LMFDB - Embedded newform 585.2.bf.b.244.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [585,2,Mod(199,585)]

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, 1]))

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

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

chi := DirichletCharacter("585.199");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 585 = 3^{2} \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	585.bf (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:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			244.3
Character	$\chi$	$=$	585.244
Dual form			585.2.bf.b.199.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.779103 - 1.34945i) q^{2} +(-0.214003 + 0.370665i) q^{4} +(2.08241 - 0.814609i) q^{5} +(1.92183 - 3.32870i) q^{7} -2.44949 q^{8} +O(q^{10})$	\(q+(-0.779103 - 1.34945i) q^{2} +(-0.214003 + 0.370665i) q^{4} +(2.08241 - 0.814609i) q^{5} +(1.92183 - 3.32870i) q^{7} -2.44949 q^{8} +(-2.72168 - 2.17543i) q^{10} +(-3.29655 + 1.90326i) q^{11} +(-0.193779 - 3.60034i) q^{13} -5.98920 q^{14} +(2.33641 + 4.04678i) q^{16} +(0.412019 + 0.237879i) q^{17} +(0.642010 + 0.370665i) q^{19} +(-0.143695 + 0.946203i) q^{20} +(5.13670 + 2.96568i) q^{22} +(4.49827 - 2.59708i) q^{23} +(3.67282 - 3.39269i) q^{25} +(-4.70749 + 3.06653i) q^{26} +(0.822554 + 1.42471i) q^{28} +(-2.99460 - 5.18680i) q^{29} +5.62019i q^{31} +(1.19112 - 2.06308i) q^{32} -0.741329i q^{34} +(1.29043 - 8.49724i) q^{35} +(1.29305 + 2.23963i) q^{37} -1.15514i q^{38} +(-5.10083 + 1.99538i) q^{40} +(-5.00944 + 2.89220i) q^{41} +(-4.03743 - 2.33101i) q^{43} -1.62922i q^{44} +(-7.00924 - 4.04678i) q^{46} -5.05609 q^{47} +(-3.88683 - 6.73218i) q^{49} +(-7.43977 - 2.31302i) q^{50} +(1.37599 + 0.698658i) q^{52} +0.951516i q^{53} +(-5.31433 + 6.64876i) q^{55} +(-4.70749 + 8.15362i) q^{56} +(-4.66621 + 8.08210i) q^{58} +(9.58770 + 5.53546i) q^{59} +(6.29523 - 10.9037i) q^{61} +(7.58414 - 4.37871i) q^{62} +5.63362 q^{64} +(-3.33640 - 7.33951i) q^{65} +(3.13194 + 5.42467i) q^{67} +(-0.176347 + 0.101814i) q^{68} +(-12.4719 + 4.87886i) q^{70} +(0.505104 + 0.291622i) q^{71} -14.1171 q^{73} +(2.01484 - 3.48980i) q^{74} +(-0.274785 + 0.158647i) q^{76} +14.6310i q^{77} -6.20561 q^{79} +(8.16190 + 6.52378i) q^{80} +(7.80574 + 4.50665i) q^{82} +3.18366 q^{83} +(1.05177 + 0.159726i) q^{85} +7.26439i q^{86} +(8.07486 - 4.66202i) q^{88} +(14.4983 - 8.37062i) q^{89} +(-12.3569 - 6.27420i) q^{91} +2.22313i q^{92} +(3.93922 + 6.82293i) q^{94} +(1.63887 + 0.248887i) q^{95} +(5.84842 - 10.1298i) q^{97} +(-6.05648 + 10.4901i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 8 q^{4}+O(q^{10}) $ 24 * q - 8 * q^4	$ 24 q - 8 q^{4} + 4 q^{10} + 16 q^{16} + 24 q^{19} + 8 q^{25} - 48 q^{40} - 48 q^{46} - 16 q^{49} + 28 q^{61} - 48 q^{64} - 144 q^{76} + 40 q^{79} + 12 q^{85} + 4 q^{91} - 40 q^{94}+O(q^{100}) $ 24 * q - 8 * q^4 + 4 * q^10 + 16 * q^16 + 24 * q^19 + 8 * q^25 - 48 * q^40 - 48 * q^46 - 16 * q^49 + 28 * q^61 - 48 * q^64 - 144 * q^76 + 40 * q^79 + 12 * q^85 + 4 * q^91 - 40 * q^94

Display 100 coefficients 10 coefficients

Character values

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

$n$	$326$	$352$	$496$
$\chi(n)$	$1$	$-1$	$e\left(\frac{5}{6}\right)$

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 $

$2$	−0.779103	−	1.34945i	−0.550909	−	0.954203i	−0.998209	−	0.0598187i	$-0.980948\pi$
$2$	−0.779103	−	1.34945i	−0.550909	−	0.954203i	0.447300	−	0.894384i	$-0.352386\pi$
$3$		0			0
$3$		0			0
$4$	−0.214003	+	0.370665i	−0.107002	+	0.185332i
$5$	2.08241	−	0.814609i	0.931280	−	0.364304i
$5$	2.08241	−	0.814609i	0.931280	−	0.364304i
$6$		0			0
$7$	1.92183	−	3.32870i	0.726382	−	1.25813i	−0.232021	−	0.972711i	$-0.574534\pi$
$7$	1.92183	−	3.32870i	0.726382	−	1.25813i	0.958403	−	0.285419i	$-0.0921329\pi$
$8$	−2.44949			−0.866025
$9$		0			0
$10$	−2.72168	−	2.17543i	−0.860671	−	0.687931i
$11$	−3.29655	+	1.90326i	−0.993946	+	0.573855i	−0.906452	−	0.422310i	$-0.861219\pi$
$11$	−3.29655	+	1.90326i	−0.993946	+	0.573855i	−0.0874949	+	0.996165i	$0.527886\pi$
$12$		0			0
$13$	−0.193779	−	3.60034i	−0.0537445	−	0.998555i
$13$	−0.193779	−	3.60034i	−0.0537445	−	0.998555i
$14$	−5.98920			−1.60068
$15$		0			0
$16$	2.33641	+	4.04678i	0.584103	+	1.01170i
$17$	0.412019	+	0.237879i	0.0999292	+	0.0576942i	0.549132	−	0.835736i	$-0.314959\pi$
$17$	0.412019	+	0.237879i	0.0999292	+	0.0576942i	−0.449203	+	0.893430i	$0.648292\pi$
$18$		0			0
$19$	0.642010	+	0.370665i	0.147287	+	0.0850363i	0.571833	−	0.820370i	$-0.306233\pi$
$19$	0.642010	+	0.370665i	0.147287	+	0.0850363i	−0.424545	+	0.905407i	$0.639566\pi$
$20$	−0.143695	+	0.946203i	−0.0321311	+	0.211577i
$21$		0			0
$22$	5.13670	+	2.96568i	1.09515	+	0.632284i
$23$	4.49827	−	2.59708i	0.937955	−	0.541528i	0.0486360	−	0.998817i	$-0.484513\pi$
$23$	4.49827	−	2.59708i	0.937955	−	0.541528i	0.889319	+	0.457288i	$0.151179\pi$
$24$		0			0
$25$	3.67282	−	3.39269i	0.734565	−	0.678539i
$26$	−4.70749	+	3.06653i	−0.923215	+	0.601396i
$27$		0			0
$28$	0.822554	+	1.42471i	0.155448	+	0.269244i
$29$	−2.99460	−	5.18680i	−0.556083	−	0.963165i	−0.997818	−	0.0660191i	$-0.978970\pi$
$29$	−2.99460	−	5.18680i	−0.556083	−	0.963165i	0.441735	−	0.897146i	$-0.354363\pi$
$30$		0			0
$31$			5.62019i			1.00942i	0.863290	+	0.504708i	$0.168400\pi$
$31$			5.62019i			1.00942i	−0.863290	+	0.504708i	$0.831600\pi$
$32$	1.19112	−	2.06308i	0.210563	−	0.364705i
$33$		0			0
$34$		−	0.741329i		−	0.127137i
$35$	1.29043	−	8.49724i	0.218123	−	1.43630i
$36$		0			0
$37$	1.29305	+	2.23963i	0.212576	+	0.368193i	0.952520	−	0.304476i	$-0.0984813\pi$
$37$	1.29305	+	2.23963i	0.212576	+	0.368193i	−0.739944	+	0.672669i	$0.765148\pi$
$38$		−	1.15514i		−	0.187389i
$39$		0			0
$40$	−5.10083	+	1.99538i	−0.806512	+	0.315497i
$41$	−5.00944	+	2.89220i	−0.782343	+	0.451686i	−0.837260	−	0.546805i	$-0.815844\pi$
$41$	−5.00944	+	2.89220i	−0.782343	+	0.451686i	0.0549171	+	0.998491i	$0.482511\pi$
$42$		0			0
$43$	−4.03743	−	2.33101i	−0.615702	−	0.355476i	0.159492	−	0.987199i	$-0.449015\pi$
$43$	−4.03743	−	2.33101i	−0.615702	−	0.355476i	−0.775194	+	0.631723i	$0.782348\pi$
$44$		−	1.62922i		−	0.245614i
$45$		0			0
$46$	−7.00924	−	4.04678i	−1.03346	−	0.596666i
$47$	−5.05609			−0.737507			−0.368754	−	0.929527i	$-0.620215\pi$
$47$	−5.05609			−0.737507			−0.368754	+	0.929527i	$0.620215\pi$
$48$		0			0
$49$	−3.88683	−	6.73218i	−0.555261	−	0.961740i
$50$	−7.43977	−	2.31302i	−1.05214	−	0.327110i
$51$		0			0
$52$	1.37599	+	0.698658i	0.190815	+	0.0968864i
$53$			0.951516i			0.130701i	0.997862	+	0.0653504i	$0.0208165\pi$
$53$			0.951516i			0.130701i	−0.997862	+	0.0653504i	$0.979183\pi$
$54$		0			0
$55$	−5.31433	+	6.64876i	−0.716584	+	0.896519i
$56$	−4.70749	+	8.15362i	−0.629065	+	1.08957i
$57$		0			0
$58$	−4.66621	+	8.08210i	−0.612703	+	1.06123i
$59$	9.58770	+	5.53546i	1.24821	+	0.720655i	0.970753	−	0.240082i	$-0.0771744\pi$
$59$	9.58770	+	5.53546i	1.24821	+	0.720655i	0.277459	+	0.960737i	$0.410508\pi$
$60$		0			0
$61$	6.29523	−	10.9037i	0.806022	−	1.39607i	−0.109577	−	0.993978i	$-0.534950\pi$
$61$	6.29523	−	10.9037i	0.806022	−	1.39607i	0.915599	−	0.402093i	$-0.131717\pi$
$62$	7.58414	−	4.37871i	0.963187	−	0.556096i
$63$		0			0
$64$	5.63362			0.704203
$65$	−3.33640	−	7.33951i	−0.413829	−	0.910355i
$66$		0			0
$67$	3.13194	+	5.42467i	0.382627	+	0.662729i	0.991437	−	0.130587i	$-0.0416861\pi$
$67$	3.13194	+	5.42467i	0.382627	+	0.662729i	−0.608810	+	0.793316i	$0.708353\pi$
$68$	−0.176347	+	0.101814i	−0.0213852	+	0.0123467i
$69$		0			0
$70$	−12.4719	+	4.87886i	−1.49068	+	0.583135i
$71$	0.505104	+	0.291622i	0.0599448	+	0.0346091i	0.529673	−	0.848202i	$-0.322315\pi$
$71$	0.505104	+	0.291622i	0.0599448	+	0.0346091i	−0.469728	+	0.882811i	$0.655648\pi$
$72$		0			0
$73$	−14.1171			−1.65228			−0.826138	−	0.563468i	$-0.809467\pi$
$73$	−14.1171			−1.65228			−0.826138	+	0.563468i	$0.809467\pi$
$74$	2.01484	−	3.48980i	0.234220	−	0.405681i
$75$		0			0
$76$	−0.274785	+	0.158647i	−0.0315200	+	0.0181981i
$77$			14.6310i			1.66735i
$78$		0			0
$79$	−6.20561			−0.698186			−0.349093	−	0.937088i	$-0.613510\pi$
$79$	−6.20561			−0.698186			−0.349093	+	0.937088i	$0.613510\pi$
$80$	8.16190	+	6.52378i	0.912529	+	0.729381i
$81$		0			0
$82$	7.80574	+	4.50665i	0.862000	+	0.497676i
$83$	3.18366			0.349452			0.174726	−	0.984617i	$-0.444096\pi$
$83$	3.18366			0.349452			0.174726	+	0.984617i	$0.444096\pi$
$84$		0			0
$85$	1.05177	+	0.159726i	0.114080	+	0.0173248i
$86$			7.26439i			0.783340i
$87$		0			0
$88$	8.07486	−	4.66202i	0.860783	−	0.496973i
$89$	14.4983	−	8.37062i	1.53682	−	0.887284i	0.537799	−	0.843073i	$-0.319256\pi$
$89$	14.4983	−	8.37062i	1.53682	−	0.887284i	0.999022	−	0.0442114i	$-0.0140775\pi$
$90$		0			0
$91$	−12.3569	−	6.27420i	−1.29535	−	0.657714i
$92$			2.22313i			0.231778i
$93$		0			0
$94$	3.93922	+	6.82293i	0.406299	+	0.703731i
$95$	1.63887	+	0.248887i	0.168145	+	0.0255352i
$96$		0			0
$97$	5.84842	−	10.1298i	0.593817	−	1.02852i	−0.399896	−	0.916560i	$-0.630954\pi$
$97$	5.84842	−	10.1298i	0.593817	−	1.02852i	0.993713	−	0.111960i	$-0.0357129\pi$
$98$	−6.05648	+	10.4901i	−0.611797	+	1.05966i
$99$		0			0
$100$	0.471555	+	2.08743i	0.0471555	+	0.208743i
$101$	−0.474658	−	0.822133i	−0.0472303	−	0.0818052i	0.841444	−	0.540345i	$-0.181706\pi$
$101$	−0.474658	−	0.822133i	−0.0472303	−	0.0818052i	−0.888674	+	0.458539i	$0.848373\pi$
$102$		0			0
$103$			16.2688i			1.60301i	0.597990	+	0.801504i	$0.295966\pi$
$103$			16.2688i			1.60301i	−0.597990	+	0.801504i	$0.704034\pi$
$104$	0.474658	+	8.81900i	0.0465441	+	0.864774i
$105$		0			0
$106$	1.28402	−	0.741329i	0.124715	−	0.0720043i
$107$	10.6107	−	6.12608i	1.02577	−	0.592231i	0.110003	−	0.993931i	$-0.464914\pi$
$107$	10.6107	−	6.12608i	1.02577	−	0.592231i	0.915771	+	0.401701i	$0.131581\pi$
$108$		0			0
$109$			19.0846i			1.82797i	0.405750	+	0.913984i	$0.367010\pi$
$109$			19.0846i			1.82797i	−0.405750	+	0.913984i	$0.632990\pi$
$110$	13.1126	+	1.99133i	1.25023	+	0.189866i
$111$		0			0
$112$	17.9607			1.69713
$113$	−9.74510	−	5.62634i	−0.916742	−	0.529281i	−0.0341479	−	0.999417i	$-0.510872\pi$
$113$	−9.74510	−	5.62634i	−0.916742	−	0.529281i	−0.882594	+	0.470135i	$0.844205\pi$
$114$		0			0
$115$	7.25162	−	9.07250i	0.676217	−	0.846015i
$116$	2.56342			0.238007
$117$		0			0
$118$		−	17.2508i		−	1.58806i
$119$	1.58366	−	0.914324i	0.145174	−	0.0838160i
$120$		0			0
$121$	1.74482	−	3.02211i	0.158620	−	0.274737i
$122$	−19.6185			−1.77618
$123$		0			0
$124$	−2.08321	−	1.20274i	−0.187077	−	0.108009i
$125$	4.88459	−	10.0569i	0.436891	−	0.899515i
$126$		0			0
$127$	15.2993	−	8.83303i	1.35759	−	0.783805i	0.368291	−	0.929710i	$-0.379943\pi$
$127$	15.2993	−	8.83303i	1.35759	−	0.783805i	0.989299	+	0.145905i	$0.0466095\pi$
$128$	−6.77141	−	11.7284i	−0.598514	−	1.03666i
$129$		0			0
$130$	−7.30488	+	10.2205i	−0.640681	+	0.896399i
$131$	16.3535			1.42881			0.714406	−	0.699731i	$-0.246697\pi$
$131$	16.3535			1.42881			0.714406	+	0.699731i	$0.246697\pi$
$132$		0			0
$133$	2.46766	−	1.42471i	0.213974	−	0.123538i
$134$	4.88020	−	8.45276i	0.421585	−	0.730207i
$135$		0			0
$136$	−1.00924	−	0.582682i	−0.0865412	−	0.0499646i
$137$	2.37093	−	4.10658i	0.202562	−	0.350848i	−0.746791	−	0.665059i	$-0.768406\pi$
$137$	2.37093	−	4.10658i	0.202562	−	0.350848i	0.949353	+	0.314210i	$0.101740\pi$
$138$		0			0
$139$	3.22522	−	5.58624i	0.273559	−	0.473818i	−0.696211	−	0.717837i	$-0.745132\pi$
$139$	3.22522	−	5.58624i	0.273559	−	0.473818i	0.969771	+	0.244018i	$0.0784657\pi$
$140$	2.87347	+	2.29675i	0.242853	+	0.194111i
$141$		0			0
$142$		−	0.908814i		−	0.0762660i
$143$	7.49119	+	11.4999i	0.626445	+	0.961668i
$144$		0			0
$145$	−10.4612	−	8.36159i	−0.868754	−	0.694392i
$146$	10.9986	+	19.0502i	0.910254	+	1.57661i
$147$		0			0
$148$	−1.10687			−0.0909840
$149$	−5.05292	−	2.91730i	−0.413951	−	0.238995i	0.278535	−	0.960426i	$-0.410151\pi$
$149$	−5.05292	−	2.91730i	−0.413951	−	0.238995i	−0.692486	+	0.721431i	$0.743485\pi$
$150$		0			0
$151$			18.0938i			1.47246i	0.676734	+	0.736228i	$0.263395\pi$
$151$			18.0938i			1.47246i	−0.676734	+	0.736228i	$0.736605\pi$
$152$	−1.57260	−	0.907939i	−0.127554	−	0.0736436i
$153$		0			0
$154$	19.7437	−	11.3990i	1.59099	−	0.918559i
$155$	4.57826	+	11.7035i	0.367734	+	0.940048i
$156$		0			0
$157$			1.52530i			0.121732i	0.998146	+	0.0608662i	$0.0193863\pi$
$157$			1.52530i			0.121732i	−0.998146	+	0.0608662i	$0.980614\pi$
$158$	4.83481	+	8.37414i	0.384637	+	0.666211i
$159$		0			0
$160$	0.799792	−	5.26647i	0.0632291	−	0.416351i
$161$		−	19.9645i		−	1.57343i
$162$		0			0
$163$	−0.276717	+	0.479288i	−0.0216741	+	0.0375407i	−0.876659	−	0.481112i	$-0.840233\pi$
$163$	−0.276717	+	0.479288i	−0.0216741	+	0.0375407i	0.854985	+	0.518653i	$0.173566\pi$
$164$		−	2.47576i		−	0.193325i
$165$		0			0
$166$	−2.48040	−	4.29618i	−0.192516	−	0.333448i
$167$	−4.98885	−	8.64094i	−0.386049	−	0.668656i	0.605865	−	0.795567i	$-0.292827\pi$
$167$	−4.98885	−	8.64094i	−0.386049	−	0.668656i	−0.991914	+	0.126911i	$0.959494\pi$
$168$		0			0
$169$	−12.9249	+	1.39534i	−0.994223	+	0.107334i
$170$	−0.603894	−	1.54375i	−0.0463165	−	0.118400i
$171$		0			0
$172$	1.72805	−	0.997688i	0.131762	−	0.0760730i
$173$	22.2557	+	12.8493i	1.69207	+	0.976916i	0.952846	+	0.303456i	$0.0981404\pi$
$173$	22.2557	+	12.8493i	1.69207	+	0.976916i	0.739223	+	0.673461i	$0.235193\pi$
$174$		0			0
$175$	−4.23473	−	18.7459i	−0.320115	−	1.41706i
$176$	−15.4042	−	8.89361i	−1.16113	−	0.670381i
$177$		0			0
$178$	−22.5914	−	13.0432i	−1.69330	−	0.977626i
$179$	11.9349	+	20.6719i	0.892058	+	1.54509i	0.837404	+	0.546585i	$0.184072\pi$
$179$	11.9349	+	20.6719i	0.892058	+	1.54509i	0.0546546	+	0.998505i	$0.482594\pi$
$180$		0			0
$181$	21.2241			1.57757			0.788787	−	0.614667i	$-0.210710\pi$
$181$	21.2241			1.57757			0.788787	+	0.614667i	$0.210710\pi$
$182$	1.16058	+	21.5632i	0.0860278	+	1.59837i
$183$		0			0
$184$	−11.0185	+	6.36152i	−0.812292	+	0.468977i
$185$	4.51708	+	3.61048i	0.332102	+	0.265448i
$186$		0			0
$187$	−1.81099			−0.132432
$188$	1.08202	−	1.87412i	0.0789145	−	0.136684i
$189$		0			0
$190$	−0.940991	−	2.40548i	−0.0682667	−	0.174512i
$191$	−3.46926	+	6.00893i	−0.251027	+	0.434791i	−0.963809	−	0.266595i	$-0.914102\pi$
$191$	−3.46926	+	6.00893i	−0.251027	+	0.434791i	0.712782	+	0.701386i	$0.247435\pi$
$192$		0			0
$193$	7.57646	+	13.1228i	0.545366	+	0.944601i	0.998584	+	0.0532014i	$0.0169425\pi$
$193$	7.57646	+	13.1228i	0.545366	+	0.944601i	−0.453218	+	0.891400i	$0.649724\pi$
$194$	−18.2261			−1.30856
$195$		0			0
$196$	3.32718			0.237655
$197$	0.266215	+	0.461098i	0.0189671	+	0.0328519i	0.875353	−	0.483484i	$-0.160629\pi$
$197$	0.266215	+	0.461098i	0.0189671	+	0.0328519i	−0.856386	+	0.516336i	$0.827296\pi$
$198$		0			0
$199$	10.1297	−	17.5451i	0.718073	−	1.24374i	−0.243689	−	0.969853i	$-0.578358\pi$
$199$	10.1297	−	17.5451i	0.718073	−	1.24374i	0.961762	−	0.273886i	$-0.0883090\pi$
$200$	−8.99654	+	8.31037i	−0.636152	+	0.587632i
$201$		0			0
$202$	−0.739616	+	1.28105i	−0.0520392	+	0.0901345i
$203$	−23.0204			−1.61572
$204$		0			0
$205$	−8.07567	+	10.1035i	−0.564029	+	0.705657i
$206$	21.9538	−	12.6750i	1.52959	−	0.883112i
$207$		0			0
$208$	14.1171	−	9.19606i	0.978842	−	0.637632i
$209$	−2.82189			−0.195194
$210$		0			0
$211$	4.64399	+	8.04362i	0.319705	+	0.553746i	0.980426	−	0.196886i	$-0.0630828\pi$
$211$	4.64399	+	8.04362i	0.319705	+	0.553746i	−0.660721	+	0.750631i	$0.729749\pi$
$212$	−0.352694	−	0.203628i	−0.0242231	−	0.0139852i
$213$		0			0
$214$	−16.5336	−	9.54570i	−1.13022	−	0.652531i
$215$	−10.3064	−	1.56518i	−0.702893	−	0.106745i
$216$		0			0
$217$	18.7079	+	10.8010i	1.26998	+	0.733221i
$218$	25.7536	−	14.8688i	1.74425	−	1.00704i
$219$		0			0
$220$	−1.32718	−	3.39269i	−0.0894782	−	0.228735i
$221$	0.776605	−	1.52950i	0.0522401	−	0.102886i
$222$		0			0
$223$	2.55060	+	4.41777i	0.170801	+	0.295836i	0.938700	−	0.344735i	$-0.112031\pi$
$223$	2.55060	+	4.41777i	0.170801	+	0.295836i	−0.767899	+	0.640571i	$0.778698\pi$
$224$	−4.57826	−	7.92977i	−0.305898	−	0.529830i
$225$		0			0
$226$			17.5340i			1.16634i
$227$	4.24337	−	7.34973i	0.281642	−	0.487819i	−0.690147	−	0.723669i	$-0.742454\pi$
$227$	4.24337	−	7.34973i	0.281642	−	0.487819i	0.971789	+	0.235850i	$0.0757875\pi$
$228$		0			0
$229$			4.38692i			0.289896i	0.989439	+	0.144948i	$0.0463015\pi$
$229$			4.38692i			0.289896i	−0.989439	+	0.144948i	$0.953699\pi$
$230$	−17.8926	−	2.71726i	−1.17980	−	0.179171i
$231$		0			0
$232$	7.33524	+	12.7050i	0.481582	+	0.834125i
$233$		−	17.6686i		−	1.15751i	−0.815502	−	0.578754i	$-0.803539\pi$
$233$		−	17.6686i		−	1.15751i	0.815502	−	0.578754i	$-0.196461\pi$
$234$		0			0
$235$	−10.5288	+	4.11874i	−0.686826	+	0.268677i
$236$	−4.10360	+	2.36921i	−0.267121	+	0.154223i
$237$		0			0
$238$	−2.46766	−	1.42471i	−0.159955	−	0.0923500i
$239$			19.0326i			1.23112i	0.788091	+	0.615559i	$0.211070\pi$
$239$			19.0326i			1.23112i	−0.788091	+	0.615559i	$0.788930\pi$
$240$		0			0
$241$	−2.63277	−	1.52003i	−0.169592	−	0.0979139i	0.412801	−	0.910821i	$-0.364550\pi$
$241$	−2.63277	−	1.52003i	−0.169592	−	0.0979139i	−0.582393	+	0.812907i	$0.697884\pi$
$242$	−5.43757			−0.349540
$243$		0			0
$244$	2.69440	+	4.66684i	0.172491	+	0.298764i
$245$	−13.5780	−	10.8529i	−0.867470	−	0.693365i
$246$		0			0
$247$	1.21011	−	2.38328i	0.0769975	−	0.151645i
$248$		−	13.7666i		−	0.874179i
$249$		0			0
$250$	−17.3768	+	1.24386i	−1.09901	+	0.0786683i
$251$	3.90044	−	6.75576i	0.246194	−	0.426420i	−0.716273	−	0.697820i	$-0.754153\pi$
$251$	3.90044	−	6.75576i	0.246194	−	0.426420i	0.962467	+	0.271400i	$0.0874867\pi$
$252$		0			0
$253$	−9.88584	+	17.1228i	−0.621518	+	1.07650i
$254$	−23.8394	−	13.7637i	−1.49582	−	0.863611i
$255$		0			0
$256$	−4.91764	+	8.51760i	−0.307353	+	0.532350i
$257$	18.2288	−	10.5244i	1.13708	−	0.656493i	0.191373	−	0.981517i	$-0.438706\pi$
$257$	18.2288	−	10.5244i	1.13708	−	0.656493i	0.945706	+	0.325025i	$0.105373\pi$
$258$		0			0
$259$	9.94006			0.617646
$260$	3.43450	+	0.333997i	0.212999	+	0.0207136i
$261$		0			0
$262$	−12.7411	−	22.0682i	−0.787146	−	1.36338i
$263$	−24.4582	+	14.1209i	−1.50816	+	0.870735i	−0.508202	+	0.861238i	$0.669690\pi$
$263$	−24.4582	+	14.1209i	−1.50816	+	0.870735i	−0.999955	+	0.00949688i	$0.996977\pi$
$264$		0			0
$265$	0.775114	+	1.98144i	0.0476149	+	0.121719i
$266$	−3.84513	−	2.21999i	−0.235760	−	0.136116i
$267$		0			0
$268$	−2.68098			−0.163767
$269$	−6.08799	+	10.5447i	−0.371191	+	0.642922i	−0.989749	−	0.142817i	$-0.954384\pi$
$269$	−6.08799	+	10.5447i	−0.371191	+	0.642922i	0.618558	+	0.785739i	$0.287717\pi$
$270$		0			0
$271$	−10.9320	+	6.31157i	−0.664069	+	0.383401i	−0.793826	−	0.608145i	$-0.791914\pi$
$271$	−10.9320	+	6.31157i	−0.664069	+	0.383401i	0.129756	+	0.991546i	$0.458580\pi$
$272$			2.22313i			0.134797i
$273$		0			0
$274$	−7.38880			−0.446374
$275$	−5.65045	+	18.1745i	−0.340735	+	1.09596i
$276$		0			0
$277$	12.2706	+	7.08442i	0.737267	+	0.425661i	0.821075	−	0.570821i	$-0.193375\pi$
$277$	12.2706	+	7.08442i	0.737267	+	0.425661i	−0.0838078	+	0.996482i	$0.526708\pi$
$278$	−10.0511			−0.602825
$279$		0			0
$280$	−3.16090	+	20.8139i	−0.188900	+	1.24387i
$281$		−	27.0646i		−	1.61454i	−0.590181	−	0.807271i	$-0.700944\pi$
$281$		−	27.0646i		−	1.61454i	0.590181	−	0.807271i	$-0.299056\pi$
$282$		0			0
$283$	−21.3973	+	12.3537i	−1.27194	+	0.734352i	−0.975352	−	0.220655i	$-0.929181\pi$
$283$	−21.3973	+	12.3537i	−1.27194	+	0.734352i	−0.296583	+	0.955007i	$0.595847\pi$
$284$	−0.216188	+	0.124816i	−0.0128284	+	0.00740647i
$285$		0			0
$286$	9.68206	−	19.0686i	0.572512	−	1.12755i
$287$			22.2332i			1.31239i
$288$		0			0
$289$	−8.38683	−	14.5264i	−0.493343	−	0.854495i
$290$	−3.13317	+	20.6314i	−0.183986	+	1.21151i
$291$		0			0
$292$	3.02110	−	5.23269i	0.176796	−	0.306220i
$293$	−4.29622	+	7.44128i	−0.250988	+	0.434724i	−0.963798	−	0.266633i	$-0.914089\pi$
$293$	−4.29622	+	7.44128i	−0.250988	+	0.434724i	0.712810	+	0.701357i	$0.247422\pi$
$294$		0			0
$295$	24.4747	+	3.71684i	1.42497	+	0.216403i
$296$	−3.16731	−	5.48595i	−0.184096	−	0.318864i
$297$		0			0
$298$			9.09152i			0.526657i
$299$	−10.2220	−	15.6921i	−0.591156	−	0.907495i
$300$		0			0
$301$	−15.5185	+	8.95959i	−0.894470	+	0.516422i
$302$	24.4167	−	14.0970i	1.40502	−	0.811189i
$303$		0			0
$304$			3.46410i			0.198680i
$305$	4.22700	−	27.8340i	0.242037	−	1.59377i
$306$		0			0
$307$	−13.1761			−0.751998			−0.375999	−	0.926620i	$-0.622700\pi$
$307$	−13.1761			−0.751998			−0.375999	+	0.926620i	$0.622700\pi$
$308$	−5.42318	−	3.13107i	−0.309014	−	0.178409i
$309$		0			0
$310$	12.2263	−	15.2964i	0.694408	−	0.868774i
$311$	−15.8105			−0.896531			−0.448266	−	0.893900i	$-0.647958\pi$
$311$	−15.8105			−0.896531			−0.448266	+	0.893900i	$0.647958\pi$
$312$		0			0
$313$			2.97740i			0.168293i	0.996453	+	0.0841463i	$0.0268163\pi$
$313$			2.97740i			0.168293i	−0.996453	+	0.0841463i	$0.973184\pi$
$314$	2.05831	−	1.18837i	0.116157	−	0.0670635i
$315$		0			0
$316$	1.32802	−	2.30020i	0.0747071	−	0.129396i
$317$	3.36340			0.188907			0.0944536	−	0.995529i	$-0.469890\pi$
$317$	3.36340			0.188907			0.0944536	+	0.995529i	$0.469890\pi$
$318$		0			0
$319$	19.7437	+	11.3990i	1.10543	+	0.638223i
$320$	11.7315	−	4.58920i	0.655810	−	0.256544i
$321$		0			0
$322$	−26.9411	+	15.5544i	−1.50137	+	0.866814i
$323$	0.176347	+	0.305442i	0.00981220	+	0.0169952i
$324$		0			0
$325$	−12.9266	−	12.5660i	−0.717037	−	0.697035i
$326$	0.862364			0.0477619
$327$		0			0
$328$	12.2706	−	7.08442i	0.677529	−	0.391171i
$329$	−9.71693	+	16.8302i	−0.535712	+	0.927880i
$330$		0			0
$331$	−8.81173	−	5.08745i	−0.484336	−	0.279632i	0.237886	−	0.971293i	$-0.423546\pi$
$331$	−8.81173	−	5.08745i	−0.484336	−	0.279632i	−0.722222	+	0.691662i	$0.756879\pi$
$332$	−0.681314	+	1.18007i	−0.0373919	+	0.0647647i
$333$		0			0
$334$	−7.77365	+	13.4644i	−0.425355	+	0.736737i
$335$	10.9410	+	8.74506i	0.597768	+	0.477794i
$336$		0			0
$337$			0.415294i			0.0226225i	0.999936	+	0.0113113i	$0.00360056\pi$
$337$			0.415294i			0.0226225i	−0.999936	+	0.0113113i	$0.996399\pi$
$338$	11.9528	+	16.3543i	0.650145	+	0.889559i
$339$		0			0
$340$	−0.284287	+	0.355671i	−0.0154176	+	0.0192890i
$341$	−10.6967	−	18.5272i	−0.579258	−	1.00331i
$342$		0			0
$343$	−2.97366			−0.160562
$344$	9.88964	+	5.70979i	0.533214	+	0.307851i
$345$		0			0
$346$		−	40.0438i		−	2.15277i
$347$	−26.2411	−	15.1503i	−1.40869	−	0.813310i	−0.413432	−	0.910535i	$-0.635670\pi$
$347$	−26.2411	−	15.1503i	−1.40869	−	0.813310i	−0.995262	+	0.0972248i	$0.969003\pi$
$348$		0			0
$349$	−8.44450	+	4.87544i	−0.452024	+	0.260976i	−0.708685	−	0.705525i	$-0.750711\pi$
$349$	−8.44450	+	4.87544i	−0.452024	+	0.260976i	0.256661	+	0.966502i	$0.417378\pi$
$350$	−21.9973	+	20.3195i	−1.17580	+	1.08612i
$351$		0			0
$352$			9.06807i			0.483330i
$353$	−12.3565	−	21.4022i	−0.657673	−	1.13912i	−0.981217	−	0.192909i	$-0.938208\pi$
$353$	−12.3565	−	21.4022i	−0.657673	−	1.13912i	0.323544	−	0.946213i	$-0.395126\pi$
$354$		0			0
$355$	1.28939	+	0.195813i	0.0684337	+	0.0103927i
$356$			7.16537i			0.379764i
$357$		0			0
$358$	18.5971	−	32.2111i	0.982886	−	1.70241i
$359$			10.8363i			0.571920i	0.958242	+	0.285960i	$0.0923124\pi$
$359$			10.8363i			0.571920i	−0.958242	+	0.285960i	$0.907688\pi$
$360$		0			0
$361$	−9.22522	−	15.9785i	−0.485538	−	0.840976i
$362$	−16.5358	−	28.6408i	−0.869100	−	1.50532i
$363$		0			0
$364$	4.97003	−	3.23755i	0.260500	−	0.169694i
$365$	−29.3974	+	11.4999i	−1.53873	+	0.601931i
$366$		0			0
$367$	0.581336	−	0.335634i	0.0303455	−	0.0175200i	−0.484751	−	0.874652i	$-0.661090\pi$
$367$	0.581336	−	0.335634i	0.0303455	−	0.0175200i	0.515096	+	0.857132i	$0.327756\pi$
$368$	21.0196	+	12.1357i	1.09572	+	0.632617i
$369$		0			0
$370$	1.35288	−	8.90849i	0.0703331	−	0.463130i
$371$	3.16731	+	1.82865i	0.164439	+	0.0949387i
$372$		0			0
$373$	−21.3973	−	12.3537i	−1.10791	−	0.639651i	−0.169621	−	0.985509i	$-0.554254\pi$
$373$	−21.3973	−	12.3537i	−1.10791	−	0.639651i	−0.938287	+	0.345858i	$0.887588\pi$
$374$	1.41094	+	2.44383i	0.0729582	+	0.126367i
$375$		0			0
$376$	12.3849			0.638700
$377$	−18.0940	+	11.7867i	−0.931886	+	0.607044i
$378$		0			0
$379$	−8.44450	+	4.87544i	−0.433765	+	0.250434i	−0.700949	−	0.713211i	$-0.747240\pi$
$379$	−8.44450	+	4.87544i	−0.433765	+	0.250434i	0.267184	+	0.963645i	$0.413907\pi$
$380$	−0.442978	+	0.554209i	−0.0227243	+	0.0284303i
$381$		0			0
$382$	10.8116			0.553172
$383$	9.08949	−	15.7435i	0.464451	−	0.804453i	−0.534725	−	0.845026i	$-0.679585\pi$
$383$	9.08949	−	15.7435i	0.464451	−	0.804453i	0.999177	+	0.0405726i	$0.0129182\pi$
$384$		0			0
$385$	11.9185	+	30.4676i	0.607424	+	1.55277i
$386$	11.8057	−	20.4481i	0.600894	−	1.04078i
$387$		0			0
$388$	2.50316	+	4.33560i	0.127079	+	0.220107i
$389$	3.77121			0.191208			0.0956039	−	0.995419i	$-0.469522\pi$
$389$	3.77121			0.191208			0.0956039	+	0.995419i	$0.469522\pi$
$390$		0			0
$391$	2.47116			0.124972
$392$	9.52074	+	16.4904i	0.480870	+	0.832892i
$393$		0			0
$394$	0.414818	−	0.718486i	0.0208982	−	0.0361968i
$395$	−12.9226	+	5.05515i	−0.650207	+	0.254352i
$396$		0			0
$397$	−7.14147	+	12.3694i	−0.358420	+	0.620801i	−0.987697	−	0.156380i	$-0.950018\pi$
$397$	−7.14147	+	12.3694i	−0.358420	+	0.620801i	0.629277	+	0.777181i	$0.283351\pi$
$398$	−31.5682			−1.58237
$399$		0			0
$400$	22.3107	+	6.93640i	1.11554	+	0.346820i
$401$	1.66942	−	0.963837i	0.0833666	−	0.0481317i	−0.457737	−	0.889088i	$-0.651340\pi$
$401$	1.66942	−	0.963837i	0.0833666	−	0.0481317i	0.541104	+	0.840956i	$0.318007\pi$
$402$		0			0
$403$	20.2346	−	1.08907i	1.00796	−	0.0542505i
$404$	0.406314			0.0202149
$405$		0			0
$406$	17.9353	+	31.0648i	0.890112	+	1.54172i
$407$	−8.52520	−	4.92203i	−0.422578	−	0.243976i
$408$		0			0
$409$	21.0218	+	12.1369i	1.03946	+	0.600133i	0.919680	−	0.392668i	$-0.128448\pi$
$409$	21.0218	+	12.1369i	1.03946	+	0.600133i	0.119780	+	0.992800i	$0.461781\pi$
$410$	19.9259	+	3.02604i	0.984068	+	0.149445i
$411$		0			0
$412$	−6.03025	−	3.48157i	−0.297089	−	0.171525i
$413$	36.8518	−	21.2764i	1.81336	−	1.04694i
$414$		0			0
$415$	6.62967	−	2.59344i	0.325438	−	0.127307i
$416$	−7.65862	−	3.88866i	−0.375495	−	0.190657i
$417$		0			0
$418$	2.19854	+	3.80799i	0.107534	+	0.186255i
$419$	13.0874	+	22.6680i	0.639361	+	1.10741i	0.985573	+	0.169250i	$0.0541345\pi$
$419$	13.0874	+	22.6680i	0.639361	+	1.10741i	−0.346212	+	0.938156i	$0.612532\pi$
$420$		0			0
$421$		−	23.4715i		−	1.14393i	−0.820278	−	0.571965i	$-0.806181\pi$
$421$		−	23.4715i		−	1.14393i	0.820278	−	0.571965i	$-0.193819\pi$
$422$	7.23629	−	12.5336i	0.352257	−	0.610127i
$423$		0			0
$424$		−	2.33073i		−	0.113190i
$425$	2.32032	−	0.524165i	0.112552	−	0.0254257i
$426$		0			0
$427$	−24.1967	−	41.9099i	−1.17096	−	2.02816i
$428$			5.24401i			0.253479i
$429$		0			0
$430$	5.91764	+	15.1274i	0.285374	+	0.729508i
$431$	11.0974	−	6.40710i	0.534544	−	0.308619i	−0.208321	−	0.978061i	$-0.566800\pi$
$431$	11.0974	−	6.40710i	0.534544	−	0.308619i	0.742865	+	0.669441i	$0.233466\pi$
$432$		0			0
$433$	11.6418	+	6.72139i	0.559469	+	0.323010i	0.752932	−	0.658098i	$-0.228639\pi$
$433$	11.6418	+	6.72139i	0.559469	+	0.323010i	−0.193463	+	0.981107i	$0.561972\pi$
$434$		−	33.6604i		−	1.61575i
$435$		0			0
$436$	−7.07397	−	4.08416i	−0.338782	−	0.195596i
$437$	3.85058			0.184198
$438$		0			0
$439$	6.86723	+	11.8944i	0.327755	+	0.567688i	0.982066	−	0.188537i	$-0.0603747\pi$
$439$	6.86723	+	11.8944i	0.327755	+	0.567688i	−0.654311	+	0.756225i	$0.727041\pi$
$440$	13.0174	−	16.2861i	0.620580	−	0.776408i
$441$		0			0
$442$	−2.66904	+	0.143654i	−0.126953	+	0.00683291i
$443$			24.2527i			1.15228i	0.817350	+	0.576141i	$0.195442\pi$
$443$			24.2527i			1.15228i	−0.817350	+	0.576141i	$0.804558\pi$
$444$		0			0
$445$	23.3726	−	29.2415i	1.10797	−	1.38618i
$446$	3.97436	−	6.88380i	0.188192	−	0.325957i
$447$		0			0
$448$	10.8268	−	18.7526i	0.511520	−	0.885978i
$449$	12.0337	+	6.94767i	0.567906	+	0.327881i	0.756313	−	0.654210i	$-0.226999\pi$
$449$	12.0337	+	6.94767i	0.567906	+	0.327881i	−0.188406	+	0.982091i	$0.560332\pi$
$450$		0			0
$451$	11.0092	−	19.0686i	0.518405	−	0.897903i
$452$	4.17097	−	2.40811i	0.196186	−	0.113268i
$453$		0			0
$454$	−13.2241			−0.620637
$455$	−30.8430	−	2.99941i	−1.44594	−	0.140614i
$456$		0			0
$457$	5.84842	+	10.1298i	0.273577	+	0.473850i	0.969775	−	0.244000i	$-0.0784597\pi$
$457$	5.84842	+	10.1298i	0.273577	+	0.473850i	−0.696198	+	0.717850i	$0.745126\pi$
$458$	5.91991	−	3.41786i	0.276619	−	0.159706i
$459$		0			0
$460$	1.81099	+	4.62947i	0.0844376	+	0.215850i
$461$	23.7102	+	13.6891i	1.10429	+	0.637564i	0.937345	−	0.348402i	$-0.113276\pi$
$461$	23.7102	+	13.6891i	1.10429	+	0.637564i	0.166948	+	0.985966i	$0.446609\pi$
$462$		0			0
$463$	−3.74877			−0.174220			−0.0871101	−	0.996199i	$-0.527763\pi$
$463$	−3.74877			−0.174220			−0.0871101	+	0.996199i	$0.527763\pi$
$464$	13.9932	−	24.2370i	0.649620	−	1.12517i
$465$		0			0
$466$	−23.8428	+	13.7657i	−1.10450	+	0.637682i
$467$			29.4842i			1.36437i	0.731182	+	0.682183i	$0.238969\pi$
$467$			29.4842i			1.36437i	−0.731182	+	0.682183i	$0.761031\pi$
$468$		0			0
$469$	24.0761			1.11173
$470$	13.7611	+	10.9992i	0.634751	+	0.507354i
$471$		0			0
$472$	−23.4850	−	13.5590i	−1.08098	−	0.624106i
$473$	17.7461			0.815967
$474$		0			0
$475$	3.61554	−	0.816757i	0.165892	−	0.0374754i
$476$			0.782674i			0.0358738i
$477$		0			0
$478$	25.6835	−	14.8284i	1.17474	−	0.678234i
$479$	−25.6697	+	14.8204i	−1.17288	+	0.677162i	−0.954356	−	0.298670i	$-0.903457\pi$
$479$	−25.6697	+	14.8204i	−1.17288	+	0.677162i	−0.218522	+	0.975832i	$0.570124\pi$
$480$		0			0
$481$	7.81286	−	5.08941i	0.356236	−	0.232057i
$482$			4.73705i			0.215767i
$483$		0			0
$484$	0.746793	+	1.29348i	0.0339452	+	0.0587947i
$485$	3.92698	−	25.8584i	0.178315	−	1.17417i
$486$		0			0
$487$	1.04423	−	1.80867i	0.0473188	−	0.0819585i	−0.841396	−	0.540419i	$-0.818266\pi$
$487$	1.04423	−	1.80867i	0.0473188	−	0.0819585i	0.888715	+	0.458461i	$0.151599\pi$
$488$	−15.4201	+	26.7084i	−0.698035	+	1.20903i
$489$		0			0
$490$	−4.06669	+	26.7784i	−0.183714	+	1.20972i
$491$	19.2058	+	33.2655i	0.866747	+	1.50125i	0.865302	+	0.501251i	$0.167127\pi$
$491$	19.2058	+	33.2655i	0.866747	+	1.50125i	0.00144556	+	0.999999i	$0.499540\pi$
$492$		0			0
$493$		−	2.84941i		−	0.128331i
$494$	−4.15891	+	0.223842i	−0.187118	+	0.0100711i
$495$		0			0
$496$	−22.7437	+	13.1311i	−1.02122	+	0.589603i
$497$	1.94144	−	1.12089i	0.0870856	−	0.0502789i
$498$		0			0
$499$		−	33.2971i		−	1.49058i	−0.666739	−	0.745291i	$-0.732310\pi$
$499$		−	33.2971i		−	1.49058i	0.666739	−	0.745291i	$-0.267690\pi$
$500$	2.68241	+	3.96275i	0.119961	+	0.177220i
$501$		0			0
$502$	−12.1554			−0.542521
$503$	1.37847	+	0.795860i	0.0614629	+	0.0354856i	0.530417	−	0.847737i	$-0.322036\pi$
$503$	1.37847	+	0.795860i	0.0614629	+	0.0354856i	−0.468954	+	0.883223i	$0.655369\pi$
$504$		0			0
$505$	−1.65815	−	1.32535i	−0.0737866	−	0.0589774i
$506$	30.8084			1.36960
$507$		0			0
$508$			7.56120i			0.335474i
$509$	−16.6859	+	9.63361i	−0.739589	+	0.427002i	−0.821920	−	0.569603i	$-0.807097\pi$
$509$	−16.6859	+	9.63361i	−0.739589	+	0.427002i	0.0823307	+	0.996605i	$0.473764\pi$
$510$		0			0
$511$	−27.1305	+	46.9914i	−1.20018	+	2.07878i
$512$	−11.7603			−0.519735
$513$		0			0
$514$	−28.4042	−	16.3992i	−1.25285	−	0.723336i
$515$	13.2527	+	33.8781i	0.583983	+	1.49285i
$516$		0			0
$517$	16.6677	−	9.62307i	0.733043	−	0.423222i
$518$	−7.74434	−	13.4136i	−0.340267	−	0.589359i
$519$		0			0
$520$	8.17247	+	17.9781i	0.358386	+	0.788390i
$521$	−35.4419			−1.55274			−0.776370	−	0.630278i	$-0.782941\pi$
$521$	−35.4419			−1.55274			−0.776370	+	0.630278i	$0.782941\pi$
$522$		0			0
$523$	−9.55409	+	5.51606i	−0.417771	+	0.241200i	−0.694123	−	0.719856i	$-0.744208\pi$
$523$	−9.55409	+	5.51606i	−0.417771	+	0.241200i	0.276352	+	0.961056i	$0.410874\pi$
$524$	−3.49970	+	6.06167i	−0.152885	+	0.264805i
$525$		0			0
$526$	38.1109	+	22.0033i	1.66171	+	0.959391i
$527$	−1.33693	+	2.31562i	−0.0582374	+	0.100870i
$528$		0			0
$529$	1.98963	−	3.44615i	0.0865058	−	0.149832i
$530$	2.06996	−	2.58972i	0.0899132	−	0.112490i
$531$		0			0
$532$			1.21957i			0.0528750i
$533$	11.3836	+	17.4752i	0.493080	+	0.756937i
$534$		0			0
$535$	17.1054	−	21.4005i	0.739530	−	0.925226i
$536$	−7.67165	−	13.2877i	−0.331365	−	0.573940i
$537$		0			0
$538$	18.9727			0.817971
$539$	25.6262	+	14.7953i	1.10380	+	0.637279i
$540$		0			0
$541$		−	28.8103i		−	1.23865i	−0.785135	−	0.619325i	$-0.787406\pi$
$541$		−	28.8103i		−	1.23865i	0.785135	−	0.619325i	$-0.212594\pi$
$542$	17.0342	+	9.83473i	0.731684	+	0.422438i
$543$		0			0
$544$	0.981529	−	0.566686i	0.0420827	−	0.0242965i
$545$	15.5465	+	39.7418i	0.665937	+	1.70235i
$546$		0			0
$547$		−	9.62978i		−	0.411740i	−0.978579	−	0.205870i	$-0.933998\pi$
$547$		−	9.62978i		−	0.411740i	0.978579	−	0.205870i	$-0.0660024\pi$
$548$	1.01478	+	1.75764i	0.0433490	+	0.0750827i
$549$		0			0
$550$	28.9278	−	6.53485i	1.23349	−	0.278647i
$551$		−	4.43997i		−	0.189149i
$552$		0			0
$553$	−11.9261	+	20.6566i	−0.507150	+	0.878409i
$554$		−	22.0780i		−	0.938003i
$555$		0			0
$556$	1.38041	+	2.39095i	0.0585426	+	0.101399i
$557$	−2.71571	−	4.70374i	−0.115068	−	0.199304i	0.802739	−	0.596331i	$-0.203375\pi$
$557$	−2.71571	−	4.70374i	−0.115068	−	0.199304i	−0.917807	+	0.397027i	$0.870042\pi$
$558$		0			0
$559$	−7.61007	+	14.9878i	−0.321871	+	0.633917i
$560$	37.4015	−	14.6310i	1.58050	−	0.618271i
$561$		0			0
$562$	−36.5223	+	21.0861i	−1.54060	+	0.889466i
$563$	4.48049	+	2.58681i	0.188830	+	0.109021i	0.591435	−	0.806353i	$-0.298562\pi$
$563$	4.48049	+	2.58681i	0.188830	+	0.109021i	−0.402605	+	0.915374i	$0.631895\pi$
$564$		0			0
$565$	−24.8765	−	3.77787i	−1.04656	−	0.158936i
$566$	33.3413	+	19.2496i	1.40144	+	0.809122i
$567$		0			0
$568$	−1.23725	−	0.714325i	−0.0519137	−	0.0299724i
$569$	−16.6554	−	28.8481i	−0.698233	−	1.20937i	−0.969079	−	0.246752i	$-0.920637\pi$
$569$	−16.6554	−	28.8481i	−0.698233	−	1.20937i	0.270846	−	0.962623i	$-0.412697\pi$
$570$		0			0
$571$	4.59273			0.192200			0.0960998	−	0.995372i	$-0.469363\pi$
$571$	4.59273			0.192200			0.0960998	+	0.995372i	$0.469363\pi$
$572$	−5.86574	+	0.315708i	−0.245259	+	0.0132004i
$573$		0			0
$574$	30.0025	−	17.3220i	1.25228	−	0.723005i
$575$	7.71027	−	24.7999i	0.321540	−	1.03423i
$576$		0			0
$577$	−38.8799			−1.61859			−0.809295	−	0.587402i	$-0.800151\pi$
$577$	−38.8799			−1.61859			−0.809295	+	0.587402i	$0.800151\pi$
$578$	−13.0684	+	22.6351i	−0.543574	+	0.941498i
$579$		0			0
$580$	5.33808	−	2.08818i	0.221652	−	0.0867071i
$581$	6.11844	−	10.5974i	0.253836	−	0.439656i
$582$		0			0
$583$	−1.81099	−	3.13672i	−0.0750034	−	0.129910i
$584$	34.5796			1.43091
$585$		0			0
$586$	13.3888			0.553086
$587$	5.39748	+	9.34870i	0.222778	+	0.385862i	0.955650	−	0.294503i	$-0.0951543\pi$
$587$	5.39748	+	9.34870i	0.222778	+	0.385862i	−0.732873	+	0.680366i	$0.761821\pi$
$588$		0			0
$589$	−2.08321	+	3.60822i	−0.0858370	+	0.148674i
$590$	−14.0526	−	35.9231i	−0.578538	−	1.47893i
$591$		0			0
$592$	−6.04219	+	10.4654i	−0.248333	+	0.430125i
$593$	−44.1073			−1.81127			−0.905634	−	0.424059i	$-0.860605\pi$
$593$	−44.1073			−1.81127			−0.905634	+	0.424059i	$0.860605\pi$
$594$		0			0
$595$	2.55300	−	3.19405i	0.104663	−	0.130943i
$596$	2.16268	−	1.24862i	0.0885869	−	0.0511457i
$597$		0			0
$598$	−13.2116	+	26.0198i	−0.540261	+	1.06403i
$599$	18.5106			0.756323			0.378161	−	0.925740i	$-0.376556\pi$
$599$	18.5106			0.756323			0.378161	+	0.925740i	$0.376556\pi$
$600$		0			0
$601$	10.6852	+	18.5073i	0.435857	+	0.754927i	0.997365	−	0.0725447i	$-0.0231120\pi$
$601$	10.6852	+	18.5073i	0.435857	+	0.754927i	−0.561508	+	0.827471i	$0.689779\pi$
$602$	24.1810	+	13.9609i	0.985543	+	0.569004i
$603$		0			0
$604$	−6.70674	−	3.87214i	−0.272894	−	0.157555i
$605$	1.17158	−	7.71461i	0.0476313	−	0.313643i
$606$		0			0
$607$	−32.1252	−	18.5475i	−1.30392	−	0.752819i	−0.322847	−	0.946451i	$-0.604640\pi$
$607$	−32.1252	−	18.5475i	−1.30392	−	0.752819i	−0.981074	+	0.193632i	$0.937973\pi$
$608$	1.52942	−	0.883014i	0.0620264	−	0.0358109i
$609$		0			0
$610$	−40.8538	+	15.9814i	−1.65412	+	0.647070i
$611$	0.979762	+	18.2037i	0.0396369	+	0.736441i
$612$		0			0
$613$	2.39232	+	4.14362i	0.0966249	+	0.167359i	0.910286	−	0.413981i	$-0.135862\pi$
$613$	2.39232	+	4.14362i	0.0966249	+	0.167359i	−0.813661	+	0.581340i	$0.802529\pi$
$614$	10.2655	+	17.7804i	0.414282	+	0.717558i
$615$		0			0
$616$		−	35.8384i		−	1.44397i
$617$	5.08972	−	8.81565i	0.204904	−	0.354905i	−0.745198	−	0.666843i	$-0.767645\pi$
$617$	5.08972	−	8.81565i	0.204904	−	0.354905i	0.950102	+	0.311939i	$0.100978\pi$
$618$		0			0
$619$			12.6551i			0.508653i	0.967118	+	0.254326i	$0.0818537\pi$
$619$			12.6551i			0.508653i	−0.967118	+	0.254326i	$0.918146\pi$
$620$	−5.31784	−	0.807592i	−0.213570	−	0.0324337i
$621$		0			0
$622$	12.3180	+	21.3354i	0.493907	+	0.855472i
$623$		−	64.3475i		−	2.57803i
$624$		0			0
$625$	1.97927	−	24.9215i	0.0791707	−	0.996861i
$626$	4.01784	−	2.31970i	0.160585	−	0.0927139i
$627$		0			0
$628$	−0.565376	−	0.326420i	−0.0225610	−	0.0130256i
$629$			1.23036i			0.0490576i
$630$		0			0
$631$	8.32689	+	4.80753i	0.331488	+	0.191385i	0.656502	−	0.754325i	$-0.272035\pi$
$631$	8.32689	+	4.80753i	0.331488	+	0.191385i	−0.325013	+	0.945709i	$0.605369\pi$
$632$	15.2006			0.604647
$633$		0			0
$634$	−2.62043	−	4.53872i	−0.104071	−	0.180256i
$635$	24.6638	−	30.8569i	0.978753	−	1.22452i
$636$		0			0
$637$	−23.4850	+	15.2985i	−0.930508	+	0.606147i
$638$		−	35.5241i		−	1.40641i
$639$		0			0
$640$	−23.6549	−	18.9073i	−0.935043	−	0.747377i
$641$	−15.5334	+	26.9047i	−0.613533	+	1.06267i	0.377107	+	0.926170i	$0.376919\pi$
$641$	−15.5334	+	26.9047i	−0.613533	+	1.06267i	−0.990640	+	0.136501i	$0.956414\pi$
$642$		0			0
$643$	−17.8854	+	30.9784i	−0.705330	+	1.22167i	0.261243	+	0.965273i	$0.415868\pi$
$643$	−17.8854	+	30.9784i	−0.705330	+	1.22167i	−0.966572	+	0.256394i	$0.917466\pi$
$644$	7.40015	+	4.27248i	0.291607	+	0.168359i
$645$		0			0
$646$	0.274785	−	0.475941i	0.0108113	−	0.0187256i
$647$	6.54221	−	3.77715i	0.257201	−	0.148495i	−0.365856	−	0.930671i	$-0.619224\pi$
$647$	6.54221	−	3.77715i	0.257201	−	0.148495i	0.623057	+	0.782176i	$0.285890\pi$
$648$		0			0
$649$	−42.1417			−1.65421
$650$	−6.88599	+	27.2339i	−0.270091	+	1.06820i
$651$		0			0
$652$	−0.118437	−	0.205138i	−0.00463834	−	0.00803384i
$653$	−26.4590	+	15.2761i	−1.03542	+	0.597800i	−0.918532	−	0.395346i	$-0.870625\pi$
$653$	−26.4590	+	15.2761i	−1.03542	+	0.597800i	−0.116887	+	0.993145i	$0.537291\pi$
$654$		0			0
$655$	34.0546	−	13.3217i	1.33062	−	0.520522i
$656$	−23.4082	−	13.5147i	−0.913938	−	0.527662i
$657$		0			0
$658$	30.2820			1.18051
$659$	18.8300	−	32.6145i	0.733511	−	1.27048i	−0.221862	−	0.975078i	$-0.571213\pi$
$659$	18.8300	−	32.6145i	0.733511	−	1.27048i	0.955373	−	0.295401i	$-0.0954532\pi$
$660$		0			0
$661$	−35.3916	+	20.4334i	−1.37657	+	0.794766i	−0.991745	−	0.128222i	$-0.959073\pi$
$661$	−35.3916	+	20.4334i	−1.37657	+	0.794766i	−0.384829	+	0.922988i	$0.625740\pi$
$662$			15.8546i			0.616207i
$663$		0			0
$664$	−7.79834			−0.302634
$665$	3.97810	−	4.97700i	0.154264	−	0.193000i
$666$		0			0
$667$	−26.9411	−	15.5544i	−1.04316	−	0.602270i
$668$	4.27052			0.165231
$669$		0			0
$670$	3.27687	−	21.5775i	0.126596	−	0.833613i
$671$			47.9259i			1.85016i
$672$		0			0
$673$	3.78861	−	2.18736i	0.146040	−	0.0843164i	−0.425199	−	0.905100i	$-0.639796\pi$
$673$	3.78861	−	2.18736i	0.146040	−	0.0843164i	0.571240	+	0.820783i	$0.306463\pi$
$674$	0.560417	−	0.323557i	0.0215865	−	0.0124630i
$675$		0			0
$676$	2.24877	−	5.08941i	0.0864911	−	0.195747i
$677$		−	9.96053i		−	0.382814i	−0.981511	−	0.191407i	$-0.938695\pi$
$677$		−	9.96053i		−	0.382814i	0.981511	−	0.191407i	$-0.0613051\pi$
$678$		0			0
$679$	−22.4793	−	38.9352i	−0.862675	−	1.49420i
$680$	−2.57630	−	0.391248i	−0.0987964	−	0.0150037i
$681$		0			0
$682$	−16.6677	+	28.8692i	−0.638237	+	1.10546i
$683$	−16.5183	+	28.6105i	−0.632054	+	1.09475i	0.355077	+	0.934837i	$0.384455\pi$
$683$	−16.5183	+	28.6105i	−0.632054	+	1.09475i	−0.987131	+	0.159913i	$0.948879\pi$
$684$		0			0
$685$	1.59199	−	10.4829i	0.0608267	−	0.400532i
$686$	2.31679	+	4.01279i	0.0884553	+	0.153209i
$687$		0			0
$688$		−	21.7848i		−	0.830538i
$689$	3.42578	−	0.184383i	0.130512	−	0.00702445i
$690$		0			0
$691$	27.4814	−	15.8664i	1.04544	−	0.603587i	0.124073	−	0.992273i	$-0.460404\pi$
$691$	27.4814	−	15.8664i	1.04544	−	0.603587i	0.921370	+	0.388686i	$0.127071\pi$
$692$	−9.52558	+	5.49960i	−0.362108	+	0.209063i
$693$		0			0
$694$			47.2146i			1.79224i
$695$	2.16561	−	14.2601i	0.0821461	−	0.540916i
$696$		0			0
$697$	−2.75198			−0.104239
$698$	13.1583	+	7.59693i	0.498048	+	0.287548i
$699$		0			0
$700$	7.85469	+	2.44202i	0.296879	+	0.0922996i
$701$	−32.0162			−1.20923			−0.604617	−	0.796516i	$-0.706674\pi$
$701$	−32.0162			−1.20923			−0.604617	+	0.796516i	$0.706674\pi$
$702$		0			0
$703$			1.91715i			0.0723067i
$704$	−18.5715	+	10.7223i	−0.699940	+	0.404110i
$705$		0			0
$706$	−19.2541	+	33.3490i	−0.724636	+	1.25511i
$707$	−3.64884			−0.137229
$708$		0			0
$709$	25.9597	+	14.9878i	0.974936	+	0.562879i	0.900737	−	0.434364i	$-0.143027\pi$
$709$	25.9597	+	14.9878i	0.974936	+	0.562879i	0.0741983	+	0.997244i	$0.476360\pi$
$710$	−0.740328	−	1.89252i	−0.0277840	−	0.0710250i
$711$		0			0
$712$	−35.5135	+	20.5038i	−1.33093	+	0.768411i
$713$	14.5961	+	25.2811i	0.546627	+	0.946786i
$714$		0			0
$715$	24.9676	+	17.8450i	0.933736	+	0.667366i
$716$	−10.2165			−0.381807
$717$		0			0
$718$	14.6230	−	8.44262i	0.545727	−	0.315076i
$719$	−14.1660	+	24.5361i	−0.528301	+	0.915044i	0.471155	+	0.882051i	$0.343837\pi$
$719$	−14.1660	+	24.5361i	−0.528301	+	0.915044i	−0.999456	+	0.0329934i	$0.989496\pi$
$720$		0			0
$721$	54.1538	+	31.2657i	2.01679	+	1.16440i
$722$	−14.3748	+	24.8979i	−0.534974	+	0.926603i
$723$		0			0
$724$	−4.54203	+	7.86702i	−0.168803	+	0.292375i
$725$	−28.5959	−	8.89044i	−1.06202	−	0.330183i
$726$		0			0
$727$		−	6.23709i		−	0.231321i	−0.993289	−	0.115660i	$-0.963102\pi$
$727$		−	6.23709i		−	0.231321i	0.993289	−	0.115660i	$-0.0368984\pi$
$728$	30.2680	+	15.3686i	1.12181	+	0.569597i
$729$		0			0
$730$	38.4221	+	30.7107i	1.42207	+	1.13665i
$731$	−1.10900	−	1.92084i	−0.0410178	−	0.0710448i
$732$		0			0
$733$	19.7159			0.728223			0.364111	−	0.931355i	$-0.381373\pi$
$733$	19.7159			0.728223			0.364111	+	0.931355i	$0.381373\pi$
$734$	−0.905841	−	0.522987i	−0.0334352	−	0.0193038i
$735$		0			0
$736$		−	12.3737i		−	0.456102i
$737$	−20.6492	−	11.9218i	−0.760621	−	0.439145i
$738$		0			0
$739$	−9.45967	+	5.46154i	−0.347979	+	0.200906i	−0.663795	−	0.747915i	$-0.731055\pi$
$739$	−9.45967	+	5.46154i	−0.347979	+	0.200906i	0.315816	+	0.948821i	$0.397722\pi$
$740$	−2.30495	+	0.901665i	−0.0847316	+	0.0331459i
$741$		0			0
$742$		−	5.69882i		−	0.209210i
$743$	−5.28222	−	9.14907i	−0.193786	−	0.335647i	0.752716	−	0.658345i	$-0.228743\pi$
$743$	−5.28222	−	9.14907i	−0.193786	−	0.335647i	−0.946502	+	0.322699i	$0.895410\pi$
$744$		0			0
$745$	−12.8987	−	1.95885i	−0.472571	−	0.0717669i
$746$			38.4993i			1.40956i
$747$		0			0
$748$	0.387557	−	0.671268i	0.0141705	−	0.0245440i
$749$		−	47.0930i		−	1.72074i
$750$		0			0
$751$	−4.30955	−	7.46436i	−0.157258	−	0.272378i	0.776621	−	0.629968i	$-0.216932\pi$
$751$	−4.30955	−	7.46436i	−0.157258	−	0.272378i	−0.933879	+	0.357590i	$0.883599\pi$
$752$	−11.8131	−	20.4609i	−0.430780	−	0.746133i
$753$		0			0
$754$	30.0025	+	15.2338i	1.09263	+	0.554782i
$755$	14.7394	+	37.6787i	0.536422	+	1.37127i
$756$		0			0
$757$	31.9035	−	18.4195i	1.15955	−	0.669468i	0.208356	−	0.978053i	$-0.433189\pi$
$757$	31.9035	−	18.4195i	1.15955	−	0.669468i	0.951197	+	0.308585i	$0.0998553\pi$
$758$	13.1583	+	7.59693i	0.477930	+	0.275933i
$759$		0			0
$760$	−4.01440	−	0.609646i	−0.145618	−	0.0221142i
$761$	−13.4024	−	7.73787i	−0.485836	−	0.280497i	0.237009	−	0.971507i	$-0.423833\pi$
$761$	−13.4024	−	7.73787i	−0.485836	−	0.280497i	−0.722845	+	0.691010i	$0.757166\pi$
$762$		0			0
$763$	63.5267	+	36.6772i	2.29982	+	1.32780i
$764$	−1.48487	−	2.57186i	−0.0537206	−	0.0930468i
$765$		0			0
$766$	−28.3266			−1.02348
$767$	18.0716	−	35.5916i	0.652529	−	1.28514i
$768$		0			0
$769$	17.6605	−	10.1963i	0.636853	−	0.367687i	−0.146548	−	0.989204i	$-0.546816\pi$
$769$	17.6605	−	10.1963i	0.636853	−	0.367687i	0.783401	+	0.621516i	$0.213483\pi$
$770$	31.8286	−	39.8208i	1.14702	−	1.43504i
$771$		0			0
$772$	−6.48555			−0.233420
$773$	−11.3898	+	19.7277i	−0.409662	+	0.709556i	−0.994852	−	0.101341i	$-0.967687\pi$
$773$	−11.3898	+	19.7277i	−0.409662	+	0.709556i	0.585190	+	0.810897i	$0.301020\pi$
$774$		0			0
$775$	19.0676	+	20.6420i	0.684927	+	0.741481i
$776$	−14.3256	+	24.8127i	−0.514260	+	0.890725i
$777$		0			0
$778$	−2.93816	−	5.08904i	−0.105338	−	0.182451i
$779$	−4.28815			−0.153639
$780$		0			0
$781$	−2.22013			−0.0794426
$782$	−1.92529	−	3.33470i	−0.0688483	−	0.119249i
$783$		0			0
$784$	18.1625	−	31.4583i	0.648659	−	1.12351i
$785$	1.24253	+	3.17630i	0.0443477	+	0.113367i
$786$		0			0
$787$	3.82411	−	6.62356i	0.136315	−	0.236104i	−0.789784	−	0.613385i	$-0.789807\pi$
$787$	3.82411	−	6.62356i	0.136315	−	0.236104i	0.926099	+	0.377281i	$0.123141\pi$
$788$	−0.227884			−0.00811803
$789$		0			0
$790$	16.8897	+	13.4999i	0.600908	+	0.480304i
$791$	−37.4568	+	21.6257i	−1.33181	+	0.768921i
$792$		0			0
$793$	−40.4768	−	20.5521i	−1.43737	−	0.729826i
$794$	22.2558			0.789827
$795$		0			0
$796$	4.33557	+	7.50942i	0.153670	+	0.266164i
$797$	−13.5110	−	7.80056i	−0.478583	−	0.276310i	0.241243	−	0.970465i	$-0.422445\pi$
$797$	−13.5110	−	7.80056i	−0.478583	−	0.276310i	−0.719826	+	0.694155i	$0.755778\pi$
$798$		0			0
$799$	−2.08321	−	1.20274i	−0.0736985	−	0.0425499i
$800$	−2.62463	−	11.6185i	−0.0927946	−	0.410774i
$801$		0			0
$802$	−2.60129	−	1.50186i	−0.0918549	−	0.0530324i
$803$	46.5375	−	26.8685i	1.64227	−	0.948167i
$804$		0			0
$805$	−16.2633	−	41.5742i	−0.573206	−	1.46530i
$806$	−17.2345	−	26.4570i	−0.607058	−	0.931908i
$807$		0			0
$808$	1.16267	+	2.01381i	0.0409026	+	0.0708454i
$809$	4.37510	+	7.57789i	0.153820	+	0.266425i	0.932629	−	0.360837i	$-0.117509\pi$
$809$	4.37510	+	7.57789i	0.153820	+	0.266425i	−0.778809	+	0.627262i	$0.784176\pi$
$810$		0			0
$811$		−	27.6769i		−	0.971868i	−0.873996	−	0.485934i	$-0.838480\pi$
$811$		−	27.6769i		−	0.971868i	0.873996	−	0.485934i	$-0.161520\pi$
$812$	4.92644	−	8.53285i	0.172884	−	0.299444i
$813$		0			0
$814$			15.3391i			0.537634i
$815$	−0.185805	+	1.22349i	−0.00650845	+	0.0428569i
$816$		0			0
$817$	−1.72805	−	2.99307i	−0.0604567	−	0.104714i
$818$		−	37.8237i		−	1.32247i
$819$		0			0
$820$	−2.01678	−	5.15554i	−0.0704290	−	0.180039i
$821$	−10.7650	+	6.21520i	−0.375702	+	0.216912i	−0.675947	−	0.736950i	$-0.736265\pi$
$821$	−10.7650	+	6.21520i	−0.375702	+	0.216912i	0.300244	+	0.953862i	$0.402932\pi$
$822$		0			0
$823$	−21.1915	−	12.2349i	−0.738691	−	0.426483i	0.0829024	−	0.996558i	$-0.473581\pi$
$823$	−21.1915	−	12.2349i	−0.738691	−	0.426483i	−0.821593	+	0.570074i	$0.806914\pi$
$824$		−	39.8501i		−	1.38825i
$825$		0			0
$826$	−57.4226	−	33.1530i	−1.99799	−	1.15354i
$827$	−11.6031			−0.403481			−0.201741	−	0.979439i	$-0.564660\pi$
$827$	−11.6031			−0.403481			−0.201741	+	0.979439i	$0.564660\pi$
$828$		0			0
$829$	−2.73247	−	4.73278i	−0.0949028	−	0.164376i	0.814665	−	0.579931i	$-0.196921\pi$
$829$	−2.73247	−	4.73278i	−0.0949028	−	0.164376i	−0.909568	+	0.415555i	$0.863587\pi$
$830$	−8.66490	−	6.92582i	−0.300763	−	0.240399i
$831$		0			0
$832$	−1.09167	−	20.2830i	−0.0378470	−	0.703185i
$833$		−	3.69838i		−	0.128141i
$834$		0			0
$835$	−17.4278	−	13.9300i	−0.603114	−	0.482067i
$836$	0.603894	−	1.04597i	0.0208861	−	0.0361758i
$837$		0			0
$838$	20.3929	−	35.3215i	0.704460	−	1.22016i
$839$	−34.9120	−	20.1564i	−1.20530	−	0.695877i	−0.243567	−	0.969884i	$-0.578318\pi$
$839$	−34.9120	−	20.1564i	−1.20530	−	0.695877i	−0.961728	+	0.274007i	$0.911651\pi$
$840$		0			0
$841$	−3.43527	+	5.95005i	−0.118457	+	0.205174i
$842$	−31.6735	+	18.2867i	−1.09154	+	0.630201i
$843$		0			0
$844$	−3.97531			−0.136836
$845$	−25.7782	+	13.4344i	−0.886798	+	0.462157i
$846$		0			0
$847$	−6.70647	−	11.6159i	−0.230437	−	0.399129i
$848$	−3.85058	+	2.22313i	−0.132230	+	0.0763427i
$849$		0			0
$850$	−2.51510	−	2.72277i	−0.0862673	−	0.0933903i
$851$	11.6330	+	6.71630i	0.398773	+	0.230232i
$852$		0			0
$853$	13.7853			0.472000			0.236000	−	0.971753i	$-0.424164\pi$
$853$	13.7853			0.472000			0.236000	+	0.971753i	$0.424164\pi$
$854$	−37.7034	+	65.3042i	−1.29018	+	2.23466i
$855$		0			0
$856$	−25.9908	+	15.0058i	−0.888346	+	0.512887i
$857$			16.8727i			0.576362i	0.957576	+	0.288181i	$0.0930505\pi$
$857$			16.8727i			0.576362i	−0.957576	+	0.288181i	$0.906950\pi$
$858$		0			0
$859$	−8.77365			−0.299353			−0.149677	−	0.988735i	$-0.547823\pi$
$859$	−8.77365			−0.299353			−0.149677	+	0.988735i	$0.547823\pi$
$860$	2.78577	−	3.48527i	0.0949939	−	0.118847i
$861$		0			0
$862$	−17.2921	−	9.98359i	−0.588971	−	0.340042i
$863$	18.4583			0.628327			0.314163	−	0.949369i	$-0.398276\pi$
$863$	18.4583			0.628327			0.314163	+	0.949369i	$0.398276\pi$
$864$		0			0
$865$	56.8125	+	8.62782i	1.93168	+	0.293355i
$866$		−	20.9466i		−	0.711796i
$867$		0			0
$868$	−8.00711	+	4.62291i	−0.271779	+	0.156912i
$869$	20.4571	−	11.8109i	0.693960	−	0.400658i
$870$		0			0
$871$	18.9238	−	12.3272i	0.641207	−	0.417692i
$872$		−	46.7474i		−	1.58307i
$873$		0			0
$874$	−3.00000	−	5.19615i	−0.101477	−	0.175762i
$875$	−24.0890	−	35.5869i	−0.814357	−	1.20306i
$876$		0			0
$877$	−10.6610	+	18.4653i	−0.359995	+	0.623530i	−0.987960	−	0.154712i	$-0.950555\pi$
$877$	−10.6610	+	18.4653i	−0.359995	+	0.623530i	0.627965	+	0.778242i	$0.283888\pi$
$878$	10.7006	−	18.5339i	0.361126	−	0.625489i
$879$		0			0
$880$	−39.3226	−	5.97171i	−1.32556	−	0.201306i
$881$	5.18215	+	8.97575i	0.174591	+	0.302401i	0.940020	−	0.341120i	$-0.110806\pi$
$881$	5.18215	+	8.97575i	0.174591	+	0.302401i	−0.765429	+	0.643521i	$0.777473\pi$
$882$		0			0
$883$		−	8.99486i		−	0.302701i	−0.988480	−	0.151351i	$-0.951638\pi$
$883$		−	8.99486i		−	0.302701i	0.988480	−	0.151351i	$-0.0483622\pi$
$884$	0.400737	+	0.615179i	0.0134782	+	0.0206907i
$885$		0			0
$886$	32.7278	−	18.8954i	1.09951	−	0.634803i
$887$	−3.75895	+	2.17023i	−0.126213	+	0.0728692i	−0.561777	−	0.827288i	$-0.689882\pi$
$887$	−3.75895	+	2.17023i	−0.126213	+	0.0728692i	0.435564	+	0.900158i	$0.356549\pi$
$888$		0			0
$889$		−	67.9022i		−	2.27737i
$890$	−57.6696	−	8.75797i	−1.93309	−	0.293568i
$891$		0			0
$892$	−2.18335			−0.0731039
$893$	−3.24606	−	1.87412i	−0.108625	−	0.0627149i
$894$		0			0
$895$	41.6929	+	33.3250i	1.39364	+	1.11393i
$896$	−52.0539			−1.73900
$897$		0			0
$898$		−	21.6518i		−	0.722530i
$899$	29.1508	−	16.8302i	0.972233	−	0.561319i
$900$		0			0
$901$	−0.226346	+	0.392043i	−0.00754067	+	0.0130608i
$902$	−34.3093			−1.14238
$903$		0			0
$904$	23.8705	+	13.7817i	0.793922	+	0.458371i
$905$	44.1971	−	17.2893i	1.46916	−	0.574717i
$906$		0			0
$907$	14.2203	−	8.21009i	0.472177	−	0.272612i	−0.244973	−	0.969530i	$-0.578779\pi$
$907$	14.2203	−	8.21009i	0.472177	−	0.272612i	0.717151	+	0.696918i	$0.245446\pi$
$908$	1.81619	+	3.14573i	0.0602724	+	0.104395i
$909$		0			0
$910$	19.9823	+	43.9578i	0.662408	+	1.45719i
$911$	−42.7868			−1.41759			−0.708795	−	0.705415i	$-0.750761\pi$
$911$	−42.7868			−1.41759			−0.708795	+	0.705415i	$0.750761\pi$
$912$		0			0
$913$	−10.4951	+	6.05934i	−0.347337	+	0.200535i
$914$	9.11304	−	15.7842i	0.301432	−	0.522096i
$915$		0			0
$916$	−1.62608	−	0.938816i	−0.0537271	−	0.0310193i
$917$	31.4286	−	54.4359i	1.03786	−	1.79763i
$918$		0			0
$919$	−12.2232	+	21.1713i	−0.403207	+	0.698376i	−0.994111	−	0.108366i	$-0.965438\pi$
$919$	−12.2232	+	21.1713i	−0.403207	+	0.698376i	0.590904	+	0.806742i	$0.298771\pi$
$920$	−17.7628	+	22.2230i	−0.585621	+	0.732671i
$921$		0			0
$922$		−	42.6608i		−	1.40496i
$923$	0.952060	−	1.87506i	0.0313374	−	0.0617182i
$924$		0			0
$925$	12.3475	+	3.83884i	0.405984	+	0.126220i
$926$	2.92068	+	5.05876i	0.0959795	+	0.166241i
$927$		0			0
$928$	−14.2677			−0.468361
$929$	−34.0310	−	19.6478i	−1.11652	−	0.644624i	−0.176010	−	0.984388i	$-0.556319\pi$
$929$	−34.0310	−	19.6478i	−1.11652	−	0.644624i	−0.940510	+	0.339765i	$0.889653\pi$
$930$		0			0
$931$		−	5.76284i		−	0.188869i
$932$	6.54913	+	3.78114i	0.214524	+	0.123855i
$933$		0			0
$934$	39.7873	−	22.9712i	1.30188	−	0.751641i
$935$	−3.77121	+	1.47525i	−0.123332	+	0.0482457i
$936$		0			0
$937$			18.6246i			0.608441i	0.952602	+	0.304220i	$0.0983959\pi$
$937$			18.6246i			0.608441i	−0.952602	+	0.304220i	$0.901604\pi$
$938$	−18.7578	−	32.4895i	−0.612464	−	1.06082i
$939$		0			0
$940$	0.726535	−	4.78409i	0.0236970	−	0.156040i
$941$			33.8097i			1.10216i	0.834451	+	0.551082i	$0.185785\pi$
$941$			33.8097i			1.10216i	−0.834451	+	0.551082i	$0.814215\pi$
$942$		0			0
$943$	−15.0225	+	26.0198i	−0.489201	+	0.847322i
$944$			51.7324i			1.68375i
$945$		0			0
$946$	−13.8260	−	23.9474i	−0.449524	−	0.778598i
$947$	23.9182	+	41.4275i	0.777236	+	1.34621i	0.933529	+	0.358501i	$0.116712\pi$
$947$	23.9182	+	41.4275i	0.777236	+	1.34621i	−0.156294	+	0.987711i	$0.549955\pi$
$948$		0			0
$949$	2.73558	+	50.8262i	0.0888007	+	1.64989i
$950$	−3.91905	−	4.24264i	−0.127151	−	0.137649i
$951$		0			0
$952$	−3.87915	+	2.23963i	−0.125724	+	0.0725868i
$953$	10.8964	+	6.29106i	0.352970	+	0.203788i	0.665993	−	0.745958i	$-0.268008\pi$
$953$	10.8964	+	6.29106i	0.352970	+	0.203788i	−0.313022	+	0.949746i	$0.601341\pi$
$954$		0			0
$955$	−2.32947	+	15.3391i	−0.0753799	+	0.496362i
$956$	−7.05472	−	4.07305i	−0.228166	−	0.131732i
$957$		0			0
$958$	39.9987	+	23.0932i	1.29230	+	0.746109i
$959$	−9.11304	−	15.7842i	−0.294275	−	0.509700i
$960$		0			0
$961$	−0.586511			−0.0189197
$962$	−12.9549	−	6.57785i	−0.417683	−	0.212079i
$963$		0			0
$964$	1.12685	−	0.650584i	0.0362932	−	0.0209539i
$965$	26.4672	+	21.1552i	0.852010	+	0.681009i
$966$		0			0
$967$	46.2658			1.48781			0.743904	−	0.668286i	$-0.232972\pi$
$967$	46.2658			1.48781			0.743904	+	0.668286i	$0.232972\pi$
$968$	−4.27391	+	7.40263i	−0.137369	+	0.237930i
$969$		0			0
$970$	−37.9541	+	14.8471i	−1.21863	+	0.476713i
$971$	0.474658	−	0.822133i	0.0152325	−	0.0263835i	−0.858309	−	0.513134i	$-0.828484\pi$
$971$	0.474658	−	0.822133i	0.0152325	−	0.0263835i	0.873541	+	0.486750i	$0.161818\pi$
$972$		0			0
$973$	−12.3966	−	21.4715i	−0.397417	−	0.688346i
$974$	−3.25426			−0.104273
$975$		0			0
$976$	58.8330			1.88320
$977$	24.7131	+	42.8043i	0.790642	+	1.36943i	0.925570	+	0.378577i	$0.123586\pi$
$977$	24.7131	+	42.8043i	0.790642	+	1.36943i	−0.134928	+	0.990855i	$0.543080\pi$
$978$		0			0
$979$	−31.8630	+	55.1883i	−1.01835	+	1.76383i
$980$	6.92853	−	2.71035i	0.221324	−	0.0865789i
$981$		0			0
$982$	29.9267	−	51.8345i	0.954998	−	1.65410i
$983$	−47.8742			−1.52695			−0.763474	−	0.645838i	$-0.776508\pi$
$983$	−47.8742			−1.52695			−0.763474	+	0.645838i	$0.776508\pi$
$984$		0			0
$985$	0.929983	+	0.743332i	0.0296317	+	0.0236845i
$986$	−3.84513	+	2.21999i	−0.122454	+	0.0706987i
$987$		0			0
$988$	0.624430	+	0.958576i	0.0198658	+	0.0304964i
$989$	−24.2153			−0.770001
$990$		0			0
$991$	−1.66972	−	2.89203i	−0.0530403	−	0.0918685i	0.838286	−	0.545230i	$-0.183558\pi$
$991$	−1.66972	−	2.89203i	−0.0530403	−	0.0918685i	−0.891327	+	0.453362i	$0.850225\pi$
$992$	11.5949	+	6.69433i	0.368139	+	0.212545i
$993$		0			0
$994$	−3.02517	−	1.74658i	−0.0959525	−	0.0553982i
$995$	6.80167	−	44.7877i	0.215628	−	1.41987i
$996$		0			0
$997$	−26.8505	−	15.5022i	−0.850365	−	0.490958i	0.0104093	−	0.999946i	$-0.496687\pi$
$997$	−26.8505	−	15.5022i	−0.850365	−	0.490958i	−0.860774	+	0.508988i	$0.830020\pi$
$998$	−44.9326	+	25.9419i	−1.42232	+	0.821175i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	585.2.bf.b.244.3	yes	24
3.2	odd	2	inner	585.2.bf.b.244.10	yes	24
5.4	even	2	inner	585.2.bf.b.244.9	yes	24
13.4	even	6	inner	585.2.bf.b.199.10	yes	24
15.14	odd	2	inner	585.2.bf.b.244.4	yes	24
39.17	odd	6	inner	585.2.bf.b.199.3	✓	24
65.4	even	6	inner	585.2.bf.b.199.4	yes	24
195.134	odd	6	inner	585.2.bf.b.199.9	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
585.2.bf.b.199.3	✓	24	39.17	odd	6	inner
585.2.bf.b.199.4	yes	24	65.4	even	6	inner
585.2.bf.b.199.9	yes	24	195.134	odd	6	inner
585.2.bf.b.199.10	yes	24	13.4	even	6	inner
585.2.bf.b.244.3	yes	24	1.1	even	1	trivial
585.2.bf.b.244.4	yes	24	15.14	odd	2	inner
585.2.bf.b.244.9	yes	24	5.4	even	2	inner
585.2.bf.b.244.10	yes	24	3.2	odd	2	inner

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.bf (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.779103 - 1.34945i) q^{2} +(-0.214003 + 0.370665i) q^{4} +(2.08241 - 0.814609i) q^{5} +(1.92183 - 3.32870i) q^{7} -2.44949 q^{8} +O(q^{10})\)	\(q+(-0.779103 - 1.34945i) q^{2} +(-0.214003 + 0.370665i) q^{4} +(2.08241 - 0.814609i) q^{5} +(1.92183 - 3.32870i) q^{7} -2.44949 q^{8} +(-2.72168 - 2.17543i) q^{10} +(-3.29655 + 1.90326i) q^{11} +(-0.193779 - 3.60034i) q^{13} -5.98920 q^{14} +(2.33641 + 4.04678i) q^{16} +(0.412019 + 0.237879i) q^{17} +(0.642010 + 0.370665i) q^{19} +(-0.143695 + 0.946203i) q^{20} +(5.13670 + 2.96568i) q^{22} +(4.49827 - 2.59708i) q^{23} +(3.67282 - 3.39269i) q^{25} +(-4.70749 + 3.06653i) q^{26} +(0.822554 + 1.42471i) q^{28} +(-2.99460 - 5.18680i) q^{29} +5.62019i q^{31} +(1.19112 - 2.06308i) q^{32} -0.741329i q^{34} +(1.29043 - 8.49724i) q^{35} +(1.29305 + 2.23963i) q^{37} -1.15514i q^{38} +(-5.10083 + 1.99538i) q^{40} +(-5.00944 + 2.89220i) q^{41} +(-4.03743 - 2.33101i) q^{43} -1.62922i q^{44} +(-7.00924 - 4.04678i) q^{46} -5.05609 q^{47} +(-3.88683 - 6.73218i) q^{49} +(-7.43977 - 2.31302i) q^{50} +(1.37599 + 0.698658i) q^{52} +0.951516i q^{53} +(-5.31433 + 6.64876i) q^{55} +(-4.70749 + 8.15362i) q^{56} +(-4.66621 + 8.08210i) q^{58} +(9.58770 + 5.53546i) q^{59} +(6.29523 - 10.9037i) q^{61} +(7.58414 - 4.37871i) q^{62} +5.63362 q^{64} +(-3.33640 - 7.33951i) q^{65} +(3.13194 + 5.42467i) q^{67} +(-0.176347 + 0.101814i) q^{68} +(-12.4719 + 4.87886i) q^{70} +(0.505104 + 0.291622i) q^{71} -14.1171 q^{73} +(2.01484 - 3.48980i) q^{74} +(-0.274785 + 0.158647i) q^{76} +14.6310i q^{77} -6.20561 q^{79} +(8.16190 + 6.52378i) q^{80} +(7.80574 + 4.50665i) q^{82} +3.18366 q^{83} +(1.05177 + 0.159726i) q^{85} +7.26439i q^{86} +(8.07486 - 4.66202i) q^{88} +(14.4983 - 8.37062i) q^{89} +(-12.3569 - 6.27420i) q^{91} +2.22313i q^{92} +(3.93922 + 6.82293i) q^{94} +(1.63887 + 0.248887i) q^{95} +(5.84842 - 10.1298i) q^{97} +(-6.05648 + 10.4901i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 8 q^{4}+O(q^{10}) \) 24 * q - 8 * q^4	\( 24 q - 8 q^{4} + 4 q^{10} + 16 q^{16} + 24 q^{19} + 8 q^{25} - 48 q^{40} - 48 q^{46} - 16 q^{49} + 28 q^{61} - 48 q^{64} - 144 q^{76} + 40 q^{79} + 12 q^{85} + 4 q^{91} - 40 q^{94}+O(q^{100}) \) 24 * q - 8 * q^4 + 4 * q^10 + 16 * q^16 + 24 * q^19 + 8 * q^25 - 48 * q^40 - 48 * q^46 - 16 * q^49 + 28 * q^61 - 48 * q^64 - 144 * q^76 + 40 * q^79 + 12 * q^85 + 4 * q^91 - 40 * q^94

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