LMFDB - Embedded newform 38.8.e.a.23.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [38,8,Mod(5,38)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(38, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([16]))

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

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

chi := DirichletCharacter("38.5");

S:= CuspForms(chi, 8);

N := Newforms(S);

Level:	$ N $	$=$	$ 38 = 2 \cdot 19 $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	38.e (of order $9$, degree $6$, 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:	$11.8706309684$
Analytic rank:	$0$
Dimension:	$30$
Relative dimension:	$5$ over $\Q(\zeta_{9})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			23.1
Character	$\chi$	$=$	38.23
Dual form			38.8.e.a.5.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-7.51754 - 2.73616i) q^{2} +(-11.6345 - 65.9825i) q^{3} +(49.0268 + 41.1384i) q^{4} +(-116.114 + 97.4309i) q^{5} +(-93.0759 + 527.860i) q^{6} +(-468.313 + 811.141i) q^{7} +(-256.000 - 443.405i) q^{8} +(-2163.22 + 787.347i) q^{9} +O(q^{10})$	\(q+(-7.51754 - 2.73616i) q^{2} +(-11.6345 - 65.9825i) q^{3} +(49.0268 + 41.1384i) q^{4} +(-116.114 + 97.4309i) q^{5} +(-93.0759 + 527.860i) q^{6} +(-468.313 + 811.141i) q^{7} +(-256.000 - 443.405i) q^{8} +(-2163.22 + 787.347i) q^{9} +(1139.48 - 414.735i) q^{10} +(647.679 + 1121.81i) q^{11} +(2144.01 - 3713.54i) q^{12} +(492.820 - 2794.92i) q^{13} +(5739.97 - 4816.41i) q^{14} +(7779.66 + 6527.91i) q^{15} +(711.263 + 4033.77i) q^{16} +(8114.94 + 2953.60i) q^{17} +18416.4 q^{18} +(22173.6 + 20055.0i) q^{19} -9700.84 q^{20} +(58969.7 + 21463.2i) q^{21} +(-1799.49 - 10205.4i) q^{22} +(16532.3 + 13872.2i) q^{23} +(-26278.5 + 22050.3i) q^{24} +(-9576.67 + 54312.0i) q^{25} +(-11352.1 + 19662.5i) q^{26} +(3854.19 + 6675.65i) q^{27} +(-56329.0 + 20502.1i) q^{28} +(141843. - 51626.5i) q^{29} +(-40622.5 - 70360.2i) q^{30} +(10751.6 - 18622.4i) q^{31} +(5690.10 - 32270.2i) q^{32} +(66484.6 - 55787.2i) q^{33} +(-52922.9 - 44407.6i) q^{34} +(-24652.8 - 139813. i) q^{35} +(-138446. - 50390.2i) q^{36} -112901. q^{37} +(-111817. - 211435. i) q^{38} -190149. q^{39} +(72926.5 + 26543.1i) q^{40} +(90924.9 + 515661. i) q^{41} +(-384580. - 322701. i) q^{42} +(-571973. + 479942. i) q^{43} +(-14395.9 + 81643.4i) q^{44} +(174467. - 302186. i) q^{45} +(-86325.3 - 149520. i) q^{46} +(-959846. + 349355. i) q^{47} +(257883. - 93861.8i) q^{48} +(-26862.0 - 46526.3i) q^{49} +(220599. - 382089. i) q^{50} +(100472. - 569808. i) q^{51} +(139140. - 116752. i) q^{52} +(1.44200e6 + 1.20998e6i) q^{53} +(-10708.4 - 60730.2i) q^{54} +(-184504. - 67153.9i) q^{55} +479552. q^{56} +(1.06530e6 - 1.69640e6i) q^{57} -1.20757e6 q^{58} +(1.22335e6 + 445264. i) q^{59} +(112864. + 640086. i) q^{60} +(558573. + 468699. i) q^{61} +(-131780. + 110576. i) q^{62} +(374413. - 2.12340e6i) q^{63} +(-131072. + 227023. i) q^{64} +(215089. + 372544. i) q^{65} +(-652443. + 237470. i) q^{66} +(-2.60229e6 + 947158. i) q^{67} +(276344. + 478641. i) q^{68} +(722978. - 1.25224e6i) q^{69} +(-197222. + 1.11850e6i) q^{70} +(-1.48264e6 + 1.24408e6i) q^{71} +(902898. + 757621. i) q^{72} +(709763. + 4.02527e6i) q^{73} +(848740. + 308916. i) q^{74} +3.69506e6 q^{75} +(262068. + 1.89542e6i) q^{76} -1.21327e6 q^{77} +(1.42946e6 + 520279. i) q^{78} +(-23228.7 - 131737. i) q^{79} +(-475602. - 399077. i) q^{80} +(-3.46108e6 + 2.90419e6i) q^{81} +(727400. - 4.12529e6i) q^{82} +(4.43083e6 - 7.67442e6i) q^{83} +(2.00814e6 + 3.47819e6i) q^{84} +(-1.23003e6 + 447694. i) q^{85} +(5.61303e6 - 2.04298e6i) q^{86} +(-5.05672e6 - 8.75849e6i) q^{87} +(331612. - 574368. i) q^{88} +(-182210. + 1.03336e6i) q^{89} +(-2.13840e6 + 1.79433e6i) q^{90} +(2.03628e6 + 1.70864e6i) q^{91} +(239844. + 1.36022e6i) q^{92} +(-1.35384e6 - 492758. i) q^{93} +8.17157e6 q^{94} +(-4.52864e6 - 168272. i) q^{95} -2.19547e6 q^{96} +(-1.19138e7 - 4.33627e6i) q^{97} +(74632.6 + 423263. i) q^{98} +(-2.28433e6 - 1.91678e6i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 30 q + 45 q^{3} + 360 q^{6} + 1806 q^{7} - 7680 q^{8} - 3105 q^{9}+O(q^{10}) $ 30 * q + 45 * q^3 + 360 * q^6 + 1806 * q^7 - 7680 * q^8 - 3105 * q^9	\( 30 q + 45 q^{3} + 360 q^{6} + 1806 q^{7} - 7680 q^{8} - 3105 q^{9} + 9786 q^{11} - 11130 q^{13} + 6144 q^{14} - 1818 q^{15} - 65250 q^{17} + 29040 q^{18} + 105906 q^{19} - 47616 q^{20} + 172854 q^{21} + 102336 q^{22} + 101004 q^{23} + 23040 q^{24} - 132756 q^{25} - 92112 q^{26} + 43659 q^{27} + 96384 q^{28} - 273912 q^{29} + 58710 q^{31} - 406965 q^{33} + 84960 q^{34} + 356100 q^{35} - 198720 q^{36} - 2598852 q^{37} - 219336 q^{38} + 1769844 q^{39} + 43377 q^{41} - 79056 q^{42} + 1126698 q^{43} + 818688 q^{44} - 912546 q^{45} - 530880 q^{46} + 588306 q^{47} - 368640 q^{48} - 2778285 q^{49} + 1665288 q^{50} + 3972045 q^{51} - 430080 q^{52} + 6520866 q^{53} - 486648 q^{54} - 1666818 q^{55} - 1849344 q^{56} - 6947844 q^{57} - 4573152 q^{58} - 970467 q^{59} + 4634496 q^{60} - 4037670 q^{61} + 755952 q^{62} + 7946472 q^{63} - 3932160 q^{64} + 1497690 q^{65} + 6499272 q^{66} - 4817025 q^{67} + 1472064 q^{68} + 10299876 q^{69} + 2848800 q^{70} - 25171290 q^{71} + 3179520 q^{72} + 1347750 q^{73} - 3123936 q^{74} + 8817984 q^{75} + 1583232 q^{76} - 11476764 q^{77} - 930960 q^{78} + 10777986 q^{79} - 5365035 q^{81} + 347016 q^{82} + 9745314 q^{83} + 877056 q^{84} + 29258556 q^{85} - 9338208 q^{86} + 25598802 q^{87} + 5010432 q^{88} - 20353740 q^{89} - 30112128 q^{90} + 19748724 q^{91} - 14097792 q^{92} - 18738174 q^{93} + 12376608 q^{94} - 20427204 q^{95} - 23005029 q^{97} + 14869008 q^{98} - 45819771 q^{99}+O(q^{100}) \) 30 * q + 45 * q^3 + 360 * q^6 + 1806 * q^7 - 7680 * q^8 - 3105 * q^9 + 9786 * q^11 - 11130 * q^13 + 6144 * q^14 - 1818 * q^15 - 65250 * q^17 + 29040 * q^18 + 105906 * q^19 - 47616 * q^20 + 172854 * q^21 + 102336 * q^22 + 101004 * q^23 + 23040 * q^24 - 132756 * q^25 - 92112 * q^26 + 43659 * q^27 + 96384 * q^28 - 273912 * q^29 + 58710 * q^31 - 406965 * q^33 + 84960 * q^34 + 356100 * q^35 - 198720 * q^36 - 2598852 * q^37 - 219336 * q^38 + 1769844 * q^39 + 43377 * q^41 - 79056 * q^42 + 1126698 * q^43 + 818688 * q^44 - 912546 * q^45 - 530880 * q^46 + 588306 * q^47 - 368640 * q^48 - 2778285 * q^49 + 1665288 * q^50 + 3972045 * q^51 - 430080 * q^52 + 6520866 * q^53 - 486648 * q^54 - 1666818 * q^55 - 1849344 * q^56 - 6947844 * q^57 - 4573152 * q^58 - 970467 * q^59 + 4634496 * q^60 - 4037670 * q^61 + 755952 * q^62 + 7946472 * q^63 - 3932160 * q^64 + 1497690 * q^65 + 6499272 * q^66 - 4817025 * q^67 + 1472064 * q^68 + 10299876 * q^69 + 2848800 * q^70 - 25171290 * q^71 + 3179520 * q^72 + 1347750 * q^73 - 3123936 * q^74 + 8817984 * q^75 + 1583232 * q^76 - 11476764 * q^77 - 930960 * q^78 + 10777986 * q^79 - 5365035 * q^81 + 347016 * q^82 + 9745314 * q^83 + 877056 * q^84 + 29258556 * q^85 - 9338208 * q^86 + 25598802 * q^87 + 5010432 * q^88 - 20353740 * q^89 - 30112128 * q^90 + 19748724 * q^91 - 14097792 * q^92 - 18738174 * q^93 + 12376608 * q^94 - 20427204 * q^95 - 23005029 * q^97 + 14869008 * q^98 - 45819771 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/38\mathbb{Z}\right)^\times$.

$n$	$21$
$\chi(n)$	$e\left(\frac{1}{9}\right)$

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 $

$2$	−7.51754	−	2.73616i	−0.664463	−	0.241845i
$2$	−7.51754	−	2.73616i	−0.664463	−	0.241845i
$3$	−11.6345	−	65.9825i	−0.248784	−	1.41093i	−0.811537	−	0.584301i	$-0.801369\pi$
$3$	−11.6345	−	65.9825i	−0.248784	−	1.41093i	0.562753	−	0.826625i	$-0.309742\pi$
$4$	49.0268	+	41.1384i	0.383022	+	0.321394i
$5$	−116.114	+	97.4309i	−0.415421	+	0.348580i	−0.826418	−	0.563057i	$-0.809625\pi$
$5$	−116.114	+	97.4309i	−0.415421	+	0.348580i	0.410997	+	0.911637i	$0.365181\pi$
$6$	−93.0759	+	527.860i	−0.175917	+	0.997675i
$7$	−468.313	+	811.141i	−0.516051	+	0.893827i	0.483775	+	0.875192i	$0.339265\pi$
$7$	−468.313	+	811.141i	−0.516051	+	0.893827i	−0.999826	+	0.0186345i	$0.994068\pi$
$8$	−256.000	−	443.405i	−0.176777	−	0.306186i
$9$	−2163.22	+	787.347i	−0.989126	+	0.360013i
$10$	1139.48	−	414.735i	0.360334	−	0.131151i
$11$	647.679	+	1121.81i	0.146719	+	0.254124i	0.930013	−	0.367527i	$-0.119795\pi$
$11$	647.679	+	1121.81i	0.146719	+	0.254124i	−0.783294	+	0.621651i	$0.786462\pi$
$12$	2144.01	−	3713.54i	0.358173	−	0.620374i
$13$	492.820	−	2794.92i	0.0622137	−	0.352832i	−0.937771	−	0.347255i	$-0.887114\pi$
$13$	492.820	−	2794.92i	0.0622137	−	0.352832i	0.999984	−	0.00557656i	$-0.00177508\pi$
$14$	5739.97	−	4816.41i	0.559064	−	0.469111i
$15$	7779.66	+	6527.91i	0.595170	+	0.499407i
$16$	711.263	+	4033.77i	0.0434120	+	0.246202i
$17$	8114.94	+	2953.60i	0.400603	+	0.145808i	0.534461	−	0.845193i	$-0.320514\pi$
$17$	8114.94	+	2953.60i	0.400603	+	0.145808i	−0.133858	+	0.991000i	$0.542737\pi$
$18$	18416.4			0.744305
$19$	22173.6	+	20055.0i	0.741648	+	0.670789i
$19$	22173.6	+	20055.0i	0.741648	+	0.670789i
$20$	−9700.84			−0.271147
$21$	58969.7	+	21463.2i	1.38951	+	0.505740i
$22$	−1799.49	−	10205.4i	−0.0360305	−	0.204339i
$23$	16532.3	+	13872.2i	0.283325	+	0.237738i	0.773363	−	0.633963i	$-0.218573\pi$
$23$	16532.3	+	13872.2i	0.283325	+	0.237738i	−0.490039	+	0.871701i	$0.663017\pi$
$24$	−26278.5	+	22050.3i	−0.388027	+	0.325593i
$25$	−9576.67	+	54312.0i	−0.122581	+	0.695193i
$26$	−11352.1	+	19662.5i	−0.126669	+	0.219398i
$27$	3854.19	+	6675.65i	0.0376843	+	0.0652711i
$28$	−56329.0	+	20502.1i	−0.484929	+	0.176500i
$29$	141843.	−	51626.5i	1.07998	−	0.393079i	0.260078	−	0.965588i	$-0.416252\pi$
$29$	141843.	−	51626.5i	1.07998	−	0.393079i	0.819899	+	0.572508i	$0.194030\pi$
$30$	−40622.5	−	70360.2i	−0.274690	−	0.475776i
$31$	10751.6	−	18622.4i	0.0648200	−	0.112271i	−0.831794	−	0.555084i	$-0.812686\pi$
$31$	10751.6	−	18622.4i	0.0648200	−	0.112271i	0.896614	+	0.442813i	$0.146019\pi$
$32$	5690.10	−	32270.2i	0.0306970	−	0.174091i
$33$	66484.6	−	55787.2i	0.322049	−	0.270231i
$34$	−52922.9	−	44407.6i	−0.230923	−	0.193768i
$35$	−24652.8	−	139813.i	−0.0971913	−	0.551199i
$36$	−138446.	−	50390.2i	−0.494563	−	0.180006i
$37$	−112901.			−0.366431			−0.183216	−	0.983073i	$-0.558651\pi$
$37$	−112901.			−0.366431			−0.183216	+	0.983073i	$0.558651\pi$
$38$	−111817.	−	211435.i	−0.330571	−	0.625078i
$39$	−190149.			−0.513297
$40$	72926.5	+	26543.1i	0.180167	+	0.0655754i
$41$	90924.9	+	515661.i	0.206034	+	1.16848i	0.895804	+	0.444450i	$0.146601\pi$
$41$	90924.9	+	515661.i	0.206034	+	1.16848i	−0.689770	+	0.724029i	$0.742288\pi$
$42$	−384580.	−	322701.i	−0.800967	−	0.672091i
$43$	−571973.	+	479942.i	−1.09707	+	0.920554i	−0.997225	−	0.0744482i	$-0.976280\pi$
$43$	−571973.	+	479942.i	−1.09707	+	0.920554i	−0.0998491	+	0.995003i	$0.531836\pi$
$44$	−14395.9	+	81643.4i	−0.0254774	+	0.144490i
$45$	174467.	−	302186.i	0.285411	−	0.494346i
$46$	−86325.3	−	149520.i	−0.130763	−	0.226489i
$47$	−959846.	+	349355.i	−1.34853	+	0.490823i	−0.912487	−	0.409105i	$-0.865841\pi$
$47$	−959846.	+	349355.i	−1.34853	+	0.490823i	−0.436038	+	0.899928i	$0.643619\pi$
$48$	257883.	−	93861.8i	0.336573	−	0.122502i
$49$	−26862.0	−	46526.3i	−0.0326176	−	0.0564953i
$50$	220599.	−	382089.i	0.249580	−	0.432285i
$51$	100472.	−	569808.i	0.106060	−	0.601496i
$52$	139140.	−	116752.i	0.137227	−	0.115147i
$53$	1.44200e6	+	1.20998e6i	1.33045	+	1.11638i	0.983971	+	0.178327i	$0.0570686\pi$
$53$	1.44200e6	+	1.20998e6i	1.33045	+	1.11638i	0.346483	+	0.938056i	$0.387376\pi$
$54$	−10708.4	−	60730.2i	−0.00925434	−	0.0524840i
$55$	−184504.	−	67153.9i	−0.149533	−	0.0544254i
$56$	479552.			0.364903
$57$	1.06530e6	−	1.69640e6i	0.761923	−	1.21329i
$58$	−1.20757e6			−0.812668
$59$	1.22335e6	+	445264.i	0.775479	+	0.282251i	0.699286	−	0.714842i	$-0.253501\pi$
$59$	1.22335e6	+	445264.i	0.775479	+	0.282251i	0.0761928	+	0.997093i	$0.475724\pi$
$60$	112864.	+	640086.i	0.0674571	+	0.382568i
$61$	558573.	+	468699.i	0.315084	+	0.264387i	0.786589	−	0.617476i	$-0.211845\pi$
$61$	558573.	+	468699.i	0.315084	+	0.264387i	−0.471506	+	0.881863i	$0.656289\pi$
$62$	−131780.	+	110576.i	−0.0702227	+	0.0589239i
$63$	374413.	−	2.12340e6i	0.188651	−	1.06989i
$64$	−131072.	+	227023.i	−0.0625000	+	0.108253i
$65$	215089.	+	372544.i	0.0971450	+	0.168260i
$66$	−652443.	+	237470.i	−0.279344	+	0.101673i
$67$	−2.60229e6	+	947158.i	−1.05705	+	0.384734i	−0.811318	−	0.584604i	$-0.801250\pi$
$67$	−2.60229e6	+	947158.i	−1.05705	+	0.384734i	−0.245730	+	0.969338i	$0.579027\pi$
$68$	276344.	+	478641.i	0.106578	+	0.184599i
$69$	722978.	−	1.25224e6i	0.264944	−	0.458896i
$70$	−197222.	+	1.11850e6i	−0.0687246	+	0.389757i
$71$	−1.48264e6	+	1.24408e6i	−0.491621	+	0.412519i	−0.854607	−	0.519276i	$-0.826202\pi$
$71$	−1.48264e6	+	1.24408e6i	−0.491621	+	0.412519i	0.362986	+	0.931795i	$0.381757\pi$
$72$	902898.	+	757621.i	0.285085	+	0.239215i
$73$	709763.	+	4.02527e6i	0.213542	+	1.21106i	0.883418	+	0.468585i	$0.155236\pi$
$73$	709763.	+	4.02527e6i	0.213542	+	1.21106i	−0.669876	+	0.742473i	$0.733653\pi$
$74$	848740.	+	308916.i	0.243480	+	0.0886195i
$75$	3.69506e6			1.01136
$76$	262068.	+	1.89542e6i	0.0684804	+	0.495288i
$77$	−1.21327e6			−0.302857
$78$	1.42946e6	+	520279.i	0.341067	+	0.124138i
$79$	−23228.7	−	131737.i	−0.00530067	−	0.0300616i	0.982043	−	0.188659i	$-0.0604140\pi$
$79$	−23228.7	−	131737.i	−0.00530067	−	0.0300616i	−0.987343	+	0.158597i	$0.949303\pi$
$80$	−475602.	−	399077.i	−0.103855	−	0.0871449i
$81$	−3.46108e6	+	2.90419e6i	−0.723626	+	0.607194i
$82$	727400.	−	4.12529e6i	0.145688	−	0.826239i
$83$	4.43083e6	−	7.67442e6i	0.850573	−	1.47324i	−0.0301185	−	0.999546i	$-0.509588\pi$
$83$	4.43083e6	−	7.67442e6i	0.850573	−	1.47324i	0.880692	−	0.473690i	$-0.157078\pi$
$84$	2.00814e6	+	3.47819e6i	0.369671	+	0.640289i
$85$	−1.23003e6	+	447694.i	−0.217244	+	0.0790705i
$86$	5.61303e6	−	2.04298e6i	0.951596	−	0.346353i
$87$	−5.05672e6	−	8.75849e6i	−0.823287	−	1.42597i
$88$	331612.	−	574368.i	0.0518729	−	0.0898465i
$89$	−182210.	+	1.03336e6i	−0.0273972	+	0.155377i	−0.995437	−	0.0954184i	$-0.969581\pi$
$89$	−182210.	+	1.03336e6i	−0.0273972	+	0.155377i	0.968040	+	0.250796i	$0.0806922\pi$
$90$	−2.13840e6	+	1.79433e6i	−0.309200	+	0.259450i
$91$	2.03628e6	+	1.70864e6i	0.283265	+	0.237687i
$92$	239844.	+	1.36022e6i	0.0321123	+	0.182118i
$93$	−1.35384e6	−	492758.i	−0.174533	−	0.0635248i
$94$	8.17157e6			1.01475
$95$	−4.52864e6	−	168272.i	−0.541920	−	0.0201363i
$96$	−2.19547e6			−0.253267
$97$	−1.19138e7	−	4.33627e6i	−1.32541	−	0.482409i	−0.420221	−	0.907422i	$-0.638047\pi$
$97$	−1.19138e7	−	4.33627e6i	−1.32541	−	0.482409i	−0.905187	+	0.425013i	$0.860270\pi$
$98$	74632.6	+	423263.i	0.00801009	+	0.0454275i
$99$	−2.28433e6	−	1.91678e6i	−0.236611	−	0.198540i
$100$	−2.70382e6	+	2.26878e6i	−0.270382	+	0.226878i
$101$	1.29997e6	−	7.37252e6i	0.125548	−	0.712018i	−0.855433	−	0.517914i	$-0.826709\pi$
$101$	1.29997e6	−	7.37252e6i	0.125548	−	0.712018i	0.980981	−	0.194105i	$-0.0621801\pi$
$102$	−2.31439e6	+	4.00864e6i	−0.215942	+	0.374022i
$103$	−1.48195e6	−	2.56681e6i	−0.133630	−	0.231453i	0.791443	−	0.611242i	$-0.209330\pi$
$103$	−1.48195e6	−	2.56681e6i	−0.133630	−	0.231453i	−0.925073	+	0.379789i	$0.875997\pi$
$104$	−1.36544e6	+	496981.i	−0.119030	+	0.0433234i
$105$	−8.93837e6	+	3.25330e6i	−0.753522	+	0.274259i
$106$	−7.52959e6	−	1.30416e7i	−0.614046	−	1.06356i
$107$	−2.69688e6	+	4.67113e6i	−0.212823	+	0.368620i	−0.952597	−	0.304235i	$-0.901599\pi$
$107$	−2.69688e6	+	4.67113e6i	−0.212823	+	0.368620i	0.739774	+	0.672855i	$0.234932\pi$
$108$	−85667.0	+	485842.i	−0.00654380	+	0.0371118i
$109$	−1.46982e7	+	1.23332e7i	−1.08710	+	0.912188i	−0.996491	−	0.0836981i	$-0.973327\pi$
$109$	−1.46982e7	+	1.23332e7i	−1.08710	+	0.912188i	−0.0906123	+	0.995886i	$0.528882\pi$
$110$	1.20327e6	+	1.00966e6i	0.0861963	+	0.0723273i
$111$	1.31355e6	+	7.44951e6i	0.0911624	+	0.517008i
$112$	−3.60505e6	−	1.31213e6i	−0.242465	−	0.0882499i
$113$	2.34480e7			1.52873			0.764366	−	0.644783i	$-0.223052\pi$
$113$	2.34480e7			1.52873			0.764366	+	0.644783i	$0.223052\pi$
$114$	−1.26501e7	+	9.83790e6i	−0.799698	+	0.621921i
$115$	−3.27120e6			−0.200570
$116$	9.07794e6	+	3.30410e6i	0.539988	+	0.196540i
$117$	1.13450e6	+	6.43404e6i	0.0654866	+	0.371393i
$118$	−7.97830e6	−	6.69459e6i	−0.447016	−	0.375091i
$119$	−6.19612e6	+	5.19916e6i	−0.337058	+	0.282826i
$120$	902915.	−	5.12069e6i	0.0476994	−	0.270516i
$121$	8.90461e6	−	1.54232e7i	0.456947	−	0.791456i
$122$	−2.91666e6	−	5.05181e6i	−0.145421	−	0.251876i
$123$	3.29667e7	−	1.19989e7i	1.59738	−	0.581398i
$124$	1.29321e6	−	470691.i	0.0609108	−	0.0221697i
$125$	−1.01006e7	−	1.74948e7i	−0.462554	−	0.801167i
$126$	−8.62463e6	+	1.49383e7i	−0.384099	+	0.665280i
$127$	6.56395e6	−	3.72260e7i	0.284349	−	1.61262i	−0.423252	−	0.906012i	$-0.639111\pi$
$127$	6.56395e6	−	3.72260e7i	0.284349	−	1.61262i	0.707601	−	0.706612i	$-0.249777\pi$
$128$	1.60651e6	−	1.34802e6i	0.0677094	−	0.0568149i
$129$	3.83224e7	+	3.21563e7i	1.57177	+	1.31887i
$130$	−597596.	−	3.38913e6i	−0.0238564	−	0.135297i
$131$	4.56859e7	+	1.66283e7i	1.77555	+	0.646248i	0.999886	+	0.0151024i	$0.00480743\pi$
$131$	4.56859e7	+	1.66283e7i	1.77555	+	0.646248i	0.775665	+	0.631145i	$0.217415\pi$
$132$	5.55453e6			0.210203
$133$	−2.66516e7	+	8.59387e6i	−0.982298	+	0.316744i
$134$	2.21544e7			0.795415
$135$	−1.09794e6	−	399617.i	−0.0384070	−	0.0139790i
$136$	−767786.	−	4.35433e6i	−0.0261730	−	0.148435i
$137$	1.64056e6	+	1.37659e6i	0.0545091	+	0.0457386i	0.669635	−	0.742690i	$-0.266450\pi$
$137$	1.64056e6	+	1.37659e6i	0.0545091	+	0.0457386i	−0.615126	+	0.788429i	$0.710895\pi$
$138$	−8.86134e6	+	7.43555e6i	−0.287027	+	0.240844i
$139$	−3.52015e6	+	1.99638e7i	−0.111176	+	0.630508i	0.877397	+	0.479764i	$0.159278\pi$
$139$	−3.52015e6	+	1.99638e7i	−0.111176	+	0.630508i	−0.988573	+	0.150744i	$0.951833\pi$
$140$	4.54303e6	−	7.86875e6i	0.139926	−	0.242358i
$141$	3.42187e7	+	5.92685e7i	1.02801	+	1.78056i
$142$	1.45498e7	−	5.29569e6i	0.426430	−	0.155208i
$143$	3.45457e6	−	1.25736e6i	0.0987910	−	0.0359570i
$144$	−4.71460e6	−	8.16592e6i	−0.131576	−	0.227896i
$145$	−1.14399e7	+	1.98144e7i	−0.311625	+	0.539751i
$146$	5.67811e6	−	3.22021e7i	0.150997	−	0.856347i
$147$	−2.75740e6	+	2.31373e6i	−0.0715960	+	0.0600762i
$148$	−5.53519e6	−	4.64458e6i	−0.140351	−	0.117769i
$149$	6.82922e6	+	3.87304e7i	0.169129	+	0.959181i	0.944704	+	0.327925i	$0.106349\pi$
$149$	6.82922e6	+	3.87304e7i	0.169129	+	0.959181i	−0.775574	+	0.631256i	$0.782540\pi$
$150$	−2.77778e7	−	1.01103e7i	−0.672013	−	0.244593i
$151$	−4.04030e7			−0.954980			−0.477490	−	0.878637i	$-0.658453\pi$
$151$	−4.04030e7			−0.954980			−0.477490	+	0.878637i	$0.658453\pi$
$152$	3.21607e6	−	1.49660e7i	0.0742801	−	0.345662i
$153$	−1.98799e7			−0.448740
$154$	9.12077e6	+	3.31969e6i	0.201238	+	0.0732445i
$155$	565984.	+	3.20986e6i	0.0122080	+	0.0692348i
$156$	−9.32243e6	−	7.82244e6i	−0.196604	−	0.164971i
$157$	−4.91959e7	+	4.12802e7i	−1.01457	+	0.851321i	−0.988935	−	0.148350i	$-0.952604\pi$
$157$	−4.91959e7	+	4.12802e7i	−1.01457	+	0.851321i	−0.0256304	+	0.999671i	$0.508159\pi$
$158$	−185830.	+	1.05389e6i	−0.00374814	+	0.0212567i
$159$	6.30607e7	−	1.09224e8i	1.24414	−	2.15491i
$160$	2.48342e6	+	4.30140e6i	0.0479324	+	0.0830214i
$161$	−1.89946e7	+	6.91346e6i	−0.358707	+	0.130559i
$162$	3.39651e7	−	1.23623e7i	0.627669	−	0.228453i
$163$	−2.32279e7	−	4.02319e7i	−0.420101	−	0.727636i	0.575848	−	0.817557i	$-0.304672\pi$
$163$	−2.32279e7	−	4.02319e7i	−0.420101	−	0.727636i	−0.995949	+	0.0899206i	$0.971339\pi$
$164$	−1.67557e7	+	2.90217e7i	−0.296626	+	0.513771i
$165$	−2.28437e6	+	1.29553e7i	−0.0395889	+	0.224520i
$166$	−5.43074e7	+	4.55693e7i	−0.921469	+	0.773204i
$167$	−5.73147e7	−	4.80927e7i	−0.952265	−	0.799046i	0.0274122	−	0.999624i	$-0.491273\pi$
$167$	−5.73147e7	−	4.80927e7i	−0.952265	−	0.799046i	−0.979678	+	0.200579i	$0.935718\pi$
$168$	−5.57935e6	−	3.16420e7i	−0.0907822	−	0.514852i
$169$	5.13956e7	+	1.87065e7i	0.819073	+	0.298118i
$170$	1.04717e7			0.163474
$171$	−6.37566e7	−	2.59251e7i	−0.975076	−	0.396492i
$172$	−4.77861e7			−0.716064
$173$	1.06453e7	+	3.87457e6i	0.156313	+	0.0568934i	0.418992	−	0.907990i	$-0.362384\pi$
$173$	1.06453e7	+	3.87457e6i	0.156313	+	0.0568934i	−0.262678	+	0.964883i	$0.584606\pi$
$174$	1.40494e7	+	7.96783e7i	0.202179	+	1.14662i
$175$	−3.95698e7	−	3.32030e7i	−0.558124	−	0.468322i
$176$	−4.06447e6	+	3.41049e6i	−0.0561965	+	0.0471545i
$177$	1.51466e7	−	8.59004e7i	0.205309	−	1.16436i
$178$	4.19721e6	−	7.26979e6i	0.0557816	−	0.0966166i
$179$	1.46998e7	+	2.54609e7i	0.191570	+	0.331809i	0.945771	−	0.324835i	$-0.105309\pi$
$179$	1.46998e7	+	2.54609e7i	0.191570	+	0.331809i	−0.754201	+	0.656644i	$0.771975\pi$
$180$	2.09850e7	−	7.63793e6i	0.268198	−	0.0976162i
$181$	3.84993e7	−	1.40126e7i	0.482590	−	0.175648i	−0.0892571	−	0.996009i	$-0.528449\pi$
$181$	3.84993e7	−	1.40126e7i	0.482590	−	0.175648i	0.571847	+	0.820360i	$0.306227\pi$
$182$	−1.06327e7	−	1.84164e7i	−0.130736	−	0.226441i
$183$	2.44272e7	−	4.23091e7i	0.294642	−	0.510335i
$184$	1.91875e6	−	1.08818e7i	0.0227068	−	0.128777i
$185$	1.31094e7	−	1.10001e7i	0.152223	−	0.127731i
$186$	8.82929e6	+	7.40866e6i	0.100608	+	0.0844198i
$187$	1.94249e6	+	1.10164e7i	0.0217227	+	0.123196i
$188$	−6.14301e7	−	2.23587e7i	−0.674263	−	0.245412i
$189$	−7.21987e6			−0.0777880
$190$	3.35838e7	+	1.36561e7i	0.355216	+	0.144440i
$191$	−1.02919e8			−1.06875			−0.534376	−	0.845247i	$-0.679453\pi$
$191$	−1.02919e8			−1.06875			−0.534376	+	0.845247i	$0.679453\pi$
$192$	1.65045e7	+	6.00715e6i	0.168286	+	0.0612512i
$193$	2.35211e6	+	1.33395e7i	0.0235509	+	0.133564i	0.994316	−	0.106467i	$-0.0339537\pi$
$193$	2.35211e6	+	1.33395e7i	0.0235509	+	0.133564i	−0.970765	+	0.240030i	$0.922843\pi$
$194$	7.76978e7	+	6.51962e7i	0.764017	+	0.641086i
$195$	2.20789e7	−	1.85264e7i	0.213234	−	0.178925i
$196$	597061.	−	3.38610e6i	0.00566399	−	0.0321221i
$197$	3.57675e7	−	6.19512e7i	0.333317	−	0.577322i	−0.649843	−	0.760068i	$-0.725165\pi$
$197$	3.57675e7	−	6.19512e7i	0.333317	−	0.577322i	0.983160	+	0.182747i	$0.0584988\pi$
$198$	1.19279e7	+	2.06598e7i	0.109203	+	0.189146i
$199$	−1.08058e8	+	3.93299e7i	−0.972010	+	0.353783i	−0.778729	−	0.627361i	$-0.784135\pi$
$199$	−1.08058e8	+	3.93299e7i	−0.972010	+	0.353783i	−0.193281	+	0.981143i	$0.561913\pi$
$200$	2.65338e7	−	9.65752e6i	0.234528	−	0.0853613i
$201$	9.27722e7	+	1.60686e8i	0.805808	+	1.39570i
$202$	−2.99450e7	+	5.18663e7i	−0.255620	+	0.442747i
$203$	−2.45503e7	+	1.39232e8i	−0.205978	+	1.16816i
$204$	2.83668e7	−	2.38026e7i	0.233940	−	0.196299i
$205$	−6.07990e7	−	5.10164e7i	−0.492899	−	0.413591i
$206$	4.11740e6	+	2.33510e7i	0.0328162	+	0.186110i
$207$	−4.66851e7	−	1.69920e7i	−0.365833	−	0.133152i
$208$	1.16246e7			0.0895687
$209$	−8.13664e6	+	3.78638e7i	−0.0616500	+	0.286888i
$210$	7.60961e7			0.567016
$211$	−1.30624e8	−	4.75431e7i	−0.957266	−	0.348416i	−0.184305	−	0.982869i	$-0.559003\pi$
$211$	−1.30624e8	−	4.75431e7i	−0.957266	−	0.348416i	−0.772962	+	0.634453i	$0.781226\pi$
$212$	2.09200e7	+	1.18643e8i	0.150795	+	0.855200i
$213$	9.93372e7	+	8.33538e7i	0.704341	+	0.591013i
$214$	3.30549e7	−	2.77363e7i	0.230562	−	0.193464i
$215$	1.96527e7	−	1.11456e8i	0.134861	−	0.764835i
$216$	1.97335e6	−	3.41794e6i	0.0133234	−	0.0230768i
$217$	1.00703e7	+	1.74422e7i	0.0669008	+	0.115876i
$218$	1.44240e8	−	5.24990e7i	0.942948	−	0.343205i
$219$	2.57339e8	−	9.36639e7i	1.65559	−	0.602584i
$220$	−6.28303e6	−	1.08825e7i	−0.0397823	−	0.0689050i
$221$	1.22543e7	−	2.12250e7i	0.0763686	−	0.132274i
$222$	1.05084e7	−	5.95960e7i	0.0644616	−	0.365580i
$223$	7.39336e7	−	6.20377e7i	0.446452	−	0.374618i	−0.391665	−	0.920108i	$-0.628101\pi$
$223$	7.39336e7	−	6.20377e7i	0.446452	−	0.374618i	0.838117	+	0.545490i	$0.183656\pi$
$224$	2.35109e7	+	1.97280e7i	0.139766	+	0.117278i
$225$	−2.20460e7	−	1.25029e8i	−0.129030	−	0.731765i
$226$	−1.76271e8	−	6.41575e7i	−1.01579	−	0.369716i
$227$	−2.34912e8			−1.33295			−0.666476	−	0.745526i	$-0.732198\pi$
$227$	−2.34912e8			−1.33295			−0.666476	+	0.745526i	$0.732198\pi$
$228$	1.22016e8	−	3.93442e7i	0.681778	−	0.219841i
$229$	6.12094e7			0.336817			0.168408	−	0.985717i	$-0.446137\pi$
$229$	6.12094e7			0.336817			0.168408	+	0.985717i	$0.446137\pi$
$230$	2.45914e7	+	8.95054e6i	0.133271	+	0.0485067i
$231$	1.41157e7	+	8.00543e7i	0.0753462	+	0.427309i
$232$	−5.92032e7	−	4.96774e7i	−0.311270	−	0.261187i
$233$	−5.81584e7	+	4.88007e7i	−0.301208	+	0.252744i	−0.780847	−	0.624722i	$-0.785212\pi$
$233$	−5.81584e7	+	4.88007e7i	−0.301208	+	0.252744i	0.479639	+	0.877466i	$0.340768\pi$
$234$	9.07596e6	−	5.14723e7i	0.0463060	−	0.262614i
$235$	7.74132e7	−	1.34084e8i	0.389115	−	0.673967i
$236$	4.16597e7	+	7.21567e7i	0.206312	+	0.357343i
$237$	−8.42206e6	+	3.06538e6i	−0.0410959	+	0.0149577i
$238$	6.08053e7	−	2.21313e7i	0.292363	−	0.106411i
$239$	7.50815e7	+	1.30045e8i	0.355746	+	0.616170i	0.987245	−	0.159206i	$-0.0508935\pi$
$239$	7.50815e7	+	1.30045e8i	0.355746	+	0.616170i	−0.631499	+	0.775376i	$0.717560\pi$
$240$	−2.07987e7	+	3.60244e7i	−0.0971174	+	0.168212i
$241$	−5.52183e7	+	3.13158e8i	−0.254111	+	1.44113i	0.544234	+	0.838933i	$0.316820\pi$
$241$	−5.52183e7	+	3.13158e8i	−0.254111	+	1.44113i	−0.798345	+	0.602200i	$0.794291\pi$
$242$	−1.09141e8	+	9.15804e7i	−0.495034	+	0.415383i
$243$	2.44808e8	+	2.05418e8i	1.09447	+	0.918368i
$244$	8.10357e6	+	4.59576e7i	0.0357118	+	0.202532i
$245$	7.65215e6	+	2.78516e6i	0.0332432	+	0.0120995i
$246$	−2.80660e8			−1.20201
$247$	6.69798e7	−	5.20898e7i	0.282816	−	0.219945i
$248$	−1.10097e7			−0.0458346
$249$	−5.57928e8	−	2.03069e8i	−2.29024	−	0.833578i
$250$	2.80632e7	+	1.59155e8i	0.113592	+	0.644212i
$251$	2.78849e8	+	2.33982e8i	1.11304	+	0.933951i	0.998232	−	0.0594370i	$-0.0189305\pi$
$251$	2.78849e8	+	2.33982e8i	1.11304	+	0.933951i	0.114807	+	0.993388i	$0.463375\pi$
$252$	1.05710e8	−	8.87009e7i	0.416114	−	0.349161i
$253$	−4.85443e6	+	2.75308e7i	−0.0188459	+	0.106880i
$254$	−1.51201e8	+	2.61888e8i	−0.578944	+	1.00276i
$255$	4.38507e7	+	7.59516e7i	0.165610	+	0.286844i
$256$	−1.57654e7	+	5.73815e6i	−0.0587308	+	0.0213763i
$257$	4.30528e8	−	1.56700e8i	1.58211	−	0.575840i	0.606446	−	0.795124i	$-0.292594\pi$
$257$	4.30528e8	−	1.56700e8i	1.58211	−	0.575840i	0.975661	+	0.219284i	$0.0703722\pi$
$258$	−2.00105e8	−	3.46593e8i	−0.725420	−	1.25647i
$259$	5.28731e7	−	9.15789e7i	0.189097	−	0.327526i
$260$	−4.78077e6	+	2.71131e7i	−0.0168691	+	0.0956692i
$261$	−2.66189e8	+	2.23359e8i	−0.926720	+	0.777610i
$262$	−2.97948e8	−	2.50008e8i	−1.02350	−	0.858815i
$263$	−8.63802e7	−	4.89887e8i	−0.292799	−	1.66054i	−0.676017	−	0.736886i	$-0.736295\pi$
$263$	−8.63802e7	−	4.89887e8i	−0.292799	−	1.66054i	0.383218	−	0.923658i	$-0.374816\pi$
$264$	−4.17564e7	−	1.51981e7i	−0.139672	−	0.0508364i
$265$	−2.85326e8			−0.941847
$266$	2.23869e8	+	8.31836e6i	0.729303	+	0.0270989i
$267$	7.03037e7			0.226042
$268$	−1.66547e8	−	6.06181e7i	−0.528524	−	0.192367i
$269$	−7.62673e7	−	4.32533e8i	−0.238894	−	1.35483i	−0.834256	−	0.551377i	$-0.814102\pi$
$269$	−7.62673e7	−	4.32533e8i	−0.238894	−	1.35483i	0.595362	−	0.803458i	$-0.297009\pi$
$270$	7.16039e6	+	6.00828e6i	0.0221393	+	0.0185771i
$271$	6.00836e7	−	5.04161e7i	0.183385	−	0.153878i	−0.546474	−	0.837476i	$-0.684030\pi$
$271$	6.00836e7	−	5.04161e7i	0.183385	−	0.153878i	0.729859	+	0.683598i	$0.239586\pi$
$272$	−6.14228e6	+	3.48346e7i	−0.0185071	+	0.104959i
$273$	8.90494e7	−	1.54238e8i	0.264888	−	0.458799i
$274$	−8.56637e6	−	1.48374e7i	−0.0251576	−	0.0435743i
$275$	−6.71305e7	+	2.44335e7i	−0.194650	+	0.0708470i
$276$	8.69603e7	−	3.16510e7i	0.248966	−	0.0906161i
$277$	2.47026e8	+	4.27862e8i	0.698336	+	1.20955i	0.969043	+	0.246891i	$0.0794090\pi$
$277$	2.47026e8	+	4.27862e8i	0.698336	+	1.20955i	−0.270708	+	0.962662i	$0.587258\pi$
$278$	8.10869e7	−	1.40447e8i	0.226357	−	0.392062i
$279$	−8.59587e6	+	4.87496e7i	−0.0236960	+	0.134387i
$280$	−5.56826e7	+	4.67232e7i	−0.151588	+	0.127198i
$281$	−1.39521e7	−	1.17072e7i	−0.0375119	−	0.0314762i	0.623839	−	0.781553i	$-0.285572\pi$
$281$	−1.39521e7	−	1.17072e7i	−0.0375119	−	0.0314762i	−0.661351	+	0.750077i	$0.730017\pi$
$282$	−9.50721e7	−	5.39181e8i	−0.252453	−	1.43173i
$283$	5.76479e8	+	2.09821e8i	1.51193	+	0.550296i	0.959117	−	0.283011i	$-0.0913333\pi$
$283$	5.76479e8	+	2.09821e8i	1.51193	+	0.550296i	0.552810	+	0.833307i	$0.313556\pi$
$284$	−1.23868e8			−0.320883
$285$	4.15854e7	+	3.00768e8i	0.106410	+	0.769618i
$286$	−2.94102e7			−0.0743390
$287$	−4.60855e8	−	1.67738e8i	−1.15074	−	0.418836i
$288$	1.30989e7	+	7.42876e7i	0.0323118	+	0.183249i
$289$	−2.57209e8	−	2.15824e8i	−0.626821	−	0.525966i
$290$	1.40215e8	−	1.17654e8i	0.337600	−	0.283280i
$291$	−1.47507e8	+	8.36553e8i	−0.350903	+	1.99007i
$292$	−1.30796e8	+	2.26545e8i	−0.307435	+	0.532493i
$293$	−1.34648e8	−	2.33217e8i	−0.312725	−	0.541655i	0.666226	−	0.745750i	$-0.267908\pi$
$293$	−1.34648e8	−	2.33217e8i	−0.312725	−	0.541655i	−0.978951	+	0.204094i	$0.934575\pi$
$294$	2.70596e7	−	9.84889e6i	0.0621020	−	0.0226033i
$295$	−1.85431e8	+	6.74912e7i	−0.420537	+	0.153063i
$296$	2.89027e7	+	5.00610e7i	0.0647765	+	0.112196i
$297$	−4.99256e6	+	8.64736e6i	−0.0110580	+	0.0191530i
$298$	5.46338e7	−	3.09844e8i	0.119593	−	0.678243i
$299$	4.69191e7	−	3.93698e7i	0.101508	−	0.0851754i
$300$	1.81157e8	+	1.52009e8i	0.387374	+	0.325046i
$301$	−1.21439e8	−	6.88714e8i	−0.256670	−	1.45565i
$302$	3.03731e8	+	1.10549e8i	0.634549	+	0.230957i
$303$	−5.01582e8			−1.03584
$304$	−6.51262e7	+	1.03708e8i	−0.132953	+	0.211716i
$305$	−1.10524e8			−0.223052
$306$	1.49448e8	+	5.43946e7i	0.298171	+	0.108525i
$307$	5.04143e7	+	2.85914e8i	0.0994420	+	0.563963i	0.993295	+	0.115604i	$0.0368804\pi$
$307$	5.04143e7	+	2.85914e8i	0.0994420	+	0.563963i	−0.893853	+	0.448359i	$0.852009\pi$
$308$	−5.94826e7	−	4.99118e7i	−0.116001	−	0.0973365i
$309$	−1.52123e8	+	1.27646e8i	−0.293319	+	0.246124i
$310$	4.52787e6	−	2.56788e7i	0.00863234	−	0.0489564i
$311$	−9.99800e7	+	1.73170e8i	−0.188474	+	0.326447i	−0.944742	−	0.327816i	$-0.893687\pi$
$311$	−9.99800e7	+	1.73170e8i	−0.188474	+	0.326447i	0.756268	+	0.654262i	$0.227021\pi$
$312$	4.86783e7	+	8.43132e7i	0.0907390	+	0.157165i
$313$	4.71547e8	−	1.71629e8i	0.869200	−	0.316363i	0.131357	−	0.991335i	$-0.458067\pi$
$313$	4.71547e8	−	1.71629e8i	0.869200	−	0.316363i	0.737843	+	0.674972i	$0.235844\pi$
$314$	4.82782e8	−	1.75718e8i	0.880029	−	0.320304i
$315$	1.63411e8	+	2.83035e8i	0.294573	+	0.510216i
$316$	4.28060e6	−	7.41423e6i	0.00763133	−	0.0132179i
$317$	−3.63831e7	+	2.06339e8i	−0.0641494	+	0.363809i	0.935787	+	0.352565i	$0.114690\pi$
$317$	−3.63831e7	+	2.06339e8i	−0.0641494	+	0.363809i	−0.999937	+	0.0112444i	$0.996421\pi$
$318$	−7.72917e8	+	6.48554e8i	−1.34784	+	1.13097i
$319$	1.49784e8	+	1.25684e8i	0.258344	+	0.216776i
$320$	−6.89985e6	−	3.91310e7i	−0.0117710	−	0.0667569i
$321$	3.39590e8	+	1.23601e8i	0.573043	+	0.208570i
$322$	1.61709e8			0.269922
$323$	1.20703e8	+	2.28237e8i	0.199301	+	0.376858i
$324$	−2.89160e8			−0.472313
$325$	1.47078e8	+	5.35320e7i	0.237660	+	0.0865011i
$326$	6.45358e7	+	3.66001e8i	0.103167	+	0.585087i
$327$	9.84784e8	+	8.26332e8i	1.55748	+	1.30688i
$328$	2.05370e8	−	1.72326e8i	0.321350	−	0.269645i
$329$	1.66131e8	−	9.42178e8i	0.257197	−	1.45864i
$330$	5.26207e7	−	9.11417e7i	0.0806042	−	0.139611i
$331$	2.26025e8	+	3.91487e8i	0.342577	+	0.593361i	0.984911	−	0.173064i	$-0.0553668\pi$
$331$	2.26025e8	+	3.91487e8i	0.342577	+	0.593361i	−0.642333	+	0.766425i	$0.722034\pi$
$332$	5.32943e8	−	1.93975e8i	0.799277	−	0.290913i
$333$	2.44230e8	−	8.88925e7i	0.362447	−	0.131920i
$334$	2.99276e8	+	5.18361e8i	0.439500	+	0.761237i
$335$	2.09880e8	−	3.63522e8i	0.305009	−	0.528292i
$336$	−4.46348e7	+	2.53136e8i	−0.0641927	+	0.364055i
$337$	4.96244e8	−	4.16398e8i	0.706302	−	0.592658i	−0.217257	−	0.976114i	$-0.569711\pi$
$337$	4.96244e8	−	4.16398e8i	0.706302	−	0.592658i	0.923559	+	0.383457i	$0.125266\pi$
$338$	−3.35185e8	−	2.81253e8i	−0.472145	−	0.396177i
$339$	−2.72806e8	−	1.54716e9i	−0.380324	−	2.15693i
$340$	−7.87218e7	−	2.86524e7i	−0.108622	−	0.0395353i
$341$	2.78544e7			0.0380412
$342$	4.08357e8	+	3.69342e8i	0.552013	+	0.499271i
$343$	−7.21032e8			−0.964773
$344$	3.59234e8	+	1.30750e8i	0.475798	+	0.173176i
$345$	3.80588e7	+	2.15842e8i	0.0498986	+	0.282989i
$346$	−6.94249e7	−	5.82544e7i	−0.0901050	−	0.0756071i
$347$	−1.84861e8	+	1.55117e8i	−0.237516	+	0.199299i	−0.753774	−	0.657133i	$-0.771769\pi$
$347$	−1.84861e8	+	1.55117e8i	−0.237516	+	0.199299i	0.516259	+	0.856433i	$0.327324\pi$
$348$	1.12395e8	−	6.37426e8i	0.142962	−	0.810779i
$349$	5.87481e8	−	1.01755e9i	0.739784	−	1.28134i	−0.212808	−	0.977094i	$-0.568261\pi$
$349$	5.87481e8	−	1.01755e9i	0.739784	−	1.28134i	0.952592	−	0.304250i	$-0.0984059\pi$
$350$	2.06619e8	+	3.57874e8i	0.257592	+	0.446162i
$351$	2.05573e7	−	7.48226e6i	0.0253742	−	0.00923544i
$352$	3.98865e7	−	1.45175e7i	0.0487446	−	0.0177416i
$353$	1.48489e8	+	2.57191e8i	0.179673	+	0.311203i	0.941769	−	0.336262i	$-0.109163\pi$
$353$	1.48489e8	+	2.57191e8i	0.179673	+	0.311203i	−0.762095	+	0.647465i	$0.775829\pi$
$354$	−3.48902e8	+	6.04316e8i	−0.418015	+	0.724024i
$355$	5.09425e7	−	2.88909e8i	0.0604340	−	0.342738i
$356$	−5.14440e7	+	4.31667e7i	−0.0604310	+	0.0507077i
$357$	4.15142e8	+	3.48346e8i	0.482901	+	0.405202i
$358$	−4.08416e7	−	2.31624e8i	−0.0470449	−	0.266805i
$359$	−6.37625e8	−	2.32076e8i	−0.727335	−	0.264728i	−0.0482987	−	0.998833i	$-0.515380\pi$
$359$	−6.37625e8	−	2.32076e8i	−0.727335	−	0.264728i	−0.679036	+	0.734105i	$0.737602\pi$
$360$	−1.78655e8			−0.201816
$361$	8.94629e7	+	8.89384e8i	0.100085	+	0.994979i
$362$	−3.27761e8			−0.363143
$363$	−1.12126e9	−	4.08107e8i	−1.23037	−	0.447817i
$364$	2.95416e7	+	1.67539e8i	0.0321055	+	0.182079i
$365$	−4.74599e8	−	3.98236e8i	−0.510860	−	0.428662i
$366$	−2.99397e8	+	2.51224e8i	−0.319201	+	0.267841i
$367$	4.39409e7	−	2.49201e8i	0.0464021	−	0.263159i	−0.952777	−	0.303671i	$-0.901788\pi$
$367$	4.39409e7	−	2.49201e8i	0.0464021	−	0.263159i	0.999179	+	0.0405116i	$0.0128988\pi$
$368$	−4.41986e7	+	7.65541e7i	−0.0462318	+	0.0800758i
$369$	−6.02695e8	−	1.04390e9i	−0.624461	−	1.08160i
$370$	−1.28648e8	+	4.68241e7i	−0.132038	+	0.0480578i
$371$	−1.65677e9	+	6.03016e8i	−1.68444	+	0.613085i
$372$	−4.61033e7	−	7.98532e7i	−0.0464335	−	0.0804252i
$373$	−3.86354e8	+	6.69185e8i	−0.385483	+	0.667676i	−0.991836	−	0.127520i	$-0.959298\pi$
$373$	−3.86354e8	+	6.69185e8i	−0.385483	+	0.667676i	0.606353	+	0.795195i	$0.292632\pi$
$374$	1.55400e7	−	8.81315e7i	0.0153603	−	0.0871125i
$375$	−1.03683e9	+	8.70006e8i	−1.01531	+	0.851947i
$376$	4.00627e8	+	3.36166e8i	0.388671	+	0.326134i
$377$	−7.43891e7	−	4.21882e8i	−0.0715014	−	0.405505i
$378$	5.42756e7	+	1.97547e7i	0.0516873	+	0.0188126i
$379$	1.15131e8			0.108631			0.0543156	−	0.998524i	$-0.482702\pi$
$379$	1.15131e8			0.108631			0.0543156	+	0.998524i	$0.482702\pi$
$380$	−2.15102e8	−	1.94551e8i	−0.201096	−	0.181882i
$381$	−2.53263e9			−2.34604
$382$	7.73694e8	+	2.81602e8i	0.710146	+	0.258472i
$383$	3.37038e8	+	1.91144e9i	0.306538	+	1.73846i	0.616178	+	0.787607i	$0.288680\pi$
$383$	3.37038e8	+	1.91144e9i	0.306538	+	1.73846i	−0.309640	+	0.950854i	$0.600209\pi$
$384$	−1.07637e8	−	9.03181e7i	−0.0970067	−	0.0813983i
$385$	1.40877e8	−	1.18210e8i	0.125813	−	0.105570i
$386$	1.88169e7	−	1.06716e8i	0.0166530	−	0.0944438i
$387$	8.59422e8	−	1.48856e9i	0.753734	−	1.30550i
$388$	−4.05709e8	−	7.02709e8i	−0.352618	−	0.610751i
$389$	−1.24994e9	+	4.54939e8i	−1.07662	+	0.391859i	−0.818650	−	0.574293i	$-0.805277\pi$
$389$	−1.24994e9	+	4.54939e8i	−1.07662	+	0.391859i	−0.257974	+	0.966152i	$0.583055\pi$
$390$	−2.16671e8	+	7.88617e7i	−0.184958	+	0.0673194i
$391$	9.31854e7	+	1.61402e8i	0.0788368	+	0.136549i
$392$	−1.37533e7	+	2.38215e7i	−0.0115321	+	0.0199741i
$393$	5.65645e8	−	3.20793e9i	0.470078	−	2.66595i
$394$	−4.38392e8	+	3.67855e8i	−0.361099	+	0.302998i
$395$	1.55324e7	+	1.30332e7i	0.0126809	+	0.0106405i
$396$	−3.31402e7	−	1.87947e8i	−0.0268177	−	0.152091i
$397$	1.62803e9	+	5.92555e8i	1.30586	+	0.475293i	0.898900	−	0.438154i	$-0.144367\pi$
$397$	1.62803e9	+	5.92555e8i	1.30586	+	0.475293i	0.406958	+	0.913447i	$0.366590\pi$
$398$	9.19943e8			0.731425
$399$	8.77123e8	+	1.65856e9i	0.691282	+	1.30715i
$400$	−2.25894e8			−0.176479
$401$	−6.16486e8	−	2.24383e8i	−0.477439	−	0.173774i	0.0920800	−	0.995752i	$-0.470648\pi$
$401$	−6.16486e8	−	2.24383e8i	−0.477439	−	0.173774i	−0.569519	+	0.821978i	$0.692871\pi$
$402$	−2.57756e8	−	1.46180e9i	−0.197887	−	1.12227i
$403$	−4.67494e7	−	3.92274e7i	−0.0355802	−	0.0298554i
$404$	3.67027e8	−	3.07973e8i	0.276926	−	0.232368i
$405$	1.18921e8	−	6.74433e8i	0.0889538	−	0.504482i
$406$	5.65519e8	−	9.79508e8i	0.419379	−	0.726385i
$407$	−7.31238e7	−	1.26654e8i	−0.0537623	−	0.0931191i
$408$	−2.78377e8	+	1.01321e8i	−0.202919	+	0.0738564i
$409$	1.87089e9	−	6.80948e8i	1.35212	−	0.492133i	0.438513	−	0.898725i	$-0.355505\pi$
$409$	1.87089e9	−	6.80948e8i	1.35212	−	0.492133i	0.913610	+	0.406592i	$0.133283\pi$
$410$	3.17470e8	+	5.49874e8i	0.227488	+	0.394021i
$411$	7.17438e7	−	1.24264e8i	0.0509727	−	0.0882873i
$412$	3.29392e7	−	1.86808e8i	0.0232046	−	0.131600i
$413$	−9.34084e8	+	7.83790e8i	−0.652471	+	0.547488i
$414$	3.04465e8	+	2.55476e8i	0.210880	+	0.176949i
$415$	2.33246e8	+	1.32281e9i	0.160194	+	0.908506i
$416$	−8.73883e7	−	3.18068e7i	−0.0595151	−	0.0216617i
$417$	1.35821e9			0.917259
$418$	1.64769e8	−	2.62380e8i	0.110347	−	0.175717i
$419$	−1.62724e9			−1.08070			−0.540348	−	0.841442i	$-0.681707\pi$
$419$	−1.62724e9			−1.08070			−0.540348	+	0.841442i	$0.681707\pi$
$420$	−5.72056e8	−	2.08211e8i	−0.376761	−	0.137130i
$421$	3.62910e8	+	2.05817e9i	0.237035	+	1.34429i	0.838286	+	0.545231i	$0.183558\pi$
$421$	3.62910e8	+	2.05817e9i	0.237035	+	1.34429i	−0.601251	+	0.799060i	$0.705331\pi$
$422$	8.51882e8	+	7.14814e8i	0.551805	+	0.463020i
$423$	1.80129e9	−	1.51146e9i	1.15716	−	0.970972i
$424$	1.67360e8	−	9.49146e8i	0.106628	−	0.604717i
$425$	−2.38130e8	+	4.12453e8i	−0.150471	+	0.260623i
$426$	−5.18702e8	−	8.98418e8i	−0.325076	−	0.563047i
$427$	−6.41768e8	+	2.33584e8i	−0.398915	+	0.145193i
$428$	−3.24382e8	+	1.18066e8i	−0.199988	+	0.0727897i
$429$	−1.23156e8	−	2.13312e8i	−0.0753103	−	0.130441i
$430$	−4.52700e8	+	7.84100e8i	−0.274582	+	0.475589i
$431$	2.21564e8	−	1.25655e9i	0.133300	−	0.755979i	−0.842729	−	0.538338i	$-0.819052\pi$
$431$	2.21564e8	−	1.25655e9i	0.133300	−	0.755979i	0.976029	−	0.217642i	$-0.0698364\pi$
$432$	−2.41867e7	+	2.02951e7i	−0.0144339	+	0.0121115i
$433$	1.66899e9	+	1.40045e9i	0.987974	+	0.829009i	0.985273	−	0.170987i	$-0.0546957\pi$
$433$	1.66899e9	+	1.40045e9i	0.987974	+	0.829009i	0.00270117	+	0.999996i	$0.499140\pi$
$434$	−2.79789e7	−	1.58676e8i	−0.0164292	−	0.0931747i
$435$	1.44050e9	+	5.24300e8i	0.839076	+	0.305399i
$436$	−1.22798e9			−0.709556
$437$	8.83715e7	+	6.39151e8i	0.0506556	+	0.366369i
$438$	−2.19084e9			−1.24581
$439$	2.33623e9	+	8.50318e8i	1.31792	+	0.479685i	0.902792	−	0.430077i	$-0.141514\pi$
$439$	2.33623e9	+	8.50318e8i	1.31792	+	0.479685i	0.415130	+	0.909762i	$0.363736\pi$
$440$	1.74566e7	+	9.90013e7i	0.00976956	+	0.0554059i
$441$	9.47408e7	+	7.94970e7i	0.0526020	+	0.0441383i
$442$	−1.50197e8	+	1.26030e8i	−0.0827339	+	0.0694220i
$443$	−4.05788e7	+	2.30134e8i	−0.0221762	+	0.125767i	−0.993886	−	0.110410i	$-0.964784\pi$
$443$	−4.05788e7	+	2.30134e8i	−0.0221762	+	0.125767i	0.971710	+	0.236177i	$0.0758947\pi$
$444$	−2.42062e8	+	4.19263e8i	−0.131246	+	0.227324i
$445$	−7.95244e7	−	1.37740e8i	−0.0427800	−	0.0740971i
$446$	−7.25544e8	+	2.64076e8i	−0.387250	+	0.140948i
$447$	2.47608e9	−	9.01218e8i	1.31126	−	0.477258i
$448$	−1.22765e8	−	2.12636e8i	−0.0645064	−	0.111728i
$449$	4.02385e7	−	6.96950e7i	0.0209787	−	0.0363362i	−0.855345	−	0.518058i	$-0.826655\pi$
$449$	4.02385e7	−	6.96950e7i	0.0209787	−	0.0363362i	0.876324	+	0.481722i	$0.159988\pi$
$450$	−1.76368e8	+	1.00023e9i	−0.0912379	+	0.517436i
$451$	−5.19585e8	+	4.35984e8i	−0.266710	+	0.223796i
$452$	1.14958e9	+	9.64613e8i	0.585538	+	0.491325i
$453$	4.70068e8	+	2.66589e9i	0.237584	+	1.34741i
$454$	1.76596e9	+	6.42757e8i	0.885698	+	0.322368i
$455$	−4.02915e8			−0.200527
$456$	−1.02491e9	−	3.80828e7i	−0.506184	−	0.0188084i
$457$	−1.08118e9			−0.529896			−0.264948	−	0.964263i	$-0.585355\pi$
$457$	−1.08118e9			−0.529896			−0.264948	+	0.964263i	$0.585355\pi$
$458$	−4.60144e8	−	1.67479e8i	−0.223802	−	0.0814574i
$459$	1.15593e7	+	6.55563e7i	0.00557942	+	0.0316424i
$460$	−1.60377e8	−	1.34572e8i	−0.0768226	−	0.0644618i
$461$	−1.15465e9	+	9.68870e8i	−0.548907	+	0.460588i	−0.874571	−	0.484898i	$-0.838857\pi$
$461$	−1.15465e9	+	9.68870e8i	−0.548907	+	0.460588i	0.325664	+	0.945486i	$0.394412\pi$
$462$	1.12926e8	−	6.40434e8i	0.0532778	−	0.302153i
$463$	1.00177e9	−	1.73512e9i	0.469067	−	0.812448i	−0.530307	−	0.847805i	$-0.677924\pi$
$463$	1.00177e9	−	1.73512e9i	0.469067	−	0.812448i	0.999375	+	0.0353571i	$0.0112569\pi$
$464$	3.09137e8	+	5.35441e8i	0.143661	+	0.248828i
$465$	2.05209e8	−	7.46901e7i	0.0946481	−	0.0344491i
$466$	5.70735e8	−	2.07731e8i	0.261267	−	0.0950932i
$467$	−8.50318e8	−	1.47279e9i	−0.386342	−	0.669165i	0.605612	−	0.795760i	$-0.292928\pi$
$467$	−8.50318e8	−	1.47279e9i	−0.386342	−	0.669165i	−0.991954	+	0.126595i	$0.959595\pi$
$468$	−2.09066e8	+	3.62112e8i	−0.0942805	+	0.163299i
$469$	4.50409e8	−	2.55439e9i	0.201605	−	1.14336i
$470$	−9.48832e8	+	7.96164e8i	−0.421548	+	0.353720i
$471$	3.29614e9	+	2.76579e9i	1.45356	+	1.21968i
$472$	−1.15746e8	−	6.56429e8i	−0.0506652	−	0.287336i
$473$	−9.08860e8	−	3.30798e8i	−0.394896	−	0.143731i
$474$	7.17005e7			0.0309242
$475$	−1.30158e9	+	1.01223e9i	−0.557240	+	0.433363i
$476$	−5.17661e8			−0.219999
$477$	−4.07204e9	−	1.48210e9i	−1.71790	−	0.625264i
$478$	−2.08604e8	−	1.18305e9i	−0.0873625	−	0.495458i
$479$	2.27636e6	+	1.91009e6i	0.000946381	+	0.000794108i	0.643261	−	0.765647i	$-0.277581\pi$
$479$	2.27636e6	+	1.91009e6i	0.000946381	+	0.000794108i	−0.642314	+	0.766441i	$0.722026\pi$
$480$	2.54924e8	−	2.13907e8i	0.105212	−	0.0882835i
$481$	−5.56400e7	+	3.15550e8i	−0.0227971	+	0.129289i
$482$	1.27196e9	−	2.20309e9i	0.517378	−	0.896125i
$483$	6.77160e8	+	1.17288e9i	0.273449	+	0.473628i
$484$	1.07105e9	−	3.89831e8i	0.429390	−	0.156285i
$485$	1.80584e9	−	6.57273e8i	0.718760	−	0.261607i
$486$	−1.27830e9	−	2.21407e9i	−0.505131	−	0.874913i
$487$	−4.99699e8	+	8.65504e8i	−0.196045	+	0.339561i	−0.947243	−	0.320517i	$-0.896143\pi$
$487$	−4.99699e8	+	8.65504e8i	−0.196045	+	0.339561i	0.751197	+	0.660078i	$0.229477\pi$
$488$	6.48286e7	−	3.67661e8i	0.0252521	−	0.143212i
$489$	−2.38436e9	+	2.00071e9i	−0.922126	+	0.773756i
$490$	−4.99047e7	−	4.18750e7i	−0.0191626	−	0.0160794i
$491$	−7.76183e8	−	4.40195e9i	−0.295923	−	1.67826i	−0.663427	−	0.748241i	$-0.730899\pi$
$491$	−7.76183e8	−	4.40195e9i	−0.295923	−	1.67826i	0.367504	−	0.930022i	$-0.380213\pi$
$492$	2.10987e9	+	7.67930e8i	0.798690	+	0.290699i
$493$	1.30353e9			0.489956
$494$	−6.46049e8	+	2.08320e8i	−0.241113	+	0.0777475i
$495$	4.51995e8			0.167500
$496$	8.27657e7	+	3.01243e7i	0.0304554	+	0.0110849i
$497$	−3.14787e8	−	1.78525e9i	−0.115019	−	0.652305i
$498$	3.63862e9	+	3.05316e9i	1.32018	+	1.10776i
$499$	1.29396e9	−	1.08576e9i	0.466195	−	0.391184i	−0.379210	−	0.925311i	$-0.623804\pi$
$499$	1.29396e9	−	1.08576e9i	0.466195	−	0.391184i	0.845404	+	0.534127i	$0.179360\pi$
$500$	2.24506e8	−	1.27324e9i	0.0803217	−	0.455527i
$501$	−2.50645e9	+	4.34130e9i	−0.890486	+	1.54237i
$502$	−1.45604e9	−	2.52194e9i	−0.513702	−	0.889758i
$503$	−2.24454e9	+	8.16945e8i	−0.786392	+	0.286223i	−0.703835	−	0.710363i	$-0.748531\pi$
$503$	−2.24454e9	+	8.16945e8i	−0.786392	+	0.286223i	−0.0825566	+	0.996586i	$0.526309\pi$
$504$	−1.03738e9	+	3.77574e8i	−0.360935	+	0.131370i
$505$	5.67367e8	+	9.82708e8i	0.196040	+	0.339551i
$506$	1.11822e8	−	1.93682e8i	0.0383708	−	0.0664602i
$507$	6.36338e8	−	3.60885e9i	0.216850	−	1.22982i
$508$	1.85323e9	−	1.55504e9i	0.627199	−	0.526283i
$509$	−4.51126e8	−	3.78539e8i	−0.151630	−	0.127233i	0.563817	−	0.825900i	$-0.309332\pi$
$509$	−4.51126e8	−	3.78539e8i	−0.151630	−	0.127233i	−0.715447	+	0.698667i	$0.753777\pi$
$510$	−1.21833e8	−	6.90952e8i	−0.0406697	−	0.230649i
$511$	−3.59745e9	−	1.30937e9i	−1.19267	−	0.434098i
$512$	1.34218e8			0.0441942
$513$	−4.84193e7	+	2.25319e8i	−0.0158346	+	0.0736864i
$514$	−3.66527e9			−1.19052
$515$	4.22161e8	+	1.53654e8i	0.136192	+	0.0495700i
$516$	5.55967e8	+	3.15305e9i	0.178146	+	1.01031i
$517$	−1.01358e9	−	8.50498e8i	−0.322584	−	0.270680i
$518$	−6.48050e8	+	5.43779e8i	−0.204859	+	0.171897i
$519$	1.31801e8	−	7.47481e8i	0.0413841	−	0.234701i
$520$	1.10125e8	−	1.90743e8i	0.0343459	−	0.0594889i
$521$	9.83345e8	+	1.70320e9i	0.304631	+	0.527636i	0.977179	−	0.212417i	$-0.0681336\pi$
$521$	9.83345e8	+	1.70320e9i	0.304631	+	0.527636i	−0.672548	+	0.740053i	$0.734800\pi$
$522$	2.61223e9	−	9.50775e8i	0.803832	−	0.292571i
$523$	−2.50001e9	+	9.09930e8i	−0.764163	+	0.278133i	−0.694553	−	0.719442i	$-0.744398\pi$
$523$	−2.50001e9	+	9.09930e8i	−0.764163	+	0.278133i	−0.0696101	+	0.997574i	$0.522176\pi$
$524$	1.55577e9	+	2.69468e9i	0.472375	+	0.818178i
$525$	−1.73044e9	+	2.99721e9i	−0.521915	+	0.903983i
$526$	−6.91042e8	+	3.91909e9i	−0.207040	+	1.17418i
$527$	1.42252e8	−	1.19364e8i	0.0423371	−	0.0355251i
$528$	2.72321e8	+	2.28504e8i	0.0805123	+	0.0675578i
$529$	−5.10364e8	−	2.89442e9i	−0.149894	−	0.850094i
$530$	2.14495e9	+	7.80697e8i	0.625823	+	0.227781i
$531$	−2.99696e9			−0.868661
$532$	−1.66018e9	−	6.75075e8i	−0.478041	−	0.194384i
$533$	1.48604e9			0.425094
$534$	−5.28511e8	−	1.92362e8i	−0.150196	−	0.0546670i
$535$	−1.41968e8	−	8.05142e8i	−0.0400823	−	0.227318i
$536$	1.08616e9	+	9.11398e8i	0.304662	+	0.255642i
$537$	1.50895e9	−	1.26616e9i	0.420498	−	0.352840i
$538$	−6.10138e8	+	3.46026e9i	−0.168924	+	0.958013i
$539$	3.47959e7	−	6.02683e7i	0.00957122	−	0.0165778i
$540$	−3.73889e7	−	6.47595e7i	−0.0102180	−	0.0176980i
$541$	8.57158e8	−	3.11980e8i	0.232740	−	0.0847104i	−0.223018	−	0.974814i	$-0.571591\pi$
$541$	8.57158e8	−	3.11980e8i	0.232740	−	0.0847104i	0.455757	+	0.890104i	$0.349368\pi$
$542$	−5.89628e8	+	2.14607e8i	−0.159067	+	0.0578957i
$543$	−1.37251e9	−	2.37725e9i	−0.367888	−	0.637200i
$544$	1.41488e8	−	2.45064e8i	0.0376811	−	0.0652656i
$545$	5.05021e8	−	2.86412e9i	0.133635	−	0.757884i
$546$	−1.09145e9	+	9.15837e8i	−0.286966	+	0.240793i
$547$	−4.78019e9	−	4.01105e9i	−1.24879	−	1.04786i	−0.996784	−	0.0801331i	$-0.974465\pi$
$547$	−4.78019e9	−	4.01105e9i	−1.24879	−	1.04786i	−0.252005	−	0.967726i	$-0.581090\pi$
$548$	2.38006e7	+	1.34980e8i	0.00617810	+	0.0350378i
$549$	−1.57735e9	−	5.74107e8i	−0.406840	−	0.148078i
$550$	5.71510e8			0.146472
$551$	4.18053e9	+	1.69992e9i	1.06464	+	0.432909i
$552$	−7.40330e8			−0.187343
$553$	1.17735e8	+	4.28522e7i	0.0296053	+	0.0107754i
$554$	−6.86331e8	−	3.89238e9i	−0.171494	−	0.972592i
$555$	−8.78333e8	−	7.37009e8i	−0.218089	−	0.182998i
$556$	−9.93859e8	+	8.33947e8i	−0.245224	+	0.205767i
$557$	1.28472e8	−	7.28602e8i	0.0315004	−	0.178647i	−0.964998	−	0.262256i	$-0.915533\pi$
$557$	1.28472e8	−	7.28602e8i	0.0315004	−	0.178647i	0.996499	+	0.0836087i	$0.0266446\pi$
$558$	1.98006e8	−	3.42957e8i	0.0482458	−	0.0835642i
$559$	1.05952e9	+	1.83514e9i	0.256548	+	0.444354i
$560$	5.46438e8	−	1.98887e8i	0.131487	−	0.0478574i
$561$	7.04292e8	−	2.56341e8i	0.168416	−	0.0612983i
$562$	7.28529e7	+	1.26185e8i	0.0173129	+	0.0299868i
$563$	6.42971e8	−	1.11366e9i	0.151849	−	0.263010i	−0.780058	−	0.625707i	$-0.784811\pi$
$563$	6.42971e8	−	1.11366e9i	0.151849	−	0.263010i	0.931907	+	0.362697i	$0.118144\pi$
$564$	−7.60577e8	+	4.31345e9i	−0.178512	+	1.01239i
$565$	−2.72263e9	+	2.28456e9i	−0.635067	+	0.532884i
$566$	−3.75960e9	−	3.15468e9i	−0.871533	−	0.731303i
$567$	−7.34842e8	−	4.16749e9i	−0.169298	−	0.960139i
$568$	9.31186e8	+	3.38924e8i	0.213215	+	0.0776038i
$569$	6.01815e9			1.36953			0.684763	−	0.728766i	$-0.259906\pi$
$569$	6.01815e9			1.36953			0.684763	+	0.728766i	$0.259906\pi$
$570$	5.10331e8	−	2.37482e9i	0.115422	−	0.537118i
$571$	5.50177e9			1.23673			0.618366	−	0.785890i	$-0.287795\pi$
$571$	5.50177e9			1.23673			0.618366	+	0.785890i	$0.287795\pi$
$572$	2.21092e8	+	8.04710e7i	0.0493955	+	0.0179785i
$573$	1.19741e9	+	6.79082e9i	0.265889	+	1.50793i
$574$	3.00554e9	+	2.52195e9i	0.663332	+	0.556602i
$575$	−9.11751e8	+	7.65050e8i	−0.200004	+	0.167823i
$576$	1.04791e8	−	5.94301e8i	0.0228479	−	0.129577i
$577$	2.35381e9	−	4.07691e9i	0.510100	−	0.883520i	−0.489831	−	0.871817i	$-0.662942\pi$
$577$	2.35381e9	−	4.07691e9i	0.510100	−	0.883520i	0.999932	−	0.0117024i	$-0.00372507\pi$
$578$	1.34305e9	+	2.32623e9i	0.289298	+	0.501078i
$579$	8.52806e8	−	3.10396e8i	0.182589	−	0.0664571i
$580$	−1.37599e9	+	5.00821e8i	−0.292832	+	0.106582i
$581$	4.15003e9	+	7.18806e9i	0.877879	+	1.52053i
$582$	3.39783e9	−	5.88522e9i	0.714450	−	1.23746i
$583$	−4.23420e8	+	2.40134e9i	−0.0884976	+	0.501895i
$584$	1.60312e9	−	1.34518e9i	0.333060	−	0.279470i
$585$	−7.58605e8	−	6.36545e8i	−0.156664	−	0.131457i
$586$	3.74101e8	+	2.12163e9i	0.0767976	+	0.435541i
$587$	−5.08658e9	−	1.85136e9i	−1.03799	−	0.377797i	−0.233871	−	0.972268i	$-0.575139\pi$
$587$	−5.08658e9	−	1.85136e9i	−1.03799	−	0.377797i	−0.804117	+	0.594470i	$0.797362\pi$
$588$	−2.30370e8			−0.0467310
$589$	6.11875e8	−	1.97300e8i	0.123384	−	0.0397854i
$590$	1.57865e9			0.316449
$591$	−4.50383e9	−	1.63926e9i	−0.897482	−	0.326657i
$592$	−8.03025e7	−	4.55418e8i	−0.0159075	−	0.0902161i
$593$	−2.65279e8	−	2.22595e8i	−0.0522409	−	0.0438353i	0.616293	−	0.787517i	$-0.288634\pi$
$593$	−2.65279e8	−	2.22595e8i	−0.0522409	−	0.0438353i	−0.668534	+	0.743681i	$0.733078\pi$
$594$	6.11923e7	−	5.13465e7i	0.0119797	−	0.0100521i
$595$	2.12895e8	−	1.20739e9i	0.0414339	−	0.234983i
$596$	−1.25849e9	+	2.17977e9i	−0.243494	+	0.421745i
$597$	3.85228e9	+	6.67235e9i	0.740982	+	1.28342i
$598$	−4.60439e8	+	1.67586e8i	−0.0880476	+	0.0320467i
$599$	5.68182e9	−	2.06802e9i	1.08017	−	0.393151i	0.260202	−	0.965554i	$-0.416211\pi$
$599$	5.68182e9	−	2.06802e9i	1.08017	−	0.393151i	0.819973	+	0.572403i	$0.193989\pi$
$600$	−9.45935e8	−	1.63841e9i	−0.178785	−	0.309665i
$601$	1.13335e9	−	1.96302e9i	0.212962	−	0.368862i	−0.739678	−	0.672961i	$-0.765022\pi$
$601$	1.13335e9	−	1.96302e9i	0.212962	−	0.368862i	0.952640	+	0.304099i	$0.0983555\pi$
$602$	−9.71511e8	+	5.50971e9i	−0.181493	+	1.02930i
$603$	4.88359e9	−	4.09782e9i	0.907045	−	0.761101i
$604$	−1.98083e9	−	1.66211e9i	−0.365778	−	0.306925i
$605$	4.68753e8	+	2.65843e9i	0.0860599	+	0.488070i
$606$	3.77066e9	+	1.37241e9i	0.688277	+	0.250512i
$607$	−1.07558e10			−1.95201			−0.976004	−	0.217753i	$-0.930127\pi$
$607$	−1.07558e10			−1.95201			−0.976004	+	0.217753i	$0.930127\pi$
$608$	7.73350e8	−	6.01430e8i	0.139545	−	0.108523i
$609$	9.47250e9			1.69943
$610$	8.30867e8	+	3.02411e8i	0.148210	+	0.0539440i
$611$	5.03389e8	+	2.85486e9i	0.0892811	+	0.506338i
$612$	−9.74649e8	−	8.17828e8i	−0.171877	−	0.144222i
$613$	−6.58822e9	+	5.52818e9i	−1.15520	+	0.969327i	−0.999828	−	0.0185295i	$-0.994102\pi$
$613$	−6.58822e9	+	5.52818e9i	−1.15520	+	0.969327i	−0.155370	+	0.987856i	$0.549657\pi$
$614$	4.03315e8	−	2.28731e9i	0.0703161	−	0.398782i
$615$	−2.65882e9	+	4.60522e9i	−0.460921	+	0.798339i
$616$	3.10596e8	+	5.37968e8i	0.0535381	+	0.0927308i
$617$	2.78762e9	−	1.01461e9i	0.477789	−	0.173901i	−0.0918887	−	0.995769i	$-0.529290\pi$
$617$	2.78762e9	−	1.01461e9i	0.477789	−	0.173901i	0.569677	+	0.821868i	$0.307068\pi$
$618$	1.49285e9	−	5.43353e8i	0.254423	−	0.0926024i
$619$	3.92262e9	+	6.79418e9i	0.664751	+	1.15138i	0.979353	+	0.202159i	$0.0647957\pi$
$619$	3.92262e9	+	6.79418e9i	0.664751	+	1.15138i	−0.314602	+	0.949224i	$0.601871\pi$
$620$	−1.04300e8	+	1.80653e8i	−0.0175757	+	0.0304420i
$621$	−2.88876e7	+	1.63830e8i	−0.00484051	+	0.0274519i
$622$	1.22543e9	−	1.02825e9i	0.204184	−	0.171330i
$623$	−7.52872e8	−	6.31734e8i	−0.124742	−	0.104671i
$624$	−1.35246e8	−	7.67020e8i	−0.0222833	−	0.126375i
$625$	−1.17139e9	−	4.26351e8i	−0.191921	−	0.0698534i
$626$	−4.01448e9			−0.654062
$627$	2.59302e9	+	9.63494e7i	0.420115	+	0.0156103i
$628$	−4.11012e9			−0.662210
$629$	−9.16187e8	−	3.33465e8i	−0.146794	−	0.0534285i
$630$	−4.54015e8	−	2.57485e9i	−0.0723400	−	0.410260i
$631$	−8.95319e9	−	7.51262e9i	−1.41865	−	1.19039i	−0.952059	−	0.305915i	$-0.901038\pi$
$631$	−8.95319e9	−	7.51262e9i	−1.41865	−	1.19039i	−0.466590	−	0.884474i	$-0.654518\pi$
$632$	−5.24661e7	+	4.40243e7i	−0.00826741	+	0.00693718i
$633$	−1.61727e9	+	9.17200e9i	−0.253437	+	1.43731i
$634$	8.38088e8	−	1.45161e9i	0.130610	−	0.226224i
$635$	2.86480e9	+	4.96198e9i	0.444003	+	0.769036i
$636$	7.58498e9	−	2.76071e9i	1.16911	−	0.425521i
$637$	−1.43276e8	+	5.21480e7i	−0.0219626	+	0.00799374i
$638$	−7.82116e8	−	1.35466e9i	−0.119234	−	0.206519i
$639$	2.22774e9	−	3.85857e9i	0.337763	−	0.585023i
$640$	−5.51988e7	+	3.13048e8i	−0.00832338	+	0.0472042i
$641$	3.17077e9	−	2.66059e9i	0.475512	−	0.399002i	−0.373288	−	0.927715i	$-0.621770\pi$
$641$	3.17077e9	−	2.66059e9i	0.475512	−	0.399002i	0.848800	+	0.528713i	$0.177325\pi$
$642$	−2.21469e9	−	1.85834e9i	−0.330324	−	0.277175i
$643$	−8.20149e8	−	4.65130e9i	−0.121662	−	0.689978i	−0.983235	−	0.182345i	$-0.941631\pi$
$643$	−8.20149e8	−	4.65130e9i	−0.121662	−	0.689978i	0.861573	−	0.507634i	$-0.169480\pi$
$644$	−1.21565e9	−	4.42462e8i	−0.179353	−	0.0652793i
$645$	−7.58278e9			−1.11268
$646$	−2.82894e8	−	2.04605e9i	−0.0412867	−	0.298608i
$647$	1.05042e10			1.52474			0.762371	−	0.647140i	$-0.224035\pi$
$647$	1.05042e10			1.52474			0.762371	+	0.647140i	$0.224035\pi$
$648$	2.17377e9	+	7.91187e8i	0.313835	+	0.114226i
$649$	2.92837e8	+	1.66076e9i	0.0420504	+	0.238480i
$650$	−9.59193e8	−	8.04858e8i	−0.136996	−	0.114954i
$651$	1.03372e9	−	8.67392e8i	0.146848	−	0.123220i
$652$	5.16286e8	−	2.92800e9i	0.0729498	−	0.413719i
$653$	3.32880e8	−	5.76565e8i	0.0467834	−	0.0810311i	−0.841685	−	0.539968i	$-0.818436\pi$
$653$	3.32880e8	−	5.76565e8i	0.0467834	−	0.0810311i	0.888469	+	0.458937i	$0.151770\pi$
$654$	−5.14218e9	−	8.90651e9i	−0.718828	−	1.24505i
$655$	−6.92488e9	+	2.52045e9i	−0.962870	+	0.350456i
$656$	−2.01539e9	+	7.33541e8i	−0.278737	+	0.101452i
$657$	−4.70466e9	−	8.14871e9i	−0.647216	−	1.12101i
$658$	−3.82685e9	+	6.62830e9i	−0.523662	+	0.907009i
$659$	−1.30015e9	+	7.37352e9i	−0.176968	+	1.00363i	0.758880	+	0.651231i	$0.225747\pi$
$659$	−1.30015e9	+	7.37352e9i	−0.176968	+	1.00363i	−0.935848	+	0.352404i	$0.885364\pi$
$660$	−6.44956e8	+	5.41183e8i	−0.0873226	+	0.0732724i
$661$	−1.02375e9	−	8.59026e8i	−0.137876	−	0.115691i	0.571242	−	0.820782i	$-0.306462\pi$
$661$	−1.02375e9	−	8.59026e8i	−0.137876	−	0.115691i	−0.709117	+	0.705091i	$0.750906\pi$
$662$	−6.27981e8	−	3.56146e9i	−0.0841286	−	0.477117i
$663$	−1.54305e9	−	5.61625e8i	−0.205628	−	0.0748426i
$664$	−4.53717e9			−0.601446
$665$	2.25731e9	−	3.59456e9i	0.297657	−	0.473991i
$666$	−2.07923e9			−0.272737
$667$	3.06116e9	+	1.11417e9i	0.399434	+	0.145382i
$668$	−8.31499e8	−	4.71567e9i	−0.107931	−	0.612104i
$669$	−4.95358e9	−	4.15655e9i	−0.639628	−	0.536712i
$670$	−2.57243e9	+	2.15853e9i	−0.330432	+	0.277265i
$671$	−1.64016e8	+	9.30181e8i	−0.0209584	+	0.118861i
$672$	1.02817e9	−	1.78083e9i	0.130698	−	0.226376i
$673$	−7.76909e9	−	1.34565e10i	−0.982465	−	1.70168i	−0.652699	−	0.757617i	$-0.726363\pi$
$673$	−7.76909e9	−	1.34565e10i	−0.982465	−	1.70168i	−0.329766	−	0.944063i	$-0.606970\pi$
$674$	−4.86987e9	+	1.77249e9i	−0.612643	+	0.222984i
$675$	−3.99478e8	+	1.45398e8i	−0.0499954	+	0.0181968i
$676$	1.75021e9	+	3.03145e9i	0.217910	+	0.377431i
$677$	2.09116e9	−	3.62199e9i	0.259016	−	0.448629i	−0.706963	−	0.707251i	$-0.749935\pi$
$677$	2.09116e9	−	3.62199e9i	0.259016	−	0.448629i	0.965979	+	0.258622i	$0.0832685\pi$
$678$	−2.18244e9	+	1.23773e10i	−0.268930	+	1.52518i
$679$	9.09672e9	−	7.63305e9i	1.11517	−	0.935738i
$680$	5.13397e8	+	4.30791e8i	0.0626141	+	0.0525394i
$681$	2.73308e9	+	1.55001e10i	0.331618	+	1.88070i
$682$	−2.09397e8	−	7.62143e7i	−0.0252770	−	0.00920006i
$683$	3.22916e9			0.387808			0.193904	−	0.981021i	$-0.437885\pi$
$683$	3.22916e9			0.387808			0.193904	+	0.981021i	$0.437885\pi$
$684$	−2.05927e9	−	3.89387e9i	−0.246046	−	0.465249i
$685$	−3.24613e8			−0.0385877
$686$	5.42039e9	+	1.97286e9i	0.641056	+	0.233325i
$687$	−7.12140e8	−	4.03875e9i	−0.0837948	−	0.475224i
$688$	−2.34280e9	−	1.96584e9i	−0.274268	−	0.230139i
$689$	4.09245e9	−	3.43397e9i	0.476668	−	0.399972i
$690$	3.04470e8	−	1.72674e9i	0.0352836	−	0.200103i
$691$	−5.00360e9	+	8.66649e9i	−0.576912	+	0.999240i	0.418919	+	0.908023i	$0.362409\pi$
$691$	−5.00360e9	+	8.66649e9i	−0.576912	+	0.999240i	−0.995831	+	0.0912170i	$0.970924\pi$
$692$	3.62511e8	+	6.27888e8i	0.0415863	+	0.0720295i
$693$	2.62456e9	−	9.55261e8i	0.299564	−	0.109032i
$694$	1.81413e9	−	6.60288e8i	0.206020	−	0.0749851i
$695$	−1.53635e9	−	2.66104e9i	−0.173598	−	0.300680i
$696$	−2.58904e9	+	4.48435e9i	−0.291076	+	0.504158i
$697$	−7.85205e8	+	4.45312e9i	−0.0878351	+	0.498138i
$698$	−7.20059e9	+	6.04201e9i	−0.801446	+	0.672493i
$699$	3.89664e9	+	3.26967e9i	0.431539	+	0.362104i
$700$	−5.74064e8	−	3.25568e9i	−0.0632582	−	0.358755i
$701$	−1.54769e10	−	5.63313e9i	−1.69696	−	0.617641i	−0.701483	−	0.712686i	$-0.747478\pi$
$701$	−1.54769e10	−	5.63313e9i	−1.69696	−	0.617641i	−0.995473	+	0.0950447i	$0.969701\pi$
$702$	−1.75013e8			−0.0190937
$703$	−2.50342e9	−	2.26424e9i	−0.271763	−	0.245798i
$704$	−3.39570e8			−0.0366797
$705$	−9.74784e9	−	3.54792e9i	−1.04772	−	0.381340i
$706$	−4.12558e8	−	2.33973e9i	−0.0441234	−	0.250236i
$707$	5.37136e9	+	4.50711e9i	0.571632	+	0.479656i
$708$	4.27639e9	−	3.58832e9i	0.452857	−	0.379992i
$709$	−2.36604e9	+	1.34185e10i	−0.249322	+	1.41397i	0.560916	+	0.827873i	$0.310449\pi$
$709$	−2.36604e9	+	1.34185e10i	−0.249322	+	1.41397i	−0.810238	+	0.586101i	$0.800662\pi$
$710$	−1.17346e9	+	2.03250e9i	−0.123046	+	0.213121i
$711$	1.53971e8	+	2.66686e8i	0.0160656	+	0.0278264i
$712$	5.04844e8	−	1.83748e8i	0.0524176	−	0.0190784i
$713$	4.36082e8	−	1.58721e8i	0.0450563	−	0.0163991i
$714$	−2.16772e9	−	3.75460e9i	−0.222874	−	0.386029i
$715$	−2.78617e8	+	4.82578e8i	−0.0285060	+	0.0493738i
$716$	−3.26733e8	+	1.85299e9i	−0.0332658	+	0.188659i
$717$	7.70715e9	−	6.46707e9i	0.780867	−	0.655225i
$718$	4.15837e9	+	3.48929e9i	0.419264	+	0.351804i
$719$	1.24414e9	+	7.05585e9i	0.124829	+	0.707943i	0.981409	+	0.191928i	$0.0614740\pi$
$719$	1.24414e9	+	7.05585e9i	0.124829	+	0.707943i	−0.856580	+	0.516015i	$0.827415\pi$
$720$	1.34304e9	+	4.88828e8i	0.134099	+	0.0488081i
$721$	2.77606e9			0.275839
$722$	1.76096e9	−	6.93076e9i	0.174128	−	0.685332i
$723$	2.13054e10			2.09655
$724$	2.46396e9	+	8.96807e8i	0.241295	+	0.0878242i
$725$	1.44556e9	+	8.19817e9i	0.140881	+	0.798976i
$726$	7.31250e9	+	6.13592e9i	0.709231	+	0.595116i
$727$	−8.44822e9	+	7.08889e9i	−0.815445	+	0.684239i	−0.951901	−	0.306407i	$-0.900873\pi$
$727$	−8.44822e9	+	7.08889e9i	−0.815445	+	0.684239i	0.136456	+	0.990646i	$0.456429\pi$
$728$	2.36333e8	−	1.34031e9i	0.0227020	−	0.128749i
$729$	5.76522e9	−	9.98566e9i	0.551150	−	0.954619i
$730$	2.47818e9	+	4.29233e9i	0.235778	+	0.408379i
$731$	−6.05909e9	+	2.20533e9i	−0.573715	+	0.208815i
$732$	2.93812e9	−	1.06939e9i	0.276873	−	0.100774i
$733$	8.73863e8	+	1.51358e9i	0.0819558	+	0.141952i	0.904090	−	0.427342i	$-0.140550\pi$
$733$	8.73863e8	+	1.51358e9i	0.0819558	+	0.141952i	−0.822134	+	0.569294i	$0.807217\pi$
$734$	−1.01218e9	+	1.75315e9i	−0.0944762	+	0.163638i
$735$	9.47426e7	−	5.37312e8i	0.00880115	−	0.0499138i
$736$	5.41729e8	−	4.54565e8i	0.0500852	−	0.0420265i
$737$	−2.74799e9	−	2.30583e9i	−0.252859	−	0.212174i
$738$	1.67451e9	+	9.49662e9i	0.153352	+	0.869705i
$739$	5.49695e9	+	2.00073e9i	0.501033	+	0.182361i	0.580159	−	0.814503i	$-0.302991\pi$
$739$	5.49695e9	+	2.00073e9i	0.501033	+	0.182361i	−0.0791254	+	0.996865i	$0.525213\pi$
$740$	1.09524e9			0.0993567
$741$	−4.21629e9	−	3.81345e9i	−0.380686	−	0.344314i
$742$	1.41048e10			1.26752
$743$	2.75931e9	+	1.00431e9i	0.246797	+	0.0898267i	0.462457	−	0.886642i	$-0.346968\pi$
$743$	2.75931e9	+	1.00431e9i	0.246797	+	0.0898267i	−0.215660	+	0.976469i	$0.569190\pi$
$744$	1.28092e8	+	7.26446e8i	0.0114029	+	0.0646693i
$745$	−4.56651e9	−	3.83176e9i	−0.404611	−	0.339509i
$746$	4.73543e9	−	3.97350e9i	0.417613	−	0.350419i
$747$	−3.54242e9	+	2.00901e10i	−0.310941	+	1.76343i
$748$	−3.57964e8	+	6.20012e8i	−0.0312740	+	0.0541682i
$749$	−2.52597e9	−	4.37510e9i	−0.219655	−	0.380454i
$750$	1.01749e10	−	3.70336e9i	0.880676	−	0.320540i
$751$	6.70877e9	−	2.44179e9i	0.577967	−	0.210363i	−0.0364617	−	0.999335i	$-0.511609\pi$
$751$	6.70877e9	−	2.44179e9i	0.577967	−	0.210363i	0.614429	+	0.788972i	$0.289386\pi$
$752$	−2.09192e9	−	3.62332e9i	−0.179384	−	0.310702i
$753$	1.21944e10	−	2.11214e10i	1.04083	−	1.80277i
$754$	−5.95113e8	+	3.37505e9i	−0.0505591	+	0.286735i
$755$	4.69134e9	−	3.93650e9i	0.396719	−	0.332886i
$756$	−3.53967e8	−	2.97014e8i	−0.0297945	−	0.0250006i
$757$	2.43478e9	+	1.38083e10i	0.203997	+	1.15692i	0.899010	+	0.437927i	$0.144287\pi$
$757$	2.43478e9	+	1.38083e10i	0.203997	+	1.15692i	−0.695014	+	0.718997i	$0.744602\pi$
$758$	−8.65500e8	−	3.15016e8i	−0.0721814	−	0.0262719i
$759$	1.87303e9			0.155489
$760$	1.08472e9	+	2.05110e9i	0.0896333	+	0.169488i
$761$	−2.02956e9			−0.166938			−0.0834690	−	0.996510i	$-0.526600\pi$
$761$	−2.02956e9			−0.166938			−0.0834690	+	0.996510i	$0.526600\pi$
$762$	1.90392e10	+	6.92969e9i	1.55885	+	0.567376i
$763$	−3.12066e9	−	1.76981e10i	−0.254337	−	1.44242i
$764$	−5.04577e9	−	4.23391e9i	−0.409356	−	0.343490i
$765$	2.30833e9	−	1.93692e9i	0.186416	−	0.156421i
$766$	2.69631e9	−	1.52915e10i	0.216755	−	1.22928i
$767$	1.84737e9	−	3.19974e9i	0.147833	−	0.256054i
$768$	5.62040e8	+	9.73482e8i	0.0447716	+	0.0775467i
$769$	6.00382e9	−	2.18521e9i	0.476086	−	0.173281i	−0.0928214	−	0.995683i	$-0.529589\pi$
$769$	6.00382e9	−	2.18521e9i	0.476086	−	0.173281i	0.568907	+	0.822402i	$0.307366\pi$
$770$	−1.38249e9	+	5.03184e8i	−0.109130	+	0.0397200i
$771$	−1.53484e10	−	2.65842e10i	−1.20607	−	2.08898i
$772$	−4.33448e8	+	7.50755e8i	−0.0339060	+	0.0587270i
$773$	1.07383e9	−	6.08997e9i	0.0836191	−	0.474227i	−0.914027	−	0.405653i	$-0.867044\pi$
$773$	1.07383e9	−	6.08997e9i	0.0836191	−	0.474227i	0.997646	−	0.0685740i	$-0.0218449\pi$
$774$	−1.05337e10	+	8.83881e9i	−0.816558	+	0.685173i
$775$	9.08454e8	+	7.62283e8i	0.0701046	+	0.0588248i
$776$	1.12721e9	+	6.39273e9i	0.0865943	+	0.491100i
$777$	−6.65775e9	−	2.42322e9i	−0.509160	−	0.185319i
$778$	1.06412e10			0.810146
$779$	−8.32547e9	+	1.32575e10i	−0.630997	+	1.00481i
$780$	1.84461e9			0.139179
$781$	−2.35590e9	−	8.57476e8i	−0.176961	−	0.0644086i
$782$	−2.58904e8	−	1.46832e9i	−0.0193604	−	0.109798i
$783$	8.91330e8	+	7.47915e8i	0.0663548	+	0.0556783i
$784$	1.68571e8	−	1.41448e8i	0.0124933	−	0.0104831i
$785$	1.69034e9	−	9.58640e9i	0.124718	−	0.707313i
$786$	−1.30297e10	+	2.25681e10i	−0.957095	+	1.65774i
$787$	1.23868e10	+	2.14545e10i	0.905830	+	1.56894i	0.819799	+	0.572651i	$0.194085\pi$
$787$	1.23868e10	+	2.14545e10i	0.905830	+	1.56894i	0.0860310	+	0.996292i	$0.472582\pi$
$788$	4.30214e9	−	1.56585e9i	0.313215	−	0.114001i
$789$	−3.13189e10	+	1.13992e10i	−2.27006	+	0.826235i
$790$	−8.11044e7	−	1.40477e8i	−0.00585261	−	0.0101370i
$791$	−1.09810e10	+	1.90196e10i	−0.788904	+	1.36642i
$792$	−2.65121e8	+	1.50358e9i	−0.0189630	+	0.107544i
$793$	1.58525e9	−	1.33018e9i	0.112886	−	0.0947230i
$794$	−1.06175e10	−	8.90911e9i	−0.752747	−	0.631630i
$795$	3.31962e9	+	1.88265e10i	0.234317	+	1.32888i
$796$	−6.91571e9	−	2.51711e9i	−0.486005	−	0.176891i
$797$	2.40216e10			1.68073			0.840364	−	0.542023i	$-0.182341\pi$
$797$	2.40216e10			1.68073			0.840364	+	0.542023i	$0.182341\pi$
$798$	−2.05574e9	−	1.48682e10i	−0.143205	−	1.03573i
$799$	−8.82095e9			−0.611789
$800$	1.69816e9	+	6.18081e8i	0.117264	+	0.0426806i
$801$	−4.19456e8	−	2.37885e9i	−0.0288385	−	0.163551i
$802$	4.02051e9	+	3.37361e9i	0.275215	+	0.230932i
$803$	−4.05590e9	+	3.40330e9i	−0.276428	+	0.231951i
$804$	−2.06204e9	+	1.16944e10i	−0.139927	+	0.793566i
$805$	1.53195e9	−	2.65341e9i	0.103504	−	0.179274i
$806$	2.44108e8	+	4.22808e8i	0.0164214	+	0.0284427i
$807$	−2.76523e10	+	1.00646e10i	−1.85214	+	0.674123i
$808$	−3.60181e9	+	1.31095e9i	−0.240204	+	0.0874272i
$809$	4.84420e9	+	8.39041e9i	0.321664	+	0.557139i	0.980832	−	0.194858i	$-0.0624245\pi$
$809$	4.84420e9	+	8.39041e9i	0.321664	+	0.557139i	−0.659167	+	0.751996i	$0.729091\pi$
$810$	−2.73935e9	+	4.74469e9i	−0.181113	+	0.313697i
$811$	2.38526e9	−	1.35275e10i	0.157023	−	0.890521i	−0.799890	−	0.600147i	$-0.795109\pi$
$811$	2.38526e9	−	1.35275e10i	0.157023	−	0.890521i	0.956913	−	0.290375i	$-0.0937800\pi$
$812$	−6.93140e9	+	5.81614e9i	−0.454334	+	0.381231i
$813$	−4.02562e9	−	3.37790e9i	−0.262734	−	0.220460i
$814$	2.03165e8	+	1.15221e9i	0.0132027	+	0.0748763i
$815$	6.61691e9	+	2.40836e9i	0.428158	+	0.155837i
$816$	2.36994e9			0.152694
$817$	−2.23079e10	−	8.28902e8i	−1.43114	−	0.0531773i
$818$	−1.59277e10			−1.01746
$819$	−5.75022e9	−	2.09291e9i	−0.365755	−	0.133124i
$820$	−8.82049e8	−	5.00235e9i	−0.0558655	−	0.316829i
$821$	−8.11229e9	−	6.80702e9i	−0.511614	−	0.429295i	0.350083	−	0.936719i	$-0.386154\pi$
$821$	−8.11229e9	−	6.80702e9i	−0.511614	−	0.429295i	−0.861697	+	0.507424i	$0.830598\pi$
$822$	−8.79343e8	+	7.37856e8i	−0.0552213	+	0.0463362i
$823$	4.38617e9	−	2.48752e10i	0.274275	−	1.55549i	−0.466981	−	0.884267i	$-0.654658\pi$
$823$	4.38617e9	−	2.48752e10i	0.274275	−	1.55549i	0.741256	−	0.671223i	$-0.234231\pi$
$824$	−7.58758e8	+	1.31421e9i	−0.0472452	+	0.0818311i
$825$	2.39321e9	+	4.14516e9i	0.148386	+	0.257012i
$826$	9.16659e9	−	3.33637e9i	0.565950	−	0.205989i
$827$	−1.76837e10	+	6.43633e9i	−1.08718	+	0.395702i	−0.822577	−	0.568654i	$-0.807464\pi$
$827$	−1.76837e10	+	6.43633e9i	−1.08718	+	0.395702i	−0.264607	+	0.964356i	$0.585242\pi$
$828$	−1.58980e9	−	2.75362e9i	−0.0973277	−	0.168577i
$829$	1.36102e10	−	2.35736e10i	0.829706	−	1.43709i	−0.0685631	−	0.997647i	$-0.521841\pi$
$829$	1.36102e10	−	2.35736e10i	0.829706	−	1.43709i	0.898269	−	0.439446i	$-0.144825\pi$
$830$	1.86597e9	−	1.05824e10i	0.113274	−	0.642410i
$831$	2.53574e10	−	2.12774e10i	1.53285	−	1.28622i
$832$	5.69917e8	+	4.78217e8i	0.0343068	+	0.0287868i
$833$	−8.05635e7	−	4.56898e8i	−0.00482926	−	0.0273881i
$834$	−1.02104e10	−	3.71629e9i	−0.609485	−	0.221834i
$835$	1.13407e10			0.674122
$836$	−1.95657e9	+	1.52162e9i	−0.115817	+	0.0900706i
$837$	1.65755e8			0.00977077
$838$	1.22329e10	+	4.45240e9i	0.718082	+	0.261360i
$839$	−2.00838e9	−	1.13901e10i	−0.117403	−	0.665826i	−0.985532	−	0.169488i	$-0.945789\pi$
$839$	−2.00838e9	−	1.13901e10i	−0.117403	−	0.665826i	0.868129	−	0.496338i	$-0.165322\pi$
$840$	3.73075e9	+	3.13047e9i	0.217180	+	0.182235i
$841$	4.23990e9	−	3.55770e9i	0.245793	−	0.206245i
$842$	2.90328e9	−	1.64653e10i	0.167609	−	0.950557i
$843$	−6.10147e8	+	1.05680e9i	−0.0350782	+	0.0607573i
$844$	−4.44821e9	−	7.70453e9i	−0.254675	−	0.441111i
$845$	−7.79032e9	+	2.83545e9i	−0.444178	+	0.161668i
$846$	−1.76769e10	+	6.43387e9i	−1.00371	+	0.365322i
$847$	8.34028e9	+	1.44458e10i	0.471616	+	0.816863i
$848$	−3.85515e9	+	6.67732e9i	−0.217098	+	0.376025i
$849$	7.13748e9	−	4.04787e10i	0.400284	−	2.27012i
$850$	2.91869e9	−	2.44907e9i	0.163013	−	0.136784i
$851$	−1.86651e9	−	1.56619e9i	−0.103819	−	0.0871146i
$852$	1.44115e9	+	8.17315e9i	0.0798306	+	0.452742i
$853$	1.11636e10	+	4.06322e9i	0.615862	+	0.224155i	0.631066	−	0.775729i	$-0.282618\pi$
$853$	1.11636e10	+	4.06322e9i	0.615862	+	0.224155i	−0.0152043	+	0.999884i	$0.504840\pi$
$854$	5.46364e9			0.300179
$855$	9.92892e9	−	3.20160e9i	0.543276	−	0.175181i
$856$	2.76160e9			0.150488
$857$	7.61339e9	+	2.77105e9i	0.413185	+	0.150387i	0.540245	−	0.841508i	$-0.318332\pi$
$857$	7.61339e9	+	2.77105e9i	0.413185	+	0.150387i	−0.127059	+	0.991895i	$0.540554\pi$
$858$	3.42172e8	+	1.94056e9i	0.0184944	+	0.104887i
$859$	2.69868e9	+	2.26446e9i	0.145270	+	0.121896i	0.712527	−	0.701645i	$-0.247551\pi$
$859$	2.69868e9	+	2.26446e9i	0.145270	+	0.121896i	−0.567257	+	0.823541i	$0.691995\pi$
$860$	5.54862e9	−	4.65584e9i	0.297468	−	0.249605i
$861$	−5.70593e9	+	3.23599e10i	−0.304660	+	1.72781i
$862$	−5.10374e9	+	8.83995e9i	−0.271402	+	0.470083i
$863$	−3.90888e9	−	6.77038e9i	−0.207021	−	0.358571i	0.743754	−	0.668454i	$-0.233044\pi$
$863$	−3.90888e9	−	6.77038e9i	−0.207021	−	0.358571i	−0.950775	+	0.309883i	$0.899710\pi$
$864$	2.37355e8	−	8.63903e7i	0.0125199	−	0.00455687i
$865$	−1.61357e9	+	5.87290e8i	−0.0847677	+	0.0308529i
$866$	−8.71484e9	−	1.50945e10i	−0.455981	−	0.789782i
$867$	−1.12481e10	+	1.94823e10i	−0.586155	+	1.01525i
$868$	−2.23831e8	+	1.26941e9i	−0.0116172	+	0.0658845i
$869$	1.32739e8	−	1.11381e8i	0.00686167	−	0.00575762i
$870$	−9.39446e9	−	7.88289e9i	−0.483676	−	0.405852i
$871$	1.36477e9	+	7.73998e9i	0.0699834	+	0.396896i
$872$	9.23135e9	+	3.35994e9i	0.471474	+	0.171603i
$873$	2.91863e10			1.48467
$874$	1.08448e9	−	5.04665e9i	0.0549457	−	0.255689i
$875$	1.89210e10			0.954806
$876$	1.64697e10	+	5.99449e9i	0.827794	+	0.301292i
$877$	−3.58474e9	−	2.03301e10i	−0.179456	−	1.01775i	−0.932873	−	0.360205i	$-0.882707\pi$
$877$	−3.58474e9	−	2.03301e10i	−0.179456	−	1.01775i	0.753417	−	0.657543i	$-0.228404\pi$
$878$	−1.52361e10	−	1.27846e10i	−0.759702	−	0.637465i
$879$	−1.38217e10	+	1.15978e10i	−0.686435	+	0.575987i
$880$	1.39653e8	−	7.92010e8i	0.00690812	−	0.0391779i
$881$	−5.61850e9	+	9.73153e9i	−0.276825	+	0.479474i	−0.970594	−	0.240723i	$-0.922615\pi$
$881$	−5.61850e9	+	9.73153e9i	−0.276825	+	0.479474i	0.693769	+	0.720197i	$0.255949\pi$
$882$	−4.94701e8	−	8.56848e8i	−0.0242774	−	0.0420498i
$883$	−2.89035e10	+	1.05200e10i	−1.41282	+	0.514226i	−0.931957	−	0.362568i	$-0.881900\pi$
$883$	−2.89035e10	+	1.05200e10i	−1.41282	+	0.514226i	−0.480867	+	0.876794i	$0.659678\pi$
$884$	1.47395e9	−	5.36475e8i	0.0717630	−	0.0261196i
$885$	6.61063e9	+	1.14499e10i	0.320584	+	0.555267i
$886$	9.34737e8	−	1.61901e9i	0.0451514	−	0.0782045i
$887$	−2.18874e9	+	1.24130e10i	−0.105308	+	0.597232i	0.885789	+	0.464089i	$0.153618\pi$
$887$	−2.18874e9	+	1.24130e10i	−0.105308	+	0.597232i	−0.991097	+	0.133143i	$0.957493\pi$
$888$	2.96688e9	−	2.48951e9i	0.142185	−	0.119308i
$889$	2.71216e10	+	2.27577e10i	1.29467	+	1.08636i
$890$	2.20948e8	+	1.25306e9i	0.0105057	+	0.0595809i
$891$	−5.49963e9	−	2.00170e9i	−0.260472	−	0.0948041i
$892$	6.17686e9			0.291401
$893$	−2.82896e10	−	1.15033e10i	−1.32937	−	0.540558i
$894$	−2.10799e10			−0.986704
$895$	−4.18753e9	−	1.52414e9i	−0.195244	−	0.0710630i
$896$	3.41088e8	+	1.93440e9i	0.0158412	+	0.0898399i
$897$	−3.14360e9	−	2.63779e9i	−0.145430	−	0.122030i
$898$	−4.93191e8	+	4.13836e8i	−0.0227273	+	0.0190705i
$899$	5.63633e8	−	3.19652e9i	0.0258724	−	0.146730i
$900$	4.06264e9	−	7.03671e9i	0.185763	−	0.321752i
$901$	8.12795e9	+	1.40780e10i	0.370207	+	0.641217i
$902$	5.09892e9	−	1.85586e9i	0.231343	−	0.0842018i
$903$	−4.40302e10	+	1.60257e10i	−1.98996	+	0.724285i
$904$	−6.00269e9	−	1.03970e10i	−0.270244	−	0.468076i
$905$	−3.10504e9	+	5.37808e9i	−0.139251	+	0.241189i
$906$	3.76055e9	−	2.13271e10i	0.167997	−	0.952760i
$907$	2.53922e10	−	2.13065e10i	1.12999	−	0.948173i	0.130923	−	0.991393i	$-0.458206\pi$
$907$	2.53922e10	−	2.13065e10i	1.12999	−	0.948173i	0.999066	+	0.0432196i	$0.0137615\pi$
$908$	−1.15170e10	−	9.66390e9i	−0.510550	−	0.428403i
$909$	2.99261e9	+	1.69719e10i	0.132153	+	0.749475i
$910$	3.02893e9	+	1.10244e9i	0.133243	+	0.0484964i
$911$	2.89526e10			1.26874			0.634371	−	0.773029i	$-0.281259\pi$
$911$	2.89526e10			1.26874			0.634371	+	0.773029i	$0.281259\pi$
$912$	7.60059e9	+	3.09060e9i	0.331792	+	0.134915i
$913$	1.14790e10			0.499180
$914$	8.12780e9	+	2.95828e9i	0.352096	+	0.128153i
$915$	1.28589e9	+	7.29263e9i	0.0554919	+	0.314710i
$916$	3.00090e9	+	2.51806e9i	0.129008	+	0.108251i
$917$	−3.48832e10	+	2.92705e10i	−1.49391	+	1.25354i
$918$	9.24748e7	−	5.24450e8i	0.00394524	−	0.0223746i
$919$	−9.46743e8	+	1.63981e9i	−0.0402372	+	0.0696929i	−0.885443	−	0.464749i	$-0.846145\pi$
$919$	−9.46743e8	+	1.63981e9i	−0.0402372	+	0.0696929i	0.845205	+	0.534442i	$0.179478\pi$
$920$	8.37428e8	+	1.45047e9i	0.0354560	+	0.0614117i
$921$	1.82788e10	−	6.65293e9i	0.770971	−	0.280611i
$922$	1.13311e10	−	4.12420e9i	0.476119	−	0.173293i
$923$	2.74643e9	+	4.75696e9i	0.114964	+	0.199124i
$924$	−2.60125e9	+	4.50551e9i	−0.108475	+	0.187885i
$925$	1.08122e9	−	6.13189e9i	0.0449177	−	0.254741i
$926$	−1.22784e10	+	1.03028e10i	−0.508164	+	0.426400i
$927$	5.22675e9	+	4.38577e9i	0.215503	+	0.180828i
$928$	−8.58898e8	−	4.87105e9i	−0.0352796	−	0.200081i
$929$	1.43217e9	+	5.21269e8i	0.0586058	+	0.0213308i	0.371157	−	0.928570i	$-0.378961\pi$
$929$	1.43217e9	+	5.21269e8i	0.0586058	+	0.0213308i	−0.312551	+	0.949901i	$0.601183\pi$
$930$	−1.74703e9			−0.0712215
$931$	3.37461e8	−	1.57037e9i	0.0137057	−	0.0637792i
$932$	−4.85891e9			−0.196600
$933$	1.25894e10	+	4.58218e9i	0.507482	+	0.184708i
$934$	2.36250e9	+	1.33984e10i	0.0948763	+	0.538070i
$935$	−1.29889e9	−	1.08990e9i	−0.0519676	−	0.0436060i
$936$	2.56246e9	−	2.15016e9i	0.102139	−	0.0857047i
$937$	−4.64380e9	+	2.63363e10i	−0.184410	+	1.04584i	0.742301	+	0.670067i	$0.233734\pi$
$937$	−4.64380e9	+	2.63363e10i	−0.184410	+	1.04584i	−0.926711	+	0.375775i	$0.877377\pi$
$938$	−1.03752e10	+	1.79704e10i	−0.410475	+	0.710963i
$939$	−1.68107e10	−	2.91170e10i	−0.662608	−	1.14767i
$940$	9.31131e9	−	3.38904e9i	0.365648	−	0.133085i
$941$	3.40068e10	−	1.23775e10i	1.33046	−	0.484249i	0.423666	−	0.905818i	$-0.360743\pi$
$941$	3.40068e10	−	1.23775e10i	1.33046	−	0.484249i	0.906796	+	0.421569i	$0.138521\pi$
$942$	−1.72112e10	−	2.98107e10i	−0.670863	−	1.16197i
$943$	−5.65016e9	+	9.78637e9i	−0.219417	+	0.380041i
$944$	−9.25969e8	+	5.25143e9i	−0.0358257	+	0.203178i
$945$	8.38325e8	−	7.03438e8i	0.0323148	−	0.0271153i
$946$	5.92728e9	+	4.97358e9i	0.227634	+	0.191007i
$947$	1.75300e9	+	9.94178e9i	0.0670746	+	0.380399i	0.999804	+	0.0198207i	$0.00630953\pi$
$947$	1.75300e9	+	9.94178e9i	0.0670746	+	0.380399i	−0.932729	+	0.360578i	$0.882579\pi$
$948$	−5.39012e8	−	1.96184e8i	−0.0205480	−	0.00747885i
$949$	1.16001e10			0.440585
$950$	1.25543e10	−	4.04816e9i	0.475072	−	0.153188i
$951$	1.40381e10			0.529267
$952$	3.89154e9	+	1.41640e9i	0.146181	+	0.0532057i
$953$	−6.39114e9	−	3.62459e10i	−0.239196	−	1.35655i	−0.833595	−	0.552375i	$-0.813721\pi$
$953$	−6.39114e9	−	3.62459e10i	−0.239196	−	1.35655i	0.594400	−	0.804170i	$-0.297390\pi$
$954$	2.65565e10	+	2.22835e10i	0.990264	+	0.830930i
$955$	1.19503e10	−	1.00275e10i	0.443982	−	0.372545i
$956$	−1.66883e9	+	9.46442e9i	−0.0617746	+	0.350341i
$957$	6.55026e9	−	1.13454e10i	0.241583	−	0.418434i
$958$	−1.18863e7	−	2.05877e7i	−0.000436784	−	0.000756533i
$959$	−1.88490e9	+	6.86048e8i	−0.0690118	+	0.0251183i
$960$	−2.50168e9	+	9.10538e8i	−0.0912605	+	0.0332161i
$961$	1.35251e10	+	2.34262e10i	0.491597	+	0.851471i
$962$	1.28167e9	−	2.21992e9i	0.0464156	−	0.0803942i
$963$	2.15614e9	−	1.22281e10i	0.0778009	−	0.441231i
$964$	−1.55900e10	+	1.30816e10i	−0.560501	+	0.470317i
$965$	−1.57279e9	−	1.31973e9i	−0.0563411	−	0.0472758i
$966$	−1.88140e9	−	1.06700e10i	−0.0671524	−	0.380840i
$967$	3.60892e10	+	1.31354e10i	1.28347	+	0.467143i	0.891577	−	0.452870i	$-0.149600\pi$
$967$	3.60892e10	+	1.31354e10i	1.28347	+	0.467143i	0.391889	+	0.920013i	$0.371822\pi$
$968$	−9.11832e9			−0.323111
$969$	1.36554e10	−	1.06197e10i	0.482136	−	0.374955i
$970$	−1.53739e10			−0.540858
$971$	4.62125e10	+	1.68200e10i	1.61992	+	0.589601i	0.983366	−	0.181634i	$-0.0581387\pi$
$971$	4.62125e10	+	1.68200e10i	1.61992	+	0.589601i	0.636550	+	0.771236i	$0.280361\pi$
$972$	3.55158e9	+	2.01420e10i	0.124048	+	0.703511i
$973$	−1.45449e10	−	1.22046e10i	−0.506193	−	0.424746i
$974$	6.12466e9	−	5.13920e9i	0.212386	−	0.178213i
$975$	1.82100e9	−	1.03274e10i	0.0629207	−	0.356841i
$976$	−1.49333e9	+	2.58653e9i	−0.0514141	+	0.0890518i
$977$	−1.99766e10	−	3.46005e10i	−0.685315	−	1.18700i	−0.973338	−	0.229377i	$-0.926331\pi$
$977$	−1.99766e10	−	3.46005e10i	−0.685315	−	1.18700i	0.288022	−	0.957624i	$-0.407002\pi$
$978$	2.33988e10	−	8.51646e9i	0.799848	−	0.291121i
$979$	−1.27725e9	+	4.64882e8i	−0.0435048	+	0.0158345i
$980$	2.60584e8	+	4.51345e8i	0.00884416	+	0.0153185i
$981$	2.20848e10	−	3.82521e10i	0.746884	−	1.29364i
$982$	−6.20946e9	+	3.52156e10i	−0.209249	+	1.18671i
$983$	7.74926e9	−	6.50240e9i	0.260209	−	0.218342i	−0.503344	−	0.864086i	$-0.667897\pi$
$983$	7.74926e9	−	6.50240e9i	0.260209	−	0.218342i	0.763554	+	0.645744i	$0.223453\pi$
$984$	−1.37599e10	−	1.15459e10i	−0.460396	−	0.386318i
$985$	1.88286e9	+	1.06782e10i	0.0627757	+	0.356019i
$986$	−9.79934e9	−	3.56667e9i	−0.325558	−	0.118493i
$987$	−6.41001e10			−2.12202
$988$	5.42670e9	+	2.01641e8i	0.179014	+	0.00665166i
$989$	−1.61139e10			−0.529679
$990$	−3.39789e9	−	1.23673e9i	−0.111298	−	0.0405091i
$991$	−4.00880e9	−	2.27350e10i	−0.130845	−	0.742057i	−0.977664	−	0.210176i	$-0.932596\pi$
$991$	−4.00880e9	−	2.27350e10i	−0.130845	−	0.742057i	0.846819	−	0.531881i	$-0.178515\pi$
$992$	−5.39770e8	−	4.52921e8i	−0.0175557	−	0.0147310i
$993$	2.32016e10	−	1.94684e10i	0.751961	−	0.630970i
$994$	−2.51830e9	+	1.42820e10i	−0.0813307	+	0.461249i
$995$	8.71506e9	−	1.50949e10i	0.280472	−	0.485792i
$996$	−1.89995e10	−	3.29081e10i	−0.609305	−	1.05535i
$997$	−4.39411e10	+	1.59932e10i	−1.40423	+	0.511097i	−0.929430	−	0.368998i	$-0.879701\pi$
$997$	−4.39411e10	+	1.59932e10i	−1.40423	+	0.511097i	−0.474798	+	0.880095i	$0.657479\pi$
$998$	−1.26982e10	+	4.62176e9i	−0.404375	+	0.147180i
$999$	−4.35143e8	−	7.53690e8i	−0.0138087	−	0.0239174i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	38.8.e.a.23.1	yes	30
19.5	even	9	inner	38.8.e.a.5.1	✓	30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
38.8.e.a.5.1	✓	30	19.5	even	9	inner
38.8.e.a.23.1	yes	30	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 38 = 2 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	38.e (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-7.51754 - 2.73616i) q^{2} +(-11.6345 - 65.9825i) q^{3} +(49.0268 + 41.1384i) q^{4} +(-116.114 + 97.4309i) q^{5} +(-93.0759 + 527.860i) q^{6} +(-468.313 + 811.141i) q^{7} +(-256.000 - 443.405i) q^{8} +(-2163.22 + 787.347i) q^{9} +O(q^{10})\)	\(q+(-7.51754 - 2.73616i) q^{2} +(-11.6345 - 65.9825i) q^{3} +(49.0268 + 41.1384i) q^{4} +(-116.114 + 97.4309i) q^{5} +(-93.0759 + 527.860i) q^{6} +(-468.313 + 811.141i) q^{7} +(-256.000 - 443.405i) q^{8} +(-2163.22 + 787.347i) q^{9} +(1139.48 - 414.735i) q^{10} +(647.679 + 1121.81i) q^{11} +(2144.01 - 3713.54i) q^{12} +(492.820 - 2794.92i) q^{13} +(5739.97 - 4816.41i) q^{14} +(7779.66 + 6527.91i) q^{15} +(711.263 + 4033.77i) q^{16} +(8114.94 + 2953.60i) q^{17} +18416.4 q^{18} +(22173.6 + 20055.0i) q^{19} -9700.84 q^{20} +(58969.7 + 21463.2i) q^{21} +(-1799.49 - 10205.4i) q^{22} +(16532.3 + 13872.2i) q^{23} +(-26278.5 + 22050.3i) q^{24} +(-9576.67 + 54312.0i) q^{25} +(-11352.1 + 19662.5i) q^{26} +(3854.19 + 6675.65i) q^{27} +(-56329.0 + 20502.1i) q^{28} +(141843. - 51626.5i) q^{29} +(-40622.5 - 70360.2i) q^{30} +(10751.6 - 18622.4i) q^{31} +(5690.10 - 32270.2i) q^{32} +(66484.6 - 55787.2i) q^{33} +(-52922.9 - 44407.6i) q^{34} +(-24652.8 - 139813. i) q^{35} +(-138446. - 50390.2i) q^{36} -112901. q^{37} +(-111817. - 211435. i) q^{38} -190149. q^{39} +(72926.5 + 26543.1i) q^{40} +(90924.9 + 515661. i) q^{41} +(-384580. - 322701. i) q^{42} +(-571973. + 479942. i) q^{43} +(-14395.9 + 81643.4i) q^{44} +(174467. - 302186. i) q^{45} +(-86325.3 - 149520. i) q^{46} +(-959846. + 349355. i) q^{47} +(257883. - 93861.8i) q^{48} +(-26862.0 - 46526.3i) q^{49} +(220599. - 382089. i) q^{50} +(100472. - 569808. i) q^{51} +(139140. - 116752. i) q^{52} +(1.44200e6 + 1.20998e6i) q^{53} +(-10708.4 - 60730.2i) q^{54} +(-184504. - 67153.9i) q^{55} +479552. q^{56} +(1.06530e6 - 1.69640e6i) q^{57} -1.20757e6 q^{58} +(1.22335e6 + 445264. i) q^{59} +(112864. + 640086. i) q^{60} +(558573. + 468699. i) q^{61} +(-131780. + 110576. i) q^{62} +(374413. - 2.12340e6i) q^{63} +(-131072. + 227023. i) q^{64} +(215089. + 372544. i) q^{65} +(-652443. + 237470. i) q^{66} +(-2.60229e6 + 947158. i) q^{67} +(276344. + 478641. i) q^{68} +(722978. - 1.25224e6i) q^{69} +(-197222. + 1.11850e6i) q^{70} +(-1.48264e6 + 1.24408e6i) q^{71} +(902898. + 757621. i) q^{72} +(709763. + 4.02527e6i) q^{73} +(848740. + 308916. i) q^{74} +3.69506e6 q^{75} +(262068. + 1.89542e6i) q^{76} -1.21327e6 q^{77} +(1.42946e6 + 520279. i) q^{78} +(-23228.7 - 131737. i) q^{79} +(-475602. - 399077. i) q^{80} +(-3.46108e6 + 2.90419e6i) q^{81} +(727400. - 4.12529e6i) q^{82} +(4.43083e6 - 7.67442e6i) q^{83} +(2.00814e6 + 3.47819e6i) q^{84} +(-1.23003e6 + 447694. i) q^{85} +(5.61303e6 - 2.04298e6i) q^{86} +(-5.05672e6 - 8.75849e6i) q^{87} +(331612. - 574368. i) q^{88} +(-182210. + 1.03336e6i) q^{89} +(-2.13840e6 + 1.79433e6i) q^{90} +(2.03628e6 + 1.70864e6i) q^{91} +(239844. + 1.36022e6i) q^{92} +(-1.35384e6 - 492758. i) q^{93} +8.17157e6 q^{94} +(-4.52864e6 - 168272. i) q^{95} -2.19547e6 q^{96} +(-1.19138e7 - 4.33627e6i) q^{97} +(74632.6 + 423263. i) q^{98} +(-2.28433e6 - 1.91678e6i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q + 45 q^{3} + 360 q^{6} + 1806 q^{7} - 7680 q^{8} - 3105 q^{9}+O(q^{10}) \) 30 * q + 45 * q^3 + 360 * q^6 + 1806 * q^7 - 7680 * q^8 - 3105 * q^9	\( 30 q + 45 q^{3} + 360 q^{6} + 1806 q^{7} - 7680 q^{8} - 3105 q^{9} + 9786 q^{11} - 11130 q^{13} + 6144 q^{14} - 1818 q^{15} - 65250 q^{17} + 29040 q^{18} + 105906 q^{19} - 47616 q^{20} + 172854 q^{21} + 102336 q^{22} + 101004 q^{23} + 23040 q^{24} - 132756 q^{25} - 92112 q^{26} + 43659 q^{27} + 96384 q^{28} - 273912 q^{29} + 58710 q^{31} - 406965 q^{33} + 84960 q^{34} + 356100 q^{35} - 198720 q^{36} - 2598852 q^{37} - 219336 q^{38} + 1769844 q^{39} + 43377 q^{41} - 79056 q^{42} + 1126698 q^{43} + 818688 q^{44} - 912546 q^{45} - 530880 q^{46} + 588306 q^{47} - 368640 q^{48} - 2778285 q^{49} + 1665288 q^{50} + 3972045 q^{51} - 430080 q^{52} + 6520866 q^{53} - 486648 q^{54} - 1666818 q^{55} - 1849344 q^{56} - 6947844 q^{57} - 4573152 q^{58} - 970467 q^{59} + 4634496 q^{60} - 4037670 q^{61} + 755952 q^{62} + 7946472 q^{63} - 3932160 q^{64} + 1497690 q^{65} + 6499272 q^{66} - 4817025 q^{67} + 1472064 q^{68} + 10299876 q^{69} + 2848800 q^{70} - 25171290 q^{71} + 3179520 q^{72} + 1347750 q^{73} - 3123936 q^{74} + 8817984 q^{75} + 1583232 q^{76} - 11476764 q^{77} - 930960 q^{78} + 10777986 q^{79} - 5365035 q^{81} + 347016 q^{82} + 9745314 q^{83} + 877056 q^{84} + 29258556 q^{85} - 9338208 q^{86} + 25598802 q^{87} + 5010432 q^{88} - 20353740 q^{89} - 30112128 q^{90} + 19748724 q^{91} - 14097792 q^{92} - 18738174 q^{93} + 12376608 q^{94} - 20427204 q^{95} - 23005029 q^{97} + 14869008 q^{98} - 45819771 q^{99}+O(q^{100}) \) 30 * q + 45 * q^3 + 360 * q^6 + 1806 * q^7 - 7680 * q^8 - 3105 * q^9 + 9786 * q^11 - 11130 * q^13 + 6144 * q^14 - 1818 * q^15 - 65250 * q^17 + 29040 * q^18 + 105906 * q^19 - 47616 * q^20 + 172854 * q^21 + 102336 * q^22 + 101004 * q^23 + 23040 * q^24 - 132756 * q^25 - 92112 * q^26 + 43659 * q^27 + 96384 * q^28 - 273912 * q^29 + 58710 * q^31 - 406965 * q^33 + 84960 * q^34 + 356100 * q^35 - 198720 * q^36 - 2598852 * q^37 - 219336 * q^38 + 1769844 * q^39 + 43377 * q^41 - 79056 * q^42 + 1126698 * q^43 + 818688 * q^44 - 912546 * q^45 - 530880 * q^46 + 588306 * q^47 - 368640 * q^48 - 2778285 * q^49 + 1665288 * q^50 + 3972045 * q^51 - 430080 * q^52 + 6520866 * q^53 - 486648 * q^54 - 1666818 * q^55 - 1849344 * q^56 - 6947844 * q^57 - 4573152 * q^58 - 970467 * q^59 + 4634496 * q^60 - 4037670 * q^61 + 755952 * q^62 + 7946472 * q^63 - 3932160 * q^64 + 1497690 * q^65 + 6499272 * q^66 - 4817025 * q^67 + 1472064 * q^68 + 10299876 * q^69 + 2848800 * q^70 - 25171290 * q^71 + 3179520 * q^72 + 1347750 * q^73 - 3123936 * q^74 + 8817984 * q^75 + 1583232 * q^76 - 11476764 * q^77 - 930960 * q^78 + 10777986 * q^79 - 5365035 * q^81 + 347016 * q^82 + 9745314 * q^83 + 877056 * q^84 + 29258556 * q^85 - 9338208 * q^86 + 25598802 * q^87 + 5010432 * q^88 - 20353740 * q^89 - 30112128 * q^90 + 19748724 * q^91 - 14097792 * q^92 - 18738174 * q^93 + 12376608 * q^94 - 20427204 * q^95 - 23005029 * q^97 + 14869008 * q^98 - 45819771 * q^99

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