LMFDB - Embedded newform 38.5.b.a.37.1

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			37.1
Root			$-13.9305i$ of defining polynomial
Character	$\chi$	$=$	38.37
Dual form			38.5.b.a.37.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.82843i q^{2} -15.3447i q^{3} -8.00000 q^{4} +41.6240 q^{5} -43.4013 q^{6} -62.4342 q^{7} +22.6274i q^{8} -154.460 q^{9} +O(q^{10})$	\(q-2.82843i q^{2} -15.3447i q^{3} -8.00000 q^{4} +41.6240 q^{5} -43.4013 q^{6} -62.4342 q^{7} +22.6274i q^{8} -154.460 q^{9} -117.730i q^{10} +122.938 q^{11} +122.758i q^{12} +68.9610i q^{13} +176.591i q^{14} -638.707i q^{15} +64.0000 q^{16} +297.375 q^{17} +436.878i q^{18} +(-195.642 - 303.390i) q^{19} -332.992 q^{20} +958.034i q^{21} -347.721i q^{22} +268.685 q^{23} +347.211 q^{24} +1107.56 q^{25} +195.051 q^{26} +1127.21i q^{27} +499.474 q^{28} -561.405i q^{29} -1806.54 q^{30} -252.423i q^{31} -181.019i q^{32} -1886.44i q^{33} -841.104i q^{34} -2598.76 q^{35} +1235.68 q^{36} +2407.33i q^{37} +(-858.116 + 553.358i) q^{38} +1058.18 q^{39} +941.843i q^{40} -690.246i q^{41} +2709.73 q^{42} +218.905 q^{43} -983.502 q^{44} -6429.22 q^{45} -759.956i q^{46} -83.1049 q^{47} -982.060i q^{48} +1497.03 q^{49} -3132.64i q^{50} -4563.13i q^{51} -551.688i q^{52} +4389.68i q^{53} +3188.24 q^{54} +5117.16 q^{55} -1412.73i q^{56} +(-4655.42 + 3002.06i) q^{57} -1587.89 q^{58} -476.981i q^{59} +5109.66i q^{60} +3965.09 q^{61} -713.960 q^{62} +9643.57 q^{63} -512.000 q^{64} +2870.43i q^{65} -5335.66 q^{66} +5111.96i q^{67} -2379.00 q^{68} -4122.89i q^{69} +7350.41i q^{70} +8182.93i q^{71} -3495.02i q^{72} -7345.23 q^{73} +6808.95 q^{74} -16995.1i q^{75} +(1565.13 + 2427.12i) q^{76} -7675.53 q^{77} -2993.00i q^{78} -1485.61i q^{79} +2663.94 q^{80} +4785.54 q^{81} -1952.31 q^{82} +5347.30 q^{83} -7664.27i q^{84} +12377.9 q^{85} -619.156i q^{86} -8614.59 q^{87} +2781.76i q^{88} -11172.3i q^{89} +18184.6i q^{90} -4305.53i q^{91} -2149.48 q^{92} -3873.35 q^{93} +235.056i q^{94} +(-8143.39 - 12628.3i) q^{95} -2777.69 q^{96} +1078.13i q^{97} -4234.25i q^{98} -18988.9 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$		−	15.3447i		−	1.70497i	−0.522755	−	0.852483i	$-0.675096\pi$
$3$		−	15.3447i		−	1.70497i	0.522755	−	0.852483i	$-0.324904\pi$
$4$	−8.00000			−0.500000
$5$	41.6240			1.66496			0.832480	−	0.554055i	$-0.186920\pi$
$5$	41.6240			1.66496			0.832480	+	0.554055i	$0.186920\pi$
$6$	−43.4013			−1.20559
$7$	−62.4342			−1.27417			−0.637084	−	0.770794i	$-0.719860\pi$
$7$	−62.4342			−1.27417			−0.637084	+	0.770794i	$0.719860\pi$
$8$			22.6274i			0.353553i
$9$	−154.460			−1.90691
$10$		−	117.730i		−	1.17730i
$11$	122.938			1.01601			0.508007	−	0.861353i	$-0.330382\pi$
$11$	122.938			1.01601			0.508007	+	0.861353i	$0.330382\pi$
$12$			122.758i			0.852483i
$13$			68.9610i			0.408053i	0.978965	+	0.204027i	$0.0654029\pi$
$13$			68.9610i			0.408053i	−0.978965	+	0.204027i	$0.934597\pi$
$14$			176.591i			0.900973i
$15$		−	638.707i		−	2.83870i
$16$	64.0000			0.250000
$17$	297.375			1.02898			0.514490	−	0.857496i	$-0.327981\pi$
$17$	297.375			1.02898			0.514490	+	0.857496i	$0.327981\pi$
$18$			436.878i			1.34839i
$19$	−195.642	−	303.390i	−0.541944	−	0.840415i
$19$	−195.642	−	303.390i	−0.541944	−	0.840415i
$20$	−332.992			−0.832480
$21$			958.034i			2.17241i
$22$		−	347.721i		−	0.718431i
$23$	268.685			0.507911			0.253956	−	0.967216i	$-0.418268\pi$
$23$	268.685			0.507911			0.253956	+	0.967216i	$0.418268\pi$
$24$	347.211			0.602796
$25$	1107.56			1.77209
$26$	195.051			0.288537
$27$			1127.21i			1.54625i
$28$	499.474			0.637084
$29$		−	561.405i		−	0.667545i	−0.942654	−	0.333772i	$-0.891678\pi$
$29$		−	561.405i		−	0.667545i	0.942654	−	0.333772i	$-0.108322\pi$
$30$	−1806.54			−2.00726
$31$		−	252.423i		−	0.262667i	−0.991338	−	0.131333i	$-0.958074\pi$
$31$		−	252.423i		−	0.262667i	0.991338	−	0.131333i	$-0.0419259\pi$
$32$		−	181.019i		−	0.176777i
$33$		−	1886.44i		−	1.73227i
$34$		−	841.104i		−	0.727599i
$35$	−2598.76			−2.12144
$36$	1235.68			0.953454
$37$			2407.33i			1.75846i	0.476400	+	0.879228i	$0.341941\pi$
$37$			2407.33i			1.75846i	−0.476400	+	0.879228i	$0.658059\pi$
$38$	−858.116	+	553.358i	−0.594263	+	0.383212i
$39$	1058.18			0.695717
$40$			941.843i			0.588652i
$41$		−	690.246i		−	0.410616i	−0.978697	−	0.205308i	$-0.934180\pi$
$41$		−	690.246i		−	0.410616i	0.978697	−	0.205308i	$-0.0658197\pi$
$42$	2709.73			1.53613
$43$	218.905			0.118391			0.0591954	−	0.998246i	$-0.481146\pi$
$43$	218.905			0.118391			0.0591954	+	0.998246i	$0.481146\pi$
$44$	−983.502			−0.508007
$45$	−6429.22			−3.17493
$46$		−	759.956i		−	0.359148i
$47$	−83.1049			−0.0376211			−0.0188105	−	0.999823i	$-0.505988\pi$
$47$	−83.1049			−0.0376211			−0.0188105	+	0.999823i	$0.505988\pi$
$48$		−	982.060i		−	0.426241i
$49$	1497.03			0.623505
$50$		−	3132.64i		−	1.25306i
$51$		−	4563.13i		−	1.75438i
$52$		−	551.688i		−	0.204027i
$53$			4389.68i			1.56272i	0.624080	+	0.781360i	$0.285474\pi$
$53$			4389.68i			1.56272i	−0.624080	+	0.781360i	$0.714526\pi$
$54$	3188.24			1.09336
$55$	5117.16			1.69162
$56$		−	1412.73i		−	0.450486i
$57$	−4655.42	+	3002.06i	−1.43288	+	0.923996i
$58$	−1587.89			−0.472025
$59$		−	476.981i		−	0.137024i	−0.997650	−	0.0685120i	$-0.978175\pi$
$59$		−	476.981i		−	0.137024i	0.997650	−	0.0685120i	$-0.0218252\pi$
$60$			5109.66i			1.41935i
$61$	3965.09			1.06560			0.532799	−	0.846242i	$-0.321140\pi$
$61$	3965.09			1.06560			0.532799	+	0.846242i	$0.321140\pi$
$62$	−713.960			−0.185734
$63$	9643.57			2.42972
$64$	−512.000			−0.125000
$65$			2870.43i			0.679392i
$66$	−5335.66			−1.22490
$67$			5111.96i			1.13878i	0.822069	+	0.569388i	$0.192820\pi$
$67$			5111.96i			1.13878i	−0.822069	+	0.569388i	$0.807180\pi$
$68$	−2379.00			−0.514490
$69$		−	4122.89i		−	0.865972i
$70$			7350.41i			1.50008i
$71$			8182.93i			1.62327i	0.584161	+	0.811637i	$0.301423\pi$
$71$			8182.93i			1.62327i	−0.584161	+	0.811637i	$0.698577\pi$
$72$		−	3495.02i		−	0.674194i
$73$	−7345.23			−1.37835			−0.689175	−	0.724595i	$-0.742027\pi$
$73$	−7345.23			−1.37835			−0.689175	+	0.724595i	$0.742027\pi$
$74$	6808.95			1.24342
$75$		−	16995.1i		−	3.02135i
$76$	1565.13	+	2427.12i	0.270972	+	0.420207i
$77$	−7675.53			−1.29457
$78$		−	2993.00i		−	0.491946i
$79$		−	1485.61i		−	0.238041i	−0.992892	−	0.119021i	$-0.962025\pi$
$79$		−	1485.61i		−	0.238041i	0.992892	−	0.119021i	$-0.0379754\pi$
$80$	2663.94			0.416240
$81$	4785.54			0.729391
$82$	−1952.31			−0.290350
$83$	5347.30			0.776209			0.388104	−	0.921615i	$-0.373130\pi$
$83$	5347.30			0.776209			0.388104	+	0.921615i	$0.373130\pi$
$84$		−	7664.27i		−	1.08621i
$85$	12377.9			1.71321
$86$		−	619.156i		−	0.0837150i
$87$	−8614.59			−1.13814
$88$			2781.76i			0.359215i
$89$		−	11172.3i		−	1.41047i	−0.708975	−	0.705234i	$-0.750842\pi$
$89$		−	11172.3i		−	1.41047i	0.708975	−	0.705234i	$-0.249158\pi$
$90$			18184.6i			2.24501i
$91$		−	4305.53i		−	0.519928i
$92$	−2149.48			−0.253956
$93$	−3873.35			−0.447838
$94$			235.056i			0.0266021i
$95$	−8143.39	−	12628.3i	−0.902315	−	1.39926i
$96$	−2777.69			−0.301398
$97$			1078.13i			0.114585i	0.998357	+	0.0572927i	$0.0182468\pi$
$97$			1078.13i			0.114585i	−0.998357	+	0.0572927i	$0.981753\pi$
$98$		−	4234.25i		−	0.440884i
$99$	−18988.9			−1.93745
$100$	−8860.45			−0.886045
$101$	1393.71			0.136625			0.0683126	−	0.997664i	$-0.478238\pi$
$101$	1393.71			0.136625			0.0683126	+	0.997664i	$0.478238\pi$
$102$	−12906.5			−1.24053
$103$			11163.2i			1.05224i	0.850411	+	0.526119i	$0.176353\pi$
$103$			11163.2i			1.05224i	−0.850411	+	0.526119i	$0.823647\pi$
$104$	−1560.41			−0.144269
$105$			39877.2i			3.61698i
$106$	12415.9			1.10501
$107$			502.078i			0.0438534i	0.999760	+	0.0219267i	$0.00698005\pi$
$107$			502.078i			0.0438534i	−0.999760	+	0.0219267i	$0.993020\pi$
$108$		−	9017.72i		−	0.773124i
$109$		−	11387.7i		−	0.958477i	−0.877685	−	0.479238i	$-0.840913\pi$
$109$		−	11387.7i		−	0.958477i	0.877685	−	0.479238i	$-0.159087\pi$
$110$		−	14473.5i		−	1.19616i
$111$	36939.7			2.99811
$112$	−3995.79			−0.318542
$113$			4779.02i			0.374267i	0.982334	+	0.187133i	$0.0599197\pi$
$113$			4779.02i			0.374267i	−0.982334	+	0.187133i	$0.940080\pi$
$114$	8491.12	+	13167.5i	0.653364	+	1.01320i
$115$	11183.7			0.845652
$116$			4491.24i			0.333772i
$117$		−	10651.7i		−	0.778120i
$118$	−1349.11			−0.0968906
$119$	−18566.4			−1.31109
$120$	14452.3			1.00363
$121$	472.695			0.0322857
$122$		−	11215.0i		−	0.753491i
$123$	−10591.6			−0.700087
$124$			2019.38i			0.131333i
$125$	20085.9			1.28550
$126$		−	27276.1i		−	1.71807i
$127$		−	17552.6i		−	1.08826i	−0.839001	−	0.544130i	$-0.816860\pi$
$127$		−	17552.6i		−	1.08826i	0.839001	−	0.544130i	$-0.183140\pi$
$128$			1448.15i			0.0883883i
$129$		−	3359.02i		−	0.201852i
$130$	8118.80			0.480403
$131$	−7401.84			−0.431317			−0.215659	−	0.976469i	$-0.569190\pi$
$131$	−7401.84			−0.431317			−0.215659	+	0.976469i	$0.569190\pi$
$132$			15091.5i			0.866135i
$133$	12214.7	+	18941.9i	0.690528	+	1.07083i
$134$	14458.8			0.805236
$135$			46919.2i			2.57444i
$136$			6728.83i			0.363799i
$137$	1692.77			0.0901896			0.0450948	−	0.998983i	$-0.485641\pi$
$137$	1692.77			0.0901896			0.0450948	+	0.998983i	$0.485641\pi$
$138$	−11661.3			−0.612334
$139$	−37366.7			−1.93399			−0.966996	−	0.254791i	$-0.917993\pi$
$139$	−37366.7			−1.93399			−0.966996	+	0.254791i	$0.917993\pi$
$140$	20790.1			1.06072
$141$			1275.22i			0.0641426i
$142$	23144.8			1.14783
$143$			8477.91i			0.414588i
$144$	−9885.41			−0.476727
$145$		−	23367.9i		−	1.11143i
$146$			20775.4i			0.974641i
$147$		−	22971.5i		−	1.06305i
$148$		−	19258.6i		−	0.879228i
$149$	−6037.22			−0.271935			−0.135967	−	0.990713i	$-0.543414\pi$
$149$	−6037.22			−0.271935			−0.135967	+	0.990713i	$0.543414\pi$
$150$	−48069.4			−2.13642
$151$			20619.1i			0.904307i	0.891940	+	0.452153i	$0.149344\pi$
$151$			20619.1i			0.904307i	−0.891940	+	0.452153i	$0.850656\pi$
$152$	6864.92	−	4426.87i	0.297131	−	0.191606i
$153$	−45932.4			−1.96217
$154$			21709.7i			0.915402i
$155$		−	10506.8i		−	0.437330i
$156$	−8465.48			−0.347858
$157$	−1043.55			−0.0423362			−0.0211681	−	0.999776i	$-0.506739\pi$
$157$	−1043.55			−0.0423362			−0.0211681	+	0.999776i	$0.506739\pi$
$158$	−4201.95			−0.168321
$159$	67358.3			2.66439
$160$		−	7534.75i		−	0.294326i
$161$	−16775.2			−0.647165
$162$		−	13535.5i		−	0.515757i
$163$	1587.92			0.0597658			0.0298829	−	0.999553i	$-0.490487\pi$
$163$	1587.92			0.0597658			0.0298829	+	0.999553i	$0.490487\pi$
$164$			5521.97i			0.205308i
$165$		−	78521.3i		−	2.88416i
$166$		−	15124.5i		−	0.548862i
$167$		−	21277.9i		−	0.762948i	−0.924380	−	0.381474i	$-0.875417\pi$
$167$		−	21277.9i		−	0.762948i	0.924380	−	0.381474i	$-0.124583\pi$
$168$	−21677.8			−0.768064
$169$	23805.4			0.833493
$170$		−	35010.1i		−	1.21142i
$171$	30218.7	+	46861.4i	1.03344	+	1.60259i
$172$	−1751.24			−0.0591954
$173$			23629.3i			0.789513i	0.918786	+	0.394756i	$0.129171\pi$
$173$			23629.3i			0.789513i	−0.918786	+	0.394756i	$0.870829\pi$
$174$			24365.7i			0.804787i
$175$	−69149.5			−2.25794
$176$	7868.02			0.254004
$177$	−7319.12			−0.233621
$178$	−31600.1			−0.997351
$179$			54580.1i			1.70345i	0.523993	+	0.851723i	$0.324442\pi$
$179$			54580.1i			1.70345i	−0.523993	+	0.851723i	$0.675558\pi$
$180$	51433.8			1.58746
$181$		−	48461.8i		−	1.47925i	−0.673017	−	0.739627i	$-0.735002\pi$
$181$		−	48461.8i		−	1.47925i	0.673017	−	0.739627i	$-0.264998\pi$
$182$	−12177.9			−0.367645
$183$		−	60843.0i		−	1.81681i
$184$			6079.65i			0.179574i
$185$			100203.i			2.92776i
$186$			10955.5i			0.316669i
$187$	36558.6			1.04546
$188$	664.839			0.0188105
$189$		−	70376.8i		−	1.97018i
$190$	−35718.2	+	23033.0i	−0.989424	+	0.638033i
$191$	10718.8			0.293819			0.146909	−	0.989150i	$-0.453067\pi$
$191$	10718.8			0.293819			0.146909	+	0.989150i	$0.453067\pi$
$192$			7856.48i			0.213121i
$193$		−	25358.2i		−	0.680776i	−0.940285	−	0.340388i	$-0.889442\pi$
$193$		−	25358.2i		−	0.680776i	0.940285	−	0.340388i	$-0.110558\pi$
$194$	3049.42			0.0810241
$195$	44045.9			1.15834
$196$	−11976.3			−0.311752
$197$	−4536.94			−0.116904			−0.0584521	−	0.998290i	$-0.518617\pi$
$197$	−4536.94			−0.116904			−0.0584521	+	0.998290i	$0.518617\pi$
$198$			53708.8i			1.36998i
$199$	−67698.1			−1.70951			−0.854753	−	0.519035i	$-0.826291\pi$
$199$	−67698.1			−1.70951			−0.854753	+	0.519035i	$0.826291\pi$
$200$			25061.1i			0.626529i
$201$	78441.5			1.94157
$202$		−	3942.01i		−	0.0966085i
$203$			35050.9i			0.850564i
$204$			36505.0i			0.877188i
$205$		−	28730.8i		−	0.683660i
$206$	31574.2			0.744044
$207$	−41501.0			−0.968540
$208$			4413.50i			0.102013i
$209$	−24051.8	−	37298.1i	−0.550623	−	0.853874i
$210$	112790.			2.55759
$211$		−	2816.81i		−	0.0632691i	−0.999500	−	0.0316346i	$-0.989929\pi$
$211$		−	2816.81i		−	0.0632691i	0.999500	−	0.0316346i	$-0.0100713\pi$
$212$		−	35117.5i		−	0.781360i
$213$	125565.			2.76763
$214$	1420.09			0.0310090
$215$	9111.68			0.197116
$216$	−25506.0			−0.546681
$217$			15759.8i			0.334682i
$218$	−32209.2			−0.677746
$219$			112710.i			2.35004i
$220$	−40937.3			−0.845812
$221$			20507.3i			0.419878i
$222$		−	104481.i		−	2.11998i
$223$		−	36870.4i		−	0.741426i	−0.928747	−	0.370713i	$-0.879113\pi$
$223$		−	36870.4i		−	0.741426i	0.928747	−	0.370713i	$-0.120887\pi$
$224$			11301.8i			0.225243i
$225$	−171073.			−3.37921
$226$	13517.1			0.264647
$227$		−	56826.9i		−	1.10281i	−0.834236	−	0.551407i	$-0.814091\pi$
$227$		−	56826.9i		−	1.10281i	0.834236	−	0.551407i	$-0.185909\pi$
$228$	37243.4	−	24016.5i	0.716439	−	0.461998i
$229$	7632.64			0.145547			0.0727736	−	0.997348i	$-0.476815\pi$
$229$	7632.64			0.145547			0.0727736	+	0.997348i	$0.476815\pi$
$230$		−	31632.4i		−	0.597966i
$231$			117779.i			2.20720i
$232$	12703.1			0.236013
$233$	91249.2			1.68080			0.840402	−	0.541964i	$-0.182319\pi$
$233$	91249.2			1.68080			0.840402	+	0.541964i	$0.182319\pi$
$234$	−30127.5			−0.550214
$235$	−3459.16			−0.0626375
$236$			3815.85i			0.0685120i
$237$	−22796.3			−0.405852
$238$			52513.7i			0.927083i
$239$	−110161.			−1.92856			−0.964280	−	0.264884i	$-0.914666\pi$
$239$	−110161.			−1.92856			−0.964280	+	0.264884i	$0.914666\pi$
$240$		−	40877.3i		−	0.709675i
$241$			58423.0i			1.00589i	0.864319	+	0.502944i	$0.167750\pi$
$241$			58423.0i			1.00589i	−0.864319	+	0.502944i	$0.832250\pi$
$242$		−	1336.98i		−	0.0228295i
$243$			17871.8i			0.302661i
$244$	−31720.7			−0.532799
$245$	62312.6			1.03811
$246$			29957.6i			0.495036i
$247$	20922.0	−	13491.6i	0.342934	−	0.221142i
$248$	5711.68			0.0928668
$249$		−	82052.7i		−	1.32341i
$250$		−	56811.6i		−	0.908985i
$251$	−17258.3			−0.273936			−0.136968	−	0.990575i	$-0.543736\pi$
$251$	−17258.3			−0.273936			−0.136968	+	0.990575i	$0.543736\pi$
$252$	−77148.5			−1.21486
$253$	33031.5			0.516045
$254$	−49646.1			−0.769517
$255$		−	189936.i		−	2.92096i
$256$	4096.00			0.0625000
$257$			41195.7i			0.623714i	0.950129	+	0.311857i	$0.100951\pi$
$257$			41195.7i			0.623714i	−0.950129	+	0.311857i	$0.899049\pi$
$258$	−9500.75			−0.142731
$259$		−	150300.i		−	2.24057i
$260$		−	22963.4i		−	0.339696i
$261$			86714.4i			1.27295i
$262$			20935.6i			0.304987i
$263$	−41179.7			−0.595349			−0.297675	−	0.954667i	$-0.596211\pi$
$263$	−41179.7			−0.595349			−0.297675	+	0.954667i	$0.596211\pi$
$264$	42685.3			0.612450
$265$			182716.i			2.60187i
$266$	53575.8	−	34548.5i	0.757191	−	0.488277i
$267$	−171436.			−2.40480
$268$		−	40895.7i		−	0.569388i
$269$		−	19858.8i		−	0.274440i	−0.990541	−	0.137220i	$-0.956183\pi$
$269$		−	19858.8i		−	0.274440i	0.990541	−	0.137220i	$-0.0438168\pi$
$270$	132707.			1.82040
$271$	110976.			1.51110			0.755549	−	0.655093i	$-0.227370\pi$
$271$	110976.			1.51110			0.755549	+	0.655093i	$0.227370\pi$
$272$	19032.0			0.257245
$273$	−66067.0			−0.886460
$274$		−	4787.87i		−	0.0637737i
$275$	136161.			1.80047
$276$			32983.1i			0.432986i
$277$	−87534.8			−1.14083			−0.570415	−	0.821357i	$-0.693218\pi$
$277$	−87534.8			−1.14083			−0.570415	+	0.821357i	$0.693218\pi$
$278$			105689.i			1.36754i
$279$			38989.1i			0.500882i
$280$		−	58803.3i		−	0.750042i
$281$		−	133298.i		−	1.68815i	−0.536228	−	0.844073i	$-0.680151\pi$
$281$		−	133298.i		−	1.68815i	0.536228	−	0.844073i	$-0.319849\pi$
$282$	3606.86			0.0453557
$283$	29905.8			0.373407			0.186704	−	0.982416i	$-0.440220\pi$
$283$	29905.8			0.373407			0.186704	+	0.982416i	$0.440220\pi$
$284$		−	65463.4i		−	0.811637i
$285$	−193777.	+	124958.i	−2.38568	+	1.53842i
$286$	23979.1			0.293158
$287$			43095.0i			0.523194i
$288$			27960.2i			0.337097i
$289$	4910.99			0.0587994
$290$	−66094.5			−0.785903
$291$	16543.6			0.195364
$292$	58761.8			0.689175
$293$		−	42625.4i		−	0.496516i	−0.968694	−	0.248258i	$-0.920142\pi$
$293$		−	42625.4i		−	0.496516i	0.968694	−	0.248258i	$-0.0798580\pi$
$294$	−64973.3			−0.751693
$295$		−	19853.8i		−	0.228140i
$296$	−54471.6			−0.621708
$297$			138577.i			1.57101i
$298$			17075.8i			0.192287i
$299$			18528.8i			0.207255i
$300$			135961.i			1.51068i
$301$	−13667.1			−0.150850
$302$	58319.6			0.639441
$303$		−	21386.1i		−	0.232941i
$304$	−12521.1	−	19416.9i	−0.135486	−	0.210104i
$305$	165043.			1.77418
$306$			129917.i			1.38746i
$307$			39047.5i			0.414302i	0.978309	+	0.207151i	$0.0664191\pi$
$307$			39047.5i			0.414302i	−0.978309	+	0.207151i	$0.933581\pi$
$308$	61404.2			0.647287
$309$	171296.			1.79403
$310$	−29717.9			−0.309239
$311$	79232.0			0.819180			0.409590	−	0.912270i	$-0.365672\pi$
$311$	79232.0			0.819180			0.409590	+	0.912270i	$0.365672\pi$
$312$			23944.0i			0.245973i
$313$	−107079.			−1.09298			−0.546492	−	0.837464i	$-0.684037\pi$
$313$	−107079.			−1.09298			−0.546492	+	0.837464i	$0.684037\pi$
$314$			2951.59i			0.0299362i
$315$	401404.			4.04539
$316$			11884.9i			0.119021i
$317$		−	132924.i		−	1.32277i	−0.750046	−	0.661385i	$-0.769969\pi$
$317$		−	132924.i		−	1.32277i	0.750046	−	0.661385i	$-0.230031\pi$
$318$		−	190518.i		−	1.88401i
$319$		−	69017.9i		−	0.678235i
$320$	−21311.5			−0.208120
$321$	7704.23			0.0747686
$322$			47447.3i			0.457614i
$323$	−58179.0	−	90220.6i	−0.557649	−	0.864770i
$324$	−38284.3			−0.364696
$325$			76378.2i			0.723107i
$326$		−	4491.31i		−	0.0422608i
$327$	−174740.			−1.63417
$328$	15618.5			0.145175
$329$	5188.59			0.0479356
$330$	−222092.			−2.03941
$331$		−	44623.1i		−	0.407290i	−0.979045	−	0.203645i	$-0.934721\pi$
$331$		−	44623.1i		−	0.407290i	0.979045	−	0.203645i	$-0.0652788\pi$
$332$	−42778.4			−0.388104
$333$		−	371835.i		−	3.35322i
$334$	−60182.9			−0.539486
$335$			212780.i			1.89602i
$336$			61314.2i			0.543103i
$337$			5142.51i			0.0452810i	0.999744	+	0.0226405i	$0.00720730\pi$
$337$			5142.51i			0.0452810i	−0.999744	+	0.0226405i	$0.992793\pi$
$338$		−	67331.8i		−	0.589368i
$339$	73332.5			0.638112
$340$	−99023.5			−0.856605
$341$		−	31032.3i		−	0.266873i
$342$	132544.	−	85471.5i	1.13320	−	0.730751i
$343$	56438.4			0.479718
$344$			4953.25i			0.0418575i
$345$		−	171611.i		−	1.44181i
$346$	66833.8			0.558270
$347$	−175661.			−1.45887			−0.729436	−	0.684049i	$-0.760218\pi$
$347$	−175661.			−1.45887			−0.729436	+	0.684049i	$0.760218\pi$
$348$	68916.7			0.569070
$349$	137125.			1.12581			0.562906	−	0.826521i	$-0.309683\pi$
$349$	137125.			1.12581			0.562906	+	0.826521i	$0.309683\pi$
$350$			195584.i			1.59661i
$351$	−77733.8			−0.630951
$352$		−	22254.1i		−	0.179608i
$353$	−199391.			−1.60013			−0.800065	−	0.599913i	$-0.795202\pi$
$353$	−199391.			−1.60013			−0.800065	+	0.599913i	$0.795202\pi$
$354$			20701.6i			0.165195i
$355$			340606.i			2.70269i
$356$			89378.5i			0.705234i
$357$			284896.i			2.23537i
$358$	154376.			1.20452
$359$	6307.95			0.0489440			0.0244720	−	0.999701i	$-0.492210\pi$
$359$	6307.95			0.0489440			0.0244720	+	0.999701i	$0.492210\pi$
$360$		−	145477.i		−	1.12251i
$361$	−53769.6	+	118711.i	−0.412594	+	0.910915i
$362$	−137071.			−1.04599
$363$		−	7253.36i		−	0.0550460i
$364$			34444.2i			0.259964i
$365$	−305738.			−2.29490
$366$	−172090.			−1.28468
$367$	52946.3			0.393100			0.196550	−	0.980494i	$-0.437026\pi$
$367$	52946.3			0.393100			0.196550	+	0.980494i	$0.437026\pi$
$368$	17195.8			0.126978
$369$			106615.i			0.783008i
$370$	283416.			2.07024
$371$		−	274067.i		−	1.99117i
$372$	30986.8			0.223919
$373$		−	9312.99i		−	0.0669378i	−0.999440	−	0.0334689i	$-0.989345\pi$
$373$		−	9312.99i		−	0.0669378i	0.999440	−	0.0334689i	$-0.0106555\pi$
$374$		−	103403.i		−	0.739251i
$375$		−	308212.i		−	2.19173i
$376$		−	1880.45i		−	0.0133011i
$377$	38715.0			0.272394
$378$	−199056.			−1.39313
$379$		−	178291.i		−	1.24123i	−0.784117	−	0.620613i	$-0.786884\pi$
$379$		−	178291.i		−	1.24123i	0.784117	−	0.620613i	$-0.213116\pi$
$380$	65147.1	+	101026.i	0.451157	+	0.699628i
$381$	−269339.			−1.85545
$382$		−	30317.3i		−	0.207761i
$383$			27764.8i			0.189276i	0.995512	+	0.0946382i	$0.0301694\pi$
$383$			27764.8i			0.189276i	−0.995512	+	0.0946382i	$0.969831\pi$
$384$	22221.5			0.150699
$385$	−319486.			−2.15541
$386$	−71723.9			−0.481381
$387$	−33811.9			−0.225760
$388$		−	8625.07i		−	0.0572927i
$389$	241135.			1.59353			0.796765	−	0.604289i	$-0.206543\pi$
$389$	241135.			1.59353			0.796765	+	0.604289i	$0.206543\pi$
$390$		−	124581.i		−	0.819070i
$391$	79900.3			0.522631
$392$			33874.0i			0.220442i
$393$			113579.i			0.735381i
$394$			12832.4i			0.0826638i
$395$		−	61837.2i		−	0.396329i
$396$	151911.			0.968723
$397$	234920.			1.49052			0.745261	−	0.666772i	$-0.232325\pi$
$397$	234920.			1.49052			0.745261	+	0.666772i	$0.232325\pi$
$398$			191479.i			1.20880i
$399$	290658.	−	187432.i	1.82573	−	1.17733i
$400$	70883.6			0.443023
$401$		−	311500.i		−	1.93718i	−0.248667	−	0.968589i	$-0.579993\pi$
$401$		−	311500.i		−	1.93718i	0.248667	−	0.968589i	$-0.420007\pi$
$402$		−	221866.i		−	1.37290i
$403$	17407.3			0.107182
$404$	−11149.7			−0.0683126
$405$	199193.			1.21441
$406$	99138.9			0.601440
$407$			295951.i			1.78662i
$408$	103252.			0.620265
$409$			243636.i			1.45645i	0.685338	+	0.728225i	$0.259655\pi$
$409$			243636.i			1.45645i	−0.685338	+	0.728225i	$0.740345\pi$
$410$	−81263.0			−0.483420
$411$		−	25975.0i		−	0.153770i
$412$		−	89305.5i		−	0.526119i
$413$			29779.9i			0.174592i
$414$			117383.i			0.684862i
$415$	222576.			1.29236
$416$	12483.3			0.0721343
$417$			573380.i			3.29739i
$418$	−105495.	+	68028.7i	−0.603780	+	0.389349i
$419$	−193805.			−1.10392			−0.551960	−	0.833871i	$-0.686120\pi$
$419$	−193805.			−1.10392			−0.551960	+	0.833871i	$0.686120\pi$
$420$		−	319018.i		−	1.80849i
$421$			136536.i			0.770339i	0.922846	+	0.385169i	$0.125857\pi$
$421$			136536.i			0.770339i	−0.922846	+	0.385169i	$0.874143\pi$
$422$	−7967.13			−0.0447380
$423$	12836.3			0.0717399
$424$	−99327.2			−0.552505
$425$	329360.			1.82345
$426$		−	355150.i		−	1.95701i
$427$	−247557.			−1.35775
$428$		−	4016.62i		−	0.0219267i
$429$	130091.			0.706858
$430$		−	25771.7i		−	0.139382i
$431$			323841.i			1.74332i	0.490113	+	0.871659i	$0.336956\pi$
$431$			323841.i			1.74332i	−0.490113	+	0.871659i	$0.663044\pi$
$432$			72141.7i			0.386562i
$433$			286129.i			1.52611i	0.646333	+	0.763056i	$0.276302\pi$
$433$			286129.i			1.52611i	−0.646333	+	0.763056i	$0.723698\pi$
$434$	44575.5			0.236656
$435$	−358574.			−1.89496
$436$			91101.3i			0.479238i
$437$	−52566.0	−	81516.3i	−0.275259	−	0.426856i
$438$	318793.			1.66173
$439$		−	26283.3i		−	0.136380i	−0.997672	−	0.0681901i	$-0.978278\pi$
$439$		−	26283.3i		−	0.136380i	0.997672	−	0.0681901i	$-0.0217224\pi$
$440$			115788.i			0.598079i
$441$	−231231.			−1.18897
$442$	58003.3			0.296899
$443$	−317887.			−1.61981			−0.809907	−	0.586558i	$-0.800482\pi$
$443$	−317887.			−1.61981			−0.809907	+	0.586558i	$0.800482\pi$
$444$	−295518.			−1.49905
$445$		−	465036.i		−	2.34837i
$446$	−104285.			−0.524267
$447$			92639.3i			0.463639i
$448$	31966.3			0.159271
$449$		−	68728.7i		−	0.340915i	−0.985365	−	0.170457i	$-0.945476\pi$
$449$		−	68728.7i		−	0.340915i	0.985365	−	0.170457i	$-0.0545245\pi$
$450$			483867.i			2.38947i
$451$		−	84857.3i		−	0.417192i
$452$		−	38232.1i		−	0.187133i
$453$	316394.			1.54181
$454$	−160731.			−0.779808
$455$		−	179213.i		−	0.865660i
$456$	−67928.9	−	105340.i	−0.326682	−	0.506599i
$457$	182859.			0.875555			0.437778	−	0.899083i	$-0.355766\pi$
$457$	182859.			0.875555			0.437778	+	0.899083i	$0.355766\pi$
$458$		−	21588.4i		−	0.102917i
$459$			335206.i			1.59106i
$460$	−89470.0			−0.422826
$461$	142804.			0.671951			0.335976	−	0.941871i	$-0.390934\pi$
$461$	142804.			0.671951			0.335976	+	0.941871i	$0.390934\pi$
$462$	333128.			1.56073
$463$	96212.9			0.448819			0.224409	−	0.974495i	$-0.427955\pi$
$463$	96212.9			0.448819			0.224409	+	0.974495i	$0.427955\pi$
$464$		−	35929.9i		−	0.166886i
$465$	−161224.			−0.745632
$466$		−	258092.i		−	1.18851i
$467$	287321.			1.31745			0.658724	−	0.752384i	$-0.271096\pi$
$467$	287321.			1.31745			0.658724	+	0.752384i	$0.271096\pi$
$468$			85213.5i			0.389060i
$469$		−	319162.i		−	1.45099i
$470$			9783.98i			0.0442914i
$471$			16012.9i			0.0721818i
$472$	10792.8			0.0484453
$473$	26911.6			0.120287
$474$			64477.7i			0.286981i
$475$	−216684.	−	336021.i	−0.960374	−	1.48929i
$476$	148531.			0.655547
$477$		−	678029.i		−	2.97997i
$478$			311583.i			1.36370i
$479$	101492.			0.442346			0.221173	−	0.975235i	$-0.429011\pi$
$479$	101492.			0.442346			0.221173	+	0.975235i	$0.429011\pi$
$480$	−115618.			−0.501816
$481$	−166012.			−0.717544
$482$	165245.			0.711270
$483$			257410.i			1.10339i
$484$	−3781.56			−0.0161429
$485$			44876.2i			0.190780i
$486$	50549.1			0.214014
$487$			203340.i			0.857363i	0.903456	+	0.428682i	$0.141022\pi$
$487$			203340.i			0.857363i	−0.903456	+	0.428682i	$0.858978\pi$
$488$			89719.7i			0.376745i
$489$		−	24366.1i		−	0.101899i
$490$		−	176247.i		−	0.734055i
$491$	−227758.			−0.944735			−0.472368	−	0.881402i	$-0.656601\pi$
$491$	−227758.			−0.944735			−0.472368	+	0.881402i	$0.656601\pi$
$492$	84732.9			0.350043
$493$		−	166948.i		−	0.686890i
$494$	−38160.1	−	59176.5i	−0.156371	−	0.242491i
$495$	−790394.			−3.22577
$496$		−	16155.1i		−	0.0656667i
$497$		−	510895.i		−	2.06833i
$498$	−232080.			−0.935792
$499$	−132829.			−0.533447			−0.266724	−	0.963773i	$-0.585941\pi$
$499$	−132829.			−0.533447			−0.266724	+	0.963773i	$0.585941\pi$
$500$	−160687.			−0.642750
$501$	−326502.			−1.30080
$502$			48813.8i			0.193702i
$503$	279294.			1.10389			0.551945	−	0.833880i	$-0.313886\pi$
$503$	279294.			1.10389			0.551945	+	0.833880i	$0.313886\pi$
$504$			218209.i			0.859036i
$505$	58011.9			0.227475
$506$		−	93427.3i		−	0.364899i
$507$		−	365286.i		−	1.42108i
$508$			140420.i			0.544130i
$509$			304788.i			1.17642i	0.808709	+	0.588209i	$0.200167\pi$
$509$			304788.i			1.17642i	−0.808709	+	0.588209i	$0.799833\pi$
$510$	−537219.			−2.06543
$511$	458594.			1.75625
$512$		−	11585.2i		−	0.0441942i
$513$	341985.	−	220530.i	1.29949	−	0.837980i
$514$	116519.			0.441032
$515$			464656.i			1.75193i
$516$			26872.2i			0.100926i
$517$	−10216.7			−0.0382235
$518$	−425112.			−1.58432
$519$	362585.			1.34609
$520$	−64950.4			−0.240201
$521$		−	181301.i		−	0.667919i	−0.942587	−	0.333959i	$-0.891615\pi$
$521$		−	181301.i		−	0.667919i	0.942587	−	0.333959i	$-0.108385\pi$
$522$	245265.			0.900109
$523$			5966.86i			0.0218144i	0.999941	+	0.0109072i	$0.00347193\pi$
$523$			5966.86i			0.0218144i	−0.999941	+	0.0109072i	$0.996528\pi$
$524$	59214.7			0.215659
$525$			1.06108e6i			3.84971i
$526$			116474.i			0.420976i
$527$		−	75064.3i		−	0.270279i
$528$		−	120732.i		−	0.433068i
$529$	−207649.			−0.742026
$530$	516799.			1.83980
$531$			73674.2i			0.261292i
$532$	−97718.0	−	151535.i	−0.345264	−	0.535415i
$533$	47600.1			0.167553
$534$			484893.i			1.70045i
$535$			20898.5i			0.0730142i
$536$	−115671.			−0.402618
$537$	837515.			2.90432
$538$	−56169.1			−0.194058
$539$	184042.			0.633490
$540$		−	375353.i		−	1.28722i
$541$	−121383.			−0.414727			−0.207364	−	0.978264i	$-0.566488\pi$
$541$	−121383.			−0.414727			−0.207364	+	0.978264i	$0.566488\pi$
$542$		−	313889.i		−	1.06851i
$543$	−743632.			−2.52208
$544$		−	53830.7i		−	0.181900i
$545$		−	474000.i		−	1.59583i
$546$			186866.i			0.626822i
$547$			297533.i			0.994399i	0.867636	+	0.497200i	$0.165638\pi$
$547$			297533.i			0.994399i	−0.867636	+	0.497200i	$0.834362\pi$
$548$	−13542.2			−0.0450948
$549$	−612446.			−2.03200
$550$		−	385120.i		−	1.27312i
$551$	−170325.	+	109834.i	−0.561014	+	0.361772i
$552$	93290.4			0.306167
$553$			92753.2i			0.303304i
$554$			247586.i			0.806689i
$555$	1.53758e6			4.99173
$556$	298933.			0.966996
$557$	192568.			0.620687			0.310344	−	0.950624i	$-0.399556\pi$
$557$	192568.			0.620687			0.310344	+	0.950624i	$0.399556\pi$
$558$	110278.			0.354177
$559$			15095.9i			0.0483097i
$560$	−166321.			−0.530360
$561$		−	560981.i		−	1.78247i
$562$	−377023.			−1.19370
$563$			21470.7i			0.0677376i	0.999426	+	0.0338688i	$0.0107828\pi$
$563$			21470.7i			0.0677376i	−0.999426	+	0.0338688i	$0.989217\pi$
$564$		−	10201.8i		−	0.0320713i
$565$			198922.i			0.623139i
$566$		−	84586.4i		−	0.264039i
$567$	−298781.			−0.929367
$568$	−185159.			−0.573914
$569$			51249.7i			0.158295i	0.996863	+	0.0791474i	$0.0252198\pi$
$569$			51249.7i			0.158295i	−0.996863	+	0.0791474i	$0.974780\pi$
$570$	353434.	+	548085.i	1.08782	+	1.68693i
$571$	515089.			1.57983			0.789914	−	0.613218i	$-0.210125\pi$
$571$	515089.			1.57983			0.789914	+	0.613218i	$0.210125\pi$
$572$		−	67823.3i		−	0.207294i
$573$		−	164477.i		−	0.500951i
$574$	121891.			0.369954
$575$	297584.			0.900065
$576$	79083.3			0.238364
$577$	−419849.			−1.26108			−0.630538	−	0.776159i	$-0.717166\pi$
$577$	−419849.			−1.26108			−0.630538	+	0.776159i	$0.717166\pi$
$578$		−	13890.4i		−	0.0415775i
$579$	−389114.			−1.16070
$580$			186943.i			0.555717i
$581$	−333855.			−0.989020
$582$		−	46792.5i		−	0.138143i
$583$			539658.i			1.58775i
$584$		−	166204.i		−	0.487320i
$585$		−	443366.i		−	1.29554i
$586$	−120563.			−0.351090
$587$	311469.			0.903939			0.451970	−	0.892033i	$-0.350722\pi$
$587$	311469.			0.903939			0.451970	+	0.892033i	$0.350722\pi$
$588$			183772.i			0.531527i
$589$	−76582.5	+	49384.5i	−0.220749	+	0.142351i
$590$	−56155.1			−0.161319
$591$			69617.9i			0.199318i
$592$			154069.i			0.439614i
$593$	−131604.			−0.374247			−0.187124	−	0.982336i	$-0.559917\pi$
$593$	−131604.			−0.374247			−0.187124	+	0.982336i	$0.559917\pi$
$594$	391956.			1.11087
$595$	−772807.			−2.18292
$596$	48297.8			0.135967
$597$			1.03881e6i			2.91465i
$598$	52407.3			0.146551
$599$			199776.i			0.556788i	0.960467	+	0.278394i	$0.0898021\pi$
$599$			199776.i			0.556788i	−0.960467	+	0.278394i	$0.910198\pi$
$600$	384556.			1.06821
$601$		−	328476.i		−	0.909399i	−0.890645	−	0.454700i	$-0.849747\pi$
$601$		−	328476.i		−	0.909399i	0.890645	−	0.454700i	$-0.150253\pi$
$602$			38656.5i			0.106667i
$603$		−	789592.i		−	2.17154i
$604$		−	164953.i		−	0.452153i
$605$	19675.5			0.0537544
$606$	−60489.0			−0.164714
$607$		−	275312.i		−	0.747219i	−0.927586	−	0.373610i	$-0.878120\pi$
$607$		−	275312.i		−	0.747219i	0.927586	−	0.373610i	$-0.121880\pi$
$608$	−54919.4	+	35414.9i	−0.148566	+	0.0958031i
$609$	537845.			1.45018
$610$		−	466811.i		−	1.25453i
$611$		−	5731.00i		−	0.0153514i
$612$	367460.			0.981085
$613$	−473140.			−1.25912			−0.629562	−	0.776950i	$-0.716766\pi$
$613$	−473140.			−1.25912			−0.629562	+	0.776950i	$0.716766\pi$
$614$	110443.			0.292956
$615$	−440865.			−1.16562
$616$		−	173677.i		−	0.457701i
$617$	10864.2			0.0285382			0.0142691	−	0.999898i	$-0.495458\pi$
$617$	10864.2			0.0285382			0.0142691	+	0.999898i	$0.495458\pi$
$618$		−	484497.i		−	1.26857i
$619$	8963.62			0.0233939			0.0116969	−	0.999932i	$-0.496277\pi$
$619$	8963.62			0.0233939			0.0116969	+	0.999932i	$0.496277\pi$
$620$			84054.8i			0.218665i
$621$			302866.i			0.785357i
$622$		−	224102.i		−	0.579248i
$623$			697535.i			1.79717i
$624$	67723.8			0.173929
$625$	143834.			0.368214
$626$			302864.i			0.772857i
$627$	−572327.	+	369067.i	−1.45583	+	0.938793i
$628$	8348.36			0.0211681
$629$			715879.i			1.80942i
$630$		−	1.13534e6i		−	2.86052i
$631$	−439268.			−1.10324			−0.551621	−	0.834095i	$-0.685991\pi$
$631$	−439268.			−1.10324			−0.551621	+	0.834095i	$0.685991\pi$
$632$	33615.6			0.0841603
$633$	−43223.0			−0.107872
$634$	−375966.			−0.935340
$635$		−	730608.i		−	1.81191i
$636$	−538867.			−1.33219
$637$			103237.i			0.254423i
$638$	−195212.			−0.479585
$639$		−	1.26393e6i		−	3.09544i
$640$			60278.0i			0.147163i
$641$		−	351470.i		−	0.855406i	−0.903919	−	0.427703i	$-0.859323\pi$
$641$		−	351470.i		−	0.855406i	0.903919	−	0.427703i	$-0.140677\pi$
$642$		−	21790.8i		−	0.0528694i
$643$	−257336.			−0.622412			−0.311206	−	0.950342i	$-0.600733\pi$
$643$	−257336.			−0.622412			−0.311206	+	0.950342i	$0.600733\pi$
$644$	134201.			0.323582
$645$		−	139816.i		−	0.336076i
$646$	−255182.	+	164555.i	−0.611485	+	0.394318i
$647$	352433.			0.841915			0.420957	−	0.907080i	$-0.361694\pi$
$647$	352433.			0.841915			0.420957	+	0.907080i	$0.361694\pi$
$648$			108284.i			0.257879i
$649$		−	58639.0i		−	0.139218i
$650$	216030.			0.511314
$651$	241830.			0.570621
$652$	−12703.3			−0.0298829
$653$	−51680.8			−0.121200			−0.0606001	−	0.998162i	$-0.519301\pi$
$653$	−51680.8			−0.121200			−0.0606001	+	0.998162i	$0.519301\pi$
$654$			494240.i			1.15553i
$655$	−308094.			−0.718126
$656$		−	44175.8i		−	0.102654i
$657$	1.13454e6			2.62839
$658$		−	14675.6i		−	0.0338956i
$659$			144227.i			0.332105i	0.986117	+	0.166053i	$0.0531021\pi$
$659$			144227.i			0.332105i	−0.986117	+	0.166053i	$0.946898\pi$
$660$			628170.i			1.44208i
$661$		−	615181.i		−	1.40799i	−0.710205	−	0.703995i	$-0.751398\pi$
$661$		−	615181.i		−	1.40799i	0.710205	−	0.703995i	$-0.248602\pi$
$662$	−126213.			−0.287997
$663$	314678.			0.715878
$664$			120996.i			0.274431i
$665$	508426.	+	788438.i	1.14970	+	1.78289i
$666$	−1.05171e6			−2.37108
$667$		−	150841.i		−	0.339054i
$668$			170223.i			0.381474i
$669$	−565765.			−1.26411
$670$	601834.			1.34069
$671$	487459.			1.08266
$672$	173423.			0.384032
$673$			334936.i			0.739489i	0.929133	+	0.369745i	$0.120555\pi$
$673$			334936.i			0.739489i	−0.929133	+	0.369745i	$0.879445\pi$
$674$	14545.2			0.0320185
$675$			1.24845e6i			2.74009i
$676$	−190443.			−0.416746
$677$		−	504808.i		−	1.10141i	−0.834700	−	0.550705i	$-0.814359\pi$
$677$		−	504808.i		−	1.10141i	0.834700	−	0.550705i	$-0.185641\pi$
$678$		−	207416.i		−	0.451214i
$679$		−	67312.5i		−	0.146001i
$680$			280081.i			0.605711i
$681$	−871992.			−1.88026
$682$	−87772.6			−0.188708
$683$			690506.i			1.48022i	0.672486	+	0.740110i	$0.265227\pi$
$683$			690506.i			1.48022i	−0.672486	+	0.740110i	$0.734773\pi$
$684$	−241750.	−	374892.i	−0.516719	−	0.801297i
$685$	70459.8			0.150162
$686$		−	159632.i		−	0.339212i
$687$		−	117121.i		−	0.248153i
$688$	14009.9			0.0295977
$689$	−302717.			−0.637673
$690$	−485390.			−1.01951
$691$	461905.			0.967379			0.483690	−	0.875240i	$-0.339296\pi$
$691$	461905.			0.967379			0.483690	+	0.875240i	$0.339296\pi$
$692$		−	189035.i		−	0.394756i
$693$	1.18556e6			2.46863
$694$			496846.i			1.03158i
$695$	−1.55535e6			−3.22002
$696$		−	194926.i		−	0.402394i
$697$		−	205262.i		−	0.422516i
$698$		−	387848.i		−	0.796069i
$699$		−	1.40019e6i		−	2.86571i
$700$	553196.			1.12897
$701$	−410170.			−0.834694			−0.417347	−	0.908747i	$-0.637040\pi$
$701$	−410170.			−0.834694			−0.417347	+	0.908747i	$0.637040\pi$
$702$			219864.i			0.446150i
$703$	730358.	−	470974.i	1.47783	−	0.952985i
$704$	−62944.1			−0.127002
$705$			53079.7i			0.106795i
$706$			563962.i			1.13146i
$707$	−87015.4			−0.174083
$708$	58553.0			0.116811
$709$	368245.			0.732562			0.366281	−	0.930504i	$-0.380631\pi$
$709$	368245.			0.732562			0.366281	+	0.930504i	$0.380631\pi$
$710$	963380.			1.91109
$711$			229467.i			0.453923i
$712$	252801.			0.498675
$713$		−	67822.3i		−	0.133411i
$714$	805806.			1.58064
$715$			352884.i			0.690272i
$716$		−	436641.i		−	0.851723i
$717$			1.69039e6i			3.28813i
$718$		−	17841.6i		−	0.0346086i
$719$	−460066.			−0.889943			−0.444971	−	0.895545i	$-0.646786\pi$
$719$	−460066.			−0.889943			−0.444971	+	0.895545i	$0.646786\pi$
$720$	−411470.			−0.793731
$721$		−	696965.i		−	1.34073i
$722$	335766.	+	152083.i	0.644114	+	0.291748i
$723$	896482.			1.71500
$724$			387695.i			0.739627i
$725$		−	621788.i		−	1.18295i
$726$	−20515.6			−0.0389234
$727$	196263.			0.371339			0.185670	−	0.982612i	$-0.440555\pi$
$727$	196263.			0.371339			0.185670	+	0.982612i	$0.440555\pi$
$728$	97422.9			0.183822
$729$	661866.			1.24542
$730$			864757.i			1.62274i
$731$	65096.8			0.121822
$732$			486744.i			0.908403i
$733$	578892.			1.07743			0.538716	−	0.842487i	$-0.318910\pi$
$733$	578892.			1.07743			0.538716	+	0.842487i	$0.318910\pi$
$734$		−	149755.i		−	0.277964i
$735$		−	956167.i		−	1.76994i
$736$		−	48637.2i		−	0.0897869i
$737$			628453.i			1.15701i
$738$	301553.			0.553670
$739$	721624.			1.32136			0.660681	−	0.750667i	$-0.270268\pi$
$739$	721624.			1.32136			0.660681	+	0.750667i	$0.270268\pi$
$740$		−	801621.i		−	1.46388i
$741$	−207025.	−	321042.i	−0.377039	−	0.584690i
$742$	−775177.			−1.40797
$743$		−	963975.i		−	1.74618i	−0.487562	−	0.873088i	$-0.662114\pi$
$743$		−	963975.i		−	1.74618i	0.487562	−	0.873088i	$-0.337886\pi$
$744$		−	87643.9i		−	0.158335i
$745$	−251293.			−0.452760
$746$	−26341.1			−0.0473322
$747$	−825942.			−1.48016
$748$	−292469.			−0.522729
$749$		−	31346.8i		−	0.0558766i
$750$	−871756.			−1.54979
$751$		−	632486.i		−	1.12143i	−0.828010	−	0.560713i	$-0.810527\pi$
$751$		−	632486.i		−	1.12143i	0.828010	−	0.560713i	$-0.189473\pi$
$752$	−5318.71			−0.00940526
$753$			264823.i			0.467052i
$754$		−	109503.i		−	0.192611i
$755$			858249.i			1.50563i
$756$			563014.i			0.985090i
$757$	684418.			1.19434			0.597172	−	0.802113i	$-0.296291\pi$
$757$	684418.			1.19434			0.597172	+	0.802113i	$0.296291\pi$
$758$	−504283.			−0.877680
$759$		−	506859.i		−	0.879840i
$760$	285746.	−	184264.i	0.494712	−	0.319016i
$761$	−201444.			−0.347845			−0.173923	−	0.984759i	$-0.555644\pi$
$761$	−201444.			−0.347845			−0.173923	+	0.984759i	$0.555644\pi$
$762$			761805.i			1.31200i
$763$			710980.i			1.22126i
$764$	−85750.4			−0.146909
$765$	−1.91189e6			−3.26693
$766$	78530.6			0.133839
$767$	32893.1			0.0559131
$768$		−	62851.9i		−	0.106560i
$769$	343992.			0.581695			0.290847	−	0.956769i	$-0.406063\pi$
$769$	343992.			0.581695			0.290847	+	0.956769i	$0.406063\pi$
$770$			903643.i			1.52411i
$771$	632135.			1.06341
$772$			202866.i			0.340388i
$773$		−	323326.i		−	0.541105i	−0.962705	−	0.270553i	$-0.912794\pi$
$773$		−	323326.i		−	0.541105i	0.962705	−	0.270553i	$-0.0872064\pi$
$774$			95634.5i			0.159637i
$775$		−	279573.i		−	0.465469i
$776$	−24395.4			−0.0405121
$777$	−2.30630e6			−3.82010
$778$		−	682032.i		−	1.12680i
$779$	−209414.	+	135041.i	−0.345088	+	0.222531i
$780$	−352367.			−0.579170
$781$			1.00599e6i			1.64927i
$782$		−	225992.i		−	0.369556i
$783$	632824.			1.03219
$784$	95810.2			0.155876
$785$	−43436.5			−0.0704881
$786$	321250.			0.519993
$787$		−	526771.i		−	0.850496i	−0.905077	−	0.425248i	$-0.860187\pi$
$787$		−	526771.i		−	0.850496i	0.905077	−	0.425248i	$-0.139813\pi$
$788$	36295.5			0.0584521
$789$			631890.i			1.01505i
$790$	−174902.			−0.280247
$791$		−	298374.i		−	0.476879i
$792$		−	429670.i		−	0.684991i
$793$			273436.i			0.434820i
$794$		−	664454.i		−	1.05396i
$795$	2.80372e6			4.43609
$796$	541585.			0.854753
$797$			937353.i			1.47566i	0.674986	+	0.737831i	$0.264150\pi$
$797$			937353.i			1.47566i	−0.674986	+	0.737831i	$0.735850\pi$
$798$	−530136.	−	822104.i	−0.832495	−	1.29098i
$799$	−24713.3			−0.0387113
$800$		−	200489.i		−	0.313264i
$801$			1.72567e6i			2.68963i
$802$	−881055.			−1.36979
$803$	−903006.			−1.40042
$804$	−627532.			−0.970787
$805$	−698249.			−1.07750
$806$		−	49235.4i		−	0.0757891i
$807$	−304727.			−0.467911
$808$			31536.1i			0.0483043i
$809$	−339941.			−0.519405			−0.259702	−	0.965689i	$-0.583624\pi$
$809$	−339941.			−0.519405			−0.259702	+	0.965689i	$0.583624\pi$
$810$		−	563403.i		−	0.858715i
$811$		−	421572.i		−	0.640958i	−0.947256	−	0.320479i	$-0.896156\pi$
$811$		−	421572.i		−	0.640958i	0.947256	−	0.320479i	$-0.103844\pi$
$812$		−	280407.i		−	0.425282i
$813$		−	1.70290e6i		−	2.57637i
$814$	837077.			1.26333
$815$	66095.4			0.0995076
$816$		−	292040.i		−	0.438594i
$817$	−42826.9	−	66413.4i	−0.0641612	−	0.0994974i
$818$	689108.			1.02987
$819$			665030.i			0.991456i
$820$			229846.i			0.341830i
$821$	−832671.			−1.23534			−0.617671	−	0.786437i	$-0.711923\pi$
$821$	−832671.			−1.23534			−0.617671	+	0.786437i	$0.711923\pi$
$822$	−73468.5			−0.108732
$823$	193463.			0.285627			0.142813	−	0.989750i	$-0.454385\pi$
$823$	193463.			0.285627			0.142813	+	0.989750i	$0.454385\pi$
$824$	−252594.			−0.372022
$825$		−	2.08934e6i		−	3.06974i
$826$	84230.4			0.123455
$827$		−	414119.i		−	0.605500i	−0.953070	−	0.302750i	$-0.902095\pi$
$827$		−	414119.i		−	0.605500i	0.953070	−	0.302750i	$-0.0979047\pi$
$828$	332008.			0.484270
$829$		−	1.10281e6i		−	1.60469i	−0.596858	−	0.802347i	$-0.703585\pi$
$829$		−	1.10281e6i		−	1.60469i	0.596858	−	0.802347i	$-0.296415\pi$
$830$		−	629540.i		−	0.913834i
$831$			1.34319e6i			1.94508i
$832$		−	35308.0i		−	0.0510066i
$833$	445181.			0.641574
$834$	1.62176e6			2.33161
$835$		−	885669.i		−	1.27028i
$836$	192414.	+	298384.i	0.275311	+	0.426937i
$837$	284535.			0.406148
$838$			548164.i			0.780589i
$839$			420379.i			0.597196i	0.954379	+	0.298598i	$0.0965189\pi$
$839$			420379.i			0.597196i	−0.954379	+	0.298598i	$0.903481\pi$
$840$	−902318.			−1.27880
$841$	392105.			0.554384
$842$	386181.			0.544712
$843$	−2.04541e6			−2.87823
$844$			22534.4i			0.0316346i
$845$	990875.			1.38773
$846$		−	36306.7i		−	0.0507278i
$847$	−29512.4			−0.0411374
$848$			280940.i			0.390680i
$849$		−	458895.i		−	0.636646i
$850$		−	931570.i		−	1.28937i
$851$			646813.i			0.893140i
$852$	−1.00452e6			−1.38381
$853$	−1.00746e6			−1.38462			−0.692310	−	0.721600i	$-0.743407\pi$
$853$	−1.00746e6			−1.38462			−0.692310	+	0.721600i	$0.743407\pi$
$854$			700198.i			0.960074i
$855$	1.25782e6	+	1.95056e6i	1.72063	+	2.66825i
$856$	−11360.7			−0.0155045
$857$		−	425334.i		−	0.579119i	−0.957160	−	0.289560i	$-0.906491\pi$
$857$		−	425334.i		−	0.579119i	0.957160	−	0.289560i	$-0.0935089\pi$
$858$		−	367953.i		−	0.499824i
$859$	−101991.			−0.138221			−0.0691105	−	0.997609i	$-0.522016\pi$
$859$	−101991.			−0.138221			−0.0691105	+	0.997609i	$0.522016\pi$
$860$	−72893.5			−0.0985580
$861$	661280.			0.892029
$862$	915959.			1.23271
$863$		−	295578.i		−	0.396872i	−0.980114	−	0.198436i	$-0.936414\pi$
$863$		−	295578.i		−	0.396872i	0.980114	−	0.198436i	$-0.0635862\pi$
$864$	204048.			0.273341
$865$			983547.i			1.31451i
$866$	809295.			1.07912
$867$		−	75357.6i		−	0.100251i
$868$		−	126079.i		−	0.167341i
$869$		−	182638.i		−	0.241853i
$870$			1.01420e6i			1.33994i
$871$	−352526.			−0.464681
$872$	257673.			0.338873
$873$		−	166528.i		−	0.218504i
$874$	−230563.	+	148679.i	−0.301833	+	0.194638i
$875$	−1.25405e6			−1.63794
$876$		−	901682.i		−	1.17502i
$877$			267600.i			0.347926i	0.984752	+	0.173963i	$0.0556573\pi$
$877$			267600.i			0.347926i	−0.984752	+	0.173963i	$0.944343\pi$
$878$	−74340.5			−0.0964354
$879$	−654073.			−0.846542
$880$	327498.			0.422906
$881$	1.32998e6			1.71353			0.856765	−	0.515707i	$-0.172471\pi$
$881$	1.32998e6			1.71353			0.856765	+	0.515707i	$0.172471\pi$
$882$			654021.i			0.840726i
$883$	−229460.			−0.294296			−0.147148	−	0.989114i	$-0.547009\pi$
$883$	−229460.			−0.294296			−0.147148	+	0.989114i	$0.547009\pi$
$884$		−	164058.i		−	0.209939i
$885$	−304651.			−0.388970
$886$			899120.i			1.14538i
$887$			161937.i			0.205825i	0.994690	+	0.102913i	$0.0328162\pi$
$887$			161937.i			0.205825i	−0.994690	+	0.102913i	$0.967184\pi$
$888$			835850.i			1.05999i
$889$			1.09588e6i			1.38663i
$890$	−1.31532e6			−1.66055
$891$	588323.			0.741072
$892$			294963.i			0.370713i
$893$	16258.8	+	25213.2i	0.0203885	+	0.0316173i
$894$	262023.			0.327842
$895$			2.27184e6i			2.83617i
$896$		−	90414.4i		−	0.112622i
$897$	284319.			0.353362
$898$	−194394.			−0.241063
$899$	−141711.			−0.175342
$900$	1.36858e6			1.68961
$901$			1.30538e6i			1.60801i
$902$	−240013.			−0.295000
$903$			209718.i			0.257194i
$904$	−108137.			−0.132323
$905$		−	2.01717e6i		−	2.46290i
$906$		−	894897.i		−	1.09023i
$907$		−	530320.i		−	0.644649i	−0.946629	−	0.322325i	$-0.895536\pi$
$907$		−	530320.i		−	0.644649i	0.946629	−	0.322325i	$-0.104464\pi$
$908$			454615.i			0.551407i
$909$	−215272.			−0.260532
$910$	−506891.			−0.612114
$911$			969623.i			1.16833i	0.811634	+	0.584166i	$0.198578\pi$
$911$			969623.i			1.16833i	−0.811634	+	0.584166i	$0.801422\pi$
$912$	−297947.	+	192132.i	−0.358220	+	0.230999i
$913$	657385.			0.788639
$914$		−	517203.i		−	0.619111i
$915$		−	2.53253e6i		−	3.02491i
$916$	−61061.1			−0.0727736
$917$	462128.			0.549571
$918$	948105.			1.12505
$919$	853445.			1.01052			0.505260	−	0.862967i	$-0.331397\pi$
$919$	853445.			1.01052			0.505260	+	0.862967i	$0.331397\pi$
$920$			253059.i			0.298983i
$921$	599172.			0.706370
$922$		−	403910.i		−	0.475141i
$923$	−564303.			−0.662382
$924$		−	942229.i		−	1.10360i
$925$			2.66625e6i			3.11614i
$926$		−	272131.i		−	0.317363i
$927$		−	1.72426e6i		−	2.00652i
$928$	−101625.			−0.118006
$929$	580185.			0.672257			0.336128	−	0.941816i	$-0.390882\pi$
$929$	580185.			0.672257			0.336128	+	0.941816i	$0.390882\pi$
$930$			456011.i			0.527242i
$931$	−292882.	−	454185.i	−0.337905	−	0.524002i
$932$	−729993.			−0.840402
$933$		−	1.21579e6i		−	1.39667i
$934$		−	812667.i		−	0.931577i
$935$	1.52172e6			1.74065
$936$	241020.			0.275107
$937$	−173996.			−0.198180			−0.0990901	−	0.995078i	$-0.531593\pi$
$937$	−173996.			−0.198180			−0.0990901	+	0.995078i	$0.531593\pi$
$938$	−902725.			−1.02601
$939$			1.64309e6i			1.86350i
$940$	27673.3			0.0313188
$941$			288487.i			0.325797i	0.986643	+	0.162899i	$0.0520844\pi$
$941$			288487.i			0.325797i	−0.986643	+	0.162899i	$0.947916\pi$
$942$	45291.3			0.0510402
$943$		−	185459.i		−	0.208557i
$944$		−	30526.8i		−	0.0342560i
$945$		−	2.92936e6i		−	3.28027i
$946$		−	76117.6i		−	0.0850556i
$947$	484204.			0.539919			0.269959	−	0.962872i	$-0.412990\pi$
$947$	484204.			0.539919			0.269959	+	0.962872i	$0.412990\pi$
$948$	182370.			0.202926
$949$		−	506534.i		−	0.562440i
$950$	−950412.	+	612876.i	−1.05309	+	0.679087i
$951$	−2.03968e6			−2.25528
$952$		−	420110.i		−	0.463542i
$953$			834271.i			0.918590i	0.888284	+	0.459295i	$0.151898\pi$
$953$			834271.i			0.918590i	−0.888284	+	0.459295i	$0.848102\pi$
$954$	−1.91775e6			−2.10715
$955$	446159.			0.489196
$956$	881290.			0.964280
$957$	−1.05906e6			−1.15637
$958$		−	287064.i		−	0.312786i
$959$	−105687.			−0.114917
$960$			327018.i			0.354837i
$961$	859804.			0.931006
$962$			469552.i			0.507380i
$963$		−	77550.7i		−	0.0836244i
$964$		−	467384.i		−	0.502944i
$965$		−	1.05551e6i		−	1.13346i
$966$	728064.			0.780217
$967$	−268509.			−0.287148			−0.143574	−	0.989640i	$-0.545859\pi$
$967$	−268509.			−0.287148			−0.143574	+	0.989640i	$0.545859\pi$
$968$			10695.9i			0.0114147i
$969$	−1.38441e6	+	892739.i	−1.47440	+	0.950773i
$970$	126929.			0.134902
$971$		−	513847.i		−	0.544999i	−0.962156	−	0.272499i	$-0.912150\pi$
$971$		−	513847.i		−	0.544999i	0.962156	−	0.272499i	$-0.0878503\pi$
$972$		−	142975.i		−	0.151330i
$973$	2.33296e6			2.46423
$974$	575132.			0.606248
$975$	1.17200e6			1.23287
$976$	253766.			0.266399
$977$		−	880047.i		−	0.921970i	−0.887408	−	0.460985i	$-0.847496\pi$
$977$		−	880047.i		−	0.921970i	0.887408	−	0.460985i	$-0.152504\pi$
$978$	−68917.7			−0.0720532
$979$		−	1.37350e6i		−	1.43306i
$980$	−498500.			−0.519055
$981$			1.75893e6i			1.82773i
$982$			644196.i			0.668029i
$983$			1.15115e6i			1.19131i	0.803239	+	0.595656i	$0.203108\pi$
$983$			1.15115e6i			1.19131i	−0.803239	+	0.595656i	$0.796892\pi$
$984$		−	239661.i		−	0.247518i
$985$	−188845.			−0.194641
$986$	−472200.			−0.485705
$987$		−	79617.3i		−	0.0817285i
$988$	−167376.	+	107933.i	−0.171467	+	0.110571i
$989$	58816.4			0.0601320
$990$			2.23557e6i			2.28096i
$991$		−	1.55344e6i		−	1.58178i	−0.611956	−	0.790892i	$-0.709617\pi$
$991$		−	1.55344e6i		−	1.58178i	0.611956	−	0.790892i	$-0.290383\pi$
$992$	−45693.4			−0.0464334
$993$	−684727.			−0.694415
$994$	−1.44503e6			−1.46253
$995$	−2.81787e6			−2.84626
$996$			656422.i			0.661705i
$997$	−1.19520e6			−1.20240			−0.601200	−	0.799099i	$-0.705310\pi$
$997$	−1.19520e6			−1.20240			−0.601200	+	0.799099i	$0.705310\pi$
$998$			375697.i			0.377204i
$999$	−2.71357e6			−2.71901

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	38.5.b.a.37.1	✓	8
3.2	odd	2		342.5.d.a.37.5		8
4.3	odd	2		304.5.e.e.113.8		8
19.18	odd	2	inner	38.5.b.a.37.8	yes	8
57.56	even	2		342.5.d.a.37.1		8
76.75	even	2		304.5.e.e.113.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
38.5.b.a.37.1	✓	8	1.1	even	1	trivial
38.5.b.a.37.8	yes	8	19.18	odd	2	inner
304.5.e.e.113.1		8	76.75	even	2
304.5.e.e.113.8		8	4.3	odd	2
342.5.d.a.37.1		8	57.56	even	2
342.5.d.a.37.5		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)

\(f(q)\)	\(=\)	\(q-2.82843i q^{2} -15.3447i q^{3} -8.00000 q^{4} +41.6240 q^{5} -43.4013 q^{6} -62.4342 q^{7} +22.6274i q^{8} -154.460 q^{9} +O(q^{10})\)	\(q-2.82843i q^{2} -15.3447i q^{3} -8.00000 q^{4} +41.6240 q^{5} -43.4013 q^{6} -62.4342 q^{7} +22.6274i q^{8} -154.460 q^{9} -117.730i q^{10} +122.938 q^{11} +122.758i q^{12} +68.9610i q^{13} +176.591i q^{14} -638.707i q^{15} +64.0000 q^{16} +297.375 q^{17} +436.878i q^{18} +(-195.642 - 303.390i) q^{19} -332.992 q^{20} +958.034i q^{21} -347.721i q^{22} +268.685 q^{23} +347.211 q^{24} +1107.56 q^{25} +195.051 q^{26} +1127.21i q^{27} +499.474 q^{28} -561.405i q^{29} -1806.54 q^{30} -252.423i q^{31} -181.019i q^{32} -1886.44i q^{33} -841.104i q^{34} -2598.76 q^{35} +1235.68 q^{36} +2407.33i q^{37} +(-858.116 + 553.358i) q^{38} +1058.18 q^{39} +941.843i q^{40} -690.246i q^{41} +2709.73 q^{42} +218.905 q^{43} -983.502 q^{44} -6429.22 q^{45} -759.956i q^{46} -83.1049 q^{47} -982.060i q^{48} +1497.03 q^{49} -3132.64i q^{50} -4563.13i q^{51} -551.688i q^{52} +4389.68i q^{53} +3188.24 q^{54} +5117.16 q^{55} -1412.73i q^{56} +(-4655.42 + 3002.06i) q^{57} -1587.89 q^{58} -476.981i q^{59} +5109.66i q^{60} +3965.09 q^{61} -713.960 q^{62} +9643.57 q^{63} -512.000 q^{64} +2870.43i q^{65} -5335.66 q^{66} +5111.96i q^{67} -2379.00 q^{68} -4122.89i q^{69} +7350.41i q^{70} +8182.93i q^{71} -3495.02i q^{72} -7345.23 q^{73} +6808.95 q^{74} -16995.1i q^{75} +(1565.13 + 2427.12i) q^{76} -7675.53 q^{77} -2993.00i q^{78} -1485.61i q^{79} +2663.94 q^{80} +4785.54 q^{81} -1952.31 q^{82} +5347.30 q^{83} -7664.27i q^{84} +12377.9 q^{85} -619.156i q^{86} -8614.59 q^{87} +2781.76i q^{88} -11172.3i q^{89} +18184.6i q^{90} -4305.53i q^{91} -2149.48 q^{92} -3873.35 q^{93} +235.056i q^{94} +(-8143.39 - 12628.3i) q^{95} -2777.69 q^{96} +1078.13i q^{97} -4234.25i q^{98} -18988.9 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 64 q^{4} + 18 q^{5} - 32 q^{6} - 162 q^{7} - 268 q^{9}+O(q^{10}) \) 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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