LMFDB - Embedded newform 108.6.h.a.35.1

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			35.1
Character	$\chi$	$=$	108.35
Dual form			108.6.h.a.71.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-5.65362 + 0.191212i) q^{2} +(31.9269 - 2.16208i) q^{4} +(-3.68052 + 2.12495i) q^{5} +(-13.9322 - 8.04377i) q^{7} +(-180.089 + 18.3284i) q^{8} +O(q^{10})$	\(q+(-5.65362 + 0.191212i) q^{2} +(31.9269 - 2.16208i) q^{4} +(-3.68052 + 2.12495i) q^{5} +(-13.9322 - 8.04377i) q^{7} +(-180.089 + 18.3284i) q^{8} +(20.4019 - 12.7174i) q^{10} +(-43.3121 + 75.0187i) q^{11} +(162.502 + 281.462i) q^{13} +(80.3056 + 42.8124i) q^{14} +(1014.65 - 138.057i) q^{16} -1863.80i q^{17} +416.071i q^{19} +(-112.913 + 75.8006i) q^{20} +(230.526 - 432.409i) q^{22} +(1293.41 + 2240.24i) q^{23} +(-1553.47 + 2690.69i) q^{25} +(-972.544 - 1560.21i) q^{26} +(-462.204 - 226.690i) q^{28} +(-4342.80 - 2507.32i) q^{29} +(-6396.76 + 3693.17i) q^{31} +(-5710.05 + 974.537i) q^{32} +(356.382 + 10537.2i) q^{34} +68.3704 q^{35} -10519.2 q^{37} +(-79.5579 - 2352.31i) q^{38} +(623.874 - 450.138i) q^{40} +(-13207.4 + 7625.29i) q^{41} +(6794.45 + 3922.78i) q^{43} +(-1220.62 + 2488.76i) q^{44} +(-7740.79 - 12418.2i) q^{46} +(-14244.6 + 24672.4i) q^{47} +(-8274.10 - 14331.2i) q^{49} +(8268.23 - 15509.2i) q^{50} +(5796.72 + 8634.85i) q^{52} +5483.31i q^{53} -368.144i q^{55} +(2656.47 + 1193.24i) q^{56} +(25032.0 + 13345.0i) q^{58} +(1901.12 + 3292.83i) q^{59} +(16590.1 - 28734.9i) q^{61} +(35458.7 - 22102.9i) q^{62} +(32096.1 - 6601.49i) q^{64} +(-1196.18 - 690.617i) q^{65} +(-57592.1 + 33250.8i) q^{67} +(-4029.69 - 59505.3i) q^{68} +(-386.540 + 13.0733i) q^{70} +43573.3 q^{71} +22901.9 q^{73} +(59471.5 - 2011.40i) q^{74} +(899.581 + 13283.8i) q^{76} +(1206.87 - 696.785i) q^{77} +(-31941.7 - 18441.5i) q^{79} +(-3441.08 + 2664.20i) q^{80} +(73211.6 - 45635.9i) q^{82} +(-27504.3 + 47638.8i) q^{83} +(3960.48 + 6859.75i) q^{85} +(-39163.3 - 20878.7i) q^{86} +(6425.06 - 14303.9i) q^{88} -40969.8i q^{89} -5228.51i q^{91} +(46138.0 + 68727.5i) q^{92} +(75816.1 - 142212. i) q^{94} +(-884.130 - 1531.36i) q^{95} +(23339.8 - 40425.7i) q^{97} +(49518.9 + 79440.8i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−5.65362	+	0.191212i	−0.999429	+	0.0338019i
$2$	−5.65362	+	0.191212i	−0.999429	+	0.0338019i
$3$		0			0
$3$		0			0
$4$	31.9269	−	2.16208i	0.997715	−	0.0675651i
$5$	−3.68052	+	2.12495i	−0.0658391	+	0.0380122i	−0.532558	−	0.846393i	$-0.678769\pi$
$5$	−3.68052	+	2.12495i	−0.0658391	+	0.0380122i	0.466719	+	0.884406i	$0.345436\pi$
$6$		0			0
$7$	−13.9322	−	8.04377i	−0.107467	−	0.0620461i	0.445303	−	0.895380i	$-0.353096\pi$
$7$	−13.9322	−	8.04377i	−0.107467	−	0.0620461i	−0.552770	+	0.833334i	$0.686429\pi$
$8$	−180.089	+	18.3284i	−0.994861	+	0.101251i
$9$		0			0
$10$	20.4019	−	12.7174i	0.0645166	−	0.0402160i
$11$	−43.3121	+	75.0187i	−0.107926	+	0.186934i	−0.914930	−	0.403613i	$-0.867754\pi$
$11$	−43.3121	+	75.0187i	−0.107926	+	0.186934i	0.807004	+	0.590546i	$0.201088\pi$
$12$		0			0
$13$	162.502	+	281.462i	0.266686	+	0.461914i	0.968004	−	0.250935i	$-0.0807380\pi$
$13$	162.502	+	281.462i	0.266686	+	0.461914i	−0.701318	+	0.712849i	$0.747405\pi$
$14$	80.3056	+	42.8124i	0.109503	+	0.0583781i
$15$		0			0
$16$	1014.65	−	138.057i	0.990870	−	0.134821i
$17$		−	1863.80i		−	1.56415i	−0.623187	−	0.782073i	$-0.714163\pi$
$17$		−	1863.80i		−	1.56415i	0.623187	−	0.782073i	$-0.285837\pi$
$18$		0			0
$19$			416.071i			0.264413i	0.991222	+	0.132207i	$0.0422063\pi$
$19$			416.071i			0.264413i	−0.991222	+	0.132207i	$0.957794\pi$
$20$	−112.913	+	75.8006i	−0.0631204	+	0.0423738i
$21$		0			0
$22$	230.526	−	432.409i	0.101546	−	0.190475i
$23$	1293.41	+	2240.24i	0.509818	+	0.883030i	0.999935	+	0.0113741i	$0.00362056\pi$
$23$	1293.41	+	2240.24i	0.509818	+	0.883030i	−0.490117	+	0.871656i	$0.663046\pi$
$24$		0			0
$25$	−1553.47	+	2690.69i	−0.497110	+	0.861020i
$26$	−972.544	−	1560.21i	−0.282147	−	0.452635i
$27$		0			0
$28$	−462.204	−	226.690i	−0.111414	−	0.0546433i
$29$	−4342.80	−	2507.32i	−0.958904	−	0.553623i	−0.0630683	−	0.998009i	$-0.520089\pi$
$29$	−4342.80	−	2507.32i	−0.958904	−	0.553623i	−0.895835	+	0.444386i	$0.853422\pi$
$30$		0			0
$31$	−6396.76	+	3693.17i	−1.19552	+	0.690232i	−0.959553	−	0.281530i	$-0.909158\pi$
$31$	−6396.76	+	3693.17i	−1.19552	+	0.690232i	−0.235964	+	0.971762i	$0.575825\pi$
$32$	−5710.05	+	974.537i	−0.985746	+	0.168238i
$33$		0			0
$34$	356.382	+	10537.2i	0.0528711	+	1.56325i
$35$	68.3704			0.00943405
$36$		0			0
$37$	−10519.2			−1.26322			−0.631609	−	0.775287i	$-0.717605\pi$
$37$	−10519.2			−1.26322			−0.631609	+	0.775287i	$0.717605\pi$
$38$	−79.5579	−	2352.31i	−0.00893767	−	0.264262i
$39$		0			0
$40$	623.874	−	450.138i	0.0616520	−	0.0444832i
$41$	−13207.4	+	7625.29i	−1.22704	+	0.708430i	−0.966409	−	0.257009i	$-0.917263\pi$
$41$	−13207.4	+	7625.29i	−1.22704	+	0.708430i	−0.260628	+	0.965439i	$0.583930\pi$
$42$		0			0
$43$	6794.45	+	3922.78i	0.560381	+	0.323536i	0.753298	−	0.657679i	$-0.228462\pi$
$43$	6794.45	+	3922.78i	0.560381	+	0.323536i	−0.192917	+	0.981215i	$0.561795\pi$
$44$	−1220.62	+	2488.76i	−0.0950495	+	0.193799i
$45$		0			0
$46$	−7740.79	−	12418.2i	−0.539375	−	0.865293i
$47$	−14244.6	+	24672.4i	−0.940604	+	1.62917i	−0.176280	+	0.984340i	$0.556406\pi$
$47$	−14244.6	+	24672.4i	−0.940604	+	1.62917i	−0.764323	+	0.644833i	$0.776927\pi$
$48$		0			0
$49$	−8274.10	−	14331.2i	−0.492301	−	0.852690i
$50$	8268.23	−	15509.2i	0.467722	−	0.877331i
$51$		0			0
$52$	5796.72	+	8634.85i	0.297286	+	0.442840i
$53$			5483.31i			0.268135i	0.990972	+	0.134067i	$0.0428038\pi$
$53$			5483.31i			0.268135i	−0.990972	+	0.134067i	$0.957196\pi$
$54$		0			0
$55$		−	368.144i		−	0.0164101i
$56$	2656.47	+	1193.24i	0.113197	+	0.0508461i
$57$		0			0
$58$	25032.0	+	13345.0i	0.977069	+	0.520894i
$59$	1901.12	+	3292.83i	0.0711015	+	0.123151i	0.899384	−	0.437159i	$-0.144015\pi$
$59$	1901.12	+	3292.83i	0.0711015	+	0.123151i	−0.828283	+	0.560310i	$0.810682\pi$
$60$		0			0
$61$	16590.1	−	28734.9i	0.570853	−	0.988747i	−0.425625	−	0.904900i	$-0.639946\pi$
$61$	16590.1	−	28734.9i	0.570853	−	0.988747i	0.996479	−	0.0838475i	$-0.0267209\pi$
$62$	35458.7	−	22102.9i	1.17150	−	0.730248i
$63$		0			0
$64$	32096.1	−	6601.49i	0.979496	−	0.201462i
$65$	−1196.18	−	690.617i	−0.0351168	−	0.0202747i
$66$		0			0
$67$	−57592.1	+	33250.8i	−1.56738	+	0.904930i	−0.570912	+	0.821011i	$0.693410\pi$
$67$	−57592.1	+	33250.8i	−1.56738	+	0.904930i	−0.996473	+	0.0839192i	$0.973256\pi$
$68$	−4029.69	−	59505.3i	−0.105682	−	1.56057i
$69$		0			0
$70$	−386.540	+	13.0733i	−0.00942866	+	0.000318889i
$71$	43573.3			1.02583			0.512914	−	0.858440i	$-0.328566\pi$
$71$	43573.3			1.02583			0.512914	+	0.858440i	$0.328566\pi$
$72$		0			0
$73$	22901.9			0.502996			0.251498	−	0.967858i	$-0.419077\pi$
$73$	22901.9			0.502996			0.251498	+	0.967858i	$0.419077\pi$
$74$	59471.5	−	2011.40i	1.26250	−	0.0426991i
$75$		0			0
$76$	899.581	+	13283.8i	0.0178651	+	0.263809i
$77$	1206.87	−	696.785i	0.0231970	−	0.0133928i
$78$		0			0
$79$	−31941.7	−	18441.5i	−0.575824	−	0.332452i	0.183648	−	0.982992i	$-0.441209\pi$
$79$	−31941.7	−	18441.5i	−0.575824	−	0.332452i	−0.759472	+	0.650540i	$0.774543\pi$
$80$	−3441.08	+	2664.20i	−0.0601132	+	0.0465417i
$81$		0			0
$82$	73211.6	−	45635.9i	1.20239	−	0.749501i
$83$	−27504.3	+	47638.8i	−0.438233	+	0.759041i	−0.997553	−	0.0699102i	$-0.977729\pi$
$83$	−27504.3	+	47638.8i	−0.438233	+	0.759041i	0.559321	+	0.828951i	$0.311062\pi$
$84$		0			0
$85$	3960.48	+	6859.75i	0.0594567	+	0.102982i
$86$	−39163.3	−	20878.7i	−0.570997	−	0.304409i
$87$		0			0
$88$	6425.06	−	14303.9i	0.0884444	−	0.196901i
$89$		−	40969.8i		−	0.548263i	−0.961692	−	0.274132i	$-0.911610\pi$
$89$		−	40969.8i		−	0.548263i	0.961692	−	0.274132i	$-0.0883904\pi$
$90$		0			0
$91$		−	5228.51i		−	0.0661873i
$92$	46138.0	+	68727.5i	0.568315	+	0.846567i
$93$		0			0
$94$	75816.1	−	142212.i	0.884997	−	1.66004i
$95$	−884.130	−	1531.36i	−0.0100509	−	0.0174087i
$96$		0			0
$97$	23339.8	−	40425.7i	0.251865	−	0.436243i	−0.712174	−	0.702003i	$-0.752289\pi$
$97$	23339.8	−	40425.7i	0.251865	−	0.436243i	0.964039	+	0.265760i	$0.0856227\pi$
$98$	49518.9	+	79440.8i	0.520842	+	0.835562i
$99$		0			0
$100$	−43779.9	+	89264.0i	−0.437799	+	0.892640i
$101$	65827.1	+	38005.3i	0.642098	+	0.370716i	0.785422	−	0.618960i	$-0.212446\pi$
$101$	65827.1	+	38005.3i	0.642098	+	0.370716i	−0.143324	+	0.989676i	$0.545779\pi$
$102$		0			0
$103$	3270.29	−	1888.10i	0.0303734	−	0.0175361i	−0.484736	−	0.874660i	$-0.661084\pi$
$103$	3270.29	−	1888.10i	0.0303734	−	0.0175361i	0.515110	+	0.857124i	$0.327751\pi$
$104$	−34423.6	−	47709.8i	−0.312085	−	0.432538i
$105$		0			0
$106$	−1048.48	−	31000.6i	−0.00906346	−	0.267981i
$107$	57656.6			0.486844			0.243422	−	0.969920i	$-0.421730\pi$
$107$	57656.6			0.486844			0.243422	+	0.969920i	$0.421730\pi$
$108$		0			0
$109$	−176304.			−1.42133			−0.710667	−	0.703529i	$-0.751607\pi$
$109$	−176304.			−1.42133			−0.710667	+	0.703529i	$0.751607\pi$
$110$	70.3936	+	2081.35i	0.000554692	+	0.0164007i
$111$		0			0
$112$	−15246.8	−	6238.18i	−0.114851	−	0.0469908i
$113$	−111854.	+	64579.2i	−0.824057	+	0.475769i	−0.851813	−	0.523845i	$-0.824497\pi$
$113$	−111854.	+	64579.2i	−0.824057	+	0.475769i	0.0277568	+	0.999615i	$0.491164\pi$
$114$		0			0
$115$	−9520.81	−	5496.84i	−0.0671319	−	0.0387586i
$116$	−144073.	−	70661.3i	−0.994118	−	0.487570i
$117$		0			0
$118$	−11377.8	−	18252.9i	−0.0752236	−	0.120678i
$119$	−14992.0	+	25966.9i	−0.0970491	+	0.168094i
$120$		0			0
$121$	76773.6	+	132976.i	0.476704	+	0.825675i
$122$	−88299.7	+	165629.i	−0.537106	+	1.00748i
$123$		0			0
$124$	−196244.	+	131742.i	−1.14615	+	0.769430i
$125$		−	26485.1i		−	0.151610i
$126$		0			0
$127$			43254.5i			0.237970i	0.992896	+	0.118985i	$0.0379640\pi$
$127$			43254.5i			0.237970i	−0.992896	+	0.118985i	$0.962036\pi$
$128$	−180197.	+	43459.5i	−0.972127	+	0.234455i
$129$		0			0
$130$	6894.82	+	3675.76i	0.0357820	+	0.0190761i
$131$	−104818.	−	181550.i	−0.533650	−	0.924309i	−0.999227	−	0.0393020i	$-0.987487\pi$
$131$	−104818.	−	181550.i	−0.533650	−	0.924309i	0.465577	−	0.885007i	$-0.345847\pi$
$132$		0			0
$133$	3346.78	−	5796.79i	0.0164058	−	0.0284157i
$134$	319246.	−	199000.i	1.53590	−	0.957394i
$135$		0			0
$136$	34160.5	+	335650.i	0.158372	+	1.55611i
$137$	−99563.4	−	57483.0i	−0.453209	−	0.261660i	0.255976	−	0.966683i	$-0.417603\pi$
$137$	−99563.4	−	57483.0i	−0.453209	−	0.261660i	−0.709184	+	0.705023i	$0.750937\pi$
$138$		0			0
$139$	186853.	−	107880.i	0.820281	−	0.473590i	−0.0302321	−	0.999543i	$-0.509625\pi$
$139$	186853.	−	107880.i	0.820281	−	0.473590i	0.850514	+	0.525953i	$0.176291\pi$
$140$	2182.85	−	147.823i	0.00941249	−	0.000637413i
$141$		0			0
$142$	−246347.	+	8331.75i	−1.02524	+	0.0346749i
$143$	−28153.2			−0.115130
$144$		0			0
$145$	21311.7			0.0841779
$146$	−129479.	+	4379.13i	−0.502709	+	0.0170022i
$147$		0			0
$148$	−335845.	+	22743.4i	−1.26033	+	0.0853495i
$149$	192038.	−	110873.i	0.708633	−	0.409129i	−0.101922	−	0.994792i	$-0.532499\pi$
$149$	192038.	−	110873.i	0.708633	−	0.409129i	0.810555	+	0.585663i	$0.199166\pi$
$150$		0			0
$151$	364405.	+	210389.i	1.30059	+	0.750898i	0.980506	−	0.196490i	$-0.0629543\pi$
$151$	364405.	+	210389.i	1.30059	+	0.750898i	0.320088	+	0.947388i	$0.396288\pi$
$152$	−7625.92	−	74929.8i	−0.0267722	−	0.263055i
$153$		0			0
$154$	−6689.94	+	4170.13i	−0.0227311	+	0.0141693i
$155$	15695.6	−	27185.6i	0.0524745	−	0.0908886i
$156$		0			0
$157$	110672.	+	191690.i	0.358335	+	0.620654i	0.987683	−	0.156470i	$-0.0500113\pi$
$157$	110672.	+	191690.i	0.358335	+	0.620654i	−0.629348	+	0.777124i	$0.716678\pi$
$158$	184112.	+	98153.8i	0.586733	+	0.312798i
$159$		0			0
$160$	18945.1	−	15720.4i	0.0585056	−	0.0485471i
$161$		−	41615.4i		−	0.126529i
$162$		0			0
$163$		−	324082.i		−	0.955402i	−0.878522	−	0.477701i	$-0.841470\pi$
$163$		−	324082.i		−	0.955402i	0.878522	−	0.477701i	$-0.158530\pi$
$164$	−405184.	+	272007.i	−1.17637	+	0.789716i
$165$		0			0
$166$	146390.	−	274591.i	0.412325	−	0.773421i
$167$	−125104.	−	216686.i	−0.347120	−	0.601229i	0.638617	−	0.769525i	$-0.279507\pi$
$167$	−125104.	−	216686.i	−0.347120	−	0.601229i	−0.985737	+	0.168296i	$0.946174\pi$
$168$		0			0
$169$	132833.	−	230073.i	0.357757	−	0.619654i
$170$	−23702.7	−	38025.2i	−0.0629037	−	0.100913i
$171$		0			0
$172$	225407.	+	110552.i	0.580960	+	0.284935i
$173$	267332.	+	154344.i	0.679102	+	0.392080i	0.799517	−	0.600644i	$-0.205089\pi$
$173$	267332.	+	154344.i	0.679102	+	0.392080i	−0.120414	+	0.992724i	$0.538422\pi$
$174$		0			0
$175$	43286.5	−	24991.5i	0.106846	−	0.0616875i
$176$	−33589.8	+	82097.4i	−0.0817382	+	0.199778i
$177$		0			0
$178$	7833.94	+	231628.i	0.0185323	+	0.547950i
$179$	7856.73			0.0183278			0.00916388	−	0.999958i	$-0.497083\pi$
$179$	7856.73			0.0183278			0.00916388	+	0.999958i	$0.497083\pi$
$180$		0			0
$181$	−449713.			−1.02033			−0.510163	−	0.860078i	$-0.670415\pi$
$181$	−449713.			−1.02033			−0.510163	+	0.860078i	$0.670415\pi$
$182$	999.756	+	29560.0i	0.00223726	+	0.0661495i
$183$		0			0
$184$	−273988.	−	379737.i	−0.596606	−	0.826873i
$185$	38716.1	−	22352.7i	0.0831691	−	0.0480177i
$186$		0			0
$187$	139820.	+	80725.1i	0.292392	+	0.168812i
$188$	−401443.	+	818512.i	−0.828379	+	1.68900i
$189$		0			0
$190$	5291.35	+	8488.66i	0.0106337	+	0.0170591i
$191$	255380.	−	442331.i	0.506527	−	0.877331i	−0.493444	−	0.869777i	$-0.664262\pi$
$191$	255380.	−	442331.i	0.506527	−	0.877331i	0.999971	−	0.00755354i	$-0.00240439\pi$
$192$		0			0
$193$	439991.	+	762087.i	0.850257	+	1.47269i	0.880976	+	0.473161i	$0.156887\pi$
$193$	439991.	+	762087.i	0.850257	+	1.47269i	−0.0307186	+	0.999528i	$0.509780\pi$
$194$	−124225.	+	233015.i	−0.236975	+	0.444507i
$195$		0			0
$196$	−295151.	−	439660.i	−0.548788	−	0.817479i
$197$			162799.i			0.298873i	0.988771	+	0.149437i	$0.0477460\pi$
$197$			162799.i			0.298873i	−0.988771	+	0.149437i	$0.952254\pi$
$198$		0			0
$199$		−	786472.i		−	1.40783i	−0.710283	−	0.703916i	$-0.751433\pi$
$199$		−	786472.i		−	1.40783i	0.710283	−	0.703916i	$-0.248567\pi$
$200$	230447.	−	513036.i	0.407376	−	0.906928i
$201$		0			0
$202$	−379429.	−	202281.i	−0.654262	−	0.348800i
$203$	40336.6	+	69865.0i	0.0687004	+	0.118993i
$204$		0			0
$205$	32406.7	−	56130.1i	0.0538580	−	0.0932848i
$206$	−18128.0	+	11299.9i	−0.0297633	+	0.0185527i
$207$		0			0
$208$	203741.	+	263151.i	0.326527	+	0.421741i
$209$	−31213.1	−	18020.9i	−0.0494278	−	0.0285372i
$210$		0			0
$211$	−879851.	+	507982.i	−1.36051	+	0.785493i	−0.989692	−	0.143212i	$-0.954257\pi$
$211$	−879851.	+	507982.i	−1.36051	+	0.785493i	−0.370821	+	0.928704i	$0.620924\pi$
$212$	11855.4	+	175065.i	0.0181166	+	0.267522i
$213$		0			0
$214$	−325969.	+	11024.7i	−0.486566	+	0.0164562i
$215$	−33342.8			−0.0491933
$216$		0			0
$217$	118828.			0.171305
$218$	996757.	−	33711.5i	1.42052	−	0.0480438i
$219$		0			0
$220$	−795.958	−	11753.7i	−0.00110875	−	0.0163726i
$221$	524588.	−	302871.i	0.722500	−	0.417136i
$222$		0			0
$223$	201948.	+	116595.i	0.271942	+	0.157006i	0.629770	−	0.776782i	$-0.283149\pi$
$223$	201948.	+	116595.i	0.271942	+	0.157006i	−0.357828	+	0.933788i	$0.616482\pi$
$224$	87392.7	+	32352.9i	0.116374	+	0.0430817i
$225$		0			0
$226$	620034.	−	386494.i	0.807504	−	0.503352i
$227$	439493.	−	761224.i	0.566092	−	0.980501i	−0.430855	−	0.902421i	$-0.641788\pi$
$227$	439493.	−	761224.i	0.566092	−	0.980501i	0.996947	−	0.0780796i	$-0.0248788\pi$
$228$		0			0
$229$	−191288.	−	331320.i	−0.241045	−	0.417503i	0.719967	−	0.694008i	$-0.244157\pi$
$229$	−191288.	−	331320.i	−0.241045	−	0.417503i	−0.961012	+	0.276506i	$0.910824\pi$
$230$	54878.1	+	29256.6i	0.0684037	+	0.0364673i
$231$		0			0
$232$	828046.	+	371944.i	1.01003	+	0.453688i
$233$			224357.i			0.270738i	0.990795	+	0.135369i	$0.0432220\pi$
$233$			224357.i			0.270738i	−0.990795	+	0.135369i	$0.956778\pi$
$234$		0			0
$235$		−	121076.i		−	0.143018i
$236$	67816.1	+	101019.i	0.0792598	+	0.118066i
$237$		0			0
$238$	79793.8	−	149674.i	0.0913118	−	0.171278i
$239$	769108.	+	1.33213e6i	0.870949	+	1.50853i	0.861017	+	0.508577i	$0.169828\pi$
$239$	769108.	+	1.33213e6i	0.870949	+	1.50853i	0.00993200	+	0.999951i	$0.496838\pi$
$240$		0			0
$241$	692903.	−	1.20014e6i	0.768475	−	1.33104i	−0.169914	−	0.985459i	$-0.554349\pi$
$241$	692903.	−	1.20014e6i	0.768475	−	1.33104i	0.938390	−	0.345579i	$-0.112318\pi$
$242$	−459476.	−	737115.i	−0.504341	−	0.809090i
$243$		0			0
$244$	467543.	−	953285.i	0.502744	−	1.02506i
$245$	60905.9	+	35164.1i	0.0648253	+	0.0374269i
$246$		0			0
$247$	−117108.	+	67612.4i	−0.122136	+	0.0705154i
$248$	1.08430e6	−	782342.i	1.11949	−	0.807732i
$249$		0			0
$250$	5064.28	+	149737.i	0.00512469	+	0.151523i
$251$	−1.31402e6			−1.31649			−0.658246	−	0.752803i	$-0.728701\pi$
$251$	−1.31402e6			−1.31649			−0.658246	+	0.752803i	$0.728701\pi$
$252$		0			0
$253$	−224080.			−0.220091
$254$	−8270.79	−	244544.i	−0.00804382	−	0.237834i
$255$		0			0
$256$	1.01046e6	−	280160.i	0.963646	−	0.267181i
$257$	−542479.	+	313201.i	−0.512331	+	0.295794i	−0.733791	−	0.679375i	$-0.762251\pi$
$257$	−542479.	+	313201.i	−0.512331	+	0.295794i	0.221461	+	0.975169i	$0.428918\pi$
$258$		0			0
$259$	146556.	+	84614.0i	0.135754	+	0.0783777i
$260$	−39683.6	−	19463.0i	−0.0364064	−	0.0178557i
$261$		0			0
$262$	627315.	+	1.00637e6i	0.564589	+	0.905743i
$263$	−750127.	+	1.29926e6i	−0.668722	+	1.15826i	0.309540	+	0.950887i	$0.399825\pi$
$263$	−750127.	+	1.29926e6i	−0.668722	+	1.15826i	−0.978262	+	0.207374i	$0.933508\pi$
$264$		0			0
$265$	−11651.8	−	20181.4i	−0.0101924	−	0.0176538i
$266$	−17813.0	+	33412.8i	−0.0154359	+	0.0289540i
$267$		0			0
$268$	−1.76684e6	+	1.18611e6i	−1.50266	+	1.00876i
$269$			264637.i			0.222982i	0.993765	+	0.111491i	$0.0355626\pi$
$269$			264637.i			0.222982i	−0.993765	+	0.111491i	$0.964437\pi$
$270$		0			0
$271$			650898.i			0.538381i	0.963087	+	0.269190i	$0.0867561\pi$
$271$			650898.i			0.538381i	−0.963087	+	0.269190i	$0.913244\pi$
$272$	−257311.	−	1.89111e6i	−0.210880	−	1.54986i
$273$		0			0
$274$	573886.	+	305949.i	0.461795	+	0.246191i
$275$	−134568.	−	233079.i	−0.107303	−	0.185853i
$276$		0			0
$277$	237366.	−	411129.i	0.185874	−	0.321943i	−0.757997	−	0.652258i	$-0.773822\pi$
$277$	237366.	−	411129.i	0.185874	−	0.321943i	0.943871	+	0.330315i	$0.107155\pi$
$278$	−1.03577e6	+	645639.i	−0.803804	+	0.501046i
$279$		0			0
$280$	−12312.8	+	1253.12i	−0.00938557	+	0.000955208i
$281$	−1.41561e6	−	817304.i	−1.06949	−	0.617473i	−0.141451	−	0.989945i	$-0.545177\pi$
$281$	−1.41561e6	−	817304.i	−1.06949	−	0.617473i	−0.928043	+	0.372472i	$0.878510\pi$
$282$		0			0
$283$	−1.06078e6	+	612441.i	−0.787333	+	0.454567i	−0.839023	−	0.544096i	$-0.816873\pi$
$283$	−1.06078e6	+	612441.i	−0.787333	+	0.454567i	0.0516895	+	0.998663i	$0.483539\pi$
$284$	1.39116e6	−	94209.1i	1.02348	−	0.0693102i
$285$		0			0
$286$	159168.	−	5383.24i	0.115064	−	0.00389160i
$287$	245345.			0.175821
$288$		0			0
$289$	−2.05390e6			−1.44655
$290$	−120488.	+	4075.06i	−0.0841298	+	0.00284537i
$291$		0			0
$292$	731186.	−	49515.9i	0.501847	−	0.0339850i
$293$	−963120.	+	556058.i	−0.655407	+	0.378400i	−0.790525	−	0.612430i	$-0.790192\pi$
$293$	−963120.	+	556058.i	−0.655407	+	0.378400i	0.135117	+	0.990830i	$0.456859\pi$
$294$		0			0
$295$	−13994.2	−	8079.55i	−0.00936253	−	0.00540546i
$296$	1.89439e6	−	192800.i	1.25673	−	0.127902i
$297$		0			0
$298$	−1.06451e6	+	663555.i	−0.694399	+	0.432849i
$299$	−420362.	+	728088.i	−0.271923	+	0.470984i
$300$		0			0
$301$	−63107.9	−	109306.i	−0.0401483	−	0.0695389i
$302$	−2.10044e6	−	1.11978e6i	−1.32523	−	0.706506i
$303$		0			0
$304$	57441.6	+	422167.i	0.0356486	+	0.261999i
$305$			141013.i			0.0867977i
$306$		0			0
$307$			1.54327e6i			0.934537i	0.884115	+	0.467269i	$0.154762\pi$
$307$			1.54327e6i			0.934537i	−0.884115	+	0.467269i	$0.845238\pi$
$308$	37025.0	−	24855.5i	0.0222391	−	0.0149295i
$309$		0			0
$310$	−83538.7	+	156698.i	−0.0493723	+	0.0926104i
$311$	1.17389e6	+	2.03323e6i	0.688218	+	1.19203i	0.972414	+	0.233262i	$0.0749399\pi$
$311$	1.17389e6	+	2.03323e6i	0.688218	+	1.19203i	−0.284196	+	0.958766i	$0.591727\pi$
$312$		0			0
$313$	−705005.	+	1.22110e6i	−0.406753	+	0.704517i	−0.994524	−	0.104510i	$-0.966672\pi$
$313$	−705005.	+	1.22110e6i	−0.406753	+	0.704517i	0.587770	+	0.809028i	$0.300006\pi$
$314$	−662351.	−	1.06258e6i	−0.379109	−	0.608187i
$315$		0			0
$316$	−1.05967e6	−	519720.i	−0.596971	−	0.292787i
$317$	−1.72360e6	−	995122.i	−0.963360	−	0.556196i	−0.0661546	−	0.997809i	$-0.521073\pi$
$317$	−1.72360e6	−	995122.i	−0.963360	−	0.556196i	−0.897206	+	0.441613i	$0.854406\pi$
$318$		0			0
$319$	376192.	−	217194.i	0.206982	−	0.119501i
$320$	−104103.	+	92499.6i	−0.0568312	+	0.0504969i
$321$		0			0
$322$	7957.38	+	235278.i	0.00427691	+	0.126457i
$323$	775473.			0.413581
$324$		0			0
$325$	−1.00977e6			−0.530289
$326$	61968.5	+	1.83224e6i	0.0322944	+	0.954856i
$327$		0			0
$328$	2.23875e6	−	1.61530e6i	1.14900	−	0.829028i
$329$	396919.	−	229161.i	0.202168	−	0.116722i
$330$		0			0
$331$	−2.45201e6	−	1.41567e6i	−1.23013	−	0.710218i	−0.263076	−	0.964775i	$-0.584737\pi$
$331$	−2.45201e6	−	1.41567e6i	−1.23013	−	0.710218i	−0.967058	+	0.254557i	$0.918070\pi$
$332$	−775126.	+	1.58042e6i	−0.385946	+	0.786916i
$333$		0			0
$334$	748723.	+	1.20114e6i	0.367244	+	0.589152i
$335$	141312.	−	244760.i	0.0687968	−	0.119160i
$336$		0			0
$337$	−360837.	−	624988.i	−0.173076	−	0.299776i	0.766418	−	0.642342i	$-0.222037\pi$
$337$	−360837.	−	624988.i	−0.173076	−	0.299776i	−0.939494	+	0.342566i	$0.888704\pi$
$338$	−706993.	+	1.32615e6i	−0.336607	+	0.631392i
$339$		0			0
$340$	141277.	+	210448.i	0.0662788	+	0.0987295i
$341$		−	639836.i		−	0.297977i
$342$		0			0
$343$			536603.i			0.246274i
$344$	−1.29550e6	−	581918.i	−0.590259	−	0.265134i
$345$		0			0
$346$	−1.54090e6	−	821486.i	−0.691967	−	0.368901i
$347$	−751022.	−	1.30081e6i	−0.334833	−	0.579948i	0.648619	−	0.761113i	$-0.275347\pi$
$347$	−751022.	−	1.30081e6i	−0.334833	−	0.579948i	−0.983453	+	0.181165i	$0.942013\pi$
$348$		0			0
$349$	−506792.	+	877790.i	−0.222724	+	0.385769i	−0.955634	−	0.294556i	$-0.904828\pi$
$349$	−506792.	+	877790.i	−0.222724	+	0.385769i	0.732910	+	0.680325i	$0.238161\pi$
$350$	−239947.	+	149569.i	−0.104700	+	0.0652638i
$351$		0			0
$352$	174206.	−	470570.i	0.0749387	−	0.202427i
$353$	1.78252e6	+	1.02914e6i	0.761374	+	0.439579i	0.829789	−	0.558077i	$-0.188461\pi$
$353$	1.78252e6	+	1.02914e6i	0.761374	+	0.439579i	−0.0684149	+	0.997657i	$0.521794\pi$
$354$		0			0
$355$	−160372.	+	92591.0i	−0.0675396	+	0.0389940i
$356$	−88580.2	−	1.30804e6i	−0.0370435	−	0.547010i
$357$		0			0
$358$	−44419.0	+	1502.30i	−0.0183173	+	0.000619513i
$359$	301586.			0.123502			0.0617512	−	0.998092i	$-0.480331\pi$
$359$	301586.			0.123502			0.0617512	+	0.998092i	$0.480331\pi$
$360$		0			0
$361$	2.30298e6			0.930086
$362$	2.54251e6	−	85990.7i	1.01974	−	0.0344889i
$363$		0			0
$364$	−11304.5	−	166930.i	−0.00447196	−	0.0660361i
$365$	−84290.9	+	48665.4i	−0.0331168	+	0.0191200i
$366$		0			0
$367$	1.93072e6	+	1.11470e6i	0.748261	+	0.432009i	0.825065	−	0.565037i	$-0.191138\pi$
$367$	1.93072e6	+	1.11470e6i	0.748261	+	0.432009i	−0.0768040	+	0.997046i	$0.524472\pi$
$368$	1.62164e6	+	2.09450e6i	0.624215	+	0.806234i
$369$		0			0
$370$	−214612.	+	133777.i	−0.0814985	+	0.0508016i
$371$	44106.5	−	76394.7i	0.0166367	−	0.0288156i
$372$		0			0
$373$	898552.	+	1.55634e6i	0.334404	+	0.579204i	0.983370	−	0.181613i	$-0.0581318\pi$
$373$	898552.	+	1.55634e6i	0.334404	+	0.579204i	−0.648966	+	0.760817i	$0.724798\pi$
$374$	−805925.	−	429654.i	−0.297931	−	0.158833i
$375$		0			0
$376$	2.11310e6	−	4.70432e6i	0.770814	−	1.71604i
$377$		−	1.62978e6i		−	0.590574i
$378$		0			0
$379$		−	2.14708e6i		−	0.767804i	−0.923374	−	0.383902i	$-0.874580\pi$
$379$		−	2.14708e6i		−	0.767804i	0.923374	−	0.383902i	$-0.125420\pi$
$380$	−31538.4	−	46979.9i	−0.0112042	−	0.0166899i
$381$		0			0
$382$	−1.35924e6	+	2.54960e6i	−0.476582	+	0.893951i
$383$	−1.30237e6	−	2.25578e6i	−0.453669	−	0.785777i	0.544942	−	0.838474i	$-0.316552\pi$
$383$	−1.30237e6	−	2.25578e6i	−0.453669	−	0.785777i	−0.998611	+	0.0526965i	$0.983218\pi$
$384$		0			0
$385$	−2961.27	+	5129.06i	−0.00101818	+	0.00176354i
$386$	−2.63326e6	−	4.22442e6i	−0.899551	−	1.44311i
$387$		0			0
$388$	657764.	−	1.34113e6i	0.221815	−	0.452264i
$389$	3.00548e6	+	1.73521e6i	1.00702	+	0.581405i	0.910319	−	0.413908i	$-0.135836\pi$
$389$	3.00548e6	+	1.73521e6i	1.00702	+	0.581405i	0.0967049	+	0.995313i	$0.469170\pi$
$390$		0			0
$391$	4.17537e6	−	2.41065e6i	1.38119	−	0.797429i
$392$	1.75274e6	+	2.42923e6i	0.576106	+	0.798462i
$393$		0			0
$394$	−31129.2	−	920406.i	−0.0101025	−	0.298703i
$395$	156749.			0.0505490
$396$		0			0
$397$	5.78885e6			1.84338			0.921692	−	0.387922i	$-0.126807\pi$
$397$	5.78885e6			1.84338			0.921692	+	0.387922i	$0.126807\pi$
$398$	150383.	+	4.44642e6i	0.0475874	+	1.40703i
$399$		0			0
$400$	−1.20476e6	+	2.94458e6i	−0.376487	+	0.920180i
$401$	2.02846e6	−	1.17113e6i	0.629950	−	0.363702i	−0.150782	−	0.988567i	$-0.548179\pi$
$401$	2.02846e6	−	1.17113e6i	0.629950	−	0.363702i	0.780733	+	0.624865i	$0.214846\pi$
$402$		0			0
$403$	−2.07897e6	−	1.20029e6i	−0.637655	−	0.368150i
$404$	2.18382e6	+	1.07107e6i	0.665678	+	0.326485i
$405$		0			0
$406$	−241407.	−	387278.i	−0.0726833	−	0.116602i
$407$	455608.	−	789137.i	0.136334	−	0.236138i
$408$		0			0
$409$	−1.17070e6	−	2.02771e6i	−0.346048	−	0.599373i	0.639495	−	0.768795i	$-0.279143\pi$
$409$	−1.17070e6	−	2.02771e6i	−0.346048	−	0.599373i	−0.985544	+	0.169422i	$0.945810\pi$
$410$	−172483.	+	323535.i	−0.0506741	+	0.0950520i
$411$		0			0
$412$	100328.	−	67351.9i	0.0291192	−	0.0195482i
$413$		−	61168.6i		−	0.0176463i
$414$		0			0
$415$		−	233781.i		−	0.0666328i
$416$	−1.20219e6	−	1.44880e6i	−0.340596	−	0.410463i
$417$		0			0
$418$	179913.	+	95915.0i	0.0503642	+	0.0268501i
$419$	−2.33383e6	−	4.04232e6i	−0.649434	−	1.12485i	−0.983258	−	0.182217i	$-0.941673\pi$
$419$	−2.33383e6	−	4.04232e6i	−0.649434	−	1.12485i	0.333824	−	0.942635i	$-0.391661\pi$
$420$		0			0
$421$	2.03900e6	−	3.53165e6i	0.560676	−	0.971119i	−0.436762	−	0.899577i	$-0.643875\pi$
$421$	2.03900e6	−	3.53165e6i	0.560676	−	0.971119i	0.997438	−	0.0715416i	$-0.0227919\pi$
$422$	4.87721e6	−	3.04018e6i	1.33318	−	0.831032i
$423$		0			0
$424$	−100500.	−	987484.i	−0.0271489	−	0.266757i
$425$	5.01490e6	+	2.89536e6i	1.34676	+	0.777553i
$426$		0			0
$427$	−462274.	+	266894.i	−0.122696	+	0.0708385i
$428$	1.84080e6	−	124658.i	0.485731	−	0.0328937i
$429$		0			0
$430$	188508.	−	6375.56i	0.0491652	−	0.00166283i
$431$	4.54361e6			1.17817			0.589085	−	0.808071i	$-0.299488\pi$
$431$	4.54361e6			1.17817			0.589085	+	0.808071i	$0.299488\pi$
$432$		0			0
$433$	−6726.40			−0.00172410			−0.000862051	−	1.00000i	$-0.500274\pi$
$433$	−6726.40			−0.00172410			−0.000862051		1.00000i	$0.500274\pi$
$434$	−671809.	+	22721.4i	−0.171207	+	0.00579043i
$435$		0			0
$436$	−5.62884e6	+	381184.i	−1.41809	+	0.0960326i
$437$	−932101.	+	538148.i	−0.233485	+	0.134803i
$438$		0			0
$439$	4.27223e6	+	2.46657e6i	1.05802	+	0.610847i	0.924883	−	0.380251i	$-0.124162\pi$
$439$	4.27223e6	+	2.46657e6i	1.05802	+	0.610847i	0.133134	+	0.991098i	$0.457496\pi$
$440$	6747.49	+	66298.7i	0.00166154	+	0.0163258i
$441$		0			0
$442$	−2.90791e6	+	1.81263e6i	−0.707987	+	0.441319i
$443$	2.52747e6	−	4.37771e6i	0.611895	−	1.05983i	−0.379025	−	0.925386i	$-0.623741\pi$
$443$	2.52747e6	−	4.37771e6i	0.611895	−	1.05983i	0.990921	−	0.134448i	$-0.0429260\pi$
$444$		0			0
$445$	87058.8	+	150790.i	0.0208407	+	0.0360972i
$446$	−1.16403e6	−	620567.i	−0.277094	−	0.147724i
$447$		0			0
$448$	−500271.	−	166201.i	−0.117763	−	0.0391235i
$449$			3.95256e6i			0.925257i	0.886552	+	0.462628i	$0.153094\pi$
$449$			3.95256e6i			0.925257i	−0.886552	+	0.462628i	$0.846906\pi$
$450$		0			0
$451$		−	1.32107e6i		−	0.305833i
$452$	−3.43154e6	+	2.30365e6i	−0.790028	+	0.530360i
$453$		0			0
$454$	−2.33917e6	+	4.38771e6i	−0.532626	+	0.999076i
$455$	11110.3	+	19243.6i	0.00251593	+	0.00435772i
$456$		0			0
$457$	−3.74368e6	+	6.48424e6i	−0.838509	+	1.45234i	0.0526320	+	0.998614i	$0.483239\pi$
$457$	−3.74368e6	+	6.48424e6i	−0.838509	+	1.45234i	−0.891141	+	0.453726i	$0.850094\pi$
$458$	1.14482e6	+	1.83658e6i	0.255020	+	0.409116i
$459$		0			0
$460$	−315854.	−	154912.i	−0.0695973	−	0.0341343i
$461$	−4.43539e6	−	2.56077e6i	−0.972029	−	0.561201i	−0.0721745	−	0.997392i	$-0.522994\pi$
$461$	−4.43539e6	−	2.56077e6i	−0.972029	−	0.561201i	−0.899854	+	0.436191i	$0.856327\pi$
$462$		0			0
$463$	3.47662e6	−	2.00723e6i	0.753711	−	0.435155i	−0.0733224	−	0.997308i	$-0.523360\pi$
$463$	3.47662e6	−	2.00723e6i	0.753711	−	0.435155i	0.827033	+	0.562153i	$0.190027\pi$
$464$	−4.75258e6	−	1.94450e6i	−1.02479	−	0.419288i
$465$		0			0
$466$	−42899.8	−	1.26843e6i	−0.00915146	−	0.270583i
$467$	−5.43636e6			−1.15350			−0.576748	−	0.816922i	$-0.695679\pi$
$467$	−5.43636e6			−1.15350			−0.576748	+	0.816922i	$0.695679\pi$
$468$		0			0
$469$	1.06985e6			0.224590
$470$	23151.3	+	684521.i	0.00483427	+	0.142936i
$471$		0			0
$472$	−402723.	−	558159.i	−0.0832054	−	0.115319i
$473$	−588564.	+	339807.i	−0.120960	+	0.0698361i
$474$		0			0
$475$	−1.11952e6	−	646353.i	−0.227665	−	0.131443i
$476$	−422505.	+	861455.i	−0.0854701	+	0.174267i
$477$		0			0
$478$	−4.60297e6	−	7.38432e6i	−0.921442	−	1.47823i
$479$	−4.63944e6	+	8.03575e6i	−0.923904	+	1.60025i	−0.130589	+	0.991437i	$0.541687\pi$
$479$	−4.63944e6	+	8.03575e6i	−0.923904	+	1.60025i	−0.793315	+	0.608812i	$0.791646\pi$
$480$		0			0
$481$	−1.70939e6	−	2.96075e6i	−0.336882	−	0.583497i
$482$	−3.68793e6	+	6.91765e6i	−0.723045	+	1.35625i
$483$		0			0
$484$	2.73865e6	+	4.07951e6i	0.531401	+	0.791580i
$485$			198384.i			0.0382958i
$486$		0			0
$487$		−	2.35999e6i		−	0.450908i	−0.974254	−	0.225454i	$-0.927614\pi$
$487$		−	2.35999e6i		−	0.450908i	0.974254	−	0.225454i	$-0.0723865\pi$
$488$	−2.46103e6	+	5.47891e6i	−0.467808	+	1.04147i
$489$		0			0
$490$	−351063.	−	187158.i	−0.0660533	−	0.0352143i
$491$	−4.26271e6	−	7.38323e6i	−0.797961	−	1.38211i	−0.920942	−	0.389701i	$-0.872579\pi$
$491$	−4.26271e6	−	7.38323e6i	−0.797961	−	1.38211i	0.122980	−	0.992409i	$-0.460755\pi$
$492$		0			0
$493$	−4.67314e6	+	8.09412e6i	−0.865947	+	1.49986i
$494$	649156.	−	404647.i	0.119683	−	0.0746035i
$495$		0			0
$496$	−5.98061e6	+	4.63040e6i	−1.09154	+	0.845111i
$497$	−607073.	−	350494.i	−0.110243	−	0.0636486i
$498$		0			0
$499$	218746.	−	126293.i	0.0393268	−	0.0227054i	−0.480208	−	0.877155i	$-0.659439\pi$
$499$	218746.	−	126293.i	0.0393268	−	0.0227054i	0.519535	+	0.854449i	$0.326105\pi$
$500$	−57263.0	−	845587.i	−0.0102435	−	0.151263i
$501$		0			0
$502$	7.42898e6	−	251257.i	1.31574	−	0.0444999i
$503$	6.25307e6			1.10198			0.550989	−	0.834512i	$-0.314251\pi$
$503$	6.25307e6			1.10198			0.550989	+	0.834512i	$0.314251\pi$
$504$		0			0
$505$	−323037.			−0.0563669
$506$	1.26687e6	−	42846.9i	0.219965	−	0.00743949i
$507$		0			0
$508$	93519.8	+	1.38098e6i	0.0160785	+	0.237426i
$509$	−431856.	+	249332.i	−0.0738830	+	0.0426564i	−0.536486	−	0.843909i	$-0.680249\pi$
$509$	−431856.	+	249332.i	−0.0738830	+	0.0426564i	0.462603	+	0.886565i	$0.346915\pi$
$510$		0			0
$511$	−319074.	−	184218.i	−0.0540555	−	0.0312090i
$512$	−5.65917e6	+	1.77713e6i	−0.954064	+	0.299601i
$513$		0			0
$514$	3.00708e6	−	1.87445e6i	0.502039	−	0.312943i
$515$	−8024.25	+	13898.4i	−0.00133317	+	0.00230912i
$516$		0			0
$517$	−1.23393e6	−	2.13723e6i	−0.203032	−	0.351661i
$518$	−844750.	−	450352.i	−0.138326	−	0.0737442i
$519$		0			0
$520$	228077.	+	102448.i	0.0369891	+	0.0166149i
$521$		−	9.81352e6i		−	1.58391i	−0.610579	−	0.791955i	$-0.709063\pi$
$521$		−	9.81352e6i		−	1.58391i	0.610579	−	0.791955i	$-0.290937\pi$
$522$		0			0
$523$			1.10853e7i			1.77211i	0.463576	+	0.886057i	$0.346566\pi$
$523$			1.10853e7i			1.77211i	−0.463576	+	0.886057i	$0.653434\pi$
$524$	−3.73903e6	−	5.56969e6i	−0.594882	−	0.886141i
$525$		0			0
$526$	3.99250e6	−	7.48895e6i	0.629188	−	1.18020i
$527$	6.88333e6	+	1.19223e7i	1.07962	+	1.86996i
$528$		0			0
$529$	−127624.	+	221050.i	−0.0198286	+	0.0343441i
$530$	69733.5	+	111870.i	0.0107833	+	0.0172991i
$531$		0			0
$532$	94319.1	−	192310.i	0.0144484	−	0.0294592i
$533$	−4.29246e6	−	2.47825e6i	−0.654467	−	0.377857i
$534$		0			0
$535$	−212206.	+	122517.i	−0.0320534	+	0.0185060i
$536$	9.76227e6	−	7.04368e6i	1.46770	−	1.05898i
$537$		0			0
$538$	−50601.9	−	1.49616e6i	−0.00753722	−	0.222855i
$539$	1.43347e6			0.212529
$540$		0			0
$541$	2.27509e6			0.334200			0.167100	−	0.985940i	$-0.446560\pi$
$541$	2.27509e6			0.334200			0.167100	+	0.985940i	$0.446560\pi$
$542$	−124460.	−	3.67993e6i	−0.0181983	−	0.538073i
$543$		0			0
$544$	1.81634e6	+	1.06424e7i	0.263148	+	1.54185i
$545$	648891.	−	374637.i	0.0935794	−	0.0540281i
$546$		0			0
$547$	−7.20659e6	−	4.16072e6i	−1.02982	−	0.594567i	−0.112887	−	0.993608i	$-0.536010\pi$
$547$	−7.20659e6	−	4.16072e6i	−1.02982	−	0.594567i	−0.916933	+	0.399041i	$0.869343\pi$
$548$	−3.30303e6	−	1.61999e6i	−0.469852	−	0.230441i
$549$		0			0
$550$	805364.	+	1.29201e6i	0.113523	+	0.182120i
$551$	1.04322e6	−	1.80691e6i	0.146385	−	0.253547i
$552$		0			0
$553$	296679.	+	513863.i	0.0412547	+	0.0714553i
$554$	−1.26336e6	+	2.36976e6i	−0.174885	+	0.328042i
$555$		0			0
$556$	5.73239e6	−	3.84825e6i	0.786409	−	0.527930i
$557$		−	1.46783e6i		−	0.200465i	−0.994964	−	0.100232i	$-0.968041\pi$
$557$		−	1.46783e6i		−	0.200465i	0.994964	−	0.100232i	$-0.0319586\pi$
$558$		0			0
$559$			2.54984e6i			0.345130i
$560$	69372.1	−	9439.03i	0.00934791	−	0.00127191i
$561$		0			0
$562$	8.15962e6	+	4.35005e6i	1.08976	+	0.580969i
$563$	1.07987e6	+	1.87039e6i	0.143582	+	0.248691i	0.928843	−	0.370474i	$-0.120805\pi$
$563$	1.07987e6	+	1.87039e6i	0.143582	+	0.248691i	−0.785261	+	0.619165i	$0.787471\pi$
$564$		0			0
$565$	274455.	−	475370.i	0.0361701	−	0.0626485i
$566$	5.88014e6	−	3.66534e6i	0.771518	−	0.480921i
$567$		0			0
$568$	−7.84707e6	+	798630.i	−1.02056	+	0.103866i
$569$	−2.42463e6	−	1.39986e6i	−0.313954	−	0.181261i	0.334741	−	0.942310i	$-0.391351\pi$
$569$	−2.42463e6	−	1.39986e6i	−0.313954	−	0.181261i	−0.648694	+	0.761049i	$0.724685\pi$
$570$		0			0
$571$	−9.90022e6	+	5.71589e6i	−1.27073	+	0.733658i	−0.975126	−	0.221651i	$-0.928855\pi$
$571$	−9.90022e6	+	5.71589e6i	−1.27073	+	0.733658i	−0.295607	+	0.955310i	$0.595522\pi$
$572$	−898844.	+	60869.6i	−0.114867	+	0.00777876i
$573$		0			0
$574$	−1.38709e6	+	46912.9i	−0.175721	+	0.00594309i
$575$	−8.03706e6			−1.01374
$576$		0			0
$577$	669533.			0.0837206			0.0418603	−	0.999123i	$-0.486672\pi$
$577$	669533.			0.0837206			0.0418603	+	0.999123i	$0.486672\pi$
$578$	1.16119e7	−	392730.i	1.44572	−	0.0488961i
$579$		0			0
$580$	680416.	−	46077.7i	0.0839855	−	0.00568749i
$581$	766391.	−	442476.i	0.0941911	−	0.0543813i
$582$		0			0
$583$	−411351.	−	237494.i	−0.0501235	−	0.0289388i
$584$	−4.12438e6	+	419756.i	−0.500411	+	0.0509289i
$585$		0			0
$586$	5.33879e6	−	3.32790e6i	0.642242	−	0.400337i
$587$	197174.	−	341516.i	0.0236187	−	0.0409087i	−0.853974	−	0.520315i	$-0.825815\pi$
$587$	197174.	−	341516.i	0.0236187	−	0.0409087i	0.877593	+	0.479406i	$0.159148\pi$
$588$		0			0
$589$	−1.53662e6	−	2.66151e6i	−0.182507	−	0.316111i
$590$	80662.8	+	43002.9i	0.00953989	+	0.00508590i
$591$		0			0
$592$	−1.06733e7	+	1.45225e6i	−1.25168	+	0.170309i
$593$			5.00148e6i			0.584066i	0.956408	+	0.292033i	$0.0943317\pi$
$593$			5.00148e6i			0.584066i	−0.956408	+	0.292033i	$0.905668\pi$
$594$		0			0
$595$		−	127429.i		−	0.0147562i
$596$	5.89145e6	−	3.95504e6i	0.679371	−	0.456073i
$597$		0			0
$598$	2.23735e6	−	4.19671e6i	0.255847	−	0.479906i
$599$	5.30363e6	+	9.18615e6i	0.603957	+	1.04608i	0.992215	+	0.124533i	$0.0397434\pi$
$599$	5.30363e6	+	9.18615e6i	0.603957	+	1.04608i	−0.388259	+	0.921550i	$0.626923\pi$
$600$		0			0
$601$	3.48253e6	−	6.03191e6i	0.393286	−	0.681191i	−0.599595	−	0.800304i	$-0.704672\pi$
$601$	3.48253e6	−	6.03191e6i	0.393286	−	0.681191i	0.992881	+	0.119113i	$0.0380050\pi$
$602$	377689.	+	605908.i	0.0424759	+	0.0681421i
$603$		0			0
$604$	1.20892e7	+	5.92919e6i	1.34836	+	0.661307i
$605$	−565134.	−	326280.i	−0.0627715	−	0.0362412i
$606$		0			0
$607$	1.36935e7	−	7.90597e6i	1.50850	−	0.870930i	0.508544	−	0.861036i	$-0.330184\pi$
$607$	1.36935e7	−	7.90597e6i	1.50850	−	0.870930i	0.999951	−	0.00989422i	$-0.00314948\pi$
$608$	−405477.	−	2.37579e6i	−0.0444843	−	0.260645i
$609$		0			0
$610$	−26963.3	−	797231.i	−0.00293392	−	0.0867481i
$611$	−9.25912e6			−1.00338
$612$		0			0
$613$	133521.			0.0143515			0.00717575	−	0.999974i	$-0.497716\pi$
$613$	133521.			0.0143515			0.00717575	+	0.999974i	$0.497716\pi$
$614$	−295093.	−	8.72508e6i	−0.0315891	−	0.934003i
$615$		0			0
$616$	−204573.	+	147603.i	−0.0217218	+	0.0156727i
$617$	−1.06772e7	+	6.16447e6i	−1.12913	+	0.651902i	−0.943715	−	0.330758i	$-0.892696\pi$
$617$	−1.06772e7	+	6.16447e6i	−1.12913	+	0.651902i	−0.185413	+	0.982661i	$0.559362\pi$
$618$		0			0
$619$	−8.56059e6	−	4.94246e6i	−0.898001	−	0.518461i	−0.0214502	−	0.999770i	$-0.506828\pi$
$619$	−8.56059e6	−	4.94246e6i	−0.898001	−	0.518461i	−0.876551	+	0.481309i	$0.840162\pi$
$620$	442334.	−	901886.i	0.0462137	−	0.0942263i
$621$		0			0
$622$	−7.02550e6	−	1.12707e7i	−0.728117	−	1.16808i
$623$	−329552.	+	570801.i	−0.0340176	+	0.0589202i
$624$		0			0
$625$	−4.79831e6	−	8.31092e6i	−0.491347	−	0.851038i
$626$	3.75234e6	−	7.03847e6i	0.382707	−	0.717864i
$627$		0			0
$628$	3.94786e6	+	5.88077e6i	0.399450	+	0.595025i
$629$			1.96057e7i			1.97586i
$630$		0			0
$631$			1.28910e7i			1.28888i	0.764653	+	0.644442i	$0.222910\pi$
$631$			1.28910e7i			1.28888i	−0.764653	+	0.644442i	$0.777090\pi$
$632$	6.09035e6	+	2.73568e6i	0.606526	+	0.272441i
$633$		0			0
$634$	9.93487e6	+	5.29647e6i	0.981610	+	0.523315i
$635$	−91913.5	−	159199.i	−0.00904576	−	0.0156677i
$636$		0			0
$637$	2.68911e6	−	4.65768e6i	0.262579	−	0.454801i
$638$	−2.08532e6	+	1.29987e6i	−0.202824	+	0.126429i
$639$		0			0
$640$	570870.	−	542863.i	0.0550918	−	0.0523891i
$641$	7.67906e6	+	4.43351e6i	0.738181	+	0.426189i	0.821408	−	0.570342i	$-0.193189\pi$
$641$	7.67906e6	+	4.43351e6i	0.738181	+	0.426189i	−0.0832264	+	0.996531i	$0.526522\pi$
$642$		0			0
$643$	−9.18917e6	+	5.30537e6i	−0.876494	+	0.506044i	−0.869501	−	0.493932i	$-0.835559\pi$
$643$	−9.18917e6	+	5.30537e6i	−0.876494	+	0.506044i	−0.00699288	+	0.999976i	$0.502226\pi$
$644$	−89976.1	−	1.32865e6i	−0.00854894	−	0.126240i
$645$		0			0
$646$	−4.38423e6	+	148280.i	−0.413345	+	0.0139798i
$647$	2.37142e6			0.222714			0.111357	−	0.993780i	$-0.464480\pi$
$647$	2.37142e6			0.222714			0.111357	+	0.993780i	$0.464480\pi$
$648$		0			0
$649$	−329365.			−0.0306949
$650$	5.70884e6	−	193080.i	0.529986	−	0.0179248i
$651$		0			0
$652$	−700693.	−	1.03469e7i	−0.0645519	−	0.953219i
$653$	8.07136e6	−	4.66000e6i	0.740737	−	0.427665i	−0.0816004	−	0.996665i	$-0.526003\pi$
$653$	8.07136e6	−	4.66000e6i	0.740737	−	0.427665i	0.822337	+	0.569001i	$0.192670\pi$
$654$		0			0
$655$	771568.	+	445465.i	0.0702701	+	0.0405705i
$656$	−1.23482e7	+	9.56039e6i	−1.12032	+	0.867393i
$657$		0			0
$658$	−2.20021e6	+	1.37149e6i	−0.198107	+	0.123489i
$659$	971185.	−	1.68214e6i	0.0871141	−	0.150886i	−0.819176	−	0.573542i	$-0.805569\pi$
$659$	971185.	−	1.68214e6i	0.0871141	−	0.150886i	0.906290	+	0.422656i	$0.138902\pi$
$660$		0			0
$661$	−8.93142e6	−	1.54697e7i	−0.795091	−	1.37714i	−0.922781	−	0.385324i	$-0.874090\pi$
$661$	−8.93142e6	−	1.54697e7i	−0.795091	−	1.37714i	0.127690	−	0.991814i	$-0.459244\pi$
$662$	1.41334e7	+	7.53480e6i	1.25344	+	0.668232i
$663$		0			0
$664$	4.08007e6	−	9.08333e6i	0.359127	−	0.799512i
$665$			28446.9i			0.00249449i
$666$		0			0
$667$		−	1.29719e7i		−	1.12899i
$668$	−4.46267e6	−	6.64763e6i	−0.386949	−	0.576402i
$669$		0			0
$670$	−752126.	+	1.41080e6i	−0.0647297	+	0.121417i
$671$	1.43710e6	+	2.48914e6i	0.123220	+	0.213424i
$672$		0			0
$673$	3.31863e6	−	5.74803e6i	0.282436	−	0.489194i	−0.689548	−	0.724240i	$-0.742191\pi$
$673$	3.31863e6	−	5.74803e6i	0.282436	−	0.489194i	0.971984	+	0.235046i	$0.0755241\pi$
$674$	2.15954e6	+	3.46445e6i	0.183110	+	0.293754i
$675$		0			0
$676$	3.74350e6	−	7.63271e6i	0.315073	−	0.642409i
$677$	2.38918e6	+	1.37940e6i	0.200345	+	0.115669i	0.596816	−	0.802378i	$-0.296432\pi$
$677$	2.38918e6	+	1.37940e6i	0.200345	+	0.115669i	−0.396472	+	0.918047i	$0.629765\pi$
$678$		0			0
$679$	−650351.	+	375480.i	−0.0541344	+	0.0312545i
$680$	−838968.	−	1.16278e6i	−0.0695782	−	0.0964327i
$681$		0			0
$682$	122344.	+	3.61739e6i	0.0100722	+	0.297807i
$683$	462361.			0.0379253			0.0189627	−	0.999820i	$-0.493964\pi$
$683$	462361.			0.0379253			0.0189627	+	0.999820i	$0.493964\pi$
$684$		0			0
$685$	488594.			0.0397852
$686$	−102605.	−	3.03375e6i	−0.00832451	−	0.246133i
$687$		0			0
$688$	7.43556e6	+	3.04223e6i	0.598884	+	0.245031i
$689$	−1.54334e6	+	891048.i	−0.123855	+	0.0715078i
$690$		0			0
$691$	4.14382e6	+	2.39243e6i	0.330146	+	0.190610i	0.655906	−	0.754843i	$-0.272287\pi$
$691$	4.14382e6	+	2.39243e6i	0.330146	+	0.190610i	−0.325760	+	0.945452i	$0.605620\pi$
$692$	8.86877e6	+	4.34973e6i	0.704041	+	0.345300i
$693$		0			0
$694$	4.49472e6	+	7.21067e6i	0.354245	+	0.568299i
$695$	−458477.	+	794106.i	−0.0360044	+	0.0623615i
$696$		0			0
$697$	1.42120e7	+	2.46160e7i	1.10809	+	1.91926i
$698$	2.69737e6	−	5.05960e6i	0.209557	−	0.393077i
$699$		0			0
$700$	1.32797e6	−	891490.i	0.102434	−	0.0687656i
$701$		−	1.31247e7i		−	1.00877i	−0.863478	−	0.504387i	$-0.831719\pi$
$701$		−	1.31247e7i		−	1.00877i	0.863478	−	0.504387i	$-0.168281\pi$
$702$		0			0
$703$		−	4.37673e6i		−	0.334012i
$704$	−894915.	+	2.69374e6i	−0.0680534	+	0.204844i
$705$		0			0
$706$	−1.02745e7	−	5.47752e6i	−0.775797	−	0.413592i
$707$	−611412.	−	1.05900e6i	−0.0460029	−	0.0796794i
$708$		0			0
$709$	−3.98415e6	+	6.90074e6i	−0.297659	+	0.515561i	−0.975600	−	0.219555i	$-0.929539\pi$
$709$	−3.98415e6	+	6.90074e6i	−0.297659	+	0.515561i	0.677941	+	0.735117i	$0.262873\pi$
$710$	888980.	−	554140.i	0.0661830	−	0.0412547i
$711$		0			0
$712$	750912.	+	7.37822e6i	0.0555123	+	0.545446i
$713$	−1.65472e7	−	9.55353e6i	−1.21899	−	0.703785i
$714$		0			0
$715$	103618.	−	59824.1i	0.00758004	−	0.00437634i
$716$	250841.	−	16986.9i	0.0182859	−	0.00123832i
$717$		0			0
$718$	−1.70505e6	+	57667.0i	−0.123432	+	0.00417461i
$719$	5.58804e6			0.403123			0.201561	−	0.979476i	$-0.435398\pi$
$719$	5.58804e6			0.403123			0.201561	+	0.979476i	$0.435398\pi$
$720$		0			0
$721$	−60749.9			−0.00435219
$722$	−1.30202e7	+	440359.i	−0.929554	+	0.0314386i
$723$		0			0
$724$	−1.43579e7	+	972317.i	−1.01799	+	0.0689385i
$725$	1.34928e7	−	7.79008e6i	0.953362	−	0.550424i
$726$		0			0
$727$	2.72597e6	+	1.57384e6i	0.191287	+	0.110439i	0.592585	−	0.805508i	$-0.298107\pi$
$727$	2.72597e6	+	1.57384e6i	0.191287	+	0.110439i	−0.401298	+	0.915948i	$0.631441\pi$
$728$	95830.4	+	941598.i	0.00670154	+	0.0658472i
$729$		0			0
$730$	467244.	−	291253.i	0.0324516	−	0.0202285i
$731$	7.31128e6	−	1.26635e7i	0.506057	−	0.876517i
$732$		0			0
$733$	1.20330e7	+	2.08418e7i	0.827209	+	1.43277i	0.900219	+	0.435438i	$0.143406\pi$
$733$	1.20330e7	+	2.08418e7i	0.827209	+	1.43277i	−0.0730095	+	0.997331i	$0.523260\pi$
$734$	−1.11287e7	−	5.93291e6i	−0.762436	−	0.406469i
$735$		0			0
$736$	−9.56861e6	−	1.15314e7i	−0.651110	−	0.784674i
$737$		−	5.76065e6i		−	0.390663i
$738$		0			0
$739$			4.89450e6i			0.329683i	0.986320	+	0.164842i	$0.0527113\pi$
$739$			4.89450e6i			0.329683i	−0.986320	+	0.164842i	$0.947289\pi$
$740$	1.18776e6	−	797361.i	0.0797348	−	0.0535273i
$741$		0			0
$742$	−234754.	+	440340.i	−0.0156532	+	0.0293615i
$743$	−2.80417e6	−	4.85696e6i	−0.186351	−	0.322770i	0.757680	−	0.652626i	$-0.226333\pi$
$743$	−2.80417e6	−	4.85696e6i	−0.186351	−	0.322770i	−0.944031	+	0.329857i	$0.893000\pi$
$744$		0			0
$745$	−471200.	+	816142.i	−0.0311039	+	0.0538735i
$746$	−5.37766e6	−	8.62713e6i	−0.353791	−	0.567570i
$747$		0			0
$748$	4.63855e6	+	2.27500e6i	0.303129	+	0.148671i
$749$	−803285.	−	463777.i	−0.0523197	−	0.0302068i
$750$		0			0
$751$	−1.23051e7	+	7.10437e6i	−0.796134	+	0.459648i	−0.842118	−	0.539294i	$-0.818691\pi$
$751$	−1.23051e7	+	7.10437e6i	−0.796134	+	0.459648i	0.0459832	+	0.998942i	$0.485358\pi$
$752$	−1.10471e7	+	2.70005e7i	−0.712368	+	1.74111i
$753$		0			0
$754$	311633.	+	9.21414e6i	0.0199625	+	0.590237i
$755$	−1.78826e6			−0.114173
$756$		0			0
$757$	−1.75241e7			−1.11147			−0.555733	−	0.831361i	$-0.687562\pi$
$757$	−1.75241e7			−1.11147			−0.555733	+	0.831361i	$0.687562\pi$
$758$	410548.	+	1.21388e7i	0.0259532	+	0.767365i
$759$		0			0
$760$	187289.	+	259576.i	0.0117619	+	0.0163016i
$761$	9.78403e6	−	5.64882e6i	0.612430	−	0.353587i	−0.161486	−	0.986875i	$-0.551629\pi$
$761$	9.78403e6	−	5.64882e6i	0.612430	−	0.353587i	0.773916	+	0.633288i	$0.218295\pi$
$762$		0			0
$763$	2.45631e6	+	1.41815e6i	0.152747	+	0.0881883i
$764$	7.19712e6	−	1.46744e7i	0.446093	−	0.909550i
$765$		0			0
$766$	7.79446e6	+	1.25043e7i	0.479970	+	0.769993i
$767$	−617871.	+	1.07018e6i	−0.0379236	+	0.0656855i
$768$		0			0
$769$	−465579.	−	806407.i	−0.0283908	−	0.0491743i	0.851481	−	0.524386i	$-0.175705\pi$
$769$	−465579.	−	806407.i	−0.0283908	−	0.0491743i	−0.879872	+	0.475211i	$0.842372\pi$
$770$	15761.1	−	29564.0i	0.000957989	−	0.00179695i
$771$		0			0
$772$	1.56952e7	+	2.33797e7i	0.947817	+	1.41188i
$773$			4.59758e6i			0.276745i	0.990380	+	0.138373i	$0.0441872\pi$
$773$			4.59758e6i			0.276745i	−0.990380	+	0.138373i	$0.955813\pi$
$774$		0			0
$775$		−	2.29489e7i		−	1.37249i
$776$	−3.46231e6	+	7.70802e6i	−0.206401	+	0.459503i
$777$		0			0
$778$	−1.73236e7	−	9.23556e6i	−1.02610	−	0.547034i
$779$	−3.17266e6	−	5.49522e6i	−0.187318	−	0.324445i
$780$		0			0
$781$	−1.88725e6	+	3.26881e6i	−0.110714	+	0.191762i
$782$	−2.31450e7	+	1.44273e7i	−1.35344	+	0.843660i
$783$		0			0
$784$	−1.03738e7	−	1.33988e7i	−0.602767	−	0.778532i
$785$	−814662.	−	470345.i	−0.0471849	−	0.0272422i
$786$		0			0
$787$	7.46443e6	−	4.30959e6i	0.429596	−	0.248027i	−0.269579	−	0.962978i	$-0.586884\pi$
$787$	7.46443e6	−	4.30959e6i	0.429596	−	0.248027i	0.699174	+	0.714951i	$0.253551\pi$
$788$	351986.	+	5.19768e6i	0.0201934	+	0.298190i
$789$		0			0
$790$	−886201.	+	29972.4i	−0.0505201	+	0.00170865i
$791$	2.07784e6			0.118079
$792$		0			0
$793$	1.07837e7			0.608954
$794$	−3.27280e7	+	1.10690e6i	−1.84233	+	0.0623099i
$795$		0			0
$796$	−1.70042e6	−	2.51096e7i	−0.0951203	−	1.40461i
$797$	−7.54210e6	+	4.35443e6i	−0.420578	+	0.242821i	−0.695324	−	0.718696i	$-0.744739\pi$
$797$	−7.54210e6	+	4.35443e6i	−0.420578	+	0.242821i	0.274747	+	0.961517i	$0.411406\pi$
$798$		0			0
$799$	4.59845e7	+	2.65492e7i	2.54826	+	1.47124i
$800$	6.24822e6	−	1.68779e7i	0.345169	−	0.932380i
$801$		0			0
$802$	−1.12442e7	+	7.00902e6i	−0.617297	+	0.384788i
$803$	−991930.	+	1.71807e6i	−0.0542865	+	0.0940270i
$804$		0			0
$805$	88430.7	+	153166.i	0.00480965	+	0.00833055i
$806$	1.19832e7	+	6.38849e6i	0.649735	+	0.346386i
$807$		0			0
$808$	−1.25513e7	−	5.63783e6i	−0.676334	−	0.303797i
$809$		−	1.21590e7i		−	0.653169i	−0.945168	−	0.326584i	$-0.894102\pi$
$809$		−	1.21590e7i		−	0.653169i	0.945168	−	0.326584i	$-0.105898\pi$
$810$		0			0
$811$		−	2.14341e7i		−	1.14433i	−0.820137	−	0.572167i	$-0.806103\pi$
$811$		−	2.14341e7i		−	1.14433i	0.820137	−	0.572167i	$-0.193897\pi$
$812$	1.43888e6	+	2.14336e6i	0.0765831	+	0.114079i
$813$		0			0
$814$	−2.42494e6	+	4.54860e6i	−0.128275	+	0.240612i
$815$	688658.	+	1.19279e6i	0.0363170	+	0.0629029i
$816$		0			0
$817$	−1.63215e6	+	2.82697e6i	−0.0855473	+	0.148172i
$818$	7.00641e6	+	1.12400e7i	0.366110	+	0.587333i
$819$		0			0
$820$	913287.	−	1.86212e6i	0.0474322	−	0.0967106i
$821$	1.88546e7	+	1.08857e7i	0.976248	+	0.563637i	0.901135	−	0.433538i	$-0.142735\pi$
$821$	1.88546e7	+	1.08857e7i	0.976248	+	0.563637i	0.0751127	+	0.997175i	$0.476068\pi$
$822$		0			0
$823$	1.63030e7	−	9.41255e6i	0.839012	−	0.484404i	−0.0179161	−	0.999839i	$-0.505703\pi$
$823$	1.63030e7	−	9.41255e6i	0.839012	−	0.484404i	0.856928	+	0.515436i	$0.172370\pi$
$824$	−554338.	+	399966.i	−0.0284418	+	0.0205213i
$825$		0			0
$826$	11696.2	+	345824.i	0.000596478	+	0.0176362i
$827$	−2.05084e7			−1.04272			−0.521361	−	0.853336i	$-0.674576\pi$
$827$	−2.05084e7			−1.04272			−0.521361	+	0.853336i	$0.674576\pi$
$828$		0			0
$829$	−3.27151e7			−1.65334			−0.826669	−	0.562688i	$-0.809767\pi$
$829$	−3.27151e7			−1.65334			−0.826669	+	0.562688i	$0.809767\pi$
$830$	44701.7	+	1.32171e6i	0.00225231	+	0.0665947i
$831$		0			0
$832$	7.07375e6	+	7.96108e6i	0.354276	+	0.398716i
$833$	−2.67104e7	+	1.54213e7i	−1.33373	+	0.770030i
$834$		0			0
$835$	920894.	+	531679.i	0.0457082	+	0.0263896i
$836$	−1.03550e6	−	507866.i	−0.0512430	−	0.0251324i
$837$		0			0
$838$	1.39676e7	+	2.24075e7i	0.687085	+	1.10226i
$839$	1.82802e6	−	3.16623e6i	0.0896555	−	0.155288i	−0.817710	−	0.575630i	$-0.804757\pi$
$839$	1.82802e6	−	3.16623e6i	0.0896555	−	0.155288i	0.907366	+	0.420342i	$0.138090\pi$
$840$		0			0
$841$	2.31771e6	+	4.01440e6i	0.112998	+	0.195718i
$842$	−1.08524e7	+	2.03565e7i	−0.527530	+	0.989516i
$843$		0			0
$844$	−2.69926e7	+	1.81206e7i	−1.30433	+	0.875621i
$845$			1.12905e6i			0.0543966i
$846$		0			0
$847$		−	2.47020e6i		−	0.118310i
$848$	757010.	+	5.56364e6i	0.0361503	+	0.265687i
$849$		0			0
$850$	−2.89060e7	−	1.54103e7i	−1.37227	−	0.731585i
$851$	−1.36056e7	−	2.35656e7i	−0.644011	−	1.11546i
$852$		0			0
$853$	1.25006e7	−	2.16517e7i	0.588245	−	1.01887i	−0.406217	−	0.913777i	$-0.633152\pi$
$853$	1.25006e7	−	2.16517e7i	0.588245	−	1.01887i	0.994462	−	0.105094i	$-0.0335144\pi$
$854$	2.56249e6	−	1.59731e6i	0.120231	−	0.0749453i
$855$		0			0
$856$	−1.03833e7	+	1.05675e6i	−0.484342	+	0.0492935i
$857$	1.66895e7	+	9.63570e6i	0.776233	+	0.448158i	0.835093	−	0.550108i	$-0.185414\pi$
$857$	1.66895e7	+	9.63570e6i	0.776233	+	0.448158i	−0.0588609	+	0.998266i	$0.518747\pi$
$858$		0			0
$859$	−1.12055e7	+	6.46950e6i	−0.518142	+	0.299149i	−0.736174	−	0.676792i	$-0.763370\pi$
$859$	−1.12055e7	+	6.46950e6i	−0.518142	+	0.299149i	0.218032	+	0.975942i	$0.430036\pi$
$860$	−1.06453e6	+	72090.0i	−0.0490809	+	0.00332375i
$861$		0			0
$862$	−2.56878e7	+	868794.i	−1.17750	+	0.0398243i
$863$	8.69765e6			0.397535			0.198767	−	0.980047i	$-0.436306\pi$
$863$	8.69765e6			0.397535			0.198767	+	0.980047i	$0.436306\pi$
$864$		0			0
$865$	−1.31189e6			−0.0596153
$866$	38028.5	−	1286.17i	0.00172312	−	5.82779e-5i
$867$		0			0
$868$	3.79381e6	−	256916.i	0.170913	−	0.0115742i
$869$	2.76692e6	−	1.59748e6i	0.124293	−	0.0717607i
$870$		0			0
$871$	−1.87176e7	−	1.08066e7i	−0.835999	−	0.482664i
$872$	3.17504e7	−	3.23138e6i	1.41403	−	0.143912i
$873$		0			0
$874$	5.16684e6	−	3.22072e6i	0.228795	−	0.142618i
$875$	−213040.	+	368996.i	−0.00940679	+	0.0162930i
$876$		0			0
$877$	1.12877e7	+	1.95509e7i	0.495573	+	0.858357i	0.999987	−	0.00510463i	$-0.00162486\pi$
$877$	1.12877e7	+	1.95509e7i	0.495573	+	0.858357i	−0.504414	+	0.863462i	$0.668292\pi$
$878$	−2.46252e7	−	1.31282e7i	−1.07806	−	0.574735i
$879$		0			0
$880$	−50824.9	−	373537.i	−0.00221243	−	0.0162603i
$881$			1.89558e7i			0.822816i	0.911451	+	0.411408i	$0.134963\pi$
$881$			1.89558e7i			0.822816i	−0.911451	+	0.411408i	$0.865037\pi$
$882$		0			0
$883$			2.38595e7i			1.02981i	0.857246	+	0.514907i	$0.172174\pi$
$883$			2.38595e7i			1.02981i	−0.857246	+	0.514907i	$0.827826\pi$
$884$	1.60936e7	−	1.08039e7i	0.692665	−	0.464998i
$885$		0			0
$886$	−1.34523e7	+	2.52332e7i	−0.575721	+	1.07991i
$887$	−1.14641e7	−	1.98564e7i	−0.489249	−	0.847405i	0.510674	−	0.859774i	$-0.329396\pi$
$887$	−1.14641e7	−	1.98564e7i	−0.489249	−	0.847405i	−0.999923	+	0.0123696i	$0.996063\pi$
$888$		0			0
$889$	347929.	−	602631.i	0.0147651	−	0.0255739i
$890$	−521030.	−	835864.i	−0.0220490	−	0.0353721i
$891$		0			0
$892$	6.69965e6	+	3.28587e6i	0.281929	+	0.138273i
$893$	−1.02655e7	−	5.92678e6i	−0.430775	−	0.248708i
$894$		0			0
$895$	−28916.9	+	16695.2i	−0.00120668	+	0.000696679i
$896$	2.86012e6	+	843977.i	0.119019	+	0.0351205i
$897$		0			0
$898$	−755778.	−	2.23463e7i	−0.0312754	−	0.924728i
$899$	3.70398e7			1.52851
$900$		0			0
$901$	1.02198e7			0.419402
$902$	252605.	+	7.46883e6i	0.0103377	+	0.305658i
$903$		0			0
$904$	1.89601e7	−	1.36801e7i	0.771649	−	0.556761i
$905$	1.65518e6	−	955617.i	0.0671774	−	0.0387849i
$906$		0			0
$907$	9.34957e6	+	5.39798e6i	0.377375	+	0.217878i	0.676676	−	0.736281i	$-0.263420\pi$
$907$	9.34957e6	+	5.39798e6i	0.377375	+	0.217878i	−0.299300	+	0.954159i	$0.596753\pi$
$908$	1.23858e7	−	2.52537e7i	0.498551	−	1.01651i
$909$		0			0
$910$	−66493.2	−	106672.i	−0.00266179	−	0.00427018i
$911$	−1.46710e6	+	2.54108e6i	−0.0585683	+	0.101443i	−0.893823	−	0.448420i	$-0.851987\pi$
$911$	−1.46710e6	+	2.54108e6i	−0.0585683	+	0.101443i	0.835255	+	0.549863i	$0.185320\pi$
$912$		0			0
$913$	−2.38253e6	−	4.12667e6i	−0.0945937	−	0.163841i
$914$	1.99255e7	−	3.73753e7i	0.788938	−	1.47985i
$915$		0			0
$916$	−6.82357e6	−	1.01644e7i	−0.268703	−	0.400263i
$917$			3.37252e6i			0.132444i
$918$		0			0
$919$		−	2.10763e7i		−	0.823201i	−0.911364	−	0.411600i	$-0.864970\pi$
$919$		−	2.10763e7i		−	0.823201i	0.911364	−	0.411600i	$-0.135030\pi$
$920$	1.81534e6	+	815420.i	0.0707113	+	0.0317623i
$921$		0			0
$922$	2.55656e7	+	1.36295e7i	0.990443	+	0.528024i
$923$	7.08075e6	+	1.22642e7i	0.273574	+	0.473844i
$924$		0			0
$925$	1.63412e7	−	2.83039e7i	0.627958	−	1.08766i
$926$	−1.92717e7	+	1.20129e7i	−0.738571	+	0.460383i
$927$		0			0
$928$	2.72411e7	+	1.00847e7i	1.03838	+	0.384409i
$929$	1.43110e7	+	8.26248e6i	0.544041	+	0.314102i	0.746715	−	0.665144i	$-0.231630\pi$
$929$	1.43110e7	+	8.26248e6i	0.544041	+	0.314102i	−0.202674	+	0.979246i	$0.564963\pi$
$930$		0			0
$931$	5.96278e6	−	3.44261e6i	0.225463	−	0.130171i
$932$	485078.	+	7.16301e6i	0.0182925	+	0.270119i
$933$		0			0
$934$	3.07351e7	−	1.03950e6i	1.15284	−	0.0389904i
$935$	−686147.			−0.0256678
$936$		0			0
$937$	1.09551e7			0.407633			0.203816	−	0.979009i	$-0.434665\pi$
$937$	1.09551e7			0.407633			0.203816	+	0.979009i	$0.434665\pi$
$938$	−6.04851e6	+	204568.i	−0.224461	+	0.00759155i
$939$		0			0
$940$	−261778.	−	3.86559e6i	−0.00966302	−	0.142691i
$941$	3.02898e7	−	1.74878e7i	1.11512	−	0.643815i	0.174970	−	0.984574i	$-0.444017\pi$
$941$	3.02898e7	−	1.74878e7i	1.11512	−	0.643815i	0.940151	+	0.340759i	$0.110684\pi$
$942$		0			0
$943$	−3.41650e7	−	1.97252e7i	−1.25113	−	0.722341i
$944$	2.38357e6	+	3.07861e6i	0.0870558	+	0.112441i
$945$		0			0
$946$	3.26254e6	−	2.03368e6i	0.118530	−	0.0738849i
$947$	−1.20408e7	+	2.08553e7i	−0.436296	+	0.755687i	−0.997400	−	0.0720580i	$-0.977043\pi$
$947$	−1.20408e7	+	2.08553e7i	−0.436296	+	0.755687i	0.561104	+	0.827745i	$0.310377\pi$
$948$		0			0
$949$	3.72161e6	+	6.44601e6i	0.134142	+	0.232341i
$950$	6.45292e6	+	3.44017e6i	0.231978	+	0.123672i
$951$		0			0
$952$	2.22396e6	−	4.95113e6i	0.0795307	−	0.177057i
$953$		−	3.19780e7i		−	1.14056i	−0.821450	−	0.570281i	$-0.806834\pi$
$953$		−	3.19780e7i		−	1.14056i	0.821450	−	0.570281i	$-0.193166\pi$
$954$		0			0
$955$			2.17067e6i			0.0770170i
$956$	2.74354e7	+	4.08680e7i	0.970882	+	1.44623i
$957$		0			0
$958$	2.46931e7	−	4.63182e7i	0.869285	−	1.63056i
$959$	924760.	+	1.60173e6i	0.0324700	+	0.0562397i
$960$		0			0
$961$	1.29644e7	−	2.24551e7i	0.452840	−	0.784343i
$962$	1.02304e7	+	1.64121e7i	0.356413	+	0.571777i
$963$		0			0
$964$	1.95274e7	−	3.98149e7i	0.676787	−	1.37992i
$965$	−3.23879e6	−	1.86992e6i	−0.111960	−	0.0646404i
$966$		0			0
$967$	−2.45189e7	+	1.41560e7i	−0.843209	+	0.486827i	−0.858354	−	0.513058i	$-0.828512\pi$
$967$	−2.45189e7	+	1.41560e7i	−0.843209	+	0.486827i	0.0151446	+	0.999885i	$0.495179\pi$
$968$	−1.62633e7	−	2.25404e7i	−0.557855	−	0.773165i
$969$		0			0
$970$	−37933.4	−	1.12159e6i	−0.00129447	−	0.0382740i
$971$	1.79971e7			0.612567			0.306284	−	0.951940i	$-0.400914\pi$
$971$	1.79971e7			0.612567			0.306284	+	0.951940i	$0.400914\pi$
$972$		0			0
$973$	−3.47103e6			−0.117538
$974$	451259.	+	1.33425e7i	0.0152415	+	0.450650i
$975$		0			0
$976$	1.28661e7	−	3.14463e7i	0.432337	−	1.05668i
$977$	6.10203e6	−	3.52301e6i	0.204521	−	0.118080i	−0.394242	−	0.919007i	$-0.628993\pi$
$977$	6.10203e6	−	3.52301e6i	0.204521	−	0.118080i	0.598763	+	0.800927i	$0.295659\pi$
$978$		0			0
$979$	3.07350e6	+	1.77449e6i	0.102489	+	0.0591720i
$980$	2.02056e6	+	990995.i	0.0672059	+	0.0329614i
$981$		0			0
$982$	2.55115e7	+	4.09269e7i	0.844223	+	1.35435i
$983$	−1.13029e7	+	1.95773e7i	−0.373085	+	0.646202i	−0.990038	−	0.140798i	$-0.955033\pi$
$983$	−1.13029e7	+	1.95773e7i	−0.373085	+	0.646202i	0.616954	+	0.787000i	$0.288367\pi$
$984$		0			0
$985$	−345940.	−	599186.i	−0.0113608	−	0.0196776i
$986$	2.48725e7	−	4.66546e7i	0.814754	−	1.52828i
$987$		0			0
$988$	−3.59271e6	+	2.41185e6i	−0.117093	+	0.0786064i
$989$			2.02950e7i			0.659778i
$990$		0			0
$991$			3.05378e7i			0.987765i	0.869529	+	0.493883i	$0.164423\pi$
$991$			3.05378e7i			0.987765i	−0.869529	+	0.493883i	$0.835577\pi$
$992$	3.29267e7	−	2.73221e7i	1.06235	−	0.881525i
$993$		0			0
$994$	3.49918e6	+	1.86548e6i	0.112331	+	0.0598859i
$995$	1.67121e6	+	2.89463e6i	0.0535148	+	0.0926904i
$996$		0			0
$997$	−1.05531e7	+	1.82786e7i	−0.336236	+	0.582377i	−0.983721	−	0.179700i	$-0.942487\pi$
$997$	−1.05531e7	+	1.82786e7i	−0.336236	+	0.582377i	0.647486	+	0.762078i	$0.275821\pi$
$998$	−1.21256e6	+	755841.i	−0.0385369	+	0.0240217i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	108.6.h.a.35.1		56
3.2	odd	2		36.6.h.a.11.28	yes	56
4.3	odd	2	inner	108.6.h.a.35.10		56
9.4	even	3		36.6.h.a.23.19	yes	56
9.5	odd	6	inner	108.6.h.a.71.10		56
12.11	even	2		36.6.h.a.11.19	✓	56
36.23	even	6	inner	108.6.h.a.71.1		56
36.31	odd	6		36.6.h.a.23.28	yes	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
36.6.h.a.11.19	✓	56	12.11	even	2
36.6.h.a.11.28	yes	56	3.2	odd	2
36.6.h.a.23.19	yes	56	9.4	even	3
36.6.h.a.23.28	yes	56	36.31	odd	6
108.6.h.a.35.1		56	1.1	even	1	trivial
108.6.h.a.35.10		56	4.3	odd	2	inner
108.6.h.a.71.1		56	36.23	even	6	inner
108.6.h.a.71.10		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)

\(f(q)\)	\(=\)	\(q+(-5.65362 + 0.191212i) q^{2} +(31.9269 - 2.16208i) q^{4} +(-3.68052 + 2.12495i) q^{5} +(-13.9322 - 8.04377i) q^{7} +(-180.089 + 18.3284i) q^{8} +O(q^{10})\)	\(q+(-5.65362 + 0.191212i) q^{2} +(31.9269 - 2.16208i) q^{4} +(-3.68052 + 2.12495i) q^{5} +(-13.9322 - 8.04377i) q^{7} +(-180.089 + 18.3284i) q^{8} +(20.4019 - 12.7174i) q^{10} +(-43.3121 + 75.0187i) q^{11} +(162.502 + 281.462i) q^{13} +(80.3056 + 42.8124i) q^{14} +(1014.65 - 138.057i) q^{16} -1863.80i q^{17} +416.071i q^{19} +(-112.913 + 75.8006i) q^{20} +(230.526 - 432.409i) q^{22} +(1293.41 + 2240.24i) q^{23} +(-1553.47 + 2690.69i) q^{25} +(-972.544 - 1560.21i) q^{26} +(-462.204 - 226.690i) q^{28} +(-4342.80 - 2507.32i) q^{29} +(-6396.76 + 3693.17i) q^{31} +(-5710.05 + 974.537i) q^{32} +(356.382 + 10537.2i) q^{34} +68.3704 q^{35} -10519.2 q^{37} +(-79.5579 - 2352.31i) q^{38} +(623.874 - 450.138i) q^{40} +(-13207.4 + 7625.29i) q^{41} +(6794.45 + 3922.78i) q^{43} +(-1220.62 + 2488.76i) q^{44} +(-7740.79 - 12418.2i) q^{46} +(-14244.6 + 24672.4i) q^{47} +(-8274.10 - 14331.2i) q^{49} +(8268.23 - 15509.2i) q^{50} +(5796.72 + 8634.85i) q^{52} +5483.31i q^{53} -368.144i q^{55} +(2656.47 + 1193.24i) q^{56} +(25032.0 + 13345.0i) q^{58} +(1901.12 + 3292.83i) q^{59} +(16590.1 - 28734.9i) q^{61} +(35458.7 - 22102.9i) q^{62} +(32096.1 - 6601.49i) q^{64} +(-1196.18 - 690.617i) q^{65} +(-57592.1 + 33250.8i) q^{67} +(-4029.69 - 59505.3i) q^{68} +(-386.540 + 13.0733i) q^{70} +43573.3 q^{71} +22901.9 q^{73} +(59471.5 - 2011.40i) q^{74} +(899.581 + 13283.8i) q^{76} +(1206.87 - 696.785i) q^{77} +(-31941.7 - 18441.5i) q^{79} +(-3441.08 + 2664.20i) q^{80} +(73211.6 - 45635.9i) q^{82} +(-27504.3 + 47638.8i) q^{83} +(3960.48 + 6859.75i) q^{85} +(-39163.3 - 20878.7i) q^{86} +(6425.06 - 14303.9i) q^{88} -40969.8i q^{89} -5228.51i q^{91} +(46138.0 + 68727.5i) q^{92} +(75816.1 - 142212. i) q^{94} +(-884.130 - 1531.36i) q^{95} +(23339.8 - 40425.7i) q^{97} +(49518.9 + 79440.8i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q + 3 q^{2} - q^{4} + 6 q^{5}+O(q^{10}) \) 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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