LMFDB - Embedded newform 252.9.z.c.73.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [252,9,Mod(73,252)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(252, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 1]))

N = Newforms(chi, 9, names="a")

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

chi := DirichletCharacter("252.73");

S:= CuspForms(chi, 9);

N := Newforms(S);

Level:	$ N $	$=$	$ 252 = 2^{2} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 9 $
Character orbit:	$[\chi]$	$=$	252.z (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$102.659409735$
Analytic rank:	$0$
Dimension:	$10$
Relative dimension:	$5$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - x^{9} + 1442 x^{8} + 59551 x^{7} + 2229058 x^{6} + 41253567 x^{5} + 582209889 x^{4} + \cdots + 63214027776 $ x^10 - x^9 + 1442x^8 + 59551x^7 + 2229058x^6 + 41253567x^5 + 582209889x^4 + 4552713792x^3 + 25685059104x^2 + 45666643968x + 63214027776
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{12}\cdot 3^{9}\cdot 7^{6} $
Twist minimal:	no (minimal twist has level 28)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			73.1
Root			$-4.78762 - 8.29240i$ of defining polynomial
Character	$\chi$	$=$	252.73
Dual form			252.9.z.c.145.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-485.304 + 280.190i) q^{5} +(-622.564 + 2318.88i) q^{7} +O(q^{10})$	$q+(-485.304 + 280.190i) q^{5} +(-622.564 + 2318.88i) q^{7} +(-5557.02 + 9625.05i) q^{11} -38682.7i q^{13} +(91862.6 + 53036.9i) q^{17} +(164173. - 94785.1i) q^{19} +(231710. + 401333. i) q^{23} +(-38299.1 + 66336.0i) q^{25} +66563.3 q^{29} +(471221. + 272060. i) q^{31} +(-347596. - 1.29980e6i) q^{35} +(459897. + 796564. i) q^{37} -2.89321e6i q^{41} +3.05504e6 q^{43} +(96022.3 - 55438.5i) q^{47} +(-4.98963e6 - 2.88730e6i) q^{49} +(-6.87405e6 + 1.19062e7i) q^{53} -6.22810e6i q^{55} +(-562742. - 324899. i) q^{59} +(-7.64311e6 + 4.41275e6i) q^{61} +(1.08385e7 + 1.87729e7i) q^{65} +(2.44951e6 - 4.24268e6i) q^{67} -1.20517e7 q^{71} +(-2.76661e7 - 1.59730e7i) q^{73} +(-1.88598e7 - 1.88783e7i) q^{77} +(3.40393e7 + 5.89577e7i) q^{79} -4.61439e7i q^{83} -5.94417e7 q^{85} +(-9.23312e6 + 5.33074e6i) q^{89} +(8.97006e7 + 2.40825e7i) q^{91} +(-5.31157e7 + 9.19992e7i) q^{95} +4.77780e7i q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + 837 q^{5} + 1526 q^{7}+O(q^{10}) $ 10 * q + 837 * q^5 + 1526 * q^7	$ 10 q + 837 q^{5} + 1526 q^{7} - 3705 q^{11} - 78003 q^{17} - 96741 q^{19} - 208533 q^{23} + 367978 q^{25} - 754764 q^{29} - 1053717 q^{31} + 1306389 q^{35} - 998075 q^{37} + 738292 q^{43} - 710883 q^{47} + 13288114 q^{49} - 10501461 q^{53} + 37089081 q^{59} - 8180481 q^{61} - 21459108 q^{65} + 48020189 q^{67} + 31918236 q^{71} - 133345593 q^{73} - 188477625 q^{77} + 53590181 q^{79} - 157179282 q^{85} + 241368273 q^{89} + 420709128 q^{91} - 347126775 q^{95}+O(q^{100}) $ 10 * q + 837 * q^5 + 1526 * q^7 - 3705 * q^11 - 78003 * q^17 - 96741 * q^19 - 208533 * q^23 + 367978 * q^25 - 754764 * q^29 - 1053717 * q^31 + 1306389 * q^35 - 998075 * q^37 + 738292 * q^43 - 710883 * q^47 + 13288114 * q^49 - 10501461 * q^53 + 37089081 * q^59 - 8180481 * q^61 - 21459108 * q^65 + 48020189 * q^67 + 31918236 * q^71 - 133345593 * q^73 - 188477625 * q^77 + 53590181 * q^79 - 157179282 * q^85 + 241368273 * q^89 + 420709128 * q^91 - 347126775 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/252\mathbb{Z}\right)^\times$.

$n$	$29$	$73$	$127$
$\chi(n)$	$1$	$e\left(\frac{1}{6}\right)$	$1$

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 $

$2$		0			0
$2$		0			0
$3$		0			0
$3$		0			0
$4$		0			0
$5$	−485.304	+	280.190i	−0.776487	+	0.448305i	−0.835184	−	0.549971i	$-0.814639\pi$
$5$	−485.304	+	280.190i	−0.776487	+	0.448305i	0.0586971	+	0.998276i	$0.481305\pi$
$6$		0			0
$7$	−622.564	+	2318.88i	−0.259294	+	0.965799i
$7$	−622.564	+	2318.88i	−0.259294	+	0.965799i
$8$		0			0
$9$		0			0
$10$		0			0
$11$	−5557.02	+	9625.05i	−0.379552	+	0.657404i	−0.990997	−	0.133883i	$-0.957255\pi$
$11$	−5557.02	+	9625.05i	−0.379552	+	0.657404i	0.611445	+	0.791287i	$0.290589\pi$
$12$		0			0
$13$		−	38682.7i		−	1.35439i	−0.735804	−	0.677194i	$-0.763196\pi$
$13$		−	38682.7i		−	1.35439i	0.735804	−	0.677194i	$-0.236804\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	91862.6	+	53036.9i	1.09987	+	0.635013i	0.936188	−	0.351499i	$-0.114328\pi$
$17$	91862.6	+	53036.9i	1.09987	+	0.635013i	0.163687	+	0.986512i	$0.447661\pi$
$18$		0			0
$19$	164173.	−	94785.1i	1.25976	−	0.727320i	0.286728	−	0.958012i	$-0.407432\pi$
$19$	164173.	−	94785.1i	1.25976	−	0.727320i	0.973027	+	0.230692i	$0.0740990\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	231710.	+	401333.i	0.828005	+	1.43415i	0.899601	+	0.436713i	$0.143857\pi$
$23$	231710.	+	401333.i	0.828005	+	1.43415i	−0.0715958	+	0.997434i	$0.522809\pi$
$24$		0			0
$25$	−38299.1	+	66336.0i	−0.0980457	+	0.169820i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	66563.3			0.0941116			0.0470558	−	0.998892i	$-0.485016\pi$
$29$	66563.3			0.0941116			0.0470558	+	0.998892i	$0.485016\pi$
$30$		0			0
$31$	471221.	+	272060.i	0.510244	+	0.294590i	0.732934	−	0.680300i	$-0.238150\pi$
$31$	471221.	+	272060.i	0.510244	+	0.294590i	−0.222690	+	0.974889i	$0.571484\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	−347596.	−	1.29980e6i	−0.231634	−	0.866172i
$36$		0			0
$37$	459897.	+	796564.i	0.245388	+	0.425024i	0.962241	−	0.272200i	$-0.0877513\pi$
$37$	459897.	+	796564.i	0.245388	+	0.425024i	−0.716853	+	0.697225i	$0.754418\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$		−	2.89321e6i		−	1.02387i	−0.859024	−	0.511935i	$-0.828929\pi$
$41$		−	2.89321e6i		−	1.02387i	0.859024	−	0.511935i	$-0.171071\pi$
$42$		0			0
$43$	3.05504e6			0.893599			0.446799	−	0.894634i	$-0.352564\pi$
$43$	3.05504e6			0.893599			0.446799	+	0.894634i	$0.352564\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	96022.3	−	55438.5i	0.0196780	−	0.0113611i	−0.490129	−	0.871650i	$-0.663050\pi$
$47$	96022.3	−	55438.5i	0.0196780	−	0.0113611i	0.509807	+	0.860289i	$0.329717\pi$
$48$		0			0
$49$	−4.98963e6	−	2.88730e6i	−0.865534	−	0.500851i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	−6.87405e6	+	1.19062e7i	−0.871183	+	1.50893i	−0.0104095	+	0.999946i	$0.503313\pi$
$53$	−6.87405e6	+	1.19062e7i	−0.871183	+	1.50893i	−0.860774	+	0.508988i	$0.830020\pi$
$54$		0			0
$55$		−	6.22810e6i		−	0.680620i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	−562742.	−	324899.i	−0.0464409	−	0.0268127i	0.476600	−	0.879120i	$-0.341869\pi$
$59$	−562742.	−	324899.i	−0.0464409	−	0.0268127i	−0.523041	+	0.852308i	$0.675202\pi$
$60$		0			0
$61$	−7.64311e6	+	4.41275e6i	−0.552015	+	0.318706i	−0.749934	−	0.661512i	$-0.769915\pi$
$61$	−7.64311e6	+	4.41275e6i	−0.552015	+	0.318706i	0.197919	+	0.980218i	$0.436582\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	1.08385e7	+	1.87729e7i	0.607179	+	1.05166i
$66$		0			0
$67$	2.44951e6	−	4.24268e6i	0.121557	−	0.210543i	−0.798825	−	0.601564i	$-0.794545\pi$
$67$	2.44951e6	−	4.24268e6i	0.121557	−	0.210543i	0.920382	+	0.391021i	$0.127878\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	−1.20517e7			−0.474258			−0.237129	−	0.971478i	$-0.576206\pi$
$71$	−1.20517e7			−0.474258			−0.237129	+	0.971478i	$0.576206\pi$
$72$		0			0
$73$	−2.76661e7	−	1.59730e7i	−0.974219	−	0.562466i	−0.0736992	−	0.997281i	$-0.523480\pi$
$73$	−2.76661e7	−	1.59730e7i	−0.974219	−	0.562466i	−0.900520	+	0.434815i	$0.856814\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−1.88598e7	−	1.88783e7i	−0.536504	−	0.537032i
$78$		0			0
$79$	3.40393e7	+	5.89577e7i	0.873920	+	1.51367i	0.857909	+	0.513802i	$0.171763\pi$
$79$	3.40393e7	+	5.89577e7i	0.873920	+	1.51367i	0.0160110	+	0.999872i	$0.494903\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$		−	4.61439e7i		−	0.972304i	−0.873874	−	0.486152i	$-0.838400\pi$
$83$		−	4.61439e7i		−	0.972304i	0.873874	−	0.486152i	$-0.161600\pi$
$84$		0			0
$85$	−5.94417e7			−1.13872
$86$		0			0
$87$		0			0
$88$		0			0
$89$	−9.23312e6	+	5.33074e6i	−0.147160	+	0.0849626i	−0.571772	−	0.820413i	$-0.693744\pi$
$89$	−9.23312e6	+	5.33074e6i	−0.147160	+	0.0849626i	0.424612	+	0.905375i	$0.360410\pi$
$90$		0			0
$91$	8.97006e7	+	2.40825e7i	1.30807	+	0.351184i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	−5.31157e7	+	9.19992e7i	−0.652122	+	1.12951i
$96$		0			0
$97$			4.77780e7i			0.539685i	0.962904	+	0.269843i	$0.0869717\pi$
$97$			4.77780e7i			0.539685i	−0.962904	+	0.269843i	$0.913028\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	1.11796e8	+	6.45453e7i	1.07434	+	0.620268i	0.929363	−	0.369168i	$-0.120357\pi$
$101$	1.11796e8	+	6.45453e7i	1.07434	+	0.620268i	0.144973	+	0.989436i	$0.453691\pi$
$102$		0			0
$103$	−8.58034e7	+	4.95386e7i	−0.762352	+	0.440144i	−0.830140	−	0.557555i	$-0.811739\pi$
$103$	−8.58034e7	+	4.95386e7i	−0.762352	+	0.440144i	0.0677874	+	0.997700i	$0.478406\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−3.79322e6	−	6.57005e6i	−0.0289383	−	0.0501226i	0.851194	−	0.524852i	$-0.175879\pi$
$107$	−3.79322e6	−	6.57005e6i	−0.0289383	−	0.0501226i	−0.880132	+	0.474729i	$0.842546\pi$
$108$		0			0
$109$	1.40975e8	−	2.44175e8i	0.998700	−	1.72980i	0.455213	−	0.890383i	$-0.349563\pi$
$109$	1.40975e8	−	2.44175e8i	0.998700	−	1.72980i	0.543488	−	0.839417i	$-0.317104\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−2.35145e8			−1.44219			−0.721094	−	0.692837i	$-0.756361\pi$
$113$	−2.35145e8			−1.44219			−0.721094	+	0.692837i	$0.756361\pi$
$114$		0			0
$115$	−2.24899e8	−	1.29846e8i	−1.28587	−	0.742397i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	−1.80177e8	+	1.80000e8i	−0.898485	+	0.897603i
$120$		0			0
$121$	4.54184e7	+	7.86670e7i	0.211880	+	0.366987i
$122$		0			0
$123$		0			0
$124$		0			0
$125$		−	2.61823e8i		−	1.07243i
$126$		0			0
$127$	−3.06482e8			−1.17812			−0.589060	−	0.808089i	$-0.700502\pi$
$127$	−3.06482e8			−1.17812			−0.589060	+	0.808089i	$0.700502\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	−6.51594e7	+	3.76198e7i	−0.221254	+	0.127741i	−0.606531	−	0.795060i	$-0.707439\pi$
$131$	−6.51594e7	+	3.76198e7i	−0.221254	+	0.127741i	0.385277	+	0.922801i	$0.374106\pi$
$132$		0			0
$133$	1.17588e8	+	4.39707e8i	0.375798	+	1.40526i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−2.87998e8	+	4.98827e8i	−0.817536	+	1.41601i	0.0899571	+	0.995946i	$0.471327\pi$
$137$	−2.87998e8	+	4.98827e8i	−0.817536	+	1.41601i	−0.907493	+	0.420068i	$0.862006\pi$
$138$		0			0
$139$			6.51562e8i			1.74541i	0.488250	+	0.872704i	$0.337635\pi$
$139$			6.51562e8i			1.74541i	−0.488250	+	0.872704i	$0.662365\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	3.72323e8	+	2.14961e8i	0.890380	+	0.514061i
$144$		0			0
$145$	−3.23035e7	+	1.86504e7i	−0.0730764	+	0.0421907i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−1.22483e8	−	2.12147e8i	−0.248502	−	0.430418i	0.714608	−	0.699525i	$-0.246605\pi$
$149$	−1.22483e8	−	2.12147e8i	−0.248502	−	0.430418i	−0.963110	+	0.269106i	$0.913272\pi$
$150$		0			0
$151$	−7.39074e7	+	1.28011e8i	−0.142161	+	0.246230i	−0.928310	−	0.371807i	$-0.878738\pi$
$151$	−7.39074e7	+	1.28011e8i	−0.142161	+	0.246230i	0.786149	+	0.618037i	$0.212072\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	−3.04914e8			−0.528264
$156$		0			0
$157$	−1.03500e8	−	5.97555e7i	−0.170349	−	0.0983511i	0.412401	−	0.911002i	$-0.364690\pi$
$157$	−1.03500e8	−	5.97555e7i	−0.170349	−	0.0983511i	−0.582750	+	0.812651i	$0.698023\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	−1.07490e9	+	2.87452e8i	−1.59979	+	0.427821i
$162$		0			0
$163$	−4.44759e8	−	7.70346e8i	−0.630050	−	1.09128i	−0.987541	−	0.157362i	$-0.949701\pi$
$163$	−4.44759e8	−	7.70346e8i	−0.630050	−	1.09128i	0.357491	−	0.933916i	$-0.383632\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$			7.73849e8i			0.994925i	0.867485	+	0.497463i	$0.165735\pi$
$167$			7.73849e8i			0.994925i	−0.867485	+	0.497463i	$0.834265\pi$
$168$		0			0
$169$	−6.80621e8			−0.834369
$170$		0			0
$171$		0			0
$172$		0			0
$173$	−6.64406e8	+	3.83595e8i	−0.741735	+	0.428241i	−0.822700	−	0.568476i	$-0.807533\pi$
$173$	−6.64406e8	+	3.83595e8i	−0.741735	+	0.428241i	0.0809647	+	0.996717i	$0.474200\pi$
$174$		0			0
$175$	−1.29982e8	−	1.30110e8i	−0.138589	−	0.138726i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	−7.29610e8	+	1.26372e9i	−0.710687	+	1.23095i	0.253912	+	0.967227i	$0.418283\pi$
$179$	−7.29610e8	+	1.26372e9i	−0.710687	+	1.23095i	−0.964599	+	0.263719i	$0.915051\pi$
$180$		0			0
$181$		−	3.92574e8i		−	0.365769i	−0.983134	−	0.182885i	$-0.941456\pi$
$181$		−	3.92574e8i		−	0.365769i	0.983134	−	0.182885i	$-0.0585435\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	−4.46379e8	−	2.57717e8i	−0.381081	−	0.220017i
$186$		0			0
$187$	−1.02097e9	+	5.89455e8i	−0.834920	+	0.482041i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−4.83147e8	−	8.36836e8i	−0.363033	−	0.628792i	0.625425	−	0.780284i	$-0.284925\pi$
$191$	−4.83147e8	−	8.36836e8i	−0.363033	−	0.628792i	−0.988458	+	0.151492i	$0.951592\pi$
$192$		0			0
$193$	4.59523e8	−	7.95917e8i	0.331190	−	0.573639i	−0.651555	−	0.758601i	$-0.725883\pi$
$193$	4.59523e8	−	7.95917e8i	0.331190	−	0.573639i	0.982746	+	0.184963i	$0.0592164\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	9.27924e8			0.616095			0.308047	−	0.951371i	$-0.400325\pi$
$197$	9.27924e8			0.616095			0.308047	+	0.951371i	$0.400325\pi$
$198$		0			0
$199$	1.25198e9	+	7.22828e8i	0.798332	+	0.460917i	0.842887	−	0.538090i	$-0.180854\pi$
$199$	1.25198e9	+	7.22828e8i	0.798332	+	0.460917i	−0.0445558	+	0.999007i	$0.514187\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	−4.14399e7	+	1.54353e8i	−0.0244025	+	0.0908928i
$204$		0			0
$205$	8.10651e8	+	1.40409e9i	0.459006	+	0.795022i
$206$		0			0
$207$		0			0
$208$		0			0
$209$			2.10689e9i			1.10422i
$210$		0			0
$211$	1.15403e9			0.582220			0.291110	−	0.956690i	$-0.405975\pi$
$211$	1.15403e9			0.582220			0.291110	+	0.956690i	$0.405975\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	−1.48262e9	+	8.55992e8i	−0.693867	+	0.400605i
$216$		0			0
$217$	−9.24240e8	+	9.23332e8i	−0.416817	+	0.416408i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	2.05161e9	−	3.55349e9i	0.860054	−	1.48966i
$222$		0			0
$223$			1.34884e9i			0.545431i	0.962095	+	0.272715i	$0.0879217\pi$
$223$			1.34884e9i			0.545431i	−0.962095	+	0.272715i	$0.912078\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−2.03477e9	−	1.17477e9i	−0.766322	−	0.442436i	0.0652389	−	0.997870i	$-0.479219\pi$
$227$	−2.03477e9	−	1.17477e9i	−0.766322	−	0.442436i	−0.831561	+	0.555433i	$0.812552\pi$
$228$		0			0
$229$	−2.03484e9	+	1.17481e9i	−0.739925	+	0.427196i	−0.822042	−	0.569427i	$-0.807165\pi$
$229$	−2.03484e9	+	1.17481e9i	−0.739925	+	0.427196i	0.0821168	+	0.996623i	$0.473832\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	1.76336e9	+	3.05423e9i	0.598298	+	1.03628i	0.993072	+	0.117505i	$0.0374895\pi$
$233$	1.76336e9	+	3.05423e9i	0.598298	+	1.03628i	−0.394774	+	0.918778i	$0.629177\pi$
$234$		0			0
$235$	−3.10667e7	+	5.38091e7i	−0.0101865	+	0.0176435i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	−3.11328e9			−0.954171			−0.477085	−	0.878857i	$-0.658307\pi$
$239$	−3.11328e9			−0.954171			−0.477085	+	0.878857i	$0.658307\pi$
$240$		0			0
$241$	3.35829e9	+	1.93891e9i	0.995519	+	0.574763i	0.906919	−	0.421304i	$-0.138428\pi$
$241$	3.35829e9	+	1.93891e9i	0.995519	+	0.574763i	0.0885994	+	0.996067i	$0.471761\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	3.23048e9	+	3.17446e6i	0.896609	+	0.000881061i
$246$		0			0
$247$	−3.66654e9	−	6.35064e9i	−0.985074	−	1.70620i
$248$		0			0
$249$		0			0
$250$		0			0
$251$			6.47407e8i			0.163111i	0.996669	+	0.0815554i	$0.0259888\pi$
$251$			6.47407e8i			0.163111i	−0.996669	+	0.0815554i	$0.974011\pi$
$252$		0			0
$253$	−5.15047e9			−1.25708
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−5.35799e9	+	3.09344e9i	−1.22820	+	0.709102i	−0.966653	−	0.256089i	$-0.917566\pi$
$257$	−5.35799e9	+	3.09344e9i	−1.22820	+	0.709102i	−0.261547	+	0.965191i	$0.584233\pi$
$258$		0			0
$259$	−2.13345e9	+	5.70534e8i	−0.474116	+	0.126789i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	3.36120e9	−	5.82177e9i	0.702541	−	1.21684i	−0.265031	−	0.964240i	$-0.585382\pi$
$263$	3.36120e9	−	5.82177e9i	0.702541	−	1.21684i	0.967572	−	0.252596i	$-0.0812845\pi$
$264$		0			0
$265$		−	7.70418e9i		−	1.56222i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	4.61865e9	+	2.66658e9i	0.882076	+	0.509267i	0.871342	−	0.490676i	$-0.163250\pi$
$269$	4.61865e9	+	2.66658e9i	0.882076	+	0.509267i	0.0107336	+	0.999942i	$0.496583\pi$
$270$		0			0
$271$	4.03199e9	−	2.32787e9i	0.747554	−	0.431601i	−0.0772553	−	0.997011i	$-0.524616\pi$
$271$	4.03199e9	−	2.32787e9i	0.747554	−	0.431601i	0.824809	+	0.565411i	$0.191282\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−4.25658e8	−	7.37262e8i	−0.0744270	−	0.128911i
$276$		0			0
$277$	−2.39960e9	+	4.15622e9i	−0.407586	+	0.705960i	−0.994619	−	0.103604i	$-0.966963\pi$
$277$	−2.39960e9	+	4.15622e9i	−0.407586	+	0.705960i	0.587033	+	0.809563i	$0.300296\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	−9.99466e9			−1.60303			−0.801517	−	0.597972i	$-0.795973\pi$
$281$	−9.99466e9			−1.60303			−0.801517	+	0.597972i	$0.795973\pi$
$282$		0			0
$283$	8.79731e9	+	5.07913e9i	1.37153	+	0.791851i	0.991120	−	0.132969i	$-0.0424511\pi$
$283$	8.79731e9	+	5.07913e9i	1.37153	+	0.791851i	0.380406	+	0.924820i	$0.375784\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	6.70902e9	+	1.80121e9i	0.988853	+	0.265483i
$288$		0			0
$289$	2.13795e9	+	3.70304e9i	0.306483	+	0.530844i
$290$		0			0
$291$		0			0
$292$		0			0
$293$		−	9.14279e9i		−	1.24053i	−0.784391	−	0.620266i	$-0.787024\pi$
$293$		−	9.14279e9i		−	1.24053i	0.784391	−	0.620266i	$-0.212976\pi$
$294$		0			0
$295$	3.64134e8			0.0480810
$296$		0			0
$297$		0			0
$298$		0			0
$299$	1.55246e10	−	8.96316e9i	1.94239	−	1.12144i
$300$		0			0
$301$	−1.90196e9	+	7.08427e9i	−0.231704	+	0.863036i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	2.47282e9	−	4.28305e9i	0.285755	−	0.494942i
$306$		0			0
$307$		−	7.30031e9i		−	0.821841i	−0.911671	−	0.410920i	$-0.865207\pi$
$307$		−	7.30031e9i		−	0.821841i	0.911671	−	0.410920i	$-0.134793\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	−5.41215e9	−	3.12471e9i	−0.578533	−	0.334016i	0.182017	−	0.983295i	$-0.441737\pi$
$311$	−5.41215e9	−	3.12471e9i	−0.578533	−	0.334016i	−0.760550	+	0.649279i	$0.775071\pi$
$312$		0			0
$313$	1.35138e10	−	7.80218e9i	1.40799	−	0.812903i	0.412795	−	0.910824i	$-0.364553\pi$
$313$	1.35138e10	−	7.80218e9i	1.40799	−	0.812903i	0.995194	+	0.0979211i	$0.0312193\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−7.91639e8	−	1.37116e9i	−0.0783954	−	0.135785i	0.824162	−	0.566354i	$-0.191646\pi$
$317$	−7.91639e8	−	1.37116e9i	−0.0783954	−	0.135785i	−0.902558	+	0.430569i	$0.858313\pi$
$318$		0			0
$319$	−3.69894e8	+	6.40675e8i	−0.0357203	+	0.0618693i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	2.01084e10			1.84743
$324$		0			0
$325$	2.56606e9	+	1.48151e9i	0.230003	+	0.132792i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	6.87753e7	+	2.57178e8i	0.00587015	+	0.0219508i
$330$		0			0
$331$	−4.25368e9	−	7.36758e9i	−0.354366	−	0.613781i	0.632643	−	0.774444i	$-0.281970\pi$
$331$	−4.25368e9	−	7.36758e9i	−0.354366	−	0.613781i	−0.987009	+	0.160663i	$0.948637\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$			2.74532e9i			0.217979i
$336$		0			0
$337$	3.55473e9			0.275605			0.137802	−	0.990460i	$-0.455996\pi$
$337$	3.55473e9			0.275605			0.137802	+	0.990460i	$0.455996\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	−5.23717e9	+	3.02368e9i	−0.387329	+	0.223624i
$342$		0			0
$343$	9.80168e9	−	9.77283e9i	0.708148	−	0.706064i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	1.12545e9	−	1.94934e9i	0.0776265	−	0.134453i	−0.824599	−	0.565718i	$-0.808599\pi$
$347$	1.12545e9	−	1.94934e9i	0.0776265	−	0.134453i	0.902225	+	0.431265i	$0.141933\pi$
$348$		0			0
$349$			1.94104e9i			0.130838i	0.997858	+	0.0654189i	$0.0208384\pi$
$349$			1.94104e9i			0.130838i	−0.997858	+	0.0654189i	$0.979162\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	1.90536e10	+	1.10006e10i	1.22709	+	0.708462i	0.966421	−	0.256966i	$-0.0827227\pi$
$353$	1.90536e10	+	1.10006e10i	1.22709	+	0.708462i	0.260672	+	0.965428i	$0.416056\pi$
$354$		0			0
$355$	5.84873e9	−	3.37677e9i	0.368255	−	0.212612i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	7.98313e9	+	1.38272e10i	0.480613	+	0.832446i	0.999753	−	0.0222434i	$-0.00708087\pi$
$359$	7.98313e9	+	1.38272e10i	0.480613	+	0.832446i	−0.519140	+	0.854689i	$0.673748\pi$
$360$		0			0
$361$	9.47664e9	−	1.64140e10i	0.557989	−	0.966465i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	1.79020e10			1.00862
$366$		0			0
$367$	−2.75030e10	−	1.58789e10i	−1.51606	−	0.875296i	−0.999822	−	0.0188484i	$-0.994000\pi$
$367$	−2.75030e10	−	1.58789e10i	−1.51606	−	0.875296i	−0.516234	−	0.856447i	$-0.672667\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	−2.33296e10	−	2.33525e10i	−1.23143	−	1.23264i
$372$		0			0
$373$	6.25659e9	+	1.08367e10i	0.323223	+	0.559839i	0.981151	−	0.193242i	$-0.0619002\pi$
$373$	6.25659e9	+	1.08367e10i	0.323223	+	0.559839i	−0.657928	+	0.753081i	$0.728567\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$		−	2.57485e9i		−	0.127464i
$378$		0			0
$379$	−5.11054e9			−0.247691			−0.123845	−	0.992302i	$-0.539523\pi$
$379$	−5.11054e9			−0.247691			−0.123845	+	0.992302i	$0.539523\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	2.39710e10	−	1.38397e10i	1.11402	−	0.643178i	0.174150	−	0.984719i	$-0.444282\pi$
$383$	2.39710e10	−	1.38397e10i	1.11402	−	0.643178i	0.939867	+	0.341542i	$0.110949\pi$
$384$		0			0
$385$	1.44422e10	+	3.87739e9i	0.657342	+	0.176480i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	−8.15078e8	+	1.41176e9i	−0.0355960	+	0.0616540i	−0.883275	−	0.468856i	$-0.844666\pi$
$389$	−8.15078e8	+	1.41176e9i	−0.0355960	+	0.0616540i	0.847679	+	0.530510i	$0.178000\pi$
$390$		0			0
$391$			4.91567e10i			2.10318i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	−3.30388e10	−	1.90749e10i	−1.35717	−	0.783565i
$396$		0			0
$397$	−2.51635e10	+	1.45281e10i	−1.01300	+	0.584854i	−0.912068	−	0.410039i	$-0.865515\pi$
$397$	−2.51635e10	+	1.45281e10i	−1.01300	+	0.584854i	−0.100929	+	0.994894i	$0.532182\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−1.68376e10	−	2.91636e10i	−0.651184	−	1.12788i	−0.982836	−	0.184482i	$-0.940939\pi$
$401$	−1.68376e10	−	2.91636e10i	−0.651184	−	1.12788i	0.331652	−	0.943402i	$-0.392394\pi$
$402$		0			0
$403$	1.05240e10	−	1.82281e10i	0.398989	−	0.691069i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−1.02226e10			−0.372550
$408$		0			0
$409$	−4.28975e10	−	2.47669e10i	−1.53299	−	0.885072i	−0.999222	−	0.0394403i	$-0.987443\pi$
$409$	−4.28975e10	−	2.47669e10i	−1.53299	−	0.885072i	−0.533767	−	0.845631i	$-0.679224\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	1.10375e9	−	1.10266e9i	0.0379375	−	0.0379002i
$414$		0			0
$415$	1.29291e10	+	2.23938e10i	0.435888	+	0.754981i
$416$		0			0
$417$		0			0
$418$		0			0
$419$		−	3.65134e10i		−	1.18467i	−0.805693	−	0.592333i	$-0.798207\pi$
$419$		−	3.65134e10i		−	1.18467i	0.805693	−	0.592333i	$-0.201793\pi$
$420$		0			0
$421$	2.76738e10			0.880929			0.440464	−	0.897770i	$-0.354814\pi$
$421$	2.76738e10			0.880929			0.440464	+	0.897770i	$0.354814\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	−7.03651e9	+	4.06253e9i	−0.215676	+	0.124521i
$426$		0			0
$427$	−5.47433e9	−	2.04707e10i	−0.164672	−	0.615774i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	−1.55146e10	+	2.68720e10i	−0.449605	+	0.778738i	−0.998360	−	0.0572447i	$-0.981768\pi$
$431$	−1.55146e10	+	2.68720e10i	−0.449605	+	0.778738i	0.548755	+	0.835983i	$0.315102\pi$
$432$		0			0
$433$		−	9.99332e8i		−	0.0284288i	−0.999899	−	0.0142144i	$-0.995475\pi$
$433$		−	9.99332e8i		−	0.0284288i	0.999899	−	0.0142144i	$-0.00452473\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	7.60808e10	+	4.39252e10i	2.08617	+	1.20445i
$438$		0			0
$439$	−2.96332e9	+	1.71087e9i	−0.0797848	+	0.0460638i	−0.539362	−	0.842074i	$-0.681334\pi$
$439$	−2.96332e9	+	1.71087e9i	−0.0797848	+	0.0460638i	0.459577	+	0.888138i	$0.348001\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	1.37156e10	+	2.37560e10i	0.356122	+	0.616821i	0.987309	−	0.158809i	$-0.0507655\pi$
$443$	1.37156e10	+	2.37560e10i	0.356122	+	0.616821i	−0.631187	+	0.775630i	$0.717432\pi$
$444$		0			0
$445$	2.98725e9	−	5.17406e9i	0.0761783	−	0.131945i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	4.31322e10			1.06125			0.530623	−	0.847608i	$-0.321958\pi$
$449$	4.31322e10			1.06125			0.530623	+	0.847608i	$0.321958\pi$
$450$		0			0
$451$	2.78473e10	+	1.60777e10i	0.673096	+	0.388612i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	−5.02798e10	+	1.34459e10i	−1.17313	+	0.313723i
$456$		0			0
$457$	−1.10397e10	−	1.91213e10i	−0.253100	−	0.438382i	0.711278	−	0.702911i	$-0.248117\pi$
$457$	−1.10397e10	−	1.91213e10i	−0.253100	−	0.438382i	−0.964378	+	0.264529i	$0.914783\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$			7.83306e10i			1.73431i	0.498034	+	0.867157i	$0.334055\pi$
$461$			7.83306e10i			1.73431i	−0.498034	+	0.867157i	$0.665945\pi$
$462$		0			0
$463$	1.78071e10			0.387498			0.193749	−	0.981051i	$-0.437935\pi$
$463$	1.78071e10			0.387498			0.193749	+	0.981051i	$0.437935\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	5.48239e9	−	3.16526e9i	0.115266	−	0.0665490i	−0.441258	−	0.897380i	$-0.645468\pi$
$467$	5.48239e9	−	3.16526e9i	0.115266	−	0.0665490i	0.556525	+	0.830831i	$0.312134\pi$
$468$		0			0
$469$	8.31330e9	+	8.32147e9i	0.171823	+	0.171992i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	−1.69769e10	+	2.94049e10i	−0.339167	+	0.587455i
$474$		0			0
$475$			1.45207e10i			0.285242i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	−4.14563e9	−	2.39348e9i	−0.0787496	−	0.0454661i	0.460108	−	0.887863i	$-0.347811\pi$
$479$	−4.14563e9	−	2.39348e9i	−0.0787496	−	0.0454661i	−0.538858	+	0.842397i	$0.681144\pi$
$480$		0			0
$481$	3.08133e10	−	1.77900e10i	0.575648	−	0.332351i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−1.33869e10	−	2.31868e10i	−0.241944	−	0.419059i
$486$		0			0
$487$	−4.79735e10	+	8.30926e10i	−0.852875	+	1.47722i	0.0257266	+	0.999669i	$0.491810\pi$
$487$	−4.79735e10	+	8.30926e10i	−0.852875	+	1.47722i	−0.878602	+	0.477555i	$0.841523\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	−1.00845e11			−1.73512			−0.867561	−	0.497331i	$-0.834313\pi$
$491$	−1.00845e11			−1.73512			−0.867561	+	0.497331i	$0.834313\pi$
$492$		0			0
$493$	6.11468e9	+	3.53031e9i	0.103511	+	0.0597621i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	7.50295e9	−	2.79465e10i	0.122972	−	0.458038i
$498$		0			0
$499$	−4.25959e10	−	7.37782e10i	−0.687014	−	1.18994i	−0.972799	−	0.231649i	$-0.925588\pi$
$499$	−4.25959e10	−	7.37782e10i	−0.687014	−	1.18994i	0.285786	−	0.958293i	$-0.407745\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$		−	4.97340e10i		−	0.776929i	−0.921464	−	0.388464i	$-0.873006\pi$
$503$		−	4.97340e10i		−	0.776929i	0.921464	−	0.388464i	$-0.126994\pi$
$504$		0			0
$505$	−7.23399e10			−1.11228
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−8.74867e10	+	5.05105e10i	−1.30338	+	0.752506i	−0.980982	−	0.194098i	$-0.937822\pi$
$509$	−8.74867e10	+	5.05105e10i	−1.30338	+	0.752506i	−0.322397	+	0.946604i	$0.604489\pi$
$510$		0			0
$511$	5.42635e10	−	5.42102e10i	0.795837	−	0.795056i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	2.77605e10	−	4.80826e10i	0.394638	−	0.683532i
$516$		0			0
$517$			1.23229e9i			0.0172485i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	−9.20083e10	−	5.31210e10i	−1.24875	−	0.720967i	−0.277891	−	0.960613i	$-0.589636\pi$
$521$	−9.20083e10	−	5.31210e10i	−1.24875	−	0.720967i	−0.970861	+	0.239645i	$0.922969\pi$
$522$		0			0
$523$	−4.92629e10	+	2.84420e10i	−0.658436	+	0.380148i	−0.791681	−	0.610935i	$-0.790794\pi$
$523$	−4.92629e10	+	2.84420e10i	−0.658436	+	0.380148i	0.133245	+	0.991083i	$0.457460\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	2.88584e10	+	4.99842e10i	0.374136	+	0.648023i
$528$		0			0
$529$	−6.82233e10	+	1.18166e11i	−0.871185	+	1.50894i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	−1.11917e11			−1.38672
$534$		0			0
$535$	3.68173e9	+	2.12565e9i	0.0449404	+	0.0259463i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	5.55179e10	−	3.19806e10i	0.657776	−	0.378906i
$540$		0			0
$541$	8.29883e10	+	1.43740e11i	0.968786	+	1.67799i	0.699079	+	0.715044i	$0.253594\pi$
$541$	8.29883e10	+	1.43740e11i	0.968786	+	1.67799i	0.269707	+	0.962942i	$0.413073\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$			1.57999e11i			1.79089i
$546$		0			0
$547$	−6.89085e10			−0.769703			−0.384852	−	0.922978i	$-0.625747\pi$
$547$	−6.89085e10			−0.769703			−0.384852	+	0.922978i	$0.625747\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	1.09279e10	−	6.30921e9i	0.118558	−	0.0684492i
$552$		0			0
$553$	−1.57908e11	+	4.22281e10i	−1.68851	+	0.451545i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−9.38818e10	+	1.62608e11i	−0.975351	+	1.68936i	−0.296578	+	0.955009i	$0.595846\pi$
$557$	−9.38818e10	+	1.62608e11i	−0.975351	+	1.68936i	−0.678773	+	0.734349i	$0.737488\pi$
$558$		0			0
$559$		−	1.18177e11i		−	1.21028i
$560$		0			0
$561$		0			0
$562$		0			0
$563$	−6.00510e10	−	3.46705e10i	−0.597705	−	0.345085i	0.170433	−	0.985369i	$-0.445483\pi$
$563$	−6.00510e10	−	3.46705e10i	−0.597705	−	0.345085i	−0.768138	+	0.640284i	$0.778817\pi$
$564$		0			0
$565$	1.14117e11	−	6.58854e10i	1.11984	−	0.646540i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	5.36170e10	+	9.28673e10i	0.511509	+	0.885959i	0.999911	+	0.0133408i	$0.00424662\pi$
$569$	5.36170e10	+	9.28673e10i	0.511509	+	0.885959i	−0.488402	+	0.872619i	$0.662420\pi$
$570$		0			0
$571$	−8.56535e9	+	1.48356e10i	−0.0805751	+	0.139560i	−0.903497	−	0.428594i	$-0.859009\pi$
$571$	−8.56535e9	+	1.48356e10i	−0.0805751	+	0.139560i	0.822922	+	0.568154i	$0.192342\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	−3.54971e10			−0.324729
$576$		0			0
$577$	−3.58005e10	−	2.06694e10i	−0.322987	−	0.186477i	0.329736	−	0.944073i	$-0.393040\pi$
$577$	−3.58005e10	−	2.06694e10i	−0.322987	−	0.186477i	−0.652723	+	0.757596i	$0.726374\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	1.07002e11	+	2.87275e10i	0.939050	+	0.252112i
$582$		0			0
$583$	−7.63986e10	−	1.32326e11i	−0.661319	−	1.14544i
$584$		0			0
$585$		0			0
$586$		0			0
$587$			6.96187e10i			0.586372i	0.956055	+	0.293186i	$0.0947155\pi$
$587$			6.96187e10i			0.586372i	−0.956055	+	0.293186i	$0.905284\pi$
$588$		0			0
$589$	1.03149e11			0.857043
$590$		0			0
$591$		0			0
$592$		0			0
$593$	−5.79574e10	+	3.34617e10i	−0.468695	+	0.270601i	−0.715693	−	0.698415i	$-0.753889\pi$
$593$	−5.79574e10	+	3.34617e10i	−0.468695	+	0.270601i	0.246998	+	0.969016i	$0.420556\pi$
$594$		0			0
$595$	3.70063e10	−	1.37838e11i	0.295262	−	1.09977i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	8.99155e10	−	1.55738e11i	0.698437	−	1.20973i	−0.270571	−	0.962700i	$-0.587212\pi$
$599$	8.99155e10	−	1.55738e11i	0.698437	−	1.20973i	0.969008	−	0.247029i	$-0.0794542\pi$
$600$		0			0
$601$			1.52360e11i			1.16781i	0.811821	+	0.583907i	$0.198477\pi$
$601$			1.52360e11i			1.16781i	−0.811821	+	0.583907i	$0.801523\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	−4.40835e10	−	2.54516e10i	−0.329044	−	0.189974i
$606$		0			0
$607$	−1.33105e10	+	7.68485e9i	−0.0980485	+	0.0566083i	−0.548222	−	0.836333i	$-0.684695\pi$
$607$	−1.33105e10	+	7.68485e9i	−0.0980485	+	0.0566083i	0.450174	+	0.892941i	$0.351362\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−2.14451e9	−	3.71440e9i	−0.0153873	−	0.0266517i
$612$		0			0
$613$	2.80966e10	−	4.86648e10i	0.198981	−	0.344646i	−0.749217	−	0.662325i	$-0.769570\pi$
$613$	2.80966e10	−	4.86648e10i	0.198981	−	0.344646i	0.948198	+	0.317679i	$0.102903\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	2.68409e10			0.185207			0.0926033	−	0.995703i	$-0.470481\pi$
$617$	2.68409e10			0.185207			0.0926033	+	0.995703i	$0.470481\pi$
$618$		0			0
$619$	1.28543e11	+	7.42143e10i	0.875560	+	0.505505i	0.869192	−	0.494475i	$-0.164640\pi$
$619$	1.28543e11	+	7.42143e10i	0.875560	+	0.505505i	0.00636782	+	0.999980i	$0.497973\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	−6.61316e9	−	2.47292e10i	−0.0438992	−	0.164157i
$624$		0			0
$625$	5.83997e10	+	1.01151e11i	0.382728	+	0.662905i
$626$		0			0
$627$		0			0
$628$		0			0
$629$			9.75660e10i			0.623298i
$630$		0			0
$631$	1.25823e10			0.0793674			0.0396837	−	0.999212i	$-0.487365\pi$
$631$	1.25823e10			0.0793674			0.0396837	+	0.999212i	$0.487365\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	1.48737e11	−	8.58732e10i	0.914794	−	0.528157i
$636$		0			0
$637$	−1.11689e11	+	1.93012e11i	−0.678347	+	1.17227i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	1.07329e11	−	1.85900e11i	0.635750	−	1.10115i	−0.350606	−	0.936523i	$-0.614024\pi$
$641$	1.07329e11	−	1.85900e11i	0.635750	−	1.10115i	0.986356	−	0.164628i	$-0.0526425\pi$
$642$		0			0
$643$			4.39520e10i			0.257119i	0.991702	+	0.128560i	$0.0410354\pi$
$643$			4.39520e10i			0.257119i	−0.991702	+	0.128560i	$0.958965\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−1.29305e11	−	7.46545e10i	−0.737903	−	0.426029i	0.0834031	−	0.996516i	$-0.473421\pi$
$647$	−1.29305e11	−	7.46545e10i	−0.737903	−	0.426029i	−0.821307	+	0.570487i	$0.806754\pi$
$648$		0			0
$649$	6.25434e9	−	3.61094e9i	0.0352535	−	0.0203536i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	3.70178e10	+	6.41167e10i	0.203591	+	0.352629i	0.949683	−	0.313213i	$-0.101406\pi$
$653$	3.70178e10	+	6.41167e10i	0.203591	+	0.352629i	−0.746092	+	0.665843i	$0.768072\pi$
$654$		0			0
$655$	2.10814e10	−	3.65141e10i	0.114534	−	0.198379i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	−1.00382e11			−0.532248			−0.266124	−	0.963939i	$-0.585743\pi$
$659$	−1.00382e11			−0.532248			−0.266124	+	0.963939i	$0.585743\pi$
$660$		0			0
$661$	3.59591e10	+	2.07610e10i	0.188366	+	0.108753i	0.591217	−	0.806512i	$-0.298647\pi$
$661$	3.59591e10	+	2.07610e10i	0.188366	+	0.108753i	−0.402851	+	0.915265i	$0.631981\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	−1.80267e11	−	1.80445e11i	−0.921786	−	0.922693i
$666$		0			0
$667$	1.54234e10	+	2.67141e10i	0.0779249	+	0.134970i
$668$		0			0
$669$		0			0
$670$		0			0
$671$		−	9.80871e10i		−	0.483862i
$672$		0			0
$673$	−1.21560e11			−0.592559			−0.296279	−	0.955101i	$-0.595746\pi$
$673$	−1.21560e11			−0.592559			−0.296279	+	0.955101i	$0.595746\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	6.95265e10	−	4.01411e10i	0.330975	−	0.191089i	−0.325299	−	0.945611i	$-0.605465\pi$
$677$	6.95265e10	−	4.01411e10i	0.330975	−	0.191089i	0.656274	+	0.754523i	$0.272132\pi$
$678$		0			0
$679$	−1.10791e11	−	2.97448e10i	−0.521227	−	0.139937i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	8.50224e10	−	1.47263e11i	0.390706	−	0.676723i	−0.601837	−	0.798619i	$-0.705564\pi$
$683$	8.50224e10	−	1.47263e11i	0.390706	−	0.676723i	0.992543	+	0.121896i	$0.0388975\pi$
$684$		0			0
$685$		−	3.22777e11i		−	1.46602i
$686$		0			0
$687$		0			0
$688$		0			0
$689$	4.60564e11	+	2.65907e11i	2.04368	+	1.17992i
$690$		0			0
$691$	1.59262e11	−	9.19498e10i	0.698553	−	0.403310i	−0.108255	−	0.994123i	$-0.534526\pi$
$691$	1.59262e11	−	9.19498e10i	0.698553	−	0.403310i	0.806808	+	0.590813i	$0.201193\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−1.82562e11	−	3.16206e11i	−0.782475	−	1.35529i
$696$		0			0
$697$	1.53447e11	−	2.65778e11i	0.650171	−	1.12613i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	1.10072e11			0.455832			0.227916	−	0.973681i	$-0.426809\pi$
$701$	1.10072e11			0.455832			0.227916	+	0.973681i	$0.426809\pi$
$702$		0			0
$703$	1.51005e11	+	8.71827e10i	0.618258	+	0.356951i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−2.19273e11	+	2.19058e11i	−0.877622	+	0.876760i
$708$		0			0
$709$	9.26532e10	+	1.60480e11i	0.366670	+	0.635092i	0.989043	−	0.147630i	$-0.0471644\pi$
$709$	9.26532e10	+	1.60480e11i	0.366670	+	0.635092i	−0.622372	+	0.782721i	$0.713831\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$			2.52155e11i			0.975687i
$714$		0			0
$715$	−2.40920e11			−0.921825
$716$		0			0
$717$		0			0
$718$		0			0
$719$	3.95549e11	−	2.28370e11i	1.48008	−	0.854524i	0.480333	−	0.877086i	$-0.340516\pi$
$719$	3.95549e11	−	2.28370e11i	1.48008	−	0.854524i	0.999745	+	0.0225623i	$0.00718240\pi$
$720$		0			0
$721$	−6.14561e10	−	2.29809e11i	−0.227418	−	0.850405i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	−2.54932e9	+	4.41555e9i	−0.00922724	+	0.0159820i
$726$		0			0
$727$			1.49697e11i			0.535889i	0.963434	+	0.267944i	$0.0863443\pi$
$727$			1.49697e11i			0.535889i	−0.963434	+	0.267944i	$0.913656\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	2.80644e11	+	1.62030e11i	0.982846	+	0.567447i
$732$		0			0
$733$	−2.82600e11	+	1.63159e11i	−0.978941	+	0.565192i	−0.901950	−	0.431840i	$-0.857865\pi$
$733$	−2.82600e11	+	1.63159e11i	−0.978941	+	0.565192i	−0.0769910	+	0.997032i	$0.524531\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	2.72240e10	+	4.71534e10i	0.0922746	+	0.159824i
$738$		0			0
$739$	2.51525e11	−	4.35654e11i	0.843342	−	1.46071i	−0.0437118	−	0.999044i	$-0.513918\pi$
$739$	2.51525e11	−	4.35654e11i	0.843342	−	1.46071i	0.887054	−	0.461667i	$-0.152748\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−1.93930e11			−0.636340			−0.318170	−	0.948034i	$-0.603068\pi$
$743$	−1.93930e11			−0.636340			−0.318170	+	0.948034i	$0.603068\pi$
$744$		0			0
$745$	1.18883e11	+	6.86371e10i	0.385917	+	0.222809i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	1.75967e10	−	4.70575e9i	0.0559118	−	0.0149521i
$750$		0			0
$751$	−2.79070e11	−	4.83363e11i	−0.877311	−	1.51955i	−0.854281	−	0.519812i	$-0.826002\pi$
$751$	−2.79070e11	−	4.83363e11i	−0.877311	−	1.51955i	−0.0230297	−	0.999735i	$-0.507331\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$		−	8.28326e10i		−	0.254926i
$756$		0			0
$757$	4.76743e10			0.145178			0.0725891	−	0.997362i	$-0.476874\pi$
$757$	4.76743e10			0.145178			0.0725891	+	0.997362i	$0.476874\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	2.24854e11	−	1.29820e11i	0.670443	−	0.387081i	−0.125801	−	0.992055i	$-0.540150\pi$
$761$	2.24854e11	−	1.29820e11i	0.670443	−	0.387081i	0.796245	+	0.604975i	$0.206817\pi$
$762$		0			0
$763$	4.78448e11	+	4.78919e11i	1.41168	+	1.41307i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−1.25680e10	+	2.17684e10i	−0.0363148	+	0.0628991i
$768$		0			0
$769$			4.46473e11i			1.27670i	0.769745	+	0.638352i	$0.220384\pi$
$769$			4.46473e11i			1.27670i	−0.769745	+	0.638352i	$0.779616\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	3.19567e11	+	1.84502e11i	0.895044	+	0.516754i	0.875589	−	0.483057i	$-0.160474\pi$
$773$	3.19567e11	+	1.84502e11i	0.895044	+	0.516754i	0.0194548	+	0.999811i	$0.493807\pi$
$774$		0			0
$775$	−3.60947e10	+	2.08393e10i	−0.100055	+	0.0577665i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−2.74233e11	−	4.74986e11i	−0.744681	−	1.28983i
$780$		0			0
$781$	6.69715e10	−	1.15998e11i	0.180006	−	0.311779i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	6.69717e10			0.176365
$786$		0			0
$787$	−3.43177e11	−	1.98133e11i	−0.894579	−	0.516486i	−0.0191418	−	0.999817i	$-0.506093\pi$
$787$	−3.43177e11	−	1.98133e11i	−0.894579	−	0.516486i	−0.875438	+	0.483331i	$0.839427\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	1.46393e11	−	5.45274e11i	0.373950	−	1.39286i
$792$		0			0
$793$	1.70697e11	+	2.95656e11i	0.431652	+	0.747643i
$794$		0			0
$795$		0			0
$796$		0			0
$797$		−	3.46928e11i		−	0.859816i	−0.902873	−	0.429908i	$-0.858546\pi$
$797$		−	3.46928e11i		−	0.859816i	0.902873	−	0.429908i	$-0.141454\pi$
$798$		0			0
$799$	1.17611e10			0.0288578
$800$		0			0
$801$		0			0
$802$		0			0
$803$	3.07482e11	−	1.77525e11i	0.739534	−	0.426970i
$804$		0			0
$805$	4.41111e11	−	4.40678e11i	1.05042	−	1.04939i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	−3.30434e10	+	5.72329e10i	−0.0771420	+	0.133614i	−0.902016	−	0.431703i	$-0.857913\pi$
$809$	−3.30434e10	+	5.72329e10i	−0.0771420	+	0.133614i	0.824874	+	0.565317i	$0.191246\pi$
$810$		0			0
$811$			4.93459e11i			1.14069i	0.821406	+	0.570345i	$0.193190\pi$
$811$			4.93459e11i			1.14069i	−0.821406	+	0.570345i	$0.806810\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	4.31687e11	+	2.49235e11i	0.978450	+	0.564908i
$816$		0			0
$817$	5.01553e11	−	2.89572e11i	1.12572	−	0.649932i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	2.37112e11	+	4.10691e11i	0.521893	+	0.903945i	0.999676	+	0.0254672i	$0.00810734\pi$
$821$	2.37112e11	+	4.10691e11i	0.521893	+	0.903945i	−0.477783	+	0.878478i	$0.658559\pi$
$822$		0			0
$823$	1.40210e11	−	2.42851e11i	0.305618	−	0.529347i	−0.671780	−	0.740750i	$-0.734470\pi$
$823$	1.40210e11	−	2.42851e11i	0.305618	−	0.529347i	0.977399	+	0.211404i	$0.0678035\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−6.21966e11			−1.32967			−0.664836	−	0.746989i	$-0.731499\pi$
$827$	−6.21966e11			−1.32967			−0.664836	+	0.746989i	$0.731499\pi$
$828$		0			0
$829$	1.38570e11	+	8.00035e10i	0.293394	+	0.169391i	0.639472	−	0.768815i	$-0.279153\pi$
$829$	1.38570e11	+	8.00035e10i	0.293394	+	0.169391i	−0.346077	+	0.938206i	$0.612487\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	−3.05227e11	−	5.29870e11i	−0.633932	−	1.10050i
$834$		0			0
$835$	−2.16825e11	−	3.75552e11i	−0.446030	−	0.772546i
$836$		0			0
$837$		0			0
$838$		0			0
$839$		−	3.71047e10i		−	0.0748826i	−0.999299	−	0.0374413i	$-0.988079\pi$
$839$		−	3.71047e10i		−	0.0748826i	0.999299	−	0.0374413i	$-0.0119207\pi$
$840$		0			0
$841$	−4.95816e11			−0.991143
$842$		0			0
$843$		0			0
$844$		0			0
$845$	3.30308e11	−	1.90703e11i	0.647877	−	0.374052i
$846$		0			0
$847$	−2.10695e11	+	5.63447e10i	−0.409375	+	0.109476i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	−2.13125e11	+	3.69143e11i	−0.406365	+	0.703845i
$852$		0			0
$853$			2.15873e11i			0.407758i	0.978996	+	0.203879i	$0.0653549\pi$
$853$			2.15873e11i			0.407758i	−0.978996	+	0.203879i	$0.934645\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−5.18905e11	−	2.99590e11i	−0.961977	−	0.555398i	−0.0651960	−	0.997872i	$-0.520767\pi$
$857$	−5.18905e11	−	2.99590e11i	−0.961977	−	0.555398i	−0.896781	+	0.442475i	$0.854101\pi$
$858$		0			0
$859$	1.76726e11	−	1.02033e11i	0.324584	−	0.187399i	−0.328850	−	0.944382i	$-0.606661\pi$
$859$	1.76726e11	−	1.02033e11i	0.324584	−	0.187399i	0.653434	+	0.756984i	$0.273328\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	2.63077e11	+	4.55662e11i	0.474285	+	0.821485i	0.999566	−	0.0294434i	$-0.00937347\pi$
$863$	2.63077e11	+	4.55662e11i	0.474285	+	0.821485i	−0.525282	+	0.850928i	$0.676040\pi$
$864$		0			0
$865$	2.14959e11	−	3.72320e11i	0.383965	−	0.665047i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	−7.56628e11			−1.32679
$870$		0			0
$871$	−1.64118e11	−	9.47538e10i	−0.285157	−	0.164636i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	6.07137e11	+	1.63002e11i	1.03575	+	0.278073i
$876$		0			0
$877$	1.97790e11	+	3.42583e11i	0.334354	+	0.579118i	0.983360	−	0.181665i	$-0.0581486\pi$
$877$	1.97790e11	+	3.42583e11i	0.334354	+	0.579118i	−0.649007	+	0.760783i	$0.724815\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$			1.15955e12i			1.92480i	0.271629	+	0.962402i	$0.412438\pi$
$881$			1.15955e12i			1.92480i	−0.271629	+	0.962402i	$0.587562\pi$
$882$		0			0
$883$	−2.07674e11			−0.341616			−0.170808	−	0.985304i	$-0.554638\pi$
$883$	−2.07674e11			−0.341616			−0.170808	+	0.985304i	$0.554638\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	2.70909e11	−	1.56410e11i	0.437652	−	0.252679i	−0.264949	−	0.964262i	$-0.585355\pi$
$887$	2.70909e11	−	1.56410e11i	0.437652	−	0.252679i	0.702601	+	0.711584i	$0.252022\pi$
$888$		0			0
$889$	1.90804e11	−	7.10695e11i	0.305479	−	1.13783i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	1.05095e10	−	1.82030e10i	0.0165263	−	0.0286244i
$894$		0			0
$895$		−	8.17719e11i		−	1.27442i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	3.13660e10	+	1.81092e10i	0.0480199	+	0.0277243i
$900$		0			0
$901$	−1.26294e12	+	7.29157e11i	−1.91638	+	1.10643i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	1.09996e11	+	1.90518e11i	0.163976	+	0.284015i
$906$		0			0
$907$	−4.22186e11	+	7.31247e11i	−0.623842	+	1.08053i	0.364922	+	0.931038i	$0.381096\pi$
$907$	−4.22186e11	+	7.31247e11i	−0.623842	+	1.08053i	−0.988764	+	0.149487i	$0.952238\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	1.25686e11			0.182480			0.0912398	−	0.995829i	$-0.470917\pi$
$911$	1.25686e11			0.182480			0.0912398	+	0.995829i	$0.470917\pi$
$912$		0			0
$913$	4.44137e11	+	2.56423e11i	0.639196	+	0.369040i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−4.66700e10	−	1.74518e11i	−0.0660025	−	0.246810i
$918$		0			0
$919$	6.38886e11	+	1.10658e12i	0.895697	+	1.55139i	0.832940	+	0.553364i	$0.186656\pi$
$919$	6.38886e11	+	1.10658e12i	0.895697	+	1.55139i	0.0627571	+	0.998029i	$0.480011\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$			4.66192e11i			0.642330i
$924$		0			0
$925$	−7.04545e10			−0.0962370
$926$		0			0
$927$		0			0
$928$		0			0
$929$	−5.39814e11	+	3.11662e11i	−0.724738	+	0.418428i	−0.816494	−	0.577354i	$-0.804085\pi$
$929$	−5.39814e11	+	3.11662e11i	−0.724738	+	0.418428i	0.0917561	+	0.995782i	$0.470752\pi$
$930$		0			0
$931$	−1.09283e12	−	1.07388e9i	−1.45464	−	0.00142941i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	3.30319e11	−	5.72130e11i	0.432203	−	0.748597i
$936$		0			0
$937$			5.70009e11i			0.739474i	0.929136	+	0.369737i	$0.120552\pi$
$937$			5.70009e11i			0.739474i	−0.929136	+	0.369737i	$0.879448\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	6.73718e10	+	3.88971e10i	0.0859250	+	0.0496088i	0.542347	−	0.840155i	$-0.317536\pi$
$941$	6.73718e10	+	3.88971e10i	0.0859250	+	0.0496088i	−0.456422	+	0.889764i	$0.650869\pi$
$942$		0			0
$943$	1.16114e12	−	6.70386e11i	1.46838	−	0.847770i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−4.17821e11	−	7.23688e11i	−0.519506	−	0.899811i	−0.999743	−	0.0226722i	$-0.992783\pi$
$947$	−4.17821e11	−	7.23688e11i	−0.519506	−	0.899811i	0.480237	−	0.877139i	$-0.340551\pi$
$948$		0			0
$949$	−6.17880e11	+	1.07020e12i	−0.761797	+	1.31947i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	−1.20610e12			−1.46222			−0.731110	−	0.682259i	$-0.760998\pi$
$953$	−1.20610e12			−1.46222			−0.731110	+	0.682259i	$0.760998\pi$
$954$		0			0
$955$	4.68947e11	+	2.70747e11i	0.563781	+	0.325499i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	−9.77423e11	−	9.78384e11i	−1.15560	−	1.15674i
$960$		0			0
$961$	−2.78413e11	−	4.82225e11i	−0.326434	−	0.565400i
$962$		0			0
$963$		0			0
$964$		0			0
$965$			5.15016e11i			0.593897i
$966$		0			0
$967$	−5.78416e11			−0.661507			−0.330753	−	0.943717i	$-0.607303\pi$
$967$	−5.78416e11			−0.661507			−0.330753	+	0.943717i	$0.607303\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	−5.31318e11	+	3.06757e11i	−0.597693	+	0.345078i	−0.768133	−	0.640290i	$-0.778814\pi$
$971$	−5.31318e11	+	3.06757e11i	−0.597693	+	0.345078i	0.170441	+	0.985368i	$0.445481\pi$
$972$		0			0
$973$	−1.51090e12	−	4.05639e11i	−1.68571	−	0.452573i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	1.02395e11	−	1.77354e11i	0.112383	−	0.194654i	−0.804347	−	0.594159i	$-0.797485\pi$
$977$	1.02395e11	−	1.77354e11i	0.112383	−	0.194654i	0.916731	+	0.399506i	$0.130818\pi$
$978$		0			0
$979$		−	1.18492e11i		−	0.128991i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	−7.28311e11	−	4.20491e11i	−0.780015	−	0.450342i	0.0564205	−	0.998407i	$-0.482031\pi$
$983$	−7.28311e11	−	4.20491e11i	−0.780015	−	0.450342i	−0.836436	+	0.548065i	$0.815365\pi$
$984$		0			0
$985$	−4.50325e11	+	2.59995e11i	−0.478389	+	0.276198i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	7.07882e11	+	1.22609e12i	0.739904	+	1.28155i
$990$		0			0
$991$	−3.41709e11	+	5.91858e11i	−0.354293	+	0.613653i	−0.986997	−	0.160741i	$-0.948612\pi$
$991$	−3.41709e11	+	5.91858e11i	−0.354293	+	0.613653i	0.632704	+	0.774394i	$0.281945\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	−8.10118e11			−0.826525
$996$		0			0
$997$	1.12565e12	+	6.49894e11i	1.13926	+	0.657751i	0.946247	−	0.323445i	$-0.104841\pi$
$997$	1.12565e12	+	6.49894e11i	1.13926	+	0.657751i	0.193012	+	0.981196i	$0.438174\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	252.9.z.c.73.1		10
3.2	odd	2		28.9.h.a.17.3	yes	10
7.5	odd	6	inner	252.9.z.c.145.1		10
12.11	even	2		112.9.s.b.17.3		10
21.2	odd	6		196.9.h.a.117.3		10
21.5	even	6		28.9.h.a.5.3	✓	10
21.11	odd	6		196.9.b.a.97.6		10
21.17	even	6		196.9.b.a.97.5		10
21.20	even	2		196.9.h.a.129.3		10
84.47	odd	6		112.9.s.b.33.3		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
28.9.h.a.5.3	✓	10	21.5	even	6
28.9.h.a.17.3	yes	10	3.2	odd	2
112.9.s.b.17.3		10	12.11	even	2
112.9.s.b.33.3		10	84.47	odd	6
196.9.b.a.97.5		10	21.17	even	6
196.9.b.a.97.6		10	21.11	odd	6
196.9.h.a.117.3		10	21.2	odd	6
196.9.h.a.129.3		10	21.20	even	2
252.9.z.c.73.1		10	1.1	even	1	trivial
252.9.z.c.145.1		10	7.5	odd	6	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 252 = 2^{2} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 9 \)
Character orbit:	\([\chi]\)	\(=\)	252.z (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-485.304 + 280.190i) q^{5} +(-622.564 + 2318.88i) q^{7} +O(q^{10})\)	\(q+(-485.304 + 280.190i) q^{5} +(-622.564 + 2318.88i) q^{7} +(-5557.02 + 9625.05i) q^{11} -38682.7i q^{13} +(91862.6 + 53036.9i) q^{17} +(164173. - 94785.1i) q^{19} +(231710. + 401333. i) q^{23} +(-38299.1 + 66336.0i) q^{25} +66563.3 q^{29} +(471221. + 272060. i) q^{31} +(-347596. - 1.29980e6i) q^{35} +(459897. + 796564. i) q^{37} -2.89321e6i q^{41} +3.05504e6 q^{43} +(96022.3 - 55438.5i) q^{47} +(-4.98963e6 - 2.88730e6i) q^{49} +(-6.87405e6 + 1.19062e7i) q^{53} -6.22810e6i q^{55} +(-562742. - 324899. i) q^{59} +(-7.64311e6 + 4.41275e6i) q^{61} +(1.08385e7 + 1.87729e7i) q^{65} +(2.44951e6 - 4.24268e6i) q^{67} -1.20517e7 q^{71} +(-2.76661e7 - 1.59730e7i) q^{73} +(-1.88598e7 - 1.88783e7i) q^{77} +(3.40393e7 + 5.89577e7i) q^{79} -4.61439e7i q^{83} -5.94417e7 q^{85} +(-9.23312e6 + 5.33074e6i) q^{89} +(8.97006e7 + 2.40825e7i) q^{91} +(-5.31157e7 + 9.19992e7i) q^{95} +4.77780e7i q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 837 q^{5} + 1526 q^{7}+O(q^{10}) \) 10 * q + 837 * q^5 + 1526 * q^7	\( 10 q + 837 q^{5} + 1526 q^{7} - 3705 q^{11} - 78003 q^{17} - 96741 q^{19} - 208533 q^{23} + 367978 q^{25} - 754764 q^{29} - 1053717 q^{31} + 1306389 q^{35} - 998075 q^{37} + 738292 q^{43} - 710883 q^{47} + 13288114 q^{49} - 10501461 q^{53} + 37089081 q^{59} - 8180481 q^{61} - 21459108 q^{65} + 48020189 q^{67} + 31918236 q^{71} - 133345593 q^{73} - 188477625 q^{77} + 53590181 q^{79} - 157179282 q^{85} + 241368273 q^{89} + 420709128 q^{91} - 347126775 q^{95}+O(q^{100}) \) 10 * q + 837 * q^5 + 1526 * q^7 - 3705 * q^11 - 78003 * q^17 - 96741 * q^19 - 208533 * q^23 + 367978 * q^25 - 754764 * q^29 - 1053717 * q^31 + 1306389 * q^35 - 998075 * q^37 + 738292 * q^43 - 710883 * q^47 + 13288114 * q^49 - 10501461 * q^53 + 37089081 * q^59 - 8180481 * q^61 - 21459108 * q^65 + 48020189 * q^67 + 31918236 * q^71 - 133345593 * q^73 - 188477625 * q^77 + 53590181 * q^79 - 157179282 * q^85 + 241368273 * q^89 + 420709128 * q^91 - 347126775 * q^95

Introduction

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