LMFDB - Embedded newform 38.5.b.a.37.5

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			37.5
Root			$-12.2418i$ of defining polynomial
Character	$\chi$	$=$	38.37
Dual form			38.5.b.a.37.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.82843i q^{2} -10.8276i q^{3} -8.00000 q^{4} -26.2296 q^{5} +30.6250 q^{6} -86.0910 q^{7} -22.6274i q^{8} -36.2364 q^{9} +O(q^{10})$	\(q+2.82843i q^{2} -10.8276i q^{3} -8.00000 q^{4} -26.2296 q^{5} +30.6250 q^{6} -86.0910 q^{7} -22.6274i q^{8} -36.2364 q^{9} -74.1886i q^{10} +114.743 q^{11} +86.6206i q^{12} -231.848i q^{13} -243.502i q^{14} +284.003i q^{15} +64.0000 q^{16} -244.466 q^{17} -102.492i q^{18} +(253.655 + 256.866i) q^{19} +209.837 q^{20} +932.157i q^{21} +324.543i q^{22} -269.052 q^{23} -245.000 q^{24} +62.9931 q^{25} +655.766 q^{26} -484.681i q^{27} +688.728 q^{28} -1131.05i q^{29} -803.282 q^{30} +1037.59i q^{31} +181.019i q^{32} -1242.39i q^{33} -691.455i q^{34} +2258.14 q^{35} +289.891 q^{36} +302.815i q^{37} +(-726.527 + 717.444i) q^{38} -2510.36 q^{39} +593.509i q^{40} -1769.82i q^{41} -2636.54 q^{42} -2316.56 q^{43} -917.946 q^{44} +950.467 q^{45} -760.993i q^{46} -835.757 q^{47} -692.965i q^{48} +5010.66 q^{49} +178.171i q^{50} +2646.98i q^{51} +1854.79i q^{52} -656.208i q^{53} +1370.89 q^{54} -3009.67 q^{55} +1948.02i q^{56} +(2781.24 - 2746.47i) q^{57} +3199.09 q^{58} -4923.33i q^{59} -2272.03i q^{60} -1576.71 q^{61} -2934.75 q^{62} +3119.63 q^{63} -512.000 q^{64} +6081.30i q^{65} +3514.01 q^{66} +7000.44i q^{67} +1955.73 q^{68} +2913.18i q^{69} +6386.97i q^{70} -4101.26i q^{71} +819.936i q^{72} +7018.02 q^{73} -856.490 q^{74} -682.062i q^{75} +(-2029.24 - 2054.93i) q^{76} -9878.36 q^{77} -7100.36i q^{78} +1264.00i q^{79} -1678.70 q^{80} -8183.07 q^{81} +5005.79 q^{82} +1020.09 q^{83} -7457.26i q^{84} +6412.25 q^{85} -6552.21i q^{86} -12246.5 q^{87} -2596.34i q^{88} -3746.30i q^{89} +2688.33i q^{90} +19960.1i q^{91} +2152.41 q^{92} +11234.6 q^{93} -2363.88i q^{94} +(-6653.27 - 6737.50i) q^{95} +1960.00 q^{96} -13041.0i q^{97} +14172.3i q^{98} -4157.88 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$		−	10.8276i		−	1.20306i	−0.798849	−	0.601532i	$-0.794557\pi$
$3$		−	10.8276i		−	1.20306i	0.798849	−	0.601532i	$-0.205443\pi$
$4$	−8.00000			−0.500000
$5$	−26.2296			−1.04918			−0.524592	−	0.851353i	$-0.675782\pi$
$5$	−26.2296			−1.04918			−0.524592	+	0.851353i	$0.675782\pi$
$6$	30.6250			0.850695
$7$	−86.0910			−1.75696			−0.878480	−	0.477779i	$-0.841442\pi$
$7$	−86.0910			−1.75696			−0.878480	+	0.477779i	$0.841442\pi$
$8$		−	22.6274i		−	0.353553i
$9$	−36.2364			−0.447363
$10$		−	74.1886i		−	0.741886i
$11$	114.743			0.948291			0.474145	−	0.880447i	$-0.342757\pi$
$11$	114.743			0.948291			0.474145	+	0.880447i	$0.342757\pi$
$12$			86.6206i			0.601532i
$13$		−	231.848i		−	1.37188i	−0.727656	−	0.685942i	$-0.759390\pi$
$13$		−	231.848i		−	1.37188i	0.727656	−	0.685942i	$-0.240610\pi$
$14$		−	243.502i		−	1.24236i
$15$			284.003i			1.26224i
$16$	64.0000			0.250000
$17$	−244.466			−0.845903			−0.422952	−	0.906152i	$-0.639006\pi$
$17$	−244.466			−0.845903			−0.422952	+	0.906152i	$0.639006\pi$
$18$		−	102.492i		−	0.316333i
$19$	253.655	+	256.866i	0.702645	+	0.711540i
$19$	253.655	+	256.866i	0.702645	+	0.711540i
$20$	209.837			0.524592
$21$			932.157i			2.11373i
$22$			324.543i			0.670543i
$23$	−269.052			−0.508604			−0.254302	−	0.967125i	$-0.581846\pi$
$23$	−269.052			−0.508604			−0.254302	+	0.967125i	$0.581846\pi$
$24$	−245.000			−0.425347
$25$	62.9931			0.100789
$26$	655.766			0.970069
$27$		−	484.681i		−	0.664858i
$28$	688.728			0.878480
$29$		−	1131.05i		−	1.34489i	−0.740148	−	0.672443i	$-0.765245\pi$
$29$		−	1131.05i		−	1.34489i	0.740148	−	0.672443i	$-0.234755\pi$
$30$	−803.282			−0.892536
$31$			1037.59i			1.07970i	0.841762	+	0.539850i	$0.181519\pi$
$31$			1037.59i			1.07970i	−0.841762	+	0.539850i	$0.818481\pi$
$32$			181.019i			0.176777i
$33$		−	1242.39i		−	1.14085i
$34$		−	691.455i		−	0.598144i
$35$	2258.14			1.84338
$36$	289.891			0.223681
$37$			302.815i			0.221194i	0.993865	+	0.110597i	$0.0352763\pi$
$37$			302.815i			0.221194i	−0.993865	+	0.110597i	$0.964724\pi$
$38$	−726.527	+	717.444i	−0.503135	+	0.496845i
$39$	−2510.36			−1.65046
$40$			593.509i			0.370943i
$41$		−	1769.82i		−	1.05283i	−0.850226	−	0.526417i	$-0.823535\pi$
$41$		−	1769.82i		−	1.05283i	0.850226	−	0.526417i	$-0.176465\pi$
$42$	−2636.54			−1.49464
$43$	−2316.56			−1.25287			−0.626435	−	0.779474i	$-0.715487\pi$
$43$	−2316.56			−1.25287			−0.626435	+	0.779474i	$0.715487\pi$
$44$	−917.946			−0.474145
$45$	950.467			0.469366
$46$		−	760.993i		−	0.359638i
$47$	−835.757			−0.378342			−0.189171	−	0.981944i	$-0.560580\pi$
$47$	−835.757			−0.378342			−0.189171	+	0.981944i	$0.560580\pi$
$48$		−	692.965i		−	0.300766i
$49$	5010.66			2.08691
$50$			178.171i			0.0712685i
$51$			2646.98i			1.01768i
$52$			1854.79i			0.685942i
$53$		−	656.208i		−	0.233609i	−0.993155	−	0.116805i	$-0.962735\pi$
$53$		−	656.208i		−	0.233609i	0.993155	−	0.116805i	$-0.0372651\pi$
$54$	1370.89			0.470125
$55$	−3009.67			−0.994932
$56$			1948.02i			0.621179i
$57$	2781.24	−	2746.47i	0.856029	−	0.845327i
$58$	3199.09			0.950979
$59$		−	4923.33i		−	1.41434i	−0.707042	−	0.707171i	$-0.749971\pi$
$59$		−	4923.33i		−	1.41434i	0.707042	−	0.707171i	$-0.250029\pi$
$60$		−	2272.03i		−	0.631118i
$61$	−1576.71			−0.423733			−0.211866	−	0.977299i	$-0.567954\pi$
$61$	−1576.71			−0.423733			−0.211866	+	0.977299i	$0.567954\pi$
$62$	−2934.75			−0.763463
$63$	3119.63			0.785999
$64$	−512.000			−0.125000
$65$			6081.30i			1.43936i
$66$	3514.01			0.806706
$67$			7000.44i			1.55946i	0.626113	+	0.779732i	$0.284645\pi$
$67$			7000.44i			1.55946i	−0.626113	+	0.779732i	$0.715355\pi$
$68$	1955.73			0.422952
$69$			2913.18i			0.611884i
$70$			6386.97i			1.30346i
$71$		−	4101.26i		−	0.813581i	−0.913521	−	0.406790i	$-0.866648\pi$
$71$		−	4101.26i		−	0.813581i	0.913521	−	0.406790i	$-0.133352\pi$
$72$			819.936i			0.158167i
$73$	7018.02			1.31695			0.658474	−	0.752603i	$-0.271202\pi$
$73$	7018.02			1.31695			0.658474	+	0.752603i	$0.271202\pi$
$74$	−856.490			−0.156408
$75$		−	682.062i		−	0.121256i
$76$	−2029.24	−	2054.93i	−0.351323	−	0.355770i
$77$	−9878.36			−1.66611
$78$		−	7100.36i		−	1.16705i
$79$			1264.00i			0.202532i	0.994859	+	0.101266i	$0.0322893\pi$
$79$			1264.00i			0.202532i	−0.994859	+	0.101266i	$0.967711\pi$
$80$	−1678.70			−0.262296
$81$	−8183.07			−1.24723
$82$	5005.79			0.744467
$83$	1020.09			0.148075			0.0740377	−	0.997255i	$-0.476411\pi$
$83$	1020.09			0.148075			0.0740377	+	0.997255i	$0.476411\pi$
$84$		−	7457.26i		−	1.05687i
$85$	6412.25			0.887509
$86$		−	6552.21i		−	0.885913i
$87$	−12246.5			−1.61799
$88$		−	2596.34i		−	0.335271i
$89$		−	3746.30i		−	0.472958i	−0.971637	−	0.236479i	$-0.924007\pi$
$89$		−	3746.30i		−	0.472958i	0.971637	−	0.236479i	$-0.0759934\pi$
$90$			2688.33i			0.331892i
$91$			19960.1i			2.41034i
$92$	2152.41			0.254302
$93$	11234.6			1.29895
$94$		−	2363.88i		−	0.267528i
$95$	−6653.27	−	6737.50i	−0.737205	−	0.746537i
$96$	1960.00			0.212674
$97$		−	13041.0i		−	1.38601i	−0.720933	−	0.693005i	$-0.756287\pi$
$97$		−	13041.0i		−	1.38601i	0.720933	−	0.693005i	$-0.243713\pi$
$98$			14172.3i			1.47567i
$99$	−4157.88			−0.424230
$100$	−503.945			−0.0503945
$101$	−4755.84			−0.466213			−0.233106	−	0.972451i	$-0.574889\pi$
$101$	−4755.84			−0.466213			−0.233106	+	0.972451i	$0.574889\pi$
$102$	−7486.78			−0.719606
$103$		−	8727.79i		−	0.822678i	−0.911483	−	0.411339i	$-0.865061\pi$
$103$		−	8727.79i		−	0.822678i	0.911483	−	0.411339i	$-0.134939\pi$
$104$	−5246.13			−0.485034
$105$		−	24450.1i		−	2.21770i
$106$	1856.04			0.165187
$107$			16884.9i			1.47479i	0.675462	+	0.737395i	$0.263944\pi$
$107$			16884.9i			1.47479i	−0.675462	+	0.737395i	$0.736056\pi$
$108$			3877.45i			0.332429i
$109$			205.403i			0.0172883i	0.999963	+	0.00864416i	$0.00275156\pi$
$109$			205.403i			0.0172883i	−0.999963	+	0.00864416i	$0.997248\pi$
$110$		−	8512.63i		−	0.703524i
$111$	3278.75			0.266111
$112$	−5509.83			−0.439240
$113$			4276.02i			0.334875i	0.985883	+	0.167438i	$0.0535492\pi$
$113$			4276.02i			0.334875i	−0.985883	+	0.167438i	$0.946451\pi$
$114$	7768.18	+	7866.53i	0.597737	+	0.605304i
$115$	7057.13			0.533620
$116$			9048.40i			0.672443i
$117$			8401.35i			0.613730i
$118$	13925.3			1.00009
$119$	21046.3			1.48622
$120$	6426.26			0.446268
$121$	−1475.00			−0.100744
$122$		−	4459.61i		−	0.299624i
$123$	−19162.8			−1.26663
$124$		−	8300.73i		−	0.539850i
$125$	14741.2			0.943439
$126$			8823.64i			0.555785i
$127$			4501.00i			0.279063i	0.990218	+	0.139531i	$0.0445596\pi$
$127$			4501.00i			0.279063i	−0.990218	+	0.139531i	$0.955440\pi$
$128$		−	1448.15i		−	0.0883883i
$129$			25082.7i			1.50728i
$130$	−17200.5			−1.01778
$131$	27606.3			1.60866			0.804332	−	0.594180i	$-0.202523\pi$
$131$	27606.3			1.60866			0.804332	+	0.594180i	$0.202523\pi$
$132$			9939.13i			0.570427i
$133$	−21837.4	−	22113.9i	−1.23452	−	1.25015i
$134$	−19800.2			−1.10271
$135$			12713.0i			0.697559i
$136$			5531.64i			0.299072i
$137$	8250.29			0.439570			0.219785	−	0.975548i	$-0.429464\pi$
$137$	8250.29			0.439570			0.219785	+	0.975548i	$0.429464\pi$
$138$	−8239.71			−0.432667
$139$	27435.0			1.41996			0.709978	−	0.704224i	$-0.248705\pi$
$139$	27435.0			1.41996			0.709978	+	0.704224i	$0.248705\pi$
$140$	−18065.1			−0.921688
$141$			9049.22i			0.455169i
$142$	11600.1			0.575289
$143$		−	26603.0i		−	1.30095i
$144$	−2319.13			−0.111841
$145$			29667.0i			1.41104i
$146$			19850.0i			0.931223i
$147$		−	54253.3i		−	2.51068i
$148$		−	2422.52i		−	0.110597i
$149$	−40247.3			−1.81286			−0.906430	−	0.422355i	$-0.861204\pi$
$149$	−40247.3			−1.81286			−0.906430	+	0.422355i	$0.861204\pi$
$150$	1929.16			0.0857406
$151$			16932.1i			0.742605i	0.928512	+	0.371303i	$0.121089\pi$
$151$			16932.1i			0.742605i	−0.928512	+	0.371303i	$0.878911\pi$
$152$	5812.22	−	5739.56i	0.251568	−	0.248423i
$153$	8858.57			0.378426
$154$		−	27940.2i		−	1.17812i
$155$		−	27215.6i		−	1.13280i
$156$	20082.8			0.825232
$157$	5684.97			0.230637			0.115319	−	0.993329i	$-0.463211\pi$
$157$	5684.97			0.230637			0.115319	+	0.993329i	$0.463211\pi$
$158$	−3575.14			−0.143212
$159$	−7105.14			−0.281047
$160$		−	4748.07i		−	0.185471i
$161$	23162.9			0.893597
$162$		−	23145.2i		−	0.881924i
$163$	−30550.6			−1.14986			−0.574929	−	0.818203i	$-0.694970\pi$
$163$	−30550.6			−1.14986			−0.574929	+	0.818203i	$0.694970\pi$
$164$			14158.5i			0.526417i
$165$			32587.4i			1.19697i
$166$			2885.26i			0.104705i
$167$		−	28241.5i		−	1.01264i	−0.862345	−	0.506320i	$-0.831005\pi$
$167$		−	28241.5i		−	1.01264i	0.862345	−	0.506320i	$-0.168995\pi$
$168$	21092.3			0.747318
$169$	−25192.7			−0.882066
$170$			18136.6i			0.627564i
$171$	−9191.54	−	9307.90i	−0.314337	−	0.318317i
$172$	18532.4			0.626435
$173$		−	35673.0i		−	1.19192i	−0.803013	−	0.595961i	$-0.796771\pi$
$173$		−	35673.0i		−	1.19192i	0.803013	−	0.595961i	$-0.203229\pi$
$174$		−	34638.4i		−	1.14409i
$175$	−5423.14			−0.177082
$176$	7343.56			0.237073
$177$	−53307.7			−1.70154
$178$	10596.1			0.334432
$179$			34371.5i			1.07273i	0.843985	+	0.536367i	$0.180204\pi$
$179$			34371.5i			1.07273i	−0.843985	+	0.536367i	$0.819796\pi$
$180$	−7603.74			−0.234683
$181$			29195.1i			0.891153i	0.895244	+	0.445577i	$0.147001\pi$
$181$			29195.1i			0.891153i	−0.895244	+	0.445577i	$0.852999\pi$
$182$	−56455.6			−1.70437
$183$			17071.9i			0.509777i
$184$			6087.95i			0.179819i
$185$		−	7942.72i		−	0.232074i
$186$			31776.2i			0.918494i
$187$	−28050.8			−0.802163
$188$	6686.05			0.189171
$189$			41726.7i			1.16813i
$190$	19056.5	−	18818.3i	0.527882	−	0.521282i
$191$	13498.2			0.370008			0.185004	−	0.982738i	$-0.440770\pi$
$191$	13498.2			0.370008			0.185004	+	0.982738i	$0.440770\pi$
$192$			5543.72i			0.150383i
$193$		−	20819.7i		−	0.558933i	−0.960155	−	0.279467i	$-0.909842\pi$
$193$		−	20819.7i		−	0.558933i	0.960155	−	0.279467i	$-0.0901577\pi$
$194$	36885.4			0.980056
$195$	65845.7			1.73164
$196$	−40085.3			−1.04345
$197$	34233.5			0.882101			0.441051	−	0.897482i	$-0.354606\pi$
$197$	34233.5			0.882101			0.441051	+	0.897482i	$0.354606\pi$
$198$		−	11760.3i		−	0.299976i
$199$	−55504.1			−1.40158			−0.700792	−	0.713366i	$-0.747170\pi$
$199$	−55504.1			−1.40158			−0.700792	+	0.713366i	$0.747170\pi$
$200$		−	1425.37i		−	0.0356343i
$201$	75797.8			1.87614
$202$		−	13451.5i		−	0.329662i
$203$			97373.2i			2.36291i
$204$		−	21175.8i		−	0.508838i
$205$			46421.6i			1.10462i
$206$	24685.9			0.581721
$207$	9749.46			0.227531
$208$		−	14838.3i		−	0.342971i
$209$	29105.2	+	29473.6i	0.666312	+	0.674747i
$210$	69155.4			1.56815
$211$		−	77552.5i		−	1.74193i	−0.491345	−	0.870965i	$-0.663495\pi$
$211$		−	77552.5i		−	1.74193i	0.491345	−	0.870965i	$-0.336505\pi$
$212$			5249.66i			0.116805i
$213$	−44406.7			−0.978790
$214$	−47757.6			−1.04283
$215$	60762.4			1.31449
$216$	−10967.1			−0.235063
$217$		−	89327.3i		−	1.89699i
$218$	−580.966			−0.0122247
$219$		−	75988.1i		−	1.58437i
$220$	24077.4			0.497466
$221$			56679.1i			1.16048i
$222$			9273.71i			0.188169i
$223$			30754.3i			0.618438i	0.950991	+	0.309219i	$0.100068\pi$
$223$			30754.3i			0.618438i	−0.950991	+	0.309219i	$0.899932\pi$
$224$		−	15584.1i		−	0.310590i
$225$	−2282.64			−0.0450892
$226$	−12094.4			−0.236792
$227$		−	81299.3i		−	1.57774i	−0.614561	−	0.788869i	$-0.710667\pi$
$227$		−	81299.3i		−	1.57774i	0.614561	−	0.788869i	$-0.289333\pi$
$228$	−22249.9	+	21971.7i	−0.428014	+	0.422664i
$229$	−93187.0			−1.77699			−0.888494	−	0.458889i	$-0.848248\pi$
$229$	−93187.0			−1.77699			−0.888494	+	0.458889i	$0.848248\pi$
$230$			19960.6i			0.377326i
$231$			106959.i			2.00444i
$232$	−25592.7			−0.475489
$233$	−3379.09			−0.0622426			−0.0311213	−	0.999516i	$-0.509908\pi$
$233$	−3379.09			−0.0622426			−0.0311213	+	0.999516i	$0.509908\pi$
$234$	−23762.6			−0.433973
$235$	21921.6			0.396950
$236$			39386.6i			0.707171i
$237$	13686.1			0.243659
$238$			59528.0i			1.05091i
$239$	35917.8			0.628802			0.314401	−	0.949290i	$-0.398196\pi$
$239$	35917.8			0.628802			0.314401	+	0.949290i	$0.398196\pi$
$240$			18176.2i			0.315559i
$241$		−	57352.1i		−	0.987451i	−0.869618	−	0.493726i	$-0.835635\pi$
$241$		−	57352.1i		−	0.987451i	0.869618	−	0.493726i	$-0.164365\pi$
$242$		−	4171.92i		−	0.0712370i
$243$			49343.6i			0.835639i
$244$	12613.7			0.211866
$245$	−131428.			−2.18955
$246$		−	54200.6i		−	0.895641i
$247$	59554.0	−	58809.5i	0.976151	−	0.963948i
$248$	23478.0			0.381731
$249$		−	11045.1i		−	0.178144i
$250$			41694.5i			0.667112i
$251$	−52486.8			−0.833110			−0.416555	−	0.909110i	$-0.636763\pi$
$251$	−52486.8			−0.833110			−0.416555	+	0.909110i	$0.636763\pi$
$252$	−24957.0			−0.392999
$253$	−30871.9			−0.482305
$254$	−12730.8			−0.197327
$255$		−	69429.2i		−	1.06773i
$256$	4096.00			0.0625000
$257$		−	85222.5i		−	1.29029i	−0.764059	−	0.645146i	$-0.776796\pi$
$257$		−	85222.5i		−	1.29029i	0.764059	−	0.645146i	$-0.223204\pi$
$258$	−70944.5			−1.06581
$259$		−	26069.6i		−	0.388629i
$260$		−	48650.4i		−	0.719680i
$261$			40985.2i			0.601653i
$262$			78082.4i			1.13750i
$263$	−27539.5			−0.398149			−0.199074	−	0.979984i	$-0.563794\pi$
$263$	−27539.5			−0.398149			−0.199074	+	0.979984i	$0.563794\pi$
$264$	−28112.1			−0.403353
$265$			17212.1i			0.245099i
$266$	62547.5	−	61765.5i	0.883988	−	0.872937i
$267$	−40563.3			−0.568999
$268$		−	56003.5i		−	0.779732i
$269$		−	58880.0i		−	0.813697i	−0.913496	−	0.406849i	$-0.866628\pi$
$269$		−	58880.0i		−	0.813697i	0.913496	−	0.406849i	$-0.133372\pi$
$270$	−35957.8			−0.493249
$271$	99955.1			1.36103			0.680513	−	0.732736i	$-0.261757\pi$
$271$	99955.1			1.36103			0.680513	+	0.732736i	$0.261757\pi$
$272$	−15645.8			−0.211476
$273$	216119.			2.89980
$274$			23335.4i			0.310823i
$275$	7228.03			0.0955772
$276$		−	23305.4i		−	0.305942i
$277$	66298.2			0.864056			0.432028	−	0.901860i	$-0.357798\pi$
$277$	66298.2			0.864056			0.432028	+	0.901860i	$0.357798\pi$
$278$			77597.8i			1.00406i
$279$		−	37598.6i		−	0.483017i
$280$		−	51095.8i		−	0.651732i
$281$		−	55021.9i		−	0.696824i	−0.937341	−	0.348412i	$-0.886721\pi$
$281$		−	55021.9i		−	0.696824i	0.937341	−	0.348412i	$-0.113279\pi$
$282$	−25595.1			−0.321853
$283$	10575.2			0.132044			0.0660219	−	0.997818i	$-0.478969\pi$
$283$	10575.2			0.132044			0.0660219	+	0.997818i	$0.478969\pi$
$284$			32810.1i			0.406790i
$285$	−72950.8	+	72038.8i	−0.898132	+	0.886904i
$286$	75244.7			0.919907
$287$			152365.i			1.84979i
$288$		−	6559.49i		−	0.0790833i
$289$	−23757.3			−0.284447
$290$	−83911.0			−0.997752
$291$	−141202.			−1.66746
$292$	−56144.2			−0.658474
$293$			9449.70i			0.110074i	0.998484	+	0.0550368i	$0.0175276\pi$
$293$			9449.70i			0.110074i	−0.998484	+	0.0550368i	$0.982472\pi$
$294$	153452.			1.77532
$295$			129137.i			1.48391i
$296$	6851.92			0.0782040
$297$		−	55613.9i		−	0.630479i
$298$		−	113837.i		−	1.28189i
$299$			62379.2i			0.697746i
$300$			5456.50i			0.0606278i
$301$	199435.			2.20124
$302$	−47891.3			−0.525101
$303$			51494.2i			0.560884i
$304$	16233.9	+	16439.4i	0.175661	+	0.177885i
$305$	41356.5			0.444574
$306$			25055.8i			0.267587i
$307$			112622.i			1.19494i	0.801890	+	0.597472i	$0.203828\pi$
$307$			112622.i			1.19494i	−0.801890	+	0.597472i	$0.796172\pi$
$308$	79026.9			0.833054
$309$	−94500.8			−0.989734
$310$	76977.4			0.801013
$311$	−75878.9			−0.784513			−0.392257	−	0.919856i	$-0.628305\pi$
$311$	−75878.9			−0.784513			−0.392257	+	0.919856i	$0.628305\pi$
$312$			56802.9i			0.583527i
$313$	−110960.			−1.13260			−0.566301	−	0.824199i	$-0.691626\pi$
$313$	−110960.			−1.13260			−0.566301	+	0.824199i	$0.691626\pi$
$314$			16079.5i			0.163085i
$315$	−81826.7			−0.824658
$316$		−	10112.0i		−	0.101266i
$317$			63970.1i			0.636589i	0.947992	+	0.318294i	$0.103110\pi$
$317$			63970.1i			0.636589i	−0.947992	+	0.318294i	$0.896890\pi$
$318$		−	20096.4i		−	0.198730i
$319$		−	129780.i		−	1.27534i
$320$	13429.6			0.131148
$321$	182822.			1.77427
$322$			65514.7i			0.631869i
$323$	−62010.0	−	62795.0i	−0.594370	−	0.601894i
$324$	65464.6			0.623615
$325$		−	14604.8i		−	0.138271i
$326$		−	86410.0i		−	0.813072i
$327$	2224.01			0.0207990
$328$	−40046.4			−0.372233
$329$	71951.1			0.664731
$330$	−92171.2			−0.846384
$331$			79462.6i			0.725282i	0.931929	+	0.362641i	$0.118125\pi$
$331$			79462.6i			0.725282i	−0.931929	+	0.362641i	$0.881875\pi$
$332$	−8160.74			−0.0740377
$333$		−	10972.9i		−	0.0989541i
$334$	79879.1			0.716045
$335$		−	183619.i		−	1.63617i
$336$			59658.1i			0.528434i
$337$			2779.80i			0.0244767i	0.999925	+	0.0122384i	$0.00389569\pi$
$337$			2779.80i			0.0244767i	−0.999925	+	0.0122384i	$0.996104\pi$
$338$		−	71255.7i		−	0.623715i
$339$	46298.9			0.402876
$340$	−51298.0			−0.443755
$341$			119057.i			1.02387i
$342$	26326.7	−	25997.6i	0.225084	−	0.222270i
$343$	−224669.			−1.90965
$344$			52417.7i			0.442956i
$345$		−	76411.6i		−	0.641979i
$346$	100899.			0.842816
$347$	−15728.1			−0.130622			−0.0653110	−	0.997865i	$-0.520804\pi$
$347$	−15728.1			−0.130622			−0.0653110	+	0.997865i	$0.520804\pi$
$348$	97972.2			0.808993
$349$	−41782.5			−0.343039			−0.171519	−	0.985181i	$-0.554868\pi$
$349$	−41782.5			−0.343039			−0.171519	+	0.985181i	$0.554868\pi$
$350$		−	15339.0i		−	0.125216i
$351$	−112373.			−0.912108
$352$			20770.7i			0.167636i
$353$	39292.1			0.315323			0.157661	−	0.987493i	$-0.449605\pi$
$353$	39292.1			0.315323			0.157661	+	0.987493i	$0.449605\pi$
$354$		−	150777.i		−	1.20317i
$355$			107575.i			0.853597i
$356$			29970.4i			0.236479i
$357$		−	227881.i		−	1.78802i
$358$	−97217.2			−0.758537
$359$	160964.			1.24894			0.624468	−	0.781050i	$-0.285316\pi$
$359$	160964.			1.24894			0.624468	+	0.781050i	$0.285316\pi$
$360$		−	21506.6i		−	0.165946i
$361$	−1639.37	+	130311.i	−0.0125794	+	0.999921i
$362$	−82576.1			−0.630141
$363$			15970.7i			0.121202i
$364$		−	159681.i		−	1.20517i
$365$	−184080.			−1.38172
$366$	−48286.7			−0.360467
$367$	19835.4			0.147268			0.0736340	−	0.997285i	$-0.476540\pi$
$367$	19835.4			0.147268			0.0736340	+	0.997285i	$0.476540\pi$
$368$	−17219.3			−0.127151
$369$			64131.7i			0.470999i
$370$	22465.4			0.164101
$371$			56493.6i			0.410442i
$372$	−89876.8			−0.649474
$373$		−	14463.5i		−	0.103958i	−0.998648	−	0.0519788i	$-0.983447\pi$
$373$		−	14463.5i		−	0.103958i	0.998648	−	0.0519788i	$-0.0165528\pi$
$374$		−	79339.7i		−	0.567215i
$375$		−	159612.i		−	1.13502i
$376$			18911.0i			0.133764i
$377$	−262232.			−1.84503
$378$	−118021.			−0.825991
$379$		−	25932.7i		−	0.180539i	−0.995917	−	0.0902693i	$-0.971227\pi$
$379$		−	25932.7i		−	0.180539i	0.995917	−	0.0902693i	$-0.0287728\pi$
$380$	53226.2	+	53900.0i	0.368602	+	0.373269i
$381$	48734.9			0.335730
$382$			38178.8i			0.261635i
$383$		−	9634.98i		−	0.0656831i	−0.999461	−	0.0328415i	$-0.989544\pi$
$383$		−	9634.98i		−	0.0656831i	0.999461	−	0.0328415i	$-0.0104557\pi$
$384$	−15680.0			−0.106337
$385$	259106.			1.74806
$386$	58887.0			0.395226
$387$	83943.6			0.560487
$388$			104328.i			0.693005i
$389$	101890.			0.673335			0.336668	−	0.941624i	$-0.390700\pi$
$389$	101890.			0.673335			0.336668	+	0.941624i	$0.390700\pi$
$390$			186240.i			1.22446i
$391$	65774.0			0.430230
$392$		−	113378.i		−	0.737833i
$393$		−	298909.i		−	1.93533i
$394$			96826.9i			0.623740i
$395$		−	33154.3i		−	0.212494i
$396$	33263.0			0.212115
$397$	100161.			0.635503			0.317752	−	0.948174i	$-0.397072\pi$
$397$	100161.			0.635503			0.317752	+	0.948174i	$0.397072\pi$
$398$		−	156989.i		−	0.991069i
$399$	−239440.	+	236446.i	−1.50401	+	1.48521i
$400$	4031.56			0.0251972
$401$			16696.5i			0.103833i	0.998651	+	0.0519165i	$0.0165330\pi$
$401$			16696.5i			0.103833i	−0.998651	+	0.0519165i	$0.983467\pi$
$402$			214388.i			1.32663i
$403$	240564.			1.48122
$404$	38046.7			0.233106
$405$	214639.			1.30857
$406$	−275413.			−1.67083
$407$			34745.9i			0.209756i
$408$	59894.2			0.359803
$409$			1173.94i			0.00701780i	0.999994	+	0.00350890i	$0.00111692\pi$
$409$			1173.94i			0.00701780i	−0.999994	+	0.00350890i	$0.998883\pi$
$410$	−131300.			−0.781083
$411$		−	89330.7i		−	0.528831i
$412$			69822.3i			0.411339i
$413$			423854.i			2.48494i
$414$			27575.7i			0.160889i
$415$	−26756.6			−0.155359
$416$	41969.0			0.242517
$417$		−	297054.i		−	1.70830i
$418$	−83364.0	+	82321.9i	−0.477118	+	0.471154i
$419$	−209961.			−1.19595			−0.597973	−	0.801517i	$-0.704027\pi$
$419$	−209961.			−1.19595			−0.597973	+	0.801517i	$0.704027\pi$
$420$			195601.i			1.10885i
$421$		−	249117.i		−	1.40552i	−0.711425	−	0.702762i	$-0.751950\pi$
$421$		−	249117.i		−	1.40552i	0.711425	−	0.702762i	$-0.248050\pi$
$422$	219351.			1.23173
$423$	30284.8			0.169256
$424$	−14848.3			−0.0825933
$425$	−15399.7			−0.0852577
$426$		−	125601.i		−	0.692109i
$427$	135741.			0.744481
$428$		−	135079.i		−	0.737395i
$429$	−288046.			−1.56512
$430$			171862.i			0.929486i
$431$		−	126947.i		−	0.683387i	−0.939811	−	0.341694i	$-0.888999\pi$
$431$		−	126947.i		−	0.683387i	0.939811	−	0.341694i	$-0.111001\pi$
$432$		−	31019.6i		−	0.166214i
$433$			327343.i			1.74593i	0.487783	+	0.872965i	$0.337806\pi$
$433$			327343.i			1.74593i	−0.487783	+	0.872965i	$0.662194\pi$
$434$	252656.			1.34137
$435$	321222.			1.69757
$436$		−	1643.22i		−	0.00864416i
$437$	−68246.3	−	69110.3i	−0.357368	−	0.361893i
$438$	214927.			1.12032
$439$			323562.i			1.67891i	0.543425	+	0.839457i	$0.317127\pi$
$439$			323562.i			1.67891i	−0.543425	+	0.839457i	$0.682873\pi$
$440$			68101.1i			0.351762i
$441$	−181568.			−0.933605
$442$	−160313.			−0.820584
$443$	188338.			0.959689			0.479845	−	0.877354i	$-0.340693\pi$
$443$	188338.			0.959689			0.479845	+	0.877354i	$0.340693\pi$
$444$	−26230.0			−0.133055
$445$			98264.0i			0.496220i
$446$	−86986.3			−0.437302
$447$			435781.i			2.18099i
$448$	44078.6			0.219620
$449$		−	31205.6i		−	0.154789i	−0.997001	−	0.0773945i	$-0.975340\pi$
$449$		−	31205.6i		−	0.154789i	0.997001	−	0.0773945i	$-0.0246601\pi$
$450$		−	6456.29i		−	0.0318829i
$451$		−	203074.i		−	0.998394i
$452$		−	34208.2i		−	0.167438i
$453$	183334.			0.893402
$454$	229949.			1.11563
$455$		−	523545.i		−	2.52890i
$456$	−62145.5	−	62932.2i	−0.298868	−	0.302652i
$457$	89688.2			0.429440			0.214720	−	0.976676i	$-0.431116\pi$
$457$	89688.2			0.429440			0.214720	+	0.976676i	$0.431116\pi$
$458$		−	263573.i		−	1.25652i
$459$			118488.i			0.562405i
$460$	−56457.0			−0.266810
$461$	−71209.7			−0.335071			−0.167536	−	0.985866i	$-0.553581\pi$
$461$	−71209.7			−0.335071			−0.167536	+	0.985866i	$0.553581\pi$
$462$	−302525.			−1.41735
$463$	−96472.6			−0.450030			−0.225015	−	0.974355i	$-0.572243\pi$
$463$	−96472.6			−0.450030			−0.225015	+	0.974355i	$0.572243\pi$
$464$		−	72387.2i		−	0.336222i
$465$	−294679.			−1.36284
$466$		−	9557.51i		−	0.0440122i
$467$	337202.			1.54617			0.773084	−	0.634304i	$-0.218713\pi$
$467$	337202.			1.54617			0.773084	+	0.634304i	$0.218713\pi$
$468$		−	67210.8i		−	0.306865i
$469$		−	602675.i		−	2.73992i
$470$			62003.6i			0.280686i
$471$		−	61554.5i		−	0.277471i
$472$	−111402.			−0.500046
$473$	−265809.			−1.18808
$474$			38710.1i			0.172293i
$475$	15978.5	+	16180.8i	0.0708189	+	0.0717154i
$476$	−168371.			−0.743109
$477$			23778.6i			0.104508i
$478$			101591.i			0.444630i
$479$	126684.			0.552143			0.276071	−	0.961137i	$-0.410967\pi$
$479$	126684.			0.552143			0.276071	+	0.961137i	$0.410967\pi$
$480$	−51410.1			−0.223134
$481$	70207.1			0.303453
$482$	162216.			0.698233
$483$		−	250798.i		−	1.07505i
$484$	11800.0			0.0503722
$485$			342059.i			1.45418i
$486$	−139565.			−0.590886
$487$		−	233861.i		−	0.986053i	−0.870014	−	0.493027i	$-0.835891\pi$
$487$		−	233861.i		−	0.986053i	0.870014	−	0.493027i	$-0.164109\pi$
$488$			35676.9i			0.149812i
$489$			330789.i			1.38335i
$490$		−	371734.i		−	1.54825i
$491$	−423929.			−1.75845			−0.879226	−	0.476406i	$-0.841939\pi$
$491$	−423929.			−1.75845			−0.879226	+	0.476406i	$0.841939\pi$
$492$	153302.			0.633314
$493$			276503.i			1.13764i
$494$	166338.	+	168444.i	0.681614	+	0.690243i
$495$	109060.			0.445096
$496$			66405.8i			0.269925i
$497$			353082.i			1.42943i
$498$	31240.3			0.125967
$499$	−175944.			−0.706600			−0.353300	−	0.935510i	$-0.614941\pi$
$499$	−175944.			−0.706600			−0.353300	+	0.935510i	$0.614941\pi$
$500$	−117930.			−0.471719
$501$	−305787.			−1.21827
$502$		−	148455.i		−	0.589098i
$503$	108798.			0.430017			0.215009	−	0.976612i	$-0.431022\pi$
$503$	108798.			0.430017			0.215009	+	0.976612i	$0.431022\pi$
$504$		−	70589.1i		−	0.277892i
$505$	124744.			0.489143
$506$		−	87318.8i		−	0.341041i
$507$			272776.i			1.06118i
$508$		−	36008.0i		−	0.139531i
$509$		−	72826.1i		−	0.281094i	−0.990074	−	0.140547i	$-0.955114\pi$
$509$		−	72826.1i		−	0.281094i	0.990074	−	0.140547i	$-0.0448861\pi$
$510$	196375.			0.754999
$511$	−604188.			−2.31383
$512$			11585.2i			0.0441942i
$513$	124498.	−	122942.i	0.473073	−	0.467159i
$514$	241046.			0.912375
$515$			228927.i			0.863141i
$516$		−	200661.i		−	0.753641i
$517$	−95897.4			−0.358778
$518$	73736.1			0.274802
$519$	−386253.			−1.43396
$520$	137604.			0.508891
$521$		−	93748.1i		−	0.345372i	−0.984977	−	0.172686i	$-0.944755\pi$
$521$		−	93748.1i		−	0.345372i	0.984977	−	0.172686i	$-0.0552446\pi$
$522$	−115924.			−0.425433
$523$		−	87245.8i		−	0.318964i	−0.987201	−	0.159482i	$-0.949018\pi$
$523$		−	87245.8i		−	0.318964i	0.987201	−	0.159482i	$-0.0509823\pi$
$524$	−220850.			−0.804332
$525$			58719.4i			0.213041i
$526$		−	77893.6i		−	0.281534i
$527$		−	253656.i		−	0.913321i
$528$		−	79513.0i		−	0.285214i
$529$	−207452.			−0.741322
$530$	−48683.1			−0.173311
$531$			178404.i			0.632724i
$532$	174699.	+	176911.i	0.617260	+	0.625074i
$533$	−410329.			−1.44437
$534$		−	114730.i		−	0.402343i
$535$		−	442884.i		−	1.54733i
$536$	158402.			0.551354
$537$	372160.			1.29057
$538$	166538.			0.575371
$539$	574940.			1.97900
$540$		−	101704.i		−	0.348779i
$541$	374060.			1.27805			0.639024	−	0.769187i	$-0.279338\pi$
$541$	374060.			1.27805			0.639024	+	0.769187i	$0.279338\pi$
$542$			282716.i			0.962391i
$543$	316112.			1.07211
$544$		−	44253.1i		−	0.149536i
$545$		−	5387.63i		−	0.0181386i
$546$			611277.i			2.05047i
$547$		−	160411.i		−	0.536118i	−0.963402	−	0.268059i	$-0.913618\pi$
$547$		−	160411.i		−	0.536118i	0.963402	−	0.268059i	$-0.0863823\pi$
$548$	−66002.3			−0.219785
$549$	57134.3			0.189562
$550$			20443.9i			0.0675833i
$551$	290528.	−	286896.i	0.956941	−	0.944978i
$552$	65917.7			0.216334
$553$		−	108819.i		−	0.355841i
$554$			187520.i			0.610980i
$555$	−86000.4			−0.279199
$556$	−219480.			−0.709978
$557$	460605.			1.48463			0.742314	−	0.670052i	$-0.233728\pi$
$557$	460605.			1.48463			0.742314	+	0.670052i	$0.233728\pi$
$558$	106345.			0.341545
$559$			537090.i			1.71879i
$560$	144521.			0.460844
$561$			303722.i			0.965053i
$562$	155626.			0.492729
$563$			73084.0i			0.230571i	0.993332	+	0.115286i	$0.0367783\pi$
$563$			73084.0i			0.230571i	−0.993332	+	0.115286i	$0.963222\pi$
$564$		−	72393.7i		−	0.227585i
$565$		−	112158.i		−	0.351346i
$566$			29911.3i			0.0933690i
$567$	704489.			2.19133
$568$	−92801.0			−0.287644
$569$			609592.i			1.88285i	0.337227	+	0.941424i	$0.390511\pi$
$569$			609592.i			1.88285i	−0.337227	+	0.941424i	$0.609489\pi$
$570$	−203757.	−	206336.i	−0.627136	−	0.635075i
$571$	−11273.0			−0.0345755			−0.0172877	−	0.999851i	$-0.505503\pi$
$571$	−11273.0			−0.0345755			−0.0172877	+	0.999851i	$0.505503\pi$
$572$			212824.i			0.650473i
$573$		−	146153.i		−	0.445143i
$574$	−430954.			−1.30800
$575$	−16948.4			−0.0512617
$576$	18553.0			0.0559204
$577$	−186962.			−0.561567			−0.280783	−	0.959771i	$-0.590594\pi$
$577$	−186962.			−0.561567			−0.280783	+	0.959771i	$0.590594\pi$
$578$		−	67195.9i		−	0.201135i
$579$	−225427.			−0.672433
$580$		−	237336.i		−	0.705518i
$581$	−87820.8			−0.260163
$582$		−	399379.i		−	1.17907i
$583$		−	75295.4i		−	0.221529i
$584$		−	158800.i		−	0.465612i
$585$		−	220364.i		−	0.643916i
$586$	−26727.8			−0.0778337
$587$	−258778.			−0.751020			−0.375510	−	0.926818i	$-0.622532\pi$
$587$	−258778.			−0.751020			−0.375510	+	0.926818i	$0.622532\pi$
$588$			434027.i			1.25534i
$589$	−266522.	+	263190.i	−0.768250	+	0.758645i
$590$	−365255.			−1.04928
$591$		−	370665.i		−	1.06122i
$592$			19380.2i			0.0552986i
$593$	−603214.			−1.71539			−0.857693	−	0.514162i	$-0.828103\pi$
$593$	−603214.			−1.71539			−0.857693	+	0.514162i	$0.828103\pi$
$594$	157300.			0.445816
$595$	−552037.			−1.55932
$596$	321979.			0.906430
$597$			600975.i			1.68619i
$598$	−176435.			−0.493381
$599$		−	32971.2i		−	0.0918927i	−0.998944	−	0.0459464i	$-0.985370\pi$
$599$		−	32971.2i		−	0.0918927i	0.998944	−	0.0459464i	$-0.0146303\pi$
$600$	−15433.3			−0.0428703
$601$		−	61000.3i		−	0.168882i	−0.996428	−	0.0844410i	$-0.973090\pi$
$601$		−	61000.3i		−	0.168882i	0.996428	−	0.0844410i	$-0.0269104\pi$
$602$			564086.i			1.55651i
$603$		−	253671.i		−	0.697647i
$604$		−	135457.i		−	0.371303i
$605$	38688.6			0.105699
$606$	−145648.			−0.396605
$607$		−	252238.i		−	0.684594i	−0.939592	−	0.342297i	$-0.888795\pi$
$607$		−	252238.i		−	0.684594i	0.939592	−	0.342297i	$-0.111205\pi$
$608$	−46497.7	+	45916.4i	−0.125784	+	0.124211i
$609$	1.05432e6			2.84273
$610$			116974.i			0.314361i
$611$			193769.i			0.519041i
$612$	−70868.6			−0.189213
$613$	384604.			1.02351			0.511757	−	0.859131i	$-0.328995\pi$
$613$	384604.			1.02351			0.511757	+	0.859131i	$0.328995\pi$
$614$	−318544.			−0.844953
$615$	502633.			1.32893
$616$			223522.i			0.589058i
$617$	89917.4			0.236197			0.118098	−	0.993002i	$-0.462320\pi$
$617$	89917.4			0.236197			0.118098	+	0.993002i	$0.462320\pi$
$618$		−	267289.i		−	0.699847i
$619$	−133253.			−0.347772			−0.173886	−	0.984766i	$-0.555632\pi$
$619$	−133253.			−0.347772			−0.173886	+	0.984766i	$0.555632\pi$
$620$			217725.i			0.566402i
$621$			130404.i			0.338150i
$622$		−	214618.i		−	0.554735i
$623$			322523.i			0.830968i
$624$	−160663.			−0.412616
$625$	−426028.			−1.09063
$626$		−	313842.i		−	0.800870i
$627$	319128.	−	315139.i	0.811764	−	0.801616i
$628$	−45479.8			−0.115319
$629$		−	74028.0i		−	0.187109i
$630$		−	231441.i		−	0.583121i
$631$	250184.			0.628348			0.314174	−	0.949365i	$-0.398273\pi$
$631$	250184.			0.628348			0.314174	+	0.949365i	$0.398273\pi$
$632$	28601.1			0.0716059
$633$	−839705.			−2.09565
$634$	−180935.			−0.450136
$635$		−	118060.i		−	0.292788i
$636$	56841.1			0.140523
$637$		−	1.16171e6i		−	2.86299i
$638$	367074.			0.901804
$639$			148615.i			0.363966i
$640$			37984.6i			0.0927357i
$641$		−	601164.i		−	1.46311i	−0.681782	−	0.731555i	$-0.738795\pi$
$641$		−	601164.i		−	1.46311i	0.681782	−	0.731555i	$-0.261205\pi$
$642$			517099.i			1.25460i
$643$	379057.			0.916816			0.458408	−	0.888742i	$-0.348420\pi$
$643$	379057.			0.916816			0.458408	+	0.888742i	$0.348420\pi$
$644$	−185304.			−0.446799
$645$		−	657909.i		−	1.58142i
$646$	177611.	−	175391.i	0.425604	−	0.420283i
$647$	245678.			0.586892			0.293446	−	0.955976i	$-0.405198\pi$
$647$	245678.			0.586892			0.293446	+	0.955976i	$0.405198\pi$
$648$			185162.i			0.440962i
$649$		−	564918.i		−	1.34121i
$650$	41308.7			0.0977722
$651$	−967198.			−2.28220
$652$	244405.			0.574929
$653$	−15905.7			−0.0373016			−0.0186508	−	0.999826i	$-0.505937\pi$
$653$	−15905.7			−0.0373016			−0.0186508	+	0.999826i	$0.505937\pi$
$654$			6290.45i			0.0147071i
$655$	−724102.			−1.68779
$656$		−	113268.i		−	0.263209i
$657$	−254308.			−0.589154
$658$			203509.i			0.470036i
$659$		−	481053.i		−	1.10770i	−0.832617	−	0.553850i	$-0.813158\pi$
$659$		−	481053.i		−	1.10770i	0.832617	−	0.553850i	$-0.186842\pi$
$660$		−	260700.i		−	0.598484i
$661$			468775.i			1.07290i	0.843931	+	0.536452i	$0.180236\pi$
$661$			468775.i			1.07290i	−0.843931	+	0.536452i	$0.819764\pi$
$662$	−224754.			−0.512852
$663$	613697.			1.39613
$664$		−	23082.0i		−	0.0523526i
$665$	572787.	+	580038.i	1.29524	+	1.31164i
$666$	31036.1			0.0699711
$667$			304311.i			0.684015i
$668$			225932.i			0.506320i
$669$	332994.			0.744020
$670$	519352.			1.15694
$671$	−180917.			−0.401822
$672$	−168738.			−0.373659
$673$		−	229158.i		−	0.505947i	−0.967473	−	0.252973i	$-0.918592\pi$
$673$		−	229158.i		−	0.505947i	0.967473	−	0.252973i	$-0.0814085\pi$
$674$	−7862.46			−0.0173077
$675$		−	30531.6i		−	0.0670103i
$676$	201541.			0.441033
$677$			38248.1i			0.0834512i	0.999129	+	0.0417256i	$0.0132855\pi$
$677$			38248.1i			0.0834512i	−0.999129	+	0.0417256i	$0.986714\pi$
$678$			130953.i			0.284876i
$679$			1.12271e6i			2.43516i
$680$		−	145093.i		−	0.313782i
$681$	−880274.			−1.89812
$682$	−336743.			−0.723985
$683$		−	31694.5i		−	0.0679426i	−0.999423	−	0.0339713i	$-0.989185\pi$
$683$		−	31694.5i		−	0.0679426i	0.999423	−	0.0339713i	$-0.0108155\pi$
$684$	73532.3	+	74463.2i	0.157169	+	0.159158i
$685$	−216402.			−0.461190
$686$		−	635459.i		−	1.35033i
$687$			1.00899e6i			2.13783i
$688$	−148260.			−0.313217
$689$	−152141.			−0.320484
$690$	216125.			0.453948
$691$	140291.			0.293815			0.146907	−	0.989150i	$-0.453068\pi$
$691$	140291.			0.293815			0.146907	+	0.989150i	$0.453068\pi$
$692$			285384.i			0.595961i
$693$	357956.			0.745355
$694$		−	44485.7i		−	0.0923637i
$695$	−719609.			−1.48980
$696$			277107.i			0.572044i
$697$			432660.i			0.890597i
$698$		−	118179.i		−	0.242565i
$699$			36587.3i			0.0748818i
$700$	43385.1			0.0885410
$701$	550797.			1.12087			0.560436	−	0.828198i	$-0.310634\pi$
$701$	550797.			1.12087			0.560436	+	0.828198i	$0.310634\pi$
$702$		−	317838.i		−	0.644958i
$703$	−77782.9	+	76810.5i	−0.157389	+	0.155421i
$704$	−58748.5			−0.118536
$705$		−	237358.i		−	0.477557i
$706$			111135.i			0.222967i
$707$	409435.			0.819117
$708$	426461.			0.850772
$709$	725719.			1.44370			0.721848	−	0.692051i	$-0.243293\pi$
$709$	725719.			1.44370			0.721848	+	0.692051i	$0.243293\pi$
$710$	−304267.			−0.603584
$711$		−	45802.9i		−	0.0906053i
$712$	−84769.1			−0.167216
$713$		−	279166.i		−	0.549140i
$714$	644544.			1.26432
$715$			697787.i			1.36493i
$716$		−	274972.i		−	0.536367i
$717$		−	388903.i		−	0.756489i
$718$			455275.i			0.883131i
$719$	184282.			0.356472			0.178236	−	0.983988i	$-0.442961\pi$
$719$	184282.			0.356472			0.178236	+	0.983988i	$0.442961\pi$
$720$	60829.9			0.117342
$721$			751384.i			1.44541i
$722$	−368574.	−	4636.83i	−0.707051	−	0.00889501i
$723$	−620985.			−1.18797
$724$		−	233561.i		−	0.445577i
$725$		−	71248.3i		−	0.135550i
$726$	−45171.8			−0.0857027
$727$	−30302.5			−0.0573336			−0.0286668	−	0.999589i	$-0.509126\pi$
$727$	−30302.5			−0.0573336			−0.0286668	+	0.999589i	$0.509126\pi$
$728$	451645.			0.852186
$729$	−128557.			−0.241902
$730$		−	520657.i		−	0.977025i
$731$	566319.			1.05981
$732$		−	136575.i		−	0.254889i
$733$	210592.			0.391954			0.195977	−	0.980609i	$-0.437212\pi$
$733$	210592.			0.391954			0.195977	+	0.980609i	$0.437212\pi$
$734$			56102.9i			0.104134i
$735$			1.42304e6i			2.63417i
$736$		−	48703.6i		−	0.0899094i
$737$			803252.i			1.47883i
$738$	−181392.			−0.333047
$739$	−257029.			−0.470645			−0.235323	−	0.971917i	$-0.575615\pi$
$739$	−257029.			−0.470645			−0.235323	+	0.971917i	$0.575615\pi$
$740$			63541.8i			0.116037i
$741$	−636764.	−	644825.i	−1.15969	−	1.17437i
$742$	−159788.			−0.290226
$743$		−	459249.i		−	0.831899i	−0.909388	−	0.415949i	$-0.863449\pi$
$743$		−	459249.i		−	0.831899i	0.909388	−	0.415949i	$-0.136551\pi$
$744$		−	254210.i		−	0.459247i
$745$	1.05567e6			1.90203
$746$	40909.0			0.0735091
$747$	−36964.5			−0.0662435
$748$	224407.			0.401081
$749$		−	1.45364e6i		−	2.59115i
$750$	451450.			0.802578
$751$		−	705805.i		−	1.25142i	−0.780054	−	0.625712i	$-0.784808\pi$
$751$		−	705805.i		−	1.25142i	0.780054	−	0.625712i	$-0.215192\pi$
$752$	−53488.4			−0.0945854
$753$			568305.i			1.00228i
$754$		−	741704.i		−	1.30463i
$755$		−	444124.i		−	0.779130i
$756$		−	333814.i		−	0.584064i
$757$	128249.			0.223801			0.111901	−	0.993719i	$-0.464306\pi$
$757$	128249.			0.223801			0.111901	+	0.993719i	$0.464306\pi$
$758$	73348.8			0.127660
$759$			334267.i			0.580244i
$760$	−152452.	+	150546.i	−0.263941	+	0.260641i
$761$	779962.			1.34680			0.673402	−	0.739277i	$-0.264833\pi$
$761$	779962.			1.34680			0.673402	+	0.739277i	$0.264833\pi$
$762$			137843.i			0.237397i
$763$		−	17683.3i		−	0.0303749i
$764$	−107986.			−0.185004
$765$	−232357.			−0.397039
$766$	27251.8			0.0464449
$767$	−1.14147e6			−1.94031
$768$		−	44349.7i		−	0.0751915i
$769$	−50722.8			−0.0857730			−0.0428865	−	0.999080i	$-0.513655\pi$
$769$	−50722.8			−0.0857730			−0.0428865	+	0.999080i	$0.513655\pi$
$770$			732861.i			1.23606i
$771$	−922754.			−1.55230
$772$			166558.i			0.279467i
$773$			942086.i			1.57664i	0.615267	+	0.788318i	$0.289048\pi$
$773$			942086.i			1.57664i	−0.615267	+	0.788318i	$0.710952\pi$
$774$			237428.i			0.396324i
$775$			65361.0i			0.108822i
$776$	−295083.			−0.490028
$777$	−282271.			−0.467546
$778$			288188.i			0.476120i
$779$	454606.	−	448922.i	0.749135	−	0.739769i
$780$	−526766.			−0.865821
$781$		−	470592.i		−	0.771511i
$782$			186037.i			0.304219i
$783$	−548199.			−0.894159
$784$	320683.			0.521727
$785$	−149115.			−0.241981
$786$	845443.			1.36848
$787$		−	764737.i		−	1.23470i	−0.786687	−	0.617352i	$-0.788206\pi$
$787$		−	764737.i		−	1.23470i	0.786687	−	0.617352i	$-0.211794\pi$
$788$	−273868.			−0.441051
$789$			298186.i			0.478998i
$790$	93774.6			0.150256
$791$		−	368127.i		−	0.588362i
$792$			94082.1i			0.149988i
$793$			365557.i			0.581312i
$794$			283298.i			0.449368i
$795$	186365.			0.294870
$796$	444033.			0.700792
$797$		−	555222.i		−	0.874077i	−0.899443	−	0.437039i	$-0.856027\pi$
$797$		−	555222.i		−	0.874077i	0.899443	−	0.437039i	$-0.143973\pi$
$798$	−668771.	−	677237.i	−1.05020	−	1.06349i
$799$	204314.			0.320040
$800$			11403.0i			0.0178171i
$801$			135752.i			0.211584i
$802$	−47224.7			−0.0734211
$803$	805270.			1.24885
$804$	−606382.			−0.938068
$805$	−607555.			−0.937549
$806$			680417.i			1.04738i
$807$	−637527.			−0.978930
$808$			107612.i			0.164831i
$809$	−94777.3			−0.144813			−0.0724065	−	0.997375i	$-0.523068\pi$
$809$	−94777.3			−0.144813			−0.0724065	+	0.997375i	$0.523068\pi$
$810$			607090.i			0.925302i
$811$			68642.4i			0.104364i	0.998638	+	0.0521820i	$0.0166176\pi$
$811$			68642.4i			0.104364i	−0.998638	+	0.0521820i	$0.983382\pi$
$812$		−	778986.i		−	1.18146i
$813$		−	1.08227e6i		−	1.63740i
$814$	−98276.4			−0.148320
$815$	801330.			1.20641
$816$			169406.i			0.254419i
$817$	−587606.	−	595045.i	−0.880323	−	0.891467i
$818$	−3320.42			−0.00496233
$819$		−	723281.i		−	1.07830i
$820$		−	371373.i		−	0.552309i
$821$	601916.			0.892996			0.446498	−	0.894785i	$-0.352671\pi$
$821$	601916.			0.892996			0.446498	+	0.894785i	$0.352671\pi$
$822$	252665.			0.373940
$823$	−307730.			−0.454329			−0.227165	−	0.973856i	$-0.572946\pi$
$823$	−307730.			−0.454329			−0.227165	+	0.973856i	$0.572946\pi$
$824$	−197487.			−0.290860
$825$		−	78262.0i		−	0.114986i
$826$	−1.19884e6			−1.75712
$827$			194825.i			0.284862i	0.989805	+	0.142431i	$0.0454919\pi$
$827$			194825.i			0.284862i	−0.989805	+	0.142431i	$0.954508\pi$
$828$	−77995.7			−0.113765
$829$			1.14738e6i			1.66955i	0.550592	+	0.834774i	$0.314402\pi$
$829$			1.14738e6i			1.66955i	−0.550592	+	0.834774i	$0.685598\pi$
$830$		−	75679.2i		−	0.109855i
$831$		−	717848.i		−	1.03951i
$832$			118706.i			0.171486i
$833$	−1.22494e6			−1.76532
$834$	840196.			1.20795
$835$			740765.i			1.06245i
$836$	−232841.	−	235789.i	−0.333156	−	0.337374i
$837$	502901.			0.717846
$838$		−	593860.i		−	0.845661i
$839$		−	283733.i		−	0.403075i	−0.979481	−	0.201538i	$-0.935406\pi$
$839$		−	283733.i		−	0.403075i	0.979481	−	0.201538i	$-0.0645938\pi$
$840$	−553243.			−0.784075
$841$	−571993.			−0.808721
$842$	704608.			0.993856
$843$	−595754.			−0.838324
$844$			620420.i			0.870965i
$845$	660795.			0.925450
$846$			85658.4i			0.119682i
$847$	126984.			0.177004
$848$		−	41997.3i		−	0.0584023i
$849$		−	114504.i		−	0.158857i
$850$		−	43556.8i		−	0.0602863i
$851$		−	81472.9i		−	0.112500i
$852$	355254.			0.489395
$853$	975341.			1.34047			0.670237	−	0.742147i	$-0.266193\pi$
$853$	975341.			1.34047			0.670237	+	0.742147i	$0.266193\pi$
$854$			383932.i			0.526428i
$855$	241091.	+	244143.i	0.329798	+	0.333973i
$856$	382061.			0.521417
$857$		−	5569.67i		−	0.00758347i	−0.999993	−	0.00379173i	$-0.998793\pi$
$857$		−	5569.67i		−	0.00758347i	0.999993	−	0.00379173i	$-0.00120695\pi$
$858$		−	814718.i		−	1.10671i
$859$	312767.			0.423871			0.211936	−	0.977284i	$-0.432023\pi$
$859$	312767.			0.423871			0.211936	+	0.977284i	$0.432023\pi$
$860$	−486099.			−0.657246
$861$	1.64975e6			2.22541
$862$	359060.			0.483228
$863$			359441.i			0.482621i	0.970448	+	0.241311i	$0.0775773\pi$
$863$			359441.i			0.482621i	−0.970448	+	0.241311i	$0.922423\pi$
$864$	87736.7			0.117531
$865$			935690.i			1.25055i
$866$	−925865.			−1.23456
$867$			257234.i			0.342208i
$868$			714618.i			0.948494i
$869$			145036.i			0.192059i
$870$			908553.i			1.20036i
$871$	1.62304e6			2.13940
$872$	4647.73			0.00611234
$873$			472557.i			0.620049i
$874$	195473.	−	193030.i	0.255897	−	0.252698i
$875$	−1.26909e6			−1.65758
$876$			607905.i			0.792187i
$877$			415375.i			0.540059i	0.962852	+	0.270030i	$0.0870335\pi$
$877$			415375.i			0.540059i	−0.962852	+	0.270030i	$0.912967\pi$
$878$	−915172.			−1.18717
$879$	102317.			0.132425
$880$	−192619.			−0.248733
$881$	−403508.			−0.519876			−0.259938	−	0.965625i	$-0.583702\pi$
$881$	−403508.			−0.519876			−0.259938	+	0.965625i	$0.583702\pi$
$882$		−	513553.i		−	0.660158i
$883$	265307.			0.340273			0.170137	−	0.985420i	$-0.445579\pi$
$883$	265307.			0.340273			0.170137	+	0.985420i	$0.445579\pi$
$884$		−	453433.i		−	0.580241i
$885$	1.39824e6			1.78523
$886$			532700.i			0.678603i
$887$			264831.i			0.336605i	0.985735	+	0.168303i	$0.0538286\pi$
$887$			264831.i			0.336605i	−0.985735	+	0.168303i	$0.946171\pi$
$888$		−	74189.7i		−	0.0940844i
$889$		−	387496.i		−	0.490302i
$890$	−277933.			−0.350881
$891$	−938952.			−1.18274
$892$		−	246034.i		−	0.309219i
$893$	−211994.	−	214678.i	−0.265840	−	0.269205i
$894$	−1.23257e6			−1.54219
$895$		−	901551.i		−	1.12550i
$896$			124673.i			0.155295i
$897$	675416.			0.839433
$898$	88262.9			0.109452
$899$	1.17357e6			1.45207
$900$	18261.1			0.0225446
$901$			160421.i			0.197611i
$902$	574381.			0.705971
$903$		−	2.15939e6i		−	2.64823i
$904$	96755.3			0.118396
$905$		−	765776.i		−	0.934985i
$906$			518547.i			0.631731i
$907$			1.43037e6i			1.73874i	0.494165	+	0.869368i	$0.335474\pi$
$907$			1.43037e6i			1.73874i	−0.494165	+	0.869368i	$0.664526\pi$
$908$			650394.i			0.788869i
$909$	172334.			0.208566
$910$	1.48081e6			1.78820
$911$			1.14296e6i			1.37719i	0.725148	+	0.688593i	$0.241771\pi$
$911$			1.14296e6i			1.37719i	−0.725148	+	0.688593i	$0.758229\pi$
$912$	177999.	−	175774.i	0.214007	−	0.211332i
$913$	117049.			0.140419
$914$			253676.i			0.303660i
$915$		−	447790.i		−	0.534851i
$916$	745496.			0.888494
$917$	−2.37665e6			−2.82636
$918$	−335135.			−0.397681
$919$	−627508.			−0.742999			−0.371500	−	0.928433i	$-0.621156\pi$
$919$	−627508.			−0.742999			−0.371500	+	0.928433i	$0.621156\pi$
$920$		−	159685.i		−	0.188663i
$921$	1.21943e6			1.43759
$922$		−	201411.i		−	0.236931i
$923$	−950871.			−1.11614
$924$		−	855669.i		−	1.00222i
$925$			19075.2i			0.0222939i
$926$		−	272866.i		−	0.318220i
$927$			316263.i			0.368035i
$928$	204742.			0.237745
$929$	−1.63447e6			−1.89385			−0.946924	−	0.321458i	$-0.895827\pi$
$929$	−1.63447e6			−1.89385			−0.946924	+	0.321458i	$0.895827\pi$
$930$		−	833479.i		−	0.963670i
$931$	1.27098e6	+	1.28707e6i	1.46636	+	1.48492i
$932$	27032.7			0.0311213
$933$			821585.i			0.943820i
$934$			953752.i			1.09331i
$935$	735762.			0.841617
$936$	190101.			0.216986
$937$	−55506.2			−0.0632211			−0.0316106	−	0.999500i	$-0.510064\pi$
$937$	−55506.2			−0.0632211			−0.0316106	+	0.999500i	$0.510064\pi$
$938$	1.70462e6			1.93741
$939$			1.20143e6i			1.36259i
$940$	−175373.			−0.198475
$941$		−	1.60327e6i		−	1.81062i	−0.424747	−	0.905312i	$-0.639637\pi$
$941$		−	1.60327e6i		−	1.81062i	0.424747	−	0.905312i	$-0.360363\pi$
$942$	174102.			0.196202
$943$			476172.i			0.535476i
$944$		−	315093.i		−	0.353586i
$945$		−	1.09448e6i		−	1.22558i
$946$		−	751822.i		−	0.840103i
$947$	165986.			0.185086			0.0925428	−	0.995709i	$-0.470501\pi$
$947$	165986.			0.185086			0.0925428	+	0.995709i	$0.470501\pi$
$948$	−109489.			−0.121830
$949$		−	1.62712e6i		−	1.80670i
$950$	−45766.2	+	45194.0i	−0.0507104	+	0.0500765i
$951$	692642.			0.765857
$952$		−	476224.i		−	0.525457i
$953$			821794.i			0.904851i	0.891802	+	0.452426i	$0.149441\pi$
$953$			821794.i			0.904851i	−0.891802	+	0.452426i	$0.850559\pi$
$954$	−67256.0			−0.0738983
$955$	−354054.			−0.388206
$956$	−287342.			−0.314401
$957$	−1.40521e6			−1.53432
$958$			358317.i			0.390424i
$959$	−710276.			−0.772307
$960$		−	145410.i		−	0.157780i
$961$	−153074.			−0.165750
$962$			198576.i			0.214574i
$963$		−	611847.i		−	0.659766i
$964$			458817.i			0.493726i
$965$			546093.i			0.586424i
$966$	709365.			0.760179
$967$	−859901.			−0.919593			−0.459796	−	0.888024i	$-0.652078\pi$
$967$	−859901.			−0.919593			−0.459796	+	0.888024i	$0.652078\pi$
$968$			33375.4i			0.0356185i
$969$	−679918.	+	671418.i	−0.724118	+	0.715065i
$970$	−967490.			−1.02826
$971$			1.15671e6i			1.22684i	0.789759	+	0.613418i	$0.210206\pi$
$971$			1.15671e6i			1.22684i	−0.789759	+	0.613418i	$0.789794\pi$
$972$		−	394749.i		−	0.417819i
$973$	−2.36191e6			−2.49481
$974$	661459.			0.697245
$975$	−158135.			−0.166349
$976$	−100909.			−0.105933
$977$			627667.i			0.657567i	0.944405	+	0.328784i	$0.106639\pi$
$977$			627667.i			0.657567i	−0.944405	+	0.328784i	$0.893361\pi$
$978$	−935611.			−0.978178
$979$		−	429862.i		−	0.448502i
$980$	1.05142e6			1.09478
$981$		−	7443.05i		−	0.00773415i
$982$		−	1.19905e6i		−	1.24341i
$983$		−	1.45983e6i		−	1.51075i	−0.655290	−	0.755377i	$-0.727454\pi$
$983$		−	1.45983e6i		−	1.51075i	0.655290	−	0.755377i	$-0.272546\pi$
$984$			433605.i			0.447820i
$985$	−897931.			−0.925487
$986$	−782070.			−0.804436
$987$		−	779056.i		−	0.799714i
$988$	−476432.	+	470476.i	−0.488075	+	0.481974i
$989$	623273.			0.637215
$990$			308467.i			0.314730i
$991$		−	977409.i		−	0.995243i	−0.867394	−	0.497621i	$-0.834207\pi$
$991$		−	977409.i		−	0.995243i	0.867394	−	0.497621i	$-0.165793\pi$
$992$	−187824.			−0.190866
$993$	860388.			0.872561
$994$	−998666.			−1.01076
$995$	1.45585e6			1.47052
$996$			88361.0i			0.0890721i
$997$	1.39372e6			1.40212			0.701059	−	0.713104i	$-0.252711\pi$
$997$	1.39372e6			1.40212			0.701059	+	0.713104i	$0.252711\pi$
$998$		−	497645.i		−	0.499642i
$999$	146769.			0.147063

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	38.5.b.a.37.5	yes	8
3.2	odd	2		342.5.d.a.37.3		8
4.3	odd	2		304.5.e.e.113.7		8
19.18	odd	2	inner	38.5.b.a.37.4	✓	8
57.56	even	2		342.5.d.a.37.7		8
76.75	even	2		304.5.e.e.113.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
38.5.b.a.37.4	✓	8	19.18	odd	2	inner
38.5.b.a.37.5	yes	8	1.1	even	1	trivial
304.5.e.e.113.2		8	76.75	even	2
304.5.e.e.113.7		8	4.3	odd	2
342.5.d.a.37.3		8	3.2	odd	2
342.5.d.a.37.7		8	57.56	even	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)

\(f(q)\)	\(=\)	\(q+2.82843i q^{2} -10.8276i q^{3} -8.00000 q^{4} -26.2296 q^{5} +30.6250 q^{6} -86.0910 q^{7} -22.6274i q^{8} -36.2364 q^{9} +O(q^{10})\)	\(q+2.82843i q^{2} -10.8276i q^{3} -8.00000 q^{4} -26.2296 q^{5} +30.6250 q^{6} -86.0910 q^{7} -22.6274i q^{8} -36.2364 q^{9} -74.1886i q^{10} +114.743 q^{11} +86.6206i q^{12} -231.848i q^{13} -243.502i q^{14} +284.003i q^{15} +64.0000 q^{16} -244.466 q^{17} -102.492i q^{18} +(253.655 + 256.866i) q^{19} +209.837 q^{20} +932.157i q^{21} +324.543i q^{22} -269.052 q^{23} -245.000 q^{24} +62.9931 q^{25} +655.766 q^{26} -484.681i q^{27} +688.728 q^{28} -1131.05i q^{29} -803.282 q^{30} +1037.59i q^{31} +181.019i q^{32} -1242.39i q^{33} -691.455i q^{34} +2258.14 q^{35} +289.891 q^{36} +302.815i q^{37} +(-726.527 + 717.444i) q^{38} -2510.36 q^{39} +593.509i q^{40} -1769.82i q^{41} -2636.54 q^{42} -2316.56 q^{43} -917.946 q^{44} +950.467 q^{45} -760.993i q^{46} -835.757 q^{47} -692.965i q^{48} +5010.66 q^{49} +178.171i q^{50} +2646.98i q^{51} +1854.79i q^{52} -656.208i q^{53} +1370.89 q^{54} -3009.67 q^{55} +1948.02i q^{56} +(2781.24 - 2746.47i) q^{57} +3199.09 q^{58} -4923.33i q^{59} -2272.03i q^{60} -1576.71 q^{61} -2934.75 q^{62} +3119.63 q^{63} -512.000 q^{64} +6081.30i q^{65} +3514.01 q^{66} +7000.44i q^{67} +1955.73 q^{68} +2913.18i q^{69} +6386.97i q^{70} -4101.26i q^{71} +819.936i q^{72} +7018.02 q^{73} -856.490 q^{74} -682.062i q^{75} +(-2029.24 - 2054.93i) q^{76} -9878.36 q^{77} -7100.36i q^{78} +1264.00i q^{79} -1678.70 q^{80} -8183.07 q^{81} +5005.79 q^{82} +1020.09 q^{83} -7457.26i q^{84} +6412.25 q^{85} -6552.21i q^{86} -12246.5 q^{87} -2596.34i q^{88} -3746.30i q^{89} +2688.33i q^{90} +19960.1i q^{91} +2152.41 q^{92} +11234.6 q^{93} -2363.88i q^{94} +(-6653.27 - 6737.50i) q^{95} +1960.00 q^{96} -13041.0i q^{97} +14172.3i q^{98} -4157.88 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 64 q^{4} + 18 q^{5} - 32 q^{6} - 162 q^{7} - 268 q^{9}+O(q^{10}) \) 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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