LMFDB - Embedded newform 100.9.j.b.11.76

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			11.76
Character	$\chi$	$=$	100.11
Dual form			100.9.j.b.91.76

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(7.53864 + 14.1127i) q^{2} +(36.9043 + 11.9909i) q^{3} +(-142.338 + 212.781i) q^{4} +(-624.781 - 16.5320i) q^{5} +(108.984 + 611.216i) q^{6} -802.640i q^{7} +(-4075.96 - 404.691i) q^{8} +(-4089.81 - 2971.42i) q^{9} +(-4476.69 - 8941.99i) q^{10} +(13197.2 + 18164.3i) q^{11} +(-7804.33 + 6145.80i) q^{12} +(-16151.5 - 11734.7i) q^{13} +(11327.4 - 6050.81i) q^{14} +(-22858.9 - 8101.82i) q^{15} +(-25015.9 - 60573.7i) q^{16} +(-25864.7 - 79603.4i) q^{17} +(11103.2 - 80118.9i) q^{18} +(135137. - 43908.6i) q^{19} +(92447.7 - 130589. i) q^{20} +(9624.41 - 29620.9i) q^{21} +(-156860. + 323182. i) q^{22} +(152647. + 210100. i) q^{23} +(-145568. - 63809.5i) q^{24} +(390078. + 20657.8i) q^{25} +(43848.8 - 316405. i) q^{26} +(-264946. - 364667. i) q^{27} +(170787. + 114246. i) q^{28} +(30864.7 - 94991.6i) q^{29} +(-57986.3 - 383678. i) q^{30} +(1.36260e6 - 442736. i) q^{31} +(666274. - 809686. i) q^{32} +(269225. + 828590. i) q^{33} +(928436. - 965123. i) q^{34} +(-13269.2 + 501474. i) q^{35} +(1.21440e6 - 447291. i) q^{36} +(-2.18913e6 - 1.59049e6i) q^{37} +(1.63842e6 + 1.57614e6i) q^{38} +(-455349. - 626734. i) q^{39} +(2.53989e6 + 320227. i) q^{40} +(-2.37789e6 - 1.72764e6i) q^{41} +(490586. - 87474.6i) q^{42} -729028. i q^{43} +(-5.74349e6 + 222640. i) q^{44} +(2.50612e6 + 1.92410e6i) q^{45} +(-1.81434e6 + 3.73813e6i) q^{46} +(-1.50061e6 - 487578. i) q^{47} +(-196860. - 2.53540e6i) q^{48} +5.12057e6 q^{49} +(2.64912e6 + 5.66080e6i) q^{50} -3.24785e6i q^{51} +(4.79590e6 - 1.76644e6i) q^{52} +(-638611. + 1.96544e6i) q^{53} +(3.14911e6 - 6.48820e6i) q^{54} +(-7.94505e6 - 1.15669e7i) q^{55} +(-324821. + 3.27153e6i) q^{56} +5.51364e6 q^{57} +(1.57327e6 - 280524. i) q^{58} +(-5.70995e6 + 7.85907e6i) q^{59} +(4.97760e6 - 3.71076e6i) q^{60} +(2.23671e7 - 1.62507e7i) q^{61} +(1.65204e7 + 1.58924e7i) q^{62} +(-2.38498e6 + 3.28265e6i) q^{63} +(1.64497e7 + 3.29901e6i) q^{64} +(9.89714e6 + 7.59865e6i) q^{65} +(-9.66407e6 + 1.00459e7i) q^{66} +(1.74623e7 - 5.67384e6i) q^{67} +(2.06197e7 + 5.82704e6i) q^{68} +(3.11403e6 + 9.58398e6i) q^{69} +(-7.17720e6 + 3.59317e6i) q^{70} +(-3.19530e7 - 1.03821e7i) q^{71} +(1.54674e7 + 1.37665e7i) q^{72} +(-3.24076e7 + 2.35455e7i) q^{73} +(5.94315e6 - 4.28847e7i) q^{74} +(1.41479e7 + 5.43977e6i) q^{75} +(-9.89213e6 + 3.50044e7i) q^{76} +(1.45794e7 - 1.05926e7i) q^{77} +(5.41221e6 - 1.11509e7i) q^{78} +(-2.86034e7 - 9.29380e6i) q^{79} +(1.46281e7 + 3.82589e7i) q^{80} +(4.84444e6 + 1.49097e7i) q^{81} +(6.45561e6 - 4.65825e7i) q^{82} +(6.50527e7 - 2.11369e7i) q^{83} +(4.93286e6 + 6.26407e6i) q^{84} +(1.48438e7 + 5.01623e7i) q^{85} +(1.02886e7 - 5.49588e6i) q^{86} +(2.27808e6 - 3.13551e6i) q^{87} +(-4.64402e7 - 7.93779e7i) q^{88} +(6.65941e7 - 4.83835e7i) q^{89} +(-8.26162e6 + 4.98732e7i) q^{90} +(-9.41876e6 + 1.29638e7i) q^{91} +(-6.64328e7 + 2.57519e6i) q^{92} +5.55947e7 q^{93} +(-4.43151e6 - 2.48534e7i) q^{94} +(-8.51568e7 + 2.51992e7i) q^{95} +(3.42973e7 - 2.18917e7i) q^{96} +(9.40676e6 - 2.89510e7i) q^{97} +(3.86021e7 + 7.22652e7i) q^{98} -1.13503e8i 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 $

$2$	7.53864	+	14.1127i	0.471165	+	0.882045i
$2$	7.53864	+	14.1127i	0.471165	+	0.882045i
$3$	36.9043	+	11.9909i	0.455609	+	0.148036i	0.527826	−	0.849353i	$-0.323007\pi$
$3$	36.9043	+	11.9909i	0.455609	+	0.148036i	−0.0722168	+	0.997389i	$0.523007\pi$
$4$	−142.338	+	212.781i	−0.556007	+	0.831178i
$5$	−624.781	−	16.5320i	−0.999650	−	0.0264512i
$5$	−624.781	−	16.5320i	−0.999650	−	0.0264512i
$6$	108.984	+	611.216i	0.0840923	+	0.471617i
$7$		−	802.640i		−	0.334294i	−0.985932	−	0.167147i	$-0.946545\pi$
$7$		−	802.640i		−	0.334294i	0.985932	−	0.167147i	$-0.0534554\pi$
$8$	−4075.96	−	404.691i	−0.995107	−	0.0988014i
$9$	−4089.81	−	2971.42i	−0.623352	−	0.452892i
$10$	−4476.69	−	8941.99i	−0.447669	−	0.894199i
$11$	13197.2	+	18164.3i	0.901384	+	1.24065i	0.970024	+	0.243008i	$0.0781341\pi$
$11$	13197.2	+	18164.3i	0.901384	+	1.24065i	−0.0686399	+	0.997642i	$0.521866\pi$
$12$	−7804.33	+	6145.80i	−0.376366	+	0.296383i
$13$	−16151.5	−	11734.7i	−0.565508	−	0.410865i	0.267963	−	0.963429i	$-0.413650\pi$
$13$	−16151.5	−	11734.7i	−0.565508	−	0.410865i	−0.833471	+	0.552564i	$0.813650\pi$
$14$	11327.4	−	6050.81i	0.294862	−	0.157508i
$15$	−22858.9	−	8101.82i	−0.451534	−	0.160036i
$16$	−25015.9	−	60573.7i	−0.381712	−	0.924281i
$17$	−25864.7	−	79603.4i	−0.309679	−	0.953094i	−0.977890	−	0.209122i	$-0.932939\pi$
$17$	−25864.7	−	79603.4i	−0.309679	−	0.953094i	0.668210	−	0.743972i	$-0.267061\pi$
$18$	11103.2	−	80118.9i	0.105769	−	0.763211i
$19$	135137.	−	43908.6i	1.03695	−	0.336926i	0.259417	−	0.965765i	$-0.416470\pi$
$19$	135137.	−	43908.6i	1.03695	−	0.336926i	0.777535	+	0.628839i	$0.216470\pi$
$20$	92447.7	−	130589.i	0.577798	−	0.816180i
$21$	9624.41	−	29620.9i	0.0494877	−	0.152307i
$22$	−156860.	+	323182.i	−0.669608	+	1.37961i
$23$	152647.	+	210100.i	0.545476	+	0.750784i	0.989390	−	0.145286i	$-0.0464102\pi$
$23$	152647.	+	210100.i	0.545476	+	0.750784i	−0.443913	+	0.896070i	$0.646410\pi$
$24$	−145568.	−	63809.5i	−0.438754	−	0.192327i
$25$	390078.	+	20657.8i	0.998601	+	0.0528839i
$26$	43848.8	−	316405.i	0.0959544	−	0.692389i
$27$	−264946.	−	364667.i	−0.498542	−	0.686185i
$28$	170787.	+	114246.i	0.277858	+	0.185870i
$29$	30864.7	−	94991.6i	0.0436385	−	0.134305i	−0.926864	−	0.375398i	$-0.877506\pi$
$29$	30864.7	−	94991.6i	0.0436385	−	0.134305i	0.970502	+	0.241093i	$0.0775059\pi$
$30$	−57986.3	−	383678.i	−0.0715881	−	0.473677i
$31$	1.36260e6	−	442736.i	1.47544	−	0.479400i	0.542694	−	0.839930i	$-0.317404\pi$
$31$	1.36260e6	−	442736.i	1.47544	−	0.479400i	0.932748	+	0.360530i	$0.117404\pi$
$32$	666274.	−	809686.i	0.635408	−	0.772176i
$33$	269225.	+	828590.i	0.227018	+	0.698689i
$34$	928436.	−	965123.i	0.694762	−	0.722216i
$35$	−13269.2	+	501474.i	−0.00884247	+	0.334177i
$36$	1.21440e6	−	447291.i	0.723022	−	0.266305i
$37$	−2.18913e6	−	1.59049e6i	−1.16806	−	0.848642i	−0.177281	−	0.984160i	$-0.556730\pi$
$37$	−2.18913e6	−	1.59049e6i	−1.16806	−	0.848642i	−0.990775	+	0.135518i	$0.956730\pi$
$38$	1.63842e6	+	1.57614e6i	0.785760	+	0.755891i
$39$	−455349.	−	626734.i	−0.196827	−	0.270910i
$40$	2.53989e6	+	320227.i	0.992146	+	0.125089i
$41$	−2.37789e6	−	1.72764e6i	−0.841503	−	0.611388i	0.0812868	−	0.996691i	$-0.474097\pi$
$41$	−2.37789e6	−	1.72764e6i	−0.841503	−	0.611388i	−0.922790	+	0.385303i	$0.874097\pi$
$42$	490586.	−	87474.6i	0.157659	−	0.0281116i
$43$		−	729028.i		−	0.213241i	−0.994300	−	0.106620i	$-0.965997\pi$
$43$		−	729028.i		−	0.213241i	0.994300	−	0.106620i	$-0.0340030\pi$
$44$	−5.74349e6	+	222640.i	−1.53238	+	0.0594009i
$45$	2.50612e6	+	1.92410e6i	0.611154	+	0.469222i
$46$	−1.81434e6	+	3.73813e6i	−0.405216	+	0.834878i
$47$	−1.50061e6	−	487578.i	−0.307522	−	0.0999200i	0.151191	−	0.988505i	$-0.451689\pi$
$47$	−1.50061e6	−	487578.i	−0.307522	−	0.0999200i	−0.458713	+	0.888585i	$0.651689\pi$
$48$	−196860.	−	2.53540e6i	−0.0370844	−	0.477618i
$49$	5.12057e6			0.888248
$50$	2.64912e6	+	5.66080e6i	0.423860	+	0.905728i
$51$		−	3.24785e6i		−	0.480082i
$52$	4.79590e6	−	1.76644e6i	0.655928	−	0.241593i
$53$	−638611.	+	1.96544e6i	−0.0809343	+	0.249090i	−0.983334	−	0.181811i	$-0.941804\pi$
$53$	−638611.	+	1.96544e6i	−0.0809343	+	0.249090i	0.902399	+	0.430901i	$0.141804\pi$
$54$	3.14911e6	−	6.48820e6i	0.370350	−	0.763043i
$55$	−7.94505e6	−	1.15669e7i	−0.868252	−	1.26406i
$56$	−324821.	+	3.27153e6i	−0.0330287	+	0.332658i
$57$	5.51364e6			0.522322
$58$	1.57327e6	−	280524.i	0.139024	−	0.0247889i
$59$	−5.70995e6	+	7.85907e6i	−0.471221	+	0.648579i	−0.976788	−	0.214208i	$-0.931283\pi$
$59$	−5.70995e6	+	7.85907e6i	−0.471221	+	0.648579i	0.505568	+	0.862787i	$0.331283\pi$
$60$	4.97760e6	−	3.71076e6i	0.384074	−	0.286324i
$61$	2.23671e7	−	1.62507e7i	1.61544	−	1.17369i	0.774454	−	0.632631i	$-0.218025\pi$
$61$	2.23671e7	−	1.62507e7i	1.61544	−	1.17369i	0.840987	−	0.541055i	$-0.181975\pi$
$62$	1.65204e7	+	1.58924e7i	1.11803	+	1.07553i
$63$	−2.38498e6	+	3.28265e6i	−0.151399	+	0.208383i
$64$	1.64497e7	+	3.29901e6i	0.980477	+	0.196636i
$65$	9.89714e6	+	7.59865e6i	0.554442	+	0.425680i
$66$	−9.66407e6	+	1.00459e7i	−0.509312	+	0.529438i
$67$	1.74623e7	−	5.67384e6i	0.866567	−	0.281565i	0.158198	−	0.987407i	$-0.449431\pi$
$67$	1.74623e7	−	5.67384e6i	0.866567	−	0.281565i	0.708369	+	0.705843i	$0.249431\pi$
$68$	2.06197e7	+	5.82704e6i	0.964375	+	0.272529i
$69$	3.11403e6	+	9.58398e6i	0.137381	+	0.422814i
$70$	−7.17720e6	+	3.59317e6i	−0.298925	+	0.149653i
$71$	−3.19530e7	−	1.03821e7i	−1.25741	−	0.408558i	−0.396841	−	0.917887i	$-0.629893\pi$
$71$	−3.19530e7	−	1.03821e7i	−1.25741	−	0.408558i	−0.860572	+	0.509329i	$0.829893\pi$
$72$	1.54674e7	+	1.37665e7i	0.575556	+	0.512264i
$73$	−3.24076e7	+	2.35455e7i	−1.14118	+	0.829119i	−0.987284	−	0.158968i	$-0.949183\pi$
$73$	−3.24076e7	+	2.35455e7i	−1.14118	+	0.829119i	−0.153900	+	0.988086i	$0.549183\pi$
$74$	5.94315e6	−	4.28847e7i	0.198194	−	1.43013i
$75$	1.41479e7	+	5.43977e6i	0.447143	+	0.171924i
$76$	−9.89213e6	+	3.50044e7i	−0.296507	+	1.04923i
$77$	1.45794e7	−	1.05926e7i	0.414741	−	0.301327i
$78$	5.41221e6	−	1.11509e7i	0.146216	−	0.301254i
$79$	−2.86034e7	−	9.29380e6i	−0.734359	−	0.238608i	−0.0821217	−	0.996622i	$-0.526170\pi$
$79$	−2.86034e7	−	9.29380e6i	−0.734359	−	0.238608i	−0.652238	+	0.758014i	$0.726170\pi$
$80$	1.46281e7	+	3.82589e7i	0.357130	+	0.934055i
$81$	4.84444e6	+	1.49097e7i	0.112539	+	0.346360i
$82$	6.45561e6	−	4.65825e7i	0.142785	−	1.03031i
$83$	6.50527e7	−	2.11369e7i	1.37073	−	0.445378i	0.471121	−	0.882068i	$-0.343849\pi$
$83$	6.50527e7	−	2.11369e7i	1.37073	−	0.445378i	0.899612	+	0.436690i	$0.143849\pi$
$84$	4.93286e6	+	6.26407e6i	0.0990790	+	0.125817i
$85$	1.48438e7	+	5.01623e7i	0.284360	+	0.960952i
$86$	1.02886e7	−	5.49588e6i	0.188088	−	0.100472i
$87$	2.27808e6	−	3.13551e6i	0.0397642	−	0.0547307i
$88$	−4.64402e7	−	7.93779e7i	−0.774396	−	1.32364i
$89$	6.65941e7	−	4.83835e7i	1.06139	−	0.771147i	0.0870470	−	0.996204i	$-0.472257\pi$
$89$	6.65941e7	−	4.83835e7i	1.06139	−	0.771147i	0.974346	+	0.225057i	$0.0722570\pi$
$90$	−8.26162e6	+	4.98732e7i	−0.125920	+	0.760147i
$91$	−9.41876e6	+	1.29638e7i	−0.137350	+	0.189046i
$92$	−6.64328e7	+	2.57519e6i	−0.927323	+	0.0359467i
$93$	5.55947e7			0.743193
$94$	−4.43151e6	−	2.48534e7i	−0.0567597	−	0.318327i
$95$	−8.51568e7	+	2.51992e7i	−1.04550	+	0.309380i
$96$	3.42973e7	−	2.18917e7i	0.403808	−	0.257747i
$97$	9.40676e6	−	2.89510e7i	0.106256	−	0.327022i	−0.883767	−	0.467927i	$-0.845001\pi$
$97$	9.40676e6	−	2.89510e7i	0.106256	−	0.327022i	0.990023	+	0.140905i	$0.0450011\pi$
$98$	3.86021e7	+	7.22652e7i	0.418511	+	0.783474i
$99$		−	1.13503e8i		−	1.18159i
$100$	−5.99185e7	+	8.00611e7i	−0.599185	+	0.800611i
$101$	−1.01600e8			−0.976353			−0.488177	−	0.872745i	$-0.662338\pi$
$101$	−1.01600e8			−0.976353			−0.488177	+	0.872745i	$0.662338\pi$
$102$	4.58361e7	−	2.44844e7i	0.423454	−	0.226198i
$103$	817360.	+	265576.i	0.00726214	+	0.00235961i	0.312646	−	0.949870i	$-0.398785\pi$
$103$	817360.	+	265576.i	0.00726214	+	0.00235961i	−0.305384	+	0.952229i	$0.598785\pi$
$104$	6.10838e7	+	5.43666e7i	0.522147	+	0.464728i
$105$	−6.50284e6	+	1.83475e7i	−0.0534991	+	0.150945i
$106$	−3.25520e7	+	5.80422e6i	−0.257842	+	0.0459749i
$107$		−	2.34293e8i		−	1.78741i	−0.448658	−	0.893704i	$-0.648098\pi$
$107$		−	2.34293e8i		−	1.78741i	0.448658	−	0.893704i	$-0.351902\pi$
$108$	1.15306e8	−	4.46971e6i	0.847534	−	0.0328537i
$109$	−1.41189e8	−	1.02580e8i	−1.00022	−	0.726700i	−0.0380825	−	0.999275i	$-0.512125\pi$
$109$	−1.41189e8	−	1.02580e8i	−1.00022	−	0.726700i	−0.962135	+	0.272574i	$0.912125\pi$
$110$	1.03346e8	−	1.99325e8i	0.705866	−	1.36142i
$111$	−6.17167e7	−	8.49458e7i	−0.406547	−	0.559564i
$112$	−4.86188e7	+	2.00788e7i	−0.308982	+	0.127604i
$113$	−8.03495e7	−	5.83773e7i	−0.492798	−	0.358039i	0.313461	−	0.949601i	$-0.398511\pi$
$113$	−8.03495e7	−	5.83773e7i	−0.492798	−	0.358039i	−0.806259	+	0.591562i	$0.798511\pi$
$114$	4.15653e7	+	7.78124e7i	0.246100	+	0.460712i
$115$	−9.18974e7	−	1.33790e8i	−0.525426	−	0.764950i
$116$	1.58193e7	+	2.00883e7i	0.0873683	+	0.110946i
$117$	3.11876e7	+	9.59857e7i	0.166433	+	0.512228i
$118$	−1.53958e8	−	2.13362e7i	−0.794099	−	0.110050i
$119$	−6.38928e7	+	2.07600e7i	−0.318614	+	0.103524i
$120$	8.98932e7	+	4.22735e7i	0.433513	+	0.203865i
$121$	−8.95376e7	+	2.75569e8i	−0.417700	+	1.28555i
$122$	3.97959e8	+	1.93153e8i	1.79638	+	0.871891i
$123$	−6.70384e7	−	9.22704e7i	−0.292889	−	0.403127i
$124$	−9.97437e7	+	3.52954e8i	−0.421889	+	1.49290i
$125$	−2.43372e8	−	1.93554e7i	−0.996852	−	0.0792795i
$126$	−6.43066e7	−	8.91190e6i	−0.255137	−	0.0353580i
$127$	−1.16361e8	−	1.60158e8i	−0.447295	−	0.615648i	0.524519	−	0.851399i	$-0.324245\pi$
$127$	−1.16361e8	−	1.60158e8i	−0.447295	−	0.615648i	−0.971814	+	0.235750i	$0.924245\pi$
$128$	7.74502e7	+	2.57020e8i	0.288524	+	0.957473i
$129$	8.74173e6	−	2.69043e7i	0.0315674	−	0.0971544i
$130$	−3.26267e7	+	1.96959e8i	−0.114235	+	0.689608i
$131$	−1.63526e8	+	5.31328e7i	−0.555266	+	0.180417i	−0.573190	−	0.819422i	$-0.694294\pi$
$131$	−1.63526e8	+	5.31328e7i	−0.555266	+	0.180417i	0.0179238	+	0.999839i	$0.494294\pi$
$132$	−2.14629e8	−	6.06535e7i	−0.706958	−	0.199784i
$133$	−3.52428e7	−	1.08466e8i	−0.112632	−	0.346647i
$134$	2.11715e8	+	2.03667e8i	0.656649	+	0.631688i
$135$	1.59505e8	+	2.32217e8i	0.480218	+	0.699132i
$136$	7.32088e7	+	3.34927e8i	0.213997	+	0.979028i
$137$	−3.14632e8	−	2.28594e8i	−0.893143	−	0.648906i	0.0435527	−	0.999051i	$-0.486132\pi$
$137$	−3.14632e8	−	2.28594e8i	−0.893143	−	0.648906i	−0.936696	+	0.350145i	$0.886132\pi$
$138$	−1.11781e8	+	1.16198e8i	−0.308212	+	0.320391i
$139$	9.38694e7	+	1.29200e8i	0.251458	+	0.346102i	0.916021	−	0.401130i	$-0.131382\pi$
$139$	9.38694e7	+	1.29200e8i	0.251458	+	0.346102i	−0.664563	+	0.747232i	$0.731382\pi$
$140$	−1.04816e8	−	7.42022e7i	−0.272844	−	0.193154i
$141$	−4.95325e7	−	3.59875e7i	−0.125318	−	0.0910490i
$142$	−9.43616e7	−	5.29211e8i	−0.232082	−	1.30159i
$143$		−	4.48246e8i		−	1.07194i
$144$	−7.76797e7	+	3.22068e8i	−0.180658	+	0.749027i
$145$	−2.08541e7	+	5.88387e7i	−0.0471757	+	0.133104i
$146$	−5.76601e8	−	2.79858e8i	−1.26901	−	0.615924i
$147$	1.88971e8	+	6.14005e7i	0.404694	+	0.131493i
$148$	6.50023e8	−	2.39418e8i	1.35482	−	0.499011i
$149$	2.20328e8			0.447018			0.223509	−	0.974702i	$-0.428249\pi$
$149$	2.20328e8			0.447018			0.223509	+	0.974702i	$0.428249\pi$
$150$	2.98858e7	+	2.40674e8i	0.0590337	+	0.475405i
$151$		−	2.34652e8i		−	0.451353i	−0.974202	−	0.225677i	$-0.927541\pi$
$151$		−	2.34652e8i		−	0.451353i	0.974202	−	0.225677i	$-0.0724592\pi$
$152$	−5.68581e8	+	1.24281e8i	−1.06517	+	0.232825i
$153$	−1.30754e8	+	4.02418e8i	−0.238609	+	0.734365i
$154$	2.59399e8	+	1.25902e8i	0.461196	+	0.223846i
$155$	−8.58647e8	+	2.54087e8i	−1.48761	+	0.440205i
$156$	1.98171e8	−	7.68187e6i	0.334612	−	0.0129708i
$157$	−7.59257e7			−0.124966			−0.0624828	−	0.998046i	$-0.519902\pi$
$157$	−7.59257e7			−0.124966			−0.0624828	+	0.998046i	$0.519902\pi$
$158$	−8.44697e7	−	4.73734e8i	−0.135542	−	0.760162i
$159$	−4.71350e7	+	6.48758e7i	−0.0737488	+	0.101507i
$160$	−4.29661e8	+	4.94862e8i	−0.655611	+	0.755099i
$161$	1.68635e8	−	1.22520e8i	0.250982	−	0.182349i
$162$	−1.73895e8	+	1.80767e8i	−0.252480	+	0.262457i
$163$	1.13640e8	−	1.56412e8i	0.160983	−	0.221575i	−0.720904	−	0.693035i	$-0.756273\pi$
$163$	1.13640e8	−	1.56412e8i	0.160983	−	0.221575i	0.881887	+	0.471461i	$0.156273\pi$
$164$	7.06072e8	−	2.60062e8i	0.976054	−	0.359503i
$165$	−1.54509e8	−	5.22138e8i	−0.208457	−	0.704449i
$166$	7.88708e8	+	7.58727e8i	1.03869	+	0.999202i
$167$	−1.34259e9	+	4.36233e8i	−1.72614	+	0.560858i	−0.992883	−	0.119092i	$-0.962002\pi$
$167$	−1.34259e9	+	4.36233e8i	−1.72614	+	0.560858i	−0.733259	+	0.679950i	$0.762002\pi$
$168$	−5.12160e7	+	1.16839e8i	−0.0642937	+	0.146673i
$169$	−1.28909e8	−	3.96740e8i	−0.158028	−	0.486361i
$170$	−5.96025e8	+	5.87642e8i	−0.713623	+	0.703586i
$171$	−6.83155e8	−	2.21970e8i	−0.798978	−	0.259604i
$172$	1.55124e8	+	1.03768e8i	0.177241	+	0.118563i
$173$	−3.31196e8	+	2.40628e8i	−0.369744	+	0.268634i	−0.757105	−	0.653294i	$-0.773387\pi$
$173$	−3.31196e8	+	2.40628e8i	−0.369744	+	0.268634i	0.387361	+	0.921928i	$0.373387\pi$
$174$	6.14242e7	+	8.51244e6i	0.0670104	+	0.00928660i
$175$	1.65807e7	−	3.13092e8i	0.0176788	−	0.333826i
$176$	7.70142e8	−	1.25380e9i	0.802639	−	1.30670i
$177$	−3.04960e8	+	2.21566e8i	−0.310706	+	0.225741i
$178$	1.18485e9	+	5.75079e8i	1.18028	+	0.572859i
$179$	6.84272e8	+	2.22333e8i	0.666525	+	0.216567i	0.622686	−	0.782472i	$-0.286041\pi$
$179$	6.84272e8	+	2.22333e8i	0.666525	+	0.216567i	0.0438387	+	0.999039i	$0.486041\pi$
$180$	−7.66128e8	+	2.59382e8i	−0.729813	+	0.247087i
$181$	1.55875e8	+	4.79733e8i	0.145232	+	0.446977i	0.997041	−	0.0768755i	$-0.0244944\pi$
$181$	1.55875e8	+	4.79733e8i	0.145232	+	0.446977i	−0.851809	+	0.523852i	$0.824494\pi$
$182$	−2.53959e8	−	3.51948e7i	−0.231461	−	0.0320770i
$183$	1.02031e9	−	3.31517e8i	0.909758	−	0.295598i
$184$	−5.37156e8	−	9.18134e8i	−0.468629	−	0.801004i
$185$	1.34143e9	+	1.02990e9i	1.14520	+	0.879242i
$186$	4.19109e8	+	7.84593e8i	0.350167	+	0.655530i
$187$	1.10460e9	−	1.52036e9i	0.903316	−	1.24331i
$188$	3.17341e8	−	2.49901e8i	0.254036	−	0.200049i
$189$	−2.92696e8	+	2.12656e8i	−0.229387	+	0.166660i
$190$	−9.97595e8	−	1.01183e9i	−0.765491	−	0.776411i
$191$	4.97692e8	−	6.85014e8i	0.373961	−	0.514714i	−0.580011	−	0.814609i	$-0.696952\pi$
$191$	4.97692e8	−	6.85014e8i	0.373961	−	0.514714i	0.953972	+	0.299895i	$0.0969517\pi$
$192$	5.67506e8	+	3.18995e8i	0.417605	+	0.234735i
$193$	4.27868e8			0.308376			0.154188	−	0.988042i	$-0.450724\pi$
$193$	4.27868e8			0.308376			0.154188	+	0.988042i	$0.450724\pi$
$194$	4.79492e8	−	8.54964e7i	0.338512	−	0.0603589i
$195$	2.74132e8	+	3.99099e8i	0.189593	+	0.276021i
$196$	−7.28851e8	+	1.08956e9i	−0.493872	+	0.738291i
$197$	6.37990e8	−	1.96353e9i	0.423593	−	1.30369i	−0.480741	−	0.876862i	$-0.659632\pi$
$197$	6.37990e8	−	1.96353e9i	0.423593	−	1.30369i	0.904335	−	0.426824i	$-0.140368\pi$
$198$	1.60184e9	−	8.55659e8i	1.04222	−	0.556724i
$199$		−	3.41119e8i		−	0.217517i	−0.994068	−	0.108759i	$-0.965312\pi$
$199$		−	3.41119e8i		−	0.217517i	0.994068	−	0.108759i	$-0.0346875\pi$
$200$	−1.58158e9	−	2.42061e8i	−0.988490	−	0.151288i
$201$	7.12469e8			0.436498
$202$	−7.65924e8	−	1.43385e9i	−0.460024	−	0.861188i
$203$	−7.62440e7	−	2.47732e7i	−0.0448975	−	0.0145881i
$204$	6.91083e8	+	4.62292e8i	0.399034	+	0.266929i
$205$	1.45710e9	+	1.11871e9i	0.825037	+	0.633433i
$206$	2.41378e6	+	1.35373e7i	0.00134038	+	0.00751730i
$207$		−	1.31285e9i		−	0.715044i
$208$	−3.06772e8	+	1.27191e9i	−0.163894	+	0.679521i
$209$	2.58099e9	+	1.87520e9i	1.35270	+	0.982794i
$210$	−3.07955e8	+	4.65421e7i	−0.158347	+	0.0239315i
$211$	−6.86972e8	−	9.45536e8i	−0.346584	−	0.477033i	0.599766	−	0.800176i	$-0.295260\pi$
$211$	−6.86972e8	−	9.45536e8i	−0.346584	−	0.477033i	−0.946350	+	0.323143i	$0.895260\pi$
$212$	−3.27311e8	−	4.15641e8i	−0.162038	−	0.205767i
$213$	−1.05471e9	−	7.66293e8i	−0.512407	−	0.372286i
$214$	3.30651e9	−	1.76625e9i	1.57657	−	0.842164i
$215$	−1.20523e7	+	4.55483e8i	−0.00564047	+	0.213166i
$216$	9.32331e8	+	1.59359e9i	0.428307	+	0.732084i
$217$	−3.55358e8	−	1.09368e9i	−0.160261	−	0.493231i
$218$	3.83307e8	−	2.76587e9i	0.169715	−	1.22463i
$219$	−1.47831e9	+	4.80334e8i	−0.642674	+	0.208817i
$220$	3.59211e9	−	4.41500e7i	1.53341	−	0.0188469i
$221$	−5.16371e8	+	1.58923e9i	−0.216468	+	0.666219i
$222$	7.33556e8	−	1.51137e9i	0.302010	−	0.622240i
$223$	9.02310e8	+	1.24192e9i	0.364868	+	0.502198i	0.951497	−	0.307658i	$-0.0995452\pi$
$223$	9.02310e8	+	1.24192e9i	0.364868	+	0.502198i	−0.586629	+	0.809856i	$0.699545\pi$
$224$	−6.49886e8	−	5.34778e8i	−0.258134	−	0.212413i
$225$	−1.53396e9	−	1.24357e9i	−0.598529	−	0.485223i
$226$	2.18137e8	−	1.57404e9i	0.0836172	−	0.603366i
$227$	9.26171e8	+	1.27477e9i	0.348809	+	0.480095i	0.946988	−	0.321268i	$-0.104109\pi$
$227$	9.26171e8	+	1.27477e9i	0.348809	+	0.480095i	−0.598179	+	0.801362i	$0.704109\pi$
$228$	−7.84799e8	+	1.17320e9i	−0.290415	+	0.434143i
$229$	1.53791e9	−	4.73319e9i	0.559226	−	1.72112i	−0.125286	−	0.992121i	$-0.539985\pi$
$229$	1.53791e9	−	4.73319e9i	0.559226	−	1.72112i	0.684512	−	0.729001i	$-0.260015\pi$
$230$	1.19536e9	−	2.30552e9i	0.427157	−	0.823867i
$231$	6.65059e8	−	2.16091e8i	0.233567	−	0.0758907i
$232$	−1.64245e8	+	3.74691e8i	−0.0566945	+	0.129337i
$233$	1.11051e9	+	3.41779e9i	0.376789	+	1.15964i	0.942264	+	0.334871i	$0.108693\pi$
$233$	1.11051e9	+	3.41779e9i	0.376789	+	1.15964i	−0.565475	+	0.824765i	$0.691307\pi$
$234$	−1.11951e9	+	1.16374e9i	−0.373391	+	0.388145i
$235$	9.29493e8	+	3.29438e8i	0.304772	+	0.108019i
$236$	−8.59523e8	−	2.33361e9i	−0.277083	−	0.752283i
$237$	−9.44147e8	−	6.85963e8i	−0.299258	−	0.217424i
$238$	−7.74646e8	−	7.45199e8i	−0.241432	−	0.232255i
$239$	2.66662e9	+	3.67029e9i	0.817277	+	1.12489i	0.990160	+	0.139943i	$0.0446919\pi$
$239$	2.66662e9	+	3.67029e9i	0.817277	+	1.12489i	−0.172883	+	0.984942i	$0.555308\pi$
$240$	8.10790e7	+	1.58732e9i	0.0244379	+	0.478432i
$241$	−1.13252e9	−	8.22824e8i	−0.335720	−	0.243915i	0.407134	−	0.913369i	$-0.366528\pi$
$241$	−1.13252e9	−	8.22824e8i	−0.335720	−	0.243915i	−0.742854	+	0.669453i	$0.766528\pi$
$242$	−4.56401e9	+	8.13792e8i	−1.33072	+	0.237275i
$243$			3.56571e9i			1.02264i
$244$	2.74154e8	+	7.07240e9i	0.0773454	+	1.99530i
$245$	−3.19924e9	−	8.46532e7i	−0.887937	−	0.0234952i
$246$	7.96808e8	−	1.64169e9i	0.217577	−	0.448281i
$247$	−2.69791e9	−	8.76604e8i	−0.724836	−	0.235514i
$248$	−5.73308e9	+	1.25314e9i	−1.51559	+	0.331279i
$249$	2.65418e9			0.690451
$250$	−1.56154e9	−	3.58056e9i	−0.399754	−	0.916623i
$251$			2.51075e9i			0.632570i	0.948664	+	0.316285i	$0.102436\pi$
$251$			2.51075e9i			0.632570i	−0.948664	+	0.316285i	$0.897564\pi$
$252$	−3.59013e8	−	9.74725e8i	−0.0890242	−	0.241702i
$253$	−1.80183e9	+	5.54545e9i	−0.439775	+	1.35349i
$254$	1.38305e9	−	2.84955e9i	0.332280	−	0.684606i
$255$	−5.36935e7	+	2.02920e9i	−0.0126987	+	0.479914i
$256$	−3.04338e9	+	3.03061e9i	−0.708591	+	0.705619i
$257$	7.85276e9			1.80007			0.900036	−	0.435815i	$-0.143540\pi$
$257$	7.85276e9			1.80007			0.900036	+	0.435815i	$0.143540\pi$
$258$	4.45594e8	−	7.94521e7i	0.100568	−	0.0179319i
$259$	−1.27659e9	+	1.75708e9i	−0.283696	+	0.390474i
$260$	−3.02559e9	+	1.02435e9i	−0.662089	+	0.224159i
$261$	−4.08491e8	+	2.96786e8i	−0.0880279	+	0.0639560i
$262$	−1.98261e9	−	1.90725e9i	−0.420758	−	0.404764i
$263$	−3.71644e9	+	5.11523e9i	−0.776790	+	1.06916i	0.218839	+	0.975761i	$0.429773\pi$
$263$	−3.71644e9	+	5.11523e9i	−0.776790	+	1.06916i	−0.995629	+	0.0933987i	$0.970227\pi$
$264$	−7.62028e8	−	3.48625e9i	−0.156876	−	0.717700i
$265$	4.31485e8	−	1.21741e9i	0.0874947	−	0.246862i
$266$	1.26507e9	−	1.31506e9i	0.252690	−	0.262675i
$267$	3.03778e9	−	9.87034e8i	0.597738	−	0.194217i
$268$	−1.27826e9	+	4.52325e9i	−0.247787	+	0.876823i
$269$	−2.92992e9	−	9.01736e9i	−0.559560	−	1.72215i	−0.683587	−	0.729869i	$-0.739581\pi$
$269$	−2.92992e9	−	9.01736e9i	−0.559560	−	1.72215i	0.124027	−	0.992279i	$-0.460419\pi$
$270$	−2.07477e9	+	4.00164e9i	−0.390404	+	0.752980i
$271$	7.21651e9	+	2.34479e9i	1.33798	+	0.434737i	0.888633	−	0.458620i	$-0.151656\pi$
$271$	7.21651e9	+	2.34479e9i	1.33798	+	0.434737i	0.449349	+	0.893356i	$0.351656\pi$
$272$	−4.17484e9	+	3.55807e9i	−0.762719	+	0.650039i
$273$	−5.03041e8	+	3.65481e8i	−0.0905635	+	0.0657982i
$274$	8.54180e8	−	6.16360e9i	0.151547	−	1.09353i
$275$	4.77270e9	+	7.35814e9i	0.834513	+	1.28658i
$276$	−2.48254e9	−	7.01556e8i	−0.427818	−	0.120900i
$277$	−3.24686e9	+	2.35898e9i	−0.551498	+	0.400687i	−0.828337	−	0.560229i	$-0.810713\pi$
$277$	−3.24686e9	+	2.35898e9i	−0.551498	+	0.400687i	0.276840	+	0.960916i	$0.410713\pi$
$278$	−1.11572e9	+	2.29875e9i	−0.186799	+	0.384868i
$279$	−6.88834e9	−	2.23816e9i	−1.13684	−	0.369380i
$280$	2.57027e8	−	2.03862e9i	0.0418164	−	0.331668i
$281$	1.34285e9	+	4.13285e9i	0.215378	+	0.662864i	0.999127	+	0.0417865i	$0.0133049\pi$
$281$	1.34285e9	+	4.13285e9i	0.215378	+	0.662864i	−0.783749	+	0.621078i	$0.786695\pi$
$282$	1.34473e8	−	9.70335e8i	0.0212638	−	0.153435i
$283$	7.34402e9	−	2.38622e9i	1.14495	−	0.372018i	0.325713	−	0.945469i	$-0.394396\pi$
$283$	7.34402e9	−	2.38622e9i	1.14495	−	0.372018i	0.819240	+	0.573451i	$0.194396\pi$
$284$	6.75724e9	−	5.32123e9i	1.03871	−	0.817972i
$285$	−3.44482e9	−	9.11514e7i	−0.522140	−	0.0138160i
$286$	6.32597e9	−	3.37917e9i	0.945503	−	0.505063i
$287$	−1.38667e9	+	1.90859e9i	−0.204383	+	0.281309i
$288$	−5.13085e9	+	1.33168e9i	−0.745795	+	0.193567i
$289$	−2.42119e7	+	1.75910e7i	−0.00347086	+	0.00252173i
$290$	−9.87586e8	+	1.49257e8i	−0.139631	+	0.0211029i
$291$	6.94300e8	−	9.55623e8i	0.0968223	−	0.133264i
$292$	−3.97220e8	−	1.02472e10i	−0.0546386	−	1.40952i
$293$	−7.29957e9			−0.990437			−0.495218	−	0.868769i	$-0.664912\pi$
$293$	−7.29957e9			−0.990437			−0.495218	+	0.868769i	$0.664912\pi$
$294$	5.58059e8	+	3.12978e9i	0.0746948	+	0.418913i
$295$	3.69740e9	−	4.81580e9i	0.488211	−	0.635888i
$296$	8.27913e9	+	7.36870e9i	1.07849	+	0.959896i
$297$	3.12740e9	−	9.62514e9i	0.401936	−	1.23703i
$298$	1.66097e9	+	3.10943e9i	0.210619	+	0.394290i
$299$		−	5.18469e9i		−	0.648691i
$300$	−3.17126e9	+	2.23612e9i	−0.391514	+	0.276064i
$301$	−5.85147e8			−0.0712851
$302$	3.31158e9	−	1.76896e9i	0.398114	−	0.212662i
$303$	−3.74947e9	−	1.21828e9i	−0.444836	−	0.144536i
$304$	−6.04027e9	−	7.08732e9i	−0.707232	−	0.829827i
$305$	−1.42432e10	+	9.78334e9i	−1.64592	+	1.13055i
$306$	−6.66492e9	+	1.18840e9i	−0.760167	+	0.135543i
$307$			1.52043e10i			1.71164i	0.517272	+	0.855821i	$0.326948\pi$
$307$			1.52043e10i			1.71164i	−0.517272	+	0.855821i	$0.673052\pi$
$308$	1.78700e8	+	4.60995e9i	0.0198573	+	0.512264i
$309$	2.69796e7	+	1.96019e7i	0.00295939	+	0.00215012i
$310$	−1.00589e10	−	1.02024e10i	−1.08919	−	1.10473i
$311$	2.54204e9	+	3.49882e9i	0.271732	+	0.374007i	0.922973	−	0.384864i	$-0.125751\pi$
$311$	2.54204e9	+	3.49882e9i	0.271732	+	0.374007i	−0.651241	+	0.758871i	$0.725751\pi$
$312$	1.60235e9	+	2.73882e9i	0.169098	+	0.289031i
$313$	6.79602e7	+	4.93760e7i	0.00708072	+	0.00514444i	0.591320	−	0.806437i	$-0.298607\pi$
$313$	6.79602e7	+	4.93760e7i	0.00708072	+	0.00514444i	−0.584239	+	0.811581i	$0.698607\pi$
$314$	−5.72377e8	−	1.07152e9i	−0.0588794	−	0.110225i
$315$	1.54436e9	−	2.01151e9i	0.156858	−	0.204305i
$316$	6.04889e9	−	4.76341e9i	0.606635	−	0.477715i
$317$	−1.46233e9	−	4.50059e9i	−0.144813	−	0.445690i	0.852174	−	0.523259i	$-0.175284\pi$
$317$	−1.46233e9	−	4.50059e9i	−0.144813	−	0.445690i	−0.996987	+	0.0775695i	$0.975284\pi$
$318$	−1.27091e9	−	1.76128e8i	−0.124281	−	0.0172235i
$319$	2.13279e9	−	6.92984e8i	0.205961	−	0.0669207i
$320$	−1.02229e10	−	2.33310e9i	−0.974932	−	0.222502i
$321$	2.80939e9	−	8.64642e9i	0.264601	−	0.814359i
$322$	3.00037e9	+	1.45626e9i	0.279095	+	0.135461i
$323$	−6.99054e9	−	9.62166e9i	−0.642245	−	0.883975i
$324$	−3.86204e9	−	1.09140e9i	−0.350459	−	0.0990385i
$325$	−6.05793e9	−	4.91112e9i	−0.542988	−	0.440197i
$326$	3.06409e9	+	4.24636e8i	0.271289	+	0.0375964i
$327$	−3.98045e9	−	5.47862e9i	−0.348130	−	0.479160i
$328$	8.99301e9	+	8.00408e9i	0.776980	+	0.691538i
$329$	−3.91349e8	+	1.20445e9i	−0.0334027	+	0.102803i
$330$	6.20401e9	−	6.11675e9i	0.523138	−	0.515781i
$331$	1.26568e10	−	4.11246e9i	1.05442	−	0.342602i	0.270018	−	0.962855i	$-0.412970\pi$
$331$	1.26568e10	−	4.11246e9i	1.05442	−	0.342602i	0.784401	+	0.620254i	$0.212970\pi$
$332$	−4.76192e9	+	1.68506e10i	−0.391949	+	1.38696i
$333$	4.22709e9	+	1.30096e10i	0.343767	+	1.05801i
$334$	−1.62777e10	−	1.56590e10i	−1.30800	−	1.25828i
$335$	−1.10039e10	+	3.25622e9i	−0.873711	+	0.258544i
$336$	−2.03501e9	+	1.58007e8i	−0.159665	+	0.0123971i
$337$	−1.83050e10	−	1.32993e10i	−1.41922	−	1.03112i	−0.991900	−	0.127022i	$-0.959458\pi$
$337$	−1.83050e10	−	1.32993e10i	−1.41922	−	1.03112i	−0.427319	−	0.904101i	$-0.640542\pi$
$338$	4.62728e9	−	4.81013e9i	0.354535	−	0.368545i
$339$	−2.26525e9	−	3.11784e9i	−0.171521	−	0.236078i
$340$	−1.27864e10	−	3.98151e9i	−0.956828	−	0.297942i
$341$	2.60245e10	+	1.89079e10i	1.92471	+	1.39838i
$342$	−2.01745e9	−	1.13145e10i	−0.147468	−	0.827050i
$343$		−	8.73703e9i		−	0.631230i
$344$	−2.95031e8	+	2.97149e9i	−0.0210685	+	0.212197i
$345$	−1.78714e9	−	6.03937e9i	−0.126149	−	0.426300i
$346$	−5.89268e9	−	2.86007e9i	−0.411158	−	0.199559i
$347$	2.14268e9	+	6.96199e8i	0.147788	+	0.0480193i	0.381977	−	0.924172i	$-0.375243\pi$
$347$	2.14268e9	+	6.96199e8i	0.147788	+	0.0480193i	−0.234189	+	0.972191i	$0.575243\pi$
$348$	3.42921e8	+	9.31034e8i	0.0233818	+	0.0634817i
$349$	2.58260e10			1.74082			0.870412	−	0.492323i	$-0.163852\pi$
$349$	2.58260e10			1.74082			0.870412	+	0.492323i	$0.163852\pi$
$350$	4.54358e9	−	2.12629e9i	0.302779	−	0.141694i
$351$			8.99897e9i			0.592877i
$352$	2.35003e10	+	1.41687e9i	1.53075	+	0.0922907i
$353$	−6.33448e9	+	1.94955e10i	−0.407955	+	1.25556i	0.510447	+	0.859909i	$0.329480\pi$
$353$	−6.33448e9	+	1.94955e10i	−0.407955	+	1.25556i	−0.918402	+	0.395648i	$0.870520\pi$
$354$	−5.42588e9	−	2.63350e9i	−0.345507	−	0.167695i
$355$	1.97920e10	+	7.01482e9i	1.24617	+	0.441675i
$356$	8.16243e8	+	2.10568e10i	0.0508183	+	1.31097i
$357$	−2.60686e9			−0.160489
$358$	2.02075e9	+	1.13330e10i	0.123021	+	0.689944i
$359$	2.38164e9	−	3.27805e9i	0.143383	−	0.197350i	−0.731285	−	0.682072i	$-0.761079\pi$
$359$	2.38164e9	−	3.27805e9i	0.143383	−	0.197350i	0.874668	+	0.484722i	$0.161079\pi$
$360$	−9.43616e9	−	8.85676e9i	−0.561804	−	0.527309i
$361$	2.59397e9	−	1.88463e9i	0.152734	−	0.110968i
$362$	−5.59525e9	+	5.81635e9i	−0.325826	+	0.338701i
$363$	−6.60866e9	+	9.09603e9i	−0.380616	+	0.523872i
$364$	−1.41781e9	−	3.84938e9i	−0.0807632	−	0.219273i
$365$	2.06369e10	−	1.41750e10i	1.16272	−	0.798643i
$366$	1.23703e10	+	1.19001e10i	0.689377	+	0.663172i
$367$	−7.49650e9	+	2.43576e9i	−0.413232	+	0.134267i	−0.508253	−	0.861208i	$-0.669708\pi$
$367$	−7.49650e9	+	2.43576e9i	−0.413232	+	0.134267i	0.0950204	+	0.995475i	$0.469708\pi$
$368$	8.90794e9	−	1.45022e10i	0.485720	−	0.790757i
$369$	4.59158e9	+	1.41314e10i	0.247660	+	0.762220i
$370$	−4.42214e9	+	2.66953e10i	−0.235953	+	1.42439i
$371$	1.57754e9	+	5.12574e8i	0.0832693	+	0.0270559i
$372$	−7.91323e9	+	1.18295e10i	−0.413221	+	0.617726i
$373$	6.63143e9	−	4.81802e9i	0.342588	−	0.248905i	−0.403165	−	0.915127i	$-0.632090\pi$
$373$	6.63143e9	−	4.81802e9i	0.342588	−	0.248905i	0.745753	+	0.666223i	$0.232090\pi$
$374$	2.97836e10	+	4.12754e9i	1.52226	+	0.210962i
$375$	−8.74940e9	−	3.63256e9i	−0.442439	−	0.183691i
$376$	5.91911e9	+	2.59463e9i	0.296145	+	0.129815i
$377$	−1.61321e9	+	1.17207e9i	−0.0798593	+	0.0580212i
$378$	−5.20769e9	−	2.52760e9i	−0.255081	−	0.123806i
$379$	−2.07144e10	−	6.73052e9i	−1.00396	−	0.326206i	−0.239513	−	0.970893i	$-0.576988\pi$
$379$	−2.07144e10	−	6.73052e9i	−1.00396	−	0.326206i	−0.764446	+	0.644687i	$0.776988\pi$
$380$	6.75911e9	−	2.17066e10i	0.324157	−	1.04101i
$381$	−2.37380e9	−	7.30580e9i	−0.112653	−	0.346711i
$382$	1.34193e10	+	1.85971e9i	0.630198	+	0.0873357i
$383$	−1.11815e10	+	3.63309e9i	−0.519642	+	0.168842i	−0.557083	−	0.830457i	$-0.688079\pi$
$383$	−1.11815e10	+	3.63309e9i	−0.519642	+	0.168842i	0.0374407	+	0.999299i	$0.488079\pi$
$384$	−2.23660e8	+	1.04138e10i	−0.0102864	+	0.478945i
$385$	−9.28407e9	+	6.37701e9i	−0.422567	+	0.290251i
$386$	3.22554e9	+	6.03838e9i	0.145296	+	0.272001i
$387$	−2.16625e9	+	2.98159e9i	−0.0965750	+	0.132924i
$388$	4.82130e9	+	6.12241e9i	0.212734	+	0.270144i
$389$	−2.00727e10	+	1.45837e10i	−0.876613	+	0.636897i	−0.932353	−	0.361548i	$-0.882248\pi$
$389$	−2.00727e10	+	1.45837e10i	−0.876613	+	0.636897i	0.0557399	+	0.998445i	$0.482248\pi$
$390$	−3.56579e9	+	6.87742e9i	−0.154134	+	0.297281i
$391$	1.27765e10	−	1.75854e10i	0.546645	−	0.752393i
$392$	−2.08712e10	−	2.07225e9i	−0.883902	−	0.0877601i
$393$	−6.67193e9			−0.279693
$394$	3.25204e10	−	5.79858e9i	1.34949	−	0.240623i
$395$	1.77172e10	+	6.27946e9i	0.727791	+	0.257949i
$396$	2.41514e10	+	1.61558e10i	0.982112	+	0.656973i
$397$	5.02527e9	−	1.54662e10i	0.202301	−	0.622617i	−0.797513	−	0.603302i	$-0.793851\pi$
$397$	5.02527e9	−	1.54662e10i	0.202301	−	0.622617i	0.999813	−	0.0193153i	$-0.00614864\pi$
$398$	4.81411e9	−	2.57157e9i	0.191860	−	0.102486i
$399$		−	4.42546e9i		−	0.174609i
$400$	−8.50685e9	−	2.41453e10i	−0.332299	−	0.943174i
$401$	3.37735e10			1.30617			0.653084	−	0.757285i	$-0.273475\pi$
$401$	3.37735e10			1.30617			0.653084	+	0.757285i	$0.273475\pi$
$402$	5.37105e9	+	1.00549e10i	0.205662	+	0.385011i
$403$	−2.72034e10	−	8.83892e9i	−1.03134	−	0.335104i
$404$	1.44615e10	−	2.16185e10i	0.542859	−	0.811523i
$405$	−2.78023e9	−	9.39536e9i	−0.103338	−	0.349215i
$406$	−2.25159e8	−	1.26277e9i	−0.00828678	−	0.0464750i
$407$		−	6.07540e10i		−	2.21410i
$408$	−1.31438e9	+	1.32381e10i	−0.0474328	+	0.477733i
$409$	1.47269e9	+	1.06997e9i	0.0526282	+	0.0382366i	0.613788	−	0.789471i	$-0.289645\pi$
$409$	1.47269e9	+	1.06997e9i	0.0526282	+	0.0382366i	−0.561160	+	0.827707i	$0.689645\pi$
$410$	−4.80345e9	+	2.89971e10i	−0.169988	+	1.02617i
$411$	−8.87024e9	−	1.22088e10i	−0.310862	−	0.427865i
$412$	−1.72851e8	+	1.36118e8i	−0.00599906	+	0.00472417i
$413$	6.30800e9	+	4.58303e9i	0.216816	+	0.157526i
$414$	1.85279e10	−	9.89709e9i	0.630701	−	0.336904i
$415$	−4.09931e10	+	1.21305e10i	−1.38203	+	0.408965i
$416$	−2.02627e10	+	5.25907e9i	−0.676589	+	0.175605i
$417$	1.91496e9	+	5.89363e9i	0.0633308	+	0.194912i
$418$	−7.00701e9	+	5.05613e10i	−0.229524	+	1.65620i
$419$	−2.23007e10	+	7.24592e9i	−0.723538	+	0.235092i	−0.647557	−	0.762017i	$-0.724209\pi$
$419$	−2.23007e10	+	7.24592e9i	−0.723538	+	0.235092i	−0.0759817	+	0.997109i	$0.524209\pi$
$420$	−2.97840e9	−	3.99522e9i	−0.0957163	−	0.128394i
$421$	−6.65166e9	+	2.04717e10i	−0.211739	+	0.651667i	0.787630	+	0.616149i	$0.211308\pi$
$421$	−6.65166e9	+	2.04717e10i	−0.211739	+	0.651667i	−0.999369	+	0.0355180i	$0.988692\pi$
$422$	8.16525e9	−	1.68231e10i	0.257466	−	0.530464i
$423$	4.68841e9	+	6.45305e9i	0.146442	+	0.201560i
$424$	3.39835e9	−	7.75262e9i	0.105149	−	0.239875i
$425$	−8.44484e9	−	3.15859e10i	−0.258842	−	0.968138i
$426$	2.86338e9	−	2.06617e10i	0.0869443	−	0.627374i
$427$	−1.30434e10	−	1.79527e10i	−0.392356	−	0.540032i
$428$	4.98531e10	+	3.33487e10i	1.48565	+	0.993811i
$429$	5.37490e9	−	1.65422e10i	0.158687	−	0.488388i
$430$	−6.51896e9	+	3.26363e9i	−0.190680	+	0.0954613i
$431$	4.11426e10	−	1.33681e10i	1.19229	−	0.387399i	0.355373	−	0.934725i	$-0.384354\pi$
$431$	4.11426e10	−	1.33681e10i	1.19229	−	0.387399i	0.836920	+	0.547325i	$0.184354\pi$
$432$	−1.54613e10	+	2.51712e10i	−0.443928	+	0.722719i
$433$	−5.99426e9	−	1.84484e10i	−0.170523	−	0.524817i	0.828877	−	0.559430i	$-0.188980\pi$
$433$	−5.99426e9	−	1.84484e10i	−0.170523	−	0.524817i	−0.999401	+	0.0346132i	$0.988980\pi$
$434$	1.27559e10	−	1.32599e10i	0.359543	−	0.373750i
$435$	−1.47514e9	+	1.92135e9i	−0.0411979	+	0.0536597i
$436$	4.19236e10	−	1.54414e10i	1.16014	−	0.427308i
$437$	2.98534e10	+	2.16897e10i	0.818592	+	0.594742i
$438$	−1.79233e10	−	1.72420e10i	−0.486992	−	0.468480i
$439$	−6.63526e8	−	9.13266e8i	−0.0178649	−	0.0245889i	0.799991	−	0.600012i	$-0.204837\pi$
$439$	−6.63526e8	−	9.13266e8i	−0.0178649	−	0.0245889i	−0.817856	+	0.575423i	$0.804837\pi$
$440$	2.77027e10	+	5.03616e10i	0.739113	+	1.34366i
$441$	−2.09422e10	−	1.52154e10i	−0.553691	−	0.402280i
$442$	−2.63211e10	+	4.69321e9i	−0.689627	+	0.122965i
$443$		−	5.58401e10i		−	1.44988i	−0.688814	−	0.724938i	$-0.741868\pi$
$443$		−	5.58401e10i		−	1.44988i	0.688814	−	0.724938i	$-0.258132\pi$
$444$	2.68595e10	−	1.04118e9i	0.691140	−	0.0267913i
$445$	−4.24067e10	+	2.91282e10i	−1.08142	+	0.742802i
$446$	−1.07247e10	+	2.20965e10i	−0.271048	+	0.558449i
$447$	8.13106e9	+	2.64194e9i	0.203665	+	0.0661749i
$448$	2.64791e9	−	1.32032e10i	0.0657342	−	0.327767i
$449$	5.27476e10			1.29783			0.648915	−	0.760861i	$-0.275223\pi$
$449$	5.27476e10			1.29783			0.648915	+	0.760861i	$0.275223\pi$
$450$	5.98621e9	−	3.10233e10i	0.145983	−	0.756550i
$451$		−	6.59927e10i		−	1.59511i
$452$	2.38584e10	−	8.78758e9i	0.571593	−	0.210531i
$453$	2.81370e9	−	8.65968e9i	0.0668167	−	0.205641i
$454$	−1.10083e10	+	2.26808e10i	−0.259118	+	0.533869i
$455$	6.09898e9	−	7.94383e9i	0.142302	−	0.185347i
$456$	−2.24734e10	−	2.23132e9i	−0.519767	−	0.0516062i
$457$	−5.87114e10			−1.34604			−0.673020	−	0.739625i	$-0.735003\pi$
$457$	−5.87114e10			−1.34604			−0.673020	+	0.739625i	$0.735003\pi$
$458$	7.83918e10	−	1.39778e10i	1.78160	−	0.317670i
$459$	−2.21760e10	+	3.05226e10i	−0.499611	+	0.687655i
$460$	4.15485e10	−	5.10666e8i	0.927950	−	0.0114053i
$461$	−1.41676e10	+	1.02934e10i	−0.313685	+	0.227906i	−0.733476	−	0.679715i	$-0.762103\pi$
$461$	−1.41676e10	+	1.02934e10i	−0.313685	+	0.227906i	0.419791	+	0.907621i	$0.362103\pi$
$462$	8.06327e9	+	7.75676e9i	0.176988	+	0.170260i
$463$	−1.51247e10	+	2.08174e10i	−0.329126	+	0.453004i	−0.941226	−	0.337777i	$-0.890325\pi$
$463$	−1.51247e10	+	2.08174e10i	−0.329126	+	0.453004i	0.612100	+	0.790781i	$0.290325\pi$
$464$	−6.52610e9	+	5.06716e8i	−0.140793	+	0.0109318i
$465$	−3.47346e10	−	9.19092e8i	−0.742933	−	0.0196583i
$466$	−3.98626e10	+	4.14378e10i	−0.845322	+	0.878725i
$467$	2.37809e10	−	7.72687e9i	0.499989	−	0.162456i	−0.0481558	−	0.998840i	$-0.515334\pi$
$467$	2.37809e10	−	7.72687e9i	0.499989	−	0.162456i	0.548144	+	0.836384i	$0.315334\pi$
$468$	−2.48632e10	−	7.02624e9i	−0.518290	−	0.146467i
$469$	−4.55405e9	−	1.40159e10i	−0.0941253	−	0.289688i
$470$	2.35785e9	+	1.56012e10i	0.0483198	+	0.319717i
$471$	−2.80199e9	−	9.10422e8i	−0.0569355	−	0.0184995i
$472$	2.64540e10	−	2.97225e10i	0.532996	−	0.598849i
$473$	1.32423e10	−	9.62110e9i	0.264557	−	0.192212i
$474$	2.56322e9	−	1.84957e10i	0.0507776	−	0.366402i
$475$	5.36210e10	−	1.43362e10i	1.05332	−	0.281617i
$476$	4.67701e9	−	1.65502e10i	0.0911047	−	0.322385i
$477$	8.45196e9	−	6.14071e9i	0.163261	−	0.118616i
$478$	−3.16950e10	+	6.53022e10i	−0.607127	+	1.25088i
$479$	−1.83548e10	−	5.96382e9i	−0.348664	−	0.113288i	0.129449	−	0.991586i	$-0.458679\pi$
$479$	−1.83548e10	−	5.96382e9i	−0.348664	−	0.113288i	−0.478113	+	0.878298i	$0.658679\pi$
$480$	−2.17902e10	+	1.31105e10i	−0.410484	+	0.246976i
$481$	1.66936e10	+	5.13776e10i	0.311867	+	0.959828i
$482$	3.07462e9	−	2.21859e10i	0.0569644	−	0.411045i
$483$	7.69249e9	−	2.49944e9i	0.141344	−	0.0459255i
$484$	−4.58913e10	−	5.82758e10i	−0.836274	−	1.06196i
$485$	−6.35578e9	+	1.79325e10i	−0.114869	+	0.324097i
$486$	−5.03219e10	+	2.68806e10i	−0.902011	+	0.481830i
$487$	2.93440e10	−	4.03886e10i	0.521679	−	0.718030i	−0.464155	−	0.885754i	$-0.653642\pi$
$487$	2.93440e10	−	4.03886e10i	0.521679	−	0.718030i	0.985834	+	0.167724i	$0.0536419\pi$
$488$	−9.77440e10	+	5.71853e10i	−1.72350	+	1.00834i
$489$	6.06934e9	−	4.40964e9i	0.106147	−	0.0771201i
$490$	−2.29232e10	−	4.57881e10i	−0.397641	−	0.794270i
$491$	−3.46739e10	+	4.77246e10i	−0.596592	+	0.821138i	−0.995391	−	0.0959002i	$-0.969427\pi$
$491$	−3.46739e10	+	4.77246e10i	−0.596592	+	0.821138i	0.398799	+	0.917038i	$0.369427\pi$
$492$	2.91755e10	−	1.13096e9i	0.497919	−	0.0193013i
$493$	−8.35996e9			−0.141520
$494$	−7.96731e9	−	4.46833e10i	−0.133784	−	0.750304i
$495$	−1.87643e9	+	7.09146e10i	−0.0312545	+	1.18118i
$496$	−6.09049e10	−	7.14624e10i	−1.00629	−	1.18073i
$497$	−8.33312e9	+	2.56467e10i	−0.136578	+	0.420345i
$498$	2.00089e10	+	3.74577e10i	0.325316	+	0.609009i
$499$			1.21059e11i			1.95251i	0.216617	+	0.976257i	$0.430498\pi$
$499$			1.21059e11i			1.95251i	−0.216617	+	0.976257i	$0.569502\pi$
$500$	3.87595e10	−	4.90301e10i	0.620152	−	0.784481i
$501$	−5.47781e10			−0.869473
$502$	−3.54335e10	+	1.89276e10i	−0.557955	+	0.298045i
$503$	−1.17187e10	−	3.80763e9i	−0.183066	−	0.0594816i	0.216050	−	0.976382i	$-0.430683\pi$
$503$	−1.17187e10	−	3.80763e9i	−0.183066	−	0.0594816i	−0.399115	+	0.916901i	$0.630683\pi$
$504$	1.10495e10	−	1.24148e10i	0.171247	−	0.192405i
$505$	6.34776e10	+	1.67965e9i	0.976012	+	0.0258257i
$506$	−9.18448e10	+	1.63765e10i	−1.40105	+	0.249815i
$507$		−	1.61872e10i		−	0.244985i
$508$	5.06412e10	−	1.96305e9i	0.760412	−	0.0294765i
$509$	−1.72238e10	−	1.25138e10i	−0.256600	−	0.186431i	0.452047	−	0.891994i	$-0.350694\pi$
$509$	−1.72238e10	−	1.25138e10i	−0.256600	−	0.186431i	−0.708647	+	0.705563i	$0.750694\pi$
$510$	−2.90423e10	+	1.45396e10i	−0.429289	+	0.214918i
$511$	1.88986e10	+	2.60116e10i	0.277169	+	0.381491i
$512$	−6.57131e10	−	2.01036e10i	−0.956251	−	0.292546i
$513$	−5.18159e10	−	3.76465e10i	−0.748158	−	0.543569i
$514$	5.91992e10	+	1.10824e11i	0.848131	+	1.58774i
$515$	−5.06281e8	−	1.79440e8i	−0.00719719	−	0.00255088i
$516$	4.48045e9	+	5.68958e9i	0.0632009	+	0.0802567i
$517$	−1.09473e10	−	3.36922e10i	−0.153230	−	0.471594i
$518$	−3.44209e10	−	4.77021e9i	−0.478083	−	0.0662549i
$519$	−1.51079e10	+	4.90886e9i	−0.208226	+	0.0676568i
$520$	−3.72652e10	−	3.49771e10i	−0.509671	−	0.478377i
$521$	1.75727e10	−	5.40831e10i	0.238499	−	0.734025i	−0.758139	−	0.652093i	$-0.773891\pi$
$521$	1.75727e10	−	5.40831e10i	0.238499	−	0.734025i	0.996638	−	0.0819317i	$-0.0261089\pi$
$522$	−7.26792e9	−	3.52756e9i	−0.0978878	−	0.0475107i
$523$	−2.86767e10	−	3.94701e10i	−0.383286	−	0.527548i	0.573166	−	0.819440i	$-0.305715\pi$
$523$	−2.86767e10	−	3.94701e10i	−0.383286	−	0.527548i	−0.956451	+	0.291892i	$0.905715\pi$
$524$	1.19702e10	−	4.23581e10i	0.158773	−	0.561838i
$525$	4.36618e9	−	1.13557e10i	0.0574730	−	0.149477i
$526$	−1.00207e11	−	1.38871e10i	−1.30904	−	0.181413i
$527$	−7.04866e10	−	9.70165e10i	−0.913827	−	1.25778i
$528$	4.34558e10	−	3.70359e10i	0.559130	−	0.476526i
$529$	3.35838e9	−	1.03360e10i	0.0428852	−	0.131987i
$530$	2.04338e10	−	3.08822e9i	0.258968	−	0.0391386i
$531$	4.67052e10	−	1.51755e10i	0.587473	−	0.190881i
$532$	2.80959e10	+	7.93981e9i	0.350750	+	0.0991206i
$533$	1.81330e10	+	5.58077e10i	0.224679	+	0.691489i
$534$	3.68304e10	+	3.54304e10i	0.452941	+	0.435724i
$535$	−3.87332e9	+	1.46382e11i	−0.0472791	+	1.78678i
$536$	−7.34717e10	+	1.60595e10i	−0.890146	+	0.194569i
$537$	2.25866e10	+	1.64101e10i	0.271615	+	0.197340i
$538$	1.05172e11	−	1.09328e11i	1.25537	−	1.30497i
$539$	6.75770e10	+	9.30118e10i	0.800653	+	1.10200i
$540$	−7.21150e10	+	8.86354e8i	−0.848107	+	0.0104239i
$541$	−3.66117e10	−	2.66000e10i	−0.427397	−	0.310522i	0.353210	−	0.935544i	$-0.385090\pi$
$541$	−3.66117e10	−	2.66000e10i	−0.427397	−	0.310522i	−0.780607	+	0.625022i	$0.785090\pi$
$542$	2.13114e10	+	1.19521e11i	0.246953	+	1.38499i
$543$			1.95733e10i			0.225146i
$544$	−8.16867e10	−	3.20954e10i	−0.932730	−	0.366477i
$545$	8.65163e10	+	6.64240e10i	0.980645	+	0.752903i
$546$	−8.95018e9	−	4.34405e9i	−0.100707	−	0.0488793i
$547$	−5.22052e10	−	1.69625e10i	−0.583129	−	0.189470i	0.00257281	−	0.999997i	$-0.499181\pi$
$547$	−5.22052e10	−	1.69625e10i	−0.583129	−	0.189470i	−0.585702	+	0.810527i	$0.699181\pi$
$548$	9.34246e10	−	3.44104e10i	1.03595	−	0.381564i
$549$	−1.39765e11			−1.53854
$550$	−6.78638e10	+	1.22826e11i	−0.741630	+	1.34227i
$551$		−	1.41921e10i		−	0.153971i
$552$	−8.81409e9	−	4.03241e10i	−0.0949339	−	0.434319i
$553$	−7.45957e9	+	2.29582e10i	−0.0797652	+	0.245492i
$554$	−5.77685e10	−	2.80385e10i	−0.613270	−	0.297656i
$555$	3.71551e10	+	5.40928e10i	0.391604	+	0.570122i
$556$	−4.08526e10	+	1.58360e9i	−0.427484	+	0.0165710i
$557$	−7.97183e10			−0.828204			−0.414102	−	0.910230i	$-0.635904\pi$
$557$	−7.97183e10			−0.828204			−0.414102	+	0.910230i	$0.635904\pi$
$558$	−2.03422e10	−	1.14086e11i	−0.209827	−	1.17678i
$559$	−8.55494e9	+	1.17749e10i	−0.0876133	+	0.120589i
$560$	3.07081e10	−	1.17411e10i	0.312249	−	0.119387i
$561$	5.89951e10	−	4.28625e10i	0.595614	−	0.432739i
$562$	−4.82026e10	+	5.01073e10i	−0.483198	+	0.502291i
$563$	−2.91808e10	+	4.01640e10i	−0.290445	+	0.399763i	−0.929159	−	0.369681i	$-0.879467\pi$
$563$	−2.91808e10	+	4.01640e10i	−0.290445	+	0.399763i	0.638714	+	0.769445i	$0.279467\pi$
$564$	1.47078e10	−	5.41722e9i	0.145356	−	0.0535378i
$565$	4.92358e10	+	3.78014e10i	0.483155	+	0.370949i
$566$	8.90399e10	+	8.56552e10i	0.867599	+	0.834619i
$567$	1.19671e10	−	3.88834e9i	0.115786	−	0.0376211i
$568$	1.26037e11	+	5.52483e10i	1.21089	+	0.530793i
$569$	5.36406e10	+	1.65089e11i	0.511735	+	1.57496i	0.789146	+	0.614206i	$0.210524\pi$
$569$	5.36406e10	+	1.65089e11i	0.511735	+	1.57496i	−0.277411	+	0.960751i	$0.589476\pi$
$570$	−2.46828e10	−	4.93029e10i	−0.233828	−	0.467060i
$571$	1.45356e11	+	4.72291e10i	1.36738	+	0.444288i	0.898500	−	0.438974i	$-0.144658\pi$
$571$	1.45356e11	+	4.72291e10i	1.36738	+	0.444288i	0.468879	+	0.883262i	$0.344658\pi$
$572$	9.53784e10	+	6.38024e10i	0.890976	+	0.596009i
$573$	2.65809e10	−	1.93122e10i	0.246577	−	0.179148i
$574$	−3.73890e10	−	5.18153e9i	−0.344426	−	0.0477321i
$575$	5.52040e10	+	8.51088e10i	0.505009	+	0.778580i
$576$	−5.74733e10	−	6.23712e10i	−0.522127	−	0.566623i
$577$	−5.79393e10	+	4.20954e10i	−0.522721	+	0.379779i	−0.817628	−	0.575747i	$-0.804711\pi$
$577$	−5.79393e10	+	4.20954e10i	−0.522721	+	0.379779i	0.294907	+	0.955526i	$0.404711\pi$
$578$	−4.30781e8	−	2.09084e8i	−0.00385963	−	0.00187331i
$579$	1.57902e10	+	5.13054e9i	0.140499	+	0.0456508i
$580$	−9.55147e9	−	1.28123e10i	−0.0844031	−	0.113218i
$581$	−1.69653e10	−	5.22139e10i	−0.148887	−	0.458228i
$582$	1.87205e10	+	2.59437e9i	0.163165	+	0.0226121i
$583$	−4.41288e10	+	1.43383e10i	−0.381987	+	0.124115i
$584$	1.41621e11	−	8.28555e10i	1.21752	−	0.712311i
$585$	−1.78986e10	−	6.04857e10i	−0.152826	−	0.516451i
$586$	−5.50288e10	−	1.03017e11i	−0.466659	−	0.873610i
$587$	1.18377e11	−	1.62932e11i	0.997044	−	1.37231i	0.0699223	−	0.997552i	$-0.477725\pi$
$587$	1.18377e11	−	1.62932e11i	0.997044	−	1.37231i	0.927122	−	0.374761i	$-0.122275\pi$
$588$	−3.99626e10	+	3.14700e10i	−0.334307	+	0.263261i
$589$	1.64698e11	−	1.19660e11i	1.36844	−	0.994230i
$590$	9.58374e10	+	1.58757e10i	0.790910	+	0.131016i
$591$	4.70892e10	−	6.48128e10i	0.385986	−	0.531264i
$592$	−4.15791e10	+	1.72391e11i	−0.338523	+	1.40355i
$593$	3.20722e10			0.259364			0.129682	−	0.991556i	$-0.458604\pi$
$593$	3.20722e10			0.259364			0.129682	+	0.991556i	$0.458604\pi$
$594$	1.59413e11	−	2.84244e10i	1.28050	−	0.228321i
$595$	4.02623e10	−	1.19142e10i	0.321241	−	0.0950599i
$596$	−3.13610e10	+	4.68817e10i	−0.248545	+	0.371551i
$597$	4.09034e9	−	1.25888e10i	0.0322004	−	0.0991028i
$598$	7.31701e10	−	3.90855e10i	0.572175	−	0.305641i
$599$			1.16139e10i			0.0902131i	0.998982	+	0.0451066i	$0.0143627\pi$
$599$			1.16139e10i			0.0902131i	−0.998982	+	0.0451066i	$0.985637\pi$
$600$	−5.54648e10	−	2.78978e10i	−0.427969	−	0.215261i
$601$	−2.42278e9			−0.0185701			−0.00928507	−	0.999957i	$-0.502956\pi$
$601$	−2.42278e9			−0.0185701			−0.00928507	+	0.999957i	$0.502956\pi$
$602$	−4.41121e9	−	8.25801e9i	−0.0335870	−	0.0628767i
$603$	−8.82769e10	−	2.86829e10i	−0.667694	−	0.216947i
$604$	4.99296e10	+	3.33998e10i	0.375155	+	0.250955i
$605$	6.04971e10	−	1.70690e11i	0.451558	−	1.27405i
$606$	−1.10727e10	−	6.20994e10i	−0.0821038	−	0.460465i
$607$		−	3.66781e10i		−	0.270179i	−0.990833	−	0.135090i	$-0.956868\pi$
$607$		−	3.66781e10i		−	0.270179i	0.990833	−	0.135090i	$-0.0431323\pi$
$608$	5.44859e10	−	1.38673e11i	0.398721	−	1.01480i
$609$	−2.51668e9	−	1.82848e9i	−0.0182961	−	0.0132929i
$610$	−2.45444e11	−	1.27258e11i	−1.77269	−	0.919103i
$611$	1.85155e10	+	2.54843e10i	0.132853	+	0.182856i
$612$	−6.70159e10	−	8.51012e10i	−0.477719	−	0.606639i
$613$	−3.70908e10	−	2.69480e10i	−0.262678	−	0.190847i	0.448649	−	0.893708i	$-0.351905\pi$
$613$	−3.70908e10	−	2.69480e10i	−0.262678	−	0.190847i	−0.711327	+	0.702861i	$0.751905\pi$
$614$	−2.14574e11	+	1.14620e11i	−1.50975	+	0.806466i
$615$	4.03589e10	+	5.87571e10i	0.282123	+	0.410733i
$616$	−6.37119e10	+	3.72747e10i	−0.442484	+	0.258876i
$617$	4.81883e10	+	1.48308e11i	0.332507	+	1.02335i	0.967937	+	0.251193i	$0.0808230\pi$
$617$	4.81883e10	+	1.48308e11i	0.332507	+	1.02335i	−0.635430	+	0.772159i	$0.719177\pi$
$618$	−7.32457e7	+	5.28527e8i	−0.000502144	+	0.00362338i
$619$	−2.39674e11	+	7.78747e10i	−1.63252	+	0.530437i	−0.974848	−	0.222871i	$-0.928457\pi$
$619$	−2.39674e11	+	7.78747e10i	−1.63252	+	0.530437i	−0.657668	+	0.753307i	$0.728457\pi$
$620$	6.81530e10	−	2.18870e11i	0.461231	−	1.48122i
$621$	3.61734e10	−	1.11330e11i	0.243233	−	0.748595i
$622$	−3.02143e10	+	6.22514e10i	−0.201860	+	0.415899i
$623$	−3.88345e10	−	5.34511e10i	−0.257790	−	0.354817i
$624$	−2.65726e10	+	4.32605e10i	−0.175265	+	0.285334i
$625$	1.51734e11	+	1.61163e10i	0.994407	+	0.105620i
$626$	−1.84502e8	+	1.33133e9i	−0.00120144	+	0.00866939i
$627$	7.27644e10	+	1.00152e11i	0.470813	+	0.648019i
$628$	1.08071e10	−	1.61556e10i	0.0694817	−	0.103869i
$629$	−6.99875e10	+	2.15399e11i	−0.447114	+	1.37607i
$630$	4.00302e10	+	6.63110e9i	0.254112	+	0.0420943i
$631$	−1.59146e11	+	5.17097e10i	−1.00387	+	0.326178i	−0.764412	−	0.644728i	$-0.776970\pi$
$631$	−1.59146e11	+	5.17097e10i	−1.00387	+	0.326178i	−0.239460	+	0.970906i	$0.576970\pi$
$632$	1.12825e11	+	4.94566e10i	0.707192	+	0.309996i
$633$	−1.40144e10	−	4.31318e10i	−0.0872889	−	0.268648i
$634$	5.24916e10	−	5.45658e10i	0.324887	−	0.337725i
$635$	7.00527e10	+	1.01987e11i	0.430854	+	0.627264i
$636$	−7.09527e9	−	1.92637e10i	−0.0433651	−	0.117737i
$637$	−8.27047e10	−	6.00885e10i	−0.502311	−	0.364950i
$638$	2.58582e10	+	2.48753e10i	0.156069	+	0.150136i
$639$	9.98319e10	+	1.37407e11i	0.598778	+	0.824147i
$640$	−4.41404e10	−	1.61861e11i	−0.263097	−	0.964769i
$641$	−4.48731e10	−	3.26022e10i	−0.265799	−	0.193114i	0.446901	−	0.894584i	$-0.352528\pi$
$641$	−4.48731e10	−	3.26022e10i	−0.265799	−	0.193114i	−0.712700	+	0.701469i	$0.752528\pi$
$642$	1.43203e11	−	2.55341e10i	0.842973	−	0.150307i
$643$		−	2.53512e11i		−	1.48305i	−0.670926	−	0.741524i	$-0.734103\pi$
$643$		−	2.53512e11i		−	1.48305i	0.670926	−	0.741524i	$-0.265897\pi$
$644$	2.06695e9	+	5.33216e10i	0.0120168	+	0.309999i
$645$	−5.90645e9	+	1.66648e10i	−0.0341262	+	0.0962855i
$646$	8.30886e10	−	1.71190e11i	0.477102	−	0.982987i
$647$	1.67032e11	+	5.42719e10i	0.953196	+	0.309712i	0.744014	−	0.668164i	$-0.232920\pi$
$647$	1.67032e11	+	5.42719e10i	0.953196	+	0.309712i	0.209182	+	0.977877i	$0.432920\pi$
$648$	−1.37119e10	−	6.27316e10i	−0.0777676	−	0.355784i
$649$	−2.18110e11			−1.22941
$650$	2.36407e10	−	1.22517e11i	0.132436	−	0.686345i
$651$		−	4.46225e10i		−	0.248445i
$652$	1.71063e10	+	4.64439e10i	0.0946600	+	0.257003i
$653$	5.85342e10	−	1.80150e11i	0.321927	−	0.990789i	−0.650882	−	0.759179i	$-0.725601\pi$
$653$	5.85342e10	−	1.80150e11i	0.321927	−	0.990789i	0.972809	−	0.231610i	$-0.0743993\pi$
$654$	4.73111e10	−	9.74764e10i	0.258614	−	0.532830i
$655$	1.03046e11	−	3.04930e10i	0.559844	−	0.165666i
$656$	−4.51643e10	+	1.87256e11i	−0.243882	+	1.01116i
$657$	2.02505e11			1.08686
$658$	−1.99483e10	+	3.55691e9i	−0.106415	+	0.0189744i
$659$	−7.35473e10	+	1.01229e11i	−0.389965	+	0.536740i	−0.958190	−	0.286133i	$-0.907630\pi$
$659$	−7.35473e10	+	1.01229e11i	−0.389965	+	0.536740i	0.568225	+	0.822873i	$0.307630\pi$
$660$	1.33094e11	+	4.14434e10i	0.701426	+	0.218414i
$661$	−1.32073e11	+	9.59568e10i	−0.691845	+	0.502655i	−0.877266	−	0.480004i	$-0.840635\pi$
$661$	−1.32073e11	+	9.59568e10i	−0.691845	+	0.502655i	0.185421	+	0.982659i	$0.440635\pi$
$662$	1.53453e11	+	1.47620e11i	0.798996	+	0.768624i
$663$	−3.81127e10	+	5.24576e10i	−0.197249	+	0.271490i
$664$	−2.73706e11	+	5.98269e10i	−1.40803	+	0.307769i
$665$	2.02259e10	+	6.83502e10i	0.103424	+	0.349505i
$666$	−1.51735e11	+	1.57731e11i	−0.771238	+	0.801713i
$667$	2.46691e10	−	8.01549e9i	0.124638	−	0.0404973i
$668$	9.82786e10	−	3.47770e11i	0.493575	−	1.74657i
$669$	1.84073e10	+	5.66519e10i	0.0918938	+	0.282820i
$670$	−1.28909e11	−	1.30748e11i	−0.639710	−	0.648836i
$671$	5.90366e11	+	1.91821e11i	2.91227	+	0.946253i
$672$	−1.75711e10	−	2.75284e10i	−0.0861633	−	0.134991i
$673$	2.04701e11	−	1.48724e11i	0.997837	−	0.724971i	0.0362135	−	0.999344i	$-0.488470\pi$
$673$	2.04701e11	−	1.48724e11i	0.997837	−	0.724971i	0.961623	+	0.274373i	$0.0884704\pi$
$674$	4.96953e10	−	3.58592e11i	0.240811	−	1.73764i
$675$	−9.58165e10	−	1.47722e11i	−0.461557	−	0.711589i
$676$	1.02767e11	+	2.90417e10i	0.492118	+	0.139071i
$677$	2.27054e11	−	1.64965e11i	1.08087	−	0.785301i	0.103039	−	0.994677i	$-0.467143\pi$
$677$	2.27054e11	−	1.64965e11i	1.08087	−	0.785301i	0.977835	+	0.209376i	$0.0671433\pi$
$678$	2.69244e10	−	5.54731e10i	0.127417	−	0.262521i
$679$	−2.32372e10	−	7.55024e9i	−0.109321	−	0.0355207i
$680$	−4.02024e10	−	2.10467e11i	−0.188026	−	0.984346i
$681$	1.88941e10	+	5.81501e10i	0.0878492	+	0.270372i
$682$	−7.06526e10	+	5.09816e11i	−0.326581	+	2.35655i
$683$	−1.68873e11	+	5.48702e10i	−0.776029	+	0.252147i	−0.670144	−	0.742231i	$-0.733768\pi$
$683$	−1.68873e11	+	5.48702e10i	−0.776029	+	0.252147i	−0.105885	+	0.994378i	$0.533768\pi$
$684$	1.44470e11	−	1.13768e11i	0.660014	−	0.519751i
$685$	1.92797e11	+	1.48023e11i	0.875666	+	0.672304i
$686$	1.23303e11	−	6.58653e10i	0.556773	−	0.297413i
$687$	1.13511e11	−	1.56234e11i	0.509577	−	0.701373i
$688$	−4.41599e10	+	1.82373e10i	−0.197094	+	0.0813966i
$689$	3.33784e10	−	2.42508e10i	0.148112	−	0.107609i
$690$	7.17594e10	−	7.07501e10i	0.316579	−	0.312127i
$691$	9.21560e10	−	1.26842e11i	0.404214	−	0.556353i	−0.557581	−	0.830122i	$-0.688271\pi$
$691$	9.21560e10	−	1.26842e11i	0.404214	−	0.556353i	0.961795	+	0.273770i	$0.0882706\pi$
$692$	−4.05946e9	−	1.04723e11i	−0.0177029	−	0.456685i
$693$	−9.11021e10			−0.394999
$694$	6.32763e9	+	3.54874e10i	0.0272774	+	0.152981i
$695$	−5.65119e10	−	8.22737e10i	−0.242215	−	0.352632i
$696$	−1.05543e10	+	1.18583e10i	−0.0449771	+	0.0505341i
$697$	−7.60224e10	+	2.33973e11i	−0.322114	+	0.991366i
$698$	1.94693e11	+	3.64475e11i	0.820216	+	1.53549i
$699$			1.39447e11i			0.584119i
$700$	6.42602e10	+	4.80930e10i	0.267639	+	0.200304i
$701$	−3.53512e11			−1.46397			−0.731985	−	0.681320i	$-0.761406\pi$
$701$	−3.53512e11			−1.46397			−0.731985	+	0.681320i	$0.761406\pi$
$702$	−1.27000e11	+	6.78400e10i	−0.522944	+	0.279343i
$703$	−3.65667e11	−	1.18813e11i	−1.49715	−	0.486453i
$704$	1.57165e11	+	3.42335e11i	0.639830	+	1.39367i
$705$	3.03520e10	+	2.33032e10i	0.122866	+	0.0943319i
$706$	−3.22888e11	+	5.75730e10i	−1.29967	+	0.231740i
$707$			8.15480e10i			0.326389i
$708$	−3.73789e9	−	9.64270e10i	−0.0148762	−	0.383765i
$709$	−2.91983e11	−	2.12138e11i	−1.15551	−	0.839524i	−0.166303	−	0.986075i	$-0.553183\pi$
$709$	−2.91983e11	−	2.12138e11i	−1.15551	−	0.839524i	−0.989203	+	0.146550i	$0.953183\pi$
$710$	5.02064e10	+	3.32201e11i	0.197572	+	1.30728i
$711$	8.93666e10	+	1.23003e11i	0.349701	+	0.481322i
$712$	−2.91015e11	+	1.70259e11i	−1.13239	+	0.662507i
$713$	3.01015e11	+	2.18700e11i	1.16474	+	0.846236i
$714$	−1.96522e10	−	3.67898e10i	−0.0756166	−	0.141558i
$715$	−7.41040e9	+	2.80056e11i	−0.0283542	+	1.07157i
$716$	−1.44706e11	+	1.13954e11i	−0.550598	+	0.433588i
$717$	5.43996e10	+	1.67425e11i	0.205835	+	0.633495i
$718$	6.42165e10	+	8.89942e9i	0.241629	+	0.0334860i
$719$	−1.65223e11	+	5.36842e10i	−0.618237	+	0.200877i	−0.601358	−	0.798980i	$-0.705373\pi$
$719$	−1.65223e11	+	5.36842e10i	−0.618237	+	0.200877i	−0.0168797	+	0.999858i	$0.505373\pi$
$720$	5.38572e10	−	1.99938e11i	0.200408	−	0.743986i
$721$	2.13162e8	−	6.56046e8i	0.000788804	−	0.00242769i
$722$	4.61523e10	+	2.24004e10i	0.169842	+	0.0824342i
$723$	−3.19285e10	−	4.39458e10i	−0.116849	−	0.160829i
$724$	−1.24265e11	−	3.51169e10i	−0.452267	−	0.127809i
$725$	1.40019e10	−	3.64166e10i	0.0506800	−	0.131810i
$726$	−1.78190e11	−	2.46944e10i	−0.641412	−	0.0888897i
$727$	−2.46840e11	−	3.39747e11i	−0.883646	−	1.21624i	−0.975398	−	0.220453i	$-0.929246\pi$
$727$	−2.46840e11	−	3.39747e11i	−0.883646	−	1.21624i	0.0917511	−	0.995782i	$-0.470754\pi$
$728$	4.36368e10	−	4.90283e10i	0.155356	−	0.174550i
$729$	−1.09719e10	+	3.37680e10i	−0.0388482	+	0.119562i
$730$	3.55623e11	+	1.84383e11i	1.25227	+	0.649275i
$731$	−5.80331e10	+	1.88561e10i	−0.203239	+	0.0660362i
$732$	−7.46873e10	+	2.64290e11i	−0.260137	+	0.920525i
$733$	−1.23159e10	−	3.79046e10i	−0.0426631	−	0.131303i	0.927456	−	0.373932i	$-0.121991\pi$
$733$	−1.23159e10	−	3.79046e10i	−0.0426631	−	0.131303i	−0.970119	+	0.242628i	$0.921991\pi$
$734$	−9.08886e10	−	8.74337e10i	−0.313130	−	0.301227i
$735$	−1.17051e11	−	4.14860e10i	−0.401074	−	0.142152i
$736$	2.71819e11	+	1.63883e10i	0.926338	+	0.0558501i
$737$	3.33514e11	+	2.42312e11i	1.13043	+	0.821307i
$738$	−1.64819e11	+	1.71331e11i	−0.555623	+	0.577579i
$739$	−2.89315e11	−	3.98208e11i	−0.970049	−	1.33516i	−0.942022	−	0.335551i	$-0.891078\pi$
$739$	−2.89315e11	−	3.98208e11i	−0.970049	−	1.33516i	−0.0280267	−	0.999607i	$-0.508922\pi$
$740$	−4.10080e11	+	1.38838e11i	−1.36755	+	0.463000i
$741$	−8.90533e10	−	6.47010e10i	−0.295377	−	0.214604i
$742$	4.65870e9	+	2.61275e10i	0.0153691	+	0.0861951i
$743$			7.72300e10i			0.253414i	0.991940	+	0.126707i	$0.0404408\pi$
$743$			7.72300e10i			0.253414i	−0.991940	+	0.126707i	$0.959559\pi$
$744$	−2.26602e11	−	2.24987e10i	−0.739557	−	0.0734286i
$745$	−1.37657e11	−	3.64246e9i	−0.446861	−	0.0118241i
$746$	1.17987e11	+	5.72663e10i	0.380961	+	0.184903i
$747$	−3.28860e11	−	1.06853e11i	−1.05616	−	0.343166i
$748$	1.66277e11	+	4.51443e11i	0.531160	+	1.44210i
$749$	−1.88053e11			−0.597519
$750$	−1.46933e10	−	1.50862e11i	−0.0464380	−	0.476800i
$751$		−	5.54731e11i		−	1.74390i	−0.489592	−	0.871952i	$-0.662854\pi$
$751$		−	5.54731e11i		−	1.74390i	0.489592	−	0.871952i	$-0.337146\pi$
$752$	8.00473e9	+	1.03095e11i	0.0250308	+	0.322378i
$753$	−3.01063e10	+	9.26575e10i	−0.0936433	+	0.288205i
$754$	−2.87025e10	−	1.39310e10i	−0.0888042	−	0.0431020i
$755$	−3.87926e9	+	1.46606e11i	−0.0119388	+	0.451195i
$756$	−3.58757e9	−	9.25493e10i	−0.0109828	−	0.283326i
$757$	−2.98110e11			−0.907807			−0.453904	−	0.891051i	$-0.649969\pi$
$757$	−2.98110e11			−0.907807			−0.453904	+	0.891051i	$0.649969\pi$
$758$	−6.11726e10	−	3.43076e11i	−0.185302	−	1.03923i
$759$	−1.32990e11	+	1.83046e11i	−0.400731	+	0.551560i
$760$	3.57293e11	−	6.82487e10i	1.07095	−	0.204569i
$761$	1.69004e11	−	1.22789e11i	0.503917	−	0.366117i	−0.306594	−	0.951840i	$-0.599189\pi$
$761$	1.69004e11	−	1.22789e11i	0.503917	−	0.366117i	0.810511	+	0.585723i	$0.199189\pi$
$762$	8.52095e10	−	8.85765e10i	0.252736	−	0.262723i
$763$	−8.23345e10	+	1.13324e11i	−0.242931	+	0.334367i
$764$	7.49179e10	+	2.03403e11i	0.219893	+	0.597013i
$765$	8.83451e10	−	2.49262e11i	0.257951	−	0.727796i
$766$	−1.35566e11	−	1.30413e11i	−0.393764	−	0.378795i
$767$	1.84448e11	−	5.99308e10i	0.532958	−	0.173168i
$768$	−1.48654e11	+	7.53497e10i	−0.427298	+	0.216589i
$769$	−6.87369e10	−	2.11550e11i	−0.196555	−	0.604935i	−0.999955	−	0.00949457i	$-0.996978\pi$
$769$	−6.87369e10	−	2.11550e11i	−0.196555	−	0.604935i	0.803400	−	0.595440i	$-0.203022\pi$
$770$	−1.59986e11	−	8.29495e10i	−0.455114	−	0.235967i
$771$	2.89801e11	+	9.41621e10i	0.820130	+	0.266476i
$772$	−6.09017e10	+	9.10423e10i	−0.171459	+	0.256315i
$773$	−4.26109e11	+	3.09586e11i	−1.19345	+	0.867089i	−0.993624	−	0.112744i	$-0.964036\pi$
$773$	−4.26109e11	+	3.09586e11i	−1.19345	+	0.867089i	−0.199821	+	0.979832i	$0.564036\pi$
$774$	−5.84089e10	−	8.09457e9i	−0.162748	−	0.0225543i
$775$	5.40667e11	−	1.44553e11i	1.49873	−	0.400702i
$776$	−5.00578e10	+	1.14196e11i	−0.138046	+	0.314924i
$777$	−6.81808e10	+	4.95363e10i	−0.187059	+	0.135906i
$778$	−3.57137e11	−	1.73340e11i	−0.974801	−	0.473129i
$779$	−3.97198e11	−	1.29057e11i	−1.07859	−	0.350456i
$780$	−1.23940e11	+	1.52333e9i	−0.334838	+	0.00411544i
$781$	−2.33104e11	−	7.17420e11i	−0.626535	−	1.92828i
$782$	3.44495e11	+	4.77417e10i	0.921204	+	0.127665i
$783$	−4.28177e10	+	1.39123e10i	−0.113914	+	0.0370129i
$784$	−1.28096e11	−	3.10172e11i	−0.339055	−	0.820991i
$785$	4.74370e10	+	1.25520e9i	0.124922	+	0.00330549i
$786$	−5.02973e10	−	9.41591e10i	−0.131781	−	0.246702i
$787$	1.46488e11	−	2.01624e11i	0.381860	−	0.525585i	−0.574216	−	0.818704i	$-0.694693\pi$
$787$	1.46488e11	−	2.01624e11i	0.381860	−	0.525585i	0.956076	+	0.293119i	$0.0946931\pi$
$788$	3.26993e11	+	4.15237e11i	0.848074	+	1.07694i
$789$	−1.98489e11	+	1.44211e11i	−0.512187	+	0.372126i
$790$	4.49433e10	+	2.97376e11i	0.115387	+	0.763481i
$791$	−4.68560e10	+	6.44917e10i	−0.119690	+	0.164740i
$792$	−4.59337e10	+	4.62634e11i	−0.116743	+	1.17581i
$793$	−5.51959e11			−1.39577
$794$	2.56154e11	−	4.56738e10i	0.644494	−	0.114917i
$795$	3.05216e10	−	3.97539e10i	0.0764080	−	0.0995203i
$796$	7.25838e10	+	4.85541e10i	0.180795	+	0.120941i
$797$	1.06878e10	−	3.28936e10i	0.0264883	−	0.0815226i	−0.936938	−	0.349494i	$-0.886353\pi$
$797$	1.06878e10	−	3.28936e10i	0.0264883	−	0.0815226i	0.963427	+	0.267972i	$0.0863534\pi$
$798$	6.24553e10	−	3.33620e10i	0.154013	−	0.0822698i
$799$			1.32065e11i			0.324041i
$800$	2.76625e11	−	3.02077e11i	0.675355	−	0.737493i
$801$	−4.16125e11			−1.01087
$802$	2.54607e11	+	4.76637e11i	0.615421	+	1.15210i
$803$	−8.55378e11	−	2.77929e11i	−2.05729	−	0.668454i
$804$	−1.01411e11	+	1.51600e11i	−0.242696	+	0.362807i
$805$	−1.07385e11	+	7.37605e10i	−0.255718	+	0.175647i
$806$	−8.03354e10	−	4.50547e11i	−0.190356	−	1.06758i
$807$		−	3.67912e11i		−	0.867462i
$808$	4.14116e11	+	4.11165e10i	0.971576	+	0.0964651i
$809$	6.03704e11	+	4.38616e11i	1.40939	+	1.02398i	0.993411	+	0.114602i	$0.0365593\pi$
$809$	6.03704e11	+	4.38616e11i	1.40939	+	1.02398i	0.415974	+	0.909377i	$0.363441\pi$
$810$	1.11635e11	−	1.10065e11i	0.259334	−	0.255687i
$811$	2.46302e11	+	3.39006e11i	0.569358	+	0.783654i	0.992478	−	0.122420i	$-0.0390654\pi$
$811$	2.46302e11	+	3.39006e11i	0.569358	+	0.783654i	−0.423121	+	0.906073i	$0.639065\pi$
$812$	1.61237e10	−	1.26972e10i	0.0370886	−	0.0292067i
$813$	2.38204e11	+	1.73066e11i	0.545240	+	0.396140i
$814$	8.57405e11	−	4.58003e11i	1.95294	−	1.04321i
$815$	−7.35860e10	+	9.58447e10i	−0.166788	+	0.217239i
$816$	−1.96734e11	+	8.12480e10i	−0.443731	+	0.183253i
$817$	−3.20106e10	−	9.85184e10i	−0.0718464	−	0.221121i
$818$	−3.99814e9	+	2.88498e10i	−0.00892986	+	0.0644362i
$819$	7.70419e10	−	2.50324e10i	0.171235	−	0.0556375i
$820$	−4.45440e11	+	1.50809e11i	−0.985222	+	0.333559i
$821$	1.13343e11	−	3.48834e11i	0.249472	−	0.767797i	−0.745396	−	0.666622i	$-0.767740\pi$
$821$	1.13343e11	−	3.48834e11i	0.249472	−	0.767797i	0.994869	−	0.101175i	$-0.0322603\pi$
$822$	1.05430e11	−	2.17221e11i	0.230929	−	0.475790i
$823$	−1.97219e11	−	2.71449e11i	−0.429882	−	0.591682i	0.538044	−	0.842917i	$-0.319163\pi$
$823$	−1.97219e11	−	2.71449e11i	−0.429882	−	0.591682i	−0.967926	+	0.251235i	$0.919163\pi$
$824$	−3.22405e9	−	1.41326e9i	−0.00699348	−	0.00306558i
$825$	8.79021e10	+	3.28777e11i	0.189751	+	0.709717i
$826$	−1.71253e10	+	1.23573e11i	−0.0367890	+	0.265462i
$827$	−1.45995e11	−	2.00945e11i	−0.312116	−	0.429591i	0.623924	−	0.781485i	$-0.285538\pi$
$827$	−1.45995e11	−	2.00945e11i	−0.312116	−	0.429591i	−0.936040	+	0.351895i	$0.885538\pi$
$828$	2.79350e11	+	1.86868e11i	0.594329	+	0.397570i
$829$	−5.76662e10	+	1.77478e11i	−0.122097	+	0.375775i	−0.993361	−	0.115039i	$-0.963301\pi$
$829$	−5.76662e10	+	1.77478e11i	−0.122097	+	0.375775i	0.871264	+	0.490814i	$0.163301\pi$
$830$	−4.80227e11	−	4.87077e11i	−1.01189	−	1.02633i
$831$	−1.48109e11	+	4.81237e10i	−0.310584	+	0.100915i
$832$	−2.26973e11	−	2.46316e11i	−0.473676	−	0.514043i
$833$	−1.32442e11	−	4.07615e11i	−0.275072	−	0.846584i
$834$	−6.87390e10	+	7.14552e10i	−0.142082	+	0.147696i
$835$	8.46035e11	−	2.50355e11i	1.74037	−	0.515003i
$836$	−7.66381e11	+	2.82275e11i	−1.56899	+	0.577894i
$837$	−5.22467e11	−	3.79594e11i	−1.06453	−	0.773424i
$838$	−2.70376e11	−	2.60099e11i	−0.548268	−	0.527426i
$839$	3.18716e11	+	4.38674e11i	0.643214	+	0.885308i	0.998782	−	0.0493423i	$-0.0157125\pi$
$839$	3.18716e11	+	4.38674e11i	0.643214	+	0.885308i	−0.355568	+	0.934650i	$0.615713\pi$
$840$	3.39304e10	−	7.21519e10i	0.0681509	−	0.144921i
$841$	3.96637e11	+	2.88174e11i	0.792883	+	0.576063i
$842$	−3.39056e11	+	6.04558e10i	−0.674564	+	0.120279i
$843$			1.68622e11i			0.333891i
$844$	2.98975e11	−	1.15894e10i	0.589202	−	0.0228398i
$845$	7.39808e10	+	2.50007e11i	0.145108	+	0.490371i
$846$	−5.57258e10	+	1.14814e11i	−0.108786	+	0.224136i
$847$	2.21182e11	+	7.18665e10i	0.429751	+	0.139634i
$848$	1.35029e11	−	1.04843e10i	0.261123	−	0.0202748i
$849$	2.99639e11			0.576724
$850$	3.82100e11	−	3.57294e11i	0.731984	−	0.684463i
$851$		−	7.02719e11i		−	1.33987i
$852$	3.13178e11	−	1.15351e11i	0.594337	−	0.218908i
$853$	6.13886e10	−	1.88935e11i	0.115956	−	0.356875i	−0.876190	−	0.481967i	$-0.839923\pi$
$853$	6.13886e10	−	1.88935e11i	0.115956	−	0.356875i	0.992145	+	0.125092i	$0.0399226\pi$
$854$	1.55032e11	−	3.19418e11i	0.291468	−	0.600520i
$855$	4.23153e11	+	1.49977e11i	0.791831	+	0.280647i
$856$	−9.48161e10	+	9.54967e11i	−0.176598	+	1.77866i
$857$	1.39895e11			0.259346			0.129673	−	0.991557i	$-0.458607\pi$
$857$	1.39895e11			0.259346			0.129673	+	0.991557i	$0.458607\pi$
$858$	2.73975e11	−	4.88515e10i	0.505548	−	0.0901423i
$859$	1.46029e11	−	2.00992e11i	0.268205	−	0.369153i	−0.653578	−	0.756860i	$-0.726733\pi$
$859$	1.46029e11	−	2.00992e11i	0.268205	−	0.369153i	0.921783	+	0.387707i	$0.126733\pi$
$860$	−9.52028e10	−	6.73969e10i	−0.174043	−	0.123210i
$861$	−7.40599e10	+	5.38077e10i	−0.134763	+	0.0979110i
$862$	4.98819e11	+	4.79858e11i	0.903471	+	0.869127i
$863$	3.03283e11	−	4.17433e11i	0.546770	−	0.752564i	−0.442800	−	0.896620i	$-0.646015\pi$
$863$	3.03283e11	−	4.17433e11i	0.546770	−	0.752564i	0.989569	+	0.144057i	$0.0460148\pi$
$864$	−4.71792e11	−	2.84449e10i	−0.846634	−	0.0510446i
$865$	2.10903e11	−	1.44865e11i	0.376720	−	0.258760i
$866$	2.15169e11	−	2.23672e11i	0.382568	−	0.397685i
$867$	−1.10446e9	+	3.58860e8i	−0.00195467	+	0.000635109i
$868$	2.83295e11	+	8.00582e10i	0.499069	+	0.141035i
$869$	−2.08668e11	−	6.42213e11i	−0.365912	−	1.12616i
$870$	−3.82359e10	−	6.33388e9i	−0.0667413	−	0.0110559i
$871$	−3.48623e11	−	1.13274e11i	−0.605735	−	0.196815i
$872$	5.33967e11	+	4.75248e11i	0.923524	+	0.821968i
$873$	−1.24498e11	+	9.04528e10i	−0.214340	+	0.155727i
$874$	−8.10474e10	+	5.84823e11i	−0.138897	+	1.00226i
$875$	−1.55354e10	+	1.95340e11i	−0.0265027	+	0.333242i
$876$	1.08214e11	−	3.82928e11i	0.183767	−	0.650280i
$877$	1.12031e11	−	8.13952e10i	0.189382	−	0.137594i	−0.489054	−	0.872253i	$-0.662658\pi$
$877$	1.12031e11	−	8.13952e10i	0.189382	−	0.137594i	0.678436	+	0.734659i	$0.262658\pi$
$878$	7.88658e9	−	1.62489e10i	0.0132712	−	0.0273431i
$879$	−2.69386e11	−	8.75288e10i	−0.451252	−	0.146621i
$880$	−5.01898e11	+	7.70618e11i	−0.836922	+	1.28502i
$881$	1.74465e11	+	5.36949e11i	0.289604	+	0.891310i	0.984981	+	0.172665i	$0.0552377\pi$
$881$	1.74465e11	+	5.36949e11i	0.289604	+	0.891310i	−0.695376	+	0.718646i	$0.744762\pi$
$882$	5.68549e10	−	4.10254e11i	0.0939493	−	0.677921i
$883$	3.65788e10	−	1.18852e10i	0.0601710	−	0.0195507i	−0.278777	−	0.960356i	$-0.589929\pi$
$883$	3.65788e10	−	1.18852e10i	0.0601710	−	0.0195507i	0.338948	+	0.940805i	$0.389929\pi$
$884$	−2.64659e11	−	3.36081e11i	−0.433389	−	0.550345i
$885$	1.94196e11	−	1.33389e11i	0.316568	−	0.217443i
$886$	7.88055e11	−	4.20958e11i	1.27886	−	0.683131i
$887$	−6.71260e11	+	9.23910e11i	−1.08442	+	1.49257i	−0.229853	+	0.973225i	$0.573824\pi$
$887$	−6.71260e11	+	9.23910e11i	−1.08442	+	1.49257i	−0.854564	+	0.519346i	$0.826176\pi$
$888$	2.17178e11	+	3.71212e11i	0.349272	+	0.596994i
$889$	−1.28549e11	+	9.33962e10i	−0.205808	+	0.149528i
$890$	−7.30766e11	−	3.78887e11i	−1.16471	−	0.603878i
$891$	−2.06891e11	+	2.84761e11i	−0.328270	+	0.451825i
$892$	−3.92691e11	+	1.52222e10i	−0.620285	+	0.0240447i
$893$	−2.24196e11			−0.352552
$894$	2.40122e10	+	1.34668e11i	0.0375908	+	0.210821i
$895$	−4.23845e11	−	1.50222e11i	−0.660563	−	0.234122i
$896$	2.06294e11	−	6.21646e10i	0.320077	−	0.0964520i
$897$	6.21694e10	−	1.91338e11i	0.0960299	−	0.295550i
$898$	3.97645e11	+	7.44413e11i	0.611492	+	1.14474i
$899$		−	1.43101e11i		−	0.219080i
$900$	4.82951e11	−	1.49392e11i	0.736093	−	0.227696i
$901$	1.72973e11			0.262470
$902$	9.31336e11	−	4.97495e11i	1.40696	−	0.751558i
$903$	−2.15944e10	−	7.01646e9i	−0.0324781	−	0.0105528i
$904$	3.03876e11	+	2.70460e11i	0.455012	+	0.404976i
$905$	−8.94566e10	−	3.02305e11i	−0.133358	−	0.450662i
$906$	1.43423e11	−	2.55732e10i	0.212866	−	0.0379553i
$907$		−	1.08346e12i		−	1.60098i	−0.599348	−	0.800489i	$-0.704573\pi$
$907$		−	1.08346e12i		−	1.60098i	0.599348	−	0.800489i	$-0.295427\pi$
$908$	−4.03076e11	+	1.56248e10i	−0.592984	+	0.0229864i
$909$	4.15524e11	+	3.01896e11i	0.608612	+	0.442182i
$910$	1.58087e11	+	2.61875e10i	0.230532	+	0.0381882i
$911$	6.66674e10	+	9.17598e10i	0.0967921	+	0.133223i	0.854666	−	0.519178i	$-0.173762\pi$
$911$	6.66674e10	+	9.17598e10i	0.0967921	+	0.133223i	−0.757874	+	0.652401i	$0.773762\pi$
$912$	−1.37929e11	−	3.33981e11i	−0.199377	−	0.482773i
$913$	1.24245e12	+	9.02692e11i	1.78812	+	1.29914i
$914$	−4.42604e11	−	8.28578e11i	−0.634207	−	1.18727i
$915$	−6.42948e11	+	1.90258e11i	−0.917258	+	0.271431i
$916$	7.88232e11	+	1.00095e12i	1.11962	+	1.42177i
$917$	4.26465e10	+	1.31252e11i	0.0603123	+	0.185622i
$918$	−5.97933e11	−	8.28643e10i	−0.841942	−	0.116680i
$919$	−4.19153e11	+	1.36191e11i	−0.587639	+	0.190935i	−0.587720	−	0.809065i	$-0.699974\pi$
$919$	−4.19153e11	+	1.36191e11i	−0.587639	+	0.190935i	8.09630e−5		1.00000i	$0.499974\pi$
$920$	3.20426e11	+	5.82513e11i	0.447277	+	0.813120i
$921$	−1.82314e11	+	5.61105e11i	−0.253385	+	0.779840i
$922$	−2.52073e11	−	1.22346e11i	−0.348821	−	0.169303i
$923$	3.94256e11	+	5.42646e11i	0.543214	+	0.747670i
$924$	−4.86829e10	+	1.72270e11i	−0.0667865	+	0.236332i
$925$	−8.21074e11	−	6.65639e11i	−1.12154	−	0.909226i
$926$	−4.07809e11	−	5.65160e10i	−0.554642	−	0.0768648i
$927$	−2.55371e9	−	3.51488e9i	−0.00345822	−	0.00475983i
$928$	−5.63491e10	−	8.82811e10i	−0.0759792	−	0.119035i
$929$	−1.20696e9	+	3.71464e9i	−0.00162043	+	0.00498717i	−0.951863	−	0.306522i	$-0.900835\pi$
$929$	−1.20696e9	+	3.71464e9i	−0.00162043	+	0.00498717i	0.950243	+	0.311510i	$0.100835\pi$
$930$	−2.48880e11	−	4.97128e11i	−0.332705	−	0.664563i
$931$	6.91977e11	−	2.24837e11i	0.921071	−	0.299274i
$932$	−8.85310e11	−	2.50185e11i	−1.17336	−	0.331588i
$933$	5.18582e10	+	1.59603e11i	0.0684370	+	0.210627i
$934$	2.88323e11	+	2.77363e11i	0.378871	+	0.364469i
$935$	−7.15270e11	+	9.31628e11i	−0.935887	+	1.21898i
$936$	−8.82750e10	−	4.03855e11i	−0.115010	−	0.526165i
$937$	−3.24092e11	−	2.35467e11i	−0.420446	−	0.305472i	0.357371	−	0.933962i	$-0.383673\pi$
$937$	−3.24092e11	−	2.35467e11i	−0.420446	−	0.305472i	−0.777817	+	0.628490i	$0.783673\pi$
$938$	1.63472e11	−	1.69931e11i	0.211169	−	0.219514i
$939$	1.91596e9	+	2.63710e9i	0.00246448	+	0.00339206i
$940$	−2.02400e11	+	1.50887e11i	−0.259238	+	0.193260i
$941$	1.04002e12	+	7.55615e11i	1.32642	+	0.963701i	0.999828	+	0.0185352i	$0.00590029\pi$
$941$	1.04002e12	+	7.55615e11i	1.32642	+	0.963701i	0.326592	+	0.945165i	$0.394100\pi$
$942$	−8.27467e9	−	4.64070e10i	−0.0105086	−	0.0589359i
$943$		−	7.63312e11i		−	0.965285i
$944$	6.18892e11	+	1.49271e11i	0.779340	+	0.187969i
$945$	1.86387e11	−	1.28025e11i	0.233715	−	0.160534i
$946$	2.35609e11	+	1.14355e11i	0.294190	+	0.142788i
$947$	−7.11567e10	−	2.31202e10i	−0.0884740	−	0.0287470i	0.264446	−	0.964401i	$-0.414811\pi$
$947$	−7.11567e10	−	2.31202e10i	−0.0884740	−	0.0287470i	−0.352920	+	0.935654i	$0.614811\pi$
$948$	2.80348e11	−	1.03259e11i	0.347108	−	0.127848i
$949$	7.99731e11			0.986005
$950$	6.06551e11	+	6.48662e11i	0.744686	+	0.796387i
$951$		−	1.83626e11i		−	0.224498i
$952$	2.68826e11	−	5.87603e10i	0.327283	−	0.0715378i
$953$	2.57869e11	−	7.93641e11i	0.312628	−	0.962171i	−0.664091	−	0.747651i	$-0.731181\pi$
$953$	2.57869e11	−	7.93641e11i	0.312628	−	0.962171i	0.976720	−	0.214520i	$-0.0688186\pi$
$954$	1.50378e11	+	7.29875e10i	0.181548	+	0.0881161i
$955$	−3.22273e11	+	4.19756e11i	−0.387445	+	0.504642i
$956$	−1.16053e12	+	4.49866e10i	−1.38939	+	0.0538582i
$957$	8.70186e10			0.103744
$958$	−5.42041e10	−	3.03995e11i	−0.0643532	−	0.360914i
$959$	−1.83478e11	+	2.52536e11i	−0.216925	+	0.298572i
$960$	−3.49294e11	−	2.08684e11i	−0.411250	−	0.245699i
$961$	9.70664e11	−	7.05229e11i	1.13809	−	0.826868i
$962$	−5.99230e11	+	6.22909e11i	−0.699670	+	0.727318i
$963$	−6.96183e11	+	9.58213e11i	−0.809502	+	1.11418i
$964$	3.36282e11	−	1.23860e11i	0.389400	−	0.143425i
$965$	−2.67324e11	−	7.07350e9i	−0.308268	−	0.00815690i
$966$	9.32648e10	+	8.97195e10i	0.107105	+	0.103033i
$967$	4.07188e11	−	1.32303e11i	0.465682	−	0.151309i	−0.0667720	−	0.997768i	$-0.521270\pi$
$967$	4.07188e11	−	1.32303e11i	0.465682	−	0.151309i	0.532454	+	0.846459i	$0.321270\pi$
$968$	4.76472e11	−	1.08697e12i	0.542670	−	1.23799i
$969$	−1.42609e11	−	4.38904e11i	−0.161752	−	0.497823i
$970$	−3.00991e11	+	4.54896e10i	−0.339990	+	0.0513837i
$971$	1.17860e12	+	3.82952e11i	1.32584	+	0.430791i	0.884496	−	0.466547i	$-0.154502\pi$
$971$	1.17860e12	+	3.82952e11i	1.32584	+	0.430791i	0.441343	+	0.897339i	$0.354502\pi$
$972$	−7.58717e11	−	5.07535e11i	−0.849992	−	0.568593i
$973$	1.03701e11	−	7.53433e10i	0.115700	−	0.0840608i
$974$	7.91206e11	+	1.09649e11i	0.879132	+	0.121834i
$975$	−1.64675e11	−	2.53882e11i	−0.182225	−	0.280940i
$976$	−1.54390e12	−	9.48334e11i	−1.70145	−	1.04511i
$977$	−5.97718e10	+	4.34268e10i	−0.0656022	+	0.0476628i	−0.620103	−	0.784520i	$-0.712909\pi$
$977$	−5.97718e10	+	4.34268e10i	−0.0656022	+	0.0476628i	0.554501	+	0.832183i	$0.312909\pi$
$978$	1.07987e11	+	5.24123e10i	0.118036	+	0.0572899i
$979$	1.75771e12	+	5.71114e11i	1.91345	+	0.621716i
$980$	4.73385e11	−	6.68689e11i	0.513228	−	0.724970i
$981$	2.72628e11	+	8.39063e11i	0.294371	+	0.905980i
$982$	−9.34918e11	−	1.29565e11i	−1.00537	−	0.139329i
$983$	1.19682e12	−	3.88871e11i	1.28179	−	0.416478i	0.412578	−	0.910922i	$-0.364628\pi$
$983$	1.19682e12	−	3.88871e11i	1.28179	−	0.416478i	0.869209	+	0.494444i	$0.164628\pi$
$984$	2.35905e11	+	4.03220e11i	0.251626	+	0.430093i
$985$	−4.31066e11	+	1.21623e12i	−0.457929	+	1.29203i
$986$	−6.30227e10	−	1.17982e11i	−0.0666791	−	0.124827i
$987$	−2.88850e10	+	3.97568e10i	−0.0304371	+	0.0418931i
$988$	5.70540e11	−	4.49291e11i	0.598767	−	0.471520i
$989$	1.53169e11	−	1.11284e11i	0.160098	−	0.116318i
$990$	−1.01494e12	+	5.08118e11i	−1.05658	+	0.528962i
$991$	2.40938e11	−	3.31622e11i	0.249810	−	0.343834i	−0.665635	−	0.746278i	$-0.731839\pi$
$991$	2.40938e11	−	3.31622e11i	0.249810	−	0.343834i	0.915445	+	0.402444i	$0.131839\pi$
$992$	5.49388e11	−	1.39826e12i	0.567326	−	1.44392i
$993$	5.16405e11			0.531121
$994$	−4.24765e11	+	7.57383e10i	−0.435114	+	0.0775836i
$995$	−5.63937e9	+	2.13125e11i	−0.00575358	+	0.217441i
$996$	−3.77790e11	+	5.64760e11i	−0.383896	+	0.573887i
$997$	−8.24666e10	+	2.53806e11i	−0.0834637	+	0.256875i	−0.984076	−	0.177749i	$-0.943119\pi$
$997$	−8.24666e10	+	2.53806e11i	−0.0834637	+	0.256875i	0.900612	+	0.434624i	$0.143119\pi$
$998$	−1.70847e12	+	9.12618e11i	−1.72220	+	0.919956i
$999$			1.21970e12i			1.22459i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	100.9.j.b.11.76	yes	464
4.3	odd	2	inner	100.9.j.b.11.28	✓	464
25.16	even	5	inner	100.9.j.b.91.28	yes	464
100.91	odd	10	inner	100.9.j.b.91.76	yes	464

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
100.9.j.b.11.28	✓	464	4.3	odd	2	inner
100.9.j.b.11.76	yes	464	1.1	even	1	trivial
100.9.j.b.91.28	yes	464	25.16	even	5	inner
100.9.j.b.91.76	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+(7.53864 + 14.1127i) q^{2} +(36.9043 + 11.9909i) q^{3} +(-142.338 + 212.781i) q^{4} +(-624.781 - 16.5320i) q^{5} +(108.984 + 611.216i) q^{6} -802.640i q^{7} +(-4075.96 - 404.691i) q^{8} +(-4089.81 - 2971.42i) q^{9} +(-4476.69 - 8941.99i) q^{10} +(13197.2 + 18164.3i) q^{11} +(-7804.33 + 6145.80i) q^{12} +(-16151.5 - 11734.7i) q^{13} +(11327.4 - 6050.81i) q^{14} +(-22858.9 - 8101.82i) q^{15} +(-25015.9 - 60573.7i) q^{16} +(-25864.7 - 79603.4i) q^{17} +(11103.2 - 80118.9i) q^{18} +(135137. - 43908.6i) q^{19} +(92447.7 - 130589. i) q^{20} +(9624.41 - 29620.9i) q^{21} +(-156860. + 323182. i) q^{22} +(152647. + 210100. i) q^{23} +(-145568. - 63809.5i) q^{24} +(390078. + 20657.8i) q^{25} +(43848.8 - 316405. i) q^{26} +(-264946. - 364667. i) q^{27} +(170787. + 114246. i) q^{28} +(30864.7 - 94991.6i) q^{29} +(-57986.3 - 383678. i) q^{30} +(1.36260e6 - 442736. i) q^{31} +(666274. - 809686. i) q^{32} +(269225. + 828590. i) q^{33} +(928436. - 965123. i) q^{34} +(-13269.2 + 501474. i) q^{35} +(1.21440e6 - 447291. i) q^{36} +(-2.18913e6 - 1.59049e6i) q^{37} +(1.63842e6 + 1.57614e6i) q^{38} +(-455349. - 626734. i) q^{39} +(2.53989e6 + 320227. i) q^{40} +(-2.37789e6 - 1.72764e6i) q^{41} +(490586. - 87474.6i) q^{42} -729028. i q^{43} +(-5.74349e6 + 222640. i) q^{44} +(2.50612e6 + 1.92410e6i) q^{45} +(-1.81434e6 + 3.73813e6i) q^{46} +(-1.50061e6 - 487578. i) q^{47} +(-196860. - 2.53540e6i) q^{48} +5.12057e6 q^{49} +(2.64912e6 + 5.66080e6i) q^{50} -3.24785e6i q^{51} +(4.79590e6 - 1.76644e6i) q^{52} +(-638611. + 1.96544e6i) q^{53} +(3.14911e6 - 6.48820e6i) q^{54} +(-7.94505e6 - 1.15669e7i) q^{55} +(-324821. + 3.27153e6i) q^{56} +5.51364e6 q^{57} +(1.57327e6 - 280524. i) q^{58} +(-5.70995e6 + 7.85907e6i) q^{59} +(4.97760e6 - 3.71076e6i) q^{60} +(2.23671e7 - 1.62507e7i) q^{61} +(1.65204e7 + 1.58924e7i) q^{62} +(-2.38498e6 + 3.28265e6i) q^{63} +(1.64497e7 + 3.29901e6i) q^{64} +(9.89714e6 + 7.59865e6i) q^{65} +(-9.66407e6 + 1.00459e7i) q^{66} +(1.74623e7 - 5.67384e6i) q^{67} +(2.06197e7 + 5.82704e6i) q^{68} +(3.11403e6 + 9.58398e6i) q^{69} +(-7.17720e6 + 3.59317e6i) q^{70} +(-3.19530e7 - 1.03821e7i) q^{71} +(1.54674e7 + 1.37665e7i) q^{72} +(-3.24076e7 + 2.35455e7i) q^{73} +(5.94315e6 - 4.28847e7i) q^{74} +(1.41479e7 + 5.43977e6i) q^{75} +(-9.89213e6 + 3.50044e7i) q^{76} +(1.45794e7 - 1.05926e7i) q^{77} +(5.41221e6 - 1.11509e7i) q^{78} +(-2.86034e7 - 9.29380e6i) q^{79} +(1.46281e7 + 3.82589e7i) q^{80} +(4.84444e6 + 1.49097e7i) q^{81} +(6.45561e6 - 4.65825e7i) q^{82} +(6.50527e7 - 2.11369e7i) q^{83} +(4.93286e6 + 6.26407e6i) q^{84} +(1.48438e7 + 5.01623e7i) q^{85} +(1.02886e7 - 5.49588e6i) q^{86} +(2.27808e6 - 3.13551e6i) q^{87} +(-4.64402e7 - 7.93779e7i) q^{88} +(6.65941e7 - 4.83835e7i) q^{89} +(-8.26162e6 + 4.98732e7i) q^{90} +(-9.41876e6 + 1.29638e7i) q^{91} +(-6.64328e7 + 2.57519e6i) q^{92} +5.55947e7 q^{93} +(-4.43151e6 - 2.48534e7i) q^{94} +(-8.51568e7 + 2.51992e7i) q^{95} +(3.42973e7 - 2.18917e7i) q^{96} +(9.40676e6 - 2.89510e7i) q^{97} +(3.86021e7 + 7.22652e7i) q^{98} -1.13503e8i 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

Downloads

Learn more