LMFDB - Embedded newform 578.4.a.g.1.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [578,4,Mod(1,578)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("578.1"); S:= CuspForms(chi, 4); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(578, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0])) N = Newforms(chi, 4, names="a")

Level:	$ N $	$=$	$ 578 = 2 \cdot 17^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	578.a (trivial)

Newform invariants

comment:select newform

sage:traces = [2,-4,7,8,-1,-14,19] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

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

Self dual:	yes
Analytic conductor:	$34.1031039833$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\sqrt{13}) $
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 3 $ x^2 - x - 3
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$2.30278$ of defining polynomial
Character	$\chi$	$=$	578.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-2.00000 q^{2} +8.90833 q^{3} +4.00000 q^{4} +1.30278 q^{5} -17.8167 q^{6} +32.9361 q^{7} -8.00000 q^{8} +52.3583 q^{9} -2.60555 q^{10} +39.2389 q^{11} +35.6333 q^{12} +67.5694 q^{13} -65.8722 q^{14} +11.6056 q^{15} +16.0000 q^{16} -104.717 q^{18} -26.0639 q^{19} +5.21110 q^{20} +293.405 q^{21} -78.4777 q^{22} -50.0917 q^{23} -71.2666 q^{24} -123.303 q^{25} -135.139 q^{26} +225.900 q^{27} +131.744 q^{28} -215.902 q^{29} -23.2111 q^{30} -93.8999 q^{31} -32.0000 q^{32} +349.553 q^{33} +42.9083 q^{35} +209.433 q^{36} -193.761 q^{37} +52.1278 q^{38} +601.930 q^{39} -10.4222 q^{40} -282.955 q^{41} -586.811 q^{42} +124.522 q^{43} +156.955 q^{44} +68.2111 q^{45} +100.183 q^{46} +202.817 q^{47} +142.533 q^{48} +741.786 q^{49} +246.606 q^{50} +270.278 q^{52} -569.258 q^{53} -451.800 q^{54} +51.1194 q^{55} -263.489 q^{56} -232.186 q^{57} +431.805 q^{58} +137.566 q^{59} +46.4222 q^{60} -3.34988 q^{61} +187.800 q^{62} +1724.48 q^{63} +64.0000 q^{64} +88.0278 q^{65} -699.105 q^{66} -764.560 q^{67} -446.233 q^{69} -85.8167 q^{70} -492.934 q^{71} -418.866 q^{72} +342.739 q^{73} +387.522 q^{74} -1098.42 q^{75} -104.256 q^{76} +1292.37 q^{77} -1203.86 q^{78} -645.643 q^{79} +20.8444 q^{80} +598.717 q^{81} +565.911 q^{82} -1274.67 q^{83} +1173.62 q^{84} -249.045 q^{86} -1923.33 q^{87} -313.911 q^{88} -830.700 q^{89} -136.422 q^{90} +2225.47 q^{91} -200.367 q^{92} -836.491 q^{93} -405.633 q^{94} -33.9554 q^{95} -285.066 q^{96} +956.748 q^{97} -1483.57 q^{98} +2054.48 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 4 q^{2} + 7 q^{3} + 8 q^{4} - q^{5} - 14 q^{6} + 19 q^{7} - 16 q^{8} + 29 q^{9} + 2 q^{10} + 28 q^{11} + 28 q^{12} + 45 q^{13} - 38 q^{14} + 16 q^{15} + 32 q^{16} - 58 q^{18} - 99 q^{19} - 4 q^{20}+ \cdots + 2317 q^{99}+O(q^{100}) $ 2 * q - 4 * q^2 + 7 * q^3 + 8 * q^4 - q^5 - 14 * q^6 + 19 * q^7 - 16 * q^8 + 29 * q^9 + 2 * q^10 + 28 * q^11 + 28 * q^12 + 45 * q^13 - 38 * q^14 + 16 * q^15 + 32 * q^16 - 58 * q^18 - 99 * q^19 - 4 * q^20 + 320 * q^21 - 56 * q^22 - 111 * q^23 - 56 * q^24 - 243 * q^25 - 90 * q^26 + 322 * q^27 + 76 * q^28 + 91 * q^29 - 32 * q^30 - 58 * q^31 - 64 * q^32 + 371 * q^33 + 75 * q^35 + 116 * q^36 - 438 * q^37 + 198 * q^38 + 645 * q^39 + 8 * q^40 - 364 * q^41 - 640 * q^42 + 350 * q^43 + 112 * q^44 + 122 * q^45 + 222 * q^46 + 384 * q^47 + 112 * q^48 + 593 * q^49 + 486 * q^50 + 180 * q^52 - 933 * q^53 - 644 * q^54 + 77 * q^55 - 152 * q^56 - 93 * q^57 - 182 * q^58 - 720 * q^59 + 64 * q^60 + 188 * q^61 + 116 * q^62 + 2050 * q^63 + 128 * q^64 + 140 * q^65 - 742 * q^66 - 22 * q^67 - 330 * q^69 - 150 * q^70 - 1332 * q^71 - 232 * q^72 + 1284 * q^73 + 876 * q^74 - 870 * q^75 - 396 * q^76 + 1449 * q^77 - 1290 * q^78 + 324 * q^79 - 16 * q^80 + 1046 * q^81 + 728 * q^82 + 7 * q^83 + 1280 * q^84 - 700 * q^86 - 2509 * q^87 - 224 * q^88 - 1272 * q^89 - 244 * q^90 + 2540 * q^91 - 444 * q^92 - 905 * q^93 - 768 * q^94 + 134 * q^95 - 224 * q^96 + 2631 * q^97 - 1186 * q^98 + 2317 * q^99

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 $

$2$	−2.00000	−0.707107
$2$	−2.00000	−0.707107
$3$	8.90833	1.71441	0.857204	−	0.514977i	$-0.172199\pi$
$3$	8.90833	1.71441	0.857204	+	0.514977i	$0.172199\pi$
$4$	4.00000	0.500000
$5$	1.30278	0.116524	0.0582619	−	0.998301i	$-0.481444\pi$
$5$	1.30278	0.116524	0.0582619	+	0.998301i	$0.481444\pi$
$6$	−17.8167	−1.21227
$7$	32.9361	1.77838	0.889191	−	0.457537i	$-0.151268\pi$
$7$	32.9361	1.77838	0.889191	+	0.457537i	$0.151268\pi$
$8$	−8.00000	−0.353553
$9$	52.3583	1.93920
$10$	−2.60555	−0.0823948
$11$	39.2389	1.07554	0.537771	−	0.843091i	$-0.319267\pi$
$11$	39.2389	1.07554	0.537771	+	0.843091i	$0.319267\pi$
$12$	35.6333	0.857204
$13$	67.5694	1.44157	0.720784	−	0.693160i	$-0.243782\pi$
$13$	67.5694	1.44157	0.720784	+	0.693160i	$0.243782\pi$
$14$	−65.8722	−1.25751
$15$	11.6056	0.199769
$16$	16.0000	0.250000
$17$	0	0
$17$	0	0
$18$	−104.717	−1.37122
$19$	−26.0639	−0.314709	−0.157355	−	0.987542i	$-0.550297\pi$
$19$	−26.0639	−0.314709	−0.157355	+	0.987542i	$0.550297\pi$
$20$	5.21110	0.0582619
$21$	293.405	3.04887
$22$	−78.4777	−0.760523
$23$	−50.0917	−0.454123	−0.227062	−	0.973880i	$-0.572912\pi$
$23$	−50.0917	−0.454123	−0.227062	+	0.973880i	$0.572912\pi$
$24$	−71.2666	−0.606135
$25$	−123.303	−0.986422
$26$	−135.139	−1.01934
$27$	225.900	1.61017
$28$	131.744	0.889191
$29$	−215.902	−1.38249	−0.691243	−	0.722623i	$-0.742936\pi$
$29$	−215.902	−1.38249	−0.691243	+	0.722623i	$0.742936\pi$
$30$	−23.2111	−0.141258
$31$	−93.8999	−0.544030	−0.272015	−	0.962293i	$-0.587690\pi$
$31$	−93.8999	−0.544030	−0.272015	+	0.962293i	$0.587690\pi$
$32$	−32.0000	−0.176777
$33$	349.553	1.84392
$34$	0	0
$35$	42.9083	0.207224
$36$	209.433	0.969598
$37$	−193.761	−0.860923	−0.430461	−	0.902609i	$-0.641649\pi$
$37$	−193.761	−0.860923	−0.430461	+	0.902609i	$0.641649\pi$
$38$	52.1278	0.222533
$39$	601.930	2.47144
$40$	−10.4222	−0.0411974
$41$	−282.955	−1.07781	−0.538905	−	0.842367i	$-0.681162\pi$
$41$	−282.955	−1.07781	−0.538905	+	0.842367i	$0.681162\pi$
$42$	−586.811	−2.15588
$43$	124.522	0.441616	0.220808	−	0.975317i	$-0.429131\pi$
$43$	124.522	0.441616	0.220808	+	0.975317i	$0.429131\pi$
$44$	156.955	0.537771
$45$	68.2111	0.225962
$46$	100.183	0.321114
$47$	202.817	0.629444	0.314722	−	0.949184i	$-0.398089\pi$
$47$	202.817	0.629444	0.314722	+	0.949184i	$0.398089\pi$
$48$	142.533	0.428602
$49$	741.786	2.16264
$50$	246.606	0.697506
$51$	0	0
$52$	270.278	0.720784
$53$	−569.258	−1.47535	−0.737676	−	0.675155i	$-0.764077\pi$
$53$	−569.258	−1.47535	−0.737676	+	0.675155i	$0.764077\pi$
$54$	−451.800	−1.13856
$55$	51.1194	0.125326
$56$	−263.489	−0.628753
$57$	−232.186	−0.539540
$58$	431.805	0.977565
$59$	137.566	0.303552	0.151776	−	0.988415i	$-0.451501\pi$
$59$	137.566	0.303552	0.151776	+	0.988415i	$0.451501\pi$
$60$	46.4222	0.0998847
$61$	−3.34988	−0.00703129	−0.00351565	−	0.999994i	$-0.501119\pi$
$61$	−3.34988	−0.00703129	−0.00351565	+	0.999994i	$0.501119\pi$
$62$	187.800	0.384687
$63$	1724.48	3.44863
$64$	64.0000	0.125000
$65$	88.0278	0.167977
$66$	−699.105	−1.30385
$67$	−764.560	−1.39412	−0.697059	−	0.717014i	$-0.745508\pi$
$67$	−764.560	−1.39412	−0.697059	+	0.717014i	$0.745508\pi$
$68$	0	0
$69$	−446.233	−0.778553
$70$	−85.8167	−0.146529
$71$	−492.934	−0.823950	−0.411975	−	0.911195i	$-0.635161\pi$
$71$	−492.934	−0.823950	−0.411975	+	0.911195i	$0.635161\pi$
$72$	−418.866	−0.685609
$73$	342.739	0.549515	0.274757	−	0.961514i	$-0.411402\pi$
$73$	342.739	0.549515	0.274757	+	0.961514i	$0.411402\pi$
$74$	387.522	0.608764
$75$	−1098.42	−1.69113
$76$	−104.256	−0.157355
$77$	1292.37	1.91272
$78$	−1203.86	−1.74757
$79$	−645.643	−0.919501	−0.459750	−	0.888048i	$-0.652061\pi$
$79$	−645.643	−0.919501	−0.459750	+	0.888048i	$0.652061\pi$
$80$	20.8444	0.0291309
$81$	598.717	0.821285
$82$	565.911	0.762127
$83$	−1274.67	−1.68570	−0.842849	−	0.538150i	$-0.819124\pi$
$83$	−1274.67	−1.68570	−0.842849	+	0.538150i	$0.819124\pi$
$84$	1173.62	1.52444
$85$	0	0
$86$	−249.045	−0.312269
$87$	−1923.33	−2.37014
$88$	−313.911	−0.380261
$89$	−830.700	−0.989371	−0.494685	−	0.869072i	$-0.664717\pi$
$89$	−830.700	−0.989371	−0.494685	+	0.869072i	$0.664717\pi$
$90$	−136.422	−0.159780
$91$	2225.47	2.56366
$92$	−200.367	−0.227062
$93$	−836.491	−0.932689
$94$	−405.633	−0.445084
$95$	−33.9554	−0.0366711
$96$	−285.066	−0.303067
$97$	956.748	1.00147	0.500737	−	0.865599i	$-0.333062\pi$
$97$	956.748	1.00147	0.500737	+	0.865599i	$0.333062\pi$
$98$	−1483.57	−1.52922
$99$	2054.48	2.08569
$100$	−493.211	−0.493211
$101$	1229.79	1.21158	0.605788	−	0.795626i	$-0.292858\pi$
$101$	1229.79	1.21158	0.605788	+	0.795626i	$0.292858\pi$
$102$	0	0
$103$	483.810	0.462827	0.231414	−	0.972855i	$-0.425665\pi$
$103$	483.810	0.462827	0.231414	+	0.972855i	$0.425665\pi$
$104$	−540.555	−0.509671
$105$	382.241	0.355266
$106$	1138.52	1.04323
$107$	729.239	0.658862	0.329431	−	0.944180i	$-0.393143\pi$
$107$	729.239	0.658862	0.329431	+	0.944180i	$0.393143\pi$
$108$	903.600	0.805083
$109$	2235.27	1.96422	0.982108	−	0.188316i	$-0.0603030\pi$
$109$	2235.27	1.96422	0.982108	+	0.188316i	$0.0603030\pi$
$110$	−102.239	−0.0886190
$111$	−1726.09	−1.47597
$112$	526.977	0.444595
$113$	241.664	0.201185	0.100592	−	0.994928i	$-0.467926\pi$
$113$	241.664	0.201185	0.100592	+	0.994928i	$0.467926\pi$
$114$	464.372	0.381512
$115$	−65.2582	−0.0529162
$116$	−863.610	−0.691243
$117$	3537.82	2.79548
$118$	−275.132	−0.214644
$119$	0	0
$120$	−92.8444	−0.0706291
$121$	208.688	0.156790
$122$	6.69977	0.00497187
$123$	−2520.66	−1.84781
$124$	−375.600	−0.272015
$125$	−323.483	−0.231465
$126$	−3448.95	−2.43855
$127$	951.589	0.664881	0.332440	−	0.943124i	$-0.392128\pi$
$127$	951.589	0.664881	0.332440	+	0.943124i	$0.392128\pi$
$128$	−128.000	−0.0883883
$129$	1109.29	0.757109
$130$	−176.056	−0.118778
$131$	−74.6493	−0.0497874	−0.0248937	−	0.999690i	$-0.507925\pi$
$131$	−74.6493	−0.0497874	−0.0248937	+	0.999690i	$0.507925\pi$
$132$	1398.21	0.921959
$133$	−858.443	−0.559673
$134$	1529.12	0.985790
$135$	294.297	0.187623
$136$	0	0
$137$	−544.661	−0.339661	−0.169830	−	0.985473i	$-0.554322\pi$
$137$	−544.661	−0.339661	−0.169830	+	0.985473i	$0.554322\pi$
$138$	892.466	0.550520
$139$	−1385.49	−0.845437	−0.422718	−	0.906261i	$-0.638924\pi$
$139$	−1385.49	−0.845437	−0.422718	+	0.906261i	$0.638924\pi$
$140$	171.633	0.103612
$141$	1806.76	1.07912
$142$	985.867	0.582621
$143$	2651.35	1.55047
$144$	837.733	0.484799
$145$	−281.272	−0.161092
$146$	−685.478	−0.388566
$147$	6608.07	3.70765
$148$	−775.045	−0.430461
$149$	481.628	0.264809	0.132404	−	0.991196i	$-0.457730\pi$
$149$	481.628	0.264809	0.132404	+	0.991196i	$0.457730\pi$
$150$	2196.84	1.19581
$151$	−202.793	−0.109292	−0.0546460	−	0.998506i	$-0.517403\pi$
$151$	−202.793	−0.109292	−0.0546460	+	0.998506i	$0.517403\pi$
$152$	208.511	0.111266
$153$	0	0
$154$	−2584.75	−1.35250
$155$	−122.331	−0.0633924
$156$	2407.72	1.23572
$157$	2186.07	1.11126	0.555628	−	0.831431i	$-0.312478\pi$
$157$	2186.07	1.11126	0.555628	+	0.831431i	$0.312478\pi$
$158$	1291.29	0.650185
$159$	−5071.14	−2.52935
$160$	−41.6888	−0.0205987
$161$	−1649.82	−0.807604
$162$	−1197.43	−0.580736
$163$	354.790	0.170486	0.0852432	−	0.996360i	$-0.472833\pi$
$163$	354.790	0.170486	0.0852432	+	0.996360i	$0.472833\pi$
$164$	−1131.82	−0.538905
$165$	455.389	0.214860
$166$	2549.34	1.19197
$167$	−1120.78	−0.519333	−0.259666	−	0.965698i	$-0.583613\pi$
$167$	−1120.78	−0.519333	−0.259666	+	0.965698i	$0.583613\pi$
$168$	−2347.24	−1.07794
$169$	2368.62	1.07812
$170$	0	0
$171$	−1364.66	−0.610283
$172$	498.089	0.220808
$173$	1731.68	0.761025	0.380512	−	0.924776i	$-0.375748\pi$
$173$	1731.68	0.761025	0.380512	+	0.924776i	$0.375748\pi$
$174$	3846.66	1.67595
$175$	−4061.11	−1.75423
$176$	627.822	0.268885
$177$	1225.48	0.520412
$178$	1661.40	0.699591
$179$	4198.04	1.75294	0.876470	−	0.481457i	$-0.159892\pi$
$179$	4198.04	1.75294	0.876470	+	0.481457i	$0.159892\pi$
$180$	272.844	0.112981
$181$	47.4660	0.0194924	0.00974619	−	0.999953i	$-0.496898\pi$
$181$	47.4660	0.0194924	0.00974619	+	0.999953i	$0.496898\pi$
$182$	−4450.94	−1.81278
$183$	−29.8419	−0.0120545
$184$	400.733	0.160557
$185$	−252.427	−0.100318
$186$	1672.98	0.659511
$187$	0	0
$188$	811.267	0.314722
$189$	7440.26	2.86349
$190$	67.9109	0.0259304
$191$	1349.60	0.511276	0.255638	−	0.966773i	$-0.417715\pi$
$191$	1349.60	0.511276	0.255638	+	0.966773i	$0.417715\pi$
$192$	570.133	0.214301
$193$	2853.94	1.06441	0.532205	−	0.846615i	$-0.321364\pi$
$193$	2853.94	1.06441	0.532205	+	0.846615i	$0.321364\pi$
$194$	−1913.50	−0.708149
$195$	784.180	0.287981
$196$	2967.14	1.08132
$197$	−4980.68	−1.80131	−0.900657	−	0.434530i	$-0.856914\pi$
$197$	−4980.68	−1.80131	−0.900657	+	0.434530i	$0.856914\pi$
$198$	−4108.96	−1.47480
$199$	−2954.72	−1.05254	−0.526268	−	0.850319i	$-0.676409\pi$
$199$	−2954.72	−1.05254	−0.526268	+	0.850319i	$0.676409\pi$
$200$	986.422	0.348753
$201$	−6810.95	−2.39009
$202$	−2459.59	−0.856713
$203$	−7110.98	−2.45859
$204$	0	0
$205$	−368.627	−0.125591
$206$	−967.620	−0.327268
$207$	−2622.71	−0.880634
$208$	1081.11	0.360392
$209$	−1022.72	−0.338483
$210$	−764.483	−0.251211
$211$	2142.09	0.698899	0.349449	−	0.936955i	$-0.386369\pi$
$211$	2142.09	0.698899	0.349449	+	0.936955i	$0.386369\pi$
$212$	−2277.03	−0.737676
$213$	−4391.21	−1.41259
$214$	−1458.48	−0.465885
$215$	162.225	0.0514587
$216$	−1807.20	−0.569279
$217$	−3092.70	−0.967492
$218$	−4470.53	−1.38891
$219$	3053.23	0.942093
$220$	204.478	0.0626631
$221$	0	0
$222$	3452.18	1.04367
$223$	−3170.14	−0.951966	−0.475983	−	0.879454i	$-0.657908\pi$
$223$	−3170.14	−0.951966	−0.475983	+	0.879454i	$0.657908\pi$
$224$	−1053.95	−0.314376
$225$	−6455.92	−1.91287
$226$	−483.329	−0.142259
$227$	−2228.79	−0.651674	−0.325837	−	0.945426i	$-0.605646\pi$
$227$	−2228.79	−0.651674	−0.325837	+	0.945426i	$0.605646\pi$
$228$	−928.744	−0.269770
$229$	−1977.95	−0.570772	−0.285386	−	0.958413i	$-0.592122\pi$
$229$	−1977.95	−0.570772	−0.285386	+	0.958413i	$0.592122\pi$
$230$	130.516	0.0374174
$231$	11512.9	3.27919
$232$	1727.22	0.488782
$233$	4826.83	1.35715	0.678576	−	0.734530i	$-0.262597\pi$
$233$	4826.83	1.35715	0.678576	+	0.734530i	$0.262597\pi$
$234$	−7075.64	−1.97670
$235$	264.225	0.0733452
$236$	550.264	0.151776
$237$	−5751.60	−1.57640
$238$	0	0
$239$	149.720	0.0405212	0.0202606	−	0.999795i	$-0.493550\pi$
$239$	149.720	0.0405212	0.0202606	+	0.999795i	$0.493550\pi$
$240$	185.689	0.0499423
$241$	7345.74	1.96340	0.981702	−	0.190422i	$-0.0609856\pi$
$241$	7345.74	1.96340	0.981702	+	0.190422i	$0.0609856\pi$
$242$	−417.376	−0.110868
$243$	−765.735	−0.202148
$244$	−13.3995	−0.00351565
$245$	966.380	0.251999
$246$	5041.32	1.30660
$247$	−1761.12	−0.453674
$248$	751.199	0.192344
$249$	−11355.2	−2.88998
$250$	646.966	0.163671
$251$	1960.43	0.492992	0.246496	−	0.969144i	$-0.420721\pi$
$251$	1960.43	0.492992	0.246496	+	0.969144i	$0.420721\pi$
$252$	6897.91	1.72431
$253$	−1965.54	−0.488429
$254$	−1903.18	−0.470142
$255$	0	0
$256$	256.000	0.0625000
$257$	−4022.21	−0.976259	−0.488129	−	0.872771i	$-0.662321\pi$
$257$	−4022.21	−0.976259	−0.488129	+	0.872771i	$0.662321\pi$
$258$	−2218.57	−0.535357
$259$	−6381.73	−1.53105
$260$	352.111	0.0839885
$261$	−11304.3	−2.68091
$262$	149.299	0.0352050
$263$	970.195	0.227471	0.113735	−	0.993511i	$-0.463718\pi$
$263$	970.195	0.227471	0.113735	+	0.993511i	$0.463718\pi$
$264$	−2796.42	−0.651923
$265$	−741.616	−0.171914
$266$	1716.89	0.395748
$267$	−7400.15	−1.69619
$268$	−3058.24	−0.697059
$269$	1617.17	0.366545	0.183272	−	0.983062i	$-0.441331\pi$
$269$	1617.17	0.366545	0.183272	+	0.983062i	$0.441331\pi$
$270$	−588.594	−0.132669
$271$	−4493.83	−1.00731	−0.503655	−	0.863905i	$-0.668012\pi$
$271$	−4493.83	−1.00731	−0.503655	+	0.863905i	$0.668012\pi$
$272$	0	0
$273$	19825.2	4.39515
$274$	1089.32	0.240176
$275$	−4838.26	−1.06094
$276$	−1784.93	−0.389276
$277$	2694.17	0.584394	0.292197	−	0.956358i	$-0.405614\pi$
$277$	2694.17	0.584394	0.292197	+	0.956358i	$0.405614\pi$
$278$	2770.98	0.597814
$279$	−4916.44	−1.05498
$280$	−343.267	−0.0732647
$281$	2980.66	0.632779	0.316390	−	0.948629i	$-0.397529\pi$
$281$	2980.66	0.632779	0.316390	+	0.948629i	$0.397529\pi$
$282$	−3613.51	−0.763055
$283$	−2863.55	−0.601486	−0.300743	−	0.953705i	$-0.597235\pi$
$283$	−2863.55	−0.601486	−0.300743	+	0.953705i	$0.597235\pi$
$284$	−1971.73	−0.411975
$285$	−302.486	−0.0628692
$286$	−5302.69	−1.09635
$287$	−9319.44	−1.91676
$288$	−1675.47	−0.342805
$289$	0	0
$290$	562.545	0.113910
$291$	8523.02	1.71694
$292$	1370.96	0.274757
$293$	−754.928	−0.150524	−0.0752618	−	0.997164i	$-0.523979\pi$
$293$	−754.928	−0.150524	−0.0752618	+	0.997164i	$0.523979\pi$
$294$	−13216.1	−2.62170
$295$	179.218	0.0353711
$296$	1550.09	0.304382
$297$	8864.06	1.73180
$298$	−963.256	−0.187248
$299$	−3384.66	−0.654649
$300$	−4393.69	−0.845565
$301$	4101.28	0.785361
$302$	405.586	0.0772810
$303$	10955.4	2.07713
$304$	−417.023	−0.0786773
$305$	−4.36415	−0.000819313 0
$306$	0	0
$307$	−7983.00	−1.48408	−0.742042	−	0.670354i	$-0.766142\pi$
$307$	−7983.00	−1.48408	−0.742042	+	0.670354i	$0.766142\pi$
$308$	5169.50	0.956362
$309$	4309.94	0.793475
$310$	244.661	0.0448252
$311$	−3528.06	−0.643272	−0.321636	−	0.946863i	$-0.604233\pi$
$311$	−3528.06	−0.643272	−0.321636	+	0.946863i	$0.604233\pi$
$312$	−4815.44	−0.873784
$313$	2801.14	0.505846	0.252923	−	0.967486i	$-0.418608\pi$
$313$	2801.14	0.505846	0.252923	+	0.967486i	$0.418608\pi$
$314$	−4372.13	−0.785776
$315$	2246.61	0.401847
$316$	−2582.57	−0.459750
$317$	−9021.98	−1.59850	−0.799251	−	0.600998i	$-0.794770\pi$
$317$	−9021.98	−1.59850	−0.799251	+	0.600998i	$0.794770\pi$
$318$	10142.3	1.78852
$319$	−8471.77	−1.48692
$320$	83.3776	0.0145655
$321$	6496.30	1.12956
$322$	3299.65	0.571063
$323$	0	0
$324$	2394.87	0.410642
$325$	−8331.49	−1.42199
$326$	−709.579	−0.120552
$327$	19912.5	3.36747
$328$	2263.64	0.381063
$329$	6679.99	1.11939
$330$	−910.777	−0.151929
$331$	10122.6	1.68093	0.840464	−	0.541867i	$-0.182282\pi$
$331$	10122.6	1.68093	0.840464	+	0.541867i	$0.182282\pi$
$332$	−5098.67	−0.842849
$333$	−10145.0	−1.66950
$334$	2241.56	0.367224
$335$	−996.050	−0.162448
$336$	4694.49	0.762218
$337$	−1939.05	−0.313433	−0.156716	−	0.987644i	$-0.550091\pi$
$337$	−1939.05	−0.313433	−0.156716	+	0.987644i	$0.550091\pi$
$338$	−4737.25	−0.762344
$339$	2152.83	0.344913
$340$	0	0
$341$	−3684.53	−0.585127
$342$	2729.32	0.431535
$343$	13134.4	2.06762
$344$	−996.178	−0.156135
$345$	−581.341	−0.0907199
$346$	−3463.36	−0.538126
$347$	−6610.95	−1.02275	−0.511375	−	0.859358i	$-0.670864\pi$
$347$	−6610.95	−1.02275	−0.511375	+	0.859358i	$0.670864\pi$
$348$	−7693.32	−1.18507
$349$	4923.51	0.755156	0.377578	−	0.925978i	$-0.376757\pi$
$349$	4923.51	0.755156	0.377578	+	0.925978i	$0.376757\pi$
$350$	8122.22	1.24043
$351$	15263.9	2.32116
$352$	−1255.64	−0.190131
$353$	2041.87	0.307869	0.153934	−	0.988081i	$-0.450806\pi$
$353$	2041.87	0.307869	0.153934	+	0.988081i	$0.450806\pi$
$354$	−2450.97	−0.367987
$355$	−642.182	−0.0960098
$356$	−3322.80	−0.494685
$357$	0	0
$358$	−8396.08	−1.23952
$359$	505.112	0.0742585	0.0371293	−	0.999310i	$-0.488179\pi$
$359$	505.112	0.0742585	0.0371293	+	0.999310i	$0.488179\pi$
$360$	−545.689	−0.0798898
$361$	−6179.67	−0.900958
$362$	−94.9320	−0.0137832
$363$	1859.06	0.268803
$364$	8901.88	1.28183
$365$	446.512	0.0640316
$366$	59.6837	0.00852382
$367$	9550.08	1.35834	0.679169	−	0.733982i	$-0.262340\pi$
$367$	9550.08	1.35834	0.679169	+	0.733982i	$0.262340\pi$
$368$	−801.467	−0.113531
$369$	−14815.1	−2.09008
$370$	504.855	0.0709355
$371$	−18749.1	−2.62374
$372$	−3345.96	−0.466345
$373$	1068.56	0.148332	0.0741662	−	0.997246i	$-0.476370\pi$
$373$	1068.56	0.148332	0.0741662	+	0.997246i	$0.476370\pi$
$374$	0	0
$375$	−2881.69	−0.396826
$376$	−1622.53	−0.222542
$377$	−14588.4	−1.99295
$378$	−14880.5	−2.02479
$379$	8247.52	1.11780	0.558901	−	0.829234i	$-0.311223\pi$
$379$	8247.52	1.11780	0.558901	+	0.829234i	$0.311223\pi$
$380$	−135.822	−0.0183355
$381$	8477.06	1.13988
$382$	−2699.20	−0.361526
$383$	4557.54	0.608040	0.304020	−	0.952666i	$-0.401671\pi$
$383$	4557.54	0.608040	0.304020	+	0.952666i	$0.401671\pi$
$384$	−1140.27	−0.151534
$385$	1683.67	0.222878
$386$	−5707.88	−0.752652
$387$	6519.77	0.856379
$388$	3826.99	0.500737
$389$	8456.75	1.10225	0.551123	−	0.834424i	$-0.314199\pi$
$389$	8456.75	1.10225	0.551123	+	0.834424i	$0.314199\pi$
$390$	−1568.36	−0.203633
$391$	0	0
$392$	−5934.28	−0.764609
$393$	−665.001	−0.0853559
$394$	9961.36	1.27372
$395$	−841.129	−0.107144
$396$	8217.92	1.04284
$397$	3414.24	0.431627	0.215814	−	0.976435i	$-0.430760\pi$
$397$	3414.24	0.431627	0.215814	+	0.976435i	$0.430760\pi$
$398$	5909.44	0.744255
$399$	−7647.29	−0.959508
$400$	−1972.84	−0.246606
$401$	5788.46	0.720852	0.360426	−	0.932788i	$-0.382631\pi$
$401$	5788.46	0.720852	0.360426	+	0.932788i	$0.382631\pi$
$402$	13621.9	1.69005
$403$	−6344.76	−0.784256
$404$	4919.18	0.605788
$405$	779.993	0.0956992
$406$	14222.0	1.73848
$407$	−7602.97	−0.925958
$408$	0	0
$409$	−12554.4	−1.51779	−0.758897	−	0.651211i	$-0.774261\pi$
$409$	−12554.4	−1.51779	−0.758897	+	0.651211i	$0.774261\pi$
$410$	737.255	0.0888059
$411$	−4852.02	−0.582317
$412$	1935.24	0.231414
$413$	4530.89	0.539832
$414$	5245.43	0.622702
$415$	−1660.61	−0.196424
$416$	−2162.22	−0.254836
$417$	−12342.4	−1.44942
$418$	2045.44	0.239343
$419$	5105.66	0.595293	0.297647	−	0.954676i	$-0.403798\pi$
$419$	5105.66	0.595293	0.297647	+	0.954676i	$0.403798\pi$
$420$	1528.97	0.177633
$421$	10075.1	1.16634	0.583170	−	0.812350i	$-0.301812\pi$
$421$	10075.1	1.16634	0.583170	+	0.812350i	$0.301812\pi$
$422$	−4284.18	−0.494196
$423$	10619.1	1.22061
$424$	4554.07	0.521616
$425$	0	0
$426$	8782.43	0.998850
$427$	−110.332	−0.0125043
$428$	2916.96	0.329431
$429$	23619.1	2.65813
$430$	−324.449	−0.0363868
$431$	13974.2	1.56175	0.780873	−	0.624690i	$-0.214774\pi$
$431$	13974.2	1.56175	0.780873	+	0.624690i	$0.214774\pi$
$432$	3614.40	0.402541
$433$	1828.71	0.202962	0.101481	−	0.994838i	$-0.467642\pi$
$433$	1828.71	0.202962	0.101481	+	0.994838i	$0.467642\pi$
$434$	6185.39	0.684120
$435$	−2505.67	−0.276178
$436$	8941.06	0.982108
$437$	1305.59	0.142917
$438$	−6106.47	−0.666160
$439$	9759.54	1.06104	0.530521	−	0.847672i	$-0.321996\pi$
$439$	9759.54	1.06104	0.530521	+	0.847672i	$0.321996\pi$
$440$	−408.955	−0.0443095
$441$	38838.6	4.19378
$442$	0	0
$443$	8806.00	0.944438	0.472219	−	0.881481i	$-0.343453\pi$
$443$	8806.00	0.944438	0.472219	+	0.881481i	$0.343453\pi$
$444$	−6904.35	−0.737986
$445$	−1082.22	−0.115285
$446$	6340.29	0.673142
$447$	4290.50	0.453991
$448$	2107.91	0.222298
$449$	−17257.7	−1.81390	−0.906952	−	0.421235i	$-0.861597\pi$
$449$	−17257.7	−1.81390	−0.906952	+	0.421235i	$0.861597\pi$
$450$	12911.8	1.35260
$451$	−11102.8	−1.15923
$452$	966.658	0.100592
$453$	−1806.55	−0.187371
$454$	4457.58	0.460803
$455$	2899.29	0.298727
$456$	1857.49	0.190756
$457$	−8456.02	−0.865549	−0.432775	−	0.901502i	$-0.642465\pi$
$457$	−8456.02	−0.865549	−0.432775	+	0.901502i	$0.642465\pi$
$458$	3955.90	0.403597
$459$	0	0
$460$	−261.033	−0.0264581
$461$	13792.9	1.39349	0.696743	−	0.717321i	$-0.254632\pi$
$461$	13792.9	1.39349	0.696743	+	0.717321i	$0.254632\pi$
$462$	−23025.8	−2.31874
$463$	−12478.0	−1.25249	−0.626243	−	0.779628i	$-0.715408\pi$
$463$	−12478.0	−1.25249	−0.626243	+	0.779628i	$0.715408\pi$
$464$	−3454.44	−0.345621
$465$	−1089.76	−0.108680
$466$	−9653.67	−0.959651
$467$	−16066.1	−1.59197	−0.795985	−	0.605316i	$-0.793047\pi$
$467$	−16066.1	−1.59197	−0.795985	+	0.605316i	$0.793047\pi$
$468$	14151.3	1.39774
$469$	−25181.6	−2.47927
$470$	−528.449	−0.0518629
$471$	19474.2	1.90515
$472$	−1100.53	−0.107322
$473$	4886.11	0.474976
$474$	11503.2	1.11468
$475$	3213.75	0.310436
$476$	0	0
$477$	−29805.4	−2.86100
$478$	−299.439	−0.0286528
$479$	13352.5	1.27368	0.636838	−	0.770997i	$-0.280242\pi$
$479$	13352.5	1.27368	0.636838	+	0.770997i	$0.280242\pi$
$480$	−371.378	−0.0353146
$481$	−13092.3	−1.24108
$482$	−14691.5	−1.38834
$483$	−14697.2	−1.38456
$484$	834.752	0.0783952
$485$	1246.43	0.116696
$486$	1531.47	0.142940
$487$	11085.4	1.03147	0.515736	−	0.856748i	$-0.327519\pi$
$487$	11085.4	1.03147	0.515736	+	0.856748i	$0.327519\pi$
$488$	26.7991	0.00248594
$489$	3160.58	0.292283
$490$	−1932.76	−0.178190
$491$	−13437.6	−1.23510	−0.617548	−	0.786533i	$-0.711874\pi$
$491$	−13437.6	−1.23510	−0.617548	+	0.786533i	$0.711874\pi$
$492$	−10082.6	−0.923903
$493$	0	0
$494$	3522.25	0.320796
$495$	2676.53	0.243032
$496$	−1502.40	−0.136007
$497$	−16235.3	−1.46530
$498$	22710.3	2.04352
$499$	13165.2	1.18107	0.590535	−	0.807012i	$-0.298917\pi$
$499$	13165.2	1.18107	0.590535	+	0.807012i	$0.298917\pi$
$500$	−1293.93	−0.115733
$501$	−9984.28	−0.890349
$502$	−3920.86	−0.348598
$503$	−7873.67	−0.697951	−0.348976	−	0.937132i	$-0.613470\pi$
$503$	−7873.67	−0.697951	−0.348976	+	0.937132i	$0.613470\pi$
$504$	−13795.8	−1.21927
$505$	1602.15	0.141177
$506$	3931.08	0.345371
$507$	21100.5	1.84833
$508$	3806.35	0.332440
$509$	8039.79	0.700113	0.350056	−	0.936729i	$-0.386162\pi$
$509$	8039.79	0.700113	0.350056	+	0.936729i	$0.386162\pi$
$510$	0	0
$511$	11288.5	0.977247
$512$	−512.000	−0.0441942
$513$	−5887.84	−0.506734
$514$	8044.42	0.690319
$515$	630.296	0.0539304
$516$	4437.14	0.378555
$517$	7958.29	0.676993
$518$	12763.5	1.08261
$519$	15426.4	1.30471
$520$	−704.222	−0.0593888
$521$	−11806.6	−0.992813	−0.496407	−	0.868090i	$-0.665347\pi$
$521$	−11806.6	−0.992813	−0.496407	+	0.868090i	$0.665347\pi$
$522$	22608.6	1.89569
$523$	−2991.18	−0.250086	−0.125043	−	0.992151i	$-0.539907\pi$
$523$	−2991.18	−0.250086	−0.125043	+	0.992151i	$0.539907\pi$
$524$	−298.597	−0.0248937
$525$	−36177.7	−3.00747
$526$	−1940.39	−0.160846
$527$	0	0
$528$	5592.84	0.460980
$529$	−9657.82	−0.793772
$530$	1483.23	0.121561
$531$	7202.72	0.588647
$532$	−3433.77	−0.279836
$533$	−19119.1	−1.55374
$534$	14800.3	1.19938
$535$	950.035	0.0767730
$536$	6116.48	0.492895
$537$	37397.5	3.00525
$538$	−3234.34	−0.259186
$539$	29106.8	2.32601
$540$	1177.19	0.0938113
$541$	17360.1	1.37961	0.689805	−	0.723995i	$-0.257696\pi$
$541$	17360.1	1.37961	0.689805	+	0.723995i	$0.257696\pi$
$542$	8987.66	0.712275
$543$	422.843	0.0334179
$544$	0	0
$545$	2912.05	0.228878
$546$	−39650.4	−3.10784
$547$	−3124.54	−0.244234	−0.122117	−	0.992516i	$-0.538968\pi$
$547$	−3124.54	−0.244234	−0.122117	+	0.992516i	$0.538968\pi$
$548$	−2178.64	−0.169830
$549$	−175.394	−0.0136351
$550$	9676.52	0.750197
$551$	5627.26	0.435081
$552$	3569.86	0.275260
$553$	−21265.0	−1.63522
$554$	−5388.35	−0.413229
$555$	−2248.70	−0.171986
$556$	−5541.96	−0.422718
$557$	−7434.65	−0.565559	−0.282779	−	0.959185i	$-0.591256\pi$
$557$	−7434.65	−0.565559	−0.282779	+	0.959185i	$0.591256\pi$
$558$	9832.88	0.745984
$559$	8413.89	0.636619
$560$	686.533	0.0518059
$561$	0	0
$562$	−5961.31	−0.447443
$563$	−22605.6	−1.69221	−0.846105	−	0.533017i	$-0.821058\pi$
$563$	−22605.6	−1.69221	−0.846105	+	0.533017i	$0.821058\pi$
$564$	7227.03	0.539562
$565$	314.834	0.0234428
$566$	5727.11	0.425315
$567$	19719.4	1.46056
$568$	3943.47	0.291310
$569$	−22968.0	−1.69222	−0.846108	−	0.533012i	$-0.821060\pi$
$569$	−22968.0	−1.69222	−0.846108	+	0.533012i	$0.821060\pi$
$570$	604.972	0.0444553
$571$	−20889.0	−1.53096	−0.765479	−	0.643461i	$-0.777498\pi$
$571$	−20889.0	−1.53096	−0.765479	+	0.643461i	$0.777498\pi$
$572$	10605.4	0.775233
$573$	12022.7	0.876535
$574$	18638.9	1.35535
$575$	6176.44	0.447957
$576$	3350.93	0.242399
$577$	−14649.6	−1.05697	−0.528485	−	0.848942i	$-0.677240\pi$
$577$	−14649.6	−1.05697	−0.528485	+	0.848942i	$0.677240\pi$
$578$	0	0
$579$	25423.8	1.82483
$580$	−1125.09	−0.0805462
$581$	−41982.6	−2.99781
$582$	−17046.0	−1.21406
$583$	−22337.0	−1.58680
$584$	−2741.91	−0.194283
$585$	4608.98	0.325740
$586$	1509.86	0.106436
$587$	13888.4	0.976548	0.488274	−	0.872690i	$-0.337627\pi$
$587$	13888.4	0.976548	0.488274	+	0.872690i	$0.337627\pi$
$588$	26432.3	1.85382
$589$	2447.40	0.171211
$590$	−358.435	−0.0250111
$591$	−44369.5	−3.08819
$592$	−3100.18	−0.215231
$593$	14653.3	1.01474	0.507368	−	0.861729i	$-0.330618\pi$
$593$	14653.3	1.01474	0.507368	+	0.861729i	$0.330618\pi$
$594$	−17728.1	−1.22457
$595$	0	0
$596$	1926.51	0.132404
$597$	−26321.6	−1.80448
$598$	6769.33	0.462907
$599$	−7698.71	−0.525143	−0.262572	−	0.964913i	$-0.584571\pi$
$599$	−7698.71	−0.525143	−0.262572	+	0.964913i	$0.584571\pi$
$600$	8787.37	0.597905
$601$	19478.7	1.32205	0.661026	−	0.750363i	$-0.270121\pi$
$601$	19478.7	1.32205	0.661026	+	0.750363i	$0.270121\pi$
$602$	−8202.55	−0.555334
$603$	−40031.1	−2.70347
$604$	−811.173	−0.0546460
$605$	271.874	0.0182698
$606$	−21910.8	−1.46876
$607$	−3136.14	−0.209707	−0.104853	−	0.994488i	$-0.533437\pi$
$607$	−3136.14	−0.209707	−0.104853	+	0.994488i	$0.533437\pi$
$608$	834.045	0.0556332
$609$	−63346.9	−4.21502
$610$	8.72830	0.000579342 0
$611$	13704.2	0.907385
$612$	0	0
$613$	2865.35	0.188793	0.0943967	−	0.995535i	$-0.469908\pi$
$613$	2865.35	0.188793	0.0943967	+	0.995535i	$0.469908\pi$
$614$	15966.0	1.04941
$615$	−3283.85	−0.215313
$616$	−10339.0	−0.676250
$617$	15952.4	1.04087	0.520437	−	0.853900i	$-0.325769\pi$
$617$	15952.4	1.04087	0.520437	+	0.853900i	$0.325769\pi$
$618$	−8619.88	−0.561072
$619$	−14278.9	−0.927171	−0.463585	−	0.886052i	$-0.653437\pi$
$619$	−14278.9	−0.927171	−0.463585	+	0.886052i	$0.653437\pi$
$620$	−489.322	−0.0316962
$621$	−11315.7	−0.731214
$622$	7056.11	0.454862
$623$	−27360.0	−1.75948
$624$	9630.88	0.617859
$625$	14991.4	0.959451
$626$	−5602.28	−0.357687
$627$	−9110.71	−0.580298
$628$	8744.27	0.555628
$629$	0	0
$630$	−4493.21	−0.284149
$631$	22216.4	1.40162	0.700808	−	0.713349i	$-0.252823\pi$
$631$	22216.4	1.40162	0.700808	+	0.713349i	$0.252823\pi$
$632$	5165.15	0.325093
$633$	19082.5	1.19820
$634$	18044.0	1.13031
$635$	1239.71	0.0774744
$636$	−20284.6	−1.26468
$637$	50122.0	3.11759
$638$	16943.5	1.05141
$639$	−25809.2	−1.59780
$640$	−166.755	−0.0102993
$641$	−22674.5	−1.39718	−0.698589	−	0.715523i	$-0.746188\pi$
$641$	−22674.5	−1.39718	−0.698589	+	0.715523i	$0.746188\pi$
$642$	−12992.6	−0.798718
$643$	22509.4	1.38053	0.690267	−	0.723555i	$-0.257493\pi$
$643$	22509.4	1.38053	0.690267	+	0.723555i	$0.257493\pi$
$644$	−6599.29	−0.403802
$645$	1445.15	0.0882213
$646$	0	0
$647$	−75.5368	−0.00458989	−0.00229494	−	0.999997i	$-0.500731\pi$
$647$	−75.5368	−0.00458989	−0.00229494	+	0.999997i	$0.500731\pi$
$648$	−4789.73	−0.290368
$649$	5397.94	0.326483
$650$	16663.0	1.00550
$651$	−27550.7	−1.65868
$652$	1419.16	0.0852432
$653$	−1134.04	−0.0679610	−0.0339805	−	0.999422i	$-0.510818\pi$
$653$	−1134.04	−0.0679610	−0.0339805	+	0.999422i	$0.510818\pi$
$654$	−39825.0	−2.38116
$655$	−97.2513	−0.00580141
$656$	−4527.29	−0.269453
$657$	17945.2	1.06562
$658$	−13360.0	−0.791529
$659$	−33374.8	−1.97283	−0.986416	−	0.164264i	$-0.947475\pi$
$659$	−33374.8	−1.97283	−0.986416	+	0.164264i	$0.947475\pi$
$660$	1821.55	0.107430
$661$	−4598.54	−0.270594	−0.135297	−	0.990805i	$-0.543199\pi$
$661$	−4598.54	−0.270594	−0.135297	+	0.990805i	$0.543199\pi$
$662$	−20245.2	−1.18860
$663$	0	0
$664$	10197.3	0.595984
$665$	−1118.36	−0.0652152
$666$	20290.0	1.18051
$667$	10814.9	0.627819
$668$	−4483.12	−0.259666
$669$	−28240.7	−1.63206
$670$	1992.10	0.114868
$671$	−131.446	−0.00756245
$672$	−9388.97	−0.538969
$673$	−2426.84	−0.139001	−0.0695007	−	0.997582i	$-0.522141\pi$
$673$	−2426.84	−0.139001	−0.0695007	+	0.997582i	$0.522141\pi$
$674$	3878.10	0.221630
$675$	−27854.1	−1.58830
$676$	9474.49	0.539058
$677$	24830.9	1.40964	0.704821	−	0.709385i	$-0.251027\pi$
$677$	24830.9	1.40964	0.704821	+	0.709385i	$0.251027\pi$
$678$	−4305.65	−0.243890
$679$	31511.5	1.78100
$680$	0	0
$681$	−19854.8	−1.11724
$682$	7369.05	0.413747
$683$	6611.10	0.370376	0.185188	−	0.982703i	$-0.440711\pi$
$683$	6611.10	0.370376	0.185188	+	0.982703i	$0.440711\pi$
$684$	−5458.65	−0.305141
$685$	−709.571	−0.0395786
$686$	−26268.9	−1.46203
$687$	−17620.2	−0.978536
$688$	1992.36	0.110404
$689$	−38464.4	−2.12682
$690$	1162.68	0.0641487
$691$	1055.68	0.0581186	0.0290593	−	0.999578i	$-0.490749\pi$
$691$	1055.68	0.0581186	0.0290593	+	0.999578i	$0.490749\pi$
$692$	6926.73	0.380512
$693$	67666.5	3.70915
$694$	13221.9	0.723193
$695$	−1804.98	−0.0985135
$696$	15386.6	0.837973
$697$	0	0
$698$	−9847.01	−0.533976
$699$	42999.0	2.32671
$700$	−16244.4	−0.877117
$701$	13811.1	0.744137	0.372068	−	0.928205i	$-0.378649\pi$
$701$	13811.1	0.744137	0.372068	+	0.928205i	$0.378649\pi$
$702$	−30527.8	−1.64131
$703$	5050.17	0.270940
$704$	2511.29	0.134443
$705$	2353.80	0.125744
$706$	−4083.74	−0.217696
$707$	40504.6	2.15464
$708$	4901.93	0.260206
$709$	15046.7	0.797025	0.398512	−	0.917163i	$-0.369527\pi$
$709$	15046.7	0.797025	0.398512	+	0.917163i	$0.369527\pi$
$710$	1284.36	0.0678892
$711$	−33804.8	−1.78309
$712$	6645.60	0.349795
$713$	4703.60	0.247057
$714$	0	0
$715$	3454.11	0.180666
$716$	16792.2	0.876470
$717$	1333.75	0.0694698
$718$	−1010.22	−0.0525087
$719$	36534.1	1.89498	0.947492	−	0.319779i	$-0.103609\pi$
$719$	36534.1	1.89498	0.947492	+	0.319779i	$0.103609\pi$
$720$	1091.38	0.0564906
$721$	15934.8	0.823084
$722$	12359.3	0.637074
$723$	65438.2	3.36608
$724$	189.864	0.00974619
$725$	26621.4	1.36371
$726$	−3718.12	−0.190072
$727$	18950.4	0.966756	0.483378	−	0.875412i	$-0.339410\pi$
$727$	18950.4	0.966756	0.483378	+	0.875412i	$0.339410\pi$
$728$	−17803.8	−0.906390
$729$	−22986.8	−1.16785
$730$	−893.025	−0.0452772
$731$	0	0
$732$	−119.367	−0.00602725
$733$	35398.9	1.78375	0.891874	−	0.452283i	$-0.149390\pi$
$733$	35398.9	1.78375	0.891874	+	0.452283i	$0.149390\pi$
$734$	−19100.2	−0.960491
$735$	8608.83	0.432029
$736$	1602.93	0.0802784
$737$	−30000.5	−1.49943
$738$	29630.1	1.47791
$739$	19350.5	0.963220	0.481610	−	0.876386i	$-0.340052\pi$
$739$	19350.5	0.963220	0.481610	+	0.876386i	$0.340052\pi$
$740$	−1009.71	−0.0501590
$741$	−15688.7	−0.777783
$742$	37498.3	1.85526
$743$	−17426.3	−0.860443	−0.430221	−	0.902723i	$-0.641564\pi$
$743$	−17426.3	−0.860443	−0.430221	+	0.902723i	$0.641564\pi$
$744$	6691.93	0.329755
$745$	627.454	0.0308565
$746$	−2137.12	−0.104887
$747$	−66739.4	−3.26890
$748$	0	0
$749$	24018.3	1.17171
$750$	5763.38	0.280599
$751$	11096.1	0.539152	0.269576	−	0.962979i	$-0.413116\pi$
$751$	11096.1	0.539152	0.269576	+	0.962979i	$0.413116\pi$
$752$	3245.07	0.157361
$753$	17464.1	0.845190
$754$	29176.8	1.40923
$755$	−264.194	−0.0127351
$756$	29761.0	1.43174
$757$	13378.2	0.642326	0.321163	−	0.947024i	$-0.395926\pi$
$757$	13378.2	0.642326	0.321163	+	0.947024i	$0.395926\pi$
$758$	−16495.0	−0.790405
$759$	−17509.7	−0.837366
$760$	271.643	0.0129652
$761$	−6331.90	−0.301618	−0.150809	−	0.988563i	$-0.548188\pi$
$761$	−6331.90	−0.301618	−0.150809	+	0.988563i	$0.548188\pi$
$762$	−16954.1	−0.806015
$763$	73620.9	3.49313
$764$	5398.40	0.255638
$765$	0	0
$766$	−9115.08	−0.429949
$767$	9295.26	0.437591
$768$	2280.53	0.107151
$769$	−14799.5	−0.693996	−0.346998	−	0.937866i	$-0.612799\pi$
$769$	−14799.5	−0.693996	−0.346998	+	0.937866i	$0.612799\pi$
$770$	−3367.35	−0.157598
$771$	−35831.2	−1.67371
$772$	11415.8	0.532205
$773$	9139.21	0.425245	0.212623	−	0.977134i	$-0.431800\pi$
$773$	9139.21	0.425245	0.212623	+	0.977134i	$0.431800\pi$
$774$	−13039.5	−0.605551
$775$	11578.1	0.536643
$776$	−7653.98	−0.354075
$777$	−56850.6	−2.62484
$778$	−16913.5	−0.779406
$779$	7374.93	0.339197
$780$	3136.72	0.143991
$781$	−19342.1	−0.886193
$782$	0	0
$783$	−48772.4	−2.22603
$784$	11868.6	0.540660
$785$	2847.95	0.129488
$786$	1330.00	0.0603557
$787$	−14159.4	−0.641332	−0.320666	−	0.947192i	$-0.603907\pi$
$787$	−14159.4	−0.641332	−0.320666	+	0.947192i	$0.603907\pi$
$788$	−19922.7	−0.900657
$789$	8642.82	0.389978
$790$	1682.26	0.0757621
$791$	7959.48	0.357783
$792$	−16435.8	−0.737402
$793$	−226.350	−0.0101361
$794$	−6828.49	−0.305207
$795$	−6606.56	−0.294730
$796$	−11818.9	−0.526268
$797$	−35152.0	−1.56229	−0.781146	−	0.624349i	$-0.785364\pi$
$797$	−35152.0	−1.56229	−0.781146	+	0.624349i	$0.785364\pi$
$798$	15294.6	0.678474
$799$	0	0
$800$	3945.69	0.174376
$801$	−43494.0	−1.91858
$802$	−11576.9	−0.509720
$803$	13448.7	0.591026
$804$	−27243.8	−1.19504
$805$	−2149.35	−0.0941051
$806$	12689.5	0.554553
$807$	14406.3	0.628408
$808$	−9838.35	−0.428356
$809$	16641.9	0.723234	0.361617	−	0.932327i	$-0.382225\pi$
$809$	16641.9	0.723234	0.361617	+	0.932327i	$0.382225\pi$
$810$	−1559.99	−0.0676696
$811$	5699.29	0.246768	0.123384	−	0.992359i	$-0.460625\pi$
$811$	5699.29	0.246768	0.123384	+	0.992359i	$0.460625\pi$
$812$	−28443.9	−1.22929
$813$	−40032.5	−1.72694
$814$	15205.9	0.654751
$815$	462.211	0.0198657
$816$	0	0
$817$	−3245.54	−0.138980
$818$	25108.9	1.07324
$819$	116522.	4.97143
$820$	−1474.51	−0.0627953
$821$	−9843.36	−0.418436	−0.209218	−	0.977869i	$-0.567092\pi$
$821$	−9843.36	−0.418436	−0.209218	+	0.977869i	$0.567092\pi$
$822$	9704.04	0.411761
$823$	25466.1	1.07860	0.539302	−	0.842112i	$-0.318688\pi$
$823$	25466.1	1.07860	0.539302	+	0.842112i	$0.318688\pi$
$824$	−3870.48	−0.163634
$825$	−43100.8	−1.81888
$826$	−9061.78	−0.381719
$827$	20037.3	0.842521	0.421260	−	0.906940i	$-0.361588\pi$
$827$	20037.3	0.842521	0.421260	+	0.906940i	$0.361588\pi$
$828$	−10490.9	−0.440317
$829$	−21911.2	−0.917982	−0.458991	−	0.888441i	$-0.651789\pi$
$829$	−21911.2	−0.917982	−0.458991	+	0.888441i	$0.651789\pi$
$830$	3321.21	0.138893
$831$	24000.6	1.00189
$832$	4324.44	0.180196
$833$	0	0
$834$	24684.8	1.02490
$835$	−1460.13	−0.0605146
$836$	−4090.87	−0.169241
$837$	−21212.0	−0.875978
$838$	−10211.3	−0.420936
$839$	39532.6	1.62672	0.813360	−	0.581761i	$-0.197636\pi$
$839$	39532.6	1.62672	0.813360	+	0.581761i	$0.197636\pi$
$840$	−3057.93	−0.125606
$841$	22224.9	0.911266
$842$	−20150.1	−0.824726
$843$	26552.7	1.08484
$844$	8568.37	0.349449
$845$	3085.78	0.125626
$846$	−21238.3	−0.863105
$847$	6873.37	0.278833
$848$	−9108.13	−0.368838
$849$	−25509.5	−1.03119
$850$	0	0
$851$	9705.82	0.390965
$852$	−17564.9	−0.706293
$853$	32412.3	1.30103	0.650513	−	0.759495i	$-0.274554\pi$
$853$	32412.3	1.30103	0.650513	+	0.759495i	$0.274554\pi$
$854$	220.664	0.00884189
$855$	−1777.85	−0.0711124
$856$	−5833.91	−0.232943
$857$	−41373.5	−1.64912	−0.824559	−	0.565777i	$-0.808576\pi$
$857$	−41373.5	−1.64912	−0.824559	+	0.565777i	$0.808576\pi$
$858$	−47238.1	−1.87958
$859$	−19281.0	−0.765843	−0.382922	−	0.923781i	$-0.625082\pi$
$859$	−19281.0	−0.765843	−0.382922	+	0.923781i	$0.625082\pi$
$860$	648.898	0.0257294
$861$	−83020.7	−3.28610
$862$	−27948.4	−1.10432
$863$	36539.7	1.44128	0.720640	−	0.693309i	$-0.243848\pi$
$863$	36539.7	1.44128	0.720640	+	0.693309i	$0.243848\pi$
$864$	−7228.80	−0.284640
$865$	2255.99	0.0886775
$866$	−3657.43	−0.143515
$867$	0	0
$868$	−12370.8	−0.483746
$869$	−25334.3	−0.988962
$870$	5011.33	0.195288
$871$	−51660.9	−2.00971
$872$	−17882.1	−0.694456
$873$	50093.7	1.94205
$874$	−2611.17	−0.101057
$875$	−10654.3	−0.411634
$876$	12212.9	0.471047
$877$	−42217.1	−1.62551	−0.812753	−	0.582608i	$-0.802032\pi$
$877$	−42217.1	−1.62551	−0.812753	+	0.582608i	$0.802032\pi$
$878$	−19519.1	−0.750270
$879$	−6725.15	−0.258059
$880$	817.911	0.0313316
$881$	18566.8	0.710023	0.355012	−	0.934862i	$-0.384477\pi$
$881$	18566.8	0.710023	0.355012	+	0.934862i	$0.384477\pi$
$882$	−77677.2	−2.96545
$883$	1627.71	0.0620347	0.0310174	−	0.999519i	$-0.490125\pi$
$883$	1627.71	0.0620347	0.0310174	+	0.999519i	$0.490125\pi$
$884$	0	0
$885$	1596.53	0.0606404
$886$	−17612.0	−0.667818
$887$	−32502.7	−1.23037	−0.615183	−	0.788384i	$-0.710918\pi$
$887$	−32502.7	−1.23037	−0.615183	+	0.788384i	$0.710918\pi$
$888$	13808.7	0.521835
$889$	31341.6	1.18241
$890$	2164.43	0.0815190
$891$	23493.0	0.883326
$892$	−12680.6	−0.475983
$893$	−5286.20	−0.198092
$894$	−8581.00	−0.321020
$895$	5469.10	0.204259
$896$	−4215.82	−0.157188
$897$	−30151.7	−1.12234
$898$	34515.5	1.28262
$899$	20273.2	0.752113
$900$	−25823.7	−0.956433
$901$	0	0
$902$	22205.7	0.819699
$903$	36535.5	1.34643
$904$	−1933.32	−0.0711295
$905$	61.8375	0.00227133
$906$	3613.10	0.132491
$907$	9352.99	0.342404	0.171202	−	0.985236i	$-0.445235\pi$
$907$	9352.99	0.342404	0.171202	+	0.985236i	$0.445235\pi$
$908$	−8915.16	−0.325837
$909$	64389.9	2.34948
$910$	−5798.58	−0.211232
$911$	−20763.9	−0.755148	−0.377574	−	0.925979i	$-0.623242\pi$
$911$	−20763.9	−0.755148	−0.377574	+	0.925979i	$0.623242\pi$
$912$	−3714.97	−0.134885
$913$	−50016.5	−1.81304
$914$	16912.0	0.612036
$915$	−38.8773	−0.00140464
$916$	−7911.81	−0.285386
$917$	−2458.66	−0.0885409
$918$	0	0
$919$	7827.21	0.280953	0.140477	−	0.990084i	$-0.455137\pi$
$919$	7827.21	0.280953	0.140477	+	0.990084i	$0.455137\pi$
$920$	522.066	0.0187087
$921$	−71115.1	−2.54433
$922$	−27585.7	−0.985343
$923$	−33307.2	−1.18778
$924$	46051.6	1.63959
$925$	23891.3	0.849233
$926$	24956.0	0.885641
$927$	25331.5	0.897513
$928$	6908.88	0.244391
$929$	−36622.2	−1.29336	−0.646682	−	0.762759i	$-0.723844\pi$
$929$	−36622.2	−1.29336	−0.646682	+	0.762759i	$0.723844\pi$
$930$	2179.52	0.0768487
$931$	−19333.8	−0.680603
$932$	19307.3	0.678576
$933$	−31429.1	−1.10283
$934$	32132.2	1.12569
$935$	0	0
$936$	−28302.5	−0.988352
$937$	−17041.0	−0.594136	−0.297068	−	0.954856i	$-0.596009\pi$
$937$	−17041.0	−0.594136	−0.297068	+	0.954856i	$0.596009\pi$
$938$	50363.2	1.75311
$939$	24953.5	0.867227
$940$	1056.90	0.0366726
$941$	−41668.5	−1.44352	−0.721760	−	0.692143i	$-0.756667\pi$
$941$	−41668.5	−1.44352	−0.721760	+	0.692143i	$0.756667\pi$
$942$	−38948.4	−1.34714
$943$	14173.7	0.489459
$944$	2201.06	0.0758880
$945$	9692.99	0.333664
$946$	−9772.22	−0.335859
$947$	52253.7	1.79305	0.896524	−	0.442995i	$-0.146084\pi$
$947$	52253.7	1.79305	0.896524	+	0.442995i	$0.146084\pi$
$948$	−23006.4	−0.788200
$949$	23158.7	0.792163
$950$	−6427.51	−0.219511
$951$	−80370.7	−2.74048
$952$	0	0
$953$	55894.2	1.89988	0.949942	−	0.312425i	$-0.101141\pi$
$953$	55894.2	1.89988	0.949942	+	0.312425i	$0.101141\pi$
$954$	59610.8	2.02303
$955$	1758.23	0.0595758
$956$	598.879	0.0202606
$957$	−75469.3	−2.54919
$958$	−26705.0	−0.900625
$959$	−17939.0	−0.604046
$960$	742.755	0.0249712
$961$	−20973.8	−0.704032
$962$	26184.6	0.877575
$963$	38181.7	1.27766
$964$	29382.9	0.981702
$965$	3718.04	0.124029
$966$	29394.3	0.979034
$967$	−27667.3	−0.920082	−0.460041	−	0.887898i	$-0.652165\pi$
$967$	−27667.3	−0.920082	−0.460041	+	0.887898i	$0.652165\pi$
$968$	−1669.50	−0.0554338
$969$	0	0
$970$	−2492.86	−0.0825162
$971$	−42803.0	−1.41464	−0.707319	−	0.706894i	$-0.750096\pi$
$971$	−42803.0	−1.41464	−0.707319	+	0.706894i	$0.750096\pi$
$972$	−3062.94	−0.101074
$973$	−45632.6	−1.50351
$974$	−22170.8	−0.729360
$975$	−74219.7	−2.43788
$976$	−53.5982	−0.00175782
$977$	30623.7	1.00280	0.501401	−	0.865215i	$-0.332818\pi$
$977$	30623.7	1.00280	0.501401	+	0.865215i	$0.332818\pi$
$978$	−6321.16	−0.206675
$979$	−32595.7	−1.06411
$980$	3865.52	0.126000
$981$	117035.	3.80900
$982$	26875.3	0.873344
$983$	−17370.2	−0.563603	−0.281802	−	0.959473i	$-0.590932\pi$
$983$	−17370.2	−0.563603	−0.281802	+	0.959473i	$0.590932\pi$
$984$	20165.3	0.653298
$985$	−6488.71	−0.209896
$986$	0	0
$987$	59507.5	1.91909
$988$	−7044.49	−0.226837
$989$	−6237.53	−0.200548
$990$	−5353.05	−0.171850
$991$	56024.6	1.79584	0.897922	−	0.440155i	$-0.145077\pi$
$991$	56024.6	1.79584	0.897922	+	0.440155i	$0.145077\pi$
$992$	3004.80	0.0961718
$993$	90175.3	2.88180
$994$	32470.6	1.03612
$995$	−3849.34	−0.122645
$996$	−45420.6	−1.44499
$997$	11709.6	0.371962	0.185981	−	0.982553i	$-0.440454\pi$
$997$	11709.6	0.371962	0.185981	+	0.982553i	$0.440454\pi$
$998$	−26330.3	−0.835142
$999$	−43770.6	−1.38623

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	578.4.a.g.1.2	yes	2
17.4	even	4		578.4.b.f.577.1		4
17.13	even	4		578.4.b.f.577.4		4
17.16	even	2		578.4.a.e.1.1	✓	2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
578.4.a.e.1.1	✓	2	17.16	even	2
578.4.a.g.1.2	yes	2	1.1	even	1	trivial
578.4.b.f.577.1		4	17.4	even	4
578.4.b.f.577.4		4	17.13	even	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 578 = 2 \cdot 17^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	578.a (trivial)

\(f(q)\)	\(=\)	\(q-2.00000 q^{2} +8.90833 q^{3} +4.00000 q^{4} +1.30278 q^{5} -17.8167 q^{6} +32.9361 q^{7} -8.00000 q^{8} +52.3583 q^{9} -2.60555 q^{10} +39.2389 q^{11} +35.6333 q^{12} +67.5694 q^{13} -65.8722 q^{14} +11.6056 q^{15} +16.0000 q^{16} -104.717 q^{18} -26.0639 q^{19} +5.21110 q^{20} +293.405 q^{21} -78.4777 q^{22} -50.0917 q^{23} -71.2666 q^{24} -123.303 q^{25} -135.139 q^{26} +225.900 q^{27} +131.744 q^{28} -215.902 q^{29} -23.2111 q^{30} -93.8999 q^{31} -32.0000 q^{32} +349.553 q^{33} +42.9083 q^{35} +209.433 q^{36} -193.761 q^{37} +52.1278 q^{38} +601.930 q^{39} -10.4222 q^{40} -282.955 q^{41} -586.811 q^{42} +124.522 q^{43} +156.955 q^{44} +68.2111 q^{45} +100.183 q^{46} +202.817 q^{47} +142.533 q^{48} +741.786 q^{49} +246.606 q^{50} +270.278 q^{52} -569.258 q^{53} -451.800 q^{54} +51.1194 q^{55} -263.489 q^{56} -232.186 q^{57} +431.805 q^{58} +137.566 q^{59} +46.4222 q^{60} -3.34988 q^{61} +187.800 q^{62} +1724.48 q^{63} +64.0000 q^{64} +88.0278 q^{65} -699.105 q^{66} -764.560 q^{67} -446.233 q^{69} -85.8167 q^{70} -492.934 q^{71} -418.866 q^{72} +342.739 q^{73} +387.522 q^{74} -1098.42 q^{75} -104.256 q^{76} +1292.37 q^{77} -1203.86 q^{78} -645.643 q^{79} +20.8444 q^{80} +598.717 q^{81} +565.911 q^{82} -1274.67 q^{83} +1173.62 q^{84} -249.045 q^{86} -1923.33 q^{87} -313.911 q^{88} -830.700 q^{89} -136.422 q^{90} +2225.47 q^{91} -200.367 q^{92} -836.491 q^{93} -405.633 q^{94} -33.9554 q^{95} -285.066 q^{96} +956.748 q^{97} -1483.57 q^{98} +2054.48 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 4 q^{2} + 7 q^{3} + 8 q^{4} - q^{5} - 14 q^{6} + 19 q^{7} - 16 q^{8} + 29 q^{9} + 2 q^{10} + 28 q^{11} + 28 q^{12} + 45 q^{13} - 38 q^{14} + 16 q^{15} + 32 q^{16} - 58 q^{18} - 99 q^{19} - 4 q^{20}+ \cdots + 2317 q^{99}+O(q^{100}) \) 2 * q - 4 * q^2 + 7 * q^3 + 8 * q^4 - q^5 - 14 * q^6 + 19 * q^7 - 16 * q^8 + 29 * q^9 + 2 * q^10 + 28 * q^11 + 28 * q^12 + 45 * q^13 - 38 * q^14 + 16 * q^15 + 32 * q^16 - 58 * q^18 - 99 * q^19 - 4 * q^20 + 320 * q^21 - 56 * q^22 - 111 * q^23 - 56 * q^24 - 243 * q^25 - 90 * q^26 + 322 * q^27 + 76 * q^28 + 91 * q^29 - 32 * q^30 - 58 * q^31 - 64 * q^32 + 371 * q^33 + 75 * q^35 + 116 * q^36 - 438 * q^37 + 198 * q^38 + 645 * q^39 + 8 * q^40 - 364 * q^41 - 640 * q^42 + 350 * q^43 + 112 * q^44 + 122 * q^45 + 222 * q^46 + 384 * q^47 + 112 * q^48 + 593 * q^49 + 486 * q^50 + 180 * q^52 - 933 * q^53 - 644 * q^54 + 77 * q^55 - 152 * q^56 - 93 * q^57 - 182 * q^58 - 720 * q^59 + 64 * q^60 + 188 * q^61 + 116 * q^62 + 2050 * q^63 + 128 * q^64 + 140 * q^65 - 742 * q^66 - 22 * q^67 - 330 * q^69 - 150 * q^70 - 1332 * q^71 - 232 * q^72 + 1284 * q^73 + 876 * q^74 - 870 * q^75 - 396 * q^76 + 1449 * q^77 - 1290 * q^78 + 324 * q^79 - 16 * q^80 + 1046 * q^81 + 728 * q^82 + 7 * q^83 + 1280 * q^84 - 700 * q^86 - 2509 * q^87 - 224 * q^88 - 1272 * q^89 - 244 * q^90 + 2540 * q^91 - 444 * q^92 - 905 * q^93 - 768 * q^94 + 134 * q^95 - 224 * q^96 + 2631 * q^97 - 1186 * q^98 + 2317 * q^99

Introduction

L-functions

Modular forms

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Groups

Database

Properties

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