LMFDB - Embedded newform 27.8.e.a.4.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [27,8,Mod(4,27)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(27, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([2]))

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

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

chi := DirichletCharacter("27.4");

S:= CuspForms(chi, 8);

N := Newforms(S);

Level:	$ N $	$=$	$ 27 = 3^{3} $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	27.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:	$8.43439568807$
Analytic rank:	$0$
Dimension:	$120$
Relative dimension:	$20$ over $\Q(\zeta_{9})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			4.6
Character	$\chi$	$=$	27.4
Dual form			27.8.e.a.7.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-9.62864 - 3.50454i) q^{2} +(31.7200 - 34.3634i) q^{3} +(-17.6248 - 14.7890i) q^{4} +(40.7285 - 230.983i) q^{5} +(-425.848 + 219.708i) q^{6} +(500.665 - 420.108i) q^{7} +(773.656 + 1340.01i) q^{8} +(-174.680 - 2180.01i) q^{9} +O(q^{10})$	\(q+(-9.62864 - 3.50454i) q^{2} +(31.7200 - 34.3634i) q^{3} +(-17.6248 - 14.7890i) q^{4} +(40.7285 - 230.983i) q^{5} +(-425.848 + 219.708i) q^{6} +(500.665 - 420.108i) q^{7} +(773.656 + 1340.01i) q^{8} +(-174.680 - 2180.01i) q^{9} +(-1201.65 + 2081.32i) q^{10} +(-328.263 - 1861.67i) q^{11} +(-1067.26 + 136.541i) q^{12} +(-13604.6 + 4951.67i) q^{13} +(-6293.01 + 2290.47i) q^{14} +(-6645.44 - 8726.35i) q^{15} +(-2241.74 - 12713.6i) q^{16} +(-7312.15 + 12665.0i) q^{17} +(-5958.01 + 21602.7i) q^{18} +(-21696.6 - 37579.6i) q^{19} +(-4133.84 + 3468.70i) q^{20} +(1444.80 - 30530.4i) q^{21} +(-3363.57 + 19075.8i) q^{22} +(61924.7 + 51961.0i) q^{23} +(70587.6 + 15919.8i) q^{24} +(21719.2 + 7905.14i) q^{25} +148347. q^{26} +(-80453.4 - 63147.5i) q^{27} -15037.1 q^{28} +(85205.2 + 31012.1i) q^{29} +(33404.7 + 107312. i) q^{30} +(-114762. - 96296.5i) q^{31} +(11421.8 - 64776.5i) q^{32} +(-74385.8 - 47772.1i) q^{33} +(114791. - 96321.1i) q^{34} +(-76646.4 - 132756. i) q^{35} +(-29161.5 + 41005.7i) q^{36} +(40221.7 - 69666.1i) q^{37} +(77209.6 + 437877. i) q^{38} +(-261382. + 624567. i) q^{39} +(341029. - 124125. i) q^{40} +(181176. - 65942.8i) q^{41} +(-120906. + 288903. i) q^{42} +(-86932.1 - 493016. i) q^{43} +(-21746.7 + 37666.3i) q^{44} +(-510660. - 48440.7i) q^{45} +(-414151. - 717331. i) q^{46} +(615804. - 516721. i) q^{47} +(-507988. - 326240. i) q^{48} +(-68831.8 + 390364. i) q^{49} +(-181422. - 152232. i) q^{50} +(203271. + 653004. i) q^{51} +(313009. + 113926. i) q^{52} -1.14077e6 q^{53} +(553354. + 889976. i) q^{54} -443384. q^{55} +(950292. + 345878. i) q^{56} +(-1.97958e6 - 446459. i) q^{57} +(-711726. - 597209. i) q^{58} +(299570. - 1.69894e6i) q^{59} +(-11929.2 + 252080. i) q^{60} +(1.71084e6 - 1.43556e6i) q^{61} +(767524. + 1.32939e6i) q^{62} +(-1.00330e6 - 1.01807e6i) q^{63} +(-1.16321e6 + 2.01474e6i) q^{64} +(589656. + 3.34410e6i) q^{65} +(548815. + 720668. i) q^{66} +(-117367. + 42717.9i) q^{67} +(316178. - 115079. i) q^{68} +(3.74981e6 - 479736. i) q^{69} +(272754. + 1.54686e6i) q^{70} +(850034. - 1.47230e6i) q^{71} +(2.78610e6 - 1.92065e6i) q^{72} +(-868776. - 1.50476e6i) q^{73} +(-631428. + 529831. i) q^{74} +(960581. - 495593. i) q^{75} +(-173366. + 983206. i) q^{76} +(-946453. - 794169. i) q^{77} +(4.70557e6 - 5.09770e6i) q^{78} +(2.67970e6 + 975329. i) q^{79} -3.02792e6 q^{80} +(-4.72194e6 + 761608. i) q^{81} -1.97558e6 q^{82} +(2.05276e6 + 747144. i) q^{83} +(-476978. + 516726. i) q^{84} +(2.62759e6 + 2.20481e6i) q^{85} +(-890757. + 5.05173e6i) q^{86} +(3.76839e6 - 1.94423e6i) q^{87} +(2.24070e6 - 1.88017e6i) q^{88} +(-5.87690e6 - 1.01791e7i) q^{89} +(4.74720e6 + 2.25604e6i) q^{90} +(-4.73111e6 + 8.19453e6i) q^{91} +(-322962. - 1.83161e6i) q^{92} +(-6.94932e6 + 889069. i) q^{93} +(-7.74022e6 + 2.81721e6i) q^{94} +(-9.56393e6 + 3.48098e6i) q^{95} +(-1.86364e6 - 2.44720e6i) q^{96} +(1.94881e6 + 1.10522e7i) q^{97} +(2.03080e6 - 3.51745e6i) q^{98} +(-4.00113e6 + 1.04081e6i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 120 q - 6 q^{2} - 6 q^{3} - 6 q^{4} - 219 q^{5} + 1386 q^{6} - 6 q^{7} - 4611 q^{8} - 1728 q^{9}+O(q^{10}) $ 120 * q - 6 * q^2 - 6 * q^3 - 6 * q^4 - 219 * q^5 + 1386 * q^6 - 6 * q^7 - 4611 * q^8 - 1728 * q^9	\( 120 q - 6 q^{2} - 6 q^{3} - 6 q^{4} - 219 q^{5} + 1386 q^{6} - 6 q^{7} - 4611 q^{8} - 1728 q^{9} - 3 q^{10} + 9399 q^{11} - 10545 q^{12} - 6 q^{13} + 16647 q^{14} + 11709 q^{15} + 378 q^{16} - 58959 q^{17} - 156051 q^{18} - 3 q^{19} + 240243 q^{20} - 516 q^{21} + 105762 q^{22} - 144084 q^{23} - 150894 q^{24} - 107997 q^{25} + 443202 q^{26} + 114363 q^{27} - 12 q^{28} + 107886 q^{29} - 179901 q^{30} + 297975 q^{31} - 639576 q^{32} - 31338 q^{33} - 265806 q^{34} - 450672 q^{35} + 51264 q^{36} - 3 q^{37} - 145596 q^{38} + 1919661 q^{39} + 283521 q^{40} + 227085 q^{41} + 3792042 q^{42} - 1080969 q^{43} - 1205115 q^{44} - 4430925 q^{45} - 3 q^{46} - 5184339 q^{47} - 2424039 q^{48} + 976008 q^{49} + 2324559 q^{50} + 2918034 q^{51} - 3366135 q^{52} + 5631750 q^{53} + 11971422 q^{54} - 12 q^{55} + 5254923 q^{56} - 284637 q^{57} + 3884295 q^{58} - 12534492 q^{59} - 29390886 q^{60} + 3865440 q^{61} - 9923646 q^{62} + 3292389 q^{63} - 10223619 q^{64} + 17158395 q^{65} + 39100653 q^{66} + 5567061 q^{67} + 19858455 q^{68} - 12682935 q^{69} - 1020993 q^{70} - 18563877 q^{71} - 33138540 q^{72} + 3770934 q^{73} - 36278085 q^{74} - 26317941 q^{75} - 1156998 q^{76} + 8471751 q^{77} + 36593658 q^{78} + 16415526 q^{79} + 101080590 q^{80} + 45736524 q^{81} - 12 q^{82} + 3147699 q^{83} - 27588054 q^{84} - 7672131 q^{85} - 70854834 q^{86} - 55384731 q^{87} - 34323078 q^{88} - 54647613 q^{89} - 25256970 q^{90} + 3315066 q^{91} + 73858515 q^{92} + 69808065 q^{93} + 22126539 q^{94} + 32541447 q^{95} + 33014034 q^{96} + 41250117 q^{97} - 88493274 q^{98} - 111262167 q^{99}+O(q^{100}) \) 120 * q - 6 * q^2 - 6 * q^3 - 6 * q^4 - 219 * q^5 + 1386 * q^6 - 6 * q^7 - 4611 * q^8 - 1728 * q^9 - 3 * q^10 + 9399 * q^11 - 10545 * q^12 - 6 * q^13 + 16647 * q^14 + 11709 * q^15 + 378 * q^16 - 58959 * q^17 - 156051 * q^18 - 3 * q^19 + 240243 * q^20 - 516 * q^21 + 105762 * q^22 - 144084 * q^23 - 150894 * q^24 - 107997 * q^25 + 443202 * q^26 + 114363 * q^27 - 12 * q^28 + 107886 * q^29 - 179901 * q^30 + 297975 * q^31 - 639576 * q^32 - 31338 * q^33 - 265806 * q^34 - 450672 * q^35 + 51264 * q^36 - 3 * q^37 - 145596 * q^38 + 1919661 * q^39 + 283521 * q^40 + 227085 * q^41 + 3792042 * q^42 - 1080969 * q^43 - 1205115 * q^44 - 4430925 * q^45 - 3 * q^46 - 5184339 * q^47 - 2424039 * q^48 + 976008 * q^49 + 2324559 * q^50 + 2918034 * q^51 - 3366135 * q^52 + 5631750 * q^53 + 11971422 * q^54 - 12 * q^55 + 5254923 * q^56 - 284637 * q^57 + 3884295 * q^58 - 12534492 * q^59 - 29390886 * q^60 + 3865440 * q^61 - 9923646 * q^62 + 3292389 * q^63 - 10223619 * q^64 + 17158395 * q^65 + 39100653 * q^66 + 5567061 * q^67 + 19858455 * q^68 - 12682935 * q^69 - 1020993 * q^70 - 18563877 * q^71 - 33138540 * q^72 + 3770934 * q^73 - 36278085 * q^74 - 26317941 * q^75 - 1156998 * q^76 + 8471751 * q^77 + 36593658 * q^78 + 16415526 * q^79 + 101080590 * q^80 + 45736524 * q^81 - 12 * q^82 + 3147699 * q^83 - 27588054 * q^84 - 7672131 * q^85 - 70854834 * q^86 - 55384731 * q^87 - 34323078 * q^88 - 54647613 * q^89 - 25256970 * q^90 + 3315066 * q^91 + 73858515 * q^92 + 69808065 * q^93 + 22126539 * q^94 + 32541447 * q^95 + 33014034 * q^96 + 41250117 * q^97 - 88493274 * q^98 - 111262167 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/27\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{1}{9}\right)$

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 $

$2$	−9.62864	−	3.50454i	−0.851059	−	0.309760i	−0.120587	−	0.992703i	$-0.538478\pi$
$2$	−9.62864	−	3.50454i	−0.851059	−	0.309760i	−0.730472	+	0.682943i	$0.760700\pi$
$3$	31.7200	−	34.3634i	0.678280	−	0.734803i
$3$	31.7200	−	34.3634i	0.678280	−	0.734803i
$4$	−17.6248	−	14.7890i	−0.137694	−	0.115539i
$5$	40.7285	−	230.983i	0.145715	−	0.826389i	−0.821076	−	0.570819i	$-0.806626\pi$
$5$	40.7285	−	230.983i	0.145715	−	0.826389i	0.966790	−	0.255570i	$-0.0822632\pi$
$6$	−425.848	+	219.708i	−0.804870	+	0.415257i
$7$	500.665	−	420.108i	0.551702	−	0.462933i	−0.323815	−	0.946120i	$-0.604966\pi$
$7$	500.665	−	420.108i	0.551702	−	0.462933i	0.875517	+	0.483188i	$0.160521\pi$
$8$	773.656	+	1340.01i	0.534236	+	0.925323i
$9$	−174.680	−	2180.01i	−0.0798718	−	0.996805i
$10$	−1201.65	+	2081.32i	−0.379994	+	0.658170i
$11$	−328.263	−	1861.67i	−0.0743614	−	0.421724i	−0.999149	−	0.0412412i	$-0.986869\pi$
$11$	−328.263	−	1861.67i	−0.0743614	−	0.421724i	0.924788	−	0.380483i	$-0.124242\pi$
$12$	−1067.26	+	136.541i	−0.178294	+	0.0228102i
$13$	−13604.6	+	4951.67i	−1.71745	+	0.625101i	−0.997614	−	0.0690437i	$-0.978005\pi$
$13$	−13604.6	+	4951.67i	−1.71745	+	0.625101i	−0.719836	+	0.694144i	$0.755783\pi$
$14$	−6293.01	+	2290.47i	−0.612929	+	0.223088i
$15$	−6645.44	−	8726.35i	−0.508398	−	0.667595i
$16$	−2241.74	−	12713.6i	−0.136825	−	0.775974i
$17$	−7312.15	+	12665.0i	−0.360972	+	0.625222i	−0.988121	−	0.153677i	$-0.950888\pi$
$17$	−7312.15	+	12665.0i	−0.360972	+	0.625222i	0.627149	+	0.778899i	$0.284222\pi$
$18$	−5958.01	+	21602.7i	−0.240795	+	0.873081i
$19$	−21696.6	−	37579.6i	−0.725696	−	1.25694i	−0.958687	−	0.284463i	$-0.908185\pi$
$19$	−21696.6	−	37579.6i	−0.725696	−	1.25694i	0.232992	−	0.972479i	$-0.425149\pi$
$20$	−4133.84	+	3468.70i	−0.115544	+	0.0969531i
$21$	1444.80	−	30530.4i	0.0340439	−	0.719390i
$22$	−3363.57	+	19075.8i	−0.0673475	+	0.381947i
$23$	61924.7	+	51961.0i	1.06125	+	0.890492i	0.994231	−	0.107260i	$-0.0342077\pi$
$23$	61924.7	+	51961.0i	1.06125	+	0.890492i	0.0670161	+	0.997752i	$0.478652\pi$
$24$	70587.6	+	15919.8i	1.04229	+	0.235070i
$25$	21719.2	+	7905.14i	0.278006	+	0.101186i
$26$	148347.			1.65528
$27$	−80453.4	−	63147.5i	−0.786631	−	0.617423i
$28$	−15037.1			−0.129453
$29$	85205.2	+	31012.1i	0.648743	+	0.236123i	0.645369	−	0.763871i	$-0.276704\pi$
$29$	85205.2	+	31012.1i	0.648743	+	0.236123i	0.00337448	+	0.999994i	$0.498926\pi$
$30$	33404.7	+	107312.i	0.225883	+	0.725645i
$31$	−114762.	−	96296.5i	−0.691881	−	0.580557i	0.227570	−	0.973762i	$-0.426922\pi$
$31$	−114762.	−	96296.5i	−0.691881	−	0.580557i	−0.919451	+	0.393205i	$0.871366\pi$
$32$	11421.8	−	64776.5i	0.0616185	−	0.349456i
$33$	−74385.8	−	47772.1i	−0.360322	−	0.231406i
$34$	114791.	−	96321.1i	0.500878	−	0.420286i
$35$	−76646.4	−	132756.i	−0.302172	−	0.523377i
$36$	−29161.5	+	41005.7i	−0.104172	+	0.146482i
$37$	40221.7	−	69666.1i	0.130543	−	0.226108i	−0.793343	−	0.608775i	$-0.791661\pi$
$37$	40221.7	−	69666.1i	0.130543	−	0.226108i	0.923886	+	0.382667i	$0.124995\pi$
$38$	77209.6	+	437877.i	0.228259	+	1.29452i
$39$	−261382.	+	624567.i	−0.705586	+	1.68598i
$40$	341029.	−	124125.i	0.842523	−	0.306653i
$41$	181176.	−	65942.8i	0.410543	−	0.149425i	−0.128489	−	0.991711i	$-0.541013\pi$
$41$	181176.	−	65942.8i	0.410543	−	0.149425i	0.539031	+	0.842286i	$0.318790\pi$
$42$	−120906.	+	288903.i	−0.251812	+	0.601698i
$43$	−86932.1	−	493016.i	−0.166740	−	0.945631i	−0.947252	−	0.320490i	$-0.896152\pi$
$43$	−86932.1	−	493016.i	−0.166740	−	0.945631i	0.780512	−	0.625141i	$-0.214959\pi$
$44$	−21746.7	+	37666.3i	−0.0384865	+	0.0666606i
$45$	−510660.	−	48440.7i	−0.835388	−	0.0792440i
$46$	−414151.	−	717331.i	−0.627345	−	1.08659i
$47$	615804.	−	516721.i	0.865167	−	0.725962i	−0.0979075	−	0.995196i	$-0.531215\pi$
$47$	615804.	−	516721.i	0.865167	−	0.725962i	0.963075	+	0.269234i	$0.0867705\pi$
$48$	−507988.	−	326240.i	−0.662994	−	0.425788i
$49$	−68831.8	+	390364.i	−0.0835801	+	0.474006i
$50$	−181422.	−	152232.i	−0.205256	−	0.172230i
$51$	203271.	+	653004.i	0.214575	+	0.689319i
$52$	313009.	+	113926.i	0.308706	+	0.112360i
$53$	−1.14077e6			−1.05253			−0.526264	−	0.850321i	$-0.676408\pi$
$53$	−1.14077e6			−1.05253			−0.526264	+	0.850321i	$0.676408\pi$
$54$	553354.	+	889976.i	0.478217	+	0.769131i
$55$	−443384.			−0.359344
$56$	950292.	+	345878.i	0.723101	+	0.263187i
$57$	−1.97958e6	−	446459.i	−1.41583	−	0.319315i
$58$	−711726.	−	597209.i	−0.478977	−	0.401910i
$59$	299570.	−	1.69894e6i	0.189896	−	1.07695i	−0.729606	−	0.683868i	$-0.760296\pi$
$59$	299570.	−	1.69894e6i	0.189896	−	1.07695i	0.919502	−	0.393086i	$-0.128592\pi$
$60$	−11929.2	+	252080.i	−0.00712990	+	0.150664i
$61$	1.71084e6	−	1.43556e6i	0.965061	−	0.809782i	−0.0167084	−	0.999860i	$-0.505319\pi$
$61$	1.71084e6	−	1.43556e6i	0.965061	−	0.809782i	0.981769	+	0.190078i	$0.0608742\pi$
$62$	767524.	+	1.32939e6i	0.408998	+	0.708405i
$63$	−1.00330e6	−	1.01807e6i	−0.505519	−	0.512964i
$64$	−1.16321e6	+	2.01474e6i	−0.554661	+	0.960701i
$65$	589656.	+	3.34410e6i	0.266319	+	1.51037i
$66$	548815.	+	720668.i	0.234975	+	0.308554i
$67$	−117367.	+	42717.9i	−0.0476741	+	0.0173520i	−0.365747	−	0.930714i	$-0.619186\pi$
$67$	−117367.	+	42717.9i	−0.0476741	+	0.0173520i	0.318073	+	0.948066i	$0.396964\pi$
$68$	316178.	−	115079.i	0.121941	−	0.0443830i
$69$	3.74981e6	−	479736.i	1.37416	−	0.175805i
$70$	272754.	+	1.54686e6i	0.0950447	+	0.539025i
$71$	850034.	−	1.47230e6i	0.281859	−	0.488194i	−0.689984	−	0.723825i	$-0.742382\pi$
$71$	850034.	−	1.47230e6i	0.281859	−	0.488194i	0.971843	+	0.235631i	$0.0757156\pi$
$72$	2.78610e6	−	1.92065e6i	0.879696	−	0.606436i
$73$	−868776.	−	1.50476e6i	−0.261383	−	0.452729i	0.705226	−	0.708982i	$-0.250845\pi$
$73$	−868776.	−	1.50476e6i	−0.261383	−	0.452729i	−0.966610	+	0.256253i	$0.917512\pi$
$74$	−631428.	+	529831.i	−0.181139	+	0.151994i
$75$	960581.	−	495593.i	0.262918	−	0.135647i
$76$	−173366.	+	983206.i	−0.0453018	+	0.256919i
$77$	−946453.	−	794169.i	−0.236255	−	0.198242i
$78$	4.70557e6	−	5.09770e6i	1.12275	−	1.21631i
$79$	2.67970e6	+	975329.i	0.611492	+	0.222565i	0.629156	−	0.777279i	$-0.283401\pi$
$79$	2.67970e6	+	975329.i	0.611492	+	0.222565i	−0.0176641	+	0.999844i	$0.505623\pi$
$80$	−3.02792e6			−0.661194
$81$	−4.72194e6	+	761608.i	−0.987241	+	0.159233i
$82$	−1.97558e6			−0.395682
$83$	2.05276e6	+	747144.i	0.394062	+	0.143427i	0.531449	−	0.847091i	$-0.321648\pi$
$83$	2.05276e6	+	747144.i	0.394062	+	0.143427i	−0.137386	+	0.990518i	$0.543870\pi$
$84$	−476978.	+	516726.i	−0.0878053	+	0.0951223i
$85$	2.62759e6	+	2.20481e6i	0.464078	+	0.389408i
$86$	−890757.	+	5.05173e6i	−0.151013	+	0.856438i
$87$	3.76839e6	−	1.94423e6i	0.613534	−	0.316541i
$88$	2.24070e6	−	1.88017e6i	0.350505	−	0.294108i
$89$	−5.87690e6	−	1.01791e7i	−0.883656	−	1.53054i	−0.847246	−	0.531201i	$-0.821741\pi$
$89$	−5.87690e6	−	1.01791e7i	−0.883656	−	1.53054i	−0.0364102	−	0.999337i	$-0.511592\pi$
$90$	4.74720e6	+	2.25604e6i	0.686418	+	0.326211i
$91$	−4.73111e6	+	8.19453e6i	−0.658140	+	1.13993i
$92$	−322962.	−	1.83161e6i	−0.0432408	−	0.245231i
$93$	−6.94932e6	+	889069.i	−0.895884	+	0.114616i
$94$	−7.74022e6	+	2.81721e6i	−0.961183	+	0.349842i
$95$	−9.56393e6	+	3.48098e6i	−1.14447	+	0.416552i
$96$	−1.86364e6	−	2.44720e6i	−0.214987	−	0.282307i
$97$	1.94881e6	+	1.10522e7i	0.216804	+	1.22956i	0.877748	+	0.479123i	$0.159045\pi$
$97$	1.94881e6	+	1.10522e7i	0.216804	+	1.22956i	−0.660943	+	0.750436i	$0.729844\pi$
$98$	2.03080e6	−	3.51745e6i	0.217960	−	0.377517i
$99$	−4.00113e6	+	1.04081e6i	−0.414438	+	0.107808i
$100$	−265888.	−	460532.i	−0.0265888	−	0.0460532i
$101$	−5.41482e6	+	4.54357e6i	−0.522949	+	0.438806i	−0.865658	−	0.500635i	$-0.833100\pi$
$101$	−5.41482e6	+	4.54357e6i	−0.522949	+	0.438806i	0.342709	+	0.939441i	$0.388655\pi$
$102$	331259.	−	6.99991e6i	0.0309077	−	0.653118i
$103$	2.04951e6	−	1.16234e7i	0.184808	−	1.04810i	−0.741394	−	0.671070i	$-0.765835\pi$
$103$	2.04951e6	−	1.16234e7i	0.184808	−	1.04810i	0.926202	−	0.377028i	$-0.123054\pi$
$104$	−1.71606e7	−	1.43994e7i	−1.49594	−	1.25524i
$105$	−6.99315e6	−	1.57718e6i	−0.589536	−	0.132959i
$106$	1.09841e7	+	3.99788e6i	0.895764	+	0.326032i
$107$	1.36780e7			1.07940			0.539698	−	0.841859i	$-0.318539\pi$
$107$	1.36780e7			1.07940			0.539698	+	0.841859i	$0.318539\pi$
$108$	484090.	+	2.30279e6i	0.0369779	+	0.175902i
$109$	6.11021e6			0.451922			0.225961	−	0.974136i	$-0.427448\pi$
$109$	6.11021e6			0.451922			0.225961	+	0.974136i	$0.427448\pi$
$110$	4.26918e6	+	1.55386e6i	0.305823	+	0.111311i
$111$	−1.11813e6	−	3.59196e6i	−0.0775997	−	0.249288i
$112$	−6.46343e6	−	5.42346e6i	−0.434710	−	0.364765i
$113$	316170.	−	1.79309e6i	0.0206132	−	0.116904i	−0.972765	−	0.231794i	$-0.925541\pi$
$113$	316170.	−	1.79309e6i	0.0206132	−	0.116904i	0.993378	+	0.114890i	$0.0366516\pi$
$114$	1.74960e7	+	1.12363e7i	1.10604	+	0.710324i
$115$	1.45242e7	−	1.21873e7i	0.890533	−	0.747246i
$116$	−1.04309e6	−	1.80668e6i	−0.0620466	−	0.107468i
$117$	1.31711e7	+	2.87932e7i	0.760279	+	1.66203i
$118$	−8.83846e6	+	1.53087e7i	−0.495210	+	0.857729i
$119$	1.65974e6	+	9.41283e6i	0.0902868	+	0.512042i
$120$	6.55213e6	−	1.56561e7i	0.346137	−	0.827086i
$121$	1.49539e7	−	5.44277e6i	0.767371	−	0.279300i
$122$	−2.15040e7	+	7.82683e6i	−1.07216	+	0.390235i
$123$	3.48091e6	−	8.31754e6i	0.168665	−	0.403020i
$124$	598528.	+	3.39442e6i	0.0281909	+	0.159878i
$125$	1.18725e7	−	2.05638e7i	0.543697	−	0.941712i
$126$	6.09251e6	+	1.33187e7i	0.271331	+	0.593152i
$127$	1.66734e7	+	2.88791e7i	0.722288	+	1.25104i	0.960080	+	0.279724i	$0.0902430\pi$
$127$	1.66734e7	+	2.88791e7i	0.722288	+	1.25104i	−0.237792	+	0.971316i	$0.576424\pi$
$128$	1.18113e7	−	9.91083e6i	0.497808	−	0.417710i
$129$	−1.96992e7	−	1.26512e7i	−0.807950	−	0.518882i
$130$	6.04195e6	−	3.42656e7i	0.241199	−	1.36791i
$131$	3.80495e7	+	3.19273e7i	1.47877	+	1.24083i	0.907491	+	0.420072i	$0.137995\pi$
$131$	3.80495e7	+	3.19273e7i	1.47877	+	1.24083i	0.571275	+	0.820759i	$0.306449\pi$
$132$	604536.	+	1.94207e6i	0.0228778	+	0.0734945i
$133$	−2.66503e7	−	9.69990e6i	−0.982247	−	0.357509i
$134$	1.27979e6			0.0459484
$135$	−1.78627e7	+	1.60115e7i	−0.624856	+	0.560096i
$136$	−2.26283e7			−0.771377
$137$	3.63910e7	+	1.32452e7i	1.20913	+	0.440086i	0.866401	−	0.499349i	$-0.166428\pi$
$137$	3.63910e7	+	1.32452e7i	1.20913	+	0.440086i	0.342726	+	0.939435i	$0.388650\pi$
$138$	−3.77868e7	−	8.52214e6i	−1.22395	−	0.276040i
$139$	−4.58471e7	−	3.84703e7i	−1.44797	−	1.21499i	−0.934043	−	0.357162i	$-0.883744\pi$
$139$	−4.58471e7	−	3.84703e7i	−1.44797	−	1.21499i	−0.513930	−	0.857832i	$-0.671811\pi$
$140$	−612439.	+	3.47332e6i	−0.0188632	+	0.106978i
$141$	1.77706e6	−	3.75515e7i	0.0533869	−	1.12813i
$142$	−1.33444e7	+	1.11973e7i	−0.391102	+	0.328173i
$143$	1.36843e7	+	2.37018e7i	0.391332	+	0.677807i
$144$	−2.73241e7	+	7.10783e6i	−0.762566	+	0.198366i
$145$	1.06336e7	−	1.84179e7i	0.289661	−	0.501708i
$146$	3.09163e6	+	1.75335e7i	0.0822152	+	0.466266i
$147$	1.12309e7	+	1.47477e7i	0.291611	+	0.382924i
$148$	−1.73919e6	+	633014.i	−0.0440993	+	0.0160508i
$149$	−3.49514e7	+	1.27213e7i	−0.865591	+	0.315049i	−0.736380	−	0.676568i	$-0.763467\pi$
$149$	−3.49514e7	+	1.27213e7i	−0.865591	+	0.315049i	−0.129210	+	0.991617i	$0.541244\pi$
$150$	−1.09859e7	+	1.40550e6i	−0.265777	+	0.0340024i
$151$	4.67429e6	+	2.65092e7i	0.110483	+	0.626582i	0.988888	+	0.148664i	$0.0474973\pi$
$151$	4.67429e6	+	2.65092e7i	0.110483	+	0.626582i	−0.878404	+	0.477918i	$0.841392\pi$
$152$	3.35714e7	−	5.81474e7i	0.775385	−	1.34301i
$153$	2.88872e7	+	1.37283e7i	0.652056	+	0.309881i
$154$	6.32986e6	+	1.09636e7i	0.139660	+	0.241898i
$155$	−2.69169e7	+	2.25860e7i	−0.580583	+	0.487167i
$156$	1.38435e7	−	7.14230e6i	0.291951	−	0.150627i
$157$	9.19247e6	−	5.21331e7i	0.189576	−	1.07514i	−0.730358	−	0.683065i	$-0.760647\pi$
$157$	9.19247e6	−	5.21331e7i	0.189576	−	1.07514i	0.919934	−	0.392074i	$-0.128242\pi$
$158$	−2.23837e7	−	1.87822e7i	−0.451474	−	0.378832i
$159$	−3.61854e7	+	3.92008e7i	−0.713909	+	0.773402i
$160$	−1.44971e7	−	5.27650e6i	−0.279808	−	0.101842i
$161$	5.28328e7			0.997730
$162$	4.81350e7	+	9.21498e6i	0.889525	+	0.170291i
$163$	−7.24867e7			−1.31100			−0.655499	−	0.755196i	$-0.727541\pi$
$163$	−7.24867e7			−1.31100			−0.655499	+	0.755196i	$0.727541\pi$
$164$	−4.16843e6	−	1.51719e6i	−0.0737937	−	0.0268587i
$165$	−1.40642e7	+	1.52362e7i	−0.243736	+	0.264047i
$166$	−1.71469e7	−	1.43880e7i	−0.290943	−	0.244130i
$167$	−9.57358e6	+	5.42945e7i	−0.159062	+	0.902086i	0.795916	+	0.605408i	$0.206990\pi$
$167$	−9.57358e6	+	5.42945e7i	−0.159062	+	0.902086i	−0.954978	+	0.296678i	$0.904121\pi$
$168$	4.20288e7	−	2.16840e7i	0.683856	−	0.352822i
$169$	1.12498e8	−	9.43970e7i	1.79284	−	1.50437i
$170$	−1.75733e7	−	3.04378e7i	−0.274335	−	0.475162i
$171$	−7.81342e7	+	5.38633e7i	−1.19496	+	0.823771i
$172$	−5.75905e6	+	9.97497e6i	−0.0862981	+	0.149473i
$173$	−45494.7	−	258013.i	−0.000668036	−	0.00378862i	0.984472	−	0.175542i	$-0.0561678\pi$
$173$	−45494.7	−	258013.i	−0.000668036	−	0.00378862i	−0.985140	+	0.171754i	$0.945057\pi$
$174$	−4.30981e7	+	5.51381e6i	−0.620206	+	0.0793467i
$175$	1.41951e7	−	5.16658e6i	0.200219	−	0.0728736i
$176$	−2.29326e7	+	8.34678e6i	−0.317073	+	0.115405i
$177$	−4.88791e7	−	6.41848e7i	−0.662547	−	0.870013i
$178$	2.09135e7	+	1.18607e8i	0.277944	+	1.57630i
$179$	−1.97153e7	+	3.41478e7i	−0.256931	+	0.445018i	−0.965418	−	0.260706i	$-0.916045\pi$
$179$	−1.97153e7	+	3.41478e7i	−0.256931	+	0.445018i	0.708487	+	0.705724i	$0.249378\pi$
$180$	8.28391e6	+	8.40590e6i	0.105872	+	0.107431i
$181$	−3.34406e7	−	5.79208e7i	−0.419178	−	0.726038i	0.576679	−	0.816971i	$-0.304348\pi$
$181$	−3.34406e7	−	5.79208e7i	−0.419178	−	0.726038i	−0.995857	+	0.0909330i	$0.971015\pi$
$182$	7.42722e7	−	6.23218e7i	0.913222	−	0.766285i
$183$	4.93706e6	−	1.04326e8i	0.0595510	−	1.25839i
$184$	−2.17199e7	+	1.23180e8i	−0.257037	+	1.45773i
$185$	−1.44535e7	−	1.21279e7i	−0.167831	−	0.140827i
$186$	7.00282e7	+	1.57936e7i	0.797954	+	0.179964i
$187$	2.59784e7	+	9.45537e6i	0.290514	+	0.105738i
$188$	−1.84952e7			−0.203005
$189$	−6.68090e7	+	2.18336e6i	−0.719811	+	0.0235239i
$190$	1.04287e8			1.10304
$191$	−4.44089e7	−	1.61635e7i	−0.461161	−	0.167849i	0.100983	−	0.994888i	$-0.467801\pi$
$191$	−4.44089e7	−	1.61635e7i	−0.461161	−	0.167849i	−0.562144	+	0.827039i	$0.690023\pi$
$192$	3.23361e7	+	1.03879e8i	0.329711	+	1.05919i
$193$	4.78792e7	+	4.01754e7i	0.479398	+	0.402263i	0.850209	−	0.526446i	$-0.176476\pi$
$193$	4.78792e7	+	4.01754e7i	0.479398	+	0.402263i	−0.370811	+	0.928709i	$0.620920\pi$
$194$	1.99686e7	−	1.13248e8i	0.196355	−	1.11359i
$195$	1.33618e8	+	8.58125e7i	1.29046	+	0.828761i
$196$	6.98624e6	−	5.86215e6i	0.0662746	−	0.0556110i
$197$	−4.50661e7	−	7.80567e7i	−0.419970	−	0.727409i	0.575966	−	0.817473i	$-0.304626\pi$
$197$	−4.50661e7	−	7.80567e7i	−0.419970	−	0.727409i	−0.995936	+	0.0900647i	$0.971293\pi$
$198$	4.21730e7	+	4.00048e6i	0.386106	+	0.0366256i
$199$	−4.99770e6	+	8.65627e6i	−0.0449557	+	0.0778655i	−0.887628	−	0.460562i	$-0.847648\pi$
$199$	−4.99770e6	+	8.65627e6i	−0.0449557	+	0.0778655i	0.842672	+	0.538427i	$0.180981\pi$
$200$	6.21021e6	+	3.52198e7i	0.0548910	+	0.311302i
$201$	−2.25494e6	+	5.38812e6i	−0.0195861	+	0.0468006i
$202$	6.80605e7	−	2.47720e7i	0.580985	−	0.211461i
$203$	5.56877e7	−	2.02687e7i	0.467222	−	0.170055i
$204$	6.07466e6	−	1.45153e7i	0.0500976	−	0.119707i
$205$	−7.85262e6	−	4.45344e7i	−0.0636614	−	0.361042i
$206$	−6.04685e7	+	1.04735e8i	−0.481941	+	0.834747i
$207$	1.02459e8	−	1.44073e8i	0.802883	−	1.12898i
$208$	9.34513e7	+	1.61862e8i	0.720052	+	1.24717i
$209$	−6.28388e7	+	5.27280e7i	−0.476119	+	0.399511i
$210$	6.18072e7	+	3.96939e7i	0.460545	+	0.295771i
$211$	−1.34821e7	+	7.64607e7i	−0.0988026	+	0.560337i	0.894713	+	0.446641i	$0.147380\pi$
$211$	−1.34821e7	+	7.64607e7i	−0.0988026	+	0.560337i	−0.993516	+	0.113696i	$0.963731\pi$
$212$	2.01059e7	+	1.68709e7i	0.144927	+	0.121608i
$213$	−2.36301e7	−	7.59115e7i	−0.167547	−	0.538243i
$214$	−1.31701e8	−	4.79352e7i	−0.918629	−	0.334354i
$215$	−1.17419e8			−0.805756
$216$	2.23751e7	−	1.56663e8i	0.151070	−	1.05774i
$217$	−9.79122e7			−0.650471
$218$	−5.88330e7	−	2.14135e7i	−0.384612	−	0.139987i
$219$	−7.92664e7	−	1.78771e7i	−0.509958	−	0.115012i
$220$	7.81457e6	+	6.55720e6i	0.0494795	+	0.0415183i
$221$	3.67659e7	−	2.08510e8i	0.229125	−	1.29943i
$222$	−1.82214e6	+	3.85042e7i	−0.0111776	+	0.236196i
$223$	7.52079e7	−	6.31069e7i	0.454147	−	0.381075i	−0.386825	−	0.922153i	$-0.626428\pi$
$223$	7.52079e7	−	6.31069e7i	0.454147	−	0.381075i	0.840972	+	0.541078i	$0.181984\pi$
$224$	−2.14946e7	−	3.72298e7i	−0.127780	−	0.221321i
$225$	1.34394e7	−	4.87290e7i	0.0786577	−	0.285200i
$226$	−9.32824e6	+	1.61570e7i	−0.0537552	+	0.0931067i
$227$	2.17289e7	+	1.23231e8i	0.123296	+	0.699245i	0.982305	+	0.187286i	$0.0599690\pi$
$227$	2.17289e7	+	1.23231e8i	0.123296	+	0.699245i	−0.859010	+	0.511959i	$0.828920\pi$
$228$	2.82871e7	+	3.71447e7i	0.158058	+	0.207551i
$229$	−3.17049e8	+	1.15396e8i	−1.74462	+	0.634991i	−0.999490	−	0.0319238i	$-0.989837\pi$
$229$	−3.17049e8	+	1.15396e8i	−1.74462	+	0.634991i	−0.745134	+	0.666915i	$0.767614\pi$
$230$	−1.82559e8	+	6.64460e7i	−0.989363	+	0.360099i
$231$	−5.73118e7	+	7.33226e6i	−0.305916	+	0.0391377i
$232$	2.43629e7	+	1.38169e8i	0.128091	+	0.726443i
$233$	−9.13771e7	+	1.58270e8i	−0.473251	+	0.819695i	−0.999531	−	0.0306162i	$-0.990253\pi$
$233$	−9.13771e7	+	1.58270e8i	−0.473251	+	0.819695i	0.526280	+	0.850311i	$0.323586\pi$
$234$	−2.59132e7	−	3.23398e8i	−0.132210	−	1.64999i
$235$	−9.42729e7	−	1.63285e8i	−0.473859	−	0.820748i
$236$	−3.04055e7	+	2.55133e7i	−0.150578	+	0.126350i
$237$	1.18516e8	−	6.11458e7i	0.578304	−	0.298365i
$238$	1.70066e7	−	9.64493e7i	0.0817708	−	0.463745i
$239$	1.94053e8	+	1.62830e8i	0.919449	+	0.771510i	0.973893	−	0.227007i	$-0.0728941\pi$
$239$	1.94053e8	+	1.62830e8i	0.919449	+	0.771510i	−0.0544437	+	0.998517i	$0.517339\pi$
$240$	−9.60456e7	+	1.04049e8i	−0.448475	+	0.485848i
$241$	−2.05548e8	−	7.48132e7i	−0.945916	−	0.344285i	−0.177417	−	0.984136i	$-0.556774\pi$
$241$	−2.05548e8	−	7.48132e7i	−0.945916	−	0.344285i	−0.768499	+	0.639851i	$0.778996\pi$
$242$	−1.63060e8			−0.739594
$243$	−1.23609e8	+	1.86420e8i	−0.552621	+	0.833433i
$244$	−5.13838e7			−0.226444
$245$	8.73641e7	+	3.17979e7i	0.379535	+	0.138139i
$246$	−6.26655e7	+	6.78876e7i	−0.268383	+	0.290749i
$247$	4.81256e8	+	4.03822e8i	2.03206	+	1.70510i
$248$	4.02523e7	−	2.28282e8i	0.167575	−	0.950367i
$249$	9.07880e7	−	4.68403e7i	0.372675	−	0.192275i
$250$	−1.86383e8	+	1.56394e8i	−0.754424	+	0.633036i
$251$	1.19420e8	+	2.06842e8i	0.476673	+	0.825622i	0.999643	−	0.0267291i	$-0.00850915\pi$
$251$	1.19420e8	+	2.06842e8i	0.476673	+	0.825622i	−0.522969	+	0.852351i	$0.675176\pi$
$252$	2.62668e6	+	3.27811e7i	0.0103396	+	0.129039i
$253$	7.64067e7	−	1.32340e8i	0.296626	−	0.513772i
$254$	−5.93339e7	−	3.36499e8i	−0.227188	−	1.28845i
$255$	1.59112e8	−	2.03562e7i	0.600913	−	0.0768785i
$256$	1.31364e8	−	4.78124e7i	0.489368	−	0.178115i
$257$	1.34696e8	−	4.90255e7i	0.494983	−	0.180159i	−0.0824534	−	0.996595i	$-0.526276\pi$
$257$	1.34696e8	−	4.90255e7i	0.494983	−	0.180159i	0.577436	+	0.816436i	$0.304053\pi$
$258$	1.45340e8	+	1.90851e8i	0.526884	+	0.691870i
$259$	−9.12966e6	−	5.17769e7i	−0.0326517	−	0.185177i
$260$	3.90633e7	−	6.76597e7i	0.137836	−	0.238739i
$261$	5.27233e7	−	1.91166e8i	0.183553	−	0.665530i
$262$	−2.54474e8	−	4.40762e8i	−0.874157	−	1.51408i
$263$	7.33625e7	−	6.15585e7i	0.248673	−	0.208662i	−0.509927	−	0.860217i	$-0.670328\pi$
$263$	7.33625e7	−	6.15585e7i	0.248673	−	0.208662i	0.758601	+	0.651556i	$0.225883\pi$
$264$	6.46610e6	−	1.36637e8i	0.0216286	−	0.457040i
$265$	−4.64620e7	+	2.63499e8i	−0.153369	+	0.869799i
$266$	2.22612e8	+	1.86794e8i	0.725208	+	0.608522i
$267$	−5.36203e8	−	1.20931e8i	−1.72401	−	0.388820i
$268$	2.70032e6	+	982836.i	0.00856926	+	0.00311896i
$269$	6.32296e7			0.198056			0.0990279	−	0.995085i	$-0.468427\pi$
$269$	6.32296e7			0.198056			0.0990279	+	0.995085i	$0.468427\pi$
$270$	2.28107e8	−	9.15678e7i	0.705285	−	0.283119i
$271$	5.76999e8			1.76109			0.880547	−	0.473959i	$-0.157176\pi$
$271$	5.76999e8			1.76109			0.880547	+	0.473959i	$0.157176\pi$
$272$	1.77409e8	+	6.45717e7i	0.534546	+	0.194559i
$273$	1.31520e8	+	4.22508e8i	0.391223	+	1.25680i
$274$	−3.03977e8	−	2.55067e8i	−0.892717	−	0.749079i
$275$	7.58717e6	−	4.30290e7i	0.0219996	−	0.124766i
$276$	−7.31845e7	−	4.70006e7i	−0.209526	−	0.134562i
$277$	3.72124e8	−	3.12249e8i	1.05198	−	0.882719i	0.0586828	−	0.998277i	$-0.481310\pi$
$277$	3.72124e8	−	3.12249e8i	1.05198	−	0.882719i	0.993301	+	0.115558i	$0.0368655\pi$
$278$	3.06625e8	+	5.31090e8i	0.855954	+	1.48256i
$279$	−1.89881e8	+	2.67003e8i	−0.523440	+	0.736040i
$280$	1.18596e8	−	2.05414e8i	0.322862	−	0.559213i
$281$	−8.79465e7	−	4.98770e8i	−0.236454	−	1.34100i	−0.839530	−	0.543313i	$-0.817170\pi$
$281$	−8.79465e7	−	4.98770e8i	−0.236454	−	1.34100i	0.603076	−	0.797684i	$-0.293942\pi$
$282$	−1.48711e8	+	3.55342e8i	−0.394886	+	0.943571i
$283$	7.72926e7	−	2.81322e7i	0.202715	−	0.0737821i	−0.238667	−	0.971101i	$-0.576711\pi$
$283$	7.72926e7	−	2.81322e7i	0.202715	−	0.0737821i	0.441382	+	0.897319i	$0.354488\pi$
$284$	−3.67556e7	+	1.33779e7i	−0.0952158	+	0.0346557i
$285$	−1.83750e8	+	4.39065e8i	−0.470186	+	1.12350i
$286$	−4.86968e7	−	2.76173e8i	−0.123089	−	0.698073i
$287$	6.30057e7	−	1.09129e8i	0.157323	−	0.272492i
$288$	−1.43209e8	−	1.35846e7i	−0.353261	−	0.0335100i
$289$	9.82343e7	+	1.70147e8i	0.239398	+	0.414650i
$290$	−1.66933e8	+	1.40073e8i	−0.401928	+	0.337258i
$291$	4.41608e8	+	2.83610e8i	1.05054	+	0.674677i
$292$	−6.94191e6	+	3.93696e7i	−0.0163170	+	0.0925381i
$293$	5.79154e8	+	4.85968e8i	1.34511	+	1.12868i	0.980282	+	0.197606i	$0.0633167\pi$
$293$	5.79154e8	+	4.85968e8i	1.34511	+	1.12868i	0.364828	+	0.931075i	$0.381128\pi$
$294$	−5.64544e7	−	1.81359e8i	−0.129563	−	0.416220i
$295$	−3.80226e8	−	1.38391e8i	−0.862313	−	0.313856i
$296$	1.24471e8			0.278963
$297$	−9.11500e7	+	1.70507e8i	−0.201887	+	0.377654i
$298$	3.81116e8			0.834259
$299$	−1.09975e9	−	4.00278e8i	−2.37929	−	0.865989i
$300$	−2.42594e7	−	5.47128e6i	−0.0518747	−	0.0116994i
$301$	−2.50644e8	−	2.10315e8i	−0.529755	−	0.444517i
$302$	4.78955e7	−	2.71629e8i	0.100062	−	0.567482i
$303$	−1.56258e7	+	3.30194e8i	−0.0322696	+	0.681898i
$304$	−4.29133e8	+	3.60085e8i	−0.876060	+	0.735102i
$305$	−2.61911e8	−	4.53643e8i	−0.528572	−	0.915513i
$306$	−2.30033e8	−	2.33421e8i	−0.458950	−	0.465708i
$307$	−2.39067e7	+	4.14077e7i	−0.0471559	+	0.0816764i	−0.888640	−	0.458606i	$-0.848349\pi$
$307$	−2.39067e7	+	4.14077e7i	−0.0471559	+	0.0816764i	0.841484	+	0.540282i	$0.181682\pi$
$308$	4.93613e6	+	2.79942e7i	0.00962629	+	0.0545934i
$309$	−3.34407e8	−	4.39122e8i	−0.644794	−	0.846701i
$310$	3.38327e8	−	1.23141e8i	0.645016	−	0.234767i
$311$	2.06722e7	−	7.52407e6i	0.0389696	−	0.0141838i	−0.322462	−	0.946582i	$-0.604510\pi$
$311$	2.06722e7	−	7.52407e6i	0.0389696	−	0.0141838i	0.361431	+	0.932399i	$0.382288\pi$
$312$	−1.03915e9	+	1.32944e8i	−1.93703	+	0.247816i
$313$	1.36196e7	+	7.72409e7i	0.0251050	+	0.142378i	0.994784	−	0.102005i	$-0.0325258\pi$
$313$	1.36196e7	+	7.72409e7i	0.0251050	+	0.142378i	−0.969679	+	0.244383i	$0.921415\pi$
$314$	−2.71213e8	+	4.69755e8i	−0.494376	+	0.856284i
$315$	−2.76020e8	+	1.90280e8i	−0.497570	+	0.343009i
$316$	−3.28050e7	−	5.68200e7i	−0.0584838	−	0.101297i
$317$	2.03372e7	−	1.70650e7i	0.0358579	−	0.0300883i	−0.624683	−	0.780879i	$-0.714772\pi$
$317$	2.03372e7	−	1.70650e7i	0.0358579	−	0.0300883i	0.660540	+	0.750790i	$0.270327\pi$
$318$	4.85796e8	−	2.50637e8i	0.847148	−	0.437070i
$319$	2.97647e7	−	1.68804e8i	0.0513375	−	0.291149i
$320$	4.17994e8	+	3.50738e8i	0.713091	+	0.598354i
$321$	4.33868e8	−	4.70023e8i	0.732132	−	0.793143i
$322$	−5.08708e8	−	1.85154e8i	−0.849127	−	0.309057i
$323$	6.34596e8			1.04782
$324$	9.44869e7	+	5.64096e7i	0.154335	+	0.0921393i
$325$	−3.34625e8			−0.540712
$326$	6.97948e8	+	2.54032e8i	1.11574	+	0.406095i
$327$	1.93816e8	−	2.09967e8i	0.306530	−	0.332074i
$328$	2.28532e8	+	1.91761e8i	0.357593	+	0.300056i
$329$	9.12331e7	−	5.17409e8i	0.141243	−	0.801029i
$330$	1.88814e8	−	9.74151e7i	0.289225	−	0.149220i
$331$	−8.64870e8	+	7.25712e8i	−1.31085	+	1.09993i	−0.322689	+	0.946505i	$0.604587\pi$
$331$	−8.64870e8	+	7.25712e8i	−1.31085	+	1.09993i	−0.988160	+	0.153428i	$0.950969\pi$
$332$	−2.51301e7	−	4.35265e7i	−0.0376886	−	0.0652786i
$333$	−1.58899e8	−	7.55146e7i	−0.235812	−	0.112067i
$334$	2.82457e8	−	4.89231e8i	0.414802	−	0.718457i
$335$	5.08695e6	+	2.88495e7i	0.00739265	+	0.0419258i
$336$	−3.91388e8	+	5.00727e7i	−0.562886	+	0.0720135i
$337$	−2.80186e7	+	1.01980e7i	−0.0398788	+	0.0145147i	−0.361883	−	0.932224i	$-0.617866\pi$
$337$	−2.80186e7	+	1.01980e7i	−0.0398788	+	0.0145147i	0.322004	+	0.946738i	$0.395644\pi$
$338$	−1.41402e9	+	5.14661e8i	−1.99181	+	0.724958i
$339$	−5.15877e7	−	6.77415e7i	−0.0719195	−	0.0944400i
$340$	−1.37039e7	−	7.77187e7i	−0.0189090	−	0.107238i
$341$	−1.41601e8	+	2.45259e8i	−0.193386	+	0.334954i
$342$	9.41091e8	−	2.44806e8i	1.27216	−	0.330926i
$343$	3.98656e8	+	6.90492e8i	0.533419	+	0.923910i
$344$	5.93392e8	−	4.97915e8i	0.785936	−	0.659478i
$345$	4.19133e7	−	8.85680e8i	0.0549522	−	1.16121i
$346$	−466165.	+	2.64375e6i	−0.000605025	+	0.00343127i
$347$	−2.55480e7	−	2.14373e7i	−0.0328249	−	0.0275434i	0.626228	−	0.779640i	$-0.284598\pi$
$347$	−2.55480e7	−	2.14373e7i	−0.0328249	−	0.0275434i	−0.659053	+	0.752097i	$0.729043\pi$
$348$	−9.51704e7	−	2.14640e7i	−0.121053	−	0.0273013i
$349$	6.26000e8	+	2.27845e8i	0.788289	+	0.286914i	0.704625	−	0.709580i	$-0.251115\pi$
$349$	6.26000e8	+	2.27845e8i	0.788289	+	0.286914i	0.0836642	+	0.996494i	$0.473338\pi$
$350$	−1.54786e8			−0.192971
$351$	1.40722e9	+	4.60718e8i	1.73695	+	0.568670i
$352$	−1.24342e8			−0.151956
$353$	−5.04698e8	−	1.83695e8i	−0.610688	−	0.222272i	0.0181160	−	0.999836i	$-0.494233\pi$
$353$	−5.04698e8	−	1.83695e8i	−0.610688	−	0.222272i	−0.628804	+	0.777563i	$0.716455\pi$
$354$	2.45701e8	+	7.89310e8i	0.294371	+	0.945663i
$355$	−3.05456e8	−	2.56308e8i	−0.362368	−	0.304062i
$356$	−4.69591e7	+	2.66318e8i	−0.0551626	+	0.312843i
$357$	3.76103e8	+	2.41541e8i	0.437490	+	0.280965i
$358$	3.09504e8	−	2.59704e8i	0.356513	−	0.299150i
$359$	3.26243e8	+	5.65069e8i	0.372143	+	0.644571i	0.989895	−	0.141802i	$-0.0452897\pi$
$359$	3.26243e8	+	5.65069e8i	0.372143	+	0.644571i	−0.617752	+	0.786373i	$0.711956\pi$
$360$	−3.30164e8	−	7.21767e8i	−0.372968	−	0.815339i
$361$	−4.94551e8	+	8.56587e8i	−0.553268	+	0.958288i
$362$	1.19002e8	+	6.74892e8i	0.131848	+	0.747746i
$363$	2.87306e8	−	6.86510e8i	0.315262	−	0.753310i
$364$	2.04574e8	−	7.44588e7i	0.222329	−	0.0809210i
$365$	−3.82959e8	+	1.39386e8i	−0.412218	+	0.150035i
$366$	−4.13152e8	+	9.87218e8i	−0.440480	+	1.05252i
$367$	−1.03104e8	−	5.84735e8i	−0.108880	−	0.617487i	−0.989600	−	0.143849i	$-0.954052\pi$
$367$	−1.03104e8	−	5.84735e8i	−0.108880	−	0.617487i	0.880720	−	0.473637i	$-0.157059\pi$
$368$	5.21790e8	−	9.03766e8i	0.545793	−	0.945342i
$369$	−1.75404e8	−	3.83448e8i	−0.181739	−	0.397296i
$370$	9.66647e7	+	1.67428e8i	0.0992115	+	0.171839i
$371$	−5.71146e8	+	4.79248e8i	−0.580682	+	0.487250i
$372$	1.35629e8	+	8.71037e7i	0.136600	+	0.0877276i
$373$	−8.30356e7	+	4.70918e8i	−0.0828483	+	0.469856i	0.914952	+	0.403563i	$0.132228\pi$
$373$	−8.30356e7	+	4.70918e8i	−0.0828483	+	0.469856i	−0.997800	+	0.0662931i	$0.978883\pi$
$374$	−2.17000e8	−	1.82085e8i	−0.214491	−	0.179979i
$375$	−3.30044e8	−	1.06026e9i	−0.323194	−	1.03825i
$376$	1.16883e9	+	4.25420e8i	1.13395	+	0.412725i
$377$	−1.31274e9			−1.26178
$378$	6.50931e8	+	2.13112e8i	0.619889	+	0.202949i
$379$	−3.37822e8			−0.318750			−0.159375	−	0.987218i	$-0.550948\pi$
$379$	−3.37822e8			−0.318750			−0.159375	+	0.987218i	$0.550948\pi$
$380$	2.20043e8	+	8.00890e7i	0.205714	+	0.0748739i
$381$	1.52126e9	+	3.43094e8i	1.40918	+	0.317816i
$382$	3.70951e8	+	3.11265e8i	0.340483	+	0.285699i
$383$	3.36446e8	−	1.90808e9i	0.305999	−	1.73540i	−0.312768	−	0.949830i	$-0.601256\pi$
$383$	3.36446e8	−	1.90808e9i	0.305999	−	1.73540i	0.618766	−	0.785575i	$-0.287633\pi$
$384$	3.40844e7	−	7.20246e8i	0.0307182	−	0.649115i
$385$	−2.21987e8	+	1.86269e8i	−0.198251	+	0.166352i
$386$	−3.20215e8	−	5.54629e8i	−0.283391	−	0.490848i
$387$	−1.05960e9	+	2.75633e8i	−0.929292	+	0.241737i
$388$	1.29104e8	−	2.23615e8i	0.112209	−	0.194352i
$389$	−7.67737e7	−	4.35405e8i	−0.0661285	−	0.375033i	−0.999855	−	0.0170454i	$-0.994574\pi$
$389$	−7.67737e7	−	4.35405e8i	−0.0661285	−	0.375033i	0.933726	−	0.357988i	$-0.116537\pi$
$390$	−9.85831e8	−	1.29453e9i	−0.841543	−	1.10506i
$391$	−1.11089e9	+	4.04331e8i	−0.939836	+	0.342072i
$392$	−5.76345e8	+	2.09772e8i	−0.483260	+	0.175892i
$393$	2.30406e9	−	2.94773e8i	1.91478	−	0.244970i
$394$	1.60372e8	+	9.09515e8i	0.132097	+	0.749158i
$395$	3.34424e8	−	5.79240e8i	0.273029	−	0.472899i
$396$	8.59118e7	+	4.08285e7i	0.0695216	+	0.0330392i
$397$	6.96996e8	+	1.20723e9i	0.559066	+	0.968331i	0.997575	+	0.0696042i	$0.0221736\pi$
$397$	6.96996e8	+	1.20723e9i	0.559066	+	0.968331i	−0.438508	+	0.898727i	$0.644493\pi$
$398$	7.84572e7	−	6.58334e7i	0.0623795	−	0.0523427i
$399$	−1.17867e9	+	6.08111e8i	−0.928937	+	0.479267i
$400$	5.18136e7	−	2.93850e8i	0.0404794	−	0.229570i
$401$	1.08073e9	+	9.06841e8i	0.836975	+	0.702305i	0.956881	−	0.290480i	$-0.0938149\pi$
$401$	1.08073e9	+	9.06841e8i	0.836975	+	0.702305i	−0.119906	+	0.992785i	$0.538259\pi$
$402$	4.05949e7	−	4.39777e7i	0.0311659	−	0.0337631i
$403$	2.03812e9	+	7.41814e8i	1.55118	+	0.564582i
$404$	1.62630e8			0.122706
$405$	−1.63994e7	+	1.12171e9i	−0.0122669	+	0.839048i
$406$	−6.07229e8			−0.450310
$407$	−1.42899e8	−	5.20108e7i	−0.105062	−	0.0382396i
$408$	−7.17772e8	+	7.77586e8i	−0.523210	+	0.566810i
$409$	1.37147e8	+	1.15080e8i	0.0991186	+	0.0831704i	0.691000	−	0.722854i	$-0.257170\pi$
$409$	1.37147e8	+	1.15080e8i	0.0991186	+	0.0831704i	−0.591882	+	0.806025i	$0.701615\pi$
$410$	−8.04625e7	+	4.56325e8i	−0.0576567	+	0.326988i
$411$	1.60947e9	−	8.30377e8i	1.14350	−	0.589969i
$412$	−2.08020e8	+	1.74550e8i	−0.146543	+	0.122964i
$413$	−5.63756e8	−	9.76454e8i	−0.393791	−	0.682066i
$414$	−1.49145e9	+	1.02816e9i	−1.03302	+	0.712129i
$415$	2.56183e8	−	4.43723e8i	0.175947	−	0.304750i
$416$	1.65362e8	+	9.37815e8i	0.112618	+	0.638691i
$417$	−2.77624e9	+	3.55182e8i	−1.87491	+	0.239869i
$418$	7.89839e8	−	2.87478e8i	0.528958	−	0.192525i
$419$	−2.58729e9	+	9.41698e8i	−1.71829	+	0.625407i	−0.997689	−	0.0679431i	$-0.978356\pi$
$419$	−2.58729e9	+	9.41698e8i	−1.71829	+	0.625407i	−0.720601	+	0.693350i	$0.756134\pi$
$420$	9.99282e7	+	1.31219e8i	0.0658136	+	0.0864221i
$421$	−5.01180e8	−	2.84233e9i	−0.327345	−	1.85647i	−0.492653	−	0.870226i	$-0.663973\pi$
$421$	−5.01180e8	−	2.84233e9i	−0.327345	−	1.85647i	0.165307	−	0.986242i	$-0.447138\pi$
$422$	3.97773e8	−	6.88963e8i	0.257657	−	0.446275i
$423$	−1.23403e9	−	1.25220e9i	−0.792745	−	0.804419i
$424$	−8.82566e8	−	1.52865e9i	−0.562298	−	0.973929i
$425$	−2.58933e8	+	2.17270e8i	−0.163616	+	0.137290i
$426$	−3.85087e7	+	8.13737e8i	−0.0241337	+	0.509977i
$427$	2.53465e8	−	1.43747e9i	0.157551	−	0.893516i
$428$	−2.41073e8	−	2.02284e8i	−0.148626	−	0.124712i
$429$	1.24854e9	+	2.81586e8i	0.763488	+	0.172191i
$430$	1.13058e9	+	4.11499e8i	0.685746	+	0.249591i
$431$	−1.23472e9			−0.742844			−0.371422	−	0.928464i	$-0.621130\pi$
$431$	−1.23472e9			−0.742844			−0.371422	+	0.928464i	$0.621130\pi$
$432$	−6.22473e8	+	1.16441e9i	−0.371473	+	0.694884i
$433$	−2.51517e9			−1.48888			−0.744440	−	0.667690i	$-0.767283\pi$
$433$	−2.51517e9			−1.48888			−0.744440	+	0.667690i	$0.767283\pi$
$434$	9.42761e8	+	3.43137e8i	0.553589	+	0.201490i
$435$	−2.95603e8	−	9.49620e8i	−0.172185	−	0.553143i
$436$	−1.07691e8	−	9.03638e7i	−0.0622269	−	0.0522146i
$437$	6.09119e8	−	3.45449e9i	0.349154	−	1.98015i
$438$	7.00576e8	+	4.49924e8i	0.398379	+	0.255847i
$439$	9.80830e8	−	8.23014e8i	0.553309	−	0.464281i	−0.322751	−	0.946484i	$-0.604608\pi$
$439$	9.80830e8	−	8.23014e8i	0.553309	−	0.464281i	0.876060	+	0.482203i	$0.160163\pi$
$440$	−3.43027e8	−	5.94139e8i	−0.191974	−	0.332509i
$441$	8.63023e8	+	8.18654e7i	0.479167	+	0.0454533i
$442$	−1.08474e9	+	1.87882e9i	−0.597511	+	1.03492i
$443$	2.96016e8	+	1.67879e9i	0.161772	+	0.917453i	0.952331	+	0.305067i	$0.0986790\pi$
$443$	2.96016e8	+	1.67879e9i	0.161772	+	0.917453i	−0.790559	+	0.612386i	$0.790210\pi$
$444$	−3.34147e7	+	7.98437e7i	−0.0181175	+	0.0432912i
$445$	−2.59055e9	+	9.42884e8i	−1.39358	+	0.507222i
$446$	−9.45310e8	+	3.44065e8i	−0.504548	+	0.183640i
$447$	−6.71514e8	+	1.60457e9i	−0.355614	+	0.849731i
$448$	2.64029e8	+	1.49738e9i	0.138732	+	0.786791i
$449$	−3.77958e8	+	6.54642e8i	−0.197052	+	0.341304i	−0.947571	−	0.319544i	$-0.896470\pi$
$449$	−3.77958e8	+	6.54642e8i	−0.197052	+	0.341304i	0.750519	+	0.660849i	$0.229803\pi$
$450$	−3.00176e8	+	4.22095e8i	−0.155286	+	0.218357i
$451$	−1.82237e8	−	3.15645e8i	−0.0935448	−	0.162024i
$452$	−3.20904e7	+	2.69271e7i	−0.0163452	+	0.0137153i
$453$	1.05921e9	+	6.80249e8i	0.535353	+	0.343815i
$454$	2.22647e8	−	1.26270e9i	0.111666	−	0.633291i
$455$	1.70011e9	+	1.42656e9i	0.846128	+	0.709985i
$456$	−9.33253e8	−	2.99806e9i	−0.460917	−	1.48069i
$457$	1.03487e9	+	3.76661e8i	0.507198	+	0.184605i	0.582929	−	0.812523i	$-0.301907\pi$
$457$	1.03487e9	+	3.76661e8i	0.507198	+	0.184605i	−0.0757307	+	0.997128i	$0.524129\pi$
$458$	3.45716e9			1.68147
$459$	1.38805e9	−	5.57199e8i	0.669979	−	0.268947i
$460$	−4.36224e8			−0.208957
$461$	3.67619e9	+	1.33802e9i	1.74761	+	0.636078i	0.999618	−	0.0276295i	$-0.00879587\pi$
$461$	3.67619e9	+	1.33802e9i	1.74761	+	0.636078i	0.747992	+	0.663708i	$0.231018\pi$
$462$	5.77531e8	+	1.30252e8i	0.272476	+	0.0614521i
$463$	−1.44193e9	−	1.20992e9i	−0.675165	−	0.566531i	0.239424	−	0.970915i	$-0.423041\pi$
$463$	−1.44193e9	−	1.20992e9i	−0.675165	−	0.566531i	−0.914589	+	0.404384i	$0.867486\pi$
$464$	2.03267e8	−	1.15278e9i	0.0944611	−	0.535715i
$465$	−7.76756e7	+	1.64138e9i	−0.0358261	+	0.757051i
$466$	1.43450e9	−	1.20369e9i	0.656674	−	0.551015i
$467$	1.18916e9	+	2.05968e9i	0.540294	+	0.935817i	0.998887	+	0.0471703i	$0.0150204\pi$
$467$	1.18916e9	+	2.05968e9i	0.540294	+	0.935817i	−0.458593	+	0.888647i	$0.651646\pi$
$468$	1.93684e8	−	7.02264e8i	0.0873439	−	0.316694i
$469$	−4.08152e7	+	7.06940e7i	−0.0182691	+	0.0316430i
$470$	3.35480e8	+	1.90260e9i	0.149047	+	0.845288i
$471$	−1.49988e9	−	1.96955e9i	−0.661430	−	0.868547i
$472$	2.50837e9	−	9.12971e8i	1.09798	−	0.399632i
$473$	−8.89298e8	+	3.23678e8i	−0.386397	+	0.140637i
$474$	−1.35543e9	+	1.73409e8i	−0.584593	+	0.0747906i
$475$	−1.74161e8	−	9.87715e8i	−0.0745629	−	0.422867i
$476$	1.09954e8	−	1.90445e8i	0.0467289	−	0.0809368i
$477$	1.99270e8	+	2.48690e9i	0.0840674	+	1.04917i
$478$	−1.29782e9	−	2.24790e9i	−0.543523	−	0.941409i
$479$	1.72599e9	−	1.44828e9i	0.717571	−	0.602114i	−0.209141	−	0.977886i	$-0.567067\pi$
$479$	1.72599e9	−	1.44828e9i	0.717571	−	0.602114i	0.926712	+	0.375772i	$0.122622\pi$
$480$	−6.41166e8	+	3.30797e8i	−0.264622	+	0.136527i
$481$	−2.02237e8	+	1.14694e9i	−0.0828615	+	0.469931i
$482$	1.71696e9	+	1.44070e9i	0.698385	+	0.586014i
$483$	1.67586e9	−	1.81551e9i	0.676741	−	0.733135i
$484$	−3.44053e8	−	1.25225e8i	−0.137932	−	0.0502033i
$485$	2.63225e9			1.04769
$486$	1.84350e9	−	1.36178e9i	0.728477	−	0.538121i
$487$	3.01715e9			1.18371			0.591856	−	0.806044i	$-0.298395\pi$
$487$	3.01715e9			1.18371			0.591856	+	0.806044i	$0.298395\pi$
$488$	3.24727e9	+	1.18191e9i	1.26488	+	0.460379i
$489$	−2.29928e9	+	2.49089e9i	−0.889224	+	0.963325i
$490$	−7.29760e8	−	6.12341e8i	−0.280217	−	0.235130i
$491$	−4.34057e8	+	2.46166e9i	−0.165486	+	0.938518i	0.783076	+	0.621926i	$0.213650\pi$
$491$	−4.34057e8	+	2.46166e9i	−0.165486	+	0.938518i	−0.948562	+	0.316592i	$0.897461\pi$
$492$	−1.84358e8	+	9.51161e7i	−0.0697887	+	0.0360061i
$493$	−1.01580e9	+	8.52359e8i	−0.381808	+	0.320375i
$494$	−3.21863e9	−	5.57483e9i	−1.20123	−	2.08059i
$495$	7.74502e7	+	9.66583e8i	0.0287015	+	0.358196i
$496$	−9.67005e8	+	1.67490e9i	−0.355830	+	0.616316i
$497$	−1.92943e8	−	1.09424e9i	−0.0704989	−	0.399819i
$498$	−1.03832e9	+	1.32838e8i	−0.376728	+	0.0481971i
$499$	1.07293e9	−	3.90513e8i	0.386561	−	0.140697i	−0.141427	−	0.989949i	$-0.545169\pi$
$499$	1.07293e9	−	3.90513e8i	0.386561	−	0.140697i	0.527987	+	0.849252i	$0.322947\pi$
$500$	−5.13368e8	+	1.86851e8i	−0.183668	+	0.0668498i
$501$	1.56207e9	+	2.05120e9i	0.554967	+	0.728746i
$502$	−4.24970e8	−	2.41012e9i	−0.149932	−	0.850308i
$503$	−9.44778e8	+	1.63640e9i	−0.331010	+	0.573327i	−0.982710	−	0.185150i	$-0.940723\pi$
$503$	−9.44778e8	+	1.63640e9i	−0.331010	+	0.573327i	0.651700	+	0.758477i	$0.274056\pi$
$504$	5.88022e8	−	2.13207e9i	0.204591	−	0.741812i
$505$	8.28950e8	+	1.43578e9i	0.286423	+	0.496100i
$506$	−1.19948e9	+	1.00649e9i	−0.411593	+	0.345367i
$507$	3.24641e8	−	6.86008e9i	0.110631	−	2.33777i
$508$	1.33228e8	−	7.55573e8i	0.0450891	−	0.255713i
$509$	−2.96163e9	−	2.48510e9i	−0.995448	−	0.835280i	−0.00910105	−	0.999959i	$-0.502897\pi$
$509$	−2.96163e9	−	2.48510e9i	−0.995448	−	0.835280i	−0.986347	+	0.164678i	$0.947341\pi$
$510$	−1.60337e9	−	3.61611e8i	−0.535227	−	0.120711i
$511$	−1.06713e9	−	3.88404e8i	−0.353789	−	0.128769i
$512$	−3.40598e9			−1.12150
$513$	−6.27494e8	+	4.39350e9i	−0.205210	+	1.43681i
$514$	−1.46875e9			−0.477066
$515$	−2.60133e9	−	9.46805e8i	−0.839207	−	0.305447i
$516$	1.60096e8	+	5.14307e8i	0.0512988	+	0.164797i
$517$	−1.16411e9	−	9.76805e8i	−0.370491	−	0.310879i
$518$	−9.35478e7	+	5.30536e8i	−0.0295719	+	0.167711i
$519$	−1.03093e7	−	6.62084e6i	−0.00323700	−	0.00207887i
$520$	−4.02494e9	+	3.37733e9i	−1.25530	+	1.05332i
$521$	2.61938e9	+	4.53690e9i	0.811458	+	1.40549i	0.911843	+	0.410538i	$0.134659\pi$
$521$	2.61938e9	+	4.53690e9i	0.811458	+	1.40549i	−0.100385	+	0.994949i	$0.532008\pi$
$522$	−1.17760e9	+	1.65589e9i	−0.362369	+	0.509549i
$523$	4.73456e7	−	8.20049e7i	0.0144718	−	0.0250659i	−0.858699	−	0.512481i	$-0.828727\pi$
$523$	4.73456e7	−	8.20049e7i	0.0144718	−	0.0250659i	0.873171	+	0.487415i	$0.162060\pi$
$524$	−1.98443e8	−	1.12543e9i	−0.0602527	−	0.341710i
$525$	2.72727e8	−	6.51674e8i	0.0822565	−	0.196550i
$526$	−9.22115e8	+	3.35623e8i	−0.276271	+	0.100554i
$527$	2.05875e9	−	7.49324e8i	0.612727	−	0.223014i
$528$	−4.40599e8	+	1.05280e9i	−0.130264	+	0.311263i
$529$	5.43482e8	+	3.08224e9i	0.159621	+	0.905257i
$530$	1.37081e9	−	2.37431e9i	0.399955	−	0.692743i
$531$	−3.75605e9	−	3.56295e8i	−1.08868	−	0.103271i
$532$	3.26255e8	+	5.65090e8i	0.0939433	+	0.162715i
$533$	−2.13831e9	+	1.79425e9i	−0.611680	+	0.513261i
$534$	4.73910e9	+	3.04354e9i	1.34679	+	0.864939i
$535$	5.57086e8	−	3.15939e9i	0.157284	−	0.892001i
$536$	−1.48044e8	−	1.24223e8i	−0.0415254	−	0.0348439i
$537$	5.48066e8	+	1.76065e9i	0.152729	+	0.490641i
$538$	−6.08815e8	−	2.21591e8i	−0.168557	−	0.0613498i
$539$	7.49325e8			0.206115
$540$	5.51621e8	−	1.80273e7i	0.150752	−	0.00492667i
$541$	3.36457e9			0.913566			0.456783	−	0.889578i	$-0.349002\pi$
$541$	3.36457e9			0.913566			0.456783	+	0.889578i	$0.349002\pi$
$542$	−5.55571e9	−	2.02211e9i	−1.49879	−	0.545517i
$543$	−3.05109e9	−	6.88118e8i	−0.817815	−	0.184444i
$544$	7.36877e8	+	6.18313e8i	0.196245	+	0.164669i
$545$	2.48860e8	−	1.41135e9i	0.0658517	−	0.373463i
$546$	2.14331e8	−	4.52909e9i	0.0563523	−	1.19079i
$547$	4.42019e9	−	3.70898e9i	1.15474	−	0.968944i	0.154923	−	0.987927i	$-0.450487\pi$
$547$	4.42019e9	−	3.70898e9i	1.15474	−	0.968944i	0.999820	+	0.0189821i	$0.00604254\pi$
$548$	−4.45501e8	−	7.71631e8i	−0.115642	−	0.200298i
$549$	−3.42840e9	−	3.47889e9i	−0.884276	−	0.897299i
$550$	−2.23851e8	+	3.87721e8i	−0.0573706	+	0.0993688i
$551$	−6.83239e8	−	3.87484e9i	−0.173997	−	0.986786i
$552$	3.54391e9	+	4.65363e9i	0.896801	+	1.17762i
$553$	1.75137e9	−	6.37448e8i	0.440394	−	0.160290i
$554$	−4.67734e9	+	1.70241e9i	−1.16873	+	0.425384i
$555$	−8.75221e8	+	1.11972e8i	−0.217316	+	0.0278026i
$556$	2.39111e8	+	1.35607e9i	0.0589981	+	0.334595i
$557$	1.34591e9	−	2.33119e9i	0.330007	−	0.571590i	−0.652505	−	0.757784i	$-0.726282\pi$
$557$	1.34591e9	−	2.33119e9i	0.330007	−	0.571590i	0.982513	+	0.186194i	$0.0596154\pi$
$558$	2.76402e9	−	1.90543e9i	0.673475	−	0.464273i
$559$	3.62393e9	+	6.27683e9i	0.877483	+	1.51984i
$560$	−1.51597e9	+	1.27205e9i	−0.364782	+	0.306088i
$561$	1.14895e9	−	5.92780e8i	0.274747	−	0.141750i
$562$	−9.01151e8	+	5.11068e9i	−0.214151	+	1.21451i
$563$	1.55263e9	+	1.30282e9i	0.366682	+	0.307683i	0.807447	−	0.589940i	$-0.200848\pi$
$563$	1.55263e9	+	1.30282e9i	0.366682	+	0.307683i	−0.440765	+	0.897622i	$0.645293\pi$
$564$	−5.86669e8	+	6.35558e8i	−0.137694	+	0.149169i
$565$	−4.01296e8	−	1.46060e8i	−0.0936042	−	0.0340691i
$566$	−8.42812e8			−0.195377
$567$	−2.04416e9	+	2.36504e9i	−0.470948	+	0.544875i
$568$	2.63053e9			0.602316
$569$	−4.17244e9	−	1.51865e9i	−0.949506	−	0.345592i	−0.179593	−	0.983741i	$-0.557478\pi$
$569$	−4.17244e9	−	1.51865e9i	−0.949506	−	0.345592i	−0.769913	+	0.638149i	$0.779700\pi$
$570$	3.30798e9	−	3.58364e9i	0.748171	−	0.810518i
$571$	−1.76542e9	−	1.48136e9i	−0.396846	−	0.332993i	0.422427	−	0.906397i	$-0.361178\pi$
$571$	−1.76542e9	−	1.48136e9i	−0.396846	−	0.332993i	−0.819273	+	0.573404i	$0.805623\pi$
$572$	1.09343e8	−	6.20118e8i	0.0244291	−	0.138544i
$573$	−1.96408e9	+	1.01333e9i	−0.436133	+	0.225014i
$574$	−9.89105e8	+	8.29958e8i	−0.218299	+	0.183174i
$575$	9.34196e8	+	1.61808e9i	0.204928	+	0.354945i
$576$	4.59534e9	+	2.18387e9i	1.00193	+	0.476156i
$577$	1.43171e9	−	2.47980e9i	0.310271	−	0.537404i	−0.668150	−	0.744026i	$-0.732914\pi$
$577$	1.43171e9	−	2.47980e9i	0.310271	−	0.537404i	0.978421	+	0.206622i	$0.0662470\pi$
$578$	−3.49577e8	−	1.98255e9i	−0.0753000	−	0.427048i
$579$	2.89929e9	−	3.70924e8i	0.620750	−	0.0794164i
$580$	−4.59796e8	+	1.67352e8i	−0.0978515	+	0.0356150i
$581$	1.34163e9	−	4.88312e8i	0.283802	−	0.103295i
$582$	−3.25817e9	−	4.27841e9i	−0.685082	−	0.899605i
$583$	3.74474e8	+	2.12375e9i	0.0782675	+	0.443877i
$584$	1.34427e9	−	2.32834e9i	0.279281	−	0.483728i
$585$	7.18719e9	−	1.86960e9i	1.48427	−	0.386104i
$586$	−3.87337e9	−	6.70888e9i	−0.795148	−	1.37724i
$587$	5.34892e9	−	4.48828e9i	1.09152	−	0.915896i	0.0946967	−	0.995506i	$-0.469812\pi$
$587$	5.34892e9	−	4.48828e9i	1.09152	−	0.915896i	0.996826	+	0.0796098i	$0.0253674\pi$
$588$	2.01606e7	−	4.26018e8i	0.00408961	−	0.0864187i
$589$	−1.12885e9	+	6.40202e9i	−0.227631	+	1.29096i
$590$	3.17606e9	+	2.66503e9i	0.636659	+	0.534220i
$591$	−4.11179e9	−	9.27340e8i	−0.819359	−	0.184792i
$592$	−9.75870e8	−	3.55188e8i	−0.193315	−	0.0703610i
$593$	−2.38323e9			−0.469325			−0.234663	−	0.972077i	$-0.575399\pi$
$593$	−2.38323e9			−0.469325			−0.234663	+	0.972077i	$0.575399\pi$
$594$	1.47520e9	−	1.32231e9i	0.288800	−	0.258869i
$595$	2.24180e9			0.436302
$596$	8.04147e8	+	2.92686e8i	0.155587	+	0.0566291i
$597$	1.38931e8	+	4.46315e8i	0.0267233	+	0.0858482i
$598$	9.18635e9	+	7.70826e9i	1.75666	+	1.47402i
$599$	−6.27748e8	+	3.56014e9i	−0.119342	+	0.676820i	0.865167	+	0.501484i	$0.167212\pi$
$599$	−6.27748e8	+	3.56014e9i	−0.119342	+	0.676820i	−0.984509	+	0.175336i	$0.943899\pi$
$600$	1.40726e9	+	9.03771e8i	0.265977	+	0.170816i
$601$	−4.57245e9	+	3.83674e9i	−0.859188	+	0.720944i	−0.961793	−	0.273778i	$-0.911727\pi$
$601$	−4.57245e9	+	3.83674e9i	−0.859188	+	0.720944i	0.102605	+	0.994722i	$0.467282\pi$
$602$	1.67630e9	+	2.90344e9i	0.313159	+	0.542407i
$603$	1.13627e8	+	2.48399e8i	0.0211043	+	0.0461359i
$604$	3.09661e8	−	5.36349e8i	0.0571818	−	0.0990417i
$605$	−6.48137e8	−	3.67577e9i	−0.118993	−	0.674845i
$606$	1.30763e9	−	3.12455e9i	0.238688	−	0.570340i
$607$	−3.55983e8	+	1.29567e8i	−0.0646054	+	0.0235145i	−0.374121	−	0.927380i	$-0.622055\pi$
$607$	−3.55983e8	+	1.29567e8i	−0.0646054	+	0.0235145i	0.309515	+	0.950894i	$0.399833\pi$
$608$	−2.68209e9	+	9.76202e8i	−0.483962	+	0.176148i
$609$	1.06992e9	−	2.55654e9i	0.191951	−	0.458661i
$610$	9.32036e8	+	5.28584e9i	0.166256	+	0.942886i
$611$	−5.81914e9	+	1.00790e10i	−1.03208	+	1.78762i
$612$	−3.06104e8	−	6.69170e8i	−0.0539808	−	0.118007i
$613$	−3.04856e7	−	5.28025e7i	−0.00534543	−	0.00925855i	0.863340	−	0.504622i	$-0.168368\pi$
$613$	−3.04856e7	−	5.28025e7i	−0.00534543	−	0.00925855i	−0.868686	+	0.495364i	$0.835035\pi$
$614$	3.75304e8	−	3.14917e8i	0.0654325	−	0.0549044i
$615$	−1.77944e9	−	1.14279e9i	−0.308475	−	0.198109i
$616$	3.31966e8	−	1.88267e9i	0.0572217	−	0.324520i
$617$	1.66391e9	+	1.39619e9i	0.285189	+	0.239302i	0.774148	−	0.633005i	$-0.218179\pi$
$617$	1.66391e9	+	1.39619e9i	0.285189	+	0.239302i	−0.488959	+	0.872307i	$0.662623\pi$
$618$	1.68097e9	+	5.40009e9i	0.286483	+	0.920324i
$619$	−8.01647e9	−	2.91776e9i	−1.35852	−	0.494461i	−0.442924	−	0.896559i	$-0.646059\pi$
$619$	−8.01647e9	−	2.91776e9i	−1.35852	−	0.494461i	−0.915596	+	0.402099i	$0.868281\pi$
$620$	8.08430e8			0.136230
$621$	−1.70085e9	−	8.09083e9i	−0.285000	−	1.35573i
$622$	−2.25414e8			−0.0375590
$623$	−7.21868e9	−	2.62738e9i	−1.19605	−	0.435327i
$624$	8.52641e9	+	1.92298e9i	1.40482	+	0.316832i
$625$	−2.88308e9	−	2.41919e9i	−0.472363	−	0.396360i
$626$	1.39555e8	−	7.91455e8i	0.0227371	−	0.128948i
$627$	−1.81337e8	+	3.83188e9i	−0.0293799	+	0.620835i
$628$	−9.33011e8	+	7.82889e8i	−0.150324	+	0.126137i
$629$	5.88214e8	+	1.01882e9i	0.0942450	+	0.163237i
$630$	3.32454e9	−	8.64813e8i	0.529712	−	0.137794i
$631$	3.47776e9	−	6.02365e9i	0.551057	−	0.954458i	−0.447142	−	0.894463i	$-0.647558\pi$
$631$	3.47776e9	−	6.02365e9i	0.551057	−	0.954458i	0.998199	−	0.0599954i	$-0.0191086\pi$
$632$	7.66210e8	+	4.34539e9i	0.120736	+	0.684730i
$633$	2.19979e9	+	2.88862e9i	0.344722	+	0.452666i
$634$	−2.55625e8	+	9.30397e7i	−0.0398373	+	0.0144996i
$635$	7.34967e9	−	2.67506e9i	1.13909	−	0.414597i
$636$	1.21750e9	−	1.55762e8i	0.187659	−	0.0240084i
$637$	−9.96527e8	−	5.65158e9i	−0.152757	−	0.866327i
$638$	−8.78174e8	+	1.52104e9i	−0.133878	+	0.231883i
$639$	−3.35812e9	−	1.59590e9i	−0.509147	−	0.241966i
$640$	−1.80818e9	−	3.13185e9i	−0.272653	−	0.472249i
$641$	4.27059e8	−	3.58345e8i	0.0640449	−	0.0537401i	−0.610203	−	0.792245i	$-0.708912\pi$
$641$	4.27059e8	−	3.58345e8i	0.0640449	−	0.0537401i	0.674248	+	0.738505i	$0.264468\pi$
$642$	−5.82477e9	+	3.00518e9i	−0.868772	+	0.448226i
$643$	8.51622e8	−	4.82979e9i	0.126331	−	0.716457i	−0.854178	−	0.519981i	$-0.825939\pi$
$643$	8.51622e8	−	4.82979e9i	0.126331	−	0.716457i	0.980509	−	0.196476i	$-0.0629497\pi$
$644$	−9.31169e8	−	7.81344e8i	−0.137381	−	0.115277i
$645$	−3.72453e9	+	4.03491e9i	−0.546529	+	0.592072i
$646$	−6.11029e9	−	2.22396e9i	−0.891760	−	0.324574i
$647$	−4.81759e8			−0.0699302			−0.0349651	−	0.999389i	$-0.511132\pi$
$647$	−4.81759e8			−0.0699302			−0.0349651	+	0.999389i	$0.511132\pi$
$648$	−4.67372e9	−	5.73823e9i	−0.674761	−	0.828449i
$649$	−3.26121e9			−0.468299
$650$	3.22198e9	+	1.17270e9i	0.460178	+	0.167491i
$651$	−3.10578e9	+	3.36459e9i	−0.441201	+	0.477968i
$652$	1.27757e9	+	1.07201e9i	0.180516	+	0.151471i
$653$	1.35275e9	−	7.67184e9i	0.190118	−	1.07821i	−0.729085	−	0.684424i	$-0.760054\pi$
$653$	1.35275e9	−	7.67184e9i	0.190118	−	1.07821i	0.919202	−	0.393786i	$-0.128835\pi$
$654$	−2.60202e9	+	1.34246e9i	−0.363738	+	0.187664i
$655$	8.92436e9	−	7.48843e9i	1.24089	−	1.04123i
$656$	−1.24452e9	−	2.15557e9i	−0.172123	−	0.298125i
$657$	−3.12865e9	+	2.15680e9i	−0.430406	+	0.296709i
$658$	−2.69173e9	+	4.66221e9i	−0.368333	+	0.637971i
$659$	1.55001e9	+	8.79056e9i	0.210978	+	1.19651i	0.887752	+	0.460323i	$0.152266\pi$
$659$	1.55001e9	+	8.79056e9i	0.210978	+	1.19651i	−0.676774	+	0.736191i	$0.736623\pi$
$660$	4.73206e8	−	6.05401e7i	0.0640687	−	0.00819671i
$661$	−4.12137e9	+	1.50005e9i	−0.555055	+	0.202024i	−0.604291	−	0.796764i	$-0.706544\pi$
$661$	−4.12137e9	+	1.50005e9i	−0.555055	+	0.202024i	0.0492360	+	0.998787i	$0.484321\pi$
$662$	1.08708e10	−	3.95665e9i	1.45633	−	0.530059i
$663$	−5.99888e9	−	7.87733e9i	−0.799416	−	1.04974i
$664$	5.86949e8	+	3.32875e9i	0.0778058	+	0.441259i
$665$	−3.32594e9	+	5.76069e9i	−0.438569	+	0.759624i
$666$	1.26534e9	+	1.28397e9i	0.165976	+	0.168420i
$667$	3.66488e9	+	6.34776e9i	0.478211	+	0.828286i
$668$	9.71693e8	−	8.15347e8i	0.126128	−	0.105834i
$669$	2.17032e8	−	4.58615e9i	0.0280241	−	0.592184i
$670$	5.21238e7	−	2.95609e8i	0.00669536	−	0.0379713i
$671$	−3.23415e9	−	2.71378e9i	−0.413268	−	0.346773i
$672$	−1.96115e9	−	4.42302e8i	−0.249298	−	0.0562246i
$673$	−1.12582e10	−	4.09766e9i	−1.42370	−	0.518183i	−0.488578	−	0.872520i	$-0.662484\pi$
$673$	−1.12582e10	−	4.09766e9i	−1.42370	−	0.518183i	−0.935118	+	0.354338i	$0.884706\pi$
$674$	3.05520e8			0.0384353
$675$	−1.24819e9	−	2.00751e9i	−0.156214	−	0.251243i
$676$	−3.37879e9			−0.420676
$677$	3.99817e9	+	1.45522e9i	0.495224	+	0.180247i	0.577544	−	0.816359i	$-0.304011\pi$
$677$	3.99817e9	+	1.45522e9i	0.495224	+	0.180247i	−0.0823209	+	0.996606i	$0.526233\pi$
$678$	2.59316e8	+	8.33050e8i	0.0319540	+	0.102652i
$679$	5.61884e9	+	4.71477e9i	0.688815	+	0.577984i
$680$	−9.21619e8	+	5.22676e9i	−0.112401	+	0.637458i
$681$	4.92387e9	+	3.16221e9i	0.597437	+	0.383686i
$682$	2.22294e9	−	1.86527e9i	0.268338	−	0.225162i
$683$	1.45095e8	+	2.51312e8i	0.0174253	+	0.0301815i	0.874607	−	0.484833i	$-0.161120\pi$
$683$	1.45095e8	+	2.51312e8i	0.0174253	+	0.0301815i	−0.857181	+	0.515015i	$0.827786\pi$
$684$	2.17369e9	+	2.06193e8i	0.259717	+	0.0246365i
$685$	4.54157e9	−	7.86623e9i	0.539870	−	0.935082i
$686$	−1.41866e9	−	8.04560e9i	−0.167781	−	0.951534i
$687$	−6.09139e9	+	1.45552e10i	−0.716750	+	1.71266i
$688$	−6.07311e9	+	2.21043e9i	−0.710971	+	0.258772i
$689$	1.55198e10	−	5.64873e9i	1.80767	−	0.657936i
$690$	−3.50747e9	+	8.38101e9i	−0.406464	+	0.971235i
$691$	−7.48833e7	−	4.24684e8i	−0.00863399	−	0.0489658i	0.980186	−	0.198077i	$-0.0634697\pi$
$691$	−7.48833e7	−	4.24684e8i	−0.00863399	−	0.0489658i	−0.988820	+	0.149112i	$0.952359\pi$
$692$	−3.01392e6	+	5.22026e6i	−0.000345749	+	0.000598854i
$693$	−1.56597e9	+	2.20201e9i	−0.178738	+	0.251334i
$694$	1.70864e8	+	2.95946e8i	0.0194041	+	0.0336089i
$695$	−1.07533e10	+	9.02307e9i	−1.21505	+	1.01955i
$696$	5.52073e9	+	3.54552e9i	0.620674	+	0.398610i
$697$	−4.89622e8	+	2.77679e9i	−0.0547705	+	0.310619i
$698$	−5.22903e9	−	4.38768e9i	−0.582006	−	0.488361i
$699$	2.54020e9	+	8.16035e9i	0.281318	+	0.903730i
$700$	−3.26594e8	−	1.18871e8i	−0.0359886	−	0.0130988i
$701$	1.10118e9			0.120738			0.0603691	−	0.998176i	$-0.480772\pi$
$701$	1.10118e9			0.120738			0.0603691	+	0.998176i	$0.480772\pi$
$702$	−1.19350e10	−	9.36774e9i	−1.30210	−	1.02201i
$703$	−3.49070e9			−0.378939
$704$	4.13261e9	+	1.50415e9i	0.446396	+	0.162475i
$705$	−8.60138e9	−	1.93989e9i	−0.924498	−	0.208504i
$706$	4.21578e9	+	3.53746e9i	0.450881	+	0.378334i
$707$	−8.02221e8	+	4.54962e9i	−0.0853741	+	0.484180i
$708$	−8.77429e7	+	1.85412e9i	−0.00929171	+	0.196345i
$709$	4.73358e9	−	3.97195e9i	0.498802	−	0.418544i	−0.358366	−	0.933581i	$-0.616666\pi$
$709$	4.73358e9	−	3.97195e9i	0.498802	−	0.418544i	0.857168	+	0.515037i	$0.172222\pi$
$710$	2.04288e9	+	3.53838e9i	0.214210	+	0.371022i
$711$	1.65814e9	−	6.01214e9i	0.173013	−	0.627315i
$712$	9.09340e9	−	1.57502e10i	0.944161	−	1.63534i
$713$	−2.10292e9	−	1.19263e10i	−0.217275	−	1.23223i
$714$	−2.77487e9	−	3.64378e9i	−0.285298	−	0.374635i
$715$	6.03206e9	−	2.19549e9i	0.617155	−	0.224626i
$716$	8.52490e8	−	3.10281e8i	0.0867948	−	0.0315907i
$717$	1.17507e10	−	1.50335e9i	1.19055	−	0.152315i
$718$	−1.16097e9	−	6.58417e9i	−0.117053	−	0.663843i
$719$	−7.56941e8	+	1.31106e9i	−0.0759470	+	0.131544i	−0.901498	−	0.432784i	$-0.857531\pi$
$719$	−7.56941e8	+	1.31106e9i	−0.0759470	+	0.131544i	0.825551	+	0.564328i	$0.190865\pi$
$720$	5.28915e8	+	6.60090e9i	0.0528108	+	0.659082i
$721$	−3.85695e9	−	6.68043e9i	−0.383240	−	0.663791i
$722$	7.76379e9	−	6.51459e9i	0.767704	−	0.644180i
$723$	−9.09080e9	+	4.69023e9i	−0.894578	+	0.461540i
$724$	−2.67205e8	+	1.51540e9i	−0.0261674	+	0.148403i
$725$	1.60543e9	+	1.34712e9i	0.156462	+	0.131287i
$726$	−5.17226e9	+	5.60328e9i	−0.501652	+	0.543456i
$727$	8.60802e9	+	3.13306e9i	0.830870	+	0.302412i	0.722216	−	0.691668i	$-0.243124\pi$
$727$	8.60802e9	+	3.13306e9i	0.830870	+	0.302412i	0.108654	+	0.994080i	$0.465346\pi$
$728$	−1.46410e10			−1.40641
$729$	2.48514e9	+	1.01609e10i	0.237577	+	0.971369i
$730$	4.17585e9			0.397297
$731$	6.87972e9	+	2.50401e9i	0.651418	+	0.237097i
$732$	−1.62989e9	+	1.76572e9i	−0.153593	+	0.166392i
$733$	−3.13125e9	−	2.62743e9i	−0.293666	−	0.246415i	0.484036	−	0.875048i	$-0.339170\pi$
$733$	−3.13125e9	−	2.62743e9i	−0.293666	−	0.246415i	−0.777702	+	0.628633i	$0.783615\pi$
$734$	−1.05647e9	+	5.99153e9i	−0.0986099	+	0.559244i
$735$	3.86387e9	−	1.99349e9i	0.358936	−	0.185186i
$736$	4.07315e9	−	3.41777e9i	0.376580	−	0.315988i
$737$	1.18054e8	+	2.04475e8i	0.0108629	+	0.0188150i
$738$	3.45094e8	+	4.30679e9i	0.0316038	+	0.394418i
$739$	1.38299e9	−	2.39541e9i	0.126056	−	0.218336i	−0.796089	−	0.605179i	$-0.793101\pi$
$739$	1.38299e9	−	2.39541e9i	0.126056	−	0.218336i	0.922145	+	0.386844i	$0.126435\pi$
$740$	7.53807e7	+	4.27505e8i	0.00683832	+	0.0387820i
$741$	2.91421e10	−	3.72833e9i	2.63122	−	0.336628i
$742$	7.17890e9	−	2.61291e9i	0.645125	−	0.234806i
$743$	9.85051e8	−	3.58529e8i	0.0881045	−	0.0320674i	−0.297592	−	0.954693i	$-0.596183\pi$
$743$	9.85051e8	−	3.58529e8i	0.0881045	−	0.0320674i	0.385696	+	0.922626i	$0.373961\pi$
$744$	−6.56774e9	−	8.62433e9i	−0.584670	−	0.767750i
$745$	1.51488e9	+	8.59129e9i	0.134224	+	0.761222i
$746$	2.44987e9	−	4.24330e9i	0.216052	−	0.374212i
$747$	1.27021e9	−	4.60556e9i	0.111494	−	0.404259i
$748$	−3.18030e8	−	5.50844e8i	−0.0277851	−	0.0481252i
$749$	6.84812e9	−	5.74625e9i	0.595504	−	0.499687i
$750$	−5.37854e8	+	1.13655e10i	−0.0465533	+	0.983729i
$751$	−3.33526e9	+	1.89152e10i	−0.287336	+	1.62956i	0.409484	+	0.912317i	$0.365709\pi$
$751$	−3.33526e9	+	1.89152e10i	−0.287336	+	1.62956i	−0.696820	+	0.717246i	$0.745402\pi$
$752$	−7.94983e9	−	6.67070e9i	−0.681704	−	0.572017i
$753$	1.08958e10	+	2.45736e9i	0.929988	+	0.209742i
$754$	1.26399e10	+	4.60056e9i	1.07385	+	0.390851i
$755$	6.31356e9			0.533900
$756$	1.20979e9	+	9.49556e8i	0.101832	+	0.0799272i
$757$	−8.43102e9			−0.706390			−0.353195	−	0.935550i	$-0.614905\pi$
$757$	−8.43102e9			−0.706390			−0.353195	+	0.935550i	$0.614905\pi$
$758$	3.25277e9	+	1.18391e9i	0.271275	+	0.0987362i
$759$	−2.12403e9	−	6.82343e9i	−0.176326	−	0.566444i
$760$	−1.20637e10	−	1.01227e10i	−0.996861	−	0.836466i
$761$	−1.35072e9	+	7.66030e9i	−0.111101	+	0.630086i	0.877506	+	0.479566i	$0.159206\pi$
$761$	−1.35072e9	+	7.66030e9i	−0.111101	+	0.630086i	−0.988607	+	0.150520i	$0.951905\pi$
$762$	−1.34453e10	−	8.63485e9i	−1.10085	−	0.706989i
$763$	3.05917e9	−	2.56695e9i	0.249326	−	0.209209i
$764$	5.43657e8	+	9.41641e8i	0.0441061	+	0.0763939i
$765$	4.34752e9	−	6.11331e9i	0.351097	−	0.493698i
$766$	−9.92645e9	+	1.71931e10i	−0.797982	+	1.38215i
$767$	4.33708e9	+	2.45968e10i	0.347068	+	1.96832i
$768$	2.52386e9	−	6.03071e9i	0.201049	−	0.480401i
$769$	−6.57994e8	+	2.39490e8i	−0.0521771	+	0.0189909i	−0.367977	−	0.929835i	$-0.619949\pi$
$769$	−6.57994e8	+	2.39490e8i	−0.0521771	+	0.0189909i	0.315800	+	0.948826i	$0.397727\pi$
$770$	2.79022e9	−	1.01556e9i	0.220252	−	0.0801653i
$771$	2.58789e9	−	6.18371e9i	0.203356	−	0.485913i
$772$	−2.49709e8	−	1.41617e9i	−0.0195332	−	0.110778i
$773$	8.88428e9	−	1.53880e10i	0.691822	−	1.19827i	−0.279419	−	0.960169i	$-0.590142\pi$
$773$	8.88428e9	−	1.53880e10i	0.691822	−	1.19827i	0.971240	−	0.238101i	$-0.0765249\pi$
$774$	1.11684e10	+	1.05943e9i	0.865763	+	0.0821254i
$775$	−1.73130e9	−	2.99869e9i	−0.133603	−	0.231407i
$776$	−1.33024e10	+	1.11621e10i	−1.02191	+	0.857488i
$777$	−2.06882e9	−	1.32864e9i	−0.158215	−	0.101609i
$778$	−7.86667e8	+	4.46141e9i	−0.0598911	+	0.339660i
$779$	−6.40903e9	−	5.37781e9i	−0.485748	−	0.407591i
$780$	−1.08592e9	−	3.48851e9i	−0.0819347	−	0.263214i
$781$	−3.01998e9	−	1.09918e9i	−0.226843	−	0.0825640i
$782$	1.21133e10			0.905817
$783$	−4.89671e9	−	7.87553e9i	−0.364534	−	0.586291i
$784$	5.11722e9			0.379252
$785$	−1.16675e10	−	4.24661e9i	−0.860860	−	0.313327i
$786$	−2.32180e10	−	5.23640e9i	−1.70548	−	0.384640i
$787$	−3.09148e9	−	2.59406e9i	−0.226076	−	0.189700i	0.522713	−	0.852509i	$-0.324920\pi$
$787$	−3.09148e9	−	2.59406e9i	−0.226076	−	0.189700i	−0.748789	+	0.662808i	$0.769364\pi$
$788$	−3.60098e8	+	2.04222e9i	−0.0262168	+	0.148683i
$789$	2.11706e8	−	4.47362e9i	0.0153449	−	0.324257i
$790$	−5.25002e9	+	4.40529e9i	−0.378849	+	0.317892i
$791$	−5.94996e8	−	1.03056e9i	−0.0427461	−	0.0740384i
$792$	−4.49020e9	−	4.55632e9i	−0.321164	−	0.325894i
$793$	−1.61668e10	+	2.80018e10i	−1.15125	+	1.99402i
$794$	−2.48033e9	−	1.40666e10i	−0.175848	−	0.997284i
$795$	7.58094e9	+	9.95479e9i	0.535104	+	0.702663i
$796$	2.16101e8	−	7.86543e7i	0.0151866	−	0.00552748i
$797$	−1.85481e10	+	6.75097e9i	−1.29776	+	0.472348i	−0.896268	−	0.443513i	$-0.853732\pi$
$797$	−1.85481e10	+	6.75097e9i	−1.29776	+	0.472348i	−0.401497	+	0.915860i	$0.631510\pi$
$798$	1.34801e10	−	1.72459e9i	0.939039	−	0.120137i
$799$	2.04143e9	+	1.15775e10i	0.141586	+	0.802974i
$800$	7.60141e8	−	1.31660e9i	0.0524903	−	0.0909159i
$801$	−2.11640e10	+	1.45898e10i	−1.45507	+	1.00308i
$802$	−7.22791e9	−	1.25191e10i	−0.494769	−	0.856965i
$803$	−2.51619e9	+	2.11134e9i	−0.171490	+	0.143897i
$804$	1.19428e8	−	6.16165e7i	0.00810418	−	0.00418120i
$805$	2.15180e9	−	1.22035e10i	0.145384	−	0.824514i
$806$	−1.70246e10	−	1.42853e10i	−1.14526	−	0.960986i
$807$	2.00565e9	−	2.17278e9i	0.134337	−	0.145532i
$808$	−1.02776e10	−	3.74076e9i	−0.685415	−	0.249471i
$809$	−1.59220e10			−1.05725			−0.528624	−	0.848856i	$-0.677292\pi$
$809$	−1.59220e10			−1.05725			−0.528624	+	0.848856i	$0.677292\pi$
$810$	4.08897e9	−	1.07430e10i	0.270344	−	0.710280i
$811$	−8.45100e9			−0.556333			−0.278167	−	0.960533i	$-0.589727\pi$
$811$	−8.45100e9			−0.556333			−0.278167	+	0.960533i	$0.589727\pi$
$812$	−1.28124e9	−	4.66333e8i	−0.0839817	−	0.0305668i
$813$	1.83024e10	−	1.98276e10i	1.19451	−	1.29406i
$814$	1.19365e9	+	1.00159e9i	0.0775693	+	0.0650884i
$815$	−2.95228e9	+	1.67432e10i	−0.191032	+	1.08339i
$816$	7.84633e9	−	4.04816e9i	0.505534	−	0.260821i
$817$	−1.66413e10	+	1.39637e10i	−1.06760	+	0.895823i
$818$	−9.17237e8	−	1.58870e9i	−0.0585929	−	0.101486i
$819$	1.86906e10	+	8.88247e9i	1.18886	+	0.564989i
$820$	−5.20218e8	+	9.01044e8i	−0.0329486	+	0.0570686i
$821$	5.14796e8	+	2.91955e9i	0.0324664	+	0.184126i	0.996728	−	0.0808247i	$-0.0257554\pi$
$821$	5.14796e8	+	2.91955e9i	0.0324664	+	0.184126i	−0.964262	+	0.264951i	$0.914644\pi$
$822$	−1.84071e10	+	2.35494e9i	−1.15594	+	0.147886i
$823$	−1.57951e9	+	5.74896e8i	−0.0987697	+	0.0359492i	−0.390932	−	0.920419i	$-0.627847\pi$
$823$	−1.57951e9	+	5.74896e8i	−0.0987697	+	0.0359492i	0.292163	+	0.956369i	$0.405625\pi$
$824$	1.71611e10	−	6.24611e9i	1.06856	−	0.388924i
$825$	−1.23796e9	−	1.62560e9i	−0.0767567	−	0.100792i
$826$	2.00618e9	+	1.13776e10i	0.123863	+	0.702460i
$827$	−2.24057e9	+	3.88078e9i	−0.137749	+	0.238589i	−0.926644	−	0.375939i	$-0.877320\pi$
$827$	−2.24057e9	+	3.88078e9i	−0.137749	+	0.238589i	0.788895	+	0.614528i	$0.210654\pi$
$828$	−3.93651e9	+	1.02401e9i	−0.240994	+	0.0626897i
$829$	1.50705e10	+	2.61029e10i	0.918728	+	1.59128i	0.801350	+	0.598196i	$0.204115\pi$
$829$	1.50705e10	+	2.61029e10i	0.918728	+	1.59128i	0.117377	+	0.993087i	$0.462551\pi$
$830$	−4.02174e9	+	3.37464e9i	−0.244141	+	0.204859i
$831$	1.07386e9	−	2.26920e10i	0.0649148	−	1.37173i
$832$	5.84868e9	−	3.31695e10i	0.352067	−	1.99667i
$833$	−4.44066e9	−	3.72616e9i	−0.266189	−	0.223359i
$834$	2.79762e10	+	6.30953e9i	1.66996	+	0.376631i
$835$	1.21512e10	+	4.42266e9i	0.722296	+	0.262894i
$836$	1.88732e9			0.111718
$837$	3.15209e9	+	1.49943e10i	0.185806	+	0.883867i
$838$	2.82123e10			1.65609
$839$	−5.59417e9	−	2.03611e9i	−0.327016	−	0.119024i	0.173295	−	0.984870i	$-0.444559\pi$
$839$	−5.59417e9	−	2.03611e9i	−0.327016	−	0.119024i	−0.500311	+	0.865846i	$0.666781\pi$
$840$	−3.29685e9	−	1.05911e10i	−0.191921	−	0.616543i
$841$	−6.91600e9	−	5.80322e9i	−0.400931	−	0.336421i
$842$	−5.13538e9	+	2.91242e10i	−0.296470	+	1.68136i
$843$	−1.99291e10	−	1.27988e10i	−1.14575	−	0.735825i
$844$	1.36840e9	−	1.14822e9i	0.0783453	−	0.0657395i
$845$	−1.72222e10	−	2.98297e10i	−0.981952	−	1.70079i
$846$	7.49361e9	+	1.63817e10i	0.425496	+	0.930169i
$847$	5.20034e9	−	9.00725e9i	0.294063	−	0.509331i
$848$	2.55732e9	+	1.45033e10i	0.144012	+	0.816735i
$849$	1.48501e9	−	3.54839e9i	0.0832820	−	0.199000i
$850$	3.25460e9	−	1.18458e9i	0.181774	−	0.0661603i
$851$	6.11064e9	−	2.22409e9i	0.339886	−	0.123708i
$852$	−7.06177e8	+	1.68739e9i	−0.0391178	+	0.0934711i
$853$	−3.92528e9	−	2.22614e10i	−0.216545	−	1.22809i	−0.878205	−	0.478285i	$-0.841259\pi$
$853$	−3.92528e9	−	2.22614e10i	−0.216545	−	1.22809i	0.661659	−	0.749805i	$-0.269853\pi$
$854$	−7.47821e9	+	1.29526e10i	−0.410861	+	0.711632i
$855$	9.25921e9	+	2.02414e10i	0.506632	+	1.10754i
$856$	1.05821e10	+	1.83287e10i	0.576651	+	0.998789i
$857$	2.23643e10	−	1.87659e10i	1.21373	−	1.01844i	0.214604	−	0.976701i	$-0.431154\pi$
$857$	2.23643e10	−	1.87659e10i	1.21373	−	1.01844i	0.999128	−	0.0417410i	$-0.0132904\pi$
$858$	−1.10349e10	−	7.08684e9i	−0.596435	−	0.383043i
$859$	−2.12011e8	+	1.20238e9i	−0.0114126	+	0.0647238i	−0.989982	−	0.141192i	$-0.954906\pi$
$859$	−2.12011e8	+	1.20238e9i	−0.0114126	+	0.0647238i	0.978570	+	0.205916i	$0.0660175\pi$
$860$	2.06949e9	+	1.73651e9i	0.110948	+	0.0930963i
$861$	−1.75150e9	−	5.62666e9i	−0.0935187	−	0.300427i
$862$	1.18887e10	+	4.32712e9i	0.632204	+	0.230103i
$863$	1.31348e10			0.695641			0.347821	−	0.937561i	$-0.386922\pi$
$863$	1.31348e10			0.695641			0.347821	+	0.937561i	$0.386922\pi$
$864$	−5.00940e9	+	4.49023e9i	−0.264233	+	0.236848i
$865$	−6.14496e7			−0.00322822
$866$	2.42176e10	+	8.81450e9i	1.26712	+	0.461196i
$867$	8.96281e9	+	2.02140e9i	0.467065	+	0.105338i
$868$	1.72569e9	+	1.44802e9i	0.0895659	+	0.0751547i
$869$	9.36099e8	−	5.30888e9i	0.0483896	−	0.274431i
$870$	−4.81727e8	+	1.01795e10i	−0.0248018	+	0.524093i
$871$	1.38520e9	−	1.16232e9i	0.0710311	−	0.0596022i
$872$	4.72720e9	+	8.18775e9i	0.241433	+	0.418174i
$873$	2.37536e10	−	6.17903e9i	1.20831	−	0.314319i
$874$	−1.79714e10	+	3.11273e10i	−0.910523	+	1.57707i
$875$	−2.69486e9	−	1.52833e10i	−0.135990	−	0.771239i
$876$	1.13267e9	+	1.48735e9i	0.0569298	+	0.0747565i
$877$	−6.47173e9	+	2.35552e9i	−0.323983	+	0.117920i	−0.498891	−	0.866665i	$-0.666259\pi$
$877$	−6.47173e9	+	2.35552e9i	−0.323983	+	0.117920i	0.174909	+	0.984585i	$0.444037\pi$
$878$	−1.23283e10	+	4.48715e9i	−0.614715	+	0.223738i
$879$	3.50703e10	−	4.48676e9i	1.74172	−	0.222829i
$880$	9.93953e8	+	5.63699e9i	0.0491673	+	0.278842i
$881$	1.33545e10	−	2.31307e10i	0.657981	−	1.13966i	−0.323157	−	0.946345i	$-0.604744\pi$
$881$	1.33545e10	−	2.31307e10i	0.657981	−	1.13966i	0.981138	−	0.193310i	$-0.0619225\pi$
$882$	−8.02283e9	−	3.81275e9i	−0.393720	−	0.187110i
$883$	2.76893e9	+	4.79593e9i	0.135347	+	0.234428i	0.925730	−	0.378185i	$-0.123452\pi$
$883$	2.76893e9	+	4.79593e9i	0.135347	+	0.234428i	−0.790383	+	0.612613i	$0.790118\pi$
$884$	−3.73164e9	+	3.13122e9i	−0.181684	+	0.152451i
$885$	−1.68164e10	+	8.67607e9i	−0.815512	+	0.420748i
$886$	3.03316e9	−	1.72019e10i	0.146513	−	0.830917i
$887$	−1.99202e10	−	1.67150e10i	−0.958432	−	0.804220i	0.0222654	−	0.999752i	$-0.492912\pi$
$887$	−1.99202e10	−	1.67150e10i	−0.958432	−	0.804220i	−0.980697	+	0.195532i	$0.937357\pi$
$888$	3.94822e9	−	4.27724e9i	0.189215	−	0.204983i
$889$	2.04801e10	+	7.45416e9i	0.977635	+	0.355830i
$890$	2.82479e10			1.34314
$891$	2.96790e9	+	8.54070e9i	0.140565	+	0.404503i
$892$	−2.25881e9			−0.106562
$893$	−3.27791e10	−	1.19306e10i	−1.54034	−	0.560638i
$894$	1.20890e10	−	1.30964e10i	0.565861	−	0.613016i
$895$	7.08459e9	+	5.94468e9i	0.330320	+	0.277171i
$896$	1.74987e9	−	9.92402e9i	0.0812696	−	0.460903i
$897$	−4.86391e10	+	2.50944e10i	−2.25015	+	1.16092i
$898$	5.93344e9	−	4.97874e9i	0.273426	−	0.229431i
$899$	−6.79193e9	−	1.17640e10i	−0.311770	−	0.540002i
$900$	−9.57520e8	+	6.60085e8i	−0.0437824	+	0.0301822i
$901$	8.34151e9	−	1.44479e10i	0.379934	−	0.658064i
$902$	6.48510e8	+	3.67788e9i	0.0294235	+	0.166869i
$903$	−1.51776e10	+	1.94176e9i	−0.685955	+	0.0877584i
$904$	2.64737e9	−	9.63563e8i	0.119186	−	0.0433801i
$905$	−1.47407e10	+	5.36517e9i	−0.661071	+	0.240610i
$906$	−7.81484e9	−	1.02619e10i	−0.349117	−	0.458438i
$907$	5.53364e7	+	3.13829e8i	0.00246255	+	0.0139658i	0.986014	−	0.166661i	$-0.0532985\pi$
$907$	5.53364e7	+	3.13829e8i	0.00246255	+	0.0139658i	−0.983552	+	0.180627i	$0.942187\pi$
$908$	1.43949e9	−	2.49327e9i	0.0638130	−	0.110527i
$909$	1.08509e10	+	1.10107e10i	0.479173	+	0.486230i
$910$	−1.13703e10	−	1.96939e10i	−0.500180	−	0.866336i
$911$	−4.41401e9	+	3.70379e9i	−0.193428	+	0.162305i	−0.734358	−	0.678762i	$-0.762517\pi$
$911$	−4.41401e9	+	3.70379e9i	−0.193428	+	0.162305i	0.540930	+	0.841067i	$0.318072\pi$
$912$	−1.23837e9	+	2.61683e10i	−0.0540591	+	1.14234i
$913$	7.17091e8	−	4.06683e9i	0.0311836	−	0.176851i
$914$	−8.64433e9	−	7.25345e9i	−0.374472	−	0.314220i
$915$	−2.38965e10	−	5.38943e9i	−1.03124	−	0.232578i
$916$	7.29453e9	+	2.65499e9i	0.313590	+	0.114138i
$917$	3.24630e10			1.39026
$918$	−1.53178e10	+	5.00594e8i	−0.653500	+	0.0213568i
$919$	−2.24544e10			−0.954327			−0.477163	−	0.878815i	$-0.658335\pi$
$919$	−2.24544e10			−0.954327			−0.477163	+	0.878815i	$0.658335\pi$
$920$	2.75678e10	+	1.00339e10i	1.16720	+	0.424825i
$921$	6.64584e8	+	2.13497e9i	0.0280312	+	0.0900498i
$922$	−3.07075e10	−	2.57667e10i	−1.29029	−	1.08268i
$923$	−4.27402e9	+	2.42392e10i	−0.178908	+	1.01464i
$924$	1.11855e9	+	7.18354e8i	0.0466447	+	0.0299562i
$925$	1.42430e9	−	1.19513e9i	0.0591707	−	0.0496501i
$926$	9.64359e9	+	1.67032e10i	0.399117	+	0.691291i
$927$	−2.56971e10	−	2.43760e9i	−1.05951	−	0.100504i
$928$	2.98206e9	−	5.16508e9i	0.122489	−	0.212158i
$929$	5.12439e9	+	2.90618e10i	0.209694	+	1.18924i	0.889880	+	0.456196i	$0.150788\pi$
$929$	5.12439e9	+	2.90618e10i	0.209694	+	1.18924i	−0.680185	+	0.733040i	$0.738101\pi$
$930$	6.50020e9	−	1.55321e10i	0.264994	−	0.633197i
$931$	1.61632e10	−	5.88291e9i	0.656452	−	0.238929i
$932$	3.95116e9	−	1.43810e9i	0.159871	−	0.0581881i
$933$	3.97171e8	−	9.49030e8i	0.0160100	−	0.0382555i
$934$	−4.23174e9	−	2.39994e10i	−0.169943	−	0.963797i
$935$	3.24209e9	−	5.61546e9i	0.129713	−	0.224670i
$936$	−2.83933e10	+	3.99255e10i	−1.13175	+	1.59142i
$937$	−1.17032e10	−	2.02706e10i	−0.464748	−	0.804967i	0.534442	−	0.845205i	$-0.320522\pi$
$937$	−1.17032e10	−	2.02706e10i	−0.464748	−	0.804967i	−0.999190	+	0.0402378i	$0.987188\pi$
$938$	6.40745e8	−	5.37649e8i	0.0253498	−	0.0212710i
$939$	3.08627e9	+	1.98207e9i	0.121648	+	0.0781247i
$940$	−7.53283e8	+	4.27208e9i	−0.0295809	+	0.167761i
$941$	−2.22808e9	−	1.86958e9i	−0.0871699	−	0.0731442i	0.598161	−	0.801376i	$-0.295898\pi$
$941$	−2.22808e9	−	1.86958e9i	−0.0871699	−	0.0731442i	−0.685331	+	0.728231i	$0.740343\pi$
$942$	7.53947e9	+	2.42204e10i	0.293875	+	0.944069i
$943$	1.46458e10	+	5.33062e9i	0.568749	+	0.207008i
$944$	−2.22712e10			−0.861670
$945$	−2.21671e9	+	1.55207e10i	−0.0854472	+	0.598272i
$946$	9.69707e9			0.372410
$947$	2.71238e10	+	9.87225e9i	1.03783	+	0.377738i	0.804056	−	0.594553i	$-0.202671\pi$
$947$	2.71238e10	+	9.87225e9i	1.03783	+	0.377738i	0.233772	+	0.972292i	$0.424893\pi$
$948$	−2.99310e9	−	6.75041e8i	−0.114102	−	0.0257336i
$949$	1.92705e10	+	1.61698e10i	0.731914	+	0.614149i
$950$	−1.78455e9	+	1.01207e10i	−0.0675300	+	0.382982i
$951$	5.86882e7	−	1.24016e9i	0.00221268	−	0.0467568i
$952$	−1.13292e10	+	9.50635e9i	−0.425570	+	0.357096i
$953$	−4.29747e8	−	7.44344e8i	−0.0160838	−	0.0278579i	0.857871	−	0.513864i	$-0.171787\pi$
$953$	−4.29747e8	−	7.44344e8i	−0.0160838	−	0.0278579i	−0.873955	+	0.486006i	$0.838453\pi$
$954$	6.79674e9	−	2.46438e10i	0.253444	−	0.918943i
$955$	−5.54220e9	+	9.59937e9i	−0.205907	+	0.356641i
$956$	−1.01206e9	−	5.73970e9i	−0.0374632	−	0.212464i
$957$	−4.85654e9	−	6.37729e9i	−0.179116	−	0.235204i
$958$	−2.16945e10	+	7.89616e9i	−0.797207	+	0.290160i
$959$	2.37841e10	−	8.65672e9i	0.870808	−	0.316948i
$960$	2.53113e10	−	3.23823e9i	0.923348	−	0.118130i
$961$	−8.80280e8	−	4.99231e9i	−0.0319955	−	0.181455i
$962$	5.96677e9	−	1.03348e10i	0.216086	−	0.374272i
$963$	−2.38927e9	−	2.98183e10i	−0.0862133	−	1.07595i
$964$	2.51633e9	+	4.35841e9i	0.0904686	+	0.156696i
$965$	1.12299e10	−	9.42299e9i	0.402281	−	0.337554i
$966$	−2.24988e10	+	1.16078e10i	−0.803042	+	0.414314i
$967$	3.88128e9	−	2.20118e10i	0.138033	−	0.782822i	−0.834667	−	0.550755i	$-0.814340\pi$
$967$	3.88128e9	−	2.20118e10i	0.138033	−	0.782822i	0.972700	−	0.232067i	$-0.0745490\pi$
$968$	1.88625e10	+	1.58275e10i	0.668400	+	0.560854i
$969$	2.01294e10	−	2.18068e10i	0.710718	−	0.769944i
$970$	−2.53450e10	−	9.22482e9i	−0.891643	−	0.324532i
$971$	−4.15665e10			−1.45706			−0.728528	−	0.685016i	$-0.759795\pi$
$971$	−4.15665e10			−1.45706			−0.728528	+	0.685016i	$0.759795\pi$
$972$	4.93555e9	−	1.45757e9i	0.172387	−	0.0509094i
$973$	−3.91158e10			−1.36131
$974$	−2.90511e10	−	1.05737e10i	−1.00741	−	0.366667i
$975$	−1.06143e10	+	1.14988e10i	−0.366755	+	0.397317i
$976$	−2.20864e10	−	1.85327e10i	−0.760414	−	0.638063i
$977$	−4.84523e9	+	2.74787e10i	−0.166220	+	0.942681i	0.781577	+	0.623808i	$0.214415\pi$
$977$	−4.84523e9	+	2.74787e10i	−0.166220	+	0.942681i	−0.947798	+	0.318873i	$0.896696\pi$
$978$	3.08683e10	−	1.59259e10i	1.05518	−	0.544401i
$979$	−1.70210e10	+	1.42823e10i	−0.579755	+	0.486472i
$980$	−1.06952e9	−	1.85246e9i	−0.0362992	−	0.0628720i
$981$	−1.06733e9	−	1.33203e10i	−0.0360958	−	0.450478i
$982$	1.28064e10	−	2.21813e10i	0.431554	−	0.747474i
$983$	1.93013e9	+	1.09463e10i	0.0648109	+	0.367561i	0.999913	+	0.0131829i	$0.00419635\pi$
$983$	1.93013e9	+	1.09463e10i	0.0648109	+	0.367561i	−0.935102	+	0.354378i	$0.884693\pi$
$984$	1.38386e10	−	1.77046e9i	0.463031	−	0.0592384i
$985$	−1.98652e10	+	7.23036e9i	−0.662319	+	0.241064i
$986$	1.27679e10	−	4.64714e9i	0.424180	−	0.154389i
$987$	−1.48860e10	−	1.95473e10i	−0.492796	−	0.647108i
$988$	−2.50994e9	−	1.42346e10i	−0.0827969	−	0.469564i
$989$	2.02344e10	−	3.50470e10i	0.665124	−	1.15203i
$990$	2.64169e9	−	9.57830e9i	0.0865283	−	0.313737i
$991$	−1.31684e10	−	2.28083e10i	−0.429808	−	0.744449i	0.567048	−	0.823685i	$-0.308085\pi$
$991$	−1.31684e10	−	2.28083e10i	−0.429808	−	0.744449i	−0.996856	+	0.0792357i	$0.974752\pi$
$992$	−7.54854e9	+	6.33398e9i	−0.245512	+	0.206009i
$993$	−2.49580e9	+	5.27394e10i	−0.0808886	+	1.70928i
$994$	−1.97701e9	+	1.12122e10i	−0.0638494	+	0.362108i
$995$	1.79590e9	+	1.50694e9i	0.0577965	+	0.0484970i
$996$	−2.29284e9	−	5.17110e8i	−0.0735304	−	0.0165835i
$997$	1.21902e10	+	4.43689e9i	0.389565	+	0.141790i	0.529374	−	0.848389i	$-0.322427\pi$
$997$	1.21902e10	+	4.43689e9i	0.389565	+	0.141790i	−0.139810	+	0.990178i	$0.544649\pi$
$998$	−1.16994e10			−0.372568
$999$	−7.63521e9	+	3.06497e9i	−0.242294	+	0.0972629i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	27.8.e.a.4.6	✓	120
3.2	odd	2		81.8.e.a.64.15		120
27.7	even	9	inner	27.8.e.a.7.6	yes	120
27.20	odd	18		81.8.e.a.19.15		120

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
27.8.e.a.4.6	✓	120	1.1	even	1	trivial
27.8.e.a.7.6	yes	120	27.7	even	9	inner
81.8.e.a.19.15		120	27.20	odd	18
81.8.e.a.64.15		120	3.2	odd	2

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:	\( N \)	\(=\)	\( 27 = 3^{3} \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	27.e (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-9.62864 - 3.50454i) q^{2} +(31.7200 - 34.3634i) q^{3} +(-17.6248 - 14.7890i) q^{4} +(40.7285 - 230.983i) q^{5} +(-425.848 + 219.708i) q^{6} +(500.665 - 420.108i) q^{7} +(773.656 + 1340.01i) q^{8} +(-174.680 - 2180.01i) q^{9} +O(q^{10})\)	\(q+(-9.62864 - 3.50454i) q^{2} +(31.7200 - 34.3634i) q^{3} +(-17.6248 - 14.7890i) q^{4} +(40.7285 - 230.983i) q^{5} +(-425.848 + 219.708i) q^{6} +(500.665 - 420.108i) q^{7} +(773.656 + 1340.01i) q^{8} +(-174.680 - 2180.01i) q^{9} +(-1201.65 + 2081.32i) q^{10} +(-328.263 - 1861.67i) q^{11} +(-1067.26 + 136.541i) q^{12} +(-13604.6 + 4951.67i) q^{13} +(-6293.01 + 2290.47i) q^{14} +(-6645.44 - 8726.35i) q^{15} +(-2241.74 - 12713.6i) q^{16} +(-7312.15 + 12665.0i) q^{17} +(-5958.01 + 21602.7i) q^{18} +(-21696.6 - 37579.6i) q^{19} +(-4133.84 + 3468.70i) q^{20} +(1444.80 - 30530.4i) q^{21} +(-3363.57 + 19075.8i) q^{22} +(61924.7 + 51961.0i) q^{23} +(70587.6 + 15919.8i) q^{24} +(21719.2 + 7905.14i) q^{25} +148347. q^{26} +(-80453.4 - 63147.5i) q^{27} -15037.1 q^{28} +(85205.2 + 31012.1i) q^{29} +(33404.7 + 107312. i) q^{30} +(-114762. - 96296.5i) q^{31} +(11421.8 - 64776.5i) q^{32} +(-74385.8 - 47772.1i) q^{33} +(114791. - 96321.1i) q^{34} +(-76646.4 - 132756. i) q^{35} +(-29161.5 + 41005.7i) q^{36} +(40221.7 - 69666.1i) q^{37} +(77209.6 + 437877. i) q^{38} +(-261382. + 624567. i) q^{39} +(341029. - 124125. i) q^{40} +(181176. - 65942.8i) q^{41} +(-120906. + 288903. i) q^{42} +(-86932.1 - 493016. i) q^{43} +(-21746.7 + 37666.3i) q^{44} +(-510660. - 48440.7i) q^{45} +(-414151. - 717331. i) q^{46} +(615804. - 516721. i) q^{47} +(-507988. - 326240. i) q^{48} +(-68831.8 + 390364. i) q^{49} +(-181422. - 152232. i) q^{50} +(203271. + 653004. i) q^{51} +(313009. + 113926. i) q^{52} -1.14077e6 q^{53} +(553354. + 889976. i) q^{54} -443384. q^{55} +(950292. + 345878. i) q^{56} +(-1.97958e6 - 446459. i) q^{57} +(-711726. - 597209. i) q^{58} +(299570. - 1.69894e6i) q^{59} +(-11929.2 + 252080. i) q^{60} +(1.71084e6 - 1.43556e6i) q^{61} +(767524. + 1.32939e6i) q^{62} +(-1.00330e6 - 1.01807e6i) q^{63} +(-1.16321e6 + 2.01474e6i) q^{64} +(589656. + 3.34410e6i) q^{65} +(548815. + 720668. i) q^{66} +(-117367. + 42717.9i) q^{67} +(316178. - 115079. i) q^{68} +(3.74981e6 - 479736. i) q^{69} +(272754. + 1.54686e6i) q^{70} +(850034. - 1.47230e6i) q^{71} +(2.78610e6 - 1.92065e6i) q^{72} +(-868776. - 1.50476e6i) q^{73} +(-631428. + 529831. i) q^{74} +(960581. - 495593. i) q^{75} +(-173366. + 983206. i) q^{76} +(-946453. - 794169. i) q^{77} +(4.70557e6 - 5.09770e6i) q^{78} +(2.67970e6 + 975329. i) q^{79} -3.02792e6 q^{80} +(-4.72194e6 + 761608. i) q^{81} -1.97558e6 q^{82} +(2.05276e6 + 747144. i) q^{83} +(-476978. + 516726. i) q^{84} +(2.62759e6 + 2.20481e6i) q^{85} +(-890757. + 5.05173e6i) q^{86} +(3.76839e6 - 1.94423e6i) q^{87} +(2.24070e6 - 1.88017e6i) q^{88} +(-5.87690e6 - 1.01791e7i) q^{89} +(4.74720e6 + 2.25604e6i) q^{90} +(-4.73111e6 + 8.19453e6i) q^{91} +(-322962. - 1.83161e6i) q^{92} +(-6.94932e6 + 889069. i) q^{93} +(-7.74022e6 + 2.81721e6i) q^{94} +(-9.56393e6 + 3.48098e6i) q^{95} +(-1.86364e6 - 2.44720e6i) q^{96} +(1.94881e6 + 1.10522e7i) q^{97} +(2.03080e6 - 3.51745e6i) q^{98} +(-4.00113e6 + 1.04081e6i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 120 q - 6 q^{2} - 6 q^{3} - 6 q^{4} - 219 q^{5} + 1386 q^{6} - 6 q^{7} - 4611 q^{8} - 1728 q^{9}+O(q^{10}) \) 120 * q - 6 * q^2 - 6 * q^3 - 6 * q^4 - 219 * q^5 + 1386 * q^6 - 6 * q^7 - 4611 * q^8 - 1728 * q^9	\( 120 q - 6 q^{2} - 6 q^{3} - 6 q^{4} - 219 q^{5} + 1386 q^{6} - 6 q^{7} - 4611 q^{8} - 1728 q^{9} - 3 q^{10} + 9399 q^{11} - 10545 q^{12} - 6 q^{13} + 16647 q^{14} + 11709 q^{15} + 378 q^{16} - 58959 q^{17} - 156051 q^{18} - 3 q^{19} + 240243 q^{20} - 516 q^{21} + 105762 q^{22} - 144084 q^{23} - 150894 q^{24} - 107997 q^{25} + 443202 q^{26} + 114363 q^{27} - 12 q^{28} + 107886 q^{29} - 179901 q^{30} + 297975 q^{31} - 639576 q^{32} - 31338 q^{33} - 265806 q^{34} - 450672 q^{35} + 51264 q^{36} - 3 q^{37} - 145596 q^{38} + 1919661 q^{39} + 283521 q^{40} + 227085 q^{41} + 3792042 q^{42} - 1080969 q^{43} - 1205115 q^{44} - 4430925 q^{45} - 3 q^{46} - 5184339 q^{47} - 2424039 q^{48} + 976008 q^{49} + 2324559 q^{50} + 2918034 q^{51} - 3366135 q^{52} + 5631750 q^{53} + 11971422 q^{54} - 12 q^{55} + 5254923 q^{56} - 284637 q^{57} + 3884295 q^{58} - 12534492 q^{59} - 29390886 q^{60} + 3865440 q^{61} - 9923646 q^{62} + 3292389 q^{63} - 10223619 q^{64} + 17158395 q^{65} + 39100653 q^{66} + 5567061 q^{67} + 19858455 q^{68} - 12682935 q^{69} - 1020993 q^{70} - 18563877 q^{71} - 33138540 q^{72} + 3770934 q^{73} - 36278085 q^{74} - 26317941 q^{75} - 1156998 q^{76} + 8471751 q^{77} + 36593658 q^{78} + 16415526 q^{79} + 101080590 q^{80} + 45736524 q^{81} - 12 q^{82} + 3147699 q^{83} - 27588054 q^{84} - 7672131 q^{85} - 70854834 q^{86} - 55384731 q^{87} - 34323078 q^{88} - 54647613 q^{89} - 25256970 q^{90} + 3315066 q^{91} + 73858515 q^{92} + 69808065 q^{93} + 22126539 q^{94} + 32541447 q^{95} + 33014034 q^{96} + 41250117 q^{97} - 88493274 q^{98} - 111262167 q^{99}+O(q^{100}) \) 120 * q - 6 * q^2 - 6 * q^3 - 6 * q^4 - 219 * q^5 + 1386 * q^6 - 6 * q^7 - 4611 * q^8 - 1728 * q^9 - 3 * q^10 + 9399 * q^11 - 10545 * q^12 - 6 * q^13 + 16647 * q^14 + 11709 * q^15 + 378 * q^16 - 58959 * q^17 - 156051 * q^18 - 3 * q^19 + 240243 * q^20 - 516 * q^21 + 105762 * q^22 - 144084 * q^23 - 150894 * q^24 - 107997 * q^25 + 443202 * q^26 + 114363 * q^27 - 12 * q^28 + 107886 * q^29 - 179901 * q^30 + 297975 * q^31 - 639576 * q^32 - 31338 * q^33 - 265806 * q^34 - 450672 * q^35 + 51264 * q^36 - 3 * q^37 - 145596 * q^38 + 1919661 * q^39 + 283521 * q^40 + 227085 * q^41 + 3792042 * q^42 - 1080969 * q^43 - 1205115 * q^44 - 4430925 * q^45 - 3 * q^46 - 5184339 * q^47 - 2424039 * q^48 + 976008 * q^49 + 2324559 * q^50 + 2918034 * q^51 - 3366135 * q^52 + 5631750 * q^53 + 11971422 * q^54 - 12 * q^55 + 5254923 * q^56 - 284637 * q^57 + 3884295 * q^58 - 12534492 * q^59 - 29390886 * q^60 + 3865440 * q^61 - 9923646 * q^62 + 3292389 * q^63 - 10223619 * q^64 + 17158395 * q^65 + 39100653 * q^66 + 5567061 * q^67 + 19858455 * q^68 - 12682935 * q^69 - 1020993 * q^70 - 18563877 * q^71 - 33138540 * q^72 + 3770934 * q^73 - 36278085 * q^74 - 26317941 * q^75 - 1156998 * q^76 + 8471751 * q^77 + 36593658 * q^78 + 16415526 * q^79 + 101080590 * q^80 + 45736524 * q^81 - 12 * q^82 + 3147699 * q^83 - 27588054 * q^84 - 7672131 * q^85 - 70854834 * q^86 - 55384731 * q^87 - 34323078 * q^88 - 54647613 * q^89 - 25256970 * q^90 + 3315066 * q^91 + 73858515 * q^92 + 69808065 * q^93 + 22126539 * q^94 + 32541447 * q^95 + 33014034 * q^96 + 41250117 * q^97 - 88493274 * q^98 - 111262167 * q^99

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