LMFDB - Embedded newform 585.2.bs.b.334.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [585,2,Mod(289,585)]

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

lf = mfeigenbasis(mf)

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")

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

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

Self dual:	no
Analytic conductor:	$4.67124851824$
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			334.5
Character	$\chi$	$=$	585.334
Dual form			585.2.bs.b.289.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.729738 - 0.421315i) q^{2} +(-0.644988 - 1.11715i) q^{4} +(-2.23540 + 0.0545741i) q^{5} +(-0.347589 + 0.200681i) q^{7} +2.77223i q^{8} +O(q^{10})$	\(q+(-0.729738 - 0.421315i) q^{2} +(-0.644988 - 1.11715i) q^{4} +(-2.23540 + 0.0545741i) q^{5} +(-0.347589 + 0.200681i) q^{7} +2.77223i q^{8} +(1.65425 + 0.901983i) q^{10} +(-2.45354 + 4.24965i) q^{11} +(3.55974 - 0.572960i) q^{13} +0.338199 q^{14} +(-0.121995 + 0.211302i) q^{16} +(6.13203 - 3.54033i) q^{17} +(1.12724 + 1.95244i) q^{19} +(1.50278 + 2.46208i) q^{20} +(3.58088 - 2.06742i) q^{22} +(-0.861695 - 0.497500i) q^{23} +(4.99404 - 0.243990i) q^{25} +(-2.83907 - 1.08166i) q^{26} +(0.448381 + 0.258873i) q^{28} +(3.94133 - 6.82658i) q^{29} -6.30120 q^{31} +(4.97969 - 2.87503i) q^{32} -5.96637 q^{34} +(0.766049 - 0.467571i) q^{35} +(7.62688 + 4.40338i) q^{37} -1.89969i q^{38} +(-0.151292 - 6.19705i) q^{40} +(2.65994 - 4.60715i) q^{41} +(1.74416 - 1.00699i) q^{43} +6.33001 q^{44} +(0.419208 + 0.726090i) q^{46} +4.62317i q^{47} +(-3.41945 + 5.92267i) q^{49} +(-3.74714 - 1.92601i) q^{50} +(-2.93607 - 3.60721i) q^{52} +10.8496i q^{53} +(5.25272 - 9.63357i) q^{55} +(-0.556333 - 0.963596i) q^{56} +(-5.75228 + 3.32108i) q^{58} +(1.52224 + 2.63659i) q^{59} +(3.55088 + 6.15031i) q^{61} +(4.59822 + 2.65479i) q^{62} -4.35718 q^{64} +(-7.92617 + 1.47507i) q^{65} +(5.32891 + 3.07665i) q^{67} +(-7.91018 - 4.56694i) q^{68} +(-0.756010 + 0.0184569i) q^{70} +(3.16446 + 5.48101i) q^{71} +1.01273i q^{73} +(-3.71042 - 6.42663i) q^{74} +(1.45411 - 2.51860i) q^{76} -1.96951i q^{77} +10.2755 q^{79} +(0.261177 - 0.479002i) q^{80} +(-3.88212 + 2.24134i) q^{82} -10.5337i q^{83} +(-13.5143 + 8.24871i) q^{85} -1.69704 q^{86} +(-11.7810 - 6.80177i) q^{88} +(-0.262260 + 0.454247i) q^{89} +(-1.12234 + 0.913524i) q^{91} +1.28353i q^{92} +(1.94781 - 3.37371i) q^{94} +(-2.62639 - 4.30297i) q^{95} +(8.15979 - 4.71106i) q^{97} +(4.99061 - 2.88133i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 8 q^{4} - 4 q^{5}+O(q^{10}) $ 24 * q + 8 * q^4 - 4 * q^5	$ 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}+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

Display 100 coefficients 10 coefficients

Character values

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

$n$	$326$	$352$	$496$
$\chi(n)$	$1$	$-1$	$e\left(\frac{2}{3}\right)$

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	$-0.429624\pi$
$2$	−0.729738	−	0.421315i	−0.516003	−	0.297914i	−0.735298	+	0.677744i	$0.762958\pi$
$3$		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	$-0.690834\pi$
$7$	−0.347589	+	0.200681i	−0.131376	+	0.0758501i	0.432871	+	0.901456i	$0.357500\pi$
$8$			2.77223i			0.980131i
$9$		0			0
$10$	1.65425	+	0.901983i	0.523120	+	0.285232i
$11$	−2.45354	+	4.24965i	−0.739769	+	1.28132i	0.212830	+	0.977089i	$0.431732\pi$
$11$	−2.45354	+	4.24965i	−0.739769	+	1.28132i	−0.952599	+	0.304228i	$0.901601\pi$
$12$		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	$-0.337966\pi$
$17$	6.13203	−	3.54033i	1.48724	−	0.858656i	0.999894	+	0.0145544i	$0.00463296\pi$
$18$		0			0
$19$	1.12724	+	1.95244i	0.258607	+	0.447920i	0.965869	−	0.259031i	$-0.0834032\pi$
$19$	1.12724	+	1.95244i	0.258607	+	0.447920i	−0.707262	+	0.706952i	$0.750070\pi$
$20$	1.50278	+	2.46208i	0.336031	+	0.550539i
$21$		0			0
$22$	3.58088	−	2.06742i	0.763446	−	0.440776i
$23$	−0.861695	−	0.497500i	−0.179676	−	0.103736i	0.407465	−	0.913221i	$-0.366413\pi$
$23$	−0.861695	−	0.497500i	−0.179676	−	0.103736i	−0.587140	+	0.809485i	$0.699746\pi$
$24$		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	−0.224190	−	0.974546i	$-0.571973\pi$
$29$	3.94133	−	6.82658i	0.731886	−	1.26766i	0.956076	−	0.293119i	$-0.0946932\pi$
$30$		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
$35$	0.766049	−	0.467571i	0.129486	−	0.0790339i
$36$		0			0
$37$	7.62688	+	4.40338i	1.25385	+	0.723912i	0.971872	−	0.235509i	$-0.0756756\pi$
$37$	7.62688	+	4.40338i	1.25385	+	0.723912i	0.281980	+	0.959420i	$0.409009\pi$
$38$		−	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	−0.580059	−	0.814575i	$-0.696970\pi$
$41$	2.65994	−	4.60715i	0.415413	−	0.719517i	0.995472	+	0.0950582i	$0.0303037\pi$
$42$		0			0
$43$	1.74416	−	1.00699i	0.265982	−	0.153565i	−0.361078	−	0.932536i	$-0.617591\pi$
$43$	1.74416	−	1.00699i	0.265982	−	0.153565i	0.627060	+	0.778971i	$0.284258\pi$
$44$	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
$50$	−3.74714	−	1.92601i	−0.529926	−	0.272380i
$51$		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
$55$	5.25272	−	9.63357i	0.708276	−	1.29899i
$56$	−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	0.947938	−	0.318455i	$-0.103164\pi$
$59$	1.52224	+	2.63659i	0.198178	+	0.343255i	−0.749759	+	0.661711i	$0.769831\pi$
$60$		0			0
$61$	3.55088	+	6.15031i	0.454644	+	0.787466i	0.998668	−	0.0516038i	$-0.0164333\pi$
$61$	3.55088	+	6.15031i	0.454644	+	0.787466i	−0.544024	+	0.839070i	$0.683100\pi$
$62$	4.59822	+	2.65479i	0.583975	+	0.337158i
$63$		0			0
$64$	−4.35718			−0.544648
$65$	−7.92617	+	1.47507i	−0.983120	+	0.182959i
$66$		0			0
$67$	5.32891	+	3.07665i	0.651030	+	0.375873i	0.788851	−	0.614585i	$-0.210676\pi$
$67$	5.32891	+	3.07665i	0.651030	+	0.375873i	−0.137821	+	0.990457i	$0.544010\pi$
$68$	−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	0.990410	−	0.138162i	$-0.0441196\pi$
$71$	3.16446	+	5.48101i	0.375553	+	0.650476i	−0.614857	+	0.788639i	$0.710786\pi$
$72$		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	$0.303817\pi$
$80$	0.261177	−	0.479002i	0.0292004	−	0.0535541i
$81$		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
$85$	−13.5143	+	8.24871i	−1.46584	+	0.894699i
$86$	−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	−0.879590	−	0.475732i	$-0.842183\pi$
$89$	−0.262260	+	0.454247i	−0.0277995	+	0.0481501i	0.851791	+	0.523882i	$0.175517\pi$
$90$		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
$95$	−2.62639	−	4.30297i	−0.269462	−	0.441475i
$96$		0			0
$97$	8.15979	−	4.71106i	0.828502	−	0.478336i	−0.0248378	−	0.999691i	$-0.507907\pi$
$97$	8.15979	−	4.71106i	0.828502	−	0.478336i	0.853339	+	0.521356i	$0.174574\pi$
$98$	4.99061	−	2.88133i	0.504128	−	0.291059i
$99$		0			0
$100$	−3.49367	−	5.42173i	−0.349367	−	0.542173i
$101$	−2.87707	+	4.98324i	−0.286280	+	0.495851i	−0.972919	−	0.231148i	$-0.925752\pi$
$101$	−2.87707	+	4.98324i	−0.286280	+	0.495851i	0.686639	+	0.726998i	$0.259085\pi$
$102$		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	$-0.0774106\pi$
$107$	12.9024	+	7.44919i	1.24732	+	0.720141i	0.276746	+	0.960943i	$0.410744\pi$
$108$		0			0
$109$	1.69762			0.162602			0.0813011	−	0.996690i	$-0.474092\pi$
$109$	1.69762			0.162602			0.0813011	+	0.996690i	$0.474092\pi$
$110$	−7.89187	+	4.81694i	−0.752461	+	0.459277i
$111$		0			0
$112$		−	0.0979282i		−	0.00925335i
$113$	−1.94685	+	1.12402i	−0.183145	+	0.105739i	−0.588769	−	0.808301i	$-0.700387\pi$
$113$	−1.94685	+	1.12402i	−0.183145	+	0.105739i	0.405625	+	0.914040i	$0.367054\pi$
$114$		0			0
$115$	1.95339	+	1.06509i	0.182154	+	0.0993198i
$116$	−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	$-0.611061\pi$
$127$	−14.9506	−	8.63173i	−1.32665	−	0.765942i	−0.984780	+	0.173804i	$0.944394\pi$
$128$	−6.77978	−	3.91431i	−0.599254	−	0.345979i
$129$		0			0
$130$	6.40550	+	2.26300i	0.561799	+	0.198478i
$131$	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	$-0.598840\pi$
$137$	4.28724	−	2.47524i	0.366284	−	0.211474i	0.671834	+	0.740702i	$0.265507\pi$
$138$		0			0
$139$	−6.63214	−	11.4872i	−0.562530	−	0.974331i	−0.997275	−	0.0737774i	$-0.976495\pi$
$139$	−6.63214	−	11.4872i	−0.562530	−	0.974331i	0.434744	−	0.900554i	$-0.356839\pi$
$140$	−1.01644	−	0.554215i	−0.0859049	−	0.0468397i
$141$		0			0
$142$		−	5.33294i		−	0.447530i
$143$	−6.29906	+	16.5334i	−0.526754	+	1.38259i
$144$		0			0
$145$	−8.43790	+	15.4752i	−0.700729	+	1.28515i
$146$	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	0.923423	−	0.383783i	$-0.125379\pi$
$149$	1.57886	+	2.73467i	0.129345	+	0.224033i	−0.794078	+	0.607816i	$0.792046\pi$
$150$		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
$160$	−10.9747	+	6.69860i	−0.867627	+	0.529571i
$161$	0.399354			0.0314735
$162$		0			0
$163$	−1.36302	+	0.786941i	−0.106760	+	0.0616380i	−0.552429	−	0.833560i	$-0.686299\pi$
$163$	−1.36302	+	0.786941i	−0.106760	+	0.0616380i	0.445669	+	0.895198i	$0.352966\pi$
$164$	−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	$-0.531453\pi$
$167$	−13.0492	−	7.53397i	−1.00978	−	0.582996i	−0.911127	+	0.412126i	$0.864786\pi$
$168$		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	$-0.625335\pi$
$173$	2.94981	−	1.70307i	0.224270	−	0.129482i	0.607926	+	0.793994i	$0.292002\pi$
$174$		0			0
$175$	−1.68691	+	1.08702i	−0.127518	+	0.0821707i
$176$	−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	−0.854576	−	0.519326i	$-0.826183\pi$
$179$	0.300516	−	0.520508i	0.0224616	−	0.0389046i	0.877038	+	0.480422i	$0.159516\pi$
$180$		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
$185$	−17.2895	−	9.42710i	−1.27115	−	0.693094i
$186$		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	0.956130	−	0.292944i	$-0.0946349\pi$
$191$	3.10083	+	5.37079i	0.224368	+	0.388617i	−0.731762	+	0.681561i	$0.761302\pi$
$192$		0			0
$193$	−7.91367	−	4.56896i	−0.569639	−	0.328881i	0.187366	−	0.982290i	$-0.440005\pi$
$193$	−7.91367	−	4.56896i	−0.569639	−	0.328881i	−0.757005	+	0.653409i	$0.773338\pi$
$194$	−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	$-0.0536780\pi$
$197$	18.7148	+	10.8050i	1.33337	+	0.769823i	0.347557	+	0.937659i	$0.387011\pi$
$198$		0			0
$199$	1.27223	+	2.20357i	0.0901860	+	0.156207i	0.907589	−	0.419859i	$-0.137921\pi$
$199$	1.27223	+	2.20357i	0.0901860	+	0.156207i	−0.817403	+	0.576066i	$0.804587\pi$
$200$	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
$205$	−5.69461	+	10.4440i	−0.397729	+	0.729441i
$206$	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	−0.609836	−	0.792528i	$-0.708765\pi$
$211$	5.54061	−	9.59663i	0.381432	−	0.660659i	0.991267	+	0.131869i	$0.0420978\pi$
$212$	12.1207	−	6.99789i	0.832453	−	0.480617i
$213$		0			0
$214$	−6.27691	−	10.8719i	−0.429081	−	0.743189i
$215$	−3.84394	+	2.34622i	−0.262155	+	0.160011i
$216$		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	$-0.327668\pi$
$223$	0.460340	+	0.265778i	0.0308267	+	0.0177978i	−0.484507	+	0.874787i	$0.661001\pi$
$224$	−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	$-0.415468\pi$
$227$	18.5220	−	10.6937i	1.22935	−	0.709764i	0.966894	+	0.255180i	$0.0821348\pi$
$228$		0			0
$229$	0.406502			0.0268624			0.0134312	−	0.999910i	$-0.495725\pi$
$229$	0.406502			0.0268624			0.0134312	+	0.999910i	$0.495725\pi$
$230$	−0.976724	−	1.60022i	−0.0644033	−	0.105516i
$231$		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	0.947390	+	0.320083i	$0.103711\pi$
$241$	11.6570	+	20.1906i	0.750895	+	1.30059i	−0.196495	+	0.980505i	$0.562956\pi$
$242$			11.0210i			0.708460i
$243$		0			0
$244$	4.58055	−	7.93375i	0.293240	−	0.507906i
$245$	7.32063	−	13.4262i	0.467698	−	0.857766i
$246$		0			0
$247$	5.13135	+	6.30431i	0.326500	+	0.401133i
$248$		−	17.4684i		−	1.10924i
$249$		0			0
$250$	8.48148	+	4.10092i	0.536416	+	0.259365i
$251$	0.650814	+	1.12724i	0.0410790	+	0.0711509i	0.885834	−	0.464002i	$-0.153587\pi$
$251$	0.650814	+	1.12724i	0.0410790	+	0.0711509i	−0.844755	+	0.535153i	$0.820254\pi$
$252$		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	$-0.432979\pi$
$257$	−8.55103	−	4.93694i	−0.533399	−	0.307958i	−0.742399	+	0.669958i	$0.766312\pi$
$258$		0			0
$259$	−3.53469			−0.219635
$260$	6.76016	+	7.90334i	0.419247	+	0.490144i
$261$		0			0
$262$	−3.35001	−	1.93413i	−0.206965	−	0.119491i
$263$	−0.462121	−	0.266805i	−0.0284956	−	0.0164519i	0.485685	−	0.874134i	$-0.338570\pi$
$263$	−0.462121	−	0.266805i	−0.0284956	−	0.0164519i	−0.514180	+	0.857682i	$0.671904\pi$
$264$		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	0.995400	−	0.0958112i	$-0.0305445\pi$
$269$	6.80199	+	11.7814i	0.414725	+	0.718324i	−0.580675	+	0.814136i	$0.697211\pi$
$270$		0			0
$271$	11.9163	−	20.6396i	0.723862	−	1.25377i	−0.235579	−	0.971855i	$-0.575699\pi$
$271$	11.9163	−	20.6396i	0.723862	−	1.25377i	0.959441	−	0.281911i	$-0.0909681\pi$
$272$			1.72761i			0.104752i
$273$		0			0
$274$	−4.17142			−0.252004
$275$	−11.2162	+	21.8216i	−0.676362	+	1.31589i
$276$		0			0
$277$	16.6388	−	9.60639i	0.999726	−	0.577192i	0.0915586	−	0.995800i	$-0.470815\pi$
$277$	16.6388	−	9.60639i	0.999726	−	0.577192i	0.908167	+	0.418608i	$0.137482\pi$
$278$			11.1769i			0.670344i
$279$		0			0
$280$	1.29621	+	2.12366i	0.0774636	+	0.126913i
$281$	−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	0.997725	+	0.0674193i	$0.0214765\pi$
$283$	26.1587	+	15.1027i	1.55497	+	0.897765i	0.557249	+	0.830345i	$0.311857\pi$
$284$	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
$290$	12.6774	−	7.73787i	0.744443	−	0.454383i
$291$		0			0
$292$	1.13137	−	0.653199i	0.0662086	−	0.0382256i
$293$	6.18072	−	3.56844i	0.361081	−	0.208470i	−0.308474	−	0.951233i	$-0.599818\pi$
$293$	6.18072	−	3.56844i	0.361081	−	0.208470i	0.669555	+	0.742762i	$0.266485\pi$
$294$		0			0
$295$	−3.54670	−	5.81077i	−0.206497	−	0.338316i
$296$	−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
$305$	−8.27329	−	13.5546i	−0.473727	−	0.776135i
$306$		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
$310$	−10.4238	−	5.68357i	−0.592030	−	0.322805i
$311$	−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
$325$	17.6377	−	3.72993i	0.978362	−	0.206899i
$326$	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	0.614348	−	0.789035i	$-0.289419\pi$
$331$	−6.84346	−	11.8532i	−0.376150	−	0.651512i	−0.990499	+	0.137524i	$0.956086\pi$
$332$	−11.7678	+	6.79413i	−0.645841	+	0.372877i
$333$		0			0
$334$	6.34834	+	10.9956i	0.347366	+	0.601655i
$335$	−12.0802	−	6.58673i	−0.660010	−	0.359871i
$336$		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
$340$	17.9317	+	9.77726i	0.972481	+	0.530246i
$341$	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	$-0.760847\pi$
$347$	−9.40767	+	5.43152i	−0.505030	+	0.291579i	0.225758	+	0.974183i	$0.427514\pi$
$348$		0			0
$349$	−9.86492	+	17.0865i	−0.528057	+	0.914622i	0.471408	+	0.881915i	$0.343746\pi$
$349$	−9.86492	+	17.0865i	−0.528057	+	0.914622i	−0.999465	+	0.0327066i	$0.989587\pi$
$350$	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	$-0.168538\pi$
$353$	16.1051	+	9.29831i	0.857190	+	0.494899i	−0.00588009	+	0.999983i	$0.501872\pi$
$354$		0			0
$355$	−7.37297	−	12.0796i	−0.391317	−	0.641117i
$356$	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	$-0.633850\pi$
$367$	−26.8759	−	15.5168i	−1.40291	−	0.809971i	−0.994690	+	0.102913i	$0.967184\pi$
$368$	0.210245	−	0.121385i	0.0109598	−	0.00632764i
$369$		0			0
$370$	8.64501	+	14.1636i	0.449432	+	0.736331i
$371$	−2.17731	−	3.77121i	−0.113040	−	0.195792i
$372$		0			0
$373$	−9.03380	+	5.21567i	−0.467752	+	0.270057i	−0.715298	−	0.698819i	$-0.753709\pi$
$373$	−9.03380	+	5.21567i	−0.467752	+	0.270057i	0.247546	+	0.968876i	$0.420376\pi$
$374$	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	0.137420	+	0.990513i	$0.456119\pi$
$379$	−15.3621	+	26.6080i	−0.789099	+	1.36676i	−0.926519	+	0.376247i	$0.877214\pi$
$380$	−3.11308	+	5.70944i	−0.159698	+	0.292888i
$381$		0			0
$382$		−	5.22569i		−	0.267370i
$383$	−7.37251	+	4.25652i	−0.376718	+	0.217498i	−0.676389	−	0.736544i	$-0.736456\pi$
$383$	−7.37251	+	4.25652i	−0.376718	+	0.217498i	0.299672	+	0.954042i	$0.403123\pi$
$384$		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	$-0.492026\pi$
$397$	17.9986	−	10.3915i	0.903325	−	0.521535i	0.878278	+	0.478151i	$0.158693\pi$
$398$		−	2.14404i		−	0.107471i
$399$		0			0
$400$	−0.557693	+	1.08502i	−0.0278847	+	0.0542508i
$401$	−18.3709	+	31.8194i	−0.917400	+	1.58898i	−0.114050	+	0.993475i	$0.536382\pi$
$401$	−18.3709	+	31.8194i	−0.917400	+	1.58898i	−0.803350	+	0.595508i	$0.796951\pi$
$402$		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	0.823598	−	0.567174i	$-0.191963\pi$
$409$	−1.60553	−	2.78087i	−0.0793885	−	0.137505i	−0.902986	+	0.429669i	$0.858630\pi$
$410$	8.55578	−	5.22217i	0.422540	−	0.257905i
$411$		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	−0.617401	−	0.786649i	$-0.711814\pi$
$419$	7.62605	−	13.2087i	0.372557	−	0.645288i	0.989958	+	0.141361i	$0.0451477\pi$
$420$		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
$425$	29.7598	−	19.1767i	1.44356	−	0.930208i
$426$		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	−0.845880	−	0.533373i	$-0.820924\pi$
$431$	0.809141	−	1.40147i	0.0389750	−	0.0675066i	0.884855	+	0.465867i	$0.154257\pi$
$432$		0			0
$433$	13.4785	−	7.78179i	0.647733	−	0.373969i	−0.139854	−	0.990172i	$-0.544663\pi$
$433$	13.4785	−	7.78179i	0.647733	−	0.373969i	0.787587	+	0.616203i	$0.211330\pi$
$434$	−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	−0.944151	−	0.329514i	$-0.893115\pi$
$439$	−3.91196	+	6.77571i	−0.186708	+	0.323387i	0.757443	+	0.652901i	$0.226448\pi$
$440$	26.7065	+	14.5617i	1.27318	+	0.694204i
$441$		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
$445$	0.561466	−	1.02974i	0.0266160	−	0.0488143i
$446$	−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	0.924959	+	0.380066i	$0.124099\pi$
$449$	16.7743	+	29.0539i	0.791626	+	1.37114i	−0.133333	+	0.991071i	$0.542568\pi$
$450$		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
$455$	2.45903	−	2.10334i	0.115281	−	0.0986063i
$456$		0			0
$457$	−15.9839	−	9.22831i	−0.747696	−	0.431682i	0.0771651	−	0.997018i	$-0.475413\pi$
$457$	−15.9839	−	9.22831i	−0.747696	−	0.431682i	−0.824861	+	0.565336i	$0.808746\pi$
$458$	−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	0.935475	−	0.353394i	$-0.114972\pi$
$461$	3.47162	+	6.01302i	0.161689	+	0.280054i	−0.773785	+	0.633448i	$0.781639\pi$
$462$		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
$470$	−4.17002	+	7.64789i	−0.192349	+	0.352771i
$471$		0			0
$472$	−7.30924	+	4.21999i	−0.336435	+	0.194241i
$473$			9.88276i			0.454410i
$474$		0			0
$475$	6.10587	+	9.47553i	0.280157	+	0.434767i
$476$	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	−0.547483	−	0.836817i	$-0.684414\pi$
$479$	9.86981	−	17.0950i	0.450963	−	0.781091i	0.998446	+	0.0557257i	$0.0177472\pi$
$480$		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
$485$	−17.9833	+	10.9764i	−0.816580	+	0.498414i
$486$		0			0
$487$	−21.0473	+	12.1517i	−0.953745	+	0.550645i	−0.894242	−	0.447583i	$-0.852285\pi$
$487$	−21.0473	+	12.1517i	−0.953745	+	0.550645i	−0.0595026	+	0.998228i	$0.518951\pi$
$488$	−17.0501	+	9.84386i	−0.771820	+	0.445610i
$489$		0			0
$490$	−10.9988	+	6.71329i	−0.496874	+	0.303276i
$491$	3.45543	−	5.98497i	0.155941	−	0.270098i	−0.777460	−	0.628932i	$-0.783492\pi$
$491$	3.45543	−	5.98497i	0.155941	−	0.270098i	0.933401	+	0.358834i	$0.116826\pi$
$492$		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	$0.515755\pi$
$500$	8.10565	+	11.9291i	0.362496	+	0.533485i
$501$		0			0
$502$		−	1.09679i		−	0.0489521i
$503$	25.3122	−	14.6140i	1.12862	−	0.651607i	0.185030	−	0.982733i	$-0.440762\pi$
$503$	25.3122	−	14.6140i	1.12862	−	0.651607i	0.943587	+	0.331126i	$0.107428\pi$
$504$		0			0
$505$	6.15946	−	11.2966i	0.274092	−	0.502690i
$506$	−4.11417			−0.182897
$507$		0			0
$508$			22.2695i			0.988047i
$509$	3.60746	−	6.24830i	0.159898	−	0.276951i	−0.774934	−	0.632042i	$-0.782217\pi$
$509$	3.60746	−	6.24830i	0.159898	−	0.276951i	0.934832	+	0.355091i	$0.115550\pi$
$510$		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
$520$	−4.08922	−	21.9732i	−0.179324	−	0.963587i
$521$	−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	$-0.332781\pi$
$523$	0.0687721	+	0.0397056i	0.00300719	+	0.00173620i	−0.498496	+	0.866892i	$0.666114\pi$
$524$	−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
$530$	−9.78618	+	17.9480i	−0.425085	+	0.779612i
$531$		0			0
$532$			1.16725i			0.0506067i
$533$	6.82897	−	17.9243i	0.295796	−	0.776387i
$534$		0			0
$535$	−29.2485	−	15.9478i	−1.26452	−	0.689484i
$536$	−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
$550$	17.3786	−	11.1985i	0.741027	−	0.477505i
$551$	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	$-0.571275\pi$
$557$	−27.7896	−	16.0443i	−1.17748	−	0.679820i	−0.955431	+	0.295215i	$0.904609\pi$
$558$		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	$-0.656472\pi$
$563$	1.31596	−	0.759773i	0.0554613	−	0.0320206i	0.527474	+	0.849571i	$0.323139\pi$
$564$		0			0
$565$	4.29066	−	2.61888i	0.180509	−	0.110177i
$566$	−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	−0.995474	−	0.0950394i	$-0.969702\pi$
$569$	−9.90956	+	17.1639i	−0.415430	+	0.719546i	0.580043	+	0.814586i	$0.303036\pi$
$570$		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
$575$	−4.42473	−	2.27429i	−0.184524	−	0.0948445i
$576$		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	$-0.511992\pi$
$587$	−22.3360	−	12.8957i	−0.921907	−	0.532263i	−0.884243	+	0.467027i	$0.845325\pi$
$588$		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
$595$	3.04208	−	5.57923i	0.124713	−	0.228726i
$596$	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	−0.386297	−	0.922375i	$-0.626246\pi$
$601$	14.8477	−	25.7170i	0.605652	−	1.04902i	0.991948	−	0.126645i	$-0.0404208\pi$
$602$	0.589873	−	0.340563i	0.0240414	−	0.0138803i
$603$		0			0
$604$	11.9889	+	20.7654i	0.487823	+	0.844933i
$605$	15.2370	+	24.9636i	0.619471	+	1.01492i
$606$		0			0
$607$	−14.0175	+	8.09298i	−0.568951	+	0.328484i	−0.756730	−	0.653727i	$-0.773204\pi$
$607$	−14.0175	+	8.09298i	−0.568951	+	0.328484i	0.187779	+	0.982211i	$0.439871\pi$
$608$	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	$-0.505559\pi$
$613$	−22.0871	−	12.7520i	−0.892089	−	0.515048i	−0.874625	+	0.484799i	$0.838893\pi$
$614$	−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	$-0.742665\pi$
$617$	−10.1748	+	5.87440i	−0.409620	+	0.236494i	0.281006	+	0.959706i	$0.409332\pi$
$618$		0			0
$619$	9.49031			0.381448			0.190724	−	0.981644i	$-0.438917\pi$
$619$	9.49031			0.381448			0.190724	+	0.981644i	$0.438917\pi$
$620$	−9.46928	−	15.5141i	−0.380295	−	0.623060i
$621$		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	0.531322	−	0.847170i	$-0.321695\pi$
$631$	−11.7563	−	20.3625i	−0.468010	−	0.810617i	−0.999332	+	0.0365534i	$0.988362\pi$
$632$			28.4861i			1.13311i
$633$		0			0
$634$	−10.5663	+	18.3014i	−0.419641	+	0.726839i
$635$	33.8917	+	18.4795i	1.34495	+	0.733336i
$636$		0			0
$637$	−8.77890	+	23.0423i	−0.347833	+	0.912971i
$638$		−	32.5935i		−	1.29039i
$639$		0			0
$640$	15.3692	+	8.38005i	0.607519	+	0.331251i
$641$	9.54940	+	16.5400i	0.377179	+	0.653292i	0.990651	−	0.136424i	$-0.0435610\pi$
$641$	9.54940	+	16.5400i	0.377179	+	0.653292i	−0.613472	+	0.789717i	$0.710228\pi$
$642$		0			0
$643$	37.7938	−	21.8202i	1.49044	−	0.860506i	0.490500	−	0.871441i	$-0.336814\pi$
$643$	37.7938	−	21.8202i	1.49044	−	0.860506i	0.999940	+	0.0109350i	$0.00348080\pi$
$644$	−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	$-0.354059\pi$
$647$	−2.86660	−	1.65503i	−0.112698	−	0.0650661i	−0.555289	+	0.831657i	$0.687392\pi$
$648$		0			0
$649$	−14.9395			−0.586425
$650$	−14.4424	−	4.70914i	−0.566476	−	0.184708i
$651$		0			0
$652$	1.75827	+	1.01514i	0.0688590	+	0.0397558i
$653$	3.12790	+	1.80589i	0.122404	+	0.0706701i	0.559952	−	0.828525i	$-0.310820\pi$
$653$	3.12790	+	1.80589i	0.122404	+	0.0706701i	−0.437548	+	0.899195i	$0.644153\pi$
$654$		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	−0.891441	−	0.453136i	$-0.850305\pi$
$659$	−21.5161	−	37.2670i	−0.838148	−	1.45172i	0.0532932	−	0.998579i	$-0.483028\pi$
$660$		0			0
$661$	−18.8524	+	32.6533i	−0.733273	+	1.27007i	0.222204	+	0.975000i	$0.428675\pi$
$661$	−18.8524	+	32.6533i	−0.733273	+	1.27007i	−0.955477	+	0.295066i	$0.904658\pi$
$662$			11.5330i			0.448242i
$663$		0			0
$664$	29.2019			1.13325
$665$	1.77643	+	0.968599i	0.0688869	+	0.0375607i
$666$		0			0
$667$	−6.79245	+	3.92162i	−0.263005	+	0.151846i
$668$			19.4373i			0.752051i
$669$		0			0
$670$	6.04028	+	9.89614i	0.233356	+	0.382321i
$671$	−34.8489			−1.34532
$672$		0			0
$673$	38.7794	+	22.3893i	1.49484	+	0.863045i	0.999982	−	0.00593030i	$-0.00188768\pi$
$673$	38.7794	+	22.3893i	1.49484	+	0.863045i	0.494855	+	0.868975i	$0.335221\pi$
$674$	−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
$680$	−22.8673	−	37.4649i	−0.876922	−	1.43671i
$681$		0			0
$682$	−22.5638	+	13.0272i	−0.864013	+	0.498838i
$683$	17.7354	−	10.2395i	0.678627	−	0.391805i	−0.120711	−	0.992688i	$-0.538517\pi$
$683$	17.7354	−	10.2395i	0.678627	−	0.391805i	0.799338	+	0.600882i	$0.205184\pi$
$684$		0			0
$685$	−9.44862	+	5.76712i	−0.361013	+	0.220351i
$686$	−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	0.471832	+	0.881689i	$0.343593\pi$
$691$	−13.8702	+	24.0240i	−0.527649	+	0.913915i	−0.999481	+	0.0322263i	$0.989740\pi$
$692$	−3.80518	−	2.19692i	−0.144651	−	0.0835145i
$693$		0			0
$694$	9.15352			0.347463
$695$	15.4524	+	25.3166i	0.586143	+	0.960312i
$696$		0			0
$697$		−	37.6683i		−	1.42679i
$698$	14.3976	−	8.31247i	0.544958	−	0.314632i
$699$		0			0
$700$	2.30240	+	1.18342i	0.0870225	+	0.0447292i
$701$	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	0.569037	−	0.822312i	$-0.307316\pi$
$709$	−11.3864	−	19.7218i	−0.427625	−	0.740668i	−0.996662	+	0.0816444i	$0.973983\pi$
$710$	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
$715$	13.1786	−	37.3026i	0.492853	−	1.39504i
$716$	−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	0.508310	−	0.861174i	$-0.330270\pi$
$719$	−13.1830	−	22.8336i	−0.491643	−	0.851551i	−0.999954	+	0.00962269i	$0.996937\pi$
$720$		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
$725$	18.0175	−	35.0539i	0.669155	−	1.30187i
$726$		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
$730$	−0.913465	+	1.67531i	−0.0338089	+	0.0620060i
$731$	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	−0.882268	−	0.470748i	$-0.843984\pi$
$739$	−0.909425	+	1.57517i	−0.0334538	+	0.0579436i	0.848814	+	0.528692i	$0.177317\pi$
$740$	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	$-0.281741\pi$
$743$	7.61880	+	4.39871i	0.279507	+	0.161373i	−0.353693	+	0.935361i	$0.615074\pi$
$744$		0			0
$745$	−3.67863	−	6.02692i	−0.134775	−	0.220809i
$746$	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	0.321156	+	0.947026i	$0.395929\pi$
$751$	−18.0751	+	31.3070i	−0.659571	+	1.14241i	−0.980727	+	0.195384i	$0.937405\pi$
$752$	−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	$-0.510665\pi$
$757$	−25.1967	−	14.5473i	−0.915789	−	0.528731i	−0.882289	+	0.470708i	$0.843999\pi$
$758$	22.4207	−	12.9446i	0.814355	−	0.470168i
$759$		0			0
$760$	11.9288	−	7.28096i	0.432704	−	0.264108i
$761$	−13.2927	−	23.0236i	−0.481859	−	0.834603i	0.517925	−	0.855426i	$-0.326705\pi$
$761$	−13.2927	−	23.0236i	−0.481859	−	0.834603i	−0.999783	+	0.0208228i	$0.993371\pi$
$762$		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	−0.550556	−	0.834799i	$-0.685584\pi$
$769$	12.4145	−	21.5026i	0.447679	−	0.775403i	0.998235	+	0.0593958i	$0.0189174\pi$
$770$	1.77646	−	3.25806i	0.0640192	−	0.117412i
$771$		0			0
$772$			11.7877i			0.424249i
$773$	15.4061	−	8.89469i	0.554117	−	0.319920i	−0.196664	−	0.980471i	$-0.563011\pi$
$773$	15.4061	−	8.89469i	0.554117	−	0.319920i	0.750781	+	0.660551i	$0.229677\pi$
$774$		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	$-0.533722\pi$
$787$	19.7092	−	11.3791i	0.702557	−	0.405622i	0.808299	+	0.588772i	$0.200388\pi$
$788$		−	27.8763i		−	0.993053i
$789$		0			0
$790$	16.9983	+	9.26832i	0.604771	+	0.329752i
$791$	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	$-0.805973\pi$
$797$	−20.7232	+	11.9646i	−0.734055	+	0.423807i	0.0858488	+	0.996308i	$0.472640\pi$
$798$		0			0
$799$	16.3676	+	28.3495i	0.579043	+	1.00293i
$800$	24.1673	−	15.5730i	0.854444	−	0.550589i
$801$		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	−0.975018	−	0.222125i	$-0.928701\pi$
$809$	−8.39474	+	14.5401i	−0.295143	+	0.511203i	0.679875	+	0.733328i	$0.262034\pi$
$810$		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
$815$	3.00396	−	1.83352i	0.105224	−	0.0642253i
$816$		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	−0.294734	−	0.955579i	$-0.595231\pi$
$821$	19.4895	−	33.7568i	0.680189	−	1.17812i	0.974923	−	0.222542i	$-0.0714355\pi$
$822$		0			0
$823$	9.60038	−	5.54278i	0.334648	−	0.193209i	−0.323255	−	0.946312i	$-0.604777\pi$
$823$	9.60038	−	5.54278i	0.334648	−	0.193209i	0.657903	+	0.753103i	$0.271444\pi$
$824$	−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	−0.624332	−	0.781159i	$-0.714629\pi$
$829$	10.4901	−	18.1694i	0.364337	−	0.631051i	0.988670	+	0.150108i	$0.0479622\pi$
$830$	9.50125	−	17.4254i	0.329793	−	0.604846i
$831$		0			0
$832$	−15.5104	+	2.49649i	−0.537727	+	0.0865503i
$833$			48.4240i			1.67779i
$834$		0			0
$835$	29.5814	+	16.1293i	1.02371	+	0.558177i
$836$	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	0.942627	−	0.333848i	$-0.108347\pi$
$839$	5.27731	+	9.14057i	0.182193	+	0.315568i	−0.760434	+	0.649415i	$0.775014\pi$
$840$		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
$845$	−27.3699	+	9.79223i	−0.941554	+	0.336863i
$846$		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	$0.614656\pi$
$860$	5.10038	+	2.78099i	0.173921	+	0.0948309i
$861$		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
$865$	−6.50107	+	3.96804i	−0.221043	+	0.134917i
$866$	−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
$875$	3.71160	−	2.52198i	0.125475	−	0.0852584i
$876$		0			0
$877$	−17.6624	+	10.1974i	−0.596417	+	0.344342i	−0.767631	−	0.640892i	$-0.778565\pi$
$877$	−17.6624	+	10.1974i	−0.596417	+	0.344342i	0.171214	+	0.985234i	$0.445231\pi$
$878$	5.70941	−	3.29633i	0.192683	−	0.111246i
$879$		0			0
$880$	1.39479	+	2.28516i	0.0470182	+	0.0770327i
$881$	−12.6173	+	21.8538i	−0.425087	+	0.736272i	−0.996429	−	0.0844405i	$-0.973090\pi$
$881$	−12.6173	+	21.8538i	−0.425087	+	0.736272i	0.571342	+	0.820712i	$0.306423\pi$
$882$		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	$-0.117400\pi$
$887$	32.3709	+	18.6894i	1.08691	+	0.627527i	0.154157	+	0.988046i	$0.450734\pi$
$888$		0			0
$889$	6.92888			0.232387
$890$	−0.843567	+	0.514885i	−0.0282764	+	0.0172590i
$891$		0			0
$892$		−	0.685693i		−	0.0229587i
$893$	−9.02647	+	5.21144i	−0.302059	+	0.174394i
$894$		0			0
$895$	−0.643367	+	1.17995i	−0.0215054	+	0.0394412i
$896$	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	$-0.0297662\pi$
$907$	42.5419	+	24.5616i	1.41258	+	0.815553i	0.416948	+	0.908930i	$0.363100\pi$
$908$	−23.8929	−	13.7946i	−0.792915	−	0.457789i
$909$		0			0
$910$	−2.68062	+	0.498865i	−0.0888617	+	0.0165372i
$911$	−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	0.513996	−	0.857793i	$-0.328165\pi$
$919$	−14.7292	−	25.5118i	−0.485872	−	0.841556i	−0.999868	+	0.0162371i	$0.994831\pi$
$920$	−2.95266	+	5.41523i	−0.0973464	+	0.178535i
$921$		0			0
$922$		−	5.85057i		−	0.192678i
$923$	14.4051	+	17.6978i	0.474148	+	0.582531i
$924$		0			0
$925$	39.1634	+	20.1298i	1.28768	+	0.661864i
$926$	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	0.616351	−	0.787472i	$-0.288610\pi$
$929$	−11.3931	−	19.7334i	−0.373795	−	0.647432i	−0.990146	+	0.140040i	$0.955277\pi$
$930$		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
$940$	−11.3826	+	6.94759i	−0.371261	+	0.226605i
$941$	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	$-0.283212\pi$
$947$	8.35815	+	4.82558i	0.271603	+	0.156810i	−0.358013	+	0.933717i	$0.616546\pi$
$948$		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	$-0.851690\pi$
$953$	−29.3593	+	16.9506i	−0.951040	+	0.549083i	−0.0576363	+	0.998338i	$0.518356\pi$
$954$		0			0
$955$	−7.22470	−	11.8366i	−0.233786	−	0.383025i
$956$	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
$965$	17.9396	+	9.78158i	0.577496	+	0.314880i
$966$		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	0.935609	+	0.353038i	$0.114851\pi$
$971$	24.1043	+	41.7499i	0.773545	+	1.33982i	−0.162064	+	0.986780i	$0.551815\pi$
$972$		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	$-0.156783\pi$
$977$	28.5119	+	16.4614i	0.912177	+	0.526646i	0.0310460	+	0.999518i	$0.490116\pi$
$978$		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
$985$	−42.4247	−	23.1321i	−1.35176	−	0.737051i
$986$	−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	−0.778938	−	0.627101i	$-0.784241\pi$
$991$	4.83587	−	8.37598i	0.153617	−	0.266072i	0.932554	+	0.361029i	$0.117575\pi$
$992$	−31.3780	+	18.1161i	−0.996253	+	0.575187i
$993$		0			0
$994$	1.07022	+	1.85367i	0.0339452	+	0.0587948i
$995$	−2.96420	−	4.85643i	−0.0939715	−	0.153959i
$996$		0			0
$997$	43.6735	−	25.2149i	1.38315	−	0.798565i	0.390623	−	0.920551i	$-0.372260\pi$
$997$	43.6735	−	25.2149i	1.38315	−	0.798565i	0.992532	+	0.121986i	$0.0389263\pi$
$998$	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.334.5		24
3.2	odd	2		195.2.ba.a.139.8	yes	24
5.4	even	2	inner	585.2.bs.b.334.8		24
13.3	even	3	inner	585.2.bs.b.289.8		24
15.2	even	4		975.2.i.o.451.3		12
15.8	even	4		975.2.i.q.451.4		12
15.14	odd	2		195.2.ba.a.139.5	yes	24
39.29	odd	6		195.2.ba.a.94.5	✓	24
65.29	even	6	inner	585.2.bs.b.289.5		24
195.29	odd	6		195.2.ba.a.94.8	yes	24
195.68	even	12		975.2.i.q.601.4		12
195.107	even	12		975.2.i.o.601.3		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
195.2.ba.a.94.5	✓	24	39.29	odd	6
195.2.ba.a.94.8	yes	24	195.29	odd	6
195.2.ba.a.139.5	yes	24	15.14	odd	2
195.2.ba.a.139.8	yes	24	3.2	odd	2
585.2.bs.b.289.5		24	65.29	even	6	inner
585.2.bs.b.289.8		24	13.3	even	3	inner
585.2.bs.b.334.5		24	1.1	even	1	trivial
585.2.bs.b.334.8		24	5.4	even	2	inner
975.2.i.o.451.3		12	15.2	even	4
975.2.i.o.601.3		12	195.107	even	12
975.2.i.q.451.4		12	15.8	even	4
975.2.i.q.601.4		12	195.68	even	12

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

\(f(q)\)	\(=\)	\(q+(-0.729738 - 0.421315i) q^{2} +(-0.644988 - 1.11715i) q^{4} +(-2.23540 + 0.0545741i) q^{5} +(-0.347589 + 0.200681i) q^{7} +2.77223i q^{8} +O(q^{10})\)	\(q+(-0.729738 - 0.421315i) q^{2} +(-0.644988 - 1.11715i) q^{4} +(-2.23540 + 0.0545741i) q^{5} +(-0.347589 + 0.200681i) q^{7} +2.77223i q^{8} +(1.65425 + 0.901983i) q^{10} +(-2.45354 + 4.24965i) q^{11} +(3.55974 - 0.572960i) q^{13} +0.338199 q^{14} +(-0.121995 + 0.211302i) q^{16} +(6.13203 - 3.54033i) q^{17} +(1.12724 + 1.95244i) q^{19} +(1.50278 + 2.46208i) q^{20} +(3.58088 - 2.06742i) q^{22} +(-0.861695 - 0.497500i) q^{23} +(4.99404 - 0.243990i) q^{25} +(-2.83907 - 1.08166i) q^{26} +(0.448381 + 0.258873i) q^{28} +(3.94133 - 6.82658i) q^{29} -6.30120 q^{31} +(4.97969 - 2.87503i) q^{32} -5.96637 q^{34} +(0.766049 - 0.467571i) q^{35} +(7.62688 + 4.40338i) q^{37} -1.89969i q^{38} +(-0.151292 - 6.19705i) q^{40} +(2.65994 - 4.60715i) q^{41} +(1.74416 - 1.00699i) q^{43} +6.33001 q^{44} +(0.419208 + 0.726090i) q^{46} +4.62317i q^{47} +(-3.41945 + 5.92267i) q^{49} +(-3.74714 - 1.92601i) q^{50} +(-2.93607 - 3.60721i) q^{52} +10.8496i q^{53} +(5.25272 - 9.63357i) q^{55} +(-0.556333 - 0.963596i) q^{56} +(-5.75228 + 3.32108i) q^{58} +(1.52224 + 2.63659i) q^{59} +(3.55088 + 6.15031i) q^{61} +(4.59822 + 2.65479i) q^{62} -4.35718 q^{64} +(-7.92617 + 1.47507i) q^{65} +(5.32891 + 3.07665i) q^{67} +(-7.91018 - 4.56694i) q^{68} +(-0.756010 + 0.0184569i) q^{70} +(3.16446 + 5.48101i) q^{71} +1.01273i q^{73} +(-3.71042 - 6.42663i) q^{74} +(1.45411 - 2.51860i) q^{76} -1.96951i q^{77} +10.2755 q^{79} +(0.261177 - 0.479002i) q^{80} +(-3.88212 + 2.24134i) q^{82} -10.5337i q^{83} +(-13.5143 + 8.24871i) q^{85} -1.69704 q^{86} +(-11.7810 - 6.80177i) q^{88} +(-0.262260 + 0.454247i) q^{89} +(-1.12234 + 0.913524i) q^{91} +1.28353i q^{92} +(1.94781 - 3.37371i) q^{94} +(-2.62639 - 4.30297i) q^{95} +(8.15979 - 4.71106i) q^{97} +(4.99061 - 2.88133i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 8 q^{4} - 4 q^{5}+O(q^{10}) \) 24 * q + 8 * q^4 - 4 * q^5	\( 24 q + 8 q^{4} - 4 q^{5} - 4 q^{10} - 4 q^{11} - 24 q^{14} + 16 q^{16} - 16 q^{19} + 16 q^{20} - 16 q^{25} + 48 q^{26} + 12 q^{29} + 8 q^{31} - 32 q^{34} - 10 q^{35} - 48 q^{40} + 40 q^{41} - 40 q^{44} - 24 q^{46} - 16 q^{49} - 20 q^{50} + 20 q^{55} + 24 q^{56} - 12 q^{59} + 20 q^{61} + 48 q^{64} - 14 q^{65} - 56 q^{70} - 4 q^{71} + 12 q^{74} + 8 q^{76} + 136 q^{79} + 4 q^{80} - 4 q^{85} - 48 q^{86} + 64 q^{89} + 60 q^{91} - 48 q^{94} + 28 q^{95}+O(q^{100}) \) 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

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