LMFDB - Embedded newform 108.6.h.a.35.2

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			35.2
Character	$\chi$	$=$	108.35
Dual form			108.6.h.a.71.2

$q$-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 $\left(\mathbb{Z}/108\mathbb{Z}\right)^\times$.

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

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−5.52836	+	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	−0.308872	−	0.951104i	$-0.599951\pi$
$5$	20.1454	−	11.6310i	0.360372	−	0.208061i	0.669244	+	0.743043i	$0.266618\pi$
$6$		0			0
$7$	156.832	+	90.5473i	1.20974	+	0.698442i	0.962702	−	0.270565i	$-0.0872104\pi$
$7$	156.832	+	90.5473i	1.20974	+	0.698442i	0.247035	+	0.969007i	$0.420544\pi$
$8$	−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	$-0.800546\pi$
$11$	41.2642	−	71.4718i	0.102823	−	0.178095i	0.912847	+	0.408302i	$0.133879\pi$
$12$		0			0
$13$	−70.1922	−	121.577i	−0.115194	−	0.199522i	0.802663	−	0.596433i	$-0.203416\pi$
$13$	−70.1922	−	121.577i	−0.115194	−	0.199522i	−0.917857	+	0.396910i	$0.870082\pi$
$14$	−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	$0.123530\pi$
$17$			901.814i			0.756824i	−0.925637	+	0.378412i	$0.876470\pi$
$18$		0			0
$19$		−	2363.52i		−	1.50202i	−0.660290	−	0.751011i	$-0.729567\pi$
$19$		−	2363.52i		−	1.50202i	0.660290	−	0.751011i	$-0.270433\pi$
$20$	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	0.895868	−	0.444320i	$-0.146555\pi$
$23$	160.190	+	277.458i	0.0631417	+	0.109365i	−0.832726	+	0.553685i	$0.813221\pi$
$24$		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	0.997809	+	0.0661569i	$0.0210738\pi$
$29$	7037.98	+	4063.38i	1.55401	+	0.897207i	0.556198	+	0.831050i	$0.312260\pi$
$30$		0			0
$31$	−1533.72	+	885.495i	−0.286644	+	0.165494i	−0.636427	−	0.771337i	$-0.719588\pi$
$31$	−1533.72	+	885.495i	−0.286644	+	0.165494i	0.349784	+	0.936831i	$0.386255\pi$
$32$	−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	−0.282840	−	0.959167i	$-0.591277\pi$
$41$	4374.37	−	2525.55i	0.406402	−	0.234637i	0.689243	+	0.724530i	$0.257943\pi$
$42$		0			0
$43$	17261.6	+	9966.01i	1.42367	+	0.821959i	0.996611	−	0.0822625i	$-0.0262146\pi$
$43$	17261.6	+	9966.01i	1.42367	+	0.821959i	0.427064	+	0.904221i	$0.359548\pi$
$44$	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	$-0.689304\pi$
$47$	6620.98	−	11467.9i	0.437197	−	0.757248i	0.997472	+	0.0710587i	$0.0226378\pi$
$48$		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	$0.209559\pi$
$53$			25022.9i			1.22362i	−0.791003	+	0.611812i	$0.790441\pi$
$54$		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	−0.945335	−	0.326101i	$-0.894265\pi$
$59$	−20189.4	−	34969.0i	−0.755079	−	1.30784i	0.190256	−	0.981735i	$-0.439068\pi$
$60$		0			0
$61$	−8934.10	+	15474.3i	−0.307416	+	0.532460i	−0.977796	−	0.209558i	$-0.932798\pi$
$61$	−8934.10	+	15474.3i	−0.307416	+	0.532460i	0.670381	+	0.742017i	$0.266131\pi$
$62$	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	$-0.515566\pi$
$67$	29089.1	−	16794.6i	0.791668	−	0.457070i	0.840549	+	0.541735i	$0.182232\pi$
$68$	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	0.767576	−	0.640958i	$-0.221463\pi$
$79$	33076.3	+	19096.6i	0.596278	+	0.344261i	−0.171298	+	0.985219i	$0.554796\pi$
$80$	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	$-0.890039\pi$
$83$	−11121.7	+	19263.4i	−0.177205	+	0.306929i	0.763717	+	0.645551i	$0.223372\pi$
$84$		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	$-0.769756\pi$
$89$		−	98921.0i		−	1.32377i	0.749604	−	0.661886i	$-0.230244\pi$
$90$		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	−0.956035	−	0.293254i	$-0.905262\pi$
$97$	−20762.4	+	35961.6i	−0.224052	+	0.388069i	0.731983	+	0.681323i	$0.238595\pi$
$98$	−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	0.903150	−	0.429324i	$-0.141248\pi$
$101$	100768.	+	58178.3i	0.982920	+	0.567489i	0.0797694	+	0.996813i	$0.474582\pi$
$102$		0			0
$103$	−34298.4	+	19802.2i	−0.318552	+	0.183916i	−0.650747	−	0.759295i	$-0.725544\pi$
$103$	−34298.4	+	19802.2i	−0.318552	+	0.183916i	0.332195	+	0.943211i	$0.392211\pi$
$104$	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	−0.552886	−	0.833257i	$-0.686473\pi$
$113$	−14619.7	+	8440.70i	−0.107707	+	0.0621845i	0.445179	+	0.895442i	$0.353140\pi$
$114$		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	$-0.959719\pi$
$127$		−	45880.3i		−	0.252416i	0.992004	−	0.126208i	$-0.0402807\pi$
$128$	−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	0.833935	−	0.551862i	$-0.186082\pi$
$131$	−11973.3	−	20738.4i	−0.0609588	−	0.105584i	−0.894894	+	0.446278i	$0.852749\pi$
$132$		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	0.0335896	−	0.999436i	$-0.489306\pi$
$137$	−179077.	−	103390.i	−0.815152	−	0.470628i	−0.848742	+	0.528807i	$0.822639\pi$
$138$		0			0
$139$	−150292.	+	86771.1i	−0.659780	+	0.380924i	−0.792193	−	0.610271i	$-0.791061\pi$
$139$	−150292.	+	86771.1i	−0.659780	+	0.380924i	0.132413	+	0.991195i	$0.457727\pi$
$140$	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	−0.815942	−	0.578134i	$-0.803781\pi$
$149$	−195995.	+	113158.i	−0.723234	+	0.417559i	0.0927081	+	0.995693i	$0.470448\pi$
$150$		0			0
$151$	−48433.2	−	27962.9i	−0.172862	−	0.0998021i	0.411072	−	0.911603i	$-0.365154\pi$
$151$	−48433.2	−	27962.9i	−0.172862	−	0.0998021i	−0.583935	+	0.811801i	$0.698488\pi$
$152$	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	0.736210	−	0.676754i	$-0.236614\pi$
$157$	−67323.6	−	116608.i	−0.217981	−	0.377554i	−0.954191	+	0.299200i	$0.903280\pi$
$158$	−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	$-0.955832\pi$
$163$		−	93835.4i		−	0.276629i	0.990388	−	0.138314i	$-0.0441685\pi$
$164$	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	0.757168	−	0.653220i	$-0.226582\pi$
$167$	−67439.6	−	116809.i	−0.187121	−	0.324104i	−0.944289	+	0.329116i	$0.893249\pi$
$168$		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	0.253917	−	0.967226i	$-0.418281\pi$
$173$	−179808.	−	103812.i	−0.456767	−	0.263715i	−0.710684	+	0.703511i	$0.751614\pi$
$174$		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	−0.989856	−	0.142076i	$-0.954622\pi$
$191$	−187497.	+	324754.i	−0.371886	+	0.644126i	0.617970	+	0.786202i	$0.287955\pi$
$192$		0			0
$193$	238572.	+	413219.i	0.461027	+	0.798522i	0.999012	−	0.0444321i	$-0.0141478\pi$
$193$	238572.	+	413219.i	0.461027	+	0.798522i	−0.537985	+	0.842954i	$0.680814\pi$
$194$	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	$-0.866404\pi$
$197$		−	443928.i		−	0.814979i	0.913210	−	0.407490i	$-0.133596\pi$
$198$		0			0
$199$		−	601252.i		−	1.07628i	−0.842857	−	0.538138i	$-0.819128\pi$
$199$		−	601252.i		−	1.07628i	0.842857	−	0.538138i	$-0.180872\pi$
$200$	−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	−0.742588	−	0.669748i	$-0.766402\pi$
$211$	−345252.	+	199331.i	−0.533863	+	0.308226i	0.208725	+	0.977974i	$0.433069\pi$
$212$	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	0.682439	−	0.730942i	$-0.260919\pi$
$223$	290097.	+	167488.i	0.390644	+	0.225538i	−0.291795	+	0.956481i	$0.594253\pi$
$224$	−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	−0.450890	−	0.892580i	$-0.648893\pi$
$227$	425099.	−	736293.i	0.547552	−	0.948388i	0.998442	−	0.0558079i	$-0.0177734\pi$
$228$		0			0
$229$	−204162.	−	353618.i	−0.257268	−	0.445601i	0.708241	−	0.705971i	$-0.249489\pi$
$229$	−204162.	−	353618.i	−0.257268	−	0.445601i	−0.965509	+	0.260370i	$0.916156\pi$
$230$	−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	$-0.865939\pi$
$233$		−	677571.i		−	0.817645i	0.912614	−	0.408823i	$-0.134061\pi$
$234$		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	−0.948940	−	0.315458i	$-0.897842\pi$
$239$	−660239.	−	1.14357e6i	−0.747664	−	1.29499i	0.201275	−	0.979535i	$-0.435491\pi$
$240$		0			0
$241$	−418674.	+	725165.i	−0.464337	+	0.804256i	−0.999171	−	0.0407014i	$-0.987041\pi$
$241$	−418674.	+	725165.i	−0.464337	+	0.804256i	0.534834	+	0.844957i	$0.320374\pi$
$242$	−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	−0.856508	−	0.516134i	$-0.827371\pi$
$257$	−887077.	+	512154.i	−0.837777	+	0.483691i	0.0187311	+	0.999825i	$0.494037\pi$
$258$		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	−0.197323	−	0.980339i	$-0.563225\pi$
$263$	841677.	−	1.45783e6i	0.750337	−	1.29962i	0.947660	−	0.319283i	$-0.103442\pi$
$264$		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	$0.351026\pi$
$269$			2.11837e6i			1.78493i	−0.451117	+	0.892465i	$0.648974\pi$
$270$		0			0
$271$		−	596748.i		−	0.493592i	−0.969067	−	0.246796i	$-0.920622\pi$
$271$		−	596748.i		−	0.493592i	0.969067	−	0.246796i	$-0.0793778\pi$
$272$	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	−0.578835	−	0.815445i	$-0.696492\pi$
$277$	532237.	−	921861.i	0.416779	−	0.721882i	0.995613	+	0.0935631i	$0.0298257\pi$
$278$	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	0.797043	−	0.603923i	$-0.206397\pi$
$281$	890207.	+	513961.i	0.672551	+	0.388298i	−0.124492	+	0.992221i	$0.539730\pi$
$282$		0			0
$283$	958119.	−	553170.i	0.711137	−	0.410575i	−0.100345	−	0.994953i	$-0.531995\pi$
$283$	958119.	−	553170.i	0.711137	−	0.410575i	0.811482	+	0.584377i	$0.198661\pi$
$284$	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	−0.124129	−	0.992266i	$-0.539614\pi$
$293$	989169.	−	571097.i	0.673134	−	0.388634i	0.797263	+	0.603632i	$0.206280\pi$
$294$		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	$0.131135\pi$
$307$			1.32248e6i			0.800836i	−0.916333	+	0.400418i	$0.868865\pi$
$308$	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	0.904010	−	0.427511i	$-0.140609\pi$
$311$	139474.	+	241576.i	0.0817698	+	0.141629i	−0.822240	+	0.569140i	$0.807276\pi$
$312$		0			0
$313$	68921.8	−	119376.i	0.0397645	−	0.0688742i	−0.845458	−	0.534042i	$-0.820673\pi$
$313$	68921.8	−	119376.i	0.0397645	−	0.0688742i	0.885223	+	0.465167i	$0.154006\pi$
$314$	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	0.781446	−	0.623973i	$-0.214482\pi$
$317$	1.13038e6	+	652623.i	0.631793	+	0.364766i	−0.149653	+	0.988739i	$0.547816\pi$
$318$		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	0.354896	−	0.934906i	$-0.384516\pi$
$331$	−552755.	−	319133.i	−0.277308	−	0.160104i	−0.632204	+	0.774802i	$0.717850\pi$
$332$	−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	0.723756	−	0.690056i	$-0.242414\pi$
$337$	−491457.	−	851229.i	−0.235728	−	0.408293i	−0.959484	+	0.281763i	$0.909081\pi$
$338$	−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	0.976410	−	0.215923i	$-0.0692760\pi$
$347$	675607.	+	1.17018e6i	0.301211	+	0.521712i	−0.675200	+	0.737635i	$0.735943\pi$
$348$		0			0
$349$	−376947.	+	652891.i	−0.165660	+	0.286931i	−0.936889	−	0.349626i	$-0.886309\pi$
$349$	−376947.	+	652891.i	−0.165660	+	0.286931i	0.771230	+	0.636557i	$0.219642\pi$
$350$	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	0.414404	−	0.910093i	$-0.363990\pi$
$353$	−389941.	−	225133.i	−0.166557	−	0.0961616i	−0.580961	+	0.813931i	$0.697323\pi$
$354$		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	−0.0266788	−	0.999644i	$-0.508493\pi$
$367$	−2.33704e6	−	1.34929e6i	−0.905735	−	0.522927i	−0.879057	+	0.476718i	$0.841826\pi$
$368$	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	0.641579	−	0.767057i	$-0.278279\pi$
$373$	−922996.	−	1.59868e6i	−0.343501	−	0.594961i	−0.985080	+	0.172096i	$0.944946\pi$
$374$	−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	$0.0780739\pi$
$379$			1.35806e6i			0.485649i	−0.970070	+	0.242824i	$0.921926\pi$
$380$	−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	−0.984825	−	0.173548i	$-0.944477\pi$
$383$	−1.84507e6	−	3.19575e6i	−0.642710	−	1.11321i	0.342115	−	0.939658i	$-0.388857\pi$
$384$		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	−0.0649663	−	0.997887i	$-0.520694\pi$
$389$	−2.87005e6	−	1.65702e6i	−0.961645	−	0.555206i	−0.896679	+	0.442681i	$0.854027\pi$
$390$		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	−0.975325	−	0.220772i	$-0.929142\pi$
$401$	−4.09522e6	+	2.36438e6i	−1.27179	+	0.734271i	−0.296469	+	0.955043i	$0.595809\pi$
$402$		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	−0.797085	−	0.603867i	$-0.793626\pi$
$409$	−3.11750e6	−	5.39967e6i	−0.921507	−	1.59610i	−0.124422	−	0.992229i	$-0.539708\pi$
$410$	−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	0.910332	−	0.413880i	$-0.135827\pi$
$419$	347632.	+	602117.i	0.0967353	+	0.167551i	−0.813596	+	0.581430i	$0.802493\pi$
$420$		0			0
$421$	−585766.	+	1.01458e6i	−0.161071	+	0.278984i	−0.935253	−	0.353979i	$-0.884828\pi$
$421$	−585766.	+	1.01458e6i	−0.161071	+	0.278984i	0.774182	+	0.632963i	$0.218162\pi$
$422$	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	0.103256	−	0.994655i	$-0.467074\pi$
$439$	−2.85286e6	−	1.64710e6i	−0.706512	−	0.407905i	−0.809768	+	0.586750i	$0.800407\pi$
$440$	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	0.214681	+	0.976684i	$0.431129\pi$
$443$	−3.05039e6	+	5.28344e6i	−0.738493	+	1.27911i	−0.953174	+	0.302423i	$0.902204\pi$
$444$		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	$0.216962\pi$
$449$			5.38289e6i			1.26008i	−0.776561	+	0.630042i	$0.783038\pi$
$450$		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	−0.890832	−	0.454332i	$-0.849878\pi$
$457$	−231952.	+	401752.i	−0.0519526	+	0.0899846i	0.838880	+	0.544317i	$0.183211\pi$
$458$	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	0.0491256	−	0.998793i	$-0.484357\pi$
$461$	−3.61068e6	−	2.08463e6i	−0.791291	−	0.456852i	−0.840417	+	0.541940i	$0.817690\pi$
$462$		0			0
$463$	−5.46488e6	+	3.15515e6i	−1.18475	+	0.684018i	−0.957110	−	0.289726i	$-0.906436\pi$
$463$	−5.46488e6	+	3.15515e6i	−1.18475	+	0.684018i	−0.227644	+	0.973744i	$0.573102\pi$
$464$	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	−0.992839	−	0.119463i	$-0.961883\pi$
$479$	−1.97328e6	+	3.41782e6i	−0.392962	+	0.680629i	0.599877	+	0.800092i	$0.295216\pi$
$480$		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	$-0.939473\pi$
$487$		−	1.97847e6i		−	0.378012i	0.981976	−	0.189006i	$-0.0605266\pi$
$488$	−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	0.810230	−	0.586112i	$-0.199342\pi$
$491$	−547411.	−	948143.i	−0.102473	−	0.177488i	−0.912703	+	0.408624i	$0.866009\pi$
$492$		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	0.646978	−	0.762508i	$-0.276032\pi$
$499$	9.07104e6	−	5.23717e6i	1.63082	−	0.941554i	0.983841	−	0.179045i	$-0.0573009\pi$
$500$	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	−0.245722	−	0.969340i	$-0.579025\pi$
$509$	2.75241e6	−	1.58911e6i	0.470890	−	0.271868i	0.716612	+	0.697472i	$0.245692\pi$
$510$		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	$0.0454190\pi$
$521$			1.76213e6i			0.284408i	−0.989837	+	0.142204i	$0.954581\pi$
$522$		0			0
$523$			8.86393e6i			1.41701i	0.705708	+	0.708503i	$0.250629\pi$
$523$			8.86393e6i			1.41701i	−0.705708	+	0.708503i	$0.749371\pi$
$524$	−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	0.460623	−	0.887596i	$-0.347626\pi$
$547$	−544056.	−	314111.i	−0.0777455	−	0.0448864i	−0.538369	+	0.842709i	$0.680959\pi$
$548$	−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	$0.0509142\pi$
$557$			2.33240e6i			0.318541i	−0.987235	+	0.159270i	$0.949086\pi$
$558$		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	0.998872	+	0.0474781i	$0.0151184\pi$
$563$	4.06546e6	+	7.04158e6i	0.540553	+	0.936266i	−0.458319	+	0.888788i	$0.651548\pi$
$564$		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	0.826892	−	0.562361i	$-0.190107\pi$
$569$	5.81782e6	+	3.35892e6i	0.753320	+	0.434929i	−0.0735725	+	0.997290i	$0.523440\pi$
$570$		0			0
$571$	1.04309e7	−	6.02229e6i	1.33885	−	0.772985i	0.352213	−	0.935920i	$-0.385429\pi$
$571$	1.04309e7	−	6.02229e6i	1.33885	−	0.772985i	0.986637	+	0.162935i	$0.0520961\pi$
$572$	−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	0.422508	+	0.906359i	$0.361150\pi$
$587$	−4.78919e6	+	8.29511e6i	−0.573676	+	0.993636i	−0.996184	+	0.0872766i	$0.972184\pi$
$588$		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	$-0.876698\pi$
$593$		−	6.46951e6i		−	0.755501i	0.925907	−	0.377750i	$-0.123302\pi$
$594$		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	0.697904	−	0.716192i	$-0.254116\pi$
$599$	−2.38231e6	−	4.12628e6i	−0.271288	−	0.469885i	−0.969192	+	0.246306i	$0.920783\pi$
$600$		0			0
$601$	−7.09387e6	+	1.22869e7i	−0.801119	+	1.38758i	0.117761	+	0.993042i	$0.462428\pi$
$601$	−7.09387e6	+	1.22869e7i	−0.801119	+	1.38758i	−0.918880	+	0.394537i	$0.870905\pi$
$602$	−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	$-0.520969\pi$
$607$	6.94805e6	−	4.01146e6i	0.765404	−	0.441906i	0.831233	+	0.555924i	$0.187636\pi$
$608$	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	−0.592759	−	0.805380i	$-0.701961\pi$
$617$	−1.81236e6	+	1.04636e6i	−0.191660	+	0.110655i	0.401100	+	0.916034i	$0.368628\pi$
$618$		0			0
$619$	7.46071e6	+	4.30745e6i	0.782625	+	0.451849i	0.837360	−	0.546652i	$-0.184098\pi$
$619$	7.46071e6	+	4.30745e6i	0.782625	+	0.451849i	−0.0547347	+	0.998501i	$0.517431\pi$
$620$	−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	$0.196554\pi$
$631$			1.15818e7i			1.15798i	−0.815334	+	0.578991i	$0.803446\pi$
$632$	−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	−0.454771	−	0.890608i	$-0.650279\pi$
$641$	−1.51197e7	−	8.72938e6i	−1.45345	−	0.839147i	−0.998675	+	0.0514611i	$0.983612\pi$
$642$		0			0
$643$	−8.37838e6	+	4.83726e6i	−0.799158	+	0.461394i	−0.843177	−	0.537637i	$-0.819317\pi$
$643$	−8.37838e6	+	4.83726e6i	−0.799158	+	0.461394i	0.0440186	+	0.999031i	$0.485984\pi$
$644$	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	0.517036	−	0.855964i	$-0.327035\pi$
$653$	1.65281e7	−	9.54250e6i	1.51684	−	0.875748i	0.999804	−	0.0197840i	$-0.00629786\pi$
$654$		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	$-0.674597\pi$
$659$	5.33197e6	−	9.23524e6i	0.478271	−	0.828390i	0.999690	+	0.0249112i	$0.00793029\pi$
$660$		0			0
$661$	1.35400e6	+	2.34520e6i	0.120535	+	0.208774i	0.919979	−	0.391968i	$-0.128206\pi$
$661$	1.35400e6	+	2.34520e6i	0.120535	+	0.208774i	−0.799443	+	0.600741i	$0.794872\pi$
$662$	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	−0.955615	−	0.294618i	$-0.904808\pi$
$673$	−2.61627e6	+	4.53151e6i	−0.222661	+	0.385660i	0.732954	+	0.680278i	$0.238141\pi$
$674$	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	0.566855	−	0.823817i	$-0.308160\pi$
$677$	1.63183e6	+	942135.i	0.136837	+	0.0790026i	−0.430019	+	0.902820i	$0.641493\pi$
$678$		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	0.900364	−	0.435138i	$-0.143300\pi$
$691$	1.22215e7	+	7.05606e6i	0.973706	+	0.562169i	0.0733417	+	0.997307i	$0.476634\pi$
$692$	−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	$-0.969104\pi$
$701$		−	2.52168e6i		−	0.193818i	0.995293	−	0.0969090i	$-0.0308956\pi$
$702$		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	−0.429401	−	0.903114i	$-0.641275\pi$
$709$	7.59486e6	−	1.31547e7i	0.567419	−	0.982799i	0.996820	−	0.0796849i	$-0.0253914\pi$
$710$	−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	0.0905324	−	0.995894i	$-0.471143\pi$
$727$	−1.03556e7	−	5.97878e6i	−0.726670	−	0.419543i	−0.817203	+	0.576350i	$0.804476\pi$
$728$	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	0.567209	−	0.823574i	$-0.308023\pi$
$733$	−6.24966e6	−	1.08247e7i	−0.429632	−	0.744144i	−0.996840	+	0.0794302i	$0.974690\pi$
$734$	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	$-0.964058\pi$
$739$		−	3.34559e6i		−	0.225352i	0.993632	−	0.112676i	$-0.0359422\pi$
$740$	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	0.798276	−	0.602291i	$-0.205745\pi$
$743$	−1.84277e6	−	3.19177e6i	−0.122461	−	0.212109i	−0.920738	+	0.390182i	$0.872412\pi$
$744$		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	$-0.803137\pi$
$751$	−1.11291e7	+	6.42540e6i	−0.720048	+	0.415720i	0.0947225	+	0.995504i	$0.469804\pi$
$752$	−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	−0.581506	−	0.813542i	$-0.697536\pi$
$761$	−2.67932e6	+	1.54691e6i	−0.167712	+	0.0968283i	0.413795	+	0.910370i	$0.364203\pi$
$762$		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	0.883798	−	0.467869i	$-0.154978\pi$
$769$	602040.	+	1.04276e6i	0.0367122	+	0.0635873i	−0.847086	+	0.531457i	$0.821645\pi$
$770$	−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	$0.312523\pi$
$773$			2.76278e7i			1.66302i	−0.555510	+	0.831510i	$0.687477\pi$
$774$		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	−0.659292	−	0.751887i	$-0.729144\pi$
$787$	−5.86919e6	+	3.38858e6i	−0.337786	+	0.195021i	0.321507	+	0.946907i	$0.395811\pi$
$788$	−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	−0.275737	−	0.961233i	$-0.588922\pi$
$797$	7.51105e6	−	4.33650e6i	0.418846	−	0.241821i	0.694584	+	0.719412i	$0.255589\pi$
$798$		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	$-0.782550\pi$
$809$		−	2.35011e7i		−	1.26246i	0.775596	−	0.631230i	$-0.217450\pi$
$810$		0			0
$811$		−	335741.i		−	0.0179247i	−0.999960	−	0.00896235i	$-0.997147\pi$
$811$		−	335741.i		−	0.0179247i	0.999960	−	0.00896235i	$-0.00285284\pi$
$812$	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	−0.154168	−	0.988045i	$-0.549270\pi$
$821$	−2.09922e7	−	1.21198e7i	−1.08692	−	0.627536i	−0.932756	+	0.360509i	$0.882603\pi$
$822$		0			0
$823$	−3.59148e6	+	2.07354e6i	−0.184831	+	0.106712i	−0.589560	−	0.807724i	$-0.700699\pi$
$823$	−3.59148e6	+	2.07354e6i	−0.184831	+	0.106712i	0.404730	+	0.914436i	$0.367366\pi$
$824$	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	−0.940007	−	0.341156i	$-0.889181\pi$
$839$	−3.55904e6	+	6.16444e6i	−0.174553	+	0.302335i	0.765453	+	0.643491i	$0.222515\pi$
$840$		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	−0.703108	−	0.711083i	$-0.748205\pi$
$853$	5.61575e6	−	9.72676e6i	0.264262	−	0.457715i	0.967370	+	0.253368i	$0.0815383\pi$
$854$	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	0.891412	−	0.453193i	$-0.149715\pi$
$857$	2.03104e7	+	1.17262e7i	0.944641	+	0.545389i	0.0532292	+	0.998582i	$0.483049\pi$
$858$		0			0
$859$	−3.00517e7	+	1.73504e7i	−1.38959	+	0.802279i	−0.993269	−	0.115834i	$-0.963046\pi$
$859$	−3.00517e7	+	1.73504e7i	−1.38959	+	0.802279i	−0.396319	+	0.918113i	$0.629713\pi$
$860$	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	−0.964736	−	0.263219i	$-0.915216\pi$
$877$	−1.61791e7	−	2.80230e7i	−0.710323	−	1.23031i	0.254414	−	0.967096i	$-0.418118\pi$
$878$	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	$-0.960289\pi$
$881$		−	5.73331e6i		−	0.248866i	0.992228	−	0.124433i	$-0.0397112\pi$
$882$		0			0
$883$		−	2.49947e7i		−	1.07881i	−0.842046	−	0.539406i	$-0.818649\pi$
$883$		−	2.49947e7i		−	1.07881i	0.842046	−	0.539406i	$-0.181351\pi$
$884$	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	0.813472	−	0.581605i	$-0.197575\pi$
$887$	−2.27170e6	−	3.93469e6i	−0.0969485	−	0.167920i	−0.910420	+	0.413685i	$0.864242\pi$
$888$		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	0.936315	−	0.351161i	$-0.114213\pi$
$907$	2.72617e7	+	1.57395e7i	1.10036	+	0.635292i	0.164043	+	0.986453i	$0.447546\pi$
$908$	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	$-0.866883\pi$
$911$	−2.63528e6	+	4.56443e6i	−0.105204	+	0.182218i	0.808618	+	0.588334i	$0.200216\pi$
$912$		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	$-0.777341\pi$
$919$		−	3.29683e7i		−	1.28768i	0.765161	−	0.643839i	$-0.222659\pi$
$920$	−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	0.532045	−	0.846716i	$-0.321424\pi$
$929$	1.70431e6	+	983982.i	0.0647901	+	0.0374066i	−0.467255	+	0.884123i	$0.654757\pi$
$930$		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	−0.100588	−	0.994928i	$-0.532072\pi$
$941$	1.93060e7	−	1.11463e7i	0.710751	−	0.410352i	0.811339	+	0.584576i	$0.198739\pi$
$942$		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	−0.138921	−	0.990304i	$-0.544363\pi$
$947$	2.17517e7	−	3.76751e7i	0.788168	−	1.36515i	0.927088	−	0.374843i	$-0.122303\pi$
$948$		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	$0.0433274\pi$
$953$			7.60909e6i			0.271394i	−0.990750	+	0.135697i	$0.956673\pi$
$954$		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	−0.708463	−	0.705748i	$-0.750611\pi$
$967$	−1.31287e7	+	7.57986e6i	−0.451498	+	0.260672i	0.256965	+	0.966421i	$0.417278\pi$
$968$	−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	−0.492774	−	0.870157i	$-0.664017\pi$
$977$	430133.	−	248338.i	0.0144167	−	0.00832350i	0.507191	+	0.861834i	$0.330684\pi$
$978$		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	0.228373	+	0.973574i	$0.426659\pi$
$983$	−2.20843e7	+	3.82511e7i	−0.728953	+	1.26258i	−0.957326	+	0.289010i	$0.906674\pi$
$984$		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	$0.0436364\pi$
$991$			8.44990e6i			0.273317i	−0.990618	+	0.136659i	$0.956364\pi$
$992$	−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	−0.686758	−	0.726887i	$-0.740967\pi$
$997$	8.98031e6	−	1.55544e7i	0.286123	−	0.495580i	0.972881	+	0.231306i	$0.0742999\pi$
$998$	−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.35.2		56
3.2	odd	2		36.6.h.a.11.27	yes	56
4.3	odd	2	inner	108.6.h.a.35.12		56
9.4	even	3		36.6.h.a.23.17	yes	56
9.5	odd	6	inner	108.6.h.a.71.12		56
12.11	even	2		36.6.h.a.11.17	✓	56
36.23	even	6	inner	108.6.h.a.71.2		56
36.31	odd	6		36.6.h.a.23.27	yes	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
36.6.h.a.11.17	✓	56	12.11	even	2
36.6.h.a.11.27	yes	56	3.2	odd	2
36.6.h.a.23.17	yes	56	9.4	even	3
36.6.h.a.23.27	yes	56	36.31	odd	6
108.6.h.a.35.2		56	1.1	even	1	trivial
108.6.h.a.35.12		56	4.3	odd	2	inner
108.6.h.a.71.2		56	36.23	even	6	inner
108.6.h.a.71.12		56	9.5	odd	6	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 108 = 2^{2} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	108.h (of order \(6\), degree \(2\), not minimal)

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