LMFDB - Embedded newform 38.10.e.b.5.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [38,10,Mod(5,38)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(38, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([16]))

N = Newforms(chi, 10, names="a")

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

chi := DirichletCharacter("38.5");

S:= CuspForms(chi, 10);

N := Newforms(S);

Level:	$ N $	$=$	$ 38 = 2 \cdot 19 $
Weight:	$ k $	$=$	$ 10 $
Character orbit:	$[\chi]$	$=$	38.e (of order $9$, degree $6$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$19.5713617742$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$8$ over $\Q(\zeta_{9})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			5.8
Character	$\chi$	$=$	38.5
Dual form			38.10.e.b.23.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-15.0351 + 5.47232i) q^{2} +(48.1038 - 272.810i) q^{3} +(196.107 - 164.554i) q^{4} +(-1032.82 - 866.635i) q^{5} +(769.661 + 4364.97i) q^{6} +(-4220.81 - 7310.67i) q^{7} +(-2048.00 + 3547.24i) q^{8} +(-53615.6 - 19514.5i) q^{9} +O(q^{10})$	\(q+(-15.0351 + 5.47232i) q^{2} +(48.1038 - 272.810i) q^{3} +(196.107 - 164.554i) q^{4} +(-1032.82 - 866.635i) q^{5} +(769.661 + 4364.97i) q^{6} +(-4220.81 - 7310.67i) q^{7} +(-2048.00 + 3547.24i) q^{8} +(-53615.6 - 19514.5i) q^{9} +(20271.0 + 7378.03i) q^{10} +(22307.6 - 38638.0i) q^{11} +(-35458.4 - 61415.8i) q^{12} +(2571.31 + 14582.6i) q^{13} +(103467. + 86818.8i) q^{14} +(-286109. + 240074. i) q^{15} +(11380.2 - 64540.4i) q^{16} +(531597. - 193485. i) q^{17} +912904. q^{18} +(553507. - 127742. i) q^{19} -345151. q^{20} +(-2.19746e6 + 799811. i) q^{21} +(-123958. + 703000. i) q^{22} +(197348. - 165595. i) q^{23} +(869207. + 729351. i) q^{24} +(-23505.4 - 133305. i) q^{25} +(-118461. - 205180. i) q^{26} +(-5.17658e6 + 8.96610e6i) q^{27} +(-2.03073e6 - 739125. i) q^{28} +(-2.67815e6 - 974768. i) q^{29} +(2.98791e6 - 5.17522e6i) q^{30} +(484230. + 838712. i) q^{31} +(182083. + 1.03265e6i) q^{32} +(-9.46775e6 - 7.94439e6i) q^{33} +(-6.93379e6 + 5.81814e6i) q^{34} +(-1.97636e6 + 1.12085e7i) q^{35} +(-1.37256e7 + 4.99570e6i) q^{36} +1.96280e7 q^{37} +(-7.62297e6 + 4.94958e6i) q^{38} +4.10198e6 q^{39} +(5.18937e6 - 1.88878e6i) q^{40} +(314812. - 1.78539e6i) q^{41} +(2.86622e7 - 2.40504e7i) q^{42} +(1.46654e7 + 1.23057e7i) q^{43} +(-1.98332e6 - 1.12480e7i) q^{44} +(3.84630e7 + 6.66199e7i) q^{45} +(-2.06096e6 + 3.56969e6i) q^{46} +(5.24121e6 + 1.90764e6i) q^{47} +(-1.70598e7 - 6.20928e6i) q^{48} +(-1.54537e7 + 2.67667e7i) q^{49} +(1.08290e6 + 1.87563e6i) q^{50} +(-2.72130e7 - 1.54333e8i) q^{51} +(2.90388e6 + 2.43664e6i) q^{52} +(-1.47585e7 + 1.23839e7i) q^{53} +(2.87649e7 - 1.63134e8i) q^{54} +(-5.65247e7 + 2.05733e7i) q^{55} +3.45769e7 q^{56} +(-8.22360e6 - 1.57147e8i) q^{57} +4.56005e7 q^{58} +(-1.43703e8 + 5.23036e7i) q^{59} +(-1.66031e7 + 9.41607e7i) q^{60} +(8.15154e7 - 6.83996e7i) q^{61} +(-1.18701e7 - 9.96023e6i) q^{62} +(8.36376e7 + 4.74332e8i) q^{63} +(-8.38861e6 - 1.45295e7i) q^{64} +(9.98212e6 - 1.72895e7i) q^{65} +(1.85823e8 + 6.76339e7i) q^{66} +(-1.02415e8 - 3.72759e7i) q^{67} +(7.24114e7 - 1.25420e8i) q^{68} +(-3.56828e7 - 6.18044e7i) q^{69} +(-3.16217e7 - 1.79336e8i) q^{70} +(1.71859e8 + 1.44207e8i) q^{71} +(1.79027e8 - 1.50222e8i) q^{72} +(6.78679e7 - 3.84898e8i) q^{73} +(-2.95109e8 + 1.07411e8i) q^{74} -3.74978e7 q^{75} +(8.75263e7 - 1.16133e8i) q^{76} -3.76626e8 q^{77} +(-6.16736e7 + 2.24474e7i) q^{78} +(3.96818e7 - 2.25047e8i) q^{79} +(-6.76866e7 + 5.67958e7i) q^{80} +(1.33673e9 + 1.12165e9i) q^{81} +(5.03700e6 + 2.85662e7i) q^{82} +(-5.77224e7 - 9.99781e7i) q^{83} +(-2.99327e8 + 5.18449e8i) q^{84} +(-7.16723e8 - 2.60866e8i) q^{85} +(-2.87835e8 - 1.04764e8i) q^{86} +(-3.94756e8 + 6.83738e8i) q^{87} +(9.13721e7 + 1.58261e8i) q^{88} +(-4.82939e7 - 2.73888e8i) q^{89} +(-9.42861e8 - 7.91154e8i) q^{90} +(9.57556e7 - 8.03485e7i) q^{91} +(1.14522e7 - 6.49488e7i) q^{92} +(2.52103e8 - 9.17578e7i) q^{93} -8.92412e7 q^{94} +(-6.82376e8 - 3.47754e8i) q^{95} +2.90475e8 q^{96} +(6.40413e8 - 2.33091e8i) q^{97} +(8.58725e7 - 4.87007e8i) q^{98} +(-1.95004e9 + 1.63627e9i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 33 q^{3} + 528 q^{6} - 25809 q^{7} - 98304 q^{8} + 7953 q^{9}+O(q^{10}) $ 48 * q + 33 * q^3 + 528 * q^6 - 25809 * q^7 - 98304 * q^8 + 7953 * q^9	\( 48 q + 33 q^{3} + 528 q^{6} - 25809 q^{7} - 98304 q^{8} + 7953 q^{9} - 55221 q^{11} - 62208 q^{12} + 21777 q^{13} + 28464 q^{14} - 280011 q^{15} + 1055055 q^{17} + 6083232 q^{18} + 2408220 q^{19} + 523776 q^{20} - 5105673 q^{21} - 2513280 q^{22} - 456708 q^{23} + 135168 q^{24} + 19417530 q^{25} - 1077120 q^{26} - 11729661 q^{27} - 30720 q^{28} + 4679889 q^{29} + 4879158 q^{31} - 12360834 q^{33} + 9206400 q^{34} - 47475759 q^{35} + 2035968 q^{36} + 119843604 q^{37} - 39471312 q^{38} + 16552668 q^{39} + 60082911 q^{41} + 59187024 q^{42} + 109939059 q^{43} - 40212480 q^{44} + 3067236 q^{45} - 4919424 q^{46} + 198627789 q^{47} - 4325376 q^{48} - 182954115 q^{49} - 229688016 q^{50} - 228228021 q^{51} - 49495296 q^{52} - 370799859 q^{53} + 111760416 q^{54} - 60369543 q^{55} + 211427328 q^{56} + 128158266 q^{57} + 166196064 q^{58} - 382689396 q^{59} - 36777216 q^{60} - 850085550 q^{61} + 42954480 q^{62} - 803298357 q^{63} - 402653184 q^{64} + 261122181 q^{65} + 516819888 q^{66} + 1146400764 q^{67} + 125611008 q^{68} - 178115667 q^{69} - 759612144 q^{70} + 363378456 q^{71} - 65150976 q^{72} + 1407478230 q^{73} - 12153360 q^{74} + 1715917770 q^{75} - 128288256 q^{76} - 193134048 q^{77} - 1199414208 q^{78} - 2098405449 q^{79} + 3082805319 q^{81} + 961326576 q^{82} + 358330707 q^{83} + 502249728 q^{84} - 1961566422 q^{85} - 588638592 q^{86} - 1222269090 q^{87} - 226185216 q^{88} - 368108670 q^{89} + 1740707616 q^{90} - 3296437032 q^{91} - 819648768 q^{92} + 6597152658 q^{93} + 2953278144 q^{94} - 881990403 q^{95} + 509607936 q^{96} - 3752161206 q^{97} - 458055696 q^{98} + 6061589742 q^{99}+O(q^{100}) \) 48 * q + 33 * q^3 + 528 * q^6 - 25809 * q^7 - 98304 * q^8 + 7953 * q^9 - 55221 * q^11 - 62208 * q^12 + 21777 * q^13 + 28464 * q^14 - 280011 * q^15 + 1055055 * q^17 + 6083232 * q^18 + 2408220 * q^19 + 523776 * q^20 - 5105673 * q^21 - 2513280 * q^22 - 456708 * q^23 + 135168 * q^24 + 19417530 * q^25 - 1077120 * q^26 - 11729661 * q^27 - 30720 * q^28 + 4679889 * q^29 + 4879158 * q^31 - 12360834 * q^33 + 9206400 * q^34 - 47475759 * q^35 + 2035968 * q^36 + 119843604 * q^37 - 39471312 * q^38 + 16552668 * q^39 + 60082911 * q^41 + 59187024 * q^42 + 109939059 * q^43 - 40212480 * q^44 + 3067236 * q^45 - 4919424 * q^46 + 198627789 * q^47 - 4325376 * q^48 - 182954115 * q^49 - 229688016 * q^50 - 228228021 * q^51 - 49495296 * q^52 - 370799859 * q^53 + 111760416 * q^54 - 60369543 * q^55 + 211427328 * q^56 + 128158266 * q^57 + 166196064 * q^58 - 382689396 * q^59 - 36777216 * q^60 - 850085550 * q^61 + 42954480 * q^62 - 803298357 * q^63 - 402653184 * q^64 + 261122181 * q^65 + 516819888 * q^66 + 1146400764 * q^67 + 125611008 * q^68 - 178115667 * q^69 - 759612144 * q^70 + 363378456 * q^71 - 65150976 * q^72 + 1407478230 * q^73 - 12153360 * q^74 + 1715917770 * q^75 - 128288256 * q^76 - 193134048 * q^77 - 1199414208 * q^78 - 2098405449 * q^79 + 3082805319 * q^81 + 961326576 * q^82 + 358330707 * q^83 + 502249728 * q^84 - 1961566422 * q^85 - 588638592 * q^86 - 1222269090 * q^87 - 226185216 * q^88 - 368108670 * q^89 + 1740707616 * q^90 - 3296437032 * q^91 - 819648768 * q^92 + 6597152658 * q^93 + 2953278144 * q^94 - 881990403 * q^95 + 509607936 * q^96 - 3752161206 * q^97 - 458055696 * q^98 + 6061589742 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/38\mathbb{Z}\right)^\times$.

$n$	$21$
$\chi(n)$	$e\left(\frac{8}{9}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−15.0351	+	5.47232i	−0.664463	+	0.241845i
$2$	−15.0351	+	5.47232i	−0.664463	+	0.241845i
$3$	48.1038	−	272.810i	0.342874	−	1.94453i	0.0147699	−	0.999891i	$-0.495298\pi$
$3$	48.1038	−	272.810i	0.342874	−	1.94453i	0.328104	−	0.944642i	$-0.393590\pi$
$4$	196.107	−	164.554i	0.383022	−	0.321394i
$5$	−1032.82	−	866.635i	−0.739022	−	0.620113i	0.193553	−	0.981090i	$-0.437999\pi$
$5$	−1032.82	−	866.635i	−0.739022	−	0.620113i	−0.932575	+	0.360977i	$0.882443\pi$
$6$	769.661	+	4364.97i	0.242448	+	1.37499i
$7$	−4220.81	−	7310.67i	−0.664439	−	1.15084i	−0.979437	−	0.201750i	$-0.935337\pi$
$7$	−4220.81	−	7310.67i	−0.664439	−	1.15084i	0.314998	−	0.949092i	$-0.397996\pi$
$8$	−2048.00	+	3547.24i	−0.176777	+	0.306186i
$9$	−53615.6	−	19514.5i	−2.72395	−	0.991438i
$10$	20271.0	+	7378.03i	0.641024	+	0.233314i
$11$	22307.6	−	38638.0i	0.459395	−	0.795696i	−0.539534	−	0.841964i	$-0.681399\pi$
$11$	22307.6	−	38638.0i	0.459395	−	0.795696i	0.998929	+	0.0462680i	$0.0147328\pi$
$12$	−35458.4	−	61415.8i	−0.493633	−	0.854997i
$13$	2571.31	+	14582.6i	0.0249695	+	0.141609i	0.994744	−	0.102394i	$-0.0326504\pi$
$13$	2571.31	+	14582.6i	0.0249695	+	0.141609i	−0.969774	+	0.244003i	$0.921539\pi$
$14$	103467.	+	86818.8i	0.719820	+	0.604001i
$15$	−286109.	+	240074.i	−1.45922	+	1.22443i
$16$	11380.2	−	64540.4i	0.0434120	−	0.246202i
$17$	531597.	−	193485.i	1.54370	−	0.561860i	0.576769	−	0.816907i	$-0.304313\pi$
$17$	531597.	−	193485.i	1.54370	−	0.561860i	0.966929	+	0.255047i	$0.0820909\pi$
$18$	912904.			2.04974
$19$	553507.	−	127742.i	0.974387	−	0.224876i
$19$	553507.	−	127742.i	0.974387	−	0.224876i
$20$	−345151.			−0.482363
$21$	−2.19746e6	+	799811.i	−2.46567	+	0.897430i
$22$	−123958.	+	703000.i	−0.112816	+	0.639813i
$23$	197348.	−	165595.i	0.147048	−	0.123388i	−0.566296	−	0.824202i	$-0.691624\pi$
$23$	197348.	−	165595.i	0.147048	−	0.123388i	0.713344	+	0.700814i	$0.247180\pi$
$24$	869207.	+	729351.i	0.534777	+	0.448731i
$25$	−23505.4	−	133305.i	−0.0120347	−	0.0682524i
$26$	−118461.	−	205180.i	−0.0508387	−	0.0880551i
$27$	−5.17658e6	+	8.96610e6i	−1.87459	+	3.24688i
$28$	−2.03073e6	−	739125.i	−0.624368	−	0.227252i
$29$	−2.67815e6	−	974768.i	−0.703144	−	0.255924i	−0.0343915	−	0.999408i	$-0.510949\pi$
$29$	−2.67815e6	−	974768.i	−0.703144	−	0.255924i	−0.668753	+	0.743485i	$0.733172\pi$
$30$	2.98791e6	−	5.17522e6i	0.673476	−	1.16650i
$31$	484230.	+	838712.i	0.0941726	+	0.163112i	0.909263	−	0.416222i	$-0.136646\pi$
$31$	484230.	+	838712.i	0.0941726	+	0.163112i	−0.815090	+	0.579334i	$0.803313\pi$
$32$	182083.	+	1.03265e6i	0.0306970	+	0.174091i
$33$	−9.46775e6	−	7.94439e6i	−1.38974	−	1.16613i
$34$	−6.93379e6	+	5.81814e6i	−0.889847	+	0.746671i
$35$	−1.97636e6	+	1.12085e7i	−0.222617	+	1.26253i
$36$	−1.37256e7	+	4.99570e6i	−1.36198	+	0.495719i
$37$	1.96280e7			1.72174			0.860871	−	0.508822i	$-0.169919\pi$
$37$	1.96280e7			1.72174			0.860871	+	0.508822i	$0.169919\pi$
$38$	−7.62297e6	+	4.94958e6i	−0.593059	+	0.385072i
$39$	4.10198e6			0.283924
$40$	5.18937e6	−	1.88878e6i	0.320512	−	0.116657i
$41$	314812.	−	1.78539e6i	0.0173990	−	0.0986747i	−0.974872	−	0.222767i	$-0.928491\pi$
$41$	314812.	−	1.78539e6i	0.0173990	−	0.0986747i	0.992271	+	0.124093i	$0.0396020\pi$
$42$	2.86622e7	−	2.40504e7i	1.42131	−	1.19262i
$43$	1.46654e7	+	1.23057e7i	0.654161	+	0.548906i	0.908330	−	0.418254i	$-0.137358\pi$
$43$	1.46654e7	+	1.23057e7i	0.654161	+	0.548906i	−0.254170	+	0.967160i	$0.581802\pi$
$44$	−1.98332e6	−	1.12480e7i	−0.0797732	−	0.452416i
$45$	3.84630e7	+	6.66199e7i	1.39826	+	2.42185i
$46$	−2.06096e6	+	3.56969e6i	−0.0678671	+	0.117549i
$47$	5.24121e6	+	1.90764e6i	0.156672	+	0.0570239i	0.419166	−	0.907910i	$-0.362323\pi$
$47$	5.24121e6	+	1.90764e6i	0.156672	+	0.0570239i	−0.262494	+	0.964934i	$0.584545\pi$
$48$	−1.70598e7	−	6.20928e6i	−0.463863	−	0.168832i
$49$	−1.54537e7	+	2.67667e7i	−0.382958	+	0.663303i
$50$	1.08290e6	+	1.87563e6i	0.0245031	+	0.0424407i
$51$	−2.72130e7	−	1.54333e8i	−0.563262	−	3.19442i
$52$	2.90388e6	+	2.43664e6i	0.0550761	+	0.0462143i
$53$	−1.47585e7	+	1.23839e7i	−0.256923	+	0.215584i	−0.762146	−	0.647405i	$-0.775854\pi$
$53$	−1.47585e7	+	1.23839e7i	−0.256923	+	0.215584i	0.505224	+	0.862988i	$0.331410\pi$
$54$	2.87649e7	−	1.63134e8i	0.460353	−	2.61079i
$55$	−5.65247e7	+	2.05733e7i	−0.832925	+	0.303160i
$56$	3.45769e7			0.469829
$57$	−8.22360e6	−	1.57147e8i	−0.103187	−	1.97183i
$58$	4.56005e7			0.529107
$59$	−1.43703e8	+	5.23036e7i	−1.54394	+	0.561949i	−0.966987	−	0.254826i	$-0.917982\pi$
$59$	−1.43703e8	+	5.23036e7i	−1.54394	+	0.561949i	−0.576956	+	0.816775i	$0.695760\pi$
$60$	−1.66031e7	+	9.41607e7i	−0.165389	+	0.937970i
$61$	8.15154e7	−	6.83996e7i	0.753799	−	0.632512i	−0.182706	−	0.983168i	$-0.558486\pi$
$61$	8.15154e7	−	6.83996e7i	0.753799	−	0.632512i	0.936505	+	0.350655i	$0.114041\pi$
$62$	−1.18701e7	−	9.96023e6i	−0.102022	−	0.0856065i
$63$	8.36376e7	+	4.74332e8i	0.668912	+	3.79359i
$64$	−8.38861e6	−	1.45295e7i	−0.0625000	−	0.108253i
$65$	9.98212e6	−	1.72895e7i	0.0693606	−	0.120136i
$66$	1.85823e8	+	6.76339e7i	1.20546	+	0.438750i
$67$	−1.02415e8	−	3.72759e7i	−0.620907	−	0.225992i	0.0123621	−	0.999924i	$-0.496065\pi$
$67$	−1.02415e8	−	3.72759e7i	−0.620907	−	0.225992i	−0.633269	+	0.773932i	$0.718287\pi$
$68$	7.24114e7	−	1.25420e8i	0.410692	−	0.711340i
$69$	−3.56828e7	−	6.18044e7i	−0.189513	−	0.328245i
$70$	−3.16217e7	−	1.79336e8i	−0.157414	−	0.892740i
$71$	1.71859e8	+	1.44207e8i	0.802618	+	0.673476i	0.948834	−	0.315776i	$-0.102265\pi$
$71$	1.71859e8	+	1.44207e8i	0.802618	+	0.673476i	−0.146216	+	0.989253i	$0.546709\pi$
$72$	1.79027e8	−	1.50222e8i	0.785096	−	0.658774i
$73$	6.78679e7	−	3.84898e8i	0.279712	−	1.58633i	−0.443872	−	0.896090i	$-0.646396\pi$
$73$	6.78679e7	−	3.84898e8i	0.279712	−	1.58633i	0.723584	−	0.690236i	$-0.242493\pi$
$74$	−2.95109e8	+	1.07411e8i	−1.14403	+	0.416395i
$75$	−3.74978e7			−0.136845
$76$	8.75263e7	−	1.16133e8i	0.300938	−	0.399295i
$77$	−3.76626e8			−1.22096
$78$	−6.16736e7	+	2.24474e7i	−0.188657	+	0.0686656i
$79$	3.96818e7	−	2.25047e8i	0.114622	−	0.650056i	−0.872314	−	0.488946i	$-0.837382\pi$
$79$	3.96818e7	−	2.25047e8i	0.114622	−	0.650056i	0.986936	−	0.161110i	$-0.0515074\pi$
$80$	−6.76866e7	+	5.67958e7i	−0.184756	+	0.155028i
$81$	1.33673e9	+	1.12165e9i	3.45034	+	2.89518i
$82$	5.03700e6	+	2.85662e7i	0.0123030	+	0.0697735i
$83$	−5.77224e7	−	9.99781e7i	−0.133504	−	0.231235i	0.791521	−	0.611142i	$-0.209289\pi$
$83$	−5.77224e7	−	9.99781e7i	−0.133504	−	0.231235i	−0.925025	+	0.379907i	$0.875956\pi$
$84$	−2.99327e8	+	5.18449e8i	−0.655977	+	1.13619i
$85$	−7.16723e8	−	2.60866e8i	−1.48924	−	0.542041i
$86$	−2.87835e8	−	1.04764e8i	−0.567416	−	0.206522i
$87$	−3.94756e8	+	6.83738e8i	−0.738741	+	1.27954i
$88$	9.13721e7	+	1.58261e8i	0.162421	+	0.281321i
$89$	−4.82939e7	−	2.73888e8i	−0.0815900	−	0.462720i	−0.998040	−	0.0625718i	$-0.980070\pi$
$89$	−4.82939e7	−	2.73888e8i	−0.0815900	−	0.462720i	0.916450	−	0.400148i	$-0.131041\pi$
$90$	−9.42861e8	−	7.91154e8i	−1.51480	−	1.27107i
$91$	9.57556e7	−	8.03485e7i	0.146379	−	0.122826i
$92$	1.14522e7	−	6.49488e7i	0.0166665	−	0.0945204i
$93$	2.52103e8	−	9.17578e7i	0.349465	−	0.127195i
$94$	−8.92412e7			−0.117894
$95$	−6.82376e8	−	3.47754e8i	−0.859543	−	0.438042i
$96$	2.90475e8			0.349051
$97$	6.40413e8	−	2.33091e8i	0.734492	−	0.267333i	0.0524272	−	0.998625i	$-0.483304\pi$
$97$	6.40413e8	−	2.33091e8i	0.734492	−	0.267333i	0.682065	+	0.731291i	$0.261082\pi$
$98$	8.58725e7	−	4.87007e8i	0.0940452	−	0.533357i
$99$	−1.95004e9	+	1.63627e9i	−2.04025	+	1.71198i
$100$	−2.65455e7	−	2.22743e7i	−0.0265455	−	0.0222743i
$101$	−1.68936e8	−	9.58082e8i	−0.161538	−	0.916128i	−0.952562	−	0.304344i	$-0.901563\pi$
$101$	−1.68936e8	−	9.58082e8i	−0.161538	−	0.916128i	0.791024	−	0.611785i	$-0.209548\pi$
$102$	1.25371e9	+	2.17148e9i	1.14682	+	1.98635i
$103$	−7.20750e8	+	1.24838e9i	−0.630982	+	1.09289i	0.356369	+	0.934345i	$0.384014\pi$
$103$	−7.20750e8	+	1.24838e9i	−0.630982	+	1.09289i	−0.987351	+	0.158548i	$0.949319\pi$
$104$	−5.69941e7	−	2.07442e7i	−0.0477727	−	0.0173878i
$105$	2.96272e9	+	1.07834e9i	2.37869	+	0.865773i
$106$	1.54127e8	−	2.66956e8i	0.118578	−	0.205383i
$107$	−2.39031e8	−	4.14014e8i	−0.176290	−	0.305343i	0.764317	−	0.644841i	$-0.223076\pi$
$107$	−2.39031e8	−	4.14014e8i	−0.176290	−	0.305343i	−0.940607	+	0.339498i	$0.889743\pi$
$108$	4.60239e8	+	2.61014e9i	0.325519	+	1.84611i
$109$	1.91213e8	+	1.60447e8i	0.129747	+	0.108871i	0.705352	−	0.708857i	$-0.250789\pi$
$109$	1.91213e8	+	1.60447e8i	0.129747	+	0.108871i	−0.575605	+	0.817728i	$0.695233\pi$
$110$	7.37269e8	−	6.18642e8i	0.480130	−	0.402877i
$111$	9.44182e8	−	5.35472e9i	0.590340	−	3.34799i
$112$	−5.19867e8	+	1.89216e8i	−0.312184	+	0.113626i
$113$	−5.80148e8			−0.334723			−0.167362	−	0.985896i	$-0.553525\pi$
$113$	−5.80148e8			−0.334723			−0.167362	+	0.985896i	$0.553525\pi$
$114$	9.83603e8	+	2.31772e9i	0.545441	+	1.28525i
$115$	−3.47335e8			−0.185186
$116$	−6.85607e8	+	2.49541e8i	−0.351572	+	0.127962i
$117$	1.46710e8	−	8.32033e8i	0.0723807	−	0.410491i
$118$	1.87436e9	−	1.57278e9i	0.889989	−	0.746789i
$119$	−3.65828e9	−	3.06966e9i	−1.67231	−	1.40323i
$120$	−2.65649e8	−	1.50657e9i	−0.116948	−	0.663245i
$121$	1.83712e8	+	3.18199e8i	0.0779120	+	0.134947i
$122$	−8.51287e8	+	1.47447e9i	−0.347902	+	0.602584i
$123$	−4.71929e8	−	1.71768e8i	−0.185910	−	0.0676659i
$124$	2.32974e8	+	8.47957e7i	0.0884933	+	0.0322089i
$125$	−1.40790e9	+	2.43855e9i	−0.515793	+	0.893379i
$126$	−3.85320e9	−	6.67393e9i	−1.36193	−	2.35893i
$127$	6.06998e8	+	3.44245e9i	0.207048	+	1.17423i	0.894185	+	0.447698i	$0.147756\pi$
$127$	6.06998e8	+	3.44245e9i	0.207048	+	1.17423i	−0.687137	+	0.726528i	$0.741133\pi$
$128$	2.05633e8	+	1.72547e8i	0.0677094	+	0.0568149i
$129$	4.06258e9	−	3.40891e9i	1.29166	−	1.08383i
$130$	−5.54681e7	+	3.14575e8i	−0.0170333	+	0.0966004i
$131$	3.60457e9	−	1.31196e9i	1.06938	−	0.389223i	0.253436	−	0.967352i	$-0.418439\pi$
$131$	3.60457e9	−	1.31196e9i	1.06938	−	0.389223i	0.815945	+	0.578129i	$0.196217\pi$
$132$	−3.16397e9			−0.907090
$133$	−3.27013e9	−	3.50733e9i	−0.906218	−	0.971950i
$134$	1.74380e9			0.467224
$135$	1.31168e10	−	4.77412e9i	3.39880	−	1.23706i
$136$	−4.02371e8	+	2.28196e9i	−0.100856	+	0.571983i
$137$	−1.61458e9	+	1.35480e9i	−0.391577	+	0.328572i	−0.817227	−	0.576315i	$-0.804490\pi$
$137$	−1.61458e9	+	1.35480e9i	−0.391577	+	0.328572i	0.425650	+	0.904888i	$0.360046\pi$
$138$	8.74708e8	+	7.33967e8i	0.205309	+	0.172274i
$139$	−5.39495e8	−	3.05963e9i	−0.122580	−	0.695187i	−0.982716	−	0.185122i	$-0.940732\pi$
$139$	−5.39495e8	−	3.05963e9i	−0.122580	−	0.695187i	0.860135	−	0.510066i	$-0.170379\pi$
$140$	1.45682e9	+	2.52328e9i	0.320501	+	0.555123i
$141$	7.72547e8	−	1.33809e9i	0.164603	−	0.285102i
$142$	−3.37305e9	−	1.22769e9i	−0.696187	−	0.253391i
$143$	6.20803e8	+	2.25954e8i	0.124148	+	0.0451863i
$144$	−1.86963e9	+	3.23829e9i	−0.362346	+	0.627602i
$145$	1.92127e9	+	3.32774e9i	0.360938	+	0.625162i
$146$	1.08589e9	+	6.15836e9i	0.197786	+	1.12170i
$147$	6.55884e9	+	5.50352e9i	1.15851	+	0.972104i
$148$	3.84920e9	−	3.22986e9i	0.659466	−	0.553358i
$149$	−1.07799e9	+	6.11358e9i	−0.179175	+	1.01615i	0.754040	+	0.656829i	$0.228103\pi$
$149$	−1.07799e9	+	6.11358e9i	−0.179175	+	1.01615i	−0.933214	+	0.359321i	$0.883008\pi$
$150$	5.63783e8	−	2.05200e8i	0.0909287	−	0.0330953i
$151$	8.21798e9			1.28638			0.643190	−	0.765707i	$-0.277611\pi$
$151$	8.21798e9			1.28638			0.643190	+	0.765707i	$0.277611\pi$
$152$	−6.80449e8	+	2.22504e9i	−0.103395	+	0.338097i
$153$	−3.22776e10			−4.76201
$154$	5.66260e9	−	2.06102e9i	0.811283	−	0.295283i
$155$	2.26736e8	−	1.28588e9i	0.0315521	−	0.178941i
$156$	8.04429e8	−	6.74996e8i	0.108749	−	0.0912516i
$157$	1.74357e8	+	1.46303e8i	0.0229030	+	0.0192179i	0.654167	−	0.756350i	$-0.273019\pi$
$157$	1.74357e8	+	1.46303e8i	0.0229030	+	0.0192179i	−0.631264	+	0.775568i	$0.717464\pi$
$158$	6.34909e8	+	3.60075e9i	0.0810503	+	0.459659i
$159$	2.66851e9	+	4.62200e9i	0.331117	+	0.573512i
$160$	7.06868e8	−	1.22433e9i	0.0852705	−	0.147693i
$161$	−2.04358e9	−	7.43802e8i	−0.239704	−	0.0872451i
$162$	−2.62359e10	−	9.54909e9i	−2.99280	−	1.08929i
$163$	3.79229e9	−	6.56843e9i	0.420782	−	0.728815i	−0.575234	−	0.817989i	$-0.695089\pi$
$163$	3.79229e9	−	6.56843e9i	0.420782	−	0.728815i	0.996016	+	0.0891732i	$0.0284225\pi$
$164$	−2.32055e8	−	4.01932e8i	−0.0250492	−	0.0433865i
$165$	2.89356e9	+	1.64102e10i	0.303916	+	1.72360i
$166$	1.41497e9	+	1.18730e9i	0.144631	+	0.121360i
$167$	−1.30241e10	+	1.09285e10i	−1.29576	+	1.08727i	−0.304896	+	0.952386i	$0.598622\pi$
$167$	−1.30241e10	+	1.09285e10i	−1.29576	+	1.08727i	−0.990861	+	0.134884i	$0.956934\pi$
$168$	1.66328e9	−	9.43294e9i	0.161092	−	0.913598i
$169$	9.75893e9	−	3.55196e9i	0.920263	−	0.334948i
$170$	1.22035e10			1.12064
$171$	−3.21694e10	−	3.95242e9i	−2.87714	−	0.353493i
$172$	4.90093e9			0.426973
$173$	−1.57418e10	+	5.72956e9i	−1.33613	+	0.486311i	−0.908591	−	0.417687i	$-0.862841\pi$
$173$	−1.57418e10	+	5.72956e9i	−1.33613	+	0.486311i	−0.427537	+	0.903998i	$0.640619\pi$
$174$	2.19356e9	−	1.24403e10i	0.181417	−	1.02887i
$175$	−8.75340e8	+	7.34497e8i	−0.0705514	+	0.0591996i
$176$	−2.23984e9	−	1.87945e9i	−0.175959	−	0.147647i
$177$	7.35630e9	+	4.17196e10i	0.563352	+	3.19493i
$178$	2.22491e9	+	3.85365e9i	0.166120	+	0.287728i
$179$	8.04903e8	−	1.39413e9i	0.0586009	−	0.101500i	−0.835237	−	0.549891i	$-0.814669\pi$
$179$	8.04903e8	−	1.39413e9i	0.0586009	−	0.101500i	0.893838	+	0.448391i	$0.148003\pi$
$180$	1.85054e10	+	6.73543e9i	1.31393	+	0.478232i
$181$	−1.64151e9	−	5.97460e8i	−0.113681	−	0.0413766i	0.284553	−	0.958660i	$-0.408155\pi$
$181$	−1.64151e9	−	5.97460e8i	−0.113681	−	0.0413766i	−0.398235	+	0.917284i	$0.630377\pi$
$182$	−1.00000e9	+	1.73205e9i	−0.0675584	+	0.117015i
$183$	−1.47389e10	−	2.55285e10i	−0.971483	−	1.68266i
$184$	1.83236e8	+	1.03918e9i	0.0117850	+	0.0668360i
$185$	−2.02721e10	−	1.70103e10i	−1.27241	−	1.06768i
$186$	−3.28825e9	+	2.75917e9i	−0.201445	+	0.169033i
$187$	4.38279e9	−	2.48560e10i	0.262098	−	1.48643i
$188$	1.34175e9	−	4.88357e8i	0.0783359	−	0.0285119i
$189$	8.73975e10			4.98220
$190$	1.21626e10	+	1.49433e9i	0.677073	+	0.0831870i
$191$	1.57960e10			0.858810			0.429405	−	0.903112i	$-0.358723\pi$
$191$	1.57960e10			0.858810			0.429405	+	0.903112i	$0.358723\pi$
$192$	−4.36732e9	+	1.58957e9i	−0.231931	+	0.0844161i
$193$	−2.66853e9	+	1.51340e10i	−0.138441	+	0.785138i	0.833961	+	0.551824i	$0.186068\pi$
$193$	−2.66853e9	+	1.51340e10i	−0.138441	+	0.785138i	−0.972402	+	0.233314i	$0.925043\pi$
$194$	−8.35311e9	+	7.00909e9i	−0.423390	+	0.355266i
$195$	−4.23659e9	−	3.55492e9i	−0.209827	−	0.176065i
$196$	1.37396e9	+	7.79211e9i	0.0665000	+	0.377140i
$197$	1.04153e10	+	1.80399e10i	0.492691	+	0.853367i	0.999965	−	0.00841867i	$-0.00267978\pi$
$197$	1.04153e10	+	1.80399e10i	0.492691	+	0.853367i	−0.507273	+	0.861785i	$0.669346\pi$
$198$	2.03647e10	−	3.52727e10i	0.941641	−	1.63097i
$199$	−1.03354e10	−	3.76179e9i	−0.467186	−	0.170042i	0.0976912	−	0.995217i	$-0.468854\pi$
$199$	−1.03354e10	−	3.76179e9i	−0.467186	−	0.170042i	−0.564877	+	0.825175i	$0.691076\pi$
$200$	5.21005e8	+	1.89630e8i	0.0230254	+	0.00838056i
$201$	−1.50958e10	+	2.61467e10i	−0.652340	+	1.12989i
$202$	7.78289e9	+	1.34804e10i	0.328897	+	0.569666i
$203$	4.17779e9	+	2.36934e10i	0.172669	+	0.979254i
$204$	−3.07327e10	−	2.57878e10i	−1.24241	−	1.04250i
$205$	−1.87242e9	+	1.57115e9i	−0.0740477	+	0.0621334i
$206$	4.00502e9	−	2.27136e10i	0.154954	−	0.878787i
$207$	−1.38124e10	+	5.02732e9i	−0.522882	+	0.190314i
$208$	9.70430e8			0.0359484
$209$	7.41173e9	−	2.42360e10i	0.268696	−	0.878623i
$210$	−5.04457e10			−1.78994
$211$	4.24491e10	−	1.54502e10i	1.47434	−	0.536615i	0.525064	−	0.851063i	$-0.324041\pi$
$211$	4.24491e10	−	1.54502e10i	1.47434	−	0.536615i	0.949275	+	0.314447i	$0.101819\pi$
$212$	−8.56446e8	+	4.85715e9i	−0.0291198	+	0.165147i
$213$	4.76081e10	−	3.99479e10i	1.58479	−	1.32980i
$214$	5.85947e9	+	4.91668e9i	0.190984	+	0.160254i
$215$	−4.48206e9	−	2.54190e10i	−0.143055	−	0.811308i
$216$	−2.12033e10	−	3.67251e10i	−0.662767	−	1.14795i
$217$	4.08769e9	−	7.08009e9i	0.125144	−	0.216755i
$218$	−3.75292e9	−	1.36595e9i	−0.112542	−	0.0409619i
$219$	−1.01739e11	−	3.70301e10i	−2.98876	−	1.08782i
$220$	−7.69949e9	+	1.33359e10i	−0.221595	+	0.383814i
$221$	4.18843e9	+	7.25457e9i	0.118110	+	0.204572i
$222$	1.51069e10	+	8.56756e10i	0.417434	+	2.36738i
$223$	−1.17189e10	−	9.83332e9i	−0.317333	−	0.266274i	0.470182	−	0.882569i	$-0.344188\pi$
$223$	−1.17189e10	−	9.83332e9i	−0.317333	−	0.266274i	−0.787515	+	0.616296i	$0.788633\pi$
$224$	6.78079e9	−	5.68976e9i	0.179955	−	0.151000i
$225$	−1.34113e9	+	7.60594e9i	−0.0348859	+	0.197848i
$226$	8.72257e9	−	3.17476e9i	0.222411	−	0.0809511i
$227$	3.00803e10			0.751911			0.375955	−	0.926638i	$-0.377315\pi$
$227$	3.00803e10			0.751911			0.375955	+	0.926638i	$0.377315\pi$
$228$	−2.74719e10	−	2.94645e10i	−0.673258	−	0.722092i
$229$	2.52051e10			0.605659			0.302829	−	0.953045i	$-0.402069\pi$
$229$	2.52051e10			0.605659			0.302829	+	0.953045i	$0.402069\pi$
$230$	5.22221e9	−	1.90073e9i	0.123049	−	0.0447862i
$231$	−1.81171e10	+	1.02747e11i	−0.418635	+	2.37420i
$232$	8.94259e9	−	7.50373e9i	0.202660	−	0.170052i
$233$	−2.94229e10	−	2.46887e10i	−0.654008	−	0.548778i	0.254276	−	0.967132i	$-0.418163\pi$
$233$	−2.94229e10	−	2.46887e10i	−0.654008	−	0.548778i	−0.908284	+	0.418354i	$0.862607\pi$
$234$	2.34736e9	+	1.33125e10i	0.0511809	+	0.290261i
$235$	−3.75997e9	−	6.51246e9i	−0.0804227	−	0.139296i
$236$	−1.95744e10	+	3.39039e10i	−0.410758	+	0.711453i
$237$	−5.94862e10	−	2.16512e10i	−1.22475	−	0.445774i
$238$	7.18007e10	+	2.61333e10i	1.45055	+	0.527957i
$239$	−1.96263e10	+	3.39938e10i	−0.389088	+	0.673921i	−0.992327	−	0.123640i	$-0.960543\pi$
$239$	−1.96263e10	+	3.39938e10i	−0.389088	+	0.673921i	0.603239	+	0.797561i	$0.293877\pi$
$240$	1.22385e10	+	2.11977e10i	0.238110	+	0.412418i
$241$	5.46737e9	+	3.10070e10i	0.104400	+	0.592083i	0.991458	+	0.130425i	$0.0416342\pi$
$241$	5.46737e9	+	3.10070e10i	0.104400	+	0.592083i	−0.887058	+	0.461658i	$0.847255\pi$
$242$	−4.50342e9	−	3.77882e9i	−0.0844060	−	0.0708250i
$243$	2.14194e11	−	1.79730e11i	3.94076	−	3.30669i
$244$	4.73038e9	−	2.68273e10i	0.0854362	−	0.484533i
$245$	3.91578e10	−	1.42523e10i	0.694338	−	0.252718i
$246$	8.03546e9			0.139895
$247$	3.28605e9	+	7.74311e9i	0.0561744	+	0.132367i
$248$	−3.96681e9			−0.0665901
$249$	−3.00517e10	+	1.09379e10i	−0.495419	+	0.180318i
$250$	7.82331e9	−	4.43682e10i	0.126666	−	0.718359i
$251$	−6.21032e10	+	5.21107e10i	−0.987602	+	0.828697i	−0.985219	−	0.171301i	$-0.945203\pi$
$251$	−6.21032e10	+	5.21107e10i	−0.987602	+	0.828697i	−0.00238334	+	0.999997i	$0.500759\pi$
$252$	9.44550e10	+	7.92572e10i	1.47544	+	1.23804i
$253$	−1.99588e9	−	1.13192e10i	−0.0306261	−	0.173689i
$254$	−2.79645e10	−	4.84359e10i	−0.421556	−	0.730156i
$255$	−1.05644e11	+	1.82981e11i	−1.56464	+	2.71003i
$256$	−4.03595e9	−	1.46897e9i	−0.0587308	−	0.0213763i
$257$	−2.47621e10	−	9.01266e9i	−0.354069	−	0.128871i	0.158861	−	0.987301i	$-0.449218\pi$
$257$	−2.47621e10	−	9.01266e9i	−0.354069	−	0.128871i	−0.512930	+	0.858430i	$0.671440\pi$
$258$	−4.24266e10	+	7.34850e10i	−0.596141	+	1.03255i
$259$	−8.28462e10	−	1.43494e11i	−1.14399	−	1.98145i
$260$	−8.87489e8	−	5.03320e9i	−0.0120443	−	0.0683068i
$261$	1.24569e11	+	1.04525e11i	1.66160	+	1.39425i
$262$	−4.70156e10	+	3.94507e10i	−0.616433	+	0.517249i
$263$	−4.03708e9	+	2.28954e10i	−0.0520316	+	0.295086i	−0.999708	−	0.0241454i	$-0.992314\pi$
$263$	−4.03708e9	+	2.28954e10i	−0.0520316	+	0.295086i	0.947677	+	0.319231i	$0.103425\pi$
$264$	4.75706e10	−	1.73143e10i	0.602728	−	0.219375i
$265$	2.59752e10			0.323558
$266$	6.83599e10	+	3.48377e10i	0.837209	+	0.426661i
$267$	−7.70427e10			−0.927749
$268$	−2.62182e10	+	9.54264e9i	−0.310453	+	0.112996i
$269$	8.89815e9	−	5.04639e10i	0.103613	−	0.587619i	−0.888152	−	0.459550i	$-0.848011\pi$
$269$	8.89815e9	−	5.04639e10i	0.103613	−	0.587619i	0.991765	−	0.128069i	$-0.0408780\pi$
$270$	−1.71086e11	+	1.43559e11i	−1.95920	+	1.64396i
$271$	−1.18122e11	−	9.91157e10i	−1.33035	−	1.11630i	−0.983995	−	0.178197i	$-0.942973\pi$
$271$	−1.18122e11	−	9.91157e10i	−1.33035	−	1.11630i	−0.346359	−	0.938102i	$-0.612582\pi$
$272$	−6.43794e9	−	3.65114e10i	−0.0713160	−	0.404453i
$273$	−1.73137e10	−	2.99882e10i	−0.188650	−	0.326752i
$274$	1.68615e10	−	2.92050e10i	0.180725	−	0.313025i
$275$	−5.67500e9	−	2.06553e9i	−0.0598369	−	0.0217788i
$276$	−1.71678e10	−	6.24857e9i	−0.178084	−	0.0648171i
$277$	−2.32334e10	+	4.02414e10i	−0.237112	+	0.410690i	−0.959884	−	0.280396i	$-0.909534\pi$
$277$	−2.32334e10	+	4.02414e10i	−0.237112	+	0.410690i	0.722773	+	0.691086i	$0.242867\pi$
$278$	2.48546e10	+	4.30495e10i	0.249578	+	0.432281i
$279$	−9.59527e9	−	5.44175e10i	−0.0948065	−	0.537675i
$280$	−3.57116e10	−	2.99656e10i	−0.347214	−	0.291347i
$281$	5.67626e10	−	4.76294e10i	0.543105	−	0.455719i	−0.329493	−	0.944158i	$-0.606878\pi$
$281$	5.67626e10	−	4.76294e10i	0.543105	−	0.455719i	0.872598	+	0.488439i	$0.162434\pi$
$282$	−4.29284e9	+	2.43459e10i	−0.0404226	+	0.229248i
$283$	1.06355e11	−	3.87102e10i	0.985644	−	0.358745i	0.201612	−	0.979465i	$-0.435382\pi$
$283$	1.06355e11	−	3.87102e10i	0.985644	−	0.358745i	0.784032	+	0.620720i	$0.213160\pi$
$284$	5.74325e10			0.523872
$285$	−1.27696e11	+	1.69431e11i	−1.14650	+	1.52122i
$286$	−1.05703e10			−0.0934201
$287$	−1.43812e10	+	5.23431e9i	−0.125120	+	0.0455398i
$288$	1.03890e10	−	5.89191e10i	0.0889834	−	0.504650i
$289$	1.54315e11	−	1.29486e11i	1.30127	−	1.09190i
$290$	−4.70969e10	−	3.95190e10i	−0.391022	−	0.328106i
$291$	−3.27834e10	−	1.85924e11i	−0.268000	−	1.51991i
$292$	−5.00269e10	−	8.66492e10i	−0.402699	−	0.697496i
$293$	−6.04047e10	+	1.04624e11i	−0.478813	+	0.829329i	−0.999705	−	0.0242939i	$-0.992266\pi$
$293$	−6.04047e10	+	1.04624e11i	−0.478813	+	0.829329i	0.520892	+	0.853623i	$0.325600\pi$
$294$	−1.28730e11	−	4.68538e10i	−1.00488	−	0.365748i
$295$	1.93747e11	+	7.05180e10i	1.48948	+	0.542127i
$296$	−4.01981e10	+	6.96252e10i	−0.304364	+	0.527174i
$297$	2.30955e11	+	4.00025e11i	1.72235	+	2.98321i
$298$	−1.72478e10	−	9.78173e10i	−0.126696	−	0.718526i
$299$	2.92225e9	+	2.45206e9i	0.0211445	+	0.0177423i
$300$	−7.35360e9	+	6.17040e9i	−0.0524148	+	0.0439813i
$301$	2.80631e10	−	1.59154e11i	0.197054	−	1.11755i
$302$	−1.23558e11	+	4.49715e10i	−0.854751	+	0.311104i
$303$	−2.69501e11			−1.83683
$304$	−1.94551e9	−	3.71773e10i	−0.0130648	−	0.249658i
$305$	−1.43468e11			−0.949304
$306$	4.85297e11	−	1.76634e11i	3.16418	−	1.15167i
$307$	−2.31247e10	+	1.31147e11i	−0.148578	+	0.842627i	0.815847	+	0.578268i	$0.196271\pi$
$307$	−2.31247e10	+	1.31147e11i	−0.148578	+	0.842627i	−0.964425	+	0.264358i	$0.914840\pi$
$308$	−7.38591e10	+	6.19751e10i	−0.467655	+	0.392409i
$309$	3.05899e11	+	2.56680e11i	1.90882	+	1.60169i
$310$	3.62778e9	+	2.05742e10i	0.0223107	+	0.126530i
$311$	9.11680e10	+	1.57908e11i	0.552613	+	0.957153i	0.998085	+	0.0618574i	$0.0197024\pi$
$311$	9.11680e10	+	1.57908e11i	0.552613	+	0.957153i	−0.445472	+	0.895296i	$0.646964\pi$
$312$	−8.40085e9	+	1.45507e10i	−0.0501912	+	0.0869338i
$313$	3.92304e10	+	1.42787e10i	0.231033	+	0.0840890i	0.454942	−	0.890521i	$-0.349660\pi$
$313$	3.92304e10	+	1.42787e10i	0.231033	+	0.0840890i	−0.223910	+	0.974610i	$0.571882\pi$
$314$	−3.42210e9	−	1.24554e9i	−0.0198659	−	0.00723060i
$315$	3.24691e11	−	5.62381e11i	1.85811	−	3.21835i
$316$	−2.92504e10	−	5.06631e10i	−0.165021	−	0.285825i
$317$	−5.48880e10	−	3.11285e11i	−0.305289	−	1.73138i	−0.622143	−	0.782903i	$-0.713738\pi$
$317$	−5.48880e10	−	3.11285e11i	−0.305289	−	1.73138i	0.316855	−	0.948474i	$-0.397373\pi$
$318$	−6.54144e10	−	5.48892e10i	−0.358716	−	0.300999i
$319$	−9.74063e10	+	8.17336e10i	−0.526659	+	0.441919i
$320$	−3.92789e9	+	2.22761e10i	−0.0209403	+	0.118759i
$321$	−1.24446e11	+	4.52945e10i	−0.654194	+	0.238107i
$322$	3.47957e10			0.180374
$323$	2.69526e11	−	1.75003e11i	1.37781	−	0.894610i
$324$	4.46715e11			2.25205
$325$	1.88350e9	−	6.85539e8i	0.00936464	−	0.00340845i
$326$	−2.10728e10	+	1.19510e11i	−0.103334	+	0.586035i
$327$	5.29696e10	−	4.44468e10i	0.256190	−	0.214969i
$328$	5.68847e9	+	4.77319e9i	0.0271371	+	0.0227707i
$329$	−8.17602e9	−	4.63685e10i	−0.0384734	−	0.218193i
$330$	−1.33307e11	−	2.30894e11i	−0.618784	−	1.07176i
$331$	−7.70405e10	+	1.33438e11i	−0.352771	+	0.611018i	−0.986734	−	0.162346i	$-0.948094\pi$
$331$	−7.70405e10	+	1.33438e11i	−0.352771	+	0.611018i	0.633963	+	0.773364i	$0.281427\pi$
$332$	−2.77716e10	−	1.01080e10i	−0.125452	−	0.0456609i
$333$	−1.05237e12	−	3.83030e11i	−4.68995	−	1.70700i
$334$	1.36014e11	−	2.35583e11i	0.598033	−	1.03582i
$335$	7.34710e10	+	1.27255e11i	0.318723	+	0.552045i
$336$	2.66125e10	+	1.50927e11i	0.113909	+	0.646012i
$337$	3.02907e11	+	2.54169e11i	1.27930	+	1.07346i	0.993339	+	0.115224i	$0.0367587\pi$
$337$	3.02907e11	+	2.54169e11i	1.27930	+	1.07346i	0.285965	+	0.958240i	$0.407686\pi$
$338$	−1.27289e11	+	1.06808e11i	−0.530475	+	0.445122i
$339$	−2.79073e10	+	1.58270e11i	−0.114768	+	0.650880i
$340$	−1.83481e11	+	6.67816e10i	−0.744622	+	0.271020i
$341$	4.32081e10			0.173050
$342$	5.05298e11	−	1.16616e11i	1.99724	−	0.460937i
$343$	−7.97406e10			−0.311068
$344$	−7.36859e10	+	2.68195e10i	−0.283708	+	0.103261i
$345$	−1.67081e10	+	9.47565e10i	−0.0634954	+	0.360100i
$346$	2.05326e11	−	1.72289e11i	0.770196	−	0.646271i
$347$	−1.15812e11	−	9.71776e10i	−0.428815	−	0.359818i	0.402689	−	0.915337i	$-0.368075\pi$
$347$	−1.15812e11	−	9.71776e10i	−0.428815	−	0.359818i	−0.831504	+	0.555518i	$0.812520\pi$
$348$	3.50969e10	+	1.99045e11i	0.128281	+	0.727518i
$349$	1.69169e10	+	2.93010e10i	0.0610389	+	0.105722i	0.894930	−	0.446206i	$-0.147225\pi$
$349$	1.69169e10	+	2.93010e10i	0.0610389	+	0.105722i	−0.833891	+	0.551929i	$0.813892\pi$
$350$	9.14140e9	−	1.58334e10i	0.0325617	−	0.0563985i
$351$	−1.44060e11	−	5.24335e10i	−0.506595	−	0.184385i
$352$	4.39612e10	+	1.60006e10i	0.152626	+	0.0555512i
$353$	1.11159e11	−	1.92533e11i	0.381030	−	0.659963i	−0.610180	−	0.792263i	$-0.708903\pi$
$353$	1.11159e11	−	1.92533e11i	0.381030	−	0.659963i	0.991210	+	0.132300i	$0.0422361\pi$
$354$	−3.38906e11	−	5.87002e11i	−1.14700	−	1.98667i
$355$	−5.25238e10	−	2.97877e11i	−0.175521	−	0.995428i
$356$	−5.45401e10	−	4.57646e10i	−0.179966	−	0.151010i
$357$	−1.01341e12	+	8.50354e11i	−3.30202	+	2.77072i
$358$	−4.47264e9	+	2.53656e10i	−0.0143910	+	0.0816152i
$359$	2.24158e11	−	8.15868e10i	0.712244	−	0.259236i	0.0396146	−	0.999215i	$-0.487387\pi$
$359$	2.24158e11	−	8.15868e10i	0.712244	−	0.259236i	0.672630	+	0.739979i	$0.265165\pi$
$360$	−3.15089e11			−0.988718
$361$	2.90052e11	−	1.41412e11i	0.898862	−	0.438233i
$362$	2.79497e10			0.0855438
$363$	9.56453e10	−	3.48120e10i	0.289124	−	0.105232i
$364$	5.55675e9	−	3.15139e10i	0.0165907	−	0.0940905i
$365$	−4.03661e11	+	3.38712e11i	−1.19042	+	0.998877i
$366$	3.61301e11	+	3.03168e11i	1.05246	+	0.883116i
$367$	9.66236e10	+	5.47980e11i	0.278026	+	1.57677i	0.729182	+	0.684320i	$0.239901\pi$
$367$	9.66236e10	+	5.47980e11i	0.278026	+	1.57677i	−0.451156	+	0.892445i	$0.648988\pi$
$368$	−8.44169e9	−	1.46214e10i	−0.0239946	−	0.0415599i
$369$	−5.17198e10	+	8.95813e10i	−0.145224	+	0.251535i
$370$	3.97879e11	+	1.44816e11i	1.10368	+	0.401706i
$371$	1.52828e11	+	5.56247e10i	0.418812	+	0.152435i
$372$	3.43401e10	−	5.94788e10i	0.0929733	−	0.161034i
$373$	2.18547e11	+	3.78534e11i	0.584594	+	1.01255i	0.994926	+	0.100610i	$0.0320795\pi$
$373$	2.18547e11	+	3.78534e11i	0.584594	+	1.01255i	−0.410332	+	0.911936i	$0.634587\pi$
$374$	7.01246e10	+	3.97696e11i	0.185331	+	1.05106i
$375$	5.97536e11	+	5.01392e11i	1.56035	+	1.30929i
$376$	−1.75009e10	+	1.46850e10i	−0.0451559	+	0.0378903i
$377$	7.32831e9	−	4.15609e10i	0.0186839	−	0.105962i
$378$	−1.31403e12	+	4.78268e11i	−3.31049	+	1.20492i
$379$	−7.40815e9			−0.0184431			−0.00922153	−	0.999957i	$-0.502935\pi$
$379$	−7.40815e9			−0.0184431			−0.00922153	+	0.999957i	$0.502935\pi$
$380$	−1.91043e11	+	4.40903e10i	−0.470008	+	0.108472i
$381$	9.68336e11			2.35431
$382$	−2.37494e11	+	8.64409e10i	−0.570648	+	0.207699i
$383$	−5.55143e10	+	3.14837e11i	−0.131829	+	0.747638i	0.845187	+	0.534471i	$0.179489\pi$
$383$	−5.55143e10	+	3.14837e11i	−0.131829	+	0.747638i	−0.977016	+	0.213167i	$0.931622\pi$
$384$	5.69644e10	−	4.77988e10i	0.133694	−	0.112183i
$385$	3.88985e11	+	3.26397e11i	0.902317	+	0.757134i
$386$	−4.26965e10	−	2.42144e11i	−0.0978926	−	0.555176i
$387$	−5.46152e11	−	9.45963e11i	−1.23770	−	2.14375i
$388$	8.72337e10	−	1.51093e11i	0.195408	−	0.338456i
$389$	2.55941e11	+	9.31549e10i	0.566717	+	0.206268i	0.609459	−	0.792818i	$-0.291387\pi$
$389$	2.55941e11	+	9.31549e10i	0.566717	+	0.206268i	−0.0427413	+	0.999086i	$0.513609\pi$
$390$	8.31511e10	+	3.02645e10i	0.182002	+	0.0662435i
$391$	7.28696e10	−	1.26214e11i	0.157671	−	0.273094i
$392$	−6.32986e10	−	1.09636e11i	−0.135396	−	0.234513i
$393$	−1.84522e11	−	1.04647e12i	−0.390194	−	2.21290i
$394$	−2.55315e11	−	2.14235e11i	−0.533758	−	0.447876i
$395$	−2.36017e11	+	1.98042e11i	−0.487817	+	0.409327i
$396$	−1.13162e11	+	6.41771e11i	−0.231244	+	1.31145i
$397$	7.34921e11	−	2.67490e11i	1.48485	−	0.540443i	0.532765	−	0.846263i	$-0.321153\pi$
$397$	7.34921e11	−	2.67490e11i	1.48485	−	0.540443i	0.952089	+	0.305821i	$0.0989309\pi$
$398$	1.75980e11			0.351552
$399$	−1.11414e12	+	7.23409e11i	−2.20071	+	1.42891i
$400$	−8.87108e9			−0.0173263
$401$	−7.39354e11	+	2.69103e11i	−1.42792	+	0.519719i	−0.936334	−	0.351112i	$-0.885804\pi$
$401$	−7.39354e11	+	2.69103e11i	−1.42792	+	0.519719i	−0.491583	+	0.870831i	$0.663581\pi$
$402$	8.38835e10	−	4.75727e11i	0.160199	−	0.908533i
$403$	−1.09855e10	+	9.21793e9i	−0.0207466	+	0.0174085i
$404$	−1.90785e11	−	1.60088e11i	−0.356311	−	0.298980i
$405$	−4.08535e11	−	2.31692e12i	−0.754538	−	4.27920i
$406$	−1.92471e11	−	3.33370e11i	−0.351559	−	0.608919i
$407$	4.37854e11	−	7.58386e11i	0.790961	−	1.36998i
$408$	6.03187e11	+	2.19542e11i	1.07766	+	0.392236i
$409$	−3.78148e11	−	1.37635e11i	−0.668201	−	0.243205i	−0.0144281	−	0.999896i	$-0.504593\pi$
$409$	−3.78148e11	−	1.37635e11i	−0.668201	−	0.243205i	−0.653773	+	0.756691i	$0.726815\pi$
$410$	1.95542e10	−	3.38689e10i	0.0341753	−	0.0591934i
$411$	2.91935e11	+	5.05646e11i	0.504658	+	0.874094i
$412$	6.40803e10	+	3.63418e11i	0.109569	+	0.621396i
$413$	9.88917e11	+	8.29800e11i	1.67257	+	1.40345i
$414$	1.80160e11	−	1.51172e11i	0.301410	−	0.252913i
$415$	−2.70280e10	+	1.53283e11i	−0.0447298	+	0.253675i
$416$	−1.45905e10	+	5.31050e9i	−0.0238864	+	0.00869392i
$417$	−8.60650e11			−1.39384
$418$	2.11912e10	+	4.04950e11i	0.0339518	+	0.648795i
$419$	5.45339e11			0.864378			0.432189	−	0.901783i	$-0.357741\pi$
$419$	5.45339e11			0.864378			0.432189	+	0.901783i	$0.357741\pi$
$420$	7.58456e11	−	2.76055e11i	1.18935	−	0.432887i
$421$	−1.46250e9	+	8.29426e9i	−0.00226896	+	0.0128679i	−0.985921	−	0.167211i	$-0.946524\pi$
$421$	−1.46250e9	+	8.29426e9i	−0.00226896	+	0.0128679i	0.983652	+	0.180078i	$0.0576352\pi$
$422$	−5.53677e11	+	4.64590e11i	−0.849866	+	0.713122i
$423$	−2.43784e11	−	2.04559e11i	−0.370231	−	0.310661i
$424$	−1.37031e10	−	7.77143e10i	−0.0205908	−	0.116776i
$425$	−3.82880e10	−	6.63168e10i	−0.0569263	−	0.0985993i
$426$	−4.97184e11	+	8.61147e11i	−0.731431	+	1.26688i
$427$	−8.44108e11	−	3.07230e11i	−1.22878	−	0.447238i
$428$	−1.15003e11	−	4.18577e10i	−0.165658	−	0.0602947i
$429$	9.15055e10	−	1.58492e11i	0.130434	−	0.225918i
$430$	2.06489e11	+	3.57650e11i	0.291266	+	0.504487i
$431$	−2.97359e10	−	1.68641e11i	−0.0415081	−	0.235404i	0.956995	−	0.290106i	$-0.0936904\pi$
$431$	−2.97359e10	−	1.68641e11i	−0.0415081	−	0.235404i	−0.998503	+	0.0547014i	$0.982579\pi$
$432$	5.19765e11	+	4.36134e11i	0.718009	+	0.602481i
$433$	3.44153e11	−	2.88779e11i	0.470497	−	0.394794i	−0.376479	−	0.926425i	$-0.622865\pi$
$433$	3.44153e11	−	2.88779e11i	0.470497	−	0.394794i	0.846976	+	0.531632i	$0.178421\pi$
$434$	−2.27143e10	+	1.28819e11i	−0.0307323	+	0.174291i
$435$	1.00026e12	−	3.64065e11i	1.33940	−	0.487503i
$436$	6.39003e10			0.0846864
$437$	8.80802e10	−	1.16868e11i	0.115535	−	0.153295i
$438$	1.73230e12			2.24900
$439$	3.22602e10	−	1.17418e10i	0.0414550	−	0.0150884i	−0.321209	−	0.947008i	$-0.604089\pi$
$439$	3.22602e10	−	1.17418e10i	0.0414550	−	0.0150884i	0.362664	+	0.931920i	$0.381867\pi$
$440$	4.27841e10	−	2.42641e11i	0.0544184	−	0.308622i
$441$	1.35090e12	−	1.13354e12i	1.70078	−	1.42713i
$442$	−1.02673e11	−	8.61526e10i	−0.127954	−	0.107366i
$443$	−1.18394e10	−	6.71448e10i	−0.0146054	−	0.0828315i	0.976634	−	0.214910i	$-0.0689459\pi$
$443$	−1.18394e10	−	6.71448e10i	−0.0146054	−	0.0828315i	−0.991239	+	0.132079i	$0.957835\pi$
$444$	−6.95978e11	−	1.20547e12i	−0.849908	−	1.47208i
$445$	−1.87482e11	+	3.24729e11i	−0.226642	+	0.392555i
$446$	2.30006e11	+	8.37152e10i	0.275253	+	0.100184i
$447$	1.61599e12	+	5.88174e11i	1.91450	+	0.696822i
$448$	−7.08135e10	+	1.22653e11i	−0.0830549	+	0.143855i
$449$	−4.68244e11	−	8.11022e11i	−0.543705	−	0.941725i	−0.998687	−	0.0512242i	$-0.983688\pi$
$449$	−4.68244e11	−	8.11022e11i	−0.543705	−	0.941725i	0.454982	−	0.890501i	$-0.349646\pi$
$450$	−2.14581e10	−	1.21695e11i	−0.0246681	−	0.139900i
$451$	−6.19611e10	−	5.19915e10i	−0.0705220	−	0.0591750i
$452$	−1.13771e11	+	9.54655e10i	−0.128206	+	0.107578i
$453$	3.95316e11	−	2.24195e12i	0.441065	−	2.50141i
$454$	−4.52260e11	+	1.64609e11i	−0.499617	+	0.181846i
$455$	−1.68531e11			−0.184343
$456$	5.74281e11	+	2.92666e11i	0.621989	+	0.316980i
$457$	−1.16391e12			−1.24824			−0.624118	−	0.781330i	$-0.714542\pi$
$457$	−1.16391e12			−1.24824			−0.624118	+	0.781330i	$0.714542\pi$
$458$	−3.78960e11	+	1.37930e11i	−0.402438	+	0.146475i
$459$	−1.01704e12	+	5.76795e12i	−1.06950	+	6.06546i
$460$	−6.81149e10	+	5.71552e10i	−0.0709303	+	0.0595176i
$461$	−3.96064e10	−	3.32338e10i	−0.0408424	−	0.0342709i	0.622138	−	0.782908i	$-0.286264\pi$
$461$	−3.96064e10	−	3.32338e10i	−0.0408424	−	0.0342709i	−0.662980	+	0.748637i	$0.730709\pi$
$462$	−2.89874e11	−	1.64396e12i	−0.296020	−	1.67881i
$463$	−8.82081e11	−	1.52781e12i	−0.892060	−	1.54509i	−0.837401	−	0.546588i	$-0.815926\pi$
$463$	−8.82081e11	−	1.52781e12i	−0.892060	−	1.54509i	−0.0546586	−	0.998505i	$-0.517407\pi$
$464$	−9.33898e10	+	1.61756e11i	−0.0935338	+	0.162005i
$465$	−3.39896e11	−	1.23712e11i	−0.337138	−	0.122708i
$466$	5.77480e11	+	2.10185e11i	0.567283	+	0.206474i
$467$	−5.45954e10	+	9.45620e10i	−0.0531166	+	0.0920007i	−0.891361	−	0.453294i	$-0.850249\pi$
$467$	−5.45954e10	+	9.45620e10i	−0.0531166	+	0.0920007i	0.838245	+	0.545294i	$0.183582\pi$
$468$	−1.08143e11	−	1.87309e11i	−0.104206	−	0.180490i
$469$	1.59762e11	+	9.06055e11i	0.152474	+	0.864723i
$470$	9.21697e10	+	7.73396e10i	0.0871260	+	0.0731074i
$471$	4.83003e10	−	4.05288e10i	0.0452226	−	0.0379463i
$472$	1.08770e11	−	6.16866e11i	0.100872	−	0.572074i
$473$	8.02616e11	−	2.92128e11i	0.737281	−	0.268348i
$474$	1.01286e12			0.921612
$475$	−3.00391e10	−	7.07828e10i	−0.0270748	−	0.0637980i
$476$	−1.22254e12			−1.09152
$477$	1.03295e12	−	3.75964e11i	0.913582	−	0.332517i
$478$	1.09058e11	−	6.18501e11i	0.0955506	−	0.541894i
$479$	−9.22782e11	+	7.74306e11i	−0.800920	+	0.672052i	−0.948422	−	0.317010i	$-0.897321\pi$
$479$	−9.22782e11	+	7.74306e11i	−0.800920	+	0.672052i	0.147502	+	0.989062i	$0.452877\pi$
$480$	−3.00007e11	−	2.51736e11i	−0.257956	−	0.216451i
$481$	5.04697e10	+	2.86228e11i	0.0429910	+	0.243814i
$482$	−2.51883e11	−	4.36273e11i	−0.212562	−	0.368169i
$483$	−3.01221e11	+	5.21730e11i	−0.251839	+	0.436198i
$484$	8.83882e10	+	3.21707e10i	0.0732133	+	0.0266475i
$485$	−8.63433e11	−	3.14264e11i	−0.708583	−	0.257903i
$486$	−2.23689e12	+	3.87440e12i	−1.81878	+	3.15022i
$487$	5.65923e11	+	9.80208e11i	0.455908	+	0.789656i	0.998740	−	0.0501855i	$-0.0159813\pi$
$487$	5.65923e11	+	9.80208e11i	0.455908	+	0.789656i	−0.542832	+	0.839841i	$0.682648\pi$
$488$	7.56861e10	+	4.29237e11i	0.0604125	+	0.342616i
$489$	−1.60951e12	−	1.35054e12i	−1.27293	−	1.06812i
$490$	−5.10748e11	+	4.28568e11i	−0.400243	+	0.335844i
$491$	1.49044e11	−	8.45272e11i	0.115731	−	0.656341i	−0.870655	−	0.491894i	$-0.836305\pi$
$491$	1.49044e11	−	8.45272e11i	0.115731	−	0.656341i	0.986386	−	0.164447i	$-0.0525840\pi$
$492$	−1.20814e11	+	4.39727e10i	−0.0929552	+	0.0338329i
$493$	−1.61230e12			−1.22924
$494$	−9.17789e10	−	9.84360e10i	−0.0693380	−	0.0743674i
$495$	3.43208e12			2.56941
$496$	5.96414e10	−	2.17077e10i	0.0442466	−	0.0161045i
$497$	3.28862e11	−	1.86507e12i	0.241774	−	1.37117i
$498$	3.91974e11	−	3.28906e11i	0.285579	−	0.239629i
$499$	−1.62238e12	−	1.36134e12i	−1.17139	−	0.982912i	−0.171391	−	0.985203i	$-0.554826\pi$
$499$	−1.62238e12	−	1.36134e12i	−1.17139	−	0.982912i	−0.999997	+	0.00229113i	$0.999271\pi$
$500$	1.25173e11	+	7.09891e11i	0.0895665	+	0.507957i
$501$	2.35490e12	+	4.07882e12i	1.66995	+	2.89244i
$502$	6.48559e11	−	1.12334e12i	0.455809	−	0.789485i
$503$	−1.49489e12	−	5.44096e11i	−1.04125	−	0.378983i	−0.235895	−	0.971779i	$-0.575802\pi$
$503$	−1.49489e12	−	5.44096e11i	−1.04125	−	0.378983i	−0.805353	+	0.592796i	$0.798024\pi$
$504$	−1.85386e12	−	6.74750e11i	−1.27979	−	0.465806i
$505$	−6.55828e11	+	1.13593e12i	−0.448723	+	0.777211i
$506$	9.19503e10	+	1.59263e11i	0.0623557	+	0.108003i
$507$	−4.99570e11	−	2.83320e12i	−0.335784	−	1.90433i
$508$	6.85505e11	+	5.75207e11i	0.456693	+	0.383211i
$509$	2.12480e12	−	1.78292e12i	1.40310	−	1.17734i	0.443395	−	0.896326i	$-0.353774\pi$
$509$	2.12480e12	−	1.78292e12i	1.40310	−	1.17734i	0.959704	−	0.281014i	$-0.0906707\pi$
$510$	5.87036e11	−	3.32925e12i	0.384237	−	2.17912i
$511$	−3.10032e12	+	1.12842e12i	−2.01146	+	0.732113i
$512$	6.87195e10			0.0441942
$513$	−1.71992e12	+	5.62406e12i	−1.09643	+	3.58527i
$514$	4.21620e11			0.266433
$515$	1.82629e12	−	6.64714e11i	1.14403	−	0.416392i
$516$	2.35754e11	−	1.33702e12i	0.146398	−	0.830263i
$517$	1.90626e11	−	1.59955e11i	0.117348	−	0.0984667i
$518$	2.03084e12	+	1.70408e12i	1.23935	+	1.03993i
$519$	8.05841e11	+	4.57015e12i	0.487524	+	2.76489i
$520$	4.08868e10	+	7.08179e10i	0.0245227	+	0.0424745i
$521$	9.65880e11	−	1.67295e12i	0.574320	−	0.994751i	−0.421796	−	0.906691i	$-0.638600\pi$
$521$	9.65880e11	−	1.67295e12i	0.574320	−	0.994751i	0.996115	−	0.0880597i	$-0.0280666\pi$
$522$	−2.44490e12	−	8.89869e11i	−1.44126	−	0.524577i
$523$	−2.00558e12	−	7.29970e11i	−1.17215	−	0.426626i	−0.318724	−	0.947848i	$-0.603254\pi$
$523$	−2.00558e12	−	7.29970e11i	−1.17215	−	0.426626i	−0.853421	+	0.521222i	$0.825477\pi$
$524$	4.90996e11	−	8.50429e11i	0.284503	−	0.492774i
$525$	1.58271e11	+	2.74134e11i	0.0909254	+	0.157487i
$526$	−6.45933e10	−	3.66327e11i	−0.0367919	−	0.208657i
$527$	4.19694e11	+	3.52165e11i	0.237020	+	0.198883i
$528$	−6.20479e11	+	5.20644e11i	−0.347436	+	0.291533i
$529$	−3.01242e11	+	1.70843e12i	−0.167250	+	0.948520i
$530$	−3.90539e11	+	1.42144e11i	−0.214992	+	0.0782508i
$531$	8.72538e12			4.76277
$532$	−1.21844e12	−	1.49701e11i	−0.659480	−	0.0810255i
$533$	2.68451e10			0.0144077
$534$	1.15834e12	−	4.21602e11i	0.616455	−	0.224371i
$535$	−1.11924e11	+	6.34752e11i	−0.0590651	+	0.334975i
$536$	3.41972e11	−	2.86949e11i	0.178957	−	0.150163i
$537$	−3.41615e11	−	2.86649e11i	−0.177277	−	0.148753i
$538$	1.42370e11	+	8.07423e11i	0.0732655	+	0.415509i
$539$	6.89473e11	+	1.19420e12i	0.351858	+	0.609437i
$540$	1.78670e12	−	3.09465e12i	0.904232	−	1.56617i
$541$	8.77618e11	+	3.19427e11i	0.440471	+	0.160318i	0.552730	−	0.833361i	$-0.313586\pi$
$541$	8.77618e11	+	3.19427e11i	0.440471	+	0.160318i	−0.112258	+	0.993679i	$0.535808\pi$
$542$	2.31836e12	+	8.43814e11i	1.15394	+	0.420001i
$543$	−2.41956e11	+	4.19080e11i	−0.119437	+	0.206870i
$544$	2.96597e11	+	5.13721e11i	0.145202	+	0.251497i
$545$	−5.84389e10	−	3.31423e11i	−0.0283738	−	0.160916i
$546$	4.24418e11	+	3.56129e11i	0.204375	+	0.171491i
$547$	−3.96027e11	+	3.32306e11i	−0.189139	+	0.158707i	−0.732440	−	0.680831i	$-0.761619\pi$
$547$	−3.96027e11	+	3.32306e11i	−0.189139	+	0.158707i	0.543301	+	0.839538i	$0.317174\pi$
$548$	−9.36950e10	+	5.31371e11i	−0.0443817	+	0.251701i
$549$	−5.70528e12	+	2.07655e12i	−2.68041	+	0.975589i
$550$	9.66274e10			0.0450265
$551$	−1.60689e12	−	1.97427e11i	−0.742686	−	0.0912484i
$552$	2.92314e11			0.134006
$553$	−1.81273e12	+	6.59780e11i	−0.824271	+	0.300010i
$554$	1.29102e11	−	7.32173e11i	0.0582289	−	0.330232i
$555$	−5.61575e12	+	4.71218e12i	−2.51241	+	2.10816i
$556$	−6.09272e11	−	5.11240e11i	−0.270380	−	0.226876i
$557$	−1.82130e11	−	1.03291e12i	−0.0801737	−	0.454688i	−0.998294	−	0.0583861i	$-0.981405\pi$
$557$	−1.82130e11	−	1.03291e12i	−0.0801737	−	0.454688i	0.918120	−	0.396302i	$-0.129707\pi$
$558$	4.42056e11	+	7.65663e11i	0.193029	+	0.334336i
$559$	−1.41740e11	+	2.45501e11i	−0.0613959	+	0.106341i
$560$	7.00907e11	+	2.55109e11i	0.301172	+	0.109618i
$561$	−6.57015e12	−	2.39134e12i	−2.80055	−	1.01932i
$562$	−5.92786e11	+	1.02674e12i	−0.250660	+	0.434155i
$563$	−2.14227e12	−	3.71053e12i	−0.898643	−	1.55650i	−0.829230	−	0.558908i	$-0.811221\pi$
$563$	−2.14227e12	−	3.71053e12i	−0.898643	−	1.55650i	−0.0694134	−	0.997588i	$-0.522113\pi$
$564$	−6.86855e10	−	3.89535e11i	−0.0285831	−	0.162103i
$565$	5.99186e11	+	5.02776e11i	0.247368	+	0.207566i
$566$	−1.38723e12	+	1.16402e12i	−0.568163	+	0.476746i
$567$	2.55792e12	−	1.45067e13i	1.03935	−	5.89446i
$568$	−8.63502e11	+	3.14289e11i	−0.348093	+	0.126696i
$569$	3.31616e12			1.32627			0.663133	−	0.748501i	$-0.269226\pi$
$569$	3.31616e12			1.32627			0.663133	+	0.748501i	$0.269226\pi$
$570$	9.92736e11	−	3.24620e12i	0.393910	−	1.28807i
$571$	−6.37976e11			−0.251155			−0.125577	−	0.992084i	$-0.540078\pi$
$571$	−6.37976e11			−0.251155			−0.125577	+	0.992084i	$0.540078\pi$
$572$	1.58925e11	−	5.78441e10i	0.0620742	−	0.0225932i
$573$	7.59849e11	−	4.30932e12i	0.294463	−	1.66998i
$574$	1.87578e11	−	1.57397e11i	0.0721238	−	0.0605190i
$575$	−2.67135e10	−	2.24153e10i	−0.0101912	−	0.00855142i
$576$	1.66225e11	+	9.42706e11i	0.0629208	+	0.356841i
$577$	−1.73774e12	−	3.00985e12i	−0.652669	−	1.13046i	−0.982473	−	0.186407i	$-0.940316\pi$
$577$	−1.73774e12	−	3.00985e12i	−0.652669	−	1.13046i	0.329803	−	0.944050i	$-0.393018\pi$
$578$	−1.61155e12	+	2.79129e12i	−0.600578	+	1.04023i
$579$	4.00035e12	+	1.45601e12i	1.47926	+	0.538406i
$580$	9.24366e11	+	3.36442e11i	0.339170	+	0.123448i
$581$	−4.87271e11	+	8.43978e11i	−0.177410	+	0.307283i
$582$	1.51034e12	+	2.61598e12i	0.545658	+	0.945107i
$583$	1.49260e11	+	8.46496e11i	0.0535100	+	0.303470i
$584$	1.22633e12	+	1.02901e12i	0.436265	+	0.366070i
$585$	−8.72593e11	+	7.32192e11i	−0.308042	+	0.258478i
$586$	3.35653e11	−	1.90358e12i	0.117585	−	0.666857i
$587$	8.81471e11	−	3.20829e11i	0.306434	−	0.111533i	−0.184226	−	0.982884i	$-0.558978\pi$
$587$	8.81471e11	−	3.20829e11i	0.306434	−	0.111533i	0.490660	+	0.871351i	$0.336756\pi$
$588$	2.19186e12			0.756163
$589$	3.75164e11	+	4.02376e11i	0.128440	+	0.137757i
$590$	−3.29889e12			−1.12082
$591$	5.42248e12	−	1.97362e12i	1.82833	−	0.665458i
$592$	2.23371e11	−	1.26680e12i	0.0747444	−	0.423896i
$593$	2.82118e12	−	2.36725e12i	0.936880	−	0.786136i	−0.0401594	−	0.999193i	$-0.512787\pi$
$593$	2.82118e12	−	2.36725e12i	0.936880	−	0.786136i	0.977040	+	0.213057i	$0.0683421\pi$
$594$	−5.66149e12	−	4.75055e12i	−1.86591	−	1.56569i
$595$	1.11805e12	+	6.34079e12i	0.365709	+	2.07404i
$596$	7.94611e11	+	1.37631e12i	0.257956	+	0.446793i
$597$	−1.52343e12	+	2.63866e12i	−0.490838	+	0.850156i
$598$	−5.73548e10	−	2.08754e10i	−0.0183406	−	0.00667544i
$599$	1.89608e12	+	6.90118e11i	0.601778	+	0.219029i	0.624902	−	0.780703i	$-0.285139\pi$
$599$	1.89608e12	+	6.90118e11i	0.601778	+	0.219029i	−0.0231236	+	0.999733i	$0.507361\pi$
$600$	7.67955e10	−	1.33014e11i	0.0241911	−	0.0419002i
$601$	2.52444e12	+	4.37245e12i	0.789276	+	1.36707i	0.926411	+	0.376514i	$0.122877\pi$
$601$	2.52444e12	+	4.37245e12i	0.789276	+	1.36707i	−0.137134	+	0.990552i	$0.543789\pi$
$602$	4.49009e11	+	2.54646e12i	0.139338	+	0.790227i
$603$	4.76361e12	+	3.99714e12i	1.46726	+	1.23118i
$604$	1.61161e12	−	1.35230e12i	0.492712	−	0.413434i
$605$	8.60215e10	−	4.87852e11i	0.0261041	−	0.148043i
$606$	4.05197e12	−	1.47480e12i	1.22050	−	0.444227i
$607$	3.75473e12			1.12261			0.561306	−	0.827608i	$-0.310299\pi$
$607$	3.75473e12			1.12261			0.561306	+	0.827608i	$0.310299\pi$
$608$	2.32697e11	+	5.48317e11i	0.0690596	+	0.162729i
$609$	6.66477e12			1.96339
$610$	2.15705e12	−	7.85102e11i	0.630777	−	0.229584i
$611$	−1.43417e10	+	8.13357e10i	−0.00416308	+	0.0236100i
$612$	−6.32988e12	+	5.31140e12i	−1.82396	+	1.53048i
$613$	−4.48922e12	−	3.76690e12i	−1.28410	−	1.07749i	−0.992665	−	0.120898i	$-0.961423\pi$
$613$	−4.48922e12	−	3.76690e12i	−1.28410	−	1.07749i	−0.291435	−	0.956591i	$-0.594133\pi$
$614$	−3.69996e11	−	2.09835e12i	−0.105060	−	0.595827i
$615$	3.38555e11	+	5.86395e11i	0.0954315	+	0.165292i
$616$	7.71329e11	−	1.33598e12i	0.215837	−	0.373841i
$617$	−7.87536e11	−	2.86640e11i	−0.218770	−	0.0796257i	0.230310	−	0.973117i	$-0.426026\pi$
$617$	−7.87536e11	−	2.86640e11i	−0.218770	−	0.0796257i	−0.449080	+	0.893492i	$0.648248\pi$
$618$	−6.00385e12	−	2.18522e12i	−1.65570	−	0.602625i
$619$	−6.91344e11	+	1.19744e12i	−0.189272	+	0.327829i	−0.945008	−	0.327048i	$-0.893946\pi$
$619$	−6.91344e11	+	1.19744e12i	−0.189272	+	0.327829i	0.755736	+	0.654877i	$0.227279\pi$
$620$	−1.67132e11	−	2.89482e11i	−0.0454253	−	0.0786790i
$621$	4.63151e11	+	2.62666e12i	0.124971	+	0.708748i
$622$	−2.23484e12	−	1.87525e12i	−0.598673	−	0.502346i
$623$	−1.79847e12	+	1.50909e12i	−0.478306	+	0.401346i
$624$	4.66814e10	−	2.64743e11i	0.0123257	−	0.0699027i
$625$	3.31899e12	−	1.20801e12i	0.870053	−	0.316674i
$626$	−6.67970e11			−0.173849
$627$	−6.25530e12	−	3.18784e12i	−1.61638	−	0.823745i
$628$	5.82675e10			0.0149489
$629$	1.04342e13	−	3.79773e12i	2.65785	−	0.967379i
$630$	−1.80422e12	+	1.02323e13i	−0.456308	+	2.58785i
$631$	−1.09552e10	+	9.19255e9i	−0.00275100	+	0.00230836i	−0.644162	−	0.764889i	$-0.722794\pi$
$631$	−1.09552e10	+	9.19255e9i	−0.00275100	+	0.00230836i	0.641411	+	0.767197i	$0.278349\pi$
$632$	7.17026e11	+	6.01656e11i	0.178776	+	0.150011i
$633$	−2.17301e12	−	1.23238e13i	−0.537954	−	3.05089i
$634$	2.52870e12	+	4.37983e12i	0.621578	+	1.07660i
$635$	2.35643e12	−	4.08146e12i	0.575140	−	0.996172i
$636$	1.28388e12	+	4.67295e11i	0.311149	+	0.113249i
$637$	−4.30065e11	−	1.56531e11i	−0.103492	−	0.0376680i
$638$	1.01724e12	−	1.76191e12i	0.243069	−	0.421008i
$639$	−6.40018e12	−	1.10854e13i	−1.51858	−	2.63026i
$640$	−6.28462e10	−	3.56418e11i	−0.0148071	−	0.0839750i
$641$	2.98559e11	+	2.50521e11i	0.0698505	+	0.0586115i	0.677044	−	0.735942i	$-0.263260\pi$
$641$	2.98559e11	+	2.50521e11i	0.0698505	+	0.0586115i	−0.607194	+	0.794554i	$0.707705\pi$
$642$	1.62318e12	−	1.36201e12i	0.377103	−	0.316427i
$643$	−1.29133e12	+	7.32349e12i	−0.297912	+	1.68954i	0.357215	+	0.934022i	$0.383726\pi$
$643$	−1.29133e12	+	7.32349e12i	−0.297912	+	1.68954i	−0.655127	+	0.755519i	$0.727385\pi$
$644$	−5.23156e11	+	1.90413e11i	−0.119852	+	0.0436226i
$645$	−7.15017e12			−1.62666
$646$	−3.09468e12	+	4.10612e12i	−0.699148	+	0.927652i
$647$	−4.11927e12			−0.924169			−0.462084	−	0.886836i	$-0.652898\pi$
$647$	−4.11927e12			−0.924169			−0.462084	+	0.886836i	$0.652898\pi$
$648$	−6.71639e12	+	2.44457e12i	−1.49640	+	0.544646i
$649$	−1.18477e12	+	6.71915e12i	−0.262139	+	1.48667i
$650$	−2.45671e10	+	2.06143e10i	−0.00539814	+	0.00452958i
$651$	−1.73489e12	−	1.45574e12i	−0.378580	−	0.317666i
$652$	−3.37164e11	−	1.91215e12i	−0.0730680	−	0.414389i
$653$	2.02861e12	+	3.51365e12i	0.436605	+	0.756223i	0.997425	−	0.0717152i	$-0.0228473\pi$
$653$	2.02861e12	+	3.51365e12i	0.436605	+	0.756223i	−0.560820	+	0.827938i	$0.689514\pi$
$654$	−5.53175e11	+	9.58127e11i	−0.118240	+	0.204797i
$655$	−4.85984e12	−	1.76884e12i	−1.03166	−	0.375493i
$656$	−1.11647e11	−	4.06362e10i	−0.0235386	−	0.00856734i
$657$	−1.11498e13	+	1.93121e13i	−2.33467	+	4.04376i
$658$	3.76671e11	+	6.52413e11i	0.0783331	+	0.135677i
$659$	3.26425e11	+	1.85125e12i	0.0674216	+	0.382367i	0.999783	+	0.0208390i	$0.00663374\pi$
$659$	3.26425e11	+	1.85125e12i	0.0674216	+	0.382367i	−0.932361	+	0.361528i	$0.882255\pi$
$660$	3.26780e12	+	2.74201e12i	0.670360	+	0.562499i
$661$	−6.76026e11	+	5.67253e11i	−0.137739	+	0.115577i	−0.709054	−	0.705154i	$-0.750878\pi$
$661$	−6.76026e11	+	5.67253e11i	−0.137739	+	0.115577i	0.571315	+	0.820731i	$0.306433\pi$
$662$	4.28094e11	−	2.42784e12i	0.0866320	−	0.491315i
$663$	2.18060e12	−	7.93674e11i	0.438294	−	0.159526i
$664$	4.72862e11			0.0944013
$665$	3.37868e11	+	6.45643e12i	0.0669962	+	1.28025i
$666$	1.79185e13			3.52912
$667$	−6.89946e11	+	2.51120e11i	−0.134974	+	0.0491264i
$668$	−7.55795e11	+	4.28633e12i	−0.146862	+	0.832897i
$669$	−3.24636e12	+	2.72402e12i	−0.626583	+	0.525766i
$670$	−1.80102e12	−	1.51124e12i	−0.345289	−	0.289732i
$671$	−8.24403e11	−	4.67542e12i	−0.156996	−	0.890368i
$672$	−1.22604e12	−	2.12357e12i	−0.231923	−	0.401702i
$673$	2.26446e12	−	3.92215e12i	0.425496	−	0.736981i	−0.570970	−	0.820971i	$-0.693433\pi$
$673$	2.26446e12	−	3.92215e12i	0.425496	−	0.736981i	0.996467	+	0.0839893i	$0.0267662\pi$
$674$	−5.94512e12	−	2.16385e12i	−1.10966	−	0.403884i
$675$	1.31691e12	+	4.79315e11i	0.244168	+	0.0888698i
$676$	1.32931e12	−	2.30243e12i	0.244831	−	0.424059i
$677$	1.92764e12	+	3.33877e12i	0.352677	+	0.610855i	0.986718	−	0.162445i	$-0.0519380\pi$
$677$	1.92764e12	+	3.33877e12i	0.352677	+	0.610855i	−0.634040	+	0.773300i	$0.718605\pi$
$678$	−4.46517e11	−	2.53233e12i	−0.0811530	−	0.460242i
$679$	−4.40712e12	−	3.69801e12i	−0.795684	−	0.667658i
$680$	2.39320e12	−	2.00813e12i	0.429229	−	0.360166i
$681$	1.44698e12	−	8.20623e12i	0.257810	−	1.46211i
$682$	−6.49638e11	+	2.36449e11i	−0.114985	+	0.0418512i
$683$	−8.66881e12			−1.52429			−0.762143	−	0.647409i	$-0.775852\pi$
$683$	−8.66881e12			−1.52429			−0.762143	+	0.647409i	$0.775852\pi$
$684$	−6.95904e12	+	4.51849e12i	−1.21562	+	0.789298i
$685$	2.84168e12			0.493137
$686$	1.19891e12	−	4.36366e11i	0.206693	−	0.0752302i
$687$	1.21246e12	−	6.87620e12i	0.207664	−	1.17772i
$688$	9.61109e11	−	8.06466e11i	0.163540	−	0.137227i
$689$	−2.18538e11	−	1.83375e11i	−0.0369438	−	0.0309995i
$690$	−2.67330e11	−	1.51610e12i	−0.0448980	−	0.254629i
$691$	−2.80167e12	−	4.85263e12i	−0.467482	−	0.809703i	0.531827	−	0.846853i	$-0.321506\pi$
$691$	−2.80167e12	−	4.85263e12i	−0.467482	−	0.809703i	−0.999310	+	0.0371496i	$0.988172\pi$
$692$	−2.14427e12	+	3.71399e12i	−0.355469	+	0.615691i
$693$	2.01930e13	+	7.34965e12i	3.32584	+	1.21051i
$694$	2.27303e12	+	8.27314e11i	0.371952	+	0.135379i
$695$	−2.09438e12	+	3.62757e12i	−0.340505	+	0.589773i
$696$	−1.61692e12	−	2.80059e12i	−0.261185	−	0.452385i
$697$	−1.78094e11	−	1.01002e12i	−0.0285826	−	0.162100i
$698$	−4.14691e11	−	3.47967e11i	−0.0661265	−	0.0554867i
$699$	−8.15069e12	+	6.83924e12i	−1.29136	+	1.08358i
$700$	−5.07964e10	+	2.88081e11i	−0.00799635	+	0.0453496i
$701$	6.10302e12	−	2.22132e12i	0.954583	−	0.347440i	0.182674	−	0.983173i	$-0.441525\pi$
$701$	6.10302e12	−	2.22132e12i	0.954583	−	0.347440i	0.771908	+	0.635734i	$0.219302\pi$
$702$	2.45288e12			0.381206
$703$	1.08642e13	−	2.50732e12i	1.67764	−	0.387179i
$704$	−7.48520e11			−0.114849
$705$	−1.95753e12	+	7.12484e11i	−0.298441	+	0.108624i
$706$	−6.17683e11	+	3.50305e12i	−0.0935717	+	0.530671i
$707$	−6.29117e12	+	5.27892e12i	−0.946987	+	0.794616i
$708$	8.30774e12	+	6.97102e12i	1.24261	+	1.04267i
$709$	−7.71271e11	−	4.37409e12i	−0.114630	−	0.650100i	−0.986933	−	0.161133i	$-0.948485\pi$
$709$	−7.71271e11	−	4.37409e12i	−0.114630	−	0.650100i	0.872303	−	0.488966i	$-0.162626\pi$
$710$	2.41978e12	+	4.19118e12i	0.357366	+	0.618976i
$711$	−6.51923e12	+	1.12916e13i	−0.956716	+	1.65708i
$712$	1.07045e12	+	3.89613e11i	0.156102	+	0.0568164i
$713$	2.34448e11	+	8.53323e10i	0.0339738	+	0.0123655i
$714$	1.05833e13	−	1.83309e13i	1.52398	−	2.63962i
$715$	−4.45355e11	−	7.71377e11i	−0.0637278	−	0.110380i
$716$	−7.15622e10	−	4.05849e11i	−0.0101759	−	0.0577107i
$717$	8.32975e12	+	6.98949e12i	1.17705	+	0.987665i
$718$	−2.92376e12	+	2.45333e12i	−0.410565	+	0.344505i
$719$	−3.83339e11	+	2.17403e12i	−0.0534938	+	0.303378i	−0.999802	−	0.0198868i	$-0.993669\pi$
$719$	−3.83339e11	+	2.17403e12i	−0.0534938	+	0.303378i	0.946308	+	0.323265i	$0.104781\pi$
$720$	4.73739e12	−	1.72427e12i	0.656966	−	0.239116i
$721$	1.21686e13			1.67700
$722$	−3.58710e12	+	3.71340e12i	−0.491276	+	0.508574i
$723$	8.72203e12			1.18712
$724$	−4.20226e11	+	1.52950e11i	−0.0568407	+	0.0206883i
$725$	−6.69910e10	+	3.79925e11i	−0.00900524	+	0.0510713i
$726$	−1.24753e12	+	1.04680e12i	−0.166662	+	0.139846i
$727$	5.35717e12	+	4.49520e12i	0.711263	+	0.596821i	0.924953	−	0.380081i	$-0.124104\pi$
$727$	5.35717e12	+	4.49520e12i	0.711263	+	0.596821i	−0.213690	+	0.976901i	$0.568548\pi$
$728$	8.89079e10	+	5.04222e11i	0.0117314	+	0.0665320i
$729$	−2.15555e13	−	3.73353e13i	−2.82673	−	4.89605i
$730$	4.21553e12	−	7.30152e12i	0.549414	−	0.951613i
$731$	1.01770e13	+	3.70414e12i	1.31824	+	0.479798i
$732$	−7.09122e12	−	2.58099e12i	−0.912896	−	0.332267i
$733$	4.94657e12	−	8.56770e12i	0.632901	−	1.09622i	−0.354055	−	0.935225i	$-0.615197\pi$
$733$	4.94657e12	−	8.56770e12i	0.632901	−	1.09622i	0.986956	−	0.160992i	$-0.0514694\pi$
$734$	−4.45146e12	−	7.71016e12i	−0.566071	−	0.980463i
$735$	−2.00453e12	−	1.13682e13i	−0.253349	−	1.43681i
$736$	2.06935e11	+	1.73639e11i	0.0259946	+	0.0218121i
$737$	−3.72490e12	+	3.12556e12i	−0.465062	+	0.390233i
$738$	2.87393e11	−	1.62989e12i	0.0356634	−	0.202257i
$739$	−7.79309e12	+	2.83645e12i	−0.961192	+	0.349845i	−0.774500	−	0.632573i	$-0.781999\pi$
$739$	−7.79309e12	+	2.83645e12i	−0.961192	+	0.349845i	−0.186691	+	0.982419i	$0.559776\pi$
$740$	−6.77462e12			−0.830504
$741$	2.27047e12	−	5.23996e11i	0.276652	−	0.0638478i
$742$	−2.60217e12			−0.315151
$743$	4.67781e12	−	1.70259e12i	0.563110	−	0.204955i	−0.0447517	−	0.998998i	$-0.514250\pi$
$743$	4.67781e12	−	1.70259e12i	0.563110	−	0.204955i	0.607862	+	0.794043i	$0.292027\pi$
$744$	−1.90819e11	+	1.08219e12i	−0.0228320	+	0.129487i
$745$	6.41161e12	−	5.37998e12i	0.762542	−	0.639849i
$746$	−5.35733e12	−	4.49533e12i	−0.633320	−	0.531419i
$747$	1.14380e12	+	6.48680e12i	0.134402	+	0.762234i
$748$	−3.23065e12	−	5.59565e12i	−0.377340	−	0.653572i
$749$	−2.01781e12	+	3.49495e12i	−0.234268	+	0.405763i
$750$	−1.17278e13	−	4.26856e12i	−1.35344	−	0.492613i
$751$	−4.94119e12	−	1.79844e12i	−0.566828	−	0.206309i	0.0426793	−	0.999089i	$-0.486411\pi$
$751$	−4.94119e12	−	1.79844e12i	−0.566828	−	0.206309i	−0.609508	+	0.792780i	$0.708633\pi$
$752$	1.82766e11	−	3.16560e11i	0.0208408	−	0.0360974i
$753$	1.12290e13	+	1.94491e13i	1.27280	+	2.20456i
$754$	1.17253e11	+	6.64975e11i	0.0132115	+	0.0749263i
$755$	−8.48766e12	−	7.12199e12i	−0.950663	−	0.797701i
$756$	1.71393e13	−	1.43816e13i	1.90829	−	1.60125i
$757$	−5.25465e11	+	2.98006e12i	−0.0581584	+	0.329833i	−0.999980	−	0.00627974i	$-0.998001\pi$
$757$	−5.25465e11	+	2.98006e12i	−0.0581584	+	0.329833i	0.941822	+	0.336112i	$0.109112\pi$
$758$	1.11382e11	−	4.05398e10i	0.0122547	−	0.00446036i
$759$	−3.18400e12			−0.348245
$760$	2.63107e12	−	1.70835e12i	0.286070	−	0.185744i
$761$	−5.12859e12			−0.554328			−0.277164	−	0.960823i	$-0.589395\pi$
$761$	−5.12859e12			−0.554328			−0.277164	+	0.960823i	$0.589395\pi$
$762$	−1.45590e13	+	5.29905e12i	−1.56435	+	0.569378i
$763$	3.65898e11	−	2.07511e12i	0.0390840	−	0.221656i
$764$	3.09771e12	−	2.59929e12i	0.328943	−	0.276016i
$765$	3.33368e13	+	2.79729e13i	3.51923	+	2.95299i
$766$	−8.88229e11	−	5.03740e12i	−0.0932171	−	0.528660i
$767$	−1.13223e12	−	1.96108e12i	−0.118128	−	0.204604i
$768$	−5.94894e11	+	1.03039e12i	−0.0617041	+	0.106875i
$769$	−1.13117e13	−	4.11712e12i	−1.16643	−	0.424547i	−0.315041	−	0.949078i	$-0.602018\pi$
$769$	−1.13117e13	−	4.11712e12i	−1.16643	−	0.424547i	−0.851391	+	0.524531i	$0.824241\pi$
$770$	−7.63457e12	−	2.77875e12i	−0.782665	−	0.284867i
$771$	−3.64990e12	+	6.32181e12i	−0.371994	+	0.644313i
$772$	1.96704e12	+	3.40701e12i	0.199312	+	0.345219i
$773$	−1.19220e12	−	6.76129e12i	−0.120099	−	0.681117i	−0.984098	−	0.177624i	$-0.943159\pi$
$773$	−1.19220e12	−	6.76129e12i	−0.120099	−	0.681117i	0.863999	−	0.503493i	$-0.167952\pi$
$774$	1.33881e13	+	1.12339e13i	1.34086	+	1.12511i
$775$	1.00423e11	−	8.42648e10i	0.00999942	−	0.00839051i
$776$	−4.84735e11	+	2.74907e12i	−0.0479873	+	0.272150i
$777$	−4.31318e13	+	1.56987e13i	−4.24525	+	1.54514i
$778$	−4.35787e12			−0.426448
$779$	−5.38188e10	−	1.02844e12i	−0.00523619	−	0.100060i
$780$	−1.41580e12			−0.136955
$781$	9.40561e12	−	3.42336e12i	0.904601	−	0.329248i
$782$	−4.04917e11	+	2.29640e12i	−0.0387201	+	0.219592i
$783$	2.26035e13	−	1.89666e13i	2.14906	−	1.80328i
$784$	1.55166e12	+	1.30200e12i	0.146682	+	0.123080i
$785$	−5.32875e10	−	3.02208e11i	−0.00500855	−	0.0284049i
$786$	8.50094e12	+	1.47241e13i	0.794448	+	1.37602i
$787$	3.97801e12	−	6.89012e12i	0.369641	−	0.640236i	−0.619869	−	0.784706i	$-0.712814\pi$
$787$	3.97801e12	−	6.89012e12i	0.369641	−	0.640236i	0.989509	+	0.144469i	$0.0461475\pi$
$788$	5.01105e12	+	1.82387e12i	0.462979	+	0.168510i
$789$	6.05191e12	+	2.20272e12i	0.555964	+	0.202354i
$790$	2.46479e12	−	4.26914e12i	0.225143	−	0.389959i
$791$	2.44870e12	+	4.24127e12i	0.222403	+	0.385214i
$792$	−1.81058e12	−	1.02683e13i	−0.163514	−	0.927335i
$793$	1.20705e12	+	1.01283e12i	0.108391	+	0.0909511i
$794$	−9.58582e12	+	8.04345e12i	−0.855927	+	0.718208i
$795$	1.24950e12	−	7.08629e12i	0.110939	−	0.629169i
$796$	−2.64587e12	+	9.63018e11i	−0.233593	+	0.0850209i
$797$	−3.68465e12			−0.323470			−0.161735	−	0.986834i	$-0.551709\pi$
$797$	−3.68465e12			−0.323470			−0.161735	+	0.986834i	$0.551709\pi$
$798$	1.27925e13	−	1.69735e13i	1.11671	−	1.48169i
$799$	3.15531e12			0.273894
$800$	1.33377e11	−	4.85454e10i	0.0115127	−	0.00419028i
$801$	−2.75548e12	+	1.56271e13i	−0.236511	+	1.34132i
$802$	9.64363e12	−	8.09197e12i	0.823106	−	0.690668i
$803$	−1.33577e13	−	1.12084e13i	−1.13373	−	0.951317i
$804$	1.34214e12	+	7.61163e12i	0.113278	+	0.642430i
$805$	1.46604e12	+	2.53925e12i	0.123045	+	0.213120i
$806$	1.14724e11	−	1.98709e11i	0.00957521	−	0.0165848i
$807$	−1.33390e13	−	4.85502e12i	−1.10712	−	0.402958i
$808$	3.74453e12	+	1.36290e12i	0.309062	+	0.112489i
$809$	1.00926e13	−	1.74808e13i	0.828387	−	1.43481i	−0.0709152	−	0.997482i	$-0.522592\pi$
$809$	1.00926e13	−	1.74808e13i	0.828387	−	1.43481i	0.899303	−	0.437327i	$-0.144075\pi$
$810$	1.88213e13	+	3.25994e13i	1.53627	+	2.66089i
$811$	8.53922e11	+	4.84283e12i	0.0693146	+	0.393102i	0.999652	+	0.0263967i	$0.00840331\pi$
$811$	8.53922e11	+	4.84283e12i	0.0693146	+	0.393102i	−0.930337	+	0.366706i	$0.880486\pi$
$812$	4.71813e12	+	3.95898e12i	0.380862	+	0.319581i
$813$	−3.27219e13	+	2.74569e13i	−2.62682	+	2.20417i
$814$	−2.43304e12	+	1.37985e13i	−0.194241	+	1.10159i
$815$	−9.60916e12	+	3.49745e12i	−0.762915	+	0.277678i
$816$	−1.02704e13			−0.810924
$817$	9.68933e12	+	4.93790e12i	0.760842	+	0.387742i
$818$	6.43867e12			0.502813
$819$	−6.70195e12	+	2.43931e12i	−0.520503	+	0.189448i
$820$	−1.08658e11	+	6.16228e11i	−0.00839263	+	0.0475970i
$821$	−7.82550e12	+	6.56638e12i	−0.601130	+	0.504408i	−0.891809	−	0.452413i	$-0.850563\pi$
$821$	−7.82550e12	+	6.56638e12i	−0.601130	+	0.504408i	0.290679	+	0.956821i	$0.406119\pi$
$822$	−7.15632e12	−	6.00486e12i	−0.546722	−	0.458754i
$823$	9.60089e11	+	5.44494e12i	0.0729478	+	0.413708i	0.999312	+	0.0370795i	$0.0118055\pi$
$823$	9.60089e11	+	5.44494e12i	0.0729478	+	0.413708i	−0.926364	+	0.376628i	$0.877083\pi$
$824$	−2.95219e12	−	5.11334e12i	−0.223086	−	0.386396i
$825$	−8.36488e11	+	1.44884e12i	−0.0628661	+	0.108887i
$826$	−1.94094e13	−	7.06444e12i	−1.45078	−	0.528041i
$827$	2.29042e12	+	8.33644e11i	0.170271	+	0.0619735i	0.425749	−	0.904841i	$-0.360011\pi$
$827$	2.29042e12	+	8.33644e11i	0.170271	+	0.0619735i	−0.255478	+	0.966815i	$0.582233\pi$
$828$	−1.88146e12	+	3.25878e12i	−0.139110	+	0.240945i
$829$	−1.45777e12	−	2.52493e12i	−0.107200	−	0.185675i	0.807435	−	0.589956i	$-0.200855\pi$
$829$	−1.45777e12	−	2.52493e12i	−0.107200	−	0.185675i	−0.914635	+	0.404281i	$0.867522\pi$
$830$	−4.32447e11	−	2.45253e12i	−0.0316287	−	0.179375i
$831$	9.86065e12	+	8.27407e12i	0.717300	+	0.601886i
$832$	1.90308e11	−	1.59688e11i	0.0137690	−	0.0115536i
$833$	−3.03620e12	+	1.72192e13i	−0.218488	+	1.23911i
$834$	1.29399e13	−	4.70975e12i	0.926158	−	0.337094i
$835$	2.29225e13			1.63182
$836$	−2.53463e12	−	5.97248e12i	−0.179467	−	0.422889i
$837$	−1.00266e13			−0.706139
$838$	−8.19922e12	+	2.98427e12i	−0.574347	+	0.209045i
$839$	2.37617e12	−	1.34759e13i	0.165557	−	0.938923i	−0.782930	−	0.622109i	$-0.786276\pi$
$839$	2.37617e12	−	1.34759e13i	0.165557	−	0.938923i	0.948488	−	0.316814i	$-0.102613\pi$
$840$	−9.89278e12	+	8.30103e12i	−0.685585	+	0.575274i
$841$	−4.89079e12	−	4.10386e12i	−0.337129	−	0.282885i
$842$	−2.34000e10	−	1.32708e11i	−0.00160440	−	0.00909899i
$843$	−1.02633e13	−	1.77766e13i	−0.699944	−	1.21234i
$844$	5.78219e12	−	1.00150e13i	0.392240	−	0.679379i
$845$	−1.31574e13	−	4.78891e12i	−0.887801	−	0.323133i
$846$	4.78472e12	+	1.74149e12i	0.321137	+	0.116884i
$847$	1.55083e12	−	2.68612e12i	0.103535	−	0.179329i
$848$	6.31306e11	+	1.09345e12i	0.0419236	+	0.0726138i
$849$	−5.44444e12	−	3.08769e13i	−0.359640	−	2.03962i
$850$	9.38571e11	+	7.87555e11i	0.0616711	+	0.0517482i
$851$	3.87355e12	−	3.25030e12i	0.253178	−	0.212442i
$852$	2.76272e12	−	1.56682e13i	0.179622	−	1.01869i
$853$	−1.41521e13	+	5.15093e12i	−0.915271	+	0.333131i	−0.756355	−	0.654161i	$-0.773022\pi$
$853$	−1.41521e13	+	5.15093e12i	−0.915271	+	0.333131i	−0.158915	+	0.987292i	$0.550800\pi$
$854$	1.43725e13			0.924638
$855$	2.97997e13	+	3.19612e13i	1.90706	+	2.04539i
$856$	1.95814e12			0.124656
$857$	7.17606e12	−	2.61187e12i	0.454436	−	0.165401i	−0.104653	−	0.994509i	$-0.533373\pi$
$857$	7.17606e12	−	2.61187e12i	0.454436	−	0.165401i	0.559089	+	0.829108i	$0.311151\pi$
$858$	−5.08472e11	+	2.88369e12i	−0.0320313	+	0.181659i
$859$	5.60882e12	−	4.70636e12i	0.351481	−	0.294928i	−0.449903	−	0.893077i	$-0.648542\pi$
$859$	5.60882e12	−	4.70636e12i	0.351481	−	0.294928i	0.801385	+	0.598149i	$0.204097\pi$
$860$	−5.06175e12	−	4.24732e12i	−0.315543	−	0.264772i
$861$	7.36186e11	+	4.17512e12i	0.0456534	+	0.258913i
$862$	1.36994e12	+	2.37280e12i	0.0845119	+	0.146379i
$863$	−1.45954e13	+	2.52799e13i	−0.895709	+	1.55141i	−0.0627833	+	0.998027i	$0.519998\pi$
$863$	−1.45954e13	+	2.52799e13i	−0.895709	+	1.55141i	−0.832925	+	0.553386i	$0.813336\pi$
$864$	−1.02014e13	−	3.71300e12i	−0.622797	−	0.226680i
$865$	2.12238e13	+	7.72485e12i	1.28900	+	0.469156i
$866$	−3.59408e12	+	6.22513e12i	−0.217149	+	0.376113i
$867$	−2.79019e13	−	4.83275e13i	−1.67706	−	2.90475i
$868$	−3.63428e11	−	2.06110e12i	−0.0217310	−	0.123243i
$869$	−7.81014e12	−	6.55348e12i	−0.464590	−	0.389837i
$870$	−1.30467e13	+	1.09475e13i	−0.772085	+	0.647856i
$871$	2.80241e11	−	1.58932e12i	0.0164987	−	0.0935688i
$872$	−9.60747e11	+	3.49683e11i	−0.0562710	+	0.0204810i
$873$	−3.88847e13			−2.26577
$874$	−6.84755e11	+	2.23912e12i	−0.0396948	+	0.129800i
$875$	2.37699e13			1.37085
$876$	−2.60453e13	+	9.47971e12i	−1.49438	+	0.543909i
$877$	4.51924e12	−	2.56299e13i	0.257969	−	1.46301i	−0.530368	−	0.847768i	$-0.677946\pi$
$877$	4.51924e12	−	2.56299e13i	0.257969	−	1.46301i	0.788336	−	0.615245i	$-0.210943\pi$
$878$	−4.20780e11	+	3.53077e11i	−0.0238963	+	0.0200513i
$879$	2.56368e13	+	2.15118e13i	1.44848	+	1.21542i
$880$	6.84546e11	+	3.88225e12i	0.0384796	+	0.218229i
$881$	5.55043e12	+	9.61362e12i	0.310409	+	0.537645i	0.978451	−	0.206479i	$-0.0662006\pi$
$881$	5.55043e12	+	9.61362e12i	0.310409	+	0.537645i	−0.668042	+	0.744124i	$0.732867\pi$
$882$	−1.41078e13	+	2.44354e13i	−0.784965	+	1.35960i
$883$	−2.28588e12	−	8.31994e11i	−0.126541	−	0.0460571i	0.277974	−	0.960589i	$-0.410337\pi$
$883$	−2.28588e12	−	8.31994e11i	−0.126541	−	0.0460571i	−0.404514	+	0.914532i	$0.632559\pi$
$884$	2.01515e12	+	7.33453e11i	0.110987	+	0.0403959i
$885$	2.85580e13	−	4.94639e13i	1.56489	−	2.71046i
$886$	5.45445e11	+	9.44738e11i	0.0297371	+	0.0515062i
$887$	4.79552e12	+	2.71968e13i	0.260124	+	1.47523i	0.782570	+	0.622562i	$0.213908\pi$
$887$	4.79552e12	+	2.71968e13i	0.260124	+	1.47523i	−0.522447	+	0.852672i	$0.674981\pi$
$888$	1.70608e13	+	1.43157e13i	0.920749	+	0.772600i
$889$	2.26046e13	−	1.89675e13i	1.21378	−	1.01848i
$890$	1.04179e12	−	5.90829e12i	0.0556577	−	0.315651i
$891$	7.31576e13	−	2.66272e13i	3.88875	−	1.41539i
$892$	−3.91627e12			−0.207124
$893$	3.14473e12	+	3.86370e11i	0.165482	+	0.0203316i
$894$	−2.75153e13			−1.44064
$895$	−2.03952e12	+	7.42324e11i	−0.106249	+	0.0386714i
$896$	3.93492e11	−	2.23161e12i	0.0203963	−	0.115673i
$897$	8.09519e11	−	6.79267e11i	0.0417504	−	0.0350328i
$898$	1.14783e13	+	9.63140e12i	0.589023	+	0.494249i
$899$	−4.79294e11	−	2.71821e12i	−0.0244728	−	0.138792i
$900$	9.88579e11	+	1.71227e12i	0.0502250	+	0.0869923i
$901$	−5.44950e12	+	9.43881e12i	−0.275483	+	0.477151i
$902$	1.21610e12	+	4.42626e11i	0.0611704	+	0.0222642i
$903$	−4.20688e13	−	1.53118e13i	−2.10555	−	0.766357i
$904$	1.18814e12	−	2.05792e12i	0.0591713	−	0.102488i
$905$	1.17759e12	+	2.03965e12i	0.0583549	+	0.101074i
$906$	6.32506e12	+	3.58712e13i	0.311880	+	1.76876i
$907$	6.39704e11	+	5.36775e11i	0.0313867	+	0.0263366i	0.658346	−	0.752715i	$-0.271256\pi$
$907$	6.39704e11	+	5.36775e11i	0.0313867	+	0.0263366i	−0.626959	+	0.779052i	$0.715701\pi$
$908$	5.89897e12	−	4.94983e12i	0.287998	−	0.241659i
$909$	−9.63887e12	+	5.46648e13i	−0.468262	+	2.65564i
$910$	2.53387e12	−	9.22254e11i	0.122489	−	0.0445825i
$911$	−2.37291e13			−1.14143			−0.570714	−	0.821149i	$-0.693334\pi$
$911$	−2.37291e13			−1.14143			−0.570714	+	0.821149i	$0.693334\pi$
$912$	−1.02359e13	−	1.25761e12i	−0.489948	−	0.0601964i
$913$	−5.15060e12			−0.245324
$914$	1.74995e13	−	6.36930e12i	0.829407	−	0.301879i
$915$	−6.90135e12	+	3.91395e13i	−0.325491	+	1.84595i
$916$	4.94290e12	−	4.14758e12i	0.231981	−	0.194655i
$917$	−2.48055e13	−	2.08143e13i	−1.15847	−	0.972074i
$918$	−1.62727e13	−	9.22871e13i	−0.756254	−	4.28893i
$919$	−1.23767e13	−	2.14370e13i	−0.572379	−	0.991390i	−0.996321	−	0.0857007i	$-0.972687\pi$
$919$	−1.23767e13	−	2.14370e13i	−0.572379	−	0.991390i	0.423941	−	0.905690i	$-0.360646\pi$
$920$	7.11342e11	−	1.23208e12i	0.0327366	−	0.0567014i
$921$	3.46658e13	+	1.26173e13i	1.58757	+	0.577829i
$922$	7.77352e11	+	2.82933e11i	0.0354265	+	0.0128942i
$923$	−1.66101e12	+	2.87695e12i	−0.0753293	+	0.130474i
$924$	1.33546e13	+	2.31308e13i	0.602706	+	1.04392i
$925$	−4.61363e11	−	2.61652e12i	−0.0207207	−	0.117513i
$926$	2.16228e13	+	1.81437e13i	0.966414	+	0.810917i
$927$	6.30048e13	−	5.28673e13i	2.80230	−	2.35141i
$928$	5.18943e11	−	2.94307e12i	0.0229696	−	0.130267i
$929$	2.78981e13	−	1.01541e13i	1.22886	−	0.447270i	0.355655	−	0.934617i	$-0.384258\pi$
$929$	2.78981e13	−	1.01541e13i	1.22886	−	0.447270i	0.873208	+	0.487347i	$0.162035\pi$
$930$	5.78735e12			0.253692
$931$	−5.13452e12	+	1.67896e13i	−0.223989	+	0.732432i
$932$	−9.83265e12			−0.426873
$933$	4.74644e13	−	1.72756e13i	2.05069	−	0.746391i
$934$	3.03373e11	−	1.72051e12i	0.0130441	−	0.0739770i
$935$	−2.60677e13	+	2.18734e13i	−1.11545	+	0.935975i
$936$	2.65096e12	+	2.22442e12i	0.112892	+	0.0947273i
$937$	5.51524e12	+	3.12785e13i	0.233742	+	1.32562i	0.845247	+	0.534376i	$0.179453\pi$
$937$	5.51524e12	+	3.12785e13i	0.233742	+	1.32562i	−0.611505	+	0.791240i	$0.709436\pi$
$938$	−7.36026e12	−	1.27483e13i	−0.310442	−	0.537701i
$939$	5.78251e12	−	1.00156e13i	0.242729	−	0.420419i
$940$	−1.80901e12	−	6.58424e11i	−0.0755726	−	0.0275062i
$941$	1.47935e13	+	5.38440e12i	0.615061	+	0.223864i	0.630716	−	0.776014i	$-0.282761\pi$
$941$	1.47935e13	+	5.38440e12i	0.615061	+	0.223864i	−0.0156553	+	0.999877i	$0.504983\pi$
$942$	−5.04412e11	+	8.73668e11i	−0.0208716	+	0.0361507i
$943$	−2.33524e11	−	4.04475e11i	−0.00961675	−	0.0166567i
$944$	1.74032e12	+	9.86986e12i	0.0713273	+	0.404517i
$945$	−9.02655e13	−	7.57418e13i	−3.68196	−	3.08953i
$946$	−1.04688e13	+	8.78435e12i	−0.424997	+	0.356615i
$947$	−3.11950e12	+	1.76916e13i	−0.126041	+	0.714811i	0.854644	+	0.519215i	$0.173775\pi$
$947$	−3.11950e12	+	1.76916e13i	−0.126041	+	0.714811i	−0.980684	+	0.195597i	$0.937336\pi$
$948$	−1.52285e13	+	5.54271e12i	−0.612377	+	0.222887i
$949$	5.78733e12			0.231622
$950$	8.38987e11	+	8.99842e11i	0.0334194	+	0.0358435i
$951$	−8.75621e13			−3.47140
$952$	1.83810e13	−	6.69013e12i	0.725275	−	0.263978i
$953$	−3.73363e12	+	2.11744e13i	−0.146627	+	0.831561i	0.819420	+	0.573193i	$0.194296\pi$
$953$	−3.73363e12	+	2.11744e13i	−0.146627	+	0.831561i	−0.966047	+	0.258367i	$0.916815\pi$
$954$	−1.34731e13	+	1.13053e13i	−0.526624	+	0.441890i
$955$	−1.63144e13	−	1.36894e13i	−0.634680	−	0.532560i
$956$	1.74493e12	+	9.89601e12i	0.0675645	+	0.383177i
$957$	1.76122e13	+	3.05052e13i	0.678749	+	1.17563i
$958$	9.63685e12	−	1.66915e13i	0.369650	−	0.640252i
$959$	1.67193e13	+	6.08533e12i	0.638314	+	0.232327i
$960$	5.88822e12	+	2.14314e12i	0.223750	+	0.0814384i
$961$	1.27509e13	−	2.20851e13i	0.482263	−	0.835304i
$962$	−2.32515e12	−	4.02727e12i	−0.0875311	−	0.151608i
$963$	4.73652e12	+	2.68621e13i	0.177477	+	1.00652i
$964$	6.17450e12	+	5.18102e12i	0.230280	+	0.193228i
$965$	1.58718e13	−	1.33180e13i	0.589186	−	0.494385i
$966$	1.67381e12	−	9.49263e12i	0.0618455	−	0.350744i
$967$	−1.68130e13	+	6.11943e12i	−0.618338	+	0.225057i	−0.632147	−	0.774848i	$-0.717826\pi$
$967$	−1.68130e13	+	6.11943e12i	−0.618338	+	0.225057i	0.0138097	+	0.999905i	$0.495604\pi$
$968$	−1.50497e12			−0.0550921
$969$	−3.47774e13	−	8.19479e13i	−1.26718	−	2.98594i
$970$	1.47015e13			0.533200
$971$	1.94566e13	−	7.08161e12i	0.702392	−	0.255650i	0.0339602	−	0.999423i	$-0.489188\pi$
$971$	1.94566e13	−	7.08161e12i	0.702392	−	0.255650i	0.668432	+	0.743773i	$0.266966\pi$
$972$	1.24298e13	−	7.04929e13i	0.446649	−	2.53307i
$973$	−2.00908e13	+	1.68582e13i	−0.718604	+	0.602980i
$974$	−1.38727e13	−	1.16406e13i	−0.493908	−	0.414438i
$975$	−9.64185e10	−	5.46816e11i	−0.00341696	−	0.0193785i
$976$	−3.48687e12	−	6.03944e12i	−0.123002	−	0.213045i
$977$	−2.99396e12	+	5.18569e12i	−0.105128	+	0.182088i	−0.913791	−	0.406185i	$-0.866859\pi$
$977$	−2.99396e12	+	5.18569e12i	−0.105128	+	0.182088i	0.808662	+	0.588273i	$0.200192\pi$
$978$	3.15898e13	+	1.14977e13i	1.10413	+	0.401872i
$979$	−1.16598e13	−	4.24382e12i	−0.405666	−	0.147651i
$980$	5.33387e12	−	9.23853e12i	0.184725	−	0.319953i
$981$	−7.12095e12	−	1.23339e13i	−0.245486	−	0.425195i
$982$	2.38471e12	+	1.35243e13i	0.0818339	+	0.464103i
$983$	2.43993e13	+	2.04735e13i	0.833464	+	0.699360i	0.956084	−	0.293094i	$-0.0946849\pi$
$983$	2.43993e13	+	2.04735e13i	0.833464	+	0.699360i	−0.122619	+	0.992454i	$0.539129\pi$
$984$	1.57581e12	−	1.32226e12i	0.0535830	−	0.0449615i
$985$	4.87688e12	−	2.76582e13i	0.165074	−	0.936182i
$986$	2.42411e13	−	8.82303e12i	0.816782	−	0.297284i
$987$	−1.30431e13			−0.437476
$988$	1.91858e12	+	9.77750e11i	0.0640579	+	0.0326454i
$989$	4.93194e12			0.163921
$990$	−5.16016e13	+	1.87814e13i	−1.70728	+	0.621399i
$991$	−9.37716e11	+	5.31805e12i	−0.0308845	+	0.175154i	−0.996348	−	0.0853830i	$-0.972789\pi$
$991$	−9.37716e11	+	5.31805e12i	−0.0308845	+	0.175154i	0.965464	+	0.260537i	$0.0838997\pi$
$992$	−7.77922e11	+	6.52754e11i	−0.0255055	+	0.0214016i
$993$	3.26974e13	+	2.74363e13i	1.06719	+	0.895477i
$994$	5.26180e12	+	2.98411e13i	0.170960	+	0.969564i
$995$	7.41449e12	+	1.28423e13i	0.239816	+	0.415373i
$996$	−4.09349e12	+	7.09013e12i	−0.131803	+	0.228290i
$997$	5.01835e13	+	1.82653e13i	1.60854	+	0.585462i	0.981151	−	0.193242i	$-0.0619002\pi$
$997$	5.01835e13	+	1.82653e13i	1.60854	+	0.585462i	0.627392	+	0.778704i	$0.284122\pi$
$998$	3.18424e13	+	1.15897e13i	1.01606	+	0.369814i
$999$	−1.01606e14	+	1.75987e14i	−3.22756	+	5.59030i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	38.10.e.b.5.8	✓	48
19.4	even	9	inner	38.10.e.b.23.8	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
38.10.e.b.5.8	✓	48	1.1	even	1	trivial
38.10.e.b.23.8	yes	48	19.4	even	9	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:	\( N \)	\(=\)	\( 38 = 2 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	38.e (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-15.0351 + 5.47232i) q^{2} +(48.1038 - 272.810i) q^{3} +(196.107 - 164.554i) q^{4} +(-1032.82 - 866.635i) q^{5} +(769.661 + 4364.97i) q^{6} +(-4220.81 - 7310.67i) q^{7} +(-2048.00 + 3547.24i) q^{8} +(-53615.6 - 19514.5i) q^{9} +O(q^{10})\)	\(q+(-15.0351 + 5.47232i) q^{2} +(48.1038 - 272.810i) q^{3} +(196.107 - 164.554i) q^{4} +(-1032.82 - 866.635i) q^{5} +(769.661 + 4364.97i) q^{6} +(-4220.81 - 7310.67i) q^{7} +(-2048.00 + 3547.24i) q^{8} +(-53615.6 - 19514.5i) q^{9} +(20271.0 + 7378.03i) q^{10} +(22307.6 - 38638.0i) q^{11} +(-35458.4 - 61415.8i) q^{12} +(2571.31 + 14582.6i) q^{13} +(103467. + 86818.8i) q^{14} +(-286109. + 240074. i) q^{15} +(11380.2 - 64540.4i) q^{16} +(531597. - 193485. i) q^{17} +912904. q^{18} +(553507. - 127742. i) q^{19} -345151. q^{20} +(-2.19746e6 + 799811. i) q^{21} +(-123958. + 703000. i) q^{22} +(197348. - 165595. i) q^{23} +(869207. + 729351. i) q^{24} +(-23505.4 - 133305. i) q^{25} +(-118461. - 205180. i) q^{26} +(-5.17658e6 + 8.96610e6i) q^{27} +(-2.03073e6 - 739125. i) q^{28} +(-2.67815e6 - 974768. i) q^{29} +(2.98791e6 - 5.17522e6i) q^{30} +(484230. + 838712. i) q^{31} +(182083. + 1.03265e6i) q^{32} +(-9.46775e6 - 7.94439e6i) q^{33} +(-6.93379e6 + 5.81814e6i) q^{34} +(-1.97636e6 + 1.12085e7i) q^{35} +(-1.37256e7 + 4.99570e6i) q^{36} +1.96280e7 q^{37} +(-7.62297e6 + 4.94958e6i) q^{38} +4.10198e6 q^{39} +(5.18937e6 - 1.88878e6i) q^{40} +(314812. - 1.78539e6i) q^{41} +(2.86622e7 - 2.40504e7i) q^{42} +(1.46654e7 + 1.23057e7i) q^{43} +(-1.98332e6 - 1.12480e7i) q^{44} +(3.84630e7 + 6.66199e7i) q^{45} +(-2.06096e6 + 3.56969e6i) q^{46} +(5.24121e6 + 1.90764e6i) q^{47} +(-1.70598e7 - 6.20928e6i) q^{48} +(-1.54537e7 + 2.67667e7i) q^{49} +(1.08290e6 + 1.87563e6i) q^{50} +(-2.72130e7 - 1.54333e8i) q^{51} +(2.90388e6 + 2.43664e6i) q^{52} +(-1.47585e7 + 1.23839e7i) q^{53} +(2.87649e7 - 1.63134e8i) q^{54} +(-5.65247e7 + 2.05733e7i) q^{55} +3.45769e7 q^{56} +(-8.22360e6 - 1.57147e8i) q^{57} +4.56005e7 q^{58} +(-1.43703e8 + 5.23036e7i) q^{59} +(-1.66031e7 + 9.41607e7i) q^{60} +(8.15154e7 - 6.83996e7i) q^{61} +(-1.18701e7 - 9.96023e6i) q^{62} +(8.36376e7 + 4.74332e8i) q^{63} +(-8.38861e6 - 1.45295e7i) q^{64} +(9.98212e6 - 1.72895e7i) q^{65} +(1.85823e8 + 6.76339e7i) q^{66} +(-1.02415e8 - 3.72759e7i) q^{67} +(7.24114e7 - 1.25420e8i) q^{68} +(-3.56828e7 - 6.18044e7i) q^{69} +(-3.16217e7 - 1.79336e8i) q^{70} +(1.71859e8 + 1.44207e8i) q^{71} +(1.79027e8 - 1.50222e8i) q^{72} +(6.78679e7 - 3.84898e8i) q^{73} +(-2.95109e8 + 1.07411e8i) q^{74} -3.74978e7 q^{75} +(8.75263e7 - 1.16133e8i) q^{76} -3.76626e8 q^{77} +(-6.16736e7 + 2.24474e7i) q^{78} +(3.96818e7 - 2.25047e8i) q^{79} +(-6.76866e7 + 5.67958e7i) q^{80} +(1.33673e9 + 1.12165e9i) q^{81} +(5.03700e6 + 2.85662e7i) q^{82} +(-5.77224e7 - 9.99781e7i) q^{83} +(-2.99327e8 + 5.18449e8i) q^{84} +(-7.16723e8 - 2.60866e8i) q^{85} +(-2.87835e8 - 1.04764e8i) q^{86} +(-3.94756e8 + 6.83738e8i) q^{87} +(9.13721e7 + 1.58261e8i) q^{88} +(-4.82939e7 - 2.73888e8i) q^{89} +(-9.42861e8 - 7.91154e8i) q^{90} +(9.57556e7 - 8.03485e7i) q^{91} +(1.14522e7 - 6.49488e7i) q^{92} +(2.52103e8 - 9.17578e7i) q^{93} -8.92412e7 q^{94} +(-6.82376e8 - 3.47754e8i) q^{95} +2.90475e8 q^{96} +(6.40413e8 - 2.33091e8i) q^{97} +(8.58725e7 - 4.87007e8i) q^{98} +(-1.95004e9 + 1.63627e9i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 33 q^{3} + 528 q^{6} - 25809 q^{7} - 98304 q^{8} + 7953 q^{9}+O(q^{10}) \) 48 * q + 33 * q^3 + 528 * q^6 - 25809 * q^7 - 98304 * q^8 + 7953 * q^9	\( 48 q + 33 q^{3} + 528 q^{6} - 25809 q^{7} - 98304 q^{8} + 7953 q^{9} - 55221 q^{11} - 62208 q^{12} + 21777 q^{13} + 28464 q^{14} - 280011 q^{15} + 1055055 q^{17} + 6083232 q^{18} + 2408220 q^{19} + 523776 q^{20} - 5105673 q^{21} - 2513280 q^{22} - 456708 q^{23} + 135168 q^{24} + 19417530 q^{25} - 1077120 q^{26} - 11729661 q^{27} - 30720 q^{28} + 4679889 q^{29} + 4879158 q^{31} - 12360834 q^{33} + 9206400 q^{34} - 47475759 q^{35} + 2035968 q^{36} + 119843604 q^{37} - 39471312 q^{38} + 16552668 q^{39} + 60082911 q^{41} + 59187024 q^{42} + 109939059 q^{43} - 40212480 q^{44} + 3067236 q^{45} - 4919424 q^{46} + 198627789 q^{47} - 4325376 q^{48} - 182954115 q^{49} - 229688016 q^{50} - 228228021 q^{51} - 49495296 q^{52} - 370799859 q^{53} + 111760416 q^{54} - 60369543 q^{55} + 211427328 q^{56} + 128158266 q^{57} + 166196064 q^{58} - 382689396 q^{59} - 36777216 q^{60} - 850085550 q^{61} + 42954480 q^{62} - 803298357 q^{63} - 402653184 q^{64} + 261122181 q^{65} + 516819888 q^{66} + 1146400764 q^{67} + 125611008 q^{68} - 178115667 q^{69} - 759612144 q^{70} + 363378456 q^{71} - 65150976 q^{72} + 1407478230 q^{73} - 12153360 q^{74} + 1715917770 q^{75} - 128288256 q^{76} - 193134048 q^{77} - 1199414208 q^{78} - 2098405449 q^{79} + 3082805319 q^{81} + 961326576 q^{82} + 358330707 q^{83} + 502249728 q^{84} - 1961566422 q^{85} - 588638592 q^{86} - 1222269090 q^{87} - 226185216 q^{88} - 368108670 q^{89} + 1740707616 q^{90} - 3296437032 q^{91} - 819648768 q^{92} + 6597152658 q^{93} + 2953278144 q^{94} - 881990403 q^{95} + 509607936 q^{96} - 3752161206 q^{97} - 458055696 q^{98} + 6061589742 q^{99}+O(q^{100}) \) 48 * q + 33 * q^3 + 528 * q^6 - 25809 * q^7 - 98304 * q^8 + 7953 * q^9 - 55221 * q^11 - 62208 * q^12 + 21777 * q^13 + 28464 * q^14 - 280011 * q^15 + 1055055 * q^17 + 6083232 * q^18 + 2408220 * q^19 + 523776 * q^20 - 5105673 * q^21 - 2513280 * q^22 - 456708 * q^23 + 135168 * q^24 + 19417530 * q^25 - 1077120 * q^26 - 11729661 * q^27 - 30720 * q^28 + 4679889 * q^29 + 4879158 * q^31 - 12360834 * q^33 + 9206400 * q^34 - 47475759 * q^35 + 2035968 * q^36 + 119843604 * q^37 - 39471312 * q^38 + 16552668 * q^39 + 60082911 * q^41 + 59187024 * q^42 + 109939059 * q^43 - 40212480 * q^44 + 3067236 * q^45 - 4919424 * q^46 + 198627789 * q^47 - 4325376 * q^48 - 182954115 * q^49 - 229688016 * q^50 - 228228021 * q^51 - 49495296 * q^52 - 370799859 * q^53 + 111760416 * q^54 - 60369543 * q^55 + 211427328 * q^56 + 128158266 * q^57 + 166196064 * q^58 - 382689396 * q^59 - 36777216 * q^60 - 850085550 * q^61 + 42954480 * q^62 - 803298357 * q^63 - 402653184 * q^64 + 261122181 * q^65 + 516819888 * q^66 + 1146400764 * q^67 + 125611008 * q^68 - 178115667 * q^69 - 759612144 * q^70 + 363378456 * q^71 - 65150976 * q^72 + 1407478230 * q^73 - 12153360 * q^74 + 1715917770 * q^75 - 128288256 * q^76 - 193134048 * q^77 - 1199414208 * q^78 - 2098405449 * q^79 + 3082805319 * q^81 + 961326576 * q^82 + 358330707 * q^83 + 502249728 * q^84 - 1961566422 * q^85 - 588638592 * q^86 - 1222269090 * q^87 - 226185216 * q^88 - 368108670 * q^89 + 1740707616 * q^90 - 3296437032 * q^91 - 819648768 * q^92 + 6597152658 * q^93 + 2953278144 * q^94 - 881990403 * q^95 + 509607936 * q^96 - 3752161206 * q^97 - 458055696 * q^98 + 6061589742 * q^99

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