LMFDB - Embedded newform 108.6.h.a.71.2

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			71.2
Character	$\chi$	$=$	108.71
Dual form			108.6.h.a.35.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-5.52836 - 1.19885i) q^{2} +(29.1255 + 13.2554i) q^{4} +(20.1454 + 11.6310i) q^{5} +(156.832 - 90.5473i) q^{7} +(-145.125 - 108.198i) q^{8} +O(q^{10})$	\(q+(-5.52836 - 1.19885i) q^{2} +(29.1255 + 13.2554i) q^{4} +(20.1454 + 11.6310i) q^{5} +(156.832 - 90.5473i) q^{7} +(-145.125 - 108.198i) q^{8} +(-97.4272 - 88.4515i) q^{10} +(41.2642 + 71.4718i) q^{11} +(-70.1922 + 121.577i) q^{13} +(-975.579 + 312.559i) q^{14} +(672.589 + 772.140i) q^{16} -901.814i q^{17} +2363.52i q^{19} +(432.572 + 605.793i) q^{20} +(-142.439 - 444.591i) q^{22} +(160.190 - 277.458i) q^{23} +(-1291.94 - 2237.71i) q^{25} +(533.800 - 587.968i) q^{26} +(5768.06 - 558.359i) q^{28} +(7037.98 - 4063.38i) q^{29} +(-1533.72 - 885.495i) q^{31} +(-2792.63 - 5075.00i) q^{32} +(-1081.14 + 4985.55i) q^{34} +4212.61 q^{35} +13713.9 q^{37} +(2833.52 - 13066.4i) q^{38} +(-1665.16 - 3867.63i) q^{40} +(4374.37 + 2525.55i) q^{41} +(17261.6 - 9966.01i) q^{43} +(254.456 + 2628.62i) q^{44} +(-1218.22 + 1341.84i) q^{46} +(6620.98 + 11467.9i) q^{47} +(7994.11 - 13846.2i) q^{49} +(4459.63 + 13919.7i) q^{50} +(-3655.93 + 2610.55i) q^{52} -25022.9i q^{53} +1919.77i q^{55} +(-32557.3 - 3828.26i) q^{56} +(-43779.9 + 14026.3i) q^{58} +(-20189.4 + 34969.0i) q^{59} +(-8934.10 - 15474.3i) q^{61} +(7417.39 + 6734.04i) q^{62} +(9354.49 + 31404.4i) q^{64} +(-2828.10 + 1632.81i) q^{65} +(29089.1 + 16794.6i) q^{67} +(11953.9 - 26265.8i) q^{68} +(-23288.8 - 5050.30i) q^{70} +55855.2 q^{71} -69860.7 q^{73} +(-75815.3 - 16441.0i) q^{74} +(-31329.4 + 68838.8i) q^{76} +(12943.1 + 7472.73i) q^{77} +(33076.3 - 19096.6i) q^{79} +(4568.86 + 23377.9i) q^{80} +(-21155.4 - 19206.4i) q^{82} +(-11121.7 - 19263.4i) q^{83} +(10489.0 - 18167.4i) q^{85} +(-107376. + 34401.5i) q^{86} +(1744.62 - 14837.0i) q^{88} +98921.0i q^{89} +25422.9i q^{91} +(8343.43 - 5957.71i) q^{92} +(-22854.8 - 71336.1i) q^{94} +(-27490.1 + 47614.2i) q^{95} +(-20762.4 - 35961.6i) q^{97} +(-60793.9 + 66963.0i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q + 3 q^{2} - q^{4} + 6 q^{5}+O(q^{10}) $ 56 * q + 3 * q^2 - q^4 + 6 * q^5	$ 56 q + 3 q^{2} - q^{4} + 6 q^{5} - 68 q^{10} - 2 q^{13} + 1518 q^{14} - q^{16} + 1242 q^{20} + 63 q^{22} + 12498 q^{25} - 2052 q^{28} + 11946 q^{29} + 7233 q^{32} + 6361 q^{34} - 8 q^{37} + 14877 q^{38} - 1526 q^{40} + 43536 q^{41} - 26880 q^{46} + 38414 q^{49} - 38631 q^{50} + 24988 q^{52} - 21186 q^{56} - 3314 q^{58} - 2 q^{61} - 106342 q^{64} - 35970 q^{65} - 31413 q^{68} + 10524 q^{70} + 53620 q^{73} + 20406 q^{74} + 26193 q^{76} - 26178 q^{77} - 151286 q^{82} + 6248 q^{85} - 279237 q^{86} - 122541 q^{88} - 435804 q^{92} + 63480 q^{94} - 58148 q^{97}+O(q^{100}) $ 56 * q + 3 * q^2 - q^4 + 6 * q^5 - 68 * q^10 - 2 * q^13 + 1518 * q^14 - q^16 + 1242 * q^20 + 63 * q^22 + 12498 * q^25 - 2052 * q^28 + 11946 * q^29 + 7233 * q^32 + 6361 * q^34 - 8 * q^37 + 14877 * q^38 - 1526 * q^40 + 43536 * q^41 - 26880 * q^46 + 38414 * q^49 - 38631 * q^50 + 24988 * q^52 - 21186 * q^56 - 3314 * q^58 - 2 * q^61 - 106342 * q^64 - 35970 * q^65 - 31413 * q^68 + 10524 * q^70 + 53620 * q^73 + 20406 * q^74 + 26193 * q^76 - 26178 * q^77 - 151286 * q^82 + 6248 * q^85 - 279237 * q^86 - 122541 * q^88 - 435804 * q^92 + 63480 * q^94 - 58148 * q^97

Display 100 coefficients 10 coefficients

Character values

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

$n$	$29$	$55$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$-1$

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 $

$2$	−5.52836	−	1.19885i	−0.977285	−	0.211929i
$2$	−5.52836	−	1.19885i	−0.977285	−	0.211929i
$3$		0			0
$3$		0			0
$4$	29.1255	+	13.2554i	0.910172	+	0.414231i
$5$	20.1454	+	11.6310i	0.360372	+	0.208061i	0.669244	−	0.743043i	$-0.266618\pi$
$5$	20.1454	+	11.6310i	0.360372	+	0.208061i	−0.308872	+	0.951104i	$0.599951\pi$
$6$		0			0
$7$	156.832	−	90.5473i	1.20974	−	0.698442i	0.247035	−	0.969007i	$-0.420544\pi$
$7$	156.832	−	90.5473i	1.20974	−	0.698442i	0.962702	+	0.270565i	$0.0872104\pi$
$8$	−145.125	−	108.198i	−0.801710	−	0.597714i
$9$		0			0
$10$	−97.4272	−	88.4515i	−0.308092	−	0.279708i
$11$	41.2642	+	71.4718i	0.102823	+	0.178095i	0.912847	−	0.408302i	$-0.133879\pi$
$11$	41.2642	+	71.4718i	0.102823	+	0.178095i	−0.810023	+	0.586398i	$0.800546\pi$
$12$		0			0
$13$	−70.1922	+	121.577i	−0.115194	+	0.199522i	−0.917857	−	0.396910i	$-0.870082\pi$
$13$	−70.1922	+	121.577i	−0.115194	+	0.199522i	0.802663	+	0.596433i	$0.203416\pi$
$14$	−975.579	+	312.559i	−1.33028	+	0.426198i
$15$		0			0
$16$	672.589	+	772.140i	0.656825	+	0.754043i
$17$		−	901.814i		−	0.756824i	−0.925637	−	0.378412i	$-0.876470\pi$
$17$		−	901.814i		−	0.756824i	0.925637	−	0.378412i	$-0.123530\pi$
$18$		0			0
$19$			2363.52i			1.50202i	0.660290	+	0.751011i	$0.270433\pi$
$19$			2363.52i			1.50202i	−0.660290	+	0.751011i	$0.729567\pi$
$20$	432.572	+	605.793i	0.241815	+	0.338648i
$21$		0			0
$22$	−142.439	−	444.591i	−0.0627441	−	0.195841i
$23$	160.190	−	277.458i	0.0631417	−	0.109365i	−0.832726	−	0.553685i	$-0.813221\pi$
$23$	160.190	−	277.458i	0.0631417	−	0.109365i	0.895868	+	0.444320i	$0.146555\pi$
$24$		0			0
$25$	−1291.94	−	2237.71i	−0.413421	−	0.716067i
$26$	533.800	−	587.968i	0.154862	−	0.170577i
$27$		0			0
$28$	5768.06	−	558.359i	1.39038	−	0.134592i
$29$	7037.98	−	4063.38i	1.55401	−	0.897207i	0.556198	−	0.831050i	$-0.312260\pi$
$29$	7037.98	−	4063.38i	1.55401	−	0.897207i	0.997809	−	0.0661569i	$-0.0210738\pi$
$30$		0			0
$31$	−1533.72	−	885.495i	−0.286644	−	0.165494i	0.349784	−	0.936831i	$-0.386255\pi$
$31$	−1533.72	−	885.495i	−0.286644	−	0.165494i	−0.636427	+	0.771337i	$0.719588\pi$
$32$	−2792.63	−	5075.00i	−0.482102	−	0.876115i
$33$		0			0
$34$	−1081.14	+	4985.55i	−0.160393	+	0.739633i
$35$	4212.61			0.581274
$36$		0			0
$37$	13713.9			1.64686			0.823429	−	0.567419i	$-0.192058\pi$
$37$	13713.9			1.64686			0.823429	+	0.567419i	$0.192058\pi$
$38$	2833.52	−	13066.4i	0.318323	−	1.46790i
$39$		0			0
$40$	−1665.16	−	3867.63i	−0.164553	−	0.382204i
$41$	4374.37	+	2525.55i	0.406402	+	0.234637i	0.689243	−	0.724530i	$-0.257943\pi$
$41$	4374.37	+	2525.55i	0.406402	+	0.234637i	−0.282840	+	0.959167i	$0.591277\pi$
$42$		0			0
$43$	17261.6	−	9966.01i	1.42367	−	0.821959i	0.427064	−	0.904221i	$-0.359548\pi$
$43$	17261.6	−	9966.01i	1.42367	−	0.821959i	0.996611	+	0.0822625i	$0.0262146\pi$
$44$	254.456	+	2628.62i	0.0198144	+	0.204690i
$45$		0			0
$46$	−1218.22	+	1341.84i	−0.0848851	+	0.0934989i
$47$	6620.98	+	11467.9i	0.437197	+	0.757248i	0.997472	−	0.0710587i	$-0.0226378\pi$
$47$	6620.98	+	11467.9i	0.437197	+	0.757248i	−0.560275	+	0.828307i	$0.689304\pi$
$48$		0			0
$49$	7994.11	−	13846.2i	0.475642	−	0.823836i
$50$	4459.63	+	13919.7i	0.252275	+	0.787417i
$51$		0			0
$52$	−3655.93	+	2610.55i	−0.187495	+	0.133883i
$53$		−	25022.9i		−	1.22362i	−0.791003	−	0.611812i	$-0.790441\pi$
$53$		−	25022.9i		−	1.22362i	0.791003	−	0.611812i	$-0.209559\pi$
$54$		0			0
$55$			1919.77i			0.0855742i
$56$	−32557.3	−	3828.26i	−1.38733	−	0.163129i
$57$		0			0
$58$	−43779.9	+	14026.3i	−1.70885	+	0.547487i
$59$	−20189.4	+	34969.0i	−0.755079	+	1.30784i	0.190256	+	0.981735i	$0.439068\pi$
$59$	−20189.4	+	34969.0i	−0.755079	+	1.30784i	−0.945335	+	0.326101i	$0.894265\pi$
$60$		0			0
$61$	−8934.10	−	15474.3i	−0.307416	−	0.532460i	0.670381	−	0.742017i	$-0.266131\pi$
$61$	−8934.10	−	15474.3i	−0.307416	−	0.532460i	−0.977796	+	0.209558i	$0.932798\pi$
$62$	7417.39	+	6734.04i	0.245060	+	0.222483i
$63$		0			0
$64$	9354.49	+	31404.4i	0.285476	+	0.958386i
$65$	−2828.10	+	1632.81i	−0.0830256	+	0.0479348i
$66$		0			0
$67$	29089.1	+	16794.6i	0.791668	+	0.457070i	0.840549	−	0.541735i	$-0.182232\pi$
$67$	29089.1	+	16794.6i	0.791668	+	0.457070i	−0.0488814	+	0.998805i	$0.515566\pi$
$68$	11953.9	−	26265.8i	0.313500	−	0.688840i
$69$		0			0
$70$	−23288.8	−	5050.30i	−0.568070	−	0.123189i
$71$	55855.2			1.31498			0.657488	−	0.753465i	$-0.271619\pi$
$71$	55855.2			1.31498			0.657488	+	0.753465i	$0.271619\pi$
$72$		0			0
$73$	−69860.7			−1.53435			−0.767177	−	0.641435i	$-0.778339\pi$
$73$	−69860.7			−1.53435			−0.767177	+	0.641435i	$0.778339\pi$
$74$	−75815.3	−	16441.0i	−1.60945	−	0.349018i
$75$		0			0
$76$	−31329.4	+	68838.8i	−0.622184	+	1.36710i
$77$	12943.1	+	7472.73i	0.248779	+	0.143632i
$78$		0			0
$79$	33076.3	−	19096.6i	0.596278	−	0.344261i	−0.171298	−	0.985219i	$-0.554796\pi$
$79$	33076.3	−	19096.6i	0.596278	−	0.344261i	0.767576	+	0.640958i	$0.221463\pi$
$80$	4568.86	+	23377.9i	0.0798148	+	0.408396i
$81$		0			0
$82$	−21155.4	−	19206.4i	−0.347445	−	0.315435i
$83$	−11121.7	−	19263.4i	−0.177205	−	0.306929i	0.763717	−	0.645551i	$-0.223372\pi$
$83$	−11121.7	−	19263.4i	−0.177205	−	0.306929i	−0.940922	+	0.338623i	$0.890039\pi$
$84$		0			0
$85$	10489.0	−	18167.4i	0.157465	−	0.272738i
$86$	−107376.	+	34401.5i	−1.56553	+	0.501570i
$87$		0			0
$88$	1744.62	−	14837.0i	0.0240156	−	0.204240i
$89$			98921.0i			1.32377i	0.749604	+	0.661886i	$0.230244\pi$
$89$			98921.0i			1.32377i	−0.749604	+	0.661886i	$0.769756\pi$
$90$		0			0
$91$			25422.9i			0.321826i
$92$	8343.43	−	5957.71i	0.102772	−	0.0733854i
$93$		0			0
$94$	−22854.8	−	71336.1i	−0.266783	−	0.832702i
$95$	−27490.1	+	47614.2i	−0.312512	+	0.541287i
$96$		0			0
$97$	−20762.4	−	35961.6i	−0.224052	−	0.388069i	0.731983	−	0.681323i	$-0.238595\pi$
$97$	−20762.4	−	35961.6i	−0.224052	−	0.388069i	−0.956035	+	0.293254i	$0.905262\pi$
$98$	−60793.9	+	66963.0i	−0.639433	+	0.704320i
$99$		0			0
$100$	−7966.74	−	82299.6i	−0.0796674	−	0.822996i
$101$	100768.	−	58178.3i	0.982920	−	0.567489i	0.0797694	−	0.996813i	$-0.474582\pi$
$101$	100768.	−	58178.3i	0.982920	−	0.567489i	0.903150	+	0.429324i	$0.141248\pi$
$102$		0			0
$103$	−34298.4	−	19802.2i	−0.318552	−	0.183916i	0.332195	−	0.943211i	$-0.392211\pi$
$103$	−34298.4	−	19802.2i	−0.318552	−	0.183916i	−0.650747	+	0.759295i	$0.725544\pi$
$104$	23340.9	−	10049.1i	0.211609	−	0.0911057i
$105$		0			0
$106$	−29998.8	+	138336.i	−0.259322	+	1.19583i
$107$	82118.9			0.693400			0.346700	−	0.937976i	$-0.387302\pi$
$107$	82118.9			0.693400			0.346700	+	0.937976i	$0.387302\pi$
$108$		0			0
$109$	−48617.2			−0.391944			−0.195972	−	0.980610i	$-0.562786\pi$
$109$	−48617.2			−0.391944			−0.195972	+	0.980610i	$0.562786\pi$
$110$	2301.52	−	10613.2i	0.0181357	−	0.0836303i
$111$		0			0
$112$	175399.	+	60195.4i	1.32124	+	0.453439i
$113$	−14619.7	−	8440.70i	−0.107707	−	0.0621845i	0.445179	−	0.895442i	$-0.353140\pi$
$113$	−14619.7	−	8440.70i	−0.107707	−	0.0621845i	−0.552886	+	0.833257i	$0.686473\pi$
$114$		0			0
$115$	6454.20	−	3726.33i	0.0455090	−	0.0262747i
$116$	258846.	−	25056.8i	1.78606	−	0.172894i
$117$		0			0
$118$	153537.	−	169117.i	1.01510	−	1.11810i
$119$	−81656.8	−	141434.i	−0.528597	−	0.915557i
$120$		0			0
$121$	77120.0	−	133576.i	0.478855	−	0.829401i
$122$	30839.5	+	96258.2i	0.187589	+	0.585515i
$123$		0			0
$124$	−32932.8	−	46120.6i	−0.192342	−	0.269364i
$125$		−	132800.i		−	0.760189i
$126$		0			0
$127$			45880.3i			0.252416i	0.992004	+	0.126208i	$0.0402807\pi$
$127$			45880.3i			0.252416i	−0.992004	+	0.126208i	$0.959719\pi$
$128$	−14065.7	−	184829.i	−0.0758815	−	0.997117i
$129$		0			0
$130$	17592.3	−	5636.25i	0.0912984	−	0.0292504i
$131$	−11973.3	+	20738.4i	−0.0609588	+	0.105584i	−0.894894	−	0.446278i	$-0.852749\pi$
$131$	−11973.3	+	20738.4i	−0.0609588	+	0.105584i	0.833935	+	0.551862i	$0.186082\pi$
$132$		0			0
$133$	214011.	+	370677.i	1.04907	+	1.81705i
$134$	−140681.	−	127720.i	−0.676819	−	0.614465i
$135$		0			0
$136$	−97574.3	+	130876.i	−0.452364	+	0.606753i
$137$	−179077.	+	103390.i	−0.815152	+	0.470628i	−0.848742	−	0.528807i	$-0.822639\pi$
$137$	−179077.	+	103390.i	−0.815152	+	0.470628i	0.0335896	+	0.999436i	$0.489306\pi$
$138$		0			0
$139$	−150292.	−	86771.1i	−0.659780	−	0.380924i	0.132413	−	0.991195i	$-0.457727\pi$
$139$	−150292.	−	86771.1i	−0.659780	−	0.380924i	−0.792193	+	0.610271i	$0.791061\pi$
$140$	122694.	+	55839.7i	0.529059	+	0.240782i
$141$		0			0
$142$	−308788.	−	66962.3i	−1.28511	−	0.278682i
$143$	−11585.7			−0.0473787
$144$		0			0
$145$	189044.			0.746695
$146$	386215.	+	83752.8i	1.49950	+	0.325175i
$147$		0			0
$148$	399424.	+	181783.i	1.49892	+	0.682180i
$149$	−195995.	−	113158.i	−0.723234	−	0.417559i	0.0927081	−	0.995693i	$-0.470448\pi$
$149$	−195995.	−	113158.i	−0.723234	−	0.417559i	−0.815942	+	0.578134i	$0.803781\pi$
$150$		0			0
$151$	−48433.2	+	27962.9i	−0.172862	+	0.0998021i	−0.583935	−	0.811801i	$-0.698488\pi$
$151$	−48433.2	+	27962.9i	−0.172862	+	0.0998021i	0.411072	+	0.911603i	$0.365154\pi$
$152$	255728.	−	343006.i	0.897779	−	1.20418i
$153$		0			0
$154$	−62595.6	−	56828.9i	−0.212688	−	0.193093i
$155$	−20598.3	−	35677.3i	−0.0688656	−	0.119279i
$156$		0			0
$157$	−67323.6	+	116608.i	−0.217981	+	0.377554i	−0.954191	−	0.299200i	$-0.903280\pi$
$157$	−67323.6	+	116608.i	−0.217981	+	0.377554i	0.736210	+	0.676754i	$0.236614\pi$
$158$	−205752.	+	65919.2i	−0.655693	+	0.210073i
$159$		0			0
$160$	2768.41	−	134719.i	0.00854930	−	0.416034i
$161$		−	58019.2i		−	0.176403i
$162$		0			0
$163$			93835.4i			0.276629i	0.990388	+	0.138314i	$0.0441685\pi$
$163$			93835.4i			0.276629i	−0.990388	+	0.138314i	$0.955832\pi$
$164$	93928.7	+	131542.i	0.272702	+	0.381904i
$165$		0			0
$166$	38390.9	+	119828.i	0.108133	+	0.337512i
$167$	−67439.6	+	116809.i	−0.187121	+	0.324104i	−0.944289	−	0.329116i	$-0.893249\pi$
$167$	−67439.6	+	116809.i	−0.187121	+	0.324104i	0.757168	+	0.653220i	$0.226582\pi$
$168$		0			0
$169$	175793.	+	304482.i	0.473461	+	0.820058i
$170$	−79766.8	+	87861.3i	−0.211690	+	0.233171i
$171$		0			0
$172$	634857.	−	61455.3i	1.63627	−	0.158394i
$173$	−179808.	+	103812.i	−0.456767	+	0.263715i	−0.710684	−	0.703511i	$-0.751614\pi$
$173$	−179808.	+	103812.i	−0.456767	+	0.263715i	0.253917	+	0.967226i	$0.418281\pi$
$174$		0			0
$175$	−405237.	−	233964.i	−1.00026	−	0.577501i
$176$	−27432.3	+	79932.9i	−0.0667545	+	0.194511i
$177$		0			0
$178$	118592.	−	546871.i	0.280546	−	1.29370i
$179$	−525249.			−1.22527			−0.612636	−	0.790365i	$-0.709891\pi$
$179$	−525249.			−1.22527			−0.612636	+	0.790365i	$0.709891\pi$
$180$		0			0
$181$	−825837.			−1.87369			−0.936846	−	0.349743i	$-0.886269\pi$
$181$	−825837.			−1.87369			−0.936846	+	0.349743i	$0.886269\pi$
$182$	30478.3	−	140547.i	0.0682044	−	0.314516i
$183$		0			0
$184$	−53267.9	+	22933.8i	−0.115990	+	0.0499380i
$185$	276272.	+	159506.i	0.593482	+	0.342647i
$186$		0			0
$187$	64454.3	−	37212.7i	0.134787	−	0.0778192i
$188$	40828.2	+	421771.i	0.0842492	+	0.870327i
$189$		0			0
$190$	209057.	−	230272.i	0.420128	−	0.462761i
$191$	−187497.	−	324754.i	−0.371886	−	0.644126i	0.617970	−	0.786202i	$-0.287955\pi$
$191$	−187497.	−	324754.i	−0.371886	−	0.644126i	−0.989856	+	0.142076i	$0.954622\pi$
$192$		0			0
$193$	238572.	−	413219.i	0.461027	−	0.798522i	−0.537985	−	0.842954i	$-0.680814\pi$
$193$	238572.	−	413219.i	0.461027	−	0.798522i	0.999012	+	0.0444321i	$0.0141478\pi$
$194$	71669.4	+	223700.i	0.136719	+	0.426737i
$195$		0			0
$196$	416369.	−	297313.i	0.774174	−	0.552807i
$197$			443928.i			0.814979i	0.913210	+	0.407490i	$0.133596\pi$
$197$			443928.i			0.814979i	−0.913210	+	0.407490i	$0.866404\pi$
$198$		0			0
$199$			601252.i			1.07628i	0.842857	+	0.538138i	$0.180872\pi$
$199$			601252.i			1.07628i	−0.842857	+	0.538138i	$0.819128\pi$
$200$	−54622.1	+	464532.i	−0.0965592	+	0.821185i
$201$		0			0
$202$	−626827.	+	200825.i	−1.08086	+	0.346289i
$203$	735856.	−	1.27454e6i	1.25329	−	2.17077i
$204$		0			0
$205$	58749.1	+	101756.i	0.0976374	+	0.169113i
$206$	165874.	+	150592.i	0.272339	+	0.247249i
$207$		0			0
$208$	−141085.	+	27572.9i	−0.226111	+	0.0441899i
$209$	−168925.	+	97529.1i	−0.267503	+	0.154443i
$210$		0			0
$211$	−345252.	−	199331.i	−0.533863	−	0.308226i	0.208725	−	0.977974i	$-0.433069\pi$
$211$	−345252.	−	199331.i	−0.533863	−	0.308226i	−0.742588	+	0.669748i	$0.766402\pi$
$212$	331688.	−	728805.i	0.506863	−	1.11371i
$213$		0			0
$214$	−453983.	−	98448.5i	−0.677649	−	0.146952i
$215$	463657.			0.684070
$216$		0			0
$217$	−320716.			−0.462351
$218$	268773.	+	58284.9i	0.383041	+	0.0830644i
$219$		0			0
$220$	−25447.3	+	55914.3i	−0.0354475	+	0.0778872i
$221$	109639.	+	63300.4i	0.151003	+	0.0871817i
$222$		0			0
$223$	290097.	−	167488.i	0.390644	−	0.225538i	−0.291795	−	0.956481i	$-0.594253\pi$
$223$	290097.	−	167488.i	0.390644	−	0.225538i	0.682439	+	0.730942i	$0.260919\pi$
$224$	−897503.	−	543060.i	−1.19513	−	0.723149i
$225$		0			0
$226$	70703.9	+	64190.1i	0.0920815	+	0.0835982i
$227$	425099.	+	736293.i	0.547552	+	0.948388i	0.998442	+	0.0558079i	$0.0177734\pi$
$227$	425099.	+	736293.i	0.547552	+	0.948388i	−0.450890	+	0.892580i	$0.648893\pi$
$228$		0			0
$229$	−204162.	+	353618.i	−0.257268	+	0.445601i	−0.965509	−	0.260370i	$-0.916156\pi$
$229$	−204162.	+	353618.i	−0.257268	+	0.445601i	0.708241	+	0.705971i	$0.249489\pi$
$230$	−40148.5	+	12862.9i	−0.0500437	+	0.0160331i
$231$		0			0
$232$	−1.46104e6	−	171796.i	−1.78214	−	0.209553i
$233$			677571.i			0.817645i	0.912614	+	0.408823i	$0.134061\pi$
$233$			677571.i			0.817645i	−0.912614	+	0.408823i	$0.865939\pi$
$234$		0			0
$235$			308033.i			0.363855i
$236$	−1.05155e6	+	750872.i	−1.22900	+	0.877578i
$237$		0			0
$238$	281870.	+	879791.i	0.322557	+	1.00679i
$239$	−660239.	+	1.14357e6i	−0.747664	+	1.29499i	0.201275	+	0.979535i	$0.435491\pi$
$239$	−660239.	+	1.14357e6i	−0.747664	+	1.29499i	−0.948940	+	0.315458i	$0.897842\pi$
$240$		0			0
$241$	−418674.	−	725165.i	−0.464337	−	0.804256i	0.534834	−	0.844957i	$-0.320374\pi$
$241$	−418674.	−	725165.i	−0.464337	−	0.804256i	−0.999171	+	0.0407014i	$0.987041\pi$
$242$	−586485.	+	645999.i	−0.643752	+	0.709077i
$243$		0			0
$244$	−55092.0	−	569122.i	−0.0592399	−	0.611971i
$245$	322089.	−	185958.i	0.342816	−	0.197925i
$246$		0			0
$247$	−287349.	−	165901.i	−0.299687	−	0.173024i
$248$	126773.	+	294453.i	0.130887	+	0.304009i
$249$		0			0
$250$	−159207.	+	734164.i	−0.161106	+	0.742921i
$251$	−1.41641e6			−1.41907			−0.709534	−	0.704671i	$-0.751095\pi$
$251$	−1.41641e6			−1.41907			−0.709534	+	0.704671i	$0.751095\pi$
$252$		0			0
$253$	26440.5			0.0259698
$254$	55003.8	−	253643.i	0.0534944	−	0.246682i
$255$		0			0
$256$	−143823.	+	1.03867e6i	−0.137161	+	0.990549i
$257$	−887077.	−	512154.i	−0.837777	−	0.483691i	0.0187311	−	0.999825i	$-0.494037\pi$
$257$	−887077.	−	512154.i	−0.837777	−	0.483691i	−0.856508	+	0.516134i	$0.827371\pi$
$258$		0			0
$259$	2.15078e6	−	1.24176e6i	1.99227	−	1.15023i
$260$	−104013.	+	10068.7i	−0.0954236	+	0.00923718i
$261$		0			0
$262$	91055.1	−	100295.i	0.0819504	−	0.0902664i
$263$	841677.	+	1.45783e6i	0.750337	+	1.29962i	0.947660	+	0.319283i	$0.103442\pi$
$263$	841677.	+	1.45783e6i	0.750337	+	1.29962i	−0.197323	+	0.980339i	$0.563225\pi$
$264$		0			0
$265$	291040.	−	504097.i	0.254588	−	0.440960i
$266$	−738740.	−	2.30581e6i	−0.640158	−	1.99811i
$267$		0			0
$268$	624615.	+	874738.i	0.531221	+	0.743945i
$269$		−	2.11837e6i		−	1.78493i	−0.451117	−	0.892465i	$-0.648974\pi$
$269$		−	2.11837e6i		−	1.78493i	0.451117	−	0.892465i	$-0.351026\pi$
$270$		0			0
$271$			596748.i			0.493592i	0.969067	+	0.246796i	$0.0793778\pi$
$271$			596748.i			0.493592i	−0.969067	+	0.246796i	$0.920622\pi$
$272$	696327.	−	606551.i	0.570677	−	0.497101i
$273$		0			0
$274$	1.11395e6	−	356891.i	0.896376	−	0.287183i
$275$	106622.	−	184675.i	0.0850188	−	0.147257i
$276$		0			0
$277$	532237.	+	921861.i	0.416779	+	0.721882i	0.995613	−	0.0935631i	$-0.0298257\pi$
$277$	532237.	+	921861.i	0.416779	+	0.721882i	−0.578835	+	0.815445i	$0.696492\pi$
$278$	726842.	+	659880.i	0.564064	+	0.512098i
$279$		0			0
$280$	−611354.	−	455795.i	−0.466013	−	0.347435i
$281$	890207.	−	513961.i	0.672551	−	0.388298i	−0.124492	−	0.992221i	$-0.539730\pi$
$281$	890207.	−	513961.i	0.672551	−	0.388298i	0.797043	+	0.603923i	$0.206397\pi$
$282$		0			0
$283$	958119.	+	553170.i	0.711137	+	0.410575i	0.811482	−	0.584377i	$-0.198661\pi$
$283$	958119.	+	553170.i	0.711137	+	0.410575i	−0.100345	+	0.994953i	$0.531995\pi$
$284$	1.62681e6	+	740383.i	1.19685	+	0.544704i
$285$		0			0
$286$	64050.0	+	13889.6i	0.0463025	+	0.0100409i
$287$	914725.			0.655520
$288$		0			0
$289$	606588.			0.427218
$290$	−1.04510e6	−	226636.i	−0.729733	−	0.158247i
$291$		0			0
$292$	−2.03473e6	−	926031.i	−1.39653	−	0.635577i
$293$	989169.	+	571097.i	0.673134	+	0.388634i	0.797263	−	0.603632i	$-0.206280\pi$
$293$	989169.	+	571097.i	0.673134	+	0.388634i	−0.124129	+	0.992266i	$0.539614\pi$
$294$		0			0
$295$	−813446.	+	469643.i	−0.544219	+	0.314205i
$296$	−1.99023e6	−	1.48381e6i	−1.32030	−	0.984350i
$297$		0			0
$298$	947869.	+	860545.i	0.618312	+	0.561349i
$299$	22488.2	+	38950.7i	0.0145471	+	0.0251964i
$300$		0			0
$301$	1.80479e6	−	3.12599e6i	1.14818	−	1.98871i
$302$	301279.	−	96524.6i	0.190087	−	0.0609005i
$303$		0			0
$304$	−1.82497e6	+	1.58968e6i	−1.13259	+	0.986566i
$305$		−	415648.i		−	0.255845i
$306$		0			0
$307$		−	1.32248e6i		−	0.800836i	−0.916333	−	0.400418i	$-0.868865\pi$
$307$		−	1.32248e6i		−	0.800836i	0.916333	−	0.400418i	$-0.131135\pi$
$308$	277922.	+	389213.i	0.166934	+	0.233782i
$309$		0			0
$310$	71102.9	+	221931.i	0.0420226	+	0.131164i
$311$	139474.	−	241576.i	0.0817698	−	0.141629i	−0.822240	−	0.569140i	$-0.807276\pi$
$311$	139474.	−	241576.i	0.0817698	−	0.141629i	0.904010	+	0.427511i	$0.140609\pi$
$312$		0			0
$313$	68921.8	+	119376.i	0.0397645	+	0.0688742i	0.885223	−	0.465167i	$-0.154006\pi$
$313$	68921.8	+	119376.i	0.0397645	+	0.0688742i	−0.845458	+	0.534042i	$0.820673\pi$
$314$	511985.	−	563939.i	0.293044	−	0.322781i
$315$		0			0
$316$	1.21650e6	−	117759.i	0.685319	−	0.0663401i
$317$	1.13038e6	−	652623.i	0.631793	−	0.364766i	−0.149653	−	0.988739i	$-0.547816\pi$
$317$	1.13038e6	−	652623.i	0.631793	−	0.364766i	0.781446	+	0.623973i	$0.214482\pi$
$318$		0			0
$319$	580834.	+	335345.i	0.319577	+	0.184508i
$320$	−176813.	+	741456.i	−0.0965250	+	0.404772i
$321$		0			0
$322$	−69556.5	+	320751.i	−0.0373851	+	0.172396i
$323$	2.13146e6			1.13677
$324$		0			0
$325$	362737.			0.190495
$326$	112495.	−	518756.i	0.0586258	−	0.270345i
$327$		0			0
$328$	−361572.	−	839817.i	−0.185571	−	0.431023i
$329$	2.07677e6	+	1.19902e6i	1.05779	+	0.610714i
$330$		0			0
$331$	−552755.	+	319133.i	−0.277308	+	0.160104i	−0.632204	−	0.774802i	$-0.717850\pi$
$331$	−552755.	+	319133.i	−0.277308	+	0.160104i	0.354896	+	0.934906i	$0.384516\pi$
$332$	−68582.0	−	708478.i	−0.0341479	−	0.352762i
$333$		0			0
$334$	512867.	−	564910.i	0.251558	−	0.277085i
$335$	390674.	+	676668.i	0.190197	+	0.329430i
$336$		0			0
$337$	−491457.	+	851229.i	−0.235728	+	0.408293i	−0.959484	−	0.281763i	$-0.909081\pi$
$337$	−491457.	+	851229.i	−0.235728	+	0.408293i	0.723756	+	0.690056i	$0.242414\pi$
$338$	−606815.	−	1.89403e6i	−0.288912	−	0.901770i
$339$		0			0
$340$	546313.	−	390100.i	0.256297	−	0.183012i
$341$		−	146157.i		−	0.0680666i
$342$		0			0
$343$			148276.i			0.0680511i
$344$	−3.58339e6	−	421354.i	−1.63267	−	0.191978i
$345$		0			0
$346$	1.11850e6	−	358348.i	0.502281	−	0.160922i
$347$	675607.	−	1.17018e6i	0.301211	−	0.521712i	−0.675200	−	0.737635i	$-0.735943\pi$
$347$	675607.	−	1.17018e6i	0.301211	−	0.521712i	0.976410	+	0.215923i	$0.0692760\pi$
$348$		0			0
$349$	−376947.	−	652891.i	−0.165660	−	0.286931i	0.771230	−	0.636557i	$-0.219642\pi$
$349$	−376947.	−	652891.i	−0.165660	−	0.286931i	−0.936889	+	0.349626i	$0.886309\pi$
$350$	1.95981e6	+	1.77925e6i	0.855151	+	0.776368i
$351$		0			0
$352$	247483.	−	409010.i	0.106461	−	0.175945i
$353$	−389941.	+	225133.i	−0.166557	+	0.0961616i	−0.580961	−	0.813931i	$-0.697323\pi$
$353$	−389941.	+	225133.i	−0.166557	+	0.0961616i	0.414404	+	0.910093i	$0.363990\pi$
$354$		0			0
$355$	1.12523e6	+	649650.i	0.473881	+	0.273595i
$356$	−1.31124e6	+	2.88112e6i	−0.548347	+	1.20486i
$357$		0			0
$358$	2.90377e6	+	629697.i	1.19744	+	0.259671i
$359$	−3.02244e6			−1.23772			−0.618860	−	0.785502i	$-0.712405\pi$
$359$	−3.02244e6			−1.23772			−0.618860	+	0.785502i	$0.712405\pi$
$360$		0			0
$361$	−3.11015e6			−1.25607
$362$	4.56552e6	+	990058.i	1.83113	+	0.397090i
$363$		0			0
$364$	−336990.	+	740453.i	−0.133310	+	0.292917i
$365$	−1.40737e6	−	812547.i	−0.552939	−	0.319239i
$366$		0			0
$367$	−2.33704e6	+	1.34929e6i	−0.905735	+	0.522927i	−0.879057	−	0.476718i	$-0.841826\pi$
$367$	−2.33704e6	+	1.34929e6i	−0.905735	+	0.522927i	−0.0266788	+	0.999644i	$0.508493\pi$
$368$	321978.	−	62925.8i	0.123939	−	0.0242220i
$369$		0			0
$370$	−1.33611e6	−	1.21301e6i	−0.507384	−	0.460640i
$371$	−2.26576e6	−	3.92440e6i	−0.854630	−	1.48026i
$372$		0			0
$373$	−922996.	+	1.59868e6i	−0.343501	+	0.594961i	−0.985080	−	0.172096i	$-0.944946\pi$
$373$	−922996.	+	1.59868e6i	−0.343501	+	0.594961i	0.641579	+	0.767057i	$0.278279\pi$
$374$	−400939.	+	128454.i	−0.148217	+	0.0474863i
$375$		0			0
$376$	279929.	−	2.38065e6i	0.102112	−	0.868412i
$377$			1.14087e6i			0.413412i
$378$		0			0
$379$		−	1.35806e6i		−	0.485649i	−0.970070	−	0.242824i	$-0.921926\pi$
$379$		−	1.35806e6i		−	0.485649i	0.970070	−	0.242824i	$-0.0780739\pi$
$380$	−1.43181e6	+	1.02240e6i	−0.508657	+	0.363212i
$381$		0			0
$382$	647216.	+	2.02014e6i	0.226930	+	0.708308i
$383$	−1.84507e6	+	3.19575e6i	−0.642710	+	1.11321i	0.342115	+	0.939658i	$0.388857\pi$
$383$	−1.84507e6	+	3.19575e6i	−0.642710	+	1.11321i	−0.984825	+	0.173548i	$0.944477\pi$
$384$		0			0
$385$	173830.	+	301082.i	0.0597686	+	0.103522i
$386$	−1.81430e6	+	1.99841e6i	−0.619785	+	0.682678i
$387$		0			0
$388$	−128031.	−	1.32261e6i	−0.0431754	−	0.446019i
$389$	−2.87005e6	+	1.65702e6i	−0.961645	+	0.555206i	−0.896679	−	0.442681i	$-0.854027\pi$
$389$	−2.87005e6	+	1.65702e6i	−0.961645	+	0.555206i	−0.0649663	+	0.997887i	$0.520694\pi$
$390$		0			0
$391$	−250215.	−	144462.i	−0.0827698	−	0.0477872i
$392$	−2.65827e6	+	1.14448e6i	−0.873745	+	0.376179i
$393$		0			0
$394$	532204.	−	2.45419e6i	0.172718	−	0.796467i
$395$	888447.			0.286509
$396$		0			0
$397$	−119467.			−0.0380427			−0.0190214	−	0.999819i	$-0.506055\pi$
$397$	−119467.			−0.0380427			−0.0190214	+	0.999819i	$0.506055\pi$
$398$	720813.	−	3.32394e6i	0.228095	−	1.05183i
$399$		0			0
$400$	858877.	−	2.50262e6i	0.268399	−	0.782068i
$401$	−4.09522e6	−	2.36438e6i	−1.27179	−	0.734271i	−0.296469	−	0.955043i	$-0.595809\pi$
$401$	−4.09522e6	−	2.36438e6i	−1.27179	−	0.734271i	−0.975325	+	0.220772i	$0.929142\pi$
$402$		0			0
$403$	215311.	−	124310.i	0.0660394	−	0.0381279i
$404$	3.70609e6	−	358756.i	1.12970	−	0.109357i
$405$		0			0
$406$	−5.59606e6	+	6.16393e6i	−1.68487	+	1.85585i
$407$	565893.	+	980156.i	0.169336	+	0.293298i
$408$		0			0
$409$	−3.11750e6	+	5.39967e6i	−0.921507	+	1.59610i	−0.124422	+	0.992229i	$0.539708\pi$
$409$	−3.11750e6	+	5.39967e6i	−0.921507	+	1.59610i	−0.797085	+	0.603867i	$0.793626\pi$
$410$	−202795.	−	632977.i	−0.0595796	−	0.185964i
$411$		0			0
$412$	−736471.	−	1.03139e6i	−0.213753	−	0.299349i
$413$			7.31236e6i			2.10952i
$414$		0			0
$415$		−	517425.i		−	0.147478i
$416$	813022.	+	16707.2i	0.230340	+	0.00473337i
$417$		0			0
$418$	1.05080e6	−	336659.i	0.294158	−	0.0942430i
$419$	347632.	−	602117.i	0.0967353	−	0.167551i	−0.813596	−	0.581430i	$-0.802493\pi$
$419$	347632.	−	602117.i	0.0967353	−	0.167551i	0.910332	+	0.413880i	$0.135827\pi$
$420$		0			0
$421$	−585766.	−	1.01458e6i	−0.161071	−	0.278984i	0.774182	−	0.632963i	$-0.218162\pi$
$421$	−585766.	−	1.01458e6i	−0.161071	−	0.278984i	−0.935253	+	0.353979i	$0.884828\pi$
$422$	1.66971e6	+	1.51588e6i	0.456414	+	0.414366i
$423$		0			0
$424$	−2.70742e6	+	3.63145e6i	−0.731377	+	0.980991i
$425$	−2.01800e6	+	1.16509e6i	−0.541936	+	0.312887i
$426$		0			0
$427$	−2.80231e6	−	1.61792e6i	−0.743784	−	0.429424i
$428$	2.39175e6	+	1.08852e6i	0.631113	+	0.287228i
$429$		0			0
$430$	−2.56326e6	−	555857.i	−0.668531	−	0.144975i
$431$	2.98148e6			0.773104			0.386552	−	0.922268i	$-0.373666\pi$
$431$	2.98148e6			0.773104			0.386552	+	0.922268i	$0.373666\pi$
$432$		0			0
$433$	5.90562e6			1.51372			0.756861	−	0.653576i	$-0.226732\pi$
$433$	5.90562e6			1.51372			0.756861	+	0.653576i	$0.226732\pi$
$434$	1.77304e6	+	384492.i	0.451849	+	0.0979858i
$435$		0			0
$436$	−1.41600e6	−	644440.i	−0.356736	−	0.162355i
$437$	655778.	+	378614.i	0.164268	+	0.0948403i
$438$		0			0
$439$	−2.85286e6	+	1.64710e6i	−0.706512	+	0.407905i	−0.809768	−	0.586750i	$-0.800407\pi$
$439$	−2.85286e6	+	1.64710e6i	−0.706512	+	0.407905i	0.103256	+	0.994655i	$0.467074\pi$
$440$	207715.	−	278607.i	0.0511489	−	0.0686056i
$441$		0			0
$442$	−530238.	−	481389.i	−0.129097	−	0.117203i
$443$	−3.05039e6	−	5.28344e6i	−0.738493	−	1.27911i	−0.953174	−	0.302423i	$-0.902204\pi$
$443$	−3.05039e6	−	5.28344e6i	−0.738493	−	1.27911i	0.214681	−	0.976684i	$-0.431129\pi$
$444$		0			0
$445$	−1.15055e6	+	1.99280e6i	−0.275425	+	0.477051i
$446$	−1.80455e6	+	578148.i	−0.429569	+	0.137626i
$447$		0			0
$448$	4.31067e6	+	4.07820e6i	1.01473	+	0.960006i
$449$		−	5.38289e6i		−	1.26008i	−0.776561	−	0.630042i	$-0.783038\pi$
$449$		−	5.38289e6i		−	1.26008i	0.776561	−	0.630042i	$-0.216962\pi$
$450$		0			0
$451$			416859.i			0.0965046i
$452$	−313922.	−	439630.i	−0.0722729	−	0.101214i
$453$		0			0
$454$	−1.46739e6	−	4.58012e6i	−0.334123	−	1.04289i
$455$	−295692.	+	512154.i	−0.0669594	+	0.115977i
$456$		0			0
$457$	−231952.	−	401752.i	−0.0519526	−	0.0899846i	0.838880	−	0.544317i	$-0.183211\pi$
$457$	−231952.	−	401752.i	−0.0519526	−	0.0899846i	−0.890832	+	0.454332i	$0.849878\pi$
$458$	1.55262e6	−	1.71017e6i	0.345860	−	0.380956i
$459$		0			0
$460$	237376.	−	22978.4i	0.0523048	−	0.00506320i
$461$	−3.61068e6	+	2.08463e6i	−0.791291	+	0.456852i	−0.840417	−	0.541940i	$-0.817690\pi$
$461$	−3.61068e6	+	2.08463e6i	−0.791291	+	0.456852i	0.0491256	+	0.998793i	$0.484357\pi$
$462$		0			0
$463$	−5.46488e6	−	3.15515e6i	−1.18475	−	0.684018i	−0.227644	−	0.973744i	$-0.573102\pi$
$463$	−5.46488e6	−	3.15515e6i	−1.18475	−	0.684018i	−0.957110	+	0.289726i	$0.906436\pi$
$464$	7.87117e6	+	2.70132e6i	1.69724	+	0.582480i
$465$		0			0
$466$	812308.	−	3.74585e6i	0.173283	−	0.799072i
$467$	−763795.			−0.162063			−0.0810316	−	0.996712i	$-0.525821\pi$
$467$	−763795.			−0.162063			−0.0810316	+	0.996712i	$0.525821\pi$
$468$		0			0
$469$	6.08282e6			1.27695
$470$	369287.	−	1.70292e6i	0.0771115	−	0.355590i
$471$		0			0
$472$	6.71355e6	−	2.89043e6i	1.38707	−	0.597183i
$473$	1.42458e6	+	822480.i	0.292774	+	0.169033i
$474$		0			0
$475$	5.28888e6	−	3.05354e6i	1.07555	−	0.620968i
$476$	−503536.	−	5.20172e6i	−0.101862	−	1.05228i
$477$		0			0
$478$	5.02101e6	−	5.53052e6i	1.00513	−	1.10712i
$479$	−1.97328e6	−	3.41782e6i	−0.392962	−	0.680629i	0.599877	−	0.800092i	$-0.295216\pi$
$479$	−1.97328e6	−	3.41782e6i	−0.392962	−	0.680629i	−0.992839	+	0.119463i	$0.961883\pi$
$480$		0			0
$481$	−962608.	+	1.66729e6i	−0.189709	+	0.328585i
$482$	1.44521e6	+	4.51090e6i	0.283344	+	0.884394i
$483$		0			0
$484$	4.01676e6	−	2.86821e6i	0.779403	−	0.556541i
$485$		−	965947.i		−	0.186466i
$486$		0			0
$487$			1.97847e6i			0.378012i	0.981976	+	0.189006i	$0.0605266\pi$
$487$			1.97847e6i			0.378012i	−0.981976	+	0.189006i	$0.939473\pi$
$488$	−377726.	+	3.21236e6i	−0.0718004	+	0.610625i
$489$		0			0
$490$	−2.00356e6	+	641907.i	−0.376975	+	0.120776i
$491$	−547411.	+	948143.i	−0.102473	+	0.177488i	−0.912703	−	0.408624i	$-0.866009\pi$
$491$	−547411.	+	948143.i	−0.102473	+	0.177488i	0.810230	+	0.586112i	$0.199342\pi$
$492$		0			0
$493$	−3.66441e6	−	6.34695e6i	−0.679027	−	1.17611i
$494$	1.38968e6	+	1.26165e6i	0.256210	+	0.232606i
$495$		0			0
$496$	−347839.	−	1.77982e6i	−0.0634855	−	0.324842i
$497$	8.75991e6	−	5.05754e6i	1.59078	−	0.918435i
$498$		0			0
$499$	9.07104e6	+	5.23717e6i	1.63082	+	0.941554i	0.983841	+	0.179045i	$0.0573009\pi$
$499$	9.07104e6	+	5.23717e6i	1.63082	+	0.941554i	0.646978	+	0.762508i	$0.276032\pi$
$500$	1.76031e6	−	3.86785e6i	0.314894	−	0.691903i
$501$		0			0
$502$	7.83040e6	+	1.69806e6i	1.38683	+	0.300742i
$503$	639826.			0.112757			0.0563783	−	0.998409i	$-0.482045\pi$
$503$	639826.			0.112757			0.0563783	+	0.998409i	$0.482045\pi$
$504$		0			0
$505$	2.70668e6			0.472289
$506$	−146173.	−	31698.3i	−0.0253799	−	0.00550377i
$507$		0			0
$508$	−608161.	+	1.33629e6i	−0.104559	+	0.229742i
$509$	2.75241e6	+	1.58911e6i	0.470890	+	0.271868i	0.716612	−	0.697472i	$-0.245692\pi$
$509$	2.75241e6	+	1.58911e6i	0.470890	+	0.271868i	−0.245722	+	0.969340i	$0.579025\pi$
$510$		0			0
$511$	−1.09564e7	+	6.32570e6i	−1.85617	+	1.07166i
$512$	2.04032e6	−	5.56969e6i	0.343971	−	0.938980i
$513$		0			0
$514$	4.29008e6	+	3.89485e6i	0.716238	+	0.650253i
$515$	−460636.	−	797845.i	−0.0765315	−	0.132556i
$516$		0			0
$517$	−546419.	+	946426.i	−0.0899083	+	0.155726i
$518$	−1.33790e7	+	4.28639e6i	−2.19078	+	0.701888i
$519$		0			0
$520$	587094.	+	69033.6i	0.0952137	+	0.0111957i
$521$		−	1.76213e6i		−	0.284408i	−0.989837	−	0.142204i	$-0.954581\pi$
$521$		−	1.76213e6i		−	0.284408i	0.989837	−	0.142204i	$-0.0454190\pi$
$522$		0			0
$523$		−	8.86393e6i		−	1.41701i	−0.705708	−	0.708503i	$-0.749371\pi$
$523$		−	8.86393e6i		−	1.41701i	0.705708	−	0.708503i	$-0.250629\pi$
$524$	−623624.	+	445305.i	−0.0992190	+	0.0708483i
$525$		0			0
$526$	−2.90537e6	−	9.06844e6i	−0.457865	−	1.42912i
$527$	−798552.	+	1.38313e6i	−0.125250	+	0.216939i
$528$		0			0
$529$	3.16685e6	+	5.48514e6i	0.492026	+	0.852214i
$530$	−2.21331e6	+	2.43791e6i	−0.342258	+	0.376989i
$531$		0			0
$532$	1.31969e6	+	1.36330e7i	0.202160	+	2.08839i
$533$	−614094.	+	354547.i	−0.0936304	+	0.0540575i
$534$		0			0
$535$	1.65432e6	+	955121.i	0.249882	+	0.144269i
$536$	−2.40441e6	−	5.58469e6i	−0.361491	−	0.839628i
$537$		0			0
$538$	−2.53962e6	+	1.17111e7i	−0.378279	+	1.74438i
$539$	1.31948e6			0.195629
$540$		0			0
$541$	−6.03815e6			−0.886974			−0.443487	−	0.896281i	$-0.646259\pi$
$541$	−6.03815e6			−0.886974			−0.443487	+	0.896281i	$0.646259\pi$
$542$	715414.	−	3.29904e6i	0.104607	−	0.482380i
$543$		0			0
$544$	−4.57671e6	+	2.51844e6i	−0.663065	+	0.364866i
$545$	−979414.	−	565465.i	−0.141246	−	0.0815482i
$546$		0			0
$547$	−544056.	+	314111.i	−0.0777455	+	0.0448864i	−0.538369	−	0.842709i	$-0.680959\pi$
$547$	−544056.	+	314111.i	−0.0777455	+	0.0448864i	0.460623	+	0.887596i	$0.347626\pi$
$548$	−6.58619e6	+	637555.i	−0.936878	+	0.0906914i
$549$		0			0
$550$	−810842.	+	893124.i	−0.114296	+	0.125894i
$551$	9.60390e6	+	1.66344e7i	1.34762	+	2.33415i
$552$		0			0
$553$	3.45829e6	−	5.98993e6i	0.480893	−	0.832931i
$554$	−1.83722e6	−	5.73445e6i	−0.254323	−	0.793812i
$555$		0			0
$556$	−3.22714e6	−	4.51943e6i	−0.442722	−	0.620007i
$557$		−	2.33240e6i		−	0.318541i	−0.987235	−	0.159270i	$-0.949086\pi$
$557$		−	2.33240e6i		−	0.318541i	0.987235	−	0.159270i	$-0.0509142\pi$
$558$		0			0
$559$			2.79815e6i			0.378740i
$560$	2.83335e6	+	3.25272e6i	0.381795	+	0.438305i
$561$		0			0
$562$	−5.53755e6	+	1.77413e6i	−0.739566	+	0.236944i
$563$	4.06546e6	−	7.04158e6i	0.540553	−	0.936266i	−0.458319	−	0.888788i	$-0.651548\pi$
$563$	4.06546e6	−	7.04158e6i	0.540553	−	0.936266i	0.998872	−	0.0474781i	$-0.0151184\pi$
$564$		0			0
$565$	−196347.	−	340083.i	−0.0258763	−	0.0448191i
$566$	−4.63366e6	−	4.20677e6i	−0.607971	−	0.551960i
$567$		0			0
$568$	−8.10599e6	−	6.04341e6i	−1.05423	−	0.785980i
$569$	5.81782e6	−	3.35892e6i	0.753320	−	0.434929i	−0.0735725	−	0.997290i	$-0.523440\pi$
$569$	5.81782e6	−	3.35892e6i	0.753320	−	0.434929i	0.826892	+	0.562361i	$0.190107\pi$
$570$		0			0
$571$	1.04309e7	+	6.02229e6i	1.33885	+	0.772985i	0.986637	−	0.162935i	$-0.0520961\pi$
$571$	1.04309e7	+	6.02229e6i	1.33885	+	0.772985i	0.352213	+	0.935920i	$0.385429\pi$
$572$	−337440.	−	153573.i	−0.0431227	−	0.0196257i
$573$		0			0
$574$	−5.05693e6	−	1.09662e6i	−0.640630	−	0.138924i
$575$	−827826.			−0.104417
$576$		0			0
$577$	−906368.			−0.113335			−0.0566676	−	0.998393i	$-0.518048\pi$
$577$	−906368.			−0.113335			−0.0566676	+	0.998393i	$0.518048\pi$
$578$	−3.35344e6	−	727211.i	−0.417513	−	0.0905400i
$579$		0			0
$580$	5.50600e6	+	2.50585e6i	0.679620	+	0.309304i
$581$	−3.48849e6	−	2.01408e6i	−0.428743	−	0.247535i
$582$		0			0
$583$	1.78843e6	−	1.03255e6i	0.217922	−	0.125817i
$584$	1.01385e7	+	7.55877e6i	1.23011	+	0.917105i
$585$		0			0
$586$	−4.78382e6	−	4.34310e6i	−0.575480	−	0.522463i
$587$	−4.78919e6	−	8.29511e6i	−0.573676	−	0.993636i	−0.996184	−	0.0872766i	$-0.972184\pi$
$587$	−4.78919e6	−	8.29511e6i	−0.573676	−	0.993636i	0.422508	−	0.906359i	$-0.361150\pi$
$588$		0			0
$589$	2.09289e6	−	3.62499e6i	0.248575	−	0.430545i
$590$	5.06005e6	−	1.62115e6i	0.598446	−	0.191732i
$591$		0			0
$592$	9.22382e6	+	1.05890e7i	1.08170	+	1.24180i
$593$			6.46951e6i			0.755501i	0.925907	+	0.377750i	$0.123302\pi$
$593$			6.46951e6i			0.755501i	−0.925907	+	0.377750i	$0.876698\pi$
$594$		0			0
$595$		−	3.79899e6i		−	0.439922i
$596$	−4.20849e6	−	5.89376e6i	−0.485301	−	0.679636i
$597$		0			0
$598$	−77626.7	−	242294.i	−0.00887684	−	0.0277070i
$599$	−2.38231e6	+	4.12628e6i	−0.271288	+	0.469885i	−0.969192	−	0.246306i	$-0.920783\pi$
$599$	−2.38231e6	+	4.12628e6i	−0.271288	+	0.469885i	0.697904	+	0.716192i	$0.254116\pi$
$600$		0			0
$601$	−7.09387e6	−	1.22869e7i	−0.801119	−	1.38758i	−0.918880	−	0.394537i	$-0.870905\pi$
$601$	−7.09387e6	−	1.22869e7i	−0.801119	−	1.38758i	0.117761	−	0.993042i	$-0.462428\pi$
$602$	−1.37251e7	+	1.51179e7i	−1.54357	+	1.70020i
$603$		0			0
$604$	−1.78130e6	+	172433.i	−0.198676	+	0.0192322i
$605$	3.10723e6	−	1.79396e6i	0.345132	−	0.199262i
$606$		0			0
$607$	6.94805e6	+	4.01146e6i	0.765404	+	0.441906i	0.831233	−	0.555924i	$-0.187636\pi$
$607$	6.94805e6	+	4.01146e6i	0.765404	+	0.441906i	−0.0658283	+	0.997831i	$0.520969\pi$
$608$	1.19949e7	−	6.60045e6i	1.31594	−	0.724127i
$609$		0			0
$610$	−498302.	+	2.29785e6i	−0.0542210	+	0.250033i
$611$	−1.85897e6			−0.201450
$612$		0			0
$613$	4.92638e6			0.529513			0.264757	−	0.964315i	$-0.414708\pi$
$613$	4.92638e6			0.529513			0.264757	+	0.964315i	$0.414708\pi$
$614$	−1.58546e6	+	7.31115e6i	−0.169721	+	0.782645i
$615$		0			0
$616$	−1.06984e6	−	2.48490e6i	−0.113597	−	0.263850i
$617$	−1.81236e6	−	1.04636e6i	−0.191660	−	0.110655i	0.401100	−	0.916034i	$-0.368628\pi$
$617$	−1.81236e6	−	1.04636e6i	−0.191660	−	0.110655i	−0.592759	+	0.805380i	$0.701961\pi$
$618$		0			0
$619$	7.46071e6	−	4.30745e6i	0.782625	−	0.451849i	−0.0547347	−	0.998501i	$-0.517431\pi$
$619$	7.46071e6	−	4.30745e6i	0.782625	−	0.451849i	0.837360	+	0.546652i	$0.184098\pi$
$620$	−127019.	−	1.31216e6i	−0.0132706	−	0.137090i
$621$		0			0
$622$	−1.06068e6	+	1.16831e6i	−0.109928	+	0.121083i
$623$	8.95702e6	+	1.55140e7i	0.924578	+	1.60142i
$624$		0			0
$625$	−2.49273e6	+	4.31754e6i	−0.255256	+	0.442116i
$626$	−237910.	−	742581.i	−0.0242648	−	0.0757369i
$627$		0			0
$628$	−3.50652e6	+	2.50386e6i	−0.354795	+	0.253345i
$629$		−	1.23674e7i		−	1.24638i
$630$		0			0
$631$		−	1.15818e7i		−	1.15798i	−0.815334	−	0.578991i	$-0.803446\pi$
$631$		−	1.15818e7i		−	1.15798i	0.815334	−	0.578991i	$-0.196554\pi$
$632$	−6.86640e6	−	807387.i	−0.683812	−	0.0804061i
$633$		0			0
$634$	−7.03152e6	+	2.25278e6i	−0.694746	+	0.222585i
$635$	−533632.	+	924277.i	−0.0525179	+	0.0909637i
$636$		0			0
$637$	1.12225e6	+	1.94379e6i	0.109582	+	0.189802i
$638$	−2.80903e6	−	2.55024e6i	−0.273215	−	0.248044i
$639$		0			0
$640$	1.86638e6	−	3.88706e6i	0.180115	−	0.375121i
$641$	−1.51197e7	+	8.72938e6i	−1.45345	+	0.839147i	−0.998675	−	0.0514611i	$-0.983612\pi$
$641$	−1.51197e7	+	8.72938e6i	−1.45345	+	0.839147i	−0.454771	+	0.890608i	$0.650279\pi$
$642$		0			0
$643$	−8.37838e6	−	4.83726e6i	−0.799158	−	0.461394i	0.0440186	−	0.999031i	$-0.485984\pi$
$643$	−8.37838e6	−	4.83726e6i	−0.799158	−	0.461394i	−0.843177	+	0.537637i	$0.819317\pi$
$644$	769067.	−	1.68984e6i	0.0730717	−	0.160557i
$645$		0			0
$646$	−1.17835e7	−	2.55531e6i	−1.11094	−	0.240914i
$647$	−1.26182e7			−1.18505			−0.592525	−	0.805552i	$-0.701869\pi$
$647$	−1.26182e7			−1.18505			−0.592525	+	0.805552i	$0.701869\pi$
$648$		0			0
$649$	−3.33239e6			−0.310559
$650$	−2.00534e6	−	434869.i	−0.186168	−	0.0403715i
$651$		0			0
$652$	−1.24382e6	+	2.73300e6i	−0.114588	+	0.251780i
$653$	1.65281e7	+	9.54250e6i	1.51684	+	0.875748i	0.999804	+	0.0197840i	$0.00629786\pi$
$653$	1.65281e7	+	9.54250e6i	1.51684	+	0.875748i	0.517036	+	0.855964i	$0.327035\pi$
$654$		0			0
$655$	−482415.	+	278522.i	−0.0439357	+	0.0253663i
$656$	992083.	+	5.07628e6i	0.0900095	+	0.460560i
$657$		0			0
$658$	−1.00437e7	−	9.11837e6i	−0.904332	−	0.821018i
$659$	5.33197e6	+	9.23524e6i	0.478271	+	0.828390i	0.999690	−	0.0249112i	$-0.00793029\pi$
$659$	5.33197e6	+	9.23524e6i	0.478271	+	0.828390i	−0.521419	+	0.853301i	$0.674597\pi$
$660$		0			0
$661$	1.35400e6	−	2.34520e6i	0.120535	−	0.208774i	−0.799443	−	0.600741i	$-0.794872\pi$
$661$	1.35400e6	−	2.34520e6i	0.120535	−	0.208774i	0.919979	+	0.391968i	$0.128206\pi$
$662$	3.43842e6	−	1.10161e6i	0.304940	−	0.0976974i
$663$		0			0
$664$	−470216.	+	3.99894e6i	−0.0413883	+	0.351986i
$665$			9.95660e6i			0.873086i
$666$		0			0
$667$		−	2.60366e6i		−	0.226605i
$668$	−3.51256e6	+	2.50818e6i	−0.304566	+	0.217479i
$669$		0			0
$670$	−1.34856e6	−	4.20922e6i	−0.116060	−	0.362256i
$671$	737317.	−	1.27707e6i	0.0632191	−	0.109499i
$672$		0			0
$673$	−2.61627e6	−	4.53151e6i	−0.222661	−	0.385660i	0.732954	−	0.680278i	$-0.238141\pi$
$673$	−2.61627e6	−	4.53151e6i	−0.222661	−	0.385660i	−0.955615	+	0.294618i	$0.904808\pi$
$674$	3.73745e6	−	4.11671e6i	0.316903	−	0.349061i
$675$		0			0
$676$	1.08402e6	+	1.11984e7i	0.0912372	+	0.942516i
$677$	1.63183e6	−	942135.i	0.136837	−	0.0790026i	−0.430019	−	0.902820i	$-0.641493\pi$
$677$	1.63183e6	−	942135.i	0.136837	−	0.0790026i	0.566855	+	0.823817i	$0.308160\pi$
$678$		0			0
$679$	−6.51244e6	−	3.75996e6i	−0.542087	−	0.312974i
$680$	−3.48788e6	+	1.50166e6i	−0.289261	+	0.124537i
$681$		0			0
$682$	−175221.	+	808009.i	−0.0144253	+	0.0665204i
$683$	8.13981e6			0.667671			0.333835	−	0.942631i	$-0.391657\pi$
$683$	8.13981e6			0.667671			0.333835	+	0.942631i	$0.391657\pi$
$684$		0			0
$685$	−4.81011e6			−0.391678
$686$	177761.	−	819722.i	0.0144220	−	0.0665053i
$687$		0			0
$688$	1.93051e7	+	6.62536e6i	1.55490	+	0.533628i
$689$	3.04220e6	+	1.75641e6i	0.244140	+	0.140954i
$690$		0			0
$691$	1.22215e7	−	7.05606e6i	0.973706	−	0.562169i	0.0733417	−	0.997307i	$-0.476634\pi$
$691$	1.22215e7	−	7.05606e6i	0.973706	−	0.562169i	0.900364	+	0.435138i	$0.143300\pi$
$692$	−6.61309e6	+	640158.i	−0.524975	+	0.0508186i
$693$		0			0
$694$	−5.13788e6	+	5.65925e6i	−0.404935	+	0.446026i
$695$	−2.01846e6	−	3.49608e6i	−0.158511	−	0.274549i
$696$		0			0
$697$	2.27757e6	−	3.94487e6i	0.177579	−	0.307575i
$698$	1.30118e6	+	4.06132e6i	0.101088	+	0.315521i
$699$		0			0
$700$	−8.70144e6	−	1.21859e7i	−0.671191	−	0.939965i
$701$			2.52168e6i			0.193818i	0.995293	+	0.0969090i	$0.0308956\pi$
$701$			2.52168e6i			0.193818i	−0.995293	+	0.0969090i	$0.969104\pi$
$702$		0			0
$703$			3.24131e7i			2.47362i
$704$	−1.85852e6	+	1.96446e6i	−0.141330	+	0.149387i
$705$		0			0
$706$	2.42564e6	−	777132.i	0.183153	−	0.0586790i
$707$	1.05358e7	−	1.82485e7i	0.792716	−	1.37302i
$708$		0			0
$709$	7.59486e6	+	1.31547e7i	0.567419	+	0.982799i	0.996820	+	0.0796849i	$0.0253914\pi$
$709$	7.59486e6	+	1.31547e7i	0.567419	+	0.982799i	−0.429401	+	0.903114i	$0.641275\pi$
$710$	−5.44182e6	−	4.94048e6i	−0.405134	−	0.367810i
$711$		0			0
$712$	1.07030e7	−	1.43559e7i	0.791237	−	1.06128i
$713$	−491375.	+	283695.i	−0.0361984	+	0.0208991i
$714$		0			0
$715$	−233399.	−	134753.i	−0.0170739	−	0.00985765i
$716$	−1.52981e7	−	6.96238e6i	−1.11521	−	0.507546i
$717$		0			0
$718$	1.67092e7	+	3.62347e6i	1.20960	+	0.262309i
$719$	−4.45507e6			−0.321390			−0.160695	−	0.987004i	$-0.551374\pi$
$719$	−4.45507e6			−0.321390			−0.160695	+	0.987004i	$0.551374\pi$
$720$		0			0
$721$	−7.17213e6			−0.513819
$722$	1.71940e7	+	3.72862e6i	1.22754	+	0.266198i
$723$		0			0
$724$	−2.40529e7	−	1.09468e7i	−1.70538	−	0.776141i
$725$	−1.81853e7	−	1.04993e7i	−1.28492	−	0.741849i
$726$		0			0
$727$	−1.03556e7	+	5.97878e6i	−0.726670	+	0.419543i	−0.817203	−	0.576350i	$-0.804476\pi$
$727$	−1.03556e7	+	5.97878e6i	−0.726670	+	0.419543i	0.0905324	+	0.995894i	$0.471143\pi$
$728$	2.75070e6	−	3.68949e6i	0.192360	−	0.258011i
$729$		0			0
$730$	6.80634e6	+	6.17929e6i	0.472722	+	0.429172i
$731$	−8.98749e6	−	1.55668e7i	−0.622078	−	1.07747i
$732$		0			0
$733$	−6.24966e6	+	1.08247e7i	−0.429632	+	0.744144i	−0.996840	−	0.0794302i	$-0.974690\pi$
$733$	−6.24966e6	+	1.08247e7i	−0.429632	+	0.744144i	0.567209	+	0.823574i	$0.308023\pi$
$734$	1.45376e7	−	4.65760e6i	0.995985	−	0.319096i
$735$		0			0
$736$	−1.85545e6	−	38128.6i	−0.126257	−	0.00259452i
$737$			2.77206e6i			0.187990i
$738$		0			0
$739$			3.34559e6i			0.225352i	0.993632	+	0.112676i	$0.0359422\pi$
$739$			3.34559e6i			0.225352i	−0.993632	+	0.112676i	$0.964058\pi$
$740$	5.93225e6	+	8.30778e6i	0.398236	+	0.557706i
$741$		0			0
$742$	7.82112e6	+	2.44118e7i	0.521506	+	1.62776i
$743$	−1.84277e6	+	3.19177e6i	−0.122461	+	0.212109i	−0.920738	−	0.390182i	$-0.872412\pi$
$743$	−1.84277e6	+	3.19177e6i	−0.122461	+	0.212109i	0.798276	+	0.602291i	$0.205745\pi$
$744$		0			0
$745$	−2.63226e6	−	4.55921e6i	−0.173755	−	0.300953i
$746$	7.01923e6	−	7.73152e6i	0.461788	−	0.508648i
$747$		0			0
$748$	2.37053e6	−	229472.i	0.154914	−	0.0149960i
$749$	1.28789e7	−	7.43564e6i	0.838831	−	0.484299i
$750$		0			0
$751$	−1.11291e7	−	6.42540e6i	−0.720048	−	0.415720i	0.0947225	−	0.995504i	$-0.469804\pi$
$751$	−1.11291e7	−	6.42540e6i	−0.720048	−	0.415720i	−0.814770	+	0.579784i	$0.803137\pi$
$752$	−4.40160e6	+	1.28255e7i	−0.283835	+	0.827045i
$753$		0			0
$754$	1.36774e6	−	6.30714e6i	0.0876142	−	0.404021i
$755$	−1.30094e6			−0.0830597
$756$		0			0
$757$	2.81332e6			0.178435			0.0892175	−	0.996012i	$-0.471563\pi$
$757$	2.81332e6			0.178435			0.0892175	+	0.996012i	$0.471563\pi$
$758$	−1.62812e6	+	7.50787e6i	−0.102923	+	0.474617i
$759$		0			0
$760$	9.14124e6	−	3.93564e6i	0.574078	−	0.247162i
$761$	−2.67932e6	−	1.54691e6i	−0.167712	−	0.0968283i	0.413795	−	0.910370i	$-0.364203\pi$
$761$	−2.67932e6	−	1.54691e6i	−0.167712	−	0.0968283i	−0.581506	+	0.813542i	$0.697536\pi$
$762$		0			0
$763$	−7.62475e6	+	4.40215e6i	−0.474149	+	0.273750i
$764$	−1.15620e6	−	1.19440e7i	−0.0716635	−	0.740312i
$765$		0			0
$766$	1.40314e7	−	1.54553e7i	0.864032	−	0.951711i
$767$	−2.83427e6	−	4.90910e6i	−0.173962	−	0.301310i
$768$		0			0
$769$	602040.	−	1.04276e6i	0.0367122	−	0.0635873i	−0.847086	−	0.531457i	$-0.821645\pi$
$769$	602040.	−	1.04276e6i	0.0367122	−	0.0635873i	0.883798	+	0.467869i	$0.154978\pi$
$770$	−600041.	−	1.87289e6i	−0.0364715	−	0.113837i
$771$		0			0
$772$	1.24259e7	−	8.87284e6i	0.750386	−	0.535821i
$773$		−	2.76278e7i		−	1.66302i	−0.555510	−	0.831510i	$-0.687477\pi$
$773$		−	2.76278e7i		−	1.66302i	0.555510	−	0.831510i	$-0.312523\pi$
$774$		0			0
$775$			4.57603e6i			0.273675i
$776$	−877816.	+	7.46537e6i	−0.0523298	+	0.445038i
$777$		0			0
$778$	1.78532e7	−	5.71985e6i	1.05747	−	0.338794i
$779$	−5.96919e6	+	1.03389e7i	−0.352429	+	0.610425i
$780$		0			0
$781$	2.30482e6	+	3.99207e6i	0.135210	+	0.234191i
$782$	1.21009e6	+	1.09861e6i	0.0707622	+	0.0642430i
$783$		0			0
$784$	1.60680e7	−	3.14024e6i	0.933621	−	0.182462i
$785$	−2.71252e6	+	1.56608e6i	−0.157108	+	0.0907066i
$786$		0			0
$787$	−5.86919e6	−	3.38858e6i	−0.337786	−	0.195021i	0.321507	−	0.946907i	$-0.395811\pi$
$787$	−5.86919e6	−	3.38858e6i	−0.337786	−	0.195021i	−0.659292	+	0.751887i	$0.729144\pi$
$788$	−5.88443e6	+	1.29296e7i	−0.337590	+	0.741771i
$789$		0			0
$790$	−4.91165e6	−	1.06512e6i	−0.280001	−	0.0607198i
$791$	−3.05713e6			−0.173729
$792$		0			0
$793$	2.50842e6			0.141650
$794$	660456.	+	143223.i	0.0371786	+	0.00806237i
$795$		0			0
$796$	−7.96983e6	+	1.75118e7i	−0.445827	+	0.979596i
$797$	7.51105e6	+	4.33650e6i	0.418846	+	0.241821i	0.694584	−	0.719412i	$-0.255589\pi$
$797$	7.51105e6	+	4.33650e6i	0.418846	+	0.241821i	−0.275737	+	0.961233i	$0.588922\pi$
$798$		0			0
$799$	1.03419e7	−	5.97089e6i	0.573103	−	0.330881i
$800$	−7.74846e6	+	1.28057e7i	−0.428046	+	0.707422i
$801$		0			0
$802$	1.98053e7	+	1.79807e7i	1.08729	+	0.987122i
$803$	−2.88275e6	−	4.99307e6i	−0.157768	−	0.273262i
$804$		0			0
$805$	674819.	−	1.16882e6i	0.0367026	−	0.0635708i
$806$	−1.33934e6	+	429102.i	−0.0726197	+	0.0232661i
$807$		0			0
$808$	−2.09187e7	−	2.45973e6i	−1.12721	−	0.132543i
$809$			2.35011e7i			1.26246i	0.775596	+	0.631230i	$0.217450\pi$
$809$			2.35011e7i			1.26246i	−0.775596	+	0.631230i	$0.782550\pi$
$810$		0			0
$811$			335741.i			0.0179247i	0.999960	+	0.00896235i	$0.00285284\pi$
$811$			335741.i			0.0179247i	−0.999960	+	0.00896235i	$0.997147\pi$
$812$	3.83267e7	−	2.73675e7i	2.03991	−	1.45662i
$813$		0			0
$814$	−1.95340e6	−	6.09708e6i	−0.103331	−	0.322523i
$815$	−1.09140e6	+	1.89035e6i	−0.0575557	+	0.0996894i
$816$		0			0
$817$	2.35549e7	+	4.07983e7i	1.23460	+	2.13839i
$818$	2.37081e7	−	2.61139e7i	1.23883	−	1.36455i
$819$		0			0
$820$	362275.	+	3.74245e6i	0.0188150	+	0.194366i
$821$	−2.09922e7	+	1.21198e7i	−1.08692	+	0.627536i	−0.932756	−	0.360509i	$-0.882603\pi$
$821$	−2.09922e7	+	1.21198e7i	−1.08692	+	0.627536i	−0.154168	+	0.988045i	$0.549270\pi$
$822$		0			0
$823$	−3.59148e6	−	2.07354e6i	−0.184831	−	0.106712i	0.404730	−	0.914436i	$-0.367366\pi$
$823$	−3.59148e6	−	2.07354e6i	−0.184831	−	0.106712i	−0.589560	+	0.807724i	$0.700699\pi$
$824$	2.83500e6	+	6.58479e6i	0.145457	+	0.337850i
$825$		0			0
$826$	8.76646e6	−	4.04254e7i	0.447068	−	2.06160i
$827$	−2.18621e6			−0.111155			−0.0555773	−	0.998454i	$-0.517700\pi$
$827$	−2.18621e6			−0.111155			−0.0555773	+	0.998454i	$0.517700\pi$
$828$		0			0
$829$	9.24847e6			0.467395			0.233697	−	0.972309i	$-0.424918\pi$
$829$	9.24847e6			0.467395			0.233697	+	0.972309i	$0.424918\pi$
$830$	−620317.	+	2.86051e6i	−0.0312549	+	0.144128i
$831$		0			0
$832$	−4.47465e6	−	1.06706e6i	−0.224104	−	0.0534416i
$833$	−1.24867e7	−	7.20920e6i	−0.623499	−	0.359977i
$834$		0			0
$835$	−2.71720e6	+	1.56877e6i	−0.134867	+	0.0778653i
$836$	−6.21282e6	+	601412.i	−0.307449	+	0.0297616i
$837$		0			0
$838$	−2.64369e6	+	2.91196e6i	−0.130047	+	0.143244i
$839$	−3.55904e6	−	6.16444e6i	−0.174553	−	0.302335i	0.765453	−	0.643491i	$-0.222515\pi$
$839$	−3.55904e6	−	6.16444e6i	−0.174553	−	0.302335i	−0.940007	+	0.341156i	$0.889181\pi$
$840$		0			0
$841$	2.27665e7	−	3.94328e7i	1.10996	−	1.92251i
$842$	2.02199e6	+	6.31119e6i	0.0982878	+	0.306783i
$843$		0			0
$844$	−7.41342e6	−	1.03821e7i	−0.358230	−	0.501681i
$845$			8.17855e6i			0.394035i
$846$		0			0
$847$		−	2.79320e7i		−	1.33781i
$848$	1.93212e7	−	1.68301e7i	0.922665	−	0.803708i
$849$		0			0
$850$	1.25530e7	−	4.02176e6i	0.595936	−	0.190928i
$851$	2.19683e6	−	3.80502e6i	0.103986	−	0.180108i
$852$		0			0
$853$	5.61575e6	+	9.72676e6i	0.264262	+	0.457715i	0.967370	−	0.253368i	$-0.0815383\pi$
$853$	5.61575e6	+	9.72676e6i	0.264262	+	0.457715i	−0.703108	+	0.711083i	$0.748205\pi$
$854$	1.35525e7	+	1.23040e7i	0.635881	+	0.577299i
$855$		0			0
$856$	−1.19175e7	−	8.88508e6i	−0.555905	−	0.414455i
$857$	2.03104e7	−	1.17262e7i	0.944641	−	0.545389i	0.0532292	−	0.998582i	$-0.483049\pi$
$857$	2.03104e7	−	1.17262e7i	0.944641	−	0.545389i	0.891412	+	0.453193i	$0.149715\pi$
$858$		0			0
$859$	−3.00517e7	−	1.73504e7i	−1.38959	−	0.802279i	−0.396319	−	0.918113i	$-0.629713\pi$
$859$	−3.00517e7	−	1.73504e7i	−1.38959	−	0.802279i	−0.993269	+	0.115834i	$0.963046\pi$
$860$	1.35042e7	+	6.14595e6i	0.622621	+	0.283363i
$861$		0			0
$862$	−1.64827e7	−	3.57435e6i	−0.755543	−	0.163844i
$863$	2.83896e7			1.29757			0.648787	−	0.760970i	$-0.275276\pi$
$863$	2.83896e7			1.29757			0.648787	+	0.760970i	$0.275276\pi$
$864$		0			0
$865$	−4.82975e6			−0.219475
$866$	−3.26484e7	−	7.07998e6i	−1.47934	−	0.320802i
$867$		0			0
$868$	−9.34103e6	−	4.25122e6i	−0.420819	−	0.191520i
$869$	2.72974e6	+	1.57601e6i	0.122623	+	0.0707963i
$870$		0			0
$871$	−4.08366e6	+	2.35770e6i	−0.182391	+	0.105304i
$872$	7.05557e6	+	5.26027e6i	0.314225	+	0.234270i
$873$		0			0
$874$	−3.17147e6	−	2.87929e6i	−0.140437	−	0.127499i
$875$	−1.20246e7	−	2.08273e7i	−0.530948	−	0.919629i
$876$		0			0
$877$	−1.61791e7	+	2.80230e7i	−0.710323	+	1.23031i	0.254414	+	0.967096i	$0.418118\pi$
$877$	−1.61791e7	+	2.80230e7i	−0.710323	+	1.23031i	−0.964736	+	0.263219i	$0.915216\pi$
$878$	1.77463e7	−	5.68560e6i	0.776911	−	0.248909i
$879$		0			0
$880$	−1.48233e6	+	1.29122e6i	−0.0645266	+	0.0562073i
$881$			5.73331e6i			0.248866i	0.992228	+	0.124433i	$0.0397112\pi$
$881$			5.73331e6i			0.248866i	−0.992228	+	0.124433i	$0.960289\pi$
$882$		0			0
$883$			2.49947e7i			1.07881i	0.842046	+	0.539406i	$0.181351\pi$
$883$			2.49947e7i			1.07881i	−0.842046	+	0.539406i	$0.818649\pi$
$884$	2.35423e6	+	3.29697e6i	0.101325	+	0.141901i
$885$		0			0
$886$	1.05296e7	+	3.28657e7i	0.450638	+	1.40656i
$887$	−2.27170e6	+	3.93469e6i	−0.0969485	+	0.167920i	−0.910420	−	0.413685i	$-0.864242\pi$
$887$	−2.27170e6	+	3.93469e6i	−0.0969485	+	0.167920i	0.813472	+	0.581605i	$0.197575\pi$
$888$		0			0
$889$	4.15433e6	+	7.19552e6i	0.176298	+	0.305357i
$890$	8.74971e6	−	9.63760e6i	0.370270	−	0.407844i
$891$		0			0
$892$	1.06693e7	−	1.03281e6i	0.448978	−	0.0434619i
$893$	−2.71046e7	+	1.56488e7i	−1.13740	+	0.656680i
$894$		0			0
$895$	−1.05814e7	−	6.10915e6i	−0.441554	−	0.254931i
$896$	−1.89417e7	−	2.77136e7i	−0.788225	−	1.15325i
$897$		0			0
$898$	−6.45329e6	+	2.97585e7i	−0.267049	+	1.23146i
$899$	−1.43924e7			−0.593928
$900$		0			0
$901$	−2.25660e7			−0.926068
$902$	499753.	−	2.30455e6i	0.0204522	−	0.0943125i
$903$		0			0
$904$	1.20842e6	+	2.80678e6i	0.0491810	+	0.114232i
$905$	−1.66368e7	−	9.60528e6i	−0.675226	−	0.389842i
$906$		0			0
$907$	2.72617e7	−	1.57395e7i	1.10036	−	0.635292i	0.164043	−	0.986453i	$-0.447546\pi$
$907$	2.72617e7	−	1.57395e7i	1.10036	−	0.635292i	0.936315	+	0.351161i	$0.114213\pi$
$908$	2.62137e6	+	2.70797e7i	0.105515	+	1.09001i
$909$		0			0
$910$	2.24869e6	−	2.47688e6i	0.0900173	−	0.0991519i
$911$	−2.63528e6	−	4.56443e6i	−0.105204	−	0.182218i	0.808618	−	0.588334i	$-0.200216\pi$
$911$	−2.63528e6	−	4.56443e6i	−0.105204	−	0.182218i	−0.913821	+	0.406116i	$0.866883\pi$
$912$		0			0
$913$	917858.	−	1.58978e6i	0.0364417	−	0.0631189i
$914$	800671.	+	2.49911e6i	0.0317021	+	0.0989509i
$915$		0			0
$916$	−1.06337e7	+	7.59307e6i	−0.418740	+	0.299005i
$917$			4.33661e6i			0.170305i
$918$		0			0
$919$			3.29683e7i			1.28768i	0.765161	+	0.643839i	$0.222659\pi$
$919$			3.29683e7i			1.28768i	−0.765161	+	0.643839i	$0.777341\pi$
$920$	−1.33985e6	−	157546.i	−0.0521898	−	0.00613674i
$921$		0			0
$922$	2.24603e7	−	7.19588e6i	0.870138	−	0.278777i
$923$	−3.92060e6	+	6.79068e6i	−0.151478	+	0.262367i
$924$		0			0
$925$	−1.77175e7	−	3.06877e7i	−0.680846	−	1.17926i
$926$	2.64293e7	+	2.39944e7i	1.01288	+	0.919565i
$927$		0			0
$928$	−4.02761e7	−	2.43702e7i	−1.53525	−	0.928945i
$929$	1.70431e6	−	983982.i	0.0647901	−	0.0374066i	−0.467255	−	0.884123i	$-0.654757\pi$
$929$	1.70431e6	−	983982.i	0.0647901	−	0.0374066i	0.532045	+	0.846716i	$0.321424\pi$
$930$		0			0
$931$	3.27259e7	+	1.88943e7i	1.23742	+	0.714424i
$932$	−8.98146e6	+	1.97346e7i	−0.338694	+	0.744198i
$933$		0			0
$934$	4.22253e6	+	915678.i	0.158382	+	0.0343460i
$935$	1.73128e6			0.0647646
$936$		0			0
$937$	−3.97561e7			−1.47929			−0.739647	−	0.672995i	$-0.765007\pi$
$937$	−3.97561e7			−1.47929			−0.739647	+	0.672995i	$0.765007\pi$
$938$	−3.36280e7	−	7.29241e6i	−1.24794	−	0.270623i
$939$		0			0
$940$	−4.08310e6	+	8.97163e6i	−0.150720	+	0.331170i
$941$	1.93060e7	+	1.11463e7i	0.710751	+	0.410352i	0.811339	−	0.584576i	$-0.198739\pi$
$941$	1.93060e7	+	1.11463e7i	0.710751	+	0.410352i	−0.100588	+	0.994928i	$0.532072\pi$
$942$		0			0
$943$	1.40146e6	−	809136.i	0.0513219	−	0.0296307i
$944$	−4.05801e7	+	7.93077e6i	−1.48212	+	0.289658i
$945$		0			0
$946$	−6.88954e6	−	6.25482e6i	−0.250301	−	0.227241i
$947$	2.17517e7	+	3.76751e7i	0.788168	+	1.36515i	0.927088	+	0.374843i	$0.122303\pi$
$947$	2.17517e7	+	3.76751e7i	0.788168	+	1.36515i	−0.138921	+	0.990304i	$0.544363\pi$
$948$		0			0
$949$	4.90368e6	−	8.49342e6i	0.176749	−	0.306138i
$950$	−3.28996e7	+	1.05404e7i	−1.18272	+	0.378922i
$951$		0			0
$952$	−3.45238e6	+	2.93606e7i	−0.123460	+	1.04996i
$953$		−	7.60909e6i		−	0.271394i	−0.990750	−	0.135697i	$-0.956673\pi$
$953$		−	7.60909e6i		−	0.271394i	0.990750	−	0.135697i	$-0.0433274\pi$
$954$		0			0
$955$		−	8.72306e6i		−	0.309500i
$956$	−3.43882e7	+	2.45553e7i	−1.21693	+	0.868960i
$957$		0			0
$958$	6.81153e6	+	2.12606e7i	0.239790	+	0.748449i
$959$	−1.87234e7	+	3.24299e7i	−0.657413	+	1.13867i
$960$		0			0
$961$	−1.27464e7	−	2.20774e7i	−0.445224	−	0.771150i
$962$	7.32048e6	−	8.06333e6i	0.255036	−	0.280916i
$963$		0			0
$964$	−2.58175e6	−	2.66705e7i	−0.0894791	−	0.924354i
$965$	9.61226e6	−	5.54964e6i	0.332282	−	0.191843i
$966$		0			0
$967$	−1.31287e7	−	7.57986e6i	−0.451498	−	0.260672i	0.256965	−	0.966421i	$-0.417278\pi$
$967$	−1.31287e7	−	7.57986e6i	−0.451498	−	0.260672i	−0.708463	+	0.705748i	$0.750611\pi$
$968$	−2.56446e7	+	1.10410e7i	−0.879647	+	0.378720i
$969$		0			0
$970$	−1.15803e6	+	5.34010e6i	−0.0395176	+	0.182230i
$971$	9.85699e6			0.335503			0.167751	−	0.985829i	$-0.446349\pi$
$971$	9.85699e6			0.335503			0.167751	+	0.985829i	$0.446349\pi$
$972$		0			0
$973$	−3.14276e7			−1.06421
$974$	2.37189e6	−	1.09377e7i	0.0801120	−	0.369426i
$975$		0			0
$976$	5.93935e6	−	1.73062e7i	0.199579	−	0.581538i
$977$	430133.	+	248338.i	0.0144167	+	0.00832350i	0.507191	−	0.861834i	$-0.330684\pi$
$977$	430133.	+	248338.i	0.0144167	+	0.00832350i	−0.492774	+	0.870157i	$0.664017\pi$
$978$		0			0
$979$	−7.07006e6	+	4.08190e6i	−0.235758	+	0.136115i
$980$	1.18460e7	−	1.14671e6i	0.394008	−	0.0381407i
$981$		0			0
$982$	4.16297e6	−	4.58541e6i	0.137760	−	0.151740i
$983$	−2.20843e7	−	3.82511e7i	−0.728953	−	1.26258i	−0.957326	−	0.289010i	$-0.906674\pi$
$983$	−2.20843e7	−	3.82511e7i	−0.728953	−	1.26258i	0.228373	−	0.973574i	$-0.426659\pi$
$984$		0			0
$985$	−5.16330e6	+	8.94311e6i	−0.169565	+	0.293696i
$986$	1.26491e7	+	3.94813e7i	0.414351	+	1.29330i
$987$		0			0
$988$	−6.17010e6	−	8.64088e6i	−0.201094	−	0.281621i
$989$		−	6.38583e6i		−	0.207600i
$990$		0			0
$991$		−	8.44990e6i		−	0.273317i	−0.990618	−	0.136659i	$-0.956364\pi$
$991$		−	8.44990e6i		−	0.273317i	0.990618	−	0.136659i	$-0.0436364\pi$
$992$	−210766.	+	1.02565e7i	−0.00680020	+	0.330918i
$993$		0			0
$994$	−5.44912e7	+	1.74580e7i	−1.74928	+	0.560440i
$995$	−6.99314e6	+	1.21125e7i	−0.223931	+	0.387860i
$996$		0			0
$997$	8.98031e6	+	1.55544e7i	0.286123	+	0.495580i	0.972881	−	0.231306i	$-0.0742999\pi$
$997$	8.98031e6	+	1.55544e7i	0.286123	+	0.495580i	−0.686758	+	0.726887i	$0.740967\pi$
$998$	−4.38694e7	−	3.98278e7i	−1.39423	−	1.26579i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	108.6.h.a.71.2		56
3.2	odd	2		36.6.h.a.23.27	yes	56
4.3	odd	2	inner	108.6.h.a.71.12		56
9.2	odd	6	inner	108.6.h.a.35.12		56
9.7	even	3		36.6.h.a.11.17	✓	56
12.11	even	2		36.6.h.a.23.17	yes	56
36.7	odd	6		36.6.h.a.11.27	yes	56
36.11	even	6	inner	108.6.h.a.35.2		56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
36.6.h.a.11.17	✓	56	9.7	even	3
36.6.h.a.11.27	yes	56	36.7	odd	6
36.6.h.a.23.17	yes	56	12.11	even	2
36.6.h.a.23.27	yes	56	3.2	odd	2
108.6.h.a.35.2		56	36.11	even	6	inner
108.6.h.a.35.12		56	9.2	odd	6	inner
108.6.h.a.71.2		56	1.1	even	1	trivial
108.6.h.a.71.12		56	4.3	odd	2	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)

\(f(q)\)	\(=\)	\(q+(-5.52836 - 1.19885i) q^{2} +(29.1255 + 13.2554i) q^{4} +(20.1454 + 11.6310i) q^{5} +(156.832 - 90.5473i) q^{7} +(-145.125 - 108.198i) q^{8} +O(q^{10})\)	\(q+(-5.52836 - 1.19885i) q^{2} +(29.1255 + 13.2554i) q^{4} +(20.1454 + 11.6310i) q^{5} +(156.832 - 90.5473i) q^{7} +(-145.125 - 108.198i) q^{8} +(-97.4272 - 88.4515i) q^{10} +(41.2642 + 71.4718i) q^{11} +(-70.1922 + 121.577i) q^{13} +(-975.579 + 312.559i) q^{14} +(672.589 + 772.140i) q^{16} -901.814i q^{17} +2363.52i q^{19} +(432.572 + 605.793i) q^{20} +(-142.439 - 444.591i) q^{22} +(160.190 - 277.458i) q^{23} +(-1291.94 - 2237.71i) q^{25} +(533.800 - 587.968i) q^{26} +(5768.06 - 558.359i) q^{28} +(7037.98 - 4063.38i) q^{29} +(-1533.72 - 885.495i) q^{31} +(-2792.63 - 5075.00i) q^{32} +(-1081.14 + 4985.55i) q^{34} +4212.61 q^{35} +13713.9 q^{37} +(2833.52 - 13066.4i) q^{38} +(-1665.16 - 3867.63i) q^{40} +(4374.37 + 2525.55i) q^{41} +(17261.6 - 9966.01i) q^{43} +(254.456 + 2628.62i) q^{44} +(-1218.22 + 1341.84i) q^{46} +(6620.98 + 11467.9i) q^{47} +(7994.11 - 13846.2i) q^{49} +(4459.63 + 13919.7i) q^{50} +(-3655.93 + 2610.55i) q^{52} -25022.9i q^{53} +1919.77i q^{55} +(-32557.3 - 3828.26i) q^{56} +(-43779.9 + 14026.3i) q^{58} +(-20189.4 + 34969.0i) q^{59} +(-8934.10 - 15474.3i) q^{61} +(7417.39 + 6734.04i) q^{62} +(9354.49 + 31404.4i) q^{64} +(-2828.10 + 1632.81i) q^{65} +(29089.1 + 16794.6i) q^{67} +(11953.9 - 26265.8i) q^{68} +(-23288.8 - 5050.30i) q^{70} +55855.2 q^{71} -69860.7 q^{73} +(-75815.3 - 16441.0i) q^{74} +(-31329.4 + 68838.8i) q^{76} +(12943.1 + 7472.73i) q^{77} +(33076.3 - 19096.6i) q^{79} +(4568.86 + 23377.9i) q^{80} +(-21155.4 - 19206.4i) q^{82} +(-11121.7 - 19263.4i) q^{83} +(10489.0 - 18167.4i) q^{85} +(-107376. + 34401.5i) q^{86} +(1744.62 - 14837.0i) q^{88} +98921.0i q^{89} +25422.9i q^{91} +(8343.43 - 5957.71i) q^{92} +(-22854.8 - 71336.1i) q^{94} +(-27490.1 + 47614.2i) q^{95} +(-20762.4 - 35961.6i) q^{97} +(-60793.9 + 66963.0i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q + 3 q^{2} - q^{4} + 6 q^{5}+O(q^{10}) \) 56 * q + 3 * q^2 - q^4 + 6 * q^5	\( 56 q + 3 q^{2} - q^{4} + 6 q^{5} - 68 q^{10} - 2 q^{13} + 1518 q^{14} - q^{16} + 1242 q^{20} + 63 q^{22} + 12498 q^{25} - 2052 q^{28} + 11946 q^{29} + 7233 q^{32} + 6361 q^{34} - 8 q^{37} + 14877 q^{38} - 1526 q^{40} + 43536 q^{41} - 26880 q^{46} + 38414 q^{49} - 38631 q^{50} + 24988 q^{52} - 21186 q^{56} - 3314 q^{58} - 2 q^{61} - 106342 q^{64} - 35970 q^{65} - 31413 q^{68} + 10524 q^{70} + 53620 q^{73} + 20406 q^{74} + 26193 q^{76} - 26178 q^{77} - 151286 q^{82} + 6248 q^{85} - 279237 q^{86} - 122541 q^{88} - 435804 q^{92} + 63480 q^{94} - 58148 q^{97}+O(q^{100}) \) 56 * q + 3 * q^2 - q^4 + 6 * q^5 - 68 * q^10 - 2 * q^13 + 1518 * q^14 - q^16 + 1242 * q^20 + 63 * q^22 + 12498 * q^25 - 2052 * q^28 + 11946 * q^29 + 7233 * q^32 + 6361 * q^34 - 8 * q^37 + 14877 * q^38 - 1526 * q^40 + 43536 * q^41 - 26880 * q^46 + 38414 * q^49 - 38631 * q^50 + 24988 * q^52 - 21186 * q^56 - 3314 * q^58 - 2 * q^61 - 106342 * q^64 - 35970 * q^65 - 31413 * q^68 + 10524 * q^70 + 53620 * q^73 + 20406 * q^74 + 26193 * q^76 - 26178 * q^77 - 151286 * q^82 + 6248 * q^85 - 279237 * q^86 - 122541 * q^88 - 435804 * q^92 + 63480 * q^94 - 58148 * q^97

Introduction

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