LMFDB - Embedded newform 162.10.c.b.55.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [162,10,Mod(55,162)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(162, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([4])) N = Newforms(chi, 10, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("162.55"); S:= CuspForms(chi, 10); N := Newforms(S);

Level:	$ N $	$=$	$ 162 = 2 \cdot 3^{4} $
Weight:	$ k $	$=$	$ 10 $
Character orbit:	$[\chi]$	$=$	162.c (of order $3$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [2,-16,0,-256,-870] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$83.4358054585$
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 2)
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			162.10.c.b.109.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-8.00000 + 13.8564i) q^{2} +(-128.000 - 221.703i) q^{4} +(-435.000 - 753.442i) q^{5} +(476.000 - 824.456i) q^{7} +4096.00 q^{8} +13920.0 q^{10} +(28074.0 - 48625.6i) q^{11} +(-89047.0 - 154234. i) q^{13} +(7616.00 + 13191.3i) q^{14} +(-32768.0 + 56755.8i) q^{16} -247662. q^{17} +315380. q^{19} +(-111360. + 192881. i) q^{20} +(449184. + 778010. i) q^{22} +(-102252. - 177106. i) q^{23} +(598112. - 1.03596e6i) q^{25} +2.84950e6 q^{26} -243712. q^{28} +(1.92023e6 - 3.32593e6i) q^{29} +(654704. + 1.13398e6i) q^{31} +(-524288. - 908093. i) q^{32} +(1.98130e6 - 3.43171e6i) q^{34} -828240. q^{35} +4.30708e6 q^{37} +(-2.52304e6 + 4.37003e6i) q^{38} +(-1.78176e6 - 3.08610e6i) q^{40} +(-756021. - 1.30947e6i) q^{41} +(-1.68353e7 + 2.91596e7i) q^{43} -1.43739e7 q^{44} +3.27206e6 q^{46} +(5.29054e6 - 9.16348e6i) q^{47} +(1.97237e7 + 3.41624e7i) q^{49} +(9.56980e6 + 1.65754e7i) q^{50} +(-2.27960e7 + 3.94839e7i) q^{52} +1.66162e7 q^{53} -4.88488e7 q^{55} +(1.94970e6 - 3.37697e6i) q^{56} +(3.07236e7 + 5.32148e7i) q^{58} +(-5.61175e7 - 9.71984e7i) q^{59} +(1.65986e7 - 2.87496e7i) q^{61} -2.09505e7 q^{62} +1.67772e7 q^{64} +(-7.74709e7 + 1.34184e8i) q^{65} +(6.06861e7 + 1.05111e8i) q^{67} +(3.17007e7 + 5.49073e7i) q^{68} +(6.62592e6 - 1.14764e7i) q^{70} -3.87173e8 q^{71} +2.55240e8 q^{73} +(-3.44566e7 + 5.96806e7i) q^{74} +(-4.03686e7 - 6.99205e7i) q^{76} +(-2.67264e7 - 4.62916e7i) q^{77} +(-2.46051e8 + 4.26173e8i) q^{79} +5.70163e7 q^{80} +2.41927e7 q^{82} +(2.28710e8 - 3.96138e8i) q^{83} +(1.07733e8 + 1.86599e8i) q^{85} +(-2.69365e8 - 4.66554e8i) q^{86} +(1.14991e8 - 1.99170e8i) q^{88} -3.18095e7 q^{89} -1.69545e8 q^{91} +(-2.61765e7 + 4.53390e7i) q^{92} +(8.46486e7 + 1.46616e8i) q^{94} +(-1.37190e8 - 2.37621e8i) q^{95} +(3.36766e8 - 5.83296e8i) q^{97} -6.31157e8 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 16 q^{2} - 256 q^{4} - 870 q^{5} + 952 q^{7} + 8192 q^{8} + 27840 q^{10} + 56148 q^{11} - 178094 q^{13} + 15232 q^{14} - 65536 q^{16} - 495324 q^{17} + 630760 q^{19} - 222720 q^{20} + 898368 q^{22}+ \cdots - 1262313696 q^{98}+O(q^{100}) $ 2 * q - 16 * q^2 - 256 * q^4 - 870 * q^5 + 952 * q^7 + 8192 * q^8 + 27840 * q^10 + 56148 * q^11 - 178094 * q^13 + 15232 * q^14 - 65536 * q^16 - 495324 * q^17 + 630760 * q^19 - 222720 * q^20 + 898368 * q^22 - 204504 * q^23 + 1196225 * q^25 + 5699008 * q^26 - 487424 * q^28 + 3840450 * q^29 + 1309408 * q^31 - 1048576 * q^32 + 3962592 * q^34 - 1656480 * q^35 + 8614156 * q^37 - 5046080 * q^38 - 3563520 * q^40 - 1512042 * q^41 - 33670604 * q^43 - 28747776 * q^44 + 6544128 * q^46 + 10581072 * q^47 + 39447303 * q^49 + 19139600 * q^50 - 45592064 * q^52 + 33232428 * q^53 - 97697520 * q^55 + 3899392 * q^56 + 61447200 * q^58 - 112235100 * q^59 + 33197218 * q^61 - 41901056 * q^62 + 33554432 * q^64 - 154941780 * q^65 + 121372252 * q^67 + 63401472 * q^68 + 13251840 * q^70 - 774345456 * q^71 + 510480148 * q^73 - 68913248 * q^74 - 80737280 * q^76 - 53452896 * q^77 - 492101840 * q^79 + 114032640 * q^80 + 48385344 * q^82 + 457420236 * q^83 + 215465940 * q^85 - 538729664 * q^86 + 229982208 * q^88 - 63619020 * q^89 - 339090976 * q^91 - 52353024 * q^92 + 169297152 * q^94 - 274380600 * q^95 + 673532062 * q^97 - 1262313696 * q^98

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 $

$2$	−8.00000	+	13.8564i	−0.353553	+	0.612372i
$2$	−8.00000	+	13.8564i	−0.353553	+	0.612372i
$3$		0			0
$3$		0			0
$4$	−128.000	−	221.703i	−0.250000	−	0.433013i
$5$	−435.000	−	753.442i	−0.311261	−	0.539119i	0.667375	−	0.744722i	$-0.267418\pi$
$5$	−435.000	−	753.442i	−0.311261	−	0.539119i	−0.978636	+	0.205603i	$0.934085\pi$
$6$		0			0
$7$	476.000	−	824.456i	0.0749317	−	0.129786i	−0.826125	−	0.563487i	$-0.809459\pi$
$7$	476.000	−	824.456i	0.0749317	−	0.129786i	0.901057	+	0.433702i	$0.142793\pi$
$8$	4096.00			0.353553
$9$		0			0
$10$	13920.0			0.440189
$11$	28074.0	−	48625.6i	0.578146	−	1.00138i	−0.417546	−	0.908656i	$-0.637110\pi$
$11$	28074.0	−	48625.6i	0.578146	−	1.00138i	0.995692	−	0.0927219i	$-0.0295568\pi$
$12$		0			0
$13$	−89047.0	−	154234.i	−0.864717	−	1.49773i	−0.867327	−	0.497738i	$-0.834164\pi$
$13$	−89047.0	−	154234.i	−0.864717	−	1.49773i	0.00261007	−	0.999997i	$-0.499169\pi$
$14$	7616.00	+	13191.3i	0.0529847	+	0.0917723i
$15$		0			0
$16$	−32768.0	+	56755.8i	−0.125000	+	0.216506i
$17$	−247662.			−0.719183			−0.359591	−	0.933110i	$-0.617084\pi$
$17$	−247662.			−0.719183			−0.359591	+	0.933110i	$0.617084\pi$
$18$		0			0
$19$	315380.			0.555192			0.277596	−	0.960698i	$-0.410462\pi$
$19$	315380.			0.555192			0.277596	+	0.960698i	$0.410462\pi$
$20$	−111360.	+	192881.i	−0.155630	+	0.269560i
$21$		0			0
$22$	449184.	+	778010.i	0.408811	+	0.708081i
$23$	−102252.	−	177106.i	−0.0761898	−	0.131965i	0.825413	−	0.564529i	$-0.190942\pi$
$23$	−102252.	−	177106.i	−0.0761898	−	0.131965i	−0.901603	+	0.432564i	$0.857609\pi$
$24$		0			0
$25$	598112.	−	1.03596e6i	0.306234	−	0.530412i
$26$	2.84950e6			1.22290
$27$		0			0
$28$	−243712.			−0.0749317
$29$	1.92023e6	−	3.32593e6i	0.504152	−	0.873216i	−0.495837	−	0.868416i	$-0.665139\pi$
$29$	1.92023e6	−	3.32593e6i	0.504152	−	0.873216i	0.999988	−	0.00480048i	$-0.00152805\pi$
$30$		0			0
$31$	654704.	+	1.13398e6i	0.127326	+	0.220535i	0.922640	−	0.385663i	$-0.126027\pi$
$31$	654704.	+	1.13398e6i	0.127326	+	0.220535i	−0.795314	+	0.606198i	$0.792694\pi$
$32$	−524288.	−	908093.i	−0.0883883	−	0.153093i
$33$		0			0
$34$	1.98130e6	−	3.43171e6i	0.254269	−	0.440408i
$35$	−828240.			−0.0932932
$36$		0			0
$37$	4.30708e6			0.377811			0.188906	−	0.981995i	$-0.439506\pi$
$37$	4.30708e6			0.377811			0.188906	+	0.981995i	$0.439506\pi$
$38$	−2.52304e6	+	4.37003e6i	−0.196290	+	0.339984i
$39$		0			0
$40$	−1.78176e6	−	3.08610e6i	−0.110047	−	0.190607i
$41$	−756021.	−	1.30947e6i	−0.0417837	−	0.0723714i	0.844377	−	0.535749i	$-0.179971\pi$
$41$	−756021.	−	1.30947e6i	−0.0417837	−	0.0723714i	−0.886161	+	0.463378i	$0.846637\pi$
$42$		0			0
$43$	−1.68353e7	+	2.91596e7i	−0.750953	+	1.30069i	0.196408	+	0.980522i	$0.437072\pi$
$43$	−1.68353e7	+	2.91596e7i	−0.750953	+	1.30069i	−0.947361	+	0.320167i	$0.896261\pi$
$44$	−1.43739e7			−0.578146
$45$		0			0
$46$	3.27206e6			0.107749
$47$	5.29054e6	−	9.16348e6i	0.158146	−	0.273918i	−0.776054	−	0.630667i	$-0.782782\pi$
$47$	5.29054e6	−	9.16348e6i	0.158146	−	0.273918i	0.934200	+	0.356749i	$0.116115\pi$
$48$		0			0
$49$	1.97237e7	+	3.41624e7i	0.488770	+	0.846575i
$50$	9.56980e6	+	1.65754e7i	0.216540	+	0.375058i
$51$		0			0
$52$	−2.27960e7	+	3.94839e7i	−0.432359	+	0.748867i
$53$	1.66162e7			0.289262			0.144631	−	0.989486i	$-0.453801\pi$
$53$	1.66162e7			0.289262			0.144631	+	0.989486i	$0.453801\pi$
$54$		0			0
$55$	−4.88488e7			−0.719816
$56$	1.94970e6	−	3.37697e6i	0.0264924	−	0.0458861i
$57$		0			0
$58$	3.07236e7	+	5.32148e7i	0.356489	+	0.617457i
$59$	−5.61175e7	−	9.71984e7i	−0.602927	−	1.04430i	−0.992375	−	0.123252i	$-0.960668\pi$
$59$	−5.61175e7	−	9.71984e7i	−0.602927	−	1.04430i	0.389449	−	0.921048i	$-0.372666\pi$
$60$		0			0
$61$	1.65986e7	−	2.87496e7i	0.153493	−	0.265857i	−0.779017	−	0.627003i	$-0.784281\pi$
$61$	1.65986e7	−	2.87496e7i	0.153493	−	0.265857i	0.932509	+	0.361146i	$0.117615\pi$
$62$	−2.09505e7			−0.180066
$63$		0			0
$64$	1.67772e7			0.125000
$65$	−7.74709e7	+	1.34184e8i	−0.538305	+	0.932372i
$66$		0			0
$67$	6.06861e7	+	1.05111e8i	0.367919	+	0.637255i	0.989240	−	0.146301i	$-0.0467369\pi$
$67$	6.06861e7	+	1.05111e8i	0.367919	+	0.637255i	−0.621321	+	0.783556i	$0.713404\pi$
$68$	3.17007e7	+	5.49073e7i	0.179796	+	0.311415i
$69$		0			0
$70$	6.62592e6	−	1.14764e7i	0.0329841	−	0.0571302i
$71$	−3.87173e8			−1.80818			−0.904091	−	0.427340i	$-0.859451\pi$
$71$	−3.87173e8			−1.80818			−0.904091	+	0.427340i	$0.859451\pi$
$72$		0			0
$73$	2.55240e8			1.05195			0.525976	−	0.850499i	$-0.323700\pi$
$73$	2.55240e8			1.05195			0.525976	+	0.850499i	$0.323700\pi$
$74$	−3.44566e7	+	5.96806e7i	−0.133576	+	0.231361i
$75$		0			0
$76$	−4.03686e7	−	6.99205e7i	−0.138798	−	0.240405i
$77$	−2.67264e7	−	4.62916e7i	−0.0866429	−	0.150070i
$78$		0			0
$79$	−2.46051e8	+	4.26173e8i	−0.710727	+	1.23102i	0.253857	+	0.967242i	$0.418301\pi$
$79$	−2.46051e8	+	4.26173e8i	−0.710727	+	1.23102i	−0.964584	+	0.263774i	$0.915033\pi$
$80$	5.70163e7			0.155630
$81$		0			0
$82$	2.41927e7			0.0590910
$83$	2.28710e8	−	3.96138e8i	0.528974	−	0.916209i	−0.470456	−	0.882424i	$-0.655910\pi$
$83$	2.28710e8	−	3.96138e8i	0.528974	−	0.916209i	0.999429	−	0.0337854i	$-0.0107563\pi$
$84$		0			0
$85$	1.07733e8	+	1.86599e8i	0.223853	+	0.387725i
$86$	−2.69365e8	−	4.66554e8i	−0.531004	−	0.919726i
$87$		0			0
$88$	1.14991e8	−	1.99170e8i	0.204405	−	0.354040i
$89$	−3.18095e7			−0.0537405			−0.0268703	−	0.999639i	$-0.508554\pi$
$89$	−3.18095e7			−0.0537405			−0.0268703	+	0.999639i	$0.508554\pi$
$90$		0			0
$91$	−1.69545e8			−0.259179
$92$	−2.61765e7	+	4.53390e7i	−0.0380949	+	0.0659823i
$93$		0			0
$94$	8.46486e7	+	1.46616e8i	0.111826	+	0.193689i
$95$	−1.37190e8	−	2.37621e8i	−0.172809	−	0.299315i
$96$		0			0
$97$	3.36766e8	−	5.83296e8i	0.386238	−	0.668985i	−0.605702	−	0.795692i	$-0.707108\pi$
$97$	3.36766e8	−	5.83296e8i	0.386238	−	0.668985i	0.991940	+	0.126707i	$0.0404409\pi$
$98$	−6.31157e8			−0.691226
$99$		0			0
$100$	−3.06234e8			−0.306234
$101$	−5.28859e8	+	9.16012e8i	−0.505701	+	0.875900i	0.494277	+	0.869305i	$0.335433\pi$
$101$	−5.28859e8	+	9.16012e8i	−0.505701	+	0.875900i	−0.999978	+	0.00659592i	$0.997900\pi$
$102$		0			0
$103$	−3.97933e8	−	6.89240e8i	−0.348371	−	0.603397i	0.637589	−	0.770377i	$-0.279932\pi$
$103$	−3.97933e8	−	6.89240e8i	−0.348371	−	0.603397i	−0.985960	+	0.166980i	$0.946599\pi$
$104$	−3.64737e8	−	6.31742e8i	−0.305724	−	0.529529i
$105$		0			0
$106$	−1.32930e8	+	2.30241e8i	−0.102269	+	0.177136i
$107$	−1.97413e9			−1.45596			−0.727981	−	0.685598i	$-0.759541\pi$
$107$	−1.97413e9			−1.45596			−0.727981	+	0.685598i	$0.759541\pi$
$108$		0			0
$109$	−1.34465e9			−0.912408			−0.456204	−	0.889875i	$-0.650791\pi$
$109$	−1.34465e9			−0.912408			−0.456204	+	0.889875i	$0.650791\pi$
$110$	3.90790e8	−	6.76868e8i	0.254493	−	0.440795i
$111$		0			0
$112$	3.11951e7	+	5.40316e7i	0.0187329	+	0.0324464i
$113$	−1.35340e9	−	2.34416e9i	−0.780861	−	1.35249i	−0.931441	−	0.363893i	$-0.881447\pi$
$113$	−1.35340e9	−	2.34416e9i	−0.780861	−	1.35249i	0.150580	−	0.988598i	$-0.451886\pi$
$114$		0			0
$115$	−8.89592e7	+	1.54082e8i	−0.0474297	+	0.0821507i
$116$	−9.83155e8			−0.504152
$117$		0			0
$118$	1.79576e9			0.852667
$119$	−1.17887e8	+	2.04186e8i	−0.0538896	+	0.0933395i
$120$		0			0
$121$	−3.97325e8	−	6.88187e8i	−0.168505	−	0.291859i
$122$	2.65578e8	+	4.59994e8i	0.108536	+	0.187989i
$123$		0			0
$124$	1.67604e8	−	2.90299e8i	0.0636630	−	0.110268i
$125$	−2.73993e9			−1.00380
$126$		0			0
$127$	1.19960e9			0.409185			0.204593	−	0.978847i	$-0.434413\pi$
$127$	1.19960e9			0.409185			0.204593	+	0.978847i	$0.434413\pi$
$128$	−1.34218e8	+	2.32472e8i	−0.0441942	+	0.0765466i
$129$		0			0
$130$	−1.23953e9	−	2.14694e9i	−0.380639	−	0.659286i
$131$	−1.39307e9	−	2.41287e9i	−0.413288	−	0.715836i	0.581959	−	0.813218i	$-0.302286\pi$
$131$	−1.39307e9	−	2.41287e9i	−0.413288	−	0.715836i	−0.995247	+	0.0973821i	$0.968953\pi$
$132$		0			0
$133$	1.50121e8	−	2.60017e8i	0.0416015	−	0.0720559i
$134$	−1.94196e9			−0.520317
$135$		0			0
$136$	−1.01442e9			−0.254269
$137$	−1.44117e9	+	2.49617e9i	−0.349519	+	0.605385i	−0.986164	−	0.165772i	$-0.946988\pi$
$137$	−1.44117e9	+	2.49617e9i	−0.349519	+	0.605385i	0.636645	+	0.771157i	$0.280322\pi$
$138$		0			0
$139$	−1.07821e9	−	1.86751e9i	−0.244982	−	0.424322i	0.717144	−	0.696925i	$-0.245449\pi$
$139$	−1.07821e9	−	1.86751e9i	−0.244982	−	0.424322i	−0.962127	+	0.272603i	$0.912116\pi$
$140$	1.06015e8	+	1.83623e8i	0.0233233	+	0.0403971i
$141$		0			0
$142$	3.09738e9	−	5.36482e9i	0.639289	−	1.10728i
$143$	−9.99962e9			−1.99973
$144$		0			0
$145$	−3.34119e9			−0.627690
$146$	−2.04192e9	+	3.53671e9i	−0.371921	+	0.644187i
$147$		0			0
$148$	−5.51306e8	−	9.54890e8i	−0.0944528	−	0.163597i
$149$	−3.77274e9	−	6.53458e9i	−0.627074	−	1.08612i	−0.988136	−	0.153582i	$-0.950919\pi$
$149$	−3.77274e9	−	6.53458e9i	−0.627074	−	1.08612i	0.361062	−	0.932542i	$-0.382414\pi$
$150$		0			0
$151$	2.15654e9	−	3.73524e9i	0.337568	−	0.584685i	−0.646407	−	0.762993i	$-0.723729\pi$
$151$	2.15654e9	−	3.73524e9i	0.337568	−	0.584685i	0.983975	+	0.178308i	$0.0570623\pi$
$152$	1.29180e9			0.196290
$153$		0			0
$154$	8.55246e8			0.122532
$155$	5.69592e8	−	9.86563e8i	0.0792632	−	0.137288i
$156$		0			0
$157$	2.11579e9	+	3.66465e9i	0.277922	+	0.481376i	0.970868	−	0.239614i	$-0.0770209\pi$
$157$	2.11579e9	+	3.66465e9i	0.277922	+	0.481376i	−0.692946	+	0.720990i	$0.743688\pi$
$158$	−3.93681e9	−	6.81876e9i	−0.502560	−	0.870460i
$159$		0			0
$160$	−4.56131e8	+	7.90041e8i	−0.0550236	+	0.0953037i
$161$	−1.94688e8			−0.0228361
$162$		0			0
$163$	8.28448e8			0.0919223			0.0459612	−	0.998943i	$-0.485365\pi$
$163$	8.28448e8			0.0919223			0.0459612	+	0.998943i	$0.485365\pi$
$164$	−1.93541e8	+	3.35223e8i	−0.0208918	+	0.0361857i
$165$		0			0
$166$	3.65936e9	+	6.33820e9i	0.374041	+	0.647858i
$167$	1.42750e9	+	2.47250e9i	0.142021	+	0.245987i	0.928257	−	0.371938i	$-0.121307\pi$
$167$	1.42750e9	+	2.47250e9i	0.142021	+	0.245987i	−0.786237	+	0.617925i	$0.787973\pi$
$168$		0			0
$169$	−1.05565e10	+	1.82844e10i	−0.995472	+	1.72421i
$170$	−3.44746e9			−0.316576
$171$		0			0
$172$	8.61967e9			0.750953
$173$	8.83451e9	−	1.53018e10i	0.749851	−	1.29878i	−0.198043	−	0.980193i	$-0.563459\pi$
$173$	8.83451e9	−	1.53018e10i	0.749851	−	1.29878i	0.947894	−	0.318587i	$-0.103208\pi$
$174$		0			0
$175$	−5.69403e8	−	9.86235e8i	−0.0458932	−	0.0794894i
$176$	1.83986e9	+	3.18673e9i	0.144536	+	0.250344i
$177$		0			0
$178$	2.54476e8	−	4.40765e8i	0.0190001	−	0.0329092i
$179$	−5.86732e8			−0.0427170			−0.0213585	−	0.999772i	$-0.506799\pi$
$179$	−5.86732e8			−0.0427170			−0.0213585	+	0.999772i	$0.506799\pi$
$180$		0			0
$181$	−5.43396e9			−0.376325			−0.188162	−	0.982138i	$-0.560253\pi$
$181$	−5.43396e9			−0.376325			−0.188162	+	0.982138i	$0.560253\pi$
$182$	1.35636e9	−	2.34929e9i	0.0916336	−	0.158714i
$183$		0			0
$184$	−4.18824e8	−	7.25425e8i	−0.0269371	−	0.0466565i
$185$	−1.87358e9	−	3.24513e9i	−0.117598	−	0.203685i
$186$		0			0
$187$	−6.95286e9	+	1.20427e10i	−0.415792	+	0.720173i
$188$	−2.70875e9			−0.158146
$189$		0			0
$190$	4.39009e9			0.244389
$191$	−1.61646e10	+	2.79979e10i	−0.878851	+	1.52222i	−0.0262486	+	0.999655i	$0.508356\pi$
$191$	−1.61646e10	+	2.79979e10i	−0.878851	+	1.52222i	−0.852603	+	0.522560i	$0.824977\pi$
$192$		0			0
$193$	6.46996e9	+	1.12063e10i	0.335655	+	0.581372i	0.983611	−	0.180306i	$-0.0577089\pi$
$193$	6.46996e9	+	1.12063e10i	0.335655	+	0.581372i	−0.647955	+	0.761679i	$0.724376\pi$
$194$	5.38826e9	+	9.33273e9i	0.273112	+	0.473044i
$195$		0			0
$196$	5.04925e9	−	8.74557e9i	0.244385	−	0.423288i
$197$	8.81090e9			0.416795			0.208397	−	0.978044i	$-0.433175\pi$
$197$	8.81090e9			0.416795			0.208397	+	0.978044i	$0.433175\pi$
$198$		0			0
$199$	−2.48534e10			−1.12343			−0.561716	−	0.827330i	$-0.689859\pi$
$199$	−2.48534e10			−1.12343			−0.561716	+	0.827330i	$0.689859\pi$
$200$	2.44987e9	−	4.24330e9i	0.108270	−	0.187529i
$201$		0			0
$202$	−8.46175e9	−	1.46562e10i	−0.357585	−	0.619355i
$203$	−1.82805e9	−	3.16628e9i	−0.0755539	−	0.130863i
$204$		0			0
$205$	−6.57738e8	+	1.13924e9i	−0.0260112	+	0.0450528i
$206$	1.27339e10			0.492672
$207$		0			0
$208$	1.16716e10			0.432359
$209$	8.85398e9	−	1.53355e10i	0.320982	−	0.555956i
$210$		0			0
$211$	2.32582e10	+	4.02843e10i	0.807801	+	1.39915i	0.914384	+	0.404848i	$0.132675\pi$
$211$	2.32582e10	+	4.02843e10i	0.807801	+	1.39915i	−0.106584	+	0.994304i	$0.533991\pi$
$212$	−2.12688e9	−	3.68386e9i	−0.0723154	−	0.125254i
$213$		0			0
$214$	1.57931e10	−	2.73544e10i	0.514760	−	0.891591i
$215$	2.92934e10			0.934969
$216$		0			0
$217$	1.24656e9			0.0381631
$218$	1.07572e10	−	1.86320e10i	0.322585	−	0.558734i
$219$		0			0
$220$	6.25264e9	+	1.08299e10i	0.179954	+	0.311689i
$221$	2.20536e10	+	3.81979e10i	0.621890	+	1.07714i
$222$		0			0
$223$	−2.33174e10	+	4.03869e10i	−0.631404	+	1.09362i	0.355860	+	0.934539i	$0.384188\pi$
$223$	−2.33174e10	+	4.03869e10i	−0.631404	+	1.09362i	−0.987265	+	0.159085i	$0.949145\pi$
$224$	−9.98244e8			−0.0264924
$225$		0			0
$226$	4.33088e10			1.10430
$227$	−1.32934e10	+	2.30248e10i	−0.332291	+	0.575545i	−0.982961	−	0.183816i	$-0.941155\pi$
$227$	−1.32934e10	+	2.30248e10i	−0.332291	+	0.575545i	0.650670	+	0.759361i	$0.274488\pi$
$228$		0			0
$229$	−1.99954e10	−	3.46330e10i	−0.480474	−	0.832205i	0.519275	−	0.854607i	$-0.326202\pi$
$229$	−1.99954e10	−	3.46330e10i	−0.480474	−	0.832205i	−0.999749	+	0.0224021i	$0.992869\pi$
$230$	−1.42335e9	−	2.46531e9i	−0.0335379	−	0.0580893i
$231$		0			0
$232$	7.86524e9	−	1.36230e10i	0.178244	−	0.308729i
$233$	6.53338e9			0.145223			0.0726116	−	0.997360i	$-0.476867\pi$
$233$	6.53338e9			0.145223			0.0726116	+	0.997360i	$0.476867\pi$
$234$		0			0
$235$	−9.20553e9			−0.196899
$236$	−1.43661e10	+	2.48828e10i	−0.301463	+	0.522150i
$237$		0			0
$238$	−1.88619e9	−	3.26698e9i	−0.0381057	−	0.0660010i
$239$	2.83386e10	+	4.90840e10i	0.561809	+	0.973082i	0.997339	+	0.0729072i	$0.0232277\pi$
$239$	2.83386e10	+	4.90840e10i	0.561809	+	0.973082i	−0.435530	+	0.900174i	$0.643439\pi$
$240$		0			0
$241$	−2.30746e9	+	3.99663e9i	−0.0440613	+	0.0763163i	−0.887215	−	0.461356i	$-0.847363\pi$
$241$	−2.30746e9	+	3.99663e9i	−0.0440613	+	0.0763163i	0.843154	+	0.537673i	$0.180696\pi$
$242$	1.27144e10			0.238302
$243$		0			0
$244$	−8.49849e9			−0.153493
$245$	1.71596e10	−	2.97213e10i	0.304270	−	0.527011i
$246$		0			0
$247$	−2.80836e10	−	4.86423e10i	−0.480084	−	0.831530i
$248$	2.68167e9	+	4.64478e9i	0.0450166	+	0.0779710i
$249$		0			0
$250$	2.19195e10	−	3.79656e10i	0.354895	−	0.614697i
$251$	6.80194e10			1.08169			0.540843	−	0.841124i	$-0.318105\pi$
$251$	6.80194e10			1.08169			0.540843	+	0.841124i	$0.318105\pi$
$252$		0			0
$253$	−1.14825e10			−0.176195
$254$	−9.59681e9	+	1.66222e10i	−0.144669	+	0.250574i
$255$		0			0
$256$	−2.14748e9	−	3.71955e9i	−0.0312500	−	0.0541266i
$257$	4.67979e10	+	8.10563e10i	0.669156	+	1.15901i	0.978141	+	0.207945i	$0.0666774\pi$
$257$	4.67979e10	+	8.10563e10i	0.669156	+	1.15901i	−0.308985	+	0.951067i	$0.599989\pi$
$258$		0			0
$259$	2.05017e9	−	3.55100e9i	0.0283101	−	0.0490345i
$260$	3.96651e10			0.538305
$261$		0			0
$262$	4.45783e10			0.584478
$263$	4.70200e10	−	8.14411e10i	0.606013	−	1.04965i	−0.385877	−	0.922550i	$-0.626101\pi$
$263$	4.70200e10	−	8.14411e10i	0.606013	−	1.04965i	0.991890	−	0.127096i	$-0.0405655\pi$
$264$		0			0
$265$	−7.22805e9	−	1.25194e10i	−0.0900357	−	0.155946i
$266$	2.40193e9	+	4.16027e9i	0.0294167	+	0.0509512i
$267$		0			0
$268$	1.55356e10	−	2.69085e10i	0.183960	−	0.318628i
$269$	1.22724e11			1.42904			0.714522	−	0.699613i	$-0.246644\pi$
$269$	1.22724e11			1.42904			0.714522	+	0.699613i	$0.246644\pi$
$270$		0			0
$271$	−1.64257e11			−1.84996			−0.924982	−	0.380012i	$-0.875920\pi$
$271$	−1.64257e11			−1.84996			−0.924982	+	0.380012i	$0.875920\pi$
$272$	8.11539e9	−	1.40563e10i	0.0898978	−	0.155708i
$273$		0			0
$274$	−2.30586e10	−	3.99387e10i	−0.247147	−	0.428072i
$275$	−3.35828e10	−	5.81672e10i	−0.354095	−	0.613311i
$276$		0			0
$277$	−3.25067e10	+	5.63033e10i	−0.331752	+	0.574612i	−0.982856	−	0.184377i	$-0.940973\pi$
$277$	−3.25067e10	+	5.63033e10i	−0.331752	+	0.574612i	0.651103	+	0.758989i	$0.274306\pi$
$278$	3.45026e10			0.346458
$279$		0			0
$280$	−3.39247e9			−0.0329841
$281$	−2.60482e10	+	4.51168e10i	−0.249230	+	0.431678i	−0.963312	−	0.268383i	$-0.913511\pi$
$281$	−2.60482e10	+	4.51168e10i	−0.249230	+	0.431678i	0.714083	+	0.700061i	$0.246844\pi$
$282$		0			0
$283$	4.53496e10	+	7.85478e10i	0.420276	+	0.727939i	0.995966	−	0.0897286i	$-0.0286000\pi$
$283$	4.53496e10	+	7.85478e10i	0.420276	+	0.727939i	−0.575690	+	0.817668i	$0.695267\pi$
$284$	4.95581e10	+	8.58372e10i	0.452046	+	0.782966i
$285$		0			0
$286$	7.99970e10	−	1.38559e11i	0.707011	−	1.22458i
$287$	−1.43946e9			−0.0125237
$288$		0			0
$289$	−5.72514e10			−0.482776
$290$	2.67295e10	−	4.62969e10i	0.221922	−	0.384380i
$291$		0			0
$292$	−3.26707e10	−	5.65874e10i	−0.262988	−	0.455509i
$293$	−3.62784e10	−	6.28361e10i	−0.287571	−	0.498087i	0.685659	−	0.727923i	$-0.259514\pi$
$293$	−3.62784e10	−	6.28361e10i	−0.287571	−	0.498087i	−0.973229	+	0.229836i	$0.926181\pi$
$294$		0			0
$295$	−4.88223e10	+	8.45626e10i	−0.375335	+	0.650099i
$296$	1.76418e10			0.133576
$297$		0			0
$298$	1.20728e11			0.886816
$299$	−1.82105e10	+	3.15415e10i	−0.131765	+	0.228224i
$300$		0			0
$301$	1.60272e10	+	2.77599e10i	0.112540	+	0.194926i
$302$	3.45047e10	+	5.97638e10i	0.238697	+	0.413435i
$303$		0			0
$304$	−1.03344e10	+	1.78997e10i	−0.0693990	+	0.120203i
$305$	−2.88816e10			−0.191105
$306$		0			0
$307$	1.81977e11			1.16921			0.584607	−	0.811317i	$-0.301249\pi$
$307$	1.81977e11			1.16921			0.584607	+	0.811317i	$0.301249\pi$
$308$	−6.84197e9	+	1.18506e10i	−0.0433215	+	0.0750350i
$309$		0			0
$310$	9.11348e9	+	1.57850e10i	0.0560475	+	0.0970772i
$311$	4.49148e10	+	7.77946e10i	0.272250	+	0.471550i	0.969438	−	0.245338i	$-0.0788990\pi$
$311$	4.49148e10	+	7.77946e10i	0.272250	+	0.471550i	−0.697188	+	0.716888i	$0.745566\pi$
$312$		0			0
$313$	−2.75697e9	+	4.77521e9i	−0.0162361	+	0.0281218i	−0.874029	−	0.485873i	$-0.838502\pi$
$313$	−2.75697e9	+	4.77521e9i	−0.0162361	+	0.0281218i	0.857793	+	0.513995i	$0.171835\pi$
$314$	−6.77052e10			−0.393041
$315$		0			0
$316$	1.25978e11			0.710727
$317$	9.74028e9	−	1.68707e10i	0.0541757	−	0.0938351i	−0.837666	−	0.546183i	$-0.816080\pi$
$317$	9.74028e9	−	1.68707e10i	0.0541757	−	0.0938351i	0.891841	+	0.452348i	$0.149414\pi$
$318$		0			0
$319$	−1.07817e11	−	1.86744e11i	−0.582946	−	1.00969i
$320$	−7.29809e9	−	1.26407e10i	−0.0389076	−	0.0673899i
$321$		0			0
$322$	1.55750e9	−	2.69767e9i	0.00807379	−	0.0139842i
$323$	−7.81076e10			−0.399284
$324$		0			0
$325$	−2.13040e11			−1.05922
$326$	−6.62758e9	+	1.14793e10i	−0.0324995	+	0.0562907i
$327$		0			0
$328$	−3.09666e9	−	5.36358e9i	−0.0147728	−	0.0255872i
$329$	−5.03659e9	−	8.72363e9i	−0.0237004	−	0.0410502i
$330$		0			0
$331$	5.34005e10	−	9.24924e10i	0.244523	−	0.423526i	−0.717475	−	0.696585i	$-0.754702\pi$
$331$	5.34005e10	−	9.24924e10i	0.244523	−	0.423526i	0.961997	+	0.273059i	$0.0880354\pi$
$332$	−1.17100e11			−0.528974
$333$		0			0
$334$	−4.56800e10			−0.200848
$335$	5.27969e10	−	9.14470e10i	0.229038	−	0.396705i
$336$		0			0
$337$	8.78882e10	+	1.52227e11i	0.371190	+	0.642920i	0.989749	−	0.142819i	$-0.0456166\pi$
$337$	8.78882e10	+	1.52227e11i	0.371190	+	0.642920i	−0.618559	+	0.785738i	$0.712283\pi$
$338$	−1.68904e11	−	2.92550e11i	−0.703905	−	1.21920i
$339$		0			0
$340$	2.75796e10	−	4.77693e10i	0.111927	−	0.193863i
$341$	7.35206e10			0.294452
$342$		0			0
$343$	7.59705e10			0.296361
$344$	−6.89574e10	+	1.19438e11i	−0.265502	+	0.459863i
$345$		0			0
$346$	1.41352e11	+	2.44829e11i	0.530225	+	0.918376i
$347$	−4.16513e10	−	7.21422e10i	−0.154222	−	0.267120i	0.778554	−	0.627578i	$-0.215954\pi$
$347$	−4.16513e10	−	7.21422e10i	−0.154222	−	0.267120i	−0.932775	+	0.360458i	$0.882620\pi$
$348$		0			0
$349$	−1.60684e11	+	2.78313e11i	−0.579773	+	1.00420i	0.415732	+	0.909487i	$0.363525\pi$
$349$	−1.60684e11	+	2.78313e11i	−0.579773	+	1.00420i	−0.995505	+	0.0947093i	$0.969808\pi$
$350$	1.82209e10			0.0649028
$351$		0			0
$352$	−5.88754e10			−0.204405
$353$	−2.03844e11	+	3.53069e11i	−0.698735	+	1.21024i	0.270171	+	0.962812i	$0.412920\pi$
$353$	−2.03844e11	+	3.53069e11i	−0.698735	+	1.21024i	−0.968905	+	0.247431i	$0.920414\pi$
$354$		0			0
$355$	1.68420e11	+	2.91712e11i	0.562816	+	0.974826i
$356$	4.07162e9	+	7.05225e9i	0.0134351	+	0.0232703i
$357$		0			0
$358$	4.69386e9	−	8.13000e9i	0.0151028	−	0.0261587i
$359$	−5.60079e11			−1.77961			−0.889804	−	0.456343i	$-0.849159\pi$
$359$	−5.60079e11			−1.77961			−0.889804	+	0.456343i	$0.849159\pi$
$360$		0			0
$361$	−2.23223e11			−0.691762
$362$	4.34717e10	−	7.52951e10i	0.133051	−	0.230451i
$363$		0			0
$364$	2.17018e10	+	3.75887e10i	0.0647948	+	0.112228i
$365$	−1.11029e11	−	1.92309e11i	−0.327431	−	0.567128i
$366$		0			0
$367$	−1.88028e11	+	3.25674e11i	−0.541036	+	0.937101i	0.457809	+	0.889050i	$0.348634\pi$
$367$	−1.88028e11	+	3.25674e11i	−0.541036	+	0.937101i	−0.998845	+	0.0480506i	$0.984699\pi$
$368$	1.34024e10			0.0380949
$369$		0			0
$370$	5.99545e10			0.166308
$371$	7.90932e9	−	1.36993e10i	0.0216749	−	0.0375420i
$372$		0			0
$373$	4.06122e10	+	7.03424e10i	0.108634	+	0.188160i	0.915217	−	0.402961i	$-0.132019\pi$
$373$	4.06122e10	+	7.03424e10i	0.108634	+	0.188160i	−0.806583	+	0.591121i	$0.798686\pi$
$374$	−1.11246e11	−	1.92683e11i	−0.294010	−	0.509239i
$375$		0			0
$376$	2.16700e10	−	3.75336e10i	0.0559132	−	0.0968445i
$377$	−6.83961e11			−1.74379
$378$		0			0
$379$	2.02729e11			0.504708			0.252354	−	0.967635i	$-0.418795\pi$
$379$	2.02729e11			0.504708			0.252354	+	0.967635i	$0.418795\pi$
$380$	−3.51207e10	+	6.08309e10i	−0.0864047	+	0.149657i
$381$		0			0
$382$	−2.58634e11	−	4.47967e11i	−0.621442	−	1.07637i
$383$	2.38408e10	+	4.12935e10i	0.0566143	+	0.0980589i	0.892944	−	0.450169i	$-0.148636\pi$
$383$	2.38408e10	+	4.12935e10i	0.0566143	+	0.0980589i	−0.836329	+	0.548228i	$0.815303\pi$
$384$		0			0
$385$	−2.32520e10	+	4.02737e10i	−0.0539371	+	0.0934217i
$386$	−2.07039e11			−0.474688
$387$		0			0
$388$	−1.72424e11			−0.386238
$389$	9.48973e10	−	1.64367e11i	0.210126	−	0.363950i	−0.741627	−	0.670812i	$-0.765946\pi$
$389$	9.48973e10	−	1.64367e11i	0.210126	−	0.363950i	0.951754	+	0.306862i	$0.0992791\pi$
$390$		0			0
$391$	2.53239e10	+	4.38623e10i	0.0547943	+	0.0949066i
$392$	8.07881e10	+	1.39929e11i	0.172806	+	0.299310i
$393$		0			0
$394$	−7.04872e10	+	1.22087e11i	−0.147359	+	0.255234i
$395$	4.28129e11			0.884886
$396$		0			0
$397$	4.00237e11			0.808649			0.404325	−	0.914616i	$-0.367507\pi$
$397$	4.00237e11			0.808649			0.404325	+	0.914616i	$0.367507\pi$
$398$	1.98827e11	−	3.44379e11i	0.397193	−	0.687959i
$399$		0			0
$400$	3.91979e10	+	6.78928e10i	0.0765584	+	0.132603i
$401$	−4.38093e11	−	7.58799e11i	−0.846090	−	1.46547i	−0.884671	−	0.466215i	$-0.845617\pi$
$401$	−4.38093e11	−	7.58799e11i	−0.846090	−	1.46547i	0.0385813	−	0.999255i	$-0.487716\pi$
$402$		0			0
$403$	1.16599e11	−	2.01955e11i	0.220202	−	0.381401i
$404$	2.70776e11			0.505701
$405$		0			0
$406$	5.84977e10			0.106849
$407$	1.20917e11	−	2.09434e11i	0.218430	−	0.378332i
$408$		0			0
$409$	−2.86150e11	−	4.95626e11i	−0.505637	−	0.875789i	−0.999979	−	0.00652133i	$-0.997924\pi$
$409$	−2.86150e11	−	4.95626e11i	−0.505637	−	0.875789i	0.494342	−	0.869268i	$-0.335409\pi$
$410$	−1.05238e10	−	1.82278e10i	−0.0183927	−	0.0318571i
$411$		0			0
$412$	−1.01871e11	+	1.76445e11i	−0.174186	+	0.301698i
$413$	−1.06848e11			−0.180713
$414$		0			0
$415$	−3.97956e11			−0.658595
$416$	−9.33725e10	+	1.61726e11i	−0.152862	+	0.264765i
$417$		0			0
$418$	1.41664e11	+	2.45369e11i	0.226968	+	0.393121i
$419$	−2.08346e11	−	3.60866e11i	−0.330235	−	0.571983i	0.652323	−	0.757941i	$-0.273795\pi$
$419$	−2.08346e11	−	3.60866e11i	−0.330235	−	0.571983i	−0.982558	+	0.185958i	$0.940461\pi$
$420$		0			0
$421$	5.95217e11	−	1.03095e12i	0.923434	−	1.59943i	0.129374	−	0.991596i	$-0.458703\pi$
$421$	5.95217e11	−	1.03095e12i	0.923434	−	1.59943i	0.794060	−	0.607839i	$-0.207963\pi$
$422$	−7.44261e11			−1.14240
$423$		0			0
$424$	6.80600e10			0.102269
$425$	−1.48130e11	+	2.56568e11i	−0.220238	+	0.381463i
$426$		0			0
$427$	−1.58019e10	−	2.73697e10i	−0.0230029	−	0.0398422i
$428$	2.52689e11	+	4.37671e11i	0.363990	+	0.630450i
$429$		0			0
$430$	−2.34347e11	+	4.05902e11i	−0.330561	+	0.572549i
$431$	−4.36455e11			−0.609245			−0.304622	−	0.952473i	$-0.598530\pi$
$431$	−4.36455e11			−0.609245			−0.304622	+	0.952473i	$0.598530\pi$
$432$		0			0
$433$	4.48430e11			0.613055			0.306527	−	0.951862i	$-0.400833\pi$
$433$	4.48430e11			0.613055			0.306527	+	0.951862i	$0.400833\pi$
$434$	−9.97245e9	+	1.72728e10i	−0.0134927	+	0.0233700i
$435$		0			0
$436$	1.72115e11	+	2.98112e11i	0.228102	+	0.395084i
$437$	−3.22482e10	−	5.58556e10i	−0.0422999	−	0.0732656i
$438$		0			0
$439$	3.29851e11	−	5.71319e11i	0.423866	−	0.734157i	−0.572448	−	0.819941i	$-0.694006\pi$
$439$	3.29851e11	−	5.71319e11i	0.423866	−	0.734157i	0.996314	+	0.0857843i	$0.0273396\pi$
$440$	−2.00085e11			−0.254493
$441$		0			0
$442$	−7.05714e11			−0.879485
$443$	−4.74253e11	+	8.21431e11i	−0.585051	+	1.01334i	0.409818	+	0.912167i	$0.365592\pi$
$443$	−4.74253e11	+	8.21431e11i	−0.585051	+	1.01334i	−0.994869	+	0.101171i	$0.967741\pi$
$444$		0			0
$445$	1.38371e10	+	2.39666e10i	0.0167273	+	0.0289726i
$446$	−3.73078e11	−	6.46190e11i	−0.446470	−	0.773309i
$447$		0			0
$448$	7.98595e9	−	1.38321e10i	0.00936647	−	0.0162232i
$449$	−6.11763e11			−0.710354			−0.355177	−	0.934799i	$-0.615579\pi$
$449$	−6.11763e11			−0.710354			−0.355177	+	0.934799i	$0.615579\pi$
$450$		0			0
$451$	−8.48981e10			−0.0966282
$452$	−3.46471e11	+	6.00105e11i	−0.390430	+	0.676245i
$453$		0			0
$454$	−2.12694e11	−	3.68397e11i	−0.234965	−	0.406972i
$455$	7.37523e10	+	1.27743e11i	0.0806723	+	0.139728i
$456$		0			0
$457$	1.89516e11	−	3.28252e11i	0.203247	−	0.352034i	−0.746326	−	0.665581i	$-0.768184\pi$
$457$	1.89516e11	−	3.28252e11i	0.203247	−	0.352034i	0.949573	+	0.313547i	$0.101517\pi$
$458$	6.39852e11			0.679492
$459$		0			0
$460$	4.55471e10			0.0474297
$461$	4.45031e11	−	7.70817e11i	0.458919	−	0.794872i	−0.539985	−	0.841675i	$-0.681570\pi$
$461$	4.45031e11	−	7.70817e11i	0.458919	−	0.794872i	0.998904	+	0.0468032i	$0.0149034\pi$
$462$		0			0
$463$	−6.64261e11	−	1.15053e12i	−0.671776	−	1.16355i	−0.977400	−	0.211397i	$-0.932199\pi$
$463$	−6.64261e11	−	1.15053e12i	−0.671776	−	1.16355i	0.305625	−	0.952152i	$-0.401135\pi$
$464$	1.25844e11	+	2.17968e11i	0.126038	+	0.218304i
$465$		0			0
$466$	−5.22670e10	+	9.05291e10i	−0.0513441	+	0.0889307i
$467$	1.65638e12			1.61151			0.805755	−	0.592249i	$-0.201760\pi$
$467$	1.65638e12			1.61151			0.805755	+	0.592249i	$0.201760\pi$
$468$		0			0
$469$	1.15546e11			0.110275
$470$	7.36443e10	−	1.27556e11i	0.0696143	−	0.120576i
$471$		0			0
$472$	−2.29857e11	−	3.98125e11i	−0.213167	−	0.369216i
$473$	9.45269e11	+	1.63725e12i	0.868321	+	1.50398i
$474$		0			0
$475$	1.88633e11	−	3.26721e11i	0.170018	−	0.294480i
$476$	6.03582e10			0.0538896
$477$		0			0
$478$	−9.06837e11			−0.794518
$479$	5.39866e11	−	9.35075e11i	0.468571	−	0.811590i	−0.530783	−	0.847508i	$-0.678102\pi$
$479$	5.39866e11	−	9.35075e11i	0.468571	−	0.811590i	0.999355	+	0.0359180i	$0.0114355\pi$
$480$		0			0
$481$	−3.83532e11	−	6.64298e11i	−0.326700	−	0.565861i
$482$	−3.69193e10	−	6.39461e10i	−0.0311560	−	0.0539638i
$483$		0			0
$484$	−1.01715e11	+	1.76176e11i	−0.0842523	+	0.145929i
$485$	−5.85973e11			−0.480883
$486$		0			0
$487$	1.60549e12			1.29338			0.646690	−	0.762753i	$-0.276153\pi$
$487$	1.60549e12			1.29338			0.646690	+	0.762753i	$0.276153\pi$
$488$	6.79879e10	−	1.17759e11i	0.0542678	−	0.0939946i
$489$		0			0
$490$	2.74553e11	+	4.75540e11i	0.215151	+	0.372653i
$491$	−3.96815e11	−	6.87303e11i	−0.308121	−	0.533681i	0.669831	−	0.742514i	$-0.266367\pi$
$491$	−3.96815e11	−	6.87303e11i	−0.308121	−	0.533681i	−0.977951	+	0.208833i	$0.933033\pi$
$492$		0			0
$493$	−4.75567e11	+	8.23706e11i	−0.362577	+	0.628002i
$494$	8.98677e11			0.678941
$495$		0			0
$496$	−8.58134e10			−0.0636630
$497$	−1.84294e11	+	3.19207e11i	−0.135490	+	0.234676i
$498$		0			0
$499$	9.84754e11	+	1.70564e12i	0.711010	+	1.23150i	0.964479	+	0.264161i	$0.0850951\pi$
$499$	9.84754e11	+	1.70564e12i	0.711010	+	1.23150i	−0.253469	+	0.967344i	$0.581572\pi$
$500$	3.50712e11	+	6.07450e11i	0.250949	+	0.434656i
$501$		0			0
$502$	−5.44155e11	+	9.42504e11i	−0.382434	+	0.662394i
$503$	−5.42230e11			−0.377683			−0.188842	−	0.982008i	$-0.560473\pi$
$503$	−5.42230e11			−0.377683			−0.188842	+	0.982008i	$0.560473\pi$
$504$		0			0
$505$	9.20216e11			0.629620
$506$	9.18599e10	−	1.59106e11i	0.0622944	−	0.107897i
$507$		0			0
$508$	−1.53549e11	−	2.65954e11i	−0.102296	−	0.177182i
$509$	8.46074e11	+	1.46544e12i	0.558699	+	0.967696i	0.997605	+	0.0691628i	$0.0220328\pi$
$509$	8.46074e11	+	1.46544e12i	0.558699	+	0.967696i	−0.438906	+	0.898533i	$0.644634\pi$
$510$		0			0
$511$	1.21494e11	−	2.10434e11i	0.0788246	−	0.136528i
$512$	6.87195e10			0.0441942
$513$		0			0
$514$	−1.49753e12			−0.946329
$515$	−3.46202e11	+	5.99639e11i	−0.216869	+	0.375627i
$516$		0			0
$517$	−2.97053e11	−	5.14511e11i	−0.182863	−	0.316729i
$518$	3.28027e10	+	5.68160e10i	0.0200182	+	0.0346726i
$519$		0			0
$520$	−3.17321e11	+	5.49616e11i	−0.190320	+	0.329643i
$521$	2.97596e12			1.76953			0.884764	−	0.466040i	$-0.154320\pi$
$521$	2.97596e12			1.76953			0.884764	+	0.466040i	$0.154320\pi$
$522$		0			0
$523$	−1.07989e12			−0.631137			−0.315568	−	0.948903i	$-0.602195\pi$
$523$	−1.07989e12			−0.631137			−0.315568	+	0.948903i	$0.602195\pi$
$524$	−3.56627e11	+	6.17695e11i	−0.206644	+	0.357918i
$525$		0			0
$526$	7.52321e11	+	1.30306e12i	0.428516	+	0.742212i
$527$	−1.62145e11	−	2.80844e11i	−0.0915707	−	0.158605i
$528$		0			0
$529$	8.79665e11	−	1.52363e12i	0.488390	−	0.845917i
$530$	2.31298e11			0.127330
$531$		0			0
$532$	−7.68619e10			−0.0416015
$533$	−1.34643e11	+	2.33208e11i	−0.0722621	+	0.125162i
$534$		0			0
$535$	8.58749e11	+	1.48740e12i	0.453183	+	0.784937i
$536$	2.48570e11	+	4.30537e11i	0.130079	+	0.225304i
$537$		0			0
$538$	−9.81795e11	+	1.70052e12i	−0.505244	+	0.875107i
$539$	2.21489e12			1.13032
$540$		0			0
$541$	−2.02167e12			−1.01467			−0.507333	−	0.861750i	$-0.669369\pi$
$541$	−2.02167e12			−1.01467			−0.507333	+	0.861750i	$0.669369\pi$
$542$	1.31406e12	−	2.27602e12i	0.654061	−	1.13287i
$543$		0			0
$544$	1.29846e11	+	2.24900e11i	0.0635674	+	0.110102i
$545$	5.84922e11	+	1.01311e12i	0.283997	+	0.491897i
$546$		0			0
$547$	1.31306e12	−	2.27429e12i	0.627107	−	1.08618i	−0.361022	−	0.932557i	$-0.617572\pi$
$547$	1.31306e12	−	2.27429e12i	0.627107	−	1.08618i	0.988129	−	0.153624i	$-0.0490944\pi$
$548$	7.37876e11			0.349519
$549$		0			0
$550$	1.07465e12			0.500766
$551$	6.05601e11	−	1.04893e12i	0.279901	−	0.484802i
$552$		0			0
$553$	2.34240e11	+	4.05716e11i	0.106512	+	0.184484i
$554$	−5.20107e11	−	9.00852e11i	−0.234584	−	0.406312i
$555$		0			0
$556$	−2.76021e11	+	4.78082e11i	−0.122491	+	0.212161i
$557$	3.48482e12			1.53402			0.767012	−	0.641633i	$-0.221743\pi$
$557$	3.48482e12			1.53402			0.767012	+	0.641633i	$0.221743\pi$
$558$		0			0
$559$	5.99653e12			2.59745
$560$	2.71398e10	−	4.70075e10i	0.0116617	−	0.0201986i
$561$		0			0
$562$	−4.16772e11	−	7.21870e11i	−0.176232	−	0.305243i
$563$	1.38546e12	+	2.39968e12i	0.581173	+	1.00662i	0.995341	+	0.0964202i	$0.0307393\pi$
$563$	1.38546e12	+	2.39968e12i	0.581173	+	1.00662i	−0.414168	+	0.910200i	$0.635927\pi$
$564$		0			0
$565$	−1.17746e12	+	2.03942e12i	−0.486102	+	0.841954i
$566$	−1.45119e12			−0.594360
$567$		0			0
$568$	−1.58586e12			−0.639289
$569$	3.35191e11	−	5.80568e11i	0.134056	−	0.232192i	−0.791180	−	0.611583i	$-0.790533\pi$
$569$	3.35191e11	−	5.80568e11i	0.134056	−	0.232192i	0.925237	+	0.379391i	$0.123866\pi$
$570$		0			0
$571$	−1.33562e12	−	2.31336e12i	−0.525798	−	0.910710i	−0.999548	−	0.0300503i	$-0.990433\pi$
$571$	−1.33562e12	−	2.31336e12i	−0.525798	−	0.910710i	0.473750	−	0.880659i	$-0.342900\pi$
$572$	1.27995e12	+	2.21694e12i	0.499933	+	0.865909i
$573$		0			0
$574$	1.15157e10	−	1.99458e10i	0.00442779	−	0.00766916i
$575$	−2.44633e11			−0.0933274
$576$		0			0
$577$	−6.59284e11			−0.247618			−0.123809	−	0.992306i	$-0.539511\pi$
$577$	−6.59284e11			−0.247618			−0.123809	+	0.992306i	$0.539511\pi$
$578$	4.58011e11	−	7.93299e11i	0.170687	−	0.295639i
$579$		0			0
$580$	4.27673e11	+	7.40751e11i	0.156923	+	0.271798i
$581$	−2.17732e11	−	3.77123e11i	−0.0792738	−	0.137306i
$582$		0			0
$583$	4.66484e11	−	8.07973e11i	0.167235	−	0.289660i
$584$	1.04546e12			0.371921
$585$		0			0
$586$	1.16091e12			0.406686
$587$	−5.24733e11	+	9.08864e11i	−0.182418	+	0.315956i	−0.942703	−	0.333632i	$-0.891726\pi$
$587$	−5.24733e11	+	9.08864e11i	−0.182418	+	0.315956i	0.760286	+	0.649589i	$0.225059\pi$
$588$		0			0
$589$	2.06481e11	+	3.57635e11i	0.0706904	+	0.122439i
$590$	−7.81156e11	−	1.35300e12i	−0.265402	−	0.459689i
$591$		0			0
$592$	−1.41134e11	+	2.44452e11i	−0.0472264	+	0.0817986i
$593$	−1.31188e12			−0.435662			−0.217831	−	0.975987i	$-0.569898\pi$
$593$	−1.31188e12			−0.435662			−0.217831	+	0.975987i	$0.569898\pi$
$594$		0			0
$595$	2.05124e11			0.0670949
$596$	−9.65821e11	+	1.67285e12i	−0.313537	+	0.543062i
$597$		0			0
$598$	−2.91367e11	−	5.04663e11i	−0.0931721	−	0.161379i
$599$	1.68801e12	+	2.92373e12i	0.535742	+	0.927932i	0.999127	+	0.0417749i	$0.0133012\pi$
$599$	1.68801e12	+	2.92373e12i	0.535742	+	0.927932i	−0.463385	+	0.886157i	$0.653365\pi$
$600$		0			0
$601$	−1.31940e12	+	2.28527e12i	−0.412517	+	0.714501i	−0.995164	−	0.0982246i	$-0.968684\pi$
$601$	−1.31940e12	+	2.28527e12i	−0.412517	+	0.714501i	0.582647	+	0.812725i	$0.302017\pi$
$602$	−5.12871e11			−0.159156
$603$		0			0
$604$	−1.10415e12			−0.337568
$605$	−3.45673e11	+	5.98723e11i	−0.104898	+	0.181688i
$606$		0			0
$607$	2.57969e12	+	4.46816e12i	0.771293	+	1.33592i	0.936855	+	0.349719i	$0.113723\pi$
$607$	2.57969e12	+	4.46816e12i	0.771293	+	1.33592i	−0.165562	+	0.986199i	$0.552944\pi$
$608$	−1.65350e11	−	2.86395e11i	−0.0490725	−	0.0849960i
$609$		0			0
$610$	2.31053e11	−	4.00195e11i	0.0675658	−	0.117027i
$611$	−1.88443e12			−0.547008
$612$		0			0
$613$	−5.37354e11			−0.153705			−0.0768525	−	0.997042i	$-0.524487\pi$
$613$	−5.37354e11			−0.153705			−0.0768525	+	0.997042i	$0.524487\pi$
$614$	−1.45582e12	+	2.52155e12i	−0.413380	+	0.715995i
$615$		0			0
$616$	−1.09472e11	−	1.89610e11i	−0.0306329	−	0.0530577i
$617$	−2.31679e12	−	4.01280e12i	−0.643582	−	1.11472i	−0.984627	−	0.174669i	$-0.944114\pi$
$617$	−2.31679e12	−	4.01280e12i	−0.643582	−	1.11472i	0.341046	−	0.940047i	$-0.389219\pi$
$618$		0			0
$619$	−1.53134e12	+	2.65235e12i	−0.419240	+	0.726145i	−0.995863	−	0.0908655i	$-0.971037\pi$
$619$	−1.53134e12	+	2.65235e12i	−0.419240	+	0.726145i	0.576623	+	0.817010i	$0.304370\pi$
$620$	−2.91631e11			−0.0792632
$621$		0			0
$622$	−1.43727e12			−0.385019
$623$	−1.51413e10	+	2.62255e10i	−0.00402687	+	0.00697475i
$624$		0			0
$625$	2.36830e10	+	4.10202e10i	0.00620836	+	0.0107532i
$626$	−4.41115e10	−	7.64034e10i	−0.0114807	−	0.0198851i
$627$		0			0
$628$	5.41641e11	−	9.38150e11i	0.138961	−	0.240688i
$629$	−1.06670e12			−0.271715
$630$		0			0
$631$	−5.46928e10			−0.0137340			−0.00686702	−	0.999976i	$-0.502186\pi$
$631$	−5.46928e10			−0.0137340			−0.00686702	+	0.999976i	$0.502186\pi$
$632$	−1.00782e12	+	1.74560e12i	−0.251280	+	0.435230i
$633$		0			0
$634$	1.55844e11	+	2.69930e11i	0.0383080	+	0.0663514i
$635$	−5.21826e11	−	9.03830e11i	−0.127363	−	0.220600i
$636$		0			0
$637$	3.51266e12	−	6.08411e12i	0.845297	−	1.46410i
$638$	3.45014e12			0.824410
$639$		0			0
$640$	2.33539e11			0.0550236
$641$	2.39034e12	−	4.14019e12i	0.559240	−	0.968633i	−0.438320	−	0.898819i	$-0.644426\pi$
$641$	2.39034e12	−	4.14019e12i	0.559240	−	0.968633i	0.997560	−	0.0698136i	$-0.0222404\pi$
$642$		0			0
$643$	−2.05242e12	−	3.55490e12i	−0.473497	−	0.820121i	0.526043	−	0.850458i	$-0.323675\pi$
$643$	−2.05242e12	−	3.55490e12i	−0.473497	−	0.820121i	−0.999540	+	0.0303374i	$0.990342\pi$
$644$	2.49200e10	+	4.31628e10i	0.00570903	+	0.00988833i
$645$		0			0
$646$	6.24861e11	−	1.08229e12i	0.141168	−	0.244511i
$647$	−5.49263e12			−1.23228			−0.616142	−	0.787635i	$-0.711305\pi$
$647$	−5.49263e12			−1.23228			−0.616142	+	0.787635i	$0.711305\pi$
$648$		0			0
$649$	−6.30178e12			−1.39432
$650$	1.70432e12	−	2.95198e12i	0.374492	−	0.648638i
$651$		0			0
$652$	−1.06041e11	−	1.83669e11i	−0.0229806	−	0.0398035i
$653$	−2.07997e12	−	3.60262e12i	−0.447660	−	0.775369i	0.550573	−	0.834787i	$-0.314409\pi$
$653$	−2.07997e12	−	3.60262e12i	−0.447660	−	0.775369i	−0.998233	+	0.0594172i	$0.981076\pi$
$654$		0			0
$655$	−1.21197e12	+	2.09920e12i	−0.257281	+	0.445623i
$656$	9.90932e10			0.0208918
$657$		0			0
$658$	1.61171e11			0.0335174
$659$	−1.07647e12	+	1.86451e12i	−0.222341	+	0.385105i	−0.955518	−	0.294932i	$-0.904703\pi$
$659$	−1.07647e12	+	1.86451e12i	−0.222341	+	0.385105i	0.733178	+	0.680037i	$0.238036\pi$
$660$		0			0
$661$	−4.31989e12	−	7.48227e12i	−0.880169	−	1.52450i	−0.851152	−	0.524919i	$-0.824096\pi$
$661$	−4.31989e12	−	7.48227e12i	−0.880169	−	1.52450i	−0.0290173	−	0.999579i	$-0.509238\pi$
$662$	8.54408e11	+	1.47988e12i	0.172904	+	0.299478i
$663$		0			0
$664$	9.36797e11	−	1.62258e12i	0.187020	−	0.323929i
$665$	−2.61210e11			−0.0517956
$666$		0			0
$667$	−7.85387e11			−0.153645
$668$	3.65440e11	−	6.32960e11i	0.0710104	−	0.122994i
$669$		0			0
$670$	8.44751e11	+	1.46315e12i	0.161954	+	0.280513i
$671$	−9.31979e11	−	1.61423e12i	−0.177482	−	0.307408i
$672$		0			0
$673$	1.45394e12	−	2.51830e12i	0.273199	−	0.473195i	−0.696480	−	0.717576i	$-0.745252\pi$
$673$	1.45394e12	−	2.51830e12i	0.273199	−	0.473195i	0.969679	+	0.244381i	$0.0785849\pi$
$674$	−2.81242e12			−0.524942
$675$		0			0
$676$	5.40492e12			0.995472
$677$	−2.13411e12	+	3.69639e12i	−0.390452	+	0.676283i	−0.992509	−	0.122170i	$-0.961015\pi$
$677$	−2.13411e12	+	3.69639e12i	−0.390452	+	0.676283i	0.602057	+	0.798453i	$0.294348\pi$
$678$		0			0
$679$	−3.20601e11	−	5.55298e11i	−0.0578830	−	0.100256i
$680$	4.41274e11	+	7.64309e11i	0.0791441	+	0.137082i
$681$		0			0
$682$	−5.88165e11	+	1.01873e12i	−0.104105	+	0.180314i
$683$	−7.69165e11			−0.135247			−0.0676233	−	0.997711i	$-0.521542\pi$
$683$	−7.69165e11			−0.135247			−0.0676233	+	0.997711i	$0.521542\pi$
$684$		0			0
$685$	2.50763e12			0.435166
$686$	−6.07764e11	+	1.05268e12i	−0.104779	+	0.181483i
$687$		0			0
$688$	−1.10332e12	−	1.91100e12i	−0.187738	−	0.325172i
$689$	−1.47962e12	−	2.56278e12i	−0.250129	−	0.433237i
$690$		0			0
$691$	−6.93242e11	+	1.20073e12i	−0.115673	+	0.200352i	−0.918049	−	0.396467i	$-0.870236\pi$
$691$	−6.93242e11	+	1.20073e12i	−0.115673	+	0.200352i	0.802375	+	0.596820i	$0.203569\pi$
$692$	−4.52327e12			−0.749851
$693$		0			0
$694$	1.33284e12			0.218103
$695$	−9.38039e11	+	1.62473e12i	−0.152507	+	0.264150i
$696$		0			0
$697$	1.87238e11	+	3.24305e11i	0.0300501	+	0.0520483i
$698$	−2.57094e12	−	4.45300e12i	−0.409962	−	0.710074i
$699$		0			0
$700$	−1.45767e11	+	2.52476e11i	−0.0229466	+	0.0397447i
$701$	−5.51186e12			−0.862119			−0.431059	−	0.902324i	$-0.641860\pi$
$701$	−5.51186e12			−0.862119			−0.431059	+	0.902324i	$0.641860\pi$
$702$		0			0
$703$	1.35837e12			0.209758
$704$	4.71004e11	−	8.15802e11i	0.0722682	−	0.125172i
$705$		0			0
$706$	−3.26151e12	−	5.64910e12i	−0.494080	−	0.855772i
$707$	5.03474e11	+	8.72043e11i	0.0757862	+	0.131265i
$708$		0			0
$709$	−1.21576e12	+	2.10576e12i	−0.180693	+	0.312969i	−0.942117	−	0.335286i	$-0.891167\pi$
$709$	−1.21576e12	+	2.10576e12i	−0.180693	+	0.312969i	0.761424	+	0.648254i	$0.224501\pi$
$710$	−5.38944e12			−0.795942
$711$		0			0
$712$	−1.30292e11			−0.0190001
$713$	1.33890e11	−	2.31904e11i	0.0194019	−	0.0336050i
$714$		0			0
$715$	4.34984e12	+	7.53414e12i	0.622437	+	1.07809i
$716$	7.51017e10	+	1.30080e11i	0.0106793	+	0.0184970i
$717$		0			0
$718$	4.48063e12	−	7.76068e12i	0.629186	−	1.08978i
$719$	−2.70890e12			−0.378018			−0.189009	−	0.981975i	$-0.560528\pi$
$719$	−2.70890e12			−0.378018			−0.189009	+	0.981975i	$0.560528\pi$
$720$		0			0
$721$	−7.57664e11			−0.104416
$722$	1.78579e12	−	3.09307e12i	0.244575	−	0.423616i
$723$		0			0
$724$	6.95546e11	+	1.20472e12i	0.0940811	+	0.162953i
$725$	−2.29702e12	−	3.97856e12i	−0.308776	−	0.534816i
$726$		0			0
$727$	−2.63323e11	+	4.56089e11i	−0.0349611	+	0.0605543i	−0.882977	−	0.469417i	$-0.844464\pi$
$727$	−2.63323e11	+	4.56089e11i	−0.0349611	+	0.0605543i	0.848015	+	0.529971i	$0.177797\pi$
$728$	−6.94458e11			−0.0916336
$729$		0			0
$730$	3.55294e12			0.463058
$731$	4.16946e12	−	7.22172e12i	0.540073	−	0.935433i
$732$		0			0
$733$	1.39005e12	+	2.40763e12i	0.177853	+	0.308051i	0.941145	−	0.338003i	$-0.109751\pi$
$733$	1.39005e12	+	2.40763e12i	0.177853	+	0.308051i	−0.763292	+	0.646054i	$0.776418\pi$
$734$	−3.00845e12	−	5.21079e12i	−0.382570	−	0.662630i
$735$		0			0
$736$	−1.07219e11	+	1.85709e11i	−0.0134686	+	0.0233283i
$737$	6.81481e12			0.850844
$738$		0			0
$739$	−2.36558e12			−0.291768			−0.145884	−	0.989302i	$-0.546603\pi$
$739$	−2.36558e12			−0.291768			−0.145884	+	0.989302i	$0.546603\pi$
$740$	−4.79636e11	+	8.30754e11i	−0.0587989	+	0.101843i
$741$		0			0
$742$	1.26549e11	+	2.19189e11i	0.0153264	+	0.0265462i
$743$	−6.56989e12	−	1.13794e13i	−0.790876	−	1.36984i	−0.925425	−	0.378930i	$-0.876292\pi$
$743$	−6.56989e12	−	1.13794e13i	−0.790876	−	1.36984i	0.134550	−	0.990907i	$-0.457041\pi$
$744$		0			0
$745$	−3.28228e12	+	5.68508e12i	−0.390367	+	0.676135i
$746$	−1.29959e12			−0.153632
$747$		0			0
$748$	3.55987e12			0.415792
$749$	−9.39688e11	+	1.62759e12i	−0.109098	+	0.188963i
$750$		0			0
$751$	3.64718e12	+	6.31710e12i	0.418387	+	0.724667i	0.995777	−	0.0918011i	$-0.0292624\pi$
$751$	3.64718e12	+	6.31710e12i	0.418387	+	0.724667i	−0.577391	+	0.816468i	$0.695929\pi$
$752$	3.46721e11	+	6.00538e11i	0.0395366	+	0.0684794i
$753$		0			0
$754$	5.47169e12	−	9.47724e12i	0.616524	−	1.06785i
$755$	−3.75238e12			−0.420287
$756$		0			0
$757$	−1.63020e13			−1.80430			−0.902150	−	0.431423i	$-0.858012\pi$
$757$	−1.63020e13			−1.80430			−0.902150	+	0.431423i	$0.858012\pi$
$758$	−1.62183e12	+	2.80910e12i	−0.178441	+	0.309069i
$759$		0			0
$760$	−5.61931e11	−	9.73294e11i	−0.0610973	−	0.105824i
$761$	4.84472e12	+	8.39131e12i	0.523646	+	0.906982i	0.999621	+	0.0275231i	$0.00876197\pi$
$761$	4.84472e12	+	8.39131e12i	0.523646	+	0.906982i	−0.475975	+	0.879459i	$0.657905\pi$
$762$		0			0
$763$	−6.40052e11	+	1.10860e12i	−0.0683683	+	0.118417i
$764$	8.27629e12			0.878851
$765$		0			0
$766$	−7.62906e11			−0.0800648
$767$	−9.99420e12	+	1.73105e13i	−1.04272	+	1.80605i
$768$		0			0
$769$	−6.06644e12	−	1.05074e13i	−0.625554	−	1.08349i	−0.988433	−	0.151656i	$-0.951539\pi$
$769$	−6.06644e12	−	1.05074e13i	−0.625554	−	1.08349i	0.362879	−	0.931836i	$-0.381794\pi$
$770$	−3.72032e11	−	6.44379e11i	−0.0381393	−	0.0660591i
$771$		0			0
$772$	1.65631e12	−	2.86881e12i	0.167828	−	0.290686i
$773$	−1.68647e13			−1.69891			−0.849454	−	0.527663i	$-0.823068\pi$
$773$	−1.68647e13			−1.69891			−0.849454	+	0.527663i	$0.823068\pi$
$774$		0			0
$775$	1.56635e12			0.155966
$776$	1.37939e12	−	2.38918e12i	0.136556	−	0.236522i
$777$		0			0
$778$	1.51836e12	+	2.62987e12i	0.148582	+	0.257351i
$779$	−2.38434e11	−	4.12980e11i	−0.0231979	−	0.0401800i
$780$		0			0
$781$	−1.08695e13	+	1.88265e13i	−1.04539	+	1.81067i
$782$	−8.10366e11			−0.0774909
$783$		0			0
$784$	−2.58522e12			−0.244385
$785$	1.84073e12	−	3.18825e12i	0.173013	−	0.299667i
$786$		0			0
$787$	3.00058e12	+	5.19716e12i	0.278817	+	0.482925i	0.971091	−	0.238710i	$-0.0767245\pi$
$787$	3.00058e12	+	5.19716e12i	0.278817	+	0.482925i	−0.692274	+	0.721635i	$0.743391\pi$
$788$	−1.12779e12	−	1.95340e12i	−0.104199	−	0.180477i
$789$		0			0
$790$	−3.42503e12	+	5.93232e12i	−0.312854	+	0.541880i
$791$	−2.57688e12			−0.234045
$792$		0			0
$793$	−5.91223e12			−0.530911
$794$	−3.20190e12	+	5.54585e12i	−0.285901	+	0.495195i
$795$		0			0
$796$	3.18123e12	+	5.51006e12i	0.280858	+	0.486460i
$797$	7.15775e12	+	1.23976e13i	0.628368	+	1.08837i	0.987879	+	0.155225i	$0.0496102\pi$
$797$	7.15775e12	+	1.23976e13i	0.628368	+	1.08837i	−0.359511	+	0.933141i	$0.617056\pi$
$798$		0			0
$799$	−1.31026e12	+	2.26945e12i	−0.113736	+	0.196997i
$800$	−1.25433e12			−0.108270
$801$		0			0
$802$	1.40190e13			1.19655
$803$	7.16561e12	−	1.24112e13i	0.608181	−	1.05340i
$804$		0			0
$805$	8.46892e10	+	1.46686e11i	0.00710799	+	0.0123114i
$806$	1.86558e12	+	3.23128e12i	0.155706	+	0.269691i
$807$		0			0
$808$	−2.16621e12	+	3.75198e12i	−0.178792	+	0.309678i
$809$	−1.09893e13			−0.901992			−0.450996	−	0.892526i	$-0.648931\pi$
$809$	−1.09893e13			−0.901992			−0.450996	+	0.892526i	$0.648931\pi$
$810$		0			0
$811$	2.15444e13			1.74880			0.874399	−	0.485207i	$-0.161256\pi$
$811$	2.15444e13			1.74880			0.874399	+	0.485207i	$0.161256\pi$
$812$	−4.67982e11	+	8.10568e11i	−0.0377770	+	0.0654316i
$813$		0			0
$814$	1.93467e12	+	3.35095e12i	0.154453	+	0.267521i
$815$	−3.60375e11	−	6.24188e11i	−0.0286118	−	0.0495571i
$816$		0			0
$817$	−5.30952e12	+	9.19635e12i	−0.416923	+	0.722132i
$818$	9.15680e12			0.715079
$819$		0			0
$820$	3.36762e11			0.0260112
$821$	−2.85874e12	+	4.95148e12i	−0.219599	+	0.380357i	−0.954685	−	0.297617i	$-0.903808\pi$
$821$	−2.85874e12	+	4.95148e12i	−0.219599	+	0.380357i	0.735086	+	0.677973i	$0.237142\pi$
$822$		0			0
$823$	5.02622e12	+	8.70567e12i	0.381893	+	0.661459i	0.991333	−	0.131374i	$-0.0419388\pi$
$823$	5.02622e12	+	8.70567e12i	0.381893	+	0.661459i	−0.609440	+	0.792833i	$0.708605\pi$
$824$	−1.62993e12	−	2.82313e12i	−0.123168	−	0.213333i
$825$		0			0
$826$	8.54783e11	−	1.48053e12i	0.0638918	−	0.110664i
$827$	2.29581e13			1.70672			0.853359	−	0.521324i	$-0.174562\pi$
$827$	2.29581e13			1.70672			0.853359	+	0.521324i	$0.174562\pi$
$828$		0			0
$829$	−1.57277e13			−1.15657			−0.578283	−	0.815836i	$-0.696277\pi$
$829$	−1.57277e13			−1.15657			−0.578283	+	0.815836i	$0.696277\pi$
$830$	3.18364e12	−	5.51423e12i	0.232848	−	0.403305i
$831$		0			0
$832$	−1.49396e12	−	2.58762e12i	−0.108090	−	0.187217i
$833$	−4.88480e12	−	8.46072e12i	−0.351515	−	0.608842i
$834$		0			0
$835$	1.24192e12	−	2.15108e12i	0.0884109	−	0.153132i
$836$	−4.53324e12			−0.320982
$837$		0			0
$838$	6.66708e12			0.467022
$839$	4.26084e12	−	7.37999e12i	0.296870	−	0.514194i	−0.678548	−	0.734556i	$-0.737391\pi$
$839$	4.26084e12	−	7.37999e12i	0.296870	−	0.514194i	0.975418	+	0.220362i	$0.0707239\pi$
$840$		0			0
$841$	−1.20955e11	−	2.09500e11i	−0.00833762	−	0.0144412i
$842$	9.52347e12	+	1.64951e13i	0.652966	+	1.13097i
$843$		0			0
$844$	5.95409e12	−	1.03128e13i	0.403900	−	0.699576i
$845$	1.83683e13			1.23941
$846$		0			0
$847$	−7.56507e11			−0.0505054
$848$	−5.44480e11	+	9.43067e11i	−0.0361577	+	0.0626270i
$849$		0			0
$850$	−2.37008e12	−	4.10509e12i	−0.155732	−	0.269735i
$851$	−4.40407e11	−	7.62808e11i	−0.0287854	−	0.0498577i
$852$		0			0
$853$	9.15802e11	−	1.58621e12i	0.0592285	−	0.102587i	−0.834891	−	0.550416i	$-0.814469\pi$
$853$	9.15802e11	−	1.58621e12i	0.0592285	−	0.102587i	0.894119	+	0.447829i	$0.147803\pi$
$854$	5.05660e11			0.0325311
$855$		0			0
$856$	−8.08606e12			−0.514760
$857$	3.10036e11	−	5.36998e11i	0.0196335	−	0.0340063i	−0.856042	−	0.516907i	$-0.827083\pi$
$857$	3.10036e11	−	5.36998e11i	0.0196335	−	0.0340063i	0.875675	+	0.482900i	$0.160417\pi$
$858$		0			0
$859$	2.85791e12	+	4.95004e12i	0.179093	+	0.310198i	0.941570	−	0.336817i	$-0.109350\pi$
$859$	2.85791e12	+	4.95004e12i	0.179093	+	0.310198i	−0.762477	+	0.647015i	$0.776017\pi$
$860$	−3.74956e12	−	6.49443e12i	−0.233742	−	0.404853i
$861$		0			0
$862$	3.49164e12	−	6.04770e12i	0.215401	−	0.373085i
$863$	2.02596e13			1.24332			0.621658	−	0.783289i	$-0.286460\pi$
$863$	2.02596e13			1.24332			0.621658	+	0.783289i	$0.286460\pi$
$864$		0			0
$865$	−1.53720e13			−0.933596
$866$	−3.58744e12	+	6.21363e12i	−0.216748	+	0.375418i
$867$		0			0
$868$	−1.59559e11	−	2.76365e11i	−0.00954076	−	0.0165251i
$869$	1.38153e13	+	2.39287e13i	0.821808	+	1.42341i
$870$		0			0
$871$	1.08078e13	−	1.87197e13i	0.636293	−	1.10209i
$872$	−5.50768e12			−0.322585
$873$		0			0
$874$	1.03194e12			0.0598211
$875$	−1.30421e12	+	2.25896e12i	−0.0752161	+	0.130278i
$876$		0			0
$877$	4.57286e10	+	7.92043e10i	0.00261030	+	0.00452117i	0.867328	−	0.497738i	$-0.165836\pi$
$877$	4.57286e10	+	7.92043e10i	0.00261030	+	0.00452117i	−0.864717	+	0.502259i	$0.832502\pi$
$878$	5.27762e12	+	9.14111e12i	0.299718	+	0.519127i
$879$		0			0
$880$	1.60068e12	−	2.77245e12i	0.0899770	−	0.155845i
$881$	1.73150e13			0.968347			0.484174	−	0.874972i	$-0.339120\pi$
$881$	1.73150e13			0.968347			0.484174	+	0.874972i	$0.339120\pi$
$882$		0			0
$883$	1.38781e13			0.768259			0.384130	−	0.923279i	$-0.374502\pi$
$883$	1.38781e13			0.768259			0.384130	+	0.923279i	$0.374502\pi$
$884$	5.64571e12	−	9.77866e12i	0.310945	−	0.538572i
$885$		0			0
$886$	−7.58805e12	−	1.31429e13i	−0.413693	−	0.716538i
$887$	−8.82928e12	−	1.52928e13i	−0.478926	−	0.829525i	0.520782	−	0.853690i	$-0.325641\pi$
$887$	−8.82928e12	−	1.52928e13i	−0.478926	−	0.829525i	−0.999708	+	0.0241651i	$0.992307\pi$
$888$		0			0
$889$	5.71010e11	−	9.89018e11i	0.0306610	−	0.0531063i
$890$	−4.42788e11			−0.0236560
$891$		0			0
$892$	1.19385e13			0.631404
$893$	1.66853e12	−	2.88998e12i	0.0878016	−	0.152077i
$894$		0			0
$895$	2.55228e11	+	4.42069e11i	0.0132961	+	0.0230296i
$896$	1.27775e11	+	2.21313e11i	0.00662309	+	0.0114715i
$897$		0			0
$898$	4.89410e12	−	8.47684e12i	0.251148	−	0.435001i
$899$	5.02872e12			0.256767
$900$		0			0
$901$	−4.11520e12			−0.208032
$902$	6.79185e11	−	1.17638e12i	0.0341632	−	0.0591724i
$903$		0			0
$904$	−5.54353e12	−	9.60168e12i	−0.276076	−	0.478178i
$905$	2.36377e12	+	4.09417e12i	0.117135	+	0.202884i
$906$		0			0
$907$	−6.19619e12	+	1.07321e13i	−0.304013	+	0.526565i	−0.977041	−	0.213051i	$-0.931660\pi$
$907$	−6.19619e12	+	1.07321e13i	−0.304013	+	0.526565i	0.673028	+	0.739617i	$0.264993\pi$
$908$	6.80620e12			0.332291
$909$		0			0
$910$	−2.36007e12			−0.114088
$911$	6.90519e12	−	1.19601e13i	0.332157	−	0.575312i	−0.650778	−	0.759268i	$-0.725557\pi$
$911$	6.90519e12	−	1.19601e13i	0.332157	−	0.575312i	0.982934	+	0.183956i	$0.0588904\pi$
$912$		0			0
$913$	−1.28416e13	−	2.22423e13i	−0.611647	−	1.05940i
$914$	3.03226e12	+	5.25203e12i	0.143717	+	0.248925i
$915$		0			0
$916$	−5.11881e12	+	8.86604e12i	−0.240237	+	0.416102i
$917$	−2.65241e12			−0.123874
$918$		0			0
$919$	8.56606e11			0.0396152			0.0198076	−	0.999804i	$-0.493695\pi$
$919$	8.56606e11			0.0396152			0.0198076	+	0.999804i	$0.493695\pi$
$920$	−3.64377e11	+	6.31120e11i	−0.0167689	+	0.0290447i
$921$		0			0
$922$	7.12050e12	+	1.23331e13i	0.324505	+	0.562059i
$923$	3.44766e13	+	5.97152e13i	1.56357	+	2.70818i
$924$		0			0
$925$	2.57612e12	−	4.46197e12i	0.115699	−	0.200396i
$926$	2.12563e13			0.950034
$927$		0			0
$928$	−4.02700e12			−0.178244
$929$	−6.45846e12	+	1.11864e13i	−0.284484	+	0.492741i	−0.972484	−	0.232970i	$-0.925156\pi$
$929$	−6.45846e12	+	1.11864e13i	−0.284484	+	0.492741i	0.688000	+	0.725711i	$0.258489\pi$
$930$		0			0
$931$	6.22045e12	+	1.07741e13i	0.271361	+	0.470012i
$932$	−8.36272e11	−	1.44847e12i	−0.0363058	−	0.0628835i
$933$		0			0
$934$	−1.32510e13	+	2.29514e13i	−0.569755	+	0.986844i
$935$	1.20980e13			0.517679
$936$		0			0
$937$	−3.67867e12			−0.155906			−0.0779530	−	0.996957i	$-0.524838\pi$
$937$	−3.67867e12			−0.155906			−0.0779530	+	0.996957i	$0.524838\pi$
$938$	−9.24371e11	+	1.60106e12i	−0.0389882	+	0.0675296i
$939$		0			0
$940$	1.17831e12	+	2.04089e12i	0.0492248	+	0.0852598i
$941$	−2.22573e13	−	3.85507e13i	−0.925376	−	1.60280i	−0.790955	−	0.611874i	$-0.790416\pi$
$941$	−2.22573e13	−	3.85507e13i	−0.925376	−	1.60280i	−0.134421	−	0.990924i	$-0.542917\pi$
$942$		0			0
$943$	−1.54609e11	+	2.67791e11i	−0.00636697	+	0.0110279i
$944$	7.35544e12			0.301463
$945$		0			0
$946$	−3.02486e13			−1.22799
$947$	9.97716e12	−	1.72810e13i	0.403118	−	0.698221i	−0.590982	−	0.806684i	$-0.701260\pi$
$947$	9.97716e12	−	1.72810e13i	0.403118	−	0.698221i	0.994100	+	0.108464i	$0.0345931\pi$
$948$		0			0
$949$	−2.27284e13	−	3.93667e13i	−0.909641	−	1.57555i
$950$	3.01812e12	+	5.22754e12i	0.120221	+	0.208229i
$951$		0			0
$952$	−4.82866e11	+	8.36348e11i	−0.0190529	+	0.0330005i
$953$	7.13202e12			0.280088			0.140044	−	0.990145i	$-0.455276\pi$
$953$	7.13202e12			0.280088			0.140044	+	0.990145i	$0.455276\pi$
$954$		0			0
$955$	2.81264e13			1.09421
$956$	7.25469e12	−	1.25655e13i	0.280904	−	0.486541i
$957$		0			0
$958$	8.63785e12	+	1.49612e13i	0.331330	+	0.573880i
$959$	1.37199e12	+	2.37635e12i	0.0523802	+	0.0907251i
$960$		0			0
$961$	1.23625e13	−	2.14125e13i	0.467576	−	0.809866i
$962$	1.22730e13			0.462024
$963$		0			0
$964$	1.18142e12			0.0440613
$965$	5.62886e12	−	9.74948e12i	0.208953	−	0.361917i
$966$		0			0
$967$	−1.42088e12	−	2.46103e12i	−0.0522562	−	0.0905104i	0.838714	−	0.544572i	$-0.183308\pi$
$967$	−1.42088e12	−	2.46103e12i	−0.0522562	−	0.0905104i	−0.890970	+	0.454062i	$0.849975\pi$
$968$	−1.62744e12	−	2.81882e12i	−0.0595754	−	0.103188i
$969$		0			0
$970$	4.68778e12	−	8.11948e12i	0.170018	−	0.294480i
$971$	−3.90309e13			−1.40903			−0.704517	−	0.709687i	$-0.748836\pi$
$971$	−3.90309e13			−1.40903			−0.704517	+	0.709687i	$0.748836\pi$
$972$		0			0
$973$	−2.05290e12			−0.0734278
$974$	−1.28439e13	+	2.22463e13i	−0.457279	+	0.792030i
$975$		0			0
$976$	1.08781e12	+	1.88414e12i	0.0383731	+	0.0664642i
$977$	1.08778e13	+	1.88409e13i	0.381958	+	0.661570i	0.991342	−	0.131305i	$-0.0419167\pi$
$977$	1.08778e13	+	1.88409e13i	0.381958	+	0.661570i	−0.609384	+	0.792875i	$0.708583\pi$
$978$		0			0
$979$	−8.93020e11	+	1.54676e12i	−0.0310699	+	0.0538146i
$980$	−8.78570e12			−0.304270
$981$		0			0
$982$	1.26981e13			0.435749
$983$	−2.32499e13	+	4.02700e13i	−0.794201	+	1.37560i	0.129144	+	0.991626i	$0.458777\pi$
$983$	−2.32499e13	+	4.02700e13i	−0.794201	+	1.37560i	−0.923345	+	0.383971i	$0.874556\pi$
$984$		0			0
$985$	−3.83274e12	−	6.63850e12i	−0.129732	−	0.224702i
$986$	−7.60907e12	−	1.31793e13i	−0.256381	−	0.444064i
$987$		0			0
$988$	−7.18941e12	+	1.24524e13i	−0.240042	+	0.415765i
$989$	6.88577e12			0.228860
$990$		0			0
$991$	−1.55209e13			−0.511194			−0.255597	−	0.966783i	$-0.582272\pi$
$991$	−1.55209e13			−0.511194			−0.255597	+	0.966783i	$0.582272\pi$
$992$	6.86507e11	−	1.18906e12i	0.0225083	−	0.0389855i
$993$		0			0
$994$	−2.94871e12	−	5.10731e12i	−0.0958061	−	0.165941i
$995$	1.08112e13	+	1.87256e13i	0.349680	+	0.605664i
$996$		0			0
$997$	2.13167e13	−	3.69216e13i	0.683268	−	1.18346i	−0.290709	−	0.956811i	$-0.593891\pi$
$997$	2.13167e13	−	3.69216e13i	0.683268	−	1.18346i	0.973978	−	0.226644i	$-0.0727754\pi$
$998$	−3.15121e13			−1.00552
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	162.10.c.b.55.1		2
3.2	odd	2		162.10.c.i.55.1		2
9.2	odd	6		18.10.a.a.1.1		1
9.4	even	3	inner	162.10.c.b.109.1		2
9.5	odd	6		162.10.c.i.109.1		2
9.7	even	3		2.10.a.a.1.1	✓	1
36.7	odd	6		16.10.a.d.1.1		1
36.11	even	6		144.10.a.d.1.1		1
45.7	odd	12		50.10.b.a.49.2		2
45.34	even	6		50.10.a.c.1.1		1
45.43	odd	12		50.10.b.a.49.1		2
63.16	even	3		98.10.c.c.67.1		2
63.25	even	3		98.10.c.c.79.1		2
63.34	odd	6		98.10.a.c.1.1		1
63.52	odd	6		98.10.c.b.79.1		2
63.61	odd	6		98.10.c.b.67.1		2
72.43	odd	6		64.10.a.b.1.1		1
72.61	even	6		64.10.a.h.1.1		1
99.43	odd	6		242.10.a.a.1.1		1
117.25	even	6		338.10.a.a.1.1		1
144.43	odd	12		256.10.b.e.129.1		2
144.61	even	12		256.10.b.g.129.1		2
144.115	odd	12		256.10.b.e.129.2		2
144.133	even	12		256.10.b.g.129.2		2
180.7	even	12		400.10.c.d.49.1		2
180.43	even	12		400.10.c.d.49.2		2
180.79	odd	6		400.10.a.b.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2.10.a.a.1.1	✓	1	9.7	even	3
16.10.a.d.1.1		1	36.7	odd	6
18.10.a.a.1.1		1	9.2	odd	6
50.10.a.c.1.1		1	45.34	even	6
50.10.b.a.49.1		2	45.43	odd	12
50.10.b.a.49.2		2	45.7	odd	12
64.10.a.b.1.1		1	72.43	odd	6
64.10.a.h.1.1		1	72.61	even	6
98.10.a.c.1.1		1	63.34	odd	6
98.10.c.b.67.1		2	63.61	odd	6
98.10.c.b.79.1		2	63.52	odd	6
98.10.c.c.67.1		2	63.16	even	3
98.10.c.c.79.1		2	63.25	even	3
144.10.a.d.1.1		1	36.11	even	6
162.10.c.b.55.1		2	1.1	even	1	trivial
162.10.c.b.109.1		2	9.4	even	3	inner
162.10.c.i.55.1		2	3.2	odd	2
162.10.c.i.109.1		2	9.5	odd	6
242.10.a.a.1.1		1	99.43	odd	6
256.10.b.e.129.1		2	144.43	odd	12
256.10.b.e.129.2		2	144.115	odd	12
256.10.b.g.129.1		2	144.61	even	12
256.10.b.g.129.2		2	144.133	even	12
338.10.a.a.1.1		1	117.25	even	6
400.10.a.b.1.1		1	180.79	odd	6
400.10.c.d.49.1		2	180.7	even	12
400.10.c.d.49.2		2	180.43	even	12

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 162 = 2 \cdot 3^{4} \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	162.c (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-8.00000 + 13.8564i) q^{2} +(-128.000 - 221.703i) q^{4} +(-435.000 - 753.442i) q^{5} +(476.000 - 824.456i) q^{7} +4096.00 q^{8} +13920.0 q^{10} +(28074.0 - 48625.6i) q^{11} +(-89047.0 - 154234. i) q^{13} +(7616.00 + 13191.3i) q^{14} +(-32768.0 + 56755.8i) q^{16} -247662. q^{17} +315380. q^{19} +(-111360. + 192881. i) q^{20} +(449184. + 778010. i) q^{22} +(-102252. - 177106. i) q^{23} +(598112. - 1.03596e6i) q^{25} +2.84950e6 q^{26} -243712. q^{28} +(1.92023e6 - 3.32593e6i) q^{29} +(654704. + 1.13398e6i) q^{31} +(-524288. - 908093. i) q^{32} +(1.98130e6 - 3.43171e6i) q^{34} -828240. q^{35} +4.30708e6 q^{37} +(-2.52304e6 + 4.37003e6i) q^{38} +(-1.78176e6 - 3.08610e6i) q^{40} +(-756021. - 1.30947e6i) q^{41} +(-1.68353e7 + 2.91596e7i) q^{43} -1.43739e7 q^{44} +3.27206e6 q^{46} +(5.29054e6 - 9.16348e6i) q^{47} +(1.97237e7 + 3.41624e7i) q^{49} +(9.56980e6 + 1.65754e7i) q^{50} +(-2.27960e7 + 3.94839e7i) q^{52} +1.66162e7 q^{53} -4.88488e7 q^{55} +(1.94970e6 - 3.37697e6i) q^{56} +(3.07236e7 + 5.32148e7i) q^{58} +(-5.61175e7 - 9.71984e7i) q^{59} +(1.65986e7 - 2.87496e7i) q^{61} -2.09505e7 q^{62} +1.67772e7 q^{64} +(-7.74709e7 + 1.34184e8i) q^{65} +(6.06861e7 + 1.05111e8i) q^{67} +(3.17007e7 + 5.49073e7i) q^{68} +(6.62592e6 - 1.14764e7i) q^{70} -3.87173e8 q^{71} +2.55240e8 q^{73} +(-3.44566e7 + 5.96806e7i) q^{74} +(-4.03686e7 - 6.99205e7i) q^{76} +(-2.67264e7 - 4.62916e7i) q^{77} +(-2.46051e8 + 4.26173e8i) q^{79} +5.70163e7 q^{80} +2.41927e7 q^{82} +(2.28710e8 - 3.96138e8i) q^{83} +(1.07733e8 + 1.86599e8i) q^{85} +(-2.69365e8 - 4.66554e8i) q^{86} +(1.14991e8 - 1.99170e8i) q^{88} -3.18095e7 q^{89} -1.69545e8 q^{91} +(-2.61765e7 + 4.53390e7i) q^{92} +(8.46486e7 + 1.46616e8i) q^{94} +(-1.37190e8 - 2.37621e8i) q^{95} +(3.36766e8 - 5.83296e8i) q^{97} -6.31157e8 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 16 q^{2} - 256 q^{4} - 870 q^{5} + 952 q^{7} + 8192 q^{8} + 27840 q^{10} + 56148 q^{11} - 178094 q^{13} + 15232 q^{14} - 65536 q^{16} - 495324 q^{17} + 630760 q^{19} - 222720 q^{20} + 898368 q^{22}+ \cdots - 1262313696 q^{98}+O(q^{100}) \) 2 * q - 16 * q^2 - 256 * q^4 - 870 * q^5 + 952 * q^7 + 8192 * q^8 + 27840 * q^10 + 56148 * q^11 - 178094 * q^13 + 15232 * q^14 - 65536 * q^16 - 495324 * q^17 + 630760 * q^19 - 222720 * q^20 + 898368 * q^22 - 204504 * q^23 + 1196225 * q^25 + 5699008 * q^26 - 487424 * q^28 + 3840450 * q^29 + 1309408 * q^31 - 1048576 * q^32 + 3962592 * q^34 - 1656480 * q^35 + 8614156 * q^37 - 5046080 * q^38 - 3563520 * q^40 - 1512042 * q^41 - 33670604 * q^43 - 28747776 * q^44 + 6544128 * q^46 + 10581072 * q^47 + 39447303 * q^49 + 19139600 * q^50 - 45592064 * q^52 + 33232428 * q^53 - 97697520 * q^55 + 3899392 * q^56 + 61447200 * q^58 - 112235100 * q^59 + 33197218 * q^61 - 41901056 * q^62 + 33554432 * q^64 - 154941780 * q^65 + 121372252 * q^67 + 63401472 * q^68 + 13251840 * q^70 - 774345456 * q^71 + 510480148 * q^73 - 68913248 * q^74 - 80737280 * q^76 - 53452896 * q^77 - 492101840 * q^79 + 114032640 * q^80 + 48385344 * q^82 + 457420236 * q^83 + 215465940 * q^85 - 538729664 * q^86 + 229982208 * q^88 - 63619020 * q^89 - 339090976 * q^91 - 52353024 * q^92 + 169297152 * q^94 - 274380600 * q^95 + 673532062 * q^97 - 1262313696 * q^98

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