LMFDB - Embedded newform 108.6.h.a.35.4

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			35.4
Character	$\chi$	$=$	108.35
Dual form			108.6.h.a.71.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-5.12358 - 2.39768i) q^{2} +(20.5022 + 24.5695i) q^{4} +(-61.0162 + 35.2277i) q^{5} +(-181.157 - 104.591i) q^{7} +(-46.1351 - 175.042i) q^{8} +O(q^{10})$	\(q+(-5.12358 - 2.39768i) q^{2} +(20.5022 + 24.5695i) q^{4} +(-61.0162 + 35.2277i) q^{5} +(-181.157 - 104.591i) q^{7} +(-46.1351 - 175.042i) q^{8} +(397.087 - 34.1946i) q^{10} +(75.3585 - 130.525i) q^{11} +(-210.949 - 365.375i) q^{13} +(677.397 + 970.239i) q^{14} +(-183.317 + 1007.46i) q^{16} +662.619i q^{17} +624.161i q^{19} +(-2116.49 - 776.889i) q^{20} +(-699.063 + 488.069i) q^{22} +(1186.88 + 2055.74i) q^{23} +(919.485 - 1592.59i) q^{25} +(204.763 + 2377.82i) q^{26} +(-1144.38 - 6595.28i) q^{28} +(3944.46 + 2277.34i) q^{29} +(8615.25 - 4974.02i) q^{31} +(3354.81 - 4722.26i) q^{32} +(1588.75 - 3394.98i) q^{34} +14738.0 q^{35} -5944.72 q^{37} +(1496.54 - 3197.94i) q^{38} +(8981.30 + 9055.14i) q^{40} +(-10531.7 + 6080.46i) q^{41} +(15161.2 + 8753.33i) q^{43} +(4751.94 - 824.530i) q^{44} +(-1152.08 - 13378.5i) q^{46} +(9291.01 - 16092.5i) q^{47} +(13475.1 + 23339.5i) q^{49} +(-8529.60 + 5955.16i) q^{50} +(4652.14 - 12673.9i) q^{52} -32790.2i q^{53} +10618.8i q^{55} +(-9950.10 + 36535.3i) q^{56} +(-14749.5 - 21125.7i) q^{58} +(1808.33 + 3132.12i) q^{59} +(7916.16 - 13711.2i) q^{61} +(-56067.1 + 4828.15i) q^{62} +(-28511.1 + 16151.1i) q^{64} +(25742.7 + 14862.5i) q^{65} +(-41652.4 + 24048.0i) q^{67} +(-16280.2 + 13585.2i) q^{68} +(-75511.5 - 35337.1i) q^{70} +32192.2 q^{71} -34777.5 q^{73} +(30458.3 + 14253.6i) q^{74} +(-15335.3 + 12796.7i) q^{76} +(-27303.5 + 15763.7i) q^{77} +(73506.0 + 42438.7i) q^{79} +(-24305.1 - 67929.1i) q^{80} +(68538.9 - 5902.15i) q^{82} +(-7548.53 + 13074.4i) q^{83} +(-23342.6 - 40430.5i) q^{85} +(-56692.0 - 81200.2i) q^{86} +(-26323.9 - 7169.11i) q^{88} +40174.5i q^{89} +88253.7i q^{91} +(-26174.7 + 71308.4i) q^{92} +(-86188.0 + 60174.4i) q^{94} +(-21987.8 - 38083.9i) q^{95} +(4298.65 - 7445.49i) q^{97} +(-13079.9 - 151891. i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−5.12358	−	2.39768i	−0.905730	−	0.423855i
$2$	−5.12358	−	2.39768i	−0.905730	−	0.423855i
$3$		0			0
$3$		0			0
$4$	20.5022	+	24.5695i	0.640695	+	0.767796i
$5$	−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	−0.403250	−	0.915090i	$-0.632120\pi$
$7$	−181.157	−	104.591i	−1.39737	−	0.806770i	−0.994116	+	0.108320i	$0.965453\pi$
$8$	−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	−0.756729	−	0.653728i	$-0.773204\pi$
$11$	75.3585	−	130.525i	0.187781	−	0.325246i	0.944510	+	0.328483i	$0.106537\pi$
$12$		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	$0.945860\pi$
$14$	677.397	+	970.239i	0.923684	+	1.32300i
$15$		0			0
$16$	−183.317	+	1007.46i	−0.179021	+	0.983845i
$17$			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	$0.0635509\pi$
$19$			624.161i			0.396655i	−0.980136	+	0.198327i	$0.936449\pi$
$20$	−2116.49	−	776.889i	−1.18316	−	0.434294i
$21$		0			0
$22$	−699.063	+	488.069i	−0.307935	+	0.214993i
$23$	1186.88	+	2055.74i	0.467830	+	0.810306i	0.999324	−	0.0367563i	$-0.0117025\pi$
$23$	1186.88	+	2055.74i	0.467830	+	0.810306i	−0.531494	+	0.847062i	$0.678369\pi$
$24$		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	$-0.286806\pi$
$31$	8615.25	−	4974.02i	1.61014	−	0.929615i	0.989336	−	0.145649i	$-0.0465270\pi$
$32$	3354.81	−	4722.26i	0.579152	−	0.815220i
$33$		0			0
$34$	1588.75	−	3394.98i	0.235699	−	0.503663i
$35$	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	$0.616180\pi$
$38$	1496.54	−	3197.94i	0.168124	−	0.359262i
$39$		0			0
$40$	8981.30	+	9055.14i	0.887543	+	0.894840i
$41$	−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	0.971197	−	0.238279i	$-0.0765833\pi$
$43$	15161.2	+	8753.33i	1.25044	+	0.721941i	0.279243	+	0.960221i	$0.409917\pi$
$44$	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	$-0.623092\pi$
$47$	9291.01	−	16092.5i	0.613505	−	1.06262i	0.990645	−	0.136466i	$-0.0435744\pi$
$48$		0			0
$49$	13475.1	+	23339.5i	0.801755	+	1.38868i
$50$	−8529.60	+	5955.16i	−0.482507	+	0.336875i
$51$		0			0
$52$	4652.14	−	12673.9i	0.238586	−	0.649984i
$53$		−	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
$56$	−9950.10	+	36535.3i	−0.423992	+	1.55684i
$57$		0			0
$58$	−14749.5	−	21125.7i	−0.575713	−	0.824596i
$59$	1808.33	+	3132.12i	0.0676312	+	0.117141i	0.897858	−	0.440285i	$-0.145123\pi$
$59$	1808.33	+	3132.12i	0.0676312	+	0.117141i	−0.830227	+	0.557426i	$0.811789\pi$
$60$		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	−0.944833	−	0.327552i	$-0.893776\pi$
$67$	−41652.4	+	24048.0i	−1.13358	+	0.654474i	−0.188749	+	0.982025i	$0.560443\pi$
$68$	−16280.2	+	13585.2i	−0.426960	+	0.356281i
$69$		0			0
$70$	−75511.5	−	35337.1i	−1.84191	−	0.861958i
$71$	32192.2			0.757887			0.378944	−	0.925420i	$-0.376287\pi$
$71$	32192.2			0.757887			0.378944	+	0.925420i	$0.376287\pi$
$72$		0			0
$73$	−34777.5			−0.763820			−0.381910	−	0.924200i	$-0.624734\pi$
$73$	−34777.5			−0.763820			−0.381910	+	0.924200i	$0.624734\pi$
$74$	30458.3	+	14253.6i	0.646585	+	0.302582i
$75$		0			0
$76$	−15335.3	+	12796.7i	−0.304550	+	0.254135i
$77$	−27303.5	+	15763.7i	−0.524797	+	0.302991i
$78$		0			0
$79$	73506.0	+	42438.7i	1.32512	+	0.765058i	0.984540	−	0.175158i	$-0.0560435\pi$
$79$	73506.0	+	42438.7i	1.32512	+	0.765058i	0.340579	+	0.940216i	$0.389377\pi$
$80$	−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	−0.919875	−	0.392211i	$-0.871710\pi$
$83$	−7548.53	+	13074.4i	−0.120273	+	0.208318i	0.799602	+	0.600530i	$0.205044\pi$
$84$		0			0
$85$	−23342.6	−	40430.5i	−0.350430	−	0.606962i
$86$	−56692.0	−	81200.2i	−0.826563	−	1.18389i
$87$		0			0
$88$	−26323.9	−	7169.11i	−0.362363	−	0.0986866i
$89$			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
$92$	−26174.7	+	71308.4i	−0.322413	+	0.878357i
$93$		0			0
$94$	−86188.0	+	60174.4i	−1.00607	+	0.702412i
$95$	−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	−0.114156	−	0.993463i	$-0.536416\pi$
$103$	74198.4	−	42838.4i	0.689130	−	0.397869i	0.803286	+	0.595593i	$0.203083\pi$
$104$	−54223.7	+	53781.5i	−0.491593	+	0.487584i
$105$		0			0
$106$	−78620.5	+	168003.i	−0.679628	+	1.45229i
$107$	−10199.1			−0.0861200			−0.0430600	−	0.999072i	$-0.513711\pi$
$107$	−10199.1			−0.0861200			−0.0430600	+	0.999072i	$0.513711\pi$
$108$		0			0
$109$	30565.5			0.246414			0.123207	−	0.992381i	$-0.460682\pi$
$109$	30565.5			0.246414			0.123207	+	0.992381i	$0.460682\pi$
$110$	25460.6	−	54406.5i	0.200626	−	0.428715i
$111$		0			0
$112$	138580.	−	163335.i	1.04389	−	1.23036i
$113$	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
$122$	−73434.2	+	51270.0i	−0.446682	+	0.311863i
$123$		0			0
$124$	298841.	+	109694.i	1.74536	+	0.640660i
$125$		−	90607.8i		−	0.518670i
$126$		0			0
$127$		−	142174.i		−	0.782189i	−0.920350	−	0.391095i	$-0.872096\pi$
$127$		−	142174.i		−	0.782189i	0.920350	−	0.391095i	$-0.127904\pi$
$128$	184804.	−	14390.9i	0.996982	−	0.0776362i
$129$		0			0
$130$	−96259.1	−	137872.i	−0.499555	−	0.715514i
$131$	44178.9	+	76520.1i	0.224925	+	0.389581i	0.956297	−	0.292398i	$-0.0944531\pi$
$131$	44178.9	+	76520.1i	0.224925	+	0.389581i	−0.731372	+	0.681978i	$0.761120\pi$
$132$		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	−0.316919	−	0.948453i	$-0.602648\pi$
$139$	78817.2	−	45505.1i	0.346006	−	0.199767i	0.662925	+	0.748686i	$0.269315\pi$
$140$	302162.	+	362105.i	1.30293	+	1.56140i
$141$		0			0
$142$	−164939.	−	77186.7i	−0.686442	−	0.321234i
$143$	−63587.4			−0.260034
$144$		0			0
$145$	−320902.			−1.26751
$146$	178185.	+	83385.4i	0.691815	+	0.323749i
$147$		0			0
$148$	−121880.	−	146059.i	−0.457381	−	0.548116i
$149$	−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	0.191913	−	0.981412i	$-0.438531\pi$
$151$	−157479.	−	90920.8i	−0.562059	−	0.324505i	−0.753971	+	0.656907i	$0.771864\pi$
$152$	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	$0.633088\pi$
$158$	−274860.	−	393682.i	−0.875928	−	1.25459i
$159$		0			0
$160$	−38343.3	+	406316.i	−0.118410	+	1.25477i
$161$		−	496549.i		−	1.50972i
$162$		0			0
$163$		−	342002.i		−	1.00823i	−0.863636	−	0.504115i	$-0.831819\pi$
$163$		−	342002.i		−	1.00823i	0.863636	−	0.504115i	$-0.168181\pi$
$164$	−365316.	−	134094.i	−1.06062	−	0.389315i
$165$		0			0
$166$	70023.9	−	48889.0i	0.197231	−	0.137702i
$167$	8208.18	+	14217.0i	0.0227749	+	0.0394472i	0.877188	−	0.480147i	$-0.159417\pi$
$167$	8208.18	+	14217.0i	0.0227749	+	0.0394472i	−0.854413	+	0.519594i	$0.826083\pi$
$168$		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
$176$	117684.	+	99848.0i	0.286375	+	0.242973i
$177$		0			0
$178$	96325.7	−	205837.i	0.227873	−	0.486938i
$179$	−146989.			−0.342888			−0.171444	−	0.985194i	$-0.554843\pi$
$179$	−146989.			−0.342888			−0.171444	+	0.985194i	$0.554843\pi$
$180$		0			0
$181$	238346.			0.540768			0.270384	−	0.962752i	$-0.412849\pi$
$181$	238346.			0.540768			0.270384	+	0.962752i	$0.412849\pi$
$182$	211605.	−	452175.i	0.473529	−	1.01188i
$183$		0			0
$184$	305083.	−	302596.i	0.664315	−	0.658898i
$185$	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	−0.553831	−	0.832629i	$-0.686835\pi$
$191$	223937.	−	387870.i	0.444162	−	0.769312i	0.997993	+	0.0633172i	$0.0201680\pi$
$192$		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	$0.851749\pi$
$194$	−39876.4	+	27840.8i	−0.0760698	+	0.0531101i
$195$		0			0
$196$	−297171.	+	809588.i	−0.552543	+	1.50530i
$197$			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	$-0.879454\pi$
$199$		−	413079.i		−	0.739435i	0.929144	−	0.369718i	$-0.120546\pi$
$200$	−321191.	−	87473.6i	−0.567790	−	0.154633i
$201$		0			0
$202$	−20707.3	−	29659.1i	−0.0357063	−	0.0511422i
$203$	−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	−0.786143	−	0.618044i	$-0.787925\pi$
$211$	−416461.	+	240444.i	−0.643973	+	0.371798i	0.142170	+	0.989842i	$0.454592\pi$
$212$	805637.	−	672272.i	1.23112	−	1.02732i
$213$		0			0
$214$	52256.1	+	24454.3i	0.0780015	+	0.0365024i
$215$	−1.23344e6			−1.81979
$216$		0			0
$217$	−2.08095e6			−2.99994
$218$	−156605.	−	73286.4i	−0.223185	−	0.104444i
$219$		0			0
$220$	−260899.	+	217710.i	−0.363426	+	0.303264i
$221$	242105.	−	139779.i	0.333443	−	0.192514i
$222$		0			0
$223$	−202627.	−	116987.i	−0.272858	−	0.157534i	0.357328	−	0.933979i	$-0.383688\pi$
$223$	−202627.	−	116987.i	−0.272858	−	0.157534i	−0.630186	+	0.776445i	$0.717021\pi$
$224$	−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	−0.824098	−	0.566448i	$-0.808317\pi$
$227$	60951.8	−	105572.i	0.0785094	−	0.135982i	0.902607	+	0.430466i	$0.141651\pi$
$228$		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	$0.636289\pi$
$230$	541591.	+	775722.i	0.675074	+	0.966911i
$231$		0			0
$232$	216651.	−	795511.i	0.264265	−	0.970345i
$233$			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
$236$	−39879.7	+	108645.i	−0.0466092	+	0.126978i
$237$		0			0
$238$	−642899.	+	448856.i	−0.735699	+	0.513647i
$239$	812725.	+	1.40768e6i	0.920341	+	1.59408i	0.798887	+	0.601481i	$0.205422\pi$
$239$	812725.	+	1.40768e6i	0.920341	+	1.59408i	0.121454	+	0.992597i	$0.461244\pi$
$240$		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
$248$	−1.26813e6	−	1.27855e6i	−1.30928	−	1.32004i
$249$		0			0
$250$	−217249.	+	464237.i	−0.219840	+	0.469775i
$251$	1.48383e6			1.48662			0.743311	−	0.668946i	$-0.233254\pi$
$251$	1.48383e6			1.48662			0.743311	+	0.668946i	$0.233254\pi$
$252$		0			0
$253$	357767.			0.351398
$254$	−340889.	+	728442.i	−0.331535	+	0.708453i
$255$		0			0
$256$	−981365.	−	369369.i	−0.935903	−	0.352258i
$257$	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	−0.825482	−	0.564428i	$-0.809097\pi$
$263$	85328.1	−	147793.i	0.0760681	−	0.131754i	0.901550	+	0.432674i	$0.142430\pi$
$264$		0			0
$265$	1.15512e6	+	2.00073e6i	1.01045	+	1.75015i
$266$	−605585.	+	422805.i	−0.524773	+	0.366384i
$267$		0			0
$268$	−1.44481e6	−	530339.i	−1.22878	−	0.451042i
$269$			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	$0.0643862\pi$
$271$			485769.i			0.401797i	−0.979612	+	0.200899i	$0.935614\pi$
$272$	−667561.	−	121470.i	−0.547102	−	0.0995510i
$273$		0			0
$274$	−330517.	−	473400.i	−0.265960	−	0.380936i
$275$	−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	0.175139	−	0.984544i	$-0.443962\pi$
$283$	1.50272e6	−	867593.i	1.11535	−	0.643947i	0.940209	+	0.340597i	$0.110629\pi$
$284$	660012.	+	790945.i	0.485574	+	0.581903i
$285$		0			0
$286$	325795.	+	152462.i	0.235521	+	0.110217i
$287$	2.54385e6			1.82300
$288$		0			0
$289$	980793.			0.690769
$290$	1.64417e6	+	769421.i	1.14802	+	0.537241i
$291$		0			0
$292$	−713016.	−	854464.i	−0.489375	−	0.586458i
$293$	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
$302$	588860.	+	843426.i	0.371531	+	0.532145i
$303$		0			0
$304$	−628816.	−	114420.i	−0.390247	−	0.0710095i
$305$			1.11547e6i			0.686609i
$306$		0			0
$307$		−	48971.1i		−	0.0296547i	−0.999890	−	0.0148274i	$-0.995280\pi$
$307$		−	48971.1i		−	0.0296547i	0.999890	−	0.0148274i	$-0.00471987\pi$
$308$	−947087.	−	347641.i	−0.568870	−	0.208812i
$309$		0			0
$310$	3.25092e6	−	2.26971e6i	1.92133	−	1.34142i
$311$	−36344.9	−	62951.1i	−0.0213080	−	0.0369065i	0.855175	−	0.518340i	$-0.173450\pi$
$311$	−36344.9	−	62951.1i	−0.0213080	−	0.0369065i	−0.876483	+	0.481433i	$0.840116\pi$
$312$		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
$320$	1.17067e6	−	1.98986e6i	0.639088	−	1.08630i
$321$		0			0
$322$	−1.19057e6	+	2.54411e6i	−0.639904	+	1.36740i
$323$	−413581.			−0.220574
$324$		0			0
$325$	−775859.			−0.407450
$326$	−820013.	+	1.75228e6i	−0.427343	+	0.913185i
$327$		0			0
$328$	1.55021e6	+	1.56296e6i	0.795622	+	0.802163i
$329$	−3.36626e6	+	1.94351e6i	−1.71458	+	0.989915i
$330$		0			0
$331$	2.68009e6	+	1.54735e6i	1.34456	+	0.776280i	0.987472	−	0.157793i	$-0.0504377\pi$
$331$	2.68009e6	+	1.54735e6i	1.34456	+	0.776280i	0.357084	+	0.934072i	$0.383771\pi$
$332$	−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	$0.823219\pi$
$338$	−896547.	+	625947.i	−0.426856	+	0.298020i
$339$		0			0
$340$	514781.	−	1.40243e6i	0.241505	−	0.657936i
$341$		−	1.49934e6i		−	0.698255i
$342$		0			0
$343$		−	2.12177e6i		−	0.973786i
$344$	832733.	−	3.05768e6i	0.379411	−	1.39314i
$345$		0			0
$346$	−224817.	−	322006.i	−0.100958	−	0.144602i
$347$	840739.	+	1.45620e6i	0.374833	+	0.649229i	0.990302	−	0.138932i	$-0.0443668\pi$
$347$	840739.	+	1.45620e6i	0.374833	+	0.649229i	−0.615469	+	0.788161i	$0.711033\pi$
$348$		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
$356$	−987065.	+	823666.i	−0.412782	+	0.344450i
$357$		0			0
$358$	753111.	+	352433.i	0.310564	+	0.145335i
$359$	−207171.			−0.0848386			−0.0424193	−	0.999100i	$-0.513507\pi$
$359$	−207171.			−0.0848386			−0.0424193	+	0.999100i	$0.513507\pi$
$360$		0			0
$361$	2.08652e6			0.842665
$362$	−1.22119e6	−	571478.i	−0.489790	−	0.229207i
$363$		0			0
$364$	−2.16835e6	+	1.80940e6i	−0.857779	+	0.715782i
$365$	2.12199e6	−	1.22513e6i	0.833703	−	0.481338i
$366$		0			0
$367$	−1.53243e6	−	884750.i	−0.593904	−	0.342891i	0.172736	−	0.984968i	$-0.444739\pi$
$367$	−1.53243e6	−	884750.i	−0.593904	−	0.342891i	−0.766640	+	0.642078i	$0.778073\pi$
$368$	−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	$0.813060\pi$
$374$	−323404.	−	463212.i	−0.119555	−	0.171238i
$375$		0			0
$376$	−3.24550e6	−	883884.i	−1.18389	−	0.322423i
$377$		−	1.92161e6i		−	0.696326i
$378$		0			0
$379$			1.91370e6i			0.684345i	0.939637	+	0.342172i	$0.111163\pi$
$379$			1.91370e6i			0.684345i	−0.939637	+	0.342172i	$0.888837\pi$
$380$	484904.	−	1.32103e6i	0.172265	−	0.469305i
$381$		0			0
$382$	−2.07735e6	+	1.45035e6i	−0.728368	+	0.508529i
$383$	−1.50852e6	−	2.61283e6i	−0.525477	−	0.910153i	−0.999560	−	0.0296726i	$-0.990554\pi$
$383$	−1.50852e6	−	2.61283e6i	−0.525477	−	0.910153i	0.474083	−	0.880480i	$-0.342780\pi$
$384$		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
$392$	3.46372e6	−	3.43547e6i	1.13848	−	1.12920i
$393$		0			0
$394$	2.00042e6	−	4.27467e6i	0.649202	−	1.38727i
$395$	−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	$0.508113\pi$
$398$	−990432.	+	2.11644e6i	−0.313413	+	0.669729i
$399$		0			0
$400$	1.43591e6	+	1.21829e6i	0.448723	+	0.380716i
$401$	−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	$0.886816\pi$
$410$	−3.97406e6	+	2.77460e6i	−1.16755	+	0.815155i
$411$		0			0
$412$	2.57375e6	+	944731.i	0.747004	+	0.274198i
$413$		−	756540.i		−	0.218251i
$414$		0			0
$415$		−	1.06367e6i		−	0.303170i
$416$	−2.43309e6	−	229606.i	−0.689326	−	0.0650503i
$417$		0			0
$418$	−304634.	−	436328.i	−0.0852780	−	0.122144i
$419$	−257000.	−	445137.i	−0.0715152	−	0.123868i	0.828050	−	0.560654i	$-0.189450\pi$
$419$	−257000.	−	445137.i	−0.0715152	−	0.123868i	−0.899566	+	0.436786i	$0.856117\pi$
$420$		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
$428$	−209105.	−	250587.i	−0.0551766	−	0.0661226i
$429$		0			0
$430$	6.31963e6	+	2.95740e6i	1.64824	+	0.771327i
$431$	680530.			0.176463			0.0882316	−	0.996100i	$-0.471878\pi$
$431$	680530.			0.176463			0.0882316	+	0.996100i	$0.471878\pi$
$432$		0			0
$433$	−1.78685e6			−0.458003			−0.229002	−	0.973426i	$-0.573546\pi$
$433$	−1.78685e6			−0.458003			−0.229002	+	0.973426i	$0.573546\pi$
$434$	1.06619e7	+	4.98946e6i	2.71714	+	1.27154i
$435$		0			0
$436$	626661.	+	750978.i	0.157876	+	0.189196i
$437$	−1.28311e6	+	740806.i	−0.321412	+	0.185567i
$438$		0			0
$439$	−5.72585e6	−	3.30582e6i	−1.41801	−	0.818687i	−0.421884	−	0.906650i	$-0.638631\pi$
$439$	−5.72585e6	−	3.30582e6i	−1.41801	−	0.818687i	−0.996124	+	0.0879624i	$0.971964\pi$
$440$	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	−0.977848	−	0.209317i	$-0.932876\pi$
$443$	−1.27077e6	+	2.20104e6i	−0.307650	+	0.532866i	0.670198	+	0.742183i	$0.266209\pi$
$444$		0			0
$445$	−1.41526e6	−	2.45129e6i	−0.338793	−	0.586807i
$446$	757681.	+	1.08523e6i	0.180364	+	0.258336i
$447$		0			0
$448$	6.85425e6	+	56120.1i	1.61349	+	0.0132106i
$449$		−	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
$452$	1.93626e6	+	710732.i	0.445777	+	0.163629i
$453$		0			0
$454$	−565419.	+	394762.i	−0.128745	+	0.0898867i
$455$	−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	0.381637	−	0.924312i	$-0.375360\pi$
$463$	6.33289e6	−	3.65630e6i	1.37293	−	0.792664i	0.991296	+	0.131648i	$0.0420270\pi$
$464$	−3.01741e6	+	3.55641e6i	−0.650638	+	0.766860i
$465$		0			0
$466$	1.35264e6	−	2.89043e6i	0.288547	−	0.616592i
$467$	−5.59542e6			−1.18724			−0.593622	−	0.804744i	$-0.702303\pi$
$467$	−5.59542e6			−1.18724			−0.593622	+	0.804744i	$0.702303\pi$
$468$		0			0
$469$	1.00608e7			2.11204
$470$	3.13906e6	−	6.70782e6i	0.655473	−	1.40067i
$471$		0			0
$472$	464823.	−	461033.i	0.0960358	−	0.0952527i
$473$	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	$-0.560367\pi$
$479$	3.79751e6	−	6.57748e6i	0.756241	−	1.30985i	0.944755	−	0.327777i	$-0.106299\pi$
$480$		0			0
$481$	1.25403e6	+	2.17205e6i	0.247142	+	0.428063i
$482$	−5.52634e6	+	3.85836e6i	−1.08348	+	0.756458i
$483$		0			0
$484$	−1.52538e6	+	4.15562e6i	−0.295981	+	0.806348i
$485$			605727.i			0.116929i
$486$		0			0
$487$		−	9.63136e6i		−	1.84020i	−0.391682	−	0.920101i	$-0.628107\pi$
$487$		−	9.63136e6i		−	1.84020i	0.391682	−	0.920101i	$-0.371893\pi$
$488$	−2.76524e6	−	753090.i	−0.525634	−	0.143152i
$489$		0			0
$490$	6.14887e6	+	8.80704e6i	1.15692	+	1.65707i
$491$	3.74298e6	+	6.48304e6i	0.700671	+	1.21360i	0.968231	+	0.250056i	$0.0804492\pi$
$491$	3.74298e6	+	6.48304e6i	0.700671	+	1.21360i	−0.267560	+	0.963541i	$0.586218\pi$
$492$		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	−0.408961	−	0.912552i	$-0.634109\pi$
$499$	983698.	−	567938.i	0.176852	−	0.102106i	0.585813	+	0.810446i	$0.300775\pi$
$500$	2.22619e6	−	1.85766e6i	0.398232	−	0.332309i
$501$		0			0
$502$	−7.60254e6	−	3.55776e6i	−1.34648	−	0.630112i
$503$	9.15158e6			1.61278			0.806391	−	0.591382i	$-0.201417\pi$
$503$	9.15158e6			1.61278			0.806391	+	0.591382i	$0.201417\pi$
$504$		0			0
$505$	−450525.			−0.0786123
$506$	−1.83305e6	−	857812.i	−0.318272	−	0.148942i
$507$		0			0
$508$	3.49315e6	−	2.91489e6i	0.600562	−	0.501145i
$509$	−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
$518$	−4.02693e6	−	5.76779e6i	−0.659402	−	0.944464i
$519$		0			0
$520$	1.41392e6	−	5.19172e6i	0.229307	−	0.841982i
$521$			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	$0.221644\pi$
$523$			8.02433e6i			1.28279i	−0.767212	+	0.641394i	$0.778356\pi$
$524$	−974293.	+	2.65429e6i	−0.155011	+	0.422298i
$525$		0			0
$526$	−791545.	+	552638.i	−0.124742	+	0.0870916i
$527$	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
$536$	6.13104e6	+	6.18144e6i	0.921769	+	0.929347i
$537$		0			0
$538$	68415.6	−	146197.i	0.0101906	−	0.0217762i
$539$	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	$0.698096\pi$
$542$	1.16472e6	−	2.48888e6i	0.170304	−	0.363920i
$543$		0			0
$544$	3.12906e6	+	2.22296e6i	0.453332	+	0.322058i
$545$	−1.86499e6	+	1.07675e6i	−0.268959	+	0.155283i
$546$		0			0
$547$	5.32459e6	+	3.07415e6i	0.760883	+	0.439296i	0.829613	−	0.558339i	$-0.188561\pi$
$547$	5.32459e6	+	3.07415e6i	0.760883	+	0.439296i	−0.0687298	+	0.997635i	$0.521895\pi$
$548$	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
$554$	6.46258e6	−	4.51202e6i	0.894605	−	0.624592i
$555$		0			0
$556$	2.73397e6	+	1.00354e6i	0.375065	+	0.137673i
$557$			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
$560$	−2.70174e6	+	1.48479e7i	−0.364060	+	2.00076i
$561$		0			0
$562$	2.58500e6	+	3.70251e6i	0.345239	+	0.494488i
$563$	−744431.	−	1.28939e6i	−0.0989814	−	0.171441i	0.812282	−	0.583265i	$-0.198225\pi$
$563$	−744431.	−	1.28939e6i	−0.0989814	−	0.171441i	−0.911263	+	0.411824i	$0.864892\pi$
$564$		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	−0.796502	−	0.604636i	$-0.793319\pi$
$571$	−5.22869e6	+	3.01878e6i	−0.671123	+	0.387473i	0.125379	+	0.992109i	$0.459985\pi$
$572$	−1.30368e6	−	1.56231e6i	−0.166603	−	0.199653i
$573$		0			0
$574$	−1.30336e7	−	6.09934e6i	−1.65115	−	0.772687i
$575$	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	$0.0357546\pi$
$578$	−5.02518e6	−	2.35163e6i	−0.625650	−	0.292786i
$579$		0			0
$580$	−6.57920e6	−	7.88438e6i	−0.812088	−	0.973190i
$581$	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	$-0.513523\pi$
$587$	7.04599e6	−	1.22040e7i	0.844008	−	1.46186i	0.886480	−	0.462767i	$-0.153143\pi$
$588$		0			0
$589$	3.10459e6	+	5.37730e6i	0.368736	+	0.638670i
$590$	825165.	+	1.18189e6i	0.0975912	+	0.139780i
$591$		0			0
$592$	1.08977e6	−	5.98905e6i	0.127800	−	0.702350i
$593$		−	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
$596$	−1.38264e7	−	5.07519e6i	−1.59439	−	0.585244i
$597$		0			0
$598$	−4.64515e6	+	3.24313e6i	−0.531187	+	0.370862i
$599$	−5.44302e6	−	9.42759e6i	−0.619831	−	1.07358i	−0.989516	−	0.144422i	$-0.953868\pi$
$599$	−5.44302e6	−	9.42759e6i	−0.619831	−	1.07358i	0.369685	−	0.929157i	$-0.379465\pi$
$600$		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	−0.601463	−	0.798900i	$-0.705415\pi$
$607$	−1.90927e6	+	1.10232e6i	−0.210327	+	0.121432i	0.391136	+	0.920333i	$0.372082\pi$
$608$	2.94745e6	+	2.09394e6i	0.323361	+	0.229723i
$609$		0			0
$610$	2.67455e6	−	5.71522e6i	0.291022	−	0.621882i
$611$	−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	$0.457062\pi$
$614$	−117417.	+	250908.i	−0.0125693	+	0.0268592i
$615$		0			0
$616$	4.01894e6	+	4.05198e6i	0.426737	+	0.430245i
$617$	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	0.894020	−	0.448026i	$-0.147873\pi$
$619$	9.08516e6	+	5.24532e6i	0.953028	+	0.550231i	0.0590081	+	0.998258i	$0.481206\pi$
$620$	−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
$626$	2.96632e6	−	2.07102e6i	0.302540	−	0.211226i
$627$		0			0
$628$	−4.00777e6	+	1.09184e7i	−0.405512	+	1.10474i
$629$		−	3.93908e6i		−	0.396980i
$630$		0			0
$631$			1.25868e7i			1.25846i	0.777218	+	0.629231i	$0.216630\pi$
$631$			1.25868e7i			1.25846i	−0.777218	+	0.629231i	$0.783370\pi$
$632$	4.03733e6	−	1.48245e7i	0.402070	−	1.47635i
$633$		0			0
$634$	−9.09090e6	−	1.30209e7i	−0.898222	−	1.28653i
$635$	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	0.0809407	−	0.996719i	$-0.474208\pi$
$643$	1.03225e7	−	5.95970e6i	0.984595	−	0.568456i	0.903654	+	0.428263i	$0.140874\pi$
$644$	1.22000e7	−	1.01804e7i	1.15916	−	0.967273i
$645$		0			0
$646$	2.11902e6	+	991636.i	0.199781	+	0.0934913i
$647$	1.43126e7			1.34418			0.672092	−	0.740468i	$-0.265396\pi$
$647$	1.43126e7			1.34418			0.672092	+	0.740468i	$0.265396\pi$
$648$		0			0
$649$	545092.			0.0507993
$650$	3.97518e6	+	1.86027e6i	0.369040	+	0.172700i
$651$		0			0
$652$	8.40281e6	−	7.01181e6i	0.774115	−	0.645968i
$653$	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	−0.930830	−	0.365453i	$-0.880914\pi$
$659$	−1.66026e6	+	2.87565e6i	−0.148923	+	0.257942i	0.781907	+	0.623396i	$0.214247\pi$
$660$		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	$0.957350\pi$
$662$	−1.00216e7	−	1.43540e7i	−0.888775	−	1.27300i
$663$		0			0
$664$	2.63682e6	+	718116.i	0.232092	+	0.0632084i
$665$			9.19890e6i			0.806644i
$666$		0			0
$667$			1.08117e7i			0.940981i
$668$	−181018.	+	493151.i	−0.0156957	+	0.0427601i
$669$		0			0
$670$	−1.57173e7	+	1.09734e7i	−1.35267	+	0.944399i
$671$	−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
$680$	−6.00011e6	+	5.95118e6i	−0.497607	+	0.493550i
$681$		0			0
$682$	−3.59494e6	+	7.68199e6i	−0.295958	+	0.632430i
$683$	−1.79967e7			−1.47618			−0.738092	−	0.674700i	$-0.764273\pi$
$683$	−1.79967e7			−1.47618			−0.738092	+	0.674700i	$0.764273\pi$
$684$		0			0
$685$	−7.19100e6			−0.585548
$686$	−5.08734e6	+	1.08711e7i	−0.412744	+	0.881988i
$687$		0			0
$688$	−1.15979e7	+	1.36696e7i	−0.934134	+	1.10100i
$689$	−1.19807e7	+	6.91707e6i	−0.961468	+	0.555104i
$690$		0			0
$691$	9.29000e6	+	5.36359e6i	0.740152	+	0.427327i	0.822124	−	0.569308i	$-0.192789\pi$
$691$	9.29000e6	+	5.36359e6i	0.740152	+	0.427327i	−0.0819727	+	0.996635i	$0.526122\pi$
$692$	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
$698$	79808.9	−	55720.6i	0.00620030	−	0.00432890i
$699$		0			0
$700$	−1.15558e7	−	4.24174e6i	−0.891367	−	0.327189i
$701$			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
$704$	−40434.9	+	4.93853e6i	−0.00307485	+	0.375549i
$705$		0			0
$706$	−6.21724e6	−	8.90498e6i	−0.469446	−	0.672390i
$707$	−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
$716$	−3.01360e6	−	3.61144e6i	−0.219687	−	0.263268i
$717$		0			0
$718$	1.06146e6	+	496731.i	0.0768409	+	0.0359592i
$719$	−482918.			−0.0348378			−0.0174189	−	0.999848i	$-0.505545\pi$
$719$	−482918.			−0.0348378			−0.0174189	+	0.999848i	$0.505545\pi$
$720$		0			0
$721$	−1.79221e7			−1.28396
$722$	−1.06905e7	−	5.00282e6i	−0.763227	−	0.357167i
$723$		0			0
$724$	4.88662e6	+	5.85603e6i	0.346467	+	0.415200i
$725$	7.25375e6	−	4.18796e6i	0.512528	−	0.295908i
$726$		0			0
$727$	−2.15466e7	−	1.24399e7i	−1.51197	−	0.872935i	−0.999902	−	0.0139889i	$-0.995547\pi$
$727$	−2.15466e7	−	1.24399e7i	−1.51197	−	0.872935i	−0.512066	−	0.858946i	$-0.671120\pi$
$728$	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	$0.706079\pi$
$734$	5.73019e6	+	8.20738e6i	0.392581	+	0.562295i
$735$		0			0
$736$	1.36895e7	+	1.29185e6i	0.931522	+	0.0879058i
$737$			7.24889e6i			0.491590i
$738$		0			0
$739$		−	2.22042e7i		−	1.49563i	−0.663909	−	0.747814i	$-0.731104\pi$
$739$		−	2.22042e7i		−	1.49563i	0.663909	−	0.747814i	$-0.268896\pi$
$740$	1.25820e7	+	4.61839e6i	0.844635	+	0.310035i
$741$		0			0
$742$	3.18143e7	−	2.22120e7i	2.12135	−	1.48108i
$743$	650311.	+	1.12637e6i	0.0432165	+	0.0748531i	0.886825	−	0.462106i	$-0.152906\pi$
$743$	650311.	+	1.12637e6i	0.0432165	+	0.0748531i	−0.843608	+	0.536959i	$0.819573\pi$
$744$		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	−0.868759	−	0.495235i	$-0.835082\pi$
$751$	−1.35125e7	+	7.80146e6i	−0.874253	+	0.504750i	−0.00549352	+	0.999985i	$0.501749\pi$
$752$	1.45093e7	+	1.23103e7i	0.935626	+	0.793826i
$753$		0			0
$754$	−4.60742e6	+	9.84554e6i	−0.295141	+	0.630683i
$755$	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	$0.510803\pi$
$758$	4.58844e6	−	9.80498e6i	0.290063	−	0.619832i
$759$		0			0
$760$	−5.65187e6	+	5.60578e6i	−0.354942	+	0.352048i
$761$	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	$0.694572\pi$
$770$	−1.03028e7	+	7.19317e6i	−0.626223	+	0.437214i
$771$		0			0
$772$	659880.	−	1.79772e6i	0.0398494	−	0.108562i
$773$			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
$776$	−1.50159e6	−	408945.i	−0.0895152	−	0.0243787i
$777$		0			0
$778$	8.08473e6	+	1.15798e7i	0.478869	+	0.685886i
$779$	−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	−0.737946	−	0.674860i	$-0.764204\pi$
$787$	−9.07822e6	+	5.24131e6i	−0.522473	+	0.301650i	0.215473	+	0.976510i	$0.430871\pi$
$788$	−2.04986e7	+	1.71053e7i	−1.17600	+	0.981328i
$789$		0			0
$790$	3.06394e7	+	1.43383e7i	1.74668	+	0.817393i
$791$	−1.34830e7			−0.766205
$792$		0			0
$793$	−6.67964e6			−0.377198
$794$	820082.	+	383774.i	0.0461643	+	0.0216035i
$795$		0			0
$796$	1.01491e7	−	8.46904e6i	0.567735	−	0.473752i
$797$	−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
$806$	1.35914e7	+	1.94670e7i	0.736931	+	1.05551i
$807$		0			0
$808$	304163.	−	1.11684e6i	0.0163900	−	0.0601817i
$809$		−	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	$-0.889653\pi$
$811$		−	1.27280e7i		−	0.679528i	0.940511	−	0.339764i	$-0.110347\pi$
$812$	1.05057e7	−	2.86210e7i	0.559160	−	1.52333i
$813$		0			0
$814$	4.15573e6	−	2.90143e6i	0.219830	−	0.153480i
$815$	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	−0.129305	−	0.991605i	$-0.541275\pi$
$823$	1.29178e7	−	7.45811e6i	0.664798	−	0.383821i	0.794103	+	0.607784i	$0.207941\pi$
$824$	−1.09217e7	−	1.10114e7i	−0.560364	−	0.564971i
$825$		0			0
$826$	−1.81394e6	+	3.87620e6i	−0.0925068	+	0.197677i
$827$	−1.67161e7			−0.849909			−0.424954	−	0.905215i	$-0.639710\pi$
$827$	−1.67161e7			−0.849909			−0.424954	+	0.905215i	$0.639710\pi$
$828$		0			0
$829$	−2.17816e7			−1.10079			−0.550395	−	0.834904i	$-0.685523\pi$
$829$	−2.17816e7			−1.10079			−0.550395	+	0.834904i	$0.685523\pi$
$830$	−2.55034e6	+	5.44980e6i	−0.128500	+	0.274590i
$831$		0			0
$832$	1.19156e7	+	7.01018e6i	0.596772	+	0.351092i
$833$	−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	−0.668130	−	0.744045i	$-0.732905\pi$
$839$	6.32677e6	−	1.09583e7i	0.310297	−	0.537449i	0.978427	+	0.206595i	$0.0662383\pi$
$840$		0			0
$841$	116961.	+	202582.i	0.00570231	+	0.00987669i
$842$	3.00671e7	−	2.09921e7i	1.46154	−	1.02041i
$843$		0			0
$844$	−1.44459e7	−	5.30259e6i	−0.698055	−	0.256231i
$845$			1.36186e7i			0.656133i
$846$		0			0
$847$		−	2.89373e7i		−	1.38596i
$848$	3.30347e7	+	6.01101e6i	1.57754	+	0.287050i
$849$		0			0
$850$	−3.94600e6	−	5.65187e6i	−0.187331	−	0.268315i
$851$	−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	−0.582731	−	0.812665i	$-0.698016\pi$
$859$	−3.68314e6	+	2.12646e6i	−0.170308	+	0.0983274i	0.412423	+	0.910992i	$0.364683\pi$
$860$	−2.52882e7	−	3.03049e7i	−1.16593	−	1.39723i
$861$		0			0
$862$	−3.48675e6	−	1.63170e6i	−0.159828	−	0.0747947i
$863$	−2.00613e7			−0.916920			−0.458460	−	0.888715i	$-0.651599\pi$
$863$	−2.00613e7			−0.916920			−0.458460	+	0.888715i	$0.651599\pi$
$864$		0			0
$865$	−4.89131e6			−0.222272
$866$	9.15508e6	+	4.28430e6i	0.414827	+	0.194127i
$867$		0			0
$868$	−4.26641e7	−	5.11279e7i	−1.92205	−	2.30334i
$869$	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	$0.869691\pi$
$878$	2.14106e7	+	3.06664e7i	0.937328	+	1.34254i
$879$		0			0
$880$	−1.06980e7	−	1.94662e6i	−0.465690	−	0.0847372i
$881$		−	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	$0.224491\pi$
$883$			3.00373e7i			1.29646i	−0.761444	+	0.648231i	$0.775509\pi$
$884$	8.39798e6	+	3.08260e6i	0.361447	+	0.132674i
$885$		0			0
$886$	1.17883e7	−	8.23029e6i	0.504506	−	0.352234i
$887$	−4.98101e6	−	8.62736e6i	−0.212573	−	0.368187i	0.739946	−	0.672666i	$-0.234851\pi$
$887$	−4.98101e6	−	8.62736e6i	−0.212573	−	0.368187i	−0.952519	+	0.304479i	$0.901518\pi$
$888$		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
$896$	−3.49838e7	−	1.67219e7i	−1.45578	−	0.695848i
$897$		0			0
$898$	−1.03039e7	+	2.20182e7i	−0.426392	+	0.911152i
$899$	4.53101e7			1.86980
$900$		0			0
$901$	2.17274e7			0.891653
$902$	4.39462e6	−	9.39080e6i	0.179848	−	0.384314i
$903$		0			0
$904$	−8.21649e6	−	8.28404e6i	−0.334399	−	0.337148i
$905$	−1.45430e7	+	8.39639e6i	−0.590244	+	0.340777i
$906$		0			0
$907$	−3.42191e7	−	1.97564e7i	−1.38118	−	0.797425i	−0.388882	−	0.921288i	$-0.627139\pi$
$907$	−3.42191e7	−	1.97564e7i	−1.38118	−	0.797425i	−0.992299	+	0.123862i	$0.960472\pi$
$908$	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	−0.936445	−	0.350813i	$-0.885905\pi$
$911$	−4.11834e6	+	7.13318e6i	−0.164409	+	0.284765i	0.772036	+	0.635579i	$0.219238\pi$
$912$		0			0
$913$	1.13769e6	+	1.97054e6i	0.0451698	+	0.0782363i
$914$	−7.37715e6	+	5.15055e6i	−0.292094	+	0.203933i
$915$		0			0
$916$	−1.01549e7	+	2.76653e7i	−0.399888	+	1.08942i
$917$		−	1.84829e7i		−	0.725849i
$918$		0			0
$919$			3.26323e7i			1.27455i	0.770635	+	0.637277i	$0.219939\pi$
$919$			3.26323e7i			1.27455i	−0.770635	+	0.637277i	$0.780061\pi$
$920$	−7.95527e6	+	2.92106e7i	−0.309874	+	1.13781i
$921$		0			0
$922$	−1.46770e7	−	2.10219e7i	−0.568604	−	0.814414i
$923$	−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
$932$	−1.38607e7	+	1.15662e7i	−0.522691	+	0.436164i
$933$		0			0
$934$	2.86686e7	+	1.34160e7i	1.07532	+	0.503219i
$935$	−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	$0.511930\pi$
$938$	−5.15475e7	−	2.41227e7i	−1.91294	−	0.895197i
$939$		0			0
$940$	−3.21665e7	+	2.68416e7i	−1.18736	+	0.990807i
$941$	−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	−0.965729	−	0.259553i	$-0.916425\pi$
$947$	−7.12259e6	+	1.23367e7i	−0.258085	+	0.447016i	0.707644	+	0.706569i	$0.249758\pi$
$948$		0			0
$949$	7.33629e6	+	1.27068e7i	0.264430	+	0.458006i
$950$	−3.71698e6	−	5.32384e6i	−0.133623	−	0.191389i
$951$		0			0
$952$	−2.42090e7	−	6.59312e6i	−0.865734	−	0.235776i
$953$		−	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
$956$	−1.79233e7	+	4.88288e7i	−0.634269	+	1.72795i
$957$		0			0
$958$	−3.52276e7	+	2.45950e7i	−1.24013	+	0.865832i
$959$	−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	−0.771252	−	0.636530i	$-0.780369\pi$
$967$	−1.76105e7	+	1.01674e7i	−0.605627	+	0.349659i	0.165625	+	0.986189i	$0.447036\pi$
$968$	1.77793e7	−	1.76343e7i	0.609853	−	0.604881i
$969$		0			0
$970$	1.45234e6	−	3.10349e6i	0.0495609	−	0.105906i
$971$	−4.20472e7			−1.43116			−0.715581	−	0.698530i	$-0.753838\pi$
$971$	−4.20472e7			−1.43116			−0.715581	+	0.698530i	$0.753838\pi$
$972$		0			0
$973$	−1.90377e7			−0.644663
$974$	−2.30930e7	+	4.93471e7i	−0.779978	+	1.66673i
$975$		0			0
$976$	1.23623e7	+	1.04887e7i	0.415407	+	0.352449i
$977$	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	−0.522578	−	0.852591i	$-0.675030\pi$
$983$	1.44535e7	−	2.50341e7i	0.477077	−	0.826321i	0.999655	+	0.0262705i	$0.00836312\pi$
$984$		0			0
$985$	−2.93909e7	−	5.09066e7i	−0.965212	−	1.67180i
$986$	1.39983e7	−	9.77327e6i	0.458546	−	0.320146i
$987$		0			0
$988$	7.91057e6	+	2.90368e6i	0.257819	+	0.0946362i
$989$			4.15567e7i			1.35098i
$990$		0			0
$991$			1.38437e7i			0.447782i	0.974614	+	0.223891i	$0.0718760\pi$
$991$			1.38437e7i			0.447782i	−0.974614	+	0.223891i	$0.928124\pi$
$992$	5.41392e6	−	5.73703e7i	0.174676	−	1.85101i
$993$		0			0
$994$	2.18069e7	+	3.12341e7i	0.700048	+	1.00268i
$995$	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.35.4		56
3.2	odd	2		36.6.h.a.11.25	yes	56
4.3	odd	2	inner	108.6.h.a.35.6		56
9.4	even	3		36.6.h.a.23.23	yes	56
9.5	odd	6	inner	108.6.h.a.71.6		56
12.11	even	2		36.6.h.a.11.23	✓	56
36.23	even	6	inner	108.6.h.a.71.4		56
36.31	odd	6		36.6.h.a.23.25	yes	56

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

\(f(q)\)	\(=\)	\(q+(-5.12358 - 2.39768i) q^{2} +(20.5022 + 24.5695i) q^{4} +(-61.0162 + 35.2277i) q^{5} +(-181.157 - 104.591i) q^{7} +(-46.1351 - 175.042i) q^{8} +O(q^{10})\)	\(q+(-5.12358 - 2.39768i) q^{2} +(20.5022 + 24.5695i) q^{4} +(-61.0162 + 35.2277i) q^{5} +(-181.157 - 104.591i) q^{7} +(-46.1351 - 175.042i) q^{8} +(397.087 - 34.1946i) q^{10} +(75.3585 - 130.525i) q^{11} +(-210.949 - 365.375i) q^{13} +(677.397 + 970.239i) q^{14} +(-183.317 + 1007.46i) q^{16} +662.619i q^{17} +624.161i q^{19} +(-2116.49 - 776.889i) q^{20} +(-699.063 + 488.069i) q^{22} +(1186.88 + 2055.74i) q^{23} +(919.485 - 1592.59i) q^{25} +(204.763 + 2377.82i) q^{26} +(-1144.38 - 6595.28i) q^{28} +(3944.46 + 2277.34i) q^{29} +(8615.25 - 4974.02i) q^{31} +(3354.81 - 4722.26i) q^{32} +(1588.75 - 3394.98i) q^{34} +14738.0 q^{35} -5944.72 q^{37} +(1496.54 - 3197.94i) q^{38} +(8981.30 + 9055.14i) q^{40} +(-10531.7 + 6080.46i) q^{41} +(15161.2 + 8753.33i) q^{43} +(4751.94 - 824.530i) q^{44} +(-1152.08 - 13378.5i) q^{46} +(9291.01 - 16092.5i) q^{47} +(13475.1 + 23339.5i) q^{49} +(-8529.60 + 5955.16i) q^{50} +(4652.14 - 12673.9i) q^{52} -32790.2i q^{53} +10618.8i q^{55} +(-9950.10 + 36535.3i) q^{56} +(-14749.5 - 21125.7i) q^{58} +(1808.33 + 3132.12i) q^{59} +(7916.16 - 13711.2i) q^{61} +(-56067.1 + 4828.15i) q^{62} +(-28511.1 + 16151.1i) q^{64} +(25742.7 + 14862.5i) q^{65} +(-41652.4 + 24048.0i) q^{67} +(-16280.2 + 13585.2i) q^{68} +(-75511.5 - 35337.1i) q^{70} +32192.2 q^{71} -34777.5 q^{73} +(30458.3 + 14253.6i) q^{74} +(-15335.3 + 12796.7i) q^{76} +(-27303.5 + 15763.7i) q^{77} +(73506.0 + 42438.7i) q^{79} +(-24305.1 - 67929.1i) q^{80} +(68538.9 - 5902.15i) q^{82} +(-7548.53 + 13074.4i) q^{83} +(-23342.6 - 40430.5i) q^{85} +(-56692.0 - 81200.2i) q^{86} +(-26323.9 - 7169.11i) q^{88} +40174.5i q^{89} +88253.7i q^{91} +(-26174.7 + 71308.4i) q^{92} +(-86188.0 + 60174.4i) q^{94} +(-21987.8 - 38083.9i) q^{95} +(4298.65 - 7445.49i) q^{97} +(-13079.9 - 151891. i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q + 3 q^{2} - q^{4} + 6 q^{5}+O(q^{10}) \) 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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