LMFDB - Embedded newform 144.9.q.b.65.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [144,9,Mod(65,144)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(144, 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("144.65");

S:= CuspForms(chi, 9);

N := Newforms(S);

Level:	$ N $	$=$	$ 144 = 2^{4} \cdot 3^{2} $
Weight:	$ k $	$=$	$ 9 $
Character orbit:	$[\chi]$	$=$	144.q (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$58.6625198488$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 4 x^{15} - 150208 x^{14} - 1927740 x^{13} + 8702363206 x^{12} + 239206241152 x^{11} + \cdots + 81\!\cdots\!61 $ x^16 - 4x^15 - 150208x^14 - 1927740x^13 + 8702363206x^12 + 239206241152x^11 - 241960304158448x^10 - 9458863275320348x^9 + 3259352971808015407x^8 + 150983052056025751536x^7 - 18744835998632687401792x^6 - 866018994869774202180460x^5 + 35643731791394373752805382x^4 + 1485002234815673954960734644x^3 + 16292568366453217677347743656x^2 + 62373298381917691066182105696*x + 81301302751102601946916438161
Coefficient ring:	$\Z[a_1, \ldots, a_{19}]$
Coefficient ring index:	$ 2^{32}\cdot 3^{25} $
Twist minimal:	no (minimal twist has level 18)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			65.5
Root			$220.333 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	144.65
Dual form			144.9.q.b.113.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-7.38176 - 80.6629i) q^{3} +(935.250 - 539.967i) q^{5} +(2056.09 - 3561.25i) q^{7} +(-6452.02 + 1190.87i) q^{9} +(-8419.53 - 4861.02i) q^{11} +(-4116.02 - 7129.16i) q^{13} +(-50459.1 - 71454.1i) q^{15} -87809.9i q^{17} -123643. q^{19} +(-302439. - 139562. i) q^{21} +(-92029.4 + 53133.2i) q^{23} +(387816. - 671717. i) q^{25} +(143686. + 511648. i) q^{27} +(430885. + 248772. i) q^{29} +(577977. + 1.00109e6i) q^{31} +(-329953. + 715027. i) q^{33} -4.44088e6i q^{35} +1.20145e6 q^{37} +(-544675. + 384636. i) q^{39} +(1.53952e6 - 888843. i) q^{41} +(528726. - 915780. i) q^{43} +(-5.39122e6 + 4.59764e6i) q^{45} +(3.80689e6 + 2.19791e6i) q^{47} +(-5.57261e6 - 9.65205e6i) q^{49} +(-7.08301e6 + 648192. i) q^{51} +1.04810e6i q^{53} -1.04991e7 q^{55} +(912700. + 9.97337e6i) q^{57} +(8.70048e6 - 5.02323e6i) q^{59} +(-4.15770e6 + 7.20135e6i) q^{61} +(-9.02495e6 + 2.54258e7i) q^{63} +(-7.69902e6 - 4.44503e6i) q^{65} +(-6.19183e6 - 1.07246e7i) q^{67} +(4.96522e6 + 7.03114e6i) q^{69} +1.69579e7i q^{71} -2.42736e7 q^{73} +(-5.70454e7 - 2.63239e7i) q^{75} +(-3.46226e7 + 1.99894e7i) q^{77} +(-6.39004e6 + 1.10679e7i) q^{79} +(4.02104e7 - 1.53670e7i) q^{81} +(2.79188e7 + 1.61189e7i) q^{83} +(-4.74144e7 - 8.21242e7i) q^{85} +(1.68860e7 - 3.65928e7i) q^{87} +2.10088e7i q^{89} -3.38516e7 q^{91} +(7.64841e7 - 5.40111e7i) q^{93} +(-1.15637e8 + 6.67629e7i) q^{95} +(-4.46651e7 + 7.73622e7i) q^{97} +(6.01118e7 + 2.13368e7i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 126 q^{3} - 882 q^{5} + 1846 q^{7} - 28662 q^{9} - 45756 q^{11} - 3370 q^{13} - 128754 q^{15} - 362180 q^{19} - 299166 q^{21} - 1311138 q^{23} + 963394 q^{25} + 208656 q^{27} - 2851290 q^{29} - 542438 q^{31}+ \cdots - 366888330 q^{99}+O(q^{100}) $ 16 * q - 126 * q^3 - 882 * q^5 + 1846 * q^7 - 28662 * q^9 - 45756 * q^11 - 3370 * q^13 - 128754 * q^15 - 362180 * q^19 - 299166 * q^21 - 1311138 * q^23 + 963394 * q^25 + 208656 * q^27 - 2851290 * q^29 - 542438 * q^31 + 3875796 * q^33 + 3343328 * q^37 + 5896002 * q^39 + 9218592 * q^41 - 339512 * q^43 - 32740578 * q^45 + 34980606 * q^47 - 2364654 * q^49 - 50877810 * q^51 + 4584276 * q^55 - 34049898 * q^57 - 93924216 * q^59 - 841954 * q^61 + 14043234 * q^63 - 126568134 * q^65 - 29946644 * q^67 + 70499610 * q^69 - 7547764 * q^73 - 114494910 * q^75 + 9309294 * q^77 - 33813002 * q^79 - 46018134 * q^81 - 114200226 * q^83 - 125696772 * q^85 + 159599970 * q^87 - 268578316 * q^91 + 120711534 * q^93 + 143949240 * q^95 - 89415484 * q^97 - 366888330 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/144\mathbb{Z}\right)^\times$.

$n$	$37$	$65$	$127$
$\chi(n)$	$1$	$e\left(\frac{1}{6}\right)$	$1$

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
$3$	−7.38176	−	80.6629i	−0.0911329	−	0.995839i
$3$	−7.38176	−	80.6629i	−0.0911329	−	0.995839i
$4$		0			0
$5$	935.250	−	539.967i	1.49640	−	0.863947i	0.496408	−	0.868089i	$-0.334652\pi$
$5$	935.250	−	539.967i	1.49640	−	0.863947i	0.999991	+	0.00414227i	$0.00131853\pi$
$6$		0			0
$7$	2056.09	−	3561.25i	0.856347	−	1.48324i	−0.0190419	−	0.999819i	$-0.506062\pi$
$7$	2056.09	−	3561.25i	0.856347	−	1.48324i	0.875389	−	0.483419i	$-0.160605\pi$
$8$		0			0
$9$	−6452.02	+	1190.87i	−0.983390	+	0.181507i
$10$		0			0
$11$	−8419.53	−	4861.02i	−0.575065	−	0.332014i	0.184105	−	0.982907i	$-0.441061\pi$
$11$	−8419.53	−	4861.02i	−0.575065	−	0.332014i	−0.759170	+	0.650893i	$0.774395\pi$
$12$		0			0
$13$	−4116.02	−	7129.16i	−0.144113	−	0.249612i	0.784928	−	0.619586i	$-0.212700\pi$
$13$	−4116.02	−	7129.16i	−0.144113	−	0.249612i	−0.929042	+	0.369975i	$0.879366\pi$
$14$		0			0
$15$	−50459.1	−	71454.1i	−0.996723	−	1.41144i
$16$		0			0
$17$		−	87809.9i		−	1.05135i	−0.850685	−	0.525676i	$-0.823813\pi$
$17$		−	87809.9i		−	1.05135i	0.850685	−	0.525676i	$-0.176187\pi$
$18$		0			0
$19$	−123643.			−0.948754			−0.474377	−	0.880322i	$-0.657327\pi$
$19$	−123643.			−0.948754			−0.474377	+	0.880322i	$0.657327\pi$
$20$		0			0
$21$	−302439.	−	139562.i	−1.55511	−	0.717612i
$22$		0			0
$23$	−92029.4	+	53133.2i	−0.328863	+	0.189869i	−0.655336	−	0.755337i	$-0.727473\pi$
$23$	−92029.4	+	53133.2i	−0.328863	+	0.189869i	0.326473	+	0.945206i	$0.394140\pi$
$24$		0			0
$25$	387816.	−	671717.i	0.992808	−	1.71959i
$26$		0			0
$27$	143686.	+	511648.i	0.270371	+	0.962756i
$28$		0			0
$29$	430885.	+	248772.i	0.609213	+	0.351729i	0.772657	−	0.634823i	$-0.218927\pi$
$29$	430885.	+	248772.i	0.609213	+	0.351729i	−0.163444	+	0.986553i	$0.552260\pi$
$30$		0			0
$31$	577977.	+	1.00109e6i	0.625841	+	1.08399i	0.988378	+	0.152019i	$0.0485775\pi$
$31$	577977.	+	1.00109e6i	0.625841	+	1.08399i	−0.362536	+	0.931970i	$0.618089\pi$
$32$		0			0
$33$	−329953.	+	715027.i	−0.278225	+	0.602929i
$34$		0			0
$35$		−	4.44088e6i		−	2.95935i
$36$		0			0
$37$	1.20145e6			0.641061			0.320531	−	0.947238i	$-0.396139\pi$
$37$	1.20145e6			0.641061			0.320531	+	0.947238i	$0.396139\pi$
$38$		0			0
$39$	−544675.	+	384636.i	−0.235439	+	0.166261i
$40$		0			0
$41$	1.53952e6	−	888843.i	0.544816	−	0.314550i	−0.202212	−	0.979342i	$-0.564813\pi$
$41$	1.53952e6	−	888843.i	0.544816	−	0.314550i	0.747029	+	0.664792i	$0.231480\pi$
$42$		0			0
$43$	528726.	−	915780.i	0.154652	−	0.267866i	−0.778280	−	0.627917i	$-0.783908\pi$
$43$	528726.	−	915780.i	0.154652	−	0.267866i	0.932932	+	0.360052i	$0.117241\pi$
$44$		0			0
$45$	−5.39122e6	+	4.59764e6i	−1.31473	+	1.12120i
$46$		0			0
$47$	3.80689e6	+	2.19791e6i	0.780151	+	0.450420i	0.836484	−	0.547992i	$-0.184607\pi$
$47$	3.80689e6	+	2.19791e6i	0.780151	+	0.450420i	−0.0563327	+	0.998412i	$0.517941\pi$
$48$		0			0
$49$	−5.57261e6	−	9.65205e6i	−0.966662	−	1.67431i
$50$		0			0
$51$	−7.08301e6	+	648192.i	−1.04698	+	0.0958127i
$52$		0			0
$53$			1.04810e6i			0.132831i	0.997792	+	0.0664157i	$0.0211563\pi$
$53$			1.04810e6i			0.132831i	−0.997792	+	0.0664157i	$0.978844\pi$
$54$		0			0
$55$	−1.04991e7			−1.14737
$56$		0			0
$57$	912700.	+	9.97337e6i	0.0864627	+	0.944806i
$58$		0			0
$59$	8.70048e6	−	5.02323e6i	0.718018	−	0.414548i	−0.0960047	−	0.995381i	$-0.530606\pi$
$59$	8.70048e6	−	5.02323e6i	0.718018	−	0.414548i	0.814023	+	0.580833i	$0.197273\pi$
$60$		0			0
$61$	−4.15770e6	+	7.20135e6i	−0.300285	+	0.520109i	−0.976200	−	0.216870i	$-0.930415\pi$
$61$	−4.15770e6	+	7.20135e6i	−0.300285	+	0.520109i	0.675915	+	0.736979i	$0.263749\pi$
$62$		0			0
$63$	−9.02495e6	+	2.54258e7i	−0.572905	+	1.61403i
$64$		0			0
$65$	−7.69902e6	−	4.44503e6i	−0.431302	−	0.249013i
$66$		0			0
$67$	−6.19183e6	−	1.07246e7i	−0.307270	−	0.532207i	0.670494	−	0.741915i	$-0.266082\pi$
$67$	−6.19183e6	−	1.07246e7i	−0.307270	−	0.532207i	−0.977764	+	0.209708i	$0.932749\pi$
$68$		0			0
$69$	4.96522e6	+	7.03114e6i	0.219049	+	0.310191i
$70$		0			0
$71$			1.69579e7i			0.667328i	0.942692	+	0.333664i	$0.108285\pi$
$71$			1.69579e7i			0.667328i	−0.942692	+	0.333664i	$0.891715\pi$
$72$		0			0
$73$	−2.42736e7			−0.854757			−0.427378	−	0.904073i	$-0.640563\pi$
$73$	−2.42736e7			−0.854757			−0.427378	+	0.904073i	$0.640563\pi$
$74$		0			0
$75$	−5.70454e7	−	2.63239e7i	−1.80292	−	0.831965i
$76$		0			0
$77$	−3.46226e7	+	1.99894e7i	−0.984911	+	0.568639i
$78$		0			0
$79$	−6.39004e6	+	1.10679e7i	−0.164057	+	0.284155i	−0.936320	−	0.351148i	$-0.885791\pi$
$79$	−6.39004e6	+	1.10679e7i	−0.164057	+	0.284155i	0.772263	+	0.635303i	$0.219125\pi$
$80$		0			0
$81$	4.02104e7	−	1.53670e7i	0.934110	−	0.356985i
$82$		0			0
$83$	2.79188e7	+	1.61189e7i	0.588281	+	0.339644i	0.764418	−	0.644722i	$-0.223027\pi$
$83$	2.79188e7	+	1.61189e7i	0.588281	+	0.339644i	−0.176136	+	0.984366i	$0.556360\pi$
$84$		0			0
$85$	−4.74144e7	−	8.21242e7i	−0.908312	−	1.57324i
$86$		0			0
$87$	1.68860e7	−	3.65928e7i	0.294746	−	0.638732i
$88$		0			0
$89$			2.10088e7i			0.334843i	0.985885	+	0.167422i	$0.0535441\pi$
$89$			2.10088e7i			0.334843i	−0.985885	+	0.167422i	$0.946456\pi$
$90$		0			0
$91$	−3.38516e7			−0.493644
$92$		0			0
$93$	7.64841e7	−	5.40111e7i	1.02244	−	0.722024i
$94$		0			0
$95$	−1.15637e8	+	6.67629e7i	−1.41972	+	0.819673i
$96$		0			0
$97$	−4.46651e7	+	7.73622e7i	−0.504523	+	0.873860i	0.495463	+	0.868629i	$0.334998\pi$
$97$	−4.46651e7	+	7.73622e7i	−0.504523	+	0.873860i	−0.999986	+	0.00523116i	$0.998335\pi$
$98$		0			0
$99$	6.01118e7	+	2.13368e7i	0.625776	+	0.222121i
$100$		0			0
$101$	−3.08430e7	−	1.78072e7i	−0.296395	−	0.171124i	0.344427	−	0.938813i	$-0.388073\pi$
$101$	−3.08430e7	−	1.78072e7i	−0.296395	−	0.171124i	−0.640822	+	0.767689i	$0.721406\pi$
$102$		0			0
$103$	4.35300e6	+	7.53962e6i	0.0386759	+	0.0669886i	0.884715	−	0.466132i	$-0.154353\pi$
$103$	4.35300e6	+	7.53962e6i	0.0386759	+	0.0669886i	−0.846040	+	0.533120i	$0.821019\pi$
$104$		0			0
$105$	−3.58215e8	+	3.27815e7i	−2.94704	+	0.269694i
$106$		0			0
$107$		−	2.34341e8i		−	1.78778i	−0.448290	−	0.893888i	$-0.647967\pi$
$107$		−	2.34341e8i		−	1.78778i	0.448290	−	0.893888i	$-0.352033\pi$
$108$		0			0
$109$	2.66492e8			1.88789			0.943947	−	0.330098i	$-0.107082\pi$
$109$	2.66492e8			1.88789			0.943947	+	0.330098i	$0.107082\pi$
$110$		0			0
$111$	−8.86883e6	−	9.69126e7i	−0.0584217	−	0.638393i
$112$		0			0
$113$	−2.47560e8	+	1.42929e8i	−1.51833	+	0.876610i	−0.518565	+	0.855038i	$0.673534\pi$
$113$	−2.47560e8	+	1.42929e8i	−1.51833	+	0.876610i	−0.999767	+	0.0215714i	$0.993133\pi$
$114$		0			0
$115$	−5.73803e7	+	9.93856e7i	−0.328074	+	0.568241i
$116$		0			0
$117$	3.50465e7	+	4.10958e7i	0.187026	+	0.219308i
$118$		0			0
$119$	−3.12713e8	−	1.80545e8i	−1.55940	−	0.900322i
$120$		0			0
$121$	−5.99205e7	−	1.03785e8i	−0.279534	−	0.484166i
$122$		0			0
$123$	−8.30610e7	−	1.17621e8i	−0.362892	−	0.513883i
$124$		0			0
$125$		−	4.15781e8i		−	1.70304i
$126$		0			0
$127$	8.18752e7			0.314730			0.157365	−	0.987541i	$-0.449700\pi$
$127$	8.18752e7			0.314730			0.157365	+	0.987541i	$0.449700\pi$
$128$		0			0
$129$	−7.77724e7	−	3.58885e7i	−0.280845	−	0.129597i
$130$		0			0
$131$	−3.27800e8	+	1.89256e8i	−1.11308	+	0.642634i	−0.939624	−	0.342208i	$-0.888825\pi$
$131$	−3.27800e8	+	1.89256e8i	−1.11308	+	0.642634i	−0.173451	+	0.984843i	$0.555492\pi$
$132$		0			0
$133$	−2.54220e8	+	4.40322e8i	−0.812463	+	1.40723i
$134$		0			0
$135$	4.10656e8	+	4.00933e8i	1.23635	+	1.20708i
$136$		0			0
$137$	8.36881e7	+	4.83174e7i	0.237565	+	0.137158i	0.614057	−	0.789262i	$-0.289537\pi$
$137$	8.36881e7	+	4.83174e7i	0.237565	+	0.137158i	−0.376492	+	0.926420i	$0.622870\pi$
$138$		0			0
$139$	2.13230e8	+	3.69325e8i	0.571200	+	0.989348i	0.996443	+	0.0842686i	$0.0268554\pi$
$139$	2.13230e8	+	3.69325e8i	0.571200	+	0.989348i	−0.425243	+	0.905079i	$0.639811\pi$
$140$		0			0
$141$	1.49188e8	−	3.23299e8i	0.377449	−	0.817953i
$142$		0			0
$143$			8.00322e7i			0.191391i
$144$		0			0
$145$	5.37313e8			1.21550
$146$		0			0
$147$	−7.37427e8	+	5.20752e8i	−1.57925	+	1.11522i
$148$		0			0
$149$	3.73436e8	−	2.15603e8i	0.757653	−	0.437431i	−0.0707992	−	0.997491i	$-0.522555\pi$
$149$	3.73436e8	−	2.15603e8i	0.757653	−	0.437431i	0.828453	+	0.560059i	$0.189222\pi$
$150$		0			0
$151$	4.20280e8	−	7.27947e8i	0.808409	−	1.40021i	−0.105556	−	0.994413i	$-0.533662\pi$
$151$	4.20280e8	−	7.27947e8i	0.808409	−	1.40021i	0.913965	−	0.405793i	$-0.133004\pi$
$152$		0			0
$153$	1.04570e8	+	5.66551e8i	0.190828	+	1.03389i
$154$		0			0
$155$	1.08111e9	+	6.24177e8i	1.87302	+	1.08139i
$156$		0			0
$157$	2.10919e8	+	3.65323e8i	0.347150	+	0.601282i	0.985742	−	0.168264i	$-0.0538160\pi$
$157$	2.10919e8	+	3.65323e8i	0.347150	+	0.601282i	−0.638592	+	0.769546i	$0.720483\pi$
$158$		0			0
$159$	8.45431e7	−	7.73685e6i	0.132279	−	0.0121053i
$160$		0			0
$161$			4.36987e8i			0.650376i
$162$		0			0
$163$	5.50818e8			0.780293			0.390146	−	0.920753i	$-0.372424\pi$
$163$	5.50818e8			0.780293			0.390146	+	0.920753i	$0.372424\pi$
$164$		0			0
$165$	7.75022e7	+	8.46892e8i	0.104563	+	1.14259i
$166$		0			0
$167$	−5.25550e8	+	3.03427e8i	−0.675691	+	0.390111i	−0.798230	−	0.602353i	$-0.794230\pi$
$167$	−5.25550e8	+	3.03427e8i	−0.675691	+	0.390111i	0.122538	+	0.992464i	$0.460897\pi$
$168$		0			0
$169$	3.73982e8	−	6.47756e8i	0.458463	−	0.794081i
$170$		0			0
$171$	7.97744e8	−	1.47242e8i	0.932995	−	0.172206i
$172$		0			0
$173$	−8.26617e8	−	4.77248e8i	−0.922826	−	0.532794i	−0.0382907	−	0.999267i	$-0.512191\pi$
$173$	−8.26617e8	−	4.77248e8i	−0.922826	−	0.532794i	−0.884536	+	0.466473i	$0.845525\pi$
$174$		0			0
$175$	−1.59477e9	−	2.76222e9i	−1.70038	−	2.94514i
$176$		0			0
$177$	−4.69413e8	−	6.64726e8i	−0.478258	−	0.677251i
$178$		0			0
$179$		−	9.44019e8i		−	0.919536i	−0.888039	−	0.459768i	$-0.847933\pi$
$179$		−	9.44019e8i		−	0.919536i	0.888039	−	0.459768i	$-0.152067\pi$
$180$		0			0
$181$	−8.68230e8			−0.808948			−0.404474	−	0.914550i	$-0.632545\pi$
$181$	−8.68230e8			−0.808948			−0.404474	+	0.914550i	$0.632545\pi$
$182$		0			0
$183$	6.11573e8	+	2.82214e8i	0.545311	+	0.251637i
$184$		0			0
$185$	1.12366e9	−	6.48744e8i	0.959284	−	0.553843i
$186$		0			0
$187$	−4.26845e8	+	7.39318e8i	−0.349063	+	0.604595i
$188$		0			0
$189$	2.11754e9	+	5.40291e8i	1.65953	+	0.423429i
$190$		0			0
$191$	6.09956e7	+	3.52159e7i	0.0458316	+	0.0264609i	0.522741	−	0.852492i	$-0.324910\pi$
$191$	6.09956e7	+	3.52159e7i	0.0458316	+	0.0264609i	−0.476909	+	0.878953i	$0.658243\pi$
$192$		0			0
$193$	−1.36871e9	−	2.37068e9i	−0.986467	−	1.70861i	−0.635225	−	0.772327i	$-0.719093\pi$
$193$	−1.36871e9	−	2.37068e9i	−0.986467	−	1.70861i	−0.351242	−	0.936285i	$-0.614241\pi$
$194$		0			0
$195$	−3.01717e8	+	6.53838e8i	−0.208671	+	0.452201i
$196$		0			0
$197$			5.47276e8i			0.363364i	0.983357	+	0.181682i	$0.0581541\pi$
$197$			5.47276e8i			0.363364i	−0.983357	+	0.181682i	$0.941846\pi$
$198$		0			0
$199$	2.66467e9			1.69915			0.849574	−	0.527469i	$-0.176859\pi$
$199$	2.66467e9			1.69915			0.849574	+	0.527469i	$0.176859\pi$
$200$		0			0
$201$	−8.19368e8	+	5.78617e8i	−0.501990	+	0.354493i
$202$		0			0
$203$	1.77188e9	−	1.02299e9i	1.04340	−	0.602405i
$204$		0			0
$205$	9.59891e8	−	1.66258e9i	0.543509	−	0.941385i
$206$		0			0
$207$	5.30501e8	−	4.52411e8i	0.288938	−	0.246406i
$208$		0			0
$209$	1.04101e9	+	6.01029e8i	0.545595	+	0.315000i
$210$		0			0
$211$	9.39137e8	+	1.62663e9i	0.473804	+	0.820653i	0.999550	−	0.0299884i	$-0.00954702\pi$
$211$	9.39137e8	+	1.62663e9i	0.473804	+	0.820653i	−0.525746	+	0.850642i	$0.676214\pi$
$212$		0			0
$213$	1.36788e9	−	1.25179e8i	0.664551	−	0.0608155i
$214$		0			0
$215$		−	1.14198e9i		−	0.534446i
$216$		0			0
$217$	4.75349e9			2.14375
$218$		0			0
$219$	1.79182e8	+	1.95798e9i	0.0778964	+	0.851200i
$220$		0			0
$221$	−6.26011e8	+	3.61427e8i	−0.262430	+	0.151514i
$222$		0			0
$223$	−1.45052e9	+	2.51237e9i	−0.586548	+	1.01593i	0.408132	+	0.912923i	$0.366180\pi$
$223$	−1.45052e9	+	2.51237e9i	−0.586548	+	1.01593i	−0.994680	+	0.103009i	$0.967153\pi$
$224$		0			0
$225$	−1.70227e9	+	4.79577e9i	−0.664198	+	1.87123i
$226$		0			0
$227$	−3.60966e9	−	2.08404e9i	−1.35945	−	0.784877i	−0.369898	−	0.929072i	$-0.620607\pi$
$227$	−3.60966e9	−	2.08404e9i	−1.35945	−	0.784877i	−0.989549	+	0.144195i	$0.953941\pi$
$228$		0			0
$229$	1.80018e9	+	3.11801e9i	0.654599	+	1.13380i	0.981994	+	0.188911i	$0.0604957\pi$
$229$	1.80018e9	+	3.11801e9i	0.654599	+	1.13380i	−0.327396	+	0.944887i	$0.606171\pi$
$230$		0			0
$231$	1.86798e9	+	2.64520e9i	0.656030	+	0.928991i
$232$		0			0
$233$			2.86365e9i			0.971618i	0.874065	+	0.485809i	$0.161475\pi$
$233$			2.86365e9i			0.971618i	−0.874065	+	0.485809i	$0.838525\pi$
$234$		0			0
$235$	4.74719e9			1.55656
$236$		0			0
$237$	9.39937e8	+	4.33739e8i	0.297924	+	0.137479i
$238$		0			0
$239$	−1.21500e9	+	7.01479e8i	−0.372378	+	0.214992i	−0.674497	−	0.738278i	$-0.735639\pi$
$239$	−1.21500e9	+	7.01479e8i	−0.372378	+	0.214992i	0.302119	+	0.953270i	$0.402306\pi$
$240$		0			0
$241$	2.21808e9	−	3.84182e9i	0.657519	−	1.13886i	−0.323737	−	0.946147i	$-0.604939\pi$
$241$	2.21808e9	−	3.84182e9i	0.657519	−	1.13886i	0.981256	−	0.192709i	$-0.0617273\pi$
$242$		0			0
$243$	−1.53637e9	−	3.13005e9i	−0.440627	−	0.897690i
$244$		0			0
$245$	−1.04236e10	−	6.01805e9i	−2.89303	−	1.67029i
$246$		0			0
$247$	5.08916e8	+	8.81468e8i	0.136728	+	0.236820i
$248$		0			0
$249$	1.09411e9	−	2.37100e9i	0.284619	−	0.616786i
$250$		0			0
$251$			2.42084e9i			0.609916i	0.952366	+	0.304958i	$0.0986425\pi$
$251$			2.42084e9i			0.609916i	−0.952366	+	0.304958i	$0.901357\pi$
$252$		0			0
$253$	1.03313e9			0.252157
$254$		0			0
$255$	−6.27438e9	+	4.43081e9i	−1.48392	+	1.04791i
$256$		0			0
$257$	−2.08915e9	+	1.20617e9i	−0.478891	+	0.276488i	−0.719954	−	0.694022i	$-0.755837\pi$
$257$	−2.08915e9	+	1.20617e9i	−0.478891	+	0.276488i	0.241063	+	0.970509i	$0.422504\pi$
$258$		0			0
$259$	2.47029e9	−	4.27867e9i	0.548971	−	0.950846i
$260$		0			0
$261$	−3.07633e9	−	1.09195e9i	−0.662935	−	0.235310i
$262$		0			0
$263$	−5.65030e9	−	3.26220e9i	−1.18100	−	0.681849i	−0.224752	−	0.974416i	$-0.572157\pi$
$263$	−5.65030e9	−	3.26220e9i	−1.18100	−	0.681849i	−0.956245	+	0.292567i	$0.905490\pi$
$264$		0			0
$265$	5.65941e8	+	9.80238e8i	0.114759	+	0.198769i
$266$		0			0
$267$	1.69463e9	−	1.55082e8i	0.333450	−	0.0305152i
$268$		0			0
$269$		−	6.64127e9i		−	1.26836i	−0.773186	−	0.634180i	$-0.781338\pi$
$269$		−	6.64127e9i		−	1.26836i	0.773186	−	0.634180i	$-0.218662\pi$
$270$		0			0
$271$	2.72229e9			0.504728			0.252364	−	0.967632i	$-0.418792\pi$
$271$	2.72229e9			0.504728			0.252364	+	0.967632i	$0.418792\pi$
$272$		0			0
$273$	2.49885e8	+	2.73057e9i	0.0449872	+	0.491590i
$274$		0			0
$275$	−6.53045e9	+	3.77036e9i	−1.14186	+	0.659252i
$276$		0			0
$277$	−5.00946e9	+	8.67663e9i	−0.850886	+	1.47378i	0.0295233	+	0.999564i	$0.490601\pi$
$277$	−5.00946e9	+	8.67663e9i	−0.850886	+	1.47378i	−0.880410	+	0.474214i	$0.842732\pi$
$278$		0			0
$279$	−4.92128e9	−	5.77073e9i	−0.812198	−	0.952388i
$280$		0			0
$281$	−6.83019e9	−	3.94341e9i	−1.09549	−	0.632480i	−0.160456	−	0.987043i	$-0.551296\pi$
$281$	−6.83019e9	−	3.94341e9i	−1.09549	−	0.632480i	−0.935032	+	0.354563i	$0.884630\pi$
$282$		0			0
$283$	−4.86855e8	−	8.43258e8i	−0.0759021	−	0.131466i	0.825576	−	0.564291i	$-0.190850\pi$
$283$	−4.86855e8	−	8.43258e8i	−0.0759021	−	0.131466i	−0.901478	+	0.432824i	$0.857517\pi$
$284$		0			0
$285$	6.23889e9	+	8.83477e9i	0.945645	+	1.33911i
$286$		0			0
$287$		−	7.31016e9i		−	1.07746i
$288$		0			0
$289$	−7.34822e8			−0.105339
$290$		0			0
$291$	6.56997e9	+	3.03175e9i	0.916203	+	0.422787i
$292$		0			0
$293$	−4.59420e9	+	2.65246e9i	−0.623361	+	0.359898i	−0.778176	−	0.628046i	$-0.783855\pi$
$293$	−4.59420e9	+	2.65246e9i	−0.623361	+	0.359898i	0.154815	+	0.987943i	$0.450522\pi$
$294$		0			0
$295$	5.42475e9	−	9.39595e9i	0.716295	−	1.24066i
$296$		0			0
$297$	1.27736e9	−	5.00630e9i	0.164167	−	0.643414i
$298$		0			0
$299$	7.57590e8	+	4.37395e8i	0.0947871	+	0.0547254i
$300$		0			0
$301$	−2.17422e9	−	3.76585e9i	−0.264872	−	0.458772i
$302$		0			0
$303$	−1.20871e9	+	2.61933e9i	−0.143400	+	0.310756i
$304$		0			0
$305$			8.98008e9i			1.03772i
$306$		0			0
$307$	−1.34241e10			−1.51124			−0.755618	−	0.655013i	$-0.772663\pi$
$307$	−1.34241e10			−1.51124			−0.755618	+	0.655013i	$0.772663\pi$
$308$		0			0
$309$	5.76035e8	−	4.06782e8i	0.0631852	−	0.0446198i
$310$		0			0
$311$	−1.98291e9	+	1.14483e9i	−0.211964	+	0.122377i	−0.602224	−	0.798327i	$-0.705718\pi$
$311$	−1.98291e9	+	1.14483e9i	−0.211964	+	0.122377i	0.390260	+	0.920705i	$0.372385\pi$
$312$		0			0
$313$	8.94161e9	−	1.54873e10i	0.931619	−	1.61361i	0.151065	−	0.988524i	$-0.451730\pi$
$313$	8.94161e9	−	1.54873e10i	0.931619	−	1.61361i	0.780555	−	0.625088i	$-0.214937\pi$
$314$		0			0
$315$	5.28851e9	+	2.86527e10i	0.537144	+	2.91020i
$316$		0			0
$317$	5.77404e9	+	3.33364e9i	0.571798	+	0.330128i	0.757867	−	0.652409i	$-0.226242\pi$
$317$	5.77404e9	+	3.33364e9i	0.571798	+	0.330128i	−0.186069	+	0.982537i	$0.559575\pi$
$318$		0			0
$319$	−2.41856e9	−	4.18908e9i	−0.233558	−	0.404535i
$320$		0			0
$321$	−1.89026e10	+	1.72985e9i	−1.78034	+	0.162925i
$322$		0			0
$323$			1.08570e10i			0.997474i
$324$		0			0
$325$	−6.38503e9			−0.572308
$326$		0			0
$327$	−1.96718e9	−	2.14960e10i	−0.172049	−	1.88004i
$328$		0			0
$329$	1.56546e10	−	9.03820e9i	1.33616	−	0.771433i
$330$		0			0
$331$	7.84292e9	−	1.35843e10i	0.653380	−	1.13169i	−0.328918	−	0.944359i	$-0.606684\pi$
$331$	7.84292e9	−	1.35843e10i	0.653380	−	1.13169i	0.982297	−	0.187328i	$-0.0599828\pi$
$332$		0			0
$333$	−7.75179e9	+	1.43077e9i	−0.630413	+	0.116357i
$334$		0			0
$335$	−1.15818e10	−	6.68676e9i	−0.919597	−	0.530929i
$336$		0			0
$337$	−1.29188e9	−	2.23761e9i	−0.100162	−	0.173486i	0.811589	−	0.584229i	$-0.198603\pi$
$337$	−1.29188e9	−	2.23761e9i	−0.100162	−	0.173486i	−0.911751	+	0.410743i	$0.865270\pi$
$338$		0			0
$339$	1.33565e10	+	1.89139e10i	1.01133	+	1.43213i
$340$		0			0
$341$		−	1.12382e10i		−	0.831152i
$342$		0			0
$343$	−2.21253e10			−1.59850
$344$		0			0
$345$	8.44030e9	+	3.89482e9i	0.595774	+	0.274923i
$346$		0			0
$347$	−1.45626e10	+	8.40775e9i	−1.00444	+	0.579912i	−0.909558	−	0.415577i	$-0.863580\pi$
$347$	−1.45626e10	+	8.40775e9i	−1.00444	+	0.579912i	−0.0948784	+	0.995489i	$0.530246\pi$
$348$		0			0
$349$	1.22366e10	−	2.11945e10i	0.824822	−	1.42863i	−0.0772336	−	0.997013i	$-0.524609\pi$
$349$	1.22366e10	−	2.11945e10i	0.824822	−	1.42863i	0.902055	−	0.431620i	$-0.142058\pi$
$350$		0			0
$351$	3.05620e9	−	3.13032e9i	0.201351	−	0.206234i
$352$		0			0
$353$	−9.05088e9	−	5.22553e9i	−0.582897	−	0.336536i	0.179387	−	0.983779i	$-0.442589\pi$
$353$	−9.05088e9	−	5.22553e9i	−0.582897	−	0.336536i	−0.762284	+	0.647243i	$0.775922\pi$
$354$		0			0
$355$	9.15672e9	+	1.58599e10i	0.576536	+	0.998590i
$356$		0			0
$357$	−1.22549e10	+	2.65571e10i	−0.754463	+	1.63496i
$358$		0			0
$359$		−	2.37497e10i		−	1.42982i	−0.699219	−	0.714908i	$-0.746469\pi$
$359$		−	2.37497e10i		−	1.42982i	0.699219	−	0.714908i	$-0.253531\pi$
$360$		0			0
$361$	−1.69607e9			−0.0998656
$362$		0			0
$363$	−7.92931e9	+	5.59948e9i	−0.456677	+	0.322494i
$364$		0			0
$365$	−2.27019e10	+	1.31069e10i	−1.27906	+	0.738464i
$366$		0			0
$367$	5.17433e9	−	8.96220e9i	0.285226	−	0.494027i	−0.687438	−	0.726243i	$-0.741265\pi$
$367$	5.17433e9	−	8.96220e9i	0.285226	−	0.494027i	0.972664	+	0.232217i	$0.0745979\pi$
$368$		0			0
$369$	−8.87452e9	+	7.56820e9i	−0.478674	+	0.408213i
$370$		0			0
$371$	3.73256e9	+	2.15499e9i	0.197020	+	0.113750i
$372$		0			0
$373$	4.02672e9	+	6.97448e9i	0.208025	+	0.360310i	0.951092	−	0.308907i	$-0.0999631\pi$
$373$	4.02672e9	+	6.97448e9i	0.208025	+	0.360310i	−0.743067	+	0.669217i	$0.766630\pi$
$374$		0			0
$375$	−3.35382e10	+	3.06920e9i	−1.69595	+	0.155203i
$376$		0			0
$377$		−	4.09580e9i		−	0.202756i
$378$		0			0
$379$	2.63218e10			1.27573			0.637864	−	0.770149i	$-0.279818\pi$
$379$	2.63218e10			1.27573			0.637864	+	0.770149i	$0.279818\pi$
$380$		0			0
$381$	−6.04383e8	−	6.60429e9i	−0.0286822	−	0.313420i
$382$		0			0
$383$	2.64941e10	−	1.52964e10i	1.23127	−	0.710876i	0.263978	−	0.964529i	$-0.414965\pi$
$383$	2.64941e10	−	1.52964e10i	1.23127	−	0.710876i	0.967295	+	0.253653i	$0.0816321\pi$
$384$		0			0
$385$	−2.15872e10	+	3.73901e10i	−0.982547	+	1.70182i
$386$		0			0
$387$	−2.32077e9	+	6.53827e9i	−0.103464	+	0.291487i
$388$		0			0
$389$	3.76791e10	+	2.17540e10i	1.64552	+	0.950039i	0.978824	+	0.204704i	$0.0656233\pi$
$389$	3.76791e10	+	2.17540e10i	1.64552	+	0.950039i	0.666691	+	0.745334i	$0.267710\pi$
$390$		0			0
$391$	4.66562e9	+	8.08109e9i	0.199619	+	0.345751i
$392$		0			0
$393$	1.76857e10	+	2.50443e10i	0.741398	+	1.04988i
$394$		0			0
$395$			1.38016e10i			0.566947i
$396$		0			0
$397$	4.31419e10			1.73675			0.868375	−	0.495908i	$-0.165165\pi$
$397$	4.31419e10			1.73675			0.868375	+	0.495908i	$0.165165\pi$
$398$		0			0
$399$	3.73943e10	+	1.72558e10i	1.47541	+	0.680838i
$400$		0			0
$401$	−1.57455e10	+	9.09069e9i	−0.608948	+	0.351576i	−0.772554	−	0.634950i	$-0.781021\pi$
$401$	−1.57455e10	+	9.09069e9i	−0.608948	+	0.351576i	0.163606	+	0.986526i	$0.447688\pi$
$402$		0			0
$403$	4.75794e9	−	8.24099e9i	0.180384	−	0.312434i
$404$		0			0
$405$	2.93091e10	−	3.60843e10i	1.08939	−	1.34121i
$406$		0			0
$407$	−1.01157e10	−	5.84028e9i	−0.368652	−	0.212841i
$408$		0			0
$409$	3.23724e9	+	5.60707e9i	0.115686	+	0.200374i	0.918054	−	0.396456i	$-0.129760\pi$
$409$	3.23724e9	+	5.60707e9i	0.115686	+	0.200374i	−0.802368	+	0.596830i	$0.796427\pi$
$410$		0			0
$411$	3.27965e9	−	7.10720e9i	0.114937	−	0.249076i
$412$		0			0
$413$		−	4.13128e10i		−	1.41999i
$414$		0			0
$415$	3.48148e10			1.17374
$416$		0			0
$417$	2.82168e10	−	1.99260e10i	0.933176	−	0.658985i
$418$		0			0
$419$	3.28096e10	−	1.89427e10i	1.06450	−	0.614589i	0.137826	−	0.990456i	$-0.455989\pi$
$419$	3.28096e10	−	1.89427e10i	1.06450	−	0.614589i	0.926673	+	0.375868i	$0.122655\pi$
$420$		0			0
$421$	2.38781e10	−	4.13581e10i	0.760102	−	1.31654i	−0.182696	−	0.983170i	$-0.558482\pi$
$421$	2.38781e10	−	4.13581e10i	0.760102	−	1.31654i	0.942798	−	0.333366i	$-0.108184\pi$
$422$		0			0
$423$	−2.71795e10	−	9.64744e9i	−0.848947	−	0.301336i
$424$		0			0
$425$	−5.89834e10	−	3.40541e10i	−1.80790	−	1.04379i
$426$		0			0
$427$	1.70972e10	+	2.96133e10i	0.514297	+	0.890789i
$428$		0			0
$429$	6.45563e9	−	5.90779e8i	0.190594	−	0.0174420i
$430$		0			0
$431$			2.73395e10i			0.792285i	0.918189	+	0.396143i	$0.129651\pi$
$431$			2.73395e10i			0.792285i	−0.918189	+	0.396143i	$0.870349\pi$
$432$		0			0
$433$	−6.96958e9			−0.198269			−0.0991345	−	0.995074i	$-0.531607\pi$
$433$	−6.96958e9			−0.198269			−0.0991345	+	0.995074i	$0.531607\pi$
$434$		0			0
$435$	−3.96632e9	−	4.33413e10i	−0.110772	−	1.21044i
$436$		0			0
$437$	1.13788e10	−	6.56953e9i	0.312010	−	0.180139i
$438$		0			0
$439$	−4.26214e9	+	7.38223e9i	−0.114754	+	0.198760i	−0.917682	−	0.397317i	$-0.869941\pi$
$439$	−4.26214e9	+	7.38223e9i	−0.114754	+	0.198760i	0.802927	+	0.596077i	$0.203275\pi$
$440$		0			0
$441$	4.74489e10	+	5.56389e10i	1.25450	+	1.47104i
$442$		0			0
$443$	1.77214e10	+	1.02315e10i	0.460134	+	0.265658i	0.712101	−	0.702077i	$-0.247744\pi$
$443$	1.77214e10	+	1.02315e10i	0.460134	+	0.265658i	−0.251967	+	0.967736i	$0.581077\pi$
$444$		0			0
$445$	1.13441e10	+	1.96485e10i	0.289287	+	0.501060i
$446$		0			0
$447$	−2.01478e10	−	2.85309e10i	−0.504658	−	0.714636i
$448$		0			0
$449$			1.52992e10i			0.376430i	0.982128	+	0.188215i	$0.0602702\pi$
$449$			1.52992e10i			0.376430i	−0.982128	+	0.188215i	$0.939730\pi$
$450$		0			0
$451$	−1.72827e10			−0.417740
$452$		0			0
$453$	−6.18207e10	−	2.85275e10i	−1.46805	−	0.677440i
$454$		0			0
$455$	−3.16597e10	+	1.82788e10i	−0.738689	+	0.426483i
$456$		0			0
$457$	−1.20106e10	+	2.08029e10i	−0.275359	+	0.476935i	−0.970226	−	0.242203i	$-0.922130\pi$
$457$	−1.20106e10	+	2.08029e10i	−0.275359	+	0.476935i	0.694867	+	0.719138i	$0.255463\pi$
$458$		0			0
$459$	4.49278e10	−	1.26171e10i	1.01219	−	0.284255i
$460$		0			0
$461$	4.96796e10	+	2.86825e10i	1.09995	+	0.635058i	0.936209	−	0.351445i	$-0.114310\pi$
$461$	4.96796e10	+	2.86825e10i	1.09995	+	0.635058i	0.163744	+	0.986503i	$0.447643\pi$
$462$		0			0
$463$	−3.03202e10	−	5.25162e10i	−0.659795	−	1.14280i	−0.980669	−	0.195676i	$-0.937310\pi$
$463$	−3.03202e10	−	5.25162e10i	−0.659795	−	1.14280i	0.320874	−	0.947122i	$-0.396023\pi$
$464$		0			0
$465$	4.23675e10	−	9.18128e10i	0.906194	−	1.96377i
$466$		0			0
$467$		−	1.01091e10i		−	0.212543i	−0.994337	−	0.106271i	$-0.966109\pi$
$467$		−	1.01091e10i		−	0.212543i	0.994337	−	0.106271i	$-0.0338912\pi$
$468$		0			0
$469$	−5.09238e10			−1.05252
$470$		0			0
$471$	2.79111e10	−	1.97101e10i	0.567143	−	0.400502i
$472$		0			0
$473$	−8.90324e9	+	5.14029e9i	−0.177870	+	0.102693i
$474$		0			0
$475$	−4.79505e10	+	8.30528e10i	−0.941931	+	1.63147i
$476$		0			0
$477$	−1.24815e9	−	6.76238e9i	−0.0241099	−	0.130625i
$478$		0			0
$479$	−1.87971e10	−	1.08525e10i	−0.357067	−	0.206153i	0.310727	−	0.950499i	$-0.399428\pi$
$479$	−1.87971e10	−	1.08525e10i	−0.357067	−	0.206153i	−0.667793	+	0.744347i	$0.732761\pi$
$480$		0			0
$481$	−4.94520e9	−	8.56534e9i	−0.0923855	−	0.160016i
$482$		0			0
$483$	3.52486e10	−	3.22573e9i	0.647670	−	0.0592706i
$484$		0			0
$485$			9.64707e10i			1.74353i
$486$		0			0
$487$	5.82792e9			0.103609			0.0518045	−	0.998657i	$-0.483503\pi$
$487$	5.82792e9			0.103609			0.0518045	+	0.998657i	$0.483503\pi$
$488$		0			0
$489$	−4.06601e9	−	4.44306e10i	−0.0711103	−	0.777046i
$490$		0			0
$491$	2.15718e10	−	1.24545e10i	0.371159	−	0.214288i	−0.302806	−	0.953052i	$-0.597923\pi$
$491$	2.15718e10	−	1.24545e10i	0.371159	−	0.214288i	0.673964	+	0.738764i	$0.264590\pi$
$492$		0			0
$493$	2.18446e10	−	3.78360e10i	0.369791	−	0.640497i
$494$		0			0
$495$	6.77407e10	−	1.25031e10i	1.12831	−	0.208256i
$496$		0			0
$497$	6.03915e10	+	3.48670e10i	0.989806	+	0.571465i
$498$		0			0
$499$	8.19755e9	+	1.41986e10i	0.132215	+	0.229004i	0.924530	−	0.381109i	$-0.124458\pi$
$499$	8.19755e9	+	1.41986e10i	0.132215	+	0.229004i	−0.792315	+	0.610112i	$0.791124\pi$
$500$		0			0
$501$	2.83548e10	+	4.01526e10i	0.450065	+	0.637328i
$502$		0			0
$503$			4.61285e10i			0.720606i	0.932835	+	0.360303i	$0.117327\pi$
$503$			4.61285e10i			0.720606i	−0.932835	+	0.360303i	$0.882673\pi$
$504$		0			0
$505$	−3.84612e10			−0.591367
$506$		0			0
$507$	−5.50105e10	−	2.53849e10i	−0.832557	−	0.384188i
$508$		0			0
$509$	−6.69443e9	+	3.86503e9i	−0.0997339	+	0.0575814i	−0.549037	−	0.835798i	$-0.685006\pi$
$509$	−6.69443e9	+	3.86503e9i	−0.0997339	+	0.0575814i	0.449303	+	0.893379i	$0.351672\pi$
$510$		0			0
$511$	−4.99087e10	+	8.64444e10i	−0.731969	+	1.26781i
$512$		0			0
$513$	−1.77657e10	−	6.32615e10i	−0.256516	−	0.913419i
$514$		0			0
$515$	8.14229e9	+	4.70095e9i	0.115749	+	0.0668278i
$516$		0			0
$517$	−2.13681e10	−	3.70107e10i	−0.299092	−	0.518042i
$518$		0			0
$519$	−3.23943e10	+	7.02003e10i	−0.446477	+	0.967541i
$520$		0			0
$521$			3.97902e10i			0.540039i	0.962855	+	0.270019i	$0.0870301\pi$
$521$			3.97902e10i			0.540039i	−0.962855	+	0.270019i	$0.912970\pi$
$522$		0			0
$523$	3.49978e10			0.467772			0.233886	−	0.972264i	$-0.424856\pi$
$523$	3.49978e10			0.467772			0.233886	+	0.972264i	$0.424856\pi$
$524$		0			0
$525$	−2.11037e11	+	1.49029e11i	−2.77792	+	1.96170i
$526$		0			0
$527$	8.79053e10	−	5.07521e10i	1.13965	−	0.657979i
$528$		0			0
$529$	−3.35092e10	+	5.80397e10i	−0.427899	+	0.741143i
$530$		0			0
$531$	−5.01537e10	+	4.27711e10i	−0.630848	+	0.537988i
$532$		0			0
$533$	−1.26734e10	−	7.31699e9i	−0.157031	−	0.0906617i
$534$		0			0
$535$	−1.26536e11	−	2.19167e11i	−1.54454	−	2.67523i
$536$		0			0
$537$	−7.61474e10	+	6.96853e9i	−0.915709	+	0.0838000i
$538$		0			0
$539$			1.08354e11i			1.28378i
$540$		0			0
$541$	2.34001e10			0.273168			0.136584	−	0.990629i	$-0.456388\pi$
$541$	2.34001e10			0.273168			0.136584	+	0.990629i	$0.456388\pi$
$542$		0			0
$543$	6.40907e9	+	7.00340e10i	0.0737218	+	0.805582i
$544$		0			0
$545$	2.49236e11	−	1.43897e11i	2.82504	−	1.63104i
$546$		0			0
$547$	1.16091e10	−	2.01075e10i	0.129673	−	0.224600i	−0.793877	−	0.608078i	$-0.791941\pi$
$547$	1.16091e10	−	2.01075e10i	0.129673	−	0.224600i	0.923550	+	0.383478i	$0.125274\pi$
$548$		0			0
$549$	1.82497e10	−	5.14145e10i	0.200894	−	0.565974i
$550$		0			0
$551$	−5.32757e10	−	3.07588e10i	−0.577994	−	0.333705i
$552$		0			0
$553$	2.62770e10	+	4.55131e10i	0.280980	+	0.486671i
$554$		0			0
$555$	−6.06242e10	−	8.58486e10i	−0.638960	−	0.904819i
$556$		0			0
$557$		−	3.65617e10i		−	0.379844i	−0.981799	−	0.189922i	$-0.939176\pi$
$557$		−	3.65617e10i		−	0.379844i	0.981799	−	0.189922i	$-0.0608236\pi$
$558$		0			0
$559$	−8.70499e9			−0.0891499
$560$		0			0
$561$	6.27864e10	+	2.89731e10i	0.633891	+	0.292512i
$562$		0			0
$563$	1.15433e11	−	6.66450e10i	1.14893	−	0.663337i	0.200306	−	0.979733i	$-0.435806\pi$
$563$	1.15433e11	−	6.66450e10i	1.14893	−	0.663337i	0.948627	+	0.316397i	$0.102473\pi$
$564$		0			0
$565$	−1.54354e11	+	2.67348e11i	−1.51469	+	2.62352i
$566$		0			0
$567$	2.79503e10	−	1.74795e11i	0.270430	−	1.69121i
$568$		0			0
$569$	−1.42643e11	−	8.23549e10i	−1.36082	−	0.785670i	−0.371087	−	0.928598i	$-0.621015\pi$
$569$	−1.42643e11	−	8.23549e10i	−1.36082	−	0.785670i	−0.989733	+	0.142928i	$0.954348\pi$
$570$		0			0
$571$	6.84597e10	+	1.18576e11i	0.644007	+	1.11545i	0.984530	+	0.175216i	$0.0560625\pi$
$571$	6.84597e10	+	1.18576e11i	0.644007	+	1.11545i	−0.340523	+	0.940236i	$0.610604\pi$
$572$		0			0
$573$	2.39036e9	−	5.18004e9i	0.0221740	−	0.0480524i
$574$		0			0
$575$			8.24235e10i			0.754015i
$576$		0			0
$577$	−1.01555e11			−0.916218			−0.458109	−	0.888896i	$-0.651473\pi$
$577$	−1.01555e11			−0.916218			−0.458109	+	0.888896i	$0.651473\pi$
$578$		0			0
$579$	−1.81122e11	+	1.27904e11i	−1.61160	+	1.13807i
$580$		0			0
$581$	1.14807e11	−	6.62840e10i	1.00755	−	0.581707i
$582$		0			0
$583$	5.09485e9	−	8.82453e9i	0.0441018	−	0.0763866i
$584$		0			0
$585$	5.49677e10	+	1.95109e10i	0.469336	+	0.166592i
$586$		0			0
$587$	3.25669e10	+	1.88025e10i	0.274299	+	0.158367i	0.630840	−	0.775913i	$-0.282711\pi$
$587$	3.25669e10	+	1.88025e10i	0.274299	+	0.158367i	−0.356541	+	0.934280i	$0.616044\pi$
$588$		0			0
$589$	−7.14626e10	−	1.23777e11i	−0.593769	−	1.02844i
$590$		0			0
$591$	4.41449e10	−	4.03986e9i	0.361852	−	0.0331144i
$592$		0			0
$593$			1.30215e11i			1.05304i	0.850163	+	0.526519i	$0.176503\pi$
$593$			1.30215e11i			1.05304i	−0.850163	+	0.526519i	$0.823497\pi$
$594$		0			0
$595$	−3.89953e11			−3.11132
$596$		0			0
$597$	−1.96700e10	−	2.14940e11i	−0.154848	−	1.69208i
$598$		0			0
$599$	−1.13848e11	+	6.57304e10i	−0.884341	+	0.510575i	−0.872087	−	0.489350i	$-0.837234\pi$
$599$	−1.13848e11	+	6.57304e10i	−0.884341	+	0.510575i	−0.0122537	+	0.999925i	$0.503901\pi$
$600$		0			0
$601$	2.15092e10	−	3.72550e10i	0.164864	−	0.285553i	−0.771743	−	0.635935i	$-0.780615\pi$
$601$	2.15092e10	−	3.72550e10i	0.164864	−	0.285553i	0.936607	+	0.350382i	$0.113948\pi$
$602$		0			0
$603$	5.27213e10	+	6.18214e10i	0.398765	+	0.467595i
$604$		0			0
$605$	−1.12081e11	−	6.47102e10i	−0.836588	−	0.483004i
$606$		0			0
$607$	1.29606e10	+	2.24485e10i	0.0954710	+	0.165361i	0.909805	−	0.415036i	$-0.136231\pi$
$607$	1.29606e10	+	2.24485e10i	0.0954710	+	0.165361i	−0.814334	+	0.580396i	$0.802898\pi$
$608$		0			0
$609$	−9.55972e10	−	1.35373e11i	−0.694986	−	0.984156i
$610$		0			0
$611$		−	3.61866e10i		−	0.259646i
$612$		0			0
$613$	1.28485e11			0.909933			0.454967	−	0.890508i	$-0.349651\pi$
$613$	1.28485e11			0.909933			0.454967	+	0.890508i	$0.349651\pi$
$614$		0			0
$615$	−1.41194e11	−	6.51549e10i	−0.986999	−	0.455456i
$616$		0			0
$617$	−1.02289e11	+	5.90563e10i	−0.705808	+	0.407498i	−0.809507	−	0.587110i	$-0.800265\pi$
$617$	−1.02289e11	+	5.90563e10i	−0.705808	+	0.407498i	0.103699	+	0.994609i	$0.466932\pi$
$618$		0			0
$619$	6.40218e10	−	1.10889e11i	0.436079	−	0.755312i	−0.561304	−	0.827610i	$-0.689700\pi$
$619$	6.40218e10	−	1.10889e11i	0.436079	−	0.755312i	0.997383	+	0.0722982i	$0.0230333\pi$
$620$		0			0
$621$	−4.04089e10	−	3.94521e10i	−0.271713	−	0.265280i
$622$		0			0
$623$	7.48177e10	+	4.31960e10i	0.496652	+	0.286742i
$624$		0			0
$625$	−7.30176e10	−	1.26470e11i	−0.478528	−	0.828835i
$626$		0			0
$627$	4.07962e10	−	8.84077e10i	0.263967	−	0.572032i
$628$		0			0
$629$		−	1.05499e11i		−	0.673980i
$630$		0			0
$631$	2.40613e11			1.51775			0.758877	−	0.651233i	$-0.225748\pi$
$631$	2.40613e11			1.51775			0.758877	+	0.651233i	$0.225748\pi$
$632$		0			0
$633$	1.24277e11	−	8.77610e10i	0.774059	−	0.546621i
$634$		0			0
$635$	7.65738e10	−	4.42099e10i	0.470961	−	0.271910i
$636$		0			0
$637$	−4.58740e10	+	7.94561e10i	−0.278618	+	0.482580i
$638$		0			0
$639$	−2.01947e10	−	1.09413e11i	−0.121125	−	0.656244i
$640$		0			0
$641$	1.87111e11	+	1.08029e11i	1.10833	+	0.639893i	0.938396	−	0.345563i	$-0.112312\pi$
$641$	1.87111e11	+	1.08029e11i	1.10833	+	0.639893i	0.169932	+	0.985456i	$0.445645\pi$
$642$		0			0
$643$	1.85669e10	+	3.21588e10i	0.108616	+	0.188129i	0.915210	−	0.402977i	$-0.132025\pi$
$643$	1.85669e10	+	3.21588e10i	0.108616	+	0.188129i	−0.806594	+	0.591106i	$0.798691\pi$
$644$		0			0
$645$	−9.21153e10	+	8.42981e9i	−0.532222	+	0.0487056i
$646$		0			0
$647$		−	5.88598e10i		−	0.335894i	−0.985796	−	0.167947i	$-0.946286\pi$
$647$		−	5.88598e10i		−	0.335894i	0.985796	−	0.167947i	$-0.0537137\pi$
$648$		0			0
$649$	−9.76719e10			−0.550543
$650$		0			0
$651$	−3.50892e10	−	3.83431e11i	−0.195366	−	2.13483i
$652$		0			0
$653$	−1.48938e11	+	8.59893e10i	−0.819129	+	0.472925i	−0.850116	−	0.526595i	$-0.823468\pi$
$653$	−1.48938e11	+	8.59893e10i	−0.819129	+	0.472925i	0.0309867	+	0.999520i	$0.490135\pi$
$654$		0			0
$655$	−2.04384e11	+	3.54003e11i	−1.11040	+	1.92328i
$656$		0			0
$657$	1.56614e11	−	2.89067e10i	0.840559	−	0.155145i
$658$		0			0
$659$	−2.34850e11	−	1.35591e11i	−1.24523	−	0.718934i	−0.275075	−	0.961423i	$-0.588703\pi$
$659$	−2.34850e11	−	1.35591e11i	−1.24523	−	0.718934i	−0.970154	+	0.242489i	$0.922036\pi$
$660$		0			0
$661$	1.21597e11	+	2.10613e11i	0.636968	+	1.10326i	0.986095	+	0.166185i	$0.0531451\pi$
$661$	1.21597e11	+	2.10613e11i	0.636968	+	1.10326i	−0.349126	+	0.937076i	$0.613522\pi$
$662$		0			0
$663$	3.37749e10	+	4.78279e10i	0.174799	+	0.247530i
$664$		0			0
$665$			5.49082e11i			2.80770i
$666$		0			0
$667$	−5.28721e10			−0.267130
$668$		0			0
$669$	2.13363e11	+	9.84574e10i	1.06516	+	0.491523i
$670$		0			0
$671$	7.00118e10	−	4.04213e10i	0.345367	−	0.199398i
$672$		0			0
$673$	1.44609e10	−	2.50471e10i	0.0704914	−	0.122095i	−0.828625	−	0.559804i	$-0.810877\pi$
$673$	1.44609e10	−	2.50471e10i	0.0704914	−	0.122095i	0.899117	+	0.437709i	$0.144210\pi$
$674$		0			0
$675$	3.99406e11	+	1.01909e11i	1.92398	+	0.490904i
$676$		0			0
$677$	1.58076e11	+	9.12654e10i	0.752509	+	0.434462i	0.826600	−	0.562790i	$-0.190272\pi$
$677$	1.58076e11	+	9.12654e10i	0.752509	+	0.434462i	−0.0740905	+	0.997252i	$0.523605\pi$
$678$		0			0
$679$	1.83671e11	+	3.18127e11i	0.864095	+	1.49666i
$680$		0			0
$681$	−1.41459e11	+	3.06549e11i	−0.657721	+	1.42532i
$682$		0			0
$683$			3.71514e11i			1.70723i	0.520903	+	0.853616i	$0.325595\pi$
$683$			3.71514e11i			1.70723i	−0.520903	+	0.853616i	$0.674405\pi$
$684$		0			0
$685$	1.04359e11			0.473989
$686$		0			0
$687$	2.38219e11	−	1.68225e11i	1.06942	−	0.755201i
$688$		0			0
$689$	7.47209e9	−	4.31401e9i	0.0331562	−	0.0191428i
$690$		0			0
$691$	9.88238e10	−	1.71168e11i	0.433460	−	0.750775i	−0.563708	−	0.825974i	$-0.690626\pi$
$691$	9.88238e10	−	1.71168e11i	0.433460	−	0.750775i	0.997169	+	0.0751987i	$0.0239591\pi$
$692$		0			0
$693$	1.99581e11	−	1.70203e11i	0.865339	−	0.737962i
$694$		0			0
$695$	3.98846e11	+	2.30274e11i	1.70949	+	0.986973i
$696$		0			0
$697$	−7.80492e10	−	1.35185e11i	−0.330702	−	0.572793i
$698$		0			0
$699$	2.30990e11	−	2.11388e10i	0.967575	−	0.0885464i
$700$		0			0
$701$		−	6.70096e10i		−	0.277501i	−0.990327	−	0.138751i	$-0.955691\pi$
$701$		−	6.70096e10i		−	0.277501i	0.990327	−	0.138751i	$-0.0443087\pi$
$702$		0			0
$703$	−1.48551e11			−0.608209
$704$		0			0
$705$	−3.50426e10	−	3.82922e11i	−0.141854	−	1.55008i
$706$		0			0
$707$	−1.26832e11	+	7.32264e10i	−0.507634	+	0.293083i
$708$		0			0
$709$	5.70291e10	−	9.87774e10i	0.225690	−	0.390906i	−0.730836	−	0.682553i	$-0.760870\pi$
$709$	5.70291e10	−	9.87774e10i	0.225690	−	0.390906i	0.956526	+	0.291647i	$0.0942031\pi$
$710$		0			0
$711$	2.80483e10	−	7.90198e10i	0.109756	−	0.309213i
$712$		0			0
$713$	−1.06382e11	−	6.14196e10i	−0.411632	−	0.237656i
$714$		0			0
$715$	4.32147e10	+	7.48501e10i	0.165351	+	0.286397i
$716$		0			0
$717$	6.55522e10	+	9.28271e10i	0.248034	+	0.351235i
$718$		0			0
$719$		−	2.31072e11i		−	0.864633i	−0.901722	−	0.432317i	$-0.857696\pi$
$719$		−	2.31072e11i		−	0.864633i	0.901722	−	0.432317i	$-0.142304\pi$
$720$		0			0
$721$	3.58007e10			0.132480
$722$		0			0
$723$	−3.26266e11	−	1.50557e11i	−1.19404	−	0.550995i
$724$		0			0
$725$	3.34208e11	−	1.92955e11i	1.20966	−	0.698400i
$726$		0			0
$727$	−1.70637e11	+	2.95551e11i	−0.610850	+	1.05802i	0.380248	+	0.924885i	$0.375839\pi$
$727$	−1.70637e11	+	2.95551e11i	−0.610850	+	1.05802i	−0.991097	+	0.133138i	$0.957495\pi$
$728$		0			0
$729$	−2.41138e11	+	1.47034e11i	−0.853799	+	0.520603i
$730$		0			0
$731$	−8.04145e10	−	4.64274e10i	−0.281621	−	0.162594i
$732$		0			0
$733$	2.07203e11	+	3.58887e11i	0.717763	+	1.24320i	0.961884	+	0.273457i	$0.0881670\pi$
$733$	2.07203e11	+	3.58887e11i	0.717763	+	1.24320i	−0.244122	+	0.969745i	$0.578500\pi$
$734$		0			0
$735$	−4.08489e11	+	8.85220e11i	−1.39969	+	3.03320i
$736$		0			0
$737$			1.20394e11i			0.408071i
$738$		0			0
$739$	−2.71838e11			−0.911449			−0.455725	−	0.890121i	$-0.650620\pi$
$739$	−2.71838e11			−0.911449			−0.455725	+	0.890121i	$0.650620\pi$
$740$		0			0
$741$	6.73451e10	−	4.75574e10i	0.223374	−	0.157741i
$742$		0			0
$743$	2.96676e11	−	1.71286e11i	0.973479	−	0.562039i	0.0731842	−	0.997318i	$-0.476684\pi$
$743$	2.96676e11	−	1.71286e11i	0.973479	−	0.562039i	0.900295	+	0.435280i	$0.143351\pi$
$744$		0			0
$745$	2.32837e11	−	4.03286e11i	0.755835	−	1.30914i
$746$		0			0
$747$	−1.99328e11	−	7.07521e10i	−0.640157	−	0.227225i
$748$		0			0
$749$	−8.34547e11	−	4.81826e11i	−2.65170	−	1.53096i
$750$		0			0
$751$	5.25839e10	+	9.10780e10i	0.165308	+	0.286321i	0.936765	−	0.349960i	$-0.113805\pi$
$751$	5.25839e10	+	9.10780e10i	0.165308	+	0.286321i	−0.771457	+	0.636282i	$0.780472\pi$
$752$		0			0
$753$	1.95272e11	−	1.78700e10i	0.607378	−	0.0555834i
$754$		0			0
$755$		−	9.07750e11i		−	2.79369i
$756$		0			0
$757$	−4.23531e11			−1.28974			−0.644869	−	0.764293i	$-0.723088\pi$
$757$	−4.23531e11			−1.28974			−0.644869	+	0.764293i	$0.723088\pi$
$758$		0			0
$759$	−7.62628e9	−	8.33349e10i	−0.0229798	−	0.251108i
$760$		0			0
$761$	4.62418e11	−	2.66977e11i	1.37878	−	0.796041i	0.386770	−	0.922176i	$-0.373591\pi$
$761$	4.62418e11	−	2.66977e11i	1.37878	−	0.796041i	0.992013	+	0.126135i	$0.0402574\pi$
$762$		0			0
$763$	5.47931e11	−	9.49044e11i	1.61669	−	2.80019i
$764$		0			0
$765$	4.03718e11	+	4.73403e11i	1.17878	+	1.38224i
$766$		0			0
$767$	−7.16228e10	−	4.13514e10i	−0.206952	−	0.119484i
$768$		0			0
$769$	−5.66789e10	−	9.81707e10i	−0.162075	−	0.280722i	0.773538	−	0.633750i	$-0.218485\pi$
$769$	−5.66789e10	−	9.81707e10i	−0.162075	−	0.280722i	−0.935613	+	0.353028i	$0.885152\pi$
$770$		0			0
$771$	1.12715e11	+	1.59613e11i	0.318980	+	0.451701i
$772$		0			0
$773$		−	2.83942e11i		−	0.795265i	−0.917545	−	0.397632i	$-0.869832\pi$
$773$		−	2.83942e11i		−	0.795265i	0.917545	−	0.397632i	$-0.130168\pi$
$774$		0			0
$775$	8.96595e11			2.48536
$776$		0			0
$777$	−3.63365e11	−	1.67677e11i	−0.996918	−	0.460033i
$778$		0			0
$779$	−1.90350e11	+	1.09899e11i	−0.516897	+	0.298430i
$780$		0			0
$781$	8.24328e10	−	1.42778e11i	0.221562	−	0.383757i
$782$		0			0
$783$	−6.53712e10	+	2.56207e11i	−0.173916	+	0.681621i
$784$		0			0
$785$	3.94524e11	+	2.27779e11i	1.03895	+	0.599839i
$786$		0			0
$787$	−3.25568e11	−	5.63900e11i	−0.848678	−	1.46995i	−0.882389	−	0.470521i	$-0.844066\pi$
$787$	−3.25568e11	−	5.63900e11i	−0.848678	−	1.46995i	0.0337110	−	0.999432i	$-0.489267\pi$
$788$		0			0
$789$	−2.21430e11	+	4.79851e11i	−0.571384	+	1.23822i
$790$		0			0
$791$			1.17550e12i			3.00273i
$792$		0			0
$793$	6.84528e10			0.173100
$794$		0			0
$795$	7.48913e10	−	5.28863e10i	0.187483	−	0.132396i
$796$		0			0
$797$	4.16469e11	−	2.40448e11i	1.03216	−	0.595921i	0.114561	−	0.993416i	$-0.463454\pi$
$797$	4.16469e11	−	2.40448e11i	1.03216	−	0.595921i	0.917604	+	0.397496i	$0.130121\pi$
$798$		0			0
$799$	1.92998e11	−	3.34283e11i	0.473550	−	0.820213i
$800$		0			0
$801$	−2.50188e10	−	1.35549e11i	−0.0607765	−	0.329281i
$802$		0			0
$803$	2.04372e11	+	1.17994e11i	0.491541	+	0.283791i
$804$		0			0
$805$	2.35958e11	+	4.08692e11i	0.561890	+	0.973223i
$806$		0			0
$807$	−5.35705e11	+	4.90243e10i	−1.26308	+	0.115589i
$808$		0			0
$809$			1.97505e11i			0.461089i	0.973062	+	0.230545i	$0.0740508\pi$
$809$			1.97505e11i			0.461089i	−0.973062	+	0.230545i	$0.925949\pi$
$810$		0			0
$811$	1.30697e11			0.302121			0.151061	−	0.988524i	$-0.451731\pi$
$811$	1.30697e11			0.302121			0.151061	+	0.988524i	$0.451731\pi$
$812$		0			0
$813$	−2.00953e10	−	2.19588e11i	−0.0459973	−	0.502627i
$814$		0			0
$815$	5.15152e11	−	2.97423e11i	1.16763	−	0.674131i
$816$		0			0
$817$	−6.53730e10	+	1.13229e11i	−0.146727	+	0.254139i
$818$		0			0
$819$	2.18411e11	−	4.03129e10i	0.485445	−	0.0896001i
$820$		0			0
$821$	2.25465e10	+	1.30172e10i	0.0496256	+	0.0286514i	0.524608	−	0.851344i	$-0.324212\pi$
$821$	2.25465e10	+	1.30172e10i	0.0496256	+	0.0286514i	−0.474982	+	0.879996i	$0.657545\pi$
$822$		0			0
$823$	−1.02310e11	−	1.77206e11i	−0.223007	−	0.386260i	0.732712	−	0.680539i	$-0.238254\pi$
$823$	−1.02310e11	−	1.77206e11i	−0.223007	−	0.386260i	−0.955720	+	0.294278i	$0.904921\pi$
$824$		0			0
$825$	3.52334e11	+	4.98933e11i	0.760570	+	1.07703i
$826$		0			0
$827$			2.31574e11i			0.495072i	0.968879	+	0.247536i	$0.0796208\pi$
$827$			2.31574e11i			0.495072i	−0.968879	+	0.247536i	$0.920379\pi$
$828$		0			0
$829$	7.98205e11			1.69004			0.845019	−	0.534736i	$-0.179589\pi$
$829$	7.98205e11			1.69004			0.845019	+	0.534736i	$0.179589\pi$
$830$		0			0
$831$	7.36861e11	+	3.40029e11i	1.54519	+	0.713036i
$832$		0			0
$833$	−8.47545e11	+	4.89331e11i	−1.76029	+	1.01630i
$834$		0			0
$835$	−3.27681e11	+	5.67559e11i	−0.674070	+	1.16752i
$836$		0			0
$837$	−4.29156e11	+	4.39563e11i	−0.874407	+	0.895612i
$838$		0			0
$839$	−5.56790e11	−	3.21463e11i	−1.12368	−	0.648758i	−0.181343	−	0.983420i	$-0.558045\pi$
$839$	−5.56790e11	−	3.21463e11i	−1.12368	−	0.648758i	−0.942338	+	0.334662i	$0.891378\pi$
$840$		0			0
$841$	−1.26349e11	−	2.18842e11i	−0.252573	−	0.437469i
$842$		0			0
$843$	−2.67669e11	+	5.80053e11i	−0.530014	+	1.14857i
$844$		0			0
$845$		−	8.07752e11i		−	1.58435i
$846$		0			0
$847$	−4.92808e11			−0.957511
$848$		0			0
$849$	−6.44258e10	+	4.54959e10i	−0.124002	+	0.0875672i
$850$		0			0
$851$	−1.10569e11	+	6.38370e10i	−0.210821	+	0.121718i
$852$		0			0
$853$	9.75384e10	−	1.68942e11i	0.184238	−	0.319110i	−0.759081	−	0.650996i	$-0.774352\pi$
$853$	9.75384e10	−	1.68942e11i	0.184238	−	0.319110i	0.943320	+	0.331886i	$0.107685\pi$
$854$		0			0
$855$	6.66584e11	−	5.68464e11i	1.24736	−	1.06375i
$856$		0			0
$857$	−3.84904e10	−	2.22224e10i	−0.0713557	−	0.0411972i	0.463898	−	0.885889i	$-0.346451\pi$
$857$	−3.84904e10	−	2.22224e10i	−0.0713557	−	0.0411972i	−0.535253	+	0.844692i	$0.679784\pi$
$858$		0			0
$859$	1.25294e11	+	2.17015e11i	0.230122	+	0.398582i	0.957844	−	0.287290i	$-0.0927543\pi$
$859$	1.25294e11	+	2.17015e11i	0.230122	+	0.398582i	−0.727722	+	0.685872i	$0.759421\pi$
$860$		0			0
$861$	−5.89659e11	+	5.39619e10i	−1.07297	+	0.0981916i
$862$		0			0
$863$		−	3.91558e11i		−	0.705915i	−0.935639	−	0.352958i	$-0.885176\pi$
$863$		−	3.91558e11i		−	0.705915i	0.935639	−	0.352958i	$-0.114824\pi$
$864$		0			0
$865$	−1.03079e12			−1.84122
$866$		0			0
$867$	5.42428e9	+	5.92729e10i	0.00959988	+	0.104901i
$868$		0			0
$869$	1.07602e11	−	6.21242e10i	0.188687	−	0.108939i
$870$		0			0
$871$	−5.09714e10	+	8.82851e10i	−0.0885633	+	0.153396i
$872$		0			0
$873$	1.96052e11	−	5.52333e11i	0.337531	−	0.950920i
$874$		0			0
$875$	−1.48070e12	−	8.54884e11i	−2.52601	−	1.45839i
$876$		0			0
$877$	3.99055e10	+	6.91184e10i	0.0674582	+	0.116841i	0.897782	−	0.440441i	$-0.145178\pi$
$877$	3.99055e10	+	6.91184e10i	0.0674582	+	0.116841i	−0.830324	+	0.557282i	$0.811844\pi$
$878$		0			0
$879$	2.47869e11	+	3.51002e11i	0.415209	+	0.587968i
$880$		0			0
$881$			5.84453e11i			0.970166i	0.874468	+	0.485083i	$0.161211\pi$
$881$			5.84453e11i			0.970166i	−0.874468	+	0.485083i	$0.838789\pi$
$882$		0			0
$883$	−7.52384e10			−0.123765			−0.0618823	−	0.998083i	$-0.519710\pi$
$883$	−7.52384e10			−0.123765			−0.0618823	+	0.998083i	$0.519710\pi$
$884$		0			0
$885$	−7.97949e11	−	3.68218e11i	−1.30077	−	0.600249i
$886$		0			0
$887$	−6.05896e11	+	3.49814e11i	−0.978822	+	0.565123i	−0.901914	−	0.431915i	$-0.857838\pi$
$887$	−6.05896e11	+	3.49814e11i	−0.978822	+	0.565123i	−0.0769076	+	0.997038i	$0.524505\pi$
$888$		0			0
$889$	1.68343e11	−	2.91578e11i	0.269518	−	0.466819i
$890$		0			0
$891$	−4.13252e11	−	6.60802e10i	−0.655698	−	0.104848i
$892$		0			0
$893$	−4.70694e11	−	2.71755e11i	−0.740172	−	0.427338i
$894$		0			0
$895$	−5.09739e11	−	8.82894e11i	−0.794430	−	1.37599i
$896$		0			0
$897$	2.96892e10	−	6.43382e10i	0.0458594	−	0.0993800i
$898$		0			0
$899$			5.75137e11i			0.880507i
$900$		0			0
$901$	9.20338e10			0.139652
$902$		0			0
$903$	−2.87715e11	+	2.03177e11i	−0.432725	+	0.305579i
$904$		0			0
$905$	−8.12012e11	+	4.68815e11i	−1.21051	+	0.698888i
$906$		0			0
$907$	5.79947e10	−	1.00450e11i	0.0856958	−	0.148429i	−0.819992	−	0.572375i	$-0.806022\pi$
$907$	5.79947e10	−	1.00450e11i	0.0856958	−	0.148429i	0.905687	+	0.423946i	$0.139355\pi$
$908$		0			0
$909$	2.20205e11	+	7.81624e10i	0.322532	+	0.114483i
$910$		0			0
$911$	−9.81176e11	−	5.66482e11i	−1.42454	−	0.822456i	−0.427854	−	0.903848i	$-0.640730\pi$
$911$	−9.81176e11	−	5.66482e11i	−1.42454	−	0.822456i	−0.996682	+	0.0813913i	$0.974064\pi$
$912$		0			0
$913$	−1.56709e11	−	2.71428e11i	−0.225533	−	0.390635i
$914$		0			0
$915$	7.24360e11	−	6.62889e10i	1.03340	−	0.0945706i
$916$		0			0
$917$			1.55651e12i			2.20127i
$918$		0			0
$919$	3.06256e11			0.429361			0.214680	−	0.976684i	$-0.431129\pi$
$919$	3.06256e11			0.429361			0.214680	+	0.976684i	$0.431129\pi$
$920$		0			0
$921$	9.90936e10	+	1.08283e12i	0.137723	+	1.50495i
$922$		0			0
$923$	1.20896e11	−	6.97992e10i	0.166573	−	0.0961709i
$924$		0			0
$925$	4.65942e11	−	8.07035e11i	0.636451	−	1.10237i
$926$		0			0
$927$	−3.70644e10	−	4.34619e10i	−0.0501923	−	0.0588559i
$928$		0			0
$929$	−8.75115e11	−	5.05248e11i	−1.17490	−	0.678331i	−0.220074	−	0.975483i	$-0.570630\pi$
$929$	−8.75115e11	−	5.05248e11i	−1.17490	−	0.678331i	−0.954830	+	0.297152i	$0.903963\pi$
$930$		0			0
$931$	6.89012e11	+	1.19340e12i	0.917124	+	1.58851i
$932$		0			0
$933$	1.06983e11	+	1.51496e11i	0.141185	+	0.199929i
$934$		0			0
$935$			9.21929e11i			1.20629i
$936$		0			0
$937$	−3.80033e11			−0.493018			−0.246509	−	0.969141i	$-0.579283\pi$
$937$	−3.80033e11			−0.493018			−0.246509	+	0.969141i	$0.579283\pi$
$938$		0			0
$939$	−1.31526e12	−	6.06933e11i	−1.69180	−	0.780689i
$940$		0			0
$941$	4.20722e11	−	2.42904e11i	0.536583	−	0.309796i	−0.207110	−	0.978318i	$-0.566406\pi$
$941$	4.20722e11	−	2.42904e11i	0.536583	−	0.309796i	0.743693	+	0.668521i	$0.233072\pi$
$942$		0			0
$943$	−9.44541e10	+	1.63599e11i	−0.119447	+	0.206888i
$944$		0			0
$945$	2.27217e12	−	6.38094e11i	2.84914	−	0.800124i
$946$		0			0
$947$	−4.64773e9	−	2.68337e9i	−0.00577885	−	0.00333642i	0.497108	−	0.867689i	$-0.334395\pi$
$947$	−4.64773e9	−	2.68337e9i	−0.00577885	−	0.00333642i	−0.502887	+	0.864352i	$0.667729\pi$
$948$		0			0
$949$	9.99106e10	+	1.73050e11i	0.123182	+	0.213357i
$950$		0			0
$951$	2.26279e11	−	4.90359e11i	0.276644	−	0.599504i
$952$		0			0
$953$		−	2.87948e11i		−	0.349094i	−0.984649	−	0.174547i	$-0.944154\pi$
$953$		−	2.87948e11i		−	0.349094i	0.984649	−	0.174547i	$-0.0558462\pi$
$954$		0			0
$955$	7.60616e10			0.0914433
$956$		0			0
$957$	−3.20050e11	+	2.26011e11i	−0.381566	+	0.269453i
$958$		0			0
$959$	3.44141e11	−	1.98690e11i	0.406876	−	0.234910i
$960$		0			0
$961$	−2.41670e11	+	4.18585e11i	−0.283354	+	0.490784i
$962$		0			0
$963$	2.79069e11	+	1.51197e12i	0.324494	+	1.75808i
$964$		0			0
$965$	−2.56017e12	−	1.47812e12i	−2.95230	−	1.70451i
$966$		0			0
$967$	4.51417e11	+	7.81877e11i	0.516264	+	0.894195i	0.999822	+	0.0188827i	$0.00601091\pi$
$967$	4.51417e11	+	7.81877e11i	0.516264	+	0.894195i	−0.483558	+	0.875312i	$0.660656\pi$
$968$		0			0
$969$	8.75761e11	−	8.01441e10i	0.993323	−	0.0909027i
$970$		0			0
$971$			8.08040e11i			0.908983i	0.890751	+	0.454492i	$0.150179\pi$
$971$			8.08040e11i			0.908983i	−0.890751	+	0.454492i	$0.849821\pi$
$972$		0			0
$973$	1.75368e12			1.95658
$974$		0			0
$975$	4.71328e10	+	5.15035e11i	0.0521561	+	0.569926i
$976$		0			0
$977$	1.39658e12	−	8.06317e11i	1.53281	−	0.884968i	0.533579	−	0.845750i	$-0.320847\pi$
$977$	1.39658e12	−	8.06317e11i	1.53281	−	0.884968i	0.999231	−	0.0392176i	$-0.0124866\pi$
$978$		0			0
$979$	1.02124e11	−	1.76884e11i	0.111173	−	0.192557i
$980$		0			0
$981$	−1.71941e12	+	3.17357e11i	−1.85653	+	0.342666i
$982$		0			0
$983$	−1.24469e12	−	7.18625e11i	−1.33306	−	0.769641i	−0.347290	−	0.937758i	$-0.612898\pi$
$983$	−1.24469e12	−	7.18625e11i	−1.33306	−	0.769641i	−0.985767	+	0.168117i	$0.946231\pi$
$984$		0			0
$985$	2.95511e11	+	5.11840e11i	0.313927	+	0.543737i
$986$		0			0
$987$	−8.44606e11	−	1.19603e12i	−0.889991	−	1.26030i
$988$		0			0
$989$			1.12372e11i			0.117455i
$990$		0			0
$991$	1.11953e12			1.16075			0.580377	−	0.814348i	$-0.302905\pi$
$991$	1.11953e12			1.16075			0.580377	+	0.814348i	$0.302905\pi$
$992$		0			0
$993$	−1.15365e12	−	5.32356e11i	−1.18652	−	0.547527i
$994$		0			0
$995$	2.49213e12	−	1.43883e12i	2.54261	−	1.46797i
$996$		0			0
$997$	−4.45668e11	+	7.71920e11i	−0.451057	+	0.781253i	−0.998452	−	0.0556212i	$-0.982286\pi$
$997$	−4.45668e11	+	7.71920e11i	−0.451057	+	0.781253i	0.547395	+	0.836874i	$0.315619\pi$
$998$		0			0
$999$	1.72632e11	+	6.14721e11i	0.173324	+	0.617186i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	144.9.q.b.65.5		16
3.2	odd	2		432.9.q.c.305.1		16
4.3	odd	2		18.9.d.a.11.6	yes	16
9.4	even	3		432.9.q.c.17.1		16
9.5	odd	6	inner	144.9.q.b.113.5		16
12.11	even	2		54.9.d.a.35.1		16
36.7	odd	6		162.9.b.c.161.8		16
36.11	even	6		162.9.b.c.161.9		16
36.23	even	6		18.9.d.a.5.6	✓	16
36.31	odd	6		54.9.d.a.17.1		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
18.9.d.a.5.6	✓	16	36.23	even	6
18.9.d.a.11.6	yes	16	4.3	odd	2
54.9.d.a.17.1		16	36.31	odd	6
54.9.d.a.35.1		16	12.11	even	2
144.9.q.b.65.5		16	1.1	even	1	trivial
144.9.q.b.113.5		16	9.5	odd	6	inner
162.9.b.c.161.8		16	36.7	odd	6
162.9.b.c.161.9		16	36.11	even	6
432.9.q.c.17.1		16	9.4	even	3
432.9.q.c.305.1		16	3.2	odd	2

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:	\( N \)	\(=\)	\( 144 = 2^{4} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 9 \)
Character orbit:	\([\chi]\)	\(=\)	144.q (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-7.38176 - 80.6629i) q^{3} +(935.250 - 539.967i) q^{5} +(2056.09 - 3561.25i) q^{7} +(-6452.02 + 1190.87i) q^{9} +(-8419.53 - 4861.02i) q^{11} +(-4116.02 - 7129.16i) q^{13} +(-50459.1 - 71454.1i) q^{15} -87809.9i q^{17} -123643. q^{19} +(-302439. - 139562. i) q^{21} +(-92029.4 + 53133.2i) q^{23} +(387816. - 671717. i) q^{25} +(143686. + 511648. i) q^{27} +(430885. + 248772. i) q^{29} +(577977. + 1.00109e6i) q^{31} +(-329953. + 715027. i) q^{33} -4.44088e6i q^{35} +1.20145e6 q^{37} +(-544675. + 384636. i) q^{39} +(1.53952e6 - 888843. i) q^{41} +(528726. - 915780. i) q^{43} +(-5.39122e6 + 4.59764e6i) q^{45} +(3.80689e6 + 2.19791e6i) q^{47} +(-5.57261e6 - 9.65205e6i) q^{49} +(-7.08301e6 + 648192. i) q^{51} +1.04810e6i q^{53} -1.04991e7 q^{55} +(912700. + 9.97337e6i) q^{57} +(8.70048e6 - 5.02323e6i) q^{59} +(-4.15770e6 + 7.20135e6i) q^{61} +(-9.02495e6 + 2.54258e7i) q^{63} +(-7.69902e6 - 4.44503e6i) q^{65} +(-6.19183e6 - 1.07246e7i) q^{67} +(4.96522e6 + 7.03114e6i) q^{69} +1.69579e7i q^{71} -2.42736e7 q^{73} +(-5.70454e7 - 2.63239e7i) q^{75} +(-3.46226e7 + 1.99894e7i) q^{77} +(-6.39004e6 + 1.10679e7i) q^{79} +(4.02104e7 - 1.53670e7i) q^{81} +(2.79188e7 + 1.61189e7i) q^{83} +(-4.74144e7 - 8.21242e7i) q^{85} +(1.68860e7 - 3.65928e7i) q^{87} +2.10088e7i q^{89} -3.38516e7 q^{91} +(7.64841e7 - 5.40111e7i) q^{93} +(-1.15637e8 + 6.67629e7i) q^{95} +(-4.46651e7 + 7.73622e7i) q^{97} +(6.01118e7 + 2.13368e7i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 126 q^{3} - 882 q^{5} + 1846 q^{7} - 28662 q^{9} - 45756 q^{11} - 3370 q^{13} - 128754 q^{15} - 362180 q^{19} - 299166 q^{21} - 1311138 q^{23} + 963394 q^{25} + 208656 q^{27} - 2851290 q^{29} - 542438 q^{31}+ \cdots - 366888330 q^{99}+O(q^{100}) \) 16 * q - 126 * q^3 - 882 * q^5 + 1846 * q^7 - 28662 * q^9 - 45756 * q^11 - 3370 * q^13 - 128754 * q^15 - 362180 * q^19 - 299166 * q^21 - 1311138 * q^23 + 963394 * q^25 + 208656 * q^27 - 2851290 * q^29 - 542438 * q^31 + 3875796 * q^33 + 3343328 * q^37 + 5896002 * q^39 + 9218592 * q^41 - 339512 * q^43 - 32740578 * q^45 + 34980606 * q^47 - 2364654 * q^49 - 50877810 * q^51 + 4584276 * q^55 - 34049898 * q^57 - 93924216 * q^59 - 841954 * q^61 + 14043234 * q^63 - 126568134 * q^65 - 29946644 * q^67 + 70499610 * q^69 - 7547764 * q^73 - 114494910 * q^75 + 9309294 * q^77 - 33813002 * q^79 - 46018134 * q^81 - 114200226 * q^83 - 125696772 * q^85 + 159599970 * q^87 - 268578316 * q^91 + 120711534 * q^93 + 143949240 * q^95 - 89415484 * q^97 - 366888330 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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