LMFDB - Embedded newform 100.9.j.b.11.102

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [100,9,Mod(11,100)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(100, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([5, 8])) N = Newforms(chi, 9, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("100.11"); S:= CuspForms(chi, 9); N := Newforms(S);

Level:	$ N $	$=$	$ 100 = 2^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 9 $
Character orbit:	$[\chi]$	$=$	100.j (of order $10$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [464] 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:	$40.7378610061$
Analytic rank:	$0$
Dimension:	$464$
Relative dimension:	$116$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			11.102
Character	$\chi$	$=$	100.11
Dual form			100.9.j.b.91.102

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(14.6306 - 6.47656i) q^{2} +(-23.9193 - 7.77186i) q^{3} +(172.108 - 189.512i) q^{4} +(-439.267 - 444.600i) q^{5} +(-400.289 + 41.2081i) q^{6} +3464.57i q^{7} +(1290.66 - 3887.34i) q^{8} +(-4796.23 - 3484.66i) q^{9} +(-9306.22 - 3659.81i) q^{10} +(-1192.15 - 1640.85i) q^{11} +(-5589.57 + 3195.39i) q^{12} +(8835.97 + 6419.71i) q^{13} +(22438.5 + 50688.7i) q^{14} +(7051.61 + 14048.5i) q^{15} +(-6293.50 - 65233.1i) q^{16} +(31685.0 + 97516.3i) q^{17} +(-92740.3 - 19919.6i) q^{18} +(-162540. + 52812.3i) q^{19} +(-159859. + 6727.09i) q^{20} +(26926.2 - 82870.2i) q^{21} +(-28069.0 - 16285.6i) q^{22} +(56834.9 + 78226.6i) q^{23} +(-61083.5 + 82951.7i) q^{24} +(-4713.17 + 390597. i) q^{25} +(170853. + 36697.4i) q^{26} +(184631. + 254123. i) q^{27} +(656578. + 596282. i) q^{28} +(-98761.9 + 303958. i) q^{29} +(194155. + 159867. i) q^{30} +(803046. - 260926. i) q^{31} +(-514564. - 913639. i) q^{32} +(15762.9 + 48513.4i) q^{33} +(1.09514e6 + 1.22151e6i) q^{34} +(1.54035e6 - 1.52187e6i) q^{35} +(-1.48586e6 + 309203. i) q^{36} +(1.01903e6 + 740371. i) q^{37} +(-2.03601e6 + 1.82537e6i) q^{38} +(-161457. - 222227. i) q^{39} +(-2.29526e6 + 1.13376e6i) q^{40} +(-2.18509e6 - 1.58756e6i) q^{41} +(-142769. - 1.38683e6i) q^{42} +5.79619e6i q^{43} +(-516140. - 56477.9i) q^{44} +(557546. + 3.66310e6i) q^{45} +(1.33817e6 + 776406. i) q^{46} +(3.45085e6 + 1.12125e6i) q^{47} +(-356446. + 1.60924e6i) q^{48} -6.23846e6 q^{49} +(2.46077e6 + 5.74518e6i) q^{50} -2.57877e6i q^{51} +(2.73735e6 - 569637. i) q^{52} +(-1.99603e6 + 6.14316e6i) q^{53} +(4.34711e6 + 2.52219e6i) q^{54} +(-205851. + 1.25080e6i) q^{55} +(1.34680e7 + 4.47158e6i) q^{56} +4.29829e6 q^{57} +(523658. + 5.08672e6i) q^{58} +(-9.22018e6 + 1.26905e7i) q^{59} +(3.87599e6 + 1.08149e6i) q^{60} +(1.63904e6 - 1.19083e6i) q^{61} +(1.00591e7 - 9.01848e6i) q^{62} +(1.20729e7 - 1.66169e7i) q^{63} +(-1.34456e7 - 1.00345e7i) q^{64} +(-1.02715e6 - 6.74844e6i) q^{65} +(544821. + 607689. i) q^{66} +(-7.74657e6 + 2.51701e6i) q^{67} +(2.39337e7 + 1.07787e7i) q^{68} +(-751487. - 2.31284e6i) q^{69} +(1.26797e7 - 3.22421e7i) q^{70} +(-6.69742e6 - 2.17612e6i) q^{71} +(-1.97364e7 + 1.41471e7i) q^{72} +(-1.94672e7 + 1.41437e7i) q^{73} +(1.97041e7 + 4.23223e6i) q^{74} +(3.14840e6 - 9.30617e6i) q^{75} +(-1.79658e7 + 3.98926e7i) q^{76} +(5.68486e6 - 4.13029e6i) q^{77} +(-3.80148e6 - 2.20562e6i) q^{78} +(-4.62870e7 - 1.50396e7i) q^{79} +(-2.62381e7 + 3.14529e7i) q^{80} +(9.57848e6 + 2.94795e7i) q^{81} +(-4.22511e7 - 9.07508e6i) q^{82} +(8.40252e7 - 2.73014e7i) q^{83} +(-1.10707e7 - 1.93655e7i) q^{84} +(2.94376e7 - 5.69229e7i) q^{85} +(3.75394e7 + 8.48017e7i) q^{86} +(4.72463e6 - 6.50290e6i) q^{87} +(-7.91722e6 + 2.51651e6i) q^{88} +(1.73204e7 - 1.25840e7i) q^{89} +(3.18815e7 + 4.99824e7i) q^{90} +(-2.22415e7 + 3.06129e7i) q^{91} +(2.46066e7 + 2.69254e6i) q^{92} -2.12362e7 q^{93} +(5.77499e7 - 5.94512e6i) q^{94} +(9.48787e7 + 4.90664e7i) q^{95} +(5.20735e6 + 2.58527e7i) q^{96} +(-4.13620e6 + 1.27299e7i) q^{97} +(-9.12724e7 + 4.04038e7i) q^{98} +1.20242e7i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 464 q + 29 q^{2} + 509 q^{4} - 1230 q^{5} - 515 q^{6} + 21284 q^{8} + 262434 q^{9} + 3445 q^{10} - 35805 q^{12} - 29522 q^{13} - 33705 q^{14} - 63391 q^{16} - 319922 q^{17} - 569696 q^{18} + 1244935 q^{20}+ \cdots + 209675864 q^{98}+O(q^{100}) $ 464 * q + 29 * q^2 + 509 * q^4 - 1230 * q^5 - 515 * q^6 + 21284 * q^8 + 262434 * q^9 + 3445 * q^10 - 35805 * q^12 - 29522 * q^13 - 33705 * q^14 - 63391 * q^16 - 319922 * q^17 - 569696 * q^18 + 1244935 * q^20 + 39360 * q^21 + 140220 * q^22 + 989900 * q^24 - 431710 * q^25 - 855842 * q^26 - 2358605 * q^28 - 2884562 * q^29 + 7229675 * q^30 - 7078666 * q^32 - 1866570 * q^33 + 1448973 * q^34 + 777029 * q^36 - 7317972 * q^37 + 4012465 * q^38 - 4154830 * q^40 + 1687438 * q^41 - 21337315 * q^42 + 510580 * q^44 + 2596050 * q^45 + 1721385 * q^46 + 41153690 * q^48 - 396068336 * q^49 - 60015715 * q^50 - 8419912 * q^52 + 26717388 * q^53 - 13729145 * q^54 + 7138890 * q^56 - 19745300 * q^57 - 41444182 * q^58 + 96768050 * q^60 + 26136558 * q^61 - 87505940 * q^62 + 19616924 * q^64 + 22030140 * q^65 - 69968200 * q^66 + 276958 * q^68 - 73697610 * q^69 + 39639840 * q^70 - 145994351 * q^72 - 39004722 * q^73 + 4922908 * q^74 - 19181080 * q^76 + 111211200 * q^77 - 197089615 * q^78 - 395680960 * q^80 - 539852286 * q^81 + 186999258 * q^82 - 377672700 * q^84 - 283475540 * q^85 - 340843785 * q^86 - 29231040 * q^88 - 206040612 * q^89 + 351285695 * q^90 + 43044280 * q^92 + 241823660 * q^93 - 442380075 * q^94 - 474931550 * q^96 + 2388718 * q^97 + 209675864 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/100\mathbb{Z}\right)^\times$.

$n$	$51$	$77$
$\chi(n)$	$-1$	$e\left(\frac{4}{5}\right)$

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 $

$2$	14.6306	−	6.47656i	0.914412	−	0.404785i
$2$	14.6306	−	6.47656i	0.914412	−	0.404785i
$3$	−23.9193	−	7.77186i	−0.295300	−	0.0959489i	0.157620	−	0.987500i	$-0.449618\pi$
$3$	−23.9193	−	7.77186i	−0.295300	−	0.0959489i	−0.452920	+	0.891551i	$0.649618\pi$
$4$	172.108	−	189.512i	0.672298	−	0.740281i
$5$	−439.267	−	444.600i	−0.702828	−	0.711360i
$5$	−439.267	−	444.600i	−0.702828	−	0.711360i
$6$	−400.289	+	41.2081i	−0.308865	+	0.0317964i
$7$			3464.57i			1.44297i	0.692430	+	0.721485i	$0.256540\pi$
$7$			3464.57i			1.44297i	−0.692430	+	0.721485i	$0.743460\pi$
$8$	1290.66	−	3887.34i	0.315102	−	0.949058i
$9$	−4796.23	−	3484.66i	−0.731021	−	0.531118i
$10$	−9306.22	−	3659.81i	−0.930622	−	0.365981i
$11$	−1192.15	−	1640.85i	−0.0814255	−	0.112073i	0.766361	−	0.642410i	$-0.222065\pi$
$11$	−1192.15	−	1640.85i	−0.0814255	−	0.112073i	−0.847787	+	0.530337i	$0.822065\pi$
$12$	−5589.57	+	3195.39i	−0.269559	+	0.154099i
$13$	8835.97	+	6419.71i	0.309372	+	0.224772i	0.731627	−	0.681705i	$-0.238761\pi$
$13$	8835.97	+	6419.71i	0.309372	+	0.224772i	−0.422255	+	0.906477i	$0.638761\pi$
$14$	22438.5	+	50688.7i	0.584093	+	1.31947i
$15$	7051.61	+	14048.5i	0.139291	+	0.277500i
$16$	−6293.50	−	65233.1i	−0.0960313	−	0.995378i
$17$	31685.0	+	97516.3i	0.379365	+	1.16757i	0.940486	+	0.339832i	$0.110370\pi$
$17$	31685.0	+	97516.3i	0.379365	+	1.16757i	−0.561121	+	0.827734i	$0.689630\pi$
$18$	−92740.3	−	19919.6i	−0.883443	−	0.189754i
$19$	−162540.	+	52812.3i	−1.24722	+	0.405248i	−0.856926	−	0.515440i	$-0.827628\pi$
$19$	−162540.	+	52812.3i	−1.24722	+	0.405248i	−0.390299	+	0.920688i	$0.627628\pi$
$20$	−159859.	+	6727.09i	−0.999116	+	0.0420443i
$21$	26926.2	−	82870.2i	0.138451	−	0.426110i
$22$	−28069.0	−	16285.6i	−0.119822	−	0.0695207i
$23$	56834.9	+	78226.6i	0.203097	+	0.279539i	0.898401	−	0.439177i	$-0.144730\pi$
$23$	56834.9	+	78226.6i	0.203097	+	0.279539i	−0.695303	+	0.718716i	$0.744730\pi$
$24$	−61083.5	+	82951.7i	−0.184111	+	0.250023i
$25$	−4713.17	+	390597.i	−0.0120657	+	0.999927i
$26$	170853.	+	36697.4i	0.373878	+	0.0803048i
$27$	184631.	+	254123.i	0.347416	+	0.478177i
$28$	656578.	+	596282.i	1.06820	+	0.970106i
$29$	−98761.9	+	303958.i	−0.139636	+	0.429755i	−0.996282	−	0.0861489i	$-0.972544\pi$
$29$	−98761.9	+	303958.i	−0.139636	+	0.429755i	0.856646	+	0.515904i	$0.172544\pi$
$30$	194155.	+	159867.i	0.239697	+	0.197367i
$31$	803046.	−	260926.i	0.869549	−	0.282533i	0.159938	−	0.987127i	$-0.448871\pi$
$31$	803046.	−	260926.i	0.869549	−	0.282533i	0.709611	+	0.704594i	$0.248871\pi$
$32$	−514564.	−	913639.i	−0.490727	−	0.871314i
$33$	15762.9	+	48513.4i	0.0132917	+	0.0409077i
$34$	1.09514e6	+	1.22151e6i	0.819510	+	0.914075i
$35$	1.54035e6	−	1.52187e6i	1.02647	−	1.01416i
$36$	−1.48586e6	+	309203.i	−0.884640	+	0.184091i
$37$	1.01903e6	+	740371.i	0.543728	+	0.395041i	0.825468	−	0.564449i	$-0.190911\pi$
$37$	1.01903e6	+	740371.i	0.543728	+	0.395041i	−0.281740	+	0.959491i	$0.590911\pi$
$38$	−2.03601e6	+	1.82537e6i	−0.976439	+	0.875422i
$39$	−161457.	−	222227.i	−0.0697910	−	0.0960591i
$40$	−2.29526e6	+	1.13376e6i	−0.896584	+	0.442873i
$41$	−2.18509e6	−	1.58756e6i	−0.773275	−	0.561817i	0.129678	−	0.991556i	$-0.458606\pi$
$41$	−2.18509e6	−	1.58756e6i	−0.773275	−	0.561817i	−0.902953	+	0.429739i	$0.858606\pi$
$42$	−142769.	−	1.38683e6i	−0.0458813	−	0.445683i
$43$			5.79619e6i			1.69539i	0.530487	+	0.847693i	$0.322009\pi$
$43$			5.79619e6i			1.69539i	−0.530487	+	0.847693i	$0.677991\pi$
$44$	−516140.	−	56477.9i	−0.137707	−	0.0150684i
$45$	557546.	+	3.66310e6i	0.135966	+	0.893303i
$46$	1.33817e6	+	776406.i	0.298868	+	0.173403i
$47$	3.45085e6	+	1.12125e6i	0.707188	+	0.229779i	0.640460	−	0.767992i	$-0.278744\pi$
$47$	3.45085e6	+	1.12125e6i	0.707188	+	0.229779i	0.0667287	+	0.997771i	$0.478744\pi$
$48$	−356446.	+	1.60924e6i	−0.0671474	+	0.303150i
$49$	−6.23846e6			−1.08216
$50$	2.46077e6	+	5.74518e6i	0.393723	+	0.919229i
$51$		−	2.57877e6i		−	0.381182i
$52$	2.73735e6	−	569637.i	0.374384	−	0.0779084i
$53$	−1.99603e6	+	6.14316e6i	−0.252967	+	0.778553i	0.741256	+	0.671222i	$0.234230\pi$
$53$	−1.99603e6	+	6.14316e6i	−0.252967	+	0.778553i	−0.994223	+	0.107331i	$0.965770\pi$
$54$	4.34711e6	+	2.52219e6i	0.511240	+	0.296622i
$55$	−205851.	+	1.25080e6i	−0.0224958	+	0.136691i
$56$	1.34680e7	+	4.47158e6i	1.36946	+	0.454683i
$57$	4.29829e6			0.407189
$58$	523658.	+	5.08672e6i	0.0462738	+	0.449496i
$59$	−9.22018e6	+	1.26905e7i	−0.760907	+	1.04730i	0.236231	+	0.971697i	$0.424088\pi$
$59$	−9.22018e6	+	1.26905e7i	−0.760907	+	1.04730i	−0.997138	+	0.0756014i	$0.975912\pi$
$60$	3.87599e6	+	1.08149e6i	0.299073	+	0.0834483i
$61$	1.63904e6	−	1.19083e6i	0.118377	−	0.0860062i	−0.527021	−	0.849852i	$-0.676691\pi$
$61$	1.63904e6	−	1.19083e6i	0.118377	−	0.0860062i	0.645399	+	0.763846i	$0.276691\pi$
$62$	1.00591e7	−	9.01848e6i	0.680760	−	0.610332i
$63$	1.20729e7	−	1.66169e7i	0.766387	−	1.05484i
$64$	−1.34456e7	−	1.00345e7i	−0.801421	−	0.598101i
$65$	−1.02715e6	−	6.74844e6i	−0.0575415	−	0.378051i
$66$	544821.	+	607689.i	0.0287130	+	0.0320262i
$67$	−7.74657e6	+	2.51701e6i	−0.384424	+	0.124907i	−0.494852	−	0.868977i	$-0.664778\pi$
$67$	−7.74657e6	+	2.51701e6i	−0.384424	+	0.124907i	0.110428	+	0.993884i	$0.464778\pi$
$68$	2.39337e7	+	1.07787e7i	1.11937	+	0.504115i
$69$	−751487.	−	2.31284e6i	−0.0331532	−	0.102035i
$70$	1.26797e7	−	3.22421e7i	0.528101	−	1.34286i
$71$	−6.69742e6	−	2.17612e6i	−0.263557	−	0.0856348i	0.174258	−	0.984700i	$-0.444247\pi$
$71$	−6.69742e6	−	2.17612e6i	−0.263557	−	0.0856348i	−0.437815	+	0.899065i	$0.644247\pi$
$72$	−1.97364e7	+	1.41471e7i	−0.734408	+	0.526425i
$73$	−1.94672e7	+	1.41437e7i	−0.685507	+	0.498050i	−0.875180	−	0.483797i	$-0.839257\pi$
$73$	−1.94672e7	+	1.41437e7i	−0.685507	+	0.498050i	0.189673	+	0.981847i	$0.439257\pi$
$74$	1.97041e7	+	4.23223e6i	0.657098	+	0.141138i
$75$	3.14840e6	−	9.30617e6i	0.0995049	−	0.294121i
$76$	−1.79658e7	+	3.98926e7i	−0.538509	+	1.19574i
$77$	5.68486e6	−	4.13029e6i	0.161717	−	0.117495i
$78$	−3.80148e6	−	2.20562e6i	−0.102701	−	0.0595872i
$79$	−4.62870e7	−	1.50396e7i	−1.18837	−	0.386124i	−0.352898	−	0.935662i	$-0.614804\pi$
$79$	−4.62870e7	−	1.50396e7i	−1.18837	−	0.386124i	−0.835469	+	0.549538i	$0.814804\pi$
$80$	−2.62381e7	+	3.14529e7i	−0.640579	+	0.767893i
$81$	9.57848e6	+	2.94795e7i	0.222514	+	0.684827i
$82$	−4.22511e7	−	9.07508e6i	−0.934507	−	0.200722i
$83$	8.40252e7	−	2.73014e7i	1.77050	−	0.575272i	0.772305	−	0.635252i	$-0.219104\pi$
$83$	8.40252e7	−	2.73014e7i	1.77050	−	0.575272i	0.998200	+	0.0599807i	$0.0191039\pi$
$84$	−1.10707e7	−	1.93655e7i	−0.222360	−	0.388966i
$85$	2.94376e7	−	5.69229e7i	0.563931	−	1.09046i
$86$	3.75394e7	+	8.48017e7i	0.686267	+	1.55028i
$87$	4.72463e6	−	6.50290e6i	0.0824691	−	0.113509i
$88$	−7.91722e6	+	2.51651e6i	−0.132021	+	0.0419632i
$89$	1.73204e7	−	1.25840e7i	0.276057	−	0.200567i	−0.441139	−	0.897439i	$-0.645425\pi$
$89$	1.73204e7	−	1.25840e7i	0.276057	−	0.200567i	0.717196	+	0.696872i	$0.245425\pi$
$90$	3.18815e7	+	4.99824e7i	0.485925	+	0.761810i
$91$	−2.22415e7	+	3.06129e7i	−0.324339	+	0.446415i
$92$	2.46066e7	+	2.69254e6i	0.343479	+	0.0375847i
$93$	−2.12362e7			−0.283887
$94$	5.77499e7	−	5.94512e6i	0.739673	−	0.0761464i
$95$	9.48787e7	+	4.90664e7i	1.16486	+	0.602406i
$96$	5.20735e6	+	2.58527e7i	0.0613101	+	0.304384i
$97$	−4.13620e6	+	1.27299e7i	−0.0467212	+	0.143793i	−0.971696	−	0.236236i	$-0.924086\pi$
$97$	−4.13620e6	+	1.27299e7i	−0.0467212	+	0.143793i	0.924974	+	0.380029i	$0.124086\pi$
$98$	−9.12724e7	+	4.04038e7i	−0.989544	+	0.438044i
$99$			1.20242e7i			0.125174i
$100$	7.32115e7	+	6.81181e7i	0.732115	+	0.681181i
$101$	−1.00930e8			−0.969921			−0.484960	−	0.874536i	$-0.661166\pi$
$101$	−1.00930e8			−0.969921			−0.484960	+	0.874536i	$0.661166\pi$
$102$	−1.67016e7	−	3.77290e7i	−0.154297	−	0.348558i
$103$	−1.55361e8	−	5.04798e7i	−1.38036	−	0.448507i	−0.477573	−	0.878592i	$-0.658484\pi$
$103$	−1.55361e8	−	5.04798e7i	−1.38036	−	0.448507i	−0.902788	+	0.430085i	$0.858484\pi$
$104$	3.63598e7	−	2.60628e7i	0.310805	−	0.222786i
$105$	−4.86719e7	+	2.44308e7i	−0.400425	+	0.200993i
$106$	1.05834e7	+	1.02805e8i	0.0838305	+	0.814315i
$107$			1.87567e8i			1.43094i	0.698643	+	0.715470i	$0.253787\pi$
$107$			1.87567e8i			1.43094i	−0.698643	+	0.715470i	$0.746213\pi$
$108$	7.99359e7	+	8.74686e6i	0.587553	+	0.0642921i
$109$	−1.81443e8	−	1.31826e8i	−1.28539	−	0.933887i	−0.285684	−	0.958324i	$-0.592221\pi$
$109$	−1.81443e8	−	1.31826e8i	−1.28539	−	0.933887i	−0.999701	+	0.0244370i	$0.992221\pi$
$110$	5.08919e6	+	1.96332e7i	0.0347599	+	0.134097i
$111$	−1.86205e7	−	2.56290e7i	−0.122659	−	0.168826i
$112$	2.26005e8	−	2.18043e7i	1.43630	−	0.138570i
$113$	−1.57722e8	−	1.14592e8i	−0.967340	−	0.702814i	−0.0124963	−	0.999922i	$-0.503978\pi$
$113$	−1.57722e8	−	1.14592e8i	−0.967340	−	0.702814i	−0.954844	+	0.297108i	$0.903978\pi$
$114$	6.28865e7	−	2.78381e7i	0.372338	−	0.164824i
$115$	9.81379e6	−	5.96312e7i	0.0561107	−	0.340943i
$116$	4.06059e7	+	7.10302e7i	0.224263	+	0.392293i
$117$	−2.00088e7	−	6.15808e7i	−0.106777	−	0.328626i
$118$	−5.27059e7	+	2.45384e8i	−0.271851	+	1.26567i
$119$	−3.37852e8	+	1.09775e8i	−1.68476	+	0.547413i
$120$	6.37123e7	−	9.28025e6i	0.307255	−	0.0447543i
$121$	6.49694e7	−	1.99955e8i	0.303087	−	0.932805i
$122$	1.62676e7	−	2.80378e7i	0.0734317	−	0.126563i
$123$	3.99276e7	+	5.49556e7i	0.174443	+	0.240100i
$124$	8.87624e7	−	1.97094e8i	0.375442	−	0.833657i
$125$	1.75730e8	−	1.69481e8i	0.719788	−	0.694194i
$126$	6.90129e7	−	3.21306e8i	0.273809	−	1.27478i
$127$	−4.00416e7	−	5.51125e7i	−0.153920	−	0.211853i	0.725092	−	0.688652i	$-0.241797\pi$
$127$	−4.00416e7	−	5.51125e7i	−0.153920	−	0.211853i	−0.879013	+	0.476799i	$0.841797\pi$
$128$	−2.61706e8	−	5.97287e7i	−0.974931	−	0.222507i
$129$	4.50472e7	−	1.38641e8i	0.162670	−	0.500648i
$130$	−5.87346e7	−	9.20812e7i	−0.205646	−	0.322402i
$131$	1.25876e8	−	4.08997e7i	0.427424	−	0.138878i	−0.0874022	−	0.996173i	$-0.527857\pi$
$131$	1.25876e8	−	4.08997e7i	0.427424	−	0.138878i	0.514826	+	0.857295i	$0.327857\pi$
$132$	1.19068e7	+	5.36228e6i	0.0392192	+	0.0176626i
$133$	−1.82972e8	−	5.63130e8i	−0.584761	−	1.79971i
$134$	−9.70352e7	+	8.69965e7i	−0.300961	+	0.269825i
$135$	3.18806e7	−	1.93715e8i	0.0959824	−	0.583214i
$136$	4.19974e8	+	2.69005e6i	1.22763	+	0.00786331i
$137$	−3.13928e8	−	2.28082e8i	−0.891144	−	0.647454i	0.0450323	−	0.998986i	$-0.485661\pi$
$137$	−3.13928e8	−	2.28082e8i	−0.891144	−	0.647454i	−0.936176	+	0.351532i	$0.885661\pi$
$138$	−2.59740e7	−	2.89712e7i	−0.0716179	−	0.0798821i
$139$	−7.12932e6	−	9.81267e6i	−0.0190981	−	0.0262862i	0.799361	−	0.600851i	$-0.205171\pi$
$139$	−7.12932e6	−	9.81267e6i	−0.0190981	−	0.0262862i	−0.818459	+	0.574565i	$0.805171\pi$
$140$	−2.33065e7	−	5.53842e8i	−0.0606688	−	1.44169i
$141$	−7.38279e7	−	5.36391e7i	−0.186786	−	0.135708i
$142$	−1.12081e8	+	1.15383e7i	−0.275663	+	0.0283784i
$143$		−	2.21518e7i		−	0.0529743i
$144$	−1.97130e8	+	3.34804e8i	−0.458462	+	0.778646i
$145$	1.78522e8	−	8.96092e7i	0.403851	−	0.202713i
$146$	−1.93214e8	+	3.33012e8i	−0.425232	+	0.732906i
$147$	1.49220e8	+	4.84845e7i	0.319564	+	0.103832i
$148$	3.15693e8	−	6.56950e7i	0.657989	−	0.136926i
$149$	6.45551e8			1.30974			0.654870	−	0.755741i	$-0.272723\pi$
$149$	6.45551e8			1.30974			0.654870	+	0.755741i	$0.272723\pi$
$150$	−1.42091e7	−	1.56546e8i	−0.0280674	−	0.309226i
$151$		−	2.16983e8i		−	0.417366i	−0.977983	−	0.208683i	$-0.933082\pi$
$151$		−	2.16983e8i		−	0.417366i	0.977983	−	0.208683i	$-0.0669177\pi$
$152$	−4.48377e6	+	7.00009e8i	−0.00839979	+	1.31138i
$153$	1.87843e8	−	5.78122e8i	0.342791	−	1.05500i
$154$	5.64228e7	−	9.72470e7i	0.100316	−	0.172899i
$155$	−4.68760e8	−	2.42418e8i	−0.812126	−	0.419990i
$156$	−6.99028e7	−	7.64901e6i	−0.118031	−	0.0129154i
$157$	−4.30892e8			−0.709202			−0.354601	−	0.935018i	$-0.615383\pi$
$157$	−4.30892e8			−0.709202			−0.354601	+	0.935018i	$0.615383\pi$
$158$	−7.74611e8	+	7.97431e7i	−1.24295	+	0.127957i
$159$	9.54875e7	−	1.31427e8i	0.149403	−	0.205635i
$160$	−1.80172e8	+	6.30107e8i	−0.274921	+	0.961467i
$161$	−2.71022e8	+	1.96909e8i	−0.403367	+	0.293063i
$162$	3.31065e8	+	3.69267e8i	0.480677	+	0.536143i
$163$	−6.87915e8	+	9.46834e8i	−0.974506	+	1.34129i	−0.0347684	+	0.999395i	$0.511069\pi$
$163$	−6.87915e8	+	9.46834e8i	−0.974506	+	1.34129i	−0.939737	+	0.341897i	$0.888931\pi$
$164$	−6.76934e8	+	1.40868e8i	−0.935774	+	0.194732i
$165$	1.46449e7	−	2.83185e7i	0.0197583	−	0.0382063i
$166$	1.05252e9	−	9.43630e8i	1.38611	−	1.24271i
$167$	1.76511e8	−	5.73520e7i	0.226938	−	0.0737366i	−0.193341	−	0.981132i	$-0.561932\pi$
$167$	1.76511e8	−	5.73520e7i	0.226938	−	0.0737366i	0.420279	+	0.907395i	$0.361932\pi$
$168$	−2.87392e8	−	2.11628e8i	−0.360776	−	0.265667i
$169$	−2.15213e8	−	6.62357e8i	−0.263828	−	0.811980i
$170$	6.20243e7	−	1.02347e9i	0.0742619	−	1.22540i
$171$	9.63610e8	+	3.13096e8i	1.12698	+	0.366179i
$172$	1.09845e9	+	9.97572e8i	1.25506	+	1.13980i
$173$	5.29750e7	−	3.84886e7i	0.0591407	−	0.0429682i	−0.557822	−	0.829961i	$-0.688363\pi$
$173$	5.29750e7	−	3.84886e7i	0.0591407	−	0.0429682i	0.616963	+	0.786992i	$0.288363\pi$
$174$	2.70077e7	−	1.25741e8i	0.0294639	−	0.137176i
$175$	−1.35325e9	−	1.63291e7i	−1.44287	−	0.0174105i
$176$	−9.95353e7	+	8.80944e7i	−0.103735	+	0.0918116i
$177$	3.19169e8	−	2.31890e8i	0.325183	−	0.236259i
$178$	1.71907e8	−	2.96289e8i	0.171243	−	0.295145i
$179$	8.02598e8	+	2.60780e8i	0.781783	+	0.254017i	0.672601	−	0.740005i	$-0.265177\pi$
$179$	8.02598e8	+	2.60780e8i	0.781783	+	0.254017i	0.109182	+	0.994022i	$0.465177\pi$
$180$	7.90160e8	+	5.24789e8i	0.752705	+	0.499913i
$181$	3.23446e8	+	9.95465e8i	0.301362	+	0.927496i	0.981010	+	0.193957i	$0.0621324\pi$
$181$	3.23446e8	+	9.95465e8i	0.301362	+	0.927496i	−0.679648	+	0.733538i	$0.737868\pi$
$182$	−1.27141e8	+	5.91933e8i	−0.115878	+	0.539494i
$183$	−4.84596e7	+	1.57455e7i	−0.0432091	+	0.0140395i
$184$	3.77448e8	−	1.19973e8i	0.329295	−	0.104667i
$185$	−1.18459e8	−	7.78283e8i	−0.101131	−	0.664432i
$186$	−3.10698e8	+	1.37538e8i	−0.259589	+	0.114913i
$187$	1.22237e8	−	1.68245e8i	0.0999622	−	0.137586i
$188$	8.06411e8	−	4.61001e8i	0.645543	−	0.369038i
$189$	−8.80428e8	+	6.39668e8i	−0.689996	+	0.501311i
$190$	1.70591e9	+	1.03382e8i	1.30901	+	0.0793285i
$191$	−3.24386e8	+	4.46480e8i	−0.243741	+	0.335481i	−0.913307	−	0.407272i	$-0.866480\pi$
$191$	−3.24386e8	+	4.46480e8i	−0.243741	+	0.335481i	0.669566	+	0.742753i	$0.266480\pi$
$192$	2.43624e8	+	3.44515e8i	0.179273	+	0.253515i
$193$	−1.63881e9			−1.18114			−0.590568	−	0.806988i	$-0.701096\pi$
$193$	−1.63881e9			−1.18114			−0.590568	+	0.806988i	$0.701096\pi$
$194$	2.19311e7	+	2.13034e8i	0.0154829	+	0.150398i
$195$	−2.78791e7	+	1.69401e8i	−0.0192815	+	0.117159i
$196$	−1.07369e9	+	1.18226e9i	−0.727537	+	0.801106i
$197$	−6.50063e8	+	2.00069e9i	−0.431609	+	1.32836i	0.464913	+	0.885356i	$0.346086\pi$
$197$	−6.50063e8	+	2.00069e9i	−0.431609	+	1.32836i	−0.896522	+	0.443000i	$0.853914\pi$
$198$	7.78752e7	+	1.75921e8i	0.0506686	+	0.114461i
$199$		−	1.50650e9i		−	0.960629i	−0.877096	−	0.480315i	$-0.840523\pi$
$199$		−	1.50650e9i		−	0.960629i	0.877096	−	0.480315i	$-0.159477\pi$
$200$	1.51230e9	+	5.22449e8i	0.945187	+	0.326530i
$201$	2.04854e8			0.125505
$202$	−1.47667e9	+	6.53682e8i	−0.886907	+	0.392610i
$203$	−1.05308e9	−	3.42168e8i	−0.620124	−	0.201491i
$204$	−4.88708e8	−	4.43828e8i	−0.282182	−	0.256268i
$205$	2.54010e8	+	1.66886e9i	0.143825	+	0.944938i
$206$	−2.59996e9	+	2.67655e8i	−1.44377	+	0.148630i
$207$		−	5.73243e8i		−	0.312218i
$208$	3.63168e8	−	6.16800e8i	0.194024	−	0.329527i
$209$	2.80429e8	+	2.03744e8i	0.146973	+	0.106782i
$210$	−5.53871e8	+	6.72664e8i	−0.284794	+	0.345876i
$211$	1.84943e9	+	2.54552e9i	0.933055	+	1.28424i	0.958656	+	0.284567i	$0.0918499\pi$
$211$	1.84943e9	+	2.54552e9i	0.933055	+	1.28424i	−0.0256014	+	0.999672i	$0.508150\pi$
$212$	8.20667e8	+	1.43556e9i	0.406278	+	0.710686i
$213$	1.43285e8	+	1.04103e8i	0.0696118	+	0.0505760i
$214$	1.21479e9	+	2.74422e9i	0.579224	+	1.30847i
$215$	2.57699e9	−	2.54608e9i	1.20603	−	1.19157i
$216$	1.22616e9	−	3.89738e8i	0.563289	−	0.179043i
$217$	9.03996e8	+	2.78221e9i	0.407688	+	1.25473i
$218$	−3.50839e9	−	7.53564e8i	−1.55339	−	0.333652i
$219$	5.75565e8	−	1.87013e8i	0.250218	−	0.0813007i
$220$	2.01614e8	+	2.54285e8i	0.0860655	+	0.108550i
$221$	−3.46059e8	+	1.06506e9i	−0.145071	+	0.446483i
$222$	−4.38417e8	−	2.54370e8i	−0.180499	−	0.104726i
$223$	1.71556e9	+	2.36127e9i	0.693725	+	0.954830i	0.999996	+	0.00288605i	$0.000918659\pi$
$223$	1.71556e9	+	2.36127e9i	0.693725	+	0.954830i	−0.306271	+	0.951944i	$0.599081\pi$
$224$	3.16537e9	−	1.78274e9i	1.25728	−	0.708104i
$225$	1.38370e9	−	1.85697e9i	0.539899	−	0.724559i
$226$	−3.04973e9	−	6.55049e8i	−1.16904	−	0.251096i
$227$	−7.60375e8	−	1.04657e9i	−0.286368	−	0.394152i	0.641462	−	0.767155i	$-0.278328\pi$
$227$	−7.60375e8	−	1.04657e9i	−0.286368	−	0.394152i	−0.927830	+	0.373003i	$0.878328\pi$
$228$	7.39771e8	−	8.14576e8i	0.273752	−	0.301434i
$229$	−6.78367e8	+	2.08780e9i	−0.246674	+	0.759183i	0.748683	+	0.662928i	$0.230686\pi$
$229$	−6.78367e8	+	2.08780e9i	−0.246674	+	0.759183i	−0.995357	+	0.0962551i	$0.969314\pi$
$230$	−2.42624e8	−	9.35999e8i	−0.0867006	−	0.334475i
$231$	−1.68078e8	+	5.46119e7i	−0.0590287	+	0.0191796i
$232$	1.05412e9	+	7.76227e8i	0.363863	+	0.267939i
$233$	−1.95782e8	−	6.02556e8i	−0.0664278	−	0.204444i	0.912333	−	0.409449i	$-0.134279\pi$
$233$	−1.95782e8	−	6.02556e8i	−0.0664278	−	0.204444i	−0.978761	+	0.205005i	$0.934279\pi$
$234$	−6.91572e8	−	7.71375e8i	−0.230661	−	0.257278i
$235$	−1.01734e9	−	2.02678e9i	−0.333576	−	0.664561i
$236$	8.18130e8	+	3.93147e9i	0.263739	+	1.26738i
$237$	9.90268e8	+	7.19472e8i	0.313877	+	0.228045i
$238$	−4.23201e9	+	3.79419e9i	−1.31898	+	1.18253i
$239$	2.78749e9	+	3.83665e9i	0.854323	+	1.17587i	0.982894	+	0.184174i	$0.0589609\pi$
$239$	2.78749e9	+	3.83665e9i	0.854323	+	1.17587i	−0.128571	+	0.991700i	$0.541039\pi$
$240$	8.72045e8	−	5.48413e8i	0.262841	−	0.165296i
$241$	−1.46664e9	−	1.06558e9i	−0.434765	−	0.315876i	0.348786	−	0.937202i	$-0.386594\pi$
$241$	−1.46664e9	−	1.06558e9i	−0.434765	−	0.315876i	−0.783552	+	0.621327i	$0.786594\pi$
$242$	−3.44482e8	−	3.34624e9i	−0.100440	−	0.975653i
$243$		−	2.84047e9i		−	0.814639i
$244$	5.64153e7	−	5.15568e8i	0.0159161	−	0.145454i
$245$	2.74035e9	+	2.77362e9i	0.760576	+	0.769809i
$246$	9.40087e8	+	5.45439e8i	0.256701	+	0.148938i
$247$	−1.77523e9	−	5.76809e8i	−0.476945	−	0.154969i
$248$	2.21526e7	−	3.45848e9i	0.00585622	−	0.914279i
$249$	−2.22201e9			−0.578027
$250$	1.47337e9	−	3.61773e9i	0.377183	−	0.926139i
$251$		−	1.85764e9i		−	0.468023i	−0.972234	−	0.234011i	$-0.924815\pi$
$251$		−	1.85764e9i		−	0.468023i	0.972234	−	0.234011i	$-0.0751853\pi$
$252$	−1.07126e9	−	5.14786e9i	−0.265639	−	1.27651i
$253$	6.06026e7	−	1.86516e8i	0.0147914	−	0.0455233i
$254$	−9.42771e8	−	5.46996e8i	−0.226502	−	0.131416i
$255$	−1.14652e9	+	1.13277e9i	−0.271158	+	0.267906i
$256$	−4.21575e9	+	8.21090e8i	−0.981556	+	0.191175i
$257$	7.76046e9			1.77891			0.889456	−	0.457020i	$-0.151083\pi$
$257$	7.76046e9			1.77891			0.889456	+	0.457020i	$0.151083\pi$
$258$	−2.38850e8	−	2.32015e9i	−0.0539072	−	0.523645i
$259$	−2.56507e9	+	3.53052e9i	−0.570033	+	0.784583i
$260$	−1.45569e9	−	9.66805e8i	−0.318549	−	0.211566i
$261$	1.53287e9	−	1.11370e9i	0.330327	−	0.239997i
$262$	1.57675e9	−	1.41363e9i	0.334625	−	0.300007i
$263$	−1.67073e9	+	2.29957e9i	−0.349208	+	0.480644i	−0.947103	−	0.320931i	$-0.896004\pi$
$263$	−1.67073e9	+	2.29957e9i	−0.349208	+	0.480644i	0.597894	+	0.801575i	$0.296004\pi$
$264$	2.08933e8	+	1.33827e6i	0.0430121	+	0.000275505i
$265$	3.60804e9	−	1.81105e9i	0.731624	−	0.367238i
$266$	−6.32414e9	−	7.05390e9i	−1.26321	−	1.40897i
$267$	−5.12095e8	+	1.66390e8i	−0.100764	+	0.0327402i
$268$	−8.56244e8	+	1.90126e9i	−0.165981	+	0.368556i
$269$	2.20205e9	+	6.77721e9i	0.420550	+	1.29432i	0.907191	+	0.420718i	$0.138222\pi$
$269$	2.20205e9	+	6.77721e9i	0.420550	+	1.29432i	−0.486641	+	0.873602i	$0.661778\pi$
$270$	−7.88175e8	−	3.04064e9i	−0.148309	−	0.572150i
$271$	−5.83782e9	−	1.89682e9i	−1.08236	−	0.351682i	−0.287073	−	0.957909i	$-0.592682\pi$
$271$	−5.83782e9	−	1.89682e9i	−1.08236	−	0.351682i	−0.795292	+	0.606227i	$0.792682\pi$
$272$	6.16188e9	−	2.68063e9i	1.12574	−	0.489735i
$273$	7.69922e8	−	5.59381e8i	0.138610	−	0.100706i
$274$	−6.07014e9	−	1.30380e9i	−1.07695	−	0.231318i
$275$	6.46531e8	−	4.57916e8i	0.113047	−	0.0800673i
$276$	−5.67648e8	−	2.55643e8i	−0.0978234	−	0.0440552i
$277$	5.50037e9	−	3.99625e9i	0.934271	−	0.678788i	−0.0127639	−	0.999919i	$-0.504063\pi$
$277$	5.50037e9	−	3.99625e9i	0.934271	−	0.678788i	0.947035	+	0.321131i	$0.104063\pi$
$278$	−1.67859e8	−	9.73916e7i	−0.0281038	−	0.0163058i
$279$	−4.76083e9	−	1.54689e9i	−0.785717	−	0.255295i
$280$	−3.92798e9	−	7.95208e9i	−0.639053	−	1.29374i
$281$	2.14215e9	+	6.59285e9i	0.343577	+	1.05742i	0.962341	+	0.271845i	$0.0876337\pi$
$281$	2.14215e9	+	6.59285e9i	0.343577	+	1.05742i	−0.618764	+	0.785577i	$0.712366\pi$
$282$	−1.42754e9	−	3.06621e8i	−0.225732	−	0.0484847i
$283$	6.65383e9	−	2.16196e9i	1.03735	−	0.337056i	0.259659	−	0.965700i	$-0.416390\pi$
$283$	6.65383e9	−	2.16196e9i	1.03735	−	0.337056i	0.777693	+	0.628644i	$0.216390\pi$
$284$	−1.56508e9	+	8.94712e8i	−0.240583	+	0.137534i
$285$	−1.88810e9	−	1.91102e9i	−0.286184	−	0.289658i
$286$	−1.43468e8	−	3.24094e8i	−0.0214432	−	0.0484403i
$287$	5.50022e9	−	7.57041e9i	0.810686	−	1.11581i
$288$	−7.15756e8	+	6.17510e9i	−0.104039	+	0.897582i
$289$	−2.86199e9	+	2.07936e9i	−0.410276	+	0.298083i
$290$	2.03153e9	−	2.46725e9i	0.287231	−	0.348836i
$291$	1.97870e8	−	2.72345e8i	0.0275936	−	0.0379793i
$292$	−6.70057e8	+	6.12352e9i	−0.0921681	+	0.842306i
$293$	7.81142e9			1.05989			0.529943	−	0.848033i	$-0.322213\pi$
$293$	7.81142e9			1.05989			0.529943	+	0.848033i	$0.322213\pi$
$294$	2.49719e9	−	2.57076e8i	0.334243	−	0.0344090i
$295$	9.69232e9	−	1.47523e9i	1.27979	−	0.194792i
$296$	4.19330e9	−	3.00576e9i	0.546247	−	0.391551i
$297$	1.96871e8	−	6.05906e8i	0.0253020	−	0.0778716i
$298$	9.44479e9	−	4.18095e9i	1.19764	−	0.530164i
$299$			1.05607e9i			0.132132i
$300$	−1.22177e9	−	2.19833e9i	−0.150835	−	0.271399i
$301$	−2.00813e10			−2.44639
$302$	−1.40530e9	−	3.17458e9i	−0.168944	−	0.381644i
$303$	2.41419e9	+	7.84417e8i	0.286418	+	0.0930628i
$304$	4.46806e9	+	1.02706e10i	0.523148	+	1.20254i
$305$	−1.24942e9	−	2.05623e8i	−0.144380	−	0.0237614i
$306$	−9.95987e8	−	9.67484e9i	−0.113597	−	1.10346i
$307$			8.82727e9i			0.993740i	0.867825	+	0.496870i	$0.165517\pi$
$307$			8.82727e9i			0.993740i	−0.867825	+	0.496870i	$0.834483\pi$
$308$	1.95672e8	−	1.78821e9i	0.0217433	−	0.198708i
$309$	3.32381e9	+	2.41489e9i	0.364587	+	0.264888i
$310$	−8.42827e9	−	5.10770e8i	−0.912623	−	0.0553068i
$311$	6.24118e9	+	8.59024e9i	0.667152	+	0.918256i	0.999692	−	0.0248332i	$-0.00790547\pi$
$311$	6.24118e9	+	8.59024e9i	0.667152	+	0.918256i	−0.332539	+	0.943089i	$0.607905\pi$
$312$	−1.07226e9	+	3.40820e8i	−0.113157	+	0.0359672i
$313$	−1.40012e10	−	1.01725e10i	−1.45877	−	1.05986i	−0.983681	−	0.179922i	$-0.942415\pi$
$313$	−1.40012e10	−	1.01725e10i	−1.45877	−	1.05986i	−0.475090	−	0.879937i	$-0.657585\pi$
$314$	−6.30420e9	+	2.79070e9i	−0.648502	+	0.287074i
$315$	−1.26911e10	+	1.93166e9i	−1.28901	+	0.196195i
$316$	−1.08165e10	+	6.18350e9i	−1.08478	+	0.620135i
$317$	−1.46148e9	−	4.49797e9i	−0.144729	−	0.445430i	0.852247	−	0.523139i	$-0.175239\pi$
$317$	−1.46148e9	−	4.49797e9i	−0.144729	−	0.445430i	−0.996976	+	0.0777096i	$0.975239\pi$
$318$	5.45841e8	−	2.54129e9i	0.0533774	−	0.248511i
$319$	6.16489e8	−	2.00310e8i	0.0595337	−	0.0193437i
$320$	1.44490e9	+	1.03857e10i	0.137796	+	0.990461i
$321$	1.45774e9	−	4.48648e9i	0.137297	−	0.422557i
$322$	−2.68991e9	+	4.63618e9i	−0.250216	+	0.431258i
$323$	−1.03001e10	−	1.41769e10i	−0.946308	−	1.30248i
$324$	7.23526e9	+	3.25844e9i	0.656559	+	0.295685i
$325$	−2.54916e9	+	3.42104e9i	−0.228488	+	0.306637i
$326$	−3.93237e9	+	1.83081e10i	−0.348164	+	1.62096i
$327$	3.31545e9	+	4.56333e9i	0.289969	+	0.399108i
$328$	−8.99160e9	+	6.44519e9i	−0.776858	+	0.556853i
$329$	−3.88465e9	+	1.19557e10i	−0.331565	+	1.02045i
$330$	3.08564e7	−	5.09166e8i	0.00260190	−	0.0429342i
$331$	−1.98698e9	+	6.45609e8i	−0.165532	+	0.0537846i	−0.390611	−	0.920556i	$-0.627736\pi$
$331$	−1.98698e9	+	6.45609e8i	−0.165532	+	0.0537846i	0.225079	+	0.974341i	$0.427736\pi$
$332$	9.28748e9	−	2.06226e10i	0.764444	−	1.69742i
$333$	−2.30757e9	−	7.10198e9i	−0.187663	−	0.577567i
$334$	2.21102e9	−	1.98228e9i	0.177667	−	0.159287i
$335$	4.52188e9	+	2.33848e9i	0.359037	+	0.185676i
$336$	−5.57534e9	−	1.23493e9i	−0.437436	−	0.0968917i
$337$	1.62370e10	+	1.17968e10i	1.25888	+	0.914631i	0.998702	−	0.0509293i	$-0.0162183\pi$
$337$	1.62370e10	+	1.17968e10i	1.25888	+	0.914631i	0.260179	+	0.965560i	$0.416218\pi$
$338$	−7.43849e9	−	8.29684e9i	−0.569925	−	0.635691i
$339$	2.88202e9	+	3.96676e9i	0.218222	+	0.300356i
$340$	−5.72111e9	−	1.53757e10i	−0.428119	−	1.15058i
$341$	−1.38549e9	−	1.00662e9i	−0.102468	−	0.0744471i
$342$	1.61260e10	−	1.66011e9i	1.17875	−	0.121348i
$343$		−	1.64104e9i		−	0.118561i
$344$	2.25318e10	+	7.48090e9i	1.60902	+	0.534220i
$345$	−6.98184e8	+	1.35007e9i	−0.0492826	+	0.0952969i
$346$	5.25781e8	−	9.06206e8i	0.0366860	−	0.0632299i
$347$	−2.29216e10	−	7.44769e9i	−1.58099	−	0.513693i	−0.618675	−	0.785647i	$-0.712330\pi$
$347$	−2.29216e10	−	7.44769e9i	−1.58099	−	0.513693i	−0.962310	+	0.271953i	$0.912330\pi$
$348$	−4.19228e8	−	2.01458e9i	−0.0285847	−	0.137362i
$349$	−7.47328e9			−0.503744			−0.251872	−	0.967761i	$-0.581046\pi$
$349$	−7.47328e9			−0.503744			−0.251872	+	0.967761i	$0.581046\pi$
$350$	−1.99046e10	+	8.52551e9i	−1.32642	+	0.568130i
$351$			3.43070e9i			0.226024i
$352$	−8.85710e8	+	1.93352e9i	−0.0576927	+	0.125944i
$353$	3.30154e9	−	1.01611e10i	0.212626	−	0.654397i	−0.786687	−	0.617352i	$-0.788206\pi$
$353$	3.30154e9	−	1.01611e10i	0.212626	−	0.654397i	0.999314	−	0.0370450i	$-0.0117945\pi$
$354$	3.16778e9	−	5.45981e9i	0.201717	−	0.347668i
$355$	1.97446e9	+	3.93357e9i	0.124318	+	0.247670i
$356$	5.96166e8	−	5.44825e9i	0.0371165	−	0.339201i
$357$	8.93435e9			0.550035
$358$	1.34314e10	−	1.38271e9i	0.817693	−	0.0841783i
$359$	1.27535e10	−	1.75537e10i	0.767807	−	1.05680i	−0.228717	−	0.973493i	$-0.573453\pi$
$359$	1.27535e10	−	1.75537e10i	0.767807	−	1.05680i	0.996524	−	0.0833026i	$-0.0265468\pi$
$360$	1.49593e10	+	2.56045e9i	0.890640	+	0.152442i
$361$	9.88999e9	−	7.18550e9i	0.582327	−	0.423086i
$362$	1.11794e10	+	1.24694e10i	0.651005	+	0.726126i
$363$	−3.10805e9	+	4.27786e9i	−0.179003	+	0.246377i
$364$	1.97355e9	+	9.48376e9i	0.112420	+	0.540226i
$365$	1.48396e10	+	2.44223e9i	0.836086	+	0.137599i
$366$	−6.07015e8	+	5.44217e8i	−0.0338279	+	0.0303283i
$367$	1.15797e10	−	3.76247e9i	0.638311	−	0.207400i	0.0280579	−	0.999606i	$-0.491068\pi$
$367$	1.15797e10	−	3.76247e9i	0.638311	−	0.207400i	0.610253	+	0.792206i	$0.291068\pi$
$368$	4.74527e9	−	4.19984e9i	0.258744	−	0.229003i
$369$	4.94808e9	+	1.52286e10i	0.266889	+	0.821400i
$370$	−6.77373e9	−	1.06195e10i	−0.361427	−	0.566629i
$371$	−2.12834e10	−	6.91540e9i	−1.12343	−	0.365024i
$372$	−3.65493e9	+	4.02451e9i	−0.190856	+	0.210156i
$373$	1.75503e10	−	1.27510e10i	0.906668	−	0.658733i	−0.0335020	−	0.999439i	$-0.510666\pi$
$373$	1.75503e10	−	1.27510e10i	0.906668	−	0.658733i	0.940170	+	0.340706i	$0.110666\pi$
$374$	6.98750e8	−	3.25319e9i	0.0357138	−	0.166274i
$375$	−5.52051e9	+	2.68812e9i	−0.279161	+	0.135933i
$376$	8.81256e9	−	1.19675e10i	0.440911	−	0.598759i
$377$	−2.82398e9	+	2.05174e9i	−0.139796	+	0.101568i
$378$	−8.73832e9	+	1.50609e10i	−0.428017	+	0.737705i
$379$	2.39038e10	+	7.76682e9i	1.15854	+	0.376432i	0.824353	−	0.566076i	$-0.191539\pi$
$379$	2.39038e10	+	7.76682e9i	1.15854	+	0.376432i	0.334185	+	0.942507i	$0.391539\pi$
$380$	2.56281e10	−	9.53592e9i	1.22908	−	0.457328i
$381$	5.29441e8	+	1.62945e9i	0.0251256	+	0.0773288i
$382$	−1.85431e9	+	8.63317e9i	−0.0870821	+	0.405431i
$383$	−2.69126e10	+	8.74445e9i	−1.25072	+	0.406385i	−0.858180	−	0.513349i	$-0.828405\pi$
$383$	−2.69126e10	+	8.74445e9i	−1.25072	+	0.406385i	−0.392543	+	0.919733i	$0.628405\pi$
$384$	5.79563e9	+	3.46261e9i	0.266548	+	0.159250i
$385$	−4.33350e9	−	7.13185e8i	−0.197241	−	0.0324608i
$386$	−2.39768e10	+	1.06139e10i	−1.08004	+	0.478106i
$387$	2.01978e10	−	2.77998e10i	0.900450	−	1.23936i
$388$	1.70060e9	+	2.97478e9i	0.0750368	+	0.131259i
$389$	−3.04611e10	+	2.21313e10i	−1.33029	+	0.966514i	−0.330551	+	0.943788i	$0.607235\pi$
$389$	−3.04611e10	+	2.21313e10i	−1.33029	+	0.966514i	−0.999742	+	0.0227260i	$0.992765\pi$
$390$	6.89248e8	+	2.65900e9i	0.0297932	+	0.114937i
$391$	−5.82755e9	+	8.02094e9i	−0.249333	+	0.343177i
$392$	−8.05173e9	+	2.42510e10i	−0.340993	+	1.02704i
$393$	−3.32874e9			−0.139544
$394$	3.44678e9	+	3.34814e10i	0.143031	+	1.38937i
$395$	1.36458e10	+	2.71856e10i	0.560545	+	1.11674i
$396$	2.27872e9	+	2.06946e9i	0.0926639	+	0.0841542i
$397$	7.39580e9	−	2.27619e10i	0.297730	−	0.916320i	−0.684560	−	0.728956i	$-0.740006\pi$
$397$	7.39580e9	−	2.27619e10i	0.297730	−	0.916320i	0.982291	−	0.187364i	$-0.0599943\pi$
$398$	−9.75692e9	−	2.20409e10i	−0.388848	−	0.878411i
$399$			1.48917e10i			0.587562i
$400$	2.55095e10	−	2.15077e9i	0.996465	−	0.0840143i
$401$	−1.23172e10			−0.476357			−0.238179	−	0.971221i	$-0.576550\pi$
$401$	−1.23172e10			−0.476357			−0.238179	+	0.971221i	$0.576550\pi$
$402$	2.99714e9	−	1.32675e9i	0.114763	−	0.0508026i
$403$	8.77076e9	+	2.84979e9i	0.332519	+	0.108042i
$404$	−1.73709e10	+	1.91275e10i	−0.652076	+	0.718014i
$405$	8.89908e9	−	1.72080e10i	0.330769	−	0.639603i
$406$	−1.76233e10	+	1.81425e9i	−0.648609	+	0.0667718i
$407$		−	2.55472e9i		−	0.0931034i
$408$	−1.00246e10	−	3.32832e9i	−0.361764	−	0.120111i
$409$	−2.87948e10	−	2.09206e10i	−1.02901	−	0.747621i	−0.0609016	−	0.998144i	$-0.519398\pi$
$409$	−2.87948e10	−	2.09206e10i	−1.02901	−	0.747621i	−0.968111	+	0.250523i	$0.919398\pi$
$410$	1.45248e10	+	2.27712e10i	0.514012	+	0.805844i
$411$	5.73632e9	+	7.89537e9i	0.201033	+	0.276698i
$412$	−3.63054e10	+	2.07547e10i	−1.26004	+	0.720325i
$413$	−4.39671e10	−	3.19440e10i	−1.51122	−	1.09797i
$414$	−3.71265e9	−	8.38689e9i	−0.126381	−	0.285496i
$415$	−4.90477e10	−	2.53649e10i	−1.65359	−	0.855149i
$416$	1.31862e9	−	1.13762e10i	0.0440298	−	0.379861i
$417$	9.42659e7	+	2.90121e8i	0.00311753	+	0.00959476i
$418$	5.42240e9	+	1.16467e9i	0.177618	+	0.0381504i
$419$	2.88691e10	−	9.38013e9i	0.936649	−	0.304336i	0.199370	−	0.979924i	$-0.436110\pi$
$419$	2.88691e10	−	9.38013e9i	0.936649	−	0.304336i	0.737279	+	0.675589i	$0.236110\pi$
$420$	−3.74690e9	+	1.34286e10i	−0.120413	+	0.431554i
$421$	−1.25600e9	+	3.86558e9i	−0.0399818	+	0.123051i	−0.969055	−	0.246844i	$-0.920606\pi$
$421$	−1.25600e9	+	3.86558e9i	−0.0399818	+	0.123051i	0.929073	+	0.369895i	$0.120606\pi$
$422$	4.35444e10	+	2.52645e10i	1.37304	+	0.796637i
$423$	−1.26439e10	−	1.74028e10i	−0.394930	−	0.543574i
$424$	2.13043e10	+	1.56880e10i	0.659181	+	0.485404i
$425$	−3.82389e10	+	1.19164e10i	−1.17206	+	0.365250i
$426$	2.77058e9	+	5.95090e8i	0.0841263	+	0.0180694i
$427$	4.12571e9	+	5.67856e9i	0.124104	+	0.170815i
$428$	3.55462e10	+	3.22818e10i	1.05930	+	0.962018i
$429$	−1.72161e8	+	5.29856e8i	−0.00508282	+	0.0156433i
$430$	2.12130e10	−	5.39406e10i	0.620480	−	1.57776i
$431$	5.68231e10	−	1.84629e10i	1.64670	−	0.535047i	0.668682	−	0.743548i	$-0.266859\pi$
$431$	5.68231e10	−	1.84629e10i	1.64670	−	0.535047i	0.978022	+	0.208502i	$0.0668587\pi$
$432$	1.54153e10	−	1.36434e10i	0.442604	−	0.391730i
$433$	−5.63126e9	−	1.73312e10i	−0.160197	−	0.493035i	0.838453	−	0.544973i	$-0.183460\pi$
$433$	−5.63126e9	−	1.73312e10i	−0.160197	−	0.493035i	−0.998650	+	0.0519380i	$0.983460\pi$
$434$	3.12452e10	+	3.48506e10i	0.880692	+	0.982317i
$435$	−4.96657e9	+	7.55941e8i	−0.138707	+	0.0211121i
$436$	−5.62103e10	+	1.16972e10i	−1.55550	+	0.323696i
$437$	−1.33693e10	−	9.71333e9i	−0.366591	−	0.266344i
$438$	7.20966e9	−	6.46379e9i	0.195893	−	0.175627i
$439$	7.92249e9	+	1.09044e10i	0.213306	+	0.293591i	0.902241	−	0.431233i	$-0.141921\pi$
$439$	7.92249e9	+	1.09044e10i	0.213306	+	0.293591i	−0.688934	+	0.724824i	$0.741921\pi$
$440$	4.59662e9	+	2.41457e9i	0.122639	+	0.0644214i
$441$	2.99211e10	+	2.17390e10i	0.791085	+	0.574757i
$442$	1.83488e9	+	1.78237e10i	0.0480750	+	0.466992i
$443$			6.25024e10i			1.62286i	0.584448	+	0.811431i	$0.301311\pi$
$443$			6.25024e10i			1.62286i	−0.584448	+	0.811431i	$0.698689\pi$
$444$	−8.06174e9	−	8.82144e8i	−0.207442	−	0.0226990i
$445$	−1.32032e10	−	2.17291e9i	−0.336696	−	0.0554117i
$446$	4.03926e10	+	2.34358e10i	1.02085	+	0.592299i
$447$	−1.54411e10	−	5.01713e9i	−0.386767	−	0.125668i
$448$	3.47651e10	−	4.65833e10i	0.863042	−	1.15643i
$449$	−3.15632e10			−0.776598			−0.388299	−	0.921533i	$-0.626937\pi$
$449$	−3.15632e10			−0.776598			−0.388299	+	0.921533i	$0.626937\pi$
$450$	8.21763e9	−	3.61302e10i	0.200399	−	0.881089i
$451$			5.47803e9i			0.132409i
$452$	−4.88618e10	+	1.01680e10i	−1.17062	+	0.243603i
$453$	−1.68636e9	+	5.19008e9i	−0.0400458	+	0.123248i
$454$	−1.79029e10	−	1.03873e10i	−0.421405	−	0.244500i
$455$	2.33805e10	−	3.55865e9i	0.545516	−	0.0830308i
$456$	5.54762e9	−	1.67089e10i	0.128306	−	0.386446i
$457$	5.82091e10			1.33452			0.667261	−	0.744824i	$-0.267466\pi$
$457$	5.82091e10			1.33452			0.667261	+	0.744824i	$0.267466\pi$
$458$	3.59685e9	+	3.49392e10i	0.0817449	+	0.794056i
$459$	−1.89311e10	+	2.60564e10i	−0.426506	+	0.587035i
$460$	−9.61179e9	−	1.21229e10i	−0.214671	−	0.270753i
$461$	−2.88614e9	+	2.09690e9i	−0.0639019	+	0.0464275i	−0.619278	−	0.785172i	$-0.712574\pi$
$461$	−2.88614e9	+	2.09690e9i	−0.0639019	+	0.0464275i	0.555376	+	0.831600i	$0.312574\pi$
$462$	−2.10538e9	+	1.88757e9i	−0.0462129	+	0.0414320i
$463$	−2.85953e10	+	3.93581e10i	−0.622258	+	0.856465i	−0.997515	−	0.0704559i	$-0.977555\pi$
$463$	−2.85953e10	+	3.93581e10i	−0.622258	+	0.856465i	0.375257	+	0.926921i	$0.377555\pi$
$464$	2.04497e10	+	4.52958e9i	0.441178	+	0.0977207i
$465$	9.32837e9	+	9.44161e9i	0.199524	+	0.201946i
$466$	−6.76691e9	−	7.54776e9i	−0.143498	−	0.160057i
$467$	4.21899e9	−	1.37083e9i	0.0887036	−	0.0288215i	−0.264329	−	0.964433i	$-0.585150\pi$
$467$	4.21899e9	−	1.37083e9i	0.0887036	−	0.0288215i	0.353033	+	0.935611i	$0.385150\pi$
$468$	−1.51140e10	−	6.80665e9i	−0.315061	−	0.141889i
$469$	−8.72037e9	−	2.68385e10i	−0.180237	−	0.554712i
$470$	−2.80108e10	−	2.30641e10i	−0.574030	−	0.472656i
$471$	1.03066e10	+	3.34883e9i	0.209427	+	0.0680471i
$472$	3.74321e10	+	5.22211e10i	0.754183	+	1.05215i
$473$	9.51070e9	−	6.90993e9i	0.190006	−	0.138048i
$474$	1.91479e10	+	4.11276e9i	0.379322	+	0.0814743i
$475$	−1.98622e10	−	6.37363e10i	−0.390170	−	1.25202i
$476$	−3.73435e10	+	8.29202e10i	−0.727424	+	1.61522i
$477$	3.09803e10	−	2.25085e10i	0.598428	−	0.434783i
$478$	6.56310e10	+	3.80791e10i	1.25718	+	0.729416i
$479$	−8.65100e10	−	2.81088e10i	−1.64333	−	0.533950i	−0.666050	−	0.745907i	$-0.732016\pi$
$479$	−8.65100e10	−	2.81088e10i	−1.64333	−	0.533950i	−0.977279	+	0.211957i	$0.932016\pi$
$480$	9.20670e9	−	1.36715e10i	0.173436	−	0.257543i
$481$	4.25118e9	+	1.30838e10i	0.0794199	+	0.244429i
$482$	−2.83591e10	−	6.09122e9i	−0.525416	−	0.112854i
$483$	8.01300e9	−	2.60358e9i	0.147234	−	0.0478391i
$484$	−2.67121e10	−	4.67264e10i	−0.486773	−	0.851492i
$485$	7.47661e9	−	3.75288e9i	0.135126	−	0.0678263i
$486$	−1.83965e10	−	4.15578e10i	−0.329754	−	0.744916i
$487$	1.20061e10	−	1.65250e10i	0.213445	−	0.293782i	−0.688847	−	0.724906i	$-0.741883\pi$
$487$	1.20061e10	−	1.65250e10i	0.213445	−	0.293782i	0.902292	+	0.431125i	$0.141883\pi$
$488$	−2.51372e9	−	7.90844e9i	−0.0443239	−	0.139448i
$489$	2.38131e10	−	1.73012e10i	0.416467	−	0.302581i
$490$	5.80565e10	+	2.28316e10i	1.00709	+	0.396052i
$491$	−3.68642e10	+	5.07393e10i	−0.634277	+	0.873008i	−0.998294	−	0.0583844i	$-0.981405\pi$
$491$	−3.68642e10	+	5.07393e10i	−0.634277	+	0.873008i	0.364017	+	0.931392i	$0.381405\pi$
$492$	1.72866e10	+	1.89156e9i	0.295019	+	0.0322820i
$493$	−3.27701e10			−0.554741
$494$	−2.97085e10	+	3.05837e9i	−0.498853	+	0.0513549i
$495$	5.34594e9	−	5.28182e9i	0.0890437	−	0.0879757i
$496$	−2.20750e10	−	5.07431e10i	−0.364732	−	0.838398i
$497$	7.53934e9	−	2.32037e10i	0.123569	−	0.380305i
$498$	−3.25093e10	+	1.43910e10i	−0.528555	+	0.233977i
$499$		−	3.96359e10i		−	0.639274i	−0.947540	−	0.319637i	$-0.896439\pi$
$499$		−	3.96359e10i		−	0.639274i	0.947540	−	0.319637i	$-0.103561\pi$
$500$	−1.87414e9	−	6.24719e10i	−0.0299862	−	0.999550i
$501$	−4.66777e9			−0.0740898
$502$	−1.20311e10	−	2.71784e10i	−0.189449	−	0.427966i
$503$	5.71150e9	+	1.85578e9i	0.0892233	+	0.0289904i	0.353288	−	0.935514i	$-0.385063\pi$
$503$	5.71150e9	+	1.85578e9i	0.0892233	+	0.0289904i	−0.264065	+	0.964505i	$0.585063\pi$
$504$	−4.90135e10	−	6.83781e10i	−0.759615	−	1.05973i
$505$	4.43354e10	+	4.48736e10i	0.681688	+	0.689963i
$506$	−3.21329e8	−	3.12133e9i	−0.00490171	−	0.0476144i
$507$			1.75157e10i			0.265092i
$508$	−1.73360e10	−	1.89696e9i	−0.260311	−	0.0284842i
$509$	−7.29382e10	−	5.29927e10i	−1.08664	−	0.789487i	−0.107807	−	0.994172i	$-0.534383\pi$
$509$	−7.29382e10	−	5.29927e10i	−1.08664	−	0.789487i	−0.978828	+	0.204685i	$0.934383\pi$
$510$	−9.43784e9	+	2.39987e10i	−0.139506	+	0.354737i
$511$	−4.90020e10	−	6.74455e10i	−0.718672	−	0.989167i
$512$	−5.63611e10	+	3.93166e10i	−0.820162	+	0.572132i
$513$	−4.34307e10	−	3.15543e10i	−0.627086	−	0.455605i
$514$	1.13540e11	−	5.02611e10i	1.62666	−	0.720078i
$515$	4.58017e10	+	9.12476e10i	0.651107	+	1.29716i
$516$	−1.85211e10	−	3.23982e10i	−0.261257	−	0.457006i
$517$	−2.27413e9	−	6.99905e9i	−0.0318312	−	0.0979663i
$518$	−1.46629e10	+	6.82664e10i	−0.203657	+	0.948173i
$519$	−1.56625e9	+	5.08906e8i	−0.0215870	+	0.00701405i
$520$	−2.75592e10	−	4.71704e9i	−0.376923	−	0.0645144i
$521$	1.03612e10	−	3.18886e10i	0.140624	−	0.432797i	−0.855798	−	0.517310i	$-0.826933\pi$
$521$	1.03612e10	−	3.18886e10i	0.140624	−	0.432797i	0.996422	+	0.0845131i	$0.0269335\pi$
$522$	1.52139e10	−	2.62218e10i	0.204908	−	0.353168i
$523$	−3.19783e10	−	4.40143e10i	−0.427413	−	0.588284i	0.539944	−	0.841701i	$-0.318446\pi$
$523$	−3.19783e10	−	4.40143e10i	−0.427413	−	0.588284i	−0.967357	+	0.253417i	$0.918446\pi$
$524$	1.39134e10	−	3.08942e10i	0.184547	−	0.409781i
$525$	3.22419e10	+	1.09079e10i	0.424408	+	0.143583i
$526$	−9.55053e9	+	4.44647e10i	−0.124763	+	0.580861i
$527$	5.08890e10	+	7.00427e10i	0.659753	+	0.908072i
$528$	3.06547e9	−	1.33359e9i	0.0394423	−	0.0171587i
$529$	2.13102e10	−	6.55862e10i	0.272123	−	0.837509i
$530$	4.10583e10	−	4.98645e10i	0.520353	−	0.631957i
$531$	8.84442e10	−	2.87373e10i	1.11248	−	0.361466i
$532$	−1.38211e11	−	6.22440e10i	−1.72542	−	0.777053i
$533$	−9.11571e9	−	2.80553e10i	−0.112949	−	0.347621i
$534$	−6.41461e9	+	5.75099e9i	−0.0788870	+	0.0707258i
$535$	8.33923e10	−	8.23921e10i	1.01791	−	1.00570i
$536$	−2.13694e8	+	3.33621e10i	−0.00258901	+	0.404199i
$537$	−1.71709e10	−	1.24754e10i	−0.206488	−	0.150022i
$538$	7.61103e10	+	8.48928e10i	0.908477	+	1.01331i
$539$	7.43719e9	+	1.02364e10i	0.0881158	+	0.121281i
$540$	−3.12244e10	−	3.93817e10i	−0.367214	−	0.463148i
$541$	1.28810e11	+	9.35858e10i	1.50369	+	1.09250i	0.968881	+	0.247528i	$0.0796183\pi$
$541$	1.28810e11	+	9.35858e10i	1.50369	+	1.09250i	0.534814	+	0.844970i	$0.320382\pi$
$542$	−9.76957e10	+	1.00574e10i	−1.13208	+	0.116543i
$543$		−	2.63246e10i		−	0.302805i
$544$	7.27907e10	−	7.91270e10i	0.831152	−	0.903502i
$545$	2.10921e10	+	1.38576e11i	0.239075	+	1.57073i
$546$	7.64154e9	−	1.31705e10i	0.0859825	−	0.148195i
$547$	−1.17480e11	−	3.81715e10i	−1.31224	−	0.426374i	−0.432419	−	0.901673i	$-0.642340\pi$
$547$	−1.17480e11	−	3.81715e10i	−1.31224	−	0.426374i	−0.879824	+	0.475299i	$0.842340\pi$
$548$	−9.72538e10	+	2.02383e10i	−1.07841	+	0.224415i
$549$	−1.20108e10			−0.132216
$550$	6.49340e9	−	1.08869e10i	0.0709613	−	0.118974i
$551$		−	5.46210e10i		−	0.592589i
$552$	−9.96071e9	−	6.38013e7i	−0.107284	−	0.000687184i
$553$	5.21056e10	−	1.60365e11i	0.557166	−	1.71478i
$554$	5.45917e10	−	9.40910e10i	0.579545	−	0.998870i
$555$	−3.21524e9	+	1.95367e10i	−0.0338877	+	0.205910i
$556$	−3.08663e9	−	3.37750e8i	−0.0322988	−	0.00353424i
$557$	−1.79428e10			−0.186410			−0.0932050	−	0.995647i	$-0.529711\pi$
$557$	−1.79428e10			−0.186410			−0.0932050	+	0.995647i	$0.529711\pi$
$558$	−7.96723e10	+	8.20195e9i	−0.821808	+	0.0846019i
$559$	−3.72098e10	+	5.12150e10i	−0.381075	+	0.524505i
$560$	−1.08971e11	−	9.09038e10i	−1.10805	−	0.924336i
$561$	−4.23140e9	+	3.07429e9i	−0.0427201	+	0.0310380i
$562$	7.40399e10	+	8.25836e10i	0.742200	+	0.827844i
$563$	3.38043e10	−	4.65276e10i	0.336463	−	0.463102i	−0.606941	−	0.794747i	$-0.707604\pi$
$563$	3.38043e10	−	4.65276e10i	0.336463	−	0.463102i	0.943404	+	0.331645i	$0.107604\pi$
$564$	−2.28716e10	+	4.75953e9i	−0.226038	+	0.0470379i
$565$	1.83347e10	+	1.20460e11i	0.179920	+	1.18208i
$566$	8.33474e10	−	7.47247e10i	0.812132	−	0.728113i
$567$	−1.02134e11	+	3.31854e10i	−0.988185	+	0.321081i
$568$	−1.71034e10	+	2.32265e10i	−0.164320	+	0.223147i
$569$	2.20454e9	+	6.78487e9i	0.0210314	+	0.0647280i	0.961021	−	0.276474i	$-0.0891660\pi$
$569$	2.20454e9	+	6.78487e9i	0.0210314	+	0.0647280i	−0.939990	+	0.341202i	$0.889166\pi$
$570$	−4.00008e10	−	1.57309e10i	−0.378939	−	0.149024i
$571$	−1.33445e11	−	4.33590e10i	−1.25533	−	0.407882i	−0.395504	−	0.918464i	$-0.629430\pi$
$571$	−1.33445e11	−	4.33590e10i	−1.25533	−	0.407882i	−0.859829	+	0.510582i	$0.829430\pi$
$572$	−4.19803e9	−	3.81251e9i	−0.0392158	−	0.0356145i
$573$	1.12291e10	−	8.15840e9i	0.104166	−	0.0756810i
$574$	3.14413e10	−	1.46382e11i	0.289636	−	1.34847i
$575$	−3.08229e10	+	2.18308e10i	−0.281970	+	0.199710i
$576$	2.95215e10	+	9.49810e10i	0.268194	+	0.862873i
$577$	5.29049e10	−	3.84376e10i	0.477301	−	0.346779i	−0.322979	−	0.946406i	$-0.604684\pi$
$577$	5.29049e10	−	3.84376e10i	0.477301	−	0.346779i	0.800280	+	0.599627i	$0.204684\pi$
$578$	−2.84055e10	+	4.89580e10i	−0.254502	+	0.438644i
$579$	3.91992e10	+	1.27366e10i	0.348790	+	0.113329i
$580$	1.37432e10	−	4.92546e10i	0.121444	−	0.435246i
$581$	9.45878e10	+	2.91111e11i	0.830100	+	2.55479i
$582$	1.13110e9	−	5.26608e9i	0.00985844	−	0.0458982i
$583$	1.24596e10	−	4.04837e9i	0.107852	−	0.0350434i
$584$	2.98560e10	+	9.39304e10i	0.256673	+	0.807523i
$585$	−1.85896e10	+	3.59463e10i	−0.158725	+	0.306924i
$586$	1.14286e11	−	5.05911e10i	0.969172	−	0.429026i
$587$	8.05310e10	−	1.10841e11i	0.678282	−	0.933576i	−0.321629	−	0.946866i	$-0.604230\pi$
$587$	8.05310e10	−	1.10841e11i	0.678282	−	0.933576i	0.999912	+	0.0132899i	$0.00423045\pi$
$588$	3.48703e10	−	1.99344e10i	0.291707	−	0.166760i
$589$	−1.16747e11	+	8.48215e10i	−0.970027	+	0.704766i
$590$	1.32250e11	−	8.43564e10i	1.09141	−	0.696161i
$591$	3.10981e10	−	4.28029e10i	0.254909	−	0.350851i
$592$	4.18834e10	−	7.11343e10i	0.341001	−	0.579151i
$593$	−1.43738e11			−1.16239			−0.581197	−	0.813763i	$-0.697416\pi$
$593$	−1.43738e11			−1.16239			−0.581197	+	0.813763i	$0.697416\pi$
$594$	−1.04385e9	−	1.01398e10i	−0.00838482	−	0.0814486i
$595$	1.97213e11	+	1.01989e11i	1.57351	+	0.813736i
$596$	1.11105e11	−	1.22340e11i	0.880536	−	0.969576i
$597$	−1.17083e10	+	3.60344e10i	−0.0921713	+	0.283674i
$598$	6.83971e9	+	1.54509e10i	0.0534851	+	0.120823i
$599$			4.20154e10i			0.326363i	0.986596	+	0.163182i	$0.0521756\pi$
$599$			4.20154e10i			0.326363i	−0.986596	+	0.163182i	$0.947824\pi$
$600$	−3.21128e10	−	2.42500e10i	−0.247784	−	0.187114i
$601$	2.17535e11			1.66737			0.833683	−	0.552243i	$-0.186228\pi$
$601$	2.17535e11			1.66737			0.833683	+	0.552243i	$0.186228\pi$
$602$	−2.93802e11	+	1.30058e11i	−2.23701	+	0.990264i
$603$	4.59252e10	+	1.49220e10i	0.347362	+	0.112865i
$604$	−4.11208e10	−	3.73445e10i	−0.308968	−	0.280594i
$605$	−1.17439e11	+	5.89484e10i	−0.876578	+	0.439998i
$606$	4.04013e10	−	4.15915e9i	0.299574	−	0.0308400i
$607$			2.53898e11i			1.87027i	0.354288	+	0.935136i	$0.384723\pi$
$607$			2.53898e11i			1.87027i	−0.354288	+	0.935136i	$0.615277\pi$
$608$	1.31888e11	+	1.21327e11i	0.965145	+	0.887858i
$609$	2.25298e10	+	1.63688e10i	0.163790	+	0.119000i
$610$	−1.96114e10	+	5.08355e9i	−0.141641	+	0.0367154i
$611$	2.32935e10	+	3.20608e10i	0.167136	+	0.230043i
$612$	−7.72316e10	−	1.35098e11i	−0.550541	−	0.963038i
$613$	1.46554e11	+	1.06478e11i	1.03790	+	0.754080i	0.969875	−	0.243604i	$-0.0783296\pi$
$613$	1.46554e11	+	1.06478e11i	1.03790	+	0.754080i	0.0680270	+	0.997683i	$0.478330\pi$
$614$	5.71704e10	+	1.29148e11i	0.402251	+	0.908688i
$615$	6.89437e9	−	4.18920e10i	0.0481941	−	0.292840i
$616$	−8.71864e9	−	2.74298e10i	−0.0605516	−	0.190502i
$617$	−1.90443e10	−	5.86122e10i	−0.131408	−	0.404434i	0.863606	−	0.504168i	$-0.168201\pi$
$617$	−1.90443e10	−	5.86122e10i	−0.131408	−	0.404434i	−0.995014	+	0.0997343i	$0.968201\pi$
$618$	6.42694e10	+	1.38044e10i	0.440606	+	0.0946374i
$619$	−1.71875e11	+	5.58457e10i	−1.17071	+	0.380388i	−0.828910	−	0.559383i	$-0.811038\pi$
$619$	−1.71875e11	+	5.58457e10i	−1.17071	+	0.380388i	−0.341805	+	0.939771i	$0.611038\pi$
$620$	−1.26619e11	+	4.71134e10i	−0.856901	+	0.318843i
$621$	−9.38567e9	+	2.88861e10i	−0.0631101	+	0.194233i
$622$	1.46947e11	+	8.52589e10i	0.981748	+	0.569611i
$623$	4.35983e10	+	6.00079e10i	0.289413	+	0.398342i
$624$	−1.34804e10	+	1.19310e10i	−0.0889130	+	0.0786931i
$625$	−1.52543e11	−	3.68189e9i	−0.999709	−	0.0241297i
$626$	−2.70728e11	−	5.81494e10i	−1.76293	−	0.378659i
$627$	−5.12421e9	−	7.05286e9i	−0.0331556	−	0.0456347i
$628$	−7.41600e10	+	8.16591e10i	−0.476795	+	0.525008i
$629$	−3.99102e10	+	1.22831e11i	−0.254966	+	0.784703i
$630$	−1.73168e11	+	1.10456e11i	−1.09927	+	0.701176i
$631$	2.35172e11	−	7.64119e10i	1.48343	−	0.481996i	0.548295	−	0.836285i	$-0.315277\pi$
$631$	2.35172e11	−	7.64119e10i	1.48343	−	0.481996i	0.935136	+	0.354289i	$0.115277\pi$
$632$	−1.18205e11	+	1.60522e11i	−0.740911	+	1.00616i
$633$	−2.44536e10	−	7.52605e10i	−0.152310	−	0.468762i
$634$	−5.05137e10	−	5.63425e10i	−0.312645	−	0.348722i
$635$	−6.91405e9	+	4.20116e10i	−0.0425243	+	0.258389i
$636$	−8.47284e9	−	4.07157e10i	−0.0517846	−	0.248848i
$637$	−5.51229e10	−	4.00491e10i	−0.334791	−	0.243240i
$638$	7.72229e9	−	6.92338e9i	0.0466083	−	0.0417865i
$639$	2.45393e10	+	3.37755e10i	0.147183	+	0.202581i
$640$	8.84036e10	+	1.42591e11i	0.526926	+	0.849911i
$641$	1.55495e11	+	1.12974e11i	0.921051	+	0.669182i	0.943785	−	0.330559i	$-0.107237\pi$
$641$	1.55495e11	+	1.12974e11i	0.921051	+	0.669182i	−0.0227347	+	0.999742i	$0.507237\pi$
$642$	−7.72929e9	−	7.50810e10i	−0.0454988	−	0.441967i
$643$		−	8.41991e10i		−	0.492565i	−0.969198	−	0.246283i	$-0.920791\pi$
$643$		−	8.41991e10i		−	0.492565i	0.969198	−	0.246283i	$-0.0792091\pi$
$644$	−9.32851e9	+	8.52515e10i	−0.0542337	+	0.495631i
$645$	−8.14275e10	+	4.08725e10i	−0.470470	+	0.236152i
$646$	−2.42515e11	−	1.40707e11i	−1.39254	−	0.807952i
$647$	2.03938e11	+	6.62634e10i	1.16381	+	0.378144i	0.826328	−	0.563190i	$-0.190426\pi$
$647$	2.03938e11	+	6.62634e10i	1.16381	+	0.378144i	0.337479	+	0.941333i	$0.390426\pi$
$648$	1.26960e11	+	8.13213e8i	0.720055	+	0.00461216i
$649$	3.18151e10			0.179331
$650$	−1.51391e10	+	6.65617e10i	−0.0848101	+	0.372881i
$651$		−	7.35744e10i		−	0.409640i
$652$	6.10404e10	+	2.93326e11i	0.337775	+	1.62316i
$653$	−1.05900e11	+	3.25926e11i	−0.582428	+	1.79253i	0.0269360	+	0.999637i	$0.491425\pi$
$653$	−1.05900e11	+	3.25926e11i	−0.582428	+	1.79253i	−0.609364	+	0.792891i	$0.708575\pi$
$654$	7.80617e10	+	4.52914e10i	0.426704	+	0.247574i
$655$	−7.34774e10	−	3.79987e10i	−0.399198	−	0.206445i
$656$	−8.98097e10	+	1.52532e11i	−0.484962	+	0.823653i
$657$	1.42655e11			0.765643
$658$	2.05973e10	+	2.00079e11i	0.109877	+	1.06733i
$659$	1.29239e11	−	1.77882e11i	0.685254	−	0.943172i	−0.314728	−	0.949182i	$-0.601913\pi$
$659$	1.29239e11	−	1.77882e11i	0.685254	−	0.943172i	0.999982	+	0.00601044i	$0.00191319\pi$
$660$	−2.84620e9	−	7.64923e9i	−0.0149999	−	0.0403127i
$661$	1.22923e11	−	8.93089e10i	0.643914	−	0.467831i	−0.217279	−	0.976110i	$-0.569718\pi$
$661$	1.22923e11	−	8.93089e10i	0.643914	−	0.467831i	0.861193	+	0.508279i	$0.169718\pi$
$662$	−2.48894e10	+	2.23145e10i	−0.129593	+	0.116186i
$663$	1.65550e10	−	2.27860e10i	0.0856790	−	0.117927i
$664$	2.31789e9	−	3.61871e11i	0.0119240	−	1.86158i
$665$	−1.69994e11	+	3.28714e11i	−0.869255	+	1.68086i
$666$	−7.97576e10	−	8.89610e10i	−0.405392	−	0.452171i
$667$	−2.93907e10	+	9.54962e9i	−0.148493	+	0.0482484i
$668$	1.95102e10	−	4.33218e10i	0.0979841	−	0.217571i
$669$	−2.26837e10	−	6.98131e10i	−0.113242	−	0.348524i
$670$	8.13031e10	+	4.92713e9i	0.403467	+	0.0244509i
$671$	−3.90795e9	−	1.26977e9i	−0.0192779	−	0.00626376i
$672$	−8.95687e10	+	1.80413e10i	−0.439217	+	0.0884687i
$673$	1.93412e11	−	1.40522e11i	0.942806	−	0.684989i	−0.00628815	−	0.999980i	$-0.502002\pi$
$673$	1.93412e11	−	1.40522e11i	0.942806	−	0.684989i	0.949095	+	0.314991i	$0.102002\pi$
$674$	3.13959e11	+	6.74350e10i	1.52137	+	0.326773i
$675$	−1.00130e11	+	7.09186e10i	−0.482334	+	0.341621i
$676$	−1.62565e11	−	7.32117e10i	−0.778465	−	0.350586i
$677$	1.79053e11	−	1.30089e11i	0.852366	−	0.619280i	−0.0734311	−	0.997300i	$-0.523395\pi$
$677$	1.79053e11	−	1.30089e11i	0.852366	−	0.619280i	0.925797	+	0.378020i	$0.123395\pi$
$678$	6.78566e10	+	3.93704e10i	0.321124	+	0.186316i
$679$	−4.41037e10	−	1.43302e10i	−0.207489	−	0.0674174i
$680$	−1.83285e11	−	1.87902e11i	−0.857217	−	0.878811i
$681$	1.00539e10	+	3.09427e10i	0.0467461	+	0.143870i
$682$	−2.67900e10	−	5.75421e9i	−0.123833	−	0.0265979i
$683$	−2.79983e10	+	9.09719e9i	−0.128661	+	0.0418047i	−0.372640	−	0.927976i	$-0.621547\pi$
$683$	−2.79983e10	+	9.09719e9i	−0.128661	+	0.0418047i	0.243979	+	0.969781i	$0.421547\pi$
$684$	2.25181e11	−	1.28729e11i	1.02874	−	0.588102i
$685$	3.64931e10	+	2.39761e11i	0.165748	+	1.08897i
$686$	−1.06283e10	−	2.40094e10i	−0.0479919	−	0.108414i
$687$	3.24521e10	−	4.46665e10i	0.145686	−	0.200519i
$688$	3.78103e11	−	3.64783e10i	1.68755	−	0.162810i
$689$	−5.70741e10	+	4.14668e10i	−0.253258	+	0.184002i
$690$	−1.47106e9	+	2.42741e10i	−0.00648983	+	0.107089i
$691$	8.19248e10	−	1.12760e11i	0.359338	−	0.494587i	−0.590626	−	0.806945i	$-0.701119\pi$
$691$	8.19248e10	−	1.12760e11i	0.359338	−	0.494587i	0.949964	+	0.312359i	$0.101119\pi$
$692$	1.82339e9	−	1.66636e10i	0.00795160	−	0.0726682i
$693$	−4.16586e10			−0.180622
$694$	−3.83593e11	+	3.94894e10i	−1.65361	+	0.170232i
$695$	−1.23103e9	+	7.48008e9i	−0.00527631	+	0.0320603i
$696$	−1.91811e10	−	2.67593e10i	−0.0817403	−	0.114035i
$697$	8.55786e10	−	2.63384e11i	0.362605	−	1.11598i
$698$	−1.09339e11	+	4.84012e10i	−0.460629	+	0.203908i
$699$			1.59343e10i			0.0667460i
$700$	−2.36000e11	+	2.53647e11i	−0.982924	+	1.05642i
$701$	2.23129e11			0.924025			0.462013	−	0.886873i	$-0.347127\pi$
$701$	2.23129e11			0.924025			0.462013	+	0.886873i	$0.347127\pi$
$702$	2.22192e10	+	5.01932e10i	0.0914912	+	0.206679i
$703$	−2.04734e11	−	6.65221e10i	−0.838241	−	0.272361i
$704$	−4.35897e8	+	3.40249e10i	−0.00177457	+	0.138518i
$705$	8.58225e9	+	5.63858e10i	0.0347412	+	0.228251i
$706$	−1.75055e10	−	1.70045e11i	−0.0704621	−	0.684456i
$707$		−	3.49681e11i		−	1.39957i
$708$	1.09857e10	−	1.00397e11i	0.0437216	−	0.399563i
$709$	−3.10106e11	−	2.25305e11i	−1.22723	−	0.891634i	−0.230550	−	0.973060i	$-0.574053\pi$
$709$	−3.10106e11	−	2.25305e11i	−1.22723	−	0.891634i	−0.996679	+	0.0814261i	$0.974053\pi$
$710$	5.43635e10	+	4.47628e10i	0.213931	+	0.176151i
$711$	1.69595e11	+	2.33428e11i	0.663644	+	0.913428i
$712$	−2.65636e10	−	8.35721e10i	−0.103364	−	0.325193i
$713$	6.60524e10	+	4.79899e10i	0.255582	+	0.185691i
$714$	1.30715e11	−	5.78639e10i	0.502958	−	0.222646i
$715$	−9.84869e9	+	9.73057e9i	−0.0376838	+	0.0372318i
$716$	1.87555e11	−	1.07220e11i	0.713634	−	0.407964i
$717$	−3.68570e10	−	1.13434e11i	−0.139458	−	0.429207i
$718$	7.29037e10	−	3.39420e11i	0.274316	−	1.27714i
$719$	−1.39189e11	+	4.52251e10i	−0.520821	+	0.169225i	−0.557618	−	0.830098i	$-0.688284\pi$
$719$	−1.39189e11	+	4.52251e10i	−0.520821	+	0.169225i	0.0367971	+	0.999323i	$0.488284\pi$
$720$	2.35447e11	−	5.94242e10i	0.876118	−	0.221123i
$721$	1.74891e11	−	5.38259e11i	0.647182	−	1.99182i
$722$	9.81591e10	−	1.69181e11i	0.361228	−	0.622592i
$723$	2.67995e10	+	3.68864e10i	0.0980784	+	0.134993i
$724$	2.44320e11	+	1.10031e11i	0.889212	+	0.400461i
$725$	−1.18259e11	−	4.00086e10i	−0.428039	−	0.144811i
$726$	−1.77667e10	+	8.27170e10i	−0.0639530	+	0.297748i
$727$	−2.86354e11	−	3.94132e11i	−1.02510	−	1.41092i	−0.908568	−	0.417737i	$-0.862823\pi$
$727$	−2.86354e11	−	3.94132e11i	−1.02510	−	1.41092i	−0.116529	−	0.993187i	$-0.537177\pi$
$728$	9.02964e10	+	1.25971e11i	0.321473	+	0.448483i
$729$	4.07687e10	−	1.25473e11i	0.144350	−	0.444263i
$730$	2.32930e11	−	6.03785e10i	0.820225	−	0.212614i
$731$	−5.65223e11	+	1.83652e11i	−1.97948	+	0.643171i
$732$	−5.35634e9	+	1.18936e10i	−0.0186562	+	0.0414256i
$733$	−1.65412e11	−	5.09085e11i	−0.572995	−	1.76350i	−0.642908	−	0.765943i	$-0.722272\pi$
$733$	−1.65412e11	−	5.09085e11i	−0.572995	−	1.76350i	0.0699133	−	0.997553i	$-0.477728\pi$
$734$	1.45050e11	−	1.30044e11i	0.499727	−	0.448028i
$735$	−4.39912e10	−	8.76408e10i	−0.150736	−	0.300301i
$736$	4.22256e10	−	9.21792e10i	0.143901	−	0.314139i
$737$	1.33651e10	+	9.71033e9i	0.0453005	+	0.0329127i
$738$	1.71022e11	+	1.90757e11i	0.576537	+	0.643065i
$739$	1.14640e11	+	1.57788e11i	0.384378	+	0.529051i	0.956738	−	0.290952i	$-0.0939719\pi$
$739$	1.14640e11	+	1.57788e11i	0.384378	+	0.529051i	−0.572360	+	0.820003i	$0.693972\pi$
$740$	−1.67882e11	−	1.11500e11i	−0.559856	−	0.371831i
$741$	3.79795e10	+	2.75937e10i	0.125973	+	0.0915246i
$742$	−3.56177e11	+	3.66670e10i	−1.17503	+	0.120965i
$743$			5.75184e11i			1.88735i	0.330878	+	0.943673i	$0.392655\pi$
$743$			5.75184e11i			1.88735i	−0.330878	+	0.943673i	$0.607345\pi$
$744$	−2.74087e10	+	8.25523e10i	−0.0894534	+	0.269425i
$745$	−2.83569e11	−	2.87012e11i	−0.920522	−	0.931697i
$746$	1.74188e11	−	3.00220e11i	0.562423	−	0.969359i
$747$	−4.98140e11	−	1.61856e11i	−1.59981	−	0.519811i
$748$	−1.08464e10	−	5.21216e10i	−0.0346480	−	0.166499i
$749$	−6.49840e11			−2.06481
$750$	−6.33586e10	+	7.50828e10i	−0.200244	+	0.237299i
$751$			2.79969e11i			0.880138i	0.897964	+	0.440069i	$0.145046\pi$
$751$			2.79969e11i			0.880138i	−0.897964	+	0.440069i	$0.854954\pi$
$752$	5.14247e10	−	2.32167e11i	0.160805	−	0.725986i
$753$	−1.44373e10	+	4.44335e10i	−0.0449063	+	0.138207i
$754$	−2.80282e10	+	4.83078e10i	−0.0867182	+	0.149462i
$755$	−9.64704e10	+	9.53134e10i	−0.296897	+	0.293337i
$756$	−3.03041e10	+	2.76944e11i	−0.0927716	+	0.847821i
$757$	1.77947e10			0.0541884			0.0270942	−	0.999633i	$-0.491375\pi$
$757$	1.77947e10			0.0541884			0.0270942	+	0.999633i	$0.491375\pi$
$758$	4.00029e11	−	4.11814e10i	1.21176	−	0.124745i
$759$	−2.89915e9	+	3.99034e9i	−0.00873581	+	0.0120238i
$760$	3.13194e11	−	3.05498e11i	0.938769	−	0.915701i
$761$	1.00511e11	−	7.30252e10i	0.299690	−	0.217738i	−0.427770	−	0.903888i	$-0.640701\pi$
$761$	1.00511e11	−	7.30252e10i	0.299690	−	0.217738i	0.727460	+	0.686150i	$0.240701\pi$
$762$	1.82993e10	+	2.04109e10i	0.0542767	+	0.0605399i
$763$	4.56720e11	−	6.28621e11i	1.34757	−	1.85477i
$764$	2.87836e10	+	1.38318e11i	0.0844835	+	0.405980i
$765$	−3.39546e11	+	1.70435e11i	−0.991410	+	0.497638i
$766$	−3.37114e11	+	3.02238e11i	−0.979178	+	0.877877i
$767$	−1.62938e11	+	5.29419e10i	−0.470806	+	0.152974i
$768$	1.07219e11	+	1.31243e10i	0.308197	+	0.0377252i
$769$	−1.43340e11	−	4.41156e11i	−0.409886	−	1.26150i	−0.916746	−	0.399470i	$-0.869194\pi$
$769$	−1.43340e11	−	4.41156e11i	−0.409886	−	1.26150i	0.506860	−	0.862028i	$-0.330806\pi$
$770$	−6.80207e10	+	1.76319e10i	−0.193499	+	0.0501575i
$771$	−1.85625e11	−	6.03132e10i	−0.525313	−	0.170685i
$772$	−2.82053e11	+	3.10574e11i	−0.794075	+	0.874372i
$773$	1.64137e10	−	1.19252e10i	0.0459715	−	0.0334002i	−0.564562	−	0.825391i	$-0.690955\pi$
$773$	1.64137e10	−	1.19252e10i	0.0459715	−	0.0334002i	0.610534	+	0.791990i	$0.290955\pi$
$774$	1.15458e11	−	5.37540e11i	0.321706	−	1.49778i
$775$	9.81318e10	+	3.14897e11i	0.272021	+	0.872894i
$776$	4.41471e10	+	3.25088e10i	0.121746	+	0.0896507i
$777$	8.87934e10	−	6.45122e10i	0.243611	−	0.176994i
$778$	−3.02329e11	+	5.21077e11i	−0.825205	+	1.42227i
$779$	4.39007e11	+	1.42642e11i	1.19212	+	0.387344i
$780$	2.73053e10	+	3.44387e10i	0.0737680	+	0.0930398i
$781$	4.41363e9	+	1.35838e10i	0.0118629	+	0.0365104i
$782$	−3.33124e10	+	1.55094e11i	−0.0890798	+	0.414731i
$783$	−9.54772e10	+	3.10224e10i	−0.254011	+	0.0825332i
$784$	3.92618e10	+	4.06954e11i	0.103922	+	1.07716i
$785$	1.89277e11	+	1.91574e11i	0.498447	+	0.504498i
$786$	−4.87015e10	+	2.15588e10i	−0.127600	+	0.0564852i
$787$	−2.42304e11	+	3.33503e11i	−0.631628	+	0.869362i	−0.998134	−	0.0610540i	$-0.980554\pi$
$787$	−2.42304e11	+	3.33503e11i	−0.631628	+	0.869362i	0.366506	+	0.930416i	$0.380554\pi$
$788$	2.67273e11	+	4.67530e11i	0.693187	+	1.21256i
$789$	5.78348e10	−	4.20194e10i	0.149239	−	0.108428i
$790$	3.75715e11	+	3.09363e11i	0.964607	+	0.794256i
$791$	3.97012e11	−	5.46440e11i	1.01414	−	1.39584i
$792$	4.67420e10	+	1.55191e10i	0.118797	+	0.0394426i
$793$	2.21272e10			0.0559544
$794$	−3.92142e10	−	3.80920e11i	−0.0986646	−	0.958411i
$795$	−1.00377e11	+	1.52780e10i	−0.251285	+	0.0382470i
$796$	−2.85499e11	−	2.59280e11i	−0.711135	−	0.645829i
$797$	1.55447e11	−	4.78416e11i	0.385255	−	1.18569i	−0.551040	−	0.834479i	$-0.685769\pi$
$797$	1.55447e11	−	4.78416e11i	0.385255	−	1.18569i	0.936295	−	0.351214i	$-0.114231\pi$
$798$	9.64472e10	+	2.17875e11i	0.237836	+	0.537273i
$799$			3.72041e11i			0.912860i
$800$	3.59289e11	−	1.96681e11i	0.877171	−	0.480178i
$801$	−1.26924e11			−0.308328
$802$	−1.80207e11	+	7.97728e10i	−0.435587	+	0.192822i
$803$	4.64157e10	+	1.50814e10i	0.111636	+	0.0362726i
$804$	3.52571e10	−	3.88224e10i	0.0843768	−	0.0929090i
$805$	2.06597e11	+	3.40006e10i	0.491971	+	0.0809661i
$806$	1.46778e11	−	1.51102e10i	0.347794	−	0.0358040i
$807$		−	1.79220e11i		−	0.422564i
$808$	−1.30267e11	+	3.92351e11i	−0.305624	+	0.920511i
$809$	1.15794e11	+	8.41292e10i	0.270329	+	0.196405i	0.714688	−	0.699443i	$-0.246569\pi$
$809$	1.15794e11	+	8.41292e10i	0.270329	+	0.196405i	−0.444359	+	0.895849i	$0.646569\pi$
$810$	1.87502e10	−	3.09399e11i	0.0435577	−	0.718751i
$811$	1.47000e11	+	2.02328e11i	0.339808	+	0.467705i	0.944385	−	0.328841i	$-0.106658\pi$
$811$	1.47000e11	+	2.02328e11i	0.339808	+	0.467705i	−0.604577	+	0.796546i	$0.706658\pi$
$812$	−2.46089e11	+	1.40682e11i	−0.566068	+	0.323604i
$813$	1.24895e11	+	9.07415e10i	0.285879	+	0.207703i
$814$	−1.65458e10	−	3.73771e10i	−0.0376869	−	0.0851349i
$815$	7.23141e11	−	1.10066e11i	1.63905	−	0.249473i
$816$	−1.68222e11	+	1.62295e10i	−0.379421	+	0.0366054i
$817$	−3.06110e11	−	9.42110e11i	−0.687052	−	2.11453i
$818$	−5.56778e11	−	1.19590e11i	−1.24357	−	0.267105i
$819$	2.13351e11	−	6.93220e10i	0.474197	−	0.154076i
$820$	3.59985e11	+	2.39086e11i	0.796213	+	0.528809i
$821$	−1.00941e11	+	3.10664e11i	−0.222174	+	0.683782i	0.776392	+	0.630251i	$0.217048\pi$
$821$	−1.00941e11	+	3.10664e11i	−0.222174	+	0.683782i	−0.998566	+	0.0535318i	$0.982952\pi$
$822$	1.35061e11	+	7.83623e10i	0.295830	+	0.171640i
$823$	−9.59342e10	−	1.32042e11i	−0.209110	−	0.287815i	0.691560	−	0.722319i	$-0.256924\pi$
$823$	−9.59342e10	−	1.32042e11i	−0.209110	−	0.287815i	−0.900670	+	0.434504i	$0.856924\pi$
$824$	−3.96750e11	+	5.38789e11i	−0.860614	+	1.16872i
$825$	−1.90234e10	+	5.92830e9i	−0.0410651	+	0.0127972i
$826$	−8.50152e11	−	1.82603e11i	−1.82632	−	0.392273i
$827$	6.09143e10	+	8.38414e10i	0.130226	+	0.179241i	0.869151	−	0.494547i	$-0.164666\pi$
$827$	6.09143e10	+	8.38414e10i	0.130226	+	0.179241i	−0.738925	+	0.673788i	$0.764666\pi$
$828$	−1.08636e11	−	9.86599e10i	−0.231129	−	0.209903i
$829$	−6.56104e10	+	2.01928e11i	−0.138917	+	0.427542i	−0.996179	−	0.0873388i	$-0.972164\pi$
$829$	−6.56104e10	+	2.01928e11i	−0.138917	+	0.427542i	0.857262	+	0.514881i	$0.172164\pi$
$830$	−8.81875e11	−	5.34434e10i	−1.85821	−	0.112611i
$831$	−1.62623e11	+	5.28396e10i	−0.341019	+	0.110804i
$832$	−5.43867e10	−	1.74981e11i	−0.113501	−	0.365172i
$833$	−1.97666e11	−	6.08352e11i	−0.410536	−	1.26350i
$834$	3.25815e9	+	3.63412e9i	0.00673452	+	0.00751164i
$835$	−1.03034e11	−	5.32841e10i	−0.211952	−	0.109610i
$836$	8.68760e10	−	1.80787e10i	0.177859	−	0.0370119i
$837$	2.14575e11	+	1.55898e11i	0.437196	+	0.317642i
$838$	3.61621e11	−	3.24209e11i	0.733292	−	0.657430i
$839$	−5.72264e11	−	7.87653e11i	−1.15491	−	1.58960i	−0.728462	−	0.685086i	$-0.759765\pi$
$839$	−5.72264e11	−	7.87653e11i	−1.15491	−	1.58960i	−0.426448	−	0.904512i	$-0.640235\pi$
$840$	3.21521e10	+	2.20736e11i	0.0645792	+	0.443360i
$841$	3.22071e11	+	2.33999e11i	0.643826	+	0.467767i
$842$	6.65962e9	+	6.46903e10i	0.0132495	+	0.128704i
$843$		−	1.74345e11i		−	0.345223i
$844$	8.00707e11	+	8.76162e10i	1.57799	+	0.172669i
$845$	−1.99948e11	+	3.86636e11i	−0.392184	+	0.758359i
$846$	−2.97698e11	−	1.72725e11i	−0.581159	−	0.337189i
$847$	6.92759e11	+	2.25091e11i	1.34601	+	0.437345i
$848$	4.13299e11	+	9.15454e10i	0.799247	+	0.177033i
$849$	−1.75958e11			−0.338670
$850$	−4.82280e11	+	4.22001e11i	−0.923896	+	0.808421i
$851$			1.21794e11i			0.232225i
$852$	4.43893e10	−	9.23730e9i	0.0842403	−	0.0175302i
$853$	6.37165e10	−	1.96099e11i	0.120353	−	0.370408i	−0.872673	−	0.488305i	$-0.837615\pi$
$853$	6.37165e10	−	1.96099e11i	0.120353	−	0.370408i	0.993026	+	0.117897i	$0.0376154\pi$
$854$	9.71391e10	+	5.63602e10i	0.182626	+	0.105960i
$855$	−2.84080e11	−	5.65954e11i	−0.531590	−	1.05905i
$856$	7.29137e11	+	2.42085e11i	1.35804	+	0.450893i
$857$	5.70275e11			1.05721			0.528605	−	0.848868i	$-0.322715\pi$
$857$	5.70275e11			1.05721			0.528605	+	0.848868i	$0.322715\pi$
$858$	9.12835e8	+	8.86712e9i	0.00168439	+	0.0163619i
$859$	−2.72726e11	+	3.75375e11i	−0.500903	+	0.689434i	−0.982352	−	0.187040i	$-0.940111\pi$
$859$	−2.72726e11	+	3.75375e11i	−0.500903	+	0.689434i	0.481449	+	0.876474i	$0.340111\pi$
$860$	−3.89915e10	−	9.26570e11i	−0.0712814	−	1.69389i
$861$	−1.90398e11	+	1.38332e11i	−0.346457	+	0.251716i
$862$	7.11778e11	−	6.38142e11i	1.28919	−	1.15581i
$863$	−4.95473e11	+	6.81960e11i	−0.893258	+	1.22946i	0.0793116	+	0.996850i	$0.474728\pi$
$863$	−4.95473e11	+	6.81960e11i	−0.893258	+	1.22946i	−0.972569	+	0.232614i	$0.925272\pi$
$864$	1.37172e11	−	2.99449e11i	0.246156	−	0.537363i
$865$	−4.03822e10	−	6.64589e9i	−0.0721316	−	0.0118710i
$866$	−1.94636e11	−	2.17095e11i	−0.346059	−	0.385992i
$867$	8.46172e10	−	2.74938e10i	0.149755	−	0.0486585i
$868$	6.82848e11	+	3.07524e11i	1.20294	+	0.541751i
$869$	3.05034e10	+	9.38797e10i	0.0534895	+	0.164624i
$870$	−6.77679e10	+	4.32261e10i	−0.118290	+	0.0754518i
$871$	−8.46069e10	−	2.74904e10i	−0.147005	−	0.0477649i
$872$	−7.46632e11	+	5.35187e11i	−1.29134	+	0.925635i
$873$	6.41976e10	−	4.66423e10i	0.110525	−	0.0803014i
$874$	−2.58509e11	−	5.55249e10i	−0.443027	−	0.0951574i
$875$	5.87179e11	+	6.08828e11i	1.00170	+	1.03863i
$876$	6.36184e10	−	1.41263e11i	0.108036	−	0.239890i
$877$	−6.28734e11	+	4.56802e11i	−1.06284	+	0.772199i	−0.974612	−	0.223901i	$-0.928121\pi$
$877$	−6.28734e11	+	4.56802e11i	−1.06284	+	0.772199i	−0.0882293	+	0.996100i	$0.528121\pi$
$878$	1.86534e11	+	1.08227e11i	0.313891	+	0.182120i
$879$	−1.86844e11	−	6.07092e10i	−0.312985	−	0.101695i
$880$	8.28894e10	+	5.55635e9i	0.138219	+	0.00926528i
$881$	1.13216e11	+	3.48444e11i	0.187934	+	0.578401i	0.999987	−	0.00518288i	$-0.00164977\pi$
$881$	1.13216e11	+	3.48444e11i	0.187934	+	0.578401i	−0.812053	+	0.583584i	$0.801650\pi$
$882$	5.78557e11	+	1.24268e11i	0.956031	+	0.205345i
$883$	−9.49886e10	+	3.08637e10i	−0.156253	+	0.0507697i	−0.386099	−	0.922457i	$-0.626178\pi$
$883$	−9.49886e10	+	3.08637e10i	−0.156253	+	0.0507697i	0.229846	+	0.973227i	$0.426178\pi$
$884$	1.42282e11	+	2.48888e11i	0.232992	+	0.407563i
$885$	−2.43299e11	−	4.00409e10i	−0.396613	−	0.0652725i
$886$	4.04801e11	+	9.14447e11i	0.656911	+	1.48396i
$887$	−3.41841e11	+	4.70504e11i	−0.552242	+	0.760096i	−0.990314	−	0.138844i	$-0.955661\pi$
$887$	−3.41841e11	+	4.70504e11i	−0.552242	+	0.760096i	0.438072	+	0.898940i	$0.355661\pi$
$888$	−1.23661e11	+	3.93061e10i	−0.198876	+	0.0632132i
$889$	1.90941e11	−	1.38727e11i	0.305698	−	0.222103i
$890$	−2.07243e11	+	5.37202e10i	−0.330309	+	0.0856205i
$891$	3.69526e10	−	5.08610e10i	0.0586320	−	0.0807000i
$892$	7.42751e11	+	8.12745e10i	1.17323	+	0.128379i
$893$	−6.20116e11			−0.975141
$894$	−2.58407e11	+	2.66019e10i	−0.404533	+	0.0416450i
$895$	−2.36613e11	−	4.71387e11i	−0.368762	−	0.734659i
$896$	2.06934e11	−	9.06700e11i	0.321071	−	1.40680i
$897$	8.20764e9	−	2.52605e10i	0.0126779	−	0.0390187i
$898$	−4.61789e11	+	2.04421e11i	−0.710130	+	0.314355i
$899$			2.69862e11i			0.413145i
$900$	−1.13770e11	−	5.81827e11i	−0.173404	−	0.886797i
$901$	−6.62302e11			−1.00498
$902$	3.54788e10	+	8.01468e10i	0.0535973	+	0.121077i
$903$	4.80332e11	+	1.56069e11i	0.722421	+	0.234729i
$904$	−6.49023e11	+	4.65221e11i	−0.971822	+	0.696603i
$905$	3.00504e11	−	5.81080e11i	0.447978	−	0.866246i
$906$	8.94145e9	+	8.68557e10i	0.0132707	+	0.128910i
$907$		−	1.44384e11i		−	0.213349i	−0.994294	−	0.106674i	$-0.965980\pi$
$907$		−	1.44384e11i		−	0.213349i	0.994294	−	0.106674i	$-0.0340202\pi$
$908$	−3.29204e11	−	3.60226e10i	−0.484308	−	0.0529947i
$909$	4.84085e11	+	3.51708e11i	0.709033	+	0.515142i
$910$	3.19022e11	−	2.03490e11i	0.465217	−	0.296741i
$911$	−6.87415e11	−	9.46146e11i	−0.998035	−	1.37368i	−0.926524	−	0.376237i	$-0.877218\pi$
$911$	−6.87415e11	−	9.46146e11i	−0.998035	−	1.37368i	−0.0715110	−	0.997440i	$-0.522782\pi$
$912$	−2.70513e10	−	2.80391e11i	−0.0391029	−	0.405307i
$913$	−1.44968e11	−	1.05326e11i	−0.208636	−	0.151583i
$914$	8.51633e11	−	3.76995e11i	1.22030	−	0.540195i
$915$	2.82871e10	+	1.46286e10i	0.0403557	+	0.0208699i
$916$	2.78910e11	+	4.87886e11i	0.396171	+	0.693005i
$917$	1.41700e11	+	4.36108e11i	0.200398	+	0.616760i
$918$	−1.08217e11	+	5.03829e11i	−0.152379	+	0.709435i
$919$	−7.09728e11	+	2.30605e11i	−0.995015	+	0.323300i	−0.760872	−	0.648902i	$-0.775229\pi$
$919$	−7.09728e11	+	2.30605e11i	−0.995015	+	0.323300i	−0.234143	+	0.972202i	$0.575229\pi$
$920$	−2.19141e11	−	1.15113e11i	−0.305894	−	0.160684i
$921$	6.86043e10	−	2.11142e11i	0.0953483	−	0.293452i
$922$	−2.86452e10	+	4.93712e10i	−0.0396395	+	0.0683204i
$923$	−4.52081e10	−	6.22237e10i	−0.0622888	−	0.0857332i
$924$	−1.85780e10	+	4.12519e10i	−0.0254866	+	0.0565922i
$925$	−2.93989e11	+	3.94541e11i	−0.401573	+	0.538922i
$926$	−1.63461e11	+	7.61031e11i	−0.222316	+	1.03504i
$927$	5.69241e11	+	7.83493e11i	0.770863	+	1.06100i
$928$	3.28527e11	−	6.61731e10i	0.442975	−	0.0892256i
$929$	−1.80536e11	+	5.55632e11i	−0.242382	+	0.745975i	0.753674	+	0.657249i	$0.228280\pi$
$929$	−1.80536e11	+	5.55632e11i	−0.242382	+	0.745975i	−0.996056	+	0.0887268i	$0.971720\pi$
$930$	1.97629e11	+	7.77206e10i	0.264191	+	0.103897i
$931$	1.01400e12	−	3.29468e11i	1.34970	−	0.438545i
$932$	−1.47887e11	−	6.66018e10i	−0.196005	−	0.0882719i
$933$	−8.25226e10	−	2.53978e11i	−0.108905	−	0.335174i
$934$	5.28480e10	−	4.73807e10i	0.0694451	−	0.0622607i
$935$	−1.28496e11	+	1.95579e10i	−0.168129	+	0.0255903i
$936$	−2.65210e11	−	1.69875e9i	−0.345531	−	0.00221322i
$937$	1.09534e12	+	7.95809e11i	1.42099	+	1.03241i	0.991608	+	0.129281i	$0.0412670\pi$
$937$	1.09534e12	+	7.95809e11i	1.42099	+	1.03241i	0.429377	+	0.903125i	$0.358733\pi$
$938$	−3.01406e11	−	3.36186e11i	−0.389350	−	0.434278i
$939$	2.55840e11	+	3.52133e11i	0.329083	+	0.452944i
$940$	−5.59191e11	−	1.56027e11i	−0.716224	−	0.199843i
$941$	−6.51321e10	−	4.73212e10i	−0.0830685	−	0.0603528i	0.545476	−	0.838127i	$-0.316349\pi$
$941$	−6.51321e10	−	4.73212e10i	−0.0830685	−	0.0603528i	−0.628544	+	0.777774i	$0.716349\pi$
$942$	1.72481e11	−	1.77563e10i	0.219047	−	0.0225501i
$943$		−	2.61161e11i		−	0.330264i
$944$	8.85867e11	+	5.21593e11i	1.11553	+	0.656817i
$945$	6.71140e11	+	1.10453e11i	0.841561	+	0.138500i
$946$	9.43946e10	−	1.62693e11i	0.117864	−	0.203144i
$947$	6.39643e11	+	2.07833e11i	0.795312	+	0.258413i	0.678365	−	0.734725i	$-0.262689\pi$
$947$	6.39643e11	+	2.07833e11i	0.795312	+	0.258413i	0.116948	+	0.993138i	$0.462689\pi$
$948$	3.06782e11	−	6.38405e10i	0.379836	−	0.0790430i
$949$	−2.62810e11			−0.324024
$950$	−7.03389e11	−	8.03861e11i	−0.863577	−	0.986930i
$951$			1.18947e11i			0.145422i
$952$	−9.31989e9	+	1.45503e12i	−0.0113465	+	1.77143i
$953$	1.02687e11	−	3.16039e11i	0.124493	−	0.383150i	−0.869315	−	0.494258i	$-0.835440\pi$
$953$	1.02687e11	−	3.16039e11i	0.124493	−	0.383150i	0.993808	+	0.111108i	$0.0354399\pi$
$954$	3.07482e11	−	5.29958e11i	0.371215	−	0.639805i
$955$	3.40997e11	−	5.19018e10i	0.409956	−	0.0623978i
$956$	1.20684e12	+	1.32057e11i	1.44484	+	0.158099i
$957$	−1.63028e10			−0.0194363
$958$	−1.44774e12	+	1.49039e11i	−1.71881	+	0.176945i
$959$	7.90207e11	−	1.08763e12i	0.934257	−	1.28589i
$960$	4.61554e10	−	2.59649e11i	0.0543423	−	0.305705i
$961$	−1.13202e11	+	8.22460e10i	−0.132727	+	0.0964320i
$962$	1.46935e11	+	1.63891e11i	0.171564	+	0.191361i
$963$	6.53608e11	−	8.99615e11i	0.759998	−	1.04605i
$964$	−4.54360e11	+	9.45512e10i	−0.526129	+	0.109486i
$965$	7.19876e11	+	7.28615e11i	0.830135	+	0.840212i
$966$	1.00373e11	−	8.99887e10i	0.115268	−	0.103343i
$967$	1.98103e11	−	6.43675e10i	0.226561	−	0.0736140i	−0.193537	−	0.981093i	$-0.561996\pi$
$967$	1.98103e11	−	6.43675e10i	0.226561	−	0.0736140i	0.420097	+	0.907479i	$0.361996\pi$
$968$	−6.93440e11	−	5.10632e11i	−0.789783	−	0.581576i
$969$	1.36191e11	+	4.19153e11i	0.154473	+	0.475420i
$970$	8.50815e10	−	1.03330e11i	0.0961055	−	0.116718i
$971$	−5.06931e11	−	1.64712e11i	−0.570259	−	0.185288i	0.00967299	−	0.999953i	$-0.496921\pi$
$971$	−5.06931e11	−	1.64712e11i	−0.570259	−	0.185288i	−0.579932	+	0.814665i	$0.696921\pi$
$972$	−5.38303e11	−	4.88868e11i	−0.603062	−	0.547680i
$973$	3.39967e10	−	2.47001e10i	0.0379302	−	0.0275579i
$974$	6.86312e10	−	3.19528e11i	0.0762581	−	0.355037i
$975$	8.75621e10	−	6.20173e10i	0.0968941	−	0.0686269i
$976$	−8.79967e10	−	9.94249e10i	−0.0969767	−	0.109571i
$977$	−7.52045e11	+	5.46393e11i	−0.825402	+	0.599690i	−0.918255	−	0.395990i	$-0.870401\pi$
$977$	−7.52045e11	+	5.46393e11i	−0.825402	+	0.599690i	0.0928527	+	0.995680i	$0.470401\pi$
$978$	2.36347e11	−	4.07355e11i	0.258342	−	0.445264i
$979$	−4.12971e10	−	1.34183e10i	−0.0449562	−	0.0146071i
$980$	9.97272e11	−	4.19667e10i	1.08121	−	0.0454989i
$981$	4.10872e11	+	1.26453e12i	0.443639	+	1.36538i
$982$	−2.10729e11	+	9.81099e11i	−0.226610	+	1.05503i
$983$	−9.30659e11	+	3.02389e11i	−0.996728	+	0.323856i	−0.761557	−	0.648098i	$-0.775565\pi$
$983$	−9.30659e11	+	3.02389e11i	−0.996728	+	0.323856i	−0.235170	+	0.971954i	$0.575565\pi$
$984$	2.65164e11	−	8.42831e10i	0.282836	−	0.0899001i
$985$	1.17506e12	−	5.89819e11i	1.24829	−	0.626576i
$986$	−4.79446e11	+	2.12238e11i	−0.507262	+	0.224551i
$987$	1.85837e11	−	2.55782e11i	0.195823	−	0.269527i
$988$	−4.14845e11	+	2.37155e11i	−0.435369	+	0.248888i
$989$	−4.53416e11	+	3.29426e11i	−0.473927	+	0.344328i
$990$	4.40062e10	−	1.11899e11i	0.0458113	−	0.116490i
$991$	−2.23072e11	+	3.07032e11i	−0.231286	+	0.318338i	−0.908848	−	0.417128i	$-0.863037\pi$
$991$	−2.23072e11	+	3.07032e11i	−0.231286	+	0.318338i	0.677561	+	0.735466i	$0.263037\pi$
$992$	−6.51611e11	−	5.99431e11i	−0.672886	−	0.619003i
$993$	5.25448e10			0.0540422
$994$	−3.99753e10	−	3.88313e11i	−0.0409493	−	0.397774i
$995$	−6.69788e11	+	6.61755e11i	−0.683353	+	0.675157i
$996$	−3.82426e11	+	4.21097e11i	−0.388606	+	0.427902i
$997$	−1.03652e11	+	3.19008e11i	−0.104905	+	0.322865i	−0.989708	−	0.143101i	$-0.954293\pi$
$997$	−1.03652e11	+	3.19008e11i	−0.104905	+	0.322865i	0.884803	+	0.465965i	$0.154293\pi$
$998$	−2.56705e11	−	5.79897e11i	−0.258769	−	0.584560i
$999$			3.95655e11i			0.397242i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	100.9.j.b.11.102	yes	464
4.3	odd	2	inner	100.9.j.b.11.85	✓	464
25.16	even	5	inner	100.9.j.b.91.85	yes	464
100.91	odd	10	inner	100.9.j.b.91.102	yes	464

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
100.9.j.b.11.85	✓	464	4.3	odd	2	inner
100.9.j.b.11.102	yes	464	1.1	even	1	trivial
100.9.j.b.91.85	yes	464	25.16	even	5	inner
100.9.j.b.91.102	yes	464	100.91	odd	10	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:	\( N \)	\(=\)	\( 100 = 2^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 9 \)
Character orbit:	\([\chi]\)	\(=\)	100.j (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(14.6306 - 6.47656i) q^{2} +(-23.9193 - 7.77186i) q^{3} +(172.108 - 189.512i) q^{4} +(-439.267 - 444.600i) q^{5} +(-400.289 + 41.2081i) q^{6} +3464.57i q^{7} +(1290.66 - 3887.34i) q^{8} +(-4796.23 - 3484.66i) q^{9} +(-9306.22 - 3659.81i) q^{10} +(-1192.15 - 1640.85i) q^{11} +(-5589.57 + 3195.39i) q^{12} +(8835.97 + 6419.71i) q^{13} +(22438.5 + 50688.7i) q^{14} +(7051.61 + 14048.5i) q^{15} +(-6293.50 - 65233.1i) q^{16} +(31685.0 + 97516.3i) q^{17} +(-92740.3 - 19919.6i) q^{18} +(-162540. + 52812.3i) q^{19} +(-159859. + 6727.09i) q^{20} +(26926.2 - 82870.2i) q^{21} +(-28069.0 - 16285.6i) q^{22} +(56834.9 + 78226.6i) q^{23} +(-61083.5 + 82951.7i) q^{24} +(-4713.17 + 390597. i) q^{25} +(170853. + 36697.4i) q^{26} +(184631. + 254123. i) q^{27} +(656578. + 596282. i) q^{28} +(-98761.9 + 303958. i) q^{29} +(194155. + 159867. i) q^{30} +(803046. - 260926. i) q^{31} +(-514564. - 913639. i) q^{32} +(15762.9 + 48513.4i) q^{33} +(1.09514e6 + 1.22151e6i) q^{34} +(1.54035e6 - 1.52187e6i) q^{35} +(-1.48586e6 + 309203. i) q^{36} +(1.01903e6 + 740371. i) q^{37} +(-2.03601e6 + 1.82537e6i) q^{38} +(-161457. - 222227. i) q^{39} +(-2.29526e6 + 1.13376e6i) q^{40} +(-2.18509e6 - 1.58756e6i) q^{41} +(-142769. - 1.38683e6i) q^{42} +5.79619e6i q^{43} +(-516140. - 56477.9i) q^{44} +(557546. + 3.66310e6i) q^{45} +(1.33817e6 + 776406. i) q^{46} +(3.45085e6 + 1.12125e6i) q^{47} +(-356446. + 1.60924e6i) q^{48} -6.23846e6 q^{49} +(2.46077e6 + 5.74518e6i) q^{50} -2.57877e6i q^{51} +(2.73735e6 - 569637. i) q^{52} +(-1.99603e6 + 6.14316e6i) q^{53} +(4.34711e6 + 2.52219e6i) q^{54} +(-205851. + 1.25080e6i) q^{55} +(1.34680e7 + 4.47158e6i) q^{56} +4.29829e6 q^{57} +(523658. + 5.08672e6i) q^{58} +(-9.22018e6 + 1.26905e7i) q^{59} +(3.87599e6 + 1.08149e6i) q^{60} +(1.63904e6 - 1.19083e6i) q^{61} +(1.00591e7 - 9.01848e6i) q^{62} +(1.20729e7 - 1.66169e7i) q^{63} +(-1.34456e7 - 1.00345e7i) q^{64} +(-1.02715e6 - 6.74844e6i) q^{65} +(544821. + 607689. i) q^{66} +(-7.74657e6 + 2.51701e6i) q^{67} +(2.39337e7 + 1.07787e7i) q^{68} +(-751487. - 2.31284e6i) q^{69} +(1.26797e7 - 3.22421e7i) q^{70} +(-6.69742e6 - 2.17612e6i) q^{71} +(-1.97364e7 + 1.41471e7i) q^{72} +(-1.94672e7 + 1.41437e7i) q^{73} +(1.97041e7 + 4.23223e6i) q^{74} +(3.14840e6 - 9.30617e6i) q^{75} +(-1.79658e7 + 3.98926e7i) q^{76} +(5.68486e6 - 4.13029e6i) q^{77} +(-3.80148e6 - 2.20562e6i) q^{78} +(-4.62870e7 - 1.50396e7i) q^{79} +(-2.62381e7 + 3.14529e7i) q^{80} +(9.57848e6 + 2.94795e7i) q^{81} +(-4.22511e7 - 9.07508e6i) q^{82} +(8.40252e7 - 2.73014e7i) q^{83} +(-1.10707e7 - 1.93655e7i) q^{84} +(2.94376e7 - 5.69229e7i) q^{85} +(3.75394e7 + 8.48017e7i) q^{86} +(4.72463e6 - 6.50290e6i) q^{87} +(-7.91722e6 + 2.51651e6i) q^{88} +(1.73204e7 - 1.25840e7i) q^{89} +(3.18815e7 + 4.99824e7i) q^{90} +(-2.22415e7 + 3.06129e7i) q^{91} +(2.46066e7 + 2.69254e6i) q^{92} -2.12362e7 q^{93} +(5.77499e7 - 5.94512e6i) q^{94} +(9.48787e7 + 4.90664e7i) q^{95} +(5.20735e6 + 2.58527e7i) q^{96} +(-4.13620e6 + 1.27299e7i) q^{97} +(-9.12724e7 + 4.04038e7i) q^{98} +1.20242e7i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 464 q + 29 q^{2} + 509 q^{4} - 1230 q^{5} - 515 q^{6} + 21284 q^{8} + 262434 q^{9} + 3445 q^{10} - 35805 q^{12} - 29522 q^{13} - 33705 q^{14} - 63391 q^{16} - 319922 q^{17} - 569696 q^{18} + 1244935 q^{20}+ \cdots + 209675864 q^{98}+O(q^{100}) \) 464 * q + 29 * q^2 + 509 * q^4 - 1230 * q^5 - 515 * q^6 + 21284 * q^8 + 262434 * q^9 + 3445 * q^10 - 35805 * q^12 - 29522 * q^13 - 33705 * q^14 - 63391 * q^16 - 319922 * q^17 - 569696 * q^18 + 1244935 * q^20 + 39360 * q^21 + 140220 * q^22 + 989900 * q^24 - 431710 * q^25 - 855842 * q^26 - 2358605 * q^28 - 2884562 * q^29 + 7229675 * q^30 - 7078666 * q^32 - 1866570 * q^33 + 1448973 * q^34 + 777029 * q^36 - 7317972 * q^37 + 4012465 * q^38 - 4154830 * q^40 + 1687438 * q^41 - 21337315 * q^42 + 510580 * q^44 + 2596050 * q^45 + 1721385 * q^46 + 41153690 * q^48 - 396068336 * q^49 - 60015715 * q^50 - 8419912 * q^52 + 26717388 * q^53 - 13729145 * q^54 + 7138890 * q^56 - 19745300 * q^57 - 41444182 * q^58 + 96768050 * q^60 + 26136558 * q^61 - 87505940 * q^62 + 19616924 * q^64 + 22030140 * q^65 - 69968200 * q^66 + 276958 * q^68 - 73697610 * q^69 + 39639840 * q^70 - 145994351 * q^72 - 39004722 * q^73 + 4922908 * q^74 - 19181080 * q^76 + 111211200 * q^77 - 197089615 * q^78 - 395680960 * q^80 - 539852286 * q^81 + 186999258 * q^82 - 377672700 * q^84 - 283475540 * q^85 - 340843785 * q^86 - 29231040 * q^88 - 206040612 * q^89 + 351285695 * q^90 + 43044280 * q^92 + 241823660 * q^93 - 442380075 * q^94 - 474931550 * q^96 + 2388718 * q^97 + 209675864 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

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