LMFDB - Embedded newform 71.10.g.a.2.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [71,10,Mod(2,71)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("71.2"); S:= CuspForms(chi, 10); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(71, base_ring=CyclotomicField(70)) chi = DirichletCharacter(H, H._module([6])) N = Newforms(chi, 10, names="a")

Level:	$ N $	$=$	$ 71 $
Weight:	$ k $	$=$	$ 10 $
Character orbit:	$[\chi]$	$=$	71.g (of order $35$, degree $24$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$36.5675443676$
Analytic rank:	$0$
Dimension:	$1272$
Relative dimension:	$53$ over $\Q(\zeta_{35})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{35}]$

Embedding invariants

Embedding label			2.3
Character	$\chi$	$=$	71.2
Dual form			71.10.g.a.36.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.94237 + 43.2502i) q^{2} +(-65.2666 - 57.0217i) q^{3} +(-1356.87 - 122.121i) q^{4} +(57.5622 + 177.158i) q^{5} +(2592.98 - 2712.04i) q^{6} +(10262.9 + 2832.38i) q^{7} +(4941.81 - 36481.9i) q^{8} +(-1633.86 - 12061.6i) q^{9} +(-7773.94 + 2145.47i) q^{10} +(-17350.6 + 32242.9i) q^{11} +(81594.8 + 85341.5i) q^{12} +(50178.1 + 93246.6i) q^{13} +(-142435. + 438371. i) q^{14} +(6344.98 - 14844.8i) q^{15} +(881936. + 160048. i) q^{16} +(-351550. - 255416. i) q^{17} +(524842. - 47236.6i) q^{18} +(426576. + 998025. i) q^{19} +(-56469.7 - 247410. i) q^{20} +(-508317. - 770068. i) q^{21} +(-1.36081e6 - 813046. i) q^{22} +(484403. + 607423. i) q^{23} +(-2.40280e6 + 2.09926e6i) q^{24} +(1.55204e6 - 1.12762e6i) q^{25} +(-4.13040e6 + 1.98910e6i) q^{26} +(-1.52090e6 + 2.30406e6i) q^{27} +(-1.35795e7 - 5.09648e6i) q^{28} +(3.16478e6 - 1.89087e6i) q^{29} +(629717. + 303256. i) q^{30} +(-3.81282e6 + 691925. i) q^{31} +(-4.44078e6 + 1.94563e7i) q^{32} +(2.97096e6 - 1.11502e6i) q^{33} +(1.17296e7 - 1.47085e7i) q^{34} +(88975.4 + 1.98119e6i) q^{35} +(743962. + 1.65656e7i) q^{36} +(6.04608e6 - 7.58154e6i) q^{37} +(-4.39934e7 + 1.65110e7i) q^{38} +(2.04213e6 - 8.94714e6i) q^{39} +(6.74753e6 - 1.22450e6i) q^{40} +(9.06735e6 + 4.36661e6i) q^{41} +(3.42929e7 - 2.04891e7i) q^{42} +(-1.77728e7 - 6.67025e6i) q^{43} +(2.74801e7 - 4.16305e7i) q^{44} +(2.04277e6 - 983745. i) q^{45} +(-2.72121e7 + 1.97707e7i) q^{46} +(-4.52970e7 + 3.95748e7i) q^{47} +(-4.84348e7 - 6.07353e7i) q^{48} +(6.26630e7 + 3.74394e7i) q^{49} +(4.57553e7 + 6.93163e7i) q^{50} +(8.38022e6 + 3.67161e7i) q^{51} +(-5.66979e7 - 1.32651e8i) q^{52} +(3.36685e6 - 303022. i) q^{53} +(-9.66971e7 - 7.02545e7i) q^{54} +(-6.71083e6 - 1.21784e6i) q^{55} +(1.54048e8 - 3.60413e8i) q^{56} +(2.90679e7 - 8.94619e7i) q^{57} +(7.56334e7 + 1.40550e8i) q^{58} +(-7.97113e7 - 8.33715e7i) q^{59} +(-1.04222e7 + 1.93676e7i) q^{60} +(-1.10913e8 + 3.06099e7i) q^{61} +(-2.25200e7 - 1.66249e8i) q^{62} +(1.73950e7 - 1.28415e8i) q^{63} +(-3.90476e8 - 1.07765e8i) q^{64} +(-1.36310e7 + 1.42569e7i) q^{65} +(4.24542e7 + 1.30661e8i) q^{66} +(-1.78263e7 - 1.60439e6i) q^{67} +(4.45816e8 + 3.89498e8i) q^{68} +(3.02092e6 - 6.72660e7i) q^{69} -8.58598e7 q^{70} +(3.96172e7 + 2.10426e8i) q^{71} -4.48105e8 q^{72} +(-2.09083e7 + 4.65560e8i) q^{73} +(3.16160e8 + 2.76220e8i) q^{74} +(-1.65595e8 - 1.49039e7i) q^{75} +(-4.56929e8 - 1.40628e9i) q^{76} +(-2.69392e8 + 2.81762e8i) q^{77} +(3.82999e8 + 1.05701e8i) q^{78} +(-1.81289e7 + 1.33833e8i) q^{79} +(2.24124e7 + 1.65455e8i) q^{80} +(-297995. + 82241.4i) q^{81} +(-2.06469e8 + 3.83684e8i) q^{82} +(7.39581e7 + 7.73541e7i) q^{83} +(5.95679e8 + 1.10696e9i) q^{84} +(2.50130e7 - 7.69822e7i) q^{85} +(3.23011e8 - 7.55722e8i) q^{86} +(-3.14375e8 - 5.70507e7i) q^{87} +(1.09054e9 + 7.92323e8i) q^{88} +(-5.41473e8 + 4.87334e7i) q^{89} +(3.85794e7 + 9.02609e7i) q^{90} +(2.50863e8 + 1.09910e9i) q^{91} +(-5.83094e8 - 8.83349e8i) q^{92} +(2.88305e8 + 1.72254e8i) q^{93} +(-1.62364e9 - 2.03597e9i) q^{94} +(-1.52254e8 + 1.33020e8i) q^{95} +(1.39927e9 - 1.01663e9i) q^{96} +(1.01168e8 - 4.87201e7i) q^{97} +(-1.74098e9 + 2.63747e9i) q^{98} +(4.17250e8 + 1.56597e8i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 1272 q - 76 q^{2} - 395 q^{3} + 13542 q^{4} - 1610 q^{5} - 4334 q^{6} - 4827 q^{7} - 18627 q^{8} + 286810 q^{9} - 53448 q^{10} - 170685 q^{11} + 138323 q^{12} - 93291 q^{13} + 985964 q^{14} - 966194 q^{15}+ \cdots - 4074592265 q^{99}+O(q^{100}) $ 1272 * q - 76 * q^2 - 395 * q^3 + 13542 * q^4 - 1610 * q^5 - 4334 * q^6 - 4827 * q^7 - 18627 * q^8 + 286810 * q^9 - 53448 * q^10 - 170685 * q^11 + 138323 * q^12 - 93291 * q^13 + 985964 * q^14 - 966194 * q^15 + 4755334 * q^16 + 2558412 * q^17 - 2619769 * q^18 - 172269 * q^19 + 738120 * q^20 + 1797929 * q^21 + 3015622 * q^22 + 6635088 * q^23 + 4803145 * q^24 - 115100016 * q^25 + 19254293 * q^26 - 17686931 * q^27 + 15761532 * q^28 - 10052927 * q^29 + 62637435 * q^30 - 23748991 * q^31 + 10388192 * q^32 - 15097203 * q^33 + 33217854 * q^34 - 24823174 * q^35 + 27856812 * q^36 - 27156308 * q^37 - 43400577 * q^38 + 251072838 * q^39 - 129856160 * q^40 + 62087988 * q^41 - 91873950 * q^42 - 167299067 * q^43 + 60914131 * q^44 - 31536191 * q^45 - 50201490 * q^46 - 23317743 * q^47 + 10641329 * q^48 + 338745866 * q^49 + 303770229 * q^50 + 448039613 * q^51 - 979580293 * q^52 + 12085215 * q^53 - 182583505 * q^54 - 243892552 * q^55 + 30440435 * q^56 + 714581966 * q^57 - 244549660 * q^58 - 859013315 * q^59 - 1894499000 * q^60 - 876373921 * q^61 + 186553636 * q^62 - 196611021 * q^63 + 5528242635 * q^64 + 867018244 * q^65 + 2727701199 * q^66 - 286780089 * q^67 - 1689988351 * q^68 - 3073308182 * q^69 - 41489396 * q^70 - 2538053548 * q^71 - 6821388000 * q^72 + 128479023 * q^73 + 3282772334 * q^74 + 3407782757 * q^75 + 7133788844 * q^76 + 1087098389 * q^77 + 2715049934 * q^78 + 144243625 * q^79 - 7443877603 * q^80 - 4083269278 * q^81 - 10375744380 * q^82 + 1543773955 * q^83 - 4117054288 * q^84 + 7843382686 * q^85 + 3545751759 * q^86 + 5261609811 * q^87 - 818728797 * q^88 - 1369081479 * q^89 + 10041256259 * q^90 - 7299574322 * q^91 + 602797624 * q^92 - 2146129677 * q^93 - 683447510 * q^94 - 7007204038 * q^95 + 6601829126 * q^96 - 10081488030 * q^97 - 5942379880 * q^98 - 4074592265 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/71\mathbb{Z}\right)^\times$.

$n$	$7$
$\chi(n)$	$e\left(\frac{3}{35}\right)$

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 $

$2$	−1.94237	+	43.2502i	−0.0858414	+	1.91141i	0.247970	+	0.968768i	$0.420237\pi$
$2$	−1.94237	+	43.2502i	−0.0858414	+	1.91141i	−0.333811	+	0.942640i	$0.608335\pi$
$3$	−65.2666	−	57.0217i	−0.465206	−	0.406439i	0.393165	−	0.919468i	$-0.371380\pi$
$3$	−65.2666	−	57.0217i	−0.465206	−	0.406439i	−0.858371	+	0.513030i	$0.828523\pi$
$4$	−1356.87	−	122.121i	−2.65014	−	0.238517i
$5$	57.5622	+	177.158i	0.0411881	+	0.126764i	0.969536	−	0.244948i	$-0.0787709\pi$
$5$	57.5622	+	177.158i	0.0411881	+	0.126764i	−0.928348	+	0.371712i	$0.878771\pi$
$6$	2592.98	−	2712.04i	0.816804	−	0.854310i
$7$	10262.9	+	2832.38i	1.61558	+	0.445872i	0.952963	−	0.303087i	$-0.0980171\pi$
$7$	10262.9	+	2832.38i	1.61558	+	0.445872i	0.662617	+	0.748958i	$0.269446\pi$
$8$	4941.81	−	36481.9i	0.426561	−	3.14900i
$9$	−1633.86	−	12061.6i	−0.0830086	−	0.612794i
$10$	−7773.94	+	2145.47i	−0.245833	+	0.0678457i
$11$	−17350.6	+	32242.9i	−0.357313	+	0.663998i	−0.994270	−	0.106901i	$-0.965907\pi$
$11$	−17350.6	+	32242.9i	−0.357313	+	0.663998i	0.636957	+	0.770899i	$0.280193\pi$
$12$	81594.8	+	85341.5i	1.13592	+	1.18808i
$13$	50178.1	+	93246.6i	0.487270	+	0.905499i	0.998927	+	0.0463094i	$0.0147460\pi$
$13$	50178.1	+	93246.6i	0.487270	+	0.905499i	−0.511657	+	0.859190i	$0.670968\pi$
$14$	−142435.	+	438371.i	−0.990927	+	3.04976i
$15$	6344.98	−	14844.8i	0.0323608	−	0.0757119i
$16$	881936.	+	160048.i	3.36432	+	0.610534i
$17$	−351550.	−	255416.i	−1.02086	−	0.741699i	−0.0544022	−	0.998519i	$-0.517325\pi$
$17$	−351550.	−	255416.i	−1.02086	−	0.741699i	−0.966459	+	0.256820i	$0.917325\pi$
$18$	524842.	−	47236.6i	1.17843	−	0.106060i
$19$	426576.	+	998025.i	0.750941	+	1.75691i	0.647216	+	0.762307i	$0.275933\pi$
$19$	426576.	+	998025.i	0.750941	+	1.75691i	0.103725	+	0.994606i	$0.466924\pi$
$20$	−56469.7	−	247410.i	−0.0789189	−	0.345766i
$21$	−508317.	−	770068.i	−0.570359	−	0.864056i
$22$	−1.36081e6	−	813046.i	−1.23850	−	0.739969i
$23$	484403.	+	607423.i	0.360937	+	0.452601i	0.928833	−	0.370500i	$-0.120814\pi$
$23$	484403.	+	607423.i	0.360937	+	0.452601i	−0.567895	+	0.823101i	$0.692242\pi$
$24$	−2.40280e6	+	2.09926e6i	−1.47831	+	1.29156i
$25$	1.55204e6	−	1.12762e6i	0.794644	−	0.577343i
$26$	−4.13040e6	+	1.98910e6i	−1.77261	+	0.853642i
$27$	−1.52090e6	+	2.30406e6i	−0.550761	+	0.834367i
$28$	−1.35795e7	−	5.09648e6i	−4.17516	−	1.56696i
$29$	3.16478e6	−	1.89087e6i	0.830908	−	0.496444i	−0.0333794	−	0.999443i	$-0.510627\pi$
$29$	3.16478e6	−	1.89087e6i	0.830908	−	0.496444i	0.864287	+	0.502998i	$0.167770\pi$
$30$	629717.	+	303256.i	0.141938	+	0.0683539i
$31$	−3.81282e6	+	691925.i	−0.741513	+	0.134565i	−0.536152	−	0.844122i	$-0.680123\pi$
$31$	−3.81282e6	+	691925.i	−0.741513	+	0.134565i	−0.205361	+	0.978686i	$0.565837\pi$
$32$	−4.44078e6	+	1.94563e7i	−0.748659	+	3.28009i
$33$	2.97096e6	−	1.11502e6i	0.436098	−	0.163670i
$34$	1.17296e7	−	1.47085e7i	1.50532	−	1.88761i
$35$	88975.4	+	1.98119e6i	0.0100222	+	0.223162i
$36$	743962.	+	1.65656e7i	0.0738226	+	1.64379i
$37$	6.04608e6	−	7.58154e6i	0.530354	−	0.665043i	−0.442417	−	0.896809i	$-0.645879\pi$
$37$	6.04608e6	−	7.58154e6i	0.530354	−	0.665043i	0.972771	+	0.231766i	$0.0744505\pi$
$38$	−4.39934e7	+	1.65110e7i	−3.42264	+	1.28454i
$39$	2.04213e6	−	8.94714e6i	0.141349	−	0.619289i
$40$	6.74753e6	−	1.22450e6i	0.416749	−	0.0756288i
$41$	9.06735e6	+	4.36661e6i	0.501133	+	0.241333i	0.667334	−	0.744759i	$-0.267436\pi$
$41$	9.06735e6	+	4.36661e6i	0.501133	+	0.241333i	−0.166200	+	0.986092i	$0.553150\pi$
$42$	3.42929e7	−	2.04891e7i	1.70052	−	1.01602i
$43$	−1.77728e7	−	6.67025e6i	−0.792772	−	0.297532i	−0.0780575	−	0.996949i	$-0.524872\pi$
$43$	−1.77728e7	−	6.67025e6i	−0.792772	−	0.297532i	−0.714714	+	0.699417i	$0.753443\pi$
$44$	2.74801e7	−	4.16305e7i	1.10530	−	1.67446i
$45$	2.04277e6	−	983745.i	0.0742613	−	0.0357624i
$46$	−2.72121e7	+	1.97707e7i	−0.896089	+	0.651047i
$47$	−4.52970e7	+	3.95748e7i	−1.35403	+	1.18298i	−0.388882	+	0.921288i	$0.627139\pi$
$47$	−4.52970e7	+	3.95748e7i	−1.35403	+	1.18298i	−0.965151	+	0.261695i	$0.915719\pi$
$48$	−4.84348e7	−	6.07353e7i	−1.31696	−	1.65141i
$49$	6.26630e7	+	3.74394e7i	1.55285	+	0.927784i
$50$	4.57553e7	+	6.93163e7i	1.03532	+	1.56845i
$51$	8.38022e6	+	3.67161e7i	0.173456	+	0.759961i
$52$	−5.66979e7	−	1.32651e8i	−1.07536	−	2.51592i
$53$	3.36685e6	−	303022.i	0.0586114	−	0.00527512i	−0.0602948	−	0.998181i	$-0.519204\pi$
$53$	3.36685e6	−	303022.i	0.0586114	−	0.00527512i	0.118906	+	0.992905i	$0.462061\pi$
$54$	−9.66971e7	−	7.02545e7i	−1.54754	−	1.12435i
$55$	−6.71083e6	−	1.21784e6i	−0.0988881	−	0.0179455i
$56$	1.54048e8	−	3.60413e8i	2.09319	−	4.89727i
$57$	2.90679e7	−	8.94619e7i	0.364735	−	1.12254i
$58$	7.56334e7	+	1.40550e8i	0.877581	+	1.63082i
$59$	−7.97113e7	−	8.33715e7i	−0.856419	−	0.895744i	0.139103	−	0.990278i	$-0.455578\pi$
$59$	−7.97113e7	−	8.33715e7i	−0.856419	−	0.895744i	−0.995522	+	0.0945343i	$0.969864\pi$
$60$	−1.04222e7	+	1.93676e7i	−0.103819	+	0.192928i
$61$	−1.10913e8	+	3.06099e7i	−1.02564	+	0.283060i	−0.738088	−	0.674704i	$-0.764271\pi$
$61$	−1.10913e8	+	3.06099e7i	−1.02564	+	0.283060i	−0.287556	+	0.957764i	$0.592843\pi$
$62$	−2.25200e7	−	1.66249e8i	−0.193556	−	1.42888i
$63$	1.73950e7	−	1.28415e8i	0.139121	−	1.02703i
$64$	−3.90476e8	−	1.07765e8i	−2.90928	−	0.802909i
$65$	−1.36310e7	+	1.42569e7i	−0.0947150	+	0.0990641i
$66$	4.24542e7	+	1.30661e8i	0.275406	+	0.847612i
$67$	−1.78263e7	−	1.60439e6i	−0.108075	−	0.00972689i	0.0354700	−	0.999371i	$-0.488707\pi$
$67$	−1.78263e7	−	1.60439e6i	−0.108075	−	0.00972689i	−0.143545	+	0.989644i	$0.545850\pi$
$68$	4.45816e8	+	3.89498e8i	2.52852	+	2.20910i
$69$	3.02092e6	−	6.72660e7i	0.0160442	−	0.357252i
$70$	−8.58598e7			−0.427414
$71$	3.96172e7	+	2.10426e8i	0.185021	+	0.982735i
$71$	3.96172e7	+	2.10426e8i	0.185021	+	0.982735i
$72$	−4.48105e8			−1.96510
$73$	−2.09083e7	+	4.65560e8i	−0.0861721	+	1.91877i	0.235422	+	0.971893i	$0.424353\pi$
$73$	−2.09083e7	+	4.65560e8i	−0.0861721	+	1.91877i	−0.321594	+	0.946878i	$0.604219\pi$
$74$	3.16160e8	+	2.76220e8i	1.22564	+	1.07081i
$75$	−1.65595e8	−	1.49039e7i	−0.604328	−	0.0543905i
$76$	−4.56929e8	−	1.40628e9i	−1.57104	−	4.83517i
$77$	−2.69392e8	+	2.81762e8i	−0.873325	+	0.913426i
$78$	3.82999e8	+	1.05701e8i	1.17158	+	0.323336i
$79$	−1.81289e7	+	1.33833e8i	−0.0523661	+	0.386582i	0.945733	+	0.324946i	$0.105346\pi$
$79$	−1.81289e7	+	1.33833e8i	−0.0523661	+	0.386582i	−0.998099	+	0.0616361i	$0.980368\pi$
$80$	2.24124e7	+	1.65455e8i	0.0611763	+	0.451621i
$81$	−297995.	+	82241.4i	−0.000769177	+	0.000212279i
$82$	−2.06469e8	+	3.83684e8i	−0.504304	+	0.937154i
$83$	7.39581e7	+	7.73541e7i	0.171054	+	0.178909i	0.802765	−	0.596295i	$-0.203361\pi$
$83$	7.39581e7	+	7.73541e7i	0.171054	+	0.178909i	−0.631711	+	0.775204i	$0.717647\pi$
$84$	5.95679e8	+	1.10696e9i	1.30544	+	2.42591i
$85$	2.50130e7	−	7.69822e7i	0.0519734	−	0.159958i
$86$	3.23011e8	−	7.55722e8i	0.636758	−	1.48977i
$87$	−3.14375e8	−	5.70507e7i	−0.588318	−	0.106764i
$88$	1.09054e9	+	7.92323e8i	1.93851	+	1.40841i
$89$	−5.41473e8	+	4.87334e7i	−0.914791	+	0.0823326i	−0.537023	−	0.843568i	$-0.680451\pi$
$89$	−5.41473e8	+	4.87334e7i	−0.914791	+	0.0823326i	−0.377768	+	0.925900i	$0.623308\pi$
$90$	3.85794e7	+	9.02609e7i	0.0619818	+	0.145014i
$91$	2.50863e8	+	1.09910e9i	0.383487	+	1.68017i
$92$	−5.83094e8	−	8.83349e8i	−0.848581	−	1.28555i
$93$	2.88305e8	+	1.72254e8i	0.399649	+	0.238779i
$94$	−1.62364e9	−	2.03597e9i	−2.14493	−	2.68966i
$95$	−1.52254e8	+	1.33020e8i	−0.191784	+	0.167556i
$96$	1.39927e9	−	1.01663e9i	1.68144	−	1.22163i
$97$	1.01168e8	−	4.87201e7i	0.116030	−	0.0558772i	−0.374968	−	0.927038i	$-0.622346\pi$
$97$	1.01168e8	−	4.87201e7i	0.116030	−	0.0558772i	0.490998	+	0.871160i	$0.336632\pi$
$98$	−1.74098e9	+	2.63747e9i	−1.90667	+	2.88848i
$99$	4.17250e8	+	1.56597e8i	0.436554	+	0.163842i
$100$	−2.24362e9	+	1.34050e9i	−2.24362	+	1.34050i
$101$	−8.38931e8	−	4.04008e8i	−0.802196	−	0.386317i	−0.0125815	−	0.999921i	$-0.504005\pi$
$101$	−8.38931e8	−	4.04008e8i	−0.802196	−	0.386317i	−0.789614	+	0.613604i	$0.789719\pi$
$102$	−1.60426e9	+	2.91130e8i	−1.46748	+	0.266309i
$103$	−2.42255e8	+	1.06139e9i	−0.212083	+	0.929196i	0.751066	+	0.660227i	$0.229540\pi$
$103$	−2.42255e8	+	1.06139e9i	−0.212083	+	0.929196i	−0.963149	+	0.268969i	$0.913317\pi$
$104$	3.64979e9	−	1.36979e9i	3.05927	−	1.14816i
$105$	1.07164e8	−	1.34379e8i	0.0860393	−	0.107890i
$106$	6.56610e6	+	1.46206e8i	0.00505162	+	0.112483i
$107$	−5.88004e7	−	1.30929e9i	−0.0433664	−	0.965627i	−0.896256	−	0.443536i	$-0.853724\pi$
$107$	−5.88004e7	−	1.30929e9i	−0.0433664	−	0.965627i	0.852890	−	0.522091i	$-0.174848\pi$
$108$	2.34503e9	−	2.94058e9i	1.65860	−	2.07982i
$109$	−6.47408e8	+	2.42976e8i	−0.439298	+	0.164871i	−0.561217	−	0.827669i	$-0.689667\pi$
$109$	−6.47408e8	+	2.42976e8i	−0.439298	+	0.164871i	0.121919	+	0.992540i	$0.461095\pi$
$110$	6.57066e7	−	2.87879e8i	0.0427900	−	0.187475i
$111$	−8.26920e8	+	1.50064e8i	−0.517023	+	0.0938259i
$112$	8.59790e9	+	4.14053e9i	5.16311	+	2.48642i
$113$	1.36189e9	−	8.13690e8i	0.785757	−	0.469468i	−0.0631537	−	0.998004i	$-0.520116\pi$
$113$	1.36189e9	−	8.13690e8i	0.785757	−	0.469468i	0.848911	+	0.528536i	$0.177259\pi$
$114$	3.81279e9	+	1.43096e9i	2.11432	+	0.793517i
$115$	−7.97266e7	+	1.20781e8i	−0.0425072	+	0.0643957i
$116$	−4.52511e9	+	2.17918e9i	−2.32043	+	1.11746i
$117$	1.04272e9	−	7.57582e8i	0.514437	−	0.373760i
$118$	3.76067e9	−	3.28560e9i	1.78565	−	1.56007i
$119$	−2.88448e9	−	3.61703e9i	−1.31858	−	1.65345i
$120$	−5.10211e8	−	3.04837e8i	−0.224613	−	0.134200i
$121$	5.60427e8	+	8.49011e8i	0.237676	+	0.360064i
$122$	−1.10845e9	−	4.85645e9i	−0.453000	−	1.98472i
$123$	−3.42804e8	−	8.02030e8i	−0.135043	−	0.315950i
$124$	5.25800e9	−	4.73229e8i	1.99721	−	0.179752i
$125$	5.83442e8	+	4.23895e8i	0.213748	+	0.155297i
$126$	5.52018e9	+	1.00177e9i	1.95113	+	0.354078i
$127$	−2.20972e9	+	5.16989e9i	−0.753737	+	1.76346i	−0.115933	+	0.993257i	$0.536986\pi$
$127$	−2.20972e9	+	5.16989e9i	−0.753737	+	1.76346i	−0.637804	+	0.770199i	$0.720157\pi$
$128$	2.26182e9	−	6.96115e9i	0.744753	−	2.29211i
$129$	7.79623e8	+	1.44878e9i	0.247874	+	0.460627i
$130$	−5.90139e8	−	6.17237e8i	−0.181221	−	0.189543i
$131$	−1.34166e9	+	2.49322e9i	−0.398035	+	0.739672i	−0.998185	−	0.0602145i	$-0.980822\pi$
$131$	−1.34166e9	+	2.49322e9i	−0.398035	+	0.739672i	0.600151	+	0.799887i	$0.295107\pi$
$132$	−4.16738e9	+	1.15012e9i	−1.19476	+	0.329732i
$133$	1.55112e9	+	1.14508e10i	0.429847	+	3.17326i
$134$	1.04015e8	−	7.67873e8i	0.0278693	−	0.205740i
$135$	−4.95730e8	−	1.36813e8i	−0.128453	−	0.0354507i
$136$	−1.10554e10	+	1.15630e10i	−2.77107	+	2.89831i
$137$	−8.42301e8	−	2.59234e9i	−0.204279	−	0.628707i	−0.999742	−	0.0227050i	$-0.992772\pi$
$137$	−8.42301e8	−	2.59234e9i	−0.204279	−	0.628707i	0.795463	−	0.606002i	$-0.207228\pi$
$138$	2.90340e9	+	2.61311e8i	0.681477	+	0.0613340i
$139$	−3.55497e9	−	3.10588e9i	−0.807735	−	0.705697i	0.151453	−	0.988464i	$-0.451605\pi$
$139$	−3.55497e9	−	3.10588e9i	−0.807735	−	0.705697i	−0.959189	+	0.282767i	$0.908748\pi$
$140$	1.21216e8	−	2.69909e9i	0.0266676	−	0.593801i
$141$	5.21301e9			1.11071
$142$	−9.17791e9	+	1.30473e9i	−1.89429	+	0.269291i
$143$	−3.87716e9			−0.775357
$144$	4.89478e8	−	1.08991e10i	0.0948641	−	2.11231i
$145$	5.17155e8	+	4.51824e8i	0.0971548	+	0.0848816i
$146$	−2.00950e10	−	1.80858e9i	−3.66016	−	0.329420i
$147$	−1.95495e9	−	6.01670e9i	−0.345308	−	1.06275i
$148$	−9.12960e9	+	9.54881e9i	−1.56413	+	1.63596i
$149$	4.39597e9	+	1.21321e9i	0.730662	+	0.201650i	0.611522	−	0.791227i	$-0.290558\pi$
$149$	4.39597e9	+	1.21321e9i	0.730662	+	0.201650i	0.119140	+	0.992877i	$0.461986\pi$
$150$	9.66243e8	−	7.13309e9i	0.155839	−	1.15045i
$151$	8.46800e8	+	6.25133e9i	0.132551	+	0.978534i	0.928018	+	0.372536i	$0.121512\pi$
$151$	8.46800e8	+	6.25133e9i	0.132551	+	0.978534i	−0.795466	+	0.605998i	$0.792774\pi$
$152$	3.85179e10	−	1.06303e10i	5.85284	−	1.61528i
$153$	−2.50635e9	+	4.65758e9i	−0.369769	+	0.687145i
$154$	−1.16630e10	−	1.21985e10i	−1.67096	−	1.74769i
$155$	−3.42054e8	−	6.35643e8i	−0.0475995	−	0.0884547i
$156$	−3.86353e9	+	1.18907e10i	−0.522304	+	1.60749i
$157$	3.47506e9	−	8.13030e9i	0.456471	−	1.06797i	−0.520358	−	0.853948i	$-0.674202\pi$
$157$	3.47506e9	−	8.13030e9i	0.456471	−	1.06797i	0.976829	−	0.214019i	$-0.0686556\pi$
$158$	−5.75310e9	−	1.04403e9i	−0.734421	−	0.133278i
$159$	−2.37022e8	−	1.72206e8i	−0.0294104	−	0.0213679i
$160$	−3.70247e9	+	3.33228e8i	−0.446633	+	0.0401977i
$161$	3.25093e9	+	7.60593e9i	0.381321	+	0.892145i
$162$	−2.97814e6	−	1.30481e7i	−0.000339725	−	0.00148843i
$163$	6.84231e9	+	1.03657e10i	0.759204	+	1.15014i	0.984420	+	0.175836i	$0.0562627\pi$
$163$	6.84231e9	+	1.03657e10i	0.759204	+	1.15014i	−0.225216	+	0.974309i	$0.572309\pi$
$164$	−1.17700e10	−	7.03223e9i	−1.27051	−	0.759094i
$165$	3.68550e8	+	4.62147e8i	0.0387096	+	0.0485403i
$166$	−3.48924e9	+	3.04845e9i	−0.356651	+	0.311597i
$167$	−7.00562e9	+	5.08988e9i	−0.696983	+	0.506388i	−0.878948	−	0.476917i	$-0.841754\pi$
$167$	−7.00562e9	+	5.08988e9i	−0.696983	+	0.506388i	0.181965	+	0.983305i	$0.441754\pi$
$168$	−3.06055e10	+	1.47389e10i	−2.96421	+	1.42749i
$169$	−3.35099e8	+	5.07653e8i	−0.0315997	+	0.0478715i
$170$	3.28091e9	+	1.23135e9i	0.301283	+	0.113073i
$171$	1.13408e10	−	6.77584e9i	1.01429	−	0.606011i
$172$	2.33008e10	+	1.12211e10i	2.02999	+	0.977590i
$173$	−1.10063e9	+	1.99735e8i	−0.0934189	+	0.0169530i	−0.225065	−	0.974344i	$-0.572259\pi$
$173$	−1.10063e9	+	1.99735e8i	−0.0934189	+	0.0169530i	0.131646	+	0.991297i	$0.457974\pi$
$174$	3.07809e9	−	1.34860e10i	0.254571	−	1.11535i
$175$	1.91223e10	−	7.17671e9i	1.54123	−	0.578434i
$176$	−2.04626e10	+	2.56592e10i	−1.60751	+	2.01575i
$177$	4.48501e8	+	9.98666e9i	0.0343466	+	0.764787i
$178$	−1.05599e9	−	2.35135e10i	−0.0788443	−	1.75561i
$179$	3.61996e9	−	4.53929e9i	0.263551	−	0.330483i	−0.632394	−	0.774647i	$-0.717928\pi$
$179$	3.61996e9	−	4.53929e9i	0.263551	−	0.330483i	0.895946	+	0.444164i	$0.146499\pi$
$180$	−2.89190e9	+	1.08535e9i	−0.205333	+	0.0770626i
$181$	2.97863e9	−	1.30502e10i	0.206283	−	0.903783i	−0.760733	−	0.649065i	$-0.775160\pi$
$181$	2.97863e9	−	1.30502e10i	0.206283	−	0.903783i	0.967015	−	0.254718i	$-0.0819826\pi$
$182$	−4.80237e10	+	8.71502e9i	−3.24440	+	0.588772i
$183$	8.98432e9	+	4.32662e9i	0.592182	+	0.285180i
$184$	2.45538e10	−	1.46702e10i	1.57920	−	0.943530i
$185$	1.69116e9	+	6.34702e8i	0.106148	+	0.0398379i
$186$	−8.01002e9	+	1.21347e10i	−0.490711	+	0.743395i
$187$	1.43350e10	−	6.90335e9i	0.857254	−	0.412832i
$188$	6.62950e10	−	4.81662e10i	3.87053	−	2.81211i
$189$	−2.21348e10	+	1.93386e10i	−1.26182	+	1.10242i
$190$	−5.45741e9	−	6.84338e9i	−0.303805	−	0.380960i
$191$	2.75648e9	+	1.64692e9i	0.149867	+	0.0895412i	0.585875	−	0.810401i	$-0.300751\pi$
$191$	2.75648e9	+	1.64692e9i	0.149867	+	0.0895412i	−0.436008	+	0.899943i	$0.643608\pi$
$192$	1.93402e10	+	2.92991e10i	1.02708	+	1.55596i
$193$	−3.41594e8	−	1.49662e9i	−0.0177216	−	0.0776433i	0.965294	−	0.261166i	$-0.0841070\pi$
$193$	−3.41594e8	−	1.49662e9i	−0.0177216	−	0.0776433i	−0.983015	+	0.183523i	$0.941250\pi$
$194$	1.91065e9	+	4.47018e9i	0.0968440	+	0.226578i
$195$	1.70261e9	−	1.53237e8i	0.0843255	−	0.00758943i
$196$	−8.04535e10	−	5.84529e10i	−3.89397	−	2.82913i
$197$	1.42057e10	+	2.57796e9i	0.671995	+	0.121949i	0.503821	−	0.863808i	$-0.331927\pi$
$197$	1.42057e10	+	2.57796e9i	0.671995	+	0.121949i	0.168174	+	0.985757i	$0.446213\pi$
$198$	−7.58329e9	+	1.77420e10i	−0.350642	+	0.820369i
$199$	−8.27461e8	+	2.54666e9i	−0.0374032	+	0.115115i	−0.968015	−	0.250893i	$-0.919276\pi$
$199$	−8.27461e8	+	2.54666e9i	−0.0374032	+	0.115115i	0.930612	+	0.366008i	$0.119276\pi$
$200$	−3.34679e10	−	6.21939e10i	−1.47909	−	2.74861i
$201$	1.07197e9	+	1.12120e9i	0.0463236	+	0.0484507i
$202$	1.91030e10	−	3.54992e10i	0.807271	−	1.50016i
$203$	3.78355e10	−	1.04419e10i	1.56375	−	0.431567i
$204$	−6.88707e9	−	5.08424e10i	−0.278419	−	2.05537i
$205$	−2.51643e8	+	1.85771e9i	−0.00995161	+	0.0734657i
$206$	−4.54348e10	−	1.25392e10i	−1.75787	−	0.485140i
$207$	6.53506e9	−	6.83514e9i	0.247391	−	0.258750i
$208$	2.93300e10	+	9.02684e10i	1.08649	+	3.34388i
$209$	−3.95806e10	−	3.56232e9i	−1.43491	−	0.129144i
$210$	5.60378e9	+	4.89588e9i	0.198836	+	0.173718i
$211$	−4.14572e8	+	9.23116e9i	−0.0143989	+	0.320616i	0.978847	+	0.204591i	$0.0655866\pi$
$211$	−4.14572e8	+	9.23116e9i	−0.0143989	+	0.320616i	−0.993246	+	0.116025i	$0.962985\pi$
$212$	−4.60538e9			−0.156587
$213$	9.41316e9	−	1.59928e10i	0.313348	−	0.532374i
$214$	5.67414e10			1.84943
$215$	1.58647e8	−	3.53255e9i	0.00506360	−	0.112750i
$216$	7.65406e10	+	6.68715e10i	2.39249	+	2.09025i
$217$	−4.10904e10	−	3.69820e9i	−1.25797	−	0.113220i
$218$	−9.25128e9	−	2.84725e10i	−0.277426	−	0.853830i
$219$	2.79117e10	−	2.91933e10i	0.819950	−	0.857601i
$220$	8.95700e9	+	2.47198e9i	0.257787	+	0.0711446i
$221$	6.17655e9	−	4.55971e10i	0.174173	−	1.28580i
$222$	−4.88411e9	−	3.60559e10i	−0.134957	−	0.996296i
$223$	−2.72170e10	+	7.51142e9i	−0.737002	+	0.203400i	−0.614332	−	0.789048i	$-0.710574\pi$
$223$	−2.72170e10	+	7.51142e9i	−0.737002	+	0.203400i	−0.122670	+	0.992447i	$0.539146\pi$
$224$	−1.00683e11	+	1.87100e11i	−2.67202	+	4.96544i
$225$	−1.61368e10	−	1.68777e10i	−0.419755	−	0.439029i
$226$	3.25470e10	+	6.04825e10i	0.829895	+	1.54220i
$227$	−9.14058e9	+	2.81318e10i	−0.228485	+	0.703204i	0.769434	+	0.638726i	$0.220538\pi$
$227$	−9.14058e9	+	2.81318e10i	−0.228485	+	0.703204i	−0.997919	+	0.0644781i	$0.979462\pi$
$228$	−5.03665e10	+	1.17838e11i	−1.23434	+	2.88788i
$229$	3.49881e10	+	6.34940e9i	0.840737	+	0.152571i	0.581809	−	0.813325i	$-0.302345\pi$
$229$	3.49881e10	+	6.34940e9i	0.840737	+	0.152571i	0.258928	+	0.965897i	$0.416631\pi$
$230$	−5.06893e9	−	3.68279e9i	−0.119438	−	0.0867765i
$231$	3.36488e10	−	3.02845e9i	0.777528	−	0.0699788i
$232$	−5.33428e10	−	1.24802e11i	−1.20887	−	2.82829i
$233$	5.28496e8	+	2.31549e9i	0.0117474	+	0.0514685i	0.980462	−	0.196709i	$-0.0630255\pi$
$233$	5.28496e8	+	2.31549e9i	0.0117474	+	0.0514685i	−0.968715	+	0.248178i	$0.920168\pi$
$234$	3.07402e10	+	4.65695e10i	0.670248	+	1.01538i
$235$	−9.61839e9	−	5.74672e9i	−0.205730	−	0.122918i
$236$	9.79766e10	+	1.22859e11i	2.05598	+	2.57811i
$237$	8.81461e9	−	7.70109e9i	0.181483	−	0.158557i
$238$	1.62040e11	−	1.17729e11i	3.27360	−	2.37841i
$239$	8.04401e10	−	3.87379e10i	1.59471	−	0.767973i	0.595342	−	0.803472i	$-0.297017\pi$
$239$	8.04401e10	−	3.87379e10i	1.59471	−	0.767973i	0.999370	+	0.0354996i	$0.0113023\pi$
$240$	7.97174e9	−	1.20767e10i	0.155097	−	0.234962i
$241$	−5.63643e9	−	2.11539e9i	−0.107629	−	0.0403937i	0.296980	−	0.954884i	$-0.404021\pi$
$241$	−5.63643e9	−	2.11539e9i	−0.107629	−	0.0403937i	−0.404608	+	0.914490i	$0.632592\pi$
$242$	−3.78085e10	+	2.25895e10i	−0.708631	+	0.423387i
$243$	4.89829e10	+	2.35889e10i	0.901191	+	0.433991i
$244$	1.54232e11	−	2.79890e10i	2.78561	−	0.505514i
$245$	−3.02568e9	+	1.32564e10i	−0.0536507	+	0.235059i
$246$	3.53538e10	−	1.32685e10i	0.615501	−	0.231001i
$247$	−7.16577e10	+	8.98559e10i	−1.22497	+	1.53607i
$248$	6.40051e9	+	1.42518e11i	0.107444	+	2.39242i
$249$	−4.16130e8	−	9.26586e9i	−0.00686013	−	0.152753i
$250$	−1.94668e10	+	2.44106e10i	−0.315185	+	0.395229i
$251$	−2.49454e10	+	9.36215e9i	−0.396696	+	0.148883i	−0.541747	−	0.840542i	$-0.682237\pi$
$251$	−2.49454e10	+	9.36215e9i	−0.396696	+	0.148883i	0.145051	+	0.989424i	$0.453665\pi$
$252$	−3.92848e10	+	1.72118e11i	−0.613652	+	2.68859i
$253$	−2.79898e10	+	5.07939e9i	−0.429494	+	0.0779416i
$254$	−2.19307e11	−	1.05613e11i	−3.30598	−	1.59208i
$255$	−6.02218e9	+	3.59808e9i	−0.0891914	+	0.0532894i
$256$	1.02505e11	+	3.84708e10i	1.49164	+	0.559823i
$257$	7.91559e8	−	1.19916e9i	0.0113184	−	0.0171466i	−0.828870	−	0.559441i	$-0.811016\pi$
$257$	7.91559e8	−	1.19916e9i	0.0113184	−	0.0171466i	0.840188	+	0.542295i	$0.182444\pi$
$258$	−6.41744e10	+	3.09048e10i	−0.901724	+	0.434247i
$259$	8.35240e10	−	6.06837e10i	1.15335	−	0.837960i
$260$	2.02366e10	−	1.76802e10i	0.274636	−	0.239942i
$261$	−2.79778e10	−	3.50830e10i	−0.373191	−	0.467966i
$262$	−1.05226e11	−	6.28698e10i	−1.37965	−	0.824301i
$263$	3.03773e10	+	4.60196e10i	0.391515	+	0.593119i	0.975863	−	0.218384i	$-0.0700784\pi$
$263$	3.03773e10	+	4.60196e10i	0.391515	+	0.593119i	−0.584348	+	0.811503i	$0.698650\pi$
$264$	−2.59962e10	−	1.13897e11i	−0.329376	−	1.44309i
$265$	2.47486e8	+	5.79022e8i	0.00308279	+	0.00721255i
$266$	−4.98265e11	+	4.48446e10i	−6.10229	+	0.549216i
$267$	3.81190e10	+	2.76951e10i	0.459030	+	0.333504i
$268$	2.39920e10	+	4.35390e9i	0.284092	+	0.0515552i
$269$	−3.03764e9	+	7.10690e9i	−0.0353712	+	0.0827551i	−0.936282	−	0.351249i	$-0.885757\pi$
$269$	−3.03764e9	+	7.10690e9i	−0.0353712	+	0.0827551i	0.900911	+	0.434004i	$0.142900\pi$
$270$	6.88007e9	−	2.11747e10i	0.0787872	−	0.242482i
$271$	1.02551e10	+	1.90572e10i	0.115499	+	0.214633i	0.931781	−	0.363020i	$-0.118254\pi$
$271$	1.02551e10	+	1.90572e10i	0.115499	+	0.214633i	−0.816282	+	0.577653i	$0.803969\pi$
$272$	−2.69166e11	−	2.81525e11i	−2.98167	−	3.11858i
$273$	4.62998e10	−	8.60394e10i	0.504484	−	0.937488i
$274$	1.13755e11	−	3.13944e10i	1.21925	−	0.336492i
$275$	9.42894e9	+	6.96072e10i	0.0994181	+	0.733934i
$276$	−1.23136e10	+	9.09023e10i	−0.127730	+	0.942940i
$277$	1.68048e11	+	4.63782e10i	1.71504	+	0.473320i	0.979041	−	0.203665i	$-0.0652855\pi$
$277$	1.68048e11	+	4.63782e10i	1.71504	+	0.473320i	0.735996	+	0.676986i	$0.236714\pi$
$278$	1.41235e11	−	1.47720e11i	1.41821	−	1.48333i
$279$	1.45754e10	+	4.48583e10i	0.144012	+	0.443225i
$280$	7.27174e10	+	6.54468e9i	0.707012	+	0.0636323i
$281$	−2.39399e10	−	2.09156e10i	−0.229057	−	0.200121i	0.535757	−	0.844372i	$-0.320026\pi$
$281$	−2.39399e10	−	2.09156e10i	−0.229057	−	0.200121i	−0.764814	+	0.644251i	$0.777169\pi$
$282$	−1.01256e10	+	2.25464e11i	−0.0953453	+	2.12303i
$283$	−1.60087e11			−1.48361			−0.741803	−	0.670618i	$-0.766029\pi$
$283$	−1.60087e11			−1.48361			−0.741803	+	0.670618i	$0.766029\pi$
$284$	−2.80580e10	−	2.90358e11i	−0.255932	−	2.64851i
$285$	1.75221e10			0.157320
$286$	7.53088e9	−	1.67688e11i	0.0665578	−	1.48202i
$287$	8.06894e10	+	7.04962e10i	0.702017	+	0.613334i
$288$	2.41930e11	+	2.17741e10i	2.07216	+	0.186498i
$289$	2.17044e10	+	6.67991e10i	0.183023	+	0.563288i
$290$	−2.05460e10	+	2.14894e10i	−0.170583	+	0.178416i
$291$	−9.38101e9	−	2.58900e9i	−0.0766887	−	0.0211647i
$292$	8.52244e10	−	6.29152e11i	0.686027	−	5.06445i
$293$	3.05301e10	+	2.25382e11i	0.242005	+	1.78655i	0.550000	+	0.835164i	$0.314628\pi$
$293$	3.05301e10	+	2.25382e11i	0.242005	+	1.78655i	−0.307995	+	0.951388i	$0.599658\pi$
$294$	2.64021e11	−	7.28651e10i	2.06099	−	0.568796i
$295$	1.01816e10	−	1.89206e10i	0.0782738	−	0.145457i
$296$	−2.46710e11	−	2.58039e11i	−1.86799	−	1.95377i
$297$	−4.79011e10	−	8.90151e10i	−0.357224	−	0.663834i
$298$	−6.10103e10	+	1.87770e11i	−0.448157	+	1.37928i
$299$	−3.23336e10	+	7.56483e10i	−0.233956	+	0.547367i
$300$	2.22871e11	+	4.04452e10i	1.58858	+	0.288285i
$301$	−1.63508e11	−	1.18795e11i	−1.14813	−	0.834162i
$302$	−2.72016e11	+	2.44819e10i	−1.88176	+	0.169361i
$303$	3.17170e10	+	7.42056e10i	0.216172	+	0.505760i
$304$	2.16481e11	+	9.48467e11i	1.45375	+	6.36929i
$305$	−1.18072e10	−	1.78871e10i	−0.0781261	−	0.118356i
$306$	−1.96573e11	−	1.17447e11i	−1.28167	−	0.765764i
$307$	2.95278e10	+	3.70267e10i	0.189718	+	0.237899i	0.867589	−	0.497282i	$-0.165669\pi$
$307$	2.95278e10	+	3.70267e10i	0.189718	+	0.237899i	−0.677871	+	0.735181i	$0.737097\pi$
$308$	3.99938e11	−	3.49416e11i	2.53230	−	2.21240i
$309$	7.63334e10	−	5.54595e10i	0.476323	−	0.346069i
$310$	2.81561e10	−	1.35593e10i	0.173159	−	0.0833890i
$311$	5.07260e10	−	7.68466e10i	0.307474	−	0.465804i	−0.647680	−	0.761913i	$-0.724261\pi$
$311$	5.07260e10	−	7.68466e10i	0.307474	−	0.465804i	0.955154	+	0.296109i	$0.0956892\pi$
$312$	−3.16317e11	−	1.18716e11i	−1.88985	−	0.709272i
$313$	−4.93037e10	+	2.94576e10i	−0.290356	+	0.173479i	−0.650689	−	0.759344i	$-0.725520\pi$
$313$	−4.93037e10	+	2.94576e10i	−0.290356	+	0.173479i	0.360334	+	0.932823i	$0.382663\pi$
$314$	3.44887e11	+	1.66089e11i	2.00214	+	0.964179i
$315$	2.37510e10	−	4.31018e9i	0.135920	−	0.0246659i
$316$	4.09424e10	−	1.79380e11i	0.230984	−	1.01200i
$317$	2.14988e11	−	8.06865e10i	1.19577	−	0.448781i	0.327492	−	0.944854i	$-0.393797\pi$
$317$	2.14988e11	−	8.06865e10i	1.19577	−	0.448781i	0.868281	+	0.496073i	$0.165225\pi$
$318$	7.90835e9	−	9.91676e9i	0.0433674	−	0.0543811i
$319$	6.05610e9	+	1.34850e11i	0.0327442	+	0.729107i
$320$	−3.38529e9	−	7.53792e10i	−0.0180476	−	0.401862i
$321$	−7.08204e10	+	8.88060e10i	−0.372294	+	0.466842i
$322$	−3.35273e11	+	1.25830e11i	−1.73799	+	0.652277i
$323$	1.04949e11	−	4.59810e11i	0.536495	−	2.35054i
$324$	4.14384e8	−	7.51996e7i	0.00208906	−	0.000379108i
$325$	1.83025e11	+	8.81404e10i	0.909990	+	0.438228i
$326$	−4.61607e11	+	2.75797e11i	−2.26357	+	1.35242i
$327$	5.61091e10	+	2.10581e10i	0.271374	+	0.101848i
$328$	2.04111e11	−	3.09215e11i	0.973722	−	1.47513i
$329$	−5.76969e11	+	2.77854e11i	−2.71501	+	1.30748i
$330$	−2.07038e10	+	1.50422e10i	−0.0961032	+	0.0698231i
$331$	−1.51900e11	+	1.32711e11i	−0.695556	+	0.607689i	−0.931355	−	0.364113i	$-0.881372\pi$
$331$	−1.51900e11	+	1.32711e11i	−0.695556	+	0.607689i	0.235799	+	0.971802i	$0.424229\pi$
$332$	−9.09050e10	−	1.13991e11i	−0.410645	−	0.514932i
$333$	−1.01324e11	−	6.05384e10i	−0.451558	−	0.269794i
$334$	−2.06531e11	−	3.12881e11i	−0.908084	−	1.37569i
$335$	−7.41887e8	−	3.25042e9i	−0.00321837	−	0.0141006i
$336$	−3.25056e11	−	7.60505e11i	−1.39133	−	3.25518i
$337$	−4.60560e10	+	4.14511e9i	−0.194514	+	0.0175066i	−0.186468	−	0.982461i	$-0.559704\pi$
$337$	−4.60560e10	+	4.14511e9i	−0.194514	+	0.0175066i	−0.00804622	+	0.999968i	$0.502561\pi$
$338$	−2.13052e10	−	1.54791e10i	−0.0887893	−	0.0645092i
$339$	−1.35284e11	−	2.45504e10i	−0.556349	−	0.100963i
$340$	−4.33406e10	+	1.01400e11i	−0.175889	+	0.411513i
$341$	4.38452e10	−	1.34942e11i	0.175601	−	0.540445i
$342$	2.71028e11	+	5.03655e11i	1.07127	+	1.99075i
$343$	2.40162e11	+	2.51190e11i	0.936873	+	0.979893i
$344$	−3.31173e11	+	6.15423e11i	−1.27509	+	2.36952i
$345$	1.20906e10	−	3.33679e9i	0.0459475	−	0.0126807i
$346$	−6.50076e9	−	4.79905e10i	−0.0243849	−	0.180017i
$347$	2.16954e10	−	1.60162e11i	0.0803312	−	0.593028i	−0.905382	−	0.424597i	$-0.860416\pi$
$347$	2.16954e10	−	1.60162e11i	0.0803312	−	0.593028i	0.985713	−	0.168431i	$-0.0538701\pi$
$348$	4.19600e11	+	1.15802e11i	1.53366	+	0.423263i
$349$	−2.19651e10	+	2.29737e10i	−0.0792537	+	0.0828928i	−0.761232	−	0.648479i	$-0.775405\pi$
$349$	−2.19651e10	+	2.29737e10i	−0.0792537	+	0.0828928i	0.681979	+	0.731372i	$0.261120\pi$
$350$	2.73252e11	+	8.40982e11i	0.973322	+	2.99558i
$351$	−2.91162e11	−	2.62050e10i	−1.02389	−	0.0921516i
$352$	−5.50277e11	−	4.80763e11i	−1.91047	−	1.66913i
$353$	1.66796e10	−	3.71400e11i	0.0571742	−	1.27308i	−0.741350	−	0.671119i	$-0.765814\pi$
$353$	1.66796e10	−	3.71400e11i	0.0571742	−	1.27308i	0.798524	−	0.601963i	$-0.205614\pi$
$354$	−4.32796e11			−1.46477
$355$	−3.49982e10	+	1.91311e10i	−0.116955	+	0.0639310i
$356$	7.40660e11			2.44396
$357$	−1.79887e10	+	4.00550e11i	−0.0586128	+	1.30512i
$358$	1.89294e11	+	1.65381e11i	0.609064	+	0.532123i
$359$	−4.79409e11	−	4.31476e10i	−1.52328	−	0.137098i	−0.703882	−	0.710317i	$-0.748552\pi$
$359$	−4.79409e11	−	4.31476e10i	−1.52328	−	0.137098i	−0.819402	+	0.573219i	$0.805694\pi$
$360$	−2.57939e10	−	7.93855e10i	−0.0809387	−	0.249104i
$361$	−5.91089e11	+	6.18231e11i	−1.83177	+	1.91588i
$362$	5.58639e11	+	1.54175e11i	1.70979	+	0.471872i
$363$	1.18349e10	−	8.73686e10i	0.0357754	−	0.264104i
$364$	−2.06166e11	−	1.52198e12i	−0.615545	−	4.54414i
$365$	−8.36813e10	+	2.30946e10i	−0.246780	+	0.0681071i
$366$	−2.04578e11	+	3.80170e11i	−0.595929	+	1.10742i
$367$	1.38748e11	+	1.45119e11i	0.399235	+	0.417567i	0.891601	−	0.452821i	$-0.149582\pi$
$367$	1.38748e11	+	1.45119e11i	0.399235	+	0.417567i	−0.492367	+	0.870388i	$0.663868\pi$
$368$	3.29996e11	+	6.13236e11i	0.937980	+	1.74306i
$369$	3.78536e10	−	1.16501e11i	0.106289	−	0.327124i
$370$	−3.07358e10	+	7.19101e10i	−0.0852584	+	0.199472i
$371$	3.54119e10	+	6.42631e9i	0.0970435	+	0.0176108i
$372$	−3.70156e11	−	2.68934e11i	−1.00217	−	0.728120i
$373$	−2.86825e11	+	2.58147e10i	−0.767234	+	0.0690523i	−0.466340	−	0.884605i	$-0.654428\pi$
$373$	−2.86825e11	+	2.58147e10i	−0.767234	+	0.0690523i	−0.300894	+	0.953658i	$0.597285\pi$
$374$	2.70728e11	+	6.33399e11i	0.715502	+	1.67400i
$375$	−1.39080e10	−	6.09351e10i	−0.0363183	−	0.159121i
$376$	1.21992e12	+	1.84809e12i	3.14763	+	4.76846i
$377$	3.35120e11	+	2.00225e11i	0.854406	+	0.510484i
$378$	−7.93404e11	−	9.94897e11i	−1.99885	−	2.50648i
$379$	5.37949e10	−	4.69992e10i	0.133926	−	0.117008i	−0.588370	−	0.808592i	$-0.700230\pi$
$379$	5.37949e10	−	4.69992e10i	0.133926	−	0.117008i	0.722295	+	0.691585i	$0.243087\pi$
$380$	2.22833e11	−	1.61898e11i	0.548218	−	0.398303i
$381$	4.39017e11	−	2.11419e11i	1.06738	−	0.514023i
$382$	−7.65839e10	+	1.16020e11i	−0.184015	+	0.278770i
$383$	3.69114e11	+	1.38531e11i	0.876528	+	0.328966i	0.748763	−	0.662838i	$-0.230648\pi$
$383$	3.69114e11	+	1.38531e11i	0.876528	+	0.328966i	0.127765	+	0.991804i	$0.459220\pi$
$384$	−5.44558e11	+	3.25358e11i	−1.27807	+	0.763610i
$385$	−6.54231e10	−	3.15061e10i	−0.151760	−	0.0730839i
$386$	6.53927e10	−	1.18670e10i	0.149929	−	0.0272081i
$387$	−5.14158e10	+	2.25267e11i	−0.116519	+	0.510504i
$388$	−1.43222e11	+	5.37521e10i	−0.320824	+	0.120407i
$389$	−1.59100e11	+	1.99505e11i	−0.352288	+	0.441755i	−0.926126	−	0.377214i	$-0.876882\pi$
$389$	−1.59100e11	+	1.99505e11i	−0.352288	+	0.441755i	0.573839	+	0.818968i	$0.305454\pi$
$390$	3.32046e9	+	7.39358e10i	0.00726788	+	0.161832i
$391$	−1.51465e10	−	3.37264e11i	−0.0327731	−	0.729750i
$392$	1.67553e12	−	2.10105e12i	3.58398	−	4.49416i
$393$	2.29733e11	−	8.62203e10i	0.485800	−	0.182324i
$394$	−1.39090e11	+	6.09394e11i	−0.290779	+	1.27399i
$395$	−2.47532e10	+	4.49204e9i	−0.0511615	+	0.00928445i
$396$	−5.47031e11	−	2.63436e11i	−1.11785	−	0.538328i
$397$	−2.51884e10	+	1.50494e10i	−0.0508912	+	0.0304061i	−0.538120	−	0.842869i	$-0.680865\pi$
$397$	−2.51884e10	+	1.50494e10i	−0.0508912	+	0.0304061i	0.487228	+	0.873275i	$0.338008\pi$
$398$	−1.08537e11	−	4.07345e10i	−0.216821	−	0.0813744i
$399$	5.51711e11	−	8.35806e11i	1.08977	−	1.65093i
$400$	1.54927e12	−	7.46091e11i	3.02592	−	1.45721i
$401$	2.91431e11	−	2.11737e11i	0.562841	−	0.408928i	−0.269657	−	0.962957i	$-0.586910\pi$
$401$	2.91431e11	−	2.11737e11i	0.562841	−	0.408928i	0.832498	+	0.554029i	$0.186910\pi$
$402$	−5.05742e10	+	4.41854e10i	−0.0965855	+	0.0843842i
$403$	−2.55840e11	−	3.20813e11i	−0.483165	−	0.605870i
$404$	1.08898e12	+	6.50637e11i	2.03379	+	1.21513i
$405$	−3.17230e7	−	4.80582e7i	−5.85904e−5	−	8.87606e-5i
$406$	3.78125e11	+	1.65667e12i	0.690667	+	3.02601i
$407$	1.39547e11	+	3.26487e11i	0.252085	+	0.589782i
$408$	1.38089e12	−	1.24282e11i	2.46711	−	0.222044i
$409$	3.79346e11	+	2.75611e11i	0.670317	+	0.487014i	0.870131	−	0.492820i	$-0.164034\pi$
$409$	3.79346e11	+	2.75611e11i	0.670317	+	0.487014i	−0.199814	+	0.979834i	$0.564034\pi$
$410$	−7.98575e10	−	1.44920e10i	−0.139569	−	0.0253280i
$411$	−9.28453e10	+	2.17222e11i	−0.160499	+	0.375506i
$412$	4.58326e11	−	1.41058e12i	0.783677	−	2.41191i
$413$	−5.81929e11	−	1.08141e12i	−0.984226	−	1.82900i
$414$	2.82928e11	+	2.95919e11i	0.473341	+	0.495076i
$415$	−9.44672e9	+	1.75549e10i	−0.0156338	+	0.0290525i
$416$	−2.03707e12	+	5.62194e11i	−3.33492	+	0.920379i
$417$	5.49180e10	+	4.05421e11i	0.0889411	+	0.656590i
$418$	2.30951e11	−	1.70495e12i	0.370021	−	2.73161i
$419$	−1.09348e12	−	3.01780e11i	−1.73319	−	0.478330i	−0.750080	−	0.661347i	$-0.769985\pi$
$419$	−1.09348e12	−	3.01780e11i	−1.73319	−	0.478330i	−0.983110	+	0.183017i	$0.941414\pi$
$420$	−1.61818e11	+	1.69248e11i	−0.253749	+	0.265401i
$421$	−2.96581e11	−	9.12782e11i	−0.460123	−	1.41611i	−0.865014	−	0.501747i	$-0.832691\pi$
$421$	−2.96581e11	−	9.12782e11i	−0.460123	−	1.41611i	0.404892	−	0.914365i	$-0.367309\pi$
$422$	−3.98445e11	−	3.58607e10i	−0.611592	−	0.0550443i
$423$	5.51345e11	+	4.81696e11i	0.837321	+	0.731546i
$424$	5.58351e9	−	1.24327e11i	0.00838998	−	0.186818i
$425$	−8.33632e11			−1.23944
$426$	6.73409e11	+	4.38185e11i	0.990686	+	0.644636i
$427$	−1.22498e12			−1.78322
$428$	−8.01069e10	+	1.78372e12i	−0.115391	+	2.56939i
$429$	2.53049e11	+	2.21083e11i	0.360701	+	0.315135i
$430$	1.52476e11	+	1.37230e10i	0.215076	+	0.0193572i
$431$	4.05721e11	+	1.24868e12i	0.566343	+	1.74303i	0.663926	+	0.747798i	$0.268889\pi$
$431$	4.05721e11	+	1.24868e12i	0.566343	+	1.74303i	−0.0975826	+	0.995227i	$0.531111\pi$
$432$	−1.71009e12	+	1.78862e12i	−2.36235	+	2.47082i
$433$	4.60729e11	+	1.27153e11i	0.629869	+	0.173833i	0.566373	−	0.824149i	$-0.308346\pi$
$433$	4.60729e11	+	1.27153e11i	0.629869	+	0.173833i	0.0634963	+	0.997982i	$0.479775\pi$
$434$	2.39761e11	−	1.76998e12i	0.324395	−	2.39478i
$435$	−7.98913e9	−	5.89781e10i	−0.0106979	−	0.0789749i
$436$	9.08121e11	−	2.50626e11i	1.20352	−	0.332152i
$437$	−3.99588e11	+	7.42559e11i	−0.524138	+	0.974012i
$438$	1.20840e12	+	1.26389e12i	1.56884	+	1.64088i
$439$	−1.17291e11	−	2.17964e11i	−0.150722	−	0.280088i	0.794028	−	0.607882i	$-0.207980\pi$
$439$	−1.17291e11	−	2.17964e11i	−0.150722	−	0.280088i	−0.944749	+	0.327794i	$0.893695\pi$
$440$	−7.75926e10	+	2.38806e11i	−0.0986923	+	0.303744i
$441$	3.49198e11	−	8.16989e11i	0.439641	−	1.02859i
$442$	1.96009e12	+	3.55704e11i	2.44273	+	0.443290i
$443$	−8.60509e11	−	6.25197e11i	−1.06155	−	0.771258i	−0.0871721	−	0.996193i	$-0.527783\pi$
$443$	−8.60509e11	−	6.25197e11i	−1.06155	−	0.771258i	−0.974374	+	0.224935i	$0.927783\pi$
$444$	1.14035e12	−	1.02633e11i	1.39256	−	0.125333i
$445$	−3.98019e10	−	9.31211e10i	−0.0481153	−	0.112571i
$446$	−2.72005e11	−	1.19173e12i	−0.325514	−	1.42617i
$447$	−2.17731e11	−	3.29848e11i	−0.257950	−	0.390778i
$448$	−3.70219e12	−	2.21195e12i	−4.34217	−	2.59433i
$449$	−5.69512e11	−	7.14146e11i	−0.661294	−	0.829236i	0.332190	−	0.943213i	$-0.392213\pi$
$449$	−5.69512e11	−	7.14146e11i	−0.661294	−	0.829236i	−0.993483	+	0.113976i	$0.963641\pi$
$450$	7.61310e11	−	6.65137e11i	0.875196	−	0.764636i
$451$	−2.98116e11	+	2.16594e11i	−0.339306	+	0.246520i
$452$	−1.94727e12	+	9.37758e11i	−2.19434	+	1.05674i
$453$	3.01194e11	−	4.56289e11i	0.336050	−	0.509094i
$454$	−1.19895e12	−	4.49975e11i	−1.32450	−	0.497092i
$455$	−1.80275e11	+	1.07709e11i	−0.197190	+	0.117815i
$456$	−3.12009e12	−	1.50256e12i	−3.37929	−	1.62738i
$457$	4.65084e11	−	8.44004e10i	0.498780	−	0.0905152i	0.0766637	−	0.997057i	$-0.475573\pi$
$457$	4.65084e11	−	8.44004e10i	0.498780	−	0.0905152i	0.422116	+	0.906542i	$0.361287\pi$
$458$	−3.42573e11	+	1.50091e12i	−0.363796	+	1.59389i
$459$	1.12317e12	−	4.21531e11i	1.18110	−	0.443274i
$460$	1.22928e11	−	1.54147e11i	0.128009	−	0.160519i
$461$	−3.53433e10	−	7.86980e11i	−0.0364463	−	0.811539i	−0.931097	−	0.364772i	$-0.881147\pi$
$461$	−3.53433e10	−	7.86980e11i	−0.0364463	−	0.811539i	0.894651	−	0.446767i	$-0.147425\pi$
$462$	6.56226e10	+	1.46120e12i	0.0670139	+	1.49218i
$463$	9.86260e11	−	1.23673e12i	0.997417	−	1.25072i	0.0294709	−	0.999566i	$-0.490618\pi$
$463$	9.86260e11	−	1.23673e12i	0.997417	−	1.25072i	0.967947	−	0.251156i	$-0.0808108\pi$
$464$	3.09377e12	−	1.16111e12i	3.09854	−	1.16290i
$465$	−1.39208e10	+	6.09909e10i	−0.0138078	+	0.0604960i
$466$	−1.01172e11	+	1.83600e10i	−0.0993857	+	0.0180359i
$467$	−1.79947e12	−	8.66578e11i	−1.75073	−	0.843105i	−0.978069	−	0.208280i	$-0.933213\pi$
$467$	−1.79947e12	−	8.66578e11i	−1.75073	−	0.843105i	−0.772656	−	0.634825i	$-0.781072\pi$
$468$	−1.50735e12	+	9.00603e11i	−1.45248	+	0.867814i
$469$	−1.78405e11	−	6.69564e10i	−0.170266	−	0.0639020i
$470$	2.67229e11	−	4.04835e11i	0.252606	−	0.382682i
$471$	−6.90409e11	+	3.32484e11i	−0.646417	+	0.311298i
$472$	−3.43547e12	+	2.49602e12i	−3.18601	+	2.31477i
$473$	5.23438e11	−	4.57314e11i	0.480828	−	0.420087i
$474$	3.15953e11	+	3.96192e11i	0.287488	+	0.360498i
$475$	1.78746e12	+	1.06796e12i	1.61107	+	0.962571i
$476$	3.47216e12	+	5.26009e12i	3.10004	+	4.69637i
$477$	−9.15589e9	−	4.01146e10i	−0.00809782	−	0.0354789i
$478$	1.51918e12	+	3.55430e12i	1.33102	+	3.11407i
$479$	1.15205e12	−	1.03686e11i	0.999908	−	0.0899933i	0.422426	−	0.906397i	$-0.361178\pi$
$479$	1.15205e12	−	1.03686e11i	0.999908	−	0.0899933i	0.577481	+	0.816404i	$0.304036\pi$
$480$	2.60649e11	+	1.89372e11i	0.224115	+	0.162829i
$481$	1.01033e12	+	1.83349e11i	0.860621	+	0.156180i
$482$	1.02439e11	−	2.39668e11i	0.0864478	−	0.202255i
$483$	2.21526e11	−	6.81787e11i	0.185209	−	0.570015i
$484$	−6.56745e11	−	1.22044e12i	−0.543992	−	1.01091i
$485$	1.44546e10	+	1.51183e10i	0.0118623	+	0.0124070i
$486$	−1.11537e12	+	2.07270e12i	−0.906892	+	1.68529i
$487$	7.62819e11	−	2.10525e11i	0.614527	−	0.169599i	0.0551036	−	0.998481i	$-0.482451\pi$
$487$	7.62819e11	−	2.10525e11i	0.614527	−	0.169599i	0.559424	+	0.828882i	$0.311023\pi$
$488$	5.68600e11	+	4.19757e12i	0.453855	+	3.35049i
$489$	1.44493e11	−	1.06669e12i	0.114277	−	0.843624i
$490$	−5.67464e11	−	1.56610e11i	−0.444688	−	0.122726i
$491$	1.56184e12	−	1.63356e12i	1.21275	−	1.26843i	0.259671	−	0.965697i	$-0.416386\pi$
$491$	1.56184e12	−	1.63356e12i	1.21275	−	1.26843i	0.953075	−	0.302735i	$-0.0978997\pi$
$492$	3.67196e11	+	1.13011e12i	0.282524	+	0.869520i
$493$	−1.59554e12	−	1.43601e11i	−1.21645	−	0.109483i
$494$	−3.74710e12	−	3.27374e12i	−2.83090	−	2.47328i
$495$	−3.72454e9	+	8.29333e10i	−0.00278836	+	0.0620877i
$496$	−3.47340e12			−2.57684
$497$	−1.89419e11	+	2.27179e12i	−0.139258	+	1.67018i
$498$	4.01559e11			0.292562
$499$	6.49621e10	−	1.44649e12i	0.0469038	−	1.04439i	−0.828192	−	0.560444i	$-0.810630\pi$
$499$	6.49621e10	−	1.44649e12i	0.0469038	−	1.04439i	0.875096	−	0.483949i	$-0.160798\pi$
$500$	−7.39888e11	−	6.46421e11i	−0.529421	−	0.462541i
$501$	7.47467e11	+	6.72733e10i	0.530057	+	0.0477060i
$502$	−3.56462e11	−	1.09708e12i	−0.250522	−	0.771029i
$503$	4.73248e11	−	4.94978e11i	0.329634	−	0.344771i	−0.537120	−	0.843506i	$-0.680488\pi$
$503$	4.73248e11	−	4.94978e11i	0.329634	−	0.344771i	0.866754	+	0.498735i	$0.166202\pi$
$504$	−4.59886e12	−	1.26920e12i	−3.17477	−	0.876181i
$505$	2.32826e10	−	1.71879e11i	0.0159302	−	0.117601i
$506$	−1.65318e11	−	1.22043e12i	−0.112110	−	0.827629i
$507$	5.08180e10	−	1.40249e10i	0.0341572	−	0.00942678i
$508$	3.62965e12	−	6.74502e12i	2.41812	−	4.49362i
$509$	7.78605e11	+	8.14357e11i	0.514147	+	0.537756i	0.927996	−	0.372590i	$-0.121530\pi$
$509$	7.78605e11	+	8.14357e11i	0.514147	+	0.537756i	−0.413849	+	0.910346i	$0.635816\pi$
$510$	−1.43921e11	−	2.67449e11i	−0.0942014	−	0.175055i
$511$	−1.53322e12	+	4.71877e12i	−0.994744	+	3.06151i
$512$	−3.90099e11	+	9.12682e11i	−0.250877	+	0.586955i
$513$	−2.94829e12	−	5.35036e11i	−1.87950	−	0.341079i
$514$	5.03264e10	+	3.65643e10i	0.0318026	+	0.0231059i
$515$	−2.01978e11	+	1.81784e10i	−0.126524	+	0.0113874i
$516$	−8.80921e11	−	2.06102e12i	−0.547033	−	1.27985i
$517$	−4.90074e11	−	2.14715e12i	−0.301685	−	1.32177i
$518$	2.46235e12	+	3.73030e12i	1.50268	+	2.27646i
$519$	8.32238e10	+	4.97239e10i	0.0503494	+	0.0300824i
$520$	4.52759e11	+	5.67741e11i	0.271551	+	0.340514i
$521$	1.68175e12	−	1.46930e12i	0.999982	−	0.873658i	0.00799142	−	0.999968i	$-0.497456\pi$
$521$	1.68175e12	−	1.46930e12i	0.999982	−	0.873658i	0.991991	+	0.126310i	$0.0403134\pi$
$522$	1.57169e12	−	1.14190e12i	0.926510	−	0.673149i
$523$	2.37104e11	−	1.14183e11i	0.138574	−	0.0667336i	−0.363312	−	0.931668i	$-0.618354\pi$
$523$	2.37104e11	−	1.14183e11i	0.138574	−	0.0667336i	0.501886	+	0.864934i	$0.332640\pi$
$524$	2.12493e12	−	3.21913e12i	1.23127	−	1.86530i
$525$	−1.65727e12	−	6.21986e11i	−0.952089	−	0.357325i
$526$	−2.04936e12	+	1.22444e12i	−1.16730	+	0.697430i
$527$	1.51713e12	+	7.30609e11i	0.856789	+	0.412608i
$528$	2.79866e12	−	5.07881e11i	1.56710	−	0.284387i
$529$	2.66479e11	−	1.16752e12i	0.147949	−	0.648206i
$530$	−2.55235e10	+	9.57915e9i	−0.0140508	+	0.00527334i
$531$	−8.75359e11	+	1.09767e12i	−0.477816	+	0.599163i
$532$	−7.06289e11	−	1.57267e13i	−0.382278	−	8.51209i
$533$	4.78116e10	+	1.06461e12i	0.0256603	+	0.571370i
$534$	−1.27186e12	+	1.59486e12i	−0.676867	+	0.848764i
$535$	2.28567e11	−	8.57826e10i	0.120621	−	0.0452697i
$536$	−1.46625e11	+	6.42407e11i	−0.0767304	+	0.336178i
$537$	−4.95101e11	+	8.98476e10i	−0.256927	+	0.0466253i
$538$	−3.01475e11	−	1.45183e11i	−0.155143	−	0.0747127i
$539$	−2.29440e12	+	1.37084e12i	−1.17090	+	0.699580i
$540$	6.55933e11	+	2.46176e11i	0.331961	+	0.124587i
$541$	1.45805e12	−	2.20885e12i	0.731788	−	1.10861i	−0.258011	−	0.966142i	$-0.583067\pi$
$541$	1.45805e12	−	2.20885e12i	0.731788	−	1.10861i	0.989799	−	0.142470i	$-0.0455044\pi$
$542$	−8.44147e11	+	4.06520e11i	−0.420166	+	0.202341i
$543$	−9.38551e11	+	6.81897e11i	−0.463296	+	0.336604i
$544$	6.53061e12	−	5.70562e12i	3.19712	−	2.79324i
$545$	−8.03115e10	−	1.00707e11i	−0.0389936	−	0.0488964i
$546$	3.63129e12	+	2.16960e12i	1.74862	+	1.04475i
$547$	−5.21800e10	−	7.90494e10i	−0.0249208	−	0.0377533i	0.821899	−	0.569633i	$-0.192915\pi$
$547$	−5.21800e10	−	7.90494e10i	−0.0249208	−	0.0377533i	−0.846820	+	0.531879i	$0.821486\pi$
$548$	8.26315e11	+	3.62032e12i	0.391411	+	1.71488i
$549$	5.50421e11	+	1.28777e12i	0.258595	+	0.605012i
$550$	−3.02884e12	+	2.72601e11i	−1.41138	+	0.127027i
$551$	3.23716e12	+	2.35193e12i	1.49617	+	1.08703i
$552$	−2.43906e12	−	4.42625e11i	−1.11814	−	0.202913i
$553$	−5.65121e11	+	1.32217e12i	−0.256968	+	0.601206i
$554$	−2.33228e12	+	7.17801e12i	−1.05193	+	3.23750i
$555$	−7.41843e10	−	1.37858e11i	−0.0331890	−	0.0616754i
$556$	4.44434e12	+	4.64841e12i	1.97229	+	2.06285i
$557$	−5.72116e11	+	1.06317e12i	−0.251847	+	0.468009i	−0.974858	−	0.222827i	$-0.928472\pi$
$557$	−5.72116e11	+	1.06317e12i	−0.251847	+	0.468009i	0.723012	+	0.690836i	$0.242757\pi$
$558$	−1.96844e12	+	5.43256e11i	−0.859546	+	0.237220i
$559$	−2.69829e11	−	1.99196e12i	−0.116879	−	0.862833i
$560$	−2.38615e11	+	1.76152e12i	−0.102530	+	0.756907i
$561$	−1.32924e12	−	3.66846e11i	−0.566590	−	0.156369i
$562$	9.51105e11	−	9.94778e11i	0.402175	−	0.420642i
$563$	−2.24912e11	−	6.92208e11i	−0.0943463	−	0.290368i	0.892736	−	0.450579i	$-0.148782\pi$
$563$	−2.24912e11	−	6.92208e11i	−0.0943463	−	0.290368i	−0.987083	+	0.160211i	$0.948782\pi$
$564$	−7.07337e12	−	6.36615e11i	−2.94355	−	0.264924i
$565$	2.22545e11	+	1.94432e11i	0.0918756	+	0.0802693i
$566$	3.10949e11	−	6.92382e12i	0.127355	−	2.83577i
$567$	−3.29123e9			−0.00133732
$568$	7.87251e12	−	4.05426e11i	3.17355	−	0.163435i
$569$	2.93540e12			1.17398			0.586991	−	0.809593i	$-0.300312\pi$
$569$	2.93540e12			1.17398			0.586991	+	0.809593i	$0.300312\pi$
$570$	−3.40344e10	+	7.57835e11i	−0.0135046	+	0.300703i
$571$	3.00273e12	+	2.62341e12i	1.18210	+	1.03277i	0.998763	+	0.0497194i	$0.0158327\pi$
$571$	3.00273e12	+	2.62341e12i	1.18210	+	1.03277i	0.183337	+	0.983050i	$0.441310\pi$
$572$	5.26081e12	+	4.73481e11i	2.05480	+	0.184936i
$573$	−8.59961e10	−	2.64669e11i	−0.0333260	−	0.102567i
$574$	−3.20570e12	+	3.35290e12i	−1.23259	+	1.28919i
$575$	1.43676e12	+	3.96520e11i	0.548123	+	0.151272i
$576$	−6.61834e11	+	4.88585e12i	−0.250523	+	1.84944i
$577$	4.45792e11	+	3.29097e12i	0.167433	+	1.23604i	0.858334	+	0.513091i	$0.171500\pi$
$577$	4.45792e11	+	3.29097e12i	0.167433	+	1.23604i	−0.690901	+	0.722949i	$0.742786\pi$
$578$	−2.93123e12	+	8.08969e11i	−1.09238	+	0.301479i
$579$	−6.30452e10	+	1.17158e11i	−0.0233130	+	0.0433229i
$580$	−6.46535e11	−	6.76222e11i	−0.237228	−	0.248121i
$581$	5.39928e11	+	1.00335e12i	0.196582	+	0.365310i
$582$	1.30196e11	−	4.00702e11i	0.0470375	−	0.144767i
$583$	−4.86467e10	+	1.13815e11i	−0.0174399	+	0.0408027i
$584$	1.68812e13	+	3.06349e12i	6.00545	+	1.08983i
$585$	1.94233e11	+	1.41119e11i	0.0685681	+	0.0498176i
$586$	−9.80714e12	+	8.82659e11i	−3.43560	+	0.309210i
$587$	2.13525e11	+	4.99566e11i	0.0742296	+	0.173669i	0.952533	−	0.304434i	$-0.0984674\pi$
$587$	2.13525e11	+	4.99566e11i	0.0742296	+	0.173669i	−0.878304	+	0.478103i	$0.841325\pi$
$588$	1.91784e12	+	8.40262e12i	0.661630	+	2.89879i
$589$	−2.31702e12	−	3.51013e12i	−0.793251	−	1.20172i
$590$	7.98542e11	+	4.77107e11i	0.271309	+	0.162099i
$591$	−7.80161e11	−	9.78291e11i	−0.263051	−	0.329856i
$592$	6.54566e12	−	5.71877e12i	2.19031	−	1.91362i
$593$	2.23840e12	−	1.62630e12i	0.743348	−	0.540074i	−0.150410	−	0.988624i	$-0.548059\pi$
$593$	2.23840e12	−	1.62630e12i	0.743348	−	0.540074i	0.893758	+	0.448550i	$0.148059\pi$
$594$	3.94296e12	−	1.89883e12i	1.29952	−	0.625817i
$595$	4.74749e11	−	7.19214e11i	0.155288	−	0.235251i
$596$	−5.81661e12	−	2.18301e12i	−1.88826	−	0.708675i
$597$	1.99221e11	−	1.19029e11i	0.0641875	−	0.0383502i
$598$	−3.20900e12	−	1.54537e12i	−1.02616	−	0.494172i
$599$	2.30227e12	−	4.17800e11i	0.730693	−	0.132601i	0.199555	−	0.979887i	$-0.436050\pi$
$599$	2.30227e12	−	4.17800e11i	0.730693	−	0.132601i	0.531138	+	0.847285i	$0.321765\pi$
$600$	−1.36206e12	+	5.96759e12i	−0.429058	+	1.87983i
$601$	−5.21186e12	+	1.95604e12i	−1.62951	+	0.611566i	−0.987848	−	0.155422i	$-0.950326\pi$
$601$	−5.21186e12	+	1.95604e12i	−1.62951	+	0.611566i	−0.641662	+	0.766987i	$0.721755\pi$
$602$	5.45552e12	−	6.84100e12i	1.69298	−	2.12293i
$603$	9.77400e9	+	2.17635e11i	0.00301054	+	0.0670349i
$604$	−3.85582e11	−	8.58565e12i	−0.117883	−	2.62486i
$605$	−1.18150e11	+	1.48155e11i	−0.0358537	+	0.0449591i
$606$	−3.27101e12	+	1.22763e12i	−0.985271	+	0.369778i
$607$	−8.72286e10	+	3.82174e11i	−0.0260801	+	0.114265i	−0.986293	−	0.165006i	$-0.947236\pi$
$607$	−8.72286e10	+	3.82174e11i	−0.0260801	+	0.114265i	0.960212	+	0.279271i	$0.0900927\pi$
$608$	−2.13122e13	+	3.86760e12i	−6.32503	+	1.14782i
$609$	−3.06481e12	−	1.47594e12i	−0.902871	−	0.434800i
$610$	7.96555e11	−	4.75919e11i	0.232933	−	0.139171i
$611$	−5.96314e12	−	2.23800e12i	−1.73097	−	0.649644i
$612$	3.96958e12	−	6.01365e12i	1.14383	−	1.73283i
$613$	−2.08870e11	+	1.00587e11i	−0.0597454	+	0.0287718i	−0.463518	−	0.886088i	$-0.653413\pi$
$613$	−2.08870e11	+	1.00587e11i	−0.0597454	+	0.0287718i	0.403773	+	0.914859i	$0.367699\pi$
$614$	−1.65877e12	+	1.20516e12i	−0.471007	+	0.342207i
$615$	1.22354e11	−	1.06897e11i	0.0344889	−	0.0301320i
$616$	8.94792e12	+	1.12203e13i	2.50385	+	3.13973i
$617$	−3.55873e12	−	2.12624e12i	−0.988580	−	0.590649i	−0.0749465	−	0.997188i	$-0.523879\pi$
$617$	−3.55873e12	−	2.12624e12i	−0.988580	−	0.590649i	−0.913634	+	0.406538i	$0.866736\pi$
$618$	2.25037e12	+	3.40916e12i	0.620591	+	0.940155i
$619$	6.82036e11	+	2.98819e12i	0.186724	+	0.818089i	0.978329	+	0.207057i	$0.0663885\pi$
$619$	6.82036e11	+	2.98819e12i	0.186724	+	0.818089i	−0.791605	+	0.611033i	$0.790754\pi$
$620$	3.86498e11	+	9.04257e11i	0.105047	+	0.245770i
$621$	−2.13627e12	+	1.92268e11i	−0.576426	+	0.0518793i
$622$	3.22510e12	+	2.34317e12i	0.863947	+	0.627694i
$623$	−5.69511e12	−	1.03351e12i	−1.51463	−	0.274864i
$624$	3.23299e12	−	7.56397e12i	0.853639	−	1.99719i
$625$	1.11635e12	−	3.43578e12i	0.292645	−	0.900668i
$626$	−1.17828e12	−	2.18961e12i	−0.306665	−	0.569880i
$627$	2.38016e12	+	2.48945e12i	0.615039	+	0.643280i
$628$	−5.70808e12	+	1.06074e13i	−1.46444	+	2.72138i
$629$	−4.06194e12	+	1.12103e12i	−1.03468	+	0.285553i
$630$	1.40283e11	+	1.03561e12i	0.0354791	+	0.261917i
$631$	−1.72528e11	+	1.27365e12i	−0.0433239	+	0.319830i	0.956300	+	0.292389i	$0.0944501\pi$
$631$	−1.72528e11	+	1.27365e12i	−0.0433239	+	0.319830i	−0.999623	+	0.0274411i	$0.991264\pi$
$632$	4.79290e12	+	1.32276e12i	1.19501	+	0.329802i
$633$	5.53435e11	−	5.78847e11i	0.137009	−	0.143300i
$634$	3.07212e12	+	9.45502e12i	0.755156	+	2.32413i
$635$	−1.04308e12	−	9.38793e10i	−0.254588	−	0.0229133i
$636$	3.00578e11	+	2.62607e11i	0.0728450	+	0.0636428i
$637$	−3.46785e11	+	7.72176e12i	−0.0834511	+	1.85818i
$638$	−5.84403e12			−1.39643
$639$	2.47335e12	−	8.21653e11i	0.586856	−	0.194955i
$640$	1.36342e12			0.321233
$641$	1.65681e10	−	3.68917e11i	0.00387624	−	0.0863112i	−0.996122	−	0.0879786i	$-0.971959\pi$
$641$	1.65681e10	−	3.68917e11i	0.00387624	−	0.0863112i	0.999999	+	0.00166733i	$0.000530727\pi$
$642$	−3.70332e12	−	3.23549e12i	−0.860366	−	0.751679i
$643$	−4.10506e12	−	3.69462e11i	−0.947045	−	0.0852356i	−0.394662	−	0.918826i	$-0.629138\pi$
$643$	−4.10506e12	−	3.69462e11i	−0.947045	−	0.0852356i	−0.552383	+	0.833591i	$0.686281\pi$
$644$	−3.48225e12	−	1.07173e13i	−0.797762	−	2.45526i
$645$	−2.11787e11	+	2.21511e11i	−0.0481815	+	0.0503939i
$646$	1.96830e13	+	5.43217e12i	4.44678	+	1.22723i
$647$	−7.90396e11	+	5.83493e12i	−0.177327	+	1.30908i	0.655351	+	0.755324i	$0.272521\pi$
$647$	−7.90396e11	+	5.83493e12i	−0.177327	+	1.30908i	−0.832678	+	0.553757i	$0.813194\pi$
$648$	1.52769e9	+	1.12778e10i	0.000340367	+	0.00251269i
$649$	4.07118e12	−	1.12357e12i	0.900781	−	0.248600i
$650$	−4.16760e12	+	7.74469e12i	−0.915747	+	1.70174i
$651$	2.47095e12	+	2.58441e12i	0.539200	+	0.563959i
$652$	−8.01826e12	−	1.49004e13i	−1.73767	−	3.22912i
$653$	−1.53537e12	+	4.72538e12i	−0.330448	+	1.01701i	0.638473	+	0.769644i	$0.279566\pi$
$653$	−1.53537e12	+	4.72538e12i	−0.330448	+	1.01701i	−0.968921	+	0.247370i	$0.920434\pi$
$654$	−1.01975e12	+	2.38583e12i	−0.217969	+	0.509964i
$655$	−5.18923e11	−	9.41706e10i	−0.110158	−	0.0199908i
$656$	7.29796e12	+	5.30228e12i	1.53863	+	1.11788i
$657$	5.64958e12	−	5.08471e11i	1.18296	−	0.106469i
$658$	−1.08965e13	−	2.54937e13i	−2.26606	−	5.30172i
$659$	1.19138e12	+	5.21980e12i	0.246075	+	1.07813i	0.935377	+	0.353652i	$0.115060\pi$
$659$	1.19138e12	+	5.21980e12i	0.246075	+	1.07813i	−0.689302	+	0.724474i	$0.742083\pi$
$660$	−4.43637e11	−	6.72081e11i	−0.0910081	−	0.137871i
$661$	−2.85552e9	−	1.70609e9i	−0.000581806	−	0.000347613i	0.512608	−	0.858623i	$-0.328679\pi$
$661$	−2.85552e9	−	1.70609e9i	−0.000581806	−	0.000347613i	−0.513190	+	0.858275i	$0.671536\pi$
$662$	−5.44474e12	−	6.82748e12i	−1.10183	−	1.38166i
$663$	−3.00315e12	+	2.62377e12i	−0.603624	+	0.527370i
$664$	3.18751e12	−	2.31586e12i	0.636349	−	0.462335i
$665$	−1.93932e12	+	9.33930e11i	−0.384550	+	0.185190i
$666$	2.81511e12	−	4.26470e12i	0.554448	−	0.839953i
$667$	2.68159e12	+	1.00642e12i	0.524597	+	0.196885i
$668$	1.01273e13	−	6.05078e12i	1.96788	−	1.17576i
$669$	2.20468e12	+	1.06172e12i	0.425527	+	0.204923i
$670$	1.42022e11	−	2.57733e10i	0.0272283	−	0.00494120i
$671$	9.37451e11	−	4.10724e12i	0.178524	−	0.782166i
$672$	1.72400e13	−	6.47028e12i	3.26119	−	1.22394i
$673$	−2.44997e12	+	3.07217e12i	−0.460356	+	0.577268i	−0.956780	−	0.290812i	$-0.906075\pi$
$673$	−2.44997e12	+	3.07217e12i	−0.460356	+	0.577268i	0.496424	+	0.868080i	$0.334646\pi$
$674$	−8.98193e10	−	1.99998e12i	−0.0167649	−	0.373299i
$675$	2.37619e11	+	5.29100e12i	0.0440569	+	0.981003i
$676$	5.16680e11	−	6.47897e11i	0.0951616	−	0.119329i
$677$	8.60613e12	−	3.22994e12i	1.57456	−	0.590942i	0.597119	−	0.802153i	$-0.296312\pi$
$677$	8.60613e12	−	3.22994e12i	1.57456	−	0.590942i	0.977441	+	0.211211i	$0.0677406\pi$
$678$	1.32458e12	−	5.80337e12i	0.240738	−	1.05474i
$679$	1.17627e12	−	2.13462e11i	0.212370	−	0.0385395i
$680$	−2.68485e12	−	1.29295e12i	−0.481537	−	0.231896i
$681$	2.20070e12	−	1.31486e12i	0.392102	−	0.234270i
$682$	5.75109e12	+	2.15842e12i	1.01794	+	0.382038i
$683$	2.65339e12	−	4.01972e12i	0.466561	−	0.706809i	−0.522774	−	0.852472i	$-0.675103\pi$
$683$	2.65339e12	−	4.01972e12i	0.466561	−	0.706809i	0.989334	+	0.145662i	$0.0465312\pi$
$684$	−1.62155e13	+	7.80898e12i	−2.83256	+	1.36409i
$685$	4.10769e11	−	2.98441e11i	0.0712836	−	0.0517906i
$686$	−1.13305e13	+	9.89916e12i	−1.95340	+	1.70663i
$687$	−1.92150e12	−	2.40948e12i	−0.329105	−	0.412685i
$688$	−1.46069e13	−	8.72723e12i	−2.48548	−	1.48501i
$689$	1.97198e11	+	2.98742e11i	0.0333362	+	0.0505022i
$690$	1.20833e11	+	5.29403e11i	0.0202938	+	0.0889130i
$691$	−2.09891e12	−	4.91065e12i	−0.350222	−	0.819385i	−0.998326	−	0.0578335i	$-0.981581\pi$
$691$	−2.09891e12	−	4.91065e12i	−0.350222	−	0.819385i	0.648104	−	0.761552i	$-0.275562\pi$
$692$	1.51781e12	−	1.36605e11i	0.251616	−	0.0226459i
$693$	3.83865e12	+	2.78894e12i	0.632236	+	0.459346i
$694$	6.88488e12	+	1.24942e12i	1.12662	+	0.204452i
$695$	3.45601e11	−	8.08573e11i	0.0561879	−	0.131458i
$696$	−3.63490e12	+	1.11871e13i	−0.587153	+	1.80707i
$697$	−2.07233e12	−	3.85103e12i	−0.332591	−	0.618058i
$698$	−9.50954e11	−	9.94620e11i	−0.151639	−	0.158602i
$699$	9.75402e10	−	1.81260e11i	0.0154538	−	0.0287181i
$700$	−2.68229e13	+	7.40264e12i	−4.22244	+	1.16532i
$701$	6.33725e11	+	4.67835e12i	0.0991220	+	0.731748i	0.970494	+	0.241125i	$0.0775164\pi$
$701$	6.33725e11	+	4.67835e12i	0.0991220	+	0.731748i	−0.871372	+	0.490623i	$0.836769\pi$
$702$	1.69892e12	−	1.25419e13i	0.264031	−	1.94916i
$703$	1.01457e13	+	2.80003e12i	1.56669	+	0.432378i
$704$	1.02497e13	−	1.07203e13i	1.57265	−	1.64486i
$705$	3.00072e11	+	9.23527e11i	0.0457482	+	0.140799i
$706$	1.60308e13	+	1.44279e12i	2.42847	+	0.218566i
$707$	−7.46556e12	−	6.52246e12i	−1.12376	−	0.981803i
$708$	6.11018e11	−	1.36054e13i	0.0913912	−	2.03498i
$709$	1.05567e13			1.56899			0.784495	−	0.620136i	$-0.212922\pi$
$709$	1.05567e13			1.56899			0.784495	+	0.620136i	$0.212922\pi$
$710$	−7.59443e11	−	1.55084e12i	−0.112159	−	0.229036i
$711$	1.64386e12			0.241242
$712$	−8.97967e11	+	1.99948e13i	−0.130949	+	2.91580i
$713$	−2.26723e12	−	1.98082e12i	−0.328544	−	0.287040i
$714$	−1.72889e13	−	1.55603e12i	−2.48958	−	0.224066i
$715$	−2.23178e11	−	6.86871e11i	−0.0319355	−	0.0982874i
$716$	−5.46616e12	+	5.71715e12i	−0.777273	+	0.812964i
$717$	−7.45896e12	−	2.05854e12i	−1.05400	−	0.290887i
$718$	2.79733e12	−	2.06507e13i	0.392811	−	2.89985i
$719$	1.95486e11	+	1.44313e12i	0.0272794	+	0.201385i	0.999460	−	0.0328461i	$-0.0104571\pi$
$719$	1.95486e11	+	1.44313e12i	0.0272794	+	0.201385i	−0.972181	+	0.234231i	$0.924743\pi$
$720$	1.95904e12	−	5.40660e11i	0.271673	−	0.0749769i
$721$	−5.49249e12	+	1.02068e13i	−0.756939	+	1.40663i
$722$	−2.55905e13	−	2.67656e13i	−3.50479	−	3.66572i
$723$	2.47248e11	+	4.59464e11i	0.0336520	+	0.0625358i
$724$	−5.63531e12	+	1.73437e13i	−0.762244	+	2.34595i
$725$	2.77968e12	−	6.50339e12i	0.373658	−	0.874216i
$726$	3.75573e12	+	6.81564e11i	0.501740	+	0.0910525i
$727$	6.92750e12	+	5.03312e12i	0.919754	+	0.668240i	0.943463	−	0.331479i	$-0.107548\pi$
$727$	6.92750e12	+	5.03312e12i	0.919754	+	0.668240i	−0.0237090	+	0.999719i	$0.507548\pi$
$728$	4.13371e13	−	3.72041e12i	5.45442	−	0.490907i
$729$	−1.84948e12	−	4.32707e12i	−0.242536	−	0.567440i
$730$	−8.36306e11	−	3.66409e12i	−0.108996	−	0.477544i
$731$	4.54434e12	+	6.88439e12i	0.588631	+	0.891737i
$732$	−1.16622e13	−	6.96783e12i	−1.50134	−	0.897011i
$733$	5.25288e11	+	6.58690e11i	0.0672093	+	0.0842779i	0.814300	−	0.580445i	$-0.197121\pi$
$733$	5.25288e11	+	6.58690e11i	0.0672093	+	0.0842779i	−0.747090	+	0.664722i	$0.768550\pi$
$734$	−6.54591e12	+	5.71899e12i	−0.832411	+	0.727256i
$735$	9.53377e11	−	6.92669e11i	0.120496	−	0.0875453i
$736$	−1.39693e13	+	6.72728e12i	−1.75479	+	0.845063i
$737$	3.61027e11	−	5.46933e11i	0.0450750	−	0.0682858i
$738$	4.96519e12	+	1.86347e12i	0.616144	+	0.231243i
$739$	−5.87282e12	+	3.50885e12i	−0.724347	+	0.432777i	−0.827191	−	0.561920i	$-0.810063\pi$
$739$	−5.87282e12	+	3.50885e12i	−0.724347	+	0.432777i	0.102844	+	0.994697i	$0.467206\pi$
$740$	−2.21717e12	−	1.06773e12i	−0.271804	−	0.130894i
$741$	9.80059e12	−	1.77855e12i	1.19418	−	0.216712i
$742$	−3.46722e11	+	1.51909e12i	−0.0419918	+	0.183978i
$743$	−9.15572e12	+	3.43620e12i	−1.10216	+	0.413646i	−0.835135	−	0.550045i	$-0.814611\pi$
$743$	−9.15572e12	+	3.43620e12i	−1.10216	+	0.413646i	−0.267021	+	0.963691i	$0.586039\pi$
$744$	7.70891e12	−	9.66666e12i	0.922390	−	1.15664i
$745$	3.81115e10	+	8.48617e11i	0.00453265	+	0.100927i
$746$	−5.59373e11	−	1.24554e13i	−0.0661267	−	1.47242i
$747$	8.12179e11	−	1.01844e12i	0.0954353	−	0.119672i
$748$	−2.02937e13	+	7.61636e12i	−2.37031	+	0.889591i
$749$	3.10495e12	−	1.36037e13i	0.360484	−	1.57938i
$750$	2.66247e12	−	4.83167e11i	0.307262	−	0.0557599i
$751$	1.54544e13	+	7.44247e12i	1.77286	+	0.853763i	0.964064	+	0.265671i	$0.0855934\pi$
$751$	1.54544e13	+	7.44247e12i	1.77286	+	0.853763i	0.808794	+	0.588093i	$0.200121\pi$
$752$	−4.62829e13	+	2.76528e13i	−5.27765	+	3.15325i
$753$	2.16195e12	+	8.11392e11i	0.245057	+	0.0919715i
$754$	−9.31070e12	+	1.41051e13i	−1.04909	+	1.58930i
$755$	−1.05873e12	+	5.09857e11i	−0.118583	+	0.0571067i
$756$	3.23957e13	−	2.35368e13i	3.60694	−	2.62059i
$757$	1.49531e12	−	1.30641e12i	0.165500	−	0.144593i	−0.571204	−	0.820808i	$-0.693524\pi$
$757$	1.49531e12	−	1.30641e12i	0.165500	−	0.144593i	0.736705	+	0.676214i	$0.236381\pi$
$758$	1.92824e12	+	2.41793e12i	0.212153	+	0.266031i
$759$	2.11643e12	+	1.26451e12i	0.231482	+	0.138304i
$760$	4.10041e12	+	6.21186e12i	0.445827	+	0.675399i
$761$	1.00703e12	+	4.41211e12i	0.108846	+	0.476886i	0.999743	+	0.0226802i	$0.00721994\pi$
$761$	1.00703e12	+	4.41211e12i	0.108846	+	0.476886i	−0.890897	+	0.454206i	$0.849923\pi$
$762$	8.29120e12	+	1.93982e13i	0.890882	+	2.08432i
$763$	−7.33248e12	+	6.59935e11i	−0.783232	+	0.0704922i
$764$	−3.53907e12	−	2.57128e12i	−0.375810	−	0.273042i
$765$	−9.69399e11	−	1.75920e11i	−0.102335	−	0.0185711i
$766$	−6.70844e12	+	1.56952e13i	−0.704032	+	1.64716i
$767$	3.77435e12	−	1.16162e13i	0.393788	−	1.21196i
$768$	−4.49649e12	−	8.35587e12i	−0.466388	−	0.866695i
$769$	6.98000e11	+	7.30051e11i	0.0719759	+	0.0752809i	0.757802	−	0.652485i	$-0.226273\pi$
$769$	6.98000e11	+	7.30051e11i	0.0719759	+	0.0752809i	−0.685826	+	0.727765i	$0.740559\pi$
$770$	1.48972e12	−	2.76837e12i	0.152720	−	0.283802i
$771$	−1.20041e11	+	3.31291e10i	−0.0122344	+	0.00337649i
$772$	2.80730e11	+	2.07244e12i	0.0284454	+	0.209992i
$773$	9.78313e11	−	7.22219e12i	0.0985530	−	0.727548i	−0.872488	−	0.488635i	$-0.837495\pi$
$773$	9.78313e11	−	7.22219e12i	0.0985530	−	0.727548i	0.971041	−	0.238912i	$-0.0767909\pi$
$774$	−9.64299e12	−	2.66130e12i	−0.965779	−	0.266538i
$775$	−5.13742e12	+	5.37332e12i	−0.511549	+	0.535038i
$776$	−1.27745e12	−	3.93158e12i	−0.126463	−	0.389214i
$777$	−8.91162e12	−	8.02061e11i	−0.877127	−	0.0789428i
$778$	−8.31962e12	−	7.26863e12i	−0.814133	−	0.711286i
$779$	−4.90065e11	+	1.09121e13i	−0.0476799	+	1.06167i
$780$	−2.32893e12			−0.225284
$781$	−7.47211e12	−	2.37365e12i	−0.718644	−	0.228290i
$782$	1.46162e13			1.39766
$783$	−4.56631e11	+	1.01677e13i	−0.0434148	+	0.966705i
$784$	4.92727e13	+	4.30483e13i	4.65783	+	4.06943i
$785$	1.64038e12	+	1.47637e11i	0.154181	+	0.0138765i
$786$	3.28282e12	+	1.01035e13i	0.306793	+	0.944212i
$787$	1.04137e13	−	1.08919e13i	0.967650	−	1.01208i	−0.0322704	−	0.999479i	$-0.510274\pi$
$787$	1.04137e13	−	1.08919e13i	0.967650	−	1.01208i	0.999921	−	0.0126036i	$-0.00401194\pi$
$788$	−1.89605e13	−	5.23277e12i	−1.75179	−	0.483464i
$789$	6.41496e11	−	4.73571e12i	0.0589315	−	0.435049i
$790$	−1.46202e11	−	1.07930e12i	−0.0133546	−	0.0985876i
$791$	1.62816e13	−	4.49343e12i	1.47878	−	0.408116i
$792$	7.77491e12	−	1.44482e13i	0.702154	−	1.30482i
$793$	−8.41966e12	−	8.80627e12i	−0.756076	−	0.790793i
$794$	−6.01963e11	−	1.11863e12i	−0.0537499	−	0.0998840i
$795$	1.68643e10	−	5.19029e10i	0.00149732	−	0.00460829i
$796$	1.43376e12	−	3.35444e12i	0.126581	−	0.296150i
$797$	−1.51874e13	−	2.75612e12i	−1.33328	−	0.241955i	−0.535314	−	0.844653i	$-0.679807\pi$
$797$	−1.51874e13	−	2.75612e12i	−1.33328	−	0.241955i	−0.797969	+	0.602698i	$0.794092\pi$
$798$	3.50772e13	+	2.54851e13i	3.06205	+	2.22471i
$799$	2.60322e13	−	2.34294e12i	2.25970	−	0.203376i
$800$	1.50471e13	+	3.52045e13i	1.29882	+	3.03874i
$801$	1.47249e12	+	6.45142e12i	0.126388	+	0.553744i
$802$	8.59160e12	+	1.30157e13i	0.733313	+	1.11092i
$803$	−1.46482e13	−	8.75191e12i	−1.24327	−	0.742819i
$804$	−1.31761e12	−	1.65223e12i	−0.111208	−	0.139450i
$805$	−1.16032e12	+	1.01374e12i	−0.0973861	+	0.0850836i
$806$	1.43722e13	−	1.04420e13i	1.19954	−	0.871517i
$807$	6.03504e11	−	2.90632e11i	0.0500898	−	0.0241220i
$808$	−1.88848e13	+	2.86093e13i	−1.55870	+	2.36133i
$809$	1.38543e13	+	5.19960e12i	1.13714	+	0.426778i	0.847731	−	0.530426i	$-0.177968\pi$
$809$	1.38543e13	+	5.19960e12i	1.13714	+	0.426778i	0.289414	+	0.957204i	$0.406540\pi$
$810$	2.14015e9	−	1.27868e9i	0.000174687	−	0.000104371i
$811$	−8.87767e12	−	4.27526e12i	−0.720618	−	0.347031i	0.0373687	−	0.999302i	$-0.488102\pi$
$811$	−8.87767e12	−	4.27526e12i	−0.720618	−	0.347031i	−0.757986	+	0.652270i	$0.773817\pi$
$812$	−5.26130e13	+	9.54785e12i	−4.24708	+	0.770732i
$813$	4.17358e11	−	1.82856e12i	0.0335043	−	0.146792i
$814$	−1.43917e13	+	5.40130e12i	−1.14895	+	0.431210i
$815$	−1.44250e12	+	1.80884e12i	−0.114527	+	0.143612i
$816$	1.51448e12	+	3.37225e13i	0.119580	+	2.66265i
$817$	−9.24387e11	−	2.05831e13i	−0.0725863	−	1.61626i
$818$	−1.26571e13	+	1.58714e13i	−0.988423	+	1.23944i
$819$	1.28471e13	−	4.82160e12i	0.997763	−	0.374467i
$820$	5.68312e11	−	2.48994e12i	0.0438959	−	0.192321i
$821$	−1.94428e13	+	3.52835e12i	−1.49353	+	0.271036i	−0.863031	−	0.505151i	$-0.831437\pi$
$821$	−1.94428e13	+	3.52835e12i	−1.49353	+	0.271036i	−0.630502	+	0.776187i	$0.717151\pi$
$822$	−9.21458e12	−	4.43751e12i	−0.703967	−	0.339013i
$823$	−1.43327e10	+	8.56339e9i	−0.00108900	+	0.000650648i	−0.513444	−	0.858123i	$-0.671630\pi$
$823$	−1.43327e10	+	8.56339e9i	−0.00108900	+	0.000650648i	0.512355	+	0.858774i	$0.328773\pi$
$824$	3.75243e13	+	1.40831e13i	2.83557	+	1.06421i
$825$	3.35373e12	−	5.08068e12i	0.252049	−	0.381838i
$826$	4.79014e13	−	2.30681e13i	3.58045	−	1.72425i
$827$	−3.60541e12	+	2.61949e12i	−0.268028	+	0.194734i	−0.713679	−	0.700473i	$-0.752972\pi$
$827$	−3.60541e12	+	2.61949e12i	−0.268028	+	0.194734i	0.445651	+	0.895207i	$0.352972\pi$
$828$	−9.70194e12	+	8.47633e12i	−0.717335	+	0.626717i
$829$	5.88251e12	+	7.37643e12i	0.432581	+	0.542439i	0.949571	−	0.313552i	$-0.101519\pi$
$829$	5.88251e12	+	7.37643e12i	0.432581	+	0.542439i	−0.516990	+	0.855991i	$0.672948\pi$
$830$	−7.40906e11	−	4.42671e11i	−0.0541891	−	0.0323765i
$831$	−8.32334e12	−	1.26093e13i	−0.605470	−	0.917249i
$832$	−9.54469e12	−	4.18180e13i	−0.690569	−	3.02558i
$833$	−1.24666e13	−	2.91670e13i	−0.897107	−	2.09889i
$834$	−1.76412e13	+	1.58774e12i	−1.26265	+	0.113640i
$835$	−1.30497e12	−	9.48118e11i	−0.0928992	−	0.0674952i
$836$	5.32707e13	+	9.66720e12i	3.77190	+	0.684499i
$837$	4.20467e12	−	9.83732e12i	0.296120	−	0.692807i
$838$	1.51760e13	−	4.67069e13i	1.06306	−	3.27177i
$839$	−2.89685e12	−	5.38325e12i	−0.201835	−	0.375073i	0.759477	−	0.650534i	$-0.225455\pi$
$839$	−2.89685e12	−	5.38325e12i	−0.201835	−	0.375073i	−0.961312	+	0.275462i	$0.911169\pi$
$840$	−4.37283e12	−	4.57362e12i	−0.303044	−	0.316959i
$841$	−4.34020e11	+	8.06544e11i	−0.0299177	+	0.0555963i
$842$	4.00541e13	−	1.10542e13i	2.74627	−	0.757921i
$843$	3.69829e11	+	2.73018e12i	0.0252218	+	0.186195i
$844$	1.68983e12	−	1.24749e13i	0.114631	−	0.846242i
$845$	−1.09224e11	−	3.01439e10i	−0.00736991	−	0.00203397i
$846$	−2.19044e13	+	2.29102e13i	−1.47016	+	1.53767i
$847$	3.34688e12	+	1.03006e13i	0.223442	+	0.687684i
$848$	3.01784e12	+	2.71611e11i	0.200408	+	0.0180371i
$849$	1.04484e13	+	9.12847e12i	0.690183	+	0.602994i
$850$	1.61922e12	−	3.60548e13i	0.106395	−	2.36907i
$851$	7.53394e12			0.492424
$852$	−1.47255e13	+	2.05506e13i	−0.957396	+	1.33613i
$853$	1.05075e13			0.679562			0.339781	−	0.940505i	$-0.389647\pi$
$853$	1.05075e13			0.679562			0.339781	+	0.940505i	$0.389647\pi$
$854$	2.37937e12	−	5.29808e13i	0.153074	−	3.40846i
$855$	1.85320e12	+	1.61909e12i	0.118597	+	0.103615i
$856$	−4.80560e13	−	4.32512e12i	−3.05926	−	0.275338i
$857$	−6.62444e12	−	2.03879e13i	−0.419504	−	1.29110i	−0.908160	−	0.418623i	$-0.862513\pi$
$857$	−6.62444e12	−	2.03879e13i	−0.419504	−	1.29110i	0.488657	−	0.872476i	$-0.337487\pi$
$858$	−1.00534e13	+	1.05150e13i	−0.633315	+	0.662395i
$859$	2.72934e13	+	7.53249e12i	1.71036	+	0.472030i	0.977951	−	0.208834i	$-0.0669670\pi$
$859$	2.72934e13	+	7.53249e12i	1.71036	+	0.472030i	0.732410	+	0.680864i	$0.238396\pi$
$860$	−6.46661e11	+	4.77384e12i	−0.0403119	+	0.297595i
$861$	−1.24651e12	−	9.20210e12i	−0.0773003	−	0.570654i
$862$	−5.47938e13	+	1.51221e13i	−3.38025	+	0.932889i
$863$	−1.16066e13	+	2.15686e13i	−0.712287	+	1.32365i	0.224749	+	0.974417i	$0.427844\pi$
$863$	−1.16066e13	+	2.15686e13i	−0.712287	+	1.32365i	−0.937036	+	0.349233i	$0.886442\pi$
$864$	−3.80746e13	−	3.98229e13i	−2.32447	−	2.43120i
$865$	−9.87395e10	−	1.83489e11i	−0.00599678	−	0.0111439i
$866$	−6.39431e12	+	1.96797e13i	−0.386334	+	1.18901i
$867$	2.39243e12	−	5.59737e12i	0.143798	−	0.336433i
$868$	5.53026e13	+	1.00360e13i	3.30679	+	0.600095i
$869$	−4.00062e12	−	2.90662e12i	−0.237979	−	0.172902i
$870$	2.56634e12	−	2.30974e11i	0.151872	−	0.0136687i
$871$	−7.44884e11	−	1.74274e12i	−0.0438538	−	0.102601i
$872$	5.66487e12	+	2.48194e13i	0.331792	+	1.45368i
$873$	−7.52938e11	−	1.14065e12i	−0.0438728	−	0.0664644i
$874$	−3.13397e13	−	1.87246e13i	−1.81674	−	1.08545i
$875$	4.78717e12	+	6.00292e12i	0.276085	+	0.346199i
$876$	−4.14376e13	+	3.62030e13i	−2.37753	+	2.07719i
$877$	−7.48729e12	+	5.43984e12i	−0.427392	+	0.310519i	−0.780605	−	0.625024i	$-0.785089\pi$
$877$	−7.48729e12	+	5.43984e12i	−0.427392	+	0.310519i	0.353213	+	0.935543i	$0.385089\pi$
$878$	9.65480e12	−	4.64951e12i	0.548300	−	0.264047i
$879$	1.08591e13	−	1.64508e13i	0.613541	−	0.929476i
$880$	−5.72361e12	−	2.14811e12i	−0.321735	−	0.120749i
$881$	−9.97363e12	+	5.95897e12i	−0.557779	+	0.333257i	−0.763967	−	0.645255i	$-0.776751\pi$
$881$	−9.97363e12	+	5.95897e12i	−0.557779	+	0.333257i	0.206189	+	0.978512i	$0.433894\pi$
$882$	3.46567e13	+	1.66898e13i	1.92832	+	0.928629i
$883$	2.08204e13	−	3.77834e12i	1.15256	−	0.209160i	0.431556	−	0.902086i	$-0.357965\pi$
$883$	2.08204e13	−	3.77834e12i	1.15256	−	0.209160i	0.721008	+	0.692927i	$0.243679\pi$
$884$	−1.39491e13	+	6.11151e13i	−0.768266	+	3.36599i
$885$	−1.74340e12	+	6.54309e11i	−0.0955328	+	0.0358541i
$886$	2.87113e13	−	3.60029e13i	1.56531	−	1.96284i
$887$	−2.67530e11	−	5.95701e12i	−0.0145116	−	0.323126i	−0.993098	−	0.117289i	$-0.962580\pi$
$887$	−2.67530e11	−	5.95701e12i	−0.0145116	−	0.323126i	0.978586	−	0.205837i	$-0.0659918\pi$
$888$	1.38813e12	+	3.09092e13i	0.0749157	+	1.66813i
$889$	−3.73212e13	+	4.67993e13i	−2.00400	+	2.51293i
$890$	4.10482e12	−	1.54056e12i	0.219300	−	0.0823047i
$891$	2.51870e9	−	1.10352e10i	0.000133884	−	0.000586582i
$892$	3.78473e13	−	6.86826e12i	2.00167	−	0.363250i
$893$	−5.88193e13	−	2.83259e13i	−3.09520	−	1.49057i
$894$	1.46889e13	−	8.77623e12i	0.769079	−	0.459504i
$895$	1.01254e12	+	3.80014e11i	0.0527486	+	0.0197969i
$896$	4.29294e13	−	6.50352e13i	2.22520	−	3.37103i
$897$	6.42391e12	−	3.09359e12i	0.331309	−	0.159550i
$898$	3.19932e13	−	2.32444e13i	1.64178	−	1.19282i
$899$	−1.07584e13	+	9.39934e12i	−0.549325	+	0.479931i
$900$	1.98344e13	+	2.48715e13i	1.00769	+	1.26361i
$901$	−1.26101e12	−	7.53420e11i	−0.0637467	−	0.0380869i
$902$	−8.78870e12	−	1.33143e13i	−0.442074	−	0.669714i
$903$	3.89768e12	+	1.70769e13i	0.195080	+	0.854700i
$904$	−2.29548e13	−	5.37054e13i	−1.14318	−	2.67461i
$905$	2.48341e12	−	2.23511e11i	0.123064	−	0.0110759i
$906$	1.91496e13	+	1.39130e13i	0.944239	+	0.686030i
$907$	3.81404e13	+	6.92147e12i	1.87134	+	0.339598i	0.990905	−	0.134567i	$-0.0429643\pi$
$907$	3.81404e13	+	6.92147e12i	1.87134	+	0.339598i	0.880436	+	0.474165i	$0.157250\pi$
$908$	1.58381e13	−	3.70550e13i	0.773242	−	1.80909i
$909$	−3.50230e12	+	1.07790e13i	−0.170144	+	0.523648i
$910$	−4.30829e12	−	8.00614e12i	−0.208266	−	0.387023i
$911$	5.94747e12	+	6.22057e12i	0.286088	+	0.299225i	0.850185	−	0.526484i	$-0.176490\pi$
$911$	5.94747e12	+	6.22057e12i	0.286088	+	0.299225i	−0.564097	+	0.825709i	$0.690776\pi$
$912$	3.99542e13	−	7.42474e13i	1.91243	−	3.55389i
$913$	−3.77734e12	+	1.04248e12i	−0.179915	+	0.0496534i
$914$	2.74697e12	+	2.02789e13i	0.130195	+	0.961141i
$915$	−2.49339e11	+	1.84070e12i	−0.0117597	+	0.0868135i
$916$	−4.66989e13	−	1.28881e13i	−2.19168	−	0.604864i
$917$	−2.08310e13	+	2.17875e13i	−0.972856	+	1.01753i
$918$	1.60497e13	+	4.93959e13i	0.745891	+	2.29562i
$919$	−1.88630e13	−	1.69771e12i	−0.872353	−	0.0785132i	−0.355590	−	0.934642i	$-0.615720\pi$
$919$	−1.88630e13	−	1.69771e12i	−0.872353	−	0.0785132i	−0.516762	+	0.856129i	$0.672863\pi$
$920$	4.01231e12	+	3.50545e12i	0.184650	+	0.161324i
$921$	1.84146e11	−	4.10033e12i	0.00843324	−	0.187781i
$922$	3.41057e13			1.55431
$923$	−1.76336e13	+	1.42529e13i	−0.799710	+	0.646393i
$924$	−4.60269e13			−2.07725
$925$	8.34633e11	−	1.85845e13i	0.0374850	−	0.834669i
$926$	5.15732e13	+	4.50582e13i	2.30502	+	2.01384i
$927$	1.31979e13	+	1.18783e12i	0.587010	+	0.0528319i
$928$	2.27353e13	+	6.99719e13i	1.00632	+	3.09712i
$929$	7.39252e12	−	7.73197e12i	0.325628	−	0.340580i	−0.539634	−	0.841900i	$-0.681437\pi$
$929$	7.39252e12	−	7.73197e12i	0.325628	−	0.340580i	0.865262	+	0.501319i	$0.167152\pi$
$930$	−2.61083e12	−	7.20543e11i	−0.114447	−	0.0315854i
$931$	−1.06349e13	+	7.85101e13i	−0.463938	+	3.42493i
$932$	−4.34331e11	−	3.20636e12i	−0.0188560	−	0.139201i
$933$	−7.69264e12	+	2.12303e12i	−0.332359	+	0.0917254i
$934$	4.09749e13	−	7.61442e13i	1.76180	−	3.27398i
$935$	2.04814e12	+	2.14218e12i	0.0876409	+	0.0916652i
$936$	−2.24851e13	−	4.17843e13i	−0.957532	−	1.77939i
$937$	1.08982e13	−	3.35412e13i	0.461877	−	1.42151i	−0.400992	−	0.916082i	$-0.631334\pi$
$937$	1.08982e13	−	3.35412e13i	0.461877	−	1.42151i	0.862869	−	0.505428i	$-0.168666\pi$
$938$	3.24241e12	−	7.58599e12i	0.136759	−	0.319963i
$939$	4.89761e12	+	8.88785e11i	0.205584	+	0.0373080i
$940$	1.23491e13	+	8.97216e12i	0.515894	+	0.374819i
$941$	3.31402e13	−	2.98267e12i	1.37785	−	0.124009i	0.624189	−	0.781274i	$-0.285430\pi$
$941$	3.31402e13	−	2.98267e12i	1.37785	−	0.124009i	0.753659	+	0.657265i	$0.228287\pi$
$942$	−1.30390e13	−	3.05062e13i	−0.539528	−	1.26229i
$943$	1.73988e12	+	7.62292e12i	0.0716501	+	0.313920i
$944$	−5.69569e13	−	8.62860e13i	−2.33438	−	3.53644i
$945$	−4.70011e12	−	2.80819e12i	−0.191719	−	0.114547i
$946$	1.87622e13	+	2.35271e13i	0.761682	+	0.955119i
$947$	1.38224e11	−	1.20763e11i	0.00558481	−	0.00487930i	−0.655142	−	0.755506i	$-0.727391\pi$
$947$	1.38224e11	−	1.20763e11i	0.00558481	−	0.00487930i	0.660727	+	0.750627i	$0.270248\pi$
$948$	−1.29007e13	+	9.37294e12i	−0.518773	+	0.376911i
$949$	−4.44611e13	+	2.14113e13i	−1.77943	+	0.856930i
$950$	−4.96613e13	+	7.52337e13i	−1.97816	+	2.99679i
$951$	−1.86325e13	−	6.99288e12i	−0.738683	−	0.277232i
$952$	−1.46211e14	+	8.73568e13i	−5.76916	+	3.44691i
$953$	1.81867e13	+	8.75826e12i	0.714227	+	0.343954i	0.755459	−	0.655196i	$-0.227414\pi$
$953$	1.81867e13	+	8.75826e12i	0.714227	+	0.343954i	−0.0412318	+	0.999150i	$0.513128\pi$
$954$	1.75275e12	−	3.18077e11i	0.0685097	−	0.0124327i
$955$	−1.33097e11	+	5.83134e11i	−0.00517788	+	0.0226858i
$956$	−1.13878e14	+	4.27389e13i	−4.40938	+	1.65487i
$957$	7.29409e12	−	9.14650e12i	0.281104	−	0.352494i
$958$	2.24674e12	+	5.00276e13i	0.0861804	+	1.91896i
$959$	−1.30197e12	−	2.89906e13i	−0.0497069	−	1.10681i
$960$	−4.07731e12	+	5.11278e12i	−0.154936	+	0.194284i
$961$	−1.06949e13	+	4.01385e12i	−0.404501	+	0.151812i
$962$	−9.89231e12	+	4.33410e13i	−0.372400	+	1.63159i
$963$	−1.56961e13	+	2.84843e12i	−0.588131	+	0.106730i
$964$	7.38958e12	+	3.55863e12i	0.275596	+	0.132720i
$965$	2.45476e11	−	1.46665e11i	0.00911246	−	0.00544444i
$966$	2.90572e13	+	1.09053e13i	1.07363	+	0.402941i
$967$	1.06575e13	−	1.61454e13i	0.391954	−	0.593785i	−0.584002	−	0.811752i	$-0.698514\pi$
$967$	1.06575e13	−	1.61454e13i	0.391954	−	0.593785i	0.975956	+	0.217967i	$0.0699426\pi$
$968$	3.37431e13	−	1.62498e13i	1.23522	−	0.594852i
$969$	−3.30688e13	+	2.40259e13i	−1.20493	+	0.875433i
$970$	−6.81948e11	+	5.95800e11i	−0.0247331	+	0.0216087i
$971$	−2.95007e13	−	3.69928e13i	−1.06499	−	1.33546i	−0.939188	−	0.343403i	$-0.888420\pi$
$971$	−2.95007e13	−	3.69928e13i	−1.06499	−	1.33546i	−0.125804	−	0.992055i	$-0.540151\pi$
$972$	−6.35828e13	−	3.79890e13i	−2.28476	−	1.36508i
$973$	−2.76872e13	−	4.19443e13i	−0.990311	−	1.50026i
$974$	7.62356e12	+	3.34010e13i	0.271420	+	1.18917i
$975$	−6.91954e12	−	1.61891e13i	−0.245220	−	0.573721i
$976$	−1.02717e14	+	9.24468e12i	−3.62341	+	0.326113i
$977$	−8.85016e12	−	6.43002e12i	−0.310760	−	0.225781i	0.421462	−	0.906846i	$-0.361517\pi$
$977$	−8.85016e12	−	6.43002e12i	−0.310760	−	0.225781i	−0.732223	+	0.681065i	$0.761517\pi$
$978$	4.58540e13	+	8.32127e12i	1.60270	+	0.290847i
$979$	7.82359e12	−	1.83042e13i	0.272197	−	0.636838i
$980$	5.72433e12	−	1.76177e13i	0.198247	−	0.610142i
$981$	3.98846e12	+	7.41181e12i	0.137498	+	0.255513i
$982$	6.76180e13	+	7.07229e13i	2.32039	+	2.42693i
$983$	−9.44665e12	+	1.75548e13i	−0.322691	+	0.599661i	−0.989325	−	0.145724i	$-0.953449\pi$
$983$	−9.44665e12	+	1.75548e13i	−0.322691	+	0.599661i	0.666634	+	0.745385i	$0.267734\pi$
$984$	−3.09537e13	+	8.54267e12i	−1.05253	+	0.290480i
$985$	3.61006e11	+	2.66505e12i	0.0122194	+	0.0902076i
$986$	9.30990e12	−	6.87284e13i	0.313689	−	2.31574i
$987$	5.35005e13	+	1.47652e13i	1.79445	+	0.495236i
$988$	1.08203e14	−	1.13172e14i	3.61272	−	3.77861i
$989$	−4.55755e12	−	1.40267e13i	−0.151478	−	0.466200i
$990$	−3.57965e12	−	3.22174e11i	−0.118436	−	0.0106594i
$991$	−1.94579e11	−	1.69999e11i	−0.00640863	−	0.00559905i	0.654728	−	0.755864i	$-0.272783\pi$
$991$	−1.94579e11	−	1.69999e11i	−0.00640863	−	0.00559905i	−0.661137	+	0.750265i	$0.729926\pi$
$992$	3.46958e12	−	7.72561e13i	0.113756	−	2.53297i
$993$	1.74814e13			0.570565
$994$	−9.78874e13	−	1.26050e13i	−3.18045	−	0.409549i
$995$	−4.98793e11			−0.0161330
$996$	−5.66917e11	+	1.26234e13i	−0.0182538	+	0.406452i
$997$	−3.63099e13	−	3.17230e13i	−1.16385	−	1.01683i	−0.999537	−	0.0304167i	$-0.990317\pi$
$997$	−3.63099e13	−	3.17230e13i	−1.16385	−	1.01683i	−0.164313	−	0.986408i	$-0.552541\pi$
$998$	6.24350e13	+	5.61925e12i	1.99224	+	0.179304i
$999$	8.27287e12	+	2.54613e13i	0.262792	+	0.808790i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	71.10.g.a.2.3	✓	1272
71.36	even	35	inner	71.10.g.a.36.3	yes	1272

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
71.10.g.a.2.3	✓	1272	1.1	even	1	trivial
71.10.g.a.36.3	yes	1272	71.36	even	35	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:	\( N \)	\(=\)	\( 71 \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	71.g (of order \(35\), degree \(24\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.94237 + 43.2502i) q^{2} +(-65.2666 - 57.0217i) q^{3} +(-1356.87 - 122.121i) q^{4} +(57.5622 + 177.158i) q^{5} +(2592.98 - 2712.04i) q^{6} +(10262.9 + 2832.38i) q^{7} +(4941.81 - 36481.9i) q^{8} +(-1633.86 - 12061.6i) q^{9} +(-7773.94 + 2145.47i) q^{10} +(-17350.6 + 32242.9i) q^{11} +(81594.8 + 85341.5i) q^{12} +(50178.1 + 93246.6i) q^{13} +(-142435. + 438371. i) q^{14} +(6344.98 - 14844.8i) q^{15} +(881936. + 160048. i) q^{16} +(-351550. - 255416. i) q^{17} +(524842. - 47236.6i) q^{18} +(426576. + 998025. i) q^{19} +(-56469.7 - 247410. i) q^{20} +(-508317. - 770068. i) q^{21} +(-1.36081e6 - 813046. i) q^{22} +(484403. + 607423. i) q^{23} +(-2.40280e6 + 2.09926e6i) q^{24} +(1.55204e6 - 1.12762e6i) q^{25} +(-4.13040e6 + 1.98910e6i) q^{26} +(-1.52090e6 + 2.30406e6i) q^{27} +(-1.35795e7 - 5.09648e6i) q^{28} +(3.16478e6 - 1.89087e6i) q^{29} +(629717. + 303256. i) q^{30} +(-3.81282e6 + 691925. i) q^{31} +(-4.44078e6 + 1.94563e7i) q^{32} +(2.97096e6 - 1.11502e6i) q^{33} +(1.17296e7 - 1.47085e7i) q^{34} +(88975.4 + 1.98119e6i) q^{35} +(743962. + 1.65656e7i) q^{36} +(6.04608e6 - 7.58154e6i) q^{37} +(-4.39934e7 + 1.65110e7i) q^{38} +(2.04213e6 - 8.94714e6i) q^{39} +(6.74753e6 - 1.22450e6i) q^{40} +(9.06735e6 + 4.36661e6i) q^{41} +(3.42929e7 - 2.04891e7i) q^{42} +(-1.77728e7 - 6.67025e6i) q^{43} +(2.74801e7 - 4.16305e7i) q^{44} +(2.04277e6 - 983745. i) q^{45} +(-2.72121e7 + 1.97707e7i) q^{46} +(-4.52970e7 + 3.95748e7i) q^{47} +(-4.84348e7 - 6.07353e7i) q^{48} +(6.26630e7 + 3.74394e7i) q^{49} +(4.57553e7 + 6.93163e7i) q^{50} +(8.38022e6 + 3.67161e7i) q^{51} +(-5.66979e7 - 1.32651e8i) q^{52} +(3.36685e6 - 303022. i) q^{53} +(-9.66971e7 - 7.02545e7i) q^{54} +(-6.71083e6 - 1.21784e6i) q^{55} +(1.54048e8 - 3.60413e8i) q^{56} +(2.90679e7 - 8.94619e7i) q^{57} +(7.56334e7 + 1.40550e8i) q^{58} +(-7.97113e7 - 8.33715e7i) q^{59} +(-1.04222e7 + 1.93676e7i) q^{60} +(-1.10913e8 + 3.06099e7i) q^{61} +(-2.25200e7 - 1.66249e8i) q^{62} +(1.73950e7 - 1.28415e8i) q^{63} +(-3.90476e8 - 1.07765e8i) q^{64} +(-1.36310e7 + 1.42569e7i) q^{65} +(4.24542e7 + 1.30661e8i) q^{66} +(-1.78263e7 - 1.60439e6i) q^{67} +(4.45816e8 + 3.89498e8i) q^{68} +(3.02092e6 - 6.72660e7i) q^{69} -8.58598e7 q^{70} +(3.96172e7 + 2.10426e8i) q^{71} -4.48105e8 q^{72} +(-2.09083e7 + 4.65560e8i) q^{73} +(3.16160e8 + 2.76220e8i) q^{74} +(-1.65595e8 - 1.49039e7i) q^{75} +(-4.56929e8 - 1.40628e9i) q^{76} +(-2.69392e8 + 2.81762e8i) q^{77} +(3.82999e8 + 1.05701e8i) q^{78} +(-1.81289e7 + 1.33833e8i) q^{79} +(2.24124e7 + 1.65455e8i) q^{80} +(-297995. + 82241.4i) q^{81} +(-2.06469e8 + 3.83684e8i) q^{82} +(7.39581e7 + 7.73541e7i) q^{83} +(5.95679e8 + 1.10696e9i) q^{84} +(2.50130e7 - 7.69822e7i) q^{85} +(3.23011e8 - 7.55722e8i) q^{86} +(-3.14375e8 - 5.70507e7i) q^{87} +(1.09054e9 + 7.92323e8i) q^{88} +(-5.41473e8 + 4.87334e7i) q^{89} +(3.85794e7 + 9.02609e7i) q^{90} +(2.50863e8 + 1.09910e9i) q^{91} +(-5.83094e8 - 8.83349e8i) q^{92} +(2.88305e8 + 1.72254e8i) q^{93} +(-1.62364e9 - 2.03597e9i) q^{94} +(-1.52254e8 + 1.33020e8i) q^{95} +(1.39927e9 - 1.01663e9i) q^{96} +(1.01168e8 - 4.87201e7i) q^{97} +(-1.74098e9 + 2.63747e9i) q^{98} +(4.17250e8 + 1.56597e8i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 1272 q - 76 q^{2} - 395 q^{3} + 13542 q^{4} - 1610 q^{5} - 4334 q^{6} - 4827 q^{7} - 18627 q^{8} + 286810 q^{9} - 53448 q^{10} - 170685 q^{11} + 138323 q^{12} - 93291 q^{13} + 985964 q^{14} - 966194 q^{15}+ \cdots - 4074592265 q^{99}+O(q^{100}) \) 1272 * q - 76 * q^2 - 395 * q^3 + 13542 * q^4 - 1610 * q^5 - 4334 * q^6 - 4827 * q^7 - 18627 * q^8 + 286810 * q^9 - 53448 * q^10 - 170685 * q^11 + 138323 * q^12 - 93291 * q^13 + 985964 * q^14 - 966194 * q^15 + 4755334 * q^16 + 2558412 * q^17 - 2619769 * q^18 - 172269 * q^19 + 738120 * q^20 + 1797929 * q^21 + 3015622 * q^22 + 6635088 * q^23 + 4803145 * q^24 - 115100016 * q^25 + 19254293 * q^26 - 17686931 * q^27 + 15761532 * q^28 - 10052927 * q^29 + 62637435 * q^30 - 23748991 * q^31 + 10388192 * q^32 - 15097203 * q^33 + 33217854 * q^34 - 24823174 * q^35 + 27856812 * q^36 - 27156308 * q^37 - 43400577 * q^38 + 251072838 * q^39 - 129856160 * q^40 + 62087988 * q^41 - 91873950 * q^42 - 167299067 * q^43 + 60914131 * q^44 - 31536191 * q^45 - 50201490 * q^46 - 23317743 * q^47 + 10641329 * q^48 + 338745866 * q^49 + 303770229 * q^50 + 448039613 * q^51 - 979580293 * q^52 + 12085215 * q^53 - 182583505 * q^54 - 243892552 * q^55 + 30440435 * q^56 + 714581966 * q^57 - 244549660 * q^58 - 859013315 * q^59 - 1894499000 * q^60 - 876373921 * q^61 + 186553636 * q^62 - 196611021 * q^63 + 5528242635 * q^64 + 867018244 * q^65 + 2727701199 * q^66 - 286780089 * q^67 - 1689988351 * q^68 - 3073308182 * q^69 - 41489396 * q^70 - 2538053548 * q^71 - 6821388000 * q^72 + 128479023 * q^73 + 3282772334 * q^74 + 3407782757 * q^75 + 7133788844 * q^76 + 1087098389 * q^77 + 2715049934 * q^78 + 144243625 * q^79 - 7443877603 * q^80 - 4083269278 * q^81 - 10375744380 * q^82 + 1543773955 * q^83 - 4117054288 * q^84 + 7843382686 * q^85 + 3545751759 * q^86 + 5261609811 * q^87 - 818728797 * q^88 - 1369081479 * q^89 + 10041256259 * q^90 - 7299574322 * q^91 + 602797624 * q^92 - 2146129677 * q^93 - 683447510 * q^94 - 7007204038 * q^95 + 6601829126 * q^96 - 10081488030 * q^97 - 5942379880 * q^98 - 4074592265 * q^99

Introduction

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