LMFDB - Embedded newform 162.8.c.d.55.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [162,8,Mod(55,162)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(162, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4]))

N = Newforms(chi, 8, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("162.55");

S:= CuspForms(chi, 8);

N := Newforms(S);

Level:	$ N $	$=$	$ 162 = 2 \cdot 3^{4} $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	162.c (of order $3$, 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:	$50.6063741284$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 1 $ x^2 - x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{25}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 6)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			55.1
Root			$0.500000 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	162.55
Dual form			162.8.c.d.109.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-4.00000 + 6.92820i) q^{2} +(-32.0000 - 55.4256i) q^{4} +(57.0000 + 98.7269i) q^{5} +(788.000 - 1364.86i) q^{7} +512.000 q^{8} +O(q^{10})$	\(q+(-4.00000 + 6.92820i) q^{2} +(-32.0000 - 55.4256i) q^{4} +(57.0000 + 98.7269i) q^{5} +(788.000 - 1364.86i) q^{7} +512.000 q^{8} -912.000 q^{10} +(-3666.00 + 6349.70i) q^{11} +(1901.00 + 3292.63i) q^{13} +(6304.00 + 10918.8i) q^{14} +(-2048.00 + 3547.24i) q^{16} -6606.00 q^{17} +24860.0 q^{19} +(3648.00 - 6318.52i) q^{20} +(-29328.0 - 50797.6i) q^{22} +(-20724.0 - 35895.0i) q^{23} +(32564.5 - 56403.4i) q^{25} -30416.0 q^{26} -100864. q^{28} +(20805.0 - 36035.3i) q^{29} +(-16576.0 - 28710.5i) q^{31} +(-16384.0 - 28377.9i) q^{32} +(26424.0 - 45767.7i) q^{34} +179664. q^{35} -36466.0 q^{37} +(-99440.0 + 172235. i) q^{38} +(29184.0 + 50548.2i) q^{40} +(319539. + 553458. i) q^{41} +(78206.0 - 135457. i) q^{43} +469248. q^{44} +331584. q^{46} +(216888. - 375661. i) q^{47} +(-830116. - 1.43780e6i) q^{49} +(260516. + 451227. i) q^{50} +(121664. - 210728. i) q^{52} +786078. q^{53} -835848. q^{55} +(403456. - 698806. i) q^{56} +(166440. + 288283. i) q^{58} +(-372570. - 645310. i) q^{59} +(830309. - 1.43814e6i) q^{61} +265216. q^{62} +262144. q^{64} +(-216714. + 375360. i) q^{65} +(1.64542e6 + 2.84995e6i) q^{67} +(211392. + 366142. i) q^{68} +(-718656. + 1.24475e6i) q^{70} +5.71615e6 q^{71} +2.65990e6 q^{73} +(145864. - 252644. i) q^{74} +(-795520. - 1.37788e6i) q^{76} +(5.77762e6 + 1.00071e7i) q^{77} +(-1.90372e6 + 3.29734e6i) q^{79} -466944. q^{80} -5.11262e6 q^{82} +(-1.11473e6 + 1.93078e6i) q^{83} +(-376542. - 652190. i) q^{85} +(625648. + 1.08365e6i) q^{86} +(-1.87699e6 + 3.25105e6i) q^{88} +5.99121e6 q^{89} +5.99195e6 q^{91} +(-1.32634e6 + 2.29728e6i) q^{92} +(1.73510e6 + 3.00529e6i) q^{94} +(1.41702e6 + 2.45435e6i) q^{95} +(2.03006e6 - 3.51617e6i) q^{97} +1.32819e7 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 8 q^{2} - 64 q^{4} + 114 q^{5} + 1576 q^{7} + 1024 q^{8}+O(q^{10}) $ 2 * q - 8 * q^2 - 64 * q^4 + 114 * q^5 + 1576 * q^7 + 1024 * q^8	\( 2 q - 8 q^{2} - 64 q^{4} + 114 q^{5} + 1576 q^{7} + 1024 q^{8} - 1824 q^{10} - 7332 q^{11} + 3802 q^{13} + 12608 q^{14} - 4096 q^{16} - 13212 q^{17} + 49720 q^{19} + 7296 q^{20} - 58656 q^{22} - 41448 q^{23} + 65129 q^{25} - 60832 q^{26} - 201728 q^{28} + 41610 q^{29} - 33152 q^{31} - 32768 q^{32} + 52848 q^{34} + 359328 q^{35} - 72932 q^{37} - 198880 q^{38} + 58368 q^{40} + 639078 q^{41} + 156412 q^{43} + 938496 q^{44} + 663168 q^{46} + 433776 q^{47} - 1660233 q^{49} + 521032 q^{50} + 243328 q^{52} + 1572156 q^{53} - 1671696 q^{55} + 806912 q^{56} + 332880 q^{58} - 745140 q^{59} + 1660618 q^{61} + 530432 q^{62} + 524288 q^{64} - 433428 q^{65} + 3290836 q^{67} + 422784 q^{68} - 1437312 q^{70} + 11432304 q^{71} + 5319796 q^{73} + 291728 q^{74} - 1591040 q^{76} + 11555232 q^{77} - 3807440 q^{79} - 933888 q^{80} - 10225248 q^{82} - 2229468 q^{83} - 753084 q^{85} + 1251296 q^{86} - 3753984 q^{88} + 11982420 q^{89} + 11983904 q^{91} - 2652672 q^{92} + 3470208 q^{94} + 2834040 q^{95} + 4060126 q^{97} + 26563728 q^{98}+O(q^{100}) \) 2 * q - 8 * q^2 - 64 * q^4 + 114 * q^5 + 1576 * q^7 + 1024 * q^8 - 1824 * q^10 - 7332 * q^11 + 3802 * q^13 + 12608 * q^14 - 4096 * q^16 - 13212 * q^17 + 49720 * q^19 + 7296 * q^20 - 58656 * q^22 - 41448 * q^23 + 65129 * q^25 - 60832 * q^26 - 201728 * q^28 + 41610 * q^29 - 33152 * q^31 - 32768 * q^32 + 52848 * q^34 + 359328 * q^35 - 72932 * q^37 - 198880 * q^38 + 58368 * q^40 + 639078 * q^41 + 156412 * q^43 + 938496 * q^44 + 663168 * q^46 + 433776 * q^47 - 1660233 * q^49 + 521032 * q^50 + 243328 * q^52 + 1572156 * q^53 - 1671696 * q^55 + 806912 * q^56 + 332880 * q^58 - 745140 * q^59 + 1660618 * q^61 + 530432 * q^62 + 524288 * q^64 - 433428 * q^65 + 3290836 * q^67 + 422784 * q^68 - 1437312 * q^70 + 11432304 * q^71 + 5319796 * q^73 + 291728 * q^74 - 1591040 * q^76 + 11555232 * q^77 - 3807440 * q^79 - 933888 * q^80 - 10225248 * q^82 - 2229468 * q^83 - 753084 * q^85 + 1251296 * q^86 - 3753984 * q^88 + 11982420 * q^89 + 11983904 * q^91 - 2652672 * q^92 + 3470208 * q^94 + 2834040 * q^95 + 4060126 * q^97 + 26563728 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/162\mathbb{Z}\right)^\times$.

$n$	$83$
$\chi(n)$	$e\left(\frac{2}{3}\right)$

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 $

$2$	−4.00000	+	6.92820i	−0.353553	+	0.612372i
$2$	−4.00000	+	6.92820i	−0.353553	+	0.612372i
$3$		0			0
$3$		0			0
$4$	−32.0000	−	55.4256i	−0.250000	−	0.433013i
$5$	57.0000	+	98.7269i	0.203929	+	0.353216i	0.949791	−	0.312885i	$-0.101295\pi$
$5$	57.0000	+	98.7269i	0.203929	+	0.353216i	−0.745862	+	0.666101i	$0.767962\pi$
$6$		0			0
$7$	788.000	−	1364.86i	0.868327	−	1.50399i	0.00462077	−	0.999989i	$-0.498529\pi$
$7$	788.000	−	1364.86i	0.868327	−	1.50399i	0.863706	−	0.503996i	$-0.168138\pi$
$8$	512.000			0.353553
$9$		0			0
$10$	−912.000			−0.288400
$11$	−3666.00	+	6349.70i	−0.830459	+	1.43840i	0.0672162	+	0.997738i	$0.478588\pi$
$11$	−3666.00	+	6349.70i	−0.830459	+	1.43840i	−0.897675	+	0.440658i	$0.854745\pi$
$12$		0			0
$13$	1901.00	+	3292.63i	0.239983	+	0.415663i	0.960709	−	0.277557i	$-0.0895248\pi$
$13$	1901.00	+	3292.63i	0.239983	+	0.415663i	−0.720726	+	0.693220i	$0.756191\pi$
$14$	6304.00	+	10918.8i	0.614000	+	1.06348i
$15$		0			0
$16$	−2048.00	+	3547.24i	−0.125000	+	0.216506i
$17$	−6606.00			−0.326112			−0.163056	−	0.986617i	$-0.552135\pi$
$17$	−6606.00			−0.326112			−0.163056	+	0.986617i	$0.552135\pi$
$18$		0			0
$19$	24860.0			0.831502			0.415751	−	0.909478i	$-0.363519\pi$
$19$	24860.0			0.831502			0.415751	+	0.909478i	$0.363519\pi$
$20$	3648.00	−	6318.52i	0.101965	−	0.176608i
$21$		0			0
$22$	−29328.0	−	50797.6i	−0.587223	−	1.01710i
$23$	−20724.0	−	35895.0i	−0.355162	−	0.615158i	0.631984	−	0.774982i	$-0.282241\pi$
$23$	−20724.0	−	35895.0i	−0.355162	−	0.615158i	−0.987146	+	0.159823i	$0.948908\pi$
$24$		0			0
$25$	32564.5	−	56403.4i	0.416826	−	0.721963i
$26$	−30416.0			−0.339387
$27$		0			0
$28$	−100864.			−0.868327
$29$	20805.0	−	36035.3i	0.158407	−	0.274369i	−0.775887	−	0.630872i	$-0.782697\pi$
$29$	20805.0	−	36035.3i	0.158407	−	0.274369i	0.934294	+	0.356502i	$0.116031\pi$
$30$		0			0
$31$	−16576.0	−	28710.5i	−0.0999341	−	0.173091i	0.811723	−	0.584043i	$-0.198530\pi$
$31$	−16576.0	−	28710.5i	−0.0999341	−	0.173091i	−0.911657	+	0.410952i	$0.865197\pi$
$32$	−16384.0	−	28377.9i	−0.0883883	−	0.153093i
$33$		0			0
$34$	26424.0	−	45767.7i	0.115298	−	0.199702i
$35$	179664.			0.708309
$36$		0			0
$37$	−36466.0			−0.118354			−0.0591769	−	0.998248i	$-0.518848\pi$
$37$	−36466.0			−0.118354			−0.0591769	+	0.998248i	$0.518848\pi$
$38$	−99440.0	+	172235.i	−0.293981	+	0.509189i
$39$		0			0
$40$	29184.0	+	50548.2i	0.0720999	+	0.124881i
$41$	319539.	+	553458.i	0.724070	+	1.25413i	0.959356	+	0.282199i	$0.0910640\pi$
$41$	319539.	+	553458.i	0.724070	+	1.25413i	−0.235286	+	0.971926i	$0.575603\pi$
$42$		0			0
$43$	78206.0	−	135457.i	0.150003	−	0.259813i	−0.781225	−	0.624249i	$-0.785405\pi$
$43$	78206.0	−	135457.i	0.150003	−	0.259813i	0.931228	+	0.364436i	$0.118738\pi$
$44$	469248.			0.830459
$45$		0			0
$46$	331584.			0.502275
$47$	216888.	−	375661.i	0.304714	−	0.527781i	−0.672483	−	0.740112i	$-0.734772\pi$
$47$	216888.	−	375661.i	0.304714	−	0.527781i	0.977198	+	0.212331i	$0.0681056\pi$
$48$		0			0
$49$	−830116.	−	1.43780e6i	−1.00798	−	1.74588i
$50$	260516.	+	451227.i	0.294740	+	0.510505i
$51$		0			0
$52$	121664.	−	210728.i	0.119991	−	0.207831i
$53$	786078.			0.725271			0.362635	−	0.931931i	$-0.381877\pi$
$53$	786078.			0.725271			0.362635	+	0.931931i	$0.381877\pi$
$54$		0			0
$55$	−835848.			−0.677420
$56$	403456.	−	698806.i	0.307000	−	0.531739i
$57$		0			0
$58$	166440.	+	288283.i	0.112011	+	0.194008i
$59$	−372570.	−	645310.i	−0.236171	−	0.409059i	0.723442	−	0.690386i	$-0.242559\pi$
$59$	−372570.	−	645310.i	−0.236171	−	0.409059i	−0.959612	+	0.281326i	$0.909226\pi$
$60$		0			0
$61$	830309.	−	1.43814e6i	0.468366	−	0.811234i	−0.530980	−	0.847384i	$-0.678176\pi$
$61$	830309.	−	1.43814e6i	0.468366	−	0.811234i	0.999346	+	0.0361505i	$0.0115096\pi$
$62$	265216.			0.141328
$63$		0			0
$64$	262144.			0.125000
$65$	−216714.	+	375360.i	−0.0978792	+	0.169532i
$66$		0			0
$67$	1.64542e6	+	2.84995e6i	0.668366	+	1.15764i	0.978361	+	0.206906i	$0.0663394\pi$
$67$	1.64542e6	+	2.84995e6i	0.668366	+	1.15764i	−0.309995	+	0.950738i	$0.600327\pi$
$68$	211392.	+	366142.i	0.0815281	+	0.141211i
$69$		0			0
$70$	−718656.	+	1.24475e6i	−0.250425	+	0.433749i
$71$	5.71615e6			1.89539			0.947697	−	0.319171i	$-0.103404\pi$
$71$	5.71615e6			1.89539			0.947697	+	0.319171i	$0.103404\pi$
$72$		0			0
$73$	2.65990e6			0.800267			0.400134	−	0.916457i	$-0.368964\pi$
$73$	2.65990e6			0.800267			0.400134	+	0.916457i	$0.368964\pi$
$74$	145864.	−	252644.i	0.0418444	−	0.0724766i
$75$		0			0
$76$	−795520.	−	1.37788e6i	−0.207876	−	0.360051i
$77$	5.77762e6	+	1.00071e7i	1.44222	+	2.49800i
$78$		0			0
$79$	−1.90372e6	+	3.29734e6i	−0.434418	+	0.752435i	−0.997248	−	0.0741382i	$-0.976379\pi$
$79$	−1.90372e6	+	3.29734e6i	−0.434418	+	0.752435i	0.562830	+	0.826573i	$0.309713\pi$
$80$	−466944.			−0.101965
$81$		0			0
$82$	−5.11262e6			−1.02399
$83$	−1.11473e6	+	1.93078e6i	−0.213992	+	0.370645i	−0.952960	−	0.303095i	$-0.901980\pi$
$83$	−1.11473e6	+	1.93078e6i	−0.213992	+	0.370645i	0.738968	+	0.673740i	$0.235313\pi$
$84$		0			0
$85$	−376542.	−	652190.i	−0.0665039	−	0.115188i
$86$	625648.	+	1.08365e6i	0.106068	+	0.183716i
$87$		0			0
$88$	−1.87699e6	+	3.25105e6i	−0.293612	+	0.508550i
$89$	5.99121e6			0.900844			0.450422	−	0.892816i	$-0.351274\pi$
$89$	5.99121e6			0.900844			0.450422	+	0.892816i	$0.351274\pi$
$90$		0			0
$91$	5.99195e6			0.833534
$92$	−1.32634e6	+	2.29728e6i	−0.177581	+	0.307579i
$93$		0			0
$94$	1.73510e6	+	3.00529e6i	0.215466	+	0.373197i
$95$	1.41702e6	+	2.45435e6i	0.169568	+	0.293700i
$96$		0			0
$97$	2.03006e6	−	3.51617e6i	0.225844	−	0.391173i	−0.730728	−	0.682668i	$-0.760819\pi$
$97$	2.03006e6	−	3.51617e6i	0.225844	−	0.391173i	0.956572	+	0.291495i	$0.0941527\pi$
$98$	1.32819e7			1.42550
$99$		0			0
$100$	−4.16826e6			−0.416826
$101$	8.64097e6	−	1.49666e7i	0.834522	−	1.44543i	−0.0598975	−	0.998205i	$-0.519077\pi$
$101$	8.64097e6	−	1.49666e7i	0.834522	−	1.44543i	0.894419	−	0.447229i	$-0.147589\pi$
$102$		0			0
$103$	7.18116e6	+	1.24381e7i	0.647536	+	1.12157i	0.983709	+	0.179765i	$0.0575339\pi$
$103$	7.18116e6	+	1.24381e7i	0.647536	+	1.12157i	−0.336173	+	0.941800i	$0.609133\pi$
$104$	973312.	+	1.68583e6i	0.0848468	+	0.146959i
$105$		0			0
$106$	−3.14431e6	+	5.44611e6i	−0.256422	+	0.444136i
$107$	6.45440e6			0.509346			0.254673	−	0.967027i	$-0.418032\pi$
$107$	6.45440e6			0.509346			0.254673	+	0.967027i	$0.418032\pi$
$108$		0			0
$109$	−884410.			−0.0654125			−0.0327063	−	0.999465i	$-0.510413\pi$
$109$	−884410.			−0.0654125			−0.0327063	+	0.999465i	$0.510413\pi$
$110$	3.34339e6	−	5.79092e6i	0.239504	−	0.414833i
$111$		0			0
$112$	3.22765e6	+	5.59045e6i	0.217082	+	0.375996i
$113$	−6.06625e6	−	1.05071e7i	−0.395499	−	0.685025i	0.597666	−	0.801746i	$-0.296095\pi$
$113$	−6.06625e6	−	1.05071e7i	−0.395499	−	0.685025i	−0.993165	+	0.116721i	$0.962762\pi$
$114$		0			0
$115$	2.36254e6	−	4.09203e6i	0.144856	−	0.250898i
$116$	−2.66304e6			−0.158407
$117$		0			0
$118$	5.96112e6			0.333996
$119$	−5.20553e6	+	9.01624e6i	−0.283172	+	0.490468i
$120$		0			0
$121$	−1.71355e7	−	2.96796e7i	−0.879323	−	1.52303i
$122$	6.64247e6	+	1.15051e7i	0.331185	+	0.573629i
$123$		0			0
$124$	−1.06086e6	+	1.83747e6i	−0.0499671	+	0.0865455i
$125$	1.63310e7			0.747871
$126$		0			0
$127$	6.86806e6			0.297524			0.148762	−	0.988873i	$-0.452471\pi$
$127$	6.86806e6			0.297524			0.148762	+	0.988873i	$0.452471\pi$
$128$	−1.04858e6	+	1.81619e6i	−0.0441942	+	0.0765466i
$129$		0			0
$130$	−1.73371e6	−	3.00288e6i	−0.0692110	−	0.119877i
$131$	1.97604e7	+	3.42260e7i	0.767973	+	1.33017i	0.938660	+	0.344843i	$0.112068\pi$
$131$	1.97604e7	+	3.42260e7i	0.767973	+	1.33017i	−0.170687	+	0.985325i	$0.554599\pi$
$132$		0			0
$133$	1.95897e7	−	3.39303e7i	0.722016	−	1.25057i
$134$	−2.63267e7			−0.945212
$135$		0			0
$136$	−3.38227e6			−0.115298
$137$	−9.58704e6	+	1.66052e7i	−0.318539	+	0.551725i	−0.980183	−	0.198092i	$-0.936525\pi$
$137$	−9.58704e6	+	1.66052e7i	−0.318539	+	0.551725i	0.661645	+	0.749818i	$0.269859\pi$
$138$		0			0
$139$	−6.62245e6	−	1.14704e7i	−0.209154	−	0.362266i	0.742294	−	0.670074i	$-0.233738\pi$
$139$	−6.62245e6	−	1.14704e7i	−0.209154	−	0.362266i	−0.951448	+	0.307808i	$0.900404\pi$
$140$	−5.74925e6	−	9.95799e6i	−0.177077	−	0.306707i
$141$		0			0
$142$	−2.28646e7	+	3.96027e7i	−0.670123	+	1.16069i
$143$	−2.78763e7			−0.797184
$144$		0			0
$145$	4.74354e6			0.129215
$146$	−1.06396e7	+	1.84283e7i	−0.282937	+	0.490062i
$147$		0			0
$148$	1.16691e6	+	2.02115e6i	0.0295884	+	0.0512487i
$149$	−2.86812e7	−	4.96773e7i	−0.710306	−	1.23029i	−0.964742	−	0.263197i	$-0.915223\pi$
$149$	−2.86812e7	−	4.96773e7i	−0.710306	−	1.23029i	0.254436	−	0.967090i	$-0.418110\pi$
$150$		0			0
$151$	1.55436e7	−	2.69224e7i	0.367395	−	0.636347i	−0.621762	−	0.783206i	$-0.713583\pi$
$151$	1.55436e7	−	2.69224e7i	0.367395	−	0.636347i	0.989157	+	0.146859i	$0.0469163\pi$
$152$	1.27283e7			0.293981
$153$		0			0
$154$	−9.24419e7			−2.03961
$155$	1.88966e6	−	3.27299e6i	0.0407590	−	0.0705967i
$156$		0			0
$157$	1.68917e7	+	2.92573e7i	0.348358	+	0.603373i	0.985958	−	0.166994i	$-0.0534061\pi$
$157$	1.68917e7	+	2.92573e7i	0.348358	+	0.603373i	−0.637600	+	0.770367i	$0.720073\pi$
$158$	−1.52298e7	−	2.63787e7i	−0.307180	−	0.532052i
$159$		0			0
$160$	1.86778e6	−	3.23508e6i	0.0360500	−	0.0624404i
$161$	−6.53220e7			−1.23359
$162$		0			0
$163$	6.26659e7			1.13338			0.566689	−	0.823932i	$-0.308224\pi$
$163$	6.26659e7			1.13338			0.566689	+	0.823932i	$0.308224\pi$
$164$	2.04505e7	−	3.54213e7i	0.362035	−	0.627063i
$165$		0			0
$166$	−8.91787e6	−	1.54462e7i	−0.151315	−	0.262086i
$167$	−3.13536e7	−	5.43060e7i	−0.520931	−	0.902278i	−0.999704	−	0.0243397i	$-0.992252\pi$
$167$	−3.13536e7	−	5.43060e7i	−0.520931	−	0.902278i	0.478773	−	0.877939i	$-0.341082\pi$
$168$		0			0
$169$	2.41467e7	−	4.18232e7i	0.384816	−	0.666522i
$170$	6.02467e6			0.0940507
$171$		0			0
$172$	−1.00104e7			−0.150003
$173$	1.35261e7	−	2.34278e7i	0.198614	−	0.344010i	−0.749465	−	0.662044i	$-0.769689\pi$
$173$	1.35261e7	−	2.34278e7i	0.198614	−	0.344010i	0.948079	+	0.318034i	$0.103023\pi$
$174$		0			0
$175$	−5.13217e7	−	8.88917e7i	−0.723881	−	1.25380i
$176$	−1.50159e7	−	2.60084e7i	−0.207615	−	0.359599i
$177$		0			0
$178$	−2.39648e7	+	4.15083e7i	−0.318496	+	0.551652i
$179$	−1.34281e8			−1.74996			−0.874981	−	0.484157i	$-0.839126\pi$
$179$	−1.34281e8			−1.74996			−0.874981	+	0.484157i	$0.839126\pi$
$180$		0			0
$181$	1.14661e8			1.43727			0.718636	−	0.695386i	$-0.244767\pi$
$181$	1.14661e8			1.43727			0.718636	+	0.695386i	$0.244767\pi$
$182$	−2.39678e7	+	4.15135e7i	−0.294699	+	0.510433i
$183$		0			0
$184$	−1.06107e7	−	1.83783e7i	−0.125569	−	0.217491i
$185$	−2.07856e6	−	3.60017e6i	−0.0241358	−	0.0418045i
$186$		0			0
$187$	2.42176e7	−	4.19461e7i	0.270823	−	0.469079i
$188$	−2.77617e7			−0.304714
$189$		0			0
$190$	−2.26723e7			−0.239805
$191$	−8.18026e6	+	1.41686e7i	−0.0849474	+	0.147133i	−0.905369	−	0.424626i	$-0.860406\pi$
$191$	−8.18026e6	+	1.41686e7i	−0.0849474	+	0.147133i	0.820421	+	0.571759i	$0.193739\pi$
$192$		0			0
$193$	7.70992e7	+	1.33540e8i	0.771968	+	1.33709i	0.936483	+	0.350714i	$0.114061\pi$
$193$	7.70992e7	+	1.33540e8i	0.771968	+	1.33709i	−0.164514	+	0.986375i	$0.552606\pi$
$194$	1.62405e7	+	2.81294e7i	0.159696	+	0.276601i
$195$		0			0
$196$	−5.31275e7	+	9.20195e7i	−0.503991	+	0.872938i
$197$	8.32288e7			0.775607			0.387804	−	0.921742i	$-0.373234\pi$
$197$	8.32288e7			0.775607			0.387804	+	0.921742i	$0.373234\pi$
$198$		0			0
$199$	−7.61722e7			−0.685190			−0.342595	−	0.939483i	$-0.611306\pi$
$199$	−7.61722e7			−0.685190			−0.342595	+	0.939483i	$0.611306\pi$
$200$	1.66730e7	−	2.88785e7i	0.147370	−	0.255253i
$201$		0			0
$202$	6.91278e7	+	1.19733e8i	0.590096	+	1.02208i
$203$	−3.27887e7	−	5.67917e7i	−0.275098	−	0.476484i
$204$		0			0
$205$	−3.64274e7	+	6.30942e7i	−0.295318	+	0.511506i
$206$	−1.14898e8			−0.915755
$207$		0			0
$208$	−1.55730e7			−0.119991
$209$	−9.11368e7	+	1.57853e8i	−0.690528	+	1.19603i
$210$		0			0
$211$	−1.76223e7	−	3.05227e7i	−0.129144	−	0.223684i	0.794201	−	0.607655i	$-0.207890\pi$
$211$	−1.76223e7	−	3.05227e7i	−0.129144	−	0.223684i	−0.923345	+	0.383971i	$0.874556\pi$
$212$	−2.51545e7	−	4.35689e7i	−0.181318	−	0.314051i
$213$		0			0
$214$	−2.58176e7	+	4.47174e7i	−0.180081	+	0.311909i
$215$	1.78310e7			0.122360
$216$		0			0
$217$	−5.22476e7			−0.347102
$218$	3.53764e6	−	6.12737e6i	0.0231268	−	0.0400568i
$219$		0			0
$220$	2.67471e7	+	4.63274e7i	0.169355	+	0.293331i
$221$	−1.25580e7	−	2.17511e7i	−0.0782614	−	0.135553i
$222$		0			0
$223$	9.45657e7	−	1.63793e8i	0.571040	−	0.989070i	−0.425419	−	0.904996i	$-0.639873\pi$
$223$	9.45657e7	−	1.63793e8i	0.571040	−	0.989070i	0.996460	−	0.0840741i	$-0.0267933\pi$
$224$	−5.16424e7			−0.307000
$225$		0			0
$226$	9.70600e7			0.559320
$227$	8.80501e7	−	1.52507e8i	0.499620	−	0.865367i	−0.500380	−	0.865806i	$-0.666806\pi$
$227$	8.80501e7	−	1.52507e8i	0.499620	−	0.865367i	1.00000		0.000439095i	$0.000139768\pi$
$228$		0			0
$229$	−3.25198e7	−	5.63260e7i	−0.178947	−	0.309945i	0.762573	−	0.646902i	$-0.223936\pi$
$229$	−3.25198e7	−	5.63260e7i	−0.178947	−	0.309945i	−0.941520	+	0.336957i	$0.890602\pi$
$230$	1.89003e7	+	3.27363e7i	0.102429	+	0.177411i
$231$		0			0
$232$	1.06522e7	−	1.84501e7i	0.0560054	−	0.0970042i
$233$	−2.51319e8			−1.30160			−0.650802	−	0.759248i	$-0.725567\pi$
$233$	−2.51319e8			−1.30160			−0.650802	+	0.759248i	$0.725567\pi$
$234$		0			0
$235$	4.94505e7			0.248561
$236$	−2.38445e7	+	4.12999e7i	−0.118085	+	0.204530i
$237$		0			0
$238$	−4.16442e7	−	7.21299e7i	−0.200233	−	0.346814i
$239$	−1.06540e8	−	1.84532e8i	−0.504799	−	0.874338i	−0.999985	−	0.00555086i	$-0.998233\pi$
$239$	−1.06540e8	−	1.84532e8i	−0.504799	−	0.874338i	0.495185	−	0.868787i	$-0.335100\pi$
$240$		0			0
$241$	−1.28642e8	+	2.22814e8i	−0.592001	+	1.02538i	0.401962	+	0.915657i	$0.368329\pi$
$241$	−1.28642e8	+	2.22814e8i	−0.592001	+	1.02538i	−0.993963	+	0.109719i	$0.965005\pi$
$242$	2.74168e8			1.24355
$243$		0			0
$244$	−1.06280e8			−0.468366
$245$	9.46333e7	−	1.63910e8i	0.411114	−	0.712071i
$246$		0			0
$247$	4.72589e7	+	8.18547e7i	0.199546	+	0.345625i
$248$	−8.48691e6	−	1.46998e7i	−0.0353320	−	0.0611969i
$249$		0			0
$250$	−6.53238e7	+	1.13144e8i	−0.264412	+	0.457975i
$251$	1.23058e8			0.491193			0.245596	−	0.969372i	$-0.421016\pi$
$251$	1.23058e8			0.491193			0.245596	+	0.969372i	$0.421016\pi$
$252$		0			0
$253$	3.03897e8			1.17979
$254$	−2.74723e7	+	4.75833e7i	−0.105190	+	0.182195i
$255$		0			0
$256$	−8.38861e6	−	1.45295e7i	−0.0312500	−	0.0541266i
$257$	2.21667e8	+	3.83938e8i	0.814582	+	1.41090i	0.909627	+	0.415425i	$0.136367\pi$
$257$	2.21667e8	+	3.83938e8i	0.814582	+	1.41090i	−0.0950450	+	0.995473i	$0.530300\pi$
$258$		0			0
$259$	−2.87352e7	+	4.97708e7i	−0.102770	+	0.178002i
$260$	2.77394e7			0.0978792
$261$		0			0
$262$	−3.16166e8			−1.08608
$263$	−1.49462e8	+	2.58876e8i	−0.506625	+	0.877500i	0.493345	+	0.869833i	$0.335774\pi$
$263$	−1.49462e8	+	2.58876e8i	−0.506625	+	0.877500i	−0.999971	+	0.00766701i	$0.997559\pi$
$264$		0			0
$265$	4.48064e7	+	7.76070e7i	0.147904	+	0.256177i
$266$	1.56717e8	+	2.71443e8i	0.510542	+	0.884285i
$267$		0			0
$268$	1.05307e8	−	1.82397e8i	0.334183	−	0.578822i
$269$	2.08908e8			0.654368			0.327184	−	0.944961i	$-0.393900\pi$
$269$	2.08908e8			0.654368			0.327184	+	0.944961i	$0.393900\pi$
$270$		0			0
$271$	−1.12749e7			−0.0344129			−0.0172064	−	0.999852i	$-0.505477\pi$
$271$	−1.12749e7			−0.0344129			−0.0172064	+	0.999852i	$0.505477\pi$
$272$	1.35291e7	−	2.34331e7i	0.0407641	−	0.0706054i
$273$		0			0
$274$	−7.66963e7	−	1.32842e8i	−0.225241	−	0.390129i
$275$	2.38763e8	+	4.13549e8i	0.692313	+	1.19912i
$276$		0			0
$277$	3.29482e8	−	5.70680e8i	0.931435	−	1.61329i	0.150565	−	0.988600i	$-0.451891\pi$
$277$	3.29482e8	−	5.70680e8i	0.931435	−	1.61329i	0.780870	−	0.624693i	$-0.214776\pi$
$278$	1.05959e8			0.295789
$279$		0			0
$280$	9.19880e7			0.250425
$281$	5.25614e7	−	9.10390e7i	0.141317	−	0.244769i	−0.786676	−	0.617366i	$-0.788200\pi$
$281$	5.25614e7	−	9.10390e7i	0.141317	−	0.244769i	0.927993	+	0.372598i	$0.121533\pi$
$282$		0			0
$283$	−1.65081e8	−	2.85928e8i	−0.432956	−	0.749901i	0.564171	−	0.825658i	$-0.309196\pi$
$283$	−1.65081e8	−	2.85928e8i	−0.432956	−	0.749901i	−0.997126	+	0.0757570i	$0.975863\pi$
$284$	−1.82917e8	−	3.16821e8i	−0.473849	−	0.820730i
$285$		0			0
$286$	1.11505e8	−	1.93132e8i	0.281847	−	0.488173i
$287$	1.00719e9			2.51492
$288$		0			0
$289$	−3.66699e8			−0.893651
$290$	−1.89742e7	+	3.28642e7i	−0.0456846	+	0.0791280i
$291$		0			0
$292$	−8.51167e7	−	1.47427e8i	−0.200067	−	0.346526i
$293$	4.35501e7	+	7.54310e7i	0.101147	+	0.175192i	0.912157	−	0.409840i	$-0.134415\pi$
$293$	4.35501e7	+	7.54310e7i	0.101147	+	0.175192i	−0.811011	+	0.585032i	$0.801082\pi$
$294$		0			0
$295$	4.24730e7	−	7.35654e7i	0.0963243	−	0.166839i
$296$	−1.86706e7			−0.0418444
$297$		0			0
$298$	4.58899e8			1.00452
$299$	7.87926e7	−	1.36473e8i	0.170466	−	0.295255i
$300$		0			0
$301$	−1.23253e8	−	2.13480e8i	−0.260503	−	0.451205i
$302$	1.24349e8	+	2.15379e8i	0.259788	+	0.449965i
$303$		0			0
$304$	−5.09133e7	+	8.81844e7i	−0.103938	+	0.180026i
$305$	1.89310e8			0.382054
$306$		0			0
$307$	−3.91709e8			−0.772644			−0.386322	−	0.922364i	$-0.626255\pi$
$307$	−3.91709e8			−0.772644			−0.386322	+	0.922364i	$0.626255\pi$
$308$	3.69767e8	−	6.40456e8i	0.721109	−	1.24900i
$309$		0			0
$310$	1.51173e7	+	2.61840e7i	0.0288210	+	0.0499194i
$311$	1.02468e8	+	1.77480e8i	0.193164	+	0.334570i	0.946297	−	0.323298i	$-0.104792\pi$
$311$	1.02468e8	+	1.77480e8i	0.193164	+	0.334570i	−0.753133	+	0.657868i	$0.771458\pi$
$312$		0			0
$313$	−4.38601e8	+	7.59680e8i	−0.808471	+	1.40031i	0.105451	+	0.994424i	$0.466371\pi$
$313$	−4.38601e8	+	7.59680e8i	−0.808471	+	1.40031i	−0.913922	+	0.405889i	$0.866962\pi$
$314$	−2.70268e8			−0.492652
$315$		0			0
$316$	2.43676e8			0.434418
$317$	2.20415e8	−	3.81770e8i	0.388628	−	0.673124i	−0.603637	−	0.797259i	$-0.706282\pi$
$317$	2.20415e8	−	3.81770e8i	0.388628	−	0.673124i	0.992265	+	0.124136i	$0.0396158\pi$
$318$		0			0
$319$	1.52542e8	+	2.64211e8i	0.263101	+	0.455705i
$320$	1.49422e7	+	2.58807e7i	0.0254912	+	0.0441520i
$321$		0			0
$322$	2.61288e8	−	4.52564e8i	0.436138	−	0.755414i
$323$	−1.64225e8			−0.271163
$324$		0			0
$325$	2.47620e8			0.400124
$326$	−2.50663e8	+	4.34162e8i	−0.400709	+	0.694049i
$327$		0			0
$328$	1.63604e8	+	2.83370e8i	0.255997	+	0.443400i
$329$	−3.41815e8	−	5.92042e8i	−0.529183	−	0.916572i
$330$		0			0
$331$	−5.56115e8	+	9.63219e8i	−0.842882	+	1.45991i	0.0445664	+	0.999006i	$0.485809\pi$
$331$	−5.56115e8	+	9.63219e8i	−0.842882	+	1.45991i	−0.887448	+	0.460908i	$0.847524\pi$
$332$	1.42686e8			0.213992
$333$		0			0
$334$	5.01658e8			0.736707
$335$	−1.87578e8	+	3.24894e8i	−0.272599	+	0.472155i
$336$		0			0
$337$	−1.44099e8	−	2.49587e8i	−0.205096	−	0.355236i	0.745068	−	0.666989i	$-0.232417\pi$
$337$	−1.44099e8	−	2.49587e8i	−0.205096	−	0.355236i	−0.950163	+	0.311753i	$0.899084\pi$
$338$	1.93173e8	+	3.34586e8i	0.272106	+	0.471302i
$339$		0			0
$340$	−2.40987e7	+	4.17402e7i	−0.0332520	+	0.0575941i
$341$	2.43070e8			0.331965
$342$		0			0
$343$	−1.31862e9			−1.76438
$344$	4.00415e7	−	6.93539e7i	0.0530341	−	0.0918578i
$345$		0			0
$346$	1.08208e8	+	1.87423e8i	0.140441	+	0.243252i
$347$	5.53003e8	+	9.57830e8i	0.710517	+	1.23065i	0.964663	+	0.263486i	$0.0848722\pi$
$347$	5.53003e8	+	9.57830e8i	0.710517	+	1.23065i	−0.254146	+	0.967166i	$0.581794\pi$
$348$		0			0
$349$	6.60922e8	−	1.14475e9i	0.832264	−	1.44152i	−0.0639747	−	0.997952i	$-0.520378\pi$
$349$	6.60922e8	−	1.14475e9i	0.832264	−	1.44152i	0.896239	−	0.443572i	$-0.146289\pi$
$350$	8.21146e8			1.02372
$351$		0			0
$352$	2.40255e8			0.293612
$353$	−6.01976e8	+	1.04265e9i	−0.728396	+	1.26162i	0.229165	+	0.973388i	$0.426400\pi$
$353$	−6.01976e8	+	1.04265e9i	−0.728396	+	1.26162i	−0.957561	+	0.288231i	$0.906933\pi$
$354$		0			0
$355$	3.25821e8	+	5.64338e8i	0.386527	+	0.669484i
$356$	−1.91719e8	−	3.32067e8i	−0.225211	−	0.390077i
$357$		0			0
$358$	5.37124e8	−	9.30325e8i	0.618705	−	1.07163i
$359$	−1.32057e9			−1.50637			−0.753185	−	0.657809i	$-0.771484\pi$
$359$	−1.32057e9			−1.50637			−0.753185	+	0.657809i	$0.771484\pi$
$360$		0			0
$361$	−2.75852e8			−0.308604
$362$	−4.58642e8	+	7.94392e8i	−0.508152	+	0.880146i
$363$		0			0
$364$	−1.91742e8	−	3.32108e8i	−0.208384	−	0.360931i
$365$	1.51614e8	+	2.62603e8i	0.163198	+	0.282667i
$366$		0			0
$367$	−8.75535e8	+	1.51647e9i	−0.924575	+	1.60141i	−0.132332	+	0.991205i	$0.542247\pi$
$367$	−8.75535e8	+	1.51647e9i	−0.924575	+	1.60141i	−0.792243	+	0.610206i	$0.791087\pi$
$368$	1.69771e8			0.177581
$369$		0			0
$370$	3.32570e7			0.0341332
$371$	6.19429e8	−	1.07288e9i	0.629772	−	1.09080i
$372$		0			0
$373$	2.43973e8	+	4.22573e8i	0.243422	+	0.421620i	0.961687	−	0.274150i	$-0.0883966\pi$
$373$	2.43973e8	+	4.22573e8i	0.243422	+	0.421620i	−0.718265	+	0.695770i	$0.755063\pi$
$374$	1.93741e8	+	3.35569e8i	0.191501	+	0.331689i
$375$		0			0
$376$	1.11047e8	−	1.92338e8i	0.107733	−	0.186599i
$377$	1.58201e8			0.152060
$378$		0			0
$379$	1.11007e9			1.04740			0.523700	−	0.851903i	$-0.324551\pi$
$379$	1.11007e9			1.04740			0.523700	+	0.851903i	$0.324551\pi$
$380$	9.06893e7	−	1.57078e8i	0.0847839	−	0.146850i
$381$		0			0
$382$	−6.54420e7	−	1.13349e8i	−0.0600669	−	0.104039i
$383$	−9.34558e8	−	1.61870e9i	−0.849983	−	1.47221i	−0.881222	−	0.472702i	$-0.843279\pi$
$383$	−9.34558e8	−	1.61870e9i	−0.849983	−	1.47221i	0.0312391	−	0.999512i	$-0.490055\pi$
$384$		0			0
$385$	−6.58648e8	+	1.14081e9i	−0.588222	+	1.01883i
$386$	−1.23359e9			−1.09173
$387$		0			0
$388$	−2.59848e8			−0.225844
$389$	1.36948e8	−	2.37200e8i	0.117959	−	0.204311i	−0.801000	−	0.598665i	$-0.795698\pi$
$389$	1.36948e8	−	2.37200e8i	0.117959	−	0.204311i	0.918959	+	0.394354i	$0.129032\pi$
$390$		0			0
$391$	1.36903e8	+	2.37123e8i	0.115823	+	0.200611i
$392$	−4.25020e8	−	7.36156e8i	−0.356375	−	0.617260i
$393$		0			0
$394$	−3.32915e8	+	5.76626e8i	−0.274219	+	0.474961i
$395$	−4.34048e8			−0.354363
$396$		0			0
$397$	6.24552e8			0.500958			0.250479	−	0.968122i	$-0.419412\pi$
$397$	6.24552e8			0.500958			0.250479	+	0.968122i	$0.419412\pi$
$398$	3.04689e8	−	5.27736e8i	0.242251	−	0.419591i
$399$		0			0
$400$	1.33384e8	+	2.31028e8i	0.104206	+	0.180491i
$401$	−2.77750e8	−	4.81077e8i	−0.215104	−	0.372571i	0.738201	−	0.674581i	$-0.235676\pi$
$401$	−2.77750e8	−	4.81077e8i	−0.215104	−	0.372571i	−0.953305	+	0.302010i	$0.902342\pi$
$402$		0			0
$403$	6.30220e7	−	1.09157e8i	0.0479650	−	0.0830778i
$404$	−1.10604e9			−0.834522
$405$		0			0
$406$	5.24619e8			0.389048
$407$	1.33684e8	−	2.31548e8i	0.0982879	−	0.170240i
$408$		0			0
$409$	1.07885e9	+	1.86862e9i	0.779704	+	1.35049i	0.932112	+	0.362169i	$0.117964\pi$
$409$	1.07885e9	+	1.86862e9i	0.779704	+	1.35049i	−0.152409	+	0.988318i	$0.548703\pi$
$410$	−2.91420e8	−	5.04753e8i	−0.208822	−	0.361689i
$411$		0			0
$412$	4.59594e8	−	7.96040e8i	0.323768	−	0.560783i
$413$	−1.17434e9			−0.820293
$414$		0			0
$415$	−2.54159e8			−0.174557
$416$	6.22920e7	−	1.07893e8i	0.0424234	−	0.0734795i
$417$		0			0
$418$	−7.29094e8	−	1.26283e9i	−0.488277	−	0.845721i
$419$	−8.38984e8	−	1.45316e9i	−0.557191	−	0.965084i	−0.997729	−	0.0673500i	$-0.978546\pi$
$419$	−8.38984e8	−	1.45316e9i	−0.557191	−	0.965084i	0.440538	−	0.897734i	$-0.354788\pi$
$420$		0			0
$421$	2.62617e8	−	4.54866e8i	0.171528	−	0.297095i	−0.767426	−	0.641137i	$-0.778463\pi$
$421$	2.62617e8	−	4.54866e8i	0.171528	−	0.297095i	0.938954	+	0.344042i	$0.111796\pi$
$422$	2.81957e8			0.182637
$423$		0			0
$424$	4.02472e8			0.256422
$425$	−2.15121e8	+	3.72601e8i	−0.135932	+	0.235441i
$426$		0			0
$427$	−1.30857e9	−	2.26650e9i	−0.813389	−	1.40883i
$428$	−2.06541e8	−	3.57739e8i	−0.127337	−	0.220553i
$429$		0			0
$430$	−7.13239e7	+	1.23537e8i	−0.0432609	+	0.0749300i
$431$	1.70593e8			0.102634			0.0513169	−	0.998682i	$-0.483658\pi$
$431$	1.70593e8			0.102634			0.0513169	+	0.998682i	$0.483658\pi$
$432$		0			0
$433$	−1.68797e9			−0.999210			−0.499605	−	0.866253i	$-0.666522\pi$
$433$	−1.68797e9			−0.999210			−0.499605	+	0.866253i	$0.666522\pi$
$434$	2.08990e8	−	3.61982e8i	0.122719	−	0.212556i
$435$		0			0
$436$	2.83011e7	+	4.90190e7i	0.0163531	+	0.0283245i
$437$	−5.15199e8	−	8.92350e8i	−0.295318	−	0.511505i
$438$		0			0
$439$	5.89248e8	−	1.02061e9i	0.332409	−	0.575749i	−0.650575	−	0.759442i	$-0.725472\pi$
$439$	5.89248e8	−	1.02061e9i	0.332409	−	0.575749i	0.982984	+	0.183693i	$0.0588053\pi$
$440$	−4.27954e8			−0.239504
$441$		0			0
$442$	2.00928e8			0.110678
$443$	−3.57877e8	+	6.19862e8i	−0.195579	+	0.338752i	−0.947090	−	0.320968i	$-0.895992\pi$
$443$	−3.57877e8	+	6.19862e8i	−0.195579	+	0.338752i	0.751511	+	0.659720i	$0.229325\pi$
$444$		0			0
$445$	3.41499e8	+	5.91494e8i	0.183709	+	0.318193i
$446$	7.56526e8	+	1.31034e9i	0.403786	+	0.699378i
$447$		0			0
$448$	2.06569e8	−	3.57789e8i	0.108541	−	0.187998i
$449$	−1.37358e9			−0.716132			−0.358066	−	0.933696i	$-0.616564\pi$
$449$	−1.37358e9			−0.716132			−0.358066	+	0.933696i	$0.616564\pi$
$450$		0			0
$451$	−4.68572e9			−2.40524
$452$	−3.88240e8	+	6.72451e8i	−0.197750	+	0.342512i
$453$		0			0
$454$	7.04401e8	+	1.22006e9i	0.353284	+	0.611907i
$455$	3.41541e8	+	5.91567e8i	0.169982	+	0.294418i
$456$		0			0
$457$	−9.23760e8	+	1.60000e9i	−0.452744	+	0.784175i	−0.998555	−	0.0537327i	$-0.982888\pi$
$457$	−9.23760e8	+	1.60000e9i	−0.452744	+	0.784175i	0.545812	+	0.837908i	$0.316221\pi$
$458$	5.20317e8			0.253069
$459$		0			0
$460$	−3.02405e8			−0.144856
$461$	−1.54707e9	+	2.67960e9i	−0.735455	+	1.27385i	0.219068	+	0.975710i	$0.429698\pi$
$461$	−1.54707e9	+	2.67960e9i	−0.735455	+	1.27385i	−0.954523	+	0.298136i	$0.903635\pi$
$462$		0			0
$463$	−1.50225e9	−	2.60198e9i	−0.703412	−	1.21835i	−0.967261	−	0.253782i	$-0.918325\pi$
$463$	−1.50225e9	−	2.60198e9i	−0.703412	−	1.21835i	0.263849	−	0.964564i	$-0.415008\pi$
$464$	8.52173e7	+	1.47601e8i	0.0396018	+	0.0685923i
$465$		0			0
$466$	1.00527e9	−	1.74119e9i	0.460186	−	0.797066i
$467$	−2.99252e9			−1.35965			−0.679825	−	0.733374i	$-0.737944\pi$
$467$	−2.99252e9			−1.35965			−0.679825	+	0.733374i	$0.737944\pi$
$468$		0			0
$469$	5.18636e9			2.32144
$470$	−1.97802e8	+	3.42603e8i	−0.0878796	+	0.152212i
$471$		0			0
$472$	−1.90756e8	−	3.30399e8i	−0.0834989	−	0.144624i
$473$	5.73406e8	+	9.93169e8i	0.249143	+	0.431528i
$474$		0			0
$475$	8.09553e8	−	1.40219e9i	0.346591	−	0.600314i
$476$	6.66308e8			0.283172
$477$		0			0
$478$	1.70464e9			0.713894
$479$	−9.20207e8	+	1.59385e9i	−0.382570	+	0.662631i	−0.991429	−	0.130647i	$-0.958294\pi$
$479$	−9.20207e8	+	1.59385e9i	−0.382570	+	0.662631i	0.608858	+	0.793279i	$0.291628\pi$
$480$		0			0
$481$	−6.93219e7	−	1.20069e8i	−0.0284029	−	0.0491952i
$482$	−1.02913e9	−	1.78251e9i	−0.418608	−	0.725050i
$483$		0			0
$484$	−1.09667e9	+	1.89949e9i	−0.439662	+	0.761516i
$485$	4.62854e8			0.184225
$486$		0			0
$487$	−4.26676e8			−0.167397			−0.0836983	−	0.996491i	$-0.526673\pi$
$487$	−4.26676e8			−0.167397			−0.0836983	+	0.996491i	$0.526673\pi$
$488$	4.25118e8	−	7.36326e8i	0.165592	−	0.286814i
$489$		0			0
$490$	7.57066e8	+	1.31128e9i	0.290702	+	0.503510i
$491$	−3.03773e7	−	5.26151e7i	−0.0115815	−	0.0200597i	0.860177	−	0.509996i	$-0.170353\pi$
$491$	−3.03773e7	−	5.26151e7i	−0.0115815	−	0.0200597i	−0.871758	+	0.489937i	$0.837020\pi$
$492$		0			0
$493$	−1.37438e8	+	2.38049e8i	−0.0516585	+	0.0894752i
$494$	−7.56142e8			−0.282201
$495$		0			0
$496$	1.35791e8			0.0499671
$497$	4.50433e9	−	7.80172e9i	1.64582	−	2.85065i
$498$		0			0
$499$	−1.62294e9	−	2.81101e9i	−0.584723	−	1.01277i	−0.994910	−	0.100769i	$-0.967870\pi$
$499$	−1.62294e9	−	2.81101e9i	−0.584723	−	1.01277i	0.410187	−	0.912002i	$-0.365463\pi$
$500$	−5.22591e8	−	9.05153e8i	−0.186968	−	0.323838i
$501$		0			0
$502$	−4.92232e8	+	8.52571e8i	−0.173663	+	0.300793i
$503$	−7.44381e8			−0.260800			−0.130400	−	0.991461i	$-0.541626\pi$
$503$	−7.44381e8			−0.260800			−0.130400	+	0.991461i	$0.541626\pi$
$504$		0			0
$505$	1.97014e9			0.680734
$506$	−1.21559e9	+	2.10546e9i	−0.417118	+	0.722470i
$507$		0			0
$508$	−2.19778e8	−	3.80667e8i	−0.0743809	−	0.128831i
$509$	2.22078e8	+	3.84650e8i	0.0746436	+	0.129287i	0.900931	−	0.433962i	$-0.142885\pi$
$509$	2.22078e8	+	3.84650e8i	0.0746436	+	0.129287i	−0.826288	+	0.563248i	$0.809551\pi$
$510$		0			0
$511$	2.09600e9	−	3.63038e9i	0.694893	−	1.20359i
$512$	1.34218e8			0.0441942
$513$		0			0
$514$	−3.54667e9			−1.15199
$515$	−8.18652e8	+	1.41795e9i	−0.264103	+	0.457440i
$516$		0			0
$517$	1.59022e9	+	2.75435e9i	0.506106	+	0.876600i
$518$	−2.29882e8	−	3.98167e8i	−0.0726692	−	0.125867i
$519$		0			0
$520$	−1.10958e8	+	1.92184e8i	−0.0346055	+	0.0599385i
$521$	3.04963e9			0.944745			0.472372	−	0.881399i	$-0.343398\pi$
$521$	3.04963e9			0.944745			0.472372	+	0.881399i	$0.343398\pi$
$522$		0			0
$523$	−1.40306e9			−0.428866			−0.214433	−	0.976739i	$-0.568790\pi$
$523$	−1.40306e9			−0.428866			−0.214433	+	0.976739i	$0.568790\pi$
$524$	1.26467e9	−	2.19046e9i	0.383987	−	0.665084i
$525$		0			0
$526$	−1.19570e9	−	2.07101e9i	−0.358238	−	0.620487i
$527$	1.09501e8	+	1.89661e8i	0.0325898	+	0.0564471i
$528$		0			0
$529$	8.43444e8	−	1.46089e9i	0.247720	−	0.429064i
$530$	−7.16903e8			−0.209168
$531$		0			0
$532$	−2.50748e9			−0.722016
$533$	−1.21489e9	+	2.10425e9i	−0.347529	+	0.601937i
$534$		0			0
$535$	3.67901e8	+	6.37223e8i	0.103871	+	0.179909i
$536$	8.42454e8	+	1.45917e9i	0.236303	+	0.409289i
$537$		0			0
$538$	−8.35632e8	+	1.44736e9i	−0.231354	+	0.400717i
$539$	1.21728e10			3.34835
$540$		0			0
$541$	4.21106e9			1.14341			0.571704	−	0.820460i	$-0.306283\pi$
$541$	4.21106e9			1.14341			0.571704	+	0.820460i	$0.306283\pi$
$542$	4.50997e7	−	7.81150e7i	0.0121668	−	0.0210735i
$543$		0			0
$544$	1.08233e8	+	1.87465e8i	0.0288245	+	0.0499256i
$545$	−5.04114e7	−	8.73151e7i	−0.0133395	−	0.0231048i
$546$		0			0
$547$	−9.99780e8	+	1.73167e9i	−0.261185	+	0.452386i	−0.966557	−	0.256451i	$-0.917447\pi$
$547$	−9.99780e8	+	1.73167e9i	−0.261185	+	0.452386i	0.705372	+	0.708837i	$0.250780\pi$
$548$	1.22714e9			0.318539
$549$		0			0
$550$	−3.82021e9			−0.979078
$551$	5.17212e8	−	8.95838e8i	0.131716	−	0.228139i
$552$		0			0
$553$	3.00026e9	+	5.19661e9i	0.754434	+	1.30672i
$554$	2.63586e9	+	4.56544e9i	0.658624	+	1.14077i
$555$		0			0
$556$	−4.23837e8	+	7.34107e8i	−0.104577	+	0.181133i
$557$	−3.37403e9			−0.827287			−0.413643	−	0.910439i	$-0.635744\pi$
$557$	−3.37403e9			−0.827287			−0.413643	+	0.910439i	$0.635744\pi$
$558$		0			0
$559$	5.94678e8			0.143993
$560$	−3.67952e8	+	6.37311e8i	−0.0885387	+	0.153353i
$561$		0			0
$562$	4.20491e8	+	7.28312e8i	0.0999263	+	0.173077i
$563$	2.79011e9	+	4.83261e9i	0.658933	+	1.14131i	0.980892	+	0.194552i	$0.0623254\pi$
$563$	2.79011e9	+	4.83261e9i	0.658933	+	1.14131i	−0.321959	+	0.946754i	$0.604341\pi$
$564$		0			0
$565$	6.91552e8	−	1.19780e9i	0.161308	−	0.279393i
$566$	2.64129e9			0.612292
$567$		0			0
$568$	2.92667e9			0.670123
$569$	4.44155e8	−	7.69299e8i	0.101074	−	0.175066i	−0.811053	−	0.584972i	$-0.801105\pi$
$569$	4.44155e8	−	7.69299e8i	0.101074	−	0.175066i	0.912128	+	0.409906i	$0.134439\pi$
$570$		0			0
$571$	8.95853e8	+	1.55166e9i	0.201377	+	0.348796i	0.948972	−	0.315359i	$-0.102125\pi$
$571$	8.95853e8	+	1.55166e9i	0.201377	+	0.348796i	−0.747595	+	0.664155i	$0.768792\pi$
$572$	8.92040e8	+	1.54506e9i	0.199296	+	0.345191i
$573$		0			0
$574$	−4.02875e9	+	6.97800e9i	−0.889157	+	1.54007i
$575$	−2.69947e9			−0.592162
$576$		0			0
$577$	3.82103e9			0.828066			0.414033	−	0.910262i	$-0.364120\pi$
$577$	3.82103e9			0.828066			0.414033	+	0.910262i	$0.364120\pi$
$578$	1.46680e9	−	2.54057e9i	0.315953	−	0.547247i
$579$		0			0
$580$	−1.51793e8	−	2.62914e8i	−0.0323039	−	0.0559519i
$581$	1.75682e9	+	3.04290e9i	0.371630	+	0.643682i
$582$		0			0
$583$	−2.88176e9	+	4.99136e9i	−0.602307	+	1.04323i
$584$	1.36187e9			0.282937
$585$		0			0
$586$	−6.96802e8			−0.143043
$587$	−2.18109e9	+	3.77777e9i	−0.445083	+	0.770907i	−0.998058	−	0.0622913i	$-0.980159\pi$
$587$	−2.18109e9	+	3.77777e9i	−0.445083	+	0.770907i	0.552975	+	0.833198i	$0.313493\pi$
$588$		0			0
$589$	−4.12079e8	−	7.13742e8i	−0.0830955	−	0.143926i
$590$	3.39784e8	+	5.88523e8i	0.0681115	+	0.117973i
$591$		0			0
$592$	7.46824e7	−	1.29354e8i	0.0147942	−	0.0256243i
$593$	6.38531e9			1.25745			0.628724	−	0.777628i	$-0.283577\pi$
$593$	6.38531e9			1.25745			0.628724	+	0.777628i	$0.283577\pi$
$594$		0			0
$595$	−1.18686e9			−0.230988
$596$	−1.83560e9	+	3.17935e9i	−0.355153	+	0.615143i
$597$		0			0
$598$	6.30341e8	+	1.09178e9i	0.120537	+	0.208777i
$599$	−4.02148e8	−	6.96542e8i	−0.0764527	−	0.132420i	0.825264	−	0.564747i	$-0.191026\pi$
$599$	−4.02148e8	−	6.96542e8i	−0.0764527	−	0.132420i	−0.901717	+	0.432327i	$0.857693\pi$
$600$		0			0
$601$	2.43581e9	−	4.21894e9i	0.457702	−	0.792762i	−0.541137	−	0.840934i	$-0.682006\pi$
$601$	2.43581e9	−	4.21894e9i	0.457702	−	0.792762i	0.998839	+	0.0481717i	$0.0153395\pi$
$602$	1.97204e9			0.368408
$603$		0			0
$604$	−1.98959e9			−0.367395
$605$	1.95345e9	−	3.38347e9i	0.358640	−	0.621182i
$606$		0			0
$607$	−3.58758e9	−	6.21388e9i	−0.651091	−	1.12772i	−0.982859	−	0.184361i	$-0.940978\pi$
$607$	−3.58758e9	−	6.21388e9i	−0.651091	−	1.12772i	0.331768	−	0.943361i	$-0.392355\pi$
$608$	−4.07306e8	−	7.05475e8i	−0.0734951	−	0.127297i
$609$		0			0
$610$	−7.57242e8	+	1.31158e9i	−0.135077	+	0.233960i
$611$	1.64922e9			0.292505
$612$		0			0
$613$	3.47891e9			0.610002			0.305001	−	0.952352i	$-0.401343\pi$
$613$	3.47891e9			0.610002			0.305001	+	0.952352i	$0.401343\pi$
$614$	1.56684e9	−	2.71384e9i	0.273171	−	0.473146i
$615$		0			0
$616$	2.95814e9	+	5.12365e9i	0.509901	+	0.883175i
$617$	1.19689e8	+	2.07308e8i	0.0205143	+	0.0355318i	0.876100	−	0.482129i	$-0.160136\pi$
$617$	1.19689e8	+	2.07308e8i	0.0205143	+	0.0355318i	−0.855586	+	0.517661i	$0.826803\pi$
$618$		0			0
$619$	2.76479e9	−	4.78876e9i	0.468539	−	0.811533i	−0.530815	−	0.847488i	$-0.678114\pi$
$619$	2.76479e9	−	4.78876e9i	0.468539	−	0.811533i	0.999353	+	0.0359550i	$0.0114473\pi$
$620$	−2.41877e8			−0.0407590
$621$		0			0
$622$	−1.63949e9			−0.273175
$623$	4.72107e9	−	8.17714e9i	0.782227	−	1.35486i
$624$		0			0
$625$	−1.61324e9	−	2.79421e9i	−0.264313	−	0.457803i
$626$	−3.50881e9	−	6.07744e9i	−0.571676	−	0.990171i
$627$		0			0
$628$	1.08107e9	−	1.87247e9i	0.174179	−	0.301687i
$629$	2.40894e8			0.0385966
$630$		0			0
$631$	−6.13683e9			−0.972392			−0.486196	−	0.873850i	$-0.661616\pi$
$631$	−6.13683e9			−0.972392			−0.486196	+	0.873850i	$0.661616\pi$
$632$	−9.74705e8	+	1.68824e9i	−0.153590	+	0.266026i
$633$		0			0
$634$	1.76332e9	+	3.05416e9i	0.274802	+	0.475970i
$635$	3.91480e8	+	6.78063e8i	0.0606738	+	0.105090i
$636$		0			0
$637$	3.15610e9	−	5.46653e9i	0.483797	−	0.837961i
$638$	−2.44068e9			−0.372081
$639$		0			0
$640$	−2.39075e8			−0.0360500
$641$	−5.35190e9	+	9.26976e9i	−0.802611	+	1.39016i	0.115282	+	0.993333i	$0.463223\pi$
$641$	−5.35190e9	+	9.26976e9i	−0.802611	+	1.39016i	−0.917892	+	0.396830i	$0.870110\pi$
$642$		0			0
$643$	6.99013e8	+	1.21073e9i	0.103692	+	0.179601i	0.913203	−	0.407504i	$-0.133601\pi$
$643$	6.99013e8	+	1.21073e9i	0.103692	+	0.179601i	−0.809511	+	0.587105i	$0.800268\pi$
$644$	2.09031e9	+	3.62052e9i	0.308396	+	0.534158i
$645$		0			0
$646$	6.56901e8	−	1.13779e9i	0.0958707	−	0.166053i
$647$	−5.31605e9			−0.771656			−0.385828	−	0.922571i	$-0.626084\pi$
$647$	−5.31605e9			−0.771656			−0.385828	+	0.922571i	$0.626084\pi$
$648$		0			0
$649$	5.46337e9			0.784520
$650$	−9.90482e8	+	1.71556e9i	−0.141465	+	0.245025i
$651$		0			0
$652$	−2.00531e9	−	3.47329e9i	−0.283344	−	0.490767i
$653$	−1.62202e9	−	2.80942e9i	−0.227960	−	0.394839i	0.729243	−	0.684255i	$-0.239872\pi$
$653$	−1.62202e9	−	2.80942e9i	−0.227960	−	0.394839i	−0.957203	+	0.289416i	$0.906539\pi$
$654$		0			0
$655$	−2.25268e9	+	3.90176e9i	−0.313225	+	0.542521i
$656$	−2.61766e9			−0.362035
$657$		0			0
$658$	5.46905e9			0.748378
$659$	2.58253e9	−	4.47307e9i	0.351517	−	0.608845i	−0.634998	−	0.772513i	$-0.718999\pi$
$659$	2.58253e9	−	4.47307e9i	0.351517	−	0.608845i	0.986515	+	0.163668i	$0.0523326\pi$
$660$		0			0
$661$	1.61258e9	+	2.79307e9i	0.217178	+	0.376163i	0.953944	−	0.299985i	$-0.0969815\pi$
$661$	1.61258e9	+	2.79307e9i	0.217178	+	0.376163i	−0.736766	+	0.676147i	$0.763648\pi$
$662$	−4.44892e9	−	7.70576e9i	−0.596007	−	1.03232i
$663$		0			0
$664$	−5.70744e8	+	9.88557e8i	−0.0756577	+	0.131043i
$665$	4.46645e9			0.588961
$666$		0			0
$667$	−1.72465e9			−0.225041
$668$	−2.00663e9	+	3.47559e9i	−0.260465	+	0.451139i
$669$		0			0
$670$	−1.50062e9	−	2.59915e9i	−0.192757	−	0.333864i
$671$	6.08783e9	+	1.05444e10i	0.777917	+	1.34739i
$672$		0			0
$673$	1.00317e9	−	1.73754e9i	0.126859	−	0.219726i	−0.795599	−	0.605823i	$-0.792844\pi$
$673$	1.00317e9	−	1.73754e9i	0.126859	−	0.219726i	0.922458	+	0.386097i	$0.126177\pi$
$674$	2.30559e9			0.290049
$675$		0			0
$676$	−3.09077e9			−0.384816
$677$	−5.01055e9	+	8.67853e9i	−0.620619	+	1.07494i	0.368751	+	0.929528i	$0.379785\pi$
$677$	−5.01055e9	+	8.67853e9i	−0.620619	+	1.07494i	−0.989371	+	0.145416i	$0.953548\pi$
$678$		0			0
$679$	−3.19938e9	−	5.54149e9i	−0.392213	−	0.679332i
$680$	−1.92790e8	−	3.33921e8i	−0.0235127	−	0.0407252i
$681$		0			0
$682$	−9.72282e8	+	1.68404e9i	−0.117367	+	0.203286i
$683$	−5.84861e9			−0.702393			−0.351196	−	0.936302i	$-0.614225\pi$
$683$	−5.84861e9			−0.702393			−0.351196	+	0.936302i	$0.614225\pi$
$684$		0			0
$685$	−2.18584e9			−0.259838
$686$	5.27449e9	−	9.13569e9i	0.623801	−	1.08046i
$687$		0			0
$688$	3.20332e8	+	5.54831e8i	0.0375008	+	0.0649533i
$689$	1.49433e9	+	2.58826e9i	0.174053	+	0.301468i
$690$		0			0
$691$	−1.29343e9	+	2.24028e9i	−0.149131	+	0.258303i	−0.930907	−	0.365257i	$-0.880981\pi$
$691$	−1.29343e9	+	2.24028e9i	−0.149131	+	0.258303i	0.781775	+	0.623560i	$0.214314\pi$
$692$	−1.73134e9			−0.198614
$693$		0			0
$694$	−8.84805e9			−1.00482
$695$	7.54959e8	−	1.30763e9i	0.0853054	−	0.147753i
$696$		0			0
$697$	−2.11087e9	−	3.65614e9i	−0.236128	−	0.408986i
$698$	5.28737e9	+	9.15800e9i	0.588500	+	1.01931i
$699$		0			0
$700$	−3.28459e9	+	5.68907e9i	−0.361941	+	0.626900i
$701$	−1.74460e9			−0.191286			−0.0956429	−	0.995416i	$-0.530491\pi$
$701$	−1.74460e9			−0.191286			−0.0956429	+	0.995416i	$0.530491\pi$
$702$		0			0
$703$	−9.06545e8			−0.0984114
$704$	−9.61020e8	+	1.66454e9i	−0.103807	+	0.179800i
$705$		0			0
$706$	−4.81580e9	−	8.34122e9i	−0.515054	−	0.892099i
$707$	−1.36182e10	−	2.35874e10i	−1.44927	−	2.51022i
$708$		0			0
$709$	5.60254e9	−	9.70388e9i	0.590368	−	1.02255i	−0.403814	−	0.914841i	$-0.632316\pi$
$709$	5.60254e9	−	9.70388e9i	0.590368	−	1.02255i	0.994183	−	0.107707i	$-0.0343508\pi$
$710$	−5.21313e9			−0.546631
$711$		0			0
$712$	3.06750e9			0.318496
$713$	−6.87042e8	+	1.18999e9i	−0.0709856	+	0.122951i
$714$		0			0
$715$	−1.58895e9	−	2.75214e9i	−0.162569	−	0.281578i
$716$	4.29699e9	+	7.44260e9i	0.437491	+	0.757756i
$717$		0			0
$718$	5.28229e9	−	9.14919e9i	0.532582	−	0.922460i
$719$	−9.36568e8			−0.0939698			−0.0469849	−	0.998896i	$-0.514961\pi$
$719$	−9.36568e8			−0.0939698			−0.0469849	+	0.998896i	$0.514961\pi$
$720$		0			0
$721$	2.26350e10			2.24909
$722$	1.10341e9	−	1.91116e9i	0.109108	−	0.188980i
$723$		0			0
$724$	−3.66914e9	−	6.35513e9i	−0.359318	−	0.622357i
$725$	−1.35501e9	−	2.34694e9i	−0.132056	−	0.228728i
$726$		0			0
$727$	−2.10223e9	+	3.64116e9i	−0.202913	+	0.351455i	−0.949466	−	0.313871i	$-0.898374\pi$
$727$	−2.10223e9	+	3.64116e9i	−0.202913	+	0.351455i	0.746553	+	0.665326i	$0.231707\pi$
$728$	3.06788e9			0.294699
$729$		0			0
$730$	−2.42583e9			−0.230797
$731$	−5.16629e8	+	8.94827e8i	−0.0489179	+	0.0847283i
$732$		0			0
$733$	5.77457e9	+	1.00018e10i	0.541571	+	0.938029i	0.998814	+	0.0486872i	$0.0155037\pi$
$733$	5.77457e9	+	1.00018e10i	0.541571	+	0.938029i	−0.457243	+	0.889342i	$0.651163\pi$
$734$	−7.00428e9	−	1.21318e10i	−0.653773	−	1.13237i
$735$		0			0
$736$	−6.79084e8	+	1.17621e9i	−0.0627843	+	0.108746i
$737$	−2.41284e10			−2.22020
$738$		0			0
$739$	−1.39655e10			−1.27292			−0.636460	−	0.771310i	$-0.719602\pi$
$739$	−1.39655e10			−1.27292			−0.636460	+	0.771310i	$0.719602\pi$
$740$	−1.33028e8	+	2.30411e8i	−0.0120679	+	0.0209022i
$741$		0			0
$742$	4.95544e9	+	8.58307e9i	0.445316	+	0.771310i
$743$	−7.19162e9	−	1.24563e10i	−0.643230	−	1.11411i	−0.984707	−	0.174217i	$-0.944261\pi$
$743$	−7.19162e9	−	1.24563e10i	−0.643230	−	1.11411i	0.341478	−	0.939890i	$-0.389073\pi$
$744$		0			0
$745$	3.26966e9	−	5.66321e9i	0.289705	−	0.501783i
$746$	−3.90356e9			−0.344251
$747$		0			0
$748$	−3.09985e9			−0.270823
$749$	5.08607e9	−	8.80933e9i	0.442279	−	0.766049i
$750$		0			0
$751$	3.35420e8	+	5.80965e8i	0.0288968	+	0.0500507i	0.880112	−	0.474766i	$-0.157467\pi$
$751$	3.35420e8	+	5.80965e8i	0.0288968	+	0.0500507i	−0.851215	+	0.524817i	$0.824134\pi$
$752$	8.88373e8	+	1.53871e9i	0.0761786	+	0.131945i
$753$		0			0
$754$	−6.32805e8	+	1.09605e9i	−0.0537613	+	0.0931174i
$755$	3.54395e9			0.299691
$756$		0			0
$757$	−1.91569e10			−1.60506			−0.802529	−	0.596613i	$-0.796513\pi$
$757$	−1.91569e10			−1.60506			−0.802529	+	0.596613i	$0.796513\pi$
$758$	−4.44027e9	+	7.69078e9i	−0.370312	+	0.641399i
$759$		0			0
$760$	7.25514e8	+	1.25663e9i	0.0599513	+	0.103839i
$761$	−8.95599e9	−	1.55122e10i	−0.736660	−	1.27593i	−0.953991	−	0.299835i	$-0.903068\pi$
$761$	−8.95599e9	−	1.55122e10i	−0.736660	−	1.27593i	0.217331	−	0.976098i	$-0.430265\pi$
$762$		0			0
$763$	−6.96915e8	+	1.20709e9i	−0.0567994	+	0.0983795i
$764$	1.04707e9			0.0849474
$765$		0			0
$766$	1.49529e10			1.20206
$767$	1.41651e9	−	2.45347e9i	0.113354	−	0.196335i
$768$		0			0
$769$	1.07036e10	+	1.85392e10i	0.848765	+	1.47010i	0.882311	+	0.470666i	$0.155986\pi$
$769$	1.07036e10	+	1.85392e10i	0.848765	+	1.47010i	−0.0335468	+	0.999437i	$0.510680\pi$
$770$	−5.26919e9	−	9.12650e9i	−0.415935	−	0.720421i
$771$		0			0
$772$	4.93435e9	−	8.54655e9i	0.385984	−	0.668544i
$773$	−7.55163e8			−0.0588047			−0.0294024	−	0.999568i	$-0.509360\pi$
$773$	−7.55163e8			−0.0588047			−0.0294024	+	0.999568i	$0.509360\pi$
$774$		0			0
$775$	−2.15916e9			−0.166620
$776$	1.03939e9	−	1.80028e9i	0.0798479	−	0.138301i
$777$		0			0
$778$	1.09558e9	+	1.89760e9i	0.0834096	+	0.144470i
$779$	7.94374e9	+	1.37590e10i	0.602066	+	1.04281i
$780$		0			0
$781$	−2.09554e10	+	3.62958e10i	−1.57405	+	2.72633i
$782$	−2.19044e9			−0.163798
$783$		0			0
$784$	6.80031e9			0.503991
$785$	−1.92566e9	+	3.33534e9i	−0.142081	+	0.246091i
$786$		0			0
$787$	−1.02333e10	−	1.77245e10i	−0.748347	−	1.29617i	−0.948615	−	0.316434i	$-0.897515\pi$
$787$	−1.02333e10	−	1.77245e10i	−0.748347	−	1.29617i	0.200268	−	0.979741i	$-0.435819\pi$
$788$	−2.66332e9	−	4.61301e9i	−0.193902	−	0.335848i
$789$		0			0
$790$	1.73619e9	−	3.00717e9i	0.125286	−	0.217002i
$791$	−1.91208e10			−1.37369
$792$		0			0
$793$	6.31367e9			0.449599
$794$	−2.49821e9	+	4.32702e9i	−0.177116	+	0.306773i
$795$		0			0
$796$	2.43751e9	+	4.22189e9i	0.171297	+	0.296696i
$797$	5.15489e9	+	8.92853e9i	0.360674	+	0.624706i	0.988072	−	0.153993i	$-0.0492133\pi$
$797$	5.15489e9	+	8.92853e9i	0.360674	+	0.624706i	−0.627398	+	0.778699i	$0.715880\pi$
$798$		0			0
$799$	−1.43276e9	+	2.48162e9i	−0.0993712	+	0.172116i
$800$	−2.13415e9			−0.147370
$801$		0			0
$802$	4.44400e9			0.304203
$803$	−9.75119e9	+	1.68895e10i	−0.664589	+	1.15110i
$804$		0			0
$805$	−3.72336e9	−	6.44904e9i	−0.251564	−	0.435722i
$806$	5.04176e8	+	8.73258e8i	0.0339164	+	0.0587449i
$807$		0			0
$808$	4.42418e9	−	7.66290e9i	0.295048	−	0.511038i
$809$	−4.16428e8			−0.0276516			−0.0138258	−	0.999904i	$-0.504401\pi$
$809$	−4.16428e8			−0.0276516			−0.0138258	+	0.999904i	$0.504401\pi$
$810$		0			0
$811$	−5.82687e9			−0.383586			−0.191793	−	0.981435i	$-0.561430\pi$
$811$	−5.82687e9			−0.383586			−0.191793	+	0.981435i	$0.561430\pi$
$812$	−2.09848e9	+	3.63467e9i	−0.137549	+	0.238242i
$813$		0			0
$814$	1.06947e9	+	1.85238e9i	0.0695001	+	0.120378i
$815$	3.57195e9	+	6.18681e9i	0.231129	+	0.400327i
$816$		0			0
$817$	1.94420e9	−	3.36746e9i	0.124728	−	0.216035i
$818$	−1.72616e10			−1.10267
$819$		0			0
$820$	4.66271e9			0.295318
$821$	1.04166e10	−	1.80421e10i	0.656941	−	1.13786i	−0.324462	−	0.945899i	$-0.605183\pi$
$821$	1.04166e10	−	1.80421e10i	0.656941	−	1.13786i	0.981403	−	0.191957i	$-0.0614833\pi$
$822$		0			0
$823$	−2.11701e9	−	3.66677e9i	−0.132381	−	0.229290i	0.792213	−	0.610244i	$-0.208929\pi$
$823$	−2.11701e9	−	3.66677e9i	−0.132381	−	0.229290i	−0.924594	+	0.380955i	$0.875595\pi$
$824$	3.67675e9	+	6.36832e9i	0.228939	+	0.396533i
$825$		0			0
$826$	4.69736e9	−	8.13607e9i	0.290017	−	0.502325i
$827$	5.70597e9			0.350800			0.175400	−	0.984497i	$-0.443878\pi$
$827$	5.70597e9			0.350800			0.175400	+	0.984497i	$0.443878\pi$
$828$		0			0
$829$	2.51612e10			1.53388			0.766940	−	0.641719i	$-0.221779\pi$
$829$	2.51612e10			1.53388			0.766940	+	0.641719i	$0.221779\pi$
$830$	1.01664e9	−	1.76087e9i	0.0617153	−	0.106894i
$831$		0			0
$832$	4.98336e8	+	8.63143e8i	0.0299979	+	0.0519578i
$833$	5.48375e9	+	9.49813e9i	0.328715	+	0.569352i
$834$		0			0
$835$	3.57431e9	−	6.19089e9i	0.212466	−	0.368002i
$836$	1.16655e10			0.690528
$837$		0			0
$838$	1.34237e10			0.787988
$839$	−1.13524e10	+	1.96629e10i	−0.663622	+	1.14943i	0.316035	+	0.948748i	$0.397648\pi$
$839$	−1.13524e10	+	1.96629e10i	−0.663622	+	1.14943i	−0.979657	+	0.200679i	$0.935685\pi$
$840$		0			0
$841$	7.75924e9	+	1.34394e10i	0.449814	+	0.779101i
$842$	2.10093e9	+	3.63892e9i	0.121289	+	0.210078i
$843$		0			0
$844$	−1.12783e9	+	1.95345e9i	−0.0645719	+	0.111842i
$845$	5.50544e9			0.313901
$846$		0			0
$847$	−5.40112e10			−3.05416
$848$	−1.60989e9	+	2.78841e9i	−0.0906588	+	0.157026i
$849$		0			0
$850$	−1.72097e9	−	2.98081e9i	−0.0961184	−	0.166482i
$851$	7.55721e8	+	1.30895e9i	0.0420347	+	0.0728063i
$852$		0			0
$853$	−1.43436e10	+	2.48439e10i	−0.791292	+	1.37056i	0.133875	+	0.990998i	$0.457258\pi$
$853$	−1.43436e10	+	2.48439e10i	−0.791292	+	1.37056i	−0.925167	+	0.379560i	$0.876075\pi$
$854$	2.09371e10			1.15031
$855$		0			0
$856$	3.30465e9			0.180081
$857$	−2.67475e9	+	4.63280e9i	−0.145161	+	0.251426i	−0.929433	−	0.368991i	$-0.879703\pi$
$857$	−2.67475e9	+	4.63280e9i	−0.145161	+	0.251426i	0.784272	+	0.620417i	$0.213037\pi$
$858$		0			0
$859$	7.01649e9	+	1.21529e10i	0.377697	+	0.654191i	0.990727	−	0.135869i	$-0.0433827\pi$
$859$	7.01649e9	+	1.21529e10i	0.377697	+	0.654191i	−0.613030	+	0.790060i	$0.710049\pi$
$860$	−5.70591e8	−	9.88293e8i	−0.0305901	−	0.0529835i
$861$		0			0
$862$	−6.82372e8	+	1.18190e9i	−0.0362865	+	0.0628501i
$863$	3.24994e10			1.72122			0.860612	−	0.509261i	$-0.170081\pi$
$863$	3.24994e10			1.72122			0.860612	+	0.509261i	$0.170081\pi$
$864$		0			0
$865$	3.08394e9			0.162013
$866$	6.75188e9	−	1.16946e10i	0.353274	−	0.611889i
$867$		0			0
$868$	1.67192e9	+	2.89585e9i	0.0867755	+	0.150299i
$869$	−1.39581e10	−	2.41761e10i	−0.721533	−	1.24973i
$870$		0			0
$871$	−6.25588e9	+	1.08355e10i	−0.320793	+	0.555630i
$872$	−4.52818e8			−0.0231268
$873$		0			0
$874$	8.24318e9			0.417642
$875$	1.28688e10	−	2.22894e10i	0.649396	−	1.12479i
$876$		0			0
$877$	1.69347e10	+	2.93318e10i	0.847772	+	1.46838i	0.883192	+	0.469011i	$0.155390\pi$
$877$	1.69347e10	+	2.93318e10i	0.847772	+	1.46838i	−0.0354204	+	0.999372i	$0.511277\pi$
$878$	4.71399e9	+	8.16486e9i	0.235048	+	0.407116i
$879$		0			0
$880$	1.71182e9	−	2.96495e9i	0.0846775	−	0.146666i
$881$	−1.52708e10			−0.752397			−0.376198	−	0.926539i	$-0.622769\pi$
$881$	−1.52708e10			−0.752397			−0.376198	+	0.926539i	$0.622769\pi$
$882$		0			0
$883$	−1.12045e10			−0.547685			−0.273842	−	0.961775i	$-0.588295\pi$
$883$	−1.12045e10			−0.547685			−0.273842	+	0.961775i	$0.588295\pi$
$884$	−8.03712e8	+	1.39207e9i	−0.0391307	+	0.0677764i
$885$		0			0
$886$	−2.86302e9	−	4.95890e9i	−0.138295	−	0.239534i
$887$	−3.48616e9	−	6.03821e9i	−0.167732	−	0.290520i	0.769890	−	0.638176i	$-0.220311\pi$
$887$	−3.48616e9	−	6.03821e9i	−0.167732	−	0.290520i	−0.937622	+	0.347657i	$0.886978\pi$
$888$		0			0
$889$	5.41203e9	−	9.37392e9i	0.258348	−	0.447471i
$890$	−5.46398e9			−0.259803
$891$		0			0
$892$	−1.21044e10			−0.571040
$893$	5.39184e9	−	9.33893e9i	0.253371	−	0.438851i
$894$		0			0
$895$	−7.65401e9	−	1.32571e10i	−0.356869	−	0.618115i
$896$	1.65256e9	+	2.86231e9i	0.0767499	+	0.132935i
$897$		0			0
$898$	5.49434e9	−	9.51647e9i	0.253191	−	0.438539i
$899$	−1.37945e9			−0.0633211
$900$		0			0
$901$	−5.19283e9			−0.236520
$902$	1.87429e10	−	3.24636e10i	0.850381	−	1.47290i
$903$		0			0
$904$	−3.10592e9	−	5.37961e9i	−0.139830	−	0.242193i
$905$	6.53565e9	+	1.13201e10i	0.293102	+	0.507668i
$906$		0			0
$907$	−5.90474e8	+	1.02273e9i	−0.0262770	+	0.0455130i	−0.878865	−	0.477071i	$-0.841699\pi$
$907$	−5.90474e8	+	1.02273e9i	−0.0262770	+	0.0455130i	0.852588	+	0.522584i	$0.175032\pi$
$908$	−1.12704e10			−0.499620
$909$		0			0
$910$	−5.46466e9			−0.240391
$911$	−6.39576e9	+	1.10778e10i	−0.280271	+	0.485443i	−0.971451	−	0.237239i	$-0.923758\pi$
$911$	−6.39576e9	+	1.10778e10i	−0.280271	+	0.485443i	0.691181	+	0.722682i	$0.257091\pi$
$912$		0			0
$913$	−8.17323e9	−	1.41564e10i	−0.355423	−	0.615611i
$914$	−7.39008e9	−	1.28000e10i	−0.320138	−	0.554496i
$915$		0			0
$916$	−2.08127e9	+	3.60486e9i	−0.0894734	+	0.154972i
$917$	6.22848e10			2.66741
$918$		0			0
$919$	3.52353e10			1.49752			0.748761	−	0.662840i	$-0.230649\pi$
$919$	3.52353e10			1.49752			0.748761	+	0.662840i	$0.230649\pi$
$920$	1.20962e9	−	2.09512e9i	0.0512143	−	0.0887057i
$921$		0			0
$922$	−1.23765e10	−	2.14368e10i	−0.520045	−	0.900745i
$923$	1.08664e10	+	1.88212e10i	0.454862	+	0.787845i
$924$		0			0
$925$	−1.18750e9	+	2.05681e9i	−0.0493329	+	0.0854471i
$926$	2.40361e10			0.994775
$927$		0			0
$928$	−1.36348e9			−0.0560054
$929$	1.08882e10	−	1.88590e10i	0.445556	−	0.771725i	−0.552535	−	0.833490i	$-0.686339\pi$
$929$	1.08882e10	−	1.88590e10i	0.445556	−	0.771725i	0.998091	+	0.0617646i	$0.0196728\pi$
$930$		0			0
$931$	−2.06367e10	−	3.57438e10i	−0.838139	−	1.45170i
$932$	8.04219e9	+	1.39295e10i	0.325401	+	0.563611i
$933$		0			0
$934$	1.19701e10	−	2.07328e10i	0.480709	−	0.832613i
$935$	5.52161e9			0.220915
$936$		0			0
$937$	1.15795e10			0.459833			0.229916	−	0.973210i	$-0.426155\pi$
$937$	1.15795e10			0.459833			0.229916	+	0.973210i	$0.426155\pi$
$938$	−2.07454e10	+	3.59321e10i	−0.820753	+	1.42159i
$939$		0			0
$940$	−1.58241e9	−	2.74082e9i	−0.0621402	−	0.107630i
$941$	1.91965e10	+	3.32493e10i	0.751033	+	1.30083i	0.947323	+	0.320281i	$0.103777\pi$
$941$	1.91965e10	+	3.32493e10i	0.751033	+	1.30083i	−0.196290	+	0.980546i	$0.562889\pi$
$942$		0			0
$943$	1.32443e10	−	2.29397e10i	0.514324	−	0.890835i
$944$	3.05209e9			0.118085
$945$		0			0
$946$	−9.17450e9			−0.352341
$947$	−5.59205e9	+	9.68571e9i	−0.213966	+	0.370601i	−0.952952	−	0.303120i	$-0.901972\pi$
$947$	−5.59205e9	+	9.68571e9i	−0.213966	+	0.370601i	0.738986	+	0.673721i	$0.235305\pi$
$948$		0			0
$949$	5.05647e9	+	8.75806e9i	0.192050	+	0.332641i
$950$	6.47643e9	+	1.12175e10i	0.245077	+	0.424486i
$951$		0			0
$952$	−2.66523e9	+	4.61631e9i	−0.100116	+	0.173407i
$953$	−5.19835e9			−0.194554			−0.0972770	−	0.995257i	$-0.531013\pi$
$953$	−5.19835e9			−0.194554			−0.0972770	+	0.995257i	$0.531013\pi$
$954$		0			0
$955$	−1.86510e9			−0.0692931
$956$	−6.81854e9	+	1.18101e10i	−0.252400	+	0.437169i
$957$		0			0
$958$	−7.36166e9	−	1.27508e10i	−0.270518	−	0.468551i
$959$	1.51092e10	+	2.61699e10i	0.553191	+	0.958156i
$960$		0			0
$961$	1.32068e10	−	2.28748e10i	0.480026	−	0.831430i
$962$	1.10915e9			0.0401677
$963$		0			0
$964$	1.64662e10			0.592001
$965$	−8.78931e9	+	1.52235e10i	−0.314854	+	0.545343i
$966$		0			0
$967$	1.34622e8	+	2.33171e8i	0.00478765	+	0.00829245i	0.868409	−	0.495848i	$-0.165143\pi$
$967$	1.34622e8	+	2.33171e8i	0.00478765	+	0.00829245i	−0.863622	+	0.504140i	$0.831809\pi$
$968$	−8.77339e9	−	1.51960e10i	−0.310888	−	0.538473i
$969$		0			0
$970$	−1.85142e9	+	3.20675e9i	−0.0651333	+	0.112814i
$971$	4.37283e9			0.153284			0.0766418	−	0.997059i	$-0.475580\pi$
$971$	4.37283e9			0.153284			0.0766418	+	0.997059i	$0.475580\pi$
$972$		0			0
$973$	−2.08740e10			−0.726457
$974$	1.70670e9	−	2.95610e9i	0.0591837	−	0.102509i
$975$		0			0
$976$	3.40095e9	+	5.89061e9i	0.117091	+	0.202808i
$977$	1.87495e10	+	3.24752e10i	0.643220	+	1.11409i	0.984710	+	0.174204i	$0.0557353\pi$
$977$	1.87495e10	+	3.24752e10i	0.643220	+	1.11409i	−0.341489	+	0.939886i	$0.610931\pi$
$978$		0			0
$979$	−2.19638e10	+	3.80424e10i	−0.748114	+	1.29577i
$980$	−1.21131e10			−0.411114
$981$		0			0
$982$	4.86038e8			0.0163787
$983$	1.53095e10	−	2.65168e10i	0.514071	−	0.890397i	−0.485796	−	0.874072i	$-0.661470\pi$
$983$	1.53095e10	−	2.65168e10i	0.514071	−	0.890397i	0.999867	−	0.0163250i	$-0.00519663\pi$
$984$		0			0
$985$	4.74404e9	+	8.21692e9i	0.158169	+	0.273957i
$986$	−1.09950e9	−	1.90439e9i	−0.0365281	−	0.0632685i
$987$		0			0
$988$	3.02457e9	−	5.23870e9i	0.0997732	−	0.172812i
$989$	−6.48296e9			−0.213102
$990$		0			0
$991$	−1.72703e10			−0.563693			−0.281847	−	0.959459i	$-0.590947\pi$
$991$	−1.72703e10			−0.563693			−0.281847	+	0.959459i	$0.590947\pi$
$992$	−5.43162e8	+	9.40785e8i	−0.0176660	+	0.0305985i
$993$		0			0
$994$	3.60346e10	+	6.24138e10i	1.16377	+	2.01571i
$995$	−4.34182e9	−	7.52024e9i	−0.139730	−	0.242020i
$996$		0			0
$997$	1.87539e9	−	3.24827e9i	0.0599319	−	0.103805i	−0.834503	−	0.551004i	$-0.814245\pi$
$997$	1.87539e9	−	3.24827e9i	0.0599319	−	0.103805i	0.894435	+	0.447199i	$0.147578\pi$
$998$	2.59670e10			0.826923
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	162.8.c.d.55.1		2
3.2	odd	2		162.8.c.i.55.1		2
9.2	odd	6		18.8.a.a.1.1		1
9.4	even	3	inner	162.8.c.d.109.1		2
9.5	odd	6		162.8.c.i.109.1		2
9.7	even	3		6.8.a.a.1.1	✓	1
36.7	odd	6		48.8.a.b.1.1		1
36.11	even	6		144.8.a.h.1.1		1
45.2	even	12		450.8.c.a.199.1		2
45.7	odd	12		150.8.c.k.49.2		2
45.29	odd	6		450.8.a.ba.1.1		1
45.34	even	6		150.8.a.e.1.1		1
45.38	even	12		450.8.c.a.199.2		2
45.43	odd	12		150.8.c.k.49.1		2
63.16	even	3		294.8.e.c.67.1		2
63.25	even	3		294.8.e.c.79.1		2
63.34	odd	6		294.8.a.l.1.1		1
63.52	odd	6		294.8.e.d.79.1		2
63.61	odd	6		294.8.e.d.67.1		2
72.11	even	6		576.8.a.i.1.1		1
72.29	odd	6		576.8.a.h.1.1		1
72.43	odd	6		192.8.a.n.1.1		1
72.61	even	6		192.8.a.f.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6.8.a.a.1.1	✓	1	9.7	even	3
18.8.a.a.1.1		1	9.2	odd	6
48.8.a.b.1.1		1	36.7	odd	6
144.8.a.h.1.1		1	36.11	even	6
150.8.a.e.1.1		1	45.34	even	6
150.8.c.k.49.1		2	45.43	odd	12
150.8.c.k.49.2		2	45.7	odd	12
162.8.c.d.55.1		2	1.1	even	1	trivial
162.8.c.d.109.1		2	9.4	even	3	inner
162.8.c.i.55.1		2	3.2	odd	2
162.8.c.i.109.1		2	9.5	odd	6
192.8.a.f.1.1		1	72.61	even	6
192.8.a.n.1.1		1	72.43	odd	6
294.8.a.l.1.1		1	63.34	odd	6
294.8.e.c.67.1		2	63.16	even	3
294.8.e.c.79.1		2	63.25	even	3
294.8.e.d.67.1		2	63.61	odd	6
294.8.e.d.79.1		2	63.52	odd	6
450.8.a.ba.1.1		1	45.29	odd	6
450.8.c.a.199.1		2	45.2	even	12
450.8.c.a.199.2		2	45.38	even	12
576.8.a.h.1.1		1	72.29	odd	6
576.8.a.i.1.1		1	72.11	even	6

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:	\( N \)	\(=\)	\( 162 = 2 \cdot 3^{4} \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	162.c (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-4.00000 + 6.92820i) q^{2} +(-32.0000 - 55.4256i) q^{4} +(57.0000 + 98.7269i) q^{5} +(788.000 - 1364.86i) q^{7} +512.000 q^{8} +O(q^{10})\)	\(q+(-4.00000 + 6.92820i) q^{2} +(-32.0000 - 55.4256i) q^{4} +(57.0000 + 98.7269i) q^{5} +(788.000 - 1364.86i) q^{7} +512.000 q^{8} -912.000 q^{10} +(-3666.00 + 6349.70i) q^{11} +(1901.00 + 3292.63i) q^{13} +(6304.00 + 10918.8i) q^{14} +(-2048.00 + 3547.24i) q^{16} -6606.00 q^{17} +24860.0 q^{19} +(3648.00 - 6318.52i) q^{20} +(-29328.0 - 50797.6i) q^{22} +(-20724.0 - 35895.0i) q^{23} +(32564.5 - 56403.4i) q^{25} -30416.0 q^{26} -100864. q^{28} +(20805.0 - 36035.3i) q^{29} +(-16576.0 - 28710.5i) q^{31} +(-16384.0 - 28377.9i) q^{32} +(26424.0 - 45767.7i) q^{34} +179664. q^{35} -36466.0 q^{37} +(-99440.0 + 172235. i) q^{38} +(29184.0 + 50548.2i) q^{40} +(319539. + 553458. i) q^{41} +(78206.0 - 135457. i) q^{43} +469248. q^{44} +331584. q^{46} +(216888. - 375661. i) q^{47} +(-830116. - 1.43780e6i) q^{49} +(260516. + 451227. i) q^{50} +(121664. - 210728. i) q^{52} +786078. q^{53} -835848. q^{55} +(403456. - 698806. i) q^{56} +(166440. + 288283. i) q^{58} +(-372570. - 645310. i) q^{59} +(830309. - 1.43814e6i) q^{61} +265216. q^{62} +262144. q^{64} +(-216714. + 375360. i) q^{65} +(1.64542e6 + 2.84995e6i) q^{67} +(211392. + 366142. i) q^{68} +(-718656. + 1.24475e6i) q^{70} +5.71615e6 q^{71} +2.65990e6 q^{73} +(145864. - 252644. i) q^{74} +(-795520. - 1.37788e6i) q^{76} +(5.77762e6 + 1.00071e7i) q^{77} +(-1.90372e6 + 3.29734e6i) q^{79} -466944. q^{80} -5.11262e6 q^{82} +(-1.11473e6 + 1.93078e6i) q^{83} +(-376542. - 652190. i) q^{85} +(625648. + 1.08365e6i) q^{86} +(-1.87699e6 + 3.25105e6i) q^{88} +5.99121e6 q^{89} +5.99195e6 q^{91} +(-1.32634e6 + 2.29728e6i) q^{92} +(1.73510e6 + 3.00529e6i) q^{94} +(1.41702e6 + 2.45435e6i) q^{95} +(2.03006e6 - 3.51617e6i) q^{97} +1.32819e7 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 8 q^{2} - 64 q^{4} + 114 q^{5} + 1576 q^{7} + 1024 q^{8}+O(q^{10}) \) 2 * q - 8 * q^2 - 64 * q^4 + 114 * q^5 + 1576 * q^7 + 1024 * q^8	\( 2 q - 8 q^{2} - 64 q^{4} + 114 q^{5} + 1576 q^{7} + 1024 q^{8} - 1824 q^{10} - 7332 q^{11} + 3802 q^{13} + 12608 q^{14} - 4096 q^{16} - 13212 q^{17} + 49720 q^{19} + 7296 q^{20} - 58656 q^{22} - 41448 q^{23} + 65129 q^{25} - 60832 q^{26} - 201728 q^{28} + 41610 q^{29} - 33152 q^{31} - 32768 q^{32} + 52848 q^{34} + 359328 q^{35} - 72932 q^{37} - 198880 q^{38} + 58368 q^{40} + 639078 q^{41} + 156412 q^{43} + 938496 q^{44} + 663168 q^{46} + 433776 q^{47} - 1660233 q^{49} + 521032 q^{50} + 243328 q^{52} + 1572156 q^{53} - 1671696 q^{55} + 806912 q^{56} + 332880 q^{58} - 745140 q^{59} + 1660618 q^{61} + 530432 q^{62} + 524288 q^{64} - 433428 q^{65} + 3290836 q^{67} + 422784 q^{68} - 1437312 q^{70} + 11432304 q^{71} + 5319796 q^{73} + 291728 q^{74} - 1591040 q^{76} + 11555232 q^{77} - 3807440 q^{79} - 933888 q^{80} - 10225248 q^{82} - 2229468 q^{83} - 753084 q^{85} + 1251296 q^{86} - 3753984 q^{88} + 11982420 q^{89} + 11983904 q^{91} - 2652672 q^{92} + 3470208 q^{94} + 2834040 q^{95} + 4060126 q^{97} + 26563728 q^{98}+O(q^{100}) \) 2 * q - 8 * q^2 - 64 * q^4 + 114 * q^5 + 1576 * q^7 + 1024 * q^8 - 1824 * q^10 - 7332 * q^11 + 3802 * q^13 + 12608 * q^14 - 4096 * q^16 - 13212 * q^17 + 49720 * q^19 + 7296 * q^20 - 58656 * q^22 - 41448 * q^23 + 65129 * q^25 - 60832 * q^26 - 201728 * q^28 + 41610 * q^29 - 33152 * q^31 - 32768 * q^32 + 52848 * q^34 + 359328 * q^35 - 72932 * q^37 - 198880 * q^38 + 58368 * q^40 + 639078 * q^41 + 156412 * q^43 + 938496 * q^44 + 663168 * q^46 + 433776 * q^47 - 1660233 * q^49 + 521032 * q^50 + 243328 * q^52 + 1572156 * q^53 - 1671696 * q^55 + 806912 * q^56 + 332880 * q^58 - 745140 * q^59 + 1660618 * q^61 + 530432 * q^62 + 524288 * q^64 - 433428 * q^65 + 3290836 * q^67 + 422784 * q^68 - 1437312 * q^70 + 11432304 * q^71 + 5319796 * q^73 + 291728 * q^74 - 1591040 * q^76 + 11555232 * q^77 - 3807440 * q^79 - 933888 * q^80 - 10225248 * q^82 - 2229468 * q^83 - 753084 * q^85 + 1251296 * q^86 - 3753984 * q^88 + 11982420 * q^89 + 11983904 * q^91 - 2652672 * q^92 + 3470208 * q^94 + 2834040 * q^95 + 4060126 * q^97 + 26563728 * q^98

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