LMFDB - Embedded newform 585.2.bs.b.289.8

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [585,2,Mod(289,585)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(585, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 3, 2])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("585.289"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 585 = 3^{2} \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	585.bs (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [24] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$4.67124851824$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 195)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			289.8
Character	$\chi$	$=$	585.289
Dual form			585.2.bs.b.334.8

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.729738 - 0.421315i) q^{2} +(-0.644988 + 1.11715i) q^{4} +(-2.23540 + 0.0545741i) q^{5} +(0.347589 + 0.200681i) q^{7} +2.77223i q^{8} +(-1.60827 + 0.981632i) q^{10} +(-2.45354 - 4.24965i) q^{11} +(-3.55974 - 0.572960i) q^{13} +0.338199 q^{14} +(-0.121995 - 0.211302i) q^{16} +(-6.13203 - 3.54033i) q^{17} +(1.12724 - 1.95244i) q^{19} +(1.38084 - 2.53248i) q^{20} +(-3.58088 - 2.06742i) q^{22} +(0.861695 - 0.497500i) q^{23} +(4.99404 - 0.243990i) q^{25} +(-2.83907 + 1.08166i) q^{26} +(-0.448381 + 0.258873i) q^{28} +(3.94133 + 6.82658i) q^{29} -6.30120 q^{31} +(-4.97969 - 2.87503i) q^{32} -5.96637 q^{34} +(-0.787953 - 0.429632i) q^{35} +(-7.62688 + 4.40338i) q^{37} -1.89969i q^{38} +(-0.151292 - 6.19705i) q^{40} +(2.65994 + 4.60715i) q^{41} +(-1.74416 - 1.00699i) q^{43} +6.33001 q^{44} +(0.419208 - 0.726090i) q^{46} +4.62317i q^{47} +(-3.41945 - 5.92267i) q^{49} +(3.54155 - 2.28211i) q^{50} +(2.93607 - 3.60721i) q^{52} +10.8496i q^{53} +(5.71656 + 9.36577i) q^{55} +(-0.556333 + 0.963596i) q^{56} +(5.75228 + 3.32108i) q^{58} +(1.52224 - 2.63659i) q^{59} +(3.55088 - 6.15031i) q^{61} +(-4.59822 + 2.65479i) q^{62} -4.35718 q^{64} +(7.98871 + 1.08653i) q^{65} +(-5.32891 + 3.07665i) q^{67} +(7.91018 - 4.56694i) q^{68} +(-0.756010 + 0.0184569i) q^{70} +(3.16446 - 5.48101i) q^{71} +1.01273i q^{73} +(-3.71042 + 6.42663i) q^{74} +(1.45411 + 2.51860i) q^{76} -1.96951i q^{77} +10.2755 q^{79} +(0.284240 + 0.465687i) q^{80} +(3.88212 + 2.24134i) q^{82} -10.5337i q^{83} +(13.9008 + 7.57941i) q^{85} -1.69704 q^{86} +(11.7810 - 6.80177i) q^{88} +(-0.262260 - 0.454247i) q^{89} +(-1.12234 - 0.913524i) q^{91} +1.28353i q^{92} +(1.94781 + 3.37371i) q^{94} +(-2.41329 + 4.42601i) q^{95} +(-8.15979 - 4.71106i) q^{97} +(-4.99061 - 2.88133i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 8 q^{4} - 4 q^{5} - 4 q^{10} - 4 q^{11} - 24 q^{14} + 16 q^{16} - 16 q^{19} + 16 q^{20} - 16 q^{25} + 48 q^{26} + 12 q^{29} + 8 q^{31} - 32 q^{34} - 10 q^{35} - 48 q^{40} + 40 q^{41} - 40 q^{44}+ \cdots + 28 q^{95}+O(q^{100}) $ 24 * q + 8 * q^4 - 4 * q^5 - 4 * q^10 - 4 * q^11 - 24 * q^14 + 16 * q^16 - 16 * q^19 + 16 * q^20 - 16 * q^25 + 48 * q^26 + 12 * q^29 + 8 * q^31 - 32 * q^34 - 10 * q^35 - 48 * q^40 + 40 * q^41 - 40 * q^44 - 24 * q^46 - 16 * q^49 - 20 * q^50 + 20 * q^55 + 24 * q^56 - 12 * q^59 + 20 * q^61 + 48 * q^64 - 14 * q^65 - 56 * q^70 - 4 * q^71 + 12 * q^74 + 8 * q^76 + 136 * q^79 + 4 * q^80 - 4 * q^85 - 48 * q^86 + 64 * q^89 + 60 * q^91 - 48 * q^94 + 28 * q^95

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/585\mathbb{Z}\right)^\times$.

$n$	$326$	$352$	$496$
$\chi(n)$	$1$	$-1$	$e\left(\frac{1}{3}\right)$

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 $

$2$	0.729738	−	0.421315i	0.516003	−	0.297914i	−0.219295	−	0.975659i	$-0.570376\pi$
$2$	0.729738	−	0.421315i	0.516003	−	0.297914i	0.735298	+	0.677744i	$0.237042\pi$
$3$		0			0
$3$		0			0
$4$	−0.644988	+	1.11715i	−0.322494	+	0.558576i
$5$	−2.23540	+	0.0545741i	−0.999702	+	0.0244063i
$5$	−2.23540	+	0.0545741i	−0.999702	+	0.0244063i
$6$		0			0
$7$	0.347589	+	0.200681i	0.131376	+	0.0758501i	0.564248	−	0.825606i	$-0.309166\pi$
$7$	0.347589	+	0.200681i	0.131376	+	0.0758501i	−0.432871	+	0.901456i	$0.642500\pi$
$8$			2.77223i			0.980131i
$9$		0			0
$10$	−1.60827	+	0.981632i	−0.508578	+	0.310419i
$11$	−2.45354	−	4.24965i	−0.739769	−	1.28132i	−0.952599	−	0.304228i	$-0.901601\pi$
$11$	−2.45354	−	4.24965i	−0.739769	−	1.28132i	0.212830	−	0.977089i	$-0.431732\pi$
$12$		0			0
$13$	−3.55974	−	0.572960i	−0.987293	−	0.158911i
$13$	−3.55974	−	0.572960i	−0.987293	−	0.158911i
$14$	0.338199			0.0903874
$15$		0			0
$16$	−0.121995	−	0.211302i	−0.0304988	−	0.0528254i
$17$	−6.13203	−	3.54033i	−1.48724	−	0.858656i	−0.487343	−	0.873211i	$-0.662034\pi$
$17$	−6.13203	−	3.54033i	−1.48724	−	0.858656i	−0.999894	+	0.0145544i	$0.995367\pi$
$18$		0			0
$19$	1.12724	−	1.95244i	0.258607	−	0.447920i	−0.707262	−	0.706952i	$-0.750070\pi$
$19$	1.12724	−	1.95244i	0.258607	−	0.447920i	0.965869	+	0.259031i	$0.0834032\pi$
$20$	1.38084	−	2.53248i	0.308765	−	0.566281i
$21$		0			0
$22$	−3.58088	−	2.06742i	−0.763446	−	0.440776i
$23$	0.861695	−	0.497500i	0.179676	−	0.103736i	−0.407465	−	0.913221i	$-0.633587\pi$
$23$	0.861695	−	0.497500i	0.179676	−	0.103736i	0.587140	+	0.809485i	$0.300254\pi$
$24$		0			0
$25$	4.99404	−	0.243990i	0.998809	−	0.0487981i
$26$	−2.83907	+	1.08166i	−0.556788	+	0.212130i
$27$		0			0
$28$	−0.448381	+	0.258873i	−0.0847361	+	0.0489224i
$29$	3.94133	+	6.82658i	0.731886	+	1.26766i	0.956076	+	0.293119i	$0.0946932\pi$
$29$	3.94133	+	6.82658i	0.731886	+	1.26766i	−0.224190	+	0.974546i	$0.571973\pi$
$30$		0			0
$31$	−6.30120			−1.13173			−0.565864	−	0.824499i	$-0.691457\pi$
$31$	−6.30120			−1.13173			−0.565864	+	0.824499i	$0.691457\pi$
$32$	−4.97969	−	2.87503i	−0.880293	−	0.508238i
$33$		0			0
$34$	−5.96637			−1.02322
$35$	−0.787953	−	0.429632i	−0.133188	−	0.0726211i
$36$		0			0
$37$	−7.62688	+	4.40338i	−1.25385	+	0.723912i	−0.971872	−	0.235509i	$-0.924324\pi$
$37$	−7.62688	+	4.40338i	−1.25385	+	0.723912i	−0.281980	+	0.959420i	$0.590991\pi$
$38$		−	1.89969i		−	0.308171i
$39$		0			0
$40$	−0.151292	−	6.19705i	−0.0239214	−	0.979839i
$41$	2.65994	+	4.60715i	0.415413	+	0.719517i	0.995472	−	0.0950582i	$-0.0303037\pi$
$41$	2.65994	+	4.60715i	0.415413	+	0.719517i	−0.580059	+	0.814575i	$0.696970\pi$
$42$		0			0
$43$	−1.74416	−	1.00699i	−0.265982	−	0.153565i	0.361078	−	0.932536i	$-0.382409\pi$
$43$	−1.74416	−	1.00699i	−0.265982	−	0.153565i	−0.627060	+	0.778971i	$0.715742\pi$
$44$	6.33001			0.954284
$45$		0			0
$46$	0.419208	−	0.726090i	0.0618088	−	0.107056i
$47$			4.62317i			0.674359i	0.941440	+	0.337180i	$0.109473\pi$
$47$			4.62317i			0.674359i	−0.941440	+	0.337180i	$0.890527\pi$
$48$		0			0
$49$	−3.41945	−	5.92267i	−0.488494	−	0.846096i
$50$	3.54155	−	2.28211i	0.500851	−	0.322739i
$51$		0			0
$52$	2.93607	−	3.60721i	0.407160	−	0.500230i
$53$			10.8496i			1.49031i	0.666890	+	0.745156i	$0.267625\pi$
$53$			10.8496i			1.49031i	−0.666890	+	0.745156i	$0.732375\pi$
$54$		0			0
$55$	5.71656	+	9.36577i	0.770821	+	1.26288i
$56$	−0.556333	+	0.963596i	−0.0743431	+	0.128766i
$57$		0			0
$58$	5.75228	+	3.32108i	0.755311	+	0.436079i
$59$	1.52224	−	2.63659i	0.198178	−	0.343255i	−0.749759	−	0.661711i	$-0.769831\pi$
$59$	1.52224	−	2.63659i	0.198178	−	0.343255i	0.947938	+	0.318455i	$0.103164\pi$
$60$		0			0
$61$	3.55088	−	6.15031i	0.454644	−	0.787466i	−0.544024	−	0.839070i	$-0.683100\pi$
$61$	3.55088	−	6.15031i	0.454644	−	0.787466i	0.998668	+	0.0516038i	$0.0164333\pi$
$62$	−4.59822	+	2.65479i	−0.583975	+	0.337158i
$63$		0			0
$64$	−4.35718			−0.544648
$65$	7.98871	+	1.08653i	0.990877	+	0.134767i
$66$		0			0
$67$	−5.32891	+	3.07665i	−0.651030	+	0.375873i	−0.788851	−	0.614585i	$-0.789324\pi$
$67$	−5.32891	+	3.07665i	−0.651030	+	0.375873i	0.137821	+	0.990457i	$0.455990\pi$
$68$	7.91018	−	4.56694i	0.959250	−	0.553823i
$69$		0			0
$70$	−0.756010	+	0.0184569i	−0.0903604	+	0.00220602i
$71$	3.16446	−	5.48101i	0.375553	−	0.650476i	−0.614857	−	0.788639i	$-0.710786\pi$
$71$	3.16446	−	5.48101i	0.375553	−	0.650476i	0.990410	+	0.138162i	$0.0441196\pi$
$72$		0			0
$73$			1.01273i			0.118531i	0.998242	+	0.0592655i	$0.0188759\pi$
$73$			1.01273i			0.118531i	−0.998242	+	0.0592655i	$0.981124\pi$
$74$	−3.71042	+	6.42663i	−0.431327	+	0.747081i
$75$		0			0
$76$	1.45411	+	2.51860i	0.166798	+	0.288903i
$77$		−	1.96951i		−	0.224446i
$78$		0			0
$79$	10.2755			1.15608			0.578042	−	0.816007i	$-0.303817\pi$
$79$	10.2755			1.15608			0.578042	+	0.816007i	$0.303817\pi$
$80$	0.284240	+	0.465687i	0.0317790	+	0.0520653i
$81$		0			0
$82$	3.88212	+	2.24134i	0.428709	+	0.247515i
$83$		−	10.5337i		−	1.15623i	−0.815956	−	0.578114i	$-0.803789\pi$
$83$		−	10.5337i		−	1.15623i	0.815956	−	0.578114i	$-0.196211\pi$
$84$		0			0
$85$	13.9008	+	7.57941i	1.50775	+	0.822103i
$86$	−1.69704			−0.182997
$87$		0			0
$88$	11.7810	−	6.80177i	1.25586	−	0.725071i
$89$	−0.262260	−	0.454247i	−0.0277995	−	0.0481501i	0.851791	−	0.523882i	$-0.175517\pi$
$89$	−0.262260	−	0.454247i	−0.0277995	−	0.0481501i	−0.879590	+	0.475732i	$0.842183\pi$
$90$		0			0
$91$	−1.12234	−	0.913524i	−0.117653	−	0.0957634i
$92$			1.28353i			0.133817i
$93$		0			0
$94$	1.94781	+	3.37371i	0.200901	+	0.347971i
$95$	−2.41329	+	4.42601i	−0.247598	+	0.454099i
$96$		0			0
$97$	−8.15979	−	4.71106i	−0.828502	−	0.478336i	0.0248378	−	0.999691i	$-0.492093\pi$
$97$	−8.15979	−	4.71106i	−0.828502	−	0.478336i	−0.853339	+	0.521356i	$0.825426\pi$
$98$	−4.99061	−	2.88133i	−0.504128	−	0.291059i
$99$		0			0
$100$	−2.94852	+	5.73648i	−0.294852	+	0.573648i
$101$	−2.87707	−	4.98324i	−0.286280	−	0.495851i	0.686639	−	0.726998i	$-0.259085\pi$
$101$	−2.87707	−	4.98324i	−0.286280	−	0.495851i	−0.972919	+	0.231148i	$0.925752\pi$
$102$		0			0
$103$			15.3992i			1.51733i	0.651481	+	0.758665i	$0.274148\pi$
$103$			15.3992i			1.51733i	−0.651481	+	0.758665i	$0.725852\pi$
$104$	1.58838	−	9.86840i	0.155753	−	0.967677i
$105$		0			0
$106$	4.57111	+	7.91739i	0.443985	+	0.769005i
$107$	−12.9024	+	7.44919i	−1.24732	+	0.720141i	−0.970574	−	0.240802i	$-0.922589\pi$
$107$	−12.9024	+	7.44919i	−1.24732	+	0.720141i	−0.276746	+	0.960943i	$0.589256\pi$
$108$		0			0
$109$	1.69762			0.162602			0.0813011	−	0.996690i	$-0.474092\pi$
$109$	1.69762			0.162602			0.0813011	+	0.996690i	$0.474092\pi$
$110$	8.11753	+	4.42609i	0.773976	+	0.422011i
$111$		0			0
$112$		−	0.0979282i		−	0.00925335i
$113$	1.94685	+	1.12402i	0.183145	+	0.105739i	0.588769	−	0.808301i	$-0.299613\pi$
$113$	1.94685	+	1.12402i	0.183145	+	0.105739i	−0.405625	+	0.914040i	$0.632946\pi$
$114$		0			0
$115$	−1.89908	+	1.15914i	−0.177091	+	0.108090i
$116$	−10.1684			−0.944116
$117$		0			0
$118$		−	2.56536i		−	0.236161i
$119$	−1.42095	−	2.46116i	−0.130258	−	0.225614i
$120$		0			0
$121$	−6.53968	+	11.3271i	−0.594516	+	1.02973i
$122$		−	5.98415i		−	0.541780i
$123$		0			0
$124$	4.06420	−	7.03939i	0.364976	−	0.632156i
$125$	−11.1504	+	0.817962i	−0.997320	+	0.0731607i
$126$		0			0
$127$	14.9506	−	8.63173i	1.32665	−	0.765942i	0.341871	−	0.939747i	$-0.388939\pi$
$127$	14.9506	−	8.63173i	1.32665	−	0.765942i	0.984780	+	0.173804i	$0.0556060\pi$
$128$	6.77978	−	3.91431i	0.599254	−	0.345979i
$129$		0			0
$130$	6.28744	−	2.57288i	0.551445	−	0.225656i
$131$	4.59071			0.401092			0.200546	−	0.979684i	$-0.435728\pi$
$131$	4.59071			0.401092			0.200546	+	0.979684i	$0.435728\pi$
$132$		0			0
$133$	0.783633	−	0.452431i	0.0679496	−	0.0392307i
$134$	−2.59247	+	4.49030i	−0.223956	+	0.387903i
$135$		0			0
$136$	9.81461	−	16.9994i	0.841596	−	1.45769i
$137$	−4.28724	−	2.47524i	−0.366284	−	0.211474i	0.305550	−	0.952176i	$-0.401160\pi$
$137$	−4.28724	−	2.47524i	−0.366284	−	0.211474i	−0.671834	+	0.740702i	$0.734493\pi$
$138$		0			0
$139$	−6.63214	+	11.4872i	−0.562530	+	0.974331i	0.434744	+	0.900554i	$0.356839\pi$
$139$	−6.63214	+	11.4872i	−0.562530	+	0.974331i	−0.997275	+	0.0737774i	$0.976495\pi$
$140$	0.988185	−	0.603155i	0.0835169	−	0.0509759i
$141$		0			0
$142$		−	5.33294i		−	0.447530i
$143$	6.29906	+	16.5334i	0.526754	+	1.38259i
$144$		0			0
$145$	−9.18301	−	15.0451i	−0.762607	−	1.24942i
$146$	0.426678	+	0.739028i	0.0353121	+	0.0611624i
$147$		0			0
$148$		−	11.3605i		−	0.933829i
$149$	1.57886	−	2.73467i	0.129345	−	0.224033i	−0.794078	−	0.607816i	$-0.792046\pi$
$149$	1.57886	−	2.73467i	0.129345	−	0.224033i	0.923423	+	0.383783i	$0.125379\pi$
$150$		0			0
$151$	−18.5878			−1.51266			−0.756328	−	0.654193i	$-0.773009\pi$
$151$	−18.5878			−1.51266			−0.756328	+	0.654193i	$0.773009\pi$
$152$	5.41261	+	3.12497i	0.439021	+	0.253469i
$153$		0			0
$154$	−0.829782	−	1.43723i	−0.0668658	−	0.115815i
$155$	14.0857	−	0.343882i	1.13139	−	0.0276213i
$156$		0			0
$157$		−	10.7802i		−	0.860351i	−0.902745	−	0.430175i	$-0.858452\pi$
$157$		−	10.7802i		−	0.860351i	0.902745	−	0.430175i	$-0.141548\pi$
$158$	7.49843	−	4.32922i	0.596543	−	0.344414i
$159$		0			0
$160$	11.2885	+	6.15508i	0.892435	+	0.486602i
$161$	0.399354			0.0314735
$162$		0			0
$163$	1.36302	+	0.786941i	0.106760	+	0.0616380i	0.552429	−	0.833560i	$-0.313701\pi$
$163$	1.36302	+	0.786941i	0.106760	+	0.0616380i	−0.445669	+	0.895198i	$0.647034\pi$
$164$	−6.86252			−0.535873
$165$		0			0
$166$	−4.43802	−	7.68687i	−0.344457	−	0.596617i
$167$	13.0492	−	7.53397i	1.00978	−	0.582996i	0.0986516	−	0.995122i	$-0.468547\pi$
$167$	13.0492	−	7.53397i	1.00978	−	0.582996i	0.911127	+	0.412126i	$0.135214\pi$
$168$		0			0
$169$	12.3434	+	4.07917i	0.949495	+	0.313783i
$170$	13.3372	−	0.325610i	1.02292	−	0.0249731i
$171$		0			0
$172$	2.24993	−	1.29900i	0.171555	−	0.0990475i
$173$	−2.94981	−	1.70307i	−0.224270	−	0.129482i	0.383656	−	0.923476i	$-0.374665\pi$
$173$	−2.94981	−	1.70307i	−0.224270	−	0.129482i	−0.607926	+	0.793994i	$0.707998\pi$
$174$		0			0
$175$	1.78484	+	0.917399i	0.134921	+	0.0693488i
$176$	−0.598639	+	1.03687i	−0.0451241	+	0.0781572i
$177$		0			0
$178$	−0.382762	−	0.220988i	−0.0286892	−	0.0165637i
$179$	0.300516	+	0.520508i	0.0224616	+	0.0389046i	0.877038	−	0.480422i	$-0.159516\pi$
$179$	0.300516	+	0.520508i	0.0224616	+	0.0389046i	−0.854576	+	0.519326i	$0.826183\pi$
$180$		0			0
$181$	−17.0607			−1.26811			−0.634056	−	0.773287i	$-0.718611\pi$
$181$	−17.0607			−1.26811			−0.634056	+	0.773287i	$0.718611\pi$
$182$	−1.20390	−	0.193774i	−0.0892388	−	0.0143635i
$183$		0			0
$184$	1.37918	+	2.38882i	0.101675	+	0.176106i
$185$	16.8088	−	10.2596i	1.23581	−	0.754298i
$186$		0			0
$187$			34.7453i			2.54083i
$188$	−5.16479	−	2.98189i	−0.376681	−	0.217477i
$189$		0			0
$190$	0.103674	+	4.24658i	0.00752131	+	0.308079i
$191$	3.10083	−	5.37079i	0.224368	−	0.388617i	−0.731762	−	0.681561i	$-0.761302\pi$
$191$	3.10083	−	5.37079i	0.224368	−	0.388617i	0.956130	+	0.292944i	$0.0946349\pi$
$192$		0			0
$193$	7.91367	−	4.56896i	0.569639	−	0.328881i	−0.187366	−	0.982290i	$-0.559995\pi$
$193$	7.91367	−	4.56896i	0.569639	−	0.328881i	0.757005	+	0.653409i	$0.226662\pi$
$194$	−7.93935			−0.570012
$195$		0			0
$196$	8.82203			0.630145
$197$	−18.7148	+	10.8050i	−1.33337	+	0.769823i	−0.985815	−	0.167836i	$-0.946322\pi$
$197$	−18.7148	+	10.8050i	−1.33337	+	0.769823i	−0.347557	+	0.937659i	$0.612989\pi$
$198$		0			0
$199$	1.27223	−	2.20357i	0.0901860	−	0.156207i	−0.817403	−	0.576066i	$-0.804587\pi$
$199$	1.27223	−	2.20357i	0.0901860	−	0.156207i	0.907589	+	0.419859i	$0.137921\pi$
$200$	0.676397	+	13.8446i	0.0478285	+	0.978964i
$201$		0			0
$202$	−4.19902	−	2.42431i	−0.295442	−	0.170574i
$203$			3.16379i			0.222055i
$204$		0			0
$205$	−6.19747	−	10.1537i	−0.432850	−	0.709164i
$206$	6.48792	+	11.2374i	0.452034	+	0.782947i
$207$		0			0
$208$	0.313203	+	0.822077i	0.0217167	+	0.0570008i
$209$	−11.0629			−0.765238
$210$		0			0
$211$	5.54061	+	9.59663i	0.381432	+	0.660659i	0.991267	−	0.131869i	$-0.0420978\pi$
$211$	5.54061	+	9.59663i	0.381432	+	0.660659i	−0.609836	+	0.792528i	$0.708765\pi$
$212$	−12.1207	−	6.99789i	−0.832453	−	0.480617i
$213$		0			0
$214$	−6.27691	+	10.8719i	−0.429081	+	0.743189i
$215$	3.95386	+	2.15585i	0.269651	+	0.147027i
$216$		0			0
$217$	−2.19023	−	1.26453i	−0.148682	−	0.0858417i
$218$	1.23882	−	0.715231i	0.0839032	−	0.0484416i
$219$		0			0
$220$	−14.1501	+	0.345455i	−0.954000	+	0.0232905i
$221$	19.7999	+	16.1161i	1.33189	+	1.08408i
$222$		0			0
$223$	−0.460340	+	0.265778i	−0.0308267	+	0.0177978i	−0.515334	−	0.856989i	$-0.672332\pi$
$223$	−0.460340	+	0.265778i	−0.0308267	+	0.0177978i	0.484507	+	0.874787i	$0.338999\pi$
$224$	−1.15392	−	1.99865i	−0.0770998	−	0.133541i
$225$		0			0
$226$	1.89426			0.126004
$227$	−18.5220	−	10.6937i	−1.22935	−	0.709764i	−0.262454	−	0.964944i	$-0.584532\pi$
$227$	−18.5220	−	10.6937i	−1.22935	−	0.709764i	−0.966894	+	0.255180i	$0.917865\pi$
$228$		0			0
$229$	0.406502			0.0268624			0.0134312	−	0.999910i	$-0.495725\pi$
$229$	0.406502			0.0268624			0.0134312	+	0.999910i	$0.495725\pi$
$230$	−0.897473	+	1.64598i	−0.0591776	+	0.108533i
$231$		0			0
$232$	−18.9249	+	10.9263i	−1.24248	+	0.717345i
$233$			2.66379i			0.174510i	0.996186	+	0.0872552i	$0.0278096\pi$
$233$			2.66379i			0.174510i	−0.996186	+	0.0872552i	$0.972190\pi$
$234$		0			0
$235$	−0.252306	−	10.3347i	−0.0164586	−	0.674158i
$236$	1.96365	+	3.40114i	0.127823	+	0.221395i
$237$		0			0
$238$	−2.07385	−	1.19734i	−0.134427	−	0.0776117i
$239$	−15.8317			−1.02407			−0.512034	−	0.858965i	$-0.671108\pi$
$239$	−15.8317			−1.02407			−0.512034	+	0.858965i	$0.671108\pi$
$240$		0			0
$241$	11.6570	−	20.1906i	0.750895	−	1.30059i	−0.196495	−	0.980505i	$-0.562956\pi$
$241$	11.6570	−	20.1906i	0.750895	−	1.30059i	0.947390	−	0.320083i	$-0.103711\pi$
$242$			11.0210i			0.708460i
$243$		0			0
$244$	4.58055	+	7.93375i	0.293240	+	0.507906i
$245$	7.96708	+	13.0529i	0.508998	+	0.833921i
$246$		0			0
$247$	−5.13135	+	6.30431i	−0.326500	+	0.401133i
$248$		−	17.4684i		−	1.10924i
$249$		0			0
$250$	−7.79224	+	5.29472i	−0.492824	+	0.334867i
$251$	0.650814	−	1.12724i	0.0410790	−	0.0711509i	−0.844755	−	0.535153i	$-0.820254\pi$
$251$	0.650814	−	1.12724i	0.0410790	−	0.0711509i	0.885834	+	0.464002i	$0.153587\pi$
$252$		0			0
$253$	−4.22840	−	2.44127i	−0.265837	−	0.153481i
$254$	7.27335	−	12.5978i	0.456371	−	0.790457i
$255$		0			0
$256$	7.65549	−	13.2597i	0.478468	−	0.828731i
$257$	8.55103	−	4.93694i	0.533399	−	0.307958i	−0.209001	−	0.977915i	$-0.567021\pi$
$257$	8.55103	−	4.93694i	0.533399	−	0.307958i	0.742399	+	0.669958i	$0.233688\pi$
$258$		0			0
$259$	−3.53469			−0.219635
$260$	−6.36644	+	8.22380i	−0.394830	+	0.510019i
$261$		0			0
$262$	3.35001	−	1.93413i	0.206965	−	0.119491i
$263$	0.462121	−	0.266805i	0.0284956	−	0.0164519i	−0.485685	−	0.874134i	$-0.661430\pi$
$263$	0.462121	−	0.266805i	0.0284956	−	0.0164519i	0.514180	+	0.857682i	$0.328096\pi$
$264$		0			0
$265$	−0.592110	−	24.2533i	−0.0363730	−	1.48987i
$266$	0.381232	−	0.660312i	0.0233748	−	0.0404864i
$267$		0			0
$268$		−	7.93761i		−	0.484867i
$269$	6.80199	−	11.7814i	0.414725	−	0.718324i	−0.580675	−	0.814136i	$-0.697211\pi$
$269$	6.80199	−	11.7814i	0.414725	−	0.718324i	0.995400	+	0.0958112i	$0.0305445\pi$
$270$		0			0
$271$	11.9163	+	20.6396i	0.723862	+	1.25377i	0.959441	+	0.281911i	$0.0909681\pi$
$271$	11.9163	+	20.6396i	0.723862	+	1.25377i	−0.235579	+	0.971855i	$0.575699\pi$
$272$			1.72761i			0.104752i
$273$		0			0
$274$	−4.17142			−0.252004
$275$	−13.2899	−	20.6243i	−0.801413	−	1.24369i
$276$		0			0
$277$	−16.6388	−	9.60639i	−0.999726	−	0.577192i	−0.0915586	−	0.995800i	$-0.529185\pi$
$277$	−16.6388	−	9.60639i	−0.999726	−	0.577192i	−0.908167	+	0.418608i	$0.862518\pi$
$278$			11.1769i			0.670344i
$279$		0			0
$280$	1.19104	−	2.18439i	0.0711782	−	0.130542i
$281$	−6.31792			−0.376895			−0.188448	−	0.982083i	$-0.560346\pi$
$281$	−6.31792			−0.376895			−0.188448	+	0.982083i	$0.560346\pi$
$282$		0			0
$283$	−26.1587	+	15.1027i	−1.55497	+	0.897765i	−0.557249	+	0.830345i	$0.688143\pi$
$283$	−26.1587	+	15.1027i	−1.55497	+	0.897765i	−0.997725	+	0.0674193i	$0.978523\pi$
$284$	4.08208	+	7.07037i	0.242227	+	0.419549i
$285$		0			0
$286$	11.5624	+	9.41117i	0.683701	+	0.556494i
$287$			2.13519i			0.126037i
$288$		0			0
$289$	16.5679	+	28.6964i	0.974582	+	1.68803i
$290$	−13.0399	−	7.11002i	−0.765729	−	0.417515i
$291$		0			0
$292$	−1.13137	−	0.653199i	−0.0662086	−	0.0382256i
$293$	−6.18072	−	3.56844i	−0.361081	−	0.208470i	0.308474	−	0.951233i	$-0.400182\pi$
$293$	−6.18072	−	3.56844i	−0.361081	−	0.208470i	−0.669555	+	0.742762i	$0.733515\pi$
$294$		0			0
$295$	−3.25892	+	5.97692i	−0.189742	+	0.347990i
$296$	−12.2072	−	21.1435i	−0.709528	−	1.22894i
$297$		0			0
$298$		−	2.66079i		−	0.154135i
$299$	−3.35245	+	1.27725i	−0.193877	+	0.0738653i
$300$		0			0
$301$	−0.404167	−	0.700038i	−0.0232958	−	0.0403495i
$302$	−13.5642	+	7.83132i	−0.780535	+	0.450642i
$303$		0			0
$304$	−0.550072			−0.0315488
$305$	−7.60200	+	13.9422i	−0.435289	+	0.798328i
$306$		0			0
$307$		−	9.91349i		−	0.565793i	−0.959150	−	0.282897i	$-0.908705\pi$
$307$		−	9.91349i		−	0.565793i	0.959150	−	0.282897i	$-0.0912953\pi$
$308$	2.20024	+	1.27031i	0.125370	+	0.0723826i
$309$		0			0
$310$	10.1340	−	6.18546i	0.575572	−	0.351310i
$311$	−6.04584			−0.342828			−0.171414	−	0.985199i	$-0.554834\pi$
$311$	−6.04584			−0.342828			−0.171414	+	0.985199i	$0.554834\pi$
$312$		0			0
$313$			4.62017i			0.261148i	0.991439	+	0.130574i	$0.0416820\pi$
$313$			4.62017i			0.261148i	−0.991439	+	0.130574i	$0.958318\pi$
$314$	−4.54184	−	7.86670i	−0.256311	−	0.443944i
$315$		0			0
$316$	−6.62758	+	11.4793i	−0.372830	+	0.645761i
$317$		−	25.0793i		−	1.40860i	−0.709905	−	0.704298i	$-0.751262\pi$
$317$		−	25.0793i		−	1.40860i	0.709905	−	0.704298i	$-0.248738\pi$
$318$		0			0
$319$	19.3404	−	33.4985i	1.08285	−	1.87556i
$320$	9.74005	−	0.237789i	0.544486	−	0.0132928i
$321$		0			0
$322$	0.291424	−	0.168254i	0.0162404	−	0.00937642i
$323$	−13.8246	+	7.98162i	−0.769220	+	0.444109i
$324$		0			0
$325$	−17.9173	−	1.99285i	−0.993871	−	0.110543i
$326$	1.32620			0.0734514
$327$		0			0
$328$	−12.7721	+	7.37397i	−0.705221	+	0.407159i
$329$	−0.927781	+	1.60696i	−0.0511502	+	0.0885948i
$330$		0			0
$331$	−6.84346	+	11.8532i	−0.376150	+	0.651512i	−0.990499	−	0.137524i	$-0.956086\pi$
$331$	−6.84346	+	11.8532i	−0.376150	+	0.651512i	0.614348	+	0.789035i	$0.289419\pi$
$332$	11.7678	+	6.79413i	0.645841	+	0.372877i
$333$		0			0
$334$	6.34834	−	10.9956i	0.347366	−	0.601655i
$335$	11.7444	−	7.16837i	0.641663	−	0.391650i
$336$		0			0
$337$		−	9.01512i		−	0.491085i	−0.969386	−	0.245543i	$-0.921034\pi$
$337$		−	9.01512i		−	0.491085i	0.969386	−	0.245543i	$-0.0789661\pi$
$338$	10.7261	−	2.22374i	0.583422	−	0.120955i
$339$		0			0
$340$	−17.4332	+	10.6406i	−0.945447	+	0.577070i
$341$	15.4602	+	26.7779i	0.837217	+	1.45010i
$342$		0			0
$343$		−	5.55440i		−	0.299909i
$344$	2.79161	−	4.83521i	0.150514	−	0.260697i
$345$		0			0
$346$	−2.87012			−0.154299
$347$	9.40767	+	5.43152i	0.505030	+	0.291579i	0.730788	−	0.682604i	$-0.239153\pi$
$347$	9.40767	+	5.43152i	0.505030	+	0.291579i	−0.225758	+	0.974183i	$0.572486\pi$
$348$		0			0
$349$	−9.86492	−	17.0865i	−0.528057	−	0.914622i	−0.999465	−	0.0327066i	$-0.989587\pi$
$349$	−9.86492	−	17.0865i	−0.528057	−	0.914622i	0.471408	−	0.881915i	$-0.343746\pi$
$350$	1.68898	−	0.0825172i	0.0902797	−	0.00441073i
$351$		0			0
$352$			28.2159i			1.50391i
$353$	−16.1051	+	9.29831i	−0.857190	+	0.494899i	−0.863070	−	0.505084i	$-0.831462\pi$
$353$	−16.1051	+	9.29831i	−0.857190	+	0.494899i	0.00588009	+	0.999983i	$0.498128\pi$
$354$		0			0
$355$	−6.77473	+	12.4250i	−0.359565	+	0.659448i
$356$	0.676618			0.0358607
$357$		0			0
$358$	0.438595	+	0.253223i	0.0231805	+	0.0133833i
$359$	12.1448			0.640976			0.320488	−	0.947253i	$-0.396153\pi$
$359$	12.1448			0.640976			0.320488	+	0.947253i	$0.396153\pi$
$360$		0			0
$361$	6.95865	+	12.0527i	0.366245	+	0.634355i
$362$	−12.4498	+	7.18792i	−0.654350	+	0.377789i
$363$		0			0
$364$	1.74444	−	0.664615i	0.0914337	−	0.0348353i
$365$	−0.0552689	−	2.26386i	−0.00289291	−	0.118496i
$366$		0			0
$367$	26.8759	−	15.5168i	1.40291	−	0.809971i	0.408220	−	0.912884i	$-0.366150\pi$
$367$	26.8759	−	15.5168i	1.40291	−	0.809971i	0.994690	+	0.102913i	$0.0328163\pi$
$368$	−0.210245	−	0.121385i	−0.0109598	−	0.00632764i
$369$		0			0
$370$	7.94355	−	14.5686i	0.412965	−	0.757386i
$371$	−2.17731	+	3.77121i	−0.113040	+	0.195792i
$372$		0			0
$373$	9.03380	+	5.21567i	0.467752	+	0.270057i	0.715298	−	0.698819i	$-0.246291\pi$
$373$	9.03380	+	5.21567i	0.467752	+	0.270057i	−0.247546	+	0.968876i	$0.579624\pi$
$374$	14.6387	+	25.3550i	0.756950	+	1.31108i
$375$		0			0
$376$	−12.8165			−0.660961
$377$	−10.1187	−	26.5591i	−0.521141	−	1.36786i
$378$		0			0
$379$	−15.3621	−	26.6080i	−0.789099	−	1.36676i	−0.926519	−	0.376247i	$-0.877214\pi$
$379$	−15.3621	−	26.6080i	−0.789099	−	1.36676i	0.137420	−	0.990513i	$-0.456119\pi$
$380$	−3.38798	−	5.55073i	−0.173800	−	0.284746i
$381$		0			0
$382$		−	5.22569i		−	0.267370i
$383$	7.37251	+	4.25652i	0.376718	+	0.217498i	0.676389	−	0.736544i	$-0.263544\pi$
$383$	7.37251	+	4.25652i	0.376718	+	0.217498i	−0.299672	+	0.954042i	$0.596877\pi$
$384$		0			0
$385$	0.107484	+	4.40264i	0.00547790	+	0.224379i
$386$	3.84994	−	6.66829i	0.195957	−	0.339407i
$387$		0			0
$388$	10.5259	−	6.07715i	0.534374	−	0.308521i
$389$	−21.6832			−1.09938			−0.549691	−	0.835368i	$-0.685255\pi$
$389$	−21.6832			−1.09938			−0.549691	+	0.835368i	$0.685255\pi$
$390$		0			0
$391$	−7.04526			−0.356294
$392$	16.4190	−	9.47951i	0.829285	−	0.478788i
$393$		0			0
$394$	−9.10459	+	15.7696i	−0.458683	+	0.794461i
$395$	−22.9699	+	0.560777i	−1.15574	+	0.0282157i
$396$		0			0
$397$	−17.9986	−	10.3915i	−0.903325	−	0.521535i	−0.0250477	−	0.999686i	$-0.507974\pi$
$397$	−17.9986	−	10.3915i	−0.903325	−	0.521535i	−0.878278	+	0.478151i	$0.841307\pi$
$398$		−	2.14404i		−	0.107471i
$399$		0			0
$400$	−0.660805	−	1.02548i	−0.0330402	−	0.0512742i
$401$	−18.3709	−	31.8194i	−0.917400	−	1.58898i	−0.803350	−	0.595508i	$-0.796951\pi$
$401$	−18.3709	−	31.8194i	−0.917400	−	1.58898i	−0.114050	−	0.993475i	$-0.536382\pi$
$402$		0			0
$403$	22.4306	+	3.61034i	1.11735	+	0.179844i
$404$	7.42271			0.369294
$405$		0			0
$406$	1.33295	+	2.30874i	0.0661533	+	0.114581i
$407$	37.4257	+	21.6077i	1.85512	+	1.07105i
$408$		0			0
$409$	−1.60553	+	2.78087i	−0.0793885	+	0.137505i	−0.902986	−	0.429669i	$-0.858630\pi$
$409$	−1.60553	+	2.78087i	−0.0793885	+	0.137505i	0.823598	+	0.567174i	$0.191963\pi$
$410$	−8.80042	−	4.79844i	−0.434622	−	0.236978i
$411$		0			0
$412$	−17.2033	−	9.93231i	−0.847544	−	0.489330i
$413$	1.05823	−	0.610967i	0.0520719	−	0.0300637i
$414$		0			0
$415$	0.574870	+	23.5471i	0.0282192	+	1.15588i
$416$	16.0791	+	13.0875i	0.788343	+	0.641667i
$417$		0			0
$418$	−8.07303	+	4.66097i	−0.394865	+	0.227975i
$419$	7.62605	+	13.2087i	0.372557	+	0.645288i	0.989958	−	0.141361i	$-0.0451477\pi$
$419$	7.62605	+	13.2087i	0.372557	+	0.645288i	−0.617401	+	0.786649i	$0.711814\pi$
$420$		0			0
$421$	0.122664			0.00597828			0.00298914	−	0.999996i	$-0.499049\pi$
$421$	0.122664			0.00597828			0.00298914	+	0.999996i	$0.499049\pi$
$422$	8.08640	+	4.66868i	0.393640	+	0.227268i
$423$		0			0
$424$	−30.0777			−1.46070
$425$	−31.4874	−	16.1844i	−1.52737	−	0.785059i
$426$		0			0
$427$	2.46849	−	1.42519i	0.119459	−	0.0689695i
$428$		−	19.2186i		−	0.928964i
$429$		0			0
$430$	3.79357	−	0.0926146i	0.182942	−	0.00446627i
$431$	0.809141	+	1.40147i	0.0389750	+	0.0675066i	0.884855	−	0.465867i	$-0.154257\pi$
$431$	0.809141	+	1.40147i	0.0389750	+	0.0675066i	−0.845880	+	0.533373i	$0.820924\pi$
$432$		0			0
$433$	−13.4785	−	7.78179i	−0.647733	−	0.373969i	0.139854	−	0.990172i	$-0.455337\pi$
$433$	−13.4785	−	7.78179i	−0.647733	−	0.373969i	−0.787587	+	0.616203i	$0.788670\pi$
$434$	−2.13106			−0.102294
$435$		0			0
$436$	−1.09494	+	1.89650i	−0.0524383	+	0.0908257i
$437$		−	2.24321i		−	0.107307i
$438$		0			0
$439$	−3.91196	−	6.77571i	−0.186708	−	0.323387i	0.757443	−	0.652901i	$-0.226448\pi$
$439$	−3.91196	−	6.77571i	−0.186708	−	0.323387i	−0.944151	+	0.329514i	$0.893115\pi$
$440$	−25.9641	+	15.8476i	−1.23779	+	0.755506i
$441$		0			0
$442$	21.2387	+	3.41850i	1.01022	+	0.162601i
$443$			24.8136i			1.17893i	0.807794	+	0.589465i	$0.200662\pi$
$443$			24.8136i			1.17893i	−0.807794	+	0.589465i	$0.799338\pi$
$444$		0			0
$445$	0.611046	+	1.00111i	0.0289664	+	0.0474573i
$446$	−0.223952	+	0.387896i	−0.0106044	+	0.0183674i
$447$		0			0
$448$	−1.51451	−	0.874402i	−0.0715538	−	0.0413116i
$449$	16.7743	−	29.0539i	0.791626	−	1.37114i	−0.133333	−	0.991071i	$-0.542568\pi$
$449$	16.7743	−	29.0539i	0.791626	−	1.37114i	0.924959	−	0.380066i	$-0.124099\pi$
$450$		0			0
$451$	13.0525	−	22.6076i	0.614619	−	1.06455i
$452$	−2.51140	+	1.44995i	−0.118126	+	0.0682001i
$453$		0			0
$454$	−18.0216			−0.845796
$455$	2.55874	+	1.98084i	0.119956	+	0.0928634i
$456$		0			0
$457$	15.9839	−	9.22831i	0.747696	−	0.431682i	−0.0771651	−	0.997018i	$-0.524587\pi$
$457$	15.9839	−	9.22831i	0.747696	−	0.431682i	0.824861	+	0.565336i	$0.191254\pi$
$458$	0.296640	−	0.171265i	0.0138611	−	0.00800271i
$459$		0			0
$460$	−0.0700473	−	2.86920i	−0.00326597	−	0.133777i
$461$	3.47162	−	6.01302i	0.161689	−	0.280054i	−0.773785	−	0.633448i	$-0.781639\pi$
$461$	3.47162	−	6.01302i	0.161689	−	0.280054i	0.935475	+	0.353394i	$0.114972\pi$
$462$		0			0
$463$			41.2459i			1.91686i	0.285329	+	0.958430i	$0.407897\pi$
$463$			41.2459i			1.91686i	−0.285329	+	0.958430i	$0.592103\pi$
$464$	0.961646	−	1.66562i	0.0446433	−	0.0773245i
$465$		0			0
$466$	1.12229	+	1.94387i	0.0519892	+	0.0900479i
$467$			29.7045i			1.37456i	0.726393	+	0.687280i	$0.241195\pi$
$467$			29.7045i			1.37456i	−0.726393	+	0.687280i	$0.758805\pi$
$468$		0			0
$469$	−2.46969			−0.114040
$470$	−4.53826	−	7.43529i	−0.209334	−	0.342964i
$471$		0			0
$472$	7.30924	+	4.21999i	0.336435	+	0.194241i
$473$			9.88276i			0.454410i
$474$		0			0
$475$	5.15312	−	10.0256i	0.236441	−	0.460006i
$476$	3.66599			0.168030
$477$		0			0
$478$	−11.5530	+	6.67013i	−0.528422	+	0.305084i
$479$	9.86981	+	17.0950i	0.450963	+	0.781091i	0.998446	−	0.0557257i	$-0.0177472\pi$
$479$	9.86981	+	17.0950i	0.450963	+	0.781091i	−0.547483	+	0.836817i	$0.684414\pi$
$480$		0			0
$481$	29.6726	−	11.3050i	1.35296	−	0.515463i
$482$		−	19.6451i		−	0.894809i
$483$		0			0
$484$	−8.43603	−	14.6116i	−0.383456	−	0.664165i
$485$	18.4975	+	10.0858i	0.839929	+	0.457972i
$486$		0			0
$487$	21.0473	+	12.1517i	0.953745	+	0.550645i	0.894242	−	0.447583i	$-0.147715\pi$
$487$	21.0473	+	12.1517i	0.953745	+	0.550645i	0.0595026	+	0.998228i	$0.481049\pi$
$488$	17.0501	+	9.84386i	0.771820	+	0.445610i
$489$		0			0
$490$	11.3133	+	6.16858i	0.511082	+	0.278668i
$491$	3.45543	+	5.98497i	0.155941	+	0.270098i	0.933401	−	0.358834i	$-0.116826\pi$
$491$	3.45543	+	5.98497i	0.155941	+	0.270098i	−0.777460	+	0.628932i	$0.783492\pi$
$492$		0			0
$493$		−	55.8144i		−	2.51376i
$494$	−1.08845	+	6.76241i	−0.0489716	+	0.304255i
$495$		0			0
$496$	0.768715	+	1.33145i	0.0345163	+	0.0597840i
$497$	2.19986	−	1.27009i	0.0986774	−	0.0569714i
$498$		0			0
$499$	−2.21036			−0.0989495			−0.0494747	−	0.998775i	$-0.515755\pi$
$499$	−2.21036			−0.0989495			−0.0494747	+	0.998775i	$0.515755\pi$
$500$	6.27807	−	12.9842i	0.280764	−	0.580673i
$501$		0			0
$502$		−	1.09679i		−	0.0489521i
$503$	−25.3122	−	14.6140i	−1.12862	−	0.651607i	−0.185030	−	0.982733i	$-0.559238\pi$
$503$	−25.3122	−	14.6140i	−1.12862	−	0.651607i	−0.943587	+	0.331126i	$0.892572\pi$
$504$		0			0
$505$	6.70337	+	10.9825i	0.298296	+	0.488716i
$506$	−4.11417			−0.182897
$507$		0			0
$508$			22.2695i			0.988047i
$509$	3.60746	+	6.24830i	0.159898	+	0.276951i	0.934832	−	0.355091i	$-0.115550\pi$
$509$	3.60746	+	6.24830i	0.159898	+	0.276951i	−0.774934	+	0.632042i	$0.782217\pi$
$510$		0			0
$511$	−0.203235	+	0.352014i	−0.00899060	+	0.0155722i
$512$			2.75575i			0.121788i
$513$		0			0
$514$	4.16001	−	7.20535i	0.183490	−	0.317814i
$515$	−0.840399	−	34.4234i	−0.0370324	−	1.51688i
$516$		0			0
$517$	19.6469	−	11.3431i	0.864068	−	0.498870i
$518$	−2.57940	+	1.48922i	−0.113332	+	0.0654325i
$519$		0			0
$520$	−3.01210	+	22.1465i	−0.132089	+	0.971190i
$521$	−38.0923			−1.66886			−0.834428	−	0.551118i	$-0.814202\pi$
$521$	−38.0923			−1.66886			−0.834428	+	0.551118i	$0.814202\pi$
$522$		0			0
$523$	−0.0687721	+	0.0397056i	−0.00300719	+	0.00173620i	−0.501503	−	0.865156i	$-0.667219\pi$
$523$	−0.0687721	+	0.0397056i	−0.00300719	+	0.00173620i	0.498496	+	0.866892i	$0.333886\pi$
$524$	−2.96095	+	5.12852i	−0.129350	+	0.224040i
$525$		0			0
$526$	0.224818	−	0.389396i	0.00980253	−	0.0169785i
$527$	38.6391	+	22.3083i	1.68315	+	0.971766i
$528$		0			0
$529$	−11.0050	+	19.0612i	−0.478478	+	0.828748i
$530$	−10.6504	−	17.4491i	−0.462622	−	0.757940i
$531$		0			0
$532$			1.16725i			0.0506067i
$533$	−6.82897	−	17.9243i	−0.295796	−	0.776387i
$534$		0			0
$535$	28.4355	−	17.3561i	1.22937	−	0.750369i
$536$	−8.52918	−	14.7730i	−0.368404	−	0.638095i
$537$		0			0
$538$		−	11.4631i		−	0.494210i
$539$	−16.7795	+	29.0630i	−0.722745	+	1.25183i
$540$		0			0
$541$	−29.1429			−1.25295			−0.626476	−	0.779441i	$-0.715503\pi$
$541$	−29.1429			−1.25295			−0.626476	+	0.779441i	$0.715503\pi$
$542$	17.3915	+	10.0410i	0.747030	+	0.431298i
$543$		0			0
$544$	20.3571	+	35.2595i	0.872803	+	1.51174i
$545$	−3.79486	+	0.0926460i	−0.162554	+	0.00396852i
$546$		0			0
$547$			12.9652i			0.554354i	0.960819	+	0.277177i	$0.0893988\pi$
$547$			12.9652i			0.554354i	−0.960819	+	0.277177i	$0.910601\pi$
$548$	5.53043	−	3.19300i	0.236248	−	0.136398i
$549$		0			0
$550$	−18.3875	−	9.45109i	−0.784045	−	0.402996i
$551$	17.7713			0.757084
$552$		0			0
$553$	3.57165	+	2.06209i	0.151882	+	0.0876891i
$554$	−16.1892			−0.687815
$555$		0			0
$556$	−8.55530	−	14.8182i	−0.362825	−	0.628432i
$557$	27.7896	−	16.0443i	1.17748	−	0.679820i	0.222051	−	0.975035i	$-0.428725\pi$
$557$	27.7896	−	16.0443i	1.17748	−	0.679820i	0.955431	+	0.295215i	$0.0953914\pi$
$558$		0			0
$559$	5.63178	+	4.58396i	0.238199	+	0.193881i
$560$	0.00534435	+	0.218909i	0.000225840	+	0.00925059i
$561$		0			0
$562$	−4.61043	+	2.66183i	−0.194479	+	0.112283i
$563$	−1.31596	−	0.759773i	−0.0554613	−	0.0320206i	0.472013	−	0.881592i	$-0.343528\pi$
$563$	−1.31596	−	0.759773i	−0.0554613	−	0.0320206i	−0.527474	+	0.849571i	$0.676861\pi$
$564$		0			0
$565$	−4.41334	−	2.40638i	−0.185671	−	0.101237i
$566$	−12.7260	+	22.0421i	−0.534914	+	0.926498i
$567$		0			0
$568$	15.1946	+	8.77262i	0.637552	+	0.368091i
$569$	−9.90956	−	17.1639i	−0.415430	−	0.719546i	0.580043	−	0.814586i	$-0.303036\pi$
$569$	−9.90956	−	17.1639i	−0.415430	−	0.719546i	−0.995474	+	0.0950394i	$0.969702\pi$
$570$		0			0
$571$	43.8106			1.83342			0.916708	−	0.399558i	$-0.130836\pi$
$571$	43.8106			1.83342			0.916708	+	0.399558i	$0.130836\pi$
$572$	−22.5331	−	3.62684i	−0.942158	−	0.151646i
$573$		0			0
$574$	0.899588	+	1.55813i	0.0375481	+	0.0650352i
$575$	4.18196	−	2.69478i	0.174400	−	0.112380i
$576$		0			0
$577$			11.7411i			0.488787i	0.969676	+	0.244393i	$0.0785888\pi$
$577$			11.7411i			0.488787i	−0.969676	+	0.244393i	$0.921411\pi$
$578$	24.1805	+	13.9606i	1.00577	+	0.580684i
$579$		0			0
$580$	22.7306	−	0.554934i	0.943835	−	0.0230424i
$581$	2.11392	−	3.66141i	0.0877000	−	0.151901i
$582$		0			0
$583$	46.1071	−	26.6200i	1.90956	−	1.10249i
$584$	−2.80752			−0.116176
$585$		0			0
$586$	−6.01374			−0.248425
$587$	22.3360	−	12.8957i	0.921907	−	0.532263i	0.0376643	−	0.999290i	$-0.488008\pi$
$587$	22.3360	−	12.8957i	0.921907	−	0.532263i	0.884243	+	0.467027i	$0.154675\pi$
$588$		0			0
$589$	−7.10297	+	12.3027i	−0.292673	+	0.506924i
$590$	0.140003	+	5.73462i	0.00576381	+	0.236091i
$591$		0			0
$592$	1.86089	+	1.07438i	0.0764819	+	0.0441569i
$593$		−	10.5017i		−	0.431252i	−0.976476	−	0.215626i	$-0.930821\pi$
$593$		−	10.5017i		−	0.431252i	0.976476	−	0.215626i	$-0.0691792\pi$
$594$		0			0
$595$	3.31071	+	5.42413i	0.135726	+	0.222368i
$596$	2.03669	+	3.52766i	0.0834262	+	0.144498i
$597$		0			0
$598$	−1.90829	+	2.34450i	−0.0780358	+	0.0958736i
$599$	37.8214			1.54534			0.772669	−	0.634809i	$-0.218921\pi$
$599$	37.8214			1.54534			0.772669	+	0.634809i	$0.218921\pi$
$600$		0			0
$601$	14.8477	+	25.7170i	0.605652	+	1.04902i	0.991948	+	0.126645i	$0.0404208\pi$
$601$	14.8477	+	25.7170i	0.605652	+	1.04902i	−0.386297	+	0.922375i	$0.626246\pi$
$602$	−0.589873	−	0.340563i	−0.0240414	−	0.0138803i
$603$		0			0
$604$	11.9889	−	20.7654i	0.487823	−	0.844933i
$605$	14.0006	−	25.6774i	0.569207	−	1.04394i
$606$		0			0
$607$	14.0175	+	8.09298i	0.568951	+	0.328484i	0.756730	−	0.653727i	$-0.226796\pi$
$607$	14.0175	+	8.09298i	0.568951	+	0.328484i	−0.187779	+	0.982211i	$0.560129\pi$
$608$	−11.2266	+	6.48170i	−0.455300	+	0.262868i
$609$		0			0
$610$	0.326580	+	13.3770i	0.0132228	+	0.541618i
$611$	2.64890	−	16.4573i	0.107163	−	0.665790i
$612$		0			0
$613$	22.0871	−	12.7520i	0.892089	−	0.515048i	0.0174640	−	0.999847i	$-0.494441\pi$
$613$	22.0871	−	12.7520i	0.892089	−	0.515048i	0.874625	+	0.484799i	$0.161107\pi$
$614$	−4.17670	−	7.23426i	−0.168558	−	0.291951i
$615$		0			0
$616$	5.45993			0.219987
$617$	10.1748	+	5.87440i	0.409620	+	0.236494i	0.690626	−	0.723212i	$-0.257335\pi$
$617$	10.1748	+	5.87440i	0.409620	+	0.236494i	−0.281006	+	0.959706i	$0.590668\pi$
$618$		0			0
$619$	9.49031			0.381448			0.190724	−	0.981644i	$-0.438917\pi$
$619$	9.49031			0.381448			0.190724	+	0.981644i	$0.438917\pi$
$620$	−8.70094	+	15.9577i	−0.349438	+	0.640876i
$621$		0			0
$622$	−4.41188	+	2.54720i	−0.176900	+	0.102133i
$623$		−	0.210522i		−	0.00843438i
$624$		0			0
$625$	24.8809	−	2.43700i	0.995237	−	0.0974798i
$626$	1.94655	+	3.37152i	0.0777997	+	0.134753i
$627$		0			0
$628$	12.0431	+	6.95308i	0.480571	+	0.277458i
$629$	62.3577			2.48637
$630$		0			0
$631$	−11.7563	+	20.3625i	−0.468010	+	0.810617i	−0.999332	−	0.0365534i	$-0.988362\pi$
$631$	−11.7563	+	20.3625i	−0.468010	+	0.810617i	0.531322	+	0.847170i	$0.321695\pi$
$632$			28.4861i			1.13311i
$633$		0			0
$634$	−10.5663	−	18.3014i	−0.419641	−	0.726839i
$635$	−32.9495	+	20.1113i	−1.30756	+	0.798093i
$636$		0			0
$637$	8.77890	+	23.0423i	0.347833	+	0.912971i
$638$		−	32.5935i		−	1.29039i
$639$		0			0
$640$	−14.9419	+	9.12005i	−0.590631	+	0.360502i
$641$	9.54940	−	16.5400i	0.377179	−	0.653292i	−0.613472	−	0.789717i	$-0.710228\pi$
$641$	9.54940	−	16.5400i	0.377179	−	0.653292i	0.990651	+	0.136424i	$0.0435610\pi$
$642$		0			0
$643$	−37.7938	−	21.8202i	−1.49044	−	0.860506i	−0.490500	−	0.871441i	$-0.663186\pi$
$643$	−37.7938	−	21.8202i	−1.49044	−	0.860506i	−0.999940	+	0.0109350i	$0.996519\pi$
$644$	−0.257579	+	0.446139i	−0.0101500	+	0.0175804i
$645$		0			0
$646$	−6.72555	+	11.6490i	−0.264613	+	0.458323i
$647$	2.86660	−	1.65503i	0.112698	−	0.0650661i	−0.442592	−	0.896723i	$-0.645941\pi$
$647$	2.86660	−	1.65503i	0.112698	−	0.0650661i	0.555289	+	0.831657i	$0.312608\pi$
$648$		0			0
$649$	−14.9395			−0.586425
$650$	−13.9145	+	6.09455i	−0.545773	+	0.239048i
$651$		0			0
$652$	−1.75827	+	1.01514i	−0.0688590	+	0.0397558i
$653$	−3.12790	+	1.80589i	−0.122404	+	0.0706701i	−0.559952	−	0.828525i	$-0.689180\pi$
$653$	−3.12790	+	1.80589i	−0.122404	+	0.0706701i	0.437548	+	0.899195i	$0.355847\pi$
$654$		0			0
$655$	−10.2621	+	0.250534i	−0.400972	+	0.00978917i
$656$	0.649000	−	1.12410i	0.0253392	−	0.0438888i
$657$		0			0
$658$			1.56355i			0.0609536i
$659$	−21.5161	+	37.2670i	−0.838148	+	1.45172i	0.0532932	+	0.998579i	$0.483028\pi$
$659$	−21.5161	+	37.2670i	−0.838148	+	1.45172i	−0.891441	+	0.453136i	$0.850305\pi$
$660$		0			0
$661$	−18.8524	−	32.6533i	−0.733273	−	1.27007i	−0.955477	−	0.295066i	$-0.904658\pi$
$661$	−18.8524	−	32.6533i	−0.733273	−	1.27007i	0.222204	−	0.975000i	$-0.428675\pi$
$662$			11.5330i			0.448242i
$663$		0			0
$664$	29.2019			1.13325
$665$	−1.72704	+	1.05413i	−0.0669719	+	0.0408775i
$666$		0			0
$667$	6.79245	+	3.92162i	0.263005	+	0.151846i
$668$			19.4373i			0.752051i
$669$		0			0
$670$	5.55017	−	10.1791i	0.214422	−	0.393253i
$671$	−34.8489			−1.34532
$672$		0			0
$673$	−38.7794	+	22.3893i	−1.49484	+	0.863045i	−0.999982	−	0.00593030i	$-0.998112\pi$
$673$	−38.7794	+	22.3893i	−1.49484	+	0.863045i	−0.494855	+	0.868975i	$0.664779\pi$
$674$	−3.79820	−	6.57868i	−0.146301	−	0.253401i
$675$		0			0
$676$	−12.5184	+	11.1585i	−0.481478	+	0.429172i
$677$		−	41.0024i		−	1.57585i	−0.615770	−	0.787926i	$-0.711155\pi$
$677$		−	41.0024i		−	1.57585i	0.615770	−	0.787926i	$-0.288845\pi$
$678$		0			0
$679$	−1.89084	−	3.27502i	−0.0725636	−	0.125684i
$680$	−21.0119	+	38.5361i	−0.805769	+	1.47779i
$681$		0			0
$682$	22.5638	+	13.0272i	0.864013	+	0.498838i
$683$	−17.7354	−	10.2395i	−0.678627	−	0.391805i	0.120711	−	0.992688i	$-0.461483\pi$
$683$	−17.7354	−	10.2395i	−0.678627	−	0.391805i	−0.799338	+	0.600882i	$0.794816\pi$
$684$		0			0
$685$	9.71879	+	5.29918i	0.371336	+	0.202471i
$686$	−2.34015	−	4.05326i	−0.0893473	−	0.154754i
$687$		0			0
$688$			0.491392i			0.0187342i
$689$	6.21641	−	38.6218i	0.236826	−	1.47137i
$690$		0			0
$691$	−13.8702	−	24.0240i	−0.527649	−	0.913915i	−0.999481	−	0.0322263i	$-0.989740\pi$
$691$	−13.8702	−	24.0240i	−0.527649	−	0.913915i	0.471832	−	0.881689i	$-0.343593\pi$
$692$	3.80518	−	2.19692i	0.144651	−	0.0835145i
$693$		0			0
$694$	9.15352			0.347463
$695$	14.1986	−	26.0404i	0.538583	−	0.987770i
$696$		0			0
$697$		−	37.6683i		−	1.42679i
$698$	−14.3976	−	8.31247i	−0.544958	−	0.314632i
$699$		0			0
$700$	−2.17607	+	1.40222i	−0.0822478	+	0.0529991i
$701$	6.02633			0.227611			0.113806	−	0.993503i	$-0.463696\pi$
$701$	6.02633			0.227611			0.113806	+	0.993503i	$0.463696\pi$
$702$		0			0
$703$			19.8547i			0.748835i
$704$	10.6905	+	18.5165i	0.402913	+	0.697867i
$705$		0			0
$706$	−7.83503	+	13.5707i	−0.294875	+	0.510739i
$707$		−	2.30949i		−	0.0868573i
$708$		0			0
$709$	−11.3864	+	19.7218i	−0.427625	+	0.740668i	−0.996662	−	0.0816444i	$-0.973983\pi$
$709$	−11.3864	+	19.7218i	−0.427625	+	0.740668i	0.569037	+	0.822312i	$0.307316\pi$
$710$	0.291041	+	11.9213i	0.0109226	+	0.447397i
$711$		0			0
$712$	1.25928	−	0.727045i	0.0471934	−	0.0272471i
$713$	−5.42971	+	3.13484i	−0.203344	+	0.117401i
$714$		0			0
$715$	−14.9832	−	36.6150i	−0.560341	−	1.36932i
$716$	−0.775316			−0.0289749
$717$		0			0
$718$	8.86250	−	5.11677i	0.330746	−	0.190956i
$719$	−13.1830	+	22.8336i	−0.491643	+	0.851551i	−0.999954	−	0.00962269i	$-0.996937\pi$
$719$	−13.1830	+	22.8336i	−0.491643	+	0.851551i	0.508310	+	0.861174i	$0.330270\pi$
$720$		0			0
$721$	−3.09032	+	5.35260i	−0.115090	+	0.199341i
$722$	10.1560	+	5.86356i	0.377967	+	0.218219i
$723$		0			0
$724$	11.0039	−	19.0594i	0.408959	−	0.708337i
$725$	21.3488	+	33.1306i	0.792874	+	1.23044i
$726$		0			0
$727$			1.91130i			0.0708862i	0.999372	+	0.0354431i	$0.0112842\pi$
$727$			1.91130i			0.0708862i	−0.999372	+	0.0354431i	$0.988716\pi$
$728$	2.53250	−	3.11139i	0.0938607	−	0.115316i
$729$		0			0
$730$	−0.994129	−	1.62874i	−0.0367944	−	0.0602823i
$731$	7.13017	+	12.3498i	0.263719	+	0.456774i
$732$		0			0
$733$			18.4077i			0.679904i	0.940443	+	0.339952i	$0.110411\pi$
$733$			18.4077i			0.679904i	−0.940443	+	0.339952i	$0.889589\pi$
$734$	13.0749	−	22.6464i	0.482604	−	0.835894i
$735$		0			0
$736$	−5.72130			−0.210890
$737$	26.1494	+	15.0973i	0.963224	+	0.556118i
$738$		0			0
$739$	−0.909425	−	1.57517i	−0.0334538	−	0.0579436i	0.848814	−	0.528692i	$-0.177317\pi$
$739$	−0.909425	−	1.57517i	−0.0334538	−	0.0579436i	−0.882268	+	0.470748i	$0.843984\pi$
$740$	0.619990	+	25.3953i	0.0227913	+	0.933551i
$741$		0			0
$742$			3.66933i			0.134705i
$743$	−7.61880	+	4.39871i	−0.279507	+	0.161373i	−0.633200	−	0.773988i	$-0.718259\pi$
$743$	−7.61880	+	4.39871i	−0.279507	+	0.161373i	0.353693	+	0.935361i	$0.384926\pi$
$744$		0			0
$745$	−3.38015	+	6.19925i	−0.123839	+	0.227123i
$746$	8.78974			0.321815
$747$		0			0
$748$	−38.8158	−	22.4103i	−1.41925	−	0.819402i
$749$	−5.97963			−0.218491
$750$		0			0
$751$	−18.0751	−	31.3070i	−0.659571	−	1.14241i	−0.980727	−	0.195384i	$-0.937405\pi$
$751$	−18.0751	−	31.3070i	−0.659571	−	1.14241i	0.321156	−	0.947026i	$-0.395929\pi$
$752$	0.976885	−	0.564005i	0.0356233	−	0.0205671i
$753$		0			0
$754$	−18.5737	−	15.1180i	−0.676416	−	0.550565i
$755$	41.5513	−	1.01441i	1.51221	−	0.0369183i
$756$		0			0
$757$	25.1967	−	14.5473i	0.915789	−	0.528731i	0.0334996	−	0.999439i	$-0.489335\pi$
$757$	25.1967	−	14.5473i	0.915789	−	0.528731i	0.882289	+	0.470708i	$0.156001\pi$
$758$	−22.4207	−	12.9446i	−0.814355	−	0.470168i
$759$		0			0
$760$	−12.2699	−	6.69018i	−0.445076	−	0.242678i
$761$	−13.2927	+	23.0236i	−0.481859	+	0.834603i	−0.999783	−	0.0208228i	$-0.993371\pi$
$761$	−13.2927	+	23.0236i	−0.481859	+	0.834603i	0.517925	+	0.855426i	$0.326705\pi$
$762$		0			0
$763$	0.590073	+	0.340679i	0.0213621	+	0.0123334i
$764$	3.99999	+	6.92819i	0.144715	+	0.250653i
$765$		0			0
$766$	7.17334			0.259183
$767$	−6.92943	+	8.51339i	−0.250207	+	0.307401i
$768$		0			0
$769$	12.4145	+	21.5026i	0.447679	+	0.775403i	0.998235	−	0.0593958i	$-0.0189174\pi$
$769$	12.4145	+	21.5026i	0.447679	+	0.775403i	−0.550556	+	0.834799i	$0.685584\pi$
$770$	1.93333	+	3.16749i	0.0696725	+	0.114148i
$771$		0			0
$772$			11.7877i			0.424249i
$773$	−15.4061	−	8.89469i	−0.554117	−	0.319920i	0.196664	−	0.980471i	$-0.436989\pi$
$773$	−15.4061	−	8.89469i	−0.554117	−	0.319920i	−0.750781	+	0.660551i	$0.770323\pi$
$774$		0			0
$775$	−31.4684	+	1.53743i	−1.13038	+	0.0552261i
$776$	13.0601	−	22.6208i	0.468832	−	0.812040i
$777$		0			0
$778$	−15.8231	+	9.13545i	−0.567285	+	0.327522i
$779$	11.9936			0.429715
$780$		0			0
$781$	−31.0565			−1.11129
$782$	−5.14120	+	2.96827i	−0.183849	+	0.106145i
$783$		0			0
$784$	−0.834314	+	1.44507i	−0.0297969	+	0.0516098i
$785$	0.588318	+	24.0980i	0.0209980	+	0.860095i
$786$		0			0
$787$	−19.7092	−	11.3791i	−0.702557	−	0.405622i	0.105742	−	0.994394i	$-0.466278\pi$
$787$	−19.7092	−	11.3791i	−0.702557	−	0.405622i	−0.808299	+	0.588772i	$0.799612\pi$
$788$		−	27.8763i		−	0.993053i
$789$		0			0
$790$	−16.5257	+	10.0868i	−0.587959	+	0.358871i
$791$	0.451137	+	0.781392i	0.0160406	+	0.0277831i
$792$		0			0
$793$	−16.1641	+	19.8589i	−0.574003	+	0.705212i
$794$	−17.5124			−0.621491
$795$		0			0
$796$	1.64115	+	2.84255i	0.0581689	+	0.100751i
$797$	20.7232	+	11.9646i	0.734055	+	0.423807i	0.819904	−	0.572501i	$-0.194027\pi$
$797$	20.7232	+	11.9646i	0.734055	+	0.423807i	−0.0858488	+	0.996308i	$0.527360\pi$
$798$		0			0
$799$	16.3676	−	28.3495i	0.579043	−	1.00293i
$800$	−25.5703	−	13.1430i	−0.904046	−	0.464676i
$801$		0			0
$802$	−26.8119	−	15.4799i	−0.946762	−	0.546613i
$803$	4.30375	−	2.48477i	0.151876	−	0.0876856i
$804$		0			0
$805$	−0.892717	+	0.0217944i	−0.0314641	+	0.000768152i
$806$	17.8895	−	6.81574i	0.630132	−	0.240074i
$807$		0			0
$808$	13.8147	−	7.97591i	0.485999	−	0.280592i
$809$	−8.39474	−	14.5401i	−0.295143	−	0.511203i	0.679875	−	0.733328i	$-0.262034\pi$
$809$	−8.39474	−	14.5401i	−0.295143	−	0.511203i	−0.975018	+	0.222125i	$0.928701\pi$
$810$		0			0
$811$	14.0218			0.492373			0.246186	−	0.969222i	$-0.420822\pi$
$811$	14.0218			0.492373			0.246186	+	0.969222i	$0.420822\pi$
$812$	−3.53444	−	2.04061i	−0.124034	−	0.0716113i
$813$		0			0
$814$	36.4146			1.27633
$815$	−3.08985	−	1.68474i	−0.108233	−	0.0590140i
$816$		0			0
$817$	−3.93218	+	2.27025i	−0.137570	+	0.0794259i
$818$			2.70574i			0.0946040i
$819$		0			0
$820$	15.3405	−	0.374516i	0.535713	−	0.0130787i
$821$	19.4895	+	33.7568i	0.680189	+	1.17812i	0.974923	+	0.222542i	$0.0714355\pi$
$821$	19.4895	+	33.7568i	0.680189	+	1.17812i	−0.294734	+	0.955579i	$0.595231\pi$
$822$		0			0
$823$	−9.60038	−	5.54278i	−0.334648	−	0.193209i	0.323255	−	0.946312i	$-0.395223\pi$
$823$	−9.60038	−	5.54278i	−0.334648	−	0.193209i	−0.657903	+	0.753103i	$0.728556\pi$
$824$	−42.6902			−1.48718
$825$		0			0
$826$	0.514819	−	0.891692i	0.0179128	−	0.0310259i
$827$		−	41.0529i		−	1.42755i	−0.700375	−	0.713775i	$-0.746984\pi$
$827$		−	41.0529i		−	1.42755i	0.700375	−	0.713775i	$-0.253016\pi$
$828$		0			0
$829$	10.4901	+	18.1694i	0.364337	+	0.631051i	0.988670	−	0.150108i	$-0.0479622\pi$
$829$	10.4901	+	18.1694i	0.364337	+	0.631051i	−0.624332	+	0.781159i	$0.714629\pi$
$830$	10.3403	+	16.9410i	0.358916	+	0.588032i
$831$		0			0
$832$	15.5104	+	2.49649i	0.537727	+	0.0865503i
$833$			48.4240i			1.67779i
$834$		0			0
$835$	−28.7591	+	17.5536i	−0.995249	+	0.607467i
$836$	7.13545	−	12.3590i	0.246785	−	0.427443i
$837$		0			0
$838$	11.1300	+	6.42594i	0.384481	+	0.221980i
$839$	5.27731	−	9.14057i	0.182193	−	0.315568i	−0.760434	−	0.649415i	$-0.775014\pi$
$839$	5.27731	−	9.14057i	0.182193	−	0.315568i	0.942627	+	0.333848i	$0.108347\pi$
$840$		0			0
$841$	−16.5682	+	28.6969i	−0.571316	+	0.989548i
$842$	0.0895126	−	0.0516801i	0.00308481	−	0.00178101i
$843$		0			0
$844$	−14.2945			−0.492038
$845$	−27.8152	−	8.44496i	−0.956870	−	0.290516i
$846$		0			0
$847$	−4.54624	+	2.62477i	−0.156211	+	0.0901882i
$848$	2.29255	−	1.32360i	0.0787264	−	0.0454527i
$849$		0			0
$850$	−29.7963	+	1.45574i	−1.02201	+	0.0499314i
$851$	−4.38137	+	7.58875i	−0.150191	+	0.260139i
$852$		0			0
$853$		−	32.3455i		−	1.10749i	−0.832687	−	0.553744i	$-0.813199\pi$
$853$		−	32.3455i		−	1.10749i	0.832687	−	0.553744i	$-0.186801\pi$
$854$	1.20090	−	2.08002i	0.0410940	−	0.0711770i
$855$		0			0
$856$	−20.6509	−	35.7684i	−0.705832	−	1.22254i
$857$		−	23.8618i		−	0.815103i	−0.913182	−	0.407551i	$-0.866383\pi$
$857$		−	23.8618i		−	0.815103i	0.913182	−	0.407551i	$-0.133617\pi$
$858$		0			0
$859$	−20.6605			−0.704926			−0.352463	−	0.935826i	$-0.614656\pi$
$859$	−20.6605			−0.704926			−0.352463	+	0.935826i	$0.614656\pi$
$860$	−4.95860	+	3.02656i	−0.169087	+	0.103205i
$861$		0			0
$862$	1.18092	+	0.681806i	0.0402224	+	0.0232224i
$863$		−	0.461666i		−	0.0157153i	−0.999969	−	0.00785765i	$-0.997499\pi$
$863$		−	0.461666i		−	0.0157153i	0.999969	−	0.00785765i	$-0.00250119\pi$
$864$		0			0
$865$	6.68695	+	3.64607i	0.227363	+	0.123970i
$866$	−13.1143			−0.445643
$867$		0			0
$868$	2.82534	−	1.63121i	0.0958982	−	0.0553669i
$869$	−25.2113	−	43.6673i	−0.855235	−	1.48131i
$870$		0			0
$871$	20.7323	−	7.89880i	0.702488	−	0.267641i
$872$			4.70619i			0.159372i
$873$		0			0
$874$	−0.945098	−	1.63696i	−0.0319684	−	0.0553709i
$875$	−4.03990	−	1.95335i	−0.136573	−	0.0660353i
$876$		0			0
$877$	17.6624	+	10.1974i	0.596417	+	0.344342i	0.767631	−	0.640892i	$-0.221435\pi$
$877$	17.6624	+	10.1974i	0.596417	+	0.344342i	−0.171214	+	0.985234i	$0.554769\pi$
$878$	−5.70941	−	3.29633i	−0.192683	−	0.111246i
$879$		0			0
$880$	1.28161	−	2.35050i	0.0432031	−	0.0792353i
$881$	−12.6173	−	21.8538i	−0.425087	−	0.736272i	0.571342	−	0.820712i	$-0.306423\pi$
$881$	−12.6173	−	21.8538i	−0.425087	−	0.736272i	−0.996429	+	0.0844405i	$0.973090\pi$
$882$		0			0
$883$			8.44125i			0.284071i	0.989862	+	0.142035i	$0.0453647\pi$
$883$			8.44125i			0.284071i	−0.989862	+	0.142035i	$0.954635\pi$
$884$	−30.7748	+	11.7249i	−1.03507	+	0.394351i
$885$		0			0
$886$	10.4543	+	18.1075i	0.351221	+	0.608332i
$887$	−32.3709	+	18.6894i	−1.08691	+	0.627527i	−0.932752	−	0.360519i	$-0.882600\pi$
$887$	−32.3709	+	18.6894i	−1.08691	+	0.627527i	−0.154157	+	0.988046i	$0.549266\pi$
$888$		0			0
$889$	6.92888			0.232387
$890$	0.867687	+	0.473108i	0.0290849	+	0.0158586i
$891$		0			0
$892$		−	0.685693i		−	0.0229587i
$893$	9.02647	+	5.21144i	0.302059	+	0.174394i
$894$		0			0
$895$	−0.700179	−	1.14714i	−0.0234044	−	0.0383448i
$896$	3.14210			0.104970
$897$		0			0
$898$		−	28.2690i		−	0.943348i
$899$	−24.8351	−	43.0156i	−0.828297	−	1.43465i
$900$		0			0
$901$	38.4113	−	66.5303i	1.27967	−	2.21645i
$902$		−	21.9969i		−	0.732416i
$903$		0			0
$904$	−3.11603	+	5.39713i	−0.103638	+	0.179506i
$905$	38.1375	−	0.931073i	1.26773	−	0.0309499i
$906$		0			0
$907$	−42.5419	+	24.5616i	−1.41258	+	0.815553i	−0.995631	−	0.0933771i	$-0.970234\pi$
$907$	−42.5419	+	24.5616i	−1.41258	+	0.815553i	−0.416948	+	0.908930i	$0.636900\pi$
$908$	23.8929	−	13.7946i	0.792915	−	0.457789i
$909$		0			0
$910$	2.70177	+	0.367462i	0.0895628	+	0.0121812i
$911$	−46.1927			−1.53043			−0.765217	−	0.643773i	$-0.777368\pi$
$911$	−46.1927			−1.53043			−0.765217	+	0.643773i	$0.777368\pi$
$912$		0			0
$913$	−44.7647	+	25.8449i	−1.48149	+	0.855341i
$914$	7.77604	−	13.4685i	0.257209	−	0.445499i
$915$		0			0
$916$	−0.262189	+	0.454125i	−0.00866297	+	0.0150047i
$917$	1.59568	+	0.921265i	0.0526939	+	0.0304229i
$918$		0			0
$919$	−14.7292	+	25.5118i	−0.485872	+	0.841556i	−0.999868	−	0.0162371i	$-0.994831\pi$
$919$	−14.7292	+	25.5118i	−0.485872	+	0.841556i	0.513996	+	0.857793i	$0.328165\pi$
$920$	−3.21340	−	5.26470i	−0.105943	−	0.173572i
$921$		0			0
$922$		−	5.85057i		−	0.192678i
$923$	−14.4051	+	17.6978i	−0.474148	+	0.582531i
$924$		0			0
$925$	−37.0146	+	23.8516i	−1.21703	+	0.784235i
$926$	17.3775	+	30.0987i	0.571060	+	0.989105i
$927$		0			0
$928$		−	45.3257i		−	1.48789i
$929$	−11.3931	+	19.7334i	−0.373795	+	0.647432i	−0.990146	−	0.140040i	$-0.955277\pi$
$929$	−11.3931	+	19.7334i	−0.373795	+	0.647432i	0.616351	+	0.787472i	$0.288610\pi$
$930$		0			0
$931$	−15.4182			−0.505311
$932$	−2.97585	−	1.71811i	−0.0974773	−	0.0562786i
$933$		0			0
$934$	12.5149	+	21.6765i	0.409501	+	0.709277i
$935$	−1.89620	−	77.6698i	−0.0620122	−	2.54007i
$936$		0			0
$937$		−	33.3968i		−	1.09103i	−0.838102	−	0.545513i	$-0.816335\pi$
$937$		−	33.3968i		−	1.09103i	0.838102	−	0.545513i	$-0.183665\pi$
$938$	−1.80223	+	1.04052i	−0.0588449	+	0.0339741i
$939$		0			0
$940$	11.7081	+	6.38386i	0.381877	+	0.208219i
$941$	4.59203			0.149696			0.0748480	−	0.997195i	$-0.476153\pi$
$941$	4.59203			0.149696			0.0748480	+	0.997195i	$0.476153\pi$
$942$		0			0
$943$	4.58412	+	2.64664i	0.149279	+	0.0861865i
$944$	−0.742822			−0.0241768
$945$		0			0
$946$	4.16375	+	7.21183i	0.135375	+	0.234477i
$947$	−8.35815	+	4.82558i	−0.271603	+	0.156810i	−0.629616	−	0.776906i	$-0.716788\pi$
$947$	−8.35815	+	4.82558i	−0.271603	+	0.156810i	0.358013	+	0.933717i	$0.383454\pi$
$948$		0			0
$949$	0.580254	−	3.60505i	0.0188359	−	0.117025i
$950$	−0.463507	−	9.48715i	−0.0150381	−	0.307804i
$951$		0			0
$952$	6.82290	−	3.93920i	0.221131	−	0.127670i
$953$	29.3593	+	16.9506i	0.951040	+	0.549083i	0.893404	−	0.449254i	$-0.148310\pi$
$953$	29.3593	+	16.9506i	0.951040	+	0.549083i	0.0576363	+	0.998338i	$0.481644\pi$
$954$		0			0
$955$	−6.63849	+	12.1751i	−0.214816	+	0.393977i
$956$	10.2113	−	17.6864i	0.330256	−	0.572020i
$957$		0			0
$958$	14.4048	+	8.31659i	0.465397	+	0.268697i
$959$	−0.993464	−	1.72073i	−0.0320806	−	0.0555653i
$960$		0			0
$961$	8.70507			0.280809
$962$	16.8903	−	20.7512i	0.544566	−	0.669045i
$963$		0			0
$964$	15.0373	+	26.0453i	0.484318	+	0.838863i
$965$	−17.4409	+	10.6453i	−0.561442	+	0.342686i
$966$		0			0
$967$			20.9057i			0.672283i	0.941812	+	0.336141i	$0.109122\pi$
$967$			20.9057i			0.672283i	−0.941812	+	0.336141i	$0.890878\pi$
$968$	−31.4012	−	18.1295i	−1.00927	−	0.582704i
$969$		0			0
$970$	17.7476	−	0.433283i	0.569842	−	0.0139119i
$971$	24.1043	−	41.7499i	0.773545	−	1.33982i	−0.162064	−	0.986780i	$-0.551815\pi$
$971$	24.1043	−	41.7499i	0.773545	−	1.33982i	0.935609	−	0.353038i	$-0.114851\pi$
$972$		0			0
$973$	−4.61051	+	2.66188i	−0.147806	+	0.0853360i
$974$	20.4787			0.656180
$975$		0			0
$976$	−1.73276			−0.0554643
$977$	−28.5119	+	16.4614i	−0.912177	+	0.526646i	−0.881131	−	0.472872i	$-0.843217\pi$
$977$	−28.5119	+	16.4614i	−0.912177	+	0.526646i	−0.0310460	+	0.999518i	$0.509884\pi$
$978$		0			0
$979$	−1.28693	+	2.22902i	−0.0411304	+	0.0712399i
$980$	−19.7208	+	0.481455i	−0.629957	+	0.0153795i
$981$		0			0
$982$	5.04311	+	2.91164i	0.160932	+	0.0929143i
$983$		−	11.0460i		−	0.352312i	−0.984362	−	0.176156i	$-0.943634\pi$
$983$		−	11.0460i		−	0.352312i	0.984362	−	0.176156i	$-0.0563663\pi$
$984$		0			0
$985$	41.2454	−	25.1748i	1.31419	−	0.802136i
$986$	−23.5154	−	40.7299i	−0.748884	−	1.29711i
$987$		0			0
$988$	−3.73321	−	9.79870i	−0.118769	−	0.311738i
$989$	−2.00391			−0.0637207
$990$		0			0
$991$	4.83587	+	8.37598i	0.153617	+	0.266072i	0.932554	−	0.361029i	$-0.117575\pi$
$991$	4.83587	+	8.37598i	0.153617	+	0.266072i	−0.778938	+	0.627101i	$0.784241\pi$
$992$	31.3780	+	18.1161i	0.996253	+	0.575187i
$993$		0			0
$994$	1.07022	−	1.85367i	0.0339452	−	0.0587948i
$995$	−2.72369	+	4.99529i	−0.0863467	+	0.158361i
$996$		0			0
$997$	−43.6735	−	25.2149i	−1.38315	−	0.798565i	−0.390623	−	0.920551i	$-0.627740\pi$
$997$	−43.6735	−	25.2149i	−1.38315	−	0.798565i	−0.992532	+	0.121986i	$0.961074\pi$
$998$	−1.61299	+	0.931258i	−0.0510582	+	0.0294785i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	585.2.bs.b.289.8		24
3.2	odd	2		195.2.ba.a.94.5	✓	24
5.4	even	2	inner	585.2.bs.b.289.5		24
13.9	even	3	inner	585.2.bs.b.334.5		24
15.2	even	4		975.2.i.o.601.3		12
15.8	even	4		975.2.i.q.601.4		12
15.14	odd	2		195.2.ba.a.94.8	yes	24
39.35	odd	6		195.2.ba.a.139.8	yes	24
65.9	even	6	inner	585.2.bs.b.334.8		24
195.74	odd	6		195.2.ba.a.139.5	yes	24
195.113	even	12		975.2.i.q.451.4		12
195.152	even	12		975.2.i.o.451.3		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
195.2.ba.a.94.5	✓	24	3.2	odd	2
195.2.ba.a.94.8	yes	24	15.14	odd	2
195.2.ba.a.139.5	yes	24	195.74	odd	6
195.2.ba.a.139.8	yes	24	39.35	odd	6
585.2.bs.b.289.5		24	5.4	even	2	inner
585.2.bs.b.289.8		24	1.1	even	1	trivial
585.2.bs.b.334.5		24	13.9	even	3	inner
585.2.bs.b.334.8		24	65.9	even	6	inner
975.2.i.o.451.3		12	195.152	even	12
975.2.i.o.601.3		12	15.2	even	4
975.2.i.q.451.4		12	195.113	even	12
975.2.i.q.601.4		12	15.8	even	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:	\( N \)	\(=\)	\( 585 = 3^{2} \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	585.bs (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.729738 - 0.421315i) q^{2} +(-0.644988 + 1.11715i) q^{4} +(-2.23540 + 0.0545741i) q^{5} +(0.347589 + 0.200681i) q^{7} +2.77223i q^{8} +(-1.60827 + 0.981632i) q^{10} +(-2.45354 - 4.24965i) q^{11} +(-3.55974 - 0.572960i) q^{13} +0.338199 q^{14} +(-0.121995 - 0.211302i) q^{16} +(-6.13203 - 3.54033i) q^{17} +(1.12724 - 1.95244i) q^{19} +(1.38084 - 2.53248i) q^{20} +(-3.58088 - 2.06742i) q^{22} +(0.861695 - 0.497500i) q^{23} +(4.99404 - 0.243990i) q^{25} +(-2.83907 + 1.08166i) q^{26} +(-0.448381 + 0.258873i) q^{28} +(3.94133 + 6.82658i) q^{29} -6.30120 q^{31} +(-4.97969 - 2.87503i) q^{32} -5.96637 q^{34} +(-0.787953 - 0.429632i) q^{35} +(-7.62688 + 4.40338i) q^{37} -1.89969i q^{38} +(-0.151292 - 6.19705i) q^{40} +(2.65994 + 4.60715i) q^{41} +(-1.74416 - 1.00699i) q^{43} +6.33001 q^{44} +(0.419208 - 0.726090i) q^{46} +4.62317i q^{47} +(-3.41945 - 5.92267i) q^{49} +(3.54155 - 2.28211i) q^{50} +(2.93607 - 3.60721i) q^{52} +10.8496i q^{53} +(5.71656 + 9.36577i) q^{55} +(-0.556333 + 0.963596i) q^{56} +(5.75228 + 3.32108i) q^{58} +(1.52224 - 2.63659i) q^{59} +(3.55088 - 6.15031i) q^{61} +(-4.59822 + 2.65479i) q^{62} -4.35718 q^{64} +(7.98871 + 1.08653i) q^{65} +(-5.32891 + 3.07665i) q^{67} +(7.91018 - 4.56694i) q^{68} +(-0.756010 + 0.0184569i) q^{70} +(3.16446 - 5.48101i) q^{71} +1.01273i q^{73} +(-3.71042 + 6.42663i) q^{74} +(1.45411 + 2.51860i) q^{76} -1.96951i q^{77} +10.2755 q^{79} +(0.284240 + 0.465687i) q^{80} +(3.88212 + 2.24134i) q^{82} -10.5337i q^{83} +(13.9008 + 7.57941i) q^{85} -1.69704 q^{86} +(11.7810 - 6.80177i) q^{88} +(-0.262260 - 0.454247i) q^{89} +(-1.12234 - 0.913524i) q^{91} +1.28353i q^{92} +(1.94781 + 3.37371i) q^{94} +(-2.41329 + 4.42601i) q^{95} +(-8.15979 - 4.71106i) q^{97} +(-4.99061 - 2.88133i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 8 q^{4} - 4 q^{5} - 4 q^{10} - 4 q^{11} - 24 q^{14} + 16 q^{16} - 16 q^{19} + 16 q^{20} - 16 q^{25} + 48 q^{26} + 12 q^{29} + 8 q^{31} - 32 q^{34} - 10 q^{35} - 48 q^{40} + 40 q^{41} - 40 q^{44}+ \cdots + 28 q^{95}+O(q^{100}) \) 24 * q + 8 * q^4 - 4 * q^5 - 4 * q^10 - 4 * q^11 - 24 * q^14 + 16 * q^16 - 16 * q^19 + 16 * q^20 - 16 * q^25 + 48 * q^26 + 12 * q^29 + 8 * q^31 - 32 * q^34 - 10 * q^35 - 48 * q^40 + 40 * q^41 - 40 * q^44 - 24 * q^46 - 16 * q^49 - 20 * q^50 + 20 * q^55 + 24 * q^56 - 12 * q^59 + 20 * q^61 + 48 * q^64 - 14 * q^65 - 56 * q^70 - 4 * q^71 + 12 * q^74 + 8 * q^76 + 136 * q^79 + 4 * q^80 - 4 * q^85 - 48 * q^86 + 64 * q^89 + 60 * q^91 - 48 * q^94 + 28 * q^95

Introduction

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