LMFDB - Embedded newform 585.2.c.d.469.12

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [585,2,Mod(469,585)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(585, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 1, 0])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("585.469"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 585 = 3^{2} \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	585.c (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [12] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$4.67124851824$
Analytic rank:	$0$
Dimension:	$12$
Coefficient field:	12.0.2593100598870016.1
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 4x^{10} + 9x^{8} - 16x^{6} + 36x^{4} - 64x^{2} + 64 $ x^12 - 4x^10 + 9x^8 - 16x^6 + 36x^4 - 64*x^2 + 64
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			469.12
Root			$0.721581 + 1.21627i$ of defining polynomial
Character	$\chi$	$=$	585.469
Dual form			585.2.c.d.469.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+2.43255i q^{2} -3.91729 q^{4} +(1.11567 + 1.93785i) q^{5} +4.51056i q^{7} -4.66389i q^{8} +(-4.71392 + 2.71392i) q^{10} +5.03230 q^{11} +1.00000i q^{13} -10.9721 q^{14} +3.51056 q^{16} -2.06414i q^{17} +2.81346 q^{19} +(-4.37040 - 7.59113i) q^{20} +12.2413i q^{22} -4.04291i q^{23} +(-2.51056 + 4.32401i) q^{25} -2.43255 q^{26} -17.6691i q^{28} -7.83457 q^{31} -0.788180i q^{32} +5.02112 q^{34} +(-8.74080 + 5.03230i) q^{35} -6.34513i q^{37} +6.84387i q^{38} +(9.03794 - 5.20336i) q^{40} +1.47716 q^{41} -6.81346i q^{43} -19.7129 q^{44} +9.83457 q^{46} -9.07521i q^{47} -13.3451 q^{49} +(-10.5184 - 6.10705i) q^{50} -3.91729i q^{52} +9.81556i q^{53} +(5.61439 + 9.75186i) q^{55} +21.0367 q^{56} +13.2035 q^{59} +8.34513 q^{61} -19.0580i q^{62} +8.93840 q^{64} +(-1.93785 + 1.11567i) q^{65} +15.8346i q^{67} +8.08582i q^{68} +(-12.2413 - 21.2624i) q^{70} +0.569614 q^{71} -0.373086i q^{73} +15.4348 q^{74} -11.0211 q^{76} +22.6985i q^{77} -6.13747 q^{79} +(3.91663 + 6.80295i) q^{80} +3.59327i q^{82} -0.654981i q^{83} +(4.00000 - 2.30290i) q^{85} +16.5741 q^{86} -23.4701i q^{88} +5.93985 q^{89} -4.51056 q^{91} +15.8372i q^{92} +22.0759 q^{94} +(3.13889 + 5.45207i) q^{95} +2.67599i q^{97} -32.4627i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 8 q^{4} - 20 q^{10} + 8 q^{16} + 24 q^{19} + 4 q^{25} - 16 q^{31} - 8 q^{34} + 28 q^{40} + 40 q^{46} - 48 q^{49} + 4 q^{55} - 12 q^{61} - 64 q^{70} - 64 q^{76} - 20 q^{79} + 48 q^{85} - 20 q^{91}+ \cdots + 104 q^{94}+O(q^{100}) $ 12 * q - 8 * q^4 - 20 * q^10 + 8 * q^16 + 24 * q^19 + 4 * q^25 - 16 * q^31 - 8 * q^34 + 28 * q^40 + 40 * q^46 - 48 * q^49 + 4 * q^55 - 12 * q^61 - 64 * q^70 - 64 * q^76 - 20 * q^79 + 48 * q^85 - 20 * q^91 + 104 * q^94

Character values

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

$n$	$326$	$352$	$496$
$\chi(n)$	$1$	$-1$	$1$

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 $

$2$			2.43255i			1.72007i	0.510235	+	0.860035i	$0.329559\pi$
$2$			2.43255i			1.72007i	−0.510235	+	0.860035i	$0.670441\pi$
$3$		0			0
$3$		0			0
$4$	−3.91729			−1.95864
$5$	1.11567	+	1.93785i	0.498943	+	0.866635i
$5$	1.11567	+	1.93785i	0.498943	+	0.866635i
$6$		0			0
$7$			4.51056i			1.70483i	0.522865	+	0.852415i	$0.324863\pi$
$7$			4.51056i			1.70483i	−0.522865	+	0.852415i	$0.675137\pi$
$8$		−	4.66389i		−	1.64893i
$9$		0			0
$10$	−4.71392	+	2.71392i	−1.49067	+	0.858217i
$11$	5.03230			1.51729			0.758647	−	0.651502i	$-0.225861\pi$
$11$	5.03230			1.51729			0.758647	+	0.651502i	$0.225861\pi$
$12$		0			0
$13$			1.00000i			0.277350i
$13$			1.00000i			0.277350i
$14$	−10.9721			−2.93243
$15$		0			0
$16$	3.51056			0.877639
$17$		−	2.06414i		−	0.500627i	−0.968165	−	0.250314i	$-0.919466\pi$
$17$		−	2.06414i		−	0.500627i	0.968165	−	0.250314i	$-0.0805337\pi$
$18$		0			0
$19$	2.81346			0.645451			0.322726	−	0.946493i	$-0.395401\pi$
$19$	2.81346			0.645451			0.322726	+	0.946493i	$0.395401\pi$
$20$	−4.37040	−	7.59113i	−0.977251	−	1.69743i
$21$		0			0
$22$			12.2413i			2.60985i
$23$		−	4.04291i		−	0.843005i	−0.906827	−	0.421503i	$-0.861503\pi$
$23$		−	4.04291i		−	0.843005i	0.906827	−	0.421503i	$-0.138497\pi$
$24$		0			0
$25$	−2.51056	+	4.32401i	−0.502112	+	0.864803i
$26$	−2.43255			−0.477062
$27$		0			0
$28$		−	17.6691i		−	3.33915i
$29$		0			0			−	1.00000i	$-0.5\pi$
$29$		0			0				1.00000i	$0.5\pi$
$30$		0			0
$31$	−7.83457			−1.40713			−0.703565	−	0.710631i	$-0.748410\pi$
$31$	−7.83457			−1.40713			−0.703565	+	0.710631i	$0.748410\pi$
$32$		−	0.788180i		−	0.139332i
$33$		0			0
$34$	5.02112			0.861114
$35$	−8.74080	+	5.03230i	−1.47747	+	0.850613i
$36$		0			0
$37$		−	6.34513i		−	1.04313i	−0.853211	−	0.521566i	$-0.825348\pi$
$37$		−	6.34513i		−	1.04313i	0.853211	−	0.521566i	$-0.174652\pi$
$38$			6.84387i			1.11022i
$39$		0			0
$40$	9.03794	−	5.20336i	1.42902	−	0.822724i
$41$	1.47716			0.230694			0.115347	−	0.993325i	$-0.463202\pi$
$41$	1.47716			0.230694			0.115347	+	0.993325i	$0.463202\pi$
$42$		0			0
$43$		−	6.81346i		−	1.03904i	−0.854458	−	0.519521i	$-0.826110\pi$
$43$		−	6.81346i		−	1.03904i	0.854458	−	0.519521i	$-0.173890\pi$
$44$	−19.7129			−2.97184
$45$		0			0
$46$	9.83457			1.45003
$47$		−	9.07521i		−	1.32376i	−0.749612	−	0.661878i	$-0.769760\pi$
$47$		−	9.07521i		−	1.32376i	0.749612	−	0.661878i	$-0.230240\pi$
$48$		0			0
$49$	−13.3451			−1.90645
$50$	−10.5184	−	6.10705i	−1.48752	−	0.863667i
$51$		0			0
$52$		−	3.91729i		−	0.543230i
$53$			9.81556i			1.34827i	0.738608	+	0.674135i	$0.235483\pi$
$53$			9.81556i			1.34827i	−0.738608	+	0.674135i	$0.764517\pi$
$54$		0			0
$55$	5.61439	+	9.75186i	0.757044	+	1.31494i
$56$	21.0367			2.81115
$57$		0			0
$58$		0			0
$59$	13.2035			1.71895			0.859474	−	0.511180i	$-0.170791\pi$
$59$	13.2035			1.71895			0.859474	+	0.511180i	$0.170791\pi$
$60$		0			0
$61$	8.34513			1.06848			0.534242	−	0.845331i	$-0.320597\pi$
$61$	8.34513			1.06848			0.534242	+	0.845331i	$0.320597\pi$
$62$		−	19.0580i		−	2.42036i
$63$		0			0
$64$	8.93840			1.11730
$65$	−1.93785	+	1.11567i	−0.240361	+	0.138382i
$66$		0			0
$67$			15.8346i			1.93450i	0.253824	+	0.967250i	$0.418312\pi$
$67$			15.8346i			1.93450i	−0.253824	+	0.967250i	$0.581688\pi$
$68$			8.08582i			0.980550i
$69$		0			0
$70$	−12.2413	−	21.2624i	−1.46312	−	2.54134i
$71$	0.569614			0.0676008			0.0338004	−	0.999429i	$-0.489239\pi$
$71$	0.569614			0.0676008			0.0338004	+	0.999429i	$0.489239\pi$
$72$		0			0
$73$		−	0.373086i		−	0.0436664i	−0.999762	−	0.0218332i	$-0.993050\pi$
$73$		−	0.373086i		−	0.0436664i	0.999762	−	0.0218332i	$-0.00695028\pi$
$74$	15.4348			1.79426
$75$		0			0
$76$	−11.0211			−1.26421
$77$			22.6985i			2.58673i
$78$		0			0
$79$	−6.13747			−0.690519			−0.345260	−	0.938507i	$-0.612209\pi$
$79$	−6.13747			−0.690519			−0.345260	+	0.938507i	$0.612209\pi$
$80$	3.91663	+	6.80295i	0.437892	+	0.760593i
$81$		0			0
$82$			3.59327i			0.396810i
$83$		−	0.654981i		−	0.0718935i	−0.999354	−	0.0359467i	$-0.988555\pi$
$83$		−	0.654981i		−	0.0718935i	0.999354	−	0.0359467i	$-0.0114447\pi$
$84$		0			0
$85$	4.00000	−	2.30290i	0.433861	−	0.249784i
$86$	16.5741			1.78723
$87$		0			0
$88$		−	23.4701i		−	2.50192i
$89$	5.93985			0.629623			0.314811	−	0.949154i	$-0.398059\pi$
$89$	5.93985			0.629623			0.314811	+	0.949154i	$0.398059\pi$
$90$		0			0
$91$	−4.51056			−0.472835
$92$			15.8372i			1.65115i
$93$		0			0
$94$	22.0759			2.27695
$95$	3.13889	+	5.45207i	0.322043	+	0.559370i
$96$		0			0
$97$			2.67599i			0.271705i	0.990729	+	0.135853i	$0.0433774\pi$
$97$			2.67599i			0.271705i	−0.990729	+	0.135853i	$0.956623\pi$
$98$		−	32.4627i		−	3.27922i
$99$		0			0
$100$	9.83457	−	16.9384i	0.983457	−	1.69384i
$101$	11.8797			1.18207			0.591037	−	0.806645i	$-0.298719\pi$
$101$	11.8797			1.18207			0.591037	+	0.806645i	$0.298719\pi$
$102$		0			0
$103$			2.20766i			0.217527i	0.994068	+	0.108764i	$0.0346891\pi$
$103$			2.20766i			0.217527i	−0.994068	+	0.108764i	$0.965311\pi$
$104$	4.66389			0.457332
$105$		0			0
$106$	−23.8768			−2.31912
$107$		−	10.1500i		−	0.981234i	−0.871375	−	0.490617i	$-0.836771\pi$
$107$		−	10.1500i		−	0.981234i	0.871375	−	0.490617i	$-0.163229\pi$
$108$		0			0
$109$	−0.373086			−0.0357352			−0.0178676	−	0.999840i	$-0.505688\pi$
$109$	−0.373086			−0.0357352			−0.0178676	+	0.999840i	$0.505688\pi$
$110$	−23.7219	+	13.6573i	−2.26179	+	1.30217i
$111$		0			0
$112$			15.8346i			1.49623i
$113$		−	6.91187i		−	0.650214i	−0.945677	−	0.325107i	$-0.894600\pi$
$113$		−	6.91187i		−	0.650214i	0.945677	−	0.325107i	$-0.105400\pi$
$114$		0			0
$115$	7.83457	−	4.51056i	0.730578	−	0.420612i
$116$		0			0
$117$		0			0
$118$			32.1181i			2.95671i
$119$	9.31042			0.853485
$120$		0			0
$121$	14.3240			1.30218
$122$			20.2999i			1.83787i
$123$		0			0
$124$	30.6903			2.75607
$125$	−11.1803	−	0.0409180i	−0.999993	−	0.00365982i
$126$		0			0
$127$		−	3.66914i		−	0.325584i	−0.986660	−	0.162792i	$-0.947950\pi$
$127$		−	3.66914i		−	0.325584i	0.986660	−	0.162792i	$-0.0520499\pi$
$128$			20.1667i			1.78250i
$129$		0			0
$130$	−2.71392	−	4.71392i	−0.238027	−	0.413438i
$131$	−18.9900			−1.65916			−0.829580	−	0.558387i	$-0.811420\pi$
$131$	−18.9900			−1.65916			−0.829580	+	0.558387i	$0.811420\pi$
$132$		0			0
$133$			12.6903i			1.10039i
$134$	−38.5183			−3.32748
$135$		0			0
$136$	−9.62691			−0.825501
$137$			7.02843i			0.600479i	0.953864	+	0.300240i	$0.0970667\pi$
$137$			7.02843i			0.600479i	−0.953864	+	0.300240i	$0.902933\pi$
$138$		0			0
$139$	−18.9932			−1.61098			−0.805489	−	0.592610i	$-0.798097\pi$
$139$	−18.9932			−1.61098			−0.805489	+	0.592610i	$0.798097\pi$
$140$	34.2402	−	19.7129i	2.89383	−	1.66605i
$141$		0			0
$142$			1.38561i			0.116278i
$143$			5.03230i			0.420822i
$144$		0			0
$145$		0			0
$146$	0.907550			0.0751094
$147$		0			0
$148$			24.8557i			2.04312i
$149$	18.9588			1.55316			0.776581	−	0.630017i	$-0.216952\pi$
$149$	18.9588			1.55316			0.776581	+	0.630017i	$0.216952\pi$
$150$		0			0
$151$	−16.8557			−1.37170			−0.685848	−	0.727745i	$-0.740569\pi$
$151$	−16.8557			−1.37170			−0.685848	+	0.727745i	$0.740569\pi$
$152$		−	13.1216i		−	1.06431i
$153$		0			0
$154$	−55.2151			−4.44936
$155$	−8.74080	−	15.1823i	−0.702078	−	1.21947i
$156$		0			0
$157$			9.02112i			0.719963i	0.932959	+	0.359982i	$0.117217\pi$
$157$			9.02112i			0.719963i	−0.932959	+	0.359982i	$0.882783\pi$
$158$		−	14.9297i		−	1.18774i
$159$		0			0
$160$	1.52738	−	0.879350i	0.120750	−	0.0695187i
$161$	18.2358			1.43718
$162$		0			0
$163$		−	0.841414i		−	0.0659046i	−0.999457	−	0.0329523i	$-0.989509\pi$
$163$		−	0.841414i		−	0.0659046i	0.999457	−	0.0329523i	$-0.0104909\pi$
$164$	−5.78647			−0.451848
$165$		0			0
$166$	1.59327			0.123662
$167$			9.91475i			0.767227i	0.923494	+	0.383613i	$0.125320\pi$
$167$			9.91475i			0.767227i	−0.923494	+	0.383613i	$0.874680\pi$
$168$		0			0
$169$	−1.00000			−0.0769231
$170$	5.60191	+	9.73019i	0.429647	+	0.746271i
$171$		0			0
$172$			26.6903i			2.03511i
$173$			4.79709i			0.364716i	0.983232	+	0.182358i	$0.0583730\pi$
$173$			4.79709i			0.364716i	−0.983232	+	0.182358i	$0.941627\pi$
$174$		0			0
$175$	−19.5037	−	11.3240i	−1.47434	−	0.856015i
$176$	17.6662			1.33164
$177$		0			0
$178$			14.4490i			1.08300i
$179$	−7.41701			−0.554373			−0.277187	−	0.960816i	$-0.589402\pi$
$179$	−7.41701			−0.554373			−0.277187	+	0.960816i	$0.589402\pi$
$180$		0			0
$181$	3.69710			0.274803			0.137402	−	0.990515i	$-0.456125\pi$
$181$	3.69710			0.274803			0.137402	+	0.990515i	$0.456125\pi$
$182$		−	10.9721i		−	0.813309i
$183$		0			0
$184$	−18.8557			−1.39006
$185$	12.2959	−	7.07908i	0.904015	−	0.520464i
$186$		0			0
$187$		−	10.3874i		−	0.759599i
$188$			35.5502i			2.59276i
$189$		0			0
$190$	−13.2624	+	7.63550i	−0.962157	+	0.553938i
$191$	−8.55624			−0.619108			−0.309554	−	0.950882i	$-0.600180\pi$
$191$	−8.55624			−0.619108			−0.309554	+	0.950882i	$0.600180\pi$
$192$		0			0
$193$		−	15.3662i		−	1.10609i	−0.833153	−	0.553043i	$-0.813466\pi$
$193$		−	15.3662i		−	1.10609i	0.833153	−	0.553043i	$-0.186534\pi$
$194$	−6.50946			−0.467352
$195$		0			0
$196$	52.2767			3.73405
$197$			11.2927i			0.804573i	0.915514	+	0.402286i	$0.131784\pi$
$197$			11.2927i			0.804573i	−0.915514	+	0.402286i	$0.868216\pi$
$198$		0			0
$199$	17.8768			1.26725			0.633626	−	0.773639i	$-0.281566\pi$
$199$	17.8768			1.26725			0.633626	+	0.773639i	$0.281566\pi$
$200$	20.1667	+	11.7090i	1.42600	+	0.827949i
$201$		0			0
$202$			28.8979i			2.03325i
$203$		0			0
$204$		0			0
$205$	1.64803	+	2.86253i	0.115103	+	0.199928i
$206$	−5.37023			−0.374162
$207$		0			0
$208$			3.51056i			0.243413i
$209$	14.1582			0.979340
$210$		0			0
$211$	15.8346			1.09010			0.545048	−	0.838405i	$-0.316511\pi$
$211$	15.8346			1.09010			0.545048	+	0.838405i	$0.316511\pi$
$212$		−	38.4503i		−	2.64078i
$213$		0			0
$214$	24.6903			1.68779
$215$	13.2035	−	7.60157i	0.900470	−	0.518423i
$216$		0			0
$217$		−	35.3383i		−	2.39892i
$218$		−	0.907550i		−	0.0614670i
$219$		0			0
$220$	−21.9932	−	38.2008i	−1.48278	−	2.57550i
$221$	2.06414			0.138849
$222$		0			0
$223$			1.46149i			0.0978683i	0.998802	+	0.0489342i	$0.0155825\pi$
$223$			1.46149i			0.0978683i	−0.998802	+	0.0489342i	$0.984418\pi$
$224$	3.55513			0.237537
$225$		0			0
$226$	16.8135			1.11841
$227$		−	12.2279i		−	0.811596i	−0.913963	−	0.405798i	$-0.866994\pi$
$227$		−	12.2279i		−	0.811596i	0.913963	−	0.405798i	$-0.133006\pi$
$228$		0			0
$229$	24.3172			1.60692			0.803462	−	0.595356i	$-0.202989\pi$
$229$	24.3172			1.60692			0.803462	+	0.595356i	$0.202989\pi$
$230$	10.9721	+	19.0580i	0.723482	+	1.25665i
$231$		0			0
$232$		0			0
$233$		−	14.9470i		−	0.979214i	−0.871943	−	0.489607i	$-0.837140\pi$
$233$		−	14.9470i		−	0.979214i	0.871943	−	0.489607i	$-0.162860\pi$
$234$		0			0
$235$	17.5864	−	10.1249i	1.14721	−	0.660479i
$236$	−51.7218			−3.36680
$237$		0			0
$238$			22.6480i			1.46805i
$239$	−9.49498			−0.614179			−0.307090	−	0.951681i	$-0.599355\pi$
$239$	−9.49498			−0.614179			−0.307090	+	0.951681i	$0.599355\pi$
$240$		0			0
$241$	−2.60580			−0.167854			−0.0839271	−	0.996472i	$-0.526746\pi$
$241$	−2.60580			−0.167854			−0.0839271	+	0.996472i	$0.526746\pi$
$242$			34.8438i			2.23985i
$243$		0			0
$244$	−32.6903			−2.09278
$245$	−14.8888	−	25.8609i	−0.951209	−	1.65219i
$246$		0			0
$247$			2.81346i			0.179016i
$248$			36.5396i			2.32027i
$249$		0			0
$250$	0.0995351	−	27.1965i	0.00629515	−	1.72006i
$251$	1.50835			0.0952065			0.0476033	−	0.998866i	$-0.484842\pi$
$251$	1.50835			0.0952065			0.0476033	+	0.998866i	$0.484842\pi$
$252$		0			0
$253$		−	20.3451i		−	1.27909i
$254$	8.92537			0.560027
$255$		0			0
$256$	−31.1797			−1.94873
$257$		−	7.41701i		−	0.462660i	−0.972875	−	0.231330i	$-0.925692\pi$
$257$		−	7.41701i		−	0.462660i	0.972875	−	0.231330i	$-0.0743078\pi$
$258$		0			0
$259$	28.6201			1.77836
$260$	7.59113	−	4.37040i	0.470782	−	0.271041i
$261$		0			0
$262$		−	46.1940i		−	2.85387i
$263$			22.7491i			1.40277i	0.712782	+	0.701385i	$0.247435\pi$
$263$			22.7491i			1.40277i	−0.712782	+	0.701385i	$0.752565\pi$
$264$		0			0
$265$	−19.0211	+	10.9509i	−1.16846	+	0.672710i
$266$	−30.8697			−1.89274
$267$		0			0
$268$		−	62.0285i		−	3.78900i
$269$	8.92537			0.544189			0.272095	−	0.962271i	$-0.412284\pi$
$269$	8.92537			0.544189			0.272095	+	0.962271i	$0.412284\pi$
$270$		0			0
$271$	−8.16543			−0.496014			−0.248007	−	0.968758i	$-0.579776\pi$
$271$	−8.16543			−0.496014			−0.248007	+	0.968758i	$0.579776\pi$
$272$		−	7.24628i		−	0.439370i
$273$		0			0
$274$	−17.0970			−1.03287
$275$	−12.6339	+	21.7597i	−0.761851	+	1.31216i
$276$		0			0
$277$			26.3172i			1.58125i	0.612303	+	0.790623i	$0.290243\pi$
$277$			26.3172i			1.58125i	−0.612303	+	0.790623i	$0.709757\pi$
$278$		−	46.2018i		−	2.77100i
$279$		0			0
$280$	23.4701	+	40.7661i	1.40261	+	2.43624i
$281$	−19.7129			−1.17598			−0.587988	−	0.808870i	$-0.700080\pi$
$281$	−19.7129			−1.17598			−0.587988	+	0.808870i	$0.700080\pi$
$282$		0			0
$283$		−	27.0633i		−	1.60875i	−0.594123	−	0.804374i	$-0.702501\pi$
$283$		−	27.0633i		−	1.60875i	0.594123	−	0.804374i	$-0.297499\pi$
$284$	−2.23134			−0.132406
$285$		0			0
$286$	−12.2413			−0.723843
$287$			6.66283i			0.393295i
$288$		0			0
$289$	12.7393			0.749372
$290$		0			0
$291$		0			0
$292$			1.46149i			0.0855270i
$293$			4.87892i			0.285030i	0.989793	+	0.142515i	$0.0455189\pi$
$293$			4.87892i			0.285030i	−0.989793	+	0.142515i	$0.954481\pi$
$294$		0			0
$295$	14.7307	+	25.5864i	0.857657	+	1.48970i
$296$	−29.5930			−1.72006
$297$		0			0
$298$			46.1181i			2.67155i
$299$	4.04291			0.233808
$300$		0			0
$301$	30.7325			1.77139
$302$		−	41.0023i		−	2.35941i
$303$		0			0
$304$	9.87680			0.566473
$305$	9.31042	+	16.1716i	0.533113	+	0.925986i
$306$		0			0
$307$		−	12.7855i		−	0.729707i	−0.931065	−	0.364854i	$-0.881119\pi$
$307$		−	12.7855i		−	0.729707i	0.931065	−	0.364854i	$-0.118881\pi$
$308$		−	88.9164i		−	5.06648i
$309$		0			0
$310$	36.9316	−	21.2624i	2.09757	−	1.20762i
$311$	−27.5462			−1.56200			−0.781001	−	0.624530i	$-0.785291\pi$
$311$	−27.5462			−1.56200			−0.781001	+	0.624530i	$0.785291\pi$
$312$		0			0
$313$		−	31.2961i		−	1.76896i	−0.466580	−	0.884479i	$-0.654514\pi$
$313$		−	31.2961i		−	1.76896i	0.466580	−	0.884479i	$-0.345486\pi$
$314$	−21.9443			−1.23839
$315$		0			0
$316$	24.0422			1.35248
$317$			3.70498i			0.208092i	0.994572	+	0.104046i	$0.0331789\pi$
$317$			3.70498i			0.208092i	−0.994572	+	0.104046i	$0.966821\pi$
$318$		0			0
$319$		0			0
$320$	9.97231	+	17.3213i	0.557469	+	0.968291i
$321$		0			0
$322$			44.3594i			2.47205i
$323$		−	5.80737i		−	0.323130i
$324$		0			0
$325$	−4.32401	−	2.51056i	−0.239853	−	0.139261i
$326$	2.04678			0.113361
$327$		0			0
$328$		−	6.88933i		−	0.380400i
$329$	40.9342			2.25678
$330$		0			0
$331$	−16.5807			−0.911360			−0.455680	−	0.890144i	$-0.650604\pi$
$331$	−16.5807			−0.911360			−0.455680	+	0.890144i	$0.650604\pi$
$332$			2.56575i			0.140814i
$333$		0			0
$334$	−24.1181			−1.31968
$335$	−30.6851	+	17.6662i	−1.67651	+	0.965206i
$336$		0			0
$337$			4.04223i			0.220194i	0.993921	+	0.110097i	$0.0351162\pi$
$337$			4.04223i			0.220194i	−0.993921	+	0.110097i	$0.964884\pi$
$338$		−	2.43255i		−	0.132313i
$339$		0			0
$340$	−15.6691	+	9.02112i	−0.849779	+	0.489239i
$341$	−39.4259			−2.13503
$342$		0			0
$343$		−	28.6201i		−	1.54534i
$344$	−31.7772			−1.71331
$345$		0			0
$346$	−11.6691			−0.627337
$347$		−	6.86123i		−	0.368330i	−0.982895	−	0.184165i	$-0.941042\pi$
$347$		−	6.86123i		−	0.368330i	0.982895	−	0.184165i	$-0.0589581\pi$
$348$		0			0
$349$	−26.9652			−1.44341			−0.721707	−	0.692199i	$-0.756642\pi$
$349$	−26.9652			−1.44341			−0.721707	+	0.692199i	$0.756642\pi$
$350$	27.5462	−	47.4437i	1.47241	−	2.53597i
$351$		0			0
$352$		−	3.96636i		−	0.211408i
$353$		−	13.4352i		−	0.715082i	−0.933898	−	0.357541i	$-0.883615\pi$
$353$		−	13.4352i		−	0.715082i	0.933898	−	0.357541i	$-0.116385\pi$
$354$		0			0
$355$	0.635502	+	1.10383i	0.0337289	+	0.0585852i
$356$	−23.2681			−1.23321
$357$		0			0
$358$		−	18.0422i		−	0.953561i
$359$	11.3884			0.601056			0.300528	−	0.953773i	$-0.402837\pi$
$359$	11.3884			0.601056			0.300528	+	0.953773i	$0.402837\pi$
$360$		0			0
$361$	−11.0845			−0.583393
$362$			8.99337i			0.472681i
$363$		0			0
$364$	17.6691			0.926115
$365$	0.722987	−	0.416241i	0.0378429	−	0.0217871i
$366$		0			0
$367$		−	6.81346i		−	0.355660i	−0.984061	−	0.177830i	$-0.943092\pi$
$367$		−	6.81346i		−	0.355660i	0.984061	−	0.177830i	$-0.0569076\pi$
$368$		−	14.1929i		−	0.739855i
$369$		0			0
$370$	17.2202	+	29.9104i	0.895235	+	1.55497i
$371$	−44.2736			−2.29857
$372$		0			0
$373$			9.39420i			0.486413i	0.969974	+	0.243207i	$0.0781993\pi$
$373$			9.39420i			0.486413i	−0.969974	+	0.243207i	$0.921801\pi$
$374$	25.2677			1.30656
$375$		0			0
$376$	−42.3258			−2.18278
$377$		0			0
$378$		0			0
$379$	29.8768			1.53467			0.767334	−	0.641247i	$-0.221583\pi$
$379$	29.8768			1.53467			0.767334	+	0.641247i	$0.221583\pi$
$380$	−12.2959	−	21.3573i	−0.630768	−	1.09561i
$381$		0			0
$382$		−	20.8135i		−	1.06491i
$383$		−	1.65820i		−	0.0847299i	−0.999102	−	0.0423650i	$-0.986511\pi$
$383$		−	1.65820i		−	0.0847299i	0.999102	−	0.0423650i	$-0.0134892\pi$
$384$		0			0
$385$	−43.9863	+	25.3240i	−2.24175	+	1.29063i
$386$	37.3791			1.90255
$387$		0			0
$388$		−	10.4826i		−	0.532173i
$389$	23.0835			1.17038			0.585190	−	0.810896i	$-0.301020\pi$
$389$	23.0835			1.17038			0.585190	+	0.810896i	$0.301020\pi$
$390$		0			0
$391$	−8.34513			−0.422031
$392$			62.2402i			3.14360i
$393$		0			0
$394$	−27.4701			−1.38392
$395$	−6.84740	−	11.8935i	−0.344530	−	0.598428i
$396$		0			0
$397$		−	7.09130i		−	0.355902i	−0.984039	−	0.177951i	$-0.943053\pi$
$397$		−	7.09130i		−	0.355902i	0.984039	−	0.177951i	$-0.0569469\pi$
$398$			43.4862i			2.17976i
$399$		0			0
$400$	−8.81346	+	15.1797i	−0.440673	+	0.758985i
$401$	33.1010			1.65298			0.826492	−	0.562948i	$-0.190333\pi$
$401$	33.1010			1.65298			0.826492	+	0.562948i	$0.190333\pi$
$402$		0			0
$403$		−	7.83457i		−	0.390268i
$404$	−46.5362			−2.31526
$405$		0			0
$406$		0			0
$407$		−	31.9306i		−	1.58274i
$408$		0			0
$409$	16.0422			0.793237			0.396619	−	0.917983i	$-0.370184\pi$
$409$	16.0422			0.793237			0.396619	+	0.917983i	$0.370184\pi$
$410$	−6.96324	+	4.00891i	−0.343890	+	0.197986i
$411$		0			0
$412$		−	8.64803i		−	0.426058i
$413$			59.5551i			2.93051i
$414$		0			0
$415$	1.26926	−	0.730743i	0.0623054	−	0.0358708i
$416$	0.788180			0.0386437
$417$		0			0
$418$			34.4404i			1.68453i
$419$	−2.64758			−0.129343			−0.0646714	−	0.997907i	$-0.520600\pi$
$419$	−2.64758			−0.129343			−0.0646714	+	0.997907i	$0.520600\pi$
$420$		0			0
$421$	−29.0074			−1.41374			−0.706868	−	0.707346i	$-0.749892\pi$
$421$	−29.0074			−1.41374			−0.706868	+	0.707346i	$0.749892\pi$
$422$			38.5183i			1.87504i
$423$		0			0
$424$	45.7787			2.22321
$425$	8.92537	+	5.18214i	0.432944	+	0.251371i
$426$		0			0
$427$			37.6412i			1.82158i
$428$			39.7603i			1.92189i
$429$		0			0
$430$	18.4912	+	32.1181i	0.891724	+	1.54887i
$431$	17.2970			0.833169			0.416585	−	0.909097i	$-0.363227\pi$
$431$	17.2970			0.833169			0.416585	+	0.909097i	$0.363227\pi$
$432$		0			0
$433$			21.3383i			1.02545i	0.858552	+	0.512726i	$0.171364\pi$
$433$			21.3383i			1.02545i	−0.858552	+	0.512726i	$0.828636\pi$
$434$	85.9621			4.12631
$435$		0			0
$436$	1.46149			0.0699925
$437$		−	11.3746i		−	0.544119i
$438$		0			0
$439$	0.675986			0.0322630			0.0161315	−	0.999870i	$-0.494865\pi$
$439$	0.675986			0.0322630			0.0161315	+	0.999870i	$0.494865\pi$
$440$	45.4816	−	26.1849i	2.16825	−	1.24831i
$441$		0			0
$442$			5.02112i			0.238830i
$443$		−	11.6583i		−	0.553903i	−0.960884	−	0.276952i	$-0.910676\pi$
$443$		−	11.6583i		−	0.553903i	0.960884	−	0.276952i	$-0.0893242\pi$
$444$		0			0
$445$	6.62691	+	11.5106i	0.314146	+	0.545653i
$446$	−3.55513			−0.168340
$447$		0			0
$448$			40.3172i			1.90481i
$449$	2.98552			0.140895			0.0704477	−	0.997515i	$-0.477557\pi$
$449$	2.98552			0.140895			0.0704477	+	0.997515i	$0.477557\pi$
$450$		0			0
$451$	7.43353			0.350031
$452$			27.0758i			1.27354i
$453$		0			0
$454$	29.7450			1.39600
$455$	−5.03230	−	8.74080i	−0.235918	−	0.409775i
$456$		0			0
$457$			28.0565i			1.31243i	0.754575	+	0.656214i	$0.227843\pi$
$457$			28.0565i			1.31243i	−0.754575	+	0.656214i	$0.772157\pi$
$458$			59.1527i			2.76402i
$459$		0			0
$460$	−30.6903	+	17.6691i	−1.43094	+	0.823828i
$461$	23.4215			1.09085			0.545423	−	0.838161i	$-0.316369\pi$
$461$	23.4215			1.09085			0.545423	+	0.838161i	$0.316369\pi$
$462$		0			0
$463$		−	4.51056i		−	0.209623i	−0.994492	−	0.104812i	$-0.966576\pi$
$463$		−	4.51056i		−	0.209623i	0.994492	−	0.104812i	$-0.0334240\pi$
$464$		0			0
$465$		0			0
$466$	36.3594			1.68432
$467$		−	24.3428i		−	1.12645i	−0.826303	−	0.563226i	$-0.809560\pi$
$467$		−	24.3428i		−	1.12645i	0.826303	−	0.563226i	$-0.190440\pi$
$468$		0			0
$469$	−71.4227			−3.29800
$470$	24.6294	+	42.7798i	1.13607	+	1.97329i
$471$		0			0
$472$		−	61.5796i		−	2.83443i
$473$		−	34.2873i		−	1.57653i
$474$		0			0
$475$	−7.06335	+	12.1654i	−0.324089	+	0.558188i
$476$	−36.4716			−1.67167
$477$		0			0
$478$		−	23.0970i		−	1.05643i
$479$	−16.9120			−0.772729			−0.386364	−	0.922346i	$-0.626269\pi$
$479$	−16.9120			−0.772729			−0.386364	+	0.922346i	$0.626269\pi$
$480$		0			0
$481$	6.34513			0.289313
$482$		−	6.33873i		−	0.288721i
$483$		0			0
$484$	−56.1113			−2.55051
$485$	−5.18567	+	2.98552i	−0.235469	+	0.135565i
$486$		0			0
$487$			31.5739i			1.43075i	0.698741	+	0.715375i	$0.253744\pi$
$487$			31.5739i			1.43075i	−0.698741	+	0.715375i	$0.746256\pi$
$488$		−	38.9208i		−	1.76186i
$489$		0			0
$490$	62.9079	−	36.2176i	2.84189	−	1.63615i
$491$	−14.8340			−0.669450			−0.334725	−	0.942316i	$-0.608643\pi$
$491$	−14.8340			−0.669450			−0.334725	+	0.942316i	$0.608643\pi$
$492$		0			0
$493$		0			0
$494$	−6.84387			−0.307920
$495$		0			0
$496$	−27.5037			−1.23495
$497$			2.56928i			0.115248i
$498$		0			0
$499$	−0.771227			−0.0345248			−0.0172624	−	0.999851i	$-0.505495\pi$
$499$	−0.771227			−0.0345248			−0.0172624	+	0.999851i	$0.505495\pi$
$500$	43.7963	+	0.160288i	1.95863	+	0.00716828i
$501$		0			0
$502$			3.66914i			0.163762i
$503$		−	41.5407i		−	1.85221i	−0.377269	−	0.926104i	$-0.623137\pi$
$503$		−	41.5407i		−	1.85221i	0.377269	−	0.926104i	$-0.376863\pi$
$504$		0			0
$505$	13.2538	+	23.0211i	0.589788	+	1.02443i
$506$	49.4905			2.20012
$507$		0			0
$508$			14.3731i			0.637703i
$509$	−33.8552			−1.50060			−0.750302	−	0.661095i	$-0.770092\pi$
$509$	−33.8552			−1.50060			−0.750302	+	0.661095i	$0.770092\pi$
$510$		0			0
$511$	1.68283			0.0744439
$512$		−	35.5127i		−	1.56945i
$513$		0			0
$514$	18.0422			0.795809
$515$	−4.27812	+	2.46302i	−0.188516	+	0.108534i
$516$		0			0
$517$		−	45.6691i		−	2.00853i
$518$			69.6197i			3.05891i
$519$		0			0
$520$	5.20336	+	9.03794i	0.228183	+	0.396340i
$521$	−25.2677			−1.10700			−0.553500	−	0.832849i	$-0.686708\pi$
$521$	−25.2677			−1.10700			−0.553500	+	0.832849i	$0.686708\pi$
$522$		0			0
$523$		−	11.2288i		−	0.491000i	−0.969397	−	0.245500i	$-0.921048\pi$
$523$		−	11.2288i		−	0.491000i	0.969397	−	0.245500i	$-0.0789521\pi$
$524$	74.3891			3.24970
$525$		0			0
$526$	−55.3383			−2.41286
$527$			16.1716i			0.704448i
$528$		0			0
$529$	6.65487			0.289342
$530$	−26.6386	−	46.2698i	−1.15711	−	2.00983i
$531$		0			0
$532$		−	49.7114i		−	2.15526i
$533$			1.47716i			0.0639831i
$534$		0			0
$535$	19.6691	−	11.3240i	0.850371	−	0.489580i
$536$	73.8507			3.18986
$537$		0			0
$538$			21.7114i			0.936044i
$539$	−67.1567			−2.89264
$540$		0			0
$541$	6.41532			0.275816			0.137908	−	0.990445i	$-0.455962\pi$
$541$	6.41532			0.275816			0.137908	+	0.990445i	$0.455962\pi$
$542$		−	19.8628i		−	0.853180i
$543$		0			0
$544$	−1.62691			−0.0697533
$545$	−0.416241	−	0.722987i	−0.0178298	−	0.0309694i
$546$		0			0
$547$			24.8557i			1.06275i	0.847136	+	0.531376i	$0.178325\pi$
$547$			24.8557i			1.06275i	−0.847136	+	0.531376i	$0.821675\pi$
$548$		−	27.5324i		−	1.17612i
$549$		0			0
$550$	−52.9316	−	30.7325i	−2.25701	−	1.31044i
$551$		0			0
$552$		0			0
$553$		−	27.6834i		−	1.17722i
$554$	−64.0178			−2.71985
$555$		0			0
$556$	74.4016			3.15533
$557$		−	35.0450i		−	1.48491i	−0.669898	−	0.742453i	$-0.733662\pi$
$557$		−	35.0450i		−	1.48491i	0.669898	−	0.742453i	$-0.266338\pi$
$558$		0			0
$559$	6.81346			0.288179
$560$	−30.6851	+	17.6662i	−1.29668	+	0.746532i
$561$		0			0
$562$		−	47.9527i		−	2.02276i
$563$		−	31.7598i		−	1.33852i	−0.743029	−	0.669259i	$-0.766612\pi$
$563$		−	31.7598i		−	1.33852i	0.743029	−	0.669259i	$-0.233388\pi$
$564$		0			0
$565$	13.3942	−	7.71137i	0.563498	−	0.324420i
$566$	65.8329			2.76716
$567$		0			0
$568$		−	2.65662i		−	0.111469i
$569$	2.95433			0.123852			0.0619259	−	0.998081i	$-0.480276\pi$
$569$	2.95433			0.123852			0.0619259	+	0.998081i	$0.480276\pi$
$570$		0			0
$571$	−12.7855			−0.535057			−0.267528	−	0.963550i	$-0.586207\pi$
$571$	−12.7855			−0.535057			−0.267528	+	0.963550i	$0.586207\pi$
$572$		−	19.7129i		−	0.824240i
$573$		0			0
$574$	−16.2077			−0.676495
$575$	17.4816	+	10.1500i	0.729033	+	0.423283i
$576$		0			0
$577$			10.0143i			0.416900i	0.978033	+	0.208450i	$0.0668418\pi$
$577$			10.0143i			0.416900i	−0.978033	+	0.208450i	$0.933158\pi$
$578$			30.9890i			1.28897i
$579$		0			0
$580$		0			0
$581$	2.95433			0.122566
$582$		0			0
$583$			49.3948i			2.04572i
$584$	−1.74003			−0.0720031
$585$		0			0
$586$	−11.8682			−0.490271
$587$			17.9659i			0.741530i	0.928727	+	0.370765i	$0.120904\pi$
$587$			17.9659i			0.741530i	−0.928727	+	0.370765i	$0.879096\pi$
$588$		0			0
$589$	−22.0422			−0.908234
$590$	−62.2402	+	35.8332i	−2.56239	+	1.47523i
$591$		0			0
$592$		−	22.2749i		−	0.915494i
$593$		−	6.18889i		−	0.254147i	−0.991893	−	0.127074i	$-0.959442\pi$
$593$		−	6.18889i		−	0.254147i	0.991893	−	0.127074i	$-0.0405584\pi$
$594$		0			0
$595$	10.3874	+	18.0422i	0.425840	+	0.739659i
$596$	−74.2669			−3.04209
$597$		0			0
$598$			9.83457i			0.402166i
$599$	37.6108			1.53674			0.768368	−	0.640009i	$-0.221069\pi$
$599$	37.6108			1.53674			0.768368	+	0.640009i	$0.221069\pi$
$600$		0			0
$601$	7.32401			0.298753			0.149376	−	0.988780i	$-0.452273\pi$
$601$	7.32401			0.298753			0.149376	+	0.988780i	$0.452273\pi$
$602$			74.7582i			3.04692i
$603$		0			0
$604$	66.0285			2.68666
$605$	15.9809	+	27.7579i	0.649715	+	1.12852i
$606$		0			0
$607$			18.7575i			0.761345i	0.924710	+	0.380673i	$0.124308\pi$
$607$			18.7575i			0.761345i	−0.924710	+	0.380673i	$0.875692\pi$
$608$		−	2.21751i		−	0.0899320i
$609$		0			0
$610$	−39.3383	+	22.6480i	−1.59276	+	0.916992i
$611$	9.07521			0.367144
$612$		0			0
$613$			1.73933i			0.0702509i	0.999383	+	0.0351255i	$0.0111831\pi$
$613$			1.73933i			0.0702509i	−0.999383	+	0.0351255i	$0.988817\pi$
$614$	31.1013			1.25515
$615$		0			0
$616$	105.863			4.26535
$617$		−	1.39180i		−	0.0560317i	−0.999607	−	0.0280158i	$-0.991081\pi$
$617$		−	1.39180i		−	0.0560317i	0.999607	−	0.0280158i	$-0.00891888\pi$
$618$		0			0
$619$	−14.2077			−0.571054			−0.285527	−	0.958371i	$-0.592169\pi$
$619$	−14.2077			−0.571054			−0.285527	+	0.958371i	$0.592169\pi$
$620$	34.2402	+	59.4732i	1.37512	+	2.38850i
$621$		0			0
$622$		−	67.0074i		−	2.68675i
$623$			26.7920i			1.07340i
$624$		0			0
$625$	−12.3942	−	21.7114i	−0.495768	−	0.868455i
$626$	76.1291			3.04273
$627$		0			0
$628$		−	35.3383i		−	1.41015i
$629$	−13.0972			−0.522221
$630$		0			0
$631$	−35.2288			−1.40244			−0.701218	−	0.712947i	$-0.747360\pi$
$631$	−35.2288			−1.40244			−0.701218	+	0.712947i	$0.747360\pi$
$632$			28.6245i			1.13862i
$633$		0			0
$634$	−9.01253			−0.357933
$635$	7.11027	−	4.09356i	0.282162	−	0.162448i
$636$		0			0
$637$		−	13.3451i		−	0.528753i
$638$		0			0
$639$		0			0
$640$	−39.0802	+	22.4994i	−1.54478	+	0.889368i
$641$	−35.7957			−1.41384			−0.706922	−	0.707291i	$-0.749917\pi$
$641$	−35.7957			−1.41384			−0.706922	+	0.707291i	$0.749917\pi$
$642$		0			0
$643$		−	21.8066i		−	0.859969i	−0.902836	−	0.429984i	$-0.858519\pi$
$643$		−	21.8066i		−	0.859969i	0.902836	−	0.429984i	$-0.141481\pi$
$644$	−71.4348			−2.81492
$645$		0			0
$646$	14.1267			0.555807
$647$		−	27.4608i		−	1.07960i	−0.841794	−	0.539798i	$-0.818500\pi$
$647$		−	27.4608i		−	1.07960i	0.841794	−	0.539798i	$-0.181500\pi$
$648$		0			0
$649$	66.4439			2.60815
$650$	6.10705	−	10.5184i	0.239538	−	0.412564i
$651$		0			0
$652$			3.29606i			0.129084i
$653$		−	1.34468i		−	0.0526215i	−0.999654	−	0.0263107i	$-0.991624\pi$
$653$		−	1.34468i		−	0.0526215i	0.999654	−	0.0263107i	$-0.00837594\pi$
$654$		0			0
$655$	−21.1865	−	36.7998i	−0.827827	−	1.43789i
$656$	5.18567			0.202466
$657$		0			0
$658$			99.5745i			3.88182i
$659$	−24.8986			−0.969912			−0.484956	−	0.874538i	$-0.661164\pi$
$659$	−24.8986			−0.969912			−0.484956	+	0.874538i	$0.661164\pi$
$660$		0			0
$661$	22.3594			0.869680			0.434840	−	0.900508i	$-0.356805\pi$
$661$	22.3594			0.869680			0.434840	+	0.900508i	$0.356805\pi$
$662$		−	40.3334i		−	1.56760i
$663$		0			0
$664$	−3.05476			−0.118548
$665$	−24.5919	+	14.1582i	−0.953632	+	0.549030i
$666$		0			0
$667$		0			0
$668$		−	38.8389i		−	1.50272i
$669$		0			0
$670$	−42.9738	−	74.6429i	−1.66022	−	2.88371i
$671$	41.9952			1.62121
$672$		0			0
$673$			48.7747i			1.88013i	0.340999	+	0.940064i	$0.389235\pi$
$673$			48.7747i			1.88013i	−0.340999	+	0.940064i	$0.610765\pi$
$674$	−9.83292			−0.378750
$675$		0			0
$676$	3.91729			0.150665
$677$			21.1901i			0.814402i	0.913339	+	0.407201i	$0.133495\pi$
$677$			21.1901i			0.814402i	−0.913339	+	0.407201i	$0.866505\pi$
$678$		0			0
$679$	−12.0702			−0.463211
$680$	−10.7405	−	18.6556i	−0.411878	−	0.715408i
$681$		0			0
$682$		−	95.9053i		−	3.67241i
$683$		−	26.0517i		−	0.996840i	−0.866936	−	0.498420i	$-0.833914\pi$
$683$		−	26.0517i		−	0.996840i	0.866936	−	0.498420i	$-0.166086\pi$
$684$		0			0
$685$	−13.6201	+	7.84141i	−0.520396	+	0.299605i
$686$	69.6197			2.65809
$687$		0			0
$688$		−	23.9190i		−	0.911905i
$689$	−9.81556			−0.373943
$690$		0			0
$691$	19.8346			0.754543			0.377271	−	0.926103i	$-0.376862\pi$
$691$	19.8346			0.754543			0.377271	+	0.926103i	$0.376862\pi$
$692$		−	18.7916i		−	0.714348i
$693$		0			0
$694$	16.6903			0.633554
$695$	−21.1901	−	36.8060i	−0.803787	−	1.39613i
$696$		0			0
$697$		−	3.04907i		−	0.115492i
$698$		−	65.5941i		−	2.48277i
$699$		0			0
$700$	76.4016	+	44.3594i	2.88771	+	1.67663i
$701$	50.6297			1.91226			0.956129	−	0.292946i	$-0.0946356\pi$
$701$	50.6297			1.91226			0.956129	+	0.292946i	$0.0946356\pi$
$702$		0			0
$703$		−	17.8517i		−	0.673291i
$704$	44.9807			1.69527
$705$		0			0
$706$	32.6817			1.22999
$707$			53.5840i			2.01524i
$708$		0			0
$709$	−47.1056			−1.76909			−0.884544	−	0.466458i	$-0.845530\pi$
$709$	−47.1056			−1.76909			−0.884544	+	0.466458i	$0.845530\pi$
$710$	−2.68512	+	1.54589i	−0.100771	+	0.0580162i
$711$		0			0
$712$		−	27.7028i		−	1.03821i
$713$			31.6745i			1.18622i
$714$		0			0
$715$	−9.75186	+	5.61439i	−0.364699	+	0.209966i
$716$	29.0546			1.08582
$717$		0			0
$718$			27.7028i			1.03386i
$719$	10.4337			0.389112			0.194556	−	0.980891i	$-0.437673\pi$
$719$	10.4337			0.389112			0.194556	+	0.980891i	$0.437673\pi$
$720$		0			0
$721$	−9.95777			−0.370847
$722$		−	26.9635i		−	1.00348i
$723$		0			0
$724$	−14.4826			−0.538242
$725$		0			0
$726$		0			0
$727$		−	3.66914i		−	0.136081i	−0.997683	−	0.0680405i	$-0.978325\pi$
$727$		−	3.66914i		−	0.136081i	0.997683	−	0.0680405i	$-0.0216747\pi$
$728$			21.0367i			0.779673i
$729$		0			0
$730$	1.01253	+	1.75870i	0.0374753	+	0.0650924i
$731$	−14.0639			−0.520173
$732$		0			0
$733$			15.5567i			0.574601i	0.957841	+	0.287300i	$0.0927578\pi$
$733$			15.5567i			0.574601i	−0.957841	+	0.287300i	$0.907242\pi$
$734$	16.5741			0.611760
$735$		0			0
$736$	−3.18654			−0.117458
$737$			79.6843i			2.93521i
$738$		0			0
$739$	−13.5459			−0.498296			−0.249148	−	0.968465i	$-0.580151\pi$
$739$	−13.5459			−0.498296			−0.249148	+	0.968465i	$0.580151\pi$
$740$	−48.1667	+	27.7308i	−1.77064	+	1.01940i
$741$		0			0
$742$		−	107.698i		−	3.95371i
$743$		−	6.08616i		−	0.223280i	−0.993749	−	0.111640i	$-0.964390\pi$
$743$		−	6.08616i		−	0.223280i	0.993749	−	0.111640i	$-0.0356103\pi$
$744$		0			0
$745$	21.1517	+	36.7393i	0.774940	+	1.34602i
$746$	−22.8518			−0.836665
$747$		0			0
$748$			40.6903i			1.48778i
$749$	45.7820			1.67284
$750$		0			0
$751$	20.0702			0.732372			0.366186	−	0.930542i	$-0.380663\pi$
$751$	20.0702			0.732372			0.366186	+	0.930542i	$0.380663\pi$
$752$		−	31.8590i		−	1.16178i
$753$		0			0
$754$		0			0
$755$	−18.8054	−	32.6639i	−0.684398	−	1.18876i
$756$		0			0
$757$		−	9.39420i		−	0.341438i	−0.985320	−	0.170719i	$-0.945391\pi$
$757$		−	9.39420i		−	0.341438i	0.985320	−	0.170719i	$-0.0546090\pi$
$758$			72.6767i			2.63974i
$759$		0			0
$760$	25.4278	−	14.6394i	0.922365	−	0.531028i
$761$	−8.50912			−0.308456			−0.154228	−	0.988035i	$-0.549289\pi$
$761$	−8.50912			−0.308456			−0.154228	+	0.988035i	$0.549289\pi$
$762$		0			0
$763$		−	1.68283i		−	0.0609224i
$764$	33.5172			1.21261
$765$		0			0
$766$	4.03364			0.145741
$767$			13.2035i			0.476750i
$768$		0			0
$769$	32.6480			1.17732			0.588659	−	0.808381i	$-0.299656\pi$
$769$	32.6480			1.17732			0.588659	+	0.808381i	$0.299656\pi$
$770$	−61.6019	−	106.999i	−2.21998	−	3.85597i
$771$		0			0
$772$			60.1940i			2.16643i
$773$			7.66252i			0.275602i	0.990460	+	0.137801i	$0.0440034\pi$
$773$			7.66252i			0.275602i	−0.990460	+	0.137801i	$0.955997\pi$
$774$		0			0
$775$	19.6691	−	33.8768i	0.706537	−	1.21689i
$776$	12.4805			0.448024
$777$		0			0
$778$			56.1517i			2.01314i
$779$	4.15594			0.148902
$780$		0			0
$781$	2.86647			0.102570
$782$		−	20.2999i		−	0.725924i
$783$		0			0
$784$	−46.8488			−1.67317
$785$	−17.4816	+	10.0646i	−0.623945	+	0.359221i
$786$		0			0
$787$		−	41.2151i		−	1.46916i	−0.678522	−	0.734580i	$-0.737379\pi$
$787$		−	41.2151i		−	1.46916i	0.678522	−	0.734580i	$-0.262621\pi$
$788$		−	44.2368i		−	1.57587i
$789$		0			0
$790$	28.9316	−	16.6566i	1.02934	−	0.592616i
$791$	31.1764			1.10851
$792$		0			0
$793$			8.34513i			0.296344i
$794$	17.2499			0.612177
$795$		0			0
$796$	−70.0285			−2.48210
$797$		−	8.47087i		−	0.300054i	−0.988682	−	0.150027i	$-0.952064\pi$
$797$		−	8.47087i		−	0.300054i	0.988682	−	0.150027i	$-0.0479360\pi$
$798$		0			0
$799$	−18.7325			−0.662708
$800$	3.40810	+	1.97877i	0.120495	+	0.0699602i
$801$		0			0
$802$			80.5197i			2.84325i
$803$		−	1.87748i		−	0.0662549i
$804$		0			0
$805$	20.3451	+	35.3383i	0.717072	+	1.24551i
$806$	19.0580			0.671288
$807$		0			0
$808$		−	55.4056i		−	1.94916i
$809$	−47.6754			−1.67618			−0.838089	−	0.545534i	$-0.816327\pi$
$809$	−47.6754			−1.67618			−0.838089	+	0.545534i	$0.816327\pi$
$810$		0			0
$811$	21.5174			0.755578			0.377789	−	0.925892i	$-0.376684\pi$
$811$	21.5174			0.755578			0.377789	+	0.925892i	$0.376684\pi$
$812$		0			0
$813$		0			0
$814$	77.6726			2.72242
$815$	1.63054	−	0.938741i	0.0571152	−	0.0328826i
$816$		0			0
$817$		−	19.1694i		−	0.670651i
$818$			39.0235i			1.36442i
$819$		0			0
$820$	−6.45580	−	11.2133i	−0.225446	−	0.391587i
$821$	−10.7093			−0.373756			−0.186878	−	0.982383i	$-0.559837\pi$
$821$	−10.7093			−0.373756			−0.186878	+	0.982383i	$0.559837\pi$
$822$		0			0
$823$			3.89049i			0.135614i	0.997698	+	0.0678069i	$0.0216002\pi$
$823$			3.89049i			0.135614i	−0.997698	+	0.0678069i	$0.978400\pi$
$824$	10.2963			0.358688
$825$		0			0
$826$	−144.871			−5.04069
$827$		−	38.6072i		−	1.34251i	−0.741229	−	0.671253i	$-0.765757\pi$
$827$		−	38.6072i		−	1.34251i	0.741229	−	0.671253i	$-0.234243\pi$
$828$		0			0
$829$	20.6903			0.718602			0.359301	−	0.933222i	$-0.383015\pi$
$829$	20.6903			0.718602			0.359301	+	0.933222i	$0.383015\pi$
$830$	1.77757	+	3.08753i	0.0617002	+	0.107170i
$831$		0			0
$832$			8.93840i			0.309883i
$833$			27.5462i			0.954419i
$834$		0			0
$835$	−19.2133	+	11.0616i	−0.664905	+	0.382802i
$836$	−55.4615			−1.91818
$837$		0			0
$838$		−	6.44037i		−	0.222479i
$839$	−9.49498			−0.327803			−0.163902	−	0.986477i	$-0.552408\pi$
$839$	−9.49498			−0.327803			−0.163902	+	0.986477i	$0.552408\pi$
$840$		0			0
$841$	−29.0000			−1.00000
$842$		−	70.5619i		−	2.43173i
$843$		0			0
$844$	−62.0285			−2.13511
$845$	−1.11567	−	1.93785i	−0.0383802	−	0.0666642i
$846$		0			0
$847$			64.6093i			2.22000i
$848$			34.4581i			1.18330i
$849$		0			0
$850$	−12.6058	+	21.7114i	−0.432375	+	0.744694i
$851$	−25.6528			−0.879366
$852$		0			0
$853$		−	24.3874i		−	0.835007i	−0.908675	−	0.417504i	$-0.862905\pi$
$853$		−	24.3874i		−	0.835007i	0.908675	−	0.417504i	$-0.137095\pi$
$854$	−91.5640			−3.13325
$855$		0			0
$856$	−47.3383			−1.61799
$857$			28.1020i			0.959945i	0.877283	+	0.479973i	$0.159353\pi$
$857$			28.1020i			0.959945i	−0.877283	+	0.479973i	$0.840647\pi$
$858$		0			0
$859$	−39.1586			−1.33607			−0.668037	−	0.744128i	$-0.732865\pi$
$859$	−39.1586			−1.33607			−0.668037	+	0.744128i	$0.732865\pi$
$860$	−51.7218	+	29.7775i	−1.76370	+	1.01541i
$861$		0			0
$862$			42.0759i			1.43311i
$863$			6.62602i			0.225552i	0.993620	+	0.112776i	$0.0359743\pi$
$863$			6.62602i			0.225552i	−0.993620	+	0.112776i	$0.964026\pi$
$864$		0			0
$865$	−9.29606	+	5.35197i	−0.316075	+	0.181972i
$866$	−51.9064			−1.76385
$867$		0			0
$868$			138.430i			4.69863i
$869$	−30.8856			−1.04772
$870$		0			0
$871$	−15.8346			−0.536534
$872$			1.74003i			0.0589250i
$873$		0			0
$874$	27.6691			0.935923
$875$	0.184563	−	50.4292i	0.00623937	−	1.70482i
$876$		0			0
$877$			21.3383i			0.720543i	0.932848	+	0.360271i	$0.117316\pi$
$877$			21.3383i			0.720543i	−0.932848	+	0.360271i	$0.882684\pi$
$878$			1.64437i			0.0554947i
$879$		0			0
$880$	19.7096	+	34.2345i	0.664411	+	1.15404i
$881$	49.1214			1.65494			0.827470	−	0.561509i	$-0.189779\pi$
$881$	49.1214			1.65494			0.827470	+	0.561509i	$0.189779\pi$
$882$		0			0
$883$		−	6.28863i		−	0.211629i	−0.994386	−	0.105815i	$-0.966255\pi$
$883$		−	6.28863i		−	0.211629i	0.994386	−	0.105815i	$-0.0337450\pi$
$884$	−8.08582			−0.271956
$885$		0			0
$886$	28.3594			0.952753
$887$			42.4932i			1.42678i	0.700765	+	0.713392i	$0.252842\pi$
$887$			42.4932i			1.42678i	−0.700765	+	0.713392i	$0.747158\pi$
$888$		0			0
$889$	16.5499			0.555065
$890$	−28.0000	+	16.1203i	−0.938561	+	0.540353i
$891$		0			0
$892$		−	5.72506i		−	0.191689i
$893$		−	25.5327i		−	0.854419i
$894$		0			0
$895$	−8.27494	−	14.3731i	−0.276601	−	0.480439i
$896$	−90.9632			−3.03887
$897$		0			0
$898$			7.26242i			0.242350i
$899$		0			0
$900$		0			0
$901$	20.2607			0.674981
$902$			18.0824i			0.602078i
$903$		0			0
$904$	−32.2362			−1.07216
$905$	4.12475	+	7.16444i	0.137111	+	0.238154i
$906$		0			0
$907$			43.6132i			1.44815i	0.689719	+	0.724077i	$0.257734\pi$
$907$			43.6132i			1.44815i	−0.689719	+	0.724077i	$0.742266\pi$
$908$			47.9003i			1.58963i
$909$		0			0
$910$	21.2624	−	12.2413i	0.704842	−	0.405795i
$911$	10.0646			0.333455			0.166727	−	0.986003i	$-0.446680\pi$
$911$	10.0646			0.333455			0.166727	+	0.986003i	$0.446680\pi$
$912$		0			0
$913$		−	3.29606i		−	0.109084i
$914$	−68.2488			−2.25747
$915$		0			0
$916$	−95.2573			−3.14739
$917$		−	85.6553i		−	2.82859i
$918$		0			0
$919$	−17.3913			−0.573686			−0.286843	−	0.957978i	$-0.592606\pi$
$919$	−17.3913			−0.573686			−0.286843	+	0.957978i	$0.592606\pi$
$920$	−21.0367	−	36.5396i	−0.693561	−	1.20467i
$921$		0			0
$922$			56.9738i			1.87633i
$923$			0.569614i			0.0187491i
$924$		0			0
$925$	27.4364	+	15.9298i	0.902104	+	0.523769i
$926$	10.9721			0.360567
$927$		0			0
$928$		0			0
$929$	19.3279			0.634128			0.317064	−	0.948404i	$-0.397303\pi$
$929$	19.3279			0.634128			0.317064	+	0.948404i	$0.397303\pi$
$930$		0			0
$931$	−37.5459			−1.23052
$932$			58.5519i			1.91793i
$933$		0			0
$934$	59.2151			1.93758
$935$	20.1292	−	11.5889i	0.658295	−	0.378997i
$936$		0			0
$937$		−	15.9863i		−	0.522250i	−0.965305	−	0.261125i	$-0.915906\pi$
$937$		−	15.9863i		−	0.522250i	0.965305	−	0.261125i	$-0.0840935\pi$
$938$		−	173.739i		−	5.67279i
$939$		0			0
$940$	−68.8911	+	39.6623i	−2.24698	+	1.29364i
$941$	16.0044			0.521730			0.260865	−	0.965375i	$-0.415992\pi$
$941$	16.0044			0.521730			0.260865	+	0.965375i	$0.415992\pi$
$942$		0			0
$943$		−	5.97204i		−	0.194476i
$944$	46.3516			1.50862
$945$		0			0
$946$	83.4056			2.71175
$947$		−	46.0519i		−	1.49649i	−0.663425	−	0.748243i	$-0.730898\pi$
$947$		−	46.0519i		−	1.49649i	0.663425	−	0.748243i	$-0.269102\pi$
$948$		0			0
$949$	0.373086			0.0121109
$950$	−29.5930	−	17.1819i	−0.960123	−	0.557455i
$951$		0			0
$952$		−	43.4227i		−	1.40734i
$953$		−	50.7498i		−	1.64395i	−0.569525	−	0.821974i	$-0.692873\pi$
$953$		−	50.7498i		−	1.64395i	0.569525	−	0.821974i	$-0.307127\pi$
$954$		0			0
$955$	−9.54595	−	16.5807i	−0.308900	−	0.536540i
$956$	37.1946			1.20296
$957$		0			0
$958$		−	41.1392i		−	1.32915i
$959$	−31.7021			−1.02372
$960$		0			0
$961$	30.3805			0.980017
$962$			15.4348i			0.497639i
$963$		0			0
$964$	10.2077			0.328767
$965$	29.7775	−	17.1437i	0.958573	−	0.551874i
$966$		0			0
$967$		−	15.0884i		−	0.485210i	−0.970125	−	0.242605i	$-0.921998\pi$
$967$		−	15.0884i		−	0.485210i	0.970125	−	0.242605i	$-0.0780019\pi$
$968$		−	66.8056i		−	2.14721i
$969$		0			0
$970$	−7.26242	−	12.6144i	−0.233182	−	0.405024i
$971$	30.1938			0.968965			0.484482	−	0.874801i	$-0.339008\pi$
$971$	30.1938			0.968965			0.484482	+	0.874801i	$0.339008\pi$
$972$		0			0
$973$		−	85.6697i		−	2.74645i
$974$	−76.8050			−2.46099
$975$		0			0
$976$	29.2961			0.937744
$977$		−	23.3637i		−	0.747472i	−0.927535	−	0.373736i	$-0.878077\pi$
$977$		−	23.3637i		−	0.747472i	0.927535	−	0.373736i	$-0.121923\pi$
$978$		0			0
$979$	29.8911			0.955323
$980$	58.3236	+	101.305i	1.86308	+	3.23606i
$981$		0			0
$982$		−	36.0845i		−	1.15150i
$983$		−	25.3899i		−	0.809813i	−0.914358	−	0.404906i	$-0.867304\pi$
$983$		−	25.3899i		−	0.809813i	0.914358	−	0.404906i	$-0.132696\pi$
$984$		0			0
$985$	−21.8836	+	12.5990i	−0.697271	+	0.401436i
$986$		0			0
$987$		0			0
$988$		−	11.0211i		−	0.350628i
$989$	−27.5462			−0.875918
$990$		0			0
$991$	1.69710			0.0539102			0.0269551	−	0.999637i	$-0.491419\pi$
$991$	1.69710			0.0539102			0.0269551	+	0.999637i	$0.491419\pi$
$992$			6.17506i			0.196058i
$993$		0			0
$994$	−6.24989			−0.198234
$995$	19.9446	+	34.6426i	0.632287	+	1.09825i
$996$		0			0
$997$		−	31.6691i		−	1.00297i	−0.865166	−	0.501486i	$-0.832787\pi$
$997$		−	31.6691i		−	1.00297i	0.865166	−	0.501486i	$-0.167213\pi$
$998$		−	1.87605i		−	0.0593852i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	585.2.c.d.469.12	yes	12
3.2	odd	2	inner	585.2.c.d.469.1	✓	12
5.2	odd	4		2925.2.a.bn.1.1		6
5.3	odd	4		2925.2.a.bo.1.6		6
5.4	even	2	inner	585.2.c.d.469.2	yes	12
15.2	even	4		2925.2.a.bn.1.6		6
15.8	even	4		2925.2.a.bo.1.1		6
15.14	odd	2	inner	585.2.c.d.469.11	yes	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
585.2.c.d.469.1	✓	12	3.2	odd	2	inner
585.2.c.d.469.2	yes	12	5.4	even	2	inner
585.2.c.d.469.11	yes	12	15.14	odd	2	inner
585.2.c.d.469.12	yes	12	1.1	even	1	trivial
2925.2.a.bn.1.1		6	5.2	odd	4
2925.2.a.bn.1.6		6	15.2	even	4
2925.2.a.bo.1.1		6	15.8	even	4
2925.2.a.bo.1.6		6	5.3	odd	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 585 = 3^{2} \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	585.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+2.43255i q^{2} -3.91729 q^{4} +(1.11567 + 1.93785i) q^{5} +4.51056i q^{7} -4.66389i q^{8} +(-4.71392 + 2.71392i) q^{10} +5.03230 q^{11} +1.00000i q^{13} -10.9721 q^{14} +3.51056 q^{16} -2.06414i q^{17} +2.81346 q^{19} +(-4.37040 - 7.59113i) q^{20} +12.2413i q^{22} -4.04291i q^{23} +(-2.51056 + 4.32401i) q^{25} -2.43255 q^{26} -17.6691i q^{28} -7.83457 q^{31} -0.788180i q^{32} +5.02112 q^{34} +(-8.74080 + 5.03230i) q^{35} -6.34513i q^{37} +6.84387i q^{38} +(9.03794 - 5.20336i) q^{40} +1.47716 q^{41} -6.81346i q^{43} -19.7129 q^{44} +9.83457 q^{46} -9.07521i q^{47} -13.3451 q^{49} +(-10.5184 - 6.10705i) q^{50} -3.91729i q^{52} +9.81556i q^{53} +(5.61439 + 9.75186i) q^{55} +21.0367 q^{56} +13.2035 q^{59} +8.34513 q^{61} -19.0580i q^{62} +8.93840 q^{64} +(-1.93785 + 1.11567i) q^{65} +15.8346i q^{67} +8.08582i q^{68} +(-12.2413 - 21.2624i) q^{70} +0.569614 q^{71} -0.373086i q^{73} +15.4348 q^{74} -11.0211 q^{76} +22.6985i q^{77} -6.13747 q^{79} +(3.91663 + 6.80295i) q^{80} +3.59327i q^{82} -0.654981i q^{83} +(4.00000 - 2.30290i) q^{85} +16.5741 q^{86} -23.4701i q^{88} +5.93985 q^{89} -4.51056 q^{91} +15.8372i q^{92} +22.0759 q^{94} +(3.13889 + 5.45207i) q^{95} +2.67599i q^{97} -32.4627i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 8 q^{4} - 20 q^{10} + 8 q^{16} + 24 q^{19} + 4 q^{25} - 16 q^{31} - 8 q^{34} + 28 q^{40} + 40 q^{46} - 48 q^{49} + 4 q^{55} - 12 q^{61} - 64 q^{70} - 64 q^{76} - 20 q^{79} + 48 q^{85} - 20 q^{91}+ \cdots + 104 q^{94}+O(q^{100}) \) 12 * q - 8 * q^4 - 20 * q^10 + 8 * q^16 + 24 * q^19 + 4 * q^25 - 16 * q^31 - 8 * q^34 + 28 * q^40 + 40 * q^46 - 48 * q^49 + 4 * q^55 - 12 * q^61 - 64 * q^70 - 64 * q^76 - 20 * q^79 + 48 * q^85 - 20 * q^91 + 104 * q^94

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more