LMFDB - Embedded newform 126.10.g.e.37.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [126,10,Mod(37,126)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(126, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 2])) N = Newforms(chi, 10, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("126.37"); S:= CuspForms(chi, 10); N := Newforms(S);

Level:	$ N $	$=$	$ 126 = 2 \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 10 $
Character orbit:	$[\chi]$	$=$	126.g (of order $3$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [6,-48,0,-768,1085] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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

Self dual:	no
Analytic conductor:	$64.8945153566$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{6} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{5} + 4038x^{4} - 137923x^{3} + 16368349x^{2} - 286546260x + 5038160400 $ x^6 - x^5 + 4038x^4 - 137923x^3 + 16368349x^2 - 286546260x + 5038160400
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{6}\cdot 3\cdot 7 $
Twist minimal:	no (minimal twist has level 14)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			37.1
Root			$26.1296 + 45.2579i$ of defining polynomial
Character	$\chi$	$=$	126.37
Dual form			126.10.g.e.109.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-8.00000 + 13.8564i) q^{2} +(-128.000 - 221.703i) q^{4} +(-546.130 + 945.925i) q^{5} +(6111.84 - 1731.76i) q^{7} +4096.00 q^{8} +(-8738.08 - 15134.8i) q^{10} +(27030.4 + 46818.1i) q^{11} +37802.6 q^{13} +(-24898.8 + 98542.3i) q^{14} +(-32768.0 + 56755.8i) q^{16} +(-176735. - 306114. i) q^{17} +(-25105.3 + 43483.7i) q^{19} +279618. q^{20} -864974. q^{22} +(1.22926e6 - 2.12914e6i) q^{23} +(380047. + 658261. i) q^{25} +(-302421. + 523808. i) q^{26} +(-1.16625e6 - 1.13335e6i) q^{28} -1.40865e6 q^{29} +(-2.89162e6 - 5.00843e6i) q^{31} +(-524288. - 908093. i) q^{32} +5.65552e6 q^{34} +(-1.69974e6 + 6.72711e6i) q^{35} +(-2.72938e6 + 4.72743e6i) q^{37} +(-401685. - 695739. i) q^{38} +(-2.23695e6 + 3.87451e6i) q^{40} +1.73066e7 q^{41} +1.43644e6 q^{43} +(6.91979e6 - 1.19854e7i) q^{44} +(1.96682e7 + 3.40663e7i) q^{46} +(1.52194e7 - 2.63607e7i) q^{47} +(3.43556e7 - 2.11685e7i) q^{49} -1.21615e7 q^{50} +(-4.83873e6 - 8.38092e6i) q^{52} +(-2.15398e6 - 3.73080e6i) q^{53} -5.90485e7 q^{55} +(2.50341e7 - 7.09329e6i) q^{56} +(1.12692e7 - 1.95189e7i) q^{58} +(-3.30728e7 - 5.72837e7i) q^{59} +(1.00462e8 - 1.74006e8i) q^{61} +9.25317e7 q^{62} +1.67772e7 q^{64} +(-2.06451e7 + 3.57584e7i) q^{65} +(1.36301e8 + 2.36080e8i) q^{67} +(-4.52441e7 + 7.83651e7i) q^{68} +(-7.96156e7 - 7.73692e7i) q^{70} -1.43433e8 q^{71} +(1.84016e8 + 3.18725e8i) q^{73} +(-4.36701e7 - 7.56389e7i) q^{74} +1.28539e7 q^{76} +(2.46283e8 + 2.39334e8i) q^{77} +(-2.31998e8 + 4.01832e8i) q^{79} +(-3.57912e7 - 6.19921e7i) q^{80} +(-1.38453e8 + 2.39808e8i) q^{82} +7.47626e8 q^{83} +3.86081e8 q^{85} +(-1.14915e7 + 1.99038e7i) q^{86} +(1.10717e8 + 1.91767e8i) q^{88} +(-5.63943e8 + 9.76778e8i) q^{89} +(2.31043e8 - 6.54650e7i) q^{91} -6.29382e8 q^{92} +(2.43510e8 + 4.21771e8i) q^{94} +(-2.74215e7 - 4.74955e7i) q^{95} -1.27313e8 q^{97} +(1.84743e7 + 6.45393e8i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 48 q^{2} - 768 q^{4} + 1085 q^{5} - 6796 q^{7} + 24576 q^{8} + 17360 q^{10} - 2555 q^{11} + 36140 q^{13} - 43504 q^{14} - 196608 q^{16} - 20759 q^{17} + 1220649 q^{19} - 555520 q^{20} + 81760 q^{22}+ \cdots + 597954960 q^{98}+O(q^{100}) $ 6 * q - 48 * q^2 - 768 * q^4 + 1085 * q^5 - 6796 * q^7 + 24576 * q^8 + 17360 * q^10 - 2555 * q^11 + 36140 * q^13 - 43504 * q^14 - 196608 * q^16 - 20759 * q^17 + 1220649 * q^19 - 555520 * q^20 + 81760 * q^22 + 1960903 * q^23 - 863572 * q^25 - 289120 * q^26 + 2435840 * q^28 + 5212292 * q^29 - 9377989 * q^31 - 3145728 * q^32 + 664288 * q^34 - 20361719 * q^35 - 25814913 * q^37 + 19530384 * q^38 + 4444160 * q^40 - 418500 * q^41 + 5888616 * q^43 - 654080 * q^44 + 31374448 * q^46 - 48391269 * q^47 + 108466086 * q^49 + 27634304 * q^50 - 4625920 * q^52 - 102186411 * q^53 - 456557402 * q^55 - 27836416 * q^56 - 41698336 * q^58 - 144220135 * q^59 + 280936871 * q^61 + 300095648 * q^62 + 100663296 * q^64 + 186819738 * q^65 + 170710399 * q^67 - 5314304 * q^68 - 347247824 * q^70 - 939517376 * q^71 + 613838539 * q^73 - 413038608 * q^74 - 624972288 * q^76 + 729499715 * q^77 + 197445809 * q^79 + 71106560 * q^80 + 3348000 * q^82 + 2148362872 * q^83 + 822545038 * q^85 - 47108928 * q^86 - 10465280 * q^88 - 805730427 * q^89 + 17178248 * q^91 - 1003982336 * q^92 - 774260304 * q^94 - 1799421743 * q^95 - 4525836188 * q^97 + 597954960 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/126\mathbb{Z}\right)^\times$.

$n$	$29$	$73$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$

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
$5$	−546.130	+	945.925i	−0.390779	+	0.676849i	−0.992552	−	0.121818i	$-0.961128\pi$
$5$	−546.130	+	945.925i	−0.390779	+	0.676849i	0.601774	+	0.798667i	$0.294461\pi$
$6$		0			0
$7$	6111.84	−	1731.76i	0.962124	−	0.272613i
$7$	6111.84	−	1731.76i	0.962124	−	0.272613i
$8$	4096.00			0.353553
$9$		0			0
$10$	−8738.08	−	15134.8i	−0.276322	−	0.478604i
$11$	27030.4	+	46818.1i	0.556655	+	0.964154i	0.997773	+	0.0667050i	$0.0212486\pi$
$11$	27030.4	+	46818.1i	0.556655	+	0.964154i	−0.441118	+	0.897449i	$0.645418\pi$
$12$		0			0
$13$	37802.6			0.367093			0.183547	−	0.983011i	$-0.441242\pi$
$13$	37802.6			0.367093			0.183547	+	0.983011i	$0.441242\pi$
$14$	−24898.8	+	98542.3i	−0.173221	+	0.685561i
$15$		0			0
$16$	−32768.0	+	56755.8i	−0.125000	+	0.216506i
$17$	−176735.	−	306114.i	−0.513218	−	0.888920i	−0.999882	−	0.0153311i	$-0.995120\pi$
$17$	−176735.	−	306114.i	−0.513218	−	0.888920i	0.486664	−	0.873589i	$-0.338214\pi$
$18$		0			0
$19$	−25105.3	+	43483.7i	−0.0441952	+	0.0765483i	−0.887277	−	0.461237i	$-0.847406\pi$
$19$	−25105.3	+	43483.7i	−0.0441952	+	0.0765483i	0.843082	+	0.537786i	$0.180739\pi$
$20$	279618.			0.390779
$21$		0			0
$22$	−864974.			−0.787228
$23$	1.22926e6	−	2.12914e6i	0.915944	−	1.58646i	0.110432	−	0.993884i	$-0.464777\pi$
$23$	1.22926e6	−	2.12914e6i	0.915944	−	1.58646i	0.805513	−	0.592579i	$-0.201890\pi$
$24$		0			0
$25$	380047.	+	658261.i	0.194584	+	0.337029i
$26$	−302421.	+	523808.i	−0.129787	+	0.224798i
$27$		0			0
$28$	−1.16625e6	−	1.13335e6i	−0.358576	−	0.348459i
$29$	−1.40865e6			−0.369840			−0.184920	−	0.982754i	$-0.559203\pi$
$29$	−1.40865e6			−0.369840			−0.184920	+	0.982754i	$0.559203\pi$
$30$		0			0
$31$	−2.89162e6	−	5.00843e6i	−0.562358	−	0.974033i	−0.997290	−	0.0735696i	$-0.976561\pi$
$31$	−2.89162e6	−	5.00843e6i	−0.562358	−	0.974033i	0.434932	−	0.900463i	$-0.356772\pi$
$32$	−524288.	−	908093.i	−0.0883883	−	0.153093i
$33$		0			0
$34$	5.65552e6			0.725800
$35$	−1.69974e6	+	6.72711e6i	−0.191460	+	0.757743i
$36$		0			0
$37$	−2.72938e6	+	4.72743e6i	−0.239418	+	0.414684i	−0.960547	−	0.278116i	$-0.910290\pi$
$37$	−2.72938e6	+	4.72743e6i	−0.239418	+	0.414684i	0.721129	+	0.692800i	$0.243623\pi$
$38$	−401685.	−	695739.i	−0.0312507	−	0.0541278i
$39$		0			0
$40$	−2.23695e6	+	3.87451e6i	−0.138161	+	0.239302i
$41$	1.73066e7			0.956501			0.478251	−	0.878223i	$-0.341271\pi$
$41$	1.73066e7			0.956501			0.478251	+	0.878223i	$0.341271\pi$
$42$		0			0
$43$	1.43644e6			0.0640735			0.0320367	−	0.999487i	$-0.489801\pi$
$43$	1.43644e6			0.0640735			0.0320367	+	0.999487i	$0.489801\pi$
$44$	6.91979e6	−	1.19854e7i	0.278327	−	0.482077i
$45$		0			0
$46$	1.96682e7	+	3.40663e7i	0.647671	+	1.12180i
$47$	1.52194e7	−	2.63607e7i	0.454942	−	0.787982i	−0.543743	−	0.839252i	$-0.682993\pi$
$47$	1.52194e7	−	2.63607e7i	0.454942	−	0.787982i	0.998685	+	0.0512695i	$0.0163267\pi$
$48$		0			0
$49$	3.43556e7	−	2.11685e7i	0.851364	−	0.524575i
$50$	−1.21615e7			−0.275183
$51$		0			0
$52$	−4.83873e6	−	8.38092e6i	−0.0917733	−	0.158956i
$53$	−2.15398e6	−	3.73080e6i	−0.0374973	−	0.0649473i	0.846668	−	0.532122i	$-0.178605\pi$
$53$	−2.15398e6	−	3.73080e6i	−0.0374973	−	0.0649473i	−0.884165	+	0.467175i	$0.845272\pi$
$54$		0			0
$55$	−5.90485e7			−0.870115
$56$	2.50341e7	−	7.09329e6i	0.340162	−	0.0963833i
$57$		0			0
$58$	1.12692e7	−	1.95189e7i	0.130758	−	0.226480i
$59$	−3.30728e7	−	5.72837e7i	−0.355334	−	0.615456i	0.631841	−	0.775098i	$-0.282300\pi$
$59$	−3.30728e7	−	5.72837e7i	−0.355334	−	0.615456i	−0.987175	+	0.159642i	$0.948966\pi$
$60$		0			0
$61$	1.00462e8	−	1.74006e8i	0.929008	−	1.60909i	0.144022	−	0.989574i	$-0.453996\pi$
$61$	1.00462e8	−	1.74006e8i	0.929008	−	1.60909i	0.784986	−	0.619514i	$-0.212670\pi$
$62$	9.25317e7			0.795295
$63$		0			0
$64$	1.67772e7			0.125000
$65$	−2.06451e7	+	3.57584e7i	−0.143452	+	0.248466i
$66$		0			0
$67$	1.36301e8	+	2.36080e8i	0.826347	+	1.43127i	0.900886	+	0.434057i	$0.142918\pi$
$67$	1.36301e8	+	2.36080e8i	0.826347	+	1.43127i	−0.0745386	+	0.997218i	$0.523748\pi$
$68$	−4.52441e7	+	7.83651e7i	−0.256609	+	0.444460i
$69$		0			0
$70$	−7.96156e7	−	7.73692e7i	−0.396330	−	0.385147i
$71$	−1.43433e8			−0.669866			−0.334933	−	0.942242i	$-0.608714\pi$
$71$	−1.43433e8			−0.669866			−0.334933	+	0.942242i	$0.608714\pi$
$72$		0			0
$73$	1.84016e8	+	3.18725e8i	0.758407	+	1.31360i	0.943663	+	0.330909i	$0.107355\pi$
$73$	1.84016e8	+	3.18725e8i	0.758407	+	1.31360i	−0.185256	+	0.982690i	$0.559311\pi$
$74$	−4.36701e7	−	7.56389e7i	−0.169294	−	0.293226i
$75$		0			0
$76$	1.28539e7			0.0441952
$77$	2.46283e8	+	2.39334e8i	0.798412	+	0.775884i
$78$		0			0
$79$	−2.31998e8	+	4.01832e8i	−0.670134	+	1.16071i	0.307731	+	0.951473i	$0.400430\pi$
$79$	−2.31998e8	+	4.01832e8i	−0.670134	+	1.16071i	−0.977866	+	0.209233i	$0.932903\pi$
$80$	−3.57912e7	−	6.19921e7i	−0.0976947	−	0.169212i
$81$		0			0
$82$	−1.38453e8	+	2.39808e8i	−0.338174	+	0.585735i
$83$	7.47626e8			1.72915			0.864576	−	0.502503i	$-0.167587\pi$
$83$	7.47626e8			1.72915			0.864576	+	0.502503i	$0.167587\pi$
$84$		0			0
$85$	3.86081e8			0.802219
$86$	−1.14915e7	+	1.99038e7i	−0.0226534	+	0.0392368i
$87$		0			0
$88$	1.10717e8	+	1.91767e8i	0.196807	+	0.340880i
$89$	−5.63943e8	+	9.76778e8i	−0.952753	+	1.65022i	−0.213325	+	0.976981i	$0.568429\pi$
$89$	−5.63943e8	+	9.76778e8i	−0.952753	+	1.65022i	−0.739428	+	0.673235i	$0.764904\pi$
$90$		0			0
$91$	2.31043e8	−	6.54650e7i	0.353189	−	0.100074i
$92$	−6.29382e8			−0.915944
$93$		0			0
$94$	2.43510e8	+	4.21771e8i	0.321692	+	0.557188i
$95$	−2.74215e7	−	4.74955e7i	−0.0345410	−	0.0598269i
$96$		0			0
$97$	−1.27313e8			−0.146016			−0.0730079	−	0.997331i	$-0.523260\pi$
$97$	−1.27313e8			−0.146016			−0.0730079	+	0.997331i	$0.523260\pi$
$98$	1.84743e7	+	6.45393e8i	0.0202325	+	0.706817i
$99$		0			0
$100$	9.72920e7	−	1.68515e8i	0.0972920	−	0.168515i
$101$	7.52725e8	+	1.30376e9i	0.719764	+	1.24667i	0.961093	+	0.276225i	$0.0890834\pi$
$101$	7.52725e8	+	1.30376e9i	0.719764	+	1.24667i	−0.241329	+	0.970443i	$0.577583\pi$
$102$		0			0
$103$	2.97478e8	−	5.15246e8i	0.260428	−	0.451074i	−0.705928	−	0.708284i	$-0.749470\pi$
$103$	2.97478e8	−	5.15246e8i	0.260428	−	0.451074i	0.966356	+	0.257210i	$0.0828032\pi$
$104$	1.54839e8			0.129787
$105$		0			0
$106$	6.89274e7			0.0530292
$107$	6.77457e8	−	1.17339e9i	0.499637	−	0.865397i	−0.500363	−	0.865816i	$-0.666800\pi$
$107$	6.77457e8	−	1.17339e9i	0.499637	−	0.865397i	1.00000		0.000418881i	$0.000133334\pi$
$108$		0			0
$109$	9.68920e8	+	1.67822e9i	0.657459	+	1.13875i	0.981271	+	0.192631i	$0.0617021\pi$
$109$	9.68920e8	+	1.67822e9i	0.657459	+	1.13875i	−0.323812	+	0.946121i	$0.604965\pi$
$110$	4.72388e8	−	8.18200e8i	0.307632	−	0.532834i
$111$		0			0
$112$	−1.01985e8	+	4.03629e8i	−0.0612430	+	0.242383i
$113$	1.98306e9			1.14415			0.572074	−	0.820202i	$-0.306139\pi$
$113$	1.98306e9			1.14415			0.572074	+	0.820202i	$0.306139\pi$
$114$		0			0
$115$	1.34267e9	+	2.32558e9i	0.715863	+	1.23991i
$116$	1.80308e8	+	3.12302e8i	0.0924599	+	0.160145i
$117$		0			0
$118$	1.05833e9			0.502518
$119$	−1.61029e9	−	1.56486e9i	−0.736111	−	0.715341i
$120$		0			0
$121$	−2.82314e8	+	4.88982e8i	−0.119729	+	0.207376i
$122$	1.60740e9	+	2.78410e9i	0.656908	+	1.13780i
$123$		0			0
$124$	−7.40254e8	+	1.28216e9i	−0.281179	+	0.487016i
$125$	−2.96354e9			−1.08571
$126$		0			0
$127$	3.90286e7			0.0133127			0.00665635	−	0.999978i	$-0.497881\pi$
$127$	3.90286e7			0.0133127			0.00665635	+	0.999978i	$0.497881\pi$
$128$	−1.34218e8	+	2.32472e8i	−0.0441942	+	0.0765466i
$129$		0			0
$130$	−3.30322e8	−	5.72134e8i	−0.101436	−	0.175692i
$131$	7.96889e8	−	1.38025e9i	0.236416	−	0.409485i	−0.723267	−	0.690568i	$-0.757360\pi$
$131$	7.96889e8	−	1.38025e9i	0.236416	−	0.409485i	0.959683	+	0.281083i	$0.0906938\pi$
$132$		0			0
$133$	−7.81364e7	+	3.09242e8i	−0.0216532	+	0.0856971i
$134$	−4.36163e9			−1.16863
$135$		0			0
$136$	−7.23906e8	−	1.25384e9i	−0.181450	−	0.314281i
$137$	2.81817e9	+	4.88122e9i	0.683479	+	1.18382i	0.973912	+	0.226925i	$0.0728672\pi$
$137$	2.81817e9	+	4.88122e9i	0.683479	+	1.18382i	−0.290433	+	0.956895i	$0.593799\pi$
$138$		0			0
$139$	2.40520e9			0.546493			0.273246	−	0.961944i	$-0.411903\pi$
$139$	2.40520e9			0.546493			0.273246	+	0.961944i	$0.411903\pi$
$140$	1.70898e9	−	4.84232e8i	0.375977	−	0.106531i
$141$		0			0
$142$	1.14747e9	−	1.98747e9i	0.236833	−	0.410208i
$143$	1.02182e9	+	1.76984e9i	0.204344	+	0.353934i
$144$		0			0
$145$	7.69308e8	−	1.33248e9i	0.144525	−	0.250325i
$146$	−5.88851e9			−1.07255
$147$		0			0
$148$	1.39744e9			0.239418
$149$	2.41463e9	−	4.18227e9i	0.401341	−	0.695143i	−0.592547	−	0.805536i	$-0.701878\pi$
$149$	2.41463e9	−	4.18227e9i	0.401341	−	0.695143i	0.993888	+	0.110393i	$0.0352110\pi$
$150$		0			0
$151$	−5.33310e9	−	9.23721e9i	−0.834802	−	1.44592i	−0.894191	−	0.447685i	$-0.852248\pi$
$151$	−5.33310e9	−	9.23721e9i	−0.834802	−	1.44592i	0.0593887	−	0.998235i	$-0.481085\pi$
$152$	−1.02831e8	+	1.78109e8i	−0.0156253	+	0.0270639i
$153$		0			0
$154$	−5.28658e9	+	1.49793e9i	−0.757411	+	0.214609i
$155$	6.31679e9			0.879030
$156$		0			0
$157$	4.95301e9	+	8.57886e9i	0.650610	+	1.12689i	0.982975	+	0.183738i	$0.0588199\pi$
$157$	4.95301e9	+	8.57886e9i	0.650610	+	1.12689i	−0.332365	+	0.943151i	$0.607847\pi$
$158$	−3.71196e9	−	6.42931e9i	−0.473857	−	0.820744i
$159$		0			0
$160$	1.14532e9			0.138161
$161$	3.82589e9	−	1.51418e10i	0.448762	−	1.77607i
$162$		0			0
$163$	6.21440e9	−	1.07637e10i	0.689533	−	1.19431i	−0.282457	−	0.959280i	$-0.591149\pi$
$163$	6.21440e9	−	1.07637e10i	0.689533	−	1.19431i	0.971989	−	0.235025i	$-0.0755173\pi$
$164$	−2.21525e9	−	3.83693e9i	−0.239125	−	0.414177i
$165$		0			0
$166$	−5.98101e9	+	1.03594e10i	−0.611347	+	1.05888i
$167$	5.48234e9			0.545434			0.272717	−	0.962094i	$-0.412078\pi$
$167$	5.48234e9			0.545434			0.272717	+	0.962094i	$0.412078\pi$
$168$		0			0
$169$	−9.17547e9			−0.865243
$170$	−3.08865e9	+	5.34969e9i	−0.283627	+	0.491257i
$171$		0			0
$172$	−1.83864e8	−	3.18462e8i	−0.0160184	−	0.0277446i
$173$	−2.29883e9	+	3.98170e9i	−0.195119	+	0.337956i	−0.946940	−	0.321412i	$-0.895843\pi$
$173$	−2.29883e9	+	3.98170e9i	−0.195119	+	0.337956i	0.751820	+	0.659368i	$0.229176\pi$
$174$		0			0
$175$	3.46274e9	+	3.36504e9i	0.279093	+	0.271218i
$176$	−3.54293e9			−0.278327
$177$		0			0
$178$	−9.02309e9	−	1.56285e10i	−0.673698	−	1.16688i
$179$	1.28201e9	+	2.22051e9i	0.0933370	+	0.161664i	0.908913	−	0.416985i	$-0.136913\pi$
$179$	1.28201e9	+	2.22051e9i	0.0933370	+	0.161664i	−0.815576	+	0.578650i	$0.803580\pi$
$180$		0			0
$181$	−3.58323e9			−0.248154			−0.124077	−	0.992273i	$-0.539597\pi$
$181$	−3.58323e9			−0.248154			−0.124077	+	0.992273i	$0.539597\pi$
$182$	−9.41237e8	+	3.72515e9i	−0.0635884	+	0.251665i
$183$		0			0
$184$	5.03506e9	−	8.72097e9i	0.323835	−	0.560899i
$185$	−2.98120e9	−	5.16358e9i	−0.187119	−	0.324099i
$186$		0			0
$187$	9.55444e9	−	1.65488e10i	0.571371	−	0.989643i
$188$	−7.79231e9			−0.454942
$189$		0			0
$190$	8.77489e8			0.0488484
$191$	−3.48694e8	+	6.03956e8i	−0.0189581	+	0.0328364i	−0.875349	−	0.483492i	$-0.839368\pi$
$191$	−3.48694e8	+	6.03956e8i	−0.0189581	+	0.0328364i	0.856391	+	0.516328i	$0.172702\pi$
$192$		0			0
$193$	2.85429e8	+	4.94378e8i	0.0148078	+	0.0256479i	0.873334	−	0.487121i	$-0.161953\pi$
$193$	2.85429e8	+	4.94378e8i	0.0148078	+	0.0256479i	−0.858527	+	0.512769i	$0.828620\pi$
$194$	1.01850e9	−	1.76410e9i	0.0516244	−	0.0894161i
$195$		0			0
$196$	−9.09063e9	−	4.90716e9i	−0.439989	−	0.237508i
$197$	4.88945e9			0.231293			0.115646	−	0.993290i	$-0.463106\pi$
$197$	4.88945e9			0.231293			0.115646	+	0.993290i	$0.463106\pi$
$198$		0			0
$199$	−5.09120e9	−	8.81822e9i	−0.230134	−	0.398604i	0.727713	−	0.685882i	$-0.240583\pi$
$199$	−5.09120e9	−	8.81822e9i	−0.230134	−	0.398604i	−0.957847	+	0.287277i	$0.907250\pi$
$200$	1.55667e9	+	2.69624e9i	0.0687959	+	0.119158i
$201$		0			0
$202$	−2.40872e10			−1.01790
$203$	−8.60948e9	+	2.43945e9i	−0.355832	+	0.100823i
$204$		0			0
$205$	−9.45167e9	+	1.63708e10i	−0.373780	+	0.647406i
$206$	4.75964e9	+	8.24394e9i	0.184150	+	0.318957i
$207$		0			0
$208$	−1.23871e9	+	2.14552e9i	−0.0458866	+	0.0794780i
$209$	−2.71443e9			−0.0984058
$210$		0			0
$211$	−2.89906e10			−1.00690			−0.503450	−	0.864025i	$-0.667936\pi$
$211$	−2.89906e10			−1.00690			−0.503450	+	0.864025i	$0.667936\pi$
$212$	−5.51419e8	+	9.55086e8i	−0.0187487	+	0.0324736i
$213$		0			0
$214$	1.08393e10	+	1.87742e10i	0.353297	+	0.611928i
$215$	−7.84481e8	+	1.35876e9i	−0.0250386	+	0.0433680i
$216$		0			0
$217$	−2.63465e10	−	2.56031e10i	−0.806592	−	0.783834i
$218$	−3.10054e10			−0.929788
$219$		0			0
$220$	7.55821e9	+	1.30912e10i	0.217529	+	0.376771i
$221$	−6.68103e9	−	1.15719e10i	−0.188399	−	0.326316i
$222$		0			0
$223$	−9.01973e9			−0.244243			−0.122121	−	0.992515i	$-0.538970\pi$
$223$	−9.01973e9			−0.244243			−0.122121	+	0.992515i	$0.538970\pi$
$224$	−4.77697e9	−	4.64218e9i	−0.126776	−	0.123199i
$225$		0			0
$226$	−1.58645e10	+	2.74780e10i	−0.404517	+	0.700644i
$227$	6.63153e9	+	1.14861e10i	0.165767	+	0.287116i	0.936927	−	0.349524i	$-0.113657\pi$
$227$	6.63153e9	+	1.14861e10i	0.165767	+	0.287116i	−0.771161	+	0.636641i	$0.780323\pi$
$228$		0			0
$229$	3.83833e10	−	6.64819e10i	0.922323	−	1.59751i	0.126512	−	0.991965i	$-0.459622\pi$
$229$	3.83833e10	−	6.64819e10i	0.922323	−	1.59751i	0.795811	−	0.605545i	$-0.207045\pi$
$230$	−4.29655e10			−1.01238
$231$		0			0
$232$	−5.76985e9			−0.130758
$233$	−1.14694e9	+	1.98657e9i	−0.0254942	+	0.0441572i	−0.878491	−	0.477759i	$-0.841449\pi$
$233$	−1.14694e9	+	1.98657e9i	−0.0254942	+	0.0441572i	0.852997	+	0.521916i	$0.174783\pi$
$234$		0			0
$235$	1.66235e10	+	2.87927e10i	0.355563	+	0.615853i
$236$	−8.46663e9	+	1.46646e10i	−0.177667	+	0.307728i
$237$		0			0
$238$	3.45656e10	−	9.79400e9i	0.698310	−	0.197863i
$239$	4.06748e10			0.806372			0.403186	−	0.915118i	$-0.367903\pi$
$239$	4.06748e10			0.806372			0.403186	+	0.915118i	$0.367903\pi$
$240$		0			0
$241$	−4.71851e9	−	8.17271e9i	−0.0901008	−	0.156059i	0.817453	−	0.575996i	$-0.195386\pi$
$241$	−4.71851e9	−	8.17271e9i	−0.0901008	−	0.156059i	−0.907553	+	0.419937i	$0.862052\pi$
$242$	−4.51702e9	−	7.82372e9i	−0.0846610	−	0.146637i
$243$		0			0
$244$	−5.14367e10			−0.929008
$245$	1.26117e9	+	4.40586e10i	0.0223628	+	0.781237i
$246$		0			0
$247$	−9.49046e8	+	1.64380e9i	−0.0162237	+	0.0281003i
$248$	−1.18441e10	−	2.05145e10i	−0.198824	−	0.344373i
$249$		0			0
$250$	2.37083e10	−	4.10640e10i	0.383858	−	0.664862i
$251$	7.60552e10			1.20948			0.604738	−	0.796425i	$-0.293278\pi$
$251$	7.60552e10			1.20948			0.604738	+	0.796425i	$0.293278\pi$
$252$		0			0
$253$	1.32910e11			2.03946
$254$	−3.12229e8	+	5.40796e8i	−0.00470675	+	0.00815233i
$255$		0			0
$256$	−2.14748e9	−	3.71955e9i	−0.0312500	−	0.0541266i
$257$	4.51105e10	−	7.81337e10i	0.645028	−	1.11722i	−0.339266	−	0.940690i	$-0.610179\pi$
$257$	4.51105e10	−	7.81337e10i	0.645028	−	1.11722i	0.984295	−	0.176532i	$-0.0564878\pi$
$258$		0			0
$259$	−8.49478e9	+	3.36200e10i	−0.117301	+	0.464246i
$260$	1.05703e10			0.143452
$261$		0			0
$262$	1.27502e10	+	2.20840e10i	0.167172	+	0.289550i
$263$	−4.67841e10	−	8.10324e10i	−0.602972	−	1.04438i	−0.992368	−	0.123308i	$-0.960650\pi$
$263$	−4.67841e10	−	8.10324e10i	−0.602972	−	1.04438i	0.389396	−	0.921070i	$-0.372684\pi$
$264$		0			0
$265$	4.70541e9			0.0586126
$266$	−3.65989e9	−	3.55663e9i	−0.0448230	−	0.0435583i
$267$		0			0
$268$	3.48931e10	−	6.04365e10i	0.413173	−	0.715637i
$269$	7.42816e9	+	1.28660e10i	0.0864960	+	0.149815i	0.906028	−	0.423218i	$-0.139100\pi$
$269$	7.42816e9	+	1.28660e10i	0.0864960	+	0.149815i	−0.819532	+	0.573034i	$0.805766\pi$
$270$		0			0
$271$	−5.85924e10	+	1.01485e11i	−0.659902	+	1.14298i	0.320739	+	0.947168i	$0.396069\pi$
$271$	−5.85924e10	+	1.01485e11i	−0.659902	+	1.14298i	−0.980641	+	0.195816i	$0.937264\pi$
$272$	2.31650e10			0.256609
$273$		0			0
$274$	−9.01815e10			−0.966585
$275$	−2.05457e10	+	3.55861e10i	−0.216632	+	0.375218i
$276$		0			0
$277$	1.43612e10	+	2.48743e10i	0.146565	+	0.253859i	0.929956	−	0.367671i	$-0.119845\pi$
$277$	1.43612e10	+	2.48743e10i	0.146565	+	0.253859i	−0.783390	+	0.621530i	$0.786511\pi$
$278$	−1.92416e10	+	3.33274e10i	−0.193214	+	0.334657i
$279$		0			0
$280$	−6.96215e9	+	2.75542e10i	−0.0676912	+	0.267903i
$281$	7.39690e10			0.707736			0.353868	−	0.935295i	$-0.384866\pi$
$281$	7.39690e10			0.707736			0.353868	+	0.935295i	$0.384866\pi$
$282$		0			0
$283$	3.63744e10	+	6.30023e10i	0.337098	+	0.583872i	0.983886	−	0.178799i	$-0.0572212\pi$
$283$	3.63744e10	+	6.30023e10i	0.337098	+	0.583872i	−0.646787	+	0.762671i	$0.723888\pi$
$284$	1.83595e10	+	3.17996e10i	0.167467	+	0.290061i
$285$		0			0
$286$	−3.26982e10			−0.288986
$287$	1.05775e11	−	2.99710e10i	0.920273	−	0.260755i
$288$		0			0
$289$	−3.17652e9	+	5.50189e9i	−0.0267862	+	0.0463950i
$290$	1.23089e10	+	2.13197e10i	0.102195	+	0.177007i
$291$		0			0
$292$	4.71081e10	−	8.15935e10i	0.379204	−	0.656800i
$293$	−2.43926e11			−1.93354			−0.966771	−	0.255644i	$-0.917712\pi$
$293$	−2.43926e11			−1.93354			−0.966771	+	0.255644i	$0.917712\pi$
$294$		0			0
$295$	7.22481e10			0.555428
$296$	−1.11796e10	+	1.93636e10i	−0.0846471	+	0.146613i
$297$		0			0
$298$	3.86342e10	+	6.69163e10i	0.283791	+	0.491540i
$299$	4.64692e10	−	8.04871e10i	0.336237	−	0.582379i
$300$		0			0
$301$	8.77927e9	−	2.48756e9i	0.0616466	−	0.0174673i
$302$	1.70659e11			1.18059
$303$		0			0
$304$	−1.64530e9	−	2.84975e9i	−0.0110488	−	0.0191371i
$305$	1.09731e11	+	1.90060e11i	0.726073	+	1.25759i
$306$		0			0
$307$	1.41661e11			0.910182			0.455091	−	0.890445i	$-0.349607\pi$
$307$	1.41661e11			0.910182			0.455091	+	0.890445i	$0.349607\pi$
$308$	2.15368e10	−	8.52364e10i	0.136365	−	0.539693i
$309$		0			0
$310$	−5.05343e10	+	8.75280e10i	−0.310784	+	0.538294i
$311$	6.45871e10	+	1.11868e11i	0.391493	+	0.678086i	0.992647	−	0.121048i	$-0.0386254\pi$
$311$	6.45871e10	+	1.11868e11i	0.391493	+	0.678086i	−0.601154	+	0.799133i	$0.705292\pi$
$312$		0			0
$313$	−2.22325e10	+	3.85078e10i	−0.130930	+	0.226777i	−0.924035	−	0.382307i	$-0.875130\pi$
$313$	−2.22325e10	+	3.85078e10i	−0.130930	+	0.226777i	0.793106	+	0.609084i	$0.208463\pi$
$314$	−1.58496e11			−0.920101
$315$		0			0
$316$	1.18783e11			0.670134
$317$	−1.24213e11	+	2.15143e11i	−0.690877	+	1.19663i	0.280674	+	0.959803i	$0.409442\pi$
$317$	−1.24213e11	+	2.15143e11i	−0.690877	+	1.19663i	−0.971551	+	0.236830i	$0.923891\pi$
$318$		0			0
$319$	−3.80765e10	−	6.59505e10i	−0.205873	−	0.356583i
$320$	−9.16254e9	+	1.58700e10i	−0.0488473	+	0.0846061i
$321$		0			0
$322$	1.79204e11	+	1.74147e11i	0.928956	+	0.902745i
$323$	1.77480e10			0.0907271
$324$		0			0
$325$	1.43668e10	+	2.48839e10i	0.0714305	+	0.123721i
$326$	9.94303e10	+	1.72218e11i	0.487573	+	0.844501i
$327$		0			0
$328$	7.08880e10			0.338174
$329$	4.73679e10	−	1.87469e11i	0.222896	−	0.882159i
$330$		0			0
$331$	−1.81110e11	+	3.13691e11i	−0.829307	+	1.43640i	0.0692754	+	0.997598i	$0.477931\pi$
$331$	−1.81110e11	+	3.13691e11i	−0.829307	+	1.43640i	−0.898583	+	0.438805i	$0.855402\pi$
$332$	−9.56961e10	−	1.65751e11i	−0.432288	−	0.748744i
$333$		0			0
$334$	−4.38587e10	+	7.59656e10i	−0.192840	+	0.334009i
$335$	−2.97752e11			−1.29167
$336$		0			0
$337$	−4.33951e11			−1.83276			−0.916380	−	0.400309i	$-0.868903\pi$
$337$	−4.33951e11			−1.83276			−0.916380	+	0.400309i	$0.868903\pi$
$338$	7.34037e10	−	1.27139e11i	0.305909	−	0.529851i
$339$		0			0
$340$	−4.94183e10	−	8.55951e10i	−0.200555	−	0.347371i
$341$	1.56323e11	−	2.70760e11i	0.626079	−	1.08440i
$342$		0			0
$343$	1.73317e11	−	1.88874e11i	0.676112	−	0.736799i
$344$	5.88364e9			0.0226534
$345$		0			0
$346$	−3.67813e10	−	6.37071e10i	−0.137970	−	0.238971i
$347$	9.64888e10	+	1.67124e11i	0.357268	+	0.618807i	0.987503	−	0.157597i	$-0.0503749\pi$
$347$	9.64888e10	+	1.67124e11i	0.357268	+	0.618807i	−0.630235	+	0.776404i	$0.717042\pi$
$348$		0			0
$349$	2.85795e11			1.03119			0.515596	−	0.856832i	$-0.327570\pi$
$349$	2.85795e11			1.03119			0.515596	+	0.856832i	$0.327570\pi$
$350$	−7.43292e10	+	2.10608e10i	−0.264761	+	0.0750186i
$351$		0			0
$352$	2.83435e10	−	4.90923e10i	0.0984036	−	0.170440i
$353$	2.08069e10	+	3.60386e10i	0.0713217	+	0.123533i	0.899481	−	0.436960i	$-0.143945\pi$
$353$	2.08069e10	+	3.60386e10i	0.0713217	+	0.123533i	−0.828159	+	0.560493i	$0.810612\pi$
$354$		0			0
$355$	7.83333e10	−	1.35677e11i	0.261769	−	0.453398i
$356$	2.88739e11			0.952753
$357$		0			0
$358$	−4.10244e10			−0.131998
$359$	−2.05388e11	+	3.55742e11i	−0.652604	+	1.13034i	0.329885	+	0.944021i	$0.392990\pi$
$359$	−2.05388e11	+	3.55742e11i	−0.652604	+	1.13034i	−0.982489	+	0.186322i	$0.940343\pi$
$360$		0			0
$361$	1.60083e11	+	2.77272e11i	0.496094	+	0.859259i
$362$	2.86658e10	−	4.96507e10i	0.0877356	−	0.151962i
$363$		0			0
$364$	−4.40873e10	−	4.28434e10i	−0.131631	−	0.127917i
$365$	−4.01986e11			−1.18548
$366$		0			0
$367$	−9.15209e10	−	1.58519e11i	−0.263344	−	0.456125i	0.703785	−	0.710413i	$-0.251492\pi$
$367$	−9.15209e10	−	1.58519e11i	−0.263344	−	0.456125i	−0.967128	+	0.254289i	$0.918159\pi$
$368$	8.05609e10	+	1.39536e11i	0.228986	+	0.396616i
$369$		0			0
$370$	9.53983e10			0.264626
$371$	−1.96256e10	−	1.90719e10i	−0.0537826	−	0.0522651i
$372$		0			0
$373$	1.42882e11	−	2.47479e11i	0.382198	−	0.661987i	−0.609178	−	0.793034i	$-0.708501\pi$
$373$	1.42882e11	−	2.47479e11i	0.382198	−	0.661987i	0.991376	+	0.131047i	$0.0418338\pi$
$374$	1.52871e11	+	2.64780e11i	0.404020	+	0.699783i
$375$		0			0
$376$	6.23385e10	−	1.07973e11i	0.160846	−	0.278594i
$377$	−5.32508e10			−0.135766
$378$		0			0
$379$	4.76362e10			0.118593			0.0592967	−	0.998240i	$-0.481114\pi$
$379$	4.76362e10			0.118593			0.0592967	+	0.998240i	$0.481114\pi$
$380$	−7.01991e9	+	1.21588e10i	−0.0172705	+	0.0299134i
$381$		0			0
$382$	−5.57910e9	−	9.66329e9i	−0.0134054	−	0.0232188i
$383$	−2.04495e11	+	3.54196e11i	−0.485611	+	0.841104i	−0.999863	−	0.0165355i	$-0.994736\pi$
$383$	−2.04495e11	+	3.54196e11i	−0.485611	+	0.841104i	0.514252	+	0.857639i	$0.328070\pi$
$384$		0			0
$385$	−3.60895e11	+	1.02258e11i	−0.837158	+	0.237205i
$386$	−9.13374e9			−0.0209414
$387$		0			0
$388$	1.62961e10	+	2.82256e10i	0.0365040	+	0.0632267i
$389$	−5.61626e10	−	9.72765e10i	−0.124358	−	0.215394i	0.797124	−	0.603816i	$-0.206354\pi$
$389$	−5.61626e10	−	9.72765e10i	−0.124358	−	0.215394i	−0.921482	+	0.388421i	$0.873020\pi$
$390$		0			0
$391$	−8.69014e11			−1.88032
$392$	1.40721e11	−	8.67061e10i	0.301003	−	0.185465i
$393$		0			0
$394$	−3.91156e10	+	6.77501e10i	−0.0817743	+	0.141637i
$395$	−2.53402e11	−	4.38905e11i	−0.523748	−	0.907159i
$396$		0			0
$397$	1.92843e11	−	3.34013e11i	0.389624	−	0.674848i	−0.602775	−	0.797911i	$-0.705938\pi$
$397$	1.92843e11	−	3.34013e11i	0.389624	−	0.674848i	0.992399	+	0.123063i	$0.0392717\pi$
$398$	1.62918e11			0.325459
$399$		0			0
$400$	−4.98135e10			−0.0972920
$401$	9.03426e10	−	1.56478e11i	0.174479	−	0.302206i	−0.765502	−	0.643434i	$-0.777509\pi$
$401$	9.03426e10	−	1.56478e11i	0.174479	−	0.302206i	0.939981	+	0.341227i	$0.110843\pi$
$402$		0			0
$403$	−1.09311e11	−	1.89331e11i	−0.206438	−	0.357561i
$404$	1.92698e11	−	3.33762e11i	0.359882	−	0.623334i
$405$		0			0
$406$	3.50738e10	−	1.38812e11i	0.0640642	−	0.253548i
$407$	−2.95106e11			−0.533093
$408$		0			0
$409$	1.24009e11	+	2.14789e11i	0.219127	+	0.379540i	0.954541	−	0.298078i	$-0.0963456\pi$
$409$	1.24009e11	+	2.14789e11i	0.219127	+	0.379540i	−0.735414	+	0.677618i	$0.763012\pi$
$410$	−1.51227e11	−	2.61932e11i	−0.264303	−	0.457785i
$411$		0			0
$412$	−1.52309e11			−0.260428
$413$	−3.01337e11	−	2.92835e11i	−0.509657	−	0.495277i
$414$		0			0
$415$	−4.08301e11	+	7.07198e11i	−0.675715	+	1.17037i
$416$	−1.98194e10	−	3.43283e10i	−0.0324468	−	0.0561994i
$417$		0			0
$418$	2.17154e10	−	3.76123e10i	0.0347917	−	0.0602610i
$419$	2.26007e11			0.358227			0.179113	−	0.983828i	$-0.442677\pi$
$419$	2.26007e11			0.358227			0.179113	+	0.983828i	$0.442677\pi$
$420$		0			0
$421$	−3.76981e11			−0.584858			−0.292429	−	0.956287i	$-0.594464\pi$
$421$	−3.76981e11			−0.584858			−0.292429	+	0.956287i	$0.594464\pi$
$422$	2.31925e11	−	4.01705e11i	0.355993	−	0.616597i
$423$		0			0
$424$	−8.82271e9	−	1.52814e10i	−0.0132573	−	0.0229623i
$425$	1.34335e11	−	2.32675e11i	0.199728	−	0.345939i
$426$		0			0
$427$	3.12674e11	−	1.23747e12i	0.455162	−	1.80140i
$428$	−3.46858e11			−0.499637
$429$		0			0
$430$	−1.25517e10	−	2.17402e10i	−0.0177049	−	0.0306658i
$431$	−7.15512e10	−	1.23930e11i	−0.0998779	−	0.172994i	0.811756	−	0.583997i	$-0.198512\pi$
$431$	−7.15512e10	−	1.23930e11i	−0.0998779	−	0.172994i	−0.911634	+	0.411003i	$0.865179\pi$
$432$		0			0
$433$	−1.36985e12			−1.87275			−0.936373	−	0.351007i	$-0.885839\pi$
$433$	−1.36985e12			−1.87275			−0.936373	+	0.351007i	$0.885839\pi$
$434$	5.65539e11	−	1.60243e11i	0.765172	−	0.216808i
$435$		0			0
$436$	2.48044e11	−	4.29624e11i	0.328730	−	0.569376i
$437$	6.17220e10	+	1.06906e11i	0.0809606	+	0.140228i
$438$		0			0
$439$	5.27776e11	−	9.14136e11i	0.678203	−	1.17468i	−0.297319	−	0.954778i	$-0.596092\pi$
$439$	5.27776e11	−	9.14136e11i	0.678203	−	1.17468i	0.975522	−	0.219904i	$-0.0705743\pi$
$440$	−2.41863e11			−0.307632
$441$		0			0
$442$	2.13793e11			0.266436
$443$	3.68388e11	−	6.38067e11i	0.454453	−	0.787136i	−0.544203	−	0.838953i	$-0.683168\pi$
$443$	3.68388e11	−	6.38067e11i	0.454453	−	0.787136i	0.998657	+	0.0518173i	$0.0165014\pi$
$444$		0			0
$445$	−6.15972e11	−	1.06690e12i	−0.744631	−	1.28974i
$446$	7.21578e10	−	1.24981e11i	0.0863528	−	0.149567i
$447$		0			0
$448$	1.02540e11	−	2.90541e10i	0.120265	−	0.0340766i
$449$	1.37800e11			0.160007			0.0800036	−	0.996795i	$-0.474507\pi$
$449$	1.37800e11			0.160007			0.0800036	+	0.996795i	$0.474507\pi$
$450$		0			0
$451$	4.67806e11	+	8.10264e11i	0.532441	+	0.922215i
$452$	−2.53831e11	−	4.39649e11i	−0.286037	−	0.495430i
$453$		0			0
$454$	−2.12209e11			−0.234429
$455$	−6.42547e10	+	2.54302e11i	−0.0702835	+	0.278162i
$456$		0			0
$457$	4.08741e11	−	7.07960e11i	0.438354	−	0.759252i	−0.559209	−	0.829027i	$-0.688895\pi$
$457$	4.08741e11	−	7.07960e11i	0.438354	−	0.759252i	0.997563	+	0.0697754i	$0.0222283\pi$
$458$	6.14133e11	+	1.06371e12i	0.652181	+	1.12961i
$459$		0			0
$460$	3.43724e11	−	5.95348e11i	0.357932	−	0.619956i
$461$	−1.54090e12			−1.58899			−0.794495	−	0.607270i	$-0.792265\pi$
$461$	−1.54090e12			−1.58899			−0.794495	+	0.607270i	$0.792265\pi$
$462$		0			0
$463$	−7.47957e11			−0.756419			−0.378209	−	0.925720i	$-0.623460\pi$
$463$	−7.47957e11			−0.756419			−0.378209	+	0.925720i	$0.623460\pi$
$464$	4.61588e10	−	7.99494e10i	0.0462300	−	0.0800727i
$465$		0			0
$466$	−1.83511e10	−	3.17851e10i	−0.0180271	−	0.0312238i
$467$	1.20537e11	−	2.08776e11i	0.117272	−	0.203121i	−0.801414	−	0.598110i	$-0.795918\pi$
$467$	1.20537e11	−	2.08776e11i	0.117272	−	0.203121i	0.918686	+	0.394989i	$0.129252\pi$
$468$		0			0
$469$	1.24188e12	+	1.20684e12i	1.18523	+	1.15179i
$470$	−5.31951e11			−0.502842
$471$		0			0
$472$	−1.35466e11	−	2.34634e11i	−0.125630	−	0.217597i
$473$	3.88275e10	+	6.72512e10i	0.0356668	+	0.0617767i
$474$		0			0
$475$	−3.81648e10			−0.0343987
$476$	−1.40815e11	+	5.57307e11i	−0.125724	+	0.497581i
$477$		0			0
$478$	−3.25399e11	+	5.63607e11i	−0.285095	+	0.493800i
$479$	2.09044e11	+	3.62075e11i	0.181438	+	0.314259i	0.942370	−	0.334571i	$-0.108592\pi$
$479$	2.09044e11	+	3.62075e11i	0.181438	+	0.314259i	−0.760933	+	0.648831i	$0.775258\pi$
$480$		0			0
$481$	−1.03178e11	+	1.78709e11i	−0.0878887	+	0.152228i
$482$	1.50992e11			0.127422
$483$		0			0
$484$	1.44545e11			0.119729
$485$	6.95294e10	−	1.20428e11i	0.0570599	−	0.0988306i
$486$		0			0
$487$	8.57863e11	+	1.48586e12i	0.691095	+	1.19701i	0.971480	+	0.237123i	$0.0762046\pi$
$487$	8.57863e11	+	1.48586e12i	0.691095	+	1.19701i	−0.280385	+	0.959888i	$0.590462\pi$
$488$	4.11494e11	−	7.12728e11i	0.328454	−	0.568899i
$489$		0			0
$490$	−6.20583e11	−	3.34993e11i	−0.486315	−	0.262515i
$491$	−3.34731e11			−0.259914			−0.129957	−	0.991520i	$-0.541484\pi$
$491$	−3.34731e11			−0.259914			−0.129957	+	0.991520i	$0.541484\pi$
$492$		0			0
$493$	2.48958e11	+	4.31209e11i	0.189809	+	0.328758i
$494$	−1.51847e10	−	2.63007e10i	−0.0114719	−	0.0198699i
$495$		0			0
$496$	3.79010e11			0.281179
$497$	−8.76643e11	+	2.48392e11i	−0.644494	+	0.182614i
$498$		0			0
$499$	−3.55022e11	+	6.14916e11i	−0.256332	+	0.443980i	−0.965256	−	0.261304i	$-0.915847\pi$
$499$	−3.55022e11	+	6.14916e11i	−0.256332	+	0.443980i	0.708924	+	0.705285i	$0.249181\pi$
$500$	3.79333e11	+	6.57024e11i	0.271429	+	0.470128i
$501$		0			0
$502$	−6.08441e11	+	1.05385e12i	−0.427614	+	0.740649i
$503$	2.16835e12			1.51033			0.755167	−	0.655532i	$-0.227556\pi$
$503$	2.16835e12			1.51033			0.755167	+	0.655532i	$0.227556\pi$
$504$		0			0
$505$	−1.64434e12			−1.12507
$506$	−1.06328e12	+	1.84165e12i	−0.721058	+	1.24891i
$507$		0			0
$508$	−4.99566e9	−	8.65273e9i	−0.00332817	−	0.00576457i
$509$	3.84948e11	−	6.66750e11i	0.254198	−	0.440284i	−0.710479	−	0.703718i	$-0.751522\pi$
$509$	3.84948e11	−	6.66750e11i	0.254198	−	0.440284i	0.964677	+	0.263434i	$0.0848551\pi$
$510$		0			0
$511$	1.67663e12	+	1.62932e12i	1.08779	+	1.05709i
$512$	6.87195e10			0.0441942
$513$		0			0
$514$	7.21768e11	+	1.25014e12i	0.456104	+	0.789995i
$515$	3.24923e11	+	5.62783e11i	0.203539	+	0.352540i
$516$		0			0
$517$	1.64554e12			1.01298
$518$	−3.97893e11	−	3.86667e11i	−0.242819	−	0.235968i
$519$		0			0
$520$	−8.45624e10	+	1.46466e11i	−0.0507180	+	0.0878461i
$521$	1.16046e11	+	2.00998e11i	0.0690021	+	0.119515i	0.898462	−	0.439051i	$-0.144685\pi$
$521$	1.16046e11	+	2.00998e11i	0.0690021	+	0.119515i	−0.829460	+	0.558566i	$0.811352\pi$
$522$		0			0
$523$	1.04130e12	−	1.80358e12i	0.608580	−	1.05409i	−0.382895	−	0.923792i	$-0.625073\pi$
$523$	1.04130e12	−	1.80358e12i	0.608580	−	1.05409i	0.991475	−	0.130299i	$-0.0415938\pi$
$524$	−4.08007e11			−0.236416
$525$		0			0
$526$	1.49709e12			0.852731
$527$	−1.02210e12	+	1.77033e12i	−0.577225	+	0.999783i
$528$		0			0
$529$	−2.12159e12	−	3.67471e12i	−1.17791	−	2.04020i
$530$	−3.76433e10	+	6.52001e10i	−0.0207227	+	0.0358928i
$531$		0			0
$532$	7.85612e10	−	2.22599e10i	0.0425212	−	0.0120482i
$533$	6.54236e11			0.351125
$534$		0			0
$535$	7.39959e11	+	1.28165e12i	0.390495	+	0.676357i
$536$	5.58289e11	+	9.66985e11i	0.292158	+	0.506032i
$537$		0			0
$538$	−2.37701e11			−0.122324
$539$	1.91971e12	+	1.03627e12i	0.979687	+	0.528839i
$540$		0			0
$541$	4.19871e11	−	7.27238e11i	0.210731	−	0.364996i	−0.741213	−	0.671270i	$-0.765749\pi$
$541$	4.19871e11	−	7.27238e11i	0.210731	−	0.364996i	0.951943	+	0.306274i	$0.0990823\pi$
$542$	−9.37478e11	−	1.62376e12i	−0.466621	−	0.808212i
$543$		0			0
$544$	−1.85320e11	+	3.20984e11i	−0.0907250	+	0.157140i
$545$	−2.11662e12			−1.02768
$546$		0			0
$547$	−7.58235e11			−0.362127			−0.181064	−	0.983471i	$-0.557954\pi$
$547$	−7.58235e11			−0.362127			−0.181064	+	0.983471i	$0.557954\pi$
$548$	7.21452e11	−	1.24959e12i	0.341739	−	0.591910i
$549$		0			0
$550$	−3.28731e11	−	5.69378e11i	−0.153182	−	0.265319i
$551$	3.53647e10	−	6.12535e10i	0.0163451	−	0.0283106i
$552$		0			0
$553$	−7.22057e11	+	2.85770e12i	−0.328328	+	1.29943i
$554$	−4.59558e11			−0.207275
$555$		0			0
$556$	−3.07866e11	−	5.33239e11i	−0.136623	−	0.236638i
$557$	7.98622e11	+	1.38325e12i	0.351555	+	0.608911i	0.986522	−	0.163628i	$-0.0523198\pi$
$557$	7.98622e11	+	1.38325e12i	0.351555	+	0.608911i	−0.634967	+	0.772539i	$0.718986\pi$
$558$		0			0
$559$	5.43010e10			0.0235209
$560$	−3.26105e11	−	3.16904e11i	−0.140124	−	0.136170i
$561$		0			0
$562$	−5.91752e11	+	1.02494e12i	−0.250222	+	0.433398i
$563$	1.30480e11	+	2.25999e11i	0.0547340	+	0.0948021i	0.892094	−	0.451849i	$-0.149236\pi$
$563$	1.30480e11	+	2.25999e11i	0.0547340	+	0.0948021i	−0.837360	+	0.546652i	$0.815902\pi$
$564$		0			0
$565$	−1.08301e12	+	1.87582e12i	−0.447108	+	0.774415i
$566$	−1.16398e12			−0.476729
$567$		0			0
$568$	−5.87504e11			−0.236833
$569$	−7.66696e11	+	1.32796e12i	−0.306632	+	0.531103i	−0.977623	−	0.210363i	$-0.932535\pi$
$569$	−7.66696e11	+	1.32796e12i	−0.306632	+	0.531103i	0.670991	+	0.741465i	$0.265869\pi$
$570$		0			0
$571$	1.38056e12	+	2.39120e12i	0.543492	+	0.941355i	0.998700	+	0.0509702i	$0.0162313\pi$
$571$	1.38056e12	+	2.39120e12i	0.543492	+	0.941355i	−0.455209	+	0.890385i	$0.650435\pi$
$572$	2.61586e11	−	4.53080e11i	0.102172	−	0.176967i
$573$		0			0
$574$	−4.30914e11	+	1.70544e12i	−0.165686	+	0.655740i
$575$	1.86871e12			0.712913
$576$		0			0
$577$	2.00235e12	+	3.46817e12i	0.752054	+	1.30260i	0.946826	+	0.321747i	$0.104270\pi$
$577$	2.00235e12	+	3.46817e12i	0.752054	+	1.30260i	−0.194771	+	0.980849i	$0.562396\pi$
$578$	−5.08243e10	−	8.80302e10i	−0.0189407	−	0.0328063i
$579$		0			0
$580$	−3.93886e11			−0.144525
$581$	4.56937e12	−	1.29471e12i	1.66366	−	0.471389i
$582$		0			0
$583$	1.16446e11	−	2.01690e11i	0.0417461	−	0.0723064i
$584$	7.53729e11	+	1.30550e12i	0.268137	+	0.464428i
$585$		0			0
$586$	1.95141e12	−	3.37994e12i	0.683610	−	1.18405i
$587$	1.31451e12			0.456976			0.228488	−	0.973547i	$-0.426622\pi$
$587$	1.31451e12			0.456976			0.228488	+	0.973547i	$0.426622\pi$
$588$		0			0
$589$	2.90380e11			0.0994140
$590$	−5.77985e11	+	1.00110e12i	−0.196373	+	0.340129i
$591$		0			0
$592$	−1.78873e11	−	3.09817e11i	−0.0598545	−	0.103671i
$593$	2.09286e12	−	3.62495e12i	0.695016	−	1.20380i	−0.275159	−	0.961399i	$-0.588731\pi$
$593$	2.09286e12	−	3.62495e12i	0.695016	−	1.20380i	0.970175	−	0.242404i	$-0.0779361\pi$
$594$		0			0
$595$	2.35966e12	−	6.68599e11i	0.771834	−	0.218695i
$596$	−1.23629e12			−0.401341
$597$		0			0
$598$	7.43508e11	+	1.28779e12i	0.237755	+	0.411804i
$599$	−9.72836e11	−	1.68500e12i	−0.308758	−	0.534785i	0.669333	−	0.742963i	$-0.266580\pi$
$599$	−9.72836e11	−	1.68500e12i	−0.308758	−	0.534785i	−0.978091	+	0.208178i	$0.933247\pi$
$600$		0			0
$601$	4.58168e12			1.43248			0.716242	−	0.697852i	$-0.245861\pi$
$601$	4.58168e12			1.43248			0.716242	+	0.697852i	$0.245861\pi$
$602$	−3.57655e10	+	1.41550e11i	−0.0110989	+	0.0439263i
$603$		0			0
$604$	−1.36527e12	+	2.36472e12i	−0.417401	+	0.722960i
$605$	−3.08360e11	−	5.34096e11i	−0.0935749	−	0.162076i
$606$		0			0
$607$	1.86944e12	−	3.23796e12i	0.558936	−	0.968106i	−0.438650	−	0.898658i	$-0.644543\pi$
$607$	1.86944e12	−	3.23796e12i	0.558936	−	0.968106i	0.997586	−	0.0694474i	$-0.0221236\pi$
$608$	5.26497e10			0.0156253
$609$		0			0
$610$	−3.51139e12			−1.02682
$611$	5.75331e11	−	9.96502e11i	0.167006	−	0.289263i
$612$		0			0
$613$	−5.61986e11	−	9.73387e11i	−0.160751	−	0.278428i	0.774387	−	0.632712i	$-0.218058\pi$
$613$	−5.61986e11	−	9.73387e11i	−0.160751	−	0.278428i	−0.935138	+	0.354283i	$0.884725\pi$
$614$	−1.13329e12	+	1.96291e12i	−0.321798	+	0.557370i
$615$		0			0
$616$	1.00878e12	+	9.80314e11i	0.282281	+	0.274317i
$617$	−8.34463e11			−0.231805			−0.115903	−	0.993261i	$-0.536976\pi$
$617$	−8.34463e11			−0.231805			−0.115903	+	0.993261i	$0.536976\pi$
$618$		0			0
$619$	−1.23873e12	−	2.14554e12i	−0.339132	−	0.587394i	0.645138	−	0.764066i	$-0.276800\pi$
$619$	−1.23873e12	−	2.14554e12i	−0.339132	−	0.587394i	−0.984270	+	0.176673i	$0.943467\pi$
$620$	−8.08549e11	−	1.40045e12i	−0.219758	−	0.380631i
$621$		0			0
$622$	−2.06679e12			−0.553655
$623$	−1.75519e12	+	6.94653e12i	−0.466796	+	1.84745i
$624$		0			0
$625$	8.76198e11	−	1.51762e12i	0.229690	−	0.397835i
$626$	−3.55719e11	−	6.16124e11i	−0.0925813	−	0.160355i
$627$		0			0
$628$	1.26797e12	−	2.19619e12i	0.325305	−	0.563445i
$629$	1.92951e12			0.491495
$630$		0			0
$631$	1.00841e12			0.253223			0.126612	−	0.991952i	$-0.459590\pi$
$631$	1.00841e12			0.253223			0.126612	+	0.991952i	$0.459590\pi$
$632$	−9.50263e11	+	1.64590e12i	−0.236928	+	0.410372i
$633$		0			0
$634$	−1.98741e12	−	3.44229e12i	−0.488524	−	0.846148i
$635$	−2.13147e10	+	3.69181e10i	−0.00520232	+	0.00901068i
$636$		0			0
$637$	1.29873e12	−	8.00223e11i	0.312530	−	0.192568i
$638$	1.21845e12			0.291148
$639$		0			0
$640$	−1.46601e11	−	2.53920e11i	−0.0345403	−	0.0598255i
$641$	−3.49112e12	−	6.04681e12i	−0.816778	−	1.41470i	−0.908044	−	0.418875i	$-0.862425\pi$
$641$	−3.49112e12	−	6.04681e12i	−0.816778	−	1.41470i	0.0912655	−	0.995827i	$-0.470909\pi$
$642$		0			0
$643$	−5.09779e12			−1.17607			−0.588034	−	0.808836i	$-0.700098\pi$
$643$	−5.09779e12			−1.17607			−0.588034	+	0.808836i	$0.700098\pi$
$644$	−3.84668e12	+	1.08994e12i	−0.881252	+	0.249698i
$645$		0			0
$646$	−1.41984e11	+	2.45923e11i	−0.0320769	+	0.0555588i
$647$	1.10368e12	+	1.91163e12i	0.247613	+	0.428879i	0.962863	−	0.269990i	$-0.0870205\pi$
$647$	1.10368e12	+	1.91163e12i	0.247613	+	0.428879i	−0.715250	+	0.698869i	$0.753687\pi$
$648$		0			0
$649$	1.78794e12	−	3.09681e12i	0.395597	−	0.685193i
$650$	−4.59736e11			−0.101018
$651$		0			0
$652$	−3.18177e12			−0.689533
$653$	4.10454e12	−	7.10928e12i	0.883397	−	1.53009i	0.0358561	−	0.999357i	$-0.488584\pi$
$653$	4.10454e12	−	7.10928e12i	0.883397	−	1.53009i	0.847540	−	0.530731i	$-0.178082\pi$
$654$		0			0
$655$	8.70410e11	+	1.50759e12i	0.184773	+	0.320036i
$656$	−5.67104e11	+	9.82253e11i	−0.119563	+	0.207089i
$657$		0			0
$658$	2.21870e12	+	2.15610e12i	0.461404	+	0.448386i
$659$	−5.75171e12			−1.18799			−0.593994	−	0.804469i	$-0.702450\pi$
$659$	−5.75171e12			−1.18799			−0.593994	+	0.804469i	$0.702450\pi$
$660$		0			0
$661$	−1.70202e12	−	2.94798e12i	−0.346783	−	0.600646i	0.638893	−	0.769296i	$-0.279393\pi$
$661$	−1.70202e12	−	2.94798e12i	−0.346783	−	0.600646i	−0.985676	+	0.168650i	$0.946059\pi$
$662$	−2.89775e12	−	5.01906e12i	−0.586409	−	1.01569i
$663$		0			0
$664$	3.06228e12			0.611347
$665$	−2.49847e11	−	2.42797e11i	−0.0495423	−	0.0481445i
$666$		0			0
$667$	−1.73161e12	+	2.99923e12i	−0.338753	+	0.586737i
$668$	−7.01740e11	−	1.21545e12i	−0.136358	−	0.236180i
$669$		0			0
$670$	2.38202e12	−	4.12577e12i	0.456676	−	0.790986i
$671$	1.08622e13			2.06855
$672$		0			0
$673$	−7.13050e12			−1.33984			−0.669918	−	0.742435i	$-0.733671\pi$
$673$	−7.13050e12			−1.33984			−0.669918	+	0.742435i	$0.733671\pi$
$674$	3.47160e12	−	6.01300e12i	0.647979	−	1.12233i
$675$		0			0
$676$	1.17446e12	+	2.03422e12i	0.216311	+	0.374661i
$677$	−6.50974e11	+	1.12752e12i	−0.119101	+	0.206289i	−0.919412	−	0.393297i	$-0.871334\pi$
$677$	−6.50974e11	+	1.12752e12i	−0.119101	+	0.206289i	0.800311	+	0.599585i	$0.204668\pi$
$678$		0			0
$679$	−7.78117e11	+	2.20476e11i	−0.140485	+	0.0398058i
$680$	1.58139e12			0.283627
$681$		0			0
$682$	2.50117e12	+	4.33216e12i	0.442704	+	0.766786i
$683$	−2.31279e12	−	4.00587e12i	−0.406671	−	0.704374i	0.587844	−	0.808975i	$-0.299977\pi$
$683$	−2.31279e12	−	4.00587e12i	−0.406671	−	0.704374i	−0.994514	+	0.104600i	$0.966644\pi$
$684$		0			0
$685$	−6.15635e12			−1.06836
$686$	1.23058e12	+	3.91255e12i	0.212154	+	0.674530i
$687$		0			0
$688$	−4.70692e10	+	8.15262e10i	−0.00800919	+	0.0138723i
$689$	−8.14260e10	−	1.41034e11i	−0.0137650	−	0.0238417i
$690$		0			0
$691$	1.46317e12	−	2.53428e12i	0.244142	−	0.422866i	−0.717748	−	0.696303i	$-0.754827\pi$
$691$	1.46317e12	−	2.53428e12i	0.244142	−	0.422866i	0.961890	+	0.273437i	$0.0881604\pi$
$692$	1.17700e12			0.195119
$693$		0			0
$694$	−3.08764e12			−0.505254
$695$	−1.31355e12	+	2.27514e12i	−0.213558	+	0.369893i
$696$		0			0
$697$	−3.05869e12	−	5.29780e12i	−0.490894	−	0.850253i
$698$	−2.28636e12	+	3.96009e12i	−0.364582	+	0.631474i
$699$		0			0
$700$	3.02806e11	−	1.19842e12i	0.0476677	−	0.188655i
$701$	−5.32710e12			−0.833220			−0.416610	−	0.909085i	$-0.636782\pi$
$701$	−5.32710e12			−0.833220			−0.416610	+	0.909085i	$0.636782\pi$
$702$		0			0
$703$	−1.37044e11	−	2.37367e11i	−0.0211622	−	0.0366541i
$704$	4.53495e11	+	7.85477e11i	0.0695818	+	0.120519i
$705$		0			0
$706$	−6.65821e11			−0.100864
$707$	6.85833e12	+	6.66482e12i	1.03236	+	1.00323i
$708$		0			0
$709$	−1.57111e12	+	2.72124e12i	−0.233506	+	0.404444i	−0.958837	−	0.283956i	$-0.908353\pi$
$709$	−1.57111e12	+	2.72124e12i	−0.233506	+	0.404444i	0.725332	+	0.688400i	$0.241686\pi$
$710$	1.25333e12	+	2.17084e12i	0.185099	+	0.320601i
$711$		0			0
$712$	−2.30991e12	+	4.00088e12i	−0.336849	+	0.583440i
$713$	−1.42182e13			−2.06036
$714$		0			0
$715$	−2.23218e12			−0.319413
$716$	3.28195e11	−	5.68451e11i	0.0466685	−	0.0808322i
$717$		0			0
$718$	−3.28620e12	−	5.69187e12i	−0.461460	−	0.799273i
$719$	7.96174e11	−	1.37901e12i	0.111104	−	0.192437i	−0.805112	−	0.593123i	$-0.797895\pi$
$719$	7.96174e11	−	1.37901e12i	0.111104	−	0.192437i	0.916216	+	0.400686i	$0.131228\pi$
$720$		0			0
$721$	9.25853e11	−	3.66426e12i	0.127595	−	0.504985i
$722$	−5.12267e12			−0.701582
$723$		0			0
$724$	4.58653e11	+	7.94410e11i	0.0620384	+	0.107454i
$725$	−5.35355e11	−	9.27262e11i	−0.0719649	−	0.124647i
$726$		0			0
$727$	6.30493e11			0.0837096			0.0418548	−	0.999124i	$-0.486673\pi$
$727$	6.30493e11			0.0837096			0.0418548	+	0.999124i	$0.486673\pi$
$728$	9.46353e11	−	2.68145e11i	0.124871	−	0.0353816i
$729$		0			0
$730$	3.21589e12	−	5.57008e12i	0.419129	−	0.725954i
$731$	−2.53868e11	−	4.39713e11i	−0.0328837	−	0.0569562i
$732$		0			0
$733$	5.97049e12	−	1.03412e13i	0.763910	−	1.32313i	−0.176911	−	0.984227i	$-0.556610\pi$
$733$	5.97049e12	−	1.03412e13i	0.763910	−	1.32313i	0.940821	−	0.338904i	$-0.110056\pi$
$734$	2.92867e12			0.372424
$735$		0			0
$736$	−2.57795e12			−0.323835
$737$	−7.36855e12	+	1.27627e13i	−0.919980	+	1.59345i
$738$		0			0
$739$	2.68231e11	+	4.64590e11i	0.0330833	+	0.0573020i	0.882093	−	0.471075i	$-0.156134\pi$
$739$	2.68231e11	+	4.64590e11i	0.0330833	+	0.0573020i	−0.849010	+	0.528377i	$0.822801\pi$
$740$	−7.63186e11	+	1.32188e12i	−0.0935595	+	0.162050i
$741$		0			0
$742$	4.21273e11	−	1.19366e11i	0.0510207	−	0.0144565i
$743$	−7.16300e12			−0.862274			−0.431137	−	0.902286i	$-0.641888\pi$
$743$	−7.16300e12			−0.862274			−0.431137	+	0.902286i	$0.641888\pi$
$744$		0			0
$745$	2.63741e12	+	4.56812e12i	0.313671	+	0.543294i
$746$	2.28612e12	+	3.95967e12i	0.270255	+	0.468095i
$747$		0			0
$748$	−4.89187e12			−0.571371
$749$	2.10848e12	−	8.34477e12i	0.244794	−	0.968827i
$750$		0			0
$751$	−6.44748e12	+	1.11674e13i	−0.739623	+	1.28106i	0.213042	+	0.977043i	$0.431663\pi$
$751$	−6.44748e12	+	1.11674e13i	−0.739623	+	1.28106i	−0.952665	+	0.304021i	$0.901671\pi$
$752$	9.97415e11	+	1.72757e12i	0.113735	+	0.196996i
$753$		0			0
$754$	4.26006e11	−	7.37864e11i	0.0480004	−	0.0831391i
$755$	1.16503e13			1.30489
$756$		0			0
$757$	−1.53380e13			−1.69761			−0.848804	−	0.528708i	$-0.822677\pi$
$757$	−1.53380e13			−1.69761			−0.848804	+	0.528708i	$0.822677\pi$
$758$	−3.81090e11	+	6.60067e11i	−0.0419291	+	0.0726234i
$759$		0			0
$760$	−1.12319e11	−	1.94542e11i	−0.0122121	−	0.0211520i
$761$	4.27674e12	−	7.40753e12i	0.462256	−	0.800650i	−0.536817	−	0.843698i	$-0.680374\pi$
$761$	4.27674e12	−	7.40753e12i	0.462256	−	0.800650i	0.999073	+	0.0430484i	$0.0137070\pi$
$762$		0			0
$763$	8.82816e12	+	8.57907e12i	0.942996	+	0.916389i
$764$	1.78531e11			0.0189581
$765$		0			0
$766$	−3.27193e12	−	5.66714e12i	−0.343379	−	0.594750i
$767$	−1.25024e12	−	2.16547e12i	−0.130441	−	0.225930i
$768$		0			0
$769$	5.63703e12			0.581275			0.290638	−	0.956833i	$-0.406133\pi$
$769$	5.63703e12			0.581275			0.290638	+	0.956833i	$0.406133\pi$
$770$	1.47023e12	−	5.81877e12i	0.150723	−	0.596517i
$771$		0			0
$772$	7.30699e10	−	1.26561e11i	0.00740390	−	0.0128239i
$773$	−1.24471e12	−	2.15590e12i	−0.125390	−	0.217181i	0.796496	−	0.604644i	$-0.206685\pi$
$773$	−1.24471e12	−	2.15590e12i	−0.125390	−	0.217181i	−0.921885	+	0.387463i	$0.873351\pi$
$774$		0			0
$775$	2.19790e12	−	3.80687e12i	0.218852	−	0.379063i
$776$	−5.21474e11			−0.0516244
$777$		0			0
$778$	1.79720e12			0.175869
$779$	−4.34489e11	+	7.52557e11i	−0.0422727	+	0.0732185i
$780$		0			0
$781$	−3.87707e12	−	6.71528e12i	−0.372884	−	0.645854i
$782$	6.95211e12	−	1.20414e13i	0.664793	−	1.15145i
$783$		0			0
$784$	7.56706e10	+	2.64353e12i	0.00715327	+	0.249898i
$785$	−1.08199e13			−1.01698
$786$		0			0
$787$	6.87537e12	+	1.19085e13i	0.638866	+	1.10655i	0.985682	+	0.168615i	$0.0539294\pi$
$787$	6.87537e12	+	1.19085e13i	0.638866	+	1.10655i	−0.346816	+	0.937933i	$0.612737\pi$
$788$	−6.25849e11	−	1.08400e12i	−0.0578231	−	0.100153i
$789$		0			0
$790$	8.10886e12			0.740692
$791$	1.21201e13	−	3.43418e12i	1.10081	−	0.311910i
$792$		0			0
$793$	3.79774e12	−	6.57787e12i	0.341032	−	0.590685i
$794$	3.08548e12	+	5.34421e12i	0.275506	+	0.477190i
$795$		0			0
$796$	−1.30335e12	+	2.25746e12i	−0.115067	+	0.199302i
$797$	−1.44214e12			−0.126603			−0.0633016	−	0.997994i	$-0.520163\pi$
$797$	−1.44214e12			−0.126603			−0.0633016	+	0.997994i	$0.520163\pi$
$798$		0			0
$799$	−1.07592e13			−0.933938
$800$	3.98508e11	−	6.90236e11i	0.0343979	−	0.0595790i
$801$		0			0
$802$	1.44548e12	+	2.50365e12i	0.123375	+	0.213692i
$803$	−9.94805e12	+	1.72305e13i	−0.844342	+	1.46244i
$804$		0			0
$805$	1.22335e13	+	1.18884e13i	1.02676	+	0.997794i
$806$	3.49794e12			0.291947
$807$		0			0
$808$	3.08316e12	+	5.34019e12i	0.254475	+	0.440764i
$809$	1.35494e11	+	2.34683e11i	0.0111212	+	0.0192625i	0.871532	−	0.490338i	$-0.163127\pi$
$809$	1.35494e11	+	2.34683e11i	0.0111212	+	0.0192625i	−0.860411	+	0.509600i	$0.829793\pi$
$810$		0			0
$811$	1.23287e13			1.00075			0.500373	−	0.865810i	$-0.333196\pi$
$811$	1.23287e13			1.00075			0.500373	+	0.865810i	$0.333196\pi$
$812$	1.64285e12	+	1.59649e12i	0.132616	+	0.128874i
$813$		0			0
$814$	2.36085e12	−	4.08910e12i	0.188477	−	0.326451i
$815$	6.78773e12	+	1.17567e13i	0.538909	+	0.933418i
$816$		0			0
$817$	−3.60622e10	+	6.24616e10i	−0.00283174	+	0.00490471i
$818$	−3.96827e12			−0.309893
$819$		0			0
$820$	4.83926e12			0.373780
$821$	−4.37808e12	+	7.58306e12i	−0.336310	+	0.582506i	−0.983736	−	0.179623i	$-0.942512\pi$
$821$	−4.37808e12	+	7.58306e12i	−0.336310	+	0.582506i	0.647426	+	0.762129i	$0.275846\pi$
$822$		0			0
$823$	−6.64063e12	−	1.15019e13i	−0.504557	−	0.873918i	−0.999986	−	0.00526950i	$-0.998323\pi$
$823$	−6.64063e12	−	1.15019e13i	−0.504557	−	0.873918i	0.495430	−	0.868648i	$-0.335011\pi$
$824$	1.21847e12	−	2.11045e12i	0.0920750	−	0.159479i
$825$		0			0
$826$	6.46834e12	−	1.83277e12i	0.483485	−	0.136993i
$827$	1.28106e13			0.952345			0.476173	−	0.879352i	$-0.342024\pi$
$827$	1.28106e13			0.952345			0.476173	+	0.879352i	$0.342024\pi$
$828$		0			0
$829$	−7.12962e12	−	1.23489e13i	−0.524289	−	0.908095i	−0.999600	−	0.0282773i	$-0.990998\pi$
$829$	−7.12962e12	−	1.23489e13i	−0.524289	−	0.908095i	0.475311	−	0.879818i	$-0.342335\pi$
$830$	−6.53281e12	−	1.13152e13i	−0.477803	−	0.827579i
$831$		0			0
$832$	6.34222e11			0.0458866
$833$	−1.25518e13	−	6.77552e12i	−0.903241	−	0.487573i
$834$		0			0
$835$	−2.99407e12	+	5.18588e12i	−0.213144	+	0.369176i
$836$	3.47447e11	+	6.01796e11i	0.0246014	+	0.0426109i
$837$		0			0
$838$	−1.80805e12	+	3.13164e12i	−0.126652	+	0.219368i
$839$	−5.62810e12			−0.392133			−0.196066	−	0.980591i	$-0.562817\pi$
$839$	−5.62810e12			−0.392133			−0.196066	+	0.980591i	$0.562817\pi$
$840$		0			0
$841$	−1.25228e13			−0.863219
$842$	3.01585e12	−	5.22361e12i	0.206779	−	0.358151i
$843$		0			0
$844$	3.71080e12	+	6.42729e12i	0.251725	+	0.436000i
$845$	5.01099e12	−	8.67930e12i	0.338118	−	0.585638i
$846$		0			0
$847$	−8.78659e11	+	3.47748e12i	−0.0586604	+	0.232161i
$848$	2.82327e11			0.0187487
$849$		0			0
$850$	2.14936e12	+	3.72280e12i	0.141229	+	0.244616i
$851$	6.71025e12	+	1.16225e13i	0.438587	+	0.759655i
$852$		0			0
$853$	1.54422e13			0.998709			0.499354	−	0.866398i	$-0.333571\pi$
$853$	1.54422e13			0.998709			0.499354	+	0.866398i	$0.333571\pi$
$854$	1.46456e13	+	1.42323e13i	0.942205	+	0.915620i
$855$		0			0
$856$	2.77486e12	−	4.80621e12i	0.176648	−	0.305964i
$857$	−8.04165e12	−	1.39286e13i	−0.509251	−	0.882048i	−0.999943	−	0.0107150i	$-0.996589\pi$
$857$	−8.04165e12	−	1.39286e13i	−0.509251	−	0.882048i	0.490692	−	0.871333i	$-0.336744\pi$
$858$		0			0
$859$	1.51461e12	−	2.62338e12i	0.0949141	−	0.164396i	−0.814659	−	0.579941i	$-0.803076\pi$
$859$	1.51461e12	−	2.62338e12i	0.0949141	−	0.164396i	0.909573	+	0.415545i	$0.136409\pi$
$860$	4.01654e11			0.0250386
$861$		0			0
$862$	2.28964e12			0.141249
$863$	6.78181e12	−	1.17464e13i	0.416195	−	0.720871i	−0.579358	−	0.815073i	$-0.696697\pi$
$863$	6.78181e12	−	1.17464e13i	0.416195	−	0.720871i	0.995553	+	0.0942019i	$0.0300299\pi$
$864$		0			0
$865$	−2.51092e12	−	4.34904e12i	−0.152497	−	0.264132i
$866$	1.09588e13	−	1.89813e13i	0.662116	−	1.14682i
$867$		0			0
$868$	−2.30393e12	+	9.11828e12i	−0.137762	+	0.545223i
$869$	−2.50840e13			−1.49213
$870$		0			0
$871$	5.15253e12	+	8.92444e12i	0.303346	+	0.525411i
$872$	3.96870e12	+	6.87399e12i	0.232447	+	0.402610i
$873$		0			0
$874$	−1.97511e12			−0.114496
$875$	−1.81127e13	+	5.13214e12i	−1.04459	+	0.295980i
$876$		0			0
$877$	−1.04192e13	+	1.80465e13i	−0.594751	+	1.03014i	0.398831	+	0.917024i	$0.369416\pi$
$877$	−1.04192e13	+	1.80465e13i	−0.594751	+	1.03014i	−0.993582	+	0.113114i	$0.963917\pi$
$878$	8.44442e12	+	1.46262e13i	0.479562	+	0.830626i
$879$		0			0
$880$	1.93490e12	−	3.35135e12i	0.108764	−	0.188385i
$881$	1.45413e13			0.813225			0.406612	−	0.913601i	$-0.366710\pi$
$881$	1.45413e13			0.813225			0.406612	+	0.913601i	$0.366710\pi$
$882$		0			0
$883$	6.56890e12			0.363638			0.181819	−	0.983332i	$-0.441802\pi$
$883$	6.56890e12			0.363638			0.181819	+	0.983332i	$0.441802\pi$
$884$	−1.71034e12	+	2.96240e12i	−0.0941995	+	0.163158i
$885$		0			0
$886$	5.89421e12	+	1.02091e13i	0.321347	+	0.556589i
$887$	6.13102e11	−	1.06192e12i	0.0332565	−	0.0576020i	−0.848918	−	0.528524i	$-0.822746\pi$
$887$	6.13102e11	−	1.06192e12i	0.0332565	−	0.0576020i	0.882175	+	0.470922i	$0.156079\pi$
$888$		0			0
$889$	2.38537e11	−	6.75881e10i	0.0128085	−	0.00362921i
$890$	1.97111e13			1.05307
$891$		0			0
$892$	1.15453e12	+	1.99970e12i	0.0610607	+	0.105760i
$893$	7.64174e11	+	1.32359e12i	0.0402124	+	0.0696500i
$894$		0			0
$895$	−2.80058e12			−0.145896
$896$	−4.17732e11	+	1.65326e12i	−0.0216527	+	0.0856952i
$897$		0			0
$898$	−1.10240e12	+	1.90941e12i	−0.0565711	+	0.0979840i
$899$	4.07329e12	+	7.05514e12i	0.207982	+	0.360236i
$900$		0			0
$901$	−7.61367e11	+	1.31873e12i	−0.0384886	+	0.0666643i
$902$	−1.49698e13			−0.752985
$903$		0			0
$904$	8.12260e12			0.404517
$905$	1.95691e12	−	3.38946e12i	0.0969732	−	0.167962i
$906$		0			0
$907$	6.95770e12	+	1.20511e13i	0.341376	+	0.591280i	0.984688	−	0.174323i	$-0.0557737\pi$
$907$	6.95770e12	+	1.20511e13i	0.341376	+	0.591280i	−0.643313	+	0.765604i	$0.722440\pi$
$908$	1.69767e12	−	2.94045e12i	0.0828833	−	0.143558i
$909$		0			0
$910$	−3.00967e12	−	2.92475e12i	−0.145490	−	0.141385i
$911$	−5.99228e11			−0.0288243			−0.0144122	−	0.999896i	$-0.504588\pi$
$911$	−5.99228e11			−0.0288243			−0.0144122	+	0.999896i	$0.504588\pi$
$912$		0			0
$913$	2.02086e13	+	3.50024e13i	0.962540	+	1.66717i
$914$	6.53985e12	+	1.13274e13i	0.309963	+	0.536872i
$915$		0			0
$916$	−1.96523e13			−0.922323
$917$	2.48020e12	−	9.81591e12i	0.115831	−	0.458425i
$918$		0			0
$919$	2.60385e12	−	4.51000e12i	0.120419	−	0.208572i	−0.799514	−	0.600648i	$-0.794909\pi$
$919$	2.60385e12	−	4.51000e12i	0.120419	−	0.208572i	0.919933	+	0.392075i	$0.128243\pi$
$920$	5.49959e12	+	9.52557e12i	0.253096	+	0.438375i
$921$		0			0
$922$	1.23272e13	−	2.13514e13i	0.561793	−	0.973054i
$923$	−5.42215e12			−0.245903
$924$		0			0
$925$	−4.14918e12			−0.186348
$926$	5.98366e12	−	1.03640e13i	0.267434	−	0.463210i
$927$		0			0
$928$	7.38541e11	+	1.27919e12i	0.0326895	+	0.0566199i
$929$	−1.01430e13	+	1.75682e13i	−0.446783	+	0.773850i	−0.998174	−	0.0603962i	$-0.980764\pi$
$929$	−1.01430e13	+	1.75682e13i	−0.446783	+	0.773850i	0.551392	+	0.834246i	$0.314097\pi$
$930$		0			0
$931$	5.79753e10	+	2.02535e12i	0.00252912	+	0.0883541i
$932$	5.87236e11			0.0254942
$933$		0			0
$934$	1.92859e12	+	3.34042e12i	0.0829238	+	0.143628i
$935$	1.04359e13	+	1.80756e13i	0.446559	+	0.773463i
$936$		0			0
$937$	−3.47244e13			−1.47166			−0.735828	−	0.677169i	$-0.763207\pi$
$937$	−3.47244e13			−1.47166			−0.735828	+	0.677169i	$0.763207\pi$
$938$	−2.66576e13	+	7.55330e12i	−1.12437	+	0.318584i
$939$		0			0
$940$	4.25561e12	−	7.37094e12i	0.177782	−	0.307927i
$941$	−2.32792e12	−	4.03208e12i	−0.0967866	−	0.167639i	0.813566	−	0.581472i	$-0.197523\pi$
$941$	−2.32792e12	−	4.03208e12i	−0.0967866	−	0.167639i	−0.910353	+	0.413833i	$0.864190\pi$
$942$		0			0
$943$	2.12744e13	−	3.68483e13i	0.876102	−	1.51745i
$944$	4.33492e12			0.177667
$945$		0			0
$946$	−1.24248e12			−0.0504405
$947$	−1.98170e13	+	3.43240e13i	−0.800687	+	1.38683i	0.118478	+	0.992957i	$0.462198\pi$
$947$	−1.98170e13	+	3.43240e13i	−0.800687	+	1.38683i	−0.919165	+	0.393873i	$0.871135\pi$
$948$		0			0
$949$	6.95627e12	+	1.20486e13i	0.278406	+	0.482213i
$950$	3.05319e11	−	5.28827e11i	0.0121618	−	0.0210648i
$951$		0			0
$952$	−6.59575e12	−	6.40965e12i	−0.260254	−	0.252911i
$953$	3.33592e13			1.31008			0.655040	−	0.755594i	$-0.272652\pi$
$953$	3.33592e13			1.31008			0.655040	+	0.755594i	$0.272652\pi$
$954$		0			0
$955$	−3.80864e11	−	6.59676e11i	−0.0148168	−	0.0256635i
$956$	−5.20638e12	−	9.01771e12i	−0.201593	−	0.349169i
$957$		0			0
$958$	−6.68941e12			−0.256592
$959$	2.56773e13	+	2.49528e13i	0.980316	+	0.952656i
$960$		0			0
$961$	−3.50307e12	+	6.06750e12i	−0.132493	+	0.229485i
$962$	−1.65084e12	−	2.85934e12i	−0.0621467	−	0.107641i
$963$		0			0
$964$	−1.20794e12	+	2.09221e12i	−0.0450504	+	0.0780296i
$965$	−6.23526e11			−0.0231463
$966$		0			0
$967$	3.72454e13			1.36979			0.684893	−	0.728643i	$-0.259849\pi$
$967$	3.72454e13			1.36979			0.684893	+	0.728643i	$0.259849\pi$
$968$	−1.15636e12	+	2.00287e12i	−0.0423305	+	0.0733186i
$969$		0			0
$970$	1.11247e12	+	1.92686e12i	0.0403474	+	0.0698838i
$971$	1.23678e13	−	2.14217e13i	0.446485	−	0.773334i	−0.551670	−	0.834063i	$-0.686009\pi$
$971$	1.23678e13	−	2.14217e13i	0.446485	−	0.773334i	0.998154	+	0.0607287i	$0.0193424\pi$
$972$		0			0
$973$	1.47002e13	−	4.16523e12i	0.525794	−	0.148981i
$974$	−2.74516e13			−0.977356
$975$		0			0
$976$	6.58390e12	+	1.14037e13i	0.232252	+	0.402272i
$977$	−1.96826e13	−	3.40912e13i	−0.691125	−	1.19706i	−0.971470	−	0.237164i	$-0.923782\pi$
$977$	−1.96826e13	−	3.40912e13i	−0.691125	−	1.19706i	0.280345	−	0.959899i	$-0.409551\pi$
$978$		0			0
$979$	−6.09745e13			−2.12142
$980$	9.60647e12	−	5.91910e12i	0.332695	−	0.204993i
$981$		0			0
$982$	2.67785e12	−	4.63817e12i	0.0918935	−	0.159164i
$983$	−1.85175e13	−	3.20732e13i	−0.632544	−	1.09560i	−0.987030	−	0.160537i	$-0.948677\pi$
$983$	−1.85175e13	−	3.20732e13i	−0.632544	−	1.09560i	0.354486	−	0.935062i	$-0.384656\pi$
$984$		0			0
$985$	−2.67027e12	+	4.62505e12i	−0.0903842	+	0.156550i
$986$	−7.96667e12			−0.268430
$987$		0			0
$988$	4.85911e11			0.0162237
$989$	1.76576e12	−	3.05838e12i	0.0586878	−	0.101650i
$990$		0			0
$991$	−1.41148e13	−	2.44476e13i	−0.464883	−	0.805201i	0.534313	−	0.845287i	$-0.320570\pi$
$991$	−1.41148e13	−	2.44476e13i	−0.464883	−	0.805201i	−0.999196	+	0.0400853i	$0.987237\pi$
$992$	−3.03208e12	+	5.25172e12i	−0.0994118	+	0.172186i
$993$		0			0
$994$	3.57132e12	−	1.41343e13i	0.116035	−	0.459234i
$995$	1.11218e13			0.359726
$996$		0			0
$997$	−1.72255e13	−	2.98354e13i	−0.552132	−	0.956321i	−0.998120	−	0.0612823i	$-0.980481\pi$
$997$	−1.72255e13	−	2.98354e13i	−0.552132	−	0.956321i	0.445988	−	0.895039i	$-0.352852\pi$
$998$	−5.68035e12	−	9.83866e12i	−0.181254	−	0.313941i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	126.10.g.e.37.1		6
3.2	odd	2		14.10.c.b.9.2	✓	6
7.4	even	3	inner	126.10.g.e.109.1		6
12.11	even	2		112.10.i.a.65.2		6
21.2	odd	6		98.10.a.g.1.2		3
21.5	even	6		98.10.a.h.1.2		3
21.11	odd	6		14.10.c.b.11.2	yes	6
21.17	even	6		98.10.c.l.67.2		6
21.20	even	2		98.10.c.l.79.2		6
84.11	even	6		112.10.i.a.81.2		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
14.10.c.b.9.2	✓	6	3.2	odd	2
14.10.c.b.11.2	yes	6	21.11	odd	6
98.10.a.g.1.2		3	21.2	odd	6
98.10.a.h.1.2		3	21.5	even	6
98.10.c.l.67.2		6	21.17	even	6
98.10.c.l.79.2		6	21.20	even	2
112.10.i.a.65.2		6	12.11	even	2
112.10.i.a.81.2		6	84.11	even	6
126.10.g.e.37.1		6	1.1	even	1	trivial
126.10.g.e.109.1		6	7.4	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 126 = 2 \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	126.g (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-8.00000 + 13.8564i) q^{2} +(-128.000 - 221.703i) q^{4} +(-546.130 + 945.925i) q^{5} +(6111.84 - 1731.76i) q^{7} +4096.00 q^{8} +(-8738.08 - 15134.8i) q^{10} +(27030.4 + 46818.1i) q^{11} +37802.6 q^{13} +(-24898.8 + 98542.3i) q^{14} +(-32768.0 + 56755.8i) q^{16} +(-176735. - 306114. i) q^{17} +(-25105.3 + 43483.7i) q^{19} +279618. q^{20} -864974. q^{22} +(1.22926e6 - 2.12914e6i) q^{23} +(380047. + 658261. i) q^{25} +(-302421. + 523808. i) q^{26} +(-1.16625e6 - 1.13335e6i) q^{28} -1.40865e6 q^{29} +(-2.89162e6 - 5.00843e6i) q^{31} +(-524288. - 908093. i) q^{32} +5.65552e6 q^{34} +(-1.69974e6 + 6.72711e6i) q^{35} +(-2.72938e6 + 4.72743e6i) q^{37} +(-401685. - 695739. i) q^{38} +(-2.23695e6 + 3.87451e6i) q^{40} +1.73066e7 q^{41} +1.43644e6 q^{43} +(6.91979e6 - 1.19854e7i) q^{44} +(1.96682e7 + 3.40663e7i) q^{46} +(1.52194e7 - 2.63607e7i) q^{47} +(3.43556e7 - 2.11685e7i) q^{49} -1.21615e7 q^{50} +(-4.83873e6 - 8.38092e6i) q^{52} +(-2.15398e6 - 3.73080e6i) q^{53} -5.90485e7 q^{55} +(2.50341e7 - 7.09329e6i) q^{56} +(1.12692e7 - 1.95189e7i) q^{58} +(-3.30728e7 - 5.72837e7i) q^{59} +(1.00462e8 - 1.74006e8i) q^{61} +9.25317e7 q^{62} +1.67772e7 q^{64} +(-2.06451e7 + 3.57584e7i) q^{65} +(1.36301e8 + 2.36080e8i) q^{67} +(-4.52441e7 + 7.83651e7i) q^{68} +(-7.96156e7 - 7.73692e7i) q^{70} -1.43433e8 q^{71} +(1.84016e8 + 3.18725e8i) q^{73} +(-4.36701e7 - 7.56389e7i) q^{74} +1.28539e7 q^{76} +(2.46283e8 + 2.39334e8i) q^{77} +(-2.31998e8 + 4.01832e8i) q^{79} +(-3.57912e7 - 6.19921e7i) q^{80} +(-1.38453e8 + 2.39808e8i) q^{82} +7.47626e8 q^{83} +3.86081e8 q^{85} +(-1.14915e7 + 1.99038e7i) q^{86} +(1.10717e8 + 1.91767e8i) q^{88} +(-5.63943e8 + 9.76778e8i) q^{89} +(2.31043e8 - 6.54650e7i) q^{91} -6.29382e8 q^{92} +(2.43510e8 + 4.21771e8i) q^{94} +(-2.74215e7 - 4.74955e7i) q^{95} -1.27313e8 q^{97} +(1.84743e7 + 6.45393e8i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 48 q^{2} - 768 q^{4} + 1085 q^{5} - 6796 q^{7} + 24576 q^{8} + 17360 q^{10} - 2555 q^{11} + 36140 q^{13} - 43504 q^{14} - 196608 q^{16} - 20759 q^{17} + 1220649 q^{19} - 555520 q^{20} + 81760 q^{22}+ \cdots + 597954960 q^{98}+O(q^{100}) \) 6 * q - 48 * q^2 - 768 * q^4 + 1085 * q^5 - 6796 * q^7 + 24576 * q^8 + 17360 * q^10 - 2555 * q^11 + 36140 * q^13 - 43504 * q^14 - 196608 * q^16 - 20759 * q^17 + 1220649 * q^19 - 555520 * q^20 + 81760 * q^22 + 1960903 * q^23 - 863572 * q^25 - 289120 * q^26 + 2435840 * q^28 + 5212292 * q^29 - 9377989 * q^31 - 3145728 * q^32 + 664288 * q^34 - 20361719 * q^35 - 25814913 * q^37 + 19530384 * q^38 + 4444160 * q^40 - 418500 * q^41 + 5888616 * q^43 - 654080 * q^44 + 31374448 * q^46 - 48391269 * q^47 + 108466086 * q^49 + 27634304 * q^50 - 4625920 * q^52 - 102186411 * q^53 - 456557402 * q^55 - 27836416 * q^56 - 41698336 * q^58 - 144220135 * q^59 + 280936871 * q^61 + 300095648 * q^62 + 100663296 * q^64 + 186819738 * q^65 + 170710399 * q^67 - 5314304 * q^68 - 347247824 * q^70 - 939517376 * q^71 + 613838539 * q^73 - 413038608 * q^74 - 624972288 * q^76 + 729499715 * q^77 + 197445809 * q^79 + 71106560 * q^80 + 3348000 * q^82 + 2148362872 * q^83 + 822545038 * q^85 - 47108928 * q^86 - 10465280 * q^88 - 805730427 * q^89 + 17178248 * q^91 - 1003982336 * q^92 - 774260304 * q^94 - 1799421743 * q^95 - 4525836188 * q^97 + 597954960 * q^98

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