LMFDB - Embedded newform 108.6.h.a.35.6

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			35.6
Character	$\chi$	$=$	108.35
Dual form			108.6.h.a.71.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-4.63825 - 3.23831i) q^{2} +(11.0267 + 30.0402i) q^{4} +(-61.0162 + 35.2277i) q^{5} +(181.157 + 104.591i) q^{7} +(46.1351 - 175.042i) q^{8} +O(q^{10})$	\(q+(-4.63825 - 3.23831i) q^{2} +(11.0267 + 30.0402i) q^{4} +(-61.0162 + 35.2277i) q^{5} +(181.157 + 104.591i) q^{7} +(46.1351 - 175.042i) q^{8} +(397.087 + 34.1946i) q^{10} +(-75.3585 + 130.525i) q^{11} +(-210.949 - 365.375i) q^{13} +(-501.553 - 1071.76i) q^{14} +(-780.825 + 662.486i) q^{16} +662.619i q^{17} -624.161i q^{19} +(-1731.05 - 1444.49i) q^{20} +(772.212 - 361.372i) q^{22} +(-1186.88 - 2055.74i) q^{23} +(919.485 - 1592.59i) q^{25} +(-204.763 + 2377.82i) q^{26} +(-1144.38 + 6595.28i) q^{28} +(3944.46 + 2277.34i) q^{29} +(-8615.25 + 4974.02i) q^{31} +(5767.00 - 544.220i) q^{32} +(2145.77 - 3073.39i) q^{34} -14738.0 q^{35} -5944.72 q^{37} +(-2021.23 + 2895.01i) q^{38} +(3351.33 + 12305.6i) q^{40} +(-10531.7 + 6080.46i) q^{41} +(-15161.2 - 8753.33i) q^{43} +(-4751.94 - 824.530i) q^{44} +(-1152.08 + 13378.5i) q^{46} +(-9291.01 + 16092.5i) q^{47} +(13475.1 + 23339.5i) q^{49} +(-9422.12 + 4409.27i) q^{50} +(8649.87 - 10365.8i) q^{52} -32790.2i q^{53} -10618.8i q^{55} +(26665.5 - 26884.7i) q^{56} +(-10920.7 - 23336.3i) q^{58} +(-1808.33 - 3132.12i) q^{59} +(7916.16 - 13711.2i) q^{61} +(56067.1 + 4828.15i) q^{62} +(-28511.1 - 16151.1i) q^{64} +(25742.7 + 14862.5i) q^{65} +(41652.4 - 24048.0i) q^{67} +(-19905.2 + 7306.48i) q^{68} +(68358.6 + 47726.3i) q^{70} -32192.2 q^{71} -34777.5 q^{73} +(27573.1 + 19250.9i) q^{74} +(18749.9 - 6882.42i) q^{76} +(-27303.5 + 15763.7i) q^{77} +(-73506.0 - 42438.7i) q^{79} +(24305.1 - 67929.1i) q^{80} +(68538.9 + 5902.15i) q^{82} +(7548.53 - 13074.4i) q^{83} +(-23342.6 - 40430.5i) q^{85} +(41975.4 + 89696.8i) q^{86} +(19370.6 + 19212.6i) q^{88} +40174.5i q^{89} -88253.7i q^{91} +(48667.5 - 58322.2i) q^{92} +(95206.5 - 44553.8i) q^{94} +(21987.8 + 38083.9i) q^{95} +(4298.65 - 7445.49i) q^{97} +(13079.9 - 151891. i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−4.63825	−	3.23831i	−0.819934	−	0.572458i
$2$	−4.63825	−	3.23831i	−0.819934	−	0.572458i
$3$		0			0
$3$		0			0
$4$	11.0267	+	30.0402i	0.344583	+	0.938756i
$5$	−61.0162	+	35.2277i	−1.09149	+	0.630173i	−0.933973	−	0.357343i	$-0.883683\pi$
$5$	−61.0162	+	35.2277i	−1.09149	+	0.630173i	−0.157518	+	0.987516i	$0.550349\pi$
$6$		0			0
$7$	181.157	+	104.591i	1.39737	+	0.806770i	0.994116	−	0.108320i	$-0.0345472\pi$
$7$	181.157	+	104.591i	1.39737	+	0.806770i	0.403250	+	0.915090i	$0.367880\pi$
$8$	46.1351	−	175.042i	0.254863	−	0.966977i
$9$		0			0
$10$	397.087	+	34.1946i	1.25570	+	0.108133i
$11$	−75.3585	+	130.525i	−0.187781	+	0.325246i	−0.944510	−	0.328483i	$-0.893463\pi$
$11$	−75.3585	+	130.525i	−0.187781	+	0.325246i	0.756729	+	0.653728i	$0.226796\pi$
$12$		0			0
$13$	−210.949	−	365.375i	−0.346194	−	0.599626i	0.639376	−	0.768895i	$-0.279193\pi$
$13$	−210.949	−	365.375i	−0.346194	−	0.599626i	−0.985570	+	0.169268i	$0.945860\pi$
$14$	−501.553	−	1071.76i	−0.683906	−	1.46143i
$15$		0			0
$16$	−780.825	+	662.486i	−0.762525	+	0.646959i
$17$			662.619i			0.556086i	0.960569	+	0.278043i	$0.0896857\pi$
$17$			662.619i			0.556086i	−0.960569	+	0.278043i	$0.910314\pi$
$18$		0			0
$19$		−	624.161i		−	0.396655i	−0.980136	−	0.198327i	$-0.936449\pi$
$19$		−	624.161i		−	0.396655i	0.980136	−	0.198327i	$-0.0635509\pi$
$20$	−1731.05	−	1444.49i	−0.967688	−	0.807496i
$21$		0			0
$22$	772.212	−	361.372i	0.340157	−	0.159183i
$23$	−1186.88	−	2055.74i	−0.467830	−	0.810306i	0.531494	−	0.847062i	$-0.321631\pi$
$23$	−1186.88	−	2055.74i	−0.467830	−	0.810306i	−0.999324	+	0.0367563i	$0.988297\pi$
$24$		0			0
$25$	919.485	−	1592.59i	0.294235	−	0.509630i
$26$	−204.763	+	2377.82i	−0.0594044	+	0.689836i
$27$		0			0
$28$	−1144.38	+	6595.28i	−0.275850	+	1.58978i
$29$	3944.46	+	2277.34i	0.870950	+	0.502843i	0.867664	−	0.497152i	$-0.165621\pi$
$29$	3944.46	+	2277.34i	0.870950	+	0.502843i	0.00328601	+	0.999995i	$0.498954\pi$
$30$		0			0
$31$	−8615.25	+	4974.02i	−1.61014	+	0.929615i	−0.620804	+	0.783966i	$0.713194\pi$
$31$	−8615.25	+	4974.02i	−1.61014	+	0.929615i	−0.989336	+	0.145649i	$0.953473\pi$
$32$	5767.00	−	544.220i	0.995577	−	0.0939506i
$33$		0			0
$34$	2145.77	−	3073.39i	0.318336	−	0.455953i
$35$	−14738.0			−2.03362
$36$		0			0
$37$	−5944.72			−0.713883			−0.356941	−	0.934127i	$-0.616180\pi$
$37$	−5944.72			−0.713883			−0.356941	+	0.934127i	$0.616180\pi$
$38$	−2021.23	+	2895.01i	−0.227068	+	0.325231i
$39$		0			0
$40$	3351.33	+	12305.6i	0.331182	+	1.21605i
$41$	−10531.7	+	6080.46i	−0.978447	+	0.564907i	−0.901801	−	0.432151i	$-0.857755\pi$
$41$	−10531.7	+	6080.46i	−0.978447	+	0.564907i	−0.0766464	+	0.997058i	$0.524421\pi$
$42$		0			0
$43$	−15161.2	−	8753.33i	−1.25044	−	0.721941i	−0.279243	−	0.960221i	$-0.590083\pi$
$43$	−15161.2	−	8753.33i	−1.25044	−	0.721941i	−0.971197	+	0.238279i	$0.923417\pi$
$44$	−4751.94	−	824.530i	−0.370032	−	0.0642059i
$45$		0			0
$46$	−1152.08	+	13378.5i	−0.0802762	+	0.932210i
$47$	−9291.01	+	16092.5i	−0.613505	+	1.06262i	0.377139	+	0.926156i	$0.376908\pi$
$47$	−9291.01	+	16092.5i	−0.613505	+	1.06262i	−0.990645	+	0.136466i	$0.956426\pi$
$48$		0			0
$49$	13475.1	+	23339.5i	0.801755	+	1.38868i
$50$	−9422.12	+	4409.27i	−0.532995	+	0.249426i
$51$		0			0
$52$	8649.87	−	10365.8i	0.443610	−	0.531613i
$53$		−	32790.2i		−	1.60345i	−0.597696	−	0.801723i	$-0.703917\pi$
$53$		−	32790.2i		−	1.60345i	0.597696	−	0.801723i	$-0.296083\pi$
$54$		0			0
$55$		−	10618.8i		−	0.473337i
$56$	26665.5	−	26884.7i	1.13626	−	1.14561i
$57$		0			0
$58$	−10920.7	−	23336.3i	−0.426265	−	0.910880i
$59$	−1808.33	−	3132.12i	−0.0676312	−	0.117141i	0.830227	−	0.557426i	$-0.188211\pi$
$59$	−1808.33	−	3132.12i	−0.0676312	−	0.117141i	−0.897858	+	0.440285i	$0.854877\pi$
$60$		0			0
$61$	7916.16	−	13711.2i	0.272389	−	0.471792i	−0.697084	−	0.716990i	$-0.745520\pi$
$61$	7916.16	−	13711.2i	0.272389	−	0.471792i	0.969473	+	0.245198i	$0.0788528\pi$
$62$	56067.1	+	4828.15i	1.85237	+	0.159515i
$63$		0			0
$64$	−28511.1	−	16151.1i	−0.870090	−	0.492893i
$65$	25742.7	+	14862.5i	0.755736	+	0.436324i
$66$		0			0
$67$	41652.4	−	24048.0i	1.13358	−	0.654474i	0.188749	−	0.982025i	$-0.439557\pi$
$67$	41652.4	−	24048.0i	1.13358	−	0.654474i	0.944833	+	0.327552i	$0.106224\pi$
$68$	−19905.2	+	7306.48i	−0.522028	+	0.191618i
$69$		0			0
$70$	68358.6	+	47726.3i	1.66743	+	1.16416i
$71$	−32192.2			−0.757887			−0.378944	−	0.925420i	$-0.623713\pi$
$71$	−32192.2			−0.757887			−0.378944	+	0.925420i	$0.623713\pi$
$72$		0			0
$73$	−34777.5			−0.763820			−0.381910	−	0.924200i	$-0.624734\pi$
$73$	−34777.5			−0.763820			−0.381910	+	0.924200i	$0.624734\pi$
$74$	27573.1	+	19250.9i	0.585337	+	0.408668i
$75$		0			0
$76$	18749.9	−	6882.42i	0.372362	−	0.136681i
$77$	−27303.5	+	15763.7i	−0.524797	+	0.302991i
$78$		0			0
$79$	−73506.0	−	42438.7i	−1.32512	−	0.765058i	−0.340579	−	0.940216i	$-0.610623\pi$
$79$	−73506.0	−	42438.7i	−1.32512	−	0.765058i	−0.984540	+	0.175158i	$0.943956\pi$
$80$	24305.1	−	67929.1i	0.424593	−	1.18667i
$81$		0			0
$82$	68538.9	+	5902.15i	1.12565	+	0.0969338i
$83$	7548.53	−	13074.4i	0.120273	−	0.208318i	−0.799602	−	0.600530i	$-0.794956\pi$
$83$	7548.53	−	13074.4i	0.120273	−	0.208318i	0.919875	+	0.392211i	$0.128290\pi$
$84$		0			0
$85$	−23342.6	−	40430.5i	−0.350430	−	0.606962i
$86$	41975.4	+	89696.8i	0.611996	+	1.30777i
$87$		0			0
$88$	19370.6	+	19212.6i	0.266647	+	0.264473i
$89$			40174.5i			0.537620i	0.963193	+	0.268810i	$0.0866303\pi$
$89$			40174.5i			0.537620i	−0.963193	+	0.268810i	$0.913370\pi$
$90$		0			0
$91$		−	88253.7i		−	1.11720i
$92$	48667.5	−	58322.2i	0.599473	−	0.718396i
$93$		0			0
$94$	95206.5	−	44553.8i	1.11134	−	0.520074i
$95$	21987.8	+	38083.9i	0.249961	+	0.432945i
$96$		0			0
$97$	4298.65	−	7445.49i	0.0463877	−	0.0803459i	−0.841899	−	0.539635i	$-0.818562\pi$
$97$	4298.65	−	7445.49i	0.0463877	−	0.0803459i	0.888287	+	0.459289i	$0.151896\pi$
$98$	13079.9	−	151891.i	0.137575	−	1.59760i
$99$		0			0
$100$	57980.7	+	10060.5i	0.579807	+	0.100605i
$101$	5537.77	+	3197.23i	0.0540171	+	0.0311868i	0.526765	−	0.850011i	$-0.323405\pi$
$101$	5537.77	+	3197.23i	0.0540171	+	0.0311868i	−0.472748	+	0.881198i	$0.656738\pi$
$102$		0			0
$103$	−74198.4	+	42838.4i	−0.689130	+	0.397869i	−0.803286	−	0.595593i	$-0.796917\pi$
$103$	−74198.4	+	42838.4i	−0.689130	+	0.397869i	0.114156	+	0.993463i	$0.463584\pi$
$104$	−73688.0	+	20068.3i	−0.668057	+	0.181940i
$105$		0			0
$106$	−106185.	+	152089.i	−0.917905	+	1.31472i
$107$	10199.1			0.0861200			0.0430600	−	0.999072i	$-0.486289\pi$
$107$	10199.1			0.0861200			0.0430600	+	0.999072i	$0.486289\pi$
$108$		0			0
$109$	30565.5			0.246414			0.123207	−	0.992381i	$-0.460682\pi$
$109$	30565.5			0.246414			0.123207	+	0.992381i	$0.460682\pi$
$110$	−34387.1	+	49252.8i	−0.270966	+	0.388105i
$111$		0			0
$112$	−210742.	+	38346.7i	−1.58747	+	0.288857i
$113$	55820.3	−	32227.9i	0.411241	−	0.237430i	−0.280082	−	0.959976i	$-0.590362\pi$
$113$	55820.3	−	32227.9i	0.411241	−	0.237430i	0.691323	+	0.722546i	$0.257028\pi$
$114$		0			0
$115$	144838.	+	83622.4i	1.02126	+	0.589628i
$116$	−24917.3	+	143604.i	−0.171932	+	0.990880i
$117$		0			0
$118$	−1755.30	+	20383.5i	−0.0116050	+	0.134764i
$119$	−69304.0	+	120038.i	−0.448633	+	0.777055i
$120$		0			0
$121$	69167.7	+	119802.i	0.429477	+	0.743876i
$122$	−81118.2	+	37960.9i	−0.493422	+	0.230907i
$123$		0			0
$124$	−244418.	−	203957.i	−1.42751	−	1.19120i
$125$		−	90607.8i		−	0.518670i
$126$		0			0
$127$			142174.i			0.782189i	0.920350	+	0.391095i	$0.127904\pi$
$127$			142174.i			0.782189i	−0.920350	+	0.391095i	$0.872096\pi$
$128$	79939.2	+	167241.i	0.431256	+	0.902230i
$129$		0			0
$130$	−71271.3	−	152299.i	−0.369876	−	0.790384i
$131$	−44178.9	−	76520.1i	−0.224925	−	0.389581i	0.731372	−	0.681978i	$-0.238880\pi$
$131$	−44178.9	−	76520.1i	−0.224925	−	0.389581i	−0.956297	+	0.292398i	$0.905547\pi$
$132$		0			0
$133$	65281.7	−	113071.i	0.320009	−	0.554272i
$134$	−271069.	−	23342.8i	−1.30412	−	0.112303i
$135$		0			0
$136$	115986.	+	30570.0i	0.537722	+	0.141725i
$137$	88390.4	+	51032.2i	0.402350	+	0.232297i	0.687497	−	0.726187i	$-0.258709\pi$
$137$	88390.4	+	51032.2i	0.402350	+	0.232297i	−0.285148	+	0.958484i	$0.592043\pi$
$138$		0			0
$139$	−78817.2	+	45505.1i	−0.346006	+	0.199767i	−0.662925	−	0.748686i	$-0.730685\pi$
$139$	−78817.2	+	45505.1i	−0.346006	+	0.199767i	0.316919	+	0.948453i	$0.397352\pi$
$140$	−162511.	−	442733.i	−0.700751	−	1.90907i
$141$		0			0
$142$	149315.	+	104248.i	0.621418	+	0.433859i
$143$	63587.4			0.260034
$144$		0			0
$145$	−320902.			−1.26751
$146$	161307.	+	112620.i	0.626282	+	0.437255i
$147$		0			0
$148$	−65550.4	−	178580.i	−0.245992	−	0.670162i
$149$	−398601.	+	230133.i	−1.47087	+	0.849205i	−0.999465	−	0.0327141i	$-0.989585\pi$
$149$	−398601.	+	230133.i	−1.47087	+	0.849205i	−0.471401	+	0.881919i	$0.656252\pi$
$150$		0			0
$151$	157479.	+	90920.8i	0.562059	+	0.324505i	0.753971	−	0.656907i	$-0.228136\pi$
$151$	157479.	+	90920.8i	0.562059	+	0.324505i	−0.191913	+	0.981412i	$0.561469\pi$
$152$	−109254.	−	28795.7i	−0.383556	−	0.101092i
$153$		0			0
$154$	177688.	+	15301.4i	0.603748	+	0.0519911i
$155$	350447.	−	606991.i	1.17164	−	2.02933i
$156$		0			0
$157$	181731.	+	314767.i	0.588408	+	1.01915i	0.994441	+	0.105295i	$0.0335786\pi$
$157$	181731.	+	314767.i	0.588408	+	1.01915i	−0.406033	+	0.913859i	$0.633088\pi$
$158$	203509.	+	434877.i	0.648547	+	1.38587i
$159$		0			0
$160$	−332709.	+	236364.i	−1.02746	+	0.729932i
$161$		−	496549.i		−	1.50972i
$162$		0			0
$163$			342002.i			1.00823i	0.863636	+	0.504115i	$0.168181\pi$
$163$			342002.i			1.00823i	−0.863636	+	0.504115i	$0.831819\pi$
$164$	−298787.	−	249326.i	−0.867466	−	0.723866i
$165$		0			0
$166$	−77351.0	+	36198.0i	−0.217869	+	0.101956i
$167$	−8208.18	−	14217.0i	−0.0227749	−	0.0394472i	0.854413	−	0.519594i	$-0.173917\pi$
$167$	−8208.18	−	14217.0i	−0.0227749	−	0.0394472i	−0.877188	+	0.480147i	$0.840583\pi$
$168$		0			0
$169$	96647.2	−	167398.i	0.260299	−	0.450851i
$170$	−22658.0	+	263117.i	−0.0601312	+	0.698276i
$171$		0			0
$172$	95773.9	−	551965.i	0.246846	−	1.42263i
$173$	60123.0	+	34712.1i	0.152730	+	0.0881790i	0.574418	−	0.818562i	$-0.305229\pi$
$173$	60123.0	+	34712.1i	0.152730	+	0.0881790i	−0.421687	+	0.906741i	$0.638562\pi$
$174$		0			0
$175$	333142.	−	192340.i	0.822308	−	0.474760i
$176$	−27629.1	−	151841.i	−0.0672333	−	0.369494i
$177$		0			0
$178$	130097.	−	186339.i	0.307765	−	0.440813i
$179$	146989.			0.342888			0.171444	−	0.985194i	$-0.445157\pi$
$179$	146989.			0.342888			0.171444	+	0.985194i	$0.445157\pi$
$180$		0			0
$181$	238346.			0.540768			0.270384	−	0.962752i	$-0.412849\pi$
$181$	238346.			0.540768			0.270384	+	0.962752i	$0.412849\pi$
$182$	−285793.	+	409343.i	−0.639548	+	0.916027i
$183$		0			0
$184$	−414597.	+	112912.i	−0.902780	+	0.245865i
$185$	362724.	−	209419.i	0.779197	−	0.449869i
$186$		0			0
$187$	−86488.2	−	49934.0i	−0.180864	−	0.104422i
$188$	−585871.	−	101657.i	−1.20895	−	0.209770i
$189$		0			0
$190$	21343.0	−	247846.i	0.0428914	−	0.498079i
$191$	−223937.	+	387870.i	−0.444162	+	0.769312i	−0.997993	−	0.0633172i	$-0.979832\pi$
$191$	−223937.	+	387870.i	−0.444162	+	0.769312i	0.553831	+	0.832629i	$0.313165\pi$
$192$		0			0
$193$	−29922.0	−	51826.4i	−0.0578226	−	0.100152i	0.835665	−	0.549239i	$-0.185082\pi$
$193$	−29922.0	−	51826.4i	−0.0578226	−	0.100152i	−0.893488	+	0.449088i	$0.851749\pi$
$194$	−44049.0	+	20613.6i	−0.0840295	+	0.0393233i
$195$		0			0
$196$	−552539.	+	662152.i	−1.02736	+	1.23117i
$197$			834312.i			1.53166i	0.643042	+	0.765831i	$0.277672\pi$
$197$			834312.i			1.53166i	−0.643042	+	0.765831i	$0.722328\pi$
$198$		0			0
$199$			413079.i			0.739435i	0.929144	+	0.369718i	$0.120546\pi$
$199$			413079.i			0.739435i	−0.929144	+	0.369718i	$0.879454\pi$
$200$	−236350.	−	234423.i	−0.417811	−	0.414404i
$201$		0			0
$202$	−15331.9	−	32762.6i	−0.0264373	−	0.0564936i
$203$	476378.	+	825112.i	0.811357	+	1.40531i
$204$		0			0
$205$	428402.	−	742013.i	0.711978	−	1.23318i
$206$	482875.	+	41582.2i	0.792805	+	0.0682714i
$207$		0			0
$208$	406771.	+	145543.i	0.651915	+	0.233256i
$209$	81468.5	+	47035.9i	0.129010	+	0.0744841i
$210$		0			0
$211$	416461.	−	240444.i	0.643973	−	0.371798i	−0.142170	−	0.989842i	$-0.545408\pi$
$211$	416461.	−	240444.i	0.643973	−	0.371798i	0.786143	+	0.618044i	$0.212075\pi$
$212$	985023.	−	361567.i	1.50524	−	0.552521i
$213$		0			0
$214$	−47306.1	−	33028.0i	−0.0706127	−	0.0493001i
$215$	1.23344e6			1.81979
$216$		0			0
$217$	−2.08095e6			−2.99994
$218$	−141770.	−	98980.7i	−0.202043	−	0.141062i
$219$		0			0
$220$	318992.	−	117090.i	0.444348	−	0.163104i
$221$	242105.	−	139779.i	0.333443	−	0.192514i
$222$		0			0
$223$	202627.	+	116987.i	0.272858	+	0.157534i	0.630186	−	0.776445i	$-0.282979\pi$
$223$	202627.	+	116987.i	0.272858	+	0.157534i	−0.357328	+	0.933979i	$0.616312\pi$
$224$	1.10165e6	+	504587.i	1.46698	+	0.671918i
$225$		0			0
$226$	−363272.	−	31282.8i	−0.473109	−	0.0407412i
$227$	−60951.8	+	105572.i	−0.0785094	+	0.135982i	−0.902607	−	0.430466i	$-0.858349\pi$
$227$	−60951.8	+	105572.i	−0.0785094	+	0.135982i	0.824098	+	0.566448i	$0.191683\pi$
$228$		0			0
$229$	460471.	+	797559.i	0.580248	+	1.00502i	0.995450	+	0.0952893i	$0.0303776\pi$
$229$	460471.	+	797559.i	0.580248	+	1.00502i	−0.415202	+	0.909729i	$0.636289\pi$
$230$	−401000.	−	856892.i	−0.499833	−	1.06809i
$231$		0			0
$232$	580607.	−	585380.i	0.708210	−	0.714033i
$233$			564143.i			0.680768i	0.940287	+	0.340384i	$0.110557\pi$
$233$			564143.i			0.680768i	−0.940287	+	0.340384i	$0.889443\pi$
$234$		0			0
$235$		−	1.30920e6i		−	1.54646i
$236$	74149.5	−	88859.4i	0.0866619	−	0.103854i
$237$		0			0
$238$	710170.	−	332338.i	0.812681	−	0.380310i
$239$	−812725.	−	1.40768e6i	−0.920341	−	1.59408i	−0.798887	−	0.601481i	$-0.794578\pi$
$239$	−812725.	−	1.40768e6i	−0.920341	−	1.59408i	−0.121454	−	0.992597i	$-0.538756\pi$
$240$		0			0
$241$	595736.	−	1.03184e6i	0.660710	−	1.14438i	−0.319719	−	0.947512i	$-0.603589\pi$
$241$	595736.	−	1.03184e6i	0.660710	−	1.14438i	0.980429	−	0.196871i	$-0.0630781\pi$
$242$	67139.3	−	779658.i	0.0736950	−	0.855787i
$243$		0			0
$244$	499175.	+	86614.1i	0.536758	+	0.0931352i
$245$	−1.64440e6	−	949394.i	−1.75022	−	1.01049i
$246$		0			0
$247$	−228053.	+	131666.i	−0.237845	+	0.137320i
$248$	473195.	+	1.73750e6i	0.488552	+	1.79389i
$249$		0			0
$250$	−293416.	+	420262.i	−0.296917	+	0.425275i
$251$	−1.48383e6			−1.48662			−0.743311	−	0.668946i	$-0.766746\pi$
$251$	−1.48383e6			−1.48662			−0.743311	+	0.668946i	$0.766746\pi$
$252$		0			0
$253$	357767.			0.351398
$254$	460405.	−	659440.i	0.447771	−	0.641344i
$255$		0			0
$256$	170800.	−	1.03457e6i	0.162887	−	0.986645i
$257$	1.18845e6	−	686154.i	1.12240	−	0.648020i	0.180390	−	0.983595i	$-0.442264\pi$
$257$	1.18845e6	−	686154.i	1.12240	−	0.648020i	0.942014	+	0.335575i	$0.108931\pi$
$258$		0			0
$259$	−1.07693e6	−	621764.i	−0.997556	−	0.575939i
$260$	−162617.	+	937199.i	−0.149188	+	0.859802i
$261$		0			0
$262$	−42883.3	+	497984.i	−0.0385954	+	0.448190i
$263$	−85328.1	+	147793.i	−0.0760681	+	0.131754i	−0.901550	−	0.432674i	$-0.857570\pi$
$263$	−85328.1	+	147793.i	−0.0760681	+	0.131754i	0.825482	+	0.564428i	$0.190903\pi$
$264$		0			0
$265$	1.15512e6	+	2.00073e6i	1.01045	+	1.75015i
$266$	−668952.	+	313050.i	−0.579684	+	0.271275i
$267$		0			0
$268$	1.18169e6	+	986076.i	1.00500	+	0.838636i
$269$			28534.0i			0.0240427i	0.999928	+	0.0120213i	$0.00382660\pi$
$269$			28534.0i			0.0240427i	−0.999928	+	0.0120213i	$0.996173\pi$
$270$		0			0
$271$		−	485769.i		−	0.401797i	−0.979612	−	0.200899i	$-0.935614\pi$
$271$		−	485769.i		−	0.401797i	0.979612	−	0.200899i	$-0.0643862\pi$
$272$	−438976.	−	517390.i	−0.359765	−	0.424029i
$273$		0			0
$274$	−244718.	−	522936.i	−0.196920	−	0.420796i
$275$	138582.	+	240031.i	0.110503	+	0.191397i
$276$		0			0
$277$	−696662.	+	1.20665e6i	−0.545535	+	0.944894i	0.453038	+	0.891491i	$0.350340\pi$
$277$	−696662.	+	1.20665e6i	−0.545535	+	0.944894i	−0.998573	+	0.0534030i	$0.982993\pi$
$278$	512934.	+	44170.7i	0.398061	+	0.0342785i
$279$		0			0
$280$	−679940.	+	2.57977e6i	−0.518293	+	1.96646i
$281$	−691310.	−	399128.i	−0.522285	−	0.301541i	0.215584	−	0.976485i	$-0.430834\pi$
$281$	−691310.	−	399128.i	−0.522285	−	0.301541i	−0.737869	+	0.674944i	$0.764168\pi$
$282$		0			0
$283$	−1.50272e6	+	867593.i	−1.11535	+	0.643947i	−0.940209	−	0.340597i	$-0.889371\pi$
$283$	−1.50272e6	+	867593.i	−1.11535	+	0.643947i	−0.175139	+	0.984544i	$0.556038\pi$
$284$	−354973.	−	967059.i	−0.261155	−	0.711471i
$285$		0			0
$286$	−294934.	−	205916.i	−0.213211	−	0.148859i
$287$	−2.54385e6			−1.82300
$288$		0			0
$289$	980793.			0.690769
$290$	1.48842e6	+	1.03918e6i	1.03928	+	0.725597i
$291$		0			0
$292$	−383480.	−	1.04472e6i	−0.263200	−	0.717040i
$293$	376330.	−	217274.i	0.256094	−	0.147856i	−0.366457	−	0.930435i	$-0.619429\pi$
$293$	376330.	−	217274.i	0.256094	−	0.147856i	0.622551	+	0.782579i	$0.286096\pi$
$294$		0			0
$295$	220675.	+	127407.i	0.147638	+	0.0852387i
$296$	−274260.	+	1.04057e6i	−0.181942	+	0.690308i
$297$		0			0
$298$	2.59405e6	+	223384.i	1.69215	+	0.145717i
$299$	−500745.	+	867315.i	−0.323920	+	0.561047i
$300$		0			0
$301$	−1.83104e6	−	3.17145e6i	−1.16488	−	2.01763i
$302$	−435999.	−	931681.i	−0.275086	−	0.587827i
$303$		0			0
$304$	413498.	+	487361.i	0.256620	+	0.302459i
$305$			1.11547e6i			0.686609i
$306$		0			0
$307$			48971.1i			0.0296547i	0.999890	+	0.0148274i	$0.00471987\pi$
$307$			48971.1i			0.0296547i	−0.999890	+	0.0148274i	$0.995280\pi$
$308$	−774610.	−	646380.i	−0.465271	−	0.388250i
$309$		0			0
$310$	−3.59109e6	+	1.68052e6i	−2.12237	+	0.993206i
$311$	36344.9	+	62951.1i	0.0213080	+	0.0369065i	0.876483	−	0.481433i	$-0.159884\pi$
$311$	36344.9	+	62951.1i	0.0213080	+	0.0369065i	−0.855175	+	0.518340i	$0.826550\pi$
$312$		0			0
$313$	−319768.	+	553854.i	−0.184490	+	0.319547i	−0.943405	−	0.331644i	$-0.892397\pi$
$313$	−319768.	+	553854.i	−0.184490	+	0.319547i	0.758914	+	0.651191i	$0.225730\pi$
$314$	176401.	−	2.04847e6i	0.100967	−	1.17248i
$315$		0			0
$316$	464340.	−	2.67609e6i	0.261588	−	1.50759i
$317$	2.43119e6	+	1.40365e6i	1.35885	+	0.784531i	0.989469	−	0.144748i	$-0.0462373\pi$
$317$	2.43119e6	+	1.40365e6i	1.35885	+	0.784531i	0.369379	+	0.929279i	$0.379571\pi$
$318$		0			0
$319$	−594498.	+	343234.i	−0.327095	+	0.188848i
$320$	2.30861e6	−	18902.0i	1.26030	−	0.0103189i
$321$		0			0
$322$	−1.60798e6	+	2.30312e6i	−0.864254	+	1.23787i
$323$	413581.			0.220574
$324$		0			0
$325$	−775859.			−0.407450
$326$	1.10751e6	−	1.58629e6i	0.577170	−	0.826683i
$327$		0			0
$328$	578454.	+	2.12400e6i	0.296882	+	1.09011i
$329$	−3.36626e6	+	1.94351e6i	−1.71458	+	0.989915i
$330$		0			0
$331$	−2.68009e6	−	1.54735e6i	−1.34456	−	0.776280i	−0.357084	−	0.934072i	$-0.616229\pi$
$331$	−2.68009e6	−	1.54735e6i	−1.34456	−	0.776280i	−0.987472	+	0.157793i	$0.949562\pi$
$332$	475994.	+	82591.7i	0.237004	+	0.0411236i
$333$		0			0
$334$	−7967.47	+	92522.6i	−0.00390800	+	0.0453818i
$335$	−1.69431e6	+	2.93464e6i	−0.824863	+	1.42870i
$336$		0			0
$337$	66234.5	+	114721.i	0.0317694	+	0.0550263i	0.881473	−	0.472234i	$-0.156552\pi$
$337$	66234.5	+	114721.i	0.0317694	+	0.0550263i	−0.849704	+	0.527261i	$0.823219\pi$
$338$	−990360.	+	463459.i	−0.471521	+	0.220658i
$339$		0			0
$340$	957149.	−	1.14703e6i	0.449037	−	0.538117i
$341$		−	1.49934e6i		−	0.698255i
$342$		0			0
$343$			2.12177e6i			0.973786i
$344$	−2.23166e6	+	2.25001e6i	−1.01679	+	1.02515i
$345$		0			0
$346$	−166457.	−	355700.i	−0.0747501	−	0.159733i
$347$	−840739.	−	1.45620e6i	−0.374833	−	0.649229i	0.615469	−	0.788161i	$-0.288967\pi$
$347$	−840739.	−	1.45620e6i	−0.374833	−	0.649229i	−0.990302	+	0.138932i	$0.955633\pi$
$348$		0			0
$349$	−8603.35	+	14901.4i	−0.00378097	+	0.00654884i	−0.867910	−	0.496722i	$-0.834537\pi$
$349$	−8603.35	+	14901.4i	−0.00378097	+	0.00654884i	0.864129	+	0.503271i	$0.167870\pi$
$350$	−2.16805e6	−	186699.i	−0.946019	−	0.0814653i
$351$		0			0
$352$	−363558.	+	793748.i	−0.156393	+	0.341449i
$353$	1.66268e6	+	959951.i	0.710187	+	0.410027i	0.811130	−	0.584865i	$-0.198853\pi$
$353$	1.66268e6	+	959951.i	0.710187	+	0.410027i	−0.100943	+	0.994892i	$0.532186\pi$
$354$		0			0
$355$	1.96425e6	−	1.13406e6i	0.827227	−	0.477600i
$356$	−1.20685e6	+	442991.i	−0.504694	+	0.185255i
$357$		0			0
$358$	−681772.	−	475997.i	−0.281146	−	0.196289i
$359$	207171.			0.0848386			0.0424193	−	0.999100i	$-0.486493\pi$
$359$	207171.			0.0848386			0.0424193	+	0.999100i	$0.486493\pi$
$360$		0			0
$361$	2.08652e6			0.842665
$362$	−1.10551e6	−	771839.i	−0.443394	−	0.309567i
$363$		0			0
$364$	2.65116e6	−	973145.i	1.04877	−	0.384967i
$365$	2.12199e6	−	1.22513e6i	0.833703	−	0.481338i
$366$		0			0
$367$	1.53243e6	+	884750.i	0.593904	+	0.342891i	0.766640	−	0.642078i	$-0.221927\pi$
$367$	1.53243e6	+	884750.i	0.593904	+	0.342891i	−0.172736	+	0.984968i	$0.555261\pi$
$368$	2.28865e6	+	818881.i	0.880967	+	0.315211i
$369$		0			0
$370$	−2.36057e6	−	203277.i	−0.896421	−	0.0771942i
$371$	3.42956e6	−	5.94017e6i	1.29361	−	2.24060i
$372$		0			0
$373$	171024.	+	296222.i	0.0636481	+	0.110242i	0.896093	−	0.443865i	$-0.146393\pi$
$373$	171024.	+	296222.i	0.0636481	+	0.110242i	−0.832445	+	0.554107i	$0.813060\pi$
$374$	239452.	+	511682.i	0.0885196	+	0.189156i
$375$		0			0
$376$	2.38822e6	+	2.36874e6i	0.871172	+	0.864068i
$377$		−	1.92161e6i		−	0.696326i
$378$		0			0
$379$		−	1.91370e6i		−	0.684345i	−0.939637	−	0.342172i	$-0.888837\pi$
$379$		−	1.91370e6i		−	0.684345i	0.939637	−	0.342172i	$-0.111163\pi$
$380$	−901597.	+	1.08046e6i	−0.320297	+	0.383838i
$381$		0			0
$382$	2.29472e6	−	1.07386e6i	0.804583	−	0.376521i
$383$	1.50852e6	+	2.61283e6i	0.525477	+	0.910153i	0.999560	+	0.0296726i	$0.00944646\pi$
$383$	1.50852e6	+	2.61283e6i	0.525477	+	0.910153i	−0.474083	+	0.880480i	$0.657220\pi$
$384$		0			0
$385$	1.11064e6	−	1.92368e6i	0.381874	−	0.661425i
$386$	−29044.5	+	337280.i	−0.00992192	+	0.115219i
$387$		0			0
$388$	271064.	+	47033.4i	0.0914096	+	0.0158609i
$389$	−2.16211e6	−	1.24829e6i	−0.724442	−	0.418257i	0.0919434	−	0.995764i	$-0.470692\pi$
$389$	−2.16211e6	−	1.24829e6i	−0.724442	−	0.418257i	−0.816385	+	0.577507i	$0.804025\pi$
$390$		0			0
$391$	1.36217e6	−	786451.i	0.450599	−	0.260154i
$392$	4.70706e6	−	1.28193e6i	1.54716	−	0.421356i
$393$		0			0
$394$	2.70176e6	−	3.86975e6i	0.876812	−	1.25586i
$395$	5.98008e6			1.92848
$396$		0			0
$397$	−160060.			−0.0509692			−0.0254846	−	0.999675i	$-0.508113\pi$
$397$	−160060.			−0.0509692			−0.0254846	+	0.999675i	$0.508113\pi$
$398$	1.33768e6	−	1.91596e6i	0.423296	−	0.606288i
$399$		0			0
$400$	337115.	+	1.85268e6i	0.105349	+	0.578964i
$401$	−2.51150e6	+	1.45002e6i	−0.779960	+	0.450310i	−0.836416	−	0.548095i	$-0.815353\pi$
$401$	−2.51150e6	+	1.45002e6i	−0.779960	+	0.450310i	0.0564561	+	0.998405i	$0.482020\pi$
$402$		0			0
$403$	3.63476e6	+	2.09853e6i	1.11484	+	0.643655i
$404$	−34982.3	+	201610.i	−0.0106634	+	0.0614553i
$405$		0			0
$406$	462408.	−	5.36973e6i	0.139223	−	1.61673i
$407$	447985.	−	775933.i	0.134053	−	0.232187i
$408$		0			0
$409$	−565751.	−	979909.i	−0.167231	−	0.289653i	0.770214	−	0.637785i	$-0.220149\pi$
$409$	−565751.	−	979909.i	−0.167231	−	0.289653i	−0.937445	+	0.348133i	$0.886816\pi$
$410$	−4.38990e6	+	2.05434e6i	−1.28972	+	0.603550i
$411$		0			0
$412$	−2.10504e6	−	1.75657e6i	−0.610965	−	0.509826i
$413$		−	756540.i		−	0.218251i
$414$		0			0
$415$			1.06367e6i			0.303170i
$416$	−1.41539e6	−	1.99231e6i	−0.400998	−	0.564449i
$417$		0			0
$418$	−225554.	−	481984.i	−0.0631408	−	0.134925i
$419$	257000.	+	445137.i	0.0715152	+	0.123868i	0.899566	−	0.436786i	$-0.143883\pi$
$419$	257000.	+	445137.i	0.0715152	+	0.123868i	−0.828050	+	0.560654i	$0.810550\pi$
$420$		0			0
$421$	−3.24121e6	+	5.61394e6i	−0.891255	+	1.54370i	−0.0528829	+	0.998601i	$0.516841\pi$
$421$	−3.24121e6	+	5.61394e6i	−0.891255	+	1.54370i	−0.838372	+	0.545098i	$0.816492\pi$
$422$	−2.71028e6	−	233392.i	−0.740854	−	0.0637978i
$423$		0			0
$424$	−5.73965e6	−	1.51278e6i	−1.55050	−	0.408658i
$425$	1.05528e6	+	609268.i	0.283398	+	0.163620i
$426$		0			0
$427$	2.86814e6	−	1.65592e6i	0.761255	−	0.439511i
$428$	112463.	+	306384.i	0.0296755	+	0.0808457i
$429$		0			0
$430$	−5.72100e6	−	3.99426e6i	−1.49211	−	1.04175i
$431$	−680530.			−0.176463			−0.0882316	−	0.996100i	$-0.528122\pi$
$431$	−680530.			−0.176463			−0.0882316	+	0.996100i	$0.528122\pi$
$432$		0			0
$433$	−1.78685e6			−0.458003			−0.229002	−	0.973426i	$-0.573546\pi$
$433$	−1.78685e6			−0.458003			−0.229002	+	0.973426i	$0.573546\pi$
$434$	9.65197e6	+	6.73877e6i	2.45975	+	1.71734i
$435$		0			0
$436$	337036.	+	918193.i	0.0849102	+	0.231323i
$437$	−1.28311e6	+	740806.i	−0.321412	+	0.185567i
$438$		0			0
$439$	5.72585e6	+	3.30582e6i	1.41801	+	0.818687i	0.996124	−	0.0879624i	$-0.0280355\pi$
$439$	5.72585e6	+	3.30582e6i	1.41801	+	0.818687i	0.421884	+	0.906650i	$0.361369\pi$
$440$	−1.85874e6	−	489901.i	−0.457706	−	0.120636i
$441$		0			0
$442$	−1.57559e6	−	135680.i	−0.383608	−	0.0330339i
$443$	1.27077e6	−	2.20104e6i	0.307650	−	0.532866i	−0.670198	−	0.742183i	$-0.733791\pi$
$443$	1.27077e6	−	2.20104e6i	0.307650	−	0.532866i	0.977848	+	0.209317i	$0.0671240\pi$
$444$		0			0
$445$	−1.41526e6	−	2.45129e6i	−0.338793	−	0.586807i
$446$	−560996.	−	1.19879e6i	−0.133543	−	0.285367i
$447$		0			0
$448$	−3.47573e6	−	5.90790e6i	−0.818183	−	1.39071i
$449$		−	4.29742e6i		−	1.00599i	−0.864290	−	0.502993i	$-0.832232\pi$
$449$		−	4.29742e6i		−	1.00599i	0.864290	−	0.502993i	$-0.167768\pi$
$450$		0			0
$451$		−	1.83286e6i		−	0.424314i
$452$	1.58364e6	+	1.32149e6i	0.364595	+	0.304240i
$453$		0			0
$454$	624583.	−	292286.i	0.142217	−	0.0665532i
$455$	3.10898e6	+	5.38491e6i	0.704027	+	1.21941i
$456$		0			0
$457$	795252.	−	1.37742e6i	0.178121	−	0.308514i	−0.763116	−	0.646261i	$-0.776332\pi$
$457$	795252.	−	1.37742e6i	0.178121	−	0.308514i	0.941237	+	0.337747i	$0.109665\pi$
$458$	446967.	−	5.19042e6i	0.0995662	−	1.15622i
$459$		0			0
$460$	−914948.	+	5.27304e6i	−0.201605	+	1.16189i
$461$	3.92509e6	+	2.26615e6i	0.860195	+	0.496634i	0.864078	−	0.503359i	$-0.167903\pi$
$461$	3.92509e6	+	2.26615e6i	0.860195	+	0.496634i	−0.00388260	+	0.999992i	$0.501236\pi$
$462$		0			0
$463$	−6.33289e6	+	3.65630e6i	−1.37293	+	0.792664i	−0.991296	−	0.131648i	$-0.957973\pi$
$463$	−6.33289e6	+	3.65630e6i	−1.37293	+	0.792664i	−0.381637	+	0.924312i	$0.624640\pi$
$464$	−4.58864e6	+	834951.i	−0.989440	+	0.180039i
$465$		0			0
$466$	1.82687e6	−	2.61663e6i	0.389711	−	0.558185i
$467$	5.59542e6			1.18724			0.593622	−	0.804744i	$-0.297697\pi$
$467$	5.59542e6			1.18724			0.593622	+	0.804744i	$0.297697\pi$
$468$		0			0
$469$	1.00608e7			2.11204
$470$	−4.23961e6	+	6.07241e6i	−0.885282	+	1.26799i
$471$		0			0
$472$	−631678.	+	172032.i	−0.130509	+	0.0355431i
$473$	2.28505e6	−	1.31928e6i	0.469617	−	0.271133i
$474$		0			0
$475$	−994036.	−	573907.i	−0.202147	−	0.116710i
$476$	−4.37016e6	−	758285.i	−0.884056	−	0.153396i
$477$		0			0
$478$	−788891.	+	9.16103e6i	−0.157924	+	1.83390i
$479$	−3.79751e6	+	6.57748e6i	−0.756241	+	1.30985i	0.188515	+	0.982070i	$0.439633\pi$
$479$	−3.79751e6	+	6.57748e6i	−0.756241	+	1.30985i	−0.944755	+	0.327777i	$0.893701\pi$
$480$		0			0
$481$	1.25403e6	+	2.17205e6i	0.247142	+	0.428063i
$482$	−6.10460e6	+	2.85677e6i	−1.19685	+	0.560090i
$483$		0			0
$484$	−2.83618e6	+	3.39883e6i	−0.550327	+	0.659501i
$485$			605727.i			0.116929i
$486$		0			0
$487$			9.63136e6i			1.84020i	0.391682	+	0.920101i	$0.371893\pi$
$487$			9.63136e6i			1.84020i	−0.391682	+	0.920101i	$0.628107\pi$
$488$	−2.03482e6	−	2.01822e6i	−0.386790	−	0.383636i
$489$		0			0
$490$	4.55269e6	+	9.72860e6i	0.856600	+	1.83046i
$491$	−3.74298e6	−	6.48304e6i	−0.700671	−	1.21360i	−0.968231	−	0.250056i	$-0.919551\pi$
$491$	−3.74298e6	−	6.48304e6i	−0.700671	−	1.21360i	0.267560	−	0.963541i	$-0.413782\pi$
$492$		0			0
$493$	−1.50901e6	+	2.61368e6i	−0.279624	+	0.484323i
$494$	1.48414e6	+	127805.i	0.273627	+	0.0235630i
$495$		0			0
$496$	3.43179e6	−	9.59132e6i	0.626348	−	1.75055i
$497$	−5.83184e6	−	3.36702e6i	−1.05905	−	0.611441i
$498$		0			0
$499$	−983698.	+	567938.i	−0.176852	+	0.102106i	−0.585813	−	0.810446i	$-0.699225\pi$
$499$	−983698.	+	567938.i	−0.176852	+	0.102106i	0.408961	+	0.912552i	$0.365891\pi$
$500$	2.72188e6	−	999103.i	0.486904	−	0.178725i
$501$		0			0
$502$	6.88239e6	+	4.80512e6i	1.21893	+	0.851029i
$503$	−9.15158e6			−1.61278			−0.806391	−	0.591382i	$-0.798583\pi$
$503$	−9.15158e6			−1.61278			−0.806391	+	0.591382i	$0.798583\pi$
$504$		0			0
$505$	−450525.			−0.0786123
$506$	−1.65941e6	−	1.15856e6i	−0.288123	−	0.201160i
$507$		0			0
$508$	−4.27094e6	+	1.56771e6i	−0.734285	+	0.269530i
$509$	−659417.	+	380714.i	−0.112815	+	0.0651336i	−0.555346	−	0.831620i	$-0.687414\pi$
$509$	−659417.	+	380714.i	−0.112815	+	0.0651336i	0.442531	+	0.896753i	$0.354081\pi$
$510$		0			0
$511$	−6.30019e6	−	3.63741e6i	−1.06734	−	0.616227i
$512$	−4.14248e6	+	4.24550e6i	−0.698370	+	0.715737i
$513$		0			0
$514$	−7.73432e6	−	666032.i	−1.29126	−	0.111195i
$515$	3.01820e6	−	5.22768e6i	0.501453	−	0.868542i
$516$		0			0
$517$	−1.40031e6	−	2.42541e6i	−0.230409	−	0.399080i
$518$	2.98159e6	+	6.37133e6i	0.488229	+	1.04329i
$519$		0			0
$520$	3.78920e6	−	3.82035e6i	0.614525	−	0.619577i
$521$			8.50821e6i			1.37323i	0.727020	+	0.686616i	$0.240905\pi$
$521$			8.50821e6i			1.37323i	−0.727020	+	0.686616i	$0.759095\pi$
$522$		0			0
$523$		−	8.02433e6i		−	1.28279i	−0.767212	−	0.641394i	$-0.778356\pi$
$523$		−	8.02433e6i		−	1.28279i	0.767212	−	0.641394i	$-0.221644\pi$
$524$	1.81153e6	−	2.17091e6i	0.288216	−	0.345392i
$525$		0			0
$526$	874371.	−	409179.i	0.137794	−	0.0644836i
$527$	−3.29588e6	−	5.70863e6i	−0.516945	−	0.895376i
$528$		0			0
$529$	400790.	−	694188.i	0.0622698	−	0.107854i
$530$	1.12125e6	−	1.30205e7i	0.173385	−	2.01344i
$531$		0			0
$532$	4.11652e6	+	714275.i	0.630596	+	0.109417i
$533$	4.44330e6	+	2.56534e6i	0.677466	+	0.391135i
$534$		0			0
$535$	−622313.	+	359292.i	−0.0939992	+	0.0542705i
$536$	−2.28777e6	−	8.40036e6i	−0.343954	−	1.26295i
$537$		0			0
$538$	92402.1	−	132348.i	0.0137634	−	0.0197134i
$539$	−4.06185e6			−0.602216
$540$		0			0
$541$	−7.93678e6			−1.16587			−0.582937	−	0.812518i	$-0.698096\pi$
$541$	−7.93678e6			−1.16587			−0.582937	+	0.812518i	$0.698096\pi$
$542$	−1.57307e6	+	2.25312e6i	−0.230012	+	0.329447i
$543$		0			0
$544$	360610.	+	3.82132e6i	0.0522446	+	0.553626i
$545$	−1.86499e6	+	1.07675e6i	−0.268959	+	0.155283i
$546$		0			0
$547$	−5.32459e6	−	3.07415e6i	−0.760883	−	0.439296i	0.0687298	−	0.997635i	$-0.478105\pi$
$547$	−5.32459e6	−	3.07415e6i	−0.760883	−	0.439296i	−0.829613	+	0.558339i	$0.811439\pi$
$548$	−558366.	+	3.21798e6i	−0.0794268	+	0.457754i
$549$		0			0
$550$	134518.	−	1.56210e6i	0.0189615	−	0.220192i
$551$	1.42143e6	−	2.46198e6i	0.199455	−	0.345466i
$552$		0			0
$553$	−8.87742e6	−	1.53761e7i	−1.23445	−	2.13813i
$554$	7.13881e6	−	3.34075e6i	0.988215	−	0.462455i
$555$		0			0
$556$	−2.23607e6	−	1.86591e6i	−0.306760	−	0.255979i
$557$			6.19751e6i			0.846407i	0.906035	+	0.423203i	$0.139094\pi$
$557$			6.19751e6i			0.846407i	−0.906035	+	0.423203i	$0.860906\pi$
$558$		0			0
$559$			7.38604e6i			0.999728i
$560$	1.15078e7	−	9.76374e6i	1.55068	−	1.31567i
$561$		0			0
$562$	1.91397e6	+	4.08993e6i	0.255619	+	0.546230i
$563$	744431.	+	1.28939e6i	0.0989814	+	0.171441i	0.911263	−	0.411824i	$-0.135108\pi$
$563$	744431.	+	1.28939e6i	0.0989814	+	0.171441i	−0.812282	+	0.583265i	$0.801775\pi$
$564$		0			0
$565$	−2.27063e6	+	3.93284e6i	−0.299244	+	0.518305i
$566$	9.77950e6	+	842150.i	1.28315	+	0.110497i
$567$		0			0
$568$	−1.48519e6	+	5.63497e6i	−0.193157	+	0.732860i
$569$	−149856.	−	86519.3i	−0.0194041	−	0.0112029i	0.490267	−	0.871573i	$-0.336899\pi$
$569$	−149856.	−	86519.3i	−0.0194041	−	0.0112029i	−0.509671	+	0.860370i	$0.670233\pi$
$570$		0			0
$571$	5.22869e6	−	3.01878e6i	0.671123	−	0.387473i	−0.125379	−	0.992109i	$-0.540015\pi$
$571$	5.22869e6	−	3.01878e6i	0.671123	−	0.387473i	0.796502	+	0.604636i	$0.206681\pi$
$572$	701157.	+	1.91018e6i	0.0896035	+	0.244109i
$573$		0			0
$574$	1.17990e7	+	8.23777e6i	1.49474	+	1.04359i
$575$	−4.36528e6			−0.550608
$576$		0			0
$577$	1.58937e7			1.98740			0.993698	−	0.112090i	$-0.0357546\pi$
$577$	1.58937e7			1.98740			0.993698	+	0.112090i	$0.0357546\pi$
$578$	−4.54916e6	−	3.17611e6i	−0.566385	−	0.395436i
$579$		0			0
$580$	−3.53848e6	−	9.63995e6i	−0.436764	−	1.18988i
$581$	2.73494e6	−	1.57902e6i	0.336130	−	0.194065i
$582$		0			0
$583$	4.27993e6	+	2.47102e6i	0.521514	+	0.301096i
$584$	−1.60446e6	+	6.08751e6i	−0.194669	+	0.738597i
$585$		0			0
$586$	−2.44911e6	−	210902.i	−0.294622	−	0.0253710i
$587$	−7.04599e6	+	1.22040e7i	−0.844008	+	1.46186i	0.0424722	+	0.999098i	$0.486477\pi$
$587$	−7.04599e6	+	1.22040e7i	−0.844008	+	1.46186i	−0.886480	+	0.462767i	$0.846857\pi$
$588$		0			0
$589$	3.10459e6	+	5.37730e6i	0.368736	+	0.638670i
$590$	−610962.	−	1.30556e6i	−0.0722576	−	0.154407i
$591$		0			0
$592$	4.64178e6	−	3.93829e6i	0.544353	−	0.461853i
$593$		−	1.07696e7i		−	1.25766i	−0.777544	−	0.628828i	$-0.783535\pi$
$593$		−	1.07696e7i		−	1.25766i	0.777544	−	0.628828i	$-0.216465\pi$
$594$		0			0
$595$		−	9.76569e6i		−	1.13086i
$596$	−1.13085e7	−	9.43646e6i	−1.30403	−	1.08816i
$597$		0			0
$598$	5.13121e6	−	2.40125e6i	0.586769	−	0.274590i
$599$	5.44302e6	+	9.42759e6i	0.619831	+	1.07358i	0.989516	+	0.144422i	$0.0461321\pi$
$599$	5.44302e6	+	9.42759e6i	0.619831	+	1.07358i	−0.369685	+	0.929157i	$0.620535\pi$
$600$		0			0
$601$	−6.66377e6	+	1.15420e7i	−0.752548	+	1.30345i	0.194036	+	0.980994i	$0.437842\pi$
$601$	−6.66377e6	+	1.15420e7i	−0.752548	+	1.30345i	−0.946584	+	0.322457i	$0.895491\pi$
$602$	−1.77734e6	+	2.06395e7i	−0.199885	+	2.32117i
$603$		0			0
$604$	−994804.	+	5.73327e6i	−0.110955	+	0.639455i
$605$	−8.44070e6	−	4.87324e6i	−0.937540	−	0.541289i
$606$		0			0
$607$	1.90927e6	−	1.10232e6i	0.210327	−	0.121432i	−0.391136	−	0.920333i	$-0.627918\pi$
$607$	1.90927e6	−	1.10232e6i	0.210327	−	0.121432i	0.601463	+	0.798900i	$0.294585\pi$
$608$	−339681.	−	3.59954e6i	−0.0372659	−	0.394900i
$609$		0			0
$610$	3.61225e6	−	5.17384e6i	0.393055	−	0.562974i
$611$	7.83973e6			0.849568
$612$		0			0
$613$	2.50240e6			0.268971			0.134485	−	0.990916i	$-0.457062\pi$
$613$	2.50240e6			0.268971			0.134485	+	0.990916i	$0.457062\pi$
$614$	158584.	−	227140.i	0.0169761	−	0.0243149i
$615$		0			0
$616$	1.49965e6	+	5.50650e6i	0.159235	+	0.584688i
$617$	6.29534e6	−	3.63461e6i	0.665742	−	0.384366i	−0.128719	−	0.991681i	$-0.541087\pi$
$617$	6.29534e6	−	3.63461e6i	0.665742	−	0.384366i	0.794461	+	0.607315i	$0.207753\pi$
$618$		0			0
$619$	−9.08516e6	−	5.24532e6i	−0.953028	−	0.550231i	−0.0590081	−	0.998258i	$-0.518794\pi$
$619$	−9.08516e6	−	5.24532e6i	−0.953028	−	0.550231i	−0.894020	+	0.448026i	$0.852127\pi$
$620$	2.20984e7	+	3.83439e6i	2.30877	+	0.400605i
$621$		0			0
$622$	35279.0	−	409679.i	0.00365629	−	0.0424588i
$623$	−4.20189e6	+	7.27789e6i	−0.433735	+	0.751252i
$624$		0			0
$625$	6.06530e6	+	1.05054e7i	0.621087	+	1.07575i
$626$	3.27671e6	−	1.53340e6i	0.334197	−	0.156394i
$627$		0			0
$628$	−7.45176e6	+	8.93005e6i	−0.753980	+	0.903555i
$629$		−	3.93908e6i		−	0.396980i
$630$		0			0
$631$		−	1.25868e7i		−	1.25846i	−0.777218	−	0.629231i	$-0.783370\pi$
$631$		−	1.25868e7i		−	1.25846i	0.777218	−	0.629231i	$-0.216630\pi$
$632$	−1.08197e7	+	1.09087e7i	−1.07752	+	1.08638i
$633$		0			0
$634$	−6.73101e6	−	1.43834e7i	−0.665054	−	1.42115i
$635$	−5.00848e6	−	8.67494e6i	−0.492914	−	0.853753i
$636$		0			0
$637$	5.68513e6	−	9.84693e6i	0.555126	−	0.961506i
$638$	3.86893e6	+	333168.i	0.376304	+	0.0324050i
$639$		0			0
$640$	−1.07691e7	−	7.38832e6i	−1.03927	−	0.713010i
$641$	4.75044e6	+	2.74267e6i	0.456655	+	0.263650i	0.710637	−	0.703559i	$-0.248407\pi$
$641$	4.75044e6	+	2.74267e6i	0.456655	+	0.263650i	−0.253981	+	0.967209i	$0.581740\pi$
$642$		0			0
$643$	−1.03225e7	+	5.95970e6i	−0.984595	+	0.568456i	−0.903654	−	0.428263i	$-0.859126\pi$
$643$	−1.03225e7	+	5.95970e6i	−0.984595	+	0.568456i	−0.0809407	+	0.996719i	$0.525792\pi$
$644$	1.49164e7	−	5.47529e6i	1.41726	−	0.520226i
$645$		0			0
$646$	−1.91829e6	−	1.33930e6i	−0.180856	−	0.126269i
$647$	−1.43126e7			−1.34418			−0.672092	−	0.740468i	$-0.734604\pi$
$647$	−1.43126e7			−1.34418			−0.672092	+	0.740468i	$0.734604\pi$
$648$		0			0
$649$	545092.			0.0507993
$650$	3.59863e6	+	2.51247e6i	0.334082	+	0.233248i
$651$		0			0
$652$	−1.02738e7	+	3.77115e6i	−0.946482	+	0.347420i
$653$	3.09615e6	−	1.78757e6i	0.284145	−	0.164051i	−0.351154	−	0.936318i	$-0.614211\pi$
$653$	3.09615e6	−	1.78757e6i	0.284145	−	0.164051i	0.635298	+	0.772267i	$0.280877\pi$
$654$		0			0
$655$	5.39126e6	+	3.11265e6i	0.491006	+	0.283483i
$656$	4.19517e6	−	1.17249e7i	0.380618	−	1.06377i
$657$		0			0
$658$	2.19073e7	+	1.88652e6i	1.97253	+	0.169862i
$659$	1.66026e6	−	2.87565e6i	0.148923	−	0.257942i	−0.781907	−	0.623396i	$-0.785753\pi$
$659$	1.66026e6	−	2.87565e6i	0.148923	−	0.257942i	0.930830	+	0.365453i	$0.119086\pi$
$660$		0			0
$661$	−4.26668e6	−	7.39011e6i	−0.379828	−	0.657881i	0.611209	−	0.791469i	$-0.290683\pi$
$661$	−4.26668e6	−	7.39011e6i	−0.379828	−	0.657881i	−0.991037	+	0.133588i	$0.957350\pi$
$662$	7.42011e6	+	1.58559e7i	0.658060	+	1.40620i
$663$		0			0
$664$	−1.94032e6	−	1.92450e6i	−0.170786	−	0.169394i
$665$			9.19890e6i			0.806644i
$666$		0			0
$667$		−	1.08117e7i		−	0.940981i
$668$	336572.	−	403341.i	0.0291835	−	0.0349729i
$669$		0			0
$670$	1.73619e7	−	8.12486e6i	1.49421	−	0.699244i
$671$	1.19310e6	+	2.06651e6i	0.102299	+	0.177187i
$672$		0			0
$673$	−9.81452e6	+	1.69992e7i	−0.835279	+	1.44675i	0.0585245	+	0.998286i	$0.481360\pi$
$673$	−9.81452e6	+	1.69992e7i	−0.835279	+	1.44675i	−0.893803	+	0.448459i	$0.851973\pi$
$674$	64292.1	−	746594.i	0.00545140	−	0.0633046i
$675$		0			0
$676$	6.09436e6	+	1.05746e6i	0.512934	+	0.0890013i
$677$	−1.67817e7	−	9.68890e6i	−1.40722	−	0.812461i	−0.412104	−	0.911137i	$-0.635206\pi$
$677$	−1.67817e7	−	9.68890e6i	−1.40722	−	0.812461i	−0.995120	+	0.0986755i	$0.968539\pi$
$678$		0			0
$679$	1.55746e6	−	899202.i	0.129641	−	0.0748484i
$680$	−8.15393e6	+	2.22065e6i	−0.676230	+	0.184166i
$681$		0			0
$682$	−4.85533e6	+	6.95430e6i	−0.399722	+	0.572523i
$683$	1.79967e7			1.47618			0.738092	−	0.674700i	$-0.235727\pi$
$683$	1.79967e7			1.47618			0.738092	+	0.674700i	$0.235727\pi$
$684$		0			0
$685$	−7.19100e6			−0.585548
$686$	6.87096e6	−	9.84131e6i	0.557452	−	0.798440i
$687$		0			0
$688$	1.76372e7	−	3.20927e6i	1.42056	−	0.258485i
$689$	−1.19807e7	+	6.91707e6i	−0.961468	+	0.555104i
$690$		0			0
$691$	−9.29000e6	−	5.36359e6i	−0.740152	−	0.427327i	0.0819727	−	0.996635i	$-0.473878\pi$
$691$	−9.29000e6	−	5.36359e6i	−0.740152	−	0.427327i	−0.822124	+	0.569308i	$0.807211\pi$
$692$	−379800.	+	2.18887e6i	−0.0301501	+	0.173762i
$693$		0			0
$694$	−816083.	+	9.47680e6i	−0.0643185	+	0.746901i
$695$	3.20608e6	−	5.55310e6i	0.251775	−	0.436088i
$696$		0			0
$697$	−4.02903e6	−	6.97848e6i	−0.314137	−	0.544100i
$698$	88159.9	−	41256.2i	0.00684909	−	0.00320517i
$699$		0			0
$700$	9.45137e6	+	7.88679e6i	0.729038	+	0.608352i
$701$			3.82293e6i			0.293834i	0.989149	+	0.146917i	$0.0469350\pi$
$701$			3.82293e6i			0.293834i	−0.989149	+	0.146917i	$0.953065\pi$
$702$		0			0
$703$			3.71046e6i			0.283165i
$704$	4.25668e6	−	2.50428e6i	0.323697	−	0.190437i
$705$		0			0
$706$	−4.60332e6	−	9.83678e6i	−0.347584	−	0.742748i
$707$	668804.	+	1.15840e6i	0.0503211	+	0.0871587i
$708$		0			0
$709$	1.02820e7	−	1.78090e7i	0.768181	−	1.33053i	−0.170368	−	0.985381i	$-0.554496\pi$
$709$	1.02820e7	−	1.78090e7i	0.768181	−	1.33053i	0.938549	−	0.345147i	$-0.112171\pi$
$710$	−1.27831e7	−	1.10080e6i	−0.951678	−	0.0819526i
$711$		0			0
$712$	7.03220e6	+	1.85345e6i	0.519866	+	0.137019i
$713$	2.04506e7	+	1.18072e7i	1.50654	+	0.869804i
$714$		0			0
$715$	−3.87986e6	+	2.24004e6i	−0.283825	+	0.163867i
$716$	1.62080e6	+	4.41558e6i	0.118154	+	0.321888i
$717$		0			0
$718$	−960912.	−	670886.i	−0.0695621	−	0.0485666i
$719$	482918.			0.0348378			0.0174189	−	0.999848i	$-0.494455\pi$
$719$	482918.			0.0348378			0.0174189	+	0.999848i	$0.494455\pi$
$720$		0			0
$721$	−1.79221e7			−1.28396
$722$	−9.67780e6	−	6.75681e6i	−0.690930	−	0.482390i
$723$		0			0
$724$	2.62816e6	+	7.15996e6i	0.186340	+	0.507649i
$725$	7.25375e6	−	4.18796e6i	0.512528	−	0.295908i
$726$		0			0
$727$	2.15466e7	+	1.24399e7i	1.51197	+	0.872935i	0.999902	+	0.0139889i	$0.00445295\pi$
$727$	2.15466e7	+	1.24399e7i	1.51197	+	0.872935i	0.512066	+	0.858946i	$0.328880\pi$
$728$	−1.54481e7	−	4.07159e6i	−1.08030	−	0.284732i
$729$		0			0
$730$	−1.38097e7	−	1.18920e6i	−0.959127	−	0.0825941i
$731$	5.80012e6	−	1.00461e7i	0.401461	−	0.695351i
$732$		0			0
$733$	5.66177e6	+	9.80648e6i	0.389218	+	0.674145i	0.992344	−	0.123501i	$-0.0394121\pi$
$733$	5.66177e6	+	9.80648e6i	0.389218	+	0.674145i	−0.603127	+	0.797645i	$0.706079\pi$
$734$	−4.24270e6	−	9.06618e6i	−0.290671	−	0.621133i
$735$		0			0
$736$	−7.96353e6	−	1.12095e7i	−0.541890	−	0.762769i
$737$			7.24889e6i			0.491590i
$738$		0			0
$739$			2.22042e7i			1.49563i	0.663909	+	0.747814i	$0.268896\pi$
$739$			2.22042e7i			1.49563i	−0.663909	+	0.747814i	$0.731104\pi$
$740$	1.02906e7	+	8.58711e6i	0.690816	+	0.576458i
$741$		0			0
$742$	−3.51433e7	+	1.64460e7i	−2.34333	+	1.09661i
$743$	−650311.	−	1.12637e6i	−0.0432165	−	0.0748531i	0.843608	−	0.536959i	$-0.180427\pi$
$743$	−650311.	−	1.12637e6i	−0.0432165	−	0.0748531i	−0.886825	+	0.462106i	$0.847094\pi$
$744$		0			0
$745$	1.62141e7	−	2.80836e7i	1.07029	−	1.85380i
$746$	166009.	−	1.92778e6i	0.0109215	−	0.126827i
$747$		0			0
$748$	546349.	−	3.14873e6i	0.0357040	−	0.205770i
$749$	1.84765e6	+	1.06674e6i	0.120341	+	0.0694790i
$750$		0			0
$751$	1.35125e7	−	7.80146e6i	0.874253	−	0.504750i	0.00549352	−	0.999985i	$-0.498251\pi$
$751$	1.35125e7	−	7.80146e6i	0.874253	−	0.504750i	0.868759	+	0.495235i	$0.164918\pi$
$752$	−3.40641e6	−	1.87206e7i	−0.219661	−	1.20719i
$753$		0			0
$754$	−6.22278e6	+	8.91291e6i	−0.398617	+	0.570941i
$755$	−1.28117e7			−0.817976
$756$		0			0
$757$	−1.06995e6			−0.0678613			−0.0339307	−	0.999424i	$-0.510803\pi$
$757$	−1.06995e6			−0.0678613			−0.0339307	+	0.999424i	$0.510803\pi$
$758$	−6.19714e6	+	8.87619e6i	−0.391759	+	0.561117i
$759$		0			0
$760$	7.68068e6	−	2.09177e6i	0.482354	−	0.131365i
$761$	1.68821e7	−	9.74690e6i	1.05673	−	0.610105i	0.132207	−	0.991222i	$-0.457794\pi$
$761$	1.68821e7	−	9.74690e6i	1.05673	−	0.610105i	0.924527	+	0.381117i	$0.124460\pi$
$762$		0			0
$763$	5.53716e6	+	3.19688e6i	0.344331	+	0.198799i
$764$	−1.41210e7	−	2.45019e6i	−0.875247	−	0.151868i
$765$		0			0
$766$	1.46428e6	−	1.70040e7i	0.0901679	−	1.04708i
$767$	−762932.	+	1.32144e6i	−0.0468271	+	0.0811069i
$768$		0			0
$769$	6.92454e6	+	1.19937e7i	0.422255	+	0.731368i	0.996160	−	0.0875545i	$-0.0279052\pi$
$769$	6.92454e6	+	1.19937e7i	0.422255	+	0.731368i	−0.573904	+	0.818922i	$0.694572\pi$
$770$	−1.13809e7	+	5.32591e6i	−0.691749	+	0.323718i
$771$		0			0
$772$	1.22693e6	−	1.47033e6i	0.0740932	−	0.0887918i
$773$			1.41475e7i			0.851588i	0.904820	+	0.425794i	$0.140005\pi$
$773$			1.41475e7i			0.851588i	−0.904820	+	0.425794i	$0.859995\pi$
$774$		0			0
$775$			1.82941e7i			1.09410i
$776$	−1.10495e6	−	1.09594e6i	−0.0658702	−	0.0653331i
$777$		0			0
$778$	5.98603e6	+	1.27915e7i	0.354560	+	0.757656i
$779$	3.79519e6	+	6.57346e6i	0.224073	+	0.388106i
$780$		0			0
$781$	2.42596e6	−	4.20188e6i	0.142317	−	0.246500i
$782$	−8.86487e6	−	763388.i	−0.518389	−	0.0446404i
$783$		0			0
$784$	−2.59838e7	−	9.29704e6i	−1.50978	−	0.540200i
$785$	−2.21770e7	−	1.28039e7i	−1.28448	−	0.741598i
$786$		0			0
$787$	9.07822e6	−	5.24131e6i	0.522473	−	0.301650i	−0.215473	−	0.976510i	$-0.569129\pi$
$787$	9.07822e6	−	5.24131e6i	0.522473	−	0.301650i	0.737946	+	0.674860i	$0.235796\pi$
$788$	−2.50629e7	+	9.19968e6i	−1.43786	+	0.527785i
$789$		0			0
$790$	−2.77371e7	−	1.93654e7i	−1.58122	−	1.10397i
$791$	1.34830e7			0.766205
$792$		0			0
$793$	−6.67964e6			−0.377198
$794$	742399.	+	518325.i	0.0417913	+	0.0291777i
$795$		0			0
$796$	−1.24090e7	+	4.55488e6i	−0.694149	+	0.254797i
$797$	−6.94849e6	+	4.01172e6i	−0.387476	+	0.223709i	−0.681066	−	0.732222i	$-0.738483\pi$
$797$	−6.94849e6	+	4.01172e6i	−0.387476	+	0.223709i	0.293590	+	0.955931i	$0.405150\pi$
$798$		0			0
$799$	−1.06632e7	−	6.15640e6i	−0.590909	−	0.341161i
$800$	4.43595e6	−	9.68489e6i	0.245054	−	0.535020i
$801$		0			0
$802$	1.63446e7	+	1.40749e6i	0.897299	+	0.0772699i
$803$	2.62078e6	−	4.53932e6i	0.143431	−	0.248429i
$804$		0			0
$805$	1.74923e7	+	3.02976e7i	0.951387	+	1.64785i
$806$	−1.00632e7	−	2.15040e7i	−0.545632	−	1.16596i
$807$		0			0
$808$	815134.	−	821835.i	0.0439239	−	0.0442850i
$809$		−	2.34652e7i		−	1.26053i	−0.776380	−	0.630265i	$-0.782946\pi$
$809$		−	2.34652e7i		−	1.26053i	0.776380	−	0.630265i	$-0.217054\pi$
$810$		0			0
$811$			1.27280e7i			0.679528i	0.940511	+	0.339764i	$0.110347\pi$
$811$			1.27280e7i			0.679528i	−0.940511	+	0.339764i	$0.889653\pi$
$812$	−1.95336e7	+	2.34087e7i	−1.03966	+	1.24591i
$813$		0			0
$814$	−4.59058e6	+	2.14825e6i	−0.242832	+	0.113638i
$815$	−1.20480e7	−	2.08677e7i	−0.635360	−	1.10047i
$816$		0			0
$817$	−5.46349e6	+	9.46304e6i	−0.286362	+	0.495993i
$818$	−549160.	+	6.37714e6i	−0.0286956	+	0.333229i
$819$		0			0
$820$	2.70141e7	+	4.68733e6i	1.40299	+	0.243439i
$821$	−1.40331e7	−	8.10200e6i	−0.726599	−	0.419502i	0.0905775	−	0.995889i	$-0.471129\pi$
$821$	−1.40331e7	−	8.10200e6i	−0.726599	−	0.419502i	−0.817177	+	0.576387i	$0.804462\pi$
$822$		0			0
$823$	−1.29178e7	+	7.45811e6i	−0.664798	+	0.383821i	−0.794103	−	0.607784i	$-0.792059\pi$
$823$	−1.29178e7	+	7.45811e6i	−0.664798	+	0.383821i	0.129305	+	0.991605i	$0.458725\pi$
$824$	4.07536e6	+	1.49642e7i	0.209097	+	0.767775i
$825$		0			0
$826$	−2.44991e6	+	3.50902e6i	−0.124940	+	0.178952i
$827$	1.67161e7			0.849909			0.424954	−	0.905215i	$-0.360290\pi$
$827$	1.67161e7			0.849909			0.424954	+	0.905215i	$0.360290\pi$
$828$		0			0
$829$	−2.17816e7			−1.10079			−0.550395	−	0.834904i	$-0.685523\pi$
$829$	−2.17816e7			−1.10079			−0.550395	+	0.834904i	$0.685523\pi$
$830$	3.44449e6	−	4.93356e6i	0.173552	−	0.248580i
$831$		0			0
$832$	113188.	+	1.38243e7i	0.00566883	+	0.692366i
$833$	−1.54652e7	+	8.92885e6i	−0.772225	+	0.445844i
$834$		0			0
$835$	1.00166e6	+	578311.i	0.0497171	+	0.0287042i
$836$	−514640.	+	2.96598e6i	−0.0254676	+	0.146775i
$837$		0			0
$838$	249463.	−	2.89690e6i	0.0122715	−	0.142503i
$839$	−6.32677e6	+	1.09583e7i	−0.310297	+	0.537449i	−0.978427	−	0.206595i	$-0.933762\pi$
$839$	−6.32677e6	+	1.09583e7i	−0.310297	+	0.537449i	0.668130	+	0.744045i	$0.267095\pi$
$840$		0			0
$841$	116961.	+	202582.i	0.00570231	+	0.00987669i
$842$	3.32132e7	−	1.55428e7i	1.61447	−	0.755525i
$843$		0			0
$844$	1.18151e7	+	9.85926e6i	0.570930	+	0.476418i
$845$			1.36186e7i			0.656133i
$846$		0			0
$847$			2.89373e7i			1.38596i
$848$	2.17230e7	+	2.56034e7i	1.03736	+	1.22267i
$849$		0			0
$850$	−2.92166e6	−	6.24327e6i	−0.138702	−	0.296391i
$851$	7.05568e6	+	1.22208e7i	0.333976	+	0.578463i
$852$		0			0
$853$	1.57491e7	−	2.72782e7i	0.741109	−	1.28364i	−0.210881	−	0.977512i	$-0.567633\pi$
$853$	1.57491e7	−	2.72782e7i	0.741109	−	1.28364i	0.951991	−	0.306127i	$-0.0990334\pi$
$854$	−1.86655e7	−	1.60736e6i	−0.875780	−	0.0754168i
$855$		0			0
$856$	470538.	−	1.78527e6i	0.0219488	−	0.0832761i
$857$	2.78616e7	+	1.60859e7i	1.29585	+	0.748158i	0.979684	−	0.200547i	$-0.0642718\pi$
$857$	2.78616e7	+	1.60859e7i	1.29585	+	0.748158i	0.316164	+	0.948705i	$0.397605\pi$
$858$		0			0
$859$	3.68314e6	−	2.12646e6i	0.170308	−	0.0983274i	−0.412423	−	0.910992i	$-0.635317\pi$
$859$	3.68314e6	−	2.12646e6i	0.170308	−	0.0983274i	0.582731	+	0.812665i	$0.301984\pi$
$860$	1.36007e7	+	3.70527e7i	0.627070	+	1.70834i
$861$		0			0
$862$	3.15647e6	+	2.20377e6i	0.144688	+	0.101018i
$863$	2.00613e7			0.916920			0.458460	−	0.888715i	$-0.348401\pi$
$863$	2.00613e7			0.916920			0.458460	+	0.888715i	$0.348401\pi$
$864$		0			0
$865$	−4.89131e6			−0.222272
$866$	8.28785e6	+	5.78638e6i	0.375532	+	0.262188i
$867$		0			0
$868$	−2.29460e7	−	6.25122e7i	−1.03373	−	2.81621i
$869$	1.10786e7	−	6.39624e6i	0.497664	−	0.287326i
$870$		0			0
$871$	−1.75731e7	−	1.01458e7i	−0.784879	−	0.453150i
$872$	1.41014e6	−	5.35023e6i	0.0628017	−	0.238277i
$873$		0			0
$874$	8.35036e6	+	719081.i	0.369766	+	0.0318419i
$875$	9.47677e6	−	1.64143e7i	0.418447	−	0.724771i
$876$		0			0
$877$	−2.59598e6	−	4.49637e6i	−0.113973	−	0.197407i	0.803396	−	0.595445i	$-0.203024\pi$
$877$	−2.59598e6	−	4.49637e6i	−0.113973	−	0.197407i	−0.917369	+	0.398038i	$0.869691\pi$
$878$	−1.58526e7	−	3.38753e7i	−0.694009	−	1.48302i
$879$		0			0
$880$	7.03484e6	+	8.29146e6i	0.306230	+	0.360931i
$881$		−	3.46088e7i		−	1.50227i	−0.660150	−	0.751134i	$-0.729507\pi$
$881$		−	3.46088e7i		−	1.50227i	0.660150	−	0.751134i	$-0.270493\pi$
$882$		0			0
$883$		−	3.00373e7i		−	1.29646i	−0.761444	−	0.648231i	$-0.775509\pi$
$883$		−	3.00373e7i		−	1.29646i	0.761444	−	0.648231i	$-0.224491\pi$
$884$	6.86860e6	+	5.73157e6i	0.295622	+	0.246685i
$885$		0			0
$886$	−1.30218e7	+	6.09380e6i	−0.557296	+	0.260798i
$887$	4.98101e6	+	8.62736e6i	0.212573	+	0.368187i	0.952519	−	0.304479i	$-0.0984823\pi$
$887$	4.98101e6	+	8.62736e6i	0.212573	+	0.368187i	−0.739946	+	0.672666i	$0.765149\pi$
$888$		0			0
$889$	−1.48702e7	+	2.57559e7i	−0.631047	+	1.09301i
$890$	−1.37375e6	+	1.59527e7i	−0.0581344	+	0.675088i
$891$		0			0
$892$	−1.28001e6	+	7.37694e6i	−0.0538641	+	0.310430i
$893$	1.00443e7	+	5.79909e6i	0.421494	+	0.243350i
$894$		0			0
$895$	−8.96872e6	+	5.17809e6i	−0.374259	+	0.216079i
$896$	−3.01033e6	+	3.86578e7i	−0.125269	+	1.60867i
$897$		0			0
$898$	−1.39164e7	+	1.99325e7i	−0.575885	+	0.824842i
$899$	−4.53101e7			−1.86980
$900$		0			0
$901$	2.17274e7			0.891653
$902$	−5.93537e6	+	8.50125e6i	−0.242902	+	0.347910i
$903$		0			0
$904$	−3.06594e6	−	1.12577e7i	−0.124779	−	0.458172i
$905$	−1.45430e7	+	8.39639e6i	−0.590244	+	0.340777i
$906$		0			0
$907$	3.42191e7	+	1.97564e7i	1.38118	+	0.797425i	0.992299	−	0.123862i	$-0.0395281\pi$
$907$	3.42191e7	+	1.97564e7i	1.38118	+	0.797425i	0.388882	+	0.921288i	$0.372861\pi$
$908$	−3.84349e6	−	666900.i	−0.154707	−	0.0268439i
$909$		0			0
$910$	3.01780e6	−	3.50444e7i	0.120806	−	1.40286i
$911$	4.11834e6	−	7.13318e6i	0.164409	−	0.284765i	−0.772036	−	0.635579i	$-0.780762\pi$
$911$	4.11834e6	−	7.13318e6i	0.164409	−	0.284765i	0.936445	+	0.350813i	$0.114095\pi$
$912$		0			0
$913$	1.13769e6	+	1.97054e6i	0.0451698	+	0.0782363i
$914$	−8.14908e6	+	3.81352e6i	−0.322658	+	0.150994i
$915$		0			0
$916$	−1.88814e7	+	2.26270e7i	−0.743523	+	0.891024i
$917$		−	1.84829e7i		−	0.725849i
$918$		0			0
$919$		−	3.26323e7i		−	1.27455i	−0.770635	−	0.637277i	$-0.780061\pi$
$919$		−	3.26323e7i		−	1.27455i	0.770635	−	0.637277i	$-0.219939\pi$
$920$	2.13195e7	−	2.14948e7i	0.830439	−	0.837266i
$921$		0			0
$922$	−1.08670e7	−	2.32216e7i	−0.421001	−	0.899633i
$923$	6.79093e6	+	1.17622e7i	0.262376	+	0.454449i
$924$		0			0
$925$	−5.46608e6	+	9.46752e6i	−0.210049	+	0.363816i
$926$	4.12137e7	+	3.54907e6i	1.57948	+	0.136015i
$927$		0			0
$928$	2.39871e7	+	1.09867e7i	0.914340	+	0.418793i
$929$	2.44741e7	+	1.41302e7i	0.930397	+	0.537165i	0.886937	−	0.461890i	$-0.152829\pi$
$929$	2.44741e7	+	1.41302e7i	0.930397	+	0.537165i	0.0434598	+	0.999055i	$0.486162\pi$
$930$		0			0
$931$	1.45676e7	−	8.41063e6i	0.550827	−	0.318020i
$932$	−1.69469e7	+	6.22062e6i	−0.639075	+	0.234581i
$933$		0			0
$934$	−2.59529e7	−	1.81197e7i	−0.973462	−	0.679648i
$935$	7.03624e6			0.263216
$936$		0			0
$937$	−2.01407e6			−0.0749419			−0.0374710	−	0.999298i	$-0.511930\pi$
$937$	−2.01407e6			−0.0749419			−0.0374710	+	0.999298i	$0.511930\pi$
$938$	−4.66646e7	−	3.25801e7i	−1.73173	−	1.20905i
$939$		0			0
$940$	3.93287e7	−	1.44362e7i	1.45175	−	0.532883i
$941$	−3.56931e7	+	2.06074e7i	−1.31404	+	0.758664i	−0.982763	−	0.184868i	$-0.940814\pi$
$941$	−3.56931e7	+	2.06074e7i	−1.31404	+	0.758664i	−0.331281	+	0.943532i	$0.607481\pi$
$942$		0			0
$943$	2.49997e7	+	1.44336e7i	0.915494	+	0.528561i
$944$	3.48697e6	+	1.24764e6i	0.127356	+	0.0455680i
$945$		0			0
$946$	−1.48709e7	−	1.28059e6i	−0.540267	−	0.0465244i
$947$	7.12259e6	−	1.23367e7i	0.258085	−	0.447016i	−0.707644	−	0.706569i	$-0.750242\pi$
$947$	7.12259e6	−	1.23367e7i	0.258085	−	0.447016i	0.965729	+	0.259553i	$0.0835752\pi$
$948$		0			0
$949$	7.33629e6	+	1.27068e7i	0.264430	+	0.458006i
$950$	2.75209e6	+	5.88092e6i	0.0989360	+	0.211415i
$951$		0			0
$952$	1.78143e7	+	1.76691e7i	0.637055	+	0.631860i
$953$		−	4.10100e7i		−	1.46271i	−0.681998	−	0.731354i	$-0.738889\pi$
$953$		−	4.10100e7i		−	1.46271i	0.681998	−	0.731354i	$-0.261111\pi$
$954$		0			0
$955$		−	3.15551e7i		−	1.11960i
$956$	3.33253e7	−	3.99364e7i	1.17932	−	1.41327i
$957$		0			0
$958$	3.89137e7	−	1.82104e7i	1.36990	−	0.641072i
$959$	1.06750e7	+	1.84897e7i	0.374820	+	0.649207i
$960$		0			0
$961$	3.51671e7	−	6.09112e7i	1.22837	−	2.12760i
$962$	1.21726e6	−	1.41355e7i	0.0424078	−	0.492462i
$963$		0			0
$964$	3.75658e7	+	6.51820e6i	1.30197	+	0.225910i
$965$	3.65145e6	+	2.10817e6i	0.126226	+	0.0728764i
$966$		0			0
$967$	1.76105e7	−	1.01674e7i	0.605627	−	0.349659i	−0.165625	−	0.986189i	$-0.552964\pi$
$967$	1.76105e7	−	1.01674e7i	0.605627	−	0.349659i	0.771252	+	0.636530i	$0.219631\pi$
$968$	2.41614e7	−	6.58015e6i	0.828769	−	0.225708i
$969$		0			0
$970$	1.96153e6	−	2.80951e6i	0.0669370	−	0.0958742i
$971$	4.20472e7			1.43116			0.715581	−	0.698530i	$-0.246162\pi$
$971$	4.20472e7			1.43116			0.715581	+	0.698530i	$0.246162\pi$
$972$		0			0
$973$	−1.90377e7			−0.644663
$974$	3.11894e7	−	4.46726e7i	1.05344	−	1.50884i
$975$		0			0
$976$	2.90234e6	+	1.59504e7i	0.0975267	+	0.535978i
$977$	6.47483e6	−	3.73824e6i	0.217016	−	0.125294i	−0.387552	−	0.921848i	$-0.626679\pi$
$977$	6.47483e6	−	3.73824e6i	0.217016	−	0.125294i	0.604568	+	0.796554i	$0.293346\pi$
$978$		0			0
$979$	−5.24377e6	−	3.02749e6i	−0.174858	−	0.100955i
$980$	1.03877e7	−	5.98667e7i	0.345506	−	1.99122i
$981$		0			0
$982$	−3.63322e6	+	4.21909e7i	−0.120230	+	1.39617i
$983$	−1.44535e7	+	2.50341e7i	−0.477077	+	0.826321i	−0.999655	−	0.0262705i	$-0.991637\pi$
$983$	−1.44535e7	+	2.50341e7i	−0.477077	+	0.826321i	0.522578	+	0.852591i	$0.324970\pi$
$984$		0			0
$985$	−2.93909e7	−	5.09066e7i	−0.965212	−	1.67180i
$986$	1.54631e7	−	7.23624e6i	0.506527	−	0.237040i
$987$		0			0
$988$	−6.46995e6	−	5.39891e6i	−0.210867	−	0.175960i
$989$			4.15567e7i			1.35098i
$990$		0			0
$991$		−	1.38437e7i		−	0.447782i	−0.974614	−	0.223891i	$-0.928124\pi$
$991$		−	1.38437e7i		−	0.447782i	0.974614	−	0.223891i	$-0.0718760\pi$
$992$	−4.69772e7	+	3.33737e7i	−1.51568	+	1.07678i
$993$		0			0
$994$	1.61461e7	+	3.45024e7i	0.518324	+	1.10760i
$995$	−1.45518e7	−	2.52045e7i	−0.465972	−	0.807087i
$996$		0			0
$997$	−1.66200e7	+	2.87867e7i	−0.529533	+	0.917178i	0.469873	+	0.882734i	$0.344300\pi$
$997$	−1.66200e7	+	2.87867e7i	−0.529533	+	0.917178i	−0.999407	+	0.0344446i	$0.989034\pi$
$998$	6.40180e6	+	551283.i	0.203458	+	0.0175206i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	108.6.h.a.35.6		56
3.2	odd	2		36.6.h.a.11.23	✓	56
4.3	odd	2	inner	108.6.h.a.35.4		56
9.4	even	3		36.6.h.a.23.25	yes	56
9.5	odd	6	inner	108.6.h.a.71.4		56
12.11	even	2		36.6.h.a.11.25	yes	56
36.23	even	6	inner	108.6.h.a.71.6		56
36.31	odd	6		36.6.h.a.23.23	yes	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
36.6.h.a.11.23	✓	56	3.2	odd	2
36.6.h.a.11.25	yes	56	12.11	even	2
36.6.h.a.23.23	yes	56	36.31	odd	6
36.6.h.a.23.25	yes	56	9.4	even	3
108.6.h.a.35.4		56	4.3	odd	2	inner
108.6.h.a.35.6		56	1.1	even	1	trivial
108.6.h.a.71.4		56	9.5	odd	6	inner
108.6.h.a.71.6		56	36.23	even	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)

\(f(q)\)	\(=\)	\(q+(-4.63825 - 3.23831i) q^{2} +(11.0267 + 30.0402i) q^{4} +(-61.0162 + 35.2277i) q^{5} +(181.157 + 104.591i) q^{7} +(46.1351 - 175.042i) q^{8} +O(q^{10})\)	\(q+(-4.63825 - 3.23831i) q^{2} +(11.0267 + 30.0402i) q^{4} +(-61.0162 + 35.2277i) q^{5} +(181.157 + 104.591i) q^{7} +(46.1351 - 175.042i) q^{8} +(397.087 + 34.1946i) q^{10} +(-75.3585 + 130.525i) q^{11} +(-210.949 - 365.375i) q^{13} +(-501.553 - 1071.76i) q^{14} +(-780.825 + 662.486i) q^{16} +662.619i q^{17} -624.161i q^{19} +(-1731.05 - 1444.49i) q^{20} +(772.212 - 361.372i) q^{22} +(-1186.88 - 2055.74i) q^{23} +(919.485 - 1592.59i) q^{25} +(-204.763 + 2377.82i) q^{26} +(-1144.38 + 6595.28i) q^{28} +(3944.46 + 2277.34i) q^{29} +(-8615.25 + 4974.02i) q^{31} +(5767.00 - 544.220i) q^{32} +(2145.77 - 3073.39i) q^{34} -14738.0 q^{35} -5944.72 q^{37} +(-2021.23 + 2895.01i) q^{38} +(3351.33 + 12305.6i) q^{40} +(-10531.7 + 6080.46i) q^{41} +(-15161.2 - 8753.33i) q^{43} +(-4751.94 - 824.530i) q^{44} +(-1152.08 + 13378.5i) q^{46} +(-9291.01 + 16092.5i) q^{47} +(13475.1 + 23339.5i) q^{49} +(-9422.12 + 4409.27i) q^{50} +(8649.87 - 10365.8i) q^{52} -32790.2i q^{53} -10618.8i q^{55} +(26665.5 - 26884.7i) q^{56} +(-10920.7 - 23336.3i) q^{58} +(-1808.33 - 3132.12i) q^{59} +(7916.16 - 13711.2i) q^{61} +(56067.1 + 4828.15i) q^{62} +(-28511.1 - 16151.1i) q^{64} +(25742.7 + 14862.5i) q^{65} +(41652.4 - 24048.0i) q^{67} +(-19905.2 + 7306.48i) q^{68} +(68358.6 + 47726.3i) q^{70} -32192.2 q^{71} -34777.5 q^{73} +(27573.1 + 19250.9i) q^{74} +(18749.9 - 6882.42i) q^{76} +(-27303.5 + 15763.7i) q^{77} +(-73506.0 - 42438.7i) q^{79} +(24305.1 - 67929.1i) q^{80} +(68538.9 + 5902.15i) q^{82} +(7548.53 - 13074.4i) q^{83} +(-23342.6 - 40430.5i) q^{85} +(41975.4 + 89696.8i) q^{86} +(19370.6 + 19212.6i) q^{88} +40174.5i q^{89} -88253.7i q^{91} +(48667.5 - 58322.2i) q^{92} +(95206.5 - 44553.8i) q^{94} +(21987.8 + 38083.9i) q^{95} +(4298.65 - 7445.49i) q^{97} +(13079.9 - 151891. i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q + 3 q^{2} - q^{4} + 6 q^{5}+O(q^{10}) \) 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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