LMFDB - Embedded newform 43.8.g.a.24.2

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			24.2
Character	$\chi$	$=$	43.24
Dual form			43.8.g.a.9.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-12.0734 + 15.1396i) q^{2} +(-73.9419 + 11.1450i) q^{3} +(-54.9571 - 240.783i) q^{4} +(-26.8606 + 18.3132i) q^{5} +(724.002 - 1254.01i) q^{6} +(53.2365 + 92.2083i) q^{7} +(2075.71 + 999.609i) q^{8} +(3253.36 - 1003.53i) q^{9} +O(q^{10})$	\(q+(-12.0734 + 15.1396i) q^{2} +(-73.9419 + 11.1450i) q^{3} +(-54.9571 - 240.783i) q^{4} +(-26.8606 + 18.3132i) q^{5} +(724.002 - 1254.01i) q^{6} +(53.2365 + 92.2083i) q^{7} +(2075.71 + 999.609i) q^{8} +(3253.36 - 1003.53i) q^{9} +(47.0442 - 627.761i) q^{10} +(407.040 - 1783.36i) q^{11} +(6747.15 + 17191.4i) q^{12} +(-222.107 - 2963.82i) q^{13} +(-2038.74 - 307.291i) q^{14} +(1782.02 - 1653.47i) q^{15} +(-11712.4 + 5640.41i) q^{16} +(-22380.2 - 15258.6i) q^{17} +(-24086.2 + 61370.6i) q^{18} +(12680.4 + 3911.39i) q^{19} +(5885.69 + 5461.12i) q^{20} +(-4964.06 - 6224.74i) q^{21} +(22085.0 + 27693.7i) q^{22} +(-79701.0 - 73951.7i) q^{23} +(-164623. - 50779.3i) q^{24} +(-28156.2 + 71740.7i) q^{25} +(47552.6 + 32420.8i) q^{26} +(-82033.4 + 39505.2i) q^{27} +(19276.4 - 17885.9i) q^{28} +(119505. + 18012.5i) q^{29} +(3517.83 + 46942.2i) q^{30} +(107987. + 275147. i) q^{31} +(-9604.52 + 42080.1i) q^{32} +(-10221.9 + 136402. i) q^{33} +(501214. - 154604. i) q^{34} +(-3118.59 - 1501.83i) q^{35} +(-420428. - 728203. i) q^{36} +(35047.9 - 60704.8i) q^{37} +(-212313. + 144753. i) q^{38} +(49454.6 + 216675. i) q^{39} +(-74060.7 + 11162.9i) q^{40} +(240046. - 301009. i) q^{41} +154173. q^{42} +(-446290. + 269524. i) q^{43} -451772. q^{44} +(-69009.3 + 86534.9i) q^{45} +(2.08186e6 - 313790. i) q^{46} +(61816.6 + 270836. i) q^{47} +(803178. - 547598. i) q^{48} +(406103. - 703391. i) q^{49} +(-746184. - 1.29243e6i) q^{50} +(1.82489e6 + 878821. i) q^{51} +(-701430. + 216362. i) q^{52} +(-26654.6 + 355681. i) q^{53} +(392331. - 1.71892e6i) q^{54} +(21725.7 + 55356.3i) q^{55} +(18331.2 + 244613. i) q^{56} +(-981208. - 147893. i) q^{57} +(-1.71554e6 + 1.59179e6i) q^{58} +(-2.05129e6 + 987849. i) q^{59} +(-496063. - 338210. i) q^{60} +(493673. - 1.25786e6i) q^{61} +(-5.46939e6 - 1.68708e6i) q^{62} +(265731. + 246563. i) q^{63} +(-1.55859e6 - 1.95441e6i) q^{64} +(60242.9 + 75542.3i) q^{65} +(-1.94165e6 - 1.80159e6i) q^{66} +(3.08590e6 + 951873. i) q^{67} +(-2.44405e6 + 6.22733e6i) q^{68} +(6.71743e6 + 4.57987e6i) q^{69} +(60389.2 - 29081.9i) q^{70} +(-264027. + 244982. i) q^{71} +(7.75617e6 + 1.16905e6i) q^{72} +(243335. + 3.24708e6i) q^{73} +(495897. + 1.26353e6i) q^{74} +(1.28237e6 - 5.61845e6i) q^{75} +(244917. - 3.26819e6i) q^{76} +(186110. - 57407.3i) q^{77} +(-3.87746e6 - 1.86729e6i) q^{78} +(2.82551e6 + 4.89392e6i) q^{79} +(211308. - 365997. i) q^{80} +(-526672. + 359079. i) q^{81} +(1.65897e6 + 7.26841e6i) q^{82} +(30885.4 - 4655.23i) q^{83} +(-1.22600e6 + 1.53735e6i) q^{84} +880578. q^{85} +(1.30776e6 - 1.00107e7i) q^{86} -9.03719e6 q^{87} +(2.62756e6 - 3.29485e6i) q^{88} +(3.41839e6 - 515240. i) q^{89} +(-476925. - 2.08955e6i) q^{90} +(261464. - 178263. i) q^{91} +(-1.34262e7 + 2.32548e7i) q^{92} +(-1.10513e7 - 1.91414e7i) q^{93} +(-4.84669e6 - 2.33404e6i) q^{94} +(-412234. + 127157. i) q^{95} +(241195. - 3.21853e6i) q^{96} +(2.85628e6 - 1.25142e7i) q^{97} +(5.74601e6 + 1.46406e7i) q^{98} +(-465405. - 6.21039e6i) 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 $

$2$	−12.0734	+	15.1396i	−1.06715	+	1.33816i	−0.129113	+	0.991630i	$0.541213\pi$
$2$	−12.0734	+	15.1396i	−1.06715	+	1.33816i	−0.938037	+	0.346534i	$0.887359\pi$
$3$	−73.9419	+	11.1450i	−1.58113	+	0.238316i	−0.880089	−	0.474809i	$-0.842517\pi$
$3$	−73.9419	+	11.1450i	−1.58113	+	0.238316i	−0.701037	+	0.713125i	$0.747279\pi$
$4$	−54.9571	−	240.783i	−0.429352	−	1.88112i
$5$	−26.8606	+	18.3132i	−0.0960992	+	0.0655194i	−0.610416	−	0.792081i	$-0.708998\pi$
$5$	−26.8606	+	18.3132i	−0.0960992	+	0.0655194i	0.514317	+	0.857600i	$0.328045\pi$
$6$	724.002	−	1254.01i	1.36839	−	2.37012i
$7$	53.2365	+	92.2083i	0.0586632	+	0.101608i	0.893866	−	0.448335i	$-0.147983\pi$
$7$	53.2365	+	92.2083i	0.0586632	+	0.101608i	−0.835202	+	0.549943i	$0.814650\pi$
$8$	2075.71	+	999.609i	1.43335	+	0.690264i
$9$	3253.36	−	1003.53i	1.48759	−	0.458861i
$10$	47.0442	−	627.761i	0.0148767	−	0.198516i
$11$	407.040	−	1783.36i	0.0922068	−	0.403984i	−0.907670	−	0.419685i	$-0.862141\pi$
$11$	407.040	−	1783.36i	0.0922068	−	0.403984i	0.999877	+	0.0157003i	$0.00499778\pi$
$12$	6747.15	+	17191.4i	1.12716	+	2.87196i
$13$	−222.107	−	2963.82i	−0.0280389	−	0.374153i	−0.993518	−	0.113673i	$-0.963738\pi$
$13$	−222.107	−	2963.82i	−0.0280389	−	0.374153i	0.965479	−	0.260480i	$-0.0838808\pi$
$14$	−2038.74	−	307.291i	−0.198570	−	0.0299297i
$15$	1782.02	−	1653.47i	0.136331	−	0.126496i
$16$	−11712.4	+	5640.41i	−0.714870	+	0.344263i
$17$	−22380.2	−	15258.6i	−1.10482	−	0.753256i	−0.133507	−	0.991048i	$-0.542624\pi$
$17$	−22380.2	−	15258.6i	−1.10482	−	0.753256i	−0.971316	+	0.237792i	$0.923576\pi$
$18$	−24086.2	+	61370.6i	−0.973452	+	2.48032i
$19$	12680.4	+	3911.39i	0.424127	+	0.130826i	0.499469	−	0.866332i	$-0.333528\pi$
$19$	12680.4	+	3911.39i	0.424127	+	0.130826i	−0.0753415	+	0.997158i	$0.524005\pi$
$20$	5885.69	+	5461.12i	0.164510	+	0.152643i
$21$	−4964.06	−	6224.74i	−0.116969	−	0.146674i
$22$	22085.0	+	27693.7i	0.442199	+	0.554500i
$23$	−79701.0	−	73951.7i	−1.36589	−	1.26736i	−0.930096	−	0.367316i	$-0.880277\pi$
$23$	−79701.0	−	73951.7i	−1.36589	−	1.26736i	−0.435795	−	0.900046i	$-0.643533\pi$
$24$	−164623.	−	50779.3i	−2.43080	−	0.749804i
$25$	−28156.2	+	71740.7i	−0.360399	+	0.918281i
$26$	47552.6	+	32420.8i	0.530600	+	0.361757i
$27$	−82033.4	+	39505.2i	−0.802079	+	0.386261i
$28$	19276.4	−	17885.9i	0.165949	−	0.153978i
$29$	119505.	+	18012.5i	0.909900	+	0.137145i	0.587280	−	0.809384i	$-0.300199\pi$
$29$	119505.	+	18012.5i	0.909900	+	0.137145i	0.322619	+	0.946529i	$0.395437\pi$
$30$	3517.83	+	46942.2i	0.0237876	+	0.317423i
$31$	107987.	+	275147.i	0.651038	+	1.65882i	0.748138	+	0.663543i	$0.230948\pi$
$31$	107987.	+	275147.i	0.651038	+	1.65882i	−0.0971004	+	0.995275i	$0.530957\pi$
$32$	−9604.52	+	42080.1i	−0.0518144	+	0.227014i
$33$	−10221.9	+	136402.i	−0.0495145	+	0.660725i
$34$	501214.	−	154604.i	2.18699	−	0.674598i
$35$	−3118.59	−	1501.83i	−0.0122948	−	0.00592085i
$36$	−420428.	−	728203.i	−1.50187	−	2.60132i
$37$	35047.9	−	60704.8i	0.113751	−	0.197023i	−0.803529	−	0.595266i	$-0.797047\pi$
$37$	35047.9	−	60704.8i	0.113751	−	0.197023i	0.917280	+	0.398243i	$0.130380\pi$
$38$	−212313.	+	144753.i	−0.627674	+	0.427941i
$39$	49454.6	+	216675.i	0.133500	+	0.584901i
$40$	−74060.7	+	11162.9i	−0.182969	+	0.0275782i
$41$	240046.	−	301009.i	0.543941	−	0.682080i	−0.431558	−	0.902085i	$-0.642036\pi$
$41$	240046.	−	301009.i	0.543941	−	0.682080i	0.975499	+	0.220005i	$0.0706074\pi$
$42$	154173.			0.321097
$43$	−446290.	+	269524.i	−0.856008	+	0.516962i
$43$	−446290.	+	269524.i	−0.856008	+	0.516962i
$44$	−451772.			−0.799530
$45$	−69009.3	+	86534.9i	−0.112892	+	0.141562i
$46$	2.08186e6	−	313790.i	3.15355	−	0.475321i
$47$	61816.6	+	270836.i	0.0868486	+	0.380509i	0.999608	−	0.0279885i	$-0.00891017\pi$
$47$	61816.6	+	270836.i	0.0868486	+	0.380509i	−0.912760	+	0.408497i	$0.866053\pi$
$48$	803178.	−	547598.i	1.04826	−	0.714689i
$49$	406103.	−	703391.i	0.493117	−	0.854104i
$50$	−746184.	−	1.29243e6i	−0.844211	−	1.46222i
$51$	1.82489e6	+	878821.i	1.92638	+	0.927695i
$52$	−701430.	+	216362.i	−0.691787	+	0.213388i
$53$	−26654.6	+	355681.i	−0.0245927	+	0.328167i	0.971315	+	0.237795i	$0.0764247\pi$
$53$	−26654.6	+	355681.i	−0.0245927	+	0.328167i	−0.995908	+	0.0903721i	$0.971194\pi$
$54$	392331.	−	1.71892e6i	0.339058	−	1.48551i
$55$	21725.7	+	55356.3i	0.0176078	+	0.0448639i
$56$	18331.2	+	244613.i	0.0139487	+	0.186132i
$57$	−981208.	−	147893.i	−0.701777	−	0.105776i
$58$	−1.71554e6	+	1.59179e6i	−1.15452	+	1.07124i
$59$	−2.05129e6	+	987849.i	−1.30030	+	0.626193i	−0.950528	−	0.310640i	$-0.899457\pi$
$59$	−2.05129e6	+	987849.i	−1.30030	+	0.626193i	−0.349776	+	0.936833i	$0.613742\pi$
$60$	−496063.	−	338210.i	−0.296488	−	0.202142i
$61$	493673.	−	1.25786e6i	0.278474	−	0.709541i	−0.721381	−	0.692538i	$-0.756492\pi$
$61$	493673.	−	1.25786e6i	0.278474	−	0.709541i	0.999855	−	0.0170028i	$-0.00541243\pi$
$62$	−5.46939e6	−	1.68708e6i	−2.91452	−	0.899012i
$63$	265731.	+	246563.i	0.133891	+	0.124233i
$64$	−1.55859e6	−	1.95441e6i	−0.743194	−	0.931935i
$65$	60242.9	+	75542.3i	0.0272088	+	0.0341188i
$66$	−1.94165e6	−	1.80159e6i	−0.831318	−	0.771351i
$67$	3.08590e6	+	951873.i	1.25349	+	0.386649i	0.849243	−	0.528003i	$-0.177059\pi$
$67$	3.08590e6	+	951873.i	1.25349	+	0.386649i	0.404243	+	0.914652i	$0.367535\pi$
$68$	−2.44405e6	+	6.22733e6i	−0.942602	+	2.40171i
$69$	6.71743e6	+	4.57987e6i	2.46168	+	1.67834i
$70$	60389.2	−	29081.9i	0.0210434	−	0.0101340i
$71$	−264027.	+	244982.i	−0.0875477	+	0.0812324i	−0.722733	−	0.691128i	$-0.757114\pi$
$71$	−264027.	+	244982.i	−0.0875477	+	0.0812324i	0.635185	+	0.772360i	$0.280924\pi$
$72$	7.75617e6	+	1.16905e6i	2.44897	+	0.369123i
$73$	243335.	+	3.24708e6i	0.0732108	+	0.976930i	0.905983	+	0.423314i	$0.139133\pi$
$73$	243335.	+	3.24708e6i	0.0732108	+	0.976930i	−0.832772	+	0.553616i	$0.813248\pi$
$74$	495897.	+	1.26353e6i	0.142259	+	0.362471i
$75$	1.28237e6	−	5.61845e6i	0.350994	−	1.53781i
$76$	244917.	−	3.26819e6i	0.0639987	−	0.854003i
$77$	186110.	−	57407.3i	0.0464571	−	0.0143301i
$78$	−3.87746e6	−	1.86729e6i	−0.925158	−	0.445533i
$79$	2.82551e6	+	4.89392e6i	0.644766	+	1.11677i	0.984356	+	0.176193i	$0.0563783\pi$
$79$	2.82551e6	+	4.89392e6i	0.644766	+	1.11677i	−0.339590	+	0.940574i	$0.610288\pi$
$80$	211308.	−	365997.i	0.0461426	−	0.0799213i
$81$	−526672.	+	359079.i	−0.110114	+	0.0750745i
$82$	1.65897e6	+	7.26841e6i	0.332269	+	1.45576i
$83$	30885.4	−	4655.23i	0.00592898	−	0.000893651i	−0.146077	−	0.989273i	$-0.546665\pi$
$83$	30885.4	−	4655.23i	0.00592898	−	0.000893651i	0.152006	+	0.988380i	$0.451427\pi$
$84$	−1.22600e6	+	1.53735e6i	−0.225690	+	0.283007i
$85$	880578.			0.155526
$86$	1.30776e6	−	1.00107e7i	0.221710	−	1.69716i
$87$	−9.03719e6			−1.47135
$88$	2.62756e6	−	3.29485e6i	0.411020	−	0.515403i
$89$	3.41839e6	−	515240.i	0.513992	−	0.0774719i	0.113076	−	0.993586i	$-0.463930\pi$
$89$	3.41839e6	−	515240.i	0.513992	−	0.0774719i	0.400917	+	0.916114i	$0.368692\pi$
$90$	−476925.	−	2.08955e6i	−0.0689607	−	0.302136i
$91$	261464.	−	178263.i	0.0363720	−	0.0247980i
$92$	−1.34262e7	+	2.32548e7i	−1.79761	+	3.11354i
$93$	−1.10513e7	−	1.91414e7i	−1.42470	−	2.46765i
$94$	−4.84669e6	−	2.33404e6i	−0.601863	−	0.289842i
$95$	−412234.	+	127157.i	−0.0493300	+	0.0152163i
$96$	241195.	−	3.21853e6i	0.0278240	−	0.371286i
$97$	2.85628e6	−	1.25142e7i	0.317760	−	1.39220i	−0.523711	−	0.851896i	$-0.675453\pi$
$97$	2.85628e6	−	1.25142e7i	0.317760	−	1.39220i	0.841471	−	0.540302i	$-0.181690\pi$
$98$	5.74601e6	+	1.46406e7i	0.616701	+	1.57133i
$99$	−465405.	−	6.21039e6i	−0.0482067	−	0.643274i
$100$	1.88213e7	+	2.83686e6i	1.88213	+	0.283686i
$101$	570824.	−	529647.i	0.0551286	−	0.0511519i	−0.652127	−	0.758109i	$-0.726123\pi$
$101$	570824.	−	529647.i	0.0551286	−	0.0511519i	0.707256	+	0.706957i	$0.249933\pi$
$102$	−3.53377e7	+	1.70177e7i	−3.29714	+	1.58782i
$103$	5.87946e6	+	4.00855e6i	0.530160	+	0.361457i	0.798622	−	0.601833i	$-0.205563\pi$
$103$	5.87946e6	+	4.00855e6i	0.530160	+	0.361457i	−0.268461	+	0.963290i	$0.586515\pi$
$104$	2.50163e6	−	6.37404e6i	0.218075	−	0.555646i
$105$	247333.	+	76292.0i	0.0208506	+	0.00643156i
$106$	−5.06305e6	−	4.69783e6i	−0.412897	−	0.383113i
$107$	7.59629e6	+	9.52545e6i	0.599458	+	0.751696i	0.985293	−	0.170871i	$-0.0546582\pi$
$107$	7.59629e6	+	9.52545e6i	0.599458	+	0.751696i	−0.385836	+	0.922568i	$0.626087\pi$
$108$	1.40205e7	+	1.75811e7i	1.07098	+	1.34296i
$109$	−8.86773e6	−	8.22805e6i	−0.655873	−	0.608561i	0.280380	−	0.959889i	$-0.409540\pi$
$109$	−8.86773e6	−	8.22805e6i	−0.655873	−	0.608561i	−0.936252	+	0.351328i	$0.885730\pi$
$110$	−1.10038e6	−	339421.i	−0.0788254	−	0.0243144i
$111$	−1.91496e6	+	4.87923e6i	−0.132901	+	0.338627i
$112$	−1.14362e6	−	779708.i	−0.0769165	−	0.0524407i
$113$	426408.	−	205347.i	0.0278004	−	0.0133880i	−0.419932	−	0.907556i	$-0.637946\pi$
$113$	426408.	−	205347.i	0.0278004	−	0.0133880i	0.447732	+	0.894168i	$0.352232\pi$
$114$	1.40856e7	−	1.30695e7i	0.890447	−	0.826214i
$115$	3.49511e6	+	526802.i	0.214298	+	0.0323002i
$116$	−2.23055e6	−	2.97647e7i	−0.132681	−	1.77051i
$117$	−3.69687e6	−	9.41948e6i	−0.213395	−	0.543721i
$118$	9.81045e6	−	4.29824e7i	0.549670	−	2.40826i
$119$	215523.	−	2.87595e6i	0.0117241	−	0.156447i
$120$	5.35178e6	−	1.65081e6i	0.282725	−	0.0872091i
$121$	1.45426e7	+	7.00337e6i	0.746268	+	0.359384i
$122$	1.30832e7	+	2.26607e7i	0.652308	+	1.12983i
$123$	−1.43948e7	+	2.49325e7i	−0.697488	+	1.20808i
$124$	6.03160e7	−	4.11227e7i	2.84090	−	1.93689i
$125$	−1.12267e6	−	4.91875e6i	−0.0514124	−	0.225252i
$126$	−6.94114e6	+	1.04621e6i	−0.309125	+	0.0465931i
$127$	2.68628e6	−	3.36849e6i	0.116369	−	0.145922i	−0.720235	−	0.693730i	$-0.755966\pi$
$127$	2.68628e6	−	3.36849e6i	0.116369	−	0.145922i	0.836604	+	0.547808i	$0.184537\pi$
$128$	4.28817e7			1.80733
$129$	2.99957e7	−	2.49030e7i	1.23026	−	1.02138i
$130$	−1.87102e6			−0.0746924
$131$	−1.73527e7	+	2.17596e7i	−0.674399	+	0.845669i	−0.994825	−	0.101604i	$-0.967602\pi$
$131$	−1.73527e7	+	2.17596e7i	−0.674399	+	0.845669i	0.320426	+	0.947273i	$0.396174\pi$
$132$	3.34049e7	−	5.03498e6i	1.26416	−	0.190541i
$133$	314398.	+	1.37747e6i	0.0115878	+	0.0507693i
$134$	−5.16683e7	+	3.52268e7i	−1.85506	+	1.26476i
$135$	1.47999e6	−	2.56343e6i	0.0517717	−	0.0896711i
$136$	−3.12022e7	−	5.40438e7i	−1.06365	−	1.84230i
$137$	4.69650e7	+	2.26172e7i	1.56046	+	0.751478i	0.997198	−	0.0748011i	$-0.0238322\pi$
$137$	4.69650e7	+	2.26172e7i	1.56046	+	0.751478i	0.563261	+	0.826279i	$0.309546\pi$
$138$	−1.50440e8	+	4.64045e7i	−4.87288	+	1.50308i
$139$	−2.73661e6	+	3.65175e7i	−0.0864294	+	1.15332i	0.770345	+	0.637628i	$0.220084\pi$
$139$	−2.73661e6	+	3.65175e7i	−0.0864294	+	1.15332i	−0.856774	+	0.515692i	$0.827535\pi$
$140$	−190227.	+	833439.i	−0.00585901	+	0.0256700i
$141$	−7.58930e6	−	1.93372e7i	−0.228000	−	0.580935i
$142$	−521208.	−	6.95504e6i	−0.0152757	−	0.203840i
$143$	−5.37596e6	−	810295.i	−0.153737	−	0.0231722i
$144$	−3.24445e7	+	3.01041e7i	−0.905466	+	0.840150i
$145$	−3.53984e6	+	1.70470e6i	−0.0964263	+	0.0464365i
$146$	−5.20974e7	−	3.55194e7i	−1.38542	−	0.944563i
$147$	−2.21888e7	+	5.65361e7i	−0.576133	+	1.46796i
$148$	−1.65428e7	−	5.10277e6i	−0.419462	−	0.129387i
$149$	4.15832e7	+	3.85836e7i	1.02983	+	0.955545i	0.999032	−	0.0439811i	$-0.0140041\pi$
$149$	4.15832e7	+	3.85836e7i	1.02983	+	0.955545i	0.0307997	+	0.999526i	$0.490195\pi$
$150$	6.95784e7	+	8.72485e7i	1.68327	+	2.11076i
$151$	3.86813e7	+	4.85048e7i	0.914286	+	1.14648i	0.988798	+	0.149258i	$0.0476885\pi$
$151$	3.86813e7	+	4.85048e7i	0.914286	+	1.14648i	−0.0745126	+	0.997220i	$0.523740\pi$
$152$	2.24110e7	+	2.07944e7i	0.517617	+	0.480279i
$153$	−8.81233e7	−	2.71824e7i	−1.98917	−	0.613576i
$154$	−1.37786e6	+	3.51073e6i	−0.0304006	+	0.0774596i
$155$	−7.93942e6	−	5.41300e6i	−0.171249	−	0.116756i
$156$	4.94537e7	−	2.38157e7i	1.04295	−	0.502257i
$157$	3.39274e7	−	3.14801e7i	0.699685	−	0.649213i	−0.247875	−	0.968792i	$-0.579732\pi$
$157$	3.39274e7	−	3.14801e7i	0.699685	−	0.649213i	0.947559	+	0.319580i	$0.103542\pi$
$158$	−1.08206e8	−	1.63094e7i	−2.18248	−	0.328956i
$159$	−1.99316e6	−	2.65968e7i	−0.0393234	−	0.524734i
$160$	−512640.	−	1.30619e6i	−0.00989447	−	0.0252107i
$161$	2.57596e6	−	1.12860e7i	0.0486462	−	0.213133i
$162$	922426.	−	1.23089e7i	0.0170462	−	0.227466i
$163$	−3.27636e7	+	1.01062e7i	−0.592563	+	0.182782i	−0.576511	−	0.817090i	$-0.695586\pi$
$163$	−3.27636e7	+	1.01062e7i	−0.592563	+	0.182782i	−0.0160527	+	0.999871i	$0.505110\pi$
$164$	−8.56699e7	−	4.12565e7i	−1.51661	−	0.730363i
$165$	−2.22339e6	−	3.85102e6i	−0.0385319	−	0.0667393i
$166$	−302415.	+	523797.i	−0.00513126	+	0.00888761i
$167$	2.51157e7	−	1.71236e7i	0.417290	−	0.284504i	−0.336418	−	0.941713i	$-0.609216\pi$
$167$	2.51157e7	−	1.71236e7i	0.417290	−	0.284504i	0.753708	+	0.657209i	$0.228263\pi$
$168$	−4.08165e6	−	1.78829e7i	−0.0664130	−	0.290974i
$169$	5.33128e7	−	8.03561e6i	0.849626	−	0.128061i
$170$	−1.06316e7	+	1.33316e7i	−0.165969	+	0.208119i
$171$	4.51792e7			0.690959
$172$	8.94237e7	+	9.26468e7i	1.33999	+	1.38829i
$173$	−1.34384e8			−1.97326			−0.986631	−	0.162972i	$-0.947892\pi$
$173$	−1.34384e8			−1.97326			−0.986631	+	0.162972i	$0.947892\pi$
$174$	1.09110e8	−	1.36819e8i	1.57015	−	1.96891i
$175$	−8.11402e6	+	1.22299e6i	−0.114447	+	0.0172501i
$176$	5.29145e6	+	2.31834e7i	0.0731611	+	0.320540i
$177$	1.40667e8	−	9.59050e7i	1.90671	−	1.29997i
$178$	−3.34712e7	+	5.79738e7i	−0.444837	+	0.770480i
$179$	−2.71301e7	−	4.69907e7i	−0.353562	−	0.612387i	0.633309	−	0.773899i	$-0.281696\pi$
$179$	−2.71301e7	−	4.69907e7i	−0.353562	−	0.612387i	−0.986871	+	0.161512i	$0.948363\pi$
$180$	2.46287e7	+	1.18605e7i	0.314765	+	0.151583i
$181$	−1.25224e8	+	3.86264e7i	−1.56968	+	0.484183i	−0.952985	−	0.303018i	$-0.902006\pi$
$181$	−1.25224e8	+	3.86264e7i	−1.56968	+	0.484183i	−0.616697	+	0.787201i	$0.711530\pi$
$182$	−457934.	+	6.11071e6i	−0.00563058	+	0.0751349i
$183$	−2.24844e7	+	9.85105e7i	−0.271208	+	1.18824i
$184$	−9.15132e7	−	2.33172e8i	−1.08298	−	2.75940i
$185$	170293.	+	2.27240e6i	0.00197741	+	0.0263867i
$186$	4.23220e8	+	6.37901e7i	4.82248	+	0.726872i
$187$	−3.63212e7	+	3.37011e7i	−0.406176	+	0.376876i
$188$	6.18155e7	−	2.97688e7i	0.678492	−	0.326744i
$189$	−8.00987e6	−	5.46104e6i	−0.0862997	−	0.0588381i
$190$	3.05196e6	−	7.77627e6i	0.0322806	−	0.0822496i
$191$	6.40635e6	+	1.97610e6i	0.0665264	+	0.0205207i	0.327840	−	0.944733i	$-0.393679\pi$
$191$	6.40635e6	+	1.97610e6i	0.0665264	+	0.0205207i	−0.261313	+	0.965254i	$0.584156\pi$
$192$	1.37027e8	+	1.27142e8i	1.39718	+	1.29639i
$193$	7.56757e7	+	9.48944e7i	0.757715	+	0.950145i	0.999798	−	0.0201109i	$-0.00640192\pi$
$193$	7.56757e7	+	9.48944e7i	0.757715	+	0.950145i	−0.242083	+	0.970256i	$0.577830\pi$
$194$	1.54975e8	+	1.94332e8i	1.52389	+	1.91090i
$195$	−5.29640e6	−	4.91434e6i	−0.0511516	−	0.0474618i
$196$	−1.91683e8	−	5.91263e7i	−1.81839	−	0.560899i
$197$	2.53075e7	−	6.44824e7i	0.235840	−	0.600910i	−0.763132	−	0.646242i	$-0.776339\pi$
$197$	2.53075e7	−	6.44824e7i	0.235840	−	0.600910i	0.998972	+	0.0453325i	$0.0144347\pi$
$198$	9.96419e7	+	6.79347e7i	0.912250	+	0.621961i
$199$	5.61301e7	−	2.70308e7i	0.504905	−	0.243150i	−0.164050	−	0.986452i	$-0.552456\pi$
$199$	5.61301e7	−	2.70308e7i	0.504905	−	0.243150i	0.668956	+	0.743302i	$0.266742\pi$
$200$	−1.30157e8	+	1.20768e8i	−1.15043	+	1.06745i
$201$	−2.38786e8	−	3.59911e7i	−2.07406	−	0.312615i
$202$	1.12684e6	+	1.50367e7i	0.00961910	+	0.128358i
$203$	4.70113e6	+	1.19783e7i	0.0394426	+	0.100498i
$204$	1.11314e8	−	4.87700e8i	0.918006	−	4.02205i
$205$	−935343.	+	1.24813e7i	−0.00758284	+	0.101186i
$206$	−1.31673e8	+	4.06158e7i	−1.04945	+	0.323712i
$207$	−3.33509e8	−	1.60609e8i	−2.61343	−	1.25856i
$208$	1.93186e7	+	3.34607e7i	0.148852	+	0.257818i
$209$	1.21369e7	−	2.10217e7i	0.0919591	−	0.159278i
$210$	−4.14118e6	+	2.82341e6i	−0.0308572	+	0.0210381i
$211$	−4.62734e7	−	2.02737e8i	−0.339111	−	1.48574i	−0.800924	−	0.598767i	$-0.795658\pi$
$211$	−4.62734e7	−	2.02737e8i	−0.339111	−	1.48574i	0.461812	−	0.886978i	$-0.347199\pi$
$212$	8.71067e7	−	1.31292e7i	0.627879	−	0.0946376i
$213$	1.67924e7	−	2.10570e7i	0.119065	−	0.149303i
$214$	−2.35925e8			−1.64560
$215$	7.05175e6	−	1.54126e7i	0.0483908	−	0.105765i
$216$	−2.09767e8			−1.41628
$217$	−1.96220e7	+	2.46052e7i	−0.130357	+	0.163462i
$218$	2.31633e8	−	3.49131e7i	1.51427	−	0.228239i
$219$	−5.41813e7	−	2.37384e8i	−0.348574	−	1.52720i
$220$	1.21348e7	−	8.27340e6i	0.0768343	−	0.0523847i
$221$	−4.02528e7	+	6.97198e7i	−0.250855	+	0.434494i
$222$	−5.07495e7	−	8.79008e7i	−0.311313	−	0.539209i
$223$	1.35724e8	+	6.53613e7i	0.819577	+	0.394688i	0.796196	−	0.605039i	$-0.206843\pi$
$223$	1.35724e8	+	6.53613e7i	0.819577	+	0.394688i	0.0233813	+	0.999727i	$0.492557\pi$
$224$	−4.39145e6	+	1.35458e6i	−0.0261060	+	0.00805262i
$225$	−1.96083e7	+	2.61654e8i	−0.114763	+	1.53140i
$226$	−2.03933e6	+	8.93489e6i	−0.0117519	+	0.0514884i
$227$	8.36289e7	+	2.13083e8i	0.474533	+	1.20909i	0.945116	+	0.326734i	$0.105948\pi$
$227$	8.36289e7	+	2.13083e8i	0.474533	+	1.20909i	−0.470584	+	0.882355i	$0.655957\pi$
$228$	1.83142e7	+	2.44386e8i	0.102333	+	1.36554i
$229$	−1.02576e8	−	1.54608e7i	−0.564444	−	0.0850762i	−0.139379	−	0.990239i	$-0.544511\pi$
$229$	−1.02576e8	−	1.54608e7i	−0.564444	−	0.0850762i	−0.425065	+	0.905163i	$0.639749\pi$
$230$	−5.01735e7	+	4.65542e7i	−0.271911	+	0.252297i
$231$	−1.31215e7	+	6.31899e6i	−0.0700394	+	0.0337292i
$232$	2.30052e8	+	1.56847e8i	1.20954	+	0.824647i
$233$	1.10061e8	−	2.80431e8i	0.570018	−	1.45238i	−0.297377	−	0.954760i	$-0.596112\pi$
$233$	1.10061e8	−	2.80431e8i	0.570018	−	1.45238i	0.867394	−	0.497621i	$-0.165793\pi$
$234$	1.87241e8	+	5.77562e7i	0.955313	+	0.294675i
$235$	−6.62031e6	−	6.14275e6i	−0.0332768	−	0.0308763i
$236$	3.50590e8	+	4.39626e8i	1.73623	+	2.17716i
$237$	−2.63466e8	−	3.30376e8i	−1.28560	−	1.61209i
$238$	4.09386e7	+	3.79855e7i	0.196840	+	0.182641i
$239$	3.04560e8	+	9.39443e7i	1.44305	+	0.445120i	0.914778	−	0.403958i	$-0.132366\pi$
$239$	3.04560e8	+	9.39443e7i	1.44305	+	0.445120i	0.528267	+	0.849078i	$0.322842\pi$
$240$	−1.15455e7	+	2.94176e7i	−0.0539107	+	0.137362i
$241$	3.51106e7	+	2.39380e7i	0.161577	+	0.110161i	0.641409	−	0.767199i	$-0.278350\pi$
$241$	3.51106e7	+	2.39380e7i	0.161577	+	0.110161i	−0.479832	+	0.877360i	$0.659303\pi$
$242$	−2.81608e8	+	1.35615e8i	−1.27729	+	0.615112i
$243$	1.80911e8	−	1.67861e8i	0.808806	−	0.750462i
$244$	−3.30002e8	−	4.97397e7i	−1.45429	−	0.219199i
$245$	1.97320e6	+	2.63305e7i	0.00857216	+	0.114387i
$246$	−2.03673e8	−	5.18951e8i	−0.872291	−	2.22256i
$247$	8.77624e6	−	3.84512e7i	0.0370569	−	0.162357i
$248$	−5.08892e7	+	6.79070e8i	−0.211858	+	2.82705i
$249$	−2.23185e6	+	688433.i	−0.00916150	+	0.00282595i
$250$	8.80223e7	+	4.23893e7i	0.356289	+	0.171580i
$251$	−1.13691e8	−	1.96919e8i	−0.453805	−	0.786013i	0.544814	−	0.838557i	$-0.316600\pi$
$251$	−1.13691e8	−	1.96919e8i	−0.453805	−	0.786013i	−0.998619	+	0.0525441i	$0.983267\pi$
$252$	4.47642e7	−	7.75339e7i	0.176209	−	0.305204i
$253$	−1.64324e8	+	1.12034e8i	−0.637939	+	0.434939i
$254$	1.85650e7	+	8.13384e7i	0.0710847	+	0.311442i
$255$	−6.51116e7	+	9.81400e6i	−0.245905	+	0.0370643i
$256$	−3.18230e8	+	3.99047e8i	−1.18550	+	1.48657i
$257$	1.12008e8			0.411608			0.205804	−	0.978593i	$-0.434019\pi$
$257$	1.12008e8			0.411608			0.205804	+	0.978593i	$0.434019\pi$
$258$	1.48706e7	+	7.54789e8i	0.0539089	+	2.73625i
$259$	7.46331e6			0.0266921
$260$	1.48785e7	−	1.86570e7i	0.0524992	−	0.0658319i
$261$	4.06870e8	−	6.13257e7i	1.41649	−	0.213501i
$262$	−1.19925e8	−	5.25425e8i	−0.411959	−	1.80491i
$263$	−1.00330e8	+	6.84040e7i	−0.340084	+	0.231865i	−0.721303	−	0.692619i	$-0.756457\pi$
$263$	−1.00330e8	+	6.84040e7i	−0.340084	+	0.231865i	0.381219	+	0.924485i	$0.375504\pi$
$264$	−1.57566e8	+	2.72912e8i	−0.527046	+	0.912870i
$265$	−5.79771e6	−	1.00419e7i	−0.0191380	−	0.0331479i
$266$	−2.46502e7	−	1.18709e7i	−0.0803035	−	0.0386721i
$267$	−2.47020e8	+	7.61956e7i	−0.794224	+	0.244986i
$268$	5.96027e7	−	7.95342e8i	0.189145	−	2.52396i
$269$	7.34395e6	−	3.21760e7i	0.0230037	−	0.100786i	−0.962123	−	0.272616i	$-0.912111\pi$
$269$	7.34395e6	−	3.21760e7i	0.0230037	−	0.100786i	0.985126	+	0.171831i	$0.0549682\pi$
$270$	2.09406e7	+	5.33559e7i	0.0647465	+	0.164972i
$271$	−9.27775e6	−	1.23803e8i	−0.0283172	−	0.377867i	−0.993301	−	0.115557i	$-0.963135\pi$
$271$	−9.27775e6	−	1.23803e8i	−0.0283172	−	0.377867i	0.964984	−	0.262310i	$-0.0844843\pi$
$272$	3.48191e8	+	5.24814e7i	1.04912	+	0.158130i
$273$	−1.73464e7	+	1.60951e7i	−0.0515990	+	0.0478768i
$274$	−9.09443e8	+	4.37965e8i	−2.67085	+	1.28621i
$275$	1.16479e8	+	7.94139e7i	0.337740	+	0.230267i
$276$	7.33583e8	−	1.86914e9i	2.10023	−	5.35130i
$277$	6.59928e8	+	2.03561e8i	1.86560	+	0.575460i	0.996767	+	0.0803482i	$0.0256032\pi$
$277$	6.59928e8	+	2.03561e8i	1.86560	+	0.575460i	0.868829	+	0.495112i	$0.164873\pi$
$278$	−5.19821e8	−	4.82323e8i	−1.45110	−	1.34642i
$279$	6.27439e8	+	7.86784e8i	1.72965	+	2.16891i
$280$	−4.97204e6	−	6.23474e6i	−0.0135357	−	0.0169733i
$281$	−3.23597e8	−	3.00254e8i	−0.870025	−	0.807265i	0.112450	−	0.993657i	$-0.464130\pi$
$281$	−3.23597e8	−	3.00254e8i	−0.870025	−	0.807265i	−0.982475	+	0.186392i	$0.940321\pi$
$282$	3.84387e8	+	1.18568e8i	1.02070	+	0.314843i
$283$	−1.07437e8	+	2.73744e8i	−0.281773	+	0.717947i	0.717987	+	0.696057i	$0.245064\pi$
$283$	−1.07437e8	+	2.73744e8i	−0.281773	+	0.717947i	−0.999760	+	0.0218904i	$0.993032\pi$
$284$	7.34975e7	+	5.01098e7i	0.190396	+	0.129810i
$285$	2.90642e7	−	1.39966e7i	0.0743706	−	0.0358150i
$286$	7.71738e7	−	7.16068e7i	0.195069	−	0.180998i
$287$	4.05347e7	+	6.10962e6i	0.101214	+	0.0152555i
$288$	1.09817e7	+	1.46540e8i	0.0270891	+	0.361479i
$289$	1.18136e8	+	3.01006e8i	0.287899	+	0.733555i
$290$	1.69296e7	−	7.41733e7i	0.0407618	−	0.178589i
$291$	−7.17289e7	+	9.57156e8i	−0.170635	+	2.27697i
$292$	7.68469e8	−	2.37041e8i	1.80629	−	0.557165i
$293$	2.59024e8	+	1.24739e8i	0.601594	+	0.289712i	0.709786	−	0.704418i	$-0.248792\pi$
$293$	2.59024e8	+	1.24739e8i	0.601594	+	0.289712i	−0.108192	+	0.994130i	$0.534506\pi$
$294$	−5.88039e8	−	1.01851e9i	−1.34956	−	2.33750i
$295$	3.70081e7	−	6.40999e7i	0.0839304	−	0.145372i
$296$	1.33430e8	−	9.09712e7i	0.299043	−	0.203884i
$297$	3.70611e7	+	1.62375e8i	0.0820863	+	0.359643i
$298$	−1.08619e9	+	1.63717e8i	−2.37766	+	0.358375i
$299$	−2.01477e8	+	2.52644e8i	−0.435890	+	0.546588i
$300$	−1.42330e9			−3.04349
$301$	−4.86113e7	−	2.68031e7i	−0.102744	−	0.0566504i
$302$	−1.20136e9			−2.50986
$303$	−3.63049e7	+	4.55249e7i	−0.0749750	+	0.0940157i
$304$	−1.70581e8	+	2.57109e7i	−0.348235	+	0.0524879i
$305$	9.77511e6	+	4.28275e7i	0.0197275	+	0.0864318i
$306$	1.47548e9	−	1.00597e9i	2.94380	−	2.00705i
$307$	8.04756e7	−	1.39388e8i	0.158738	−	0.274942i	−0.775676	−	0.631131i	$-0.782591\pi$
$307$	8.04756e7	−	1.39388e8i	0.158738	−	0.274942i	0.934414	+	0.356190i	$0.115924\pi$
$308$	−2.40507e7	−	4.16571e7i	−0.0469031	−	0.0812385i
$309$	−4.79414e8	−	2.30874e8i	−0.924391	−	0.445163i
$310$	1.77807e8	−	5.48461e7i	0.338986	−	0.104563i
$311$	5.37380e7	−	7.17083e8i	0.101302	−	1.35179i	−0.682550	−	0.730839i	$-0.739129\pi$
$311$	5.37380e7	−	7.17083e8i	0.101302	−	1.35179i	0.783852	−	0.620947i	$-0.213252\pi$
$312$	−1.13937e8	+	4.99189e8i	−0.212384	+	0.930517i
$313$	2.95075e8	+	7.51839e8i	0.543910	+	1.38586i	0.893545	+	0.448974i	$0.148211\pi$
$313$	2.95075e8	+	7.51839e8i	0.543910	+	1.38586i	−0.349634	+	0.936886i	$0.613694\pi$
$314$	6.69751e7	+	8.93720e8i	0.122084	+	1.62910i
$315$	−1.16530e7	−	1.75641e6i	−0.0210064	−	0.00316621i
$316$	1.02309e9	−	9.49290e8i	1.82394	−	1.69236i
$317$	3.94177e8	−	1.89826e8i	0.694998	−	0.334693i	−0.0528135	−	0.998604i	$-0.516819\pi$
$317$	3.94177e8	−	1.89826e8i	0.694998	−	0.334693i	0.747812	+	0.663911i	$0.231105\pi$
$318$	4.26729e8	+	2.90939e8i	0.744145	+	0.507349i
$319$	8.07661e7	−	2.05789e8i	0.139303	−	0.354939i
$320$	7.76561e7	+	2.39537e7i	0.132480	+	0.0408647i
$321$	−6.67845e8	−	6.19670e8i	−1.12696	−	1.04567i
$322$	1.39765e8	+	1.75260e8i	0.233294	+	0.292541i
$323$	−2.24108e8	−	2.81023e8i	−0.370040	−	0.464016i
$324$	1.15404e8	+	1.07080e8i	0.188501	+	0.174904i
$325$	2.18880e8	+	6.75155e7i	0.353683	+	0.109097i
$326$	2.42565e8	−	6.18044e8i	0.387762	−	0.988002i
$327$	7.47398e8	+	5.09567e8i	1.18205	+	0.805906i
$328$	7.99157e8	−	3.84854e8i	1.25047	−	0.602195i
$329$	−2.16825e7	+	2.01184e7i	−0.0335678	+	0.0311464i
$330$	8.51467e7	+	1.28338e7i	0.130427	+	0.0196588i
$331$	4.39601e6	+	5.86607e7i	0.00666286	+	0.0889097i	0.999544	−	0.0302010i	$-0.00961473\pi$
$331$	4.39601e6	+	5.86607e7i	0.00666286	+	0.0889097i	−0.992881	+	0.119111i	$0.961996\pi$
$332$	−2.81827e6	−	7.18084e6i	−0.00422668	−	0.0107694i
$333$	5.31045e7	−	2.32666e8i	0.0788092	−	0.345286i
$334$	−4.39883e7	+	5.86983e8i	−0.0645988	+	0.862011i
$335$	−1.00321e8	+	3.09448e7i	−0.145792	+	0.0449709i
$336$	9.32514e7	+	4.49075e7i	0.134112	+	0.0645850i
$337$	−1.76028e8	−	3.04890e8i	−0.250541	−	0.433949i	0.713134	−	0.701028i	$-0.247275\pi$
$337$	−1.76028e8	−	3.04890e8i	−0.250541	−	0.433949i	−0.963675	+	0.267079i	$0.913942\pi$
$338$	−5.22012e8	+	9.04151e8i	−0.735313	+	1.27360i
$339$	−2.92409e7	+	1.99361e7i	−0.0407653	+	0.0277933i
$340$	−4.83940e7	−	2.12028e8i	−0.0667752	−	0.292561i
$341$	5.34641e8	−	8.05842e7i	0.730166	−	0.110055i
$342$	−5.45468e8	+	6.83995e8i	−0.737357	+	0.924617i
$343$	1.74163e8			0.233038
$344$	−1.19579e9	+	1.13338e8i	−1.58380	+	0.150114i
$345$	−2.64306e8			−0.346530
$346$	1.62247e9	−	2.03451e9i	2.10577	−	2.64055i
$347$	−1.19759e9	+	1.80508e8i	−1.53871	+	0.231923i	−0.862984	−	0.505231i	$-0.831407\pi$
$347$	−1.19759e9	+	1.80508e8i	−1.53871	+	0.231923i	−0.675724	+	0.737154i	$0.736169\pi$
$348$	4.96658e8	+	2.17600e9i	0.631727	+	2.76778i
$349$	9.48508e8	−	6.46682e8i	1.19441	−	0.814332i	0.207915	−	0.978147i	$-0.433332\pi$
$349$	9.48508e8	−	6.46682e8i	1.19441	−	0.814332i	0.986491	+	0.163815i	$0.0523800\pi$
$350$	7.94484e7	−	1.37609e8i	0.0990483	−	0.171557i
$351$	1.35306e8	+	2.34357e8i	0.167010	+	0.289270i
$352$	7.11346e7	+	3.42566e7i	0.0869324	+	0.0418644i
$353$	−3.15759e8	+	9.73987e7i	−0.382071	+	0.117853i	−0.479840	−	0.877356i	$-0.659305\pi$
$353$	−3.15759e8	+	9.73987e7i	−0.382071	+	0.117853i	0.0977694	+	0.995209i	$0.468829\pi$
$354$	−2.46367e8	+	3.28754e9i	−0.295169	+	3.93876i
$355$	2.60552e6	−	1.14155e7i	0.00309097	−	0.0135424i
$356$	−3.11926e8	−	7.94774e8i	−0.366417	−	0.933616i
$357$	1.61162e7	+	2.15055e8i	0.0187466	+	0.250156i
$358$	1.03897e9	+	1.56600e8i	1.19678	+	0.180385i
$359$	2.84986e8	−	2.64428e8i	0.325082	−	0.301632i	−0.500701	−	0.865620i	$-0.666924\pi$
$359$	2.84986e8	−	2.64428e8i	0.325082	−	0.301632i	0.825783	+	0.563989i	$0.190734\pi$
$360$	−2.29744e8	+	1.10639e8i	−0.259529	+	0.124983i
$361$	−5.93057e8	−	4.04340e8i	−0.663470	−	0.452346i
$362$	9.27091e8	−	2.36219e9i	1.02717	−	2.61719i
$363$	−1.15336e9	−	3.55766e8i	−1.26559	−	0.390383i
$364$	−5.72920e7	−	5.31592e7i	−0.0622643	−	0.0577729i
$365$	−6.60007e7	−	8.27622e7i	−0.0710434	−	0.0890855i
$366$	−1.21995e9	−	1.52976e9i	−1.30064	−	1.63095i
$367$	1.07817e9	+	1.00040e9i	1.13856	+	1.05643i	0.997794	+	0.0663883i	$0.0211476\pi$
$367$	1.07817e9	+	1.00040e9i	1.13856	+	1.05643i	0.140768	+	0.990043i	$0.455043\pi$
$368$	1.35061e9	+	4.16608e8i	1.41274	+	0.435773i
$369$	4.78887e8	−	1.22018e9i	0.496182	−	1.26425i
$370$	−3.64593e7	−	2.48575e7i	−0.0374199	−	0.0255124i
$371$	−3.42157e7	+	1.64774e7i	−0.0347870	+	0.0167525i
$372$	−4.00157e9	+	3.71291e9i	−4.03023	+	3.73951i
$373$	−1.00344e9	−	1.51245e8i	−1.00118	−	0.150904i	−0.372058	−	0.928210i	$-0.621348\pi$
$373$	−1.00344e9	−	1.51245e8i	−1.00118	−	0.150904i	−0.629123	+	0.777306i	$0.716586\pi$
$374$	−7.17004e7	−	9.56775e8i	−0.0708714	−	0.945713i
$375$	1.37832e8	+	3.51190e8i	0.134971	+	0.343900i
$376$	−1.42417e8	+	6.23970e8i	−0.138167	+	0.605349i
$377$	2.68428e7	−	3.58192e8i	0.0258008	−	0.344287i
$378$	1.79385e8	−	5.53328e7i	0.170830	−	0.0526940i
$379$	9.10947e8	+	4.38689e8i	0.859520	+	0.413923i	0.811102	−	0.584904i	$-0.198868\pi$
$379$	9.10947e8	+	4.38689e8i	0.859520	+	0.413923i	0.0484175	+	0.998827i	$0.484582\pi$
$380$	5.32724e7	+	9.22706e7i	0.0498035	+	0.0862622i
$381$	−1.61087e8	+	2.79011e8i	−0.149219	+	0.258454i
$382$	−1.07264e8	+	7.31313e7i	−0.0984537	+	0.0671246i
$383$	−4.50718e7	−	1.97472e8i	−0.0409930	−	0.179602i	0.950287	−	0.311376i	$-0.100790\pi$
$383$	−4.50718e7	−	1.97472e8i	−0.0409930	−	0.179602i	−0.991280	+	0.131774i	$0.957933\pi$
$384$	−3.17076e9	+	4.77915e8i	−2.85761	+	0.430716i
$385$	−3.94770e6	+	4.95026e6i	−0.00352559	+	0.00442095i
$386$	−2.35033e9			−2.08005
$387$	−1.18147e9	+	1.32473e9i	−1.03618	+	1.16182i
$388$	−3.17017e9			−2.75532
$389$	−2.86049e7	+	3.58694e7i	−0.0246386	+	0.0308959i	−0.793998	−	0.607920i	$-0.792004\pi$
$389$	−2.86049e7	+	3.58694e7i	−0.0246386	+	0.0308959i	0.769360	+	0.638816i	$0.220575\pi$
$390$	1.38347e8	−	2.08524e7i	0.118098	−	0.0178004i
$391$	6.55327e8	+	2.87118e9i	0.554421	+	2.42908i
$392$	1.54607e9	−	1.05409e9i	1.29637	−	0.883847i
$393$	1.04058e9	−	1.80234e9i	0.864772	−	1.49783i
$394$	6.70689e8	+	1.16167e9i	0.552440	+	0.956853i
$395$	−1.65518e8	−	7.97094e7i	−0.135131	−	0.0650758i
$396$	−1.46978e9	+	4.53367e8i	−1.18937	+	0.366873i
$397$	6.66153e7	−	8.88919e8i	0.0534327	−	0.713009i	−0.904584	−	0.426296i	$-0.859818\pi$
$397$	6.66153e7	−	8.88919e8i	0.0534327	−	0.713009i	0.958016	−	0.286713i	$-0.0925628\pi$
$398$	−2.68447e8	+	1.17614e9i	−0.213436	+	0.935123i
$399$	−3.85991e7	−	9.83488e7i	−0.0304209	−	0.0775111i
$400$	−7.48700e7	−	9.99071e8i	−0.0584922	−	0.780524i
$401$	−3.60238e8	−	5.42972e7i	−0.278987	−	0.0420506i	0.00805815	−	0.999968i	$-0.497435\pi$
$401$	−3.60238e8	−	5.42972e7i	−0.278987	−	0.0420506i	−0.287045	+	0.957917i	$0.592673\pi$
$402$	3.42785e9	−	3.18058e9i	2.63167	−	2.44183i
$403$	7.91500e8	−	3.81166e8i	0.602398	−	0.290099i
$404$	−1.58901e8	−	1.08337e8i	−0.119892	−	0.0817411i
$405$	7.57081e6	−	1.92901e7i	0.00566305	−	0.0144292i
$406$	−2.38105e8	−	7.34457e7i	−0.176574	−	0.0544660i
$407$	−9.39925e7	−	8.72123e7i	−0.0691055	−	0.0641206i
$408$	2.90947e9	+	3.64835e9i	2.12081	+	2.65942i
$409$	7.17475e8	+	8.99685e8i	0.518532	+	0.650218i	0.970296	−	0.241919i	$-0.0777768\pi$
$409$	7.17475e8	+	8.99685e8i	0.518532	+	0.650218i	−0.451765	+	0.892137i	$0.649205\pi$
$410$	−1.77669e8	−	1.64852e8i	−0.127311	−	0.118128i
$411$	−3.72475e9	−	1.14893e9i	−2.64637	−	0.816298i
$412$	6.42071e8	−	1.63597e9i	0.452317	−	1.15249i
$413$	−2.00291e8	−	1.36556e8i	−0.139906	−	0.0953864i
$414$	6.45816e9	−	3.11008e9i	4.47309	−	2.15413i
$415$	−744348.	+	690654.i	−0.000511220	+	0.000474342i
$416$	1.26851e8	+	1.91197e7i	0.0863908	+	0.0130213i
$417$	−2.04636e8	−	2.73068e9i	−0.138199	−	1.84414i
$418$	1.71726e8	+	4.37551e8i	0.115006	+	0.293030i
$419$	−4.42950e8	+	1.94069e9i	−0.294175	+	1.28887i	0.584480	+	0.811408i	$0.301299\pi$
$419$	−4.42950e8	+	1.94069e9i	−0.294175	+	1.28887i	−0.878655	+	0.477457i	$0.841559\pi$
$420$	4.77712e6	−	6.37462e7i	0.00314625	−	0.0419838i
$421$	1.71610e9	−	5.29348e8i	1.12087	−	0.345743i	0.321697	−	0.946843i	$-0.395747\pi$
$421$	1.71610e9	−	5.29348e8i	1.12087	−	0.345743i	0.799174	+	0.601099i	$0.205270\pi$
$422$	3.62803e9	+	1.74717e9i	2.35005	+	1.13173i
$423$	4.72904e8	+	8.19094e8i	0.303796	+	0.526190i
$424$	−4.10869e8	+	7.11646e8i	−0.261772	+	0.453402i
$425$	1.72480e9	−	1.17595e9i	1.08988	−	0.743066i
$426$	1.16053e8	+	5.08460e8i	0.0727313	+	0.318657i
$427$	1.42266e8	−	2.14432e7i	0.0884311	−	0.0133288i
$428$	1.87609e9	−	2.35255e9i	1.15665	−	1.45039i
$429$	4.06539e8			0.248601
$430$	1.48202e8	+	2.92843e8i	0.0898904	+	0.177622i
$431$	2.58860e9			1.55738			0.778691	−	0.627408i	$-0.215884\pi$
$431$	2.58860e9			1.55738			0.778691	+	0.627408i	$0.215884\pi$
$432$	7.37985e8	−	9.25404e8i	0.440407	−	0.552253i
$433$	−2.28855e9	+	3.44944e8i	−1.35473	+	0.204193i	−0.785947	−	0.618293i	$-0.787824\pi$
$433$	−2.28855e9	+	3.44944e8i	−1.35473	+	0.204193i	−0.568785	+	0.822486i	$0.692586\pi$
$434$	−1.35608e8	−	5.94137e8i	−0.0796289	−	0.348877i
$435$	2.42744e8	−	1.65500e8i	0.141396	−	0.0964019i
$436$	−1.49383e9	+	2.58738e9i	−0.863173	+	1.49506i
$437$	−7.21388e8	−	1.24948e9i	−0.413508	−	0.716217i
$438$	4.24805e9	+	2.04575e9i	2.41563	+	1.16331i
$439$	−1.58630e9	+	4.89308e8i	−0.894868	+	0.276030i	−0.707881	−	0.706332i	$-0.750348\pi$
$439$	−1.58630e9	+	4.89308e8i	−0.894868	+	0.276030i	−0.186987	+	0.982362i	$0.559872\pi$
$440$	−1.02383e7	+	1.36621e8i	−0.00572986	+	0.0764596i
$441$	6.15327e8	−	2.69592e9i	0.341642	−	1.49683i
$442$	−5.69541e8	−	1.45117e9i	−0.313724	−	0.799355i
$443$	−1.15033e7	−	1.53501e8i	−0.00628650	−	0.0838875i	0.993178	−	0.116608i	$-0.0372020\pi$
$443$	−1.15033e7	−	1.53501e8i	−0.00628650	−	0.0838875i	−0.999465	+	0.0327202i	$0.989583\pi$
$444$	1.28008e9	+	1.92940e8i	0.694057	+	0.104612i
$445$	−8.23842e7	+	7.64414e7i	−0.0443184	+	0.0411214i
$446$	−2.62820e9	+	1.26567e9i	−1.40277	+	0.675538i
$447$	−3.50476e9	−	2.38950e9i	−1.85602	−	1.26541i
$448$	9.72389e7	−	2.47761e8i	0.0510937	−	0.130185i
$449$	9.70889e8	+	2.99480e8i	0.506183	+	0.156137i	0.537320	−	0.843378i	$-0.319437\pi$
$449$	9.70889e8	+	2.99480e8i	0.506183	+	0.156137i	−0.0311373	+	0.999515i	$0.509913\pi$
$450$	−3.72460e9	−	3.45592e9i	−1.92680	−	1.78780i
$451$	−4.39098e8	−	5.50612e8i	−0.225395	−	0.282636i
$452$	−7.28782e7	−	9.13864e7i	−0.0371205	−	0.0465476i
$453$	−3.40076e9	−	3.15544e9i	−1.71883	−	1.59484i
$454$	−4.23568e9	−	1.30653e9i	−2.12436	−	0.655277i
$455$	−3.75850e6	+	9.57650e6i	−0.00187057	+	0.00476614i
$456$	−1.88887e9	−	1.28781e9i	−0.932877	−	0.636025i
$457$	2.42630e8	−	1.16845e8i	0.118915	−	0.0572666i	−0.373480	−	0.927638i	$-0.621836\pi$
$457$	2.42630e8	−	1.16845e8i	0.118915	−	0.0572666i	0.492396	+	0.870372i	$0.336121\pi$
$458$	1.47251e9	−	1.36629e9i	0.716192	−	0.664529i
$459$	2.43872e9	+	3.67577e8i	1.17711	+	0.177421i
$460$	−6.52359e7	−	8.70513e8i	−0.0312489	−	0.416987i
$461$	2.11191e8	+	5.38106e8i	0.100397	+	0.255808i	0.972243	−	0.233972i	$-0.0751723\pi$
$461$	2.11191e8	+	5.38106e8i	0.100397	+	0.255808i	−0.871846	+	0.489780i	$0.837077\pi$
$462$	6.27547e7	−	2.74946e8i	0.0296074	−	0.129718i
$463$	−2.61501e8	+	3.48949e9i	−0.122445	+	1.63391i	0.510615	+	0.859809i	$0.329418\pi$
$463$	−2.61501e8	+	3.48949e9i	−0.122445	+	1.63391i	−0.633060	+	0.774103i	$0.718201\pi$
$464$	−1.50129e9	+	4.63088e8i	−0.697674	+	0.215204i
$465$	6.47384e8	+	3.11764e8i	0.298591	+	0.143794i
$466$	2.91680e9	+	5.05205e9i	1.33523	+	2.31269i
$467$	−2.03157e9	+	3.51878e9i	−0.923045	+	1.59876i	−0.128370	+	0.991726i	$0.540975\pi$
$467$	−2.03157e9	+	3.51878e9i	−0.923045	+	1.59876i	−0.794675	+	0.607035i	$0.792359\pi$
$468$	−2.06488e9	+	1.40781e9i	−0.931181	+	0.634868i
$469$	7.65116e7	+	3.35219e8i	0.0342470	+	0.150046i
$470$	1.72929e8	−	2.60648e7i	0.0768289	−	0.0115801i
$471$	−2.15782e9	+	2.70582e9i	−0.951572	+	1.19323i
$472$	−5.24534e9			−2.29603
$473$	2.99001e8	+	9.05604e8i	0.129915	+	0.393481i
$474$	8.18270e9			3.52917
$475$	−6.37638e8	+	7.99573e8i	−0.272990	+	0.342319i
$476$	−7.04324e8	+	1.06160e8i	−0.299329	+	0.0451165i
$477$	2.70219e8	+	1.18391e9i	0.113999	+	0.499463i
$478$	−5.09936e9	+	3.47668e9i	−2.13559	+	1.45602i
$479$	5.42069e7	−	9.38892e7i	0.0225362	−	0.0390338i	−0.854537	−	0.519390i	$-0.826159\pi$
$479$	5.42069e7	−	9.38892e7i	0.0225362	−	0.0390338i	0.877074	+	0.480356i	$0.159493\pi$
$480$	5.24630e7	+	9.08685e7i	0.0216525	+	0.0375033i
$481$	−1.87702e8	−	9.03926e7i	−0.0769062	−	0.0370361i
$482$	−7.86317e8	+	2.42547e8i	−0.319840	+	0.0986576i
$483$	−6.46893e7	+	8.63219e8i	−0.0261227	+	0.348583i
$484$	8.87069e8	−	3.88650e9i	0.355630	−	1.55812i
$485$	1.52454e8	+	3.88445e8i	0.0606794	+	0.154609i
$486$	3.57131e8	+	4.76559e9i	0.141124	+	1.88317i
$487$	−1.24585e8	−	1.87782e7i	−0.0488782	−	0.00736721i	0.124558	−	0.992212i	$-0.460249\pi$
$487$	−1.24585e8	−	1.87782e7i	−0.0488782	−	0.00736721i	−0.173436	+	0.984845i	$0.555487\pi$
$488$	2.28209e9	−	2.11747e9i	0.888921	−	0.824798i
$489$	2.30997e9	−	1.11242e9i	0.893358	−	0.430218i
$490$	−4.22457e8	−	2.88026e8i	−0.162217	−	0.110598i
$491$	1.18235e9	−	3.01258e9i	0.450776	−	1.14856i	−0.507231	−	0.861810i	$-0.669331\pi$
$491$	1.18235e9	−	3.01258e9i	0.450776	−	1.14856i	0.958006	−	0.286747i	$-0.0925740\pi$
$492$	6.79440e9	+	2.09580e9i	2.57201	+	0.793361i
$493$	−2.39970e9	−	2.22660e9i	−0.901973	−	0.836908i
$494$	4.76177e8	+	5.97107e8i	0.177715	+	0.222847i
$495$	1.26233e8	+	1.58292e8i	0.0467795	+	0.0586597i
$496$	−2.81673e9	−	2.61355e9i	−1.03648	−	0.961711i
$497$	−3.66452e7	−	1.13036e7i	−0.0133897	−	0.00413017i
$498$	1.65234e7	−	4.21010e7i	0.00599511	−	0.0152753i
$499$	6.46073e8	+	4.40485e8i	0.232771	+	0.158701i	0.674089	−	0.738650i	$-0.264536\pi$
$499$	6.46073e8	+	4.40485e8i	0.232771	+	0.158701i	−0.441318	+	0.897351i	$0.645489\pi$
$500$	−1.12265e9	+	5.40640e8i	−0.401652	+	0.193425i
$501$	−1.66626e9	+	1.54607e9i	−0.591987	+	0.549283i
$502$	4.35392e9	+	6.56248e8i	1.53609	+	0.231529i
$503$	8.89470e7	+	1.18692e9i	0.0311633	+	0.415845i	0.990868	+	0.134835i	$0.0430505\pi$
$503$	8.89470e7	+	1.18692e9i	0.0311633	+	0.415845i	−0.959705	+	0.281010i	$0.909330\pi$
$504$	3.05115e8	+	7.77419e8i	0.106159	+	0.270488i
$505$	−5.63310e6	+	2.46802e7i	−0.00194638	+	0.00852765i
$506$	2.87801e8	−	3.84044e9i	0.0987564	−	1.31781i
$507$	−3.85249e9	+	1.18834e9i	−1.31285	+	0.404960i
$508$	−9.58704e8	−	4.61687e8i	−0.324460	−	0.156252i
$509$	5.92605e8	+	1.02642e9i	0.199183	+	0.344996i	0.948264	−	0.317483i	$-0.102838\pi$
$509$	5.92605e8	+	1.02642e9i	0.199183	+	0.344996i	−0.749080	+	0.662479i	$0.769504\pi$
$510$	6.37541e8	−	1.10425e9i	0.212820	−	0.368615i
$511$	−2.86454e8	+	1.95301e8i	−0.0949689	+	0.0647487i
$512$	−9.77908e8	−	4.28449e9i	−0.321998	−	1.41077i
$513$	−1.19474e9	+	1.80078e8i	−0.390717	+	0.0588911i
$514$	−1.35232e9	+	1.69576e9i	−0.439248	+	0.550799i
$515$	−2.31335e8			−0.0746305
$516$	−7.64470e9	−	5.85386e9i	−2.44955	−	1.87572i
$517$	5.08161e8			0.161728
$518$	−9.01077e7	+	1.12991e8i	−0.0284844	+	0.0357184i
$519$	9.93658e9	−	1.49770e9i	3.11997	−	0.470261i
$520$	4.95341e7	+	2.17023e8i	0.0154487	+	0.0676853i
$521$	−2.91390e9	+	1.98666e9i	−0.902698	+	0.615449i	−0.923191	−	0.384341i	$-0.874429\pi$
$521$	−2.91390e9	+	1.98666e9i	−0.902698	+	0.615449i	0.0204934	+	0.999790i	$0.493476\pi$
$522$	−3.98386e9	+	6.90025e9i	−1.22591	+	2.12333i
$523$	−2.08283e9	−	3.60757e9i	−0.636646	−	1.10270i	−0.986164	−	0.165773i	$-0.946988\pi$
$523$	−2.08283e9	−	3.60757e9i	−0.636646	−	1.10270i	0.349518	−	0.936930i	$-0.386345\pi$
$524$	6.19298e9	+	2.98238e9i	1.88036	+	0.905532i
$525$	5.86336e8	−	1.80861e8i	0.176844	−	0.0545490i
$526$	1.75721e8	−	2.34483e9i	0.0526469	−	0.702524i
$527$	1.78157e9	−	7.80557e9i	0.530232	−	2.32310i
$528$	−6.49638e8	−	1.65525e9i	−0.192067	−	0.489378i
$529$	6.28949e8	+	8.39274e9i	0.184723	+	2.46495i
$530$	2.22029e8	+	3.34655e7i	0.0647804	+	0.00976408i
$531$	−5.68225e9	+	5.27236e9i	−1.64699	+	1.52818i
$532$	3.14392e8	−	1.51403e8i	0.0905277	−	0.0435958i
$533$	−9.45450e8	−	6.44597e8i	−0.270454	−	0.184392i
$534$	1.82881e9	−	4.65973e9i	0.519725	−	1.32424i
$535$	−3.78482e8	−	1.16746e8i	−0.106858	−	0.0329614i
$536$	5.45392e9	+	5.06050e9i	1.52979	+	1.41944i
$537$	2.52976e9	+	3.17222e9i	0.704968	+	0.884002i
$538$	3.98464e8	+	4.99658e8i	0.110319	+	0.138336i
$539$	−1.08910e9	−	1.01054e9i	−0.299576	−	0.277966i
$540$	−6.98565e8	−	2.15479e8i	−0.190910	−	0.0588879i
$541$	−1.03297e9	+	2.63196e9i	−0.280476	+	0.714642i	0.719324	+	0.694674i	$0.244452\pi$
$541$	−1.03297e9	+	2.63196e9i	−0.280476	+	0.714642i	−0.999801	+	0.0199676i	$0.993644\pi$
$542$	1.98634e9	+	1.35426e9i	0.535866	+	0.365347i
$543$	8.82879e9	−	4.25172e9i	2.36648	−	1.13963i
$544$	8.57033e8	−	7.95211e8i	0.228245	−	0.211781i
$545$	3.88874e8	+	5.86133e7i	0.102901	+	0.0155099i
$546$	−3.42430e7	−	4.56941e8i	−0.00900322	−	0.120140i
$547$	1.19669e9	+	3.04912e9i	0.312627	+	0.796562i	0.997681	+	0.0680688i	$0.0216837\pi$
$547$	1.19669e9	+	3.04912e9i	0.312627	+	0.796562i	−0.685053	+	0.728493i	$0.740221\pi$
$548$	2.86476e9	−	1.25513e10i	0.743629	−	3.25805i
$549$	3.43800e8	−	4.58769e9i	0.0886752	−	1.18329i
$550$	−2.60859e9	+	8.04644e8i	−0.668554	+	0.206222i
$551$	1.44492e9	+	6.95838e8i	0.367971	+	0.177206i
$552$	9.36536e9	+	1.62213e10i	2.36994	+	4.10486i
$553$	−3.00840e8	+	5.21071e8i	−0.0756481	+	0.131026i
$554$	−1.10494e10	+	7.53337e9i	−2.76093	+	1.88237i
$555$	−3.79176e7	−	1.66128e8i	−0.00941490	−	0.0412494i
$556$	8.94319e9	−	1.34797e9i	2.20664	−	0.332597i
$557$	−1.47294e9	+	1.84701e9i	−0.361153	+	0.452872i	−0.928900	−	0.370332i	$-0.879244\pi$
$557$	−1.47294e9	+	1.84701e9i	−0.361153	+	0.452872i	0.567746	+	0.823204i	$0.307815\pi$
$558$	−1.94869e10			−4.74814
$559$	8.97945e8	+	1.26286e9i	0.217425	+	0.305783i
$560$	4.49973e7			0.0108275
$561$	2.31006e9	−	2.89672e9i	0.552399	−	0.692687i
$562$	8.45264e9	−	1.27403e9i	2.00870	−	0.302763i
$563$	−4.11730e7	−	1.80391e8i	−0.00972373	−	0.0426024i	0.969833	−	0.243769i	$-0.0783839\pi$
$563$	−4.11730e7	−	1.80391e8i	−0.00972373	−	0.0426024i	−0.979557	+	0.201167i	$0.935527\pi$
$564$	−4.23898e9	+	2.89009e9i	−0.994912	+	0.678320i
$565$	−7.69299e6	+	1.33246e7i	−0.00179443	+	0.00310804i
$566$	−2.84725e9	−	4.93158e9i	−0.660036	−	1.14322i
$567$	−6.11482e7	−	2.94474e7i	−0.0140878	−	0.00678433i
$568$	−7.92930e8	+	2.44586e8i	−0.181558	+	0.0560032i
$569$	3.24218e8	−	4.32638e9i	0.0737809	−	0.984537i	−0.830339	−	0.557258i	$-0.811853\pi$
$569$	3.24218e8	−	4.32638e9i	0.0737809	−	0.984537i	0.904120	−	0.427279i	$-0.140528\pi$
$570$	−1.39002e8	+	6.09007e8i	−0.0314383	+	0.137740i
$571$	−1.42986e9	−	3.64323e9i	−0.321416	−	0.818956i	−0.996683	−	0.0813820i	$-0.974067\pi$
$571$	−1.42986e9	−	3.64323e9i	−0.321416	−	0.818956i	0.675267	−	0.737574i	$-0.264029\pi$
$572$	1.00342e8	+	1.33897e9i	0.0224180	+	0.299147i
$573$	−4.95722e8	−	7.47180e7i	−0.110077	−	0.0165914i
$574$	−5.81890e8	+	5.39915e8i	−0.128425	+	0.119161i
$575$	7.54942e9	−	3.63561e9i	1.65606	−	0.797517i
$576$	−7.03197e9	−	4.79431e9i	−1.53320	−	1.04532i
$577$	−1.85392e9	+	4.72370e9i	−0.401767	+	1.02369i	0.576640	+	0.816999i	$0.304364\pi$
$577$	−1.85392e9	+	4.72370e9i	−0.401767	+	1.02369i	−0.978407	+	0.206688i	$0.933732\pi$
$578$	−5.98342e9	−	1.84564e9i	−1.28885	−	0.397557i
$579$	−6.65320e9	−	6.17327e9i	−1.42448	−	1.32172i
$580$	6.05001e8	+	7.58647e8i	0.128753	+	0.161451i
$581$	2.07348e6	+	2.60006e6i	0.000438615	+	0.000550006i
$582$	−1.36249e10	−	1.26421e10i	−2.86486	−	2.65821i
$583$	6.23458e8	+	1.92311e8i	0.130307	+	0.0401943i
$584$	−2.74072e9	+	6.98324e9i	−0.569403	+	1.45082i
$585$	2.71801e8	+	1.85311e8i	0.0561314	+	0.0382697i
$586$	−5.01581e9	+	2.41549e9i	−1.02967	+	0.495865i
$587$	1.36166e9	−	1.26344e9i	0.277866	−	0.257822i	−0.528912	−	0.848677i	$-0.677400\pi$
$587$	1.36166e9	−	1.26344e9i	0.277866	−	0.257822i	0.806778	+	0.590855i	$0.201209\pi$
$588$	1.48324e10	+	2.23562e9i	3.00877	+	0.453500i
$589$	2.93116e8	+	3.91136e9i	0.0591066	+	0.788723i
$590$	5.23632e8	+	1.33419e9i	0.104965	+	0.267446i
$591$	−1.15263e9	+	5.05000e9i	−0.229686	+	1.00632i
$592$	−6.80965e7	+	9.08685e8i	−0.0134896	+	0.180006i
$593$	3.38109e8	−	1.04293e8i	0.0665833	−	0.0205382i	−0.261285	−	0.965262i	$-0.584146\pi$
$593$	3.38109e8	−	1.04293e8i	0.0665833	−	0.0205382i	0.327868	+	0.944724i	$0.393670\pi$
$594$	−2.90575e9	−	1.39934e9i	−0.568860	−	0.273949i
$595$	4.68789e7	+	8.11966e7i	0.00912363	+	0.0158026i
$596$	7.00497e9	−	1.21330e10i	1.35533	−	2.34750i
$597$	−3.84911e9	+	2.62428e9i	−0.740372	+	0.504777i
$598$	−1.39241e9	−	6.10056e9i	−0.266265	−	1.16658i
$599$	−4.57023e9	+	6.88851e8i	−0.868848	+	0.130958i	−0.568313	−	0.822813i	$-0.692404\pi$
$599$	−4.57023e9	+	6.88851e8i	−0.868848	+	0.130958i	−0.300536	+	0.953771i	$0.597165\pi$
$600$	8.27808e9	−	1.03804e10i	1.56459	−	1.96193i
$601$	4.97651e9			0.935113			0.467556	−	0.883963i	$-0.345135\pi$
$601$	4.97651e9			0.935113			0.467556	+	0.883963i	$0.345135\pi$
$602$	9.92694e8	−	4.12350e8i	0.185450	−	0.0770332i
$603$	1.09948e10			2.04209
$604$	9.55331e9	−	1.19795e10i	1.76411	−	2.21212i
$605$	−5.18878e8	+	7.82082e7i	−0.0952623	+	0.0143585i
$606$	−2.50904e8	−	1.09928e9i	−0.0457988	−	0.200658i
$607$	3.39764e9	−	2.31647e9i	0.616619	−	0.420404i	−0.214323	−	0.976763i	$-0.568754\pi$
$607$	3.39764e9	−	2.31647e9i	0.616619	−	0.420404i	0.830942	+	0.556359i	$0.187802\pi$
$608$	−2.86381e8	+	4.96027e8i	−0.0516752	+	0.0895041i
$609$	−4.81108e8	−	8.33303e8i	−0.0863142	−	0.149500i
$610$	−7.66411e8	−	3.69084e8i	−0.136712	−	0.0658371i
$611$	7.88979e8	−	2.43368e8i	0.139933	−	0.0431637i
$612$	−1.70206e9	+	2.27124e10i	−0.300155	+	4.00529i
$613$	2.26219e9	−	9.91128e9i	0.396658	−	1.73787i	−0.243749	−	0.969838i	$-0.578377\pi$
$613$	2.26219e9	−	9.91128e9i	0.396658	−	1.73787i	0.640408	−	0.768035i	$-0.278765\pi$
$614$	1.13866e9	+	2.90126e9i	0.198520	+	0.505821i
$615$	−6.99422e7	−	9.33314e8i	−0.0121249	−	0.161795i
$616$	4.43695e8	+	6.68762e7i	0.0764807	+	0.0115276i
$617$	−2.01262e9	+	1.86744e9i	−0.344957	+	0.320073i	−0.833556	−	0.552436i	$-0.813699\pi$
$617$	−2.01262e9	+	1.86744e9i	−0.344957	+	0.320073i	0.488599	+	0.872508i	$0.337508\pi$
$618$	9.28350e9	−	4.47070e9i	1.58217	−	0.761931i
$619$	−7.08238e9	−	4.82869e9i	−1.20022	−	0.818299i	−0.212909	−	0.977072i	$-0.568294\pi$
$619$	−7.08238e9	−	4.82869e9i	−1.20022	−	0.818299i	−0.987315	+	0.158773i	$0.949246\pi$
$620$	−8.67031e8	+	2.20916e9i	−0.146104	+	0.372268i
$621$	9.45962e9	+	2.91791e9i	1.58509	+	0.488934i
$622$	1.02075e10	+	9.47122e9i	1.70081	+	1.57812i
$623$	2.29492e8	+	2.87774e8i	0.0380242	+	0.0476809i
$624$	−1.80137e9	−	2.25885e9i	−0.296795	−	0.372170i
$625$	−4.29343e9	−	3.98372e9i	−0.703436	−	0.652693i
$626$	−1.49451e10	−	4.60995e9i	−2.43494	−	0.751080i
$627$	−6.63138e8	+	1.68965e9i	−0.107440	+	0.273754i
$628$	−9.44441e9	−	6.43909e9i	−1.52165	−	1.03745i
$629$	−1.71065e9	+	8.23804e8i	−0.274084	+	0.131992i
$630$	1.67284e8	−	1.55216e8i	0.0266539	−	0.0247312i
$631$	−4.62646e9	−	6.97327e8i	−0.733071	−	0.110493i	−0.228111	−	0.973635i	$-0.573255\pi$
$631$	−4.62646e9	−	6.97327e8i	−0.733071	−	0.110493i	−0.504960	+	0.863142i	$0.668493\pi$
$632$	9.72924e8	+	1.29828e10i	0.153309	+	2.04577i
$633$	5.68103e9	+	1.44750e10i	0.890255	+	2.26833i
$634$	−1.88518e9	+	8.25952e9i	−0.293793	+	1.28719i
$635$	−1.04671e7	+	1.39674e8i	−0.00162225	+	0.0216475i
$636$	−6.29451e9	+	1.94160e9i	−0.970202	+	0.299268i
$637$	−2.17492e9	−	1.04739e9i	−0.333392	−	0.160553i
$638$	2.14043e9	+	3.70734e9i	0.326309	+	0.565185i
$639$	−6.13131e8	+	1.06197e9i	−0.0929608	+	0.161013i
$640$	−1.15183e9	+	7.85302e8i	−0.173683	+	0.118415i
$641$	−1.47365e8	−	6.45646e8i	−0.0220999	−	0.0968259i	0.962675	−	0.270659i	$-0.0872417\pi$
$641$	−1.47365e8	−	6.45646e8i	−0.0220999	−	0.0968259i	−0.984775	+	0.173833i	$0.944385\pi$
$642$	1.74447e10	−	2.62937e9i	2.60191	−	0.392174i
$643$	6.78771e9	−	8.51152e9i	1.00690	−	1.26261i	0.0422368	−	0.999108i	$-0.486552\pi$
$643$	6.78771e9	−	8.51152e9i	1.00690	−	1.26261i	0.964659	−	0.263500i	$-0.0848770\pi$
$644$	−2.85905e9			−0.421814
$645$	−3.49648e8	+	1.21823e9i	−0.0513064	+	0.178760i
$646$	6.96033e9			1.01582
$647$	−6.51173e9	+	8.16545e9i	−0.945217	+	1.18526i	0.0373399	+	0.999303i	$0.488112\pi$
$647$	−6.51173e9	+	8.16545e9i	−0.945217	+	1.18526i	−0.982557	+	0.185962i	$0.940460\pi$
$648$	−1.45216e9	+	2.18877e8i	−0.209653	+	0.0316001i
$649$	9.26733e8	+	4.06028e9i	0.133075	+	0.583042i
$650$	−3.66479e9	+	2.49861e9i	−0.523422	+	0.356863i
$651$	1.17666e9	−	2.03804e9i	0.167155	−	0.289520i
$652$	4.23400e9	+	7.33350e9i	0.598252	+	1.03620i
$653$	9.08575e9	+	4.37547e9i	1.27692	+	0.614934i	0.944598	−	0.328231i	$-0.106452\pi$
$653$	9.08575e9	+	4.37547e9i	1.27692	+	0.614934i	0.332326	+	0.943165i	$0.392167\pi$
$654$	−1.67383e10	+	5.16308e9i	−2.33986	+	0.721750i
$655$	6.76148e7	−	9.02257e8i	0.00940150	−	0.125454i
$656$	−1.11372e9	+	4.87950e9i	−0.154032	+	0.674858i
$657$	4.05020e9	+	1.03197e10i	0.557183	+	1.41968i
$658$	−4.28026e7	−	5.71161e8i	−0.00585706	−	0.0781570i
$659$	6.97305e8	+	1.05102e8i	0.0949126	+	0.0143058i	0.196327	−	0.980539i	$-0.437099\pi$
$659$	6.97305e8	+	1.05102e8i	0.0949126	+	0.0143058i	−0.101414	+	0.994844i	$0.532337\pi$
$660$	−8.05068e8	+	7.46994e8i	−0.109001	+	0.101138i
$661$	−4.58705e9	+	2.20901e9i	−0.617772	+	0.297503i	−0.716474	−	0.697614i	$-0.754245\pi$
$661$	−4.58705e9	+	2.20901e9i	−0.617772	+	0.297503i	0.0987020	+	0.995117i	$0.468531\pi$
$662$	−9.41173e8	−	6.41681e8i	−0.126086	−	0.0859639i
$663$	2.19934e9	−	5.60384e9i	0.293086	−	0.746772i
$664$	6.87625e7	+	2.12104e7i	0.00911515	+	0.00281165i
$665$	−3.36708e7	−	3.12419e7i	−0.00443995	−	0.00411967i
$666$	2.88132e9	+	3.61306e9i	0.377947	+	0.473931i
$667$	−8.19262e9	−	1.02732e10i	−1.06901	−	1.34050i
$668$	−5.50336e9	−	5.10637e9i	−0.714349	−	0.662819i
$669$	−1.07641e10	−	3.32030e9i	−1.38992	−	0.428732i
$670$	7.42722e8	−	1.89243e9i	0.0954036	−	0.243084i
$671$	−2.04227e9	−	1.39240e9i	−0.260966	−	0.177924i
$672$	3.09615e8	−	1.49103e8i	0.0393577	−	0.0189537i
$673$	1.00638e10	−	9.33783e9i	1.27265	−	1.18085i	0.298632	−	0.954368i	$-0.403470\pi$
$673$	1.00638e10	−	9.33783e9i	1.27265	−	1.18085i	0.974016	−	0.226477i	$-0.0727209\pi$
$674$	6.74118e9	+	1.01607e9i	0.848059	+	0.127824i
$675$	−5.24386e8	−	6.99745e9i	−0.0656278	−	0.875742i
$676$	−4.86475e9	−	1.23952e10i	−0.605686	−	1.54326i
$677$	−2.31334e9	+	1.01354e10i	−0.286536	+	1.25539i	0.602708	+	0.797961i	$0.294088\pi$
$677$	−2.31334e9	+	1.01354e10i	−0.286536	+	1.25539i	−0.889244	+	0.457433i	$0.848769\pi$
$678$	5.12131e7	−	6.83391e8i	0.00631069	−	0.0842104i
$679$	1.30597e9	−	4.02838e8i	0.160099	−	0.0493840i
$680$	1.82782e9	+	8.80233e8i	0.222922	+	0.107354i
$681$	−8.55849e9	−	1.48237e10i	−1.03844	−	1.79863i
$682$	−5.23494e9	+	9.06717e9i	−0.631926	+	1.09453i
$683$	1.49440e9	−	1.01886e9i	0.179470	−	0.122361i	−0.470253	−	0.882532i	$-0.655837\pi$
$683$	1.49440e9	−	1.01886e9i	0.179470	−	0.122361i	0.649723	+	0.760171i	$0.274885\pi$
$684$	−2.48292e9	−	1.08784e10i	−0.296665	−	1.29977i
$685$	−1.67570e9	+	2.52571e8i	−0.199195	+	0.0300239i
$686$	−2.10274e9	+	2.63676e9i	−0.248686	+	0.311843i
$687$	7.75696e9			0.912732
$688$	3.70692e9	−	5.67405e9i	0.433964	−	0.664253i
$689$	1.06009e9			0.123474
$690$	3.19108e9	−	4.00149e9i	0.369799	−	0.463713i
$691$	−4.70166e9	+	7.08662e8i	−0.542099	+	0.0817082i	−0.414383	−	0.910103i	$-0.636003\pi$
$691$	−4.70166e9	+	7.08662e8i	−0.542099	+	0.0817082i	−0.127716	+	0.991811i	$0.540764\pi$
$692$	7.38533e9	+	3.23572e10i	0.847224	+	3.71193i
$693$	5.47873e8	−	3.73534e8i	0.0625336	−	0.0426347i
$694$	1.17262e10	−	2.03104e10i	1.33168	−	2.30654i
$695$	−5.95247e8	−	1.03100e9i	−0.0672590	−	0.116496i
$696$	−1.87586e10	−	9.03365e9i	−2.10895	−	1.01562i
$697$	−9.96524e9	+	3.07387e9i	−1.11474	+	0.343851i
$698$	−1.66124e9	+	2.21677e10i	−0.184900	+	2.46733i
$699$	−5.01274e9	+	2.19623e10i	−0.555144	+	2.43224i
$700$	7.40398e8	+	1.88650e9i	0.0815872	+	0.207881i
$701$	5.32459e8	+	7.10517e9i	0.0583812	+	0.779043i	0.947171	+	0.320728i	$0.103928\pi$
$701$	5.32459e8	+	7.10517e9i	0.0583812	+	0.779043i	−0.888790	+	0.458315i	$0.848453\pi$
$702$	−5.18169e9	−	7.81014e8i	−0.565316	−	0.0852077i
$703$	6.81863e8	−	6.32676e8i	0.0740207	−	0.0686812i
$704$	−4.11982e9	+	1.98400e9i	−0.445015	+	0.214308i
$705$	5.57980e8	+	3.80424e8i	0.0599731	+	0.0408890i
$706$	2.33771e9	−	5.95640e9i	0.250020	−	0.637041i
$707$	7.92265e7	+	2.44381e7i	0.00843145	+	0.00260076i
$708$	−3.08229e10	−	2.85995e10i	−3.26405	−	3.02860i
$709$	3.43369e9	+	4.30571e9i	0.361826	+	0.453715i	0.929108	−	0.369808i	$-0.120577\pi$
$709$	3.43369e9	+	4.30571e9i	0.361826	+	0.453715i	−0.567282	+	0.823523i	$0.692005\pi$
$710$	1.41369e8	+	1.77271e8i	0.0148235	+	0.0185880i
$711$	1.41036e10	+	1.30862e10i	1.47159	+	1.36543i
$712$	7.61062e9	+	2.34757e9i	0.790206	+	0.243746i
$713$	1.17409e10	−	2.99153e10i	1.21308	−	3.09087i
$714$	−3.45043e9	−	2.35246e9i	−0.354756	−	0.241868i
$715$	1.59240e8	−	7.66861e7i	0.0162923	−	0.00784595i
$716$	−9.82356e9	+	9.11493e9i	−1.00017	+	0.928021i
$717$	−2.35667e10	−	3.55212e9i	−2.38772	−	0.359890i
$718$	5.62581e8	+	7.50712e9i	0.0567217	+	0.756899i
$719$	−6.07593e9	−	1.54812e10i	−0.609624	−	1.55330i	−0.817982	−	0.575243i	$-0.804907\pi$
$719$	−6.07593e9	−	1.54812e10i	−0.609624	−	1.55330i	0.208359	−	0.978053i	$-0.433188\pi$
$720$	3.20174e8	−	1.40278e9i	0.0319685	−	0.140063i
$721$	−5.66196e7	+	7.55536e8i	−0.00562592	+	0.0750726i
$722$	1.32818e10	−	4.09688e9i	1.31334	−	0.405110i
$723$	−2.86293e9	−	1.37872e9i	−0.281726	−	0.135672i
$724$	1.61825e10	+	2.80289e10i	1.58475	+	2.74487i
$725$	−4.65703e9	+	8.06622e9i	−0.453865	+	0.786116i
$726$	1.93112e10	−	1.31661e10i	1.87297	−	1.27697i
$727$	−2.36774e9	−	1.03738e10i	−0.228541	−	1.00130i	−0.950830	−	0.309713i	$-0.899767\pi$
$727$	−2.36774e9	−	1.03738e10i	−0.228541	−	1.00130i	0.722289	−	0.691591i	$-0.243090\pi$
$728$	7.20917e8	−	1.08661e8i	0.0692509	−	0.0104379i
$729$	−1.06370e10	+	1.33383e10i	−1.01688	+	1.27513i
$730$	2.04984e9			0.195025
$731$	1.41006e10	+	7.77741e8i	1.33514	+	0.0736417i
$732$	2.49553e10			2.35166
$733$	−1.09732e9	+	1.37599e9i	−0.102913	+	0.129048i	−0.830621	−	0.556839i	$-0.812014\pi$
$733$	−1.09732e9	+	1.37599e9i	−0.102913	+	0.129048i	0.727708	+	0.685887i	$0.240586\pi$
$734$	−2.81628e10	+	4.24486e9i	−2.62869	+	0.396212i
$735$	−4.39355e8	−	1.92494e9i	−0.0408141	−	0.178818i
$736$	3.87739e9	−	2.64356e9i	0.358481	−	0.244409i
$737$	2.95361e9	−	5.11581e9i	0.271780	−	0.470737i
$738$	1.26913e10	+	2.19819e10i	1.16227	+	2.01312i
$739$	4.07934e9	+	1.96451e9i	0.371821	+	0.179060i	0.610457	−	0.792049i	$-0.290986\pi$
$739$	4.07934e9	+	1.96451e9i	0.371821	+	0.179060i	−0.238636	+	0.971109i	$0.576700\pi$
$740$	5.37797e8	−	1.65888e8i	0.0487873	−	0.0150489i
$741$	−2.20395e8	+	2.94097e9i	−0.0198993	+	0.265538i
$742$	1.63639e8	−	7.16951e8i	0.0147053	−	0.0644282i
$743$	6.65087e9	+	1.69461e10i	0.594864	+	1.51569i	0.837985	+	0.545693i	$0.183734\pi$
$743$	6.65087e9	+	1.69461e10i	0.594864	+	1.51569i	−0.243121	+	0.969996i	$0.578171\pi$
$744$	−3.80535e9	−	5.07789e10i	−0.338758	−	4.52041i
$745$	−1.82354e9	−	2.74854e8i	−0.161573	−	0.0243532i
$746$	1.44048e10	−	1.33657e10i	1.27034	−	1.17871i
$747$	9.58098e7	−	4.61396e7i	0.00840985	−	0.00404997i
$748$	1.01107e10	+	6.89339e9i	0.883340	+	0.602251i
$749$	−4.73926e8	+	1.20754e9i	−0.0412120	+	0.105006i
$750$	−6.98097e9	−	2.15334e9i	−0.604229	−	0.186380i
$751$	−3.89826e8	−	3.61706e8i	−0.0335839	−	0.0311613i	0.663202	−	0.748440i	$-0.269197\pi$
$751$	−3.89826e8	−	3.61706e8i	−0.0335839	−	0.0311613i	−0.696786	+	0.717279i	$0.745387\pi$
$752$	−2.25165e9	−	2.82348e9i	−0.193081	−	0.242116i
$753$	1.06012e10	+	1.32935e10i	0.904842	+	1.13464i
$754$	5.09880e9	+	4.73099e9i	0.433180	+	0.401932i
$755$	−1.92728e9	−	5.94488e8i	−0.162979	−	0.0502723i
$756$	−8.74725e8	+	2.22876e9i	−0.0736284	+	0.187602i
$757$	1.57276e10	+	1.07229e10i	1.31773	+	0.898413i	0.998781	−	0.0493588i	$-0.0157178\pi$
$757$	1.57276e10	+	1.07229e10i	1.31773	+	0.898413i	0.318949	+	0.947772i	$0.396670\pi$
$758$	−1.76398e10	+	8.49489e9i	−1.47113	+	0.708461i
$759$	1.09018e10	−	1.01154e10i	0.905009	−	0.839725i
$760$	−9.82784e8	−	1.48131e8i	−0.0812102	−	0.0122405i
$761$	1.27325e9	+	1.69904e10i	0.104729	+	1.39752i	0.763809	+	0.645442i	$0.223327\pi$
$761$	1.27325e9	+	1.69904e10i	0.104729	+	1.39752i	−0.659080	+	0.752073i	$0.729054\pi$
$762$	−2.27924e9	−	5.80741e9i	−0.186616	−	0.475489i
$763$	2.86608e8	−	1.25571e9i	0.0233589	−	0.102342i
$764$	1.23736e8	−	1.65114e9i	0.0100385	−	0.133954i
$765$	2.86484e9	−	8.83686e8i	0.231358	−	0.0713646i
$766$	3.53382e9	+	1.70180e9i	0.284082	+	0.136807i
$767$	3.38341e9	+	5.86024e9i	0.270751	+	0.468955i
$768$	1.90832e10	−	3.30530e10i	1.52015	−	2.63297i
$769$	−1.19283e10	+	8.13259e9i	−0.945883	+	0.644892i	−0.934848	−	0.355047i	$-0.884465\pi$
$769$	−1.19283e10	+	8.13259e9i	−0.945883	+	0.644892i	−0.0110342	+	0.999939i	$0.503512\pi$
$770$	−2.72827e7	−	1.19533e8i	−0.00215362	−	0.00943564i
$771$	−8.28210e9	+	1.24833e9i	−0.650804	+	0.0980929i
$772$	1.86900e10	−	2.34365e10i	1.46201	−	1.83330i
$773$	1.02297e10			0.796586			0.398293	−	0.917258i	$-0.369603\pi$
$773$	1.02297e10			0.796586			0.398293	+	0.917258i	$0.369603\pi$
$774$	−5.79144e9	−	3.38809e10i	−0.448945	−	2.62641i
$775$	−2.27797e10			−1.75789
$776$	1.84381e10	−	2.31206e10i	1.41644	−	1.77617i
$777$	−5.51851e8	+	8.31782e7i	−0.0422035	+	0.00636116i
$778$	−1.97689e8	−	8.66133e8i	−0.0150506	−	0.0659411i
$779$	4.22125e9	−	2.87800e9i	0.319934	−	0.218127i
$780$	−8.92213e8	+	1.54536e9i	−0.0673190	+	0.116600i
$781$	3.29421e8	+	5.70573e8i	0.0247441	+	0.0428581i
$782$	−5.13805e10	−	2.47435e10i	−3.84215	−	1.85028i
$783$	−1.05150e10	+	3.24345e9i	−0.782786	+	0.241457i
$784$	−7.89041e8	+	1.05290e10i	−0.0584781	+	0.780336i
$785$	−3.34809e8	+	1.46689e9i	−0.0247032	+	0.108232i
$786$	1.47233e10	+	3.75144e10i	1.08150	+	2.75562i
$787$	−1.90930e8	−	2.54778e9i	−0.0139625	−	0.186316i	−0.999824	−	0.0187548i	$-0.994030\pi$
$787$	−1.90930e8	−	2.54778e9i	−0.0139625	−	0.186316i	0.985862	−	0.167561i	$-0.0535892\pi$
$788$	−1.69171e10	−	2.54984e9i	−1.23164	−	0.185640i
$789$	6.65625e9	−	6.17610e9i	0.482459	−	0.447656i
$790$	3.20514e9	−	1.54351e9i	0.231288	−	0.111382i
$791$	4.16352e7	+	2.83864e7i	0.00299118	+	0.00203935i
$792$	5.24192e9	−	1.33562e10i	0.374932	−	0.955310i
$793$	−3.83771e9	−	1.18378e9i	−0.273285	−	0.0842974i
$794$	1.26536e10	+	1.17408e10i	0.897103	+	0.832390i
$795$	5.40610e8	+	6.77904e8i	0.0381592	+	0.0478501i
$796$	−9.59330e9	−	1.20296e10i	−0.674175	−	0.845388i
$797$	−3.35482e9	−	3.11282e9i	−0.234728	−	0.217796i	0.554035	−	0.832494i	$-0.313088\pi$
$797$	−3.35482e9	−	3.11282e9i	−0.234728	−	0.217796i	−0.788763	+	0.614698i	$0.789278\pi$
$798$	1.95498e9	+	6.03033e8i	0.136186	+	0.0420079i
$799$	2.74910e9	−	7.00460e9i	0.190668	−	0.485814i
$800$	−2.74843e9	−	1.87385e9i	−0.189789	−	0.129396i
$801$	1.06042e10	−	5.10672e9i	0.729062	−	0.351098i
$802$	5.17135e9	−	4.79831e9i	0.353992	−	0.328456i
$803$	5.88977e9	+	8.87740e8i	0.401415	+	0.0605036i
$804$	4.45692e9	+	5.94734e10i	0.302439	+	4.03577i
$805$	1.37492e8	+	3.50323e8i	0.00928946	+	0.0236692i
$806$	−3.78541e9	+	1.65850e10i	−0.254648	+	1.11569i
$807$	−1.84426e8	+	2.46100e9i	−0.0123528	+	0.164837i
$808$	1.71430e9	−	5.28793e8i	0.114327	−	0.0352651i
$809$	1.64979e10	+	7.94495e9i	1.09549	+	0.527559i	0.892237	−	0.451567i	$-0.149135\pi$
$809$	1.64979e10	+	7.94495e9i	1.09549	+	0.527559i	0.203251	+	0.979127i	$0.434849\pi$
$810$	2.00639e8	+	3.47517e8i	0.0132653	+	0.0229762i
$811$	−6.26463e9	+	1.08507e10i	−0.412403	+	0.714304i	−0.995152	−	0.0983488i	$-0.968644\pi$
$811$	−6.26463e9	+	1.08507e10i	−0.412403	+	0.714304i	0.582749	+	0.812653i	$0.301977\pi$
$812$	2.62580e9	−	1.79024e9i	0.172114	−	0.117345i
$813$	2.06579e9	+	9.05083e9i	0.134825	+	0.590706i
$814$	2.45517e9	−	3.70057e8i	0.159550	−	0.0240483i
$815$	6.94971e8	−	8.71466e8i	0.0449692	−	0.0563896i
$816$	−2.63308e10			−1.69648
$817$	−6.71337e9	+	1.67207e9i	−0.430689	+	0.107270i
$818$	−2.22832e10			−1.42345
$819$	6.71745e8	−	8.42342e8i	0.0427279	−	0.0535790i
$820$	3.05668e9	−	4.60720e8i	0.193598	−	0.0291802i
$821$	−2.72800e8	−	1.19521e9i	−0.0172045	−	0.0753779i	0.965597	−	0.260044i	$-0.0837369\pi$
$821$	−2.72800e8	−	1.19521e9i	−0.0172045	−	0.0753779i	−0.982801	+	0.184666i	$0.940880\pi$
$822$	6.23649e10	−	4.25197e10i	3.91642	−	2.67017i
$823$	1.19604e10	−	2.07160e10i	0.747904	−	1.29541i	−0.200921	−	0.979607i	$-0.564394\pi$
$823$	1.19604e10	−	2.07160e10i	0.747904	−	1.29541i	0.948825	−	0.315801i	$-0.102273\pi$
$824$	8.19707e9	+	1.41977e10i	0.510403	+	0.884044i
$825$	−9.49773e9	−	4.57387e9i	−0.588886	−	0.283592i
$826$	4.48561e9	−	1.38363e9i	0.276943	−	0.0854257i
$827$	2.19734e9	−	2.93215e10i	0.135091	−	1.80267i	−0.359082	−	0.933306i	$-0.616910\pi$
$827$	2.19734e9	−	2.93215e10i	0.135091	−	1.80267i	0.494173	−	0.869364i	$-0.335471\pi$
$828$	−2.03433e10	+	8.91298e10i	−1.24542	+	5.45653i
$829$	−1.27081e9	−	3.23798e9i	−0.0774714	−	0.197394i	0.886891	−	0.461979i	$-0.152860\pi$
$829$	−1.27081e9	−	3.23798e9i	−0.0774714	−	0.197394i	−0.964362	+	0.264585i	$0.914765\pi$
$830$	−1.46939e6	−	1.96077e7i	−8.91999e−5	−	0.00119029i
$831$	−5.10651e10	−	7.69682e9i	−3.08688	−	0.465273i
$832$	−5.44634e9	+	5.05346e9i	−0.327848	+	0.304199i
$833$	−1.98214e10	+	9.54549e9i	−1.18817	+	0.572191i
$834$	4.38120e10	+	2.98705e10i	2.61524	+	1.78304i
$835$	−3.61034e8	+	9.19900e8i	−0.0214608	+	0.0546812i
$836$	−5.72866e9	−	1.76706e9i	−0.339103	−	0.104599i
$837$	−1.97283e10	−	1.83052e10i	−1.16292	−	1.07903i
$838$	−2.40334e10	−	3.01369e10i	−1.41078	−	1.76907i
$839$	−6.47749e9	−	8.12252e9i	−0.378652	−	0.474814i	0.555589	−	0.831457i	$-0.312493\pi$
$839$	−6.47749e9	−	8.12252e9i	−0.378652	−	0.474814i	−0.934241	+	0.356643i	$0.883921\pi$
$840$	4.37128e8	+	4.05596e8i	0.0254467	+	0.0236111i
$841$	−2.52649e9	−	7.79320e8i	−0.146465	−	0.0451783i
$842$	−1.27051e10	+	3.23721e10i	−0.733477	+	1.86887i
$843$	2.72737e10	+	1.85949e10i	1.56800	+	1.06905i
$844$	−4.62725e10	+	2.22837e10i	−2.64926	+	1.27582i
$845$	−1.28485e9	+	1.19217e9i	−0.0732580	+	0.0679735i
$846$	−1.81103e10	−	2.72969e9i	−1.02832	−	0.154995i
$847$	1.28431e8	+	1.71379e9i	0.00726234	+	0.0969092i
$848$	−1.69400e9	−	4.31623e9i	−0.0953953	−	0.243063i
$849$	4.89321e9	−	2.14386e10i	0.274421	−	1.20232i
$850$	−3.02086e9	+	4.03105e10i	−0.168719	+	2.25140i
$851$	−7.28257e9	+	2.24638e9i	−0.405071	+	0.124948i
$852$	−5.99302e9	−	2.88609e9i	−0.331976	−	0.159871i
$853$	−1.24460e10	−	2.15571e10i	−0.686608	−	1.18924i	−0.972929	−	0.231106i	$-0.925766\pi$
$853$	−1.24460e10	−	2.15571e10i	−0.686608	−	1.18924i	0.286321	−	0.958134i	$-0.407568\pi$
$854$	−1.39300e9	+	2.41275e9i	−0.0765331	+	0.132559i
$855$	−1.21354e9	+	8.27377e8i	−0.0664007	+	0.0452712i
$856$	6.24597e9	+	2.73654e10i	0.340363	+	1.49123i
$857$	3.29723e9	−	4.96978e8i	0.178944	−	0.0269714i	−0.0589590	−	0.998260i	$-0.518778\pi$
$857$	3.29723e9	−	4.96978e8i	0.178944	−	0.0269714i	0.237903	+	0.971289i	$0.423540\pi$
$858$	−4.90832e9	+	6.15484e9i	−0.265294	+	0.332668i
$859$	−1.59296e10			−0.857489			−0.428744	−	0.903426i	$-0.641044\pi$
$859$	−1.59296e10			−0.857489			−0.428744	+	0.903426i	$0.641044\pi$
$860$	−4.09863e9	−	8.50909e8i	−0.219732	−	0.0456182i
$861$	−3.06531e9			−0.163668
$862$	−3.12533e10	+	3.91904e10i	−1.66196	+	2.08403i
$863$	1.71892e10	−	2.59086e9i	0.910371	−	0.137216i	0.322873	−	0.946442i	$-0.395351\pi$
$863$	1.71892e10	−	2.59086e9i	0.910371	−	0.137216i	0.587498	+	0.809226i	$0.300113\pi$
$864$	−8.74493e8	−	3.83140e9i	−0.0461273	−	0.202097i
$865$	3.60962e9	−	2.46099e9i	0.189629	−	0.129287i
$866$	2.24084e10	−	3.88124e10i	1.17246	−	2.03076i
$867$	−1.20899e10	−	2.09403e10i	−0.630023	−	1.09123i
$868$	7.00286e9	+	3.37240e9i	0.363460	+	0.175033i
$869$	9.87772e9	−	3.04687e9i	0.510608	−	0.157502i
$870$	−4.25147e8	+	5.67320e9i	−0.0218888	+	0.292086i
$871$	2.13578e9	−	9.35744e9i	0.109520	−	0.479837i
$872$	−1.01820e10	−	2.59433e10i	−0.520026	−	1.32500i
$873$	−3.26583e9	−	4.35795e10i	−0.166129	−	2.21683i
$874$	2.76263e10	+	4.16399e9i	1.39969	+	0.210969i
$875$	3.93782e8	−	3.65376e8i	0.0198714	−	0.0184379i
$876$	−5.41803e10	+	2.60918e10i	−2.72318	+	1.31142i
$877$	−9.86096e9	−	6.72309e9i	−0.493652	−	0.336566i	0.290771	−	0.956793i	$-0.406088\pi$
$877$	−9.86096e9	−	6.72309e9i	−0.493652	−	0.336566i	−0.784423	+	0.620227i	$0.787041\pi$
$878$	1.17441e10	−	2.99235e10i	0.585585	−	1.49205i
$879$	−2.05430e10	−	6.33667e9i	−1.02024	−	0.314702i
$880$	−5.66693e8	−	5.25815e8i	−0.0280323	−	0.0260102i
$881$	6.87208e9	+	8.61732e9i	0.338589	+	0.424577i	0.921753	−	0.387777i	$-0.126757\pi$
$881$	6.87208e9	+	8.61732e9i	0.338589	+	0.424577i	−0.583164	+	0.812354i	$0.698186\pi$
$882$	3.33861e10	+	4.18648e10i	1.63842	+	2.05452i
$883$	1.12767e10	+	1.04632e10i	0.551211	+	0.511450i	0.905875	−	0.423544i	$-0.139214\pi$
$883$	1.12767e10	+	1.04632e10i	0.551211	+	0.511450i	−0.354664	+	0.934994i	$0.615405\pi$
$884$	1.89995e10	+	5.86057e9i	0.925038	+	0.285336i
$885$	−2.02206e9	+	5.15212e9i	−0.0980601	+	0.249853i
$886$	2.46282e9	+	1.67912e9i	0.118964	+	0.0811082i
$887$	−2.11729e10	+	1.01963e10i	−1.01870	+	0.490582i	−0.867245	−	0.497882i	$-0.834111\pi$
$887$	−2.11729e10	+	1.01963e10i	−1.01870	+	0.490582i	−0.151459	+	0.988464i	$0.548397\pi$
$888$	−8.85222e9	+	8.21366e9i	−0.424235	+	0.393633i
$889$	4.53611e8	+	6.83708e7i	0.0216534	+	0.00326373i
$890$	−1.62632e8	−	2.17017e9i	−0.00773287	−	0.103188i
$891$	4.25990e8	+	1.08541e9i	0.0201757	+	0.0514067i
$892$	8.27886e9	−	3.62721e10i	0.390565	−	1.71118i
$893$	−2.75486e8	+	3.67611e9i	−0.0129455	+	0.172746i
$894$	7.84906e10	−	2.42111e10i	3.67397	−	1.13327i
$895$	1.58928e9	+	7.65357e8i	0.0741003	+	0.0356848i
$896$	2.28287e9	+	3.95405e9i	0.106024	+	0.183639i
$897$	1.20819e10	−	2.09265e10i	0.558935	−	0.968104i
$898$	−1.62560e10	+	1.10831e10i	−0.749109	+	0.510734i
$899$	7.94894e9	+	3.48266e10i	0.364880	+	1.59864i
$900$	6.40794e10	−	9.65842e9i	2.93001	−	0.441629i
$901$	6.02372e9	−	7.55350e9i	0.274364	−	0.344042i
$902$	1.36375e10			0.618743
$903$	3.89313e9	+	1.44011e9i	0.175951	+	0.0650860i
$904$	1.09037e9			0.0490888
$905$	2.65621e9	−	3.33078e9i	0.119122	−	0.149374i
$906$	8.88309e10	−	1.33891e10i	3.96840	−	0.598140i
$907$	2.96724e9	+	1.30003e10i	0.132047	+	0.578534i	0.997049	+	0.0767663i	$0.0244595\pi$
$907$	2.96724e9	+	1.30003e10i	0.132047	+	0.578534i	−0.865003	+	0.501767i	$0.832683\pi$
$908$	4.67107e10	−	3.18468e10i	2.07070	−	1.41178i
$909$	1.32558e9	−	2.29597e9i	0.0585373	−	0.101390i
$910$	−9.96064e7	−	1.72523e8i	−0.00438170	−	0.00758932i
$911$	3.15870e10	+	1.52115e10i	1.38418	+	0.666588i	0.969887	−	0.243553i	$-0.0783131\pi$
$911$	3.15870e10	+	1.52115e10i	1.38418	+	0.666588i	0.414297	+	0.910142i	$0.364027\pi$
$912$	1.23265e10	−	3.80223e9i	0.538094	−	0.165980i
$913$	4.26966e6	−	5.69747e7i	0.000185672	−	0.00247762i
$914$	−1.16040e9	+	5.08404e9i	−0.0502684	+	0.220240i
$915$	−1.20010e9	−	3.05781e9i	−0.0517898	−	0.131958i
$916$	1.91457e9	+	2.55482e10i	0.0823071	+	1.09831i
$917$	−2.93021e9	−	4.41657e8i	−0.125489	−	0.0189144i
$918$	−3.50086e10	+	3.24833e10i	−1.49357	+	1.38583i
$919$	−9.95917e9	+	4.79608e9i	−0.423271	+	0.203837i	−0.633379	−	0.773841i	$-0.718333\pi$
$919$	−9.95917e9	+	4.79608e9i	−0.423271	+	0.203837i	0.210108	+	0.977678i	$0.432618\pi$
$920$	6.72822e9	+	4.58723e9i	0.284868	+	0.194219i
$921$	−4.39705e9	+	1.12035e10i	−0.185461	+	0.472547i
$922$	−1.06965e10	−	3.29944e9i	−0.449453	−	0.138638i
$923$	7.84723e8	+	7.28117e8i	0.0328481	+	0.0304786i
$924$	2.24263e9	+	2.81216e9i	0.0935201	+	0.117270i
$925$	3.36819e9	+	4.22357e9i	0.139927	+	0.175462i
$926$	−4.96723e10	−	4.60891e10i	−2.05578	−	1.90748i
$927$	2.31507e10	+	7.14105e9i	0.954521	+	0.294431i
$928$	−1.90576e9	+	4.85579e9i	−0.0782798	+	0.199454i
$929$	1.18400e10	+	8.07236e9i	0.484502	+	0.330328i	0.780814	−	0.624763i	$-0.214804\pi$
$929$	1.18400e10	+	8.07236e9i	0.484502	+	0.330328i	−0.296312	+	0.955091i	$0.595757\pi$
$930$	−1.25361e10	+	6.03707e9i	−0.511061	+	0.246114i
$931$	7.90081e9	−	7.33088e9i	0.320884	−	0.297736i
$932$	−7.35717e10	−	1.10891e10i	−2.97684	−	0.448686i
$933$	4.01837e9	+	5.36214e10i	0.161981	+	2.16149i
$934$	−2.87450e10	−	7.32409e10i	−1.15438	−	2.94130i
$935$	3.58431e8	−	1.57039e9i	0.0143405	−	0.0628299i
$936$	1.74216e9	−	2.32475e10i	0.0694421	−	0.926640i
$937$	1.04526e10	−	3.22420e9i	0.415084	−	0.128036i	−0.0801772	−	0.996781i	$-0.525549\pi$
$937$	1.04526e10	−	3.22420e9i	0.415084	−	0.128036i	0.495261	+	0.868744i	$0.335072\pi$
$938$	−5.99884e9	−	2.88889e9i	−0.237333	−	0.114293i
$939$	−3.01976e10	−	5.23038e10i	−1.19026	−	2.06160i
$940$	−1.11524e9	+	1.93165e9i	−0.0437945	+	0.0758542i
$941$	6.43709e9	−	4.38873e9i	0.251841	−	0.171702i	−0.430819	−	0.902438i	$-0.641775\pi$
$941$	6.43709e9	−	4.38873e9i	0.251841	−	0.171702i	0.682660	+	0.730736i	$0.260823\pi$
$942$	−1.49127e10	−	6.53370e10i	−0.581272	−	2.54672i
$943$	−4.13920e10	+	6.23884e9i	−1.60741	+	0.242278i
$944$	1.84537e10	−	2.31402e10i	0.713973	−	0.895294i
$945$	3.15159e8			0.0121484
$946$	−1.73204e10	−	6.40699e9i	−0.665181	−	0.246057i
$947$	4.38592e10			1.67817			0.839084	−	0.544001i	$-0.183091\pi$
$947$	4.38592e10			1.67817			0.839084	+	0.544001i	$0.183091\pi$
$948$	−6.50695e10	+	8.15946e10i	−2.48055	+	3.11052i
$949$	9.56972e9	−	1.44240e9i	0.363469	−	0.0547841i
$950$	−4.40674e9	−	1.93072e10i	−0.166757	−	0.730611i
$951$	−2.70306e10	+	1.84292e10i	−1.01912	+	0.694822i
$952$	3.32219e9	−	5.75420e9i	0.124794	−	0.216150i
$953$	6.85509e9	+	1.18734e10i	0.256560	+	0.444374i	0.965318	−	0.261077i	$-0.0840777\pi$
$953$	6.85509e9	+	1.18734e10i	0.256560	+	0.444374i	−0.708758	+	0.705451i	$0.750744\pi$
$954$	−2.11864e10	−	1.02028e10i	−0.790018	−	0.380453i
$955$	−2.08267e8	+	6.42418e7i	−0.00773764	+	0.00238675i
$956$	5.88244e9	−	7.84957e10i	0.217748	−	2.90565i
$957$	−3.67850e9	+	1.61166e10i	−0.135668	+	0.594402i
$958$	7.66981e8	+	1.95423e9i	0.0281842	+	0.0718121i
$959$	4.14763e8	+	5.53462e9i	0.0151857	+	0.202639i
$960$	−6.00901e9	−	9.05712e8i	−0.219207	−	0.0330401i
$961$	−4.38764e10	+	4.07113e10i	−1.59477	+	1.47973i
$962$	3.63471e9	−	1.75039e9i	0.131631	−	0.0633901i
$963$	3.42726e10	+	2.33666e10i	1.23667	+	0.843149i
$964$	3.83428e9	−	9.76959e9i	0.137852	−	0.351242i
$965$	−3.77051e9	−	1.16305e9i	−0.135069	−	0.0416632i
$966$	−1.22878e10	−	1.14014e10i	−0.438584	−	0.406947i
$967$	9.31787e8	+	1.16842e9i	0.0331378	+	0.0415535i	0.798124	−	0.602493i	$-0.205826\pi$
$967$	9.31787e8	+	1.16842e9i	0.0331378	+	0.0415535i	−0.764986	+	0.644046i	$0.777254\pi$
$968$	2.31857e10	+	2.90739e10i	0.821591	+	1.03024i
$969$	1.97030e10	+	1.82817e10i	0.695663	+	0.645481i
$970$	−7.72154e9	−	2.38178e9i	−0.271646	−	0.0837916i
$971$	8.69014e9	−	2.21421e10i	0.304621	−	0.776161i	−0.693810	−	0.720158i	$-0.744069\pi$
$971$	8.69014e9	−	2.21421e10i	0.304621	−	0.776161i	0.998431	−	0.0560026i	$-0.0178355\pi$
$972$	−5.03605e10	−	3.43352e10i	−1.75897	−	1.19924i
$973$	−3.51291e9	+	1.69173e9i	−0.122256	+	0.0588756i
$974$	1.78847e9	−	1.65945e9i	0.0620189	−	0.0575451i
$975$	−1.69369e10	−	2.55282e9i	−0.585217	−	0.0882073i
$976$	1.31273e9	+	1.75171e10i	0.0451960	+	0.603099i
$977$	1.30839e10	+	3.33373e10i	0.448857	+	1.14367i	0.958957	+	0.283553i	$0.0915131\pi$
$977$	1.30839e10	+	3.33373e10i	0.448857	+	1.14367i	−0.510100	+	0.860115i	$0.670392\pi$
$978$	−1.10476e10	+	4.84028e10i	−0.377644	+	1.65457i
$979$	4.72565e8	−	6.30594e9i	0.0160962	−	0.214788i
$980$	6.23150e9	−	1.92216e9i	0.211496	−	0.0652377i
$981$	−3.71070e10	−	1.78698e10i	−1.25492	−	0.604335i
$982$	3.13342e10	+	5.42724e10i	1.05591	+	1.82889i
$983$	2.27020e10	−	3.93210e10i	0.762301	−	1.32034i	−0.179361	−	0.983783i	$-0.557403\pi$
$983$	2.27020e10	−	3.93210e10i	0.762301	−	1.32034i	0.941662	−	0.336561i	$-0.109264\pi$
$984$	−5.48020e10	+	3.73634e10i	−1.83364	+	1.25015i
$985$	5.01107e8	+	2.19549e9i	0.0167072	+	0.0731991i
$986$	6.26824e10	−	9.44786e9i	2.08246	−	0.313880i
$987$	1.37902e9	−	1.72924e9i	0.0456522	−	0.0572461i
$988$	−9.74071e9			−0.321323
$989$	5.55016e10	+	1.15226e10i	1.82439	+	0.378759i
$990$	−3.92054e9			−0.128417
$991$	2.79667e10	−	3.50691e10i	0.912816	−	1.14463i	−0.0762398	−	0.997090i	$-0.524291\pi$
$991$	2.79667e10	−	3.50691e10i	0.912816	−	1.14463i	0.989055	−	0.147545i	$-0.0471371\pi$
$992$	−1.26154e10	+	1.90146e9i	−0.410308	+	0.0618439i
$993$	−9.78820e8	−	4.28849e9i	−0.0317234	−	0.138989i
$994$	6.13565e8	−	4.18321e8i	0.0198156	−	0.0135101i
$995$	−1.01266e9	+	1.75399e9i	−0.0325900	+	0.0564476i
$996$	2.88419e8	+	4.99556e8i	0.00924944	+	0.0160205i
$997$	−5.34930e10	−	2.57609e10i	−1.70948	−	0.823243i	−0.991937	−	0.126729i	$-0.959552\pi$
$997$	−5.34930e10	−	2.57609e10i	−1.70948	−	0.823243i	−0.717544	−	0.696514i	$-0.754734\pi$
$998$	−1.44691e10	+	4.46312e9i	−0.460770	+	0.142129i
$999$	−4.76945e8	+	6.36439e9i	−0.0151352	+	0.201966i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	43.8.g.a.24.2	yes	300
43.9	even	21	inner	43.8.g.a.9.2	✓	300

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
43.8.g.a.9.2	✓	300	43.9	even	21	inner
43.8.g.a.24.2	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)

\(f(q)\)	\(=\)	\(q+(-12.0734 + 15.1396i) q^{2} +(-73.9419 + 11.1450i) q^{3} +(-54.9571 - 240.783i) q^{4} +(-26.8606 + 18.3132i) q^{5} +(724.002 - 1254.01i) q^{6} +(53.2365 + 92.2083i) q^{7} +(2075.71 + 999.609i) q^{8} +(3253.36 - 1003.53i) q^{9} +O(q^{10})\)	\(q+(-12.0734 + 15.1396i) q^{2} +(-73.9419 + 11.1450i) q^{3} +(-54.9571 - 240.783i) q^{4} +(-26.8606 + 18.3132i) q^{5} +(724.002 - 1254.01i) q^{6} +(53.2365 + 92.2083i) q^{7} +(2075.71 + 999.609i) q^{8} +(3253.36 - 1003.53i) q^{9} +(47.0442 - 627.761i) q^{10} +(407.040 - 1783.36i) q^{11} +(6747.15 + 17191.4i) q^{12} +(-222.107 - 2963.82i) q^{13} +(-2038.74 - 307.291i) q^{14} +(1782.02 - 1653.47i) q^{15} +(-11712.4 + 5640.41i) q^{16} +(-22380.2 - 15258.6i) q^{17} +(-24086.2 + 61370.6i) q^{18} +(12680.4 + 3911.39i) q^{19} +(5885.69 + 5461.12i) q^{20} +(-4964.06 - 6224.74i) q^{21} +(22085.0 + 27693.7i) q^{22} +(-79701.0 - 73951.7i) q^{23} +(-164623. - 50779.3i) q^{24} +(-28156.2 + 71740.7i) q^{25} +(47552.6 + 32420.8i) q^{26} +(-82033.4 + 39505.2i) q^{27} +(19276.4 - 17885.9i) q^{28} +(119505. + 18012.5i) q^{29} +(3517.83 + 46942.2i) q^{30} +(107987. + 275147. i) q^{31} +(-9604.52 + 42080.1i) q^{32} +(-10221.9 + 136402. i) q^{33} +(501214. - 154604. i) q^{34} +(-3118.59 - 1501.83i) q^{35} +(-420428. - 728203. i) q^{36} +(35047.9 - 60704.8i) q^{37} +(-212313. + 144753. i) q^{38} +(49454.6 + 216675. i) q^{39} +(-74060.7 + 11162.9i) q^{40} +(240046. - 301009. i) q^{41} +154173. q^{42} +(-446290. + 269524. i) q^{43} -451772. q^{44} +(-69009.3 + 86534.9i) q^{45} +(2.08186e6 - 313790. i) q^{46} +(61816.6 + 270836. i) q^{47} +(803178. - 547598. i) q^{48} +(406103. - 703391. i) q^{49} +(-746184. - 1.29243e6i) q^{50} +(1.82489e6 + 878821. i) q^{51} +(-701430. + 216362. i) q^{52} +(-26654.6 + 355681. i) q^{53} +(392331. - 1.71892e6i) q^{54} +(21725.7 + 55356.3i) q^{55} +(18331.2 + 244613. i) q^{56} +(-981208. - 147893. i) q^{57} +(-1.71554e6 + 1.59179e6i) q^{58} +(-2.05129e6 + 987849. i) q^{59} +(-496063. - 338210. i) q^{60} +(493673. - 1.25786e6i) q^{61} +(-5.46939e6 - 1.68708e6i) q^{62} +(265731. + 246563. i) q^{63} +(-1.55859e6 - 1.95441e6i) q^{64} +(60242.9 + 75542.3i) q^{65} +(-1.94165e6 - 1.80159e6i) q^{66} +(3.08590e6 + 951873. i) q^{67} +(-2.44405e6 + 6.22733e6i) q^{68} +(6.71743e6 + 4.57987e6i) q^{69} +(60389.2 - 29081.9i) q^{70} +(-264027. + 244982. i) q^{71} +(7.75617e6 + 1.16905e6i) q^{72} +(243335. + 3.24708e6i) q^{73} +(495897. + 1.26353e6i) q^{74} +(1.28237e6 - 5.61845e6i) q^{75} +(244917. - 3.26819e6i) q^{76} +(186110. - 57407.3i) q^{77} +(-3.87746e6 - 1.86729e6i) q^{78} +(2.82551e6 + 4.89392e6i) q^{79} +(211308. - 365997. i) q^{80} +(-526672. + 359079. i) q^{81} +(1.65897e6 + 7.26841e6i) q^{82} +(30885.4 - 4655.23i) q^{83} +(-1.22600e6 + 1.53735e6i) q^{84} +880578. q^{85} +(1.30776e6 - 1.00107e7i) q^{86} -9.03719e6 q^{87} +(2.62756e6 - 3.29485e6i) q^{88} +(3.41839e6 - 515240. i) q^{89} +(-476925. - 2.08955e6i) q^{90} +(261464. - 178263. i) q^{91} +(-1.34262e7 + 2.32548e7i) q^{92} +(-1.10513e7 - 1.91414e7i) q^{93} +(-4.84669e6 - 2.33404e6i) q^{94} +(-412234. + 127157. i) q^{95} +(241195. - 3.21853e6i) q^{96} +(2.85628e6 - 1.25142e7i) q^{97} +(5.74601e6 + 1.46406e7i) q^{98} +(-465405. - 6.21039e6i) 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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