LMFDB - Embedded newform 108.6.h.a.71.12

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			71.12
Character	$\chi$	$=$	108.71
Dual form			108.6.h.a.35.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.72594 + 5.38713i) q^{2} +(-26.0423 - 18.5957i) q^{4} +(20.1454 + 11.6310i) q^{5} +(-156.832 + 90.5473i) q^{7} +(145.125 - 108.198i) q^{8} +O(q^{10})$	\(q+(-1.72594 + 5.38713i) q^{2} +(-26.0423 - 18.5957i) q^{4} +(20.1454 + 11.6310i) q^{5} +(-156.832 + 90.5473i) q^{7} +(145.125 - 108.198i) q^{8} +(-97.4272 + 88.4515i) q^{10} +(-41.2642 - 71.4718i) q^{11} +(-70.1922 + 121.577i) q^{13} +(-217.106 - 1001.16i) q^{14} +(332.398 + 968.549i) q^{16} -901.814i q^{17} -2363.52i q^{19} +(-308.346 - 677.515i) q^{20} +(456.247 - 98.9396i) q^{22} +(-160.190 + 277.458i) q^{23} +(-1291.94 - 2237.71i) q^{25} +(-533.800 - 587.968i) q^{26} +(5768.06 + 558.359i) q^{28} +(7037.98 - 4063.38i) q^{29} +(1533.72 + 885.495i) q^{31} +(-5791.40 + 119.010i) q^{32} +(4858.19 + 1556.48i) q^{34} -4212.61 q^{35} +13713.9 q^{37} +(12732.6 + 4079.30i) q^{38} +(4182.05 - 491.747i) q^{40} +(4374.37 + 2525.55i) q^{41} +(-17261.6 + 9966.01i) q^{43} +(-254.456 + 2628.62i) q^{44} +(-1218.22 - 1341.84i) q^{46} +(-6620.98 - 11467.9i) q^{47} +(7994.11 - 13846.2i) q^{49} +(14284.6 - 3097.70i) q^{50} +(4088.77 - 1860.85i) q^{52} -25022.9i q^{53} -1919.77i q^{55} +(-12963.3 + 30109.6i) q^{56} +(9742.80 + 44927.6i) q^{58} +(20189.4 - 34969.0i) q^{59} +(-8934.10 - 15474.3i) q^{61} +(-7417.39 + 6734.04i) q^{62} +(9354.49 - 31404.4i) q^{64} +(-2828.10 + 1632.81i) q^{65} +(-29089.1 - 16794.6i) q^{67} +(-16769.9 + 23485.3i) q^{68} +(7270.71 - 22693.8i) q^{70} -55855.2 q^{71} -69860.7 q^{73} +(-23669.4 + 73878.5i) q^{74} +(-43951.5 + 61551.5i) q^{76} +(12943.1 + 7472.73i) q^{77} +(-33076.3 + 19096.6i) q^{79} +(-4568.86 + 23377.9i) q^{80} +(-21155.4 + 19206.4i) q^{82} +(11121.7 + 19263.4i) q^{83} +(10489.0 - 18167.4i) q^{85} +(-23895.6 - 110191. i) q^{86} +(-13721.6 - 5907.63i) q^{88} +98921.0i q^{89} -25422.9i q^{91} +(9331.24 - 4246.77i) q^{92} +(73206.3 - 15875.2i) q^{94} +(27490.1 - 47614.2i) q^{95} +(-20762.4 - 35961.6i) q^{97} +(60793.9 + 66963.0i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−1.72594	+	5.38713i	−0.305106	+	0.952318i
$2$	−1.72594	+	5.38713i	−0.305106	+	0.952318i
$3$		0			0
$3$		0			0
$4$	−26.0423	−	18.5957i	−0.813820	−	0.581116i
$5$	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	−0.962702	−	0.270565i	$-0.912790\pi$
$7$	−156.832	+	90.5473i	−1.20974	+	0.698442i	−0.247035	+	0.969007i	$0.579456\pi$
$8$	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	0.810023	−	0.586398i	$-0.199454\pi$
$11$	−41.2642	−	71.4718i	−0.102823	−	0.178095i	−0.912847	+	0.408302i	$0.866121\pi$
$12$		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	$0.203416\pi$
$14$	−217.106	−	1001.16i	−0.296041	−	1.36515i
$15$		0			0
$16$	332.398	+	968.549i	0.324607	+	0.945849i
$17$		−	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	$-0.729567\pi$
$19$		−	2363.52i		−	1.50202i	0.660290	−	0.751011i	$-0.270433\pi$
$20$	−308.346	−	677.515i	−0.172371	−	0.378742i
$21$		0			0
$22$	456.247	−	98.9396i	0.200976	−	0.0435826i
$23$	−160.190	+	277.458i	−0.0631417	+	0.109365i	−0.895868	−	0.444320i	$-0.853445\pi$
$23$	−160.190	+	277.458i	−0.0631417	+	0.109365i	0.832726	+	0.553685i	$0.186779\pi$
$24$		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	0.636427	−	0.771337i	$-0.280412\pi$
$31$	1533.72	+	885.495i	0.286644	+	0.165494i	−0.349784	+	0.936831i	$0.613745\pi$
$32$	−5791.40	+	119.010i	−0.999789	+	0.0205452i
$33$		0			0
$34$	4858.19	+	1556.48i	0.720737	+	0.230912i
$35$	−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	$0.192058\pi$
$38$	12732.6	+	4079.30i	1.43040	+	0.458276i
$39$		0			0
$40$	4182.05	−	491.747i	0.413275	−	0.0485950i
$41$	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	−0.996611	−	0.0822625i	$-0.973785\pi$
$43$	−17261.6	+	9966.01i	−1.42367	+	0.821959i	−0.427064	+	0.904221i	$0.640452\pi$
$44$	−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	0.560275	−	0.828307i	$-0.310696\pi$
$47$	−6620.98	−	11467.9i	−0.437197	−	0.757248i	−0.997472	+	0.0710587i	$0.977362\pi$
$48$		0			0
$49$	7994.11	−	13846.2i	0.475642	−	0.823836i
$50$	14284.6	−	3097.70i	0.808061	−	0.175232i
$51$		0			0
$52$	4088.77	−	1860.85i	0.209693	−	0.0954340i
$53$		−	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
$56$	−12963.3	+	30109.6i	−0.552389	+	1.28302i
$57$		0			0
$58$	9742.80	+	44927.6i	0.380289	+	1.75365i
$59$	20189.4	−	34969.0i	0.755079	−	1.30784i	−0.190256	−	0.981735i	$-0.560932\pi$
$59$	20189.4	−	34969.0i	0.755079	−	1.30784i	0.945335	−	0.326101i	$-0.105735\pi$
$60$		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	0.0488814	−	0.998805i	$-0.484434\pi$
$67$	−29089.1	−	16794.6i	−0.791668	−	0.457070i	−0.840549	+	0.541735i	$0.817768\pi$
$68$	−16769.9	+	23485.3i	−0.439803	+	0.615919i
$69$		0			0
$70$	7270.71	−	22693.8i	0.177350	−	0.553558i
$71$	−55855.2			−1.31498			−0.657488	−	0.753465i	$-0.728381\pi$
$71$	−55855.2			−1.31498			−0.657488	+	0.753465i	$0.728381\pi$
$72$		0			0
$73$	−69860.7			−1.53435			−0.767177	−	0.641435i	$-0.778339\pi$
$73$	−69860.7			−1.53435			−0.767177	+	0.641435i	$0.778339\pi$
$74$	−23669.4	+	73878.5i	−0.502467	+	1.56833i
$75$		0			0
$76$	−43951.5	+	61551.5i	−0.872849	+	1.22238i
$77$	12943.1	+	7472.73i	0.248779	+	0.143632i
$78$		0			0
$79$	−33076.3	+	19096.6i	−0.596278	+	0.344261i	−0.767576	−	0.640958i	$-0.778537\pi$
$79$	−33076.3	+	19096.6i	−0.596278	+	0.344261i	0.171298	+	0.985219i	$0.445204\pi$
$80$	−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	0.940922	−	0.338623i	$-0.109961\pi$
$83$	11121.7	+	19263.4i	0.177205	+	0.306929i	−0.763717	+	0.645551i	$0.776628\pi$
$84$		0			0
$85$	10489.0	−	18167.4i	0.157465	−	0.272738i
$86$	−23895.6	−	110191.i	−0.348395	−	1.60658i
$87$		0			0
$88$	−13721.6	−	5907.63i	−0.188885	−	0.0813218i
$89$			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
$92$	9331.24	−	4246.77i	0.114940	−	0.0523105i
$93$		0			0
$94$	73206.3	−	15875.2i	0.854533	−	0.185310i
$95$	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	0.650747	−	0.759295i	$-0.274456\pi$
$103$	34298.4	+	19802.2i	0.318552	+	0.183916i	−0.332195	+	0.943211i	$0.607789\pi$
$104$	2967.67	+	25238.4i	0.0269049	+	0.228812i
$105$		0			0
$106$	134802.	+	43188.1i	1.16528	+	0.373335i
$107$	−82118.9			−0.693400			−0.346700	−	0.937976i	$-0.612698\pi$
$107$	−82118.9			−0.693400			−0.346700	+	0.937976i	$0.612698\pi$
$108$		0			0
$109$	−48617.2			−0.391944			−0.195972	−	0.980610i	$-0.562786\pi$
$109$	−48617.2			−0.391944			−0.195972	+	0.980610i	$0.562786\pi$
$110$	10342.0	+	3313.41i	0.0814938	+	0.0261092i
$111$		0			0
$112$	−139830.	−	121802.i	−1.05331	−	0.917509i
$113$	−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
$122$	98781.8	−	21421.4i	0.600865	−	0.130301i
$123$		0			0
$124$	−23475.2	−	51580.9i	−0.137105	−	0.301256i
$125$		−	132800.i		−	0.760189i
$126$		0			0
$127$		−	45880.3i		−	0.252416i	−0.992004	−	0.126208i	$-0.959719\pi$
$127$		−	45880.3i		−	0.252416i	0.992004	−	0.126208i	$-0.0402807\pi$
$128$	153034.	+	104596.i	0.825588	+	0.564274i
$129$		0			0
$130$	−3914.99	−	18053.5i	−0.0203176	−	0.0936920i
$131$	11973.3	−	20738.4i	0.0609588	−	0.105584i	−0.833935	−	0.551862i	$-0.813918\pi$
$131$	11973.3	−	20738.4i	0.0609588	−	0.105584i	0.894894	+	0.446278i	$0.147251\pi$
$132$		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	0.792193	−	0.610271i	$-0.208939\pi$
$139$	150292.	+	86771.1i	0.659780	+	0.380924i	−0.132413	+	0.991195i	$0.542273\pi$
$140$	109706.	+	78336.5i	0.473052	+	0.337788i
$141$		0			0
$142$	96402.9	−	300899.i	0.401207	−	1.25228i
$143$	11585.7			0.0473787
$144$		0			0
$145$	189044.			0.746695
$146$	120575.	−	376348.i	0.468141	−	1.46119i
$147$		0			0
$148$	−357141.	−	255020.i	−1.34025	−	0.957017i
$149$	−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	−0.411072	−	0.911603i	$-0.634846\pi$
$151$	48433.2	−	27962.9i	0.172862	−	0.0998021i	0.583935	+	0.811801i	$0.301512\pi$
$152$	−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	$0.236614\pi$
$158$	−45788.1	−	211146.i	−0.145918	−	0.672883i
$159$		0			0
$160$	−118054.	−	64962.0i	−0.364571	−	0.200613i
$161$		−	58019.2i		−	0.176403i
$162$		0			0
$163$		−	93835.4i		−	0.276629i	−0.990388	−	0.138314i	$-0.955832\pi$
$163$		−	93835.4i		−	0.276629i	0.990388	−	0.138314i	$-0.0441685\pi$
$164$	−66954.2	−	147116.i	−0.194387	−	0.427119i
$165$		0			0
$166$	−122970.	+	26666.6i	−0.346360	+	0.0751100i
$167$	67439.6	−	116809.i	0.187121	−	0.324104i	−0.757168	−	0.653220i	$-0.773418\pi$
$167$	67439.6	−	116809.i	0.187121	−	0.324104i	0.944289	+	0.329116i	$0.106751\pi$
$168$		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
$176$	55507.8	−	63723.5i	0.135074	−	0.155067i
$177$		0			0
$178$	−532900.	−	170732.i	−1.26065	−	0.403891i
$179$	525249.			1.22527			0.612636	−	0.790365i	$-0.290109\pi$
$179$	525249.			1.22527			0.612636	+	0.790365i	$0.290109\pi$
$180$		0			0
$181$	−825837.			−1.87369			−0.936846	−	0.349743i	$-0.886269\pi$
$181$	−825837.			−1.87369			−0.936846	+	0.349743i	$0.886269\pi$
$182$	136956.	+	43878.4i	0.306481	+	0.0981910i
$183$		0			0
$184$	6772.70	+	57598.3i	0.0147475	+	0.125419i
$185$	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	0.989856	−	0.142076i	$-0.0453778\pi$
$191$	187497.	+	324754.i	0.371886	+	0.644126i	−0.617970	+	0.786202i	$0.712045\pi$
$192$		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	$0.0141478\pi$
$194$	229564.	−	49782.2i	0.437925	−	0.0949664i
$195$		0			0
$196$	−465665.	+	211930.i	−0.865832	+	0.394051i
$197$			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	$-0.819128\pi$
$199$		−	601252.i		−	1.07628i	0.842857	−	0.538138i	$-0.180872\pi$
$200$	−429608.	−	184962.i	−0.759447	−	0.326970i
$201$		0			0
$202$	139495.	+	643261.i	0.240535	+	1.10920i
$203$	−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	0.742588	−	0.669748i	$-0.233598\pi$
$211$	345252.	+	199331.i	0.533863	+	0.308226i	−0.208725	+	0.977974i	$0.566931\pi$
$212$	−465319.	+	651653.i	−0.711068	+	0.995811i
$213$		0			0
$214$	141732.	−	442385.i	0.211560	−	0.660337i
$215$	−463657.			−0.684070
$216$		0			0
$217$	−320716.			−0.462351
$218$	83910.4	−	261907.i	0.119584	−	0.373255i
$219$		0			0
$220$	−35699.5	+	49995.2i	−0.0497286	+	0.0696420i
$221$	109639.	+	63300.4i	0.151003	+	0.0871817i
$222$		0			0
$223$	−290097.	+	167488.i	−0.390644	+	0.225538i	−0.682439	−	0.730942i	$-0.739081\pi$
$223$	−290097.	+	167488.i	−0.390644	+	0.225538i	0.291795	+	0.956481i	$0.405747\pi$
$224$	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	$-0.982227\pi$
$227$	−425099.	−	736293.i	−0.547552	−	0.948388i	0.450890	−	0.892580i	$-0.351107\pi$
$228$		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	$0.249489\pi$
$230$	−8934.66	−	41201.0i	−0.0111367	−	0.0513557i
$231$		0			0
$232$	581738.	−	1.35119e6i	0.709590	−	1.64815i
$233$			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
$236$	−1.17605e6	+	535236.i	−1.37450	+	0.625554i
$237$		0			0
$238$	−902856.	+	195789.i	−1.03318	+	0.224051i
$239$	660239.	−	1.14357e6i	0.747664	−	1.29499i	−0.201275	−	0.979535i	$-0.564509\pi$
$239$	660239.	−	1.14357e6i	0.747664	−	1.29499i	0.948940	−	0.315458i	$-0.102158\pi$
$240$		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
$248$	318390.	−	37437.9i	0.328723	−	0.0386529i
$249$		0			0
$250$	715408.	+	229204.i	0.723942	+	0.231938i
$251$	1.41641e6			1.41907			0.709534	−	0.704671i	$-0.248905\pi$
$251$	1.41641e6			1.41907			0.709534	+	0.704671i	$0.248905\pi$
$252$		0			0
$253$	26440.5			0.0259698
$254$	247163.	+	79186.7i	0.240380	+	0.0770137i
$255$		0			0
$256$	−827599.	+	643888.i	−0.789260	+	0.614059i
$257$	−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	$-0.896558\pi$
$263$	−841677.	−	1.45783e6i	−0.750337	−	1.29962i	0.197323	−	0.980339i	$-0.436775\pi$
$264$		0			0
$265$	291040.	−	504097.i	0.254588	−	0.440960i
$266$	−2.36626e6	+	513135.i	−2.05049	+	0.444660i
$267$		0			0
$268$	445238.	+	978302.i	0.378665	+	0.832024i
$269$		−	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	$-0.920622\pi$
$271$		−	596748.i		−	0.493592i	0.969067	−	0.246796i	$-0.0793778\pi$
$272$	873451.	−	299761.i	0.715841	−	0.245671i
$273$		0			0
$274$	−247900.	−	1.14316e6i	−0.199480	−	0.919876i
$275$	−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	0.100345	−	0.994953i	$-0.468005\pi$
$283$	−958119.	−	553170.i	−0.711137	−	0.410575i	−0.811482	+	0.584377i	$0.801339\pi$
$284$	1.45460e6	+	1.03867e6i	1.07015	+	0.764154i
$285$		0			0
$286$	−19996.3	+	62413.7i	−0.0144555	+	0.0451196i
$287$	−914725.			−0.655520
$288$		0			0
$289$	606588.			0.427218
$290$	−326279.	+	1.01840e6i	−0.227821	+	0.711091i
$291$		0			0
$292$	1.81933e6	+	1.29911e6i	1.24869	+	0.891639i
$293$	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
$302$	67046.9	+	309178.i	0.0423020	+	0.195070i
$303$		0			0
$304$	2.28919e6	−	785631.i	1.42069	−	0.487567i
$305$		−	415648.i		−	0.255845i
$306$		0			0
$307$			1.32248e6i			0.800836i	0.916333	+	0.400418i	$0.131135\pi$
$307$			1.32248e6i			0.800836i	−0.916333	+	0.400418i	$0.868865\pi$
$308$	−198108.	−	435294.i	−0.118994	−	0.261460i
$309$		0			0
$310$	−227750.	+	49388.7i	−0.134603	+	0.0291893i
$311$	−139474.	+	241576.i	−0.0817698	+	0.141629i	−0.904010	−	0.427511i	$-0.859391\pi$
$311$	−139474.	+	241576.i	−0.0817698	+	0.141629i	0.822240	+	0.569140i	$0.192724\pi$
$312$		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
$320$	553713.	−	523853.i	0.302280	−	0.285979i
$321$		0			0
$322$	312557.	+	100138.i	0.167992	+	0.0538217i
$323$	−2.13146e6			−1.13677
$324$		0			0
$325$	362737.			0.190495
$326$	505503.	+	161954.i	0.263439	+	0.0844012i
$327$		0			0
$328$	908089.	−	106778.i	0.466062	−	0.0548020i
$329$	2.07677e6	+	1.19902e6i	1.05779	+	0.610714i
$330$		0			0
$331$	552755.	−	319133.i	0.277308	−	0.160104i	−0.354896	−	0.934906i	$-0.615484\pi$
$331$	552755.	−	319133.i	0.277308	−	0.160104i	0.632204	+	0.774802i	$0.282150\pi$
$332$	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	$0.242414\pi$
$338$	−1.94369e6	+	421499.i	−0.925412	+	0.200680i
$339$		0			0
$340$	−610993.	+	278071.i	−0.286641	+	0.130454i
$341$		−	146157.i		−	0.0680666i
$342$		0			0
$343$		−	148276.i		−	0.0680511i
$344$	−1.42679e6	+	3.31399e6i	−0.650077	+	1.50992i
$345$		0			0
$346$	−248912.	−	1.14783e6i	−0.111778	−	0.515449i
$347$	−675607.	+	1.17018e6i	−0.301211	+	0.521712i	−0.976410	−	0.215923i	$-0.930724\pi$
$347$	−675607.	+	1.17018e6i	−0.301211	+	0.521712i	0.675200	+	0.737635i	$0.264057\pi$
$348$		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
$356$	1.83951e6	−	2.57612e6i	0.769266	−	1.07731i
$357$		0			0
$358$	−906549.	+	2.82958e6i	−0.373838	+	1.16685i
$359$	3.02244e6			1.23772			0.618860	−	0.785502i	$-0.287595\pi$
$359$	3.02244e6			1.23772			0.618860	+	0.785502i	$0.287595\pi$
$360$		0			0
$361$	−3.11015e6			−1.25607
$362$	1.42535e6	−	4.44889e6i	0.571675	−	1.78435i
$363$		0			0
$364$	−472756.	+	662068.i	−0.187018	+	0.261908i
$365$	−1.40737e6	−	812547.i	−0.552939	−	0.319239i
$366$		0			0
$367$	2.33704e6	−	1.34929e6i	0.905735	−	0.522927i	0.0266788	−	0.999644i	$-0.491507\pi$
$367$	2.33704e6	−	1.34929e6i	0.905735	−	0.522927i	0.879057	+	0.476718i	$0.158174\pi$
$368$	−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	$0.278279\pi$
$374$	−89225.1	−	411450.i	−0.0329844	−	0.152103i
$375$		0			0
$376$	−2.20167e6	−	947899.i	−0.803123	−	0.345774i
$377$			1.14087e6i			0.413412i
$378$		0			0
$379$			1.35806e6i			0.485649i	0.970070	+	0.242824i	$0.0780739\pi$
$379$			1.35806e6i			0.485649i	−0.970070	+	0.242824i	$0.921926\pi$
$380$	−1.60132e6	+	728783.i	−0.568879	+	0.258904i
$381$		0			0
$382$	−2.07310e6	+	449562.i	−0.726877	+	0.157627i
$383$	1.84507e6	−	3.19575e6i	0.642710	−	1.11321i	−0.342115	−	0.939658i	$-0.611143\pi$
$383$	1.84507e6	−	3.19575e6i	0.642710	−	1.11321i	0.984825	−	0.173548i	$-0.0555233\pi$
$384$		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
$392$	−337984.	−	2.87438e6i	−0.111092	−	0.944775i
$393$		0			0
$394$	−2.39149e6	−	766193.i	−0.776120	−	0.248655i
$395$	−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	$0.506055\pi$
$398$	3.23902e6	+	1.03773e6i	1.02496	+	0.328379i
$399$		0			0
$400$	1.73789e6	−	1.99512e6i	0.543091	−	0.623475i
$401$	−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	$0.793626\pi$
$410$	−649572.	+	140863.i	−0.190839	+	0.0413845i
$411$		0			0
$412$	−524971.	−	1.15350e6i	−0.152367	−	0.334790i
$413$			7.31236e6i			2.10952i
$414$		0			0
$415$			517425.i			0.147478i
$416$	392042.	−	712451.i	0.111071	−	0.201847i
$417$		0			0
$418$	−233846.	−	1.07835e6i	−0.0654621	−	0.301870i
$419$	−347632.	+	602117.i	−0.0967353	+	0.167551i	−0.910332	−	0.413880i	$-0.864173\pi$
$419$	−347632.	+	602117.i	−0.0967353	+	0.167551i	0.813596	+	0.581430i	$0.197507\pi$
$420$		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
$428$	2.13856e6	+	1.52706e6i	0.564303	+	0.402946i
$429$		0			0
$430$	800245.	−	2.49778e6i	0.208714	−	0.651453i
$431$	−2.98148e6			−0.773104			−0.386552	−	0.922268i	$-0.626334\pi$
$431$	−2.98148e6			−0.773104			−0.386552	+	0.922268i	$0.626334\pi$
$432$		0			0
$433$	5.90562e6			1.51372			0.756861	−	0.653576i	$-0.226732\pi$
$433$	5.90562e6			1.51372			0.756861	+	0.653576i	$0.226732\pi$
$434$	553538.	−	1.72774e6i	0.141066	−	0.440305i
$435$		0			0
$436$	1.26610e6	+	904072.i	0.318972	+	0.227765i
$437$	655778.	+	378614.i	0.164268	+	0.0948403i
$438$		0			0
$439$	2.85286e6	−	1.64710e6i	0.706512	−	0.407905i	−0.103256	−	0.994655i	$-0.532926\pi$
$439$	2.85286e6	−	1.64710e6i	0.706512	−	0.407905i	0.809768	+	0.586750i	$0.199593\pi$
$440$	−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	$0.0977956\pi$
$443$	3.05039e6	+	5.28344e6i	0.738493	+	1.27911i	−0.214681	+	0.976684i	$0.568871\pi$
$444$		0			0
$445$	−1.15055e6	+	1.99280e6i	−0.275425	+	0.477051i
$446$	−401586.	−	1.85186e6i	−0.0955965	−	0.440831i
$447$		0			0
$448$	1.37649e6	+	5.77225e6i	0.324026	+	1.35878i
$449$		−	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
$452$	223770.	+	491679.i	0.0515175	+	0.113197i
$453$		0			0
$454$	4.70020e6	−	1.01926e6i	1.07023	−	0.232085i
$455$	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	0.957110	−	0.289726i	$-0.0935643\pi$
$463$	5.46488e6	+	3.15515e6i	1.18475	+	0.684018i	0.227644	+	0.973744i	$0.426898\pi$
$464$	6.27499e6	+	5.46597e6i	1.35306	+	1.17862i
$465$		0			0
$466$	−3.65016e6	−	1.16945e6i	−0.778658	−	0.249469i
$467$	763795.			0.162063			0.0810316	−	0.996712i	$-0.474179\pi$
$467$	763795.			0.162063			0.0810316	+	0.996712i	$0.474179\pi$
$468$		0			0
$469$	6.08282e6			1.27695
$470$	1.65941e6	+	531648.i	0.346506	+	0.111014i
$471$		0			0
$472$	−853588.	−	7.25932e6i	−0.176357	−	1.49983i
$473$	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	0.992839	−	0.119463i	$-0.0381172\pi$
$479$	1.97328e6	+	3.41782e6i	0.392962	+	0.680629i	−0.599877	+	0.800092i	$0.704784\pi$
$480$		0			0
$481$	−962608.	+	1.66729e6i	−0.189709	+	0.328585i
$482$	4.62916e6	−	1.00386e6i	0.907580	−	0.196813i
$483$		0			0
$484$	−4.49232e6	+	2.04451e6i	−0.871680	+	0.396713i
$485$		−	965947.i		−	0.186466i
$486$		0			0
$487$		−	1.97847e6i		−	0.378012i	−0.981976	−	0.189006i	$-0.939473\pi$
$487$		−	1.97847e6i		−	0.378012i	0.981976	−	0.189006i	$-0.0605266\pi$
$488$	−2.97085e6	−	1.27906e6i	−0.564717	−	0.243131i
$489$		0			0
$490$	445874.	+	2.05609e6i	0.0838923	+	0.386858i
$491$	547411.	−	948143.i	0.102473	−	0.177488i	−0.810230	−	0.586112i	$-0.800658\pi$
$491$	547411.	−	948143.i	0.102473	−	0.177488i	0.912703	+	0.408624i	$0.133991\pi$
$492$		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	$-0.942699\pi$
$499$	−9.07104e6	−	5.23717e6i	−1.63082	−	0.941554i	−0.646978	−	0.762508i	$-0.723968\pi$
$500$	−2.46950e6	+	3.45840e6i	−0.441758	+	0.618657i
$501$		0			0
$502$	−2.44463e6	+	7.63035e6i	−0.432967	+	1.35140i
$503$	−639826.			−0.112757			−0.0563783	−	0.998409i	$-0.517955\pi$
$503$	−639826.			−0.112757			−0.0563783	+	0.998409i	$0.517955\pi$
$504$		0			0
$505$	2.70668e6			0.472289
$506$	−45634.8	+	142438.i	−0.00792355	+	0.0247315i
$507$		0			0
$508$	−853177.	+	1.19483e6i	−0.146683	+	0.205421i
$509$	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
$518$	−2.97737e6	−	1.37297e7i	−0.487537	−	2.24821i
$519$		0			0
$520$	−233762.	+	542955.i	−0.0379111	+	0.0880553i
$521$		−	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	$0.250629\pi$
$523$			8.86393e6i			1.41701i	−0.705708	+	0.708503i	$0.749371\pi$
$524$	−697458.	+	317422.i	−0.110966	+	0.0505020i
$525$		0			0
$526$	9.30619e6	−	2.01810e6i	1.46659	−	0.318037i
$527$	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
$536$	−6.03869e6	+	710060.i	−0.907885	+	0.106754i
$537$		0			0
$538$	1.14119e7	+	3.65618e6i	1.69982	+	0.544593i
$539$	−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	$0.646259\pi$
$542$	3.21476e6	+	1.02995e6i	0.470057	+	0.150598i
$543$		0			0
$544$	107325.	+	5.22276e6i	0.0155491	+	0.756664i
$545$	−979414.	−	565465.i	−0.141246	−	0.0815482i
$546$		0			0
$547$	544056.	−	314111.i	0.0777455	−	0.0448864i	−0.460623	−	0.887596i	$-0.652374\pi$
$547$	544056.	−	314111.i	0.0777455	−	0.0448864i	0.538369	+	0.842709i	$0.319041\pi$
$548$	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
$554$	−5.88479e6	+	1.27615e6i	−0.814623	+	0.176655i
$555$		0			0
$556$	−2.30037e6	−	5.05451e6i	−0.315581	−	0.693413i
$557$		−	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
$560$	−1.40026e6	−	4.08012e6i	−0.188686	−	0.549797i
$561$		0			0
$562$	1.23233e6	+	5.68272e6i	0.164583	+	0.758955i
$563$	−4.06546e6	+	7.04158e6i	−0.540553	+	0.936266i	0.458319	+	0.888788i	$0.348452\pi$
$563$	−4.06546e6	+	7.04158e6i	−0.540553	+	0.936266i	−0.998872	+	0.0474781i	$0.984882\pi$
$564$		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	−0.352213	−	0.935920i	$-0.614571\pi$
$571$	−1.04309e7	−	6.02229e6i	−1.33885	−	0.772985i	−0.986637	+	0.162935i	$0.947904\pi$
$572$	−301718.	−	215445.i	−0.0385577	−	0.0275325i
$573$		0			0
$574$	1.57876e6	−	4.92774e6i	0.200003	−	0.624264i
$575$	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	$0.518048\pi$
$578$	−1.04694e6	+	3.26777e6i	−0.130347	+	0.406847i
$579$		0			0
$580$	−4.92313e6	−	3.51541e6i	−0.607675	−	0.433916i
$581$	−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	$0.0278164\pi$
$587$	4.78919e6	+	8.29511e6i	0.573676	+	0.993636i	−0.422508	+	0.906359i	$0.638850\pi$
$588$		0			0
$589$	2.09289e6	−	3.62499e6i	0.248575	−	0.430545i
$590$	1.12607e6	+	5.19271e6i	0.133179	+	0.614136i
$591$		0			0
$592$	4.55847e6	+	1.32826e7i	0.534582	+	1.55768i
$593$			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
$596$	2.99990e6	+	6.59154e6i	0.345932	+	0.760101i
$597$		0			0
$598$	248646.	−	53920.2i	0.0284334	−	0.00616593i
$599$	2.38231e6	−	4.12628e6i	0.271288	−	0.469885i	−0.697904	−	0.716192i	$-0.745884\pi$
$599$	2.38231e6	−	4.12628e6i	0.271288	−	0.469885i	0.969192	+	0.246306i	$0.0792169\pi$
$600$		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	0.0658283	−	0.997831i	$-0.479031\pi$
$607$	−6.94805e6	−	4.01146e6i	−0.765404	−	0.441906i	−0.831233	+	0.555924i	$0.812364\pi$
$608$	281284.	+	1.36881e7i	0.0308593	+	1.50170i
$609$		0			0
$610$	2.23915e6	+	717385.i	0.243646	+	0.0780598i
$611$	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	$0.414708\pi$
$614$	−7.12437e6	−	2.28252e6i	−0.762651	−	0.244340i
$615$		0			0
$616$	2.68691e6	−	315940.i	0.285299	−	0.0335470i
$617$	−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	−0.837360	−	0.546652i	$-0.815902\pi$
$619$	−7.46071e6	+	4.30745e6i	−0.782625	+	0.451849i	0.0547347	+	0.998501i	$0.482569\pi$
$620$	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
$626$	−762049.	+	165254.i	−0.0777225	+	0.0168545i
$627$		0			0
$628$	3.92167e6	−	1.78480e6i	0.396800	−	0.180589i
$629$		−	1.23674e7i		−	1.24638i
$630$		0			0
$631$			1.15818e7i			1.15798i	0.815334	+	0.578991i	$0.196554\pi$
$631$			1.15818e7i			1.15798i	−0.815334	+	0.578991i	$0.803446\pi$
$632$	−2.73398e6	+	6.35017e6i	−0.272272	+	0.632401i
$633$		0			0
$634$	1.56480e6	+	7.21587e6i	0.154609	+	0.712960i
$635$	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	0.843177	−	0.537637i	$-0.180683\pi$
$643$	8.37838e6	+	4.83726e6i	0.799158	+	0.461394i	−0.0440186	+	0.999031i	$0.514016\pi$
$644$	−1.07891e6	+	1.51095e6i	−0.102511	+	0.143561i
$645$		0			0
$646$	3.67878e6	−	1.14824e7i	0.346834	−	1.08256i
$647$	1.26182e7			1.18505			0.592525	−	0.805552i	$-0.298131\pi$
$647$	1.26182e7			1.18505			0.592525	+	0.805552i	$0.298131\pi$
$648$		0			0
$649$	−3.33239e6			−0.310559
$650$	−626063.	+	1.95411e6i	−0.0581212	+	0.181412i
$651$		0			0
$652$	−1.74494e6	+	2.44368e6i	−0.160754	+	0.225126i
$653$	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	0.521419	−	0.853301i	$-0.325403\pi$
$659$	−5.33197e6	−	9.23524e6i	−0.478271	−	0.828390i	−0.999690	+	0.0249112i	$0.992070\pi$
$660$		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	$0.128206\pi$
$662$	765188.	+	3.52857e6i	0.0678615	+	0.312934i
$663$		0			0
$664$	3.69829e6	+	1.59225e6i	0.325523	+	0.140149i
$665$			9.95660e6i			0.873086i
$666$		0			0
$667$			2.60366e6i			0.226605i
$668$	−3.92842e6	+	1.78788e6i	−0.340625	+	0.155023i
$669$		0			0
$670$	4.31958e6	−	936723.i	0.371753	−	0.0806166i
$671$	−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
$680$	−443464.	−	3.77143e6i	−0.0367778	−	0.312776i
$681$		0			0
$682$	787366.	+	252259.i	0.0648210	+	0.0207675i
$683$	−8.13981e6			−0.667671			−0.333835	−	0.942631i	$-0.608343\pi$
$683$	−8.13981e6			−0.667671			−0.333835	+	0.942631i	$0.608343\pi$
$684$		0			0
$685$	−4.81011e6			−0.391678
$686$	798780.	+	255915.i	0.0648063	+	0.0207628i
$687$		0			0
$688$	−1.53903e7	−	1.34061e7i	−1.23958	−	1.07977i
$689$	3.04220e6	+	1.75641e6i	0.244140	+	0.140954i
$690$		0			0
$691$	−1.22215e7	+	7.05606e6i	−0.973706	+	0.562169i	−0.900364	−	0.435138i	$-0.856700\pi$
$691$	−1.22215e7	+	7.05606e6i	−0.973706	+	0.562169i	−0.0733417	+	0.997307i	$0.523366\pi$
$692$	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
$698$	4.16779e6	−	903808.i	0.323793	−	0.0702163i
$699$		0			0
$700$	−6.20256e6	−	1.36286e7i	−0.478438	−	1.05125i
$701$			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
$704$	−2.63053e6	+	627297.i	−0.200038	+	0.0477025i
$705$		0			0
$706$	−539802.	−	2.48923e6i	−0.0407590	−	0.187955i
$707$	−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
$716$	−1.36787e7	−	9.76739e6i	−0.997152	−	0.712026i
$717$		0			0
$718$	−5.21656e6	+	1.62823e7i	−0.377636	+	1.17870i
$719$	4.45507e6			0.321390			0.160695	−	0.987004i	$-0.448626\pi$
$719$	4.45507e6			0.321390			0.160695	+	0.987004i	$0.448626\pi$
$720$		0			0
$721$	−7.17213e6			−0.513819
$722$	5.36794e6	−	1.67548e7i	0.383234	−	1.19618i
$723$		0			0
$724$	2.15067e7	+	1.53570e7i	1.52485	+	1.08883i
$725$	−1.81853e7	−	1.04993e7i	−1.28492	−	0.741849i
$726$		0			0
$727$	1.03556e7	−	5.97878e6i	0.726670	−	0.419543i	−0.0905324	−	0.995894i	$-0.528857\pi$
$727$	1.03556e7	−	5.97878e6i	0.726670	−	0.419543i	0.817203	+	0.576350i	$0.195524\pi$
$728$	−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	$0.308023\pi$
$734$	3.23521e6	+	1.49187e7i	0.221647	+	1.02210i
$735$		0			0
$736$	894705.	−	1.62593e6i	0.0608815	−	0.110639i
$737$			2.77206e6i			0.187990i
$738$		0			0
$739$		−	3.34559e6i		−	0.225352i	−0.993632	−	0.112676i	$-0.964058\pi$
$739$		−	3.34559e6i		−	0.225352i	0.993632	−	0.112676i	$-0.0359422\pi$
$740$	−4.22862e6	−	9.29137e6i	−0.283870	−	0.623735i
$741$		0			0
$742$	−2.50518e7	+	5.43262e6i	−1.67044	+	0.362243i
$743$	1.84277e6	−	3.19177e6i	0.122461	−	0.212109i	−0.798276	−	0.602291i	$-0.794255\pi$
$743$	1.84277e6	−	3.19177e6i	0.122461	−	0.212109i	0.920738	+	0.390182i	$0.127588\pi$
$744$		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	0.814770	−	0.579784i	$-0.196863\pi$
$751$	1.11291e7	+	6.42540e6i	0.720048	+	0.415720i	−0.0947225	+	0.995504i	$0.530196\pi$
$752$	8.90640e6	−	1.02246e7i	0.574325	−	0.659331i
$753$		0			0
$754$	−6.14601e6	−	1.96908e6i	−0.393700	−	0.126135i
$755$	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	$0.471563\pi$
$758$	−7.31606e6	−	2.34394e6i	−0.462492	−	0.148174i
$759$		0			0
$760$	−1.16226e6	−	9.88437e6i	−0.0729907	−	0.620747i
$761$	−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	$0.154978\pi$
$770$	−1.92199e6	+	416794.i	−0.116822	+	0.0253334i
$771$		0			0
$772$	−1.38971e7	+	6.32473e6i	−0.839227	+	0.381943i
$773$		−	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
$776$	−6.90410e6	−	2.97247e6i	−0.411579	−	0.177200i
$777$		0			0
$778$	−3.97305e6	−	1.83212e7i	−0.235329	−	1.08519i
$779$	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	0.659292	−	0.751887i	$-0.270856\pi$
$787$	5.86919e6	+	3.38858e6i	0.337786	+	0.195021i	−0.321507	+	0.946907i	$0.604189\pi$
$788$	8.25516e6	−	1.15609e7i	0.473598	−	0.663247i
$789$		0			0
$790$	1.53341e6	−	4.78618e6i	0.0874158	−	0.272848i
$791$	3.05713e6			0.173729
$792$		0			0
$793$	2.50842e6			0.141650
$794$	206193.	−	643584.i	0.0116071	−	0.0362288i
$795$		0			0
$796$	−1.11807e7	+	1.56580e7i	−0.625442	+	0.875896i
$797$	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
$806$	−298058.	−	1.37446e6i	−0.0161608	−	0.0745236i
$807$		0			0
$808$	8.32915e6	−	1.93460e7i	0.448820	−	1.04247i
$809$			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	$-0.997147\pi$
$811$		−	335741.i		−	0.0179247i	0.999960	−	0.00896235i	$-0.00285284\pi$
$812$	4.28643e7	−	1.95081e7i	2.28142	−	1.03831i
$813$		0			0
$814$	6.25692e6	−	1.35685e6i	0.330978	−	0.0717744i
$815$	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	0.589560	−	0.807724i	$-0.299301\pi$
$823$	3.59148e6	+	2.07354e6i	0.184831	+	0.106712i	−0.404730	+	0.914436i	$0.632634\pi$
$824$	7.12010e6	−	837218.i	0.365315	−	0.0429557i
$825$		0			0
$826$	−3.93926e7	−	1.26207e7i	−2.00893	−	0.643626i
$827$	2.18621e6			0.111155			0.0555773	−	0.998454i	$-0.482300\pi$
$827$	2.18621e6			0.111155			0.0555773	+	0.998454i	$0.482300\pi$
$828$		0			0
$829$	9.24847e6			0.467395			0.233697	−	0.972309i	$-0.424918\pi$
$829$	9.24847e6			0.467395			0.233697	+	0.972309i	$0.424918\pi$
$830$	−2.78743e6	−	893045.i	−0.140446	−	0.0449964i
$831$		0			0
$832$	3.16142e6	+	3.34163e6i	0.158334	+	0.167359i
$833$	−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	0.940007	−	0.341156i	$-0.110819\pi$
$839$	3.55904e6	+	6.16444e6i	0.174553	+	0.302335i	−0.765453	+	0.643491i	$0.777485\pi$
$840$		0			0
$841$	2.27665e7	−	3.94328e7i	1.10996	−	1.92251i
$842$	6.47664e6	−	1.40449e6i	0.314825	−	0.0682716i
$843$		0			0
$844$	−5.28443e6	−	1.16112e7i	−0.255353	−	0.561077i
$845$			8.17855e6i			0.394035i
$846$		0			0
$847$			2.79320e7i			1.33781i
$848$	2.42359e7	−	8.31756e6i	1.15736	−	0.397198i
$849$		0			0
$850$	−2.79355e6	−	1.28821e7i	−0.132620	−	0.611560i
$851$	−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	0.993269	−	0.115834i	$-0.0369540\pi$
$859$	3.00517e7	+	1.73504e7i	1.38959	+	0.802279i	0.396319	+	0.918113i	$0.370287\pi$
$860$	1.20747e7	+	8.62204e6i	0.556710	+	0.397524i
$861$		0			0
$862$	5.14585e6	−	1.60616e7i	0.235879	−	0.736242i
$863$	−2.83896e7			−1.29757			−0.648787	−	0.760970i	$-0.724724\pi$
$863$	−2.83896e7			−1.29757			−0.648787	+	0.760970i	$0.724724\pi$
$864$		0			0
$865$	−4.82975e6			−0.219475
$866$	−1.01928e7	+	3.18143e7i	−0.461846	+	1.44154i
$867$		0			0
$868$	8.35218e6	+	5.96396e6i	0.376271	+	0.268680i
$869$	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	$0.915216\pi$
$878$	3.94927e6	+	1.82115e7i	0.172894	+	0.797279i
$879$		0			0
$880$	1.85939e6	−	638128.i	0.0809402	−	0.0277780i
$881$			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	$-0.818649\pi$
$883$		−	2.49947e7i		−	1.07881i	0.842046	−	0.539406i	$-0.181351\pi$
$884$	−1.67814e6	−	3.68731e6i	−0.0722267	−	0.158701i
$885$		0			0
$886$	−3.37273e7	+	7.31395e6i	−1.44344	+	0.313017i
$887$	2.27170e6	−	3.93469e6i	0.0969485	−	0.167920i	−0.813472	−	0.581605i	$-0.802425\pi$
$887$	2.27170e6	−	3.93469e6i	0.0969485	−	0.167920i	0.910420	+	0.413685i	$0.135758\pi$
$888$		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
$896$	−3.34716e7	−	2.54722e6i	−1.39286	−	0.105998i
$897$		0			0
$898$	2.89983e7	+	9.29054e6i	1.20000	+	0.384459i
$899$	1.43924e7			0.593928
$900$		0			0
$901$	−2.25660e7			−0.926068
$902$	2.24567e6	+	719474.i	0.0919031	+	0.0294441i
$903$		0			0
$904$	−3.03495e6	+	356865.i	−0.123518	+	0.0145239i
$905$	−1.66368e7	−	9.60528e6i	−0.675226	−	0.389842i
$906$		0			0
$907$	−2.72617e7	+	1.57395e7i	−1.10036	+	0.635292i	−0.936315	−	0.351161i	$-0.885787\pi$
$907$	−2.72617e7	+	1.57395e7i	−1.10036	+	0.635292i	−0.164043	+	0.986453i	$0.552454\pi$
$908$	−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	0.913821	−	0.406116i	$-0.133117\pi$
$911$	2.63528e6	+	4.56443e6i	0.105204	+	0.182218i	−0.808618	+	0.588334i	$0.799784\pi$
$912$		0			0
$913$	917858.	−	1.58978e6i	0.0364417	−	0.0631189i
$914$	2.56463e6	−	556153.i	0.101545	−	0.0220206i
$915$		0			0
$916$	1.18926e7	−	5.41248e6i	0.468316	−	0.213137i
$917$			4.33661e6i			0.170305i
$918$		0			0
$919$		−	3.29683e7i		−	1.28768i	−0.765161	−	0.643839i	$-0.777341\pi$
$919$		−	3.29683e7i		−	1.28768i	0.765161	−	0.643839i	$-0.222659\pi$
$920$	−533484.	+	1.23911e6i	−0.0207803	+	0.0482660i
$921$		0			0
$922$	−4.99832e6	−	2.30491e7i	−0.193641	−	0.892950i
$923$	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
$932$	1.25999e7	−	1.76455e7i	0.475147	−	0.665416i
$933$		0			0
$934$	−1.31826e6	+	4.11466e6i	−0.0494465	+	0.154336i
$935$	−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	$0.765007\pi$
$938$	−1.04986e7	+	3.27689e7i	−0.389604	+	1.21606i
$939$		0			0
$940$	−5.72810e6	+	8.02188e6i	−0.211442	+	0.296112i
$941$	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	$-0.877697\pi$
$947$	−2.17517e7	−	3.76751e7i	−0.788168	−	1.36515i	0.138921	−	0.990304i	$-0.455637\pi$
$948$		0			0
$949$	4.90368e6	−	8.49342e6i	0.176749	−	0.306138i
$950$	−7.32149e6	−	3.37621e7i	−0.263203	−	1.21372i
$951$		0			0
$952$	2.71533e7	+	1.16905e7i	0.971023	+	0.418061i
$953$		−	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
$956$	−3.84596e7	+	1.75035e7i	−1.36101	+	0.619411i
$957$		0			0
$958$	−2.18180e7	+	4.73135e6i	−0.768071	+	0.166560i
$959$	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	0.708463	−	0.705748i	$-0.249389\pi$
$967$	1.31287e7	+	7.57986e6i	0.451498	+	0.260672i	−0.256965	+	0.966421i	$0.582722\pi$
$968$	−3.26057e6	−	2.77294e7i	−0.111842	−	0.951156i
$969$		0			0
$970$	5.20368e6	+	1.66717e6i	0.177575	+	0.0568919i
$971$	−9.85699e6			−0.335503			−0.167751	−	0.985829i	$-0.553651\pi$
$971$	−9.85699e6			−0.335503			−0.167751	+	0.985829i	$0.553651\pi$
$972$		0			0
$973$	−3.14276e7			−1.06421
$974$	1.06582e7	+	3.41471e6i	0.359988	+	0.115334i
$975$		0			0
$976$	1.20180e7	−	1.37967e7i	0.403837	−	0.463609i
$977$	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	$0.0933260\pi$
$983$	2.20843e7	+	3.82511e7i	0.728953	+	1.26258i	−0.228373	+	0.973574i	$0.573341\pi$
$984$		0			0
$985$	−5.16330e6	+	8.94311e6i	−0.169565	+	0.293696i
$986$	4.05164e7	−	8.78619e6i	1.32721	−	0.287812i
$987$		0			0
$988$	−4.39817e6	−	9.66390e6i	−0.143344	−	0.314963i
$989$		−	6.38583e6i		−	0.207600i
$990$		0			0
$991$			8.44990e6i			0.273317i	0.990618	+	0.136659i	$0.0436364\pi$
$991$			8.44990e6i			0.273317i	−0.990618	+	0.136659i	$0.956364\pi$
$992$	−8.98777e6	−	4.94572e6i	−0.289983	−	0.159570i
$993$		0			0
$994$	1.21265e7	+	5.59198e7i	0.389287	+	1.79514i
$995$	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.71.12		56
3.2	odd	2		36.6.h.a.23.17	yes	56
4.3	odd	2	inner	108.6.h.a.71.2		56
9.2	odd	6	inner	108.6.h.a.35.2		56
9.7	even	3		36.6.h.a.11.27	yes	56
12.11	even	2		36.6.h.a.23.27	yes	56
36.7	odd	6		36.6.h.a.11.17	✓	56
36.11	even	6	inner	108.6.h.a.35.12		56

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

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)

\(f(q)\)	\(=\)	\(q+(-1.72594 + 5.38713i) q^{2} +(-26.0423 - 18.5957i) q^{4} +(20.1454 + 11.6310i) q^{5} +(-156.832 + 90.5473i) q^{7} +(145.125 - 108.198i) q^{8} +O(q^{10})\)	\(q+(-1.72594 + 5.38713i) q^{2} +(-26.0423 - 18.5957i) q^{4} +(20.1454 + 11.6310i) q^{5} +(-156.832 + 90.5473i) q^{7} +(145.125 - 108.198i) q^{8} +(-97.4272 + 88.4515i) q^{10} +(-41.2642 - 71.4718i) q^{11} +(-70.1922 + 121.577i) q^{13} +(-217.106 - 1001.16i) q^{14} +(332.398 + 968.549i) q^{16} -901.814i q^{17} -2363.52i q^{19} +(-308.346 - 677.515i) q^{20} +(456.247 - 98.9396i) q^{22} +(-160.190 + 277.458i) q^{23} +(-1291.94 - 2237.71i) q^{25} +(-533.800 - 587.968i) q^{26} +(5768.06 + 558.359i) q^{28} +(7037.98 - 4063.38i) q^{29} +(1533.72 + 885.495i) q^{31} +(-5791.40 + 119.010i) q^{32} +(4858.19 + 1556.48i) q^{34} -4212.61 q^{35} +13713.9 q^{37} +(12732.6 + 4079.30i) q^{38} +(4182.05 - 491.747i) q^{40} +(4374.37 + 2525.55i) q^{41} +(-17261.6 + 9966.01i) q^{43} +(-254.456 + 2628.62i) q^{44} +(-1218.22 - 1341.84i) q^{46} +(-6620.98 - 11467.9i) q^{47} +(7994.11 - 13846.2i) q^{49} +(14284.6 - 3097.70i) q^{50} +(4088.77 - 1860.85i) q^{52} -25022.9i q^{53} -1919.77i q^{55} +(-12963.3 + 30109.6i) q^{56} +(9742.80 + 44927.6i) q^{58} +(20189.4 - 34969.0i) q^{59} +(-8934.10 - 15474.3i) q^{61} +(-7417.39 + 6734.04i) q^{62} +(9354.49 - 31404.4i) q^{64} +(-2828.10 + 1632.81i) q^{65} +(-29089.1 - 16794.6i) q^{67} +(-16769.9 + 23485.3i) q^{68} +(7270.71 - 22693.8i) q^{70} -55855.2 q^{71} -69860.7 q^{73} +(-23669.4 + 73878.5i) q^{74} +(-43951.5 + 61551.5i) q^{76} +(12943.1 + 7472.73i) q^{77} +(-33076.3 + 19096.6i) q^{79} +(-4568.86 + 23377.9i) q^{80} +(-21155.4 + 19206.4i) q^{82} +(11121.7 + 19263.4i) q^{83} +(10489.0 - 18167.4i) q^{85} +(-23895.6 - 110191. i) q^{86} +(-13721.6 - 5907.63i) q^{88} +98921.0i q^{89} -25422.9i q^{91} +(9331.24 - 4246.77i) q^{92} +(73206.3 - 15875.2i) q^{94} +(27490.1 - 47614.2i) q^{95} +(-20762.4 - 35961.6i) q^{97} +(60793.9 + 66963.0i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q + 3 q^{2} - q^{4} + 6 q^{5}+O(q^{10}) \) 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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