LMFDB - Embedded newform 43.8.g.a.9.9

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			9.9
Character	$\chi$	$=$	43.9
Dual form			43.8.g.a.24.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-5.72725 - 7.18175i) q^{2} +(9.19934 + 1.38658i) q^{3} +(9.70661 - 42.5274i) q^{4} +(445.851 + 303.976i) q^{5} +(-42.7289 - 74.0086i) q^{6} +(-356.405 + 617.311i) q^{7} +(-1420.36 + 684.008i) q^{8} +(-2007.13 - 619.118i) q^{9} +O(q^{10})$	\(q+(-5.72725 - 7.18175i) q^{2} +(9.19934 + 1.38658i) q^{3} +(9.70661 - 42.5274i) q^{4} +(445.851 + 303.976i) q^{5} +(-42.7289 - 74.0086i) q^{6} +(-356.405 + 617.311i) q^{7} +(-1420.36 + 684.008i) q^{8} +(-2007.13 - 619.118i) q^{9} +(-370.422 - 4942.94i) q^{10} +(644.393 + 2823.27i) q^{11} +(148.262 - 377.765i) q^{12} +(-615.967 + 8219.51i) q^{13} +(6474.59 - 975.887i) q^{14} +(3680.05 + 3414.59i) q^{15} +(8016.55 + 3860.57i) q^{16} +(-25301.9 + 17250.5i) q^{17} +(7049.00 + 17960.6i) q^{18} +(45077.8 - 13904.7i) q^{19} +(17255.0 - 16010.3i) q^{20} +(-4134.64 + 5184.67i) q^{21} +(16585.4 - 20797.5i) q^{22} +(-36582.7 + 33943.8i) q^{23} +(-14014.8 + 4322.99i) q^{24} +(77839.6 + 198332. i) q^{25} +(62558.3 - 42651.5i) q^{26} +(-35937.1 - 17306.4i) q^{27} +(22793.2 + 21149.0i) q^{28} +(154587. - 23300.3i) q^{29} +(3446.13 - 45985.4i) q^{30} +(49661.5 - 126536. i) q^{31} +(26715.1 + 117047. i) q^{32} +(2013.31 + 26865.7i) q^{33} +(268799. + 82913.6i) q^{34} +(-346551. + 166890. i) q^{35} +(-45812.0 + 79348.7i) q^{36} +(-157467. - 272741. i) q^{37} +(-358032. - 244102. i) q^{38} +(-17063.5 + 74760.0i) q^{39} +(-841190. - 126789. i) q^{40} +(-178082. - 223307. i) q^{41} +60915.1 q^{42} +(423568. + 303988. i) q^{43} +126321. q^{44} +(-706686. - 886156. i) q^{45} +(453294. + 68323.0i) q^{46} +(-81470.5 + 356946. i) q^{47} +(68394.0 + 46630.2i) q^{48} +(157723. + 273184. i) q^{49} +(978564. - 1.69492e6i) q^{50} +(-256680. + 123611. i) q^{51} +(343576. + 105979. i) q^{52} +(-8143.56 - 108668. i) q^{53} +(81530.8 + 357210. i) q^{54} +(-570904. + 1.45464e6i) q^{55} +(83976.2 - 1.12059e6i) q^{56} +(433966. - 65409.9i) q^{57} +(-1.05270e6 - 976759. i) q^{58} +(-168215. - 81008.2i) q^{59} +(180935. - 123359. i) q^{60} +(-29093.2 - 74128.3i) q^{61} +(-1.19317e6 + 368044. i) q^{62} +(1.09754e6 - 1.01837e6i) q^{63} +(1.39769e6 - 1.75265e6i) q^{64} +(-2.77317e6 + 3.47744e6i) q^{65} +(181412. - 168326. i) q^{66} +(-2.08697e6 + 643746. i) q^{67} +(488025. + 1.24347e6i) q^{68} +(-383602. + 261535. i) q^{69} +(3.18335e6 + 1.53302e6i) q^{70} +(2.30346e6 + 2.13730e6i) q^{71} +(3.27433e6 - 493525. i) q^{72} +(391954. - 5.23026e6i) q^{73} +(-1.05690e6 + 2.69295e6i) q^{74} +(441070. + 1.93246e6i) q^{75} +(-153777. - 2.05201e6i) q^{76} +(-1.97250e6 - 608436. i) q^{77} +(634634. - 305624. i) q^{78} +(-728587. + 1.26195e6i) q^{79} +(2.40067e6 + 4.15808e6i) q^{80} +(3.48888e6 + 2.37868e6i) q^{81} +(-583818. + 2.55787e6i) q^{82} +(3.54221e6 + 533903. i) q^{83} +(180357. + 226161. i) q^{84} -1.65246e7 q^{85} +(-242714. - 4.78297e6i) q^{86} +1.45441e6 q^{87} +(-2.84641e6 - 3.56928e6i) q^{88} +(3.86183e6 + 582077. i) q^{89} +(-2.31678e6 + 1.01505e7i) q^{90} +(-4.85446e6 - 3.30972e6i) q^{91} +(1.08845e6 + 1.88525e6i) q^{92} +(632305. - 1.09518e6i) q^{93} +(3.03009e6 - 1.45922e6i) q^{94} +(2.43247e7 + 7.50318e6i) q^{95} +(83467.3 + 1.11379e6i) q^{96} +(-3.21483e6 - 1.40851e7i) q^{97} +(1.05862e6 - 2.69732e6i) q^{98} +(454557. - 6.06564e6i) 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 $\left(\mathbb{Z}/43\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{1}{21}\right)$

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 $

$2$	−5.72725	−	7.18175i	−0.506222	−	0.634783i	0.461398	−	0.887193i	$-0.347348\pi$
$2$	−5.72725	−	7.18175i	−0.506222	−	0.634783i	−0.967620	+	0.252411i	$0.918777\pi$
$3$	9.19934	+	1.38658i	0.196713	+	0.0296497i	0.246659	−	0.969102i	$-0.420667\pi$
$3$	9.19934	+	1.38658i	0.196713	+	0.0296497i	−0.0499468	+	0.998752i	$0.515905\pi$
$4$	9.70661	−	42.5274i	0.0758329	−	0.332246i
$5$	445.851	+	303.976i	1.59513	+	1.08754i	0.944683	+	0.327984i	$0.106369\pi$
$5$	445.851	+	303.976i	1.59513	+	1.08754i	0.650443	+	0.759555i	$0.274583\pi$
$6$	−42.7289	−	74.0086i	−0.0807593	−	0.139879i
$7$	−356.405	+	617.311i	−0.392736	+	0.680238i	−0.992809	−	0.119707i	$-0.961805\pi$
$7$	−356.405	+	617.311i	−0.392736	+	0.680238i	0.600074	+	0.799945i	$0.295138\pi$
$8$	−1420.36	+	684.008i	−0.980804	+	0.472331i
$9$	−2007.13	−	619.118i	−0.917756	−	0.283090i
$10$	−370.422	−	4942.94i	−0.117138	−	1.56310i
$11$	644.393	+	2823.27i	0.145974	+	0.639555i	0.993979	+	0.109567i	$0.0349465\pi$
$11$	644.393	+	2823.27i	0.145974	+	0.639555i	−0.848005	+	0.529988i	$0.822196\pi$
$12$	148.262	−	377.765i	0.0247683	−	0.0631085i
$13$	−615.967	+	8219.51i	−0.0777600	+	1.03763i	0.812733	+	0.582637i	$0.197979\pi$
$13$	−615.967	+	8219.51i	−0.0777600	+	1.03763i	−0.890493	+	0.454998i	$0.849640\pi$
$14$	6474.59	−	975.887i	0.630615	−	0.0950499i
$15$	3680.05	+	3414.59i	0.281536	+	0.261228i
$16$	8016.55	+	3860.57i	0.489291	+	0.235630i
$17$	−25301.9	+	17250.5i	−1.24906	+	0.851591i	−0.993347	−	0.115163i	$-0.963261\pi$
$17$	−25301.9	+	17250.5i	−1.24906	+	0.851591i	−0.255708	+	0.966754i	$0.582309\pi$
$18$	7049.00	+	17960.6i	0.284888	+	0.725882i
$19$	45077.8	−	13904.7i	1.50774	−	0.465075i	0.572741	−	0.819736i	$-0.305880\pi$
$19$	45077.8	−	13904.7i	1.50774	−	0.465075i	0.934995	+	0.354661i	$0.115404\pi$
$20$	17255.0	−	16010.3i	0.482293	−	0.447503i
$21$	−4134.64	+	5184.67i	−0.0974249	+	0.122167i
$22$	16585.4	−	20797.5i	0.332083	−	0.416419i
$23$	−36582.7	+	33943.8i	−0.626943	+	0.581718i	−0.928318	−	0.371788i	$-0.878745\pi$
$23$	−36582.7	+	33943.8i	−0.626943	+	0.581718i	0.301375	+	0.953506i	$0.402554\pi$
$24$	−14014.8	+	4322.99i	−0.206941	+	0.0638329i
$25$	77839.6	+	198332.i	0.996347	+	2.53865i
$26$	62558.3	−	42651.5i	0.698036	−	0.475913i
$27$	−35937.1	−	17306.4i	−0.351375	−	0.169213i
$28$	22793.2	+	21149.0i	0.196224	+	0.182069i
$29$	154587.	−	23300.3i	1.17701	−	0.177406i	0.468733	−	0.883340i	$-0.344711\pi$
$29$	154587.	−	23300.3i	1.17701	−	0.177406i	0.708278	+	0.705934i	$0.249473\pi$
$30$	3446.13	−	45985.4i	0.0233028	−	0.310954i
$31$	49661.5	−	126536.i	0.299402	−	0.762863i	−0.699437	−	0.714694i	$-0.746566\pi$
$31$	49661.5	−	126536.i	0.299402	−	0.762863i	0.998839	−	0.0481694i	$-0.0153387\pi$
$32$	26715.1	+	117047.i	0.144123	+	0.631442i
$33$	2013.31	+	26865.7i	0.00975240	+	0.130137i
$34$	268799.	+	82913.6i	1.17287	+	0.361784i
$35$	−346551.	+	166890.i	−1.36625	+	0.657950i
$36$	−45812.0	+	79348.7i	−0.163652	+	0.283453i
$37$	−157467.	−	272741.i	−0.511074	−	0.885206i	−0.999918	−	0.0128348i	$-0.995914\pi$
$37$	−157467.	−	272741.i	−0.511074	−	0.885206i	0.488844	−	0.872371i	$-0.337419\pi$
$38$	−358032.	−	244102.i	−1.05847	−	0.721654i
$39$	−17063.5	+	74760.0i	−0.0460619	+	0.201810i
$40$	−841190.	−	126789.i	−2.07819	−	0.313236i
$41$	−178082.	−	223307.i	−0.403530	−	0.506010i	0.537998	−	0.842946i	$-0.319181\pi$
$41$	−178082.	−	223307.i	−0.403530	−	0.506010i	−0.941528	+	0.336936i	$0.890609\pi$
$42$	60915.1			0.126868
$43$	423568.	+	303988.i	0.812425	+	0.583065i
$43$	423568.	+	303988.i	0.812425	+	0.583065i
$44$	126321.			0.223559
$45$	−706686.	−	886156.i	−1.15607	−	1.44966i
$46$	453294.	+	68323.0i	0.686637	+	0.103494i
$47$	−81470.5	+	356946.i	−0.114461	+	0.501487i	0.884901	+	0.465779i	$0.154226\pi$
$47$	−81470.5	+	356946.i	−0.114461	+	0.501487i	−0.999362	+	0.0357080i	$0.988631\pi$
$48$	68394.0	+	46630.2i	0.0892634	+	0.0608588i
$49$	157723.	+	273184.i	0.191518	+	0.331718i
$50$	978564.	−	1.69492e6i	1.10712	−	1.91759i
$51$	−256680.	+	123611.i	−0.270954	+	0.130485i
$52$	343576.	+	105979.i	0.338853	+	0.104522i
$53$	−8143.56	−	108668.i	−0.00751362	−	0.100262i	0.992186	−	0.124767i	$-0.0398182\pi$
$53$	−8143.56	−	108668.i	−0.00751362	−	0.100262i	−0.999700	+	0.0245045i	$0.992199\pi$
$54$	81530.8	+	357210.i	0.0704601	+	0.308706i
$55$	−570904.	+	1.45464e6i	−0.462694	+	1.17892i
$56$	83976.2	−	1.12059e6i	0.0638996	−	0.852681i
$57$	433966.	−	65409.9i	0.310380	−	0.0467823i
$58$	−1.05270e6	−	976759.i	−0.708443	−	0.657339i
$59$	−168215.	−	81008.2i	−0.106631	−	0.0513508i	0.379808	−	0.925065i	$-0.375990\pi$
$59$	−168215.	−	81008.2i	−0.106631	−	0.0513508i	−0.486439	+	0.873715i	$0.661704\pi$
$60$	180935.	−	123359.i	0.108141	−	0.0737296i
$61$	−29093.2	−	74128.3i	−0.0164111	−	0.0418147i	0.922433	−	0.386156i	$-0.126197\pi$
$61$	−29093.2	−	74128.3i	−0.0164111	−	0.0418147i	−0.938844	+	0.344341i	$0.888102\pi$
$62$	−1.19317e6	+	368044.i	−0.635816	+	0.196123i
$63$	1.09754e6	−	1.01837e6i	0.553004	−	0.513113i
$64$	1.39769e6	−	1.75265e6i	0.666471	−	0.835728i
$65$	−2.77317e6	+	3.47744e6i	−1.25250	+	1.57059i
$66$	181412.	−	168326.i	0.0776717	−	0.0720688i
$67$	−2.08697e6	+	643746.i	−0.847725	+	0.261488i	−0.688034	−	0.725679i	$-0.741526\pi$
$67$	−2.08697e6	+	643746.i	−0.847725	+	0.261488i	−0.159691	+	0.987167i	$0.551050\pi$
$68$	488025.	+	1.24347e6i	0.188218	+	0.479572i
$69$	−383602.	+	261535.i	−0.140575	+	0.0958426i
$70$	3.18335e6	+	1.53302e6i	1.10928	+	0.534201i
$71$	2.30346e6	+	2.13730e6i	0.763796	+	0.708699i	0.962476	−	0.271365i	$-0.0874751\pi$
$71$	2.30346e6	+	2.13730e6i	0.763796	+	0.708699i	−0.198680	+	0.980064i	$0.563666\pi$
$72$	3.27433e6	−	493525.i	1.03385	−	0.155828i
$73$	391954.	−	5.23026e6i	0.117925	−	1.57360i	−0.553707	−	0.832711i	$-0.686787\pi$
$73$	391954.	−	5.23026e6i	0.117925	−	1.57360i	0.671632	−	0.740885i	$-0.265594\pi$
$74$	−1.05690e6	+	2.69295e6i	−0.303197	+	0.772532i
$75$	441070.	+	1.93246e6i	0.120724	+	0.528926i
$76$	−153777.	−	2.05201e6i	−0.0401831	−	0.536207i
$77$	−1.97250e6	−	608436.i	−0.492379	−	0.151879i
$78$	634634.	−	305624.i	0.151423	−	0.0729216i
$79$	−728587.	+	1.26195e6i	−0.166260	+	0.287970i	−0.937102	−	0.349056i	$-0.886502\pi$
$79$	−728587.	+	1.26195e6i	−0.166260	+	0.287970i	0.770842	+	0.637026i	$0.219836\pi$
$80$	2.40067e6	+	4.15808e6i	0.524224	+	0.907983i
$81$	3.48888e6	+	2.37868e6i	0.729438	+	0.497322i
$82$	−583818.	+	2.55787e6i	−0.116931	+	0.512307i
$83$	3.54221e6	+	533903.i	0.679989	+	0.102492i	0.479949	−	0.877296i	$-0.340655\pi$
$83$	3.54221e6	+	533903.i	0.679989	+	0.102492i	0.200039	+	0.979788i	$0.435893\pi$
$84$	180357.	+	226161.i	0.0332014	+	0.0416333i
$85$	−1.65246e7			−2.91854
$86$	−242714.	−	4.78297e6i	−0.0411481	−	0.810874i
$87$	1.45441e6			0.236793
$88$	−2.84641e6	−	3.56928e6i	−0.445254	−	0.558331i
$89$	3.86183e6	+	582077.i	0.580669	+	0.0875217i	0.432807	−	0.901486i	$-0.357523\pi$
$89$	3.86183e6	+	582077.i	0.580669	+	0.0875217i	0.147861	+	0.989008i	$0.452761\pi$
$90$	−2.31678e6	+	1.01505e7i	−0.334993	+	1.46770i
$91$	−4.85446e6	−	3.30972e6i	−0.675299	−	0.460411i
$92$	1.08845e6	+	1.88525e6i	0.145730	+	0.252412i
$93$	632305.	−	1.09518e6i	0.0815148	−	0.141188i
$94$	3.03009e6	−	1.45922e6i	0.376278	−	0.181206i
$95$	2.43247e7	+	7.50318e6i	2.91082	+	0.897868i
$96$	83467.3	+	1.11379e6i	0.00962869	+	0.128486i
$97$	−3.21483e6	−	1.40851e7i	−0.357649	−	1.56696i	−0.759032	−	0.651054i	$-0.774327\pi$
$97$	−3.21483e6	−	1.40851e7i	−0.357649	−	1.56696i	0.401382	−	0.915911i	$-0.368530\pi$
$98$	1.05862e6	−	2.69732e6i	0.113619	−	0.289495i
$99$	454557.	−	6.06564e6i	0.0470831	−	0.628280i
$100$	9.19011e6	−	1.38519e6i	0.919011	−	0.138519i
$101$	2.29742e6	+	2.13169e6i	0.221878	+	0.205873i	0.783278	−	0.621672i	$-0.213546\pi$
$101$	2.29742e6	+	2.13169e6i	0.221878	+	0.205873i	−0.561399	+	0.827545i	$0.689737\pi$
$102$	2.35781e6	+	1.13546e6i	0.219993	+	0.105943i
$103$	−1.69238e7	+	1.15385e7i	−1.52605	+	1.04044i	−0.546921	+	0.837185i	$0.684200\pi$
$103$	−1.69238e7	+	1.15385e7i	−1.52605	+	1.04044i	−0.979126	+	0.203256i	$0.934848\pi$
$104$	−4.74732e6	−	1.20960e7i	−0.413839	−	1.05444i
$105$	−3.41945e6	+	1.05476e6i	−0.288266	+	0.0889184i
$106$	−733788.	+	680856.i	−0.0598412	+	0.0555245i
$107$	−217852.	+	273178.i	−0.0171917	+	0.0215577i	−0.790353	−	0.612652i	$-0.790103\pi$
$107$	−217852.	+	273178.i	−0.0171917	+	0.0215577i	0.773161	+	0.634209i	$0.218674\pi$
$108$	−1.08483e6	+	1.36033e6i	−0.0828661	+	0.103911i
$109$	1.08421e6	−	1.00600e6i	0.0801901	−	0.0744055i	−0.639059	−	0.769157i	$-0.720676\pi$
$109$	1.08421e6	−	1.00600e6i	0.0801901	−	0.0744055i	0.719250	+	0.694752i	$0.244486\pi$
$110$	1.37166e7	−	4.23100e6i	0.982587	−	0.303088i
$111$	−1.07042e6	−	2.72738e6i	−0.0742887	−	0.189284i
$112$	−5.24030e6	+	3.57278e6i	−0.352447	+	0.240294i
$113$	−2.02967e7	−	9.77435e6i	−1.32327	−	0.637255i	−0.367135	−	0.930168i	$-0.619661\pi$
$113$	−2.02967e7	−	9.77435e6i	−1.32327	−	0.637255i	−0.956139	+	0.292912i	$0.905376\pi$
$114$	−2.95519e6	−	2.74202e6i	−0.186818	−	0.173342i
$115$	−2.66285e7	+	4.01361e6i	−1.63269	+	0.246089i
$116$	509617.	−	6.80036e6i	0.0303138	−	0.404510i
$117$	6.32518e6	−	1.61163e7i	0.365109	−	0.930282i
$118$	381631.	+	1.67203e6i	0.0213824	+	0.0936824i
$119$	−1.63123e6	−	2.17673e7i	−0.0887364	−	1.18410i
$120$	−7.56259e6	−	2.33275e6i	−0.399518	−	0.123235i
$121$	1.00017e7	−	4.81657e6i	0.513246	−	0.247166i
$122$	−365746.	+	633491.i	−0.0182356	+	0.0315850i
$123$	−1.32860e6	−	2.30120e6i	−0.0643764	−	0.111503i
$124$	−4.89919e6	−	3.34021e6i	−0.230753	−	0.157325i
$125$	−1.62024e7	+	7.09875e7i	−0.741986	+	3.25085i
$126$	−1.35995e7	−	2.04980e6i	−0.605658	−	0.0912883i
$127$	−1.82349e7	−	2.28659e7i	−0.789935	−	0.990547i	−0.999918	−	0.0128420i	$-0.995912\pi$
$127$	−1.82349e7	−	2.28659e7i	−0.789935	−	0.990547i	0.209983	−	0.977705i	$-0.432659\pi$
$128$	−5.22475e6			−0.220207
$129$	3.47504e6	+	3.38380e6i	0.142527	+	0.138784i
$130$	4.08567e7			1.63103
$131$	4.90233e6	+	6.14733e6i	0.190526	+	0.238912i	0.867915	−	0.496713i	$-0.165460\pi$
$131$	4.90233e6	+	6.14733e6i	0.190526	+	0.238912i	−0.677389	+	0.735625i	$0.736889\pi$
$132$	1.16207e6	+	175154.i	0.0439769	+	0.00662845i
$133$	−7.48244e6	+	3.27827e7i	−0.275780	+	1.20827i
$134$	1.65758e7	+	1.13012e7i	0.595125	+	0.405750i
$135$	−1.07619e7	−	1.86401e7i	−0.376461	−	0.652050i
$136$	2.41382e7	−	4.18086e7i	0.822846	−	1.42521i
$137$	2.84199e7	−	1.36863e7i	0.944280	−	0.454741i	0.102603	−	0.994722i	$-0.467283\pi$
$137$	2.84199e7	−	1.36863e7i	0.944280	−	0.454741i	0.841677	+	0.539981i	$0.181569\pi$
$138$	4.07527e6	+	1.25705e6i	0.132002	+	0.0407171i
$139$	1.43059e6	+	1.90899e7i	0.0451819	+	0.602911i	0.973138	+	0.230222i	$0.0739451\pi$
$139$	1.43059e6	+	1.90899e7i	0.0451819	+	0.602911i	−0.927956	+	0.372689i	$0.878436\pi$
$140$	3.73358e6	+	1.63579e7i	0.114995	+	0.503824i
$141$	−1.24441e6	+	3.17070e6i	−0.0373849	+	0.0952551i
$142$	2.15705e6	−	2.87838e7i	0.0632194	−	0.843604i
$143$	−2.36028e7	+	3.55756e6i	−0.674976	+	0.101736i
$144$	−1.37001e7	−	1.27119e7i	−0.382345	−	0.354765i
$145$	7.60056e7	+	3.66024e7i	2.07042	+	0.997060i
$146$	−3.98072e7	+	2.71401e7i	−1.05859	+	0.721733i
$147$	1.07216e6	+	2.73181e6i	0.0278386	+	0.0709316i
$148$	−1.31275e7	+	4.04928e6i	−0.332862	+	0.102674i
$149$	−1.37657e7	+	1.27727e7i	−0.340915	+	0.316323i	−0.831986	−	0.554797i	$-0.812796\pi$
$149$	−1.37657e7	+	1.27727e7i	−0.340915	+	0.316323i	0.491071	+	0.871119i	$0.336606\pi$
$150$	1.13523e7	−	1.42353e7i	0.274640	−	0.344388i
$151$	−2.38184e6	+	2.98673e6i	−0.0562980	+	0.0705955i	−0.809183	−	0.587556i	$-0.800090\pi$
$151$	−2.38184e6	+	2.98673e6i	−0.0562980	+	0.0705955i	0.752885	+	0.658152i	$0.228662\pi$
$152$	−5.45157e7	+	5.05832e7i	−1.25913	+	1.16830i
$153$	6.14643e7	−	1.89592e7i	1.38741	−	0.427958i
$154$	6.92738e6	+	1.76507e7i	0.152843	+	0.389438i
$155$	6.06055e7	−	4.13201e7i	1.30723	−	0.891252i
$156$	3.01372e6	+	1.45133e6i	0.0635576	+	0.0306077i
$157$	−1.52727e7	−	1.41710e7i	−0.314969	−	0.292248i	0.506807	−	0.862060i	$-0.330826\pi$
$157$	−1.52727e7	−	1.41710e7i	−0.314969	−	0.292248i	−0.821775	+	0.569812i	$0.807016\pi$
$158$	1.32358e7	−	1.99498e6i	0.266963	−	0.0402381i
$159$	75761.6	−	1.01097e6i	0.00149472	−	0.0199456i
$160$	−2.36684e7	+	6.03061e7i	−0.456824	+	1.16397i
$161$	−7.91562e6	−	3.46806e7i	−0.149484	−	0.654932i
$162$	−2.89863e6	−	3.86795e7i	−0.0535661	−	0.714790i
$163$	1.01656e8	+	3.13567e7i	1.83855	+	0.567118i	0.999742	+	0.0226944i	$0.00722448\pi$
$163$	1.01656e8	+	3.13567e7i	1.83855	+	0.567118i	0.838810	+	0.544424i	$0.183252\pi$
$164$	−1.12253e7	+	5.40580e6i	−0.198721	+	0.0956988i
$165$	−7.26891e6	+	1.25901e7i	−0.125972	+	0.218191i
$166$	−1.64528e7	−	2.84971e7i	−0.279165	−	0.483529i
$167$	7.01069e7	+	4.77981e7i	1.16480	+	0.794150i	0.981978	−	0.188995i	$-0.0605230\pi$
$167$	7.01069e7	+	4.77981e7i	1.16480	+	0.794150i	0.182826	+	0.983145i	$0.441475\pi$
$168$	2.32630e6	−	1.01922e7i	0.0378516	−	0.165839i
$169$	−5.13332e6	−	773723.i	−0.0818078	−	0.0123305i
$170$	9.46407e7	+	1.18676e8i	1.47743	+	1.85264i
$171$	−9.90858e7			−1.51539
$172$	1.70392e7	−	1.50626e7i	0.255329	−	0.225709i
$173$	5.18097e7			0.760763			0.380382	−	0.924830i	$-0.375793\pi$
$173$	5.18097e7			0.760763			0.380382	+	0.924830i	$0.375793\pi$
$174$	−8.32976e6	−	1.04452e7i	−0.119870	−	0.150312i
$175$	−1.50175e8	−	2.26352e7i	−2.11819	−	0.319265i
$176$	−5.73362e6	+	2.51206e7i	−0.0792746	+	0.347325i
$177$	−1.43515e6	−	978466.i	−0.0194531	−	0.0132629i
$178$	−1.79373e7	−	3.10684e7i	−0.238390	−	0.412904i
$179$	−1.40117e7	+	2.42689e7i	−0.182601	+	0.316275i	−0.942766	−	0.333456i	$-0.891785\pi$
$179$	−1.40117e7	+	2.42689e7i	−0.182601	+	0.316275i	0.760164	+	0.649731i	$0.225118\pi$
$180$	−4.45454e7	+	2.14520e7i	−0.569311	+	0.274166i
$181$	−5.28286e7	−	1.62955e7i	−0.662208	−	0.204264i	−0.0546087	−	0.998508i	$-0.517391\pi$
$181$	−5.28286e7	−	1.62955e7i	−0.662208	−	0.204264i	−0.607599	+	0.794244i	$0.707867\pi$
$182$	4.03318e6	+	5.38191e7i	0.0495905	+	0.661739i
$183$	−164854.	−	722271.i	−0.00198847	−	0.00871207i
$184$	2.87426e7	−	7.32351e7i	0.340145	−	0.866676i
$185$	1.26999e7	−	1.69468e8i	0.147468	−	1.96783i
$186$	−1.14867e7	+	1.73134e6i	−0.130888	+	0.0197282i
$187$	−6.50073e7	−	6.03179e7i	−0.726970	−	0.674529i
$188$	1.43892e7	+	6.92946e6i	0.157937	+	0.0760584i
$189$	2.34916e7	−	1.60163e7i	0.253102	−	0.172562i
$190$	−8.54278e7	−	2.17666e8i	−0.903570	−	2.30226i
$191$	−2.00032e6	+	617018.i	−0.0207722	+	0.00640739i	−0.305124	−	0.952313i	$-0.598698\pi$
$191$	−2.00032e6	+	617018.i	−0.0207722	+	0.00640739i	0.284352	+	0.958720i	$0.408222\pi$
$192$	1.52880e7	−	1.41852e7i	0.155882	−	0.144638i
$193$	−4.86420e7	+	6.09951e7i	−0.487036	+	0.610723i	−0.963250	−	0.268606i	$-0.913437\pi$
$193$	−4.86420e7	+	6.09951e7i	−0.487036	+	0.610723i	0.476215	+	0.879329i	$0.342009\pi$
$194$	−8.27435e7	+	1.03757e8i	−0.813632	+	1.02026i
$195$	−3.03331e7	+	2.81450e7i	−0.292951	+	0.271819i
$196$	1.31488e7	−	4.05586e6i	0.124735	−	0.0384757i
$197$	1.16031e7	+	2.95643e7i	0.108129	+	0.275509i	0.974689	−	0.223564i	$-0.0717691\pi$
$197$	1.16031e7	+	2.95643e7i	0.108129	+	0.275509i	−0.866560	+	0.499073i	$0.833674\pi$
$198$	−4.61652e7	+	3.14749e7i	−0.422656	+	0.288162i
$199$	1.65351e8	+	7.96287e7i	1.48737	+	0.716282i	0.988616	−	0.150459i	$-0.0480753\pi$
$199$	1.65351e8	+	7.96287e7i	1.48737	+	0.716282i	0.498758	+	0.866741i	$0.333790\pi$
$200$	−2.46221e8	−	2.28459e8i	−2.17630	−	2.01931i
$201$	−2.00914e7	+	3.02829e6i	−0.174511	+	0.0263033i
$202$	2.15138e6	−	2.87082e7i	0.0183649	−	0.245062i
$203$	−4.07121e7	+	1.03733e8i	−0.341576	+	0.870321i
$204$	2.76535e6	+	1.21158e7i	0.0228057	+	0.0999184i
$205$	−1.15178e7	−	1.53694e8i	−0.0933752	−	1.24600i
$206$	1.79793e8	+	5.54588e7i	1.43297	+	0.442013i
$207$	9.44415e7	−	4.54806e7i	0.740059	−	0.356394i
$208$	−3.66699e7	+	6.35141e7i	−0.282545	+	0.489383i
$209$	6.83045e7	+	1.18307e8i	0.517532	+	0.896392i
$210$	2.71591e7	+	1.85168e7i	0.202371	+	0.137974i
$211$	4.07726e7	−	1.78636e8i	0.298799	−	1.30912i	−0.573119	−	0.819472i	$-0.694267\pi$
$211$	4.07726e7	−	1.78636e8i	0.298799	−	1.30912i	0.871918	−	0.489652i	$-0.162876\pi$
$212$	−4.70043e6	−	708476.i	−0.0338815	−	0.00510681i
$213$	1.82268e7	+	2.28557e7i	0.129236	+	0.162056i
$214$	3.20959e6			0.0223873
$215$	9.64431e7	+	2.64288e8i	0.661815	+	1.81361i
$216$	6.28813e7			0.424554
$217$	6.04122e7	+	7.57545e7i	0.401343	+	0.503268i
$218$	−1.34344e7	−	2.02491e6i	−0.0878254	−	0.0132375i
$219$	1.08579e7	−	4.75715e7i	0.0698539	−	0.306050i
$220$	5.63206e7	+	3.83987e7i	0.356605	+	0.243129i
$221$	−1.26206e8	−	2.18595e8i	−0.786514	−	1.36228i
$222$	−1.34568e7	+	2.33078e7i	−0.0825479	+	0.142977i
$223$	1.68282e8	−	8.10404e7i	1.01618	−	0.489367i	0.149781	−	0.988719i	$-0.452143\pi$
$223$	1.68282e8	−	8.10404e7i	1.01618	−	0.489367i	0.866399	+	0.499352i	$0.166429\pi$
$224$	−8.17755e7	−	2.52244e7i	−0.486133	−	0.149952i
$225$	−3.34434e7	−	4.46271e8i	−0.195736	−	2.61192i
$226$	4.60471e7	+	2.01746e8i	0.265352	+	1.16258i
$227$	2.89622e7	−	7.37945e7i	0.164339	−	0.418730i	−0.824854	−	0.565345i	$-0.808743\pi$
$227$	2.89622e7	−	7.37945e7i	0.164339	−	0.418730i	0.989194	+	0.146616i	$0.0468381\pi$
$228$	1.43063e6	−	1.90904e7i	0.00799382	−	0.106670i
$229$	−1.80499e8	+	2.72058e7i	−0.993229	+	0.149705i	−0.625497	−	0.780227i	$-0.715104\pi$
$229$	−1.80499e8	+	2.72058e7i	−0.993229	+	0.149705i	−0.367732	+	0.929932i	$0.619866\pi$
$230$	1.81333e8	+	1.68252e8i	0.982719	+	0.911830i
$231$	−1.73021e7	−	8.33224e6i	−0.0923541	−	0.0444754i
$232$	−2.03631e8	+	1.38833e8i	−1.07062	+	0.729939i
$233$	1.91332e7	+	4.87507e7i	0.0990929	+	0.252485i	0.971820	−	0.235723i	$-0.0757460\pi$
$233$	1.91332e7	+	4.87507e7i	0.0990929	+	0.252485i	−0.872727	+	0.488208i	$0.837651\pi$
$234$	−1.51969e8	+	4.68762e7i	−0.775353	+	0.239165i
$235$	−1.44827e8	+	1.34380e8i	−0.727966	+	0.675454i
$236$	−5.07787e6	+	6.36745e6i	−0.0251472	+	0.0315336i
$237$	−8.45231e6	+	1.05989e7i	−0.0412436	+	0.0517178i
$238$	−1.46985e8	+	1.36382e8i	−0.706729	+	0.655749i
$239$	1.15235e8	−	3.55453e7i	0.546000	−	0.168419i	−0.00947034	−	0.999955i	$-0.503015\pi$
$239$	1.15235e8	−	3.55453e7i	0.546000	−	0.168419i	0.555470	+	0.831537i	$0.312538\pi$
$240$	1.63191e7	+	4.15803e7i	0.0762002	+	0.194155i
$241$	2.68940e8	−	1.83360e8i	1.23764	−	0.843810i	0.245558	−	0.969382i	$-0.421029\pi$
$241$	2.68940e8	−	1.83360e8i	1.23764	−	0.843810i	0.992085	+	0.125571i	$0.0400764\pi$
$242$	−9.18737e7	−	4.42441e7i	−0.416714	−	0.200679i
$243$	9.27437e7	+	8.60536e7i	0.414632	+	0.384722i
$244$	−3.43488e6	+	517725.i	−0.0151373	+	0.00228158i
$245$	−1.27205e7	+	1.69744e8i	−0.0552617	+	0.737416i
$246$	−8.91743e6	+	2.27212e7i	−0.0381915	+	0.0973104i
$247$	8.65231e7	+	3.79083e8i	0.365336	+	1.60064i
$248$	1.60142e7	+	2.13695e8i	0.0666690	+	0.889636i
$249$	3.18457e7	+	9.82311e6i	0.130724	+	0.0403229i
$250$	6.02610e8	−	2.90202e8i	2.43919	−	1.17465i
$251$	7.52805e7	−	1.30390e8i	0.300486	−	0.520458i	−0.675760	−	0.737122i	$-0.736184\pi$
$251$	7.52805e7	−	1.30390e8i	0.300486	−	0.520458i	0.976246	+	0.216664i	$0.0695177\pi$
$252$	−3.26552e7	−	5.65605e7i	−0.128544	−	0.222644i
$253$	−1.19406e8	−	8.14097e7i	−0.463558	−	0.316049i
$254$	−5.97809e7	+	2.61917e8i	−0.228899	+	1.00287i
$255$	−1.52016e8	−	2.29127e7i	−0.574114	−	0.0865337i
$256$	−1.48981e8	−	1.86816e8i	−0.554997	−	0.695944i
$257$	−1.20519e8			−0.442884			−0.221442	−	0.975174i	$-0.571076\pi$
$257$	−1.20519e8			−0.442884			−0.221442	+	0.975174i	$0.571076\pi$
$258$	4.39916e6	−	4.43368e7i	0.0159478	−	0.160729i
$259$	2.24488e8			0.802868
$260$	1.20969e8	+	1.51690e8i	0.426841	+	0.535242i
$261$	−3.24703e8	−	4.89410e7i	−1.13043	−	0.170385i
$262$	1.60717e7	−	7.04146e7i	0.0552086	−	0.241885i
$263$	1.93577e8	+	1.31979e8i	0.656159	+	0.447361i	0.845087	−	0.534630i	$-0.179549\pi$
$263$	1.93577e8	+	1.31979e8i	0.656159	+	0.447361i	−0.188928	+	0.981991i	$0.560501\pi$
$264$	−2.12360e7	−	3.67818e7i	−0.0710328	−	0.123032i
$265$	2.94018e7	−	5.09254e7i	0.0970539	−	0.168102i
$266$	2.78291e8	−	1.34018e8i	0.906595	−	0.436593i
$267$	3.47192e7	+	1.07095e7i	0.111630	+	0.0344333i
$268$	7.11943e6	+	9.50021e7i	0.0225930	+	0.301482i
$269$	−2.00797e7	−	8.79750e7i	−0.0628962	−	0.275566i	0.933694	−	0.358071i	$-0.116565\pi$
$269$	−2.00797e7	−	8.79750e7i	−0.0628962	−	0.275566i	−0.996591	+	0.0825044i	$0.973708\pi$
$270$	−7.22327e7	+	1.84046e8i	−0.223337	+	0.569053i
$271$	−1.21791e7	+	1.62519e8i	−0.0371727	+	0.496035i	0.947283	+	0.320399i	$0.103817\pi$
$271$	−1.21791e7	+	1.62519e8i	−0.0371727	+	0.496035i	−0.984455	+	0.175636i	$0.943802\pi$
$272$	−2.69431e8	+	4.06101e7i	−0.811812	+	0.122361i
$273$	−4.00687e7	−	3.71783e7i	−0.119189	−	0.110591i
$274$	−2.61060e8	−	1.25720e8i	−0.766677	−	0.369212i
$275$	−5.09786e8	+	3.47566e8i	−1.47817	+	1.00780i
$276$	7.39896e6	+	1.88522e7i	0.0211831	+	0.0539736i
$277$	−2.97260e8	+	9.16926e7i	−0.840345	+	0.259212i	−0.684904	−	0.728633i	$-0.740156\pi$
$277$	−2.97260e8	+	9.16926e7i	−0.840345	+	0.259212i	−0.155441	+	0.987845i	$0.549680\pi$
$278$	1.28906e8	−	1.19607e8i	0.359845	−	0.333887i
$279$	−1.78018e8	+	2.23227e8i	−0.490737	+	0.615365i
$280$	3.78072e8	−	4.74088e8i	1.02925	−	1.29064i
$281$	5.87532e7	−	5.45150e7i	0.157965	−	0.146570i	−0.597231	−	0.802069i	$-0.703732\pi$
$281$	5.87532e7	−	5.45150e7i	0.157965	−	0.146570i	0.755195	+	0.655500i	$0.227542\pi$
$282$	2.98982e7	−	9.22237e6i	0.0793913	−	0.0244890i
$283$	1.68469e8	+	4.29251e8i	0.441842	+	1.12579i	0.962320	+	0.271919i	$0.0876584\pi$
$283$	1.68469e8	+	4.29251e8i	0.441842	+	1.12579i	−0.520478	+	0.853875i	$0.674246\pi$
$284$	1.13253e8	−	7.72145e7i	0.293383	−	0.200025i
$285$	2.13368e8	+	1.02752e8i	0.545973	+	0.262927i
$286$	1.60729e8	+	1.49135e8i	0.406268	+	0.376962i
$287$	2.01319e8	−	3.03440e7i	0.502688	−	0.0757680i
$288$	1.88449e7	−	2.51468e8i	0.0464858	−	0.620310i
$289$	1.92691e8	−	4.90968e8i	0.469590	−	1.19650i
$290$	−1.72434e8	−	7.55484e8i	−0.415175	−	1.81900i
$291$	−1.00443e7	−	1.34031e8i	−0.0238942	−	0.318846i
$292$	−2.18625e8	−	6.74369e7i	−0.513878	−	0.158510i
$293$	−4.42110e7	+	2.12909e7i	−0.102682	+	0.0494490i	−0.484520	−	0.874780i	$-0.661006\pi$
$293$	−4.42110e7	+	2.12909e7i	−0.102682	+	0.0494490i	0.381838	+	0.924229i	$0.375291\pi$
$294$	1.34787e7	−	2.33457e7i	0.0309336	−	0.0535786i
$295$	−5.03745e7	−	8.72511e7i	−0.114244	−	0.197876i
$296$	4.10216e8	+	2.79681e8i	0.919374	+	0.626818i
$297$	2.57031e7	−	1.12612e8i	0.0569295	−	0.249424i
$298$	1.70570e8	+	2.57092e7i	0.373375	+	0.0562772i
$299$	−2.56467e8	−	3.21600e8i	−0.554860	−	0.695772i
$300$	8.64637e7			0.184888
$301$	−3.38617e8	+	1.53130e8i	−0.715691	+	0.323652i
$302$	3.50913e7			0.0733121
$303$	1.81790e7	+	2.27957e7i	0.0375422	+	0.0470764i
$304$	4.15048e8	+	6.25585e7i	0.847308	+	0.127711i
$305$	9.56200e6	−	4.18938e7i	0.0192974	−	0.0845475i
$306$	−4.88182e8	−	3.32837e8i	−0.973996	−	0.664059i
$307$	−3.84803e7	−	6.66498e7i	−0.0759021	−	0.131466i	0.825576	−	0.564291i	$-0.190850\pi$
$307$	−3.84803e7	−	6.66498e7i	−0.0759021	−	0.131466i	−0.901478	+	0.432824i	$0.857517\pi$
$308$	−4.50215e7	+	7.79796e7i	−0.0877996	+	0.152073i
$309$	−1.71687e8	+	8.26800e7i	−0.331041	+	0.159421i
$310$	−6.43854e8	−	1.98603e8i	−1.22750	−	0.378633i
$311$	2.42024e7	+	3.22958e8i	0.0456243	+	0.608814i	0.972418	+	0.233244i	$0.0749341\pi$
$311$	2.42024e7	+	3.22958e8i	0.0456243	+	0.608814i	−0.926794	+	0.375570i	$0.877447\pi$
$312$	−2.69002e7	−	1.17857e8i	−0.0501435	−	0.219693i
$313$	1.75495e7	−	4.47153e7i	0.0323488	−	0.0824235i	−0.913787	−	0.406195i	$-0.866856\pi$
$313$	1.75495e7	−	4.47153e7i	0.0323488	−	0.0824235i	0.946135	+	0.323771i	$0.104951\pi$
$314$	−1.43019e7	+	1.90846e8i	−0.0260699	+	0.347879i
$315$	7.98899e8	−	1.20415e8i	1.44014	−	0.217066i
$316$	4.65954e7	+	4.32342e7i	0.0830688	+	0.0770766i
$317$	−5.79239e8	−	2.78947e8i	−1.02129	−	0.491829i	−0.153181	−	0.988198i	$-0.548952\pi$
$317$	−5.79239e8	−	2.78947e8i	−1.02129	−	0.491829i	−0.868111	+	0.496370i	$0.834666\pi$
$318$	−7.69443e6	+	5.24597e6i	−0.0134178	+	0.00914810i
$319$	1.65398e8	+	4.21427e8i	0.285274	+	0.726867i
$320$	1.15593e9	−	3.56556e8i	1.97199	−	0.608279i
$321$	−2.38288e6	+	2.21099e6i	−0.00402100	+	0.00373094i
$322$	−2.03732e8	+	2.55472e8i	−0.340067	+	0.426431i
$323$	−9.00691e8	+	1.12943e9i	−1.48719	+	1.86488i
$324$	1.35024e8	−	1.25284e8i	0.220548	−	0.204639i
$325$	−1.67814e9	+	5.17638e8i	−2.71167	+	0.836439i
$326$	−3.57013e8	−	9.09655e8i	−0.570719	−	1.45417i
$327$	1.13689e7	−	7.75120e6i	0.0179805	−	0.0122589i
$328$	4.05683e8	+	1.95367e8i	0.634788	+	0.305698i
$329$	−1.91310e8	−	1.77510e8i	−0.296177	−	0.274812i
$330$	1.32050e8	−	1.99033e7i	0.202274	−	0.0304879i
$331$	7.16134e7	−	9.55614e8i	0.108542	−	1.44839i	−0.631265	−	0.775567i	$-0.717464\pi$
$331$	7.16134e7	−	9.55614e8i	0.108542	−	1.44839i	0.739807	−	0.672820i	$-0.234917\pi$
$332$	5.70884e7	−	1.45459e8i	0.0856179	−	0.218151i
$333$	1.47198e8	+	6.44918e8i	0.218448	+	0.957083i
$334$	−5.82462e7	−	7.77241e8i	−0.0855372	−	1.14141i
$335$	−1.12616e9	−	3.47375e8i	−1.63661	−	0.504826i
$336$	−5.31613e7	+	2.56011e7i	−0.0764554	+	0.0368190i
$337$	4.80829e8	−	8.32820e8i	0.684362	−	1.18535i	−0.289274	−	0.957246i	$-0.593414\pi$
$337$	4.80829e8	−	8.32820e8i	0.684362	−	1.18535i	0.973637	−	0.228104i	$-0.0732526\pi$
$338$	2.38431e7	+	4.12975e7i	0.0335857	+	0.0581722i
$339$	−1.73163e8	−	1.18061e8i	−0.241410	−	0.164591i
$340$	−1.60398e8	+	7.02750e8i	−0.221321	+	0.969672i
$341$	3.89246e8	+	5.86694e7i	0.531598	+	0.0801256i
$342$	5.67489e8	+	7.11609e8i	0.767125	+	0.961945i
$343$	−8.11882e8			−1.08633
$344$	−8.09548e8	−	1.42048e8i	−1.07223	−	0.188140i
$345$	−2.50530e8			−0.328468
$346$	−2.96727e8	−	3.72084e8i	−0.385115	−	0.482919i
$347$	1.19269e9	+	1.79770e8i	1.53241	+	0.230974i	0.860421	−	0.509584i	$-0.170201\pi$
$347$	1.19269e9	+	1.79770e8i	1.53241	+	0.230974i	0.671992	+	0.740558i	$0.265439\pi$
$348$	1.41174e7	−	6.18522e7i	0.0179567	−	0.0786734i
$349$	2.12735e8	+	1.45040e8i	0.267886	+	0.182642i	0.689812	−	0.723989i	$-0.257693\pi$
$349$	2.12735e8	+	1.45040e8i	0.267886	+	0.182642i	−0.421925	+	0.906631i	$0.638646\pi$
$350$	6.97529e8	+	1.20816e9i	0.869609	+	1.50621i
$351$	1.64386e8	−	2.84726e8i	0.202904	−	0.351440i
$352$	−3.13239e8	+	1.50848e8i	−0.382804	+	0.184349i
$353$	6.24930e8	+	1.92765e8i	0.756170	+	0.233248i	0.648787	−	0.760970i	$-0.275277\pi$
$353$	6.24930e8	+	1.92765e8i	0.756170	+	0.233248i	0.107383	+	0.994218i	$0.465753\pi$
$354$	1.19235e6	+	1.59108e7i	0.00142854	+	0.0190625i
$355$	3.77314e8	+	1.65312e9i	0.447613	+	1.96112i
$356$	6.22396e7	−	1.58584e8i	0.0731125	−	0.186288i
$357$	1.51758e7	−	2.02507e8i	0.0176527	−	0.235559i
$358$	2.54542e8	−	3.83660e7i	0.293203	−	0.0441932i
$359$	3.11042e8	+	2.88605e8i	0.354804	+	0.329210i	0.837357	−	0.546657i	$-0.184100\pi$
$359$	3.11042e8	+	2.88605e8i	0.354804	+	0.329210i	−0.482553	+	0.875867i	$0.660290\pi$
$360$	1.60988e9	+	7.75279e8i	1.81859	+	0.875788i
$361$	1.10012e9	−	7.50049e8i	1.23074	−	0.839101i
$362$	1.85533e8	+	4.72730e8i	0.205561	+	0.523761i
$363$	9.86878e7	−	3.04411e7i	0.108290	−	0.0334032i
$364$	−1.87874e8	+	1.74322e8i	−0.204179	+	0.189451i
$365$	1.76463e9	−	2.21277e9i	1.89945	−	2.38184i
$366$	−4.24301e6	+	5.32057e6i	−0.00452366	+	0.00567250i
$367$	−5.60536e8	+	5.20101e8i	−0.591932	+	0.549233i	−0.918237	−	0.396032i	$-0.870387\pi$
$367$	−5.60536e8	+	5.20101e8i	−0.591932	+	0.549233i	0.326304	+	0.945265i	$0.394197\pi$
$368$	−4.24309e8	+	1.30882e8i	−0.443828	+	0.136903i
$369$	2.19180e8	+	5.58461e8i	0.227095	+	0.578629i
$370$	−1.28981e9	+	8.79380e8i	−1.32380	+	0.902549i
$371$	6.99845e7	+	3.37028e7i	0.0711530	+	0.0342655i
$372$	−4.04378e7	−	3.75208e7i	−0.0407275	−	0.0377896i
$373$	1.41287e9	−	2.12956e8i	1.40969	−	0.212476i	0.600310	−	0.799768i	$-0.295044\pi$
$373$	1.41287e9	−	2.12956e8i	1.40969	−	0.212476i	0.809375	+	0.587292i	$0.199806\pi$
$374$	−6.08751e7	+	8.12322e8i	−0.0601713	+	0.802930i
$375$	−2.47482e8	+	6.30573e8i	−0.242345	+	0.617484i
$376$	−1.28436e8	−	5.62716e8i	−0.124604	−	0.545924i
$377$	9.62962e7	+	1.28498e9i	0.0925581	+	1.23510i
$378$	−2.49567e8	−	7.69813e7i	−0.237666	−	0.0733102i
$379$	−1.72569e9	+	8.31047e8i	−1.62826	+	0.784131i	−0.628283	+	0.777985i	$0.716242\pi$
$379$	−1.72569e9	+	8.31047e8i	−1.62826	+	0.784131i	−0.999981	+	0.00614547i	$0.998044\pi$
$380$	5.55201e8	−	9.61637e8i	0.519049	−	0.899018i
$381$	−1.36044e8	−	2.35635e8i	−0.126021	−	0.218274i
$382$	1.58876e7	+	1.08320e7i	0.0145827	+	0.00994229i
$383$	1.41362e7	−	6.19347e7i	0.0128569	−	0.0563298i	−0.968093	−	0.250593i	$-0.919374\pi$
$383$	1.41362e7	−	6.19347e7i	0.0128569	−	0.0563298i	0.980949	+	0.194263i	$0.0622316\pi$
$384$	−4.80643e7	−	7.24452e6i	−0.0433175	−	0.00652906i
$385$	−6.94492e8	−	8.70866e8i	−0.620233	−	0.777747i
$386$	7.16636e8			0.634225
$387$	−6.61952e8	−	8.72383e8i	−0.580548	−	0.765101i
$388$	−6.30209e8			−0.547739
$389$	7.12625e7	+	8.93604e7i	0.0613815	+	0.0769700i	0.811574	−	0.584249i	$-0.198611\pi$
$389$	7.12625e7	+	8.93604e7i	0.0613815	+	0.0769700i	−0.750193	+	0.661219i	$0.770039\pi$
$390$	3.75855e8	+	5.66510e7i	0.320844	+	0.0483595i
$391$	3.40063e8	−	1.48991e9i	0.287700	−	1.26050i
$392$	−4.10883e8	−	2.80135e8i	−0.344522	−	0.234891i
$393$	3.65745e7	+	6.33489e7i	0.0303952	+	0.0526460i
$394$	1.45869e8	−	2.52653e8i	0.120151	−	0.208108i
$395$	−7.08444e8	+	3.41169e8i	−0.578383	+	0.278535i
$396$	−2.53544e8	−	7.82079e7i	−0.205173	−	0.0632874i
$397$	−5.41045e7	−	7.21975e8i	−0.0433977	−	0.579102i	−0.975940	−	0.218041i	$-0.930033\pi$
$397$	−5.41045e7	−	7.21975e8i	−0.0433977	−	0.579102i	0.932542	−	0.361062i	$-0.117586\pi$
$398$	−3.75132e8	−	1.64356e9i	−0.298259	−	1.30676i
$399$	−1.14289e8	+	2.91205e8i	−0.0900742	+	0.229505i
$400$	−1.41669e8	+	1.89044e9i	−0.110679	+	1.47691i
$401$	−2.08278e8	+	3.13929e7i	−0.161302	+	0.0243123i	−0.229197	−	0.973380i	$-0.573610\pi$
$401$	−2.08278e8	+	3.13929e7i	−0.161302	+	0.0243123i	0.0678949	+	0.997692i	$0.478372\pi$
$402$	1.36817e8	+	1.26947e8i	0.105038	+	0.0974614i
$403$	1.00947e9	+	4.86136e8i	0.768292	+	0.369990i
$404$	1.12955e8	−	7.70117e7i	0.0852261	−	0.0581062i
$405$	8.32460e8	+	2.12107e9i	0.622688	+	1.58658i
$406$	9.78150e8	−	3.01719e8i	0.725378	−	0.223749i
$407$	6.68551e8	−	6.20325e8i	0.491535	−	0.456078i
$408$	2.80026e8	−	3.51142e8i	0.204121	−	0.255960i
$409$	4.21918e8	−	5.29069e8i	0.304928	−	0.382367i	−0.605632	−	0.795745i	$-0.707080\pi$
$409$	4.21918e8	−	5.29069e8i	0.304928	−	0.382367i	0.910560	+	0.413378i	$0.135651\pi$
$410$	−1.03783e9	+	9.62965e8i	−0.743674	+	0.690028i
$411$	2.80422e8	−	8.64986e7i	0.199235	−	0.0614558i
$412$	3.26428e8	+	8.31725e8i	0.229957	+	0.585922i
$413$	1.09960e8	−	7.49695e7i	0.0768085	−	0.0523672i
$414$	−8.67520e8	−	4.17776e8i	−0.600867	−	0.289362i
$415$	1.41701e9	+	1.31479e9i	0.973204	+	0.903001i
$416$	−9.78521e8	+	1.47488e8i	−0.666413	+	0.100446i
$417$	−1.33092e7	+	1.77599e8i	−0.00898824	+	0.119940i
$418$	4.58453e8	−	1.16812e9i	0.307028	−	0.782294i
$419$	3.74925e7	+	1.64265e8i	0.0248998	+	0.109093i	0.985851	−	0.167626i	$-0.0536100\pi$
$419$	3.74925e7	+	1.64265e8i	0.0248998	+	0.109093i	−0.960951	+	0.276719i	$0.910753\pi$
$420$	1.16650e7	+	1.55659e8i	0.00768267	+	0.102518i
$421$	−1.63198e9	−	5.03399e8i	−1.06593	−	0.328795i	−0.288313	−	0.957536i	$-0.593094\pi$
$421$	−1.63198e9	−	5.03399e8i	−1.06593	−	0.328795i	−0.777615	+	0.628741i	$0.783571\pi$
$422$	−1.51644e9	+	7.30277e8i	−0.982269	+	0.473036i
$423$	3.84514e8	−	6.65997e8i	0.247013	−	0.427840i
$424$	8.58967e7	+	1.48777e8i	0.0547263	+	0.0947887i
$425$	−5.39082e9	−	3.67540e9i	−3.40638	−	2.32243i
$426$	5.97543e7	−	2.61801e8i	0.0374486	−	0.164073i
$427$	5.61291e7	+	8.46011e6i	0.0348892	+	0.00525870i
$428$	9.50295e6	+	1.19163e7i	0.00585875	+	0.00734664i
$429$	−2.22063e8			−0.135793
$430$	1.34570e9	−	2.20628e9i	0.816221	−	1.33820i
$431$	1.00831e9			0.606631			0.303315	−	0.952890i	$-0.401906\pi$
$431$	1.00831e9			0.606631			0.303315	+	0.952890i	$0.401906\pi$
$432$	−2.21279e8	−	2.77475e8i	−0.132053	−	0.165589i
$433$	−1.35996e8	−	2.04980e7i	−0.0805039	−	0.0121340i	0.108667	−	0.994078i	$-0.465342\pi$
$433$	−1.35996e8	−	2.04980e7i	−0.0805039	−	0.0121340i	−0.189171	+	0.981944i	$0.560580\pi$
$434$	1.98054e8	−	8.67730e8i	0.116297	−	0.509531i
$435$	6.48450e8	+	4.42106e8i	0.377715	+	0.257522i
$436$	−3.22586e7	−	5.58735e7i	−0.0186399	−	0.0322852i
$437$	−1.17709e9	+	2.03878e9i	−0.674722	+	1.16865i
$438$	−4.03832e8	+	1.94475e8i	−0.229637	+	0.110587i
$439$	−8.06287e8	−	2.48707e8i	−0.454845	−	0.140301i	0.0588631	−	0.998266i	$-0.481252\pi$
$439$	−8.06287e8	−	2.48707e8i	−0.454845	−	0.140301i	−0.513708	+	0.857965i	$0.671729\pi$
$440$	−1.84097e8	−	2.45661e9i	−0.103030	−	1.37484i
$441$	−1.47438e8	−	6.45966e8i	−0.0818603	−	0.358653i
$442$	−8.47081e8	+	2.15833e9i	−0.466602	+	1.18888i
$443$	2.31360e8	−	3.08728e9i	0.126437	−	1.68719i	−0.468537	−	0.883444i	$-0.655219\pi$
$443$	2.31360e8	−	3.08728e9i	0.126437	−	1.68719i	0.594974	−	0.803745i	$-0.297162\pi$
$444$	−1.26379e8	+	1.90485e7i	−0.0685225	+	0.0103281i
$445$	1.54487e9	+	1.43343e9i	0.831057	+	0.771108i
$446$	−1.54581e9	−	7.44421e8i	−0.825055	−	0.397325i
$447$	−1.44346e8	+	9.84131e7i	−0.0764411	+	0.0521167i
$448$	5.83785e8	+	1.48746e9i	0.306747	+	0.781578i
$449$	1.40707e9	−	4.34022e8i	0.733588	−	0.226282i	0.0946180	−	0.995514i	$-0.469837\pi$
$449$	1.40707e9	−	4.34022e8i	0.733588	−	0.226282i	0.638970	+	0.769232i	$0.279361\pi$
$450$	−3.01346e9	+	2.79609e9i	−1.55891	+	1.44646i
$451$	5.15702e8	−	6.46670e8i	0.264717	−	0.331944i
$452$	−6.12690e8	+	7.68289e8i	−0.312073	+	0.391327i
$453$	−2.60527e7	+	2.41734e7i	−0.0131677	+	0.0122178i
$454$	−6.95848e8	+	2.14641e8i	−0.348995	+	0.107651i
$455$	−1.15829e9	−	2.95128e9i	−0.576473	−	1.46883i
$456$	−5.71646e8	+	3.89742e8i	−0.282326	+	0.192486i
$457$	−6.98659e8	−	3.36456e8i	−0.342420	−	0.164901i	0.254768	−	0.967002i	$-0.418001\pi$
$457$	−6.98659e8	−	3.36456e8i	−0.342420	−	0.164901i	−0.597188	+	0.802102i	$0.703715\pi$
$458$	1.22915e9	+	1.14048e9i	0.597825	+	0.554701i
$459$	1.20782e9	−	1.82050e8i	0.582987	−	0.0878711i
$460$	−8.77844e7	+	1.17140e9i	−0.0420499	+	0.561117i
$461$	8.96275e8	−	2.28367e9i	0.426077	−	1.08563i	−0.543189	−	0.839611i	$-0.682783\pi$
$461$	8.96275e8	−	2.28367e9i	0.426077	−	1.08563i	0.969266	−	0.246016i	$-0.0791216\pi$
$462$	3.92533e7	+	1.71980e8i	0.0185195	+	0.0811392i
$463$	4.82445e7	+	6.43779e8i	0.0225899	+	0.301442i	0.997043	+	0.0768492i	$0.0244860\pi$
$463$	4.82445e7	+	6.43779e8i	0.0225899	+	0.301442i	−0.974453	+	0.224592i	$0.927895\pi$
$464$	1.32921e9	+	4.10006e8i	0.617703	+	0.190536i
$465$	6.14824e8	−	2.96084e8i	0.283573	−	0.136562i
$466$	2.40534e8	−	4.16617e8i	0.110110	−	0.190716i
$467$	−5.16866e8	−	8.95238e8i	−0.234838	−	0.406752i	0.724387	−	0.689393i	$-0.242123\pi$
$467$	−5.16866e8	−	8.95238e8i	−0.234838	−	0.406752i	−0.959226	+	0.282641i	$0.908789\pi$
$468$	−6.23989e8	−	4.25428e8i	−0.281395	−	0.191852i
$469$	3.46415e8	−	1.51774e9i	0.155057	−	0.679350i
$470$	1.79454e9	+	2.70483e8i	0.797279	+	0.120171i
$471$	−1.20850e8	−	1.51541e8i	−0.0532933	−	0.0668276i
$472$	2.94336e8			0.128839
$473$	−5.85297e8	+	1.39174e9i	−0.254309	+	0.604704i
$474$	1.24527e8			0.0537080
$475$	6.26658e9	+	7.85805e9i	2.68289	+	3.36424i
$476$	−9.41541e8	−	1.41914e8i	−0.400143	−	0.0603118i
$477$	−5.09333e7	+	2.23154e8i	−0.0214876	+	0.0941433i
$478$	−9.15258e8	−	6.24013e8i	−0.383306	−	0.261334i
$479$	1.81717e9	+	3.14743e9i	0.755478	+	1.30853i	0.945136	+	0.326676i	$0.105929\pi$
$479$	1.81717e9	+	3.14743e9i	0.755478	+	1.30853i	−0.189659	+	0.981850i	$0.560738\pi$
$480$	−3.01353e8	+	5.21959e8i	−0.124374	+	0.215423i
$481$	2.33879e9	−	1.12630e9i	0.958262	−	0.461474i
$482$	−2.85713e9	−	8.81308e8i	−1.16216	−	0.358478i
$483$	−2.47311e7	−	3.30014e8i	−0.00998687	−	0.133265i
$484$	−1.07754e8	−	4.72100e8i	−0.0431990	−	0.189267i
$485$	2.84820e9	−	7.25710e9i	1.13364	−	2.88846i
$486$	8.68485e7	−	1.15891e9i	0.0343191	−	0.457956i
$487$	5.12901e7	−	7.73074e6i	0.0201225	−	0.00303298i	−0.138973	−	0.990296i	$-0.544380\pi$
$487$	5.12901e7	−	7.73074e6i	0.0201225	−	0.00303298i	0.159096	+	0.987263i	$0.449142\pi$
$488$	9.20270e7	+	8.53886e7i	0.0358464	+	0.0332606i
$489$	8.91689e8	+	4.29415e8i	0.344852	+	0.166072i
$490$	1.29191e9	−	8.80809e8i	0.496073	−	0.338217i
$491$	1.74226e9	+	4.43920e9i	0.664243	+	1.69246i	0.719960	+	0.694016i	$0.244160\pi$
$491$	1.74226e9	+	4.43920e9i	0.664243	+	1.69246i	−0.0557173	+	0.998447i	$0.517745\pi$
$492$	−1.10761e8	+	3.41651e7i	−0.0419283	+	0.0129332i
$493$	−3.50940e9	+	3.25625e9i	−1.31907	+	1.22392i
$494$	2.22694e9	−	2.79249e9i	0.831119	−	1.04219i
$495$	2.04647e9	−	2.56620e9i	0.758382	−	0.950981i
$496$	8.86613e8	−	8.22657e8i	0.326248	−	0.302714i
$497$	−2.14035e9	+	6.60209e8i	−0.782054	+	0.241232i
$498$	−1.11842e8	−	2.84968e8i	−0.0405789	−	0.103393i
$499$	−1.70179e9	+	1.16026e9i	−0.613133	+	0.418027i	−0.829675	−	0.558246i	$-0.811474\pi$
$499$	−1.70179e9	+	1.16026e9i	−0.613133	+	0.418027i	0.216543	+	0.976273i	$0.430522\pi$
$500$	2.86165e9	+	1.37810e9i	1.02381	+	0.493043i
$501$	5.78661e8	+	5.36919e8i	0.205585	+	0.190755i
$502$	−1.36758e9	+	2.06129e8i	−0.482490	+	0.0727237i
$503$	9.30200e7	−	1.24127e9i	0.0325903	−	0.434887i	−0.956913	−	0.290376i	$-0.906220\pi$
$503$	9.30200e7	−	1.24127e9i	0.0325903	−	0.434887i	0.989503	−	0.144512i	$-0.0461612\pi$
$504$	−8.62326e8	+	2.19717e9i	−0.300030	+	0.764464i
$505$	3.76323e8	+	1.64878e9i	0.130029	+	0.569695i
$506$	9.92049e7	+	1.32380e9i	0.0340413	+	0.454250i
$507$	−4.61503e7	−	1.42355e7i	−0.0157270	−	0.00485115i
$508$	−1.14943e9	+	5.53535e8i	−0.389008	+	0.187336i
$509$	−1.31085e9	+	2.27045e9i	−0.440595	+	0.763133i	−0.997734	−	0.0672866i	$-0.978566\pi$
$509$	−1.31085e9	+	2.27045e9i	−0.440595	+	0.763133i	0.557139	+	0.830419i	$0.311899\pi$
$510$	7.06079e8	+	1.22297e9i	0.235699	+	0.408243i
$511$	3.08900e9	+	2.10605e9i	1.02411	+	0.698224i
$512$	−6.37230e8	+	2.79189e9i	−0.209822	+	0.919291i
$513$	−1.86061e9	−	2.80442e8i	−0.608477	−	0.0917132i
$514$	6.90244e8	+	8.65538e8i	0.224198	+	0.281135i
$515$	−1.10529e10			−3.56576
$516$	1.77635e8	−	1.14939e8i	0.0569187	−	0.0368294i
$517$	−1.06025e9			−0.337437
$518$	−1.28570e9	−	1.61222e9i	−0.406430	−	0.509647i
$519$	4.76615e8	+	7.18381e7i	0.149652	+	0.0225564i
$520$	1.56029e9	−	6.83608e9i	0.486624	−	2.13204i
$521$	−6.41514e8	−	4.37377e8i	−0.198735	−	0.135495i	0.459864	−	0.887989i	$-0.347898\pi$
$521$	−6.41514e8	−	4.37377e8i	−0.198735	−	0.135495i	−0.658599	+	0.752494i	$0.728851\pi$
$522$	1.50817e9	+	2.61223e9i	0.464092	+	0.803830i
$523$	−6.09226e7	+	1.05521e8i	−0.0186218	+	0.0322540i	−0.875186	−	0.483786i	$-0.839261\pi$
$523$	−6.09226e7	+	1.05521e8i	−0.0186218	+	0.0322540i	0.856564	+	0.516040i	$0.172595\pi$
$524$	3.09015e8	−	1.48814e8i	0.0938254	−	0.0451840i
$525$	−1.35013e9	−	4.16458e8i	−0.407208	−	0.125607i
$526$	−1.60828e8	−	2.14610e9i	−0.0481849	−	0.642982i
$527$	9.26275e8	+	4.05828e9i	0.275678	+	1.20783i
$528$	−8.75772e7	+	2.23143e8i	−0.0258924	+	0.0659727i
$529$	−6.83299e7	+	9.11799e8i	−0.0200685	+	0.267796i
$530$	−5.34124e8	+	8.05063e7i	−0.155839	+	0.0234890i
$531$	2.87477e8	+	2.66739e8i	0.0833244	+	0.0773137i
$532$	1.32154e9	+	6.36418e8i	0.380530	+	0.183253i
$533$	1.94517e9	−	1.32619e9i	0.556432	−	0.379369i
$534$	−1.21933e8	−	3.10680e8i	−0.0346519	−	0.0882916i
$535$	−1.80169e8	+	5.55748e7i	−0.0508677	+	0.0156906i
$536$	2.52392e9	−	2.34185e9i	0.707943	−	0.656875i
$537$	−1.62549e8	+	2.03830e8i	−0.0452975	+	0.0568012i
$538$	−5.16812e8	+	6.48062e8i	−0.143085	+	0.179423i
$539$	−6.69638e8	+	6.21333e8i	−0.184196	+	0.170909i
$540$	−8.97179e8	+	2.76743e8i	−0.245189	+	0.0756307i
$541$	−5.70769e8	−	1.45429e9i	−0.154978	−	0.394877i	0.832206	−	0.554467i	$-0.187078\pi$
$541$	−5.70769e8	−	1.45429e9i	−0.154978	−	0.394877i	−0.987183	+	0.159590i	$0.948983\pi$
$542$	1.23692e9	−	8.43321e8i	0.333692	−	0.227507i
$543$	−4.63394e8	−	2.23159e8i	−0.124208	−	0.0598156i
$544$	−2.69506e9	−	2.50065e9i	−0.717748	−	0.665973i
$545$	7.89197e8	−	1.18952e8i	0.208832	−	0.0314764i
$546$	−3.75217e7	+	5.00693e8i	−0.00986526	+	0.131643i
$547$	−7.57199e8	+	1.92931e9i	−0.197813	+	0.504019i	−0.995019	−	0.0996889i	$-0.968215\pi$
$547$	−7.57199e8	+	1.92931e9i	−0.197813	+	0.504019i	0.797206	+	0.603707i	$0.206310\pi$
$548$	−3.06183e8	−	1.34147e9i	−0.0794783	−	0.348217i
$549$	1.24997e7	+	1.66797e8i	0.00322402	+	0.0430216i
$550$	5.41580e9	+	1.67055e9i	1.38801	+	0.428145i
$551$	6.64447e9	−	3.19981e9i	1.69211	−	0.814880i
$552$	3.65960e8	−	6.33860e8i	0.0926075	−	0.160401i
$553$	−5.19343e8	−	8.99529e8i	−0.130592	−	0.226192i
$554$	2.36100e9	+	1.60970e9i	0.589945	+	0.402217i
$555$	3.51812e8	−	1.54139e9i	0.0873544	−	0.382725i
$556$	8.25733e8	+	1.24459e8i	0.203741	+	0.0307090i
$557$	4.03856e9	+	5.06420e9i	0.990224	+	1.24170i	0.970301	+	0.241900i	$0.0777706\pi$
$557$	4.03856e9	+	5.06420e9i	0.990224	+	1.24170i	0.0199229	+	0.999802i	$0.493658\pi$
$558$	2.62271e9			0.639045
$559$	−2.75954e9	+	3.29428e9i	−0.668183	+	0.797661i
$560$	−3.42244e9			−0.823526
$561$	−5.14389e8	−	6.45023e8i	−0.123005	−	0.154243i
$562$	−7.28007e8	−	1.09729e8i	−0.173005	−	0.0260763i
$563$	−3.57770e8	+	1.56749e9i	−0.0844936	+	0.370191i	−0.999443	−	0.0333784i	$-0.989373\pi$
$563$	−3.57770e8	+	1.56749e9i	−0.0844936	+	0.370191i	0.914949	+	0.403569i	$0.132231\pi$
$564$	1.22763e8	+	8.36982e7i	0.0288131	+	0.0196444i
$565$	−6.07812e9	−	1.05276e10i	−1.41775	−	2.45562i
$566$	2.11791e9	−	3.66833e9i	0.490964	−	0.850375i
$567$	−2.71184e9	+	1.30595e9i	−0.624773	+	0.300875i
$568$	−4.73367e9	−	1.46014e9i	−1.08387	−	0.334331i
$569$	4.84063e7	+	6.45937e8i	0.0110156	+	0.146993i	0.999999	−	0.00103028i	$-0.000327949\pi$
$569$	4.84063e7	+	6.45937e8i	0.0110156	+	0.146993i	−0.988984	+	0.148023i	$0.952709\pi$
$570$	−4.84068e8	−	2.12084e9i	−0.109482	−	0.479674i
$571$	1.05574e9	−	2.68997e9i	0.237317	−	0.604674i	−0.761749	−	0.647872i	$-0.775659\pi$
$571$	1.05574e9	−	2.68997e9i	0.237317	−	0.604674i	0.999067	+	0.0431974i	$0.0137544\pi$
$572$	−7.78098e7	+	1.03830e9i	−0.0173839	+	0.231973i
$573$	−1.92572e7	+	2.90255e6i	−0.00427614	+	0.000644524i
$574$	−1.37093e9	−	1.27204e9i	−0.302568	−	0.280742i
$575$	−9.57972e9	−	4.61335e9i	−2.10143	−	1.01200i
$576$	−3.89045e9	+	2.65246e9i	−0.848244	+	0.578323i
$577$	2.08217e9	+	5.30529e9i	0.451234	+	1.14972i	0.957777	+	0.287511i	$0.0928276\pi$
$577$	2.08217e9	+	5.30529e9i	0.451234	+	1.14972i	−0.506544	+	0.862214i	$0.669077\pi$
$578$	−4.62960e9	+	1.42804e9i	−0.997231	+	0.307605i
$579$	−5.32049e8	+	4.93669e8i	−0.113914	+	0.105697i
$580$	2.29436e9	−	2.87704e9i	0.488275	−	0.612277i
$581$	−1.59205e9	+	1.99636e9i	−0.336774	+	0.422302i
$582$	−9.05053e8	+	8.39767e8i	−0.190302	+	0.176575i
$583$	3.01552e8	−	9.30166e7i	0.0630265	−	0.0194411i
$584$	3.02082e9	+	7.69694e9i	0.627597	+	1.59909i
$585$	7.71906e9	−	5.26277e9i	1.59411	−	1.08685i
$586$	4.06113e8	+	1.95574e8i	0.0833692	+	0.0401485i
$587$	−2.56797e9	−	2.38273e9i	−0.524030	−	0.486229i	0.373225	−	0.927741i	$-0.378252\pi$
$587$	−2.56797e9	−	2.38273e9i	−0.524030	−	0.486229i	−0.897255	+	0.441512i	$0.854442\pi$
$588$	1.26584e8	−	1.90795e7i	0.0256778	−	0.00387031i
$589$	4.79200e8	−	6.39448e9i	0.0966302	−	1.28944i
$590$	−3.38108e8	+	8.61486e8i	−0.0677757	+	0.172690i
$591$	6.57480e7	+	2.88061e8i	0.0131017	+	0.0574022i
$592$	−2.09408e8	−	2.79435e9i	−0.0414827	−	0.553548i
$593$	−1.08434e9	−	3.34474e8i	−0.213537	−	0.0658674i	0.186141	−	0.982523i	$-0.440402\pi$
$593$	−1.08434e9	−	3.34474e8i	−0.213537	−	0.0658674i	−0.399678	+	0.916656i	$0.630878\pi$
$594$	−9.55962e8	+	4.60367e8i	−0.187149	+	0.0901263i
$595$	5.88946e9	−	1.02008e10i	1.14621	−	1.98530i
$596$	4.09571e8	+	7.09399e8i	0.0792443	+	0.137255i
$597$	1.41071e9	+	9.61803e8i	0.271348	+	0.185002i
$598$	−8.40796e8	+	3.68377e9i	−0.160782	+	0.704430i
$599$	−7.74489e9	−	1.16735e9i	−1.47238	−	0.221926i	−0.636690	−	0.771120i	$-0.719697\pi$
$599$	−7.74489e9	−	1.16735e9i	−1.47238	−	0.221926i	−0.835695	+	0.549194i	$0.814935\pi$
$600$	−1.94829e9	−	2.44308e9i	−0.368235	−	0.461752i
$601$	−2.41170e9			−0.453172			−0.226586	−	0.973991i	$-0.572756\pi$
$601$	−2.41170e9			−0.453172			−0.226586	+	0.973991i	$0.572756\pi$
$602$	3.03909e9	+	1.55484e9i	0.567748	+	0.290469i
$603$	4.58738e9			0.852029
$604$	1.03898e8	+	1.30285e8i	0.0191858	+	0.0240582i
$605$	5.92340e9	+	8.92809e8i	1.08750	+	0.163914i
$606$	5.95974e7	−	2.61113e8i	0.0108786	−	0.0476623i
$607$	8.72077e9	+	5.94572e9i	1.58268	+	1.07906i	0.953327	+	0.301939i	$0.0976340\pi$
$607$	8.72077e9	+	5.94572e9i	1.58268	+	1.07906i	0.629357	+	0.777116i	$0.283318\pi$
$608$	2.83175e9	+	4.90474e9i	0.510967	+	0.885021i
$609$	−5.18358e8	+	8.97822e8i	−0.0929970	+	0.161076i
$610$	−3.55635e8	+	1.71265e8i	−0.0634381	+	0.0305502i
$611$	−2.88374e9	−	8.89515e8i	−0.511459	−	0.157764i
$612$	−2.09677e8	−	2.79795e9i	−0.0369762	−	0.493413i
$613$	−1.23432e9	−	5.40792e9i	−0.216430	−	0.948241i	−0.960092	−	0.279685i	$-0.909770\pi$
$613$	−1.23432e9	−	5.40792e9i	−0.216430	−	0.948241i	0.743662	−	0.668556i	$-0.233087\pi$
$614$	−2.58276e8	+	6.58076e8i	−0.0450292	+	0.114733i
$615$	1.07153e8	−	1.42986e9i	0.0185756	−	0.247874i
$616$	3.21783e9	−	4.85010e8i	0.554665	−	0.0836023i
$617$	3.65759e9	+	3.39375e9i	0.626898	+	0.581676i	0.928305	−	0.371819i	$-0.121266\pi$
$617$	3.65759e9	+	3.39375e9i	0.626898	+	0.581676i	−0.301407	+	0.953495i	$0.597456\pi$
$618$	1.57708e9	+	7.59482e8i	0.268778	+	0.129437i
$619$	−8.05834e9	+	5.49408e9i	−1.36562	+	0.931061i	−0.365615	+	0.930766i	$0.619141\pi$
$619$	−8.05834e9	+	5.49408e9i	−1.36562	+	0.931061i	−1.00000		0.000294534i	$0.999906\pi$
$620$	−1.16897e9	−	2.97847e9i	−0.196984	−	0.501907i
$621$	1.90212e9	−	5.86727e8i	0.318726	−	0.0983140i
$622$	2.18079e9	−	2.02348e9i	0.363369	−	0.337157i
$623$	−1.73570e9	+	2.17650e9i	−0.287585	+	0.360620i
$624$	−4.25406e8	+	5.33443e8i	−0.0700903	+	0.0878904i
$625$	−1.66005e10	+	1.54030e10i	−2.71983	+	2.52363i
$626$	−4.21644e8	+	1.30060e8i	−0.0686967	+	0.0211901i
$627$	4.64315e8	+	1.18305e9i	0.0752274	+	0.191676i
$628$	−7.50903e8	+	5.11957e8i	−0.120983	+	0.0824849i
$629$	8.68914e9	+	4.18447e9i	1.39219	+	0.670445i
$630$	−5.44029e9	−	5.04785e9i	−0.866822	−	0.804293i
$631$	9.57463e8	−	1.44314e8i	0.151712	−	0.0228669i	−0.0727472	−	0.997350i	$-0.523177\pi$
$631$	9.57463e8	−	1.44314e8i	0.151712	−	0.0228669i	0.224459	+	0.974484i	$0.427939\pi$
$632$	1.71670e8	−	2.29078e9i	0.0270511	−	0.360972i
$633$	6.22774e8	−	1.58680e9i	0.0975927	−	0.248662i
$634$	1.31412e9	+	5.75754e9i	0.204797	+	0.897273i
$635$	−1.17938e9	−	1.57378e10i	−0.182788	−	2.43913i
$636$	−4.22585e7	−	1.30350e7i	−0.00651350	−	0.00200915i
$637$	−2.34259e9	+	1.12813e9i	−0.359095	+	0.172931i
$638$	2.07931e9	−	3.60146e9i	0.316990	−	0.549043i
$639$	−3.30012e9	−	5.71597e9i	−0.500353	−	0.866636i
$640$	−2.32946e9	−	1.58820e9i	−0.351258	−	0.239483i
$641$	−2.44254e9	+	1.07015e10i	−0.366301	+	1.60487i	0.370548	+	0.928813i	$0.379170\pi$
$641$	−2.44254e9	+	1.07015e10i	−0.366301	+	1.60487i	−0.736849	+	0.676057i	$0.763687\pi$
$642$	2.95261e7	+	4.45034e6i	0.00440386	+	0.000663775i
$643$	−3.66695e9	−	4.59822e9i	−0.543960	−	0.682105i	0.431542	−	0.902093i	$-0.357970\pi$
$643$	−3.66695e9	−	4.59822e9i	−0.543960	−	0.682105i	−0.975503	+	0.219988i	$0.929398\pi$
$644$	−1.55171e9			−0.228934
$645$	5.20757e8	+	2.56500e9i	0.0764146	+	0.376382i
$646$	1.32698e10			1.93664
$647$	−5.62488e9	−	7.05338e9i	−0.816486	−	1.02384i	−0.999173	−	0.0406695i	$-0.987051\pi$
$647$	−5.62488e9	−	7.05338e9i	−0.816486	−	1.02384i	0.182687	−	0.983171i	$-0.441520\pi$
$648$	−6.58248e9	−	9.92150e8i	−0.950336	−	0.143240i
$649$	1.20311e8	−	5.27119e8i	0.0172763	−	0.0756924i
$650$	1.33287e10	+	9.08733e9i	1.90366	+	1.29790i
$651$	4.50713e8	+	7.80657e8i	0.0640275	+	0.110899i
$652$	2.32025e9	−	4.01880e9i	0.327845	−	0.567845i
$653$	6.28459e9	−	3.02650e9i	0.883244	−	0.425348i	0.0634357	−	0.997986i	$-0.479794\pi$
$653$	6.28459e9	−	3.02650e9i	0.883244	−	0.425348i	0.819808	+	0.572638i	$0.194080\pi$
$654$	−1.20780e8	−	3.72556e7i	−0.0168839	−	0.00520799i
$655$	3.17069e8	+	4.23099e9i	0.0440869	+	0.588298i
$656$	−5.65507e8	−	2.47765e9i	−0.0782122	−	0.342670i
$657$	−4.02485e9	+	1.02552e10i	−0.553696	+	1.41079i
$658$	−1.79149e8	+	2.39058e9i	−0.0245146	+	0.327124i
$659$	6.38095e9	−	9.61774e8i	0.868534	−	0.130910i	0.300367	−	0.953824i	$-0.402891\pi$
$659$	6.38095e9	−	9.61774e8i	0.868534	−	0.130910i	0.568167	+	0.822913i	$0.307653\pi$
$660$	4.64869e8	+	4.31336e8i	0.0629401	+	0.0583998i
$661$	−1.73458e9	−	8.35330e8i	−0.233609	−	0.112500i	0.313418	−	0.949615i	$-0.398526\pi$
$661$	−1.73458e9	−	8.35330e8i	−0.233609	−	0.112500i	−0.547027	+	0.837115i	$0.684240\pi$
$662$	−7.27313e9	+	4.95873e9i	−0.974357	+	0.664305i
$663$	−8.57912e8	−	2.18592e9i	−0.114326	−	0.291298i
$664$	−5.39640e9	+	1.66457e9i	−0.715346	+	0.220655i
$665$	−1.33012e10	+	1.23417e10i	−1.75395	+	1.62742i
$666$	3.78860e9	−	4.75075e9i	0.496957	−	0.623164i
$667$	−4.86431e9	+	6.09965e9i	−0.634718	+	0.795912i
$668$	2.71323e9	−	2.51751e9i	0.352183	−	0.326778i
$669$	1.66045e9	−	5.12182e8i	0.214405	−	0.0661352i
$670$	3.95506e9	+	1.00773e10i	0.508032	+	1.29444i
$671$	1.90537e8	−	1.29906e8i	0.0243473	−	0.0165997i
$672$	−7.17305e8	−	3.45436e8i	−0.0911825	−	0.0439112i
$673$	−3.69698e9	−	3.43030e9i	−0.467514	−	0.433790i	0.410907	−	0.911677i	$-0.365212\pi$
$673$	−3.69698e9	−	3.43030e9i	−0.467514	−	0.433790i	−0.878421	+	0.477888i	$0.841403\pi$
$674$	−8.73493e9	+	1.31658e9i	−1.09888	+	0.165629i
$675$	6.35084e8	−	8.47461e9i	0.0794819	−	1.06061i
$676$	−8.27316e7	+	2.10797e8i	−0.0103005	+	0.0262452i
$677$	−2.30973e8	−	1.01196e9i	−0.0286089	−	0.125344i	0.958607	−	0.284733i	$-0.0919048\pi$
$677$	−2.30973e8	−	1.01196e9i	−0.0286089	−	0.125344i	−0.987216	+	0.159389i	$0.949048\pi$
$678$	1.43867e8	+	1.91977e9i	0.0177279	+	0.236563i
$679$	9.84067e9	+	3.03545e9i	1.20637	+	0.372116i
$680$	2.34709e10	−	1.13030e10i	2.86252	−	1.37852i
$681$	3.68755e8	−	6.38703e8i	0.0447428	−	0.0774968i
$682$	−1.80796e9	−	3.13148e9i	−0.218245	−	0.378011i
$683$	7.92209e9	+	5.40119e9i	0.951410	+	0.648660i	0.936291	−	0.351226i	$-0.114235\pi$
$683$	7.92209e9	+	5.40119e9i	0.951410	+	0.648660i	0.0151187	+	0.999886i	$0.495187\pi$
$684$	−9.61787e8	+	4.21387e9i	−0.114917	+	0.503482i
$685$	1.68314e10	+	2.53692e9i	2.00079	+	0.301571i
$686$	4.64985e9	+	5.83073e9i	0.549927	+	0.689586i
$687$	−1.69819e9			−0.199819
$688$	2.22199e9	+	4.07215e9i	0.260125	+	0.476721i
$689$	8.98217e8			0.104620
$690$	1.43485e9	+	1.79924e9i	0.166278	+	0.208506i
$691$	1.25312e10	+	1.88877e9i	1.44483	+	0.217774i	0.824188	−	0.566317i	$-0.191632\pi$
$691$	1.25312e10	+	1.88877e9i	1.44483	+	0.217774i	0.620646	+	0.784091i	$0.286870\pi$
$692$	5.02896e8	−	2.20333e9i	0.0576909	−	0.252760i
$693$	3.58238e9	+	2.44242e9i	0.408889	+	0.278775i
$694$	−5.53980e9	−	9.59521e9i	−0.629123	−	1.08967i
$695$	−5.16506e9	+	8.94615e9i	−0.583618	+	1.01086i
$696$	−2.06578e9	+	9.94826e8i	−0.232248	+	0.111845i
$697$	8.35797e9	+	2.57809e9i	0.934945	+	0.288392i
$698$	−1.76745e8	−	2.35849e9i	−0.0196722	−	0.262507i
$699$	1.08416e8	+	4.75004e8i	0.0120067	+	0.0526050i
$700$	−2.42031e9	+	6.16684e9i	−0.266703	+	0.679548i
$701$	1.21949e8	−	1.62730e9i	0.0133711	−	0.178424i	−0.986520	−	0.163643i	$-0.947676\pi$
$701$	1.21949e8	−	1.62730e9i	0.0133711	−	0.178424i	0.999891	−	0.0147818i	$-0.00470535\pi$
$702$	−2.98631e9	+	4.50114e8i	−0.325803	+	0.0491069i
$703$	−1.08907e10	−	1.01050e10i	−1.18225	−	1.09697i
$704$	5.84886e9	+	2.81666e9i	0.631782	+	0.304250i
$705$	−1.51864e9	+	1.03539e9i	−0.163227	+	0.111286i
$706$	−2.19474e9	−	5.59210e9i	−0.234729	−	0.598079i
$707$	−2.13473e9	+	6.58476e8i	−0.227182	+	0.0700764i
$708$	−5.55421e7	+	5.15355e7i	−0.00588174	+	0.00545745i
$709$	2.38556e9	−	2.99140e9i	0.251379	−	0.315220i	−0.640091	−	0.768299i	$-0.721103\pi$
$709$	2.38556e9	−	2.99140e9i	0.251379	−	0.315220i	0.891470	+	0.453080i	$0.149675\pi$
$710$	9.71131e9	−	1.21776e10i	1.01829	−	1.27690i
$711$	2.24367e9	−	2.08182e9i	0.234107	−	0.217220i
$712$	−5.88332e9	+	1.81476e9i	−0.610861	+	0.188426i
$713$	2.47834e9	+	6.31471e9i	0.256063	+	0.652439i
$714$	−1.54127e9	+	1.05082e9i	−0.158465	+	0.108040i
$715$	−1.16048e10	−	5.58856e9i	−1.18731	−	0.571780i
$716$	8.96089e8	+	8.31449e8i	0.0912338	+	0.0846526i
$717$	1.10937e9	−	1.67211e8i	0.112399	−	0.0169414i
$718$	2.91271e8	−	3.88674e9i	0.0293671	−	0.391877i
$719$	−6.71186e9	+	1.71016e10i	−0.673429	+	1.71587i	0.0244962	+	0.999700i	$0.492202\pi$
$719$	−6.71186e9	+	1.71016e10i	−0.673429	+	1.71587i	−0.697926	+	0.716170i	$0.745893\pi$
$720$	−2.24412e9	−	9.83211e9i	−0.224069	−	0.981710i
$721$	−1.09109e9	−	1.45596e10i	−0.108415	−	1.44669i
$722$	−1.16873e10	−	3.60506e9i	−1.15567	−	0.356478i
$723$	2.72831e9	−	1.31389e9i	0.268479	−	0.129293i
$724$	−1.20579e9	+	2.08849e9i	−0.118083	+	0.204526i
$725$	1.66542e10	+	2.88459e10i	1.62308	+	2.81126i
$726$	−7.83830e8	−	5.34406e8i	−0.0760228	−	0.0518315i
$727$	1.44902e9	−	6.34858e9i	0.139863	−	0.612782i	−0.855600	−	0.517638i	$-0.826812\pi$
$727$	1.44902e9	−	6.34858e9i	0.139863	−	0.612782i	0.995463	−	0.0951443i	$-0.0303313\pi$
$728$	9.15894e9	+	1.38049e9i	0.879803	+	0.132609i
$729$	−5.02396e9	−	6.29985e9i	−0.480286	−	0.602260i
$730$	−2.59981e10			−2.47349
$731$	−1.59610e10	−	3.84703e8i	−1.51130	−	0.0364263i
$732$	−3.23165e7			−0.00304534
$733$	−5.88635e9	−	7.38125e9i	−0.552055	−	0.692255i	0.425012	−	0.905188i	$-0.360270\pi$
$733$	−5.88635e9	−	7.38125e9i	−0.552055	−	0.692255i	−0.977067	+	0.212933i	$0.931698\pi$
$734$	6.94556e9	+	1.04688e9i	0.648293	+	0.0977144i
$735$	−3.52383e8	+	1.54389e9i	−0.0327348	+	0.143420i
$736$	−4.95031e9	−	3.37506e9i	−0.457678	−	0.312039i
$737$	−3.16230e9	−	5.47726e9i	−0.290982	−	0.503996i
$738$	2.75543e9	−	4.77254e9i	0.252343	−	0.437071i
$739$	9.53144e9	−	4.59010e9i	0.868766	−	0.418376i	0.0542573	−	0.998527i	$-0.482721\pi$
$739$	9.53144e9	−	4.59010e9i	0.868766	−	0.418376i	0.814509	+	0.580151i	$0.197007\pi$
$740$	−7.08378e9	−	2.18506e9i	−0.642620	−	0.198222i
$741$	2.70328e8	+	3.60728e9i	0.0244078	+	0.325699i
$742$	−1.58774e8	−	6.95635e8i	−0.0142681	−	0.0625127i
$743$	2.46822e9	−	6.28893e9i	0.220762	−	0.562492i	−0.776990	−	0.629513i	$-0.783254\pi$
$743$	2.46822e9	−	6.28893e9i	0.220762	−	0.562492i	0.997752	+	0.0670215i	$0.0213496\pi$
$744$	−1.48984e8	+	1.98805e9i	−0.0132628	+	0.176979i
$745$	−1.00200e10	+	1.51028e9i	−0.887815	+	0.133817i
$746$	−9.62128e9	−	8.92724e9i	−0.848490	−	0.787284i
$747$	−6.77915e9	−	3.26466e9i	−0.595049	−	0.286561i
$748$	−3.19617e9	+	2.17911e9i	−0.279238	+	0.190381i
$749$	−9.09922e7	−	2.31844e8i	−0.00791257	−	0.0201609i
$750$	5.94600e9	−	1.83410e9i	0.514648	−	0.158748i
$751$	8.24779e9	−	7.65283e9i	0.710555	−	0.659299i	−0.239673	−	0.970854i	$-0.577040\pi$
$751$	8.24779e9	−	7.65283e9i	0.710555	−	0.659299i	0.950228	+	0.311555i	$0.100850\pi$
$752$	−2.03112e9	+	2.54695e9i	−0.174170	+	0.218403i
$753$	8.73327e8	−	1.09512e9i	0.0745409	−	0.0934713i
$754$	8.67691e9	−	8.05100e9i	0.737166	−	0.683990i
$755$	−1.96984e9	+	6.07616e8i	−0.166578	+	0.0513825i
$756$	−4.53109e8	−	1.15450e9i	−0.0381396	−	0.0971781i
$757$	1.06229e9	−	7.24257e8i	0.0890036	−	0.0606816i	−0.518001	−	0.855380i	$-0.673323\pi$
$757$	1.06229e9	−	7.24257e8i	0.0890036	−	0.0606816i	0.607004	+	0.794699i	$0.292371\pi$
$758$	1.58518e10	+	7.63383e9i	1.32202	+	0.636649i
$759$	−9.85576e8	−	9.14481e8i	−0.0818171	−	0.0759152i
$760$	−3.96820e10	+	5.98110e9i	−3.27903	+	0.494235i
$761$	1.17764e9	−	1.57145e10i	0.0968647	−	1.29257i	−0.710996	−	0.703196i	$-0.751756\pi$
$761$	1.17764e9	−	1.57145e10i	0.0968647	−	1.29257i	0.807861	−	0.589373i	$-0.200625\pi$
$762$	−9.13114e8	+	2.32658e9i	−0.0747623	+	0.190491i
$763$	2.34597e8	+	1.02784e9i	0.0191200	+	0.0837700i
$764$	6.82383e6	+	9.10577e7i	0.000553607	+	0.00738737i
$765$	3.31671e10	+	1.02307e10i	2.67851	+	0.826210i
$766$	−5.25761e8	+	2.53193e8i	−0.0422656	+	0.0203541i
$767$	7.69463e8	−	1.33275e9i	0.0615750	−	0.106651i
$768$	−1.11149e9	−	1.92516e9i	−0.0885404	−	0.153357i
$769$	−1.92349e10	−	1.31141e10i	−1.52527	−	1.03991i	−0.979373	−	0.202061i	$-0.935236\pi$
$769$	−1.92349e10	−	1.31141e10i	−1.52527	−	1.03991i	−0.545899	−	0.837851i	$-0.683812\pi$
$770$	−2.27680e9	+	9.97533e9i	−0.179725	+	0.787426i
$771$	−1.10870e9	−	1.67109e8i	−0.0871210	−	0.0131314i
$772$	2.12182e9	+	2.66067e9i	0.165977	+	0.208128i
$773$	−2.11419e10			−1.64633			−0.823164	−	0.567804i	$-0.807793\pi$
$773$	−2.11419e10			−1.64633			−0.823164	+	0.567804i	$0.807793\pi$
$774$	−2.47407e9	+	9.75033e9i	−0.191787	+	0.755833i
$775$	2.89617e10			2.23495
$776$	1.42005e10	+	1.78069e10i	1.09091	+	1.36796i
$777$	2.06514e9	+	3.11270e8i	0.157934	+	0.0238048i
$778$	2.33625e8	−	1.02358e9i	0.0177865	−	0.0779278i
$779$	−1.11325e10	−	7.59004e9i	−0.843749	−	0.575259i
$780$	9.02502e8	+	1.56318e9i	0.0680953	+	0.117945i
$781$	−4.54985e9	+	7.88057e9i	−0.341758	+	0.591942i
$782$	−1.26478e10	+	6.09085e9i	−0.945782	+	0.455464i
$783$	−5.95867e9	−	1.83800e9i	−0.443591	−	0.136830i
$784$	2.09748e8	+	2.79889e9i	0.0155450	+	0.207434i
$785$	−2.50171e9	−	1.09607e10i	−0.184584	−	0.808713i
$786$	2.45484e8	−	6.25484e8i	0.0180320	−	0.0459449i
$787$	9.58368e8	−	1.27885e10i	0.0700843	−	0.935210i	−0.845731	−	0.533610i	$-0.820835\pi$
$787$	9.58368e8	−	1.27885e10i	0.0700843	−	0.935210i	0.915815	−	0.401600i	$-0.131546\pi$
$788$	1.36992e9	−	2.06483e8i	0.0997365	−	0.0150329i
$789$	1.59778e9	+	1.48253e9i	0.115811	+	0.107457i
$790$	6.50763e9	+	3.13391e9i	0.469600	+	0.226147i
$791$	1.32676e10	−	9.04572e9i	0.953182	−	0.649869i
$792$	3.50331e9	+	8.92629e9i	0.250576	+	0.638458i
$793$	6.27219e8	−	1.93471e8i	0.0446645	−	0.0137772i
$794$	−4.87517e9	+	4.52350e9i	−0.345635	+	0.320703i
$795$	3.41089e8	−	4.27712e8i	0.0240759	−	0.0301902i
$796$	4.99140e9	−	6.25902e9i	0.350773	−	0.439856i
$797$	−1.22097e10	+	1.13289e10i	−0.854281	+	0.792657i	−0.979914	−	0.199419i	$-0.936094\pi$
$797$	−1.22097e10	+	1.13289e10i	−0.854281	+	0.792657i	0.125633	+	0.992077i	$0.459904\pi$
$798$	2.74592e9	−	8.47004e8i	0.191284	−	0.0590032i
$799$	−4.09614e9	−	1.04368e10i	−0.284094	−	0.723859i
$800$	−2.11346e10	+	1.44093e10i	−1.45942	+	0.995012i
$801$	−7.39083e9	−	3.55924e9i	−0.508136	−	0.244705i
$802$	1.41832e9	+	1.31601e9i	0.0970875	+	0.0900840i
$803$	1.50190e10	−	2.26375e9i	1.02362	−	0.154285i
$804$	−6.62338e7	+	8.83829e8i	−0.00449452	+	0.0599752i
$805$	7.01289e9	−	1.78686e10i	0.473818	−	1.20727i
$806$	−2.29019e9	−	1.00340e10i	−0.154063	−	0.674995i
$807$	−6.27360e7	−	8.37154e8i	−0.00420203	−	0.0560722i
$808$	−4.72124e9	−	1.45631e9i	−0.314859	−	0.0971212i
$809$	−9.07736e9	+	4.37143e9i	−0.602754	+	0.290271i	−0.710267	−	0.703933i	$-0.751426\pi$
$809$	−9.07736e9	+	4.37143e9i	−0.602754	+	0.290271i	0.107513	+	0.994204i	$0.465711\pi$
$810$	1.04653e10	−	1.81264e10i	0.691917	−	1.19844i
$811$	−6.77799e9	−	1.17398e10i	−0.446198	−	0.772838i	0.551937	−	0.833886i	$-0.313889\pi$
$811$	−6.77799e9	−	1.17398e10i	−0.446198	−	0.772838i	−0.998135	+	0.0610483i	$0.980556\pi$
$812$	4.01631e9	+	2.73827e9i	0.263258	+	0.179486i
$813$	−3.37386e8	+	1.47818e9i	−0.0220196	+	0.0964742i
$814$	−8.28398e9	−	1.24861e9i	−0.538336	−	0.0811411i
$815$	3.57917e10	+	4.48814e10i	2.31596	+	2.90412i
$816$	−2.53489e9			−0.163322
$817$	2.33204e10	+	7.81356e9i	1.49609	+	0.501270i
$818$	−6.21607e9			−0.397081
$819$	7.69444e9	+	9.64852e9i	0.489422	+	0.613716i
$820$	−6.64803e9	−	1.00203e9i	−0.421061	−	0.0634647i
$821$	4.47620e8	−	1.96115e9i	0.0282299	−	0.123683i	−0.958850	−	0.283914i	$-0.908367\pi$
$821$	4.47620e8	−	1.96115e9i	0.0282299	−	0.123683i	0.987080	+	0.160231i	$0.0512240\pi$
$822$	−2.22726e9	−	1.51852e9i	−0.139868	−	0.0953605i
$823$	3.52120e8	+	6.09890e8i	0.0220187	+	0.0381375i	0.876825	−	0.480810i	$-0.159657\pi$
$823$	3.52120e8	+	6.09890e8i	0.0220187	+	0.0381375i	−0.854806	+	0.518948i	$0.826324\pi$
$824$	1.61454e10	−	2.79647e10i	1.00532	−	1.74127i
$825$	−5.17162e9	+	2.49052e9i	−0.320655	+	0.154419i
$826$	−1.16818e9	−	3.60336e8i	−0.0721240	−	0.0222473i
$827$	1.68829e8	+	2.25287e9i	0.0103795	+	0.138505i	0.999986	−	0.00529707i	$-0.00168612\pi$
$827$	1.68829e8	+	2.25287e9i	0.0103795	+	0.138505i	−0.989606	+	0.143802i	$0.954067\pi$
$828$	−1.01747e9	−	4.45782e9i	−0.0622894	−	0.272908i
$829$	−3.78706e9	+	9.64926e9i	−0.230866	+	0.588238i	−0.998621	−	0.0525064i	$-0.983279\pi$
$829$	−3.78706e9	+	9.64926e9i	−0.230866	+	0.588238i	0.767754	+	0.640745i	$0.221374\pi$
$830$	1.32694e9	−	1.77067e10i	0.0805521	−	1.07489i
$831$	−2.86174e9	+	4.31337e8i	−0.172992	+	0.0260744i
$832$	1.35450e10	+	1.25679e10i	0.815355	+	0.756539i
$833$	−8.70326e9	−	4.19127e9i	−0.521704	−	0.251240i
$834$	1.35169e9	−	9.21569e8i	0.0806857	−	0.0550106i
$835$	1.67278e10	+	4.26217e10i	0.994341	+	2.53354i
$836$	5.69429e9	−	1.75646e9i	0.337068	−	0.103972i
$837$	−3.97457e9	+	3.68786e9i	−0.234289	+	0.217388i
$838$	9.64984e8	−	1.21005e9i	0.0566456	−	0.0710313i
$839$	8.25170e9	−	1.03473e10i	0.482366	−	0.604867i	−0.479785	−	0.877386i	$-0.659285\pi$
$839$	8.25170e9	−	1.03473e10i	0.482366	−	0.604867i	0.962150	+	0.272519i	$0.0878567\pi$
$840$	4.13538e9	−	3.83707e9i	0.240734	−	0.223369i
$841$	6.87077e9	−	2.11935e9i	0.398309	−	0.122862i
$842$	5.73148e9	+	1.46036e10i	0.330883	+	0.843076i
$843$	6.16080e8	−	4.20036e8i	0.0354194	−	0.0241485i
$844$	−7.20118e9	−	3.46791e9i	−0.412292	−	0.198549i
$845$	−2.05350e9	−	1.90537e9i	−0.117084	−	0.108638i
$846$	−6.98523e9	+	1.05285e9i	−0.396629	+	0.0597822i
$847$	−5.91335e8	+	7.89082e9i	−0.0334381	+	0.446200i
$848$	3.54238e8	−	9.02583e8i	0.0199485	−	0.0508279i
$849$	9.54611e8	+	4.18242e9i	0.0535364	+	0.234558i
$850$	4.47880e9	+	5.97655e10i	0.250147	+	3.33798i
$851$	1.50184e10	+	4.63257e9i	0.835355	+	0.257673i
$852$	1.14892e9	−	5.53289e8i	0.0636428	−	0.0306488i
$853$	−1.81599e9	+	3.14538e9i	−0.100182	+	0.173521i	−0.911760	−	0.410724i	$-0.865276\pi$
$853$	−1.81599e9	+	3.14538e9i	−0.100182	+	0.173521i	0.811577	+	0.584245i	$0.198609\pi$
$854$	−2.60707e8	−	4.51558e8i	−0.0143236	−	0.0248091i
$855$	−4.41776e10	−	3.01197e10i	−2.41724	−	1.64805i
$856$	1.22572e8	−	5.37022e8i	0.00667932	−	0.0292640i
$857$	1.58490e10	+	2.38885e9i	0.860138	+	0.129645i	0.564276	−	0.825586i	$-0.309155\pi$
$857$	1.58490e10	+	2.38885e9i	0.860138	+	0.129645i	0.295861	+	0.955231i	$0.404393\pi$
$858$	1.27181e9	+	1.59480e9i	0.0687413	+	0.0861989i
$859$	1.16801e10			0.628740			0.314370	−	0.949301i	$-0.398207\pi$
$859$	1.16801e10			0.628740			0.314370	+	0.949301i	$0.398207\pi$
$860$	1.21756e10	−	1.53614e9i	0.652750	−	0.0823541i
$861$	1.89408e9			0.101132
$862$	−5.77486e9	−	7.24144e9i	−0.307090	−	0.385079i
$863$	2.15399e10	+	3.24662e9i	1.14079	+	0.171947i	0.692143	−	0.721761i	$-0.256667\pi$
$863$	2.15399e10	+	3.24662e9i	1.14079	+	0.171947i	0.448650	+	0.893707i	$0.351905\pi$
$864$	1.06559e9	−	4.66866e9i	0.0562073	−	0.246260i
$865$	2.30994e10	+	1.57489e10i	1.21351	+	0.827360i
$866$	6.31669e8	+	1.09408e9i	0.0330504	+	0.0572450i
$867$	2.45339e9	−	4.24940e9i	0.127850	−	0.221443i
$868$	3.80804e9	−	1.83386e9i	0.197644	−	0.0951801i
$869$	−4.03232e9	−	1.24381e9i	−0.208442	−	0.0642960i
$870$	−5.38745e8	−	7.18905e9i	−0.0277374	−	0.370130i
$871$	−4.00577e9	−	1.75504e10i	−0.205410	−	0.899962i
$872$	−8.51853e8	+	2.17049e9i	−0.0435068	+	0.110854i
$873$	−2.26775e9	+	3.02610e10i	−0.115357	+	1.53934i
$874$	2.13835e10	−	3.22304e9i	1.08340	−	0.163296i
$875$	−3.80468e10	−	3.53022e10i	−1.91995	−	1.78145i
$876$	−1.91770e9	−	9.23516e8i	−0.0963865	−	0.0464173i
$877$	1.87893e10	−	1.28103e10i	0.940614	−	0.641300i	0.00715114	−	0.999974i	$-0.497724\pi$
$877$	1.87893e10	−	1.28103e10i	0.940614	−	0.641300i	0.933463	+	0.358675i	$0.116771\pi$
$878$	2.83166e9	+	7.21495e9i	0.141192	+	0.359751i
$879$	−4.36234e8	+	1.34560e8i	−0.0216650	+	0.00668276i
$880$	−1.01924e10	+	9.45718e9i	−0.504182	+	0.467813i
$881$	−7.17614e9	+	8.99859e9i	−0.353570	+	0.443362i	−0.926530	−	0.376221i	$-0.877223\pi$
$881$	−7.17614e9	+	8.99859e9i	−0.353570	+	0.443362i	0.572960	+	0.819583i	$0.305795\pi$
$882$	−3.79475e9	+	4.75847e9i	−0.186227	+	0.233522i
$883$	−1.55344e10	+	1.44138e10i	−0.759334	+	0.704559i	−0.961504	−	0.274791i	$-0.911391\pi$
$883$	−1.55344e10	+	1.44138e10i	−0.759334	+	0.704559i	0.202170	+	0.979350i	$0.435201\pi$
$884$	−1.05213e10	+	3.24540e9i	−0.512256	+	0.158010i
$885$	−3.42431e8	−	8.72501e8i	−0.0166063	−	0.0423121i
$886$	−2.34971e10	+	1.60201e10i	−1.13500	+	0.773832i
$887$	−3.13489e10	−	1.50969e10i	−1.50831	−	0.726363i	−0.516764	−	0.856128i	$-0.672864\pi$
$887$	−3.13489e10	−	1.50969e10i	−1.50831	−	0.726363i	−0.991545	+	0.129765i	$0.958578\pi$
$888$	3.38592e9	+	3.14168e9i	0.162268	+	0.150562i
$889$	2.06144e10	−	3.10712e9i	0.984043	−	0.148321i
$890$	1.44667e9	−	1.93044e10i	0.0687865	−	0.917892i
$891$	−4.46744e9	+	1.13829e10i	−0.211586	+	0.539112i
$892$	−1.81299e9	−	7.94323e9i	−0.0855300	−	0.374732i
$893$	1.29070e9	+	1.72232e10i	0.0606519	+	0.809343i
$894$	1.53348e9	+	4.73016e8i	0.0717789	+	0.0221409i
$895$	−1.36243e10	+	6.56112e9i	−0.635234	+	0.305912i
$896$	1.86213e9	−	3.22530e9i	0.0864830	−	0.149793i
$897$	−1.91341e9	−	3.31412e9i	−0.0885185	−	0.153319i
$898$	−1.11757e10	−	7.61943e9i	−0.514998	−	0.351120i
$899$	4.72873e9	−	2.07179e10i	0.217063	−	0.951014i
$900$	−1.93034e10	−	2.90951e9i	−0.882642	−	0.133037i
$901$	2.08063e9	+	2.60903e9i	0.0947674	+	0.118835i
$902$	−7.59778e9			−0.344718
$903$	−3.32738e9	+	9.39179e8i	−0.150382	+	0.0424464i
$904$	3.55142e10			1.59887
$905$	−1.86003e10	−	2.33240e10i	−0.834160	−	1.04600i
$906$	3.22817e8	+	4.86569e7i	0.0144214	+	0.00217368i
$907$	8.59244e9	−	3.76459e10i	0.382376	−	1.67530i	−0.307638	−	0.951503i	$-0.599539\pi$
$907$	8.59244e9	−	3.76459e10i	0.382376	−	1.67530i	0.690014	−	0.723796i	$-0.257604\pi$
$908$	−2.85717e9	−	1.94798e9i	−0.126659	−	0.0863545i
$909$	−3.29145e9	−	5.70096e9i	−0.145350	−	0.251753i
$910$	−1.45615e10	+	2.52213e10i	−0.640563	+	1.10949i
$911$	−3.19008e10	+	1.53626e10i	−1.39794	+	0.673211i	−0.972742	−	0.231890i	$-0.925509\pi$
$911$	−3.19008e10	+	1.53626e10i	−1.39794	+	0.673211i	−0.425196	+	0.905101i	$0.639795\pi$
$912$	3.73143e9	+	1.15099e9i	0.162890	+	0.0502448i
$913$	7.75226e8	+	1.03447e10i	0.0337117	+	0.449852i
$914$	1.58505e9	+	6.94456e9i	0.0686644	+	0.300838i
$915$	1.46053e8	−	3.72137e8i	0.00630285	−	0.0160594i
$916$	−5.95037e8	+	7.94022e9i	−0.0255805	+	0.341349i
$917$	−5.54203e9	+	8.35327e8i	−0.237343	+	0.0357737i
$918$	−8.22494e9	−	7.63163e9i	−0.350900	−	0.325588i
$919$	−1.56490e10	−	7.53615e9i	−0.665092	−	0.320291i	0.0707017	−	0.997498i	$-0.477476\pi$
$919$	−1.56490e10	−	7.53615e9i	−0.665092	−	0.320291i	−0.735793	+	0.677206i	$0.763190\pi$
$920$	3.50767e10	−	2.39149e10i	1.48512	−	1.01254i
$921$	−2.61578e8	−	6.66490e8i	−0.0110330	−	0.0281116i
$922$	−2.15339e10	+	6.64234e9i	−0.904827	+	0.279102i
$923$	−1.89865e10	+	1.76169e10i	−0.794763	+	0.737433i
$924$	−5.22293e8	+	6.54935e8i	−0.0217802	+	0.0273115i
$925$	4.18361e10	−	5.24608e10i	1.73802	−	2.17941i
$926$	4.34715e9	−	4.03356e9i	0.179914	−	0.166936i
$927$	4.11120e10	−	1.26814e10i	1.69508	−	0.522862i
$928$	6.85703e9	+	1.74714e10i	0.281655	+	0.717646i
$929$	−2.96842e10	+	2.02383e10i	−1.21470	+	0.828170i	−0.989271	−	0.146089i	$-0.953331\pi$
$929$	−2.96842e10	+	2.02383e10i	−1.21470	+	0.828170i	−0.225431	+	0.974259i	$0.572379\pi$
$930$	−5.64765e9	−	2.71977e9i	−0.230238	−	0.110877i
$931$	1.09083e10	+	1.01215e10i	0.443032	+	0.411074i
$932$	2.25896e9	−	3.40483e8i	0.0914014	−	0.0137765i
$933$	−2.25161e8	+	3.00456e9i	−0.00907626	+	0.121114i
$934$	−3.46915e9	+	8.83926e9i	−0.139319	+	0.354978i
$935$	−1.06484e10	−	4.66535e10i	−0.426032	−	1.86657i
$936$	2.03966e9	+	2.72174e10i	0.0813003	+	1.08488i
$937$	−3.74567e9	−	1.15539e9i	−0.148744	−	0.0458816i	0.219489	−	0.975615i	$-0.429561\pi$
$937$	−3.74567e9	−	1.15539e9i	−0.148744	−	0.0458816i	−0.368233	+	0.929733i	$0.620037\pi$
$938$	−1.28841e10	+	6.20464e9i	−0.509733	+	0.245475i
$939$	2.23445e8	−	3.87018e8i	0.00880725	−	0.0152546i
$940$	4.30904e9	+	7.46348e9i	0.169213	+	0.293085i
$941$	1.25408e10	+	8.55018e9i	0.490639	+	0.334512i	0.783237	−	0.621724i	$-0.213567\pi$
$941$	1.25408e10	+	8.55018e9i	0.490639	+	0.334512i	−0.292598	+	0.956236i	$0.594520\pi$
$942$	−3.96190e8	+	1.73582e9i	−0.0154428	+	0.0676593i
$943$	1.40946e10	+	2.12442e9i	0.547345	+	0.0824990i
$944$	−1.03577e9	−	1.29881e9i	−0.0400738	−	0.0502510i
$945$	1.53423e10			0.591399
$946$	1.33472e10	−	3.76736e9i	0.512592	−	0.144683i
$947$	−2.93927e10			−1.12464			−0.562321	−	0.826919i	$-0.690091\pi$
$947$	−2.93927e10			−1.12464			−0.562321	+	0.826919i	$0.690091\pi$
$948$	3.68699e8	+	4.62334e8i	0.0140554	+	0.0176249i
$949$	4.27488e10	+	6.44334e9i	1.62365	+	0.244726i
$950$	2.05442e10	−	9.00100e10i	0.777422	−	3.40611i
$951$	−4.94183e9	−	3.36929e9i	−0.186319	−	0.127030i
$952$	1.72059e10	+	2.98015e10i	0.646322	+	1.11946i
$953$	−8.42650e9	+	1.45951e10i	−0.315371	+	0.546239i	−0.979516	−	0.201365i	$-0.935462\pi$
$953$	−8.42650e9	+	1.45951e10i	−0.315371	+	0.546239i	0.664145	+	0.747604i	$0.268796\pi$
$954$	1.89434e9	−	9.12266e8i	0.0706380	−	0.0340175i
$955$	−1.07941e9	−	3.32952e8i	−0.0401026	−	0.0123700i
$956$	−3.93109e8	−	5.24568e9i	−0.0145516	−	0.194178i
$957$	9.37211e8	+	4.10619e9i	0.0345657	+	0.151442i
$958$	1.21967e10	−	3.10766e10i	0.448190	−	1.14197i
$959$	−1.68028e9	+	2.24218e10i	−0.0615200	+	0.820928i
$960$	1.11281e10	−	1.67730e9i	0.405951	−	0.0611873i
$961$	6.62319e9	+	6.14543e9i	0.240733	+	0.223368i
$962$	−2.14837e10	−	1.03460e10i	−0.778029	−	0.374679i
$963$	6.06387e8	−	4.13428e8i	0.0218805	−	0.0149179i
$964$	−5.18734e9	−	1.32171e10i	−0.186498	−	0.475190i
$965$	−4.02282e10	+	1.24087e10i	−1.44107	+	0.444511i
$966$	−2.22844e9	+	2.06769e9i	−0.0795390	+	0.0738015i
$967$	1.90911e10	−	2.39395e10i	0.678952	−	0.851378i	−0.316306	−	0.948657i	$-0.602442\pi$
$967$	1.90911e10	−	2.39395e10i	0.678952	−	0.851378i	0.995257	+	0.0972790i	$0.0310139\pi$
$968$	−1.09114e10	+	1.36825e10i	−0.386650	+	0.484844i
$969$	−9.85181e9	+	9.14114e9i	−0.347843	+	0.322751i
$970$	−6.84310e10	+	2.11082e10i	−2.40742	+	0.742591i
$971$	−1.79807e10	−	4.58142e10i	−0.630290	−	1.60595i	−0.786054	−	0.618158i	$-0.787879\pi$
$971$	−1.79807e10	−	4.58142e10i	−0.630290	−	1.60595i	0.155765	−	0.987794i	$-0.450216\pi$
$972$	4.55987e9	−	3.10886e9i	0.159265	−	0.108585i
$973$	−1.22943e10	−	5.92062e9i	−0.427867	−	0.206050i
$974$	−3.49271e8	−	3.24077e8i	−0.0121117	−	0.0112381i
$975$	−1.61555e10	+	2.43505e9i	−0.558219	+	0.0841380i
$976$	5.29500e7	−	7.06569e8i	0.00182302	−	0.0243265i
$977$	2.85565e8	−	7.27609e8i	0.00979658	−	0.0249613i	−0.925892	−	0.377789i	$-0.876685\pi$
$977$	2.85565e8	−	7.27609e8i	0.00979658	−	0.0249613i	0.935688	+	0.352828i	$0.114780\pi$
$978$	−2.02298e9	−	8.86325e9i	−0.0691521	−	0.302975i
$979$	8.45176e8	+	1.12781e10i	0.0287877	+	0.384146i
$980$	7.09529e9	+	2.18861e9i	0.240812	+	0.0742808i
$981$	−2.79899e9	+	1.34792e9i	−0.0946584	+	0.0455851i
$982$	2.19028e10	−	3.79368e10i	0.738091	−	1.27841i
$983$	1.26125e10	+	2.18455e10i	0.423510	+	0.733540i	0.996280	−	0.0861756i	$-0.0274646\pi$
$983$	1.26125e10	+	2.18455e10i	0.423510	+	0.733540i	−0.572770	+	0.819716i	$0.694131\pi$
$984$	3.46113e9	+	2.35976e9i	0.115807	+	0.0789559i
$985$	−3.81358e9	+	1.67084e10i	−0.127147	+	0.557067i
$986$	4.34848e10	+	6.55428e9i	1.44467	+	0.217749i
$987$	−1.51379e9	−	1.89824e9i	−0.0501137	−	0.0628407i
$988$	1.69613e10			0.559511
$989$	−2.58137e10	+	3.25678e9i	−0.848524	+	0.107054i
$990$	−3.01505e10			−0.987576
$991$	−1.85893e10	−	2.33103e10i	−0.606745	−	0.760834i	0.379667	−	0.925123i	$-0.376038\pi$
$991$	−1.85893e10	−	2.33103e10i	−0.606745	−	0.760834i	−0.986412	+	0.164289i	$0.947467\pi$
$992$	1.61373e10	+	2.43230e9i	0.524855	+	0.0791091i
$993$	1.98383e9	−	8.69172e9i	0.0642957	−	0.281698i
$994$	1.69998e10	+	1.15902e10i	0.549023	+	0.374317i
$995$	4.95166e10	+	8.57653e10i	1.59357	+	2.76014i
$996$	7.26866e8	−	1.25897e9i	0.0233102	−	0.0403745i
$997$	−3.37836e10	+	1.62693e10i	−1.07963	+	0.519920i	−0.887197	−	0.461391i	$-0.847351\pi$
$997$	−3.37836e10	+	1.62693e10i	−1.07963	+	0.519920i	−0.192429	+	0.981311i	$0.561636\pi$
$998$	1.80793e10	+	5.57672e9i	0.575737	+	0.177591i
$999$	9.38748e8	+	1.25267e10i	0.0297900	+	0.397519i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	43.8.g.a.9.9	✓	300
43.24	even	21	inner	43.8.g.a.24.9	yes	300

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
43.8.g.a.9.9	✓	300	1.1	even	1	trivial
43.8.g.a.24.9	yes	300	43.24	even	21	inner

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)

\(f(q)\)	\(=\)	\(q+(-5.72725 - 7.18175i) q^{2} +(9.19934 + 1.38658i) q^{3} +(9.70661 - 42.5274i) q^{4} +(445.851 + 303.976i) q^{5} +(-42.7289 - 74.0086i) q^{6} +(-356.405 + 617.311i) q^{7} +(-1420.36 + 684.008i) q^{8} +(-2007.13 - 619.118i) q^{9} +O(q^{10})\)	\(q+(-5.72725 - 7.18175i) q^{2} +(9.19934 + 1.38658i) q^{3} +(9.70661 - 42.5274i) q^{4} +(445.851 + 303.976i) q^{5} +(-42.7289 - 74.0086i) q^{6} +(-356.405 + 617.311i) q^{7} +(-1420.36 + 684.008i) q^{8} +(-2007.13 - 619.118i) q^{9} +(-370.422 - 4942.94i) q^{10} +(644.393 + 2823.27i) q^{11} +(148.262 - 377.765i) q^{12} +(-615.967 + 8219.51i) q^{13} +(6474.59 - 975.887i) q^{14} +(3680.05 + 3414.59i) q^{15} +(8016.55 + 3860.57i) q^{16} +(-25301.9 + 17250.5i) q^{17} +(7049.00 + 17960.6i) q^{18} +(45077.8 - 13904.7i) q^{19} +(17255.0 - 16010.3i) q^{20} +(-4134.64 + 5184.67i) q^{21} +(16585.4 - 20797.5i) q^{22} +(-36582.7 + 33943.8i) q^{23} +(-14014.8 + 4322.99i) q^{24} +(77839.6 + 198332. i) q^{25} +(62558.3 - 42651.5i) q^{26} +(-35937.1 - 17306.4i) q^{27} +(22793.2 + 21149.0i) q^{28} +(154587. - 23300.3i) q^{29} +(3446.13 - 45985.4i) q^{30} +(49661.5 - 126536. i) q^{31} +(26715.1 + 117047. i) q^{32} +(2013.31 + 26865.7i) q^{33} +(268799. + 82913.6i) q^{34} +(-346551. + 166890. i) q^{35} +(-45812.0 + 79348.7i) q^{36} +(-157467. - 272741. i) q^{37} +(-358032. - 244102. i) q^{38} +(-17063.5 + 74760.0i) q^{39} +(-841190. - 126789. i) q^{40} +(-178082. - 223307. i) q^{41} +60915.1 q^{42} +(423568. + 303988. i) q^{43} +126321. q^{44} +(-706686. - 886156. i) q^{45} +(453294. + 68323.0i) q^{46} +(-81470.5 + 356946. i) q^{47} +(68394.0 + 46630.2i) q^{48} +(157723. + 273184. i) q^{49} +(978564. - 1.69492e6i) q^{50} +(-256680. + 123611. i) q^{51} +(343576. + 105979. i) q^{52} +(-8143.56 - 108668. i) q^{53} +(81530.8 + 357210. i) q^{54} +(-570904. + 1.45464e6i) q^{55} +(83976.2 - 1.12059e6i) q^{56} +(433966. - 65409.9i) q^{57} +(-1.05270e6 - 976759. i) q^{58} +(-168215. - 81008.2i) q^{59} +(180935. - 123359. i) q^{60} +(-29093.2 - 74128.3i) q^{61} +(-1.19317e6 + 368044. i) q^{62} +(1.09754e6 - 1.01837e6i) q^{63} +(1.39769e6 - 1.75265e6i) q^{64} +(-2.77317e6 + 3.47744e6i) q^{65} +(181412. - 168326. i) q^{66} +(-2.08697e6 + 643746. i) q^{67} +(488025. + 1.24347e6i) q^{68} +(-383602. + 261535. i) q^{69} +(3.18335e6 + 1.53302e6i) q^{70} +(2.30346e6 + 2.13730e6i) q^{71} +(3.27433e6 - 493525. i) q^{72} +(391954. - 5.23026e6i) q^{73} +(-1.05690e6 + 2.69295e6i) q^{74} +(441070. + 1.93246e6i) q^{75} +(-153777. - 2.05201e6i) q^{76} +(-1.97250e6 - 608436. i) q^{77} +(634634. - 305624. i) q^{78} +(-728587. + 1.26195e6i) q^{79} +(2.40067e6 + 4.15808e6i) q^{80} +(3.48888e6 + 2.37868e6i) q^{81} +(-583818. + 2.55787e6i) q^{82} +(3.54221e6 + 533903. i) q^{83} +(180357. + 226161. i) q^{84} -1.65246e7 q^{85} +(-242714. - 4.78297e6i) q^{86} +1.45441e6 q^{87} +(-2.84641e6 - 3.56928e6i) q^{88} +(3.86183e6 + 582077. i) q^{89} +(-2.31678e6 + 1.01505e7i) q^{90} +(-4.85446e6 - 3.30972e6i) q^{91} +(1.08845e6 + 1.88525e6i) q^{92} +(632305. - 1.09518e6i) q^{93} +(3.03009e6 - 1.45922e6i) q^{94} +(2.43247e7 + 7.50318e6i) q^{95} +(83467.3 + 1.11379e6i) q^{96} +(-3.21483e6 - 1.40851e7i) q^{97} +(1.05862e6 - 2.69732e6i) q^{98} +(454557. - 6.06564e6i) 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

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