LMFDB - Embedded newform 162.11.d.d.53.4

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			53.4
Root			$-2.88503 - 0.707107i$ of defining polynomial
Character	$\chi$	$=$	162.53
Dual form			162.11.d.d.107.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(19.5959 - 11.3137i) q^{2} +(256.000 - 443.405i) q^{4} +(3144.08 + 1815.24i) q^{5} +(11613.3 + 20114.8i) q^{7} -11585.2i q^{8} +O(q^{10})$	\(q+(19.5959 - 11.3137i) q^{2} +(256.000 - 443.405i) q^{4} +(3144.08 + 1815.24i) q^{5} +(11613.3 + 20114.8i) q^{7} -11585.2i q^{8} +82148.2 q^{10} +(54076.9 - 31221.3i) q^{11} +(85080.3 - 147363. i) q^{13} +(455145. + 262778. i) q^{14} +(-131072. - 227023. i) q^{16} -2.66626e6i q^{17} +766825. q^{19} +(1.60977e6 - 929401. i) q^{20} +(706458. - 1.22362e6i) q^{22} +(-1.21526e6 - 701633. i) q^{23} +(1.70736e6 + 2.95723e6i) q^{25} -3.85029e6i q^{26} +1.18920e7 q^{28} +(4.18503e6 - 2.41623e6i) q^{29} +(2.09149e7 - 3.62256e7i) q^{31} +(-5.13695e6 - 2.96582e6i) q^{32} +(-3.01653e7 - 5.22478e7i) q^{34} +8.43233e7i q^{35} +5.01619e7 q^{37} +(1.50266e7 - 8.67564e6i) q^{38} +(2.10299e7 - 3.64249e7i) q^{40} +(1.29245e8 + 7.46194e7i) q^{41} +(9.93595e7 + 1.72096e8i) q^{43} -3.19706e7i q^{44} -3.17523e7 q^{46} +(-1.34285e8 + 7.75293e7i) q^{47} +(-1.28498e8 + 2.22565e8i) q^{49} +(6.69144e7 + 3.86331e7i) q^{50} +(-4.35611e7 - 7.54501e7i) q^{52} +4.21541e7i q^{53} +2.26696e8 q^{55} +(2.33034e8 - 1.34542e8i) q^{56} +(5.46730e7 - 9.46964e7i) q^{58} +(-2.52902e8 - 1.46013e8i) q^{59} +(2.65363e8 + 4.59623e8i) q^{61} -9.46499e8i q^{62} -1.34218e8 q^{64} +(5.34999e8 - 3.08882e8i) q^{65} +(-2.61047e8 + 4.52146e8i) q^{67} +(-1.18223e9 - 6.82563e8i) q^{68} +(9.54009e8 + 1.65239e9i) q^{70} +5.71364e8i q^{71} +2.18588e9 q^{73} +(9.82968e8 - 5.67517e8i) q^{74} +(1.96307e8 - 3.40014e8i) q^{76} +(1.25602e9 + 7.25163e8i) q^{77} +(-9.82961e8 - 1.70254e9i) q^{79} -9.51707e8i q^{80} +3.37689e9 q^{82} +(-1.89277e9 + 1.09279e9i) q^{83} +(4.83989e9 - 8.38294e9i) q^{85} +(3.89408e9 + 2.24825e9i) q^{86} +(-3.61707e8 - 6.26494e8i) q^{88} -2.38742e8i q^{89} +3.95224e9 q^{91} +(-6.22215e8 + 3.59236e8i) q^{92} +(-1.75429e9 + 3.03852e9i) q^{94} +(2.41096e9 + 1.39197e9i) q^{95} +(4.42056e9 + 7.65664e9i) q^{97} +5.81517e9i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/162\mathbb{Z}\right)^\times$.

$n$	$83$
$\chi(n)$	$e\left(\frac{5}{6}\right)$

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
$5$	3144.08	+	1815.24i	1.00611	+	0.580876i	0.910049	−	0.414500i	$-0.136044\pi$
$5$	3144.08	+	1815.24i	1.00611	+	0.580876i	0.0960570	+	0.995376i	$0.469377\pi$
$6$		0			0
$7$	11613.3	+	20114.8i	0.690978	+	1.19681i	0.971518	+	0.236966i	$0.0761531\pi$
$7$	11613.3	+	20114.8i	0.690978	+	1.19681i	−0.280540	+	0.959842i	$0.590514\pi$
$8$		−	11585.2i		−	0.353553i
$9$		0			0
$10$	82148.2			0.821482
$11$	54076.9	−	31221.3i	0.335775	−	0.193860i	−0.322627	−	0.946526i	$-0.604566\pi$
$11$	54076.9	−	31221.3i	0.335775	−	0.193860i	0.658402	+	0.752666i	$0.271233\pi$
$12$		0			0
$13$	85080.3	−	147363.i	0.229146	−	0.396892i	−0.728409	−	0.685142i	$-0.759740\pi$
$13$	85080.3	−	147363.i	0.229146	−	0.396892i	0.957555	+	0.288250i	$0.0930734\pi$
$14$	455145.	+	262778.i	0.846272	+	0.488595i
$15$		0			0
$16$	−131072.	−	227023.i	−0.125000	−	0.216506i
$17$		−	2.66626e6i		−	1.87784i	−0.344139	−	0.938919i	$-0.611829\pi$
$17$		−	2.66626e6i		−	1.87784i	0.344139	−	0.938919i	$-0.388171\pi$
$18$		0			0
$19$	766825.			0.309691			0.154845	−	0.987939i	$-0.450512\pi$
$19$	766825.			0.309691			0.154845	+	0.987939i	$0.450512\pi$
$20$	1.60977e6	−	929401.i	0.503053	−	0.290438i
$21$		0			0
$22$	706458.	−	1.22362e6i	0.137080	−	0.237429i
$23$	−1.21526e6	−	701633.i	−0.188813	−	0.109011i	0.402614	−	0.915370i	$-0.368102\pi$
$23$	−1.21526e6	−	701633.i	−0.188813	−	0.109011i	−0.591427	+	0.806359i	$0.701435\pi$
$24$		0			0
$25$	1.70736e6	+	2.95723e6i	0.174833	+	0.302820i
$26$		−	3.85029e6i		−	0.324061i
$27$		0			0
$28$	1.18920e7			0.690978
$29$	4.18503e6	−	2.41623e6i	0.204037	−	0.117801i	−0.394500	−	0.918896i	$-0.629082\pi$
$29$	4.18503e6	−	2.41623e6i	0.204037	−	0.117801i	0.598537	+	0.801095i	$0.295749\pi$
$30$		0			0
$31$	2.09149e7	−	3.62256e7i	0.730544	−	1.26534i	−0.226106	−	0.974103i	$-0.572600\pi$
$31$	2.09149e7	−	3.62256e7i	0.730544	−	1.26534i	0.956651	−	0.291237i	$-0.0940670\pi$
$32$	−5.13695e6	−	2.96582e6i	−0.153093	−	0.0883883i
$33$		0			0
$34$	−3.01653e7	−	5.22478e7i	−0.663916	−	1.14994i
$35$			8.43233e7i			1.60549i
$36$		0			0
$37$	5.01619e7			0.723378			0.361689	−	0.932299i	$-0.382200\pi$
$37$	5.01619e7			0.723378			0.361689	+	0.932299i	$0.382200\pi$
$38$	1.50266e7	−	8.67564e6i	0.189646	−	0.109492i
$39$		0			0
$40$	2.10299e7	−	3.64249e7i	0.205371	−	0.355712i
$41$	1.29245e8	+	7.46194e7i	1.11556	+	0.644069i	0.940264	−	0.340447i	$-0.110578\pi$
$41$	1.29245e8	+	7.46194e7i	1.11556	+	0.644069i	0.175296	+	0.984516i	$0.443912\pi$
$42$		0			0
$43$	9.93595e7	+	1.72096e8i	0.675876	+	1.17065i	0.976212	+	0.216818i	$0.0695680\pi$
$43$	9.93595e7	+	1.72096e8i	0.675876	+	1.17065i	−0.300336	+	0.953834i	$0.597099\pi$
$44$		−	3.19706e7i		−	0.193860i
$45$		0			0
$46$	−3.17523e7			−0.154165
$47$	−1.34285e8	+	7.75293e7i	−0.585514	+	0.338047i	−0.763322	−	0.646019i	$-0.776433\pi$
$47$	−1.34285e8	+	7.75293e7i	−0.585514	+	0.338047i	0.177808	+	0.984065i	$0.443099\pi$
$48$		0			0
$49$	−1.28498e8	+	2.22565e8i	−0.454901	+	0.787911i
$50$	6.69144e7	+	3.86331e7i	0.214126	+	0.123626i
$51$		0			0
$52$	−4.35611e7	−	7.54501e7i	−0.114573	−	0.198446i
$53$			4.21541e7i			0.100800i	0.998729	+	0.0503999i	$0.0160496\pi$
$53$			4.21541e7i			0.100800i	−0.998729	+	0.0503999i	$0.983950\pi$
$54$		0			0
$55$	2.26696e8			0.450434
$56$	2.33034e8	−	1.34542e8i	0.423136	−	0.244298i
$57$		0			0
$58$	5.46730e7	−	9.46964e7i	0.0832976	−	0.144276i
$59$	−2.52902e8	−	1.46013e8i	−0.353746	−	0.204236i	0.312588	−	0.949889i	$-0.398804\pi$
$59$	−2.52902e8	−	1.46013e8i	−0.353746	−	0.204236i	−0.666334	+	0.745653i	$0.732138\pi$
$60$		0			0
$61$	2.65363e8	+	4.59623e8i	0.314190	+	0.544192i	0.979265	−	0.202584i	$-0.0649339\pi$
$61$	2.65363e8	+	4.59623e8i	0.314190	+	0.544192i	−0.665075	+	0.746776i	$0.731601\pi$
$62$		−	9.46499e8i		−	1.03315i
$63$		0			0
$64$	−1.34218e8			−0.125000
$65$	5.34999e8	−	3.08882e8i	0.461090	−	0.266211i
$66$		0			0
$67$	−2.61047e8	+	4.52146e8i	−0.193350	+	0.334892i	−0.946358	−	0.323119i	$-0.895269\pi$
$67$	−2.61047e8	+	4.52146e8i	−0.193350	+	0.334892i	0.753008	+	0.658011i	$0.228602\pi$
$68$	−1.18223e9	−	6.82563e8i	−0.813128	−	0.469459i
$69$		0			0
$70$	9.54009e8	+	1.65239e9i	0.567626	+	0.983157i
$71$			5.71364e8i			0.316681i	0.987385	+	0.158340i	$0.0506143\pi$
$71$			5.71364e8i			0.316681i	−0.987385	+	0.158340i	$0.949386\pi$
$72$		0			0
$73$	2.18588e9			1.05441			0.527207	−	0.849737i	$-0.323239\pi$
$73$	2.18588e9			1.05441			0.527207	+	0.849737i	$0.323239\pi$
$74$	9.82968e8	−	5.67517e8i	0.442977	−	0.255753i
$75$		0			0
$76$	1.96307e8	−	3.40014e8i	0.0774227	−	0.134100i
$77$	1.25602e9	+	7.25163e8i	0.464026	+	0.267906i
$78$		0			0
$79$	−9.82961e8	−	1.70254e9i	−0.319449	−	0.553301i	0.660924	−	0.750452i	$-0.270164\pi$
$79$	−9.82961e8	−	1.70254e9i	−0.319449	−	0.553301i	−0.980373	+	0.197151i	$0.936831\pi$
$80$		−	9.51707e8i		−	0.290438i
$81$		0			0
$82$	3.37689e9			0.910851
$83$	−1.89277e9	+	1.09279e9i	−0.480514	+	0.277425i	−0.720631	−	0.693319i	$-0.756148\pi$
$83$	−1.89277e9	+	1.09279e9i	−0.480514	+	0.277425i	0.240116	+	0.970744i	$0.422814\pi$
$84$		0			0
$85$	4.83989e9	−	8.38294e9i	1.09079	−	1.88930i
$86$	3.89408e9	+	2.24825e9i	0.827776	+	0.477917i
$87$		0			0
$88$	−3.61707e8	−	6.26494e8i	−0.0685398	−	0.118714i
$89$		−	2.38742e8i		−	0.0427542i	−0.999771	−	0.0213771i	$-0.993195\pi$
$89$		−	2.38742e8i		−	0.0427542i	0.999771	−	0.0213771i	$-0.00680506\pi$
$90$		0			0
$91$	3.95224e9			0.633339
$92$	−6.22215e8	+	3.59236e8i	−0.0944064	+	0.0545056i
$93$		0			0
$94$	−1.75429e9	+	3.03852e9i	−0.239035	+	0.414021i
$95$	2.41096e9	+	1.39197e9i	0.311582	+	0.179892i
$96$		0			0
$97$	4.42056e9	+	7.65664e9i	0.514776	+	0.891619i	0.999853	+	0.0171473i	$0.00545843\pi$
$97$	4.42056e9	+	7.65664e9i	0.514776	+	0.891619i	−0.485076	+	0.874472i	$0.661208\pi$
$98$			5.81517e9i			0.643327i
$99$		0			0
$100$	1.74833e9			0.174833
$101$	1.45430e10	−	8.39641e9i	1.38372	−	0.798890i	0.391120	−	0.920340i	$-0.372088\pi$
$101$	1.45430e10	−	8.39641e9i	1.38372	−	0.798890i	0.992598	+	0.121450i	$0.0387543\pi$
$102$		0			0
$103$	−4.18432e9	+	7.24746e9i	−0.360944	+	0.625173i	−0.988116	−	0.153708i	$-0.950879\pi$
$103$	−4.18432e9	+	7.24746e9i	−0.360944	+	0.625173i	0.627173	+	0.778880i	$0.284212\pi$
$104$	−1.70724e9	−	9.85675e8i	−0.140323	−	0.0810153i
$105$		0			0
$106$	4.76919e8	+	8.26048e8i	0.0356381	+	0.0617271i
$107$		−	1.43555e10i		−	1.02353i	−0.859126	−	0.511764i	$-0.828992\pi$
$107$		−	1.43555e10i		−	1.02353i	0.859126	−	0.511764i	$-0.171008\pi$
$108$		0			0
$109$	−4.72564e9			−0.307134			−0.153567	−	0.988138i	$-0.549076\pi$
$109$	−4.72564e9			−0.307134			−0.153567	+	0.988138i	$0.549076\pi$
$110$	4.44233e9	−	2.56478e9i	0.275833	−	0.159253i
$111$		0			0
$112$	3.04435e9	−	5.27296e9i	0.172744	−	0.299202i
$113$	1.14452e10	+	6.60792e9i	0.621202	+	0.358651i	0.777337	−	0.629084i	$-0.216570\pi$
$113$	1.14452e10	+	6.60792e9i	0.621202	+	0.358651i	−0.156135	+	0.987736i	$0.549903\pi$
$114$		0			0
$115$	−2.54726e9	−	4.41199e9i	−0.126644	−	0.219354i
$116$		−	2.47422e9i		−	0.117801i
$117$		0			0
$118$	−6.60779e9			−0.288833
$119$	5.36312e10	−	3.09640e10i	2.24741	−	1.29754i
$120$		0			0
$121$	−1.10192e10	+	1.90858e10i	−0.424837	+	0.735839i
$122$	1.04001e10	+	6.00449e9i	0.384802	+	0.222166i
$123$		0			0
$124$	−1.07084e10	−	1.85475e10i	−0.365272	−	0.632670i
$125$		−	2.30568e10i		−	0.755526i
$126$		0			0
$127$	−3.17814e10			−0.961953			−0.480976	−	0.876733i	$-0.659718\pi$
$127$	−3.17814e10			−0.961953			−0.480976	+	0.876733i	$0.659718\pi$
$128$	−2.63012e9	+	1.51850e9i	−0.0765466	+	0.0441942i
$129$		0			0
$130$	6.98920e9	−	1.21056e10i	0.188239	−	0.326040i
$131$	4.33960e10	+	2.50547e10i	1.12485	+	0.649430i	0.942634	−	0.333829i	$-0.108341\pi$
$131$	4.33960e10	+	2.50547e10i	1.12485	+	0.649430i	0.182213	+	0.983259i	$0.441674\pi$
$132$		0			0
$133$	8.90535e9	+	1.54245e10i	0.213990	+	0.370641i
$134$			1.18136e10i			0.273438i
$135$		0			0
$136$	−3.08893e10			−0.663916
$137$	−2.37935e10	+	1.37372e10i	−0.493010	+	0.284639i	−0.725822	−	0.687882i	$-0.758540\pi$
$137$	−2.37935e10	+	1.37372e10i	−0.493010	+	0.284639i	0.232812	+	0.972522i	$0.425207\pi$
$138$		0			0
$139$	−3.16244e10	+	5.47751e10i	−0.609464	+	1.05562i	0.381865	+	0.924218i	$0.375282\pi$
$139$	−3.16244e10	+	5.47751e10i	−0.609464	+	1.05562i	−0.991329	+	0.131405i	$0.958051\pi$
$140$	3.73894e10	+	2.15868e10i	0.695197	+	0.401372i
$141$		0			0
$142$	6.46425e9	+	1.11964e10i	0.111963	+	0.193926i
$143$		−	1.06253e10i		−	0.177689i
$144$		0			0
$145$	1.75441e10			0.273710
$146$	4.28342e10	−	2.47304e10i	0.645694	−	0.372792i
$147$		0			0
$148$	1.28414e10	−	2.22420e10i	0.180845	−	0.313232i
$149$	−2.93131e10	−	1.69239e10i	−0.399145	−	0.230446i	0.286970	−	0.957940i	$-0.407352\pi$
$149$	−2.93131e10	−	1.69239e10i	−0.399145	−	0.230446i	−0.686115	+	0.727493i	$0.740685\pi$
$150$		0			0
$151$	−6.11931e10	−	1.05990e11i	−0.779503	−	1.35014i	−0.932229	−	0.361870i	$-0.882139\pi$
$151$	−6.11931e10	−	1.05990e11i	−0.779503	−	1.35014i	0.152726	−	0.988269i	$-0.451195\pi$
$152$		−	8.88385e9i		−	0.109492i
$153$		0			0
$154$	3.28171e10			0.378876
$155$	1.31516e11	−	7.59309e10i	1.47001	−	0.848711i
$156$		0			0
$157$	7.94857e10	−	1.37673e11i	0.833279	−	1.44328i	−0.0621448	−	0.998067i	$-0.519794\pi$
$157$	7.94857e10	−	1.37673e11i	0.833279	−	1.44328i	0.895424	−	0.445215i	$-0.146873\pi$
$158$	−3.85241e10	−	2.22419e10i	−0.391243	−	0.225884i
$159$		0			0
$160$	−1.07673e10	−	1.86496e10i	−0.102685	−	0.177856i
$161$		−	3.25930e10i		−	0.301297i
$162$		0			0
$163$	−9.20831e10			−0.800280			−0.400140	−	0.916454i	$-0.631038\pi$
$163$	−9.20831e10			−0.800280			−0.400140	+	0.916454i	$0.631038\pi$
$164$	6.61732e10	−	3.82051e10i	0.557780	−	0.322034i
$165$		0			0
$166$	−2.47270e10	+	4.28284e10i	−0.196169	+	0.339775i
$167$	1.83958e11	+	1.06208e11i	1.41623	+	0.817663i	0.995966	−	0.0897362i	$-0.0286024\pi$
$167$	1.83958e11	+	1.06208e11i	1.41623	+	0.817663i	0.420269	+	0.907400i	$0.361936\pi$
$168$		0			0
$169$	5.44519e10	+	9.43135e10i	0.394984	+	0.684133i
$170$		−	2.19029e11i		−	1.54261i
$171$		0			0
$172$	1.01744e11			0.675876
$173$	2.63386e11	−	1.52066e11i	1.69966	−	0.981300i	0.753590	−	0.657345i	$-0.228320\pi$
$173$	2.63386e11	−	1.52066e11i	1.69966	−	0.981300i	0.946072	−	0.323956i	$-0.105013\pi$
$174$		0			0
$175$	−3.96560e10	+	6.86861e10i	−0.241612	+	0.418484i
$176$	−1.41759e10	−	8.18449e9i	−0.0839438	−	0.0484650i
$177$		0			0
$178$	−2.70106e9	−	4.67837e9i	−0.0151159	−	0.0261815i
$179$			7.07114e9i			0.0384791i	0.999815	+	0.0192395i	$0.00612451\pi$
$179$			7.07114e9i			0.0384791i	−0.999815	+	0.0192395i	$0.993875\pi$
$180$		0			0
$181$	−1.27309e11			−0.655337			−0.327669	−	0.944793i	$-0.606263\pi$
$181$	−1.27309e11			−0.655337			−0.327669	+	0.944793i	$0.606263\pi$
$182$	7.74478e10	−	4.47145e10i	0.387839	−	0.223919i
$183$		0			0
$184$	−8.12859e9	+	1.40791e10i	−0.0385413	+	0.0667554i
$185$	1.57713e11	+	9.10557e10i	0.727795	+	0.420193i
$186$		0			0
$187$	−8.32442e10	−	1.44183e11i	−0.364037	−	0.630531i
$188$			7.93900e10i			0.338047i
$189$		0			0
$190$	6.29934e10			0.254406
$191$	−1.78799e11	+	1.03230e11i	−0.703394	+	0.406105i	−0.808610	−	0.588345i	$-0.799780\pi$
$191$	−1.78799e11	+	1.03230e11i	−0.703394	+	0.406105i	0.105216	+	0.994449i	$0.466447\pi$
$192$		0			0
$193$	−1.55803e11	+	2.69859e11i	−0.581821	+	1.00774i	0.413442	+	0.910530i	$0.364326\pi$
$193$	−1.55803e11	+	2.69859e11i	−0.581821	+	1.00774i	−0.995264	+	0.0972136i	$0.969007\pi$
$194$	1.73250e11	+	1.00026e11i	0.630470	+	0.364002i
$195$		0			0
$196$	6.57911e10	+	1.13954e11i	0.227450	+	0.393956i
$197$		−	1.51694e11i		−	0.511255i	−0.966775	−	0.255628i	$-0.917718\pi$
$197$		−	1.51694e11i		−	0.511255i	0.966775	−	0.255628i	$-0.0822821\pi$
$198$		0			0
$199$	−1.11692e11			−0.357895			−0.178947	−	0.983859i	$-0.557269\pi$
$199$	−1.11692e11			−0.357895			−0.178947	+	0.983859i	$0.557269\pi$
$200$	3.42602e10	−	1.97801e10i	0.107063	−	0.0618129i
$201$		0			0
$202$	1.89989e11	−	3.29071e11i	0.564901	−	0.978436i
$203$	9.72037e10	+	5.61206e10i	0.281970	+	0.162795i
$204$		0			0
$205$	2.70904e11	+	4.69219e11i	0.748248	+	1.29600i
$206$			1.89361e11i			0.510451i
$207$		0			0
$208$	−4.46066e10			−0.114573
$209$	4.14676e10	−	2.39413e10i	0.103987	−	0.0600367i
$210$		0			0
$211$	−7.65329e10	+	1.32559e11i	−0.182994	+	0.316954i	−0.942899	−	0.333080i	$-0.891912\pi$
$211$	−7.65329e10	+	1.32559e11i	−0.182994	+	0.316954i	0.759905	+	0.650034i	$0.225245\pi$
$212$	1.86913e10	+	1.07914e10i	0.0436476	+	0.0252000i
$213$		0			0
$214$	−1.62414e11	−	2.81310e11i	−0.361872	−	0.626781i
$215$			7.21444e11i			1.57040i
$216$		0			0
$217$	9.71560e11			2.01916
$218$	−9.26033e10	+	5.34645e10i	−0.188081	+	0.108588i
$219$		0			0
$220$	5.80343e10	−	1.00518e11i	0.112609	−	0.195044i
$221$	−3.92909e11	−	2.26846e11i	−0.745300	−	0.430299i
$222$		0			0
$223$	3.02880e11	+	5.24603e11i	0.549219	+	0.951276i	0.998328	+	0.0577987i	$0.0184082\pi$
$223$	3.02880e11	+	5.24603e11i	0.549219	+	0.951276i	−0.449109	+	0.893477i	$0.648259\pi$
$224$		−	1.37771e11i		−	0.244298i
$225$		0			0
$226$	2.99040e11			0.507210
$227$	5.80746e11	−	3.35294e11i	0.963512	−	0.556284i	0.0662598	−	0.997802i	$-0.478893\pi$
$227$	5.80746e11	−	3.35294e11i	0.963512	−	0.556284i	0.897252	+	0.441519i	$0.145560\pi$
$228$		0			0
$229$	−1.76678e11	+	3.06015e11i	−0.280547	+	0.485921i	−0.971520	−	0.236960i	$-0.923849\pi$
$229$	−1.76678e11	+	3.06015e11i	−0.280547	+	0.485921i	0.690973	+	0.722881i	$0.257182\pi$
$230$	−9.98318e10	−	5.76379e10i	−0.155106	−	0.0895508i
$231$		0			0
$232$	−2.79926e10	−	4.84845e10i	−0.0416488	−	0.0721379i
$233$		−	1.12390e12i		−	1.63662i	−0.574779	−	0.818309i	$-0.694912\pi$
$233$		−	1.12390e12i		−	1.63662i	0.574779	−	0.818309i	$-0.305088\pi$
$234$		0			0
$235$	−5.62936e11			−0.785452
$236$	−1.29486e11	+	7.47586e10i	−0.176873	+	0.102118i
$237$		0			0
$238$	7.00635e11	−	1.21354e12i	0.917502	−	1.58916i
$239$	2.29153e11	+	1.32302e11i	0.293857	+	0.169658i	0.639680	−	0.768641i	$-0.279067\pi$
$239$	2.29153e11	+	1.32302e11i	0.293857	+	0.169658i	−0.345823	+	0.938300i	$0.612400\pi$
$240$		0			0
$241$	−4.43384e11	−	7.67964e11i	−0.545375	−	0.944617i	−0.998583	−	0.0532121i	$-0.983054\pi$
$241$	−4.43384e11	−	7.67964e11i	−0.545375	−	0.944617i	0.453209	−	0.891404i	$-0.350279\pi$
$242$			4.98671e11i			0.600810i
$243$		0			0
$244$	2.71732e11			0.314190
$245$	−8.08018e11	+	4.66509e11i	−0.915357	+	0.528482i
$246$		0			0
$247$	6.52417e10	−	1.13002e11i	0.0709644	−	0.122914i
$248$	−4.19682e11	−	2.42304e11i	−0.447365	−	0.258286i
$249$		0			0
$250$	−2.60858e11	−	4.51820e11i	−0.267119	−	0.462663i
$251$		−	8.59494e11i		−	0.862729i	−0.902178	−	0.431364i	$-0.858032\pi$
$251$		−	8.59494e11i		−	0.862729i	0.902178	−	0.431364i	$-0.141968\pi$
$252$		0			0
$253$	−8.76237e10			−0.0845316
$254$	−6.22785e11	+	3.59565e11i	−0.589073	+	0.340102i
$255$		0			0
$256$	−3.43597e10	+	5.95128e10i	−0.0312500	+	0.0541266i
$257$	−1.88707e12	−	1.08950e12i	−1.68315	−	0.971764i	−0.959549	−	0.281540i	$-0.909155\pi$
$257$	−1.88707e12	−	1.08950e12i	−1.68315	−	0.971764i	−0.723596	−	0.690224i	$-0.757512\pi$
$258$		0			0
$259$	5.82543e11	+	1.00899e12i	0.499838	+	0.865745i
$260$		−	3.16295e11i		−	0.266211i
$261$		0			0
$262$	1.13385e12			0.918433
$263$	−1.19461e12	+	6.89708e11i	−0.949395	+	0.548134i	−0.892893	−	0.450269i	$-0.851328\pi$
$263$	−1.19461e12	+	6.89708e11i	−0.949395	+	0.548134i	−0.0565021	+	0.998402i	$0.517995\pi$
$264$		0			0
$265$	−7.65196e10	+	1.32536e11i	−0.0585522	+	0.101415i
$266$	3.49017e11	+	2.01505e11i	0.262083	+	0.151313i
$267$		0			0
$268$	1.33656e11	+	2.31499e11i	0.0966750	+	0.167446i
$269$			1.18129e12i			0.838680i	0.907829	+	0.419340i	$0.137738\pi$
$269$			1.18129e12i			0.838680i	−0.907829	+	0.419340i	$0.862262\pi$
$270$		0			0
$271$	−1.42251e12			−0.973213			−0.486606	−	0.873621i	$-0.661765\pi$
$271$	−1.42251e12			−0.973213			−0.486606	+	0.873621i	$0.661765\pi$
$272$	−6.05304e11	+	3.49472e11i	−0.406564	+	0.234730i
$273$		0			0
$274$	−3.10837e11	+	5.38385e11i	−0.201270	+	0.348611i
$275$	1.84657e11	+	1.06612e11i	0.117409	+	0.0677863i
$276$		0			0
$277$	−2.64980e11	−	4.58959e11i	−0.162485	−	0.281433i	0.773274	−	0.634072i	$-0.218618\pi$
$277$	−2.64980e11	−	4.58959e11i	−0.162485	−	0.281433i	−0.935759	+	0.352639i	$0.885284\pi$
$278$			1.43116e12i			0.861913i
$279$		0			0
$280$	9.76905e11			0.567626
$281$	−1.97835e12	+	1.14220e12i	−1.12920	+	0.651946i	−0.943735	−	0.330704i	$-0.892714\pi$
$281$	−1.97835e12	+	1.14220e12i	−1.12920	+	0.651946i	−0.185469	+	0.982650i	$0.559381\pi$
$282$		0			0
$283$	−1.15637e12	+	2.00289e12i	−0.637038	+	1.10338i	0.349042	+	0.937107i	$0.386507\pi$
$283$	−1.15637e12	+	2.00289e12i	−0.637038	+	1.10338i	−0.986079	+	0.166275i	$0.946826\pi$
$284$	2.53346e11	+	1.46269e11i	0.137127	+	0.0791701i
$285$		0			0
$286$	−1.20211e11	−	2.08212e11i	−0.0628225	−	0.108812i
$287$			3.46630e12i			1.78015i
$288$		0			0
$289$	−5.09295e12			−2.52627
$290$	3.43793e11	−	1.98489e11i	0.167613	−	0.0967712i
$291$		0			0
$292$	5.59584e11	−	9.69228e11i	0.263604	−	0.456575i
$293$	−9.17894e11	−	5.29947e11i	−0.425064	−	0.245411i	0.272177	−	0.962247i	$-0.412256\pi$
$293$	−9.17894e11	−	5.29947e11i	−0.425064	−	0.245411i	−0.697242	+	0.716836i	$0.745590\pi$
$294$		0			0
$295$	−5.30096e11	−	9.18153e11i	−0.237271	−	0.410965i
$296$		−	5.81138e11i		−	0.255753i
$297$		0			0
$298$	−7.65890e11			−0.325900
$299$	−2.06790e11	+	1.19390e11i	−0.0865314	+	0.0499589i
$300$		0			0
$301$	−2.30778e12	+	3.99719e12i	−0.934031	+	1.61779i
$302$	−2.39827e12	−	1.38464e12i	−0.954692	−	0.551192i
$303$		0			0
$304$	−1.00509e11	−	1.74087e11i	−0.0387114	−	0.0670501i
$305$			1.92679e12i			0.730020i
$306$		0			0
$307$	6.89209e11			0.252731			0.126366	−	0.991984i	$-0.459669\pi$
$307$	6.89209e11			0.252731			0.126366	+	0.991984i	$0.459669\pi$
$308$	6.43082e11	−	3.71284e11i	0.232013	−	0.133953i
$309$		0			0
$310$	1.71812e12	−	2.97587e12i	0.600129	−	1.03945i
$311$	1.69458e12	+	9.78369e11i	0.582454	+	0.336280i	0.762108	−	0.647450i	$-0.224165\pi$
$311$	1.69458e12	+	9.78369e11i	0.582454	+	0.336280i	−0.179654	+	0.983730i	$0.557498\pi$
$312$		0			0
$313$	1.24410e11	+	2.15485e11i	0.0414128	+	0.0717291i	0.885989	−	0.463707i	$-0.153481\pi$
$313$	1.24410e11	+	2.15485e11i	0.0414128	+	0.0717291i	−0.844576	+	0.535436i	$0.820147\pi$
$314$		−	3.59711e12i		−	1.17843i
$315$		0			0
$316$	−1.00655e12			−0.319449
$317$	−4.01555e12	+	2.31838e12i	−1.25444	+	0.724249i	−0.971987	−	0.235034i	$-0.924480\pi$
$317$	−4.01555e12	+	2.31838e12i	−1.25444	+	0.724249i	−0.282448	+	0.959283i	$0.591147\pi$
$318$		0			0
$319$	1.50876e11	−	2.61324e11i	0.0456737	−	0.0791091i
$320$	−4.21992e11	−	2.43637e11i	−0.125763	−	0.0726095i
$321$		0			0
$322$	−3.68748e11	−	6.38690e11i	−0.106525	−	0.184506i
$323$		−	2.04456e12i		−	0.581549i
$324$		0			0
$325$	5.81050e11			0.160249
$326$	−1.80445e12	+	1.04180e12i	−0.490069	+	0.282942i
$327$		0			0
$328$	8.64483e11	−	1.49733e12i	0.227713	−	0.394410i
$329$	−3.11897e12	−	1.80074e12i	−0.809154	−	0.467165i
$330$		0			0
$331$	7.07216e11	+	1.22493e12i	0.177997	+	0.308300i	0.941194	−	0.337866i	$-0.109705\pi$
$331$	7.07216e11	+	1.22493e12i	0.177997	+	0.308300i	−0.763197	+	0.646165i	$0.776372\pi$
$332$			1.11902e12i			0.277425i
$333$		0			0
$334$	4.80642e12			1.15635
$335$	−1.64150e12	+	9.47723e11i	−0.389061	+	0.224625i
$336$		0			0
$337$	−4.33878e11	+	7.51498e11i	−0.0998201	+	0.172893i	−0.911610	−	0.411056i	$-0.865160\pi$
$337$	−4.33878e11	+	7.51498e11i	−0.0998201	+	0.172893i	0.811790	+	0.583949i	$0.198493\pi$
$338$	2.13407e12	+	1.23211e12i	0.483755	+	0.279296i
$339$		0			0
$340$	−2.47803e12	−	4.29207e12i	−0.545395	−	0.944652i
$341$		−	2.61196e12i		−	0.566493i
$342$		0			0
$343$	5.91785e11			0.124650
$344$	1.99377e12	−	1.15110e12i	0.413888	−	0.238958i
$345$		0			0
$346$	3.44086e12	−	5.95975e12i	0.693884	−	1.20184i
$347$	−4.50950e12	−	2.60356e12i	−0.896357	−	0.517512i	−0.0203407	−	0.999793i	$-0.506475\pi$
$347$	−4.50950e12	−	2.60356e12i	−0.896357	−	0.517512i	−0.876017	+	0.482281i	$0.839808\pi$
$348$		0			0
$349$	−5.59765e11	−	9.69541e11i	−0.108113	−	0.187257i	0.806893	−	0.590698i	$-0.201148\pi$
$349$	−5.59765e11	−	9.69541e11i	−0.108113	−	0.187257i	−0.915006	+	0.403441i	$0.867814\pi$
$350$			1.79462e12i			0.341691i
$351$		0			0
$352$	−3.70388e11			−0.0685398
$353$	3.23852e12	−	1.86976e12i	0.590844	−	0.341124i	−0.174587	−	0.984642i	$-0.555859\pi$
$353$	3.23852e12	−	1.86976e12i	0.590844	−	0.341124i	0.765431	+	0.643518i	$0.222526\pi$
$354$		0			0
$355$	−1.03716e12	+	1.79642e12i	−0.183952	+	0.318614i
$356$	−1.05859e11	−	6.11180e10i	−0.0185131	−	0.0106886i
$357$		0			0
$358$	8.00009e10	+	1.38566e11i	0.0136044	+	0.0235635i
$359$			3.54489e12i			0.594471i	0.954804	+	0.297235i	$0.0960646\pi$
$359$			3.54489e12i			0.594471i	−0.954804	+	0.297235i	$0.903935\pi$
$360$		0			0
$361$	−5.54305e12			−0.904092
$362$	−2.49473e12	+	1.44033e12i	−0.401310	+	0.231697i
$363$		0			0
$364$	1.01177e12	−	1.75244e12i	0.158335	−	0.274244i
$365$	6.87257e12	+	3.96788e12i	1.06085	+	0.612484i
$366$		0			0
$367$	5.05807e12	+	8.76083e12i	0.759722	+	1.31588i	0.942992	+	0.332814i	$0.107998\pi$
$367$	5.05807e12	+	8.76083e12i	0.759722	+	1.31588i	−0.183271	+	0.983062i	$0.558669\pi$
$368$			3.67858e11i			0.0545056i
$369$		0			0
$370$	4.12071e12			0.594242
$371$	−8.47919e11	+	4.89546e11i	−0.120638	+	0.0696505i
$372$		0			0
$373$	−1.90528e12	+	3.30004e12i	−0.263885	+	0.457062i	−0.967271	−	0.253746i	$-0.918337\pi$
$373$	−1.90528e12	+	3.30004e12i	−0.263885	+	0.457062i	0.703386	+	0.710808i	$0.251670\pi$
$374$	−3.26249e12	−	1.88360e12i	−0.445853	−	0.257413i
$375$		0			0
$376$	8.98195e11	+	1.55572e12i	0.119518	+	0.207010i
$377$		−	8.22293e11i		−	0.107974i
$378$		0			0
$379$	1.11052e13			1.42014			0.710069	−	0.704132i	$-0.248664\pi$
$379$	1.11052e13			1.42014			0.710069	+	0.704132i	$0.248664\pi$
$380$	1.23441e12	−	7.12688e11i	0.155791	−	0.0899460i
$381$		0			0
$382$	−2.33582e12	+	4.04576e12i	−0.287159	+	0.497375i
$383$	−3.71671e12	−	2.14585e12i	−0.450988	−	0.260378i	0.257259	−	0.966342i	$-0.417181\pi$
$383$	−3.71671e12	−	2.14585e12i	−0.450988	−	0.260378i	−0.708247	+	0.705964i	$0.750514\pi$
$384$		0			0
$385$	2.63269e12	+	4.55995e12i	0.311240	+	0.539083i
$386$			7.05084e12i			0.822820i
$387$		0			0
$388$	4.52665e12			0.514776
$389$	1.30384e13	−	7.52771e12i	1.46378	−	0.845113i	0.464595	−	0.885523i	$-0.346200\pi$
$389$	1.30384e13	−	7.52771e12i	1.46378	−	0.845113i	0.999183	+	0.0404106i	$0.0128666\pi$
$390$		0			0
$391$	−1.87074e12	+	3.24021e12i	−0.204705	+	0.354560i
$392$	2.57847e12	+	1.48868e12i	0.278569	+	0.160832i
$393$		0			0
$394$	−1.71622e12	−	2.97259e12i	−0.180756	−	0.313079i
$395$		−	7.13723e12i		−	0.742240i
$396$		0			0
$397$	−1.11669e13			−1.13235			−0.566174	−	0.824286i	$-0.691577\pi$
$397$	−1.11669e13			−1.13235			−0.566174	+	0.824286i	$0.691577\pi$
$398$	−2.18870e12	+	1.26365e12i	−0.219165	+	0.126535i
$399$		0			0
$400$	4.47573e11	−	7.75220e11i	0.0437083	−	0.0757050i
$401$	1.00186e13	+	5.78426e12i	0.966243	+	0.557861i	0.898089	−	0.439814i	$-0.144956\pi$
$401$	1.00186e13	+	5.78426e12i	0.966243	+	0.557861i	0.0681541	+	0.997675i	$0.478289\pi$
$402$		0			0
$403$	−3.55889e12	−	6.16417e12i	−0.334803	−	0.579895i
$404$		−	8.59793e12i		−	0.798890i
$405$		0			0
$406$	2.53973e12			0.230227
$407$	2.71260e12	−	1.56612e12i	0.242892	−	0.140234i
$408$		0			0
$409$	5.37056e12	−	9.30209e12i	0.469249	−	0.812763i	−0.530133	−	0.847914i	$-0.677858\pi$
$409$	5.37056e12	−	9.30209e12i	0.469249	−	0.812763i	0.999382	+	0.0351516i	$0.0111914\pi$
$410$	1.06172e13	+	6.12985e12i	0.916413	+	0.529091i
$411$		0			0
$412$	2.14237e12	+	3.71070e12i	0.180472	+	0.312586i
$413$		−	6.78275e12i		−	0.564489i
$414$		0			0
$415$	−7.93468e12			−0.644598
$416$	−8.74107e11	+	5.04666e11i	−0.0701613	+	0.0405077i
$417$		0			0
$418$	5.41730e11	−	9.38304e11i	0.0424523	−	0.0735296i
$419$	7.63589e12	+	4.40859e12i	0.591275	+	0.341373i	0.765602	−	0.643315i	$-0.222441\pi$
$419$	7.63589e12	+	4.40859e12i	0.591275	+	0.341373i	−0.174326	+	0.984688i	$0.555775\pi$
$420$		0			0
$421$	2.84871e12	+	4.93410e12i	0.215396	+	0.373076i	0.953395	−	0.301725i	$-0.0975625\pi$
$421$	2.84871e12	+	4.93410e12i	0.215396	+	0.373076i	−0.737999	+	0.674802i	$0.764229\pi$
$422$			3.46348e12i			0.258792i
$423$		0			0
$424$	4.88365e11			0.0356381
$425$	7.88474e12	−	4.55226e12i	0.568647	−	0.328309i
$426$		0			0
$427$	−6.16347e12	+	1.06754e13i	−0.434196	+	0.752050i
$428$	−6.36531e12	−	3.67501e12i	−0.443201	−	0.255882i
$429$		0			0
$430$	8.16221e12	+	1.41374e13i	0.555220	+	0.961670i
$431$		−	1.80323e13i		−	1.21245i	−0.795293	−	0.606226i	$-0.792683\pi$
$431$		−	1.80323e13i		−	1.21245i	0.795293	−	0.606226i	$-0.207317\pi$
$432$		0			0
$433$	2.06339e13			1.35563			0.677816	−	0.735232i	$-0.262927\pi$
$433$	2.06339e13			1.35563			0.677816	+	0.735232i	$0.262927\pi$
$434$	1.90386e13	−	1.09919e13i	1.23648	−	0.713881i
$435$		0			0
$436$	−1.20976e12	+	2.09537e12i	−0.0767836	+	0.132993i
$437$	−9.31896e11	−	5.38030e11i	−0.0584736	−	0.0337598i
$438$		0			0
$439$	−9.76567e12	−	1.69146e13i	−0.598935	−	1.03739i	−0.992979	−	0.118294i	$-0.962258\pi$
$439$	−9.76567e12	−	1.69146e13i	−0.598935	−	1.03739i	0.394044	−	0.919092i	$-0.371076\pi$
$440$		−	2.62633e12i		−	0.159253i
$441$		0			0
$442$	−1.02659e13			−0.608535
$443$	2.57616e13	−	1.48735e13i	1.50992	−	0.871753i	0.509987	−	0.860182i	$-0.329650\pi$
$443$	2.57616e13	−	1.48735e13i	1.50992	−	0.871753i	0.999933	−	0.0115703i	$-0.00368303\pi$
$444$		0			0
$445$	4.33373e11	−	7.50625e11i	0.0248349	−	0.0430153i
$446$	1.18704e13	+	6.85338e12i	0.672653	+	0.388357i
$447$		0			0
$448$	−1.55871e12	−	2.69976e12i	−0.0863722	−	0.149601i
$449$			1.37505e13i			0.753509i	0.926313	+	0.376754i	$0.122960\pi$
$449$			1.37505e13i			0.753509i	−0.926313	+	0.376754i	$0.877040\pi$
$450$		0			0
$451$	9.31887e12			0.499437
$452$	5.85997e12	−	3.38325e12i	0.310601	−	0.179326i
$453$		0			0
$454$	7.58684e12	−	1.31408e13i	0.393352	−	0.681306i
$455$	1.24262e13	+	7.17425e12i	0.637207	+	0.367891i
$456$		0			0
$457$	−2.05112e11	−	3.55265e11i	−0.0102899	−	0.0178226i	0.860835	−	0.508885i	$-0.169942\pi$
$457$	−2.05112e11	−	3.55265e11i	−0.0102899	−	0.0178226i	−0.871124	+	0.491062i	$0.836609\pi$
$458$			7.99554e12i			0.396753i
$459$		0			0
$460$	−2.60840e12			−0.126644
$461$	1.82657e11	−	1.05457e11i	0.00877266	−	0.00506490i	−0.495607	−	0.868547i	$-0.665054\pi$
$461$	1.82657e11	−	1.05457e11i	0.00877266	−	0.00506490i	0.504380	+	0.863482i	$0.331721\pi$
$462$		0			0
$463$	9.83688e12	−	1.70380e13i	0.462330	−	0.800779i	−0.536746	−	0.843744i	$-0.680347\pi$
$463$	9.83688e12	−	1.70380e13i	0.462330	−	0.800779i	0.999077	+	0.0429642i	$0.0136801\pi$
$464$	−1.09708e12	−	6.33399e11i	−0.0510092	−	0.0294502i
$465$		0			0
$466$	−1.27155e13	−	2.20238e13i	−0.578632	−	1.00222i
$467$			1.21902e13i			0.548815i	0.961614	+	0.274407i	$0.0884817\pi$
$467$			1.21902e13i			0.548815i	−0.961614	+	0.274407i	$0.911518\pi$
$468$		0			0
$469$	−1.21264e13			−0.534402
$470$	−1.10312e13	+	6.36889e12i	−0.480989	+	0.277699i
$471$		0			0
$472$	−1.69159e12	+	2.92993e12i	−0.0722082	+	0.125068i
$473$	1.07461e13	+	6.20427e12i	0.453885	+	0.262051i
$474$		0			0
$475$	1.30924e12	+	2.26768e12i	0.0541443	+	0.0937806i
$476$		−	3.17071e13i		−	1.29754i
$477$		0			0
$478$	5.98729e12			0.239933
$479$	−4.33780e12	+	2.50443e12i	−0.172025	+	0.0993187i	−0.583540	−	0.812084i	$-0.698333\pi$
$479$	−4.33780e12	+	2.50443e12i	−0.172025	+	0.0993187i	0.411515	+	0.911403i	$0.365000\pi$
$480$		0			0
$481$	4.26779e12	−	7.39203e12i	0.165759	−	0.287103i
$482$	−1.73770e13	−	1.00326e13i	−0.667945	−	0.385638i
$483$		0			0
$484$	5.64181e12	+	9.77191e12i	0.212418	+	0.367919i
$485$			3.20975e13i			1.19608i
$486$		0			0
$487$	−4.17000e13			−1.52227			−0.761134	−	0.648595i	$-0.775357\pi$
$487$	−4.17000e13			−1.52227			−0.761134	+	0.648595i	$0.775357\pi$
$488$	5.32484e12	−	3.07430e12i	0.192401	−	0.111083i
$489$		0			0
$490$	−1.05559e13	+	1.82834e13i	−0.373693	+	0.647255i
$491$	−1.82160e12	−	1.05170e12i	−0.0638331	−	0.0368540i	0.467744	−	0.883864i	$-0.345067\pi$
$491$	−1.82160e12	−	1.05170e12i	−0.0638331	−	0.0368540i	−0.531577	+	0.847010i	$0.678400\pi$
$492$		0			0
$493$	−6.44229e12	−	1.11584e13i	−0.221211	−	0.383148i
$494$		−	2.95250e12i		−	0.100359i
$495$		0			0
$496$	−1.09654e13			−0.365272
$497$	−1.14929e13	+	6.63541e12i	−0.379006	+	0.218819i
$498$		0			0
$499$	−1.37241e13	+	2.37708e13i	−0.443589	+	0.768319i	−0.997953	−	0.0639553i	$-0.979628\pi$
$499$	−1.37241e13	+	2.37708e13i	−0.443589	+	0.768319i	0.554363	+	0.832275i	$0.312962\pi$
$500$	−1.02235e13	−	5.90255e12i	−0.327152	−	0.188881i
$501$		0			0
$502$	−9.72406e12	−	1.68426e13i	−0.305021	−	0.528311i
$503$		−	2.26985e13i		−	0.704949i	−0.935822	−	0.352474i	$-0.885340\pi$
$503$		−	2.26985e13i		−	0.704949i	0.935822	−	0.352474i	$-0.114660\pi$
$504$		0			0
$505$	6.09659e13			1.85622
$506$	−1.71707e12	+	9.91349e11i	−0.0517648	+	0.0298864i
$507$		0			0
$508$	−8.13603e12	+	1.40920e13i	−0.240488	+	0.416538i
$509$	3.64995e13	+	2.10730e13i	1.06831	+	0.616791i	0.927720	−	0.373277i	$-0.121766\pi$
$509$	3.64995e13	+	2.10730e13i	1.06831	+	0.616791i	0.140593	+	0.990068i	$0.455099\pi$
$510$		0			0
$511$	2.53852e13	+	4.39684e13i	0.728577	+	1.26193i
$512$			1.55494e12i			0.0441942i
$513$		0			0
$514$	−4.93051e13			−1.37428
$515$	−2.63117e13	+	1.51911e13i	−0.726295	+	0.419327i
$516$		0			0
$517$	−4.84114e12	+	8.38509e12i	−0.131067	+	0.227015i
$518$	2.28309e13	+	1.31815e13i	0.612174	+	0.353439i
$519$		0			0
$520$	−3.57847e12	−	6.19809e12i	−0.0941197	−	0.163020i
$521$		−	6.54420e13i		−	1.70478i	−0.522907	−	0.852390i	$-0.675152\pi$
$521$		−	6.54420e13i		−	1.70478i	0.522907	−	0.852390i	$-0.324848\pi$
$522$		0			0
$523$	−6.14531e13			−1.57049			−0.785245	−	0.619185i	$-0.787463\pi$
$523$	−6.14531e13			−1.57049			−0.785245	+	0.619185i	$0.787463\pi$
$524$	2.22188e13	−	1.28280e13i	0.562423	−	0.324715i
$525$		0			0
$526$	−1.56063e13	+	2.70309e13i	−0.387589	+	0.671324i
$527$	−9.65869e13	−	5.57645e13i	−2.37610	−	1.37184i
$528$		0			0
$529$	−1.97287e13	−	3.41711e13i	−0.476233	−	0.824860i
$530$			3.46288e12i			0.0828053i
$531$		0			0
$532$	9.11907e12			0.213990
$533$	2.19923e13	−	1.26973e13i	0.511252	−	0.295172i
$534$		0			0
$535$	2.60587e13	−	4.51349e13i	0.594543	−	1.02978i
$536$	5.23822e12	+	3.02429e12i	0.118402	+	0.0683595i
$537$		0			0
$538$	1.33648e13	+	2.31485e13i	0.296518	+	0.513584i
$539$			1.60475e13i			0.352748i
$540$		0			0
$541$	1.50207e13			0.324118			0.162059	−	0.986781i	$-0.448187\pi$
$541$	1.50207e13			0.324118			0.162059	+	0.986781i	$0.448187\pi$
$542$	−2.78753e13	+	1.60938e13i	−0.595969	+	0.344083i
$543$		0			0
$544$	−7.90765e12	+	1.36965e13i	−0.165979	+	0.287484i
$545$	−1.48578e13	−	8.57816e12i	−0.309010	−	0.178407i
$546$		0			0
$547$	−3.57548e13	−	6.19292e13i	−0.730127	−	1.26462i	−0.956829	−	0.290652i	$-0.906128\pi$
$547$	−3.57548e13	−	6.19292e13i	−0.730127	−	1.26462i	0.226702	−	0.973964i	$-0.427206\pi$
$548$			1.40669e13i			0.284639i
$549$		0			0
$550$	4.82470e12			0.0958644
$551$	3.20919e12	−	1.85282e12i	0.0631883	−	0.0364818i
$552$		0			0
$553$	2.28308e13	−	3.95441e13i	0.441464	−	0.764638i
$554$	−1.03851e13	−	5.99581e12i	−0.199003	−	0.114894i
$555$		0			0
$556$	1.61917e13	+	2.80448e13i	0.304732	+	0.527811i
$557$			7.34107e13i			1.36925i	0.728895	+	0.684626i	$0.240034\pi$
$557$			7.34107e13i			1.36925i	−0.728895	+	0.684626i	$0.759966\pi$
$558$		0			0
$559$	3.38141e13			0.619497
$560$	1.91434e13	−	1.10524e13i	0.347599	−	0.200686i
$561$		0			0
$562$	−2.58451e13	+	4.47650e13i	−0.460996	+	0.798468i
$563$	4.13394e13	+	2.38673e13i	0.730840	+	0.421951i	0.818729	−	0.574179i	$-0.194679\pi$
$563$	4.13394e13	+	2.38673e13i	0.730840	+	0.421951i	−0.0878892	+	0.996130i	$0.528012\pi$
$564$		0			0
$565$	2.39899e13	+	4.15517e13i	0.416664	+	0.721683i
$566$			5.23314e13i			0.900907i
$567$		0			0
$568$	6.61939e12			0.111963
$569$	−1.65369e13	+	9.54756e12i	−0.277263	+	0.160078i	−0.632184	−	0.774819i	$-0.717841\pi$
$569$	−1.65369e13	+	9.54756e12i	−0.277263	+	0.160078i	0.354921	+	0.934896i	$0.384508\pi$
$570$		0			0
$571$	1.04724e13	−	1.81387e13i	0.172530	−	0.298831i	−0.766774	−	0.641918i	$-0.778139\pi$
$571$	1.04724e13	−	1.81387e13i	0.172530	−	0.298831i	0.939304	+	0.343087i	$0.111472\pi$
$572$	−4.71130e12	−	2.72007e12i	−0.0769415	−	0.0444222i
$573$		0			0
$574$	3.92167e13	+	6.79253e13i	0.629378	+	1.09011i
$575$		−	4.79175e12i		−	0.0762351i
$576$		0			0
$577$	3.56688e13			0.557711			0.278855	−	0.960333i	$-0.410045\pi$
$577$	3.56688e13			0.557711			0.278855	+	0.960333i	$0.410045\pi$
$578$	−9.98011e13	+	5.76202e13i	−1.54702	+	0.893173i
$579$		0			0
$580$	4.49129e12	−	7.77914e12i	0.0684275	−	0.118520i
$581$	−4.39624e13	−	2.53817e13i	−0.664050	−	0.383389i
$582$		0			0
$583$	1.31611e12	+	2.27956e12i	0.0195411	+	0.0338461i
$584$		−	2.53239e13i		−	0.372792i
$585$		0			0
$586$	−2.39826e13			−0.347064
$587$	−1.12079e14	+	6.47090e13i	−1.60818	+	0.928483i	−0.618402	+	0.785862i	$0.712220\pi$
$587$	−1.12079e14	+	6.47090e13i	−1.60818	+	0.928483i	−0.989777	+	0.142621i	$0.954447\pi$
$588$		0			0
$589$	1.60381e13	−	2.77787e13i	0.226243	−	0.391864i
$590$	−2.07754e13	−	1.19947e13i	−0.290596	−	0.167776i
$591$		0			0
$592$	−6.57482e12	−	1.13879e13i	−0.0904223	−	0.156616i
$593$			3.96596e13i			0.540848i	0.962741	+	0.270424i	$0.0871639\pi$
$593$			3.96596e13i			0.540848i	−0.962741	+	0.270424i	$0.912836\pi$
$594$		0			0
$595$	2.24828e14			3.01485
$596$	−1.50083e13	+	8.66505e12i	−0.199572	+	0.115223i
$597$		0			0
$598$	−2.70150e12	+	4.67913e12i	−0.0353263	+	0.0611870i
$599$	3.96254e13	+	2.28777e13i	0.513854	+	0.296674i	0.734416	−	0.678699i	$-0.237456\pi$
$599$	3.96254e13	+	2.28777e13i	0.513854	+	0.296674i	−0.220562	+	0.975373i	$0.570789\pi$
$600$		0			0
$601$	−5.30165e13	−	9.18273e13i	−0.676143	−	1.17111i	−0.976133	−	0.217172i	$-0.930317\pi$
$601$	−5.30165e13	−	9.18273e13i	−0.676143	−	1.17111i	0.299990	−	0.953942i	$-0.403017\pi$
$602$			1.04438e14i			1.32092i
$603$		0			0
$604$	−6.26617e13			−0.779503
$605$	−6.92903e13	+	4.00048e13i	−0.854862	+	0.493555i
$606$		0			0
$607$	4.77534e13	−	8.27112e13i	0.579509	−	1.00374i	−0.416026	−	0.909353i	$-0.636578\pi$
$607$	4.77534e13	−	8.27112e13i	0.579509	−	1.00374i	0.995536	−	0.0943870i	$-0.0300891\pi$
$608$	−3.93915e12	−	2.27427e12i	−0.0474115	−	0.0273731i
$609$		0			0
$610$	2.17991e13	+	3.77572e13i	0.258101	+	0.447044i
$611$			2.63849e13i			0.309848i
$612$		0			0
$613$	−5.18411e13			−0.598924			−0.299462	−	0.954108i	$-0.596807\pi$
$613$	−5.18411e13			−0.598924			−0.299462	+	0.954108i	$0.596807\pi$
$614$	1.35057e13	−	7.79751e12i	0.154766	−	0.0893540i
$615$		0			0
$616$	8.40119e12	−	1.45513e13i	0.0947190	−	0.164058i
$617$	−6.97534e13	−	4.02721e13i	−0.780081	−	0.450380i	0.0563782	−	0.998409i	$-0.482045\pi$
$617$	−6.97534e13	−	4.02721e13i	−0.780081	−	0.450380i	−0.836459	+	0.548030i	$0.815378\pi$
$618$		0			0
$619$	2.57473e13	+	4.45957e13i	0.283321	+	0.490726i	0.972201	−	0.234149i	$-0.0752305\pi$
$619$	2.57473e13	+	4.45957e13i	0.283321	+	0.490726i	−0.688880	+	0.724876i	$0.741897\pi$
$620$		−	7.77532e13i		−	0.848711i
$621$		0			0
$622$	4.42759e13			0.475571
$623$	4.80224e12	−	2.77257e12i	0.0511686	−	0.0295422i
$624$		0			0
$625$	5.85270e13	−	1.01372e14i	0.613700	−	1.06296i
$626$	4.87587e12	+	2.81508e12i	0.0507201	+	0.0292833i
$627$		0			0
$628$	−4.06967e13	−	7.04887e13i	−0.416640	−	0.721641i
$629$		−	1.33745e14i		−	1.35839i
$630$		0			0
$631$	−1.02922e13			−0.102887			−0.0514435	−	0.998676i	$-0.516382\pi$
$631$	−1.02922e13			−0.102887			−0.0514435	+	0.998676i	$0.516382\pi$
$632$	−1.97243e13	+	1.13878e13i	−0.195622	+	0.112942i
$633$		0			0
$634$	−5.24589e13	+	9.08614e13i	−0.512121	+	0.887020i
$635$	−9.99232e13	−	5.76907e13i	−0.967827	−	0.558775i
$636$		0			0
$637$	2.18653e13	+	3.78719e13i	0.208477	+	0.361093i
$638$		−	6.82785e12i		−	0.0645923i
$639$		0			0
$640$	−1.10257e13			−0.102685
$641$	−4.00494e13	+	2.31225e13i	−0.370089	+	0.213671i	−0.673497	−	0.739190i	$-0.735209\pi$
$641$	−4.00494e13	+	2.31225e13i	−0.370089	+	0.213671i	0.303408	+	0.952861i	$0.401875\pi$
$642$		0			0
$643$	−1.36551e13	+	2.36514e13i	−0.124234	+	0.215180i	−0.921433	−	0.388537i	$-0.872981\pi$
$643$	−1.36551e13	+	2.36514e13i	−0.124234	+	0.215180i	0.797199	+	0.603716i	$0.206314\pi$
$644$	−1.44519e13	−	8.34381e12i	−0.130466	−	0.0753243i
$645$		0			0
$646$	−2.31315e13	−	4.00650e13i	−0.205609	−	0.356125i
$647$			1.34984e13i			0.119059i	0.998227	+	0.0595293i	$0.0189600\pi$
$647$			1.34984e13i			0.119059i	−0.998227	+	0.0595293i	$0.981040\pi$
$648$		0			0
$649$	−1.82349e13			−0.158372
$650$	1.13862e13	−	6.57382e12i	0.0981323	−	0.0566567i
$651$		0			0
$652$	−2.35733e13	+	4.08301e13i	−0.200070	+	0.346531i
$653$	−7.29055e13	−	4.20920e13i	−0.614037	−	0.354514i	0.160507	−	0.987035i	$-0.448687\pi$
$653$	−7.29055e13	−	4.20920e13i	−0.614037	−	0.354514i	−0.774544	+	0.632520i	$0.782020\pi$
$654$		0			0
$655$	9.09604e13	+	1.57548e14i	0.754477	+	1.30679i
$656$		−	3.91220e13i		−	0.322034i
$657$		0			0
$658$	−8.14920e13			−0.660672
$659$	1.43296e14	−	8.27319e13i	1.15294	−	0.665650i	0.203338	−	0.979109i	$-0.434821\pi$
$659$	1.43296e14	−	8.27319e13i	1.15294	−	0.665650i	0.949602	+	0.313458i	$0.101488\pi$
$660$		0			0
$661$	−1.00840e14	+	1.74661e14i	−0.799148	+	1.38416i	0.121024	+	0.992650i	$0.461382\pi$
$661$	−1.00840e14	+	1.74661e14i	−0.799148	+	1.38416i	−0.920172	+	0.391515i	$0.871951\pi$
$662$	2.77171e13	+	1.60025e13i	0.218001	+	0.125863i
$663$		0			0
$664$	1.26602e13	+	2.19281e13i	0.0980846	+	0.169887i
$665$			6.46612e13i			0.497205i
$666$		0			0
$667$	−6.78122e12			−0.0513664
$668$	9.41862e13	−	5.43785e13i	0.708117	−	0.408832i
$669$		0			0
$670$	−2.14445e13	+	3.71430e13i	−0.158834	+	0.275108i
$671$	2.87001e13	+	1.65700e13i	0.210994	+	0.121818i
$672$		0			0
$673$	−3.02184e12	−	5.23398e12i	−0.0218875	−	0.0379103i	0.854874	−	0.518835i	$-0.173634\pi$
$673$	−3.02184e12	−	5.23398e12i	−0.0218875	−	0.0379103i	−0.876762	+	0.480925i	$0.840301\pi$
$674$			1.96351e13i			0.141167i
$675$		0			0
$676$	5.57588e13			0.394984
$677$	−1.05200e14	+	6.07372e13i	−0.739727	+	0.427082i	−0.821970	−	0.569530i	$-0.807125\pi$
$677$	−1.05200e14	+	6.07372e13i	−0.739727	+	0.427082i	0.0822428	+	0.996612i	$0.473792\pi$
$678$		0			0
$679$	−1.02674e14	+	1.77837e14i	−0.711398	+	1.23218i
$680$	−9.71184e13	−	5.60713e13i	−0.667970	−	0.385653i
$681$		0			0
$682$	−2.95510e13	−	5.11838e13i	−0.200286	−	0.346905i
$683$			1.51629e14i			1.02019i	0.860119	+	0.510094i	$0.170389\pi$
$683$			1.51629e14i			1.02019i	−0.860119	+	0.510094i	$0.829611\pi$
$684$		0			0
$685$	−9.97450e13			−0.661360
$686$	1.15966e13	−	6.69528e12i	0.0763324	−	0.0440705i
$687$		0			0
$688$	2.60465e13	−	4.51139e13i	0.168969	−	0.292663i
$689$	6.21197e12	+	3.58648e12i	0.0400067	+	0.0230979i
$690$		0			0
$691$	−3.31124e13	−	5.73524e13i	−0.210185	−	0.364051i	0.741588	−	0.670856i	$-0.234073\pi$
$691$	−3.31124e13	−	5.73524e13i	−0.210185	−	0.364051i	−0.951772	+	0.306806i	$0.900740\pi$
$692$		−	1.55716e14i		−	0.981300i
$693$		0			0
$694$	−1.17824e14			−0.731873
$695$	−1.98859e14	+	1.14812e14i	−1.22637	+	0.708046i
$696$		0			0
$697$	1.98955e14	−	3.44600e14i	1.20946	−	2.09484i
$698$	−2.19382e13	−	1.26660e13i	−0.132411	−	0.0764475i
$699$		0			0
$700$	2.03039e13	+	3.51673e13i	0.120806	+	0.209242i
$701$		−	5.78990e13i		−	0.342043i	−0.985267	−	0.171022i	$-0.945293\pi$
$701$		−	5.78990e13i		−	0.342043i	0.985267	−	0.171022i	$-0.0547068\pi$
$702$		0			0
$703$	3.84654e13			0.224024
$704$	−7.25808e12	+	4.19046e12i	−0.0419719	+	0.0242325i
$705$		0			0
$706$	4.23078e13	−	7.32793e13i	0.241211	−	0.417790i
$707$	3.37784e14	+	1.95020e14i	1.91224	+	1.10403i
$708$		0			0
$709$	−1.35039e14	−	2.33894e14i	−0.753750	−	1.30553i	−0.945994	−	0.324186i	$-0.894910\pi$
$709$	−1.35039e14	−	2.33894e14i	−0.753750	−	1.30553i	0.192244	−	0.981347i	$-0.438424\pi$
$710$			4.69366e13i			0.260148i
$711$		0			0
$712$	−2.76588e12			−0.0151159
$713$	−5.08342e13	+	2.93491e13i	−0.275872	+	0.159275i
$714$		0			0
$715$	1.92874e13	−	3.34068e13i	0.103215	−	0.178774i
$716$	3.13538e12	+	1.81021e12i	0.0166619	+	0.00961977i
$717$		0			0
$718$	4.01059e13	+	6.94654e13i	0.210177	+	0.364038i
$719$			1.48102e14i			0.770755i	0.922759	+	0.385377i	$0.125929\pi$
$719$			1.48102e14i			0.770755i	−0.922759	+	0.385377i	$0.874071\pi$
$720$		0			0
$721$	−1.94375e14			−0.997616
$722$	−1.08621e14	+	6.27124e13i	−0.553641	+	0.319645i
$723$		0			0
$724$	−3.25910e13	+	5.64493e13i	−0.163834	+	0.283769i
$725$	1.42907e13	+	8.25072e12i	0.0713448	+	0.0411910i
$726$		0			0
$727$	−2.60801e13	−	4.51720e13i	−0.128421	−	0.222432i	0.794644	−	0.607076i	$-0.207658\pi$
$727$	−2.60801e13	−	4.51720e13i	−0.128421	−	0.222432i	−0.923065	+	0.384644i	$0.874324\pi$
$728$		−	4.57876e13i		−	0.223919i
$729$		0			0
$730$	1.79566e14			0.866183
$731$	4.58852e14	−	2.64918e14i	2.19829	−	1.26919i
$732$		0			0
$733$	−1.60891e14	+	2.78671e14i	−0.760346	+	1.31696i	0.182326	+	0.983238i	$0.441637\pi$
$733$	−1.60891e14	+	2.78671e14i	−0.760346	+	1.31696i	−0.942672	+	0.333720i	$0.891696\pi$
$734$	1.98235e14	+	1.14451e14i	0.930465	+	0.537204i
$735$		0			0
$736$	4.16184e12	+	7.20851e12i	0.0192706	+	0.0333777i
$737$			3.26009e13i			0.149931i
$738$		0			0
$739$	1.66542e14			0.755617			0.377809	−	0.925884i	$-0.376678\pi$
$739$	1.66542e14			0.755617			0.377809	+	0.925884i	$0.376678\pi$
$740$	8.07491e13	−	4.66205e13i	0.363898	−	0.210096i
$741$		0			0
$742$	−1.10772e13	+	1.91862e13i	−0.0492503	+	0.0853041i
$743$	9.84071e13	+	5.68154e13i	0.434593	+	0.250912i	0.701301	−	0.712865i	$-0.252603\pi$
$743$	9.84071e13	+	5.68154e13i	0.434593	+	0.250912i	−0.266708	+	0.963777i	$0.585936\pi$
$744$		0			0
$745$	−6.14419e13	−	1.06420e14i	−0.267721	−	0.463707i
$746$			8.62230e13i			0.373189i
$747$		0			0
$748$	−8.52421e13			−0.364037
$749$	2.88758e14	−	1.66714e14i	1.22497	−	0.707236i
$750$		0			0
$751$	8.24781e13	−	1.42856e14i	0.345254	−	0.597998i	−0.640146	−	0.768253i	$-0.721126\pi$
$751$	8.24781e13	−	1.42856e14i	0.345254	−	0.597998i	0.985400	+	0.170256i	$0.0544594\pi$
$752$	3.52019e13	+	2.03238e13i	0.146378	+	0.0845116i
$753$		0			0
$754$	−9.30319e12	−	1.61136e13i	−0.0381746	−	0.0661204i
$755$		−	4.44320e14i		−	1.81118i
$756$		0			0
$757$	−2.67990e14			−1.07805			−0.539026	−	0.842289i	$-0.681207\pi$
$757$	−2.67990e14			−1.07805			−0.539026	+	0.842289i	$0.681207\pi$
$758$	2.17617e14	−	1.25641e14i	0.869653	−	0.502095i
$759$		0			0
$760$	1.61263e13	−	2.79316e13i	0.0636014	−	0.110161i
$761$	−1.12405e14	−	6.48973e13i	−0.440417	−	0.254275i	0.263358	−	0.964698i	$-0.415170\pi$
$761$	−1.12405e14	−	6.48973e13i	−0.440417	−	0.254275i	−0.703774	+	0.710423i	$0.748503\pi$
$762$		0			0
$763$	−5.48801e13	−	9.50552e13i	−0.212223	−	0.367581i
$764$			1.05707e14i			0.406105i
$765$		0			0
$766$	−9.71099e13			−0.368230
$767$	−4.30339e13	+	2.48456e13i	−0.162119	+	0.0935995i
$768$		0			0
$769$	1.09593e14	−	1.89820e14i	0.407521	−	0.705846i	−0.587091	−	0.809521i	$-0.699727\pi$
$769$	1.09593e14	−	1.89820e14i	0.407521	−	0.705846i	0.994611	+	0.103675i	$0.0330601\pi$
$770$	1.03180e14	+	5.95709e13i	0.381190	+	0.220080i
$771$		0			0
$772$	7.97712e13	+	1.38168e14i	0.290911	+	0.503872i
$773$		−	4.05042e14i		−	1.46758i	−0.679374	−	0.733792i	$-0.737749\pi$
$773$		−	4.05042e14i		−	1.46758i	0.679374	−	0.733792i	$-0.262251\pi$
$774$		0			0
$775$	1.42837e14			0.510894
$776$	8.87039e13	−	5.12132e13i	0.315235	−	0.182001i
$777$		0			0
$778$	1.70333e14	−	2.95025e14i	0.597585	−	1.03505i
$779$	9.91080e13	+	5.72200e13i	0.345479	+	0.199462i
$780$		0			0
$781$	1.78388e13	+	3.08976e13i	0.0613917	+	0.106333i
$782$			8.46599e13i			0.289497i
$783$		0			0
$784$	6.73701e13			0.227450
$785$	4.99819e14	−	2.88571e14i	1.67673	−	0.968063i
$786$		0			0
$787$	−2.49364e14	+	4.31912e14i	−0.825963	+	1.43061i	0.0752180	+	0.997167i	$0.476035\pi$
$787$	−2.49364e14	+	4.31912e14i	−0.825963	+	1.43061i	−0.901181	+	0.433443i	$0.857299\pi$
$788$	−6.72620e13	−	3.88337e13i	−0.221380	−	0.127814i
$789$		0			0
$790$	−8.07485e13	−	1.39861e14i	−0.262421	−	0.454527i
$791$			3.06958e14i			0.991280i
$792$		0			0
$793$	9.03088e13			0.287981
$794$	−2.18825e14	+	1.26339e14i	−0.693418	+	0.400345i
$795$		0			0
$796$	−2.85931e13	+	4.95246e13i	−0.0894737	+	0.154973i
$797$	1.28753e14	+	7.43358e13i	0.400375	+	0.231157i	0.686646	−	0.726992i	$-0.259082\pi$
$797$	1.28753e14	+	7.43358e13i	0.400375	+	0.231157i	−0.286271	+	0.958149i	$0.592416\pi$
$798$		0			0
$799$	2.06713e14	+	3.58038e14i	0.634797	+	1.09950i
$800$		−	2.02549e13i		−	0.0618129i
$801$		0			0
$802$	2.61766e14			0.788934
$803$	1.18205e14	−	6.82460e13i	0.354046	−	0.204409i
$804$		0			0
$805$	5.91640e13	−	1.02475e14i	0.175016	−	0.303137i
$806$	−1.39479e14	−	8.05284e13i	−0.410048	−	0.236741i
$807$		0			0
$808$	−9.72745e13	−	1.68484e14i	−0.282450	−	0.489218i
$809$		−	1.32296e14i		−	0.381772i	−0.981612	−	0.190886i	$-0.938864\pi$
$809$		−	1.32296e14i		−	0.381772i	0.981612	−	0.190886i	$-0.0611361\pi$
$810$		0			0
$811$	−3.75449e14			−1.07016			−0.535078	−	0.844803i	$-0.679718\pi$
$811$	−3.75449e14			−1.07016			−0.535078	+	0.844803i	$0.679718\pi$
$812$	4.97683e13	−	2.87337e13i	0.140985	−	0.0813976i
$813$		0			0
$814$	3.54373e13	−	6.13792e13i	0.0991604	−	0.171751i
$815$	−2.89517e14	−	1.67153e14i	−0.805167	−	0.464863i
$816$		0			0
$817$	7.61914e13	+	1.31967e14i	0.209313	+	0.362540i
$818$		−	2.43044e14i		−	0.663618i
$819$		0			0
$820$	2.77405e14			0.748248
$821$	−4.02252e12	+	2.32240e12i	−0.0107841	+	0.00622618i	−0.505382	−	0.862896i	$-0.668649\pi$
$821$	−4.02252e12	+	2.32240e12i	−0.0107841	+	0.00622618i	0.494598	+	0.869122i	$0.335315\pi$
$822$		0			0
$823$	−3.19073e14	+	5.52651e14i	−0.845067	+	1.46370i	0.0404962	+	0.999180i	$0.487106\pi$
$823$	−3.19073e14	+	5.52651e14i	−0.845067	+	1.46370i	−0.885563	+	0.464519i	$0.846227\pi$
$824$	8.39636e13	+	4.84764e13i	0.221032	+	0.127613i
$825$		0			0
$826$	−7.67380e13	−	1.32914e14i	−0.199577	−	0.345677i
$827$		−	5.33624e14i		−	1.37946i	−0.724068	−	0.689728i	$-0.757730\pi$
$827$		−	5.33624e14i		−	1.37946i	0.724068	−	0.689728i	$-0.242270\pi$
$828$		0			0
$829$	−8.63626e13			−0.220573			−0.110287	−	0.993900i	$-0.535177\pi$
$829$	−8.63626e13			−0.220573			−0.110287	+	0.993900i	$0.535177\pi$
$830$	−1.55487e14	+	8.97707e13i	−0.394734	+	0.227900i
$831$		0			0
$832$	−1.14193e13	+	1.97788e13i	−0.0286432	+	0.0496116i
$833$	5.93418e14	+	3.42610e14i	1.47957	+	0.854230i
$834$		0			0
$835$	3.85585e14	+	6.67853e14i	0.949922	+	1.64531i
$836$		−	2.45159e13i		−	0.0600367i
$837$		0			0
$838$	1.99510e14			0.482774
$839$	−3.71325e14	+	2.14385e14i	−0.893192	+	0.515685i	−0.874985	−	0.484149i	$-0.839129\pi$
$839$	−3.71325e14	+	2.14385e14i	−0.893192	+	0.515685i	−0.0182069	+	0.999834i	$0.505796\pi$
$840$		0			0
$841$	−1.98677e14	+	3.44119e14i	−0.472246	+	0.817954i
$842$	1.11646e14	+	6.44589e13i	0.263805	+	0.152308i
$843$		0			0
$844$	3.91848e13	+	6.78701e13i	0.0914968	+	0.158477i
$845$			3.95373e14i			0.917747i
$846$		0			0
$847$	−5.11874e14			−1.17421
$848$	9.56996e12	−	5.52522e12i	0.0218238	−	0.0126000i
$849$		0			0
$850$	1.03006e14	−	1.78411e14i	0.232149	−	0.402094i
$851$	−6.09600e13	−	3.51953e13i	−0.136583	−	0.0788563i
$852$		0			0
$853$	4.49747e10	+	7.78984e10i	9.95916e−5	+	0.000172498i	0.866075	−	0.499914i	$-0.166635\pi$
$853$	4.49747e10	+	7.78984e10i	9.95916e−5	+	0.000172498i	−0.865976	+	0.500086i	$0.833302\pi$
$854$			2.78927e14i			0.614046i
$855$		0			0
$856$	−1.66312e14			−0.361872
$857$	−1.25804e14	+	7.26327e13i	−0.272138	+	0.157119i	−0.629859	−	0.776710i	$-0.716887\pi$
$857$	−1.25804e14	+	7.26327e13i	−0.272138	+	0.157119i	0.357721	+	0.933829i	$0.383554\pi$
$858$		0			0
$859$	1.76778e14	−	3.06188e14i	0.377974	−	0.654670i	−0.612794	−	0.790243i	$-0.709954\pi$
$859$	1.76778e14	−	3.06188e14i	0.377974	−	0.654670i	0.990767	+	0.135573i	$0.0432876\pi$
$860$	3.19892e14	+	1.84690e14i	0.680003	+	0.392600i
$861$		0			0
$862$	−2.04012e14	−	3.53359e14i	−0.428666	−	0.742472i
$863$			5.16372e14i			1.07872i	0.842075	+	0.539360i	$0.181334\pi$
$863$			5.16372e14i			1.07872i	−0.842075	+	0.539360i	$0.818666\pi$
$864$		0			0
$865$	1.10414e15			2.28005
$866$	4.04340e14	−	2.33446e14i	0.830151	−	0.479288i
$867$		0			0
$868$	2.48719e14	−	4.30794e14i	0.504790	−	0.874322i
$869$	−1.06311e14	−	6.13787e13i	−0.214526	−	0.123857i
$870$		0			0
$871$	4.44199e13	+	7.69374e13i	0.0886107	+	0.153478i
$872$			5.47477e13i			0.108588i
$873$		0			0
$874$	−2.43485e13			−0.0477435
$875$	4.63782e14	−	2.67765e14i	0.904220	−	0.522052i
$876$		0			0
$877$	−1.61743e13	+	2.80148e13i	−0.0311766	+	0.0539995i	−0.881193	−	0.472757i	$-0.843259\pi$
$877$	−1.61743e13	+	2.80148e13i	−0.0311766	+	0.0539995i	0.850016	+	0.526757i	$0.176592\pi$
$878$	−3.82735e14	−	2.20972e14i	−0.733542	−	0.423511i
$879$		0			0
$880$	−2.97136e13	−	5.14654e13i	−0.0563043	−	0.0975218i
$881$		−	3.45484e14i		−	0.650950i	−0.945551	−	0.325475i	$-0.894476\pi$
$881$		−	3.45484e14i		−	0.650950i	0.945551	−	0.325475i	$-0.105524\pi$
$882$		0			0
$883$	−1.94069e14			−0.361537			−0.180769	−	0.983526i	$-0.557859\pi$
$883$	−1.94069e14			−0.361537			−0.180769	+	0.983526i	$0.557859\pi$
$884$	−2.01170e14	+	1.16145e14i	−0.372650	+	0.215149i
$885$		0			0
$886$	3.36548e14	−	5.82918e14i	0.616422	−	1.06767i
$887$	−1.78733e14	−	1.03191e14i	−0.325526	−	0.187943i	0.328327	−	0.944564i	$-0.393515\pi$
$887$	−1.78733e14	−	1.03191e14i	−0.325526	−	0.187943i	−0.653853	+	0.756622i	$0.726849\pi$
$888$		0			0
$889$	−3.69085e14	−	6.39275e14i	−0.664688	−	1.15127i
$890$		−	1.96122e13i		−	0.0351218i
$891$		0			0
$892$	3.10149e14			0.549219
$893$	−1.02973e14	+	5.94514e13i	−0.181328	+	0.104690i
$894$		0			0
$895$	−1.28358e13	+	2.22323e13i	−0.0223516	+	0.0387140i
$896$	−6.10886e13	−	3.52695e13i	−0.105784	−	0.0610744i
$897$		0			0
$898$	1.55570e14	+	2.69455e14i	0.266406	+	0.461428i
$899$		−	2.02140e14i		−	0.344234i
$900$		0			0
$901$	1.12394e14			0.189286
$902$	1.82612e14	−	1.05431e14i	0.305841	−	0.176578i
$903$		0			0
$904$	7.65543e13	−	1.32596e14i	0.126802	−	0.219628i
$905$	−4.00269e14	−	2.31095e14i	−0.659339	−	0.380669i
$906$		0			0
$907$	1.76823e14	+	3.06266e14i	0.288073	+	0.498956i	0.973350	−	0.229326i	$-0.0736522\pi$
$907$	1.76823e14	+	3.06266e14i	0.288073	+	0.498956i	−0.685277	+	0.728282i	$0.740319\pi$
$908$		−	3.43341e14i		−	0.556284i
$909$		0			0
$910$	3.24670e14			0.520277
$911$	−3.95812e14	+	2.28522e14i	−0.630807	+	0.364197i	−0.781065	−	0.624450i	$-0.785323\pi$
$911$	−3.95812e14	+	2.28522e14i	−0.630807	+	0.364197i	0.150257	+	0.988647i	$0.451990\pi$
$912$		0			0
$913$	−6.82366e13	+	1.18189e14i	−0.107563	+	0.186305i
$914$	−8.03873e12	−	4.64116e12i	−0.0126025	−	0.00727605i
$915$		0			0
$916$	9.04592e13	+	1.56680e14i	0.140273	+	0.242961i
$917$			1.16387e15i			1.79497i
$918$		0			0
$919$	4.85254e14			0.740273			0.370136	−	0.928977i	$-0.379311\pi$
$919$	4.85254e14			0.740273			0.370136	+	0.928977i	$0.379311\pi$
$920$	−5.11139e13	+	2.95106e13i	−0.0775532	+	0.0447754i
$921$		0			0
$922$	2.38622e12	−	4.13305e12i	0.00358143	−	0.00620321i
$923$	8.41982e13	+	4.86119e13i	0.125688	+	0.0725661i
$924$		0			0
$925$	8.56442e13	+	1.48340e14i	0.126471	+	0.219053i
$926$		−	4.45166e14i		−	0.653834i
$927$		0			0
$928$	−2.86644e13			−0.0416488
$929$	−7.06856e14	+	4.08104e14i	−1.02153	+	0.589783i	−0.914548	−	0.404478i	$-0.867453\pi$
$929$	−7.06856e14	+	4.08104e14i	−1.02153	+	0.589783i	−0.106986	+	0.994261i	$0.534120\pi$
$930$		0			0
$931$	−9.85357e13	+	1.70669e14i	−0.140879	+	0.244009i
$932$	−4.98342e14	−	2.87718e14i	−0.708676	−	0.409154i
$933$		0			0
$934$	1.37916e14	+	2.38878e14i	0.194035	+	0.336079i
$935$		−	6.04432e14i		−	0.845842i
$936$		0			0
$937$	−6.90133e14			−0.955510			−0.477755	−	0.878493i	$-0.658549\pi$
$937$	−6.90133e14			−0.955510			−0.477755	+	0.878493i	$0.658549\pi$
$938$	−2.37628e14	+	1.37195e14i	−0.327253	+	0.188940i
$939$		0			0
$940$	−1.44112e14	+	2.49609e14i	−0.196363	+	0.340111i
$941$	1.09535e14	+	6.32403e13i	0.148459	+	0.0857129i	0.572389	−	0.819982i	$-0.306017\pi$
$941$	1.09535e14	+	6.32403e13i	0.148459	+	0.0857129i	−0.423930	+	0.905695i	$0.639350\pi$
$942$		0			0
$943$	−1.04711e14	−	1.81365e14i	−0.140421	−	0.243217i
$944$			7.65528e13i			0.102118i
$945$		0			0
$946$	2.80773e14			0.370596
$947$	2.64781e14	−	1.52871e14i	0.347646	−	0.200713i	−0.316002	−	0.948758i	$-0.602341\pi$
$947$	2.64781e14	−	1.52871e14i	0.347646	−	0.200713i	0.663648	+	0.748045i	$0.269007\pi$
$948$		0			0
$949$	1.85975e14	−	3.22118e14i	0.241615	−	0.418489i
$950$	5.13117e13	+	2.96248e13i	0.0663129	+	0.0382858i
$951$		0			0
$952$	−3.58725e14	−	6.21330e14i	−0.458751	−	0.794580i
$953$			7.71039e14i			0.980870i	0.871478	+	0.490435i	$0.163162\pi$
$953$			7.71039e14i			0.980870i	−0.871478	+	0.490435i	$0.836838\pi$
$954$		0			0
$955$	−7.49546e14			−0.943586
$956$	1.17326e14	−	6.77384e13i	0.146929	−	0.0848292i
$957$		0			0
$958$	−5.66688e13	+	9.81532e13i	−0.0702289	+	0.121640i
$959$	−5.52640e14	−	3.19067e14i	−0.681318	−	0.393359i
$960$		0			0
$961$	−4.65049e14	−	8.05489e14i	−0.567390	−	0.982749i
$962$		−	1.93138e14i		−	0.234419i
$963$		0			0
$964$	−4.54025e14			−0.545375
$965$	−9.79716e14	+	5.65639e14i	−1.17075	+	0.675932i
$966$		0			0
$967$	−6.36819e14	+	1.10300e15i	−0.753154	+	1.30450i	0.193133	+	0.981172i	$0.438135\pi$
$967$	−6.36819e14	+	1.10300e15i	−0.753154	+	1.30450i	−0.946287	+	0.323328i	$0.895198\pi$
$968$	2.21113e14	+	1.27660e14i	0.260158	+	0.150202i
$969$		0			0
$970$	3.63141e14	+	6.28979e14i	0.422880	+	0.732449i
$971$			4.71364e14i			0.546085i	0.962002	+	0.273043i	$0.0880300\pi$
$971$			4.71364e14i			0.546085i	−0.962002	+	0.273043i	$0.911970\pi$
$972$		0			0
$973$	−1.46905e15			−1.68451
$974$	−8.17149e14	+	4.71781e14i	−0.932195	+	0.538203i
$975$		0			0
$976$	6.95634e13	−	1.20487e14i	0.0785474	−	0.136048i
$977$	9.50315e14	+	5.48665e14i	1.06757	+	0.616360i	0.927516	−	0.373785i	$-0.121940\pi$
$977$	9.50315e14	+	5.48665e14i	1.06757	+	0.616360i	0.140051	+	0.990144i	$0.455273\pi$
$978$		0			0
$979$	−7.45384e12	−	1.29104e13i	−0.00828833	−	0.0143558i
$980$			4.77706e14i			0.528482i
$981$		0			0
$982$	−4.75946e13			−0.0521195
$983$	−1.31843e15	+	7.61198e14i	−1.43645	+	0.829336i	−0.997601	−	0.0692247i	$-0.977947\pi$
$983$	−1.31843e15	+	7.61198e14i	−1.43645	+	0.829336i	−0.438850	+	0.898560i	$0.644614\pi$
$984$		0			0
$985$	2.75361e14	−	4.76939e14i	0.296976	−	0.514377i
$986$	−2.52485e14	−	1.45772e14i	−0.270926	−	0.156419i
$987$		0			0
$988$	−3.34038e13	−	5.78570e13i	−0.0354822	−	0.0614570i
$989$		−	2.78856e14i		−	0.294712i
$990$		0			0
$991$	3.79461e14			0.397008			0.198504	−	0.980100i	$-0.436392\pi$
$991$	3.79461e14			0.397008			0.198504	+	0.980100i	$0.436392\pi$
$992$	−2.14877e14	+	1.24059e14i	−0.223683	+	0.129143i
$993$		0			0
$994$	−1.50142e14	+	2.60054e14i	−0.154729	+	0.267998i
$995$	−3.51168e14	−	2.02747e14i	−0.360080	−	0.207892i
$996$		0			0
$997$	−1.62669e13	−	2.81750e13i	−0.0165131	−	0.0286015i	0.857651	−	0.514233i	$-0.171923\pi$
$997$	−1.62669e13	−	2.81750e13i	−0.0165131	−	0.0286015i	−0.874164	+	0.485631i	$0.838590\pi$
$998$			6.21082e14i			0.627330i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	162.11.d.d.53.4		8
3.2	odd	2	inner	162.11.d.d.53.1		8
9.2	odd	6	inner	162.11.d.d.107.4		8
9.4	even	3		6.11.b.a.5.3	yes	4
9.5	odd	6		6.11.b.a.5.1	✓	4
9.7	even	3	inner	162.11.d.d.107.1		8
36.23	even	6		48.11.e.d.17.3		4
36.31	odd	6		48.11.e.d.17.4		4
45.4	even	6		150.11.d.a.101.2		4
45.13	odd	12		150.11.b.a.149.7		8
45.14	odd	6		150.11.d.a.101.4		4
45.22	odd	12		150.11.b.a.149.2		8
45.23	even	12		150.11.b.a.149.1		8
45.32	even	12		150.11.b.a.149.8		8
72.5	odd	6		192.11.e.g.65.3		4
72.13	even	6		192.11.e.g.65.4		4
72.59	even	6		192.11.e.h.65.2		4
72.67	odd	6		192.11.e.h.65.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6.11.b.a.5.1	✓	4	9.5	odd	6
6.11.b.a.5.3	yes	4	9.4	even	3
48.11.e.d.17.3		4	36.23	even	6
48.11.e.d.17.4		4	36.31	odd	6
150.11.b.a.149.1		8	45.23	even	12
150.11.b.a.149.2		8	45.22	odd	12
150.11.b.a.149.7		8	45.13	odd	12
150.11.b.a.149.8		8	45.32	even	12
150.11.d.a.101.2		4	45.4	even	6
150.11.d.a.101.4		4	45.14	odd	6
162.11.d.d.53.1		8	3.2	odd	2	inner
162.11.d.d.53.4		8	1.1	even	1	trivial
162.11.d.d.107.1		8	9.7	even	3	inner
162.11.d.d.107.4		8	9.2	odd	6	inner
192.11.e.g.65.3		4	72.5	odd	6
192.11.e.g.65.4		4	72.13	even	6
192.11.e.h.65.1		4	72.67	odd	6
192.11.e.h.65.2		4	72.59	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)

\(f(q)\)	\(=\)	\(q+(19.5959 - 11.3137i) q^{2} +(256.000 - 443.405i) q^{4} +(3144.08 + 1815.24i) q^{5} +(11613.3 + 20114.8i) q^{7} -11585.2i q^{8} +O(q^{10})\)	\(q+(19.5959 - 11.3137i) q^{2} +(256.000 - 443.405i) q^{4} +(3144.08 + 1815.24i) q^{5} +(11613.3 + 20114.8i) q^{7} -11585.2i q^{8} +82148.2 q^{10} +(54076.9 - 31221.3i) q^{11} +(85080.3 - 147363. i) q^{13} +(455145. + 262778. i) q^{14} +(-131072. - 227023. i) q^{16} -2.66626e6i q^{17} +766825. q^{19} +(1.60977e6 - 929401. i) q^{20} +(706458. - 1.22362e6i) q^{22} +(-1.21526e6 - 701633. i) q^{23} +(1.70736e6 + 2.95723e6i) q^{25} -3.85029e6i q^{26} +1.18920e7 q^{28} +(4.18503e6 - 2.41623e6i) q^{29} +(2.09149e7 - 3.62256e7i) q^{31} +(-5.13695e6 - 2.96582e6i) q^{32} +(-3.01653e7 - 5.22478e7i) q^{34} +8.43233e7i q^{35} +5.01619e7 q^{37} +(1.50266e7 - 8.67564e6i) q^{38} +(2.10299e7 - 3.64249e7i) q^{40} +(1.29245e8 + 7.46194e7i) q^{41} +(9.93595e7 + 1.72096e8i) q^{43} -3.19706e7i q^{44} -3.17523e7 q^{46} +(-1.34285e8 + 7.75293e7i) q^{47} +(-1.28498e8 + 2.22565e8i) q^{49} +(6.69144e7 + 3.86331e7i) q^{50} +(-4.35611e7 - 7.54501e7i) q^{52} +4.21541e7i q^{53} +2.26696e8 q^{55} +(2.33034e8 - 1.34542e8i) q^{56} +(5.46730e7 - 9.46964e7i) q^{58} +(-2.52902e8 - 1.46013e8i) q^{59} +(2.65363e8 + 4.59623e8i) q^{61} -9.46499e8i q^{62} -1.34218e8 q^{64} +(5.34999e8 - 3.08882e8i) q^{65} +(-2.61047e8 + 4.52146e8i) q^{67} +(-1.18223e9 - 6.82563e8i) q^{68} +(9.54009e8 + 1.65239e9i) q^{70} +5.71364e8i q^{71} +2.18588e9 q^{73} +(9.82968e8 - 5.67517e8i) q^{74} +(1.96307e8 - 3.40014e8i) q^{76} +(1.25602e9 + 7.25163e8i) q^{77} +(-9.82961e8 - 1.70254e9i) q^{79} -9.51707e8i q^{80} +3.37689e9 q^{82} +(-1.89277e9 + 1.09279e9i) q^{83} +(4.83989e9 - 8.38294e9i) q^{85} +(3.89408e9 + 2.24825e9i) q^{86} +(-3.61707e8 - 6.26494e8i) q^{88} -2.38742e8i q^{89} +3.95224e9 q^{91} +(-6.22215e8 + 3.59236e8i) q^{92} +(-1.75429e9 + 3.03852e9i) q^{94} +(2.41096e9 + 1.39197e9i) q^{95} +(4.42056e9 + 7.65664e9i) q^{97} +5.81517e9i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 2048 q^{4} + 45112 q^{7}+O(q^{10}) \) 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

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