LMFDB - Embedded newform 162.11.d.d.107.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [162,11,Mod(53,162)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

chi = DirichletCharacter(H, H._module([5]))

N = Newforms(chi, 11, names="a")

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

chi := DirichletCharacter("162.53");

S:= CuspForms(chi, 11);

N := Newforms(S);

Level:	$ N $	$=$	$ 162 = 2 \cdot 3^{4} $
Weight:	$ k $	$=$	$ 11 $
Character orbit:	$[\chi]$	$=$	162.d (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$102.927874933$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	8.0.17318914560000.97
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 4x^{7} - 82x^{6} + 260x^{5} + 2477x^{4} - 5392x^{3} - 31616x^{2} + 34356x + 161859 $ x^8 - 4x^7 - 82x^6 + 260x^5 + 2477x^4 - 5392x^3 - 31616x^2 + 34356*x + 161859
Coefficient ring:	$\Z[a_1, \ldots, a_{25}]$
Coefficient ring index:	$ 2^{24}\cdot 3^{16} $
Twist minimal:	no (minimal twist has level 6)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			107.3
Root			$6.33452 + 0.707107i$ of defining polynomial
Character	$\chi$	$=$	162.107
Dual form			162.11.d.d.53.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(19.5959 + 11.3137i) q^{2} +(256.000 + 443.405i) q^{4} +(-4172.87 + 2409.21i) q^{5} +(-335.265 + 580.696i) q^{7} +11585.2i q^{8} +O(q^{10})$	\(q+(19.5959 + 11.3137i) q^{2} +(256.000 + 443.405i) q^{4} +(-4172.87 + 2409.21i) q^{5} +(-335.265 + 580.696i) q^{7} +11585.2i q^{8} -109028. q^{10} +(-202016. - 116634. i) q^{11} +(-153890. - 266546. i) q^{13} +(-13139.6 + 7586.18i) q^{14} +(-131072. + 227023. i) q^{16} +672324. i q^{17} -1.55119e6 q^{19} +(-2.13651e6 - 1.23351e6i) q^{20} +(-2.63913e6 - 4.57111e6i) q^{22} +(4.82854e6 - 2.78776e6i) q^{23} +(6.72574e6 - 1.16493e7i) q^{25} -6.96428e6i q^{26} -343311. q^{28} +(2.57481e7 + 1.48657e7i) q^{29} +(-1.54684e7 - 2.67921e7i) q^{31} +(-5.13695e6 + 2.96582e6i) q^{32} +(-7.60648e6 + 1.31748e7i) q^{34} -3.23089e6i q^{35} -8.56690e7 q^{37} +(-3.03970e7 - 1.75497e7i) q^{38} +(-2.79112e7 - 4.83437e7i) q^{40} +(3.10950e7 - 1.79527e7i) q^{41} +(1.83126e7 - 3.17184e7i) q^{43} -1.19433e8i q^{44} +1.26159e8 q^{46} +(-2.84816e7 - 1.64438e7i) q^{47} +(1.41013e8 + 2.44241e8i) q^{49} +(2.63594e8 - 1.52186e8i) q^{50} +(7.87918e7 - 1.36471e8i) q^{52} +4.59194e8i q^{53} +1.12398e9 q^{55} +(-6.72750e6 - 3.88412e6i) q^{56} +(3.36372e8 + 5.82613e8i) q^{58} +(-4.23189e8 + 2.44328e8i) q^{59} +(3.06464e7 - 5.30811e7i) q^{61} -7.00020e8i q^{62} -1.34218e8 q^{64} +(1.28433e9 + 7.41507e8i) q^{65} +(3.35388e8 + 5.80909e8i) q^{67} +(-2.98112e8 + 1.72115e8i) q^{68} +(3.65533e7 - 6.33122e7i) q^{70} +1.23330e9i q^{71} +1.08126e9 q^{73} +(-1.67876e9 - 9.69234e8i) q^{74} +(-3.97104e8 - 6.87805e8i) q^{76} +(1.35458e8 - 7.82067e7i) q^{77} +(9.33141e8 - 1.61625e9i) q^{79} -1.26312e9i q^{80} +8.12446e8 q^{82} +(9.48838e8 + 5.47812e8i) q^{83} +(-1.61977e9 - 2.80552e9i) q^{85} +(7.17706e8 - 4.14368e8i) q^{86} +(1.35123e9 - 2.34041e9i) q^{88} +5.19876e9i q^{89} +2.06376e8 q^{91} +(2.47221e9 + 1.42733e9i) q^{92} +(-3.72082e8 - 6.44464e8i) q^{94} +(6.47291e9 - 3.73714e9i) q^{95} +(5.37353e9 - 9.30722e9i) q^{97} +6.38151e9i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 2048 q^{4} + 45112 q^{7}+O(q^{10}) $ 8 * q + 2048 * q^4 + 45112 * q^7	$ 8 q + 2048 q^{4} + 45112 q^{7} - 107520 q^{10} - 275240 q^{13} - 1048576 q^{16} - 3137456 q^{19} - 7730688 q^{22} + 33732380 q^{25} + 46194688 q^{28} + 21785848 q^{31} - 151087104 q^{34} - 142028336 q^{37} - 27525120 q^{40} + 470688664 q^{43} + 377628672 q^{46} + 50058420 q^{49} + 140922880 q^{52} + 5402718720 q^{55} + 1564177920 q^{58} + 1184038744 q^{61} - 1073741824 q^{64} + 297365848 q^{67} + 3962250240 q^{70} + 13068538000 q^{73} - 803188736 q^{76} - 199282568 q^{79} + 16757336064 q^{82} + 12880512000 q^{85} + 3958112256 q^{88} + 16634464160 q^{91} - 8505477120 q^{94} + 39176355064 q^{97}+O(q^{100}) $ 8 * q + 2048 * q^4 + 45112 * q^7 - 107520 * q^10 - 275240 * q^13 - 1048576 * q^16 - 3137456 * q^19 - 7730688 * q^22 + 33732380 * q^25 + 46194688 * q^28 + 21785848 * q^31 - 151087104 * q^34 - 142028336 * q^37 - 27525120 * q^40 + 470688664 * q^43 + 377628672 * q^46 + 50058420 * q^49 + 140922880 * q^52 + 5402718720 * q^55 + 1564177920 * q^58 + 1184038744 * q^61 - 1073741824 * q^64 + 297365848 * q^67 + 3962250240 * q^70 + 13068538000 * q^73 - 803188736 * q^76 - 199282568 * q^79 + 16757336064 * q^82 + 12880512000 * q^85 + 3958112256 * q^88 + 16634464160 * q^91 - 8505477120 * q^94 + 39176355064 * q^97

Display 100 coefficients 10 coefficients

Character values

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

$n$	$83$
$\chi(n)$	$e\left(\frac{1}{6}\right)$

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 $

$2$	19.5959	+	11.3137i	0.612372	+	0.353553i
$2$	19.5959	+	11.3137i	0.612372	+	0.353553i
$3$		0			0
$3$		0			0
$4$	256.000	+	443.405i	0.250000	+	0.433013i
$5$	−4172.87	+	2409.21i	−1.33532	+	0.770946i	−0.986109	−	0.166099i	$-0.946883\pi$
$5$	−4172.87	+	2409.21i	−1.33532	+	0.770946i	−0.349209	+	0.937045i	$0.613550\pi$
$6$		0			0
$7$	−335.265	+	580.696i	−0.0199479	+	0.0345508i	−0.875827	−	0.482625i	$-0.839683\pi$
$7$	−335.265	+	580.696i	−0.0199479	+	0.0345508i	0.855879	+	0.517176i	$0.173017\pi$
$8$			11585.2i			0.353553i
$9$		0			0
$10$	−109028.			−1.09028
$11$	−202016.	−	116634.i	−1.25436	−	0.724206i	−0.282390	−	0.959300i	$-0.591127\pi$
$11$	−202016.	−	116634.i	−1.25436	−	0.724206i	−0.971973	+	0.235093i	$0.924460\pi$
$12$		0			0
$13$	−153890.	−	266546.i	−0.414471	−	0.717885i	0.580901	−	0.813974i	$-0.302700\pi$
$13$	−153890.	−	266546.i	−0.414471	−	0.717885i	−0.995373	+	0.0960885i	$0.969367\pi$
$14$	−13139.6	+	7586.18i	−0.0244311	+	0.0141053i
$15$		0			0
$16$	−131072.	+	227023.i	−0.125000	+	0.216506i
$17$			672324.i			0.473515i	0.971569	+	0.236758i	$0.0760847\pi$
$17$			672324.i			0.473515i	−0.971569	+	0.236758i	$0.923915\pi$
$18$		0			0
$19$	−1.55119e6			−0.626465			−0.313233	−	0.949676i	$-0.601412\pi$
$19$	−1.55119e6			−0.626465			−0.313233	+	0.949676i	$0.601412\pi$
$20$	−2.13651e6	−	1.23351e6i	−0.667659	−	0.385473i
$21$		0			0
$22$	−2.63913e6	−	4.57111e6i	−0.512091	−	0.886968i
$23$	4.82854e6	−	2.78776e6i	0.750199	−	0.433127i	−0.0755670	−	0.997141i	$-0.524077\pi$
$23$	4.82854e6	−	2.78776e6i	0.750199	−	0.433127i	0.825766	+	0.564013i	$0.190743\pi$
$24$		0			0
$25$	6.72574e6	−	1.16493e7i	0.688716	−	1.19289i
$26$		−	6.96428e6i		−	0.586151i
$27$		0			0
$28$	−343311.			−0.0199479
$29$	2.57481e7	+	1.48657e7i	1.25532	+	0.724760i	0.972161	−	0.234313i	$-0.0752840\pi$
$29$	2.57481e7	+	1.48657e7i	1.25532	+	0.724760i	0.283160	+	0.959073i	$0.408617\pi$
$30$		0			0
$31$	−1.54684e7	−	2.67921e7i	−0.540303	−	0.935832i	−0.998886	−	0.0471804i	$-0.984976\pi$
$31$	−1.54684e7	−	2.67921e7i	−0.540303	−	0.935832i	0.458584	−	0.888651i	$-0.348357\pi$
$32$	−5.13695e6	+	2.96582e6i	−0.153093	+	0.0883883i
$33$		0			0
$34$	−7.60648e6	+	1.31748e7i	−0.167413	+	0.289968i
$35$		−	3.23089e6i		−	0.0615151i
$36$		0			0
$37$	−8.56690e7			−1.23542			−0.617711	−	0.786406i	$-0.711940\pi$
$37$	−8.56690e7			−1.23542			−0.617711	+	0.786406i	$0.711940\pi$
$38$	−3.03970e7	−	1.75497e7i	−0.383630	−	0.221489i
$39$		0			0
$40$	−2.79112e7	−	4.83437e7i	−0.272571	−	0.472106i
$41$	3.10950e7	−	1.79527e7i	0.268393	−	0.154957i	−0.359764	−	0.933043i	$-0.617143\pi$
$41$	3.10950e7	−	1.79527e7i	0.268393	−	0.154957i	0.628157	+	0.778087i	$0.283810\pi$
$42$		0			0
$43$	1.83126e7	−	3.17184e7i	0.124569	−	0.215759i	−0.796996	−	0.603985i	$-0.793579\pi$
$43$	1.83126e7	−	3.17184e7i	0.124569	−	0.215759i	0.921564	+	0.388226i	$0.126912\pi$
$44$		−	1.19433e8i		−	0.724206i
$45$		0			0
$46$	1.26159e8			0.612535
$47$	−2.84816e7	−	1.64438e7i	−0.124187	−	0.0716992i	0.436620	−	0.899646i	$-0.356175\pi$
$47$	−2.84816e7	−	1.64438e7i	−0.124187	−	0.0716992i	−0.560806	+	0.827947i	$0.689509\pi$
$48$		0			0
$49$	1.41013e8	+	2.44241e8i	0.499204	+	0.864647i
$50$	2.63594e8	−	1.52186e8i	0.843501	−	0.486996i
$51$		0			0
$52$	7.87918e7	−	1.36471e8i	0.207236	−	0.358943i
$53$			4.59194e8i			1.09804i	0.835810	+	0.549019i	$0.184998\pi$
$53$			4.59194e8i			1.09804i	−0.835810	+	0.549019i	$0.815002\pi$
$54$		0			0
$55$	1.12398e9			2.23330
$56$	−6.72750e6	−	3.88412e6i	−0.0122156	−	0.00705266i
$57$		0			0
$58$	3.36372e8	+	5.82613e8i	0.512483	+	0.887646i
$59$	−4.23189e8	+	2.44328e8i	−0.591936	+	0.341754i	−0.765863	−	0.643004i	$-0.777688\pi$
$59$	−4.23189e8	+	2.44328e8i	−0.591936	+	0.341754i	0.173927	+	0.984759i	$0.444354\pi$
$60$		0			0
$61$	3.06464e7	−	5.30811e7i	0.0362852	−	0.0628479i	−0.847312	−	0.531095i	$-0.821781\pi$
$61$	3.06464e7	−	5.30811e7i	0.0362852	−	0.0628479i	0.883598	+	0.468247i	$0.155114\pi$
$62$		−	7.00020e8i		−	0.764103i
$63$		0			0
$64$	−1.34218e8			−0.125000
$65$	1.28433e9	+	7.41507e8i	1.10690	+	0.639070i
$66$		0			0
$67$	3.35388e8	+	5.80909e8i	0.248413	+	0.430263i	0.963086	−	0.269196i	$-0.0867578\pi$
$67$	3.35388e8	+	5.80909e8i	0.248413	+	0.430263i	−0.714673	+	0.699459i	$0.753424\pi$
$68$	−2.98112e8	+	1.72115e8i	−0.205038	+	0.118379i
$69$		0			0
$70$	3.65533e7	−	6.33122e7i	0.0217489	−	0.0376702i
$71$			1.23330e9i			0.683561i	0.939780	+	0.341781i	$0.111030\pi$
$71$			1.23330e9i			0.683561i	−0.939780	+	0.341781i	$0.888970\pi$
$72$		0			0
$73$	1.08126e9			0.521573			0.260787	−	0.965396i	$-0.416018\pi$
$73$	1.08126e9			0.521573			0.260787	+	0.965396i	$0.416018\pi$
$74$	−1.67876e9	−	9.69234e8i	−0.756538	−	0.436787i
$75$		0			0
$76$	−3.97104e8	−	6.87805e8i	−0.156616	−	0.271267i
$77$	1.35458e8	−	7.82067e7i	0.0500439	−	0.0288928i
$78$		0			0
$79$	9.33141e8	−	1.61625e9i	0.303258	−	0.525258i	−0.673614	−	0.739083i	$-0.735259\pi$
$79$	9.33141e8	−	1.61625e9i	0.303258	−	0.525258i	0.976872	+	0.213826i	$0.0685924\pi$
$80$		−	1.26312e9i		−	0.385473i
$81$		0			0
$82$	8.12446e8			0.219142
$83$	9.48838e8	+	5.47812e8i	0.240880	+	0.139072i	0.615581	−	0.788073i	$-0.288921\pi$
$83$	9.48838e8	+	5.47812e8i	0.240880	+	0.139072i	−0.374701	+	0.927146i	$0.622255\pi$
$84$		0			0
$85$	−1.61977e9	−	2.80552e9i	−0.365055	−	0.632293i
$86$	7.17706e8	−	4.14368e8i	0.152565	−	0.0880833i
$87$		0			0
$88$	1.35123e9	−	2.34041e9i	0.256046	−	0.443484i
$89$			5.19876e9i			0.931000i	0.885048	+	0.465500i	$0.154126\pi$
$89$			5.19876e9i			0.931000i	−0.885048	+	0.465500i	$0.845874\pi$
$90$		0			0
$91$	2.06376e8			0.0330714
$92$	2.47221e9	+	1.42733e9i	0.375099	+	0.216564i
$93$		0			0
$94$	−3.72082e8	−	6.44464e8i	−0.0506990	−	0.0878132i
$95$	6.47291e9	−	3.73714e9i	0.836530	−	0.482971i
$96$		0			0
$97$	5.37353e9	−	9.30722e9i	0.625750	−	1.08383i	−0.362645	−	0.931927i	$-0.618126\pi$
$97$	5.37353e9	−	9.30722e9i	0.625750	−	1.08383i	0.988395	−	0.151904i	$-0.0485403\pi$
$98$			6.38151e9i			0.705981i
$99$		0			0
$100$	6.88716e9			0.688716
$101$	9.36643e9	+	5.40771e9i	0.891183	+	0.514525i	0.874329	−	0.485333i	$-0.161302\pi$
$101$	9.36643e9	+	5.40771e9i	0.891183	+	0.514525i	0.0168540	+	0.999858i	$0.494635\pi$
$102$		0			0
$103$	1.41723e9	+	2.45471e9i	0.122251	+	0.211746i	0.920655	−	0.390377i	$-0.127655\pi$
$103$	1.41723e9	+	2.45471e9i	0.122251	+	0.211746i	−0.798404	+	0.602122i	$0.794322\pi$
$104$	3.08800e9	−	1.78286e9i	0.253811	−	0.146538i
$105$		0			0
$106$	−5.19519e9	+	8.99834e9i	−0.388215	+	0.672408i
$107$		−	2.41202e10i		−	1.71974i	−0.510515	−	0.859869i	$-0.670545\pi$
$107$		−	2.41202e10i		−	1.71974i	0.510515	−	0.859869i	$-0.329455\pi$
$108$		0			0
$109$	−5.43424e9			−0.353188			−0.176594	−	0.984284i	$-0.556508\pi$
$109$	−5.43424e9			−0.353188			−0.176594	+	0.984284i	$0.556508\pi$
$110$	2.20255e10	+	1.27164e10i	1.36761	+	0.789590i
$111$		0			0
$112$	−8.78877e7	−	1.52226e8i	−0.00498698	−	0.00863771i
$113$	1.20642e10	−	6.96526e9i	0.654795	−	0.378046i	−0.135496	−	0.990778i	$-0.543263\pi$
$113$	1.20642e10	−	6.96526e9i	0.654795	−	0.378046i	0.790291	+	0.612732i	$0.209929\pi$
$114$		0			0
$115$	−1.34326e10	+	2.32659e10i	−0.667836	+	1.15673i
$116$			1.52224e10i			0.724760i
$117$		0			0
$118$	−1.10570e10			−0.483313
$119$	−3.90416e8	−	2.25407e8i	−0.0163603	−	0.00944565i
$120$		0			0
$121$	1.42383e10	+	2.46615e10i	0.548950	+	0.950809i
$122$	1.20109e9	−	6.93449e8i	0.0444402	−	0.0256575i
$123$		0			0
$124$	7.91982e9	−	1.37175e10i	0.270151	−	0.467916i
$125$			1.77600e10i			0.581958i
$126$		0			0
$127$	4.08412e10			1.23617			0.618087	−	0.786110i	$-0.287908\pi$
$127$	4.08412e10			1.23617			0.618087	+	0.786110i	$0.287908\pi$
$128$	−2.63012e9	−	1.51850e9i	−0.0765466	−	0.0441942i
$129$		0			0
$130$	1.67784e10	+	2.90610e10i	0.451891	+	0.782698i
$131$	3.59831e10	−	2.07749e10i	0.932701	−	0.538495i	0.0450365	−	0.998985i	$-0.485660\pi$
$131$	3.59831e10	−	2.07749e10i	0.932701	−	0.538495i	0.887665	+	0.460490i	$0.152326\pi$
$132$		0			0
$133$	5.20059e8	−	9.00769e8i	0.0124967	−	0.0216449i
$134$			1.51779e10i			0.351308i
$135$		0			0
$136$	−7.78903e9			−0.167413
$137$	8.01534e10	+	4.62766e10i	1.66081	+	0.958867i	0.972331	+	0.233609i	$0.0750535\pi$
$137$	8.01534e10	+	4.62766e10i	1.66081	+	0.958867i	0.688477	+	0.725259i	$0.258280\pi$
$138$		0			0
$139$	−3.97788e10	−	6.88989e10i	−0.766615	−	1.32782i	−0.939388	−	0.342855i	$-0.888606\pi$
$139$	−3.97788e10	−	6.88989e10i	−0.766615	−	1.32782i	0.172773	−	0.984962i	$-0.444727\pi$
$140$	1.43259e9	−	8.27107e8i	0.0266368	−	0.0153788i
$141$		0			0
$142$	−1.39532e10	+	2.41677e10i	−0.241675	+	0.418594i
$143$			7.17955e10i			1.20065i
$144$		0			0
$145$	−1.43258e11			−2.23500
$146$	2.11883e10	+	1.22330e10i	0.319397	+	0.184404i
$147$		0			0
$148$	−2.19313e10	−	3.79861e10i	−0.308855	−	0.534953i
$149$	6.99579e10	−	4.03902e10i	0.952589	−	0.549977i	0.0587047	−	0.998275i	$-0.481303\pi$
$149$	6.99579e10	−	4.03902e10i	0.952589	−	0.549977i	0.893884	+	0.448298i	$0.147970\pi$
$150$		0			0
$151$	−1.54327e10	+	2.67302e10i	−0.196588	+	0.340501i	−0.947420	−	0.319993i	$-0.896320\pi$
$151$	−1.54327e10	+	2.67302e10i	−0.196588	+	0.340501i	0.750832	+	0.660493i	$0.229653\pi$
$152$		−	1.79709e10i		−	0.221489i
$153$		0			0
$154$	3.53923e9			0.0408606
$155$	1.29095e11	+	7.45332e10i	1.44295	+	0.833088i
$156$		0			0
$157$	−4.85661e10	−	8.41190e10i	−0.509138	−	0.881852i	−0.999944	−	0.0105835i	$-0.996631\pi$
$157$	−4.85661e10	−	8.41190e10i	−0.509138	−	0.881852i	0.490806	−	0.871269i	$-0.336702\pi$
$158$	3.65715e10	−	2.11146e10i	0.371413	−	0.214435i
$159$		0			0
$160$	1.42905e10	−	2.47520e10i	0.136285	−	0.236053i
$161$			3.73855e9i			0.0345600i
$162$		0			0
$163$	−1.39440e11			−1.21185			−0.605927	−	0.795520i	$-0.707198\pi$
$163$	−1.39440e11			−1.21185			−0.605927	+	0.795520i	$0.707198\pi$
$164$	1.59206e10	+	9.19178e9i	0.134196	+	0.0774784i
$165$		0			0
$166$	1.23956e10	+	2.14698e10i	0.0983390	+	0.170328i
$167$	−1.08981e11	+	6.29200e10i	−0.839009	+	0.484402i	−0.856927	−	0.515437i	$-0.827630\pi$
$167$	−1.08981e11	+	6.29200e10i	−0.839009	+	0.484402i	0.0179180	+	0.999839i	$0.494296\pi$
$168$		0			0
$169$	2.15648e10	−	3.73513e10i	0.156427	−	0.270940i
$170$		−	7.33023e10i		−	0.516265i
$171$		0			0
$172$	1.87521e10			0.124569
$173$	1.09342e11	+	6.31284e10i	0.705594	+	0.407375i	0.809428	−	0.587220i	$-0.199778\pi$
$173$	1.09342e11	+	6.31284e10i	0.705594	+	0.407375i	−0.103833	+	0.994595i	$0.533111\pi$
$174$		0			0
$175$	4.50981e9	+	7.81121e9i	0.0274769	+	0.0475914i
$176$	5.29574e10	−	3.05749e10i	0.313591	−	0.181052i
$177$		0			0
$178$	−5.88173e10	+	1.01875e11i	−0.329158	+	0.570119i
$179$			2.96543e11i			1.61370i	0.590758	+	0.806848i	$0.298829\pi$
$179$			2.96543e11i			1.61370i	−0.590758	+	0.806848i	$0.701171\pi$
$180$		0			0
$181$	2.48451e11			1.27893			0.639466	−	0.768819i	$-0.279155\pi$
$181$	2.48451e11			1.27893			0.639466	+	0.768819i	$0.279155\pi$
$182$	4.04413e9	+	2.33488e9i	0.0202520	+	0.0116925i
$183$		0			0
$184$	3.22968e10	+	5.59397e10i	0.153134	+	0.265235i
$185$	3.57485e11	−	2.06394e11i	1.64968	−	0.952443i
$186$		0			0
$187$	7.84159e10	−	1.35820e11i	0.342923	−	0.593960i
$188$		−	1.68385e10i		−	0.0716992i
$189$		0			0
$190$	1.69123e11			0.683024
$191$	1.36876e11	+	7.90252e10i	0.538468	+	0.310884i	0.744458	−	0.667670i	$-0.232708\pi$
$191$	1.36876e11	+	7.90252e10i	0.538468	+	0.310884i	−0.205990	+	0.978554i	$0.566041\pi$
$192$		0			0
$193$	1.89185e11	+	3.27677e11i	0.706479	+	1.22366i	0.966155	+	0.257962i	$0.0830508\pi$
$193$	1.89185e11	+	3.27677e11i	0.706479	+	1.22366i	−0.259676	+	0.965696i	$0.583616\pi$
$194$	2.10598e11	−	1.21589e11i	0.766384	−	0.442472i
$195$		0			0
$196$	−7.21986e10	+	1.25052e11i	−0.249602	+	0.432323i
$197$		−	1.89406e11i		−	0.638356i	−0.947695	−	0.319178i	$-0.896593\pi$
$197$		−	1.89406e11i		−	0.638356i	0.947695	−	0.319178i	$-0.103407\pi$
$198$		0			0
$199$	5.02942e10			0.161158			0.0805791	−	0.996748i	$-0.474323\pi$
$199$	5.02942e10			0.161158			0.0805791	+	0.996748i	$0.474323\pi$
$200$	1.34960e11	+	7.79193e10i	0.421750	+	0.243498i
$201$		0			0
$202$	1.22362e11	+	2.11938e11i	0.363824	+	0.630162i
$203$	−1.72649e10	+	9.96787e9i	−0.0500821	+	0.0289149i
$204$		0			0
$205$	−8.65035e10	+	1.49828e11i	−0.238927	+	0.413833i
$206$			6.41365e10i			0.172890i
$207$		0			0
$208$	8.06828e10			0.207236
$209$	3.13366e11	+	1.80922e11i	0.785814	+	0.453690i
$210$		0			0
$211$	−2.37485e11	−	4.11336e11i	−0.567837	−	0.983522i	−0.996780	−	0.0801907i	$-0.974447\pi$
$211$	−2.37485e11	−	4.11336e11i	−0.567837	−	0.983522i	0.428943	−	0.903332i	$-0.358886\pi$
$212$	−2.03609e11	+	1.17554e11i	−0.475464	+	0.274509i
$213$		0			0
$214$	2.72889e11	−	4.72658e11i	0.608019	−	1.05312i
$215$			1.76476e11i			0.384143i
$216$		0			0
$217$	2.07440e10			0.0431117
$218$	−1.06489e11	−	6.14814e10i	−0.216283	−	0.124871i
$219$		0			0
$220$	2.87740e11	+	4.98380e11i	0.558324	+	0.967046i
$221$	1.79205e11	−	1.03464e11i	0.339930	−	0.196258i
$222$		0			0
$223$	1.17790e11	−	2.04018e11i	0.213592	−	0.369951i	−0.739244	−	0.673437i	$-0.764817\pi$
$223$	1.17790e11	−	2.04018e11i	0.213592	−	0.369951i	0.952836	+	0.303486i	$0.0981505\pi$
$224$		−	3.97734e9i		−	0.00705266i
$225$		0			0
$226$	3.15211e11			0.534638
$227$	−3.69815e11	−	2.13513e11i	−0.613557	−	0.354238i	0.160799	−	0.986987i	$-0.448593\pi$
$227$	−3.69815e11	−	2.13513e11i	−0.613557	−	0.354238i	−0.774356	+	0.632750i	$0.781926\pi$
$228$		0			0
$229$	−5.18356e11	−	8.97819e11i	−0.823096	−	1.42564i	−0.903366	−	0.428871i	$-0.858911\pi$
$229$	−5.18356e11	−	8.97819e11i	−0.823096	−	1.42564i	0.0802696	−	0.996773i	$-0.474422\pi$
$230$	−5.26447e11	+	3.03944e11i	−0.817928	+	0.472231i
$231$		0			0
$232$	−1.72222e11	+	2.98298e11i	−0.256241	+	0.443823i
$233$		−	1.03766e12i		−	1.51103i	−0.655130	−	0.755516i	$-0.727386\pi$
$233$		−	1.03766e12i		−	1.51103i	0.655130	−	0.755516i	$-0.272614\pi$
$234$		0			0
$235$	1.58466e11			0.221105
$236$	−2.16673e11	−	1.25096e11i	−0.295968	−	0.170877i
$237$		0			0
$238$	−5.10037e9	−	8.83410e9i	−0.00667908	−	0.0115685i
$239$	−1.07116e12	+	6.18437e11i	−1.37362	+	0.793060i	−0.991382	−	0.131004i	$-0.958180\pi$
$239$	−1.07116e12	+	6.18437e11i	−1.37362	+	0.793060i	−0.382238	+	0.924064i	$0.624847\pi$
$240$		0			0
$241$	5.19560e11	−	8.99904e11i	0.639072	−	1.10691i	−0.346564	−	0.938026i	$-0.612652\pi$
$241$	5.19560e11	−	8.99904e11i	0.639072	−	1.10691i	0.985637	−	0.168880i	$-0.0540149\pi$
$242$			6.44354e11i			0.776333i
$243$		0			0
$244$	3.13819e10			0.0362852
$245$	−1.17686e12	−	6.79458e11i	−1.33319	−	0.769719i
$246$		0			0
$247$	2.38713e11	+	4.13463e11i	0.259652	+	0.449730i
$248$	3.10392e11	−	1.79205e11i	0.330866	−	0.191026i
$249$		0			0
$250$	−2.00931e11	+	3.48023e11i	−0.205753	+	0.356375i
$251$			5.66781e11i			0.568914i	0.958689	+	0.284457i	$0.0918133\pi$
$251$			5.66781e11i			0.568914i	−0.958689	+	0.284457i	$0.908187\pi$
$252$		0			0
$253$	−1.30059e12			−1.25469
$254$	8.00320e11	+	4.62065e11i	0.756999	+	0.437053i
$255$		0			0
$256$	−3.43597e10	−	5.95128e10i	−0.0312500	−	0.0541266i
$257$	1.10802e12	−	6.39713e11i	0.988281	−	0.570584i	0.0835208	−	0.996506i	$-0.473383\pi$
$257$	1.10802e12	−	6.39713e11i	0.988281	−	0.570584i	0.904760	+	0.425922i	$0.140050\pi$
$258$		0			0
$259$	2.87218e10	−	4.97476e10i	0.0246441	−	0.0426848i
$260$			7.59303e11i			0.639070i
$261$		0			0
$262$	9.40164e11			0.761548
$263$	−1.45997e12	−	8.42915e11i	−1.16029	−	0.669892i	−0.208914	−	0.977934i	$-0.566993\pi$
$263$	−1.45997e12	−	8.42915e11i	−1.16029	−	0.669892i	−0.951373	+	0.308042i	$0.900326\pi$
$264$		0			0
$265$	−1.10629e12	−	1.91616e12i	−0.846528	−	1.46623i
$266$	2.03821e10	−	1.17676e10i	0.0153052	−	0.00883649i
$267$		0			0
$268$	−1.71719e11	+	2.97426e11i	−0.124206	+	0.215132i
$269$		−	1.34023e12i		−	0.951523i	−0.879574	−	0.475761i	$-0.842173\pi$
$269$		−	1.34023e12i		−	0.951523i	0.879574	−	0.475761i	$-0.157827\pi$
$270$		0			0
$271$	−1.75349e12			−1.19966			−0.599829	−	0.800129i	$-0.704765\pi$
$271$	−1.75349e12			−1.19966			−0.599829	+	0.800129i	$0.704765\pi$
$272$	−1.52633e11	−	8.81228e10i	−0.102519	−	0.0591894i
$273$		0			0
$274$	1.04712e12	+	1.81366e12i	0.678022	+	1.17437i
$275$	−2.71742e12	+	1.56890e12i	−1.72780	+	0.997545i
$276$		0			0
$277$	−8.47898e11	+	1.46860e12i	−0.519930	+	0.900545i	0.479802	+	0.877377i	$0.340709\pi$
$277$	−8.47898e11	+	1.46860e12i	−0.519930	+	0.900545i	−0.999732	+	0.0231681i	$0.992625\pi$
$278$		−	1.80018e12i		−	1.08416i
$279$		0			0
$280$	3.74306e10			0.0217489
$281$	−2.11462e11	−	1.22088e11i	−0.120698	−	0.0696851i	0.438435	−	0.898763i	$-0.355533\pi$
$281$	−2.11462e11	−	1.22088e11i	−0.120698	−	0.0696851i	−0.559134	+	0.829078i	$0.688866\pi$
$282$		0			0
$283$	4.98205e11	+	8.62916e11i	0.274458	+	0.475375i	0.969998	−	0.243112i	$-0.0781683\pi$
$283$	4.98205e11	+	8.62916e11i	0.274458	+	0.475375i	−0.695540	+	0.718487i	$0.744835\pi$
$284$	−5.46852e11	+	3.15725e11i	−0.295991	+	0.170890i
$285$		0			0
$286$	−8.12273e11	+	1.40690e12i	−0.424494	+	0.735246i
$287$			2.40756e10i			0.0123643i
$288$		0			0
$289$	1.56397e12			0.775783
$290$	−2.80727e12	−	1.62078e12i	−1.36865	−	0.790193i
$291$		0			0
$292$	2.76802e11	+	4.79435e11i	0.130393	+	0.225848i
$293$	−1.36461e12	+	7.87855e11i	−0.631930	+	0.364845i	−0.781499	−	0.623906i	$-0.785545\pi$
$293$	−1.36461e12	+	7.87855e11i	−0.631930	+	0.364845i	0.149569	+	0.988751i	$0.452211\pi$
$294$		0			0
$295$	1.17728e12	−	2.03910e12i	0.526948	−	0.912701i
$296$		−	9.92496e11i		−	0.436787i
$297$		0			0
$298$	1.82785e12			0.777786
$299$	−1.48613e12	−	8.58017e11i	−0.621872	−	0.359038i
$300$		0			0
$301$	1.22792e10	+	2.12681e10i	0.00496977	+	0.00860790i
$302$	−6.04836e11	+	3.49202e11i	−0.240770	+	0.139009i
$303$		0			0
$304$	2.03317e11	−	3.52156e11i	0.0783081	−	0.135634i
$305$			2.95334e11i			0.111896i
$306$		0			0
$307$	−3.29823e12			−1.20945			−0.604726	−	0.796434i	$-0.706717\pi$
$307$	−3.29823e12			−1.20945			−0.604726	+	0.796434i	$0.706717\pi$
$308$	6.93545e10	+	4.00418e10i	0.0250219	+	0.0144464i
$309$		0			0
$310$	1.68649e12	+	2.92109e12i	0.589082	+	1.02032i
$311$	1.44887e12	−	8.36504e11i	0.497997	−	0.287519i	−0.229889	−	0.973217i	$-0.573836\pi$
$311$	1.44887e12	−	8.36504e11i	0.497997	−	0.287519i	0.727886	+	0.685698i	$0.240503\pi$
$312$		0			0
$313$	−8.66592e11	+	1.50098e12i	−0.288465	+	0.499636i	−0.973444	−	0.228927i	$-0.926478\pi$
$313$	−8.66592e11	+	1.50098e12i	−0.288465	+	0.499636i	0.684979	+	0.728563i	$0.259812\pi$
$314$		−	2.19785e12i		−	0.720029i
$315$		0			0
$316$	9.55536e11			0.303258
$317$	1.15268e12	+	6.65501e11i	0.360092	+	0.207899i	0.669121	−	0.743154i	$-0.266671\pi$
$317$	1.15268e12	+	6.65501e11i	0.360092	+	0.207899i	−0.309029	+	0.951053i	$0.600004\pi$
$318$		0			0
$319$	−3.46769e12	−	6.00621e12i	−1.04975	−	1.81822i
$320$	5.60073e11	−	3.23358e11i	0.166915	−	0.0963683i
$321$		0			0
$322$	−4.22968e10	+	7.32603e10i	−0.0122188	+	0.0211636i
$323$		−	1.04290e12i		−	0.296641i
$324$		0			0
$325$	−4.14010e12			−1.14181
$326$	−2.73246e12	−	1.57759e12i	−0.742107	−	0.428455i
$327$		0			0
$328$	2.07986e11	+	3.60243e11i	0.0547855	+	0.0948912i
$329$	1.90977e10	−	1.10261e10i	0.00495453	−	0.00286050i
$330$		0			0
$331$	−2.35980e12	+	4.08730e12i	−0.593931	+	1.02872i	0.399766	+	0.916617i	$0.369092\pi$
$331$	−2.35980e12	+	4.08730e12i	−0.593931	+	1.02872i	−0.993697	+	0.112102i	$0.964242\pi$
$332$			5.60959e11i			0.139072i
$333$		0			0
$334$	−2.84743e12			−0.685048
$335$	−2.79906e12	−	1.61604e12i	−0.663420	−	0.383025i
$336$		0			0
$337$	−2.07642e12	−	3.59646e12i	−0.477711	−	0.827419i	0.521963	−	0.852968i	$-0.325200\pi$
$337$	−2.07642e12	−	3.59646e12i	−0.477711	−	0.827419i	−0.999674	+	0.0255489i	$0.991867\pi$
$338$	8.45164e11	−	4.87956e11i	0.191583	−	0.110611i
$339$		0			0
$340$	8.29321e11	−	1.43643e12i	0.182527	−	0.316147i
$341$			7.21658e12i			1.56516i
$342$		0			0
$343$	−3.78515e11			−0.0797282
$344$	3.67466e11	+	2.12156e11i	0.0762824	+	0.0440417i
$345$		0			0
$346$	1.42843e12	+	2.47412e12i	0.288058	+	0.498931i
$347$	−3.80998e12	+	2.19969e12i	−0.757313	+	0.437235i	−0.828330	−	0.560240i	$-0.810709\pi$
$347$	−3.80998e12	+	2.19969e12i	−0.757313	+	0.437235i	0.0710170	+	0.997475i	$0.477376\pi$
$348$		0			0
$349$	4.62001e12	−	8.00209e12i	0.892310	−	1.54553i	0.0552116	−	0.998475i	$-0.482417\pi$
$349$	4.62001e12	−	8.00209e12i	0.892310	−	1.54553i	0.837099	−	0.547052i	$-0.184250\pi$
$350$			2.04091e11i			0.0388582i
$351$		0			0
$352$	1.38366e12			0.256046
$353$	−7.97378e11	−	4.60367e11i	−0.145476	−	0.0839905i	0.425495	−	0.904961i	$-0.360100\pi$
$353$	−7.97378e11	−	4.60367e11i	−0.145476	−	0.0839905i	−0.570971	+	0.820970i	$0.693433\pi$
$354$		0			0
$355$	−2.97128e12	−	5.14640e12i	−0.526989	−	0.912771i
$356$	−2.30516e12	+	1.33088e12i	−0.403135	+	0.232750i
$357$		0			0
$358$	−3.35500e12	+	5.81103e12i	−0.570528	+	0.988184i
$359$		−	6.17595e12i		−	1.03569i	−0.855473	−	0.517847i	$-0.826733\pi$
$359$		−	6.17595e12i		−	1.03569i	0.855473	−	0.517847i	$-0.173267\pi$
$360$		0			0
$361$	−3.72488e12			−0.607542
$362$	4.86862e12	+	2.81090e12i	0.783183	+	0.452171i
$363$		0			0
$364$	5.28323e10	+	9.15082e10i	0.00826784	+	0.0143203i
$365$	−4.51195e12	+	2.60497e12i	−0.696466	+	0.402105i
$366$		0			0
$367$	4.09689e12	−	7.09603e12i	0.615353	−	1.06582i	−0.374969	−	0.927037i	$-0.622347\pi$
$367$	4.09689e12	−	7.09603e12i	0.615353	−	1.06582i	0.990322	−	0.138786i	$-0.0443199\pi$
$368$			1.46159e12i			0.216564i
$369$		0			0
$370$	9.34034e12			1.34696
$371$	−2.66652e11	−	1.53952e11i	−0.0379381	−	0.0219036i
$372$		0			0
$373$	4.53661e12	+	7.85764e12i	0.628329	+	1.08830i	0.987887	+	0.155176i	$0.0495943\pi$
$373$	4.53661e12	+	7.85764e12i	0.628329	+	1.08830i	−0.359557	+	0.933123i	$0.617072\pi$
$374$	3.07326e12	−	1.77435e12i	0.419993	−	0.242483i
$375$		0			0
$376$	1.90506e11	−	3.29966e11i	0.0253495	−	0.0439066i
$377$		−	9.15072e12i		−	1.20157i
$378$		0			0
$379$	1.17817e13			1.50665			0.753324	−	0.657650i	$-0.228449\pi$
$379$	1.17817e13			1.50665			0.753324	+	0.657650i	$0.228449\pi$
$380$	3.31413e12	+	1.91341e12i	0.418265	+	0.241485i
$381$		0			0
$382$	1.78814e12	+	3.09714e12i	0.219828	+	0.380754i
$383$	5.90920e12	−	3.41168e12i	0.717026	−	0.413975i	−0.0966310	−	0.995320i	$-0.530807\pi$
$383$	5.90920e12	−	3.41168e12i	0.717026	−	0.413975i	0.813657	+	0.581345i	$0.197473\pi$
$384$		0			0
$385$	−3.76832e11	+	6.52692e11i	−0.0445496	+	0.0771622i
$386$			8.56152e12i			0.999112i
$387$		0			0
$388$	5.50249e12			0.625750
$389$	−6.12985e11	−	3.53907e11i	−0.0688180	−	0.0397321i	0.465196	−	0.885208i	$-0.345984\pi$
$389$	−6.12985e11	−	3.53907e11i	−0.0688180	−	0.0397321i	−0.534014	+	0.845476i	$0.679317\pi$
$390$		0			0
$391$	1.87428e12	+	3.24634e12i	0.205092	+	0.355230i
$392$	−2.82959e12	+	1.63367e12i	−0.305699	+	0.176495i
$393$		0			0
$394$	2.14289e12	−	3.71159e12i	0.225693	−	0.390912i
$395$			8.99251e12i			0.935181i
$396$		0			0
$397$	1.26553e12			0.128328			0.0641639	−	0.997939i	$-0.479562\pi$
$397$	1.26553e12			0.128328			0.0641639	+	0.997939i	$0.479562\pi$
$398$	9.85560e11	+	5.69013e11i	0.0986888	+	0.0569780i
$399$		0			0
$400$	1.76311e12	+	3.05380e12i	0.172179	+	0.298223i
$401$	1.30128e13	−	7.51294e12i	1.25501	−	0.724583i	0.282914	−	0.959145i	$-0.408699\pi$
$401$	1.30128e13	−	7.51294e12i	1.25501	−	0.724583i	0.972101	+	0.234562i	$0.0753656\pi$
$402$		0			0
$403$	−4.76087e12	+	8.24608e12i	−0.447880	+	0.775751i
$404$			5.53749e12i			0.514525i
$405$		0			0
$406$	−4.51094e11			−0.0408919
$407$	1.73065e13	+	9.99193e12i	1.54967	+	0.894700i
$408$		0			0
$409$	8.51808e11	+	1.47537e12i	0.0744261	+	0.128910i	0.900837	−	0.434158i	$-0.142954\pi$
$409$	8.51808e11	+	1.47537e12i	0.0744261	+	0.128910i	−0.826410	+	0.563068i	$0.809621\pi$
$410$	−3.39023e12	+	1.95735e12i	−0.292624	+	0.168947i
$411$		0			0
$412$	−7.25622e11	+	1.25681e12i	−0.0611257	+	0.105873i
$413$		−	3.27659e11i		−	0.0272692i
$414$		0			0
$415$	−5.27917e12			−0.428869
$416$	1.58105e12	+	9.12822e11i	0.126905	+	0.0732689i
$417$		0			0
$418$	4.09379e12	+	7.09065e12i	0.320807	+	0.555655i
$419$	1.92646e13	−	1.11224e13i	1.49173	−	0.861248i	0.491770	−	0.870725i	$-0.336350\pi$
$419$	1.92646e13	−	1.11224e13i	1.49173	−	0.861248i	0.999955	+	0.00947693i	$0.00301665\pi$
$420$		0			0
$421$	−9.14739e10	+	1.58437e11i	−0.00691650	+	0.0119797i	−0.869463	−	0.493998i	$-0.835535\pi$
$421$	−9.14739e10	+	1.58437e11i	−0.00691650	+	0.0119797i	0.862546	+	0.505978i	$0.168868\pi$
$422$		−	1.07473e13i		−	0.803043i
$423$		0			0
$424$	−5.31988e12			−0.388215
$425$	7.83212e12	+	4.52187e12i	0.564852	+	0.326117i
$426$		0			0
$427$	2.05493e10	+	3.55924e10i	0.00144763	+	0.00250737i
$428$	1.06950e13	−	6.17477e12i	0.744668	−	0.429934i
$429$		0			0
$430$	−1.99660e12	+	3.45820e12i	−0.135815	+	0.235239i
$431$			6.64491e12i			0.446789i	0.974728	+	0.223395i	$0.0717139\pi$
$431$			6.64491e12i			0.446789i	−0.974728	+	0.223395i	$0.928286\pi$
$432$		0			0
$433$	7.28337e12			0.478512			0.239256	−	0.970956i	$-0.423096\pi$
$433$	7.28337e12			0.478512			0.239256	+	0.970956i	$0.423096\pi$
$434$	4.06499e11	+	2.34692e11i	0.0264004	+	0.0152423i
$435$		0			0
$436$	−1.39116e12	−	2.40957e12i	−0.0882970	−	0.152935i
$437$	−7.48997e12	+	4.32434e12i	−0.469973	+	0.271339i
$438$		0			0
$439$	7.63002e12	−	1.32156e13i	0.467954	−	0.810520i	−0.531376	−	0.847136i	$-0.678325\pi$
$439$	7.63002e12	−	1.32156e13i	0.467954	−	0.810520i	0.999329	+	0.0366167i	$0.0116581\pi$
$440$			1.30216e13i			0.789590i
$441$		0			0
$442$	4.68225e12			0.277551
$443$	1.58746e13	+	9.16520e12i	0.930430	+	0.537184i	0.886948	−	0.461870i	$-0.152821\pi$
$443$	1.58746e13	+	9.16520e12i	0.930430	+	0.537184i	0.0434825	+	0.999054i	$0.486155\pi$
$444$		0			0
$445$	−1.25249e13	−	2.16937e13i	−0.717751	−	1.24318i
$446$	4.61641e12	−	2.66528e12i	0.261595	−	0.151032i
$447$		0			0
$448$	4.49985e10	−	7.79397e10i	0.00249349	−	0.00431885i
$449$			8.33876e12i			0.456951i	0.973550	+	0.228475i	$0.0733741\pi$
$449$			8.33876e12i			0.456951i	−0.973550	+	0.228475i	$0.926626\pi$
$450$		0			0
$451$	−8.37559e12			−0.448883
$452$	6.17686e12	+	3.56621e12i	0.327398	+	0.189023i
$453$		0			0
$454$	−4.83124e12	−	8.36796e12i	−0.250484	−	0.433851i
$455$	−8.61180e11	+	4.97202e11i	−0.0441608	+	0.0254962i
$456$		0			0
$457$	−2.06144e11	+	3.57052e11i	−0.0103416	+	0.0179123i	−0.871150	−	0.491017i	$-0.836625\pi$
$457$	−2.06144e11	+	3.57052e11i	−0.0103416	+	0.0179123i	0.860808	+	0.508929i	$0.169959\pi$
$458$		−	2.34581e13i		−	1.16403i
$459$		0			0
$460$	−1.37549e13			−0.667836
$461$	−1.43974e11	−	8.31235e10i	−0.00691480	−	0.00399226i	0.496539	−	0.868015i	$-0.334604\pi$
$461$	−1.43974e11	−	8.31235e10i	−0.00691480	−	0.00399226i	−0.503453	+	0.864022i	$0.667937\pi$
$462$		0			0
$463$	−6.36616e12	−	1.10265e13i	−0.299208	−	0.518243i	0.676747	−	0.736216i	$-0.263389\pi$
$463$	−6.36616e12	−	1.10265e13i	−0.299208	−	0.518243i	−0.975955	+	0.217972i	$0.930056\pi$
$464$	−6.74970e12	+	3.89694e12i	−0.313830	+	0.181190i
$465$		0			0
$466$	1.17397e13	−	2.03338e13i	0.534230	−	0.925314i
$467$		−	2.26689e13i		−	1.02058i	−0.860004	−	0.510288i	$-0.829539\pi$
$467$		−	2.26689e13i		−	1.02058i	0.860004	−	0.510288i	$-0.170461\pi$
$468$		0			0
$469$	−4.49775e11			−0.0198213
$470$	3.10530e12	+	1.79284e12i	0.135398	+	0.0781723i
$471$		0			0
$472$	−2.83060e12	−	4.90275e12i	−0.120828	−	0.209281i
$473$	−7.39891e12	+	4.27176e12i	−0.312508	+	0.180427i
$474$		0			0
$475$	−1.04329e13	+	1.80703e13i	−0.431456	+	0.747304i
$476$		−	2.30816e11i		−	0.00944565i
$477$		0			0
$478$	−2.79873e13			−1.12156
$479$	2.07547e13	+	1.19827e13i	0.823073	+	0.475201i	0.851475	−	0.524395i	$-0.175709\pi$
$479$	2.07547e13	+	1.19827e13i	0.823073	+	0.475201i	−0.0284023	+	0.999597i	$0.509042\pi$
$480$		0			0
$481$	1.31836e13	+	2.28347e13i	0.512047	+	0.886891i
$482$	2.03625e13	−	1.17563e13i	0.782701	−	0.451892i
$483$		0			0
$484$	−7.29004e12	+	1.26267e13i	−0.274475	+	0.475405i
$485$			5.17838e13i			1.92968i
$486$		0			0
$487$	−1.13824e13			−0.415516			−0.207758	−	0.978180i	$-0.566617\pi$
$487$	−1.13824e13			−0.415516			−0.207758	+	0.978180i	$0.566617\pi$
$488$	6.14957e11	+	3.55046e11i	0.0222201	+	0.0128288i
$489$		0			0
$490$	−1.53744e13	−	2.66292e13i	−0.544273	−	0.942709i
$491$	3.11346e13	−	1.79756e13i	1.09103	−	0.629906i	0.157179	−	0.987570i	$-0.449760\pi$
$491$	3.11346e13	−	1.79756e13i	1.09103	−	0.629906i	0.933850	+	0.357664i	$0.116427\pi$
$492$		0			0
$493$	−9.99454e12	+	1.73110e13i	−0.343185	+	0.594414i
$494$			1.08029e13i			0.367203i
$495$		0			0
$496$	8.10990e12			0.270151
$497$	−7.16172e11	−	4.13482e11i	−0.0236176	−	0.0136356i
$498$		0			0
$499$	6.68148e12	+	1.15727e13i	0.215958	+	0.374051i	0.953569	−	0.301176i	$-0.0973791\pi$
$499$	6.68148e12	+	1.15727e13i	0.215958	+	0.374051i	−0.737610	+	0.675227i	$0.764046\pi$
$500$	−7.87485e12	+	4.54655e12i	−0.251995	+	0.145490i
$501$		0			0
$502$	−6.41239e12	+	1.11066e13i	−0.201141	+	0.348387i
$503$			3.54934e13i			1.10232i	0.834399	+	0.551160i	$0.185815\pi$
$503$			3.54934e13i			1.10232i	−0.834399	+	0.551160i	$0.814185\pi$
$504$		0			0
$505$	−5.21132e13			−1.58668
$506$	−2.54863e13	−	1.47145e13i	−0.768340	−	0.443602i
$507$		0			0
$508$	1.04553e13	+	1.81092e13i	0.309043	+	0.535279i
$509$	−5.25969e13	+	3.03668e13i	−1.53947	+	0.888813i	−0.540600	+	0.841280i	$0.681803\pi$
$509$	−5.25969e13	+	3.03668e13i	−1.53947	+	0.888813i	−0.998870	+	0.0475339i	$0.984864\pi$
$510$		0			0
$511$	−3.62508e11	+	6.27882e11i	−0.0104043	+	0.0180208i
$512$		−	1.55494e12i		−	0.0441942i
$513$		0			0
$514$	2.89501e13			0.806928
$515$	−1.18278e13	−	6.82880e12i	−0.326489	−	0.188499i
$516$		0			0
$517$	3.83583e12	+	6.64385e12i	0.103850	+	0.179873i
$518$	1.12566e12	−	6.49900e11i	0.0301827	−	0.0174260i
$519$		0			0
$520$	−8.59053e12	+	1.48792e13i	−0.225945	+	0.391349i
$521$		−	2.06244e13i		−	0.537270i	−0.963242	−	0.268635i	$-0.913427\pi$
$521$		−	2.06244e13i		−	0.537270i	0.963242	−	0.268635i	$-0.0865726\pi$
$522$		0			0
$523$	5.24376e13			1.34009			0.670045	−	0.742320i	$-0.266275\pi$
$523$	5.24376e13			1.34009			0.670045	+	0.742320i	$0.266275\pi$
$524$	1.84234e13	+	1.06367e13i	0.466351	+	0.269248i
$525$		0			0
$526$	−1.90730e13	−	3.30354e13i	−0.473685	−	0.820447i
$527$	1.80129e13	−	1.03998e13i	0.443130	−	0.255841i
$528$		0			0
$529$	−5.17008e12	+	8.95484e12i	−0.124801	+	0.216162i
$530$		−	5.00652e13i		−	1.19717i
$531$		0			0
$532$	5.32541e11			0.0124967
$533$	−9.57043e12	−	5.52549e12i	−0.222482	−	0.128450i
$534$		0			0
$535$	5.81106e13	+	1.00650e14i	1.32582	+	2.29640i
$536$	−6.72997e12	+	3.88555e12i	−0.152121	+	0.0878271i
$537$		0			0
$538$	1.51630e13	−	2.62631e13i	0.336414	−	0.582686i
$539$		−	6.57877e13i		−	1.44611i
$540$		0			0
$541$	8.20249e13			1.76994			0.884972	−	0.465645i	$-0.154178\pi$
$541$	8.20249e13			1.76994			0.884972	+	0.465645i	$0.154178\pi$
$542$	−3.43613e13	−	1.98385e13i	−0.734637	−	0.424143i
$543$		0			0
$544$	−1.99399e12	−	3.45370e12i	−0.0418532	−	0.0724919i
$545$	2.26764e13	−	1.30922e13i	0.471618	−	0.272289i
$546$		0			0
$547$	8.11661e12	−	1.40584e13i	0.165744	−	0.287077i	−0.771175	−	0.636623i	$-0.780331\pi$
$547$	8.11661e12	−	1.40584e13i	0.165744	−	0.287077i	0.936919	+	0.349546i	$0.113664\pi$
$548$			4.73872e13i			0.958867i
$549$		0			0
$550$	−7.10004e13			−1.41074
$551$	−3.99401e13	−	2.30595e13i	−0.786415	−	0.454037i
$552$		0			0
$553$	6.25698e11	+	1.08374e12i	0.0120987	+	0.0209556i
$554$	−3.32307e13	+	1.91857e13i	−0.636782	+	0.367646i
$555$		0			0
$556$	2.03667e13	−	3.52762e13i	0.383308	−	0.663908i
$557$		−	1.12168e13i		−	0.209215i	−0.994514	−	0.104608i	$-0.966641\pi$
$557$		−	1.12168e13i		−	0.209215i	0.994514	−	0.104608i	$-0.0333587\pi$
$558$		0			0
$559$	−1.12726e13			−0.206521
$560$	7.33487e11	+	4.23479e11i	0.0133184	+	0.00768939i
$561$		0			0
$562$	−2.76253e12	−	4.78484e12i	−0.0492748	−	0.0853465i
$563$	−6.91540e13	+	3.99261e13i	−1.22258	+	0.705854i	−0.965466	−	0.260528i	$-0.916103\pi$
$563$	−6.91540e13	+	3.99261e13i	−1.22258	+	0.705854i	−0.257109	+	0.966382i	$0.582770\pi$
$564$		0			0
$565$	−3.35615e13	+	5.81302e13i	−0.582906	+	1.00962i
$566$			2.25462e13i			0.388142i
$567$		0			0
$568$	−1.42881e13			−0.241675
$569$	8.62210e11	+	4.97797e11i	0.0144561	+	0.00834624i	0.507211	−	0.861822i	$-0.330677\pi$
$569$	8.62210e11	+	4.97797e11i	0.0144561	+	0.00834624i	−0.492755	+	0.870168i	$0.664010\pi$
$570$		0			0
$571$	−5.39178e13	−	9.33883e13i	−0.888283	−	1.53855i	−0.841904	−	0.539627i	$-0.818565\pi$
$571$	−5.39178e13	−	9.33883e13i	−0.888283	−	1.53855i	−0.0463786	−	0.998924i	$-0.514768\pi$
$572$	−3.18345e13	+	1.83796e13i	−0.519897	+	0.300163i
$573$		0			0
$574$	−2.72385e11	+	4.71784e11i	−0.00437143	+	0.00757153i
$575$		−	7.49989e13i		−	1.19321i
$576$		0			0
$577$	3.31000e13			0.517546			0.258773	−	0.965938i	$-0.416682\pi$
$577$	3.31000e13			0.517546			0.258773	+	0.965938i	$0.416682\pi$
$578$	3.06475e13	+	1.76944e13i	0.475068	+	0.274281i
$579$		0			0
$580$	−3.66740e13	−	6.35212e13i	−0.558751	−	0.967785i
$581$	−6.36224e11	+	3.67324e11i	−0.00961013	+	0.00554841i
$582$		0			0
$583$	5.35578e13	−	9.27648e13i	0.795206	−	1.37734i
$584$			1.25266e13i			0.184404i
$585$		0			0
$586$	−3.56543e13			−0.515969
$587$	−1.04808e14	−	6.05110e13i	−1.50385	−	0.868248i	−0.999990	−	0.00446213i	$-0.998580\pi$
$587$	−1.04808e14	−	6.05110e13i	−1.50385	−	0.868248i	−0.503859	−	0.863786i	$-0.668087\pi$
$588$		0			0
$589$	2.39944e13	+	4.15596e13i	0.338481	+	0.586266i
$590$	4.61396e13	−	2.66387e13i	0.645377	−	0.372609i
$591$		0			0
$592$	1.12288e13	−	1.94489e13i	0.154428	−	0.267477i
$593$		−	8.43944e12i		−	0.115091i	−0.998343	−	0.0575453i	$-0.981673\pi$
$593$		−	8.43944e12i		−	0.115091i	0.998343	−	0.0575453i	$-0.0183274\pi$
$594$		0			0
$595$	2.17220e12			0.0291283
$596$	3.58185e13	+	2.06798e13i	0.476294	+	0.274989i
$597$		0			0
$598$	−1.94147e13	−	3.36273e13i	−0.253878	−	0.439730i
$599$	2.70098e13	−	1.55941e13i	0.350258	−	0.202221i	−0.314541	−	0.949244i	$-0.601851\pi$
$599$	2.70098e13	−	1.55941e13i	0.350258	−	0.202221i	0.664799	+	0.747023i	$0.268517\pi$
$600$		0			0
$601$	−1.43700e13	+	2.48896e13i	−0.183267	+	0.317428i	−0.942991	−	0.332817i	$-0.892001\pi$
$601$	−1.43700e13	+	2.48896e13i	−0.183267	+	0.317428i	0.759724	+	0.650246i	$0.225334\pi$
$602$			5.55692e11i			0.00702832i
$603$		0			0
$604$	−1.58031e13			−0.196588
$605$	−1.18830e14	−	6.86062e13i	−1.46605	−	0.846422i
$606$		0			0
$607$	2.23768e13	+	3.87578e13i	0.271553	+	0.470344i	0.969260	−	0.246040i	$-0.0791295\pi$
$607$	2.23768e13	+	3.87578e13i	0.271553	+	0.470344i	−0.697707	+	0.716384i	$0.745796\pi$
$608$	7.96839e12	−	4.60055e12i	0.0959075	−	0.0553722i
$609$		0			0
$610$	−3.34132e12	+	5.78734e12i	−0.0395612	+	0.0685219i
$611$			1.01222e13i			0.118869i
$612$		0			0
$613$	6.78051e13			0.783358			0.391679	−	0.920102i	$-0.371894\pi$
$613$	6.78051e13			0.783358			0.391679	+	0.920102i	$0.371894\pi$
$614$	−6.46318e13	−	3.73152e13i	−0.740635	−	0.427606i
$615$		0			0
$616$	9.06043e11	+	1.56931e12i	0.0102152	+	0.0176932i
$617$	−2.15001e12	+	1.24131e12i	−0.0240444	+	0.0138820i	−0.511974	−	0.859001i	$-0.671086\pi$
$617$	−2.15001e12	+	1.24131e12i	−0.0240444	+	0.0138820i	0.487930	+	0.872883i	$0.337752\pi$
$618$		0			0
$619$	−8.20000e12	+	1.42028e13i	−0.0902320	+	0.156286i	−0.907609	−	0.419817i	$-0.862094\pi$
$619$	−8.20000e12	+	1.42028e13i	−0.0902320	+	0.156286i	0.817377	+	0.576104i	$0.195428\pi$
$620$			7.63220e13i			0.833088i
$621$		0			0
$622$	3.78559e13			0.406613
$623$	−3.01890e12	−	1.74296e12i	−0.0321668	−	0.0185715i
$624$		0			0
$625$	2.28936e13	+	3.96529e13i	0.240057	+	0.415791i
$626$	−3.39633e13	+	1.96087e13i	−0.353296	+	0.203976i
$627$		0			0
$628$	2.48659e13	−	4.30689e13i	0.254569	−	0.440926i
$629$		−	5.75973e13i		−	0.584991i
$630$		0			0
$631$	−1.37258e13			−0.137211			−0.0686056	−	0.997644i	$-0.521855\pi$
$631$	−1.37258e13			−0.137211			−0.0686056	+	0.997644i	$0.521855\pi$
$632$	1.87246e13	+	1.08107e13i	0.185707	+	0.107218i
$633$		0			0
$634$	1.50586e13	+	2.60822e13i	0.147007	+	0.254623i
$635$	−1.70425e14	+	9.83948e13i	−1.65068	+	0.953023i
$636$		0			0
$637$	4.34010e13	−	7.51728e13i	0.413812	−	0.716743i
$638$		−	1.56930e14i		−	1.48457i
$639$		0			0
$640$	1.46335e13			0.136285
$641$	4.69687e13	+	2.71174e13i	0.434029	+	0.250587i	0.701061	−	0.713101i	$-0.252710\pi$
$641$	4.69687e13	+	2.71174e13i	0.434029	+	0.250587i	−0.267033	+	0.963687i	$0.586043\pi$
$642$		0			0
$643$	2.77346e13	+	4.80378e13i	0.252329	+	0.437047i	0.964167	−	0.265297i	$-0.0854700\pi$
$643$	2.77346e13	+	4.80378e13i	0.252329	+	0.437047i	−0.711837	+	0.702344i	$0.752137\pi$
$644$	−1.65769e12	+	9.57068e11i	−0.0149649	+	0.00863999i
$645$		0			0
$646$	1.17991e13	−	2.04366e13i	0.104878	−	0.181655i
$647$			5.56652e13i			0.490979i	0.969399	+	0.245489i	$0.0789486\pi$
$647$			5.56652e13i			0.490979i	−0.969399	+	0.245489i	$0.921051\pi$
$648$		0			0
$649$	1.13988e14			0.990002
$650$	−8.11291e13	−	4.68399e13i	−0.699214	−	0.403691i
$651$		0			0
$652$	−3.56967e13	−	6.18286e13i	−0.302964	−	0.524749i
$653$	−4.82196e13	+	2.78396e13i	−0.406123	+	0.234475i	−0.689123	−	0.724645i	$-0.742004\pi$
$653$	−4.82196e13	+	2.78396e13i	−0.406123	+	0.234475i	0.283000	+	0.959120i	$0.408671\pi$
$654$		0			0
$655$	−1.00102e14	+	1.73382e14i	−0.830302	+	1.43813i
$656$			9.41238e12i			0.0774784i
$657$		0			0
$658$	4.98984e11			0.00404536
$659$	−1.32241e14	−	7.63495e13i	−1.06399	−	0.614298i	−0.137460	−	0.990507i	$-0.543894\pi$
$659$	−1.32241e14	−	7.63495e13i	−1.06399	−	0.614298i	−0.926535	+	0.376210i	$0.877227\pi$
$660$		0			0
$661$	1.04018e14	+	1.80164e14i	0.824329	+	1.42778i	0.902431	+	0.430834i	$0.141780\pi$
$661$	1.04018e14	+	1.80164e14i	0.824329	+	1.42778i	−0.0781026	+	0.996945i	$0.524886\pi$
$662$	−9.24851e13	+	5.33963e13i	−0.727414	+	0.419973i
$663$		0			0
$664$	−6.34653e12	+	1.09925e13i	−0.0491695	+	0.0851641i
$665$			5.01172e12i			0.0385371i
$666$		0			0
$667$	1.65767e14			1.25565
$668$	−5.57981e13	−	3.22150e13i	−0.419505	−	0.242201i
$669$		0			0
$670$	−3.65668e13	−	6.33355e13i	−0.270840	−	0.469108i
$671$	−1.23821e13	+	7.14883e12i	−0.0910297	+	0.0525560i
$672$		0			0
$673$	4.72630e13	−	8.18619e13i	0.342331	−	0.592934i	−0.642534	−	0.766257i	$-0.722117\pi$
$673$	4.72630e13	−	8.18619e13i	0.342331	−	0.592934i	0.984865	+	0.173323i	$0.0554503\pi$
$674$		−	9.39679e13i		−	0.675585i
$675$		0			0
$676$	2.20824e13			0.156427
$677$	1.47316e14	+	8.50528e13i	1.03587	+	0.598060i	0.918661	−	0.395047i	$-0.129272\pi$
$677$	1.47316e14	+	8.50528e13i	1.03587	+	0.598060i	0.117210	+	0.993107i	$0.462605\pi$
$678$		0			0
$679$	3.60311e12	+	6.24077e12i	0.0249648	+	0.0432404i
$680$	3.25026e13	−	1.87654e13i	0.223549	−	0.129066i
$681$		0			0
$682$	−8.16463e13	+	1.41415e14i	−0.553369	+	0.958462i
$683$			2.23578e14i			1.50427i	0.659009	+	0.752135i	$0.270976\pi$
$683$			2.23578e14i			1.50427i	−0.659009	+	0.752135i	$0.729024\pi$
$684$		0			0
$685$	−4.45960e14			−2.95694
$686$	−7.41734e12	−	4.28240e12i	−0.0488234	−	0.0281882i
$687$		0			0
$688$	4.80055e12	+	8.31480e12i	0.0311422	+	0.0539398i
$689$	1.22396e14	−	7.06656e13i	0.788265	−	0.455105i
$690$		0			0
$691$	5.50672e12	−	9.53792e12i	0.0349545	−	0.0605429i	−0.848019	−	0.529966i	$-0.822205\pi$
$691$	5.50672e12	−	9.53792e12i	0.0349545	−	0.0605429i	0.882973	+	0.469423i	$0.155538\pi$
$692$			6.46435e13i			0.407375i
$693$		0			0
$694$	−9.95468e13			−0.618344
$695$	3.31983e14	+	1.91671e14i	2.04735	+	1.18204i
$696$		0			0
$697$	1.20700e13	+	2.09059e13i	0.0733744	+	0.127088i
$698$	1.81067e14	−	1.04539e14i	1.09285	−	0.630959i
$699$		0			0
$700$	−2.30902e12	+	3.99934e12i	−0.0137384	+	0.0237957i
$701$		−	1.10962e14i		−	0.655516i	−0.944762	−	0.327758i	$-0.893707\pi$
$701$		−	1.10962e14i		−	0.655516i	0.944762	−	0.327758i	$-0.106293\pi$
$702$		0			0
$703$	1.32889e14			0.773948
$704$	2.71142e13	+	1.56544e13i	0.156795	+	0.0905258i
$705$		0			0
$706$	−1.04169e13	−	1.80426e13i	−0.0593903	−	0.102867i
$707$	−6.28047e12	+	3.62603e12i	−0.0355545	+	0.0205274i
$708$		0			0
$709$	−1.04110e14	+	1.80323e14i	−0.581112	+	1.00652i	0.414236	+	0.910169i	$0.364049\pi$
$709$	−1.04110e14	+	1.80323e14i	−0.581112	+	1.00652i	−0.995348	+	0.0963458i	$0.969285\pi$
$710$		−	1.34465e14i		−	0.745275i
$711$		0			0
$712$	−6.02289e13			−0.329158
$713$	−1.49380e14	−	8.62443e13i	−0.810669	−	0.468040i
$714$		0			0
$715$	−1.72970e14	−	2.99593e14i	−0.925637	−	1.60325i
$716$	−1.31488e14	+	7.59149e13i	−0.698751	+	0.403424i
$717$		0			0
$718$	6.98730e13	−	1.21024e14i	0.366173	−	0.634231i
$719$			2.74910e14i			1.43069i	0.698771	+	0.715346i	$0.253731\pi$
$719$			2.74910e14i			1.43069i	−0.698771	+	0.715346i	$0.746269\pi$
$720$		0			0
$721$	−1.90059e12			−0.00975465
$722$	−7.29924e13	−	4.21422e13i	−0.372042	−	0.214798i
$723$		0			0
$724$	6.36034e13	+	1.10164e14i	0.319733	+	0.553794i
$725$	3.46350e14	−	1.99965e14i	1.72912	−	0.998307i
$726$		0			0
$727$	1.49536e14	−	2.59003e14i	0.736330	−	1.27536i	−0.217807	−	0.975992i	$-0.569890\pi$
$727$	1.49536e14	−	2.59003e14i	0.736330	−	1.27536i	0.954137	−	0.299370i	$-0.0967764\pi$
$728$			2.39092e12i			0.0116925i
$729$		0			0
$730$	−1.17888e14			−0.568662
$731$	2.13251e13	+	1.23120e13i	0.102165	+	0.0589852i
$732$		0			0
$733$	−5.99610e13	−	1.03856e14i	−0.283367	−	0.490806i	0.688845	−	0.724909i	$-0.258118\pi$
$733$	−5.99610e13	−	1.03856e14i	−0.283367	−	0.490806i	−0.972212	+	0.234103i	$0.924785\pi$
$734$	1.60565e14	−	9.27021e13i	0.753651	−	0.435120i
$735$		0			0
$736$	−1.65360e13	+	2.86411e13i	−0.0765668	+	0.132618i
$737$		−	1.56471e14i		−	0.719608i
$738$		0			0
$739$	−7.29345e13			−0.330911			−0.165455	−	0.986217i	$-0.552909\pi$
$739$	−7.29345e13			−0.330911			−0.165455	+	0.986217i	$0.552909\pi$
$740$	1.83033e14	+	1.05674e14i	0.824840	+	0.476221i
$741$		0			0
$742$	−3.48353e12	−	6.03365e12i	−0.0154882	−	0.0268263i
$743$	−9.27173e13	+	5.35303e13i	−0.409465	+	0.236405i	−0.690560	−	0.723275i	$-0.742636\pi$
$743$	−9.27173e13	+	5.35303e13i	−0.409465	+	0.236405i	0.281095	+	0.959680i	$0.409302\pi$
$744$		0			0
$745$	−1.94617e14	+	3.37086e14i	−0.848006	+	1.46879i
$746$			2.05304e14i			0.888592i
$747$		0			0
$748$	8.02979e13			0.342923
$749$	1.40065e13	+	8.08666e12i	0.0594183	+	0.0343052i
$750$		0			0
$751$	−9.18885e13	−	1.59156e14i	−0.384646	−	0.666227i	0.607074	−	0.794645i	$-0.292343\pi$
$751$	−9.18885e13	−	1.59156e14i	−0.384646	−	0.666227i	−0.991720	+	0.128419i	$0.959010\pi$
$752$	7.46627e12	−	4.31065e12i	0.0310466	−	0.0179248i
$753$		0			0
$754$	1.03529e14	−	1.79317e14i	0.424819	−	0.735808i
$755$		−	1.48722e14i		−	0.606236i
$756$		0			0
$757$	−1.73049e14			−0.696130			−0.348065	−	0.937470i	$-0.613161\pi$
$757$	−1.73049e14			−0.696130			−0.348065	+	0.937470i	$0.613161\pi$
$758$	2.30873e14	+	1.33295e14i	0.922629	+	0.532680i
$759$		0			0
$760$	4.32956e13	+	7.49902e13i	0.170756	+	0.295758i
$761$	−9.53979e13	+	5.50780e13i	−0.373780	+	0.215802i	−0.675108	−	0.737719i	$-0.735903\pi$
$761$	−9.53979e13	+	5.50780e13i	−0.373780	+	0.215802i	0.301329	+	0.953520i	$0.402570\pi$
$762$		0			0
$763$	1.82191e12	−	3.15564e12i	0.00704537	−	0.0122029i
$764$			8.09218e13i			0.310884i
$765$		0			0
$766$	1.54395e14			0.585449
$767$	1.30249e14	+	7.51995e13i	0.490681	+	0.283295i
$768$		0			0
$769$	−1.15229e14	−	1.99583e14i	−0.428480	−	0.742149i	0.568259	−	0.822850i	$-0.307617\pi$
$769$	−1.15229e14	−	1.99583e14i	−0.428480	−	0.742149i	−0.996738	+	0.0807014i	$0.974284\pi$
$770$	−1.47687e13	+	8.52674e12i	−0.0545619	+	0.0315013i
$771$		0			0
$772$	−9.68625e13	+	1.67771e14i	−0.353239	+	0.611829i
$773$		−	1.50965e14i		−	0.546991i	−0.961873	−	0.273495i	$-0.911820\pi$
$773$		−	1.50965e14i		−	0.546991i	0.961873	−	0.273495i	$-0.0881798\pi$
$774$		0			0
$775$	−4.16146e14			−1.48846
$776$	1.07826e14	+	6.22536e13i	0.383192	+	0.221236i
$777$		0			0
$778$	−8.00801e12	−	1.38703e13i	−0.0280948	−	0.0486617i
$779$	−4.82342e13	+	2.78480e13i	−0.168139	+	0.0970750i
$780$		0			0
$781$	1.43845e14	−	2.49147e14i	0.495039	−	0.857433i
$782$			8.48200e13i			0.290044i
$783$		0			0
$784$	−7.39313e13			−0.249602
$785$	4.05320e14	+	2.34012e14i	1.35972	+	0.785035i
$786$		0			0
$787$	1.71040e14	+	2.96250e14i	0.566532	+	0.981263i	0.996905	+	0.0786117i	$0.0250487\pi$
$787$	1.71040e14	+	2.96250e14i	0.566532	+	0.981263i	−0.430373	+	0.902651i	$0.641618\pi$
$788$	8.39837e13	−	4.84880e13i	0.276416	−	0.159589i
$789$		0			0
$790$	−1.01739e14	+	1.76217e14i	−0.330636	+	0.572679i
$791$			9.34082e12i			0.0301649i
$792$		0			0
$793$	−1.88647e13			−0.0601568
$794$	2.47993e13	+	1.43179e13i	0.0785844	+	0.0453707i
$795$		0			0
$796$	1.28753e13	+	2.23007e13i	0.0402895	+	0.0697835i
$797$	4.52919e14	−	2.61493e14i	1.40841	−	0.813146i	0.413176	−	0.910651i	$-0.364420\pi$
$797$	4.52919e14	−	2.61493e14i	1.40841	−	0.813146i	0.995235	+	0.0975050i	$0.0310862\pi$
$798$		0			0
$799$	1.10556e13	−	1.91488e13i	0.0339506	−	0.0588042i
$800$			7.97893e13i			0.243498i
$801$		0			0
$802$	3.39997e14			1.02472
$803$	−2.18432e14	−	1.26112e14i	−0.654242	−	0.377727i
$804$		0			0
$805$	−9.00693e12	−	1.56005e13i	−0.0266439	−	0.0461486i
$806$	−1.86587e14	+	1.07726e14i	−0.548539	+	0.316699i
$807$		0			0
$808$	−6.26496e13	+	1.08512e14i	−0.181912	+	0.315081i
$809$			3.45374e14i			0.996661i	0.866987	+	0.498331i	$0.166053\pi$
$809$			3.45374e14i			0.996661i	−0.866987	+	0.498331i	$0.833947\pi$
$810$		0			0
$811$	3.60870e14			1.02860			0.514301	−	0.857610i	$-0.328052\pi$
$811$	3.60870e14			1.02860			0.514301	+	0.857610i	$0.328052\pi$
$812$	−8.83960e12	−	5.10355e12i	−0.0250411	−	0.0144575i
$813$		0			0
$814$	2.26092e14	+	3.91602e14i	0.632648	+	1.09578i
$815$	5.81866e14	−	3.35941e14i	1.61821	−	0.934275i
$816$		0			0
$817$	−2.84064e13	+	4.92013e13i	−0.0780379	+	0.135166i
$818$			3.85484e13i			0.105254i
$819$		0			0
$820$	−8.85796e13			−0.238927
$821$	5.78784e14	+	3.34161e14i	1.55168	+	0.895860i	0.998006	+	0.0631235i	$0.0201062\pi$
$821$	5.78784e14	+	3.34161e14i	1.55168	+	0.895860i	0.553669	+	0.832737i	$0.313227\pi$
$822$		0			0
$823$	−2.17665e13	−	3.77008e13i	−0.0576488	−	0.0998506i	0.835761	−	0.549094i	$-0.185027\pi$
$823$	−2.17665e13	−	3.77008e13i	−0.0576488	−	0.0998506i	−0.893410	+	0.449243i	$0.851694\pi$
$824$	−2.84384e13	+	1.64189e13i	−0.0748634	+	0.0432224i
$825$		0			0
$826$	3.70704e12	−	6.42078e12i	0.00964110	−	0.0166989i
$827$		−	2.21008e13i		−	0.0571321i	−0.999592	−	0.0285661i	$-0.990906\pi$
$827$		−	2.21008e13i		−	0.0571321i	0.999592	−	0.0285661i	$-0.00909409\pi$
$828$		0			0
$829$	7.62973e14			1.94866			0.974331	−	0.225119i	$-0.0722770\pi$
$829$	7.62973e14			1.94866			0.974331	+	0.225119i	$0.0722770\pi$
$830$	−1.03450e14	−	5.97270e13i	−0.262628	−	0.151628i
$831$		0			0
$832$	2.06548e13	+	3.57752e13i	0.0518089	+	0.0897357i
$833$	−1.64209e14	+	9.48063e13i	−0.409423	+	0.236381i
$834$		0			0
$835$	3.03174e14	−	5.25113e14i	0.746896	−	1.29366i
$836$			1.85264e14i			0.453690i
$837$		0			0
$838$	5.03342e14			1.21799
$839$	7.40702e13	+	4.27644e13i	0.178170	+	0.102866i	0.586432	−	0.809998i	$-0.300532\pi$
$839$	7.40702e13	+	4.27644e13i	0.178170	+	0.102866i	−0.408263	+	0.912864i	$0.633865\pi$
$840$		0			0
$841$	2.31622e14	+	4.01181e14i	0.550554	+	0.953588i
$842$	−3.58503e12	+	2.06982e12i	−0.00847095	+	0.00489071i
$843$		0			0
$844$	1.21592e14	−	2.10604e14i	0.283918	−	0.491761i
$845$			2.07816e14i			0.482387i
$846$		0			0
$847$	−1.90945e13			−0.0438017
$848$	−1.04248e14	−	6.01875e13i	−0.237732	−	0.137255i
$849$		0			0
$850$	1.02318e14	+	1.77221e14i	0.230600	+	0.399411i
$851$	−4.13656e14	+	2.38824e14i	−0.926811	+	0.535095i
$852$		0			0
$853$	−9.10893e13	+	1.57771e14i	−0.201708	+	0.349368i	−0.949079	−	0.315039i	$-0.897982\pi$
$853$	−9.10893e13	+	1.57771e14i	−0.201708	+	0.349368i	0.747371	+	0.664407i	$0.231316\pi$
$854$			9.29956e11i			0.00204726i
$855$		0			0
$856$	2.79438e14			0.608019
$857$	−7.38198e14	−	4.26199e14i	−1.59687	−	0.921952i	−0.992086	−	0.125560i	$-0.959927\pi$
$857$	−7.38198e14	−	4.26199e14i	−1.59687	−	0.921952i	−0.604781	−	0.796392i	$-0.706739\pi$
$858$		0			0
$859$	−1.30031e14	−	2.25220e14i	−0.278023	−	0.481550i	0.692870	−	0.721062i	$-0.256346\pi$
$859$	−1.30031e14	−	2.25220e14i	−0.278023	−	0.481550i	−0.970893	+	0.239512i	$0.923013\pi$
$860$	−7.82502e13	+	4.51778e13i	−0.166339	+	0.0960357i
$861$		0			0
$862$	−7.51786e13	+	1.30213e14i	−0.157964	+	0.273601i
$863$		−	2.71494e14i		−	0.567161i	−0.958948	−	0.283580i	$-0.908478\pi$
$863$		−	2.71494e14i		−	0.567161i	0.958948	−	0.283580i	$-0.0915223\pi$
$864$		0			0
$865$	−6.08358e14			−1.25626
$866$	1.42724e14	+	8.24020e13i	0.293028	+	0.169180i
$867$		0			0
$868$	5.31048e12	+	9.19801e12i	0.0107779	+	0.0186679i
$869$	−3.77019e14	+	2.17672e14i	−0.760790	+	0.439242i
$870$		0			0
$871$	1.03226e14	−	1.78793e14i	0.205920	−	0.356664i
$872$		−	6.29569e13i		−	0.124871i
$873$		0			0
$874$	−1.95697e14			−0.383732
$875$	−1.03131e13	−	5.95429e12i	−0.0201071	−	0.0116089i
$876$		0			0
$877$	−9.50609e13	−	1.64650e14i	−0.183233	−	0.317369i	0.759747	−	0.650219i	$-0.225323\pi$
$877$	−9.50609e13	−	1.64650e14i	−0.183233	−	0.317369i	−0.942980	+	0.332850i	$0.891990\pi$
$878$	2.99034e14	−	1.72648e14i	0.573124	−	0.330893i
$879$		0			0
$880$	−1.47323e14	+	2.55170e14i	−0.279162	+	0.483523i
$881$			6.12829e14i			1.15468i	0.816506	+	0.577338i	$0.195908\pi$
$881$			6.12829e14i			1.15468i	−0.816506	+	0.577338i	$0.804092\pi$
$882$		0			0
$883$	−4.57367e14			−0.852042			−0.426021	−	0.904713i	$-0.640085\pi$
$883$	−4.57367e14			−0.852042			−0.426021	+	0.904713i	$0.640085\pi$
$884$	9.17530e13	+	5.29736e13i	0.169965	+	0.0981292i
$885$		0			0
$886$	2.07385e14	+	3.59201e14i	0.379847	+	0.657913i
$887$	5.17143e14	−	2.98573e14i	0.941874	−	0.543791i	0.0513267	−	0.998682i	$-0.483655\pi$
$887$	5.17143e14	−	2.98573e14i	0.941874	−	0.543791i	0.890547	+	0.454891i	$0.150322\pi$
$888$		0			0
$889$	−1.36926e13	+	2.37163e13i	−0.0246591	+	0.0427108i
$890$		−	5.66812e14i		−	1.01505i
$891$		0			0
$892$	1.20617e14			0.213592
$893$	4.41803e13	+	2.55075e13i	0.0777985	+	0.0449170i
$894$		0			0
$895$	−7.14432e14	−	1.23743e15i	−1.24407	−	2.15480i
$896$	1.76357e12	−	1.01820e12i	0.00305389	−	0.00176316i
$897$		0			0
$898$	−9.43423e13	+	1.63406e14i	−0.161557	+	0.279824i
$899$		−	9.19792e14i		−	1.56636i
$900$		0			0
$901$	−3.08727e14			−0.519938
$902$	−1.64127e14	−	9.47590e13i	−0.274883	−	0.158704i
$903$		0			0
$904$	8.06941e13	+	1.39766e14i	0.133659	+	0.231505i
$905$	−1.03675e15	+	5.98569e14i	−1.70778	+	0.985988i
$906$		0			0
$907$	3.98099e14	−	6.89528e14i	0.648567	−	1.12335i	−0.334898	−	0.942254i	$-0.608702\pi$
$907$	3.98099e14	−	6.89528e14i	0.648567	−	1.12335i	0.983465	−	0.181097i	$-0.0579647\pi$
$908$		−	2.18637e14i		−	0.354238i
$909$		0			0
$910$	−2.25008e13			−0.0360571
$911$	5.15739e14	+	2.97762e14i	0.821936	+	0.474545i	0.851083	−	0.525030i	$-0.175946\pi$
$911$	5.15739e14	+	2.97762e14i	0.821936	+	0.474545i	−0.0291479	+	0.999575i	$0.509279\pi$
$912$		0			0
$913$	−1.27787e14	−	2.21334e14i	−0.201434	−	0.348894i
$914$	−8.07916e12	+	4.66451e12i	−0.0126659	+	0.00731265i
$915$		0			0
$916$	2.65398e14	−	4.59683e14i	0.411548	−	0.712822i
$917$			2.78603e13i			0.0429675i
$918$		0			0
$919$	5.55318e14			0.847157			0.423579	−	0.905859i	$-0.360774\pi$
$919$	5.55318e14			0.847157			0.423579	+	0.905859i	$0.360774\pi$
$920$	−2.69541e14	−	1.55619e14i	−0.408964	−	0.236116i
$921$		0			0
$922$	−1.88087e12	−	3.25776e12i	−0.00282296	−	0.00488950i
$923$	3.28731e14	−	1.89793e14i	0.490718	−	0.283316i
$924$		0			0
$925$	−5.76187e14	+	9.97986e14i	−0.850854	+	1.47372i
$926$		−	2.88100e14i		−	0.423144i
$927$		0			0
$928$	−1.76356e14			−0.256241
$929$	1.29291e14	+	7.46462e13i	0.186849	+	0.107877i	0.590506	−	0.807033i	$-0.298928\pi$
$929$	1.29291e14	+	7.46462e13i	0.186849	+	0.107877i	−0.403658	+	0.914910i	$0.632261\pi$
$930$		0			0
$931$	−2.18738e14	−	3.78865e14i	−0.312734	−	0.541671i
$932$	4.60102e14	−	2.65640e14i	0.654296	−	0.377758i
$933$		0			0
$934$	2.56469e14	−	4.44217e14i	0.360828	−	0.624972i
$935$			7.55681e14i			1.05750i
$936$		0			0
$937$	−3.07315e14			−0.425487			−0.212743	−	0.977108i	$-0.568240\pi$
$937$	−3.07315e14			−0.425487			−0.212743	+	0.977108i	$0.568240\pi$
$938$	−8.81376e12	−	5.08863e12i	−0.0121380	−	0.00700788i
$939$		0			0
$940$	4.05674e13	+	7.02648e13i	0.0552762	+	0.0957412i
$941$	2.27895e14	−	1.31575e14i	0.308877	−	0.178330i	−0.337547	−	0.941309i	$-0.609597\pi$
$941$	2.27895e14	−	1.31575e14i	0.308877	−	0.178330i	0.646424	+	0.762978i	$0.276264\pi$
$942$		0			0
$943$	1.00096e14	−	1.73371e14i	0.134232	−	0.232497i
$944$		−	1.28098e14i		−	0.170877i
$945$		0			0
$946$	−1.93318e14			−0.255162
$947$	−1.04028e15	−	6.00604e14i	−1.36584	−	0.788566i	−0.375443	−	0.926845i	$-0.622509\pi$
$947$	−1.04028e15	−	6.00604e14i	−1.36584	−	0.788566i	−0.990393	+	0.138279i	$0.955843\pi$
$948$		0			0
$949$	−1.66395e14	−	2.88205e14i	−0.216177	−	0.374430i
$950$	−4.08884e14	+	2.36069e14i	−0.528424	+	0.305086i
$951$		0			0
$952$	2.61139e12	−	4.52306e12i	0.00333954	−	0.00578425i
$953$			3.27942e13i			0.0417189i	0.999782	+	0.0208594i	$0.00664025\pi$
$953$			3.27942e13i			0.0417189i	−0.999782	+	0.0208594i	$0.993360\pi$
$954$		0			0
$955$	−7.61552e14			−0.958700
$956$	−5.48436e14	−	3.16640e14i	−0.686810	−	0.396530i
$957$		0			0
$958$	2.71138e14	+	4.69624e14i	0.336018	+	0.582000i
$959$	−5.37452e13	+	3.10298e13i	−0.0662593	+	0.0382548i
$960$		0			0
$961$	−6.87290e13	+	1.19042e14i	−0.0838538	+	0.145239i
$962$			5.96623e14i			0.724143i
$963$		0			0
$964$	5.32029e14			0.639072
$965$	−1.57888e15	−	9.11569e14i	−1.88675	−	1.08931i
$966$		0			0
$967$	4.93527e14	+	8.54813e14i	0.583684	+	1.01097i	0.995038	+	0.0994953i	$0.0317228\pi$
$967$	4.93527e14	+	8.54813e14i	0.583684	+	1.01097i	−0.411354	+	0.911476i	$0.634944\pi$
$968$	−2.85710e14	+	1.64955e14i	−0.336162	+	0.194083i
$969$		0			0
$970$	−5.85866e14	+	1.01475e15i	−0.682244	+	1.18168i
$971$		−	5.42431e14i		−	0.628418i	−0.949354	−	0.314209i	$-0.898261\pi$
$971$		−	5.42431e14i		−	0.628418i	0.949354	−	0.314209i	$-0.101739\pi$
$972$		0			0
$973$	5.33457e13			0.0611695
$974$	−2.23048e14	−	1.28777e14i	−0.254451	−	0.146907i
$975$		0			0
$976$	8.03377e12	+	1.39149e13i	0.00907131	+	0.0157120i
$977$	−8.26067e14	+	4.76930e14i	−0.927988	+	0.535774i	−0.886175	−	0.463352i	$-0.846647\pi$
$977$	−8.26067e14	+	4.76930e14i	−0.927988	+	0.535774i	−0.0418131	+	0.999125i	$0.513313\pi$
$978$		0			0
$979$	6.06353e14	−	1.05023e15i	0.674237	−	1.16781i
$980$		−	6.95765e14i		−	0.769719i
$981$		0			0
$982$	8.13482e14			0.890821
$983$	5.46361e14	+	3.15442e14i	0.595268	+	0.343678i	0.767178	−	0.641435i	$-0.221660\pi$
$983$	5.46361e14	+	3.15442e14i	0.595268	+	0.343678i	−0.171910	+	0.985113i	$0.554994\pi$
$984$		0			0
$985$	4.56319e14	+	7.90367e14i	0.492138	+	0.852409i
$986$	−3.91704e14	+	2.26151e14i	−0.420314	+	0.242668i
$987$		0			0
$988$	−1.22221e14	+	2.11693e14i	−0.129826	+	0.224865i
$989$		−	2.04205e14i		−	0.215816i
$990$		0			0
$991$	4.94498e14			0.517364			0.258682	−	0.965963i	$-0.416712\pi$
$991$	4.94498e14			0.517364			0.258682	+	0.965963i	$0.416712\pi$
$992$	1.58921e14	+	9.17530e13i	0.165433	+	0.0955129i
$993$		0			0
$994$	−9.35604e12	−	1.62051e13i	−0.00964184	−	0.0167002i
$995$	−2.09871e14	+	1.21169e14i	−0.215197	+	0.124244i
$996$		0			0
$997$	−8.14965e14	+	1.41156e15i	−0.827301	+	1.43293i	0.0728476	+	0.997343i	$0.476791\pi$
$997$	−8.14965e14	+	1.41156e15i	−0.827301	+	1.43293i	−0.900148	+	0.435584i	$0.856542\pi$
$998$			3.02369e14i			0.305411i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	162.11.d.d.107.3		8
3.2	odd	2	inner	162.11.d.d.107.2		8
9.2	odd	6		6.11.b.a.5.4	yes	4
9.4	even	3	inner	162.11.d.d.53.2		8
9.5	odd	6	inner	162.11.d.d.53.3		8
9.7	even	3		6.11.b.a.5.2	✓	4
36.7	odd	6		48.11.e.d.17.2		4
36.11	even	6		48.11.e.d.17.1		4
45.2	even	12		150.11.b.a.149.3		8
45.7	odd	12		150.11.b.a.149.5		8
45.29	odd	6		150.11.d.a.101.1		4
45.34	even	6		150.11.d.a.101.3		4
45.38	even	12		150.11.b.a.149.6		8
45.43	odd	12		150.11.b.a.149.4		8
72.11	even	6		192.11.e.h.65.4		4
72.29	odd	6		192.11.e.g.65.1		4
72.43	odd	6		192.11.e.h.65.3		4
72.61	even	6		192.11.e.g.65.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6.11.b.a.5.2	✓	4	9.7	even	3
6.11.b.a.5.4	yes	4	9.2	odd	6
48.11.e.d.17.1		4	36.11	even	6
48.11.e.d.17.2		4	36.7	odd	6
150.11.b.a.149.3		8	45.2	even	12
150.11.b.a.149.4		8	45.43	odd	12
150.11.b.a.149.5		8	45.7	odd	12
150.11.b.a.149.6		8	45.38	even	12
150.11.d.a.101.1		4	45.29	odd	6
150.11.d.a.101.3		4	45.34	even	6
162.11.d.d.53.2		8	9.4	even	3	inner
162.11.d.d.53.3		8	9.5	odd	6	inner
162.11.d.d.107.2		8	3.2	odd	2	inner
162.11.d.d.107.3		8	1.1	even	1	trivial
192.11.e.g.65.1		4	72.29	odd	6
192.11.e.g.65.2		4	72.61	even	6
192.11.e.h.65.3		4	72.43	odd	6
192.11.e.h.65.4		4	72.11	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 162 = 2 \cdot 3^{4} \)
Weight:	\( k \)	\(=\)	\( 11 \)
Character orbit:	\([\chi]\)	\(=\)	162.d (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(19.5959 + 11.3137i) q^{2} +(256.000 + 443.405i) q^{4} +(-4172.87 + 2409.21i) q^{5} +(-335.265 + 580.696i) q^{7} +11585.2i q^{8} +O(q^{10})\)	\(q+(19.5959 + 11.3137i) q^{2} +(256.000 + 443.405i) q^{4} +(-4172.87 + 2409.21i) q^{5} +(-335.265 + 580.696i) q^{7} +11585.2i q^{8} -109028. q^{10} +(-202016. - 116634. i) q^{11} +(-153890. - 266546. i) q^{13} +(-13139.6 + 7586.18i) q^{14} +(-131072. + 227023. i) q^{16} +672324. i q^{17} -1.55119e6 q^{19} +(-2.13651e6 - 1.23351e6i) q^{20} +(-2.63913e6 - 4.57111e6i) q^{22} +(4.82854e6 - 2.78776e6i) q^{23} +(6.72574e6 - 1.16493e7i) q^{25} -6.96428e6i q^{26} -343311. q^{28} +(2.57481e7 + 1.48657e7i) q^{29} +(-1.54684e7 - 2.67921e7i) q^{31} +(-5.13695e6 + 2.96582e6i) q^{32} +(-7.60648e6 + 1.31748e7i) q^{34} -3.23089e6i q^{35} -8.56690e7 q^{37} +(-3.03970e7 - 1.75497e7i) q^{38} +(-2.79112e7 - 4.83437e7i) q^{40} +(3.10950e7 - 1.79527e7i) q^{41} +(1.83126e7 - 3.17184e7i) q^{43} -1.19433e8i q^{44} +1.26159e8 q^{46} +(-2.84816e7 - 1.64438e7i) q^{47} +(1.41013e8 + 2.44241e8i) q^{49} +(2.63594e8 - 1.52186e8i) q^{50} +(7.87918e7 - 1.36471e8i) q^{52} +4.59194e8i q^{53} +1.12398e9 q^{55} +(-6.72750e6 - 3.88412e6i) q^{56} +(3.36372e8 + 5.82613e8i) q^{58} +(-4.23189e8 + 2.44328e8i) q^{59} +(3.06464e7 - 5.30811e7i) q^{61} -7.00020e8i q^{62} -1.34218e8 q^{64} +(1.28433e9 + 7.41507e8i) q^{65} +(3.35388e8 + 5.80909e8i) q^{67} +(-2.98112e8 + 1.72115e8i) q^{68} +(3.65533e7 - 6.33122e7i) q^{70} +1.23330e9i q^{71} +1.08126e9 q^{73} +(-1.67876e9 - 9.69234e8i) q^{74} +(-3.97104e8 - 6.87805e8i) q^{76} +(1.35458e8 - 7.82067e7i) q^{77} +(9.33141e8 - 1.61625e9i) q^{79} -1.26312e9i q^{80} +8.12446e8 q^{82} +(9.48838e8 + 5.47812e8i) q^{83} +(-1.61977e9 - 2.80552e9i) q^{85} +(7.17706e8 - 4.14368e8i) q^{86} +(1.35123e9 - 2.34041e9i) q^{88} +5.19876e9i q^{89} +2.06376e8 q^{91} +(2.47221e9 + 1.42733e9i) q^{92} +(-3.72082e8 - 6.44464e8i) q^{94} +(6.47291e9 - 3.73714e9i) q^{95} +(5.37353e9 - 9.30722e9i) q^{97} +6.38151e9i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 2048 q^{4} + 45112 q^{7}+O(q^{10}) \) 8 * q + 2048 * q^4 + 45112 * q^7	\( 8 q + 2048 q^{4} + 45112 q^{7} - 107520 q^{10} - 275240 q^{13} - 1048576 q^{16} - 3137456 q^{19} - 7730688 q^{22} + 33732380 q^{25} + 46194688 q^{28} + 21785848 q^{31} - 151087104 q^{34} - 142028336 q^{37} - 27525120 q^{40} + 470688664 q^{43} + 377628672 q^{46} + 50058420 q^{49} + 140922880 q^{52} + 5402718720 q^{55} + 1564177920 q^{58} + 1184038744 q^{61} - 1073741824 q^{64} + 297365848 q^{67} + 3962250240 q^{70} + 13068538000 q^{73} - 803188736 q^{76} - 199282568 q^{79} + 16757336064 q^{82} + 12880512000 q^{85} + 3958112256 q^{88} + 16634464160 q^{91} - 8505477120 q^{94} + 39176355064 q^{97}+O(q^{100}) \) 8 * q + 2048 * q^4 + 45112 * q^7 - 107520 * q^10 - 275240 * q^13 - 1048576 * q^16 - 3137456 * q^19 - 7730688 * q^22 + 33732380 * q^25 + 46194688 * q^28 + 21785848 * q^31 - 151087104 * q^34 - 142028336 * q^37 - 27525120 * q^40 + 470688664 * q^43 + 377628672 * q^46 + 50058420 * q^49 + 140922880 * q^52 + 5402718720 * q^55 + 1564177920 * q^58 + 1184038744 * q^61 - 1073741824 * q^64 + 297365848 * q^67 + 3962250240 * q^70 + 13068538000 * q^73 - 803188736 * q^76 - 199282568 * q^79 + 16757336064 * q^82 + 12880512000 * q^85 + 3958112256 * q^88 + 16634464160 * q^91 - 8505477120 * q^94 + 39176355064 * q^97

Introduction

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