LMFDB - Embedded newform 43.8.g.a.24.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [43,8,Mod(9,43)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(43, base_ring=CyclotomicField(42))

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("43.9");

S:= CuspForms(chi, 8);

N := Newforms(S);

Level:	$ N $	$=$	$ 43 $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	43.g (of order $21$, degree $12$, 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:	$13.4325560958$
Analytic rank:	$0$
Dimension:	$300$
Relative dimension:	$25$ over $\Q(\zeta_{21})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{21}]$

Embedding invariants

Embedding label			24.8
Character	$\chi$	$=$	43.24
Dual form			43.8.g.a.9.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-6.35832 + 7.97308i) q^{2} +(-51.9023 + 7.82301i) q^{3} +(5.34089 + 23.4000i) q^{4} +(-119.077 + 81.1857i) q^{5} +(267.638 - 463.562i) q^{6} +(-639.426 - 1107.52i) q^{7} +(-1396.60 - 672.566i) q^{8} +(542.807 - 167.434i) q^{9} +O(q^{10})$	\(q+(-6.35832 + 7.97308i) q^{2} +(-51.9023 + 7.82301i) q^{3} +(5.34089 + 23.4000i) q^{4} +(-119.077 + 81.1857i) q^{5} +(267.638 - 463.562i) q^{6} +(-639.426 - 1107.52i) q^{7} +(-1396.60 - 672.566i) q^{8} +(542.807 - 167.434i) q^{9} +(109.833 - 1465.62i) q^{10} +(-1897.71 + 8314.43i) q^{11} +(-460.263 - 1172.73i) q^{12} +(-777.239 - 10371.5i) q^{13} +(12896.0 + 1943.76i) q^{14} +(5545.27 - 5145.26i) q^{15} +(11474.5 - 5525.81i) q^{16} +(13557.1 + 9243.06i) q^{17} +(-2116.38 + 5392.44i) q^{18} +(15757.4 + 4860.50i) q^{19} +(-2535.72 - 2352.81i) q^{20} +(41851.8 + 52480.5i) q^{21} +(-54225.3 - 67996.4i) q^{22} +(34949.4 + 32428.3i) q^{23} +(77748.1 + 23982.1i) q^{24} +(-20953.9 + 53389.7i) q^{25} +(87635.0 + 59748.5i) q^{26} +(76561.3 - 36870.0i) q^{27} +(22500.8 - 20877.7i) q^{28} +(-197489. - 29766.6i) q^{29} +(5764.97 + 76928.1i) q^{30} +(25635.1 + 65317.2i) q^{31} +(15250.6 - 66817.4i) q^{32} +(33451.8 - 446383. i) q^{33} +(-159896. + 49321.3i) q^{34} +(166056. + 79968.3i) q^{35} +(6817.02 + 11807.4i) q^{36} +(-11693.9 + 20254.5i) q^{37} +(-138944. + 94730.1i) q^{38} +(121477. + 532225. i) q^{39} +(220906. - 33296.2i) q^{40} +(343566. - 430818. i) q^{41} -684538. q^{42} +(-31124.4 - 520432. i) q^{43} -204693. q^{44} +(-51042.9 + 64005.7i) q^{45} +(-480773. + 72464.9i) q^{46} +(-243658. - 1.06754e6i) q^{47} +(-552322. + 376567. i) q^{48} +(-405961. + 703144. i) q^{49} +(-292449. - 506536. i) q^{50} +(-775951. - 373678. i) q^{51} +(238542. - 73580.6i) q^{52} +(-134712. + 1.79761e6i) q^{53} +(-192834. + 844860. i) q^{54} +(-449037. - 1.14413e6i) q^{55} +(148142. + 1.97682e6i) q^{56} +(-855866. - 129001. i) q^{57} +(1.49303e6 - 1.38533e6i) q^{58} +(1.93800e6 - 933290. i) q^{59} +(150016. + 102279. i) q^{60} +(267187. - 680781. i) q^{61} +(-683775. - 210917. i) q^{62} +(-532521. - 494107. i) q^{63} +(1.45217e6 + 1.82096e6i) q^{64} +(934571. + 1.17192e6i) q^{65} +(3.34635e6 + 3.10496e6i) q^{66} +(-1.30943e6 - 403905. i) q^{67} +(-143880. + 366601. i) q^{68} +(-2.06764e6 - 1.40969e6i) q^{69} +(-1.69343e6 + 815513. i) q^{70} +(3.76758e6 - 3.49581e6i) q^{71} +(-870693. - 131236. i) q^{72} +(17935.0 + 239326. i) q^{73} +(-87136.9 - 222021. i) q^{74} +(669888. - 2.93497e6i) q^{75} +(-29577.3 + 394681. i) q^{76} +(1.04218e7 - 3.21471e6i) q^{77} +(-5.01586e6 - 2.41551e6i) q^{78} +(-1.48443e6 - 2.57110e6i) q^{79} +(-917734. + 1.58956e6i) q^{80} +(-4.71171e6 + 3.21239e6i) q^{81} +(1.25044e6 + 5.47856e6i) q^{82} +(-4.42373e6 + 666770. i) q^{83} +(-1.00452e6 + 1.25962e6i) q^{84} -2.36475e6 q^{85} +(4.34735e6 + 3.06092e6i) q^{86} +1.04830e7 q^{87} +(8.24235e6 - 1.03356e7i) q^{88} +(121197. - 18267.5i) q^{89} +(-185776. - 813938. i) q^{90} +(-1.09897e7 + 7.49263e6i) q^{91} +(-572161. + 991011. i) q^{92} +(-1.84150e6 - 3.18957e6i) q^{93} +(1.00608e7 + 4.84503e6i) q^{94} +(-2.27095e6 + 700496. i) q^{95} +(-268829. + 3.58728e6i) q^{96} +(1.41501e6 - 6.19956e6i) q^{97} +(-3.02500e6 - 7.70757e6i) q^{98} +(362024. + 4.83087e6i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 300 q - 40 q^{2} - 12 q^{3} - 3028 q^{4} + 235 q^{5} + 1274 q^{6} - 4122 q^{7} + 762 q^{8} + 8097 q^{9}+O(q^{10}) $ 300 * q - 40 * q^2 - 12 * q^3 - 3028 * q^4 + 235 * q^5 + 1274 * q^6 - 4122 * q^7 + 762 * q^8 + 8097 * q^9	\( 300 q - 40 q^{2} - 12 q^{3} - 3028 q^{4} + 235 q^{5} + 1274 q^{6} - 4122 q^{7} + 762 q^{8} + 8097 q^{9} - 1681 q^{10} + 4580 q^{11} + 9330 q^{12} - 20444 q^{13} - 45798 q^{14} + 50477 q^{15} - 74504 q^{16} - 25312 q^{17} + 2046 q^{18} + 4046 q^{19} + 140781 q^{20} + 100555 q^{21} + 95810 q^{22} + 1648 q^{23} - 292592 q^{24} + 419068 q^{25} + 393435 q^{26} + 274140 q^{27} + 233644 q^{28} + 605697 q^{29} - 1216016 q^{30} + 358580 q^{31} - 19194 q^{32} + 1280291 q^{33} + 1137255 q^{34} + 652739 q^{35} - 8980975 q^{36} - 2360047 q^{37} - 308490 q^{38} + 536339 q^{39} + 3057993 q^{40} - 1376320 q^{41} + 8417790 q^{42} + 7173000 q^{43} - 3856780 q^{44} + 2761486 q^{45} - 7073993 q^{46} + 1437090 q^{47} - 9543469 q^{48} - 16053170 q^{49} - 3046893 q^{50} + 2972901 q^{51} + 17415142 q^{52} + 3320604 q^{53} + 6000486 q^{54} + 13427750 q^{55} - 5450793 q^{56} + 3333100 q^{57} - 7876190 q^{58} - 7084765 q^{59} + 7356443 q^{60} + 3354606 q^{61} - 719427 q^{62} + 14716815 q^{63} - 16086234 q^{64} - 19914646 q^{65} - 8293345 q^{66} + 13025470 q^{67} - 22191927 q^{68} - 33964295 q^{69} + 8094727 q^{70} + 30843495 q^{71} + 93841607 q^{72} - 3067637 q^{73} + 18179570 q^{74} - 41508571 q^{75} - 19751872 q^{76} - 15169179 q^{77} - 69509396 q^{78} - 12090149 q^{79} - 69662530 q^{80} + 3387954 q^{81} + 39226888 q^{82} + 16408777 q^{83} + 98603231 q^{84} - 13423424 q^{85} + 111906660 q^{86} + 49022010 q^{87} + 76213954 q^{88} - 12540205 q^{89} - 92608607 q^{90} - 59091937 q^{91} - 50489370 q^{92} - 52218334 q^{93} - 3441600 q^{94} - 79947551 q^{95} - 23449784 q^{96} - 116467587 q^{97} + 73909552 q^{98} - 20061115 q^{99}+O(q^{100}) \) 300 * q - 40 * q^2 - 12 * q^3 - 3028 * q^4 + 235 * q^5 + 1274 * q^6 - 4122 * q^7 + 762 * q^8 + 8097 * q^9 - 1681 * q^10 + 4580 * q^11 + 9330 * q^12 - 20444 * q^13 - 45798 * q^14 + 50477 * q^15 - 74504 * q^16 - 25312 * q^17 + 2046 * q^18 + 4046 * q^19 + 140781 * q^20 + 100555 * q^21 + 95810 * q^22 + 1648 * q^23 - 292592 * q^24 + 419068 * q^25 + 393435 * q^26 + 274140 * q^27 + 233644 * q^28 + 605697 * q^29 - 1216016 * q^30 + 358580 * q^31 - 19194 * q^32 + 1280291 * q^33 + 1137255 * q^34 + 652739 * q^35 - 8980975 * q^36 - 2360047 * q^37 - 308490 * q^38 + 536339 * q^39 + 3057993 * q^40 - 1376320 * q^41 + 8417790 * q^42 + 7173000 * q^43 - 3856780 * q^44 + 2761486 * q^45 - 7073993 * q^46 + 1437090 * q^47 - 9543469 * q^48 - 16053170 * q^49 - 3046893 * q^50 + 2972901 * q^51 + 17415142 * q^52 + 3320604 * q^53 + 6000486 * q^54 + 13427750 * q^55 - 5450793 * q^56 + 3333100 * q^57 - 7876190 * q^58 - 7084765 * q^59 + 7356443 * q^60 + 3354606 * q^61 - 719427 * q^62 + 14716815 * q^63 - 16086234 * q^64 - 19914646 * q^65 - 8293345 * q^66 + 13025470 * q^67 - 22191927 * q^68 - 33964295 * q^69 + 8094727 * q^70 + 30843495 * q^71 + 93841607 * q^72 - 3067637 * q^73 + 18179570 * q^74 - 41508571 * q^75 - 19751872 * q^76 - 15169179 * q^77 - 69509396 * q^78 - 12090149 * q^79 - 69662530 * q^80 + 3387954 * q^81 + 39226888 * q^82 + 16408777 * q^83 + 98603231 * q^84 - 13423424 * q^85 + 111906660 * q^86 + 49022010 * q^87 + 76213954 * q^88 - 12540205 * q^89 - 92608607 * q^90 - 59091937 * q^91 - 50489370 * q^92 - 52218334 * q^93 - 3441600 * q^94 - 79947551 * q^95 - 23449784 * q^96 - 116467587 * q^97 + 73909552 * q^98 - 20061115 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/43\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{20}{21}\right)$

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 $

$2$	−6.35832	+	7.97308i	−0.562001	+	0.704727i	−0.978926	−	0.204213i	$-0.934536\pi$
$2$	−6.35832	+	7.97308i	−0.562001	+	0.704727i	0.416925	+	0.908941i	$0.363108\pi$
$3$	−51.9023	+	7.82301i	−1.10984	+	0.167282i	−0.678282	−	0.734801i	$-0.737275\pi$
$3$	−51.9023	+	7.82301i	−1.10984	+	0.167282i	−0.431561	+	0.902084i	$0.642037\pi$
$4$	5.34089	+	23.4000i	0.0417257	+	0.182812i
$5$	−119.077	+	81.1857i	−0.426025	+	0.290459i	−0.757290	−	0.653079i	$-0.773477\pi$
$5$	−119.077	+	81.1857i	−0.426025	+	0.290459i	0.331265	+	0.943538i	$0.392525\pi$
$6$	267.638	−	463.562i	0.505845	−	0.876150i
$7$	−639.426	−	1107.52i	−0.704608	−	1.22042i	−0.966833	−	0.255410i	$-0.917790\pi$
$7$	−639.426	−	1107.52i	−0.704608	−	1.22042i	0.262225	−	0.965007i	$-0.415544\pi$
$8$	−1396.60	−	672.566i	−0.964398	−	0.464430i
$9$	542.807	−	167.434i	0.248197	−	0.0765586i
$10$	109.833	−	1465.62i	0.0347322	−	0.463469i
$11$	−1897.71	+	8314.43i	−0.429889	+	1.88347i	0.0372903	+	0.999304i	$0.488127\pi$
$11$	−1897.71	+	8314.43i	−0.429889	+	1.88347i	−0.467179	+	0.884163i	$0.654730\pi$
$12$	−460.263	−	1172.73i	−0.0768903	−	0.195913i
$13$	−777.239	−	10371.5i	−0.0981189	−	1.30931i	−0.801286	−	0.598281i	$-0.795851\pi$
$13$	−777.239	−	10371.5i	−0.0981189	−	1.30931i	0.703167	−	0.711024i	$-0.251768\pi$
$14$	12896.0	+	1943.76i	1.25605	+	0.189319i
$15$	5545.27	−	5145.26i	0.424232	−	0.393630i
$16$	11474.5	−	5525.81i	0.700346	−	0.337269i
$17$	13557.1	+	9243.06i	0.669260	+	0.456294i	0.849682	−	0.527296i	$-0.176794\pi$
$17$	13557.1	+	9243.06i	0.669260	+	0.456294i	−0.180422	+	0.983589i	$0.557746\pi$
$18$	−2116.38	+	5392.44i	−0.0855341	+	0.217937i
$19$	15757.4	+	4860.50i	0.527043	+	0.162571i	0.546847	−	0.837233i	$-0.315828\pi$
$19$	15757.4	+	4860.50i	0.527043	+	0.162571i	−0.0198039	+	0.999804i	$0.506304\pi$
$20$	−2535.72	−	2352.81i	−0.0708756	−	0.0657630i
$21$	41851.8	+	52480.5i	0.986158	+	1.23660i
$22$	−54225.3	−	67996.4i	−1.08573	−	1.36147i
$23$	34949.4	+	32428.3i	0.598952	+	0.555747i	0.920299	−	0.391215i	$-0.127945\pi$
$23$	34949.4	+	32428.3i	0.598952	+	0.555747i	−0.321347	+	0.946962i	$0.604136\pi$
$24$	77748.1	+	23982.1i	1.14802	+	0.354118i
$25$	−20953.9	+	53389.7i	−0.268210	+	0.683389i
$26$	87635.0	+	59748.5i	0.977846	+	0.666684i
$27$	76561.3	−	36870.0i	0.748576	−	0.360495i
$28$	22500.8	−	20877.7i	0.193707	−	0.179734i
$29$	−197489.	−	29766.6i	−1.50366	−	0.226640i	−0.655019	−	0.755612i	$-0.727339\pi$
$29$	−197489.	−	29766.6i	−1.50366	−	0.226640i	−0.848639	+	0.528972i	$0.822578\pi$
$30$	5764.97	+	76928.1i	0.0389828	+	0.520189i
$31$	25635.1	+	65317.2i	0.154550	+	0.393787i	0.987088	−	0.160182i	$-0.0512080\pi$
$31$	25635.1	+	65317.2i	0.154550	+	0.393787i	−0.832537	+	0.553969i	$0.813113\pi$
$32$	15250.6	−	66817.4i	0.0822740	−	0.360466i
$33$	33451.8	−	446383.i	0.162039	−	2.16227i
$34$	−159896.	+	49321.3i	−0.697687	+	0.215208i
$35$	166056.	+	79968.3i	0.654661	+	0.315268i
$36$	6817.02	+	11807.4i	0.0243521	+	0.0421790i
$37$	−11693.9	+	20254.5i	−0.0379538	+	0.0657378i	−0.884378	−	0.466771i	$-0.845417\pi$
$37$	−11693.9	+	20254.5i	−0.0379538	+	0.0657378i	0.846425	+	0.532509i	$0.178751\pi$
$38$	−138944.	+	94730.1i	−0.410767	+	0.280056i
$39$	121477.	+	532225.i	0.327920	+	1.43671i
$40$	220906.	−	33296.2i	0.545755	−	0.0822593i
$41$	343566.	−	430818.i	0.778514	−	0.976226i	−0.221485	−	0.975164i	$-0.571091\pi$
$41$	343566.	−	430818.i	0.778514	−	0.976226i	0.999999	−	0.00106196i	$-0.000338032\pi$
$42$	−684538.			−1.42569
$43$	−31124.4	−	520432.i	−0.0596983	−	0.998216i
$43$	−31124.4	−	520432.i	−0.0596983	−	0.998216i
$44$	−204693.			−0.362259
$45$	−51042.9	+	64005.7i	−0.0835009	+	0.104707i
$46$	−480773.	+	72464.9i	−0.728262	+	0.109768i
$47$	−243658.	−	1.06754e6i	−0.342325	−	1.49982i	−0.794153	−	0.607718i	$-0.792085\pi$
$47$	−243658.	−	1.06754e6i	−0.342325	−	1.49982i	0.451828	−	0.892105i	$-0.350772\pi$
$48$	−552322.	+	376567.i	−0.720855	+	0.491471i
$49$	−405961.	+	703144.i	−0.492944	+	0.853804i
$50$	−292449.	−	506536.i	−0.330868	−	0.573081i
$51$	−775951.	−	373678.i	−0.819103	−	0.394459i
$52$	238542.	−	73580.6i	0.235263	−	0.0725691i
$53$	−134712.	+	1.79761e6i	−0.124292	+	1.65856i	0.491672	+	0.870780i	$0.336386\pi$
$53$	−134712.	+	1.79761e6i	−0.124292	+	1.65856i	−0.615964	+	0.787775i	$0.711233\pi$
$54$	−192834.	+	844860.i	−0.166650	+	0.730141i
$55$	−449037.	−	1.14413e6i	−0.363926	−	0.927268i
$56$	148142.	+	1.97682e6i	0.112725	+	1.50421i
$57$	−855866.	−	129001.i	−0.612131	−	0.0922638i
$58$	1.49303e6	−	1.38533e6i	1.00478	−	0.932297i
$59$	1.93800e6	−	933290.i	1.22849	−	0.591608i	0.296825	−	0.954932i	$-0.404072\pi$
$59$	1.93800e6	−	933290.i	1.22849	−	0.591608i	0.931663	+	0.363324i	$0.118358\pi$
$60$	150016.	+	102279.i	0.0896618	+	0.0611304i
$61$	267187.	−	680781.i	0.150716	−	0.384019i	−0.835498	−	0.549494i	$-0.814820\pi$
$61$	267187.	−	680781.i	0.150716	−	0.384019i	0.986214	+	0.165475i	$0.0529157\pi$
$62$	−683775.	−	210917.i	−0.364370	−	0.112393i
$63$	−532521.	−	494107.i	−0.268315	−	0.248960i
$64$	1.45217e6	+	1.82096e6i	0.692446	+	0.868300i
$65$	934571.	+	1.17192e6i	0.422100	+	0.529297i
$66$	3.34635e6	+	3.10496e6i	1.43274	+	1.32939i
$67$	−1.30943e6	−	403905.i	−0.531887	−	0.164065i	0.0171663	−	0.999853i	$-0.494536\pi$
$67$	−1.30943e6	−	403905.i	−0.531887	−	0.164065i	−0.549054	+	0.835787i	$0.685012\pi$
$68$	−143880.	+	366601.i	−0.0554908	+	0.141388i
$69$	−2.06764e6	−	1.40969e6i	−0.757710	−	0.516598i
$70$	−1.69343e6	+	815513.i	−0.590098	+	0.284176i
$71$	3.76758e6	−	3.49581e6i	1.24928	−	1.15916i	0.268657	−	0.963236i	$-0.413420\pi$
$71$	3.76758e6	−	3.49581e6i	1.24928	−	1.15916i	0.980619	−	0.195923i	$-0.0627703\pi$
$72$	−870693.	−	131236.i	−0.274917	−	0.0414370i
$73$	17935.0	+	239326.i	0.00539599	+	0.0720045i	0.999252	−	0.0386791i	$-0.0123150\pi$
$73$	17935.0	+	239326.i	0.00539599	+	0.0720045i	−0.993856	+	0.110684i	$0.964696\pi$
$74$	−87136.9	−	222021.i	−0.0249972	−	0.0636918i
$75$	669888.	−	2.93497e6i	0.183353	−	0.803321i
$76$	−29577.3	+	394681.i	−0.00772878	+	0.103133i
$77$	1.04218e7	−	3.21471e6i	2.60152	−	0.802462i
$78$	−5.01586e6	−	2.41551e6i	−1.19678	−	0.576339i
$79$	−1.48443e6	−	2.57110e6i	−0.338738	−	0.586711i	0.645458	−	0.763796i	$-0.276667\pi$
$79$	−1.48443e6	−	2.57110e6i	−0.338738	−	0.586711i	−0.984196	+	0.177085i	$0.943333\pi$
$80$	−917734.	+	1.58956e6i	−0.200402	+	0.347106i
$81$	−4.71171e6	+	3.21239e6i	−0.985102	+	0.671632i
$82$	1.25044e6	+	5.47856e6i	0.250447	+	1.09728i
$83$	−4.42373e6	+	666770.i	−0.849210	+	0.127998i	−0.559207	−	0.829028i	$-0.688894\pi$
$83$	−4.42373e6	+	666770.i	−0.849210	+	0.127998i	−0.290003	+	0.957026i	$0.593656\pi$
$84$	−1.00452e6	+	1.25962e6i	−0.184918	+	0.231880i
$85$	−2.36475e6			−0.417656
$86$	4.34735e6	+	3.06092e6i	0.737021	+	0.518928i
$87$	1.04830e7			1.70674
$88$	8.24235e6	−	1.03356e7i	1.28932	−	1.61676i
$89$	121197.	−	18267.5i	0.0182232	−	0.00274671i	−0.139924	−	0.990162i	$-0.544686\pi$
$89$	121197.	−	18267.5i	0.0182232	−	0.00274671i	0.158148	+	0.987415i	$0.449448\pi$
$90$	−185776.	−	813938.i	−0.0268621	−	0.117691i
$91$	−1.09897e7	+	7.49263e6i	−1.52876	+	1.04229i
$92$	−572161.	+	991011.i	−0.0766056	+	0.132685i
$93$	−1.84150e6	−	3.18957e6i	−0.237400	−	0.411189i
$94$	1.00608e7	+	4.84503e6i	1.24935	+	0.601657i
$95$	−2.27095e6	+	700496.i	−0.271753	+	0.0838248i
$96$	−268829.	+	3.58728e6i	−0.0310118	+	0.413824i
$97$	1.41501e6	−	6.19956e6i	0.157419	−	0.689699i	−0.833191	−	0.552985i	$-0.813489\pi$
$97$	1.41501e6	−	6.19956e6i	0.157419	−	0.689699i	0.990611	−	0.136714i	$-0.0436541\pi$
$98$	−3.02500e6	−	7.70757e6i	−0.324664	−	0.827230i
$99$	362024.	+	4.83087e6i	0.0374985	+	0.500383i
$100$	−1.36123e6	−	205173.i	−0.136123	−	0.0205173i
$101$	−4.93757e6	+	4.58139e6i	−0.476857	+	0.442459i	−0.881618	−	0.471964i	$-0.843545\pi$
$101$	−4.93757e6	+	4.58139e6i	−0.476857	+	0.442459i	0.404761	+	0.914423i	$0.367355\pi$
$102$	7.91311e6	−	3.81075e6i	0.738324	−	0.355558i
$103$	8.62412e6	+	5.87982e6i	0.777650	+	0.530193i	0.885870	−	0.463934i	$-0.153563\pi$
$103$	8.62412e6	+	5.87982e6i	0.777650	+	0.530193i	−0.108220	+	0.994127i	$0.534515\pi$
$104$	−5.89005e6	+	1.50076e7i	−0.513455	+	1.30826i
$105$	−9.24427e6	−	2.85148e6i	−0.779310	−	0.240385i
$106$	−1.34759e7	−	1.25038e7i	−1.09898	−	1.01970i
$107$	1.20729e7	+	1.51390e7i	0.952730	+	1.19469i	0.980787	+	0.195079i	$0.0624964\pi$
$107$	1.20729e7	+	1.51390e7i	0.952730	+	1.19469i	−0.0280576	+	0.999606i	$0.508932\pi$
$108$	1.27166e6	+	1.59461e6i	0.0971379	+	0.121807i
$109$	−8.05861e6	−	7.47730e6i	−0.596029	−	0.553034i	0.323414	−	0.946258i	$-0.395169\pi$
$109$	−8.05861e6	−	7.47730e6i	−0.596029	−	0.553034i	−0.919443	+	0.393223i	$0.871360\pi$
$110$	1.19774e7	+	3.69452e6i	0.857998	+	0.264657i
$111$	448491.	−	1.14274e6i	0.0311260	−	0.0793077i
$112$	−1.34570e7	−	9.17483e6i	−0.905077	−	0.617071i
$113$	−3.78651e6	+	1.82349e6i	−0.246868	+	0.118885i	−0.553226	−	0.833031i	$-0.686604\pi$
$113$	−3.78651e6	+	1.82349e6i	−0.246868	+	0.118885i	0.306359	+	0.951916i	$0.400889\pi$
$114$	6.47041e6	−	6.00366e6i	0.409039	−	0.379533i
$115$	−6.79440e6	−	1.02409e6i	−0.416590	−	0.0627908i
$116$	−358227.	−	4.78021e6i	−0.0213086	−	0.284344i
$117$	−2.15843e6	−	5.49960e6i	−0.124591	−	0.317454i
$118$	−4.88120e6	+	2.13859e7i	−0.273489	+	1.19823i
$119$	1.56811e6	−	2.09250e7i	0.0853025	−	1.13828i
$120$	−1.12050e7	+	3.45630e6i	−0.591942	+	0.182590i
$121$	−4.79711e7	−	2.31017e7i	−2.46167	−	1.18548i
$122$	3.72906e6	+	6.45893e6i	0.185926	+	0.322033i
$123$	−1.44615e7	+	2.50481e7i	−0.700724	+	1.21369i
$124$	−1.39151e6	+	948713.i	−0.0655405	+	0.0446847i
$125$	−4.34479e6	−	1.90358e7i	−0.198968	−	0.871736i
$126$	7.32550e6	−	1.10414e6i	0.326242	−	0.0491731i
$127$	2.58062e7	−	3.23599e7i	1.11792	−	1.40183i	0.212579	−	0.977144i	$-0.431814\pi$
$127$	2.58062e7	−	3.23599e7i	1.11792	−	1.40183i	0.905341	−	0.424684i	$-0.139615\pi$
$128$	−1.49794e7			−0.631335
$129$	5.68677e6	+	2.67681e7i	0.233239	+	1.09788i
$130$	−1.52861e7			−0.610231
$131$	3.25300e6	−	4.07913e6i	0.126426	−	0.158533i	−0.714590	−	0.699543i	$-0.753387\pi$
$131$	3.25300e6	−	4.07913e6i	0.126426	−	0.158533i	0.841016	+	0.541011i	$0.181958\pi$
$132$	1.06240e7	−	1.60131e6i	0.402050	−	0.0605993i
$133$	−4.69257e6	−	2.05595e7i	−0.172954	−	0.757761i
$134$	1.15461e7	−	7.87201e6i	0.414543	−	0.282631i
$135$	−6.12341e6	+	1.06061e7i	−0.214203	+	0.371010i
$136$	−1.27172e7	−	2.20269e7i	−0.433517	−	0.750873i
$137$	−7.88450e6	−	3.79697e6i	−0.261970	−	0.126158i	0.298289	−	0.954476i	$-0.403584\pi$
$137$	−7.88450e6	−	3.79697e6i	−0.261970	−	0.126158i	−0.560259	+	0.828317i	$0.689298\pi$
$138$	2.43863e7	−	7.52218e6i	0.789895	−	0.243650i
$139$	403474.	−	5.38399e6i	0.0127428	−	0.170041i	−0.987201	−	0.159478i	$-0.949019\pi$
$139$	403474.	−	5.38399e6i	0.0127428	−	0.170041i	0.999944	−	0.0105623i	$-0.00336214\pi$
$140$	−984370.	+	4.31281e6i	−0.0303187	+	0.132835i
$141$	2.09977e7	+	5.35014e7i	0.630821	+	1.60730i
$142$	3.91685e6	+	5.22667e7i	0.114796	+	1.53185i
$143$	8.77083e7	+	1.32199e7i	2.50821	+	0.378052i
$144$	5.30321e6	−	4.92066e6i	0.148003	−	0.137327i
$145$	2.59331e7	−	1.24887e7i	0.706425	−	0.340196i
$146$	−2.02220e6	−	1.37871e6i	−0.0537761	−	0.0366639i
$147$	1.55696e7	−	3.96706e7i	0.404265	−	1.03005i
$148$	−536411.	−	165461.i	−0.0136013	−	0.00419546i
$149$	4.06587e7	+	3.77258e7i	1.00694	+	0.934300i	0.997842	−	0.0656583i	$-0.0209147\pi$
$149$	4.06587e7	+	3.77258e7i	1.00694	+	0.934300i	0.00909416	+	0.999959i	$0.497105\pi$
$150$	1.91414e7	+	2.40026e7i	0.463078	+	0.580681i
$151$	1.78571e7	+	2.23922e7i	0.422078	+	0.529269i	0.946722	−	0.322053i	$-0.104373\pi$
$151$	1.78571e7	+	2.23922e7i	0.422078	+	0.529269i	−0.524644	+	0.851322i	$0.675801\pi$
$152$	−1.87377e7	−	1.73860e7i	−0.432776	−	0.401558i
$153$	8.90647e6	+	2.74728e6i	0.201041	+	0.0620131i
$154$	−4.06342e7	+	1.03534e8i	−0.896539	+	2.28434i
$155$	−8.35538e6	−	5.69660e6i	−0.180221	−	0.122873i
$156$	−1.18053e7	+	5.68512e6i	−0.248966	+	0.119896i
$157$	−3.29669e7	+	3.05888e7i	−0.679876	+	0.630833i	−0.942555	−	0.334050i	$-0.891584\pi$
$157$	−3.29669e7	+	3.05888e7i	−0.679876	+	0.630833i	0.262679	+	0.964883i	$0.415394\pi$
$158$	2.99381e7	+	4.51244e6i	0.603843	+	0.0910147i
$159$	−7.07084e6	−	9.43539e7i	−0.139502	−	1.86153i
$160$	3.60861e6	+	9.19458e6i	0.0696497	+	0.177465i
$161$	1.35674e7	−	5.94426e7i	0.256216	−	1.12255i
$162$	4.34592e6	−	5.79923e7i	0.0803118	−	1.07169i
$163$	−2.13187e7	+	6.57596e6i	−0.385571	+	0.118933i	−0.481480	−	0.876457i	$-0.659901\pi$
$163$	−2.13187e7	+	6.57596e6i	−0.385571	+	0.118933i	0.0959085	+	0.995390i	$0.469424\pi$
$164$	1.19161e7	+	5.73848e6i	0.210950	+	0.101588i
$165$	3.22566e7	+	5.58700e7i	0.559016	+	0.968245i
$166$	2.28113e7	−	3.95103e7i	0.387054	−	0.670396i
$167$	1.71382e7	−	1.16846e7i	0.284746	−	0.194136i	−0.412521	−	0.910948i	$-0.635352\pi$
$167$	1.71382e7	−	1.16846e7i	0.284746	−	0.194136i	0.697267	+	0.716812i	$0.254399\pi$
$168$	−2.31535e7	−	1.01442e8i	−0.376734	−	1.65058i
$169$	−4.49168e7	+	6.77012e6i	−0.715823	+	0.107893i
$170$	1.50358e7	−	1.88543e7i	0.234723	−	0.294333i
$171$	9.36702e6			0.143257
$172$	1.20119e7	−	3.50788e6i	0.179995	−	0.0525649i
$173$	−5.08898e7			−0.747256			−0.373628	−	0.927579i	$-0.621886\pi$
$173$	−5.08898e7			−0.747256			−0.373628	+	0.927579i	$0.621886\pi$
$174$	−6.66541e7	+	8.35816e7i	−0.959189	+	1.20279i
$175$	7.25286e7	−	1.09319e7i	1.02300	−	0.154193i
$176$	2.41687e7	+	1.05890e8i	0.334163	+	1.46407i
$177$	−9.32852e7	+	6.36008e7i	−1.26446	+	0.862097i
$178$	−624959.	+	1.08246e6i	−0.00830581	+	0.0143861i
$179$	−1.75923e7	−	3.04707e7i	−0.229264	−	0.397097i	0.728326	−	0.685231i	$-0.240299\pi$
$179$	−1.75923e7	−	3.04707e7i	−0.229264	−	0.397097i	−0.957590	+	0.288134i	$0.906965\pi$
$180$	−1.77035e6	−	852554.i	−0.0226258	−	0.0108960i
$181$	−1.05802e7	+	3.26356e6i	−0.132623	+	0.0409088i	−0.360356	−	0.932815i	$-0.617345\pi$
$181$	−1.05802e7	+	3.26356e6i	−0.132623	+	0.0409088i	0.227733	+	0.973724i	$0.426869\pi$
$182$	1.01365e7	−	1.35262e8i	0.124634	−	1.66313i
$183$	−8.54185e6	+	3.74243e7i	−0.103032	+	0.451414i
$184$	−2.70001e7	−	6.87951e7i	−0.319523	−	0.814132i
$185$	−251890.	−	3.36123e6i	−0.00292489	−	0.0390299i
$186$	3.71395e7	+	5.59788e6i	0.423195	+	0.0637864i
$187$	−1.02578e8	+	9.51786e7i	−1.14712	+	1.06437i
$188$	2.36790e7	−	1.14032e7i	0.259902	−	0.125162i
$189$	−8.97895e7	−	6.12174e7i	−0.967407	−	0.659567i
$190$	8.85432e6	−	2.25604e7i	0.0936522	−	0.238622i
$191$	−742473.	−	229023.i	−0.00771017	−	0.00237827i	0.290898	−	0.956754i	$-0.406046\pi$
$191$	−742473.	−	229023.i	−0.00771017	−	0.00237827i	−0.298608	+	0.954376i	$0.596522\pi$
$192$	−8.96160e7	−	8.31515e7i	−0.913758	−	0.847844i
$193$	6.14586e7	+	7.70667e7i	0.615364	+	0.771642i	0.987684	−	0.156462i	$-0.0500090\pi$
$193$	6.14586e7	+	7.70667e7i	0.615364	+	0.771642i	−0.372320	+	0.928104i	$0.621438\pi$
$194$	4.04325e7	+	5.07007e7i	0.397580	+	0.498549i
$195$	−5.76742e7	−	5.35139e7i	−0.557007	−	0.516827i
$196$	−1.86218e7	−	5.74405e6i	−0.176654	−	0.0544907i
$197$	3.16676e7	−	8.06878e7i	0.295110	−	0.751928i	−0.704018	−	0.710182i	$-0.748613\pi$
$197$	3.16676e7	−	8.06878e7i	0.295110	−	0.751928i	0.999128	−	0.0417459i	$-0.0132920\pi$
$198$	−4.08188e7	−	2.78298e7i	−0.373707	−	0.254789i
$199$	5.55700e7	−	2.67611e7i	0.499867	−	0.240723i	−0.166921	−	0.985970i	$-0.553383\pi$
$199$	5.55700e7	−	2.67611e7i	0.499867	−	0.240723i	0.666789	+	0.745247i	$0.267668\pi$
$200$	6.51723e7	−	6.04711e7i	0.576048	−	0.534494i
$201$	7.11220e7	+	1.07199e7i	0.617757	+	0.0931119i
$202$	−5.13318e6	−	6.84976e7i	−0.0438185	−	0.584717i
$203$	9.33124e7	+	2.37756e8i	0.782894	+	1.99478i
$204$	4.59979e6	−	2.01530e7i	0.0379344	−	0.166201i
$205$	−5.93472e6	+	7.91933e7i	−0.0481129	+	0.642022i
$206$	−1.01715e8	+	3.13750e7i	−0.810682	+	0.250062i
$207$	2.44004e7	+	1.17506e7i	0.191205	+	0.0920797i
$208$	−6.62295e7	−	1.14713e8i	−0.510305	−	0.883874i
$209$	−7.03153e7	+	1.21790e8i	−0.532767	+	0.922780i
$210$	8.15131e7	−	5.55747e7i	0.607379	−	0.414104i
$211$	1.26743e6	+	5.55295e6i	0.00928825	+	0.0406945i	0.979360	−	0.202125i	$-0.0647848\pi$
$211$	1.26743e6	+	5.55295e6i	0.00928825	+	0.0406945i	−0.970071	+	0.242820i	$0.921928\pi$
$212$	−4.27835e7	+	6.44858e6i	−0.308391	+	0.0464824i
$213$	−1.68198e8	+	2.10914e8i	−1.19259	+	1.49547i
$214$	−1.97468e8			−1.37736
$215$	4.59579e7	+	5.94449e7i	0.315374	+	0.407925i
$216$	−1.31723e8			−0.889350
$217$	5.59483e7	−	7.01569e7i	0.371687	−	0.466081i
$218$	1.10856e8	−	1.67089e7i	0.724708	−	0.109232i
$219$	−2.80312e6	−	1.22812e7i	−0.0180338	−	0.0790111i
$220$	2.43743e7	−	1.66181e7i	0.154331	−	0.105221i
$221$	8.53275e7	−	1.47792e8i	0.531761	−	0.921036i
$222$	6.25948e6	+	1.08417e7i	0.0383975	+	0.0665064i
$223$	1.76366e8	+	8.49336e7i	1.06500	+	0.512876i	0.882491	−	0.470328i	$-0.155865\pi$
$223$	1.76366e8	+	8.49336e7i	1.06500	+	0.512876i	0.182507	+	0.983205i	$0.441579\pi$
$224$	−8.37531e7	+	2.58344e7i	−0.497890	+	0.153579i
$225$	−2.43469e6	+	3.24887e7i	−0.0142497	+	0.190149i
$226$	9.53703e6	−	4.17844e7i	0.0549583	−	0.240788i
$227$	−8.41809e7	−	2.14489e8i	−0.477665	−	1.21707i	−0.943255	−	0.332069i	$-0.892253\pi$
$227$	−8.41809e7	−	2.14489e8i	−0.477665	−	1.21707i	0.465590	−	0.885000i	$-0.345842\pi$
$228$	−1.55247e6	−	2.07162e7i	−0.00867462	−	0.115755i
$229$	1.69709e7	+	2.55795e6i	0.0933858	+	0.0140756i	0.195569	−	0.980690i	$-0.437345\pi$
$229$	1.69709e7	+	2.55795e6i	0.0933858	+	0.0140756i	−0.102183	+	0.994766i	$0.532583\pi$
$230$	5.13661e7	−	4.76608e7i	0.278374	−	0.258294i
$231$	−5.15768e8	+	2.48381e8i	−2.75304	+	1.32579i
$232$	2.55792e8	+	1.74396e8i	1.34487	+	0.916915i
$233$	5.71650e7	−	1.45654e8i	0.296063	−	0.754356i	−0.703005	−	0.711185i	$-0.748159\pi$
$233$	5.71650e7	−	1.45654e8i	0.296063	−	0.754356i	0.999068	−	0.0431712i	$-0.0137461\pi$
$234$	5.75728e7	+	1.77588e7i	0.293739	+	0.0906065i
$235$	1.15683e8	+	1.07338e8i	0.581475	+	0.539530i
$236$	3.21896e7	+	4.03645e7i	0.159413	+	0.199897i
$237$	9.71588e7	+	1.21833e8i	0.474092	+	0.594493i
$238$	1.56866e8	+	1.45550e8i	0.754239	+	0.699832i
$239$	−7.92509e7	−	2.44457e7i	−0.375501	−	0.115827i	0.101259	−	0.994860i	$-0.467713\pi$
$239$	−7.92509e7	−	2.44457e7i	−0.375501	−	0.115827i	−0.476760	+	0.879033i	$0.658189\pi$
$240$	3.51973e7	−	8.96812e7i	0.164350	−	0.418757i
$241$	−7.99396e7	−	5.45019e7i	−0.367877	−	0.250814i	0.365245	−	0.930911i	$-0.380985\pi$
$241$	−7.99396e7	−	5.45019e7i	−0.367877	−	0.250814i	−0.733122	+	0.680097i	$0.761938\pi$
$242$	4.89207e8	−	2.35590e8i	2.21890	−	1.06857i
$243$	8.31849e7	−	7.71843e7i	0.371897	−	0.345070i
$244$	1.73573e7	+	2.61619e6i	0.0764922	+	0.0115294i
$245$	−8.74447e6	−	1.16687e8i	−0.0379885	−	0.506921i
$246$	−1.07760e8	−	2.74567e8i	−0.461512	−	1.17591i
$247$	3.81636e7	−	1.67206e8i	0.161143	−	0.706012i
$248$	8.12819e6	−	1.08463e8i	0.0338386	−	0.451545i
$249$	2.24385e8	−	6.92137e7i	0.921079	−	0.284115i
$250$	1.79399e8	+	8.63941e7i	0.726157	+	0.349699i
$251$	5.20428e7	+	9.01407e7i	0.207731	+	0.359801i	0.951000	−	0.309192i	$-0.100059\pi$
$251$	5.20428e7	+	9.01407e7i	0.207731	+	0.359801i	−0.743268	+	0.668994i	$0.766725\pi$
$252$	8.71796e6	−	1.51000e7i	0.0343173	−	0.0594393i
$253$	−3.35947e8	+	2.29045e8i	−1.30421	+	0.889198i
$254$	9.39244e7	+	4.11510e8i	0.359634	+	1.57566i
$255$	1.22736e8	−	1.84994e7i	0.463532	−	0.0698663i
$256$	−9.06333e7	+	1.13651e8i	−0.337635	+	0.423381i
$257$	−3.61235e7			−0.132747			−0.0663733	−	0.997795i	$-0.521143\pi$
$257$	−3.61235e7			−0.132747			−0.0663733	+	0.997795i	$0.521143\pi$
$258$	−2.49583e8	−	1.24859e8i	−0.904785	−	0.452639i
$259$	2.99096e7			0.106970
$260$	−2.24313e7	+	2.81280e7i	−0.0791496	+	0.0992504i
$261$	−1.12182e8	+	1.69087e7i	−0.390555	+	0.0588667i
$262$	1.18396e7	+	5.18729e7i	0.0406709	+	0.178191i
$263$	3.75082e8	−	2.55727e8i	1.27140	−	0.866824i	0.275860	−	0.961198i	$-0.411037\pi$
$263$	3.75082e8	−	2.55727e8i	1.27140	−	0.866824i	0.995537	+	0.0943744i	$0.0300851\pi$
$264$	−3.46941e8	+	6.00920e8i	−1.16049	+	2.01003i
$265$	−1.29899e8	−	2.24992e8i	−0.428790	−	0.742687i
$266$	1.93760e8	+	9.33097e7i	0.631215	+	0.303977i
$267$	−6.14748e6	+	1.89625e6i	−0.0197655	+	0.00609684i
$268$	2.45785e6	−	3.27978e7i	0.00779982	−	0.104081i
$269$	2.20627e7	−	9.66630e7i	0.0691075	−	0.302780i	−0.928548	−	0.371212i	$-0.878942\pi$
$269$	2.20627e7	−	9.66630e7i	0.0691075	−	0.302780i	0.997656	+	0.0684318i	$0.0217996\pi$
$270$	−4.56284e7	−	1.16259e8i	−0.141079	−	0.359463i
$271$	7.38851e6	+	9.85928e7i	0.0225509	+	0.300921i	0.997063	+	0.0765860i	$0.0244020\pi$
$271$	7.38851e6	+	9.85928e7i	0.0225509	+	0.300921i	−0.974512	+	0.224335i	$0.927979\pi$
$272$	2.06635e8	+	3.11453e7i	0.622607	+	0.0938428i
$273$	5.11774e8	−	4.74857e8i	1.52233	−	1.41252i
$274$	8.04057e7	−	3.87214e7i	0.236135	−	0.113717i
$275$	−4.04141e8	−	2.75538e8i	−1.17184	−	0.798947i
$276$	2.19437e7	−	5.59117e7i	0.0628245	−	0.160074i
$277$	5.19709e7	+	1.60309e7i	0.146920	+	0.0453188i	0.367343	−	0.930086i	$-0.380268\pi$
$277$	5.19709e7	+	1.60309e7i	0.146920	+	0.0453188i	−0.220423	+	0.975404i	$0.570744\pi$
$278$	4.03616e7	+	3.74501e7i	0.112671	+	0.104543i
$279$	2.48512e7	+	3.11624e7i	0.0685067	+	0.0859046i
$280$	−1.78129e8	−	2.23367e8i	−0.484934	−	0.608088i
$281$	3.21643e8	+	2.98441e8i	0.864773	+	0.802392i	0.981638	−	0.190755i	$-0.0610937\pi$
$281$	3.21643e8	+	2.98441e8i	0.864773	+	0.802392i	−0.116864	+	0.993148i	$0.537284\pi$
$282$	−5.60081e8	−	1.72762e8i	−1.48723	−	0.458751i
$283$	1.70812e8	−	4.35222e8i	0.447988	−	1.14145i	−0.511395	−	0.859346i	$-0.670871\pi$
$283$	1.70812e8	−	4.35222e8i	0.447988	−	1.14145i	0.959383	−	0.282108i	$-0.0910336\pi$
$284$	1.01924e8	+	6.94906e7i	0.264036	+	0.180016i
$285$	1.12387e8	−	5.41230e7i	0.287581	−	0.138492i
$286$	−6.63081e8	+	6.15249e8i	−1.67604	+	1.55514i
$287$	−6.96824e8	−	1.05029e8i	−1.73995	−	0.262255i
$288$	−2.90934e6	−	3.88224e7i	−0.00717662	−	0.0957654i
$289$	−5.15534e7	−	1.31356e8i	−0.125636	−	0.320116i
$290$	−6.53173e7	+	2.86174e8i	−0.157266	+	0.689028i
$291$	−2.49430e7	+	3.32841e8i	−0.0593366	+	0.791791i
$292$	−5.50443e6	+	1.69789e6i	−0.0129382	+	0.00399090i
$293$	2.09758e8	+	1.01014e8i	0.487172	+	0.234610i	0.661312	−	0.750111i	$-0.270000\pi$
$293$	2.09758e8	+	1.01014e8i	0.487172	+	0.234610i	−0.174139	+	0.984721i	$0.555714\pi$
$294$	2.17301e8	+	3.76376e8i	0.498707	+	0.863786i
$295$	−1.55002e8	+	2.68471e8i	−0.351528	+	0.608865i
$296$	2.99542e7	−	2.04224e7i	0.0671331	−	0.0457706i
$297$	1.61261e8	+	7.06532e8i	0.357176	+	1.56489i
$298$	−5.59312e8	+	8.43027e7i	−1.22433	+	0.184538i
$299$	3.09167e8	−	3.87683e8i	0.668874	−	0.838741i
$300$	7.22561e7			0.154508
$301$	−5.56487e8	+	3.67249e8i	−1.17618	+	0.776208i
$302$	−2.92076e8			−0.610199
$303$	2.20431e8	−	2.76411e8i	0.455221	−	0.570830i
$304$	2.07665e8	−	3.13005e7i	0.423942	−	0.0638990i
$305$	2.34537e7	+	1.02757e8i	0.0473328	+	0.207379i
$306$	−7.85345e7	+	5.35439e7i	−0.156688	+	0.106828i
$307$	−6.76257e6	+	1.17131e7i	−0.0133391	+	0.0231040i	−0.872618	−	0.488403i	$-0.837579\pi$
$307$	−6.76257e6	+	1.17131e7i	−0.0133391	+	0.0231040i	0.859279	+	0.511508i	$0.170913\pi$
$308$	1.30886e8	+	2.26701e8i	0.255250	+	0.442106i
$309$	−4.93609e8	−	2.37710e8i	−0.951762	−	0.458344i
$310$	9.85457e7	−	3.03973e7i	0.187876	−	0.0579521i
$311$	−3.70930e7	+	4.94971e8i	−0.0699246	+	0.933079i	0.846375	+	0.532587i	$0.178780\pi$
$311$	−3.70930e7	+	4.94971e8i	−0.0699246	+	0.933079i	−0.916300	+	0.400493i	$0.868839\pi$
$312$	1.88302e8	−	8.25006e8i	0.351006	−	1.53786i
$313$	−3.39938e8	−	8.66147e8i	−0.626605	−	1.59656i	−0.792126	−	0.610358i	$-0.791026\pi$
$313$	−3.39938e8	−	8.66147e8i	−0.626605	−	1.59656i	0.165520	−	0.986206i	$-0.447070\pi$
$314$	−3.42730e7	−	4.57342e8i	−0.0624739	−	0.833656i
$315$	1.03526e8	+	1.56040e7i	0.186621	+	0.0281286i
$316$	5.22356e7	−	4.84675e7i	0.0931240	−	0.0864065i
$317$	2.85657e7	−	1.37565e7i	0.0503660	−	0.0242550i	−0.408531	−	0.912744i	$-0.633959\pi$
$317$	2.85657e7	−	1.37565e7i	0.0503660	−	0.0242550i	0.458897	+	0.888489i	$0.348245\pi$
$318$	7.97250e8	+	5.43556e8i	1.39027	+	0.947871i
$319$	6.22270e8	−	1.58552e9i	1.07328	−	2.73466i
$320$	−3.20756e8	−	9.89401e7i	−0.547205	−	0.168790i
$321$	−7.45045e8	−	6.91301e8i	−1.25723	−	1.16654i
$322$	3.87675e8	+	4.86129e8i	0.647101	+	0.811439i
$323$	1.68698e8	+	2.11540e8i	0.278548	+	0.349289i
$324$	−1.00335e8	−	9.30970e7i	−0.163887	−	0.152065i
$325$	5.70019e8	+	1.75828e8i	0.921081	+	0.284116i
$326$	8.31207e7	−	2.11788e8i	0.132876	−	0.338563i
$327$	4.76755e8	+	3.25046e8i	0.754012	+	0.514077i
$328$	−7.69577e8	+	3.70609e8i	−1.20419	+	0.579905i
$329$	−1.02651e9	+	9.52467e8i	−1.58920	+	1.47457i
$330$	−6.50554e8	−	9.80552e7i	−0.996516	−	0.150201i
$331$	3.15106e7	+	4.20480e8i	0.0477595	+	0.637306i	0.968801	+	0.247841i	$0.0797210\pi$
$331$	3.15106e7	+	4.20480e8i	0.0477595	+	0.637306i	−0.921041	+	0.389465i	$0.872660\pi$
$332$	−3.92291e7	−	9.99540e7i	−0.0588335	−	0.149905i
$333$	−2.95626e6	+	1.29522e7i	−0.00438721	+	0.0192216i
$334$	−1.58077e7	+	2.10939e8i	−0.0232143	+	0.309773i
$335$	1.88715e8	−	5.82107e7i	0.274251	−	0.0845953i
$336$	7.70224e8	+	3.70920e8i	1.10772	+	0.533449i
$337$	−6.03280e8	−	1.04491e9i	−0.858646	−	1.48722i	−0.873221	−	0.487325i	$-0.837973\pi$
$337$	−6.03280e8	−	1.04491e9i	−0.858646	−	1.48722i	0.0145742	−	0.999894i	$-0.495361\pi$
$338$	2.31617e8	−	4.01172e8i	0.326258	−	0.565096i
$339$	1.82263e8	−	1.24265e8i	0.254097	−	0.173241i
$340$	−1.26299e7	−	5.53350e7i	−0.0174270	−	0.0763526i
$341$	−5.91723e8	+	8.91879e7i	−0.808125	+	0.121805i
$342$	−5.95585e7	+	7.46840e7i	−0.0805105	+	0.100957i
$343$	−1.48628e7			−0.0198871
$344$	−3.06557e8	+	7.47768e8i	−0.406029	+	0.990404i
$345$	3.60656e8			0.472853
$346$	3.23574e8	−	4.05748e8i	0.419959	−	0.526612i
$347$	−3.02141e8	+	4.55404e7i	−0.388201	+	0.0585118i	−0.340243	−	0.940338i	$-0.610509\pi$
$347$	−3.02141e8	+	4.55404e7i	−0.388201	+	0.0585118i	−0.0479576	+	0.998849i	$0.515271\pi$
$348$	5.59884e7	+	2.45301e8i	0.0712149	+	0.312013i
$349$	1.04029e9	−	7.09257e8i	1.30998	−	0.893130i	0.311611	−	0.950210i	$-0.399131\pi$
$349$	1.04029e9	−	7.09257e8i	1.30998	−	0.893130i	0.998370	+	0.0570798i	$0.0181789\pi$
$350$	−3.73999e8	+	6.47785e8i	−0.466265	+	0.807594i
$351$	−4.41904e8	−	7.65401e8i	−0.545448	−	0.944744i
$352$	5.26607e8	+	2.53600e8i	0.643557	+	0.309921i
$353$	−1.53960e9	+	4.74903e8i	−1.86293	+	0.574637i	−0.865672	+	0.500612i	$0.833108\pi$
$353$	−1.53960e9	+	4.74903e8i	−1.86293	+	0.574637i	−0.997256	+	0.0740251i	$0.976416\pi$
$354$	8.60430e7	−	1.14816e9i	0.103087	−	1.37560i
$355$	−1.64825e8	+	7.22145e8i	−0.195535	+	0.856693i
$356$	1.07476e6	+	2.73844e6i	0.00126251	+	0.00321683i
$357$	8.23077e7	+	1.09832e9i	0.0957419	+	1.27759i
$358$	3.54802e8	+	5.34778e7i	0.408692	+	0.0616004i
$359$	5.74931e8	−	5.33458e8i	0.655821	−	0.608512i	−0.280418	−	0.959878i	$-0.590473\pi$
$359$	5.74931e8	−	5.33458e8i	0.655821	−	0.608512i	0.936238	+	0.351366i	$0.114283\pi$
$360$	1.14334e8	−	5.50606e7i	0.129157	−	0.0621988i
$361$	−5.13881e8	−	3.50358e8i	−0.574894	−	0.391956i
$362$	4.12516e7	−	1.05107e8i	0.0457047	−	0.116454i
$363$	2.67053e9	+	8.23750e8i	2.93038	+	0.903904i
$364$	−2.34022e8	−	2.17141e8i	−0.254333	−	0.235986i
$365$	−2.15655e7	−	2.70423e7i	−0.0232132	−	0.0291084i
$366$	−2.44075e8	−	3.06060e8i	−0.260219	−	0.326305i
$367$	−6.47024e8	−	6.00351e8i	−0.683265	−	0.633978i	0.260159	−	0.965566i	$-0.416225\pi$
$367$	−6.47024e8	−	6.00351e8i	−0.683265	−	0.633978i	−0.943424	+	0.331588i	$0.892416\pi$
$368$	5.80218e8	+	1.78974e8i	0.606909	+	0.187207i
$369$	1.14356e8	−	2.91375e8i	0.118486	−	0.301898i
$370$	2.84010e7	+	1.93635e7i	0.0291493	+	0.0198736i
$371$	2.07703e9	−	1.00024e9i	2.11170	−	1.01694i
$372$	6.48005e7	−	6.01261e7i	0.0652647	−	0.0605568i
$373$	1.21771e9	+	1.83540e8i	1.21496	+	0.183126i	0.725082	−	0.688662i	$-0.241802\pi$
$373$	1.21771e9	+	1.83540e8i	1.21496	+	0.183126i	0.489882	+	0.871789i	$0.337040\pi$
$374$	−1.06642e8	−	1.42304e9i	−0.105409	−	1.40659i
$375$	3.74421e8	+	9.54009e8i	0.366649	+	0.934207i
$376$	−3.77696e8	+	1.65479e9i	−0.366425	+	1.60541i
$377$	−1.55230e8	+	2.07140e9i	−0.149204	+	1.99099i
$378$	1.05900e9	−	3.26659e8i	1.00850	−	0.311081i
$379$	−4.23795e7	−	2.04089e7i	−0.0399870	−	0.0192567i	0.413783	−	0.910375i	$-0.364207\pi$
$379$	−4.23795e7	−	2.04089e7i	−0.0399870	−	0.0192567i	−0.453770	+	0.891119i	$0.649921\pi$
$380$	−2.85205e7	−	4.93989e7i	−0.0266633	−	0.0461822i
$381$	−1.08625e9	+	1.88144e9i	−1.00622	+	1.74282i
$382$	6.54690e6	−	4.46360e6i	0.00600916	−	0.00409698i
$383$	−4.31533e8	−	1.89067e9i	−0.392481	−	1.71957i	−0.655863	−	0.754880i	$-0.727695\pi$
$383$	−4.31533e8	−	1.89067e9i	−0.392481	−	1.71957i	0.263382	−	0.964692i	$-0.415162\pi$
$384$	7.77465e8	−	1.17184e8i	0.700683	−	0.105611i
$385$	−9.80018e8	+	1.22890e9i	−0.875228	+	1.09750i
$386$	−1.00523e9			−0.889633
$387$	−1.04032e8	−	2.77283e8i	−0.0912390	−	0.243184i
$388$	1.52627e8			0.132654
$389$	1.87694e8	−	2.35361e8i	0.161669	−	0.202727i	−0.694398	−	0.719591i	$-0.744329\pi$
$389$	1.87694e8	−	2.35361e8i	0.161669	−	0.202727i	0.856067	+	0.516864i	$0.172901\pi$
$390$	7.93382e8	−	1.19583e8i	0.677261	−	0.102081i
$391$	1.74075e8	+	7.62672e8i	0.147271	+	0.645237i
$392$	1.03987e9	−	7.08974e8i	0.871926	−	0.594469i
$393$	−1.36927e8	+	2.37165e8i	−0.113793	+	0.197095i
$394$	4.41977e8	+	7.65527e8i	0.364052	+	0.630556i
$395$	3.85498e8	+	1.85646e8i	0.314726	+	0.151564i
$396$	−1.11109e8	+	3.42725e7i	−0.0899115	+	0.0277340i
$397$	1.02588e8	−	1.36894e9i	0.0822866	−	1.09804i	−0.791319	−	0.611404i	$-0.790605\pi$
$397$	1.02588e8	−	1.36894e9i	0.0822866	−	1.09804i	0.873605	−	0.486635i	$-0.161776\pi$
$398$	−1.39963e8	+	6.13220e8i	−0.111282	+	0.487557i
$399$	4.04392e8	+	1.03037e9i	0.318712	+	0.812064i
$400$	5.45865e7	+	7.28406e8i	0.0426457	+	0.569067i
$401$	6.70359e8	+	1.01040e8i	0.519161	+	0.0782510i	0.403396	−	0.915026i	$-0.367830\pi$
$401$	6.70359e8	+	1.01040e8i	0.519161	+	0.0782510i	0.115765	+	0.993277i	$0.463068\pi$
$402$	−5.37687e8	+	4.98901e8i	−0.412799	+	0.383021i
$403$	6.57514e8	−	3.16642e8i	0.500423	−	0.240991i
$404$	−1.33576e8	−	9.10703e7i	−0.100784	−	0.0687135i
$405$	3.00259e8	−	7.65047e8i	0.224597	−	0.572263i
$406$	−2.48896e9	−	7.67742e8i	−1.84576	−	0.569343i
$407$	−1.46213e8	−	1.35666e8i	−0.107499	−	0.0997446i
$408$	8.32368e8	+	1.04376e9i	0.606743	+	0.760832i
$409$	−8.50718e8	−	1.06677e9i	−0.614829	−	0.770971i	0.372778	−	0.927921i	$-0.378405\pi$
$409$	−8.50718e8	−	1.06677e9i	−0.614829	−	0.770971i	−0.987607	+	0.156950i	$0.949834\pi$
$410$	−5.93680e8	−	5.50855e8i	−0.425411	−	0.394724i
$411$	4.38927e8	+	1.35391e8i	0.311850	+	0.0961930i
$412$	−9.15273e7	+	2.33208e8i	−0.0644778	+	0.164287i
$413$	−2.27284e9	−	1.54960e9i	−1.58761	−	1.08241i
$414$	−2.48834e8	+	1.19832e8i	−0.172349	+	0.0829988i
$415$	4.72634e8	−	4.38541e8i	0.324606	−	0.301191i
$416$	−7.04851e8	−	1.06239e8i	−0.480033	−	0.0723533i
$417$	2.11778e7	+	2.82598e8i	0.0143022	+	0.190850i
$418$	−5.23952e8	−	1.33501e9i	−0.350893	−	0.894060i
$419$	782479.	−	3.42826e6i	0.000519665	−	0.00227680i	−0.974667	−	0.223659i	$-0.928200\pi$
$419$	782479.	−	3.42826e6i	0.000519665	−	0.00227680i	0.975187	+	0.221382i	$0.0710569\pi$
$420$	1.73519e7	−	2.31545e8i	0.0114281	−	0.152498i
$421$	−1.59121e8	+	4.90822e7i	−0.103930	+	0.0320580i	−0.346284	−	0.938130i	$-0.612557\pi$
$421$	−1.59121e8	+	4.90822e7i	−0.103930	+	0.0320580i	0.242354	+	0.970188i	$0.422080\pi$
$422$	−5.23328e7	−	2.52022e7i	−0.0338985	−	0.0163247i
$423$	−3.11001e8	−	5.38669e8i	−0.199788	−	0.346044i
$424$	1.39715e9	−	2.41994e9i	0.890149	−	1.54178i
$425$	−7.77558e8	+	5.30130e8i	−0.491328	+	0.334982i
$426$	−6.12176e8	−	2.68212e9i	−0.383656	−	1.68091i
$427$	−9.24824e8	+	1.39395e8i	−0.574859	+	0.0866461i
$428$	−2.89772e8	+	3.63362e8i	−0.178650	+	0.224020i
$429$	−4.65568e9			−2.84697
$430$	−7.66174e8	−	1.15441e7i	−0.464716	−	0.00700197i
$431$	−2.71692e9			−1.63458			−0.817290	−	0.576226i	$-0.804525\pi$
$431$	−2.71692e9			−1.63458			−0.817290	+	0.576226i	$0.804525\pi$
$432$	6.74763e8	−	8.46126e8i	0.402678	−	0.504943i
$433$	−6.09826e8	+	9.19165e7i	−0.360993	+	0.0544109i	−0.327035	−	0.945012i	$-0.606049\pi$
$433$	−6.09826e8	+	9.19165e7i	−0.360993	+	0.0544109i	−0.0339580	+	0.999423i	$0.510811\pi$
$434$	2.03630e8	+	8.92160e8i	0.119571	+	0.523876i
$435$	−1.24829e9	+	8.51067e8i	−0.727113	+	0.495737i
$436$	1.31928e8	−	2.28507e8i	0.0762317	−	0.132037i
$437$	3.93093e8	+	6.80856e8i	0.225325	+	0.390275i
$438$	1.15742e8	+	5.57386e7i	0.0658163	+	0.0316955i
$439$	2.27739e9	−	7.02480e8i	1.28473	−	0.396286i	0.424143	−	0.905595i	$-0.360575\pi$
$439$	2.27739e9	−	7.02480e8i	1.28473	−	0.396286i	0.860583	+	0.509309i	$0.170099\pi$
$440$	−1.42377e8	+	1.89989e9i	−0.0796814	+	1.06327i
$441$	−1.02628e8	+	4.49643e8i	−0.0569811	+	0.249651i
$442$	6.35815e8	+	1.62003e9i	0.350229	+	0.892370i
$443$	1.79937e8	+	2.40109e9i	0.0983348	+	1.31219i	0.800138	+	0.599816i	$0.204760\pi$
$443$	1.79937e8	+	2.40109e9i	0.0983348	+	1.31219i	−0.701803	+	0.712371i	$0.747621\pi$
$444$	2.91353e7	+	4.39145e6i	0.0157972	+	0.00238104i
$445$	−1.29487e7	+	1.20147e7i	−0.00696575	+	0.00646327i
$446$	−1.79858e9	+	8.66149e8i	−0.959968	+	0.462296i
$447$	−2.40541e9	−	1.63998e9i	−1.27383	−	0.868485i
$448$	1.08819e9	−	2.77267e9i	0.571785	−	1.45688i
$449$	8.88804e8	+	2.74160e8i	0.463387	+	0.142936i	0.517653	−	0.855591i	$-0.326806\pi$
$449$	8.88804e8	+	2.74160e8i	0.463387	+	0.142936i	−0.0542662	+	0.998527i	$0.517282\pi$
$450$	−2.43555e8	−	2.25986e8i	−0.125995	−	0.116906i
$451$	2.93001e9	+	3.67412e9i	1.50401	+	1.88597i
$452$	−6.28929e7	−	7.88652e7i	−0.0320344	−	0.0401699i
$453$	−1.10200e9	−	1.02251e9i	−0.556978	−	0.516800i
$454$	2.24539e9	+	6.92611e8i	1.12615	+	0.347371i
$455$	7.00329e8	−	1.78441e9i	0.348548	−	0.888085i
$456$	1.10854e9	+	7.55789e8i	0.547488	+	0.373271i
$457$	1.56296e9	−	7.52682e8i	0.766022	−	0.368897i	−0.00971495	−	0.999953i	$-0.503092\pi$
$457$	1.56296e9	−	7.52682e8i	0.766022	−	0.368897i	0.775737	+	0.631056i	$0.217378\pi$
$458$	−1.28301e8	+	1.19046e8i	−0.0624024	+	0.0579010i
$459$	1.37874e9	+	2.07811e8i	0.665484	+	0.100306i
$460$	−1.23245e7	−	1.64458e8i	−0.00590358	−	0.0787778i
$461$	6.51578e8	+	1.66019e9i	0.309751	+	0.789233i	0.997967	+	0.0637275i	$0.0202988\pi$
$461$	6.51578e8	+	1.66019e9i	0.309751	+	0.789233i	−0.688216	+	0.725506i	$0.741606\pi$
$462$	1.29906e9	−	5.69154e9i	0.612889	−	2.68524i
$463$	−1.23108e8	+	1.64276e9i	−0.0576437	+	0.769202i	0.891231	+	0.453550i	$0.149842\pi$
$463$	−1.23108e8	+	1.64276e9i	−0.0576437	+	0.769202i	−0.948875	+	0.315653i	$0.897777\pi$
$464$	−2.43056e9	+	7.49729e8i	−1.12952	+	0.348410i
$465$	4.78228e8	+	2.30302e8i	0.220572	+	0.106222i
$466$	7.97838e8	+	1.38190e9i	0.365228	+	0.632593i
$467$	−6.97675e7	+	1.20841e8i	−0.0316989	+	0.0549041i	−0.881440	−	0.472297i	$-0.843425\pi$
$467$	−6.97675e7	+	1.20841e8i	−0.0316989	+	0.0549041i	0.849741	+	0.527201i	$0.176758\pi$
$468$	1.17163e8	−	7.98801e7i	0.0528358	−	0.0360229i
$469$	3.89950e8	+	1.70848e9i	0.174544	+	0.764726i
$470$	−1.59136e9	+	2.39859e8i	−0.707012	+	0.106565i
$471$	1.47176e9	−	1.84553e9i	0.649029	−	0.813857i
$472$	−3.33430e9			−1.45951
$473$	4.38616e9	+	7.28850e8i	1.90577	+	0.316683i
$474$	−1.58915e9			−0.685396
$475$	−5.89680e8	+	7.39435e8i	−0.252458	+	0.316572i
$476$	4.98019e8	−	7.50643e7i	0.211652	−	0.0319013i
$477$	2.27858e8	+	9.98310e8i	0.0961279	+	0.421164i
$478$	6.98810e8	−	4.76441e8i	0.292659	−	0.199531i
$479$	6.26871e8	−	1.08577e9i	0.260618	−	0.451403i	−0.705789	−	0.708423i	$-0.749407\pi$
$479$	6.26871e8	−	1.08577e9i	0.260618	−	0.451403i	0.966406	+	0.257020i	$0.0827405\pi$
$480$	−2.59224e8	−	4.48989e8i	−0.106987	−	0.185307i
$481$	2.19159e8	+	1.05541e8i	0.0897949	+	0.0432429i
$482$	9.42830e8	−	2.90825e8i	0.383503	−	0.118295i
$483$	−2.39158e8	+	3.19134e9i	−0.0965762	+	1.28872i
$484$	2.84370e8	−	1.24591e9i	0.114005	−	0.499490i
$485$	3.34819e8	+	8.53106e8i	0.133265	+	0.339553i
$486$	8.64805e7	+	1.15400e9i	0.0341736	+	0.456015i
$487$	2.55654e9	+	3.85337e8i	1.00300	+	0.151178i	0.629953	−	0.776634i	$-0.283074\pi$
$487$	2.55654e9	+	3.85337e8i	1.00300	+	0.151178i	0.373049	+	0.927812i	$0.378312\pi$
$488$	−8.31023e8	+	7.71077e8i	−0.323701	+	0.300350i
$489$	1.05505e9	−	5.08084e8i	0.408029	−	0.196496i
$490$	9.85954e8	+	6.72212e8i	0.378591	+	0.258119i
$491$	3.28647e8	−	8.37380e8i	0.125298	−	0.319255i	−0.854436	−	0.519557i	$-0.826097\pi$
$491$	3.28647e8	−	8.37380e8i	0.125298	−	0.319255i	0.979734	+	0.200302i	$0.0641923\pi$
$492$	−6.63364e8	−	2.04621e8i	−0.251116	−	0.0774589i
$493$	−2.40223e9	−	2.22895e9i	−0.902924	−	0.837791i
$494$	1.09049e9	+	1.36743e9i	0.406983	+	0.510341i
$495$	−4.35306e8	−	5.45857e8i	−0.161316	−	0.202284i
$496$	6.55079e8	+	6.07825e8i	0.241051	+	0.223662i
$497$	−6.28076e9	−	1.93736e9i	−2.29491	−	0.707885i
$498$	−8.74867e8	+	2.22912e9i	−0.317424	+	0.808782i
$499$	2.48588e9	+	1.69484e9i	0.895629	+	0.610629i	0.921220	−	0.389043i	$-0.127194\pi$
$499$	2.48588e9	+	1.69484e9i	0.895629	+	0.610629i	−0.0255907	+	0.999673i	$0.508147\pi$
$500$	4.22231e8	−	2.03336e8i	0.151062	−	0.0727476i
$501$	−7.98102e8	+	7.40530e8i	−0.283548	+	0.263094i
$502$	−1.04960e9	−	1.58202e8i	−0.370307	−	0.0558148i
$503$	−1.01176e8	−	1.35010e9i	−0.0354478	−	0.473018i	−0.986475	−	0.163911i	$-0.947589\pi$
$503$	−1.01176e8	−	1.35010e9i	−0.0354478	−	0.473018i	0.951027	−	0.309107i	$-0.100030\pi$
$504$	4.11398e8	+	1.04822e9i	0.143138	+	0.364710i
$505$	2.16010e8	−	9.46400e8i	0.0746369	−	0.327006i
$506$	3.09866e8	−	4.13487e9i	0.106328	−	1.41885i
$507$	2.27832e9	−	7.02769e8i	0.776403	−	0.239489i
$508$	8.95050e8	+	4.31034e8i	0.302918	+	0.145877i
$509$	1.76503e9	+	3.05712e9i	0.593253	+	1.02754i	0.993791	+	0.111264i	$0.0354898\pi$
$509$	1.76503e9	+	3.05712e9i	0.593253	+	1.02754i	−0.400538	+	0.916280i	$0.631177\pi$
$510$	−6.32895e8	+	1.09621e9i	−0.211269	+	0.365929i
$511$	2.53590e8	−	1.72895e8i	0.0840734	−	0.0573203i
$512$	−7.56523e8	−	3.31454e9i	−0.249102	−	1.09139i
$513$	1.38561e9	−	2.08847e8i	0.453138	−	0.0682996i
$514$	2.29685e8	−	2.88015e8i	0.0746038	−	0.0935502i
$515$	−1.50430e9			−0.485297
$516$	−5.96001e8	+	2.76036e8i	−0.190974	+	0.0884488i
$517$	9.33835e9			2.97203
$518$	−1.90175e8	+	2.38472e8i	−0.0601173	+	0.0753847i
$519$	2.64129e9	−	3.98111e8i	0.829337	−	0.125002i
$520$	−5.17030e8	−	2.26525e9i	−0.161251	−	0.706489i
$521$	−1.55297e9	+	1.05880e9i	−0.481095	+	0.328005i	−0.779466	−	0.626445i	$-0.784509\pi$
$521$	−1.55297e9	+	1.05880e9i	−0.481095	+	0.328005i	0.298371	+	0.954450i	$0.403557\pi$
$522$	5.78475e8	−	1.00195e9i	0.178007	−	0.308318i
$523$	−5.86063e8	−	1.01509e9i	−0.179138	−	0.310276i	0.762447	−	0.647050i	$-0.223998\pi$
$523$	−5.86063e8	−	1.01509e9i	−0.179138	−	0.310276i	−0.941586	+	0.336774i	$0.890664\pi$
$524$	1.12826e8	+	5.43340e7i	0.0342569	+	0.0164973i
$525$	−3.67888e9	+	1.13478e9i	−1.10958	+	0.342260i
$526$	−3.45963e8	+	4.61655e9i	−0.103652	+	1.38314i
$527$	−2.56193e8	+	1.12246e9i	−0.0762484	+	0.334066i
$528$	−2.08279e9	−	5.30686e9i	−0.615781	−	1.56898i
$529$	−8.45773e7	−	1.12861e9i	−0.0248404	−	0.331472i
$530$	2.61982e9	+	3.94874e8i	0.764373	+	0.115211i
$531$	8.95693e8	−	8.31082e8i	0.259614	−	0.240887i
$532$	4.56030e8	−	2.19612e8i	0.131311	−	0.0632362i
$533$	−4.73527e9	−	3.22845e9i	−1.35456	−	0.923526i
$534$	2.39687e7	−	6.10712e7i	0.00681161	−	0.0173557i
$535$	−2.66668e9	−	8.22563e8i	−0.752893	−	0.232237i
$536$	1.55709e9	+	1.44477e9i	0.436754	+	0.405249i
$537$	1.15145e9	+	1.44387e9i	0.320874	+	0.402364i
$538$	6.30420e8	+	7.90522e8i	0.174539	+	0.218865i
$539$	−5.07585e9	−	4.70970e9i	−1.39620	−	1.29548i
$540$	−2.80886e8	−	8.66419e7i	−0.0767631	−	0.0236783i
$541$	−8.35886e8	+	2.12980e9i	−0.226964	+	0.578294i	−0.998309	−	0.0581222i	$-0.981489\pi$
$541$	−8.35886e8	+	2.12980e9i	−0.226964	+	0.578294i	0.771346	+	0.636416i	$0.219584\pi$
$542$	−8.33067e8	−	5.67976e8i	−0.224741	−	0.153226i
$543$	5.23605e8	−	2.52155e8i	0.140347	−	0.0675878i
$544$	8.24350e8	−	7.64885e8i	0.219541	−	0.203704i
$545$	1.56665e9	+	2.36134e8i	0.414557	+	0.0624844i
$546$	5.32050e8	+	7.09971e9i	0.139887	+	1.86666i
$547$	−8.59319e8	−	2.18951e9i	−0.224491	−	0.571993i	0.773606	−	0.633667i	$-0.218451\pi$
$547$	−8.59319e8	−	2.18951e9i	−0.224491	−	0.571993i	−0.998096	+	0.0616742i	$0.980356\pi$
$548$	4.67389e7	−	2.04776e8i	0.0121324	−	0.0531555i
$549$	3.10452e7	−	4.14269e8i	0.00800738	−	0.106851i
$550$	4.76655e9	−	1.47028e9i	1.22161	−	0.376818i
$551$	−2.96722e9	−	1.42894e9i	−0.755647	−	0.363901i
$552$	1.93955e9	+	3.35940e9i	0.490811	+	0.850109i
$553$	−1.89836e9	+	3.28806e9i	−0.477355	+	0.826803i
$554$	−4.58263e8	+	3.12439e8i	−0.114507	+	0.0780694i
$555$	3.93686e7	+	1.72485e8i	0.00977518	+	0.0428278i
$556$	1.28140e8	−	1.93140e7i	0.0316172	−	0.00476553i
$557$	2.13663e9	−	2.67924e9i	0.523884	−	0.656930i	−0.447544	−	0.894262i	$-0.647701\pi$
$557$	2.13663e9	−	2.67924e9i	0.523884	−	0.656930i	0.971429	+	0.237332i	$0.0762728\pi$
$558$	−4.06473e8			−0.0990402
$559$	−5.37349e9	+	7.27308e8i	−1.30111	+	0.176107i
$560$	2.34729e9			0.564819
$561$	4.57946e9	−	5.74246e9i	1.09507	−	1.37318i
$562$	−4.42461e9	+	6.66902e8i	−1.05147	+	0.158484i
$563$	−1.43282e8	−	6.27761e8i	−0.0338387	−	0.148257i	0.955186	−	0.296005i	$-0.0956546\pi$
$563$	−1.43282e8	−	6.27761e8i	−0.0338387	−	0.148257i	−0.989025	+	0.147748i	$0.952797\pi$
$564$	−1.13978e9	+	7.77092e8i	−0.267514	+	0.182388i
$565$	3.02847e8	−	5.24546e8i	0.0706405	−	0.122353i
$566$	2.38398e9	+	4.12918e9i	0.552644	+	0.957208i
$567$	6.57058e9	+	3.16422e9i	1.51378	+	0.728998i
$568$	−7.61296e9	+	2.34829e9i	−1.74315	+	0.537690i
$569$	2.16049e8	−	2.88298e9i	0.0491654	−	0.656067i	−0.917123	−	0.398605i	$-0.869495\pi$
$569$	2.16049e8	−	2.88298e9i	0.0491654	−	0.656067i	0.966288	−	0.257462i	$-0.0828863\pi$
$570$	−2.83069e8	+	1.24021e9i	−0.0640221	+	0.280499i
$571$	2.76925e9	+	7.05593e9i	0.622495	+	1.58609i	0.798695	+	0.601737i	$0.205524\pi$
$571$	2.76925e9	+	7.05593e9i	0.622495	+	1.58609i	−0.176200	+	0.984354i	$0.556380\pi$
$572$	1.59095e8	+	2.12298e9i	0.0355444	+	0.474307i
$573$	4.03277e7	+	6.07842e6i	0.00895492	+	0.00134974i
$574$	5.26804e9	−	4.88802e9i	1.16267	−	1.07880i
$575$	−2.46367e9	+	1.18644e9i	−0.540436	+	0.260260i
$576$	1.09313e9	+	7.45287e8i	0.238339	+	0.162497i
$577$	2.38035e8	−	6.06503e8i	0.0515852	−	0.131437i	−0.902758	−	0.430148i	$-0.858461\pi$
$577$	2.38035e8	−	6.06503e8i	0.0515852	−	0.131437i	0.954344	+	0.298711i	$0.0965566\pi$
$578$	1.37510e9	+	4.24164e8i	0.296202	+	0.0913663i
$579$	−3.79273e9	−	3.51914e9i	−0.812040	−	0.753463i
$580$	4.30742e8	+	5.40133e8i	0.0916682	+	0.114948i
$581$	3.56711e9	+	4.47301e9i	0.754570	+	0.946201i
$582$	−2.49517e9	−	2.31518e9i	−0.524650	−	0.486804i
$583$	−1.46905e10	−	4.53141e9i	−3.07040	−	0.947094i
$584$	1.35915e8	−	3.46305e8i	0.0282372	−	0.0719471i
$585$	7.03510e8	+	4.79645e8i	0.145286	+	0.0990545i
$586$	−2.13911e9	+	1.03014e9i	−0.439127	+	0.211473i
$587$	4.03476e9	−	3.74371e9i	0.823351	−	0.763958i	−0.151110	−	0.988517i	$-0.548285\pi$
$587$	4.03476e9	−	3.74371e9i	0.823351	−	0.763958i	0.974460	+	0.224559i	$0.0720942\pi$
$588$	1.01145e9	+	1.52451e8i	0.205174	+	0.0309250i
$589$	8.64673e7	+	1.15383e9i	0.0174361	+	0.232668i
$590$	−1.15499e9	−	2.94287e9i	−0.231524	−	0.589914i
$591$	−1.01240e9	+	4.43561e9i	−0.201742	+	0.883889i
$592$	−2.22592e7	+	2.97028e8i	−0.00440943	+	0.0588398i
$593$	−7.85564e9	+	2.42314e9i	−1.54700	+	0.477186i	−0.946572	−	0.322493i	$-0.895479\pi$
$593$	−7.85564e9	+	2.42314e9i	−1.54700	+	0.477186i	−0.600427	+	0.799679i	$0.705003\pi$
$594$	−6.65859e9	−	3.20661e9i	−1.30356	−	0.627759i
$595$	1.51208e9	+	2.61900e9i	0.294283	+	0.509714i
$596$	−6.65629e8	+	1.15290e9i	−0.128787	+	0.223065i
$597$	−2.67486e9	+	1.82369e9i	−0.514506	+	0.350784i
$598$	1.12525e9	+	4.93003e9i	0.215176	+	0.942747i
$599$	1.30484e9	−	1.96674e8i	0.248064	−	0.0373897i	−0.0238329	−	0.999716i	$-0.507587\pi$
$599$	1.30484e9	−	1.96674e8i	0.248064	−	0.0373897i	0.271897	+	0.962326i	$0.412349\pi$
$600$	−2.90953e9	+	3.64843e9i	−0.549912	+	0.689567i
$601$	2.48690e9			0.467302			0.233651	−	0.972320i	$-0.424933\pi$
$601$	2.48690e9			0.467302			0.233651	+	0.972320i	$0.424933\pi$
$602$	6.10215e8	−	6.77200e9i	0.113998	−	1.26511i
$603$	−7.78393e8			−0.144573
$604$	−4.28603e8	+	5.37451e8i	−0.0791454	+	0.0992452i
$605$	7.58780e9	−	1.14368e9i	1.39307	−	0.209971i
$606$	8.02281e8	+	3.51502e9i	0.146444	+	0.641614i
$607$	6.68323e9	−	4.55655e9i	1.21290	−	0.826943i	0.223867	−	0.974620i	$-0.428132\pi$
$607$	6.68323e9	−	4.55655e9i	1.21290	−	0.826943i	0.989036	+	0.147677i	$0.0471795\pi$
$608$	5.65076e8	−	9.78740e8i	0.101963	−	0.176606i
$609$	−6.70309e9	−	1.16101e10i	−1.20258	−	2.08293i
$610$	−9.68420e8	−	4.66366e8i	−0.172746	−	0.0831903i
$611$	−1.08826e10	+	3.35684e9i	−1.93014	+	0.595369i
$612$	−1.67178e7	+	2.23084e8i	−0.00294816	+	0.0393404i
$613$	1.06450e9	−	4.66387e9i	0.186652	−	0.817777i	−0.791713	−	0.610893i	$-0.790811\pi$
$613$	1.06450e9	−	4.66387e9i	0.186652	−	0.817777i	0.978365	−	0.206884i	$-0.0663323\pi$
$614$	−5.03910e7	−	1.28394e8i	−0.00878544	−	0.0223849i
$615$	−3.11505e8	−	4.15674e9i	−0.0540010	−	0.720593i
$616$	−1.67172e10	−	2.51972e9i	−2.88159	−	0.434329i
$617$	−1.48944e9	+	1.38200e9i	−0.255285	+	0.236870i	−0.797425	−	0.603418i	$-0.793805\pi$
$617$	−1.48944e9	+	1.38200e9i	−0.255285	+	0.236870i	0.542140	+	0.840288i	$0.317614\pi$
$618$	5.03380e9	−	2.42415e9i	0.857899	−	0.413143i
$619$	7.99966e9	+	5.45407e9i	1.35567	+	0.924281i	0.999947	−	0.0103106i	$-0.00328204\pi$
$619$	7.99966e9	+	5.45407e9i	1.35567	+	0.924281i	0.355724	+	0.934591i	$0.384234\pi$
$620$	8.86752e7	−	2.25941e8i	0.0149428	−	0.0380736i
$621$	3.87140e9	+	1.19417e9i	0.648706	+	0.200099i
$622$	−3.71060e9	−	3.44293e9i	−0.618269	−	0.573670i
$623$	−9.77279e7	−	1.22547e8i	−0.0161924	−	0.0203046i
$624$	4.33486e9	+	5.43574e9i	0.714215	+	0.895597i
$625$	−1.22187e9	−	1.13373e9i	−0.200192	−	0.185751i
$626$	9.06729e9	+	2.79689e9i	1.47730	+	0.455685i
$627$	2.69676e9	−	6.87123e9i	0.436924	−	1.11326i
$628$	−8.91851e8	−	6.08054e8i	−0.143692	−	0.0979678i
$629$	−3.45749e8	+	1.66504e8i	−0.0553967	+	0.0266776i
$630$	−7.82661e8	+	7.26204e8i	−0.124704	+	0.115709i
$631$	−1.05100e10	−	1.58413e9i	−1.66533	−	0.251008i	−0.752276	−	0.658848i	$-0.771044\pi$
$631$	−1.05100e10	−	1.58413e9i	−1.66533	−	0.251008i	−0.913053	+	0.407840i	$0.866282\pi$
$632$	3.43911e8	+	4.58917e9i	0.0541921	+	0.723143i
$633$	−1.09223e8	−	2.78296e8i	−0.0171160	−	0.0436107i
$634$	−7.19481e7	+	3.15225e8i	−0.0112126	+	0.0491257i
$635$	−4.45774e8	+	5.94843e9i	−0.0690886	+	0.921923i
$636$	2.17011e9	−	6.69392e8i	0.334490	−	0.103176i
$637$	7.60821e9	+	3.66392e9i	1.16626	+	0.561640i
$638$	8.68487e9	+	1.50426e10i	1.32401	+	2.29325i
$639$	1.45975e9	−	2.52837e9i	0.221323	−	0.383343i
$640$	1.78371e9	−	1.21611e9i	0.268964	−	0.183377i
$641$	−1.91850e9	−	8.40548e9i	−0.287712	−	1.26055i	−0.887656	−	0.460507i	$-0.847668\pi$
$641$	−1.91850e9	−	8.40548e9i	−0.287712	−	1.26055i	0.599944	−	0.800042i	$-0.295189\pi$
$642$	1.02490e10	−	1.54479e9i	1.52866	−	0.230408i
$643$	4.58409e9	−	5.74827e9i	0.680010	−	0.852705i	−0.315345	−	0.948977i	$-0.602120\pi$
$643$	4.58409e9	−	5.74827e9i	0.680010	−	0.852705i	0.995355	+	0.0962718i	$0.0306918\pi$
$644$	1.46342e9			0.215908
$645$	−2.85035e9	−	2.72580e9i	−0.418254	−	0.399977i
$646$	−2.75926e9			−0.402698
$647$	6.93533e9	−	8.69663e9i	1.00670	−	1.26237i	0.0419767	−	0.999119i	$-0.486634\pi$
$647$	6.93533e9	−	8.69663e9i	1.00670	−	1.26237i	0.964728	−	0.263249i	$-0.0847941\pi$
$648$	8.74092e9	−	1.31748e9i	1.26196	−	0.190209i
$649$	4.08201e9	+	1.78844e10i	0.586162	+	2.56814i
$650$	−5.02625e9	+	3.42684e9i	−0.717873	+	0.489438i
$651$	−2.35500e9	+	4.07898e9i	−0.334548	+	0.579454i
$652$	−2.67738e8	−	4.63736e8i	−0.0378307	−	0.0655246i
$653$	−2.74870e9	−	1.32370e9i	−0.386306	−	0.186035i	0.230643	−	0.973038i	$-0.425917\pi$
$653$	−2.74870e9	−	1.32370e9i	−0.386306	−	0.186035i	−0.616949	+	0.787003i	$0.711631\pi$
$654$	−5.62298e9	+	1.73446e9i	−0.786040	+	0.242461i
$655$	−5.61920e7	+	7.49830e8i	−0.00781322	+	0.104260i
$656$	1.56161e9	−	6.84188e9i	0.215978	−	0.946264i
$657$	4.98065e7	+	1.26905e8i	0.00685184	+	0.0174582i
$658$	−1.06718e9	−	1.42406e10i	−0.146032	−	1.94866i
$659$	−1.33119e9	−	2.00645e8i	−0.181193	−	0.0273105i	0.0578189	−	0.998327i	$-0.481585\pi$
$659$	−1.33119e9	−	2.00645e8i	−0.181193	−	0.0273105i	−0.239012	+	0.971017i	$0.576824\pi$
$660$	−1.13508e9	+	1.05320e9i	−0.153682	+	0.142596i
$661$	9.62739e9	−	4.63631e9i	1.29659	−	0.624406i	0.346991	−	0.937868i	$-0.387203\pi$
$661$	9.62739e9	−	4.63631e9i	1.29659	−	0.624406i	0.949601	+	0.313462i	$0.101489\pi$
$662$	−3.55288e9	−	2.42231e9i	−0.475968	−	0.324509i
$663$	−3.27252e9	+	8.33824e9i	−0.436098	+	1.11116i
$664$	6.62662e9	+	2.04404e9i	0.878423	+	0.270957i
$665$	2.22792e9	+	2.06721e9i	0.293781	+	0.272589i
$666$	−8.44724e7	−	1.05925e8i	−0.0110804	−	0.0138944i
$667$	−5.93683e9	−	7.44455e9i	−0.774665	−	0.971400i
$668$	3.64953e8	+	3.38627e8i	0.0473717	+	0.0439546i
$669$	−9.81825e9	−	3.02853e9i	−1.26778	−	0.391057i
$670$	−7.35789e8	+	1.87476e9i	−0.0945130	+	0.240815i
$671$	5.15326e9	+	3.51343e9i	0.658496	+	0.448955i
$672$	4.14487e9	−	1.99607e9i	0.526889	−	0.253736i
$673$	−5.56259e9	+	5.16133e9i	−0.703436	+	0.652693i	−0.948487	−	0.316817i	$-0.897386\pi$
$673$	−5.56259e9	+	5.16133e9i	−0.703436	+	0.652693i	0.245051	+	0.969510i	$0.421195\pi$
$674$	1.21670e10	+	1.83388e9i	1.53064	+	0.230708i
$675$	3.64218e8	+	4.86016e9i	0.0455826	+	0.608257i
$676$	−3.98317e8	−	1.01489e9i	−0.0495924	−	0.126359i
$677$	4.30025e8	−	1.88406e9i	0.0532640	−	0.233365i	−0.941288	−	0.337604i	$-0.890384\pi$
$677$	4.30025e8	−	1.88406e9i	0.0532640	−	0.233365i	0.994552	+	0.104239i	$0.0332407\pi$
$678$	−1.68113e8	+	2.24331e9i	−0.0207156	+	0.276431i
$679$	−7.77092e9	+	2.39701e9i	−0.952639	+	0.293850i
$680$	3.30260e9	+	1.59045e9i	0.402786	+	0.193972i
$681$	6.04713e9	+	1.04739e10i	0.733727	+	1.27085i
$682$	3.05126e9	−	5.28494e9i	0.368328	−	0.637962i
$683$	−6.38138e8	+	4.35075e8i	−0.0766376	+	0.0522506i	−0.601033	−	0.799224i	$-0.705244\pi$
$683$	−6.38138e8	+	4.35075e8i	−0.0766376	+	0.0522506i	0.524395	+	0.851475i	$0.324291\pi$
$684$	5.00282e7	+	2.19188e8i	0.00597749	+	0.0261891i
$685$	1.24713e9	−	1.87974e8i	0.148250	−	0.0223450i
$686$	9.45024e7	−	1.18502e8i	0.0111766	−	0.0140150i
$687$	−9.00839e8			−0.105998
$688$	−3.23295e9	−	5.79969e9i	−0.378476	−	0.678962i
$689$	1.87487e10			2.18375
$690$	−2.29317e9	+	2.87554e9i	−0.265744	+	0.333233i
$691$	−1.16296e10	+	1.75288e9i	−1.34088	+	0.202105i	−0.779994	−	0.625786i	$-0.784778\pi$
$691$	−1.16296e10	+	1.75288e9i	−1.34088	+	0.202105i	−0.560888	+	0.827892i	$0.689540\pi$
$692$	−2.71797e8	−	1.19082e9i	−0.0311798	−	0.136608i
$693$	5.11879e9	−	3.48993e9i	0.584253	−	0.398337i
$694$	1.55801e9	−	2.69855e9i	0.176934	−	0.306459i
$695$	3.89058e8	+	6.73868e8i	0.0439610	+	0.0761427i
$696$	−1.46405e10	−	7.05049e9i	−1.64598	−	0.792660i
$697$	8.63982e9	−	2.66503e9i	0.966473	−	0.298118i
$698$	−9.59526e8	+	1.28040e10i	−0.106798	+	1.42512i
$699$	−1.82754e9	+	8.00697e9i	−0.202393	+	0.886744i
$700$	6.43175e8	+	1.63878e9i	0.0708738	+	0.180584i
$701$	−9.46335e7	−	1.26280e9i	−0.0103760	−	0.138459i	0.989610	−	0.143779i	$-0.0459255\pi$
$701$	−9.46335e7	−	1.26280e9i	−0.0103760	−	0.138459i	−0.999986	+	0.00532043i	$0.998306\pi$
$702$	8.91237e9	+	1.34332e9i	0.972329	+	0.146555i
$703$	−2.82713e8	+	2.62319e8i	−0.0306903	+	0.0284765i
$704$	−1.78960e10	+	8.61827e9i	−1.93309	+	0.930927i
$705$	−6.84391e9	−	4.66610e9i	−0.735601	−	0.501524i
$706$	6.00282e9	−	1.52949e10i	0.642006	−	1.63580i
$707$	8.23119e9	+	2.53899e9i	0.875981	+	0.270204i
$708$	−1.98648e9	−	1.84319e9i	−0.210363	−	0.195188i
$709$	−3.91397e9	−	4.90796e9i	−0.412435	−	0.517177i	0.531612	−	0.846988i	$-0.321586\pi$
$709$	−3.91397e9	−	4.90796e9i	−0.412435	−	0.517177i	−0.944047	+	0.329811i	$0.893015\pi$
$710$	−4.70971e9	−	5.90579e9i	−0.493845	−	0.619261i
$711$	−1.23625e9	−	1.14707e9i	−0.128992	−	0.119687i
$712$	−1.81549e8	−	5.60005e7i	−0.0188501	−	0.00581449i
$713$	−1.22219e9	+	3.11410e9i	−0.126278	+	0.321750i
$714$	−9.28033e9	−	6.32722e9i	−0.954157	−	0.650533i
$715$	−1.15174e10	+	5.54646e9i	−1.17837	+	0.567473i
$716$	6.19055e8	−	5.74399e8i	0.0630280	−	0.0584814i
$717$	4.30454e9	+	6.48805e8i	0.436124	+	0.0657351i
$718$	5.97708e8	+	7.97586e9i	0.0602634	+	0.804160i
$719$	6.81329e9	+	1.73600e10i	0.683606	+	1.74180i	0.670527	+	0.741885i	$0.266068\pi$
$719$	6.81329e9	+	1.73600e10i	0.683606	+	1.74180i	0.0130787	+	0.999914i	$0.495837\pi$
$720$	−2.32006e8	+	1.01648e9i	−0.0231652	+	0.101493i
$721$	9.97528e8	−	1.33111e10i	0.0991178	−	1.32263i
$722$	6.06086e9	−	1.86953e9i	0.599313	−	0.184864i
$723$	4.57542e9	+	2.20340e9i	0.450243	+	0.216825i
$724$	−1.32875e8	−	2.30146e8i	−0.0130124	−	0.0225382i
$725$	5.72740e9	−	9.92014e9i	0.558180	−	0.966796i
$726$	−2.35479e10	+	1.60547e10i	−2.28389	+	1.55713i
$727$	2.58855e9	+	1.13412e10i	0.249853	+	1.09468i	0.931713	+	0.363196i	$0.118315\pi$
$727$	2.58855e9	+	1.13412e10i	0.249853	+	1.09468i	−0.681859	+	0.731483i	$0.738828\pi$
$728$	2.03875e10	−	3.07291e9i	1.95841	−	0.295182i
$729$	4.06225e9	−	5.09390e9i	0.388347	−	0.486972i
$730$	3.52730e8			0.0335593
$731$	4.38843e9	−	7.34322e9i	0.415526	−	0.695306i
$732$	−9.21349e8			−0.0868231
$733$	−6.35971e9	+	7.97482e9i	−0.596449	+	0.747924i	−0.984820	−	0.173580i	$-0.944467\pi$
$733$	−6.35971e9	+	7.97482e9i	−0.596449	+	0.747924i	0.388371	+	0.921503i	$0.373038\pi$
$734$	8.90063e9	−	1.34155e9i	0.830777	−	0.125220i
$735$	1.36670e9	+	5.98790e9i	0.126960	+	0.556249i
$736$	2.69977e9	−	1.84067e9i	0.249606	−	0.170178i
$737$	5.84316e9	−	1.01206e10i	0.537664	−	0.931262i
$738$	1.59604e9	+	2.76443e9i	0.146166	+	0.253168i
$739$	−1.20477e10	−	5.80187e9i	−1.09812	−	0.528825i	−0.205051	−	0.978751i	$-0.565736\pi$
$739$	−1.20477e10	−	5.80187e9i	−1.09812	−	0.528825i	−0.893066	+	0.449926i	$0.851450\pi$
$740$	7.73075e7	−	2.38462e7i	0.00701311	−	0.00216326i
$741$	−6.72726e8	+	8.97691e9i	−0.0607400	+	0.810519i
$742$	−5.23138e9	+	2.29202e10i	−0.470113	+	2.05970i
$743$	3.02542e9	+	7.70864e9i	0.270598	+	0.689473i	0.999986	+	0.00537198i	$0.00170996\pi$
$743$	3.02542e9	+	7.70864e9i	0.270598	+	0.689473i	−0.729387	+	0.684101i	$0.760195\pi$
$744$	4.26637e8	+	5.69307e9i	0.0379798	+	0.506805i
$745$	−7.90434e9	−	1.19139e9i	−0.700355	−	0.105562i
$746$	−9.20598e9	+	8.54190e9i	−0.811866	+	0.753301i
$747$	−2.28959e9	+	1.10261e9i	−0.200972	+	0.0967830i
$748$	−2.77504e9	−	1.89199e9i	−0.242445	−	0.165296i
$749$	9.04696e9	−	2.30513e10i	0.786713	−	2.00451i
$750$	−9.98708e9	−	3.08061e9i	−0.864419	−	0.266638i
$751$	−9.79149e9	−	9.08518e9i	−0.843547	−	0.782697i	0.134537	−	0.990909i	$-0.457045\pi$
$751$	−9.79149e9	−	9.08518e9i	−0.843547	−	0.782697i	−0.978084	+	0.208212i	$0.933236\pi$
$752$	−8.69485e9	−	1.09030e10i	−0.745589	−	0.934939i
$753$	−3.40631e9	−	4.27137e9i	−0.290738	−	0.364574i
$754$	−1.55284e10	−	1.44083e10i	−1.31925	−	1.22408i
$755$	−3.94431e9	−	1.21666e9i	−0.333546	−	0.102885i
$756$	9.52931e8	−	2.42803e9i	0.0802112	−	0.204375i
$757$	−6.08817e9	−	4.15084e9i	−0.510095	−	0.347777i	0.280763	−	0.959777i	$-0.409413\pi$
$757$	−6.08817e9	−	4.15084e9i	−0.510095	−	0.347777i	−0.790857	+	0.612000i	$0.790365\pi$
$758$	4.32184e8	−	2.08129e8i	0.0360435	−	0.0173576i
$759$	1.56446e10	−	1.45160e10i	1.29873	−	1.20504i
$760$	3.64273e9	+	5.49054e8i	0.301009	+	0.0453699i
$761$	4.95607e8	+	6.61341e9i	0.0407653	+	0.543975i	0.979777	+	0.200091i	$0.0641238\pi$
$761$	4.95607e8	+	6.61341e9i	0.0407653	+	0.543975i	−0.939012	+	0.343884i	$0.888257\pi$
$762$	−8.09413e9	−	2.06235e10i	−0.662717	−	1.68857i
$763$	−3.12836e9	+	1.37062e10i	−0.254965	+	1.11708i
$764$	1.39366e6	−	1.85970e7i	0.000113065	−	0.00150875i
$765$	−1.28360e9	+	3.95938e8i	−0.103661	+	0.0319751i
$766$	1.78183e10	+	8.58084e9i	1.43240	+	0.689809i
$767$	−1.11859e10	−	1.93746e10i	−0.895134	−	1.55042i
$768$	3.81498e9	−	6.60775e9i	0.303898	−	0.526368i
$769$	1.02209e9	−	6.96849e8i	0.0810488	−	0.0552582i	−0.522118	−	0.852873i	$-0.674858\pi$
$769$	1.02209e9	−	6.96849e8i	0.0810488	−	0.0552582i	0.603167	+	0.797615i	$0.293905\pi$
$770$	−3.56688e9	−	1.56275e10i	−0.281560	−	1.23359i
$771$	1.87489e9	−	2.82594e8i	0.147328	−	0.0222061i
$772$	−1.47511e9	+	1.84974e9i	−0.115389	+	0.144693i
$773$	−1.18517e10			−0.922898			−0.461449	−	0.887167i	$-0.652670\pi$
$773$	−1.18517e10			−0.922898			−0.461449	+	0.887167i	$0.652670\pi$
$774$	2.87227e9	+	9.33594e8i	0.222655	+	0.0723710i
$775$	−4.02442e9			−0.310562
$776$	−6.14581e9	+	7.70660e9i	−0.472132	+	0.592034i
$777$	−1.55238e9	+	2.33983e8i	−0.118720	+	0.0178942i
$778$	6.83133e8	+	2.99300e9i	0.0520088	+	0.227865i
$779$	7.50768e9	−	5.11865e9i	0.569016	−	0.387949i
$780$	9.44192e8	−	1.63539e9i	0.0712409	−	0.123393i
$781$	2.19158e10	+	3.79593e10i	1.64619	+	2.85128i
$782$	−7.18767e9	−	3.46140e9i	−0.537483	−	0.258838i
$783$	−1.62175e10	+	5.00243e9i	−1.20731	+	0.372404i
$784$	−7.72737e8	+	1.03115e10i	−0.0572698	+	0.764212i
$785$	1.44224e9	−	6.31888e9i	0.106413	−	0.466226i
$786$	−1.02031e9	−	2.59970e9i	−0.0749466	−	0.190961i
$787$	−8.89534e8	−	1.18700e10i	−0.0650506	−	0.868039i	−0.930324	−	0.366739i	$-0.880474\pi$
$787$	−8.89534e8	−	1.18700e10i	−0.0650506	−	0.868039i	0.865273	−	0.501300i	$-0.167145\pi$
$788$	2.05723e9	+	3.10077e8i	0.149775	+	0.0225750i
$789$	−1.74670e10	+	1.62071e10i	−1.26605	+	1.17472i
$790$	−3.93129e9	+	1.89321e9i	−0.283688	+	0.136617i
$791$	4.44074e9	+	3.02764e9i	0.319034	+	0.217514i
$792$	2.74348e9	−	6.99027e9i	0.196229	−	0.499983i
$793$	−7.26841e9	−	2.24201e9i	−0.517587	−	0.159654i
$794$	1.02624e10	+	9.52210e9i	0.727573	+	0.675089i
$795$	8.50216e9	+	1.06614e10i	0.600129	+	0.752537i
$796$	9.23003e8	+	1.15741e9i	0.0648646	+	0.0813376i
$797$	−2.53476e9	−	2.35191e9i	−0.177350	−	0.164557i	0.586503	−	0.809947i	$-0.300504\pi$
$797$	−2.53476e9	−	2.35191e9i	−0.177350	−	0.164557i	−0.763853	+	0.645390i	$0.776695\pi$
$798$	−1.07865e10	−	3.32720e9i	−0.751400	−	0.231776i
$799$	6.56400e9	−	1.67248e10i	0.455255	−	1.15997i
$800$	3.24780e9	+	2.21431e9i	0.224272	+	0.152906i
$801$	6.27278e7	−	3.02081e7i	0.00431267	−	0.00207687i
$802$	−5.06796e9	+	4.70238e9i	−0.346915	+	0.321890i
$803$	−2.02389e9	−	3.05053e8i	−0.137938	−	0.0207908i
$804$	1.29009e8	+	1.72151e9i	0.00875436	+	0.116819i
$805$	3.21032e9	+	8.17976e9i	0.216901	+	0.552656i
$806$	−1.65607e9	+	7.25573e9i	−0.111406	+	0.488100i
$807$	−3.88908e8	+	5.18962e9i	−0.0260489	+	0.347599i
$808$	9.97709e9	−	3.07752e9i	0.665371	−	0.205240i
$809$	−8.92281e9	−	4.29700e9i	−0.592491	−	0.285329i	0.113513	−	0.993537i	$-0.463790\pi$
$809$	−8.92281e9	−	4.29700e9i	−0.592491	−	0.285329i	−0.706004	+	0.708208i	$0.749504\pi$
$810$	4.19064e9	+	7.25840e9i	0.277066	+	0.479892i
$811$	4.78043e9	−	8.27995e9i	0.314698	−	0.545073i	−0.664675	−	0.747133i	$-0.731430\pi$
$811$	4.78043e9	−	8.27995e9i	0.314698	−	0.545073i	0.979373	+	0.202059i	$0.0647633\pi$
$812$	−5.06511e9	+	3.45334e9i	−0.332004	+	0.226356i
$813$	−1.15477e9	−	5.05939e9i	−0.0753667	−	0.330203i
$814$	2.01134e9	−	3.03161e8i	0.130707	−	0.0197010i
$815$	2.00471e9	−	2.51382e9i	0.129718	−	0.162661i
$816$	−1.09685e10			−0.706694
$817$	2.03912e9	−	8.35192e9i	0.130818	−	0.535808i
$818$	1.39146e10			0.888859
$819$	−4.71075e9	+	5.90710e9i	−0.299638	+	0.375734i
$820$	−1.88482e9	+	2.84091e8i	−0.119377	+	0.0179932i
$821$	4.70832e9	+	2.06285e10i	0.296937	+	1.30097i	0.874661	+	0.484735i	$0.161084\pi$
$821$	4.70832e9	+	2.06285e10i	0.296937	+	1.30097i	−0.577724	+	0.816232i	$0.696059\pi$
$822$	−3.87032e9	+	2.63874e9i	−0.243050	+	0.165709i
$823$	1.21176e10	−	2.09883e10i	0.757735	−	1.31244i	−0.186268	−	0.982499i	$-0.559639\pi$
$823$	1.21176e10	−	2.09883e10i	0.757735	−	1.31244i	0.944003	−	0.329936i	$-0.107027\pi$
$824$	−8.08985e9	−	1.40120e10i	−0.503727	−	0.872481i
$825$	2.31313e10	+	1.11395e10i	1.43421	+	0.690678i
$826$	2.68065e10	−	8.26871e9i	1.65505	−	0.510514i
$827$	6.95625e8	−	9.28248e9i	0.0427667	−	0.570683i	−0.934125	−	0.356947i	$-0.883818\pi$
$827$	6.95625e8	−	9.28248e9i	0.0427667	−	0.570683i	0.976891	−	0.213736i	$-0.0685632\pi$
$828$	−1.44644e8	+	6.33727e8i	−0.00885512	+	0.0387968i
$829$	2.12700e9	+	5.41950e9i	0.129666	+	0.330384i	0.980932	−	0.194351i	$-0.0622600\pi$
$829$	2.12700e9	+	5.41950e9i	0.129666	+	0.330384i	−0.851266	+	0.524734i	$0.824165\pi$
$830$	4.91359e8	+	6.55673e9i	0.0298281	+	0.398028i
$831$	−2.82282e9	−	4.25471e8i	−0.170639	−	0.0257197i
$832$	1.77574e10	−	1.64765e10i	1.06893	−	0.991820i
$833$	−1.20028e10	+	5.78026e9i	−0.719493	+	0.346489i
$834$	−2.38783e9	−	1.62799e9i	−0.142535	−	0.0971788i
$835$	−1.09215e9	+	2.78275e9i	−0.0649201	+	0.165414i
$836$	−3.22542e9	−	9.94911e8i	−0.190926	−	0.0588928i
$837$	4.37090e9	+	4.05560e9i	0.257651	+	0.239065i
$838$	2.23586e7	+	2.80368e7i	0.00131247	+	0.00164579i
$839$	1.27046e10	+	1.59311e10i	0.742670	+	0.931279i	0.999380	−	0.0352099i	$-0.0112100\pi$
$839$	1.27046e10	+	1.59311e10i	0.742670	+	0.931279i	−0.256710	+	0.966488i	$0.582639\pi$
$840$	1.09927e10	+	1.01998e10i	0.639923	+	0.593762i
$841$	2.16322e10	+	6.67265e9i	1.25405	+	0.386823i
$842$	6.20404e8	−	1.58076e9i	0.0358164	−	0.0912587i
$843$	−1.90287e10	−	1.29736e10i	−1.09399	−	0.745869i
$844$	−1.23170e8	+	5.93155e7i	−0.00705189	+	0.00339601i
$845$	4.79895e9	−	4.45277e9i	0.273620	−	0.253882i
$846$	6.27230e9	+	9.45397e8i	0.356148	+	0.0536806i
$847$	5.08845e9	+	6.79007e10i	0.287736	+	3.83957i
$848$	8.38750e9	+	2.13710e10i	0.472332	+	1.20348i
$849$	−5.46079e9	+	2.39253e10i	−0.306251	+	1.34178i
$850$	7.17193e8	−	9.57027e9i	0.0400562	−	0.534513i
$851$	−1.06552e9	+	3.28668e8i	−0.0592661	+	0.0182812i
$852$	−5.83371e9	−	2.80937e9i	−0.323152	−	0.155622i
$853$	−2.90584e9	−	5.03305e9i	−0.160306	−	0.277658i	0.774673	−	0.632363i	$-0.217915\pi$
$853$	−2.90584e9	−	5.03305e9i	−0.160306	−	0.277658i	−0.934978	+	0.354705i	$0.884581\pi$
$854$	4.76892e9	−	8.26002e9i	0.262010	−	0.453814i
$855$	−1.11540e9	+	7.60467e8i	−0.0610309	+	0.0416101i
$856$	−6.67907e9	−	2.92629e10i	−0.363964	−	1.59463i
$857$	−3.08112e10	+	4.64405e9i	−1.67215	+	0.252037i	−0.915657	−	0.401960i	$-0.868329\pi$
$857$	−3.08112e10	+	4.64405e9i	−1.67215	+	0.252037i	−0.756497	+	0.653997i	$0.773091\pi$
$858$	2.96023e10	−	3.71201e10i	1.60000	−	2.00634i
$859$	−2.17018e10			−1.16821			−0.584104	−	0.811679i	$-0.698554\pi$
$859$	−2.17018e10			−1.16821			−0.584104	+	0.811679i	$0.698554\pi$
$860$	−1.14555e9	+	1.39290e9i	−0.0614145	+	0.0746751i
$861$	3.69884e10			1.97494
$862$	1.72750e10	−	2.16622e10i	0.918636	−	1.15193i
$863$	2.94427e10	−	4.43778e9i	1.55934	−	0.235032i	0.687998	−	0.725713i	$-0.258490\pi$
$863$	2.94427e10	−	4.43778e9i	1.55934	−	0.235032i	0.871340	+	0.490681i	$0.163252\pi$
$864$	−1.29595e9	−	5.67791e9i	−0.0683579	−	0.299496i
$865$	6.05983e9	−	4.13152e9i	0.318349	−	0.217047i
$866$	3.14461e9	−	5.44663e9i	0.164533	−	0.284980i
$867$	3.70334e9	+	6.41437e9i	0.192986	+	0.334262i
$868$	1.94048e9	+	9.34488e8i	0.100714	+	0.0485014i
$869$	2.41943e10	−	7.46294e9i	1.25067	−	0.385781i
$870$	1.15138e9	−	1.53640e10i	0.0592788	−	0.791021i
$871$	−3.17137e9	+	1.38947e10i	−0.162624	+	0.712501i
$872$	6.22566e9	+	1.58627e10i	0.317964	+	0.810159i
$873$	−2.69939e8	−	3.60208e9i	−0.0137314	−	0.183233i
$874$	−7.92793e9	−	1.19494e9i	−0.401670	−	0.0605421i
$875$	−1.83043e10	+	1.69839e10i	−0.923686	+	0.857056i
$876$	2.72410e8	−	1.31186e8i	0.0136917	−	0.00659359i
$877$	1.48135e10	+	1.00997e10i	0.741581	+	0.505601i	0.874200	−	0.485566i	$-0.161386\pi$
$877$	1.48135e10	+	1.00997e10i	0.741581	+	0.505601i	−0.132619	+	0.991167i	$0.542339\pi$
$878$	−8.87941e9	+	2.26244e10i	−0.442745	+	1.12810i
$879$	−1.16772e10	−	3.60193e9i	−0.579931	−	0.178885i
$880$	−1.14747e10	−	1.06470e10i	−0.567612	−	0.526667i
$881$	−1.11749e9	−	1.40128e9i	−0.0550588	−	0.0690416i	0.753540	−	0.657403i	$-0.228345\pi$
$881$	−1.11749e9	−	1.40128e9i	−0.0550588	−	0.0690416i	−0.808598	+	0.588361i	$0.799773\pi$
$882$	−2.93250e9	−	3.67724e9i	−0.143912	−	0.180460i
$883$	1.30669e10	+	1.21243e10i	0.638718	+	0.592644i	0.931591	−	0.363508i	$-0.118421\pi$
$883$	1.30669e10	+	1.21243e10i	0.638718	+	0.592644i	−0.292873	+	0.956151i	$0.594611\pi$
$884$	3.91405e9	+	1.20732e9i	0.190565	+	0.0587815i
$885$	5.94470e9	−	1.51468e10i	0.288289	−	0.734549i
$886$	−2.02882e10	−	1.38323e10i	−0.979999	−	0.668152i
$887$	−2.70078e10	+	1.30063e10i	−1.29944	+	0.625778i	−0.950313	−	0.311297i	$-0.899236\pi$
$887$	−2.70078e10	+	1.30063e10i	−1.29944	+	0.625778i	−0.349128	+	0.937075i	$0.613522\pi$
$888$	−1.39493e9	+	1.29430e9i	−0.0668507	+	0.0620284i
$889$	−5.23404e10	−	7.88905e9i	−2.49851	−	0.376590i
$890$	−1.34617e7	−	1.79635e8i	−0.000640083	−	0.00854132i
$891$	−1.77677e10	−	4.52714e10i	−0.841511	−	2.14414i
$892$	−1.04549e9	+	4.58059e9i	−0.0493223	+	0.216095i
$893$	1.34935e9	−	1.80059e10i	0.0634082	−	0.846123i
$894$	2.83701e10	−	8.75100e9i	1.32794	−	0.409616i
$895$	4.56862e9	+	2.20013e9i	0.213012	+	0.102581i
$896$	9.57822e9	+	1.65900e10i	0.444843	+	0.770491i
$897$	−1.30136e10	+	2.25402e10i	−0.602039	+	1.04276i
$898$	−7.83720e9	+	5.34331e9i	−0.361155	+	0.246231i
$899$	−3.11837e9	−	1.36625e10i	−0.143143	−	0.627149i
$900$	−7.73239e8	+	1.16547e8i	−0.0353561	+	0.00532908i
$901$	−1.84417e10	+	2.31252e10i	−0.839971	+	1.05329i
$902$	−4.79240e10			−2.17436
$903$	2.60099e10	−	2.34145e10i	1.17553	−	1.05822i
$904$	6.51464e9			0.293293
$905$	9.94909e8	−	1.24758e9i	0.0446183	−	0.0559496i
$906$	1.51594e10	−	2.28491e9i	0.677225	−	0.102075i
$907$	4.77107e9	+	2.09034e10i	0.212320	+	0.930233i	0.962986	+	0.269552i	$0.0868755\pi$
$907$	4.77107e9	+	2.09034e10i	0.212320	+	0.930233i	−0.750666	+	0.660682i	$0.770267\pi$
$908$	4.56945e9	−	3.11540e9i	0.202564	−	0.138106i
$909$	−1.91307e9	+	3.31353e9i	−0.0844804	+	0.146324i
$910$	9.77432e9	+	1.69296e10i	0.429973	+	0.744736i
$911$	−3.11134e10	−	1.49834e10i	−1.36343	−	0.656593i	−0.398031	−	0.917372i	$-0.630306\pi$
$911$	−3.11134e10	−	1.49834e10i	−1.36343	−	0.656593i	−0.965399	+	0.260779i	$0.916021\pi$
$912$	−1.05334e10	+	3.24914e9i	−0.459821	+	0.141836i
$913$	2.85116e9	−	3.80461e10i	0.123986	−	1.65448i
$914$	−3.93661e9	+	1.72474e10i	−0.170534	+	0.747158i
$915$	−2.02117e9	−	5.14987e9i	−0.0872227	−	0.222240i
$916$	3.07837e7	+	4.10780e8i	0.00132339	+	0.0176594i
$917$	−6.59777e9	−	9.94454e8i	−0.282556	−	0.0425885i
$918$	−1.04234e10	+	9.67146e9i	−0.444691	+	0.412613i
$919$	2.42731e10	−	1.16893e10i	1.03162	−	0.496804i	0.160071	−	0.987106i	$-0.448828\pi$
$919$	2.42731e10	−	1.16893e10i	1.03162	−	0.496804i	0.871553	+	0.490302i	$0.163113\pi$
$920$	8.80028e9	+	5.99993e9i	0.372597	+	0.254032i
$921$	2.59361e8	−	6.60840e8i	0.0109394	−	0.0278733i
$922$	−1.73798e10	−	5.36096e9i	−0.730275	−	0.225260i
$923$	−3.91852e10	−	3.63585e10i	−1.64027	−	1.52195i
$924$	−8.56677e9	−	1.07424e10i	−0.357244	−	0.447970i
$925$	−8.36348e8	−	1.04875e9i	−0.0347449	−	0.0435687i
$926$	−1.23151e10	−	1.14267e10i	−0.509682	−	0.472916i
$927$	5.66571e9	+	1.74764e9i	0.233601	+	0.0720564i
$928$	−5.00075e9	+	1.27417e10i	−0.205408	+	0.523371i
$929$	1.05588e10	+	7.19883e9i	0.432073	+	0.294583i	0.759760	−	0.650204i	$-0.225317\pi$
$929$	1.05588e10	+	7.19883e9i	0.432073	+	0.294583i	−0.327686	+	0.944787i	$0.606269\pi$
$930$	−4.87694e9	+	2.34861e9i	−0.198819	+	0.0957461i
$931$	−9.81450e9	+	9.10653e9i	−0.398607	+	0.369853i
$932$	3.71361e9	+	5.59737e8i	0.150259	+	0.0226479i
$933$	−1.94695e9	−	2.59803e10i	−0.0784820	−	1.04727i
$934$	−5.19870e8	−	1.32461e9i	−0.0208776	−	0.0531953i
$935$	4.48761e9	−	1.96615e10i	0.179546	−	0.786640i
$936$	−6.84380e8	+	9.13242e9i	−0.0272792	+	0.364016i
$937$	4.21156e10	−	1.29909e10i	1.67246	−	0.515884i	0.693587	−	0.720373i	$-0.256029\pi$
$937$	4.21156e10	−	1.29909e10i	1.67246	−	0.515884i	0.978869	+	0.204489i	$0.0655533\pi$
$938$	−1.61013e10	−	7.75398e9i	−0.637017	−	0.306771i
$939$	2.44194e10	+	4.22957e10i	0.962511	+	1.66712i
$940$	−1.89386e9	+	3.28026e9i	−0.0743703	+	0.128813i
$941$	−6.56137e8	+	4.47346e8i	−0.0256703	+	0.0175017i	−0.576087	−	0.817388i	$-0.695421\pi$
$941$	−6.56137e8	+	4.47346e8i	−0.0256703	+	0.0175017i	0.550417	+	0.834890i	$0.314469\pi$
$942$	5.35663e9	+	2.34689e10i	0.208792	+	0.914777i
$943$	2.59781e10	−	3.91557e9i	1.00883	−	0.152056i
$944$	1.70803e10	−	2.14180e10i	0.660835	−	0.828661i
$945$	1.56619e10			0.603716
$946$	−3.36998e10	+	3.03370e10i	−1.29422	+	1.16507i
$947$	−2.12442e10			−0.812861			−0.406430	−	0.913682i	$-0.633227\pi$
$947$	−2.12442e10			−0.812861			−0.406430	+	0.913682i	$0.633227\pi$
$948$	−2.33198e9	+	2.92421e9i	−0.0888989	+	0.111476i
$949$	2.46824e9	−	3.72027e8i	0.0937465	−	0.0141300i
$950$	−2.14620e9	−	9.40313e9i	−0.0812153	−	0.355828i
$951$	−1.37501e9	+	9.37465e8i	−0.0518410	+	0.0353446i
$952$	−1.62634e10	+	2.81691e10i	−0.610918	+	1.05814i
$953$	−1.76951e10	−	3.06489e10i	−0.662261	−	1.14707i	−0.980020	−	0.198898i	$-0.936264\pi$
$953$	−1.76951e10	−	3.06489e10i	−0.662261	−	1.14707i	0.317759	−	0.948171i	$-0.397070\pi$
$954$	−9.40840e9	−	4.53085e9i	−0.350830	−	0.168951i
$955$	1.07005e8	−	3.30067e7i	0.00397551	−	0.00122628i
$956$	1.48758e8	−	1.98503e9i	0.00550651	−	0.0734793i
$957$	−1.98937e10	+	8.71599e10i	−0.733708	+	3.21459i
$958$	4.67110e9	+	1.19018e10i	0.171649	+	0.437353i
$959$	8.36335e8	+	1.11601e10i	0.0306207	+	0.408605i
$960$	1.74220e10	+	2.62594e9i	0.635547	+	0.0957933i
$961$	1.65590e10	−	1.53645e10i	0.601869	−	0.558453i
$962$	−2.23497e9	+	1.07631e9i	−0.0809393	+	0.0389783i
$963$	9.08805e9	+	6.19613e9i	0.327928	+	0.223578i
$964$	8.48395e8	−	2.16168e9i	0.0305020	−	0.0777179i
$965$	−1.35750e10	−	4.18735e9i	−0.486290	−	0.150001i
$966$	−2.39242e10	−	2.21984e10i	−0.853921	−	0.792323i
$967$	8.35812e9	+	1.04808e10i	0.297246	+	0.372735i	0.907917	−	0.419150i	$-0.137672\pi$
$967$	8.35812e9	+	1.04808e10i	0.297246	+	0.372735i	−0.610671	+	0.791884i	$0.709100\pi$
$968$	5.14589e10	+	6.45274e10i	1.82346	+	2.28655i
$969$	−1.04107e10	−	9.65970e9i	−0.367575	−	0.341060i
$970$	−8.93077e9	−	2.75478e9i	−0.314187	−	0.0969138i
$971$	−7.72686e8	+	1.96877e9i	−0.0270854	+	0.0690126i	−0.943777	−	0.330584i	$-0.892754\pi$
$971$	−7.72686e8	+	1.96877e9i	−0.0270854	+	0.0690126i	0.916691	+	0.399596i	$0.130850\pi$
$972$	2.25039e9	+	1.53429e9i	0.0786007	+	0.0535890i
$973$	−6.22086e9	+	2.99581e9i	−0.216499	+	0.104260i
$974$	−1.93276e10	+	1.79334e10i	−0.670228	+	0.621880i
$975$	−3.09608e10	−	4.66659e9i	−1.06978	−	0.161244i
$976$	−6.96041e8	−	9.28802e9i	−0.0239641	−	0.319778i
$977$	−1.36644e10	−	3.48163e10i	−0.468770	−	1.19441i	−0.948440	−	0.316958i	$-0.897339\pi$
$977$	−1.36644e10	−	3.48163e10i	−0.468770	−	1.19441i	0.479670	−	0.877449i	$-0.340757\pi$
$978$	−2.65733e9	+	1.16425e10i	−0.0908364	+	0.397980i
$979$	−7.81132e7	+	1.04235e9i	−0.00266063	+	0.0355037i
$980$	2.68377e9	−	8.27832e8i	0.0910864	−	0.0280964i
$981$	−5.62622e9	−	2.70945e9i	−0.190272	−	0.0916303i
$982$	4.58685e9	+	7.94466e9i	0.154570	+	0.267723i
$983$	−1.29347e10	+	2.24035e10i	−0.434329	+	0.752280i	−0.997241	−	0.0742374i	$-0.976348\pi$
$983$	−1.29347e10	+	2.24035e10i	−0.434329	+	0.752280i	0.562912	+	0.826517i	$0.309681\pi$
$984$	3.70435e10	−	2.52558e10i	1.23945	−	0.845043i
$985$	2.77979e9	+	1.21791e10i	0.0926798	+	0.406057i
$986$	3.30457e10	−	4.98084e9i	1.09786	−	0.165476i
$987$	4.58273e10	−	5.74656e10i	1.51710	−	1.90238i
$988$	4.11644e9			0.135791
$989$	1.57890e10	−	1.91981e10i	0.518999	−	0.631061i
$990$	7.11998e9			0.233214
$991$	−7.72835e9	+	9.69104e9i	−0.252249	+	0.316310i	−0.891792	−	0.452445i	$-0.850552\pi$
$991$	−7.72835e9	+	9.69104e9i	−0.252249	+	0.316310i	0.639544	+	0.768755i	$0.279123\pi$
$992$	4.75527e9	−	7.16742e8i	0.154662	−	0.0233116i
$993$	−4.92489e9	−	2.15774e10i	−0.159615	−	0.699320i
$994$	5.53818e10	−	3.77587e10i	1.78861	−	1.21945i
$995$	−4.44452e9	+	7.69814e9i	−0.143036	+	0.247745i
$996$	2.81802e9	+	4.88095e9i	0.0903724	+	0.156530i
$997$	−1.78435e10	−	8.59296e9i	−0.570225	−	0.274606i	0.126473	−	0.991970i	$-0.459634\pi$
$997$	−1.78435e10	−	8.59296e9i	−0.570225	−	0.274606i	−0.696698	+	0.717364i	$0.745348\pi$
$998$	−2.93191e10	+	9.04376e9i	−0.933672	+	0.288000i
$999$	−1.48520e8	+	1.98187e9i	−0.00471310	+	0.0628919i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	43.8.g.a.24.8	yes	300
43.9	even	21	inner	43.8.g.a.9.8	✓	300

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
43.8.g.a.9.8	✓	300	43.9	even	21	inner
43.8.g.a.24.8	yes	300	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 43 \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	43.g (of order \(21\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(-6.35832 + 7.97308i) q^{2} +(-51.9023 + 7.82301i) q^{3} +(5.34089 + 23.4000i) q^{4} +(-119.077 + 81.1857i) q^{5} +(267.638 - 463.562i) q^{6} +(-639.426 - 1107.52i) q^{7} +(-1396.60 - 672.566i) q^{8} +(542.807 - 167.434i) q^{9} +O(q^{10})\)	\(q+(-6.35832 + 7.97308i) q^{2} +(-51.9023 + 7.82301i) q^{3} +(5.34089 + 23.4000i) q^{4} +(-119.077 + 81.1857i) q^{5} +(267.638 - 463.562i) q^{6} +(-639.426 - 1107.52i) q^{7} +(-1396.60 - 672.566i) q^{8} +(542.807 - 167.434i) q^{9} +(109.833 - 1465.62i) q^{10} +(-1897.71 + 8314.43i) q^{11} +(-460.263 - 1172.73i) q^{12} +(-777.239 - 10371.5i) q^{13} +(12896.0 + 1943.76i) q^{14} +(5545.27 - 5145.26i) q^{15} +(11474.5 - 5525.81i) q^{16} +(13557.1 + 9243.06i) q^{17} +(-2116.38 + 5392.44i) q^{18} +(15757.4 + 4860.50i) q^{19} +(-2535.72 - 2352.81i) q^{20} +(41851.8 + 52480.5i) q^{21} +(-54225.3 - 67996.4i) q^{22} +(34949.4 + 32428.3i) q^{23} +(77748.1 + 23982.1i) q^{24} +(-20953.9 + 53389.7i) q^{25} +(87635.0 + 59748.5i) q^{26} +(76561.3 - 36870.0i) q^{27} +(22500.8 - 20877.7i) q^{28} +(-197489. - 29766.6i) q^{29} +(5764.97 + 76928.1i) q^{30} +(25635.1 + 65317.2i) q^{31} +(15250.6 - 66817.4i) q^{32} +(33451.8 - 446383. i) q^{33} +(-159896. + 49321.3i) q^{34} +(166056. + 79968.3i) q^{35} +(6817.02 + 11807.4i) q^{36} +(-11693.9 + 20254.5i) q^{37} +(-138944. + 94730.1i) q^{38} +(121477. + 532225. i) q^{39} +(220906. - 33296.2i) q^{40} +(343566. - 430818. i) q^{41} -684538. q^{42} +(-31124.4 - 520432. i) q^{43} -204693. q^{44} +(-51042.9 + 64005.7i) q^{45} +(-480773. + 72464.9i) q^{46} +(-243658. - 1.06754e6i) q^{47} +(-552322. + 376567. i) q^{48} +(-405961. + 703144. i) q^{49} +(-292449. - 506536. i) q^{50} +(-775951. - 373678. i) q^{51} +(238542. - 73580.6i) q^{52} +(-134712. + 1.79761e6i) q^{53} +(-192834. + 844860. i) q^{54} +(-449037. - 1.14413e6i) q^{55} +(148142. + 1.97682e6i) q^{56} +(-855866. - 129001. i) q^{57} +(1.49303e6 - 1.38533e6i) q^{58} +(1.93800e6 - 933290. i) q^{59} +(150016. + 102279. i) q^{60} +(267187. - 680781. i) q^{61} +(-683775. - 210917. i) q^{62} +(-532521. - 494107. i) q^{63} +(1.45217e6 + 1.82096e6i) q^{64} +(934571. + 1.17192e6i) q^{65} +(3.34635e6 + 3.10496e6i) q^{66} +(-1.30943e6 - 403905. i) q^{67} +(-143880. + 366601. i) q^{68} +(-2.06764e6 - 1.40969e6i) q^{69} +(-1.69343e6 + 815513. i) q^{70} +(3.76758e6 - 3.49581e6i) q^{71} +(-870693. - 131236. i) q^{72} +(17935.0 + 239326. i) q^{73} +(-87136.9 - 222021. i) q^{74} +(669888. - 2.93497e6i) q^{75} +(-29577.3 + 394681. i) q^{76} +(1.04218e7 - 3.21471e6i) q^{77} +(-5.01586e6 - 2.41551e6i) q^{78} +(-1.48443e6 - 2.57110e6i) q^{79} +(-917734. + 1.58956e6i) q^{80} +(-4.71171e6 + 3.21239e6i) q^{81} +(1.25044e6 + 5.47856e6i) q^{82} +(-4.42373e6 + 666770. i) q^{83} +(-1.00452e6 + 1.25962e6i) q^{84} -2.36475e6 q^{85} +(4.34735e6 + 3.06092e6i) q^{86} +1.04830e7 q^{87} +(8.24235e6 - 1.03356e7i) q^{88} +(121197. - 18267.5i) q^{89} +(-185776. - 813938. i) q^{90} +(-1.09897e7 + 7.49263e6i) q^{91} +(-572161. + 991011. i) q^{92} +(-1.84150e6 - 3.18957e6i) q^{93} +(1.00608e7 + 4.84503e6i) q^{94} +(-2.27095e6 + 700496. i) q^{95} +(-268829. + 3.58728e6i) q^{96} +(1.41501e6 - 6.19956e6i) q^{97} +(-3.02500e6 - 7.70757e6i) q^{98} +(362024. + 4.83087e6i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 300 q - 40 q^{2} - 12 q^{3} - 3028 q^{4} + 235 q^{5} + 1274 q^{6} - 4122 q^{7} + 762 q^{8} + 8097 q^{9}+O(q^{10}) \) 300 * q - 40 * q^2 - 12 * q^3 - 3028 * q^4 + 235 * q^5 + 1274 * q^6 - 4122 * q^7 + 762 * q^8 + 8097 * q^9	\( 300 q - 40 q^{2} - 12 q^{3} - 3028 q^{4} + 235 q^{5} + 1274 q^{6} - 4122 q^{7} + 762 q^{8} + 8097 q^{9} - 1681 q^{10} + 4580 q^{11} + 9330 q^{12} - 20444 q^{13} - 45798 q^{14} + 50477 q^{15} - 74504 q^{16} - 25312 q^{17} + 2046 q^{18} + 4046 q^{19} + 140781 q^{20} + 100555 q^{21} + 95810 q^{22} + 1648 q^{23} - 292592 q^{24} + 419068 q^{25} + 393435 q^{26} + 274140 q^{27} + 233644 q^{28} + 605697 q^{29} - 1216016 q^{30} + 358580 q^{31} - 19194 q^{32} + 1280291 q^{33} + 1137255 q^{34} + 652739 q^{35} - 8980975 q^{36} - 2360047 q^{37} - 308490 q^{38} + 536339 q^{39} + 3057993 q^{40} - 1376320 q^{41} + 8417790 q^{42} + 7173000 q^{43} - 3856780 q^{44} + 2761486 q^{45} - 7073993 q^{46} + 1437090 q^{47} - 9543469 q^{48} - 16053170 q^{49} - 3046893 q^{50} + 2972901 q^{51} + 17415142 q^{52} + 3320604 q^{53} + 6000486 q^{54} + 13427750 q^{55} - 5450793 q^{56} + 3333100 q^{57} - 7876190 q^{58} - 7084765 q^{59} + 7356443 q^{60} + 3354606 q^{61} - 719427 q^{62} + 14716815 q^{63} - 16086234 q^{64} - 19914646 q^{65} - 8293345 q^{66} + 13025470 q^{67} - 22191927 q^{68} - 33964295 q^{69} + 8094727 q^{70} + 30843495 q^{71} + 93841607 q^{72} - 3067637 q^{73} + 18179570 q^{74} - 41508571 q^{75} - 19751872 q^{76} - 15169179 q^{77} - 69509396 q^{78} - 12090149 q^{79} - 69662530 q^{80} + 3387954 q^{81} + 39226888 q^{82} + 16408777 q^{83} + 98603231 q^{84} - 13423424 q^{85} + 111906660 q^{86} + 49022010 q^{87} + 76213954 q^{88} - 12540205 q^{89} - 92608607 q^{90} - 59091937 q^{91} - 50489370 q^{92} - 52218334 q^{93} - 3441600 q^{94} - 79947551 q^{95} - 23449784 q^{96} - 116467587 q^{97} + 73909552 q^{98} - 20061115 q^{99}+O(q^{100}) \) 300 * q - 40 * q^2 - 12 * q^3 - 3028 * q^4 + 235 * q^5 + 1274 * q^6 - 4122 * q^7 + 762 * q^8 + 8097 * q^9 - 1681 * q^10 + 4580 * q^11 + 9330 * q^12 - 20444 * q^13 - 45798 * q^14 + 50477 * q^15 - 74504 * q^16 - 25312 * q^17 + 2046 * q^18 + 4046 * q^19 + 140781 * q^20 + 100555 * q^21 + 95810 * q^22 + 1648 * q^23 - 292592 * q^24 + 419068 * q^25 + 393435 * q^26 + 274140 * q^27 + 233644 * q^28 + 605697 * q^29 - 1216016 * q^30 + 358580 * q^31 - 19194 * q^32 + 1280291 * q^33 + 1137255 * q^34 + 652739 * q^35 - 8980975 * q^36 - 2360047 * q^37 - 308490 * q^38 + 536339 * q^39 + 3057993 * q^40 - 1376320 * q^41 + 8417790 * q^42 + 7173000 * q^43 - 3856780 * q^44 + 2761486 * q^45 - 7073993 * q^46 + 1437090 * q^47 - 9543469 * q^48 - 16053170 * q^49 - 3046893 * q^50 + 2972901 * q^51 + 17415142 * q^52 + 3320604 * q^53 + 6000486 * q^54 + 13427750 * q^55 - 5450793 * q^56 + 3333100 * q^57 - 7876190 * q^58 - 7084765 * q^59 + 7356443 * q^60 + 3354606 * q^61 - 719427 * q^62 + 14716815 * q^63 - 16086234 * q^64 - 19914646 * q^65 - 8293345 * q^66 + 13025470 * q^67 - 22191927 * q^68 - 33964295 * q^69 + 8094727 * q^70 + 30843495 * q^71 + 93841607 * q^72 - 3067637 * q^73 + 18179570 * q^74 - 41508571 * q^75 - 19751872 * q^76 - 15169179 * q^77 - 69509396 * q^78 - 12090149 * q^79 - 69662530 * q^80 + 3387954 * q^81 + 39226888 * q^82 + 16408777 * q^83 + 98603231 * q^84 - 13423424 * q^85 + 111906660 * q^86 + 49022010 * q^87 + 76213954 * q^88 - 12540205 * q^89 - 92608607 * q^90 - 59091937 * q^91 - 50489370 * q^92 - 52218334 * q^93 - 3441600 * q^94 - 79947551 * q^95 - 23449784 * q^96 - 116467587 * q^97 + 73909552 * q^98 - 20061115 * q^99

Introduction

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