LMFDB - Embedded newform 27.8.e.a.4.18

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			4.18
Character	$\chi$	$=$	27.4
Dual form			27.8.e.a.7.18

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(16.7921 + 6.11184i) q^{2} +(46.7511 - 1.15397i) q^{3} +(146.567 + 122.985i) q^{4} +(-21.3907 + 121.313i) q^{5} +(792.104 + 266.358i) q^{6} +(-285.632 + 239.674i) q^{7} +(565.850 + 980.080i) q^{8} +(2184.34 - 107.899i) q^{9} +O(q^{10})$	\(q+(16.7921 + 6.11184i) q^{2} +(46.7511 - 1.15397i) q^{3} +(146.567 + 122.985i) q^{4} +(-21.3907 + 121.313i) q^{5} +(792.104 + 266.358i) q^{6} +(-285.632 + 239.674i) q^{7} +(565.850 + 980.080i) q^{8} +(2184.34 - 107.899i) q^{9} +(-1100.64 + 1906.36i) q^{10} +(-803.430 - 4556.48i) q^{11} +(6994.12 + 5580.54i) q^{12} +(933.323 - 339.702i) q^{13} +(-6261.21 + 2278.89i) q^{14} +(-860.050 + 5696.20i) q^{15} +(-740.959 - 4202.19i) q^{16} +(-11166.2 + 19340.4i) q^{17} +(37339.1 + 11538.5i) q^{18} +(-13878.2 - 24037.7i) q^{19} +(-18054.8 + 15149.8i) q^{20} +(-13077.0 + 11534.6i) q^{21} +(14357.1 - 81423.4i) q^{22} +(23315.9 + 19564.3i) q^{23} +(27585.1 + 45166.9i) q^{24} +(59154.2 + 21530.4i) q^{25} +17748.7 q^{26} +(101996. - 7565.05i) q^{27} -71340.5 q^{28} +(-146453. - 53304.7i) q^{29} +(-49256.3 + 90394.8i) q^{30} +(-245544. - 206036. i) q^{31} +(38395.0 - 217749. i) q^{32} +(-42819.3 - 212093. i) q^{33} +(-305710. + 256521. i) q^{34} +(-22965.6 - 39777.6i) q^{35} +(333423. + 252826. i) q^{36} +(-88195.2 + 152759. i) q^{37} +(-86129.5 - 488465. i) q^{38} +(43241.9 - 16958.5i) q^{39} +(-131000. + 47680.2i) q^{40} +(456882. - 166292. i) q^{41} +(-290089. + 113766. i) q^{42} +(109246. + 619565. i) q^{43} +(442620. - 766641. i) q^{44} +(-33635.0 + 267296. i) q^{45} +(271949. + 471029. i) q^{46} +(-78494.2 + 65864.5i) q^{47} +(-39489.9 - 195602. i) q^{48} +(-118865. + 674115. i) q^{49} +(861736. + 723082. i) q^{50} +(-499714. + 917072. i) q^{51} +(178573. + 64995.2i) q^{52} +2.07437e6 q^{53} +(1.75896e6 + 496348. i) q^{54} +569945. q^{55} +(-396524. - 144323. i) q^{56} +(-676558. - 1.10777e6i) q^{57} +(-2.13347e6 - 1.79020e6i) q^{58} +(-442381. + 2.50887e6i) q^{59} +(-826600. + 729104. i) q^{60} +(-1.00139e6 + 840264. i) q^{61} +(-2.86395e6 - 4.96051e6i) q^{62} +(-598056. + 554347. i) q^{63} +(1.70249e6 - 2.94880e6i) q^{64} +(21245.7 + 120491. i) q^{65} +(577253. - 3.82320e6i) q^{66} +(-2.45376e6 + 893094. i) q^{67} +(-4.01517e6 + 1.46140e6i) q^{68} +(1.11262e6 + 887749. i) q^{69} +(-142527. - 808313. i) q^{70} +(429648. - 744172. i) q^{71} +(1.34176e6 + 2.07977e6i) q^{72} +(1.52805e6 + 2.64665e6i) q^{73} +(-2.41462e6 + 2.02611e6i) q^{74} +(2.79037e6 + 938308. i) q^{75} +(922180. - 5.22994e6i) q^{76} +(1.32155e6 + 1.10891e6i) q^{77} +(829771. - 20481.4i) q^{78} +(-642214. - 233747. i) q^{79} +525629. q^{80} +(4.75968e6 - 471375. i) q^{81} +8.68838e6 q^{82} +(1.46994e6 + 535013. i) q^{83} +(-3.33525e6 + 82324.8i) q^{84} +(-2.10739e6 - 1.76831e6i) q^{85} +(-1.95221e6 + 1.10715e7i) q^{86} +(-6.90837e6 - 2.32305e6i) q^{87} +(4.01109e6 - 3.36571e6i) q^{88} +(-1.37382e6 - 2.37952e6i) q^{89} +(-2.19847e6 + 4.28290e6i) q^{90} +(-185169. + 320722. i) q^{91} +(1.01123e6 + 5.73499e6i) q^{92} +(-1.17172e7 - 9.34907e6i) q^{93} +(-1.72064e6 + 626261. i) q^{94} +(3.21294e6 - 1.16942e6i) q^{95} +(1.54374e6 - 1.02243e7i) q^{96} +(145687. + 826233. i) q^{97} +(-6.11607e6 + 1.05933e7i) q^{98} +(-2.24660e6 - 9.86619e6i) 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 $

$2$	16.7921	+	6.11184i	1.48423	+	0.540215i	0.951923	−	0.306337i	$-0.0991035\pi$
$2$	16.7921	+	6.11184i	1.48423	+	0.540215i	0.532306	+	0.846552i	$0.321326\pi$
$3$	46.7511	−	1.15397i	0.999696	−	0.0246757i
$3$	46.7511	−	1.15397i	0.999696	−	0.0246757i
$4$	146.567	+	122.985i	1.14506	+	0.960818i
$5$	−21.3907	+	121.313i	−0.0765298	+	0.434022i	0.922335	+	0.386391i	$0.126278\pi$
$5$	−21.3907	+	121.313i	−0.0765298	+	0.434022i	−0.998865	+	0.0476313i	$0.984833\pi$
$6$	792.104	+	266.358i	1.49711	+	0.503426i
$7$	−285.632	+	239.674i	−0.314748	+	0.264105i	−0.786451	−	0.617652i	$-0.788084\pi$
$7$	−285.632	+	239.674i	−0.314748	+	0.264105i	0.471703	+	0.881758i	$0.343639\pi$
$8$	565.850	+	980.080i	0.390738	+	0.676779i
$9$	2184.34	−	107.899i	0.998782	−	0.0493364i
$10$	−1100.64	+	1906.36i	−0.348053	+	0.602846i
$11$	−803.430	−	4556.48i	−0.182001	−	1.03218i	−0.929748	−	0.368195i	$-0.879976\pi$
$11$	−803.430	−	4556.48i	−0.182001	−	1.03218i	0.747747	−	0.663983i	$-0.231135\pi$
$12$	6994.12	+	5580.54i	1.16842	+	0.932270i
$13$	933.323	−	339.702i	0.117823	−	0.0428841i	−0.282436	−	0.959286i	$-0.591142\pi$
$13$	933.323	−	339.702i	0.117823	−	0.0428841i	0.400259	+	0.916402i	$0.368920\pi$
$14$	−6261.21	+	2278.89i	−0.609832	+	0.221961i
$15$	−860.050	+	5696.20i	−0.0657967	+	0.435778i
$16$	−740.959	−	4202.19i	−0.0452245	−	0.256481i
$17$	−11166.2	+	19340.4i	−0.551231	+	0.954761i	0.446955	+	0.894557i	$0.352508\pi$
$17$	−11166.2	+	19340.4i	−0.551231	+	0.954761i	−0.998186	+	0.0602040i	$0.980825\pi$
$18$	37339.1	+	11538.5i	1.50907	+	0.466331i
$19$	−13878.2	−	24037.7i	−0.464188	−	0.803998i	0.534976	−	0.844867i	$-0.320321\pi$
$19$	−13878.2	−	24037.7i	−0.464188	−	0.803998i	−0.999164	+	0.0408696i	$0.986987\pi$
$20$	−18054.8	+	15149.8i	−0.504647	+	0.423449i
$21$	−13077.0	+	11534.6i	−0.308135	+	0.271791i
$22$	14357.1	−	81423.4i	0.287467	−	1.63031i
$23$	23315.9	+	19564.3i	0.399580	+	0.335288i	0.820331	−	0.571888i	$-0.193789\pi$
$23$	23315.9	+	19564.3i	0.399580	+	0.335288i	−0.420751	+	0.907176i	$0.638233\pi$
$24$	27585.1	+	45166.9i	0.407319	+	0.666931i
$25$	59154.2	+	21530.4i	0.757174	+	0.275589i
$26$	17748.7			0.198043
$27$	101996.	−	7565.05i	0.997261	−	0.0739671i
$28$	−71340.5			−0.614162
$29$	−146453.	−	53304.7i	−1.11508	−	0.405856i	−0.282226	−	0.959348i	$-0.591073\pi$
$29$	−146453.	−	53304.7i	−1.11508	−	0.405856i	−0.832855	+	0.553492i	$0.813295\pi$
$30$	−49256.3	+	90394.8i	−0.333071	+	0.611250i
$31$	−245544.	−	206036.i	−1.48035	−	1.24216i	−0.905812	−	0.423679i	$-0.860738\pi$
$31$	−245544.	−	206036.i	−1.48035	−	1.24216i	−0.574535	−	0.818480i	$-0.694817\pi$
$32$	38395.0	−	217749.i	0.207133	−	1.17471i
$33$	−42819.3	−	212093.i	−0.207415	−	1.02737i
$34$	−305710.	+	256521.i	−1.33393	+	1.11930i
$35$	−22965.6	−	39777.6i	−0.0905399	−	0.156820i
$36$	333423.	+	252826.i	1.19107	+	0.903155i
$37$	−88195.2	+	152759.i	−0.286246	+	0.495792i	−0.972911	−	0.231182i	$-0.925741\pi$
$37$	−88195.2	+	152759.i	−0.286246	+	0.495792i	0.686665	+	0.726974i	$0.259074\pi$
$38$	−86129.5	−	488465.i	−0.254630	−	1.44408i
$39$	43241.9	−	16958.5i	0.116729	−	0.0457784i
$40$	−131000.	+	47680.2i	−0.323640	+	0.117795i
$41$	456882.	−	166292.i	1.03529	−	0.376814i	0.232196	−	0.972669i	$-0.425409\pi$
$41$	456882.	−	166292.i	1.03529	−	0.376814i	0.803092	+	0.595855i	$0.203187\pi$
$42$	−290089.	+	113766.i	−0.604169	+	0.236941i
$43$	109246.	+	619565.i	0.209540	+	1.18836i	0.890134	+	0.455698i	$0.150610\pi$
$43$	109246.	+	619565.i	0.209540	+	1.18836i	−0.680595	+	0.732660i	$0.738278\pi$
$44$	442620.	−	766641.i	0.783334	−	1.35677i
$45$	−33635.0	+	267296.i	−0.0550235	+	0.437269i
$46$	271949.	+	471029.i	0.411941	+	0.713503i
$47$	−78494.2	+	65864.5i	−0.110280	+	0.0925356i	−0.696260	−	0.717790i	$-0.745154\pi$
$47$	−78494.2	+	65864.5i	−0.110280	+	0.0925356i	0.585980	+	0.810325i	$0.300710\pi$
$48$	−39489.9	−	195602.i	−0.0515396	−	0.255287i
$49$	−118865.	+	674115.i	−0.144333	+	0.818554i
$50$	861736.	+	723082.i	0.974943	+	0.818074i
$51$	−499714.	+	917072.i	−0.527504	+	0.968072i
$52$	178573.	+	64995.2i	0.176118	+	0.0641017i
$53$	2.07437e6			1.91391			0.956953	−	0.290242i	$-0.0937358\pi$
$53$	2.07437e6			1.91391			0.956953	+	0.290242i	$0.0937358\pi$
$54$	1.75896e6	+	496348.i	1.52012	+	0.428951i
$55$	569945.			0.461917
$56$	−396524.	−	144323.i	−0.301725	−	0.109819i
$57$	−676558.	−	1.10777e6i	−0.483886	−	0.792299i
$58$	−2.13347e6	−	1.79020e6i	−1.43579	−	1.20477i
$59$	−442381.	+	2.50887e6i	−0.280424	+	1.59036i	0.440764	+	0.897623i	$0.354708\pi$
$59$	−442381.	+	2.50887e6i	−0.280424	+	1.59036i	−0.721188	+	0.692740i	$0.756404\pi$
$60$	−826600.	+	729104.i	−0.494045	+	0.435773i
$61$	−1.00139e6	+	840264.i	−0.564869	+	0.473981i	−0.879939	−	0.475087i	$-0.842417\pi$
$61$	−1.00139e6	+	840264.i	−0.564869	+	0.473981i	0.315070	+	0.949069i	$0.397972\pi$
$62$	−2.86395e6	−	4.96051e6i	−1.52614	−	2.64335i
$63$	−598056.	+	554347.i	−0.301335	+	0.279312i
$64$	1.70249e6	−	2.94880e6i	0.811812	−	1.40610i
$65$	21245.7	+	120491.i	0.00959566	+	0.0544197i
$66$	577253.	−	3.82320e6i	0.247151	−	1.63691i
$67$	−2.45376e6	+	893094.i	−0.996712	+	0.362773i	−0.788316	−	0.615271i	$-0.789047\pi$
$67$	−2.45376e6	+	893094.i	−0.996712	+	0.362773i	−0.208396	+	0.978044i	$0.566824\pi$
$68$	−4.01517e6	+	1.46140e6i	−1.54854	+	0.563624i
$69$	1.11262e6	+	887749.i	0.407732	+	0.325326i
$70$	−142527.	−	808313.i	−0.0496655	−	0.281667i
$71$	429648.	−	744172.i	0.142465	−	0.246757i	−0.785959	−	0.618278i	$-0.787830\pi$
$71$	429648.	−	744172.i	0.142465	−	0.246757i	0.928424	+	0.371522i	$0.121164\pi$
$72$	1.34176e6	+	2.07977e6i	0.423652	+	0.656677i
$73$	1.52805e6	+	2.64665e6i	0.459734	+	0.796282i	0.998947	−	0.0458875i	$-0.0146116\pi$
$73$	1.52805e6	+	2.64665e6i	0.459734	+	0.796282i	−0.539213	+	0.842169i	$0.681278\pi$
$74$	−2.41462e6	+	2.02611e6i	−0.692689	+	0.581235i
$75$	2.79037e6	+	938308.i	0.763744	+	0.256821i
$76$	922180.	−	5.22994e6i	0.240973	−	1.36662i
$77$	1.32155e6	+	1.10891e6i	0.329888	+	0.276809i
$78$	829771.	−	20481.4i	0.197983	−	0.00488686i
$79$	−642214.	−	233747.i	−0.146550	−	0.0533397i	0.267704	−	0.963501i	$-0.413735\pi$
$79$	−642214.	−	233747.i	−0.146550	−	0.0533397i	−0.414254	+	0.910162i	$0.635957\pi$
$80$	525629.			0.114779
$81$	4.75968e6	−	471375.i	0.995132	−	0.0985527i
$82$	8.68838e6			1.74016
$83$	1.46994e6	+	535013.i	0.282179	+	0.102705i	0.479233	−	0.877688i	$-0.340915\pi$
$83$	1.46994e6	+	535013.i	0.282179	+	0.102705i	−0.197053	+	0.980393i	$0.563137\pi$
$84$	−3.33525e6	+	82324.8i	−0.613975	+	0.0151549i
$85$	−2.10739e6	−	1.76831e6i	−0.372202	−	0.312314i
$86$	−1.95221e6	+	1.10715e7i	−0.330964	+	1.87699i
$87$	−6.90837e6	−	2.32305e6i	−1.12476	−	0.378217i
$88$	4.01109e6	−	3.36571e6i	0.627442	−	0.526486i
$89$	−1.37382e6	−	2.37952e6i	−0.206568	−	0.357787i	0.744063	−	0.668110i	$-0.232896\pi$
$89$	−1.37382e6	−	2.37952e6i	−0.206568	−	0.357787i	−0.950631	+	0.310323i	$0.899563\pi$
$90$	−2.19847e6	+	4.28290e6i	−0.317887	+	0.619283i
$91$	−185169.	+	320722.i	−0.0257587	+	0.0446154i
$92$	1.01123e6	+	5.73499e6i	0.135392	+	0.767848i
$93$	−1.17172e7	−	9.34907e6i	−1.51055	−	1.20525i
$94$	−1.72064e6	+	626261.i	−0.213669	+	0.0777693i
$95$	3.21294e6	−	1.16942e6i	0.384477	−	0.139938i
$96$	1.54374e6	−	1.02243e7i	0.178083	−	1.17947i
$97$	145687.	+	826233.i	0.0162077	+	0.0919182i	0.991839	−	0.127500i	$-0.0406952\pi$
$97$	145687.	+	826233.i	0.0162077	+	0.0919182i	−0.975631	+	0.219418i	$0.929584\pi$
$98$	−6.11607e6	+	1.05933e7i	−0.656419	+	1.13695i
$99$	−2.24660e6	−	9.86619e6i	−0.232703	−	1.02194i
$100$	6.02218e6	+	1.04307e7i	0.602218	+	1.04307i
$101$	7.18886e6	−	6.03217e6i	0.694281	−	0.582571i	−0.225860	−	0.974160i	$-0.572519\pi$
$101$	7.18886e6	−	6.03217e6i	0.694281	−	0.582571i	0.920140	+	0.391589i	$0.128075\pi$
$102$	−1.39963e7	+	1.23454e7i	−1.30590	+	1.15187i
$103$	375312.	−	2.12850e6i	0.0338425	−	0.191930i	−0.963200	−	0.268787i	$-0.913377\pi$
$103$	375312.	−	2.12850e6i	0.0338425	−	0.191930i	0.997042	+	0.0768565i	$0.0244883\pi$
$104$	861056.	+	722512.i	0.0750610	+	0.0629837i
$105$	−1.11957e6	−	1.83315e6i	−0.0943819	−	0.154538i
$106$	3.48331e7	+	1.26782e7i	2.84068	+	1.03392i
$107$	1.80236e7			1.42232			0.711160	−	0.703030i	$-0.248170\pi$
$107$	1.80236e7			1.42232			0.711160	+	0.703030i	$0.248170\pi$
$108$	1.58796e7	+	1.14351e7i	1.21299	+	0.873489i
$109$	−1.98533e7			−1.46838			−0.734191	−	0.678943i	$-0.762438\pi$
$109$	−1.98533e7			−1.46838			−0.734191	+	0.678943i	$0.762438\pi$
$110$	9.57060e6	+	3.48341e6i	0.685590	+	0.249534i
$111$	−3.94695e6	+	7.24341e6i	−0.273925	+	0.502705i
$112$	1.21879e6	+	1.02269e6i	0.0819723	+	0.0687830i
$113$	2.41988e6	−	1.37238e7i	0.157768	−	0.894748i	−0.798443	−	0.602071i	$-0.794343\pi$
$113$	2.41988e6	−	1.37238e7i	0.157768	−	0.894748i	0.956211	−	0.292678i	$-0.0945463\pi$
$114$	−4.59033e6	−	2.27369e7i	−0.290186	−	1.43735i
$115$	−2.87215e6	+	2.41002e6i	−0.176102	+	0.147767i
$116$	−1.49096e7	−	2.58243e7i	−0.886879	−	1.53612i
$117$	2.00204e6	−	842728.i	0.115564	−	0.0486448i
$118$	−2.27623e7	+	3.94255e7i	−1.27535	+	2.20897i
$119$	−1.44597e6	−	8.20048e6i	−0.0786581	−	0.446092i
$120$	−6.06939e6	+	2.38027e6i	−0.320635	+	0.125746i
$121$	−1.80404e6	+	656617.i	−0.0925758	+	0.0336948i
$122$	−2.19510e7	+	7.98951e6i	−1.09445	+	0.398346i
$123$	2.11679e7	−	8.30155e6i	1.02567	−	0.402246i
$124$	−1.06495e7	−	6.03964e7i	−0.501595	−	2.84469i
$125$	−8.68915e6	+	1.50501e7i	−0.397917	+	0.689212i
$126$	−1.34307e7	+	5.65345e6i	−0.598139	+	0.251777i
$127$	−3.70882e6	−	6.42387e6i	−0.160666	−	0.278281i	0.774442	−	0.632645i	$-0.218031\pi$
$127$	−3.70882e6	−	6.42387e6i	−0.160666	−	0.278281i	−0.935108	+	0.354364i	$0.884697\pi$
$128$	2.49306e7	−	2.09193e7i	1.05075	−	0.881681i
$129$	5.82234e6	+	2.88393e7i	0.238799	+	1.18283i
$130$	−379657.	+	2.15314e6i	−0.0151562	+	0.0859550i
$131$	−7.21665e6	−	6.05548e6i	−0.280470	−	0.235342i	0.491690	−	0.870770i	$-0.336379\pi$
$131$	−7.21665e6	−	6.05548e6i	−0.280470	−	0.235342i	−0.772160	+	0.635428i	$0.780824\pi$
$132$	1.98083e7	−	3.63521e7i	0.749616	−	1.37569i
$133$	9.72523e6	+	3.53970e6i	0.358442	+	0.130462i
$134$	−4.66622e7			−1.67532
$135$	−1.26402e6	+	1.25352e7i	−0.0442168	+	0.438494i
$136$	−2.52735e7			−0.861549
$137$	3.37379e7	+	1.22796e7i	1.12098	+	0.408002i	0.835008	−	0.550238i	$-0.185463\pi$
$137$	3.37379e7	+	1.22796e7i	1.12098	+	0.408002i	0.285967	+	0.958239i	$0.407685\pi$
$138$	1.32575e7	+	2.17073e7i	0.429422	+	0.703121i
$139$	−1.68732e7	−	1.41583e7i	−0.532901	−	0.447157i	0.336201	−	0.941790i	$-0.390858\pi$
$139$	−1.68732e7	−	1.41583e7i	−0.532901	−	0.447157i	−0.869102	+	0.494633i	$0.835302\pi$
$140$	1.52603e6	−	8.65452e6i	0.0470017	−	0.266560i
$141$	−3.59369e6	+	3.16982e6i	−0.107963	+	0.0952286i
$142$	1.17630e7	−	9.87029e6i	0.344752	−	0.289282i
$143$	−2.29770e6	−	3.97974e6i	−0.0657079	−	0.113809i
$144$	−2.07191e6	−	9.09904e6i	−0.0578233	−	0.253938i
$145$	9.59929e6	−	1.66265e7i	0.261488	−	0.452910i
$146$	9.48323e6	+	5.37821e7i	0.252186	+	1.43022i
$147$	−4.77915e6	+	3.16528e7i	−0.124091	+	0.821867i
$148$	−3.17135e7	+	1.15428e7i	−0.804134	+	0.292681i
$149$	−4.46405e7	+	1.62478e7i	−1.10555	+	0.402386i	−0.829358	−	0.558718i	$-0.811294\pi$
$149$	−4.46405e7	+	1.62478e7i	−1.10555	+	0.402386i	−0.276188	+	0.961104i	$0.589071\pi$
$150$	4.11215e7	+	3.28105e7i	0.994832	+	0.793767i
$151$	−1.37273e7	−	7.78516e7i	−0.324465	−	1.84013i	−0.513412	−	0.858143i	$-0.671619\pi$
$151$	−1.37273e7	−	7.78516e7i	−0.324465	−	1.84013i	0.188947	−	0.981987i	$-0.439493\pi$
$152$	1.57059e7	−	2.72034e7i	0.362752	−	0.628305i
$153$	−2.23039e7	+	4.34508e7i	−0.503455	+	0.980794i
$154$	1.54142e7	+	2.66981e7i	0.340093	+	0.589059i
$155$	3.02472e7	−	2.53804e7i	0.652415	−	0.547441i
$156$	8.42349e6	+	2.83253e6i	0.177646	+	0.0597364i
$157$	−7.23863e6	+	4.10523e7i	−0.149282	+	0.846621i	0.814546	+	0.580098i	$0.196986\pi$
$157$	−7.23863e6	+	4.10523e7i	−0.149282	+	0.846621i	−0.963829	+	0.266523i	$0.914125\pi$
$158$	−9.35551e6	−	7.85021e6i	−0.188698	−	0.158337i
$159$	9.69792e7	−	2.39376e6i	1.91332	−	0.0472270i
$160$	2.55945e7	+	9.31563e6i	0.493999	+	0.179801i
$161$	−1.13488e7			−0.214318
$162$	8.28062e7	+	2.11750e7i	1.53024	+	0.391310i
$163$	3.29063e7			0.595145			0.297572	−	0.954699i	$-0.403823\pi$
$163$	3.29063e7			0.595145			0.297572	+	0.954699i	$0.403823\pi$
$164$	8.74154e7	+	3.18166e7i	1.54751	+	0.563249i
$165$	2.66456e7	−	657700.i	0.461776	−	0.0113981i
$166$	2.14135e7	+	1.79680e7i	0.363336	+	0.304875i
$167$	−2.44163e6	+	1.38472e7i	−0.0405670	+	0.230067i	−0.998350	−	0.0574261i	$-0.981711\pi$
$167$	−2.44163e6	+	1.38472e7i	−0.0405670	+	0.230067i	0.957783	+	0.287493i	$0.0928218\pi$
$168$	−1.87045e7	−	6.28968e6i	−0.304343	−	0.102340i
$169$	−4.73125e7	+	3.96999e7i	−0.754001	+	0.632682i
$170$	−2.45799e7	−	4.25737e7i	−0.383715	−	0.664615i
$171$	−3.29082e7	−	5.10089e7i	−0.503289	−	0.780117i
$172$	−6.01851e7	+	1.04244e8i	−0.901861	+	1.56207i
$173$	−1.67728e7	−	9.51231e7i	−0.246288	−	1.39677i	−0.817482	−	0.575954i	$-0.804631\pi$
$173$	−1.67728e7	−	9.51231e7i	−0.246288	−	1.39677i	0.571194	−	0.820815i	$-0.306480\pi$
$174$	−1.01808e8	−	8.12318e7i	−1.46508	−	1.16897i
$175$	−2.20566e7	+	8.02794e6i	−0.311104	+	0.113233i
$176$	−1.85519e7	+	6.75233e6i	−0.256503	+	0.0933596i
$177$	−1.77867e7	+	1.17803e8i	−0.241095	+	1.59680i
$178$	−8.52608e6	−	4.83538e7i	−0.113313	−	0.642629i
$179$	4.83086e7	−	8.36729e7i	0.629562	−	1.09043i	−0.358077	−	0.933692i	$-0.616568\pi$
$179$	4.83086e7	−	8.36729e7i	0.629562	−	1.09043i	0.987640	−	0.156742i	$-0.0500991\pi$
$180$	−3.78031e7	+	3.50403e7i	−0.483141	+	0.447831i
$181$	−5.41120e6	−	9.37248e6i	−0.0678295	−	0.117484i	0.830116	−	0.557591i	$-0.188274\pi$
$181$	−5.41120e6	−	9.37248e6i	−0.0678295	−	0.117484i	−0.897946	+	0.440106i	$0.854941\pi$
$182$	−5.06959e6	+	4.25389e6i	−0.0623337	+	0.0523042i
$183$	−4.58464e7	+	4.04389e7i	−0.553001	+	0.487776i
$184$	−5.98134e6	+	3.39219e7i	−0.0707842	+	0.401437i
$185$	−1.66450e7	−	1.39668e7i	−0.193278	−	0.162180i
$186$	−1.39617e8	−	2.28605e8i	−1.59090	−	2.60489i
$187$	9.70954e7	+	3.53398e7i	1.08581	+	0.395202i
$188$	−1.96050e7			−0.215186
$189$	−2.73201e7	+	2.66065e7i	−0.294351	+	0.286663i
$190$	6.10994e7			0.646248
$191$	−5.06380e7	−	1.84307e7i	−0.525847	−	0.191393i	0.0654360	−	0.997857i	$-0.479156\pi$
$191$	−5.06380e7	−	1.84307e7i	−0.525847	−	0.191393i	−0.591283	+	0.806464i	$0.701378\pi$
$192$	7.61906e7	−	1.39825e8i	0.776868	−	1.42570i
$193$	−1.17237e8	−	9.83735e7i	−1.17385	−	0.984981i	−1.00000		0.000209353i	$-0.999933\pi$
$193$	−1.17237e8	−	9.83735e7i	−1.17385	−	0.984981i	−0.173854	−	0.984771i	$-0.555622\pi$
$194$	−2.60340e6	+	1.47646e7i	−0.0255997	+	0.145183i
$195$	1.13230e6	+	5.60855e6i	0.0109356	+	0.0541664i
$196$	−1.00327e8	+	8.41848e7i	−0.951752	+	0.798615i
$197$	9.88162e7	+	1.71155e8i	0.920866	+	1.59499i	0.798079	+	0.602553i	$0.205850\pi$
$197$	9.88162e7	+	1.71155e8i	0.920866	+	1.59499i	0.122787	+	0.992433i	$0.460817\pi$
$198$	2.25754e7	−	1.79405e8i	0.206684	−	1.64251i
$199$	5.71709e7	−	9.90229e7i	0.514268	−	0.890738i	−0.485595	−	0.874184i	$-0.661397\pi$
$199$	5.71709e7	−	9.90229e7i	0.514268	−	0.890738i	0.999863	−	0.0165540i	$-0.00526955\pi$
$200$	1.23709e7	+	7.01589e7i	0.109344	+	0.620123i
$201$	−1.13685e8	+	4.45847e7i	−0.987457	+	0.387258i
$202$	1.57584e8	−	5.73558e7i	1.34518	−	0.489607i
$203$	5.46075e7	−	1.98755e7i	0.458159	−	0.166756i
$204$	−1.86028e8	+	7.29557e7i	−1.53416	+	0.601663i
$205$	1.04003e7	+	5.89828e7i	0.0843152	+	0.478175i
$206$	1.93114e7	−	3.34483e7i	0.153914	−	0.266586i
$207$	5.30407e7	+	4.02193e7i	0.415636	+	0.315165i
$208$	−2.11904e6	−	3.67029e6i	−0.0163274	−	0.0282800i
$209$	−9.83770e7	+	8.25481e7i	−0.745386	+	0.625453i
$210$	−7.59608e6	−	3.76251e7i	−0.0566008	−	0.280356i
$211$	3.95214e7	−	2.24137e8i	0.289630	−	1.64257i	−0.398631	−	0.917111i	$-0.630515\pi$
$211$	3.95214e7	−	2.24137e8i	0.289630	−	1.64257i	0.688261	−	0.725463i	$-0.258374\pi$
$212$	3.04035e8	+	2.55116e8i	2.19153	+	1.83892i
$213$	1.92278e7	−	3.52867e7i	0.136333	−	0.250197i
$214$	3.02654e8	+	1.10157e8i	2.11105	+	0.768359i
$215$	−7.74981e7			−0.531810
$216$	6.51286e7	+	9.56833e7i	0.439727	+	0.646023i
$217$	1.19517e8			0.793998
$218$	−3.33379e8	−	1.21340e8i	−2.17941	−	0.793242i
$219$	7.44920e7	+	1.21971e8i	0.479242	+	0.784695i
$220$	8.35354e7	+	7.00946e7i	0.528922	+	0.443818i
$221$	−3.85169e6	+	2.18440e7i	−0.0240037	+	0.136132i
$222$	−1.10548e8	+	9.75092e7i	−0.678135	+	0.598150i
$223$	−2.24956e8	+	1.88760e8i	−1.35841	+	1.13984i	−0.381935	+	0.924189i	$0.624742\pi$
$223$	−2.24956e8	+	1.88760e8i	−1.35841	+	1.13984i	−0.976471	+	0.215649i	$0.930813\pi$
$224$	4.12219e7	+	7.13983e7i	0.245053	+	0.424444i
$225$	1.31536e8	+	4.06469e7i	0.769849	+	0.237897i
$226$	1.24513e8	−	2.15662e8i	0.717521	−	1.24278i
$227$	−3.10201e6	−	1.75923e7i	−0.0176016	−	0.0998236i	0.974741	−	0.223337i	$-0.0716950\pi$
$227$	−3.10201e6	−	1.75923e7i	−0.0176016	−	0.0998236i	−0.992343	+	0.123513i	$0.960584\pi$
$228$	3.70777e7	−	2.45570e8i	0.207177	−	1.37215i
$229$	−1.72955e8	+	6.29503e7i	−0.951717	+	0.346397i	−0.770783	−	0.637098i	$-0.780135\pi$
$229$	−1.72955e8	+	6.29503e7i	−0.951717	+	0.346397i	−0.180935	+	0.983495i	$0.557912\pi$
$230$	−6.29591e7	+	2.29152e7i	−0.341202	+	0.124187i
$231$	6.30637e7	+	5.03180e7i	0.336618	+	0.268585i
$232$	−3.06277e7	−	1.73699e8i	−0.161030	−	0.913247i
$233$	4.28350e7	−	7.41925e7i	0.221847	−	0.384250i	−0.733522	−	0.679666i	$-0.762125\pi$
$233$	4.28350e7	−	7.41925e7i	0.221847	−	0.384250i	0.955369	+	0.295416i	$0.0954581\pi$
$234$	3.87691e7	−	1.91506e6i	0.197802	−	0.00977073i
$235$	−6.31116e6	−	1.09313e7i	−0.0317228	−	0.0549455i
$236$	−3.73391e8	+	3.13313e8i	−1.84915	+	1.55162i
$237$	−3.02939e7	−	1.01868e7i	−0.147821	−	0.0497072i
$238$	2.58391e7	−	1.46541e8i	0.124239	−	0.704595i
$239$	2.49912e6	+	2.09701e6i	0.0118412	+	0.00993592i	0.648689	−	0.761054i	$-0.275318\pi$
$239$	2.49912e6	+	2.09701e6i	0.0118412	+	0.00993592i	−0.636848	+	0.770990i	$0.719762\pi$
$240$	2.45737e7	−	606560.i	0.114745	−	0.00283227i
$241$	1.04385e8	+	3.79929e7i	0.480372	+	0.174841i	0.570845	−	0.821058i	$-0.306616\pi$
$241$	1.04385e8	+	3.79929e7i	0.480372	+	0.174841i	−0.0904733	+	0.995899i	$0.528838\pi$
$242$	−3.43068e7			−0.155606
$243$	2.21977e8	−	2.75298e7i	0.992397	−	0.123078i
$244$	−2.50110e8			−1.10222
$245$	−7.92362e7	−	2.88396e7i	−0.344225	−	0.125288i
$246$	4.06191e8	−	1.00261e7i	1.73963	−	0.0429398i
$247$	−2.11184e7	−	1.77205e7i	−0.0891708	−	0.0748232i
$248$	6.29908e7	−	3.57238e8i	0.262238	−	1.48723i
$249$	6.93386e7	+	2.33162e7i	0.284628	+	0.0957106i
$250$	−2.37893e8	+	1.99616e8i	−0.962923	+	0.807988i
$251$	1.40256e8	+	2.42930e8i	0.559839	+	0.969670i	0.997509	+	0.0705344i	$0.0224705\pi$
$251$	1.40256e8	+	2.42930e8i	0.559839	+	0.969670i	−0.437670	+	0.899136i	$0.644196\pi$
$252$	−1.55832e8	+	7.69755e6i	−0.613414	+	0.0303006i
$253$	7.04118e7	−	1.21957e8i	0.273353	−	0.473461i
$254$	−2.30174e7	−	1.30538e8i	−0.0881330	−	0.499827i
$255$	−1.00563e8	−	8.02385e7i	−0.379795	−	0.303035i
$256$	1.36939e8	−	4.98418e7i	0.510139	−	0.185675i
$257$	−2.73861e8	+	9.96772e7i	−1.00638	+	0.366294i	−0.792043	−	0.610465i	$-0.790983\pi$
$257$	−2.73861e8	+	9.96772e7i	−1.00638	+	0.366294i	−0.214341	+	0.976759i	$0.568760\pi$
$258$	−7.84917e7	+	5.19859e8i	−0.284547	+	1.88459i
$259$	−1.14208e7	−	6.47708e7i	−0.0408459	−	0.231649i
$260$	−1.17046e7	+	2.02729e7i	−0.0412998	+	0.0715334i
$261$	−3.25655e8	−	1.00633e8i	−1.13375	−	0.350348i
$262$	−8.41727e7	−	1.45791e8i	−0.289146	−	0.500815i
$263$	3.64900e8	−	3.06187e8i	1.23688	−	1.03787i	0.239122	−	0.970990i	$-0.423140\pi$
$263$	3.64900e8	−	3.06187e8i	1.23688	−	1.03787i	0.997761	−	0.0668785i	$-0.0213040\pi$
$264$	1.83639e8	−	1.61979e8i	0.614259	−	0.541809i
$265$	−4.43723e7	+	2.51648e8i	−0.146471	+	0.830678i
$266$	1.41673e8	+	1.18878e8i	0.461533	+	0.387272i
$267$	−6.69734e7	−	1.09660e8i	−0.215334	−	0.352581i
$268$	−4.69478e8	−	1.70876e8i	−1.48985	−	0.542262i
$269$	4.80231e8			1.50424			0.752121	−	0.659025i	$-0.229031\pi$
$269$	4.80231e8			1.50424			0.752121	+	0.659025i	$0.229031\pi$
$270$	−9.78388e7	+	2.02767e8i	−0.302509	+	0.626939i
$271$	3.90431e8			1.19166			0.595830	−	0.803111i	$-0.296823\pi$
$271$	3.90431e8			1.19166			0.595830	+	0.803111i	$0.296823\pi$
$272$	8.95457e7	+	3.25920e7i	0.269807	+	0.0982018i
$273$	−8.28677e6	+	1.52078e7i	−0.0246499	+	0.0452374i
$274$	4.91480e8	+	4.12401e8i	1.44338	+	1.21114i
$275$	5.05764e7	−	2.86833e8i	0.146651	−	0.831697i
$276$	5.38943e7	+	2.66950e8i	0.154298	+	0.764273i
$277$	−1.45473e8	+	1.22066e8i	−0.411247	+	0.345077i	−0.824821	−	0.565393i	$-0.808724\pi$
$277$	−1.45473e8	+	1.22066e8i	−0.411247	+	0.345077i	0.413575	+	0.910470i	$0.364280\pi$
$278$	−1.96804e8	−	3.40875e8i	−0.549386	−	0.951565i
$279$	−5.58582e8	−	4.23558e8i	−1.53983	−	1.16761i
$280$	2.59902e7	−	4.50163e7i	0.0707548	−	0.122551i
$281$	−6.21788e6	−	3.52633e7i	−0.0167174	−	0.0948094i	0.975307	−	0.220852i	$-0.0708836\pi$
$281$	−6.21788e6	−	3.52633e7i	−0.0167174	−	0.0948094i	−0.992025	+	0.126042i	$0.959773\pi$
$282$	−7.97191e7	+	3.12640e7i	−0.211685	+	0.0830180i
$283$	−2.07839e8	+	7.56471e7i	−0.545097	+	0.198399i	−0.599867	−	0.800100i	$-0.704780\pi$
$283$	−2.07839e8	+	7.56471e7i	−0.545097	+	0.198399i	0.0547696	+	0.998499i	$0.482558\pi$
$284$	1.54494e8	−	5.62313e7i	0.400219	−	0.145668i
$285$	1.48859e8	−	5.83791e7i	0.380907	−	0.149383i
$286$	−1.42598e7	−	8.08715e7i	−0.0360440	−	0.204416i
$287$	−9.06445e7	+	1.57001e8i	−0.226337	+	0.392026i
$288$	6.03728e7	−	4.79780e8i	0.148925	−	1.18350i
$289$	−4.41983e7	−	7.65537e7i	−0.107712	−	0.186562i
$290$	2.62811e8	−	2.20524e8i	0.632776	−	0.530962i
$291$	7.76449e6	+	3.84592e7i	0.0184709	+	0.0914903i
$292$	−1.01536e8	+	5.75839e8i	−0.238660	+	1.35351i
$293$	−1.74642e8	−	1.46542e8i	−0.405613	−	0.340350i	0.417045	−	0.908886i	$-0.363066\pi$
$293$	−1.74642e8	−	1.46542e8i	−0.405613	−	0.340350i	−0.822658	+	0.568536i	$0.807510\pi$
$294$	−2.73709e8	+	5.02309e8i	−0.628164	+	1.15280i
$295$	−2.94895e8	−	1.07333e8i	−0.668792	−	0.243420i
$296$	−1.99621e8			−0.447389
$297$	−1.16416e8	−	4.58663e8i	−0.257850	−	1.01589i
$298$	−8.48913e8			−1.85826
$299$	2.84073e7	+	1.03394e7i	0.0614583	+	0.0223690i
$300$	2.93580e8	+	4.80699e8i	0.627773	+	1.02789i
$301$	−1.79698e8	−	1.50784e8i	−0.379804	−	0.318693i
$302$	2.45305e8	−	1.39119e9i	0.512486	−	2.90645i
$303$	3.29126e8	−	2.90306e8i	0.679694	−	0.599525i
$304$	−9.07276e7	+	7.61295e7i	−0.185217	+	0.155416i
$305$	−8.05144e7	−	1.39455e8i	−0.162489	−	0.281439i
$306$	−6.40094e8	+	5.93313e8i	−1.27708	+	1.18375i
$307$	−1.55480e8	+	2.69299e8i	−0.306683	+	0.531190i	−0.977635	−	0.210311i	$-0.932552\pi$
$307$	−1.55480e8	+	2.69299e8i	−0.306683	+	0.531190i	0.670952	+	0.741501i	$0.265886\pi$
$308$	5.73171e7	+	3.25061e8i	0.111778	+	0.633925i
$309$	1.50901e7	−	9.99430e7i	0.0290962	−	0.192707i
$310$	6.63036e8	−	2.41325e8i	1.26407	−	0.460084i
$311$	6.01550e6	−	2.18946e6i	0.0113399	−	0.00412740i	−0.336344	−	0.941739i	$-0.609190\pi$
$311$	6.01550e6	−	2.18946e6i	0.0113399	−	0.00412740i	0.347684	+	0.937612i	$0.386968\pi$
$312$	4.10891e7	+	3.27846e7i	0.0765923	+	0.0611123i
$313$	1.05376e8	+	5.97617e8i	0.194239	+	1.10158i	0.913498	+	0.406842i	$0.133370\pi$
$313$	1.05376e8	+	5.97617e8i	0.194239	+	1.10158i	−0.719259	+	0.694742i	$0.755519\pi$
$314$	−3.72457e8	+	6.45115e8i	−0.678926	+	1.17593i
$315$	−5.44566e7	−	8.44097e7i	−0.0981665	−	0.152162i
$316$	−6.53804e7	−	1.13242e8i	−0.116558	−	0.201885i
$317$	1.63022e6	−	1.36791e6i	0.00287434	−	0.00241186i	−0.641349	−	0.767249i	$-0.721625\pi$
$317$	1.63022e6	−	1.36791e6i	0.00287434	−	0.00241186i	0.644224	+	0.764837i	$0.277181\pi$
$318$	1.64312e9	+	5.52524e8i	2.86532	+	0.963511i
$319$	−1.25217e8	+	7.10138e8i	−0.215970	+	1.22483i
$320$	3.21310e8	+	2.69611e8i	0.548150	+	0.459953i
$321$	8.42622e8	−	2.07986e7i	1.42189	−	0.0350968i
$322$	−1.90571e8	−	6.93620e7i	−0.318098	−	0.115778i
$323$	6.19864e8			1.02350
$324$	7.55587e8	+	5.16280e8i	1.23418	+	0.843292i
$325$	6.25239e7			0.101031
$326$	5.52567e8	+	2.01118e8i	0.883331	+	0.321506i
$327$	−9.28162e8	+	2.29101e7i	−1.46793	+	0.0362334i
$328$	4.21506e8	+	3.53686e8i	0.659546	+	0.553425i
$329$	6.63448e6	−	3.76260e7i	0.0102712	−	0.0582508i
$330$	4.51456e8	+	1.51809e8i	0.691539	+	0.232541i
$331$	8.86662e8	−	7.43998e8i	1.34388	−	1.12765i	0.363268	−	0.931685i	$-0.381661\pi$
$331$	8.86662e8	−	7.43998e8i	1.34388	−	1.12765i	0.980611	−	0.195964i	$-0.0627836\pi$
$332$	1.49646e8	+	2.59195e8i	0.224431	+	0.388726i
$333$	−1.76166e8	+	3.43192e8i	−0.261437	+	0.509311i
$334$	−1.25632e8	+	2.17601e8i	−0.184496	+	0.319557i
$335$	−5.58562e7	−	3.16776e8i	−0.0811735	−	0.460358i
$336$	5.81602e7	+	4.64055e7i	0.0836446	+	0.0667393i
$337$	5.15855e8	−	1.87756e8i	0.734214	−	0.267232i	0.0522665	−	0.998633i	$-0.483355\pi$
$337$	5.15855e8	−	1.87756e8i	0.734214	−	0.267232i	0.681947	+	0.731401i	$0.261133\pi$
$338$	−1.03712e9	+	3.77479e8i	−1.46089	+	0.531722i
$339$	9.72953e7	−	6.44397e8i	0.135642	−	0.898369i
$340$	−9.13996e7	−	5.18353e8i	−0.126115	−	0.715236i
$341$	−7.41521e8	+	1.28435e9i	−1.01271	+	1.75406i
$342$	−2.40841e8	−	1.05768e9i	−0.325565	−	1.42976i
$343$	−2.81151e8	−	4.86969e8i	−0.376193	−	0.651586i
$344$	−5.45407e8	+	4.57651e8i	−0.722381	+	0.606149i
$345$	−1.31495e8	+	1.15985e8i	−0.172402	+	0.152068i
$346$	2.99726e8	−	1.69983e9i	0.389008	−	2.20617i
$347$	−1.06854e8	−	8.96612e7i	−0.137290	−	0.115200i	0.571557	−	0.820562i	$-0.306340\pi$
$347$	−1.06854e8	−	8.96612e7i	−0.137290	−	0.115200i	−0.708846	+	0.705363i	$0.750784\pi$
$348$	−7.26843e8	−	1.19011e9i	−0.924513	−	1.51377i
$349$	−5.05463e7	−	1.83974e7i	−0.0636503	−	0.0231668i	0.309999	−	0.950737i	$-0.399671\pi$
$349$	−5.05463e7	−	1.83974e7i	−0.0636503	−	0.0231668i	−0.373649	+	0.927570i	$0.621894\pi$
$350$	−4.19443e8			−0.522919
$351$	9.26251e7	−	4.17088e7i	0.114328	−	0.0514816i
$352$	−1.02302e9			−1.25021
$353$	−1.04945e9	−	3.81968e8i	−1.26984	−	0.462185i	−0.382782	−	0.923838i	$-0.625034\pi$
$353$	−1.04945e9	−	3.81968e8i	−1.26984	−	0.462185i	−0.887060	+	0.461654i	$0.847256\pi$
$354$	−1.01867e9	+	1.86945e9i	−1.22045	+	2.23977i
$355$	8.10871e7	+	6.80402e7i	0.0961950	+	0.0807172i
$356$	9.12878e7	−	5.17719e8i	0.107235	−	0.608162i
$357$	−7.70636e7	−	3.81713e8i	−0.0896418	−	0.444016i
$358$	1.32260e9	−	1.10979e9i	1.52348	−	1.27835i
$359$	5.58954e8	+	9.68136e8i	0.637595	+	1.10435i	0.985959	+	0.166988i	$0.0534041\pi$
$359$	5.58954e8	+	9.68136e8i	0.637595	+	1.10435i	−0.348364	+	0.937359i	$0.613263\pi$
$360$	−2.81004e8	+	1.18284e8i	−0.317434	+	0.133619i
$361$	6.17296e7	−	1.06919e8i	0.0690587	−	0.119613i
$362$	−3.35826e7	−	1.90456e8i	−0.0372078	−	0.211016i
$363$	−8.35832e7	+	3.27794e7i	−0.0917162	+	0.0359690i
$364$	−6.65837e7	+	2.42345e7i	−0.0723625	+	0.0263378i
$365$	−3.53759e8	+	1.28758e8i	−0.380787	+	0.138595i
$366$	−1.01701e9	+	3.98849e8i	−1.08428	+	0.425231i
$367$	−1.03863e7	−	5.89036e7i	−0.0109680	−	0.0622029i	0.978832	−	0.204663i	$-0.0656098\pi$
$367$	−1.03863e7	−	5.89036e7i	−0.0109680	−	0.0622029i	−0.989801	+	0.142460i	$0.954499\pi$
$368$	6.49369e7	−	1.12474e8i	0.0679241	−	0.117648i
$369$	9.80042e8	−	4.12534e8i	1.01544	−	0.427432i
$370$	−1.94142e8	−	3.36265e8i	−0.199257	−	0.345124i
$371$	−5.92506e8	+	4.97172e8i	−0.602399	+	0.505473i
$372$	−5.67572e8	−	2.81131e9i	−0.571638	−	2.83145i
$373$	−7.34937e7	+	4.16803e8i	−0.0733279	+	0.415863i	0.925942	+	0.377665i	$0.123273\pi$
$373$	−7.34937e7	+	4.16803e8i	−0.0733279	+	0.415863i	−0.999270	+	0.0381981i	$0.987838\pi$
$374$	1.41445e9	+	1.18686e9i	1.39809	+	1.17314i
$375$	−3.88860e8	+	7.13634e8i	−0.380789	+	0.698821i
$376$	−1.08968e8	−	3.96613e7i	−0.105717	−	0.0384777i
$377$	−1.54796e8			−0.148787
$378$	−6.21377e8	+	2.79804e8i	−0.591744	+	0.266460i
$379$	1.60275e9			1.51227			0.756133	−	0.654418i	$-0.227086\pi$
$379$	1.60275e9			1.51227			0.756133	+	0.654418i	$0.227086\pi$
$380$	6.14733e8	+	2.23744e8i	0.574704	+	0.209175i
$381$	−1.80805e8	−	2.96043e8i	−0.167484	−	0.274232i
$382$	−7.37674e8	−	6.18982e8i	−0.677084	−	0.568141i
$383$	1.74349e7	−	9.88780e7i	0.0158571	−	0.0899299i	−0.975852	−	0.218432i	$-0.929906\pi$
$383$	1.74349e7	−	9.88780e7i	0.0158571	−	0.0899299i	0.991709	+	0.128502i	$0.0410169\pi$
$384$	1.14139e9	−	1.00677e9i	1.02867	−	0.907341i
$385$	−1.62795e8	+	1.36601e8i	−0.145388	+	0.121995i
$386$	−1.36742e9	−	2.36843e9i	−1.21017	−	2.09607i
$387$	3.05481e8	+	1.34155e9i	0.267914	+	1.17657i
$388$	−8.02610e7	+	1.39016e8i	−0.0697579	+	0.120824i
$389$	1.37843e8	+	7.81744e8i	0.118730	+	0.673350i	0.984836	+	0.173490i	$0.0555043\pi$
$389$	1.37843e8	+	7.81744e8i	0.118730	+	0.673350i	−0.866106	+	0.499861i	$0.833385\pi$
$390$	−1.52647e7	+	1.01100e8i	−0.0130306	+	0.0863029i
$391$	−6.38731e8	+	2.32479e8i	−0.540381	+	0.196682i
$392$	−7.27946e8	+	2.64951e8i	−0.610377	+	0.222159i
$393$	−3.44374e8	−	2.74773e8i	−0.286191	−	0.228350i
$394$	6.13265e8	+	3.47800e9i	0.505140	+	2.86479i
$395$	4.20939e7	−	7.29088e7i	0.0343660	−	0.0595237i
$396$	8.84112e8	−	1.72236e9i	0.715442	−	1.39377i
$397$	1.02221e9	+	1.77051e9i	0.819920	+	1.42014i	0.905741	+	0.423832i	$0.139315\pi$
$397$	1.02221e9	+	1.77051e9i	0.819920	+	1.42014i	−0.0858208	+	0.996311i	$0.527351\pi$
$398$	1.56523e9	−	1.31339e9i	1.24448	−	1.04424i
$399$	4.58750e8	+	1.54262e8i	0.361552	+	0.121578i
$400$	4.66438e7	−	2.64530e8i	0.0364405	−	0.206664i
$401$	4.36462e8	+	3.66235e8i	0.338019	+	0.283632i	0.795958	−	0.605352i	$-0.206968\pi$
$401$	4.36462e8	+	3.66235e8i	0.338019	+	0.283632i	−0.457939	+	0.888984i	$0.651412\pi$
$402$	−2.18151e9	+	5.38468e7i	−1.67481	+	0.0413398i
$403$	−2.99163e8	−	1.08886e8i	−0.227688	−	0.0828716i
$404$	1.79552e9			1.35474
$405$	−4.46293e7	+	5.87494e8i	−0.0333832	+	0.439451i
$406$	1.03845e9			0.770096
$407$	7.66900e8	+	2.79129e8i	0.563843	+	0.205222i
$408$	−1.18157e9	+	2.91649e7i	−0.861287	+	0.0212594i
$409$	3.87627e8	+	3.25258e8i	0.280145	+	0.235069i	0.772023	−	0.635595i	$-0.219245\pi$
$409$	3.87627e8	+	3.25258e8i	0.280145	+	0.235069i	−0.491878	+	0.870664i	$0.663689\pi$
$410$	−1.85851e8	+	1.05401e9i	−0.133174	+	0.755270i
$411$	1.59146e9	+	5.35152e8i	1.13070	+	0.380217i
$412$	3.16782e8	−	2.65812e8i	0.223162	−	0.187255i
$413$	−4.74952e8	−	8.22640e8i	−0.331760	−	0.574625i
$414$	6.44852e8	+	9.99544e8i	0.446641	+	0.692310i
$415$	−9.63470e7	+	1.66878e8i	−0.0661713	+	0.114612i
$416$	−3.81348e7	−	2.16273e8i	−0.0259714	−	0.147291i
$417$	−8.05181e8	−	6.42447e8i	−0.543773	−	0.433871i
$418$	−2.15648e9	+	7.84894e8i	−1.44420	+	0.525647i
$419$	−1.66171e9	+	6.04812e8i	−1.10358	+	0.401671i	−0.828636	−	0.559788i	$-0.810883\pi$
$419$	−1.66171e9	+	6.04812e8i	−1.10358	+	0.401671i	−0.274947	+	0.961459i	$0.588660\pi$
$420$	6.13564e7	−	4.06370e8i	0.0404098	−	0.267639i
$421$	−3.50467e6	−	1.98760e7i	−0.00228908	−	0.0129820i	0.983642	−	0.180135i	$-0.0576536\pi$
$421$	−3.50467e6	−	1.98760e7i	−0.00228908	−	0.0129820i	−0.985931	+	0.167153i	$0.946542\pi$
$422$	2.03354e9	−	3.52219e9i	1.31722	−	2.28149i
$423$	−1.64351e8	+	1.52340e8i	−0.105580	+	0.0978637i
$424$	1.17378e9	+	2.03305e9i	0.747837	+	1.29529i
$425$	−1.07693e9	+	9.03655e8i	−0.680500	+	0.571007i
$426$	5.38542e8	−	4.75021e8i	0.337509	−	0.297701i
$427$	8.46391e7	−	4.80012e8i	0.0526106	−	0.298370i
$428$	2.64167e9	+	2.21662e9i	1.62864	+	1.36659i
$429$	−1.12013e8	−	1.83406e8i	−0.0684963	−	0.112153i
$430$	−1.30136e9	−	4.73656e8i	−0.789328	−	0.287292i
$431$	−1.40740e9			−0.846735			−0.423367	−	0.905958i	$-0.639152\pi$
$431$	−1.40740e9			−0.846735			−0.423367	+	0.905958i	$0.639152\pi$
$432$	−1.07364e8	−	4.23000e8i	−0.0640718	−	0.252433i
$433$	2.36842e9			1.40201			0.701006	−	0.713155i	$-0.252735\pi$
$433$	2.36842e9			1.40201			0.701006	+	0.713155i	$0.252735\pi$
$434$	2.00694e9	+	7.30466e8i	1.17847	+	0.428930i
$435$	4.29591e8	−	7.88383e8i	0.250232	−	0.459224i
$436$	−2.90984e9	−	2.44165e9i	−1.68138	−	1.41085i
$437$	1.46700e8	−	8.31976e8i	0.0840900	−	0.476898i
$438$	5.05415e8	+	2.50343e9i	0.287401	+	1.42356i
$439$	1.00116e9	−	8.40076e8i	0.564780	−	0.473906i	−0.315129	−	0.949049i	$-0.602048\pi$
$439$	1.00116e9	−	8.40076e8i	0.564780	−	0.473906i	0.879909	+	0.475142i	$0.157603\pi$
$440$	3.22503e8	+	5.58592e8i	0.180489	+	0.312616i
$441$	−1.86904e8	+	1.48532e9i	−0.103773	+	0.824678i
$442$	−1.98185e8	+	3.43267e8i	−0.109167	+	0.189084i
$443$	−2.12817e6	−	1.20694e7i	−0.00116304	−	0.00659590i	0.984221	−	0.176945i	$-0.0566215\pi$
$443$	−2.12817e6	−	1.20694e7i	−0.00116304	−	0.00659590i	−0.985384	+	0.170349i	$0.945510\pi$
$444$	−1.46932e9	+	5.76234e8i	−0.796667	+	0.312434i
$445$	3.18053e8	−	1.15762e8i	0.171096	−	0.0622739i
$446$	−4.93115e9	+	1.79479e9i	−2.63194	+	0.957949i
$447$	−2.06824e9	+	8.11117e8i	−1.09528	+	0.429543i
$448$	2.20464e8	+	1.25031e9i	0.115842	+	0.656971i
$449$	1.69912e9	−	2.94296e9i	0.885854	−	1.53434i	0.0411218	−	0.999154i	$-0.486907\pi$
$449$	1.69912e9	−	2.94296e9i	0.885854	−	1.53434i	0.844732	−	0.535190i	$-0.179760\pi$
$450$	1.96034e9	+	1.48647e9i	1.01412	+	0.768978i
$451$	−1.12478e9	−	1.94817e9i	−0.577363	−	1.00002i
$452$	2.04250e9	−	1.71386e9i	1.04034	−	0.872952i
$453$	−7.31607e8	−	3.62381e9i	−0.369772	−	1.83156i
$454$	5.54323e7	−	3.14372e8i	0.0278014	−	0.157670i
$455$	−3.49469e7	−	2.93239e7i	−0.0173927	−	0.0145942i
$456$	7.02877e8	−	1.28991e9i	0.347138	−	0.637065i
$457$	−2.35354e9	−	8.56617e8i	−1.15349	−	0.419836i	−0.306723	−	0.951799i	$-0.599233\pi$
$457$	−2.35354e9	−	8.56617e8i	−1.15349	−	0.419836i	−0.846768	+	0.531962i	$0.821455\pi$
$458$	−3.28902e9			−1.59969
$459$	−9.92592e8	+	2.05711e9i	−0.479100	+	0.992918i
$460$	−7.17359e8			−0.343624
$461$	−2.88321e9	−	1.04940e9i	−1.37064	−	0.498872i	−0.451313	−	0.892366i	$-0.649044\pi$
$461$	−2.88321e9	−	1.04940e9i	−1.37064	−	0.498872i	−0.919328	+	0.393493i	$0.871267\pi$
$462$	7.51439e8	+	1.23038e9i	0.354525	+	0.580487i
$463$	−3.19236e8	−	2.67871e8i	−0.149479	−	0.125427i	0.564982	−	0.825103i	$-0.308883\pi$
$463$	−3.19236e8	−	2.67871e8i	−0.149479	−	0.125427i	−0.714460	+	0.699676i	$0.753328\pi$
$464$	−1.15480e8	+	6.54921e8i	−0.0536654	+	0.304352i
$465$	1.38480e9	−	1.22147e9i	0.638708	−	0.563374i
$466$	1.17274e9	−	9.84049e8i	0.536849	−	0.450470i
$467$	1.69549e8	+	2.93668e8i	0.0770348	+	0.133428i	0.901969	−	0.431800i	$-0.142121\pi$
$467$	1.69549e8	+	2.93668e8i	0.0770348	+	0.133428i	−0.824935	+	0.565228i	$0.808788\pi$
$468$	3.97076e8	+	1.22704e8i	0.179066	+	0.0553346i
$469$	4.86820e8	−	8.43197e8i	0.217903	−	0.377419i
$470$	−3.91678e7	−	2.22132e8i	−0.0174015	−	0.0986889i
$471$	−2.91041e8	+	1.92760e9i	−0.128346	+	0.850047i
$472$	−2.70922e9	+	9.86074e8i	−1.18590	+	0.431631i
$473$	2.73526e9	−	9.95555e8i	1.18846	−	0.432565i
$474$	−4.46440e8	−	3.56210e8i	−0.192548	−	0.153632i
$475$	−3.03411e8	−	1.72073e9i	−0.129899	−	0.736691i
$476$	7.96602e8	−	1.37975e9i	0.338545	−	0.586378i
$477$	4.53112e9	−	2.23822e8i	1.91158	−	0.0944253i
$478$	2.91490e7	+	5.04875e7i	0.0122075	+	0.0211439i
$479$	−1.76063e9	+	1.47734e9i	−0.731971	+	0.614196i	−0.930668	−	0.365864i	$-0.880773\pi$
$479$	−1.76063e9	+	1.47734e9i	−0.731971	+	0.614196i	0.198697	+	0.980061i	$0.436329\pi$
$480$	1.20732e9	+	4.05981e8i	0.498285	+	0.167556i
$481$	−3.04223e7	+	1.72533e8i	−0.0124648	+	0.0706911i
$482$	1.52064e9	+	1.27596e9i	0.618530	+	0.519008i
$483$	−5.30569e8	+	1.30962e7i	−0.214253	+	0.00528846i
$484$	−3.45168e8	−	1.25631e8i	−0.138379	−	0.0503659i
$485$	−1.03349e8			−0.0411349
$486$	3.89572e9	+	8.94401e8i	1.53943	+	0.353431i
$487$	−2.02240e9			−0.793442			−0.396721	−	0.917939i	$-0.629852\pi$
$487$	−2.02240e9			−0.793442			−0.396721	+	0.917939i	$0.629852\pi$
$488$	−1.39016e9	−	5.05977e8i	−0.541497	−	0.197089i
$489$	1.53841e9	−	3.79729e7i	0.594964	−	0.0146856i
$490$	−1.15428e9	−	9.68557e8i	−0.443226	−	0.371911i
$491$	3.09187e8	−	1.75349e9i	0.117879	−	0.668525i	−0.867405	−	0.497602i	$-0.834214\pi$
$491$	3.09187e8	−	1.75349e9i	0.117879	−	0.668525i	0.985284	−	0.170923i	$-0.0546750\pi$
$492$	4.12349e9	+	1.38659e9i	1.56094	+	0.524892i
$493$	2.66626e9	−	2.23726e9i	1.00216	−	0.840915i
$494$	−2.46319e8	−	4.26637e8i	−0.0919292	−	0.159226i
$495$	1.24495e9	−	6.14964e7i	0.461354	−	0.0227893i
$496$	−6.83864e8	+	1.18449e9i	−0.251642	+	0.435857i
$497$	5.56372e7	+	3.15534e8i	0.0203291	+	0.115292i
$498$	1.02184e9	+	8.15315e8i	0.370748	+	0.295817i
$499$	−1.59256e9	+	5.79645e8i	−0.573779	+	0.208838i	−0.612580	−	0.790409i	$-0.709868\pi$
$499$	−1.59256e9	+	5.79645e8i	−0.573779	+	0.208838i	0.0388013	+	0.999247i	$0.487646\pi$
$500$	−3.12447e9	+	1.13722e9i	−1.11785	+	0.406862i
$501$	−9.81698e7	+	6.50189e8i	−0.0348776	+	0.230998i
$502$	8.70446e8	+	4.93654e9i	0.307099	+	1.74165i
$503$	−6.38921e8	+	1.10664e9i	−0.223851	+	0.387722i	−0.955974	−	0.293451i	$-0.905196\pi$
$503$	−6.38921e8	+	1.10664e9i	−0.223851	+	0.387722i	0.732123	+	0.681173i	$0.238530\pi$
$504$	−8.81714e8	−	2.72465e8i	−0.306776	−	0.0947992i
$505$	5.78005e8	+	1.00113e9i	0.199715	+	0.345917i
$506$	1.92774e9	−	1.61757e9i	0.661489	−	0.555055i
$507$	−2.16610e9	+	1.91061e9i	−0.738160	+	0.651095i
$508$	2.46445e8	−	1.39766e9i	0.0834059	−	0.473019i
$509$	−1.52843e9	−	1.28250e9i	−0.513727	−	0.431068i	0.348711	−	0.937230i	$-0.386619\pi$
$509$	−1.52843e9	−	1.28250e9i	−0.513727	−	0.431068i	−0.862438	+	0.506162i	$0.831064\pi$
$510$	−1.19827e9	−	1.96200e9i	−0.399998	−	0.654944i
$511$	−1.07079e9	−	3.89736e8i	−0.355003	−	0.129210i
$512$	−1.56158e9			−0.514185
$513$	−1.59736e9	−	2.34675e9i	−0.522386	−	0.767460i
$514$	−5.20792e9			−1.69158
$515$	2.50187e8	+	9.10605e7i	0.0807121	+	0.0293768i
$516$	−2.69343e9	+	4.94296e9i	−0.863041	+	1.58385i
$517$	3.63175e8	+	3.04740e8i	0.115584	+	0.0969867i
$518$	2.04088e8	−	1.15744e9i	0.0645155	−	0.365885i
$519$	−8.93915e8	−	4.42776e9i	−0.280679	−	1.39027i
$520$	−1.06069e8	+	8.90021e7i	−0.0330807	+	0.0277580i
$521$	4.49772e8	+	7.79027e8i	0.139335	+	0.241335i	0.927245	−	0.374455i	$-0.122170\pi$
$521$	4.49772e8	+	7.79027e8i	0.139335	+	0.241335i	−0.787910	+	0.615790i	$0.788837\pi$
$522$	−4.85339e9	−	3.68020e9i	−1.49348	−	1.13246i
$523$	−1.81103e9	+	3.13680e9i	−0.553567	+	0.958805i	0.444447	+	0.895805i	$0.353400\pi$
$523$	−1.81103e9	+	3.13680e9i	−0.553567	+	0.958805i	−0.998014	+	0.0630003i	$0.979933\pi$
$524$	−3.12993e8	−	1.77507e9i	−0.0950333	−	0.538961i
$525$	−1.02191e9	+	4.00768e8i	−0.308215	+	0.120875i
$526$	7.99881e9	−	2.91133e9i	2.39649	−	0.872251i
$527$	6.72661e9	−	2.44829e9i	2.00198	−	0.728661i
$528$	−8.59529e8	+	3.37087e8i	−0.254122	+	0.0996606i
$529$	−4.30375e8	−	2.44078e9i	−0.126402	−	0.716859i
$530$	−2.28314e9	+	3.95451e9i	−0.666141	+	1.15379i
$531$	−6.95606e8	+	5.52795e9i	−0.201620	+	1.60226i
$532$	9.90075e8	+	1.71486e9i	0.285087	+	0.493785i
$533$	3.69929e8	−	3.10408e8i	0.105821	−	0.0887947i
$534$	−4.54402e8	−	2.25076e9i	−0.129136	−	0.639637i
$535$	−3.85537e8	+	2.18649e9i	−0.108850	+	0.617318i
$536$	−2.26376e9	−	1.89952e9i	−0.634971	−	0.532804i
$537$	2.16192e9	−	3.96755e9i	0.602463	−	1.10564i
$538$	8.06411e9	+	2.93510e9i	2.23264	+	0.812614i
$539$	3.16709e9			0.871163
$540$	−1.72690e9	+	1.68180e9i	−0.471944	+	0.459617i
$541$	2.40561e8			0.0653182			0.0326591	−	0.999467i	$-0.489602\pi$
$541$	2.40561e8			0.0653182			0.0326591	+	0.999467i	$0.489602\pi$
$542$	6.55617e9	+	2.38625e9i	1.76870	+	0.643752i
$543$	−2.63795e8	−	4.31930e8i	−0.0707079	−	0.115775i
$544$	3.78263e9	+	3.17400e9i	1.00739	+	0.845301i
$545$	4.24676e8	−	2.40846e9i	0.112375	−	0.637310i
$546$	−2.32100e8	+	2.04724e8i	−0.0610241	+	0.0538264i
$547$	−2.72198e9	+	2.28401e9i	−0.711098	+	0.596682i	−0.924907	−	0.380193i	$-0.875857\pi$
$547$	−2.72198e9	+	2.28401e9i	−0.711098	+	0.596682i	0.213809	+	0.976876i	$0.431413\pi$
$548$	3.43468e9	+	5.94903e9i	0.891567	+	1.54424i
$549$	−2.09670e9	+	1.94347e9i	−0.540797	+	0.501273i
$550$	2.60236e9	−	4.50743e9i	0.666958	−	1.15521i
$551$	7.51183e8	+	4.26017e9i	0.191300	+	1.08492i
$552$	−2.40490e8	+	1.59279e9i	−0.0608569	+	0.403062i
$553$	2.39459e8	−	8.71561e7i	0.0602135	−	0.0219159i
$554$	−3.18884e9	+	1.16064e9i	−0.796800	+	0.290011i
$555$	−7.94291e8	−	6.33757e8i	−0.197221	−	0.157361i
$556$	−7.31810e8	−	4.15030e9i	−0.180566	−	1.02404i
$557$	−1.01299e9	+	1.75455e9i	−0.248377	+	0.430202i	−0.963076	−	0.269231i	$-0.913231\pi$
$557$	−1.01299e9	+	1.75455e9i	−0.248377	+	0.430202i	0.714699	+	0.699433i	$0.246564\pi$
$558$	−6.79107e9	−	1.05264e10i	−1.65470	−	2.56484i
$559$	3.12429e8	+	5.41144e8i	0.0756503	+	0.131030i
$560$	−1.50136e8	+	1.25979e8i	−0.0361267	+	0.0303139i
$561$	4.58010e9	+	1.54013e9i	1.09523	+	0.368288i
$562$	1.11112e8	−	6.30149e8i	0.0264049	−	0.149750i
$563$	3.25885e9	+	2.73450e9i	0.769635	+	0.645800i	0.940615	−	0.339474i	$-0.110249\pi$
$563$	3.25885e9	+	2.73450e9i	0.769635	+	0.645800i	−0.170981	+	0.985274i	$0.554694\pi$
$564$	−9.16557e8	+	2.26236e7i	−0.215121	+	0.00530988i
$565$	1.61311e9	+	5.87126e8i	0.376267	+	0.136950i
$566$	−3.95240e9			−0.916227
$567$	−1.24654e9	+	1.27541e9i	−0.287188	+	0.293839i
$568$	9.72464e8			0.222666
$569$	3.08913e9	+	1.12435e9i	0.702980	+	0.255864i	0.668683	−	0.743548i	$-0.266858\pi$
$569$	3.08913e9	+	1.12435e9i	0.702980	+	0.255864i	0.0342975	+	0.999412i	$0.489081\pi$
$570$	2.85647e9	−	7.05069e7i	0.646052	−	0.0159467i
$571$	3.49918e9	+	2.93616e9i	0.786575	+	0.660014i	0.944895	−	0.327373i	$-0.106163\pi$
$571$	3.49918e9	+	2.93616e9i	0.786575	+	0.660014i	−0.158321	+	0.987388i	$0.550608\pi$
$572$	1.52678e8	−	8.65883e8i	0.0341108	−	0.193452i
$573$	−2.38865e9	−	8.03222e8i	−0.530410	−	0.178359i
$574$	−2.48168e9	+	2.08237e9i	−0.547714	+	0.459586i
$575$	9.58004e8	+	1.65931e9i	0.210150	+	0.363991i
$576$	3.40064e9	−	6.62488e9i	0.741451	−	1.44444i
$577$	−4.25167e9	+	7.36410e9i	−0.921391	+	1.59590i	−0.124125	+	0.992267i	$0.539612\pi$
$577$	−4.25167e9	+	7.36410e9i	−0.921391	+	1.59590i	−0.797266	+	0.603629i	$0.793721\pi$
$578$	−2.74300e8	−	1.55563e9i	−0.0590852	−	0.335089i
$579$	−5.59448e9	−	4.46379e9i	−1.19780	−	0.955715i
$580$	3.45174e9	−	1.25633e9i	0.734582	−	0.267366i
$581$	−5.48089e8	+	1.99488e8i	−0.115940	+	0.0421988i
$582$	−1.04674e8	+	6.93267e8i	−0.0220094	+	0.145771i
$583$	−1.66661e9	−	9.45182e9i	−0.348333	−	1.97549i
$584$	−1.72929e9	+	2.99521e9i	−0.359271	+	0.622276i
$585$	5.94086e7	+	2.60900e8i	0.0122689	+	0.0538800i
$586$	−2.03697e9	−	3.52813e9i	−0.418160	−	0.724275i
$587$	7.72415e8	−	6.48133e8i	0.157622	−	0.132261i	−0.560566	−	0.828110i	$-0.689416\pi$
$587$	7.72415e8	−	6.48133e8i	0.157622	−	0.132261i	0.718188	+	0.695849i	$0.244972\pi$
$588$	−4.59328e9	+	4.05151e9i	−0.931756	+	0.821857i
$589$	−1.54493e9	+	8.76171e9i	−0.311533	+	1.76679i
$590$	−4.29592e9	−	3.60470e9i	−0.861141	−	0.722583i
$591$	4.81728e9	+	7.88764e9i	0.959943	+	1.57178i
$592$	7.07269e8	+	2.57425e8i	0.140107	+	0.0509946i
$593$	−2.37491e9			−0.467686			−0.233843	−	0.972274i	$-0.575130\pi$
$593$	−2.37491e9			−0.467686			−0.233843	+	0.972274i	$0.575130\pi$
$594$	8.48395e8	−	8.41345e9i	0.166091	−	1.64711i
$595$	1.02575e9			0.199634
$596$	−8.54107e9	−	3.10870e9i	−1.65253	−	0.601473i
$597$	2.55853e9	−	4.69541e9i	0.492132	−	0.903156i
$598$	4.13826e8	+	3.47241e8i	0.0791341	+	0.0664014i
$599$	1.57671e9	−	8.94197e9i	0.299749	−	1.69996i	−0.347497	−	0.937681i	$-0.612968\pi$
$599$	1.57671e9	−	8.94197e9i	0.299749	−	1.69996i	0.647246	−	0.762281i	$-0.275921\pi$
$600$	6.59315e8	+	3.26573e9i	0.124613	+	0.617236i
$601$	−7.06784e8	+	5.93062e8i	−0.132809	+	0.111440i	−0.706772	−	0.707441i	$-0.749849\pi$
$601$	−7.06784e8	+	5.93062e8i	−0.132809	+	0.111440i	0.573964	+	0.818881i	$0.305405\pi$
$602$	−2.09594e9	−	3.63027e9i	−0.391553	−	0.678190i
$603$	−5.26347e9	+	2.21558e9i	−0.977600	+	0.411506i
$604$	7.56258e9	−	1.30988e10i	1.39650	−	2.41881i
$605$	−4.10664e7	−	2.32899e8i	−0.00753950	−	0.0427586i
$606$	7.30104e9	−	2.86330e9i	1.33269	−	0.522652i
$607$	−1.24277e9	+	4.52331e8i	−0.225543	+	0.0820910i	−0.452320	−	0.891856i	$-0.649403\pi$
$607$	−1.24277e9	+	4.52331e8i	−0.225543	+	0.0820910i	0.226777	+	0.973947i	$0.427181\pi$
$608$	−5.76703e9	+	2.09903e9i	−1.04061	+	0.378753i
$609$	2.53002e9	−	9.92217e8i	0.453904	−	0.178011i
$610$	−4.99682e8	−	2.83384e9i	−0.0891332	−	0.505499i
$611$	−5.08862e7	+	8.81375e7i	−0.00902518	+	0.0156321i
$612$	−8.61281e9	+	3.62543e9i	−1.51885	+	0.639337i
$613$	−4.79933e9	−	8.31269e9i	−0.841529	−	1.45757i	−0.888602	−	0.458680i	$-0.848323\pi$
$613$	−4.79933e9	−	8.31269e9i	−0.841529	−	1.45757i	0.0470727	−	0.998891i	$-0.485011\pi$
$614$	−4.25675e9	+	3.57183e9i	−0.742144	+	0.622733i
$615$	5.54288e8	+	2.74551e9i	0.0960888	+	0.475949i
$616$	−3.39025e8	+	1.92271e9i	−0.0584385	+	0.331421i
$617$	−4.28770e8	−	3.59781e8i	−0.0734897	−	0.0616651i	0.605303	−	0.795995i	$-0.293052\pi$
$617$	−4.28770e8	−	3.59781e8i	−0.0734897	−	0.0616651i	−0.678793	+	0.734330i	$0.737496\pi$
$618$	8.64230e8	−	1.58603e9i	0.147289	−	0.270303i
$619$	−1.09196e10	−	3.97440e9i	−1.85050	−	0.673525i	−0.984987	−	0.172631i	$-0.944773\pi$
$619$	−1.09196e10	−	3.97440e9i	−1.85050	−	0.673525i	−0.865508	−	0.500894i	$-0.833004\pi$
$620$	7.55466e9			1.27304
$621$	2.52612e9	+	1.81909e9i	0.423286	+	0.304813i
$622$	1.14395e8			0.0190607
$623$	9.62714e8	+	3.50399e8i	0.159510	+	0.0580571i
$624$	−1.03303e8	−	1.69145e8i	−0.0170203	−	0.0278685i
$625$	2.12752e9	+	1.78520e9i	0.348573	+	0.292488i
$626$	−1.88305e9	+	1.06793e10i	−0.306797	+	1.73993i
$627$	−4.50398e9	+	3.97274e9i	−0.729726	+	0.643656i
$628$	−6.10976e9	+	5.12670e9i	−0.984386	+	0.825998i
$629$	−1.96961e9	−	3.41146e9i	−0.315575	−	0.546592i
$630$	−3.98544e8	−	1.75025e9i	−0.0635015	−	0.278874i
$631$	−4.49642e8	+	7.78802e8i	−0.0712466	+	0.123403i	−0.899448	−	0.437028i	$-0.856031\pi$
$631$	−4.49642e8	+	7.78802e8i	−0.0712466	+	0.123403i	0.828201	+	0.560431i	$0.189364\pi$
$632$	−1.34306e8	−	7.61686e8i	−0.0211634	−	0.120024i
$633$	1.58902e9	−	1.05243e10i	0.249010	−	1.64922i
$634$	3.57353e7	−	1.30066e7i	0.00556910	−	0.00202699i
$635$	8.58632e8	−	3.12517e8i	0.133076	−	0.0484356i
$636$	1.45084e10	+	1.15761e10i	2.23624	+	1.78428i
$637$	1.18059e8	+	6.69545e8i	0.0180972	+	0.102634i
$638$	−6.44290e9	+	1.11594e10i	−0.982221	+	1.70126i
$639$	8.58200e8	−	1.67188e9i	0.130117	−	0.253485i
$640$	2.00449e9	+	3.47188e9i	0.302256	+	0.523522i
$641$	−3.79303e9	+	3.18273e9i	−0.568831	+	0.477306i	−0.881258	−	0.472636i	$-0.843303\pi$
$641$	−3.79303e9	+	3.18273e9i	−0.568831	+	0.477306i	0.312427	+	0.949942i	$0.398858\pi$
$642$	1.42765e10	+	4.80071e9i	2.12937	+	0.716033i
$643$	2.25317e9	−	1.27784e10i	0.334238	−	1.89556i	−0.100389	−	0.994948i	$-0.532009\pi$
$643$	2.25317e9	−	1.27784e10i	0.334238	−	1.89556i	0.434627	−	0.900611i	$-0.356880\pi$
$644$	−1.66337e9	−	1.39573e9i	−0.245407	−	0.205921i
$645$	−3.62312e9	+	8.94305e7i	−0.531648	+	0.0131228i
$646$	1.04088e10	+	3.78851e9i	1.51911	+	0.552910i
$647$	1.05373e10			1.52955			0.764776	−	0.644296i	$-0.222850\pi$
$647$	1.05373e10			1.52955			0.764776	+	0.644296i	$0.222850\pi$
$648$	3.15525e9	+	4.39815e9i	0.455535	+	0.634976i
$649$	1.17870e10			1.69258
$650$	1.04991e9	+	3.82136e8i	0.149953	+	0.0545784i
$651$	5.58754e9	−	1.37919e8i	0.793756	−	0.0195925i
$652$	4.82300e9	+	4.04697e9i	0.681476	+	0.571826i
$653$	−3.69025e8	+	2.09284e9i	−0.0518632	+	0.294131i	−0.999696	−	0.0246356i	$-0.992157\pi$
$653$	−3.69025e8	+	2.09284e9i	−0.0518632	+	0.294131i	0.947833	+	0.318766i	$0.103269\pi$
$654$	−1.57258e10	−	5.28807e9i	−2.19832	−	0.739222i
$655$	8.88978e8	−	7.45941e8i	0.123608	−	0.103719i
$656$	−1.03732e9	−	1.79669e9i	−0.143466	−	0.248490i
$657$	3.62334e9	+	5.61630e9i	0.498459	+	0.772631i
$658$	3.41371e8	−	5.91272e8i	0.0467128	−	0.0809089i
$659$	8.49358e8	+	4.81695e9i	0.115609	+	0.655651i	0.986447	+	0.164081i	$0.0524659\pi$
$659$	8.49358e8	+	4.81695e9i	0.115609	+	0.655651i	−0.870838	+	0.491570i	$0.836423\pi$
$660$	3.98626e9	+	3.18060e9i	0.539712	+	0.430631i
$661$	−6.41537e9	+	2.33500e9i	−0.864006	+	0.314472i	−0.735737	−	0.677267i	$-0.763164\pi$
$661$	−6.41537e9	+	2.33500e9i	−0.864006	+	0.314472i	−0.128269	+	0.991739i	$0.540942\pi$
$662$	1.94361e10	−	7.07418e9i	2.60380	−	0.947705i
$663$	−1.54864e8	+	1.02568e9i	−0.0206373	+	0.136683i
$664$	3.07407e8	+	1.74339e9i	0.0407498	+	0.231104i
$665$	−6.37441e8	+	1.10408e9i	−0.0840551	+	0.145588i
$666$	−5.05573e9	+	4.68624e9i	−0.663169	+	0.614702i
$667$	−2.37182e9	−	4.10811e9i	−0.309486	−	0.536045i
$668$	−2.06086e9	+	1.72926e9i	−0.267504	+	0.224462i
$669$	−1.02991e10	+	9.08434e9i	−1.32987	+	1.17301i
$670$	9.98140e8	−	5.66073e9i	0.128212	−	0.727128i
$671$	4.63319e9	+	3.88771e9i	0.592040	+	0.496781i
$672$	2.00956e9	+	3.29038e9i	0.255452	+	0.418268i
$673$	5.98629e9	+	2.17883e9i	0.757015	+	0.275531i	0.691555	−	0.722324i	$-0.256926\pi$
$673$	5.98629e9	+	2.17883e9i	0.757015	+	0.275531i	0.0654607	+	0.997855i	$0.479148\pi$
$674$	9.80983e9			1.23410
$675$	6.19636e9	+	1.74850e9i	0.775485	+	0.218828i
$676$	−1.18169e10			−1.47127
$677$	−8.67542e9	−	3.15759e9i	−1.07456	−	0.391107i	−0.256679	−	0.966497i	$-0.582628\pi$
$677$	−8.67542e9	−	3.15759e9i	−1.07456	−	0.391107i	−0.817880	+	0.575390i	$0.804850\pi$
$678$	5.57225e9	−	1.02261e10i	0.686636	−	1.26011i
$679$	−2.39639e8	−	2.01081e8i	−0.0293774	−	0.0246506i
$680$	5.40620e8	−	3.06601e9i	0.0659342	−	0.373931i
$681$	−1.65323e8	−	8.18882e8i	−0.0200595	−	0.0993589i
$682$	−2.03015e10	+	1.70350e10i	−2.45065	+	2.05634i
$683$	−2.39674e9	−	4.15128e9i	−0.287839	−	0.498551i	0.685455	−	0.728115i	$-0.259603\pi$
$683$	−2.39674e9	−	4.15128e9i	−0.287839	−	0.498551i	−0.973294	+	0.229564i	$0.926270\pi$
$684$	1.45005e9	−	1.15235e10i	0.173255	−	1.37685i
$685$	−2.21135e9	+	3.83017e9i	−0.262870	+	0.455304i
$686$	−1.74486e9	−	9.89559e9i	−0.206360	−	1.17033i
$687$	−8.01318e9	+	3.14258e9i	−0.942880	+	0.369776i
$688$	2.52258e9	−	9.18145e8i	0.295315	−	0.107486i
$689$	1.93606e9	−	7.04667e8i	0.225502	−	0.0820761i
$690$	−2.91697e9	+	1.14397e9i	−0.338033	+	0.132569i
$691$	−1.70425e8	−	9.66530e8i	−0.0196499	−	0.111440i	0.973405	−	0.229090i	$-0.0735751\pi$
$691$	−1.70425e8	−	9.66530e8i	−0.0196499	−	0.111440i	−0.993055	+	0.117650i	$0.962464\pi$
$692$	9.24034e9	−	1.60047e10i	1.06003	−	1.83602i
$693$	3.00637e9	+	2.27965e9i	0.343143	+	0.260197i
$694$	−1.24631e9	−	2.15868e9i	−0.141537	−	0.245149i
$695$	2.07852e9	−	1.74408e9i	0.234859	−	0.197070i
$696$	−1.63232e9	−	8.08526e9i	−0.183516	−	0.908995i
$697$	−1.88549e9	+	1.06931e10i	−0.210916	+	1.19616i
$698$	−7.36339e8	−	6.17862e8i	−0.0819566	−	0.0687697i
$699$	1.91697e9	−	3.51801e9i	0.212298	−	0.389607i
$700$	−4.22009e9	−	1.53599e9i	−0.465028	−	0.169256i
$701$	−5.01902e9			−0.550308			−0.275154	−	0.961400i	$-0.588729\pi$
$701$	−5.01902e9			−0.550308			−0.275154	+	0.961400i	$0.588729\pi$
$702$	1.81029e9	−	1.34270e8i	0.197500	−	0.0146487i
$703$	4.89595e9			0.531488
$704$	−1.48040e10	−	5.38821e9i	−1.59910	−	0.582023i
$705$	−3.07668e8	−	5.03765e8i	−0.0330690	−	0.0541460i
$706$	−1.52880e10	−	1.28281e10i	−1.63506	−	1.37198i
$707$	−6.07615e8	+	3.44596e9i	−0.0646637	+	0.366726i
$708$	−1.70949e10	+	1.50786e10i	−1.81030	+	1.59678i
$709$	−1.26803e10	+	1.06400e10i	−1.33618	+	1.12119i	−0.353595	+	0.935398i	$0.615041\pi$
$709$	−1.26803e10	+	1.06400e10i	−1.33618	+	1.12119i	−0.982589	+	0.185793i	$0.940515\pi$
$710$	9.45775e8	+	1.63813e9i	0.0991708	+	0.171769i
$711$	−1.42803e9	−	4.41287e8i	−0.149003	−	0.0460445i
$712$	1.55475e9	−	2.69290e9i	0.161428	−	0.279602i
$713$	−1.69412e9	−	9.60781e9i	−0.175037	−	0.992684i
$714$	1.03890e9	−	6.88078e9i	0.106815	−	0.707447i
$715$	5.31943e8	−	1.93611e8i	0.0544245	−	0.0198089i
$716$	1.73710e10	−	6.32251e9i	1.76859	−	0.643716i
$717$	1.19257e8	+	9.51537e7i	0.0120827	+	0.00964070i
$718$	3.46893e9	+	1.96733e10i	0.349752	+	1.98354i
$719$	4.15265e9	−	7.19260e9i	0.416652	−	0.721663i	−0.578948	−	0.815365i	$-0.696537\pi$
$719$	4.15265e9	−	7.19260e9i	0.416652	−	0.721663i	0.995600	+	0.0937014i	$0.0298699\pi$
$720$	1.14815e9	−	5.67147e7i	0.114640	−	0.00566281i
$721$	4.02945e8	+	6.97921e8i	0.0400380	+	0.0693478i
$722$	1.69004e9	−	1.41811e9i	0.167116	−	0.140227i
$723$	4.92395e9	+	1.65576e9i	0.484540	+	0.162934i
$724$	3.59565e8	−	2.03920e9i	0.0352122	−	0.199698i
$725$	−7.51567e9	−	6.30639e9i	−0.732461	−	0.614608i
$726$	−1.60388e9	+	3.95890e7i	−0.155559	+	0.00383970i
$727$	1.77701e10	+	6.46778e9i	1.71522	+	0.624287i	0.997408	−	0.0719541i	$-0.0229235\pi$
$727$	1.77701e10	+	6.46778e9i	1.71522	+	0.624287i	0.717808	+	0.696242i	$0.245146\pi$
$728$	−4.19112e8			−0.0402597
$729$	1.03459e10	−	1.54320e9i	0.989058	−	0.147529i
$730$	−6.72731e9			−0.640047
$731$	−1.32025e10	−	4.80532e9i	−1.25010	−	0.455000i
$732$	−1.16929e10	+	2.88620e8i	−1.10188	+	0.0271980i
$733$	−5.47152e8	−	4.59115e8i	−0.0513149	−	0.0430583i	0.616770	−	0.787144i	$-0.288441\pi$
$733$	−5.47152e8	−	4.59115e8i	−0.0513149	−	0.0430583i	−0.668084	+	0.744085i	$0.732886\pi$
$734$	1.85601e8	−	1.05260e9i	0.0173238	−	0.0982484i
$735$	−3.73766e9	−	1.25685e9i	−0.347212	−	0.116755i
$736$	5.15533e9	−	4.32583e9i	0.476633	−	0.399942i
$737$	6.04079e9	+	1.04629e10i	0.555850	+	0.962760i
$738$	1.89783e10	−	9.37465e8i	1.73804	−	0.0858535i
$739$	9.91757e8	−	1.71777e9i	0.0903961	−	0.156571i	−0.817282	−	0.576238i	$-0.804520\pi$
$739$	9.91757e8	−	1.71777e9i	0.0903961	−	0.156571i	0.907678	+	0.419668i	$0.137853\pi$
$740$	−7.21912e8	−	4.09417e9i	−0.0654897	−	0.371411i
$741$	−1.00776e9	−	8.04082e8i	−0.0909899	−	0.0726000i
$742$	−1.29881e10	+	4.72727e9i	−1.16716	+	0.424812i
$743$	4.28075e9	−	1.55807e9i	0.382877	−	0.139356i	−0.143409	−	0.989664i	$-0.545806\pi$
$743$	4.28075e9	−	1.55807e9i	0.382877	−	0.139356i	0.526286	+	0.850308i	$0.323584\pi$
$744$	2.53265e9	−	1.67740e10i	0.225460	−	1.49325i
$745$	−1.01618e9	−	5.76302e9i	−0.0900371	−	0.510626i
$746$	−3.78155e9	+	6.54984e9i	−0.333491	+	0.577623i
$747$	3.26856e9	+	1.01004e9i	0.286903	+	0.0886581i
$748$	9.88477e9	+	1.71209e10i	0.863597	+	1.49579i
$749$	−5.14810e9	+	4.31977e9i	−0.447673	+	0.375642i
$750$	−1.08914e10	+	9.60679e9i	−0.942692	+	0.831503i
$751$	2.00820e9	−	1.13891e10i	0.173008	−	0.981178i	−0.767410	−	0.641157i	$-0.778455\pi$
$751$	2.00820e9	−	1.13891e10i	0.173008	−	0.981178i	0.940418	−	0.340021i	$-0.110434\pi$
$752$	3.34936e8	+	2.81045e8i	0.0287210	+	0.0240998i
$753$	6.83746e9	+	1.11954e10i	0.583596	+	0.955560i
$754$	−2.59935e9	−	9.46088e8i	−0.220834	−	0.0803770i
$755$	9.73804e9			0.823488
$756$	−7.27643e9	+	5.39694e8i	−0.612480	+	0.0454278i
$757$	7.43587e9			0.623012			0.311506	−	0.950244i	$-0.399167\pi$
$757$	7.43587e9			0.623012			0.311506	+	0.950244i	$0.399167\pi$
$758$	2.69136e10	+	9.79574e9i	2.24455	+	0.816949i
$759$	3.15110e9	−	5.78287e9i	0.261587	−	0.480062i
$760$	2.96416e9	+	2.48723e9i	0.244937	+	0.205527i
$761$	−2.22643e9	+	1.26267e10i	−0.183132	+	1.03859i	0.745201	+	0.666840i	$0.232354\pi$
$761$	−2.22643e9	+	1.26267e10i	−0.183132	+	1.03859i	−0.928333	+	0.371751i	$0.878758\pi$
$762$	−1.22673e9	−	6.07625e9i	−0.100440	−	0.497500i
$763$	5.67072e9	−	4.75830e9i	0.462171	−	0.387807i
$764$	−5.15518e9	−	8.92904e9i	−0.418232	−	0.724399i
$765$	−4.79404e9	−	3.63520e9i	−0.387157	−	0.293571i
$766$	8.97094e8	−	1.55381e9i	0.0721170	−	0.124910i
$767$	4.39383e8	+	2.49186e9i	0.0351608	+	0.199407i
$768$	6.34455e9	−	2.48819e9i	0.505402	−	0.198207i
$769$	1.82759e10	−	6.65187e9i	1.44922	−	0.527474i	0.506850	−	0.862034i	$-0.330810\pi$
$769$	1.82759e10	−	6.65187e9i	1.44922	−	0.527474i	0.942374	+	0.334560i	$0.108588\pi$
$770$	−3.56855e9	+	1.29885e9i	−0.281692	+	0.102527i
$771$	−1.26883e10	+	4.97605e9i	−0.997040	+	0.391016i
$772$	−5.08469e9	−	2.88367e10i	−0.397744	−	2.25572i
$773$	−6.09554e9	+	1.05578e10i	−0.474662	+	0.822138i	−0.999579	−	0.0290152i	$-0.990763\pi$
$773$	−6.09554e9	+	1.05578e10i	−0.474662	+	0.822138i	0.524917	+	0.851153i	$0.324096\pi$
$774$	−3.06967e9	+	2.43946e10i	−0.237957	+	1.89104i
$775$	−1.00889e10	−	1.74746e10i	−0.778556	−	1.34850i
$776$	−7.27338e8	+	6.10309e8i	−0.0558753	+	0.0468850i
$777$	−6.08681e8	−	3.01493e9i	−0.0465496	−	0.230570i
$778$	−2.46322e9	+	1.39696e10i	−0.187532	+	1.06355i
$779$	−1.03379e10	−	8.67457e9i	−0.783526	−	0.657456i
$780$	−5.23807e8	+	9.61288e8i	−0.0395221	+	0.0725308i
$781$	−3.73599e9	−	1.35979e9i	−0.280626	−	0.102139i
$782$	−1.21465e10			−0.908299
$783$	−1.53409e10	−	4.32892e9i	−1.14205	−	0.322265i
$784$	2.92083e9			0.216471
$785$	−4.82534e9	−	1.75628e9i	−0.356028	−	0.129583i
$786$	−4.10341e9	−	6.71878e9i	−0.301416	−	0.493528i
$787$	−1.53527e10	−	1.28824e10i	−1.12272	−	0.942077i	−0.123985	−	0.992284i	$-0.539567\pi$
$787$	−1.53527e10	−	1.28824e10i	−1.12272	−	0.942077i	−0.998739	+	0.0502071i	$0.984012\pi$
$788$	−6.56617e9	+	3.72386e10i	−0.478047	+	2.71114i
$789$	1.67062e10	−	1.47357e10i	1.21090	−	1.06807i
$790$	1.15245e9	−	9.67022e8i	0.0831626	−	0.0697817i
$791$	2.59804e9	+	4.49994e9i	0.186650	+	0.323288i
$792$	8.39842e9	−	7.78463e9i	0.600703	−	0.556801i
$793$	−6.49179e8	+	1.12441e9i	−0.0462283	+	0.0800698i
$794$	6.34393e9	+	3.59782e10i	0.449766	+	2.55075i
$795$	−1.78406e9	+	1.18160e10i	−0.125929	+	0.834039i
$796$	2.05577e10	−	7.48239e9i	1.44470	−	0.525829i
$797$	−1.83070e10	+	6.66322e9i	−1.28090	+	0.466208i	−0.890729	−	0.454535i	$-0.849805\pi$
$797$	−1.83070e10	+	6.66322e9i	−1.28090	+	0.466208i	−0.390168	+	0.920744i	$0.627583\pi$
$798$	6.76057e9	+	5.39420e9i	0.470948	+	0.375765i
$799$	−3.97365e8	−	2.25357e9i	−0.0275598	−	0.156299i
$800$	6.95945e9	−	1.20541e10i	0.480574	−	0.832378i
$801$	−3.25763e9	−	5.04944e9i	−0.223969	−	0.347160i
$802$	5.09076e9	+	8.81746e9i	0.348476	+	0.603578i
$803$	1.08317e10	−	9.08890e9i	0.738233	−	0.619451i
$804$	−2.21458e10	−	7.44688e9i	−1.50278	−	0.505334i
$805$	2.42759e8	−	1.37676e9i	0.0164017	−	0.0930189i
$806$	−4.35809e9	−	3.65687e9i	−0.293172	−	0.246001i
$807$	2.24514e10	−	5.54172e8i	1.50378	−	0.0371183i
$808$	9.97982e9	+	3.63236e9i	0.665554	+	0.242242i
$809$	−2.29327e10			−1.52278			−0.761388	−	0.648297i	$-0.775482\pi$
$809$	−2.29327e10			−1.52278			−0.761388	+	0.648297i	$0.775482\pi$
$810$	−4.34009e9	+	9.59251e9i	−0.286947	+	0.634212i
$811$	2.46948e10			1.62567			0.812835	−	0.582495i	$-0.197923\pi$
$811$	2.46948e10			1.62567			0.812835	+	0.582495i	$0.197923\pi$
$812$	1.04481e10	+	3.80278e9i	0.684841	+	0.249262i
$813$	1.82531e10	−	4.50546e8i	1.19130	−	0.0294051i
$814$	1.11719e10	+	9.37433e9i	0.726008	+	0.609193i
$815$	−7.03890e8	+	3.99196e9i	−0.0455463	+	0.258306i
$816$	4.22397e9	+	1.42038e9i	0.272148	+	0.0915142i
$817$	1.33768e10	−	1.12244e10i	0.858172	−	0.720091i
$818$	4.52116e9	+	7.83088e9i	0.288811	+	0.500235i
$819$	−3.69866e8	+	7.20545e8i	−0.0235262	+	0.0458319i
$820$	−5.72964e9	+	9.92403e9i	−0.362893	+	0.628550i
$821$	1.54601e9	+	8.76785e9i	0.0975013	+	0.552958i	0.993952	+	0.109814i	$0.0350256\pi$
$821$	1.54601e9	+	8.76785e9i	0.0975013	+	0.552958i	−0.896451	+	0.443143i	$0.853863\pi$
$822$	2.34532e10	+	1.87131e10i	1.47282	+	1.17515i
$823$	−2.13900e10	+	7.78532e9i	−1.33755	+	0.486829i	−0.909041	−	0.416707i	$-0.863184\pi$
$823$	−2.13900e10	+	7.78532e9i	−1.33755	+	0.486829i	−0.428512	+	0.903536i	$0.640962\pi$
$824$	2.29847e9	−	8.36576e8i	0.143118	−	0.0520907i
$825$	2.03351e9	−	1.34681e10i	0.126083	−	0.835062i
$826$	−2.94761e9	−	1.67167e10i	−0.181987	−	1.03210i
$827$	1.91120e9	−	3.31030e9i	0.117500	−	0.203516i	−0.801276	−	0.598294i	$-0.795845\pi$
$827$	1.91120e9	−	3.31030e9i	0.117500	−	0.203516i	0.918776	+	0.394779i	$0.129179\pi$
$828$	2.82767e9	+	1.24180e10i	0.173110	+	0.760233i
$829$	1.54318e9	+	2.67286e9i	0.0940751	+	0.162943i	0.909222	−	0.416311i	$-0.136677\pi$
$829$	1.54318e9	+	2.67286e9i	0.0940751	+	0.162943i	−0.815147	+	0.579254i	$0.803344\pi$
$830$	−2.63780e9	+	2.21338e9i	−0.160129	+	0.134364i
$831$	−6.66015e9	+	5.87460e9i	−0.402606	+	0.355120i
$832$	5.87262e8	−	3.33053e9i	0.0353509	−	0.200485i
$833$	−1.17104e10	−	9.82618e9i	−0.701962	−	0.589016i
$834$	−9.59418e9	−	1.57092e10i	−0.572699	−	0.937718i
$835$	−1.62761e9	−	5.92403e8i	−0.0967495	−	0.0352139i
$836$	−2.45710e10			−1.45446
$837$	−2.66031e10	−	1.91572e10i	−1.56817	−	1.12926i
$838$	−3.16001e10			−1.85496
$839$	1.58611e10	+	5.77298e9i	0.927186	+	0.337468i	0.761094	−	0.648642i	$-0.224663\pi$
$839$	1.58611e10	+	5.77298e9i	0.927186	+	0.337468i	0.166093	+	0.986110i	$0.446885\pi$
$840$	1.16312e9	−	2.13455e9i	0.0677092	−	0.124260i
$841$	5.39303e9	+	4.52529e9i	0.312642	+	0.262338i
$842$	6.26279e7	−	3.55180e8i	0.00361556	−	0.0205048i
$843$	−3.31386e8	−	1.64143e9i	−0.0190518	−	0.0943680i
$844$	3.33580e10	−	2.79907e10i	1.90986	−	1.60256i
$845$	−3.80406e9	−	6.58882e9i	−0.216894	−	0.375672i
$846$	−3.69088e9	+	1.55362e9i	−0.209572	+	0.0882162i
$847$	3.57918e8	−	6.19932e8i	0.0202391	−	0.0350551i
$848$	−1.53702e9	−	8.71689e9i	−0.0865555	−	0.490881i
$849$	−9.62940e9	+	3.77643e9i	−0.540036	+	0.211789i
$850$	−2.36070e10	+	8.59225e9i	−1.31848	+	0.479889i
$851$	−5.04497e9	+	1.83622e9i	−0.280611	+	0.102134i
$852$	7.15789e9	−	2.80716e9i	0.396503	−	0.155499i
$853$	4.41684e9	+	2.50491e10i	0.243663	+	1.38188i	0.823577	+	0.567205i	$0.191975\pi$
$853$	4.41684e9	+	2.50491e10i	0.243663	+	1.38188i	−0.579914	+	0.814678i	$0.696914\pi$
$854$	4.35503e9	−	7.54313e9i	0.239270	−	0.414428i
$855$	6.89197e9	−	2.90107e9i	0.377105	−	0.158736i
$856$	1.01986e10	+	1.76645e10i	0.555755	+	0.962596i
$857$	1.98036e10	−	1.66172e10i	1.07476	−	0.901832i	0.0792865	−	0.996852i	$-0.474736\pi$
$857$	1.98036e10	−	1.66172e10i	1.07476	−	0.901832i	0.995475	+	0.0950196i	$0.0302914\pi$
$858$	−7.59986e8	−	3.76438e9i	−0.0410771	−	0.203464i
$859$	−2.71250e9	+	1.53834e10i	−0.146014	+	0.828086i	0.820534	+	0.571598i	$0.193676\pi$
$859$	−2.71250e9	+	1.53834e10i	−0.146014	+	0.828086i	−0.966547	+	0.256488i	$0.917435\pi$
$860$	−1.13587e10	−	9.53108e9i	−0.608953	−	0.510973i
$861$	−4.05656e9	+	7.44457e9i	−0.216594	+	0.397492i
$862$	−2.36333e10	−	8.60180e9i	−1.25675	−	0.457419i
$863$	−1.60919e10			−0.852254			−0.426127	−	0.904663i	$-0.640122\pi$
$863$	−1.60919e10			−0.852254			−0.426127	+	0.904663i	$0.640122\pi$
$864$	2.26885e9	−	2.24999e10i	0.119676	−	1.18682i
$865$	1.18984e10			0.625077
$866$	3.97709e10	+	1.44754e10i	2.08091	+	0.757388i
$867$	−2.15466e9	−	3.52797e9i	−0.112283	−	0.183848i
$868$	1.75172e10	+	1.46987e10i	0.909174	+	0.762887i
$869$	−5.49088e8	+	3.11403e9i	−0.0283839	+	0.160973i
$870$	1.20322e10	−	1.06130e10i	0.619481	−	0.546415i
$871$	−1.98676e9	+	1.66709e9i	−0.101878	+	0.0854861i
$872$	−1.12340e10	−	1.94578e10i	−0.573753	−	0.993770i
$873$	4.07379e8	+	1.78905e9i	0.0207228	+	0.0910066i
$874$	7.54830e9	−	1.30740e10i	0.382436	−	0.662399i
$875$	−1.12520e9	−	6.38133e9i	−0.0567809	−	0.322020i
$876$	−4.08242e9	+	2.70383e10i	−0.205189	+	1.35899i
$877$	−2.86920e9	+	1.04430e9i	−0.143636	+	0.0522791i	−0.412838	−	0.910805i	$-0.635462\pi$
$877$	−2.86920e9	+	1.04430e9i	−0.143636	+	0.0522791i	0.269202	+	0.963084i	$0.413240\pi$
$878$	2.19461e10	−	7.98772e9i	1.09427	−	0.398283i
$879$	−8.33381e9	−	6.64947e9i	−0.413888	−	0.330237i
$880$	−4.22306e8	−	2.39502e9i	−0.0208900	−	0.118473i
$881$	6.44146e9	−	1.11569e10i	0.317372	−	0.549704i	−0.662567	−	0.749003i	$-0.730533\pi$
$881$	6.44146e9	−	1.11569e10i	0.317372	−	0.549704i	0.979939	+	0.199298i	$0.0638663\pi$
$882$	−1.22165e10	+	2.37993e10i	−0.599526	+	1.16795i
$883$	4.88974e9	+	8.46928e9i	0.239014	+	0.413984i	0.960432	−	0.278516i	$-0.0898425\pi$
$883$	4.88974e9	+	8.46928e9i	0.239014	+	0.413984i	−0.721418	+	0.692500i	$0.756509\pi$
$884$	−3.25101e9	+	2.72792e9i	−0.158284	+	0.132816i
$885$	−1.39106e10	−	4.67765e9i	−0.674595	−	0.226843i
$886$	3.80300e7	−	2.15679e8i	0.00183700	−	0.0104181i
$887$	6.77952e9	+	5.68869e9i	0.326187	+	0.273703i	0.791144	−	0.611630i	$-0.209486\pi$
$887$	6.77952e9	+	5.68869e9i	0.326187	+	0.273703i	−0.464957	+	0.885333i	$0.653930\pi$
$888$	−9.33251e9	+	2.30357e8i	−0.447253	+	0.0110396i
$889$	2.59899e9	+	9.45955e8i	0.124065	+	0.0451559i
$890$	6.04831e9			0.287587
$891$	−5.97188e9	−	2.13087e10i	−0.282839	−	1.00922i
$892$	−5.61858e10			−2.65063
$893$	2.67258e9	+	9.72741e8i	0.125589	+	0.0457106i
$894$	−3.96876e10	+	9.79619e8i	−1.85769	+	0.0458539i
$895$	9.11725e9	+	7.65028e9i	0.425092	+	0.356695i
$896$	−2.10718e9	+	1.19504e10i	−0.0978642	+	0.555015i
$897$	1.34000e9	+	4.50597e8i	0.0619915	+	0.0208456i
$898$	4.65188e10	−	3.90339e10i	2.14369	−	1.79877i
$899$	2.49781e10	+	4.32633e10i	1.14657	+	1.98592i
$900$	1.42799e10	+	2.21344e10i	0.652946	+	1.01209i
$901$	−2.31628e10	+	4.01192e10i	−1.05501	+	1.82732i
$902$	−6.98050e9	−	3.95884e10i	−0.316712	−	1.79616i
$903$	−8.57507e9	−	6.84197e9i	−0.387552	−	0.309224i
$904$	1.48197e10	−	5.39395e9i	0.667193	−	0.242838i
$905$	1.25275e9	−	4.55964e8i	0.0561817	−	0.0204485i
$906$	9.86289e9	−	6.53230e10i	0.440611	−	2.91822i
$907$	2.33954e9	+	1.32682e10i	0.104113	+	0.590453i	0.991571	+	0.129565i	$0.0413580\pi$
$907$	2.33954e9	+	1.32682e10i	0.104113	+	0.590453i	−0.887458	+	0.460888i	$0.847531\pi$
$908$	1.70894e9	−	2.95996e9i	0.0757575	−	0.131216i
$909$	1.50520e10	−	1.39520e10i	0.664693	−	0.616114i
$910$	−4.07609e8	−	7.06000e8i	−0.0179308	−	0.0310570i
$911$	3.77047e9	−	3.16380e9i	0.165227	−	0.138642i	−0.556425	−	0.830898i	$-0.687827\pi$
$911$	3.77047e9	−	3.16380e9i	0.165227	−	0.138642i	0.721652	+	0.692256i	$0.243383\pi$
$912$	−4.15377e9	+	3.66384e9i	−0.181326	+	0.159939i
$913$	1.25678e9	−	7.12758e9i	0.0546529	−	0.309952i
$914$	−3.42854e10	−	2.87689e10i	−1.48524	−	1.24627i
$915$	−3.92507e9	−	6.42677e9i	−0.169384	−	0.277344i
$916$	−3.30914e10	−	1.20443e10i	−1.42260	−	0.517783i
$917$	3.51264e9			0.150432
$918$	−2.92405e10	+	2.84767e10i	−1.24748	+	1.21490i
$919$	−1.86619e10			−0.793143			−0.396571	−	0.918004i	$-0.629800\pi$
$919$	−1.86619e10			−0.793143			−0.396571	+	0.918004i	$0.629800\pi$
$920$	−3.98722e9	−	1.45123e9i	−0.168816	−	0.0614438i
$921$	−6.95809e9	+	1.27694e10i	−0.293482	+	0.538596i
$922$	−4.20015e10	−	3.52435e10i	−1.76485	−	1.48088i
$923$	1.48204e8	−	8.40505e8i	0.00620373	−	0.0351831i
$924$	3.05475e9	+	1.51308e10i	0.127387	+	0.630974i
$925$	−8.50607e9	+	7.13744e9i	−0.353373	+	0.296515i
$926$	−3.72347e9	−	6.44925e9i	−0.154103	−	0.266913i
$927$	5.90146e8	−	4.68986e9i	0.0243321	−	0.193366i
$928$	−1.72301e10	+	2.98435e10i	−0.707735	+	1.22583i
$929$	5.74992e9	+	3.26094e10i	0.235292	+	1.33441i	0.841998	+	0.539480i	$0.181379\pi$
$929$	5.74992e9	+	3.26094e10i	0.235292	+	1.33441i	−0.606707	+	0.794926i	$0.707510\pi$
$930$	3.07192e10	−	1.20474e10i	1.25233	−	0.491135i
$931$	1.78538e10	−	6.49824e9i	0.725113	−	0.263920i
$932$	1.54028e10	−	5.60615e9i	0.623222	−	0.226834i
$933$	2.78705e8	−	1.09302e8i	0.0112346	−	0.00440596i
$934$	1.05224e9	+	5.96757e9i	0.0422574	+	0.239653i
$935$	−6.36412e9	+	1.10230e10i	−0.254623	+	0.441020i
$936$	1.95879e9	+	1.48530e9i	0.0780770	+	0.0592037i
$937$	−8.48375e9	−	1.46943e10i	−0.336899	−	0.583526i	0.646949	−	0.762533i	$-0.276045\pi$
$937$	−8.48375e9	−	1.46943e10i	−0.336899	−	0.583526i	−0.983848	+	0.179008i	$0.942711\pi$
$938$	1.33282e10	−	1.11837e10i	0.527305	−	0.442462i
$939$	5.61608e9	+	2.78177e10i	0.221362	+	1.09646i
$940$	4.19366e8	−	2.37834e9i	0.0164682	−	0.0933957i
$941$	1.46757e10	+	1.23144e10i	0.574163	+	0.481780i	0.883025	−	0.469327i	$-0.155503\pi$
$941$	1.46757e10	+	1.23144e10i	0.574163	+	0.481780i	−0.308861	+	0.951107i	$0.599948\pi$
$942$	−1.66684e10	+	3.05897e10i	−0.649703	+	1.19233i
$943$	1.39060e10	+	5.06137e9i	0.540021	+	0.196552i
$944$	1.08705e10			0.420580
$945$	−2.64331e9	−	3.88341e9i	−0.101891	−	0.149693i
$946$	5.20156e10			1.99763
$947$	−1.44414e10	−	5.25622e9i	−0.552565	−	0.201117i	0.0506210	−	0.998718i	$-0.483880\pi$
$947$	−1.44414e10	−	5.25622e9i	−0.552565	−	0.201117i	−0.603186	+	0.797601i	$0.706102\pi$
$948$	−3.18728e9	−	5.21875e9i	−0.121504	−	0.198947i
$949$	2.32523e9	+	1.95110e9i	0.0883150	+	0.0741051i
$950$	5.42191e9	−	3.07492e10i	0.205173	−	1.16359i
$951$	7.46360e7	−	6.58328e7i	0.00281395	−	0.00248205i
$952$	7.21893e9	−	6.05740e9i	0.271171	−	0.227540i
$953$	−6.19572e9	−	1.07313e10i	−0.231882	−	0.401631i	0.726480	−	0.687187i	$-0.241155\pi$
$953$	−6.19572e9	−	1.07313e10i	−0.231882	−	0.401631i	−0.958362	+	0.285557i	$0.907822\pi$
$954$	7.74552e10	+	2.39350e10i	2.88823	+	0.892513i
$955$	3.31907e9	−	5.74879e9i	0.123312	−	0.213582i
$956$	1.08389e8	+	6.14707e8i	0.00401222	+	0.0227544i
$957$	−5.03454e9	+	3.33443e10i	−0.185681	+	1.22979i
$958$	−3.85940e10	+	1.40471e10i	−1.41821	+	0.516186i
$959$	−1.25797e10	+	4.57864e9i	−0.460580	+	0.167638i
$960$	1.53327e10	+	1.22339e10i	0.559333	+	0.446287i
$961$	1.30636e10	+	7.40873e10i	0.474822	+	2.69285i
$962$	−1.56535e9	+	2.71126e9i	−0.0566890	+	0.0981882i
$963$	3.93695e10	−	1.94472e9i	1.42059	−	0.0701722i
$964$	1.06269e10	+	1.84063e10i	0.382063	+	0.661753i
$965$	1.44418e10	−	1.21181e10i	0.517338	−	0.434098i
$966$	−8.98943e9	−	3.02284e9i	−0.320858	−	0.107893i
$967$	5.80149e9	−	3.29019e10i	0.206323	−	1.17011i	−0.689022	−	0.724741i	$-0.741960\pi$
$967$	5.80149e9	−	3.29019e10i	0.206323	−	1.17011i	0.895345	−	0.445374i	$-0.146929\pi$
$968$	−1.66435e9	−	1.39656e9i	−0.0589769	−	0.0494875i
$969$	2.89794e10	−	7.15305e8i	1.02319	−	0.0252556i
$970$	−1.73545e9	−	6.31653e8i	−0.0610536	−	0.0222217i
$971$	2.73014e10			0.957014			0.478507	−	0.878084i	$-0.341178\pi$
$971$	2.73014e10			0.957014			0.478507	+	0.878084i	$0.341178\pi$
$972$	3.59203e10	+	2.32648e10i	1.25461	+	0.812581i
$973$	8.21291e9			0.285826
$974$	−3.39604e10	−	1.23606e10i	−1.17765	−	0.428629i
$975$	2.92306e9	−	7.21507e7i	0.101000	−	0.00249301i
$976$	4.27293e9	+	3.58542e9i	0.147113	+	0.123443i
$977$	−1.64451e9	+	9.32648e9i	−0.0564164	+	0.319953i	−0.999935	−	0.0113650i	$-0.996382\pi$
$977$	−1.64451e9	+	9.32648e9i	−0.0564164	+	0.319953i	0.943519	+	0.331318i	$0.107493\pi$
$978$	2.60652e10	+	8.76485e9i	0.890995	+	0.299611i
$979$	−9.73847e9	+	8.17155e9i	−0.331704	+	0.278333i
$980$	−8.06662e9	−	1.39718e10i	−0.273779	−	0.474199i
$981$	−4.33662e10	+	2.14214e9i	−1.46659	+	0.0724447i
$982$	1.59090e10	−	2.75551e10i	0.536107	−	0.928565i
$983$	−3.97074e9	−	2.25192e10i	−0.133332	−	0.756163i	−0.976007	−	0.217740i	$-0.930132\pi$
$983$	−3.97074e9	−	2.25192e10i	−0.133332	−	0.756163i	0.842675	−	0.538423i	$-0.180980\pi$
$984$	2.01140e10	+	1.60488e10i	0.673002	+	0.536982i
$985$	−2.28770e10	+	8.32655e9i	−0.762733	+	0.277612i
$986$	5.84460e10	−	2.12726e10i	1.94171	−	0.706726i
$987$	2.66750e8	−	1.76671e9i	0.00883069	−	0.0584866i
$988$	−9.15929e8	−	5.19449e9i	−0.0302143	−	0.171354i
$989$	−9.57421e9	+	1.65830e10i	−0.314714	+	0.545101i
$990$	2.12813e10	+	6.57629e9i	0.697067	+	0.215406i
$991$	−5.60807e9	−	9.71347e9i	−0.183044	−	0.317042i	0.759872	−	0.650073i	$-0.225262\pi$
$991$	−5.60807e9	−	9.71347e9i	−0.183044	−	0.317042i	−0.942916	+	0.333031i	$0.891928\pi$
$992$	−5.42918e10	+	4.55563e10i	−1.76581	+	1.48169i
$993$	4.05939e10	−	3.58059e10i	1.31564	−	1.16047i
$994$	−9.94227e8	+	5.63854e9i	−0.0321095	+	0.182102i
$995$	1.07898e10	+	9.05374e9i	0.347243	+	0.291372i
$996$	7.29524e9	+	1.19450e10i	0.233955	+	0.383070i
$997$	−4.04608e10	−	1.47265e10i	−1.29301	−	0.470617i	−0.398295	−	0.917257i	$-0.630398\pi$
$997$	−4.04608e10	−	1.47265e10i	−1.29301	−	0.470617i	−0.894713	+	0.446641i	$0.852620\pi$
$998$	−3.02852e10			−0.964436
$999$	−7.83991e9	+	1.62479e10i	−0.248789	+	0.515607i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	27.8.e.a.4.18	✓	120
3.2	odd	2		81.8.e.a.64.3		120
27.7	even	9	inner	27.8.e.a.7.18	yes	120
27.20	odd	18		81.8.e.a.19.3		120

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
27.8.e.a.4.18	✓	120	1.1	even	1	trivial
27.8.e.a.7.18	yes	120	27.7	even	9	inner
81.8.e.a.19.3		120	27.20	odd	18
81.8.e.a.64.3		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)

\(f(q)\)	\(=\)	\(q+(16.7921 + 6.11184i) q^{2} +(46.7511 - 1.15397i) q^{3} +(146.567 + 122.985i) q^{4} +(-21.3907 + 121.313i) q^{5} +(792.104 + 266.358i) q^{6} +(-285.632 + 239.674i) q^{7} +(565.850 + 980.080i) q^{8} +(2184.34 - 107.899i) q^{9} +O(q^{10})\)	\(q+(16.7921 + 6.11184i) q^{2} +(46.7511 - 1.15397i) q^{3} +(146.567 + 122.985i) q^{4} +(-21.3907 + 121.313i) q^{5} +(792.104 + 266.358i) q^{6} +(-285.632 + 239.674i) q^{7} +(565.850 + 980.080i) q^{8} +(2184.34 - 107.899i) q^{9} +(-1100.64 + 1906.36i) q^{10} +(-803.430 - 4556.48i) q^{11} +(6994.12 + 5580.54i) q^{12} +(933.323 - 339.702i) q^{13} +(-6261.21 + 2278.89i) q^{14} +(-860.050 + 5696.20i) q^{15} +(-740.959 - 4202.19i) q^{16} +(-11166.2 + 19340.4i) q^{17} +(37339.1 + 11538.5i) q^{18} +(-13878.2 - 24037.7i) q^{19} +(-18054.8 + 15149.8i) q^{20} +(-13077.0 + 11534.6i) q^{21} +(14357.1 - 81423.4i) q^{22} +(23315.9 + 19564.3i) q^{23} +(27585.1 + 45166.9i) q^{24} +(59154.2 + 21530.4i) q^{25} +17748.7 q^{26} +(101996. - 7565.05i) q^{27} -71340.5 q^{28} +(-146453. - 53304.7i) q^{29} +(-49256.3 + 90394.8i) q^{30} +(-245544. - 206036. i) q^{31} +(38395.0 - 217749. i) q^{32} +(-42819.3 - 212093. i) q^{33} +(-305710. + 256521. i) q^{34} +(-22965.6 - 39777.6i) q^{35} +(333423. + 252826. i) q^{36} +(-88195.2 + 152759. i) q^{37} +(-86129.5 - 488465. i) q^{38} +(43241.9 - 16958.5i) q^{39} +(-131000. + 47680.2i) q^{40} +(456882. - 166292. i) q^{41} +(-290089. + 113766. i) q^{42} +(109246. + 619565. i) q^{43} +(442620. - 766641. i) q^{44} +(-33635.0 + 267296. i) q^{45} +(271949. + 471029. i) q^{46} +(-78494.2 + 65864.5i) q^{47} +(-39489.9 - 195602. i) q^{48} +(-118865. + 674115. i) q^{49} +(861736. + 723082. i) q^{50} +(-499714. + 917072. i) q^{51} +(178573. + 64995.2i) q^{52} +2.07437e6 q^{53} +(1.75896e6 + 496348. i) q^{54} +569945. q^{55} +(-396524. - 144323. i) q^{56} +(-676558. - 1.10777e6i) q^{57} +(-2.13347e6 - 1.79020e6i) q^{58} +(-442381. + 2.50887e6i) q^{59} +(-826600. + 729104. i) q^{60} +(-1.00139e6 + 840264. i) q^{61} +(-2.86395e6 - 4.96051e6i) q^{62} +(-598056. + 554347. i) q^{63} +(1.70249e6 - 2.94880e6i) q^{64} +(21245.7 + 120491. i) q^{65} +(577253. - 3.82320e6i) q^{66} +(-2.45376e6 + 893094. i) q^{67} +(-4.01517e6 + 1.46140e6i) q^{68} +(1.11262e6 + 887749. i) q^{69} +(-142527. - 808313. i) q^{70} +(429648. - 744172. i) q^{71} +(1.34176e6 + 2.07977e6i) q^{72} +(1.52805e6 + 2.64665e6i) q^{73} +(-2.41462e6 + 2.02611e6i) q^{74} +(2.79037e6 + 938308. i) q^{75} +(922180. - 5.22994e6i) q^{76} +(1.32155e6 + 1.10891e6i) q^{77} +(829771. - 20481.4i) q^{78} +(-642214. - 233747. i) q^{79} +525629. q^{80} +(4.75968e6 - 471375. i) q^{81} +8.68838e6 q^{82} +(1.46994e6 + 535013. i) q^{83} +(-3.33525e6 + 82324.8i) q^{84} +(-2.10739e6 - 1.76831e6i) q^{85} +(-1.95221e6 + 1.10715e7i) q^{86} +(-6.90837e6 - 2.32305e6i) q^{87} +(4.01109e6 - 3.36571e6i) q^{88} +(-1.37382e6 - 2.37952e6i) q^{89} +(-2.19847e6 + 4.28290e6i) q^{90} +(-185169. + 320722. i) q^{91} +(1.01123e6 + 5.73499e6i) q^{92} +(-1.17172e7 - 9.34907e6i) q^{93} +(-1.72064e6 + 626261. i) q^{94} +(3.21294e6 - 1.16942e6i) q^{95} +(1.54374e6 - 1.02243e7i) q^{96} +(145687. + 826233. i) q^{97} +(-6.11607e6 + 1.05933e7i) q^{98} +(-2.24660e6 - 9.86619e6i) 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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