LMFDB - Embedded newform 13.5.f.a.11.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [13,5,Mod(2,13)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(13, base_ring=CyclotomicField(12))

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("13.2");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 13 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	13.f (of order $12$, degree $4$, 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:	$1.34380952009$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{12})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 152 x^{14} + 9190 x^{12} + 285720 x^{10} + 4862025 x^{8} + 43573680 x^{6} + 169417008 x^{4} + \cdots + 3779136 $ x^16 + 152x^14 + 9190x^12 + 285720x^10 + 4862025x^8 + 43573680x^6 + 169417008x^4 + 100636992*x^2 + 3779136
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 2^{4}\cdot 3^{2}\cdot 13^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			11.3
Root			$-3.68702i$ of defining polynomial
Character	$\chi$	$=$	13.11
Dual form			13.5.f.a.6.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.540374 - 2.01670i) q^{2} +(-8.21171 - 14.2231i) q^{3} +(10.0813 + 5.82045i) q^{4} +(17.2508 + 17.2508i) q^{5} +(-33.1212 + 8.87479i) q^{6} +(-2.95016 - 11.0101i) q^{7} +(40.8071 - 40.8071i) q^{8} +(-94.3643 + 163.444i) q^{9} +O(q^{10})$	\(q+(0.540374 - 2.01670i) q^{2} +(-8.21171 - 14.2231i) q^{3} +(10.0813 + 5.82045i) q^{4} +(17.2508 + 17.2508i) q^{5} +(-33.1212 + 8.87479i) q^{6} +(-2.95016 - 11.0101i) q^{7} +(40.8071 - 40.8071i) q^{8} +(-94.3643 + 163.444i) q^{9} +(44.1117 - 25.4679i) q^{10} +(101.675 + 27.2438i) q^{11} -191.183i q^{12} +(-166.736 + 27.5674i) q^{13} -23.7984 q^{14} +(103.701 - 387.019i) q^{15} +(32.8825 + 56.9542i) q^{16} +(65.7171 + 37.9418i) q^{17} +(278.626 + 278.626i) q^{18} +(-313.811 + 84.0854i) q^{19} +(73.5035 + 274.319i) q^{20} +(-132.372 + 132.372i) q^{21} +(109.885 - 190.327i) q^{22} +(-174.829 + 100.938i) q^{23} +(-915.499 - 245.307i) q^{24} -29.8174i q^{25} +(-34.5048 + 351.155i) q^{26} +1769.27 q^{27} +(34.3425 - 128.168i) q^{28} +(432.185 + 748.566i) q^{29} +(-724.465 - 418.270i) q^{30} +(-767.381 - 767.381i) q^{31} +(1024.52 - 274.521i) q^{32} +(-447.436 - 1669.85i) q^{33} +(112.029 - 112.029i) q^{34} +(139.041 - 240.827i) q^{35} +(-1902.63 + 1098.49i) q^{36} +(-756.260 - 202.639i) q^{37} +678.302i q^{38} +(1761.28 + 2145.13i) q^{39} +1407.91 q^{40} +(308.517 - 1151.40i) q^{41} +(195.425 + 338.486i) q^{42} +(318.080 + 183.644i) q^{43} +(866.449 + 866.449i) q^{44} +(-4447.40 + 1191.68i) q^{45} +(109.088 + 407.123i) q^{46} +(-308.850 + 308.850i) q^{47} +(540.043 - 935.382i) q^{48} +(1966.81 - 1135.54i) q^{49} +(-60.1328 - 16.1125i) q^{50} -1246.27i q^{51} +(-1841.38 - 692.566i) q^{52} -2120.08 q^{53} +(956.069 - 3568.10i) q^{54} +(1284.00 + 2223.96i) q^{55} +(-569.679 - 328.904i) q^{56} +(3772.88 + 3772.88i) q^{57} +(1743.18 - 467.083i) q^{58} +(-1468.47 - 5480.39i) q^{59} +(3298.07 - 3298.07i) q^{60} +(-2851.77 + 4939.42i) q^{61} +(-1962.25 + 1132.91i) q^{62} +(2077.93 + 556.779i) q^{63} -1162.27i q^{64} +(-3351.90 - 2400.78i) q^{65} -3609.38 q^{66} +(-525.691 + 1961.90i) q^{67} +(441.677 + 765.007i) q^{68} +(2871.29 + 1657.74i) q^{69} +(-410.542 - 410.542i) q^{70} +(1510.63 - 404.773i) q^{71} +(2818.93 + 10520.4i) q^{72} +(-1577.77 + 1577.77i) q^{73} +(-817.326 + 1415.65i) q^{74} +(-424.095 + 244.852i) q^{75} +(-3653.04 - 978.830i) q^{76} -1199.83i q^{77} +(5277.85 - 2392.81i) q^{78} +4448.61 q^{79} +(-415.256 + 1549.76i) q^{80} +(-6885.24 - 11925.6i) q^{81} +(-2155.32 - 1244.38i) q^{82} +(-4026.77 - 4026.77i) q^{83} +(-2104.95 + 564.021i) q^{84} +(479.148 + 1788.20i) q^{85} +(542.237 - 542.237i) q^{86} +(7097.95 - 12294.0i) q^{87} +(5260.81 - 3037.33i) q^{88} +(10633.9 + 2849.33i) q^{89} +9613.05i q^{90} +(795.419 + 1754.46i) q^{91} -2350.01 q^{92} +(-4613.03 + 17216.0i) q^{93} +(455.964 + 789.753i) q^{94} +(-6864.05 - 3962.96i) q^{95} +(-12317.6 - 12317.6i) q^{96} +(16595.6 - 4446.77i) q^{97} +(-1227.23 - 4580.08i) q^{98} +(-14047.3 + 14047.3i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 4 q^{2} - 2 q^{3} - 6 q^{4} + 8 q^{5} - 38 q^{6} + 56 q^{7} + 90 q^{8} - 164 q^{9}+O(q^{10}) $ 16 * q - 4 * q^2 - 2 * q^3 - 6 * q^4 + 8 * q^5 - 38 * q^6 + 56 * q^7 + 90 * q^8 - 164 * q^9	\( 16 q - 4 q^{2} - 2 q^{3} - 6 q^{4} + 8 q^{5} - 38 q^{6} + 56 q^{7} + 90 q^{8} - 164 q^{9} - 486 q^{10} - 100 q^{11} + 294 q^{13} + 808 q^{14} + 346 q^{15} + 230 q^{16} + 984 q^{17} + 2434 q^{18} - 1498 q^{19} - 3962 q^{20} - 1076 q^{21} - 1524 q^{22} - 1014 q^{23} - 2142 q^{24} + 614 q^{26} + 3352 q^{27} + 5764 q^{28} + 814 q^{29} + 9162 q^{30} + 4060 q^{31} - 4996 q^{32} - 5636 q^{33} - 2502 q^{34} - 4892 q^{35} - 15750 q^{36} - 1790 q^{37} + 6982 q^{39} + 18816 q^{40} + 4280 q^{41} - 1204 q^{42} - 1368 q^{43} + 10736 q^{44} - 6806 q^{45} - 15246 q^{46} + 1484 q^{47} - 3002 q^{48} - 11820 q^{49} - 13574 q^{50} + 1432 q^{52} + 7204 q^{53} + 13240 q^{54} + 6936 q^{55} + 8124 q^{56} + 12736 q^{57} + 3030 q^{58} - 2380 q^{59} - 6472 q^{60} - 162 q^{61} + 19614 q^{62} + 12004 q^{63} - 5248 q^{65} - 23872 q^{66} - 14854 q^{67} - 6444 q^{68} + 2412 q^{69} - 34524 q^{70} - 8050 q^{71} + 15420 q^{72} - 15448 q^{73} - 2882 q^{74} + 8280 q^{75} + 10622 q^{76} - 11672 q^{78} - 17064 q^{79} + 2564 q^{80} + 2128 q^{81} - 5346 q^{82} + 12788 q^{83} + 25948 q^{84} + 35382 q^{85} + 67260 q^{86} + 29342 q^{87} + 40836 q^{88} + 20492 q^{89} + 8996 q^{91} - 49884 q^{92} - 78920 q^{93} - 30606 q^{94} - 98574 q^{95} - 94664 q^{96} + 50944 q^{97} + 61484 q^{98} - 21632 q^{99}+O(q^{100}) \) 16 * q - 4 * q^2 - 2 * q^3 - 6 * q^4 + 8 * q^5 - 38 * q^6 + 56 * q^7 + 90 * q^8 - 164 * q^9 - 486 * q^10 - 100 * q^11 + 294 * q^13 + 808 * q^14 + 346 * q^15 + 230 * q^16 + 984 * q^17 + 2434 * q^18 - 1498 * q^19 - 3962 * q^20 - 1076 * q^21 - 1524 * q^22 - 1014 * q^23 - 2142 * q^24 + 614 * q^26 + 3352 * q^27 + 5764 * q^28 + 814 * q^29 + 9162 * q^30 + 4060 * q^31 - 4996 * q^32 - 5636 * q^33 - 2502 * q^34 - 4892 * q^35 - 15750 * q^36 - 1790 * q^37 + 6982 * q^39 + 18816 * q^40 + 4280 * q^41 - 1204 * q^42 - 1368 * q^43 + 10736 * q^44 - 6806 * q^45 - 15246 * q^46 + 1484 * q^47 - 3002 * q^48 - 11820 * q^49 - 13574 * q^50 + 1432 * q^52 + 7204 * q^53 + 13240 * q^54 + 6936 * q^55 + 8124 * q^56 + 12736 * q^57 + 3030 * q^58 - 2380 * q^59 - 6472 * q^60 - 162 * q^61 + 19614 * q^62 + 12004 * q^63 - 5248 * q^65 - 23872 * q^66 - 14854 * q^67 - 6444 * q^68 + 2412 * q^69 - 34524 * q^70 - 8050 * q^71 + 15420 * q^72 - 15448 * q^73 - 2882 * q^74 + 8280 * q^75 + 10622 * q^76 - 11672 * q^78 - 17064 * q^79 + 2564 * q^80 + 2128 * q^81 - 5346 * q^82 + 12788 * q^83 + 25948 * q^84 + 35382 * q^85 + 67260 * q^86 + 29342 * q^87 + 40836 * q^88 + 20492 * q^89 + 8996 * q^91 - 49884 * q^92 - 78920 * q^93 - 30606 * q^94 - 98574 * q^95 - 94664 * q^96 + 50944 * q^97 + 61484 * q^98 - 21632 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/13\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{7}{12}\right)$

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 $

$2$	0.540374	−	2.01670i	0.135094	−	0.504176i	−0.864904	−	0.501937i	$-0.832621\pi$
$2$	0.540374	−	2.01670i	0.135094	−	0.504176i	0.999997	−	0.00223854i	$-0.000712549\pi$
$3$	−8.21171	−	14.2231i	−0.912412	−	1.58034i	−0.810647	−	0.585536i	$-0.800884\pi$
$3$	−8.21171	−	14.2231i	−0.912412	−	1.58034i	−0.101765	−	0.994808i	$-0.532449\pi$
$4$	10.0813	+	5.82045i	0.630082	+	0.363778i
$5$	17.2508	+	17.2508i	0.690033	+	0.690033i	0.962239	−	0.272206i	$-0.0877531\pi$
$5$	17.2508	+	17.2508i	0.690033	+	0.690033i	−0.272206	+	0.962239i	$0.587753\pi$
$6$	−33.1212	+	8.87479i	−0.920032	+	0.246522i
$7$	−2.95016	−	11.0101i	−0.0602073	−	0.224697i	0.929266	−	0.369411i	$-0.120440\pi$
$7$	−2.95016	−	11.0101i	−0.0602073	−	0.224697i	−0.989474	+	0.144714i	$0.953774\pi$
$8$	40.8071	−	40.8071i	0.637611	−	0.637611i
$9$	−94.3643	+	163.444i	−1.16499	+	2.01782i
$10$	44.1117	−	25.4679i	0.441117	−	0.254679i
$11$	101.675	+	27.2438i	0.840291	+	0.225155i	0.653198	−	0.757187i	$-0.273427\pi$
$11$	101.675	+	27.2438i	0.840291	+	0.225155i	0.187093	+	0.982342i	$0.440093\pi$
$12$		−	191.183i		−	1.32766i
$13$	−166.736	+	27.5674i	−0.986606	+	0.163121i
$13$	−166.736	+	27.5674i	−0.986606	+	0.163121i
$14$	−23.7984			−0.121420
$15$	103.701	−	387.019i	0.460895	−	1.72008i
$16$	32.8825	+	56.9542i	0.128447	+	0.222477i
$17$	65.7171	+	37.9418i	0.227395	+	0.131287i	0.609370	−	0.792886i	$-0.291423\pi$
$17$	65.7171	+	37.9418i	0.227395	+	0.131287i	−0.381975	+	0.924173i	$0.624756\pi$
$18$	278.626	+	278.626i	0.859956	+	0.859956i
$19$	−313.811	+	84.0854i	−0.869283	+	0.232924i	−0.665778	−	0.746150i	$-0.731900\pi$
$19$	−313.811	+	84.0854i	−0.869283	+	0.232924i	−0.203505	+	0.979074i	$0.565233\pi$
$20$	73.5035	+	274.319i	0.183759	+	0.685797i
$21$	−132.372	+	132.372i	−0.300164	+	0.300164i
$22$	109.885	−	190.327i	0.227036	−	0.393237i
$23$	−174.829	+	100.938i	−0.330490	+	0.190809i	−0.656059	−	0.754710i	$-0.727778\pi$
$23$	−174.829	+	100.938i	−0.330490	+	0.190809i	0.325569	+	0.945518i	$0.394444\pi$
$24$	−915.499	−	245.307i	−1.58941	−	0.425881i
$25$		−	29.8174i		−	0.0477078i
$26$	−34.5048	+	351.155i	−0.0510426	+	0.519460i
$27$	1769.27			2.42698
$28$	34.3425	−	128.168i	0.0438042	−	0.163479i
$29$	432.185	+	748.566i	0.513894	+	0.890090i	0.999870	+	0.0161183i	$0.00513085\pi$
$29$	432.185	+	748.566i	0.513894	+	0.890090i	−0.485976	+	0.873972i	$0.661536\pi$
$30$	−724.465	−	418.270i	−0.804961	−	0.464745i
$31$	−767.381	−	767.381i	−0.798523	−	0.798523i	0.184339	−	0.982863i	$-0.440986\pi$
$31$	−767.381	−	767.381i	−0.798523	−	0.798523i	−0.982863	+	0.184339i	$0.940986\pi$
$32$	1024.52	−	274.521i	1.00051	−	0.268086i
$33$	−447.436	−	1669.85i	−0.410869	−	1.53338i
$34$	112.029	−	112.029i	0.0969111	−	0.0969111i
$35$	139.041	−	240.827i	0.113503	−	0.196593i
$36$	−1902.63	+	1098.49i	−1.46808	+	0.847597i
$37$	−756.260	−	202.639i	−0.552418	−	0.148020i	−0.0281971	−	0.999602i	$-0.508977\pi$
$37$	−756.260	−	202.639i	−0.552418	−	0.148020i	−0.524221	+	0.851583i	$0.675643\pi$
$38$			678.302i			0.469738i
$39$	1761.28	+	2145.13i	1.15798	+	1.41034i
$40$	1407.91			0.879945
$41$	308.517	−	1151.40i	0.183532	−	0.684950i	−0.811408	−	0.584480i	$-0.801299\pi$
$41$	308.517	−	1151.40i	0.183532	−	0.684950i	0.994940	−	0.100470i	$-0.0320348\pi$
$42$	195.425	+	338.486i	0.110785	+	0.191886i
$43$	318.080	+	183.644i	0.172028	+	0.0993205i	0.583542	−	0.812083i	$-0.301666\pi$
$43$	318.080	+	183.644i	0.172028	+	0.0993205i	−0.411514	+	0.911404i	$0.635000\pi$
$44$	866.449	+	866.449i	0.447546	+	0.447546i
$45$	−4447.40	+	1191.68i	−2.19625	+	0.588483i
$46$	109.088	+	407.123i	0.0515540	+	0.192402i
$47$	−308.850	+	308.850i	−0.139814	+	0.139814i	−0.773550	−	0.633736i	$-0.781521\pi$
$47$	−308.850	+	308.850i	−0.139814	+	0.139814i	0.633736	+	0.773550i	$0.281521\pi$
$48$	540.043	−	935.382i	0.234394	−	0.405982i
$49$	1966.81	−	1135.54i	0.819162	−	0.472943i
$50$	−60.1328	−	16.1125i	−0.0240531	−	0.00644501i
$51$		−	1246.27i		−	0.479150i
$52$	−1841.38	−	692.566i	−0.680983	−	0.256126i
$53$	−2120.08			−0.754746			−0.377373	−	0.926061i	$-0.623173\pi$
$53$	−2120.08			−0.754746			−0.377373	+	0.926061i	$0.623173\pi$
$54$	956.069	−	3568.10i	0.327870	−	1.22363i
$55$	1284.00	+	2223.96i	0.424464	+	0.735194i
$56$	−569.679	−	328.904i	−0.181658	−	0.104880i
$57$	3772.88	+	3772.88i	1.16124	+	1.16124i
$58$	1743.18	−	467.083i	0.518186	−	0.138847i
$59$	−1468.47	−	5480.39i	−0.421852	−	1.57437i	−0.770703	−	0.637194i	$-0.780095\pi$
$59$	−1468.47	−	5480.39i	−0.421852	−	1.57437i	0.348851	−	0.937178i	$-0.386572\pi$
$60$	3298.07	−	3298.07i	0.916131	−	0.916131i
$61$	−2851.77	+	4939.42i	−0.766400	+	1.32744i	0.173104	+	0.984904i	$0.444620\pi$
$61$	−2851.77	+	4939.42i	−0.766400	+	1.32744i	−0.939503	+	0.342540i	$0.888713\pi$
$62$	−1962.25	+	1132.91i	−0.510472	+	0.294721i
$63$	2077.93	+	556.779i	0.523539	+	0.140282i
$64$		−	1162.27i		−	0.283756i
$65$	−3351.90	−	2400.78i	−0.793350	−	0.568232i
$66$	−3609.38			−0.828601
$67$	−525.691	+	1961.90i	−0.117106	+	0.437047i	−0.999436	−	0.0335852i	$-0.989307\pi$
$67$	−525.691	+	1961.90i	−0.117106	+	0.437047i	0.882329	+	0.470632i	$0.155974\pi$
$68$	441.677	+	765.007i	0.0955183	+	0.165443i
$69$	2871.29	+	1657.74i	0.603086	+	0.348192i
$70$	−410.542	−	410.542i	−0.0837840	−	0.0837840i
$71$	1510.63	−	404.773i	0.299670	−	0.0802962i	−0.105851	−	0.994382i	$-0.533757\pi$
$71$	1510.63	−	404.773i	0.299670	−	0.0802962i	0.405521	+	0.914086i	$0.367090\pi$
$72$	2818.93	+	10520.4i	0.543775	+	2.02940i
$73$	−1577.77	+	1577.77i	−0.296072	+	0.296072i	−0.839473	−	0.543401i	$-0.817136\pi$
$73$	−1577.77	+	1577.77i	−0.296072	+	0.296072i	0.543401	+	0.839473i	$0.317136\pi$
$74$	−817.326	+	1415.65i	−0.149256	+	0.258519i
$75$	−424.095	+	244.852i	−0.0753947	+	0.0435292i
$76$	−3653.04	−	978.830i	−0.632452	−	0.169465i
$77$		−	1199.83i		−	0.202367i
$78$	5277.85	−	2392.81i	0.867497	−	0.393296i
$79$	4448.61			0.712804			0.356402	−	0.934333i	$-0.384003\pi$
$79$	4448.61			0.712804			0.356402	+	0.934333i	$0.384003\pi$
$80$	−415.256	+	1549.76i	−0.0648838	+	0.242150i
$81$	−6885.24	−	11925.6i	−1.04942	−	1.81765i
$82$	−2155.32	−	1244.38i	−0.320542	−	0.185065i
$83$	−4026.77	−	4026.77i	−0.584521	−	0.584521i	0.351621	−	0.936142i	$-0.385631\pi$
$83$	−4026.77	−	4026.77i	−0.584521	−	0.584521i	−0.936142	+	0.351621i	$0.885631\pi$
$84$	−2104.95	+	564.021i	−0.298321	+	0.0799349i
$85$	479.148	+	1788.20i	0.0663180	+	0.247502i
$86$	542.237	−	542.237i	0.0733149	−	0.0733149i
$87$	7097.95	−	12294.0i	0.937766	−	1.62426i
$88$	5260.81	−	3037.33i	0.679340	−	0.392217i
$89$	10633.9	+	2849.33i	1.34249	+	0.359719i	0.857357	−	0.514722i	$-0.172105\pi$
$89$	10633.9	+	2849.33i	1.34249	+	0.359719i	0.485132	+	0.874441i	$0.338772\pi$
$90$			9613.05i			1.18680i
$91$	795.419	+	1754.46i	0.0960535	+	0.211866i
$92$	−2350.01			−0.277648
$93$	−4613.03	+	17216.0i	−0.533359	+	1.99052i
$94$	455.964	+	789.753i	0.0516030	+	0.0893790i
$95$	−6864.05	−	3962.96i	−0.760559	−	0.439109i
$96$	−12317.6	−	12317.6i	−1.33655	−	1.33655i
$97$	16595.6	−	4446.77i	1.76380	−	0.472608i	0.776316	−	0.630343i	$-0.217086\pi$
$97$	16595.6	−	4446.77i	1.76380	−	0.472608i	0.987481	+	0.157735i	$0.0504193\pi$
$98$	−1227.23	−	4580.08i	−0.127783	−	0.476893i
$99$	−14047.3	+	14047.3i	−1.43326	+	1.43326i
$100$	173.551	−	300.598i	0.0173551	−	0.0300598i
$101$	5294.19	−	3056.60i	0.518987	−	0.299637i	−0.217533	−	0.976053i	$-0.569801\pi$
$101$	5294.19	−	3056.60i	0.518987	−	0.299637i	0.736520	+	0.676416i	$0.236468\pi$
$102$	−2513.35	−	673.451i	−0.241576	−	0.0647300i
$103$		−	5625.33i		−	0.530242i	−0.964215	−	0.265121i	$-0.914588\pi$
$103$		−	5625.33i		−	0.530242i	0.964215	−	0.265121i	$-0.0854119\pi$
$104$	−5679.08	+	7928.97i	−0.525063	+	0.733078i
$105$	−4567.07			−0.414246
$106$	−1145.64	+	4275.58i	−0.101961	+	0.380525i
$107$	4866.71	+	8429.38i	0.425077	+	0.736255i	0.996428	−	0.0844510i	$-0.0269137\pi$
$107$	4866.71	+	8429.38i	0.425077	+	0.736255i	−0.571351	+	0.820706i	$0.693580\pi$
$108$	17836.6	+	10298.0i	1.52920	+	0.882884i
$109$	−6384.24	−	6384.24i	−0.537349	−	0.537349i	0.385401	−	0.922749i	$-0.374063\pi$
$109$	−6384.24	−	6384.24i	−0.537349	−	0.537349i	−0.922749	+	0.385401i	$0.874063\pi$
$110$	5178.91	−	1387.69i	0.428009	−	0.114685i
$111$	3328.03	+	12420.4i	0.270110	+	1.00807i
$112$	530.065	−	530.065i	0.0422564	−	0.0422564i
$113$	−2938.86	+	5090.26i	−0.230156	+	0.398642i	−0.957854	−	0.287256i	$-0.907257\pi$
$113$	−2938.86	+	5090.26i	−0.230156	+	0.398642i	0.727698	+	0.685898i	$0.240590\pi$
$114$	9647.55	−	5570.02i	0.742348	−	0.428595i
$115$	−4757.21	−	1274.69i	−0.359714	−	0.0963850i
$116$			10062.0i			0.747774i
$117$	11228.2	−	29853.4i	0.820239	−	2.18083i
$118$	−11845.8			−0.850750
$119$	223.868	−	835.488i	0.0158088	−	0.0589993i
$120$	−11561.4	−	20024.9i	−0.802873	−	1.39062i
$121$	−3083.85	−	1780.46i	−0.210631	−	0.121608i
$122$	8420.31	+	8420.31i	0.565729	+	0.565729i
$123$	−18910.0	+	5066.91i	−1.24991	+	0.334913i
$124$	−3269.71	−	12202.7i	−0.212650	−	0.793621i
$125$	11296.1	−	11296.1i	0.722953	−	0.722953i
$126$	2245.72	−	3889.69i	0.141454	−	0.245005i
$127$	−13486.4	+	7786.40i	−0.836161	+	0.482758i	−0.855957	−	0.517047i	$-0.827031\pi$
$127$	−13486.4	+	7786.40i	−0.836161	+	0.482758i	0.0197968	+	0.999804i	$0.493698\pi$
$128$	14048.4	+	3764.27i	0.857449	+	0.229753i
$129$		−	6032.11i		−	0.362485i
$130$	−6652.95	+	5462.48i	−0.393666	+	0.323223i
$131$	−6751.71			−0.393433			−0.196717	−	0.980460i	$-0.563028\pi$
$131$	−6751.71			−0.393433			−0.196717	+	0.980460i	$0.563028\pi$
$132$	5208.56	−	19438.6i	0.298930	−	1.11562i
$133$	1851.58	+	3207.04i	0.104674	+	0.181301i
$134$	3672.51	+	2120.32i	0.204528	+	0.118084i
$135$	30521.4	+	30521.4i	1.67470	+	1.67470i
$136$	4230.02	−	1133.43i	0.228699	−	0.0612797i
$137$	3485.50	+	13008.1i	0.185705	+	0.693061i	0.994478	+	0.104941i	$0.0334652\pi$
$137$	3485.50	+	13008.1i	0.185705	+	0.693061i	−0.808773	+	0.588120i	$0.799868\pi$
$138$	4894.75	−	4894.75i	0.257023	−	0.257023i
$139$	−10454.8	+	18108.2i	−0.541110	+	0.937229i	0.457731	+	0.889091i	$0.348662\pi$
$139$	−10454.8	+	18108.2i	−0.541110	+	0.937229i	−0.998841	+	0.0481387i	$0.984671\pi$
$140$	2803.44	−	1618.57i	0.143033	−	0.0825799i
$141$	6928.98	+	1856.62i	0.348523	+	0.0933864i
$142$		−	3265.23i		−	0.161934i
$143$	−17704.0	−	1739.61i	−0.865764	−	0.0850708i
$144$	−12411.7			−0.598560
$145$	−5457.84	+	20368.9i	−0.259588	+	0.968796i
$146$	2329.30	+	4034.47i	0.109275	+	0.189270i
$147$	−32301.7	−	18649.4i	−1.49483	−	0.863038i
$148$	−6444.64	−	6444.64i	−0.294222	−	0.294222i
$149$	2638.41	−	706.961i	0.118842	−	0.0318437i	−0.198908	−	0.980018i	$-0.563739\pi$
$149$	2638.41	−	706.961i	0.118842	−	0.0318437i	0.317750	+	0.948175i	$0.397073\pi$
$150$	264.623	+	987.586i	0.0117610	+	0.0438927i
$151$	22287.7	−	22287.7i	0.977490	−	0.977490i	−0.0222623	−	0.999752i	$-0.507087\pi$
$151$	22287.7	−	22287.7i	0.977490	−	0.977490i	0.999752	+	0.0222623i	$0.00708691\pi$
$152$	−9374.43	+	16237.0i	−0.405749	+	0.702779i
$153$	−12402.7	+	7160.70i	−0.529826	+	0.305895i
$154$	−2419.70	−	648.358i	−0.102028	−	0.0273384i
$155$		−	26475.9i		−	1.10202i
$156$	5270.43	+	31877.2i	0.216569	+	1.30988i
$157$	17116.8			0.694421			0.347210	−	0.937787i	$-0.387129\pi$
$157$	17116.8			0.694421			0.347210	+	0.937787i	$0.387129\pi$
$158$	2403.91	−	8971.53i	0.0962952	−	0.359379i
$159$	17409.5	+	30154.1i	0.688639	+	1.19276i
$160$	22409.6	+	12938.2i	0.875376	+	0.505398i
$161$	1627.11	+	1627.11i	0.0627719	+	0.0627719i
$162$	−27771.0	+	7441.21i	−1.05818	+	0.283539i
$163$	−10610.4	−	39598.6i	−0.399353	−	1.49041i	−0.814238	−	0.580531i	$-0.802845\pi$
$163$	−10610.4	−	39598.6i	−0.399353	−	1.49041i	0.414885	−	0.909874i	$-0.363822\pi$
$164$	9811.94	−	9811.94i	0.364810	−	0.364810i
$165$	21087.7	−	36525.0i	0.774573	−	1.34160i
$166$	−10296.8	+	5944.83i	−0.373667	+	0.215736i
$167$	−7080.99	−	1897.35i	−0.253899	−	0.0680321i	0.129624	−	0.991563i	$-0.458623\pi$
$167$	−7080.99	−	1897.35i	−0.253899	−	0.0680321i	−0.383524	+	0.923531i	$0.625289\pi$
$168$			10803.5i			0.382776i
$169$	27041.1	−	9192.98i	0.946783	−	0.321872i
$170$	3865.19			0.133744
$171$	15869.3	−	59225.1i	0.542708	−	2.02541i
$172$	2137.78	+	3702.74i	0.0722613	+	0.125160i
$173$	−9208.34	−	5316.44i	−0.307673	−	0.177635i	0.338212	−	0.941070i	$-0.390178\pi$
$173$	−9208.34	−	5316.44i	−0.307673	−	0.177635i	−0.645885	+	0.763435i	$0.723511\pi$
$174$	−20957.8	−	20957.8i	−0.692226	−	0.692226i
$175$	−328.293	+	87.9659i	−0.0107198	+	0.00287236i
$176$	1791.69	+	6686.67i	0.0578412	+	0.215866i
$177$	−65889.5	+	65889.5i	−2.10315	+	2.10315i
$178$	11492.5	−	19905.6i	0.362723	−	0.628255i
$179$	4343.15	−	2507.52i	0.135550	−	0.0782598i	−0.430692	−	0.902499i	$-0.641730\pi$
$179$	4343.15	−	2507.52i	0.135550	−	0.0782598i	0.566241	+	0.824239i	$0.308397\pi$
$180$	−51771.8	−	13872.2i	−1.59790	−	0.428155i
$181$			60491.1i			1.84643i	0.384278	+	0.923217i	$0.374450\pi$
$181$			60491.1i			1.84643i	−0.384278	+	0.923217i	$0.625550\pi$
$182$	3968.05	−	656.059i	0.119794	−	0.0198061i
$183$	93671.7			2.79709
$184$	−3015.30	+	11253.2i	−0.0890625	+	0.332386i
$185$	−9550.42	−	16541.8i	−0.279048	−	0.483325i
$186$	32226.9	+	18606.2i	0.931521	+	0.537814i
$187$	5648.12	+	5648.12i	0.161518	+	0.161518i
$188$	−4911.26	+	1315.97i	−0.138956	+	0.0372331i
$189$	−5219.63	−	19479.9i	−0.146122	−	0.545335i
$190$	−11701.3	+	11701.3i	−0.324135	+	0.324135i
$191$	−15375.6	+	26631.3i	−0.421469	+	0.730005i	−0.996083	−	0.0884188i	$-0.971819\pi$
$191$	−15375.6	+	26631.3i	−0.421469	+	0.730005i	0.574615	+	0.818424i	$0.305152\pi$
$192$	−16531.0	+	9544.19i	−0.448433	+	0.258903i
$193$	−30011.1	−	8041.45i	−0.805689	−	0.215884i	−0.167609	−	0.985854i	$-0.553605\pi$
$193$	−30011.1	−	8041.45i	−0.805689	−	0.215884i	−0.638080	+	0.769970i	$0.720271\pi$
$194$		−	35871.3i		−	0.953111i
$195$	−6621.70	+	67389.0i	−0.174141	+	1.77223i
$196$	26437.3			0.688186
$197$	−2013.50	+	7514.50i	−0.0518824	+	0.193628i	−0.987003	−	0.160702i	$-0.948624\pi$
$197$	−2013.50	+	7514.50i	−0.0518824	+	0.193628i	0.935121	+	0.354330i	$0.115291\pi$
$198$	20738.5	+	35920.1i	0.528989	+	0.916237i
$199$	−38461.0	−	22205.5i	−0.971214	−	0.560731i	−0.0716078	−	0.997433i	$-0.522813\pi$
$199$	−38461.0	−	22205.5i	−0.971214	−	0.560731i	−0.899606	+	0.436702i	$0.856146\pi$
$200$	−1216.76	−	1216.76i	−0.0304190	−	0.0304190i
$201$	32221.2	−	8633.64i	0.797534	−	0.213699i
$202$	−3303.42	−	12328.5i	−0.0809582	−	0.302140i
$203$	6966.80	−	6966.80i	0.169060	−	0.169060i
$204$	7253.84	−	12564.0i	0.174304	−	0.301904i
$205$	25184.8	−	14540.5i	0.599282	−	0.345996i
$206$	−11344.6	−	3039.79i	−0.267335	−	0.0716322i
$207$		−	38099.7i		−	0.889162i
$208$	−7052.79	−	8589.85i	−0.163018	−	0.198545i
$209$	−34197.6			−0.782895
$210$	−2467.92	+	9210.42i	−0.0559620	+	0.208853i
$211$	7233.34	+	12528.5i	0.162470	+	0.281407i	0.935754	−	0.352653i	$-0.114721\pi$
$211$	7233.34	+	12528.5i	0.162470	+	0.281407i	−0.773284	+	0.634060i	$0.781387\pi$
$212$	−21373.2	−	12339.8i	−0.475552	−	0.274560i
$213$	−18162.0	−	18162.0i	−0.400318	−	0.400318i
$214$	19629.4	−	5259.69i	0.428627	−	0.114850i
$215$	2319.14	+	8655.16i	0.0501707	+	0.187240i
$216$	72198.8	−	72198.8i	1.54747	−	1.54747i
$217$	−6185.07	+	10712.9i	−0.131349	+	0.227502i
$218$	−16325.0	+	9425.24i	−0.343511	+	0.198326i
$219$	35396.9	+	9484.57i	0.738035	+	0.197756i
$220$			29893.9i			0.617643i
$221$	−12003.4	−	4514.63i	−0.245765	−	0.0924353i
$222$	26846.6			0.544732
$223$	9819.76	−	36647.8i	0.197465	−	0.736951i	−0.794149	−	0.607723i	$-0.792083\pi$
$223$	9819.76	−	36647.8i	0.197465	−	0.736951i	0.991615	−	0.129229i	$-0.0412501\pi$
$224$	−6045.02	−	10470.3i	−0.120476	−	0.208671i
$225$	4873.46	+	2813.70i	0.0962660	+	0.0555792i
$226$	8677.45	+	8677.45i	0.169893	+	0.169893i
$227$	−95364.8	+	25552.9i	−1.85070	+	0.495894i	−0.999577	−	0.0290718i	$-0.990745\pi$
$227$	−95364.8	+	25552.9i	−1.85070	+	0.495894i	−0.851123	+	0.524966i	$0.824078\pi$
$228$	16075.7	+	59995.5i	0.309244	+	1.15411i
$229$	−22254.1	+	22254.1i	−0.424364	+	0.424364i	−0.886703	−	0.462339i	$-0.847010\pi$
$229$	−22254.1	+	22254.1i	−0.424364	+	0.424364i	0.462339	+	0.886703i	$0.347010\pi$
$230$	−5141.35	+	8905.08i	−0.0971900	+	0.168338i
$231$	−17065.3	+	9852.66i	−0.319809	+	0.184642i
$232$	48183.0	+	12910.6i	0.895195	+	0.239867i
$233$		−	89857.7i		−	1.65517i	−0.561338	−	0.827586i	$-0.689713\pi$
$233$		−	89857.7i		−	1.65517i	0.561338	−	0.827586i	$-0.310287\pi$
$234$	−54138.0	−	38776.1i	−0.988714	−	0.708161i
$235$	−10655.8			−0.192953
$236$	17094.3	−	63796.7i	0.306921	−	1.14544i
$237$	−36530.7	−	63273.0i	−0.650371	−	1.12648i
$238$	−1563.96	−	902.953i	−0.0276103	−	0.0159408i
$239$	71939.7	+	71939.7i	1.25943	+	1.25943i	0.951367	+	0.308061i	$0.0996800\pi$
$239$	71939.7	+	71939.7i	1.25943	+	1.25943i	0.308061	+	0.951367i	$0.400320\pi$
$240$	25452.3	−	6819.93i	0.441881	−	0.118402i
$241$	12624.8	+	47116.6i	0.217366	+	0.811221i	0.985320	+	0.170717i	$0.0546082\pi$
$241$	12624.8	+	47116.6i	0.217366	+	0.811221i	−0.767954	+	0.640505i	$0.778725\pi$
$242$	−5257.10	+	5257.10i	−0.0897668	+	0.0897668i
$243$	−41423.6	+	71747.8i	−0.701512	+	1.21505i
$244$	−57499.3	+	33197.2i	−0.965790	+	0.557599i
$245$	53518.0	+	14340.1i	0.891596	+	0.238902i
$246$			40873.8i			0.675421i
$247$	50005.7	−	22671.1i	0.819645	−	0.371602i
$248$	−62629.2			−1.01829
$249$	−24206.5	+	90339.7i	−0.390420	+	1.45707i
$250$	−16676.8	−	28885.1i	−0.266829	−	0.462162i
$251$	102969.	+	59449.2i	1.63440	+	0.943623i	0.982713	+	0.185138i	$0.0592731\pi$
$251$	102969.	+	59449.2i	1.63440	+	0.943623i	0.651690	+	0.758485i	$0.274060\pi$
$252$	17707.5	+	17707.5i	0.278841	+	0.278841i
$253$	−20525.7	+	5499.85i	−0.320670	+	0.0859231i
$254$	8415.13	+	31405.7i	0.130435	+	0.486789i
$255$	21499.2	−	21499.2i	0.330629	−	0.330629i
$256$	24481.0	−	42402.3i	0.373550	−	0.647007i
$257$	101027.	−	58327.9i	1.52957	−	0.883100i	0.530195	−	0.847876i	$-0.322119\pi$
$257$	101027.	−	58327.9i	1.52957	−	0.883100i	0.999379	−	0.0352249i	$-0.0112147\pi$
$258$	−12165.0	−	3259.60i	−0.182756	−	0.0489694i
$259$			8924.34i			0.133038i
$260$	−19818.0	−	43712.6i	−0.293165	−	0.646637i
$261$	−163131.			−2.39473
$262$	−3648.45	+	13616.2i	−0.0531503	+	0.198360i
$263$	29898.7	+	51786.0i	0.432256	+	0.748688i	0.997067	−	0.0765313i	$-0.0243845\pi$
$263$	29898.7	+	51786.0i	0.432256	+	0.748688i	−0.564812	+	0.825220i	$0.691051\pi$
$264$	−86400.4	−	49883.3i	−1.23968	−	0.715727i
$265$	−36573.2	−	36573.2i	−0.520800	−	0.520800i
$266$	7468.19	−	2001.10i	0.105549	−	0.0282816i
$267$	−46795.8	−	174644.i	−0.656423	−	2.44981i
$268$	−16718.8	+	16718.8i	−0.232775	+	0.232775i
$269$	−14058.5	+	24350.0i	−0.194283	+	0.336508i	−0.946665	−	0.322219i	$-0.895571\pi$
$269$	−14058.5	+	24350.0i	−0.194283	+	0.336508i	0.752382	+	0.658727i	$0.228905\pi$
$270$	78045.6	−	45059.7i	1.07058	−	0.618102i
$271$	−82316.6	−	22056.7i	−1.12085	−	0.300332i	−0.349625	−	0.936890i	$-0.613691\pi$
$271$	−82316.6	−	22056.7i	−1.12085	−	0.300332i	−0.771229	+	0.636558i	$0.780358\pi$
$272$			4990.49i			0.0674536i
$273$	18422.1	−	25720.5i	0.247181	−	0.345107i
$274$	28116.9			0.374512
$275$	812.338	−	3031.69i	0.0107417	−	0.0400884i
$276$	19297.6	+	33424.5i	0.253329	+	0.438779i
$277$	43634.9	+	25192.6i	0.568689	+	0.328333i	0.756626	−	0.653848i	$-0.226847\pi$
$277$	43634.9	+	25192.6i	0.568689	+	0.328333i	−0.187937	+	0.982181i	$0.560180\pi$
$278$	30869.4	+	30869.4i	0.399428	+	0.399428i
$279$	197837.	−	53010.3i	2.54155	−	0.681007i
$280$	−4153.56	−	15501.3i	−0.0529791	−	0.197721i
$281$	26228.7	−	26228.7i	0.332173	−	0.332173i	−0.521238	−	0.853411i	$-0.674530\pi$
$281$	26228.7	−	26228.7i	0.332173	−	0.332173i	0.853411	+	0.521238i	$0.174530\pi$
$282$	7488.49	−	12970.4i	0.0941664	−	0.163101i
$283$	28506.3	−	16458.1i	0.355933	−	0.205498i	−0.311362	−	0.950291i	$-0.600785\pi$
$283$	28506.3	−	16458.1i	0.355933	−	0.205498i	0.667295	+	0.744793i	$0.267452\pi$
$284$	17585.2	+	4711.93i	0.218027	+	0.0584200i
$285$			130171.i			1.60259i
$286$	−13075.1	+	34763.7i	−0.159850	+	0.425005i
$287$	−13587.3			−0.164956
$288$	−51809.9	+	193357.i	−0.624637	+	2.33118i
$289$	−38881.3	−	67344.5i	−0.465528	−	0.806318i
$290$	38128.8	+	22013.7i	0.453375	+	0.261756i
$291$	−199525.	−	199525.i	−2.35619	−	2.35619i
$292$	−25089.3	+	6722.65i	−0.294254	+	0.0788452i
$293$	23314.1	+	87009.4i	0.271571	+	1.01352i	0.958105	+	0.286419i	$0.0924649\pi$
$293$	23314.1	+	87009.4i	0.271571	+	1.01352i	−0.686533	+	0.727098i	$0.740868\pi$
$294$	−55065.3	+	55065.3i	−0.637064	+	0.637064i
$295$	69209.1	−	119874.i	0.795278	−	1.37746i
$296$	−39129.9	+	22591.6i	−0.446606	+	0.257848i
$297$	179891.	+	48201.7i	2.03937	+	0.546448i
$298$		−	5702.92i		−	0.0642192i
$299$	26367.8	−	21649.6i	0.294939	−	0.242163i
$300$	−5700.59			−0.0633398
$301$	1083.55	−	4043.88i	0.0119596	−	0.0446340i
$302$	−32904.1	−	56991.5i	−0.360774	−	0.624879i
$303$	−86948.7	−	50199.8i	−0.947060	−	0.546786i
$304$	−15107.9	−	15107.9i	−0.163477	−	0.163477i
$305$	−134405.	+	36013.6i	−1.44482	+	0.387139i
$306$	7738.92	+	28882.0i	0.0826490	+	0.308450i
$307$	−102971.	+	102971.i	−1.09254	+	1.09254i	−0.0972877	+	0.995256i	$0.531017\pi$
$307$	−102971.	+	102971.i	−1.09254	+	1.09254i	−0.995256	+	0.0972877i	$0.968983\pi$
$308$	6983.56	−	12095.9i	0.0736165	−	0.127508i
$309$	−80009.7	+	46193.6i	−0.837964	+	0.483799i
$310$	−53394.1	−	14306.9i	−0.555610	−	0.148875i
$311$			123419.i			1.27603i	0.770023	+	0.638016i	$0.220244\pi$
$311$			123419.i			1.27603i	−0.770023	+	0.638016i	$0.779756\pi$
$312$	159409.	+	15663.7i	1.63759	+	0.160911i
$313$	32784.5			0.334642			0.167321	−	0.985902i	$-0.446488\pi$
$313$	32784.5			0.334642			0.167321	+	0.985902i	$0.446488\pi$
$314$	9249.46	−	34519.5i	0.0938117	−	0.350110i
$315$	26241.1	+	45450.9i	0.264460	+	0.458059i
$316$	44847.9	+	25892.9i	0.449125	+	0.259303i
$317$	80351.9	+	80351.9i	0.799609	+	0.799609i	0.983034	−	0.183425i	$-0.0587184\pi$
$317$	80351.9	+	80351.9i	0.799609	+	0.799609i	−0.183425	+	0.983034i	$0.558718\pi$
$318$	70219.6	−	18815.3i	0.694391	−	0.186061i
$319$	23548.7	+	87885.0i	0.231412	+	0.863641i
$320$	20050.1	−	20050.1i	0.195801	−	0.195801i
$321$	79928.0	−	138439.i	0.775691	−	1.34354i
$322$	4160.65	−	2402.15i	0.0401282	−	0.0231680i
$323$	−23813.1	−	6380.71i	−0.228250	−	0.0611595i
$324$		−	160301.i		−	1.52702i
$325$	821.987	+	4971.64i	0.00778213	+	0.0470688i
$326$	−85592.2			−0.805376
$327$	−38378.1	+	143229.i	−0.358912	+	1.33948i
$328$	−34395.7	−	59575.0i	−0.319710	−	0.553754i
$329$	4311.63	+	2489.32i	0.0398336	+	0.0229980i
$330$	−62264.9	−	62264.9i	−0.571762	−	0.571762i
$331$	88849.3	−	23807.1i	0.810958	−	0.217295i	0.170568	−	0.985346i	$-0.445440\pi$
$331$	88849.3	−	23807.1i	0.810958	−	0.217295i	0.640389	+	0.768050i	$0.278773\pi$
$332$	−17157.5	−	64032.7i	−0.155660	−	0.580933i
$333$	104484.	−	104484.i	0.942240	−	0.942240i
$334$	−7652.77	+	13255.0i	−0.0686002	+	0.118819i
$335$	−42913.1	+	24775.9i	−0.382384	+	0.220770i
$336$	−11891.9	−	3186.42i	−0.105335	−	0.0282244i
$337$		−	65948.7i		−	0.580693i	−0.956922	−	0.290347i	$-0.906229\pi$
$337$		−	65948.7i		−	0.580693i	0.956922	−	0.290347i	$-0.0937706\pi$
$338$	−3927.21	−	59501.5i	−0.0343757	−	0.520828i
$339$	96532.3			0.839988
$340$	−5577.71	+	20816.3i	−0.0482501	+	0.180072i
$341$	−57117.3	−	98930.0i	−0.491200	−	0.850784i
$342$	−110864.	−	64007.5i	−0.947849	−	0.547241i
$343$	−37656.8	−	37656.8i	−0.320078	−	0.320078i
$344$	20473.9	−	5485.96i	0.173015	−	0.0463592i
$345$	20934.8	+	78129.7i	0.175886	+	0.656414i
$346$	−15697.6	+	15697.6i	−0.131124	+	0.131124i
$347$	−90807.4	+	157283.i	−0.754158	+	1.30624i	0.191633	+	0.981467i	$0.438622\pi$
$347$	−90807.4	+	157283.i	−0.754158	+	1.30624i	−0.945792	+	0.324774i	$0.894712\pi$
$348$	143113.	−	82626.6i	1.18174	−	0.682278i
$349$	−67661.3	−	18129.8i	−0.555507	−	0.148848i	−0.0298656	−	0.999554i	$-0.509508\pi$
$349$	−67661.3	−	18129.8i	−0.555507	−	0.148848i	−0.525641	+	0.850706i	$0.676175\pi$
$350$			709.605i			0.00579269i
$351$	−295002.	+	48774.2i	−2.39448	+	0.395891i
$352$	111648.			0.901083
$353$	41944.9	−	156540.i	0.336612	−	1.25625i	−0.565499	−	0.824749i	$-0.691316\pi$
$353$	41944.9	−	156540.i	0.336612	−	1.25625i	0.902111	−	0.431504i	$-0.142017\pi$
$354$	97274.6	+	168485.i	0.776235	+	1.34448i
$355$	33042.4	+	19077.0i	0.262189	+	0.151375i
$356$	90618.8	+	90618.8i	0.715020	+	0.715020i
$357$	−13721.6	+	3676.68i	−0.107663	+	0.0288483i
$358$	−2710.00	−	10113.9i	−0.0211448	−	0.0789134i
$359$	122825.	−	122825.i	0.953014	−	0.953014i	−0.0459305	−	0.998945i	$-0.514625\pi$
$359$	122825.	−	122825.i	0.953014	−	0.953014i	0.998945	+	0.0459305i	$0.0146253\pi$
$360$	−132857.	+	230115.i	−1.02513	+	1.77557i
$361$	−21454.2	+	12386.6i	−0.164626	+	0.0950469i
$362$	121993.	+	32687.8i	0.930928	+	0.249441i
$363$			58482.6i			0.443826i
$364$	−2192.89	+	22317.0i	−0.0165506	+	0.168435i
$365$	−54435.6			−0.408599
$366$	50617.8	−	188908.i	0.377869	−	1.41023i
$367$	31836.7	+	55142.8i	0.236372	+	0.409408i	0.959671	−	0.281127i	$-0.0907083\pi$
$367$	31836.7	+	55142.8i	0.236372	+	0.409408i	−0.723299	+	0.690535i	$0.757375\pi$
$368$	−11497.7	−	6638.17i	−0.0849012	−	0.0490177i
$369$	159076.	+	159076.i	1.16830	+	1.16830i
$370$	−38520.7	+	10321.6i	−0.281379	+	0.0753952i
$371$	6254.57	+	23342.4i	0.0454412	+	0.169589i
$372$	−146711.	+	146711.i	−1.06017	+	1.06017i
$373$	15827.7	−	27414.4i	0.113763	−	0.197043i	−0.803522	−	0.595275i	$-0.797043\pi$
$373$	15827.7	−	27414.4i	0.113763	−	0.197043i	0.917285	+	0.398232i	$0.130376\pi$
$374$	14442.7	−	8338.49i	0.103254	−	0.0596135i
$375$	−253427.	−	67905.5i	−1.80215	−	0.482884i
$376$			25206.5i			0.178294i
$377$	−92697.0	−	112899.i	−0.652203	−	0.794342i
$378$	−42105.8			−0.294685
$379$	−1952.97	+	7288.57i	−0.0135962	+	0.0507416i	−0.972391	−	0.233359i	$-0.925028\pi$
$379$	−1952.97	+	7288.57i	−0.0135962	+	0.0507416i	0.958794	+	0.284101i	$0.0916950\pi$
$380$	−46132.4	−	79903.7i	−0.319477	−	0.553350i
$381$	221493.	+	127879.i	1.52585	+	0.880948i
$382$	45398.9	+	45398.9i	0.311113	+	0.311113i
$383$	−107444.	+	28789.6i	−0.732464	+	0.196263i	−0.605726	−	0.795673i	$-0.707117\pi$
$383$	−107444.	+	28789.6i	−0.732464	+	0.196263i	−0.126738	+	0.991936i	$0.540451\pi$
$384$	−61822.2	−	230724.i	−0.419259	−	1.56469i
$385$	20698.1	−	20698.1i	0.139640	−	0.139640i
$386$	−32434.5	+	56178.1i	−0.217687	+	0.377044i
$387$	−60030.8	+	34658.8i	−0.400823	+	0.231415i
$388$	193187.	+	51764.4i	1.28326	+	0.343849i
$389$		−	246139.i		−	1.62660i	−0.581843	−	0.813301i	$-0.697668\pi$
$389$		−	246139.i		−	1.62660i	0.581843	−	0.813301i	$-0.302332\pi$
$390$	132325.	+	49769.3i	0.869989	+	0.327214i
$391$	−15319.0			−0.100202
$392$	33921.7	−	126598.i	0.220753	−	0.823860i
$393$	55443.0	+	96030.2i	0.358973	+	0.621760i
$394$	14066.5	+	8121.28i	0.0906134	+	0.0523157i
$395$	76742.3	+	76742.3i	0.491859	+	0.491859i
$396$	−223378.	+	59853.8i	−1.42446	+	0.381682i
$397$	45095.8	+	168300.i	0.286125	+	1.06783i	0.948014	+	0.318230i	$0.103088\pi$
$397$	45095.8	+	168300.i	0.286125	+	1.06783i	−0.661889	+	0.749602i	$0.730245\pi$
$398$	−65565.2	+	65565.2i	−0.413912	+	0.413912i
$399$	30409.3	−	52670.5i	0.191012	−	0.330843i
$400$	1698.22	−	980.470i	0.0106139	−	0.00612794i
$401$	−75340.7	−	20187.5i	−0.468534	−	0.125543i	0.0168247	−	0.999858i	$-0.494644\pi$
$401$	−75340.7	−	20187.5i	−0.468534	−	0.125543i	−0.485359	+	0.874315i	$0.661311\pi$
$402$		−	69646.0i		−	0.430967i
$403$	149105.	+	106796.i	0.918084	+	0.657572i
$404$	71163.2			0.436006
$405$	86950.1	−	324502.i	0.530103	−	1.97837i
$406$	−10285.3	−	17814.6i	−0.0623971	−	0.108075i
$407$	−71372.2	−	41206.8i	−0.430864	−	0.248760i
$408$	−50856.6	−	50856.6i	−0.305511	−	0.305511i
$409$	−166456.	+	44601.7i	−0.995067	+	0.266627i	−0.719377	−	0.694619i	$-0.755573\pi$
$409$	−166456.	+	44601.7i	−0.995067	+	0.266627i	−0.275689	+	0.961247i	$0.588906\pi$
$410$	−15714.6	−	58647.6i	−0.0934835	−	0.348885i
$411$	156393.	−	156393.i	0.925835	−	0.925835i
$412$	32742.0	−	56710.8i	0.192890	−	0.334096i
$413$	−56007.6	+	32336.0i	−0.328358	+	0.189577i
$414$	−76835.8	−	20588.1i	−0.448294	−	0.120120i
$415$		−	138930.i		−	0.806678i
$416$	−163258.	+	74016.1i	−0.943381	+	0.427700i
$417$	343406.			1.97486
$418$	−18479.5	+	68966.5i	−0.105764	+	0.394717i
$419$	−2785.02	−	4823.79i	−0.0158635	−	0.0274764i	0.857985	−	0.513675i	$-0.171716\pi$
$419$	−2785.02	−	4823.79i	−0.0158635	−	0.0274764i	−0.873848	+	0.486199i	$0.838383\pi$
$420$	−46042.0	−	26582.4i	−0.261009	−	0.150694i
$421$	−145168.	−	145168.i	−0.819042	−	0.819042i	0.166927	−	0.985969i	$-0.446616\pi$
$421$	−145168.	−	145168.i	−0.819042	−	0.819042i	−0.985969	+	0.166927i	$0.946616\pi$
$422$	29175.0	−	7817.41i	0.163827	−	0.0438973i
$423$	−21335.2	−	79624.0i	−0.119238	−	0.445003i
$424$	−86514.3	+	86514.3i	−0.481234	+	0.481234i
$425$	1131.32	−	1959.51i	0.00626339	−	0.0108485i
$426$	−46441.7	+	26813.1i	−0.255911	+	0.147750i
$427$	62796.8	+	16826.4i	0.344415	+	0.0922857i
$428$			113306.i			0.618535i
$429$	120637.	+	266091.i	0.655492	+	1.44582i
$430$	18708.1			0.101179
$431$	−49471.8	+	184631.i	−0.266320	+	0.993919i	0.695118	+	0.718896i	$0.255352\pi$
$431$	−49471.8	+	184631.i	−0.266320	+	0.993919i	−0.961438	+	0.275023i	$0.911314\pi$
$432$	58178.1	+	100767.i	0.311740	+	0.539949i
$433$	−233928.	−	135058.i	−1.24769	−	0.720353i	−0.277040	−	0.960858i	$-0.589353\pi$
$433$	−233928.	−	135058.i	−1.24769	−	0.720353i	−0.970648	+	0.240506i	$0.922687\pi$
$434$	18262.4	+	18262.4i	0.0969569	+	0.0969569i
$435$	334528.	−	89636.4i	1.76788	−	0.473703i
$436$	−27202.4	−	101521.i	−0.143098	−	0.534050i
$437$	46376.0	−	46376.0i	0.242846	−	0.242846i
$438$	38255.1	−	66259.8i	0.199408	−	0.345384i
$439$	−38535.5	+	22248.5i	−0.199955	+	0.115444i	−0.596635	−	0.802513i	$-0.703496\pi$
$439$	−38535.5	+	22248.5i	−0.199955	+	0.115444i	0.396679	+	0.917957i	$0.370162\pi$
$440$	143150.	+	38356.9i	0.739410	+	0.198124i
$441$			428617.i			2.20390i
$442$	−15591.0	+	21767.7i	−0.0798049	+	0.111421i
$443$	−150334.			−0.766035			−0.383018	−	0.923741i	$-0.625115\pi$
$443$	−150334.			−0.766035			−0.383018	+	0.923741i	$0.625115\pi$
$444$	−38741.2	+	144584.i	−0.196520	+	0.733424i
$445$	134289.	+	232596.i	0.678144	+	1.17458i
$446$	−68601.5	−	39607.1i	−0.344877	−	0.199115i
$447$	−31721.1	−	31721.1i	−0.158757	−	0.158757i
$448$	−12796.7	+	3428.87i	−0.0637591	+	0.0170842i
$449$	−66489.9	−	248144.i	−0.329809	−	1.23087i	−0.909388	−	0.415949i	$-0.863449\pi$
$449$	−66489.9	−	248144.i	−0.329809	−	1.23087i	0.579579	−	0.814916i	$-0.303217\pi$
$450$	8307.88	−	8307.88i	0.0410266	−	0.0410266i
$451$	62737.1	−	108664.i	0.308440	−	0.534235i
$452$	−59255.2	+	34211.0i	−0.290034	+	0.167451i
$453$	−500021.	−	133980.i	−2.43664	−	0.652897i
$454$			206131.i			1.00007i
$455$	−16544.3	+	43987.6i	−0.0799145	+	0.212475i
$456$	307920.			1.48084
$457$	−2468.70	+	9213.31i	−0.0118205	+	0.0441147i	−0.971584	−	0.236694i	$-0.923936\pi$
$457$	−2468.70	+	9213.31i	−0.0118205	+	0.0441147i	0.959764	+	0.280809i	$0.0906027\pi$
$458$	32854.4	+	56905.4i	0.156625	+	0.271283i
$459$	116271.	+	67129.4i	0.551884	+	0.318630i
$460$	−40539.7	−	40539.7i	−0.191586	−	0.191586i
$461$	47756.1	−	12796.2i	0.224712	−	0.0602115i	−0.144706	−	0.989475i	$-0.546224\pi$
$461$	47756.1	−	12796.2i	0.224712	−	0.0602115i	0.369418	+	0.929263i	$0.379557\pi$
$462$	10648.2	+	39739.8i	0.0498878	+	0.186184i
$463$	117898.	−	117898.i	0.549978	−	0.549978i	−0.376456	−	0.926434i	$-0.622857\pi$
$463$	117898.	−	117898.i	0.549978	−	0.549978i	0.926434	+	0.376456i	$0.122857\pi$
$464$	−28422.7	+	49229.5i	−0.132017	+	0.228659i
$465$	−376570.	+	217413.i	−1.74156	+	1.00549i
$466$	−181216.	−	48556.8i	−0.834498	−	0.223603i
$467$		−	62768.3i		−	0.287811i	−0.989591	−	0.143905i	$-0.954034\pi$
$467$		−	62768.3i		−	0.287811i	0.989591	−	0.143905i	$-0.0459661\pi$
$468$	286956.	−	235608.i	1.31016	−	1.07572i
$469$	23151.7			0.105254
$470$	−5758.14	+	21489.7i	−0.0260667	+	0.0972823i
$471$	−140558.	−	243454.i	−0.633598	−	1.09742i
$472$	−283563.	−	163715.i	−1.27281	−	0.734859i
$473$	27337.7	+	27337.7i	0.122191	+	0.122191i
$474$	−147343.	+	39480.5i	−0.655803	+	0.175722i
$475$	2507.21	+	9357.02i	0.0111123	+	0.0414716i
$476$	7119.81	−	7119.81i	0.0314235	−	0.0314235i
$477$	200060.	−	346514.i	0.879273	−	1.52294i
$478$	183956.	−	106207.i	0.805113	−	0.464832i
$479$	285203.	+	76419.8i	1.24303	+	0.333070i	0.819641	−	0.572877i	$-0.194173\pi$
$479$	285203.	+	76419.8i	1.24303	+	0.333070i	0.423391	+	0.905947i	$0.360840\pi$
$480$		−	424979.i		−	1.84453i
$481$	131682.	+	12939.2i	0.569164	+	0.0559266i
$482$	101842.			0.438363
$483$	9781.20	−	36503.9i	0.0419274	−	0.156475i
$484$	−20726.2	−	35898.8i	−0.0884767	−	0.153246i
$485$	362998.	+	209577.i	1.54319	+	0.890964i
$486$	122310.	+	122310.i	0.517831	+	0.517831i
$487$	174444.	−	46742.0i	0.735525	−	0.197083i	0.128437	−	0.991718i	$-0.459004\pi$
$487$	174444.	−	46742.0i	0.735525	−	0.197083i	0.607088	+	0.794634i	$0.292337\pi$
$488$	85190.6	+	317936.i	0.357727	+	1.33506i
$489$	−476085.	+	476085.i	−1.99098	+	1.99098i
$490$	57839.5	−	100181.i	0.240898	−	0.417247i
$491$	150367.	−	86814.5i	0.623720	−	0.360105i	−0.154596	−	0.987978i	$-0.549408\pi$
$491$	150367.	−	86814.5i	0.623720	−	0.360105i	0.778316	+	0.627873i	$0.216074\pi$
$492$	−220129.	−	58983.4i	−0.909383	−	0.243668i
$493$			65591.5i			0.269869i
$494$	−18699.0	−	113098.i	−0.0766240	−	0.463446i
$495$	−484657.			−1.97799
$496$	18472.1	−	68939.0i	0.0750851	−	0.280222i
$497$	−8913.22	−	15438.1i	−0.0360846	−	0.0625003i
$498$	169108.	+	97634.5i	0.681876	+	0.393681i
$499$	−100154.	−	100154.i	−0.402223	−	0.402223i	0.476793	−	0.879016i	$-0.341799\pi$
$499$	−100154.	−	100154.i	−0.402223	−	0.402223i	−0.879016	+	0.476793i	$0.841799\pi$
$500$	179629.	−	48131.4i	0.718515	−	0.192525i
$501$	31160.9	+	116294.i	0.124147	+	0.463321i
$502$	175533.	−	175533.i	0.696549	−	0.696549i
$503$	−245718.	+	425596.i	−0.971183	+	1.68214i	−0.279187	+	0.960237i	$0.590065\pi$
$503$	−245718.	+	425596.i	−0.971183	+	1.68214i	−0.691996	+	0.721901i	$0.743268\pi$
$504$	107515.	−	62073.6i	0.423259	−	0.244369i
$505$	144058.	+	38600.3i	0.564878	+	0.151359i
$506$			44366.3i			0.173282i
$507$	−352806.	−	309118.i	−1.37252	−	1.20256i
$508$	−181281.			−0.702467
$509$	73332.8	−	273682.i	0.283050	−	1.05636i	−0.667203	−	0.744876i	$-0.732509\pi$
$509$	73332.8	−	273682.i	0.283050	−	1.05636i	0.950253	−	0.311480i	$-0.100825\pi$
$510$	−31739.8	−	54975.0i	−0.122029	−	0.211361i
$511$	22026.1	+	12716.8i	0.0843520	+	0.0487007i
$512$	92262.9	+	92262.9i	0.351955	+	0.351955i
$513$	−555217.	+	148770.i	−2.10974	+	0.565302i
$514$	−63037.8	−	235260.i	−0.238602	−	0.890476i
$515$	97041.7	−	97041.7i	0.365884	−	0.365884i
$516$	35109.6	−	60811.6i	0.131864	−	0.228395i
$517$	−39816.6	+	22988.1i	−0.148965	+	0.0860048i
$518$	17997.7	+	4822.48i	0.0670747	+	0.0179726i
$519$			174628.i			0.648305i
$520$	−234750.	+	38812.5i	−0.868159	+	0.143537i
$521$	43309.3			0.159553			0.0797766	−	0.996813i	$-0.474579\pi$
$521$	43309.3			0.159553			0.0797766	+	0.996813i	$0.474579\pi$
$522$	−88151.9	+	328987.i	−0.323512	+	1.20736i
$523$	176567.	+	305823.i	0.645515	+	1.11807i	0.984182	+	0.177159i	$0.0566908\pi$
$523$	176567.	+	305823.i	0.645515	+	1.11807i	−0.338667	+	0.940906i	$0.609976\pi$
$524$	−68066.1	−	39298.0i	−0.247895	−	0.143122i
$525$	3947.00	+	3947.00i	0.0143202	+	0.0143202i
$526$	120594.	−	32312.9i	0.435866	−	0.116790i
$527$	−21314.3	−	79545.9i	−0.0767448	−	0.286416i
$528$	80392.4	−	80392.4i	0.288368	−	0.288368i
$529$	−119544.	+	207056.i	−0.427184	+	0.739905i
$530$	−93520.5	+	53994.1i	−0.332932	+	0.192218i
$531$	1.03431e6	+	277142.i	3.66826	+	0.982908i
$532$			43108.2i			0.152313i
$533$	−19699.9	+	200486.i	−0.0693441	+	0.705714i
$534$	−377493.			−1.32381
$535$	−61459.2	+	229369.i	−0.214723	+	0.801358i
$536$	58607.7	+	101512.i	0.203998	+	0.353334i
$537$	−71329.4	−	41182.1i	−0.247355	−	0.142810i
$538$	41510.0	+	41510.0i	0.143413	+	0.143413i
$539$	230912.	−	61872.7i	0.794820	−	0.212971i
$540$	130048.	+	485344.i	0.445980	+	1.66442i
$541$	129117.	−	129117.i	0.441152	−	0.441152i	−0.451247	−	0.892399i	$-0.649021\pi$
$541$	129117.	−	129117.i	0.441152	−	0.441152i	0.892399	+	0.451247i	$0.149021\pi$
$542$	−88963.6	+	154089.i	−0.302840	+	0.524535i
$543$	860370.	−	496735.i	2.91800	−	1.68471i
$544$	77744.6	+	20831.6i	0.262708	+	0.0703923i
$545$		−	220267.i		−	0.741577i
$546$	−41915.7	−	51050.6i	−0.140602	−	0.171244i
$547$	−494292.			−1.65199			−0.825997	−	0.563674i	$-0.809387\pi$
$547$	−494292.			−1.65199			−0.825997	+	0.563674i	$0.809387\pi$
$548$	−40574.4	+	151426.i	−0.135111	+	0.504241i
$549$	−538211.	−	932209.i	−1.78570	−	3.09292i
$550$	−5675.05	−	3276.49i	−0.0187605	−	0.0108314i
$551$	−198568.	−	198568.i	−0.654042	−	0.654042i
$552$	184817.	−	49521.5i	0.606545	−	0.162523i
$553$	−13124.1	−	48979.8i	−0.0429160	−	0.160165i
$554$	74385.3	−	74385.3i	0.242364	−	0.242364i
$555$	−156850.	+	271673.i	−0.509213	+	0.881984i
$556$	−210796.	+	121703.i	−0.681887	+	0.393688i
$557$	−442425.	−	118547.i	−1.42603	−	0.382104i	−0.538412	−	0.842682i	$-0.680975\pi$
$557$	−442425.	−	118547.i	−1.42603	−	0.382104i	−0.887619	+	0.460578i	$0.847642\pi$
$558$		−	427624.i		−	1.37339i
$559$	−58098.1	−	21851.4i	−0.185925	−	0.0699289i
$560$	18288.1			0.0583167
$561$	33953.1	−	126715.i	0.107883	−	0.402625i
$562$	−38722.3	−	67068.9i	−0.122599	−	0.212348i
$563$	−26996.6	−	15586.5i	−0.0851711	−	0.0491736i	0.456810	−	0.889565i	$-0.348992\pi$
$563$	−26996.6	−	15586.5i	−0.0851711	−	0.0491736i	−0.541981	+	0.840391i	$0.682325\pi$
$564$	59046.9	+	59046.9i	0.185626	+	0.185626i
$565$	−138509.	+	37113.4i	−0.433891	+	0.116261i
$566$	−17787.1	−	66382.3i	−0.0555229	−	0.207214i
$567$	−110990.	+	110990.i	−0.345236	+	0.345236i
$568$	45127.0	−	78162.2i	0.139875	−	0.242270i
$569$	450482.	−	260086.i	1.39140	−	0.803326i	0.397931	−	0.917415i	$-0.369728\pi$
$569$	450482.	−	260086.i	1.39140	−	0.803326i	0.993471	+	0.114089i	$0.0363950\pi$
$570$	262516.	+	70340.9i	0.807989	+	0.216500i
$571$		−	167278.i		−	0.513057i	−0.966537	−	0.256528i	$-0.917421\pi$
$571$		−	167278.i		−	0.513057i	0.966537	−	0.256528i	$-0.0825787\pi$
$572$	−168354.	−	120583.i	−0.514556	−	0.368548i
$573$	505040.			1.53821
$574$	−7342.20	+	27401.5i	−0.0222845	+	0.0831668i
$575$	3009.70	+	5212.95i	0.00910306	+	0.0157670i
$576$	189965.	+	109676.i	0.572570	+	0.330574i
$577$	113625.	+	113625.i	0.341290	+	0.341290i	0.856852	−	0.515562i	$-0.172417\pi$
$577$	113625.	+	113625.i	0.341290	+	0.341290i	−0.515562	+	0.856852i	$0.672417\pi$
$578$	−156824.	+	42020.9i	−0.469416	+	0.125780i
$579$	132068.	+	492885.i	0.393950	+	1.47024i
$580$	−173579.	+	173579.i	−0.515989	+	0.515989i
$581$	−32455.6	+	56214.8i	−0.0961475	+	0.166532i
$582$	−510201.	+	294564.i	−1.50624	+	0.869630i
$583$	−215560.	−	57759.1i	−0.634206	−	0.169935i
$584$			128768.i			0.377557i
$585$	708693.	−	321300.i	2.07084	−	0.938855i
$586$	188071.			0.547678
$587$	−85863.1	+	320446.i	−0.249190	+	0.929990i	0.722041	+	0.691850i	$0.243204\pi$
$587$	−85863.1	+	320446.i	−0.249190	+	0.929990i	−0.971231	+	0.238139i	$0.923462\pi$
$588$	−217096.	−	376021.i	−0.627909	−	1.08757i
$589$	305338.	+	176287.i	0.880138	+	0.508148i
$590$	−204351.	−	204351.i	−0.587046	−	0.587046i
$591$	123414.	−	33068.6i	0.353336	−	0.0946762i
$592$	−13326.6	−	49735.5i	−0.0380255	−	0.141913i
$593$	−60427.5	+	60427.5i	−0.171840	+	0.171840i	−0.787788	−	0.615947i	$-0.788773\pi$
$593$	−60427.5	+	60427.5i	−0.171840	+	0.171840i	0.615947	+	0.787788i	$0.288773\pi$
$594$	194417.	−	336740.i	0.551012	−	0.954381i
$595$	18274.8	−	10551.0i	0.0516201	−	0.0298029i
$596$	30713.5	+	8229.66i	0.0864644	+	0.0231681i
$597$			729380.i			2.04647i
$598$	−29412.3	−	64875.0i	−0.0822483	−	0.181416i
$599$	−292574.			−0.815421			−0.407710	−	0.913111i	$-0.633673\pi$
$599$	−292574.			−0.815421			−0.407710	+	0.913111i	$0.633673\pi$
$600$	−7314.42	+	27297.8i	−0.0203178	+	0.0758271i
$601$	−6487.06	−	11235.9i	−0.0179597	−	0.0311071i	0.856906	−	0.515473i	$-0.172384\pi$
$601$	−6487.06	−	11235.9i	−0.0179597	−	0.0311071i	−0.874866	+	0.484366i	$0.839050\pi$
$602$	−7569.79	−	4370.42i	−0.0208877	−	0.0120595i
$603$	−271055.	−	271055.i	−0.745456	−	0.745456i
$604$	354415.	−	94965.1i	0.971489	−	0.260310i
$605$	−22484.6	−	83913.5i	−0.0614290	−	0.229256i
$606$	−148223.	+	148223.i	−0.403618	+	0.403618i
$607$	97043.8	−	168085.i	0.263385	−	0.456196i	−0.703755	−	0.710443i	$-0.748495\pi$
$607$	97043.8	−	168085.i	0.263385	−	0.456196i	0.967139	+	0.254248i	$0.0818278\pi$
$608$	−298424.	+	172295.i	−0.807285	+	0.466086i
$609$	−156299.	−	41880.1i	−0.421426	−	0.112921i
$610$			290515.i			0.780744i
$611$	42982.3	−	60010.7i	0.115135	−	0.160748i
$612$	−166714.			−0.445112
$613$	−79524.1	+	296788.i	−0.211630	+	0.789814i	0.775696	+	0.631107i	$0.217399\pi$
$613$	−79524.1	+	296788.i	−0.211630	+	0.789814i	−0.987326	+	0.158707i	$0.949267\pi$
$614$	152019.	+	263305.i	0.403239	+	0.698430i
$615$	−413621.	−	238804.i	−1.09358	−	0.631381i
$616$	−48961.6	−	48961.6i	−0.129031	−	0.129031i
$617$	168944.	−	45268.3i	0.443784	−	0.118912i	−0.0300055	−	0.999550i	$-0.509552\pi$
$617$	168944.	−	45268.3i	0.443784	−	0.118912i	0.473789	+	0.880638i	$0.342886\pi$
$618$	49923.7	+	186318.i	0.130716	+	0.487840i
$619$	−184299.	+	184299.i	−0.480997	+	0.480997i	−0.905450	−	0.424453i	$-0.860467\pi$
$619$	−184299.	+	184299.i	−0.480997	+	0.480997i	0.424453	+	0.905450i	$0.360467\pi$
$620$	154102.	−	266912.i	0.400889	−	0.694361i
$621$	−309321.	+	178586.i	−0.802095	+	0.463090i
$622$	248900.	+	66692.4i	0.643344	+	0.172384i
$623$		−	125486.i		−	0.323310i
$624$	−64258.8	+	170850.i	−0.165030	+	0.438779i
$625$	371100.			0.950016
$626$	17715.9	−	66116.7i	0.0452080	−	0.168718i
$627$	280821.	+	486396.i	0.714322	+	1.23724i
$628$	172560.	+	99627.4i	0.437542	+	0.252615i
$629$	−42010.7	−	42010.7i	−0.106184	−	0.106184i
$630$	105841.	−	28360.0i	0.266669	−	0.0714538i
$631$	−97664.4	−	364488.i	−0.245289	−	0.915430i	−0.973238	−	0.229799i	$-0.926193\pi$
$631$	−97664.4	−	364488.i	−0.245289	−	0.915430i	0.727949	−	0.685631i	$-0.240474\pi$
$632$	181535.	−	181535.i	0.454492	−	0.454492i
$633$	118796.	−	205761.i	0.296480	−	0.513518i
$634$	205466.	−	118626.i	0.511165	−	0.295121i
$635$	−366974.	−	98330.4i	−0.910097	−	0.243860i
$636$			405324.i			1.00205i
$637$	−296635.	+	243555.i	−0.731043	+	0.600231i
$638$	189963.			0.466689
$639$	−76392.3	+	285100.i	−0.187089	+	0.698225i
$640$	177411.	+	307284.i	0.433132	+	0.750206i
$641$	−605371.	−	349511.i	−1.47335	−	0.850638i	−0.473799	−	0.880633i	$-0.657118\pi$
$641$	−605371.	−	349511.i	−1.47335	−	0.850638i	−0.999550	+	0.0299949i	$0.990451\pi$
$642$	−236000.	−	236000.i	−0.572588	−	0.572588i
$643$	350856.	−	94011.6i	0.848608	−	0.227384i	0.191793	−	0.981435i	$-0.438570\pi$
$643$	350856.	−	94011.6i	0.848608	−	0.227384i	0.656815	+	0.754052i	$0.271903\pi$
$644$	6932.90	+	25874.0i	0.0167164	+	0.0623866i
$645$	104059.	−	104059.i	0.250127	−	0.250127i
$646$	−25736.0	+	44576.0i	−0.0616703	+	0.106816i
$647$	279880.	−	161589.i	0.668596	−	0.386014i	−0.126948	−	0.991909i	$-0.540518\pi$
$647$	279880.	−	161589.i	0.668596	−	0.386014i	0.795545	+	0.605895i	$0.207185\pi$
$648$	−767614.	−	205682.i	−1.82807	−	0.489830i
$649$		−	597227.i		−	1.41791i
$650$	10470.5	+	1028.84i	0.0247823	+	0.00243513i
$651$	203160.			0.479376
$652$	123515.	−	460963.i	0.290552	−	1.08435i
$653$	224593.	+	389006.i	0.526707	+	0.912284i	0.999516	+	0.0311188i	$0.00990701\pi$
$653$	224593.	+	389006.i	0.526707	+	0.912284i	−0.472808	+	0.881165i	$0.656760\pi$
$654$	268112.	+	154795.i	0.626846	+	0.361910i
$655$	−116473.	−	116473.i	−0.271482	−	0.271482i
$656$	75722.0	−	20289.6i	0.175960	−	0.0471484i
$657$	−108991.	−	406761.i	−0.252500	−	0.942342i
$658$	7350.12	−	7350.12i	0.0169763	−	0.0169763i
$659$	355669.	−	616037.i	0.818984	−	1.41852i	−0.0874472	−	0.996169i	$-0.527871\pi$
$659$	355669.	−	616037.i	0.818984	−	1.41852i	0.906431	−	0.422353i	$-0.138796\pi$
$660$	425184.	−	245480.i	0.976089	−	0.563545i
$661$	382899.	+	102597.i	0.876357	+	0.234819i	0.668835	−	0.743411i	$-0.266793\pi$
$661$	382899.	+	102597.i	0.876357	+	0.234819i	0.207522	+	0.978230i	$0.433460\pi$
$662$		−	192048.i		−	0.438221i
$663$	34356.4	+	207798.i	0.0781592	+	0.472732i
$664$	−328641.			−0.745394
$665$	−23382.7	+	87265.4i	−0.0528751	+	0.197333i
$666$	−154253.	−	267174.i	−0.347764	−	0.602345i
$667$	−151117.	−	87247.5i	−0.339674	−	0.196111i
$668$	−60342.3	−	60342.3i	−0.135229	−	0.135229i
$669$	−601883.	+	161274.i	−1.34481	+	0.360340i
$670$	26776.5	+	99931.2i	0.0596491	+	0.222614i
$671$	−424523.	+	424523.i	−0.942880	+	0.942880i
$672$	−99279.8	+	171958.i	−0.219848	+	0.380788i
$673$	−351802.	+	203113.i	−0.776727	+	0.448444i	−0.835269	−	0.549841i	$-0.814688\pi$
$673$	−351802.	+	203113.i	−0.776727	+	0.448444i	0.0585419	+	0.998285i	$0.481355\pi$
$674$	−132999.	−	35637.0i	−0.292771	−	0.0784479i
$675$		−	52755.0i		−	0.115786i
$676$	326117.	+	64713.9i	0.713641	+	0.141613i
$677$	−273635.			−0.597027			−0.298514	−	0.954405i	$-0.596491\pi$
$677$	−273635.			−0.597027			−0.298514	+	0.954405i	$0.596491\pi$
$678$	52163.5	−	194677.i	0.113477	−	0.423502i
$679$	−97919.1	−	169601.i	−0.212387	−	0.367865i
$680$	92524.0	+	53418.7i	0.200095	+	0.115525i
$681$	1.14655e6	+	1.14655e6i	2.47228	+	2.47228i
$682$	−230377.	+	61729.4i	−0.495303	+	0.132716i
$683$	13252.3	+	49458.3i	0.0284086	+	0.106022i	0.978674	−	0.205418i	$-0.0658553\pi$
$683$	13252.3	+	49458.3i	0.0284086	+	0.106022i	−0.950266	+	0.311440i	$0.899189\pi$
$684$	504701.	−	504701.i	1.07875	−	1.07875i
$685$	−164272.	+	284528.i	−0.350092	+	0.606378i
$686$	−96291.4	+	55593.8i	−0.204616	+	0.118135i
$687$	499266.	+	133778.i	1.05784	+	0.283446i
$688$			24154.7i			0.0510298i
$689$	353495.	−	58445.1i	0.744637	−	0.123115i
$690$	168877.			0.354709
$691$	66936.6	−	249811.i	0.140187	−	0.523185i	−0.859736	−	0.510739i	$-0.829372\pi$
$691$	66936.6	−	249811.i	0.140187	−	0.523185i	0.999923	−	0.0124455i	$-0.00396161\pi$
$692$	−61888.1	−	107193.i	−0.129239	−	0.223849i
$693$	196105.	+	113221.i	0.408340	+	0.235755i
$694$	268123.	+	268123.i	0.556693	+	0.556693i
$695$	−492735.	+	132028.i	−1.02010	+	0.273336i
$696$	−212036.	−	791329.i	−0.437715	−	1.63357i
$697$	63961.1	−	63961.1i	0.131659	−	0.131659i
$698$	−73124.8	+	126656.i	−0.150091	+	0.259965i
$699$	−1.27805e6	+	737885.i	−2.61574	+	1.51020i
$700$	−3821.63	−	1024.00i	−0.00779924	−	0.00208980i
$701$			361445.i			0.735540i	0.929917	+	0.367770i	$0.119879\pi$
$701$			361445.i			0.735540i	−0.929917	+	0.367770i	$0.880121\pi$
$702$	−61048.3	+	621288.i	−0.123880	+	1.26072i
$703$	254362.			0.514685
$704$	31664.5	−	118174.i	0.0638892	−	0.238438i
$705$	87502.6	+	151559.i	0.176053	+	0.304932i
$706$	−293030.	−	169181.i	−0.587898	−	0.339423i
$707$	−49272.3	−	49272.3i	−0.0985743	−	0.0985743i
$708$	−1.04776e6	+	280746.i	−2.09024	+	0.560077i
$709$	137117.	+	511729.i	0.272772	+	1.01800i	0.957320	+	0.289031i	$0.0933332\pi$
$709$	137117.	+	511729.i	0.272772	+	1.01800i	−0.684547	+	0.728968i	$0.740000\pi$
$710$	56328.0	−	56328.0i	0.111740	−	0.111740i
$711$	−419790.	+	727098.i	−0.830411	+	1.43831i
$712$	550209.	−	317664.i	1.08535	−	0.626624i
$713$	211618.	+	56703.0i	0.416269	+	0.111539i
$714$			29659.1i			0.0581784i
$715$	−275399.	−	335419.i	−0.538704	−	0.656108i
$716$	58379.6			0.113877
$717$	432458.	−	1.61395e6i	0.841212	−	3.13945i
$718$	−181331.	−	314074.i	−0.351741	−	0.609233i
$719$	−49890.2	−	28804.1i	−0.0965066	−	0.0557181i	0.450970	−	0.892539i	$-0.351078\pi$
$719$	−49890.2	−	28804.1i	−0.0965066	−	0.0557181i	−0.547477	+	0.836821i	$0.684411\pi$
$720$	−214113.	−	214113.i	−0.413027	−	0.413027i
$721$	−61935.7	+	16595.6i	−0.119143	+	0.0319244i
$722$	13386.8	+	49960.2i	0.0256804	+	0.0958407i
$723$	566472.	−	566472.i	1.08368	−	1.08368i
$724$	−352085.	+	609830.i	−0.671693	+	1.16341i
$725$	22320.3	−	12886.6i	0.0424643	−	0.0245167i
$726$	117942.	+	31602.5i	0.223767	+	0.0599581i
$727$			1582.61i			0.00299437i	0.999999	+	0.00149718i	$0.000476569\pi$
$727$			1582.61i			0.00299437i	−0.999999	+	0.00149718i	$0.999523\pi$
$728$	104053.	+	39135.7i	0.196333	+	0.0738432i
$729$	245225.			0.461435
$730$	−29415.6	+	109780.i	−0.0551991	+	0.206006i
$731$	13935.5	+	24137.1i	0.0260789	+	0.0451700i
$732$	944334.	+	545212.i	1.76240	+	1.01752i
$733$	364582.	+	364582.i	0.678559	+	0.678559i	0.959674	−	0.281115i	$-0.0907043\pi$
$733$	364582.	+	364582.i	0.678559	+	0.678559i	−0.281115	+	0.959674i	$0.590704\pi$
$734$	128410.	−	34407.5i	0.238346	−	0.0638647i
$735$	−235514.	−	878949.i	−0.435955	−	1.62701i
$736$	−151407.	+	151407.i	−0.279506	+	0.279506i
$737$	−106899.	+	185155.i	−0.196807	+	0.340880i
$738$	406771.	−	234849.i	0.746856	−	0.431198i
$739$	−568359.	−	152291.i	−1.04072	−	0.278860i	−0.302308	−	0.953210i	$-0.597757\pi$
$739$	−568359.	−	152291.i	−1.04072	−	0.278860i	−0.738411	+	0.674351i	$0.764424\pi$
$740$		−	222351.i		−	0.406046i
$741$	−733085.	−	525068.i	−1.33511	−	0.956267i
$742$	50454.5			0.0916414
$743$	−134191.	+	500807.i	−0.243078	+	0.907178i	0.731262	+	0.682097i	$0.238932\pi$
$743$	−134191.	+	500807.i	−0.243078	+	0.907178i	−0.974340	+	0.225082i	$0.927735\pi$
$744$	514292.	+	890781.i	0.929104	+	1.60926i
$745$	57710.5	+	33319.2i	0.103978	+	0.0600319i
$746$	−46733.8	−	46733.8i	−0.0839757	−	0.0839757i
$747$	1.03813e6	−	278167.i	1.86042	−	0.498499i
$748$	24065.9	+	89815.2i	0.0430129	+	0.160526i
$749$	78451.1	−	78451.1i	0.139841	−	0.139841i
$750$	−273891.	+	474392.i	−0.486917	+	0.843364i
$751$	−151770.	+	87624.4i	−0.269095	+	0.155362i	−0.628476	−	0.777829i	$-0.716321\pi$
$751$	−151770.	+	87624.4i	−0.269095	+	0.155362i	0.359381	+	0.933191i	$0.382988\pi$
$752$	−27746.0	−	7434.53i	−0.0490643	−	0.0131467i
$753$		−	1.95272e6i		−	3.44389i
$754$	−277775.	+	125935.i	−0.488596	+	0.221515i
$755$	768964.			1.34900
$756$	60761.2	−	226764.i	0.106312	−	0.396762i
$757$	−216745.	−	375414.i	−0.378232	−	0.655116i	0.612573	−	0.790414i	$-0.290134\pi$
$757$	−216745.	−	375414.i	−0.378232	−	0.655116i	−0.990805	+	0.135297i	$0.956801\pi$
$758$	13643.6	+	7877.11i	0.0237459	+	0.0137097i
$759$	246776.	+	246776.i	0.428371	+	0.428371i
$760$	−441819.	+	118385.i	−0.764921	+	0.204960i
$761$	439.181	+	1639.05i	0.000758358	+	0.00283023i	0.966304	−	0.257404i	$-0.0828670\pi$
$761$	439.181	+	1639.05i	0.000758358	+	0.00283023i	−0.965546	+	0.260234i	$0.916200\pi$
$762$	377584.	−	377584.i	0.650284	−	0.650284i
$763$	−51456.8	+	89125.8i	−0.0883881	+	0.153093i
$764$	−310013.	+	178986.i	−0.531120	+	0.306642i
$765$	−337485.	−	90428.9i	−0.576676	−	0.154520i
$766$			232241.i			0.395804i
$767$	395927.	+	873299.i	0.673014	+	1.48447i
$768$	−804122.			−1.36333
$769$	104274.	−	389157.i	0.176330	−	0.658071i	−0.819992	−	0.572375i	$-0.806022\pi$
$769$	104274.	−	389157.i	0.176330	−	0.658071i	0.996321	−	0.0856955i	$-0.0273112\pi$
$770$	−30557.2	−	52926.6i	−0.0515385	−	0.0892674i
$771$	−1.65921e6	−	957943.i	−2.79120	−	1.61150i
$772$	−255747.	−	255747.i	−0.429117	−	0.429117i
$773$	−87317.7	+	23396.7i	−0.146131	+	0.0391558i	−0.331143	−	0.943581i	$-0.607434\pi$
$773$	−87317.7	+	23396.7i	−0.146131	+	0.0391558i	0.185012	+	0.982736i	$0.440768\pi$
$774$	37457.5	+	139793.i	0.0625254	+	0.233348i
$775$	−22881.3	+	22881.3i	−0.0380958	+	0.0380958i
$776$	495757.	−	858677.i	0.823276	−	1.42596i
$777$	126932.	−	73284.1i	0.210246	−	0.121386i
$778$	−496390.	−	133007.i	−0.820094	−	0.219744i
$779$			387264.i			0.638165i
$780$	−458990.	+	640828.i	−0.754421	+	1.05330i
$781$	164622.			0.269889
$782$	−8278.01	+	30894.0i	−0.0135367	+	0.0505196i
$783$	764652.	+	1.32442e6i	1.24721	+	2.16024i
$784$	129347.	+	74678.6i	0.210438	+	0.121497i
$785$	295279.	+	295279.i	0.479173	+	0.479173i
$786$	223624.	−	59920.0i	0.361971	−	0.0969899i
$787$	58784.5	+	219387.i	0.0949103	+	0.354210i	0.997006	−	0.0773263i	$-0.0246383\pi$
$787$	58784.5	+	219387.i	0.0949103	+	0.354210i	−0.902096	+	0.431536i	$0.857972\pi$
$788$	−64036.5	+	64036.5i	−0.103128	+	0.103128i
$789$	491038.	−	850504.i	0.788790	−	1.36622i
$790$	196236.	−	113297.i	0.314430	−	0.181536i
$791$	64714.5	+	17340.2i	0.103430	+	0.0277141i
$792$			1.14646e6i			1.82772i
$793$	339328.	−	902197.i	0.539601	−	1.43468i
$794$	363780.			0.577028
$795$	−219856.	+	820512.i	−0.347859	+	1.29823i
$796$	−258492.	−	447721.i	−0.407963	−	0.706613i
$797$	892671.	+	515384.i	1.40532	+	0.811361i	0.994932	−	0.100551i	$-0.0320606\pi$
$797$	892671.	+	515384.i	1.40532	+	0.811361i	0.410386	+	0.911912i	$0.365394\pi$
$798$	−89788.4	−	89788.4i	−0.140998	−	0.140998i
$799$	−32015.0	+	8578.40i	−0.0501488	+	0.0134373i
$800$	−8185.48	−	30548.6i	−0.0127898	−	0.0477322i
$801$	−1.46916e6	+	1.46916e6i	−2.28984	+	2.28984i
$802$	−81424.4	+	141031.i	−0.126592	+	0.219263i
$803$	−203404.	+	117435.i	−0.315449	+	0.182124i
$804$	375084.	+	100503.i	0.580251	+	0.155478i
$805$			56138.1i			0.0866295i
$806$	295948.	−	242991.i	0.455559	−	0.374042i
$807$	461777.			0.709064
$808$	91309.4	−	340771.i	0.139860	−	0.521964i
$809$	−279770.	−	484576.i	−0.427468	−	0.740397i	0.569179	−	0.822214i	$-0.307261\pi$
$809$	−279770.	−	484576.i	−0.427468	−	0.740397i	−0.996647	+	0.0818166i	$0.973928\pi$
$810$	−607439.	−	350705.i	−0.925833	−	0.534530i
$811$	−15617.4	−	15617.4i	−0.0237447	−	0.0237447i	0.695135	−	0.718879i	$-0.255345\pi$
$811$	−15617.4	−	15617.4i	−0.0237447	−	0.0237447i	−0.718879	+	0.695135i	$0.755345\pi$
$812$	110784.	−	29684.6i	0.168022	−	0.0450214i
$813$	362246.	+	1.35192e6i	0.548053	+	2.04536i
$814$	−121670.	+	121670.i	−0.183626	+	0.183626i
$815$	500070.	−	866147.i	0.752863	−	1.30400i
$816$	70980.2	−	40980.4i	0.106600	−	0.0615455i
$817$	−115259.	−	30883.5i	−0.172675	−	0.0462682i
$818$			359794.i			0.537708i
$819$	−361815.	−	35552.3i	−0.539410	−	0.0530029i
$820$	338528.			0.503463
$821$	−104919.	+	391564.i	−0.155657	+	0.580920i	0.843391	+	0.537300i	$0.180556\pi$
$821$	−104919.	+	391564.i	−0.155657	+	0.580920i	−0.999048	+	0.0436197i	$0.986111\pi$
$822$	−230888.	−	399909.i	−0.341709	−	0.591858i
$823$	750117.	+	433080.i	1.10746	+	0.639394i	0.938171	−	0.346172i	$-0.112519\pi$
$823$	750117.	+	433080.i	1.10746	+	0.639394i	0.169292	+	0.985566i	$0.445852\pi$
$824$	−229553.	−	229553.i	−0.338088	−	0.338088i
$825$	−49790.7	+	13341.4i	−0.0731543	+	0.0196016i
$826$	34947.1	+	130424.i	0.0512213	+	0.191161i
$827$	−276075.	+	276075.i	−0.403661	+	0.403661i	−0.879521	−	0.475860i	$-0.842137\pi$
$827$	−276075.	+	276075.i	−0.403661	+	0.403661i	0.475860	+	0.879521i	$0.342137\pi$
$828$	221757.	−	384095.i	0.323458	−	0.560245i
$829$	−388574.	+	224343.i	−0.565412	+	0.326441i	−0.755315	−	0.655362i	$-0.772516\pi$
$829$	−388574.	+	224343.i	−0.565412	+	0.326441i	0.189903	+	0.981803i	$0.439183\pi$
$830$	−280181.	−	75074.3i	−0.406708	−	0.108977i
$831$		−	827499.i		−	1.19830i
$832$	32040.6	+	193792.i	0.0462865	+	0.279956i
$833$	172337.			0.248364
$834$	185568.	−	692549.i	0.266791	−	0.995677i
$835$	−89422.2	−	154884.i	−0.128254	−	0.222143i
$836$	−344757.	−	199046.i	−0.493288	−	0.284800i
$837$	−1.35771e6	−	1.35771e6i	−1.93800	−	1.93800i
$838$	−11233.1	+	3009.90i	−0.0159960	+	0.00428612i
$839$	−35296.0	−	131727.i	−0.0501420	−	0.187133i	0.936312	−	0.351168i	$-0.114215\pi$
$839$	−35296.0	−	131727.i	−0.0501420	−	0.187133i	−0.986454	+	0.164036i	$0.947549\pi$
$840$	−186369.	+	186369.i	−0.264128	+	0.264128i
$841$	−19926.9	+	34514.4i	−0.0281740	+	0.0487987i
$842$	−371206.	+	214316.i	−0.523589	+	0.302294i
$843$	−588436.	−	157671.i	−0.828027	−	0.221869i
$844$			168405.i			0.236412i
$845$	625068.	+	307895.i	0.875414	+	0.431210i
$846$	−172107.			−0.240468
$847$	−10505.3	+	39206.3i	−0.0146434	+	0.0546498i
$848$	−69713.6	−	120748.i	−0.0969451	−	0.167914i
$849$	−468171.	−	270299.i	−0.649515	−	0.374998i
$850$	−3340.42	−	3340.42i	−0.00462341	−	0.00462341i
$851$	152670.	−	40907.9i	0.210812	−	0.0564869i
$852$	−77385.9	−	288808.i	−0.106606	−	0.397860i
$853$	933402.	−	933402.i	1.28283	−	1.28283i	0.343787	−	0.939048i	$-0.388290\pi$
$853$	933402.	−	933402.i	1.28283	−	1.28283i	0.939048	−	0.343787i	$-0.111710\pi$
$854$	67867.5	−	117550.i	0.0930564	−	0.161178i
$855$	1.29544e6	−	747924.i	1.77209	−	1.02312i
$856$	542575.	+	145382.i	0.740478	+	0.198410i
$857$			1.09474e6i			1.49055i	0.666755	+	0.745277i	$0.267683\pi$
$857$			1.09474e6i			1.49055i	−0.666755	+	0.745277i	$0.732317\pi$
$858$	601816.	−	99501.3i	0.817502	−	0.135162i
$859$	639678.			0.866912			0.433456	−	0.901175i	$-0.357294\pi$
$859$	639678.			0.866912			0.433456	+	0.901175i	$0.357294\pi$
$860$	−26996.9	+	100754.i	−0.0365020	+	0.136227i
$861$	111575.	+	193253.i	0.150508	+	0.260687i
$862$	345614.	+	199540.i	0.465132	+	0.268544i
$863$	−831636.	−	831636.i	−1.11664	−	1.11664i	−0.992231	−	0.124405i	$-0.960298\pi$
$863$	−831636.	−	831636.i	−1.11664	−	1.11664i	−0.124405	−	0.992231i	$-0.539702\pi$
$864$	1.81266e6	−	485702.i	2.42823	−	0.650642i
$865$	−67138.5	−	250564.i	−0.0897304	−	0.334878i
$866$	−398781.	+	398781.i	−0.531739	+	0.531739i
$867$	−638564.	+	1.10603e6i	−0.849506	+	1.47139i
$868$	−124707.	+	71999.8i	−0.165521	+	0.0955635i
$869$	452314.	+	121197.i	0.598963	+	0.160492i
$870$		−	723080.i		−	0.955318i
$871$	33567.2	−	341613.i	0.0442465	−	0.450296i
$872$	−521044.			−0.685239
$873$	−839233.	+	3.13206e6i	−1.10117	+	4.10962i
$874$	−68466.2	−	118587.i	−0.0896300	−	0.155244i
$875$	−157697.	−	91046.7i	−0.205972	−	0.118918i
$876$	301643.	+	301643.i	0.393084	+	0.393084i
$877$	−739270.	+	198087.i	−0.961178	+	0.257547i	−0.705099	−	0.709109i	$-0.749097\pi$
$877$	−739270.	+	198087.i	−0.961178	+	0.257547i	−0.256079	+	0.966656i	$0.582431\pi$
$878$	24045.0	+	89737.3i	0.0311915	+	0.116408i
$879$	1.04609e6	−	1.04609e6i	1.35392	−	1.35392i
$880$	−84442.6	+	146259.i	−0.109043	+	0.188867i
$881$	61433.2	−	35468.5i	0.0791500	−	0.0456973i	−0.459903	−	0.887969i	$-0.652116\pi$
$881$	61433.2	−	35468.5i	0.0791500	−	0.0456973i	0.539053	+	0.842272i	$0.318782\pi$
$882$	864393.	+	231613.i	1.11115	+	0.297733i
$883$		−	230442.i		−	0.295557i	−0.989020	−	0.147778i	$-0.952788\pi$
$883$		−	230442.i		−	0.295557i	0.989020	−	0.147778i	$-0.0472123\pi$
$884$	−94732.8	−	115379.i	−0.121226	−	0.147646i
$885$	−2.27330e6			−2.90248
$886$	−81236.4	+	303178.i	−0.103486	+	0.386216i
$887$	−250826.	−	434444.i	−0.318805	−	0.552187i	0.661434	−	0.750004i	$-0.269948\pi$
$887$	−250826.	−	434444.i	−0.318805	−	0.552187i	−0.980239	+	0.197817i	$0.936615\pi$
$888$	642646.	+	371032.i	0.814978	+	0.470528i
$889$	125516.	+	125516.i	0.158817	+	0.158817i
$890$	541644.	−	145133.i	0.683808	−	0.183226i
$891$	−375160.	−	1.40012e6i	−0.472564	−	1.76363i
$892$	312303.	−	312303.i	0.392506	−	0.392506i
$893$	70950.7	−	122890.i	0.0889721	−	0.154104i
$894$	−81113.2	+	46830.7i	−0.101488	+	0.0585944i
$895$	118180.	+	31666.2i	0.147536	+	0.0395321i
$896$		−	165780.i		−	0.206499i
$897$	−524449.	−	197252.i	−0.651806	−	0.245153i
$898$	−536362.			−0.665128
$899$	242785.	−	906086.i	0.300402	−	1.12111i
$900$	32754.0	+	56731.5i	0.0404370	+	0.0700389i
$901$	−139326.	−	80439.7i	−0.171625	−	0.0990880i
$902$	−185241.	−	185241.i	−0.227680	−	0.227680i
$903$	−66414.4	+	17795.7i	−0.0814491	+	0.0218242i
$904$	87792.2	+	327645.i	0.107428	+	0.400928i
$905$	−1.04352e6	+	1.04352e6i	−1.27410	+	1.27410i
$906$	−540397.	+	935995.i	−0.658350	+	1.14029i
$907$	83825.0	−	48396.4i	0.101896	−	0.0588299i	−0.448186	−	0.893940i	$-0.647930\pi$
$907$	83825.0	−	48396.4i	0.101896	−	0.0588299i	0.550082	+	0.835110i	$0.314596\pi$
$908$	−1.11013e6	−	297459.i	−1.34649	−	0.360791i
$909$			1.15374e6i			1.39630i
$910$	79769.8	+	57134.7i	0.0963287	+	0.0689949i
$911$	583928.			0.703595			0.351798	−	0.936076i	$-0.385571\pi$
$911$	583928.			0.703595			0.351798	+	0.936076i	$0.385571\pi$
$912$	−90819.6	+	338943.i	−0.109192	+	0.407509i
$913$	−299718.	−	519127.i	−0.359560	−	0.622776i
$914$	17246.5	+	9957.27i	0.0206447	+	0.0119192i
$915$	1.61592e6	+	1.61592e6i	1.93009	+	1.93009i
$916$	−353879.	+	94821.7i	−0.421759	+	0.113010i
$917$	19918.6	+	74337.2i	0.0236875	+	0.0884031i
$918$	198210.	−	198210.i	0.235202	−	0.235202i
$919$	−395880.	+	685685.i	−0.468741	+	0.811883i	−0.999362	−	0.0357265i	$-0.988625\pi$
$919$	−395880.	+	685685.i	−0.468741	+	0.811883i	0.530621	+	0.847609i	$0.321959\pi$
$920$	−246144.	+	142112.i	−0.290813	+	0.167901i
$921$	2.31014e6	+	619000.i	2.72345	+	0.729745i
$922$		−	103225.i		−	0.121429i
$923$	−240719.	+	109135.i	−0.282558	+	0.128103i
$924$	−229388.			−0.268674
$925$	−6042.17	+	22549.7i	−0.00706170	+	0.0263546i
$926$	−174057.	−	301475.i	−0.202987	−	0.351584i
$927$	919426.	+	530831.i	1.06993	+	0.617727i
$928$	648281.	+	648281.i	0.752779	+	0.752779i
$929$	−658118.	+	176342.i	−0.762557	+	0.204327i	−0.619081	−	0.785327i	$-0.712495\pi$
$929$	−658118.	+	176342.i	−0.762557	+	0.204327i	−0.143476	+	0.989654i	$0.545828\pi$
$930$	234968.	+	876914.i	0.271671	+	1.01389i
$931$	−521724.	+	521724.i	−0.601924	+	0.601924i
$932$	523012.	−	905884.i	0.602116	−	1.04290i
$933$	1.75540e6	−	1.01348e6i	2.01657	−	1.16427i
$934$	−126585.	−	33918.4i	−0.145107	−	0.0388813i
$935$			194870.i			0.222906i
$936$	−760038.	−	1.67642e6i	−0.867529	−	1.91351i
$937$	−1.42104e6			−1.61856			−0.809278	−	0.587426i	$-0.800141\pi$
$937$	−1.42104e6			−1.61856			−0.809278	+	0.587426i	$0.800141\pi$
$938$	12510.6	−	46690.1i	0.0142191	−	0.0530664i
$939$	−269217.	−	466298.i	−0.305331	−	0.528849i
$940$	−107425.	−	62021.8i	−0.121576	−	0.0701921i
$941$	−549268.	−	549268.i	−0.620305	−	0.620305i	0.325305	−	0.945609i	$-0.394533\pi$
$941$	−549268.	−	549268.i	−0.620305	−	0.620305i	−0.945609	+	0.325305i	$0.894533\pi$
$942$	−566928.	+	151908.i	−0.638889	+	0.171190i
$943$	62282.1	+	232440.i	0.0700389	+	0.261389i
$944$	263844.	−	263844.i	0.296076	−	0.296076i
$945$	246002.	−	426088.i	0.275470	−	0.477129i
$946$	69904.7	−	40359.5i	0.0781131	−	0.0450986i
$947$	799306.	+	214173.i	0.891278	+	0.238817i	0.675267	−	0.737574i	$-0.264029\pi$
$947$	799306.	+	214173.i	0.891278	+	0.238817i	0.216011	+	0.976391i	$0.430695\pi$
$948$		−	850501.i		−	0.946363i
$949$	219576.	−	306566.i	0.243811	−	0.340402i
$950$	20225.2			0.0224102
$951$	483026.	−	1.80268e6i	0.534084	−	1.99323i
$952$	−24958.4	−	43229.3i	−0.0275387	−	0.0476984i
$953$	−702015.	−	405309.i	−0.772967	−	0.446273i	0.0609652	−	0.998140i	$-0.480582\pi$
$953$	−702015.	−	405309.i	−0.772967	−	0.446273i	−0.833932	+	0.551867i	$0.813915\pi$
$954$	−590709.	−	590709.i	−0.649048	−	0.649048i
$955$	−724655.	+	194171.i	−0.794556	+	0.212901i
$956$	306526.	+	1.14397e6i	0.335391	+	1.25170i
$957$	1.05662e6	−	1.05662e6i	1.15371	−	1.15371i
$958$	308232.	−	533874.i	0.335851	−	0.581712i
$959$	132938.	−	76751.6i	0.144548	−	0.0834546i
$960$	−449819.	−	120529.i	−0.488085	−	0.130782i
$961$			254226.i			0.275280i
$962$	97252.3	−	258572.i	0.105087	−	0.279403i
$963$	−1.83697e6			−1.98084
$964$	−146965.	+	548479.i	−0.158146	+	0.590209i
$965$	−378995.	−	656438.i	−0.406985	−	0.704919i
$966$	−68332.1	−	39451.6i	−0.0732269	−	0.0422776i
$967$	1.08406e6	+	1.08406e6i	1.15931	+	1.15931i	0.984625	+	0.174682i	$0.0558897\pi$
$967$	1.08406e6	+	1.08406e6i	1.15931	+	1.15931i	0.174682	+	0.984625i	$0.444110\pi$
$968$	−198498.	+	53187.5i	−0.211839	+	0.0567622i
$969$	104793.	+	391093.i	0.111605	+	0.416516i
$970$	618809.	−	618809.i	0.657678	−	0.657678i
$971$	181886.	−	315036.i	0.192913	−	0.334134i	−0.753302	−	0.657675i	$-0.771540\pi$
$971$	181886.	−	315036.i	0.192913	−	0.334134i	0.946214	+	0.323541i	$0.104873\pi$
$972$	−835209.	+	482208.i	−0.884021	+	0.510390i
$973$	230217.	+	61686.5i	0.243171	+	0.0651575i
$974$		−	377059.i		−	0.397459i
$975$	63962.2	−	52516.9i	0.0672844	−	0.0552446i
$976$	−375094.			−0.393768
$977$	99437.0	−	371104.i	0.104174	−	0.388782i	−0.894076	−	0.447915i	$-0.852167\pi$
$977$	99437.0	−	371104.i	0.104174	−	0.388782i	0.998250	+	0.0591326i	$0.0188335\pi$
$978$	702858.	+	1.21739e6i	0.734835	+	1.27277i
$979$	1.00357e6	+	579413.i	1.04709	+	0.604537i
$980$	456066.	+	456066.i	0.474871	+	0.474871i
$981$	1.64591e6	−	441020.i	1.71028	−	0.458269i
$982$	−93824.6	−	350158.i	−0.0972957	−	0.363112i
$983$	−200018.	+	200018.i	−0.206996	+	0.206996i	−0.802989	−	0.595993i	$-0.796758\pi$
$983$	−200018.	+	200018.i	−0.206996	+	0.206996i	0.595993	+	0.802989i	$0.296758\pi$
$984$	−564894.	+	978426.i	−0.583414	+	1.01050i
$985$	−164366.	+	94896.7i	−0.169410	+	0.0978090i
$986$	132279.	+	35443.9i	0.136062	+	0.0364576i
$987$		−	81766.3i		−	0.0839344i
$988$	636079.	+	62501.8i	0.651625	+	0.0640292i
$989$	−74146.3			−0.0758048
$990$	−261896.	+	977409.i	−0.267213	+	0.997254i
$991$	728833.	+	1.26238e6i	0.742131	+	1.28541i	0.951523	+	0.307577i	$0.0995181\pi$
$991$	728833.	+	1.26238e6i	0.742131	+	1.28541i	−0.209392	+	0.977832i	$0.567149\pi$
$992$	−996863.	−	575539.i	−1.01301	−	0.584859i
$993$	−1.06822e6	−	1.06822e6i	−1.08333	−	1.08333i
$994$	−35950.6	+	9632.94i	−0.0363860	+	0.00974959i
$995$	−280422.	−	1.04655e6i	−0.283247	−	1.05709i
$996$	−769851.	+	769851.i	−0.776047	+	0.776047i
$997$	381869.	−	661416.i	0.384170	−	0.665402i	−0.607483	−	0.794332i	$-0.707821\pi$
$997$	381869.	−	661416.i	0.384170	−	0.665402i	0.991654	+	0.128930i	$0.0411542\pi$
$998$	−256102.	+	147860.i	−0.257129	+	0.148454i
$999$	−1.33803e6	−	358524.i	−1.34071	−	0.359242i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	13.5.f.a.11.3	yes	16
3.2	odd	2		117.5.bd.c.37.2		16
13.2	odd	12		169.5.d.d.70.5		16
13.3	even	3		169.5.d.d.99.5		16
13.6	odd	12	inner	13.5.f.a.6.3	✓	16
13.10	even	6		169.5.d.c.99.4		16
13.11	odd	12		169.5.d.c.70.4		16
39.32	even	12		117.5.bd.c.19.2		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
13.5.f.a.6.3	✓	16	13.6	odd	12	inner
13.5.f.a.11.3	yes	16	1.1	even	1	trivial
117.5.bd.c.19.2		16	39.32	even	12
117.5.bd.c.37.2		16	3.2	odd	2
169.5.d.c.70.4		16	13.11	odd	12
169.5.d.c.99.4		16	13.10	even	6
169.5.d.d.70.5		16	13.2	odd	12
169.5.d.d.99.5		16	13.3	even	3

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:	\( N \)	\(=\)	\( 13 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	13.f (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.540374 - 2.01670i) q^{2} +(-8.21171 - 14.2231i) q^{3} +(10.0813 + 5.82045i) q^{4} +(17.2508 + 17.2508i) q^{5} +(-33.1212 + 8.87479i) q^{6} +(-2.95016 - 11.0101i) q^{7} +(40.8071 - 40.8071i) q^{8} +(-94.3643 + 163.444i) q^{9} +O(q^{10})\)	\(q+(0.540374 - 2.01670i) q^{2} +(-8.21171 - 14.2231i) q^{3} +(10.0813 + 5.82045i) q^{4} +(17.2508 + 17.2508i) q^{5} +(-33.1212 + 8.87479i) q^{6} +(-2.95016 - 11.0101i) q^{7} +(40.8071 - 40.8071i) q^{8} +(-94.3643 + 163.444i) q^{9} +(44.1117 - 25.4679i) q^{10} +(101.675 + 27.2438i) q^{11} -191.183i q^{12} +(-166.736 + 27.5674i) q^{13} -23.7984 q^{14} +(103.701 - 387.019i) q^{15} +(32.8825 + 56.9542i) q^{16} +(65.7171 + 37.9418i) q^{17} +(278.626 + 278.626i) q^{18} +(-313.811 + 84.0854i) q^{19} +(73.5035 + 274.319i) q^{20} +(-132.372 + 132.372i) q^{21} +(109.885 - 190.327i) q^{22} +(-174.829 + 100.938i) q^{23} +(-915.499 - 245.307i) q^{24} -29.8174i q^{25} +(-34.5048 + 351.155i) q^{26} +1769.27 q^{27} +(34.3425 - 128.168i) q^{28} +(432.185 + 748.566i) q^{29} +(-724.465 - 418.270i) q^{30} +(-767.381 - 767.381i) q^{31} +(1024.52 - 274.521i) q^{32} +(-447.436 - 1669.85i) q^{33} +(112.029 - 112.029i) q^{34} +(139.041 - 240.827i) q^{35} +(-1902.63 + 1098.49i) q^{36} +(-756.260 - 202.639i) q^{37} +678.302i q^{38} +(1761.28 + 2145.13i) q^{39} +1407.91 q^{40} +(308.517 - 1151.40i) q^{41} +(195.425 + 338.486i) q^{42} +(318.080 + 183.644i) q^{43} +(866.449 + 866.449i) q^{44} +(-4447.40 + 1191.68i) q^{45} +(109.088 + 407.123i) q^{46} +(-308.850 + 308.850i) q^{47} +(540.043 - 935.382i) q^{48} +(1966.81 - 1135.54i) q^{49} +(-60.1328 - 16.1125i) q^{50} -1246.27i q^{51} +(-1841.38 - 692.566i) q^{52} -2120.08 q^{53} +(956.069 - 3568.10i) q^{54} +(1284.00 + 2223.96i) q^{55} +(-569.679 - 328.904i) q^{56} +(3772.88 + 3772.88i) q^{57} +(1743.18 - 467.083i) q^{58} +(-1468.47 - 5480.39i) q^{59} +(3298.07 - 3298.07i) q^{60} +(-2851.77 + 4939.42i) q^{61} +(-1962.25 + 1132.91i) q^{62} +(2077.93 + 556.779i) q^{63} -1162.27i q^{64} +(-3351.90 - 2400.78i) q^{65} -3609.38 q^{66} +(-525.691 + 1961.90i) q^{67} +(441.677 + 765.007i) q^{68} +(2871.29 + 1657.74i) q^{69} +(-410.542 - 410.542i) q^{70} +(1510.63 - 404.773i) q^{71} +(2818.93 + 10520.4i) q^{72} +(-1577.77 + 1577.77i) q^{73} +(-817.326 + 1415.65i) q^{74} +(-424.095 + 244.852i) q^{75} +(-3653.04 - 978.830i) q^{76} -1199.83i q^{77} +(5277.85 - 2392.81i) q^{78} +4448.61 q^{79} +(-415.256 + 1549.76i) q^{80} +(-6885.24 - 11925.6i) q^{81} +(-2155.32 - 1244.38i) q^{82} +(-4026.77 - 4026.77i) q^{83} +(-2104.95 + 564.021i) q^{84} +(479.148 + 1788.20i) q^{85} +(542.237 - 542.237i) q^{86} +(7097.95 - 12294.0i) q^{87} +(5260.81 - 3037.33i) q^{88} +(10633.9 + 2849.33i) q^{89} +9613.05i q^{90} +(795.419 + 1754.46i) q^{91} -2350.01 q^{92} +(-4613.03 + 17216.0i) q^{93} +(455.964 + 789.753i) q^{94} +(-6864.05 - 3962.96i) q^{95} +(-12317.6 - 12317.6i) q^{96} +(16595.6 - 4446.77i) q^{97} +(-1227.23 - 4580.08i) q^{98} +(-14047.3 + 14047.3i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 4 q^{2} - 2 q^{3} - 6 q^{4} + 8 q^{5} - 38 q^{6} + 56 q^{7} + 90 q^{8} - 164 q^{9}+O(q^{10}) \) 16 * q - 4 * q^2 - 2 * q^3 - 6 * q^4 + 8 * q^5 - 38 * q^6 + 56 * q^7 + 90 * q^8 - 164 * q^9	\( 16 q - 4 q^{2} - 2 q^{3} - 6 q^{4} + 8 q^{5} - 38 q^{6} + 56 q^{7} + 90 q^{8} - 164 q^{9} - 486 q^{10} - 100 q^{11} + 294 q^{13} + 808 q^{14} + 346 q^{15} + 230 q^{16} + 984 q^{17} + 2434 q^{18} - 1498 q^{19} - 3962 q^{20} - 1076 q^{21} - 1524 q^{22} - 1014 q^{23} - 2142 q^{24} + 614 q^{26} + 3352 q^{27} + 5764 q^{28} + 814 q^{29} + 9162 q^{30} + 4060 q^{31} - 4996 q^{32} - 5636 q^{33} - 2502 q^{34} - 4892 q^{35} - 15750 q^{36} - 1790 q^{37} + 6982 q^{39} + 18816 q^{40} + 4280 q^{41} - 1204 q^{42} - 1368 q^{43} + 10736 q^{44} - 6806 q^{45} - 15246 q^{46} + 1484 q^{47} - 3002 q^{48} - 11820 q^{49} - 13574 q^{50} + 1432 q^{52} + 7204 q^{53} + 13240 q^{54} + 6936 q^{55} + 8124 q^{56} + 12736 q^{57} + 3030 q^{58} - 2380 q^{59} - 6472 q^{60} - 162 q^{61} + 19614 q^{62} + 12004 q^{63} - 5248 q^{65} - 23872 q^{66} - 14854 q^{67} - 6444 q^{68} + 2412 q^{69} - 34524 q^{70} - 8050 q^{71} + 15420 q^{72} - 15448 q^{73} - 2882 q^{74} + 8280 q^{75} + 10622 q^{76} - 11672 q^{78} - 17064 q^{79} + 2564 q^{80} + 2128 q^{81} - 5346 q^{82} + 12788 q^{83} + 25948 q^{84} + 35382 q^{85} + 67260 q^{86} + 29342 q^{87} + 40836 q^{88} + 20492 q^{89} + 8996 q^{91} - 49884 q^{92} - 78920 q^{93} - 30606 q^{94} - 98574 q^{95} - 94664 q^{96} + 50944 q^{97} + 61484 q^{98} - 21632 q^{99}+O(q^{100}) \) 16 * q - 4 * q^2 - 2 * q^3 - 6 * q^4 + 8 * q^5 - 38 * q^6 + 56 * q^7 + 90 * q^8 - 164 * q^9 - 486 * q^10 - 100 * q^11 + 294 * q^13 + 808 * q^14 + 346 * q^15 + 230 * q^16 + 984 * q^17 + 2434 * q^18 - 1498 * q^19 - 3962 * q^20 - 1076 * q^21 - 1524 * q^22 - 1014 * q^23 - 2142 * q^24 + 614 * q^26 + 3352 * q^27 + 5764 * q^28 + 814 * q^29 + 9162 * q^30 + 4060 * q^31 - 4996 * q^32 - 5636 * q^33 - 2502 * q^34 - 4892 * q^35 - 15750 * q^36 - 1790 * q^37 + 6982 * q^39 + 18816 * q^40 + 4280 * q^41 - 1204 * q^42 - 1368 * q^43 + 10736 * q^44 - 6806 * q^45 - 15246 * q^46 + 1484 * q^47 - 3002 * q^48 - 11820 * q^49 - 13574 * q^50 + 1432 * q^52 + 7204 * q^53 + 13240 * q^54 + 6936 * q^55 + 8124 * q^56 + 12736 * q^57 + 3030 * q^58 - 2380 * q^59 - 6472 * q^60 - 162 * q^61 + 19614 * q^62 + 12004 * q^63 - 5248 * q^65 - 23872 * q^66 - 14854 * q^67 - 6444 * q^68 + 2412 * q^69 - 34524 * q^70 - 8050 * q^71 + 15420 * q^72 - 15448 * q^73 - 2882 * q^74 + 8280 * q^75 + 10622 * q^76 - 11672 * q^78 - 17064 * q^79 + 2564 * q^80 + 2128 * q^81 - 5346 * q^82 + 12788 * q^83 + 25948 * q^84 + 35382 * q^85 + 67260 * q^86 + 29342 * q^87 + 40836 * q^88 + 20492 * q^89 + 8996 * q^91 - 49884 * q^92 - 78920 * q^93 - 30606 * q^94 - 98574 * q^95 - 94664 * q^96 + 50944 * q^97 + 61484 * q^98 - 21632 * q^99

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