	+	1.03131i	0.398060	+	0.917360i	$0.369684\pi$
$271$	−9.80196	+	16.9775i	−0.595427	+	1.03131i	−0.993486	+	0.113950i	$0.963650\pi$
$272$		0			0
$273$	2.72626	+	0.0772244i	0.165001	+	0.00467383i
$274$		0			0
$275$	−31.1883			−1.88072
$276$		0			0
$277$	5.46542	−	9.46639i	0.328385	−	0.568780i	−0.653806	−	0.756662i	$-0.726829\pi$
$277$	5.46542	−	9.46639i	0.328385	−	0.568780i	0.982192	+	0.187882i	$0.0601622\pi$
$278$		0			0
$279$	5.91336	−	10.2422i	0.354024	−	0.613187i
$280$		0			0
$281$	−9.01439	+	15.6134i	−0.537753	+	0.931416i	0.461271	+	0.887259i	$0.347394\pi$
$281$	−9.01439	+	15.6134i	−0.537753	+	0.931416i	−0.999025	+	0.0441571i	$0.985940\pi$
$282$		0			0
$283$	−21.7749			−1.29438			−0.647190	−	0.762328i	$-0.724056\pi$
$283$	−21.7749			−1.29438			−0.647190	+	0.762328i	$0.724056\pi$
$284$		0			0
$285$	−5.54468	−	15.5175i	−0.328438	−	0.919175i
$286$		0			0
$287$	−10.6719	+	17.3316i	−0.629942	+	1.02305i
$288$		0			0
$289$	7.11909			0.418770
$290$		0			0
$291$	−2.85037	−	4.93699i	−0.167092	−	0.289412i
$292$		0			0
$293$	−14.5570			−0.850426			−0.425213	−	0.905093i	$-0.639801\pi$
$293$	−14.5570			−0.850426			−0.425213	+	0.905093i	$0.639801\pi$
$294$		0			0
$295$	−13.4353	+	23.2706i	−0.782232	+	1.35487i
$296$		0			0
$297$	10.9606	−	18.9843i	0.635997	−	1.10158i
$298$		0			0
$299$	1.76188	−	3.05166i	0.101892	−	0.176482i
$300$		0			0
$301$	−14.6290	+	23.7582i	−0.843203	+	1.36940i
$302$		0			0
$303$	0.275738	+	0.477593i	0.0158407	+	0.0274370i
$304$		0			0
$305$	4.12717	−	7.14847i	0.236321	−	0.409320i
$306$		0			0
$307$	−7.58731	−	13.1416i	−0.433031	−	0.750032i	0.564102	−	0.825705i	$-0.309223\pi$
$307$	−7.58731	−	13.1416i	−0.433031	−	0.750032i	−0.997133	+	0.0756738i	$0.975889\pi$
$308$		0			0
$309$	−2.11858	−	3.66949i	−0.120522	−	0.208750i
$310$		0			0
$311$	8.30533	−	14.3853i	0.470952	−	0.815713i	−0.528496	−	0.848936i	$-0.677244\pi$
$311$	8.30533	−	14.3853i	0.470952	−	0.815713i	0.999448	+	0.0332227i	$0.0105771\pi$
$312$		0			0
$313$	−32.8437			−1.85644			−0.928218	−	0.372037i	$-0.878659\pi$
$313$	−32.8437			−1.85644			−0.928218	+	0.372037i	$0.878659\pi$
$314$		0			0
$315$	−17.2108	−	0.487517i	−0.969721	−	0.0274685i
$316$		0			0
$317$	27.0154			1.51734			0.758668	−	0.651477i	$-0.225850\pi$
$317$	27.0154			1.51734			0.758668	+	0.651477i	$0.225850\pi$
$318$		0			0
$319$	−9.56788	−	16.5721i	−0.535698	−	0.927857i
$320$		0			0
$321$	−7.04044	−	12.1944i	−0.392959	−	0.680625i
$322$		0			0
$323$	13.8565	−	16.3175i	0.770995	−	0.907930i
$324$		0			0
$325$	−7.10993			−0.394388
$326$		0			0
$327$	−14.5908			−0.806872
$328$		0			0
$329$	1.13434	+	2.09989i	0.0625380	+	0.115770i
$330$		0			0
$331$	0.909047	+	1.57452i	0.0499657	+	0.0865432i	0.889927	−	0.456104i	$-0.150755\pi$
$331$	0.909047	+	1.57452i	0.0499657	+	0.0865432i	−0.839961	+	0.542647i	$0.817422\pi$
$332$		0			0
$333$	−2.36770	−	4.10097i	−0.129749	−	0.224732i
$334$		0			0
$335$	38.6761			2.11310
$336$		0			0
$337$	−13.2866	−	23.0131i	−0.723769	−	1.25360i	−0.959479	−	0.281781i	$-0.909075\pi$
$337$	−13.2866	−	23.0131i	−0.723769	−	1.25360i	0.235710	−	0.971823i	$-0.424258\pi$
$338$		0			0
$339$	13.0599			0.709317
$340$		0			0
$341$	13.4814	+	23.3504i	0.730057	+	1.26450i
$342$		0			0
$343$	18.4535	+	1.57151i	0.996393	+	0.0848536i
$344$		0			0
$345$	6.93559	−	12.0128i	0.373399	−	0.646747i
$346$		0			0
$347$	21.0389			1.12943			0.564714	−	0.825287i	$-0.308986\pi$
$347$	21.0389			1.12943			0.564714	+	0.825287i	$0.308986\pi$
$348$		0			0
$349$	−25.6088			−1.37081			−0.685403	−	0.728164i	$-0.740374\pi$
$349$	−25.6088			−1.37081			−0.685403	+	0.728164i	$0.740374\pi$
$350$		0			0
$351$	2.49866	−	4.32780i	0.133368	−	0.231001i
$352$		0			0
$353$	−12.8782	+	22.3058i	−0.685440	+	1.18722i	0.287859	+	0.957673i	$0.407057\pi$
$353$	−12.8782	+	22.3058i	−0.685440	+	1.18722i	−0.973298	+	0.229543i	$0.926277\pi$
$354$		0			0
$355$	−6.54993			−0.347634
$356$		0			0
$357$	6.62890	+	12.2714i	0.350838	+	0.649473i
$358$		0			0
$359$	2.89365	−	5.01195i	0.152721	−	0.264521i	−0.779506	−	0.626395i	$-0.784530\pi$
$359$	2.89365	−	5.01195i	0.152721	−	0.264521i	0.932227	+	0.361874i	$0.117863\pi$
$360$		0			0
$361$	−3.07883	−	18.7489i	−0.162044	−	0.986784i
$362$		0			0
$363$	3.62079	+	6.27139i	0.190042	+	0.329163i
$364$		0			0
$365$	17.5252	−	30.3546i	0.917312	−	1.58883i
$366$		0			0
$367$	−3.54716	−	6.14385i	−0.185160	−	0.320707i	0.758470	−	0.651707i	$-0.225947\pi$
$367$	−3.54716	−	6.14385i	−0.185160	−	0.320707i	−0.943630	+	0.331001i	$0.892614\pi$
$368$		0			0
$369$	7.10756	+	12.3107i	0.370005	+	0.640867i
$370$		0			0
$371$	−19.1718	+	31.1359i	−0.995350	+	1.61649i
$372$		0			0
$373$	10.6060	+	18.3702i	0.549159	+	0.951172i	0.998332	+	0.0577269i	$0.0183853\pi$
$373$	10.6060	+	18.3702i	0.549159	+	0.951172i	−0.449173	+	0.893445i	$0.648281\pi$
$374$		0			0
$375$	−9.08614			−0.469206
$376$		0			0
$377$	−2.18117	−	3.77790i	−0.112336	−	0.194572i
$378$		0			0
$379$	−9.73543			−0.500076			−0.250038	−	0.968236i	$-0.580443\pi$
$379$	−9.73543			−0.500076			−0.250038	+	0.968236i	$0.580443\pi$
$380$		0			0
$381$	9.65962	−	16.7310i	0.494878	−	0.857153i
$382$		0			0
$383$	−8.60742	+	14.9085i	−0.439818	+	0.761788i	−0.997675	−	0.0681494i	$-0.978291\pi$
$383$	−8.60742	+	14.9085i	−0.439818	+	0.761788i	0.557857	+	0.829937i	$0.311624\pi$
$384$		0			0
$385$	20.5813	−	33.4250i	1.04892	−	1.70349i
$386$		0			0
$387$	9.74304	+	16.8754i	0.495266	+	0.857827i
$388$		0			0
$389$	14.6330	+	25.3451i	0.741922	+	1.28505i	0.951619	+	0.307280i	$0.0994187\pi$
$389$	14.6330	+	25.3451i	0.741922	+	1.28505i	−0.209698	+	0.977766i	$0.567248\pi$
$390$		0			0
$391$	18.0201			0.911317
$392$		0			0
$393$	−11.3786	+	19.7083i	−0.573975	+	0.994154i
$394$		0			0
$395$	15.6893	+	27.1746i	0.789413	+	1.36730i
$396$		0			0
$397$	−0.579042	+	1.00293i	−0.0290613	+	0.0503356i	−0.880190	−	0.474621i	$-0.842585\pi$
$397$	−0.579042	+	1.00293i	−0.0290613	+	0.0503356i	0.851129	+	0.524957i	$0.175918\pi$
$398$		0			0
$399$	12.1104	+	2.56526i	0.606279	+	0.128424i
$400$		0			0
$401$	18.4412	−	31.9411i	0.920909	−	1.59506i	0.122896	−	0.992419i	$-0.460782\pi$
$401$	18.4412	−	31.9411i	0.920909	−	1.59506i	0.798012	−	0.602641i	$-0.205885\pi$
$402$		0			0
$403$	3.07332	+	5.32315i	0.153093	+	0.265165i
$404$		0			0
$405$	0.0743695	−	0.128812i	0.00369545	−	0.00640071i
$406$		0			0
$407$	10.7958			0.535129
$408$		0			0
$409$	16.7816	+	29.0667i	0.829799	+	1.43725i	0.898196	+	0.439596i	$0.144878\pi$
$409$	16.7816	+	29.0667i	0.829799	+	1.43725i	−0.0683966	+	0.997658i	$0.521788\pi$
$410$		0			0
$411$	4.47384	+	7.74892i	0.220678	+	0.382226i
$412$		0			0
$413$	−9.59404	−	17.7605i	−0.472092	−	0.873937i
$414$		0			0
$415$	0.847216	−	1.46742i	0.0415882	−	0.0720329i
$416$		0			0
$417$	−3.34349	+	5.79110i	−0.163732	+	0.283591i
$418$		0			0
$419$	−34.4912			−1.68501			−0.842504	−	0.538691i	$-0.818919\pi$
$419$	−34.4912			−1.68501			−0.842504	+	0.538691i	$0.818919\pi$
$420$		0			0
$421$	−15.2416	−	26.3992i	−0.742829	−	1.28662i	−0.951202	−	0.308568i	$-0.900150\pi$
$421$	−15.2416	−	26.3992i	−0.742829	−	1.28662i	0.208373	−	0.978049i	$-0.433183\pi$
$422$		0			0
$423$	1.66686			0.0810457
$424$		0			0
$425$	−18.1797	−	31.4882i	−0.881846	−	1.52740i
$426$		0			0
$427$	2.94718	+	5.45583i	0.142624	+	0.264026i
$428$		0			0
$429$	2.17128	+	3.76077i	0.104831	+	0.181572i
$430$		0			0
$431$	−9.12562	−	15.8060i	−0.439565	−	0.761350i	0.558090	−	0.829780i	$-0.311534\pi$
$431$	−9.12562	−	15.8060i	−0.439565	−	0.761350i	−0.997656	+	0.0684304i	$0.978201\pi$
$432$		0			0
$433$	−5.46128	+	9.45922i	−0.262452	+	0.454581i	−0.966893	−	0.255182i	$-0.917865\pi$
$433$	−5.46128	+	9.45922i	−0.262452	+	0.454581i	0.704441	+	0.709763i	$0.251198\pi$
$434$		0			0
$435$	−8.58612	−	14.8716i	−0.411673	−	0.713039i
$436$		0			0
$437$	10.3526	−	12.1913i	0.495232	−	0.583189i
$438$		0			0
$439$	−8.96074	+	15.5205i	−0.427673	+	0.740751i	−0.996666	−	0.0815911i	$-0.974000\pi$
$439$	−8.96074	+	15.5205i	−0.427673	+	0.740751i	0.568993	+	0.822342i	$0.307333\pi$
$440$		0			0
$441$	7.09102	−	10.8176i	0.337668	−	0.515126i
$442$		0			0
$443$	−24.6164			−1.16956			−0.584780	−	0.811192i	$-0.698819\pi$
$443$	−24.6164			−1.16956			−0.584780	+	0.811192i	$0.698819\pi$
$444$		0			0
$445$	−30.3952	+	52.6460i	−1.44087	+	2.49566i
$446$		0			0
$447$	5.12208	−	8.87171i	0.242266	−	0.419617i
$448$		0			0
$449$	27.1518			1.28137			0.640687	−	0.767802i	$-0.278649\pi$
$449$	27.1518			1.28137			0.640687	+	0.767802i	$0.278649\pi$
$450$		0			0
$451$	−32.4078			−1.52603
$452$		0			0
$453$	−7.37723	+	12.7777i	−0.346613	+	0.600351i
$454$		0			0
$455$	4.69188	−	7.61982i	0.219958	−	0.357223i
$456$		0			0
$457$	−12.1336	−	21.0160i	−0.567585	−	0.983085i	−0.996804	−	0.0798852i	$-0.974545\pi$
$457$	−12.1336	−	21.0160i	−0.567585	−	0.983085i	0.429219	−	0.903200i	$-0.358789\pi$
$458$		0			0
$459$	25.5558			1.19284
$460$		0			0
$461$	12.9069	+	22.3555i	0.601136	+	1.04120i	0.992649	+	0.121025i	$0.0386181\pi$
$461$	12.9069	+	22.3555i	0.601136	+	1.04120i	−0.391514	+	0.920172i	$0.628049\pi$
$462$		0			0
$463$	6.85695			0.318670			0.159335	−	0.987225i	$-0.449065\pi$
$463$	6.85695			0.318670			0.159335	+	0.987225i	$0.449065\pi$
$464$		0			0
$465$	12.0981	+	20.9544i	0.561034	+	0.971739i
$466$		0			0
$467$	−2.21068	−	3.82901i	−0.102298	−	0.177186i	0.810333	−	0.585970i	$-0.199286\pi$
$467$	−2.21068	−	3.82901i	−0.102298	−	0.177186i	−0.912631	+	0.408784i	$0.865953\pi$
$468$		0			0
$469$	−15.2341	+	24.7409i	−0.703446	+	1.14243i
$470$		0			0
$471$	−1.83781			−0.0846820
$472$		0			0
$473$	−44.4246			−2.04265
$474$		0			0
$475$	−31.7473	−	5.79077i	−1.45667	−	0.265699i
$476$		0			0
$477$	12.7686	+	22.1158i	0.584632	+	1.01261i
$478$		0			0
$479$	11.6272	+	20.1389i	0.531260	+	0.920170i	0.999334	+	0.0364804i	$0.0116147\pi$
$479$	11.6272	+	20.1389i	0.531260	+	0.920170i	−0.468074	+	0.883689i	$0.655052\pi$
$480$		0			0
$481$	2.46110			0.112217
$482$		0			0
$483$	4.95265	+	9.16836i	0.225354	+	0.417175i
$484$		0			0
$485$	−18.7042			−0.849315
$486$		0			0
$487$	−7.06232	+	12.2323i	−0.320024	+	0.554299i	−0.980493	−	0.196555i	$-0.937024\pi$
$487$	−7.06232	+	12.2323i	−0.320024	+	0.554299i	0.660468	+	0.750854i	$0.270358\pi$
$488$		0			0
$489$	7.50214	+	12.9941i	0.339259	+	0.587613i
$490$		0			0
$491$	8.72265	+	15.1081i	0.393648	+	0.681818i	0.992928	−	0.118722i	$-0.0378797\pi$
$491$	8.72265	+	15.1081i	0.393648	+	0.681818i	−0.599280	+	0.800539i	$0.704546\pi$
$492$		0			0
$493$	11.1543	−	19.3198i	0.502364	−	0.870119i
$494$		0			0
$495$	−13.7073	−	23.7417i	−0.616097	−	1.06711i
$496$		0			0
$497$	2.57995	−	4.18995i	0.115726	−	0.187945i
$498$		0			0
$499$	6.39276	−	11.0726i	0.286179	−	0.495677i	−0.686715	−	0.726927i	$-0.740948\pi$
$499$	6.39276	−	11.0726i	0.286179	−	0.495677i	0.972895	+	0.231249i	$0.0742813\pi$
$500$		0			0
$501$	−4.62744	+	8.01497i	−0.206739	+	0.358082i
$502$		0			0
$503$	−9.38455	+	16.2545i	−0.418436	+	0.724753i	−0.995782	−	0.0917464i	$-0.970755\pi$
$503$	−9.38455	+	16.2545i	−0.418436	+	0.724753i	0.577346	+	0.816500i	$0.304088\pi$
$504$		0			0
$505$	1.80940			0.0805174
$506$		0			0
$507$	−6.48215	−	11.2274i	−0.287883	−	0.498627i
$508$		0			0
$509$	25.5483			1.13241			0.566205	−	0.824265i	$-0.308411\pi$
$509$	25.5483			1.13241			0.566205	+	0.824265i	$0.308411\pi$
$510$		0			0
$511$	12.5146	+	23.1671i	0.553615	+	1.02485i
$512$		0			0
$513$	14.6819	−	17.2895i	0.648220	−	0.763349i
$514$		0			0
$515$	−13.9022			−0.612603
$516$		0			0
$517$	−1.90007	+	3.29102i	−0.0835650	+	0.144739i
$518$		0			0
$519$	6.53106	−	11.3121i	0.286682	−	0.496547i
$520$		0			0
$521$	−10.0099	+	17.3376i	−0.438541	+	0.759576i	−0.997577	−	0.0695677i	$-0.977838\pi$
$521$	−10.0099	+	17.3376i	−0.438541	+	0.759576i	0.559036	+	0.829143i	$0.311171\pi$
$522$		0			0
$523$	6.29628			0.275317			0.137659	−	0.990480i	$-0.456042\pi$
$523$	6.29628			0.275317			0.137659	+	0.990480i	$0.456042\pi$
$524$		0			0
$525$	11.0242	−	17.9038i	0.481135	−	0.781386i
$526$		0			0
$527$	−15.7166	+	27.2220i	−0.684628	+	1.18581i
$528$		0			0
$529$	−9.53661			−0.414635
$530$		0			0
$531$	−14.0981			−0.611804
$532$		0			0
$533$	−7.38795			−0.320007
$534$		0			0
$535$	−46.1996			−1.99738
$536$		0			0
$537$	−2.20131	+	3.81278i	−0.0949936	+	0.164534i
$538$		0			0
$539$	13.2750	+	26.3315i	0.571794	+	1.13418i
$540$		0			0
$541$	−30.0241			−1.29084			−0.645418	−	0.763829i	$-0.723317\pi$
$541$	−30.0241			−1.29084			−0.645418	+	0.763829i	$0.723317\pi$
$542$		0			0
$543$	7.86997	−	13.6312i	0.337733	−	0.584970i
$544$		0			0
$545$	−23.9363	+	41.4589i	−1.02532	+	1.77590i
$546$		0			0
$547$	6.42453	−	11.1276i	0.274693	−	0.475782i	−0.695365	−	0.718657i	$-0.744757\pi$
$547$	6.42453	−	11.1276i	0.274693	−	0.475782i	0.970058	+	0.242875i	$0.0780904\pi$
$548$		0			0
$549$	4.33077			0.184833
$550$		0			0
$551$	−6.66241	−	18.6456i	−0.283828	−	0.794328i
$552$		0			0
$553$	−23.5633	−	0.667457i	−1.00201	−	0.0283832i
$554$		0			0
$555$	9.68807			0.411236
$556$		0			0
$557$	2.69656	+	4.67057i	0.114257	+	0.197899i	0.917482	−	0.397776i	$-0.130218\pi$
$557$	2.69656	+	4.67057i	0.114257	+	0.197899i	−0.803226	+	0.595675i	$0.796885\pi$
$558$		0			0
$559$	−10.1274			−0.428343
$560$		0			0
$561$	−11.1037	+	19.2322i	−0.468800	+	0.811985i
$562$		0			0
$563$	0.211462	−	0.366264i	0.00891208	−	0.0154362i	−0.861535	−	0.507698i	$-0.830496\pi$
$563$	0.211462	−	0.366264i	0.00891208	−	0.0154362i	0.870447	+	0.492262i	$0.163830\pi$
$564$		0			0
$565$	21.4249	−	37.1090i	0.901352	−	1.56119i
$566$		0			0
$567$	0.0531067	+	0.0983113i	0.00223027	+	0.00412868i
$568$		0			0
$569$	12.9214	+	22.3805i	0.541692	+	0.938238i	0.998807	+	0.0488304i	$0.0155494\pi$
$569$	12.9214	+	22.3805i	0.541692	+	0.938238i	−0.457115	+	0.889408i	$0.651117\pi$
$570$		0			0
$571$	−14.1729	+	24.5482i	−0.593118	+	1.02731i	0.400691	+	0.916213i	$0.368770\pi$
$571$	−14.1729	+	24.5482i	−0.593118	+	1.02731i	−0.993809	+	0.111098i	$0.964563\pi$
$572$		0			0
$573$	0.659488	+	1.14227i	0.0275505	+	0.0477189i
$574$		0			0
$575$	−13.5826	−	23.5258i	−0.566435	−	0.981094i
$576$		0			0
$577$	−12.2758	+	21.2623i	−0.511047	+	0.885160i	0.488871	+	0.872356i	$0.337409\pi$
$577$	−12.2758	+	21.2623i	−0.511047	+	0.885160i	−0.999918	+	0.0128036i	$0.995924\pi$
$578$		0			0
$579$	−15.3489			−0.637878
$580$		0			0
$581$	0.604991	+	1.11996i	0.0250993	+	0.0464638i
$582$		0			0
$583$	−58.2199			−2.41122
$584$		0			0
$585$	−3.12482	−	5.41235i	−0.129195	−	0.223773i
$586$		0			0
$587$	−11.1037	−	19.2321i	−0.458298	−	0.793796i	0.540573	−	0.841297i	$-0.318207\pi$
$587$	−11.1037	−	19.2321i	−0.458298	−	0.793796i	−0.998871	+	0.0475014i	$0.984874\pi$
$588$		0			0
$589$	9.38750	+	26.2720i	0.386805	+	1.08252i
$590$		0			0
$591$	−5.09232			−0.209470
$592$		0			0
$593$	9.25655			0.380121			0.190060	−	0.981772i	$-0.439132\pi$
$593$	9.25655			0.380121			0.190060	+	0.981772i	$0.439132\pi$
$594$		0			0
$595$	45.7433	+	1.29573i	1.87529	+	0.0531198i
$596$		0			0
$597$	7.84155	+	13.5820i	0.320933	+	0.555873i
$598$		0			0
$599$	14.6377	+	25.3532i	0.598079	+	1.03590i	0.993104	+	0.117234i	$0.0374026\pi$
$599$	14.6377	+	25.3532i	0.598079	+	1.03590i	−0.395025	+	0.918670i	$0.629264\pi$
$600$		0			0
$601$	21.0622			0.859146			0.429573	−	0.903032i	$-0.358664\pi$
$601$	21.0622			0.859146			0.429573	+	0.903032i	$0.358664\pi$
$602$		0			0
$603$	10.1460	+	17.5734i	0.413178	+	0.715646i
$604$		0			0
$605$	23.7597			0.965970
$606$		0			0
$607$	18.4078	+	31.8832i	0.747149	+	1.29410i	0.949184	+	0.314722i	$0.101911\pi$
$607$	18.4078	+	31.8832i	0.747149	+	1.29410i	−0.202035	+	0.979378i	$0.564755\pi$
$608$		0			0
$609$	12.8953	+	0.365273i	0.522542	+	0.0148016i
$610$		0			0
$611$	−0.433155	+	0.750246i	−0.0175236	+	0.0303517i
$612$		0			0
$613$	34.9124			1.41010			0.705050	−	0.709158i	$-0.250925\pi$
$613$	34.9124			1.41010			0.705050	+	0.709158i	$0.250925\pi$
$614$		0			0
$615$	−29.0825			−1.17272
$616$		0			0
$617$	5.22802	−	9.05519i	0.210472	−	0.364548i	−0.741390	−	0.671074i	$-0.765833\pi$
$617$	5.22802	−	9.05519i	0.210472	−	0.364548i	0.951862	+	0.306526i	$0.0991666\pi$
$618$		0			0
$619$	13.5466	−	23.4633i	0.544482	−	0.943070i	−0.454157	−	0.890921i	$-0.650060\pi$
$619$	13.5466	−	23.4633i	0.544482	−	0.943070i	0.998639	−	0.0521488i	$-0.0166070\pi$
$620$		0			0
$621$	19.0935			0.766196
$622$		0			0
$623$	−21.7050	−	40.1803i	−0.869592	−	1.60979i
$624$		0			0
$625$	3.60286	−	6.24034i	0.144114	−	0.249613i
$626$		0			0
$627$	6.63222	+	18.5611i	0.264865	+	0.741258i
$628$		0			0
$629$	6.29291	+	10.8996i	0.250915	+	0.434597i
$630$		0			0
$631$	1.82048	−	3.15316i	0.0724721	−	0.125525i	−0.827512	−	0.561448i	$-0.810244\pi$
$631$	1.82048	−	3.15316i	0.0724721	−	0.125525i	0.899984	+	0.435923i	$0.143578\pi$
$632$		0			0
$633$	−5.60022	−	9.69987i	−0.222589	−	0.385535i
$634$		0			0
$635$	−31.6934	−	54.8945i	−1.25771	−	2.17842i
$636$		0			0
$637$	3.02627	+	6.00273i	0.119905	+	0.237837i
$638$		0			0
$639$	−1.71826	−	2.97612i	−0.0679734	−	0.117733i
$640$		0			0
$641$	14.1379			0.558413			0.279206	−	0.960231i	$-0.409929\pi$
$641$	14.1379			0.558413			0.279206	+	0.960231i	$0.409929\pi$
$642$		0			0
$643$	−10.8348	−	18.7664i	−0.427281	−	0.740073i	0.569349	−	0.822096i	$-0.307195\pi$
$643$	−10.8348	−	18.7664i	−0.427281	−	0.740073i	−0.996630	+	0.0820231i	$0.973862\pi$
$644$		0			0
$645$	−39.8662			−1.56973
$646$		0			0
$647$	10.9743	−	19.0080i	0.431443	−	0.747281i	−0.565555	−	0.824711i	$-0.691338\pi$
$647$	10.9743	−	19.0080i	0.431443	−	0.747281i	0.996998	+	0.0774293i	$0.0246712\pi$
$648$		0			0
$649$	16.0705	−	27.8349i	0.630822	−	1.09262i
$650$		0			0
$651$	−18.1697	−	0.514678i	−0.712127	−	0.0201718i
$652$		0			0
$653$	19.2052	+	33.2644i	0.751559	+	1.30174i	0.947067	+	0.321036i	$0.104031\pi$
$653$	19.2052	+	33.2644i	0.751559	+	1.30174i	−0.195508	+	0.980702i	$0.562636\pi$
$654$		0			0
$655$	37.3334	+	64.6634i	1.45874	+	2.52661i
$656$		0			0
$657$	18.3898			0.717453
$658$		0			0
$659$	3.94165	−	6.82714i	0.153545	−	0.265948i	−0.778983	−	0.627045i	$-0.784264\pi$
$659$	3.94165	−	6.82714i	0.153545	−	0.265948i	0.932528	+	0.361097i	$0.117598\pi$
$660$		0			0
$661$	−9.68672	−	16.7779i	−0.376770	−	0.652584i	0.613820	−	0.789446i	$-0.289632\pi$
$661$	−9.68672	−	16.7779i	−0.376770	−	0.652584i	−0.990590	+	0.136861i	$0.956299\pi$
$662$		0			0
$663$	−2.53129	+	4.38433i	−0.0983073	+	0.170273i
$664$		0			0
$665$	27.1563	−	30.2027i	1.05307	−	1.17121i
$666$		0			0
$667$	8.33371	−	14.4344i	0.322682	−	0.558902i
$668$		0			0
$669$	−6.12850	−	10.6149i	−0.236942	−	0.410395i
$670$		0			0
$671$	−4.93668	+	8.55058i	−0.190578	+	0.330091i
$672$		0			0
$673$	30.3695			1.17066			0.585329	−	0.810796i	$-0.300965\pi$
$673$	30.3695			1.17066			0.585329	+	0.810796i	$0.300965\pi$
$674$		0			0
$675$	−19.2626	−	33.3638i	−0.741419	−	1.28418i
$676$		0			0
$677$	4.21573	+	7.30186i	0.162024	+	0.280633i	0.935594	−	0.353077i	$-0.114865\pi$
$677$	4.21573	+	7.30186i	0.162024	+	0.280633i	−0.773571	+	0.633710i	$0.781531\pi$
$678$		0			0
$679$	7.36740	−	11.9650i	0.282735	−	0.459174i
$680$		0			0
$681$	4.49471	−	7.78506i	0.172237	−	0.298324i
$682$		0			0
$683$	17.7336	−	30.7155i	0.678557	−	1.17529i	−0.296859	−	0.954921i	$-0.595939\pi$
$683$	17.7336	−	30.7155i	0.678557	−	1.17529i	0.975416	−	0.220373i	$-0.0707275\pi$
$684$		0			0
$685$	29.3575			1.12169
$686$		0			0
$687$	5.38275	+	9.32320i	0.205365	+	0.355702i
$688$		0			0
$689$	−13.2723			−0.505633
$690$		0			0
$691$	1.47490	+	2.55460i	0.0561077	+	0.0971814i	0.892715	−	0.450622i	$-0.148798\pi$
$691$	1.47490	+	2.55460i	0.0561077	+	0.0971814i	−0.836607	+	0.547803i	$0.815464\pi$
$692$		0			0
$693$	20.5866	+	0.583139i	0.782020	+	0.0221516i
$694$		0			0
$695$	10.9701	+	19.0007i	0.416118	+	0.720737i
$696$		0			0
$697$	−18.8906	−	32.7195i	−0.715533	−	1.23934i
$698$		0			0
$699$	0.187831	−	0.325333i	0.00710441	−	0.0123052i
$700$		0			0
$701$	−17.7395	−	30.7257i	−0.670011	−	1.16049i	−0.977900	−	0.209071i	$-0.932956\pi$
$701$	−17.7395	−	30.7257i	−0.670011	−	1.16049i	0.307889	−	0.951422i	$-0.400377\pi$
$702$		0			0
$703$	10.9893	+	2.00448i	0.414470	+	0.0756003i
$704$		0			0
$705$	−1.70510	+	2.95333i	−0.0642180	+	0.111229i
$706$		0			0
$707$	−0.712704	+	1.15746i	−0.0268040	+	0.0435309i
$708$		0			0
$709$	45.4614			1.70734			0.853670	−	0.520815i	$-0.174372\pi$
$709$	45.4614			1.70734			0.853670	+	0.520815i	$0.174372\pi$
$710$		0			0
$711$	−8.23163	+	14.2576i	−0.308710	+	0.534702i
$712$		0			0
$713$	−11.7424	+	20.3384i	−0.439756	+	0.761680i
$714$		0			0
$715$	14.2480			0.532846
$716$		0			0
$717$	−5.41052			−0.202060
$718$		0			0
$719$	3.25917	−	5.64505i	0.121547	−	0.210525i	−0.798831	−	0.601555i	$-0.794548\pi$
$719$	3.25917	−	5.64505i	0.121547	−	0.210525i	0.920378	+	0.391030i	$0.127881\pi$
$720$		0			0
$721$	5.47592	−	8.89314i	0.203934	−	0.331198i
$722$		0			0
$723$	−9.67071	−	16.7502i	−0.359657	−	0.622945i
$724$		0			0
$725$	−33.6301			−1.24899
$726$		0			0
$727$	−24.6628	−	42.7172i	−0.914693	−	1.58429i	−0.807351	−	0.590072i	$-0.799099\pi$
$727$	−24.6628	−	42.7172i	−0.914693	−	1.58429i	−0.107342	−	0.994222i	$-0.534234\pi$
$728$		0			0
$729$	16.8349			0.623516
$730$		0			0
$731$	−25.8952	−	44.8519i	−0.957770	−	1.65891i
$732$		0			0
$733$	−11.8066	−	20.4497i	−0.436088	−	0.755327i	0.561295	−	0.827616i	$-0.310303\pi$
$733$	−11.8066	−	20.4497i	−0.436088	−	0.755327i	−0.997384	+	0.0722883i	$0.976970\pi$
$734$		0			0
$735$	11.9128	+	23.6296i	0.439412	+	0.871591i
$736$		0			0
$737$	−46.2621			−1.70409
$738$		0			0
$739$	35.4122			1.30266			0.651329	−	0.758796i	$-0.274212\pi$
$739$	35.4122			1.30266			0.651329	+	0.758796i	$0.274212\pi$
$740$		0			0
$741$	1.51193	+	4.23133i	0.0555423	+	0.155442i
$742$		0			0
$743$	16.5550	+	28.6740i	0.607342	+	1.05195i	0.991677	+	0.128754i	$0.0410977\pi$
$743$	16.5550	+	28.6740i	0.607342	+	1.05195i	−0.384334	+	0.923194i	$0.625569\pi$
$744$		0			0
$745$	−16.8056	−	29.1082i	−0.615711	−	1.06644i
$746$		0			0
$747$	0.889011			0.0325272
$748$		0			0
$749$	18.1975	−	29.5536i	0.664923	−	1.07986i
$750$		0			0
$751$	−27.4985			−1.00344			−0.501718	−	0.865031i	$-0.667299\pi$
$751$	−27.4985			−1.00344			−0.501718	+	0.865031i	$0.667299\pi$
$752$		0			0
$753$	−13.7278	+	23.7772i	−0.500267	+	0.866488i
$754$		0			0
$755$	24.2048	+	41.9240i	0.880903	+	1.52577i
$756$		0			0
$757$	22.8550	+	39.5860i	0.830678	+	1.43878i	0.897502	+	0.441011i	$0.145380\pi$
$757$	22.8550	+	39.5860i	0.830678	+	1.43878i	−0.0668237	+	0.997765i	$0.521287\pi$
$758$		0			0
$759$	−8.29594	+	14.3690i	−0.301124	+	0.521561i
$760$		0			0
$761$	−12.5144	−	21.6755i	−0.453645	−	0.785737i	0.544964	−	0.838460i	$-0.316543\pi$
$761$	−12.5144	−	21.6755i	−0.453645	−	0.785737i	−0.998609	+	0.0527227i	$0.983210\pi$
$762$		0			0
$763$	−17.0927	−	31.6421i	−0.618799	−	1.14552i
$764$		0			0
$765$	15.9800	−	27.6782i	0.577759	−	1.00071i
$766$		0			0
$767$	3.66355	−	6.34546i	0.132283	−	0.229121i
$768$		0			0
$769$	−3.24446	+	5.61958i	−0.116998	+	0.202647i	−0.918577	−	0.395243i	$-0.870661\pi$
$769$	−3.24446	+	5.61958i	−0.116998	+	0.202647i	0.801578	+	0.597890i	$0.203994\pi$
$770$		0			0
$771$	6.14271			0.221224
$772$		0			0
$773$	−0.632982	−	1.09636i	−0.0227668	−	0.0394332i	0.854418	−	0.519587i	$-0.173914\pi$
$773$	−0.632982	−	1.09636i	−0.0227668	−	0.0394332i	−0.877184	+	0.480154i	$0.840581\pi$
$774$		0			0
$775$	47.3856			1.70214
$776$		0			0
$777$	−3.81603	+	6.19740i	−0.136899	+	0.222330i
$778$		0			0
$779$	−32.9887	−	6.01721i	−1.18194	−	0.215589i
$780$		0			0
$781$	7.83464			0.280345
$782$		0			0
$783$	11.8187	−	20.4706i	0.422366	−	0.731559i
$784$		0			0
$785$	−3.01495	+	5.22204i	−0.107608	+	0.186383i
$786$		0			0
$787$	7.98184	−	13.8250i	0.284522	−	0.492807i	−0.687971	−	0.725738i	$-0.741498\pi$
$787$	7.98184	−	13.8250i	0.284522	−	0.492807i	0.972493	+	0.232932i	$0.0748318\pi$
$788$		0			0
$789$	−3.72993			−0.132789
$790$		0			0
$791$	15.2994	+	28.3222i	0.543983	+	1.00702i
$792$		0			0
$793$	−1.12540	+	1.94926i	−0.0399643	+	0.0692201i
$794$		0			0
$795$	−52.2460			−1.85297
$796$		0			0
$797$	−13.6435			−0.483277			−0.241638	−	0.970366i	$-0.577685\pi$
$797$	−13.6435			−0.483277			−0.241638	+	0.970366i	$0.577685\pi$
$798$		0			0
$799$	−4.43022			−0.156730
$800$		0			0
$801$	−31.8946			−1.12694
$802$		0			0
$803$	−20.9626	+	36.3084i	−0.739755	+	1.28129i
$804$		0			0
$805$	34.1762	+	0.968081i	1.20455	+	0.0341204i
$806$		0			0
$807$	−17.8026			−0.626681
$808$		0			0
$809$	−8.89282	+	15.4028i	−0.312655	+	0.541534i	−0.978936	−	0.204166i	$-0.934552\pi$
$809$	−8.89282	+	15.4028i	−0.312655	+	0.541534i	0.666281	+	0.745701i	$0.267885\pi$
$810$		0			0
$811$	5.79398	−	10.0355i	0.203454	−	0.352393i	−0.746185	−	0.665739i	$-0.768117\pi$
$811$	5.79398	−	10.0355i	0.203454	−	0.352393i	0.949639	+	0.313346i	$0.101450\pi$
$812$		0			0
$813$	10.5215	−	18.2237i	0.369004	−	0.639134i
$814$		0			0
$815$	49.2293			1.72443
$816$		0			0
$817$	−45.2209	−	8.24839i	−1.58208	−	0.288575i
$818$		0			0
$819$	4.69308	+	0.132937i	0.163990	+	0.00464519i
$820$		0			0
$821$	−2.58772			−0.0903122			−0.0451561	−	0.998980i	$-0.514379\pi$
$821$	−2.58772			−0.0903122			−0.0451561	+	0.998980i	$0.514379\pi$
$822$		0			0
$823$	−15.9894	−	27.6944i	−0.557354	−	0.965365i	−0.997716	−	0.0675450i	$-0.978483\pi$
$823$	−15.9894	−	27.6944i	−0.557354	−	0.965365i	0.440362	−	0.897820i	$-0.354850\pi$
$824$		0			0
$825$	33.4777			1.16554
$826$		0			0
$827$	14.4731	−	25.0681i	0.503279	−	0.871705i	−0.496714	−	0.867914i	$-0.665460\pi$
$827$	14.4731	−	25.0681i	0.503279	−	0.871705i	0.999993	−	0.00379046i	$-0.00120654\pi$
$828$		0			0
$829$	9.84518	−	17.0524i	0.341937	−	0.592253i	−0.642855	−	0.765988i	$-0.722250\pi$
$829$	9.84518	−	17.0524i	0.341937	−	0.592253i	0.984792	+	0.173735i	$0.0555836\pi$
$830$		0			0
$831$	−5.86661	+	10.1613i	−0.203511	+	0.352491i
$832$		0			0
$833$	−18.8467	+	28.7513i	−0.652998	+	0.996174i
$834$		0			0
$835$	15.1827	+	26.2972i	0.525419	+	0.910053i
$836$		0			0
$837$	−16.6528	+	28.8435i	−0.575606	+	0.996979i
$838$		0			0
$839$	8.22919	+	14.2534i	0.284103	+	0.492081i	0.972391	−	0.233356i	$-0.0749708\pi$
$839$	8.22919	+	14.2534i	0.284103	+	0.492081i	−0.688288	+	0.725437i	$0.741638\pi$
$840$		0			0
$841$	4.18303	+	7.24522i	0.144242	+	0.249835i
$842$		0			0
$843$	9.67610	−	16.7595i	0.333263	−	0.577228i
$844$		0			0
$845$	−42.5361			−1.46329
$846$		0			0
$847$	−9.35870	+	15.1990i	−0.321569	+	0.522242i
$848$		0			0
$849$	23.3733			0.802168
$850$		0			0
$851$	4.70163	+	8.14346i	0.161170	+	0.279154i
$852$		0			0
$853$	24.6702	+	42.7301i	0.844692	+	1.46305i	0.885888	+	0.463899i	$0.153550\pi$
$853$	24.6702	+	42.7301i	0.844692	+	1.46305i	−0.0411963	+	0.999151i	$0.513117\pi$
$854$		0			0
$855$	−9.54482	−	26.7123i	−0.326426	−	0.913542i
$856$		0			0
$857$	29.2347			0.998637			0.499318	−	0.866419i	$-0.333584\pi$
$857$	29.2347			0.998637			0.499318	+	0.866419i	$0.333584\pi$
$858$		0			0
$859$	10.0460			0.342766			0.171383	−	0.985204i	$-0.445176\pi$
$859$	10.0460			0.342766			0.171383	+	0.985204i	$0.445176\pi$
$860$		0			0
$861$	11.4553	−	18.6039i	0.390395	−	0.634019i
$862$		0			0
$863$	6.76643	+	11.7198i	0.230332	+	0.398947i	0.957906	−	0.287083i	$-0.0926854\pi$
$863$	6.76643	+	11.7198i	0.230332	+	0.398947i	−0.727574	+	0.686029i	$0.759352\pi$
$864$		0			0
$865$	−21.4285	−	37.1152i	−0.728590	−	1.26196i
$866$		0			0
$867$	−7.64167			−0.259525
$868$		0			0
$869$	−18.7666	−	32.5047i	−0.636613	−	1.10265i
$870$		0			0
$871$	−10.5463			−0.357347
$872$		0			0
$873$	−4.90674	−	8.49872i	−0.166068	−	0.287638i
$874$		0			0
$875$	−10.6442	−	19.7045i	−0.359839	−	0.666135i
$876$		0			0
$877$	−6.16748	+	10.6824i	−0.208261	+	0.360718i	−0.951167	−	0.308677i	$-0.900114\pi$
$877$	−6.16748	+	10.6824i	−0.208261	+	0.360718i	0.742906	+	0.669396i	$0.233447\pi$
$878$		0			0
$879$	15.6255			0.527036
$880$		0			0
$881$	−46.1711			−1.55554			−0.777772	−	0.628547i	$-0.783650\pi$
$881$	−46.1711			−1.55554			−0.777772	+	0.628547i	$0.783650\pi$
$882$		0			0
$883$	0.291953	−	0.505678i	0.00982500	−	0.0170174i	−0.861071	−	0.508485i	$-0.830206\pi$
$883$	0.291953	−	0.505678i	0.00982500	−	0.0170174i	0.870896	+	0.491467i	$0.163539\pi$
$884$		0			0
$885$	14.4215	−	24.9788i	0.484773	−	0.839652i
$886$		0			0
$887$	50.9872			1.71198			0.855992	−	0.516990i	$-0.172947\pi$
$887$	50.9872			1.71198			0.855992	+	0.516990i	$0.172947\pi$
$888$		0			0
$889$	47.5994	+	1.34831i	1.59643	+	0.0452208i
$890$		0			0
$891$	−0.0889564	+	0.154077i	−0.00298015	+	0.00516178i
$892$		0			0
$893$	−2.54517	+	2.99722i	−0.0851710	+	0.100298i
$894$		0			0
$895$	7.22254	+	12.5098i	0.241423	+	0.418157i
$896$		0			0
$897$	−1.89121	+	3.27567i	−0.0631456	+	0.109371i
$898$		0			0
$899$	14.5369	+	25.1786i	0.484831	+	0.839753i
$900$		0			0
$901$	−33.9365	−	58.7798i	−1.13059	−	1.95824i
$902$		0			0
$903$	15.7029	−	25.5022i	0.522559	−	0.848660i
$904$		0			0
$905$	−25.8215	−	44.7241i	−0.858335	−	1.48668i
$906$		0			0
$907$	54.1112			1.79673			0.898366	−	0.439247i	$-0.144755\pi$
$907$	54.1112			1.79673			0.898366	+	0.439247i	$0.144755\pi$
$908$		0			0
$909$	0.474666	+	0.822146i	0.0157437	+	0.0272689i
$910$		0			0
$911$	28.7695			0.953176			0.476588	−	0.879127i	$-0.341873\pi$
$911$	28.7695			0.953176			0.476588	+	0.879127i	$0.341873\pi$
$912$		0			0
$913$	−1.01339	+	1.75524i	−0.0335383	+	0.0580901i
$914$		0			0
$915$	−4.43013	+	7.67320i	−0.146455	+	0.253668i
$916$		0			0
$917$	−56.0700	−	1.58825i	−1.85159	−	0.0524485i
$918$		0			0
$919$	−16.5467	−	28.6597i	−0.545826	−	0.945398i	−0.998554	−	0.0537494i	$-0.982883\pi$
$919$	−16.5467	−	28.6597i	−0.545826	−	0.945398i	0.452729	−	0.891648i	$-0.350451\pi$
$920$		0			0
$921$	8.14427	+	14.1063i	0.268363	+	0.464818i
$922$		0			0
$923$	1.78605			0.0587884
$924$		0			0
$925$	9.48655	−	16.4312i	0.311916	−	0.540254i
$926$		0			0
$927$	−3.64700	−	6.31679i	−0.119783	−	0.207471i
$928$		0			0
$929$	6.79934	−	11.7768i	0.223079	−	0.386384i	−0.732662	−	0.680592i	$-0.761723\pi$
$929$	6.79934	−	11.7768i	0.223079	−	0.386384i	0.955741	+	0.294208i	$0.0950559\pi$
$930$		0			0
$931$	8.62393	+	29.2682i	0.282638	+	0.959227i
$932$		0			0
$933$	−8.91499	+	15.4412i	−0.291864	+	0.505523i
$934$		0			0
$935$	36.4315	+	63.1012i	1.19144	+	2.06363i
$936$		0			0
$937$	−6.53650	+	11.3215i	−0.213538	+	0.369859i	−0.952819	−	0.303538i	$-0.901832\pi$
$937$	−6.53650	+	11.3215i	−0.213538	+	0.369859i	0.739281	+	0.673397i	$0.235165\pi$
$938$		0			0
$939$	35.2546			1.15049
$940$		0			0
$941$	3.35986	+	5.81945i	0.109528	+	0.189709i	0.915579	−	0.402138i	$-0.131733\pi$
$941$	3.35986	+	5.81945i	0.109528	+	0.189709i	−0.806051	+	0.591846i	$0.798399\pi$
$942$		0			0
$943$	−14.1138	−	24.4457i	−0.459607	−	0.796063i
$944$		0			0
$945$	48.4680	+	1.37291i	1.57667	+	0.0446609i
$946$		0			0
$947$	−1.43347	+	2.48285i	−0.0465817	+	0.0806818i	−0.888376	−	0.459116i	$-0.848166\pi$
$947$	−1.43347	+	2.48285i	−0.0465817	+	0.0806818i	0.841794	+	0.539798i	$0.181499\pi$
$948$		0			0
$949$	−4.77881	+	8.27714i	−0.155127	+	0.268687i
$950$		0			0
$951$	−28.9985			−0.940340
$952$		0			0
$953$	7.26488	+	12.5831i	0.235333	+	0.407608i	0.959369	−	0.282153i	$-0.0910487\pi$
$953$	7.26488	+	12.5831i	0.235333	+	0.407608i	−0.724037	+	0.689761i	$0.757715\pi$
$954$		0			0
$955$	4.32758			0.140037
$956$		0			0
$957$	10.2702	+	17.7885i	0.331989	+	0.575022i
$958$		0			0
$959$	−11.5636	+	18.7798i	−0.373408	+	0.606431i
$960$		0			0
$961$	−4.98278	−	8.63043i	−0.160735	−	0.278401i
$962$		0			0
$963$	−12.1197	−	20.9919i	−0.390551	−	0.676454i
$964$		0			0
$965$	−25.1800	+	43.6130i	−0.810572	+	1.40395i
$966$		0			0
$967$	24.2782	+	42.0510i	0.780733	+	1.35227i	0.931515	+	0.363703i	$0.118488\pi$
$967$	24.2782	+	42.0510i	0.780733	+	1.35227i	−0.150782	+	0.988567i	$0.548179\pi$
$968$		0			0
$969$	−14.8736	+	17.5153i	−0.477810	+	0.562672i
$970$		0			0
$971$	1.73628	−	3.00732i	0.0557198	−	0.0965095i	−0.836820	−	0.547478i	$-0.815588\pi$
$971$	1.73628	−	3.00732i	0.0557198	−	0.0965095i	0.892540	+	0.450968i	$0.148921\pi$
$972$		0			0
$973$	−16.4756	−	0.466691i	−0.528184	−	0.0149614i
$974$		0			0
$975$	7.63183			0.244414
$976$		0			0
$977$	−12.5888	+	21.8044i	−0.402750	+	0.697584i	−0.994057	−	0.108863i	$-0.965279\pi$
$977$	−12.5888	+	21.8044i	−0.402750	+	0.697584i	0.591306	+	0.806447i	$0.298612\pi$
$978$		0			0
$979$	36.3569	−	62.9721i	1.16197	−	2.01260i
$980$		0			0
$981$	−25.1171			−0.801928
$982$		0			0
$983$	11.8334			0.377426			0.188713	−	0.982032i	$-0.439568\pi$
$983$	11.8334			0.377426			0.188713	+	0.982032i	$0.439568\pi$
$984$		0			0
$985$	−8.35400	+	14.4695i	−0.266180	+	0.461038i
$986$		0			0
$987$	−1.21760	−	2.25403i	−0.0387567	−	0.0717465i
$988$		0			0
$989$	−19.3471	−	33.5102i	−0.615203	−	1.06556i
$990$		0			0
$991$	−15.1623			−0.481646			−0.240823	−	0.970569i	$-0.577417\pi$
$991$	−15.1623			−0.481646			−0.240823	+	0.970569i	$0.577417\pi$
$992$		0			0
$993$	−0.975776	−	1.69009i	−0.0309653	−	0.0536335i
$994$		0			0
$995$	51.4565			1.63128
$996$		0			0
$997$	−5.07089	−	8.78305i	−0.160597	−	0.278162i	0.774486	−	0.632591i	$-0.218009\pi$
$997$	−5.07089	−	8.78305i	−0.160597	−	0.278162i	−0.935083	+	0.354429i	$0.884675\pi$
$998$		0			0
$999$	6.66776	+	11.5489i	0.210959	+	0.365391i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	532.2.l.b.501.5	yes	24
7.2	even	3		532.2.k.b.121.8	✓	24
19.11	even	3		532.2.k.b.277.8	yes	24
133.30	even	3	inner	532.2.l.b.429.5	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
532.2.k.b.121.8	✓	24	7.2	even	3
532.2.k.b.277.8	yes	24	19.11	even	3
532.2.l.b.429.5	yes	24	133.30	even	3	inner
532.2.l.b.501.5	yes	24	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 532 = 2^{2} \cdot 7 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	532.l (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-1.07341 q^{3} +(-1.76093 + 3.05002i) q^{5} +(-1.25747 - 2.32783i) q^{7} -1.84780 q^{9} +(2.10632 - 3.64826i) q^{11} +(0.480174 - 0.831685i) q^{13} +(1.89019 - 3.27391i) q^{15} +4.91112 q^{17} +(2.82145 - 3.32256i) q^{19} +(1.34977 + 2.49870i) q^{21} +3.66925 q^{23} +(-3.70175 - 6.41162i) q^{25} +5.20366 q^{27} +(2.27123 - 3.93389i) q^{29} +(-3.20022 + 5.54294i) q^{31} +(-2.26094 + 3.91606i) q^{33} +(9.31423 + 0.263836i) q^{35} +(1.28136 + 2.21938i) q^{37} +(-0.515421 + 0.892735i) q^{39} +(-3.84650 - 6.66233i) q^{41} +(-5.27278 - 9.13272i) q^{43} +(3.25385 - 5.63583i) q^{45} -0.902080 q^{47} +(-3.83755 + 5.85433i) q^{49} -5.27162 q^{51} +(-6.91014 - 11.9687i) q^{53} +(7.41817 + 12.8486i) q^{55} +(-3.02856 + 3.56646i) q^{57} +7.62965 q^{59} -2.34374 q^{61} +(2.32355 + 4.30136i) q^{63} +(1.69110 + 2.92908i) q^{65} +(-5.49087 - 9.51046i) q^{67} -3.93859 q^{69} +(0.929896 + 1.61063i) q^{71} -9.95225 q^{73} +(3.97348 + 6.88227i) q^{75} +(-11.1411 - 0.315586i) q^{77} +(4.45483 - 7.71599i) q^{79} -0.0422331 q^{81} -0.481118 q^{83} +(-8.64814 + 14.9790i) q^{85} +(-2.43795 + 4.22265i) q^{87} +17.2609 q^{89} +(-2.53982 - 0.0719434i) q^{91} +(3.43513 - 5.94982i) q^{93} +(5.16550 + 14.4563i) q^{95} +(2.65545 + 4.59937i) q^{97} +(-3.89206 + 6.74125i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 2 q^{3} - 6 q^{5} - 6 q^{7} + 30 q^{9} + q^{11} - 7 q^{13} - 2 q^{15} - 6 q^{17} + 17 q^{19} - 18 q^{21} - 16 q^{23} - 8 q^{25} + 20 q^{27} - 22 q^{29} - 7 q^{31} + 7 q^{33} - 21 q^{35} + 9 q^{37}+ \cdots - 27 q^{99}+O(q^{100}) \) 24 * q + 2 * q^3 - 6 * q^5 - 6 * q^7 + 30 * q^9 + q^11 - 7 * q^13 - 2 * q^15 - 6 * q^17 + 17 * q^19 - 18 * q^21 - 16 * q^23 - 8 * q^25 + 20 * q^27 - 22 * q^29 - 7 * q^31 + 7 * q^33 - 21 * q^35 + 9 * q^37 + 12 * q^39 - 11 * q^41 - 9 * q^43 - 28 * q^45 - 22 * q^47 - 32 * q^49 - 16 * q^51 - 7 * q^53 - 11 * q^55 + 11 * q^57 + 16 * q^59 + 12 * q^61 + 20 * q^63 + 3 * q^65 - 27 * q^67 + 108 * q^69 - 13 * q^71 + 20 * q^73 + 25 * q^75 + 2 * q^77 - 14 * q^79 + 80 * q^81 - 12 * q^83 - 19 * q^85 + 19 * q^87 + 74 * q^89 - 21 * q^91 + 5 * q^93 + 47 * q^95 - 21 * q^97 - 27 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

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