LMFDB - Embedded newform 38.10.e.a.17.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [38,10,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, 10, names="a")

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

chi := DirichletCharacter("38.5");

S:= CuspForms(chi, 10);

N := Newforms(S);

Level:	$ N $	$=$	$ 38 = 2 \cdot 19 $
Weight:	$ k $	$=$	$ 10 $
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:	$19.5713617742$
Analytic rank:	$0$
Dimension:	$42$
Relative dimension:	$7$ over $\Q(\zeta_{9})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			17.5
Character	$\chi$	$=$	38.17
Dual form			38.10.e.a.9.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.77837 + 15.7569i) q^{2} +(74.8003 + 62.7649i) q^{3} +(-240.561 - 87.5572i) q^{4} +(1601.32 - 582.833i) q^{5} +(-1196.81 + 1004.24i) q^{6} +(2055.81 + 3560.77i) q^{7} +(2048.00 - 3547.24i) q^{8} +(-1762.26 - 9994.30i) q^{9} +O(q^{10})$	\(q+(-2.77837 + 15.7569i) q^{2} +(74.8003 + 62.7649i) q^{3} +(-240.561 - 87.5572i) q^{4} +(1601.32 - 582.833i) q^{5} +(-1196.81 + 1004.24i) q^{6} +(2055.81 + 3560.77i) q^{7} +(2048.00 - 3547.24i) q^{8} +(-1762.26 - 9994.30i) q^{9} +(4734.59 + 26851.2i) q^{10} +(29167.3 - 50519.2i) q^{11} +(-12498.5 - 21648.1i) q^{12} +(85526.6 - 71765.4i) q^{13} +(-61818.5 + 22500.1i) q^{14} +(156361. + 56910.6i) q^{15} +(50203.5 + 42125.7i) q^{16} +(51435.9 - 291707. i) q^{17} +162376. q^{18} +(72881.4 + 563361. i) q^{19} -436247. q^{20} +(-69716.0 + 395379. i) q^{21} +(714989. + 599947. i) q^{22} +(-589167. - 214439. i) q^{23} +(375833. - 136792. i) q^{24} +(728349. - 611158. i) q^{25} +(893177. + 1.54703e6i) q^{26} +(1.45645e6 - 2.52264e6i) q^{27} +(-182778. - 1.03658e6i) q^{28} +(982446. + 5.57173e6i) q^{29} +(-1.33116e6 + 2.30564e6i) q^{30} +(4.95106e6 + 8.57549e6i) q^{31} +(-803256. + 674012. i) q^{32} +(5.35255e6 - 1.94817e6i) q^{33} +(4.45350e6 + 1.62094e6i) q^{34} +(5.36734e6 + 4.50373e6i) q^{35} +(-451140. + 2.55854e6i) q^{36} +4.69775e6 q^{37} +(-9.07933e6 - 416841. i) q^{38} +1.09018e7 q^{39} +(1.21205e6 - 6.87391e6i) q^{40} +(-2.20058e7 - 1.84651e7i) q^{41} +(-6.03627e6 - 2.19702e6i) q^{42} +(924985. - 336667. i) q^{43} +(-1.14398e7 + 9.59916e6i) q^{44} +(-8.64695e6 - 1.49770e7i) q^{45} +(5.01583e6 - 8.68767e6i) q^{46} +(1.54451e6 + 8.75933e6i) q^{47} +(1.11122e6 + 6.30204e6i) q^{48} +(1.17241e7 - 2.03067e7i) q^{49} +(7.60634e6 + 1.31746e7i) q^{50} +(2.21564e7 - 1.85914e7i) q^{51} +(-2.68580e7 + 9.77550e6i) q^{52} +(1.25163e7 + 4.55554e6i) q^{53} +(3.57025e7 + 2.99579e7i) q^{54} +(1.72619e7 - 9.78970e7i) q^{55} +1.68412e7 q^{56} +(-2.99078e7 + 4.67140e7i) q^{57} -9.05229e7 q^{58} +(-5.52397e6 + 3.13280e7i) q^{59} +(-3.26314e7 - 2.73810e7i) q^{60} +(-1.39602e8 - 5.08110e7i) q^{61} +(-1.48879e8 + 5.41876e7i) q^{62} +(3.19645e7 - 2.68214e7i) q^{63} +(-8.38861e6 - 1.45295e7i) q^{64} +(9.51282e7 - 1.64767e8i) q^{65} +(1.58258e7 + 8.97525e7i) q^{66} +(-2.68365e7 - 1.52197e8i) q^{67} +(-3.79145e7 + 6.56699e7i) q^{68} +(-3.06106e7 - 5.30192e7i) q^{69} +(-8.58774e7 + 7.20597e7i) q^{70} +(-2.49113e8 + 9.06699e7i) q^{71} +(-3.90613e7 - 1.42171e7i) q^{72} +(2.21069e8 + 1.85499e8i) q^{73} +(-1.30521e7 + 7.40221e7i) q^{74} +9.28400e7 q^{75} +(3.17939e7 - 1.41904e8i) q^{76} +2.39849e8 q^{77} +(-3.02891e7 + 1.71778e8i) q^{78} +(2.57442e8 + 2.16020e8i) q^{79} +(1.04944e8 + 3.81965e7i) q^{80} +(7.95699e7 - 2.89611e7i) q^{81} +(3.52093e8 - 2.95441e8i) q^{82} +(-6.96443e7 - 1.20627e8i) q^{83} +(5.13893e7 - 8.90088e7i) q^{84} +(-8.76513e7 - 4.97095e8i) q^{85} +(2.73488e6 + 1.55103e7i) q^{86} +(-2.76222e8 + 4.78430e8i) q^{87} +(-1.19469e8 - 2.06927e8i) q^{88} +(5.06429e8 - 4.24944e8i) q^{89} +(2.60015e8 - 9.46378e7i) q^{90} +(4.31366e8 + 1.57004e8i) q^{91} +(1.22955e8 + 1.03172e8i) q^{92} +(-1.67899e8 + 9.52202e8i) q^{93} -1.42311e8 q^{94} +(4.45052e8 + 8.59644e8i) q^{95} -1.02388e8 q^{96} +(-3.28835e7 + 1.86492e8i) q^{97} +(2.87398e8 + 2.41155e8i) q^{98} +(-5.56304e8 - 2.02478e8i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 42 q - 252 q^{3} + 4032 q^{6} + 14373 q^{7} + 86016 q^{8} + 12852 q^{9}+O(q^{10}) $ 42 * q - 252 * q^3 + 4032 * q^6 + 14373 * q^7 + 86016 * q^8 + 12852 * q^9	\( 42 q - 252 q^{3} + 4032 q^{6} + 14373 q^{7} + 86016 q^{8} + 12852 q^{9} + 32625 q^{11} - 62208 q^{12} + 351237 q^{13} + 165264 q^{14} - 834165 q^{15} + 1075035 q^{17} - 3364608 q^{18} + 696762 q^{19} - 1396224 q^{20} - 3148065 q^{21} - 1462656 q^{22} - 4882824 q^{23} + 1032192 q^{24} - 483270 q^{25} - 70176 q^{26} + 2570400 q^{27} + 1519104 q^{28} + 13670499 q^{29} - 2263968 q^{31} - 5777733 q^{33} - 9526080 q^{34} + 43019613 q^{35} + 3290112 q^{36} - 50105184 q^{37} - 692160 q^{38} - 89820600 q^{39} - 94033860 q^{41} - 43526160 q^{42} + 30524217 q^{43} + 23402496 q^{44} + 39789630 q^{45} - 18312576 q^{46} + 81865791 q^{47} + 33030144 q^{48} + 40421580 q^{49} - 16761600 q^{50} - 28132314 q^{51} - 91666176 q^{52} + 126049077 q^{53} - 106214544 q^{54} + 553870071 q^{55} + 117743616 q^{56} + 384197394 q^{57} - 63148512 q^{58} + 135312639 q^{59} - 129611520 q^{60} + 132517452 q^{61} - 419324112 q^{62} + 577860735 q^{63} - 352321536 q^{64} - 184218951 q^{65} + 413765760 q^{66} + 229749621 q^{67} + 152743680 q^{68} - 517946637 q^{69} - 688313808 q^{70} - 2107934406 q^{71} + 105283584 q^{72} - 26577420 q^{73} + 322027248 q^{74} + 941894730 q^{75} - 107163648 q^{76} + 620006124 q^{77} + 122597280 q^{78} - 624601023 q^{79} - 1037387736 q^{81} + 1504541760 q^{82} + 907729401 q^{83} - 604998912 q^{84} + 1462808898 q^{85} + 222950208 q^{86} + 63648732 q^{87} - 133632000 q^{88} - 847590846 q^{89} - 4481693280 q^{90} + 957045924 q^{91} + 648163584 q^{92} + 2438307564 q^{93} + 2205393024 q^{94} - 208077987 q^{95} - 509607936 q^{96} + 535342599 q^{97} + 1861154832 q^{98} - 11757151095 q^{99}+O(q^{100}) \) 42 * q - 252 * q^3 + 4032 * q^6 + 14373 * q^7 + 86016 * q^8 + 12852 * q^9 + 32625 * q^11 - 62208 * q^12 + 351237 * q^13 + 165264 * q^14 - 834165 * q^15 + 1075035 * q^17 - 3364608 * q^18 + 696762 * q^19 - 1396224 * q^20 - 3148065 * q^21 - 1462656 * q^22 - 4882824 * q^23 + 1032192 * q^24 - 483270 * q^25 - 70176 * q^26 + 2570400 * q^27 + 1519104 * q^28 + 13670499 * q^29 - 2263968 * q^31 - 5777733 * q^33 - 9526080 * q^34 + 43019613 * q^35 + 3290112 * q^36 - 50105184 * q^37 - 692160 * q^38 - 89820600 * q^39 - 94033860 * q^41 - 43526160 * q^42 + 30524217 * q^43 + 23402496 * q^44 + 39789630 * q^45 - 18312576 * q^46 + 81865791 * q^47 + 33030144 * q^48 + 40421580 * q^49 - 16761600 * q^50 - 28132314 * q^51 - 91666176 * q^52 + 126049077 * q^53 - 106214544 * q^54 + 553870071 * q^55 + 117743616 * q^56 + 384197394 * q^57 - 63148512 * q^58 + 135312639 * q^59 - 129611520 * q^60 + 132517452 * q^61 - 419324112 * q^62 + 577860735 * q^63 - 352321536 * q^64 - 184218951 * q^65 + 413765760 * q^66 + 229749621 * q^67 + 152743680 * q^68 - 517946637 * q^69 - 688313808 * q^70 - 2107934406 * q^71 + 105283584 * q^72 - 26577420 * q^73 + 322027248 * q^74 + 941894730 * q^75 - 107163648 * q^76 + 620006124 * q^77 + 122597280 * q^78 - 624601023 * q^79 - 1037387736 * q^81 + 1504541760 * q^82 + 907729401 * q^83 - 604998912 * q^84 + 1462808898 * q^85 + 222950208 * q^86 + 63648732 * q^87 - 133632000 * q^88 - 847590846 * q^89 - 4481693280 * q^90 + 957045924 * q^91 + 648163584 * q^92 + 2438307564 * q^93 + 2205393024 * q^94 - 208077987 * q^95 - 509607936 * q^96 + 535342599 * q^97 + 1861154832 * q^98 - 11757151095 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$21$
$\chi(n)$	$e\left(\frac{5}{9}\right)$

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 $

$2$	−2.77837	+	15.7569i	−0.122788	+	0.696364i
$2$	−2.77837	+	15.7569i	−0.122788	+	0.696364i
$3$	74.8003	+	62.7649i	0.533160	+	0.447375i	0.869191	−	0.494476i	$-0.164640\pi$
$3$	74.8003	+	62.7649i	0.533160	+	0.447375i	−0.336031	+	0.941851i	$0.609085\pi$
$4$	−240.561	−	87.5572i	−0.469846	−	0.171010i
$5$	1601.32	−	582.833i	1.14581	−	0.417041i	0.301802	−	0.953371i	$-0.402412\pi$
$5$	1601.32	−	582.833i	1.14581	−	0.417041i	0.844009	+	0.536330i	$0.180190\pi$
$6$	−1196.81	+	1004.24i	−0.377001	+	0.316342i
$7$	2055.81	+	3560.77i	0.323625	+	0.560535i	0.981233	−	0.192825i	$-0.0617651\pi$
$7$	2055.81	+	3560.77i	0.323625	+	0.560535i	−0.657608	+	0.753360i	$0.728432\pi$
$8$	2048.00	−	3547.24i	0.176777	−	0.306186i
$9$	−1762.26	−	9994.30i	−0.0895323	−	0.507763i
$10$	4734.59	+	26851.2i	0.149721	+	0.849109i
$11$	29167.3	−	50519.2i	0.600660	−	1.04037i	−0.392061	−	0.919939i	$-0.628238\pi$
$11$	29167.3	−	50519.2i	0.600660	−	1.04037i	0.992721	−	0.120434i	$-0.0384287\pi$
$12$	−12498.5	−	21648.1i	−0.173998	−	0.301373i
$13$	85526.6	−	71765.4i	0.830532	−	0.696899i	−0.124881	−	0.992172i	$-0.539855\pi$
$13$	85526.6	−	71765.4i	0.830532	−	0.696899i	0.955413	+	0.295273i	$0.0954106\pi$
$14$	−61818.5	+	22500.1i	−0.430073	+	0.156534i
$15$	156361.	+	56910.6i	0.797475	+	0.290257i
$16$	50203.5	+	42125.7i	0.191511	+	0.160697i
$17$	51435.9	−	291707.i	0.149364	−	0.847085i	−0.814395	−	0.580311i	$-0.802931\pi$
$17$	51435.9	−	291707.i	0.149364	−	0.847085i	0.963759	−	0.266774i	$-0.0859578\pi$
$18$	162376.			0.364581
$19$	72881.4	+	563361.i	0.128300	+	0.991735i
$19$	72881.4	+	563361.i	0.128300	+	0.991735i
$20$	−436247.			−0.609673
$21$	−69716.0	+	395379.i	−0.0782251	+	0.443636i
$22$	714989.	+	599947.i	0.650725	+	0.546023i
$23$	−589167.	−	214439.i	−0.438999	−	0.159783i	0.113059	−	0.993588i	$-0.463935\pi$
$23$	−589167.	−	214439.i	−0.438999	−	0.159783i	−0.552058	+	0.833806i	$0.686157\pi$
$24$	375833.	−	136792.i	0.231230	−	0.0841609i
$25$	728349.	−	611158.i	0.372915	−	0.312913i
$26$	893177.	+	1.54703e6i	0.383316	+	0.663923i
$27$	1.45645e6	−	2.52264e6i	0.527421	−	0.913520i
$28$	−182778.	−	1.03658e6i	−0.0561969	−	0.318708i
$29$	982446.	+	5.57173e6i	0.257939	+	1.46285i	0.788413	+	0.615146i	$0.210903\pi$
$29$	982446.	+	5.57173e6i	0.257939	+	1.46285i	−0.530474	+	0.847701i	$0.677986\pi$
$30$	−1.33116e6	+	2.30564e6i	−0.300045	+	0.519693i
$31$	4.95106e6	+	8.57549e6i	0.962877	+	1.66775i	0.715215	+	0.698905i	$0.246329\pi$
$31$	4.95106e6	+	8.57549e6i	0.962877	+	1.66775i	0.247662	+	0.968847i	$0.420338\pi$
$32$	−803256.	+	674012.i	−0.135419	+	0.113630i
$33$	5.35255e6	−	1.94817e6i	0.785685	−	0.285966i
$34$	4.45350e6	+	1.62094e6i	0.571540	+	0.208023i
$35$	5.36734e6	+	4.50373e6i	0.604579	+	0.507302i
$36$	−451140.	+	2.55854e6i	−0.0447661	+	0.253881i
$37$	4.69775e6			0.412081			0.206040	−	0.978544i	$-0.433942\pi$
$37$	4.69775e6			0.412081			0.206040	+	0.978544i	$0.433942\pi$
$38$	−9.07933e6	−	416841.i	−0.706363	−	0.0324298i
$39$	1.09018e7			0.754581
$40$	1.21205e6	−	6.87391e6i	0.0748604	−	0.424555i
$41$	−2.20058e7	−	1.84651e7i	−1.21621	−	1.02052i	−0.999014	−	0.0443965i	$-0.985864\pi$
$41$	−2.20058e7	−	1.84651e7i	−1.21621	−	1.02052i	−0.217199	−	0.976127i	$-0.569692\pi$
$42$	−6.03627e6	−	2.19702e6i	−0.299327	−	0.108946i
$43$	924985.	−	336667.i	0.0412597	−	0.0150173i	−0.321308	−	0.946975i	$-0.604122\pi$
$43$	924985.	−	336667.i	0.0412597	−	0.0150173i	0.362568	+	0.931957i	$0.381900\pi$
$44$	−1.14398e7	+	9.59916e6i	−0.460132	+	0.386097i
$45$	−8.64695e6	−	1.49770e7i	−0.314345	−	0.544462i
$46$	5.01583e6	−	8.68767e6i	0.165171	−	0.286084i
$47$	1.54451e6	+	8.75933e6i	0.0461689	+	0.261837i	0.999151	−	0.0411885i	$-0.0131144\pi$
$47$	1.54451e6	+	8.75933e6i	0.0461689	+	0.261837i	−0.952982	+	0.303025i	$0.902003\pi$
$48$	1.11122e6	+	6.30204e6i	0.0302144	+	0.171354i
$49$	1.17241e7	−	2.03067e7i	0.290534	−	0.503220i
$50$	7.60634e6	+	1.31746e7i	0.172112	+	0.298106i
$51$	2.21564e7	−	1.85914e7i	0.458599	−	0.384811i
$52$	−2.68580e7	+	9.77550e6i	−0.509399	+	0.185406i
$53$	1.25163e7	+	4.55554e6i	0.217888	+	0.0793047i	0.448658	−	0.893704i	$-0.351902\pi$
$53$	1.25163e7	+	4.55554e6i	0.217888	+	0.0793047i	−0.230770	+	0.973008i	$0.574124\pi$
$54$	3.57025e7	+	2.99579e7i	0.571382	+	0.479446i
$55$	1.72619e7	−	9.78970e7i	0.254364	−	1.44257i
$56$	1.68412e7			0.228837
$57$	−2.99078e7	+	4.67140e7i	−0.375273	+	0.586152i
$58$	−9.05229e7			−1.05035
$59$	−5.52397e6	+	3.13280e7i	−0.0593496	+	0.336588i	−0.999996	−	0.00279976i	$-0.999109\pi$
$59$	−5.52397e6	+	3.13280e7i	−0.0593496	+	0.336588i	0.940647	+	0.339388i	$0.110220\pi$
$60$	−3.26314e7	−	2.73810e7i	−0.325054	−	0.272752i
$61$	−1.39602e8	−	5.08110e7i	−1.29094	−	0.469865i	−0.396907	−	0.917859i	$-0.629916\pi$
$61$	−1.39602e8	−	5.08110e7i	−1.29094	−	0.469865i	−0.894037	+	0.447994i	$0.852139\pi$
$62$	−1.48879e8	+	5.41876e7i	−1.27959	+	0.465733i
$63$	3.19645e7	−	2.68214e7i	0.255644	−	0.214511i
$64$	−8.38861e6	−	1.45295e7i	−0.0625000	−	0.108253i
$65$	9.51282e7	−	1.64767e8i	0.660997	−	1.14488i
$66$	1.58258e7	+	8.97525e7i	0.102664	+	0.582236i
$67$	−2.68365e7	−	1.52197e8i	−0.162700	−	0.922720i	−0.951404	−	0.307946i	$-0.900358\pi$
$67$	−2.68365e7	−	1.52197e8i	−0.162700	−	0.922720i	0.788703	−	0.614774i	$-0.210753\pi$
$68$	−3.79145e7	+	6.56699e7i	−0.215038	+	0.372457i
$69$	−3.06106e7	−	5.30192e7i	−0.162574	−	0.281587i
$70$	−8.58774e7	+	7.20597e7i	−0.427502	+	0.358717i
$71$	−2.49113e8	+	9.06699e7i	−1.16341	+	0.423448i	−0.850316	−	0.526272i	$-0.823589\pi$
$71$	−2.49113e8	+	9.06699e7i	−1.16341	+	0.423448i	−0.313099	+	0.949721i	$0.601367\pi$
$72$	−3.90613e7	−	1.42171e7i	−0.171297	−	0.0623471i
$73$	2.21069e8	+	1.85499e8i	0.911119	+	0.764519i	0.972331	−	0.233605i	$-0.0750524\pi$
$73$	2.21069e8	+	1.85499e8i	0.911119	+	0.764519i	−0.0612128	+	0.998125i	$0.519497\pi$
$74$	−1.30521e7	+	7.40221e7i	−0.0505985	+	0.286958i
$75$	9.28400e7			0.338813
$76$	3.17939e7	−	1.41904e8i	0.109316	−	0.487904i
$77$	2.39849e8			0.777554
$78$	−3.02891e7	+	1.71778e8i	−0.0926534	+	0.525464i
$79$	2.57442e8	+	2.16020e8i	0.743632	+	0.623981i	0.933810	−	0.357768i	$-0.116462\pi$
$79$	2.57442e8	+	2.16020e8i	0.743632	+	0.623981i	−0.190179	+	0.981750i	$0.560907\pi$
$80$	1.04944e8	+	3.81965e7i	0.286453	+	0.104260i
$81$	7.95699e7	−	2.89611e7i	0.205384	−	0.0747536i
$82$	3.52093e8	−	2.95441e8i	0.859992	−	0.721619i
$83$	−6.96443e7	−	1.20627e8i	−0.161077	−	0.278994i	0.774178	−	0.632968i	$-0.218163\pi$
$83$	−6.96443e7	−	1.20627e8i	−0.161077	−	0.278994i	−0.935255	+	0.353974i	$0.884830\pi$
$84$	5.13893e7	−	8.90088e7i	0.112620	−	0.195064i
$85$	−8.76513e7	−	4.97095e8i	−0.182126	−	1.03289i
$86$	2.73488e6	+	1.55103e7i	0.00539133	+	0.0305757i
$87$	−2.76222e8	+	4.78430e8i	−0.516918	+	0.895328i
$88$	−1.19469e8	−	2.06927e8i	−0.212365	−	0.367828i
$89$	5.06429e8	−	4.24944e8i	0.855586	−	0.717922i	−0.105426	−	0.994427i	$-0.533621\pi$
$89$	5.06429e8	−	4.24944e8i	0.855586	−	0.717922i	0.961012	+	0.276505i	$0.0891763\pi$
$90$	2.60015e8	−	9.46378e7i	0.417741	−	0.152045i
$91$	4.31366e8	+	1.57004e8i	0.659417	+	0.240008i
$92$	1.22955e8	+	1.03172e8i	0.178938	+	0.150146i
$93$	−1.67899e8	+	9.52202e8i	−0.232742	+	1.31995i
$94$	−1.42311e8			−0.188003
$95$	4.45052e8	+	8.59644e8i	0.560601	+	1.08284i
$96$	−1.02388e8			−0.123035
$97$	−3.28835e7	+	1.86492e8i	−0.0377142	+	0.213888i	−0.997841	−	0.0656773i	$-0.979079\pi$
$97$	−3.28835e7	+	1.86492e8i	−0.0377142	+	0.213888i	0.960127	+	0.279565i	$0.0901903\pi$
$98$	2.87398e8	+	2.41155e8i	0.314750	+	0.264107i
$99$	−5.56304e8	−	2.02478e8i	−0.582041	−	0.211846i
$100$	−2.28724e8	+	8.32487e7i	−0.228724	+	0.0832487i
$101$	1.11348e9	−	9.34324e8i	1.06473	−	0.893411i	0.0701618	−	0.997536i	$-0.477648\pi$
$101$	1.11348e9	−	9.34324e8i	1.06473	−	0.893411i	0.994564	+	0.104124i	$0.0332040\pi$
$102$	2.31385e8	+	4.00771e8i	0.211658	+	0.366602i
$103$	−5.80675e8	+	1.00576e9i	−0.508353	+	0.880494i	0.491600	+	0.870821i	$0.336412\pi$
$103$	−5.80675e8	+	1.00576e9i	−0.508353	+	0.880494i	−0.999953	+	0.00967256i	$0.996921\pi$
$104$	−7.94104e7	−	4.50359e8i	−0.0665622	−	0.377493i
$105$	1.18802e8	+	6.73761e8i	0.0953835	+	0.540946i
$106$	−1.06556e8	+	1.84561e8i	−0.0819789	+	0.141992i
$107$	−7.65152e8	−	1.32528e9i	−0.564314	−	0.977420i	−0.997113	−	0.0759299i	$-0.975807\pi$
$107$	−7.65152e8	−	1.32528e9i	−0.564314	−	0.977420i	0.432799	−	0.901490i	$-0.357526\pi$
$108$	−5.71239e8	+	4.79327e8i	−0.404028	+	0.339020i
$109$	−1.96287e9	+	7.14427e8i	−1.33190	+	0.484773i	−0.907253	−	0.420584i	$-0.861825\pi$
$109$	−1.96287e9	+	7.14427e8i	−1.33190	+	0.484773i	−0.424650	+	0.905358i	$0.639603\pi$
$110$	1.49460e9	+	5.43988e8i	0.973322	+	0.354260i
$111$	3.51393e8	+	2.94854e8i	0.219705	+	0.184354i
$112$	−4.67911e7	+	2.65365e8i	−0.0280984	+	0.159354i
$113$	−8.53758e7			−0.0492585			−0.0246293	−	0.999697i	$-0.507841\pi$
$113$	−8.53758e7			−0.0492585			−0.0246293	+	0.999697i	$0.507841\pi$
$114$	−6.52974e8	−	6.01044e8i	−0.362096	−	0.333299i
$115$	−1.06843e9			−0.569646
$116$	2.51506e8	−	1.42636e9i	0.128970	−	0.731424i
$117$	−8.67965e8	−	7.28309e8i	−0.428219	−	0.359318i
$118$	−4.78285e8	−	1.74082e8i	−0.227101	−	0.0826578i
$119$	1.14444e9	−	4.16544e8i	0.523158	−	0.190414i
$120$	5.22102e8	−	4.38096e8i	0.229848	−	0.192865i
$121$	−5.22485e8	−	9.04970e8i	−0.221584	−	0.383796i
$122$	1.18849e9	−	2.05853e9i	0.485709	−	0.841273i
$123$	−4.87083e8	−	2.76238e9i	−0.191880	−	1.08821i
$124$	−4.40188e8	−	2.49643e9i	−0.167202	−	0.948248i
$125$	−8.54032e8	+	1.47923e9i	−0.312881	+	0.541925i
$126$	3.33813e8	+	5.78182e8i	0.117988	+	0.204360i
$127$	−1.37040e9	+	1.14990e9i	−0.467444	+	0.392232i	−0.845861	−	0.533403i	$-0.820913\pi$
$127$	−1.37040e9	+	1.14990e9i	−0.467444	+	0.392232i	0.378417	+	0.925635i	$0.376468\pi$
$128$	2.52247e8	−	9.18103e7i	0.0830579	−	0.0302306i
$129$	9.03200e7	+	3.28738e7i	0.0287164	+	0.0104519i
$130$	2.33192e9	+	1.95671e9i	0.716091	+	0.600872i
$131$	−7.67546e8	+	4.35297e9i	−0.227711	+	1.29141i	0.629724	+	0.776819i	$0.283168\pi$
$131$	−7.67546e8	+	4.35297e9i	−0.227711	+	1.29141i	−0.857435	+	0.514593i	$0.827943\pi$
$132$	−1.45819e9			−0.418054
$133$	−1.85617e9	+	1.41768e9i	−0.514381	+	0.392867i
$134$	2.47272e9			0.662527
$135$	8.61959e8	−	4.88841e9i	0.223349	−	1.26668i
$136$	−9.29415e8	−	7.79872e8i	−0.232962	−	0.195478i
$137$	−5.19115e9	−	1.88942e9i	−1.25899	−	0.458234i	−0.375558	−	0.926799i	$-0.622549\pi$
$137$	−5.19115e9	−	1.88942e9i	−1.25899	−	0.458234i	−0.883429	+	0.468565i	$0.844771\pi$
$138$	9.20467e8	−	3.35023e8i	0.216049	−	0.0786354i
$139$	1.29416e9	−	1.08593e9i	0.294050	−	0.246737i	−0.483812	−	0.875172i	$-0.660748\pi$
$139$	1.29416e9	−	1.08593e9i	0.294050	−	0.246737i	0.777863	+	0.628434i	$0.216304\pi$
$140$	−8.96840e8	−	1.55337e9i	−0.197305	−	0.341743i
$141$	−4.34249e8	+	7.52142e8i	−0.0925237	+	0.160256i
$142$	−7.36549e8	−	4.17718e9i	−0.152021	−	0.862155i
$143$	−1.13095e9	−	6.41393e9i	−0.226168	−	1.28266i
$144$	3.32545e8	−	5.75985e8i	0.0644495	−	0.111630i
$145$	4.82060e9	+	8.34952e9i	0.905617	+	1.56858i
$146$	−3.53710e9	+	2.96798e9i	−0.644258	+	0.540597i
$147$	2.15152e9	−	7.83088e8i	0.380029	−	0.138319i
$148$	−1.13010e9	−	4.11322e8i	−0.193615	−	0.0704699i
$149$	−1.49677e9	−	1.25594e9i	−0.248781	−	0.208752i	0.509866	−	0.860254i	$-0.329695\pi$
$149$	−1.49677e9	−	1.25594e9i	−0.248781	−	0.208752i	−0.758647	+	0.651502i	$0.774139\pi$
$150$	−2.57944e8	+	1.46287e9i	−0.0416021	+	0.235937i
$151$	5.30494e9			0.830394			0.415197	−	0.909731i	$-0.363713\pi$
$151$	5.30494e9			0.830394			0.415197	+	0.909731i	$0.363713\pi$
$152$	2.14764e9	+	8.95236e8i	0.326336	+	0.136032i
$153$	−3.00605e9			−0.443491
$154$	−6.66391e8	+	3.77929e9i	−0.0954741	+	0.541461i
$155$	1.29263e10	+	1.08465e10i	1.79880	+	1.50937i
$156$	−2.62254e9	−	9.54528e8i	−0.354537	−	0.129041i
$157$	−1.36273e10	+	4.95993e9i	−1.79003	+	0.651519i	−0.790813	+	0.612058i	$0.790342\pi$
$157$	−1.36273e10	+	4.95993e9i	−1.79003	+	0.651519i	−0.999221	+	0.0394611i	$0.987436\pi$
$158$	−4.11908e9	+	3.45632e9i	−0.525827	+	0.441221i
$159$	6.50292e8	+	1.12634e9i	0.0806903	+	0.139760i
$160$	−8.93433e8	+	1.54747e9i	−0.107776	+	0.186674i
$161$	−4.47647e8	−	2.53873e9i	−0.0525073	−	0.297784i
$162$	2.35263e8	+	1.33424e9i	0.0268371	+	0.152201i
$163$	2.00156e9	−	3.46681e9i	0.222088	−	0.384667i	−0.733354	−	0.679847i	$-0.762046\pi$
$163$	2.00156e9	−	3.46681e9i	0.222088	−	0.384667i	0.955442	+	0.295180i	$0.0953795\pi$
$164$	3.67699e9	+	6.36874e9i	0.396913	+	0.687474i
$165$	7.43569e9	−	6.23929e9i	0.780987	−	0.655326i
$166$	2.09422e9	−	7.62232e8i	0.214060	−	0.0779114i
$167$	1.20373e10	+	4.38120e9i	1.19758	+	0.435882i	0.862378	−	0.506265i	$-0.168974\pi$
$167$	1.20373e10	+	4.38120e9i	1.19758	+	0.435882i	0.335199	+	0.942147i	$0.391196\pi$
$168$	1.25973e9	+	1.05704e9i	0.122007	+	0.102376i
$169$	3.23084e8	−	1.83230e9i	0.0304667	−	0.172785i
$170$	8.07622e9			0.741631
$171$	5.50196e9	−	1.72119e9i	0.492079	−	0.153938i
$172$	−2.51993e8			−0.0219538
$173$	−2.07922e9	+	1.17919e10i	−0.176479	+	1.00086i	0.759943	+	0.649989i	$0.225227\pi$
$173$	−2.07922e9	+	1.17919e10i	−0.176479	+	1.00086i	−0.936423	+	0.350874i	$0.885884\pi$
$174$	−6.77114e9	−	5.68166e9i	−0.560003	−	0.469898i
$175$	3.67354e9	+	1.33706e9i	0.296083	+	0.107765i
$176$	3.59246e9	−	1.30755e9i	0.282218	−	0.102719i
$177$	−2.37950e9	+	1.99663e9i	−0.182224	+	0.152904i
$178$	5.28877e9	+	9.16042e9i	0.394880	+	0.683951i
$179$	1.11310e10	−	1.92795e10i	0.810394	−	1.40364i	−0.102194	−	0.994764i	$-0.532586\pi$
$179$	1.11310e10	−	1.92795e10i	0.810394	−	1.40364i	0.912588	−	0.408879i	$-0.134080\pi$
$180$	7.68782e8	+	4.35998e9i	0.0545854	+	0.309569i
$181$	3.34266e8	+	1.89572e9i	0.0231494	+	0.131287i	0.994192	−	0.107619i	$-0.0343226\pi$
$181$	3.34266e8	+	1.89572e9i	0.0231494	+	0.131287i	−0.971043	+	0.238905i	$0.923211\pi$
$182$	−3.67240e9	+	6.36079e9i	−0.248101	+	0.429724i
$183$	−7.25313e9	−	1.25628e10i	−0.478074	−	0.828049i
$184$	−1.96728e9	+	1.65075e9i	−0.126528	+	0.106170i
$185$	7.52260e9	−	2.73800e9i	0.472166	−	0.171855i
$186$	−1.45373e10	−	5.29114e9i	−0.890585	−	0.324146i
$187$	−1.32366e10	−	1.11068e10i	−0.791568	−	0.664204i
$188$	3.95394e8	−	2.24239e9i	0.0230844	−	0.130918i
$189$	1.19767e10			0.682746
$190$	−1.47819e10	+	4.62424e9i	−0.822883	+	0.257424i
$191$	−1.97859e10			−1.07574			−0.537868	−	0.843029i	$-0.680770\pi$
$191$	−1.97859e10			−1.07574			−0.537868	+	0.843029i	$0.680770\pi$
$192$	2.84472e8	−	1.61332e9i	0.0151072	−	0.0856772i
$193$	1.64866e10	+	1.38339e10i	0.855307	+	0.717688i	0.960952	−	0.276716i	$-0.0892461\pi$
$193$	1.64866e10	+	1.38339e10i	0.855307	+	0.717688i	−0.105644	+	0.994404i	$0.533691\pi$
$194$	−2.84717e9	−	1.03629e9i	−0.144313	−	0.0525257i
$195$	1.74572e10	−	6.35390e9i	0.864608	−	0.314691i
$196$	−4.59836e9	+	3.85848e9i	−0.222562	+	0.186752i
$197$	−6.84511e9	−	1.18561e10i	−0.323804	−	0.560846i	0.657465	−	0.753485i	$-0.271629\pi$
$197$	−6.84511e9	−	1.18561e10i	−0.323804	−	0.560846i	−0.981270	+	0.192639i	$0.938295\pi$
$198$	4.73605e9	−	8.20308e9i	0.218989	−	0.379301i
$199$	−1.65505e9	−	9.38626e9i	−0.0748122	−	0.424281i	−0.999094	−	0.0425692i	$-0.986446\pi$
$199$	−1.65505e9	−	9.38626e9i	−0.0748122	−	0.424281i	0.924281	−	0.381712i	$-0.124665\pi$
$200$	−6.76263e8	−	3.83528e9i	−0.0298869	−	0.169497i
$201$	7.54527e9	−	1.30688e10i	0.326056	−	0.564746i
$202$	1.16284e10	+	2.01410e10i	0.491404	+	0.851137i
$203$	−1.78199e10	+	1.49527e10i	−0.736501	+	0.617998i
$204$	−6.95779e9	+	2.53243e9i	−0.281278	+	0.102377i
$205$	−4.60003e10	−	1.67428e10i	−1.81915	−	0.662117i
$206$	−1.42343e10	−	1.19440e10i	−0.550725	−	0.462113i
$207$	−1.10490e9	+	6.26621e9i	−0.0418271	+	0.237213i
$208$	7.31690e9			0.271046
$209$	3.05863e10	+	1.27498e10i	1.10884	+	0.462216i
$210$	−1.09465e10			−0.388408
$211$	−8.00925e8	+	4.54227e9i	−0.0278177	+	0.157762i	−0.995552	−	0.0942093i	$-0.969968\pi$
$211$	−8.00925e8	+	4.54227e9i	−0.0278177	+	0.157762i	0.967735	+	0.251971i	$0.0810788\pi$
$212$	−2.61206e9	−	2.19178e9i	−0.0888119	−	0.0745220i
$213$	−2.43247e10	−	8.85345e9i	−0.809727	−	0.294716i
$214$	2.30082e10	−	8.37432e9i	0.749931	−	0.272953i
$215$	1.28498e9	−	1.07822e9i	0.0410130	−	0.0344140i
$216$	−5.96560e9	−	1.03327e10i	−0.186471	−	0.322978i
$217$	−2.03569e10	+	3.52592e10i	−0.623222	+	1.07945i
$218$	−5.80359e9	−	3.29138e10i	−0.174037	−	0.987014i
$219$	4.89321e9	+	2.77508e10i	0.143746	+	0.815223i
$220$	−1.27241e10	+	2.20388e10i	−0.366206	+	0.634288i
$221$	−1.65353e10	−	2.86400e10i	−0.466281	−	0.807623i
$222$	−5.62229e9	+	4.71766e9i	−0.155355	+	0.130358i
$223$	4.78296e10	−	1.74085e10i	1.29516	−	0.471401i	0.399745	−	0.916627i	$-0.369099\pi$
$223$	4.78296e10	−	1.74085e10i	1.29516	−	0.471401i	0.895418	+	0.445226i	$0.146877\pi$
$224$	−4.05134e9	−	1.47457e9i	−0.107518	−	0.0391335i
$225$	−7.39163e9	−	6.20232e9i	−0.192273	−	0.161337i
$226$	2.37206e8	−	1.34526e9i	0.00604835	−	0.0343019i
$227$	−1.00906e10			−0.252233			−0.126116	−	0.992015i	$-0.540251\pi$
$227$	−1.00906e10			−0.252233			−0.126116	+	0.992015i	$0.540251\pi$
$228$	1.12848e10	−	8.61894e9i	0.276559	−	0.211226i
$229$	−5.78341e10			−1.38971			−0.694856	−	0.719149i	$-0.744532\pi$
$229$	−5.78341e10			−1.38971			−0.694856	+	0.719149i	$0.744532\pi$
$230$	2.96849e9	−	1.68351e10i	0.0699455	−	0.396681i
$231$	1.79408e10	+	1.50541e10i	0.414561	+	0.347858i
$232$	2.17763e10	+	7.92593e9i	0.493501	+	0.179620i
$233$	9.84190e8	−	3.58216e8i	0.0218765	−	0.00796239i	−0.331059	−	0.943610i	$-0.607406\pi$
$233$	9.84190e8	−	3.58216e8i	0.0218765	−	0.00796239i	0.352935	+	0.935648i	$0.385184\pi$
$234$	1.38874e10	−	1.16529e10i	0.302796	−	0.254076i
$235$	7.57847e9	+	1.31263e10i	0.162098	+	0.280761i
$236$	4.07185e9	−	7.05264e9i	0.0854451	−	0.147995i
$237$	5.69830e9	+	3.23167e10i	0.117322	+	0.665364i
$238$	3.38376e9	+	1.91902e10i	0.0683601	+	0.387689i
$239$	2.99346e10	−	5.18483e10i	0.593449	−	1.02788i	−0.400315	−	0.916378i	$-0.631099\pi$
$239$	2.99346e10	−	5.18483e10i	0.593449	−	1.02788i	0.993764	−	0.111506i	$-0.0355674\pi$
$240$	5.45245e9	+	9.44392e9i	0.106082	+	0.183739i
$241$	−7.38784e10	+	6.19913e10i	−1.41072	+	1.18373i	−0.454623	+	0.890684i	$0.650226\pi$
$241$	−7.38784e10	+	6.19913e10i	−1.41072	+	1.18373i	−0.956097	+	0.293050i	$0.905330\pi$
$242$	1.57112e10	−	5.71841e9i	0.294469	−	0.107178i
$243$	−4.61072e10	−	1.67816e10i	−0.848282	−	0.308749i
$244$	2.91340e10	+	2.44463e10i	0.526193	+	0.441529i
$245$	6.93860e9	−	3.93507e10i	0.123034	−	0.697759i
$246$	4.48800e10			0.781348
$247$	4.66631e10	+	4.29520e10i	0.797696	+	0.734256i
$248$	4.05591e10			0.680857
$249$	2.36176e9	−	1.33942e10i	0.0389348	−	0.220810i
$250$	−2.09352e10	−	1.75668e10i	−0.338960	−	0.284421i
$251$	1.36567e10	+	4.97062e9i	0.217177	+	0.0790458i	0.448317	−	0.893875i	$-0.352024\pi$
$251$	1.36567e10	+	4.97062e9i	0.217177	+	0.0790458i	−0.231141	+	0.972920i	$0.574246\pi$
$252$	−1.00378e10	+	3.65347e9i	−0.156797	+	0.0570694i
$253$	−2.80177e10	+	2.35096e10i	−0.429922	+	0.360748i
$254$	−1.43114e10	−	2.47881e10i	−0.215740	−	0.373673i
$255$	2.46438e10	−	4.26843e10i	0.364986	−	0.632175i
$256$	7.45813e8	+	4.22972e9i	0.0108530	+	0.0615505i
$257$	4.96670e9	+	2.81676e10i	0.0710181	+	0.402764i	0.999507	+	0.0314031i	$0.00999756\pi$
$257$	4.96670e9	+	2.81676e10i	0.0710181	+	0.402764i	−0.928489	+	0.371361i	$0.878891\pi$
$258$	−7.68932e8	+	1.33183e9i	−0.0108044	+	0.0187137i
$259$	9.65768e9	+	1.67276e10i	0.133360	+	0.230985i
$260$	−3.73107e10	+	3.13074e10i	−0.506353	+	0.424881i
$261$	5.39542e10	−	1.96377e10i	0.719686	−	0.261944i
$262$	−6.64569e10	−	2.41883e10i	−0.871333	−	0.317139i
$263$	6.14525e10	+	5.15648e10i	0.792025	+	0.664588i	0.946246	−	0.323448i	$-0.104842\pi$
$263$	6.14525e10	+	5.15648e10i	0.792025	+	0.664588i	−0.154221	+	0.988036i	$0.549287\pi$
$264$	4.05140e9	−	2.29766e10i	0.0513319	−	0.291118i
$265$	2.26976e10			0.282732
$266$	−1.71811e10	−	3.31863e10i	−0.210418	−	0.406436i
$267$	6.45527e10			0.777345
$268$	−6.87014e9	+	3.89625e10i	−0.0813502	+	0.461360i
$269$	−1.10230e10	−	9.24937e9i	−0.128355	−	0.107703i	0.576350	−	0.817203i	$-0.304476\pi$
$269$	−1.10230e10	−	9.24937e9i	−0.128355	−	0.107703i	−0.704705	+	0.709500i	$0.748921\pi$
$270$	7.46315e10	+	2.71636e10i	0.854644	+	0.311065i
$271$	−4.67132e10	+	1.70022e10i	−0.526111	+	0.191489i	−0.591401	−	0.806377i	$-0.701425\pi$
$271$	−4.67132e10	+	1.70022e10i	−0.526111	+	0.191489i	0.0652898	+	0.997866i	$0.479203\pi$
$272$	1.48706e10	−	1.24779e10i	0.164729	−	0.138224i
$273$	2.24120e10	+	3.88187e10i	0.244201	+	0.422969i
$274$	4.41945e10	−	7.65471e10i	0.473686	−	0.820448i
$275$	−9.63123e9	−	5.46214e10i	−0.101551	−	0.575925i
$276$	2.72153e9	+	1.54345e10i	0.0282307	+	0.160104i
$277$	−4.91530e10	+	8.51355e10i	−0.501639	+	0.868864i	0.498359	+	0.866971i	$0.333936\pi$
$277$	−4.91530e10	+	8.51355e10i	−0.501639	+	0.868864i	−0.999998	+	0.00189330i	$0.999397\pi$
$278$	1.35153e10	+	2.34091e10i	0.135713	+	0.235062i
$279$	7.69809e10	−	6.45946e10i	0.760614	−	0.638231i
$280$	2.69681e10	−	9.81560e9i	0.262204	−	0.0954345i
$281$	−4.07149e10	−	1.48190e10i	−0.389560	−	0.141788i	0.139812	−	0.990178i	$-0.455350\pi$
$281$	−4.07149e10	−	1.48190e10i	−0.389560	−	0.141788i	−0.529372	+	0.848390i	$0.677572\pi$
$282$	−1.06449e10	−	8.93216e9i	−0.100236	−	0.0841077i
$283$	−2.79783e10	+	1.58673e11i	−0.259288	+	1.47049i	0.525535	+	0.850772i	$0.323865\pi$
$283$	−2.79783e10	+	1.58673e11i	−0.259288	+	1.47049i	−0.784822	+	0.619721i	$0.787246\pi$
$284$	6.78659e10			0.619040
$285$	−2.06655e10	+	9.22353e10i	−0.185542	+	0.828124i
$286$	1.04206e11			0.920971
$287$	2.05100e10	−	1.16318e11i	0.178442	−	1.01200i
$288$	8.15182e9	+	6.84019e9i	0.0698214	+	0.0585871i
$289$	2.89887e10	+	1.05510e10i	0.244449	+	0.0889721i
$290$	−1.44956e11	+	5.27597e10i	−1.20350	+	0.438038i
$291$	−1.41648e10	+	1.18857e10i	−0.115796	+	0.0971642i
$292$	−3.69389e10	−	6.39800e10i	−0.297345	−	0.515017i
$293$	−5.86944e10	+	1.01662e11i	−0.465256	+	0.805848i	−0.999213	−	0.0396642i	$-0.987371\pi$
$293$	−5.86944e10	+	1.01662e11i	−0.465256	+	0.805848i	0.533957	+	0.845512i	$0.320705\pi$
$294$	6.36135e9	+	3.60770e10i	0.0496576	+	0.281622i
$295$	9.41334e9	+	5.33857e10i	0.0723677	+	0.410418i
$296$	9.62099e9	−	1.66640e10i	0.0728462	−	0.126173i
$297$	−8.49611e10	−	1.47157e11i	−0.633601	−	1.09743i
$298$	2.39483e10	−	2.00950e10i	0.175914	−	0.147610i
$299$	−6.57788e10	+	2.39415e10i	−0.475955	+	0.173233i
$300$	−2.23337e10	−	8.12881e9i	−0.159190	−	0.0579404i
$301$	3.10038e9	+	2.60153e9i	0.0217704	+	0.0182675i
$302$	−1.47391e10	+	8.35896e10i	−0.101962	+	0.578257i
$303$	1.41932e11			0.967359
$304$	−2.00731e10	+	3.13529e10i	−0.134798	+	0.210546i
$305$	−2.53162e11			−1.67513
$306$	8.35193e9	−	4.73661e10i	0.0544553	−	0.308831i
$307$	−1.13668e11	−	9.53791e10i	−0.730327	−	0.612817i	0.199894	−	0.979818i	$-0.435940\pi$
$307$	−1.13668e11	−	9.53791e10i	−0.730327	−	0.612817i	−0.930221	+	0.367001i	$0.880385\pi$
$308$	−5.76985e10	−	2.10005e10i	−0.365331	−	0.132970i
$309$	−1.06561e11	+	3.87851e10i	−0.664944	+	0.242020i
$310$	−2.06821e11	+	1.73543e11i	−1.27194	+	1.06728i
$311$	−1.04498e11	−	1.80996e11i	−0.633411	−	1.09710i	−0.986849	−	0.161642i	$-0.948321\pi$
$311$	−1.04498e11	−	1.80996e11i	−0.633411	−	1.09710i	0.353438	−	0.935458i	$-0.385012\pi$
$312$	2.23268e10	−	3.86712e10i	0.133392	−	0.231042i
$313$	−2.29291e10	−	1.30038e11i	−0.135032	−	0.765807i	−0.974837	−	0.222918i	$-0.928442\pi$
$313$	−2.29291e10	−	1.30038e11i	−0.135032	−	0.765807i	0.839805	−	0.542889i	$-0.182669\pi$
$314$	−4.02916e10	−	2.28505e11i	−0.233900	−	1.32651i
$315$	3.55530e10	−	6.15796e10i	0.203460	−	0.352403i
$316$	−4.30166e10	−	7.45069e10i	−0.242686	−	0.420344i
$317$	7.02135e10	−	5.89161e10i	0.390530	−	0.327693i	−0.426290	−	0.904587i	$-0.640180\pi$
$317$	7.02135e10	−	5.89161e10i	0.390530	−	0.327693i	0.816819	+	0.576893i	$0.195735\pi$
$318$	−1.95544e10	+	7.11721e9i	−0.107231	+	0.0390290i
$319$	3.10134e11	+	1.12880e11i	1.67684	+	0.610320i
$320$	−2.19011e10	−	1.83772e10i	−0.116759	−	0.0979726i
$321$	2.59476e10	−	1.47156e11i	0.136403	−	0.773581i
$322$	4.12464e10			0.213813
$323$	1.68085e11	+	7.71695e9i	0.859248	+	0.0394489i
$324$	−2.16772e10			−0.109282
$325$	1.84333e10	−	1.04540e11i	0.0916491	−	0.519768i
$326$	4.90651e10	+	4.11705e10i	0.240599	+	0.201887i
$327$	−1.91664e11	−	6.97602e10i	−0.926993	−	0.337398i
$328$	−1.10568e11	+	4.02434e10i	−0.527468	+	0.191983i
$329$	−2.80147e10	+	2.35072e10i	−0.131827	+	0.110616i
$330$	7.76528e10	+	1.34499e11i	0.360450	+	0.624317i
$331$	1.10592e10	−	1.91552e10i	0.0506407	−	0.0877122i	−0.839594	−	0.543215i	$-0.817207\pi$
$331$	1.10592e10	−	1.91552e10i	0.0506407	−	0.0877122i	0.890235	+	0.455502i	$0.150540\pi$
$332$	6.19193e9	+	3.51162e10i	0.0279708	+	0.158630i
$333$	−8.27868e9	−	4.69507e10i	−0.0368945	−	0.209239i
$334$	−1.02478e11	+	1.77498e11i	−0.450581	+	0.780429i
$335$	−1.31679e11	−	2.28075e11i	−0.571236	−	0.989410i
$336$	−2.01556e10	+	1.69126e10i	−0.0862720	+	0.0723908i
$337$	1.14724e11	−	4.17561e10i	0.484528	−	0.176354i	−0.0881941	−	0.996103i	$-0.528110\pi$
$337$	1.14724e11	−	4.17561e10i	0.484528	−	0.176354i	0.572722	+	0.819749i	$0.305887\pi$
$338$	2.79738e10	+	1.01816e10i	0.116581	+	0.0424319i
$339$	−6.38613e9	−	5.35860e9i	−0.0262627	−	0.0220370i
$340$	−2.24387e10	+	1.27256e11i	−0.0910632	+	0.516445i
$341$	5.77636e11			2.31345
$342$	1.18342e10	+	9.14761e10i	0.0467756	+	0.361568i
$343$	2.62329e11			1.02335
$344$	7.00130e8	−	3.97064e9i	0.00269566	−	0.0152879i
$345$	−7.99187e10	−	6.70598e10i	−0.303712	−	0.254845i
$346$	−1.80027e11	−	6.55243e10i	−0.675296	−	0.245788i
$347$	1.40815e11	−	5.12525e10i	0.521395	−	0.189772i	−0.0678971	−	0.997692i	$-0.521629\pi$
$347$	1.40815e11	−	5.12525e10i	0.521395	−	0.189772i	0.589292	+	0.807920i	$0.299407\pi$
$348$	1.08338e11	−	9.09066e10i	0.395982	−	0.332268i
$349$	1.50311e11	+	2.60346e11i	0.542346	+	0.939370i	0.998769	+	0.0496075i	$0.0157970\pi$
$349$	1.50311e11	+	2.60346e11i	0.542346	+	0.939370i	−0.456423	+	0.889763i	$0.650870\pi$
$350$	−3.12744e10	+	5.41688e10i	−0.111399	+	0.192949i
$351$	−5.64731e10	−	3.20275e11i	−0.198591	−	1.12627i
$352$	1.06217e10	+	6.02389e10i	0.0368769	+	0.209139i
$353$	−1.24602e11	+	2.15817e11i	−0.427108	+	0.739773i	−0.996615	−	0.0822135i	$-0.973801\pi$
$353$	−1.24602e11	+	2.15817e11i	−0.427108	+	0.739773i	0.569506	+	0.821987i	$0.307134\pi$
$354$	−2.48497e10	−	4.30409e10i	−0.0841020	−	0.145669i
$355$	−3.46065e11	+	2.90383e11i	−1.15646	+	0.970383i
$356$	−1.59034e11	+	5.78837e10i	−0.524766	+	0.190999i
$357$	1.11749e11	+	4.06734e10i	0.364114	+	0.132527i
$358$	2.72859e11	+	2.28956e11i	0.877941	+	0.736680i
$359$	2.57649e10	−	1.46120e11i	0.0818659	−	0.464285i	−0.916123	−	0.400897i	$-0.868698\pi$
$359$	2.57649e10	−	1.46120e11i	0.0818659	−	0.464285i	0.997989	−	0.0633876i	$-0.0201904\pi$
$360$	−7.08358e10			−0.222276
$361$	−3.12064e11	+	8.21171e10i	−0.967078	+	0.254479i
$362$	−3.07994e10			−0.0942658
$363$	1.77183e10	−	1.00486e11i	0.0535604	−	0.303756i
$364$	−9.00232e10	−	7.55384e10i	−0.268781	−	0.225534i
$365$	4.62117e11	+	1.68197e11i	1.36281	+	0.496021i
$366$	2.18103e11	−	7.93829e10i	0.635325	−	0.231239i
$367$	−3.70083e11	+	3.10536e11i	−1.06488	+	0.893543i	−0.994579	−	0.103983i	$-0.966841\pi$
$367$	−3.70083e11	+	3.10536e11i	−1.06488	+	0.893543i	−0.0703035	+	0.997526i	$0.522397\pi$
$368$	−2.05448e10	−	3.55847e10i	−0.0583966	−	0.101146i
$369$	−1.45765e11	+	2.52473e11i	−0.409294	+	0.708918i
$370$	2.22419e10	+	1.26140e11i	0.0616971	+	0.349901i
$371$	9.50981e9	+	5.39328e10i	0.0260609	+	0.147799i
$372$	1.23762e11	−	2.14362e11i	0.335077	−	0.580370i
$373$	−3.01493e11	−	5.22201e11i	−0.806468	−	1.39684i	−0.915295	−	0.402783i	$-0.868043\pi$
$373$	−3.01493e11	−	5.22201e11i	−0.806468	−	1.39684i	0.108827	−	0.994061i	$-0.465291\pi$
$374$	2.11785e11	−	1.77709e11i	0.559723	−	0.469663i
$375$	−1.56725e11	+	5.70434e10i	−0.409259	+	0.148958i
$376$	3.42346e10	+	1.24604e10i	0.0883324	+	0.0321504i
$377$	4.83882e11	+	4.06026e11i	1.23368	+	1.03518i
$378$	−3.32757e10	+	1.88716e11i	−0.0838329	+	0.475440i
$379$	−1.84325e11			−0.458890			−0.229445	−	0.973322i	$-0.573691\pi$
$379$	−1.84325e11			−0.458890			−0.229445	+	0.973322i	$0.573691\pi$
$380$	−3.17942e10	−	2.45764e11i	−0.0782208	−	0.604635i
$381$	−1.74679e11			−0.424697
$382$	5.49726e10	−	3.11765e11i	0.132087	−	0.749104i
$383$	3.69046e11	+	3.09667e11i	0.876368	+	0.735360i	0.965429	−	0.260666i	$-0.0839422\pi$
$383$	3.69046e11	+	3.09667e11i	0.876368	+	0.735360i	−0.0890610	+	0.996026i	$0.528387\pi$
$384$	2.46306e10	+	8.96481e9i	0.0578076	+	0.0210402i
$385$	3.84075e11	−	1.39792e11i	0.890929	−	0.324272i
$386$	−2.63785e11	+	2.21342e11i	−0.604794	+	0.507482i
$387$	−4.99482e9	−	8.65127e9i	−0.0113193	−	0.0196056i
$388$	2.42392e10	−	4.19835e10i	0.0542969	−	0.0940450i
$389$	5.29880e10	+	3.00510e11i	0.117329	+	0.665405i	0.985571	+	0.169264i	$0.0541389\pi$
$389$	5.29880e10	+	3.00510e11i	0.117329	+	0.665405i	−0.868242	+	0.496141i	$0.834750\pi$
$390$	5.16154e10	+	2.92725e11i	0.112977	+	0.640722i
$391$	−9.28579e10	+	1.60835e11i	−0.200920	+	0.348004i
$392$	−4.80219e10	−	8.31763e10i	−0.102719	−	0.177915i
$393$	−3.30627e11	+	2.77429e11i	−0.699151	+	0.586658i
$394$	2.05834e11	−	7.49173e10i	0.430312	−	0.156621i
$395$	5.38151e11	+	1.95871e11i	1.11229	+	0.404839i
$396$	1.16097e11	+	9.74168e10i	0.237242	+	0.199070i
$397$	−9.10047e10	+	5.16113e11i	−0.183868	+	1.04277i	0.743533	+	0.668700i	$0.233149\pi$
$397$	−9.10047e10	+	5.16113e11i	−0.183868	+	1.04277i	−0.927401	+	0.374069i	$0.877962\pi$
$398$	1.52497e11			0.304640
$399$	−2.27822e11	−	1.04595e10i	−0.450006	−	0.0206602i
$400$	6.23111e10			0.121701
$401$	4.81232e10	−	2.72920e11i	0.0929405	−	0.527092i	−0.902418	−	0.430861i	$-0.858210\pi$
$401$	4.81232e10	−	2.72920e11i	0.0929405	−	0.527092i	0.995359	−	0.0962313i	$-0.0306789\pi$
$402$	1.84960e11	+	1.55200e11i	0.353233	+	0.296398i
$403$	1.03887e12	+	3.78118e11i	1.96195	+	0.714093i
$404$	−3.49668e11	+	1.27269e11i	−0.653040	+	0.237687i
$405$	1.10537e11	−	9.27519e10i	0.204156	−	0.171307i
$406$	−1.86098e11	−	3.22331e11i	−0.339918	−	0.588756i
$407$	1.37021e11	−	2.37326e11i	0.247520	−	0.428718i
$408$	−2.05720e10	−	1.16669e11i	−0.0367540	−	0.208442i
$409$	−1.68004e11	−	9.52795e11i	−0.296868	−	1.68362i	−0.659511	−	0.751695i	$-0.729237\pi$
$409$	−1.68004e11	−	9.52795e11i	−0.296868	−	1.68362i	0.362643	−	0.931928i	$-0.381874\pi$
$410$	3.91620e11	−	6.78306e11i	0.684444	−	1.18549i
$411$	−2.69710e11	−	4.67152e11i	−0.466240	−	0.807551i
$412$	2.27749e11	−	1.91104e11i	0.389421	−	0.326763i
$413$	−1.22908e11	+	4.47349e10i	−0.207876	+	0.0756608i
$414$	−9.56664e10	−	3.48197e10i	−0.160051	−	0.0582537i
$415$	−1.81828e11	−	1.52572e11i	−0.300916	−	0.252498i
$416$	−2.03291e10	+	1.15292e11i	−0.0332811	+	0.188746i
$417$	1.64962e11			0.267160
$418$	−2.85878e11	+	4.46522e11i	−0.458023	+	0.715402i
$419$	−8.92559e11			−1.41473			−0.707366	−	0.706848i	$-0.750117\pi$
$419$	−8.92559e11			−1.41473			−0.707366	+	0.706848i	$0.750117\pi$
$420$	3.04134e10	−	1.72483e11i	0.0476917	−	0.270473i
$421$	−5.36986e11	−	4.50585e11i	−0.833093	−	0.699048i	0.122906	−	0.992418i	$-0.460779\pi$
$421$	−5.36986e11	−	4.50585e11i	−0.833093	−	0.699048i	−0.955999	+	0.293370i	$0.905223\pi$
$422$	−6.93469e10	−	2.52402e10i	−0.106444	−	0.0387424i
$423$	8.48215e10	−	3.08725e10i	0.128817	−	0.0468857i
$424$	4.17929e10	−	3.50684e10i	0.0627995	−	0.0526950i
$425$	−1.40816e11	−	2.43900e11i	−0.209364	−	0.362628i
$426$	2.07086e11	−	3.58684e11i	0.304655	−	0.527677i
$427$	−1.06069e11	−	6.01548e11i	−0.154406	−	0.875678i
$428$	6.80280e10	+	3.85806e11i	0.0979921	+	0.555741i
$429$	3.17975e11	−	5.50748e11i	0.453247	−	0.785046i
$430$	1.34193e10	+	2.32430e10i	0.0189288	+	0.0327856i
$431$	−3.50784e11	+	2.94343e11i	−0.489657	+	0.410871i	−0.853903	−	0.520432i	$-0.825771\pi$
$431$	−3.50784e11	+	2.94343e11i	−0.489657	+	0.410871i	0.364246	+	0.931303i	$0.381327\pi$
$432$	1.79387e11	−	6.52914e10i	0.247807	−	0.0901943i
$433$	−1.11642e12	−	4.06343e11i	−1.52627	−	0.555516i	−0.563564	−	0.826072i	$-0.690570\pi$
$433$	−1.11642e12	−	4.06343e11i	−1.52627	−	0.555516i	−0.962704	+	0.270556i	$0.912792\pi$
$434$	−4.99017e11	−	4.18725e11i	−0.675167	−	0.566533i
$435$	−1.63475e11	+	9.27111e11i	−0.218902	+	1.24145i
$436$	5.34744e11			0.708691
$437$	7.78675e10	−	3.47543e11i	0.102139	−	0.455871i
$438$	−4.50862e11			−0.585342
$439$	−2.45033e11	+	1.38965e12i	−0.314873	+	1.78573i	0.258060	+	0.966129i	$0.416917\pi$
$439$	−2.45033e11	+	1.38965e12i	−0.314873	+	1.78573i	−0.572932	+	0.819603i	$0.694194\pi$
$440$	−3.11912e11	−	2.61725e11i	−0.396730	−	0.332896i
$441$	−2.23612e11	−	8.13883e10i	−0.281528	−	0.102468i
$442$	4.97220e11	−	1.80973e11i	0.619653	−	0.225535i
$443$	−1.07752e12	+	9.04145e11i	−1.32925	+	1.11538i	−0.345003	+	0.938602i	$0.612122\pi$
$443$	−1.07752e12	+	9.04145e11i	−1.32925	+	1.11538i	−0.984251	+	0.176775i	$0.943434\pi$
$444$	−5.87150e10	−	1.01697e11i	−0.0717011	−	0.124190i
$445$	5.63283e11	−	9.75635e11i	0.680937	−	1.17942i
$446$	1.41417e11	+	8.02014e11i	0.169236	+	0.959788i
$447$	−3.31299e10	−	1.87889e11i	−0.0392497	−	0.222596i
$448$	3.44908e10	−	5.97398e10i	0.0404531	−	0.0700668i
$449$	4.05796e11	+	7.02859e11i	0.471193	+	0.816131i	0.999457	−	0.0329496i	$-0.0104901\pi$
$449$	4.05796e11	+	7.02859e11i	0.471193	+	0.816131i	−0.528264	+	0.849080i	$0.677157\pi$
$450$	1.18266e11	−	9.92371e10i	0.135958	−	0.114082i
$451$	−1.57469e12	+	5.73140e11i	−1.79226	+	0.652328i
$452$	2.05381e10	+	7.47526e9i	0.0231439	+	0.00842371i
$453$	3.96811e11	+	3.32964e11i	0.442733	+	0.371497i
$454$	2.80355e10	−	1.58997e11i	0.0309711	−	0.175646i
$455$	7.82262e11			0.855660
$456$	1.04455e11	+	2.01760e11i	0.113132	+	0.218521i
$457$	4.65017e11			0.498707			0.249354	−	0.968412i	$-0.419782\pi$
$457$	4.65017e11			0.498707			0.249354	+	0.968412i	$0.419782\pi$
$458$	1.60685e11	−	9.11288e11i	0.170640	−	0.967745i
$459$	−6.60958e11	−	5.54610e11i	−0.695051	−	0.583217i
$460$	2.57022e11	+	9.35485e10i	0.267646	+	0.0974151i
$461$	3.48552e11	−	1.26863e11i	0.359429	−	0.130821i	−0.155992	−	0.987758i	$-0.549858\pi$
$461$	3.48552e11	−	1.26863e11i	0.359429	−	0.130821i	0.515422	+	0.856937i	$0.327635\pi$
$462$	−2.87053e11	+	2.40866e11i	−0.293139	+	0.245973i
$463$	−5.11139e11	−	8.85318e11i	−0.516921	−	0.895334i	−0.999807	−	0.0196505i	$-0.993745\pi$
$463$	−5.11139e11	−	8.85318e11i	−0.516921	−	0.895334i	0.482886	−	0.875683i	$-0.339589\pi$
$464$	−1.85391e11	+	3.21107e11i	−0.185677	+	0.321602i
$465$	2.86115e11	+	1.62264e12i	0.283793	+	1.60947i
$466$	2.90994e9	+	1.65031e10i	0.00285856	+	0.0162117i
$467$	1.47800e11	−	2.55997e11i	0.143796	−	0.249063i	−0.785127	−	0.619335i	$-0.787402\pi$
$467$	1.47800e11	−	2.55997e11i	0.143796	−	0.249063i	0.928923	+	0.370272i	$0.120736\pi$
$468$	1.45030e11	+	2.51199e11i	0.139750	+	0.242054i
$469$	4.86768e11	−	4.08447e11i	0.464563	−	0.389814i
$470$	−2.27886e11	+	8.29437e10i	−0.215416	+	0.0784049i
$471$	−1.33064e12	−	4.84312e11i	−1.24585	−	0.453452i
$472$	9.98149e10	+	8.37546e10i	0.0925670	+	0.0776730i
$473$	9.97113e9	−	5.65491e10i	0.00915945	−	0.0519458i
$474$	−5.25044e11			−0.477741
$475$	3.97386e11	+	3.65782e11i	0.358171	+	0.329686i
$476$	−3.11780e11			−0.278367
$477$	2.34725e10	−	1.33119e11i	0.0207600	−	0.117736i
$478$	7.33800e11	+	6.15731e11i	0.642913	+	0.539468i
$479$	1.88229e12	+	6.85099e11i	1.63372	+	0.594625i	0.985925	−	0.167190i	$-0.0534693\pi$
$479$	1.88229e12	+	6.85099e11i	1.63372	+	0.594625i	0.647795	+	0.761815i	$0.275692\pi$
$480$	−1.63956e11	+	5.96751e10i	−0.140975	+	0.0513107i
$481$	4.01783e11	−	3.37136e11i	0.342246	−	0.287178i
$482$	−7.71531e11	−	1.33633e12i	−0.651091	−	1.12772i
$483$	1.25859e11	−	2.17995e11i	0.105226	−	0.182257i
$484$	4.64530e10	+	2.63448e11i	0.0384777	+	0.218218i
$485$	5.60364e10	+	3.17798e11i	0.0459867	+	0.260804i
$486$	3.92530e11	−	6.79881e11i	0.319161	−	0.552802i
$487$	−4.08855e11	−	7.08157e11i	−0.329374	−	0.570492i	0.653014	−	0.757346i	$-0.273504\pi$
$487$	−4.08855e11	−	7.08157e11i	−0.329374	−	0.570492i	−0.982388	+	0.186854i	$0.940171\pi$
$488$	−4.66143e11	+	3.91141e11i	−0.372075	+	0.312208i
$489$	3.67311e11	−	1.33690e11i	0.290499	−	0.105733i
$490$	6.00769e11	+	2.18662e11i	0.470787	+	0.171353i
$491$	−8.25742e11	−	6.92880e11i	−0.641177	−	0.538011i	0.263203	−	0.964741i	$-0.415221\pi$
$491$	−8.25742e11	−	6.92880e11i	−0.641177	−	0.538011i	−0.904379	+	0.426729i	$0.859666\pi$
$492$	−1.24693e11	+	7.07170e11i	−0.0959400	+	0.544103i
$493$	1.67585e12			1.27768
$494$	−8.06439e11	+	6.15931e11i	−0.609257	+	0.465329i
$495$	−1.00883e12			−0.755258
$496$	−1.12688e11	+	6.39086e11i	−0.0836009	+	0.474124i
$497$	−8.34984e11	−	7.00635e11i	−0.613867	−	0.515096i
$498$	2.04489e11	+	7.44281e10i	0.148984	+	0.0542256i
$499$	1.81743e12	−	6.61492e11i	1.31222	−	0.477608i	0.411261	−	0.911517i	$-0.365088\pi$
$499$	1.81743e12	−	6.61492e11i	1.31222	−	0.477608i	0.900957	+	0.433909i	$0.142866\pi$
$500$	3.34964e11	−	2.81068e11i	0.239681	−	0.201116i
$501$	6.25405e11	+	1.08323e12i	0.443498	+	0.768161i
$502$	−1.16265e11	+	2.01377e11i	−0.0817113	+	0.141528i
$503$	4.09743e11	+	2.32377e12i	0.285401	+	1.61859i	0.703849	+	0.710350i	$0.251463\pi$
$503$	4.09743e11	+	2.32377e12i	0.285401	+	1.61859i	−0.418448	+	0.908241i	$0.637426\pi$
$504$	−2.96786e10	−	1.68316e11i	−0.0204883	−	0.116195i
$505$	1.23849e12	−	2.14513e12i	0.847386	−	1.46771i
$506$	−2.92596e11	−	5.06791e11i	−0.198423	−	0.343678i
$507$	1.39171e11	−	1.16778e11i	0.0935435	−	0.0784923i
$508$	4.30346e11	−	1.56633e11i	0.286702	−	0.104351i
$509$	2.34014e12	+	8.51740e11i	1.54529	+	0.562441i	0.967308	−	0.253605i	$-0.0816162\pi$
$509$	2.34014e12	+	8.51740e11i	1.54529	+	0.562441i	0.577987	+	0.816046i	$0.303838\pi$
$510$	6.04104e11	+	5.06903e11i	0.395408	+	0.331787i
$511$	−2.06043e11	+	1.16853e12i	−0.133679	+	0.758131i
$512$	−6.87195e10			−0.0441942
$513$	1.52730e12	+	6.36652e11i	0.973638	+	0.405858i
$514$	−4.57634e11			−0.289190
$515$	−3.43657e11	+	1.94898e12i	−0.215275	+	1.22088i
$516$	−1.88492e10	−	1.58163e10i	−0.0117049	−	0.00982159i
$517$	4.87563e11	+	1.77459e11i	0.300140	+	0.109242i
$518$	−2.90408e11	+	1.05700e11i	−0.177225	+	0.0645046i
$519$	−8.95642e11	+	7.51533e11i	−0.541853	+	0.454668i
$520$	−3.89645e11	−	6.74885e11i	−0.233698	−	0.404776i
$521$	−7.73958e10	+	1.34053e11i	−0.0460201	+	0.0797092i	−0.888118	−	0.459616i	$-0.847987\pi$
$521$	−7.73958e10	+	1.34053e11i	−0.0460201	+	0.0797092i	0.842098	+	0.539325i	$0.181321\pi$
$522$	1.59525e11	+	9.04713e11i	0.0940399	+	0.533327i
$523$	−5.24203e11	−	2.97290e12i	−0.306367	−	1.73749i	−0.617001	−	0.786962i	$-0.711653\pi$
$523$	−5.24203e11	−	2.97290e12i	−0.306367	−	1.73749i	0.310634	−	0.950529i	$-0.399459\pi$
$524$	5.65776e11	−	9.79952e11i	0.327834	−	0.567824i
$525$	1.90861e11	+	3.30582e11i	0.109648	+	0.189916i
$526$	−9.83241e11	+	8.25037e11i	−0.560046	+	0.469935i
$527$	2.75619e12	−	1.00317e12i	1.55655	−	0.566537i
$528$	3.50785e11	+	1.27675e11i	0.196421	+	0.0714915i
$529$	−1.07863e12	−	9.05077e11i	−0.598855	−	0.502499i
$530$	−6.30625e10	+	3.57645e11i	−0.0347160	+	0.196884i
$531$	3.22836e11			0.176221
$532$	5.70650e11	−	1.78518e11i	0.308864	−	0.0966226i
$533$	−3.20723e12			−1.72131
$534$	−1.79351e11	+	1.01715e12i	−0.0954484	+	0.541315i
$535$	−1.99767e12	−	1.67624e12i	−1.05422	−	0.884597i
$536$	−5.94841e11	−	2.16504e11i	−0.311286	−	0.113299i
$537$	2.04268e12	−	7.43475e11i	1.06002	−	0.385817i
$538$	1.76368e11	−	1.47990e11i	0.0907608	−	0.0761574i
$539$	−6.83919e11	−	1.18458e12i	−0.349024	−	0.604528i
$540$	−6.35369e11	+	1.10049e12i	−0.321554	+	0.556949i
$541$	−3.50232e11	−	1.98626e12i	−0.175779	−	0.996894i	−0.937241	−	0.348683i	$-0.886629\pi$
$541$	−3.50232e11	−	1.98626e12i	−0.175779	−	0.996894i	0.761461	−	0.648210i	$-0.224482\pi$
$542$	−1.38116e11	−	7.83295e11i	−0.0687459	−	0.389878i
$543$	−9.39815e10	+	1.62781e11i	−0.0463920	+	0.0803533i
$544$	1.55298e11	+	2.68984e11i	0.0760275	+	0.131683i
$545$	−2.72679e12	+	2.28805e12i	−1.32394	+	1.11092i
$546$	−6.73931e11	+	2.45291e11i	−0.324525	+	0.118118i
$547$	2.41303e12	+	8.78273e11i	1.15245	+	0.419456i	0.846393	−	0.532558i	$-0.178769\pi$
$547$	2.41303e12	+	8.78273e11i	1.15245	+	0.419456i	0.306053	+	0.952015i	$0.400992\pi$
$548$	1.08336e12	+	9.09045e11i	0.513168	+	0.430599i
$549$	−2.61804e11	+	1.48477e12i	−0.122999	+	0.697561i
$550$	8.87424e11			0.413523
$551$	−3.06729e12	+	9.59547e11i	−1.41766	+	0.443490i
$552$	−2.50762e11			−0.114957
$553$	−2.39944e11	+	1.36079e12i	−0.109105	+	0.618767i
$554$	−1.20491e12	−	1.01104e12i	−0.543451	−	0.456009i
$555$	7.34543e11	+	2.67352e11i	0.328624	+	0.119609i
$556$	−4.06406e11	+	1.47920e11i	−0.180353	+	0.0656431i
$557$	2.24159e12	−	1.88092e12i	0.986752	−	0.827983i	0.00165771	−	0.999999i	$-0.499472\pi$
$557$	2.24159e12	−	1.88092e12i	0.986752	−	0.827983i	0.985094	+	0.172015i	$0.0550279\pi$
$558$	8.03931e11	+	1.39245e12i	0.351047	+	0.608031i
$559$	5.49498e10	−	9.51758e10i	0.0238020	−	0.0412262i
$560$	7.97362e10	+	4.52206e11i	0.0342617	+	0.194308i
$561$	−2.92982e11	−	1.66158e12i	−0.124884	−	0.708255i
$562$	3.46623e11	−	6.00368e11i	0.146570	−	0.253866i
$563$	−1.51968e12	−	2.63216e12i	−0.637477	−	1.10414i	−0.985985	−	0.166837i	$-0.946645\pi$
$563$	−1.51968e12	−	2.63216e12i	−0.637477	−	1.10414i	0.348507	−	0.937306i	$-0.386689\pi$
$564$	1.70319e11	−	1.42915e11i	0.0708773	−	0.0594731i
$565$	−1.36714e11	+	4.97598e10i	−0.0564410	+	0.0205428i
$566$	−2.42246e12	−	8.81703e11i	−0.992161	−	0.361117i
$567$	2.66704e11	+	2.23791e11i	0.108369	+	0.0909326i
$568$	−1.88557e11	+	1.06936e12i	−0.0760106	+	0.431077i
$569$	3.77945e12			1.51155			0.755777	−	0.654829i	$-0.227260\pi$
$569$	3.77945e12			1.51155			0.755777	+	0.654829i	$0.227260\pi$
$570$	−1.39593e12	−	5.81888e11i	−0.553893	−	0.230889i
$571$	5.95919e11			0.234598			0.117299	−	0.993097i	$-0.462576\pi$
$571$	5.95919e11			0.234598			0.117299	+	0.993097i	$0.462576\pi$
$572$	−2.89523e11	+	1.64197e12i	−0.113084	+	0.641331i
$573$	−1.47999e12	−	1.24186e12i	−0.573540	−	0.481257i
$574$	1.77583e12	+	6.46350e11i	0.682807	+	0.248522i
$575$	−5.60176e11	+	2.03887e11i	−0.213707	+	0.0777830i
$576$	−1.30429e11	+	1.09443e11i	−0.0493712	+	0.0414273i
$577$	−2.17018e11	−	3.75886e11i	−0.0815088	−	0.141177i	0.822389	−	0.568925i	$-0.192641\pi$
$577$	−2.17018e11	−	3.75886e11i	−0.0815088	−	0.141177i	−0.903898	+	0.427748i	$0.859307\pi$
$578$	−2.46793e11	+	4.27458e11i	−0.0919723	+	0.159301i
$579$	3.64918e11	+	2.06956e12i	0.134941	+	0.765286i
$580$	−4.28589e11	−	2.43065e12i	−0.157259	−	0.891859i
$581$	2.86351e11	−	4.95974e11i	0.104257	−	0.180579i
$582$	−1.47927e11	−	2.56217e11i	−0.0534434	−	0.0925666i
$583$	5.95207e11	−	4.99438e11i	0.213383	−	0.179050i
$584$	1.11076e12	−	4.04283e11i	0.395150	−	0.143823i
$585$	−1.81437e12	−	6.60377e11i	−0.640508	−	0.233126i
$586$	−1.43880e12	−	1.20730e12i	−0.504036	−	0.422936i
$587$	−5.92286e11	+	3.35902e12i	−0.205902	+	1.16773i	0.690113	+	0.723702i	$0.257561\pi$
$587$	−5.92286e11	+	3.35902e12i	−0.205902	+	1.16773i	−0.896015	+	0.444024i	$0.853550\pi$
$588$	−5.86137e11			−0.202209
$589$	−4.47026e12	+	3.41423e12i	−1.53043	+	1.16889i
$590$	−8.67348e11			−0.294686
$591$	2.32130e11	−	1.31647e12i	0.0782685	−	0.443882i
$592$	2.35843e11	+	1.97896e11i	0.0789180	+	0.0662201i
$593$	−9.93552e11	−	3.61623e11i	−0.329947	−	0.120091i	0.171734	−	0.985143i	$-0.445063\pi$
$593$	−9.93552e11	−	3.61623e11i	−0.329947	−	0.120091i	−0.501682	+	0.865052i	$0.667285\pi$
$594$	2.55479e12	−	9.29869e11i	0.842009	−	0.306466i
$595$	1.58985e12	−	1.33404e12i	0.520030	−	0.436357i
$596$	2.50098e11	+	4.33183e11i	0.0811900	+	0.140625i
$597$	4.65330e11	−	8.05975e11i	0.149926	−	0.259679i
$598$	−1.94487e11	−	1.10299e12i	−0.0621921	−	0.352709i
$599$	−4.36555e11	−	2.47582e12i	−0.138554	−	0.785777i	−0.972319	−	0.233658i	$-0.924931\pi$
$599$	−4.36555e11	−	2.47582e12i	−0.138554	−	0.785777i	0.833765	−	0.552119i	$-0.186181\pi$
$600$	1.90136e11	−	3.29326e11i	0.0598942	−	0.103740i
$601$	−8.22045e11	−	1.42382e12i	−0.257016	−	0.445165i	0.708425	−	0.705786i	$-0.249406\pi$
$601$	−8.22045e11	−	1.42382e12i	−0.257016	−	0.445165i	−0.965441	+	0.260621i	$0.916073\pi$
$602$	−4.96062e10	+	4.16245e10i	−0.0153940	+	0.0129171i
$603$	−1.47381e12	+	5.36423e11i	−0.453956	+	0.165227i
$604$	−1.27616e12	−	4.64486e11i	−0.390158	−	0.142006i
$605$	−1.36411e12	−	1.14462e12i	−0.413952	−	0.347347i
$606$	−3.94339e11	+	2.23641e12i	−0.118780	+	0.673634i
$607$	2.10793e12			0.630241			0.315121	−	0.949052i	$-0.397955\pi$
$607$	2.10793e12			0.630241			0.315121	+	0.949052i	$0.397955\pi$
$608$	−4.38254e11	−	4.03400e11i	−0.130065	−	0.119721i
$609$	−2.27144e12			−0.669150
$610$	7.03377e11	−	3.98905e12i	0.205686	−	1.16650i
$611$	7.60713e11	+	6.38314e11i	0.220818	+	0.185289i
$612$	7.23140e11	+	2.63201e11i	0.208373	+	0.0758415i
$613$	−8.05062e11	+	2.93018e11i	−0.230280	+	0.0838152i	−0.454583	−	0.890704i	$-0.650212\pi$
$613$	−8.05062e11	+	2.93018e11i	−0.230280	+	0.0838152i	0.224303	+	0.974520i	$0.427990\pi$
$614$	1.81870e12	−	1.52607e12i	0.516419	−	0.433327i
$615$	−2.38998e12	−	4.13957e12i	−0.673685	−	1.16686i
$616$	4.91212e11	−	8.50803e11i	0.137453	−	0.238076i
$617$	9.34330e11	+	5.29885e12i	0.259548	+	1.47197i	0.784124	+	0.620604i	$0.213112\pi$
$617$	9.34330e11	+	5.29885e12i	0.259548	+	1.47197i	−0.524577	+	0.851363i	$0.675776\pi$
$618$	−3.15067e11	−	1.78683e12i	−0.0868870	−	0.492761i
$619$	1.31433e12	−	2.27648e12i	0.359828	−	0.623241i	−0.628104	−	0.778130i	$-0.716169\pi$
$619$	1.31433e12	−	2.27648e12i	0.359828	−	0.623241i	0.987932	+	0.154889i	$0.0495020\pi$
$620$	−2.15988e12	−	3.74103e12i	−0.587040	−	1.01678i
$621$	−1.39904e12	+	1.17394e12i	−0.377502	+	0.316762i
$622$	3.14227e12	−	1.14369e12i	0.841756	−	0.306374i
$623$	2.55425e12	+	9.29671e11i	0.679309	+	0.247248i
$624$	5.47307e11	+	4.59245e11i	0.144511	+	0.121259i
$625$	−8.27904e11	+	4.69528e12i	−0.217030	+	1.23084i
$626$	2.11270e12			0.549861
$627$	1.48763e12	+	2.87344e12i	0.384405	+	0.742502i
$628$	3.71248e12			0.952457
$629$	2.41633e11	−	1.37037e12i	0.0615500	−	0.349067i
$630$	8.71525e11	+	7.31296e11i	0.220418	+	0.184953i
$631$	−2.94411e12	−	1.07157e12i	−0.739302	−	0.269084i	−0.0552049	−	0.998475i	$-0.517581\pi$
$631$	−2.94411e12	−	1.07157e12i	−0.739302	−	0.269084i	−0.684097	+	0.729391i	$0.739803\pi$
$632$	1.29352e12	−	4.70801e11i	0.322511	−	0.117384i
$633$	−3.45005e11	+	2.89493e11i	−0.0854099	+	0.0716674i
$634$	7.33258e11	+	1.27004e12i	0.180242	+	0.312188i
$635$	−1.52424e12	+	2.64007e12i	−0.372025	+	0.644367i
$636$	−5.78160e10	−	3.27891e11i	−0.0140117	−	0.0794644i
$637$	−4.54597e11	−	2.57815e12i	−0.109395	−	0.620413i
$638$	−2.64031e12	+	4.57314e12i	−0.630901	+	1.09275i
$639$	1.34519e12	+	2.32993e12i	0.319175	+	0.552827i
$640$	3.50418e11	−	2.94035e11i	0.0825612	−	0.0692771i
$641$	−4.48538e12	+	1.63254e12i	−1.04939	+	0.381948i	−0.808433	−	0.588588i	$-0.799684\pi$
$641$	−4.48538e12	+	1.63254e12i	−1.04939	+	0.381948i	−0.240959	+	0.970535i	$0.577462\pi$
$642$	2.24664e12	+	8.17709e11i	0.521946	+	0.189973i
$643$	2.47784e12	+	2.07915e12i	0.571641	+	0.479664i	0.882190	−	0.470894i	$-0.156068\pi$
$643$	2.47784e12	+	2.07915e12i	0.571641	+	0.479664i	−0.310549	+	0.950557i	$0.600513\pi$
$644$	−1.14598e11	+	6.49916e11i	−0.0262536	+	0.148892i
$645$	1.63791e11			0.0372625
$646$	−5.88599e11	+	2.62707e12i	−0.132976	+	0.593506i
$647$	4.12601e12			0.925681			0.462840	−	0.886442i	$-0.346830\pi$
$647$	4.12601e12			0.925681			0.462840	+	0.886442i	$0.346830\pi$
$648$	6.02273e10	−	3.41566e11i	0.0134186	−	0.0761004i
$649$	1.42155e12	+	1.19282e12i	0.314528	+	0.263921i
$650$	1.59602e12	+	5.80904e11i	0.350694	+	0.127642i
$651$	−3.73574e12	+	1.35970e12i	−0.815196	+	0.296707i
$652$	−7.85042e11	+	6.58729e11i	−0.170129	+	0.142755i
$653$	1.06062e12	+	1.83704e12i	0.228270	+	0.395375i	0.957296	−	0.289111i	$-0.0933597\pi$
$653$	1.06062e12	+	1.83704e12i	0.228270	+	0.395375i	−0.729025	+	0.684487i	$0.760026\pi$
$654$	1.63172e12	−	2.82622e12i	0.348775	−	0.604097i
$655$	1.30797e12	+	7.41785e12i	0.277658	+	1.57468i
$656$	−3.26914e11	−	1.85402e12i	−0.0689233	−	0.390883i
$657$	1.46435e12	−	2.53633e12i	0.306620	−	0.531081i
$658$	−2.92565e11	−	5.06738e11i	−0.0608424	−	0.105382i
$659$	4.69184e12	−	3.93692e12i	0.969077	−	0.813152i	−0.0133285	−	0.999911i	$-0.504243\pi$
$659$	4.69184e12	−	3.93692e12i	0.969077	−	0.813152i	0.982406	+	0.186759i	$0.0597983\pi$
$660$	−2.33503e12	+	8.49883e11i	−0.479011	+	0.174346i
$661$	7.74335e12	+	2.81835e12i	1.57769	+	0.574233i	0.974701	−	0.223514i	$-0.0717527\pi$
$661$	7.74335e12	+	2.81835e12i	1.57769	+	0.574233i	0.602992	+	0.797747i	$0.293975\pi$
$662$	2.71100e11	+	2.27480e11i	0.0548616	+	0.0460343i
$663$	5.60742e11	−	3.18012e12i	0.112707	−	0.639195i
$664$	−5.70526e11			−0.113899
$665$	−2.14605e12	+	3.35199e12i	−0.425542	+	0.664669i
$666$	7.62800e11			0.150237
$667$	6.15973e11	−	3.49336e12i	0.120502	−	0.683403i
$668$	−2.51209e12	−	2.10790e12i	−0.488137	−	0.409596i
$669$	4.67031e12	+	1.69985e12i	0.901422	+	0.328091i
$670$	3.95962e12	−	1.44118e12i	0.759131	−	0.276301i
$671$	−6.63873e12	+	5.57056e12i	−1.26425	+	1.06083i
$672$	−2.10490e11	−	3.64580e11i	−0.0398172	−	0.0689654i
$673$	3.18676e12	−	5.51963e12i	0.598799	−	1.03715i	−0.394199	−	0.919025i	$-0.628978\pi$
$673$	3.18676e12	−	5.51963e12i	0.598799	−	1.03715i	0.992999	−	0.118126i	$-0.0376886\pi$
$674$	3.39202e11	+	1.92371e12i	0.0633124	+	0.359062i
$675$	−4.80928e11	−	2.72748e12i	−0.0891689	−	0.505702i
$676$	−2.38153e11	+	4.12493e11i	−0.0438627	+	0.0759725i
$677$	4.66134e11	+	8.07367e11i	0.0852828	+	0.147714i	0.905512	−	0.424321i	$-0.139487\pi$
$677$	4.66134e11	+	8.07367e11i	0.0852828	+	0.147714i	−0.820229	+	0.572035i	$0.806154\pi$
$678$	1.02178e11	−	8.57377e10i	0.0185705	−	0.0155825i
$679$	−7.31655e11	+	2.66301e11i	−0.132097	+	0.0480793i
$680$	−1.94282e12	−	7.07130e11i	−0.348452	−	0.126826i
$681$	−7.54782e11	−	6.33337e11i	−0.134481	−	0.112843i
$682$	−1.60489e12	+	9.10176e12i	−0.284063	+	1.61100i
$683$	7.39657e12			1.30058			0.650290	−	0.759686i	$-0.274647\pi$
$683$	7.39657e12			1.30058			0.650290	+	0.759686i	$0.274647\pi$
$684$	−1.47426e12	−	6.76847e10i	−0.257527	−	0.0118233i
$685$	−9.41391e12			−1.63366
$686$	−7.28847e11	+	4.13349e12i	−0.125654	+	0.712621i
$687$	−4.32601e12	−	3.62996e12i	−0.740939	−	0.621722i
$688$	6.06198e10	+	2.20638e10i	0.0103149	+	0.00375433i
$689$	1.39740e12	−	5.08613e11i	0.236230	−	0.0859807i
$690$	1.27870e12	−	1.07296e12i	0.214757	−	0.180203i
$691$	8.28052e11	+	1.43423e12i	0.138168	+	0.239313i	0.926803	−	0.375548i	$-0.122545\pi$
$691$	8.28052e11	+	1.43423e12i	0.138168	+	0.239313i	−0.788635	+	0.614861i	$0.789212\pi$
$692$	1.53264e12	−	2.65461e12i	0.254076	−	0.440072i
$693$	−4.22678e11	−	2.39713e12i	−0.0696162	−	0.394813i
$694$	4.16345e11	+	2.36121e12i	0.0681297	+	0.386382i
$695$	1.43945e12	−	2.49320e12i	0.234026	−	0.405345i
$696$	1.13140e12	+	1.95965e12i	0.182758	+	0.316546i
$697$	−6.51828e12	+	5.46948e12i	−1.04613	+	0.877806i
$698$	−4.51988e12	+	1.64510e12i	−0.720737	+	0.262327i
$699$	9.61011e10	+	3.49780e10i	0.0152258	+	0.00554175i
$700$	−7.66642e11	−	6.43289e11i	−0.120684	−	0.101266i
$701$	1.73787e10	−	9.85593e10i	0.00271822	−	0.0154158i	−0.983418	−	0.181351i	$-0.941953\pi$
$701$	1.73787e10	−	9.85593e10i	0.00271822	−	0.0154158i	0.986137	+	0.165935i	$0.0530642\pi$
$702$	5.20345e12			0.808676
$703$	3.42378e11	+	2.64653e12i	0.0528698	+	0.408675i
$704$	−9.78691e11			−0.150165
$705$	−2.56999e11	+	1.45751e12i	−0.0391814	+	0.222209i
$706$	−3.05442e12	−	2.56296e12i	−0.462708	−	0.388258i
$707$	5.61602e12	+	2.04407e12i	0.845360	+	0.307686i
$708$	7.47234e11	−	2.71971e11i	0.111765	−	0.0406792i
$709$	2.61215e11	−	2.19186e11i	0.0388231	−	0.0325765i	−0.623170	−	0.782087i	$-0.714155\pi$
$709$	2.61215e11	−	2.19186e11i	0.0388231	−	0.0325765i	0.661993	+	0.749510i	$0.269711\pi$
$710$	−3.61404e12	−	6.25971e12i	−0.533741	−	0.924467i
$711$	1.70528e12	−	2.95364e12i	0.250255	−	0.433455i
$712$	−4.70213e11	−	2.66671e12i	−0.0685701	−	0.388880i
$713$	−1.07808e12	−	6.11410e12i	−0.156224	−	0.885992i
$714$	−9.51367e11	+	1.64782e12i	−0.136996	+	0.237283i
$715$	−5.54926e12	−	9.61160e12i	−0.794068	−	1.37537i
$716$	−4.36575e12	+	3.66330e12i	−0.620798	+	0.520911i
$717$	5.49337e12	−	1.99942e12i	0.776252	−	0.282533i
$718$	2.23082e12	+	8.11951e11i	0.313259	+	0.114017i
$719$	7.68907e12	+	6.45189e12i	1.07299	+	0.900341i	0.995320	−	0.0966381i	$-0.0308089\pi$
$719$	7.68907e12	+	6.45189e12i	1.07299	+	0.900341i	0.0776655	+	0.996979i	$0.475253\pi$
$720$	1.96808e11	−	1.11615e12i	0.0272927	−	0.154785i
$721$	−4.77503e12			−0.658063
$722$	−4.26882e11	−	5.14533e12i	−0.0584643	−	0.704686i
$723$	−9.41701e12			−1.28171
$724$	8.55722e10	−	4.85304e11i	0.0115747	−	0.0656433i
$725$	4.12077e12	+	3.45774e12i	0.553933	+	0.464805i
$726$	1.53412e12	+	5.58373e11i	0.204948	+	0.0745950i
$727$	−6.93810e12	+	2.52526e12i	−0.921162	+	0.335275i	−0.758701	−	0.651439i	$-0.774165\pi$
$727$	−6.93810e12	+	2.52526e12i	−0.921162	+	0.335275i	−0.162461	+	0.986715i	$0.551943\pi$
$728$	1.44037e12	−	1.20861e12i	0.190057	−	0.159476i
$729$	−3.22888e12	−	5.59258e12i	−0.423426	−	0.733395i
$730$	−3.93420e12	+	6.81423e12i	−0.512747	+	0.888104i
$731$	−5.06308e10	−	2.87141e11i	−0.00655823	−	0.0371936i
$732$	6.44860e11	+	3.65718e12i	0.0830167	+	0.470811i
$733$	6.46708e12	−	1.12013e13i	0.827448	−	1.43318i	−0.0725864	−	0.997362i	$-0.523125\pi$
$733$	6.46708e12	−	1.12013e13i	0.827448	−	1.43318i	0.900034	−	0.435819i	$-0.143541\pi$
$734$	−3.86487e12	−	6.69415e12i	−0.491477	−	0.851262i
$735$	2.98886e12	−	2.50795e12i	0.377756	−	0.316975i
$736$	6.17787e11	−	2.24856e11i	0.0776048	−	0.0282458i
$737$	−8.47162e12	−	3.08342e12i	−1.05770	−	0.384972i
$738$	−3.57320e12	−	2.99827e12i	−0.443409	−	0.372064i
$739$	9.54857e11	−	5.41526e12i	0.117771	−	0.667912i	−0.867570	−	0.497315i	$-0.834319\pi$
$739$	9.54857e11	−	5.41526e12i	0.117771	−	0.667912i	0.985341	−	0.170597i	$-0.0545696\pi$
$740$	−2.04938e12			−0.251235
$741$	7.94536e11	+	6.14163e12i	0.0968125	+	0.748345i
$742$	−8.76237e11			−0.106122
$743$	1.11742e12	−	6.33719e12i	0.134514	−	0.762864i	−0.840684	−	0.541527i	$-0.817847\pi$
$743$	1.11742e12	−	6.33719e12i	0.134514	−	0.762864i	0.975197	−	0.221338i	$-0.0710423\pi$
$744$	3.03383e12	+	2.54569e12i	0.363006	+	0.304598i
$745$	−3.12881e12	−	1.13879e12i	−0.372113	−	0.135438i
$746$	9.06594e12	−	3.29973e12i	1.07174	−	0.390080i
$747$	−1.08285e12	+	9.08623e11i	−0.127241	+	0.106768i
$748$	2.21173e12	+	3.83082e12i	0.258330	+	0.447440i
$749$	3.14601e12	−	5.44906e12i	0.365252	−	0.632635i
$750$	−4.63387e11	−	2.62800e12i	−0.0534771	−	0.303284i
$751$	7.68167e11	+	4.35649e12i	0.0881203	+	0.499755i	0.996640	+	0.0819121i	$0.0261027\pi$
$751$	7.68167e11	+	4.35649e12i	0.0881203	+	0.499755i	−0.908519	+	0.417843i	$0.862786\pi$
$752$	−2.91454e11	+	5.04813e11i	−0.0332345	+	0.0575639i
$753$	7.09542e11	+	1.22896e12i	0.0804268	+	0.139303i
$754$	−7.74212e12	+	6.49641e12i	−0.872346	+	0.731985i
$755$	8.49490e12	−	3.09189e12i	0.951475	−	0.346308i
$756$	−2.88113e12	−	1.04865e12i	−0.320786	−	0.116756i
$757$	5.18774e12	+	4.35303e12i	0.574178	+	0.481793i	0.883029	−	0.469318i	$-0.155500\pi$
$757$	5.18774e12	+	4.35303e12i	0.574178	+	0.481793i	−0.308851	+	0.951110i	$0.599945\pi$
$758$	5.12124e11	−	2.90440e12i	0.0563461	−	0.319555i
$759$	−3.57131e12			−0.390607
$760$	3.96083e12	+	1.81845e11i	0.430650	+	0.0197716i
$761$	−9.54220e12			−1.03138			−0.515689	−	0.856776i	$-0.672464\pi$
$761$	−9.54220e12			−1.03138			−0.515689	+	0.856776i	$0.672464\pi$
$762$	4.85324e11	−	2.75241e12i	0.0521476	−	0.295744i
$763$	−6.57920e12	−	5.52060e12i	−0.702769	−	0.589693i
$764$	4.75972e12	+	1.73240e12i	0.505431	+	0.183962i
$765$	−4.81365e12	+	1.75203e12i	−0.508157	+	0.184954i
$766$	−5.90474e12	+	4.95467e12i	−0.619686	+	0.519978i
$767$	1.77582e12	+	3.07581e12i	0.185276	+	0.320908i
$768$	−2.09691e11	+	3.63195e11i	−0.0217497	+	0.0376716i
$769$	−1.42679e12	−	8.09174e12i	−0.147127	−	0.834398i	−0.965635	−	0.259903i	$-0.916310\pi$
$769$	−1.42679e12	−	8.09174e12i	−0.147127	−	0.834398i	0.818508	−	0.574495i	$-0.194802\pi$
$770$	1.13559e12	+	6.44024e12i	0.116416	+	0.660228i
$771$	−1.39642e12	+	2.41868e12i	−0.142322	+	0.246509i
$772$	−2.75477e12	−	4.77141e12i	−0.279131	−	0.483469i
$773$	1.01307e13	−	8.50067e12i	1.02054	−	0.856339i	0.0308487	−	0.999524i	$-0.490179\pi$
$773$	1.01307e13	−	8.50067e12i	1.02054	−	0.856339i	0.989696	+	0.143185i	$0.0457345\pi$
$774$	1.50195e11	−	5.46665e10i	0.0150425	−	0.00547503i
$775$	8.84708e12	+	3.22007e12i	0.880931	+	0.320633i
$776$	5.94185e11	+	4.98580e11i	0.0588226	+	0.0493580i
$777$	−3.27509e11	+	1.85739e12i	−0.0322350	+	0.182814i
$778$	−4.88233e12			−0.477770
$779$	8.79868e12	−	1.37430e13i	0.856050	−	1.33709i
$780$	−4.75586e12			−0.460048
$781$	−2.68539e12	+	1.52296e13i	−0.258272	+	1.46473i
$782$	−2.27626e12	−	1.91001e12i	−0.217667	−	0.182644i
$783$	1.54863e13	+	5.63656e12i	1.47238	+	0.535903i
$784$	1.44403e12	−	5.25582e11i	0.136506	−	0.0496842i
$785$	−1.89308e13	+	1.58849e13i	−1.77933	+	1.49304i
$786$	−3.45282e12	−	5.98046e12i	−0.322680	−	0.558898i
$787$	−4.01451e12	+	6.95334e12i	−0.373032	+	0.646111i	−0.990030	−	0.140854i	$-0.955015\pi$
$787$	−4.01451e12	+	6.95334e12i	−0.373032	+	0.646111i	0.616998	+	0.786965i	$0.288349\pi$
$788$	6.08584e11	+	3.45145e12i	0.0562280	+	0.318885i
$789$	1.36021e12	+	7.71413e12i	0.124957	+	0.708664i
$790$	−4.58150e12	+	7.93540e12i	−0.418491	+	0.724848i
$791$	−1.75516e11	−	3.04003e11i	−0.0159413	−	0.0276111i
$792$	−1.85755e12	+	1.55867e12i	−0.167756	+	0.140764i
$793$	−1.55861e13	+	5.67289e12i	−1.39962	+	0.509419i
$794$	−7.87952e12	−	2.86791e12i	−0.703570	−	0.256078i
$795$	1.69779e12	+	1.42462e12i	0.150741	+	0.126487i
$796$	−4.23693e11	+	2.40288e12i	−0.0374061	+	0.212141i
$797$	2.00362e13			1.75895			0.879473	−	0.475949i	$-0.157895\pi$
$797$	2.00362e13			1.75895			0.879473	+	0.475949i	$0.157895\pi$
$798$	7.97785e11	−	3.56072e12i	0.0696423	−	0.310831i
$799$	2.63460e12			0.228694
$800$	−1.73123e11	+	9.81832e11i	−0.0149435	+	0.0847485i
$801$	−5.13948e12	−	4.31254e12i	−0.441137	−	0.370158i
$802$	4.16668e12	+	1.51655e12i	0.355636	+	0.129441i
$803$	1.58192e13	−	5.75773e12i	1.34266	−	0.488688i
$804$	−2.95937e12	+	2.48320e12i	−0.249774	+	0.209585i
$805$	−2.19648e12	−	3.80442e12i	−0.184351	−	0.319306i
$806$	−8.84434e12	+	1.53189e13i	−0.738173	+	1.27855i
$807$	−2.43986e11	−	1.38371e12i	−0.0202504	−	0.114846i
$808$	−1.03386e12	−	5.86329e12i	−0.0853315	−	0.483939i
$809$	3.31458e12	−	5.74102e12i	0.272057	−	0.471217i	−0.697331	−	0.716749i	$-0.745629\pi$
$809$	3.31458e12	−	5.74102e12i	0.272057	−	0.471217i	0.969388	+	0.245532i	$0.0789627\pi$
$810$	1.15437e12	+	1.99943e12i	0.0942242	+	0.163201i
$811$	3.79887e11	−	3.18763e11i	0.0308362	−	0.0258746i	−0.627239	−	0.778827i	$-0.715815\pi$
$811$	3.79887e11	−	3.18763e11i	0.0308362	−	0.0258746i	0.658075	+	0.752952i	$0.271371\pi$
$812$	5.59600e12	−	2.03678e12i	0.451726	−	0.164415i
$813$	−4.56130e12	−	1.66018e12i	−0.366169	−	0.133275i
$814$	3.35884e12	+	2.81840e12i	0.268151	+	0.225006i
$815$	1.18457e12	−	6.71804e12i	0.0940486	−	0.533376i
$816$	1.89551e12			0.149665
$817$	2.57079e11	+	4.96564e11i	0.0201868	+	0.0389920i
$818$	1.54799e13			1.20887
$819$	8.08968e11	−	4.58789e12i	0.0628281	−	0.356316i
$820$	9.59995e12	+	8.05532e12i	0.741492	+	0.622186i
$821$	−1.54278e13	−	5.61526e12i	−1.18511	−	0.431346i	−0.327109	−	0.944987i	$-0.606074\pi$
$821$	−1.54278e13	−	5.61526e12i	−1.18511	−	0.431346i	−0.858005	+	0.513641i	$0.828296\pi$
$822$	8.11023e12	−	2.95188e12i	0.619598	−	0.225515i
$823$	−9.31980e12	+	7.82024e12i	−0.708120	+	0.594184i	−0.924071	−	0.382221i	$-0.875159\pi$
$823$	−9.31980e12	+	7.82024e12i	−0.708120	+	0.594184i	0.215951	+	0.976404i	$0.430715\pi$
$824$	2.37844e12	+	4.11959e12i	0.179730	+	0.311302i
$825$	2.70789e12	−	4.69020e12i	0.203511	−	0.352492i
$826$	−3.63400e11	−	2.06094e12i	−0.0271628	−	0.154048i
$827$	1.82496e12	+	1.03498e13i	0.135668	+	0.769412i	0.974392	+	0.224855i	$0.0721910\pi$
$827$	1.82496e12	+	1.03498e13i	0.135668	+	0.769412i	−0.838724	+	0.544557i	$0.816698\pi$
$828$	8.14448e11	−	1.41067e12i	0.0602181	−	0.104301i
$829$	5.04811e12	+	8.74358e12i	0.371222	+	0.642975i	0.989754	−	0.142785i	$-0.0456057\pi$
$829$	5.04811e12	+	8.74358e12i	0.371222	+	0.642975i	−0.618532	+	0.785759i	$0.712272\pi$
$830$	2.90925e12	−	2.44115e12i	0.212780	−	0.178543i
$831$	−9.02018e12	+	3.28308e12i	−0.656162	+	0.238823i
$832$	−1.76016e12	−	6.40647e11i	−0.127350	−	0.0463515i
$833$	−5.32058e12	−	4.46450e12i	−0.382875	−	0.321270i
$834$	−4.58325e11	+	2.59929e12i	−0.0328040	+	0.186041i
$835$	2.18290e13			1.55398
$836$	−6.24154e12	−	5.74516e12i	−0.441941	−	0.406793i
$837$	2.88438e13			2.03136
$838$	2.47986e12	−	1.40640e13i	0.173712	−	0.985168i
$839$	−1.29675e12	−	1.08810e12i	−0.0903500	−	0.0758126i	0.596494	−	0.802618i	$-0.296560\pi$
$839$	−1.29675e12	−	1.08810e12i	−0.0903500	−	0.0758126i	−0.686844	+	0.726805i	$0.741004\pi$
$840$	2.63330e12	+	9.58443e11i	0.182492	+	0.0664216i
$841$	−1.64467e13	+	5.98611e12i	−1.13370	+	0.412632i
$842$	8.59178e12	−	7.20936e12i	0.589086	−	0.494302i
$843$	−2.11537e12	−	3.66393e12i	−0.144266	−	0.249875i
$844$	5.90380e11	−	1.02257e12i	0.0400489	−	0.0693667i
$845$	−5.50564e11	−	3.12241e12i	−0.0371495	−	0.210685i
$846$	2.50790e11	+	1.42230e12i	0.0168323	+	0.0954608i
$847$	2.14826e12	−	3.72089e12i	0.143420	−	0.248412i
$848$	4.36454e11	+	7.55961e11i	0.0289839	+	0.0502016i
$849$	−1.20519e13	+	1.01127e13i	−0.796103	+	0.668010i
$850$	4.23436e12	−	1.54118e12i	0.278229	−	0.101267i
$851$	−2.76776e12	−	1.00738e12i	−0.180903	−	0.0658433i
$852$	5.07639e12	+	4.25960e12i	0.330048	+	0.276943i
$853$	−1.99391e12	+	1.13080e13i	−0.128954	+	0.731333i	0.849927	+	0.526900i	$0.176646\pi$
$853$	−1.99391e12	+	1.13080e13i	−0.128954	+	0.731333i	−0.978881	+	0.204432i	$0.934465\pi$
$854$	9.77324e12			0.628750
$855$	7.80724e12	−	5.96290e12i	0.499631	−	0.381601i
$856$	−6.26812e12			−0.399030
$857$	−4.35837e12	+	2.47175e13i	−0.276001	+	1.56528i	0.459764	+	0.888041i	$0.347934\pi$
$857$	−4.35837e12	+	2.47175e13i	−0.276001	+	1.56528i	−0.735765	+	0.677237i	$0.763177\pi$
$858$	7.79465e12	+	6.54049e12i	0.491025	+	0.412019i
$859$	3.41568e12	+	1.24320e12i	0.214046	+	0.0779064i	0.446818	−	0.894625i	$-0.352557\pi$
$859$	3.41568e12	+	1.24320e12i	0.214046	+	0.0779064i	−0.232772	+	0.972531i	$0.574779\pi$
$860$	−4.03521e11	+	1.46870e11i	−0.0251550	+	0.00915565i
$861$	8.83486e12	−	7.41332e12i	0.547880	−	0.459726i
$862$	−3.66333e12	−	6.34507e12i	−0.225992	−	0.391430i
$863$	5.06297e12	−	8.76933e12i	0.310711	−	0.538168i	−0.667805	−	0.744336i	$-0.732766\pi$
$863$	5.06297e12	−	8.76933e12i	0.310711	−	0.538168i	0.978517	+	0.206168i	$0.0660995\pi$
$864$	5.30389e11	+	3.00798e12i	0.0323804	+	0.183639i
$865$	3.54318e12	+	2.00944e13i	0.215189	+	1.22040i
$866$	9.50453e12	−	1.64623e13i	0.574249	−	0.994628i
$867$	1.50613e12	+	2.60869e12i	0.0905266	+	0.156797i
$868$	7.98427e12	−	6.69960e12i	0.477415	−	0.400599i
$869$	1.84220e13	−	6.70507e12i	1.09584	−	0.398854i
$870$	−1.41542e13	−	5.15172e12i	−0.837625	−	0.304870i
$871$	−1.32177e13	−	1.10910e13i	−0.778171	−	0.652963i
$872$	−1.48572e12	+	8.42593e12i	−0.0870186	+	0.493507i
$873$	1.92180e12			0.111981
$874$	5.25986e12	+	2.19256e12i	0.304911	+	0.127101i
$875$	−7.02291e12			−0.405024
$876$	1.25266e12	−	7.10419e12i	0.0718729	−	0.407611i
$877$	1.64340e13	+	1.37898e13i	0.938092	+	0.787152i	0.977252	−	0.212081i	$-0.0680239\pi$
$877$	1.64340e13	+	1.37898e13i	0.938092	+	0.787152i	−0.0391605	+	0.999233i	$0.512468\pi$
$878$	−2.12159e13	−	7.72195e12i	−1.20486	−	0.438532i
$879$	−1.07711e13	+	3.92038e12i	−0.608572	+	0.221502i
$880$	4.99059e12	−	4.18760e12i	0.280530	−	0.235393i
$881$	−7.59585e12	−	1.31564e13i	−0.424800	−	0.735775i	0.571602	−	0.820531i	$-0.306322\pi$
$881$	−7.59585e12	−	1.31564e13i	−0.424800	−	0.735775i	−0.996402	+	0.0847560i	$0.972989\pi$
$882$	1.90371e12	−	3.29732e12i	0.105923	−	0.183464i
$883$	2.42450e12	+	1.37500e13i	0.134214	+	0.761167i	0.975404	+	0.220426i	$0.0707449\pi$
$883$	2.42450e12	+	1.37500e13i	0.134214	+	0.761167i	−0.841189	+	0.540741i	$0.818144\pi$
$884$	1.47012e12	+	8.33747e12i	0.0809689	+	0.459197i
$885$	−2.64663e12	+	4.58410e12i	−0.145027	+	0.251194i
$886$	−1.12528e13	−	1.94904e13i	−0.613492	−	1.06260i
$887$	3.69078e12	−	3.09693e12i	0.200199	−	0.167987i	−0.537177	−	0.843470i	$-0.680509\pi$
$887$	3.69078e12	−	3.09693e12i	0.200199	−	0.167987i	0.737376	+	0.675483i	$0.236065\pi$
$888$	1.76557e12	−	6.42615e11i	0.0952855	−	0.0346811i
$889$	−6.91180e12	−	2.51569e12i	−0.371136	−	0.135082i
$890$	1.38080e13	+	1.15863e13i	0.737693	+	0.618998i
$891$	8.57746e11	−	4.86452e12i	0.0455942	−	0.258577i
$892$	−1.30302e13			−0.689142
$893$	−4.82210e12	+	1.50851e12i	−0.253749	+	0.0793809i
$894$	3.05260e12			0.159827
$895$	6.58760e12	−	3.73601e13i	0.343181	−	1.94628i
$896$	8.45487e11	+	7.09448e11i	0.0438249	+	0.0367734i
$897$	−6.42296e12	−	2.33777e12i	−0.331260	−	0.120569i
$898$	−1.22023e13	+	4.44129e12i	−0.626181	+	0.227911i
$899$	−4.29162e13	+	3.60109e13i	−2.19130	+	1.83872i
$900$	1.23508e12	+	2.13923e12i	0.0627488	+	0.108684i
$901$	1.97267e12	−	3.41676e12i	0.0997224	−	0.172724i
$902$	−4.65585e12	−	2.64046e13i	−0.234191	−	1.32816i
$903$	6.86248e10	+	3.89191e11i	0.00343468	+	0.0194790i
$904$	−1.74850e11	+	3.02848e11i	−0.00870776	+	0.0150823i
$905$	1.64015e12	+	2.84083e12i	0.0812767	+	0.140775i
$906$	−6.34898e12	+	5.32743e12i	−0.313060	+	0.262688i
$907$	−3.26972e13	+	1.19008e13i	−1.60427	+	0.583907i	−0.980296	−	0.197536i	$-0.936706\pi$
$907$	−3.26972e13	+	1.19008e13i	−1.60427	+	0.583907i	−0.623977	+	0.781443i	$0.714484\pi$
$908$	2.42741e12	+	8.83506e11i	0.118511	+	0.0431344i
$909$	−1.13002e13	−	9.48197e12i	−0.548968	−	0.460639i
$910$	−2.17341e12	+	1.23260e13i	−0.105065	+	0.595851i
$911$	−2.89016e13			−1.39024			−0.695118	−	0.718896i	$-0.744648\pi$
$911$	−2.89016e13			−1.39024			−0.695118	+	0.718896i	$0.744648\pi$
$912$	−3.46934e12	+	1.08532e12i	−0.166062	+	0.0519494i
$913$	−8.12533e12			−0.387010
$914$	−1.29199e12	+	7.32724e12i	−0.0612352	+	0.347282i
$915$	−1.89366e13	−	1.58897e13i	−0.893113	−	0.749411i
$916$	1.39127e13	+	5.06379e12i	0.652951	+	0.237655i
$917$	−1.70778e13	+	6.21583e12i	−0.797574	+	0.290293i
$918$	1.05753e13	−	8.87376e12i	0.491476	−	0.412397i
$919$	2.11192e13	+	3.65796e13i	0.976694	+	1.69168i	0.674227	+	0.738524i	$0.264477\pi$
$919$	2.11192e13	+	3.65796e13i	0.976694	+	1.69168i	0.302467	+	0.953160i	$0.402190\pi$
$920$	−2.18814e12	+	3.78997e12i	−0.100700	+	0.174418i
$921$	−2.51597e12	−	1.42688e13i	−0.115223	−	0.653459i
$922$	1.03056e12	+	5.84458e12i	0.0469659	+	0.266357i
$923$	−1.47989e13	+	2.56324e13i	−0.671152	+	1.16247i
$924$	−2.99777e12	−	5.19229e12i	−0.135293	−	0.234334i
$925$	3.42160e12	−	2.87107e12i	0.153671	−	0.128945i
$926$	1.53700e13	−	5.59423e12i	0.686950	−	0.250029i
$927$	1.10752e13	+	4.03103e12i	0.492596	+	0.179290i
$928$	−4.54457e12	−	3.81334e12i	−0.201153	−	0.168787i
$929$	7.40414e12	−	4.19909e13i	0.326140	−	1.84963i	−0.175402	−	0.984497i	$-0.556122\pi$
$929$	7.40414e12	−	4.19909e13i	0.326140	−	1.84963i	0.501542	−	0.865133i	$-0.332766\pi$
$930$	−2.63627e13			−1.15562
$931$	1.22945e13	+	5.12492e12i	0.536336	+	0.223570i
$932$	−2.68122e11			−0.0116402
$933$	3.54370e12	−	2.00973e13i	0.153105	−	0.868302i
$934$	3.62308e12	+	3.04012e12i	0.155782	+	0.130716i
$935$	−2.76694e13	−	1.00708e13i	−1.18399	−	0.430936i
$936$	−4.36108e12	+	1.58730e12i	−0.185717	+	0.0675956i
$937$	3.49131e13	−	2.92955e13i	1.47965	−	1.24158i	0.573099	−	0.819486i	$-0.305741\pi$
$937$	3.49131e13	−	2.92955e13i	1.47965	−	1.24158i	0.906554	−	0.422090i	$-0.138703\pi$
$938$	5.08345e12	+	8.80479e12i	0.214410	+	0.371369i
$939$	6.44669e12	−	1.11660e13i	0.270609	−	0.468708i
$940$	−6.73786e11	−	3.82123e12i	−0.0281479	−	0.159635i
$941$	−3.81405e12	−	2.16306e13i	−0.158574	−	0.899320i	−0.955445	−	0.295170i	$-0.904624\pi$
$941$	−3.81405e12	−	2.16306e13i	−0.158574	−	0.899320i	0.796870	−	0.604150i	$-0.206487\pi$
$942$	1.13283e13	−	1.96211e13i	0.468743	−	0.811886i
$943$	9.00546e12	+	1.55979e13i	0.370854	+	0.642338i
$944$	−1.59704e12	+	1.34007e12i	−0.0654548	+	0.0549231i
$945$	1.91785e13	−	6.98041e12i	0.782298	−	0.284733i
$946$	8.63337e11	+	3.14229e11i	0.0350485	+	0.0127566i
$947$	1.88115e13	+	1.57848e13i	0.760063	+	0.637769i	0.938143	−	0.346247i	$-0.112544\pi$
$947$	1.88115e13	+	1.57848e13i	0.760063	+	0.637769i	−0.178080	+	0.984016i	$0.556989\pi$
$948$	1.45877e12	−	8.27307e12i	0.0586608	−	0.332682i
$949$	3.22197e13			1.28951
$950$	−6.86768e12	+	5.24530e12i	−0.273561	+	0.208936i
$951$	8.94986e12			0.354817
$952$	8.66241e11	−	4.91270e12i	0.0341800	−	0.193845i
$953$	−1.39234e13	−	1.16831e13i	−0.546798	−	0.458818i	0.327057	−	0.945005i	$-0.393943\pi$
$953$	−1.39234e13	−	1.16831e13i	−0.546798	−	0.458818i	−0.873855	+	0.486187i	$0.838388\pi$
$954$	2.03233e12	+	7.39709e11i	0.0794379	+	0.0289130i
$955$	−3.16836e13	+	1.15319e13i	−1.23259	+	0.448626i
$956$	−1.17408e13	+	9.85170e12i	−0.454608	+	0.381462i
$957$	1.61133e13	+	2.79090e13i	0.620983	+	1.07557i
$958$	−1.60248e13	+	2.77557e13i	−0.614677	+	1.06465i
$959$	−3.94422e12	−	2.23688e13i	−0.150583	−	0.854001i
$960$	−4.84766e11	−	2.74924e12i	−0.0184209	−	0.104470i
$961$	−3.58062e13	+	6.20181e13i	−1.35426	+	2.34565i
$962$	4.19592e12	+	7.26755e12i	0.157957	+	0.273590i
$963$	−1.18969e13	+	9.98265e12i	−0.445773	+	0.374048i
$964$	2.32001e13	−	8.44413e12i	0.865252	−	0.314926i
$965$	3.44631e13	+	1.25435e13i	1.27933	+	0.465636i
$966$	3.08524e12	+	2.58883e12i	0.113997	+	0.0956546i
$967$	8.56716e12	−	4.85868e13i	0.315078	−	1.78690i	−0.256704	−	0.966490i	$-0.582637\pi$
$967$	8.56716e12	−	4.85868e13i	0.315078	−	1.78690i	0.571782	−	0.820405i	$-0.306252\pi$
$968$	−4.28019e12			−0.156684
$969$	1.20885e13	+	1.11271e13i	0.440468	+	0.405438i
$970$	−5.16321e12			−0.187261
$971$	−5.23962e12	+	2.97154e13i	−0.189153	+	1.07274i	0.731349	+	0.682003i	$0.238891\pi$
$971$	−5.23962e12	+	2.97154e13i	−0.189153	+	1.07274i	−0.920502	+	0.390737i	$0.872220\pi$
$972$	9.62225e12	+	8.07402e12i	0.345763	+	0.290129i
$973$	6.52729e12	+	2.37574e12i	0.233467	+	0.0849750i
$974$	1.22943e13	−	4.47477e12i	0.437713	−	0.159315i
$975$	7.94029e12	−	6.66270e12i	0.281395	−	0.236118i
$976$	−4.86806e12	−	8.43172e12i	−0.171724	−	0.297435i
$977$	1.96397e13	−	3.40170e13i	0.689620	−	1.19446i	−0.282340	−	0.959314i	$-0.591111\pi$
$977$	1.96397e13	−	3.40170e13i	0.689620	−	1.19446i	0.971961	−	0.235143i	$-0.0755560\pi$
$978$	1.08602e12	+	6.15914e12i	0.0379589	+	0.215276i
$979$	−6.69670e12	−	3.79789e13i	−0.232991	−	1.32136i
$980$	−5.11460e12	+	8.85874e12i	−0.177131	+	0.306800i
$981$	1.05993e13	+	1.83585e13i	0.365398	+	0.632888i
$982$	1.32119e13	−	1.10861e13i	0.453380	−	0.380431i
$983$	−2.20361e13	+	8.02048e12i	−0.752738	+	0.273974i	−0.689757	−	0.724041i	$-0.742283\pi$
$983$	−2.20361e13	+	8.02048e12i	−0.752738	+	0.273974i	−0.0629804	+	0.998015i	$0.520061\pi$
$984$	−1.07964e13	−	3.92956e12i	−0.367114	−	0.133618i
$985$	−1.78713e13	−	1.49958e13i	−0.604914	−	0.507583i
$986$	−4.65612e12	+	2.64062e13i	−0.156884	+	0.889733i
$987$	−3.57094e12			−0.119772
$988$	−7.46458e12	−	1.44183e13i	−0.249229	−	0.481401i
$989$	−6.17165e11			−0.0205125
$990$	2.80291e12	−	1.58961e13i	0.0927364	−	0.525934i
$991$	7.64690e12	+	6.41651e12i	0.251857	+	0.211333i	0.759971	−	0.649956i	$-0.225213\pi$
$991$	7.64690e12	+	6.41651e12i	0.251857	+	0.211333i	−0.508114	+	0.861290i	$0.669657\pi$
$992$	−9.75695e12	−	3.55124e12i	−0.319898	−	0.116433i
$993$	2.02951e12	−	7.38680e11i	0.0662398	−	0.0241093i
$994$	1.33597e13	−	1.12102e13i	0.434070	−	0.364228i
$995$	−8.12089e12	−	1.40658e13i	−0.262663	−	0.454946i
$996$	−1.74090e12	+	3.01534e12i	−0.0560542	+	0.0970887i
$997$	−7.25170e12	−	4.11264e13i	−0.232440	−	1.31824i	−0.847938	−	0.530096i	$-0.822156\pi$
$997$	−7.25170e12	−	4.11264e13i	−0.232440	−	1.31824i	0.615497	−	0.788139i	$-0.288955\pi$
$998$	5.37357e12	+	3.04750e13i	0.171465	+	0.972426i
$999$	6.84202e12	−	1.18507e13i	0.217340	−	0.376444i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	38.10.e.a.17.5	yes	42
19.9	even	9	inner	38.10.e.a.9.5	✓	42

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
38.10.e.a.9.5	✓	42	19.9	even	9	inner
38.10.e.a.17.5	yes	42	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:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	38.e (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.77837 + 15.7569i) q^{2} +(74.8003 + 62.7649i) q^{3} +(-240.561 - 87.5572i) q^{4} +(1601.32 - 582.833i) q^{5} +(-1196.81 + 1004.24i) q^{6} +(2055.81 + 3560.77i) q^{7} +(2048.00 - 3547.24i) q^{8} +(-1762.26 - 9994.30i) q^{9} +O(q^{10})\)	\(q+(-2.77837 + 15.7569i) q^{2} +(74.8003 + 62.7649i) q^{3} +(-240.561 - 87.5572i) q^{4} +(1601.32 - 582.833i) q^{5} +(-1196.81 + 1004.24i) q^{6} +(2055.81 + 3560.77i) q^{7} +(2048.00 - 3547.24i) q^{8} +(-1762.26 - 9994.30i) q^{9} +(4734.59 + 26851.2i) q^{10} +(29167.3 - 50519.2i) q^{11} +(-12498.5 - 21648.1i) q^{12} +(85526.6 - 71765.4i) q^{13} +(-61818.5 + 22500.1i) q^{14} +(156361. + 56910.6i) q^{15} +(50203.5 + 42125.7i) q^{16} +(51435.9 - 291707. i) q^{17} +162376. q^{18} +(72881.4 + 563361. i) q^{19} -436247. q^{20} +(-69716.0 + 395379. i) q^{21} +(714989. + 599947. i) q^{22} +(-589167. - 214439. i) q^{23} +(375833. - 136792. i) q^{24} +(728349. - 611158. i) q^{25} +(893177. + 1.54703e6i) q^{26} +(1.45645e6 - 2.52264e6i) q^{27} +(-182778. - 1.03658e6i) q^{28} +(982446. + 5.57173e6i) q^{29} +(-1.33116e6 + 2.30564e6i) q^{30} +(4.95106e6 + 8.57549e6i) q^{31} +(-803256. + 674012. i) q^{32} +(5.35255e6 - 1.94817e6i) q^{33} +(4.45350e6 + 1.62094e6i) q^{34} +(5.36734e6 + 4.50373e6i) q^{35} +(-451140. + 2.55854e6i) q^{36} +4.69775e6 q^{37} +(-9.07933e6 - 416841. i) q^{38} +1.09018e7 q^{39} +(1.21205e6 - 6.87391e6i) q^{40} +(-2.20058e7 - 1.84651e7i) q^{41} +(-6.03627e6 - 2.19702e6i) q^{42} +(924985. - 336667. i) q^{43} +(-1.14398e7 + 9.59916e6i) q^{44} +(-8.64695e6 - 1.49770e7i) q^{45} +(5.01583e6 - 8.68767e6i) q^{46} +(1.54451e6 + 8.75933e6i) q^{47} +(1.11122e6 + 6.30204e6i) q^{48} +(1.17241e7 - 2.03067e7i) q^{49} +(7.60634e6 + 1.31746e7i) q^{50} +(2.21564e7 - 1.85914e7i) q^{51} +(-2.68580e7 + 9.77550e6i) q^{52} +(1.25163e7 + 4.55554e6i) q^{53} +(3.57025e7 + 2.99579e7i) q^{54} +(1.72619e7 - 9.78970e7i) q^{55} +1.68412e7 q^{56} +(-2.99078e7 + 4.67140e7i) q^{57} -9.05229e7 q^{58} +(-5.52397e6 + 3.13280e7i) q^{59} +(-3.26314e7 - 2.73810e7i) q^{60} +(-1.39602e8 - 5.08110e7i) q^{61} +(-1.48879e8 + 5.41876e7i) q^{62} +(3.19645e7 - 2.68214e7i) q^{63} +(-8.38861e6 - 1.45295e7i) q^{64} +(9.51282e7 - 1.64767e8i) q^{65} +(1.58258e7 + 8.97525e7i) q^{66} +(-2.68365e7 - 1.52197e8i) q^{67} +(-3.79145e7 + 6.56699e7i) q^{68} +(-3.06106e7 - 5.30192e7i) q^{69} +(-8.58774e7 + 7.20597e7i) q^{70} +(-2.49113e8 + 9.06699e7i) q^{71} +(-3.90613e7 - 1.42171e7i) q^{72} +(2.21069e8 + 1.85499e8i) q^{73} +(-1.30521e7 + 7.40221e7i) q^{74} +9.28400e7 q^{75} +(3.17939e7 - 1.41904e8i) q^{76} +2.39849e8 q^{77} +(-3.02891e7 + 1.71778e8i) q^{78} +(2.57442e8 + 2.16020e8i) q^{79} +(1.04944e8 + 3.81965e7i) q^{80} +(7.95699e7 - 2.89611e7i) q^{81} +(3.52093e8 - 2.95441e8i) q^{82} +(-6.96443e7 - 1.20627e8i) q^{83} +(5.13893e7 - 8.90088e7i) q^{84} +(-8.76513e7 - 4.97095e8i) q^{85} +(2.73488e6 + 1.55103e7i) q^{86} +(-2.76222e8 + 4.78430e8i) q^{87} +(-1.19469e8 - 2.06927e8i) q^{88} +(5.06429e8 - 4.24944e8i) q^{89} +(2.60015e8 - 9.46378e7i) q^{90} +(4.31366e8 + 1.57004e8i) q^{91} +(1.22955e8 + 1.03172e8i) q^{92} +(-1.67899e8 + 9.52202e8i) q^{93} -1.42311e8 q^{94} +(4.45052e8 + 8.59644e8i) q^{95} -1.02388e8 q^{96} +(-3.28835e7 + 1.86492e8i) q^{97} +(2.87398e8 + 2.41155e8i) q^{98} +(-5.56304e8 - 2.02478e8i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 42 q - 252 q^{3} + 4032 q^{6} + 14373 q^{7} + 86016 q^{8} + 12852 q^{9}+O(q^{10}) \) 42 * q - 252 * q^3 + 4032 * q^6 + 14373 * q^7 + 86016 * q^8 + 12852 * q^9	\( 42 q - 252 q^{3} + 4032 q^{6} + 14373 q^{7} + 86016 q^{8} + 12852 q^{9} + 32625 q^{11} - 62208 q^{12} + 351237 q^{13} + 165264 q^{14} - 834165 q^{15} + 1075035 q^{17} - 3364608 q^{18} + 696762 q^{19} - 1396224 q^{20} - 3148065 q^{21} - 1462656 q^{22} - 4882824 q^{23} + 1032192 q^{24} - 483270 q^{25} - 70176 q^{26} + 2570400 q^{27} + 1519104 q^{28} + 13670499 q^{29} - 2263968 q^{31} - 5777733 q^{33} - 9526080 q^{34} + 43019613 q^{35} + 3290112 q^{36} - 50105184 q^{37} - 692160 q^{38} - 89820600 q^{39} - 94033860 q^{41} - 43526160 q^{42} + 30524217 q^{43} + 23402496 q^{44} + 39789630 q^{45} - 18312576 q^{46} + 81865791 q^{47} + 33030144 q^{48} + 40421580 q^{49} - 16761600 q^{50} - 28132314 q^{51} - 91666176 q^{52} + 126049077 q^{53} - 106214544 q^{54} + 553870071 q^{55} + 117743616 q^{56} + 384197394 q^{57} - 63148512 q^{58} + 135312639 q^{59} - 129611520 q^{60} + 132517452 q^{61} - 419324112 q^{62} + 577860735 q^{63} - 352321536 q^{64} - 184218951 q^{65} + 413765760 q^{66} + 229749621 q^{67} + 152743680 q^{68} - 517946637 q^{69} - 688313808 q^{70} - 2107934406 q^{71} + 105283584 q^{72} - 26577420 q^{73} + 322027248 q^{74} + 941894730 q^{75} - 107163648 q^{76} + 620006124 q^{77} + 122597280 q^{78} - 624601023 q^{79} - 1037387736 q^{81} + 1504541760 q^{82} + 907729401 q^{83} - 604998912 q^{84} + 1462808898 q^{85} + 222950208 q^{86} + 63648732 q^{87} - 133632000 q^{88} - 847590846 q^{89} - 4481693280 q^{90} + 957045924 q^{91} + 648163584 q^{92} + 2438307564 q^{93} + 2205393024 q^{94} - 208077987 q^{95} - 509607936 q^{96} + 535342599 q^{97} + 1861154832 q^{98} - 11757151095 q^{99}+O(q^{100}) \) 42 * q - 252 * q^3 + 4032 * q^6 + 14373 * q^7 + 86016 * q^8 + 12852 * q^9 + 32625 * q^11 - 62208 * q^12 + 351237 * q^13 + 165264 * q^14 - 834165 * q^15 + 1075035 * q^17 - 3364608 * q^18 + 696762 * q^19 - 1396224 * q^20 - 3148065 * q^21 - 1462656 * q^22 - 4882824 * q^23 + 1032192 * q^24 - 483270 * q^25 - 70176 * q^26 + 2570400 * q^27 + 1519104 * q^28 + 13670499 * q^29 - 2263968 * q^31 - 5777733 * q^33 - 9526080 * q^34 + 43019613 * q^35 + 3290112 * q^36 - 50105184 * q^37 - 692160 * q^38 - 89820600 * q^39 - 94033860 * q^41 - 43526160 * q^42 + 30524217 * q^43 + 23402496 * q^44 + 39789630 * q^45 - 18312576 * q^46 + 81865791 * q^47 + 33030144 * q^48 + 40421580 * q^49 - 16761600 * q^50 - 28132314 * q^51 - 91666176 * q^52 + 126049077 * q^53 - 106214544 * q^54 + 553870071 * q^55 + 117743616 * q^56 + 384197394 * q^57 - 63148512 * q^58 + 135312639 * q^59 - 129611520 * q^60 + 132517452 * q^61 - 419324112 * q^62 + 577860735 * q^63 - 352321536 * q^64 - 184218951 * q^65 + 413765760 * q^66 + 229749621 * q^67 + 152743680 * q^68 - 517946637 * q^69 - 688313808 * q^70 - 2107934406 * q^71 + 105283584 * q^72 - 26577420 * q^73 + 322027248 * q^74 + 941894730 * q^75 - 107163648 * q^76 + 620006124 * q^77 + 122597280 * q^78 - 624601023 * q^79 - 1037387736 * q^81 + 1504541760 * q^82 + 907729401 * q^83 - 604998912 * q^84 + 1462808898 * q^85 + 222950208 * q^86 + 63648732 * q^87 - 133632000 * q^88 - 847590846 * q^89 - 4481693280 * q^90 + 957045924 * q^91 + 648163584 * q^92 + 2438307564 * q^93 + 2205393024 * q^94 - 208077987 * q^95 - 509607936 * q^96 + 535342599 * q^97 + 1861154832 * q^98 - 11757151095 * q^99

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