LMFDB - Embedded newform 108.6.h.a.35.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [108,6,Mod(35,108)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(108, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 1]))

N = Newforms(chi, 6, names="a")

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

chi := DirichletCharacter("108.35");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 108 = 2^{2} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	108.h (of order $6$, degree $2$, not 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:	$17.3214525398$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$28$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 36)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			35.14
Character	$\chi$	$=$	108.35
Dual form			108.6.h.a.71.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.216257 + 5.65272i) q^{2} +(-31.9065 - 2.44488i) q^{4} +(0.143132 - 0.0826372i) q^{5} +(192.634 + 111.217i) q^{7} +(20.7202 - 179.830i) q^{8} +O(q^{10})$	\(q+(-0.216257 + 5.65272i) q^{2} +(-31.9065 - 2.44488i) q^{4} +(0.143132 - 0.0826372i) q^{5} +(192.634 + 111.217i) q^{7} +(20.7202 - 179.830i) q^{8} +(0.436172 + 0.826955i) q^{10} +(329.552 - 570.801i) q^{11} +(43.8997 + 76.0365i) q^{13} +(-670.338 + 1064.85i) q^{14} +(1012.05 + 156.015i) q^{16} +85.1645i q^{17} +2308.11i q^{19} +(-4.76887 + 2.28672i) q^{20} +(3155.31 + 1986.31i) q^{22} +(1327.18 + 2298.74i) q^{23} +(-1562.49 + 2706.31i) q^{25} +(-439.307 + 231.709i) q^{26} +(-5874.36 - 4019.52i) q^{28} +(-1337.58 - 772.253i) q^{29} +(1202.41 - 694.212i) q^{31} +(-1100.77 + 5687.07i) q^{32} +(-481.411 - 18.4174i) q^{34} +36.7627 q^{35} +4404.71 q^{37} +(-13047.1 - 499.144i) q^{38} +(-11.8949 - 27.4516i) q^{40} +(3145.98 - 1816.33i) q^{41} +(2424.30 + 1399.67i) q^{43} +(-11910.4 + 17406.5i) q^{44} +(-13281.1 + 7005.04i) q^{46} +(-4973.66 + 8614.64i) q^{47} +(16335.1 + 28293.2i) q^{49} +(-14960.1 - 9417.55i) q^{50} +(-1214.78 - 2533.39i) q^{52} -15134.7i q^{53} -108.933i q^{55} +(23991.6 - 32336.8i) q^{56} +(4654.59 - 7393.96i) q^{58} +(17228.5 + 29840.7i) q^{59} +(22173.9 - 38406.3i) q^{61} +(3664.16 + 6947.02i) q^{62} +(-31909.3 - 7452.21i) q^{64} +(12.5669 + 7.25550i) q^{65} +(-30386.6 + 17543.7i) q^{67} +(208.217 - 2717.30i) q^{68} +(-7.95019 + 207.809i) q^{70} +6002.26 q^{71} +32902.8 q^{73} +(-952.549 + 24898.6i) q^{74} +(5643.04 - 73643.6i) q^{76} +(126966. - 73303.8i) q^{77} +(23909.7 + 13804.3i) q^{79} +(157.749 - 61.3019i) q^{80} +(9586.86 + 18176.1i) q^{82} +(49118.1 - 85075.0i) q^{83} +(7.03776 + 12.1898i) q^{85} +(-8436.22 + 13401.2i) q^{86} +(-95818.6 - 71090.4i) q^{88} +19178.8i q^{89} +19529.6i q^{91} +(-36725.4 - 76589.3i) q^{92} +(-47620.5 - 29977.7i) q^{94} +(190.736 + 330.364i) q^{95} +(-9697.23 + 16796.1i) q^{97} +(-163466. + 86219.0i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q + 3 q^{2} - q^{4} + 6 q^{5}+O(q^{10}) $ 56 * q + 3 * q^2 - q^4 + 6 * q^5	$ 56 q + 3 q^{2} - q^{4} + 6 q^{5} - 68 q^{10} - 2 q^{13} + 1518 q^{14} - q^{16} + 1242 q^{20} + 63 q^{22} + 12498 q^{25} - 2052 q^{28} + 11946 q^{29} + 7233 q^{32} + 6361 q^{34} - 8 q^{37} + 14877 q^{38} - 1526 q^{40} + 43536 q^{41} - 26880 q^{46} + 38414 q^{49} - 38631 q^{50} + 24988 q^{52} - 21186 q^{56} - 3314 q^{58} - 2 q^{61} - 106342 q^{64} - 35970 q^{65} - 31413 q^{68} + 10524 q^{70} + 53620 q^{73} + 20406 q^{74} + 26193 q^{76} - 26178 q^{77} - 151286 q^{82} + 6248 q^{85} - 279237 q^{86} - 122541 q^{88} - 435804 q^{92} + 63480 q^{94} - 58148 q^{97}+O(q^{100}) $ 56 * q + 3 * q^2 - q^4 + 6 * q^5 - 68 * q^10 - 2 * q^13 + 1518 * q^14 - q^16 + 1242 * q^20 + 63 * q^22 + 12498 * q^25 - 2052 * q^28 + 11946 * q^29 + 7233 * q^32 + 6361 * q^34 - 8 * q^37 + 14877 * q^38 - 1526 * q^40 + 43536 * q^41 - 26880 * q^46 + 38414 * q^49 - 38631 * q^50 + 24988 * q^52 - 21186 * q^56 - 3314 * q^58 - 2 * q^61 - 106342 * q^64 - 35970 * q^65 - 31413 * q^68 + 10524 * q^70 + 53620 * q^73 + 20406 * q^74 + 26193 * q^76 - 26178 * q^77 - 151286 * q^82 + 6248 * q^85 - 279237 * q^86 - 122541 * q^88 - 435804 * q^92 + 63480 * q^94 - 58148 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/108\mathbb{Z}\right)^\times$.

$n$	$29$	$55$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.216257	+	5.65272i	−0.0382292	+	0.999269i
$2$	−0.216257	+	5.65272i	−0.0382292	+	0.999269i
$3$		0			0
$3$		0			0
$4$	−31.9065	−	2.44488i	−0.997077	−	0.0764024i
$5$	0.143132	−	0.0826372i	0.00256042	−	0.00147826i	−0.498719	−	0.866764i	$-0.666196\pi$
$5$	0.143132	−	0.0826372i	0.00256042	−	0.00147826i	0.501280	+	0.865285i	$0.332863\pi$
$6$		0			0
$7$	192.634	+	111.217i	1.48589	+	0.857881i	0.999871	−	0.0160647i	$-0.00511378\pi$
$7$	192.634	+	111.217i	1.48589	+	0.857881i	0.486023	+	0.873946i	$0.338447\pi$
$8$	20.7202	−	179.830i	0.114464	−	0.993427i
$9$		0			0
$10$	0.436172	+	0.826955i	0.00137930	+	0.00261506i
$11$	329.552	−	570.801i	0.821188	−	1.42234i	−0.0836100	−	0.996499i	$-0.526645\pi$
$11$	329.552	−	570.801i	0.821188	−	1.42234i	0.904798	−	0.425841i	$-0.140022\pi$
$12$		0			0
$13$	43.8997	+	76.0365i	0.0720449	+	0.124785i	0.899797	−	0.436308i	$-0.143714\pi$
$13$	43.8997	+	76.0365i	0.0720449	+	0.124785i	−0.827752	+	0.561093i	$0.810381\pi$
$14$	−670.338	+	1064.85i	−0.914059	+	1.45201i
$15$		0			0
$16$	1012.05	+	156.015i	0.988325	+	0.152358i
$17$			85.1645i			0.0714721i	0.999361	+	0.0357360i	$0.0113776\pi$
$17$			85.1645i			0.0714721i	−0.999361	+	0.0357360i	$0.988622\pi$
$18$		0			0
$19$			2308.11i			1.46680i	0.679795	+	0.733402i	$0.262069\pi$
$19$			2308.11i			1.46680i	−0.679795	+	0.733402i	$0.737931\pi$
$20$	−4.76887	+	2.28672i	−0.00266588	+	0.00127832i
$21$		0			0
$22$	3155.31	+	1986.31i	1.38991	+	0.874963i
$23$	1327.18	+	2298.74i	0.523129	+	0.906086i	0.999638	+	0.0269164i	$0.00856881\pi$
$23$	1327.18	+	2298.74i	0.523129	+	0.906086i	−0.476509	+	0.879170i	$0.658098\pi$
$24$		0			0
$25$	−1562.49	+	2706.31i	−0.499996	+	0.866018i
$26$	−439.307	+	231.709i	−0.127448	+	0.0672218i
$27$		0			0
$28$	−5874.36	−	4019.52i	−1.41601	−	0.968900i
$29$	−1337.58	−	772.253i	−0.295342	−	0.170516i	0.345007	−	0.938600i	$-0.387877\pi$
$29$	−1337.58	−	772.253i	−0.295342	−	0.170516i	−0.640348	+	0.768085i	$0.721210\pi$
$30$		0			0
$31$	1202.41	−	694.212i	0.224724	−	0.129744i	−0.383412	−	0.923577i	$-0.625251\pi$
$31$	1202.41	−	694.212i	0.224724	−	0.129744i	0.608136	+	0.793833i	$0.291918\pi$
$32$	−1100.77	+	5687.07i	−0.190030	+	0.981778i
$33$		0			0
$34$	−481.411	−	18.4174i	−0.0714198	−	0.00273232i
$35$	36.7627			0.00507268
$36$		0			0
$37$	4404.71			0.528948			0.264474	−	0.964393i	$-0.414802\pi$
$37$	4404.71			0.528948			0.264474	+	0.964393i	$0.414802\pi$
$38$	−13047.1	−	499.144i	−1.46573	−	0.0560747i
$39$		0			0
$40$	−11.8949	−	27.4516i	−0.00117547	−	0.00271280i
$41$	3145.98	−	1816.33i	0.292278	−	0.168747i	−0.346691	−	0.937979i	$-0.612695\pi$
$41$	3145.98	−	1816.33i	0.292278	−	0.168747i	0.638969	+	0.769233i	$0.279361\pi$
$42$		0			0
$43$	2424.30	+	1399.67i	0.199947	+	0.115440i	0.596631	−	0.802516i	$-0.296506\pi$
$43$	2424.30	+	1399.67i	0.199947	+	0.115440i	−0.396684	+	0.917955i	$0.629839\pi$
$44$	−11910.4	+	17406.5i	−0.927458	+	1.35544i
$45$		0			0
$46$	−13281.1	+	7005.04i	−0.925423	+	0.488108i
$47$	−4973.66	+	8614.64i	−0.328422	+	0.568843i	−0.982199	−	0.187844i	$-0.939850\pi$
$47$	−4973.66	+	8614.64i	−0.328422	+	0.568843i	0.653777	+	0.756687i	$0.273183\pi$
$48$		0			0
$49$	16335.1	+	28293.2i	0.971921	+	1.68342i
$50$	−14960.1	−	9417.55i	−0.846270	−	0.532737i
$51$		0			0
$52$	−1214.78	−	2533.39i	−0.0623004	−	0.129925i
$53$		−	15134.7i		−	0.740087i	−0.929014	−	0.370044i	$-0.879343\pi$
$53$		−	15134.7i		−	0.740087i	0.929014	−	0.370044i	$-0.120657\pi$
$54$		0			0
$55$		−	108.933i		−	0.00485572i
$56$	23991.6	−	32336.8i	1.02232	−	1.37793i
$57$		0			0
$58$	4654.59	−	7393.96i	0.181682	−	0.288607i
$59$	17228.5	+	29840.7i	0.644344	+	1.11604i	0.984453	+	0.175651i	$0.0562029\pi$
$59$	17228.5	+	29840.7i	0.644344	+	1.11604i	−0.340108	+	0.940386i	$0.610464\pi$
$60$		0			0
$61$	22173.9	−	38406.3i	0.762986	−	1.32153i	−0.178318	−	0.983973i	$-0.557066\pi$
$61$	22173.9	−	38406.3i	0.762986	−	1.32153i	0.941305	−	0.337558i	$-0.109601\pi$
$62$	3664.16	+	6947.02i	0.121058	+	0.229519i
$63$		0			0
$64$	−31909.3	−	7452.21i	−0.973796	−	0.227423i
$65$	12.5669	+	7.25550i	0.000368930	+	0.000213002i
$66$		0			0
$67$	−30386.6	+	17543.7i	−0.826980	+	0.477457i	−0.852817	−	0.522209i	$-0.825108\pi$
$67$	−30386.6	+	17543.7i	−0.826980	+	0.477457i	0.0258378	+	0.999666i	$0.491775\pi$
$68$	208.217	−	2717.30i	0.00546064	−	0.0712632i
$69$		0			0
$70$	−7.95019	+	207.809i	−0.000193924	+	0.00506898i
$71$	6002.26			0.141309			0.0706544	−	0.997501i	$-0.477491\pi$
$71$	6002.26			0.141309			0.0706544	+	0.997501i	$0.477491\pi$
$72$		0			0
$73$	32902.8			0.722647			0.361324	−	0.932441i	$-0.382325\pi$
$73$	32902.8			0.722647			0.361324	+	0.932441i	$0.382325\pi$
$74$	−952.549	+	24898.6i	−0.0202213	+	0.528562i
$75$		0			0
$76$	5643.04	−	73643.6i	0.112067	−	1.46252i
$77$	126966.	−	73303.8i	2.44040	−	1.40896i
$78$		0			0
$79$	23909.7	+	13804.3i	0.431029	+	0.248855i	0.699785	−	0.714354i	$-0.253279\pi$
$79$	23909.7	+	13804.3i	0.431029	+	0.248855i	−0.268756	+	0.963208i	$0.586613\pi$
$80$	157.749	−	61.3019i	0.00275575	−	0.00107090i
$81$		0			0
$82$	9586.86	+	18176.1i	0.157450	+	0.298515i
$83$	49118.1	−	85075.0i	0.782611	−	1.35552i	−0.147804	−	0.989017i	$-0.547221\pi$
$83$	49118.1	−	85075.0i	0.782611	−	1.35552i	0.930416	−	0.366506i	$-0.119446\pi$
$84$		0			0
$85$	7.03776	+	12.1898i	0.000105654	+	0.000182999i
$86$	−8436.22	+	13401.2i	−0.122999	+	0.195388i
$87$		0			0
$88$	−95818.6	−	71090.4i	−1.31899	−	0.978597i
$89$			19178.8i			0.256653i	0.991732	+	0.128326i	$0.0409605\pi$
$89$			19178.8i			0.256653i	−0.991732	+	0.128326i	$0.959040\pi$
$90$		0			0
$91$			19529.6i			0.247224i
$92$	−36725.4	−	76589.3i	−0.452373	−	0.943406i
$93$		0			0
$94$	−47620.5	−	29977.7i	−0.555872	−	0.349928i
$95$	190.736	+	330.364i	0.00216832	+	0.00375563i
$96$		0			0
$97$	−9697.23	+	16796.1i	−0.104645	+	0.181250i	−0.913593	−	0.406630i	$-0.866704\pi$
$97$	−9697.23	+	16796.1i	−0.104645	+	0.181250i	0.808948	+	0.587880i	$0.200037\pi$
$98$	−163466.	+	86219.0i	−1.71934	+	0.906855i
$99$		0			0
$100$	56470.0	−	82528.6i	0.564700	−	0.825286i
$101$	18242.5	+	10532.3i	0.177943	+	0.102735i	0.586326	−	0.810075i	$-0.300574\pi$
$101$	18242.5	+	10532.3i	0.177943	+	0.102735i	−0.408383	+	0.912811i	$0.633907\pi$
$102$		0			0
$103$	−109139.	+	63011.2i	−1.01364	+	0.585228i	−0.912257	−	0.409619i	$-0.865662\pi$
$103$	−109139.	+	63011.2i	−1.01364	+	0.585228i	−0.101388	+	0.994847i	$0.532328\pi$
$104$	14583.2	−	6318.97i	0.132212	−	0.0572879i
$105$		0			0
$106$	85552.0	+	3272.97i	0.739546	+	0.0282929i
$107$	−147922.			−1.24903			−0.624516	−	0.781012i	$-0.714704\pi$
$107$	−147922.			−1.24903			−0.624516	+	0.781012i	$0.714704\pi$
$108$		0			0
$109$	121171.			0.976857			0.488429	−	0.872604i	$-0.337570\pi$
$109$	121171.			0.976857			0.488429	+	0.872604i	$0.337570\pi$
$110$	615.768	+	23.5575i	0.00485217	+	0.000185630i
$111$		0			0
$112$	177603.	+	142611.i	1.33784	+	1.07425i
$113$	−102842.	+	59376.0i	−0.757662	+	0.437436i	−0.828456	−	0.560055i	$-0.810780\pi$
$113$	−102842.	+	59376.0i	−0.757662	+	0.437436i	0.0707938	+	0.997491i	$0.477447\pi$
$114$		0			0
$115$	379.922	+	219.348i	0.00267886	+	0.00154664i
$116$	40789.4	+	27910.1i	0.281451	+	0.192582i
$117$		0			0
$118$	−172407.	+	90934.7i	−1.13985	+	0.601208i
$119$	−9471.77	+	16405.6i	−0.0613146	+	0.106200i
$120$		0			0
$121$	−136684.	−	236744.i	−0.848700	−	1.46999i
$122$	212305.	+	133648.i	1.29140	+	0.812950i
$123$		0			0
$124$	−40061.9	+	19210.1i	−0.233979	+	0.112196i
$125$			1032.96i			0.00591301i
$126$		0			0
$127$		−	215170.i		−	1.18378i	−0.806018	−	0.591891i	$-0.798381\pi$
$127$		−	215170.i		−	1.18378i	0.806018	−	0.591891i	$-0.201619\pi$
$128$	49025.9	−	178763.i	0.264485	−	0.964390i
$129$		0			0
$130$	−43.7310	+	69.4680i	−0.000226950	+	0.000360518i
$131$	123220.	+	213424.i	0.627341	+	1.08659i	0.988083	+	0.153921i	$0.0491900\pi$
$131$	123220.	+	213424.i	0.627341	+	1.08659i	−0.360742	+	0.932666i	$0.617477\pi$
$132$		0			0
$133$	−256701.	+	444620.i	−1.25834	+	2.17951i
$134$	−92598.3	−	175561.i	−0.445493	−	0.844628i
$135$		0			0
$136$	15315.1	+	1764.63i	0.0710023	+	0.00818098i
$137$	−182252.	−	105223.i	−0.829606	−	0.478973i	0.0241120	−	0.999709i	$-0.492324\pi$
$137$	−182252.	−	105223.i	−0.829606	−	0.478973i	−0.853718	+	0.520736i	$0.825658\pi$
$138$		0			0
$139$	246037.	−	142050.i	1.08010	−	0.623596i	0.149177	−	0.988811i	$-0.452338\pi$
$139$	246037.	−	142050.i	1.08010	−	0.623596i	0.930923	+	0.365214i	$0.119004\pi$
$140$	−1172.97	−	89.8804i	−0.00505786	−	0.000387565i
$141$		0			0
$142$	−1298.03	+	33929.1i	−0.00540212	+	0.141205i
$143$	57869.0			0.236650
$144$		0			0
$145$	−255.267			−0.00100827
$146$	−7115.46	+	185991.i	−0.0276262	+	0.722119i
$147$		0			0
$148$	−140539.	−	10769.0i	−0.527402	−	0.0404129i
$149$	−256622.	+	148161.i	−0.946953	+	0.546723i	−0.892133	−	0.451773i	$-0.850792\pi$
$149$	−256622.	+	148161.i	−0.946953	+	0.546723i	−0.0548196	+	0.998496i	$0.517458\pi$
$150$		0			0
$151$	381289.	+	220137.i	1.36086	+	0.785690i	0.989738	−	0.142896i	$-0.0456414\pi$
$151$	381289.	+	220137.i	1.36086	+	0.785690i	0.371118	+	0.928586i	$0.378975\pi$
$152$	415066.	+	47824.4i	1.45716	+	0.167896i
$153$		0			0
$154$	386909.	+	733555.i	1.31464	+	2.49248i
$155$	114.735	−	198.728i	0.000383591	−	0.000664399i
$156$		0			0
$157$	20432.3	+	35389.8i	0.0661558	+	0.114585i	0.897206	−	0.441612i	$-0.145593\pi$
$157$	20432.3	+	35389.8i	0.0661558	+	0.114585i	−0.831050	+	0.556197i	$0.812260\pi$
$158$	−83202.3	+	132170.i	−0.265151	+	0.421200i
$159$		0			0
$160$	312.408	+	904.965i	0.000964767	+	0.00279468i
$161$			590420.i			1.79513i
$162$		0			0
$163$		−	326446.i		−	0.962369i	−0.876619	−	0.481185i	$-0.840207\pi$
$163$		−	326446.i		−	0.962369i	0.876619	−	0.481185i	$-0.159793\pi$
$164$	−104818.	+	50261.1i	−0.304316	+	0.145923i
$165$		0			0
$166$	470283.	+	296049.i	1.32461	+	0.833860i
$167$	−232137.	−	402072.i	−0.644099	−	1.11561i	−0.984509	−	0.175335i	$-0.943899\pi$
$167$	−232137.	−	402072.i	−0.644099	−	1.11561i	0.340410	−	0.940277i	$-0.389434\pi$
$168$		0			0
$169$	181792.	−	314873.i	0.489619	−	0.848045i
$170$	−70.4272	+	37.1464i	−0.000186904	+	9.85812e-5i
$171$		0			0
$172$	−73928.9	−	50585.7i	−0.190543	−	0.130379i
$173$	−356838.	−	206020.i	−0.906474	−	0.523353i	−0.0271793	−	0.999631i	$-0.508653\pi$
$173$	−356838.	−	206020.i	−0.906474	−	0.523353i	−0.879295	+	0.476277i	$0.841986\pi$
$174$		0			0
$175$	−601976.	+	347551.i	−1.48588	+	0.857874i
$176$	422575.	−	526262.i	1.02831	−	1.28062i
$177$		0			0
$178$	−108412.	−	4147.54i	−0.256465	−	0.00981162i
$179$	−91420.4			−0.213261			−0.106630	−	0.994299i	$-0.534006\pi$
$179$	−91420.4			−0.213261			−0.106630	+	0.994299i	$0.534006\pi$
$180$		0			0
$181$	−705467.			−1.60059			−0.800295	−	0.599606i	$-0.795324\pi$
$181$	−705467.			−1.60059			−0.800295	+	0.599606i	$0.795324\pi$
$182$	−110395.	−	4223.41i	−0.247043	−	0.00945116i
$183$		0			0
$184$	440880.	−	191035.i	0.960010	−	0.415977i
$185$	630.455	−	363.993i	0.00135433	−	0.000781923i
$186$		0			0
$187$	48612.0	+	28066.2i	0.101658	+	0.0586920i
$188$	179754.	−	262703.i	0.370923	−	0.542088i
$189$		0			0
$190$	−1908.70	+	1006.73i	−0.00383578	+	0.00202316i
$191$	−65114.9	+	112782.i	−0.129151	+	0.223696i	−0.923348	−	0.383965i	$-0.874558\pi$
$191$	−65114.9	+	112782.i	−0.129151	+	0.223696i	0.794197	+	0.607660i	$0.207892\pi$
$192$		0			0
$193$	−229197.	−	396982.i	−0.442911	−	0.767144i	0.554993	−	0.831855i	$-0.312721\pi$
$193$	−229197.	−	396982.i	−0.442911	−	0.767144i	−0.997904	+	0.0647106i	$0.979388\pi$
$194$	−92846.6	−	58448.0i	−0.177117	−	0.111498i
$195$		0			0
$196$	−452021.	−	942672.i	−0.840463	−	1.75275i
$197$		−	484753.i		−	0.889928i	−0.895549	−	0.444964i	$-0.853217\pi$
$197$		−	484753.i		−	0.889928i	0.895549	−	0.444964i	$-0.146783\pi$
$198$		0			0
$199$		−	616397.i		−	1.10339i	−0.834047	−	0.551694i	$-0.813982\pi$
$199$		−	616397.i		−	1.10339i	0.834047	−	0.551694i	$-0.186018\pi$
$200$	454299.	+	337056.i	0.803094	+	0.595837i
$201$		0			0
$202$	−63481.2	+	100842.i	−0.109463	+	0.173885i
$203$	−171776.	−	297524.i	−0.292565	−	0.506737i
$204$		0			0
$205$	300.193	−	519.949i	0.000498903	−	0.000864125i
$206$	−332583.	−	630557.i	−0.546049	−	1.03528i
$207$		0			0
$208$	32565.7	+	83801.4i	0.0521917	+	0.134305i
$209$	1.31747e6	+	760642.i	2.08629	+	1.20452i
$210$		0			0
$211$	−388325.	+	224199.i	−0.600466	+	0.346679i	−0.769225	−	0.638978i	$-0.779357\pi$
$211$	−388325.	+	224199.i	−0.600466	+	0.346679i	0.168759	+	0.985657i	$0.446024\pi$
$212$	−37002.4	+	482893.i	−0.0565445	+	0.737924i
$213$		0			0
$214$	31989.1	−	836162.i	0.0477494	−	1.24812i
$215$	462.660			0.000682599
$216$		0			0
$217$	308834.			0.445220
$218$	−26204.0	+	684944.i	−0.0373444	+	0.976143i
$219$		0			0
$220$	−266.328	+	3475.67i	−0.000370988	+	0.00484152i
$221$	−6475.61	+	3738.70i	−0.00891867	+	0.00514920i
$222$		0			0
$223$	48031.9	+	27731.2i	0.0646796	+	0.0373428i	0.531991	−	0.846750i	$-0.321444\pi$
$223$	48031.9	+	27731.2i	0.0646796	+	0.0373428i	−0.467311	+	0.884093i	$0.654777\pi$
$224$	−844546.	+	973098.i	−1.12461	+	1.29580i
$225$		0			0
$226$	−313395.	−	594179.i	−0.408152	−	0.773831i
$227$	309416.	−	535925.i	0.398546	−	0.690302i	−0.595001	−	0.803725i	$-0.702848\pi$
$227$	309416.	−	535925.i	0.398546	−	0.690302i	0.993547	+	0.113423i	$0.0361815\pi$
$228$		0			0
$229$	78993.5	+	136821.i	0.0995412	+	0.172410i	0.911495	−	0.411312i	$-0.134929\pi$
$229$	78993.5	+	136821.i	0.0995412	+	0.172410i	−0.811954	+	0.583722i	$0.801596\pi$
$230$	−1322.07	+	2100.16i	−0.00164792	+	0.00261778i
$231$		0			0
$232$	−166589.	+	224535.i	−0.203201	+	0.273883i
$233$		−	824409.i		−	0.994840i	−0.867510	−	0.497420i	$-0.834281\pi$
$233$		−	824409.i		−	0.994840i	0.867510	−	0.497420i	$-0.165719\pi$
$234$		0			0
$235$			1644.04i			0.00194197i
$236$	−476744.	−	994232.i	−0.557193	−	1.16200i
$237$		0			0
$238$	−90687.8	−	57089.1i	−0.103778	−	0.0653297i
$239$	−227607.	−	394226.i	−0.257745	−	0.446427i	0.707893	−	0.706320i	$-0.249646\pi$
$239$	−227607.	−	394226.i	−0.257745	−	0.446427i	−0.965637	+	0.259893i	$0.916313\pi$
$240$		0			0
$241$	134036.	−	232158.i	0.148655	−	0.257478i	−0.782075	−	0.623184i	$-0.785839\pi$
$241$	134036.	−	232158.i	0.148655	−	0.257478i	0.930731	+	0.365705i	$0.119172\pi$
$242$	1.36780e6	−	721438.i	1.50136	−	0.791883i
$243$		0			0
$244$	−801388.	+	1.17120e6i	−0.861724	+	1.25937i
$245$	4676.14	+	2699.77i	0.00497705	+	0.00287350i
$246$		0			0
$247$	−175500.	+	101325.i	−0.183036	+	0.105676i
$248$	−99925.7	−	230613.i	−0.103169	−	0.238098i
$249$		0			0
$250$	−5839.04	−	223.385i	−0.00590869	−	0.000226049i
$251$	1.05745e6			1.05944			0.529719	−	0.848173i	$-0.322298\pi$
$251$	1.05745e6			1.05944			0.529719	+	0.848173i	$0.322298\pi$
$252$		0			0
$253$	1.74950e6			1.71835
$254$	1.21629e6	+	46531.9i	1.18292	+	0.0452550i
$255$		0			0
$256$	999895.	+	315788.i	0.953574	+	0.301159i
$257$	−18796.2	+	10852.0i	−0.0177516	+	0.0102489i	−0.508850	−	0.860855i	$-0.669929\pi$
$257$	−18796.2	+	10852.0i	−0.0177516	+	0.0102489i	0.491098	+	0.871104i	$0.336596\pi$
$258$		0			0
$259$	848497.	+	489880.i	0.785961	+	0.453775i
$260$	−383.226	−	262.222i	−0.000351578	−	0.000240567i
$261$		0			0
$262$	−1.23307e6	+	650375.i	−1.10977	+	0.585343i
$263$	−1.03830e6	+	1.79839e6i	−0.925622	+	1.60322i	−0.135063	+	0.990837i	$0.543124\pi$
$263$	−1.03830e6	+	1.79839e6i	−0.925622	+	1.60322i	−0.790558	+	0.612387i	$0.790210\pi$
$264$		0			0
$265$	−1250.69	−	2166.25i	−0.00109404	−	0.00189493i
$266$	−2.45780e6	−	1.54721e6i	−2.12982	−	1.34074i
$267$		0			0
$268$	1.01242e6	−	485466.i	0.861041	−	0.412878i
$269$		−	175156.i		−	0.147585i	−0.997274	−	0.0737927i	$-0.976490\pi$
$269$		−	175156.i		−	0.147585i	0.997274	−	0.0737927i	$-0.0235103\pi$
$270$		0			0
$271$			926017.i			0.765942i	0.923760	+	0.382971i	$0.125099\pi$
$271$			926017.i			0.765942i	−0.923760	+	0.382971i	$0.874901\pi$
$272$	−13286.9	+	86190.3i	−0.0108894	+	0.0706377i
$273$		0			0
$274$	634212.	−	1.00747e6i	0.510338	−	0.810688i
$275$	1.02984e6	+	1.78374e6i	0.821181	+	1.42233i
$276$		0			0
$277$	−561144.	+	971930.i	−0.439415	+	0.761089i	−0.997644	−	0.0685974i	$-0.978148\pi$
$277$	−561144.	+	971930.i	−0.439415	+	0.761089i	0.558229	+	0.829687i	$0.311481\pi$
$278$	749760.	+	1.42150e6i	0.581849	+	1.10315i
$279$		0			0
$280$	761.731	−	6611.03i	0.000580640	−	0.00503934i
$281$	−1.74330e6	−	1.00650e6i	−1.31707	−	0.760408i	−0.333810	−	0.942641i	$-0.608334\pi$
$281$	−1.74330e6	−	1.00650e6i	−1.31707	−	0.760408i	−0.983255	+	0.182233i	$0.941668\pi$
$282$		0			0
$283$	−28134.7	+	16243.6i	−0.0208822	+	0.0120563i	−0.510405	−	0.859934i	$-0.670504\pi$
$283$	−28134.7	+	16243.6i	−0.0208822	+	0.0120563i	0.489523	+	0.871991i	$0.337171\pi$
$284$	−191511.	−	14674.8i	−0.140896	−	0.0107963i
$285$		0			0
$286$	−12514.6	+	327117.i	−0.00904692	+	0.236477i
$287$	808029.			0.579058
$288$		0			0
$289$	1.41260e6			0.994892
$290$	55.2033	−	1442.95i	3.85452e−5	−	0.00100753i
$291$		0			0
$292$	−1.04981e6	−	80443.4i	−0.720535	−	0.0552120i
$293$	1.69871e6	−	980754.i	1.15598	−	0.667407i	0.205645	−	0.978627i	$-0.434071\pi$
$293$	1.69871e6	−	980754.i	1.15598	−	0.667407i	0.950338	+	0.311220i	$0.100737\pi$
$294$		0			0
$295$	4931.90	+	2847.43i	0.00329958	+	0.00190502i
$296$	91266.5	−	792098.i	0.0605455	−	0.525472i
$297$		0			0
$298$	−782015.	−	1.48265e6i	−0.510122	−	0.967161i
$299$	−116525.	+	201828.i	−0.0753776	+	0.130558i
$300$		0			0
$301$	311335.	+	539249.i	0.198067	+	0.343062i
$302$	−1.32683e6	+	2.10771e6i	−0.837140	+	1.32982i
$303$		0			0
$304$	−360099.	+	2.33591e6i	−0.223480	+	1.44968i
$305$		−	7329.54i		−	0.00451157i
$306$		0			0
$307$		−	2.30255e6i		−	1.39432i	−0.716915	−	0.697160i	$-0.754447\pi$
$307$		−	2.30255e6i		−	1.39432i	0.716915	−	0.697160i	$-0.245553\pi$
$308$	−4.23025e6	+	2.02845e6i	−2.54091	+	1.21839i
$309$		0			0
$310$	1098.54	+	691.544i	0.000649249	+	0.000408710i
$311$	−900581.	−	1.55985e6i	−0.527985	−	0.914498i	−0.999468	−	0.0326220i	$-0.989614\pi$
$311$	−900581.	−	1.55985e6i	−0.527985	−	0.914498i	0.471482	−	0.881875i	$-0.343719\pi$
$312$		0			0
$313$	−1.06851e6	+	1.85072e6i	−0.616480	+	1.06777i	0.373643	+	0.927573i	$0.378109\pi$
$313$	−1.06851e6	+	1.85072e6i	−0.616480	+	1.06777i	−0.990123	+	0.140202i	$0.955225\pi$
$314$	−204467.	+	107845.i	−0.117030	+	0.0617269i
$315$		0			0
$316$	−729124.	−	498902.i	−0.410756	−	0.281059i
$317$	2.21433e6	+	1.27844e6i	1.23764	+	0.714551i	0.968611	−	0.248582i	$-0.0799645\pi$
$317$	2.21433e6	+	1.27844e6i	1.23764	+	0.714551i	0.269027	+	0.963133i	$0.413298\pi$
$318$		0			0
$319$	−881606.	+	508995.i	−0.485063	+	0.280051i
$320$	−5183.07	+	1570.25i	−0.00282952	+	0.000857224i
$321$		0			0
$322$	−3.33748e6	−	127682.i	−1.79382	−	0.0686263i
$323$	−196569.			−0.104836
$324$		0			0
$325$	−274371.			−0.144089
$326$	1.84530e6	+	70596.1i	0.961666	+	0.0367906i
$327$		0			0
$328$	−261445.	−	603374.i	−0.134182	−	0.309672i
$329$	−1.91619e6	+	1.10631e6i	−0.975999	+	0.563493i
$330$		0			0
$331$	1.38965e6	+	802314.i	0.697164	+	0.402508i	0.806290	−	0.591520i	$-0.201472\pi$
$331$	1.38965e6	+	802314.i	0.697164	+	0.402508i	−0.109126	+	0.994028i	$0.534805\pi$
$332$	−1.77518e6	+	2.59436e6i	−0.883889	+	1.29177i
$333$		0			0
$334$	2.32300e6	−	1.22525e6i	1.13942	−	0.600979i
$335$	−2899.52	+	5022.12i	−0.00141161	+	0.00244498i
$336$		0			0
$337$	840067.	+	1.45504e6i	0.402939	+	0.697911i	0.994079	−	0.108658i	$-0.0346554\pi$
$337$	840067.	+	1.45504e6i	0.402939	+	0.697911i	−0.591140	+	0.806569i	$0.701322\pi$
$338$	1.74058e6	+	1.09571e6i	0.828707	+	0.521681i
$339$		0			0
$340$	−194.748	−	406.138i	−9.13639e−5	−	0.000190536i
$341$		−	915117.i		−	0.426177i
$342$		0			0
$343$			3.52851e6i			1.61941i
$344$	301934.	−	406960.i	0.137568	−	0.185420i
$345$		0			0
$346$	1.24174e6	−	1.97255e6i	0.557624	−	0.885804i
$347$	752957.	+	1.30416e6i	0.335696	+	0.581443i	0.983618	−	0.180264i	$-0.0576951\pi$
$347$	752957.	+	1.30416e6i	0.335696	+	0.581443i	−0.647922	+	0.761707i	$0.724362\pi$
$348$		0			0
$349$	1.76659e6	−	3.05983e6i	0.776377	−	1.34473i	−0.157640	−	0.987497i	$-0.550388\pi$
$349$	1.76659e6	−	3.05983e6i	0.776377	−	1.34473i	0.934017	−	0.357228i	$-0.116278\pi$
$350$	−1.83443e6	−	3.47796e6i	−0.800443	−	1.51759i
$351$		0			0
$352$	2.88342e6	+	2.50251e6i	1.24037	+	1.07651i
$353$	83593.0	+	48262.4i	0.0357053	+	0.0206145i	0.517746	−	0.855534i	$-0.326771\pi$
$353$	83593.0	+	48262.4i	0.0357053	+	0.0206145i	−0.482041	+	0.876149i	$0.660104\pi$
$354$		0			0
$355$	859.115	−	496.010i	0.000361810	−	0.000208891i
$356$	46889.7	−	611927.i	0.0196089	−	0.255902i
$357$		0			0
$358$	19770.3	−	516774.i	0.00815278	−	0.213105i
$359$	−1.43721e6			−0.588552			−0.294276	−	0.955720i	$-0.595078\pi$
$359$	−1.43721e6			−0.588552			−0.294276	+	0.955720i	$0.595078\pi$
$360$		0			0
$361$	−2.85126e6			−1.15151
$362$	152562.	−	3.98781e6i	0.0611892	−	1.59942i
$363$		0			0
$364$	47747.5	−	623121.i	0.0188885	−	0.246501i
$365$	4709.44	−	2719.00i	0.00185028	−	0.00106826i
$366$		0			0
$367$	−2.46407e6	−	1.42263e6i	−0.954968	−	0.551351i	−0.0603472	−	0.998177i	$-0.519221\pi$
$367$	−2.46407e6	−	1.42263e6i	−0.954968	−	0.551351i	−0.894621	+	0.446827i	$0.852554\pi$
$368$	984525.	+	2.53348e6i	0.378972	+	0.975211i
$369$		0			0
$370$	1921.21	+	3642.50i	0.000729576	+	0.00138323i
$371$	1.68324e6	−	2.91545e6i	0.634907	−	1.09969i
$372$		0			0
$373$	−1.92380e6	−	3.33212e6i	−0.715959	−	1.24008i	−0.962589	−	0.270967i	$-0.912657\pi$
$373$	−1.92380e6	−	3.33212e6i	−0.715959	−	1.24008i	0.246630	−	0.969110i	$-0.420677\pi$
$374$	−169163.	+	268721.i	−0.0625354	+	0.0993395i
$375$		0			0
$376$	1.44611e6	+	1.07291e6i	0.527512	+	0.391375i
$377$		−	135607.i		−	0.0491391i
$378$		0			0
$379$		−	1.26215e6i		−	0.451351i	−0.974202	−	0.225676i	$-0.927541\pi$
$379$		−	1.26215e6i		−	0.451351i	0.974202	−	0.225676i	$-0.0724589\pi$
$380$	−5278.00	−	11007.1i	−0.00187504	−	0.00391032i
$381$		0			0
$382$	−623445.	−	392466.i	−0.218595	−	0.137608i
$383$	−819424.	−	1.41928e6i	−0.285438	−	0.494393i	0.687277	−	0.726395i	$-0.258806\pi$
$383$	−819424.	−	1.41928e6i	−0.285438	−	0.494393i	−0.972715	+	0.232002i	$0.925472\pi$
$384$		0			0
$385$	12115.2	−	20984.2i	0.00416563	−	0.00721508i
$386$	2.29359e6	−	1.20974e6i	0.783516	−	0.413260i
$387$		0			0
$388$	350469.	−	512196.i	0.118187	−	0.172726i
$389$	−2.12915e6	−	1.22927e6i	−0.713400	−	0.411881i	0.0989190	−	0.995095i	$-0.468462\pi$
$389$	−2.12915e6	−	1.22927e6i	−0.713400	−	0.411881i	−0.812318	+	0.583214i	$0.801795\pi$
$390$		0			0
$391$	−195771.	+	113028.i	−0.0647599	+	0.0373891i
$392$	5.42641e6	−	2.35129e6i	1.78360	−	0.772842i
$393$		0			0
$394$	2.74017e6	+	104831.i	0.889277	+	0.0340212i
$395$	4562.99			0.00147149
$396$		0			0
$397$	176766.			0.0562890			0.0281445	−	0.999604i	$-0.491040\pi$
$397$	176766.			0.0562890			0.0281445	+	0.999604i	$0.491040\pi$
$398$	3.48432e6	+	133300.i	1.10258	+	0.0421816i
$399$		0			0
$400$	−2.00353e6	+	2.49513e6i	−0.626103	+	0.779729i
$401$	3.74356e6	−	2.16134e6i	1.16258	−	0.671217i	0.210661	−	0.977559i	$-0.432438\pi$
$401$	3.74356e6	−	2.16134e6i	1.16258	−	0.671217i	0.951921	+	0.306342i	$0.0991051\pi$
$402$		0			0
$403$	105571.	+	60951.4i	0.0323804	+	0.0186948i
$404$	−556303.	−	380649.i	−0.169573	−	0.116030i
$405$		0			0
$406$	1.71897e6	−	906658.i	0.517551	−	0.272979i
$407$	1.45158e6	−	2.51422e6i	0.434366	−	0.752344i
$408$		0			0
$409$	205225.	+	355461.i	0.0606629	+	0.105071i	0.894762	−	0.446544i	$-0.147345\pi$
$409$	205225.	+	355461.i	0.0606629	+	0.105071i	−0.834099	+	0.551615i	$0.814012\pi$
$410$	2874.21	+	1809.35i	0.000844420	+	0.000531573i
$411$		0			0
$412$	3.63628e6	−	1.74364e6i	1.05539	−	0.506072i
$413$			7.66444e6i			2.21108i
$414$		0			0
$415$		−	16235.9i		−	0.00462761i
$416$	−480748.	+	165962.i	−0.136202	+	0.0470192i
$417$		0			0
$418$	−4.58461e6	+	7.28280e6i	−1.28340	+	2.03872i
$419$	1.14156e6	+	1.97723e6i	0.317660	+	0.550203i	0.979999	−	0.199001i	$-0.0637697\pi$
$419$	1.14156e6	+	1.97723e6i	0.317660	+	0.550203i	−0.662340	+	0.749204i	$0.730436\pi$
$420$		0			0
$421$	586612.	−	1.01604e6i	0.161304	−	0.279387i	−0.774032	−	0.633146i	$-0.781763\pi$
$421$	586612.	−	1.01604e6i	0.161304	−	0.279387i	0.935337	+	0.353759i	$0.115097\pi$
$422$	−1.18336e6	−	2.24357e6i	−0.323471	−	0.613281i
$423$		0			0
$424$	−2.72166e6	−	313593.i	−0.735223	−	0.0847133i
$425$	−230481.	−	133068.i	−0.0618961	−	0.0357357i
$426$		0			0
$427$	8.54288e6	−	4.93223e6i	2.26743	−	1.30910i
$428$	4.71967e6	+	361651.i	1.24538	+	0.0954291i
$429$		0			0
$430$	−100.053	+	2615.29i	−2.60952e−5	+	0.000682100i
$431$	−6.84835e6			−1.77579			−0.887897	−	0.460042i	$-0.847834\pi$
$431$	−6.84835e6			−1.77579			−0.887897	+	0.460042i	$0.847834\pi$
$432$		0			0
$433$	−1.99773e6			−0.512054			−0.256027	−	0.966670i	$-0.582414\pi$
$433$	−1.99773e6			−0.512054			−0.256027	+	0.966670i	$0.582414\pi$
$434$	−66787.3	+	1.74575e6i	−0.0170204	+	0.444895i
$435$		0			0
$436$	−3.86613e6	−	296247.i	−0.974002	−	0.0746343i
$437$	−5.30573e6	+	3.06326e6i	−1.32905	+	0.767328i
$438$		0			0
$439$	−4.92061e6	−	2.84091e6i	−1.21859	−	0.703553i	−0.253973	−	0.967211i	$-0.581737\pi$
$439$	−4.92061e6	−	2.84091e6i	−1.21859	−	0.703553i	−0.964616	+	0.263659i	$0.915071\pi$
$440$	−19589.4	−	2257.12i	−0.00482380	−	0.000555805i
$441$		0			0
$442$	−19733.4	−	37413.3i	−0.00480448	−	0.00910900i
$443$	−1.18053e6	+	2.04473e6i	−0.285803	+	0.495025i	−0.972804	−	0.231632i	$-0.925594\pi$
$443$	−1.18053e6	+	2.04473e6i	−0.285803	+	0.495025i	0.687001	+	0.726657i	$0.258927\pi$
$444$		0			0
$445$	1584.88	+	2745.09i	0.000379399	+	0.000657139i
$446$	−167144.	+	265514.i	−0.0397881	+	0.0632047i
$447$		0			0
$448$	−5.31801e6	−	4.98442e6i	−1.25186	−	1.17333i
$449$		−	1.40173e6i		−	0.328132i	−0.986449	−	0.164066i	$-0.947539\pi$
$449$		−	1.40173e6i		−	0.328132i	0.986449	−	0.164066i	$-0.0524610\pi$
$450$		0			0
$451$		−	2.39430e6i		−	0.554291i
$452$	3.42650e6	−	1.64304e6i	0.788868	−	0.378270i
$453$		0			0
$454$	2.96252e6	+	1.86494e6i	0.674562	+	0.424645i
$455$	1613.87	+	2795.31i	0.000365461	+	0.000632997i
$456$		0			0
$457$	431178.	−	746822.i	0.0965753	−	0.167273i	−0.813690	−	0.581300i	$-0.802544\pi$
$457$	431178.	−	746822.i	0.0965753	−	0.167273i	0.910265	+	0.414026i	$0.135878\pi$
$458$	−790492.	+	416940.i	−0.176090	+	0.0928773i
$459$		0			0
$460$	−11585.7	−	7927.49i	−0.00255286	−	0.00174679i
$461$	−3.31136e6	−	1.91182e6i	−0.725696	−	0.418981i	0.0911497	−	0.995837i	$-0.470946\pi$
$461$	−3.31136e6	−	1.91182e6i	−0.725696	−	0.418981i	−0.816845	+	0.576857i	$0.804279\pi$
$462$		0			0
$463$	−1.52485e6	+	880372.i	−0.330578	+	0.190860i	−0.656098	−	0.754676i	$-0.727794\pi$
$463$	−1.52485e6	+	880372.i	−0.330578	+	0.190860i	0.325519	+	0.945535i	$0.394461\pi$
$464$	−1.23321e6	−	990237.i	−0.265914	−	0.213523i
$465$		0			0
$466$	4.66016e6	+	178284.i	0.994113	+	0.0380319i
$467$	3.33201e6			0.706991			0.353496	−	0.935436i	$-0.384993\pi$
$467$	3.33201e6			0.706991			0.353496	+	0.935436i	$0.384993\pi$
$468$		0			0
$469$	−7.80465e6			−1.63841
$470$	−9293.29	−	355.534i	−0.00194055	−	7.42399e-5i
$471$		0			0
$472$	5.72321e6	−	2.47989e6i	1.18246	−	0.512363i
$473$	1.59787e6	−	922530.i	0.328389	−	0.189595i
$474$		0			0
$475$	−6.24644e6	−	3.60639e6i	−1.27028	−	0.733395i
$476$	342320.	−	500287.i	0.0692493	−	0.101205i
$477$		0			0
$478$	2.27767e6	−	1.20134e6i	0.455954	−	0.240490i
$479$	−287756.	+	498407.i	−0.0573040	+	0.0992535i	−0.893254	−	0.449552i	$-0.851584\pi$
$479$	−287756.	+	498407.i	−0.0573040	+	0.0992535i	0.835950	+	0.548805i	$0.184917\pi$
$480$		0			0
$481$	193366.	+	334919.i	0.0381080	+	0.0660050i
$482$	1.28334e6	+	807876.i	0.251607	+	0.158390i
$483$		0			0
$484$	3.78229e6	+	7.88782e6i	0.733908	+	1.53054i
$485$			3205.41i			0.000618770i
$486$		0			0
$487$			8.10529e6i			1.54863i	0.632803	+	0.774313i	$0.281904\pi$
$487$			8.10529e6i			1.54863i	−0.632803	+	0.774313i	$0.718096\pi$
$488$	−6.44713e6	−	4.78330e6i	−1.22551	−	0.909239i
$489$		0			0
$490$	−16272.3	+	25849.0i	−0.00306167	+	0.00486356i
$491$	−747070.	−	1.29396e6i	−0.139848	−	0.242225i	0.787591	−	0.616199i	$-0.211328\pi$
$491$	−747070.	−	1.29396e6i	−0.139848	−	0.242225i	−0.927439	+	0.373974i	$0.877995\pi$
$492$		0			0
$493$	65768.5	−	113914.i	0.0121871	−	0.0211087i
$494$	−534810.	−	1.01397e6i	−0.0986012	−	0.186942i
$495$		0			0
$496$	1.32520e6	−	514980.i	0.241868	−	0.0939910i
$497$	1.15624e6	+	667555.i	0.209970	+	0.121226i
$498$		0			0
$499$	2.62531e6	−	1.51572e6i	0.471985	−	0.272501i	−0.245085	−	0.969502i	$-0.578816\pi$
$499$	2.62531e6	−	1.51572e6i	0.471985	−	0.272501i	0.717070	+	0.697001i	$0.245483\pi$
$500$	2525.46	−	32958.1i	0.000451768	−	0.00589573i
$501$		0			0
$502$	−228681.	+	5.97746e6i	−0.0405014	+	1.05866i
$503$	−7.87121e6			−1.38714			−0.693572	−	0.720388i	$-0.743964\pi$
$503$	−7.87121e6			−1.38714			−0.693572	+	0.720388i	$0.743964\pi$
$504$		0			0
$505$	3481.44			0.000607478
$506$	−378340.	+	9.88941e6i	−0.0656911	+	1.71709i
$507$		0			0
$508$	−526064.	+	6.86531e6i	−0.0904439	+	1.18032i
$509$	−5.38888e6	+	3.11127e6i	−0.921942	+	0.532284i	−0.884254	−	0.467006i	$-0.845333\pi$
$509$	−5.38888e6	+	3.11127e6i	−0.921942	+	0.532284i	−0.0376882	+	0.999290i	$0.511999\pi$
$510$		0			0
$511$	6.33821e6	+	3.65936e6i	1.07378	+	0.619945i
$512$	−2.00130e6	+	5.58383e6i	−0.337393	+	0.941364i
$513$		0			0
$514$	−57278.4	−	108596.i	−0.00956275	−	0.0181304i
$515$	−10414.1	+	18037.8i	−0.00173024	+	0.00299686i
$516$		0			0
$517$	3.27816e6	+	5.67795e6i	0.539392	+	0.934254i
$518$	−2.95265e6	+	4.69038e6i	−0.483490	+	0.768039i
$519$		0			0
$520$	1565.14	−	2109.56i	0.000253831	−	0.000342124i
$521$			636052.i			0.102659i	0.998682	+	0.0513296i	$0.0163459\pi$
$521$			636052.i			0.102659i	−0.998682	+	0.0513296i	$0.983654\pi$
$522$		0			0
$523$			5.87088e6i			0.938531i	0.883057	+	0.469266i	$0.155481\pi$
$523$			5.87088e6i			0.938531i	−0.883057	+	0.469266i	$0.844519\pi$
$524$	−3.40973e6	−	7.11085e6i	−0.542489	−	1.13134i
$525$		0			0
$526$	−9.94124e6	−	6.25813e6i	−1.56667	−	0.986235i
$527$	59122.2	+	102403.i	0.00927309	+	0.0160615i
$528$		0			0
$529$	−304621.	+	527619.i	−0.0473283	+	0.0819749i
$530$	12515.7	−	6601.31i	0.00193537	−	0.00102080i
$531$		0			0
$532$	9.27748e6	−	1.35586e7i	1.42119	−	2.07700i
$533$	276215.	+	159473.i	0.0421142	+	0.0243147i
$534$		0			0
$535$	−21172.4	+	12223.9i	−0.00319805	+	0.00184639i
$536$	2.52526e6	+	5.82791e6i	0.379659	+	0.876196i
$537$		0			0
$538$	990106.	+	37878.6i	0.147478	+	0.00564207i
$539$	2.15330e7			3.19252
$540$		0			0
$541$	2.16059e6			0.317380			0.158690	−	0.987328i	$-0.449273\pi$
$541$	2.16059e6			0.317380			0.158690	+	0.987328i	$0.449273\pi$
$542$	−5.23451e6	−	200257.i	−0.765382	−	0.0292813i
$543$		0			0
$544$	−484336.	−	93746.5i	−0.0701697	−	0.0135818i
$545$	17343.4	−	10013.2i	0.00250117	−	0.00144405i
$546$		0			0
$547$	6.31053e6	+	3.64339e6i	0.901774	+	0.520639i	0.877775	−	0.479073i	$-0.159027\pi$
$547$	6.31053e6	+	3.64339e6i	0.901774	+	0.520639i	0.0239984	+	0.999712i	$0.492360\pi$
$548$	5.55777e6	+	3.80289e6i	0.790586	+	0.540957i
$549$		0			0
$550$	−1.03057e7	+	5.43566e6i	−1.45268	+	0.766206i
$551$	1.78244e6	−	3.08728e6i	0.250113	−	0.433209i
$552$		0			0
$553$	3.07055e6	+	5.31834e6i	0.426976	+	0.739543i
$554$	−5.37270e6	−	3.38218e6i	−0.743734	−	0.468190i
$555$		0			0
$556$	−8.19748e6	+	3.93077e6i	−1.12459	+	0.539251i
$557$		−	296984.i		−	0.0405598i	−0.999794	−	0.0202799i	$-0.993544\pi$
$557$		−	296984.i		−	0.0405598i	0.999794	−	0.0202799i	$-0.00645573\pi$
$558$		0			0
$559$			245781.i			0.0332674i
$560$	37205.6	+	5735.53i	0.00501346	+	0.000772865i
$561$		0			0
$562$	6.06644e6	−	9.63674e6i	0.810202	−	1.28703i
$563$	−345248.	−	597988.i	−0.0459051	−	0.0795099i	0.842160	−	0.539228i	$-0.181284\pi$
$563$	−345248.	−	597988.i	−0.0459051	−	0.0795099i	−0.888065	+	0.459718i	$0.847951\pi$
$564$		0			0
$565$	−9813.33	+	16997.2i	−0.00129329	+	0.00224004i
$566$	−85736.1	−	162550.i	−0.0112492	−	0.0213278i
$567$		0			0
$568$	124368.	−	1.07938e6i	0.0161748	−	0.140380i
$569$	3.83851e6	+	2.21616e6i	0.497029	+	0.286960i	0.727486	−	0.686123i	$-0.240689\pi$
$569$	3.83851e6	+	2.21616e6i	0.497029	+	0.286960i	−0.230457	+	0.973083i	$0.574022\pi$
$570$		0			0
$571$	4.13165e6	−	2.38541e6i	0.530314	−	0.306177i	−0.210831	−	0.977523i	$-0.567617\pi$
$571$	4.13165e6	−	2.38541e6i	0.530314	−	0.306177i	0.741144	+	0.671346i	$0.234283\pi$
$572$	−1.84639e6	−	141483.i	−0.235958	−	0.0180806i
$573$		0			0
$574$	−174742.	+	4.56756e6i	−0.0221369	+	0.578635i
$575$	−8.29478e6			−1.04625
$576$		0			0
$577$	−2.33515e6			−0.291995			−0.145998	−	0.989285i	$-0.546639\pi$
$577$	−2.33515e6			−0.291995			−0.145998	+	0.989285i	$0.546639\pi$
$578$	−305485.	+	7.98505e6i	−0.0380339	+	0.994164i
$579$		0			0
$580$	8144.68	+	624.097i	0.00100532	+	7.70340e-5i
$581$	1.89236e7	−	1.09256e7i	2.32575	−	1.34278i
$582$		0			0
$583$	−8.63888e6	−	4.98766e6i	−1.05266	−	0.607751i
$584$	681753.	−	5.91690e6i	0.0827171	−	0.717897i
$585$		0			0
$586$	5.17657e6	+	9.81445e6i	0.622727	+	1.18065i
$587$	−3.03042e6	+	5.24884e6i	−0.363001	+	0.628736i	−0.988453	−	0.151526i	$-0.951581\pi$
$587$	−3.03042e6	+	5.24884e6i	−0.363001	+	0.628736i	0.625452	+	0.780262i	$0.284914\pi$
$588$		0			0
$589$	1.60232e6	+	2.77529e6i	0.190309	+	0.329625i
$590$	−17162.3	+	27262.9i	−0.00202976	+	0.00322434i
$591$		0			0
$592$	4.45777e6	+	687200.i	0.522773	+	0.0805896i
$593$		−	1.50413e7i		−	1.75650i	−0.478204	−	0.878249i	$-0.658712\pi$
$593$		−	1.50413e7i		−	1.75650i	0.478204	−	0.878249i	$-0.341288\pi$
$594$		0			0
$595$			3130.88i			0.000362555i
$596$	8.55014e6	−	4.09988e6i	0.985956	−	0.472776i
$597$		0			0
$598$	−1.11568e6	−	702331.i	−0.127581	−	0.0803136i
$599$	5.82159e6	+	1.00833e7i	0.662941	+	1.14825i	0.979839	+	0.199788i	$0.0640253\pi$
$599$	5.82159e6	+	1.00833e7i	0.662941	+	1.14825i	−0.316898	+	0.948460i	$0.602641\pi$
$600$		0			0
$601$	5.34600e6	−	9.25955e6i	0.603730	−	1.04569i	−0.388520	−	0.921440i	$-0.627014\pi$
$601$	5.34600e6	−	9.25955e6i	0.603730	−	1.04569i	0.992251	−	0.124252i	$-0.0396530\pi$
$602$	−3.11555e6	+	1.64328e6i	−0.350383	+	0.184807i
$603$		0			0
$604$	−1.16274e7	−	7.95601e6i	−1.29685	−	0.887366i
$605$	−39127.6	−	22590.4i	−0.00434606	−	0.00250920i
$606$		0			0
$607$	−1.36860e7	+	7.90159e6i	−1.50766	+	0.870448i	−0.507700	+	0.861534i	$0.669504\pi$
$607$	−1.36860e7	+	7.90159e6i	−1.50766	+	0.870448i	−0.999960	+	0.00891441i	$0.997162\pi$
$608$	−1.31264e7	−	2.54069e6i	−1.44008	−	0.278736i
$609$		0			0
$610$	41431.9	+	1585.06i	0.00450827	+	0.000172473i
$611$	−873369.			−0.0946444
$612$		0			0
$613$	1.38482e7			1.48848			0.744240	−	0.667912i	$-0.232812\pi$
$613$	1.38482e7			1.48848			0.744240	+	0.667912i	$0.232812\pi$
$614$	1.30157e7	+	497941.i	1.39330	+	0.0533037i
$615$		0			0
$616$	−1.05514e7	−	2.43511e7i	−1.12037	−	2.58563i
$617$	−9.84163e6	+	5.68207e6i	−1.04077	+	0.600888i	−0.920051	−	0.391799i	$-0.871853\pi$
$617$	−9.84163e6	+	5.68207e6i	−1.04077	+	0.600888i	−0.120718	+	0.992687i	$0.538520\pi$
$618$		0			0
$619$	−5.57020e6	−	3.21595e6i	−0.584311	−	0.337352i	0.178534	−	0.983934i	$-0.442865\pi$
$619$	−5.57020e6	−	3.21595e6i	−0.584311	−	0.337352i	−0.762845	+	0.646582i	$0.776198\pi$
$620$	−4146.67	+	6060.18i	−0.000433232	+	0.000633150i
$621$		0			0
$622$	9.01216e6	−	4.75340e6i	0.934013	−	0.492639i
$623$	−2.13301e6	+	3.69448e6i	−0.220177	+	0.381359i
$624$		0			0
$625$	−4.88268e6	−	8.45706e6i	−0.499987	−	0.866003i
$626$	−1.02305e7	−	6.44024e6i	−1.04343	−	0.656850i
$627$		0			0
$628$	−565398.	−	1.17912e6i	−0.0572078	−	0.119305i
$629$			375125.i			0.0378050i
$630$		0			0
$631$			189565.i			0.0189533i	0.999955	+	0.00947664i	$0.00301655\pi$
$631$			189565.i			0.0189533i	−0.999955	+	0.00947664i	$0.996983\pi$
$632$	2.97783e6	−	4.01364e6i	0.296556	−	0.399711i
$633$		0			0
$634$	−7.70554e6	+	1.22405e7i	−0.761342	+	1.20942i
$635$	−17781.0	−	30797.6i	−0.00174994	−	0.00303098i
$636$		0			0
$637$	−1.43421e6	+	2.48412e6i	−0.140044	+	0.242563i
$638$	−2.68655e6	−	5.09354e6i	−0.261303	−	0.495414i
$639$		0			0
$640$	−7755.31	−	29638.0i	−0.000748427	−	0.00286022i
$641$	1.05418e6	+	608632.i	0.101338	+	0.0585073i	0.549812	−	0.835288i	$-0.314699\pi$
$641$	1.05418e6	+	608632.i	0.101338	+	0.0585073i	−0.448475	+	0.893796i	$0.648033\pi$
$642$		0			0
$643$	1.05398e7	−	6.08518e6i	1.00532	−	0.580424i	0.0955052	−	0.995429i	$-0.469553\pi$
$643$	1.05398e7	−	6.08518e6i	1.00532	−	0.580424i	0.909819	+	0.415005i	$0.136220\pi$
$644$	1.44350e6	−	1.88382e7i	0.137152	−	1.78988i
$645$		0			0
$646$	42509.4	−	1.11115e6i	0.00400777	−	0.104759i
$647$	−3.77606e6			−0.354632			−0.177316	−	0.984154i	$-0.556741\pi$
$647$	−3.77606e6			−0.354632			−0.177316	+	0.984154i	$0.556741\pi$
$648$		0			0
$649$	2.27108e7			2.11651
$650$	59334.5	−	1.55094e6i	0.00550838	−	0.143983i
$651$		0			0
$652$	−798119.	+	1.04157e7i	−0.0735273	+	0.959556i
$653$	2.34130e6	−	1.35175e6i	0.214869	−	0.124055i	−0.388703	−	0.921363i	$-0.627077\pi$
$653$	2.34130e6	−	1.35175e6i	0.214869	−	0.124055i	0.603572	+	0.797308i	$0.293744\pi$
$654$		0			0
$655$	35273.5	+	20365.1i	0.00321251	+	0.00185474i
$656$	3.46724e6	−	1.34739e6i	0.314575	−	0.122246i
$657$		0			0
$658$	−5.83930e6	−	1.10709e7i	−0.525770	−	0.996828i
$659$	−2.57880e6	+	4.46661e6i	−0.231315	+	0.400649i	−0.958195	−	0.286115i	$-0.907636\pi$
$659$	−2.57880e6	+	4.46661e6i	−0.231315	+	0.400649i	0.726880	+	0.686764i	$0.240969\pi$
$660$		0			0
$661$	−2.13265e6	−	3.69386e6i	−0.189853	−	0.328834i	0.755348	−	0.655324i	$-0.227468\pi$
$661$	−2.13265e6	−	3.69386e6i	−0.189853	−	0.328834i	−0.945201	+	0.326489i	$0.894134\pi$
$662$	−4.83578e6	+	7.68179e6i	−0.428866	+	0.681267i
$663$		0			0
$664$	−1.42813e7	−	1.05957e7i	−1.25703	−	0.932626i
$665$			84852.4i			0.00744063i
$666$		0			0
$667$		−	4.09966e6i		−	0.356807i
$668$	6.42364e6	+	1.33963e7i	0.556981	+	1.16156i
$669$		0			0
$670$	−27761.6	−	17476.3i	−0.00238923	−	0.00150405i
$671$	−1.46149e7	−	2.53137e7i	−1.25311	−	2.17045i
$672$		0			0
$673$	−6.22631e6	+	1.07843e7i	−0.529899	+	0.917811i	0.469493	+	0.882936i	$0.344437\pi$
$673$	−6.22631e6	+	1.07843e7i	−0.529899	+	0.917811i	−0.999392	+	0.0348752i	$0.988897\pi$
$674$	−8.40659e6	+	4.43400e6i	−0.712804	+	0.375964i
$675$		0			0
$676$	−6.57017e6	+	9.60203e6i	−0.552981	+	0.808158i
$677$	1.63455e7	+	9.43705e6i	1.37065	+	0.791343i	0.991009	−	0.133793i	$-0.0427156\pi$
$677$	1.63455e7	+	9.43705e6i	1.37065	+	0.791343i	0.379637	+	0.925136i	$0.376049\pi$
$678$		0			0
$679$	−3.73603e6	+	2.15700e6i	−0.310983	+	0.179546i
$680$	2337.90	−	1013.02i	0.000193889	−	8.40131e-5i
$681$		0			0
$682$	5.17290e6	+	197900.i	0.425866	+	0.0162924i
$683$	1.32651e7			1.08807			0.544036	−	0.839062i	$-0.316896\pi$
$683$	1.32651e7			1.08807			0.544036	+	0.839062i	$0.316896\pi$
$684$		0			0
$685$	−34781.5			−0.00283219
$686$	−1.99457e7	−	763064.i	−1.61822	−	0.0619086i
$687$		0			0
$688$	2.23513e6	+	1.79476e6i	0.180025	+	0.144556i
$689$	1.15079e6	−	664407.i	0.0923521	−	0.0533195i
$690$		0			0
$691$	−4.37907e6	−	2.52826e6i	−0.348889	−	0.201431i	0.315307	−	0.948990i	$-0.397893\pi$
$691$	−4.37907e6	−	2.52826e6i	−0.348889	−	0.201431i	−0.664196	+	0.747559i	$0.731226\pi$
$692$	1.08817e7	+	7.44581e6i	0.863839	+	0.591080i
$693$		0			0
$694$	−7.53488e6	+	3.97422e6i	−0.593851	+	0.313223i
$695$	23477.2	−	40663.7i	0.00184367	−	0.00319334i
$696$		0			0
$697$	154687.	+	267926.i	0.0120607	+	0.0208897i
$698$	1.69143e7	+	1.06478e7i	1.31406	+	0.827218i
$699$		0			0
$700$	2.00566e7	−	9.61737e6i	1.54708	−	0.741841i
$701$		−	1.64236e7i		−	1.26233i	−0.775649	−	0.631165i	$-0.782577\pi$
$701$		−	1.64236e7i		−	1.26233i	0.775649	−	0.631165i	$-0.217423\pi$
$702$		0			0
$703$			1.01666e7i			0.775863i
$704$	−1.47695e7	+	1.57580e7i	−1.12314	+	1.19831i
$705$		0			0
$706$	−290891.	+	462090.i	−0.0219644	+	0.0348911i
$707$	2.34275e6	+	4.05776e6i	0.176269	+	0.305308i
$708$		0			0
$709$	1.63475e6	−	2.83147e6i	0.122134	−	0.211542i	−0.798475	−	0.602028i	$-0.794360\pi$
$709$	1.63475e6	−	2.83147e6i	0.122134	−	0.211542i	0.920609	+	0.390486i	$0.127693\pi$
$710$	2618.02	+	4963.60i	0.000194907	+	0.000369531i
$711$		0			0
$712$	3.44891e6	+	397388.i	0.254966	+	0.0293775i
$713$	3.19162e6	+	1.84268e6i	0.235119	+	0.135746i
$714$		0			0
$715$	8282.89	−	4782.13i	0.000605922	−	0.000349829i
$716$	2.91690e6	+	223512.i	0.212637	+	0.0162936i
$717$		0			0
$718$	310807.	−	8.12416e6i	0.0224998	−	0.588122i
$719$	1.65702e7			1.19538			0.597689	−	0.801728i	$-0.296086\pi$
$719$	1.65702e7			1.19538			0.597689	+	0.801728i	$0.296086\pi$
$720$		0			0
$721$	−2.80318e7			−2.00822
$722$	616605.	−	1.61174e7i	0.0440214	−	1.15067i
$723$		0			0
$724$	2.25090e7	+	1.72478e6i	1.59591	+	0.122289i
$725$	4.17990e6	−	2.41327e6i	0.295339	−	0.170514i
$726$		0			0
$727$	1.27235e7	+	7.34592e6i	0.892834	+	0.515478i	0.874868	−	0.484361i	$-0.160948\pi$
$727$	1.27235e7	+	7.34592e6i	0.892834	+	0.515478i	0.0179654	+	0.999839i	$0.494281\pi$
$728$	3.51200e6	+	404658.i	0.245599	+	0.0282982i
$729$		0			0
$730$	14351.3	+	27209.2i	0.000996744	+	0.00188977i
$731$	−119202.	+	206465.i	−0.00825071	+	0.0142907i
$732$		0			0
$733$	−4.45862e6	−	7.72256e6i	−0.306507	−	0.530886i	0.671089	−	0.741377i	$-0.265827\pi$
$733$	−4.45862e6	−	7.72256e6i	−0.306507	−	0.530886i	−0.977596	+	0.210491i	$0.932494\pi$
$734$	8.57462e6	−	1.36211e7i	0.587455	−	0.933192i
$735$		0			0
$736$	−1.45340e7	+	5.01736e6i	−0.988986	+	0.341414i
$737$			2.31263e7i			1.56833i
$738$		0			0
$739$		−	1.80178e7i		−	1.21364i	−0.794840	−	0.606820i	$-0.792445\pi$
$739$		−	1.80178e7i		−	1.21364i	0.794840	−	0.606820i	$-0.207555\pi$
$740$	−21005.5	+	10072.4i	−0.00141011	+	0.000676163i
$741$		0			0
$742$	1.61162e7	+	1.01453e7i	1.07462	+	0.676483i
$743$	−747641.	−	1.29495e6i	−0.0496845	−	0.0860561i	0.840114	−	0.542411i	$-0.182488\pi$
$743$	−747641.	−	1.29495e6i	−0.0496845	−	0.0860561i	−0.889798	+	0.456354i	$0.849155\pi$
$744$		0			0
$745$	−24487.2	+	42413.1i	−0.00161640	+	0.00279968i
$746$	1.92516e7	−	1.01541e7i	1.26654	−	0.668028i
$747$		0			0
$748$	−1.48242e6	−	1.01434e6i	−0.0968762	−	0.0662873i
$749$	−2.84948e7	−	1.64515e7i	−1.85593	−	1.07152i
$750$		0			0
$751$	−1.22754e7	+	7.08720e6i	−0.794210	+	0.458537i	−0.841443	−	0.540347i	$-0.818293\pi$
$751$	−1.22754e7	+	7.08720e6i	−0.794210	+	0.458537i	0.0472327	+	0.998884i	$0.484960\pi$
$752$	−6.37758e6	+	7.94244e6i	−0.411255	+	0.512164i
$753$		0			0
$754$	766546.	+	29325.9i	0.0491032	+	0.00187855i
$755$	72766.1			0.00464582
$756$		0			0
$757$	−2.06134e7			−1.30740			−0.653701	−	0.756753i	$-0.726784\pi$
$757$	−2.06134e7			−1.30740			−0.653701	+	0.756753i	$0.726784\pi$
$758$	7.13461e6	+	272950.i	0.451021	+	0.0172548i
$759$		0			0
$760$	63361.2	−	27454.7i	0.00397914	−	0.00172418i
$761$	−2.19743e7	+	1.26869e7i	−1.37548	+	0.794134i	−0.991612	−	0.129254i	$-0.958742\pi$
$761$	−2.19743e7	+	1.26869e7i	−1.37548	+	0.794134i	−0.383869	+	0.923388i	$0.625408\pi$
$762$		0			0
$763$	2.33416e7	+	1.34763e7i	1.45151	+	0.838028i
$764$	2.35332e6	−	3.43928e6i	0.145864	−	0.213174i
$765$		0			0
$766$	8.20002e6	−	4.32504e6i	0.504944	−	0.266329i
$767$	−1.51265e6	+	2.61999e6i	−0.0928434	+	0.160810i
$768$		0			0
$769$	7.30670e6	+	1.26556e7i	0.445559	+	0.771732i	0.998091	−	0.0617604i	$-0.0196715\pi$
$769$	7.30670e6	+	1.26556e7i	0.445559	+	0.771732i	−0.552532	+	0.833492i	$0.686338\pi$
$770$	115998.	+	73022.1i	0.00705056	+	0.00443841i
$771$		0			0
$772$	6.34231e6	+	1.32266e7i	0.383005	+	0.798742i
$773$			5.98384e6i			0.360190i	0.983649	+	0.180095i	$0.0576405\pi$
$773$			5.98384e6i			0.360190i	−0.983649	+	0.180095i	$0.942360\pi$
$774$		0			0
$775$			4.33879e6i			0.259486i
$776$	2.81951e6	+	2.09187e6i	0.168081	+	0.124704i
$777$		0			0
$778$	7.40914e6	−	1.17697e7i	0.438853	−	0.697132i
$779$	4.19228e6	+	7.26125e6i	0.247518	+	0.428714i
$780$		0			0
$781$	1.97806e6	−	3.42610e6i	0.116041	−	0.200989i
$782$	−596581.	−	1.13108e6i	−0.0348861	−	0.0661419i
$783$		0			0
$784$	1.21177e7	+	3.11825e7i	0.704092	+	1.81184i
$785$	5849.02	+	3376.93i	0.000338773	+	0.000195591i
$786$		0			0
$787$	37478.1	−	21638.0i	0.00215696	−	0.00124532i	−0.498921	−	0.866647i	$-0.666270\pi$
$787$	37478.1	−	21638.0i	0.00215696	−	0.00124532i	0.501078	+	0.865402i	$0.332937\pi$
$788$	−1.18516e6	+	1.54667e7i	−0.0679926	+	0.887327i
$789$		0			0
$790$	−986.777	+	25793.3i	−5.62537e−5	+	0.00147041i
$791$	−2.64145e7			−1.50107
$792$		0			0
$793$	3.89370e6			0.219877
$794$	−38226.9	+	999211.i	−0.00215188	+	0.0562479i
$795$		0			0
$796$	−1.50702e6	+	1.96671e7i	−0.0843015	+	1.10016i
$797$	−1.90170e7	+	1.09795e7i	−1.06047	+	0.612260i	−0.925561	−	0.378598i	$-0.876406\pi$
$797$	−1.90170e7	+	1.09795e7i	−1.06047	+	0.612260i	−0.134905	+	0.990859i	$0.543073\pi$
$798$		0			0
$799$	−733661.	−	423580.i	−0.0406564	−	0.0234730i
$800$	−1.36710e7	−	1.18650e7i	−0.755224	−	0.655454i
$801$		0			0
$802$	1.14079e7	+	2.16287e7i	0.626282	+	1.18739i
$803$	1.08432e7	−	1.87810e7i	0.593429	−	1.02785i
$804$		0			0
$805$	48790.6	+	84507.9i	0.00265367	+	0.00459629i
$806$	−367372.	+	583582.i	−0.0199190	+	0.0316420i
$807$		0			0
$808$	2.27201e6	−	3.06231e6i	0.122428	−	0.165014i
$809$			2.05647e7i			1.10472i	0.833606	+	0.552360i	$0.186272\pi$
$809$			2.05647e7i			1.10472i	−0.833606	+	0.552360i	$0.813728\pi$
$810$		0			0
$811$		−	7.88381e6i		−	0.420905i	−0.977604	−	0.210452i	$-0.932506\pi$
$811$		−	7.88381e6i		−	0.420905i	0.977604	−	0.210452i	$-0.0674937\pi$
$812$	4.75335e6	+	9.91292e6i	0.252993	+	0.527608i
$813$		0			0
$814$	1.38982e7	+	8.74911e6i	0.735189	+	0.462810i
$815$	−26976.5	−	46724.8i	−0.00142263	−	0.00246407i
$816$		0			0
$817$	−3.23059e6	+	5.59555e6i	−0.169327	+	0.293284i
$818$	−2.05370e6	+	1.08321e6i	−0.107313	+	0.0566017i
$819$		0			0
$820$	−10849.3	+	15855.8i	−0.000563465	+	0.000823481i
$821$	−1.29381e6	−	746979.i	−0.0669902	−	0.0386768i	0.466131	−	0.884716i	$-0.345648\pi$
$821$	−1.29381e6	−	746979.i	−0.0669902	−	0.0386768i	−0.533121	+	0.846039i	$0.678981\pi$
$822$		0			0
$823$	1.33652e6	−	771641.i	0.0687823	−	0.0397115i	−0.465214	−	0.885198i	$-0.654023\pi$
$823$	1.33652e6	−	771641.i	0.0687823	−	0.0397115i	0.533997	+	0.845487i	$0.320689\pi$
$824$	9.06991e6	+	2.09320e7i	0.465356	+	1.07397i
$825$		0			0
$826$	−4.33249e7	−	1.65749e6i	−2.20947	−	0.0845279i
$827$	−3.53724e7			−1.79846			−0.899229	−	0.437478i	$-0.855872\pi$
$827$	−3.53724e7			−1.79846			−0.899229	+	0.437478i	$0.855872\pi$
$828$		0			0
$829$	−6.15167e6			−0.310890			−0.155445	−	0.987845i	$-0.549681\pi$
$829$	−6.15167e6			−0.310890			−0.155445	+	0.987845i	$0.549681\pi$
$830$	91777.1	+	3511.13i	0.00462423	+	0.000176910i
$831$		0			0
$832$	−834171.	−	2.75343e6i	−0.0417779	−	0.137900i
$833$	−2.40957e6	+	1.39117e6i	−0.120317	+	0.0694652i
$834$		0			0
$835$	−66452.3	−	38366.2i	−0.00329833	−	0.00190429i
$836$	−4.01762e7	−	2.74905e7i	−1.98817	−	1.36040i
$837$		0			0
$838$	−1.14236e7	+	6.02530e6i	−0.561944	+	0.296394i
$839$	2.06799e6	−	3.58186e6i	0.101425	−	0.175672i	−0.810847	−	0.585258i	$-0.800993\pi$
$839$	2.06799e6	−	3.58186e6i	0.101425	−	0.175672i	0.912272	+	0.409585i	$0.134327\pi$
$840$		0			0
$841$	−9.06283e6	−	1.56973e7i	−0.441849	−	0.765305i
$842$	5.61654e6	+	3.53568e6i	0.273017	+	0.171867i
$843$		0			0
$844$	1.29382e7	−	6.20400e6i	0.625198	−	0.299789i
$845$		−	60091.2i		−	0.00289514i
$846$		0			0
$847$		−	6.08065e7i		−	2.91233i
$848$	2.36123e6	−	1.53170e7i	0.112758	−	0.731447i
$849$		0			0
$850$	802041.	−	1.27407e6i	0.0380758	−	0.0604847i
$851$	5.84583e6	+	1.01253e7i	0.276708	+	0.479273i
$852$		0			0
$853$	−1.95376e7	+	3.38401e7i	−0.919387	+	1.59243i	−0.119040	+	0.992890i	$0.537982\pi$
$853$	−1.95376e7	+	3.38401e7i	−0.919387	+	1.59243i	−0.800348	+	0.599536i	$0.795352\pi$
$854$	2.60331e7	+	4.93571e7i	1.22146	+	2.31582i
$855$		0			0
$856$	−3.06497e6	+	2.66008e7i	−0.142969	+	1.24082i
$857$	553414.	+	319514.i	0.0257394	+	0.0148606i	0.512814	−	0.858499i	$-0.328603\pi$
$857$	553414.	+	319514.i	0.0257394	+	0.0148606i	−0.487075	+	0.873360i	$0.661936\pi$
$858$		0			0
$859$	6.90014e6	−	3.98380e6i	0.319062	−	0.184211i	−0.331912	−	0.943310i	$-0.607694\pi$
$859$	6.90014e6	−	3.98380e6i	0.319062	−	0.184211i	0.650974	+	0.759100i	$0.274361\pi$
$860$	−14761.8	−	1131.15i	−0.000680604	−	5.21522e-5i
$861$		0			0
$862$	1.48100e6	−	3.87118e7i	0.0678871	−	1.77450i
$863$	1.19376e7			0.545622			0.272811	−	0.962068i	$-0.412047\pi$
$863$	1.19376e7			0.545622			0.272811	+	0.962068i	$0.412047\pi$
$864$		0			0
$865$	−68099.8			−0.00309461
$866$	432022.	−	1.12926e7i	0.0195754	−	0.511680i
$867$		0			0
$868$	−9.85379e6	−	755060.i	−0.443919	−	0.0340159i
$869$	1.57590e7	−	9.09846e6i	0.707912	−	0.408713i
$870$		0			0
$871$	−2.66792e6	−	1.54033e6i	−0.119159	−	0.0687967i
$872$	2.51068e6	−	2.17901e7i	0.111815	−	0.970437i
$873$		0			0
$874$	−1.61684e7	−	3.06543e7i	−0.715958	−	1.35741i
$875$	−114883.	+	198983.i	−0.00507266	+	0.00878611i
$876$		0			0
$877$	9.42773e6	+	1.63293e7i	0.413912	+	0.716917i	0.995314	−	0.0967001i	$-0.0308288\pi$
$877$	9.42773e6	+	1.63293e7i	0.413912	+	0.716917i	−0.581402	+	0.813617i	$0.697495\pi$
$878$	1.71230e7	−	2.72004e7i	0.749624	−	1.19080i
$879$		0			0
$880$	16995.2	−	110245.i	0.000739808	−	0.00479903i
$881$		−	2.77186e7i		−	1.20318i	−0.798804	−	0.601592i	$-0.794533\pi$
$881$		−	2.77186e7i		−	1.20318i	0.798804	−	0.601592i	$-0.205467\pi$
$882$		0			0
$883$		−	6.18034e6i		−	0.266754i	−0.991065	−	0.133377i	$-0.957418\pi$
$883$		−	6.18034e6i		−	0.266754i	0.991065	−	0.133377i	$-0.0425821\pi$
$884$	215755.	−	103457.i	0.00928601	−	0.00445274i
$885$		0			0
$886$	−1.13030e7	−	7.11537e6i	−0.483737	−	0.304518i
$887$	7.78341e6	+	1.34813e7i	0.332170	+	0.575336i	0.982937	−	0.183942i	$-0.0588858\pi$
$887$	7.78341e6	+	1.34813e7i	0.332170	+	0.575336i	−0.650767	+	0.759278i	$0.725552\pi$
$888$		0			0
$889$	2.39306e7	−	4.14490e7i	1.01554	−	1.75898i
$890$	−15860.0	+	8365.24i	−0.000671162	+	0.000354000i
$891$		0			0
$892$	−1.46473e6	−	1.00224e6i	−0.0616374	−	0.0421753i
$893$	−1.98835e7	−	1.14797e7i	−0.834381	−	0.481730i
$894$		0			0
$895$	−13085.2	+	7554.73i	−0.000546037	+	0.000315255i
$896$	2.93256e7	−	2.89833e7i	1.22033	−	1.20608i
$897$		0			0
$898$	7.92358e6	+	303134.i	0.327892	+	0.0125442i
$899$	−2.14443e6			−0.0884937
$900$		0			0
$901$	1.28894e6			0.0528956
$902$	1.35343e7	+	517784.i	0.553886	+	0.0211901i
$903$		0			0
$904$	8.54665e6	+	1.97244e7i	0.347836	+	0.802753i
$905$	−100975.	+	58297.8i	−0.00409818	+	0.00236609i
$906$		0			0
$907$	−135521.	−	78243.1i	−0.00547001	−	0.00315811i	0.497263	−	0.867600i	$-0.334339\pi$
$907$	−135521.	−	78243.1i	−0.00547001	−	0.00315811i	−0.502733	+	0.864442i	$0.667672\pi$
$908$	−1.11827e7	+	1.63430e7i	−0.450122	+	0.657835i
$909$		0			0
$910$	−16150.1	+	8518.27i	−0.000646505	+	0.000340995i
$911$	−2.09808e7	+	3.63398e7i	−0.837579	+	1.45073i	0.0543350	+	0.998523i	$0.482696\pi$
$911$	−2.09808e7	+	3.63398e7i	−0.837579	+	1.45073i	−0.891914	+	0.452206i	$0.850637\pi$
$912$		0			0
$913$	−3.23739e7	−	5.60733e7i	−1.28534	−	2.22628i
$914$	4.12833e6	+	2.59883e6i	0.163459	+	0.102899i
$915$		0			0
$916$	−2.18589e6	−	4.55860e6i	−0.0860776	−	0.179512i
$917$			5.48169e7i			2.15274i
$918$		0			0
$919$			2.72926e7i			1.06600i	0.846115	+	0.533000i	$0.178935\pi$
$919$			2.72926e7i			1.06600i	−0.846115	+	0.533000i	$0.821065\pi$
$920$	47317.4	−	63776.3i	0.00184311	−	0.00248422i
$921$		0			0
$922$	1.15231e7	−	1.83048e7i	0.446417	−	0.709148i
$923$	263498.	+	456391.i	0.0101806	+	0.0176333i
$924$		0			0
$925$	−6.88230e6	+	1.19205e7i	−0.264472	+	0.458079i
$926$	−4.64674e6	−	8.80993e6i	−0.178082	−	0.337633i
$927$		0			0
$928$	5.86422e6	−	6.75684e6i	0.223532	−	0.257557i
$929$	2.44081e7	+	1.40920e7i	0.927886	+	0.535715i	0.886142	−	0.463413i	$-0.153375\pi$
$929$	2.44081e7	+	1.40920e7i	0.927886	+	0.535715i	0.0417437	+	0.999128i	$0.486709\pi$
$930$		0			0
$931$	−6.53037e7	+	3.77031e7i	−2.46924	+	1.42562i
$932$	−2.01558e6	+	2.63040e7i	−0.0760082	+	0.991932i
$933$		0			0
$934$	−720570.	+	1.88349e7i	−0.0270277	+	0.706474i
$935$	9277.24			0.000347048
$936$		0			0
$937$	4.61113e7			1.71577			0.857883	−	0.513844i	$-0.171779\pi$
$937$	4.61113e7			1.71577			0.857883	+	0.513844i	$0.171779\pi$
$938$	1.68781e6	−	4.41175e7i	0.0626349	−	1.63721i
$939$		0			0
$940$	4019.47	−	52455.5i	0.000148371	−	0.00193629i
$941$	3.09579e7	−	1.78736e7i	1.13972	−	0.658017i	0.193357	−	0.981128i	$-0.438062\pi$
$941$	3.09579e7	−	1.78736e7i	1.13972	−	0.658017i	0.946361	+	0.323112i	$0.104729\pi$
$942$		0			0
$943$	8.35053e6	+	4.82118e6i	0.305798	+	0.176553i
$944$	1.27805e7	+	3.28880e7i	0.466784	+	1.20118i
$945$		0			0
$946$	4.86925e6	+	9.23181e6i	0.176903	+	0.335397i
$947$	2.69789e7	−	4.67288e7i	0.977572	−	1.69320i	0.306398	−	0.951903i	$-0.400876\pi$
$947$	2.69789e7	−	4.67288e7i	0.977572	−	1.69320i	0.671173	−	0.741300i	$-0.265791\pi$
$948$		0			0
$949$	1.44442e6	+	2.50182e6i	0.0520630	+	0.0901758i
$950$	2.17367e7	−	3.45295e7i	0.781421	−	1.24131i
$951$		0			0
$952$	2.75395e6	+	2.04323e6i	0.0984836	+	0.0730676i
$953$		−	5.27586e7i		−	1.88174i	−0.338762	−	0.940872i	$-0.610008\pi$
$953$		−	5.27586e7i		−	1.88174i	0.338762	−	0.940872i	$-0.389992\pi$
$954$		0			0
$955$			21523.6i			0.000763673i
$956$	6.29829e6	+	1.31348e7i	0.222883	+	0.464815i
$957$		0			0
$958$	−2.75513e6	−	1.73439e6i	−0.0969902	−	0.0610565i
$959$	−2.34053e7	−	4.05392e7i	−0.821804	−	1.42341i
$960$		0			0
$961$	−1.33507e7	+	2.31241e7i	−0.466333	+	0.807712i
$962$	−1.93502e6	+	1.02061e6i	−0.0674136	+	0.0355569i
$963$		0			0
$964$	−4.84422e6	+	7.07963e6i	−0.167893	+	0.245368i
$965$	−65610.9	−	37880.5i	−0.00226808	−	0.00130947i
$966$		0			0
$967$	2.97045e7	−	1.71499e7i	1.02154	−	0.589788i	0.106992	−	0.994260i	$-0.465878\pi$
$967$	2.97045e7	−	1.71499e7i	1.02154	−	0.589788i	0.914550	+	0.404472i	$0.132545\pi$
$968$	−4.54056e7	+	1.96744e7i	−1.55747	+	0.674860i
$969$		0			0
$970$	−18119.3	−	693.192i	−0.000618318	−	2.36551e-5i
$971$	2.21065e7			0.752440			0.376220	−	0.926530i	$-0.377224\pi$
$971$	2.21065e7			0.752440			0.376220	+	0.926530i	$0.377224\pi$
$972$		0			0
$973$	6.31935e7			2.13989
$974$	−4.58169e7	−	1.75282e6i	−1.54749	−	0.0592026i
$975$		0			0
$976$	2.84329e7	−	3.54094e7i	0.955425	−	1.18986i
$977$	2.47525e7	−	1.42908e7i	0.829625	−	0.478984i	−0.0240990	−	0.999710i	$-0.507672\pi$
$977$	2.47525e7	−	1.42908e7i	0.829625	−	0.478984i	0.853724	+	0.520725i	$0.174338\pi$
$978$		0			0
$979$	1.09473e7	+	6.32041e6i	0.365047	+	0.210760i
$980$	−142598.	−	97572.7i	−0.00474296	−	0.00324536i
$981$		0			0
$982$	7.47597e6	−	3.94315e6i	0.247394	−	0.130486i
$983$	2.54359e7	−	4.40562e7i	0.839582	−	1.45420i	−0.0506632	−	0.998716i	$-0.516134\pi$
$983$	2.54359e7	−	4.40562e7i	0.839582	−	1.45420i	0.890245	−	0.455482i	$-0.150533\pi$
$984$		0			0
$985$	−40058.6	−	69383.6i	−0.00131554	−	0.00227859i
$986$	629703.	+	396406.i	0.0206274	+	0.0129852i
$987$		0			0
$988$	5.84733e6	−	2.80385e6i	0.190575	−	0.0913825i
$989$			7.43044e6i			0.241559i
$990$		0			0
$991$			5.10757e7i			1.65208i	0.563615	+	0.826038i	$0.309410\pi$
$991$			5.10757e7i			1.65208i	−0.563615	+	0.826038i	$0.690590\pi$
$992$	2.62445e6	+	7.60236e6i	0.0846759	+	0.245284i
$993$		0			0
$994$	−4.02355e6	+	6.39154e6i	−0.129165	+	0.205182i
$995$	−50937.4	−	88226.1i	−0.00163109	−	0.00282514i
$996$		0			0
$997$	−4.62753e6	+	8.01512e6i	−0.147439	+	0.255371i	−0.930280	−	0.366850i	$-0.880436\pi$
$997$	−4.62753e6	+	8.01512e6i	−0.147439	+	0.255371i	0.782841	+	0.622221i	$0.213770\pi$
$998$	8.00020e6	+	1.51679e7i	0.254258	+	0.482058i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	108.6.h.a.35.14		56
3.2	odd	2		36.6.h.a.11.15	yes	56
4.3	odd	2	inner	108.6.h.a.35.24		56
9.4	even	3		36.6.h.a.23.5	yes	56
9.5	odd	6	inner	108.6.h.a.71.24		56
12.11	even	2		36.6.h.a.11.5	✓	56
36.23	even	6	inner	108.6.h.a.71.14		56
36.31	odd	6		36.6.h.a.23.15	yes	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
36.6.h.a.11.5	✓	56	12.11	even	2
36.6.h.a.11.15	yes	56	3.2	odd	2
36.6.h.a.23.5	yes	56	9.4	even	3
36.6.h.a.23.15	yes	56	36.31	odd	6
108.6.h.a.35.14		56	1.1	even	1	trivial
108.6.h.a.35.24		56	4.3	odd	2	inner
108.6.h.a.71.14		56	36.23	even	6	inner
108.6.h.a.71.24		56	9.5	odd	6	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:	\( N \)	\(=\)	\( 108 = 2^{2} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	108.h (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.216257 + 5.65272i) q^{2} +(-31.9065 - 2.44488i) q^{4} +(0.143132 - 0.0826372i) q^{5} +(192.634 + 111.217i) q^{7} +(20.7202 - 179.830i) q^{8} +O(q^{10})\)	\(q+(-0.216257 + 5.65272i) q^{2} +(-31.9065 - 2.44488i) q^{4} +(0.143132 - 0.0826372i) q^{5} +(192.634 + 111.217i) q^{7} +(20.7202 - 179.830i) q^{8} +(0.436172 + 0.826955i) q^{10} +(329.552 - 570.801i) q^{11} +(43.8997 + 76.0365i) q^{13} +(-670.338 + 1064.85i) q^{14} +(1012.05 + 156.015i) q^{16} +85.1645i q^{17} +2308.11i q^{19} +(-4.76887 + 2.28672i) q^{20} +(3155.31 + 1986.31i) q^{22} +(1327.18 + 2298.74i) q^{23} +(-1562.49 + 2706.31i) q^{25} +(-439.307 + 231.709i) q^{26} +(-5874.36 - 4019.52i) q^{28} +(-1337.58 - 772.253i) q^{29} +(1202.41 - 694.212i) q^{31} +(-1100.77 + 5687.07i) q^{32} +(-481.411 - 18.4174i) q^{34} +36.7627 q^{35} +4404.71 q^{37} +(-13047.1 - 499.144i) q^{38} +(-11.8949 - 27.4516i) q^{40} +(3145.98 - 1816.33i) q^{41} +(2424.30 + 1399.67i) q^{43} +(-11910.4 + 17406.5i) q^{44} +(-13281.1 + 7005.04i) q^{46} +(-4973.66 + 8614.64i) q^{47} +(16335.1 + 28293.2i) q^{49} +(-14960.1 - 9417.55i) q^{50} +(-1214.78 - 2533.39i) q^{52} -15134.7i q^{53} -108.933i q^{55} +(23991.6 - 32336.8i) q^{56} +(4654.59 - 7393.96i) q^{58} +(17228.5 + 29840.7i) q^{59} +(22173.9 - 38406.3i) q^{61} +(3664.16 + 6947.02i) q^{62} +(-31909.3 - 7452.21i) q^{64} +(12.5669 + 7.25550i) q^{65} +(-30386.6 + 17543.7i) q^{67} +(208.217 - 2717.30i) q^{68} +(-7.95019 + 207.809i) q^{70} +6002.26 q^{71} +32902.8 q^{73} +(-952.549 + 24898.6i) q^{74} +(5643.04 - 73643.6i) q^{76} +(126966. - 73303.8i) q^{77} +(23909.7 + 13804.3i) q^{79} +(157.749 - 61.3019i) q^{80} +(9586.86 + 18176.1i) q^{82} +(49118.1 - 85075.0i) q^{83} +(7.03776 + 12.1898i) q^{85} +(-8436.22 + 13401.2i) q^{86} +(-95818.6 - 71090.4i) q^{88} +19178.8i q^{89} +19529.6i q^{91} +(-36725.4 - 76589.3i) q^{92} +(-47620.5 - 29977.7i) q^{94} +(190.736 + 330.364i) q^{95} +(-9697.23 + 16796.1i) q^{97} +(-163466. + 86219.0i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q + 3 q^{2} - q^{4} + 6 q^{5}+O(q^{10}) \) 56 * q + 3 * q^2 - q^4 + 6 * q^5	\( 56 q + 3 q^{2} - q^{4} + 6 q^{5} - 68 q^{10} - 2 q^{13} + 1518 q^{14} - q^{16} + 1242 q^{20} + 63 q^{22} + 12498 q^{25} - 2052 q^{28} + 11946 q^{29} + 7233 q^{32} + 6361 q^{34} - 8 q^{37} + 14877 q^{38} - 1526 q^{40} + 43536 q^{41} - 26880 q^{46} + 38414 q^{49} - 38631 q^{50} + 24988 q^{52} - 21186 q^{56} - 3314 q^{58} - 2 q^{61} - 106342 q^{64} - 35970 q^{65} - 31413 q^{68} + 10524 q^{70} + 53620 q^{73} + 20406 q^{74} + 26193 q^{76} - 26178 q^{77} - 151286 q^{82} + 6248 q^{85} - 279237 q^{86} - 122541 q^{88} - 435804 q^{92} + 63480 q^{94} - 58148 q^{97}+O(q^{100}) \) 56 * q + 3 * q^2 - q^4 + 6 * q^5 - 68 * q^10 - 2 * q^13 + 1518 * q^14 - q^16 + 1242 * q^20 + 63 * q^22 + 12498 * q^25 - 2052 * q^28 + 11946 * q^29 + 7233 * q^32 + 6361 * q^34 - 8 * q^37 + 14877 * q^38 - 1526 * q^40 + 43536 * q^41 - 26880 * q^46 + 38414 * q^49 - 38631 * q^50 + 24988 * q^52 - 21186 * q^56 - 3314 * q^58 - 2 * q^61 - 106342 * q^64 - 35970 * q^65 - 31413 * q^68 + 10524 * q^70 + 53620 * q^73 + 20406 * q^74 + 26193 * q^76 - 26178 * q^77 - 151286 * q^82 + 6248 * q^85 - 279237 * q^86 - 122541 * q^88 - 435804 * q^92 + 63480 * q^94 - 58148 * q^97

Introduction

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