LMFDB - Embedded newform 196.9.h.c.117.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [196,9,Mod(117,196)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(196, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 5])) N = Newforms(chi, 9, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("196.117"); S:= CuspForms(chi, 9); N := Newforms(S);

Level:	$ N $	$=$	$ 196 = 2^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 9 $
Character orbit:	$[\chi]$	$=$	196.h (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [32] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$79.8462075720$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			117.3
Character	$\chi$	$=$	196.117
Dual form			196.9.h.c.129.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-106.882 + 61.7084i) q^{3} +(-149.792 - 86.4823i) q^{5} +(4335.35 - 7509.04i) q^{9} +(-2312.68 - 4005.68i) q^{11} +38424.8i q^{13} +21346.7 q^{15} +(18010.2 - 10398.2i) q^{17} +(59635.0 + 34430.3i) q^{19} +(-138965. + 240695. i) q^{23} +(-180354. - 312383. i) q^{25} +260371. i q^{27} -815335. q^{29} +(-1.44227e6 + 832694. i) q^{31} +(494368. + 285423. i) q^{33} +(-1.08184e6 + 1.87379e6i) q^{37} +(-2.37113e6 - 4.10692e6i) q^{39} +4.92685e6i q^{41} +2.84791e6 q^{43} +(-1.29880e6 + 749861. i) q^{45} +(3.90905e6 + 2.25689e6i) q^{47} +(-1.28331e6 + 2.22275e6i) q^{51} +(-6.74283e6 - 1.16789e7i) q^{53} +800023. i q^{55} -8.49855e6 q^{57} +(-1.10116e7 + 6.35756e6i) q^{59} +(-2.11485e6 - 1.22101e6i) q^{61} +(3.32307e6 - 5.75572e6i) q^{65} +(5.98497e6 + 1.03663e7i) q^{67} -3.43013e7i q^{69} +1.36325e6 q^{71} +(2.62076e7 - 1.51310e7i) q^{73} +(3.85532e7 + 2.22587e7i) q^{75} +(2.39976e7 - 4.15650e7i) q^{79} +(1.23771e7 + 2.14378e7i) q^{81} -3.39149e7i q^{83} -3.59703e6 q^{85} +(8.71446e7 - 5.03130e7i) q^{87} +(1.07589e7 + 6.21164e6i) q^{89} +(1.02768e8 - 1.78000e8i) q^{93} +(-5.95522e6 - 1.03147e7i) q^{95} -1.15877e8i q^{97} -4.01051e7 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 52264 q^{9} + 22776 q^{11} + 206064 q^{15} - 571560 q^{23} + 1030440 q^{25} - 5384256 q^{29} + 3376640 q^{37} + 10336136 q^{39} + 18525008 q^{43} + 16028856 q^{51} - 14106216 q^{53} - 4787360 q^{57}+ \cdots + 1119499328 q^{99}+O(q^{100}) $ 32 * q + 52264 * q^9 + 22776 * q^11 + 206064 * q^15 - 571560 * q^23 + 1030440 * q^25 - 5384256 * q^29 + 3376640 * q^37 + 10336136 * q^39 + 18525008 * q^43 + 16028856 * q^51 - 14106216 * q^53 - 4787360 * q^57 - 5623008 * q^65 - 82433680 * q^67 + 250685568 * q^71 + 138241200 * q^79 - 465637680 * q^81 + 880381104 * q^85 + 310654512 * q^93 - 811120872 * q^95 + 1119499328 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/196\mathbb{Z}\right)^\times$.

$n$	$99$	$101$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−106.882	+	61.7084i	−1.31953	+	0.761832i	−0.983653	−	0.180074i	$-0.942366\pi$
$3$	−106.882	+	61.7084i	−1.31953	+	0.761832i	−0.335878	+	0.941905i	$0.609033\pi$
$4$		0			0
$5$	−149.792	−	86.4823i	−0.239667	−	0.138372i	0.375357	−	0.926880i	$-0.377520\pi$
$5$	−149.792	−	86.4823i	−0.239667	−	0.138372i	−0.615024	+	0.788509i	$0.710853\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$		0			0
$9$	4335.35	−	7509.04i	0.660775	−	1.14450i
$10$		0			0
$11$	−2312.68	−	4005.68i	−0.157959	−	0.273593i	0.776173	−	0.630519i	$-0.217158\pi$
$11$	−2312.68	−	4005.68i	−0.157959	−	0.273593i	−0.934133	+	0.356926i	$0.883825\pi$
$12$		0			0
$13$			38424.8i			1.34536i	0.739934	+	0.672680i	$0.234857\pi$
$13$			38424.8i			1.34536i	−0.739934	+	0.672680i	$0.765143\pi$
$14$		0			0
$15$	21346.7			0.421664
$16$		0			0
$17$	18010.2	−	10398.2i	0.215636	−	0.124498i	−0.388292	−	0.921536i	$-0.626935\pi$
$17$	18010.2	−	10398.2i	0.215636	−	0.124498i	0.603928	+	0.797039i	$0.293601\pi$
$18$		0			0
$19$	59635.0	+	34430.3i	0.457601	+	0.264196i	0.711035	−	0.703157i	$-0.248227\pi$
$19$	59635.0	+	34430.3i	0.457601	+	0.264196i	−0.253434	+	0.967353i	$0.581560\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−138965.	+	240695.i	−0.496587	+	0.860114i	−0.999992	−	0.00393650i	$-0.998747\pi$
$23$	−138965.	+	240695.i	−0.496587	+	0.860114i	0.503405	+	0.864050i	$0.332080\pi$
$24$		0			0
$25$	−180354.	−	312383.i	−0.461707	−	0.799699i
$26$		0			0
$27$			260371.i			0.489935i
$28$		0			0
$29$	−815335.			−1.15277			−0.576387	−	0.817177i	$-0.695538\pi$
$29$	−815335.			−1.15277			−0.576387	+	0.817177i	$0.695538\pi$
$30$		0			0
$31$	−1.44227e6	+	832694.i	−1.56171	+	0.901652i	−0.564622	+	0.825350i	$0.690978\pi$
$31$	−1.44227e6	+	832694.i	−1.56171	+	0.901652i	−0.997085	+	0.0763019i	$0.975689\pi$
$32$		0			0
$33$	494368.	+	285423.i	0.416864	+	0.240676i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	−1.08184e6	+	1.87379e6i	−0.577237	+	0.999805i	0.418557	+	0.908190i	$0.362536\pi$
$37$	−1.08184e6	+	1.87379e6i	−0.577237	+	0.999805i	−0.995795	+	0.0916141i	$0.970797\pi$
$38$		0			0
$39$	−2.37113e6	−	4.10692e6i	−1.02494	−	1.77524i
$40$		0			0
$41$			4.92685e6i			1.74355i	0.489908	+	0.871774i	$0.337030\pi$
$41$			4.92685e6i			1.74355i	−0.489908	+	0.871774i	$0.662970\pi$
$42$		0			0
$43$	2.84791e6			0.833014			0.416507	−	0.909133i	$-0.363254\pi$
$43$	2.84791e6			0.833014			0.416507	+	0.909133i	$0.363254\pi$
$44$		0			0
$45$	−1.29880e6	+	749861.i	−0.316732	+	0.182865i
$46$		0			0
$47$	3.90905e6	+	2.25689e6i	0.801088	+	0.462508i	0.843851	−	0.536577i	$-0.180283\pi$
$47$	3.90905e6	+	2.25689e6i	0.801088	+	0.462508i	−0.0427635	+	0.999085i	$0.513616\pi$
$48$		0			0
$49$		0			0
$50$		0			0
$51$	−1.28331e6	+	2.22275e6i	−0.189692	+	0.328557i
$52$		0			0
$53$	−6.74283e6	−	1.16789e7i	−0.854552	−	1.48013i	−0.877060	−	0.480381i	$-0.840498\pi$
$53$	−6.74283e6	−	1.16789e7i	−0.854552	−	1.48013i	0.0225073	−	0.999747i	$-0.492835\pi$
$54$		0			0
$55$			800023.i			0.0874282i
$56$		0			0
$57$	−8.49855e6			−0.805092
$58$		0			0
$59$	−1.10116e7	+	6.35756e6i	−0.908747	+	0.524665i	−0.880028	−	0.474922i	$-0.842476\pi$
$59$	−1.10116e7	+	6.35756e6i	−0.908747	+	0.524665i	−0.0287191	+	0.999588i	$0.509143\pi$
$60$		0			0
$61$	−2.11485e6	−	1.22101e6i	−0.152743	−	0.0881862i	0.421681	−	0.906744i	$-0.361440\pi$
$61$	−2.11485e6	−	1.22101e6i	−0.152743	−	0.0881862i	−0.574423	+	0.818558i	$0.694774\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	3.32307e6	−	5.75572e6i	0.186160	−	0.322438i
$66$		0			0
$67$	5.98497e6	+	1.03663e7i	0.297004	+	0.514427i	0.975449	−	0.220225i	$-0.0706791\pi$
$67$	5.98497e6	+	1.03663e7i	0.297004	+	0.514427i	−0.678445	+	0.734651i	$0.737346\pi$
$68$		0			0
$69$		−	3.43013e7i		−	1.51326i
$70$		0			0
$71$	1.36325e6			0.0536464			0.0268232	−	0.999640i	$-0.491461\pi$
$71$	1.36325e6			0.0536464			0.0268232	+	0.999640i	$0.491461\pi$
$72$		0			0
$73$	2.62076e7	−	1.51310e7i	0.922860	−	0.532813i	0.0383137	−	0.999266i	$-0.487801\pi$
$73$	2.62076e7	−	1.51310e7i	0.922860	−	0.532813i	0.884546	+	0.466452i	$0.154468\pi$
$74$		0			0
$75$	3.85532e7	+	2.22587e7i	1.21847	+	0.703485i
$76$		0			0
$77$		0			0
$78$		0			0
$79$	2.39976e7	−	4.15650e7i	0.616111	−	1.06713i	−0.374078	−	0.927397i	$-0.622041\pi$
$79$	2.39976e7	−	4.15650e7i	0.616111	−	1.06713i	0.990189	−	0.139737i	$-0.0446259\pi$
$80$		0			0
$81$	1.23771e7	+	2.14378e7i	0.287527	+	0.498012i
$82$		0			0
$83$		−	3.39149e7i		−	0.714626i	−0.933985	−	0.357313i	$-0.883693\pi$
$83$		−	3.39149e7i		−	0.714626i	0.933985	−	0.357313i	$-0.116307\pi$
$84$		0			0
$85$	−3.59703e6			−0.0689077
$86$		0			0
$87$	8.71446e7	−	5.03130e7i	1.52112	−	0.878219i
$88$		0			0
$89$	1.07589e7	+	6.21164e6i	0.171478	+	0.0990026i	0.583282	−	0.812269i	$-0.301768\pi$
$89$	1.07589e7	+	6.21164e6i	0.171478	+	0.0990026i	−0.411805	+	0.911272i	$0.635101\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$	1.02768e8	−	1.78000e8i	1.37381	−	2.37952i
$94$		0			0
$95$	−5.95522e6	−	1.03147e7i	−0.0731145	−	0.126638i
$96$		0			0
$97$		−	1.15877e8i		−	1.30891i	−0.756102	−	0.654454i	$-0.772899\pi$
$97$		−	1.15877e8i		−	1.30891i	0.756102	−	0.654454i	$-0.227101\pi$
$98$		0			0
$99$	−4.01051e7			−0.417502
$100$		0			0
$101$	−5.59126e7	+	3.22811e7i	−0.537309	+	0.310215i	−0.743988	−	0.668194i	$-0.767068\pi$
$101$	−5.59126e7	+	3.22811e7i	−0.537309	+	0.310215i	0.206679	+	0.978409i	$0.433734\pi$
$102$		0			0
$103$	1.05151e8	+	6.07090e7i	0.934254	+	0.539392i	0.888155	−	0.459545i	$-0.151987\pi$
$103$	1.05151e8	+	6.07090e7i	0.934254	+	0.539392i	0.0460998	+	0.998937i	$0.485321\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−4.88872e7	+	8.46751e7i	−0.372958	+	0.645982i	−0.990019	−	0.140933i	$-0.954990\pi$
$107$	−4.88872e7	+	8.46751e7i	−0.372958	+	0.645982i	0.617061	+	0.786915i	$0.288323\pi$
$108$		0			0
$109$	−3.68434e7	−	6.38146e7i	−0.261008	−	0.452079i	0.705502	−	0.708708i	$-0.250721\pi$
$109$	−3.68434e7	−	6.38146e7i	−0.261008	−	0.452079i	−0.966510	+	0.256629i	$0.917388\pi$
$110$		0			0
$111$		−	2.67033e8i		−	1.75903i
$112$		0			0
$113$	−9.96728e7			−0.611312			−0.305656	−	0.952142i	$-0.598876\pi$
$113$	−9.96728e7			−0.611312			−0.305656	+	0.952142i	$0.598876\pi$
$114$		0			0
$115$	4.16317e7	−	2.40361e7i	0.238031	−	0.137427i
$116$		0			0
$117$	2.88534e8	+	1.66585e8i	1.53976	+	0.888981i
$118$		0			0
$119$		0			0
$120$		0			0
$121$	9.64825e7	−	1.67113e8i	0.450098	−	0.779592i
$122$		0			0
$123$	−3.04028e8	−	5.26592e8i	−1.32829	−	2.30067i
$124$		0			0
$125$			1.29954e8i			0.532292i
$126$		0			0
$127$	1.31508e8			0.505517			0.252759	−	0.967529i	$-0.418662\pi$
$127$	1.31508e8			0.505517			0.252759	+	0.967529i	$0.418662\pi$
$128$		0			0
$129$	−3.04390e8	+	1.75740e8i	−1.09919	+	0.634616i
$130$		0			0
$131$	3.62932e8	+	2.09539e8i	1.23237	+	0.711508i	0.967523	−	0.252783i	$-0.0813459\pi$
$131$	3.62932e8	+	2.09539e8i	1.23237	+	0.711508i	0.264845	+	0.964291i	$0.414679\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$	2.25175e7	−	3.90015e7i	0.0677930	−	0.117421i
$136$		0			0
$137$	−3.15734e8	−	5.46868e8i	−0.896271	−	1.55239i	−0.832223	−	0.554441i	$-0.812932\pi$
$137$	−3.15734e8	−	5.46868e8i	−0.896271	−	1.55239i	−0.0640481	−	0.997947i	$-0.520401\pi$
$138$		0			0
$139$			2.37838e8i			0.637122i	0.947902	+	0.318561i	$0.103200\pi$
$139$			2.37838e8i			0.637122i	−0.947902	+	0.318561i	$0.896800\pi$
$140$		0			0
$141$	−5.57077e8			−1.40941
$142$		0			0
$143$	1.53917e8	−	8.88643e7i	0.368081	−	0.212512i
$144$		0			0
$145$	1.22130e8	+	7.05120e7i	0.276281	+	0.159511i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	2.59717e8	−	4.49842e8i	0.526932	−	0.912673i	−0.472575	−	0.881290i	$-0.656675\pi$
$149$	2.59717e8	−	4.49842e8i	0.526932	−	0.912673i	0.999507	−	0.0313830i	$-0.00999118\pi$
$150$		0			0
$151$	−2.10947e8	−	3.65370e8i	−0.405756	−	0.702790i	0.588653	−	0.808386i	$-0.299658\pi$
$151$	−2.10947e8	−	3.65370e8i	−0.405756	−	0.702790i	−0.994409	+	0.105596i	$0.966325\pi$
$152$		0			0
$153$		−	1.80319e8i		−	0.329060i
$154$		0			0
$155$	2.88053e8			0.499052
$156$		0			0
$157$	−3.82356e8	+	2.20754e8i	−0.629317	+	0.363337i	−0.780488	−	0.625171i	$-0.785029\pi$
$157$	−3.82356e8	+	2.20754e8i	−0.629317	+	0.363337i	0.151170	+	0.988508i	$0.451696\pi$
$158$		0			0
$159$	1.44137e9	+	8.32178e8i	2.25522	+	1.30205i
$160$		0			0
$161$		0			0
$162$		0			0
$163$	−4.37137e8	+	7.57144e8i	−0.619252	+	1.07258i	0.370370	+	0.928884i	$0.379231\pi$
$163$	−4.37137e8	+	7.57144e8i	−0.619252	+	1.07258i	−0.989622	+	0.143692i	$0.954103\pi$
$164$		0			0
$165$	−4.93681e7	−	8.55081e7i	−0.0666056	−	0.115364i
$166$		0			0
$167$		−	1.27186e9i		−	1.63521i	−0.575783	−	0.817603i	$-0.695303\pi$
$167$		−	1.27186e9i		−	1.63521i	0.575783	−	0.817603i	$-0.304697\pi$
$168$		0			0
$169$	−6.60737e8			−0.809994
$170$		0			0
$171$	5.17077e8	−	2.98535e8i	0.604743	−	0.349149i
$172$		0			0
$173$	−9.99203e8	−	5.76890e8i	−1.11550	−	0.644034i	−0.175251	−	0.984524i	$-0.556074\pi$
$173$	−9.99203e8	−	5.76890e8i	−1.11550	−	0.644034i	−0.940248	+	0.340490i	$0.889407\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	7.84629e8	−	1.35902e9i	0.799413	−	1.38462i
$178$		0			0
$179$	7.49730e8	+	1.29857e9i	0.730285	+	1.26489i	0.956761	+	0.290875i	$0.0939463\pi$
$179$	7.49730e8	+	1.29857e9i	0.730285	+	1.26489i	−0.226476	+	0.974017i	$0.572720\pi$
$180$		0			0
$181$		−	8.43686e8i		−	0.786079i	−0.919521	−	0.393040i	$-0.871423\pi$
$181$		−	8.43686e8i		−	0.786079i	0.919521	−	0.393040i	$-0.128577\pi$
$182$		0			0
$183$	3.01387e8			0.268732
$184$		0			0
$185$	3.24100e8	−	1.87119e8i	0.276689	−	0.159747i
$186$		0			0
$187$	−8.33034e7	−	4.80952e7i	−0.0681234	−	0.0393311i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	7.03352e8	−	1.21824e9i	0.528493	−	0.915377i	−0.470955	−	0.882157i	$-0.656090\pi$
$191$	7.03352e8	−	1.21824e9i	0.528493	−	0.915377i	0.999448	−	0.0332199i	$-0.0105762\pi$
$192$		0			0
$193$	7.60769e7	+	1.31769e8i	0.0548307	+	0.0949695i	0.892138	−	0.451763i	$-0.149205\pi$
$193$	7.60769e7	+	1.31769e8i	0.0548307	+	0.0949695i	−0.837307	+	0.546733i	$0.815871\pi$
$194$		0			0
$195$			8.20244e8i			0.567289i
$196$		0			0
$197$	1.63587e8			0.108614			0.0543069	−	0.998524i	$-0.482705\pi$
$197$	1.63587e8			0.108614			0.0543069	+	0.998524i	$0.482705\pi$
$198$		0			0
$199$	1.91243e9	−	1.10414e9i	1.21948	−	0.704067i	0.254673	−	0.967027i	$-0.418032\pi$
$199$	1.91243e9	−	1.10414e9i	1.21948	−	0.704067i	0.964807	+	0.262961i	$0.0846990\pi$
$200$		0			0
$201$	−1.27937e9	−	7.38646e8i	−0.783813	−	0.452535i
$202$		0			0
$203$		0			0
$204$		0			0
$205$	4.26085e8	−	7.38001e8i	0.241258	−	0.417870i
$206$		0			0
$207$	1.20493e9	+	2.08699e9i	0.656265	+	1.13668i
$208$		0			0
$209$		−	3.18505e8i		−	0.166929i
$210$		0			0
$211$	3.36732e9			1.69885			0.849425	−	0.527709i	$-0.176949\pi$
$211$	3.36732e9			1.69885			0.849425	+	0.527709i	$0.176949\pi$
$212$		0			0
$213$	−1.45706e8	+	8.41237e7i	−0.0707881	+	0.0408695i
$214$		0			0
$215$	−4.26593e8	−	2.46293e8i	−0.199646	−	0.115265i
$216$		0			0
$217$		0			0
$218$		0			0
$219$	−1.86741e9	+	3.23446e9i	−0.811828	+	1.40613i
$220$		0			0
$221$	3.99548e8	+	6.92037e8i	0.167494	+	0.290108i
$222$		0			0
$223$		−	1.18163e9i		−	0.477817i	−0.971042	−	0.238908i	$-0.923210\pi$
$223$		−	1.18163e9i		−	0.477817i	0.971042	−	0.238908i	$-0.0767895\pi$
$224$		0			0
$225$	−3.12759e9			−1.22034
$226$		0			0
$227$	−8.36430e8	+	4.82913e8i	−0.315011	+	0.181872i	−0.649167	−	0.760646i	$-0.724882\pi$
$227$	−8.36430e8	+	4.82913e8i	−0.315011	+	0.181872i	0.334155	+	0.942518i	$0.391549\pi$
$228$		0			0
$229$	−9.41321e8	−	5.43472e8i	−0.342291	−	0.197622i	0.318994	−	0.947757i	$-0.396655\pi$
$229$	−9.41321e8	−	5.43472e8i	−0.342291	−	0.197622i	−0.661285	+	0.750135i	$0.729989\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−1.53281e9	+	2.65490e9i	−0.520072	+	0.900792i	0.479655	+	0.877457i	$0.340762\pi$
$233$	−1.53281e9	+	2.65490e9i	−0.520072	+	0.900792i	−0.999728	+	0.0233347i	$0.992572\pi$
$234$		0			0
$235$	−3.90362e8	−	6.76128e8i	−0.127996	−	0.221696i
$236$		0			0
$237$			5.92340e9i			1.87749i
$238$		0			0
$239$	−3.16844e8			−0.0971078			−0.0485539	−	0.998821i	$-0.515461\pi$
$239$	−3.16844e8			−0.0971078			−0.0485539	+	0.998821i	$0.515461\pi$
$240$		0			0
$241$	−5.14474e9	+	2.97031e9i	−1.52509	+	0.880510i	−0.525530	+	0.850775i	$0.676133\pi$
$241$	−5.14474e9	+	2.97031e9i	−1.52509	+	0.880510i	−0.999558	+	0.0297348i	$0.990534\pi$
$242$		0			0
$243$	−4.12521e9	−	2.38169e9i	−1.18310	−	0.683062i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	−1.32298e9	+	2.29147e9i	−0.355439	+	0.615638i
$248$		0			0
$249$	2.09284e9	+	3.62490e9i	0.544425	+	0.942971i
$250$		0			0
$251$			5.99415e9i			1.51019i	0.655613	+	0.755097i	$0.272410\pi$
$251$			5.99415e9i			1.51019i	−0.655613	+	0.755097i	$0.727590\pi$
$252$		0			0
$253$	1.28553e9			0.313762
$254$		0			0
$255$	3.84458e8	−	2.21967e8i	0.0909259	−	0.0524961i
$256$		0			0
$257$	−1.93545e9	−	1.11743e9i	−0.443658	−	0.256146i	0.261490	−	0.965206i	$-0.415786\pi$
$257$	−1.93545e9	−	1.11743e9i	−0.443658	−	0.256146i	−0.705148	+	0.709060i	$0.749120\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$	−3.53476e9	+	6.12238e9i	−0.761724	+	1.31934i
$262$		0			0
$263$	−4.64032e9	−	8.03728e9i	−0.969896	−	1.67991i	−0.695841	−	0.718195i	$-0.744968\pi$
$263$	−4.64032e9	−	8.03728e9i	−0.969896	−	1.67991i	−0.274055	−	0.961714i	$-0.588365\pi$
$264$		0			0
$265$			2.33254e9i			0.472983i
$266$		0			0
$267$	−1.53324e9			−0.301693
$268$		0			0
$269$	−2.04502e9	+	1.18069e9i	−0.390561	+	0.225490i	−0.682403	−	0.730976i	$-0.739065\pi$
$269$	−2.04502e9	+	1.18069e9i	−0.390561	+	0.225490i	0.291842	+	0.956466i	$0.405732\pi$
$270$		0			0
$271$	−1.99405e9	−	1.15126e9i	−0.369708	−	0.213451i	0.303623	−	0.952792i	$-0.401804\pi$
$271$	−1.99405e9	−	1.15126e9i	−0.369708	−	0.213451i	−0.673331	+	0.739341i	$0.735137\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−8.34202e8	+	1.44488e9i	−0.145862	+	0.252640i
$276$		0			0
$277$	4.42211e8	+	7.65932e8i	0.0751122	+	0.130098i	0.901135	−	0.433538i	$-0.142735\pi$
$277$	4.42211e8	+	7.65932e8i	0.0751122	+	0.130098i	−0.826023	+	0.563637i	$0.809402\pi$
$278$		0			0
$279$			1.44401e10i			2.38316i
$280$		0			0
$281$	1.08376e10			1.73823			0.869116	−	0.494609i	$-0.164689\pi$
$281$	1.08376e10			1.73823			0.869116	+	0.494609i	$0.164689\pi$
$282$		0			0
$283$	2.25665e9	−	1.30288e9i	0.351818	−	0.203122i	−0.313668	−	0.949533i	$-0.601558\pi$
$283$	2.25665e9	−	1.30288e9i	0.351818	−	0.203122i	0.665486	+	0.746411i	$0.268224\pi$
$284$		0			0
$285$	1.27301e9	+	7.34974e8i	0.192954	+	0.111402i
$286$		0			0
$287$		0			0
$288$		0			0
$289$	−3.27163e9	+	5.66664e9i	−0.469001	+	0.812333i
$290$		0			0
$291$	7.15056e9	+	1.23851e10i	0.997168	+	1.72714i
$292$		0			0
$293$		−	8.03400e9i		−	1.09009i	−0.838408	−	0.545043i	$-0.816513\pi$
$293$		−	8.03400e9i		−	1.09009i	0.838408	−	0.545043i	$-0.183487\pi$
$294$		0			0
$295$	2.19926e9			0.290395
$296$		0			0
$297$	1.04296e9	−	6.02155e8i	0.134043	−	0.0773896i
$298$		0			0
$299$	−9.24867e9	−	5.33972e9i	−1.15716	−	0.668088i
$300$		0			0
$301$		0			0
$302$		0			0
$303$	3.98403e9	−	6.90055e9i	0.472664	−	0.818678i
$304$		0			0
$305$	2.11192e8	+	3.65795e8i	0.0244049	+	0.0422706i
$306$		0			0
$307$		−	6.40529e9i		−	0.721083i	−0.932743	−	0.360542i	$-0.882592\pi$
$307$		−	6.40529e9i		−	0.721083i	0.932743	−	0.360542i	$-0.117408\pi$
$308$		0			0
$309$	−1.49850e10			−1.64370
$310$		0			0
$311$	−8.57644e9	+	4.95161e9i	−0.916781	+	0.529304i	−0.882607	−	0.470112i	$-0.844213\pi$
$311$	−8.57644e9	+	4.95161e9i	−0.916781	+	0.529304i	−0.0341741	+	0.999416i	$0.510880\pi$
$312$		0			0
$313$	−1.11525e10	−	6.43889e9i	−1.16197	−	0.670863i	−0.210194	−	0.977660i	$-0.567410\pi$
$313$	−1.11525e10	−	6.43889e9i	−1.16197	−	0.670863i	−0.951775	+	0.306797i	$0.900743\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−2.45499e9	+	4.25216e9i	−0.243115	+	0.421088i	−0.961600	−	0.274455i	$-0.911503\pi$
$317$	−2.45499e9	+	4.25216e9i	−0.243115	+	0.421088i	0.718485	+	0.695543i	$0.244836\pi$
$318$		0			0
$319$	1.88561e9	+	3.26597e9i	0.182091	+	0.315391i
$320$		0			0
$321$		−	1.20670e10i		−	1.13652i
$322$		0			0
$323$	1.43205e9			0.131567
$324$		0			0
$325$	1.20032e10	−	6.93008e9i	1.07588	−	0.621162i
$326$		0			0
$327$	7.87579e9	+	4.54709e9i	0.688816	+	0.397688i
$328$		0			0
$329$		0			0
$330$		0			0
$331$	1.05763e10	−	1.83187e10i	0.881096	−	1.52610i	0.0309714	−	0.999520i	$-0.490140\pi$
$331$	1.05763e10	−	1.83187e10i	0.881096	−	1.52610i	0.850124	−	0.526582i	$-0.176527\pi$
$332$		0			0
$333$	9.38027e9	+	1.62471e10i	0.762848	+	1.32129i
$334$		0			0
$335$		−	2.07037e9i		−	0.164388i
$336$		0			0
$337$	1.66609e10			1.29175			0.645876	−	0.763442i	$-0.276492\pi$
$337$	1.66609e10			1.29175			0.645876	+	0.763442i	$0.276492\pi$
$338$		0			0
$339$	1.06532e10	−	6.15065e9i	0.806645	−	0.465717i
$340$		0			0
$341$	6.67101e9	+	3.85151e9i	0.493371	+	0.284848i
$342$		0			0
$343$		0			0
$344$		0			0
$345$	−2.96646e9	+	5.13805e9i	−0.209393	+	0.362679i
$346$		0			0
$347$	−3.77345e8	−	6.53581e8i	−0.0260268	−	0.0450797i	0.852719	−	0.522370i	$-0.174952\pi$
$347$	−3.77345e8	−	6.53581e8i	−0.0260268	−	0.0450797i	−0.878745	+	0.477291i	$0.841619\pi$
$348$		0			0
$349$		−	1.22867e10i		−	0.828195i	−0.910232	−	0.414098i	$-0.864097\pi$
$349$		−	1.22867e10i		−	0.828195i	0.910232	−	0.414098i	$-0.135903\pi$
$350$		0			0
$351$	−1.00047e10			−0.659138
$352$		0			0
$353$	1.97054e10	−	1.13769e10i	1.26907	−	0.732698i	0.294258	−	0.955726i	$-0.404927\pi$
$353$	1.97054e10	−	1.13769e10i	1.26907	−	0.732698i	0.974812	+	0.223028i	$0.0715940\pi$
$354$		0			0
$355$	−2.04203e8	−	1.17897e8i	−0.0128573	−	0.00742314i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	1.33032e10	−	2.30418e10i	0.800899	−	1.38720i	−0.118126	−	0.992999i	$-0.537689\pi$
$359$	1.33032e10	−	2.30418e10i	0.800899	−	1.38720i	0.919025	−	0.394199i	$-0.128978\pi$
$360$		0			0
$361$	−6.12089e9	−	1.06017e10i	−0.360401	−	0.624232i
$362$		0			0
$363$			2.38151e10i			1.37160i
$364$		0			0
$365$	−5.23424e9			−0.294905
$366$		0			0
$367$	−1.52175e10	+	8.78584e9i	−0.838841	+	0.484305i	−0.856870	−	0.515532i	$-0.827594\pi$
$367$	−1.52175e10	+	8.78584e9i	−0.838841	+	0.484305i	0.0180288	+	0.999837i	$0.494261\pi$
$368$		0			0
$369$	3.69959e10	+	2.13596e10i	1.99548	+	1.15209i
$370$		0			0
$371$		0			0
$372$		0			0
$373$	−4.49956e9	+	7.79346e9i	−0.232453	+	0.402620i	−0.958529	−	0.284994i	$-0.908008\pi$
$373$	−4.49956e9	+	7.79346e9i	−0.232453	+	0.402620i	0.726077	+	0.687614i	$0.241342\pi$
$374$		0			0
$375$	−8.01925e9	−	1.38897e10i	−0.405517	−	0.702375i
$376$		0			0
$377$		−	3.13291e10i		−	1.55090i
$378$		0			0
$379$	1.44215e10			0.698964			0.349482	−	0.936943i	$-0.386358\pi$
$379$	1.44215e10			0.698964			0.349482	+	0.936943i	$0.386358\pi$
$380$		0			0
$381$	−1.40558e10	+	8.11512e9i	−0.667046	+	0.385119i
$382$		0			0
$383$	−2.03270e10	−	1.17358e10i	−0.944664	−	0.545402i	−0.0532446	−	0.998581i	$-0.516956\pi$
$383$	−2.03270e10	−	1.17358e10i	−0.944664	−	0.545402i	−0.891419	+	0.453180i	$0.850290\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	1.23467e10	−	2.13851e10i	0.550435	−	0.953381i
$388$		0			0
$389$	−7.60413e9	−	1.31707e10i	−0.332087	−	0.575191i	0.650834	−	0.759220i	$-0.274419\pi$
$389$	−7.60413e9	−	1.31707e10i	−0.332087	−	0.575191i	−0.982921	+	0.184029i	$0.941086\pi$
$390$		0			0
$391$			5.77994e9i			0.247296i
$392$		0			0
$393$	−5.17212e10			−2.16820
$394$		0			0
$395$	−7.18927e9	+	4.15073e9i	−0.295322	+	0.170504i
$396$		0			0
$397$	2.14552e10	+	1.23872e10i	0.863717	+	0.498667i	0.865255	−	0.501332i	$-0.167156\pi$
$397$	2.14552e10	+	1.23872e10i	0.863717	+	0.498667i	−0.00153819	+	0.999999i	$0.500490\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−1.16435e10	+	2.01672e10i	−0.450305	+	0.779951i	−0.998405	−	0.0564621i	$-0.982018\pi$
$401$	−1.16435e10	+	2.01672e10i	−0.450305	+	0.779951i	0.548100	+	0.836413i	$0.315351\pi$
$402$		0			0
$403$	−3.19961e10	−	5.54189e10i	−1.21305	−	2.10106i
$404$		0			0
$405$		−	4.28160e9i		−	0.159143i
$406$		0			0
$407$	1.00078e10			0.364720
$408$		0			0
$409$	−3.81857e10	+	2.20465e10i	−1.36461	+	0.787856i	−0.990233	−	0.139422i	$-0.955476\pi$
$409$	−3.81857e10	+	2.20465e10i	−1.36461	+	0.787856i	−0.374374	+	0.927278i	$0.622142\pi$
$410$		0			0
$411$	6.74926e10	+	3.89669e10i	2.36532	+	1.36562i
$412$		0			0
$413$		0			0
$414$		0			0
$415$	−2.93304e9	+	5.08018e9i	−0.0988839	+	0.171272i
$416$		0			0
$417$	−1.46766e10	−	2.54206e10i	−0.485380	−	0.840702i
$418$		0			0
$419$		−	1.28016e10i		−	0.415343i	−0.978199	−	0.207672i	$-0.933411\pi$
$419$		−	1.28016e10i		−	0.415343i	0.978199	−	0.207672i	$-0.0665886\pi$
$420$		0			0
$421$	−9.73575e8			−0.0309914			−0.0154957	−	0.999880i	$-0.504933\pi$
$421$	−9.73575e8			−0.0309914			−0.0154957	+	0.999880i	$0.504933\pi$
$422$		0			0
$423$	3.38942e10	−	1.95688e10i	1.05868	−	0.611228i
$424$		0			0
$425$	−6.49641e9	−	3.75070e9i	−0.199121	−	0.114963i
$426$		0			0
$427$		0			0
$428$		0			0
$429$	−1.09673e10	+	1.89960e10i	−0.323797	+	0.560832i
$430$		0			0
$431$	−1.39835e10	−	2.42201e10i	−0.405235	−	0.701887i	0.589114	−	0.808050i	$-0.299477\pi$
$431$	−1.39835e10	−	2.42201e10i	−0.405235	−	0.701887i	−0.994349	+	0.106163i	$0.966143\pi$
$432$		0			0
$433$		−	3.09448e10i		−	0.880310i	−0.897922	−	0.440155i	$-0.854923\pi$
$433$		−	3.09448e10i		−	0.880310i	0.897922	−	0.440155i	$-0.145077\pi$
$434$		0			0
$435$	−1.74047e10			−0.486083
$436$		0			0
$437$	−1.65744e10	+	9.56924e9i	−0.454478	+	0.262393i
$438$		0			0
$439$	−1.08633e10	−	6.27191e9i	−0.292484	−	0.168866i	0.346577	−	0.938021i	$-0.387344\pi$
$439$	−1.08633e10	−	6.27191e9i	−0.292484	−	0.168866i	−0.639062	+	0.769156i	$0.720677\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	1.96973e10	−	3.41167e10i	0.511437	−	0.885835i	−0.488475	−	0.872578i	$-0.662447\pi$
$443$	1.96973e10	−	3.41167e10i	0.511437	−	0.885835i	0.999912	−	0.0132570i	$-0.00421996\pi$
$444$		0			0
$445$	−1.07439e9	−	1.86091e9i	−0.0273983	−	0.0474552i
$446$		0			0
$447$			6.41068e10i			1.60573i
$448$		0			0
$449$	6.70984e10			1.65092			0.825462	−	0.564458i	$-0.190915\pi$
$449$	6.70984e10			1.65092			0.825462	+	0.564458i	$0.190915\pi$
$450$		0			0
$451$	1.97354e10	−	1.13942e10i	0.477023	−	0.275409i
$452$		0			0
$453$	4.50928e10	+	2.60343e10i	1.07082	+	0.618235i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	2.60678e10	−	4.51508e10i	0.597640	−	1.03514i	−0.395528	−	0.918454i	$-0.629438\pi$
$457$	2.60678e10	−	4.51508e10i	0.597640	−	1.03514i	0.993168	−	0.116690i	$-0.0372283\pi$
$458$		0			0
$459$	2.70738e9	+	4.68933e9i	0.0609957	+	0.105648i
$460$		0			0
$461$		−	6.17475e9i		−	0.136715i	−0.997661	−	0.0683574i	$-0.978224\pi$
$461$		−	6.17475e9i		−	0.136715i	0.997661	−	0.0683574i	$-0.0217758\pi$
$462$		0			0
$463$	1.26457e9			0.0275182			0.0137591	−	0.999905i	$-0.495620\pi$
$463$	1.26457e9			0.0275182			0.0137591	+	0.999905i	$0.495620\pi$
$464$		0			0
$465$	−3.07877e10	+	1.77753e10i	−0.658515	+	0.380194i
$466$		0			0
$467$	1.58865e10	+	9.17206e9i	0.334010	+	0.192841i	0.657620	−	0.753350i	$-0.271563\pi$
$467$	1.58865e10	+	9.17206e9i	0.334010	+	0.192841i	−0.323610	+	0.946191i	$0.604897\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$	2.72447e10	−	4.71892e10i	0.553603	−	0.958868i
$472$		0			0
$473$	−6.58630e9	−	1.14078e10i	−0.131582	−	0.227907i
$474$		0			0
$475$		−	2.48386e10i		−	0.487924i
$476$		0			0
$477$	−1.16930e11			−2.25867
$478$		0			0
$479$	7.31345e10	−	4.22243e10i	1.38925	−	0.802084i	0.396020	−	0.918242i	$-0.370391\pi$
$479$	7.31345e10	−	4.22243e10i	1.38925	−	0.802084i	0.993231	+	0.116158i	$0.0370579\pi$
$480$		0			0
$481$	−7.20002e10	−	4.15694e10i	−1.34510	−	0.776592i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−1.00213e10	+	1.73574e10i	−0.181116	+	0.313702i
$486$		0			0
$487$	4.61531e10	+	7.99394e10i	0.820511	+	1.42117i	0.905302	+	0.424769i	$0.139645\pi$
$487$	4.61531e10	+	7.99394e10i	0.820511	+	1.42117i	−0.0847905	+	0.996399i	$0.527022\pi$
$488$		0			0
$489$		−	1.07900e11i		−	1.88706i
$490$		0			0
$491$	3.08704e10			0.531149			0.265574	−	0.964090i	$-0.414438\pi$
$491$	3.08704e10			0.531149			0.265574	+	0.964090i	$0.414438\pi$
$492$		0			0
$493$	−1.46843e10	+	8.47799e9i	−0.248580	+	0.143518i
$494$		0			0
$495$	6.00740e9	+	3.46838e9i	0.100061	+	0.0577704i
$496$		0			0
$497$		0			0
$498$		0			0
$499$	−1.90238e10	+	3.29501e10i	−0.306828	+	0.531441i	−0.977667	−	0.210162i	$-0.932601\pi$
$499$	−1.90238e10	+	3.29501e10i	−0.306828	+	0.531441i	0.670839	+	0.741603i	$0.265934\pi$
$500$		0			0
$501$	7.84842e10	+	1.35939e11i	1.24575	+	2.15770i
$502$		0			0
$503$		−	1.64419e10i		−	0.256850i	−0.991719	−	0.128425i	$-0.959008\pi$
$503$		−	1.64419e10i		−	0.256850i	0.991719	−	0.128425i	$-0.0409921\pi$
$504$		0			0
$505$	1.11670e10			0.171700
$506$		0			0
$507$	7.06209e10	−	4.07730e10i	1.06881	−	0.617079i
$508$		0			0
$509$	−1.65983e10	−	9.58304e9i	−0.247282	−	0.142768i	0.371237	−	0.928538i	$-0.378934\pi$
$509$	−1.65983e10	−	9.58304e9i	−0.247282	−	0.142768i	−0.618519	+	0.785770i	$0.712267\pi$
$510$		0			0
$511$		0			0
$512$		0			0
$513$	−8.96467e9	+	1.55273e10i	−0.129439	+	0.224195i
$514$		0			0
$515$	−1.05005e10	−	1.81874e10i	−0.149273	−	0.258549i
$516$		0			0
$517$		−	2.08779e10i		−	0.292230i
$518$		0			0
$519$	1.42396e11			1.96258
$520$		0			0
$521$	−2.48583e10	+	1.43520e10i	−0.337381	+	0.194787i	−0.659113	−	0.752044i	$-0.729068\pi$
$521$	−2.48583e10	+	1.43520e10i	−0.337381	+	0.194787i	0.321732	+	0.946831i	$0.395735\pi$
$522$		0			0
$523$	6.28180e9	+	3.62680e9i	0.0839609	+	0.0484748i	0.541393	−	0.840770i	$-0.317897\pi$
$523$	6.28180e9	+	3.62680e9i	0.0839609	+	0.0484748i	−0.457432	+	0.889245i	$0.651231\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−1.73170e10	+	2.99939e10i	−0.224507	+	0.388858i
$528$		0			0
$529$	5.32724e8	+	9.22704e8i	0.00680267	+	0.0117826i
$530$		0			0
$531$			1.10249e11i			1.38674i
$532$		0			0
$533$	−1.89313e11			−2.34570
$534$		0			0
$535$	1.46458e10	−	8.45575e9i	0.178771	−	0.103214i
$536$		0			0
$537$	−1.60265e11	−	9.25292e10i	−1.92727	−	1.11271i
$538$		0			0
$539$		0			0
$540$		0			0
$541$	3.49646e10	−	6.05604e10i	0.408168	−	0.706968i	−0.586516	−	0.809937i	$-0.699501\pi$
$541$	3.49646e10	−	6.05604e10i	0.408168	−	0.706968i	0.994685	+	0.102970i	$0.0328344\pi$
$542$		0			0
$543$	5.20625e10	+	9.01749e10i	0.598860	+	1.03726i
$544$		0			0
$545$			1.27452e10i			0.144464i
$546$		0			0
$547$	1.52716e11			1.70583			0.852913	−	0.522054i	$-0.174834\pi$
$547$	1.52716e11			1.70583			0.852913	+	0.522054i	$0.174834\pi$
$548$		0			0
$549$	−1.83373e10	+	1.05870e10i	−0.201858	+	0.116543i
$550$		0			0
$551$	−4.86225e10	−	2.80722e10i	−0.527511	−	0.304558i
$552$		0			0
$553$		0			0
$554$		0			0
$555$	−2.30936e10	+	3.99994e10i	−0.243400	+	0.421581i
$556$		0			0
$557$	−8.61047e9	−	1.49138e10i	−0.0894553	−	0.154941i	0.817826	−	0.575466i	$-0.195179\pi$
$557$	−8.61047e9	−	1.49138e10i	−0.0894553	−	0.154941i	−0.907281	+	0.420525i	$0.861846\pi$
$558$		0			0
$559$			1.09430e11i			1.12070i
$560$		0			0
$561$	1.18715e10			0.119855
$562$		0			0
$563$	−2.95498e10	+	1.70606e10i	−0.294118	+	0.169809i	−0.639797	−	0.768544i	$-0.720982\pi$
$563$	−2.95498e10	+	1.70606e10i	−0.294118	+	0.169809i	0.345680	+	0.938353i	$0.387648\pi$
$564$		0			0
$565$	1.49302e10	+	8.61993e9i	0.146511	+	0.0845882i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−4.86901e10	+	8.43337e10i	−0.464506	+	0.804549i	−0.999179	−	0.0405106i	$-0.987102\pi$
$569$	−4.86901e10	+	8.43337e10i	−0.464506	+	0.804549i	0.534673	+	0.845059i	$0.320435\pi$
$570$		0			0
$571$	−2.48222e10	−	4.29933e10i	−0.233505	−	0.404442i	0.725332	−	0.688399i	$-0.241686\pi$
$571$	−2.48222e10	−	4.29933e10i	−0.233505	−	0.404442i	−0.958837	+	0.283957i	$0.908353\pi$
$572$		0			0
$573$			1.73611e11i			1.61049i
$574$		0			0
$575$	1.00252e11			0.917110
$576$		0			0
$577$	−1.08670e11	+	6.27405e10i	−0.980405	+	0.566037i	−0.902392	−	0.430915i	$-0.858191\pi$
$577$	−1.08670e11	+	6.27405e10i	−0.980405	+	0.566037i	−0.0780124	+	0.996952i	$0.524857\pi$
$578$		0			0
$579$	−1.62625e10	−	9.38916e9i	−0.144702	−	0.0835435i
$580$		0			0
$581$		0			0
$582$		0			0
$583$	−3.11880e10	+	5.40192e10i	−0.269969	+	0.467599i
$584$		0			0
$585$	−2.88133e10	−	4.99061e10i	−0.246019	−	0.426118i
$586$		0			0
$587$			1.19946e11i			1.01026i	0.863043	+	0.505130i	$0.168556\pi$
$587$			1.19946e11i			1.01026i	−0.863043	+	0.505130i	$0.831444\pi$
$588$		0			0
$589$	−1.14680e11			−0.952852
$590$		0			0
$591$	−1.74846e10	+	1.00947e10i	−0.143319	+	0.0827455i
$592$		0			0
$593$	−1.55033e11	−	8.95084e10i	−1.25374	−	0.723844i	−0.281886	−	0.959448i	$-0.590960\pi$
$593$	−1.55033e11	−	8.95084e10i	−1.25374	−	0.723844i	−0.971849	+	0.235604i	$0.924293\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	−1.36270e11	+	2.36026e11i	−1.07276	+	1.85808i
$598$		0			0
$599$	−5.45483e10	−	9.44805e10i	−0.423715	−	0.733897i	0.572584	−	0.819846i	$-0.305941\pi$
$599$	−5.45483e10	−	9.44805e10i	−0.423715	−	0.733897i	−0.996300	+	0.0859494i	$0.972608\pi$
$600$		0			0
$601$		−	1.02458e11i		−	0.785325i	−0.919683	−	0.392663i	$-0.871554\pi$
$601$		−	1.02458e11i		−	0.785325i	0.919683	−	0.392663i	$-0.128446\pi$
$602$		0			0
$603$	1.03788e11			0.785012
$604$		0			0
$605$	−2.89045e10	+	1.66880e10i	−0.215747	+	0.124562i
$606$		0			0
$607$	4.97148e10	+	2.87029e10i	0.366211	+	0.211432i	0.671802	−	0.740731i	$-0.265521\pi$
$607$	4.97148e10	+	2.87029e10i	0.366211	+	0.211432i	−0.305591	+	0.952163i	$0.598854\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−8.67207e10	+	1.50205e11i	−0.622240	+	1.07775i
$612$		0			0
$613$	7.03556e10	+	1.21860e11i	0.498261	+	0.863014i	0.999998	−	0.00200674i	$-0.000638766\pi$
$613$	7.03556e10	+	1.21860e11i	0.498261	+	0.863014i	−0.501737	+	0.865020i	$0.667305\pi$
$614$		0			0
$615$			1.05172e11i			0.735191i
$616$		0			0
$617$	−2.78345e10			−0.192063			−0.0960313	−	0.995378i	$-0.530615\pi$
$617$	−2.78345e10			−0.192063			−0.0960313	+	0.995378i	$0.530615\pi$
$618$		0			0
$619$	5.33247e10	−	3.07870e10i	0.363217	−	0.209703i	−0.307274	−	0.951621i	$-0.599417\pi$
$619$	5.33247e10	−	3.07870e10i	0.363217	−	0.209703i	0.670491	+	0.741918i	$0.266084\pi$
$620$		0			0
$621$	−6.26701e10	−	3.61826e10i	−0.421400	−	0.243295i
$622$		0			0
$623$		0			0
$624$		0			0
$625$	−5.92121e10	+	1.02558e11i	−0.388053	+	0.672127i
$626$		0			0
$627$	1.96544e10	+	3.40425e10i	0.127172	+	0.220268i
$628$		0			0
$629$			4.49964e10i			0.287459i
$630$		0			0
$631$	−1.98125e11			−1.24975			−0.624874	−	0.780726i	$-0.714850\pi$
$631$	−1.98125e11			−1.24975			−0.624874	+	0.780726i	$0.714850\pi$
$632$		0			0
$633$	−3.59906e11	+	2.07792e11i	−2.24169	+	1.29424i
$634$		0			0
$635$	−1.96987e10	−	1.13731e10i	−0.121156	−	0.0699492i
$636$		0			0
$637$		0			0
$638$		0			0
$639$	5.91014e9	−	1.02367e10i	0.0354482	−	0.0613981i
$640$		0			0
$641$	−7.76040e9	−	1.34414e10i	−0.0459676	−	0.0796183i	0.842126	−	0.539281i	$-0.181304\pi$
$641$	−7.76040e9	−	1.34414e10i	−0.0459676	−	0.0796183i	−0.888094	+	0.459662i	$0.847970\pi$
$642$		0			0
$643$			2.33886e11i			1.36824i	0.729371	+	0.684118i	$0.239813\pi$
$643$			2.33886e11i			1.36824i	−0.729371	+	0.684118i	$0.760187\pi$
$644$		0			0
$645$	6.07935e10			0.351251
$646$		0			0
$647$	1.87182e11	−	1.08069e11i	1.06818	−	0.616716i	0.140499	−	0.990081i	$-0.455129\pi$
$647$	1.87182e11	−	1.08069e11i	1.06818	−	0.616716i	0.927685	+	0.373364i	$0.121796\pi$
$648$		0			0
$649$	5.09327e10	+	2.94060e10i	0.287090	+	0.165751i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	1.60346e11	−	2.77727e11i	0.881869	−	1.52744i	0.0326087	−	0.999468i	$-0.489618\pi$
$653$	1.60346e11	−	2.77727e11i	0.881869	−	1.52744i	0.849261	−	0.527974i	$-0.177048\pi$
$654$		0			0
$655$	−3.62428e10	−	6.27744e10i	−0.196905	−	0.341049i
$656$		0			0
$657$		−	2.62392e11i		−	1.40828i
$658$		0			0
$659$	−9.25294e10			−0.490612			−0.245306	−	0.969446i	$-0.578888\pi$
$659$	−9.25294e10			−0.490612			−0.245306	+	0.969446i	$0.578888\pi$
$660$		0			0
$661$	8.25004e10	−	4.76316e10i	0.432166	−	0.249511i	−0.268103	−	0.963390i	$-0.586397\pi$
$661$	8.25004e10	−	4.76316e10i	0.432166	−	0.249511i	0.700269	+	0.713879i	$0.253063\pi$
$662$		0			0
$663$	−8.54090e10	−	4.93109e10i	−0.442027	−	0.255205i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	1.13303e11	−	1.96247e11i	0.572452	−	0.991517i
$668$		0			0
$669$	7.29163e10	+	1.26295e11i	0.364016	+	0.630494i
$670$		0			0
$671$			1.12952e10i			0.0557192i
$672$		0			0
$673$	3.91328e11			1.90757			0.953787	−	0.300485i	$-0.0971485\pi$
$673$	3.91328e11			1.90757			0.953787	+	0.300485i	$0.0971485\pi$
$674$		0			0
$675$	8.13355e10	−	4.69590e10i	0.391800	−	0.226206i
$676$		0			0
$677$	9.24478e10	+	5.33748e10i	0.440091	+	0.254086i	0.703636	−	0.710561i	$-0.251559\pi$
$677$	9.24478e10	+	5.33748e10i	0.440091	+	0.254086i	−0.263545	+	0.964647i	$0.584892\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$	5.95996e10	−	1.03230e11i	0.277112	−	0.479971i
$682$		0			0
$683$	1.34438e11	+	2.32853e11i	0.617787	+	1.07004i	0.989889	+	0.141847i	$0.0453040\pi$
$683$	1.34438e11	+	2.32853e11i	0.617787	+	1.07004i	−0.372101	+	0.928192i	$0.621363\pi$
$684$		0			0
$685$			1.09222e11i			0.496074i
$686$		0			0
$687$	1.34147e11			0.602219
$688$		0			0
$689$	4.48761e11	−	2.59092e11i	1.99131	−	1.14968i
$690$		0			0
$691$	−8.39256e10	−	4.84545e10i	−0.368114	−	0.212531i	0.304520	−	0.952506i	$-0.401504\pi$
$691$	−8.39256e10	−	4.84545e10i	−0.368114	−	0.212531i	−0.672634	+	0.739975i	$0.734837\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	2.05688e10	−	3.56262e10i	0.0881596	−	0.152697i
$696$		0			0
$697$	5.12302e10	+	8.87333e10i	0.217068	+	0.375972i
$698$		0			0
$699$		−	3.78348e11i		−	1.58483i
$700$		0			0
$701$	−4.51079e11			−1.86802			−0.934008	−	0.357252i	$-0.883714\pi$
$701$	−4.51079e11			−1.86802			−0.934008	+	0.357252i	$0.883714\pi$
$702$		0			0
$703$	−1.29031e11	+	7.44959e10i	−0.528289	+	0.305008i
$704$		0			0
$705$	8.34455e10	+	4.81773e10i	0.337790	+	0.195023i
$706$		0			0
$707$		0			0
$708$		0			0
$709$	−2.09020e11	+	3.62033e11i	−0.827184	+	1.43272i	0.0730544	+	0.997328i	$0.476725\pi$
$709$	−2.09020e11	+	3.62033e11i	−0.827184	+	1.43272i	−0.900239	+	0.435397i	$0.856608\pi$
$710$		0			0
$711$	−2.08075e11	−	3.60397e11i	−0.814221	−	1.41027i
$712$		0			0
$713$		−	4.62863e11i		−	1.79099i
$714$		0			0
$715$	−3.07407e10			−0.117622
$716$		0			0
$717$	3.38649e10	−	1.95519e10i	0.128137	−	0.0739798i
$718$		0			0
$719$	1.81302e11	+	1.04674e11i	0.678400	+	0.391675i	0.799252	−	0.600996i	$-0.205229\pi$
$719$	1.81302e11	+	1.04674e11i	0.678400	+	0.391675i	−0.120852	+	0.992671i	$0.538563\pi$
$720$		0			0
$721$		0			0
$722$		0			0
$723$	3.66587e11	−	6.34946e11i	1.34160	−	2.32372i
$724$		0			0
$725$	1.47049e11	+	2.54696e11i	0.532243	+	0.921872i
$726$		0			0
$727$		−	1.87662e11i		−	0.671797i	−0.941898	−	0.335899i	$-0.890960\pi$
$727$		−	1.87662e11i		−	0.671797i	0.941898	−	0.335899i	$-0.109040\pi$
$728$		0			0
$729$	4.25469e11			1.50646
$730$		0			0
$731$	5.12912e10	−	2.96130e10i	0.179628	−	0.103708i
$732$		0			0
$733$	3.72577e11	+	2.15107e11i	1.29062	+	0.745143i	0.978765	−	0.204986i	$-0.0657148\pi$
$733$	3.72577e11	+	2.15107e11i	1.29062	+	0.745143i	0.311860	+	0.950128i	$0.399048\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	2.76826e10	−	4.79477e10i	0.0938291	−	0.162517i
$738$		0			0
$739$	1.83158e11	+	3.17240e11i	0.614114	+	1.06368i	0.990539	+	0.137230i	$0.0438199\pi$
$739$	1.83158e11	+	3.17240e11i	0.614114	+	1.06368i	−0.376425	+	0.926447i	$0.622847\pi$
$740$		0			0
$741$		−	3.26555e11i		−	1.08314i
$742$		0			0
$743$	−3.84706e11			−1.26233			−0.631166	−	0.775648i	$-0.717423\pi$
$743$	−3.84706e11			−1.26233			−0.631166	+	0.775648i	$0.717423\pi$
$744$		0			0
$745$	−7.78068e10	+	4.49218e10i	−0.252576	+	0.145825i
$746$		0			0
$747$	−2.54669e11	−	1.47033e11i	−0.817887	−	0.472207i
$748$		0			0
$749$		0			0
$750$		0			0
$751$	2.28104e11	−	3.95088e11i	0.717090	−	1.24204i	−0.245058	−	0.969508i	$-0.578807\pi$
$751$	2.28104e11	−	3.95088e11i	0.717090	−	1.24204i	0.962148	−	0.272528i	$-0.0878597\pi$
$752$		0			0
$753$	−3.69889e11	−	6.40667e11i	−1.15051	−	1.99275i
$754$		0			0
$755$			7.29726e10i			0.224580i
$756$		0			0
$757$	−5.39134e11			−1.64177			−0.820886	−	0.571092i	$-0.806520\pi$
$757$	−5.39134e11			−1.64177			−0.820886	+	0.571092i	$0.806520\pi$
$758$		0			0
$759$	−1.37400e11	+	7.93279e10i	−0.414018	+	0.239034i
$760$		0			0
$761$	−1.54194e11	−	8.90242e10i	−0.459759	−	0.265442i	0.252184	−	0.967679i	$-0.418851\pi$
$761$	−1.54194e11	−	8.90242e10i	−0.459759	−	0.265442i	−0.711943	+	0.702237i	$0.752185\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$	−1.55944e10	+	2.70102e10i	−0.0455325	+	0.0788647i
$766$		0			0
$767$	−2.44288e11	−	4.23119e11i	−0.705864	−	1.22259i
$768$		0			0
$769$		−	3.25479e10i		−	0.0930717i	−0.998917	−	0.0465358i	$-0.985182\pi$
$769$		−	3.25479e10i		−	0.0930717i	0.998917	−	0.0465358i	$-0.0148182\pi$
$770$		0			0
$771$	2.75819e11			0.780562
$772$		0			0
$773$	6.46687e10	−	3.73365e10i	0.181124	−	0.104572i	−0.406697	−	0.913563i	$-0.633319\pi$
$773$	6.46687e10	−	3.73365e10i	0.181124	−	0.104572i	0.587821	+	0.808991i	$0.299986\pi$
$774$		0			0
$775$	5.20238e11	+	3.00360e11i	1.44210	+	0.832597i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−1.69633e11	+	2.93813e11i	−0.460639	+	0.797850i
$780$		0			0
$781$	−3.15275e9	−	5.46072e9i	−0.00847394	−	0.0146773i
$782$		0			0
$783$		−	2.12290e11i		−	0.564784i
$784$		0			0
$785$	7.63651e10			0.201102
$786$		0			0
$787$	−3.52056e11	+	2.03260e11i	−0.917727	+	0.529850i	−0.882909	−	0.469544i	$-0.844418\pi$
$787$	−3.52056e11	+	2.03260e11i	−0.917727	+	0.529850i	−0.0348175	+	0.999394i	$0.511085\pi$
$788$		0			0
$789$	9.91934e11	+	5.72694e11i	2.55962	+	1.47780i
$790$		0			0
$791$		0			0
$792$		0			0
$793$	4.69172e10	−	8.12629e10i	0.118642	−	0.205494i
$794$		0			0
$795$	−1.43937e11	−	2.49307e11i	−0.360334	−	0.624116i
$796$		0			0
$797$			7.13612e11i			1.76860i	0.466922	+	0.884298i	$0.345363\pi$
$797$			7.13612e11i			1.76860i	−0.466922	+	0.884298i	$0.654637\pi$
$798$		0			0
$799$	9.38702e10			0.230325
$800$		0			0
$801$	9.32870e10	−	5.38593e10i	0.226616	−	0.130837i
$802$		0			0
$803$	−1.21220e11	−	6.99861e10i	−0.291548	−	0.168325i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	1.45717e11	−	2.52390e11i	0.343571	−	0.595083i
$808$		0			0
$809$	−4.01982e11	−	6.96254e11i	−0.938454	−	1.62545i	−0.768356	−	0.640022i	$-0.778925\pi$
$809$	−4.01982e11	−	6.96254e11i	−0.938454	−	1.62545i	−0.170097	−	0.985427i	$-0.554408\pi$
$810$		0			0
$811$			4.34692e11i			1.00484i	0.864623	+	0.502422i	$0.167557\pi$
$811$			4.34692e11i			1.00484i	−0.864623	+	0.502422i	$0.832443\pi$
$812$		0			0
$813$	2.84171e11			0.650454
$814$		0			0
$815$	1.30959e11	−	7.56093e10i	0.296828	−	0.171374i
$816$		0			0
$817$	1.69835e11	+	9.80543e10i	0.381188	+	0.220079i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−1.42253e11	+	2.46389e11i	−0.313103	+	0.542311i	−0.979033	−	0.203704i	$-0.934702\pi$
$821$	−1.42253e11	+	2.46389e11i	−0.313103	+	0.542311i	0.665929	+	0.746015i	$0.268035\pi$
$822$		0			0
$823$	1.77486e10	+	3.07414e10i	0.0386869	+	0.0670077i	0.884721	−	0.466122i	$-0.154349\pi$
$823$	1.77486e10	+	3.07414e10i	0.0386869	+	0.0670077i	−0.846034	+	0.533130i	$0.821016\pi$
$824$		0			0
$825$		−	2.05909e11i		−	0.444488i
$826$		0			0
$827$	−8.15466e11			−1.74335			−0.871673	−	0.490087i	$-0.836965\pi$
$827$	−8.15466e11			−1.74335			−0.871673	+	0.490087i	$0.836965\pi$
$828$		0			0
$829$	5.67873e11	−	3.27861e11i	1.20236	−	0.694180i	0.241277	−	0.970456i	$-0.422434\pi$
$829$	5.67873e11	−	3.27861e11i	1.20236	−	0.694180i	0.961078	+	0.276276i	$0.0891004\pi$
$830$		0			0
$831$	−9.45288e10	−	5.45762e10i	−0.198226	−	0.114446i
$832$		0			0
$833$		0			0
$834$		0			0
$835$	−1.09993e11	+	1.90514e11i	−0.226266	+	0.391904i
$836$		0			0
$837$	−2.16810e11	−	3.75525e11i	−0.441750	−	0.765134i
$838$		0			0
$839$			9.47661e10i			0.191252i	0.995417	+	0.0956258i	$0.0304852\pi$
$839$			9.47661e10i			0.191252i	−0.995417	+	0.0956258i	$0.969515\pi$
$840$		0			0
$841$	1.64524e11			0.328887
$842$		0			0
$843$	−1.15834e12	+	6.68770e11i	−2.29365	+	1.32424i
$844$		0			0
$845$	9.89728e10	+	5.71420e10i	0.194128	+	0.112080i
$846$		0			0
$847$		0			0
$848$		0			0
$849$	−1.60797e11	+	2.78508e11i	−0.309490	+	0.536052i
$850$		0			0
$851$	−3.00676e11	−	5.20785e11i	−0.573297	−	0.992980i
$852$		0			0
$853$		−	9.59002e10i		−	0.181144i	−0.995890	−	0.0905718i	$-0.971131\pi$
$853$		−	9.59002e10i		−	0.181144i	0.995890	−	0.0905718i	$-0.0288695\pi$
$854$		0			0
$855$	−1.03272e11			−0.193249
$856$		0			0
$857$	−3.26016e10	+	1.88226e10i	−0.0604388	+	0.0348944i	−0.529915	−	0.848051i	$-0.677776\pi$
$857$	−3.26016e10	+	1.88226e10i	−0.0604388	+	0.0348944i	0.469476	+	0.882945i	$0.344443\pi$
$858$		0			0
$859$	6.33374e11	+	3.65679e11i	1.16329	+	0.671625i	0.952090	−	0.305818i	$-0.0989298\pi$
$859$	6.33374e11	+	3.65679e11i	1.16329	+	0.671625i	0.211199	+	0.977443i	$0.432263\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	1.07380e11	−	1.85987e11i	0.193588	−	0.335305i	−0.752848	−	0.658194i	$-0.771321\pi$
$863$	1.07380e11	−	1.85987e11i	0.193588	−	0.335305i	0.946437	+	0.322889i	$0.104654\pi$
$864$		0			0
$865$	9.97815e10	+	1.72827e11i	0.178232	+	0.308707i
$866$		0			0
$867$		−	8.07549e11i		−	1.42920i
$868$		0			0
$869$	−2.21995e11			−0.389281
$870$		0			0
$871$	−3.98322e11	+	2.29971e11i	−0.692089	+	0.399578i
$872$		0			0
$873$	−8.70122e11	−	5.02365e11i	−1.49804	−	0.864894i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	1.89034e11	−	3.27416e11i	0.319552	−	0.553480i	−0.660843	−	0.750524i	$-0.729801\pi$
$877$	1.89034e11	−	3.27416e11i	0.319552	−	0.553480i	0.980395	+	0.197044i	$0.0631343\pi$
$878$		0			0
$879$	4.95765e11	+	8.58690e11i	0.830463	+	1.43840i
$880$		0			0
$881$			1.50034e11i			0.249050i	0.992216	+	0.124525i	$0.0397407\pi$
$881$			1.50034e11i			0.249050i	−0.992216	+	0.124525i	$0.960259\pi$
$882$		0			0
$883$	−6.07752e11			−0.999733			−0.499866	−	0.866103i	$-0.666618\pi$
$883$	−6.07752e11			−0.999733			−0.499866	+	0.866103i	$0.666618\pi$
$884$		0			0
$885$	−2.35062e11	+	1.35713e11i	−0.383185	+	0.221232i
$886$		0			0
$887$	−3.26886e11	−	1.88727e11i	−0.528082	−	0.304888i	0.212153	−	0.977236i	$-0.431952\pi$
$887$	−3.26886e11	−	1.88727e11i	−0.528082	−	0.304888i	−0.740235	+	0.672348i	$0.765286\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$	5.72486e10	−	9.91575e10i	0.0908352	−	0.157331i
$892$		0			0
$893$	1.55411e11	+	2.69180e11i	0.244386	+	0.423289i
$894$		0			0
$895$		−	2.59353e11i		−	0.404203i
$896$		0			0
$897$	1.31802e12			2.03588
$898$		0			0
$899$	1.17593e12	−	6.78925e11i	1.80029	−	1.03940i
$900$		0			0
$901$	−2.42879e11	−	1.40226e11i	−0.368545	−	0.212779i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−7.29639e10	+	1.26377e11i	−0.108771	+	0.188397i
$906$		0			0
$907$	2.04500e11	+	3.54205e11i	0.302179	+	0.523390i	0.976629	−	0.214931i	$-0.0689525\pi$
$907$	2.04500e11	+	3.54205e11i	0.302179	+	0.523390i	−0.674450	+	0.738321i	$0.735619\pi$
$908$		0			0
$909$			5.59800e11i			0.819930i
$910$		0			0
$911$	−4.33314e11			−0.629115			−0.314557	−	0.949239i	$-0.601856\pi$
$911$	−4.33314e11			−0.629115			−0.314557	+	0.949239i	$0.601856\pi$
$912$		0			0
$913$	−1.35852e11	+	7.84344e10i	−0.195517	+	0.112882i
$914$		0			0
$915$	−4.51452e10	−	2.60646e10i	−0.0644061	−	0.0371849i
$916$		0			0
$917$		0			0
$918$		0			0
$919$	−6.35099e11	+	1.10002e12i	−0.890389	+	1.54220i	−0.0509790	+	0.998700i	$0.516234\pi$
$919$	−6.35099e11	+	1.10002e12i	−0.890389	+	1.54220i	−0.839410	+	0.543499i	$0.817099\pi$
$920$		0			0
$921$	3.95260e11	+	6.84611e11i	0.549344	+	0.951492i
$922$		0			0
$923$			5.23825e10i			0.0721737i
$924$		0			0
$925$	7.80454e11			1.06606
$926$		0			0
$927$	9.11733e11	−	5.26389e11i	1.23466	−	0.712834i
$928$		0			0
$929$	1.79688e10	+	1.03743e10i	0.0241244	+	0.0139282i	0.512014	−	0.858977i	$-0.328900\pi$
$929$	1.79688e10	+	1.03743e10i	0.0241244	+	0.0139282i	−0.487889	+	0.872906i	$0.662233\pi$
$930$		0			0
$931$		0			0
$932$		0			0
$933$	6.11112e11	−	1.05848e12i	0.806481	−	1.39687i
$934$		0			0
$935$	8.31877e9	+	1.44085e10i	0.0108846	+	0.0188527i
$936$		0			0
$937$			2.21313e11i			0.287111i	0.989642	+	0.143555i	$0.0458535\pi$
$937$			2.21313e11i			0.287111i	−0.989642	+	0.143555i	$0.954146\pi$
$938$		0			0
$939$	1.58933e12			2.04434
$940$		0			0
$941$	6.98331e11	−	4.03182e11i	0.890642	−	0.514212i	0.0164894	−	0.999864i	$-0.494751\pi$
$941$	6.98331e11	−	4.03182e11i	0.890642	−	0.514212i	0.874152	+	0.485652i	$0.161418\pi$
$942$		0			0
$943$	−1.18587e12	−	6.84662e11i	−1.49965	−	0.865824i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−9.63382e10	+	1.66863e11i	−0.119784	+	0.207472i	−0.919682	−	0.392664i	$-0.871554\pi$
$947$	−9.63382e10	+	1.66863e11i	−0.119784	+	0.207472i	0.799898	+	0.600136i	$0.204887\pi$
$948$		0			0
$949$	5.81405e11	+	1.00702e12i	0.716826	+	1.24158i
$950$		0			0
$951$		−	6.05973e11i		−	0.740851i
$952$		0			0
$953$	−1.09675e12			−1.32965			−0.664823	−	0.747000i	$-0.731493\pi$
$953$	−1.09675e12			−1.32965			−0.664823	+	0.747000i	$0.731493\pi$
$954$		0			0
$955$	−2.10713e11	+	1.21655e11i	−0.253324	+	0.146257i
$956$		0			0
$957$	−4.03075e11	−	2.32716e11i	−0.480550	−	0.277445i
$958$		0			0
$959$		0			0
$960$		0			0
$961$	9.60314e11	−	1.66331e12i	1.12595	−	1.95021i
$962$		0			0
$963$	4.23886e11	+	7.34191e11i	0.492883	+	0.853698i
$964$		0			0
$965$		−	2.63172e10i		−	0.0303480i
$966$		0			0
$967$	4.69070e10			0.0536453			0.0268226	−	0.999640i	$-0.491461\pi$
$967$	4.69070e10			0.0536453			0.0268226	+	0.999640i	$0.491461\pi$
$968$		0			0
$969$	−1.53060e11	+	8.83694e10i	−0.173607	+	0.100232i
$970$		0			0
$971$	−7.66248e11	−	4.42394e11i	−0.861971	−	0.497659i	0.00270091	−	0.999996i	$-0.499140\pi$
$971$	−7.66248e11	−	4.42394e11i	−0.861971	−	0.497659i	−0.864672	+	0.502337i	$0.832474\pi$
$972$		0			0
$973$		0			0
$974$		0			0
$975$	−8.55287e11	+	1.48140e12i	−0.946441	+	1.63928i
$976$		0			0
$977$	2.68415e11	+	4.64908e11i	0.294597	+	0.510257i	0.974891	−	0.222682i	$-0.0714813\pi$
$977$	2.68415e11	+	4.64908e11i	0.294597	+	0.510257i	−0.680294	+	0.732939i	$0.738148\pi$
$978$		0			0
$979$		−	5.74622e10i		−	0.0625534i
$980$		0			0
$981$	−6.38915e11			−0.689870
$982$		0			0
$983$	4.96400e11	−	2.86597e11i	0.531640	−	0.306943i	−0.210044	−	0.977692i	$-0.567361\pi$
$983$	4.96400e11	−	2.86597e11i	0.531640	−	0.306943i	0.741684	+	0.670749i	$0.234027\pi$
$984$		0			0
$985$	−2.45040e10	−	1.41474e10i	−0.0260311	−	0.0150291i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−3.95761e11	+	6.85478e11i	−0.413664	+	0.716487i
$990$		0			0
$991$	3.54723e11	+	6.14399e11i	0.367786	+	0.637024i	0.989219	−	0.146443i	$-0.0467826\pi$
$991$	3.54723e11	+	6.14399e11i	0.367786	+	0.637024i	−0.621433	+	0.783467i	$0.713449\pi$
$992$		0			0
$993$			2.61059e12i			2.68499i
$994$		0			0
$995$	−3.81956e11			−0.389691
$996$		0			0
$997$	−1.00436e12	+	5.79868e11i	−1.01650	+	0.586879i	−0.913089	−	0.407759i	$-0.866310\pi$
$997$	−1.00436e12	+	5.79868e11i	−1.01650	+	0.586879i	−0.103415	+	0.994638i	$0.532977\pi$
$998$		0			0
$999$	−4.87882e11	−	2.81679e11i	−0.489839	−	0.282809i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	196.9.h.c.117.3		32
7.2	even	3		196.9.b.b.97.3	✓	16
7.3	odd	6	inner	196.9.h.c.129.3		32
7.4	even	3	inner	196.9.h.c.129.14		32
7.5	odd	6		196.9.b.b.97.14	yes	16
7.6	odd	2	inner	196.9.h.c.117.14		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
196.9.b.b.97.3	✓	16	7.2	even	3
196.9.b.b.97.14	yes	16	7.5	odd	6
196.9.h.c.117.3		32	1.1	even	1	trivial
196.9.h.c.117.14		32	7.6	odd	2	inner
196.9.h.c.129.3		32	7.3	odd	6	inner
196.9.h.c.129.14		32	7.4	even	3	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 196 = 2^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 9 \)
Character orbit:	\([\chi]\)	\(=\)	196.h (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-106.882 + 61.7084i) q^{3} +(-149.792 - 86.4823i) q^{5} +(4335.35 - 7509.04i) q^{9} +(-2312.68 - 4005.68i) q^{11} +38424.8i q^{13} +21346.7 q^{15} +(18010.2 - 10398.2i) q^{17} +(59635.0 + 34430.3i) q^{19} +(-138965. + 240695. i) q^{23} +(-180354. - 312383. i) q^{25} +260371. i q^{27} -815335. q^{29} +(-1.44227e6 + 832694. i) q^{31} +(494368. + 285423. i) q^{33} +(-1.08184e6 + 1.87379e6i) q^{37} +(-2.37113e6 - 4.10692e6i) q^{39} +4.92685e6i q^{41} +2.84791e6 q^{43} +(-1.29880e6 + 749861. i) q^{45} +(3.90905e6 + 2.25689e6i) q^{47} +(-1.28331e6 + 2.22275e6i) q^{51} +(-6.74283e6 - 1.16789e7i) q^{53} +800023. i q^{55} -8.49855e6 q^{57} +(-1.10116e7 + 6.35756e6i) q^{59} +(-2.11485e6 - 1.22101e6i) q^{61} +(3.32307e6 - 5.75572e6i) q^{65} +(5.98497e6 + 1.03663e7i) q^{67} -3.43013e7i q^{69} +1.36325e6 q^{71} +(2.62076e7 - 1.51310e7i) q^{73} +(3.85532e7 + 2.22587e7i) q^{75} +(2.39976e7 - 4.15650e7i) q^{79} +(1.23771e7 + 2.14378e7i) q^{81} -3.39149e7i q^{83} -3.59703e6 q^{85} +(8.71446e7 - 5.03130e7i) q^{87} +(1.07589e7 + 6.21164e6i) q^{89} +(1.02768e8 - 1.78000e8i) q^{93} +(-5.95522e6 - 1.03147e7i) q^{95} -1.15877e8i q^{97} -4.01051e7 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 52264 q^{9} + 22776 q^{11} + 206064 q^{15} - 571560 q^{23} + 1030440 q^{25} - 5384256 q^{29} + 3376640 q^{37} + 10336136 q^{39} + 18525008 q^{43} + 16028856 q^{51} - 14106216 q^{53} - 4787360 q^{57}+ \cdots + 1119499328 q^{99}+O(q^{100}) \) 32 * q + 52264 * q^9 + 22776 * q^11 + 206064 * q^15 - 571560 * q^23 + 1030440 * q^25 - 5384256 * q^29 + 3376640 * q^37 + 10336136 * q^39 + 18525008 * q^43 + 16028856 * q^51 - 14106216 * q^53 - 4787360 * q^57 - 5623008 * q^65 - 82433680 * q^67 + 250685568 * q^71 + 138241200 * q^79 - 465637680 * q^81 + 880381104 * q^85 + 310654512 * q^93 - 811120872 * q^95 + 1119499328 * q^99

Introduction

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