LMFDB - Embedded newform 162.10.c.j.55.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [162,10,Mod(55,162)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

N = Newforms(chi, 10, names="a")

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

chi := DirichletCharacter("162.55");

S:= CuspForms(chi, 10);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$83.4358054585$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 1 $ x^2 - x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 54)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			55.1
Root			$0.500000 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	162.55
Dual form			162.10.c.j.109.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(8.00000 - 13.8564i) q^{2} +(-128.000 - 221.703i) q^{4} +(588.000 + 1018.45i) q^{5} +(5736.50 - 9935.91i) q^{7} -4096.00 q^{8} +O(q^{10})$	\(q+(8.00000 - 13.8564i) q^{2} +(-128.000 - 221.703i) q^{4} +(588.000 + 1018.45i) q^{5} +(5736.50 - 9935.91i) q^{7} -4096.00 q^{8} +18816.0 q^{10} +(-29244.0 + 50652.1i) q^{11} +(53085.5 + 91946.8i) q^{13} +(-91784.0 - 158975. i) q^{14} +(-32768.0 + 56755.8i) q^{16} -593352. q^{17} -210967. q^{19} +(150528. - 260722. i) q^{20} +(467904. + 810434. i) q^{22} +(-1.04392e6 - 1.80812e6i) q^{23} +(285074. - 493764. i) q^{25} +1.69874e6 q^{26} -2.93709e6 q^{28} +(-1.19971e6 + 2.07796e6i) q^{29} +(594386. + 1.02951e6i) q^{31} +(524288. + 908093. i) q^{32} +(-4.74682e6 + 8.22173e6i) q^{34} +1.34922e7 q^{35} +1.15782e7 q^{37} +(-1.68774e6 + 2.92324e6i) q^{38} +(-2.40845e6 - 4.17155e6i) q^{40} +(-1.19708e7 - 2.07341e7i) q^{41} +(5.32992e6 - 9.23169e6i) q^{43} +1.49729e7 q^{44} -3.34053e7 q^{46} +(-1.70270e7 + 2.94916e7i) q^{47} +(-4.56381e7 - 7.90474e7i) q^{49} +(-4.56119e6 - 7.90022e6i) q^{50} +(1.35899e7 - 2.35384e7i) q^{52} -4.27411e7 q^{53} -6.87819e7 q^{55} +(-2.34967e7 + 4.06975e7i) q^{56} +(1.91954e7 + 3.32474e7i) q^{58} +(-3.71040e7 - 6.42660e7i) q^{59} +(-4.05120e7 + 7.01689e7i) q^{61} +1.90204e7 q^{62} +1.67772e7 q^{64} +(-6.24285e7 + 1.08129e8i) q^{65} +(9.82543e6 + 1.70181e7i) q^{67} +(7.59491e7 + 1.31548e8i) q^{68} +(1.07938e8 - 1.86954e8i) q^{70} -1.84185e8 q^{71} -2.57038e8 q^{73} +(9.26255e7 - 1.60432e8i) q^{74} +(2.70038e7 + 4.67719e7i) q^{76} +(3.35516e8 + 5.81131e8i) q^{77} +(-3.25796e8 + 5.64295e8i) q^{79} -7.70703e7 q^{80} -3.83066e8 q^{82} +(8.81930e6 - 1.52755e7i) q^{83} +(-3.48891e8 - 6.04297e8i) q^{85} +(-8.52787e7 - 1.47707e8i) q^{86} +(1.19783e8 - 2.07471e8i) q^{88} -5.16255e8 q^{89} +1.21810e9 q^{91} +(-2.67242e8 + 4.62878e8i) q^{92} +(2.72432e8 + 4.71866e8i) q^{94} +(-1.24049e8 - 2.14858e8i) q^{95} +(2.17116e8 - 3.76057e8i) q^{97} -1.46042e9 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 16 q^{2} - 256 q^{4} + 1176 q^{5} + 11473 q^{7} - 8192 q^{8}+O(q^{10}) $ 2 * q + 16 * q^2 - 256 * q^4 + 1176 * q^5 + 11473 * q^7 - 8192 * q^8	\( 2 q + 16 q^{2} - 256 q^{4} + 1176 q^{5} + 11473 q^{7} - 8192 q^{8} + 37632 q^{10} - 58488 q^{11} + 106171 q^{13} - 183568 q^{14} - 65536 q^{16} - 1186704 q^{17} - 421934 q^{19} + 301056 q^{20} + 935808 q^{22} - 2087832 q^{23} + 570149 q^{25} + 3397472 q^{26} - 5874176 q^{28} - 2399424 q^{29} + 1188772 q^{31} + 1048576 q^{32} - 9493632 q^{34} + 26984496 q^{35} + 23156374 q^{37} - 3375472 q^{38} - 4816896 q^{40} - 23941632 q^{41} + 10659832 q^{43} + 29945856 q^{44} - 66810624 q^{46} - 34054008 q^{47} - 91276122 q^{49} - 9122384 q^{50} + 27179776 q^{52} - 85482144 q^{53} - 137563776 q^{55} - 46993408 q^{56} + 38390784 q^{58} - 74207928 q^{59} - 81024095 q^{61} + 38040704 q^{62} + 33554432 q^{64} - 124857096 q^{65} + 19650859 q^{67} + 151898112 q^{68} + 215875968 q^{70} - 368370720 q^{71} - 514075406 q^{73} + 185250992 q^{74} + 54007552 q^{76} + 671032824 q^{77} - 651592289 q^{79} - 154140672 q^{80} - 766132224 q^{82} + 17638608 q^{83} - 697781952 q^{85} - 170557312 q^{86} + 239566848 q^{88} - 1032509520 q^{89} + 2436199766 q^{91} - 534484992 q^{92} + 544864128 q^{94} - 248097192 q^{95} + 434232691 q^{97} - 2920835904 q^{98}+O(q^{100}) \) 2 * q + 16 * q^2 - 256 * q^4 + 1176 * q^5 + 11473 * q^7 - 8192 * q^8 + 37632 * q^10 - 58488 * q^11 + 106171 * q^13 - 183568 * q^14 - 65536 * q^16 - 1186704 * q^17 - 421934 * q^19 + 301056 * q^20 + 935808 * q^22 - 2087832 * q^23 + 570149 * q^25 + 3397472 * q^26 - 5874176 * q^28 - 2399424 * q^29 + 1188772 * q^31 + 1048576 * q^32 - 9493632 * q^34 + 26984496 * q^35 + 23156374 * q^37 - 3375472 * q^38 - 4816896 * q^40 - 23941632 * q^41 + 10659832 * q^43 + 29945856 * q^44 - 66810624 * q^46 - 34054008 * q^47 - 91276122 * q^49 - 9122384 * q^50 + 27179776 * q^52 - 85482144 * q^53 - 137563776 * q^55 - 46993408 * q^56 + 38390784 * q^58 - 74207928 * q^59 - 81024095 * q^61 + 38040704 * q^62 + 33554432 * q^64 - 124857096 * q^65 + 19650859 * q^67 + 151898112 * q^68 + 215875968 * q^70 - 368370720 * q^71 - 514075406 * q^73 + 185250992 * q^74 + 54007552 * q^76 + 671032824 * q^77 - 651592289 * q^79 - 154140672 * q^80 - 766132224 * q^82 + 17638608 * q^83 - 697781952 * q^85 - 170557312 * q^86 + 239566848 * q^88 - 1032509520 * q^89 + 2436199766 * q^91 - 534484992 * q^92 + 544864128 * q^94 - 248097192 * q^95 + 434232691 * q^97 - 2920835904 * q^98

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	8.00000	−	13.8564i	0.353553	−	0.612372i
$2$	8.00000	−	13.8564i	0.353553	−	0.612372i
$3$		0			0
$3$		0			0
$4$	−128.000	−	221.703i	−0.250000	−	0.433013i
$5$	588.000	+	1018.45i	0.420739	+	0.728741i	0.996012	−	0.0892207i	$-0.0284376\pi$
$5$	588.000	+	1018.45i	0.420739	+	0.728741i	−0.575273	+	0.817961i	$0.695104\pi$
$6$		0			0
$7$	5736.50	−	9935.91i	0.903038	−	1.56411i	0.0795075	−	0.996834i	$-0.474665\pi$
$7$	5736.50	−	9935.91i	0.903038	−	1.56411i	0.823530	−	0.567273i	$-0.192001\pi$
$8$	−4096.00			−0.353553
$9$		0			0
$10$	18816.0			0.595014
$11$	−29244.0	+	50652.1i	−0.602240	+	1.04311i	0.390241	+	0.920713i	$0.372392\pi$
$11$	−29244.0	+	50652.1i	−0.602240	+	1.04311i	−0.992481	+	0.122398i	$0.960942\pi$
$12$		0			0
$13$	53085.5	+	91946.8i	0.515503	+	0.892877i	0.999838	+	0.0179943i	$0.00572807\pi$
$13$	53085.5	+	91946.8i	0.515503	+	0.892877i	−0.484336	+	0.874882i	$0.660939\pi$
$14$	−91784.0	−	158975.i	−0.638544	−	1.10599i
$15$		0			0
$16$	−32768.0	+	56755.8i	−0.125000	+	0.216506i
$17$	−593352.			−1.72303			−0.861514	−	0.507734i	$-0.830483\pi$
$17$	−593352.			−1.72303			−0.861514	+	0.507734i	$0.830483\pi$
$18$		0			0
$19$	−210967.			−0.371384			−0.185692	−	0.982608i	$-0.559453\pi$
$19$	−210967.			−0.371384			−0.185692	+	0.982608i	$0.559453\pi$
$20$	150528.	−	260722.i	0.210369	−	0.364370i
$21$		0			0
$22$	467904.	+	810434.i	0.425848	+	0.737591i
$23$	−1.04392e6	−	1.80812e6i	−0.777840	−	1.34726i	−0.933184	−	0.359398i	$-0.882982\pi$
$23$	−1.04392e6	−	1.80812e6i	−0.777840	−	1.34726i	0.155344	−	0.987860i	$-0.450351\pi$
$24$		0			0
$25$	285074.	−	493764.i	0.145958	−	0.252807i
$26$	1.69874e6			0.729031
$27$		0			0
$28$	−2.93709e6			−0.903038
$29$	−1.19971e6	+	2.07796e6i	−0.314982	+	0.545565i	−0.979434	−	0.201766i	$-0.935332\pi$
$29$	−1.19971e6	+	2.07796e6i	−0.314982	+	0.545565i	0.664452	+	0.747331i	$0.268665\pi$
$30$		0			0
$31$	594386.	+	1.02951e6i	0.115596	+	0.200217i	0.918018	−	0.396540i	$-0.129789\pi$
$31$	594386.	+	1.02951e6i	0.115596	+	0.200217i	−0.802422	+	0.596757i	$0.796456\pi$
$32$	524288.	+	908093.i	0.0883883	+	0.153093i
$33$		0			0
$34$	−4.74682e6	+	8.22173e6i	−0.609182	+	1.05513i
$35$	1.34922e7			1.51977
$36$		0			0
$37$	1.15782e7			1.01562			0.507812	−	0.861468i	$-0.330455\pi$
$37$	1.15782e7			1.01562			0.507812	+	0.861468i	$0.330455\pi$
$38$	−1.68774e6	+	2.92324e6i	−0.131304	+	0.227425i
$39$		0			0
$40$	−2.40845e6	−	4.17155e6i	−0.148754	−	0.257649i
$41$	−1.19708e7	−	2.07341e7i	−0.661601	−	1.14593i	−0.980195	−	0.198036i	$-0.936544\pi$
$41$	−1.19708e7	−	2.07341e7i	−0.661601	−	1.14593i	0.318593	−	0.947891i	$-0.396790\pi$
$42$		0			0
$43$	5.32992e6	−	9.23169e6i	0.237746	−	0.411787i	−0.722322	−	0.691557i	$-0.756925\pi$
$43$	5.32992e6	−	9.23169e6i	0.237746	−	0.411787i	0.960067	+	0.279770i	$0.0902582\pi$
$44$	1.49729e7			0.602240
$45$		0			0
$46$	−3.34053e7			−1.10003
$47$	−1.70270e7	+	2.94916e7i	−0.508977	+	0.881573i	0.490969	+	0.871177i	$0.336643\pi$
$47$	−1.70270e7	+	2.94916e7i	−0.508977	+	0.881573i	−0.999946	+	0.0103966i	$0.996691\pi$
$48$		0			0
$49$	−4.56381e7	−	7.90474e7i	−1.13095	−	1.95887i
$50$	−4.56119e6	−	7.90022e6i	−0.103208	−	0.178761i
$51$		0			0
$52$	1.35899e7	−	2.35384e7i	0.257751	−	0.446438i
$53$	−4.27411e7			−0.744053			−0.372027	−	0.928222i	$-0.621337\pi$
$53$	−4.27411e7			−0.744053			−0.372027	+	0.928222i	$0.621337\pi$
$54$		0			0
$55$	−6.87819e7			−1.01354
$56$	−2.34967e7	+	4.06975e7i	−0.319272	+	0.552995i
$57$		0			0
$58$	1.91954e7	+	3.32474e7i	0.222726	+	0.385773i
$59$	−3.71040e7	−	6.42660e7i	−0.398645	−	0.690473i	0.594914	−	0.803789i	$-0.297186\pi$
$59$	−3.71040e7	−	6.42660e7i	−0.398645	−	0.690473i	−0.993559	+	0.113316i	$0.963853\pi$
$60$		0			0
$61$	−4.05120e7	+	7.01689e7i	−0.374628	+	0.648874i	−0.990271	−	0.139151i	$-0.955563\pi$
$61$	−4.05120e7	+	7.01689e7i	−0.374628	+	0.648874i	0.615644	+	0.788025i	$0.288896\pi$
$62$	1.90204e7			0.163477
$63$		0			0
$64$	1.67772e7			0.125000
$65$	−6.24285e7	+	1.08129e8i	−0.433784	+	0.751335i
$66$		0			0
$67$	9.82543e6	+	1.70181e7i	0.0595683	+	0.103175i	0.894272	−	0.447524i	$-0.147694\pi$
$67$	9.82543e6	+	1.70181e7i	0.0595683	+	0.103175i	−0.834703	+	0.550700i	$0.814361\pi$
$68$	7.59491e7	+	1.31548e8i	0.430757	+	0.746093i
$69$		0			0
$70$	1.07938e8	−	1.86954e8i	0.537320	−	0.930666i
$71$	−1.84185e8			−0.860186			−0.430093	−	0.902785i	$-0.641519\pi$
$71$	−1.84185e8			−0.860186			−0.430093	+	0.902785i	$0.641519\pi$
$72$		0			0
$73$	−2.57038e8			−1.05936			−0.529680	−	0.848197i	$-0.677688\pi$
$73$	−2.57038e8			−1.05936			−0.529680	+	0.848197i	$0.677688\pi$
$74$	9.26255e7	−	1.60432e8i	0.359077	−	0.621940i
$75$		0			0
$76$	2.70038e7	+	4.67719e7i	0.0928460	+	0.160814i
$77$	3.35516e8	+	5.81131e8i	1.08769	+	1.88394i
$78$		0			0
$79$	−3.25796e8	+	5.64295e8i	−0.941075	+	1.62999i	−0.177648	+	0.984094i	$0.556849\pi$
$79$	−3.25796e8	+	5.64295e8i	−0.941075	+	1.62999i	−0.763426	+	0.645895i	$0.776484\pi$
$80$	−7.70703e7			−0.210369
$81$		0			0
$82$	−3.83066e8			−0.935646
$83$	8.81930e6	−	1.52755e7i	0.0203978	−	0.0353300i	−0.855646	−	0.517561i	$-0.826840\pi$
$83$	8.81930e6	−	1.52755e7i	0.0203978	−	0.0353300i	0.876044	+	0.482231i	$0.160173\pi$
$84$		0			0
$85$	−3.48891e8	−	6.04297e8i	−0.724944	−	1.25564i
$86$	−8.52787e7	−	1.47707e8i	−0.168111	−	0.291178i
$87$		0			0
$88$	1.19783e8	−	2.07471e8i	0.212924	−	0.368795i
$89$	−5.16255e8			−0.872186			−0.436093	−	0.899902i	$-0.643638\pi$
$89$	−5.16255e8			−0.872186			−0.436093	+	0.899902i	$0.643638\pi$
$90$		0			0
$91$	1.21810e9			1.86207
$92$	−2.67242e8	+	4.62878e8i	−0.388920	+	0.673629i
$93$		0			0
$94$	2.72432e8	+	4.71866e8i	0.359901	+	0.623367i
$95$	−1.24049e8	−	2.14858e8i	−0.156256	−	0.270643i
$96$		0			0
$97$	2.17116e8	−	3.76057e8i	0.249012	−	0.431301i	−0.714240	−	0.699901i	$-0.753228\pi$
$97$	2.17116e8	−	3.76057e8i	0.249012	−	0.431301i	0.963252	+	0.268600i	$0.0865609\pi$
$98$	−1.46042e9			−1.59941
$99$		0			0
$100$	−1.45958e8			−0.145958
$101$	−4.23301e7	+	7.33180e7i	−0.0404766	+	0.0701075i	−0.885554	−	0.464537i	$-0.846221\pi$
$101$	−4.23301e7	+	7.33180e7i	−0.0404766	+	0.0701075i	0.845077	+	0.534644i	$0.179554\pi$
$102$		0			0
$103$	−3.34900e7	−	5.80065e7i	−0.0293189	−	0.0507819i	0.850994	−	0.525176i	$-0.176001\pi$
$103$	−3.34900e7	−	5.80065e7i	−0.0293189	−	0.0507819i	−0.880313	+	0.474394i	$0.842667\pi$
$104$	−2.17438e8	−	3.76614e8i	−0.182258	−	0.315680i
$105$		0			0
$106$	−3.41929e8	+	5.92238e8i	−0.263063	+	0.455638i
$107$	−2.22121e9			−1.63818			−0.819091	−	0.573663i	$-0.805522\pi$
$107$	−2.22121e9			−1.63818			−0.819091	+	0.573663i	$0.805522\pi$
$108$		0			0
$109$	−4.45158e8			−0.302061			−0.151031	−	0.988529i	$-0.548259\pi$
$109$	−4.45158e8			−0.302061			−0.151031	+	0.988529i	$0.548259\pi$
$110$	−5.50255e8	+	9.53070e8i	−0.358341	+	0.620666i
$111$		0			0
$112$	3.75947e8	+	6.51160e8i	0.225759	+	0.391027i
$113$	−3.75191e8	−	6.49850e8i	−0.216471	−	0.374939i	0.737256	−	0.675614i	$-0.236121\pi$
$113$	−3.75191e8	−	6.49850e8i	−0.216471	−	0.374939i	−0.953727	+	0.300675i	$0.902788\pi$
$114$		0			0
$115$	1.22765e9	−	2.12634e9i	0.654535	−	1.13369i
$116$	6.14253e8			0.314982
$117$		0			0
$118$	−1.18733e9			−0.563769
$119$	−3.40376e9	+	5.89549e9i	−1.55596	+	2.69500i
$120$		0			0
$121$	−5.31449e8	−	9.20497e8i	−0.225386	−	0.390381i
$122$	6.48193e8	+	1.12270e9i	0.264902	+	0.458823i
$123$		0			0
$124$	1.52163e8	−	2.63554e8i	0.0577978	−	0.100109i
$125$	2.96737e9			1.08712
$126$		0			0
$127$	4.12423e9			1.40678			0.703391	−	0.710803i	$-0.251668\pi$
$127$	4.12423e9			1.40678			0.703391	+	0.710803i	$0.251668\pi$
$128$	1.34218e8	−	2.32472e8i	0.0441942	−	0.0765466i
$129$		0			0
$130$	9.98857e8	+	1.73007e9i	0.306731	+	0.531274i
$131$	2.15181e9	+	3.72704e9i	0.638384	+	1.10571i	0.985787	+	0.167998i	$0.0537303\pi$
$131$	2.15181e9	+	3.72704e9i	0.638384	+	1.10571i	−0.347403	+	0.937716i	$0.612936\pi$
$132$		0			0
$133$	−1.21021e9	+	2.09615e9i	−0.335374	+	0.580884i
$134$	3.14414e8			0.0842422
$135$		0			0
$136$	2.43037e9			0.609182
$137$	−3.30177e9	+	5.71884e9i	−0.800764	+	1.38696i	0.118350	+	0.992972i	$0.462239\pi$
$137$	−3.30177e9	+	5.71884e9i	−0.800764	+	1.38696i	−0.919114	+	0.393992i	$0.871094\pi$
$138$		0			0
$139$	4.26538e9	+	7.38785e9i	0.969150	+	1.67862i	0.698025	+	0.716073i	$0.254062\pi$
$139$	4.26538e9	+	7.38785e9i	0.969150	+	1.67862i	0.271125	+	0.962544i	$0.412604\pi$
$140$	−1.72701e9	−	2.99127e9i	−0.379943	−	0.658080i
$141$		0			0
$142$	−1.47348e9	+	2.55215e9i	−0.304122	+	0.526754i
$143$	−6.20973e9			−1.24183
$144$		0			0
$145$	−2.82172e9			−0.530101
$146$	−2.05630e9	+	3.56162e9i	−0.374541	+	0.648723i
$147$		0			0
$148$	−1.48201e9	−	2.56691e9i	−0.253906	−	0.439778i
$149$	−3.92080e9	−	6.79103e9i	−0.651683	−	1.12875i	−0.982714	−	0.185129i	$-0.940730\pi$
$149$	−3.92080e9	−	6.79103e9i	−0.651683	−	1.12875i	0.331031	−	0.943620i	$-0.392603\pi$
$150$		0			0
$151$	1.46794e9	−	2.54255e9i	0.229780	−	0.397991i	−0.727963	−	0.685617i	$-0.759533\pi$
$151$	1.46794e9	−	2.54255e9i	0.229780	−	0.397991i	0.957743	+	0.287626i	$0.0928659\pi$
$152$	8.64121e8			0.131304
$153$		0			0
$154$	1.07365e10			1.53823
$155$	−6.98998e8	+	1.21070e9i	−0.0972710	+	0.168478i
$156$		0			0
$157$	−4.34567e9	−	7.52692e9i	−0.570832	−	0.988709i	−0.996481	−	0.0838211i	$-0.973288\pi$
$157$	−4.34567e9	−	7.52692e9i	−0.570832	−	0.988709i	0.425649	−	0.904888i	$-0.360046\pi$
$158$	5.21274e9	+	9.02873e9i	0.665440	+	1.15258i
$159$		0			0
$160$	−6.16563e8	+	1.06792e9i	−0.0743768	+	0.128824i
$161$	−2.39537e10			−2.80968
$162$		0			0
$163$	−9.70380e9			−1.07671			−0.538353	−	0.842719i	$-0.680953\pi$
$163$	−9.70380e9			−1.07671			−0.538353	+	0.842719i	$0.680953\pi$
$164$	−3.06453e9	+	5.30792e9i	−0.330801	+	0.572964i
$165$		0			0
$166$	−1.41109e8	−	2.44408e8i	−0.0144234	−	0.0249821i
$167$	9.75631e8	+	1.68984e9i	0.0970647	+	0.168121i	0.910468	−	0.413579i	$-0.135721\pi$
$167$	9.75631e8	+	1.68984e9i	0.0970647	+	0.168121i	−0.813404	+	0.581700i	$0.802388\pi$
$168$		0			0
$169$	−3.33891e8	+	5.78316e8i	−0.0314858	+	0.0545350i
$170$	−1.11645e10			−1.02523
$171$		0			0
$172$	−2.72892e9			−0.237746
$173$	2.61697e9	−	4.53273e9i	0.222122	−	0.384727i	−0.733330	−	0.679873i	$-0.762035\pi$
$173$	2.61697e9	−	4.53273e9i	0.222122	−	0.384727i	0.955452	+	0.295146i	$0.0953683\pi$
$174$		0			0
$175$	−3.27066e9	−	5.66495e9i	−0.263611	−	0.456588i
$176$	−1.91653e9	−	3.31954e9i	−0.150560	−	0.260778i
$177$		0			0
$178$	−4.13004e9	+	7.15344e9i	−0.308364	+	0.534103i
$179$	1.85510e10			1.35061			0.675304	−	0.737539i	$-0.264012\pi$
$179$	1.85510e10			1.35061			0.675304	+	0.737539i	$0.264012\pi$
$180$		0			0
$181$	−2.37080e10			−1.64188			−0.820940	−	0.571015i	$-0.806550\pi$
$181$	−2.37080e10			−1.64188			−0.820940	+	0.571015i	$0.806550\pi$
$182$	9.74480e9	−	1.68785e10i	0.658342	−	1.14028i
$183$		0			0
$184$	4.27588e9	+	7.40604e9i	0.275008	+	0.476328i
$185$	6.80797e9	+	1.17918e10i	0.427312	+	0.740126i
$186$		0			0
$187$	1.73520e10	−	3.00545e10i	1.03768	−	1.79731i
$188$	8.71783e9			0.508977
$189$		0			0
$190$	−3.96956e9			−0.220979
$191$	5.39976e9	−	9.35265e9i	0.293578	−	0.508493i	−0.681075	−	0.732214i	$-0.738487\pi$
$191$	5.39976e9	−	9.35265e9i	0.293578	−	0.508493i	0.974653	+	0.223721i	$0.0718205\pi$
$192$		0			0
$193$	−8.87551e9	−	1.53728e10i	−0.460453	−	0.797528i	0.538530	−	0.842606i	$-0.318980\pi$
$193$	−8.87551e9	−	1.53728e10i	−0.460453	−	0.797528i	−0.998983	+	0.0450781i	$0.985646\pi$
$194$	−3.47386e9	−	6.01690e9i	−0.176078	−	0.304976i
$195$		0			0
$196$	−1.16833e10	+	2.02361e10i	−0.565477	+	0.979435i
$197$	−1.21392e9			−0.0574239			−0.0287120	−	0.999588i	$-0.509141\pi$
$197$	−1.21392e9			−0.0574239			−0.0287120	+	0.999588i	$0.509141\pi$
$198$		0			0
$199$	1.57326e10			0.711151			0.355575	−	0.934648i	$-0.384285\pi$
$199$	1.57326e10			0.711151			0.355575	+	0.934648i	$0.384285\pi$
$200$	−1.16767e9	+	2.02246e9i	−0.0516040	+	0.0893807i
$201$		0			0
$202$	6.77282e8	+	1.17309e9i	0.0286212	+	0.0495735i
$203$	1.37643e10	+	2.38405e10i	0.568882	+	0.985332i
$204$		0			0
$205$	1.40777e10	−	2.43833e10i	0.556722	−	0.964271i
$206$	−1.07168e9			−0.0414632
$207$		0			0
$208$	−6.95802e9			−0.257751
$209$	6.16952e9	−	1.06859e10i	0.223662	−	0.387395i
$210$		0			0
$211$	−4.18347e9	−	7.24598e9i	−0.145300	−	0.251667i	0.784185	−	0.620527i	$-0.213081\pi$
$211$	−4.18347e9	−	7.24598e9i	−0.145300	−	0.251667i	−0.929485	+	0.368860i	$0.879748\pi$
$212$	5.47086e9	+	9.47580e9i	0.186013	+	0.322184i
$213$		0			0
$214$	−1.77697e10	+	3.07780e10i	−0.579185	+	1.00318i
$215$	1.25360e10			0.400115
$216$		0			0
$217$	1.36388e10			0.417548
$218$	−3.56126e9	+	6.16829e9i	−0.106795	+	0.184974i
$219$		0			0
$220$	8.80408e9	+	1.52491e10i	0.253386	+	0.438877i
$221$	−3.14984e10	−	5.45568e10i	−0.888225	−	1.53845i
$222$		0			0
$223$	−2.39561e10	+	4.14931e10i	−0.648699	+	1.12358i	0.334735	+	0.942312i	$0.391353\pi$
$223$	−2.39561e10	+	4.14931e10i	−0.648699	+	1.12358i	−0.983434	+	0.181267i	$0.941980\pi$
$224$	1.20303e10			0.319272
$225$		0			0
$226$	−1.20061e10			−0.306136
$227$	−1.35585e10	+	2.34841e10i	−0.338920	+	0.587026i	−0.984230	−	0.176895i	$-0.943395\pi$
$227$	−1.35585e10	+	2.34841e10i	−0.338920	+	0.587026i	0.645310	+	0.763921i	$0.276728\pi$
$228$		0			0
$229$	−2.67580e10	−	4.63463e10i	−0.642976	−	1.11367i	−0.984765	−	0.173890i	$-0.944366\pi$
$229$	−2.67580e10	−	4.63463e10i	−0.642976	−	1.11367i	0.341789	−	0.939777i	$-0.388967\pi$
$230$	−1.96423e10	−	3.40215e10i	−0.462826	−	0.801638i
$231$		0			0
$232$	4.91402e9	−	8.51133e9i	0.111363	−	0.192886i
$233$	7.18897e10			1.59796			0.798978	−	0.601360i	$-0.205374\pi$
$233$	7.18897e10			1.59796			0.798978	+	0.601360i	$0.205374\pi$
$234$		0			0
$235$	−4.00475e10			−0.856584
$236$	−9.49861e9	+	1.64521e10i	−0.199322	+	0.345237i
$237$		0			0
$238$	5.44602e10	+	9.43279e10i	1.10023	+	1.90565i
$239$	−1.38525e10	−	2.39932e10i	−0.274623	−	0.475661i	0.695417	−	0.718606i	$-0.255220\pi$
$239$	−1.38525e10	−	2.39932e10i	−0.274623	−	0.475661i	−0.970040	+	0.242946i	$0.921886\pi$
$240$		0			0
$241$	−1.16952e10	+	2.02566e10i	−0.223321	+	0.386804i	−0.955814	−	0.293971i	$-0.905023\pi$
$241$	−1.16952e10	+	2.02566e10i	−0.223321	+	0.386804i	0.732493	+	0.680774i	$0.238357\pi$
$242$	−1.70064e10			−0.318744
$243$		0			0
$244$	2.07422e10			0.374628
$245$	5.36704e10	−	9.29598e10i	0.951672	−	1.64834i
$246$		0			0
$247$	−1.11993e10	−	1.93977e10i	−0.191449	−	0.331600i
$248$	−2.43461e9	−	4.21686e9i	−0.0408692	−	0.0707875i
$249$		0			0
$250$	2.37390e10	−	4.11171e10i	0.384354	−	0.665721i
$251$	9.43150e10			1.49985			0.749927	−	0.661521i	$-0.230089\pi$
$251$	9.43150e10			1.49985			0.749927	+	0.661521i	$0.230089\pi$
$252$		0			0
$253$	1.22113e11			1.87379
$254$	3.29939e10	−	5.71471e10i	0.497372	−	0.861474i
$255$		0			0
$256$	−2.14748e9	−	3.71955e9i	−0.0312500	−	0.0541266i
$257$	5.75263e9	+	9.96384e9i	0.0822559	+	0.142471i	0.904219	−	0.427070i	$-0.140454\pi$
$257$	5.75263e9	+	9.96384e9i	0.0822559	+	0.142471i	−0.821963	+	0.569541i	$0.807121\pi$
$258$		0			0
$259$	6.64183e10	−	1.15040e11i	0.917146	−	1.58854i
$260$	3.19634e10			0.433784
$261$		0			0
$262$	6.88578e10			0.902812
$263$	8.52613e8	−	1.47677e9i	0.0109888	−	0.0190332i	−0.860479	−	0.509486i	$-0.829835\pi$
$263$	8.52613e8	−	1.47677e9i	0.0109888	−	0.0190332i	0.871468	+	0.490453i	$0.163169\pi$
$264$		0			0
$265$	−2.51318e10	−	4.35295e10i	−0.313052	−	0.542222i
$266$	1.93634e10	+	3.35384e10i	0.237145	+	0.410747i
$267$		0			0
$268$	2.51531e9	−	4.35664e9i	0.0297841	−	0.0515876i
$269$	9.57785e10			1.11528			0.557638	−	0.830084i	$-0.311708\pi$
$269$	9.57785e10			1.11528			0.557638	+	0.830084i	$0.311708\pi$
$270$		0			0
$271$	−1.62837e11			−1.83397			−0.916985	−	0.398921i	$-0.869385\pi$
$271$	−1.62837e11			−1.83397			−0.916985	+	0.398921i	$0.869385\pi$
$272$	1.94430e10	−	3.36762e10i	0.215378	−	0.373046i
$273$		0			0
$274$	5.28283e10	+	9.15014e10i	0.566225	+	0.980731i
$275$	1.66734e10	+	2.88792e10i	0.175804	+	0.304501i
$276$		0			0
$277$	−2.53483e10	+	4.39045e10i	−0.258696	+	0.448075i	−0.965893	−	0.258942i	$-0.916626\pi$
$277$	−2.53483e10	+	4.39045e10i	−0.258696	+	0.448075i	0.707197	+	0.707017i	$0.249959\pi$
$278$	1.36492e11			1.37059
$279$		0			0
$280$	−5.52642e10			−0.537320
$281$	5.57995e10	−	9.66475e10i	0.533890	−	0.924724i	−0.465326	−	0.885139i	$-0.654063\pi$
$281$	5.57995e10	−	9.66475e10i	0.533890	−	0.924724i	0.999216	−	0.0395851i	$-0.0126036\pi$
$282$		0			0
$283$	1.29405e9	+	2.24137e9i	0.0119926	+	0.0207718i	0.871959	−	0.489578i	$-0.162849\pi$
$283$	1.29405e9	+	2.24137e9i	0.0119926	+	0.0207718i	−0.859967	+	0.510350i	$0.829516\pi$
$284$	2.35757e10	+	4.08344e10i	0.215047	+	0.372472i
$285$		0			0
$286$	−4.96778e10	+	8.60445e10i	−0.439052	+	0.760460i
$287$	−2.74682e11			−2.38980
$288$		0			0
$289$	2.33479e11			1.96882
$290$	−2.25738e10	+	3.90989e10i	−0.187419	+	0.324619i
$291$		0			0
$292$	3.29008e10	+	5.69859e10i	0.264840	+	0.458717i
$293$	−3.05424e10	−	5.29009e10i	−0.242102	−	0.419333i	0.719211	−	0.694792i	$-0.244504\pi$
$293$	−3.05424e10	−	5.29009e10i	−0.242102	−	0.419333i	−0.961313	+	0.275459i	$0.911170\pi$
$294$		0			0
$295$	4.36343e10	−	7.55768e10i	0.335451	−	0.581017i
$296$	−4.74243e10			−0.359077
$297$		0			0
$298$	−1.25466e11			−0.921619
$299$	1.10834e11	−	1.91969e11i	0.801957	−	1.38903i
$300$		0			0
$301$	−6.11501e10	−	1.05915e11i	−0.429386	−	0.743719i
$302$	−2.34871e10	−	4.06808e10i	−0.162479	−	0.281422i
$303$		0			0
$304$	6.91297e9	−	1.19736e10i	0.0464230	−	0.0804070i
$305$	−9.52843e10			−0.630481
$306$		0			0
$307$	−7.67436e9			−0.0493082			−0.0246541	−	0.999696i	$-0.507848\pi$
$307$	−7.67436e9			−0.0493082			−0.0246541	+	0.999696i	$0.507848\pi$
$308$	8.58922e10	−	1.48770e11i	0.543845	−	0.941968i
$309$		0			0
$310$	1.11840e10	+	1.93712e10i	0.0687810	+	0.119132i
$311$	−4.79359e10	−	8.30274e10i	−0.290562	−	0.503268i	0.683381	−	0.730062i	$-0.260509\pi$
$311$	−4.79359e10	−	8.30274e10i	−0.290562	−	0.503268i	−0.973943	+	0.226794i	$0.927176\pi$
$312$		0			0
$313$	1.97948e10	−	3.42857e10i	0.116574	−	0.201912i	−0.801834	−	0.597547i	$-0.796142\pi$
$313$	1.97948e10	−	3.42857e10i	0.116574	−	0.201912i	0.918408	+	0.395635i	$0.129475\pi$
$314$	−1.39061e11			−0.807278
$315$		0			0
$316$	1.66808e11			0.941075
$317$	−1.39290e11	+	2.41257e11i	−0.774732	+	1.34188i	0.160212	+	0.987083i	$0.448782\pi$
$317$	−1.39290e11	+	2.41257e11i	−0.774732	+	1.34188i	−0.934945	+	0.354793i	$0.884551\pi$
$318$		0			0
$319$	−7.01688e10	−	1.21536e11i	−0.379390	−	0.657122i
$320$	9.86500e9	+	1.70867e10i	0.0525923	+	0.0910926i
$321$		0			0
$322$	−1.91630e11	+	3.31912e11i	−0.993370	+	1.72057i
$323$	1.25178e11			0.639905
$324$		0			0
$325$	6.05333e10			0.300967
$326$	−7.76304e10	+	1.34460e11i	−0.380673	+	0.659346i
$327$		0			0
$328$	4.90325e10	+	8.49267e10i	0.233911	+	0.405146i
$329$	1.95351e11	+	3.38358e11i	0.919250	+	1.59219i
$330$		0			0
$331$	5.01586e10	−	8.68773e10i	0.229678	−	0.397814i	−0.728035	−	0.685540i	$-0.759566\pi$
$331$	5.01586e10	−	8.68773e10i	0.229678	−	0.397814i	0.957713	+	0.287726i	$0.0928993\pi$
$332$	−4.51548e9			−0.0203978
$333$		0			0
$334$	3.12202e10			0.137270
$335$	−1.15547e10	+	2.00133e10i	−0.0501253	+	0.0868196i
$336$		0			0
$337$	1.44108e11	+	2.49602e11i	0.608630	+	1.05418i	0.991467	+	0.130361i	$0.0416137\pi$
$337$	1.44108e11	+	2.49602e11i	0.608630	+	1.05418i	−0.382837	+	0.923816i	$0.625053\pi$
$338$	5.34225e9	+	9.25306e9i	0.0222638	+	0.0385620i
$339$		0			0
$340$	−8.93161e10	+	1.54700e11i	−0.362472	+	0.627820i
$341$	−6.95289e10			−0.278465
$342$		0			0
$343$	−5.84234e11			−2.27910
$344$	−2.18313e10	+	3.78130e10i	−0.0840557	+	0.145589i
$345$		0			0
$346$	−4.18716e10	−	7.25237e10i	−0.157064	−	0.272043i
$347$	3.28830e10	+	5.69550e10i	0.121755	+	0.210887i	0.920460	−	0.390837i	$-0.127814\pi$
$347$	3.28830e10	+	5.69550e10i	0.121755	+	0.210887i	−0.798705	+	0.601723i	$0.794481\pi$
$348$		0			0
$349$	8.61283e10	−	1.49179e11i	0.310765	−	0.538260i	−0.667764	−	0.744373i	$-0.732748\pi$
$349$	8.61283e10	−	1.49179e11i	0.310765	−	0.538260i	0.978528	+	0.206113i	$0.0660816\pi$
$350$	−1.04661e11			−0.372803
$351$		0			0
$352$	−6.13291e10			−0.212924
$353$	−1.75594e11	+	3.04138e11i	−0.601900	+	1.04252i	0.390633	+	0.920546i	$0.372256\pi$
$353$	−1.75594e11	+	3.04138e11i	−0.601900	+	1.04252i	−0.992533	+	0.121975i	$0.961077\pi$
$354$		0			0
$355$	−1.08301e11	−	1.87583e11i	−0.361914	−	0.626853i
$356$	6.60806e10	+	1.14455e11i	0.218046	+	0.377668i
$357$		0			0
$358$	1.48408e11	−	2.57051e11i	0.477512	−	0.827075i
$359$	4.18672e11			1.33030			0.665149	−	0.746711i	$-0.268368\pi$
$359$	4.18672e11			1.33030			0.665149	+	0.746711i	$0.268368\pi$
$360$		0			0
$361$	−2.78181e11			−0.862074
$362$	−1.89664e11	+	3.28508e11i	−0.580492	+	1.00544i
$363$		0			0
$364$	−1.55917e11	−	2.70056e11i	−0.465518	−	0.806301i
$365$	−1.51138e11	−	2.61779e11i	−0.445714	−	0.771999i
$366$		0			0
$367$	2.08352e11	−	3.60876e11i	0.599515	−	1.03839i	−0.393378	−	0.919377i	$-0.628694\pi$
$367$	2.08352e11	−	3.60876e11i	0.599515	−	1.03839i	0.992893	−	0.119013i	$-0.0379731\pi$
$368$	1.36828e11			0.388920
$369$		0			0
$370$	2.17855e11			0.604310
$371$	−2.45184e11	+	4.24671e11i	−0.671908	+	1.16378i
$372$		0			0
$373$	−3.03880e11	−	5.26336e11i	−0.812855	−	1.40791i	−0.910858	−	0.412720i	$-0.864579\pi$
$373$	−3.03880e11	−	5.26336e11i	−0.812855	−	1.40791i	0.0980030	−	0.995186i	$-0.468755\pi$
$374$	−2.77632e11	−	4.80872e11i	−0.733748	−	1.27089i
$375$		0			0
$376$	6.97426e10	−	1.20798e11i	0.179950	−	0.311683i
$377$	−2.54749e11			−0.649497
$378$		0			0
$379$	−7.79404e9			−0.0194038			−0.00970189	−	0.999953i	$-0.503088\pi$
$379$	−7.79404e9			−0.0194038			−0.00970189	+	0.999953i	$0.503088\pi$
$380$	−3.17564e10	+	5.50038e10i	−0.0781278	+	0.135321i
$381$		0			0
$382$	−8.63961e10	−	1.49642e11i	−0.207591	−	0.359559i
$383$	−6.90626e10	−	1.19620e11i	−0.164002	−	0.284059i	0.772299	−	0.635260i	$-0.219107\pi$
$383$	−6.90626e10	−	1.19620e11i	−0.164002	−	0.284059i	−0.936300	+	0.351200i	$0.885774\pi$
$384$		0			0
$385$	−3.94567e11	+	6.83411e11i	−0.915267	+	1.58529i
$386$	−2.84016e11			−0.651179
$387$		0			0
$388$	−1.11164e11			−0.249012
$389$	−3.67197e10	+	6.36005e10i	−0.0813067	+	0.140827i	−0.903811	−	0.427931i	$-0.859243\pi$
$389$	−3.67197e10	+	6.36005e10i	−0.0813067	+	0.140827i	0.822505	+	0.568758i	$0.192576\pi$
$390$		0			0
$391$	6.19410e11	+	1.07285e12i	1.34024	+	2.32136i
$392$	1.86933e11	+	3.23778e11i	0.399853	+	0.692565i
$393$		0			0
$394$	−9.71138e9	+	1.68206e10i	−0.0203024	+	0.0351648i
$395$	−7.66273e11			−1.58379
$396$		0			0
$397$	2.58425e10			0.0522128			0.0261064	−	0.999659i	$-0.491689\pi$
$397$	2.58425e10			0.0522128			0.0261064	+	0.999659i	$0.491689\pi$
$398$	1.25861e11	−	2.17997e11i	0.251430	−	0.435489i
$399$		0			0
$400$	1.86826e10	+	3.23593e10i	0.0364895	+	0.0632017i
$401$	3.74006e10	+	6.47798e10i	0.0722319	+	0.125109i	0.899879	−	0.436139i	$-0.143654\pi$
$401$	3.74006e10	+	6.47798e10i	0.0722319	+	0.125109i	−0.827647	+	0.561249i	$0.810321\pi$
$402$		0			0
$403$	−6.31066e10	+	1.09304e11i	−0.119180	+	0.206425i
$404$	2.16730e10			0.0404766
$405$		0			0
$406$	4.40457e11			0.804520
$407$	−3.38593e11	+	5.86459e11i	−0.611649	+	1.05941i
$408$		0			0
$409$	−2.74745e11	−	4.75873e11i	−0.485485	−	0.840884i	0.514376	−	0.857565i	$-0.328023\pi$
$409$	−2.74745e11	−	4.75873e11i	−0.485485	−	0.840884i	−0.999861	+	0.0166806i	$0.994690\pi$
$410$	−2.25243e11	−	3.90132e11i	−0.393662	−	0.681843i
$411$		0			0
$412$	−8.57345e9	+	1.48497e10i	−0.0146595	+	0.0253909i
$413$	−8.51388e11			−1.43997
$414$		0			0
$415$	2.07430e10			0.0343285
$416$	−5.56642e10	+	9.64132e10i	−0.0911288	+	0.157840i
$417$		0			0
$418$	−9.87123e10	−	1.70975e11i	−0.158153	−	0.273929i
$419$	−1.76059e11	−	3.04943e11i	−0.279058	−	0.483342i	0.692093	−	0.721808i	$-0.256689\pi$
$419$	−1.76059e11	−	3.04943e11i	−0.279058	−	0.483342i	−0.971151	+	0.238466i	$0.923355\pi$
$420$		0			0
$421$	−6.50364e9	+	1.12646e10i	−0.0100899	+	0.0174762i	−0.871026	−	0.491236i	$-0.836545\pi$
$421$	−6.50364e9	+	1.12646e10i	−0.0100899	+	0.0174762i	0.860936	+	0.508713i	$0.169878\pi$
$422$	−1.33871e11			−0.205485
$423$		0			0
$424$	1.75067e11			0.263063
$425$	−1.69150e11	+	2.92976e11i	−0.251490	+	0.435593i
$426$		0			0
$427$	4.64795e11	+	8.05048e11i	0.676606	+	1.17192i
$428$	2.84315e11	+	4.92448e11i	0.409546	+	0.709354i
$429$		0			0
$430$	1.00288e11	−	1.73703e11i	0.141462	−	0.245019i
$431$	−6.43135e10			−0.0897748			−0.0448874	−	0.998992i	$-0.514293\pi$
$431$	−6.43135e10			−0.0897748			−0.0448874	+	0.998992i	$0.514293\pi$
$432$		0			0
$433$	7.95481e11			1.08751			0.543756	−	0.839243i	$-0.317002\pi$
$433$	7.95481e11			1.08751			0.543756	+	0.839243i	$0.317002\pi$
$434$	1.09110e11	−	1.88984e11i	0.147626	−	0.255695i
$435$		0			0
$436$	5.69802e10	+	9.86926e10i	0.0755153	+	0.130796i
$437$	2.20232e11	+	3.81453e11i	0.288877	+	0.500350i
$438$		0			0
$439$	−8.33342e10	+	1.44339e11i	−0.107086	+	0.185478i	−0.914589	−	0.404386i	$-0.867485\pi$
$439$	−8.33342e10	+	1.44339e11i	−0.107086	+	0.185478i	0.807503	+	0.589864i	$0.200819\pi$
$440$	2.81731e11			0.358341
$441$		0			0
$442$	−1.00795e12			−1.25614
$443$	5.16635e11	−	8.94839e11i	0.637334	−	1.10390i	−0.348681	−	0.937241i	$-0.613370\pi$
$443$	5.16635e11	−	8.94839e11i	0.637334	−	1.10390i	0.986015	−	0.166654i	$-0.0532964\pi$
$444$		0			0
$445$	−3.03558e11	−	5.25778e11i	−0.366962	−	0.635597i
$446$	3.83297e11	+	6.63890e11i	0.458700	+	0.794491i
$447$		0			0
$448$	9.62425e10	−	1.66697e11i	0.112880	−	0.195513i
$449$	1.05633e12			1.22656			0.613281	−	0.789865i	$-0.289849\pi$
$449$	1.05633e12			1.22656			0.613281	+	0.789865i	$0.289849\pi$
$450$		0			0
$451$	1.40030e12			1.59377
$452$	−9.60490e10	+	1.66362e11i	−0.108236	+	0.187469i
$453$		0			0
$454$	2.16937e11	+	3.75746e11i	0.239652	+	0.415090i
$455$	7.16243e11	+	1.24057e12i	0.783446	+	1.35697i
$456$		0			0
$457$	−3.14049e11	+	5.43949e11i	−0.336802	+	0.583358i	−0.983829	−	0.179108i	$-0.942679\pi$
$457$	−3.14049e11	+	5.43949e11i	−0.336802	+	0.583358i	0.647027	+	0.762467i	$0.276012\pi$
$458$	−8.56257e11			−0.909305
$459$		0			0
$460$	−6.28554e11			−0.654535
$461$	4.46492e11	−	7.73347e11i	0.460426	−	0.797481i	−0.538556	−	0.842589i	$-0.681030\pi$
$461$	4.46492e11	−	7.73347e11i	0.460426	−	0.797481i	0.998982	+	0.0451089i	$0.0143635\pi$
$462$		0			0
$463$	5.62705e11	+	9.74633e11i	0.569071	+	0.985659i	0.996658	+	0.0816854i	$0.0260303\pi$
$463$	5.62705e11	+	9.74633e11i	0.569071	+	0.985659i	−0.427587	+	0.903974i	$0.640636\pi$
$464$	−7.86243e10	−	1.36181e11i	−0.0787456	−	0.136391i
$465$		0			0
$466$	5.75117e11	−	9.96132e11i	0.564963	−	0.978544i
$467$	−1.04729e12			−1.01892			−0.509461	−	0.860494i	$-0.670155\pi$
$467$	−1.04729e12			−1.01892			−0.509461	+	0.860494i	$0.670155\pi$
$468$		0			0
$469$	2.25454e11			0.215170
$470$	−3.20380e11	+	5.54915e11i	−0.302848	+	0.524549i
$471$		0			0
$472$	1.51978e11	+	2.63233e11i	0.140942	+	0.244119i
$473$	3.11736e11	+	5.39943e11i	0.286360	+	0.495990i
$474$		0			0
$475$	−6.01413e10	+	1.04168e11i	−0.0542065	+	0.0938885i
$476$	1.74273e12			1.55596
$477$		0			0
$478$	−4.43279e11			−0.388375
$479$	6.38141e11	−	1.10529e12i	0.553869	−	0.959329i	−0.444122	−	0.895966i	$-0.646484\pi$
$479$	6.38141e11	−	1.10529e12i	0.553869	−	0.959329i	0.997991	−	0.0633624i	$-0.0201824\pi$
$480$		0			0
$481$	6.14634e11	+	1.06458e12i	0.523557	+	0.906827i
$482$	1.87123e11	+	3.24106e11i	0.157912	+	0.273512i
$483$		0			0
$484$	−1.36051e11	+	2.35647e11i	−0.112693	+	0.195190i
$485$	5.10658e11			0.419075
$486$		0			0
$487$	6.62479e11			0.533693			0.266847	−	0.963739i	$-0.414018\pi$
$487$	6.62479e11			0.533693			0.266847	+	0.963739i	$0.414018\pi$
$488$	1.65937e11	−	2.87412e11i	0.132451	−	0.229412i
$489$		0			0
$490$	−8.58726e11	−	1.48736e12i	−0.672933	−	1.16555i
$491$	−1.16275e12	−	2.01395e12i	−0.902861	−	1.56380i	−0.823763	−	0.566935i	$-0.808129\pi$
$491$	−1.16275e12	−	2.01395e12i	−0.902861	−	1.56380i	−0.0790986	−	0.996867i	$-0.525204\pi$
$492$		0			0
$493$	7.11852e11	−	1.23296e12i	0.542723	−	0.940024i
$494$	−3.58377e11			−0.270750
$495$		0			0
$496$	−7.79074e10			−0.0577978
$497$	−1.05658e12	+	1.83005e12i	−0.776781	+	1.34542i
$498$		0			0
$499$	1.55727e10	+	2.69727e10i	0.0112438	+	0.0194748i	0.871593	−	0.490231i	$-0.163088\pi$
$499$	1.55727e10	+	2.69727e10i	0.0112438	+	0.0194748i	−0.860349	+	0.509706i	$0.829754\pi$
$500$	−3.79823e11	−	6.57873e11i	−0.271779	−	0.470736i
$501$		0			0
$502$	7.54520e11	−	1.30687e12i	0.530278	−	0.918469i
$503$	5.25877e11			0.366293			0.183146	−	0.983086i	$-0.441372\pi$
$503$	5.25877e11			0.366293			0.183146	+	0.983086i	$0.441372\pi$
$504$		0			0
$505$	−9.95605e10			−0.0681202
$506$	9.76905e11	−	1.69205e12i	0.662483	−	1.14745i
$507$		0			0
$508$	−5.27902e11	−	9.14353e11i	−0.351695	−	0.609154i
$509$	−4.23815e11	−	7.34070e11i	−0.279864	−	0.484738i	0.691487	−	0.722389i	$-0.256956\pi$
$509$	−4.23815e11	−	7.34070e11i	−0.279864	−	0.484738i	−0.971351	+	0.237651i	$0.923623\pi$
$510$		0			0
$511$	−1.47450e12	+	2.55390e12i	−0.956643	+	1.65695i
$512$	−6.87195e10			−0.0441942
$513$		0			0
$514$	1.84084e11			0.116327
$515$	3.93843e10	−	6.82156e10i	0.0246712	−	0.0427318i
$516$		0			0
$517$	−9.95875e11	−	1.72491e12i	−0.613052	−	1.06184i
$518$	−1.06269e12	−	1.84064e12i	−0.648520	−	1.12327i
$519$		0			0
$520$	2.55707e11	−	4.42898e11i	0.153366	−	0.265637i
$521$	6.24007e11			0.371039			0.185520	−	0.982641i	$-0.440603\pi$
$521$	6.24007e11			0.371039			0.185520	+	0.982641i	$0.440603\pi$
$522$		0			0
$523$	−2.13963e12			−1.25049			−0.625247	−	0.780427i	$-0.715002\pi$
$523$	−2.13963e12			−1.25049			−0.625247	+	0.780427i	$0.715002\pi$
$524$	5.50862e11	−	9.54121e11i	0.319192	−	0.552857i
$525$		0			0
$526$	−1.36418e10	−	2.36283e10i	−0.00777027	−	0.0134585i
$527$	−3.52680e11	−	6.10860e11i	−0.199174	−	0.344980i
$528$		0			0
$529$	−1.27894e12	+	2.21520e12i	−0.710070	+	1.22988i
$530$	−8.04216e11			−0.442722
$531$		0			0
$532$	6.19629e11			0.335374
$533$	1.27095e12	−	2.20136e12i	0.682114	−	1.18146i
$534$		0			0
$535$	−1.30607e12	−	2.26218e12i	−0.689247	−	1.19381i
$536$	−4.02450e10	−	6.97063e10i	−0.0210606	−	0.0364780i
$537$		0			0
$538$	7.66228e11	−	1.32715e12i	0.394310	−	0.682965i
$539$	5.33856e12			2.72442
$540$		0			0
$541$	−1.28484e12			−0.644853			−0.322427	−	0.946594i	$-0.604499\pi$
$541$	−1.28484e12			−0.644853			−0.322427	+	0.946594i	$0.604499\pi$
$542$	−1.30270e12	+	2.25634e12i	−0.648407	+	1.12307i
$543$		0			0
$544$	−3.11087e11	−	5.38819e11i	−0.152296	−	0.263784i
$545$	−2.61753e11	−	4.53369e11i	−0.127089	−	0.220124i
$546$		0			0
$547$	−8.34512e11	+	1.44542e12i	−0.398556	+	0.690319i	−0.993548	−	0.113412i	$-0.963822\pi$
$547$	−8.34512e11	+	1.44542e12i	−0.398556	+	0.690319i	0.594992	+	0.803732i	$0.297155\pi$
$548$	1.69051e12			0.800764
$549$		0			0
$550$	5.33550e11			0.248624
$551$	2.53100e11	−	4.38381e11i	0.116979	−	0.202614i
$552$		0			0
$553$	3.73786e12	+	6.47416e12i	1.69965	+	2.94388i
$554$	4.05573e11	+	7.02473e11i	0.182926	+	0.316837i
$555$		0			0
$556$	1.09194e12	−	1.89129e12i	0.484575	−	0.839309i
$557$	3.34603e12			1.47293			0.736464	−	0.676477i	$-0.236494\pi$
$557$	3.34603e12			1.47293			0.736464	+	0.676477i	$0.236494\pi$
$558$		0			0
$559$	1.13177e12			0.490234
$560$	−4.42114e11	+	7.65764e11i	−0.189971	+	0.329040i
$561$		0			0
$562$	−8.92792e11	−	1.54636e12i	−0.377517	−	0.653879i
$563$	6.70548e11	+	1.16142e12i	0.281282	+	0.487195i	0.971701	−	0.236215i	$-0.0759071\pi$
$563$	6.70548e11	+	1.16142e12i	0.281282	+	0.487195i	−0.690419	+	0.723410i	$0.742574\pi$
$564$		0			0
$565$	4.41225e11	−	7.64224e11i	0.182155	−	0.315502i
$566$	4.14098e10			0.0169601
$567$		0			0
$568$	7.54423e11			0.304122
$569$	2.24935e12	−	3.89598e12i	0.899604	−	1.55816i	0.0716024	−	0.997433i	$-0.477189\pi$
$569$	2.24935e12	−	3.89598e12i	0.899604	−	1.55816i	0.828001	−	0.560726i	$-0.189478\pi$
$570$		0			0
$571$	3.68189e11	+	6.37723e11i	0.144947	+	0.251055i	0.929353	−	0.369192i	$-0.120366\pi$
$571$	3.68189e11	+	6.37723e11i	0.144947	+	0.251055i	−0.784406	+	0.620247i	$0.787032\pi$
$572$	7.94845e11	+	1.37671e12i	0.310456	+	0.537726i
$573$		0			0
$574$	−2.19746e12	+	3.80611e12i	−0.844923	+	1.46345i
$575$	−1.19038e12			−0.454128
$576$		0			0
$577$	−3.19860e11			−0.120135			−0.0600673	−	0.998194i	$-0.519132\pi$
$577$	−3.19860e11			−0.120135			−0.0600673	+	0.998194i	$0.519132\pi$
$578$	1.86783e12	−	3.23518e12i	0.696085	−	1.20565i
$579$		0			0
$580$	3.61180e11	+	6.25583e11i	0.132525	+	0.229540i
$581$	−1.01184e11	−	1.75256e11i	−0.0368399	−	0.0638086i
$582$		0			0
$583$	1.24992e12	−	2.16492e12i	0.448099	−	0.776130i
$584$	1.05283e12			0.374541
$585$		0			0
$586$	−9.77356e11			−0.342384
$587$	1.41772e11	−	2.45556e11i	0.0492855	−	0.0853649i	−0.840330	−	0.542075i	$-0.817639\pi$
$587$	1.41772e11	−	2.45556e11i	0.0492855	−	0.0853649i	0.889616	+	0.456710i	$0.150972\pi$
$588$		0			0
$589$	−1.25396e11	−	2.17192e11i	−0.0429303	−	0.0743575i
$590$	−6.98148e11	−	1.20923e12i	−0.237199	−	0.410841i
$591$		0			0
$592$	−3.79394e11	+	6.57130e11i	−0.126953	+	0.219889i
$593$	−1.27449e12			−0.423245			−0.211622	−	0.977352i	$-0.567875\pi$
$593$	−1.27449e12			−0.423245			−0.211622	+	0.977352i	$0.567875\pi$
$594$		0			0
$595$	−8.00565e12			−2.61861
$596$	−1.00372e12	+	1.73850e12i	−0.325842	+	0.564374i
$597$		0			0
$598$	−1.77334e12	−	3.07151e12i	−0.567069	−	0.982193i
$599$	1.08807e12	+	1.88460e12i	0.345333	+	0.598134i	0.985414	−	0.170173i	$-0.0544327\pi$
$599$	1.08807e12	+	1.88460e12i	0.345333	+	0.598134i	−0.640081	+	0.768307i	$0.721099\pi$
$600$		0			0
$601$	1.87450e12	−	3.24673e12i	0.586072	−	1.01511i	−0.408669	−	0.912683i	$-0.634007\pi$
$601$	1.87450e12	−	3.24673e12i	0.586072	−	1.01511i	0.994741	−	0.102423i	$-0.0326596\pi$
$602$	−1.95680e12			−0.607244
$603$		0			0
$604$	−7.51586e11			−0.229780
$605$	6.24984e11	−	1.08250e12i	0.189657	−	0.328496i
$606$		0			0
$607$	−1.39525e12	−	2.41664e12i	−0.417159	−	0.722541i	0.578493	−	0.815687i	$-0.303641\pi$
$607$	−1.39525e12	−	2.41664e12i	−0.417159	−	0.722541i	−0.995652	+	0.0931465i	$0.970308\pi$
$608$	−1.10607e11	−	1.91578e11i	−0.0328260	−	0.0568563i
$609$		0			0
$610$	−7.62275e11	+	1.32030e12i	−0.222909	+	0.386089i
$611$	−3.61555e12			−1.04952
$612$		0			0
$613$	6.25456e12			1.78906			0.894530	−	0.447008i	$-0.147510\pi$
$613$	6.25456e12			1.78906			0.894530	+	0.447008i	$0.147510\pi$
$614$	−6.13948e10	+	1.06339e11i	−0.0174331	+	0.0301950i
$615$		0			0
$616$	−1.37428e12	−	2.38031e12i	−0.384557	−	0.666072i
$617$	−1.77847e12	−	3.08039e12i	−0.494040	−	0.855703i	0.505936	−	0.862571i	$-0.331147\pi$
$617$	−1.77847e12	−	3.08039e12i	−0.494040	−	0.855703i	−0.999976	+	0.00686793i	$0.997814\pi$
$618$		0			0
$619$	−1.47650e12	+	2.55738e12i	−0.404228	+	0.700143i	−0.994231	−	0.107258i	$-0.965793\pi$
$619$	−1.47650e12	+	2.55738e12i	−0.404228	+	0.700143i	0.590004	+	0.807401i	$0.299126\pi$
$620$	3.57887e11			0.0972710
$621$		0			0
$622$	−1.53395e12			−0.410917
$623$	−2.96150e12	+	5.12946e12i	−0.787617	+	1.36419i
$624$		0			0
$625$	1.18803e12	+	2.05772e12i	0.311434	+	0.539420i
$626$	−3.16717e11	−	5.48571e11i	−0.0824304	−	0.142774i
$627$		0			0
$628$	−1.11249e12	+	1.92689e12i	−0.285416	+	0.494355i
$629$	−6.86994e12			−1.74995
$630$		0			0
$631$	1.18375e12			0.297254			0.148627	−	0.988893i	$-0.452515\pi$
$631$	1.18375e12			0.297254			0.148627	+	0.988893i	$0.452515\pi$
$632$	1.33446e12	−	2.31135e12i	0.332720	−	0.576288i
$633$		0			0
$634$	2.22863e12	+	3.86010e12i	0.547819	+	0.948850i
$635$	2.42505e12	+	4.20031e12i	0.591887	+	1.02518i
$636$		0			0
$637$	4.84544e12	−	8.39255e12i	1.16602	−	2.01960i
$638$	−2.24540e12			−0.536538
$639$		0			0
$640$	3.15680e11			0.0743768
$641$	−1.70873e12	+	2.95961e12i	−0.399772	+	0.692425i	−0.993698	−	0.112095i	$-0.964244\pi$
$641$	−1.70873e12	+	2.95961e12i	−0.399772	+	0.692425i	0.593926	+	0.804520i	$0.297577\pi$
$642$		0			0
$643$	9.88069e11	+	1.71138e12i	0.227949	+	0.394819i	0.957200	−	0.289427i	$-0.0934647\pi$
$643$	9.88069e11	+	1.71138e12i	0.227949	+	0.394819i	−0.729251	+	0.684246i	$0.760131\pi$
$644$	3.06607e12	+	5.31059e12i	0.702419	+	1.21663i
$645$		0			0
$646$	1.00142e12	−	1.73451e12i	0.226241	−	0.391860i
$647$	−1.33446e12			−0.299388			−0.149694	−	0.988732i	$-0.547829\pi$
$647$	−1.33446e12			−0.299388			−0.149694	+	0.988732i	$0.547829\pi$
$648$		0			0
$649$	4.34027e12			0.960320
$650$	4.84266e11	−	8.38774e11i	0.106408	−	0.184304i
$651$		0			0
$652$	1.24209e12	+	2.15136e12i	0.269177	+	0.466228i
$653$	1.98417e12	+	3.43669e12i	0.427042	+	0.739658i	0.996609	−	0.0822868i	$-0.0262224\pi$
$653$	1.98417e12	+	3.43669e12i	0.427042	+	0.739658i	−0.569567	+	0.821945i	$0.692889\pi$
$654$		0			0
$655$	−2.53052e12	+	4.38300e12i	−0.537186	+	0.930433i
$656$	1.56904e12			0.330801
$657$		0			0
$658$	6.25123e12			1.30002
$659$	2.48758e12	−	4.30861e12i	0.513797	−	0.889923i	−0.486075	−	0.873917i	$-0.661572\pi$
$659$	2.48758e12	−	4.30861e12i	0.513797	−	0.889923i	0.999872	−	0.0160057i	$-0.00509499\pi$
$660$		0			0
$661$	−2.46007e12	−	4.26096e12i	−0.501234	−	0.868162i	−0.999999	−	0.00142495i	$-0.999546\pi$
$661$	−2.46007e12	−	4.26096e12i	−0.501234	−	0.868162i	0.498765	−	0.866737i	$-0.333787\pi$
$662$	−8.02538e11	−	1.39004e12i	−0.162407	−	0.281297i
$663$		0			0
$664$	−3.61239e10	+	6.25684e10i	−0.00721170	+	0.0124910i
$665$	−2.84642e12			−0.564419
$666$		0			0
$667$	5.00959e12			0.980023
$668$	2.49761e11	−	4.32600e11i	0.0485324	−	0.0840605i
$669$		0			0
$670$	1.84875e11	+	3.20213e11i	0.0354440	+	0.0613907i
$671$	−2.36947e12	−	4.10404e12i	−0.451232	−	0.781556i
$672$		0			0
$673$	4.78109e10	−	8.28109e10i	0.00898377	−	0.0155604i	−0.861499	−	0.507760i	$-0.830474\pi$
$673$	4.78109e10	−	8.28109e10i	0.00898377	−	0.0155604i	0.870482	+	0.492200i	$0.163807\pi$
$674$	4.61145e12			0.860732
$675$		0			0
$676$	1.70952e11			0.0314858
$677$	−1.67940e12	+	2.90880e12i	−0.307259	+	0.532188i	−0.977762	−	0.209719i	$-0.932745\pi$
$677$	−1.67940e12	+	2.90880e12i	−0.307259	+	0.532188i	0.670503	+	0.741907i	$0.266079\pi$
$678$		0			0
$679$	−2.49098e12	−	4.31450e12i	−0.449734	−	0.778962i
$680$	1.42906e12	+	2.47520e12i	0.256306	+	0.443936i
$681$		0			0
$682$	−5.56231e11	+	9.63421e11i	−0.0984522	+	0.170524i
$683$	5.37711e12			0.945487			0.472743	−	0.881200i	$-0.343264\pi$
$683$	5.37711e12			0.945487			0.472743	+	0.881200i	$0.343264\pi$
$684$		0			0
$685$	−7.76577e12			−1.34765
$686$	−4.67387e12	+	8.09538e12i	−0.805783	+	1.39566i
$687$		0			0
$688$	3.49301e11	+	6.05008e11i	0.0594364	+	0.102947i
$689$	−2.26893e12	−	3.92990e12i	−0.383561	−	0.664348i
$690$		0			0
$691$	−3.41097e12	+	5.90797e12i	−0.569150	+	0.985797i	0.427500	+	0.904015i	$0.359394\pi$
$691$	−3.41097e12	+	5.90797e12i	−0.569150	+	0.985797i	−0.996650	+	0.0817814i	$0.973939\pi$
$692$	−1.33989e12			−0.222122
$693$		0			0
$694$	1.05226e12			0.172188
$695$	−5.01609e12	+	8.68812e12i	−0.815518	+	1.41252i
$696$		0			0
$697$	7.10291e12	+	1.23026e13i	1.13996	+	1.97446i
$698$	−1.37805e12	−	2.38686e12i	−0.219744	−	0.380607i
$699$		0			0
$700$	−8.37289e11	+	1.45023e12i	−0.131806	+	0.228294i
$701$	4.41615e12			0.690737			0.345369	−	0.938467i	$-0.387754\pi$
$701$	4.41615e12			0.690737			0.345369	+	0.938467i	$0.387754\pi$
$702$		0			0
$703$	−2.44262e12			−0.377186
$704$	−4.90633e11	+	8.49801e11i	−0.0752800	+	0.130389i
$705$		0			0
$706$	2.80951e12	+	4.86621e12i	0.425608	+	0.737174i
$707$	4.85654e11	+	8.41177e11i	0.0731037	+	0.126619i
$708$		0			0
$709$	4.10138e12	−	7.10380e12i	0.609568	−	1.05580i	−0.381744	−	0.924268i	$-0.624676\pi$
$709$	4.10138e12	−	7.10380e12i	0.609568	−	1.05580i	0.991312	−	0.131534i	$-0.0419904\pi$
$710$	−3.46563e12			−0.511823
$711$		0			0
$712$	2.11458e12			0.308364
$713$	1.24098e12	−	2.14944e12i	0.179830	−	0.311474i
$714$		0			0
$715$	−3.65132e12	−	6.32427e12i	−0.522484	−	0.904968i
$716$	−2.37453e12	−	4.11281e12i	−0.337652	−	0.584830i
$717$		0			0
$718$	3.34938e12	−	5.80129e12i	0.470331	−	0.814638i
$719$	−9.34677e12			−1.30431			−0.652156	−	0.758084i	$-0.726135\pi$
$719$	−9.34677e12			−1.30431			−0.652156	+	0.758084i	$0.726135\pi$
$720$		0			0
$721$	−7.68463e11			−0.105904
$722$	−2.22544e12	+	3.85458e12i	−0.304789	+	0.527910i
$723$		0			0
$724$	3.03462e12	+	5.25612e12i	0.410470	+	0.710955i
$725$	6.84015e11	+	1.18475e12i	0.0919484	+	0.159259i
$726$		0			0
$727$	−5.76090e12	+	9.97817e12i	−0.764866	+	1.32479i	0.175451	+	0.984488i	$0.443862\pi$
$727$	−5.76090e12	+	9.97817e12i	−0.764866	+	1.32479i	−0.940317	+	0.340299i	$0.889472\pi$
$728$	−4.98934e12			−0.658342
$729$		0			0
$730$	−4.83642e12			−0.630335
$731$	−3.16252e12	+	5.47764e12i	−0.409642	+	0.709521i
$732$		0			0
$733$	−3.71752e12	−	6.43894e12i	−0.475648	−	0.823846i	0.523963	−	0.851741i	$-0.324453\pi$
$733$	−3.71752e12	−	6.43894e12i	−0.475648	−	0.823846i	−0.999611	+	0.0278946i	$0.991120\pi$
$734$	−3.33363e12	−	5.77401e12i	−0.423921	−	0.734253i
$735$		0			0
$736$	1.09463e12	−	1.89595e12i	0.137504	−	0.238164i
$737$	−1.14934e12			−0.143498
$738$		0			0
$739$	5.94698e12			0.733494			0.366747	−	0.930321i	$-0.380471\pi$
$739$	5.94698e12			0.733494			0.366747	+	0.930321i	$0.380471\pi$
$740$	1.74284e12	−	3.01869e12i	0.213656	−	0.370063i
$741$		0			0
$742$	3.92295e12	+	6.79474e12i	0.475111	+	0.822916i
$743$	2.19039e12	+	3.79387e12i	0.263677	+	0.456702i	0.967216	−	0.253954i	$-0.0817313\pi$
$743$	2.19039e12	+	3.79387e12i	0.263677	+	0.456702i	−0.703539	+	0.710657i	$0.748398\pi$
$744$		0			0
$745$	4.61086e12	−	7.98625e12i	0.548376	−	0.949816i
$746$	−9.72418e12			−1.14955
$747$		0			0
$748$	−8.88422e12			−1.03768
$749$	−1.27420e13	+	2.20697e13i	−1.47934	+	2.56229i
$750$		0			0
$751$	2.62327e11	+	4.54363e11i	0.0300928	+	0.0521223i	0.880680	−	0.473712i	$-0.157086\pi$
$751$	2.62327e11	+	4.54363e11i	0.0300928	+	0.0521223i	−0.850587	+	0.525835i	$0.823753\pi$
$752$	−1.11588e12	−	1.93276e12i	−0.127244	−	0.220393i
$753$		0			0
$754$	−2.03799e12	+	3.52991e12i	−0.229632	+	0.397734i
$755$	3.45260e12			0.386710
$756$		0			0
$757$	3.95445e12			0.437678			0.218839	−	0.975761i	$-0.429773\pi$
$757$	3.95445e12			0.437678			0.218839	+	0.975761i	$0.429773\pi$
$758$	−6.23523e10	+	1.07997e11i	−0.00686027	+	0.0118823i
$759$		0			0
$760$	5.08103e11	+	8.80060e11i	0.0552447	+	0.0956866i
$761$	−7.21193e12	−	1.24914e13i	−0.779508	−	1.35015i	−0.932226	−	0.361877i	$-0.882136\pi$
$761$	−7.21193e12	−	1.24914e13i	−0.779508	−	1.35015i	0.152718	−	0.988270i	$-0.451197\pi$
$762$		0			0
$763$	−2.55365e12	+	4.42305e12i	−0.272773	+	0.472456i
$764$	−2.76468e12			−0.293578
$765$		0			0
$766$	−2.21000e12			−0.231933
$767$	3.93936e12	−	6.82318e12i	0.411005	−	0.711882i
$768$		0			0
$769$	−9.18862e12	−	1.59152e13i	−0.947505	−	1.64113i	−0.750656	−	0.660693i	$-0.770262\pi$
$769$	−9.18862e12	−	1.59152e13i	−0.947505	−	1.64113i	−0.196849	−	0.980434i	$-0.563071\pi$
$770$	6.31308e12	+	1.09346e13i	0.647192	+	1.12097i
$771$		0			0
$772$	−2.27213e12	+	3.93544e12i	−0.230226	+	0.398764i
$773$	−5.50573e12			−0.554635			−0.277318	−	0.960778i	$-0.589445\pi$
$773$	−5.50573e12			−0.554635			−0.277318	+	0.960778i	$0.589445\pi$
$774$		0			0
$775$	6.77777e11			0.0674884
$776$	−8.89309e11	+	1.54033e12i	−0.0880389	+	0.152488i
$777$		0			0
$778$	5.87516e11	+	1.01761e12i	0.0574925	+	0.0995800i
$779$	2.52545e12	+	4.37420e12i	0.245708	+	0.425579i
$780$		0			0
$781$	5.38632e12	−	9.32937e12i	0.518039	−	0.897269i
$782$	1.98211e13			1.89539
$783$		0			0
$784$	5.98187e12			0.565477
$785$	5.11050e12	−	8.85165e12i	0.480342	−	0.831976i
$786$		0			0
$787$	−5.95701e12	−	1.03178e13i	−0.553531	−	0.958744i	−0.998016	−	0.0629579i	$-0.979947\pi$
$787$	−5.95701e12	−	1.03178e13i	−0.553531	−	0.958744i	0.444485	−	0.895786i	$-0.353387\pi$
$788$	1.55382e11	+	2.69130e11i	0.0143560	+	0.0248653i
$789$		0			0
$790$	−6.13018e12	+	1.06178e13i	−0.559953	+	0.969867i
$791$	−8.60914e12			−0.781926
$792$		0			0
$793$	−8.60241e12			−0.772486
$794$	2.06740e11	−	3.58084e11i	0.0184600	−	0.0319737i
$795$		0			0
$796$	−2.01377e12	−	3.48796e12i	−0.177788	−	0.307937i
$797$	8.64517e12	+	1.49739e13i	0.758946	+	1.31453i	0.943388	+	0.331690i	$0.107619\pi$
$797$	8.64517e12	+	1.49739e13i	0.758946	+	1.31453i	−0.184442	+	0.982843i	$0.559048\pi$
$798$		0			0
$799$	1.01030e13	−	1.74989e13i	0.876981	−	1.51898i
$800$	5.97845e11			0.0516040
$801$		0			0
$802$	1.19682e12			0.102151
$803$	7.51681e12	−	1.30195e13i	0.637990	−	1.10503i
$804$		0			0
$805$	−1.40848e13	−	2.43955e13i	−1.18214	−	2.04752i
$806$	1.00970e12	+	1.74886e12i	0.0842727	+	0.145965i
$807$		0			0
$808$	1.73384e11	−	3.00310e11i	0.0143106	−	0.0247867i
$809$	5.01450e12			0.411584			0.205792	−	0.978596i	$-0.434023\pi$
$809$	5.01450e12			0.411584			0.205792	+	0.978596i	$0.434023\pi$
$810$		0			0
$811$	−7.01801e12			−0.569666			−0.284833	−	0.958577i	$-0.591938\pi$
$811$	−7.01801e12			−0.569666			−0.284833	+	0.958577i	$0.591938\pi$
$812$	3.52366e12	−	6.10316e12i	0.284441	−	0.492666i
$813$		0			0
$814$	5.41748e12	+	9.38335e12i	0.432501	+	0.749114i
$815$	−5.70583e12	−	9.88279e12i	−0.453012	−	0.784640i
$816$		0			0
$817$	−1.12444e12	+	1.94758e12i	−0.0882949	+	0.152931i
$818$	−8.79185e12			−0.686579
$819$		0			0
$820$	−7.20777e12			−0.556722
$821$	2.10007e12	−	3.63743e12i	0.161320	−	0.279415i	−0.774022	−	0.633159i	$-0.781758\pi$
$821$	2.10007e12	−	3.63743e12i	0.161320	−	0.279415i	0.935343	+	0.353743i	$0.115091\pi$
$822$		0			0
$823$	7.86329e12	+	1.36196e13i	0.597455	+	1.03482i	0.993195	+	0.116459i	$0.0371545\pi$
$823$	7.86329e12	+	1.36196e13i	0.597455	+	1.03482i	−0.395741	+	0.918362i	$0.629512\pi$
$824$	1.37175e11	+	2.37594e11i	0.0103658	+	0.0179541i
$825$		0			0
$826$	−6.81110e12	+	1.17972e13i	−0.509105	+	0.881795i
$827$	1.63254e13			1.21364			0.606820	−	0.794840i	$-0.292445\pi$
$827$	1.63254e13			1.21364			0.606820	+	0.794840i	$0.292445\pi$
$828$		0			0
$829$	1.72909e12			0.127152			0.0635759	−	0.997977i	$-0.479749\pi$
$829$	1.72909e12			0.127152			0.0635759	+	0.997977i	$0.479749\pi$
$830$	1.65944e11	−	2.87423e11i	0.0121370	−	0.0210218i
$831$		0			0
$832$	8.90627e11	+	1.54261e12i	0.0644378	+	0.111610i
$833$	2.70794e13	+	4.69030e13i	1.94866	+	3.37519i
$834$		0			0
$835$	−1.14734e12	+	1.98725e12i	−0.0816777	+	0.141470i
$836$	−3.15879e12			−0.223662
$837$		0			0
$838$	−5.63388e12			−0.394647
$839$	−7.34991e12	+	1.27304e13i	−0.512098	+	0.886980i	0.487804	+	0.872953i	$0.337798\pi$
$839$	−7.34991e12	+	1.27304e13i	−0.512098	+	0.886980i	−0.999902	+	0.0140265i	$0.995535\pi$
$840$		0			0
$841$	4.37496e12	+	7.57764e12i	0.301572	+	0.522339i
$842$	1.04058e11	+	1.80234e11i	0.00713464	+	0.0123576i
$843$		0			0
$844$	−1.07097e12	+	1.85497e12i	−0.0726499	+	0.125833i
$845$	−7.85311e11			−0.0529891
$846$		0			0
$847$	−1.21946e13			−0.814129
$848$	1.40054e12	−	2.42581e12i	0.0930067	−	0.161092i
$849$		0			0
$850$	2.70639e12	+	4.68761e12i	0.177830	+	0.308011i
$851$	−1.20867e13	−	2.09347e13i	−0.789993	−	1.36831i
$852$		0			0
$853$	−7.45841e12	+	1.29183e13i	−0.482365	+	0.835481i	−0.999795	−	0.0202449i	$-0.993555\pi$
$853$	−7.45841e12	+	1.29183e13i	−0.482365	+	0.835481i	0.517430	+	0.855725i	$0.326889\pi$
$854$	1.48734e13			0.956865
$855$		0			0
$856$	9.09807e12			0.579185
$857$	1.35627e13	−	2.34913e13i	0.858880	−	1.48762i	−0.0141174	−	0.999900i	$-0.504494\pi$
$857$	1.35627e13	−	2.34913e13i	0.858880	−	1.48762i	0.872998	−	0.487724i	$-0.162173\pi$
$858$		0			0
$859$	−1.81855e11	−	3.14982e11i	−0.0113961	−	0.0197386i	0.860271	−	0.509837i	$-0.170294\pi$
$859$	−1.81855e11	−	3.14982e11i	−0.0113961	−	0.0197386i	−0.871667	+	0.490098i	$0.836961\pi$
$860$	−1.60460e12	−	2.77925e12i	−0.100029	−	0.173255i
$861$		0			0
$862$	−5.14508e11	+	8.91154e11i	−0.0317402	+	0.0549756i
$863$	−2.24882e13			−1.38009			−0.690044	−	0.723768i	$-0.742409\pi$
$863$	−2.24882e13			−1.38009			−0.690044	+	0.723768i	$0.742409\pi$
$864$		0			0
$865$	6.15512e12			0.373821
$866$	6.36385e12	−	1.10225e13i	0.384494	−	0.665963i
$867$		0			0
$868$	−1.74576e12	−	3.02375e12i	−0.104387	−	0.180804i
$869$	−1.90552e13	−	3.30045e13i	−1.13351	−	1.96329i
$870$		0			0
$871$	−1.04318e12	+	1.80683e12i	−0.0614152	+	0.106374i
$872$	1.82337e12			0.106795
$873$		0			0
$874$	7.04742e12			0.408534
$875$	1.70223e13	−	2.94835e13i	0.981708	−	1.70037i
$876$		0			0
$877$	1.07666e13	+	1.86483e13i	0.614584	+	1.06449i	0.990457	+	0.137820i	$0.0440094\pi$
$877$	1.07666e13	+	1.86483e13i	0.614584	+	1.06449i	−0.375873	+	0.926671i	$0.622657\pi$
$878$	1.33335e12	+	2.30942e12i	0.0757213	+	0.131153i
$879$		0			0
$880$	2.25384e12	−	3.90377e12i	0.126693	−	0.219438i
$881$	1.34923e13			0.754558			0.377279	−	0.926100i	$-0.376860\pi$
$881$	1.34923e13			0.754558			0.377279	+	0.926100i	$0.376860\pi$
$882$		0			0
$883$	−7.07524e12			−0.391668			−0.195834	−	0.980637i	$-0.562741\pi$
$883$	−7.07524e12			−0.391668			−0.195834	+	0.980637i	$0.562741\pi$
$884$	−8.06359e12	+	1.39665e13i	−0.444113	+	0.769226i
$885$		0			0
$886$	−8.26617e12	−	1.43174e13i	−0.450664	−	0.780572i
$887$	−5.92317e12	−	1.02592e13i	−0.321291	−	0.556492i	0.659464	−	0.751736i	$-0.270783\pi$
$887$	−5.92317e12	−	1.02592e13i	−0.321291	−	0.556492i	−0.980755	+	0.195245i	$0.937450\pi$
$888$		0			0
$889$	2.36587e13	−	4.09780e13i	1.27038	−	2.20036i
$890$	−9.71385e12			−0.518963
$891$		0			0
$892$	1.22655e13			0.648699
$893$	3.59214e12	−	6.22176e12i	0.189026	−	0.327402i
$894$		0			0
$895$	1.09080e13	+	1.88932e13i	0.568253	+	0.984243i
$896$	−1.53988e12	−	2.66715e12i	−0.0798180	−	0.138249i
$897$		0			0
$898$	8.45060e12	−	1.46369e13i	0.433655	−	0.751112i
$899$	−2.85237e12			−0.145642
$900$		0			0
$901$	2.53605e13			1.28202
$902$	1.12024e13	−	1.94031e13i	0.563483	−	0.975982i
$903$		0			0
$904$	1.53678e12	+	2.66179e12i	0.0765341	+	0.132561i
$905$	−1.39403e13	−	2.41453e13i	−0.690802	−	1.19650i
$906$		0			0
$907$	−1.10486e13	+	1.91367e13i	−0.542092	+	0.938931i	0.456691	+	0.889625i	$0.349034\pi$
$907$	−1.10486e13	+	1.91367e13i	−0.542092	+	0.938931i	−0.998784	+	0.0493062i	$0.984299\pi$
$908$	6.94198e12			0.338920
$909$		0			0
$910$	2.29198e13			1.10796
$911$	−3.99076e12	+	6.91220e12i	−0.191965	+	0.332494i	−0.945902	−	0.324454i	$-0.894819\pi$
$911$	−3.99076e12	+	6.91220e12i	−0.191965	+	0.332494i	0.753936	+	0.656948i	$0.228153\pi$
$912$		0			0
$913$	5.15823e11	+	8.93432e11i	0.0245687	+	0.0425543i
$914$	5.02479e12	+	8.70319e12i	0.238155	+	0.412497i
$915$		0			0
$916$	−6.85006e12	+	1.18646e13i	−0.321488	+	0.556833i
$917$	4.93753e13			2.30594
$918$		0			0
$919$	−3.54669e13			−1.64023			−0.820113	−	0.572202i	$-0.806090\pi$
$919$	−3.54669e13			−1.64023			−0.820113	+	0.572202i	$0.806090\pi$
$920$	−5.02843e12	+	8.70950e12i	−0.231413	+	0.400819i
$921$		0			0
$922$	−7.14387e12	−	1.23735e13i	−0.325570	−	0.563904i
$923$	−9.77757e12	−	1.69353e13i	−0.443428	−	0.768040i
$924$		0			0
$925$	3.30065e12	−	5.71689e12i	0.148239	−	0.256757i
$926$	1.80066e13			0.804787
$927$		0			0
$928$	−2.51598e12			−0.111363
$929$	−9.21512e12	+	1.59611e13i	−0.405910	+	0.703058i	−0.994427	−	0.105428i	$-0.966379\pi$
$929$	−9.21512e12	+	1.59611e13i	−0.405910	+	0.703058i	0.588517	+	0.808485i	$0.299712\pi$
$930$		0			0
$931$	9.62812e12	+	1.66764e13i	0.420018	+	0.727493i
$932$	−9.20188e12	−	1.59381e13i	−0.399489	−	0.691935i
$933$		0			0
$934$	−8.37831e12	+	1.45117e13i	−0.360243	+	0.623959i
$935$	4.08119e13			1.74636
$936$		0			0
$937$	−2.09388e13			−0.887410			−0.443705	−	0.896173i	$-0.646336\pi$
$937$	−2.09388e13			−0.887410			−0.443705	+	0.896173i	$0.646336\pi$
$938$	1.80363e12	−	3.12399e12i	0.0760739	−	0.131764i
$939$		0			0
$940$	5.12608e12	+	8.87863e12i	0.214146	+	0.370912i
$941$	1.24446e13	+	2.15547e13i	0.517403	+	0.896168i	0.999796	+	0.0202133i	$0.00643453\pi$
$941$	1.24446e13	+	2.15547e13i	0.517403	+	0.896168i	−0.482393	+	0.875955i	$0.660232\pi$
$942$		0			0
$943$	−2.49931e13	+	4.32892e13i	−1.02924	+	1.78270i
$944$	4.86329e12			0.199322
$945$		0			0
$946$	9.97556e12			0.404974
$947$	−6.20740e12	+	1.07515e13i	−0.250804	+	0.434406i	−0.963747	−	0.266816i	$-0.914028\pi$
$947$	−6.20740e12	+	1.07515e13i	−0.250804	+	0.434406i	0.712943	+	0.701222i	$0.247362\pi$
$948$		0			0
$949$	−1.36450e13	−	2.36338e13i	−0.546103	−	0.945879i
$950$	9.62261e11	+	1.66668e12i	0.0383298	+	0.0663892i
$951$		0			0
$952$	1.39418e13	−	2.41479e13i	0.550114	−	0.952826i
$953$	−3.02285e13			−1.18713			−0.593566	−	0.804785i	$-0.702281\pi$
$953$	−3.02285e13			−1.18713			−0.593566	+	0.804785i	$0.702281\pi$
$954$		0			0
$955$	1.27002e13			0.494079
$956$	−3.54623e12	+	6.14226e12i	−0.137311	+	0.237830i
$957$		0			0
$958$	−1.02103e13	−	1.76847e13i	−0.391644	−	0.678348i
$959$	3.78812e13	+	6.56122e13i	1.44624	+	2.50496i
$960$		0			0
$961$	1.25132e13	−	2.16735e13i	0.473275	−	0.819737i
$962$	1.96683e13			0.740421
$963$		0			0
$964$	5.98793e12			0.223321
$965$	1.04376e13	−	1.80784e13i	0.387461	−	0.671102i
$966$		0			0
$967$	−1.05726e13	−	1.83122e13i	−0.388832	−	0.673476i	0.603461	−	0.797393i	$-0.293788\pi$
$967$	−1.05726e13	−	1.83122e13i	−0.388832	−	0.673476i	−0.992293	+	0.123916i	$0.960455\pi$
$968$	2.17682e12	+	3.77036e12i	0.0796861	+	0.138020i
$969$		0			0
$970$	4.08526e12	−	7.07588e12i	0.148165	−	0.256630i
$971$	4.31181e13			1.55659			0.778293	−	0.627901i	$-0.216086\pi$
$971$	4.31181e13			1.55659			0.778293	+	0.627901i	$0.216086\pi$
$972$		0			0
$973$	9.78734e13			3.50072
$974$	5.29983e12	−	9.17958e12i	0.188689	−	0.326819i
$975$		0			0
$976$	−2.65500e12	−	4.59859e12i	−0.0936569	−	0.162219i
$977$	−1.41929e13	−	2.45828e13i	−0.498362	−	0.863189i	0.501636	−	0.865079i	$-0.332732\pi$
$977$	−1.41929e13	−	2.45828e13i	−0.498362	−	0.863189i	−0.999998	+	0.00188990i	$0.999398\pi$
$978$		0			0
$979$	1.50974e13	−	2.61494e13i	0.525265	−	0.909786i
$980$	−2.74792e13			−0.951672
$981$		0			0
$982$	−3.72081e13			−1.27684
$983$	1.93990e13	−	3.36001e13i	0.662657	−	1.14776i	−0.317258	−	0.948339i	$-0.602762\pi$
$983$	1.93990e13	−	3.36001e13i	0.662657	−	1.14776i	0.979915	−	0.199416i	$-0.0639045\pi$
$984$		0			0
$985$	−7.13786e11	−	1.23631e12i	−0.0241605	−	0.0418471i
$986$	−1.13896e13	−	1.97274e13i	−0.383763	−	0.664697i
$987$		0			0
$988$	−2.86702e12	+	4.96582e12i	−0.0957247	+	0.165800i
$989$	−2.22559e13			−0.739712
$990$		0			0
$991$	−3.91150e13			−1.28829			−0.644143	−	0.764905i	$-0.722786\pi$
$991$	−3.91150e13			−1.28829			−0.644143	+	0.764905i	$0.722786\pi$
$992$	−6.23259e11	+	1.07952e12i	−0.0204346	+	0.0353938i
$993$		0			0
$994$	1.69053e13	+	2.92808e13i	0.549267	+	0.951358i
$995$	9.25077e12	+	1.60228e13i	0.299208	+	0.518244i
$996$		0			0
$997$	−5.14522e12	+	8.91178e12i	−0.164921	+	0.285651i	−0.936627	−	0.350328i	$-0.886070\pi$
$997$	−5.14522e12	+	8.91178e12i	−0.164921	+	0.285651i	0.771706	+	0.635979i	$0.219404\pi$
$998$	4.98326e11			0.0159011
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	162.10.c.j.55.1		2
3.2	odd	2		162.10.c.a.55.1		2
9.2	odd	6		54.10.a.d.1.1	yes	1
9.4	even	3	inner	162.10.c.j.109.1		2
9.5	odd	6		162.10.c.a.109.1		2
9.7	even	3		54.10.a.a.1.1	✓	1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
54.10.a.a.1.1	✓	1	9.7	even	3
54.10.a.d.1.1	yes	1	9.2	odd	6
162.10.c.a.55.1		2	3.2	odd	2
162.10.c.a.109.1		2	9.5	odd	6
162.10.c.j.55.1		2	1.1	even	1	trivial
162.10.c.j.109.1		2	9.4	even	3	inner

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:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	162.c (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(8.00000 - 13.8564i) q^{2} +(-128.000 - 221.703i) q^{4} +(588.000 + 1018.45i) q^{5} +(5736.50 - 9935.91i) q^{7} -4096.00 q^{8} +O(q^{10})\)	\(q+(8.00000 - 13.8564i) q^{2} +(-128.000 - 221.703i) q^{4} +(588.000 + 1018.45i) q^{5} +(5736.50 - 9935.91i) q^{7} -4096.00 q^{8} +18816.0 q^{10} +(-29244.0 + 50652.1i) q^{11} +(53085.5 + 91946.8i) q^{13} +(-91784.0 - 158975. i) q^{14} +(-32768.0 + 56755.8i) q^{16} -593352. q^{17} -210967. q^{19} +(150528. - 260722. i) q^{20} +(467904. + 810434. i) q^{22} +(-1.04392e6 - 1.80812e6i) q^{23} +(285074. - 493764. i) q^{25} +1.69874e6 q^{26} -2.93709e6 q^{28} +(-1.19971e6 + 2.07796e6i) q^{29} +(594386. + 1.02951e6i) q^{31} +(524288. + 908093. i) q^{32} +(-4.74682e6 + 8.22173e6i) q^{34} +1.34922e7 q^{35} +1.15782e7 q^{37} +(-1.68774e6 + 2.92324e6i) q^{38} +(-2.40845e6 - 4.17155e6i) q^{40} +(-1.19708e7 - 2.07341e7i) q^{41} +(5.32992e6 - 9.23169e6i) q^{43} +1.49729e7 q^{44} -3.34053e7 q^{46} +(-1.70270e7 + 2.94916e7i) q^{47} +(-4.56381e7 - 7.90474e7i) q^{49} +(-4.56119e6 - 7.90022e6i) q^{50} +(1.35899e7 - 2.35384e7i) q^{52} -4.27411e7 q^{53} -6.87819e7 q^{55} +(-2.34967e7 + 4.06975e7i) q^{56} +(1.91954e7 + 3.32474e7i) q^{58} +(-3.71040e7 - 6.42660e7i) q^{59} +(-4.05120e7 + 7.01689e7i) q^{61} +1.90204e7 q^{62} +1.67772e7 q^{64} +(-6.24285e7 + 1.08129e8i) q^{65} +(9.82543e6 + 1.70181e7i) q^{67} +(7.59491e7 + 1.31548e8i) q^{68} +(1.07938e8 - 1.86954e8i) q^{70} -1.84185e8 q^{71} -2.57038e8 q^{73} +(9.26255e7 - 1.60432e8i) q^{74} +(2.70038e7 + 4.67719e7i) q^{76} +(3.35516e8 + 5.81131e8i) q^{77} +(-3.25796e8 + 5.64295e8i) q^{79} -7.70703e7 q^{80} -3.83066e8 q^{82} +(8.81930e6 - 1.52755e7i) q^{83} +(-3.48891e8 - 6.04297e8i) q^{85} +(-8.52787e7 - 1.47707e8i) q^{86} +(1.19783e8 - 2.07471e8i) q^{88} -5.16255e8 q^{89} +1.21810e9 q^{91} +(-2.67242e8 + 4.62878e8i) q^{92} +(2.72432e8 + 4.71866e8i) q^{94} +(-1.24049e8 - 2.14858e8i) q^{95} +(2.17116e8 - 3.76057e8i) q^{97} -1.46042e9 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 16 q^{2} - 256 q^{4} + 1176 q^{5} + 11473 q^{7} - 8192 q^{8}+O(q^{10}) \) 2 * q + 16 * q^2 - 256 * q^4 + 1176 * q^5 + 11473 * q^7 - 8192 * q^8	\( 2 q + 16 q^{2} - 256 q^{4} + 1176 q^{5} + 11473 q^{7} - 8192 q^{8} + 37632 q^{10} - 58488 q^{11} + 106171 q^{13} - 183568 q^{14} - 65536 q^{16} - 1186704 q^{17} - 421934 q^{19} + 301056 q^{20} + 935808 q^{22} - 2087832 q^{23} + 570149 q^{25} + 3397472 q^{26} - 5874176 q^{28} - 2399424 q^{29} + 1188772 q^{31} + 1048576 q^{32} - 9493632 q^{34} + 26984496 q^{35} + 23156374 q^{37} - 3375472 q^{38} - 4816896 q^{40} - 23941632 q^{41} + 10659832 q^{43} + 29945856 q^{44} - 66810624 q^{46} - 34054008 q^{47} - 91276122 q^{49} - 9122384 q^{50} + 27179776 q^{52} - 85482144 q^{53} - 137563776 q^{55} - 46993408 q^{56} + 38390784 q^{58} - 74207928 q^{59} - 81024095 q^{61} + 38040704 q^{62} + 33554432 q^{64} - 124857096 q^{65} + 19650859 q^{67} + 151898112 q^{68} + 215875968 q^{70} - 368370720 q^{71} - 514075406 q^{73} + 185250992 q^{74} + 54007552 q^{76} + 671032824 q^{77} - 651592289 q^{79} - 154140672 q^{80} - 766132224 q^{82} + 17638608 q^{83} - 697781952 q^{85} - 170557312 q^{86} + 239566848 q^{88} - 1032509520 q^{89} + 2436199766 q^{91} - 534484992 q^{92} + 544864128 q^{94} - 248097192 q^{95} + 434232691 q^{97} - 2920835904 q^{98}+O(q^{100}) \) 2 * q + 16 * q^2 - 256 * q^4 + 1176 * q^5 + 11473 * q^7 - 8192 * q^8 + 37632 * q^10 - 58488 * q^11 + 106171 * q^13 - 183568 * q^14 - 65536 * q^16 - 1186704 * q^17 - 421934 * q^19 + 301056 * q^20 + 935808 * q^22 - 2087832 * q^23 + 570149 * q^25 + 3397472 * q^26 - 5874176 * q^28 - 2399424 * q^29 + 1188772 * q^31 + 1048576 * q^32 - 9493632 * q^34 + 26984496 * q^35 + 23156374 * q^37 - 3375472 * q^38 - 4816896 * q^40 - 23941632 * q^41 + 10659832 * q^43 + 29945856 * q^44 - 66810624 * q^46 - 34054008 * q^47 - 91276122 * q^49 - 9122384 * q^50 + 27179776 * q^52 - 85482144 * q^53 - 137563776 * q^55 - 46993408 * q^56 + 38390784 * q^58 - 74207928 * q^59 - 81024095 * q^61 + 38040704 * q^62 + 33554432 * q^64 - 124857096 * q^65 + 19650859 * q^67 + 151898112 * q^68 + 215875968 * q^70 - 368370720 * q^71 - 514075406 * q^73 + 185250992 * q^74 + 54007552 * q^76 + 671032824 * q^77 - 651592289 * q^79 - 154140672 * q^80 - 766132224 * q^82 + 17638608 * q^83 - 697781952 * q^85 - 170557312 * q^86 + 239566848 * q^88 - 1032509520 * q^89 + 2436199766 * q^91 - 534484992 * q^92 + 544864128 * q^94 - 248097192 * q^95 + 434232691 * q^97 - 2920835904 * q^98

Introduction

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