LMFDB - Embedded newform 69.8.g.a.5.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [69,8,Mod(5,69)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(69, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([11, 1]))

N = Newforms(chi, 8, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("69.5");

S:= CuspForms(chi, 8);

N := Newforms(S);

Level:	$ N $	$=$	$ 69 = 3 \cdot 23 $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	69.g (of order $22$, degree $10$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$21.5545667584$
Analytic rank:	$0$
Dimension:	$540$
Relative dimension:	$54$ over $\Q(\zeta_{22})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			5.14
Character	$\chi$	$=$	69.5
Dual form			69.8.g.a.14.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-3.60512 + 12.2779i) q^{2} +(46.6247 - 3.62518i) q^{3} +(-30.0694 - 19.3245i) q^{4} +(-56.5273 + 393.156i) q^{5} +(-123.578 + 585.522i) q^{6} +(-611.212 + 279.131i) q^{7} +(-892.188 + 773.086i) q^{8} +(2160.72 - 338.046i) q^{9} +O(q^{10})$	\(q+(-3.60512 + 12.2779i) q^{2} +(46.6247 - 3.62518i) q^{3} +(-30.0694 - 19.3245i) q^{4} +(-56.5273 + 393.156i) q^{5} +(-123.578 + 585.522i) q^{6} +(-611.212 + 279.131i) q^{7} +(-892.188 + 773.086i) q^{8} +(2160.72 - 338.046i) q^{9} +(-4623.34 - 2111.41i) q^{10} +(650.920 - 191.127i) q^{11} +(-1472.03 - 791.989i) q^{12} +(1256.61 - 2751.60i) q^{13} +(-1223.65 - 8510.70i) q^{14} +(-1210.30 + 18535.7i) q^{15} +(-8176.02 - 17903.0i) q^{16} +(-7513.61 + 4828.71i) q^{17} +(-3639.14 + 27747.7i) q^{18} +(-8841.70 + 13757.9i) q^{19} +(9297.27 - 10729.6i) q^{20} +(-27485.7 + 15230.2i) q^{21} +8680.97i q^{22} +(24142.2 + 53122.3i) q^{23} +(-38795.4 + 39279.2i) q^{24} +(-76416.0 - 22437.8i) q^{25} +(29253.6 + 25348.4i) q^{26} +(99517.2 - 23594.2i) q^{27} +(23772.9 + 3418.02i) q^{28} +(-116206. - 180820. i) q^{29} +(-223216. - 81683.3i) q^{30} +(50316.4 + 58068.2i) q^{31} +(99716.3 - 14337.0i) q^{32} +(29656.1 - 11271.0i) q^{33} +(-32198.9 - 109659. i) q^{34} +(-75192.0 - 256080. i) q^{35} +(-71504.1 - 31589.8i) q^{36} +(217915. - 31331.4i) q^{37} +(-137043. - 158156. i) q^{38} +(48614.1 - 132848. i) q^{39} +(-253510. - 394470. i) q^{40} +(-416216. - 59842.9i) q^{41} +(-87905.3 - 392372. i) q^{42} +(-343798. - 297903. i) q^{43} +(-23266.2 - 6831.59i) q^{44} +(10765.2 + 868608. i) q^{45} +(-739266. + 104903. i) q^{46} -139012. i q^{47} +(-446106. - 805081. i) q^{48} +(-243640. + 281176. i) q^{49} +(550977. - 857338. i) q^{50} +(-332815. + 252375. i) q^{51} +(-90958.8 + 58455.7i) q^{52} +(713053. + 1.56137e6i) q^{53} +(-69083.1 + 1.30692e6i) q^{54} +(38348.1 + 266717. i) q^{55} +(329524. - 721557. i) q^{56} +(-362366. + 673512. i) q^{57} +(2.63902e6 - 774887. i) q^{58} +(1.80634e6 + 824928. i) q^{59} +(394585. - 533969. i) q^{60} +(-919511. + 796761. i) q^{61} +(-894352. + 408437. i) q^{62} +(-1.22630e6 + 809741. i) q^{63} +(175065. - 1.21761e6i) q^{64} +(1.01077e6 + 649586. i) q^{65} +(31470.1 + 404747. i) q^{66} +(511181. - 1.74092e6i) q^{67} +319242. q^{68} +(1.31820e6 + 2.38929e6i) q^{69} +3.41520e6 q^{70} +(-1.10492e6 + 3.76301e6i) q^{71} +(-1.66643e6 + 1.97202e6i) q^{72} +(-2.74254e6 - 1.76252e6i) q^{73} +(-400924. + 2.78849e6i) q^{74} +(-3.64421e6 - 769131. i) q^{75} +(531730. - 242833. i) q^{76} +(-344501. + 298512. i) q^{77} +(1.45583e6 + 1.07581e6i) q^{78} +(1.15036e6 + 525351. i) q^{79} +(7.50084e6 - 2.20245e6i) q^{80} +(4.55442e6 - 1.46084e6i) q^{81} +(2.23525e6 - 4.89452e6i) q^{82} +(805140. + 5.59987e6i) q^{83} +(1.12079e6 + 73183.1i) q^{84} +(-1.47371e6 - 3.22698e6i) q^{85} +(4.89706e6 - 3.14715e6i) q^{86} +(-6.07356e6 - 8.00939e6i) q^{87} +(-432986. + 673739. i) q^{88} +(-4.53210e6 + 5.23032e6i) q^{89} +(-1.07035e7 - 2.99926e6i) q^{90} +2.03257e6i q^{91} +(300619. - 2.06389e6i) q^{92} +(2.55649e6 + 2.52500e6i) q^{93} +(1.70678e6 + 501156. i) q^{94} +(-4.90923e6 - 4.25387e6i) q^{95} +(4.59726e6 - 1.02995e6i) q^{96} +(1.29118e7 + 1.85644e6i) q^{97} +(-2.57389e6 - 4.00506e6i) q^{98} +(1.34184e6 - 633013. i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 540 q - 35 q^{3} + 3362 q^{4} - 1280 q^{6} - 22 q^{7} - 659 q^{9}+O(q^{10}) $ 540 * q - 35 * q^3 + 3362 * q^4 - 1280 * q^6 - 22 * q^7 - 659 * q^9	\( 540 q - 35 q^{3} + 3362 q^{4} - 1280 q^{6} - 22 q^{7} - 659 q^{9} - 22 q^{10} + 4756 q^{12} + 4970 q^{13} + 3828 q^{15} - 174622 q^{16} + 250050 q^{18} - 22 q^{19} - 221738 q^{21} + 94934 q^{24} - 788392 q^{25} + 1020934 q^{27} - 22 q^{28} - 1480875 q^{30} + 738458 q^{31} + 1215192 q^{33} + 1815924 q^{34} - 394502 q^{36} - 905234 q^{37} - 1635803 q^{39} + 10260228 q^{40} - 11 q^{42} - 1694330 q^{43} - 6978726 q^{46} + 134426 q^{48} + 7785740 q^{49} - 11 q^{51} + 16219654 q^{52} - 10697559 q^{54} - 1371960 q^{55} + 7508908 q^{57} - 21860696 q^{58} - 21971851 q^{60} - 11102850 q^{61} - 9022926 q^{63} + 2572060 q^{64} + 16582830 q^{66} + 6031564 q^{67} + 12019470 q^{69} - 2949828 q^{70} + 12828949 q^{72} - 1809596 q^{73} - 16620656 q^{75} - 42651158 q^{76} - 47106384 q^{78} - 1156914 q^{79} + 48837101 q^{81} + 47208588 q^{82} + 124183367 q^{84} + 5833252 q^{85} - 17916287 q^{87} + 360426 q^{88} - 142298860 q^{90} - 51670516 q^{93} - 18401348 q^{94} + 36462337 q^{96} - 63860500 q^{97} + 135683977 q^{99}+O(q^{100}) \) 540 * q - 35 * q^3 + 3362 * q^4 - 1280 * q^6 - 22 * q^7 - 659 * q^9 - 22 * q^10 + 4756 * q^12 + 4970 * q^13 + 3828 * q^15 - 174622 * q^16 + 250050 * q^18 - 22 * q^19 - 221738 * q^21 + 94934 * q^24 - 788392 * q^25 + 1020934 * q^27 - 22 * q^28 - 1480875 * q^30 + 738458 * q^31 + 1215192 * q^33 + 1815924 * q^34 - 394502 * q^36 - 905234 * q^37 - 1635803 * q^39 + 10260228 * q^40 - 11 * q^42 - 1694330 * q^43 - 6978726 * q^46 + 134426 * q^48 + 7785740 * q^49 - 11 * q^51 + 16219654 * q^52 - 10697559 * q^54 - 1371960 * q^55 + 7508908 * q^57 - 21860696 * q^58 - 21971851 * q^60 - 11102850 * q^61 - 9022926 * q^63 + 2572060 * q^64 + 16582830 * q^66 + 6031564 * q^67 + 12019470 * q^69 - 2949828 * q^70 + 12828949 * q^72 - 1809596 * q^73 - 16620656 * q^75 - 42651158 * q^76 - 47106384 * q^78 - 1156914 * q^79 + 48837101 * q^81 + 47208588 * q^82 + 124183367 * q^84 + 5833252 * q^85 - 17916287 * q^87 + 360426 * q^88 - 142298860 * q^90 - 51670516 * q^93 - 18401348 * q^94 + 36462337 * q^96 - 63860500 * q^97 + 135683977 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/69\mathbb{Z}\right)^\times$.

$n$	$28$	$47$
$\chi(n)$	$e\left(\frac{1}{22}\right)$	$-1$

Coefficient data

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

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

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

$2$	−3.60512	+	12.2779i	−0.318650	+	1.08522i	0.632003	+	0.774966i	$0.282233\pi$
$2$	−3.60512	+	12.2779i	−0.318650	+	1.08522i	−0.950653	+	0.310257i	$0.899585\pi$
$3$	46.6247	−	3.62518i	0.996991	−	0.0775185i
$3$	46.6247	−	3.62518i	0.996991	−	0.0775185i
$4$	−30.0694	−	19.3245i	−0.234918	−	0.150972i
$5$	−56.5273	+	393.156i	−0.202238	+	1.40660i	0.595384	+	0.803441i	$0.297000\pi$
$5$	−56.5273	+	393.156i	−0.202238	+	1.40660i	−0.797622	+	0.603157i	$0.793909\pi$
$6$	−123.578	+	585.522i	−0.233567	+	1.10666i
$7$	−611.212	+	279.131i	−0.673517	+	0.307585i	−0.722657	−	0.691207i	$-0.757079\pi$
$7$	−611.212	+	279.131i	−0.673517	+	0.307585i	0.0491396	+	0.998792i	$0.484352\pi$
$8$	−892.188	+	773.086i	−0.616086	+	0.533842i
$9$	2160.72	−	338.046i	0.987982	−	0.154570i
$10$	−4623.34	−	2111.41i	−1.46203	−	0.667687i
$11$	650.920	−	191.127i	0.147453	−	0.0432961i	−0.207173	−	0.978304i	$-0.566426\pi$
$11$	650.920	−	191.127i	0.147453	−	0.0432961i	0.354626	+	0.935008i	$0.384608\pi$
$12$	−1472.03	−	791.989i	−0.245914	−	0.132308i
$13$	1256.61	−	2751.60i	0.158635	−	0.347363i	−0.813579	−	0.581454i	$-0.802484\pi$
$13$	1256.61	−	2751.60i	0.158635	−	0.347363i	0.972215	+	0.234091i	$0.0752114\pi$
$14$	−1223.65	−	8510.70i	−0.119182	−	0.828929i
$15$	−1210.30	+	18535.7i	−0.0925924	+	1.41804i
$16$	−8176.02	−	17903.0i	−0.499025	−	1.09271i
$17$	−7513.61	+	4828.71i	−0.370918	+	0.238374i	−0.712798	−	0.701369i	$-0.752573\pi$
$17$	−7513.61	+	4828.71i	−0.370918	+	0.238374i	0.341881	+	0.939743i	$0.388936\pi$
$18$	−3639.14	+	27747.7i	−0.147077	+	1.12143i
$19$	−8841.70	+	13757.9i	−0.295732	+	0.460168i	−0.957044	−	0.289943i	$-0.906364\pi$
$19$	−8841.70	+	13757.9i	−0.295732	+	0.460168i	0.661312	+	0.750111i	$0.270000\pi$
$20$	9297.27	−	10729.6i	0.259867	−	0.299902i
$21$	−27485.7	+	15230.2i	−0.647647	+	0.358870i
$22$			8680.97i			0.173816i
$23$	24142.2	+	53122.3i	0.413741	+	0.910395i
$23$	24142.2	+	53122.3i	0.413741	+	0.910395i
$24$	−38795.4	+	39279.2i	−0.572850	+	0.579994i
$25$	−76416.0	−	22437.8i	−0.978125	−	0.287204i
$26$	29253.6	+	25348.4i	0.326417	+	0.282842i
$27$	99517.2	−	23594.2i	0.973027	−	0.230692i
$28$	23772.9	+	3418.02i	0.204658	+	0.0294254i
$29$	−116206.	−	180820.i	−0.884779	−	1.37674i	−0.925972	−	0.377592i	$-0.876752\pi$
$29$	−116206.	−	180820.i	−0.884779	−	1.37674i	0.0411925	−	0.999151i	$-0.486884\pi$
$30$	−223216.	−	81683.3i	−1.50939	−	0.552343i
$31$	50316.4	+	58068.2i	0.303350	+	0.350084i	0.886874	−	0.462011i	$-0.152872\pi$
$31$	50316.4	+	58068.2i	0.303350	+	0.350084i	−0.583524	+	0.812096i	$0.698327\pi$
$32$	99716.3	−	14337.0i	0.537949	−	0.0773454i
$33$	29656.1	−	11271.0i	0.143653	−	0.0545961i
$34$	−32198.9	−	109659.i	−0.140496	−	0.478487i
$35$	−75192.0	−	256080.i	−0.296438	−	1.00957i
$36$	−71504.1	−	31589.8i	−0.255430	−	0.112847i
$37$	217915.	−	31331.4i	0.707262	−	0.101689i	0.220708	−	0.975340i	$-0.429163\pi$
$37$	217915.	−	31331.4i	0.707262	−	0.101689i	0.486553	+	0.873651i	$0.338254\pi$
$38$	−137043.	−	158156.i	−0.405150	−	0.467568i
$39$	48614.1	−	132848.i	0.131231	−	0.358615i
$40$	−253510.	−	394470.i	−0.626305	−	0.974549i
$41$	−416216.	−	59842.9i	−0.943139	−	0.135603i	−0.346443	−	0.938071i	$-0.612611\pi$
$41$	−416216.	−	59842.9i	−0.943139	−	0.135603i	−0.596695	+	0.802468i	$0.703520\pi$
$42$	−87905.3	−	392372.i	−0.183081	−	0.817196i
$43$	−343798.	−	297903.i	−0.659423	−	0.571394i	0.259542	−	0.965732i	$-0.416428\pi$
$43$	−343798.	−	297903.i	−0.659423	−	0.571394i	−0.918965	+	0.394338i	$0.870974\pi$
$44$	−23266.2	−	6831.59i	−0.0411758	−	0.0120903i
$45$	10765.2	+	868608.i	0.0176108	+	1.42095i
$46$	−739266.	+	104903.i	−1.11982	+	0.158904i
$47$		−	139012.i		−	0.195304i	−0.995221	−	0.0976519i	$-0.968867\pi$
$47$		−	139012.i		−	0.195304i	0.995221	−	0.0976519i	$-0.0311332\pi$
$48$	−446106.	−	805081.i	−0.582229	−	1.05074i
$49$	−243640.	+	281176.i	−0.295844	+	0.341422i
$50$	550977.	−	857338.i	0.623360	−	0.969967i
$51$	−332815.	+	252375.i	−0.351323	+	0.266410i
$52$	−90958.8	+	58455.7i	−0.0897084	+	0.0576521i
$53$	713053.	+	1.56137e6i	0.657895	+	1.44059i	0.884471	+	0.466595i	$0.154519\pi$
$53$	713053.	+	1.56137e6i	0.657895	+	1.44059i	−0.226577	+	0.973993i	$0.572753\pi$
$54$	−69083.1	+	1.30692e6i	−0.0597027	+	1.12946i
$55$	38348.1	+	266717.i	0.0310796	+	0.216163i
$56$	329524.	−	721557.i	0.250743	−	0.549051i
$57$	−362366.	+	673512.i	−0.259170	+	0.481708i
$58$	2.63902e6	−	774887.i	1.77601	−	0.521483i
$59$	1.80634e6	+	824928.i	1.14503	+	0.522918i	0.895329	−	0.445404i	$-0.146940\pi$
$59$	1.80634e6	+	824928.i	1.14503	+	0.522918i	0.249702	+	0.968323i	$0.419667\pi$
$60$	394585.	−	533969.i	0.235837	−	0.319144i
$61$	−919511.	+	796761.i	−0.518684	+	0.449442i	−0.874438	−	0.485138i	$-0.838770\pi$
$61$	−919511.	+	796761.i	−0.518684	+	0.449442i	0.355754	+	0.934580i	$0.384224\pi$
$62$	−894352.	+	408437.i	−0.476582	+	0.217648i
$63$	−1.22630e6	+	809741.i	−0.617879	+	0.407994i
$64$	175065.	−	1.21761e6i	0.0834777	−	0.580600i
$65$	1.01077e6	+	649586.i	0.456518	+	0.293386i
$66$	31470.1	+	404747.i	0.0134739	+	0.173293i
$67$	511181.	−	1.74092e6i	0.207641	−	0.707160i	−0.788148	−	0.615485i	$-0.788960\pi$
$67$	511181.	−	1.74092e6i	0.207641	−	0.707160i	0.995789	−	0.0916741i	$-0.0292218\pi$
$68$	319242.			0.123123
$69$	1.31820e6	+	2.38929e6i	0.483068	+	0.875583i
$70$	3.41520e6			1.19007
$71$	−1.10492e6	+	3.76301e6i	−0.366376	+	1.24776i	0.545783	+	0.837926i	$0.316232\pi$
$71$	−1.10492e6	+	3.76301e6i	−0.366376	+	1.24776i	−0.912159	+	0.409836i	$0.865586\pi$
$72$	−1.66643e6	+	1.97202e6i	−0.526166	+	0.622655i
$73$	−2.74254e6	−	1.76252e6i	−0.825132	−	0.530280i	0.0585959	−	0.998282i	$-0.481338\pi$
$73$	−2.74254e6	−	1.76252e6i	−0.825132	−	0.530280i	−0.883727	+	0.468002i	$0.844974\pi$
$74$	−400924.	+	2.78849e6i	−0.115014	+	0.799940i
$75$	−3.64421e6	−	769131.i	−0.997446	−	0.210516i
$76$	531730.	−	242833.i	0.138945	−	0.0634541i
$77$	−344501.	+	298512.i	−0.0859949	+	0.0745150i
$78$	1.45583e6	+	1.07581e6i	0.347360	+	0.256687i
$79$	1.15036e6	+	525351.i	0.262506	+	0.119882i	0.542321	−	0.840172i	$-0.317546\pi$
$79$	1.15036e6	+	525351.i	0.262506	+	0.119882i	−0.279815	+	0.960054i	$0.590273\pi$
$80$	7.50084e6	−	2.20245e6i	1.63793	−	0.480939i
$81$	4.55442e6	−	1.46084e6i	0.952216	−	0.305426i
$82$	2.23525e6	−	4.89452e6i	0.447691	−	0.980306i
$83$	805140.	+	5.59987e6i	0.154560	+	1.07499i	0.908451	+	0.417991i	$0.137266\pi$
$83$	805140.	+	5.59987e6i	0.154560	+	1.07499i	−0.753891	+	0.656999i	$0.771825\pi$
$84$	1.12079e6	+	73183.1i	0.206323	+	0.0134720i
$85$	−1.47371e6	−	3.22698e6i	−0.260283	−	0.569941i
$86$	4.89706e6	−	3.14715e6i	0.830215	−	0.533547i
$87$	−6.07356e6	−	8.00939e6i	−0.988840	−	1.30401i
$88$	−432986.	+	673739.i	−0.0677305	+	0.105391i
$89$	−4.53210e6	+	5.23032e6i	−0.681450	+	0.786436i	−0.986122	−	0.166022i	$-0.946908\pi$
$89$	−4.53210e6	+	5.23032e6i	−0.681450	+	0.786436i	0.304672	+	0.952457i	$0.401453\pi$
$90$	−1.07035e7	−	2.99926e6i	−1.54766	−	0.433675i
$91$			2.03257e6i			0.282749i
$92$	300619.	−	2.06389e6i	0.0402494	−	0.276331i
$93$	2.55649e6	+	2.52500e6i	0.329575	+	0.325516i
$94$	1.70678e6	+	501156.i	0.211948	+	0.0622336i
$95$	−4.90923e6	−	4.25387e6i	−0.587463	−	0.509039i
$96$	4.59726e6	−	1.02995e6i	0.530335	−	0.118814i
$97$	1.29118e7	+	1.85644e6i	1.43644	+	0.206528i	0.816147	−	0.577844i	$-0.196106\pi$
$97$	1.29118e7	+	1.85644e6i	1.43644	+	0.206528i	0.620290	+	0.784373i	$0.287015\pi$
$98$	−2.57389e6	−	4.00506e6i	−0.276248	−	0.429850i
$99$	1.34184e6	−	633013.i	0.138989	−	0.0655676i
$100$	1.86419e6	+	2.15139e6i	0.186419	+	0.215139i
$101$	1.90111e7	−	2.73338e6i	1.83604	−	0.263982i	0.864804	−	0.502109i	$-0.167443\pi$
$101$	1.90111e7	−	2.73338e6i	1.83604	−	0.263982i	0.971234	+	0.238127i	$0.0765334\pi$
$102$	−1.89880e6	−	4.99611e6i	−0.177165	−	0.466156i
$103$	−181754.	−	618998.i	−0.0163891	−	0.0558161i	0.950892	−	0.309521i	$-0.100169\pi$
$103$	−181754.	−	618998.i	−0.0163891	−	0.0558161i	−0.967282	+	0.253705i	$0.918351\pi$
$104$	1.00609e6	+	3.42641e6i	0.0877038	+	0.298692i
$105$	−4.43414e6	−	1.16671e7i	−0.373806	−	0.983557i
$106$	−2.17410e7	+	3.12588e6i	−1.77300	+	0.254919i
$107$	9.38650e6	+	1.08326e7i	0.740731	+	0.854849i	0.993636	−	0.112642i	$-0.0359314\pi$
$107$	9.38650e6	+	1.08326e7i	0.740731	+	0.854849i	−0.252905	+	0.967491i	$0.581386\pi$
$108$	−3.44837e6	−	1.21365e6i	−0.263409	−	0.0927065i
$109$	1.28502e7	+	1.99952e7i	0.950420	+	1.47888i	0.876376	+	0.481628i	$0.159954\pi$
$109$	1.28502e7	+	1.99952e7i	0.950420	+	1.47888i	0.0740442	+	0.997255i	$0.476409\pi$
$110$	−3.41298e6	−	490712.i	−0.244489	−	0.0351522i
$111$	1.00466e7	−	2.25079e6i	0.697251	−	0.156209i
$112$	9.99457e6	+	8.66034e6i	0.672204	+	0.582468i
$113$	−8.02307e6	−	2.35579e6i	−0.523078	−	0.153589i	0.00952534	−	0.999955i	$-0.496968\pi$
$113$	−8.02307e6	−	2.35579e6i	−0.523078	−	0.153589i	−0.532603	+	0.846365i	$0.678786\pi$
$114$	−6.96294e6	−	6.87718e6i	−0.440176	−	0.434754i
$115$	−2.22501e7	+	6.48877e6i	−1.36423	+	0.397851i
$116$			7.68277e6i			0.456998i
$117$	1.78502e6	−	6.37022e6i	0.103037	−	0.367708i
$118$	−1.66404e7	+	1.92041e7i	−0.932347	+	1.07599i
$119$	3.24457e6	−	5.04865e6i	0.176499	−	0.274638i
$120$	−1.32499e7	−	1.74730e7i	−0.699966	−	0.923067i
$121$	−1.60065e7	+	1.02867e7i	−0.821386	+	0.527873i
$122$	−6.46761e6	−	1.41621e7i	−0.322466	−	0.706102i
$123$	−1.96229e7	−	1.28129e6i	−0.950812	−	0.0620841i
$124$	−390849.	−	2.71842e6i	−0.0184091	−	0.128038i
$125$	250327.	−	548139.i	0.0114636	−	0.0251018i
$126$	−5.52097e6	−	1.79756e7i	−0.245877	−	0.800544i
$127$	−2.02758e7	+	5.95351e6i	−0.878345	+	0.257905i	−0.689661	−	0.724133i	$-0.742240\pi$
$127$	−2.02758e7	+	5.95351e6i	−0.878345	+	0.257905i	−0.188684	+	0.982038i	$0.560422\pi$
$128$	2.60482e7	+	1.18958e7i	1.09785	+	0.501370i
$129$	−1.71094e7	−	1.26433e7i	−0.701733	−	0.518557i
$130$	−1.16195e7	+	1.00684e7i	−0.463859	+	0.401936i
$131$	1.17970e7	−	5.38751e6i	0.458481	−	0.209381i	−0.172766	−	0.984963i	$-0.555270\pi$
$131$	1.17970e7	−	5.38751e6i	0.458481	−	0.209381i	0.631248	+	0.775581i	$0.282543\pi$
$132$	−1.10955e6	−	234176.i	−0.0419891	−	0.00886204i
$133$	1.56388e6	−	1.08770e7i	0.0576398	−	0.400894i
$134$	1.95320e7	+	1.25524e7i	0.701261	+	0.450673i
$135$	3.65079e6	+	4.04595e7i	0.127708	+	1.41531i
$136$	2.97056e6	−	1.01168e7i	0.101263	−	0.344871i
$137$	−3.02951e6			−0.100659			−0.0503293	−	0.998733i	$-0.516027\pi$
$137$	−3.02951e6			−0.100659			−0.0503293	+	0.998733i	$0.516027\pi$
$138$	−3.40877e7	+	7.57102e6i	−1.10413	+	0.245232i
$139$	2.57960e6			0.0814705			0.0407352	−	0.999170i	$-0.487030\pi$
$139$	2.57960e6			0.0814705			0.0407352	+	0.999170i	$0.487030\pi$
$140$	−2.68763e6	+	9.15324e6i	−0.0827793	+	0.281920i
$141$	−503945.	−	6.48140e6i	−0.0151397	−	0.194716i
$142$	−4.22185e7	−	2.71322e7i	−1.23735	−	0.795199i
$143$	292049.	−	2.03124e6i	0.00835179	−	0.0580879i
$144$	−2.37181e7	−	3.59194e7i	−0.661928	−	1.00244i
$145$	7.76592e7	−	3.54658e7i	2.11546	−	0.966099i
$146$	3.15273e7	−	2.73185e7i	0.838400	−	0.726478i
$147$	−1.03403e7	+	1.39929e7i	−0.268487	+	0.363328i
$148$	−7.15803e6	−	3.26896e6i	−0.181500	−	0.0828884i
$149$	−2.56164e6	+	752166.i	−0.0634404	+	0.0186278i	−0.313299	−	0.949655i	$-0.601434\pi$
$149$	−2.56164e6	+	752166.i	−0.0634404	+	0.0186278i	0.249858	+	0.968282i	$0.419616\pi$
$150$	2.25811e7	−	4.19705e7i	0.546294	−	1.01537i
$151$	−739055.	+	1.61831e6i	−0.0174686	+	0.0382509i	−0.918165	−	0.396198i	$-0.870329\pi$
$151$	−739055.	+	1.61831e6i	−0.0174686	+	0.0382509i	0.900697	+	0.434449i	$0.143057\pi$
$152$	−2.74761e6	−	1.91101e7i	−0.0634604	−	0.441377i
$153$	−1.46025e7	+	1.29734e7i	−0.329614	+	0.292843i
$154$	−2.42313e6	−	5.30591e6i	−0.0534631	−	0.117068i
$155$	−2.56741e7	+	1.64998e7i	−0.553777	+	0.355891i
$156$	−4.02901e6	+	3.05522e6i	−0.0849693	+	0.0644326i
$157$	5.11117e7	−	7.95313e7i	1.05407	−	1.64017i	0.339511	−	0.940602i	$-0.389739\pi$
$157$	5.11117e7	−	7.95313e7i	1.05407	−	1.64017i	0.714564	−	0.699570i	$-0.246625\pi$
$158$	−1.05974e7	+	1.22300e7i	−0.213746	+	0.246677i
$159$	3.89061e7	+	7.02133e7i	0.767587	+	1.38525i
$160$			4.00145e7i			0.772320i
$161$	−2.95841e7	−	2.57302e7i	−0.558686	−	0.485906i
$162$	1.51685e6	+	6.11852e7i	0.0280311	+	1.13069i
$163$	9.24362e7	+	2.71417e7i	1.67180	+	0.490886i	0.974217	−	0.225614i	$-0.0724387\pi$
$163$	9.24362e7	+	2.71417e7i	1.67180	+	0.490886i	0.697587	+	0.716500i	$0.254257\pi$
$164$	1.13590e7	+	9.84259e6i	0.201088	+	0.174243i
$165$	2.75487e6	+	1.22966e7i	0.0477427	+	0.213103i
$166$	−7.16572e7	−	1.03028e7i	−1.21585	−	0.174814i
$167$	1.64145e7	+	2.55414e7i	0.272722	+	0.424363i	0.950416	−	0.310980i	$-0.100657\pi$
$167$	1.64145e7	+	2.55414e7i	0.272722	+	0.424363i	−0.677695	+	0.735343i	$0.737021\pi$
$168$	1.27482e7	−	3.48369e7i	0.207427	−	0.566836i
$169$	3.50993e7	+	4.05068e7i	0.559365	+	0.645542i
$170$	4.49334e7	−	6.46045e6i	0.701452	−	0.100854i
$171$	−1.44536e7	+	3.27159e7i	−0.221049	+	0.500349i
$172$	4.58101e6	+	1.56015e7i	0.0686455	+	0.233785i
$173$	7.21577e6	+	2.45746e7i	0.105955	+	0.360849i	0.995354	−	0.0962821i	$-0.0306951\pi$
$173$	7.21577e6	+	2.45746e7i	0.105955	+	0.360849i	−0.889399	+	0.457131i	$0.848877\pi$
$174$	1.20234e8	−	4.56958e7i	1.73024	−	0.657588i
$175$	5.29695e7	−	7.61586e6i	0.747124	−	0.107420i
$176$	−8.74369e6	−	1.00908e7i	−0.120893	−	0.139518i
$177$	8.72105e7	+	3.19137e7i	1.18212	+	0.432584i
$178$	−4.78786e7	−	7.45005e7i	−0.636314	−	0.990123i
$179$	−1.21920e8	−	1.75294e7i	−1.58887	−	0.228445i	−0.709542	−	0.704663i	$-0.751098\pi$
$179$	−1.21920e8	−	1.75294e7i	−1.58887	−	0.228445i	−0.879327	+	0.476218i	$0.842007\pi$
$180$	1.64617e7	−	2.63266e7i	0.210388	−	0.336466i
$181$	5.10931e7	+	4.42724e7i	0.640453	+	0.554956i	0.913395	−	0.407075i	$-0.133451\pi$
$181$	5.10931e7	+	4.42724e7i	0.640453	+	0.554956i	−0.272942	+	0.962031i	$0.587997\pi$
$182$	−2.49557e7	−	7.32765e6i	−0.306845	−	0.0900980i
$183$	−3.99835e7	+	4.04821e7i	−0.482283	+	0.488297i
$184$	−6.26075e7	−	2.87312e7i	−0.740907	−	0.340009i
$185$			8.74455e7i			1.01540i
$186$	−4.02182e7	+	2.22854e7i	−0.458276	+	0.253937i
$187$	−3.96787e6	+	4.57916e6i	−0.0443722	+	0.0512083i
$188$	−2.68634e6	+	4.18002e6i	−0.0294855	+	0.0458803i
$189$	−5.42402e7	+	4.21994e7i	−0.584393	+	0.454664i
$190$	6.99269e7	−	4.49393e7i	0.739616	−	0.475323i
$191$	−4.14124e7	−	9.06804e7i	−0.430044	−	0.941666i	−0.993320	−	0.115396i	$-0.963186\pi$
$191$	−4.14124e7	−	9.06804e7i	−0.430044	−	0.941666i	0.563275	−	0.826269i	$-0.309541\pi$
$192$	3.74832e6	−	5.74051e7i	0.0382193	−	0.585324i
$193$	−1.62464e7	−	1.12996e8i	−0.162670	−	1.13139i	−0.893575	−	0.448913i	$-0.851811\pi$
$193$	−1.62464e7	−	1.12996e8i	−0.162670	−	1.13139i	0.730906	−	0.682478i	$-0.239098\pi$
$194$	−6.93418e7	+	1.51837e8i	−0.681850	+	1.49304i
$195$	4.94819e7	+	2.66225e7i	0.477887	+	0.257115i
$196$	1.27597e7	−	3.74658e6i	0.121044	−	0.0355417i
$197$	6.15773e7	+	2.81214e7i	0.573837	+	0.262063i	0.681127	−	0.732165i	$-0.261490\pi$
$197$	6.15773e7	+	2.81214e7i	0.573837	+	0.262063i	−0.107290	+	0.994228i	$0.534217\pi$
$198$	2.93456e6	+	1.87571e7i	0.0268668	+	0.171727i
$199$	−2.70663e7	+	2.34531e7i	−0.243468	+	0.210967i	−0.768044	−	0.640397i	$-0.778770\pi$
$199$	−2.70663e7	+	2.34531e7i	−0.243468	+	0.210967i	0.524575	+	0.851364i	$0.324224\pi$
$200$	8.55238e7	−	3.90574e7i	0.755931	−	0.345222i
$201$	1.75225e7	−	8.30230e7i	0.152198	−	0.721128i
$202$	−3.49770e7	+	2.43270e8i	−0.298574	+	2.07663i
$203$	1.21499e8	+	7.80826e7i	1.01938	+	0.655116i
$204$	1.48846e7	−	1.15731e6i	0.122753	−	0.00954431i
$205$	4.70552e7	−	1.60255e8i	0.381478	−	1.29919i
$206$	8.25524e6			0.0657953
$207$	7.01221e7	+	1.06621e8i	0.549489	+	0.835501i
$208$	−5.95359e7			−0.458730
$209$	−3.12572e6	+	1.06452e7i	−0.0236831	+	0.0806571i
$210$	1.59233e8	−	1.23807e7i	1.18649	−	0.0922527i
$211$	−5.57861e7	−	3.58515e7i	−0.408825	−	0.262736i	0.320025	−	0.947409i	$-0.396309\pi$
$211$	−5.57861e7	−	3.58515e7i	−0.408825	−	0.262736i	−0.728850	+	0.684673i	$0.759945\pi$
$212$	8.73149e6	−	6.07288e7i	0.0629380	−	0.437743i
$213$	−3.78749e7	+	1.79455e8i	−0.268549	+	1.27241i
$214$	−1.66841e8	+	7.61937e7i	−1.16374	+	0.531460i
$215$	1.36556e8	−	1.18327e8i	0.937082	−	0.811986i
$216$	−7.05477e7	+	9.79858e7i	−0.476315	+	0.661569i
$217$	−4.69627e7	−	2.14471e7i	−0.311992	−	0.142482i
$218$	−2.91826e8	+	8.56878e7i	−1.90777	+	0.560172i
$219$	−1.34260e8	−	7.22349e7i	−0.863755	−	0.464721i
$220$	4.00106e6	−	8.76110e6i	0.0253335	−	0.0554727i
$221$	3.84496e6	+	2.67423e7i	0.0239618	+	0.166658i
$222$	−8.58416e6	+	1.31466e8i	−0.0526578	+	0.806449i
$223$	1.46883e7	+	3.21629e7i	0.0886962	+	0.194218i	0.948782	−	0.315932i	$-0.102317\pi$
$223$	1.46883e7	+	3.21629e7i	0.0886962	+	0.194218i	−0.860086	+	0.510150i	$0.829590\pi$
$224$	−5.69459e7	+	3.65969e7i	−0.338528	+	0.217559i
$225$	−1.72698e8	−	2.26496e7i	−1.01076	−	0.132563i
$226$	5.78482e7	−	9.00136e7i	0.333358	−	0.518715i
$227$	−1.89389e7	+	2.18566e7i	−0.107464	+	0.124020i	−0.806933	−	0.590642i	$-0.798874\pi$
$227$	−1.89389e7	+	2.18566e7i	−0.107464	+	0.124020i	0.699469	+	0.714663i	$0.253420\pi$
$228$	2.39114e7	−	1.32496e7i	0.133608	−	0.0740340i
$229$		−	8.34627e7i		−	0.459270i	−0.973277	−	0.229635i	$-0.926247\pi$
$229$		−	8.34627e7i		−	0.459270i	0.973277	−	0.229635i	$-0.0737533\pi$
$230$	545577.	−	2.96577e8i	0.00295671	−	1.60727i
$231$	−1.49801e7	+	1.51669e7i	−0.0799598	+	0.0809570i
$232$	2.43467e8	+	7.14883e7i	1.28006	+	0.375861i
$233$	−2.20585e8	−	1.91138e8i	−1.14243	−	0.989924i	−1.00000		0.000119309i	$-0.999962\pi$
$233$	−2.20585e8	−	1.91138e8i	−1.14243	−	0.989924i	−0.142433	−	0.989804i	$-0.545493\pi$
$234$	7.17777e7	+	4.48816e7i	0.366213	+	0.228988i
$235$	5.46536e7	+	7.85799e6i	0.274714	+	0.0394979i
$236$	−3.83743e7	−	5.97116e7i	−0.190042	−	0.295711i
$237$	5.55396e7	+	2.03241e7i	0.271009	+	0.0991725i
$238$	5.02897e7	+	5.80375e7i	0.241802	+	0.279054i
$239$	−9.99706e7	+	1.43736e7i	−0.473674	+	0.0681040i	−0.375018	−	0.927018i	$-0.622363\pi$
$239$	−9.99706e7	+	1.43736e7i	−0.473674	+	0.0681040i	−0.0986560	+	0.995122i	$0.531454\pi$
$240$	3.41740e8	−	1.29880e8i	1.59572	−	0.606462i
$241$	−5.44969e7	−	1.85599e8i	−0.250791	−	0.854116i	−0.984609	−	0.174770i	$-0.944082\pi$
$241$	−5.44969e7	−	1.85599e8i	−0.250791	−	0.854116i	0.733818	−	0.679346i	$-0.237736\pi$
$242$	−6.85943e7	−	2.33611e8i	−0.311125	−	1.05959i
$243$	2.07052e8	−	8.46218e7i	0.925674	−	0.378321i
$244$	4.30462e7	−	6.18910e6i	0.189701	−	0.0272749i
$245$	−9.67736e7	−	1.11683e8i	−0.420412	−	0.485182i
$246$	8.64743e7	−	2.36308e8i	0.370352	−	1.01206i
$247$	2.67458e7	+	4.16172e7i	0.112932	+	0.175725i
$248$	−8.97834e7	−	1.29089e7i	−0.373779	−	0.0537414i
$249$	5.78399e7	+	2.58173e8i	0.237427	+	1.05977i
$250$	5.82753e6	+	5.04959e6i	0.0235882	+	0.0204393i
$251$	−1.60554e8	−	4.71429e7i	−0.640860	−	0.188173i	−0.0548721	−	0.998493i	$-0.517475\pi$
$251$	−1.60554e8	−	4.71429e7i	−0.640860	−	0.188173i	−0.585988	+	0.810320i	$0.699293\pi$
$252$	5.25219e7	−	650938.i	0.206747	−	0.00256235i
$253$	2.58678e7	+	2.99642e7i	0.100424	+	0.116327i
$254$		−	2.70407e8i		−	1.03538i
$255$	−8.04097e7	−	1.45114e8i	−0.303681	−	0.548049i
$256$	−1.36850e8	+	1.57933e8i	−0.509806	+	0.588348i
$257$	−2.16980e8	+	3.37628e8i	−0.797361	+	1.24072i	0.169530	+	0.985525i	$0.445775\pi$
$257$	−2.16980e8	+	3.37628e8i	−0.797361	+	1.24072i	−0.966890	+	0.255192i	$0.917861\pi$
$258$	2.16915e8	−	1.64487e8i	0.786357	−	0.596298i
$259$	−1.24446e8	+	7.99769e7i	−0.445075	+	0.286032i
$260$	−1.78405e7	−	3.90654e7i	−0.0629508	−	0.137843i
$261$	−3.12213e8	−	3.51417e8i	−1.08695	−	1.22344i
$262$	2.36177e7	+	1.64265e8i	0.0811304	+	0.564274i
$263$	1.98493e8	−	4.34639e8i	0.672822	−	1.47327i	−0.197252	−	0.980353i	$-0.563202\pi$
$263$	1.98493e8	−	4.34639e8i	0.672822	−	1.47327i	0.870074	−	0.492922i	$-0.164071\pi$
$264$	−1.77454e7	+	3.29825e7i	−0.0593569	+	0.110324i
$265$	−6.54169e8	+	1.92081e8i	−2.15938	+	0.634051i
$266$	1.27909e8	+	5.84141e7i	0.416692	+	0.190297i
$267$	−1.92347e8	+	2.60291e8i	−0.618436	+	0.836894i
$268$	−4.90133e7	+	4.24702e7i	−0.155540	+	0.134776i
$269$	−2.08881e7	+	9.53926e6i	−0.0654283	+	0.0298801i	−0.447860	−	0.894103i	$-0.647814\pi$
$269$	−2.08881e7	+	9.53926e6i	−0.0654283	+	0.0298801i	0.382432	+	0.923984i	$0.375087\pi$
$270$	−5.09919e8	−	1.01037e8i	−1.57662	−	0.312398i
$271$	5.80223e7	−	4.03554e8i	0.177094	−	1.23171i	−0.686352	−	0.727270i	$-0.740789\pi$
$271$	5.80223e7	−	4.03554e8i	0.177094	−	1.23171i	0.863445	−	0.504443i	$-0.168302\pi$
$272$	1.47880e8	+	9.50366e7i	0.445572	+	0.286352i
$273$	7.36844e6	+	9.47679e7i	0.0219183	+	0.281898i
$274$	1.09217e7	−	3.71960e7i	0.0320749	−	0.109237i
$275$	−5.40292e7			−0.156662
$276$	6.53428e6	−	9.73181e7i	0.0187075	−	0.278620i
$277$	2.96200e8			0.837349			0.418675	−	0.908136i	$-0.362495\pi$
$277$	2.96200e8			0.837349			0.418675	+	0.908136i	$0.362495\pi$
$278$	−9.29975e6	+	3.16720e7i	−0.0259606	+	0.0884136i
$279$	1.28349e8	+	1.08460e8i	0.353817	+	0.298988i
$280$	2.65057e8	+	1.70342e8i	0.721584	+	0.463734i
$281$	−5.60497e7	+	3.89834e8i	−0.150696	+	1.04811i	0.764361	+	0.644788i	$0.223054\pi$
$281$	−5.60497e7	+	3.89834e8i	−0.150696	+	1.04811i	−0.915057	+	0.403324i	$0.867855\pi$
$282$	8.13948e7	+	1.71788e7i	0.216135	+	0.0456164i
$283$	−5.32765e8	+	2.43306e8i	−1.39728	+	0.638116i	−0.964669	−	0.263465i	$-0.915134\pi$
$283$	−5.32765e8	+	2.43306e8i	−1.39728	+	0.638116i	−0.432610	+	0.901581i	$0.642407\pi$
$284$	1.05943e8	−	9.17998e7i	0.274446	−	0.237808i
$285$	−2.44312e8	−	1.80538e8i	−0.625155	−	0.461968i
$286$	2.38865e7	+	1.09086e7i	0.0603771	+	0.0275733i
$287$	2.71100e8	−	7.96023e7i	0.676930	−	0.198764i
$288$	2.10612e8	−	6.46869e7i	0.519528	−	0.159567i
$289$	−1.37323e8	+	3.00695e8i	−0.334657	+	0.732797i
$290$	1.55475e8	+	1.08135e9i	0.374340	+	2.60360i
$291$	6.08739e8	+	3.97482e7i	1.44812	+	0.0945565i
$292$	4.84069e7	+	1.05996e8i	0.113780	+	0.249144i
$293$	1.03766e8	−	6.66866e7i	0.241002	−	0.154882i	−0.414565	−	0.910020i	$-0.636066\pi$
$293$	1.03766e8	−	6.66866e7i	0.241002	−	0.154882i	0.655567	+	0.755137i	$0.272430\pi$
$294$	−1.34526e8	−	1.77404e8i	−0.308738	−	0.407143i
$295$	−4.26433e8	+	6.63543e8i	−0.967105	+	1.50484i
$296$	−1.70199e8	+	1.96420e8i	−0.381449	+	0.440215i
$297$	6.02682e7	−	3.43784e7i	0.133488	−	0.0761445i
$298$		−	3.41632e7i		−	0.0747828i
$299$	1.76509e8	+	324702.i	0.381871	+	0.000702484i
$300$	9.47164e7	+	9.35498e7i	0.202535	+	0.200041i
$301$	2.93288e8	+	8.61171e7i	0.619885	+	0.182015i
$302$	−1.72050e7	−	1.49082e7i	−0.0359443	−	0.0311459i
$303$	8.76475e8	−	1.96361e8i	1.81005	−	0.405515i
$304$	3.18598e8	+	4.58075e7i	0.650408	+	0.0935146i
$305$	−2.61274e8	−	4.06550e8i	−0.527287	−	0.820474i
$306$	−1.06643e8	−	2.26058e8i	−0.212768	−	0.451019i
$307$	7.14513e7	+	8.24591e7i	0.140937	+	0.162650i	0.821830	−	0.569733i	$-0.192953\pi$
$307$	7.14513e7	+	8.24591e7i	0.140937	+	0.162650i	−0.680893	+	0.732383i	$0.738408\pi$
$308$	1.61275e7	−	2.31879e6i	0.0314514	−	0.00452203i
$309$	−1.07182e7	−	2.82017e7i	−0.0206665	−	0.0543777i
$310$	−1.10024e8	−	3.74708e8i	−0.209760	−	0.714376i
$311$	−2.41326e8	−	8.21879e8i	−0.454927	−	1.54934i	−0.793602	−	0.608437i	$-0.791797\pi$
$311$	−2.41326e8	−	8.21879e8i	−0.454927	−	1.54934i	0.338675	−	0.940903i	$-0.390021\pi$
$312$	5.93298e7	+	1.56108e8i	0.110594	+	0.290994i
$313$	1.02418e9	−	1.47255e8i	1.88787	−	0.271435i	0.901108	−	0.433596i	$-0.142755\pi$
$313$	1.02418e9	−	1.47255e8i	1.88787	−	0.271435i	0.986764	+	0.162161i	$0.0518463\pi$
$314$	7.92214e8	+	9.14264e8i	1.44407	+	1.66655i
$315$	−2.49035e8	−	5.27899e8i	−0.448925	−	0.951620i
$316$	−2.44385e7	−	3.80271e7i	−0.0435682	−	0.0677935i
$317$	−6.70020e8	−	9.63343e7i	−1.18135	−	0.169853i	−0.476480	−	0.879185i	$-0.658088\pi$
$317$	−6.70020e8	−	9.63343e7i	−1.18135	−	0.169853i	−0.704875	+	0.709332i	$0.748997\pi$
$318$	−1.00233e9	+	2.24558e8i	−1.74790	+	0.391592i
$319$	−1.10200e8	−	9.54892e7i	−0.190071	−	0.164697i
$320$	4.68814e8	+	1.37656e8i	0.799789	+	0.234839i
$321$	4.76912e8	+	4.71038e8i	0.804769	+	0.794856i
$322$	4.22567e8	−	2.70470e8i	0.705342	−	0.451464i
$323$		−	1.46066e8i		−	0.241179i
$324$	−1.65179e8	−	4.40850e7i	−0.269803	−	0.0720084i
$325$	−1.57765e8	+	1.82071e8i	−0.254929	+	0.294204i
$326$	−6.66486e8	+	1.03707e9i	−1.06544	+	1.65786i
$327$	6.71620e8	+	8.85687e8i	1.06220	+	1.40076i
$328$	4.17607e8	−	2.68380e8i	0.653445	−	0.419944i
$329$	3.88027e7	+	8.49660e7i	0.0600726	+	0.131541i
$330$	−1.60908e8	−	1.05066e7i	−0.246478	−	0.0160940i
$331$	−9.02590e7	−	6.27765e8i	−0.136802	−	0.951479i	−0.936398	−	0.350940i	$-0.885862\pi$
$331$	−9.02590e7	−	6.27765e8i	−0.136802	−	0.951479i	0.799596	−	0.600539i	$-0.205047\pi$
$332$	8.40043e7	−	1.83944e8i	0.125985	−	0.275868i
$333$	4.60260e8	−	1.41363e8i	0.683044	−	0.209789i
$334$	−3.72771e8	+	1.09455e8i	−0.547431	+	0.160740i
$335$	6.55558e8	+	2.99383e8i	0.952696	+	0.435082i
$336$	4.97389e8	+	3.67553e8i	0.715333	+	0.528607i
$337$	5.03241e8	−	4.36061e8i	0.716261	−	0.620644i	−0.218535	−	0.975829i	$-0.570128\pi$
$337$	5.03241e8	−	4.36061e8i	0.716261	−	0.620644i	0.934796	+	0.355185i	$0.115582\pi$
$338$	−6.23875e8	+	2.84914e8i	−0.878798	+	0.401334i
$339$	−3.82613e8	−	8.07526e7i	−0.533410	−	0.112579i
$340$	−1.80459e7	+	1.25512e8i	−0.0249002	+	0.173185i
$341$	4.38504e7	+	2.81809e7i	0.0598871	+	0.0384871i
$342$	−3.49576e8	−	2.95404e8i	−0.472553	−	0.399324i
$343$	2.26332e8	−	7.70816e8i	0.302842	−	1.03139i
$344$	5.37038e8			0.711296
$345$	−1.01388e9	+	3.83197e8i	−1.32929	+	0.502407i
$346$	−3.27739e8			−0.425365
$347$	2.43743e8	−	8.30112e8i	0.313169	−	1.06656i	−0.641063	−	0.767488i	$-0.721506\pi$
$347$	2.43743e8	−	8.30112e8i	0.313169	−	1.06656i	0.954232	−	0.299067i	$-0.0966756\pi$
$348$	2.78514e7	+	3.58206e8i	0.0354258	+	0.455623i
$349$	7.46098e8	+	4.79488e8i	0.939522	+	0.603794i	0.918259	−	0.395980i	$-0.129595\pi$
$349$	7.46098e8	+	4.79488e8i	0.939522	+	0.603794i	0.0212628	+	0.999774i	$0.493231\pi$
$350$	−9.74544e7	+	6.77810e8i	−0.121496	+	0.845026i
$351$	6.01326e7	−	3.03480e8i	0.0742225	−	0.374589i
$352$	6.21671e7	−	2.83908e7i	0.0759734	−	0.0346959i
$353$	1.01365e9	−	8.78332e8i	1.22652	−	1.06279i	0.230558	−	0.973059i	$-0.425945\pi$
$353$	1.01365e9	−	8.78332e8i	1.22652	−	1.06279i	0.995966	−	0.0897306i	$-0.0286006\pi$
$354$	−7.06236e8	+	9.55709e8i	−0.846133	+	1.14502i
$355$	−1.41699e9	−	6.47120e8i	−1.68100	−	0.767689i
$356$	2.37351e8	−	6.96925e7i	0.278815	−	0.0818674i
$357$	1.32975e8	−	2.47154e8i	0.154679	−	0.287494i
$358$	6.54759e8	−	1.43372e9i	0.754207	−	1.65148i
$359$	7.35537e7	+	5.11577e8i	0.0839023	+	0.583554i	0.987791	+	0.155786i	$0.0497909\pi$
$359$	7.35537e7	+	5.11577e8i	0.0839023	+	0.583554i	−0.903889	+	0.427768i	$0.859300\pi$
$360$	−6.81113e8	−	7.66639e8i	−0.769414	−	0.866029i
$361$	2.60222e8	+	5.69807e8i	0.291118	+	0.637460i
$362$	−7.27769e8	+	4.67709e8i	−0.806331	+	0.518198i
$363$	−7.09005e8	+	5.37642e8i	−0.777994	+	0.589957i
$364$	3.92783e7	−	6.11182e7i	0.0426872	−	0.0664226i
$365$	8.47976e8	−	9.78616e8i	0.912764	−	1.05339i
$366$	−3.52890e8	−	6.36856e8i	−0.376232	−	0.678980i
$367$			4.97320e8i			0.525176i	0.964908	+	0.262588i	$0.0845760\pi$
$367$			4.97320e8i			0.525176i	−0.964908	+	0.262588i	$0.915424\pi$
$368$	7.53662e8	−	8.66546e8i	0.788332	−	0.906409i
$369$	−9.19555e8	+	1.13967e7i	−0.952764	+	0.0118082i
$370$	−1.07365e9	−	3.15251e8i	−1.10193	−	0.323557i
$371$	−8.71653e8	−	7.55292e8i	−0.886207	−	0.767903i
$372$	−2.80780e7	−	1.25328e8i	−0.0282791	−	0.126226i
$373$	4.66106e8	+	6.70159e7i	0.465054	+	0.0668647i	0.370859	−	0.928689i	$-0.379063\pi$
$373$	4.66106e8	+	6.70159e7i	0.465054	+	0.0668647i	0.0941950	+	0.995554i	$0.469972\pi$
$374$	−4.19179e7	−	6.52255e7i	−0.0414332	−	0.0644713i
$375$	9.68428e6	−	2.64643e7i	0.00948327	−	0.0259149i
$376$	1.07468e8	+	1.24025e8i	0.104261	+	0.120324i
$377$	−6.43569e8	+	9.25313e7i	−0.618587	+	0.0889393i
$378$	−3.22578e8	−	8.18089e8i	−0.307195	−	0.779075i
$379$	−4.58961e8	−	1.56308e9i	−0.433050	−	1.47483i	−0.830401	−	0.557166i	$-0.811889\pi$
$379$	−4.58961e8	−	1.56308e9i	−0.433050	−	1.47483i	0.397351	−	0.917667i	$-0.369930\pi$
$380$	6.54140e7	+	2.22780e8i	0.0611544	+	0.208273i
$381$	−9.23769e8	+	3.51084e8i	−0.855709	+	0.325217i
$382$	1.26266e9	−	1.81543e8i	1.15895	−	0.166632i
$383$	2.30913e8	+	2.66488e8i	0.210016	+	0.242371i	0.850978	−	0.525201i	$-0.176010\pi$
$383$	2.30913e8	+	2.66488e8i	0.210016	+	0.242371i	−0.640962	+	0.767572i	$0.721464\pi$
$384$	1.25761e9	+	4.60208e8i	1.13341	+	0.414758i
$385$	−9.78880e7	−	1.52317e8i	−0.0874212	−	0.136030i
$386$	1.44592e9	+	2.07893e8i	1.27965	+	0.183985i
$387$	−8.43556e8	−	5.27464e8i	−0.739819	−	0.462599i
$388$	−3.52377e8	−	3.05336e8i	−0.306264	−	0.265379i
$389$	9.63734e8	+	2.82978e8i	0.830106	+	0.243741i	0.669062	−	0.743206i	$-0.266696\pi$
$389$	9.63734e8	+	2.82978e8i	0.830106	+	0.243741i	0.161044	+	0.986947i	$0.448514\pi$
$390$	−5.05256e8	+	5.11557e8i	−0.431306	+	0.436684i
$391$	−4.37907e8	−	2.82565e8i	−0.370479	−	0.239056i
$392$		−	4.39216e8i		−	0.368279i
$393$	5.30500e8	−	2.93957e8i	0.440871	−	0.244292i
$394$	−5.67265e8	+	6.54659e8i	−0.467250	+	0.539235i
$395$	−2.71572e8	+	4.22574e8i	−0.221715	+	0.344995i
$396$	−5.25811e7	−	6.89606e6i	−0.0425497	−	0.00558044i
$397$	−1.19212e9	+	7.66126e8i	−0.956206	+	0.614516i	−0.922946	−	0.384930i	$-0.874225\pi$
$397$	−1.19212e9	+	7.66126e8i	−0.956206	+	0.614516i	−0.0332604	+	0.999447i	$0.510589\pi$
$398$	−1.90377e8	−	4.16868e8i	−0.151365	−	0.331442i
$399$	3.34842e7	−	5.12807e8i	0.0263897	−	0.404155i
$400$	2.23076e8	+	1.55153e9i	0.174278	+	1.21213i
$401$	−8.22727e8	+	1.80152e9i	−0.637163	+	1.39519i	0.265191	+	0.964196i	$0.414565\pi$
$401$	−8.22727e8	+	1.80152e9i	−0.637163	+	1.39519i	−0.902354	+	0.430996i	$0.858162\pi$
$402$	9.56177e8	+	5.14446e8i	0.734086	+	0.394956i
$403$	2.23009e8	−	6.54813e7i	0.169728	−	0.0498367i
$404$	−6.24473e8	−	2.85187e8i	−0.471172	−	0.215177i
$405$	3.16890e8	+	1.87318e9i	0.237037	+	1.40115i
$406$	−1.39671e9	+	1.21025e9i	−1.03577	+	0.897502i
$407$	1.35857e8	−	6.20437e7i	0.0998851	−	0.0456160i
$408$	1.01826e8	−	4.82460e8i	0.0742246	−	0.351683i
$409$	−3.19385e8	+	2.22137e9i	−0.230825	+	1.60542i	0.463727	+	0.885978i	$0.346512\pi$
$409$	−3.19385e8	+	2.22137e9i	−0.230825	+	1.60542i	−0.694551	+	0.719443i	$0.744397\pi$
$410$	1.79796e9	+	1.15548e9i	1.28836	+	0.827976i
$411$	−1.41250e8	+	1.09825e7i	−0.100356	+	0.00780290i
$412$	−6.49656e6	+	2.21252e7i	−0.00457660	+	0.0155865i
$413$	−1.33432e9			−0.932040
$414$	−1.56188e9	+	4.76570e8i	−1.08180	+	0.330085i
$415$	−2.24714e9			−1.54334
$416$	8.58550e7	−	2.92395e8i	0.0584708	−	0.199133i
$417$	1.20273e8	−	9.35151e6i	0.0812253	−	0.00631547i
$418$	−1.19432e8	−	7.67545e7i	−0.0799843	−	0.0514028i
$419$	−3.84172e8	+	2.67198e9i	−0.255139	+	1.77453i	0.311187	+	0.950349i	$0.399273\pi$
$419$	−3.84172e8	+	2.67198e9i	−0.255139	+	1.77453i	−0.566326	+	0.824181i	$0.691636\pi$
$420$	−9.21278e7	+	4.36510e8i	−0.0606762	+	0.287489i
$421$	2.60120e9	−	1.18793e9i	1.69897	−	0.775893i	0.700935	−	0.713225i	$-0.252766\pi$
$421$	2.60120e9	−	1.18793e9i	1.69897	−	0.775893i	0.998034	−	0.0626685i	$-0.0199611\pi$
$422$	6.41297e8	−	5.55687e8i	0.415399	−	0.359945i
$423$	−4.69925e7	−	3.00366e8i	−0.0301882	−	0.192957i
$424$	−1.84325e9	−	8.41784e8i	−1.17437	−	0.536315i
$425$	6.82506e8	−	2.00402e8i	0.431266	−	0.126631i
$426$	−2.06678e9	−	1.11198e9i	−1.29527	−	0.696889i
$427$	3.39616e8	−	7.43654e8i	0.211101	−	0.462246i
$428$	−7.29127e7	−	5.07119e8i	−0.0449521	−	0.312649i
$429$	6.25305e6	−	9.57648e7i	0.00382376	−	0.0585606i
$430$	9.60503e8	+	2.10321e9i	0.582585	+	1.27568i
$431$	2.49499e9	−	1.60344e9i	1.50106	−	0.964675i	0.506312	−	0.862350i	$-0.331008\pi$
$431$	2.49499e9	−	1.60344e9i	1.50106	−	0.964675i	0.994751	−	0.102325i	$-0.0326280\pi$
$432$	−1.23606e9	−	1.58875e9i	−0.737645	−	0.948117i
$433$	−4.69364e8	+	7.30345e8i	−0.277845	+	0.432335i	−0.951929	−	0.306320i	$-0.900902\pi$
$433$	−4.69364e8	+	7.30345e8i	−0.277845	+	0.432335i	0.674084	+	0.738655i	$0.264539\pi$
$434$	4.32631e8	−	4.99283e8i	0.254041	−	0.293179i
$435$	3.49226e9	−	1.93511e9i	2.03421	−	1.12718i
$436$		−	8.49568e8i		−	0.490903i
$437$	−9.44312e8	−	1.37545e8i	−0.541291	−	0.0788424i
$438$	1.37091e9	−	1.38801e9i	0.779562	−	0.789283i
$439$	1.88802e9	+	5.54373e8i	1.06508	+	0.312735i	0.766894	−	0.641774i	$-0.221801\pi$
$439$	1.88802e9	+	5.54373e8i	1.06508	+	0.312735i	0.298183	+	0.954509i	$0.403619\pi$
$440$	−2.40409e8	−	2.08316e8i	−0.134545	−	0.116584i
$441$	−4.31387e8	+	6.89902e8i	−0.239514	+	0.383047i
$442$	−3.42200e8	−	4.92010e7i	−0.188496	−	0.0271017i
$443$	−1.87682e9	−	2.92038e9i	−1.02567	−	1.59598i	−0.779148	−	0.626840i	$-0.784348\pi$
$443$	−1.87682e9	−	2.92038e9i	−1.02567	−	1.59598i	−0.246524	−	0.969137i	$-0.579289\pi$
$444$	−3.45591e8	−	1.26465e8i	−0.187380	−	0.0685694i
$445$	−1.80014e9	−	2.07748e9i	−0.968384	−	1.11757i
$446$	−4.47846e8	+	6.43906e7i	−0.239032	+	0.0343677i
$447$	−1.16709e8	+	4.43559e7i	−0.0618056	+	0.0234896i
$448$	2.32870e8	+	7.93082e8i	0.122360	+	0.416721i
$449$	−2.68686e8	−	9.15061e8i	−0.140082	−	0.477076i	0.859328	−	0.511425i	$-0.170882\pi$
$449$	−2.68686e8	−	9.15061e8i	−0.140082	−	0.477076i	−0.999410	+	0.0343492i	$0.989064\pi$
$450$	9.00686e8	−	2.03872e9i	0.465940	−	1.05466i
$451$	−2.82361e8	+	4.05974e7i	−0.144940	+	0.0208392i
$452$	1.95725e8	+	2.25879e8i	0.0996924	+	0.115051i
$453$	−2.85915e7	+	7.81321e7i	−0.0144509	+	0.0394899i
$454$	−2.00077e8	−	3.11325e8i	−0.100346	−	0.156142i
$455$	−7.99117e8	−	1.14896e8i	−0.397714	−	0.0571826i
$456$	−1.97384e8	−	8.81040e8i	−0.0974844	−	0.435130i
$457$	2.07985e9	+	1.80220e9i	1.01935	+	0.883274i	0.993204	−	0.116384i	$-0.0371302\pi$
$457$	2.07985e9	+	1.80220e9i	1.01935	+	0.883274i	0.0261487	+	0.999658i	$0.491676\pi$
$458$	1.02475e9	+	3.00893e8i	0.498411	+	0.146347i
$459$	−6.33804e8	+	6.57817e8i	−0.305922	+	0.317513i
$460$	7.94439e8	+	2.34857e8i	0.380547	+	0.112499i
$461$		−	1.29101e9i		−	0.613731i	−0.951753	−	0.306865i	$-0.900720\pi$
$461$		−	1.29101e9i		−	0.613731i	0.951753	−	0.306865i	$-0.0992801\pi$
$462$	−1.32212e8	−	2.38602e8i	−0.0623771	−	0.112571i
$463$	−6.24444e8	+	7.20646e8i	−0.292388	+	0.337434i	−0.882870	−	0.469617i	$-0.844392\pi$
$463$	−6.24444e8	+	7.20646e8i	−0.292388	+	0.337434i	0.590482	+	0.807051i	$0.298938\pi$
$464$	−2.28711e9	+	3.55882e9i	−1.06286	+	1.65384i
$465$	−1.13723e9	+	8.62369e8i	−0.524522	+	0.397748i
$466$	3.14201e9	−	2.01925e9i	1.43832	−	0.924355i
$467$	−5.52545e8	−	1.20990e9i	−0.251049	−	0.549720i	0.741587	−	0.670857i	$-0.234073\pi$
$467$	−5.52545e8	−	1.20990e9i	−0.251049	−	0.549720i	−0.992636	+	0.121136i	$0.961346\pi$
$468$	−1.76775e8	+	1.57054e8i	−0.0797189	+	0.0708255i
$469$	1.73506e8	+	1.20676e9i	0.0776621	+	0.540151i
$470$	−2.93512e8	+	6.42702e8i	−0.130402	+	0.285540i
$471$	2.09475e9	−	3.89341e9i	0.923759	−	1.71695i
$472$	−2.24933e9	+	6.60464e8i	−0.984594	+	0.289103i
$473$	−2.80723e8	−	1.28202e8i	−0.121973	−	0.0557032i
$474$	−4.49763e8	+	6.08639e8i	−0.193981	+	0.262504i
$475$	9.84345e8	−	8.52940e8i	0.421425	−	0.365166i
$476$	−1.95125e8	+	8.91105e7i	−0.0829255	+	0.0378708i
$477$	2.06852e9	+	3.13263e9i	0.872660	+	1.32158i
$478$	1.83928e8	−	1.27925e9i	0.0770283	−	0.535743i
$479$	1.61379e9	+	1.03712e9i	0.670922	+	0.431176i	0.831258	−	0.555887i	$-0.187621\pi$
$479$	1.61379e9	+	1.03712e9i	0.670922	+	0.431176i	−0.160336	+	0.987063i	$0.551258\pi$
$480$	1.45060e8	+	1.86566e9i	0.0598691	+	0.769996i
$481$	1.87623e8	−	6.38985e8i	0.0768737	−	0.261808i
$482$	2.47524e9			1.00682
$483$	−1.47262e9	−	1.09241e9i	−0.594671	−	0.441135i
$484$	6.80092e8			0.272652
$485$	−1.45974e9	+	4.97142e9i	−0.581005	+	1.97872i
$486$	2.92530e8	+	2.84724e9i	0.115596	+	1.12512i
$487$	5.29825e7	+	3.40498e7i	0.0207865	+	0.0133587i	0.550993	−	0.834510i	$-0.314249\pi$
$487$	5.29825e7	+	3.40498e7i	0.0207865	+	0.0133587i	−0.530206	+	0.847869i	$0.677886\pi$
$488$	2.04413e8	−	1.42172e9i	0.0796230	−	0.553790i
$489$	4.40820e9	+	9.30375e8i	1.70483	+	0.359813i
$490$	1.72011e9	−	7.85547e8i	0.660495	−	0.301638i
$491$	−1.29094e9	+	1.11860e9i	−0.492176	+	0.426473i	−0.865259	−	0.501325i	$-0.832846\pi$
$491$	−1.29094e9	+	1.11860e9i	−0.492176	+	0.426473i	0.373083	+	0.927798i	$0.378301\pi$
$492$	5.65289e8	+	4.17729e8i	0.213989	+	0.158131i
$493$	1.74625e9	+	7.97487e8i	0.656361	+	0.299750i
$494$	−6.07393e8	+	1.78347e8i	−0.226687	+	0.0665612i
$495$	1.73022e8	+	5.63337e8i	0.0641185	+	0.208761i
$496$	6.28207e8	−	1.37558e9i	0.231162	−	0.506175i
$497$	−3.75034e8	−	2.60842e9i	−0.137032	−	0.953081i
$498$	−3.37834e9	−	2.20592e8i	−1.22575	−	0.0800363i
$499$	−7.21532e8	−	1.57993e9i	−0.259958	−	0.569229i	0.733980	−	0.679171i	$-0.237661\pi$
$499$	−7.21532e8	−	1.57993e9i	−0.259958	−	0.569229i	−0.993938	+	0.109942i	$0.964933\pi$
$500$	−1.81197e7	+	1.16448e7i	−0.00648269	+	0.00416617i
$501$	8.57912e8	+	1.13135e9i	0.304797	+	0.401945i
$502$	1.15763e9	−	1.80131e9i	0.408420	−	0.635514i
$503$	−1.14574e9	+	1.32225e9i	−0.401418	+	0.463261i	−0.920087	−	0.391714i	$-0.871882\pi$
$503$	−1.14574e9	+	1.32225e9i	−0.401418	+	0.463261i	0.518669	+	0.854975i	$0.326428\pi$
$504$	4.68089e8	−	1.67047e9i	0.162863	−	0.581210i
$505$			7.62883e9i			2.63596i
$506$	−4.61153e8	+	2.09577e8i	−0.158241	+	0.0719146i
$507$	1.78334e9	+	1.76137e9i	0.607723	+	0.600238i
$508$	7.24730e8	+	2.12800e8i	0.245275	+	0.0720193i
$509$	2.05695e9	+	1.78236e9i	0.691372	+	0.599077i	0.928025	−	0.372517i	$-0.121505\pi$
$509$	2.05695e9	+	1.78236e9i	0.691372	+	0.599077i	−0.236654	+	0.971594i	$0.576051\pi$
$510$	2.07158e9	−	4.64108e8i	0.691523	−	0.154926i
$511$	2.16825e9	+	3.11747e8i	0.718847	+	0.103355i
$512$	5.35935e8	+	8.33932e8i	0.176469	+	0.274591i
$513$	−5.55292e8	+	1.57777e9i	−0.181598	+	0.515979i
$514$	−3.36312e9	−	3.88125e9i	−1.09238	−	1.26067i
$515$	2.53637e8	−	3.64675e7i	0.0818253	−	0.0117647i
$516$	2.70146e8	+	7.10807e8i	0.0865616	+	0.227760i
$517$	−2.65691e7	−	9.04859e7i	−0.00845589	−	0.0287981i
$518$	−5.33304e8	−	1.81627e9i	−0.168586	−	0.574150i
$519$	4.25520e8	+	1.11963e9i	0.133609	+	0.351550i
$520$	−1.40399e9	+	2.01863e8i	−0.437876	+	0.0629571i
$521$	−2.12204e9	−	2.44897e9i	−0.657389	−	0.758667i	0.324959	−	0.945728i	$-0.394649\pi$
$521$	−2.12204e9	−	2.44897e9i	−0.657389	−	0.758667i	−0.982348	+	0.187061i	$0.940104\pi$
$522$	5.44023e9	−	2.56642e9i	1.67406	−	0.789735i
$523$	−1.94167e9	−	3.02130e9i	−0.593498	−	0.923501i	−0.999952	−	0.00982943i	$-0.996871\pi$
$523$	−1.94167e9	−	3.02130e9i	−0.593498	−	0.923501i	0.406454	−	0.913671i	$-0.366765\pi$
$524$	−4.58840e8	−	6.59712e7i	−0.139316	−	0.0200306i
$525$	2.44208e9	−	5.47111e8i	0.736549	−	0.165013i
$526$	4.62086e9	+	4.00400e9i	1.38444	+	1.19962i
$527$	−6.58453e8	−	1.93339e8i	−0.195969	−	0.0575417i
$528$	−4.44252e8	−	4.38781e8i	−0.131344	−	0.129726i
$529$	−2.23914e9	+	2.56497e9i	−0.657637	+	0.753335i
$530$		−	8.72429e9i		−	2.54545i
$531$	4.18185e9	+	1.17181e9i	1.21210	+	0.339646i
$532$	−2.57217e8	+	2.96845e8i	−0.0740644	+	0.0854749i
$533$	−6.87686e8	+	1.07006e9i	−0.196718	+	0.306100i
$534$	−2.50240e9	−	3.29999e9i	−0.711152	−	0.937818i
$535$	−4.78950e9	+	3.07802e9i	−1.35223	+	0.869028i
$536$	8.89812e8	+	1.94842e9i	0.249587	+	0.546519i
$537$	−5.74801e9	−	3.75321e8i	−1.60180	−	0.104591i
$538$	−4.18182e7	−	2.90852e8i	−0.0115778	−	0.0805255i
$539$	−1.04850e8	+	2.29589e8i	−0.0288408	+	0.0631525i
$540$	6.72081e8	−	1.28714e9i	0.183672	−	0.351762i
$541$	2.25197e9	−	6.61239e8i	0.611467	−	0.179543i	0.0386860	−	0.999251i	$-0.487683\pi$
$541$	2.25197e9	−	6.61239e8i	0.611467	−	0.179543i	0.572781	+	0.819709i	$0.305865\pi$
$542$	4.74562e9	+	2.16725e9i	1.28025	+	0.584672i
$543$	2.54269e9	+	1.87896e9i	0.681545	+	0.503639i
$544$	−6.80000e8	+	5.89224e8i	−0.181098	+	0.156922i
$545$	−8.58763e9	+	3.92184e9i	−2.27241	+	1.03777i
$546$	−1.19011e9	−	2.51180e8i	−0.312906	−	0.0660406i
$547$	3.85690e7	−	2.68253e8i	0.0100759	−	0.0700792i	−0.984163	−	0.177265i	$-0.943275\pi$
$547$	3.85690e7	−	2.68253e8i	0.0100759	−	0.0700792i	0.994239	+	0.107186i	$0.0341840\pi$
$548$	9.10958e7	+	5.85437e7i	0.0236465	+	0.0151967i
$549$	−1.71746e9	+	2.03241e9i	−0.442980	+	0.524214i
$550$	1.94782e8	−	6.63365e8i	0.0499205	−	0.170013i
$551$	3.51517e9			0.895190
$552$	−3.02321e9	−	1.11262e9i	−0.765035	−	0.281552i
$553$	−8.49755e8			−0.213676
$554$	−1.06784e9	+	3.63672e9i	−0.266821	+	0.908710i
$555$	3.17006e8	+	4.07712e9i	0.0787122	+	1.01234i
$556$	−7.75671e7	−	4.98493e7i	−0.0191388	−	0.0122998i
$557$	−6.10506e8	+	4.24616e9i	−0.149691	+	1.04113i	0.767033	+	0.641607i	$0.221732\pi$
$557$	−6.10506e8	+	4.24616e9i	−0.149691	+	1.04113i	−0.916725	+	0.399519i	$0.869177\pi$
$558$	−1.79437e9	+	1.18485e9i	−0.437212	+	0.288698i
$559$	−1.25173e9	+	5.71646e8i	−0.303089	+	0.138416i
$560$	−3.96983e9	+	3.43988e9i	−0.955244	+	0.827723i
$561$	−1.68400e8	+	2.27886e8i	−0.0402691	+	0.0544939i
$562$	−4.58428e9	−	2.09357e9i	−1.08942	−	0.497520i
$563$	5.70438e9	−	1.67496e9i	1.34719	−	0.395571i	0.472961	−	0.881084i	$-0.343185\pi$
$563$	5.70438e9	−	1.67496e9i	1.34719	−	0.395571i	0.874230	+	0.485513i	$0.161367\pi$
$564$	−1.10096e8	+	2.04631e8i	−0.0258402	+	0.0480279i
$565$	1.37972e9	−	3.02115e9i	0.321825	−	0.704699i
$566$	−1.06660e9	−	7.41838e9i	−0.247255	−	1.71969i
$567$	−2.37595e9	+	2.16416e9i	−0.547390	+	0.498597i
$568$	−1.92333e9	−	4.21152e9i	−0.440388	−	0.964316i
$569$	1.75195e9	−	1.12591e9i	0.398683	−	0.256218i	−0.325902	−	0.945404i	$-0.605668\pi$
$569$	1.75195e9	−	1.12591e9i	0.398683	−	0.256218i	0.724585	+	0.689186i	$0.242032\pi$
$570$	3.09740e9	−	2.34878e9i	0.700545	−	0.531226i
$571$	−2.80385e9	+	4.36288e9i	−0.630273	+	0.980725i	0.368422	+	0.929659i	$0.379898\pi$
$571$	−2.80385e9	+	4.36288e9i	−0.630273	+	0.980725i	−0.998695	+	0.0510659i	$0.983738\pi$
$572$	−4.80344e7	+	5.54347e7i	−0.0107317	+	0.0123850i
$573$	−2.25957e9	−	4.07782e9i	−0.501747	−	0.905496i
$574$			3.61552e9i			0.797956i
$575$	−6.52901e8	−	4.60109e9i	−0.143222	−	1.00931i
$576$	−3.33400e7	−	2.69008e9i	−0.00726920	−	0.586526i
$577$	4.97368e8	+	1.46040e8i	0.107786	+	0.0316488i	0.335181	−	0.942154i	$-0.391203\pi$
$577$	4.97368e8	+	1.46040e8i	0.107786	+	0.0316488i	−0.227395	+	0.973803i	$0.573021\pi$
$578$	−3.19684e9	−	2.77008e9i	−0.688610	−	0.596684i
$579$	−1.16711e9	−	5.20951e9i	−0.249884	−	1.11538i
$580$	−3.02053e9	−	4.34286e8i	−0.642813	−	0.0924226i
$581$	−2.05521e9	−	3.19797e9i	−0.434750	−	0.676484i
$582$	−2.68260e9	+	7.33074e9i	−0.564060	+	1.54141i
$583$	7.62561e8	+	8.80042e8i	0.159380	+	0.183935i
$584$	3.80945e9	−	5.47716e8i	0.791438	−	0.113792i
$585$	2.40359e9	+	1.06188e9i	0.496380	+	0.219296i
$586$	4.44681e8	+	1.51445e9i	0.0912867	+	0.310894i
$587$	−1.31206e9	−	4.46845e9i	−0.267744	−	0.911851i	−0.978122	−	0.208031i	$-0.933294\pi$
$587$	−1.31206e9	−	4.46845e9i	−0.267744	−	0.911851i	0.710379	−	0.703820i	$-0.248524\pi$
$588$	5.81334e8	−	2.20939e8i	0.117925	−	0.0448180i
$589$	−1.24378e9	+	1.78829e8i	−0.250808	+	0.0360607i
$590$	−6.60957e9	−	7.62785e9i	−1.32492	−	1.52904i
$591$	2.97297e9	+	1.08792e9i	0.592425	+	0.216791i
$592$	−2.34260e9	−	3.64516e9i	−0.464058	−	0.722088i
$593$	−2.75325e9	−	3.95857e8i	−0.542193	−	0.0779556i	−0.134223	−	0.990951i	$-0.542854\pi$
$593$	−2.75325e9	−	3.95857e8i	−0.542193	−	0.0779556i	−0.407970	+	0.912996i	$0.633763\pi$
$594$	2.04821e8	+	8.63905e8i	0.0400979	+	0.169127i
$595$	1.80150e9	+	1.56101e9i	0.350611	+	0.303806i
$596$	9.15623e7	+	2.68851e7i	0.0177156	+	0.00520176i
$597$	−1.17693e9	+	1.19161e9i	−0.226382	+	0.229205i
$598$	−6.40321e8	+	2.16598e9i	−0.122446	+	0.414192i
$599$		−	1.93415e9i		−	0.367702i	−0.982954	−	0.183851i	$-0.941144\pi$
$599$		−	1.93415e9i		−	0.367702i	0.982954	−	0.183851i	$-0.0588564\pi$
$600$	3.84593e9	−	2.13108e9i	0.726895	−	0.402782i
$601$	2.16818e9	−	2.50221e9i	0.407412	−	0.470178i	−0.514549	−	0.857461i	$-0.672041\pi$
$601$	2.16818e9	−	2.50221e9i	0.407412	−	0.470178i	0.921961	+	0.387282i	$0.126586\pi$
$602$	−2.11467e9	+	3.29050e9i	−0.395053	+	0.614715i
$603$	5.16005e8	−	3.93444e9i	0.0958393	−	0.730756i
$604$	5.34958e7	−	3.43797e7i	0.00987850	−	0.00634852i
$605$	−3.13949e9	−	6.87453e9i	−0.576389	−	1.26212i
$606$	−7.48890e8	+	1.14692e10i	−0.136699	+	2.09353i
$607$	−1.11204e9	−	7.73440e9i	−0.201818	−	1.40367i	−0.798885	−	0.601483i	$-0.794577\pi$
$607$	−1.11204e9	−	7.73440e9i	−0.201818	−	1.40367i	0.597067	−	0.802191i	$-0.296332\pi$
$608$	−6.84413e8	+	1.49866e9i	−0.123497	+	0.270420i
$609$	5.94791e9	+	3.20012e9i	1.06710	+	0.574124i
$610$	5.93351e9	−	1.74223e9i	1.05842	−	0.310779i
$611$	−3.82506e8	−	1.74685e8i	−0.0678413	−	0.0309821i
$612$	6.89792e8	−	1.07918e8i	0.121643	−	0.0190312i
$613$	4.66619e9	−	4.04328e9i	0.818184	−	0.708961i	−0.141531	−	0.989934i	$-0.545203\pi$
$613$	4.66619e9	−	4.04328e9i	0.818184	−	0.708961i	0.959716	+	0.280973i	$0.0906572\pi$
$614$	−1.27001e9	+	5.79996e8i	−0.221421	+	0.101120i
$615$	1.61298e9	−	7.64243e9i	0.279618	−	1.32486i
$616$	7.65845e7	−	5.32657e8i	0.0132011	−	0.0918153i
$617$	1.41372e9	+	9.08542e8i	0.242306	+	0.155721i	0.656158	−	0.754623i	$-0.272180\pi$
$617$	1.41372e9	+	9.08542e8i	0.242306	+	0.155721i	−0.413852	+	0.910344i	$0.635817\pi$
$618$	3.84898e8	−	2.99268e7i	0.0655973	−	0.00510035i
$619$	1.36010e9	−	4.63207e9i	0.230490	−	0.784978i	−0.760300	−	0.649572i	$-0.774948\pi$
$619$	1.36010e9	−	4.63207e9i	0.230490	−	0.784978i	0.990790	−	0.135406i	$-0.0432338\pi$
$620$	1.09086e9			0.183822
$621$	3.65594e9	+	4.71697e9i	0.612602	+	0.790392i
$622$	1.09610e10			1.82634
$623$	1.31013e9	−	4.46188e9i	0.217073	−	0.739282i
$624$	−2.77584e9	+	2.15829e8i	−0.457350	+	0.0355601i
$625$	−5.03296e9	−	3.23449e9i	−0.824600	−	0.529938i
$626$	−1.88431e9	+	1.31057e10i	−0.307003	+	2.13525i
$627$	−1.07145e8	+	5.07661e8i	−0.0173594	+	0.0822503i
$628$	−3.07380e9	+	1.40376e9i	−0.495241	+	0.226169i
$629$	−1.48604e9	+	1.28766e9i	−0.238096	+	0.206311i
$630$	7.37929e9	−	1.15449e9i	1.17577	−	0.183950i
$631$	3.86266e9	+	1.76402e9i	0.612046	+	0.279512i	0.697223	−	0.716854i	$-0.254419\pi$
$631$	3.86266e9	+	1.76402e9i	0.612046	+	0.279512i	−0.0851777	+	0.996366i	$0.527146\pi$
$632$	−1.43248e9	+	4.20614e8i	−0.225724	+	0.0662786i
$633$	−2.73097e9	−	1.46933e9i	−0.427962	−	0.230254i
$634$	3.59828e9	−	7.87914e9i	0.560768	−	1.22791i
$635$	−1.19452e9	−	8.30809e9i	−0.185134	−	1.28764i
$636$	1.86950e8	−	2.86311e9i	0.0288154	−	0.441305i
$637$	4.67521e8	+	1.02373e9i	0.0716660	+	0.156927i
$638$	1.56969e9	−	1.00878e9i	0.239300	−	0.153788i
$639$	−1.11535e9	+	8.50432e9i	−0.169106	+	1.28940i
$640$	−6.14934e9	+	9.56856e9i	−0.927254	+	1.44283i
$641$	−5.10955e9	+	5.89674e9i	−0.766266	+	0.884318i	−0.996038	−	0.0889263i	$-0.971656\pi$
$641$	−5.10955e9	+	5.89674e9i	−0.766266	+	0.884318i	0.229772	+	0.973244i	$0.426202\pi$
$642$	−7.50268e9	+	4.15733e9i	−1.11904	+	0.620072i
$643$			2.31051e9i			0.342744i	0.985206	+	0.171372i	$0.0548200\pi$
$643$			2.31051e9i			0.342744i	−0.985206	+	0.171372i	$0.945180\pi$
$644$	3.92355e8	+	1.34539e9i	0.0578867	+	0.198494i
$645$	5.93794e9	−	6.01199e9i	0.871318	−	0.882184i
$646$	1.79338e9	+	5.26584e8i	0.261733	+	0.0768518i
$647$	4.43819e9	+	3.84571e9i	0.644229	+	0.558228i	0.914515	−	0.404552i	$-0.132573\pi$
$647$	4.43819e9	+	3.84571e9i	0.644229	+	0.558228i	−0.270286	+	0.962780i	$0.587118\pi$
$648$	−2.93404e9	+	4.82430e9i	−0.423598	+	0.696501i
$649$	1.33345e9	+	1.91721e8i	0.191479	+	0.0275305i
$650$	−1.66668e9	−	2.59341e9i	−0.238044	−	0.370403i
$651$	−2.26737e9	−	8.29717e8i	−0.322098	−	0.117868i
$652$	−2.25501e9	−	2.60242e9i	−0.318626	−	0.367714i
$653$	6.86915e9	−	9.87635e8i	0.965400	−	0.138803i	0.358454	−	0.933547i	$-0.383304\pi$
$653$	6.86915e9	−	9.87635e8i	0.965400	−	0.138803i	0.606945	+	0.794744i	$0.292395\pi$
$654$	−1.32956e10	+	5.05308e9i	−1.85860	+	0.706373i
$655$	1.45128e9	+	4.94260e9i	0.201793	+	0.687244i
$656$	2.33163e9	+	7.94079e9i	0.322475	+	1.09825i
$657$	−6.52167e9	−	2.88121e9i	−0.897181	−	0.396366i
$658$	−1.18309e9	+	1.70103e8i	−0.161893	+	0.0232767i
$659$	3.90800e9	+	4.51008e9i	0.531932	+	0.613882i	0.956578	−	0.291477i	$-0.0941468\pi$
$659$	3.90800e9	+	4.51008e9i	0.531932	+	0.613882i	−0.424646	+	0.905360i	$0.639601\pi$
$660$	1.54787e8	−	4.22988e8i	0.0209571	−	0.0572696i
$661$	−5.17798e9	−	8.05709e9i	−0.697357	−	1.08511i	−0.991596	−	0.129376i	$-0.958703\pi$
$661$	−5.17798e9	−	8.05709e9i	−0.697357	−	1.08511i	0.294239	−	0.955732i	$-0.404934\pi$
$662$	8.03303e9	+	1.15498e9i	1.07616	+	0.154728i
$663$	2.76215e8	+	1.23291e9i	0.0368087	+	0.164299i
$664$	−5.04751e9	−	4.37370e9i	−0.669097	−	0.579776i
$665$	4.18797e9	+	1.22970e9i	0.552239	+	0.162152i
$666$	7.63531e7	+	6.16066e9i	0.0100154	+	0.808104i
$667$	6.80011e9	−	1.05385e10i	0.887311	−	1.37511i
$668$		−	1.08522e9i		−	0.140864i
$669$	8.01434e8	+	1.44634e9i	0.103485	+	0.186758i
$670$	−6.03916e9	+	6.96957e9i	−0.775738	+	0.895249i
$671$	−4.46246e8	+	6.94372e8i	−0.0570224	+	0.0887285i
$672$	−2.52241e9	+	1.91276e9i	−0.320644	+	0.243146i
$673$	−3.39815e9	+	2.18386e9i	−0.429724	+	0.276167i	−0.737572	−	0.675269i	$-0.764028\pi$
$673$	−3.39815e9	+	2.18386e9i	−0.429724	+	0.276167i	0.307848	+	0.951436i	$0.400391\pi$
$674$	3.53967e9	+	7.75079e9i	0.445300	+	0.975072i
$675$	−8.13411e9	−	4.29964e8i	−1.01800	−	0.0538108i
$676$	−2.72646e8	−	1.89629e9i	−0.0339457	−	0.236098i
$677$	−1.17113e9	+	2.56441e9i	−0.145059	+	0.317635i	−0.968190	−	0.250217i	$-0.919498\pi$
$677$	−1.17113e9	+	2.56441e9i	−0.145059	+	0.317635i	0.823131	+	0.567852i	$0.192225\pi$
$678$	2.37084e9	−	4.40656e9i	0.292145	−	0.542995i
$679$	−8.41005e9	+	2.46941e9i	−1.03099	+	0.302726i
$680$	3.80956e9	+	1.73977e9i	0.464615	+	0.212183i
$681$	−8.03784e8	+	1.08771e9i	−0.0975269	+	0.131978i
$682$	−5.04089e8	+	4.36795e8i	−0.0608501	+	0.0527269i
$683$	9.11588e9	−	4.16308e9i	1.09478	−	0.499969i	0.215610	−	0.976480i	$-0.430826\pi$
$683$	9.11588e9	−	4.16308e9i	1.09478	−	0.499969i	0.879168	+	0.476511i	$0.158099\pi$
$684$	1.06683e9	−	7.04442e8i	0.127467	−	0.0841683i
$685$	1.71250e8	−	1.19107e9i	0.0203570	−	0.141586i
$686$	8.64805e9	+	5.55776e9i	1.02278	+	0.657303i
$687$	−3.02568e8	−	3.89142e9i	−0.0356020	−	0.457888i
$688$	−2.52245e9	+	8.59068e9i	−0.295300	+	1.00570i
$689$	5.19229e9			0.604772
$690$	−1.04971e9	−	1.38298e10i	−0.121646	−	1.60267i
$691$	9.28078e9			1.07007			0.535034	−	0.844831i	$-0.320299\pi$
$691$	9.28078e9			1.07007			0.535034	+	0.844831i	$0.320299\pi$
$692$	2.57918e8	−	8.78387e8i	0.0295876	−	0.100766i
$693$	−6.43458e8	+	7.61456e8i	−0.0734436	+	0.0869117i
$694$	9.31331e9	+	5.98530e9i	1.05766	+	0.679716i
$695$	−1.45818e8	+	1.01418e9i	−0.0164765	+	0.114596i
$696$	1.16107e10	+	2.45050e9i	1.30535	+	0.275501i
$697$	3.41625e9	−	1.56015e9i	0.382151	−	0.174523i
$698$	−8.57688e9	+	7.43191e9i	−0.954630	+	0.827192i
$699$	−1.09776e10	−	8.11209e9i	−1.21573	−	0.898385i
$700$	−1.73994e9	−	7.94602e8i	−0.191730	−	0.0875601i
$701$	−1.35157e8	+	3.96856e7i	−0.0148192	+	0.00435131i	−0.289134	−	0.957289i	$-0.593367\pi$
$701$	−1.35157e8	+	3.96856e7i	−0.0148192	+	0.00435131i	0.274315	+	0.961640i	$0.411549\pi$
$702$	3.50931e9	+	1.83238e9i	0.382862	+	0.199911i
$703$	−1.49568e9	+	3.27508e9i	−0.162366	+	0.355532i
$704$	−1.18764e8	−	8.26025e8i	−0.0128287	−	0.0892255i
$705$	2.57669e9	+	1.68247e8i	0.276949	+	0.0180836i
$706$	7.12975e9	+	1.56120e10i	0.762531	+	1.66971i
$707$	−1.08568e10	+	6.97726e9i	−1.15541	+	0.742535i
$708$	−2.00566e9	−	2.64492e9i	−0.212393	−	0.280089i
$709$	−4.57011e9	+	7.11122e9i	−0.481576	+	0.749346i	−0.993999	−	0.109387i	$-0.965111\pi$
$709$	−4.57011e9	+	7.11122e9i	−0.481576	+	0.749346i	0.512424	+	0.858733i	$0.328748\pi$
$710$	1.30537e10	−	1.50648e10i	1.36877	−	1.57964i
$711$	2.66319e9	+	7.46261e8i	0.277881	+	0.0778659i
$712$		−	8.17013e9i		−	0.848299i
$713$	−1.86997e9	+	4.07482e9i	−0.193207	+	0.421012i
$714$	2.55514e9	+	2.52367e9i	0.262706	+	0.259471i
$715$	7.82088e8	+	2.29642e8i	0.0800174	+	0.0234952i
$716$	3.32731e9	+	2.88313e9i	0.338764	+	0.293541i
$717$	−4.60899e9	+	1.03258e9i	−0.466969	+	0.104618i
$718$	−6.54626e9	−	9.41211e8i	−0.660021	−	0.0948967i
$719$	−3.59241e9	−	5.58989e9i	−0.360441	−	0.560857i	0.612917	−	0.790147i	$-0.289996\pi$
$719$	−3.59241e9	−	5.58989e9i	−0.360441	−	0.560857i	−0.973358	+	0.229290i	$0.926360\pi$
$720$	1.54627e10	−	7.29449e9i	1.54390	−	0.728335i
$721$	2.83872e8	+	3.27606e8i	0.0282065	+	0.0325521i
$722$	−7.93416e9	+	1.14076e9i	−0.784551	+	0.112801i
$723$	−3.21373e9	−	8.45595e9i	−0.316246	−	0.832105i
$724$	−6.80800e8	−	2.31859e9i	−0.0666707	−	0.227059i
$725$	4.82280e9	+	1.64249e10i	0.470020	+	1.60074i
$726$	−4.04507e9	−	1.06434e10i	−0.392327	−	1.03229i
$727$	5.38300e9	−	7.73958e8i	0.519582	−	0.0747046i	0.122465	−	0.992473i	$-0.460920\pi$
$727$	5.38300e9	−	7.73958e8i	0.519582	−	0.0747046i	0.397116	+	0.917768i	$0.370011\pi$
$728$	−1.57135e9	−	1.81344e9i	−0.150943	−	0.174198i
$729$	9.34698e9	−	4.69606e9i	0.893562	−	0.448939i
$730$	8.95830e9	+	1.39394e10i	0.852306	+	1.32621i
$731$	4.02166e9	+	5.78227e8i	0.380797	+	0.0547504i
$732$	1.98458e9	−	4.44615e8i	0.187016	−	0.0418982i
$733$	4.68496e9	+	4.05954e9i	0.439382	+	0.380726i	0.846272	−	0.532750i	$-0.178842\pi$
$733$	4.68496e9	+	4.05954e9i	0.439382	+	0.380726i	−0.406891	+	0.913477i	$0.633387\pi$
$734$	−6.10605e9	−	1.79290e9i	−0.569933	−	0.167348i
$735$	−4.91690e9	−	4.85634e9i	−0.456758	−	0.451132i
$736$	3.16898e9	+	4.95103e9i	0.292986	+	0.457745i
$737$		−	1.23090e9i		−	0.113263i
$738$	3.17517e9	−	1.13313e10i	0.290784	−	1.03772i
$739$	−7.05153e9	+	8.13790e9i	−0.642729	+	0.741749i	−0.979855	−	0.199710i	$-0.936000\pi$
$739$	−7.05153e9	+	8.13790e9i	−0.642729	+	0.741749i	0.337126	+	0.941460i	$0.390545\pi$
$740$	1.68984e9	−	2.62944e9i	0.153297	−	0.238535i
$741$	1.39788e9	+	1.84343e9i	0.126214	+	0.166442i
$742$	1.24158e10	−	7.97916e9i	1.11574	−	0.717040i
$743$	−2.10068e9	−	4.59984e9i	−0.187888	−	0.411417i	0.792123	−	0.610362i	$-0.208976\pi$
$743$	−2.10068e9	−	4.59984e9i	−0.187888	−	0.411417i	−0.980011	+	0.198945i	$0.936249\pi$
$744$	−4.23292e9	−	2.76392e8i	−0.376821	−	0.0246048i
$745$	−1.50916e8	−	1.04964e9i	−0.0133717	−	0.0930025i
$746$	−2.50318e9	+	5.48120e9i	−0.220753	+	0.483381i
$747$	3.63269e9	+	1.18276e10i	0.318864	+	1.03818i
$748$	2.07801e8	−	6.10160e7i	0.0181549	−	0.00533074i
$749$	−8.76086e9	−	4.00095e9i	−0.761834	−	0.347918i
$750$	2.90012e8	+	2.14309e8i	0.0251016	+	0.0185493i
$751$	2.34640e9	−	2.03317e9i	0.202145	−	0.175160i	−0.547905	−	0.836540i	$-0.684575\pi$
$751$	2.34640e9	−	2.03317e9i	0.202145	−	0.175160i	0.750050	+	0.661381i	$0.230029\pi$
$752$	−2.48874e9	+	1.13657e9i	−0.213411	+	0.0974615i
$753$	−7.65667e9	−	1.61598e9i	−0.653518	−	0.137929i
$754$	1.18405e9	−	8.23526e9i	0.100594	−	0.699645i
$755$	−5.94470e8	−	3.82043e8i	−0.0502708	−	0.0323071i
$756$	2.44645e9	−	2.20751e8i	0.205926	−	0.0185813i
$757$	−2.25499e9	+	7.67981e9i	−0.188934	+	0.643450i	0.809480	+	0.587148i	$0.199749\pi$
$757$	−2.25499e9	+	7.67981e9i	−0.188934	+	0.643450i	−0.998414	+	0.0563022i	$0.982069\pi$
$758$	2.08459e10			1.73851
$759$	1.31470e9	+	1.30329e9i	0.109139	+	0.108192i
$760$	7.66856e9			0.633674
$761$	1.78505e9	−	6.07931e9i	0.146826	−	0.500044i	−0.852932	−	0.522021i	$-0.825178\pi$
$761$	1.78505e9	−	6.07931e9i	0.146826	−	0.500044i	0.999758	+	0.0219778i	$0.00699631\pi$
$762$	−9.80275e8	−	1.26076e10i	−0.0802612	−	1.03227i
$763$	−1.34355e10	−	8.63445e9i	−1.09501	−	0.703718i
$764$	−5.07103e8	+	3.52698e9i	−0.0411405	+	0.286139i
$765$	−4.27514e9	−	6.47440e9i	−0.345251	−	0.522859i
$766$	−4.10437e9	+	1.87441e9i	−0.329949	+	0.150682i
$767$	4.53974e9	−	3.93371e9i	0.363285	−	0.314788i
$768$	−5.80805e9	+	7.85969e9i	−0.462664	+	0.626097i
$769$	−4.68792e9	−	2.14090e9i	−0.371739	−	0.169768i	0.220781	−	0.975324i	$-0.429140\pi$
$769$	−4.68792e9	−	2.14090e9i	−0.371739	−	0.169768i	−0.592520	+	0.805556i	$0.701867\pi$
$770$	2.22303e9	−	6.52739e8i	0.175480	−	0.0515255i
$771$	−8.89268e9	+	1.65284e10i	−0.698783	+	1.29879i
$772$	−1.69507e9	+	3.71168e9i	−0.132595	+	0.290342i
$773$	−3.53113e9	−	2.45595e10i	−0.274970	−	1.91246i	−0.393165	−	0.919468i	$-0.628620\pi$
$773$	−3.53113e9	−	2.45595e10i	−0.274970	−	1.91246i	0.118195	−	0.992990i	$-0.462289\pi$
$774$	9.51727e9	−	8.45552e9i	0.737767	−	0.655461i
$775$	−2.54206e9	−	5.56633e9i	−0.196169	−	0.429549i
$776$	−1.29550e10	+	8.32565e9i	−0.995223	+	0.639591i
$777$	−5.51234e9	+	4.18003e9i	−0.421563	+	0.319673i
$778$	−6.94875e9	+	1.08125e10i	−0.529027	+	0.823182i
$779$	4.50337e9	−	5.19717e9i	0.341316	−	0.393900i
$780$	−9.73428e8	−	1.75673e9i	−0.0734468	−	0.132548i
$781$			2.66060e9i			0.199849i
$782$	5.04801e9	−	4.35790e9i	0.377483	−	0.325877i
$783$	−1.58308e10	−	1.52529e10i	−1.17852	−	1.13550i
$784$	7.02589e9	+	2.06299e9i	0.520709	+	0.152894i
$785$	2.83790e10	+	2.45906e10i	2.09389	+	1.81437i
$786$	1.69666e9	+	7.57317e9i	0.124628	+	0.556287i
$787$	−1.21792e10	−	1.75110e9i	−0.890647	−	0.128056i	−0.318225	−	0.948015i	$-0.603087\pi$
$787$	−1.21792e10	−	1.75110e9i	−0.890647	−	0.128056i	−0.572422	+	0.819959i	$0.693996\pi$
$788$	−1.30816e9	−	2.03554e9i	−0.0952402	−	0.148197i
$789$	7.67902e9	−	2.09845e10i	0.556591	−	1.52100i
$790$	−4.20927e9	−	4.85776e9i	−0.303747	−	0.350543i
$791$	5.56137e9	−	7.99605e8i	0.399544	−	0.0574457i
$792$	−7.07805e8	+	1.60213e9i	−0.0506262	+	0.114593i
$793$	1.03690e9	+	3.53135e9i	0.0738379	+	0.251469i
$794$	−5.10870e9	−	1.73986e10i	−0.362192	−	1.23351i
$795$	−2.98041e10	+	1.13272e10i	−2.10373	+	0.799535i
$796$	1.26709e9	−	1.82179e8i	0.0890451	−	0.0128028i
$797$	7.06322e9	+	8.15139e9i	0.494195	+	0.570332i	0.946982	−	0.321287i	$-0.104115\pi$
$797$	7.06322e9	+	8.15139e9i	0.494195	+	0.570332i	−0.452786	+	0.891619i	$0.649570\pi$
$798$	6.17547e9	+	2.25984e9i	0.430190	+	0.157423i
$799$	6.71250e8	+	1.04449e9i	0.0465554	+	0.0724417i
$800$	−7.94161e9	−	1.14183e9i	−0.548395	−	0.0788474i
$801$	−8.02449e9	+	1.28333e10i	−0.551701	+	0.882316i
$802$	−1.91529e10	−	1.65960e10i	−1.31106	−	1.13604i
$803$	−2.12204e9	−	6.23088e8i	−0.144627	−	0.0424664i
$804$	−2.13126e9	+	2.15784e9i	−0.144624	+	0.146428i
$805$	1.17883e10	−	1.01767e10i	0.796462	−	0.687577i
$806$			2.97415e9i			0.200073i
$807$	−9.39317e8	+	5.20488e8i	−0.0629151	+	0.0348621i
$808$	−1.48483e10	+	1.71359e10i	−0.990233	+	1.14279i
$809$	1.16386e10	−	1.81100e10i	0.772824	−	1.20254i	−0.201962	−	0.979393i	$-0.564732\pi$
$809$	1.16386e10	−	1.81100e10i	0.772824	−	1.20254i	0.974786	−	0.223144i	$-0.0716319\pi$
$810$	−2.41411e10	−	2.86228e9i	−1.59610	−	0.189240i
$811$	1.13817e10	−	7.31458e9i	0.749263	−	0.481522i	−0.109441	−	0.993993i	$-0.534906\pi$
$811$	1.13817e10	−	7.31458e9i	0.749263	−	0.481522i	0.858705	+	0.512471i	$0.171270\pi$
$812$	−2.14450e9	−	4.69580e9i	−0.140566	−	0.307796i
$813$	1.24231e9	−	1.90259e10i	0.0810801	−	1.24173i
$814$	2.71987e8	+	1.89171e9i	0.0176751	+	0.122933i
$815$	−1.58961e10	+	3.48076e10i	−1.02858	+	2.25228i
$816$	7.23937e9	+	3.89496e9i	0.466429	+	0.250950i
$817$	7.13830e9	−	2.09599e9i	0.457949	−	0.134466i
$818$	−2.61223e10	−	1.19297e10i	−1.66869	−	0.762064i
$819$	6.87101e8	+	4.39181e9i	0.0437046	+	0.279351i
$820$	−4.51177e9	+	3.90947e9i	−0.285758	+	0.247611i
$821$	−1.89802e10	+	8.66796e9i	−1.19701	+	0.546658i	−0.911334	−	0.411667i	$-0.864947\pi$
$821$	−1.89802e10	+	8.66796e9i	−1.19701	+	0.546658i	−0.285680	+	0.958325i	$0.592219\pi$
$822$	3.74380e8	−	1.77385e9i	0.0235105	−	0.111395i
$823$	3.49489e9	−	2.43075e10i	0.218542	−	1.51999i	−0.524884	−	0.851174i	$-0.675891\pi$
$823$	3.49489e9	−	2.43075e10i	0.218542	−	1.51999i	0.743426	−	0.668818i	$-0.233199\pi$
$824$	6.40698e8	+	4.11752e8i	0.0398940	+	0.0256383i
$825$	−2.51909e9	+	1.95866e8i	−0.156191	+	0.0121442i
$826$	4.81038e9	−	1.63826e10i	0.296995	−	1.01147i
$827$	1.93887e10			1.19201			0.596005	−	0.802980i	$-0.296754\pi$
$827$	1.93887e10			1.19201			0.596005	+	0.802980i	$0.296754\pi$
$828$	−4.81372e7	−	4.56111e9i	−0.00294696	−	0.279231i
$829$	1.87405e10			1.14246			0.571229	−	0.820791i	$-0.306467\pi$
$829$	1.87405e10			1.14246			0.571229	+	0.820791i	$0.306467\pi$
$830$	8.10118e9	−	2.75901e10i	0.491785	−	1.67487i
$831$	1.38102e10	−	1.07378e9i	0.834829	−	0.0649100i
$832$	−3.13038e9	−	2.01177e9i	−0.188436	−	0.121101i
$833$	4.72903e8	−	3.28911e9i	0.0283475	−	0.197161i
$834$	−3.18781e8	+	1.51041e9i	−0.0190288	+	0.0901600i
$835$	−1.09696e10	+	5.00967e9i	−0.652063	+	0.297787i
$836$	2.99702e8	−	2.59693e8i	0.0177406	−	0.0153723i
$837$	6.37742e9	+	4.59161e9i	0.375929	+	0.270661i
$838$	−3.14213e10	−	1.43496e10i	−1.84446	−	0.842337i
$839$	−1.20951e9	+	3.55144e8i	−0.0707038	+	0.0207605i	−0.316893	−	0.948461i	$-0.602640\pi$
$839$	−1.20951e9	+	3.55144e8i	−0.0707038	+	0.0207605i	0.246189	+	0.969222i	$0.420821\pi$
$840$	1.29757e10	+	6.98126e9i	0.755361	+	0.406402i
$841$	−1.20262e10	+	2.63336e10i	−0.697173	+	1.52660i
$842$	5.20762e9	+	3.62198e10i	0.300640	+	2.09100i
$843$	−1.20008e9	+	1.83791e10i	−0.0689943	+	1.05664i
$844$	9.84645e8	+	2.15607e9i	0.0563743	+	0.123442i
$845$	−1.79096e10	+	1.15098e10i	−1.02114	+	0.656249i
$846$	3.85728e9	+	5.05886e8i	0.219020	+	0.0287247i
$847$	6.91201e9	−	1.07553e10i	0.390852	−	0.608177i
$848$	2.21232e10	−	2.55316e10i	1.24584	−	1.43778i
$849$	−2.39579e10	+	1.32754e10i	−1.34361	+	0.744511i
$850$			9.10221e9i			0.508371i
$851$	6.92532e9	+	1.08197e10i	0.385200	+	0.601814i
$852$	4.60674e9	−	4.66419e9i	0.255185	−	0.258367i
$853$	−1.65403e10	−	4.85668e9i	−0.912479	−	0.267928i	−0.208395	−	0.978045i	$-0.566824\pi$
$853$	−1.65403e10	−	4.85668e9i	−0.912479	−	0.267928i	−0.704084	+	0.710117i	$0.748642\pi$
$854$	7.90616e9	+	6.85072e9i	0.434373	+	0.376386i
$855$	−1.20454e10	−	7.53186e9i	−0.659085	−	0.412117i
$856$	−1.67491e10	−	2.40815e9i	−0.912708	−	0.131228i
$857$	2.21790e9	+	3.45112e9i	0.120367	+	0.187295i	0.896209	−	0.443633i	$-0.146311\pi$
$857$	2.21790e9	+	3.45112e9i	0.120367	+	0.187295i	−0.775841	+	0.630928i	$0.782674\pi$
$858$	1.15325e9	+	4.22017e8i	0.0623328	+	0.0228100i
$859$	5.27672e9	+	6.08966e9i	0.284045	+	0.327806i	0.879785	−	0.475372i	$-0.157686\pi$
$859$	5.27672e9	+	6.08966e9i	0.284045	+	0.327806i	−0.595740	+	0.803178i	$0.703141\pi$
$860$	−6.39278e9	+	9.19143e8i	−0.342724	+	0.0492763i
$861$	1.23514e10	−	4.69422e9i	0.659485	−	0.250641i
$862$	1.06921e10	+	3.64138e10i	0.568573	+	1.93638i
$863$	−1.04089e10	−	3.54495e10i	−0.551273	−	1.87746i	−0.474152	−	0.880443i	$-0.657245\pi$
$863$	−1.04089e10	−	3.54495e10i	−0.551273	−	1.87746i	−0.0771219	−	0.997022i	$-0.524573\pi$
$864$	9.58521e9	−	3.77951e9i	0.505596	−	0.199360i
$865$	−1.00696e10	+	1.44778e9i	−0.528998	+	0.0760584i
$866$	−7.27499e9	−	8.39578e9i	−0.380644	−	0.439287i
$867$	−5.31256e9	+	1.45176e10i	−0.276845	+	0.756534i
$868$	9.97687e8	+	1.55243e9i	0.0517816	+	0.0805737i
$869$	8.49201e8	+	1.22097e8i	0.0438976	+	0.00631153i
$870$	1.11690e10	+	4.98540e10i	0.575041	+	2.56674i
$871$	−4.14796e9	−	3.59423e9i	−0.212702	−	0.184307i
$872$	−2.69228e10	−	7.90524e9i	−1.37503	−	0.403745i
$873$	2.85263e10	−	3.53546e8i	1.45110	−	0.0179844i
$874$	5.09312e9	−	1.10983e10i	0.258044	−	0.562298i
$875$			4.04903e8i			0.0204326i
$876$	2.64121e9	+	4.76655e9i	0.132751	+	0.239574i
$877$	4.86110e9	−	5.61001e9i	0.243353	−	0.280844i	−0.620913	−	0.783879i	$-0.713238\pi$
$877$	4.86110e9	−	5.61001e9i	0.243353	−	0.280844i	0.864266	+	0.503035i	$0.167784\pi$
$878$	−1.36131e10	+	2.11824e10i	−0.678774	+	1.05619i
$879$	4.59632e9	−	3.48541e9i	0.228270	−	0.173098i
$880$	4.46150e9	−	2.86723e9i	0.220695	−	0.141832i
$881$	2.31906e9	+	5.07803e9i	0.114260	+	0.250195i	0.958119	−	0.286370i	$-0.0924487\pi$
$881$	2.31906e9	+	5.07803e9i	0.114260	+	0.250195i	−0.843859	+	0.536566i	$0.819721\pi$
$882$	−6.91535e9	−	7.78370e9i	−0.339370	−	0.381985i
$883$	4.34663e9	+	3.02315e10i	0.212466	+	1.47774i	0.764884	+	0.644169i	$0.222796\pi$
$883$	4.34663e9	+	3.02315e10i	0.212466	+	1.47774i	−0.552417	+	0.833568i	$0.686294\pi$
$884$	4.01164e8	−	8.78427e8i	0.0195317	−	0.0427684i
$885$	−1.74768e10	+	3.24833e10i	−0.847542	+	1.57529i
$886$	4.26223e10	−	1.25150e10i	2.05882	−	0.604525i
$887$	1.39168e10	+	6.35558e9i	0.669586	+	0.305790i	0.721048	−	0.692885i	$-0.243661\pi$
$887$	1.39168e10	+	6.35558e9i	0.669586	+	0.305790i	−0.0514620	+	0.998675i	$0.516388\pi$
$888$	−7.22341e9	+	9.77502e9i	−0.346176	+	0.468460i
$889$	1.07310e10	−	9.29847e9i	0.512253	−	0.443869i
$890$	3.19968e10	−	1.46124e10i	1.52139	−	0.694797i
$891$	2.68536e9	−	1.82137e9i	0.127183	−	0.0862631i
$892$	1.79862e8	−	1.25096e9i	0.00848519	−	0.0590158i
$893$	1.91252e9	+	1.22910e9i	0.0898725	+	0.0577576i
$894$	−1.23848e8	−	1.59285e9i	−0.00579705	−	0.0745578i
$895$	1.37836e10	−	4.69426e10i	0.642660	−	2.18870i
$896$	−1.92414e10			−0.893634
$897$	8.23083e9	−	6.24737e8i	0.380777	−	0.0289017i
$898$	1.22037e10			0.562371
$899$	4.65283e9	−	1.58461e10i	0.213579	−	0.727382i
$900$	4.75525e9	+	4.01836e9i	0.217433	+	0.183739i
$901$	−1.28970e10	−	8.28840e9i	−0.587424	−	0.377515i
$902$	5.19494e8	−	3.61316e9i	0.0235699	−	0.163932i
$903$	1.39866e10	+	2.95196e9i	0.632129	+	0.133414i
$904$	8.97932e9	−	4.10072e9i	0.404254	−	0.184616i
$905$	−2.02941e10	+	1.75850e10i	−0.910124	+	0.788627i
$906$	−8.56222e8	−	6.32719e8i	−0.0382506	−	0.0282659i
$907$	2.94318e9	+	1.34410e9i	0.130976	+	0.0598146i	0.479825	−	0.877364i	$-0.340700\pi$
$907$	2.94318e9	+	1.34410e9i	0.130976	+	0.0598146i	−0.348849	+	0.937179i	$0.613427\pi$
$908$	9.91849e8	−	2.91233e8i	0.0439688	−	0.0129104i
$909$	4.01535e10	−	1.23327e10i	1.77317	−	0.544607i
$910$	4.29159e9	−	9.39727e9i	0.188788	−	0.413387i
$911$	1.50330e9	+	1.04557e10i	0.0658766	+	0.458182i	0.995884	+	0.0906403i	$0.0288914\pi$
$911$	1.50330e9	+	1.04557e10i	0.0658766	+	0.458182i	−0.930007	+	0.367542i	$0.880200\pi$
$912$	1.50206e10	+	9.80783e8i	0.655700	+	0.0428145i
$913$	1.59437e9	+	3.49118e9i	0.0693332	+	0.151819i
$914$	−2.96253e10	+	1.90390e10i	−1.28337	+	0.824770i
$915$	−1.36556e10	−	1.80081e10i	−0.589302	−	0.777131i
$916$	−1.61287e9	+	2.50968e9i	−0.0693371	+	0.107891i
$917$	−5.70664e9	+	6.58582e9i	−0.244393	+	0.282044i
$918$	−5.79168e9	−	1.01533e10i	−0.247090	−	0.433169i
$919$			3.46763e10i			1.47377i	0.676021	+	0.736883i	$0.263703\pi$
$919$			3.46763e10i			1.47377i	−0.676021	+	0.736883i	$0.736297\pi$
$920$	1.48349e10	−	2.29904e10i	0.628096	−	0.973395i
$921$	3.63032e9	+	3.58561e9i	0.153121	+	0.151236i
$922$	1.58509e10	+	4.65426e9i	0.666035	+	0.195565i
$923$	8.96585e9	+	7.76895e9i	0.375306	+	0.325204i
$924$	7.43534e8	−	1.66578e8i	0.0310062	−	0.00694649i
$925$	−1.73552e10	−	2.49530e9i	−0.720996	−	0.103664i
$926$	−6.59683e9	−	1.02649e10i	−0.273021	−	0.424830i
$927$	−6.01969e8	−	1.27604e9i	−0.0248196	−	0.0526120i
$928$	−1.41800e10	−	1.63646e10i	−0.582451	−	0.672184i
$929$	−3.32967e10	+	4.78735e9i	−1.36253	+	0.195903i	−0.784509	−	0.620118i	$-0.787085\pi$
$929$	−3.32967e10	+	4.78735e9i	−1.36253	+	0.195903i	−0.578023	+	0.816020i	$0.696176\pi$
$930$	−6.48822e9	−	1.70718e10i	−0.264506	−	0.695966i
$931$	−1.71421e9	−	5.83806e9i	−0.0696209	−	0.237107i
$932$	2.93923e9	+	1.00101e10i	0.118926	+	0.405026i
$933$	−1.42312e10	−	3.74450e10i	−0.573661	−	1.50941i
$934$	1.68471e10	−	2.42224e9i	0.676566	−	0.0972755i
$935$	−1.57603e9	−	1.81884e9i	−0.0630557	−	0.0727702i
$936$	3.33215e9	+	7.06340e9i	0.132819	+	0.281545i
$937$	1.19975e10	+	1.86685e10i	0.476433	+	0.741345i	0.993405	−	0.114658i	$-0.0365771\pi$
$937$	1.19975e10	+	1.86685e10i	0.476433	+	0.741345i	−0.516972	+	0.856002i	$0.672941\pi$
$938$	−1.54420e10	−	2.22022e9i	−0.610932	−	0.0878387i
$939$	4.72184e10	−	1.05786e10i	1.86115	−	0.416963i
$940$	−1.49155e9	−	1.29244e9i	−0.0585721	−	0.0507530i
$941$	5.33129e9	+	1.56541e9i	0.208578	+	0.0612441i	0.384353	−	0.923186i	$-0.374425\pi$
$941$	5.33129e9	+	1.56541e9i	0.208578	+	0.0612441i	−0.175774	+	0.984430i	$0.556243\pi$
$942$	4.02511e10	+	3.97553e10i	1.56891	+	1.54959i
$943$	−6.86936e9	−	2.35551e10i	−0.266763	−	0.914733i
$944$		−	3.90835e10i		−	1.51214i
$945$	−1.35249e10	−	2.37103e10i	−0.521343	−	0.913957i
$946$	2.58609e9	−	2.98450e9i	0.0993171	−	0.114618i
$947$	1.96099e10	−	3.05136e10i	0.750326	−	1.16753i	−0.230581	−	0.973053i	$-0.574063\pi$
$947$	1.96099e10	−	3.05136e10i	0.750326	−	1.16753i	0.980907	−	0.194477i	$-0.0623010\pi$
$948$	−1.27729e9	−	1.68441e9i	−0.0486924	−	0.0642122i
$949$	−8.29607e9	+	5.33156e9i	−0.315094	+	0.202499i
$950$	6.92363e9	+	1.51606e10i	0.262000	+	0.573700i
$951$	−3.15887e10	−	2.06261e9i	−1.19097	−	0.0777652i
$952$	1.00827e9	+	7.01268e9i	0.0378746	+	0.263423i
$953$	−1.21199e10	+	2.65388e10i	−0.453600	+	0.993246i	0.535300	+	0.844662i	$0.320199\pi$
$953$	−1.21199e10	+	2.65388e10i	−0.453600	+	0.993246i	−0.988900	+	0.148584i	$0.952529\pi$
$954$	−4.59194e10	+	1.41036e10i	−1.71229	+	0.525908i
$955$	3.79925e10	−	1.11556e10i	1.41152	−	0.414459i
$956$	3.28382e9	+	1.49967e9i	0.121556	+	0.0555128i
$957$	−5.48422e9	−	4.05265e9i	−0.202266	−	0.149468i
$958$	−1.85515e10	+	1.60750e10i	−0.681711	+	0.590706i
$959$	1.85167e9	−	8.45632e8i	0.0677953	−	0.0309611i
$960$	2.23573e10	+	4.71863e9i	0.815587	+	0.172134i
$961$	3.07527e9	−	2.13890e10i	0.111777	−	0.777425i
$962$	7.16899e9	+	4.60723e9i	0.259624	+	0.166850i
$963$	2.39435e10	+	2.02331e10i	0.863963	+	0.730080i
$964$	−1.94792e9	+	6.63399e9i	−0.0700327	+	0.238509i
$965$	4.53435e10			1.62431
$966$	1.87215e10	−	1.41424e10i	0.668222	−	0.504783i
$967$	3.40051e10			1.20935			0.604675	−	0.796472i	$-0.293303\pi$
$967$	3.40051e10			1.20935			0.604675	+	0.796472i	$0.293303\pi$
$968$	6.32827e9	−	2.15521e10i	0.224244	−	0.763705i
$969$	−5.29515e8	−	6.81027e9i	−0.0186959	−	0.240454i
$970$	−5.57761e10	−	3.58451e10i	−1.96222	−	1.26104i
$971$	−2.39897e9	+	1.66852e10i	−0.0840925	+	0.584876i	0.903589	+	0.428400i	$0.140923\pi$
$971$	−2.39897e9	+	1.66852e10i	−0.0840925	+	0.584876i	−0.987682	+	0.156476i	$0.949987\pi$
$972$	−7.86122e9	−	1.45664e9i	−0.274573	−	0.0508770i
$973$	−1.57668e9	+	7.20046e8i	−0.0548718	+	0.0250591i
$974$	−6.09068e8	+	5.27760e8i	−0.0211207	+	0.0183012i
$975$	−6.69570e9	+	9.06091e9i	−0.231356	+	0.313080i
$976$	2.17823e10	+	9.94767e9i	0.749947	+	0.342489i
$977$	−3.07058e10	+	9.01604e9i	−1.05339	+	0.309304i	−0.762187	−	0.647357i	$-0.775874\pi$
$977$	−3.07058e10	+	9.01604e9i	−1.05339	+	0.309304i	−0.291205	+	0.956661i	$0.594056\pi$
$978$	−2.73151e10	+	5.07693e10i	−0.933721	+	1.73546i
$979$	−1.95038e9	+	4.27073e9i	−0.0664323	+	0.145466i
$980$	7.51721e8	+	5.22833e9i	0.0255132	+	0.177448i
$981$	3.45248e10	+	3.88601e10i	1.16759	+	1.31420i
$982$	−9.08013e9	−	1.98827e10i	−0.305986	−	0.670016i
$983$	−2.76078e10	+	1.77424e10i	−0.927030	+	0.595766i	−0.914689	−	0.404158i	$-0.867565\pi$
$983$	−2.76078e10	+	1.77424e10i	−0.927030	+	0.595766i	−0.0123409	+	0.999924i	$0.503928\pi$
$984$	1.84979e10	−	1.40270e10i	0.618926	−	0.469334i
$985$	−1.45369e10	+	2.26199e10i	−0.484669	+	0.754160i
$986$	−1.60869e10	+	1.85653e10i	−0.534445	+	0.616783i
$987$	2.11718e9	+	3.82084e9i	0.0700886	+	0.126488i
$988$		−	1.76825e9i		−	0.0583304i
$989$	7.52527e9	−	2.54554e10i	0.247363	−	0.836744i
$990$	−7.54036e9	+	9.34526e7i	−0.246984	+	0.00306104i
$991$	8.23898e9	+	2.41918e9i	0.268915	+	0.0789607i	0.413410	−	0.910545i	$-0.364338\pi$
$991$	8.23898e9	+	2.41918e9i	0.268915	+	0.0789607i	−0.144495	+	0.989506i	$0.546156\pi$
$992$	5.84989e9	+	5.06896e9i	0.190264	+	0.164865i
$993$	−6.48406e9	−	2.89421e10i	−0.210148	−	0.938011i
$994$	3.33779e10	+	4.79902e9i	1.07797	+	0.154989i
$995$	−7.69073e9	−	1.19670e10i	−0.247507	−	0.385128i
$996$	3.24984e9	−	8.88085e9i	0.104221	−	0.284804i
$997$	1.28571e9	+	1.48379e9i	0.0410875	+	0.0474175i	0.775921	−	0.630830i	$-0.217285\pi$
$997$	1.28571e9	+	1.48379e9i	0.0410875	+	0.0474175i	−0.734834	+	0.678247i	$0.762740\pi$
$998$	2.19995e10	−	3.16305e9i	0.700576	−	0.100728i
$999$	2.09470e10	−	8.25954e9i	0.664726	−	0.262106i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	69.8.g.a.5.14	✓	540
3.2	odd	2	inner	69.8.g.a.5.41	yes	540
23.14	odd	22	inner	69.8.g.a.14.41	yes	540
69.14	even	22	inner	69.8.g.a.14.14	yes	540

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
69.8.g.a.5.14	✓	540	1.1	even	1	trivial
69.8.g.a.5.41	yes	540	3.2	odd	2	inner
69.8.g.a.14.14	yes	540	69.14	even	22	inner
69.8.g.a.14.41	yes	540	23.14	odd	22	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 69 = 3 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	69.g (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-3.60512 + 12.2779i) q^{2} +(46.6247 - 3.62518i) q^{3} +(-30.0694 - 19.3245i) q^{4} +(-56.5273 + 393.156i) q^{5} +(-123.578 + 585.522i) q^{6} +(-611.212 + 279.131i) q^{7} +(-892.188 + 773.086i) q^{8} +(2160.72 - 338.046i) q^{9} +O(q^{10})\)	\(q+(-3.60512 + 12.2779i) q^{2} +(46.6247 - 3.62518i) q^{3} +(-30.0694 - 19.3245i) q^{4} +(-56.5273 + 393.156i) q^{5} +(-123.578 + 585.522i) q^{6} +(-611.212 + 279.131i) q^{7} +(-892.188 + 773.086i) q^{8} +(2160.72 - 338.046i) q^{9} +(-4623.34 - 2111.41i) q^{10} +(650.920 - 191.127i) q^{11} +(-1472.03 - 791.989i) q^{12} +(1256.61 - 2751.60i) q^{13} +(-1223.65 - 8510.70i) q^{14} +(-1210.30 + 18535.7i) q^{15} +(-8176.02 - 17903.0i) q^{16} +(-7513.61 + 4828.71i) q^{17} +(-3639.14 + 27747.7i) q^{18} +(-8841.70 + 13757.9i) q^{19} +(9297.27 - 10729.6i) q^{20} +(-27485.7 + 15230.2i) q^{21} +8680.97i q^{22} +(24142.2 + 53122.3i) q^{23} +(-38795.4 + 39279.2i) q^{24} +(-76416.0 - 22437.8i) q^{25} +(29253.6 + 25348.4i) q^{26} +(99517.2 - 23594.2i) q^{27} +(23772.9 + 3418.02i) q^{28} +(-116206. - 180820. i) q^{29} +(-223216. - 81683.3i) q^{30} +(50316.4 + 58068.2i) q^{31} +(99716.3 - 14337.0i) q^{32} +(29656.1 - 11271.0i) q^{33} +(-32198.9 - 109659. i) q^{34} +(-75192.0 - 256080. i) q^{35} +(-71504.1 - 31589.8i) q^{36} +(217915. - 31331.4i) q^{37} +(-137043. - 158156. i) q^{38} +(48614.1 - 132848. i) q^{39} +(-253510. - 394470. i) q^{40} +(-416216. - 59842.9i) q^{41} +(-87905.3 - 392372. i) q^{42} +(-343798. - 297903. i) q^{43} +(-23266.2 - 6831.59i) q^{44} +(10765.2 + 868608. i) q^{45} +(-739266. + 104903. i) q^{46} -139012. i q^{47} +(-446106. - 805081. i) q^{48} +(-243640. + 281176. i) q^{49} +(550977. - 857338. i) q^{50} +(-332815. + 252375. i) q^{51} +(-90958.8 + 58455.7i) q^{52} +(713053. + 1.56137e6i) q^{53} +(-69083.1 + 1.30692e6i) q^{54} +(38348.1 + 266717. i) q^{55} +(329524. - 721557. i) q^{56} +(-362366. + 673512. i) q^{57} +(2.63902e6 - 774887. i) q^{58} +(1.80634e6 + 824928. i) q^{59} +(394585. - 533969. i) q^{60} +(-919511. + 796761. i) q^{61} +(-894352. + 408437. i) q^{62} +(-1.22630e6 + 809741. i) q^{63} +(175065. - 1.21761e6i) q^{64} +(1.01077e6 + 649586. i) q^{65} +(31470.1 + 404747. i) q^{66} +(511181. - 1.74092e6i) q^{67} +319242. q^{68} +(1.31820e6 + 2.38929e6i) q^{69} +3.41520e6 q^{70} +(-1.10492e6 + 3.76301e6i) q^{71} +(-1.66643e6 + 1.97202e6i) q^{72} +(-2.74254e6 - 1.76252e6i) q^{73} +(-400924. + 2.78849e6i) q^{74} +(-3.64421e6 - 769131. i) q^{75} +(531730. - 242833. i) q^{76} +(-344501. + 298512. i) q^{77} +(1.45583e6 + 1.07581e6i) q^{78} +(1.15036e6 + 525351. i) q^{79} +(7.50084e6 - 2.20245e6i) q^{80} +(4.55442e6 - 1.46084e6i) q^{81} +(2.23525e6 - 4.89452e6i) q^{82} +(805140. + 5.59987e6i) q^{83} +(1.12079e6 + 73183.1i) q^{84} +(-1.47371e6 - 3.22698e6i) q^{85} +(4.89706e6 - 3.14715e6i) q^{86} +(-6.07356e6 - 8.00939e6i) q^{87} +(-432986. + 673739. i) q^{88} +(-4.53210e6 + 5.23032e6i) q^{89} +(-1.07035e7 - 2.99926e6i) q^{90} +2.03257e6i q^{91} +(300619. - 2.06389e6i) q^{92} +(2.55649e6 + 2.52500e6i) q^{93} +(1.70678e6 + 501156. i) q^{94} +(-4.90923e6 - 4.25387e6i) q^{95} +(4.59726e6 - 1.02995e6i) q^{96} +(1.29118e7 + 1.85644e6i) q^{97} +(-2.57389e6 - 4.00506e6i) q^{98} +(1.34184e6 - 633013. i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 540 q - 35 q^{3} + 3362 q^{4} - 1280 q^{6} - 22 q^{7} - 659 q^{9}+O(q^{10}) \) 540 * q - 35 * q^3 + 3362 * q^4 - 1280 * q^6 - 22 * q^7 - 659 * q^9	\( 540 q - 35 q^{3} + 3362 q^{4} - 1280 q^{6} - 22 q^{7} - 659 q^{9} - 22 q^{10} + 4756 q^{12} + 4970 q^{13} + 3828 q^{15} - 174622 q^{16} + 250050 q^{18} - 22 q^{19} - 221738 q^{21} + 94934 q^{24} - 788392 q^{25} + 1020934 q^{27} - 22 q^{28} - 1480875 q^{30} + 738458 q^{31} + 1215192 q^{33} + 1815924 q^{34} - 394502 q^{36} - 905234 q^{37} - 1635803 q^{39} + 10260228 q^{40} - 11 q^{42} - 1694330 q^{43} - 6978726 q^{46} + 134426 q^{48} + 7785740 q^{49} - 11 q^{51} + 16219654 q^{52} - 10697559 q^{54} - 1371960 q^{55} + 7508908 q^{57} - 21860696 q^{58} - 21971851 q^{60} - 11102850 q^{61} - 9022926 q^{63} + 2572060 q^{64} + 16582830 q^{66} + 6031564 q^{67} + 12019470 q^{69} - 2949828 q^{70} + 12828949 q^{72} - 1809596 q^{73} - 16620656 q^{75} - 42651158 q^{76} - 47106384 q^{78} - 1156914 q^{79} + 48837101 q^{81} + 47208588 q^{82} + 124183367 q^{84} + 5833252 q^{85} - 17916287 q^{87} + 360426 q^{88} - 142298860 q^{90} - 51670516 q^{93} - 18401348 q^{94} + 36462337 q^{96} - 63860500 q^{97} + 135683977 q^{99}+O(q^{100}) \) 540 * q - 35 * q^3 + 3362 * q^4 - 1280 * q^6 - 22 * q^7 - 659 * q^9 - 22 * q^10 + 4756 * q^12 + 4970 * q^13 + 3828 * q^15 - 174622 * q^16 + 250050 * q^18 - 22 * q^19 - 221738 * q^21 + 94934 * q^24 - 788392 * q^25 + 1020934 * q^27 - 22 * q^28 - 1480875 * q^30 + 738458 * q^31 + 1215192 * q^33 + 1815924 * q^34 - 394502 * q^36 - 905234 * q^37 - 1635803 * q^39 + 10260228 * q^40 - 11 * q^42 - 1694330 * q^43 - 6978726 * q^46 + 134426 * q^48 + 7785740 * q^49 - 11 * q^51 + 16219654 * q^52 - 10697559 * q^54 - 1371960 * q^55 + 7508908 * q^57 - 21860696 * q^58 - 21971851 * q^60 - 11102850 * q^61 - 9022926 * q^63 + 2572060 * q^64 + 16582830 * q^66 + 6031564 * q^67 + 12019470 * q^69 - 2949828 * q^70 + 12828949 * q^72 - 1809596 * q^73 - 16620656 * q^75 - 42651158 * q^76 - 47106384 * q^78 - 1156914 * q^79 + 48837101 * q^81 + 47208588 * q^82 + 124183367 * q^84 + 5833252 * q^85 - 17916287 * q^87 + 360426 * q^88 - 142298860 * q^90 - 51670516 * q^93 - 18401348 * q^94 + 36462337 * q^96 - 63860500 * q^97 + 135683977 * q^99

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