LMFDB - Embedded newform 38.5.b.a.37.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [38,5,Mod(37,38)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(38, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1]))

N = Newforms(chi, 5, names="a")

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

chi := DirichletCharacter("38.37");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 38 = 2 \cdot 19 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	38.b (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.92805859719$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 450x^{6} + 68229x^{4} + 4001228x^{2} + 77475204 $ x^8 + 450x^6 + 68229x^4 + 4001228*x^2 + 77475204
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{5} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			37.2
Root			$-6.38941i$ of defining polynomial
Character	$\chi$	$=$	38.37
Dual form			38.5.b.a.37.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.82843i q^{2} -7.80363i q^{3} -8.00000 q^{4} -33.0971 q^{5} -22.0720 q^{6} +16.0783 q^{7} +22.6274i q^{8} +20.1034 q^{9} +O(q^{10})$	\(q-2.82843i q^{2} -7.80363i q^{3} -8.00000 q^{4} -33.0971 q^{5} -22.0720 q^{6} +16.0783 q^{7} +22.6274i q^{8} +20.1034 q^{9} +93.6127i q^{10} -215.592 q^{11} +62.4290i q^{12} -281.497i q^{13} -45.4764i q^{14} +258.277i q^{15} +64.0000 q^{16} +226.582 q^{17} -56.8610i q^{18} +(13.9969 - 360.729i) q^{19} +264.777 q^{20} -125.469i q^{21} +609.786i q^{22} +414.609 q^{23} +176.576 q^{24} +470.416 q^{25} -796.195 q^{26} -788.973i q^{27} -128.627 q^{28} +606.612i q^{29} +730.518 q^{30} -478.655i q^{31} -181.019i q^{32} +1682.40i q^{33} -640.871i q^{34} -532.145 q^{35} -160.827 q^{36} -104.604i q^{37} +(-1020.29 - 39.5893i) q^{38} -2196.70 q^{39} -748.901i q^{40} +1891.12i q^{41} -354.881 q^{42} +315.912 q^{43} +1724.73 q^{44} -665.364 q^{45} -1172.69i q^{46} -474.327 q^{47} -499.432i q^{48} -2142.49 q^{49} -1330.54i q^{50} -1768.16i q^{51} +2251.98i q^{52} -774.381i q^{53} -2231.55 q^{54} +7135.46 q^{55} +363.811i q^{56} +(-2814.99 - 109.227i) q^{57} +1715.76 q^{58} +567.212i q^{59} -2066.22i q^{60} +4799.51 q^{61} -1353.84 q^{62} +323.229 q^{63} -512.000 q^{64} +9316.74i q^{65} +4758.54 q^{66} +4464.01i q^{67} -1812.66 q^{68} -3235.45i q^{69} +1505.13i q^{70} -7636.34i q^{71} +454.888i q^{72} +8396.65 q^{73} -295.866 q^{74} -3670.95i q^{75} +(-111.975 + 2885.83i) q^{76} -3466.35 q^{77} +6213.21i q^{78} -9706.71i q^{79} -2118.21 q^{80} -4528.48 q^{81} +5348.89 q^{82} -10589.4 q^{83} +1003.75i q^{84} -7499.21 q^{85} -893.533i q^{86} +4733.77 q^{87} -4878.29i q^{88} -10281.7i q^{89} +1881.93i q^{90} -4526.01i q^{91} -3316.87 q^{92} -3735.24 q^{93} +1341.60i q^{94} +(-463.257 + 11939.1i) q^{95} -1412.61 q^{96} +15477.3i q^{97} +6059.87i q^{98} -4334.13 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 64 q^{4} + 18 q^{5} - 32 q^{6} - 162 q^{7} - 268 q^{9}+O(q^{10}) $ 8 * q - 64 * q^4 + 18 * q^5 - 32 * q^6 - 162 * q^7 - 268 * q^9	$ 8 q - 64 q^{4} + 18 q^{5} - 32 q^{6} - 162 q^{7} - 268 q^{9} - 6 q^{11} + 512 q^{16} + 510 q^{17} - 12 q^{19} - 144 q^{20} - 396 q^{23} + 256 q^{24} + 3458 q^{25} - 192 q^{26} + 1296 q^{28} - 2752 q^{30} + 1002 q^{35} + 2144 q^{36} - 3216 q^{38} - 6588 q^{39} + 1376 q^{42} - 8654 q^{43} + 48 q^{44} - 10334 q^{45} + 3210 q^{47} + 9222 q^{49} + 9088 q^{54} + 17146 q^{55} - 14076 q^{57} - 960 q^{58} + 1314 q^{61} - 15168 q^{62} + 29938 q^{63} - 4096 q^{64} + 4928 q^{66} - 4080 q^{68} + 23398 q^{73} + 13152 q^{74} + 96 q^{76} - 44622 q^{77} + 1152 q^{80} - 20368 q^{81} + 16512 q^{82} - 10440 q^{83} + 21274 q^{85} - 14316 q^{87} + 3168 q^{92} + 19416 q^{93} - 34686 q^{95} - 2048 q^{96} - 56798 q^{99}+O(q^{100}) $ 8 * q - 64 * q^4 + 18 * q^5 - 32 * q^6 - 162 * q^7 - 268 * q^9 - 6 * q^11 + 512 * q^16 + 510 * q^17 - 12 * q^19 - 144 * q^20 - 396 * q^23 + 256 * q^24 + 3458 * q^25 - 192 * q^26 + 1296 * q^28 - 2752 * q^30 + 1002 * q^35 + 2144 * q^36 - 3216 * q^38 - 6588 * q^39 + 1376 * q^42 - 8654 * q^43 + 48 * q^44 - 10334 * q^45 + 3210 * q^47 + 9222 * q^49 + 9088 * q^54 + 17146 * q^55 - 14076 * q^57 - 960 * q^58 + 1314 * q^61 - 15168 * q^62 + 29938 * q^63 - 4096 * q^64 + 4928 * q^66 - 4080 * q^68 + 23398 * q^73 + 13152 * q^74 + 96 * q^76 - 44622 * q^77 + 1152 * q^80 - 20368 * q^81 + 16512 * q^82 - 10440 * q^83 + 21274 * q^85 - 14316 * q^87 + 3168 * q^92 + 19416 * q^93 - 34686 * q^95 - 2048 * q^96 - 56798 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/38\mathbb{Z}\right)^\times$.

$n$	$21$
$\chi(n)$	$-1$

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 $

$2$		−	2.82843i		−	0.707107i
$2$		−	2.82843i		−	0.707107i
$3$		−	7.80363i		−	0.867070i	−0.901137	−	0.433535i	$-0.857266\pi$
$3$		−	7.80363i		−	0.867070i	0.901137	−	0.433535i	$-0.142734\pi$
$4$	−8.00000			−0.500000
$5$	−33.0971			−1.32388			−0.661941	−	0.749556i	$-0.730267\pi$
$5$	−33.0971			−1.32388			−0.661941	+	0.749556i	$0.730267\pi$
$6$	−22.0720			−0.613111
$7$	16.0783			0.328129			0.164064	−	0.986450i	$-0.447539\pi$
$7$	16.0783			0.328129			0.164064	+	0.986450i	$0.447539\pi$
$8$			22.6274i			0.353553i
$9$	20.1034			0.248190
$10$			93.6127i			0.936127i
$11$	−215.592			−1.78175			−0.890875	−	0.454248i	$-0.849908\pi$
$11$	−215.592			−1.78175			−0.890875	+	0.454248i	$0.849908\pi$
$12$			62.4290i			0.433535i
$13$		−	281.497i		−	1.66567i	−0.553525	−	0.832833i	$-0.686718\pi$
$13$		−	281.497i		−	1.66567i	0.553525	−	0.832833i	$-0.313282\pi$
$14$		−	45.4764i		−	0.232022i
$15$			258.277i			1.14790i
$16$	64.0000			0.250000
$17$	226.582			0.784022			0.392011	−	0.919961i	$-0.371780\pi$
$17$	226.582			0.784022			0.392011	+	0.919961i	$0.371780\pi$
$18$		−	56.8610i		−	0.175497i
$19$	13.9969	−	360.729i	0.0387726	−	0.999248i
$19$	13.9969	−	360.729i	0.0387726	−	0.999248i
$20$	264.777			0.661941
$21$		−	125.469i		−	0.284511i
$22$			609.786i			1.25989i
$23$	414.609			0.783760			0.391880	−	0.920016i	$-0.371825\pi$
$23$	414.609			0.783760			0.391880	+	0.920016i	$0.371825\pi$
$24$	176.576			0.306555
$25$	470.416			0.752666
$26$	−796.195			−1.17780
$27$		−	788.973i		−	1.08227i
$28$	−128.627			−0.164064
$29$			606.612i			0.721298i	0.932702	+	0.360649i	$0.117445\pi$
$29$			606.612i			0.721298i	−0.932702	+	0.360649i	$0.882555\pi$
$30$	730.518			0.811687
$31$		−	478.655i		−	0.498080i	−0.968493	−	0.249040i	$-0.919885\pi$
$31$		−	478.655i		−	0.498080i	0.968493	−	0.249040i	$-0.0801151\pi$
$32$		−	181.019i		−	0.176777i
$33$			1682.40i			1.54490i
$34$		−	640.871i		−	0.554387i
$35$	−532.145			−0.434404
$36$	−160.827			−0.124095
$37$		−	104.604i		−	0.0764094i	−0.999270	−	0.0382047i	$-0.987836\pi$
$37$		−	104.604i		−	0.0764094i	0.999270	−	0.0382047i	$-0.0121639\pi$
$38$	−1020.29	−	39.5893i	−0.706575	−	0.0274164i
$39$	−2196.70			−1.44425
$40$		−	748.901i		−	0.468063i
$41$			1891.12i			1.12500i	0.826799	+	0.562498i	$0.190159\pi$
$41$			1891.12i			1.12500i	−0.826799	+	0.562498i	$0.809841\pi$
$42$	−354.881			−0.201179
$43$	315.912			0.170855			0.0854277	−	0.996344i	$-0.472774\pi$
$43$	315.912			0.170855			0.0854277	+	0.996344i	$0.472774\pi$
$44$	1724.73			0.890875
$45$	−665.364			−0.328575
$46$		−	1172.69i		−	0.554202i
$47$	−474.327			−0.214725			−0.107362	−	0.994220i	$-0.534241\pi$
$47$	−474.327			−0.214725			−0.107362	+	0.994220i	$0.534241\pi$
$48$		−	499.432i		−	0.216767i
$49$	−2142.49			−0.892331
$50$		−	1330.54i		−	0.532215i
$51$		−	1768.16i		−	0.679801i
$52$			2251.98i			0.832833i
$53$		−	774.381i		−	0.275679i	−0.990455	−	0.137839i	$-0.955984\pi$
$53$		−	774.381i		−	0.275679i	0.990455	−	0.137839i	$-0.0440158\pi$
$54$	−2231.55			−0.765279
$55$	7135.46			2.35883
$56$			363.811i			0.116011i
$57$	−2814.99	−	109.227i	−0.866418	−	0.0336186i
$58$	1715.76			0.510035
$59$			567.212i			0.162945i	0.996676	+	0.0814725i	$0.0259623\pi$
$59$			567.212i			0.162945i	−0.996676	+	0.0814725i	$0.974038\pi$
$60$		−	2066.22i		−	0.573949i
$61$	4799.51			1.28984			0.644922	−	0.764248i	$-0.276890\pi$
$61$	4799.51			1.28984			0.644922	+	0.764248i	$0.276890\pi$
$62$	−1353.84			−0.352196
$63$	323.229			0.0814384
$64$	−512.000			−0.125000
$65$			9316.74i			2.20515i
$66$	4758.54			1.09241
$67$			4464.01i			0.994433i	0.867627	+	0.497216i	$0.165644\pi$
$67$			4464.01i			0.994433i	−0.867627	+	0.497216i	$0.834356\pi$
$68$	−1812.66			−0.392011
$69$		−	3235.45i		−	0.679575i
$70$			1505.13i			0.307170i
$71$		−	7636.34i		−	1.51485i	−0.652924	−	0.757423i	$-0.726458\pi$
$71$		−	7636.34i		−	1.51485i	0.652924	−	0.757423i	$-0.273542\pi$
$72$			454.888i			0.0877484i
$73$	8396.65			1.57565			0.787826	−	0.615898i	$-0.211207\pi$
$73$	8396.65			1.57565			0.787826	+	0.615898i	$0.211207\pi$
$74$	−295.866			−0.0540296
$75$		−	3670.95i		−	0.652614i
$76$	−111.975	+	2885.83i	−0.0193863	+	0.499624i
$77$	−3466.35			−0.584644
$78$			6213.21i			1.02124i
$79$		−	9706.71i		−	1.55531i	−0.628689	−	0.777657i	$-0.716408\pi$
$79$		−	9706.71i		−	1.55531i	0.628689	−	0.777657i	$-0.283592\pi$
$80$	−2118.21			−0.330971
$81$	−4528.48			−0.690212
$82$	5348.89			0.795492
$83$	−10589.4			−1.53715			−0.768575	−	0.639760i	$-0.779034\pi$
$83$	−10589.4			−1.53715			−0.768575	+	0.639760i	$0.779034\pi$
$84$			1003.75i			0.142255i
$85$	−7499.21			−1.03795
$86$		−	893.533i		−	0.120813i
$87$	4733.77			0.625416
$88$		−	4878.29i		−	0.629944i
$89$		−	10281.7i		−	1.29804i	−0.760773	−	0.649018i	$-0.775180\pi$
$89$		−	10281.7i		−	1.29804i	0.760773	−	0.649018i	$-0.224820\pi$
$90$			1881.93i			0.232337i
$91$		−	4526.01i		−	0.546553i
$92$	−3316.87			−0.391880
$93$	−3735.24			−0.431870
$94$			1341.60i			0.151833i
$95$	−463.257	+	11939.1i	−0.0513304	+	1.32289i
$96$	−1412.61			−0.153278
$97$			15477.3i			1.64494i	0.568806	+	0.822472i	$0.307406\pi$
$97$			15477.3i			1.64494i	−0.568806	+	0.822472i	$0.692594\pi$
$98$			6059.87i			0.630974i
$99$	−4334.13			−0.442213
$100$	−3763.33			−0.376333
$101$	10464.5			1.02583			0.512914	−	0.858440i	$-0.328566\pi$
$101$	10464.5			1.02583			0.512914	+	0.858440i	$0.328566\pi$
$102$	−5001.12			−0.480692
$103$		−	3224.53i		−	0.303943i	−0.988385	−	0.151972i	$-0.951438\pi$
$103$		−	3224.53i		−	0.303943i	0.988385	−	0.151972i	$-0.0485622\pi$
$104$	6369.56			0.588902
$105$			4152.66i			0.376659i
$106$	−2190.28			−0.194934
$107$		−	7740.93i		−	0.676123i	−0.941124	−	0.338061i	$-0.890229\pi$
$107$		−	7740.93i		−	0.676123i	0.941124	−	0.338061i	$-0.109771\pi$
$108$			6311.79i			0.541134i
$109$			12613.1i			1.06162i	0.847492	+	0.530809i	$0.178112\pi$
$109$			12613.1i			1.06162i	−0.847492	+	0.530809i	$0.821888\pi$
$110$		−	20182.1i		−	1.66794i
$111$	−816.294			−0.0662523
$112$	1029.01			0.0820322
$113$		−	900.876i		−	0.0705518i	−0.999378	−	0.0352759i	$-0.988769\pi$
$113$		−	900.876i		−	0.0705518i	0.999378	−	0.0352759i	$-0.0112310\pi$
$114$	−308.940	+	7962.00i	−0.0237719	+	0.612650i
$115$	−13722.3			−1.03761
$116$		−	4852.89i		−	0.360649i
$117$		−	5659.06i		−	0.413402i
$118$	1604.32			0.115220
$119$	3643.06			0.257260
$120$	−5844.15			−0.405843
$121$	31838.8			2.17464
$122$		−	13575.1i		−	0.912058i
$123$	14757.6			0.975449
$124$			3829.24i			0.249040i
$125$	5116.28			0.327442
$126$		−	914.229i		−	0.0575856i
$127$		−	16688.1i		−	1.03467i	−0.855784	−	0.517334i	$-0.826925\pi$
$127$		−	16688.1i		−	1.03467i	0.855784	−	0.517334i	$-0.173075\pi$
$128$			1448.15i			0.0883883i
$129$		−	2465.26i		−	0.148144i
$130$	26351.7			1.55927
$131$	9365.24			0.545728			0.272864	−	0.962053i	$-0.412029\pi$
$131$	9365.24			0.545728			0.272864	+	0.962053i	$0.412029\pi$
$132$		−	13459.2i		−	0.772451i
$133$	225.047	−	5799.91i	0.0127224	−	0.327882i
$134$	12626.1			0.703170
$135$			26112.7i			1.43280i
$136$			5126.97i			0.277194i
$137$	−36021.1			−1.91918			−0.959591	−	0.281399i	$-0.909201\pi$
$137$	−36021.1			−1.91918			−0.959591	+	0.281399i	$0.909201\pi$
$138$	−9151.25			−0.480532
$139$	−10371.8			−0.536813			−0.268406	−	0.963306i	$-0.586497\pi$
$139$	−10371.8			−0.536813			−0.268406	+	0.963306i	$0.586497\pi$
$140$	4257.16			0.217202
$141$			3701.47i			0.186181i
$142$	−21598.8			−1.07116
$143$			60688.6i			2.96780i
$144$	1286.62			0.0620475
$145$		−	20077.1i		−	0.954914i
$146$		−	23749.3i		−	1.11415i
$147$			16719.2i			0.773714i
$148$			836.835i			0.0382047i
$149$	1353.29			0.0609562			0.0304781	−	0.999535i	$-0.490297\pi$
$149$	1353.29			0.0609562			0.0304781	+	0.999535i	$0.490297\pi$
$150$	−10383.0			−0.461468
$151$		−	29132.7i		−	1.27769i	−0.769334	−	0.638847i	$-0.779412\pi$
$151$		−	29132.7i		−	1.27769i	0.769334	−	0.638847i	$-0.220588\pi$
$152$	8162.36	+	316.714i	0.353288	+	0.0137082i
$153$	4555.07			0.194586
$154$			9804.33i			0.413406i
$155$			15842.1i			0.659399i
$156$	17573.6			0.722124
$157$	−11934.0			−0.484156			−0.242078	−	0.970257i	$-0.577829\pi$
$157$	−11934.0			−0.484156			−0.242078	+	0.970257i	$0.577829\pi$
$158$	−27454.7			−1.09977
$159$	−6042.98			−0.239033
$160$			5991.21i			0.234032i
$161$	6666.22			0.257174
$162$			12808.5i			0.488053i
$163$	13818.7			0.520108			0.260054	−	0.965594i	$-0.416260\pi$
$163$	13818.7			0.520108			0.260054	+	0.965594i	$0.416260\pi$
$164$		−	15128.9i		−	0.562498i
$165$		−	55682.5i		−	2.04527i
$166$			29951.4i			1.08693i
$167$		−	10267.5i		−	0.368157i	−0.982912	−	0.184079i	$-0.941070\pi$
$167$		−	10267.5i		−	0.368157i	0.982912	−	0.184079i	$-0.0589301\pi$
$168$	2839.04			0.100590
$169$	−50679.8			−1.77444
$170$			21211.0i			0.733943i
$171$	281.386	−	7251.87i	0.00962298	−	0.248003i
$172$	−2527.29			−0.0854277
$173$		−	29001.7i		−	0.969015i	−0.874787	−	0.484508i	$-0.838999\pi$
$173$		−	29001.7i		−	0.969015i	0.874787	−	0.484508i	$-0.161001\pi$
$174$		−	13389.1i		−	0.442236i
$175$	7563.50			0.246971
$176$	−13797.9			−0.445438
$177$	4426.31			0.141285
$178$	−29081.2			−0.917850
$179$			25479.5i			0.795217i	0.917555	+	0.397608i	$0.130160\pi$
$179$			25479.5i			0.795217i	−0.917555	+	0.397608i	$0.869840\pi$
$180$	5322.91			0.164287
$181$			31158.1i			0.951073i	0.879696	+	0.475536i	$0.157746\pi$
$181$			31158.1i			0.951073i	−0.879696	+	0.475536i	$0.842254\pi$
$182$	−12801.5			−0.386471
$183$		−	37453.6i		−	1.11839i
$184$			9381.53i			0.277101i
$185$			3462.10i			0.101157i
$186$			10564.9i			0.305378i
$187$	−48849.3			−1.39693
$188$	3794.62			0.107362
$189$		−	12685.4i		−	0.355123i
$190$	33768.8	+	1310.29i	0.935423	+	0.0362961i
$191$	17888.8			0.490359			0.245179	−	0.969478i	$-0.421153\pi$
$191$	17888.8			0.490359			0.245179	+	0.969478i	$0.421153\pi$
$192$			3995.46i			0.108384i
$193$			784.195i			0.0210528i	0.999945	+	0.0105264i	$0.00335071\pi$
$193$			784.195i			0.0210528i	−0.999945	+	0.0105264i	$0.996649\pi$
$194$	43776.4			1.16315
$195$	72704.4			1.91202
$196$	17139.9			0.446166
$197$	42272.4			1.08924			0.544621	−	0.838682i	$-0.316673\pi$
$197$	42272.4			1.08924			0.544621	+	0.838682i	$0.316673\pi$
$198$			12258.8i			0.312692i
$199$	−15361.7			−0.387911			−0.193955	−	0.981010i	$-0.562132\pi$
$199$	−15361.7			−0.387911			−0.193955	+	0.981010i	$0.562132\pi$
$200$			10644.3i			0.266108i
$201$	34835.5			0.862243
$202$		−	29598.0i		−	0.725369i
$203$			9753.30i			0.236679i
$204$			14145.3i			0.339901i
$205$		−	62590.4i		−	1.48936i
$206$	−9120.36			−0.214920
$207$	8335.05			0.194521
$208$		−	18015.8i		−	0.416416i
$209$	−3017.62	+	77770.1i	−0.0690831	+	1.78041i
$210$	11745.5			0.266338
$211$			36036.6i			0.809429i	0.914443	+	0.404714i	$0.132629\pi$
$211$			36036.6i			0.809429i	−0.914443	+	0.404714i	$0.867371\pi$
$212$			6195.05i			0.137839i
$213$	−59591.2			−1.31348
$214$	−21894.7			−0.478091
$215$	−10455.8			−0.226193
$216$	17852.4			0.382639
$217$		−	7695.96i		−	0.163434i
$218$	35675.2			0.750677
$219$		−	65524.3i		−	1.36620i
$220$	−57083.7			−1.17941
$221$		−	63782.3i		−	1.30592i
$222$			2308.83i			0.0468474i
$223$			44099.4i			0.886795i	0.896325	+	0.443398i	$0.146227\pi$
$223$			44099.4i			0.886795i	−0.896325	+	0.443398i	$0.853773\pi$
$224$		−	2910.49i		−	0.0580056i
$225$	9456.96			0.186804
$226$	−2548.06			−0.0498876
$227$			34866.5i			0.676638i	0.941032	+	0.338319i	$0.109858\pi$
$227$			34866.5i			0.676638i	−0.941032	+	0.338319i	$0.890142\pi$
$228$	22519.9	+	873.814i	0.433209	+	0.0168093i
$229$	26085.5			0.497425			0.248712	−	0.968577i	$-0.419993\pi$
$229$	26085.5			0.497425			0.248712	+	0.968577i	$0.419993\pi$
$230$			38812.7i			0.733699i
$231$			27050.1i			0.506927i
$232$	−13726.1			−0.255017
$233$	75466.8			1.39009			0.695047	−	0.718964i	$-0.255383\pi$
$233$	75466.8			1.39009			0.695047	+	0.718964i	$0.255383\pi$
$234$	−16006.2			−0.292319
$235$	15698.8			0.284271
$236$		−	4537.69i		−	0.0814725i
$237$	−75747.5			−1.34856
$238$		−	10304.1i		−	0.181910i
$239$	−42891.8			−0.750895			−0.375447	−	0.926844i	$-0.622511\pi$
$239$	−42891.8			−0.750895			−0.375447	+	0.926844i	$0.622511\pi$
$240$			16529.7i			0.286975i
$241$			15629.3i			0.269095i	0.990907	+	0.134547i	$0.0429580\pi$
$241$			15629.3i			0.269095i	−0.990907	+	0.134547i	$0.957042\pi$
$242$		−	90053.8i		−	1.53770i
$243$		−	28568.3i		−	0.483806i
$244$	−38396.1			−0.644922
$245$	70910.1			1.18134
$246$		−	41740.7i		−	0.689747i
$247$	−101544.	−	3940.10i	−1.66441	−	0.0645822i
$248$	10830.7			0.176098
$249$			82635.9i			1.33282i
$250$		−	14471.0i		−	0.231536i
$251$	76998.8			1.22218			0.611092	−	0.791560i	$-0.290731\pi$
$251$	76998.8			1.22218			0.611092	+	0.791560i	$0.290731\pi$
$252$	−2585.83			−0.0407192
$253$	−89386.3			−1.39646
$254$	−47201.2			−0.731620
$255$			58521.0i			0.899977i
$256$	4096.00			0.0625000
$257$			8903.45i			0.134801i	0.997726	+	0.0674003i	$0.0214705\pi$
$257$			8903.45i			0.134801i	−0.997726	+	0.0674003i	$0.978530\pi$
$258$	−6972.80			−0.104753
$259$		−	1681.86i		−	0.0250721i
$260$		−	74533.9i		−	1.10257i
$261$			12195.0i			0.179019i
$262$		−	26488.9i		−	0.385888i
$263$	−79232.7			−1.14549			−0.572747	−	0.819732i	$-0.694122\pi$
$263$	−79232.7			−1.14549			−0.572747	+	0.819732i	$0.694122\pi$
$264$	−38068.3			−0.546205
$265$			25629.8i			0.364966i
$266$	−16404.6	−	636.529i	−0.231848	−	0.00899611i
$267$	−80234.9			−1.12549
$268$		−	35712.1i		−	0.497216i
$269$		−	132817.i		−	1.83548i	−0.397177	−	0.917742i	$-0.630010\pi$
$269$		−	132817.i		−	1.83548i	0.397177	−	0.917742i	$-0.369990\pi$
$270$	73857.9			1.01314
$271$	73016.0			0.994213			0.497106	−	0.867690i	$-0.334396\pi$
$271$	73016.0			0.994213			0.497106	+	0.867690i	$0.334396\pi$
$272$	14501.3			0.196005
$273$	−35319.3			−0.473900
$274$			101883.i			1.35707i
$275$	−101418.			−1.34106
$276$			25883.6i			0.339787i
$277$	66280.9			0.863831			0.431916	−	0.901914i	$-0.357838\pi$
$277$	66280.9			0.863831			0.431916	+	0.901914i	$0.357838\pi$
$278$			29335.8i			0.379584i
$279$		−	9622.59i		−	0.123619i
$280$		−	12041.1i		−	0.153585i
$281$			112860.i			1.42932i	0.699473	+	0.714659i	$0.253418\pi$
$281$			112860.i			1.42932i	−0.699473	+	0.714659i	$0.746582\pi$
$282$	10469.3			0.131650
$283$	80766.6			1.00846			0.504230	−	0.863569i	$-0.331776\pi$
$283$	80766.6			1.00846			0.504230	+	0.863569i	$0.331776\pi$
$284$			61090.7i			0.757423i
$285$	93168.0	+	3615.08i	1.14704	+	0.0445070i
$286$	171653.			2.09855
$287$			30406.0i			0.369144i
$288$		−	3639.10i		−	0.0438742i
$289$	−32181.5			−0.385310
$290$	−56786.5			−0.675226
$291$	120779.			1.42628
$292$	−67173.2			−0.787826
$293$		−	133666.i		−	1.55699i	−0.627653	−	0.778493i	$-0.715984\pi$
$293$		−	133666.i		−	1.55699i	0.627653	−	0.778493i	$-0.284016\pi$
$294$	47289.0			0.547098
$295$		−	18773.0i		−	0.215720i
$296$	2366.93			0.0270148
$297$			170096.i			1.92833i
$298$		−	3827.68i		−	0.0431025i
$299$		−	116711.i		−	1.30548i
$300$			29367.6i			0.326307i
$301$	5079.33			0.0560626
$302$	−82399.8			−0.903467
$303$		−	81660.8i		−	0.889464i
$304$	895.803	−	23086.6i	0.00969316	−	0.249812i
$305$	−158850.			−1.70760
$306$		−	12883.7i		−	0.137593i
$307$			100857.i			1.07011i	0.844816	+	0.535057i	$0.179710\pi$
$307$			100857.i			1.07011i	−0.844816	+	0.535057i	$0.820290\pi$
$308$	27730.8			0.292322
$309$	−25163.1			−0.263540
$310$	44808.1			0.466266
$311$	121531.			1.25651			0.628254	−	0.778009i	$-0.283770\pi$
$311$	121531.			1.25651			0.628254	+	0.778009i	$0.283770\pi$
$312$		−	49705.7i		−	0.510619i
$313$	189932.			1.93869			0.969346	−	0.245700i	$-0.0790180\pi$
$313$	189932.			1.93869			0.969346	+	0.245700i	$0.0790180\pi$
$314$			33754.3i			0.342350i
$315$	−10697.9			−0.107815
$316$			77653.7i			0.777657i
$317$			67336.1i			0.670085i	0.942203	+	0.335042i	$0.108751\pi$
$317$			67336.1i			0.670085i	−0.942203	+	0.335042i	$0.891249\pi$
$318$			17092.1i			0.169022i
$319$		−	130781.i		−	1.28517i
$320$	16945.7			0.165485
$321$	−60407.3			−0.586246
$322$		−	18854.9i		−	0.181850i
$323$	3171.45	−	81734.7i	0.0303986	−	0.783432i
$324$	36227.8			0.345106
$325$		−	132421.i		−	1.25369i
$326$		−	39085.3i		−	0.367772i
$327$	98427.7			0.920496
$328$	−42791.1			−0.397746
$329$	−7626.38			−0.0704574
$330$	−157494.			−1.44622
$331$		−	154310.i		−	1.40844i	−0.709984	−	0.704218i	$-0.751298\pi$
$331$		−	154310.i		−	1.40844i	0.709984	−	0.704218i	$-0.248702\pi$
$332$	84715.4			0.768575
$333$		−	2102.90i		−	0.0189640i
$334$	−29041.0			−0.260327
$335$		−	147746.i		−	1.31651i
$336$		−	8030.03i		−	0.0711277i
$337$			127543.i			1.12304i	0.827463	+	0.561521i	$0.189783\pi$
$337$			127543.i			1.12304i	−0.827463	+	0.561521i	$0.810217\pi$
$338$			143344.i			1.25472i
$339$	−7030.10			−0.0611733
$340$	59993.7			0.518976
$341$			103194.i			0.887454i
$342$	−20511.4	−	795.879i	−0.175365	−	0.00680447i
$343$	−73051.6			−0.620929
$344$			7148.26i			0.0604065i
$345$			107084.i			0.899677i
$346$	−82029.1			−0.685197
$347$	−71084.5			−0.590359			−0.295179	−	0.955442i	$-0.595379\pi$
$347$	−71084.5			−0.590359			−0.295179	+	0.955442i	$0.595379\pi$
$348$	−37870.2			−0.312708
$349$	83601.6			0.686378			0.343189	−	0.939266i	$-0.388493\pi$
$349$	83601.6			0.686378			0.343189	+	0.939266i	$0.388493\pi$
$350$		−	21392.8i		−	0.174635i
$351$	−222094.			−1.80270
$352$			39026.3i			0.314972i
$353$	−40368.7			−0.323963			−0.161981	−	0.986794i	$-0.551788\pi$
$353$	−40368.7			−0.323963			−0.161981	+	0.986794i	$0.551788\pi$
$354$		−	12519.5i		−	0.0999034i
$355$			252740.i			2.00548i
$356$			82254.0i			0.649018i
$357$		−	28429.1i		−	0.223063i
$358$	72067.0			0.562303
$359$	143079.			1.11016			0.555081	−	0.831796i	$-0.312687\pi$
$359$	143079.			1.11016			0.555081	+	0.831796i	$0.312687\pi$
$360$		−	15055.5i		−	0.116169i
$361$	−129929.	−	10098.2i	−0.996993	−	0.0774869i
$362$	88128.4			0.672510
$363$		−	248458.i		−	1.88556i
$364$			36208.0i			0.273277i
$365$	−277904.			−2.08598
$366$	−105935.			−0.790818
$367$	−30831.7			−0.228910			−0.114455	−	0.993428i	$-0.536512\pi$
$367$	−30831.7			−0.228910			−0.114455	+	0.993428i	$0.536512\pi$
$368$	26535.0			0.195940
$369$			38017.9i			0.279213i
$370$	9792.30			0.0715288
$371$		−	12450.8i		−	0.0904582i
$372$	29882.0			0.215935
$373$			199882.i			1.43666i	0.695701	+	0.718332i	$0.255094\pi$
$373$			199882.i			1.43666i	−0.695701	+	0.718332i	$0.744906\pi$
$374$			138167.i			0.987779i
$375$		−	39925.5i		−	0.283915i
$376$		−	10732.8i		−	0.0759167i
$377$	170760.			1.20144
$378$	−35879.6			−0.251110
$379$		−	49499.6i		−	0.344606i	−0.985044	−	0.172303i	$-0.944879\pi$
$379$		−	49499.6i		−	0.344606i	0.985044	−	0.172303i	$-0.0551209\pi$
$380$	3706.06	−	95512.5i	0.0256652	−	0.661444i
$381$	−130228.			−0.897129
$382$		−	50597.1i		−	0.346736i
$383$			49593.2i			0.338084i	0.985609	+	0.169042i	$0.0540674\pi$
$383$			49593.2i			0.338084i	−0.985609	+	0.169042i	$0.945933\pi$
$384$	11300.9			0.0766389
$385$	114726.			0.774000
$386$	2218.04			0.0148866
$387$	6350.90			0.0424046
$388$		−	123818.i		−	0.822472i
$389$	−15826.9			−0.104592			−0.0522958	−	0.998632i	$-0.516654\pi$
$389$	−15826.9			−0.104592			−0.0522958	+	0.998632i	$0.516654\pi$
$390$		−	205639.i		−	1.35200i
$391$	93943.1			0.614485
$392$		−	48479.0i		−	0.315487i
$393$		−	73082.8i		−	0.473184i
$394$		−	119564.i		−	0.770211i
$395$			321264.i			2.05905i
$396$	34673.0			0.221106
$397$	−2861.99			−0.0181588			−0.00907939	−	0.999959i	$-0.502890\pi$
$397$	−2861.99			−0.0181588			−0.00907939	+	0.999959i	$0.502890\pi$
$398$			43449.3i			0.274294i
$399$	−45260.3	−	1756.18i	−0.284297	−	0.0110312i
$400$	30106.6			0.188166
$401$		−	226034.i		−	1.40567i	−0.711351	−	0.702837i	$-0.751916\pi$
$401$		−	226034.i		−	1.40567i	0.711351	−	0.702837i	$-0.248084\pi$
$402$		−	98529.6i		−	0.609698i
$403$	−134740.			−0.829634
$404$	−83715.7			−0.512914
$405$	149879.			0.913759
$406$	27586.5			0.167357
$407$			22551.9i			0.136142i
$408$	40009.0			0.240346
$409$		−	300321.i		−	1.79531i	−0.440700	−	0.897655i	$-0.645270\pi$
$409$		−	300321.i		−	1.79531i	0.440700	−	0.897655i	$-0.354730\pi$
$410$	−177032.			−1.05314
$411$			281095.i			1.66406i
$412$			25796.3i			0.151972i
$413$			9119.81i			0.0534670i
$414$		−	23575.1i		−	0.137547i
$415$	350479.			2.03501
$416$	−50956.5			−0.294451
$417$			80937.4i			0.465454i
$418$	219967.	+	8535.12i	1.25894	+	0.0488492i
$419$	−88915.8			−0.506467			−0.253233	−	0.967405i	$-0.581494\pi$
$419$	−88915.8			−0.506467			−0.253233	+	0.967405i	$0.581494\pi$
$420$		−	33221.3i		−	0.188329i
$421$		−	52919.8i		−	0.298575i	−0.988794	−	0.149288i	$-0.952302\pi$
$421$		−	52919.8i		−	0.298575i	0.988794	−	0.149288i	$-0.0476980\pi$
$422$	101927.			0.572353
$423$	−9535.59			−0.0532926
$424$	17522.3			0.0974671
$425$	106588.			0.590106
$426$			168549.i			0.928769i
$427$	77168.1			0.423235
$428$			61927.4i			0.338061i
$429$	473591.			2.57329
$430$			29573.3i			0.159942i
$431$			18064.2i			0.0972442i	0.998817	+	0.0486221i	$0.0154830\pi$
$431$			18064.2i			0.0972442i	−0.998817	+	0.0486221i	$0.984517\pi$
$432$		−	50494.3i		−	0.270567i
$433$			188974.i			1.00792i	0.863726	+	0.503961i	$0.168125\pi$
$433$			188974.i			1.00792i	−0.863726	+	0.503961i	$0.831875\pi$
$434$	−21767.5			−0.115566
$435$	−156674.			−0.827977
$436$		−	100905.i		−	0.530809i
$437$	5803.25	−	149561.i	0.0303884	−	0.783171i
$438$	−185331.			−0.966049
$439$			249410.i			1.29415i	0.762427	+	0.647074i	$0.224008\pi$
$439$			249410.i			1.29415i	−0.762427	+	0.647074i	$0.775992\pi$
$440$			161457.i			0.833972i
$441$	−43071.3			−0.221468
$442$	−180404.			−0.923423
$443$	43050.1			0.219365			0.109682	−	0.993967i	$-0.465017\pi$
$443$	43050.1			0.219365			0.109682	+	0.993967i	$0.465017\pi$
$444$	6530.35			0.0331261
$445$			340296.i			1.71845i
$446$	124732.			0.627059
$447$		−	10560.6i		−	0.0528533i
$448$	−8232.10			−0.0410161
$449$			19223.8i			0.0953556i	0.998863	+	0.0476778i	$0.0151821\pi$
$449$			19223.8i			0.0953556i	−0.998863	+	0.0476778i	$0.984818\pi$
$450$		−	26748.3i		−	0.132090i
$451$		−	407709.i		−	2.00446i
$452$			7207.01i			0.0352759i
$453$	−227341.			−1.10785
$454$	98617.2			0.478455
$455$			149798.i			0.723572i
$456$	2471.52	−	63696.0i	0.0118860	−	0.306325i
$457$	38484.7			0.184271			0.0921353	−	0.995747i	$-0.470631\pi$
$457$	38484.7			0.184271			0.0921353	+	0.995747i	$0.470631\pi$
$458$		−	73780.8i		−	0.351732i
$459$		−	178767.i		−	0.848521i
$460$	109779.			0.518803
$461$	−203940.			−0.959623			−0.479812	−	0.877371i	$-0.659295\pi$
$461$	−203940.			−0.959623			−0.479812	+	0.877371i	$0.659295\pi$
$462$	76509.3			0.358452
$463$	−203200.			−0.947900			−0.473950	−	0.880552i	$-0.657172\pi$
$463$	−203200.			−0.947900			−0.473950	+	0.880552i	$0.657172\pi$
$464$			38823.2i			0.180325i
$465$	123626.			0.571745
$466$		−	213452.i		−	0.982945i
$467$	−121674.			−0.557912			−0.278956	−	0.960304i	$-0.589988\pi$
$467$	−121674.			−0.557912			−0.278956	+	0.960304i	$0.589988\pi$
$468$			45272.4i			0.206701i
$469$			71773.8i			0.326302i
$470$		−	44403.0i		−	0.201010i
$471$			93128.2i			0.419797i
$472$	−12834.5			−0.0576098
$473$	−68108.0			−0.304422
$474$			214246.i			0.953579i
$475$	6584.37	−	169693.i	0.0291828	−	0.752100i
$476$	−29144.5			−0.128630
$477$		−	15567.7i		−	0.0684207i
$478$			121316.i			0.530963i
$479$	−208037.			−0.906711			−0.453355	−	0.891330i	$-0.649773\pi$
$479$	−208037.			−0.906711			−0.453355	+	0.891330i	$0.649773\pi$
$480$	46753.2			0.202922
$481$	−29445.9			−0.127272
$482$	44206.3			0.190279
$483$		−	52020.7i		−	0.222988i
$484$	−254711.			−1.08732
$485$		−	512253.i		−	2.17771i
$486$	−80803.3			−0.342103
$487$		−	47417.7i		−	0.199932i	−0.994991	−	0.0999660i	$-0.968127\pi$
$487$		−	47417.7i		−	0.199932i	0.994991	−	0.0999660i	$-0.0318734\pi$
$488$			108601.i			0.456029i
$489$		−	107836.i		−	0.450970i
$490$		−	200564.i		−	0.835335i
$491$	−218823.			−0.907676			−0.453838	−	0.891084i	$-0.649946\pi$
$491$	−218823.			−0.907676			−0.453838	+	0.891084i	$0.649946\pi$
$492$	−118061.			−0.487725
$493$			137447.i			0.565513i
$494$	−11144.3	+	287210.i	−0.0456665	+	1.17692i
$495$	143447.			0.585438
$496$		−	30633.9i		−	0.124520i
$497$		−	122780.i		−	0.497065i
$498$	233730.			0.942443
$499$	147213.			0.591214			0.295607	−	0.955310i	$-0.404478\pi$
$499$	147213.			0.591214			0.295607	+	0.955310i	$0.404478\pi$
$500$	−40930.2			−0.163721
$501$	−80124.1			−0.319218
$502$		−	217786.i		−	0.864215i
$503$	189477.			0.748895			0.374448	−	0.927248i	$-0.377832\pi$
$503$	189477.			0.748895			0.374448	+	0.927248i	$0.377832\pi$
$504$			7313.83i			0.0287928i
$505$	−346343.			−1.35807
$506$			252823.i			0.987450i
$507$			395486.i			1.53856i
$508$			133505.i			0.517334i
$509$		−	117829.i		−	0.454797i	−0.973802	−	0.227398i	$-0.926978\pi$
$509$		−	117829.i		−	0.454797i	0.973802	−	0.227398i	$-0.0730220\pi$
$510$	165522.			0.636380
$511$	135004.			0.517017
$512$		−	11585.2i		−	0.0441942i
$513$	−284605.	−	11043.2i	−1.08145	−	0.0419624i
$514$	25182.8			0.0953185
$515$			106723.i			0.402385i
$516$			19722.1i			0.0740718i
$517$	102261.			0.382586
$518$	−4757.03			−0.0177287
$519$	−226318.			−0.840204
$520$	−210814.			−0.779637
$521$		−	254449.i		−	0.937402i	−0.883357	−	0.468701i	$-0.844722\pi$
$521$		−	254449.i		−	0.937402i	0.883357	−	0.468701i	$-0.155278\pi$
$522$	34492.6			0.126586
$523$		−	33047.5i		−	0.120819i	−0.998174	−	0.0604094i	$-0.980759\pi$
$523$		−	33047.5i		−	0.120819i	0.998174	−	0.0604094i	$-0.0192406\pi$
$524$	−74921.9			−0.272864
$525$		−	59022.7i		−	0.214141i
$526$			224104.i			0.809987i
$527$		−	108455.i		−	0.390505i
$528$			107673.i			0.386226i
$529$	−107940.			−0.385720
$530$	72491.9			0.258070
$531$			11402.9i			0.0404414i
$532$	−1800.38	+	46399.3i	−0.00636121	+	0.163941i
$533$	532345.			1.87387
$534$			226939.i			0.795840i
$535$			256202.i			0.895107i
$536$	−101009.			−0.351585
$537$	198833.			0.689508
$538$	−375665.			−1.29788
$539$	461903.			1.58991
$540$		−	208902.i		−	0.716398i
$541$	−363239.			−1.24108			−0.620538	−	0.784176i	$-0.713086\pi$
$541$	−363239.			−1.24108			−0.620538	+	0.784176i	$0.713086\pi$
$542$		−	206520.i		−	0.703014i
$543$	243146.			0.824647
$544$		−	41015.8i		−	0.138597i
$545$		−	417456.i		−	1.40546i
$546$			99898.0i			0.335098i
$547$			899.921i			0.00300767i	0.999999	+	0.00150383i	$0.000478685\pi$
$547$			899.921i			0.00300767i	−0.999999	+	0.00150383i	$0.999521\pi$
$548$	288169.			0.959591
$549$	96486.5			0.320127
$550$			286853.i			0.948274i
$551$	218822.	+	8490.69i	0.720756	+	0.0279666i
$552$	73210.0			0.240266
$553$		−	156068.i		−	0.510343i
$554$		−	187471.i		−	0.610821i
$555$	27016.9			0.0877102
$556$	82974.1			0.268406
$557$	340311.			1.09690			0.548448	−	0.836184i	$-0.315219\pi$
$557$	340311.			1.09690			0.548448	+	0.836184i	$0.315219\pi$
$558$	−27216.8			−0.0874115
$559$		−	88928.3i		−	0.284588i
$560$	−34057.3			−0.108601
$561$			381202.i			1.21124i
$562$	319217.			1.01068
$563$			631686.i			1.99289i	0.0842180	+	0.996447i	$0.473161\pi$
$563$			631686.i			1.99289i	−0.0842180	+	0.996447i	$0.526839\pi$
$564$		−	29611.8i		−	0.0930907i
$565$			29816.3i			0.0934023i
$566$		−	228442.i		−	0.713089i
$567$	−72810.3			−0.226478
$568$	172791.			0.535579
$569$			5519.19i			0.0170471i	0.999964	+	0.00852356i	$0.00271317\pi$
$569$			5519.19i			0.0170471i	−0.999964	+	0.00852356i	$0.997287\pi$
$570$	10225.0	−	263519.i	0.0314712	−	0.811077i
$571$	−478673.			−1.46814			−0.734068	−	0.679076i	$-0.762381\pi$
$571$	−478673.			−1.46814			−0.734068	+	0.679076i	$0.762381\pi$
$572$		−	485508.i		−	1.48390i
$573$		−	139597.i		−	0.425175i
$574$	86001.1			0.261024
$575$	195039.			0.589909
$576$	−10292.9			−0.0310238
$577$	65914.9			0.197985			0.0989925	−	0.995088i	$-0.468438\pi$
$577$	65914.9			0.197985			0.0989925	+	0.995088i	$0.468438\pi$
$578$			91023.0i			0.272455i
$579$	6119.56			0.0182542
$580$			160617.i			0.477457i
$581$	−170260.			−0.504383
$582$		−	341614.i		−	1.00853i
$583$			166950.i			0.491191i
$584$			189994.i			0.557077i
$585$			187298.i			0.547295i
$586$	−378064.			−1.10096
$587$	289436.			0.839994			0.419997	−	0.907526i	$-0.362031\pi$
$587$	289436.			0.839994			0.419997	+	0.907526i	$0.362031\pi$
$588$		−	133753.i		−	0.386857i
$589$	−172664.	−	6699.69i	−0.497705	−	0.0193119i
$590$	−53098.2			−0.152537
$591$		−	329878.i		−	0.944449i
$592$		−	6694.68i		−	0.0191023i
$593$	388285.			1.10418			0.552092	−	0.833783i	$-0.313830\pi$
$593$	388285.			1.10418			0.552092	+	0.833783i	$0.313830\pi$
$594$	481105.			1.36354
$595$	−120575.			−0.340582
$596$	−10826.3			−0.0304781
$597$			119877.i			0.336346i
$598$	−330110.			−0.923115
$599$			601872.i			1.67745i	0.544553	+	0.838727i	$0.316699\pi$
$599$			601872.i			1.67745i	−0.544553	+	0.838727i	$0.683301\pi$
$600$	83064.2			0.230734
$601$		−	176095.i		−	0.487527i	−0.969835	−	0.243764i	$-0.921618\pi$
$601$		−	176095.i		−	0.487527i	0.969835	−	0.243764i	$-0.0783821\pi$
$602$		−	14366.5i		−	0.0396423i
$603$			89741.7i			0.246808i
$604$			233062.i			0.638847i
$605$	−1.05377e6			−2.87896
$606$	−230972.			−0.628946
$607$		−	607939.i		−	1.64999i	−0.565137	−	0.824997i	$-0.691177\pi$
$607$		−	607939.i		−	1.64999i	0.565137	−	0.824997i	$-0.308823\pi$
$608$	−65298.8	−	2533.71i	−0.176644	−	0.00685410i
$609$	76111.1			0.205217
$610$			449295.i			1.20746i
$611$			133522.i			0.357660i
$612$	−36440.6			−0.0972932
$613$	194933.			0.518757			0.259379	−	0.965776i	$-0.416482\pi$
$613$	194933.			0.518757			0.259379	+	0.965776i	$0.416482\pi$
$614$	285267.			0.756685
$615$	−488432.			−1.29138
$616$		−	78434.6i		−	0.206703i
$617$	148271.			0.389480			0.194740	−	0.980855i	$-0.437614\pi$
$617$	148271.			0.389480			0.194740	+	0.980855i	$0.437614\pi$
$618$			71171.9i			0.186351i
$619$	−572353.			−1.49377			−0.746884	−	0.664955i	$-0.768451\pi$
$619$	−572353.			−1.49377			−0.746884	+	0.664955i	$0.768451\pi$
$620$		−	126737.i		−	0.329700i
$621$		−	327115.i		−	0.848238i
$622$		−	343741.i		−	0.888485i
$623$		−	165313.i		−	0.425923i
$624$	−140589.			−0.361062
$625$	−463344.			−1.18616
$626$		−	537208.i		−	1.37086i
$627$	606889.	+	23548.4i	1.54374	+	0.0598999i
$628$	95471.7			0.242078
$629$		−	23701.5i		−	0.0599066i
$630$			30258.3i			0.0762366i
$631$	236439.			0.593829			0.296914	−	0.954904i	$-0.404042\pi$
$631$	236439.			0.593829			0.296914	+	0.954904i	$0.404042\pi$
$632$	219638.			0.549886
$633$	281216.			0.701831
$634$	190455.			0.473821
$635$			552329.i			1.36978i
$636$	48343.9			0.119516
$637$			603105.i			1.48633i
$638$	−369903.			−0.908755
$639$		−	153516.i		−	0.375970i
$640$		−	47929.7i		−	0.117016i
$641$			247053.i			0.601275i	0.953738	+	0.300638i	$0.0971995\pi$
$641$			247053.i			0.601275i	−0.953738	+	0.300638i	$0.902801\pi$
$642$			170858.i			0.414538i
$643$	543389.			1.31428			0.657142	−	0.753767i	$-0.271765\pi$
$643$	543389.			1.31428			0.657142	+	0.753767i	$0.271765\pi$
$644$	−53329.7			−0.128587
$645$			81592.8i			0.196125i
$646$	−231181.	−	8970.22i	−0.553970	−	0.0214950i
$647$	−263444.			−0.629332			−0.314666	−	0.949202i	$-0.601893\pi$
$647$	−263444.			−0.629332			−0.314666	+	0.949202i	$0.601893\pi$
$648$		−	102468.i		−	0.244027i
$649$		−	122286.i		−	0.290327i
$650$	−374543.			−0.886492
$651$	−60056.4			−0.141709
$652$	−110550.			−0.260054
$653$	−261207.			−0.612574			−0.306287	−	0.951939i	$-0.599087\pi$
$653$	−261207.			−0.612574			−0.306287	+	0.951939i	$0.599087\pi$
$654$		−	278396.i		−	0.650889i
$655$	−309962.			−0.722480
$656$			121031.i			0.281249i
$657$	168801.			0.391061
$658$			21570.7i			0.0498209i
$659$		−	532996.i		−	1.22731i	−0.789576	−	0.613653i	$-0.789699\pi$
$659$		−	532996.i		−	1.22731i	0.789576	−	0.613653i	$-0.210301\pi$
$660$			445460.i			1.02263i
$661$			495346.i			1.13372i	0.823814	+	0.566860i	$0.191842\pi$
$661$			495346.i			1.13372i	−0.823814	+	0.566860i	$0.808158\pi$
$662$	−436454.			−0.995915
$663$	−497734.			−1.13232
$664$		−	239611.i		−	0.543465i
$665$	−7448.39	+	191960.i	−0.0168430	+	0.434078i
$666$	−5947.91			−0.0134096
$667$			251507.i			0.565325i
$668$			82140.3i			0.184079i
$669$	344136.			0.768913
$670$	−417888.			−0.930915
$671$	−1.03474e6			−2.29818
$672$	−22712.4			−0.0502949
$673$		−	425648.i		−	0.939768i	−0.882728	−	0.469884i	$-0.844296\pi$
$673$		−	425648.i		−	0.939768i	0.882728	−	0.469884i	$-0.155704\pi$
$674$	360745.			0.794110
$675$		−	371146.i		−	0.814586i
$676$	405439.			0.887221
$677$			423249.i			0.923461i	0.887020	+	0.461730i	$0.152771\pi$
$677$			423249.i			0.923461i	−0.887020	+	0.461730i	$0.847229\pi$
$678$			19884.1i			0.0432561i
$679$			248849.i			0.539754i
$680$		−	169688.i		−	0.366972i
$681$	272085.			0.586692
$682$	291877.			0.627525
$683$		−	310900.i		−	0.666467i	−0.942844	−	0.333233i	$-0.891860\pi$
$683$		−	310900.i		−	0.666467i	0.942844	−	0.333233i	$-0.108140\pi$
$684$	−2251.08	+	58015.0i	−0.00481149	+	0.124002i
$685$	1.19219e6			2.54077
$686$			206621.i			0.439063i
$687$		−	203561.i		−	0.431302i
$688$	20218.3			0.0427139
$689$	−217986.			−0.459188
$690$	302879.			0.636168
$691$	314072.			0.657769			0.328885	−	0.944370i	$-0.393327\pi$
$691$	314072.			0.657769			0.328885	+	0.944370i	$0.393327\pi$
$692$			232013.i			0.484508i
$693$	−69685.5			−0.145103
$694$			201057.i			0.417447i
$695$	343275.			0.710677
$696$			107113.i			0.221118i
$697$			428494.i			0.882021i
$698$		−	236461.i		−	0.485343i
$699$		−	588915.i		−	1.20531i
$700$	−60508.0			−0.123486
$701$	607472.			1.23620			0.618102	−	0.786098i	$-0.287902\pi$
$701$	607472.			1.23620			0.618102	+	0.786098i	$0.287902\pi$
$702$			628177.i			1.27470i
$703$	−37733.8	−	1464.14i	−0.0763519	−	0.00296259i
$704$	110383.			0.222719
$705$		−	122508.i		−	0.246482i
$706$			114180.i			0.229076i
$707$	168251.			0.336604
$708$	−35410.5			−0.0706424
$709$	−293984.			−0.584833			−0.292416	−	0.956291i	$-0.594459\pi$
$709$	−293984.			−0.584833			−0.292416	+	0.956291i	$0.594459\pi$
$710$	714858.			1.41809
$711$		−	195138.i		−	0.386013i
$712$	232649.			0.458925
$713$		−	198455.i		−	0.390375i
$714$	−80409.6			−0.157729
$715$		−	2.00861e6i		−	3.92902i
$716$		−	203836.i		−	0.397608i
$717$			334712.i			0.651078i
$718$		−	404688.i		−	0.785003i
$719$	911462.			1.76312			0.881558	−	0.472075i	$-0.156495\pi$
$719$	911462.			1.76312			0.881558	+	0.472075i	$0.156495\pi$
$720$	−42583.3			−0.0821436
$721$		−	51845.1i		−	0.0997326i
$722$	−28562.0	+	367495.i	−0.0547915	+	0.704981i
$723$	121965.			0.233324
$724$		−	249265.i		−	0.475536i
$725$			285360.i			0.542896i
$726$	−702747.			−1.33329
$727$	−174790.			−0.330710			−0.165355	−	0.986234i	$-0.552877\pi$
$727$	−174790.			−0.330710			−0.165355	+	0.986234i	$0.552877\pi$
$728$	102412.			0.193236
$729$	−589743.			−1.10971
$730$			786032.i			1.47501i
$731$	71580.0			0.133954
$732$			299629.i			0.559193i
$733$	−401715.			−0.747671			−0.373835	−	0.927495i	$-0.621958\pi$
$733$	−401715.			−0.747671			−0.373835	+	0.927495i	$0.621958\pi$
$734$			87205.3i			0.161864i
$735$		−	553356.i		−	1.02431i
$736$		−	75052.3i		−	0.138551i
$737$		−	962404.i		−	1.77183i
$738$	107531.			0.197433
$739$	−302531.			−0.553963			−0.276982	−	0.960875i	$-0.589334\pi$
$739$	−302531.			−0.553963			−0.276982	+	0.960875i	$0.589334\pi$
$740$		−	27696.8i		−	0.0505785i
$741$	−30747.0	+	792413.i	−0.0559973	+	1.44316i
$742$	−35216.0			−0.0639636
$743$			909052.i			1.64669i	0.567543	+	0.823344i	$0.307894\pi$
$743$			909052.i			1.64669i	−0.567543	+	0.823344i	$0.692106\pi$
$744$		−	84518.9i		−	0.152689i
$745$	−44789.9			−0.0806989
$746$	565350.			1.01587
$747$	−212883.			−0.381505
$748$	390794.			0.698466
$749$		−	124461.i		−	0.221855i
$750$	−112926.			−0.200758
$751$		−	370317.i		−	0.656589i	−0.944575	−	0.328295i	$-0.893526\pi$
$751$		−	370317.i		−	0.656589i	0.944575	−	0.328295i	$-0.106474\pi$
$752$	−30356.9			−0.0536812
$753$		−	600870.i		−	1.05972i
$754$		−	482981.i		−	0.849547i
$755$			964208.i			1.69152i
$756$			101483.i			0.177562i
$757$	154581.			0.269751			0.134876	−	0.990863i	$-0.456937\pi$
$757$	154581.			0.269751			0.134876	+	0.990863i	$0.456937\pi$
$758$	−140006.			−0.243674
$759$			697538.i			1.21083i
$760$	−270150.	−	10482.3i	−0.467711	−	0.0181480i
$761$	−722058.			−1.24682			−0.623409	−	0.781896i	$-0.714253\pi$
$761$	−722058.			−1.24682			−0.623409	+	0.781896i	$0.714253\pi$
$762$			368341.i			0.634366i
$763$			202797.i			0.348347i
$764$	−143110.			−0.245179
$765$	−150760.			−0.257610
$766$	140271.			0.239062
$767$	159669.			0.271412
$768$		−	31963.7i		−	0.0541919i
$769$	496131.			0.838965			0.419482	−	0.907763i	$-0.362212\pi$
$769$	496131.			0.838965			0.419482	+	0.907763i	$0.362212\pi$
$770$		−	324495.i		−	0.547301i
$771$	69479.2			0.116882
$772$		−	6273.56i		−	0.0105264i
$773$			317854.i			0.531948i	0.963980	+	0.265974i	$0.0856935\pi$
$773$			317854.i			0.531948i	−0.963980	+	0.265974i	$0.914306\pi$
$774$		−	17963.1i		−	0.0299846i
$775$		−	225167.i		−	0.374888i
$776$	−350211.			−0.581575
$777$	−13124.6			−0.0217393
$778$			44765.2i			0.0739574i
$779$	682180.	+	26469.8i	1.12415	+	0.0436190i
$780$	−581635.			−0.956008
$781$			1.64633e6i			2.69908i
$782$		−	265711.i		−	0.434506i
$783$	478601.			0.780638
$784$	−137119.			−0.223083
$785$	394979.			0.640966
$786$	−206709.			−0.334592
$787$			206097.i			0.332752i	0.986062	+	0.166376i	$0.0532066\pi$
$787$			206097.i			0.332752i	−0.986062	+	0.166376i	$0.946793\pi$
$788$	−338179.			−0.544621
$789$			618302.i			0.993223i
$790$	908671.			1.45597
$791$		−	14484.6i		−	0.0231501i
$792$		−	98070.1i		−	0.156346i
$793$		−	1.35105e6i		−	2.14845i
$794$			8094.92i			0.0128402i
$795$	200005.			0.316451
$796$	122893.			0.193955
$797$		−	406943.i		−	0.640644i	−0.947309	−	0.320322i	$-0.896209\pi$
$797$		−	406943.i		−	0.640644i	0.947309	−	0.320322i	$-0.103791\pi$
$798$	−4967.23	+	128016.i	−0.00780025	+	0.201028i
$799$	−107474.			−0.168349
$800$		−	85154.4i		−	0.133054i
$801$		−	206698.i		−	0.322160i
$802$	−639320.			−0.993961
$803$	−1.81025e6			−2.80742
$804$	−278684.			−0.431121
$805$	−220632.			−0.340469
$806$			381103.i			0.586640i
$807$	−1.03646e6			−1.59149
$808$			236784.i			0.362685i
$809$	−301170.			−0.460166			−0.230083	−	0.973171i	$-0.573900\pi$
$809$	−301170.			−0.460166			−0.230083	+	0.973171i	$0.573900\pi$
$810$		−	423923.i		−	0.646125i
$811$		−	454953.i		−	0.691711i	−0.938288	−	0.345855i	$-0.887589\pi$
$811$		−	454953.i		−	0.691711i	0.938288	−	0.345855i	$-0.112411\pi$
$812$		−	78026.4i		−	0.118339i
$813$		−	569789.i		−	0.862052i
$814$	63786.3			0.0962672
$815$	−457360.			−0.688562
$816$		−	113162.i		−	0.169950i
$817$	4421.79	−	113958.i	0.00662451	−	0.170727i
$818$	−849436.			−1.26948
$819$		−	90988.1i		−	0.135649i
$820$			500723.i			0.744681i
$821$	−833823.			−1.23705			−0.618526	−	0.785764i	$-0.712270\pi$
$821$	−833823.			−1.23705			−0.618526	+	0.785764i	$0.712270\pi$
$822$	795058.			1.17667
$823$	903550.			1.33399			0.666995	−	0.745063i	$-0.267580\pi$
$823$	903550.			1.33399			0.666995	+	0.745063i	$0.267580\pi$
$824$	72962.9			0.107460
$825$			791427.i			1.16279i
$826$	25794.7			0.0378069
$827$			273012.i			0.399182i	0.979879	+	0.199591i	$0.0639613\pi$
$827$			273012.i			0.399182i	−0.979879	+	0.199591i	$0.936039\pi$
$828$	−66680.4			−0.0972607
$829$			29206.8i			0.0424986i	0.999774	+	0.0212493i	$0.00676438\pi$
$829$			29206.8i			0.0424986i	−0.999774	+	0.0212493i	$0.993236\pi$
$830$		−	991304.i		−	1.43897i
$831$		−	517232.i		−	0.749002i
$832$			144127.i			0.208208i
$833$	−485450.			−0.699607
$834$	228925.			0.329126
$835$			339826.i			0.487397i
$836$	24141.0	−	622161.i	0.0345416	−	0.890205i
$837$	−377646.			−0.539056
$838$			251492.i			0.358126i
$839$		−	563481.i		−	0.800488i	−0.916409	−	0.400244i	$-0.868925\pi$
$839$		−	563481.i		−	0.800488i	0.916409	−	0.400244i	$-0.131075\pi$
$840$	−93964.0			−0.133169
$841$	339303.			0.479729
$842$	−149680.			−0.211125
$843$	880720.			1.23932
$844$		−	288293.i		−	0.404714i
$845$	1.67735e6			2.34915
$846$			26970.7i			0.0376835i
$847$	511915.			0.713561
$848$		−	49560.4i		−	0.0689197i
$849$		−	630272.i		−	0.874405i
$850$		−	301476.i		−	0.417268i
$851$		−	43369.9i		−	0.0598866i
$852$	476729.			0.656739
$853$	−852435.			−1.17156			−0.585778	−	0.810472i	$-0.699211\pi$
$853$	−852435.			−1.17156			−0.585778	+	0.810472i	$0.699211\pi$
$854$		−	218264.i		−	0.299273i
$855$	−9313.04	+	240016.i	−0.0127397	+	0.328328i
$856$	175157.			0.239045
$857$			103865.i			0.141419i	0.997497	+	0.0707097i	$0.0225264\pi$
$857$			103865.i			0.141419i	−0.997497	+	0.0707097i	$0.977474\pi$
$858$		−	1.33952e6i		−	1.81959i
$859$	−74101.6			−0.100425			−0.0502125	−	0.998739i	$-0.515990\pi$
$859$	−74101.6			−0.100425			−0.0502125	+	0.998739i	$0.515990\pi$
$860$	83646.0			0.113096
$861$	237277.			0.320073
$862$	51093.2			0.0687621
$863$			434232.i			0.583042i	0.956564	+	0.291521i	$0.0941613\pi$
$863$			434232.i			0.583042i	−0.956564	+	0.291521i	$0.905839\pi$
$864$	−142819.			−0.191320
$865$			959870.i			1.28286i
$866$	534500.			0.712709
$867$			251132.i			0.334091i
$868$			61567.7i			0.0817172i
$869$			2.09269e6i			2.77118i
$870$			443141.i			0.585468i
$871$	1.25661e6			1.65639
$872$	−285401.			−0.375338
$873$			311146.i			0.408259i
$874$	−423023.	−	16414.1i	−0.553785	−	0.0214879i
$875$	82261.1			0.107443
$876$			524194.i			0.683100i
$877$			493156.i			0.641188i	0.947217	+	0.320594i	$0.103883\pi$
$877$			493156.i			0.641188i	−0.947217	+	0.320594i	$0.896117\pi$
$878$	705437.			0.915101
$879$	−1.04308e6			−1.35002
$880$	456669.			0.589707
$881$	−699253.			−0.900913			−0.450456	−	0.892798i	$-0.648739\pi$
$881$	−699253.			−0.900913			−0.450456	+	0.892798i	$0.648739\pi$
$882$			121824.i			0.156601i
$883$	657183.			0.842878			0.421439	−	0.906857i	$-0.361525\pi$
$883$	657183.			0.842878			0.421439	+	0.906857i	$0.361525\pi$
$884$			510259.i			0.652959i
$885$	−146498.			−0.187044
$886$		−	121764.i		−	0.155114i
$887$		−	123664.i		−	0.157179i	−0.996907	−	0.0785895i	$-0.974958\pi$
$887$		−	123664.i		−	0.157179i	0.996907	−	0.0785895i	$-0.0250416\pi$
$888$		−	18470.6i		−	0.0234237i
$889$		−	268317.i		−	0.339504i
$890$	962502.			1.21513
$891$	976303.			1.22978
$892$		−	352796.i		−	0.443398i
$893$	−6639.12	+	171103.i	−0.00832545	+	0.214563i
$894$	−29869.8			−0.0373729
$895$		−	843298.i		−	1.05277i
$896$			23283.9i			0.0290028i
$897$	−910772.			−1.13194
$898$	54373.1			0.0674266
$899$	290358.			0.359264
$900$	−75655.7			−0.0934021
$901$		−	175461.i		−	0.216138i
$902$	−1.15318e6			−1.41737
$903$		−	39637.2i		−	0.0486102i
$904$	20384.5			0.0249438
$905$		−	1.03124e6i		−	1.25911i
$906$			643017.i			0.783368i
$907$			30174.9i			0.0366801i	0.999832	+	0.0183401i	$0.00583815\pi$
$907$			30174.9i			0.0366801i	−0.999832	+	0.0183401i	$0.994162\pi$
$908$		−	278932.i		−	0.338319i
$909$	210371.			0.254600
$910$	423691.			0.511643
$911$		−	198609.i		−	0.239311i	−0.992815	−	0.119655i	$-0.961821\pi$
$911$		−	198609.i		−	0.239311i	0.992815	−	0.119655i	$-0.0381790\pi$
$912$	−180159.	−	6990.51i	−0.216604	−	0.00840464i
$913$	2.28299e6			2.73882
$914$		−	108851.i		−	0.130299i
$915$			1.23960e6i			1.48061i
$916$	−208684.			−0.248712
$917$	150577.			0.179069
$918$	−505630.			−0.599995
$919$	−1.20577e6			−1.42769			−0.713845	−	0.700304i	$-0.753048\pi$
$919$	−1.20577e6			−1.42769			−0.713845	+	0.700304i	$0.753048\pi$
$920$		−	310501.i		−	0.366849i
$921$	787052.			0.927863
$922$			576830.i			0.678556i
$923$	−2.14961e6			−2.52323
$924$		−	216401.i		−	0.253464i
$925$		−	49207.6i		−	0.0575107i
$926$			574737.i			0.670267i
$927$		−	64824.1i		−	0.0754357i
$928$	109808.			0.127509
$929$	1.04643e6			1.21249			0.606246	−	0.795277i	$-0.292675\pi$
$929$	1.04643e6			1.21249			0.606246	+	0.795277i	$0.292675\pi$
$930$		−	349666.i		−	0.404285i
$931$	−29988.2	+	772856.i	−0.0345980	+	0.891660i
$932$	−603735.			−0.695047
$933$		−	948380.i		−	1.08948i
$934$			344147.i			0.394503i
$935$	1.61677e6			1.84937
$936$	128050.			0.146160
$937$	251416.			0.286361			0.143181	−	0.989697i	$-0.454267\pi$
$937$	251416.			0.286361			0.143181	+	0.989697i	$0.454267\pi$
$938$	203007.			0.230731
$939$		−	1.48216e6i		−	1.68098i
$940$	−125591.			−0.142135
$941$		−	1.26323e6i		−	1.42660i	−0.700858	−	0.713301i	$-0.747199\pi$
$941$		−	1.26323e6i		−	1.42660i	0.700858	−	0.713301i	$-0.252801\pi$
$942$	263406.			0.296841
$943$			784074.i			0.881726i
$944$			36301.6i			0.0407363i
$945$			419848.i			0.470142i
$946$			192638.i			0.215259i
$947$	−1.04458e6			−1.16477			−0.582386	−	0.812913i	$-0.697881\pi$
$947$	−1.04458e6			−1.16477			−0.582386	+	0.812913i	$0.697881\pi$
$948$	605980.			0.674282
$949$		−	2.36363e6i		−	2.62451i
$950$	−479963.	−	18623.4i	−0.531815	−	0.0206354i
$951$	525466.			0.581010
$952$			82433.1i			0.0909552i
$953$		−	928965.i		−	1.02285i	−0.859327	−	0.511427i	$-0.829117\pi$
$953$		−	928965.i		−	1.02285i	0.859327	−	0.511427i	$-0.170883\pi$
$954$	−44032.1			−0.0483808
$955$	−592066.			−0.649178
$956$	343135.			0.375447
$957$	−1.02056e6			−1.11434
$958$			588417.i			0.641141i
$959$	−579159.			−0.629739
$960$		−	132238.i		−	0.143487i
$961$	694411.			0.751916
$962$			83285.5i			0.0899952i
$963$		−	155619.i		−	0.167807i
$964$		−	125034.i		−	0.134547i
$965$		−	25954.5i		−	0.0278714i
$966$	−147137.			−0.157676
$967$	−72252.5			−0.0772680			−0.0386340	−	0.999253i	$-0.512301\pi$
$967$	−72252.5			−0.0772680			−0.0386340	+	0.999253i	$0.512301\pi$
$968$			720431.i			0.768850i
$969$	−637827.	−	24748.8i	−0.679290	−	0.0263577i
$970$	−1.44887e6			−1.53988
$971$		−	217697.i		−	0.230895i	−0.993314	−	0.115447i	$-0.963170\pi$
$971$		−	217697.i		−	0.230895i	0.993314	−	0.115447i	$-0.0368302\pi$
$972$			228546.i			0.241903i
$973$	−166761.			−0.176144
$974$	−134117.			−0.141373
$975$	−1.03336e6			−1.08704
$976$	307169.			0.322461
$977$		−	1.19511e6i		−	1.25204i	−0.779805	−	0.626022i	$-0.784682\pi$
$977$		−	1.19511e6i		−	1.25204i	0.779805	−	0.626022i	$-0.215318\pi$
$978$	−305007.			−0.318884
$979$			2.21666e6i			2.31278i
$980$	−567281.			−0.590671
$981$			253566.i			0.263483i
$982$			618926.i			0.641824i
$983$			743610.i			0.769552i	0.923010	+	0.384776i	$0.125721\pi$
$983$			743610.i			0.769552i	−0.923010	+	0.384776i	$0.874279\pi$
$984$			333926.i			0.344873i
$985$	−1.39909e6			−1.44203
$986$	388760.			0.399878
$987$			59513.5i			0.0610915i
$988$	812353.	+	31520.8i	0.832206	+	0.0322911i
$989$	130980.			0.133910
$990$		−	405729.i		−	0.413967i
$991$			213907.i			0.217810i	0.994052	+	0.108905i	$0.0347345\pi$
$991$			213907.i			0.217810i	−0.994052	+	0.108905i	$0.965266\pi$
$992$	−86645.8			−0.0880489
$993$	−1.20418e6			−1.22121
$994$	−347273.			−0.351478
$995$	508426.			0.513549
$996$		−	661088.i		−	0.666408i
$997$	563076.			0.566470			0.283235	−	0.959051i	$-0.408592\pi$
$997$	563076.			0.566470			0.283235	+	0.959051i	$0.408592\pi$
$998$		−	416381.i		−	0.418052i
$999$	−82530.1			−0.0826954

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	38.5.b.a.37.2	✓	8
3.2	odd	2		342.5.d.a.37.8		8
4.3	odd	2		304.5.e.e.113.6		8
19.18	odd	2	inner	38.5.b.a.37.7	yes	8
57.56	even	2		342.5.d.a.37.4		8
76.75	even	2		304.5.e.e.113.3		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
38.5.b.a.37.2	✓	8	1.1	even	1	trivial
38.5.b.a.37.7	yes	8	19.18	odd	2	inner
304.5.e.e.113.3		8	76.75	even	2
304.5.e.e.113.6		8	4.3	odd	2
342.5.d.a.37.4		8	57.56	even	2
342.5.d.a.37.8		8	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 38 = 2 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	38.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-2.82843i q^{2} -7.80363i q^{3} -8.00000 q^{4} -33.0971 q^{5} -22.0720 q^{6} +16.0783 q^{7} +22.6274i q^{8} +20.1034 q^{9} +O(q^{10})\)	\(q-2.82843i q^{2} -7.80363i q^{3} -8.00000 q^{4} -33.0971 q^{5} -22.0720 q^{6} +16.0783 q^{7} +22.6274i q^{8} +20.1034 q^{9} +93.6127i q^{10} -215.592 q^{11} +62.4290i q^{12} -281.497i q^{13} -45.4764i q^{14} +258.277i q^{15} +64.0000 q^{16} +226.582 q^{17} -56.8610i q^{18} +(13.9969 - 360.729i) q^{19} +264.777 q^{20} -125.469i q^{21} +609.786i q^{22} +414.609 q^{23} +176.576 q^{24} +470.416 q^{25} -796.195 q^{26} -788.973i q^{27} -128.627 q^{28} +606.612i q^{29} +730.518 q^{30} -478.655i q^{31} -181.019i q^{32} +1682.40i q^{33} -640.871i q^{34} -532.145 q^{35} -160.827 q^{36} -104.604i q^{37} +(-1020.29 - 39.5893i) q^{38} -2196.70 q^{39} -748.901i q^{40} +1891.12i q^{41} -354.881 q^{42} +315.912 q^{43} +1724.73 q^{44} -665.364 q^{45} -1172.69i q^{46} -474.327 q^{47} -499.432i q^{48} -2142.49 q^{49} -1330.54i q^{50} -1768.16i q^{51} +2251.98i q^{52} -774.381i q^{53} -2231.55 q^{54} +7135.46 q^{55} +363.811i q^{56} +(-2814.99 - 109.227i) q^{57} +1715.76 q^{58} +567.212i q^{59} -2066.22i q^{60} +4799.51 q^{61} -1353.84 q^{62} +323.229 q^{63} -512.000 q^{64} +9316.74i q^{65} +4758.54 q^{66} +4464.01i q^{67} -1812.66 q^{68} -3235.45i q^{69} +1505.13i q^{70} -7636.34i q^{71} +454.888i q^{72} +8396.65 q^{73} -295.866 q^{74} -3670.95i q^{75} +(-111.975 + 2885.83i) q^{76} -3466.35 q^{77} +6213.21i q^{78} -9706.71i q^{79} -2118.21 q^{80} -4528.48 q^{81} +5348.89 q^{82} -10589.4 q^{83} +1003.75i q^{84} -7499.21 q^{85} -893.533i q^{86} +4733.77 q^{87} -4878.29i q^{88} -10281.7i q^{89} +1881.93i q^{90} -4526.01i q^{91} -3316.87 q^{92} -3735.24 q^{93} +1341.60i q^{94} +(-463.257 + 11939.1i) q^{95} -1412.61 q^{96} +15477.3i q^{97} +6059.87i q^{98} -4334.13 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 64 q^{4} + 18 q^{5} - 32 q^{6} - 162 q^{7} - 268 q^{9}+O(q^{10}) \) 8 * q - 64 * q^4 + 18 * q^5 - 32 * q^6 - 162 * q^7 - 268 * q^9	\( 8 q - 64 q^{4} + 18 q^{5} - 32 q^{6} - 162 q^{7} - 268 q^{9} - 6 q^{11} + 512 q^{16} + 510 q^{17} - 12 q^{19} - 144 q^{20} - 396 q^{23} + 256 q^{24} + 3458 q^{25} - 192 q^{26} + 1296 q^{28} - 2752 q^{30} + 1002 q^{35} + 2144 q^{36} - 3216 q^{38} - 6588 q^{39} + 1376 q^{42} - 8654 q^{43} + 48 q^{44} - 10334 q^{45} + 3210 q^{47} + 9222 q^{49} + 9088 q^{54} + 17146 q^{55} - 14076 q^{57} - 960 q^{58} + 1314 q^{61} - 15168 q^{62} + 29938 q^{63} - 4096 q^{64} + 4928 q^{66} - 4080 q^{68} + 23398 q^{73} + 13152 q^{74} + 96 q^{76} - 44622 q^{77} + 1152 q^{80} - 20368 q^{81} + 16512 q^{82} - 10440 q^{83} + 21274 q^{85} - 14316 q^{87} + 3168 q^{92} + 19416 q^{93} - 34686 q^{95} - 2048 q^{96} - 56798 q^{99}+O(q^{100}) \) 8 * q - 64 * q^4 + 18 * q^5 - 32 * q^6 - 162 * q^7 - 268 * q^9 - 6 * q^11 + 512 * q^16 + 510 * q^17 - 12 * q^19 - 144 * q^20 - 396 * q^23 + 256 * q^24 + 3458 * q^25 - 192 * q^26 + 1296 * q^28 - 2752 * q^30 + 1002 * q^35 + 2144 * q^36 - 3216 * q^38 - 6588 * q^39 + 1376 * q^42 - 8654 * q^43 + 48 * q^44 - 10334 * q^45 + 3210 * q^47 + 9222 * q^49 + 9088 * q^54 + 17146 * q^55 - 14076 * q^57 - 960 * q^58 + 1314 * q^61 - 15168 * q^62 + 29938 * q^63 - 4096 * q^64 + 4928 * q^66 - 4080 * q^68 + 23398 * q^73 + 13152 * q^74 + 96 * q^76 - 44622 * q^77 + 1152 * q^80 - 20368 * q^81 + 16512 * q^82 - 10440 * q^83 + 21274 * q^85 - 14316 * q^87 + 3168 * q^92 + 19416 * q^93 - 34686 * q^95 - 2048 * q^96 - 56798 * q^99

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