LMFDB - Embedded newform 126.10.g.c.109.2

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 = [4,32,0,-512,-929] 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:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{7081})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + 1771x^{2} + 1770x + 3132900 $ x^4 - x^3 + 1771x^2 + 1770x + 3132900
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 42)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			109.2
Root			$21.2872 - 36.8705i$ of defining polynomial
Character	$\chi$	$=$	126.109
Dual form			126.10.g.c.37.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(8.00000 + 13.8564i) q^{2} +(-128.000 + 221.703i) q^{4} +(419.902 + 727.292i) q^{5} +(-6254.79 - 1109.63i) q^{7} -4096.00 q^{8} +(-6718.44 + 11636.7i) q^{10} +(-20668.9 + 35799.5i) q^{11} -91963.9 q^{13} +(-34662.9 - 95545.9i) q^{14} +(-32768.0 - 56755.8i) q^{16} +(154395. - 267420. i) q^{17} +(396459. + 686687. i) q^{19} -214990. q^{20} -661403. q^{22} +(-466522. - 808040. i) q^{23} +(623927. - 1.08067e6i) q^{25} +(-735712. - 1.27429e6i) q^{26} +(1.04662e6 - 1.24467e6i) q^{28} -5.92949e6 q^{29} +(3.31544e6 - 5.74252e6i) q^{31} +(524288. - 908093. i) q^{32} +4.94064e6 q^{34} +(-1.81938e6 - 5.01499e6i) q^{35} +(9.40187e6 + 1.62845e7i) q^{37} +(-6.34334e6 + 1.09870e7i) q^{38} +(-1.71992e6 - 2.97899e6i) q^{40} +3.06260e6 q^{41} -1.69946e7 q^{43} +(-5.29123e6 - 9.16467e6i) q^{44} +(7.46436e6 - 1.29286e7i) q^{46} +(-2.04657e7 - 3.54477e7i) q^{47} +(3.78911e7 + 1.38809e7i) q^{49} +1.99657e7 q^{50} +(1.17714e7 - 2.03886e7i) q^{52} +(3.67746e7 - 6.36954e7i) q^{53} -3.47156e7 q^{55} +(2.56196e7 + 4.54503e6i) q^{56} +(-4.74359e7 - 8.21615e7i) q^{58} +(1.10813e7 - 1.91935e7i) q^{59} +(-3.55783e7 - 6.16234e7i) q^{61} +1.06094e8 q^{62} +1.67772e7 q^{64} +(-3.86159e7 - 6.68846e7i) q^{65} +(1.09727e8 - 1.90053e8i) q^{67} +(3.95251e7 + 6.84596e7i) q^{68} +(5.49347e7 - 6.53299e7i) q^{70} +1.77453e7 q^{71} +(-2.18567e7 + 3.78569e7i) q^{73} +(-1.50430e8 + 2.60552e8i) q^{74} -2.02987e8 q^{76} +(1.69003e8 - 2.00984e8i) q^{77} +(3.03509e7 + 5.25694e7i) q^{79} +(2.75187e7 - 4.76638e7i) q^{80} +(2.45008e7 + 4.24367e7i) q^{82} +2.88693e8 q^{83} +2.59323e8 q^{85} +(-1.35957e8 - 2.35484e8i) q^{86} +(8.46596e7 - 1.46635e8i) q^{88} +(-4.38592e7 - 7.59663e7i) q^{89} +(5.75215e8 + 1.02046e8i) q^{91} +2.38859e8 q^{92} +(3.27452e8 - 5.67163e8i) q^{94} +(-3.32948e8 + 5.76683e8i) q^{95} +1.15563e9 q^{97} +(1.10789e8 + 6.36082e8i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 32 q^{2} - 512 q^{4} - 929 q^{5} - 8526 q^{7} - 16384 q^{8} + 14864 q^{10} - 41695 q^{11} - 181214 q^{13} - 204624 q^{14} - 131072 q^{16} + 472508 q^{17} + 390503 q^{19} + 475648 q^{20} - 1334240 q^{22}+ \cdots - 963050704 q^{98}+O(q^{100}) $ 4 * q + 32 * q^2 - 512 * q^4 - 929 * q^5 - 8526 * q^7 - 16384 * q^8 + 14864 * q^10 - 41695 * q^11 - 181214 * q^13 - 204624 * q^14 - 131072 * q^16 + 472508 * q^17 + 390503 * q^19 + 475648 * q^20 - 1334240 * q^22 - 2225236 * q^23 + 72309 * q^25 - 1449712 * q^26 - 1091328 * q^28 - 6665582 * q^29 - 303326 * q^31 + 2097152 * q^32 + 15120256 * q^34 + 11318510 * q^35 + 29575385 * q^37 - 6248048 * q^38 + 3805184 * q^40 + 70138308 * q^41 - 16999882 * q^43 - 10673920 * q^44 + 35603776 * q^46 + 25023696 * q^47 + 10943758 * q^49 + 2313888 * q^50 + 23195392 * q^52 + 46233651 * q^53 - 68167202 * q^55 + 34922496 * q^56 - 53324656 * q^58 - 42109697 * q^59 - 28918988 * q^61 - 9706432 * q^62 + 67108864 * q^64 - 79631898 * q^65 + 367330515 * q^67 + 120962048 * q^68 + 461924176 * q^70 + 249191216 * q^71 - 94453335 * q^73 - 473206160 * q^74 - 199937536 * q^76 + 333561865 * q^77 + 402026668 * q^79 - 60882944 * q^80 + 561106464 * q^82 + 1775352998 * q^83 - 60522968 * q^85 - 135999056 * q^86 + 170782720 * q^88 - 72113094 * q^89 + 1155834883 * q^91 + 1139320832 * q^92 - 400379136 * q^94 - 1377688234 * q^95 + 296226882 * q^97 - 963050704 * q^98

Character values

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

$n$	$29$	$73$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$

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
$5$	419.902	+	727.292i	0.300458	+	0.520408i	0.976240	−	0.216694i	$-0.0695273\pi$
$5$	419.902	+	727.292i	0.300458	+	0.520408i	−0.675782	+	0.737101i	$0.736194\pi$
$6$		0			0
$7$	−6254.79	−	1109.63i	−0.984626	−	0.174677i
$7$	−6254.79	−	1109.63i	−0.984626	−	0.174677i
$8$	−4096.00			−0.353553
$9$		0			0
$10$	−6718.44	+	11636.7i	−0.212456	+	0.367984i
$11$	−20668.9	+	35799.5i	−0.425647	+	0.737242i	−0.996481	−	0.0838239i	$-0.973287\pi$
$11$	−20668.9	+	35799.5i	−0.425647	+	0.737242i	0.570834	+	0.821066i	$0.306620\pi$
$12$		0			0
$13$	−91963.9			−0.893043			−0.446522	−	0.894773i	$-0.647337\pi$
$13$	−91963.9			−0.893043			−0.446522	+	0.894773i	$0.647337\pi$
$14$	−34662.9	−	95545.9i	−0.241151	−	0.664715i
$15$		0			0
$16$	−32768.0	−	56755.8i	−0.125000	−	0.216506i
$17$	154395.	−	267420.i	0.448346	−	0.776558i	−0.549933	−	0.835209i	$-0.685347\pi$
$17$	154395.	−	267420.i	0.448346	−	0.776558i	0.998279	+	0.0586510i	$0.0186799\pi$
$18$		0			0
$19$	396459.	+	686687.i	0.697922	+	1.20884i	0.969186	+	0.246331i	$0.0792251\pi$
$19$	396459.	+	686687.i	0.697922	+	1.20884i	−0.271264	+	0.962505i	$0.587442\pi$
$20$	−214990.			−0.300458
$21$		0			0
$22$	−661403.			−0.601955
$23$	−466522.	−	808040.i	−0.347614	−	0.602085i	0.638211	−	0.769861i	$-0.279675\pi$
$23$	−466522.	−	808040.i	−0.347614	−	0.602085i	−0.985825	+	0.167776i	$0.946341\pi$
$24$		0			0
$25$	623927.	−	1.08067e6i	0.319450	−	0.553304i
$26$	−735712.	−	1.27429e6i	−0.315738	−	0.546875i
$27$		0			0
$28$	1.04662e6	−	1.24467e6i	0.321794	−	0.382686i
$29$	−5.92949e6			−1.55678			−0.778389	−	0.627782i	$-0.783963\pi$
$29$	−5.92949e6			−1.55678			−0.778389	+	0.627782i	$0.783963\pi$
$30$		0			0
$31$	3.31544e6	−	5.74252e6i	0.644784	−	1.11680i	−0.339568	−	0.940582i	$-0.610281\pi$
$31$	3.31544e6	−	5.74252e6i	0.644784	−	1.11680i	0.984351	−	0.176217i	$-0.0563859\pi$
$32$	524288.	−	908093.i	0.0883883	−	0.153093i
$33$		0			0
$34$	4.94064e6			0.634057
$35$	−1.81938e6	−	5.01499e6i	−0.204935	−	0.564890i
$36$		0			0
$37$	9.40187e6	+	1.62845e7i	0.824719	+	1.42846i	0.902133	+	0.431457i	$0.142000\pi$
$37$	9.40187e6	+	1.62845e7i	0.824719	+	1.42846i	−0.0774140	+	0.996999i	$0.524666\pi$
$38$	−6.34334e6	+	1.09870e7i	−0.493505	+	0.854776i
$39$		0			0
$40$	−1.71992e6	−	2.97899e6i	−0.106228	−	0.183992i
$41$	3.06260e6			0.169264			0.0846318	−	0.996412i	$-0.473029\pi$
$41$	3.06260e6			0.169264			0.0846318	+	0.996412i	$0.473029\pi$
$42$		0			0
$43$	−1.69946e7			−0.758058			−0.379029	−	0.925385i	$-0.623742\pi$
$43$	−1.69946e7			−0.758058			−0.379029	+	0.925385i	$0.623742\pi$
$44$	−5.29123e6	−	9.16467e6i	−0.212823	−	0.368621i
$45$		0			0
$46$	7.46436e6	−	1.29286e7i	0.245800	−	0.425738i
$47$	−2.04657e7	−	3.54477e7i	−0.611769	−	1.05961i	−0.990942	−	0.134289i	$-0.957125\pi$
$47$	−2.04657e7	−	3.54477e7i	−0.611769	−	1.05961i	0.379174	−	0.925325i	$-0.376208\pi$
$48$		0			0
$49$	3.78911e7	+	1.38809e7i	0.938976	+	0.343983i
$50$	1.99657e7			0.451771
$51$		0			0
$52$	1.17714e7	−	2.03886e7i	0.223261	−	0.386699i
$53$	3.67746e7	−	6.36954e7i	0.640186	−	1.10883i	−0.345205	−	0.938527i	$-0.612191\pi$
$53$	3.67746e7	−	6.36954e7i	0.640186	−	1.10883i	0.985391	−	0.170307i	$-0.0544759\pi$
$54$		0			0
$55$	−3.47156e7			−0.511555
$56$	2.56196e7	+	4.54503e6i	0.348118	+	0.0617576i
$57$		0			0
$58$	−4.74359e7	−	8.21615e7i	−0.550404	−	0.953328i
$59$	1.10813e7	−	1.91935e7i	0.119058	−	0.206214i	−0.800337	−	0.599551i	$-0.795346\pi$
$59$	1.10813e7	−	1.91935e7i	0.119058	−	0.206214i	0.919395	+	0.393336i	$0.128679\pi$
$60$		0			0
$61$	−3.55783e7	−	6.16234e7i	−0.329003	−	0.569851i	0.653311	−	0.757090i	$-0.273379\pi$
$61$	−3.55783e7	−	6.16234e7i	−0.329003	−	0.569851i	−0.982314	+	0.187239i	$0.940046\pi$
$62$	1.06094e8			0.911862
$63$		0			0
$64$	1.67772e7			0.125000
$65$	−3.86159e7	−	6.68846e7i	−0.268322	−	0.464747i
$66$		0			0
$67$	1.09727e8	−	1.90053e8i	0.665240	−	1.15223i	−0.313981	−	0.949429i	$-0.601663\pi$
$67$	1.09727e8	−	1.90053e8i	0.665240	−	1.15223i	0.979220	−	0.202799i	$-0.0650039\pi$
$68$	3.95251e7	+	6.84596e7i	0.224173	+	0.388279i
$69$		0			0
$70$	5.49347e7	−	6.53299e7i	0.273468	−	0.325215i
$71$	1.77453e7			0.0828744			0.0414372	−	0.999141i	$-0.486806\pi$
$71$	1.77453e7			0.0828744			0.0414372	+	0.999141i	$0.486806\pi$
$72$		0			0
$73$	−2.18567e7	+	3.78569e7i	−0.0900806	+	0.156024i	−0.907545	−	0.419955i	$-0.862046\pi$
$73$	−2.18567e7	+	3.78569e7i	−0.0900806	+	0.156024i	0.817464	+	0.575979i	$0.195379\pi$
$74$	−1.50430e8	+	2.60552e8i	−0.583165	+	1.01007i
$75$		0			0
$76$	−2.02987e8			−0.697922
$77$	1.69003e8	−	2.00984e8i	0.547882	−	0.651557i
$78$		0			0
$79$	3.03509e7	+	5.25694e7i	0.0876699	+	0.151849i	0.906526	−	0.422150i	$-0.138725\pi$
$79$	3.03509e7	+	5.25694e7i	0.0876699	+	0.151849i	−0.818856	+	0.573999i	$0.805391\pi$
$80$	2.75187e7	−	4.76638e7i	0.0751144	−	0.130102i
$81$		0			0
$82$	2.45008e7	+	4.24367e7i	0.0598437	+	0.103652i
$83$	2.88693e8			0.667705			0.333852	−	0.942625i	$-0.391651\pi$
$83$	2.88693e8			0.667705			0.333852	+	0.942625i	$0.391651\pi$
$84$		0			0
$85$	2.59323e8			0.538836
$86$	−1.35957e8	−	2.35484e8i	−0.268014	−	0.464214i
$87$		0			0
$88$	8.46596e7	−	1.46635e8i	0.150489	−	0.260654i
$89$	−4.38592e7	−	7.59663e7i	−0.0740978	−	0.128341i	0.826596	−	0.562796i	$-0.190274\pi$
$89$	−4.38592e7	−	7.59663e7i	−0.0740978	−	0.128341i	−0.900694	+	0.434455i	$0.856941\pi$
$90$		0			0
$91$	5.75215e8	+	1.02046e8i	0.879313	+	0.155994i
$92$	2.38859e8			0.347614
$93$		0			0
$94$	3.27452e8	−	5.67163e8i	0.432586	−	0.749260i
$95$	−3.32948e8	+	5.76683e8i	−0.419392	+	0.726408i
$96$		0			0
$97$	1.15563e9			1.32539			0.662697	−	0.748888i	$-0.269412\pi$
$97$	1.15563e9			1.32539			0.662697	+	0.748888i	$0.269412\pi$
$98$	1.10789e8	+	6.36082e8i	0.121333	+	0.696619i
$99$		0			0
$100$	1.59725e8	+	2.76652e8i	0.159725	+	0.276652i
$101$	7.25186e8	−	1.25606e9i	0.693431	−	1.20106i	−0.277276	−	0.960790i	$-0.589432\pi$
$101$	7.25186e8	−	1.25606e9i	0.693431	−	1.20106i	0.970707	−	0.240267i	$-0.0772350\pi$
$102$		0			0
$103$	−5.87028e7	−	1.01676e8i	−0.0513915	−	0.0890127i	0.839185	−	0.543846i	$-0.183032\pi$
$103$	−5.87028e7	−	1.01676e8i	−0.0513915	−	0.0890127i	−0.890577	+	0.454833i	$0.849699\pi$
$104$	3.76684e8			0.315738
$105$		0			0
$106$	1.17679e9			0.905359
$107$	3.71888e7	+	6.44128e7i	0.0274274	+	0.0475057i	0.879413	−	0.476059i	$-0.157935\pi$
$107$	3.71888e7	+	6.44128e7i	0.0274274	+	0.0475057i	−0.851986	+	0.523565i	$0.824602\pi$
$108$		0			0
$109$	1.25470e9	−	2.17320e9i	0.851372	−	1.47462i	−0.0285992	−	0.999591i	$-0.509105\pi$
$109$	1.25470e9	−	2.17320e9i	0.851372	−	1.47462i	0.879971	−	0.475028i	$-0.157562\pi$
$110$	−2.77725e8	−	4.81033e8i	−0.180862	−	0.313262i
$111$		0			0
$112$	1.41979e8	+	3.91356e8i	0.0852596	+	0.235012i
$113$	−2.41014e9			−1.39056			−0.695280	−	0.718739i	$-0.744720\pi$
$113$	−2.41014e9			−1.39056			−0.695280	+	0.718739i	$0.744720\pi$
$114$		0			0
$115$	3.91788e8	−	6.78596e8i	0.208887	−	0.361802i
$116$	7.58975e8	−	1.31458e9i	0.389194	−	0.674105i
$117$		0			0
$118$	3.54603e8			0.168373
$119$	−1.26244e9	+	1.50133e9i	−0.577100	+	0.686303i
$120$		0			0
$121$	3.24571e8	+	5.62173e8i	0.137650	+	0.238416i
$122$	5.69252e8	−	9.85974e8i	0.232641	−	0.402945i
$123$		0			0
$124$	8.48754e8	+	1.47008e9i	0.322392	+	0.558399i
$125$	2.68820e9			0.984840
$126$		0			0
$127$	−3.69133e9			−1.25912			−0.629558	−	0.776954i	$-0.716764\pi$
$127$	−3.69133e9			−1.25912			−0.629558	+	0.776954i	$0.716764\pi$
$128$	1.34218e8	+	2.32472e8i	0.0441942	+	0.0765466i
$129$		0			0
$130$	6.17854e8	−	1.07015e9i	0.189732	−	0.328626i
$131$	8.90047e8	+	1.54161e9i	0.264054	+	0.457355i	0.967315	−	0.253577i	$-0.0816070\pi$
$131$	8.90047e8	+	1.54161e9i	0.264054	+	0.457355i	−0.703262	+	0.710931i	$0.748274\pi$
$132$		0			0
$133$	−1.71780e9	−	4.73500e9i	−0.476036	−	1.31216i
$134$	3.51127e9			0.940791
$135$		0			0
$136$	−6.32402e8	+	1.09535e9i	−0.158514	+	0.274555i
$137$	−3.04443e8	+	5.27310e8i	−0.0738351	+	0.127886i	−0.900579	−	0.434692i	$-0.856857\pi$
$137$	−3.04443e8	+	5.27310e8i	−0.0738351	+	0.127886i	0.826744	+	0.562578i	$0.190191\pi$
$138$		0			0
$139$	−8.68107e8			−0.197245			−0.0986226	−	0.995125i	$-0.531444\pi$
$139$	−8.68107e8			−0.197245			−0.0986226	+	0.995125i	$0.531444\pi$
$140$	1.34472e9	+	2.38558e8i	0.295838	+	0.0524830i
$141$		0			0
$142$	1.41962e8	+	2.45886e8i	0.0293005	+	0.0507500i
$143$	1.90079e9	−	3.29226e9i	0.380121	−	0.658389i
$144$		0			0
$145$	−2.48981e9	−	4.31247e9i	−0.467746	−	0.810159i
$146$	−6.99413e8			−0.127393
$147$		0			0
$148$	−4.81375e9			−0.824719
$149$	−2.89099e9	−	5.00734e9i	−0.480516	−	0.832278i	0.519234	−	0.854632i	$-0.326217\pi$
$149$	−2.89099e9	−	5.00734e9i	−0.480516	−	0.832278i	−0.999750	+	0.0223539i	$0.992884\pi$
$150$		0			0
$151$	1.94063e9	−	3.36127e9i	0.303771	−	0.526146i	−0.673216	−	0.739446i	$-0.735088\pi$
$151$	1.94063e9	−	3.36127e9i	0.303771	−	0.526146i	0.976987	+	0.213299i	$0.0684210\pi$
$152$	−1.62390e9	−	2.81267e9i	−0.246753	−	0.427388i
$153$		0			0
$154$	4.13694e9	+	7.33910e8i	0.592701	+	0.105148i
$155$	5.56865e9			0.774921
$156$		0			0
$157$	−4.99418e9	+	8.65018e9i	−0.656018	+	1.13626i	0.325619	+	0.945501i	$0.394427\pi$
$157$	−4.99418e9	+	8.65018e9i	−0.656018	+	1.13626i	−0.981637	+	0.190756i	$0.938906\pi$
$158$	−4.85615e8	+	8.41110e8i	−0.0619920	+	0.107373i
$159$		0			0
$160$	8.80599e8			0.106228
$161$	2.02137e9	+	5.57178e9i	0.237099	+	0.653549i
$162$		0			0
$163$	8.81756e8	+	1.52725e9i	0.0978372	+	0.169459i	0.910789	−	0.412872i	$-0.135474\pi$
$163$	8.81756e8	+	1.52725e9i	0.0978372	+	0.169459i	−0.812952	+	0.582331i	$0.802141\pi$
$164$	−3.92013e8	+	6.78987e8i	−0.0423159	+	0.0732933i
$165$		0			0
$166$	2.30954e9	+	4.00024e9i	0.236069	+	0.408884i
$167$	−1.81719e10			−1.80791			−0.903956	−	0.427625i	$-0.859350\pi$
$167$	−1.81719e10			−1.80791			−0.903956	+	0.427625i	$0.859350\pi$
$168$		0			0
$169$	−2.14713e9			−0.202474
$170$	2.07459e9	+	3.59329e9i	0.190507	+	0.329968i
$171$		0			0
$172$	2.17531e9	−	3.76774e9i	0.189515	−	0.328249i
$173$	−1.12913e10	−	1.95572e10i	−0.958381	−	1.65996i	−0.726434	−	0.687237i	$-0.758824\pi$
$173$	−1.12913e10	−	1.95572e10i	−0.958381	−	1.65996i	−0.231948	−	0.972728i	$-0.574510\pi$
$174$		0			0
$175$	−5.10167e9	+	6.06705e9i	−0.411189	+	0.488997i
$176$	2.70911e9			0.212823
$177$		0			0
$178$	7.01747e8	−	1.21546e9i	0.0523951	−	0.0907509i
$179$	−5.55153e9	+	9.61554e9i	−0.404180	+	0.700059i	−0.994226	−	0.107310i	$-0.965776\pi$
$179$	−5.55153e9	+	9.61554e9i	−0.404180	+	0.700059i	0.590046	+	0.807370i	$0.299110\pi$
$180$		0			0
$181$	8.45337e9			0.585432			0.292716	−	0.956199i	$-0.405441\pi$
$181$	8.45337e9			0.585432			0.292716	+	0.956199i	$0.405441\pi$
$182$	3.18773e9	+	8.78677e9i	0.215358	+	0.593620i
$183$		0			0
$184$	1.91088e9	+	3.30973e9i	0.122900	+	0.212869i
$185$	−7.89573e9	+	1.36758e10i	−0.495586	+	0.858381i
$186$		0			0
$187$	6.38234e9	+	1.10545e10i	0.381674	+	0.661079i
$188$	1.04785e10			0.611769
$189$		0			0
$190$	−1.06543e10			−0.593110
$191$	−7.82916e9	−	1.35605e10i	−0.425662	−	0.737269i	0.570820	−	0.821075i	$-0.306625\pi$
$191$	−7.82916e9	−	1.35605e10i	−0.425662	−	0.737269i	−0.996482	+	0.0838067i	$0.973292\pi$
$192$		0			0
$193$	1.78070e9	−	3.08426e9i	0.0923811	−	0.160009i	−0.816132	−	0.577866i	$-0.803886\pi$
$193$	1.78070e9	−	3.08426e9i	0.0923811	−	0.160009i	0.908513	+	0.417858i	$0.137219\pi$
$194$	9.24502e9	+	1.60128e10i	0.468597	+	0.811635i
$195$		0			0
$196$	−7.92750e9	+	6.62378e9i	−0.383693	+	0.320593i
$197$	−3.56610e10			−1.68693			−0.843463	−	0.537187i	$-0.819487\pi$
$197$	−3.56610e10			−1.68693			−0.843463	+	0.537187i	$0.819487\pi$
$198$		0			0
$199$	−1.81260e10	+	3.13951e10i	−0.819337	+	1.41913i	0.0868353	+	0.996223i	$0.472325\pi$
$199$	−1.81260e10	+	3.13951e10i	−0.819337	+	1.41913i	−0.906172	+	0.422910i	$0.861009\pi$
$200$	−2.55560e9	+	4.42644e9i	−0.112943	+	0.195623i
$201$		0			0
$202$	2.32059e10			0.980659
$203$	3.70877e10	+	6.57952e9i	1.53284	+	0.271933i
$204$		0			0
$205$	1.28599e9	+	2.22741e9i	0.0508565	+	0.0880861i
$206$	9.39245e8	−	1.62682e9i	0.0363393	−	0.0629415i
$207$		0			0
$208$	3.01347e9	+	5.21949e9i	0.111630	+	0.193350i
$209$	−3.27774e10			−1.18827
$210$		0			0
$211$	−4.13477e10			−1.43609			−0.718043	−	0.695999i	$-0.754962\pi$
$211$	−4.13477e10			−1.43609			−0.718043	+	0.695999i	$0.754962\pi$
$212$	9.41429e9	+	1.63060e10i	0.320093	+	0.554417i
$213$		0			0
$214$	−5.95020e8	+	1.03061e9i	−0.0193941	+	0.0335916i
$215$	−7.13606e9	−	1.23600e10i	−0.227764	−	0.394499i
$216$		0			0
$217$	−2.71094e10	+	3.22393e10i	−0.829950	+	0.987000i
$218$	4.01503e10			1.20402
$219$		0			0
$220$	4.44360e9	−	7.69653e9i	0.127889	−	0.221510i
$221$	−1.41988e10	+	2.45930e10i	−0.400392	+	0.693500i
$222$		0			0
$223$	−5.00444e10			−1.35514			−0.677569	−	0.735459i	$-0.736966\pi$
$223$	−5.00444e10			−1.35514			−0.677569	+	0.735459i	$0.736966\pi$
$224$	−4.28695e9	+	5.09817e9i	−0.113771	+	0.135300i
$225$		0			0
$226$	−1.92811e10	−	3.33959e10i	−0.491637	−	0.851541i
$227$	−1.37832e7	+	2.38733e7i	−0.000344536	+	0.000596755i	−0.866198	−	0.499702i	$-0.833443\pi$
$227$	−1.37832e7	+	2.38733e7i	−0.000344536	+	0.000596755i	0.865853	+	0.500298i	$0.166776\pi$
$228$		0			0
$229$	1.88467e10	+	3.26435e10i	0.452872	+	0.784398i	0.998563	−	0.0535887i	$-0.0170660\pi$
$229$	1.88467e10	+	3.26435e10i	0.452872	+	0.784398i	−0.545691	+	0.837987i	$0.683733\pi$
$230$	1.25372e10			0.295410
$231$		0			0
$232$	2.42872e10			0.550404
$233$	8.86513e9	+	1.53549e10i	0.197053	+	0.341306i	0.947572	−	0.319543i	$-0.103529\pi$
$233$	8.86513e9	+	1.53549e10i	0.197053	+	0.341306i	−0.750518	+	0.660850i	$0.770196\pi$
$234$		0			0
$235$	1.71872e10	−	2.97691e10i	0.367621	−	0.636738i
$236$	2.83682e9	+	4.91352e9i	0.0595290	+	0.103107i
$237$		0			0
$238$	−3.09027e10	−	5.48226e9i	−0.624309	−	0.110755i
$239$	7.14942e10			1.41736			0.708680	−	0.705530i	$-0.249291\pi$
$239$	7.14942e10			1.41736			0.708680	+	0.705530i	$0.249291\pi$
$240$		0			0
$241$	−5.78211e9	+	1.00149e10i	−0.110410	+	0.191236i	−0.915936	−	0.401325i	$-0.868550\pi$
$241$	−5.78211e9	+	1.00149e10i	−0.110410	+	0.191236i	0.805525	+	0.592561i	$0.201883\pi$
$242$	−5.19314e9	+	8.99478e9i	−0.0973331	+	0.168586i
$243$		0			0
$244$	1.82161e10			0.329003
$245$	5.81505e9	+	3.33865e10i	0.103111	+	0.592003i
$246$		0			0
$247$	−3.64599e10	−	6.31504e10i	−0.623274	−	1.07954i
$248$	−1.35801e10	+	2.35214e10i	−0.227966	+	0.394848i
$249$		0			0
$250$	2.15056e10	+	3.72487e10i	0.348194	+	0.603089i
$251$	−6.59260e10			−1.04840			−0.524198	−	0.851597i	$-0.675635\pi$
$251$	−6.59260e10			−1.04840			−0.524198	+	0.851597i	$0.675635\pi$
$252$		0			0
$253$	3.85699e10			0.591843
$254$	−2.95306e10	−	5.11485e10i	−0.445165	−	0.771048i
$255$		0			0
$256$	−2.14748e9	+	3.71955e9i	−0.0312500	+	0.0541266i
$257$	−4.71504e10	−	8.16669e10i	−0.674196	−	1.16774i	−0.976703	−	0.214595i	$-0.931157\pi$
$257$	−4.71504e10	−	8.16669e10i	−0.674196	−	1.16774i	0.302507	−	0.953147i	$-0.402176\pi$
$258$		0			0
$259$	−4.07369e10	−	1.12289e11i	−0.562522	−	1.55055i
$260$	1.97713e10			0.268322
$261$		0			0
$262$	−1.42408e10	+	2.46657e10i	−0.186714	+	0.323398i
$263$	3.26500e9	−	5.65515e9i	0.0420807	−	0.0728859i	−0.844218	−	0.536000i	$-0.819935\pi$
$263$	3.26500e9	−	5.65515e9i	0.0420807	−	0.0728859i	0.886299	+	0.463114i	$0.153268\pi$
$264$		0			0
$265$	6.17669e10			0.769395
$266$	5.18677e10	−	6.16825e10i	0.635228	−	0.755431i
$267$		0			0
$268$	2.80902e10	+	4.86536e10i	0.332620	+	0.576114i
$269$	6.08675e10	−	1.05426e11i	0.708761	−	1.22761i	−0.256556	−	0.966529i	$-0.582588\pi$
$269$	6.08675e10	−	1.05426e11i	0.708761	−	1.22761i	0.965317	−	0.261081i	$-0.0840790\pi$
$270$		0			0
$271$	5.02171e10	+	8.69785e10i	0.565574	+	0.979603i	0.996996	+	0.0774529i	$0.0246788\pi$
$271$	5.02171e10	+	8.69785e10i	0.565574	+	0.979603i	−0.431422	+	0.902150i	$0.641988\pi$
$272$	−2.02369e10			−0.224173
$273$		0			0
$274$	−9.74217e9			−0.104419
$275$	2.57917e10	+	4.46725e10i	0.271946	+	0.471024i
$276$		0			0
$277$	8.84945e10	−	1.53277e11i	0.903145	−	1.56429i	0.0797568	−	0.996814i	$-0.474586\pi$
$277$	8.84945e10	−	1.53277e11i	0.903145	−	1.56429i	0.823388	−	0.567479i	$-0.192081\pi$
$278$	−6.94485e9	−	1.20288e10i	−0.0697367	−	0.120788i
$279$		0			0
$280$	7.45217e9	+	2.05414e10i	0.0724555	+	0.199719i
$281$	2.19444e10			0.209964			0.104982	−	0.994474i	$-0.466521\pi$
$281$	2.19444e10			0.209964			0.104982	+	0.994474i	$0.466521\pi$
$282$		0			0
$283$	4.80386e10	−	8.32053e10i	0.445196	−	0.771102i	−0.552870	−	0.833268i	$-0.686467\pi$
$283$	4.80386e10	−	8.32053e10i	0.445196	−	0.771102i	0.998066	+	0.0621654i	$0.0198006\pi$
$284$	−2.27140e9	+	3.93417e9i	−0.0207186	+	0.0358857i
$285$		0			0
$286$	6.08253e10			0.537572
$287$	−1.91559e10	−	3.39834e9i	−0.166661	−	0.0295664i
$288$		0			0
$289$	1.16183e10	+	2.01234e10i	0.0979717	+	0.169692i
$290$	3.98369e10	−	6.89996e10i	0.330746	−	0.572869i
$291$		0			0
$292$	−5.59531e9	−	9.69136e9i	−0.0450403	−	0.0780121i
$293$	−1.81128e11			−1.43575			−0.717877	−	0.696170i	$-0.754886\pi$
$293$	−1.81128e11			−1.43575			−0.717877	+	0.696170i	$0.754886\pi$
$294$		0			0
$295$	1.86123e10			0.143087
$296$	−3.85100e10	−	6.67013e10i	−0.291582	−	0.505035i
$297$		0			0
$298$	4.62558e10	−	8.01174e10i	0.339776	−	0.588510i
$299$	4.29032e10	+	7.43106e10i	0.310434	+	0.537688i
$300$		0			0
$301$	1.06297e11	+	1.88576e10i	0.746403	+	0.132415i
$302$	6.21001e10			0.429597
$303$		0			0
$304$	2.59823e10	−	4.50027e10i	0.174480	−	0.302209i
$305$	2.98788e10	−	5.17516e10i	0.197703	−	0.342432i
$306$		0			0
$307$	−1.37295e11			−0.882131			−0.441065	−	0.897475i	$-0.645399\pi$
$307$	−1.37295e11			−0.882131			−0.441065	+	0.897475i	$0.645399\pi$
$308$	2.29261e10	+	6.31943e10i	0.145162	+	0.400129i
$309$		0			0
$310$	4.45492e10	+	7.71615e10i	0.273976	+	0.474540i
$311$	−3.15063e10	+	5.45706e10i	−0.190975	+	0.330778i	−0.945574	−	0.325408i	$-0.894498\pi$
$311$	−3.15063e10	+	5.45706e10i	−0.190975	+	0.330778i	0.754599	+	0.656187i	$0.227832\pi$
$312$		0			0
$313$	−4.14563e10	−	7.18044e10i	−0.244141	−	0.422865i	0.717749	−	0.696302i	$-0.245173\pi$
$313$	−4.14563e10	−	7.18044e10i	−0.244141	−	0.422865i	−0.961890	+	0.273438i	$0.911839\pi$
$314$	−1.59814e11			−0.927750
$315$		0			0
$316$	−1.55397e10			−0.0876699
$317$	−1.37422e11	−	2.38022e11i	−0.764346	−	1.32389i	−0.940592	−	0.339539i	$-0.889729\pi$
$317$	−1.37422e11	−	2.38022e11i	−0.764346	−	1.32389i	0.176246	−	0.984346i	$-0.443605\pi$
$318$		0			0
$319$	1.22556e11	−	2.12273e11i	0.662637	−	1.14772i
$320$	7.04479e9	+	1.22019e10i	0.0375572	+	0.0650510i
$321$		0			0
$322$	−6.10339e10	+	7.25833e10i	−0.316388	+	0.376257i
$323$	2.44845e11			1.25164
$324$		0			0
$325$	−5.73788e10	+	9.93829e10i	−0.285283	+	0.494125i
$326$	−1.41081e10	+	2.44359e10i	−0.0691814	+	0.119826i
$327$		0			0
$328$	−1.25444e10			−0.0598437
$329$	8.86751e10	+	2.44427e11i	0.417273	+	1.15019i
$330$		0			0
$331$	9.27062e10	+	1.60572e11i	0.424505	+	0.735264i	0.996374	−	0.0850806i	$-0.0271148\pi$
$331$	9.27062e10	+	1.60572e11i	0.424505	+	0.735264i	−0.571869	+	0.820345i	$0.693781\pi$
$332$	−3.69527e10	+	6.40039e10i	−0.166926	+	0.289125i
$333$		0			0
$334$	−1.45376e11	−	2.51798e11i	−0.639193	−	1.10712i
$335$	1.84299e11			0.799505
$336$		0			0
$337$	2.24906e11			0.949877			0.474939	−	0.880019i	$-0.342470\pi$
$337$	2.24906e11			0.949877			0.474939	+	0.880019i	$0.342470\pi$
$338$	−1.71771e10	−	2.97515e10i	−0.0715853	−	0.123989i
$339$		0			0
$340$	−3.31934e10	+	5.74926e10i	−0.134709	+	0.233323i
$341$	1.37053e11	+	2.37383e11i	0.548900	+	0.950723i
$342$		0			0
$343$	−2.21598e11	−	1.28867e11i	−0.864454	−	0.502711i
$344$	6.96098e10			0.268014
$345$		0			0
$346$	1.80662e11	−	3.12915e11i	0.677678	−	1.17377i
$347$	2.01514e11	−	3.49032e11i	0.746143	−	1.29236i	−0.203517	−	0.979072i	$-0.565237\pi$
$347$	2.01514e11	−	3.49032e11i	0.746143	−	1.29236i	0.949659	−	0.313285i	$-0.101430\pi$
$348$		0			0
$349$	6.38726e10			0.230462			0.115231	−	0.993339i	$-0.463239\pi$
$349$	6.38726e10			0.230462			0.115231	+	0.993339i	$0.463239\pi$
$350$	−1.24881e11	−	2.21544e10i	−0.444826	−	0.0789140i
$351$		0			0
$352$	2.16729e10	+	3.75385e10i	0.0752444	+	0.130327i
$353$	8.06303e10	−	1.39656e11i	0.276384	−	0.478710i	−0.694100	−	0.719879i	$-0.744197\pi$
$353$	8.06303e10	−	1.39656e11i	0.276384	−	0.478710i	0.970483	+	0.241168i	$0.0775306\pi$
$354$		0			0
$355$	7.45129e9	+	1.29060e10i	0.0249002	+	0.0431285i
$356$	2.24559e10			0.0740978
$357$		0			0
$358$	−1.77649e11			−0.571596
$359$	1.40109e11	+	2.42677e11i	0.445187	+	0.771086i	0.998065	−	0.0621758i	$-0.0198039\pi$
$359$	1.40109e11	+	2.42677e11i	0.445187	+	0.771086i	−0.552878	+	0.833262i	$0.686471\pi$
$360$		0			0
$361$	−1.53015e11	+	2.65030e11i	−0.474190	+	0.821321i
$362$	6.76270e10	+	1.17133e11i	0.206981	+	0.358502i
$363$		0			0
$364$	−9.62512e10	+	1.14465e11i	−0.287376	+	0.341755i
$365$	−3.67107e10			−0.108262
$366$		0			0
$367$	−2.73003e11	+	4.72856e11i	−0.785544	+	1.36060i	0.143129	+	0.989704i	$0.454283\pi$
$367$	−2.73003e11	+	4.72856e11i	−0.785544	+	1.36060i	−0.928674	+	0.370898i	$0.879050\pi$
$368$	−3.05740e10	+	5.29557e10i	−0.0869035	+	0.150521i
$369$		0			0
$370$	−2.52663e11			−0.700865
$371$	−3.00695e11	+	3.57595e11i	−0.824031	+	0.979961i
$372$		0			0
$373$	3.71787e10	+	6.43954e10i	0.0994500	+	0.172252i	0.911457	−	0.411395i	$-0.134958\pi$
$373$	3.71787e10	+	6.43954e10i	0.0994500	+	0.172252i	−0.812007	+	0.583647i	$0.801625\pi$
$374$	−1.02117e11	+	1.76873e11i	−0.269884	+	0.467453i
$375$		0			0
$376$	8.38277e10	+	1.45194e11i	0.216293	+	0.374630i
$377$	5.45300e11			1.39027
$378$		0			0
$379$	3.89616e11			0.969974			0.484987	−	0.874521i	$-0.338824\pi$
$379$	3.89616e11			0.969974			0.484987	+	0.874521i	$0.338824\pi$
$380$	−8.52346e10	−	1.47631e11i	−0.209696	−	0.363204i
$381$		0			0
$382$	1.25267e11	−	2.16968e11i	0.300989	−	0.521328i
$383$	−1.26648e11	−	2.19361e11i	−0.300749	−	0.520913i	0.675557	−	0.737308i	$-0.263903\pi$
$383$	−1.26648e11	−	2.19361e11i	−0.300749	−	0.520913i	−0.976306	+	0.216395i	$0.930570\pi$
$384$		0			0
$385$	2.17139e11	+	3.85213e10i	0.503690	+	0.0893568i
$386$	5.69824e10			0.130647
$387$		0			0
$388$	−1.47920e11	+	2.56205e11i	−0.331348	+	0.573912i
$389$	−4.03992e10	+	6.99735e10i	−0.0894540	+	0.154939i	−0.907280	−	0.420526i	$-0.861846\pi$
$389$	−4.03992e10	+	6.99735e10i	−0.0894540	+	0.154939i	0.817826	+	0.575465i	$0.195179\pi$
$390$		0			0
$391$	−2.88115e11			−0.623405
$392$	−1.55202e11	−	5.68563e10i	−0.331978	−	0.121616i
$393$		0			0
$394$	−2.85288e11	−	4.94134e11i	−0.596418	−	1.03303i
$395$	−2.54889e10	+	4.41480e10i	−0.0526822	+	0.0912482i
$396$		0			0
$397$	4.72537e10	+	8.18458e10i	0.0954725	+	0.165363i	0.909806	−	0.415034i	$-0.136230\pi$
$397$	4.72537e10	+	8.18458e10i	0.0954725	+	0.165363i	−0.814333	+	0.580398i	$0.802897\pi$
$398$	−5.80031e11			−1.15872
$399$		0			0
$400$	−8.17793e10			−0.159725
$401$	1.24237e11	+	2.15186e11i	0.239940	+	0.415589i	0.960697	−	0.277600i	$-0.0895388\pi$
$401$	1.24237e11	+	2.15186e11i	0.239940	+	0.415589i	−0.720757	+	0.693188i	$0.756206\pi$
$402$		0			0
$403$	−3.04901e11	+	5.28105e11i	−0.575820	+	0.997349i
$404$	1.85648e11	+	3.21551e11i	0.346715	+	0.600529i
$405$		0			0
$406$	2.05533e11	+	5.66539e11i	0.375418	+	1.03481i
$407$	−7.77303e11			−1.40416
$408$		0			0
$409$	1.68826e11	−	2.92414e11i	0.298321	−	0.516707i	−0.677431	−	0.735586i	$-0.736907\pi$
$409$	1.68826e11	−	2.92414e11i	0.298321	−	0.516707i	0.975752	+	0.218880i	$0.0702402\pi$
$410$	−2.05759e10	+	3.56385e10i	−0.0359610	+	0.0622863i
$411$		0			0
$412$	3.00559e10			0.0513915
$413$	−9.06090e10	+	1.07755e11i	−0.153248	+	0.182247i
$414$		0			0
$415$	1.21223e11	+	2.09964e11i	0.200617	+	0.347479i
$416$	−4.82156e10	+	8.35119e10i	−0.0789346	+	0.136719i
$417$		0			0
$418$	−2.62219e11	−	4.54177e11i	−0.420118	−	0.727665i
$419$	−9.60695e11			−1.52273			−0.761364	−	0.648324i	$-0.775470\pi$
$419$	−9.60695e11			−1.52273			−0.761364	+	0.648324i	$0.775470\pi$
$420$		0			0
$421$	8.67076e11			1.34520			0.672601	−	0.740005i	$-0.265177\pi$
$421$	8.67076e11			1.34520			0.672601	+	0.740005i	$0.265177\pi$
$422$	−3.30782e11	−	5.72931e11i	−0.507733	−	0.879419i
$423$		0			0
$424$	−1.50629e11	+	2.60896e11i	−0.226340	+	0.392032i
$425$	−1.92662e11	−	3.33701e11i	−0.286449	−	0.496144i
$426$		0			0
$427$	1.54156e11	+	4.24919e11i	0.224406	+	0.618559i
$428$	−1.90407e10			−0.0274274
$429$		0			0
$430$	1.14177e11	−	1.97760e11i	0.161054	−	0.278953i
$431$	5.02711e11	−	8.70722e11i	0.701732	−	1.21543i	−0.266127	−	0.963938i	$-0.585744\pi$
$431$	5.02711e11	−	8.70722e11i	0.701732	−	1.21543i	0.967858	−	0.251497i	$-0.0809227\pi$
$432$		0			0
$433$	−1.39530e12			−1.90753			−0.953767	−	0.300547i	$-0.902831\pi$
$433$	−1.39530e12			−1.90753			−0.953767	+	0.300547i	$0.902831\pi$
$434$	−6.63597e11	−	1.17725e11i	−0.897843	−	0.159281i
$435$		0			0
$436$	3.21202e11	+	5.56338e11i	0.425686	+	0.737309i
$437$	3.69914e11	−	6.40709e11i	0.485215	−	0.840417i
$438$		0			0
$439$	−4.67401e11	−	8.09563e11i	−0.600620	−	1.04030i	−0.992727	−	0.120384i	$-0.961587\pi$
$439$	−4.67401e11	−	8.09563e11i	−0.600620	−	1.04030i	0.392108	−	0.919919i	$-0.371746\pi$
$440$	1.42195e11			0.180862
$441$		0			0
$442$	−4.54361e11			−0.566240
$443$	5.66403e11	+	9.81038e11i	0.698729	+	1.21023i	0.968907	+	0.247424i	$0.0795839\pi$
$443$	5.66403e11	+	9.81038e11i	0.698729	+	1.21023i	−0.270179	+	0.962810i	$0.587083\pi$
$444$		0			0
$445$	3.68331e10	−	6.37969e10i	0.0445265	−	0.0771222i
$446$	−4.00355e11	−	6.93435e11i	−0.479114	−	0.829849i
$447$		0			0
$448$	−1.04938e11	−	1.86164e10i	−0.123078	−	0.0218346i
$449$	−5.33285e11			−0.619228			−0.309614	−	0.950862i	$-0.600200\pi$
$449$	−5.33285e11			−0.619228			−0.309614	+	0.950862i	$0.600200\pi$
$450$		0			0
$451$	−6.33005e10	+	1.09640e11i	−0.0720465	+	0.124788i
$452$	3.08498e11	−	5.34335e11i	0.347640	−	0.602130i
$453$		0			0
$454$	−4.41064e8			−0.000487248
$455$	1.67317e11	+	4.61198e11i	0.183016	+	0.504471i
$456$		0			0
$457$	−5.78445e11	−	1.00190e12i	−0.620353	−	1.07448i	−0.989420	−	0.145080i	$-0.953656\pi$
$457$	−5.78445e11	−	1.00190e12i	−0.620353	−	1.07448i	0.369067	−	0.929403i	$-0.379677\pi$
$458$	−3.01547e11	+	5.22295e11i	−0.320229	+	0.554653i
$459$		0			0
$460$	1.00298e11	+	1.73721e11i	0.104443	+	0.180901i
$461$	1.13012e12			1.16539			0.582693	−	0.812693i	$-0.301999\pi$
$461$	1.13012e12			1.16539			0.582693	+	0.812693i	$0.301999\pi$
$462$		0			0
$463$	8.44262e11			0.853813			0.426906	−	0.904296i	$-0.359603\pi$
$463$	8.44262e11			0.853813			0.426906	+	0.904296i	$0.359603\pi$
$464$	1.94298e11	+	3.36533e11i	0.194597	+	0.337052i
$465$		0			0
$466$	−1.41842e11	+	2.45678e11i	−0.139338	+	0.241340i
$467$	6.47542e11	+	1.12158e12i	0.630002	+	1.09120i	0.987551	+	0.157301i	$0.0502794\pi$
$467$	6.47542e11	+	1.12158e12i	0.630002	+	1.09120i	−0.357548	+	0.933895i	$0.616387\pi$
$468$		0			0
$469$	−8.97209e11	+	1.06699e12i	−0.856280	+	1.01831i
$470$	5.49991e11			0.519895
$471$		0			0
$472$	−4.53892e10	+	7.86164e10i	−0.0420933	+	0.0729078i
$473$	3.51258e11	−	6.08398e11i	0.322665	−	0.558872i
$474$		0			0
$475$	9.89445e11			0.891806
$476$	−1.71257e11	−	4.72058e11i	−0.152903	−	0.421467i
$477$		0			0
$478$	5.71953e11	+	9.90652e11i	0.501112	+	0.867952i
$479$	−3.11431e11	+	5.39414e11i	−0.270304	+	0.468180i	−0.968940	−	0.247298i	$-0.920457\pi$
$479$	−3.11431e11	+	5.39414e11i	−0.270304	+	0.468180i	0.698636	+	0.715477i	$0.253791\pi$
$480$		0			0
$481$	−8.64633e11	−	1.49759e12i	−0.736510	−	1.27567i
$482$	−1.85028e11			−0.156144
$483$		0			0
$484$	−1.66180e11			−0.137650
$485$	4.85250e11	+	8.40478e11i	0.398225	+	0.689745i
$486$		0			0
$487$	−5.62901e10	+	9.74974e10i	−0.0453473	+	0.0785439i	−0.887808	−	0.460214i	$-0.847773\pi$
$487$	−5.62901e10	+	9.74974e10i	−0.0453473	+	0.0785439i	0.842461	+	0.538758i	$0.181106\pi$
$488$	1.45729e11	+	2.52409e11i	0.116320	+	0.201473i
$489$		0			0
$490$	−4.16097e11	+	3.47668e11i	−0.326071	+	0.272447i
$491$	−2.51566e11			−0.195337			−0.0976686	−	0.995219i	$-0.531139\pi$
$491$	−2.51566e11			−0.195337			−0.0976686	+	0.995219i	$0.531139\pi$
$492$		0			0
$493$	−9.15485e11	+	1.58567e12i	−0.697975	+	1.20893i
$494$	5.83359e11	−	1.01041e12i	0.440722	−	0.763352i
$495$		0			0
$496$	−4.34562e11			−0.322392
$497$	−1.10993e11	−	1.96906e10i	−0.0816003	−	0.0144762i
$498$		0			0
$499$	−1.56510e11	−	2.71084e11i	−0.113003	−	0.195727i	0.803977	−	0.594661i	$-0.202714\pi$
$499$	−1.56510e11	−	2.71084e11i	−0.113003	−	0.195727i	−0.916980	+	0.398934i	$0.869380\pi$
$500$	−3.44089e11	+	5.95980e11i	−0.246210	+	0.426448i
$501$		0			0
$502$	−5.27408e11	−	9.13498e11i	−0.370664	−	0.642009i
$503$	−2.03277e11			−0.141590			−0.0707951	−	0.997491i	$-0.522554\pi$
$503$	−2.03277e11			−0.141590			−0.0707951	+	0.997491i	$0.522554\pi$
$504$		0			0
$505$	1.21803e12			0.833386
$506$	3.08559e11	+	5.34441e11i	0.209248	+	0.362428i
$507$		0			0
$508$	4.72490e11	−	8.18376e11i	0.314779	−	0.545213i
$509$	8.31005e11	+	1.43934e12i	0.548749	+	0.950461i	0.998361	+	0.0572371i	$0.0182291\pi$
$509$	8.31005e11	+	1.43934e12i	0.548749	+	0.950461i	−0.449612	+	0.893224i	$0.648438\pi$
$510$		0			0
$511$	1.78716e11	−	2.12534e11i	0.115949	−	0.137890i
$512$	−6.87195e10			−0.0441942
$513$		0			0
$514$	7.54406e11	−	1.30667e12i	0.476729	−	0.825718i
$515$	4.92989e10	−	8.53882e10i	0.0308820	−	0.0534891i
$516$		0			0
$517$	1.69201e12			1.04159
$518$	1.23002e12	−	1.46278e12i	0.750635	−	0.892677i
$519$		0			0
$520$	1.58171e11	+	2.73959e11i	0.0948660	+	0.164313i
$521$	−4.47801e11	+	7.75614e11i	−0.266266	+	0.461186i	−0.967894	−	0.251357i	$-0.919123\pi$
$521$	−4.47801e11	+	7.75614e11i	−0.266266	+	0.461186i	0.701629	+	0.712543i	$0.252457\pi$
$522$		0			0
$523$	1.46603e11	+	2.53924e11i	0.0856813	+	0.148404i	0.905681	−	0.423959i	$-0.139360\pi$
$523$	1.46603e11	+	2.53924e11i	0.0856813	+	0.148404i	−0.820000	+	0.572363i	$0.806027\pi$
$524$	−4.55704e11			−0.264054
$525$		0			0
$526$	1.04480e11			0.0595111
$527$	−1.02378e12	−	1.77323e12i	−0.578172	−	1.00142i
$528$		0			0
$529$	4.65290e11	−	8.05906e11i	0.258329	−	0.447439i
$530$	4.94135e11	+	8.55867e11i	0.272022	+	0.471156i
$531$		0			0
$532$	1.26964e12	+	2.25239e11i	0.687192	+	0.121911i
$533$	−2.81649e11			−0.151160
$534$		0			0
$535$	−3.12313e10	+	5.40942e10i	−0.0164815	+	0.0285469i
$536$	−4.49443e11	+	7.78458e11i	−0.235198	+	0.407374i
$537$		0			0
$538$	1.94776e12			1.00234
$539$	−1.28010e12	+	1.06958e12i	−0.653270	+	0.545837i
$540$		0			0
$541$	−1.81388e12	−	3.14174e12i	−0.910378	−	1.57682i	−0.813531	−	0.581521i	$-0.802458\pi$
$541$	−1.81388e12	−	3.14174e12i	−0.910378	−	1.57682i	−0.0968467	−	0.995299i	$-0.530876\pi$
$542$	−8.03473e11	+	1.39166e12i	−0.399921	+	0.692684i
$543$		0			0
$544$	−1.61895e11	−	2.80410e11i	−0.0792571	−	0.137277i
$545$	2.10740e12			1.02320
$546$		0			0
$547$	2.70319e12			1.29102			0.645511	−	0.763751i	$-0.276645\pi$
$547$	2.70319e12			1.29102			0.645511	+	0.763751i	$0.276645\pi$
$548$	−7.79373e10	−	1.34991e11i	−0.0369176	−	0.0639431i
$549$		0			0
$550$	−4.12667e11	+	7.14760e11i	−0.192295	+	0.333065i
$551$	−2.35080e12	−	4.07170e12i	−1.08651	−	1.88189i
$552$		0			0
$553$	−1.31506e11	−	3.62488e11i	−0.0597976	−	0.164828i
$554$	2.83182e12			1.27724
$555$		0			0
$556$	1.11118e11	−	1.92461e11i	0.0493113	−	0.0854097i
$557$	1.91724e12	−	3.32076e12i	0.843974	−	1.46181i	−0.0425353	−	0.999095i	$-0.513543\pi$
$557$	1.91724e12	−	3.32076e12i	0.843974	−	1.46181i	0.886509	−	0.462711i	$-0.153123\pi$
$558$		0			0
$559$	1.56289e12			0.676979
$560$	−2.25013e11	+	2.67591e11i	−0.0966854	+	0.114981i
$561$		0			0
$562$	1.75555e11	+	3.04070e11i	0.0742335	+	0.128576i
$563$	2.15936e10	−	3.74012e10i	0.00905810	−	0.0156891i	−0.861461	−	0.507824i	$-0.830450\pi$
$563$	2.15936e10	−	3.74012e10i	0.00905810	−	0.0156891i	0.870519	+	0.492135i	$0.163783\pi$
$564$		0			0
$565$	−1.01202e12	−	1.75288e12i	−0.417804	−	0.723659i
$566$	1.53724e12			0.629602
$567$		0			0
$568$	−7.26847e10			−0.0293005
$569$	−1.20644e12	−	2.08961e12i	−0.482503	−	0.835720i	0.517295	−	0.855807i	$-0.326939\pi$
$569$	−1.20644e12	−	2.08961e12i	−0.482503	−	0.835720i	−0.999798	+	0.0200870i	$0.993606\pi$
$570$		0			0
$571$	−8.14907e11	+	1.41146e12i	−0.320808	+	0.555656i	−0.980655	−	0.195744i	$-0.937288\pi$
$571$	−8.14907e11	+	1.41146e12i	−0.320808	+	0.555656i	0.659847	+	0.751400i	$0.270621\pi$
$572$	4.86602e11	+	8.42819e11i	0.190060	+	0.329194i
$573$		0			0
$574$	−1.06159e11	−	2.92619e11i	−0.0408180	−	0.112512i
$575$	−1.16430e12			−0.444182
$576$		0			0
$577$	−2.28526e12	+	3.95818e12i	−0.858309	+	1.48663i	0.0152322	+	0.999884i	$0.495151\pi$
$577$	−2.28526e12	+	3.95818e12i	−0.858309	+	1.48663i	−0.873541	+	0.486751i	$0.838182\pi$
$578$	−1.85892e11	+	3.21975e11i	−0.0692765	+	0.119990i
$579$		0			0
$580$	1.27478e12			0.467746
$581$	−1.80571e12	−	3.20341e11i	−0.657439	−	0.116633i
$582$		0			0
$583$	1.52018e12	+	2.63302e12i	0.544986	+	0.943943i
$584$	8.95249e10	−	1.55062e11i	0.0318483	−	0.0551629i
$585$		0			0
$586$	−1.44902e12	−	2.50978e12i	−0.507616	−	0.879217i
$587$	−3.12353e12			−1.08586			−0.542931	−	0.839778i	$-0.682685\pi$
$587$	−3.12353e12			−1.08586			−0.542931	+	0.839778i	$0.682685\pi$
$588$		0			0
$589$	5.25775e12			1.80003
$590$	1.48899e11	+	2.57900e11i	0.0505891	+	0.0876228i
$591$		0			0
$592$	6.16161e11	−	1.06722e12i	0.206180	−	0.357114i
$593$	−2.29885e12	−	3.98173e12i	−0.763423	−	1.32229i	−0.941077	−	0.338194i	$-0.890184\pi$
$593$	−2.29885e12	−	3.98173e12i	−0.763423	−	1.32229i	0.177654	−	0.984093i	$-0.443149\pi$
$594$		0			0
$595$	−1.62201e12	−	2.87752e11i	−0.530552	−	0.0941221i
$596$	1.48019e12			0.480516
$597$		0			0
$598$	−6.86452e11	+	1.18897e12i	−0.219510	+	0.380203i
$599$	−1.94675e12	+	3.37187e12i	−0.617859	+	1.07016i	0.372017	+	0.928226i	$0.378666\pi$
$599$	−1.94675e12	+	3.37187e12i	−0.617859	+	1.07016i	−0.989876	+	0.141937i	$0.954667\pi$
$600$		0			0
$601$	1.02722e12			0.321166			0.160583	−	0.987022i	$-0.448663\pi$
$601$	1.02722e12			0.321166			0.160583	+	0.987022i	$0.448663\pi$
$602$	5.89081e11	+	1.62376e12i	0.182806	+	0.503893i
$603$		0			0
$604$	4.96801e11	+	8.60484e11i	0.151885	+	0.263073i
$605$	−2.72576e11	+	4.72116e11i	−0.0827158	+	0.143268i
$606$		0			0
$607$	−1.19766e12	−	2.07441e12i	−0.358084	−	0.620219i	0.629557	−	0.776954i	$-0.283236\pi$
$607$	−1.19766e12	−	2.07441e12i	−0.358084	−	0.620219i	−0.987641	+	0.156735i	$0.949903\pi$
$608$	8.31434e11			0.246753
$609$		0			0
$610$	9.56121e11			0.279594
$611$	1.88211e12	+	3.25991e12i	0.546336	+	0.946281i
$612$		0			0
$613$	3.30884e12	−	5.73108e12i	0.946464	−	1.63932i	0.193670	−	0.981067i	$-0.437961\pi$
$613$	3.30884e12	−	5.73108e12i	0.946464	−	1.63932i	0.752794	−	0.658256i	$-0.228706\pi$
$614$	−1.09836e12	−	1.90242e12i	−0.311880	−	0.540192i
$615$		0			0
$616$	−6.92237e11	+	8.23228e11i	−0.193705	+	0.230360i
$617$	6.76229e12			1.87850			0.939249	−	0.343236i	$-0.111523\pi$
$617$	6.76229e12			1.87850			0.939249	+	0.343236i	$0.111523\pi$
$618$		0			0
$619$	4.19193e11	−	7.26064e11i	0.114764	−	0.198777i	−0.802921	−	0.596085i	$-0.796722\pi$
$619$	4.19193e11	−	7.26064e11i	0.114764	−	0.198777i	0.917685	+	0.397308i	$0.130055\pi$
$620$	−7.12787e11	+	1.23458e12i	−0.193730	+	0.335551i
$621$		0			0
$622$	−1.00820e12			−0.270079
$623$	1.90036e11	+	5.23820e11i	0.0505404	+	0.139311i
$624$		0			0
$625$	−8.98272e10	−	1.55585e11i	−0.0235477	−	0.0407858i
$626$	6.63300e11	−	1.14887e12i	0.172634	−	0.299010i
$627$		0			0
$628$	−1.27851e12	−	2.21445e12i	−0.328009	−	0.568128i
$629$	5.80641e12			1.47904
$630$		0			0
$631$	−3.32721e12			−0.835504			−0.417752	−	0.908561i	$-0.637182\pi$
$631$	−3.32721e12			−0.835504			−0.417752	+	0.908561i	$0.637182\pi$
$632$	−1.24317e11	−	2.15324e11i	−0.0309960	−	0.0536866i
$633$		0			0
$634$	2.19875e12	−	3.80835e12i	0.540474	−	0.936128i
$635$	−1.55000e12	−	2.68467e12i	−0.378311	−	0.655254i
$636$		0			0
$637$	−3.48461e12	−	1.27655e12i	−0.838546	−	0.307191i
$638$	3.92179e12			0.937111
$639$		0			0
$640$	−1.12717e11	+	1.95231e11i	−0.0265570	+	0.0459980i
$641$	−7.94940e11	+	1.37688e12i	−0.185983	+	0.322132i	−0.943907	−	0.330210i	$-0.892880\pi$
$641$	−7.94940e11	+	1.37688e12i	−0.185983	+	0.322132i	0.757924	+	0.652343i	$0.226214\pi$
$642$		0			0
$643$	−6.05393e12			−1.39665			−0.698326	−	0.715780i	$-0.746071\pi$
$643$	−6.05393e12			−1.39665			−0.698326	+	0.715780i	$0.746071\pi$
$644$	−1.49401e12	−	2.65045e11i	−0.342270	−	0.0607201i
$645$		0			0
$646$	1.95876e12	+	3.39267e12i	0.442522	+	0.766471i
$647$	−1.87293e11	+	3.24400e11i	−0.0420195	+	0.0727800i	−0.886270	−	0.463168i	$-0.846713\pi$
$647$	−1.87293e11	+	3.24400e11i	−0.0420195	+	0.0727800i	0.844251	+	0.535948i	$0.180046\pi$
$648$		0			0
$649$	4.58077e11	+	7.93413e11i	0.101353	+	0.175549i
$650$	−1.83612e12			−0.403451
$651$		0			0
$652$	−4.51459e11			−0.0978372
$653$	−6.27315e11	−	1.08654e12i	−0.135013	−	0.233850i	0.790589	−	0.612347i	$-0.209774\pi$
$653$	−6.27315e11	−	1.08654e12i	−0.135013	−	0.233850i	−0.925603	+	0.378497i	$0.876441\pi$
$654$		0			0
$655$	−7.47466e11	+	1.29465e12i	−0.158674	+	0.274831i
$656$	−1.00355e11	−	1.73821e11i	−0.0211579	−	0.0366466i
$657$		0			0
$658$	−2.67748e12	+	3.18414e12i	−0.556813	+	0.662178i
$659$	−8.56899e12			−1.76989			−0.884943	−	0.465700i	$-0.845803\pi$
$659$	−8.56899e12			−1.76989			−0.884943	+	0.465700i	$0.845803\pi$
$660$		0			0
$661$	−1.62869e12	+	2.82098e12i	−0.331843	+	0.574768i	−0.982873	−	0.184283i	$-0.941004\pi$
$661$	−1.62869e12	+	2.82098e12i	−0.331843	+	0.574768i	0.651031	+	0.759051i	$0.274337\pi$
$662$	−1.48330e12	+	2.56915e12i	−0.300170	+	0.519910i
$663$		0			0
$664$	−1.18249e12			−0.236069
$665$	2.72242e12	−	3.23758e12i	0.539831	−	0.641982i
$666$		0			0
$667$	2.76624e12	+	4.79127e12i	0.541158	+	0.937313i
$668$	2.32601e12	−	4.02877e12i	0.451978	−	0.782849i
$669$		0			0
$670$	1.47439e12	+	2.55372e12i	0.282668	+	0.489595i
$671$	2.94145e12			0.560157
$672$		0			0
$673$	−5.19754e12			−0.976630			−0.488315	−	0.872667i	$-0.662388\pi$
$673$	−5.19754e12			−0.976630			−0.488315	+	0.872667i	$0.662388\pi$
$674$	1.79925e12	+	3.11640e12i	0.335832	+	0.581679i
$675$		0			0
$676$	2.74833e11	−	4.76025e11i	0.0506184	−	0.0876737i
$677$	−3.17108e12	−	5.49246e12i	−0.580173	−	1.00489i	−0.995458	−	0.0951981i	$-0.969652\pi$
$677$	−3.17108e12	−	5.49246e12i	−0.580173	−	1.00489i	0.415285	−	0.909691i	$-0.363682\pi$
$678$		0			0
$679$	−7.22820e12	−	1.28231e12i	−1.30502	−	0.231516i
$680$	−1.06219e12			−0.190507
$681$		0			0
$682$	−2.19285e12	+	3.79812e12i	−0.388131	+	0.672263i
$683$	−4.28146e12	+	7.41571e12i	−0.752834	+	1.30395i	0.193610	+	0.981079i	$0.437980\pi$
$683$	−4.28146e12	+	7.41571e12i	−0.752834	+	1.30395i	−0.946444	+	0.322868i	$0.895353\pi$
$684$		0			0
$685$	−5.11345e11			−0.0887373
$686$	1.28533e10	−	4.10149e12i	0.00221593	−	0.707103i
$687$		0			0
$688$	5.56878e11	+	9.64542e11i	0.0947573	+	0.164124i
$689$	−3.38193e12	+	5.85768e12i	−0.571714	+	0.990237i
$690$		0			0
$691$	−5.02013e12	−	8.69511e12i	−0.837651	−	1.45085i	−0.891853	−	0.452325i	$-0.850595\pi$
$691$	−5.02013e12	−	8.69511e12i	−0.837651	−	1.45085i	0.0542018	−	0.998530i	$-0.482739\pi$
$692$	5.78117e12			0.958381
$693$		0			0
$694$	6.44844e12			1.05520
$695$	−3.64520e11	−	6.31367e11i	−0.0592638	−	0.102648i
$696$		0			0
$697$	4.72851e11	−	8.19002e11i	0.0758886	−	0.131443i
$698$	5.10981e11	+	8.85045e11i	0.0814808	+	0.141129i
$699$		0			0
$700$	−6.92067e11	−	1.90764e12i	−0.108945	−	0.300299i
$701$	6.17651e12			0.966077			0.483038	−	0.875599i	$-0.339533\pi$
$701$	6.17651e12			0.966077			0.483038	+	0.875599i	$0.339533\pi$
$702$		0			0
$703$	−7.45490e12	+	1.29123e13i	−1.15118	+	1.99390i
$704$	−3.46766e11	+	6.00616e11i	−0.0532058	+	0.0921552i
$705$		0			0
$706$	2.58017e12			0.390865
$707$	−5.92964e12	+	7.05169e12i	−0.892567	+	1.06147i
$708$		0			0
$709$	4.11116e12	+	7.12074e12i	0.611022	+	1.05832i	0.991069	+	0.133353i	$0.0425745\pi$
$709$	4.11116e12	+	7.12074e12i	0.611022	+	1.05832i	−0.380047	+	0.924967i	$0.624092\pi$
$710$	−1.19221e11	+	2.06496e11i	−0.0176071	+	0.0304964i
$711$		0			0
$712$	1.79647e11	+	3.11158e11i	0.0261975	+	0.0453755i
$713$	−6.18692e12			−0.896543
$714$		0			0
$715$	3.19258e12			0.456841
$716$	−1.42119e12	−	2.46158e12i	−0.202090	−	0.350030i
$717$		0			0
$718$	−2.24175e12	+	3.88283e12i	−0.314795	+	0.545240i
$719$	6.83153e11	+	1.18326e12i	0.0953318	+	0.165119i	0.909747	−	0.415163i	$-0.136275\pi$
$719$	6.83153e11	+	1.18326e12i	0.0953318	+	0.165119i	−0.814415	+	0.580283i	$0.802942\pi$
$720$		0			0
$721$	2.54351e11	+	7.01102e11i	0.0350530	+	0.0966212i
$722$	−4.89649e12			−0.670606
$723$		0			0
$724$	−1.08203e12	+	1.87413e12i	−0.146358	+	0.253499i
$725$	−3.69957e12	+	6.40784e12i	−0.497313	+	0.861372i
$726$		0			0
$727$	1.07392e13			1.42583			0.712915	−	0.701251i	$-0.247375\pi$
$727$	1.07392e13			1.42583			0.712915	+	0.701251i	$0.247375\pi$
$728$	−2.35608e12	−	4.17979e11i	−0.310884	−	0.0551522i
$729$		0			0
$730$	−2.93685e11	−	5.08678e11i	−0.0382762	−	0.0662964i
$731$	−2.62388e12	+	4.54469e12i	−0.339872	+	0.588676i
$732$		0			0
$733$	1.85714e12	+	3.21666e12i	0.237616	+	0.411564i	0.960030	−	0.279898i	$-0.0903006\pi$
$733$	1.85714e12	+	3.21666e12i	0.237616	+	0.411564i	−0.722413	+	0.691461i	$0.756967\pi$
$734$	−8.73610e12			−1.11093
$735$		0			0
$736$	−9.78368e11			−0.122900
$737$	4.53587e12	+	7.85636e12i	0.566314	+	0.980885i
$738$		0			0
$739$	6.48512e12	−	1.12326e13i	0.799867	−	1.38541i	−0.119835	−	0.992794i	$-0.538236\pi$
$739$	6.48512e12	−	1.12326e13i	0.799867	−	1.38541i	0.919702	−	0.392617i	$-0.128430\pi$
$740$	−2.02131e12	−	3.50101e12i	−0.247793	−	0.429190i
$741$		0			0
$742$	−7.36054e12	−	1.30579e12i	−0.891440	−	0.158145i
$743$	1.26040e13			1.51726			0.758630	−	0.651522i	$-0.225869\pi$
$743$	1.26040e13			1.51726			0.758630	+	0.651522i	$0.225869\pi$
$744$		0			0
$745$	2.42786e12	−	4.20518e12i	0.288749	−	0.500129i
$746$	−5.94860e11	+	1.03033e12i	−0.0703218	+	0.121801i
$747$		0			0
$748$	−3.26776e12			−0.381674
$749$	−1.61134e11	−	4.44154e11i	−0.0187076	−	0.0515662i
$750$		0			0
$751$	1.56887e12	+	2.71736e12i	0.179973	+	0.311722i	0.941871	−	0.335975i	$-0.109066\pi$
$751$	1.56887e12	+	2.71736e12i	0.179973	+	0.311722i	−0.761898	+	0.647697i	$0.775732\pi$
$752$	−1.34124e12	+	2.32310e12i	−0.152942	+	0.264904i
$753$		0			0
$754$	4.36240e12	+	7.55589e12i	0.491535	+	0.851363i
$755$	3.25950e12			0.365081
$756$		0			0
$757$	4.60752e12			0.509959			0.254980	−	0.966946i	$-0.417931\pi$
$757$	4.60752e12			0.509959			0.254980	+	0.966946i	$0.417931\pi$
$758$	3.11693e12	+	5.39868e12i	0.342938	+	0.593986i
$759$		0			0
$760$	1.36375e12	−	2.36209e12i	0.148277	−	0.256824i
$761$	−7.95606e12	−	1.37803e13i	−0.859938	−	1.48946i	−0.871988	−	0.489528i	$-0.837169\pi$
$761$	−7.95606e12	−	1.37803e13i	−0.859938	−	1.48946i	0.0120500	−	0.999927i	$-0.496164\pi$
$762$		0			0
$763$	−1.02593e13	+	1.22006e13i	−1.09586	+	1.30323i
$764$	4.00853e12			0.425662
$765$		0			0
$766$	2.02637e12	−	3.50978e12i	0.212662	−	0.368341i
$767$	−1.01908e12	+	1.76511e12i	−0.106324	+	0.184158i
$768$		0			0
$769$	1.13622e13			1.17164			0.585819	−	0.810442i	$-0.300773\pi$
$769$	1.13622e13			1.17164			0.585819	+	0.810442i	$0.300773\pi$
$770$	1.20334e12	+	3.31693e12i	0.123362	+	0.340039i
$771$		0			0
$772$	4.55859e11	+	7.89571e11i	0.0461905	+	0.0800043i
$773$	3.31271e12	−	5.73779e12i	0.333715	−	0.578012i	−0.649522	−	0.760343i	$-0.725031\pi$
$773$	3.31271e12	−	5.73779e12i	0.333715	−	0.578012i	0.983237	+	0.182331i	$0.0583642\pi$
$774$		0			0
$775$	−4.13719e12	−	7.16582e12i	−0.411953	−	0.713523i
$776$	−4.73345e12			−0.468597
$777$		0			0
$778$	−1.29278e12			−0.126507
$779$	1.21420e12	+	2.10305e12i	0.118133	+	0.204612i
$780$		0			0
$781$	−3.66775e11	+	6.35272e11i	−0.0352752	+	0.0610985i
$782$	−2.30492e12	−	3.99224e12i	−0.220407	−	0.381756i
$783$		0			0
$784$	−4.53790e11	−	2.60539e12i	−0.0428976	−	0.246292i
$785$	−8.38827e12			−0.788423
$786$		0			0
$787$	4.46022e11	−	7.72532e11i	0.0414448	−	0.0717844i	−0.844559	−	0.535463i	$-0.820137\pi$
$787$	4.46022e11	−	7.72532e11i	0.0414448	−	0.0717844i	0.886004	+	0.463678i	$0.153471\pi$
$788$	4.56461e12	−	7.90614e12i	0.421731	−	0.730460i
$789$		0			0
$790$	−8.15644e11			−0.0745038
$791$	1.50749e13	+	2.67436e12i	1.36918	+	0.242899i
$792$		0			0
$793$	3.27192e12	+	5.66713e12i	0.293814	+	0.508901i
$794$	−7.56059e11	+	1.30953e12i	−0.0675093	+	0.116930i
$795$		0			0
$796$	−4.64025e12	−	8.03714e12i	−0.409668	−	0.709566i
$797$	1.89547e13			1.66401			0.832004	−	0.554770i	$-0.187194\pi$
$797$	1.89547e13			1.66401			0.832004	+	0.554770i	$0.187194\pi$
$798$		0			0
$799$	−1.26392e13			−1.09714
$800$	−6.54235e11	−	1.13317e12i	−0.0564714	−	0.0978113i
$801$		0			0
$802$	−1.98780e12	+	3.44297e12i	−0.169663	+	0.293865i
$803$	−9.03504e11	−	1.56492e12i	−0.0766850	−	0.132822i
$804$		0			0
$805$	−3.20353e12	+	3.80973e12i	−0.268873	+	0.319752i
$806$	−9.75684e12			−0.814332
$807$		0			0
$808$	−2.97036e12	+	5.14482e12i	−0.245165	+	0.424638i
$809$	5.43138e12	−	9.40743e12i	0.445802	−	0.772152i	−0.552306	−	0.833642i	$-0.686252\pi$
$809$	5.43138e12	−	9.40743e12i	0.445802	−	0.772152i	0.998108	+	0.0614900i	$0.0195852\pi$
$810$		0			0
$811$	9.26752e12			0.752263			0.376131	−	0.926566i	$-0.377254\pi$
$811$	9.26752e12			0.752263			0.376131	+	0.926566i	$0.377254\pi$
$812$	−6.20592e12	+	7.38026e12i	−0.500961	+	0.595758i
$813$		0			0
$814$	−6.21842e12	−	1.07706e13i	−0.496444	−	0.859867i
$815$	−7.40503e11	+	1.28259e12i	−0.0587919	+	0.101831i
$816$		0			0
$817$	−6.73765e12	−	1.16700e13i	−0.529065	−	0.916368i
$818$	5.40242e12			0.421889
$819$		0			0
$820$	−6.58429e11			−0.0508565
$821$	−5.50162e12	−	9.52909e12i	−0.422617	−	0.731994i	0.573578	−	0.819151i	$-0.305555\pi$
$821$	−5.50162e12	−	9.52909e12i	−0.422617	−	0.731994i	−0.996195	+	0.0871574i	$0.972222\pi$
$822$		0			0
$823$	−7.42852e12	+	1.28666e13i	−0.564421	+	0.977606i	0.432682	+	0.901547i	$0.357567\pi$
$823$	−7.42852e12	+	1.28666e13i	−0.564421	+	0.977606i	−0.997103	+	0.0760596i	$0.975766\pi$
$824$	2.40447e11	+	4.16466e11i	0.0181697	+	0.0314708i
$825$		0			0
$826$	−2.21797e12	−	3.93477e11i	−0.165785	−	0.0294109i
$827$	1.90248e13			1.41431			0.707155	−	0.707058i	$-0.249978\pi$
$827$	1.90248e13			1.41431			0.707155	+	0.707058i	$0.249978\pi$
$828$		0			0
$829$	6.07299e12	−	1.05187e13i	0.446588	−	0.773513i	−0.551573	−	0.834127i	$-0.685972\pi$
$829$	6.07299e12	−	1.05187e13i	0.446588	−	0.773513i	0.998161	+	0.0606131i	$0.0193056\pi$
$830$	−1.93956e12	+	3.35942e12i	−0.141858	+	0.245705i
$831$		0			0
$832$	−1.54290e12			−0.111630
$833$	9.56224e12	−	7.98969e12i	0.688109	−	0.574946i
$834$		0			0
$835$	−7.63044e12	−	1.32163e13i	−0.543201	−	0.940852i
$836$	4.19551e12	−	7.26683e12i	0.297068	−	0.514537i
$837$		0			0
$838$	−7.68556e12	−	1.33118e13i	−0.538366	−	0.932477i
$839$	−1.47673e13			−1.02890			−0.514448	−	0.857522i	$-0.672003\pi$
$839$	−1.47673e13			−1.02890			−0.514448	+	0.857522i	$0.672003\pi$
$840$		0			0
$841$	2.06518e13			1.42356
$842$	6.93660e12	+	1.20146e13i	0.475601	+	0.823765i
$843$		0			0
$844$	5.29251e12	−	9.16689e12i	0.359021	−	0.621843i
$845$	−9.01586e11	−	1.56159e12i	−0.0608348	−	0.105369i
$846$		0			0
$847$	−1.40632e12	−	3.87643e12i	−0.0938877	−	0.258795i
$848$	−4.82011e12			−0.320093
$849$		0			0
$850$	3.08260e12	−	5.33922e12i	0.202550	−	0.350827i
$851$	8.77236e12	−	1.51942e13i	0.573368	−	0.993103i
$852$		0			0
$853$	5.05930e12			0.327205			0.163602	−	0.986526i	$-0.447689\pi$
$853$	5.05930e12			0.327205			0.163602	+	0.986526i	$0.447689\pi$
$854$	−4.65461e12	+	5.53540e12i	−0.299449	+	0.356113i
$855$		0			0
$856$	−1.52325e11	−	2.63835e11i	−0.00969705	−	0.0167958i
$857$	1.40992e12	−	2.44205e12i	0.0892854	−	0.154647i	−0.817924	−	0.575326i	$-0.804875\pi$
$857$	1.40992e12	−	2.44205e12i	0.0892854	−	0.154647i	0.907209	+	0.420680i	$0.138208\pi$
$858$		0			0
$859$	−3.29627e12	−	5.70931e12i	−0.206564	−	0.357779i	0.744066	−	0.668106i	$-0.232895\pi$
$859$	−3.29627e12	−	5.70931e12i	−0.206564	−	0.357779i	−0.950630	+	0.310327i	$0.899561\pi$
$860$	3.65366e12			0.227764
$861$		0			0
$862$	1.60868e13			0.992398
$863$	1.28478e12	+	2.22530e12i	0.0788460	+	0.136565i	0.902752	−	0.430161i	$-0.141543\pi$
$863$	1.28478e12	+	2.22530e12i	0.0788460	+	0.136565i	−0.823906	+	0.566726i	$0.808210\pi$
$864$		0			0
$865$	9.48252e12	−	1.64242e13i	0.575906	−	0.997498i
$866$	−1.11624e13	−	1.93339e13i	−0.674415	−	1.16812i
$867$		0			0
$868$	−3.67753e12	−	1.01369e13i	−0.219896	−	0.606129i
$869$	−2.50928e12			−0.149266
$870$		0			0
$871$	−1.00910e13	+	1.74780e13i	−0.594088	+	1.02899i
$872$	−5.13923e12	+	8.90141e12i	−0.301005	+	0.521356i
$873$		0			0
$874$	1.18372e13			0.686197
$875$	−1.68141e13	−	2.98289e12i	−0.969699	−	0.172029i
$876$		0			0
$877$	4.58693e12	+	7.94479e12i	0.261833	+	0.453507i	0.966729	−	0.255803i	$-0.0823398\pi$
$877$	4.58693e12	+	7.94479e12i	0.261833	+	0.453507i	−0.704896	+	0.709310i	$0.749006\pi$
$878$	7.47842e12	−	1.29530e13i	0.424702	−	0.735606i
$879$		0			0
$880$	1.13756e12	+	1.97031e12i	0.0639444	+	0.110755i
$881$	2.92110e11			0.0163363			0.00816816	−	0.999967i	$-0.497400\pi$
$881$	2.92110e11			0.0163363			0.00816816	+	0.999967i	$0.497400\pi$
$882$		0			0
$883$	2.80668e13			1.55371			0.776856	−	0.629678i	$-0.216813\pi$
$883$	2.80668e13			1.55371			0.776856	+	0.629678i	$0.216813\pi$
$884$	−3.63489e12	−	6.29581e12i	−0.200196	−	0.346750i
$885$		0			0
$886$	−9.06245e12	+	1.56966e13i	−0.494076	+	0.855765i
$887$	1.13253e13	+	1.96161e13i	0.614320	+	1.06403i	0.990503	+	0.137488i	$0.0439029\pi$
$887$	1.13253e13	+	1.96161e13i	0.614320	+	1.06403i	−0.376183	+	0.926545i	$0.622764\pi$
$888$		0			0
$889$	2.30885e13	+	4.09599e12i	1.23976	+	0.219938i
$890$	1.17866e12			0.0629700
$891$		0			0
$892$	6.40568e12	−	1.10950e13i	0.338784	−	0.586792i
$893$	1.62276e13	−	2.81071e13i	0.853933	−	1.47906i
$894$		0			0
$895$	−9.32441e12			−0.485755
$896$	−5.81546e11	−	1.60299e12i	−0.0301438	−	0.0830894i
$897$		0			0
$898$	−4.26628e12	−	7.38941e12i	−0.218930	−	0.379198i
$899$	−1.96589e13	+	3.40502e13i	−1.00379	+	1.73861i
$900$		0			0
$901$	−1.13556e13	−	1.96685e13i	−0.574049	−	0.994283i
$902$	−2.02562e12			−0.101889
$903$		0			0
$904$	9.87195e12			0.491637
$905$	3.54959e12	+	6.14807e12i	0.175897	+	0.304663i
$906$		0			0
$907$	1.67377e13	−	2.89906e13i	0.821229	−	1.42241i	−0.0835391	−	0.996505i	$-0.526622\pi$
$907$	1.67377e13	−	2.89906e13i	0.821229	−	1.42241i	0.904768	−	0.425905i	$-0.140044\pi$
$908$	−3.52851e9	−	6.11156e9i	−0.000172268	−	0.000298377i
$909$		0			0
$910$	−5.05201e12	+	6.00800e12i	−0.244218	+	0.290431i
$911$	−5.92250e12			−0.284887			−0.142444	−	0.989803i	$-0.545496\pi$
$911$	−5.92250e12			−0.284887			−0.142444	+	0.989803i	$0.545496\pi$
$912$		0			0
$913$	−5.96695e12	+	1.03351e13i	−0.284206	+	0.492260i
$914$	9.25512e12	−	1.60303e13i	0.438656	−	0.759774i
$915$		0			0
$916$	−9.64951e12			−0.452872
$917$	−3.85645e12	−	1.06300e13i	−0.180105	−	0.496447i
$918$		0			0
$919$	1.30980e13	+	2.26863e13i	0.605737	+	1.04917i	0.991935	+	0.126751i	$0.0404550\pi$
$919$	1.30980e13	+	2.26863e13i	0.605737	+	1.04917i	−0.386197	+	0.922416i	$0.626212\pi$
$920$	−1.60476e12	+	2.77953e12i	−0.0738525	+	0.127916i
$921$		0			0
$922$	9.04094e12	+	1.56594e13i	0.412026	+	0.713650i
$923$	−1.63193e12			−0.0740104
$924$		0			0
$925$	2.34643e13			1.05383
$926$	6.75409e12	+	1.16984e13i	0.301868	+	0.522851i
$927$		0			0
$928$	−3.10876e12	+	5.38453e12i	−0.137601	+	0.238332i
$929$	1.04935e13	+	1.81753e13i	0.462222	+	0.800591i	0.999071	−	0.0430866i	$-0.0137191\pi$
$929$	1.04935e13	+	1.81753e13i	0.462222	+	0.800591i	−0.536850	+	0.843678i	$0.680386\pi$
$930$		0			0
$931$	5.49039e12	+	3.15225e13i	0.239513	+	1.37514i
$932$	−4.53895e12			−0.197053
$933$		0			0
$934$	−1.03607e13	+	1.79452e13i	−0.445479	+	0.771592i
$935$	−5.35992e12	+	9.28365e12i	−0.229354	+	0.397252i
$936$		0			0
$937$	−1.48411e13			−0.628982			−0.314491	−	0.949261i	$-0.601834\pi$
$937$	−1.48411e13			−0.628982			−0.314491	+	0.949261i	$0.601834\pi$
$938$	−2.19623e13	−	3.89620e12i	−0.926327	−	0.164334i
$939$		0			0
$940$	4.39993e12	+	7.62090e12i	0.183810	+	0.318369i
$941$	−1.04462e13	+	1.80933e13i	−0.434315	+	0.752255i	−0.997239	−	0.0742532i	$-0.976343\pi$
$941$	−1.04462e13	+	1.80933e13i	−0.434315	+	0.752255i	0.562925	+	0.826508i	$0.309676\pi$
$942$		0			0
$943$	−1.42877e12	−	2.47471e12i	−0.0588384	−	0.101911i
$944$	−1.45245e12			−0.0595290
$945$		0			0
$946$	1.12403e13			0.456317
$947$	−1.70007e13	−	2.94461e13i	−0.686897	−	1.18974i	−0.972836	−	0.231493i	$-0.925639\pi$
$947$	−1.70007e13	−	2.94461e13i	−0.686897	−	1.18974i	0.285939	−	0.958248i	$-0.407695\pi$
$948$		0			0
$949$	2.01003e12	−	3.48147e12i	0.0804458	−	0.139336i
$950$	7.91556e12	+	1.37101e13i	0.315301	+	0.546117i
$951$		0			0
$952$	5.17097e12	−	6.14947e12i	0.204036	−	0.242645i
$953$	4.42130e13			1.73633			0.868165	−	0.496276i	$-0.165300\pi$
$953$	4.42130e13			1.73633			0.868165	+	0.496276i	$0.165300\pi$
$954$		0			0
$955$	6.57497e12	−	1.13882e13i	0.255787	−	0.443036i
$956$	−9.15125e12	+	1.58504e13i	−0.354340	+	0.613735i
$957$		0			0
$958$	−9.96579e12			−0.382267
$959$	2.48934e12	−	2.96039e12i	0.0950387	−	0.113023i
$960$		0			0
$961$	−8.76453e12	−	1.51806e13i	−0.331492	−	0.574162i
$962$	1.38341e13	−	2.39614e13i	0.520791	−	0.902037i
$963$		0			0
$964$	−1.48022e12	−	2.56382e12i	−0.0552052	−	0.0956182i
$965$	2.99088e12			0.111026
$966$		0			0
$967$	−5.00320e13			−1.84005			−0.920023	−	0.391864i	$-0.871830\pi$
$967$	−5.00320e13			−1.84005			−0.920023	+	0.391864i	$0.871830\pi$
$968$	−1.32944e12	−	2.30266e12i	−0.0486665	−	0.0842929i
$969$		0			0
$970$	−7.76401e12	+	1.34477e13i	−0.281587	+	0.487724i
$971$	5.24298e12	+	9.08110e12i	0.189274	+	0.327833i	0.945008	−	0.327046i	$-0.106053\pi$
$971$	5.24298e12	+	9.08110e12i	0.189274	+	0.327833i	−0.755734	+	0.654878i	$0.772720\pi$
$972$		0			0
$973$	5.42982e12	+	9.63274e11i	0.194213	+	0.0344542i
$974$	−1.80128e12			−0.0641308
$975$		0			0
$976$	−2.33166e12	+	4.03855e12i	−0.0822509	+	0.142463i
$977$	1.94596e13	−	3.37050e13i	0.683295	−	1.18350i	−0.290674	−	0.956822i	$-0.593880\pi$
$977$	1.94596e13	−	3.37050e13i	0.683295	−	1.18350i	0.973969	−	0.226680i	$-0.0727871\pi$
$978$		0			0
$979$	3.62608e12			0.126158
$980$	−8.14620e12	−	2.98426e12i	−0.282122	−	0.103352i
$981$		0			0
$982$	−2.01253e12	−	3.48580e12i	−0.0690621	−	0.119619i
$983$	−1.91410e13	+	3.31532e13i	−0.653844	+	1.13249i	0.328338	+	0.944560i	$0.393512\pi$
$983$	−1.91410e13	+	3.31532e13i	−0.653844	+	1.13249i	−0.982182	+	0.187931i	$0.939822\pi$
$984$		0			0
$985$	−1.49742e13	−	2.59360e13i	−0.506850	−	0.877889i
$986$	−2.92955e13			−0.987086
$987$		0			0
$988$	1.86675e13			0.623274
$989$	7.92835e12	+	1.37323e13i	0.263512	+	0.456415i
$990$		0			0
$991$	−9.41837e12	+	1.63131e13i	−0.310202	+	0.537285i	−0.978406	−	0.206693i	$-0.933730\pi$
$991$	−9.41837e12	+	1.63131e13i	−0.310202	+	0.537285i	0.668204	+	0.743978i	$0.267063\pi$
$992$	−3.47650e12	−	6.02147e12i	−0.113983	−	0.197424i
$993$		0			0
$994$	−6.15102e11	−	1.69549e12i	−0.0199852	−	0.0550879i
$995$	−3.04445e13			−0.984704
$996$		0			0
$997$	9.64240e12	−	1.67011e13i	0.309070	−	0.535325i	−0.669089	−	0.743182i	$-0.733316\pi$
$997$	9.64240e12	−	1.67011e13i	0.309070	−	0.535325i	0.978159	+	0.207857i	$0.0666490\pi$
$998$	2.50417e12	−	4.33734e12i	0.0799054	−	0.138400i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	126.10.g.c.109.2		4
3.2	odd	2		42.10.e.b.25.1	✓	4
7.2	even	3	inner	126.10.g.c.37.2		4
21.2	odd	6		42.10.e.b.37.1	yes	4
21.11	odd	6		294.10.a.o.1.2		2
21.17	even	6		294.10.a.n.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
42.10.e.b.25.1	✓	4	3.2	odd	2
42.10.e.b.37.1	yes	4	21.2	odd	6
126.10.g.c.37.2		4	7.2	even	3	inner
126.10.g.c.109.2		4	1.1	even	1	trivial
294.10.a.n.1.1		2	21.17	even	6
294.10.a.o.1.2		2	21.11	odd	6

Overview	Random
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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)

\(f(q)\)	\(=\)	\(q+(8.00000 + 13.8564i) q^{2} +(-128.000 + 221.703i) q^{4} +(419.902 + 727.292i) q^{5} +(-6254.79 - 1109.63i) q^{7} -4096.00 q^{8} +(-6718.44 + 11636.7i) q^{10} +(-20668.9 + 35799.5i) q^{11} -91963.9 q^{13} +(-34662.9 - 95545.9i) q^{14} +(-32768.0 - 56755.8i) q^{16} +(154395. - 267420. i) q^{17} +(396459. + 686687. i) q^{19} -214990. q^{20} -661403. q^{22} +(-466522. - 808040. i) q^{23} +(623927. - 1.08067e6i) q^{25} +(-735712. - 1.27429e6i) q^{26} +(1.04662e6 - 1.24467e6i) q^{28} -5.92949e6 q^{29} +(3.31544e6 - 5.74252e6i) q^{31} +(524288. - 908093. i) q^{32} +4.94064e6 q^{34} +(-1.81938e6 - 5.01499e6i) q^{35} +(9.40187e6 + 1.62845e7i) q^{37} +(-6.34334e6 + 1.09870e7i) q^{38} +(-1.71992e6 - 2.97899e6i) q^{40} +3.06260e6 q^{41} -1.69946e7 q^{43} +(-5.29123e6 - 9.16467e6i) q^{44} +(7.46436e6 - 1.29286e7i) q^{46} +(-2.04657e7 - 3.54477e7i) q^{47} +(3.78911e7 + 1.38809e7i) q^{49} +1.99657e7 q^{50} +(1.17714e7 - 2.03886e7i) q^{52} +(3.67746e7 - 6.36954e7i) q^{53} -3.47156e7 q^{55} +(2.56196e7 + 4.54503e6i) q^{56} +(-4.74359e7 - 8.21615e7i) q^{58} +(1.10813e7 - 1.91935e7i) q^{59} +(-3.55783e7 - 6.16234e7i) q^{61} +1.06094e8 q^{62} +1.67772e7 q^{64} +(-3.86159e7 - 6.68846e7i) q^{65} +(1.09727e8 - 1.90053e8i) q^{67} +(3.95251e7 + 6.84596e7i) q^{68} +(5.49347e7 - 6.53299e7i) q^{70} +1.77453e7 q^{71} +(-2.18567e7 + 3.78569e7i) q^{73} +(-1.50430e8 + 2.60552e8i) q^{74} -2.02987e8 q^{76} +(1.69003e8 - 2.00984e8i) q^{77} +(3.03509e7 + 5.25694e7i) q^{79} +(2.75187e7 - 4.76638e7i) q^{80} +(2.45008e7 + 4.24367e7i) q^{82} +2.88693e8 q^{83} +2.59323e8 q^{85} +(-1.35957e8 - 2.35484e8i) q^{86} +(8.46596e7 - 1.46635e8i) q^{88} +(-4.38592e7 - 7.59663e7i) q^{89} +(5.75215e8 + 1.02046e8i) q^{91} +2.38859e8 q^{92} +(3.27452e8 - 5.67163e8i) q^{94} +(-3.32948e8 + 5.76683e8i) q^{95} +1.15563e9 q^{97} +(1.10789e8 + 6.36082e8i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 32 q^{2} - 512 q^{4} - 929 q^{5} - 8526 q^{7} - 16384 q^{8} + 14864 q^{10} - 41695 q^{11} - 181214 q^{13} - 204624 q^{14} - 131072 q^{16} + 472508 q^{17} + 390503 q^{19} + 475648 q^{20} - 1334240 q^{22}+ \cdots - 963050704 q^{98}+O(q^{100}) \) 4 * q + 32 * q^2 - 512 * q^4 - 929 * q^5 - 8526 * q^7 - 16384 * q^8 + 14864 * q^10 - 41695 * q^11 - 181214 * q^13 - 204624 * q^14 - 131072 * q^16 + 472508 * q^17 + 390503 * q^19 + 475648 * q^20 - 1334240 * q^22 - 2225236 * q^23 + 72309 * q^25 - 1449712 * q^26 - 1091328 * q^28 - 6665582 * q^29 - 303326 * q^31 + 2097152 * q^32 + 15120256 * q^34 + 11318510 * q^35 + 29575385 * q^37 - 6248048 * q^38 + 3805184 * q^40 + 70138308 * q^41 - 16999882 * q^43 - 10673920 * q^44 + 35603776 * q^46 + 25023696 * q^47 + 10943758 * q^49 + 2313888 * q^50 + 23195392 * q^52 + 46233651 * q^53 - 68167202 * q^55 + 34922496 * q^56 - 53324656 * q^58 - 42109697 * q^59 - 28918988 * q^61 - 9706432 * q^62 + 67108864 * q^64 - 79631898 * q^65 + 367330515 * q^67 + 120962048 * q^68 + 461924176 * q^70 + 249191216 * q^71 - 94453335 * q^73 - 473206160 * q^74 - 199937536 * q^76 + 333561865 * q^77 + 402026668 * q^79 - 60882944 * q^80 + 561106464 * q^82 + 1775352998 * q^83 - 60522968 * q^85 - 135999056 * q^86 + 170782720 * q^88 - 72113094 * q^89 + 1155834883 * q^91 + 1139320832 * q^92 - 400379136 * q^94 - 1377688234 * q^95 + 296226882 * q^97 - 963050704 * q^98

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