LMFDB - Embedded newform 216.4.n.a.37.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [216,4,Mod(37,216)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(216, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 2]))

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("216.37");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 216 = 2^{3} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	216.n (of order $6$, degree $2$, not 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:	$12.7444125612$
Analytic rank:	$0$
Dimension:	$68$
Relative dimension:	$34$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 72)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			37.9
Character	$\chi$	$=$	216.37
Dual form			216.4.n.a.181.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.16881 - 1.81556i) q^{2} +(1.40750 + 7.87521i) q^{4} +(17.5797 + 10.1497i) q^{5} +(-10.6896 - 18.5150i) q^{7} +(11.2453 - 19.6353i) q^{8} +O(q^{10})$	\(q+(-2.16881 - 1.81556i) q^{2} +(1.40750 + 7.87521i) q^{4} +(17.5797 + 10.1497i) q^{5} +(-10.6896 - 18.5150i) q^{7} +(11.2453 - 19.6353i) q^{8} +(-19.6999 - 53.9298i) q^{10} +(1.86021 - 1.07399i) q^{11} +(13.7636 + 7.94640i) q^{13} +(-10.4312 + 59.5632i) q^{14} +(-60.0379 + 22.1688i) q^{16} +100.066 q^{17} -2.35719i q^{19} +(-55.1872 + 152.730i) q^{20} +(-5.98436 - 1.04803i) q^{22} +(-74.6153 + 129.238i) q^{23} +(143.532 + 248.604i) q^{25} +(-15.4235 - 42.2228i) q^{26} +(130.764 - 110.243i) q^{28} +(175.273 - 101.194i) q^{29} +(66.8886 - 115.855i) q^{31} +(170.460 + 60.9222i) q^{32} +(-217.024 - 181.675i) q^{34} -433.985i q^{35} +16.6443i q^{37} +(-4.27962 + 5.11231i) q^{38} +(396.981 - 231.047i) q^{40} +(65.4314 - 113.331i) q^{41} +(107.846 - 62.2650i) q^{43} +(11.0762 + 13.1379i) q^{44} +(396.465 - 144.824i) q^{46} +(139.663 + 241.903i) q^{47} +(-57.0362 + 98.7895i) q^{49} +(140.062 - 799.766i) q^{50} +(-43.2073 + 119.576i) q^{52} +342.817i q^{53} +43.6028 q^{55} +(-483.754 + 1.68757i) q^{56} +(-563.859 - 98.7477i) q^{58} +(191.251 + 110.419i) q^{59} +(367.557 - 212.209i) q^{61} +(-355.410 + 129.827i) q^{62} +(-259.087 - 441.608i) q^{64} +(161.307 + 279.391i) q^{65} +(47.7127 + 27.5469i) q^{67} +(140.843 + 788.038i) q^{68} +(-787.924 + 941.232i) q^{70} +996.571 q^{71} -910.971 q^{73} +(30.2186 - 36.0983i) q^{74} +(18.5634 - 3.31776i) q^{76} +(-39.7700 - 22.9612i) q^{77} +(163.931 + 283.937i) q^{79} +(-1280.46 - 219.643i) q^{80} +(-347.667 + 126.998i) q^{82} +(-147.974 + 85.4325i) q^{83} +(1759.13 + 1015.63i) q^{85} +(-346.944 - 60.7597i) q^{86} +(-0.169551 - 48.6032i) q^{88} -850.727 q^{89} -339.776i q^{91} +(-1122.79 - 405.709i) q^{92} +(136.286 - 778.210i) q^{94} +(23.9247 - 41.4388i) q^{95} +(-24.9396 - 43.1967i) q^{97} +(303.059 - 110.704i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 68 q + q^{2} - q^{4} - 2 q^{7} + 10 q^{8}+O(q^{10}) $ 68 * q + q^2 - q^4 - 2 * q^7 + 10 * q^8	$ 68 q + q^{2} - q^{4} - 2 q^{7} + 10 q^{8} - 20 q^{10} + 10 q^{14} - q^{16} + 8 q^{17} + 52 q^{20} - 17 q^{22} - 274 q^{23} + 648 q^{25} - 368 q^{26} + 124 q^{28} - 2 q^{31} - 259 q^{32} + 189 q^{34} - 319 q^{38} + 214 q^{40} + 22 q^{41} - 282 q^{44} - 24 q^{46} + 942 q^{47} - 1080 q^{49} - 53 q^{50} - 588 q^{52} - 508 q^{55} + 502 q^{56} + 280 q^{58} - 1744 q^{62} + 410 q^{64} + 502 q^{65} - 1149 q^{68} - 586 q^{70} + 3984 q^{71} - 8 q^{73} - 1778 q^{74} + 621 q^{76} - 2 q^{79} - 4704 q^{80} + 714 q^{82} + 2923 q^{86} - 533 q^{88} + 856 q^{89} - 3342 q^{92} + 1518 q^{94} + 2792 q^{95} - 2 q^{97} + 6414 q^{98}+O(q^{100}) $ 68 * q + q^2 - q^4 - 2 * q^7 + 10 * q^8 - 20 * q^10 + 10 * q^14 - q^16 + 8 * q^17 + 52 * q^20 - 17 * q^22 - 274 * q^23 + 648 * q^25 - 368 * q^26 + 124 * q^28 - 2 * q^31 - 259 * q^32 + 189 * q^34 - 319 * q^38 + 214 * q^40 + 22 * q^41 - 282 * q^44 - 24 * q^46 + 942 * q^47 - 1080 * q^49 - 53 * q^50 - 588 * q^52 - 508 * q^55 + 502 * q^56 + 280 * q^58 - 1744 * q^62 + 410 * q^64 + 502 * q^65 - 1149 * q^68 - 586 * q^70 + 3984 * q^71 - 8 * q^73 - 1778 * q^74 + 621 * q^76 - 2 * q^79 - 4704 * q^80 + 714 * q^82 + 2923 * q^86 - 533 * q^88 + 856 * q^89 - 3342 * q^92 + 1518 * q^94 + 2792 * q^95 - 2 * q^97 + 6414 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/216\mathbb{Z}\right)^\times$.

$n$	$55$	$109$	$137$
$\chi(n)$	$1$	$-1$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$	−2.16881	−	1.81556i	−0.766791	−	0.641896i
$2$	−2.16881	−	1.81556i	−0.766791	−	0.641896i
$3$		0			0
$3$		0			0
$4$	1.40750	+	7.87521i	0.175938	+	0.984401i
$5$	17.5797	+	10.1497i	1.57238	+	0.907814i	0.995876	+	0.0907198i	$0.0289168\pi$
$5$	17.5797	+	10.1497i	1.57238	+	0.907814i	0.576504	+	0.817094i	$0.304417\pi$
$6$		0			0
$7$	−10.6896	−	18.5150i	−0.577185	−	0.999715i	−0.995800	−	0.0915508i	$-0.970818\pi$
$7$	−10.6896	−	18.5150i	−0.577185	−	0.999715i	0.418615	−	0.908164i	$-0.362516\pi$
$8$	11.2453	−	19.6353i	0.496976	−	0.867764i
$9$		0			0
$10$	−19.6999	−	53.9298i	−0.622965	−	1.70541i
$11$	1.86021	−	1.07399i	0.0509887	−	0.0294383i	−0.474289	−	0.880369i	$-0.657295\pi$
$11$	1.86021	−	1.07399i	0.0509887	−	0.0294383i	0.525278	+	0.850931i	$0.323961\pi$
$12$		0			0
$13$	13.7636	+	7.94640i	0.293641	+	0.169534i	0.639583	−	0.768722i	$-0.279107\pi$
$13$	13.7636	+	7.94640i	0.293641	+	0.169534i	−0.345942	+	0.938256i	$0.612441\pi$
$14$	−10.4312	+	59.5632i	−0.199132	+	1.13707i
$15$		0			0
$16$	−60.0379	+	22.1688i	−0.938092	+	0.346387i
$17$	100.066			1.42762			0.713809	−	0.700341i	$-0.246969\pi$
$17$	100.066			1.42762			0.713809	+	0.700341i	$0.246969\pi$
$18$		0			0
$19$		−	2.35719i		−	0.0284619i	−0.999899	−	0.0142310i	$-0.995470\pi$
$19$		−	2.35719i		−	0.0284619i	0.999899	−	0.0142310i	$-0.00453001\pi$
$20$	−55.1872	+	152.730i	−0.617012	+	1.70757i
$21$		0			0
$22$	−5.98436	−	1.04803i	−0.0579940	−	0.0101564i
$23$	−74.6153	+	129.238i	−0.676451	+	1.17165i	0.299592	+	0.954068i	$0.403150\pi$
$23$	−74.6153	+	129.238i	−0.676451	+	1.17165i	−0.976043	+	0.217580i	$0.930184\pi$
$24$		0			0
$25$	143.532	+	248.604i	1.14825	+	1.98883i
$26$	−15.4235	−	42.2228i	−0.116338	−	0.318484i
$27$		0			0
$28$	130.764	−	110.243i	0.882571	−	0.744070i
$29$	175.273	−	101.194i	1.12233	−	0.647975i	0.180333	−	0.983606i	$-0.442283\pi$
$29$	175.273	−	101.194i	1.12233	−	0.647975i	0.941994	+	0.335630i	$0.108949\pi$
$30$		0			0
$31$	66.8886	−	115.855i	0.387534	−	0.671229i	−0.604583	−	0.796542i	$-0.706660\pi$
$31$	66.8886	−	115.855i	0.387534	−	0.671229i	0.992117	+	0.125313i	$0.0399936\pi$
$32$	170.460	+	60.9222i	0.941665	+	0.336551i
$33$		0			0
$34$	−217.024	−	181.675i	−1.09468	−	0.916383i
$35$		−	433.985i		−	2.09591i
$36$		0			0
$37$			16.6443i			0.0739541i	0.999316	+	0.0369770i	$0.0117728\pi$
$37$			16.6443i			0.0739541i	−0.999316	+	0.0369770i	$0.988227\pi$
$38$	−4.27962	+	5.11231i	−0.0182696	+	0.0218244i
$39$		0			0
$40$	396.981	−	231.047i	1.56920	−	0.913294i
$41$	65.4314	−	113.331i	0.249236	−	0.431689i	−0.714078	−	0.700066i	$-0.753154\pi$
$41$	65.4314	−	113.331i	0.249236	−	0.431689i	0.963314	+	0.268377i	$0.0864872\pi$
$42$		0			0
$43$	107.846	−	62.2650i	0.382474	−	0.220821i	−0.296420	−	0.955058i	$-0.595793\pi$
$43$	107.846	−	62.2650i	0.382474	−	0.220821i	0.678894	+	0.734236i	$0.262460\pi$
$44$	11.0762	+	13.1379i	0.0379500	+	0.0450140i
$45$		0			0
$46$	396.465	−	144.824i	1.27077	−	0.464198i
$47$	139.663	+	241.903i	0.433446	+	0.750750i	0.997167	−	0.0752150i	$-0.0239643\pi$
$47$	139.663	+	241.903i	0.433446	+	0.750750i	−0.563722	+	0.825965i	$0.690631\pi$
$48$		0			0
$49$	−57.0362	+	98.7895i	−0.166286	+	0.288016i
$50$	140.062	−	799.766i	0.396154	−	2.26208i
$51$		0			0
$52$	−43.2073	+	119.576i	−0.115226	+	0.318888i
$53$			342.817i			0.888483i	0.895907	+	0.444241i	$0.146527\pi$
$53$			342.817i			0.888483i	−0.895907	+	0.444241i	$0.853473\pi$
$54$		0			0
$55$	43.6028			0.106898
$56$	−483.754	+	1.68757i	−1.15436	+	0.00402698i
$57$		0			0
$58$	−563.859	−	98.7477i	−1.27652	−	0.223555i
$59$	191.251	+	110.419i	0.422013	+	0.243649i	0.695938	−	0.718102i	$-0.254989\pi$
$59$	191.251	+	110.419i	0.422013	+	0.243649i	−0.273925	+	0.961751i	$0.588322\pi$
$60$		0			0
$61$	367.557	−	212.209i	0.771488	−	0.445419i	−0.0619169	−	0.998081i	$-0.519721\pi$
$61$	367.557	−	212.209i	0.771488	−	0.445419i	0.833405	+	0.552662i	$0.186388\pi$
$62$	−355.410	+	129.827i	−0.728017	+	0.265936i
$63$		0			0
$64$	−259.087	−	441.608i	−0.506030	−	0.862516i
$65$	161.307	+	279.391i	0.307810	+	0.533142i
$66$		0			0
$67$	47.7127	+	27.5469i	0.0870005	+	0.0502298i	0.542869	−	0.839817i	$-0.317338\pi$
$67$	47.7127	+	27.5469i	0.0870005	+	0.0502298i	−0.455869	+	0.890047i	$0.650671\pi$
$68$	140.843	+	788.038i	0.251172	+	1.40535i
$69$		0			0
$70$	−787.924	+	941.232i	−1.34536	+	1.60712i
$71$	996.571			1.66579			0.832896	−	0.553430i	$-0.186681\pi$
$71$	996.571			1.66579			0.832896	+	0.553430i	$0.186681\pi$
$72$		0			0
$73$	−910.971			−1.46056			−0.730282	−	0.683146i	$-0.760611\pi$
$73$	−910.971			−1.46056			−0.730282	+	0.683146i	$0.760611\pi$
$74$	30.2186	−	36.0983i	0.0474709	−	0.0567074i
$75$		0			0
$76$	18.5634	−	3.31776i	0.0280180	−	0.00500754i
$77$	−39.7700	−	22.9612i	−0.0588599	−	0.0339828i
$78$		0			0
$79$	163.931	+	283.937i	0.233464	+	0.404372i	0.958825	−	0.283997i	$-0.0916605\pi$
$79$	163.931	+	283.937i	0.233464	+	0.404372i	−0.725361	+	0.688369i	$0.758327\pi$
$80$	−1280.46	−	219.643i	−1.78949	−	0.306960i
$81$		0			0
$82$	−347.667	+	126.998i	−0.468212	+	0.171032i
$83$	−147.974	+	85.4325i	−0.195689	+	0.112981i	−0.594643	−	0.803990i	$-0.702707\pi$
$83$	−147.974	+	85.4325i	−0.195689	+	0.112981i	0.398954	+	0.916971i	$0.369373\pi$
$84$		0			0
$85$	1759.13	+	1015.63i	2.24476	+	1.29601i
$86$	−346.944	−	60.7597i	−0.435022	−	0.0761847i
$87$		0			0
$88$	−0.169551	−	48.6032i	−0.000205389	−	0.0588763i
$89$	−850.727			−1.01322			−0.506612	−	0.862174i	$-0.669102\pi$
$89$	−850.727			−1.01322			−0.506612	+	0.862174i	$0.669102\pi$
$90$		0			0
$91$		−	339.776i		−	0.391409i
$92$	−1122.79	−	405.709i	−1.27238	−	0.459762i
$93$		0			0
$94$	136.286	−	778.210i	0.149541	−	0.853896i
$95$	23.9247	−	41.4388i	0.0258381	−	0.0447530i
$96$		0			0
$97$	−24.9396	−	43.1967i	−0.0261055	−	0.0452161i	0.852677	−	0.522438i	$-0.174977\pi$
$97$	−24.9396	−	43.1967i	−0.0261055	−	0.0452161i	−0.878783	+	0.477222i	$0.841644\pi$
$98$	303.059	−	110.704i	0.312383	−	0.114110i
$99$		0			0
$100$	−1755.79	+	1480.25i	−1.75579	+	1.48025i
$101$	851.839	−	491.810i	0.839220	−	0.484524i	−0.0177792	−	0.999842i	$-0.505660\pi$
$101$	851.839	−	491.810i	0.839220	−	0.484524i	0.856999	+	0.515318i	$0.172326\pi$
$102$		0			0
$103$	−270.960	+	469.316i	−0.259209	+	0.448962i	−0.966030	−	0.258430i	$-0.916795\pi$
$103$	−270.960	+	469.316i	−0.259209	+	0.448962i	0.706822	+	0.707392i	$0.250128\pi$
$104$	310.805	−	180.892i	0.293047	−	0.170557i
$105$		0			0
$106$	622.405	−	743.507i	0.570314	−	0.681281i
$107$		−	1655.94i		−	1.49613i	−0.663624	−	0.748066i	$-0.730983\pi$
$107$		−	1655.94i		−	1.49613i	0.663624	−	0.748066i	$-0.269017\pi$
$108$		0			0
$109$		−	390.839i		−	0.343445i	−0.985145	−	0.171723i	$-0.945067\pi$
$109$		−	390.839i		−	0.343445i	0.985145	−	0.171723i	$-0.0549333\pi$
$110$	−94.5663	−	79.1633i	−0.0819686	−	0.0686175i
$111$		0			0
$112$	1052.24	+	874.623i	0.887741	+	0.737894i
$113$	−854.064	+	1479.28i	−0.711005	+	1.23150i	0.253475	+	0.967342i	$0.418427\pi$
$113$	−854.064	+	1479.28i	−0.711005	+	1.23150i	−0.964480	+	0.264155i	$0.914907\pi$
$114$		0			0
$115$	−2623.44	+	1514.64i	−2.12728	+	1.22818i
$116$	1043.62	+	1237.88i	0.835328	+	0.990816i
$117$		0			0
$118$	−214.316	−	586.705i	−0.167198	−	0.457716i
$119$	−1069.66	−	1852.71i	−0.824000	−	1.42721i
$120$		0			0
$121$	−663.193	+	1148.68i	−0.498267	+	0.863023i
$122$	−1182.44	−	207.078i	−0.877483	−	0.153672i
$123$		0			0
$124$	1006.52	+	363.696i	0.728940	+	0.263394i
$125$			3289.78i			2.35397i
$126$		0			0
$127$	−1388.03			−0.969826			−0.484913	−	0.874562i	$-0.661149\pi$
$127$	−1388.03			−0.969826			−0.484913	+	0.874562i	$0.661149\pi$
$128$	−239.853	+	1428.15i	−0.165626	+	0.986189i
$129$		0			0
$130$	157.407	−	898.810i	0.106196	−	0.606391i
$131$	−1827.68	−	1055.21i	−1.21897	−	0.703772i	−0.254272	−	0.967133i	$-0.581836\pi$
$131$	−1827.68	−	1055.21i	−1.21897	−	0.703772i	−0.964697	+	0.263361i	$0.915169\pi$
$132$		0			0
$133$	−43.6433	+	25.1975i	−0.0284538	+	0.0164278i
$134$	−53.4669	−	146.369i	−0.0344689	−	0.0943610i
$135$		0			0
$136$	1125.27	−	1964.82i	0.709492	−	1.23884i
$137$	−959.737	−	1662.31i	−0.598510	−	1.03665i	−0.993041	−	0.117767i	$-0.962426\pi$
$137$	−959.737	−	1662.31i	−0.598510	−	1.03665i	0.394531	−	0.918883i	$-0.370907\pi$
$138$		0			0
$139$	−679.222	−	392.149i	−0.414467	−	0.239292i	0.278241	−	0.960511i	$-0.410249\pi$
$139$	−679.222	−	392.149i	−0.414467	−	0.239292i	−0.692707	+	0.721219i	$0.743582\pi$
$140$	3417.72	−	610.835i	2.06322	−	0.368750i
$141$		0			0
$142$	−2161.38	−	1809.33i	−1.27731	−	1.06927i
$143$	34.1376			0.0199631
$144$		0			0
$145$	4108.35			2.35297
$146$	1975.73	+	1653.92i	1.11995	+	0.937530i
$147$		0			0
$148$	−131.077	+	23.4269i	−0.0728005	+	0.0130113i
$149$	−404.617	−	233.606i	−0.222467	−	0.128441i	0.384625	−	0.923073i	$-0.374331\pi$
$149$	−404.617	−	233.606i	−0.222467	−	0.128441i	−0.607092	+	0.794632i	$0.707664\pi$
$150$		0			0
$151$	218.102	+	377.764i	0.117542	+	0.203589i	0.918793	−	0.394739i	$-0.129165\pi$
$151$	218.102	+	377.764i	0.117542	+	0.203589i	−0.801251	+	0.598329i	$0.795832\pi$
$152$	−46.2841	−	26.5073i	−0.0246983	−	0.0141449i
$153$		0			0
$154$	44.5663	+	122.003i	0.0233198	+	0.0638396i
$155$	2351.77	−	1357.80i	1.21870	−	0.703618i
$156$		0			0
$157$	114.915	+	66.3465i	0.0584156	+	0.0337263i	0.528923	−	0.848670i	$-0.322596\pi$
$157$	114.915	+	66.3465i	0.0584156	+	0.0337263i	−0.470508	+	0.882396i	$0.655929\pi$
$158$	159.968	−	913.431i	0.0805465	−	0.459928i
$159$		0			0
$160$	2378.30	+	2801.11i	1.17513	+	1.38404i
$161$	3190.44			1.56175
$162$		0			0
$163$		−	3675.16i		−	1.76601i	−0.469359	−	0.883007i	$-0.655515\pi$
$163$		−	3675.16i		−	1.76601i	0.469359	−	0.883007i	$-0.344485\pi$
$164$	984.597	+	355.773i	0.468806	+	0.169398i
$165$		0			0
$166$	476.035	+	83.3671i	0.222575	+	0.0389792i
$167$	3.78642	−	6.55827i	0.00175450	−	0.00303889i	−0.865147	−	0.501519i	$-0.832775\pi$
$167$	3.78642	−	6.55827i	0.00175450	−	0.00303889i	0.866901	+	0.498480i	$0.166108\pi$
$168$		0			0
$169$	−972.209	−	1683.92i	−0.442517	−	0.766462i
$170$	−1971.28	−	5396.52i	−0.889356	−	2.43467i
$171$		0			0
$172$	642.144	+	761.673i	0.284669	+	0.337657i
$173$	−1208.10	+	697.499i	−0.530927	+	0.306531i	−0.741394	−	0.671070i	$-0.765835\pi$
$173$	−1208.10	+	697.499i	−0.530927	+	0.306531i	0.210467	+	0.977601i	$0.432502\pi$
$174$		0			0
$175$	3068.60	−	5314.97i	1.32551	−	2.29585i
$176$	−87.8741	+	105.719i	−0.0376350	+	0.0452777i
$177$		0			0
$178$	1845.07	+	1544.54i	0.776931	+	0.650384i
$179$			3708.55i			1.54855i	0.632852	+	0.774273i	$0.281884\pi$
$179$			3708.55i			1.54855i	−0.632852	+	0.774273i	$0.718116\pi$
$180$		0			0
$181$			1909.18i			0.784024i	0.919960	+	0.392012i	$0.128221\pi$
$181$			1909.18i			0.784024i	−0.919960	+	0.392012i	$0.871779\pi$
$182$	−616.883	+	736.911i	−0.251244	+	0.300129i
$183$		0			0
$184$	1698.54	+	2918.40i	0.680534	+	1.16928i
$185$	−168.934	+	292.602i	−0.0671366	+	0.116284i
$186$		0			0
$187$	186.144	−	107.470i	0.0727923	−	0.0420267i
$188$	−1708.46	+	1440.36i	−0.662779	+	0.558770i
$189$		0			0
$190$	−127.123	+	46.4364i	−0.0485393	+	0.0177308i
$191$	528.874	+	916.036i	0.200356	+	0.347026i	0.948643	−	0.316348i	$-0.102457\pi$
$191$	528.874	+	916.036i	0.200356	+	0.347026i	−0.748287	+	0.663375i	$0.769124\pi$
$192$		0			0
$193$	601.103	−	1041.14i	0.224188	−	0.388305i	−0.731887	−	0.681426i	$-0.761360\pi$
$193$	601.103	−	1041.14i	0.224188	−	0.388305i	0.956076	+	0.293120i	$0.0946936\pi$
$194$	−24.3367	+	138.965i	−0.00900656	+	0.0514284i
$195$		0			0
$196$	−858.267	−	310.125i	−0.312779	−	0.113019i
$197$			1181.13i			0.427169i	0.976925	+	0.213584i	$0.0685138\pi$
$197$			1181.13i			0.427169i	−0.976925	+	0.213584i	$0.931486\pi$
$198$		0			0
$199$	−766.932			−0.273198			−0.136599	−	0.990626i	$-0.543617\pi$
$199$	−766.932			−0.273198			−0.136599	+	0.990626i	$0.543617\pi$
$200$	6495.46	−	22.6593i	2.29649	−	0.00801128i
$201$		0			0
$202$	−2740.39	−	479.920i	−0.954520	−	0.167163i
$203$	−3747.21	−	2163.46i	−1.29558	−	0.748004i
$204$		0			0
$205$	2300.54	−	1328.22i	0.783788	−	0.452520i
$206$	1439.73	−	525.917i	0.486946	−	0.177875i
$207$		0			0
$208$	−1002.50	−	171.963i	−0.334186	−	0.0573246i
$209$	−2.53161	−	4.38488i	−0.000837872	−	0.00145124i
$210$		0			0
$211$	−3170.24	−	1830.34i	−1.03435	−	0.597183i	−0.116123	−	0.993235i	$-0.537047\pi$
$211$	−3170.24	−	1830.34i	−1.03435	−	0.597183i	−0.918228	+	0.396052i	$0.870380\pi$
$212$	−2699.76	+	482.517i	−0.874624	+	0.156318i
$213$		0			0
$214$	−3006.46	+	3591.43i	−0.960362	+	1.14722i
$215$	2527.88			0.801860
$216$		0			0
$217$	−2860.06			−0.894716
$218$	−709.590	+	847.656i	−0.220456	+	0.263351i
$219$		0			0
$220$	61.3711	+	343.381i	0.0188074	+	0.105231i
$221$	1377.26	+	795.162i	0.419207	+	0.242029i
$222$		0			0
$223$	497.726	+	862.086i	0.149463	+	0.258877i	0.931029	−	0.364945i	$-0.118912\pi$
$223$	497.726	+	862.086i	0.149463	+	0.258877i	−0.781566	+	0.623822i	$0.785579\pi$
$224$	−694.176	−	3807.29i	−0.207061	−	1.13565i
$225$		0			0
$226$	4538.03	−	1657.69i	1.33569	−	0.487910i
$227$	73.6777	−	42.5378i	0.0215426	−	0.0124376i	−0.489190	−	0.872177i	$-0.662708\pi$
$227$	73.6777	−	42.5378i	0.0215426	−	0.0124376i	0.510733	+	0.859740i	$0.329374\pi$
$228$		0			0
$229$	−5136.14	−	2965.35i	−1.48212	−	0.855703i	−0.482326	−	0.875992i	$-0.660208\pi$
$229$	−5136.14	−	2965.35i	−1.48212	−	0.855703i	−0.999794	+	0.0202888i	$0.993541\pi$
$230$	8439.66	+	1478.02i	2.41954	+	0.423730i
$231$		0			0
$232$	−15.9755	−	4579.50i	−0.00452088	−	1.29594i
$233$	−4680.37			−1.31597			−0.657986	−	0.753030i	$-0.728591\pi$
$233$	−4680.37			−1.31597			−0.657986	+	0.753030i	$0.728591\pi$
$234$		0			0
$235$			5670.13i			1.57395i
$236$	−600.384	+	1661.56i	−0.165600	+	0.458297i
$237$		0			0
$238$	−1043.80	+	5960.23i	−0.284285	+	1.62330i
$239$	−1832.74	+	3174.40i	−0.496026	+	0.859142i	−0.999990	−	0.00458254i	$-0.998541\pi$
$239$	−1832.74	+	3174.40i	−0.496026	+	0.859142i	0.503963	+	0.863725i	$0.331875\pi$
$240$		0			0
$241$	−1037.00	−	1796.13i	−0.277173	−	0.480078i	0.693508	−	0.720449i	$-0.256064\pi$
$241$	−1037.00	−	1796.13i	−0.277173	−	0.480078i	−0.970681	+	0.240371i	$0.922731\pi$
$242$	3523.84	−	1287.22i	0.936038	−	0.341923i
$243$		0			0
$244$	2188.53	+	2595.90i	0.574205	+	0.681088i
$245$	−2005.36	+	1157.80i	−0.522930	+	0.301914i
$246$		0			0
$247$	18.7312	−	32.4434i	0.00482525	−	0.00835758i
$248$	−1522.65	−	2616.19i	−0.389873	−	0.669873i
$249$		0			0
$250$	5972.78	−	7134.92i	1.51101	−	1.80501i
$251$			2144.46i			0.539271i	0.962963	+	0.269635i	$0.0869031\pi$
$251$			2144.46i			0.539271i	−0.962963	+	0.269635i	$0.913097\pi$
$252$		0			0
$253$			320.546i			0.0796543i
$254$	3010.38	+	2520.05i	0.743654	+	0.622528i
$255$		0			0
$256$	3113.09	−	2661.93i	0.760032	−	0.649886i
$257$	−1327.47	+	2299.24i	−0.322199	+	0.558065i	−0.980941	−	0.194303i	$-0.937755\pi$
$257$	−1327.47	+	2299.24i	−0.322199	+	0.558065i	0.658742	+	0.752369i	$0.271089\pi$
$258$		0			0
$259$	308.168	−	177.921i	0.0739330	−	0.0426852i
$260$	−1973.23	+	1663.57i	−0.470670	+	0.396808i
$261$		0			0
$262$	2048.10	+	5606.81i	0.482946	+	1.32210i
$263$	−863.016	−	1494.79i	−0.202342	−	0.350466i	0.746941	−	0.664891i	$-0.231522\pi$
$263$	−863.016	−	1494.79i	−0.202342	−	0.350466i	−0.949283	+	0.314424i	$0.898189\pi$
$264$		0			0
$265$	−3479.48	+	6026.64i	−0.806577	+	1.39703i
$266$	140.402	+	24.5883i	0.0323631	+	0.00566769i
$267$		0			0
$268$	−149.782	+	414.520i	−0.0341395	+	0.0944807i
$269$		−	7311.35i		−	1.65718i	−0.559857	−	0.828589i	$-0.689144\pi$
$269$		−	7311.35i		−	1.65718i	0.559857	−	0.828589i	$-0.310856\pi$
$270$		0			0
$271$	−474.085			−0.106268			−0.0531340	−	0.998587i	$-0.516921\pi$
$271$	−474.085			−0.106268			−0.0531340	+	0.998587i	$0.516921\pi$
$272$	−6007.73	+	2218.33i	−1.33924	+	0.494508i
$273$		0			0
$274$	−936.534	+	5347.70i	−0.206489	+	1.17908i
$275$	533.999	+	308.305i	0.117096	+	0.0676053i
$276$		0			0
$277$	2119.01	−	1223.41i	0.459636	−	0.265371i	−0.252255	−	0.967661i	$-0.581172\pi$
$277$	2119.01	−	1223.41i	0.459636	−	0.265371i	0.711891	+	0.702290i	$0.247839\pi$
$278$	761.137	+	2083.66i	0.164208	+	0.449532i
$279$		0			0
$280$	−8521.41	−	4880.28i	−1.81875	−	1.04162i
$281$	−4050.94	−	7016.43i	−0.859995	−	1.48956i	−0.871932	−	0.489626i	$-0.837133\pi$
$281$	−4050.94	−	7016.43i	−0.859995	−	1.48956i	0.0119373	−	0.999929i	$-0.496200\pi$
$282$		0			0
$283$	1237.85	+	714.675i	0.260010	+	0.150117i	0.624339	−	0.781153i	$-0.285368\pi$
$283$	1237.85	+	714.675i	0.260010	+	0.150117i	−0.364329	+	0.931270i	$0.618702\pi$
$284$	1402.68	+	7848.20i	0.293076	+	1.63981i
$285$		0			0
$286$	−74.0381	−	61.9787i	−0.0153076	−	0.0128143i
$287$	−2797.75			−0.575422
$288$		0			0
$289$	5100.15			1.03809
$290$	−8910.25	−	7458.95i	−1.80423	−	1.51036i
$291$		0			0
$292$	−1282.20	−	7174.09i	−0.256969	−	1.43778i
$293$	4394.07	+	2536.92i	0.876123	+	0.505830i	0.869378	−	0.494147i	$-0.164520\pi$
$293$	4394.07	+	2536.92i	0.876123	+	0.505830i	0.00674493	+	0.999977i	$0.497853\pi$
$294$		0			0
$295$	2241.43	+	3882.27i	0.442376	+	0.766218i
$296$	326.815	+	187.169i	0.0641747	+	0.0367534i
$297$		0			0
$298$	453.414	+	1241.25i	0.0881395	+	0.241288i
$299$	−2053.95	+	1185.85i	−0.397267	+	0.229362i
$300$		0			0
$301$	−2305.67	−	1331.18i	−0.441517	−	0.254910i
$302$	212.829	−	1215.28i	0.0405528	−	0.231560i
$303$		0			0
$304$	52.2561	+	141.521i	0.00985885	+	0.0266999i
$305$	8615.40			1.61743
$306$		0			0
$307$			1214.91i			0.225858i	0.993603	+	0.112929i	$0.0360233\pi$
$307$			1214.91i			0.225858i	−0.993603	+	0.112929i	$0.963977\pi$
$308$	124.848	−	345.515i	0.0230970	−	0.0639206i
$309$		0			0
$310$	−7565.71	−	1324.97i	−1.38614	−	0.242752i
$311$	3227.06	−	5589.44i	0.588392	−	1.01913i	−0.406051	−	0.913851i	$-0.633094\pi$
$311$	3227.06	−	5589.44i	0.588392	−	1.01913i	0.994443	−	0.105275i	$-0.0335723\pi$
$312$		0			0
$313$	−1651.53	−	2860.53i	−0.298243	−	0.516572i	0.677491	−	0.735531i	$-0.263067\pi$
$313$	−1651.53	−	2860.53i	−0.298243	−	0.516572i	−0.975734	+	0.218959i	$0.929734\pi$
$314$	−128.774	−	352.529i	−0.0231438	−	0.0633578i
$315$		0			0
$316$	−2005.33	+	1690.63i	−0.356989	+	0.300967i
$317$	385.013	−	222.288i	0.0682161	−	0.0393846i	−0.465504	−	0.885046i	$-0.654127\pi$
$317$	385.013	−	222.288i	0.0682161	−	0.0393846i	0.533720	+	0.845661i	$0.320794\pi$
$318$		0			0
$319$	217.364	−	376.486i	0.0381506	−	0.0660788i
$320$	−72.5126	−	10393.0i	−0.0126674	−	1.81558i
$321$		0			0
$322$	−6919.47	−	5792.42i	−1.19754	−	1.00248i
$323$		−	235.874i		−	0.0406328i
$324$		0			0
$325$			4562.24i			0.778670i
$326$	−6672.46	+	7970.73i	−1.13360	+	1.35417i
$327$		0			0
$328$	−1489.48	−	2559.20i	−0.250740	−	0.430817i
$329$	2985.89	−	5171.71i	0.500357	−	0.866644i
$330$		0			0
$331$	5662.03	−	3268.98i	0.940222	−	0.542837i	0.0501922	−	0.998740i	$-0.484017\pi$
$331$	5662.03	−	3268.98i	0.940222	−	0.542837i	0.890030	+	0.455902i	$0.150683\pi$
$332$	−881.073	−	1045.08i	−0.145648	−	0.172759i
$333$		0			0
$334$	−20.1190	+	7.34921i	−0.00329599	+	0.00120398i
$335$	559.185	+	968.536i	0.0911986	+	0.157961i
$336$		0			0
$337$	−1151.09	+	1993.74i	−0.186065	+	0.322273i	−0.943935	−	0.330132i	$-0.892907\pi$
$337$	−1151.09	+	1993.74i	−0.186065	+	0.322273i	0.757870	+	0.652405i	$0.226240\pi$
$338$	−948.705	+	5417.20i	−0.152671	+	0.871766i
$339$		0			0
$340$	−5522.35	+	15283.0i	−0.880857	+	2.43776i
$341$		−	287.352i		−	0.0456334i
$342$		0			0
$343$	−4894.30			−0.770459
$344$	−9.82976	−	2817.78i	−0.00154066	−	0.441640i
$345$		0			0
$346$	3886.50	+	680.636i	0.603872	+	0.105755i
$347$	7921.96	+	4573.75i	1.22557	+	0.707584i	0.966100	−	0.258167i	$-0.0831185\pi$
$347$	7921.96	+	4573.75i	1.22557	+	0.707584i	0.259471	+	0.965751i	$0.416452\pi$
$348$		0			0
$349$	−8355.48	+	4824.04i	−1.28154	+	0.739900i	−0.977131	−	0.212640i	$-0.931794\pi$
$349$	−8355.48	+	4824.04i	−1.28154	+	0.739900i	−0.304413	+	0.952540i	$0.598460\pi$
$350$	−16304.9	+	5955.96i	−2.49009	+	0.909599i
$351$		0			0
$352$	382.521	−	69.7444i	0.0579218	−	0.0105608i
$353$	2352.94	+	4075.41i	0.354771	+	0.614481i	0.987079	−	0.160236i	$-0.0512255\pi$
$353$	2352.94	+	4075.41i	0.354771	+	0.614481i	−0.632308	+	0.774717i	$0.717892\pi$
$354$		0			0
$355$	17519.5	+	10114.9i	2.61926	+	1.51223i
$356$	−1197.40	−	6699.65i	−0.178264	−	0.997418i
$357$		0			0
$358$	6733.08	−	8043.14i	0.994006	−	1.18741i
$359$	−7132.26			−1.04854			−0.524271	−	0.851552i	$-0.675662\pi$
$359$	−7132.26			−1.04854			−0.524271	+	0.851552i	$0.675662\pi$
$360$		0			0
$361$	6853.44			0.999190
$362$	3466.23	−	4140.66i	0.503262	−	0.601183i
$363$		0			0
$364$	2675.81	−	478.236i	0.385304	−	0.0688637i
$365$	−16014.6	−	9246.06i	−2.29656	−	1.32592i
$366$		0			0
$367$	−2335.97	−	4046.02i	−0.332253	−	0.575479i	0.650700	−	0.759335i	$-0.274475\pi$
$367$	−2335.97	−	4046.02i	−0.332253	−	0.575479i	−0.982953	+	0.183856i	$0.941142\pi$
$368$	1614.71	−	9413.28i	0.228729	−	1.33343i
$369$		0			0
$370$	897.622	−	327.890i	0.126122	−	0.0460708i
$371$	6347.26	−	3664.59i	0.888229	−	0.512819i
$372$		0			0
$373$	5258.37	+	3035.92i	0.729941	+	0.421432i	0.818401	−	0.574648i	$-0.194861\pi$
$373$	5258.37	+	3035.92i	0.729941	+	0.421432i	−0.0884596	+	0.996080i	$0.528194\pi$
$374$	−598.829	−	104.872i	−0.0827933	−	0.0144994i
$375$		0			0
$376$	6320.39	−	22.0486i	0.866886	−	0.00302412i
$377$	3216.52			0.439414
$378$		0			0
$379$		−	7792.48i		−	1.05613i	−0.849204	−	0.528064i	$-0.822918\pi$
$379$		−	7792.48i		−	1.05613i	0.849204	−	0.528064i	$-0.177082\pi$
$380$	360.014	+	130.087i	0.0486008	+	0.0175614i
$381$		0			0
$382$	516.088	−	2946.91i	0.0691239	−	0.394705i
$383$	−6946.85	+	12032.3i	−0.926809	+	1.60528i	−0.138182	+	0.990407i	$0.544126\pi$
$383$	−6946.85	+	12032.3i	−0.926809	+	1.60528i	−0.788626	+	0.614873i	$0.789207\pi$
$384$		0			0
$385$	−466.097	−	807.304i	−0.0617001	−	0.106868i
$386$	−3193.93	+	1166.70i	−0.421157	+	0.153844i
$387$		0			0
$388$	305.081	−	257.205i	0.0399178	−	0.0336536i
$389$	11195.6	−	6463.76i	1.45922	−	0.842483i	0.460250	−	0.887790i	$-0.347760\pi$
$389$	11195.6	−	6463.76i	1.45922	−	0.842483i	0.998973	+	0.0453069i	$0.0144266\pi$
$390$		0			0
$391$	−7466.44	+	12932.2i	−0.965713	+	1.67266i
$392$	1298.37	+	2230.84i	0.167290	+	0.287434i
$393$		0			0
$394$	2144.41	−	2561.66i	0.274198	−	0.327549i
$395$			6655.38i			0.847768i
$396$		0			0
$397$		−	4139.86i		−	0.523359i	−0.965155	−	0.261680i	$-0.915724\pi$
$397$		−	4139.86i		−	0.523359i	0.965155	−	0.261680i	$-0.0842764\pi$
$398$	1663.33	+	1392.41i	0.209486	+	0.175365i
$399$		0			0
$400$	−14128.6	−	11743.7i	−1.76607	−	1.46797i
$401$	−1498.25	+	2595.05i	−0.186581	+	0.323169i	−0.944108	−	0.329635i	$-0.893074\pi$
$401$	−1498.25	+	2595.05i	−0.186581	+	0.323169i	0.757527	+	0.652804i	$0.226407\pi$
$402$		0			0
$403$	1841.25	−	1063.05i	0.227591	−	0.131400i
$404$	5072.07	+	6016.19i	0.624616	+	0.740883i
$405$		0			0
$406$	4199.13	+	11495.4i	0.513299	+	1.40519i
$407$	17.8759	+	30.9619i	0.00217708	+	0.00377082i
$408$		0			0
$409$	−709.204	+	1228.38i	−0.0857405	+	0.148507i	−0.905707	−	0.423905i	$-0.860659\pi$
$409$	−709.204	+	1228.38i	−0.0857405	+	0.148507i	0.819966	+	0.572412i	$0.193992\pi$
$410$	−7400.89	−	1296.10i	−0.891472	−	0.156122i
$411$		0			0
$412$	−4077.34	−	1473.30i	−0.487564	−	0.176176i
$413$		−	4721.34i		−	0.562523i
$414$		0			0
$415$	−3468.45			−0.410264
$416$	1862.02	+	2193.05i	0.219455	+	0.258469i
$417$		0			0
$418$	−2.47041	+	14.1063i	−0.000289071	+	0.00165062i
$419$	3590.43	+	2072.93i	0.418625	+	0.241693i	0.694489	−	0.719504i	$-0.255631\pi$
$419$	3590.43	+	2072.93i	0.418625	+	0.241693i	−0.275864	+	0.961197i	$0.588964\pi$
$420$		0			0
$421$	3018.25	−	1742.59i	0.349408	−	0.201731i	−0.315017	−	0.949086i	$-0.602010\pi$
$421$	3018.25	−	1742.59i	0.349408	−	0.201731i	0.664424	+	0.747355i	$0.268677\pi$
$422$	3552.57	+	9725.41i	0.409802	+	1.12186i
$423$		0			0
$424$	6731.31	+	3855.08i	0.770994	+	0.441555i
$425$	14362.6	+	24876.7i	1.63927	+	2.83929i
$426$		0			0
$427$	−7858.08	−	4536.87i	−0.890584	−	0.514179i
$428$	13040.9	−	2330.75i	1.47279	−	0.263226i
$429$		0			0
$430$	−5482.49	−	4589.51i	−0.614859	−	0.514711i
$431$	13182.0			1.47321			0.736606	−	0.676322i	$-0.236427\pi$
$431$	13182.0			1.47321			0.736606	+	0.676322i	$0.236427\pi$
$432$		0			0
$433$	−710.264			−0.0788293			−0.0394147	−	0.999223i	$-0.512549\pi$
$433$	−710.264			−0.0788293			−0.0394147	+	0.999223i	$0.512549\pi$
$434$	6202.93	+	5192.60i	0.686061	+	0.574315i
$435$		0			0
$436$	3077.94	−	550.107i	0.338088	−	0.0604251i
$437$	304.638	+	175.883i	0.0333473	+	0.0192531i
$438$		0			0
$439$	8935.15	+	15476.1i	0.971416	+	1.68254i	0.691289	+	0.722578i	$0.257043\pi$
$439$	8935.15	+	15476.1i	0.971416	+	1.68254i	0.280126	+	0.959963i	$0.409624\pi$
$440$	490.325	−	856.152i	0.0531258	−	0.0927624i
$441$		0			0
$442$	−1543.36	−	4225.06i	−0.166086	−	0.454673i
$443$	−7352.63	+	4245.04i	−0.788564	+	0.455278i	−0.839457	−	0.543426i	$-0.817127\pi$
$443$	−7352.63	+	4245.04i	−0.788564	+	0.455278i	0.0508927	+	0.998704i	$0.483793\pi$
$444$		0			0
$445$	−14955.6	−	8634.60i	−1.59317	−	0.919818i
$446$	485.693	−	2773.35i	0.0515655	−	0.294444i
$447$		0			0
$448$	−5406.82	+	9517.62i	−0.570197	+	1.00372i
$449$	−7525.14			−0.790942			−0.395471	−	0.918478i	$-0.629419\pi$
$449$	−7525.14			−0.790942			−0.395471	+	0.918478i	$0.629419\pi$
$450$		0			0
$451$		−	281.092i		−	0.0293484i
$452$	−12851.8	−	4643.84i	−1.33738	−	0.483247i
$453$		0			0
$454$	−237.023	−	41.5094i	−0.0245023	−	0.00429105i
$455$	3448.62	−	5973.18i	0.355327	−	0.615444i
$456$		0			0
$457$	−7076.61	−	12257.0i	−0.724354	−	1.25462i	−0.959239	−	0.282595i	$-0.908805\pi$
$457$	−7076.61	−	12257.0i	−0.724354	−	1.25462i	0.234886	−	0.972023i	$-0.424528\pi$
$458$	5755.56	+	15756.2i	0.587205	+	1.60751i
$459$		0			0
$460$	−15620.6	−	18528.3i	−1.58329	−	1.87801i
$461$	1645.56	−	950.065i	0.166250	−	0.0959847i	−0.414566	−	0.910019i	$-0.636067\pi$
$461$	1645.56	−	950.065i	0.166250	−	0.0959847i	0.580817	+	0.814034i	$0.302733\pi$
$462$		0			0
$463$	6299.69	−	10911.4i	0.632335	−	1.09524i	−0.354738	−	0.934966i	$-0.615430\pi$
$463$	6299.69	−	10911.4i	0.632335	−	1.09524i	0.987073	−	0.160271i	$-0.0512368\pi$
$464$	−8279.69	+	9961.08i	−0.828395	+	0.996620i
$465$		0			0
$466$	10150.9	+	8497.48i	1.00908	+	0.844718i
$467$		−	11691.5i		−	1.15849i	−0.815152	−	0.579247i	$-0.803347\pi$
$467$		−	11691.5i		−	1.15849i	0.815152	−	0.579247i	$-0.196653\pi$
$468$		0			0
$469$		−	1177.87i		−	0.115968i
$470$	10294.5	−	12297.5i	1.01031	−	1.20689i
$471$		0			0
$472$	4318.77	−	2513.57i	0.421160	−	0.245120i
$473$	133.745	−	231.652i	0.0130012	−	0.0225188i
$474$		0			0
$475$	586.007	−	338.332i	0.0566060	−	0.0326815i
$476$	13085.0	−	11031.5i	1.25997	−	1.06225i
$477$		0			0
$478$	9738.19	−	3557.24i	0.931829	−	0.340386i
$479$	645.134	+	1117.41i	0.0615385	+	0.106588i	0.895153	−	0.445758i	$-0.147066\pi$
$479$	645.134	+	1117.41i	0.0615385	+	0.106588i	−0.833615	+	0.552346i	$0.813733\pi$
$480$		0			0
$481$	−132.262	+	229.085i	−0.0125377	+	0.0217159i
$482$	−1011.93	+	5778.20i	−0.0956264	+	0.546037i
$483$		0			0
$484$	−9979.58	−	3606.01i	−0.937225	−	0.338656i
$485$		−	1012.52i		−	0.0947959i
$486$		0			0
$487$	−9535.19			−0.887230			−0.443615	−	0.896218i	$-0.646304\pi$
$487$	−9535.19			−0.887230			−0.443615	+	0.896218i	$0.646304\pi$
$488$	−33.5014	−	9603.42i	−0.00310766	−	0.890833i
$489$		0			0
$490$	6451.30	+	1129.81i	0.594776	+	0.104162i
$491$	7737.89	+	4467.47i	0.711214	+	0.410620i	0.811510	−	0.584338i	$-0.198646\pi$
$491$	7737.89	+	4467.47i	0.711214	+	0.410620i	−0.100296	+	0.994958i	$0.531979\pi$
$492$		0			0
$493$	17538.9	−	10126.1i	1.60225	−	0.925061i
$494$	−99.5273	+	36.3561i	−0.00906466	+	0.00331121i
$495$		0			0
$496$	−1447.50	+	8438.50i	−0.131037	+	0.763911i
$497$	−10653.0	−	18451.5i	−0.961471	−	1.66532i
$498$		0			0
$499$	16966.8	+	9795.81i	1.52212	+	0.878799i	0.999658	+	0.0261381i	$0.00832097\pi$
$499$	16966.8	+	9795.81i	1.52212	+	0.878799i	0.522465	+	0.852660i	$0.325012\pi$
$500$	−25907.7	+	4630.38i	−2.31726	+	0.414154i
$501$		0			0
$502$	3893.38	−	4650.93i	0.346156	−	0.413508i
$503$	10902.0			0.966396			0.483198	−	0.875511i	$-0.339475\pi$
$503$	10902.0			0.966396			0.483198	+	0.875511i	$0.339475\pi$
$504$		0			0
$505$	19966.8			1.75943
$506$	581.969	−	695.204i	0.0511298	−	0.0610783i
$507$		0			0
$508$	−1953.66	−	10931.0i	−0.170629	−	0.954698i
$509$	−1301.27	−	751.291i	−0.113316	−	0.0654232i	0.442271	−	0.896882i	$-0.354173\pi$
$509$	−1301.27	−	751.291i	−0.113316	−	0.0654232i	−0.555587	+	0.831458i	$0.687506\pi$
$510$		0			0
$511$	9737.94	+	16866.6i	0.843016	+	1.46015i
$512$	−11584.6	+	121.242i	−0.999945	+	0.0104652i
$513$		0			0
$514$	7053.43	−	2576.53i	0.605279	−	0.221101i
$515$	−9526.82	+	5500.31i	−0.815149	+	0.470626i
$516$		0			0
$517$	519.606	+	299.995i	0.0442016	+	0.0255198i
$518$	−991.385	−	173.620i	−0.0840907	−	0.0147267i
$519$		0			0
$520$	7299.87	−	25.4655i	0.615616	−	0.00214757i
$521$	−6339.22			−0.533064			−0.266532	−	0.963826i	$-0.585878\pi$
$521$	−6339.22			−0.533064			−0.266532	+	0.963826i	$0.585878\pi$
$522$		0			0
$523$			15909.9i			1.33019i	0.746758	+	0.665096i	$0.231610\pi$
$523$			15909.9i			1.33019i	−0.746758	+	0.665096i	$0.768390\pi$
$524$	5737.54	−	15878.6i	0.478331	−	1.32377i
$525$		0			0
$526$	−842.152	+	4808.77i	−0.0698091	+	0.398617i
$527$	6693.26	−	11593.1i	0.553250	−	0.958258i
$528$		0			0
$529$	−5051.39	−	8749.27i	−0.415172	−	0.719098i
$530$	18488.1	−	6753.46i	1.51523	−	0.553494i
$531$		0			0
$532$	−259.864	−	308.235i	−0.0211777	−	0.0251197i
$533$	1801.14	−	1039.89i	0.146372	−	0.0845077i
$534$		0			0
$535$	16807.3	−	29111.1i	1.35821	−	2.35249i
$536$	1077.43	−	627.078i	0.0868247	−	0.0505329i
$537$		0			0
$538$	−13274.2	+	15857.0i	−1.06374	+	1.27071i
$539$			245.026i			0.0195808i
$540$		0			0
$541$			974.163i			0.0774169i	0.999251	+	0.0387085i	$0.0123244\pi$
$541$			974.163i			0.0774169i	−0.999251	+	0.0387085i	$0.987676\pi$
$542$	1028.20	+	860.729i	0.0814854	+	0.0682131i
$543$		0			0
$544$	17057.2	+	6096.23i	1.34434	+	0.480466i
$545$	3966.88	−	6870.84i	0.311785	−	0.540027i
$546$		0			0
$547$	−19129.5	+	11044.4i	−1.49528	+	0.863302i	−0.999985	−	0.00542137i	$-0.998274\pi$
$547$	−19129.5	+	11044.4i	−1.49528	+	0.863302i	−0.495298	+	0.868723i	$0.664941\pi$
$548$	11740.2	−	9897.84i	0.915179	−	0.771560i
$549$		0			0
$550$	−598.400	−	1638.16i	−0.0463925	−	0.127003i
$551$	−238.534	−	413.153i	−0.0184426	−	0.0319436i
$552$		0			0
$553$	3504.72	−	6070.35i	0.269504	−	0.466795i
$554$	−6816.92	−	1193.84i	−0.522786	−	0.0915545i
$555$		0			0
$556$	2132.25	−	5900.97i	0.162639	−	0.450102i
$557$			2065.57i			0.157130i	0.996909	+	0.0785648i	$0.0250337\pi$
$557$			2065.57i			0.157130i	−0.996909	+	0.0785648i	$0.974966\pi$
$558$		0			0
$559$	1979.13			0.149747
$560$	9620.91	+	26055.5i	0.725996	+	1.96615i
$561$		0			0
$562$	−3953.00	+	22572.0i	−0.296703	+	1.69421i
$563$	11759.3	+	6789.26i	0.880280	+	0.508230i	0.870751	−	0.491725i	$-0.163633\pi$
$563$	11759.3	+	6789.26i	0.880280	+	0.508230i	0.00952895	+	0.999955i	$0.496967\pi$
$564$		0			0
$565$	−30028.5	+	17336.9i	−2.23594	+	1.29092i
$566$	−1387.14	−	3797.39i	−0.103014	−	0.282008i
$567$		0			0
$568$	11206.7	−	19567.9i	0.827858	−	1.44551i
$569$	1428.57	+	2474.35i	0.105252	+	0.182303i	0.913841	−	0.406071i	$-0.133102\pi$
$569$	1428.57	+	2474.35i	0.105252	+	0.182303i	−0.808589	+	0.588374i	$0.799768\pi$
$570$		0			0
$571$	−15562.8	−	8985.21i	−1.14060	−	0.658528i	−0.194024	−	0.980997i	$-0.562154\pi$
$571$	−15562.8	−	8985.21i	−1.14060	−	0.658528i	−0.946580	+	0.322469i	$0.895487\pi$
$572$	48.0488	+	268.841i	0.00351227	+	0.0196517i
$573$		0			0
$574$	6067.80	+	5079.48i	0.441228	+	0.369361i
$575$	−42838.6			−3.10695
$576$		0			0
$577$	−22787.6			−1.64412			−0.822062	−	0.569398i	$-0.807176\pi$
$577$	−22787.6			−1.64412			−0.822062	+	0.569398i	$0.807176\pi$
$578$	−11061.3	−	9259.61i	−0.796000	−	0.666348i
$579$		0			0
$580$	5782.52	+	32354.1i	0.413976	+	2.31626i
$581$	3163.56	+	1826.48i	0.225898	+	0.130422i
$582$		0			0
$583$	368.184	+	637.714i	0.0261555	+	0.0453026i
$584$	−10244.1	+	17887.2i	−0.725865	+	1.26742i
$585$		0			0
$586$	−4923.99	−	13479.8i	−0.347113	−	0.950246i
$587$	−7735.67	+	4466.19i	−0.543927	+	0.314037i	−0.746669	−	0.665196i	$-0.768348\pi$
$587$	−7735.67	+	4466.19i	−0.543927	+	0.314037i	0.202742	+	0.979232i	$0.435015\pi$
$588$		0			0
$589$	−273.091	−	157.669i	−0.0191045	−	0.0110300i
$590$	2187.24	−	12489.4i	0.152622	−	0.871489i
$591$		0			0
$592$	−368.983	−	999.286i	−0.0256168	−	0.0693757i
$593$	−10639.1			−0.736753			−0.368377	−	0.929677i	$-0.620086\pi$
$593$	−10639.1			−0.736753			−0.368377	+	0.929677i	$0.620086\pi$
$594$		0			0
$595$		−	43427.0i		−	2.99216i
$596$	1270.19	−	3515.24i	0.0872973	−	0.241594i
$597$		0			0
$598$	6607.60	+	1157.18i	0.451848	+	0.0791313i
$599$	−1792.27	+	3104.30i	−0.122254	+	0.211750i	−0.920656	−	0.390374i	$-0.872346\pi$
$599$	−1792.27	+	3104.30i	−0.122254	+	0.211750i	0.798402	+	0.602125i	$0.205679\pi$
$600$		0			0
$601$	11481.4	+	19886.4i	0.779261	+	1.34972i	0.932368	+	0.361510i	$0.117739\pi$
$601$	11481.4	+	19886.4i	0.779261	+	1.34972i	−0.153107	+	0.988210i	$0.548928\pi$
$602$	2583.74	+	7073.15i	0.174926	+	0.478871i
$603$		0			0
$604$	−2667.99	+	2249.30i	−0.179733	+	0.151528i
$605$	−23317.5	+	13462.4i	−1.56693	+	0.904667i
$606$		0			0
$607$	−2226.59	+	3856.57i	−0.148887	+	0.257880i	−0.930816	−	0.365487i	$-0.880902\pi$
$607$	−2226.59	+	3856.57i	−0.148887	+	0.257880i	0.781929	+	0.623367i	$0.214236\pi$
$608$	143.605	−	401.806i	0.00957889	−	0.0268016i
$609$		0			0
$610$	−18685.2	−	15641.8i	−1.24023	−	1.03822i
$611$			4439.27i			0.293934i
$612$		0			0
$613$			16761.2i			1.10437i	0.833722	+	0.552185i	$0.186206\pi$
$613$			16761.2i			1.10437i	−0.833722	+	0.552185i	$0.813794\pi$
$614$	2205.73	−	2634.91i	0.144977	−	0.173186i
$615$		0			0
$616$	−898.074	+	522.689i	−0.0587410	+	0.0341879i
$617$	12004.5	−	20792.4i	0.783278	−	1.35668i	−0.146744	−	0.989174i	$-0.546879\pi$
$617$	12004.5	−	20792.4i	0.783278	−	1.35668i	0.930022	−	0.367503i	$-0.119787\pi$
$618$		0			0
$619$	12708.3	−	7337.15i	0.825187	−	0.476422i	−0.0270152	−	0.999635i	$-0.508600\pi$
$619$	12708.3	−	7337.15i	0.825187	−	0.476422i	0.852202	+	0.523213i	$0.175267\pi$
$620$	14003.1	+	16609.6i	0.907058	+	1.07590i
$621$		0			0
$622$	−17146.8	+	6263.53i	−1.10535	+	0.403770i
$623$	9093.95	+	15751.2i	0.584818	+	1.01293i
$624$		0			0
$625$	−15448.7	+	26758.0i	−0.988718	+	1.71251i
$626$	−1611.60	+	9202.41i	−0.102895	+	0.587544i
$627$		0			0
$628$	−360.748	+	998.366i	−0.0229227	+	0.0634381i
$629$			1665.52i			0.105578i
$630$		0			0
$631$	−19515.2			−1.23120			−0.615599	−	0.788059i	$-0.711086\pi$
$631$	−19515.2			−1.23120			−0.615599	+	0.788059i	$0.711086\pi$
$632$	7418.62	−	25.8797i	0.466925	−	0.00162886i
$633$		0			0
$634$	−1238.60	−	216.914i	−0.0775884	−	0.0135879i
$635$	−24401.3	−	14088.1i	−1.52494	−	0.880422i
$636$		0			0
$637$	−1570.04	+	906.465i	−0.0976568	+	0.0563822i
$638$	−1154.95	+	421.890i	−0.0716693	+	0.0261799i
$639$		0			0
$640$	−18711.8	+	22672.2i	−1.15570	+	1.40031i
$641$	−8452.58	−	14640.3i	−0.520837	−	0.902117i	−0.999706	−	0.0242303i	$-0.992286\pi$
$641$	−8452.58	−	14640.3i	−0.520837	−	0.902117i	0.478869	−	0.877886i	$-0.341047\pi$
$642$		0			0
$643$	−3132.49	−	1808.54i	−0.192120	−	0.110921i	0.400854	−	0.916142i	$-0.368713\pi$
$643$	−3132.49	−	1808.54i	−0.192120	−	0.110921i	−0.592975	+	0.805221i	$0.702047\pi$
$644$	4490.56	+	25125.4i	0.274771	+	1.53739i
$645$		0			0
$646$	−428.243	+	511.567i	−0.0260820	+	0.0311569i
$647$	−16575.8			−1.00721			−0.503604	−	0.863935i	$-0.667993\pi$
$647$	−16575.8			−1.00721			−0.503604	+	0.863935i	$0.667993\pi$
$648$		0			0
$649$	474.357			0.0286905
$650$	8283.01	−	9894.65i	0.499825	−	0.597077i
$651$		0			0
$652$	28942.6	−	5172.80i	1.73847	−	0.310709i
$653$	11999.5	+	6927.91i	0.719106	+	0.415176i	0.814424	−	0.580271i	$-0.197053\pi$
$653$	11999.5	+	6927.91i	0.719106	+	0.415176i	−0.0953176	+	0.995447i	$0.530387\pi$
$654$		0			0
$655$	−21420.1	−	37100.7i	−1.27779	−	2.21319i
$656$	−1415.96	+	8254.66i	−0.0842745	+	0.491296i
$657$		0			0
$658$	−15865.4	+	5795.43i	−0.939965	+	0.343358i
$659$	−421.594	+	243.407i	−0.0249210	+	0.0143882i	−0.512409	−	0.858742i	$-0.671247\pi$
$659$	−421.594	+	243.407i	−0.0249210	+	0.0143882i	0.487488	+	0.873130i	$0.337913\pi$
$660$		0			0
$661$	10247.6	+	5916.48i	0.603006	+	0.348146i	0.770223	−	0.637774i	$-0.220145\pi$
$661$	10247.6	+	5916.48i	0.603006	+	0.348146i	−0.167217	+	0.985920i	$0.553478\pi$
$662$	−18214.9	−	3189.95i	−1.06940	−	0.187282i
$663$		0			0
$664$	13.4872	+	3866.21i	0.000788262	+	0.225961i
$665$	−1022.99			−0.0596536
$666$		0			0
$667$			30202.5i			1.75329i
$668$	56.9772	+	20.5881i	0.00330017	+	0.00119248i
$669$		0			0
$670$	545.666	−	3115.81i	0.0314640	−	0.179663i
$671$	455.822	−	789.508i	0.0262248	−	0.0454227i
$672$		0			0
$673$	242.006	+	419.167i	0.0138613	+	0.0240085i	0.872873	−	0.487948i	$-0.162254\pi$
$673$	242.006	+	419.167i	0.0138613	+	0.0240085i	−0.859012	+	0.511956i	$0.828921\pi$
$674$	6116.25	−	2234.19i	0.349539	−	0.127682i
$675$		0			0
$676$	11892.8	−	10026.5i	0.676650	−	0.570464i
$677$	−13099.4	+	7562.92i	−0.743648	+	0.429345i	−0.823394	−	0.567470i	$-0.807922\pi$
$677$	−13099.4	+	7562.92i	−0.743648	+	0.429345i	0.0797464	+	0.996815i	$0.474589\pi$
$678$		0			0
$679$	−533.191	+	923.514i	−0.0301355	+	0.0521962i
$680$	39724.2	−	23119.9i	2.24022	−	1.30383i
$681$		0			0
$682$	−521.704	+	623.213i	−0.0292919	+	0.0349913i
$683$		−	23035.8i		−	1.29054i	−0.763954	−	0.645271i	$-0.776744\pi$
$683$		−	23035.8i		−	1.29054i	0.763954	−	0.645271i	$-0.223256\pi$
$684$		0			0
$685$		−	38964.1i		−	2.17334i
$686$	10614.8	+	8885.89i	0.590781	+	0.494555i
$687$		0			0
$688$	−5094.51	+	6129.08i	−0.282306	+	0.339635i
$689$	−2724.17	+	4718.39i	−0.150628	+	0.260895i
$690$		0			0
$691$	−25952.9	+	14983.9i	−1.42879	+	0.824913i	−0.997025	−	0.0770728i	$-0.975443\pi$
$691$	−25952.9	+	14983.9i	−1.42879	+	0.824913i	−0.431766	+	0.901986i	$0.642109\pi$
$692$	−7193.36	−	8532.34i	−0.395160	−	0.468715i
$693$		0			0
$694$	−8877.36	−	24302.4i	−0.485562	−	1.32926i
$695$	−7960.37	−	13787.8i	−0.434466	−	0.752517i
$696$		0			0
$697$	6547.44	−	11340.5i	0.355814	−	0.616287i
$698$	26879.8	+	4707.41i	1.45762	+	0.255270i
$699$		0			0
$700$	46175.6	+	16685.0i	2.49325	+	0.900906i
$701$			18538.6i			0.998851i	0.866357	+	0.499425i	$0.166456\pi$
$701$			18538.6i			0.998851i	−0.866357	+	0.499425i	$0.833544\pi$
$702$		0			0
$703$	39.2337			0.00210488
$704$	−956.243	−	543.227i	−0.0511928	−	0.0290819i
$705$		0			0
$706$	2296.05	−	13110.7i	0.122398	−	0.698905i
$707$	−18211.7	−	10514.5i	−0.968771	−	0.559320i
$708$		0			0
$709$	22910.6	−	13227.4i	1.21358	−	0.700658i	0.250039	−	0.968236i	$-0.419556\pi$
$709$	22910.6	−	13227.4i	1.21358	−	0.700658i	0.963536	+	0.267577i	$0.0862231\pi$
$710$	−19632.3	−	53744.8i	−1.03773	−	2.84086i
$711$		0			0
$712$	−9566.66	+	16704.2i	−0.503547	+	0.879239i
$713$	9981.84	+	17289.0i	0.524295	+	0.908106i
$714$		0			0
$715$	600.130	+	346.485i	0.0313896	+	0.0181228i
$716$	−29205.6	+	5219.79i	−1.52439	+	0.272448i
$717$		0			0
$718$	15468.5	+	12949.0i	0.804012	+	0.673055i
$719$	23631.1			1.22572			0.612859	−	0.790192i	$-0.290019\pi$
$719$	23631.1			1.22572			0.612859	+	0.790192i	$0.290019\pi$
$720$		0			0
$721$	11585.8			0.598446
$722$	−14863.8	−	12442.8i	−0.766170	−	0.641376i
$723$		0			0
$724$	−15035.2	+	2687.18i	−0.771794	+	0.137940i
$725$	50314.6	+	29049.1i	2.57743	+	1.48808i
$726$		0			0
$727$	−6645.21	−	11509.8i	−0.339006	−	0.587175i	0.645240	−	0.763980i	$-0.276757\pi$
$727$	−6645.21	−	11509.8i	−0.339006	−	0.587175i	−0.984246	+	0.176805i	$0.943424\pi$
$728$	−6671.60	−	3820.88i	−0.339651	−	0.194521i
$729$		0			0
$730$	17946.0	+	49128.5i	0.909880	+	2.49086i
$731$	10791.7	−	6230.59i	0.546027	−	0.315249i
$732$		0			0
$733$	1259.88	+	727.394i	0.0634855	+	0.0366534i	0.531407	−	0.847117i	$-0.321664\pi$
$733$	1259.88	+	727.394i	0.0634855	+	0.0366534i	−0.467921	+	0.883770i	$0.654997\pi$
$734$	−2279.50	+	13016.2i	−0.114629	+	0.654544i
$735$		0			0
$736$	−20592.3	+	17484.0i	−1.03131	+	0.875639i
$737$	118.341			0.00591472
$738$		0			0
$739$		−	15723.2i		−	0.782662i	−0.920250	−	0.391331i	$-0.872015\pi$
$739$		−	15723.2i		−	0.782662i	0.920250	−	0.391331i	$-0.127985\pi$
$740$	−2542.08	−	918.551i	−0.126282	−	0.0456306i
$741$		0			0
$742$	−20419.3	−	3575.99i	−1.01026	−	0.176926i
$743$	−8319.62	+	14410.0i	−0.410790	+	0.711510i	−0.994976	−	0.100110i	$-0.968080\pi$
$743$	−8319.62	+	14410.0i	−0.410790	+	0.711510i	0.584186	+	0.811620i	$0.301414\pi$
$744$		0			0
$745$	−4742.04	−	8213.46i	−0.233201	−	0.403917i
$746$	−5892.53	−	16131.2i	−0.289197	−	0.791697i
$747$		0			0
$748$	1108.35	+	1314.66i	0.0541781	+	0.0642628i
$749$	−30659.8	+	17701.4i	−1.49570	+	0.863546i
$750$		0			0
$751$	3120.48	−	5404.83i	0.151622	−	0.262617i	−0.780202	−	0.625528i	$-0.784884\pi$
$751$	3120.48	−	5404.83i	0.151622	−	0.262617i	0.931824	+	0.362911i	$0.118217\pi$
$752$	−13747.8	−	11427.2i	−0.666662	−	0.554132i
$753$		0			0
$754$	−6976.03	−	5839.77i	−0.336939	−	0.282058i
$755$			8854.65i			0.426826i
$756$		0			0
$757$			37281.0i			1.78996i	0.446106	+	0.894980i	$0.352811\pi$
$757$			37281.0i			1.78996i	−0.446106	+	0.894980i	$0.647189\pi$
$758$	−14147.7	+	16900.4i	−0.677925	+	0.809830i
$759$		0			0
$760$	−544.622	−	935.759i	−0.0259941	−	0.0446626i
$761$	−13119.1	+	22722.9i	−0.624924	+	1.08240i	0.363632	+	0.931543i	$0.381537\pi$
$761$	−13119.1	+	22722.9i	−0.624924	+	1.08240i	−0.988556	+	0.150857i	$0.951797\pi$
$762$		0			0
$763$	−7236.36	+	4177.92i	−0.343347	+	0.198232i
$764$	−6469.59	+	5454.32i	−0.306363	+	0.258286i
$765$		0			0
$766$	36911.8	−	13483.4i	1.74109	−	0.635999i
$767$	1754.86	+	3039.51i	0.0826134	+	0.143091i
$768$		0			0
$769$	4452.51	−	7711.98i	0.208793	−	0.361640i	−0.742542	−	0.669800i	$-0.766380\pi$
$769$	4452.51	−	7711.98i	0.208793	−	0.361640i	0.951335	+	0.308160i	$0.0997132\pi$
$770$	−454.829	+	2597.12i	−0.0212869	+	0.121550i
$771$		0			0
$772$	9045.26	+	3268.40i	0.421692	+	0.152374i
$773$		−	12743.6i		−	0.592954i	−0.955040	−	0.296477i	$-0.904188\pi$
$773$		−	12743.6i		−	0.592954i	0.955040	−	0.296477i	$-0.0958119\pi$
$774$		0			0
$775$	38402.6			1.77995
$776$	−1128.63	+	3.93722i	−0.0522108	+	0.000182136i
$777$		0			0
$778$	−36016.4	−	6307.49i	−1.65971	−	0.290661i
$779$	−267.142	−	154.234i	−0.0122867	−	0.00709374i
$780$		0			0
$781$	1853.83	−	1070.31i	0.0849365	−	0.0490381i
$782$	39672.5	−	14491.9i	1.81418	−	0.662697i
$783$		0			0
$784$	1234.29	−	7195.53i	0.0562266	−	0.327785i
$785$	1346.79	+	2332.71i	0.0612344	+	0.106061i
$786$		0			0
$787$	−18346.9	−	10592.6i	−0.831001	−	0.479779i	0.0231941	−	0.999731i	$-0.492616\pi$
$787$	−18346.9	−	10592.6i	−0.831001	−	0.479779i	−0.854195	+	0.519952i	$0.825950\pi$
$788$	−9301.67	+	1662.45i	−0.420505	+	0.0751552i
$789$		0			0
$790$	12083.2	−	14434.3i	0.544179	−	0.650061i
$791$	36518.5			1.64153
$792$		0			0
$793$	6745.19			0.302054
$794$	−7516.15	+	8978.58i	−0.335942	+	0.401307i
$795$		0			0
$796$	−1079.46	−	6039.75i	−0.0480659	−	0.268936i
$797$	−13475.6	−	7780.16i	−0.598910	−	0.345781i	0.169703	−	0.985495i	$-0.445719\pi$
$797$	−13475.6	−	7780.16i	−0.598910	−	0.345781i	−0.768613	+	0.639715i	$0.779053\pi$
$798$		0			0
$799$	13975.5	+	24206.2i	0.618795	+	1.07178i
$800$	9320.84	+	51121.2i	0.411927	+	2.25926i
$801$		0			0
$802$	7960.89	−	2908.02i	0.350510	−	0.128037i
$803$	−1694.60	+	978.378i	−0.0744722	+	0.0429965i
$804$		0			0
$805$	56087.1	+	32381.9i	2.45567	+	1.41778i
$806$	−5923.36	−	1037.35i	−0.258860	−	0.0453338i
$807$		0			0
$808$	−77.6419	−	22256.6i	−0.00338049	−	0.969042i
$809$	9492.69			0.412540			0.206270	−	0.978495i	$-0.433867\pi$
$809$	9492.69			0.412540			0.206270	+	0.978495i	$0.433867\pi$
$810$		0			0
$811$		−	17607.1i		−	0.762353i	−0.924502	−	0.381177i	$-0.875519\pi$
$811$		−	17607.1i		−	0.762353i	0.924502	−	0.381177i	$-0.124481\pi$
$812$	11763.4	−	32555.2i	0.508394	−	1.40697i
$813$		0			0
$814$	17.4437	−	99.6052i	0.000751107	−	0.00428890i
$815$	37301.6	−	64608.3i	1.60321	−	2.77685i
$816$		0			0
$817$	−146.771	−	254.214i	−0.00628501	−	0.0108860i
$818$	3768.32	−	1376.52i	0.161071	−	0.0588373i
$819$		0			0
$820$	13698.0	+	16247.7i	0.583359	+	0.691946i
$821$	39628.7	−	22879.7i	1.68460	−	0.972601i	0.726058	−	0.687633i	$-0.241350\pi$
$821$	39628.7	−	22879.7i	1.68460	−	0.972601i	0.958537	−	0.284968i	$-0.0919830\pi$
$822$		0			0
$823$	−9281.64	+	16076.3i	−0.393120	+	0.680903i	−0.992859	−	0.119292i	$-0.961938\pi$
$823$	−9281.64	+	16076.3i	−0.393120	+	0.680903i	0.599739	+	0.800195i	$0.295271\pi$
$824$	6168.13	+	10598.0i	0.260773	+	0.448055i
$825$		0			0
$826$	−8571.86	+	10239.7i	−0.361081	+	0.431338i
$827$		−	4839.95i		−	0.203509i	−0.994810	−	0.101754i	$-0.967554\pi$
$827$		−	4839.95i		−	0.203509i	0.994810	−	0.101754i	$-0.0324455\pi$
$828$		0			0
$829$		−	33204.3i		−	1.39111i	−0.718472	−	0.695556i	$-0.755158\pi$
$829$		−	33204.3i		−	1.39111i	0.718472	−	0.695556i	$-0.244842\pi$
$830$	7522.42	+	6297.17i	0.314587	+	0.263347i
$831$		0			0
$832$	−56.7717	−	8136.92i	−0.00236563	−	0.339059i
$833$	−5707.36	+	9885.44i	−0.237393	+	0.411177i
$834$		0			0
$835$	133.129	−	76.8618i	0.00551749	−	0.00318553i
$836$	30.9686	−	26.1087i	0.00128119	−	0.00108013i
$837$		0			0
$838$	−4023.44	−	11014.4i	−0.165856	−	0.454042i
$839$	7993.06	+	13844.4i	0.328905	+	0.569680i	0.982295	−	0.187342i	$-0.0599871\pi$
$839$	7993.06	+	13844.4i	0.328905	+	0.569680i	−0.653390	+	0.757021i	$0.726654\pi$
$840$		0			0
$841$	8286.02	−	14351.8i	0.339744	−	0.588454i
$842$	−9709.80	−	1700.46i	−0.397413	−	0.0695983i
$843$		0			0
$844$	9952.17	−	27542.5i	0.405886	−	1.12328i
$845$		−	39470.4i		−	1.60689i
$846$		0			0
$847$	28357.1			1.15037
$848$	−7599.84	−	20582.0i	−0.307759	−	0.833478i
$849$		0			0
$850$	14015.4	−	80029.1i	0.565557	−	3.22938i
$851$	−2151.06	−	1241.92i	−0.0866481	−	0.0500263i
$852$		0			0
$853$	25966.3	−	14991.7i	1.04229	−	0.601764i	0.121805	−	0.992554i	$-0.461132\pi$
$853$	25966.3	−	14991.7i	1.04229	−	0.601764i	0.920480	+	0.390790i	$0.127798\pi$
$854$	8805.78	+	24106.4i	0.352842	+	0.965930i
$855$		0			0
$856$	−32514.9	−	18621.5i	−1.29829	−	0.743541i
$857$	−5417.14	−	9382.76i	−0.215923	−	0.373990i	0.737635	−	0.675200i	$-0.235943\pi$
$857$	−5417.14	−	9382.76i	−0.215923	−	0.373990i	−0.953558	+	0.301210i	$0.902609\pi$
$858$		0			0
$859$	−30072.5	−	17362.4i	−1.19448	−	0.689635i	−0.235162	−	0.971956i	$-0.575562\pi$
$859$	−30072.5	−	17362.4i	−1.19448	−	0.689635i	−0.959320	+	0.282322i	$0.908895\pi$
$860$	3558.00	+	19907.6i	0.141078	+	0.789352i
$861$		0			0
$862$	−28589.3	−	23932.7i	−1.12965	−	0.945650i
$863$	−10642.1			−0.419771			−0.209885	−	0.977726i	$-0.567309\pi$
$863$	−10642.1			−0.419771			−0.209885	+	0.977726i	$0.567309\pi$
$864$		0			0
$865$	−28317.5			−1.11309
$866$	1540.43	+	1289.52i	0.0604457	+	0.0506003i
$867$		0			0
$868$	−4025.54	−	22523.6i	−0.157415	−	0.880760i
$869$	609.893	+	352.122i	0.0238081	+	0.0137456i
$870$		0			0
$871$	437.798	+	758.288i	0.0170313	+	0.0294990i
$872$	−7674.22	−	4395.09i	−0.298030	−	0.170684i
$873$		0			0
$874$	−341.377	−	934.543i	−0.0132120	−	0.0361687i
$875$	60910.2	−	35166.5i	2.35330	−	1.35868i
$876$		0			0
$877$	−29723.0	−	17160.6i	−1.14444	−	0.660744i	−0.196915	−	0.980420i	$-0.563092\pi$
$877$	−29723.0	−	17160.6i	−1.14444	−	0.660744i	−0.947527	+	0.319676i	$0.896426\pi$
$878$	8719.13	−	49787.1i	0.335144	−	1.91371i
$879$		0			0
$880$	−2617.82	+	966.621i	−0.100280	+	0.0370281i
$881$	−17668.9			−0.675687			−0.337843	−	0.941202i	$-0.609697\pi$
$881$	−17668.9			−0.675687			−0.337843	+	0.941202i	$0.609697\pi$
$882$		0			0
$883$			41233.2i			1.57147i	0.618563	+	0.785735i	$0.287715\pi$
$883$			41233.2i			1.57147i	−0.618563	+	0.785735i	$0.712285\pi$
$884$	−4323.57	+	11965.4i	−0.164499	+	0.455250i
$885$		0			0
$886$	23653.6	+	4142.41i	0.896905	+	0.157073i
$887$	−5664.50	+	9811.21i	−0.214425	+	0.371396i	−0.953095	−	0.302672i	$-0.902121\pi$
$887$	−5664.50	+	9811.21i	−0.214425	+	0.371396i	0.738669	+	0.674068i	$0.235455\pi$
$888$		0			0
$889$	14837.5	+	25699.4i	0.559770	+	0.969549i
$890$	16759.2	+	45879.5i	0.631203	+	1.72796i
$891$		0			0
$892$	−6088.56	+	5133.08i	−0.228543	+	0.192678i
$893$	570.213	−	329.212i	0.0213678	−	0.0123367i
$894$		0			0
$895$	−37640.5	+	65195.3i	−1.40579	+	2.43490i
$896$	29006.2	−	10825.6i	1.08150	−	0.403635i
$897$		0			0
$898$	16320.6	+	13662.3i	0.606488	+	0.507703i
$899$		−	27075.0i		−	1.00445i
$900$		0			0
$901$			34304.3i			1.26841i
$902$	−510.339	+	609.636i	−0.0188386	+	0.0225041i
$903$		0			0
$904$	19441.9	+	33404.7i	0.715297	+	1.22901i
$905$	−19377.6	+	33562.9i	−0.711748	+	1.23278i
$906$		0			0
$907$	39893.8	−	23032.7i	1.46048	−	0.843207i	0.461444	−	0.887169i	$-0.347332\pi$
$907$	39893.8	−	23032.7i	1.46048	−	0.843207i	0.999033	+	0.0439627i	$0.0139983\pi$
$908$	438.696	+	520.355i	0.0160337	+	0.0190183i
$909$		0			0
$910$	−18324.1	+	6693.55i	−0.667513	+	0.243834i
$911$	6966.40	+	12066.2i	0.253356	+	0.438825i	0.964448	−	0.264274i	$-0.0851323\pi$
$911$	6966.40	+	12066.2i	0.253356	+	0.438825i	−0.711092	+	0.703099i	$0.751799\pi$
$912$		0			0
$913$	−183.508	+	317.846i	−0.00665196	+	0.0115215i
$914$	−6905.52	+	39431.2i	−0.249906	+	1.42699i
$915$		0			0
$916$	16123.6	−	44621.9i	0.581593	−	1.60955i
$917$			45119.2i			1.62483i
$918$		0			0
$919$	19716.4			0.707709			0.353854	−	0.935301i	$-0.384871\pi$
$919$	19716.4			0.707709			0.353854	+	0.935301i	$0.384871\pi$
$920$	239.116	+	68544.5i	0.00856894	+	2.45635i
$921$		0			0
$922$	−5293.81	−	927.096i	−0.189091	−	0.0331153i
$923$	13716.4	+	7919.15i	0.489144	+	0.282407i
$924$		0			0
$925$	−4137.83	+	2388.98i	−0.147082	+	0.0849180i
$926$	−33473.1	+	12227.3i	−1.18790	+	0.433924i
$927$		0			0
$928$	36042.0	−	6571.47i	1.27493	−	0.232456i
$929$	11948.1	+	20694.8i	0.421966	+	0.730866i	0.996132	−	0.0878730i	$-0.0280070\pi$
$929$	11948.1	+	20694.8i	0.421966	+	0.730866i	−0.574166	+	0.818739i	$0.694674\pi$
$930$		0			0
$931$	232.866	+	134.445i	0.00819750	+	0.00473283i
$932$	−6587.64	−	36858.9i	−0.231529	−	1.29544i
$933$		0			0
$934$	−21226.5	+	25356.6i	−0.743633	+	0.888323i
$935$	4363.14			0.152610
$936$		0			0
$937$	−35884.7			−1.25112			−0.625562	−	0.780174i	$-0.715130\pi$
$937$	−35884.7			−1.25112			−0.625562	+	0.780174i	$0.715130\pi$
$938$	−2138.48	+	2554.57i	−0.0744392	+	0.0889229i
$939$		0			0
$940$	−44653.5	+	7980.74i	−1.54940	+	0.276918i
$941$	−44632.1	−	25768.4i	−1.54619	−	0.892694i	−0.998427	−	0.0560607i	$-0.982146\pi$
$941$	−44632.1	−	25768.4i	−1.54619	−	0.892694i	−0.547764	−	0.836633i	$-0.684521\pi$
$942$		0			0
$943$	9764.38	+	16912.4i	0.337192	+	0.584033i
$944$	−13930.1	−	2389.51i	−0.480283	−	0.0823854i
$945$		0			0
$946$	−710.645	+	259.590i	−0.0244240	+	0.00892177i
$947$	−5450.65	+	3146.93i	−0.187035	+	0.107985i	−0.590594	−	0.806969i	$-0.701106\pi$
$947$	−5450.65	+	3146.93i	−0.187035	+	0.107985i	0.403559	+	0.914954i	$0.367773\pi$
$948$		0			0
$949$	−12538.2	−	7238.94i	−0.428881	−	0.247614i
$950$	−1885.20	−	330.152i	−0.0643832	−	0.0112753i
$951$		0			0
$952$	−48407.2	+	168.868i	−1.64799	+	0.00574899i
$953$	−3877.47			−0.131798			−0.0658991	−	0.997826i	$-0.520992\pi$
$953$	−3877.47			−0.131798			−0.0658991	+	0.997826i	$0.520992\pi$
$954$		0			0
$955$			21471.6i			0.727543i
$956$	−27578.7	−	9965.25i	−0.933011	−	0.337133i
$957$		0			0
$958$	629.537	−	3594.72i	0.0212311	−	0.121232i
$959$	−20518.5	+	35539.0i	−0.690903	+	1.19668i
$960$		0			0
$961$	5947.32	+	10301.1i	0.199635	+	0.345778i
$962$	702.768	−	256.712i	0.0235532	−	0.00860368i
$963$		0			0
$964$	12685.3	−	10694.6i	0.423824	−	0.357314i
$965$	21134.5	−	12202.0i	0.705018	−	0.407043i
$966$		0			0
$967$	5832.12	−	10101.5i	0.193949	−	0.335929i	−0.752607	−	0.658470i	$-0.771204\pi$
$967$	5832.12	−	10101.5i	0.193949	−	0.335929i	0.946555	+	0.322542i	$0.104537\pi$
$968$	15096.9	+	25939.2i	0.501274	+	0.861280i
$969$		0			0
$970$	−1838.28	+	2195.96i	−0.0608492	+	0.0726887i
$971$			10211.1i			0.337478i	0.985661	+	0.168739i	$0.0539695\pi$
$971$			10211.1i			0.337478i	−0.985661	+	0.168739i	$0.946030\pi$
$972$		0			0
$973$			16767.7i			0.552464i
$974$	20680.1	+	17311.7i	0.680320	+	0.569509i
$975$		0			0
$976$	−17362.9	+	20888.8i	−0.569439	+	0.685078i
$977$	12182.5	−	21100.6i	0.398927	−	0.690961i	−0.594667	−	0.803972i	$-0.702716\pi$
$977$	12182.5	−	21100.6i	0.398927	−	0.690961i	0.993594	+	0.113011i	$0.0360495\pi$
$978$		0			0
$979$	−1582.53	+	913.676i	−0.0516629	+	0.0298276i
$980$	−11940.4	−	14163.0i	−0.389208	−	0.461655i
$981$		0			0
$982$	−8671.09	−	23737.7i	−0.281778	−	0.771386i
$983$	3493.53	+	6050.98i	0.113353	+	0.196334i	0.917120	−	0.398610i	$-0.130507\pi$
$983$	3493.53	+	6050.98i	0.113353	+	0.196334i	−0.803767	+	0.594944i	$0.797174\pi$
$984$		0			0
$985$	−11988.1	+	20764.0i	−0.387790	+	0.671672i
$986$	−56423.0	−	9881.26i	−1.82239	−	0.319151i
$987$		0			0
$988$	281.863	+	101.848i	0.00907616	+	0.00327957i
$989$			18583.7i			0.597500i
$990$		0			0
$991$	−54914.7			−1.76026			−0.880132	−	0.474728i	$-0.842546\pi$
$991$	−54914.7			−1.76026			−0.880132	+	0.474728i	$0.842546\pi$
$992$	18459.9	−	15673.5i	0.590830	−	0.501648i
$993$		0			0
$994$	−10395.4	+	59358.9i	−0.331713	+	1.89411i
$995$	−13482.5	−	7784.11i	−0.429571	−	0.248013i
$996$		0			0
$997$	−11321.2	+	6536.29i	−0.359624	+	0.207629i	−0.668916	−	0.743338i	$-0.733241\pi$
$997$	−11321.2	+	6536.29i	−0.359624	+	0.207629i	0.309292	+	0.950967i	$0.399908\pi$
$998$	−19013.1	−	52049.5i	−0.603054	−	1.65090i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	216.4.n.a.37.9		68
3.2	odd	2		72.4.n.a.13.26	yes	68
4.3	odd	2		864.4.r.a.145.34		68
8.3	odd	2		864.4.r.a.145.1		68
8.5	even	2	inner	216.4.n.a.37.15		68
9.2	odd	6		72.4.n.a.61.20	yes	68
9.7	even	3	inner	216.4.n.a.181.15		68
12.11	even	2		288.4.r.a.49.30		68
24.5	odd	2		72.4.n.a.13.20	✓	68
24.11	even	2		288.4.r.a.49.5		68
36.7	odd	6		864.4.r.a.721.1		68
36.11	even	6		288.4.r.a.241.5		68
72.11	even	6		288.4.r.a.241.30		68
72.29	odd	6		72.4.n.a.61.26	yes	68
72.43	odd	6		864.4.r.a.721.34		68
72.61	even	6	inner	216.4.n.a.181.9		68

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
72.4.n.a.13.20	✓	68	24.5	odd	2
72.4.n.a.13.26	yes	68	3.2	odd	2
72.4.n.a.61.20	yes	68	9.2	odd	6
72.4.n.a.61.26	yes	68	72.29	odd	6
216.4.n.a.37.9		68	1.1	even	1	trivial
216.4.n.a.37.15		68	8.5	even	2	inner
216.4.n.a.181.9		68	72.61	even	6	inner
216.4.n.a.181.15		68	9.7	even	3	inner
288.4.r.a.49.5		68	24.11	even	2
288.4.r.a.49.30		68	12.11	even	2
288.4.r.a.241.5		68	36.11	even	6
288.4.r.a.241.30		68	72.11	even	6
864.4.r.a.145.1		68	8.3	odd	2
864.4.r.a.145.34		68	4.3	odd	2
864.4.r.a.721.1		68	36.7	odd	6
864.4.r.a.721.34		68	72.43	odd	6

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:	\( N \)	\(=\)	\( 216 = 2^{3} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	216.n (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-2.16881 - 1.81556i) q^{2} +(1.40750 + 7.87521i) q^{4} +(17.5797 + 10.1497i) q^{5} +(-10.6896 - 18.5150i) q^{7} +(11.2453 - 19.6353i) q^{8} +O(q^{10})\)	\(q+(-2.16881 - 1.81556i) q^{2} +(1.40750 + 7.87521i) q^{4} +(17.5797 + 10.1497i) q^{5} +(-10.6896 - 18.5150i) q^{7} +(11.2453 - 19.6353i) q^{8} +(-19.6999 - 53.9298i) q^{10} +(1.86021 - 1.07399i) q^{11} +(13.7636 + 7.94640i) q^{13} +(-10.4312 + 59.5632i) q^{14} +(-60.0379 + 22.1688i) q^{16} +100.066 q^{17} -2.35719i q^{19} +(-55.1872 + 152.730i) q^{20} +(-5.98436 - 1.04803i) q^{22} +(-74.6153 + 129.238i) q^{23} +(143.532 + 248.604i) q^{25} +(-15.4235 - 42.2228i) q^{26} +(130.764 - 110.243i) q^{28} +(175.273 - 101.194i) q^{29} +(66.8886 - 115.855i) q^{31} +(170.460 + 60.9222i) q^{32} +(-217.024 - 181.675i) q^{34} -433.985i q^{35} +16.6443i q^{37} +(-4.27962 + 5.11231i) q^{38} +(396.981 - 231.047i) q^{40} +(65.4314 - 113.331i) q^{41} +(107.846 - 62.2650i) q^{43} +(11.0762 + 13.1379i) q^{44} +(396.465 - 144.824i) q^{46} +(139.663 + 241.903i) q^{47} +(-57.0362 + 98.7895i) q^{49} +(140.062 - 799.766i) q^{50} +(-43.2073 + 119.576i) q^{52} +342.817i q^{53} +43.6028 q^{55} +(-483.754 + 1.68757i) q^{56} +(-563.859 - 98.7477i) q^{58} +(191.251 + 110.419i) q^{59} +(367.557 - 212.209i) q^{61} +(-355.410 + 129.827i) q^{62} +(-259.087 - 441.608i) q^{64} +(161.307 + 279.391i) q^{65} +(47.7127 + 27.5469i) q^{67} +(140.843 + 788.038i) q^{68} +(-787.924 + 941.232i) q^{70} +996.571 q^{71} -910.971 q^{73} +(30.2186 - 36.0983i) q^{74} +(18.5634 - 3.31776i) q^{76} +(-39.7700 - 22.9612i) q^{77} +(163.931 + 283.937i) q^{79} +(-1280.46 - 219.643i) q^{80} +(-347.667 + 126.998i) q^{82} +(-147.974 + 85.4325i) q^{83} +(1759.13 + 1015.63i) q^{85} +(-346.944 - 60.7597i) q^{86} +(-0.169551 - 48.6032i) q^{88} -850.727 q^{89} -339.776i q^{91} +(-1122.79 - 405.709i) q^{92} +(136.286 - 778.210i) q^{94} +(23.9247 - 41.4388i) q^{95} +(-24.9396 - 43.1967i) q^{97} +(303.059 - 110.704i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 68 q + q^{2} - q^{4} - 2 q^{7} + 10 q^{8}+O(q^{10}) \) 68 * q + q^2 - q^4 - 2 * q^7 + 10 * q^8	\( 68 q + q^{2} - q^{4} - 2 q^{7} + 10 q^{8} - 20 q^{10} + 10 q^{14} - q^{16} + 8 q^{17} + 52 q^{20} - 17 q^{22} - 274 q^{23} + 648 q^{25} - 368 q^{26} + 124 q^{28} - 2 q^{31} - 259 q^{32} + 189 q^{34} - 319 q^{38} + 214 q^{40} + 22 q^{41} - 282 q^{44} - 24 q^{46} + 942 q^{47} - 1080 q^{49} - 53 q^{50} - 588 q^{52} - 508 q^{55} + 502 q^{56} + 280 q^{58} - 1744 q^{62} + 410 q^{64} + 502 q^{65} - 1149 q^{68} - 586 q^{70} + 3984 q^{71} - 8 q^{73} - 1778 q^{74} + 621 q^{76} - 2 q^{79} - 4704 q^{80} + 714 q^{82} + 2923 q^{86} - 533 q^{88} + 856 q^{89} - 3342 q^{92} + 1518 q^{94} + 2792 q^{95} - 2 q^{97} + 6414 q^{98}+O(q^{100}) \) 68 * q + q^2 - q^4 - 2 * q^7 + 10 * q^8 - 20 * q^10 + 10 * q^14 - q^16 + 8 * q^17 + 52 * q^20 - 17 * q^22 - 274 * q^23 + 648 * q^25 - 368 * q^26 + 124 * q^28 - 2 * q^31 - 259 * q^32 + 189 * q^34 - 319 * q^38 + 214 * q^40 + 22 * q^41 - 282 * q^44 - 24 * q^46 + 942 * q^47 - 1080 * q^49 - 53 * q^50 - 588 * q^52 - 508 * q^55 + 502 * q^56 + 280 * q^58 - 1744 * q^62 + 410 * q^64 + 502 * q^65 - 1149 * q^68 - 586 * q^70 + 3984 * q^71 - 8 * q^73 - 1778 * q^74 + 621 * q^76 - 2 * q^79 - 4704 * q^80 + 714 * q^82 + 2923 * q^86 - 533 * q^88 + 856 * q^89 - 3342 * q^92 + 1518 * q^94 + 2792 * q^95 - 2 * q^97 + 6414 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more