LMFDB - Embedded newform 27.11.d.a.8.6

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [27,11,Mod(8,27)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("27.8"); S:= CuspForms(chi, 11); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(27, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([1])) N = Newforms(chi, 11, names="a")

Level:	$ N $	$=$	$ 27 = 3^{3} $
Weight:	$ k $	$=$	$ 11 $
Character orbit:	$[\chi]$	$=$	27.d (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$17.1546458222$
Analytic rank:	$0$
Dimension:	$18$
Relative dimension:	$9$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} - x^{17} + 2219 x^{16} + 4286 x^{15} + 3372866 x^{14} + 7237076 x^{13} + 2694115412 x^{12} + \cdots + 64\!\cdots\!96 $ x^18 - x^17 + 2219x^16 + 4286x^15 + 3372866x^14 + 7237076x^13 + 2694115412x^12 + 6418314128x^11 + 1552978472768x^10 + 3181293598208x^9 + 476242689880064x^8 + 876490866851840x^7 + 103146891634589696x^6 + 253732818059067392x^5 + 8170091944772108288x^4 + 46925087214531510272x^3 + 516504122125249937408x^2 + 1745010292035556474880x + 6469041255171695312896
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{14}\cdot 3^{52} $
Twist minimal:	no (minimal twist has level 9)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			8.6
Root			$5.37603 + 9.31155i$ of defining polynomial
Character	$\chi$	$=$	27.8
Dual form			27.11.d.a.17.6

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(16.1281 + 9.31155i) q^{2} +(-338.590 - 586.455i) q^{4} +(748.776 - 432.306i) q^{5} +(-13727.6 + 23777.0i) q^{7} -31681.3i q^{8} +16101.8 q^{10} +(198936. + 114856. i) q^{11} +(184952. + 320346. i) q^{13} +(-442801. + 255651. i) q^{14} +(-51714.5 + 89572.1i) q^{16} +1.12400e6i q^{17} +1.19782e6 q^{19} +(-507056. - 292749. i) q^{20} +(2.13897e6 + 3.70481e6i) q^{22} +(-5.59191e6 + 3.22849e6i) q^{23} +(-4.50904e6 + 7.80988e6i) q^{25} +6.88877e6i q^{26} +1.85922e7 q^{28} +(4.03415e6 + 2.32912e6i) q^{29} +(2.59975e6 + 4.50290e6i) q^{31} +(-2.97634e7 + 1.71839e7i) q^{32} +(-1.04661e7 + 1.81279e7i) q^{34} +2.37382e7i q^{35} +1.62603e7 q^{37} +(1.93186e7 + 1.11536e7i) q^{38} +(-1.36960e7 - 2.37222e7i) q^{40} +(1.34895e8 - 7.78817e7i) q^{41} +(-6.44896e6 + 1.11699e7i) q^{43} -1.55556e8i q^{44} -1.20249e8 q^{46} +(-7.70926e7 - 4.45094e7i) q^{47} +(-2.35659e8 - 4.08174e8i) q^{49} +(-1.45444e8 + 8.39722e7i) q^{50} +(1.25246e8 - 2.16932e8i) q^{52} -6.92888e8i q^{53} +1.98611e8 q^{55} +(7.53285e8 + 4.34909e8i) q^{56} +(4.33754e7 + 7.51283e7i) q^{58} +(-8.10167e8 + 4.67750e8i) q^{59} +(-1.10589e8 + 1.91546e8i) q^{61} +9.68308e7i q^{62} -5.34123e8 q^{64} +(2.76975e8 + 1.59912e8i) q^{65} +(1.27630e9 + 2.21062e9i) q^{67} +(6.59173e8 - 3.80574e8i) q^{68} +(-2.21039e8 + 3.82851e8i) q^{70} +3.93486e8i q^{71} +3.62576e8 q^{73} +(2.62247e8 + 1.51409e8i) q^{74} +(-4.05571e8 - 7.02470e8i) q^{76} +(-5.46185e9 + 3.15340e9i) q^{77} +(3.33228e7 - 5.77169e7i) q^{79} +8.94259e7i q^{80} +2.90080e9 q^{82} +(2.65058e9 + 1.53032e9i) q^{83} +(4.85910e8 + 8.41621e8i) q^{85} +(-2.08019e8 + 1.20100e8i) q^{86} +(3.63877e9 - 6.30254e9i) q^{88} -9.32017e9i q^{89} -1.01558e10 q^{91} +(3.78673e9 + 2.18627e9i) q^{92} +(-8.28904e8 - 1.43570e9i) q^{94} +(8.96902e8 - 5.17826e8i) q^{95} +(-7.85587e9 + 1.36068e10i) q^{97} -8.77741e9i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q + 3 q^{2} + 4095 q^{4} - 4956 q^{5} - 6120 q^{7} - 2052 q^{10} - 969 q^{11} + 140274 q^{13} + 2134578 q^{14} - 1571841 q^{16} + 2771370 q^{19} - 14542734 q^{20} - 3475521 q^{22} + 9944382 q^{23} + 14726277 q^{25}+ \cdots - 14510723337 q^{97}+O(q^{100}) $ 18 * q + 3 * q^2 + 4095 * q^4 - 4956 * q^5 - 6120 * q^7 - 2052 * q^10 - 969 * q^11 + 140274 * q^13 + 2134578 * q^14 - 1571841 * q^16 + 2771370 * q^19 - 14542734 * q^20 - 3475521 * q^22 + 9944382 * q^23 + 14726277 * q^25 - 22968324 * q^28 + 41383956 * q^29 + 28428390 * q^31 - 165205143 * q^32 - 66263103 * q^34 + 63695196 * q^37 + 621662181 * q^38 - 75566250 * q^40 - 452543883 * q^41 + 102086037 * q^43 + 44251488 * q^46 + 289445970 * q^47 + 6735231 * q^49 - 1915252779 * q^50 + 19035576 * q^52 - 289455552 * q^55 + 4272894318 * q^56 - 83900178 * q^58 - 3065773551 * q^59 + 141349086 * q^61 - 28980486 * q^64 + 11094862926 * q^65 + 954074115 * q^67 - 21469701105 * q^68 - 1440686628 * q^70 + 772009902 * q^73 + 30101814978 * q^74 - 40906287 * q^76 - 25001072268 * q^77 + 2079634212 * q^79 - 1423292742 * q^82 + 23396438442 * q^83 - 5975304714 * q^85 - 39111097821 * q^86 + 2974531059 * q^88 + 2180413260 * q^91 + 40885098684 * q^92 + 6395997924 * q^94 - 22335455946 * q^95 - 14510723337 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/27\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{1}{6}\right)$

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 $

$2$	16.1281	+	9.31155i	0.504003	+	0.290986i	0.730365	−	0.683057i	$-0.239350\pi$
$2$	16.1281	+	9.31155i	0.504003	+	0.290986i	−0.226362	+	0.974043i	$0.572683\pi$
$3$		0			0
$3$		0			0
$4$	−338.590	−	586.455i	−0.330654	−	0.572710i
$5$	748.776	−	432.306i	0.239608	−	0.138338i	−0.375388	−	0.926868i	$-0.622491\pi$
$5$	748.776	−	432.306i	0.239608	−	0.138338i	0.614997	+	0.788530i	$0.289157\pi$
$6$		0			0
$7$	−13727.6	+	23777.0i	−0.816782	+	1.41471i	0.0912598	+	0.995827i	$0.470911\pi$
$7$	−13727.6	+	23777.0i	−0.816782	+	1.41471i	−0.908041	+	0.418880i	$0.862423\pi$
$8$		−	31681.3i		−	0.966835i
$9$		0			0
$10$	16101.8			0.161018
$11$	198936.	+	114856.i	1.23524	+	0.713164i	0.968117	−	0.250500i	$-0.0805949\pi$
$11$	198936.	+	114856.i	1.23524	+	0.713164i	0.267119	+	0.963663i	$0.413928\pi$
$12$		0			0
$13$	184952.	+	320346.i	0.498130	+	0.862786i	0.999998	−	0.00215814i	$-0.000686959\pi$
$13$	184952.	+	320346.i	0.498130	+	0.862786i	−0.501868	+	0.864944i	$0.667354\pi$
$14$	−442801.	+	255651.i	−0.823320	+	0.475344i
$15$		0			0
$16$	−51714.5	+	89572.1i	−0.0493188	+	0.0854226i
$17$			1.12400e6i			0.791626i	0.918331	+	0.395813i	$0.129537\pi$
$17$			1.12400e6i			0.791626i	−0.918331	+	0.395813i	$0.870463\pi$
$18$		0			0
$19$	1.19782e6			0.483754			0.241877	−	0.970307i	$-0.422237\pi$
$19$	1.19782e6			0.483754			0.241877	+	0.970307i	$0.422237\pi$
$20$	−507056.	−	292749.i	−0.158455	−	0.0914840i
$21$		0			0
$22$	2.13897e6	+	3.70481e6i	0.415041	+	0.718873i
$23$	−5.59191e6	+	3.22849e6i	−0.868802	+	0.501603i	−0.866950	−	0.498395i	$-0.833923\pi$
$23$	−5.59191e6	+	3.22849e6i	−0.868802	+	0.501603i	−0.00185200	+	0.999998i	$0.500590\pi$
$24$		0			0
$25$	−4.50904e6	+	7.80988e6i	−0.461725	+	0.799732i
$26$			6.88877e6i			0.579795i
$27$		0			0
$28$	1.85922e7			1.08029
$29$	4.03415e6	+	2.32912e6i	0.196681	+	0.113554i	0.595106	−	0.803647i	$-0.297110\pi$
$29$	4.03415e6	+	2.32912e6i	0.196681	+	0.113554i	−0.398426	+	0.917201i	$0.630443\pi$
$30$		0			0
$31$	2.59975e6	+	4.50290e6i	0.0908078	+	0.157284i	0.907851	−	0.419292i	$-0.137722\pi$
$31$	2.59975e6	+	4.50290e6i	0.0908078	+	0.157284i	−0.817043	+	0.576576i	$0.804388\pi$
$32$	−2.97634e7	+	1.71839e7i	−0.887017	+	0.512120i
$33$		0			0
$34$	−1.04661e7	+	1.81279e7i	−0.230352	+	0.398982i
$35$			2.37382e7i			0.451967i
$36$		0			0
$37$	1.62603e7			0.234488			0.117244	−	0.993103i	$-0.462594\pi$
$37$	1.62603e7			0.234488			0.117244	+	0.993103i	$0.462594\pi$
$38$	1.93186e7	+	1.11536e7i	0.243813	+	0.140766i
$39$		0			0
$40$	−1.36960e7	−	2.37222e7i	−0.133750	−	0.231662i
$41$	1.34895e8	−	7.78817e7i	1.16433	−	0.672227i	0.211994	−	0.977271i	$-0.432004\pi$
$41$	1.34895e8	−	7.78817e7i	1.16433	−	0.672227i	0.952338	+	0.305044i	$0.0986710\pi$
$42$		0			0
$43$	−6.44896e6	+	1.11699e7i	−0.0438680	+	0.0759815i	−0.887126	−	0.461528i	$-0.847301\pi$
$43$	−6.44896e6	+	1.11699e7i	−0.0438680	+	0.0759815i	0.843258	+	0.537509i	$0.180635\pi$
$44$		−	1.55556e8i		−	0.943243i
$45$		0			0
$46$	−1.20249e8			−0.583838
$47$	−7.70926e7	−	4.45094e7i	−0.336142	−	0.194072i	0.322422	−	0.946596i	$-0.395503\pi$
$47$	−7.70926e7	−	4.45094e7i	−0.336142	−	0.194072i	−0.658565	+	0.752524i	$0.728836\pi$
$48$		0			0
$49$	−2.35659e8	−	4.08174e8i	−0.834265	−	1.44499i
$50$	−1.45444e8	+	8.39722e7i	−0.465421	+	0.268711i
$51$		0			0
$52$	1.25246e8	−	2.16932e8i	0.329418	−	0.570568i
$53$		−	6.92888e8i		−	1.65685i	−0.560098	−	0.828426i	$-0.689237\pi$
$53$		−	6.92888e8i		−	1.65685i	0.560098	−	0.828426i	$-0.310763\pi$
$54$		0			0
$55$	1.98611e8			0.394630
$56$	7.53285e8	+	4.34909e8i	1.36779	+	0.789693i
$57$		0			0
$58$	4.33754e7	+	7.51283e7i	0.0660850	+	0.114463i
$59$	−8.10167e8	+	4.67750e8i	−1.13322	+	0.654266i	−0.944743	−	0.327812i	$-0.893689\pi$
$59$	−8.10167e8	+	4.67750e8i	−1.13322	+	0.654266i	−0.188478	+	0.982077i	$0.560355\pi$
$60$		0			0
$61$	−1.10589e8	+	1.91546e8i	−0.130938	+	0.226790i	−0.924038	−	0.382300i	$-0.875132\pi$
$61$	−1.10589e8	+	1.91546e8i	−0.130938	+	0.226790i	0.793101	+	0.609091i	$0.208465\pi$
$62$			9.68308e7i			0.105695i
$63$		0			0
$64$	−5.34123e8			−0.497441
$65$	2.76975e8	+	1.59912e8i	0.238712	+	0.137820i
$66$		0			0
$67$	1.27630e9	+	2.21062e9i	0.945322	+	1.63735i	0.755106	+	0.655603i	$0.227585\pi$
$67$	1.27630e9	+	2.21062e9i	0.945322	+	1.63735i	0.190216	+	0.981742i	$0.439081\pi$
$68$	6.59173e8	−	3.80574e8i	0.453372	−	0.261755i
$69$		0			0
$70$	−2.21039e8	+	3.82851e8i	−0.131516	+	0.227793i
$71$			3.93486e8i			0.218091i	0.994037	+	0.109045i	$0.0347794\pi$
$71$			3.93486e8i			0.218091i	−0.994037	+	0.109045i	$0.965221\pi$
$72$		0			0
$73$	3.62576e8			0.174898			0.0874491	−	0.996169i	$-0.472128\pi$
$73$	3.62576e8			0.174898			0.0874491	+	0.996169i	$0.472128\pi$
$74$	2.62247e8	+	1.51409e8i	0.118182	+	0.0682326i
$75$		0			0
$76$	−4.05571e8	−	7.02470e8i	−0.159955	−	0.277051i
$77$	−5.46185e9	+	3.15340e9i	−2.01784	+	1.16500i
$78$		0			0
$79$	3.33228e7	−	5.77169e7i	0.0108295	−	0.0187572i	−0.860560	−	0.509349i	$-0.829886\pi$
$79$	3.33228e7	−	5.77169e7i	0.0108295	−	0.0187572i	0.871389	+	0.490592i	$0.163219\pi$
$80$			8.94259e7i			0.0272906i
$81$		0			0
$82$	2.90080e9			0.782435
$83$	2.65058e9	+	1.53032e9i	0.672901	+	0.388500i	0.797175	−	0.603748i	$-0.206327\pi$
$83$	2.65058e9	+	1.53032e9i	0.672901	+	0.388500i	−0.124274	+	0.992248i	$0.539660\pi$
$84$		0			0
$85$	4.85910e8	+	8.41621e8i	0.109512	+	0.189680i
$86$	−2.08019e8	+	1.20100e8i	−0.0442191	+	0.0255299i
$87$		0			0
$88$	3.63877e9	−	6.30254e9i	0.689512	−	1.19427i
$89$		−	9.32017e9i		−	1.66907i	−0.550957	−	0.834533i	$-0.685737\pi$
$89$		−	9.32017e9i		−	1.66907i	0.550957	−	0.834533i	$-0.314263\pi$
$90$		0			0
$91$	−1.01558e10			−1.62745
$92$	3.78673e9	+	2.18627e9i	0.574546	+	0.331714i
$93$		0			0
$94$	−8.28904e8	−	1.43570e9i	−0.112944	−	0.195626i
$95$	8.96902e8	−	5.17826e8i	0.115912	−	0.0669216i
$96$		0			0
$97$	−7.85587e9	+	1.36068e10i	−0.914819	+	1.58451i	−0.107654	+	0.994188i	$0.534334\pi$
$97$	−7.85587e9	+	1.36068e10i	−0.914819	+	1.58451i	−0.807165	+	0.590325i	$0.798999\pi$
$98$		−	8.77741e9i		−	0.971037i
$99$		0			0
$100$	6.10686e9			0.610686
$101$	5.40787e8	+	3.12224e8i	0.0514541	+	0.0297070i	0.525506	−	0.850790i	$-0.323876\pi$
$101$	5.40787e8	+	3.12224e8i	0.0514541	+	0.0297070i	−0.474052	+	0.880497i	$0.657209\pi$
$102$		0			0
$103$	−8.28905e9	−	1.43571e10i	−0.715021	−	1.23845i	−0.962951	−	0.269675i	$-0.913084\pi$
$103$	−8.28905e9	−	1.43571e10i	−0.715021	−	1.23845i	0.247930	−	0.968778i	$-0.420250\pi$
$104$	1.01490e10	−	5.85951e9i	0.834172	−	0.481609i
$105$		0			0
$106$	6.45187e9	−	1.11750e10i	0.482121	−	0.835058i
$107$			1.12101e10i			0.799266i	0.916675	+	0.399633i	$0.130862\pi$
$107$			1.12101e10i			0.799266i	−0.916675	+	0.399633i	$0.869138\pi$
$108$		0			0
$109$	1.32025e10			0.858072			0.429036	−	0.903287i	$-0.358853\pi$
$109$	1.32025e10			0.858072			0.429036	+	0.903287i	$0.358853\pi$
$110$	3.20322e9	+	1.84938e9i	0.198895	+	0.114832i
$111$		0			0
$112$	−1.41984e9	−	2.45923e9i	−0.0805653	−	0.139543i
$113$	−1.08127e10	+	6.24269e9i	−0.586868	+	0.338828i	−0.763858	−	0.645384i	$-0.776697\pi$
$113$	−1.08127e10	+	6.24269e9i	−0.586868	+	0.338828i	0.176990	+	0.984213i	$0.443364\pi$
$114$		0			0
$115$	−2.79139e9	+	4.83483e9i	−0.138781	+	0.240376i
$116$		−	3.15446e9i		−	0.150188i
$117$		0			0
$118$	−1.74219e10			−0.761529
$119$	−2.67252e10	−	1.54298e10i	−1.11992	−	0.646586i
$120$		0			0
$121$	1.34150e10	+	2.32354e10i	0.517206	+	0.895826i
$122$	−3.56719e9	+	2.05952e9i	−0.131986	+	0.0762020i
$123$		0			0
$124$	1.76050e9	−	3.04927e9i	0.0600519	−	0.104013i
$125$			1.62406e10i			0.532172i
$126$		0			0
$127$	5.68786e9			0.172159			0.0860796	−	0.996288i	$-0.472566\pi$
$127$	5.68786e9			0.172159			0.0860796	+	0.996288i	$0.472566\pi$
$128$	2.18633e10	+	1.26228e10i	0.636306	+	0.367371i
$129$		0			0
$130$	2.97805e9	+	5.15814e9i	0.0802077	+	0.138924i
$131$	1.38131e10	−	7.97498e9i	0.358042	−	0.206716i	−0.310180	−	0.950678i	$-0.600389\pi$
$131$	1.38131e10	−	7.97498e9i	0.358042	−	0.206716i	0.668221	+	0.743962i	$0.267056\pi$
$132$		0			0
$133$	−1.64433e10	+	2.84806e10i	−0.395122	+	0.684371i
$134$			4.75374e10i			1.10030i
$135$		0			0
$136$	3.56096e10			0.765372
$137$	−5.71950e10	−	3.30216e10i	−1.18510	−	0.684219i	−0.227912	−	0.973682i	$-0.573190\pi$
$137$	−5.71950e10	−	3.30216e10i	−1.18510	−	0.684219i	−0.957189	+	0.289463i	$0.906523\pi$
$138$		0			0
$139$	1.99169e10	+	3.44971e10i	0.383838	+	0.664826i	0.991607	−	0.129287i	$-0.0412689\pi$
$139$	1.99169e10	+	3.44971e10i	0.383838	+	0.664826i	−0.607770	+	0.794113i	$0.707936\pi$
$140$	1.39214e10	−	8.03751e9i	0.258846	−	0.149445i
$141$		0			0
$142$	−3.66396e9	+	6.34617e9i	−0.0634614	+	0.109918i
$143$			8.49713e10i			1.42099i
$144$		0			0
$145$	4.02756e9			0.0628351
$146$	5.84766e9	+	3.37615e9i	0.0881491	+	0.0508929i
$147$		0			0
$148$	−5.50557e9	−	9.53593e9i	−0.0775343	−	0.134293i
$149$	4.40235e10	−	2.54170e10i	0.599450	−	0.346093i	−0.169375	−	0.985552i	$-0.554175\pi$
$149$	4.40235e10	−	2.54170e10i	0.599450	−	0.346093i	0.768825	+	0.639459i	$0.220842\pi$
$150$		0			0
$151$	5.35630e10	−	9.27738e10i	0.682308	−	1.18179i	−0.291967	−	0.956428i	$-0.594310\pi$
$151$	5.35630e10	−	9.27738e10i	0.682308	−	1.18179i	0.974275	−	0.225363i	$-0.0723568\pi$
$152$		−	3.79486e10i		−	0.467711i
$153$		0			0
$154$	−1.17452e11			−1.35599
$155$	3.89326e9	+	2.24777e9i	0.0435166	+	0.0251243i
$156$		0			0
$157$	−4.18863e10	−	7.25491e10i	−0.439110	−	0.760561i	0.558511	−	0.829497i	$-0.311373\pi$
$157$	−4.18863e10	−	7.25491e10i	−0.439110	−	0.760561i	−0.997621	+	0.0689362i	$0.978040\pi$
$158$	1.07487e9	−	6.20575e8i	0.0109161	−	0.00630244i
$159$		0			0
$160$	−1.48574e10	+	2.57338e10i	−0.141691	+	0.245416i
$161$		−	1.77278e11i		−	1.63880i
$162$		0			0
$163$	−2.00013e10			−0.173828			−0.0869140	−	0.996216i	$-0.527701\pi$
$163$	−2.00013e10			−0.173828			−0.0869140	+	0.996216i	$0.527701\pi$
$164$	−9.13483e10	−	5.27399e10i	−0.769983	−	0.444550i
$165$		0			0
$166$	2.84992e10	+	4.93621e10i	0.226096	+	0.391610i
$167$	1.25866e11	−	7.26688e10i	0.969005	−	0.559455i	0.0700725	−	0.997542i	$-0.477677\pi$
$167$	1.25866e11	−	7.26688e10i	0.969005	−	0.559455i	0.898933	+	0.438086i	$0.144344\pi$
$168$		0			0
$169$	5.14674e8	−	8.91441e8i	0.00373335	−	0.00646635i
$170$			1.80983e10i			0.127466i
$171$		0			0
$172$	8.73421e9			0.0580205
$173$	8.92146e10	+	5.15081e10i	0.575712	+	0.332388i	0.759428	−	0.650592i	$-0.225479\pi$
$173$	8.92146e10	+	5.15081e10i	0.575712	+	0.332388i	−0.183715	+	0.982980i	$0.558812\pi$
$174$		0			0
$175$	−1.23797e11	−	2.14423e11i	−0.754257	−	1.30641i
$176$	−2.05757e10	+	1.18794e10i	−0.121841	+	0.0703447i
$177$		0			0
$178$	8.67852e10	−	1.50316e11i	0.485675	−	0.841214i
$179$			2.00566e11i			1.09142i	0.837974	+	0.545711i	$0.183740\pi$
$179$			2.00566e11i			1.09142i	−0.837974	+	0.545711i	$0.816260\pi$
$180$		0			0
$181$	7.87993e10			0.405629			0.202815	−	0.979217i	$-0.434991\pi$
$181$	7.87993e10			0.405629			0.202815	+	0.979217i	$0.434991\pi$
$182$	−1.63794e11	−	9.45666e10i	−0.820241	−	0.473566i
$183$		0			0
$184$	1.02283e11	+	1.77159e11i	0.484967	+	0.839988i
$185$	1.21753e10	−	7.02942e9i	0.0561852	−	0.0324385i
$186$		0			0
$187$	−1.29097e11	+	2.23603e11i	−0.564559	+	0.977845i
$188$			6.02818e10i			0.256683i
$189$		0			0
$190$	1.92871e10			0.0778930
$191$	1.07255e11	+	6.19239e10i	0.421941	+	0.243608i	0.695907	−	0.718131i	$-0.255002\pi$
$191$	1.07255e11	+	6.19239e10i	0.421941	+	0.243608i	−0.273966	+	0.961739i	$0.588336\pi$
$192$		0			0
$193$	5.47019e10	+	9.47464e10i	0.204275	+	0.353815i	0.949902	−	0.312549i	$-0.101183\pi$
$193$	5.47019e10	+	9.47464e10i	0.204275	+	0.353815i	−0.745626	+	0.666364i	$0.767850\pi$
$194$	−2.53400e11	+	1.46301e11i	−0.922143	+	0.532399i
$195$		0			0
$196$	−1.59584e11	+	2.76407e11i	−0.551706	+	0.955583i
$197$		−	4.48179e9i		−	0.0151050i	−0.999971	−	0.00755249i	$-0.997596\pi$
$197$		−	4.48179e9i		−	0.0151050i	0.999971	−	0.00755249i	$-0.00240405\pi$
$198$		0			0
$199$	3.35032e11			1.07355			0.536774	−	0.843726i	$-0.319643\pi$
$199$	3.35032e11			1.07355			0.536774	+	0.843726i	$0.319643\pi$
$200$	2.47427e11	+	1.42852e11i	0.773209	+	0.446412i
$201$		0			0
$202$	5.81457e9	+	1.00711e10i	0.0172886	+	0.0299448i
$203$	−1.10759e11	+	6.39466e10i	−0.321290	+	0.185497i
$204$		0			0
$205$	6.73375e10	−	1.16632e11i	0.185989	−	0.322143i
$206$		−	3.08736e11i		−	0.832244i
$207$		0			0
$208$	−3.82588e10			−0.0982686
$209$	2.38290e11	+	1.37577e11i	0.597551	+	0.344996i
$210$		0			0
$211$	1.02217e11	+	1.77046e11i	0.244406	+	0.423324i	0.961965	−	0.273174i	$-0.0880736\pi$
$211$	1.02217e11	+	1.77046e11i	0.244406	+	0.423324i	−0.717558	+	0.696499i	$0.754740\pi$
$212$	−4.06348e11	+	2.34605e11i	−0.948896	+	0.547845i
$213$		0			0
$214$	−1.04384e11	+	1.80798e11i	−0.232575	+	0.402832i
$215$			1.11517e10i			0.0242744i
$216$		0			0
$217$	−1.42754e11			−0.296680
$218$	2.12931e11	+	1.22936e11i	0.432470	+	0.249687i
$219$		0			0
$220$	−6.72478e10	−	1.16477e11i	−0.130486	−	0.226009i
$221$	−3.60068e11	+	2.07885e11i	−0.683004	+	0.394333i
$222$		0			0
$223$	3.24564e11	−	5.62161e11i	0.588540	−	1.01938i	−0.405884	−	0.913925i	$-0.633036\pi$
$223$	3.24564e11	−	5.62161e11i	0.588540	−	1.01938i	0.994424	−	0.105457i	$-0.0336304\pi$
$224$		−	9.43577e11i		−	1.67316i
$225$		0			0
$226$	−2.32517e11			−0.394377
$227$	−3.83282e11	−	2.21288e11i	−0.635901	−	0.367138i	0.147133	−	0.989117i	$-0.452995\pi$
$227$	−3.83282e11	−	2.21288e11i	−0.635901	−	0.367138i	−0.783034	+	0.621979i	$0.786329\pi$
$228$		0			0
$229$	−1.78303e11	−	3.08830e11i	−0.283127	−	0.490391i	0.689026	−	0.724736i	$-0.258039\pi$
$229$	−1.78303e11	−	3.08830e11i	−0.283127	−	0.490391i	−0.972153	+	0.234346i	$0.924705\pi$
$230$	−9.00395e10	+	5.19844e10i	−0.139892	+	0.0807669i
$231$		0			0
$232$	7.37893e10	−	1.27807e11i	0.109788	−	0.190158i
$233$			1.50181e11i			0.218693i	0.994004	+	0.109346i	$0.0348758\pi$
$233$			1.50181e11i			0.218693i	−0.994004	+	0.109346i	$0.965124\pi$
$234$		0			0
$235$	−7.69668e10			−0.107390
$236$	5.48629e11	+	3.16751e11i	0.749409	+	0.432671i
$237$		0			0
$238$	−2.87351e11	−	4.97707e11i	−0.376295	−	0.651762i
$239$	1.30768e12	−	7.54990e11i	1.67692	−	0.968171i	0.713315	−	0.700843i	$-0.247193\pi$
$239$	1.30768e12	−	7.54990e11i	1.67692	−	0.968171i	0.963606	−	0.267327i	$-0.0861405\pi$
$240$		0			0
$241$	6.74348e10	−	1.16800e11i	0.0829466	−	0.143668i	−0.821568	−	0.570111i	$-0.806900\pi$
$241$	6.74348e10	−	1.16800e11i	0.0829466	−	0.143668i	0.904514	+	0.426443i	$0.140234\pi$
$242$			4.99657e11i			0.601998i
$243$		0			0
$244$	1.49778e11			0.173180
$245$	−3.52912e11	−	2.03754e11i	−0.399793	−	0.230821i
$246$		0			0
$247$	2.21540e11	+	3.83719e11i	0.240973	+	0.417377i
$248$	1.42657e11	−	8.23633e10i	0.152067	−	0.0877961i
$249$		0			0
$250$	−1.51225e11	+	2.61930e11i	−0.154855	+	0.268216i
$251$		−	8.84847e11i		−	0.888178i	−0.895983	−	0.444089i	$-0.853527\pi$
$251$		−	8.84847e11i		−	0.888178i	0.895983	−	0.444089i	$-0.146473\pi$
$252$		0			0
$253$	−1.48324e12			−1.43090
$254$	9.17342e10	+	5.29628e10i	0.0867687	+	0.0500959i
$255$		0			0
$256$	5.08547e11	+	8.80828e11i	0.462520	+	0.801109i
$257$	1.90896e11	−	1.10214e11i	0.170267	−	0.0983037i	−0.412445	−	0.910983i	$-0.635325\pi$
$257$	1.90896e11	−	1.10214e11i	0.170267	−	0.0983037i	0.582712	+	0.812679i	$0.301992\pi$
$258$		0			0
$259$	−2.23216e11	+	3.86621e11i	−0.191525	+	0.331731i
$260$		−	2.16578e11i		−	0.182284i
$261$		0			0
$262$	2.97038e11			0.240605
$263$	2.11532e11	+	1.22128e11i	0.168111	+	0.0970591i	0.581695	−	0.813407i	$-0.302390\pi$
$263$	2.11532e11	+	1.22128e11i	0.168111	+	0.0970591i	−0.413584	+	0.910466i	$0.635723\pi$
$264$		0			0
$265$	−2.99540e11	−	5.18818e11i	−0.229206	−	0.396996i
$266$	−5.30398e11	+	3.06225e11i	−0.398285	+	0.229950i
$267$		0			0
$268$	8.64286e11	−	1.49699e12i	0.625149	−	1.08279i
$269$			5.44808e11i			0.386796i	0.981120	+	0.193398i	$0.0619509\pi$
$269$			5.44808e11i			0.386796i	−0.981120	+	0.193398i	$0.938049\pi$
$270$		0			0
$271$	1.13982e12			0.779814			0.389907	−	0.920854i	$-0.372507\pi$
$271$	1.13982e12			0.779814			0.389907	+	0.920854i	$0.372507\pi$
$272$	−1.00679e11	−	5.81268e10i	−0.0676228	−	0.0390420i
$273$		0			0
$274$	−6.14964e11	−	1.06515e12i	−0.398196	−	0.689696i
$275$	−1.79402e12	+	1.03578e12i	−1.14068	+	0.658572i
$276$		0			0
$277$	−3.40863e11	+	5.90391e11i	−0.209016	+	0.362027i	−0.951405	−	0.307942i	$-0.900360\pi$
$277$	−3.40863e11	+	5.90391e11i	−0.209016	+	0.362027i	0.742388	+	0.669970i	$0.233693\pi$
$278$			7.41829e11i			0.446766i
$279$		0			0
$280$	7.52055e11			0.436978
$281$	−1.70955e12	−	9.87007e11i	−0.975774	−	0.563363i	−0.0747823	−	0.997200i	$-0.523826\pi$
$281$	−1.70955e12	−	9.87007e11i	−0.975774	−	0.563363i	−0.900992	+	0.433837i	$0.857160\pi$
$282$		0			0
$283$	1.31791e12	+	2.28269e12i	0.726028	+	1.25752i	0.958550	+	0.284926i	$0.0919690\pi$
$283$	1.31791e12	+	2.28269e12i	0.726028	+	1.25752i	−0.232522	+	0.972591i	$0.574698\pi$
$284$	2.30762e11	−	1.33230e11i	0.124903	−	0.0721127i
$285$		0			0
$286$	−7.91214e11	+	1.37042e12i	−0.413489	+	0.716184i
$287$			4.27653e12i			2.19625i
$288$		0			0
$289$	7.52627e11			0.373328
$290$	6.49569e10	+	3.75029e10i	0.0316690	+	0.0182841i
$291$		0			0
$292$	−1.22765e11	−	2.12635e11i	−0.0578308	−	0.100166i
$293$	1.94796e12	−	1.12465e12i	0.902072	−	0.520811i	0.0242000	−	0.999707i	$-0.492296\pi$
$293$	1.94796e12	−	1.12465e12i	0.902072	−	0.520811i	0.877872	+	0.478896i	$0.158963\pi$
$294$		0			0
$295$	−4.04423e11	+	7.00480e11i	−0.181019	+	0.313535i
$296$		−	5.15147e11i		−	0.226711i
$297$		0			0
$298$	9.46686e11			0.402833
$299$	−2.06847e12	−	1.19423e12i	−0.865552	−	0.499727i
$300$		0			0
$301$	−1.77058e11	−	3.06674e11i	−0.0716611	−	0.124121i
$302$	1.72774e12	−	9.97509e11i	0.687770	−	0.397084i
$303$		0			0
$304$	−6.19448e10	+	1.07292e11i	−0.0238582	+	0.0413236i
$305$			1.91234e11i			0.0724545i
$306$		0			0
$307$	−1.73071e12			−0.634646			−0.317323	−	0.948318i	$-0.602784\pi$
$307$	−1.73071e12			−0.634646			−0.317323	+	0.948318i	$0.602784\pi$
$308$	3.69865e12	+	2.13542e12i	1.33441	+	0.770423i
$309$		0			0
$310$	4.18605e10	+	7.25046e10i	0.0146216	+	0.0253254i
$311$	5.77332e11	−	3.33323e11i	0.198437	−	0.114568i	−0.397489	−	0.917607i	$-0.630118\pi$
$311$	5.77332e11	−	3.33323e11i	0.198437	−	0.114568i	0.595926	+	0.803039i	$0.296785\pi$
$312$		0			0
$313$	−1.00102e12	+	1.73382e12i	−0.333212	+	0.577141i	−0.983140	−	0.182856i	$-0.941466\pi$
$313$	−1.00102e12	+	1.73382e12i	−0.333212	+	0.577141i	0.649927	+	0.759996i	$0.274799\pi$
$314$		−	1.56010e12i		−	0.511100i
$315$		0			0
$316$	−4.51311e10			−0.0143232
$317$	−4.20000e12	−	2.42487e12i	−1.31206	−	0.757518i	−0.329622	−	0.944113i	$-0.606921\pi$
$317$	−4.20000e12	−	2.42487e12i	−1.31206	−	0.757518i	−0.982437	+	0.186595i	$0.940255\pi$
$318$		0			0
$319$	5.35025e11	+	9.26690e11i	0.161965	+	0.280531i
$320$	−3.99939e11	+	2.30905e11i	−0.119191	+	0.0688150i
$321$		0			0
$322$	1.65074e12	−	2.85916e12i	0.476868	−	0.825960i
$323$			1.34635e12i			0.382953i
$324$		0			0
$325$	−3.33582e12			−0.919996
$326$	−3.22582e11	−	1.86243e11i	−0.0876098	−	0.0505815i
$327$		0			0
$328$	−2.46739e12	−	4.27365e12i	−0.649933	−	1.12572i
$329$	2.11660e12	−	1.22202e12i	0.549110	−	0.317029i
$330$		0			0
$331$	1.75905e12	−	3.04677e12i	0.442730	−	0.766830i	−0.555161	−	0.831743i	$-0.687343\pi$
$331$	1.75905e12	−	3.04677e12i	0.442730	−	0.766830i	0.997891	+	0.0649124i	$0.0206768\pi$
$332$		−	2.07260e12i		−	0.513836i
$333$		0			0
$334$	2.70664e12			0.651175
$335$	1.91133e12	+	1.10351e12i	0.453014	+	0.261548i
$336$		0			0
$337$	−2.64525e12	−	4.58171e12i	−0.608580	−	1.05409i	−0.991475	−	0.130300i	$-0.958406\pi$
$337$	−2.64525e12	−	4.58171e12i	−0.608580	−	1.05409i	0.382894	−	0.923792i	$-0.374927\pi$
$338$	1.66014e10	−	9.58482e9i	0.00376323	−	0.00217270i
$339$		0			0
$340$	3.29049e11	−	5.69929e11i	0.0724211	−	0.125437i
$341$			1.19438e12i			0.259043i
$342$		0			0
$343$	5.18474e12			1.09209
$344$	3.53877e11	+	2.04311e11i	0.0734616	+	0.0424131i
$345$		0			0
$346$	9.59241e11	+	1.66145e12i	0.193440	+	0.335048i
$347$	3.72266e12	−	2.14928e12i	0.739956	−	0.427214i	−0.0820973	−	0.996624i	$-0.526162\pi$
$347$	3.72266e12	−	2.14928e12i	0.739956	−	0.427214i	0.822053	+	0.569411i	$0.192828\pi$
$348$		0			0
$349$	−1.73279e12	+	3.00129e12i	−0.334672	+	0.579669i	−0.983422	−	0.181333i	$-0.941959\pi$
$349$	−1.73279e12	+	3.00129e12i	−0.334672	+	0.579669i	0.648750	+	0.761002i	$0.275292\pi$
$350$		−	4.61097e12i		−	0.877914i
$351$		0			0
$352$	−7.89467e12			−1.46090
$353$	−6.52014e12	−	3.76441e12i	−1.18955	−	0.686789i	−0.231348	−	0.972871i	$-0.574314\pi$
$353$	−6.52014e12	−	3.76441e12i	−1.18955	−	0.686789i	−0.958205	+	0.286083i	$0.907647\pi$
$354$		0			0
$355$	1.70106e11	+	2.94633e11i	0.0301702	+	0.0522564i
$356$	−5.46586e12	+	3.15572e12i	−0.955891	+	0.551884i
$357$		0			0
$358$	−1.86758e12	+	3.23475e12i	−0.317588	+	0.550079i
$359$		−	2.83045e11i		−	0.0474660i	−0.999718	−	0.0237330i	$-0.992445\pi$
$359$		−	2.83045e11i		−	0.0474660i	0.999718	−	0.0237330i	$-0.00755517\pi$
$360$		0			0
$361$	−4.69628e12			−0.765982
$362$	1.27088e12	+	7.33744e11i	0.204438	+	0.118032i
$363$		0			0
$364$	3.43866e12	+	5.95594e12i	0.538124	+	0.932059i
$365$	2.71488e11	−	1.56744e11i	0.0419070	−	0.0241950i
$366$		0			0
$367$	5.25168e12	−	9.09618e12i	0.788802	−	1.36625i	−0.137899	−	0.990446i	$-0.544035\pi$
$367$	5.25168e12	−	9.09618e12i	0.788802	−	1.36625i	0.926701	−	0.375799i	$-0.122632\pi$
$368$		−	6.67838e11i		−	0.0989538i
$369$		0			0
$370$	2.61819e11			0.0377566
$371$	1.64748e13	+	9.51173e12i	2.34396	+	1.35329i
$372$		0			0
$373$	6.13664e12	+	1.06290e13i	0.849936	+	1.47213i	0.881265	+	0.472623i	$0.156693\pi$
$373$	6.13664e12	+	1.06290e13i	0.849936	+	1.47213i	−0.0313289	+	0.999509i	$0.509974\pi$
$374$	−4.16419e12	+	2.40419e12i	−0.569079	+	0.328558i
$375$		0			0
$376$	−1.41011e12	+	2.44239e12i	−0.187636	+	0.324994i
$377$			1.72310e12i			0.226258i
$378$		0			0
$379$	3.56139e12			0.455431			0.227716	−	0.973728i	$-0.426874\pi$
$379$	3.56139e12			0.455431			0.227716	+	0.973728i	$0.426874\pi$
$380$	−6.07364e11	−	3.50662e11i	−0.0766533	−	0.0442558i
$381$		0			0
$382$	1.15321e12	+	1.99743e12i	0.141773	+	0.245558i
$383$	−1.03654e13	+	5.98444e12i	−1.25774	+	0.726156i	−0.972634	−	0.232341i	$-0.925361\pi$
$383$	−1.03654e13	+	5.98444e12i	−1.25774	+	0.726156i	−0.285104	+	0.958497i	$0.592028\pi$
$384$		0			0
$385$	−2.72647e12	+	4.72238e12i	−0.322327	+	0.558287i
$386$			2.03744e12i			0.237765i
$387$		0			0
$388$	1.06397e13			1.20996
$389$	−9.89240e11	−	5.71138e11i	−0.111059	−	0.0641199i	0.443442	−	0.896303i	$-0.353757\pi$
$389$	−9.89240e11	−	5.71138e11i	−0.111059	−	0.0641199i	−0.554501	+	0.832183i	$0.687091\pi$
$390$		0			0
$391$	−3.62881e12	−	6.28528e12i	−0.397082	−	0.687766i
$392$	−1.29315e13	+	7.46598e12i	−1.39707	+	0.806596i
$393$		0			0
$394$	4.17324e10	−	7.22826e10i	0.00439534	−	0.00761295i
$395$		−	5.76227e10i		−	0.00599250i
$396$		0			0
$397$	1.46229e12			0.148280			0.0741399	−	0.997248i	$-0.476379\pi$
$397$	1.46229e12			0.148280			0.0741399	+	0.997248i	$0.476379\pi$
$398$	5.40343e12	+	3.11967e12i	0.541070	+	0.312387i
$399$		0			0
$400$	−4.66365e11	−	8.07767e11i	−0.0455434	−	0.0788835i
$401$	5.79844e12	−	3.34773e12i	0.559229	−	0.322871i	−0.193607	−	0.981079i	$-0.562019\pi$
$401$	5.79844e12	−	3.34773e12i	0.559229	−	0.322871i	0.752836	+	0.658208i	$0.228685\pi$
$402$		0			0
$403$	−9.61658e11	+	1.66564e12i	−0.0904681	+	0.156695i
$404$		−	4.22863e11i		−	0.0392910i
$405$		0			0
$406$	−2.38177e12			−0.215908
$407$	3.23476e12	+	1.86759e12i	0.289648	+	0.167228i
$408$		0			0
$409$	−5.86198e12	−	1.01532e13i	−0.512186	−	0.887132i	−0.999900	−	0.0141287i	$-0.995503\pi$
$409$	−5.86198e12	−	1.01532e13i	−0.512186	−	0.887132i	0.487714	−	0.873003i	$-0.337831\pi$
$410$	2.17205e12	−	1.25403e12i	0.187478	−	0.108240i
$411$		0			0
$412$	−5.61318e12	+	9.72231e12i	−0.472849	+	0.818999i
$413$		−	2.56845e13i		−	2.13757i
$414$		0			0
$415$	2.64626e12			0.214977
$416$	−1.10096e13	−	6.35639e12i	−0.883700	−	0.510204i
$417$		0			0
$418$	2.56211e12	+	4.43771e12i	0.200778	+	0.347758i
$419$	1.39582e13	−	8.05876e12i	1.08083	−	0.624019i	0.149712	−	0.988730i	$-0.452165\pi$
$419$	1.39582e13	−	8.05876e12i	1.08083	−	0.624019i	0.931121	+	0.364710i	$0.118832\pi$
$420$		0			0
$421$	7.98485e12	−	1.38302e13i	0.603749	−	1.04572i	−0.388499	−	0.921449i	$-0.627006\pi$
$421$	7.98485e12	−	1.38302e13i	0.603749	−	1.04572i	0.992248	−	0.124275i	$-0.0396605\pi$
$422$			3.80721e12i			0.284475i
$423$		0			0
$424$	−2.19516e13			−1.60190
$425$	−8.77827e12	−	5.06814e12i	−0.633088	−	0.365514i
$426$		0			0
$427$	−3.03626e12	−	5.25896e12i	−0.213895	−	0.370477i
$428$	6.57423e12	−	3.79563e12i	0.457748	−	0.264281i
$429$		0			0
$430$	−1.03840e11	+	1.79855e11i	−0.00706351	+	0.0122344i
$431$			2.10561e13i			1.41576i	0.706331	+	0.707882i	$0.250349\pi$
$431$			2.10561e13i			1.41576i	−0.706331	+	0.707882i	$0.749651\pi$
$432$		0			0
$433$	8.40350e12			0.552104			0.276052	−	0.961143i	$-0.410974\pi$
$433$	8.40350e12			0.552104			0.276052	+	0.961143i	$0.410974\pi$
$434$	−2.30234e12	−	1.32926e12i	−0.149528	−	0.0863299i
$435$		0			0
$436$	−4.47023e12	−	7.74267e12i	−0.283725	−	0.491426i
$437$	−6.69812e12	+	3.86716e12i	−0.420287	+	0.242653i
$438$		0			0
$439$	4.48024e10	−	7.76000e10i	0.00274776	−	0.00475926i	−0.864648	−	0.502378i	$-0.832459\pi$
$439$	4.48024e10	−	7.76000e10i	0.00274776	−	0.00475926i	0.867396	+	0.497618i	$0.165792\pi$
$440$		−	6.29226e12i		−	0.381543i
$441$		0			0
$442$	−7.74294e12			−0.458981
$443$	1.68713e13	+	9.74064e12i	0.988848	+	0.570912i	0.904930	−	0.425561i	$-0.139923\pi$
$443$	1.68713e13	+	9.74064e12i	0.988848	+	0.570912i	0.0839184	+	0.996473i	$0.473257\pi$
$444$		0			0
$445$	−4.02916e12	−	6.97872e12i	−0.230895	−	0.399922i
$446$	1.04692e13	−	6.04439e12i	0.593251	−	0.342514i
$447$		0			0
$448$	7.33226e12	−	1.26998e13i	0.406301	−	0.703734i
$449$		−	1.92827e13i		−	1.05666i	−0.849038	−	0.528332i	$-0.822818\pi$
$449$		−	1.92827e13i		−	1.05666i	0.849038	−	0.528332i	$-0.177182\pi$
$450$		0			0
$451$	3.57807e13			1.91763
$452$	7.32212e12	+	4.22743e12i	0.388101	+	0.224070i
$453$		0			0
$454$	−4.12107e12	−	7.13791e12i	−0.213664	−	0.370076i
$455$	−7.60444e12	+	4.39043e12i	−0.389951	+	0.225138i
$456$		0			0
$457$	−9.86363e12	+	1.70843e13i	−0.494830	+	0.857071i	−0.999982	−	0.00595966i	$-0.998103\pi$
$457$	−9.86363e12	+	1.70843e13i	−0.494830	+	0.857071i	0.505152	+	0.863030i	$0.331436\pi$
$458$		−	6.64112e12i		−	0.329544i
$459$		0			0
$460$	3.78055e12			0.183555
$461$	−2.57387e12	−	1.48602e12i	−0.123618	−	0.0713709i	0.436916	−	0.899502i	$-0.356071\pi$
$461$	−2.57387e12	−	1.48602e12i	−0.123618	−	0.0713709i	−0.560534	+	0.828131i	$0.689404\pi$
$462$		0			0
$463$	4.55799e12	+	7.89467e12i	0.214224	+	0.371047i	0.953032	−	0.302869i	$-0.0979444\pi$
$463$	4.55799e12	+	7.89467e12i	0.214224	+	0.371047i	−0.738808	+	0.673916i	$0.764611\pi$
$464$	−4.17247e11	+	2.40898e11i	−0.0194001	+	0.0112006i
$465$		0			0
$466$	−1.39842e12	+	2.42213e12i	−0.0636366	+	0.110222i
$467$			1.72405e13i			0.776186i	0.921620	+	0.388093i	$0.126866\pi$
$467$			1.72405e13i			0.776186i	−0.921620	+	0.388093i	$0.873134\pi$
$468$		0			0
$469$	−7.00825e13			−3.08849
$470$	−1.24133e12	−	7.16680e11i	−0.0541249	−	0.0312490i
$471$		0			0
$472$	1.48189e13	+	2.56671e13i	0.632567	+	1.09564i
$473$	−2.56586e12	+	1.48140e12i	−0.108375	+	0.0625701i
$474$		0			0
$475$	−5.40103e12	+	9.35486e12i	−0.223362	+	0.386874i
$476$			2.08975e13i			0.855185i
$477$		0			0
$478$	2.81205e13			1.12690
$479$	−3.64893e13	−	2.10671e13i	−1.44707	−	0.835464i	−0.448761	−	0.893652i	$-0.648134\pi$
$479$	−3.64893e13	−	2.10671e13i	−1.44707	−	0.835464i	−0.998306	+	0.0581880i	$0.981468\pi$
$480$		0			0
$481$	3.00738e12	+	5.20893e12i	0.116805	+	0.202313i
$482$	2.17519e12	−	1.25585e12i	0.0836106	−	0.0482726i
$483$		0			0
$484$	9.08436e12	−	1.57346e13i	0.342032	−	0.592418i
$485$			1.35845e13i			0.506217i
$486$		0			0
$487$	2.83759e13			1.03587			0.517934	−	0.855420i	$-0.326701\pi$
$487$	2.83759e13			1.03587			0.517934	+	0.855420i	$0.326701\pi$
$488$	6.06843e12	+	3.50361e12i	0.219269	+	0.126595i
$489$		0			0
$490$	−3.79453e12	−	6.57231e12i	−0.134331	−	0.232669i
$491$	2.51160e13	−	1.45007e13i	0.880123	−	0.508139i	0.00942378	−	0.999956i	$-0.497000\pi$
$491$	2.51160e13	−	1.45007e13i	0.880123	−	0.508139i	0.870699	+	0.491817i	$0.163667\pi$
$492$		0			0
$493$	−2.61792e12	+	4.53436e12i	−0.0898920	+	0.155698i
$494$			8.25153e12i			0.280479i
$495$		0			0
$496$	−5.37779e11			−0.0179141
$497$	−9.35591e12	−	5.40164e12i	−0.308535	−	0.178133i
$498$		0			0
$499$	1.91727e13	+	3.32081e13i	0.619698	+	1.07335i	0.989541	+	0.144254i	$0.0460783\pi$
$499$	1.91727e13	+	3.32081e13i	0.619698	+	1.07335i	−0.369843	+	0.929094i	$0.620588\pi$
$500$	9.52439e12	−	5.49891e12i	0.304780	−	0.175965i
$501$		0			0
$502$	8.23930e12	−	1.42709e13i	0.258447	−	0.447644i
$503$			5.89393e13i			1.83048i	0.402907	+	0.915241i	$0.368000\pi$
$503$			5.89393e13i			1.83048i	−0.402907	+	0.915241i	$0.632000\pi$
$504$		0			0
$505$	5.39905e11			0.0164384
$506$	−2.39219e13	−	1.38113e13i	−0.721178	−	0.416372i
$507$		0			0
$508$	−1.92585e12	−	3.33567e12i	−0.0569252	−	0.0985973i
$509$	−2.68712e13	+	1.55141e13i	−0.786498	+	0.454085i	−0.838728	−	0.544550i	$-0.816700\pi$
$509$	−2.68712e13	+	1.55141e13i	−0.786498	+	0.454085i	0.0522302	+	0.998635i	$0.483367\pi$
$510$		0			0
$511$	−4.97732e12	+	8.62097e12i	−0.142854	+	0.247430i
$512$		−	6.91002e12i		−	0.196395i
$513$		0			0
$514$	4.10504e12			0.114420
$515$	−1.24133e13	−	7.16681e12i	−0.342650	−	0.197829i
$516$		0			0
$517$	−1.02243e13	−	1.77091e13i	−0.276810	−	0.479449i
$518$	−7.20008e12	+	4.15697e12i	−0.193058	+	0.111462i
$519$		0			0
$520$	5.06621e12	−	8.77493e12i	0.133250	−	0.230795i
$521$			2.33648e13i			0.608659i	0.952567	+	0.304329i	$0.0984323\pi$
$521$			2.33648e13i			0.608659i	−0.952567	+	0.304329i	$0.901568\pi$
$522$		0			0
$523$	−4.29833e13			−1.09848			−0.549238	−	0.835666i	$-0.685082\pi$
$523$	−4.29833e13			−1.09848			−0.549238	+	0.835666i	$0.685082\pi$
$524$	−9.35393e12	−	5.40050e12i	−0.236776	−	0.136703i
$525$		0			0
$526$	2.27440e12	+	3.93938e12i	0.0564857	+	0.0978361i
$527$	−5.06124e12	+	2.92211e12i	−0.124510	+	0.0718858i
$528$		0			0
$529$	1.33028e11	−	2.30411e11i	0.00321118	−	0.00556192i
$530$		−	1.11567e13i		−	0.266782i
$531$		0			0
$532$	2.22702e13			0.522595
$533$	4.98983e13	+	2.88088e13i	1.15998	+	0.669713i
$534$		0			0
$535$	4.84620e12	+	8.39387e12i	0.110569	+	0.191511i
$536$	7.00352e13	−	4.04349e13i	1.58304	−	0.913970i
$537$		0			0
$538$	−5.07301e12	+	8.78671e12i	−0.112552	+	0.194946i
$539$		−	1.08267e14i		−	2.37987i
$540$		0			0
$541$	7.61612e12			0.164342			0.0821708	−	0.996618i	$-0.473815\pi$
$541$	7.61612e12			0.164342			0.0821708	+	0.996618i	$0.473815\pi$
$542$	1.83832e13	+	1.06135e13i	0.393028	+	0.226915i
$543$		0			0
$544$	−1.93146e13	−	3.34539e13i	−0.405407	−	0.702186i
$545$	9.88571e12	−	5.70752e12i	0.205601	−	0.118704i
$546$		0			0
$547$	−7.05321e12	+	1.22165e13i	−0.144029	+	0.249466i	−0.929010	−	0.370054i	$-0.879339\pi$
$547$	−7.05321e12	+	1.22165e13i	−0.144029	+	0.249466i	0.784981	+	0.619520i	$0.212673\pi$
$548$			4.47231e13i			0.904959i
$549$		0			0
$550$	−3.85788e13			−0.766540
$551$	4.83220e12	+	2.78987e12i	0.0951451	+	0.0549321i
$552$		0			0
$553$	9.14889e11	+	1.58463e12i	0.0176906	+	0.0306410i
$554$	−1.09949e13	+	6.34792e12i	−0.210690	+	0.121642i
$555$		0			0
$556$	1.34873e13	−	2.33607e13i	0.253835	−	0.439655i
$557$		−	9.54351e13i		−	1.78005i	−0.455911	−	0.890025i	$-0.650687\pi$
$557$		−	9.54351e13i		−	1.78005i	0.455911	−	0.890025i	$-0.349313\pi$
$558$		0			0
$559$	−4.77100e12			−0.0874078
$560$	−2.12628e12	−	1.22761e12i	−0.0386082	−	0.0222905i
$561$		0			0
$562$	−1.83811e13	−	3.18371e13i	−0.327862	−	0.567873i
$563$	−4.54844e13	+	2.62604e13i	−0.804119	+	0.464258i	−0.844909	−	0.534909i	$-0.820346\pi$
$563$	−4.54844e13	+	2.62604e13i	−0.804119	+	0.464258i	0.0407905	+	0.999168i	$0.487012\pi$
$564$		0			0
$565$	−5.39751e12	+	9.34876e12i	−0.0937456	+	0.162372i
$566$			4.90871e13i			0.845056i
$567$		0			0
$568$	1.24661e13			0.210858
$569$	−2.05866e13	−	1.18857e13i	−0.345163	−	0.199280i	0.317390	−	0.948295i	$-0.397194\pi$
$569$	−2.05866e13	−	1.18857e13i	−0.345163	−	0.199280i	−0.662553	+	0.749015i	$0.730527\pi$
$570$		0			0
$571$	−2.70449e13	−	4.68432e13i	−0.445559	−	0.771731i	0.552532	−	0.833492i	$-0.313662\pi$
$571$	−2.70449e13	−	4.68432e13i	−0.445559	−	0.771731i	−0.998091	+	0.0617606i	$0.980328\pi$
$572$	4.98318e13	−	2.87704e13i	0.813817	−	0.469857i
$573$		0			0
$574$	−3.98212e13	+	6.89723e13i	−0.639079	+	1.10692i
$575$		−	5.82295e13i		−	0.926411i
$576$		0			0
$577$	3.00524e13			0.469894			0.234947	−	0.972008i	$-0.424508\pi$
$577$	3.00524e13			0.469894			0.234947	+	0.972008i	$0.424508\pi$
$578$	1.21384e13	+	7.00813e12i	0.188158	+	0.108633i
$579$		0			0
$580$	−1.36369e12	−	2.36198e12i	−0.0207767	−	0.0359863i
$581$	−7.27726e13	+	4.20153e13i	−1.09923	+	0.634639i
$582$		0			0
$583$	7.95822e13	−	1.37840e14i	1.18161	−	2.04660i
$584$		−	1.14869e13i		−	0.169098i
$585$		0			0
$586$	4.18891e13			0.606195
$587$	4.37799e13	+	2.52764e13i	0.628181	+	0.362680i	0.780047	−	0.625721i	$-0.215195\pi$
$587$	4.37799e13	+	2.52764e13i	0.628181	+	0.362680i	−0.151867	+	0.988401i	$0.548528\pi$
$588$		0			0
$589$	3.11404e12	+	5.39368e12i	0.0439287	+	0.0760867i
$590$	−1.30451e13	+	7.53160e12i	−0.182469	+	0.105348i
$591$		0			0
$592$	−8.40893e11	+	1.45647e12i	−0.0115646	+	0.0200305i
$593$			6.15227e13i			0.839000i	0.907755	+	0.419500i	$0.137795\pi$
$593$			6.15227e13i			0.839000i	−0.907755	+	0.419500i	$0.862205\pi$
$594$		0			0
$595$	−2.66816e13			−0.357789
$596$	−2.98118e13	−	1.72119e13i	−0.396422	−	0.228874i
$597$		0			0
$598$	−2.22403e13	−	3.85213e13i	−0.290827	−	0.503727i
$599$	−6.31964e13	+	3.64864e13i	−0.819517	+	0.473148i	−0.850250	−	0.526379i	$-0.823549\pi$
$599$	−6.31964e13	+	3.64864e13i	−0.819517	+	0.473148i	0.0307329	+	0.999528i	$0.490216\pi$
$600$		0			0
$601$	−4.58625e13	+	7.94361e13i	−0.584905	+	1.01308i	0.409983	+	0.912093i	$0.365535\pi$
$601$	−4.58625e13	+	7.94361e13i	−0.584905	+	1.01308i	−0.994887	+	0.100991i	$0.967799\pi$
$602$		−	6.59475e12i		−	0.0834095i
$603$		0			0
$604$	−7.25436e13			−0.902432
$605$	2.00896e13	+	1.15988e13i	0.247853	+	0.143098i
$606$		0			0
$607$	6.11384e13	+	1.05895e14i	0.741943	+	1.28508i	0.951609	+	0.307310i	$0.0994289\pi$
$607$	6.11384e13	+	1.05895e14i	0.741943	+	1.28508i	−0.209666	+	0.977773i	$0.567238\pi$
$608$	−3.56513e13	+	2.05833e13i	−0.429099	+	0.247740i
$609$		0			0
$610$	−1.78068e12	+	3.08423e12i	−0.0210832	+	0.0365172i
$611$		−	3.29285e13i		−	0.386692i
$612$		0			0
$613$	1.34454e14			1.55336			0.776680	−	0.629895i	$-0.216902\pi$
$613$	1.34454e14			1.55336			0.776680	+	0.629895i	$0.216902\pi$
$614$	−2.79130e13	−	1.61156e13i	−0.319863	−	0.184673i
$615$		0			0
$616$	9.99036e13	+	1.73038e14i	1.12636	+	1.95092i
$617$	1.17472e13	−	6.78227e12i	0.131374	−	0.0758489i	−0.432873	−	0.901455i	$-0.642500\pi$
$617$	1.17472e13	−	6.78227e12i	0.131374	−	0.0758489i	0.564247	+	0.825606i	$0.309167\pi$
$618$		0			0
$619$	−6.39576e13	+	1.10778e14i	−0.703783	+	1.21899i	0.263346	+	0.964701i	$0.415174\pi$
$619$	−6.39576e13	+	1.10778e14i	−0.703783	+	1.21899i	−0.967129	+	0.254286i	$0.918159\pi$
$620$		−	3.04429e12i		−	0.0332298i
$621$		0			0
$622$	1.24150e13			0.133351
$623$	2.21606e14	+	1.27944e14i	2.36124	+	1.36326i
$624$		0			0
$625$	−3.70126e13	−	6.41078e13i	−0.388106	−	0.672219i
$626$	−3.22891e13	+	1.86421e13i	−0.335880	+	0.193920i
$627$		0			0
$628$	−2.83645e13	+	4.91288e13i	−0.290387	+	0.502965i
$629$			1.82765e13i			0.185627i
$630$		0			0
$631$	3.97084e12			0.0396950			0.0198475	−	0.999803i	$-0.493682\pi$
$631$	3.97084e12			0.0396950			0.0198475	+	0.999803i	$0.493682\pi$
$632$	−1.82854e12	−	1.05571e12i	−0.0181351	−	0.0104703i
$633$		0			0
$634$	−4.51587e13	−	7.82171e13i	−0.440854	−	0.763582i
$635$	4.25893e12	−	2.45889e12i	0.0412508	−	0.0238161i
$636$		0			0
$637$	8.71713e13	−	1.50985e14i	0.831144	−	1.43958i
$638$			1.99276e13i			0.188518i
$639$		0			0
$640$	2.18276e13			0.203285
$641$	−4.96096e13	−	2.86421e13i	−0.458433	−	0.264677i	0.252952	−	0.967479i	$-0.418599\pi$
$641$	−4.96096e13	−	2.86421e13i	−0.458433	−	0.264677i	−0.711385	+	0.702802i	$0.751932\pi$
$642$		0			0
$643$	3.73138e13	+	6.46295e13i	0.339481	+	0.587998i	0.984335	−	0.176308i	$-0.0564153\pi$
$643$	3.73138e13	+	6.46295e13i	0.339481	+	0.587998i	−0.644854	+	0.764305i	$0.723082\pi$
$644$	−1.03966e14	+	6.00246e13i	−0.938558	+	0.541876i
$645$		0			0
$646$	−1.25366e13	+	2.17140e13i	−0.111434	+	0.193009i
$647$		−	7.62256e12i		−	0.0672325i	−0.999435	−	0.0336163i	$-0.989298\pi$
$647$		−	7.62256e12i		−	0.0672325i	0.999435	−	0.0336163i	$-0.0107024\pi$
$648$		0			0
$649$	−2.14895e14			−1.86639
$650$	−5.38004e13	−	3.10617e13i	−0.463681	−	0.267706i
$651$		0			0
$652$	6.77223e12	+	1.17298e13i	0.0574770	+	0.0995530i
$653$	1.32797e14	−	7.66701e13i	1.11846	−	0.645744i	0.177453	−	0.984129i	$-0.443214\pi$
$653$	1.32797e14	−	7.66701e13i	1.11846	−	0.645744i	0.941008	+	0.338386i	$0.109881\pi$
$654$		0			0
$655$	6.89526e12	−	1.19429e13i	0.0571932	−	0.0990615i
$656$			1.61104e13i			0.132614i
$657$		0			0
$658$	4.55156e13			0.369004
$659$	−1.38594e14	−	8.00171e13i	−1.11511	−	0.643807i	−0.174959	−	0.984576i	$-0.555979\pi$
$659$	−1.38594e14	−	8.00171e13i	−1.11511	−	0.643807i	−0.940147	+	0.340768i	$0.889313\pi$
$660$		0			0
$661$	2.73546e13	+	4.73796e13i	0.216782	+	0.375477i	0.953822	−	0.300371i	$-0.0971106\pi$
$661$	2.73546e13	+	4.73796e13i	0.216782	+	0.375477i	−0.737040	+	0.675849i	$0.763777\pi$
$662$	5.67403e13	−	3.27590e13i	0.446274	−	0.257656i
$663$		0			0
$664$	4.84823e13	−	8.39738e13i	0.375615	−	0.650584i
$665$			2.84342e13i			0.218641i
$666$		0			0
$667$	−3.00781e13			−0.227835
$668$	−8.52339e13	−	4.92098e13i	−0.640811	−	0.369973i
$669$		0			0
$670$	2.05507e13	+	3.55949e13i	0.152213	+	0.263641i
$671$	−4.40004e13	+	2.54036e13i	−0.323477	+	0.186760i
$672$		0			0
$673$	1.09640e14	−	1.89902e14i	0.794136	−	1.37548i	−0.129251	−	0.991612i	$-0.541257\pi$
$673$	1.09640e14	−	1.89902e14i	0.794136	−	1.37548i	0.923387	−	0.383871i	$-0.125409\pi$
$674$		−	9.85257e13i		−	0.708353i
$675$		0			0
$676$	−6.97053e11			−0.00493779
$677$	9.91733e13	+	5.72577e13i	0.697351	+	0.402616i	0.806360	−	0.591425i	$-0.201434\pi$
$677$	9.91733e13	+	5.72577e13i	0.697351	+	0.402616i	−0.109009	+	0.994041i	$0.534768\pi$
$678$		0			0
$679$	−2.15685e14	−	3.73578e14i	−1.49442	−	2.58840i
$680$	2.66636e13	−	1.53942e13i	0.183389	−	0.105880i
$681$		0			0
$682$	−1.11216e13	+	1.92631e13i	−0.0753780	+	0.130558i
$683$			2.03223e13i			0.136732i	0.997660	+	0.0683659i	$0.0217785\pi$
$683$			2.03223e13i			0.136732i	−0.997660	+	0.0683659i	$0.978221\pi$
$684$		0			0
$685$	−5.71017e13			−0.378613
$686$	8.36199e13	+	4.82780e13i	0.550414	+	0.317782i
$687$		0			0
$688$	−6.67009e11	−	1.15529e12i	−0.00432703	−	0.00749463i
$689$	2.21964e14	−	1.28151e14i	1.42951	−	0.825328i
$690$		0			0
$691$	−1.34430e13	+	2.32840e13i	−0.0853308	+	0.147797i	−0.905532	−	0.424278i	$-0.860528\pi$
$691$	−1.34430e13	+	2.32840e13i	−0.0853308	+	0.147797i	0.820201	+	0.572075i	$0.193861\pi$
$692$		−	6.97605e13i		−	0.439622i
$693$		0			0
$694$	8.00525e13			0.497253
$695$	2.98266e13	+	1.72204e13i	0.183941	+	0.106199i
$696$		0			0
$697$	8.75387e13	+	1.51622e14i	0.532153	+	0.921716i
$698$	−5.58933e13	+	3.22700e13i	−0.337351	+	0.194770i
$699$		0			0
$700$	−8.38328e13	+	1.45203e14i	−0.498797	+	0.863942i
$701$		−	8.29393e13i		−	0.489971i	−0.969527	−	0.244985i	$-0.921217\pi$
$701$		−	8.29393e13i		−	0.489971i	0.969527	−	0.244985i	$-0.0787832\pi$
$702$		0			0
$703$	1.94770e13			0.113434
$704$	−1.06256e14	−	6.13472e13i	−0.614457	−	0.354757i
$705$		0			0
$706$	−7.01050e13	−	1.21425e14i	−0.399692	−	0.692286i
$707$	−1.48475e13	+	8.57219e12i	−0.0840535	+	0.0485283i
$708$		0			0
$709$	−1.34045e14	+	2.32172e14i	−0.748201	+	1.29592i	0.200483	+	0.979697i	$0.435749\pi$
$709$	−1.34045e14	+	2.32172e14i	−0.748201	+	1.29592i	−0.948684	+	0.316225i	$0.897584\pi$
$710$			6.33582e12i			0.0351165i
$711$		0			0
$712$	−2.95275e14			−1.61371
$713$	−2.90751e13	−	1.67865e13i	−0.157788	−	0.0910989i
$714$		0			0
$715$	3.67336e13	+	6.36244e13i	0.196577	+	0.340482i
$716$	1.17623e14	−	6.79097e13i	0.625068	−	0.360883i
$717$		0			0
$718$	2.63559e12	−	4.56497e12i	0.0138120	−	0.0239230i
$719$		−	1.22028e14i		−	0.635060i	−0.948248	−	0.317530i	$-0.897147\pi$
$719$		−	1.22028e14i		−	0.635060i	0.948248	−	0.317530i	$-0.102853\pi$
$720$		0			0
$721$	4.55157e14			2.33606
$722$	−7.57421e13	−	4.37297e13i	−0.386057	−	0.222890i
$723$		0			0
$724$	−2.66806e13	−	4.62122e13i	−0.134123	−	0.232308i
$725$	−3.63802e13	+	2.10041e13i	−0.181625	+	0.104861i
$726$		0			0
$727$	3.04999e13	−	5.28274e13i	0.150185	−	0.260128i	−0.781110	−	0.624393i	$-0.785346\pi$
$727$	3.04999e13	−	5.28274e13i	0.150185	−	0.260128i	0.931295	+	0.364265i	$0.118680\pi$
$728$			3.21749e14i			1.57348i
$729$		0			0
$730$	5.83812e12			0.0281617
$731$	−1.25550e13	−	7.24861e12i	−0.0601490	−	0.0347270i
$732$		0			0
$733$	1.32031e13	+	2.28684e13i	0.0623959	+	0.108073i	0.895536	−	0.444989i	$-0.146793\pi$
$733$	1.32031e13	+	2.28684e13i	0.0623959	+	0.108073i	−0.833140	+	0.553062i	$0.813459\pi$
$734$	1.69399e14	−	9.78026e13i	0.795117	−	0.459061i
$735$		0			0
$736$	1.10956e14	−	1.92181e14i	0.513762	−	0.889861i
$737$			5.86363e14i			2.69668i
$738$		0			0
$739$	−2.40663e14			−1.09191			−0.545956	−	0.837814i	$-0.683834\pi$
$739$	−2.40663e14			−1.09191			−0.545956	+	0.837814i	$0.683834\pi$
$740$	−8.24488e12	−	4.76018e12i	−0.0371557	−	0.0214519i
$741$		0			0
$742$	1.77138e14	+	3.06812e14i	0.787575	+	1.36412i
$743$	−7.30995e13	+	4.22040e13i	−0.322827	+	0.186385i	−0.652652	−	0.757658i	$-0.726344\pi$
$743$	−7.30995e13	+	4.22040e13i	−0.322827	+	0.186385i	0.329825	+	0.944042i	$0.393010\pi$
$744$		0			0
$745$	2.19758e13	−	3.80632e13i	0.0957555	−	0.165853i
$746$			2.28566e14i			0.989278i
$747$		0			0
$748$	1.74844e14			0.746696
$749$	−2.66543e14	−	1.53889e14i	−1.13073	−	0.652826i
$750$		0			0
$751$	−7.70730e13	−	1.33494e14i	−0.322628	−	0.558809i	0.658401	−	0.752667i	$-0.271233\pi$
$751$	−7.70730e13	−	1.33494e14i	−0.322628	−	0.558809i	−0.981030	+	0.193858i	$0.937900\pi$
$752$	7.97361e12	−	4.60356e12i	0.0331563	−	0.0191428i
$753$		0			0
$754$	−1.60447e13	+	2.77903e13i	−0.0658379	+	0.114035i
$755$		−	9.26224e13i		−	0.377556i
$756$		0			0
$757$	3.54470e14			1.42594			0.712969	−	0.701196i	$-0.247350\pi$
$757$	3.54470e14			1.42594			0.712969	+	0.701196i	$0.247350\pi$
$758$	5.74383e13	+	3.31620e13i	0.229539	+	0.132524i
$759$		0			0
$760$	−1.64054e13	−	2.84150e13i	−0.0647021	−	0.112067i
$761$	−1.77896e14	+	1.02708e14i	−0.697017	+	0.402423i	−0.806235	−	0.591595i	$-0.798498\pi$
$761$	−1.77896e14	+	1.02708e14i	−0.697017	+	0.402423i	0.109219	+	0.994018i	$0.465165\pi$
$762$		0			0
$763$	−1.81239e14	+	3.13916e14i	−0.700857	+	1.21392i
$764$		−	8.38672e13i		−	0.322200i
$765$		0			0
$766$	−2.22898e14			−0.845205
$767$	−2.99684e14	−	1.73023e14i	−1.12898	−	0.651818i
$768$		0			0
$769$	1.84614e14	+	3.19761e14i	0.686488	+	1.18903i	0.972967	+	0.230945i	$0.0741818\pi$
$769$	1.84614e14	+	3.19761e14i	0.686488	+	1.18903i	−0.286479	+	0.958087i	$0.592485\pi$
$770$	−8.79454e13	+	5.07753e13i	−0.324907	+	0.187585i
$771$		0			0
$772$	3.70430e13	−	6.41604e13i	0.135089	−	0.233981i
$773$			3.25884e13i			0.118077i	0.998256	+	0.0590385i	$0.0188035\pi$
$773$			3.25884e13i			0.118077i	−0.998256	+	0.0590385i	$0.981197\pi$
$774$		0			0
$775$	−4.68894e13			−0.167713
$776$	4.31079e14	+	2.48884e14i	1.53196	+	0.884480i
$777$		0			0
$778$	−1.06364e13	−	1.84227e13i	−0.0373160	−	0.0646332i
$779$	1.61581e14	−	9.32886e13i	0.563251	−	0.325193i
$780$		0			0
$781$	−4.51941e13	+	7.82785e13i	−0.155535	+	0.269394i
$782$		−	1.35159e14i		−	0.462181i
$783$		0			0
$784$	4.87479e13			0.164580
$785$	−6.27269e13	−	3.62154e13i	−0.210429	−	0.121491i
$786$		0			0
$787$	−1.68426e14	−	2.91723e14i	−0.557874	−	0.966266i	−0.997674	−	0.0681704i	$-0.978284\pi$
$787$	−1.68426e14	−	2.91723e14i	−0.557874	−	0.966266i	0.439800	−	0.898096i	$-0.355049\pi$
$788$	−2.62837e12	+	1.51749e12i	−0.00865077	+	0.00499452i
$789$		0			0
$790$	5.36556e11	−	9.29343e11i	0.00174373	−	0.00302023i
$791$		−	3.42790e14i		−	1.10700i
$792$		0			0
$793$	−8.18149e13			−0.260896
$794$	2.35840e13	+	1.36162e13i	0.0747334	+	0.0431473i
$795$		0			0
$796$	−1.13439e14	−	1.96481e14i	−0.354973	−	0.614831i
$797$	−1.35550e14	+	7.82597e13i	−0.421509	+	0.243359i	−0.695723	−	0.718310i	$-0.744916\pi$
$797$	−1.35550e14	+	7.82597e13i	−0.421509	+	0.243359i	0.274214	+	0.961669i	$0.411582\pi$
$798$		0			0
$799$	5.00284e13	−	8.66518e13i	0.153632	−	0.266099i
$800$		−	3.09931e14i		−	0.945834i
$801$		0			0
$802$	1.24690e14			0.375804
$803$	7.21295e13	+	4.16440e13i	0.216041	+	0.124731i
$804$		0			0
$805$	−7.66385e13	−	1.32742e14i	−0.226708	−	0.392670i
$806$	−3.10194e13	+	1.79091e13i	−0.0911923	+	0.0526499i
$807$		0			0
$808$	9.89164e12	−	1.71328e13i	0.0287218	−	0.0497476i
$809$			1.57640e14i			0.454909i	0.973789	+	0.227455i	$0.0730403\pi$
$809$			1.57640e14i			0.454909i	−0.973789	+	0.227455i	$0.926960\pi$
$810$		0			0
$811$	−1.51421e14			−0.431600			−0.215800	−	0.976438i	$-0.569236\pi$
$811$	−1.51421e14			−0.431600			−0.215800	+	0.976438i	$0.569236\pi$
$812$	7.50036e13	+	4.33033e13i	0.212472	+	0.122671i
$813$		0			0
$814$	3.47803e13	+	6.02413e13i	0.0973221	+	0.168567i
$815$	−1.49765e13	+	8.64667e12i	−0.0416506	+	0.0240470i
$816$		0			0
$817$	−7.72472e12	+	1.33796e13i	−0.0212213	+	0.0367564i
$818$		−	2.18336e14i		−	0.596156i
$819$		0			0
$820$	−9.11992e13			−0.245992
$821$	6.21089e14	+	3.58586e14i	1.66509	+	0.961341i	0.970226	+	0.242202i	$0.0778696\pi$
$821$	6.21089e14	+	3.58586e14i	1.66509	+	0.961341i	0.694866	+	0.719139i	$0.255464\pi$
$822$		0			0
$823$	3.42060e14	+	5.92466e14i	0.905948	+	1.56915i	0.819639	+	0.572880i	$0.194174\pi$
$823$	3.42060e14	+	5.92466e14i	0.905948	+	1.56915i	0.0863087	+	0.996268i	$0.472493\pi$
$824$	−4.54850e14	+	2.62608e14i	−1.19738	+	0.691307i
$825$		0			0
$826$	2.39162e14	−	4.14241e14i	0.622003	−	1.07734i
$827$		−	5.83847e13i		−	0.150929i	−0.997149	−	0.0754643i	$-0.975956\pi$
$827$		−	5.83847e13i		−	0.150929i	0.997149	−	0.0754643i	$-0.0240439\pi$
$828$		0			0
$829$	−3.95133e14			−1.00918			−0.504592	−	0.863358i	$-0.668357\pi$
$829$	−3.95133e14			−1.00918			−0.504592	+	0.863358i	$0.668357\pi$
$830$	4.26791e13	+	2.46408e13i	0.108349	+	0.0625553i
$831$		0			0
$832$	−9.87873e13	−	1.71105e14i	−0.247790	−	0.429185i
$833$	4.58785e14	−	2.64880e14i	1.14389	−	0.660426i
$834$		0			0
$835$	6.28303e13	−	1.08825e14i	0.154788	−	0.268100i
$836$		−	1.86329e14i		−	0.456298i
$837$		0			0
$838$	3.00158e14			0.726324
$839$	−3.52948e14	−	2.03775e14i	−0.848987	−	0.490163i	0.0113218	−	0.999936i	$-0.496396\pi$
$839$	−3.52948e14	−	2.03775e14i	−0.848987	−	0.490163i	−0.860309	+	0.509773i	$0.829729\pi$
$840$		0			0
$841$	−1.99504e14	−	3.45551e14i	−0.474211	−	0.821358i
$842$	2.57561e14	−	1.48703e14i	0.608582	−	0.351365i
$843$		0			0
$844$	6.92196e13	−	1.19892e14i	0.161628	−	0.279948i
$845$		−	8.89986e11i		−	0.00206585i
$846$		0			0
$847$	−7.36625e14			−1.68978
$848$	6.20634e13	+	3.58323e13i	0.141533	+	0.0817139i
$849$		0			0
$850$	−9.43845e13	−	1.63479e14i	−0.212719	−	0.368440i
$851$	−9.09261e13	+	5.24962e13i	−0.203723	+	0.117620i
$852$		0			0
$853$	2.25846e14	−	3.91176e14i	0.500111	−	0.866218i	−0.499889	−	0.866090i	$-0.666626\pi$
$853$	2.25846e14	−	3.91176e14i	0.500111	−	0.866218i	1.00000		0.000128656i	$-4.09524e-5\pi$
$854$		−	1.13089e14i		−	0.248961i
$855$		0			0
$856$	3.55151e14			0.772759
$857$	−7.14349e13	−	4.12429e13i	−0.154528	−	0.0892165i	0.420742	−	0.907180i	$-0.361770\pi$
$857$	−7.14349e13	−	4.12429e13i	−0.154528	−	0.0892165i	−0.575270	+	0.817964i	$0.695103\pi$
$858$		0			0
$859$	1.72996e14	+	2.99637e14i	0.369887	+	0.640664i	0.989548	−	0.144207i	$-0.0460630\pi$
$859$	1.72996e14	+	2.99637e14i	0.369887	+	0.640664i	−0.619660	+	0.784870i	$0.712730\pi$
$860$	6.53997e12	−	3.77585e12i	0.0139022	−	0.00802644i
$861$		0			0
$862$	−1.96065e14	+	3.39594e14i	−0.411967	+	0.713548i
$863$		−	1.38386e14i		−	0.289094i	−0.989498	−	0.144547i	$-0.953827\pi$
$863$		−	1.38386e14i		−	0.289094i	0.989498	−	0.144547i	$-0.0461725\pi$
$864$		0			0
$865$	8.90690e13			0.183927
$866$	1.35532e14	+	7.82497e13i	0.278262	+	0.160655i
$867$		0			0
$868$	4.83350e13	+	8.37187e13i	0.0980987	+	0.169912i
$869$	1.32582e13	−	7.65464e12i	0.0267539	−	0.0154464i
$870$		0			0
$871$	−4.72110e14	+	8.17718e14i	−0.941786	+	1.63122i
$872$		−	4.18272e14i		−	0.829614i
$873$		0			0
$874$	−1.44037e14			−0.282434
$875$	−3.86153e14	−	2.22945e14i	−0.752868	−	0.434669i
$876$		0			0
$877$	−3.48717e14	−	6.03996e14i	−0.672164	−	1.16422i	−0.977289	−	0.211910i	$-0.932032\pi$
$877$	−3.48717e14	−	6.03996e14i	−0.672164	−	1.16422i	0.305125	−	0.952312i	$-0.401302\pi$
$878$	1.44515e12	−	8.34359e11i	0.00276975	−	0.00159912i
$879$		0			0
$880$	−1.02711e13	+	1.77900e13i	−0.0194627	+	0.0337104i
$881$			5.02536e14i			0.946864i	0.880830	+	0.473432i	$0.156985\pi$
$881$			5.02536e14i			0.946864i	−0.880830	+	0.473432i	$0.843015\pi$
$882$		0			0
$883$	6.42054e14			1.19610			0.598050	−	0.801459i	$-0.295942\pi$
$883$	6.42054e14			1.19610			0.598050	+	0.801459i	$0.295942\pi$
$884$	2.43831e14	+	1.40776e14i	0.451676	+	0.260775i
$885$		0			0
$886$	1.81401e14	+	3.14196e14i	0.332255	+	0.575482i
$887$	−7.15760e14	+	4.13244e14i	−1.30361	+	0.752642i	−0.981022	−	0.193896i	$-0.937888\pi$
$887$	−7.15760e14	+	4.13244e14i	−1.30361	+	0.752642i	−0.322592	+	0.946538i	$0.604554\pi$
$888$		0			0
$889$	−7.80809e13	+	1.35240e14i	−0.140616	+	0.243555i
$890$		−	1.50071e14i		−	0.268749i
$891$		0			0
$892$	−4.39576e14			−0.778413
$893$	−9.23434e13	−	5.33145e13i	−0.162610	−	0.0938832i
$894$		0			0
$895$	8.67059e13	+	1.50179e14i	0.150985	+	0.261514i
$896$	−6.00263e14	+	3.46562e14i	−1.03945	+	0.600124i
$897$		0			0
$898$	1.79552e14	−	3.10993e14i	0.307474	−	0.532561i
$899$			2.42205e13i			0.0412462i
$900$		0			0
$901$	7.78804e14			1.31161
$902$	5.77073e14	+	3.33173e14i	0.966492	+	0.558005i
$903$		0			0
$904$	1.97776e14	+	3.42559e14i	0.327591	+	0.567405i
$905$	5.90030e13	−	3.40654e13i	0.0971922	−	0.0561139i
$906$		0			0
$907$	3.57293e14	−	6.18849e14i	0.582087	−	1.00820i	−0.413145	−	0.910665i	$-0.635570\pi$
$907$	3.57293e14	−	6.18849e14i	0.582087	−	1.00820i	0.995232	−	0.0975388i	$-0.0310970\pi$
$908$			2.99704e14i			0.485582i
$909$		0			0
$910$	−1.63527e14			−0.262049
$911$	3.72775e14	+	2.15222e14i	0.594093	+	0.343000i	0.766714	−	0.641988i	$-0.221890\pi$
$911$	3.72775e14	+	2.15222e14i	0.594093	+	0.343000i	−0.172621	+	0.984988i	$0.555224\pi$
$912$		0			0
$913$	3.51531e14	+	6.08870e14i	0.554128	+	0.959777i
$914$	−3.18163e14	+	1.83691e14i	−0.498791	+	0.287977i
$915$		0			0
$916$	−1.20743e14	+	2.09134e14i	−0.187234	+	0.324299i
$917$			4.37911e14i			0.675366i
$918$		0			0
$919$	4.49569e14			0.685833			0.342917	−	0.939366i	$-0.388585\pi$
$919$	4.49569e14			0.685833			0.342917	+	0.939366i	$0.388585\pi$
$920$	1.53173e14	+	8.84347e13i	0.232404	+	0.134179i
$921$		0			0
$922$	−2.76744e13	−	4.79334e13i	−0.0415359	−	0.0719422i
$923$	−1.26052e14	+	7.27761e13i	−0.188166	+	0.108638i
$924$		0			0
$925$	−7.33183e13	+	1.26991e14i	−0.108269	+	0.187527i
$926$			1.69768e14i			0.249345i
$927$		0			0
$928$	−1.60093e14			−0.232612
$929$	6.11112e13	+	3.52826e13i	0.0883166	+	0.0509896i	0.543508	−	0.839404i	$-0.317096\pi$
$929$	6.11112e13	+	3.52826e13i	0.0883166	+	0.0509896i	−0.455191	+	0.890394i	$0.650429\pi$
$930$		0			0
$931$	−2.82278e14	−	4.88920e14i	−0.403579	−	0.699020i
$932$	8.80743e13	−	5.08497e13i	0.125248	−	0.0723118i
$933$		0			0
$934$	−1.60536e14	+	2.78056e14i	−0.225859	+	0.391200i
$935$			2.23238e14i			0.312400i
$936$		0			0
$937$	1.12906e14			0.156322			0.0781609	−	0.996941i	$-0.475095\pi$
$937$	1.12906e14			0.156322			0.0781609	+	0.996941i	$0.475095\pi$
$938$	−1.13030e15	−	6.52577e14i	−1.55660	−	0.898706i
$939$		0			0
$940$	2.60602e13	+	4.51376e13i	0.0355090	+	0.0615033i
$941$	6.25375e14	−	3.61060e14i	0.847602	−	0.489363i	−0.0122389	−	0.999925i	$-0.503896\pi$
$941$	6.25375e14	−	3.61060e14i	0.847602	−	0.489363i	0.859841	+	0.510562i	$0.170563\pi$
$942$		0			0
$943$	−5.02881e14	+	8.71015e14i	−0.674383	+	1.16807i
$944$		−	9.67578e13i		−	0.129070i
$945$		0			0
$946$	−5.51766e13			−0.0728281
$947$	3.10028e14	+	1.78995e14i	0.407054	+	0.235013i	0.689523	−	0.724264i	$-0.257820\pi$
$947$	3.10028e14	+	1.78995e14i	0.407054	+	0.235013i	−0.282469	+	0.959276i	$0.591154\pi$
$948$		0			0
$949$	6.70593e13	+	1.16150e14i	0.0871220	+	0.150900i
$950$	−1.74217e14	+	1.00584e14i	−0.225150	+	0.129990i
$951$		0			0
$952$	−4.88836e14	+	8.46689e14i	−0.625142	+	1.08278i
$953$		−	1.90863e14i		−	0.242805i	−0.992603	−	0.121402i	$-0.961261\pi$
$953$		−	1.90863e14i		−	0.242805i	0.992603	−	0.121402i	$-0.0387392\pi$
$954$		0			0
$955$	1.07080e14			0.134801
$956$	−8.85536e14	−	5.11264e14i	−1.10896	−	0.640260i
$957$		0			0
$958$	−3.92335e14	−	6.79545e14i	−0.486217	−	0.842152i
$959$	1.57031e15	−	9.06617e14i	1.93594	−	1.11771i
$960$		0			0
$961$	3.96297e14	−	6.86406e14i	0.483508	−	0.837460i
$962$			1.12013e14i			0.135955i
$963$		0			0
$964$	−9.13310e13			−0.109707
$965$	8.19189e13	+	4.72959e13i	0.0978920	+	0.0565180i
$966$		0			0
$967$	−1.71705e14	−	2.97401e14i	−0.203072	−	0.351731i	0.746445	−	0.665447i	$-0.231759\pi$
$967$	−1.71705e14	−	2.97401e14i	−0.203072	−	0.351731i	−0.949517	+	0.313717i	$0.898426\pi$
$968$	7.36127e14	−	4.25003e14i	0.866116	−	0.500052i
$969$		0			0
$970$	−1.26493e14	+	2.19093e14i	−0.147302	+	0.255135i
$971$		−	5.00616e14i		−	0.579975i	−0.957030	−	0.289987i	$-0.906349\pi$
$971$		−	5.00616e14i		−	0.579975i	0.957030	−	0.289987i	$-0.0936511\pi$
$972$		0			0
$973$	−1.09365e15			−1.25405
$974$	4.57649e14	+	2.64224e14i	0.522080	+	0.301423i
$975$		0			0
$976$	−1.14381e13	−	1.98114e13i	−0.0129154	−	0.0223700i
$977$	−2.87392e14	+	1.65926e14i	−0.322851	+	0.186398i	−0.652662	−	0.757649i	$-0.726348\pi$
$977$	−2.87392e14	+	1.65926e14i	−0.322851	+	0.186398i	0.329812	+	0.944047i	$0.393015\pi$
$978$		0			0
$979$	1.07048e15	−	1.85412e15i	1.19032	−	2.06169i
$980$			2.75956e14i			0.305288i
$981$		0			0
$982$	5.40097e14			0.591445
$983$	−6.01068e13	−	3.47027e13i	−0.0654871	−	0.0378090i	0.466899	−	0.884311i	$-0.345371\pi$
$983$	−6.01068e13	−	3.47027e13i	−0.0654871	−	0.0378090i	−0.532386	+	0.846502i	$0.678705\pi$
$984$		0			0
$985$	−1.93750e12	−	3.35585e12i	−0.00208959	−	0.00361928i
$986$	−8.44439e13	+	4.87537e13i	−0.0906116	+	0.0523146i
$987$		0			0
$988$	1.50022e14	−	2.59847e14i	0.159357	−	0.276015i
$989$		−	8.32816e13i		−	0.0880172i
$990$		0			0
$991$	−6.94461e14			−0.726573			−0.363287	−	0.931677i	$-0.618345\pi$
$991$	−6.94461e14			−0.726573			−0.363287	+	0.931677i	$0.618345\pi$
$992$	−1.54755e14	−	8.93476e13i	−0.161096	−	0.0930089i
$993$		0			0
$994$	−1.00595e14	−	1.74236e14i	−0.103668	−	0.179559i
$995$	2.50864e14	−	1.44836e14i	0.257231	−	0.148512i
$996$		0			0
$997$	5.20134e14	−	9.00898e14i	0.528006	−	0.914534i	−0.471461	−	0.881887i	$-0.656273\pi$
$997$	5.20134e14	−	9.00898e14i	0.528006	−	0.914534i	0.999467	−	0.0326467i	$-0.0103936\pi$
$998$			7.14110e14i			0.721294i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	27.11.d.a.8.6		18
3.2	odd	2		9.11.d.a.2.4	✓	18
9.2	odd	6		81.11.b.a.80.12		18
9.4	even	3		9.11.d.a.5.4	yes	18
9.5	odd	6	inner	27.11.d.a.17.6		18
9.7	even	3		81.11.b.a.80.7		18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
9.11.d.a.2.4	✓	18	3.2	odd	2
9.11.d.a.5.4	yes	18	9.4	even	3
27.11.d.a.8.6		18	1.1	even	1	trivial
27.11.d.a.17.6		18	9.5	odd	6	inner
81.11.b.a.80.7		18	9.7	even	3
81.11.b.a.80.12		18	9.2	odd	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 27 = 3^{3} \)
Weight:	\( k \)	\(=\)	\( 11 \)
Character orbit:	\([\chi]\)	\(=\)	27.d (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(16.1281 + 9.31155i) q^{2} +(-338.590 - 586.455i) q^{4} +(748.776 - 432.306i) q^{5} +(-13727.6 + 23777.0i) q^{7} -31681.3i q^{8} +16101.8 q^{10} +(198936. + 114856. i) q^{11} +(184952. + 320346. i) q^{13} +(-442801. + 255651. i) q^{14} +(-51714.5 + 89572.1i) q^{16} +1.12400e6i q^{17} +1.19782e6 q^{19} +(-507056. - 292749. i) q^{20} +(2.13897e6 + 3.70481e6i) q^{22} +(-5.59191e6 + 3.22849e6i) q^{23} +(-4.50904e6 + 7.80988e6i) q^{25} +6.88877e6i q^{26} +1.85922e7 q^{28} +(4.03415e6 + 2.32912e6i) q^{29} +(2.59975e6 + 4.50290e6i) q^{31} +(-2.97634e7 + 1.71839e7i) q^{32} +(-1.04661e7 + 1.81279e7i) q^{34} +2.37382e7i q^{35} +1.62603e7 q^{37} +(1.93186e7 + 1.11536e7i) q^{38} +(-1.36960e7 - 2.37222e7i) q^{40} +(1.34895e8 - 7.78817e7i) q^{41} +(-6.44896e6 + 1.11699e7i) q^{43} -1.55556e8i q^{44} -1.20249e8 q^{46} +(-7.70926e7 - 4.45094e7i) q^{47} +(-2.35659e8 - 4.08174e8i) q^{49} +(-1.45444e8 + 8.39722e7i) q^{50} +(1.25246e8 - 2.16932e8i) q^{52} -6.92888e8i q^{53} +1.98611e8 q^{55} +(7.53285e8 + 4.34909e8i) q^{56} +(4.33754e7 + 7.51283e7i) q^{58} +(-8.10167e8 + 4.67750e8i) q^{59} +(-1.10589e8 + 1.91546e8i) q^{61} +9.68308e7i q^{62} -5.34123e8 q^{64} +(2.76975e8 + 1.59912e8i) q^{65} +(1.27630e9 + 2.21062e9i) q^{67} +(6.59173e8 - 3.80574e8i) q^{68} +(-2.21039e8 + 3.82851e8i) q^{70} +3.93486e8i q^{71} +3.62576e8 q^{73} +(2.62247e8 + 1.51409e8i) q^{74} +(-4.05571e8 - 7.02470e8i) q^{76} +(-5.46185e9 + 3.15340e9i) q^{77} +(3.33228e7 - 5.77169e7i) q^{79} +8.94259e7i q^{80} +2.90080e9 q^{82} +(2.65058e9 + 1.53032e9i) q^{83} +(4.85910e8 + 8.41621e8i) q^{85} +(-2.08019e8 + 1.20100e8i) q^{86} +(3.63877e9 - 6.30254e9i) q^{88} -9.32017e9i q^{89} -1.01558e10 q^{91} +(3.78673e9 + 2.18627e9i) q^{92} +(-8.28904e8 - 1.43570e9i) q^{94} +(8.96902e8 - 5.17826e8i) q^{95} +(-7.85587e9 + 1.36068e10i) q^{97} -8.77741e9i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q + 3 q^{2} + 4095 q^{4} - 4956 q^{5} - 6120 q^{7} - 2052 q^{10} - 969 q^{11} + 140274 q^{13} + 2134578 q^{14} - 1571841 q^{16} + 2771370 q^{19} - 14542734 q^{20} - 3475521 q^{22} + 9944382 q^{23} + 14726277 q^{25}+ \cdots - 14510723337 q^{97}+O(q^{100}) \) 18 * q + 3 * q^2 + 4095 * q^4 - 4956 * q^5 - 6120 * q^7 - 2052 * q^10 - 969 * q^11 + 140274 * q^13 + 2134578 * q^14 - 1571841 * q^16 + 2771370 * q^19 - 14542734 * q^20 - 3475521 * q^22 + 9944382 * q^23 + 14726277 * q^25 - 22968324 * q^28 + 41383956 * q^29 + 28428390 * q^31 - 165205143 * q^32 - 66263103 * q^34 + 63695196 * q^37 + 621662181 * q^38 - 75566250 * q^40 - 452543883 * q^41 + 102086037 * q^43 + 44251488 * q^46 + 289445970 * q^47 + 6735231 * q^49 - 1915252779 * q^50 + 19035576 * q^52 - 289455552 * q^55 + 4272894318 * q^56 - 83900178 * q^58 - 3065773551 * q^59 + 141349086 * q^61 - 28980486 * q^64 + 11094862926 * q^65 + 954074115 * q^67 - 21469701105 * q^68 - 1440686628 * q^70 + 772009902 * q^73 + 30101814978 * q^74 - 40906287 * q^76 - 25001072268 * q^77 + 2079634212 * q^79 - 1423292742 * q^82 + 23396438442 * q^83 - 5975304714 * q^85 - 39111097821 * q^86 + 2974531059 * q^88 + 2180413260 * q^91 + 40885098684 * q^92 + 6395997924 * q^94 - 22335455946 * q^95 - 14510723337 * q^97

Introduction

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