LMFDB - Embedded newform 38.5.f.a.15.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [38,5,Mod(3,38)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(38, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([13]))

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

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

chi := DirichletCharacter("38.3");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 38 = 2 \cdot 19 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	38.f (of order $18$, degree $6$, 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:	$36$
Relative dimension:	$6$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			15.2
Character	$\chi$	$=$	38.15
Dual form			38.5.f.a.33.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.967379 + 2.65785i) q^{2} +(1.72776 - 0.304651i) q^{3} +(-6.12836 - 5.14230i) q^{4} +(-25.8893 + 21.7237i) q^{5} +(-0.861682 + 4.88684i) q^{6} +(-9.12940 + 15.8126i) q^{7} +(19.5959 - 11.3137i) q^{8} +(-73.2228 + 26.6509i) q^{9} +O(q^{10})$	\(q+(-0.967379 + 2.65785i) q^{2} +(1.72776 - 0.304651i) q^{3} +(-6.12836 - 5.14230i) q^{4} +(-25.8893 + 21.7237i) q^{5} +(-0.861682 + 4.88684i) q^{6} +(-9.12940 + 15.8126i) q^{7} +(19.5959 - 11.3137i) q^{8} +(-73.2228 + 26.6509i) q^{9} +(-32.6936 - 89.8249i) q^{10} +(4.73025 + 8.19303i) q^{11} +(-12.1549 - 7.01766i) q^{12} +(-190.918 - 33.6639i) q^{13} +(-33.1959 - 39.5614i) q^{14} +(-38.1123 + 45.4205i) q^{15} +(11.1135 + 63.0277i) q^{16} +(407.971 + 148.489i) q^{17} -220.397i q^{18} +(296.077 + 206.541i) q^{19} +270.369 q^{20} +(-10.9561 + 30.1016i) q^{21} +(-26.3518 + 4.64654i) q^{22} +(185.114 + 155.329i) q^{23} +(30.4103 - 25.5173i) q^{24} +(89.8063 - 509.317i) q^{25} +(274.163 - 474.865i) q^{26} +(-241.461 + 139.408i) q^{27} +(137.261 - 49.9590i) q^{28} +(276.647 + 760.080i) q^{29} +(-83.8519 - 145.236i) q^{30} +(-648.411 - 374.360i) q^{31} +(-178.269 - 31.4337i) q^{32} +(10.6687 + 12.7145i) q^{33} +(-789.325 + 940.681i) q^{34} +(-107.154 - 607.701i) q^{35} +(585.782 + 213.207i) q^{36} -1726.97i q^{37} +(-835.375 + 587.125i) q^{38} -340.116 q^{39} +(-261.549 + 718.599i) q^{40} +(159.104 - 28.0544i) q^{41} +(-69.4070 - 58.2394i) q^{42} +(-2363.70 + 1983.38i) q^{43} +(13.1424 - 74.5342i) q^{44} +(1316.73 - 2280.64i) q^{45} +(-591.918 + 341.744i) q^{46} +(-1585.37 + 577.028i) q^{47} +(38.4029 + 105.511i) q^{48} +(1033.81 + 1790.61i) q^{49} +(1266.81 + 731.394i) q^{50} +(750.113 + 132.265i) q^{51} +(996.901 + 1188.06i) q^{52} +(767.248 - 914.371i) q^{53} +(-136.940 - 776.627i) q^{54} +(-300.446 - 109.353i) q^{55} +413.149i q^{56} +(574.473 + 266.654i) q^{57} -2287.80 q^{58} +(863.095 - 2371.33i) q^{59} +(467.132 - 82.3680i) q^{60} +(-3074.09 - 2579.47i) q^{61} +(1622.25 - 1361.23i) q^{62} +(247.060 - 1401.15i) q^{63} +(256.000 - 443.405i) q^{64} +(5674.03 - 3275.90i) q^{65} +(-44.1140 + 16.0562i) q^{66} +(1347.91 + 3703.34i) q^{67} +(-1736.61 - 3007.90i) q^{68} +(367.154 + 211.977i) q^{69} +(1718.84 + 303.077i) q^{70} +(4927.79 + 5872.71i) q^{71} +(-1133.35 + 1350.67i) q^{72} +(364.590 + 2067.69i) q^{73} +(4590.02 + 1670.63i) q^{74} -907.337i q^{75} +(-752.368 - 2788.28i) q^{76} -172.737 q^{77} +(329.021 - 903.977i) q^{78} +(-9223.86 + 1626.42i) q^{79} +(-1656.91 - 1390.32i) q^{80} +(4460.31 - 3742.65i) q^{81} +(-79.3497 + 450.015i) q^{82} +(-4594.59 + 7958.07i) q^{83} +(221.934 - 128.134i) q^{84} +(-13787.8 + 5018.35i) q^{85} +(-2984.93 - 8201.03i) q^{86} +(709.538 + 1228.96i) q^{87} +(185.387 + 107.033i) q^{88} +(9502.28 + 1675.51i) q^{89} +(4787.83 + 5705.92i) q^{90} +(2275.28 - 2711.57i) q^{91} +(-335.696 - 1903.83i) q^{92} +(-1234.35 - 449.266i) q^{93} -4771.89i q^{94} +(-12152.1 + 1084.68i) q^{95} -317.583 q^{96} +(-1743.06 + 4789.02i) q^{97} +(-5759.26 + 1015.51i) q^{98} +(-564.714 - 473.851i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q + 12 q^{3} + 48 q^{6} + 90 q^{7} - 84 q^{9}+O(q^{10}) $ 36 * q + 12 * q^3 + 48 * q^6 + 90 * q^7 - 84 * q^9	\( 36 q + 12 q^{3} + 48 q^{6} + 90 q^{7} - 84 q^{9} + 90 q^{11} - 432 q^{12} - 330 q^{13} + 576 q^{14} + 2658 q^{15} - 522 q^{17} - 1236 q^{19} - 864 q^{20} - 1998 q^{21} - 1344 q^{22} - 1440 q^{23} - 384 q^{24} - 3276 q^{25} + 576 q^{26} + 1692 q^{27} + 1056 q^{28} + 4050 q^{29} + 2808 q^{31} + 2910 q^{33} + 1536 q^{34} + 1422 q^{35} + 672 q^{36} + 1872 q^{38} - 9024 q^{39} - 3060 q^{41} - 3456 q^{42} - 1218 q^{43} - 5760 q^{44} - 2592 q^{45} - 2880 q^{46} + 990 q^{47} + 1536 q^{48} - 9696 q^{49} + 27648 q^{50} + 35784 q^{51} - 1488 q^{52} + 17082 q^{53} + 2160 q^{54} + 4290 q^{55} + 204 q^{57} - 5376 q^{58} - 11142 q^{59} - 11856 q^{60} - 35928 q^{61} - 7200 q^{62} - 58254 q^{63} + 9216 q^{64} - 34290 q^{65} - 32928 q^{66} + 44322 q^{67} - 4752 q^{68} + 21762 q^{69} + 12864 q^{70} + 40428 q^{71} + 10752 q^{72} + 6936 q^{73} - 4032 q^{74} - 576 q^{76} - 36648 q^{77} - 11040 q^{78} - 29298 q^{79} + 24324 q^{81} - 14592 q^{82} + 23958 q^{83} + 36720 q^{84} + 2772 q^{85} + 30816 q^{86} + 14256 q^{87} + 26064 q^{89} + 14784 q^{90} + 100044 q^{91} + 9360 q^{92} + 26400 q^{93} - 38646 q^{95} - 55746 q^{97} - 64512 q^{98} - 69846 q^{99}+O(q^{100}) \) 36 * q + 12 * q^3 + 48 * q^6 + 90 * q^7 - 84 * q^9 + 90 * q^11 - 432 * q^12 - 330 * q^13 + 576 * q^14 + 2658 * q^15 - 522 * q^17 - 1236 * q^19 - 864 * q^20 - 1998 * q^21 - 1344 * q^22 - 1440 * q^23 - 384 * q^24 - 3276 * q^25 + 576 * q^26 + 1692 * q^27 + 1056 * q^28 + 4050 * q^29 + 2808 * q^31 + 2910 * q^33 + 1536 * q^34 + 1422 * q^35 + 672 * q^36 + 1872 * q^38 - 9024 * q^39 - 3060 * q^41 - 3456 * q^42 - 1218 * q^43 - 5760 * q^44 - 2592 * q^45 - 2880 * q^46 + 990 * q^47 + 1536 * q^48 - 9696 * q^49 + 27648 * q^50 + 35784 * q^51 - 1488 * q^52 + 17082 * q^53 + 2160 * q^54 + 4290 * q^55 + 204 * q^57 - 5376 * q^58 - 11142 * q^59 - 11856 * q^60 - 35928 * q^61 - 7200 * q^62 - 58254 * q^63 + 9216 * q^64 - 34290 * q^65 - 32928 * q^66 + 44322 * q^67 - 4752 * q^68 + 21762 * q^69 + 12864 * q^70 + 40428 * q^71 + 10752 * q^72 + 6936 * q^73 - 4032 * q^74 - 576 * q^76 - 36648 * q^77 - 11040 * q^78 - 29298 * q^79 + 24324 * q^81 - 14592 * q^82 + 23958 * q^83 + 36720 * q^84 + 2772 * q^85 + 30816 * q^86 + 14256 * q^87 + 26064 * q^89 + 14784 * q^90 + 100044 * q^91 + 9360 * q^92 + 26400 * q^93 - 38646 * q^95 - 55746 * q^97 - 64512 * q^98 - 69846 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$21$
$\chi(n)$	$e\left(\frac{11}{18}\right)$

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 $

$2$	−0.967379	+	2.65785i	−0.241845	+	0.664463i
$2$	−0.967379	+	2.65785i	−0.241845	+	0.664463i
$3$	1.72776	−	0.304651i	0.191973	−	0.0338501i	−0.0768347	−	0.997044i	$-0.524481\pi$
$3$	1.72776	−	0.304651i	0.191973	−	0.0338501i	0.268808	+	0.963194i	$0.413370\pi$
$4$	−6.12836	−	5.14230i	−0.383022	−	0.321394i
$5$	−25.8893	+	21.7237i	−1.03557	+	0.868948i	−0.991503	−	0.130081i	$-0.958476\pi$
$5$	−25.8893	+	21.7237i	−1.03557	+	0.868948i	−0.0440681	+	0.999029i	$0.514032\pi$
$6$	−0.861682	+	4.88684i	−0.0239356	+	0.135746i
$7$	−9.12940	+	15.8126i	−0.186314	+	0.322706i	−0.944019	−	0.329892i	$-0.892988\pi$
$7$	−9.12940	+	15.8126i	−0.186314	+	0.322706i	0.757704	+	0.652598i	$0.226321\pi$
$8$	19.5959	−	11.3137i	0.306186	−	0.176777i
$9$	−73.2228	+	26.6509i	−0.903985	+	0.329024i
$10$	−32.6936	−	89.8249i	−0.326936	−	0.898249i
$11$	4.73025	+	8.19303i	0.0390930	+	0.0677110i	0.884910	−	0.465762i	$-0.154220\pi$
$11$	4.73025	+	8.19303i	0.0390930	+	0.0677110i	−0.845817	+	0.533473i	$0.820886\pi$
$12$	−12.1549	−	7.01766i	−0.0844093	−	0.0487337i
$13$	−190.918	−	33.6639i	−1.12969	−	0.199195i	−0.422599	−	0.906317i	$-0.638882\pi$
$13$	−190.918	−	33.6639i	−1.12969	−	0.199195i	−0.707092	+	0.707122i	$0.749993\pi$
$14$	−33.1959	−	39.5614i	−0.169367	−	0.201844i
$15$	−38.1123	+	45.4205i	−0.169388	+	0.201869i
$16$	11.1135	+	63.0277i	0.0434120	+	0.246202i
$17$	407.971	+	148.489i	1.41166	+	0.513804i	0.931618	−	0.363440i	$-0.118398\pi$
$17$	407.971	+	148.489i	1.41166	+	0.513804i	0.480046	+	0.877243i	$0.340620\pi$
$18$		−	220.397i		−	0.680237i
$19$	296.077	+	206.541i	0.820158	+	0.572137i
$19$	296.077	+	206.541i	0.820158	+	0.572137i
$20$	270.369			0.675921
$21$	−10.9561	+	30.1016i	−0.0248438	+	0.0682577i
$22$	−26.3518	+	4.64654i	−0.0544459	+	0.00960028i
$23$	185.114	+	155.329i	0.349932	+	0.293628i	0.800763	−	0.598981i	$-0.204428\pi$
$23$	185.114	+	155.329i	0.349932	+	0.293628i	−0.450831	+	0.892610i	$0.648872\pi$
$24$	30.4103	−	25.5173i	0.0527957	−	0.0443008i
$25$	89.8063	−	509.317i	0.143690	−	0.814907i
$26$	274.163	−	474.865i	0.405567	−	0.702463i
$27$	−241.461	+	139.408i	−0.331222	+	0.191231i
$28$	137.261	−	49.9590i	0.175078	−	0.0637232i
$29$	276.647	+	760.080i	0.328949	+	0.903781i	0.988378	+	0.152014i	$0.0485760\pi$
$29$	276.647	+	760.080i	0.328949	+	0.903781i	−0.659429	+	0.751767i	$0.729202\pi$
$30$	−83.8519	−	145.236i	−0.0931688	−	0.161373i
$31$	−648.411	−	374.360i	−0.674726	−	0.389553i	0.123139	−	0.992389i	$-0.460704\pi$
$31$	−648.411	−	374.360i	−0.674726	−	0.389553i	−0.797865	+	0.602836i	$0.794037\pi$
$32$	−178.269	−	31.4337i	−0.174091	−	0.0306970i
$33$	10.6687	+	12.7145i	0.00979683	+	0.0116754i
$34$	−789.325	+	940.681i	−0.682807	+	0.813738i
$35$	−107.154	−	607.701i	−0.0874727	−	0.496082i
$36$	585.782	+	213.207i	0.451992	+	0.164512i
$37$		−	1726.97i		−	1.26148i	−0.775994	−	0.630741i	$-0.782751\pi$
$37$		−	1726.97i		−	1.26148i	0.775994	−	0.630741i	$-0.217249\pi$
$38$	−835.375	+	587.125i	−0.578515	+	0.406596i
$39$	−340.116			−0.223613
$40$	−261.549	+	718.599i	−0.163468	+	0.449125i
$41$	159.104	−	28.0544i	0.0946485	−	0.0166891i	−0.126123	−	0.992015i	$-0.540253\pi$
$41$	159.104	−	28.0544i	0.0946485	−	0.0166891i	0.220772	+	0.975325i	$0.429142\pi$
$42$	−69.4070	−	58.2394i	−0.0393464	−	0.0330155i
$43$	−2363.70	+	1983.38i	−1.27836	+	1.07268i	−0.284897	+	0.958558i	$0.591959\pi$
$43$	−2363.70	+	1983.38i	−1.27836	+	1.07268i	−0.993467	+	0.114117i	$0.963596\pi$
$44$	13.1424	−	74.5342i	0.00678842	−	0.0384991i
$45$	1316.73	−	2280.64i	0.650237	−	1.12624i
$46$	−591.918	+	341.744i	−0.279734	+	0.161505i
$47$	−1585.37	+	577.028i	−0.717688	+	0.261217i	−0.674944	−	0.737869i	$-0.735832\pi$
$47$	−1585.37	+	577.028i	−0.717688	+	0.261217i	−0.0427440	+	0.999086i	$0.513610\pi$
$48$	38.4029	+	105.511i	0.0166679	+	0.0457947i
$49$	1033.81	+	1790.61i	0.430574	+	0.745776i
$50$	1266.81	+	731.394i	0.506725	+	0.292558i
$51$	750.113	+	132.265i	0.288394	+	0.0508517i
$52$	996.901	+	1188.06i	0.368676	+	0.439371i
$53$	767.248	−	914.371i	0.273139	−	0.325515i	−0.611985	−	0.790869i	$-0.709629\pi$
$53$	767.248	−	914.371i	0.273139	−	0.325515i	0.885124	+	0.465355i	$0.154073\pi$
$54$	−136.940	−	776.627i	−0.0469617	−	0.266333i
$55$	−300.446	−	109.353i	−0.0993209	−	0.0361498i
$56$			413.149i			0.131744i
$57$	574.473	+	266.654i	0.176815	+	0.0820726i
$58$	−2287.80			−0.680084
$59$	863.095	−	2371.33i	0.247945	−	0.681222i	−0.751817	−	0.659372i	$-0.770822\pi$
$59$	863.095	−	2371.33i	0.247945	−	0.681222i	0.999761	−	0.0218501i	$-0.00695565\pi$
$60$	467.132	−	82.3680i	0.129759	−	0.0228800i
$61$	−3074.09	−	2579.47i	−0.826146	−	0.693219i	0.128257	−	0.991741i	$-0.459062\pi$
$61$	−3074.09	−	2579.47i	−0.826146	−	0.693219i	−0.954403	+	0.298522i	$0.903506\pi$
$62$	1622.25	−	1361.23i	0.422022	−	0.354119i
$63$	247.060	−	1401.15i	0.0622474	−	0.353023i
$64$	256.000	−	443.405i	0.0625000	−	0.108253i
$65$	5674.03	−	3275.90i	1.34296	−	0.775361i
$66$	−44.1140	+	16.0562i	−0.0101272	+	0.00368600i
$67$	1347.91	+	3703.34i	0.300269	+	0.824981i	0.994453	+	0.105184i	$0.0335431\pi$
$67$	1347.91	+	3703.34i	0.300269	+	0.824981i	−0.694184	+	0.719798i	$0.744235\pi$
$68$	−1736.61	−	3007.90i	−0.375565	−	0.650498i
$69$	367.154	+	211.977i	0.0771170	+	0.0445235i
$70$	1718.84	+	303.077i	0.350783	+	0.0618525i
$71$	4927.79	+	5872.71i	0.977541	+	1.16499i	0.986289	+	0.165027i	$0.0527710\pi$
$71$	4927.79	+	5872.71i	0.977541	+	1.16499i	−0.00874782	+	0.999962i	$0.502785\pi$
$72$	−1133.35	+	1350.67i	−0.218624	+	0.260546i
$73$	364.590	+	2067.69i	0.0684163	+	0.388008i	0.999718	+	0.0237585i	$0.00756329\pi$
$73$	364.590	+	2067.69i	0.0684163	+	0.388008i	−0.931301	+	0.364249i	$0.881326\pi$
$74$	4590.02	+	1670.63i	0.838208	+	0.305083i
$75$		−	907.337i		−	0.161304i
$76$	−752.368	−	2788.28i	−0.130258	−	0.482735i
$77$	−172.737			−0.0291343
$78$	329.021	−	903.977i	0.0540797	−	0.148583i
$79$	−9223.86	+	1626.42i	−1.47795	+	0.260602i	−0.853757	−	0.520671i	$-0.825682\pi$
$79$	−9223.86	+	1626.42i	−1.47795	+	0.260602i	−0.624189	+	0.781273i	$0.714571\pi$
$80$	−1656.91	−	1390.32i	−0.258893	−	0.217237i
$81$	4460.31	−	3742.65i	0.679822	−	0.570439i
$82$	−79.3497	+	450.015i	−0.0118010	+	0.0669266i
$83$	−4594.59	+	7958.07i	−0.666946	+	1.15518i	0.311808	+	0.950145i	$0.399066\pi$
$83$	−4594.59	+	7958.07i	−0.666946	+	1.15518i	−0.978754	+	0.205039i	$0.934268\pi$
$84$	221.934	−	128.134i	0.0314533	−	0.0181596i
$85$	−13787.8	+	5018.35i	−1.90835	+	0.694581i
$86$	−2984.93	−	8201.03i	−0.403587	−	1.10885i
$87$	709.538	+	1228.96i	0.0937426	+	0.162367i
$88$	185.387	+	107.033i	0.0239395	+	0.0138215i
$89$	9502.28	+	1675.51i	1.19963	+	0.211527i	0.737539	−	0.675305i	$-0.235988\pi$
$89$	9502.28	+	1675.51i	1.19963	+	0.211527i	0.462092	+	0.886832i	$0.347099\pi$
$90$	4787.83	+	5705.92i	0.591090	+	0.704434i
$91$	2275.28	−	2711.57i	0.274759	−	0.327445i
$92$	−335.696	−	1903.83i	−0.0396616	−	0.224932i
$93$	−1234.35	−	449.266i	−0.142716	−	0.0519443i
$94$		−	4771.89i		−	0.540051i
$95$	−12152.1	+	1084.68i	−1.34649	+	0.120186i
$96$	−317.583			−0.0344599
$97$	−1743.06	+	4789.02i	−0.185255	+	0.508983i	−0.997203	−	0.0747469i	$-0.976185\pi$
$97$	−1743.06	+	4789.02i	−0.185255	+	0.508983i	0.811948	+	0.583730i	$0.198407\pi$
$98$	−5759.26	+	1015.51i	−0.599673	+	0.105738i
$99$	−564.714	−	473.851i	−0.0576180	−	0.0483472i
$100$	−3169.43	+	2659.46i	−0.316943	+	0.265946i
$101$	1837.19	−	10419.2i	0.180099	−	1.02139i	−0.751993	−	0.659171i	$-0.770907\pi$
$101$	1837.19	−	10419.2i	0.180099	−	1.02139i	0.932092	−	0.362221i	$-0.117981\pi$
$102$	−1077.18	+	1865.74i	−0.103536	+	0.179329i
$103$	6373.66	−	3679.83i	0.600778	−	0.346860i	−0.168569	−	0.985690i	$-0.553915\pi$
$103$	6373.66	−	3679.83i	0.600778	−	0.346860i	0.769348	+	0.638830i	$0.220581\pi$
$104$	−4122.07	+	1500.31i	−0.381109	+	0.138712i
$105$	−370.273	−	1017.32i	−0.0335848	−	0.0922736i
$106$	1688.04	+	2923.78i	0.150235	+	0.260215i
$107$	−7393.13	−	4268.42i	−0.645744	−	0.372821i	0.141079	−	0.989998i	$-0.454943\pi$
$107$	−7393.13	−	4268.42i	−0.645744	−	0.372821i	−0.786824	+	0.617178i	$0.788276\pi$
$108$	2196.63	+	387.326i	0.188326	+	0.0332069i
$109$	6848.65	+	8161.91i	0.576437	+	0.686971i	0.972939	−	0.231063i	$-0.0742203\pi$
$109$	6848.65	+	8161.91i	0.576437	+	0.686971i	−0.396501	+	0.918034i	$0.629776\pi$
$110$	581.290	−	692.754i	0.0480405	−	0.0572524i
$111$	−526.122	−	2983.79i	−0.0427012	−	0.242171i
$112$	−1098.09	−	399.672i	−0.0875391	−	0.0318616i
$113$		−	1756.21i		−	0.137537i	−0.997633	−	0.0687683i	$-0.978093\pi$
$113$		−	1756.21i		−	0.137537i	0.997633	−	0.0687683i	$-0.0219069\pi$
$114$	−1264.46	+	1268.91i	−0.0972961	+	0.0976385i
$115$	−8166.80			−0.617528
$116$	2213.17	−	6080.64i	0.164475	−	0.451891i
$117$	14876.7	−	2623.16i	1.08676	−	0.191626i
$118$	5467.72	+	4587.96i	0.392683	+	0.329500i
$119$	−6072.53	+	5095.45i	−0.428820	+	0.359823i
$120$	−232.972	+	1321.25i	−0.0161786	+	0.0917534i
$121$	7275.75	−	12602.0i	0.496943	−	0.860731i
$122$	9829.65	−	5675.15i	0.660417	−	0.381292i
$123$	266.347	−	96.9424i	0.0176051	−	0.00640772i
$124$	2048.62	+	5628.54i	0.133235	+	0.366060i
$125$	−1822.05	−	3155.88i	−0.116611	−	0.201976i
$126$	3485.04	+	2012.09i	0.219516	+	0.126738i
$127$	28446.7	+	5015.92i	1.76370	+	0.310987i	0.959149	−	0.282901i	$-0.0912966\pi$
$127$	28446.7	+	5015.92i	1.76370	+	0.310987i	0.804548	+	0.593888i	$0.202408\pi$
$128$	930.856	+	1109.35i	0.0568149	+	0.0677094i
$129$	−3479.66	+	4146.90i	−0.209102	+	0.249198i
$130$	3217.93	+	18249.8i	0.190410	+	1.07987i
$131$	18968.4	+	6903.94i	1.10532	+	0.402304i	0.829275	−	0.558841i	$-0.188754\pi$
$131$	18968.4	+	6903.94i	1.10532	+	0.402304i	0.276046	+	0.961144i	$0.410976\pi$
$132$		−	132.781i		−	0.00762058i
$133$	−5968.96	+	2796.14i	−0.337439	+	0.158072i
$134$	−11146.9			−0.620788
$135$	3222.80	−	8854.58i	0.176834	−	0.485848i
$136$	9674.53	−	1705.88i	0.523060	−	0.0922297i
$137$	−2183.47	−	1832.15i	−0.116334	−	0.0976157i	0.582765	−	0.812641i	$-0.301971\pi$
$137$	−2183.47	−	1832.15i	−0.116334	−	0.0976157i	−0.699099	+	0.715025i	$0.746415\pi$
$138$	−918.580	+	770.780i	−0.0482346	+	0.0404736i
$139$	4722.00	−	26779.8i	0.244397	−	1.38605i	−0.577491	−	0.816397i	$-0.695968\pi$
$139$	4722.00	−	26779.8i	0.244397	−	1.38605i	0.821888	−	0.569648i	$-0.192921\pi$
$140$	−2468.30	+	4275.22i	−0.125934	+	0.218124i
$141$	−2563.35	+	1479.95i	−0.128935	+	0.0744405i
$142$	−20375.8	+	7416.19i	−1.01050	+	0.367794i
$143$	−627.278	−	1723.43i	−0.0306753	−	0.0842796i
$144$	−2493.51	−	4318.88i	−0.120250	−	0.208279i
$145$	−23673.9	−	13668.1i	−1.12599	−	0.650090i
$146$	−5848.32	−	1031.22i	−0.274363	−	0.0483776i
$147$	2331.68	+	2778.79i	0.107903	+	0.128594i
$148$	−8880.59	+	10583.5i	−0.405432	+	0.483175i
$149$	3849.98	+	21834.3i	0.173415	+	0.983483i	0.939958	+	0.341291i	$0.110864\pi$
$149$	3849.98	+	21834.3i	0.173415	+	0.983483i	−0.766543	+	0.642193i	$0.778025\pi$
$150$	2411.57	+	877.739i	0.107181	+	0.0390106i
$151$		−	33979.6i		−	1.49027i	−0.666914	−	0.745134i	$-0.732385\pi$
$151$		−	33979.6i		−	1.49027i	0.666914	−	0.745134i	$-0.267615\pi$
$152$	8138.65	+	697.639i	0.352262	+	0.0301956i
$153$	−33830.1			−1.44518
$154$	167.102	−	459.110i	0.00704598	−	0.0193587i
$155$	24919.4	−	4393.96i	1.03723	−	0.182891i
$156$	2084.35	+	1748.98i	0.0856488	+	0.0718679i
$157$	−24654.8	+	20687.8i	−1.00024	+	0.839298i	−0.987017	−	0.160615i	$-0.948652\pi$
$157$	−24654.8	+	20687.8i	−1.00024	+	0.839298i	−0.0132188	+	0.999913i	$0.504208\pi$
$158$	4600.20	−	26089.0i	0.184273	−	1.04507i
$159$	1047.06	−	1813.56i	0.0414168	−	0.0717360i
$160$	5298.12	−	3058.87i	0.206958	−	0.119487i
$161$	−4146.14	+	1509.07i	−0.159953	+	0.0582181i
$162$	5632.59	+	15475.4i	0.214624	+	0.589674i
$163$	9603.85	+	16634.4i	0.361468	+	0.626082i	0.988203	−	0.153151i	$-0.0489422\pi$
$163$	9603.85	+	16634.4i	0.361468	+	0.626082i	−0.626734	+	0.779233i	$0.715609\pi$
$164$	−1119.31	−	646.235i	−0.0416163	−	0.0240272i
$165$	−552.413	−	97.4053i	−0.0202906	−	0.00357779i
$166$	−16706.7	−	19910.2i	−0.606280	−	0.722536i
$167$	−33609.1	+	40053.7i	−1.20510	+	1.43618i	−0.335778	+	0.941941i	$0.608999\pi$
$167$	−33609.1	+	40053.7i	−1.20510	+	1.43618i	−0.869324	+	0.494243i	$0.835445\pi$
$168$	125.866	+	713.823i	0.00445955	+	0.0252914i
$169$	8477.72	+	3085.64i	0.296829	+	0.108037i
$170$		−	41500.6i		−	1.43601i
$171$	−27184.1	−	7232.81i	−0.929657	−	0.247352i
$172$	24684.7			0.834393
$173$	−10667.8	+	29309.5i	−0.356436	+	0.979301i	0.623820	+	0.781568i	$0.285580\pi$
$173$	−10667.8	+	29309.5i	−0.356436	+	0.979301i	−0.980256	+	0.197732i	$0.936642\pi$
$174$	−3952.77	+	696.981i	−0.130558	+	0.0230209i
$175$	7233.74	+	6069.83i	0.236204	+	0.198198i
$176$	−463.818	+	389.190i	−0.0149735	+	0.0125642i
$177$	768.793	−	4360.04i	0.0245393	−	0.139169i
$178$	−13645.6	+	23634.8i	−0.430676	+	0.745954i
$179$	−4277.91	+	2469.85i	−0.133514	+	0.0770841i	−0.565269	−	0.824907i	$-0.691228\pi$
$179$	−4277.91	+	2469.85i	−0.133514	+	0.0770841i	0.431756	+	0.901991i	$0.357894\pi$
$180$	−19797.1	+	7205.57i	−0.611022	+	0.222394i
$181$	−12800.3	−	35168.4i	−0.390716	−	1.07348i	−0.966675	−	0.256005i	$-0.917593\pi$
$181$	−12800.3	−	35168.4i	−0.390716	−	1.07348i	0.575959	−	0.817478i	$-0.304629\pi$
$182$	5005.90	+	8670.46i	0.151126	+	0.261758i
$183$	−6097.13	−	3520.18i	−0.182064	−	0.105114i
$184$	5384.83	+	949.492i	0.159051	+	0.0280450i
$185$	37516.1	+	44710.0i	1.09616	+	1.30635i
$186$	2388.17	−	2846.11i	0.0690301	−	0.0822669i
$187$	713.226	+	4044.91i	0.0203960	+	0.115671i
$188$	12683.0	+	4616.23i	0.358844	+	0.130609i
$189$		−	5090.83i		−	0.142516i
$190$	8872.74	−	33347.7i	0.245782	−	0.923759i
$191$	30485.5			0.835655			0.417828	−	0.908526i	$-0.362792\pi$
$191$	30485.5			0.835655			0.417828	+	0.908526i	$0.362792\pi$
$192$	307.223	−	844.088i	0.00833396	−	0.0228974i
$193$	65457.0	−	11541.8i	1.75728	−	0.309856i	0.800212	−	0.599717i	$-0.204720\pi$
$193$	65457.0	−	11541.8i	1.75728	−	0.309856i	0.957069	+	0.289861i	$0.0936090\pi$
$194$	−11042.3	−	9265.60i	−0.293398	−	0.246190i
$195$	8805.35	−	7388.57i	0.231567	−	0.194308i
$196$	2872.30	−	16289.6i	0.0747684	−	0.424033i
$197$	−18783.7	+	32534.4i	−0.484005	+	0.838321i	−0.999831	−	0.0183721i	$-0.994152\pi$
$197$	−18783.7	+	32534.4i	−0.484005	+	0.838321i	0.515826	+	0.856693i	$0.327485\pi$
$198$	1805.72	−	1042.53i	0.0460595	−	0.0265925i
$199$	23436.7	−	8530.26i	0.591821	−	0.215405i	−0.0287093	−	0.999588i	$-0.509140\pi$
$199$	23436.7	−	8530.26i	0.591821	−	0.215405i	0.620530	+	0.784183i	$0.286917\pi$
$200$	−4002.43	−	10996.6i	−0.100061	−	0.274914i
$201$	3457.08	+	5987.85i	0.0855693	+	0.148210i
$202$	25915.5	+	14962.3i	0.635121	+	0.366687i
$203$	−14544.4	−	2564.58i	−0.352943	−	0.0622334i
$204$	−3916.81	−	4667.87i	−0.0941179	−	0.112165i
$205$	−3509.65	+	4182.64i	−0.0835134	+	0.0995274i
$206$	3614.71	+	20500.0i	0.0851802	+	0.483081i
$207$	−17694.2	−	6440.18i	−0.412944	−	0.150299i
$208$		−	12407.2i		−	0.286779i
$209$	−291.682	+	3402.76i	−0.00667755	+	0.0779003i
$210$	3062.07			0.0694347
$211$	8430.40	−	23162.3i	0.189358	−	0.520256i	−0.808292	−	0.588782i	$-0.799607\pi$
$211$	8430.40	−	23162.3i	0.189358	−	0.520256i	0.997649	+	0.0685263i	$0.0218297\pi$
$212$	−9403.94	+	1658.17i	−0.209237	+	0.0368941i
$213$	10303.2	+	8645.38i	0.227097	+	0.190557i
$214$	18496.8	−	15520.7i	0.403896	−	0.338909i
$215$	18108.1	−	102696.i	0.391739	−	2.22166i
$216$	−3154.43	+	5463.64i	−0.0676104	+	0.117105i
$217$	11839.2	−	6835.37i	0.251422	−	0.145159i
$218$	−28318.4	+	10307.0i	−0.595875	+	0.216881i
$219$	1259.85	+	3461.41i	0.0262682	+	0.0721713i
$220$	1278.91	+	2215.14i	0.0264238	+	0.0457673i
$221$	−72890.1	−	42083.1i	−1.49240	−	0.861635i
$222$	8439.42	+	1488.10i	0.171241	+	0.0301943i
$223$	14918.7	+	17779.4i	0.300000	+	0.357526i	0.894894	−	0.446278i	$-0.147251\pi$
$223$	14918.7	+	17779.4i	0.300000	+	0.357526i	−0.594895	+	0.803804i	$0.702806\pi$
$224$	2124.54	−	2531.93i	0.0423417	−	0.0504609i
$225$	6997.89	+	39687.0i	0.138230	+	0.783941i
$226$	4667.74	+	1698.92i	0.0913880	+	0.0332625i
$227$			101622.i			1.97213i	0.166355	+	0.986066i	$0.446800\pi$
$227$			101622.i			1.97213i	−0.166355	+	0.986066i	$0.553200\pi$
$228$	−2149.36	−	4588.26i	−0.0413466	−	0.0882630i
$229$	−86807.9			−1.65534			−0.827672	−	0.561212i	$-0.810335\pi$
$229$	−86807.9			−1.65534			−0.827672	+	0.561212i	$0.810335\pi$
$230$	7900.39	−	21706.2i	0.149346	−	0.410324i
$231$	−298.449	+	52.6246i	−0.00559301	+	0.000986199i
$232$	14020.5	+	11764.6i	0.260487	+	0.218575i
$233$	35953.8	−	30168.8i	0.662266	−	0.555707i	−0.248499	−	0.968632i	$-0.579937\pi$
$233$	35953.8	−	30168.8i	0.662266	−	0.555707i	0.910765	+	0.412925i	$0.135493\pi$
$234$	−7419.42	+	42077.6i	−0.135500	+	0.768457i
$235$	28509.0	−	49379.0i	0.516233	−	0.894142i
$236$	−17483.5	+	10094.1i	−0.313909	+	0.181235i
$237$	−15441.1	+	5620.11i	−0.274905	+	0.100057i
$238$	−7668.53	−	21069.1i	−0.135381	−	0.371957i
$239$	54980.5	+	95229.0i	0.962527	+	1.66714i	0.716118	+	0.697979i	$0.245917\pi$
$239$	54980.5	+	95229.0i	0.962527	+	1.66714i	0.246408	+	0.969166i	$0.420750\pi$
$240$	−3286.31	−	1897.35i	−0.0570540	−	0.0329402i
$241$	86429.8	+	15239.9i	1.48809	+	0.262391i	0.857806	−	0.513974i	$-0.171827\pi$
$241$	86429.8	+	15239.9i	1.48809	+	0.262391i	0.630285	+	0.776364i	$0.282938\pi$
$242$	26455.8	+	31528.7i	0.451741	+	0.538364i
$243$	21082.9	−	25125.6i	0.357040	−	0.425504i
$244$	5574.72	+	31615.8i	0.0936360	+	0.531036i
$245$	−65663.2	−	23899.4i	−1.09393	−	0.398158i
$246$			801.691i			0.0132476i
$247$	−49573.3	−	49399.5i	−0.812558	−	0.809709i
$248$	−16941.6			−0.275456
$249$	−5513.92	+	15149.4i	−0.0889328	+	0.244341i
$250$	10150.5	−	1789.80i	0.162408	−	0.0286369i
$251$	−75767.0	−	63576.1i	−1.20263	−	1.00913i	−0.999551	−	0.0299657i	$-0.990460\pi$
$251$	−75767.0	−	63576.1i	−1.20263	−	1.00913i	−0.203081	−	0.979162i	$-0.565095\pi$
$252$	−8719.19	+	7316.27i	−0.137302	+	0.115210i
$253$	−396.981	+	2251.39i	−0.00620196	+	0.0351731i
$254$	−40850.3	+	70754.7i	−0.633180	+	1.09670i
$255$	−22293.2	+	12871.0i	−0.342840	+	0.197939i
$256$	−3848.98	+	1400.91i	−0.0587308	+	0.0213763i
$257$	−10385.3	−	28533.3i	−0.157236	−	0.432002i	0.835912	−	0.548863i	$-0.184939\pi$
$257$	−10385.3	−	28533.3i	−0.157236	−	0.432002i	−0.993148	+	0.116861i	$0.962717\pi$
$258$	−7655.70	−	13260.1i	−0.115013	−	0.199208i
$259$	27307.8	+	15766.2i	0.407087	+	0.235032i
$260$	−51618.1	−	9101.67i	−0.763582	−	0.134640i
$261$	−40513.6	−	48282.3i	−0.594731	−	0.708772i
$262$	−36699.3	+	43736.5i	−0.534632	+	0.637150i
$263$	−5705.17	−	32355.6i	−0.0824817	−	0.467777i	−0.997872	−	0.0652085i	$-0.979229\pi$
$263$	−5705.17	−	32355.6i	−0.0824817	−	0.467777i	0.915390	−	0.402568i	$-0.131882\pi$
$264$	352.912	+	128.450i	0.00506360	+	0.00184300i
$265$			40339.9i			0.574438i
$266$	−1657.49	−	18569.5i	−0.0234255	−	0.262445i
$267$	16928.1			0.237457
$268$	10783.2	−	29626.7i	0.150134	−	0.412491i
$269$	−5394.35	+	951.169i	−0.0745477	+	0.0131448i	−0.210798	−	0.977530i	$-0.567606\pi$
$269$	−5394.35	+	951.169i	−0.0745477	+	0.0131448i	0.136250	+	0.990675i	$0.456495\pi$
$270$	20416.5	+	17131.5i	0.280062	+	0.235000i
$271$	−55213.1	+	46329.3i	−0.751802	+	0.630837i	−0.935979	−	0.352056i	$-0.885483\pi$
$271$	−55213.1	+	46329.3i	−0.751802	+	0.630837i	0.184177	+	0.982893i	$0.441038\pi$
$272$	−4824.96	+	27363.7i	−0.0652162	+	0.369860i
$273$	3105.05	−	5378.11i	0.0416623	−	0.0721613i
$274$	6981.82	−	4030.96i	0.0929967	−	0.0536917i
$275$	4597.66	−	1673.41i	0.0607954	−	0.0221277i
$276$	−1160.00	−	3187.09i	−0.0152279	−	0.0418384i
$277$	−19873.2	−	34421.3i	−0.259005	−	0.448609i	0.706971	−	0.707243i	$-0.250061\pi$
$277$	−19873.2	−	34421.3i	−0.259005	−	0.448609i	−0.965976	+	0.258633i	$0.916728\pi$
$278$	66608.7	+	38456.6i	0.861870	+	0.497601i
$279$	57455.5	+	10131.0i	0.738114	+	0.130149i
$280$	−8975.13	−	10696.1i	−0.114479	−	0.136430i
$281$	52519.7	−	62590.5i	0.665134	−	0.792676i	−0.322978	−	0.946406i	$-0.604684\pi$
$281$	52519.7	−	62590.5i	0.665134	−	0.792676i	0.988113	+	0.153730i	$0.0491286\pi$
$282$	−1453.76	−	8244.68i	−0.0182808	−	0.103675i
$283$	−35444.4	−	12900.7i	−0.442562	−	0.161079i	0.111121	−	0.993807i	$-0.464556\pi$
$283$	−35444.4	−	12900.7i	−0.442562	−	0.161079i	−0.553683	+	0.832727i	$0.686778\pi$
$284$		−	61330.2i		−	0.760392i
$285$	−20665.4	+	5576.20i	−0.254422	+	0.0686513i
$286$	5187.45			0.0634193
$287$	−1008.91	+	2771.97i	−0.0122487	+	0.0336530i
$288$	13891.1	−	2449.38i	0.167476	−	0.0295305i
$289$	80410.3	+	67472.3i	0.962755	+	0.807848i
$290$	59229.6	−	49699.5i	0.704276	−	0.590957i
$291$	−1552.61	+	8805.31i	−0.0183348	+	0.103982i
$292$	8398.37	−	14546.4i	0.0984984	−	0.170604i
$293$	30642.8	−	17691.6i	0.356938	−	0.206078i	−0.310799	−	0.950476i	$-0.600597\pi$
$293$	30642.8	−	17691.6i	0.356938	−	0.206078i	0.667737	+	0.744398i	$0.267263\pi$
$294$	−9641.24	+	3509.12i	−0.111542	+	0.0405979i
$295$	29169.2	+	80141.8i	0.335182	+	0.920905i
$296$	−19538.4	−	33841.5i	−0.223000	−	0.386248i
$297$	−2284.34	−	1318.86i	−0.0258969	−	0.0149516i
$298$	−61756.8	−	10889.4i	−0.695428	−	0.122623i
$299$	−30112.6	−	35886.8i	−0.336826	−	0.401414i
$300$	−4665.80	+	5560.48i	−0.0518422	+	0.0617832i
$301$	−9783.18	−	55483.2i	−0.107981	−	0.612390i
$302$	90312.8	+	32871.2i	0.990228	+	0.360414i
$303$		−	18561.6i		−	0.202176i
$304$	−9727.38	+	20956.5i	−0.105256	+	0.226762i
$305$	135622.			1.45790
$306$	32726.5	−	89915.4i	0.349508	−	0.960266i
$307$	−70616.4	+	12451.6i	−0.749254	+	0.132114i	−0.535220	−	0.844713i	$-0.679771\pi$
$307$	−70616.4	+	12451.6i	−0.749254	+	0.132114i	−0.214034	+	0.976826i	$0.568660\pi$
$308$	1058.60	+	888.267i	0.0111591	+	0.00936359i
$309$	9891.09	−	8299.61i	0.103592	−	0.0869242i
$310$	−12428.0	+	70482.7i	−0.129324	+	0.733431i
$311$	−30423.1	+	52694.3i	−0.314545	+	0.544807i	−0.979341	−	0.202218i	$-0.935185\pi$
$311$	−30423.1	+	52694.3i	−0.314545	+	0.544807i	0.664796	+	0.747025i	$0.268518\pi$
$312$	−6664.88	+	3847.97i	−0.0684673	+	0.0395296i
$313$	96735.8	−	35208.9i	0.987412	−	0.359389i	0.202694	−	0.979242i	$-0.435030\pi$
$313$	96735.8	−	35208.9i	0.987412	−	0.359389i	0.784718	+	0.619853i	$0.212808\pi$
$314$	−31134.7	−	85541.8i	−0.315780	−	0.867600i
$315$	24041.9	+	41641.8i	0.242297	+	0.419670i
$316$	64890.6	+	37464.6i	0.649842	+	0.375187i
$317$	25856.6	+	4559.22i	0.257308	+	0.0453703i	0.300814	−	0.953683i	$-0.402742\pi$
$317$	25856.6	+	4559.22i	0.257308	+	0.0453703i	−0.0435060	+	0.999053i	$0.513853\pi$
$318$	3807.26	+	4537.32i	0.0376495	+	0.0448689i
$319$	−4918.75	+	5861.94i	−0.0483363	+	0.0576050i
$320$	3004.74	+	17040.7i	0.0293431	+	0.166413i
$321$	−14073.9	−	5122.49i	−0.136586	−	0.0497131i
$322$		−	12479.7i		−	0.120363i
$323$	90121.6	+	128227.i	0.863821	+	1.22906i
$324$	−46580.2			−0.443723
$325$	−34291.2	+	94214.3i	−0.324651	+	0.891970i
$326$	−53502.2	+	9433.89i	−0.503427	+	0.0887678i
$327$	14319.4	+	12015.4i	0.133915	+	0.112368i
$328$	2800.39	−	2349.81i	0.0260298	−	0.0218416i
$329$	5349.19	−	30336.8i	0.0494192	−	0.280270i
$330$	793.281	−	1374.00i	0.00728449	−	0.0126171i
$331$	12936.0	−	7468.61i	0.118071	−	0.0681685i	−0.439801	−	0.898095i	$-0.644951\pi$
$331$	12936.0	−	7468.61i	0.118071	−	0.0681685i	0.557873	+	0.829927i	$0.311618\pi$
$332$	69080.1	−	25143.1i	0.626724	−	0.228109i
$333$	46025.3	+	126453.i	0.415057	+	1.14036i
$334$	−73944.2	−	128075.i	−0.662844	−	1.14808i
$335$	−115347.	−	66595.4i	−1.02782	−	0.593409i
$336$	−2019.00	−	356.004i	−0.0178837	−	0.00315338i
$337$	−3644.76	−	4343.65i	−0.0320929	−	0.0382468i	0.749759	−	0.661711i	$-0.230169\pi$
$337$	−3644.76	−	4343.65i	−0.0320929	−	0.0382468i	−0.781852	+	0.623464i	$0.785725\pi$
$338$	−16402.3	+	19547.6i	−0.143573	+	0.171104i
$339$	−535.029	−	3034.30i	−0.00465563	−	0.0264034i
$340$	110302.	+	40146.8i	0.954173	+	0.347291i
$341$		−	7083.27i		−	0.0609151i
$342$	45521.1	−	65254.4i	0.389189	−	0.557902i
$343$	−81591.6			−0.693517
$344$	−23879.4	+	65608.2i	−0.201794	+	0.554423i
$345$	−14110.3	+	2488.02i	−0.118549	+	0.0209034i
$346$	−67580.5	−	56706.8i	−0.564507	−	0.473678i
$347$	−164198.	+	137778.i	−1.36367	+	1.14425i	−0.388836	+	0.921307i	$0.627123\pi$
$347$	−164198.	+	137778.i	−1.36367	+	1.14425i	−0.974831	+	0.222945i	$0.928433\pi$
$348$	1971.36	−	11180.1i	0.0162782	−	0.0923185i
$349$	65513.7	−	113473.i	0.537875	−	0.931627i	−0.461143	−	0.887326i	$-0.652560\pi$
$349$	65513.7	−	113473.i	0.537875	−	0.931627i	0.999018	−	0.0443014i	$-0.0141062\pi$
$350$	−23130.5	+	13354.4i	−0.188820	+	0.109015i
$351$	50792.1	−	18486.8i	0.412271	−	0.150054i
$352$	−585.721	−	1609.25i	−0.00472721	−	0.0129879i
$353$	−86006.2	−	148967.i	−0.690209	−	1.19548i	−0.971769	−	0.235933i	$-0.924185\pi$
$353$	−86006.2	−	148967.i	−0.690209	−	1.19548i	0.281561	−	0.959543i	$-0.409148\pi$
$354$	10844.6	+	6261.15i	0.0865383	+	0.0499629i
$355$	−255154.	−	44990.5i	−2.02463	−	0.356996i
$356$	−49617.4	−	59131.7i	−0.391502	−	0.466574i
$357$	−8939.53	+	10653.7i	−0.0701421	+	0.0835920i
$358$	−2426.14	−	13759.3i	−0.0189300	−	0.107357i
$359$	17293.4	+	6294.28i	0.134181	+	0.0488379i	0.408238	−	0.912876i	$-0.366143\pi$
$359$	17293.4	+	6294.28i	0.134181	+	0.0488379i	−0.274057	+	0.961713i	$0.588366\pi$
$360$		−	59588.4i		−	0.459787i
$361$	45002.3	+	122304.i	0.345319	+	0.938485i
$362$	105855.			0.807783
$363$	8731.55	−	23989.7i	0.0662641	−	0.182059i
$364$	−27887.4	+	4917.30i	−0.210477	+	0.0371128i
$365$	−54356.9	−	45610.9i	−0.408008	−	0.342360i
$366$	15254.3	−	12799.9i	0.113876	−	0.0955531i
$367$	−15606.0	+	88506.3i	−0.115867	+	0.657116i	0.870450	+	0.492257i	$0.163828\pi$
$367$	−15606.0	+	88506.3i	−0.115867	+	0.657116i	−0.986317	+	0.164859i	$0.947283\pi$
$368$	−7732.78	+	13393.6i	−0.0571005	+	0.0989010i
$369$	−10902.4	+	6294.49i	−0.0800697	+	0.0462283i
$370$	−155125.	+	56460.8i	−1.13312	+	0.412424i
$371$	7454.05	+	20479.8i	0.0541557	+	0.148792i
$372$	5254.27	+	9100.65i	0.0379687	+	0.0657638i
$373$	−47752.4	−	27569.9i	−0.343224	−	0.198160i	0.318473	−	0.947932i	$-0.396830\pi$
$373$	−47752.4	−	27569.9i	−0.343224	−	0.198160i	−0.661697	+	0.749772i	$0.730163\pi$
$374$	−11440.7	−	2017.31i	−0.0817919	−	0.0144221i
$375$	−4109.51	−	4897.52i	−0.0292232	−	0.0348268i
$376$	−24538.5	+	29243.8i	−0.173569	+	0.206852i
$377$	−27229.4	−	154426.i	−0.191582	−	1.08652i
$378$	13530.7	+	4924.76i	0.0946968	+	0.0344668i
$379$			206993.i			1.44104i	0.693432	+	0.720522i	$0.256098\pi$
$379$			206993.i			1.44104i	−0.693432	+	0.720522i	$0.743902\pi$
$380$	80049.9	+	55842.3i	0.554362	+	0.386719i
$381$	50677.1			0.349110
$382$	−29491.1	+	81026.0i	−0.202099	+	0.555262i
$383$	−80587.7	+	14209.8i	−0.549378	+	0.0968702i	−0.441446	−	0.897288i	$-0.645534\pi$
$383$	−80587.7	+	14209.8i	−0.549378	+	0.0968702i	−0.107933	+	0.994158i	$0.534423\pi$
$384$	1946.26	+	1633.11i	0.0131989	+	0.0110752i
$385$	4472.05	−	3752.49i	0.0301707	−	0.0253162i
$386$	−32645.2	+	185140.i	−0.219101	+	1.24259i
$387$	120218.	−	208223.i	0.802687	−	1.39029i
$388$	35308.7	−	20385.5i	0.234541	−	0.135412i
$389$	160297.	−	58343.3i	1.05932	−	0.385560i	0.247146	−	0.968978i	$-0.420507\pi$
$389$	160297.	−	58343.3i	1.05932	−	0.385560i	0.812172	+	0.583418i	$0.198285\pi$
$390$	11119.6	+	30550.9i	0.0731072	+	0.200860i
$391$	52456.5	+	90857.3i	0.343120	+	0.594301i
$392$	40516.8	+	23392.4i	0.263672	+	0.152231i
$393$	34876.2	+	6149.61i	0.225810	+	0.0398164i
$394$	−68300.6	−	81397.5i	−0.439979	−	0.524347i
$395$	203468.	−	242483.i	1.30407	−	1.55413i
$396$	1024.08	+	5807.85i	0.00653047	+	0.0370361i
$397$	−162551.	−	59163.8i	−1.03136	−	0.375383i	−0.229759	−	0.973247i	$-0.573794\pi$
$397$	−162551.	−	59163.8i	−1.03136	−	0.375383i	−0.801597	+	0.597864i	$0.796016\pi$
$398$			70543.3i			0.445338i
$399$	−9461.08	+	6649.51i	−0.0594285	+	0.0417680i
$400$	33099.1			0.206870
$401$	−34540.0	+	94897.9i	−0.214800	+	0.590158i	−0.999561	−	0.0296411i	$-0.990564\pi$
$401$	−34540.0	+	94897.9i	−0.214800	+	0.590158i	0.784761	+	0.619799i	$0.212786\pi$
$402$	−19259.1	+	3395.90i	−0.119175	+	0.0210137i
$403$	111191.	+	93300.1i	0.684634	+	0.574476i
$404$	−64837.7	+	54405.3i	−0.397251	+	0.333333i
$405$	−34170.2	+	193789.i	−0.208323	+	1.18146i
$406$	20886.3	−	36176.1i	0.126709	−	0.219467i
$407$	14149.1	−	8168.99i	0.0854162	−	0.0493150i
$408$	16195.6	−	5894.70i	0.0972917	−	0.0354113i
$409$	7222.99	+	19845.0i	0.0431788	+	0.118633i	0.959408	−	0.282022i	$-0.0910050\pi$
$409$	7222.99	+	19845.0i	0.0431788	+	0.118633i	−0.916229	+	0.400654i	$0.868783\pi$
$410$	−7721.67	−	13374.3i	−0.0459350	−	0.0795617i
$411$	−4330.68	−	2500.32i	−0.0256373	−	0.0148017i
$412$	−57982.8	−	10223.9i	−0.341590	−	0.0602315i
$413$	29617.4	+	35296.6i	0.173639	+	0.206935i
$414$	34234.1	−	40798.6i	0.199737	−	0.238037i
$415$	−53927.9	−	305840.i	−0.313124	−	1.77582i
$416$	32976.6	+	12002.5i	0.190554	+	0.0693561i
$417$		−	47707.6i		−	0.274357i
$418$	−8761.87	−	4067.01i	−0.0501469	−	0.0232768i
$419$	127649.			0.727091			0.363546	−	0.931576i	$-0.381566\pi$
$419$	127649.			0.727091			0.363546	+	0.931576i	$0.381566\pi$
$420$	−2962.18	+	8138.53i	−0.0167924	+	0.0461368i
$421$	−4469.39	+	788.074i	−0.0252165	+	0.00444634i	−0.186242	−	0.982504i	$-0.559631\pi$
$421$	−4469.39	+	788.074i	−0.0252165	+	0.00444634i	0.161026	+	0.986950i	$0.448520\pi$
$422$	53406.6	+	44813.5i	0.299896	+	0.251642i
$423$	100707.	−	84503.2i	0.562832	−	0.472272i
$424$	4690.01	−	26598.4i	0.0260881	−	0.147953i
$425$	112266.	−	194451.i	0.621544	−	1.07655i
$426$	−32945.2	+	19020.9i	−0.181540	+	0.104812i
$427$	68852.6	−	25060.3i	0.377628	−	0.137446i
$428$	23358.2	+	64176.1i	0.127512	+	0.350337i
$429$	−1608.83	−	2786.58i	−0.00874170	−	0.0151411i
$430$	255434.	+	147475.i	1.38147	+	0.797594i
$431$	96156.9	+	16955.1i	0.517638	+	0.0912735i	0.426363	−	0.904552i	$-0.359795\pi$
$431$	96156.9	+	16955.1i	0.517638	+	0.0912735i	0.0912749	+	0.995826i	$0.470906\pi$
$432$	−11470.0	−	13669.4i	−0.0614605	−	0.0732458i
$433$	16119.0	−	19209.9i	0.0859730	−	0.102459i	−0.721343	−	0.692578i	$-0.756475\pi$
$433$	16119.0	−	19209.9i	0.0859730	−	0.102459i	0.807316	+	0.590119i	$0.200919\pi$
$434$	6714.40	+	38079.3i	0.0356474	+	0.202166i
$435$	−45066.9	−	16403.0i	−0.238166	−	0.0866852i
$436$		−	85236.9i		−	0.448389i
$437$	22726.2	+	84223.2i	0.119004	+	0.441031i
$438$	−10418.7			−0.0543080
$439$	17594.0	−	48339.2i	0.0912928	−	0.250825i	−0.885640	−	0.464373i	$-0.846280\pi$
$439$	17594.0	−	48339.2i	0.0912928	−	0.250825i	0.976933	+	0.213548i	$0.0685020\pi$
$440$	−7124.70	+	1256.28i	−0.0368011	+	0.00648903i
$441$	−123420.	−	103561.i	−0.634610	−	0.532501i
$442$	182363.	−	153021.i	0.933453	−	0.783260i
$443$	−26720.6	+	151540.i	−0.136157	+	0.772182i	0.837891	+	0.545838i	$0.183789\pi$
$443$	−26720.6	+	151540.i	−0.136157	+	0.772182i	−0.974047	+	0.226344i	$0.927323\pi$
$444$	−12119.3	+	20991.2i	−0.0614767	+	0.106481i
$445$	−282405.	+	163047.i	−1.42611	+	0.823365i
$446$	−61687.0	+	22452.2i	−0.310116	+	0.112873i
$447$	13303.7	+	36551.6i	0.0665820	+	0.182932i
$448$	4674.25	+	8096.04i	0.0232893	+	0.0403382i
$449$	150750.	+	87035.7i	0.747765	+	0.431723i	0.824886	−	0.565299i	$-0.191239\pi$
$449$	150750.	+	87035.7i	0.747765	+	0.431723i	−0.0771205	+	0.997022i	$0.524573\pi$
$450$	−112252.	−	19793.0i	−0.554330	−	0.0977433i
$451$	982.453	+	1170.84i	0.00483013	+	0.00575632i
$452$	−9030.94	+	10762.7i	−0.0442034	+	0.0526796i
$453$	−10351.9	−	58708.6i	−0.0504457	−	0.286092i
$454$	−270096.	−	98307.0i	−1.31041	−	0.476950i
$455$			119628.i			0.577843i
$456$	14274.2	−	1274.09i	0.0686470	−	0.00612734i
$457$	−156705.			−0.750326			−0.375163	−	0.926959i	$-0.622413\pi$
$457$	−156705.			−0.750326			−0.375163	+	0.926959i	$0.622413\pi$
$458$	83976.1	−	230723.i	0.400336	−	1.09991i
$459$	−119209.	+	21019.8i	−0.565829	+	0.0997710i
$460$	50049.1	+	41996.2i	0.236527	+	0.198470i
$461$	224854.	−	188675.i	1.05803	−	0.887793i	0.0641153	−	0.997943i	$-0.479577\pi$
$461$	224854.	−	188675.i	1.05803	−	0.887793i	0.993915	+	0.110150i	$0.0351330\pi$
$462$	148.845	−	844.140i	0.000697348	−	0.00395486i
$463$	−44115.7	+	76410.6i	−0.205793	+	0.356444i	−0.950385	−	0.311076i	$-0.899311\pi$
$463$	−44115.7	+	76410.6i	−0.205793	+	0.356444i	0.744592	+	0.667520i	$0.232644\pi$
$464$	−44831.6	+	25883.5i	−0.208232	+	0.120223i
$465$	41716.1	−	15183.4i	0.192929	−	0.0702205i
$466$	45403.3	+	124744.i	0.209081	+	0.574446i
$467$	−136453.	−	236344.i	−0.625677	−	1.08370i	−0.988409	−	0.151811i	$-0.951489\pi$
$467$	−136453.	−	236344.i	−0.625677	−	1.08370i	0.362732	−	0.931893i	$-0.381844\pi$
$468$	−104659.	−	60424.8i	−0.477841	−	0.275882i
$469$	−70865.0	−	12495.4i	−0.322171	−	0.0568074i
$470$	103663.	+	123541.i	0.469276	+	0.559261i
$471$	−36295.0	+	43254.8i	−0.163608	+	0.194981i
$472$	−9915.45	−	56233.3i	−0.0445070	−	0.252412i
$473$	−27430.7	−	9983.97i	−0.122607	−	0.0446253i
$474$		−	46477.0i		−	0.206863i
$475$	131785.	−	132248.i	0.584087	−	0.586142i
$476$	63417.0			0.279893
$477$	−31811.2	+	87400.6i	−0.139812	+	0.384130i
$478$	−306292.	+	54007.5i	−1.34054	+	0.236373i
$479$	−181581.	−	152364.i	−0.791405	−	0.664068i	0.154688	−	0.987963i	$-0.450563\pi$
$479$	−181581.	−	152364.i	−0.791405	−	0.664068i	−0.946093	+	0.323896i	$0.895007\pi$
$480$	8221.99	−	6899.07i	0.0356857	−	0.0299439i
$481$	−58136.5	+	329709.i	−0.251281	+	1.42508i
$482$	−124116.	+	214975.i	−0.534236	+	0.925323i
$483$	−6703.79	+	3870.44i	−0.0287360	+	0.0165907i
$484$	−109391.	+	39815.2i	−0.466974	+	0.169965i
$485$	−58908.6	−	161850.i	−0.250435	−	0.688065i
$486$	46385.0	+	80341.2i	0.196383	+	0.340146i
$487$	108287.	+	62519.4i	0.456581	+	0.263607i	0.710605	−	0.703591i	$-0.248421\pi$
$487$	108287.	+	62519.4i	0.456581	+	0.263607i	−0.254025	+	0.967198i	$0.581754\pi$
$488$	−89422.9	−	15767.7i	−0.375499	−	0.0662107i
$489$	21660.8	+	25814.4i	0.0905852	+	0.107955i
$490$	127042.	−	151403.i	0.529123	−	0.630584i
$491$	32940.8	+	186817.i	0.136638	+	0.774913i	0.973705	+	0.227812i	$0.0731573\pi$
$491$	32940.8	+	186817.i	0.136638	+	0.774913i	−0.837067	+	0.547100i	$0.815732\pi$
$492$	−2130.78	−	775.539i	−0.00880254	−	0.00320386i
$493$			351169.i			1.44485i
$494$	179253.	−	83970.6i	0.734534	−	0.344091i
$495$	24913.8			0.101679
$496$	16389.0	−	45028.3i	0.0666175	−	0.183030i
$497$	−137850.	+	24306.7i	−0.558078	+	0.0984043i
$498$	−34930.7	−	29310.4i	−0.140848	−	0.118185i
$499$	−309.884	+	260.023i	−0.00124451	+	0.00104427i	−0.643410	−	0.765522i	$-0.722481\pi$
$499$	−309.884	+	260.023i	−0.00124451	+	0.00104427i	0.642165	+	0.766566i	$0.278036\pi$
$500$	−5062.33	+	28709.9i	−0.0202493	+	0.114840i
$501$	−45866.0	+	79442.3i	−0.182732	+	0.316502i
$502$	242271.	−	139875.i	0.961378	−	0.555052i
$503$	47483.0	−	17282.4i	0.187673	−	0.0683075i	−0.246474	−	0.969149i	$-0.579272\pi$
$503$	47483.0	−	17282.4i	0.187673	−	0.0683075i	0.434147	+	0.900842i	$0.357050\pi$
$504$	−11010.8	−	30251.9i	−0.0433469	−	0.119095i
$505$	178780.	+	309657.i	0.701031	+	1.21422i
$506$	−5599.84	−	3233.07i	−0.0218713	−	0.0126274i
$507$	15587.5	+	2748.50i	0.0606403	+	0.0106925i
$508$	−148538.	−	177021.i	−0.575586	−	0.685956i
$509$	−77181.8	+	91981.6i	−0.297906	+	0.355030i	−0.894146	−	0.447776i	$-0.852216\pi$
$509$	−77181.8	+	91981.6i	−0.297906	+	0.355030i	0.596240	+	0.802806i	$0.296661\pi$
$510$	−12643.2	−	71703.1i	−0.0486090	−	0.275675i
$511$	−36024.1	−	13111.7i	−0.137959	−	0.0502131i
$512$		−	11585.2i		−	0.0441942i
$513$	−100284.	−	8596.31i	−0.381065	−	0.0326646i
$514$	85883.9			0.325076
$515$	−85069.9	+	233728.i	−0.320746	+	0.881243i
$516$	42649.2	−	7520.21i	0.160181	−	0.0282443i
$517$	−12226.8	−	10259.5i	−0.0457438	−	0.0383836i
$518$	−68321.2	+	57328.3i	−0.254622	+	0.213653i
$519$	−9502.21	+	53889.7i	−0.0352769	+	0.200065i
$520$	74125.2	−	128389.i	0.274132	−	0.474810i
$521$	−207091.	+	119564.i	−0.762933	+	0.440480i	−0.830348	−	0.557245i	$-0.811858\pi$
$521$	−207091.	+	119564.i	−0.762933	+	0.440480i	0.0674147	+	0.997725i	$0.478525\pi$
$522$	167519.	−	60972.0i	0.614785	−	0.223764i
$523$	−80919.3	−	222324.i	−0.295835	−	0.812799i	−0.995185	−	0.0980194i	$-0.968749\pi$
$523$	−80919.3	−	222324.i	−0.295835	−	0.812799i	0.699350	−	0.714779i	$-0.253473\pi$
$524$	−80743.1	−	139851.i	−0.294064	−	0.509335i
$525$	14347.3	+	8283.44i	0.0520538	+	0.0300533i
$526$	91515.6	+	16136.7i	0.330768	+	0.0583233i
$527$	−208944.	−	249010.i	−0.752332	−	0.896594i
$528$	−682.800	+	813.729i	−0.00244921	+	0.00291885i
$529$	−38453.8	−	218082.i	−0.137413	−	0.779308i
$530$	−107217.	−	39024.0i	−0.381693	−	0.138925i
$531$			196638.i			0.697394i
$532$	50958.5	+	13558.4i	0.180050	+	0.0479055i
$533$	−31320.2			−0.110248
$534$	−16375.9	+	44992.4i	−0.0574278	+	0.157782i
$535$	284129.	−	50099.6i	0.992676	−	0.175036i
$536$	68312.0	+	57320.6i	0.237776	+	0.199517i
$537$	−6638.76	+	5570.58i	−0.0230217	+	0.0193175i
$538$	2690.31	−	15257.5i	0.00929476	−	0.0527132i
$539$	−9780.34	+	16940.0i	−0.0336648	+	0.0583092i
$540$	−65283.4	+	37691.4i	−0.223880	+	0.129257i
$541$	315291.	−	114756.i	1.07725	−	0.392087i	0.258367	−	0.966047i	$-0.416816\pi$
$541$	315291.	−	114756.i	1.07725	−	0.392087i	0.818884	+	0.573960i	$0.194593\pi$
$542$	−69724.4	−	191566.i	−0.237348	−	0.652109i
$543$	−32829.9	−	56863.0i	−0.111345	−	0.192855i
$544$	−68061.1	−	39295.1i	−0.229986	−	0.132782i
$545$	−354614.	−	62527.9i	−1.19388	−	0.210514i
$546$	11290.5	+	13455.4i	0.0378727	+	0.0451349i
$547$	283767.	−	338180.i	0.948390	−	1.13025i	−0.0429694	−	0.999076i	$-0.513682\pi$
$547$	283767.	−	338180.i	0.948390	−	1.13025i	0.991360	−	0.131171i	$-0.0418738\pi$
$548$	3959.62	+	22456.1i	0.0131854	+	0.0747780i
$549$	293838.	+	106948.i	0.974909	+	0.354838i
$550$			13838.7i			0.0457478i
$551$	−75079.3	+	282181.i	−0.247296	+	0.929448i
$552$	9592.97			0.0314829
$553$	58490.5	−	160701.i	0.191265	−	0.525496i
$554$	110712.	−	19521.5i	0.360723	−	0.0636052i
$555$	78439.8	+	65818.8i	0.254654	+	0.213680i
$556$	−166648.	+	139834.i	−0.539076	+	0.452338i
$557$	57486.5	−	326022.i	0.185292	−	1.05084i	−0.740289	−	0.672289i	$-0.765311\pi$
$557$	57486.5	−	326022.i	0.185292	−	1.05084i	0.925580	−	0.378552i	$-0.123578\pi$
$558$	−82507.8	+	142908.i	−0.264988	+	0.458973i
$559$	518039.	−	299090.i	1.65783	−	0.957147i
$560$	37111.1	−	13507.3i	0.118339	−	0.0430719i
$561$	2464.57	+	6771.35i	0.00783096	+	0.0215154i
$562$	115550.	+	200138.i	0.365845	+	0.633662i
$563$	91244.2	+	52679.8i	0.287865	+	0.166199i	0.636978	−	0.770882i	$-0.280184\pi$
$563$	91244.2	+	52679.8i	0.287865	+	0.166199i	−0.349114	+	0.937080i	$0.613517\pi$
$564$	23319.5	+	4111.85i	0.0733096	+	0.0129265i
$565$	38151.3	+	45466.9i	0.119512	+	0.142429i
$566$	68576.3	−	81726.0i	0.214063	−	0.255110i
$567$	18460.9	+	104697.i	0.0574233	+	0.325663i
$568$	163007.	+	59329.5i	0.505252	+	0.183897i
$569$			127179.i			0.392816i	0.980522	+	0.196408i	$0.0629277\pi$
$569$			127179.i			0.392816i	−0.980522	+	0.196408i	$0.937072\pi$
$570$	5170.57	−	60319.9i	0.0159144	−	0.185657i
$571$	415192.			1.27343			0.636717	−	0.771098i	$-0.280292\pi$
$571$	415192.			1.27343			0.636717	+	0.771098i	$0.280292\pi$
$572$	−5018.23	+	13787.5i	−0.0153376	+	0.0421398i
$573$	52671.7	−	9287.44i	0.160424	−	0.0282870i
$574$	−6391.48	−	5363.09i	−0.0193989	−	0.0162776i
$575$	95736.3	−	80332.3i	0.289561	−	0.242971i
$576$	−6927.88	+	39290.0i	−0.0208812	+	0.118423i
$577$	−61002.1	+	105659.i	−0.183229	+	0.317361i	−0.942978	−	0.332854i	$-0.891988\pi$
$577$	−61002.1	+	105659.i	−0.183229	+	0.317361i	0.759750	+	0.650216i	$0.225322\pi$
$578$	−257119.	+	148447.i	−0.769622	+	0.444342i
$579$	109578.	−	39883.0i	0.326863	−	0.118968i
$580$	74796.5	+	205502.i	0.222344	+	0.610885i
$581$	−83891.7	−	145305.i	−0.248523	−	0.430455i
$582$	−21901.2	−	12644.7i	−0.0646581	−	0.0373303i
$583$	11120.7	+	1960.89i	0.0327188	+	0.00576920i
$584$	30537.8	+	36393.5i	0.0895389	+	0.106708i
$585$	−328162.	+	391088.i	−0.958908	+	1.14278i
$586$	17378.5	+	98558.4i	0.0506078	+	0.287011i
$587$	−440913.	−	160479.i	−1.27961	−	0.465739i	−0.389305	−	0.921109i	$-0.627285\pi$
$587$	−440913.	−	160479.i	−1.27961	−	0.465739i	−0.890302	+	0.455370i	$0.849507\pi$
$588$		−	29019.6i		−	0.0839339i
$589$	−114659.	−	244763.i	−0.330504	−	0.705531i
$590$	−241223.			−0.692970
$591$	−22542.2	+	61934.1i	−0.0645388	+	0.177319i
$592$	108847.	−	19192.6i	0.310579	−	0.0547635i
$593$	56372.3	+	47302.0i	0.160308	+	0.134515i	0.719413	−	0.694582i	$-0.244411\pi$
$593$	56372.3	+	47302.0i	0.160308	+	0.134515i	−0.559105	+	0.829097i	$0.688855\pi$
$594$	5715.17	−	4795.60i	0.0161978	−	0.0135916i
$595$	46521.3	−	263835.i	0.131407	−	0.745245i
$596$	88684.6	−	153606.i	0.249664	−	0.432430i
$597$	37894.2	−	21878.2i	0.106322	−	0.0613852i
$598$	124512.	−	45318.7i	0.348184	−	0.126729i
$599$	185753.	+	510351.i	0.517704	+	1.42238i	0.873043	+	0.487643i	$0.162143\pi$
$599$	185753.	+	510351.i	0.517704	+	1.42238i	−0.355339	+	0.934737i	$0.615635\pi$
$600$	−10265.3	−	17780.1i	−0.0285149	−	0.0493892i
$601$	−320738.	−	185178.i	−0.887977	−	0.512674i	−0.0146971	−	0.999892i	$-0.504678\pi$
$601$	−320738.	−	185178.i	−0.887977	−	0.512674i	−0.873280	+	0.487218i	$0.838012\pi$
$602$	156930.	+	27671.0i	0.433025	+	0.0763540i
$603$	−197395.	−	235246.i	−0.542877	−	0.646975i
$604$	−174733.	+	208239.i	−0.478963	+	0.570806i
$605$	85397.3	+	484312.i	0.233310	+	1.32317i
$606$	49334.0	+	17956.1i	0.134339	+	0.0488953i
$607$		−	667026.i		−	1.81036i	−0.425027	−	0.905181i	$-0.639735\pi$
$607$		−	667026.i		−	1.81036i	0.425027	−	0.905181i	$-0.360265\pi$
$608$	−46289.1	−	46126.8i	−0.125219	−	0.124780i
$609$	−25910.6			−0.0698623
$610$	−131197.	+	360462.i	−0.352586	+	0.968723i
$611$	322101.	−	56795.0i	0.862798	−	0.152135i
$612$	207323.	+	173965.i	0.553534	+	0.464470i
$613$	−455760.	+	382428.i	−1.21287	+	1.01772i	−0.213707	+	0.976898i	$0.568554\pi$
$613$	−455760.	+	382428.i	−1.21287	+	1.01772i	−0.999166	+	0.0408237i	$0.987002\pi$
$614$	35218.4	−	199733.i	0.0934185	−	0.529802i
$615$	−4789.59	+	8295.81i	−0.0126633	+	0.0219335i
$616$	−3384.95	+	1954.30i	−0.00892052	+	0.00515027i
$617$	104710.	−	38111.3i	0.275054	−	0.100111i	−0.200810	−	0.979630i	$-0.564358\pi$
$617$	104710.	−	38111.3i	0.275054	−	0.100111i	0.475864	+	0.879519i	$0.342135\pi$
$618$	12490.7	+	34317.9i	0.0327047	+	0.0898554i
$619$	−94536.8	−	163743.i	−0.246729	−	0.427347i	0.715888	−	0.698216i	$-0.246022\pi$
$619$	−94536.8	−	163743.i	−0.246729	−	0.427347i	−0.962616	+	0.270869i	$0.912689\pi$
$620$	−175310.	−	101215.i	−0.456061	−	0.263307i
$621$	−66351.9	−	11699.6i	−0.172056	−	0.0303381i
$622$	−110623.	−	131835.i	−0.285933	−	0.340762i
$623$	−113244.	+	134959.i	−0.291769	+	0.347717i
$624$	−3779.87	−	21436.7i	−0.00970751	−	0.0550540i
$625$	419469.	+	152674.i	1.07384	+	0.390846i
$626$			291170.i			0.743015i
$627$	532.697	+	5968.02i	0.00135502	+	0.0151808i
$628$	257477.			0.652858
$629$	256436.	−	704552.i	0.648153	−	1.78079i
$630$	−133935.	+	23616.4i	−0.337453	+	0.0595022i
$631$	434962.	+	364976.i	1.09243	+	0.916656i	0.996893	−	0.0787705i	$-0.0250994\pi$
$631$	434962.	+	364976.i	1.09243	+	0.916656i	0.0955348	+	0.995426i	$0.469544\pi$
$632$	−162349.	+	136227.i	−0.406459	+	0.341059i
$633$	7509.28	−	42587.3i	0.0187409	−	0.106285i
$634$	−37130.9	+	64312.6i	−0.0923755	+	0.159999i
$635$	−845428.	+	488108.i	−2.09667	+	1.21051i
$636$	−15742.6	+	5729.84i	−0.0389190	+	0.0141654i
$637$	−137093.	−	376661.i	−0.337860	−	0.928264i
$638$	−10821.9	−	18744.0i	−0.0265865	−	0.0460492i
$639$	−517339.	−	298686.i	−1.26699	−	0.731498i
$640$	−48198.4	−	8498.68i	−0.117672	−	0.0207487i
$641$	−105428.	−	125644.i	−0.256590	−	0.305792i	0.622336	−	0.782750i	$-0.286184\pi$
$641$	−105428.	−	125644.i	−0.256590	−	0.305792i	−0.878926	+	0.476958i	$0.841739\pi$
$642$	27229.7	−	32451.0i	0.0660651	−	0.0787333i
$643$	26297.7	+	149142.i	0.0636056	+	0.360726i	0.999953	+	0.00965169i	$0.00307228\pi$
$643$	26297.7	+	149142.i	0.0636056	+	0.360726i	−0.936348	+	0.351074i	$0.885817\pi$
$644$	33169.1	+	12072.6i	0.0799764	+	0.0291090i
$645$		−	182951.i		−	0.439761i
$646$	−427990.	+	115486.i	−1.02558	+	0.276734i
$647$	−360082.			−0.860187			−0.430094	−	0.902784i	$-0.641519\pi$
$647$	−360082.			−0.860187			−0.430094	+	0.902784i	$0.641519\pi$
$648$	45060.7	−	123803.i	0.107312	−	0.294837i
$649$	23511.1	−	4145.64i	0.0558191	−	0.00984242i
$650$	−217235.	−	182282.i	−0.514166	−	0.431437i
$651$	18372.9	−	15416.7i	0.0433527	−	0.0363772i
$652$	26683.1	−	151327.i	0.0627683	−	0.355977i
$653$	62367.0	−	108023.i	0.146261	−	0.253332i	−0.783582	−	0.621289i	$-0.786609\pi$
$653$	62367.0	−	108023.i	0.146261	−	0.253332i	0.929843	+	0.367957i	$0.119943\pi$
$654$	−45787.3	+	26435.3i	−0.107051	+	0.0618058i
$655$	−641058.	+	233326.i	−1.49422	+	0.543852i
$656$	3536.40	+	9716.19i	0.00821777	+	0.0225781i
$657$	−81802.2	−	141686.i	−0.189511	−	0.328243i
$658$	75455.9	+	43564.5i	0.174278	+	0.100619i
$659$	402313.	+	70938.6i	0.926388	+	0.163347i	0.616436	−	0.787405i	$-0.288576\pi$
$659$	402313.	+	70938.6i	0.926388	+	0.163347i	0.309952	+	0.950752i	$0.399687\pi$
$660$	2884.49	+	3437.61i	0.00662189	+	0.00789166i
$661$	−52551.0	+	62627.9i	−0.120276	+	0.143339i	−0.822822	−	0.568299i	$-0.807602\pi$
$661$	−52551.0	+	62627.9i	−0.120276	+	0.143339i	0.702547	+	0.711638i	$0.252046\pi$
$662$	7336.43	+	41607.0i	0.0167405	+	0.0949402i
$663$	−138757.	−	50503.5i	−0.315667	−	0.114893i
$664$			207927.i			0.471602i
$665$	93789.5	−	202058.i	0.212086	−	0.456912i
$666$	−380618.			−0.858106
$667$	−66851.5	+	183673.i	−0.150266	+	0.412851i
$668$	411937.	−	72635.6i	0.923161	−	0.162778i
$669$	31192.4	+	26173.5i	0.0696942	+	0.0584804i
$670$	288585.	−	242151.i	0.642870	−	0.539432i
$671$	6592.45	−	37387.6i	0.0146420	−	0.0830392i
$672$	2899.34	−	5021.80i	0.00642038	−	0.0111204i
$673$	318383.	−	183819.i	0.702943	−	0.405844i	−0.105500	−	0.994419i	$-0.533644\pi$
$673$	318383.	−	183819.i	0.702943	−	0.405844i	0.808443	+	0.588575i	$0.200311\pi$
$674$	15070.7	−	5485.27i	0.0331751	−	0.0120747i
$675$	49317.9	+	135500.i	0.108242	+	0.297393i
$676$	−36087.2	−	62504.9i	−0.0789696	−	0.136779i
$677$	717595.	+	414304.i	1.56568	+	0.903944i	0.996664	+	0.0816146i	$0.0260077\pi$
$677$	717595.	+	414304.i	1.56568	+	0.903944i	0.569012	+	0.822329i	$0.307326\pi$
$678$	8582.30	+	1513.29i	0.0186700	+	0.00329203i
$679$	−59813.7	−	71283.2i	−0.129736	−	0.154614i
$680$	−213409.	+	254330.i	−0.461524	+	0.550023i
$681$	30959.2	+	175578.i	0.0667568	+	0.378597i
$682$	18826.3	+	6852.21i	0.0404759	+	0.0147320i
$683$		−	715889.i		−	1.53463i	−0.641269	−	0.767316i	$-0.721592\pi$
$683$		−	715889.i		−	1.53463i	0.641269	−	0.767316i	$-0.278408\pi$
$684$	129401.	+	184114.i	0.276582	+	0.393527i
$685$	96329.5			0.205295
$686$	78930.0	−	216858.i	0.167723	−	0.460816i
$687$	−149983.	+	26446.1i	−0.317782	+	0.0560335i
$688$	−151277.	−	126936.i	−0.319591	−	0.268169i
$689$	−177263.	+	148741.i	−0.373404	+	0.313323i
$690$	7037.19	−	39909.9i	0.0147809	−	0.0838267i
$691$	−436695.	+	756378.i	−0.914581	+	1.58410i	−0.107068	+	0.994252i	$0.534146\pi$
$691$	−436695.	+	756378.i	−0.914581	+	1.58410i	−0.807513	+	0.589850i	$0.799187\pi$
$692$	216094.	−	124762.i	0.451264	−	0.260538i
$693$	12648.3	−	4603.61i	0.0263370	−	0.00958587i
$694$	−207353.	−	569697.i	−0.430518	−	1.18284i
$695$	459507.	+	795889.i	0.951310	+	1.64772i
$696$	27808.1	+	16055.0i	0.0574054	+	0.0331430i
$697$	69075.6	+	12179.9i	0.142187	+	0.0250714i
$698$	238218.	+	283897.i	0.488950	+	0.582707i
$699$	52928.5	−	63077.8i	0.108327	−	0.129099i
$700$	−13118.0	−	74396.1i	−0.0267715	−	0.151829i
$701$	476391.	+	173392.i	0.969454	+	0.352852i	0.777731	−	0.628597i	$-0.216370\pi$
$701$	476391.	+	173392.i	0.969454	+	0.352852i	0.191723	+	0.981449i	$0.438593\pi$
$702$			152882.i			0.310228i
$703$	356690.	−	511316.i	0.721740	−	1.03461i
$704$	4843.77			0.00977324
$705$	34213.3	−	94000.4i	0.0688362	−	0.189126i
$706$	479133.	−	84484.1i	0.961273	−	0.169498i
$707$	147982.	+	124172.i	0.296054	+	0.248419i
$708$	−27132.1	+	22766.5i	−0.0541273	+	0.0454182i
$709$	−5556.93	+	31514.9i	−0.0110546	+	0.0626936i	−0.989836	−	0.142213i	$-0.954578\pi$
$709$	−5556.93	+	31514.9i	−0.0110546	+	0.0626936i	0.978781	+	0.204907i	$0.0656892\pi$
$710$	366408.	−	634638.i	0.726857	−	1.25895i
$711$	632051.	−	364915.i	1.25030	−	0.721859i
$712$	205162.	−	74672.9i	0.404704	−	0.147300i
$713$	−61881.0	−	170017.i	−0.121725	−	0.334436i
$714$	−19668.1	−	34066.1i	−0.0385803	−	0.0668231i
$715$	53679.1	+	30991.7i	0.105001	+	0.0606223i
$716$	38917.2	+	6862.16i	0.0759130	+	0.0133855i
$717$	124005.	+	147783.i	0.241212	+	0.287466i
$718$	−33458.5	+	39874.3i	−0.0649019	+	0.0773471i
$719$	62930.9	+	356899.i	0.121732	+	0.690378i	0.983195	+	0.182558i	$0.0584377\pi$
$719$	62930.9	+	356899.i	0.121732	+	0.690378i	−0.861463	+	0.507821i	$0.830451\pi$
$720$	158377.	+	57644.5i	0.305511	+	0.111197i
$721$			134379.i			0.258499i
$722$	−368601.	+	1294.73i	−0.707102	+	0.00248374i
$723$	153973.			0.294556
$724$	−102402.	+	281347.i	−0.195358	+	0.536742i
$725$	411966.	−	72640.8i	0.783764	−	0.138199i
$726$	55314.5	+	46414.3i	0.104946	+	0.0880601i
$727$	−65653.3	+	55089.7i	−0.124219	+	0.104232i	−0.702781	−	0.711406i	$-0.748059\pi$
$727$	−65653.3	+	55089.7i	−0.124219	+	0.104232i	0.578562	+	0.815638i	$0.303614\pi$
$728$	13908.2	−	78877.5i	0.0262427	−	0.148830i
$729$	−207041.	+	358605.i	−0.389584	+	0.674779i
$730$	173811.	−	100350.i	0.326160	−	0.188309i
$731$	−1.25883e6	+	458176.i	−2.35576	+	0.857428i
$732$	19263.5	+	52926.2i	0.0359513	+	0.0987753i
$733$	225386.	+	390381.i	0.419488	+	0.726575i	0.995888	−	0.0905930i	$-0.0288762\pi$
$733$	225386.	+	390381.i	0.419488	+	0.726575i	−0.576400	+	0.817168i	$0.695543\pi$
$734$	−220140.	−	127098.i	−0.408607	−	0.235910i
$735$	−120731.	−	21288.2i	−0.223483	−	0.0394061i
$736$	−28117.6	−	33509.3i	−0.0519066	−	0.0618599i
$737$	−23965.7	+	28561.2i	−0.0441219	+	0.0525825i
$738$	−6183.09	−	35066.1i	−0.0113525	−	0.0643834i
$739$	−122548.	−	44603.9i	−0.224398	−	0.0816741i	0.227375	−	0.973807i	$-0.426986\pi$
$739$	−122548.	−	44603.9i	−0.224398	−	0.0816741i	−0.451772	+	0.892133i	$0.649208\pi$
$740$		−	466918.i		−	0.852662i
$741$	−100700.	−	70248.0i	−0.183398	−	0.127937i
$742$	−61643.3			−0.111964
$743$	37859.8	−	104019.i	0.0685806	−	0.188424i	−0.900668	−	0.434509i	$-0.856922\pi$
$743$	37859.8	−	104019.i	0.0685806	−	0.188424i	0.969248	+	0.246085i	$0.0791443\pi$
$744$	−29271.1	+	5161.28i	−0.0528801	+	0.00932420i
$745$	−573995.	−	481639.i	−1.03418	−	0.867779i
$746$	119471.	−	100248.i	0.214677	−	0.180135i
$747$	124339.	−	705162.i	0.222826	−	1.26371i
$748$	16429.2	−	28456.3i	0.0293639	−	0.0508598i
$749$	134990.	−	77936.3i	0.240623	−	0.138924i
$750$	16992.3	−	6184.70i	0.0302086	−	0.0109950i
$751$	−63499.4	−	174463.i	−0.112587	−	0.309331i	0.870583	−	0.492021i	$-0.163742\pi$
$751$	−63499.4	−	174463.i	−0.112587	−	0.309331i	−0.983171	+	0.182690i	$0.941520\pi$
$752$	−53987.8	−	93509.6i	−0.0954684	−	0.165356i
$753$	−150276.	−	86761.7i	−0.265032	−	0.153016i
$754$	436782.	+	77016.4i	0.768284	+	0.135469i
$755$	738163.	+	879708.i	1.29497	+	1.54328i
$756$	−26178.6	+	31198.4i	−0.0458039	+	0.0545869i
$757$	−66108.9	−	374922.i	−0.115364	−	0.654259i	−0.986570	−	0.163341i	$-0.947773\pi$
$757$	−66108.9	−	374922.i	−0.115364	−	0.654259i	0.871206	−	0.490917i	$-0.163338\pi$
$758$	−550157.	−	200241.i	−0.957521	−	0.348509i
$759$			4010.81i			0.00696223i
$760$	−225859.	+	158740.i	−0.391030	+	0.274827i
$761$	−418830.			−0.723217			−0.361609	−	0.932330i	$-0.617772\pi$
$761$	−418830.			−0.723217			−0.361609	+	0.932330i	$0.617772\pi$
$762$	−49024.0	+	134692.i	−0.0844304	+	0.231971i
$763$	−191585.	+	33781.6i	−0.329088	+	0.0580271i
$764$	−186826.	−	156766.i	−0.320074	−	0.268574i
$765$	875838.	−	734915.i	1.49658	−	1.25578i
$766$	40191.4	−	227937.i	0.0684976	−	0.388469i
$767$	−244609.	+	423674.i	−0.415797	+	0.720181i
$768$	−6223.33	+	3593.04i	−0.0105512	+	0.00609171i
$769$	−591993.	+	215468.i	−1.00107	+	0.364359i	−0.789997	−	0.613111i	$-0.789918\pi$
$769$	−591993.	+	215468.i	−1.00107	+	0.364359i	−0.211072	+	0.977470i	$0.567696\pi$
$770$	5647.41	+	15516.1i	0.00952505	+	0.0261699i
$771$	−26636.0	−	46134.9i	−0.0448084	−	0.0776105i
$772$	−460495.	−	265867.i	−0.772664	−	0.446098i
$773$	604428.	+	106577.i	1.01155	+	0.178363i	0.654771	−	0.755827i	$-0.272765\pi$
$773$	604428.	+	106577.i	1.01155	+	0.178363i	0.356775	+	0.934190i	$0.383876\pi$
$774$	437130.	+	520951.i	0.729673	+	0.869591i
$775$	−248900.	+	296627.i	−0.414401	+	0.493864i
$776$	20024.7	+	113566.i	0.0332539	+	0.188592i
$777$	51984.5	+	18920.8i	0.0861058	+	0.0313399i
$778$			482486.i			0.797123i
$779$	52901.5	+	24555.4i	0.0871752	+	0.0404642i
$780$	−91956.6			−0.151145
$781$	−24805.6	+	68152.9i	−0.0406675	+	0.111733i
$782$	−292231.	+	51528.1i	−0.477873	+	0.0842618i
$783$	−172760.	−	144963.i	−0.281786	−	0.236447i
$784$	−101369.	+	85058.4i	−0.164919	+	0.138384i
$785$	188879.	−	1.07119e6i	0.306510	−	1.73831i
$786$	−50083.2	+	86746.7i	−0.0810676	+	0.140413i
$787$	−35312.2	+	20387.5i	−0.0570132	+	0.0329166i	−0.528236	−	0.849098i	$-0.677146\pi$
$787$	−35312.2	+	20387.5i	−0.0570132	+	0.0329166i	0.471222	+	0.882014i	$0.343813\pi$
$788$	282415.	−	102791.i	0.454816	−	0.165539i
$789$	−19714.3	−	54164.7i	−0.0316686	−	0.0870087i
$790$	447654.	+	775360.i	0.717279	+	1.24236i
$791$	27770.1	+	16033.1i	0.0443839	+	0.0256250i
$792$	−16427.1	−	2896.54i	−0.0261885	−	0.00461774i
$793$	500063.	+	595952.i	0.795203	+	0.947687i
$794$	314497.	−	374803.i	0.498856	−	0.594514i
$795$	12289.6	+	69697.6i	0.0194448	+	0.110277i
$796$	−187494.	−	68242.1i	−0.295910	−	0.107703i
$797$			48643.8i			0.0765792i	0.999267	+	0.0382896i	$0.0121909\pi$
$797$			48643.8i			0.0765792i	−0.999267	+	0.0382896i	$0.987809\pi$
$798$	−8520.97	−	31578.8i	−0.0133808	−	0.0495894i
$799$	−732468.			−1.14735
$800$	−32019.4	+	87972.6i	−0.0500303	+	0.137457i
$801$	−740437.	+	130559.i	−1.15405	+	0.203489i
$802$	−218811.	−	183605.i	−0.340190	−	0.285453i
$803$	−15216.1	+	12767.8i	−0.0235978	+	0.0198009i
$804$	9605.06	−	54473.0i	0.0148590	−	0.0842693i
$805$	74558.0	−	129138.i	0.115054	−	0.199280i
$806$	−355541.	+	205272.i	−0.547293	+	0.315980i
$807$	−9030.37	+	3286.78i	−0.0138662	+	0.00504689i
$808$	−81878.6	−	224960.i	−0.125414	−	0.344573i
$809$	−510145.	−	883597.i	−0.779465	−	1.35007i	−0.932250	−	0.361814i	$-0.882158\pi$
$809$	−510145.	−	883597.i	−0.779465	−	1.35007i	0.152786	−	0.988259i	$-0.451176\pi$
$810$	−482007.	−	278287.i	−0.734655	−	0.424153i
$811$	132368.	+	23340.1i	0.201253	+	0.0354863i	0.273366	−	0.961910i	$-0.411863\pi$
$811$	132368.	+	23340.1i	0.201253	+	0.0354863i	−0.0721128	+	0.997396i	$0.522974\pi$
$812$	75945.7	+	90508.6i	0.115184	+	0.137271i
$813$	−81280.7	+	96866.6i	−0.122972	+	0.146552i
$814$	8024.42	+	45508.7i	0.0121106	+	0.0686825i
$815$	−609997.	−	222021.i	−0.918358	−	0.334255i
$816$			48747.8i			0.0732108i
$817$	−1.10949e6	+	99031.2i	−1.66218	+	0.148364i
$818$	−59732.5			−0.0892697
$819$	−94336.3	+	259187.i	−0.140641	+	0.386407i
$820$	43016.8	−	7585.02i	0.0639750	−	0.0112805i
$821$	83777.4	+	70297.6i	0.124291	+	0.104293i	0.702815	−	0.711373i	$-0.251926\pi$
$821$	83777.4	+	70297.6i	0.124291	+	0.104293i	−0.578523	+	0.815666i	$0.696371\pi$
$822$	10834.9	−	9091.55i	0.0160354	−	0.0134553i
$823$	−147146.	+	834508.i	−0.217245	+	1.23206i	0.659723	+	0.751509i	$0.270673\pi$
$823$	−147146.	+	834508.i	−0.217245	+	1.23206i	−0.876968	+	0.480548i	$0.840438\pi$
$824$	83265.1	−	144219.i	0.122633	−	0.212407i
$825$	7433.84	−	4291.93i	0.0109221	−	0.00630587i
$826$	−122464.	+	44573.4i	−0.179494	+	0.0653305i
$827$	298354.	+	819721.i	0.436236	+	1.19855i	0.941922	+	0.335830i	$0.109017\pi$
$827$	298354.	+	819721.i	0.436236	+	1.19855i	−0.505687	+	0.862717i	$0.668761\pi$
$828$	75319.3	+	130457.i	0.109861	+	0.190286i
$829$	348451.	+	201178.i	0.507029	+	0.292733i	0.731611	−	0.681722i	$-0.238769\pi$
$829$	348451.	+	201178.i	0.507029	+	0.292733i	−0.224583	+	0.974455i	$0.572102\pi$
$830$	865047.	+	152531.i	1.25569	+	0.221412i
$831$	−44822.6	−	53417.4i	−0.0649075	−	0.0773537i
$832$	−63801.7	+	76035.9i	−0.0921691	+	0.109843i
$833$	155877.	+	884025.i	0.224643	+	1.27402i
$834$	126800.	+	46151.3i	0.182300	+	0.0663517i
$835$		−	1.76708e6i		−	2.53444i
$836$	19285.6	−	19353.4i	0.0275943	−	0.0276914i
$837$	208755.			0.297979
$838$	−123485.	+	339272.i	−0.175843	+	0.483125i
$839$	−63035.4	+	11114.8i	−0.0895490	+	0.0157899i	−0.218243	−	0.975894i	$-0.570033\pi$
$839$	−63035.4	+	11114.8i	−0.0895490	+	0.0157899i	0.128694	+	0.991684i	$0.458921\pi$
$840$	−18765.5	−	15746.1i	−0.0265950	−	0.0223159i
$841$	40620.3	−	34084.5i	0.0574316	−	0.0481909i
$842$	2229.01	−	12641.3i	0.00314404	−	0.0178307i
$843$	71673.2	−	124142.i	0.100856	−	0.174688i
$844$	−170772.	+	98595.3i	−0.239735	+	0.138411i
$845$	−286514.	+	104282.i	−0.401266	+	0.146049i
$846$	127175.	+	349411.i	0.177689	+	0.488198i
$847$	132846.	+	230097.i	0.185175	+	0.320733i
$848$	66157.5	+	38196.1i	0.0919999	+	0.0531162i
$849$	−65169.6	−	11491.2i	−0.0904127	−	0.0159422i
$850$	408218.	+	486495.i	0.565008	+	0.673350i
$851$	268249.	−	319686.i	0.370406	−	0.441433i
$852$	−18684.3	−	105964.i	−0.0257393	−	0.145975i
$853$	1.19794e6	+	436014.i	1.64640	+	0.599242i	0.988141	−	0.153548i	$-0.0490698\pi$
$853$	1.19794e6	+	436014.i	1.64640	+	0.599242i	0.658262	+	0.752789i	$0.271292\pi$
$854$			207243.i			0.284161i
$855$	860900.	−	403287.i	1.17766	−	0.551673i
$856$	−193167.			−0.263624
$857$	124994.	−	343419.i	0.170188	−	0.467587i	−0.825051	−	0.565059i	$-0.808853\pi$
$857$	124994.	−	343419.i	0.170188	−	0.467587i	0.995238	+	0.0974720i	$0.0310756\pi$
$858$	8962.66	−	1580.36i	0.0121748	−	0.00214675i
$859$	15390.8	+	12914.4i	0.0208581	+	0.0175020i	0.653157	−	0.757222i	$-0.273444\pi$
$859$	15390.8	+	12914.4i	0.0208581	+	0.0175020i	−0.632299	+	0.774724i	$0.717889\pi$
$860$	−639069.	+	536242.i	−0.864074	+	0.725044i
$861$	−898.679	+	5096.66i	−0.00121227	+	0.00687511i
$862$	−138084.	+	239169.i	−0.185836	+	0.321877i
$863$	842433.	−	486379.i	1.13113	−	0.653060i	0.186914	−	0.982376i	$-0.440151\pi$
$863$	842433.	−	486379.i	1.13113	−	0.653060i	0.944220	+	0.329316i	$0.106818\pi$
$864$	47427.1	−	17262.1i	0.0635330	−	0.0231241i
$865$	−360529.	−	990545.i	−0.481846	−	1.32386i
$866$	35463.8	+	61425.1i	0.0472879	+	0.0819050i
$867$	159485.	+	92078.8i	0.212169	+	0.122496i
$868$	−107704.	−	18991.2i	−0.142953	−	0.0252065i
$869$	−56956.5	−	67878.1i	−0.0754229	−	0.0898856i
$870$	87193.5	−	103913.i	0.115198	−	0.137288i
$871$	−132670.	−	752409.i	−0.174879	−	0.991785i
$872$	226547.	+	82456.4i	0.297938	+	0.108440i
$873$		−	397119.i		−	0.521066i
$874$	−245838.	−	21073.0i	−0.321829	−	0.0275870i
$875$	66536.9			0.0869053
$876$	10078.8	−	27691.3i	0.0131341	−	0.0360856i
$877$	658398.	−	116093.i	0.856030	−	0.150941i	0.271625	−	0.962403i	$-0.412439\pi$
$877$	658398.	−	116093.i	0.856030	−	0.150941i	0.584405	+	0.811462i	$0.301328\pi$
$878$	111458.	+	93524.7i	0.144585	+	0.121321i
$879$	47553.6	−	39902.2i	0.0615468	−	0.0516439i
$880$	3553.29	−	20151.7i	0.00458844	−	0.0260223i
$881$	519792.	−	900306.i	0.669696	−	1.15995i	−0.308293	−	0.951291i	$-0.599758\pi$
$881$	519792.	−	900306.i	0.669696	−	1.15995i	0.977989	−	0.208656i	$-0.0669089\pi$
$882$	394644.	−	227848.i	0.507304	−	0.292892i
$883$	−1.11835e6	+	407048.i	−1.43436	+	0.522064i	−0.938178	−	0.346154i	$-0.887487\pi$
$883$	−1.11835e6	+	407048.i	−1.43436	+	0.522064i	−0.496182	+	0.868218i	$0.665265\pi$
$884$	230292.	+	632723.i	0.294696	+	0.809672i
$885$	74812.7	+	129579.i	0.0955188	+	0.165443i
$886$	−376922.	−	217616.i	−0.480158	−	0.277219i
$887$	224615.	+	39605.7i	0.285491	+	0.0503397i	0.314560	−	0.949238i	$-0.398143\pi$
$887$	224615.	+	39605.7i	0.285491	+	0.0503397i	−0.0290690	+	0.999577i	$0.509254\pi$
$888$	−44067.5	−	52517.6i	−0.0558847	−	0.0666008i
$889$	−339016.	+	404023.i	−0.428959	+	0.511214i
$890$	−160161.	−	908320.i	−0.202198	−	1.14672i
$891$	51762.0	+	18839.8i	0.0652013	+	0.0237313i
$892$		−	185675.i		−	0.233358i
$893$	−588573.	−	156600.i	−0.738069	−	0.196376i
$894$	−110018.			−0.137654
$895$	57097.7	−	156875.i	0.0712808	−	0.195842i
$896$	−26039.9	+	4591.53i	−0.0324356	+	0.00571928i
$897$	−62960.3	−	52829.9i	−0.0782495	−	0.0656591i
$898$	−377161.	+	316475.i	−0.467707	+	0.392453i
$899$	105163.	−	596410.i	0.130120	−	0.737948i
$900$	161197.	−	279201.i	0.199009	−	0.344693i
$901$	448789.	−	259109.i	0.552831	−	0.319177i
$902$	−4062.33	+	1478.57i	−0.00499300	+	0.00181730i
$903$	−33806.0	−	92881.2i	−0.0414589	−	0.113907i
$904$	−19869.2	−	34414.5i	−0.0243133	−	0.0421118i
$905$	1.09538e6	+	632416.i	1.33742	+	0.772157i
$906$	166053.	+	29279.6i	0.202298	+	0.0356705i
$907$	217035.	+	258652.i	0.263824	+	0.314413i	0.881652	−	0.471900i	$-0.156432\pi$
$907$	217035.	+	258652.i	0.263824	+	0.314413i	−0.617828	+	0.786313i	$0.711987\pi$
$908$	522571.	−	622776.i	0.633831	−	0.755370i
$909$	143157.	+	811886.i	0.173255	+	0.982579i
$910$	−317954.	−	115726.i	−0.383956	−	0.139748i
$911$			287019.i			0.345839i	0.984936	+	0.172920i	$0.0553200\pi$
$911$			287019.i			0.345839i	−0.984936	+	0.172920i	$0.944680\pi$
$912$	−10422.2	+	39171.2i	−0.0125305	+	0.0470952i
$913$	−86934.2			−0.104292
$914$	151593.	−	416498.i	0.181462	−	0.498564i
$915$	234321.	−	41317.2i	0.279879	−	0.0493502i
$916$	531990.	+	446392.i	0.634033	+	0.532017i
$917$	−282339.	+	236911.i	−0.335763	+	0.281738i
$918$	59453.1	−	337175.i	0.0705487	−	0.400102i
$919$	5599.66	−	9698.90i	0.00663027	−	0.0114840i	−0.862691	−	0.505731i	$-0.831223\pi$
$919$	5599.66	−	9698.90i	0.00663027	−	0.0114840i	0.869322	+	0.494247i	$0.164556\pi$
$920$	−160036.	+	92396.8i	−0.189078	+	0.109164i
$921$	−118215.	+	43026.7i	−0.139365	+	0.0507246i
$922$	283951.	+	780148.i	0.334026	+	0.917730i
$923$	−743103.	−	1.28709e6i	−0.872259	−	1.51080i
$924$	2099.61	+	1212.21i	0.00245921	+	0.00141982i
$925$	−879574.	−	155093.i	−1.02799	−	0.181262i
$926$	−160411.	−	191171.i	−0.187074	−	0.222946i
$927$	−368626.	+	439311.i	−0.428969	+	0.511226i
$928$	−25425.5	−	144195.i	−0.0295238	−	0.167438i
$929$	1.20694e6	+	439289.i	1.39847	+	0.509002i	0.927724	−	0.373267i	$-0.121763\pi$
$929$	1.20694e6	+	439289.i	1.39847	+	0.509002i	0.470746	+	0.882269i	$0.343985\pi$
$930$			125563.i			0.145177i
$931$	−63747.9	+	743682.i	−0.0735472	+	0.858002i
$932$	−375474.			−0.432264
$933$	−36510.4	+	100312.i	−0.0419424	+	0.115236i
$934$	760170.	−	134038.i	0.871399	−	0.153651i
$935$	−106335.	−	89225.9i	−0.121634	−	0.102063i
$936$	261845.	−	219714.i	0.298877	−	0.250787i
$937$	−229424.	+	1.30113e6i	−0.261312	+	1.48197i	0.518023	+	0.855367i	$0.326668\pi$
$937$	−229424.	+	1.30113e6i	−0.261312	+	1.48197i	−0.779335	+	0.626608i	$0.784443\pi$
$938$	101764.	−	176261.i	0.115662	−	0.200332i
$939$	156410.	−	90303.2i	0.177391	−	0.102417i
$940$	−428635.	+	156010.i	−0.485100	+	0.176562i
$941$	−172765.	−	474668.i	−0.195109	−	0.536057i	0.803103	−	0.595841i	$-0.203181\pi$
$941$	−172765.	−	474668.i	−0.195109	−	0.536057i	−0.998211	+	0.0597840i	$0.980959\pi$
$942$	−79853.7	−	138311.i	−0.0899897	−	0.155867i
$943$	33810.1	+	19520.3i	0.0380210	+	0.0219514i
$944$	159052.	+	28045.1i	0.178482	+	0.0314712i
$945$	110592.	+	131798.i	0.123839	+	0.147586i
$946$	53071.8	−	63248.6i	0.0593037	−	0.0706754i
$947$	231595.	+	1.31344e6i	0.258244	+	1.46457i	0.787607	+	0.616178i	$0.211320\pi$
$947$	231595.	+	1.31344e6i	0.258244	+	1.46457i	−0.529363	+	0.848395i	$0.677569\pi$
$948$	123529.	+	44960.9i	0.137452	+	0.0500286i
$949$		−	407033.i		−	0.451957i
$950$	224011.	+	478198.i	0.248211	+	0.529860i
$951$	46063.0			0.0509321
$952$	−61348.2	+	168553.i	−0.0676906	+	0.185978i
$953$	−698106.	+	123095.i	−0.768662	+	0.135536i	−0.544210	−	0.838949i	$-0.683170\pi$
$953$	−698106.	+	123095.i	−0.768662	+	0.135536i	−0.224452	+	0.974485i	$0.572059\pi$
$954$	−201524.	−	169099.i	−0.221427	−	0.185799i
$955$	−789249.	+	662258.i	−0.865381	+	0.726140i
$956$	152756.	−	866323.i	0.167141	−	0.947904i
$957$	−6712.58	+	11626.5i	−0.00732935	+	0.0126948i
$958$	580619.	−	335221.i	0.632646	−	0.365258i
$959$	48904.8	−	17799.9i	0.0531758	−	0.0193544i
$960$	10382.9	+	28526.9i	0.0112662	+	0.0309536i
$961$	−181469.	−	314314.i	−0.196497	−	0.340343i
$962$	−820077.	−	473471.i	−0.886144	−	0.511615i
$963$	655103.	+	115512.i	0.706410	+	0.124559i
$964$	−451304.	−	537844.i	−0.485641	−	0.578764i
$965$	−1.44390e6	+	1.72078e6i	−1.55054	+	1.84786i
$966$	−3801.94	−	21561.9i	−0.00407428	−	0.0231064i
$967$	1.48501e6	+	540499.i	1.58809	+	0.578019i	0.976944	−	0.213496i	$-0.0684851\pi$
$967$	1.48501e6	+	540499.i	1.58809	+	0.578019i	0.611150	+	0.791515i	$0.290707\pi$
$968$		−	329263.i		−	0.351392i
$969$	194773.	+	194090.i	0.207435	+	0.206707i
$970$	487160.			0.517760
$971$	602694.	−	1.65589e6i	0.639232	−	1.75628i	−0.0148934	−	0.999889i	$-0.504741\pi$
$971$	602694.	−	1.65589e6i	0.639232	−	1.75628i	0.654125	−	0.756386i	$-0.273037\pi$
$972$	−258407.	+	45564.1i	−0.273509	+	0.0482270i
$973$	380348.	+	319150.i	0.401750	+	0.337108i
$974$	−270922.	+	227330.i	−0.285579	+	0.239629i
$975$	−30544.5	+	173227.i	−0.0321310	+	0.182224i
$976$	128414.	−	222420.i	0.134807	−	0.233493i
$977$	−1.29215e6	+	746022.i	−1.35370	+	0.781560i	−0.988766	−	0.149472i	$-0.952242\pi$
$977$	−1.29215e6	+	746022.i	−1.35370	+	0.781560i	−0.364936	+	0.931033i	$0.618909\pi$
$978$	−89565.0	+	32599.0i	−0.0936398	+	0.0340821i
$979$	31220.6	+	85778.0i	0.0325744	+	0.0894974i
$980$	279509.	+	484124.i	0.291034	+	0.504086i
$981$	−719000.	−	415115.i	−0.747120	−	0.431350i
$982$	−528397.	−	93170.7i	−0.547946	−	0.0966177i
$983$	−941879.	−	1.12249e6i	−0.974738	−	1.16165i	−0.986836	−	0.161721i	$-0.948295\pi$
$983$	−941879.	−	1.12249e6i	−0.974738	−	1.16165i	0.0120981	−	0.999927i	$-0.496149\pi$
$984$	4122.54	−	4913.05i	0.00425769	−	0.00507412i
$985$	−220470.	−	1.25034e6i	−0.227235	−	1.28872i
$986$	−933356.	−	339714.i	−0.960050	−	0.349430i
$987$		−	54044.3i		−	0.0554773i
$988$	49775.9	+	557659.i	0.0509924	+	0.571288i
$989$	−745630.			−0.762309
$990$	−24101.1	+	66217.3i	−0.0245905	+	0.0675617i
$991$	−813244.	+	143397.i	−0.828083	+	0.146013i	−0.571597	−	0.820535i	$-0.693676\pi$
$991$	−813244.	+	143397.i	−0.828083	+	0.146013i	−0.256486	+	0.966548i	$0.582565\pi$
$992$	103824.	+	87118.9i	0.105506	+	0.0885297i
$993$	20075.0	−	16844.9i	0.0203590	−	0.0170833i
$994$	68749.8	−	389900.i	0.0695823	−	0.394621i
$995$	−421451.	+	729974.i	−0.425697	+	0.737329i
$996$	111694.	−	64486.5i	0.112593	−	0.0650055i
$997$	517419.	−	188325.i	0.520538	−	0.189460i	−0.0683706	−	0.997660i	$-0.521780\pi$
$997$	517419.	−	188325.i	0.520538	−	0.189460i	0.588909	+	0.808200i	$0.299558\pi$
$998$	−391.328	−	1075.17i	−0.000392898	−	0.00107948i
$999$	240752.	+	416995.i	0.241234	+	0.417830i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	38.5.f.a.15.2	✓	36
19.14	odd	18	inner	38.5.f.a.33.2	yes	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
38.5.f.a.15.2	✓	36	1.1	even	1	trivial
38.5.f.a.33.2	yes	36	19.14	odd	18	inner

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.f (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.967379 + 2.65785i) q^{2} +(1.72776 - 0.304651i) q^{3} +(-6.12836 - 5.14230i) q^{4} +(-25.8893 + 21.7237i) q^{5} +(-0.861682 + 4.88684i) q^{6} +(-9.12940 + 15.8126i) q^{7} +(19.5959 - 11.3137i) q^{8} +(-73.2228 + 26.6509i) q^{9} +O(q^{10})\)	\(q+(-0.967379 + 2.65785i) q^{2} +(1.72776 - 0.304651i) q^{3} +(-6.12836 - 5.14230i) q^{4} +(-25.8893 + 21.7237i) q^{5} +(-0.861682 + 4.88684i) q^{6} +(-9.12940 + 15.8126i) q^{7} +(19.5959 - 11.3137i) q^{8} +(-73.2228 + 26.6509i) q^{9} +(-32.6936 - 89.8249i) q^{10} +(4.73025 + 8.19303i) q^{11} +(-12.1549 - 7.01766i) q^{12} +(-190.918 - 33.6639i) q^{13} +(-33.1959 - 39.5614i) q^{14} +(-38.1123 + 45.4205i) q^{15} +(11.1135 + 63.0277i) q^{16} +(407.971 + 148.489i) q^{17} -220.397i q^{18} +(296.077 + 206.541i) q^{19} +270.369 q^{20} +(-10.9561 + 30.1016i) q^{21} +(-26.3518 + 4.64654i) q^{22} +(185.114 + 155.329i) q^{23} +(30.4103 - 25.5173i) q^{24} +(89.8063 - 509.317i) q^{25} +(274.163 - 474.865i) q^{26} +(-241.461 + 139.408i) q^{27} +(137.261 - 49.9590i) q^{28} +(276.647 + 760.080i) q^{29} +(-83.8519 - 145.236i) q^{30} +(-648.411 - 374.360i) q^{31} +(-178.269 - 31.4337i) q^{32} +(10.6687 + 12.7145i) q^{33} +(-789.325 + 940.681i) q^{34} +(-107.154 - 607.701i) q^{35} +(585.782 + 213.207i) q^{36} -1726.97i q^{37} +(-835.375 + 587.125i) q^{38} -340.116 q^{39} +(-261.549 + 718.599i) q^{40} +(159.104 - 28.0544i) q^{41} +(-69.4070 - 58.2394i) q^{42} +(-2363.70 + 1983.38i) q^{43} +(13.1424 - 74.5342i) q^{44} +(1316.73 - 2280.64i) q^{45} +(-591.918 + 341.744i) q^{46} +(-1585.37 + 577.028i) q^{47} +(38.4029 + 105.511i) q^{48} +(1033.81 + 1790.61i) q^{49} +(1266.81 + 731.394i) q^{50} +(750.113 + 132.265i) q^{51} +(996.901 + 1188.06i) q^{52} +(767.248 - 914.371i) q^{53} +(-136.940 - 776.627i) q^{54} +(-300.446 - 109.353i) q^{55} +413.149i q^{56} +(574.473 + 266.654i) q^{57} -2287.80 q^{58} +(863.095 - 2371.33i) q^{59} +(467.132 - 82.3680i) q^{60} +(-3074.09 - 2579.47i) q^{61} +(1622.25 - 1361.23i) q^{62} +(247.060 - 1401.15i) q^{63} +(256.000 - 443.405i) q^{64} +(5674.03 - 3275.90i) q^{65} +(-44.1140 + 16.0562i) q^{66} +(1347.91 + 3703.34i) q^{67} +(-1736.61 - 3007.90i) q^{68} +(367.154 + 211.977i) q^{69} +(1718.84 + 303.077i) q^{70} +(4927.79 + 5872.71i) q^{71} +(-1133.35 + 1350.67i) q^{72} +(364.590 + 2067.69i) q^{73} +(4590.02 + 1670.63i) q^{74} -907.337i q^{75} +(-752.368 - 2788.28i) q^{76} -172.737 q^{77} +(329.021 - 903.977i) q^{78} +(-9223.86 + 1626.42i) q^{79} +(-1656.91 - 1390.32i) q^{80} +(4460.31 - 3742.65i) q^{81} +(-79.3497 + 450.015i) q^{82} +(-4594.59 + 7958.07i) q^{83} +(221.934 - 128.134i) q^{84} +(-13787.8 + 5018.35i) q^{85} +(-2984.93 - 8201.03i) q^{86} +(709.538 + 1228.96i) q^{87} +(185.387 + 107.033i) q^{88} +(9502.28 + 1675.51i) q^{89} +(4787.83 + 5705.92i) q^{90} +(2275.28 - 2711.57i) q^{91} +(-335.696 - 1903.83i) q^{92} +(-1234.35 - 449.266i) q^{93} -4771.89i q^{94} +(-12152.1 + 1084.68i) q^{95} -317.583 q^{96} +(-1743.06 + 4789.02i) q^{97} +(-5759.26 + 1015.51i) q^{98} +(-564.714 - 473.851i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q + 12 q^{3} + 48 q^{6} + 90 q^{7} - 84 q^{9}+O(q^{10}) \) 36 * q + 12 * q^3 + 48 * q^6 + 90 * q^7 - 84 * q^9	\( 36 q + 12 q^{3} + 48 q^{6} + 90 q^{7} - 84 q^{9} + 90 q^{11} - 432 q^{12} - 330 q^{13} + 576 q^{14} + 2658 q^{15} - 522 q^{17} - 1236 q^{19} - 864 q^{20} - 1998 q^{21} - 1344 q^{22} - 1440 q^{23} - 384 q^{24} - 3276 q^{25} + 576 q^{26} + 1692 q^{27} + 1056 q^{28} + 4050 q^{29} + 2808 q^{31} + 2910 q^{33} + 1536 q^{34} + 1422 q^{35} + 672 q^{36} + 1872 q^{38} - 9024 q^{39} - 3060 q^{41} - 3456 q^{42} - 1218 q^{43} - 5760 q^{44} - 2592 q^{45} - 2880 q^{46} + 990 q^{47} + 1536 q^{48} - 9696 q^{49} + 27648 q^{50} + 35784 q^{51} - 1488 q^{52} + 17082 q^{53} + 2160 q^{54} + 4290 q^{55} + 204 q^{57} - 5376 q^{58} - 11142 q^{59} - 11856 q^{60} - 35928 q^{61} - 7200 q^{62} - 58254 q^{63} + 9216 q^{64} - 34290 q^{65} - 32928 q^{66} + 44322 q^{67} - 4752 q^{68} + 21762 q^{69} + 12864 q^{70} + 40428 q^{71} + 10752 q^{72} + 6936 q^{73} - 4032 q^{74} - 576 q^{76} - 36648 q^{77} - 11040 q^{78} - 29298 q^{79} + 24324 q^{81} - 14592 q^{82} + 23958 q^{83} + 36720 q^{84} + 2772 q^{85} + 30816 q^{86} + 14256 q^{87} + 26064 q^{89} + 14784 q^{90} + 100044 q^{91} + 9360 q^{92} + 26400 q^{93} - 38646 q^{95} - 55746 q^{97} - 64512 q^{98} - 69846 q^{99}+O(q^{100}) \) 36 * q + 12 * q^3 + 48 * q^6 + 90 * q^7 - 84 * q^9 + 90 * q^11 - 432 * q^12 - 330 * q^13 + 576 * q^14 + 2658 * q^15 - 522 * q^17 - 1236 * q^19 - 864 * q^20 - 1998 * q^21 - 1344 * q^22 - 1440 * q^23 - 384 * q^24 - 3276 * q^25 + 576 * q^26 + 1692 * q^27 + 1056 * q^28 + 4050 * q^29 + 2808 * q^31 + 2910 * q^33 + 1536 * q^34 + 1422 * q^35 + 672 * q^36 + 1872 * q^38 - 9024 * q^39 - 3060 * q^41 - 3456 * q^42 - 1218 * q^43 - 5760 * q^44 - 2592 * q^45 - 2880 * q^46 + 990 * q^47 + 1536 * q^48 - 9696 * q^49 + 27648 * q^50 + 35784 * q^51 - 1488 * q^52 + 17082 * q^53 + 2160 * q^54 + 4290 * q^55 + 204 * q^57 - 5376 * q^58 - 11142 * q^59 - 11856 * q^60 - 35928 * q^61 - 7200 * q^62 - 58254 * q^63 + 9216 * q^64 - 34290 * q^65 - 32928 * q^66 + 44322 * q^67 - 4752 * q^68 + 21762 * q^69 + 12864 * q^70 + 40428 * q^71 + 10752 * q^72 + 6936 * q^73 - 4032 * q^74 - 576 * q^76 - 36648 * q^77 - 11040 * q^78 - 29298 * q^79 + 24324 * q^81 - 14592 * q^82 + 23958 * q^83 + 36720 * q^84 + 2772 * q^85 + 30816 * q^86 + 14256 * q^87 + 26064 * q^89 + 14784 * q^90 + 100044 * q^91 + 9360 * q^92 + 26400 * q^93 - 38646 * q^95 - 55746 * q^97 - 64512 * q^98 - 69846 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

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