LMFDB - Embedded newform 89.10.f.a.11.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [89,10,Mod(11,89)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(89, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([21]))

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

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

chi := DirichletCharacter("89.11");

S:= CuspForms(chi, 10);

N := Newforms(S);

Level:	$ N $	$=$	$ 89 $
Weight:	$ k $	$=$	$ 10 $
Character orbit:	$[\chi]$	$=$	89.f (of order $22$, degree $10$, 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:	$45.8381894186$
Analytic rank:	$0$
Dimension:	$660$
Relative dimension:	$66$ over $\Q(\zeta_{22})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			11.8
Character	$\chi$	$=$	89.11
Dual form			89.10.f.a.81.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-23.8701 - 27.5475i) q^{2} +(-96.7895 + 13.9162i) q^{3} +(-116.221 + 808.333i) q^{4} +(-236.144 + 151.761i) q^{5} +(2693.73 + 2334.13i) q^{6} +(-6039.03 - 9396.92i) q^{7} +(9341.70 - 6003.54i) q^{8} +(-9711.15 + 2851.45i) q^{9} +O(q^{10})$	\(q+(-23.8701 - 27.5475i) q^{2} +(-96.7895 + 13.9162i) q^{3} +(-116.221 + 808.333i) q^{4} +(-236.144 + 151.761i) q^{5} +(2693.73 + 2334.13i) q^{6} +(-6039.03 - 9396.92i) q^{7} +(9341.70 - 6003.54i) q^{8} +(-9711.15 + 2851.45i) q^{9} +(9817.41 + 2882.65i) q^{10} +(34646.3 + 22265.9i) q^{11} -79855.5i q^{12} +(-71877.0 + 10334.4i) q^{13} +(-114710. + 390665. i) q^{14} +(20744.4 - 17975.1i) q^{15} +(12815.9 + 3763.09i) q^{16} +(-368818. + 425639. i) q^{17} +(310356. + 199454. i) q^{18} +(-71968.1 - 245101. i) q^{19} +(-95228.4 - 208521. i) q^{20} +(715285. + 825483. i) q^{21} +(-213641. - 1.48591e6i) q^{22} +(377141. + 1.28442e6i) q^{23} +(-820632. + 711081. i) q^{24} +(-778625. + 1.70495e6i) q^{25} +(2.00040e6 + 1.73335e6i) q^{26} +(2.65102e6 - 1.21068e6i) q^{27} +(8.29770e6 - 3.78943e6i) q^{28} +(2.68694e6 + 4.18096e6i) q^{29} +(-990338. - 142389. i) q^{30} +(2.10673e6 - 7.17486e6i) q^{31} +(-2.56410e6 - 5.61459e6i) q^{32} +(-3.66326e6 - 1.67295e6i) q^{33} +2.05290e7 q^{34} +(2.85217e6 + 1.30254e6i) q^{35} +(-1.17628e6 - 8.18124e6i) q^{36} +1.37200e6i q^{37} +(-5.03403e6 + 7.83311e6i) q^{38} +(6.81313e6 - 2.00052e6i) q^{39} +(-1.29489e6 + 2.83541e6i) q^{40} +(-1.09259e7 - 1.57091e6i) q^{41} +(5.66611e6 - 3.94086e7i) q^{42} +(-8.96014e6 + 1.39423e7i) q^{43} +(-2.20248e7 + 2.54180e7i) q^{44} +(1.86049e6 - 2.14713e6i) q^{45} +(2.63803e7 - 4.10486e7i) q^{46} +(-2.16871e6 + 1.50837e7i) q^{47} +(-1.29281e6 - 185879. i) q^{48} +(-3.50687e7 + 7.67897e7i) q^{49} +(6.55530e7 - 1.92481e7i) q^{50} +(2.97744e7 - 4.63299e7i) q^{51} -5.93016e7i q^{52} +(3.97679e6 + 2.76592e7i) q^{53} +(-9.66314e7 - 4.41301e7i) q^{54} -1.15606e7 q^{55} +(-1.12830e8 - 5.15276e7i) q^{56} +(1.03766e7 + 2.27217e7i) q^{57} +(5.10377e7 - 1.73818e8i) q^{58} +(-1.24023e6 - 178319. i) q^{59} +(1.21189e7 + 1.88574e7i) q^{60} +(-1.70239e8 + 7.77456e7i) q^{61} +(-2.47937e8 + 1.13229e8i) q^{62} +(8.54408e7 + 7.40349e7i) q^{63} +(-9.06219e7 + 1.98434e8i) q^{64} +(1.54050e7 - 1.33485e7i) q^{65} +(4.13565e7 + 1.40847e8i) q^{66} +(-3.28293e7 - 2.28333e8i) q^{67} +(-3.01194e8 - 3.47596e8i) q^{68} +(-5.43777e7 - 1.19070e8i) q^{69} +(-3.21996e7 - 1.09662e8i) q^{70} +(-1.34134e8 - 8.62030e7i) q^{71} +(-7.35998e7 + 8.49387e7i) q^{72} +(1.19441e8 + 3.50709e7i) q^{73} +(3.77951e7 - 3.27497e7i) q^{74} +(5.16362e7 - 1.75857e8i) q^{75} +(2.06487e8 - 2.96884e7i) q^{76} -4.60033e8i q^{77} +(-2.17739e8 - 1.39932e8i) q^{78} +(6.77768e6 + 1.99011e6i) q^{79} +(-3.59749e6 + 1.05632e6i) q^{80} +(-7.21537e7 + 4.63703e7i) q^{81} +(2.17528e8 + 3.38480e8i) q^{82} +(-5.10882e8 - 4.42682e8i) q^{83} +(-7.50396e8 + 4.82250e8i) q^{84} +(2.24991e7 - 1.56484e8i) q^{85} +(5.97954e8 - 8.59727e7i) q^{86} +(-3.18251e8 - 3.67281e8i) q^{87} +4.57330e8 q^{88} +(5.81866e8 - 1.08573e8i) q^{89} -1.03558e8 q^{90} +(5.31179e8 + 6.13013e8i) q^{91} +(-1.08207e9 + 1.55579e8i) q^{92} +(-1.04062e8 + 7.23769e8i) q^{93} +(4.67286e8 - 3.00307e8i) q^{94} +(5.41915e7 + 4.69572e7i) q^{95} +(3.26311e8 + 5.07751e8i) q^{96} +(-8.90973e8 + 5.72594e8i) q^{97} +(2.95246e9 - 8.66919e8i) q^{98} +(-3.99946e8 - 1.17435e8i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 660 q - 9 q^{2} - 825 q^{3} - 16393 q^{4} - 5127 q^{5} - 11 q^{6} - 11 q^{7} + 1015 q^{8} + 489535 q^{9}+O(q^{10}) $ 660 * q - 9 * q^2 - 825 * q^3 - 16393 * q^4 - 5127 * q^5 - 11 * q^6 - 11 * q^7 + 1015 * q^8 + 489535 * q^9	\( 660 q - 9 q^{2} - 825 q^{3} - 16393 q^{4} - 5127 q^{5} - 11 q^{6} - 11 q^{7} + 1015 q^{8} + 489535 q^{9} - 225841 q^{10} - 224944 q^{11} - 11 q^{13} + 1940664 q^{14} - 11 q^{15} - 5125641 q^{16} + 1457606 q^{17} + 2864796 q^{18} - 11 q^{19} - 5955661 q^{20} + 856653 q^{21} + 13531907 q^{22} - 11 q^{23} + 5621 q^{24} - 31973709 q^{25} - 4206763 q^{26} - 17737896 q^{27} - 11 q^{28} + 10200729 q^{29} - 81004858 q^{30} - 11 q^{31} - 44372422 q^{32} - 19516475 q^{33} + 35594328 q^{34} - 35970209 q^{35} + 71890930 q^{36} - 87132859 q^{38} + 42308203 q^{39} - 128175356 q^{40} + 60926635 q^{41} + 121333817 q^{42} + 296517661 q^{43} + 115664209 q^{44} + 48133749 q^{45} + 311125309 q^{46} - 46792325 q^{47} - 141127426 q^{48} + 164252871 q^{49} + 103838041 q^{50} - 427287971 q^{51} + 850769769 q^{53} - 329099771 q^{54} + 793594654 q^{55} - 2036185316 q^{56} - 154197519 q^{57} + 188920501 q^{58} + 405753711 q^{59} + 21484364 q^{60} + 344711653 q^{61} - 1167226764 q^{62} - 1320295229 q^{63} - 134364169 q^{64} + 1450391239 q^{65} + 863803105 q^{66} + 646170445 q^{67} + 1285178775 q^{68} - 221829309 q^{69} + 854155808 q^{70} - 1113621013 q^{71} - 2392386072 q^{72} - 314298299 q^{73} - 479039451 q^{74} - 3075936347 q^{75} - 6170784400 q^{76} - 2037231963 q^{78} - 79886655 q^{79} + 6302566534 q^{80} + 281226707 q^{81} + 5439310019 q^{82} + 1306521271 q^{83} + 1958614914 q^{84} + 4403895759 q^{85} - 3738814827 q^{86} - 4959185007 q^{87} + 2745817562 q^{88} + 3415767517 q^{89} - 10039266258 q^{90} + 1585238913 q^{91} + 8669558172 q^{92} + 1795690413 q^{93} - 8679076027 q^{94} + 10576695701 q^{95} + 12941524981 q^{96} - 2702894895 q^{97} + 1786224002 q^{98} - 9157402144 q^{99}+O(q^{100}) \) 660 * q - 9 * q^2 - 825 * q^3 - 16393 * q^4 - 5127 * q^5 - 11 * q^6 - 11 * q^7 + 1015 * q^8 + 489535 * q^9 - 225841 * q^10 - 224944 * q^11 - 11 * q^13 + 1940664 * q^14 - 11 * q^15 - 5125641 * q^16 + 1457606 * q^17 + 2864796 * q^18 - 11 * q^19 - 5955661 * q^20 + 856653 * q^21 + 13531907 * q^22 - 11 * q^23 + 5621 * q^24 - 31973709 * q^25 - 4206763 * q^26 - 17737896 * q^27 - 11 * q^28 + 10200729 * q^29 - 81004858 * q^30 - 11 * q^31 - 44372422 * q^32 - 19516475 * q^33 + 35594328 * q^34 - 35970209 * q^35 + 71890930 * q^36 - 87132859 * q^38 + 42308203 * q^39 - 128175356 * q^40 + 60926635 * q^41 + 121333817 * q^42 + 296517661 * q^43 + 115664209 * q^44 + 48133749 * q^45 + 311125309 * q^46 - 46792325 * q^47 - 141127426 * q^48 + 164252871 * q^49 + 103838041 * q^50 - 427287971 * q^51 + 850769769 * q^53 - 329099771 * q^54 + 793594654 * q^55 - 2036185316 * q^56 - 154197519 * q^57 + 188920501 * q^58 + 405753711 * q^59 + 21484364 * q^60 + 344711653 * q^61 - 1167226764 * q^62 - 1320295229 * q^63 - 134364169 * q^64 + 1450391239 * q^65 + 863803105 * q^66 + 646170445 * q^67 + 1285178775 * q^68 - 221829309 * q^69 + 854155808 * q^70 - 1113621013 * q^71 - 2392386072 * q^72 - 314298299 * q^73 - 479039451 * q^74 - 3075936347 * q^75 - 6170784400 * q^76 - 2037231963 * q^78 - 79886655 * q^79 + 6302566534 * q^80 + 281226707 * q^81 + 5439310019 * q^82 + 1306521271 * q^83 + 1958614914 * q^84 + 4403895759 * q^85 - 3738814827 * q^86 - 4959185007 * q^87 + 2745817562 * q^88 + 3415767517 * q^89 - 10039266258 * q^90 + 1585238913 * q^91 + 8669558172 * q^92 + 1795690413 * q^93 - 8679076027 * q^94 + 10576695701 * q^95 + 12941524981 * q^96 - 2702894895 * q^97 + 1786224002 * q^98 - 9157402144 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/89\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{21}{22}\right)$

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 $

$2$	−23.8701	−	27.5475i	−1.05492	−	1.21744i	−0.975362	−	0.220609i	$-0.929195\pi$
$2$	−23.8701	−	27.5475i	−1.05492	−	1.21744i	−0.0795552	−	0.996830i	$-0.525350\pi$
$3$	−96.7895	+	13.9162i	−0.689895	+	0.0991919i	−0.478341	−	0.878174i	$-0.658762\pi$
$3$	−96.7895	+	13.9162i	−0.689895	+	0.0991919i	−0.211554	+	0.977366i	$0.567852\pi$
$4$	−116.221	+	808.333i	−0.226994	+	1.57878i
$5$	−236.144	+	151.761i	−0.168971	+	0.108591i	−0.622393	−	0.782705i	$-0.713839\pi$
$5$	−236.144	+	151.761i	−0.168971	+	0.108591i	0.453422	+	0.891296i	$0.350203\pi$
$6$	2693.73	+	2334.13i	0.848542	+	0.735266i
$7$	−6039.03	−	9396.92i	−0.950662	−	1.47926i	−0.876150	−	0.482039i	$-0.839896\pi$
$7$	−6039.03	−	9396.92i	−0.950662	−	1.47926i	−0.0745125	−	0.997220i	$-0.523740\pi$
$8$	9341.70	−	6003.54i	0.806345	−	0.518206i
$9$	−9711.15	+	2851.45i	−0.493377	+	0.144869i
$10$	9817.41	+	2882.65i	0.310454	+	0.0911575i
$11$	34646.3	+	22265.9i	0.713494	+	0.458535i	0.846368	−	0.532598i	$-0.178784\pi$
$11$	34646.3	+	22265.9i	0.713494	+	0.458535i	−0.132874	+	0.991133i	$0.542421\pi$
$12$		−	79855.5i		−	1.11170i
$13$	−71877.0	+	10334.4i	−0.697983	+	0.100355i	−0.482167	−	0.876079i	$-0.660150\pi$
$13$	−71877.0	+	10334.4i	−0.697983	+	0.100355i	−0.215816	+	0.976434i	$0.569241\pi$
$14$	−114710.	+	390665.i	−0.798039	+	2.71787i
$15$	20744.4	−	17975.1i	0.105801	−	0.0916770i
$16$	12815.9	+	3763.09i	0.0488888	+	0.0143550i
$17$	−368818.	+	425639.i	−1.07101	+	1.23601i	−0.100499	+	0.994937i	$0.532044\pi$
$17$	−368818.	+	425639.i	−1.07101	+	1.23601i	−0.970508	+	0.241070i	$0.922502\pi$
$18$	310356.	+	199454.i	0.696841	+	0.447833i
$19$	−71968.1	−	245101.i	−0.126692	−	0.431473i	0.871579	−	0.490255i	$-0.163096\pi$
$19$	−71968.1	−	245101.i	−0.126692	−	0.431473i	−0.998271	+	0.0587824i	$0.981278\pi$
$20$	−95228.4	−	208521.i	−0.133086	−	0.291417i
$21$	715285.	+	825483.i	0.802587	+	0.926235i
$22$	−213641.	−	1.48591e6i	−0.194439	−	1.35235i
$23$	377141.	+	1.28442e6i	0.281014	+	0.957047i	0.972157	+	0.234329i	$0.0752893\pi$
$23$	377141.	+	1.28442e6i	0.281014	+	0.957047i	−0.691143	+	0.722718i	$0.742892\pi$
$24$	−820632.	+	711081.i	−0.504891	+	0.437491i
$25$	−778625.	+	1.70495e6i	−0.398656	+	0.872934i
$26$	2.00040e6	+	1.73335e6i	0.858491	+	0.743887i
$27$	2.65102e6	−	1.21068e6i	0.960012	−	0.438423i
$28$	8.29770e6	−	3.78943e6i	2.55121	−	1.16510i
$29$	2.68694e6	+	4.18096e6i	0.705451	+	1.09770i	0.990275	+	0.139124i	$0.0444286\pi$
$29$	2.68694e6	+	4.18096e6i	0.705451	+	1.09770i	−0.284824	+	0.958580i	$0.591935\pi$
$30$	−990338.	−	142389.i	−0.223223	−	0.0320946i
$31$	2.10673e6	−	7.17486e6i	0.409714	−	1.39536i	−0.453832	−	0.891087i	$-0.649943\pi$
$31$	2.10673e6	−	7.17486e6i	0.409714	−	1.39536i	0.863546	−	0.504270i	$-0.168238\pi$
$32$	−2.56410e6	−	5.61459e6i	−0.432274	−	0.946548i
$33$	−3.66326e6	−	1.67295e6i	−0.537719	−	0.245568i
$34$	2.05290e7			2.63459
$35$	2.85217e6	+	1.30254e6i	0.321269	+	0.146719i
$36$	−1.17628e6	−	8.18124e6i	−0.116722	−	0.811816i
$37$			1.37200e6i			0.120350i	0.998188	+	0.0601750i	$0.0191659\pi$
$37$			1.37200e6i			0.120350i	−0.998188	+	0.0601750i	$0.980834\pi$
$38$	−5.03403e6	+	7.83311e6i	−0.391643	+	0.609408i
$39$	6.81313e6	−	2.00052e6i	0.471581	−	0.138469i
$40$	−1.29489e6	+	2.83541e6i	−0.0799764	+	0.175124i
$41$	−1.09259e7	−	1.57091e6i	−0.603853	−	0.0868209i	−0.166394	−	0.986059i	$-0.553212\pi$
$41$	−1.09259e7	−	1.57091e6i	−0.603853	−	0.0868209i	−0.437459	+	0.899238i	$0.644121\pi$
$42$	5.66611e6	−	3.94086e7i	0.280972	−	1.95420i
$43$	−8.96014e6	+	1.39423e7i	−0.399675	+	0.621906i	−0.981512	−	0.191399i	$-0.938698\pi$
$43$	−8.96014e6	+	1.39423e7i	−0.399675	+	0.621906i	0.581837	+	0.813305i	$0.302334\pi$
$44$	−2.20248e7	+	2.54180e7i	−0.885882	+	1.02236i
$45$	1.86049e6	−	2.14713e6i	0.0676351	−	0.0780551i
$46$	2.63803e7	−	4.10486e7i	0.868700	−	1.35172i
$47$	−2.16871e6	+	1.50837e7i	−0.0648278	+	0.450887i	0.931392	+	0.364018i	$0.118595\pi$
$47$	−2.16871e6	+	1.50837e7i	−0.0648278	+	0.450887i	−0.996220	+	0.0868694i	$0.972314\pi$
$48$	−1.29281e6	−	185879.i	−0.0351520	−	0.00505410i
$49$	−3.50687e7	+	7.67897e7i	−0.869034	+	1.90292i
$50$	6.55530e7	−	1.92481e7i	1.48329	−	0.435534i
$51$	2.97744e7	−	4.63299e7i	0.616280	−	0.958950i
$52$		−	5.93016e7i		−	1.12474i
$53$	3.97679e6	+	2.76592e7i	0.0692295	+	0.481502i	0.994711	+	0.102710i	$0.0327513\pi$
$53$	3.97679e6	+	2.76592e7i	0.0692295	+	0.481502i	−0.925482	+	0.378792i	$0.876340\pi$
$54$	−9.66314e7	−	4.41301e7i	−1.54649	−	0.706257i
$55$	−1.15606e7			−0.170353
$56$	−1.12830e8	−	5.15276e7i	−1.53312	−	0.700154i
$57$	1.03766e7	+	2.27217e7i	0.130203	+	0.285104i
$58$	5.10377e7	−	1.73818e8i	0.592195	−	2.01683i
$59$	−1.24023e6	−	178319.i	−0.0133251	−	0.00191586i	0.135649	−	0.990757i	$-0.456688\pi$
$59$	−1.24023e6	−	178319.i	−0.0133251	−	0.00191586i	−0.148974	+	0.988841i	$0.547597\pi$
$60$	1.21189e7	+	1.88574e7i	0.120721	+	0.187846i
$61$	−1.70239e8	+	7.77456e7i	−1.57426	+	0.718938i	−0.995338	−	0.0964477i	$-0.969252\pi$
$61$	−1.70239e8	+	7.77456e7i	−1.57426	+	0.718938i	−0.578917	+	0.815386i	$0.696525\pi$
$62$	−2.47937e8	+	1.13229e8i	−2.13098	+	0.973185i
$63$	8.54408e7	+	7.40349e7i	0.683334	+	0.592112i
$64$	−9.06219e7	+	1.98434e8i	−0.675185	+	1.47845i
$65$	1.54050e7	−	1.33485e7i	0.107041	−	0.0927519i
$66$	4.13565e7	+	1.40847e8i	0.268285	+	0.913694i
$67$	−3.28293e7	−	2.28333e8i	−0.199033	−	1.38430i	−0.807098	−	0.590417i	$-0.798963\pi$
$67$	−3.28293e7	−	2.28333e8i	−0.199033	−	1.38430i	0.608065	−	0.793887i	$-0.291946\pi$
$68$	−3.01194e8	−	3.47596e8i	−1.70827	−	1.97144i
$69$	−5.43777e7	−	1.19070e8i	−0.288802	−	0.632387i
$70$	−3.21996e7	−	1.09662e8i	−0.160291	−	0.545902i
$71$	−1.34134e8	−	8.62030e7i	−0.626438	−	0.402587i	0.188551	−	0.982063i	$-0.439621\pi$
$71$	−1.34134e8	−	8.62030e7i	−0.626438	−	0.402587i	−0.814989	+	0.579476i	$0.803257\pi$
$72$	−7.35998e7	+	8.49387e7i	−0.322760	+	0.372485i
$73$	1.19441e8	+	3.50709e7i	0.492265	+	0.144542i	0.518438	−	0.855115i	$-0.326514\pi$
$73$	1.19441e8	+	3.50709e7i	0.492265	+	0.144542i	−0.0261728	+	0.999657i	$0.508332\pi$
$74$	3.77951e7	−	3.27497e7i	0.146519	−	0.126959i
$75$	5.16362e7	−	1.75857e8i	0.188442	−	0.641776i
$76$	2.06487e8	−	2.96884e7i	0.709957	−	0.102076i
$77$		−	4.60033e8i		−	1.49135i
$78$	−2.17739e8	−	1.39932e8i	−0.666056	−	0.428048i
$79$	6.77768e6	+	1.99011e6i	0.0195776	+	0.00574849i	0.291507	−	0.956569i	$-0.405843\pi$
$79$	6.77768e6	+	1.99011e6i	0.0195776	+	0.00574849i	−0.271929	+	0.962317i	$0.587662\pi$
$80$	−3.59749e6	+	1.05632e6i	−0.00981963	+	0.00288330i
$81$	−7.21537e7	+	4.63703e7i	−0.186241	+	0.119690i
$82$	2.17528e8	+	3.38480e8i	0.531316	+	0.826743i
$83$	−5.10882e8	−	4.42682e8i	−1.18160	−	1.02386i	−0.999174	−	0.0406396i	$-0.987060\pi$
$83$	−5.10882e8	−	4.42682e8i	−1.18160	−	1.02386i	−0.182423	−	0.983220i	$-0.558394\pi$
$84$	−7.50396e8	+	4.82250e8i	−1.64450	+	1.05686i
$85$	2.24991e7	−	1.56484e8i	0.0467497	−	0.325151i
$86$	5.97954e8	−	8.59727e7i	1.17876	−	0.169480i
$87$	−3.18251e8	−	3.67281e8i	−0.595570	−	0.687325i
$88$	4.57330e8			0.812938
$89$	5.81866e8	−	1.08573e8i	0.983033	−	0.183429i
$89$	5.81866e8	−	1.08573e8i	0.983033	−	0.183429i
$90$	−1.03558e8			−0.166377
$91$	5.31179e8	+	6.13013e8i	0.811997	+	0.937095i
$92$	−1.08207e9	+	1.55579e8i	−1.57475	+	0.226415i
$93$	−1.04062e8	+	7.23769e8i	−0.144251	+	1.00329i
$94$	4.67286e8	−	3.00307e8i	0.617316	−	0.396725i
$95$	5.41915e7	+	4.69572e7i	0.0682614	+	0.0591488i
$96$	3.26311e8	+	5.07751e8i	0.392114	+	0.610141i
$97$	−8.90973e8	+	5.72594e8i	−1.02186	+	0.656710i	−0.940437	−	0.339969i	$-0.889583\pi$
$97$	−8.90973e8	+	5.72594e8i	−1.02186	+	0.656710i	−0.0814246	+	0.996680i	$0.525947\pi$
$98$	2.95246e9	−	8.66919e8i	3.23345	−	0.949426i
$99$	−3.99946e8	−	1.17435e8i	−0.418449	−	0.122868i
$100$	−1.28767e9	−	8.27538e8i	−1.28767	−	0.827538i
$101$		−	1.06811e9i		−	1.02134i	−0.859776	−	0.510671i	$-0.829397\pi$
$101$		−	1.06811e9i		−	1.02134i	0.859776	−	0.510671i	$-0.170603\pi$
$102$	−1.98699e9	+	2.85686e8i	−1.81759	+	0.261330i
$103$	4.90231e8	−	1.66957e9i	0.429174	−	1.46163i	−0.407132	−	0.913370i	$-0.633471\pi$
$103$	4.90231e8	−	1.66957e9i	0.429174	−	1.46163i	0.836306	−	0.548263i	$-0.184711\pi$
$104$	−6.09411e8	+	5.28057e8i	−0.510811	+	0.442620i
$105$	−2.94186e8	−	8.63809e7i	−0.236195	−	0.0693531i
$106$	6.67015e8	−	7.69777e8i	0.513168	−	0.592227i
$107$	−9.37687e8	−	6.02615e8i	−0.691562	−	0.444440i	0.147079	−	0.989125i	$-0.453013\pi$
$107$	−9.37687e8	−	6.02615e8i	−0.691562	−	0.444440i	−0.838641	+	0.544685i	$0.816649\pi$
$108$	6.70530e8	+	2.28362e9i	0.474255	+	1.61516i
$109$	1.16080e9	+	2.54179e9i	0.787657	+	1.72473i	0.683240	+	0.730194i	$0.260570\pi$
$109$	1.16080e9	+	2.54179e9i	0.787657	+	1.72473i	0.104417	+	0.994534i	$0.466702\pi$
$110$	2.75953e8	+	3.18466e8i	0.179708	+	0.207394i
$111$	−1.90931e7	−	1.32795e8i	−0.0119377	−	0.0830288i
$112$	−4.20342e7	−	1.43155e8i	−0.0252419	−	0.0859660i
$113$	7.47701e8	−	6.47886e8i	0.431395	−	0.373806i	−0.411925	−	0.911218i	$-0.635143\pi$
$113$	7.47701e8	−	6.47886e8i	0.431395	−	0.373806i	0.843320	+	0.537412i	$0.180598\pi$
$114$	3.78234e8	−	8.28218e8i	0.209744	−	0.459275i
$115$	−2.83985e8	−	2.46074e8i	−0.151410	−	0.131198i
$116$	−3.69189e9	+	1.68603e9i	−1.89316	+	0.864577i
$117$	6.68541e8	−	3.05312e8i	0.329831	−	0.150629i
$118$	2.46922e7	+	3.84219e7i	0.0117244	+	0.0182436i
$119$	6.22700e9	+	8.95307e8i	2.84654	+	0.409271i
$120$	8.58733e7	−	2.92458e8i	0.0378044	−	0.128750i
$121$	−2.74926e8	−	6.02004e8i	−0.116595	−	0.255308i
$122$	6.20532e9	+	2.83387e9i	2.53597	+	1.15814i
$123$	1.07938e9			0.425207
$124$	5.55483e9	+	2.53680e9i	2.10995	+	0.963584i
$125$	−1.52901e8	−	1.06345e9i	−0.0560165	−	0.389603i
$126$		−	4.12090e9i		−	1.45655i
$127$	2.30975e9	−	3.59404e9i	0.787858	−	1.22593i	−0.182249	−	0.983252i	$-0.558338\pi$
$127$	2.30975e9	−	3.59404e9i	0.787858	−	1.22593i	0.970107	−	0.242678i	$-0.0780259\pi$
$128$	4.59728e9	−	1.34988e9i	1.51376	−	0.444479i
$129$	6.73224e8	−	1.47416e9i	0.214046	−	0.468694i
$130$	−7.35437e8	−	1.05740e8i	−0.225840	−	0.0324709i
$131$	−6.63280e8	+	4.61321e9i	−0.196778	+	1.36862i	0.616780	+	0.787135i	$0.288437\pi$
$131$	−6.63280e8	+	4.61321e9i	−0.196778	+	1.36862i	−0.813558	+	0.581484i	$0.802472\pi$
$132$	1.77805e9	−	2.76670e9i	0.509755	−	0.793194i
$133$	−1.86857e9	+	2.15645e9i	−0.517819	+	0.597595i
$134$	−5.50636e9	+	6.35468e9i	−1.47534	+	1.70264i
$135$	−4.42290e8	+	6.88217e8i	−0.114606	+	0.178330i
$136$	−8.90046e8	+	6.19040e9i	−0.223094	+	1.55165i
$137$	−5.73586e9	−	8.24692e8i	−1.39109	−	0.200009i	−0.594291	−	0.804250i	$-0.702567\pi$
$137$	−5.73586e9	−	8.24692e8i	−1.39109	−	0.200009i	−0.796801	+	0.604241i	$0.793476\pi$
$138$	−1.98210e9	+	4.34019e9i	−0.465232	+	1.01872i
$139$	−7.55018e9	+	2.21693e9i	−1.71550	+	0.503716i	−0.984007	−	0.178132i	$-0.942995\pi$
$139$	−7.55018e9	+	2.21693e9i	−1.71550	+	0.503716i	−0.731493	+	0.681849i	$0.761176\pi$
$140$	−1.38437e9	+	2.15412e9i	−0.304562	+	0.473907i
$141$		−	1.49013e9i		−	0.317495i
$142$	8.27119e8	+	5.75274e9i	0.170715	+	1.18735i
$143$	−2.72038e9	−	1.24236e9i	−0.544023	−	0.248447i
$144$	−1.35187e8			−0.0262002
$145$	−1.26901e9	−	5.79538e8i	−0.238402	−	0.108875i
$146$	−1.88494e9	−	4.12743e9i	−0.343328	−	0.751783i
$147$	2.32566e9	−	7.92046e9i	0.410788	−	1.39902i
$148$	−1.10903e9	−	1.59455e8i	−0.190006	−	0.0273187i
$149$	2.26019e8	+	3.51692e8i	0.0375670	+	0.0584554i	0.859529	−	0.511087i	$-0.170757\pi$
$149$	2.26019e8	+	3.51692e8i	0.0375670	+	0.0584554i	−0.821962	+	0.569542i	$0.807121\pi$
$150$	−6.07698e9	+	2.77526e9i	−0.980115	+	0.447604i
$151$	3.60373e8	−	1.64577e8i	0.0564100	−	0.0257616i	−0.387010	−	0.922075i	$-0.626492\pi$
$151$	3.60373e8	−	1.64577e8i	0.0564100	−	0.0257616i	0.443420	+	0.896314i	$0.353765\pi$
$152$	−2.14378e9	−	1.85759e9i	−0.325749	−	0.282263i
$153$	2.36796e9	−	5.18511e9i	0.349352	−	0.764973i
$154$	−1.26728e10	+	1.09810e10i	−1.81563	+	1.57326i
$155$	5.91370e8	+	2.01402e9i	0.0822937	+	0.280267i
$156$	8.25256e8	+	5.73978e9i	0.111565	+	0.775951i
$157$	−5.86911e9	−	6.77331e9i	−0.770945	−	0.889719i	0.225475	−	0.974249i	$-0.427606\pi$
$157$	−5.86911e9	−	6.77331e9i	−0.770945	−	0.889719i	−0.996421	+	0.0845303i	$0.973061\pi$
$158$	−1.06961e8	−	2.34212e8i	−0.0136543	−	0.0298987i
$159$	−7.69823e8	−	2.62178e9i	−0.0955221	−	0.325318i
$160$	1.45757e9	+	9.36724e8i	0.175829	+	0.112998i
$161$	9.79207e9	−	1.13006e10i	1.14857	−	1.32552i
$162$	2.99970e9	+	8.80791e8i	0.342184	+	0.100474i
$163$	2.46858e8	−	2.13904e8i	0.0273907	−	0.0237342i	−0.641058	−	0.767493i	$-0.721504\pi$
$163$	2.46858e8	−	2.13904e8i	0.0273907	−	0.0237342i	0.668449	+	0.743758i	$0.266959\pi$
$164$	2.53964e9	−	8.64922e9i	0.274141	−	0.933640i
$165$	1.11895e9	−	1.60880e8i	0.117525	−	0.0168976i
$166$			2.46404e10i			2.51861i
$167$	6.16360e9	+	3.96111e9i	0.613212	+	0.394087i	0.810060	−	0.586347i	$-0.199434\pi$
$167$	6.16360e9	+	3.96111e9i	0.613212	+	0.394087i	−0.196849	+	0.980434i	$0.563071\pi$
$168$	1.16378e10	+	3.41717e9i	1.12714	+	0.330959i
$169$	−5.11543e9	+	1.50203e9i	−0.482383	+	0.141640i
$170$	−4.84781e9	+	3.11550e9i	−0.445169	+	0.286093i
$171$	1.39778e9	+	2.17500e9i	0.125014	+	0.194525i
$172$	−1.02286e10	−	8.86316e9i	−0.891127	−	0.772166i
$173$	1.25320e9	−	8.05382e8i	0.106368	−	0.0683588i	−0.486375	−	0.873750i	$-0.661681\pi$
$173$	1.25320e9	−	8.05382e8i	0.106368	−	0.0683588i	0.592743	+	0.805391i	$0.298045\pi$
$174$	−2.52102e9	+	1.75340e10i	−0.208499	+	1.45014i
$175$	2.07234e10	−	2.97958e9i	1.67028	−	0.240150i
$176$	3.60236e8	+	4.15734e8i	0.0282996	+	0.0326594i
$177$	1.22523e8			0.00938294
$178$	−1.68801e10	−	1.34373e10i	−1.26033	−	1.00328i
$179$	2.71726e10			1.97830			0.989150	−	0.146912i	$-0.0469334\pi$
$179$	2.71726e10			1.97830			0.989150	+	0.146912i	$0.0469334\pi$
$180$	1.51936e9	+	1.75344e9i	0.107879	+	0.124499i
$181$	1.22689e9	−	1.76400e8i	0.0849673	−	0.0122165i	−0.0997000	−	0.995018i	$-0.531788\pi$
$181$	1.22689e9	−	1.76400e8i	0.0849673	−	0.0122165i	0.184667	+	0.982801i	$0.440879\pi$
$182$	4.20772e9	−	2.92653e10i	0.284266	−	1.97712i
$183$	1.53954e10	−	9.89405e9i	1.01476	−	0.652145i
$184$	1.12342e10	+	9.73452e9i	0.722543	+	0.626087i
$185$	−2.08216e8	−	3.23990e8i	−0.0130689	−	0.0203357i
$186$	2.24220e10	−	1.44097e10i	1.37362	−	0.882771i
$187$	−2.22554e10	+	6.53478e9i	−1.33091	+	0.390790i
$188$	−1.19406e10	−	3.50608e9i	−0.697134	−	0.204697i
$189$	−2.73863e10	−	1.76001e10i	−1.56119	−	1.00331i
$190$		−	2.61371e9i		−	0.145501i
$191$	1.49645e10	−	2.15157e9i	0.813603	−	0.116978i	0.277061	−	0.960852i	$-0.410639\pi$
$191$	1.49645e10	−	2.15157e9i	0.813603	−	0.116978i	0.536542	+	0.843874i	$0.319730\pi$
$192$	6.00979e9	−	2.04675e10i	0.319157	−	1.08695i
$193$	−6.98030e8	+	6.04847e8i	−0.0362131	+	0.0313789i	−0.672779	−	0.739843i	$-0.734900\pi$
$193$	−6.98030e8	+	6.04847e8i	−0.0362131	+	0.0313789i	0.636566	+	0.771222i	$0.280354\pi$
$194$	3.70411e10	+	1.08763e10i	1.87748	+	0.551279i
$195$	−1.30528e9	+	1.50638e9i	−0.0646471	+	0.0746067i
$196$	−5.79959e10	−	3.72717e10i	−2.80702	−	1.80396i
$197$	−4.12134e9	−	1.40360e10i	−0.194958	−	0.663965i	−0.997709	−	0.0676508i	$-0.978450\pi$
$197$	−4.12134e9	−	1.40360e10i	−0.194958	−	0.663965i	0.802751	−	0.596314i	$-0.203369\pi$
$198$	6.31169e9	+	1.38207e10i	0.291845	+	0.639052i
$199$	3.68415e9	+	4.25174e9i	0.166532	+	0.192189i	0.832882	−	0.553451i	$-0.186689\pi$
$199$	3.68415e9	+	4.25174e9i	0.166532	+	0.192189i	−0.666349	+	0.745640i	$0.732144\pi$
$200$	2.96207e9	+	2.06016e10i	0.130906	+	0.910472i
$201$	6.35506e9	+	2.16434e10i	0.274623	+	0.935282i
$202$	−2.94239e10	+	2.54959e10i	−1.24342	+	1.07743i
$203$	2.30616e10	−	5.04979e10i	0.953143	−	2.08709i
$204$	3.39896e10	+	2.94522e10i	1.37407	+	1.19064i
$205$	2.81850e9	−	1.28717e9i	0.111462	−	0.0509028i
$206$	−5.76945e10	+	2.63482e10i	−2.23219	+	1.01941i
$207$	−7.32495e9	−	1.13978e10i	−0.277292	−	0.431475i
$208$	−9.60058e8	−	1.38036e8i	−0.0355642	−	0.00511336i
$209$	2.96395e9	−	1.00943e10i	0.107451	−	0.365946i
$210$	4.64267e9	+	1.01660e10i	0.164733	+	0.360715i
$211$	5.05894e10	+	2.31034e10i	1.75707	+	0.802426i	0.986227	+	0.165398i	$0.0528910\pi$
$211$	5.05894e10	+	2.31034e10i	1.75707	+	0.802426i	0.770841	+	0.637028i	$0.219836\pi$
$212$	−2.28200e10			−0.775898
$213$	1.41824e10	+	6.47690e9i	0.472109	+	0.215605i
$214$	5.78210e9	+	4.02154e10i	0.188462	+	1.31078i
$215$		−	4.65218e9i		−	0.148485i
$216$	1.74967e10	−	2.72254e10i	0.546907	−	0.851004i
$217$	−8.01441e10	+	2.35324e10i	−2.45360	+	0.720441i
$218$	4.23117e10	−	9.26498e10i	1.26884	−	2.77837i
$219$	−1.20486e10	−	1.73233e9i	−0.353948	−	0.0508901i
$220$	1.34358e9	−	9.34483e9i	0.0386690	−	0.268949i
$221$	2.21109e10	−	3.44052e10i	0.623505	−	0.970193i
$222$	−3.20242e9	+	3.69579e9i	−0.0884892	+	0.102122i
$223$	1.02568e10	−	1.18370e10i	0.277741	−	0.320531i	−0.599690	−	0.800232i	$-0.704710\pi$
$223$	1.02568e10	−	1.18370e10i	0.277741	−	0.320531i	0.877432	+	0.479702i	$0.159255\pi$
$224$	−3.72752e10	+	5.80013e10i	−0.989244	+	1.53929i
$225$	2.69976e9	−	1.87772e10i	0.0702269	−	0.488439i
$226$	−3.56953e10	−	5.13221e9i	−0.910171	−	0.130863i
$227$	−1.16593e10	+	2.55304e10i	−0.291446	+	0.638177i	−0.997552	−	0.0699286i	$-0.977723\pi$
$227$	−1.16593e10	+	2.55304e10i	−0.291446	+	0.638177i	0.706106	+	0.708106i	$0.250450\pi$
$228$	−1.95726e10	+	5.74705e9i	−0.479670	+	0.140844i
$229$	−1.33414e10	+	2.07596e10i	−0.320584	+	0.498838i	−0.963721	−	0.266913i	$-0.913996\pi$
$229$	−1.33414e10	+	2.07596e10i	−0.320584	+	0.498838i	0.643137	+	0.765751i	$0.277633\pi$
$230$			1.36969e10i			0.322736i
$231$	6.40193e9	+	4.45264e10i	0.147930	+	1.02888i
$232$	5.02012e10	+	2.29261e10i	1.13767	+	0.519558i
$233$	4.23227e10			0.940744			0.470372	−	0.882468i	$-0.344120\pi$
$233$	4.23227e10			0.940744			0.470372	+	0.882468i	$0.344120\pi$
$234$	−2.43687e10	−	1.11288e10i	−0.531326	−	0.242648i
$235$	−1.77699e9	−	3.89106e9i	−0.0380084	−	0.0832267i
$236$	2.88282e8	−	9.81798e8i	0.00604942	−	0.0206024i
$237$	−6.83703e8	−	9.83016e7i	−0.0140767	−	0.00202392i
$238$	−1.23975e11	−	1.92909e11i	−2.50460	−	3.89724i
$239$	−8.86307e9	+	4.04763e9i	−0.175709	+	0.0802435i	−0.501327	−	0.865258i	$-0.667155\pi$
$239$	−8.86307e9	+	4.04763e9i	−0.175709	+	0.0802435i	0.325619	+	0.945501i	$0.394427\pi$
$240$	3.33500e8	−	1.52304e8i	0.00648851	−	0.00296320i
$241$	4.00952e10	+	3.47427e10i	0.765624	+	0.663417i	0.947447	−	0.319914i	$-0.103654\pi$
$241$	4.00952e10	+	3.47427e10i	0.765624	+	0.663417i	−0.181822	+	0.983331i	$0.558199\pi$
$242$	−1.00212e10	+	2.19434e10i	−0.187824	+	0.411277i
$243$	−3.70144e10	+	3.20731e10i	−0.680992	+	0.590083i
$244$	−4.30590e10	−	1.46646e11i	−0.777696	−	2.64859i
$245$	−3.37239e9	−	2.34555e10i	−0.0597985	−	0.415908i
$246$	−2.57648e10	−	2.97341e10i	−0.448558	−	0.517663i
$247$	7.70581e9	+	1.68734e10i	0.131729	+	0.288447i
$248$	−2.33942e10	−	7.96732e10i	−0.392712	−	1.33746i
$249$	5.56085e10	+	3.57374e10i	0.916736	+	0.589150i
$250$	−2.56457e10	+	2.95967e10i	−0.415226	+	0.479196i
$251$	−4.35104e10	−	1.27758e10i	−0.691928	−	0.203168i	−0.0831831	−	0.996534i	$-0.526509\pi$
$251$	−4.35104e10	−	1.27758e10i	−0.691928	−	0.203168i	−0.608745	+	0.793366i	$0.708327\pi$
$252$	−6.97748e10	+	6.04602e10i	−1.08992	+	0.944425i
$253$	−1.55323e10	+	5.28980e10i	−0.238337	+	0.811702i
$254$	−1.54141e11	+	2.21621e10i	−2.32362	+	0.334086i
$255$			1.54591e10i			0.228957i
$256$	−5.29621e10	−	3.40367e10i	−0.770701	−	0.495299i
$257$	1.10058e11	+	3.23159e10i	1.57370	+	0.462080i	0.948075	−	0.318046i	$-0.103027\pi$
$257$	1.10058e11	+	3.23159e10i	1.57370	+	0.462080i	0.625623	+	0.780125i	$0.284845\pi$
$258$	−5.66792e10	+	1.66425e10i	−0.796407	+	0.233846i
$259$	1.28926e10	−	8.28554e9i	0.178029	−	0.114412i
$260$	8.99967e9	+	1.40038e10i	0.122137	+	0.190048i
$261$	−3.80151e10	−	3.29403e10i	−0.507077	−	0.439384i
$262$	1.42915e11	−	9.18460e10i	1.87380	−	1.20422i
$263$	8.69477e9	−	6.04735e10i	0.112062	−	0.779406i	−0.853847	−	0.520524i	$-0.825737\pi$
$263$	8.69477e9	−	6.04735e10i	0.112062	−	0.779406i	0.965909	−	0.258883i	$-0.0833542\pi$
$264$	−4.42647e10	+	6.36431e9i	−0.560841	+	0.0806368i
$265$	−5.13667e9	−	5.92804e9i	−0.0639846	−	0.0738422i
$266$	1.04008e11			1.27379
$267$	−5.48076e10	+	1.86061e10i	−0.659994	+	0.224056i
$268$	1.88384e11			2.23068
$269$	−2.78562e10	−	3.21478e10i	−0.324367	−	0.374339i	0.570022	−	0.821629i	$-0.306935\pi$
$269$	−2.78562e10	−	3.21478e10i	−0.324367	−	0.374339i	−0.894389	+	0.447290i	$0.852389\pi$
$270$	2.95162e10	−	4.24378e9i	0.338005	−	0.0485978i
$271$	−8.51635e9	+	5.92325e10i	−0.0959162	+	0.667112i	0.883968	+	0.467547i	$0.154862\pi$
$271$	−8.51635e9	+	5.92325e10i	−0.0959162	+	0.667112i	−0.979885	+	0.199565i	$0.936047\pi$
$272$	−6.32845e9	+	4.06705e9i	−0.0701032	+	0.0450526i
$273$	−5.99434e10	−	5.19413e10i	−0.653145	−	0.565953i
$274$	1.14197e11	+	1.77694e11i	1.22399	+	1.90456i
$275$	−6.49387e10	+	4.17335e10i	−0.684709	+	0.440036i
$276$	1.02568e11	−	3.01168e10i	1.06395	−	0.312405i
$277$	3.03716e10	+	8.91791e9i	0.309962	+	0.0910131i	0.433014	−	0.901387i	$-0.357450\pi$
$277$	3.03716e10	+	8.91791e9i	0.309962	+	0.0910131i	−0.123052	+	0.992400i	$0.539268\pi$
$278$	2.41294e11	+	1.55070e11i	2.42295	+	1.55714i
$279$			7.56833e10i			0.747793i
$280$	3.44639e10	−	4.95517e9i	0.335084	−	0.0481778i
$281$	−8.75411e9	+	2.98138e10i	−0.0837594	+	0.285258i	−0.990712	−	0.135973i	$-0.956584\pi$
$281$	−8.75411e9	+	2.98138e10i	−0.0837594	+	0.285258i	0.906953	+	0.421232i	$0.138402\pi$
$282$	−4.10493e10	+	3.55694e10i	−0.386531	+	0.334931i
$283$	−1.04418e11	−	3.06598e10i	−0.967689	−	0.284139i	−0.240555	−	0.970635i	$-0.577330\pi$
$283$	−1.04418e11	−	3.06598e10i	−0.967689	−	0.284139i	−0.727133	+	0.686496i	$0.759148\pi$
$284$	8.52699e10	−	9.84067e10i	0.777792	−	0.897620i
$285$	−5.89864e9	−	3.79083e9i	−0.0529603	−	0.0340355i
$286$	3.07118e10	+	1.04595e11i	0.271430	+	0.924407i
$287$	5.12203e10	+	1.12157e11i	0.445629	+	0.975792i
$288$	4.09100e10	+	4.72127e10i	0.350400	+	0.404383i
$289$	−2.82648e10	−	1.96586e11i	−0.238345	−	1.65772i
$290$	1.43265e10	+	4.87917e10i	0.118946	+	0.405094i
$291$	7.82685e10	−	6.78201e10i	0.639836	−	0.554421i
$292$	−4.22304e10	+	9.24717e10i	−0.339940	+	0.744365i
$293$	4.45368e10	+	3.85914e10i	0.353032	+	0.305904i	0.813264	−	0.581894i	$-0.197688\pi$
$293$	4.45368e10	+	3.85914e10i	0.353032	+	0.305904i	−0.460232	+	0.887799i	$0.652234\pi$
$294$	−2.73703e11	+	1.24996e11i	−2.13656	+	0.975736i
$295$	3.19936e8	−	1.46110e8i	0.00245960	−	0.00112326i
$296$	8.23685e9	+	1.28168e10i	0.0623661	+	0.0970436i
$297$	1.18805e11	+	1.70816e10i	0.885995	+	0.127387i
$298$	4.29317e9	−	1.46212e10i	0.0315358	−	0.107401i
$299$	−4.03815e10	−	8.84231e10i	−0.292188	−	0.639802i
$300$	1.36150e11	+	6.21775e10i	0.970445	+	0.443187i
$301$	1.85125e11			1.29992
$302$	−1.31358e10	−	5.99892e9i	−0.0908710	−	0.0414994i
$303$	1.48641e10	+	1.03382e11i	0.101309	+	0.704619i
$304$		−	3.41201e9i		−	0.0229128i
$305$	2.84023e10	−	4.41948e10i	0.187933	−	0.292430i
$306$	−1.99360e11	+	5.85374e10i	−1.29985	+	0.381669i
$307$	7.26885e10	−	1.59166e11i	0.467028	−	1.02265i	−0.518801	−	0.854895i	$-0.673621\pi$
$307$	7.26885e10	−	1.59166e11i	0.467028	−	1.02265i	0.985829	−	0.167754i	$-0.0536513\pi$
$308$	3.71860e11	+	5.34654e10i	2.35451	+	0.338528i
$309$	−2.42151e10	+	1.68420e11i	−0.151103	+	1.05094i
$310$	4.13652e10	−	6.43656e10i	0.254395	−	0.395846i
$311$	−1.61649e10	+	1.86553e10i	−0.0979833	+	0.113079i	−0.802623	−	0.596486i	$-0.796563\pi$
$311$	−1.61649e10	+	1.86553e10i	−0.0979833	+	0.113079i	0.704640	+	0.709565i	$0.251109\pi$
$312$	5.16360e10	−	5.95911e10i	0.308501	−	0.356030i
$313$	−5.83000e10	+	9.07165e10i	−0.343336	+	0.534241i	−0.969386	−	0.245542i	$-0.921034\pi$
$313$	−5.83000e10	+	9.07165e10i	−0.343336	+	0.534241i	0.626050	+	0.779783i	$0.284670\pi$
$314$	−4.64920e10	+	3.23359e11i	−0.269895	+	1.87716i
$315$	−3.14120e10	−	4.51636e9i	−0.179762	−	0.0258458i
$316$	−2.39637e9	+	5.24733e9i	−0.0135196	+	0.0296037i
$317$	1.36586e11	−	4.01052e10i	0.759695	−	0.223067i	0.121132	−	0.992636i	$-0.461347\pi$
$317$	1.36586e11	−	4.01052e10i	0.759695	−	0.223067i	0.638563	+	0.769570i	$0.279529\pi$
$318$	−5.38477e10	+	8.37887e10i	−0.295288	+	0.459476i
$319$			2.04682e11i			1.10668i
$320$	−8.71469e9	−	6.06120e10i	−0.0464597	−	0.323135i
$321$	9.91444e10	+	4.52777e10i	0.521189	+	0.238019i
$322$	−5.45042e11			−2.82539
$323$	1.30867e11	+	5.97652e10i	0.668991	+	0.305518i
$324$	−2.90969e10	−	6.37134e10i	−0.146688	−	0.321202i
$325$	3.83457e10	−	1.30593e11i	0.190652	−	0.649301i
$326$	−1.17850e10	−	1.69443e9i	−0.0577899	−	0.00830893i
$327$	−1.47725e11	−	2.29865e11i	−0.714479	−	1.11175i
$328$	−1.11498e11	+	5.09193e10i	−0.531905	+	0.242913i
$329$	1.54837e11	−	7.07119e10i	0.728609	−	0.332744i
$330$	−3.11412e10	−	2.69840e10i	−0.144551	−	0.125255i
$331$	−6.71114e10	+	1.46954e11i	−0.307306	+	0.672905i	−0.998774	−	0.0495012i	$-0.984237\pi$
$331$	−6.71114e10	+	1.46954e11i	−0.307306	+	0.672905i	0.691468	+	0.722407i	$0.256964\pi$
$332$	4.17210e11	−	3.61514e11i	1.88466	−	1.63307i
$333$	−3.91219e9	−	1.33237e10i	−0.0174349	−	0.0593779i
$334$	−3.80069e10	−	2.64344e11i	−0.167110	−	1.16228i
$335$	4.24044e10	+	4.89373e10i	0.183954	+	0.212294i
$336$	6.06066e9	+	1.32710e10i	0.0259414	+	0.0568037i
$337$	−6.99745e10	−	2.38311e11i	−0.295532	−	1.00649i	−0.964694	−	0.263374i	$-0.915165\pi$
$337$	−6.99745e10	−	2.38311e11i	−0.295532	−	1.00649i	0.669162	−	0.743117i	$-0.266653\pi$
$338$	1.63483e11	+	1.05064e11i	0.681313	+	0.437853i
$339$	−6.33535e10	+	7.31138e10i	−0.260538	+	0.300677i
$340$	1.23877e11	+	3.63735e10i	0.502729	+	0.147615i
$341$	2.32745e11	−	2.01674e11i	0.932148	−	0.807711i
$342$	2.65505e10	−	9.04228e10i	0.104944	−	0.357405i
$343$	4.87200e11	−	7.00487e10i	1.90057	−	0.273260i
$344$			1.84037e11i			0.708585i
$345$	3.09112e10	+	1.98654e10i	0.117471	+	0.0754939i
$346$	−5.21002e10	−	1.52980e10i	−0.195432	−	0.0573842i
$347$	3.00240e10	−	8.81584e9i	0.111170	−	0.0326423i	−0.225675	−	0.974203i	$-0.572459\pi$
$347$	3.00240e10	−	8.81584e9i	0.111170	−	0.0326423i	0.336844	+	0.941560i	$0.390640\pi$
$348$	3.33873e11	−	2.14567e11i	1.22032	−	0.784253i
$349$	1.92961e11	+	3.00254e11i	0.696235	+	1.08336i	0.991770	+	0.128032i	$0.0408659\pi$
$349$	1.92961e11	+	3.00254e11i	0.696235	+	1.08336i	−0.295535	+	0.955332i	$0.595498\pi$
$350$	−5.76749e11	−	4.99756e11i	−2.05438	−	1.78013i
$351$	−1.78036e11	+	1.14417e11i	−0.626075	+	0.402354i
$352$	3.61770e10	−	2.51617e11i	0.125600	−	0.873569i
$353$	−4.14290e11	+	5.95659e10i	−1.42010	+	0.204179i	−0.809202	−	0.587531i	$-0.800100\pi$
$353$	−4.14290e11	+	5.95659e10i	−1.42010	+	0.204179i	−0.610897	+	0.791710i	$0.709191\pi$
$354$	−2.92464e9	−	3.37521e9i	−0.00989822	−	0.0114232i
$355$	4.47573e10			0.149567
$356$	2.01384e10	+	4.82960e11i	0.0664509	+	1.59363i
$357$	−6.15168e11			−2.00441
$358$	−6.48611e11	−	7.48537e11i	−2.08694	−	2.40846i
$359$	4.06135e11	−	5.83934e10i	1.29046	−	0.185541i	0.537309	−	0.843385i	$-0.319441\pi$
$359$	4.06135e11	−	5.83934e10i	1.29046	−	0.185541i	0.753154	+	0.657845i	$0.228532\pi$
$360$	4.48982e9	−	3.12274e10i	0.0140886	−	0.0979882i
$361$	2.16567e11	−	1.39179e11i	0.671136	−	0.431313i
$362$	−3.41453e10	−	2.95871e10i	−0.104506	−	0.0905553i
$363$	3.49876e10	+	5.44417e10i	0.105763	+	0.164571i
$364$	−5.57253e11	+	3.58125e11i	−1.66378	+	1.06925i
$365$	−3.35276e10	+	9.84459e9i	−0.0988746	+	0.0290322i
$366$	−6.40047e11	−	1.87935e11i	−1.86443	−	0.547447i
$367$	−4.87313e11	−	3.13177e11i	−1.40220	−	0.901141i	−0.402306	−	0.915505i	$-0.631791\pi$
$367$	−4.87313e11	−	3.13177e11i	−1.40220	−	0.901141i	−0.999897	+	0.0143638i	$0.995428\pi$
$368$			1.78803e10i			0.0508229i
$369$	1.10583e11	−	1.58994e10i	0.310505	−	0.0446439i
$370$	−3.95499e9	+	1.34695e10i	−0.0109708	+	0.0373631i
$371$	2.35895e11	−	2.04404e11i	0.646452	−	0.560154i
$372$	−5.72952e11	−	1.68234e11i	−1.55123	−	0.455481i
$373$	−2.38831e11	+	2.75626e11i	−0.638853	+	0.737276i	−0.979172	−	0.203034i	$-0.934920\pi$
$373$	−2.38831e11	+	2.75626e11i	−0.638853	+	0.737276i	0.340318	+	0.940310i	$0.389465\pi$
$374$	7.11255e11	+	4.57096e11i	1.87976	+	1.20805i
$375$	2.95985e10	+	1.00803e11i	0.0772910	+	0.263229i
$376$	7.02963e10	+	1.53928e11i	0.181379	+	0.397165i
$377$	−2.36337e11	−	2.72747e11i	−0.602553	−	0.695384i
$378$	1.68873e11	+	1.17454e12i	0.425450	+	2.95907i
$379$	−9.46106e10	−	3.22214e11i	−0.235539	−	0.802173i	−0.989410	−	0.145150i	$-0.953634\pi$
$379$	−9.46106e10	−	3.22214e11i	−0.235539	−	0.802173i	0.753870	−	0.657023i	$-0.228185\pi$
$380$	−4.42553e10	+	3.83474e10i	−0.108878	+	0.0943430i
$381$	−1.73544e11	+	3.80008e11i	−0.421936	+	0.923912i
$382$	−4.16474e11	−	3.60877e11i	−1.00070	−	0.867110i
$383$	−4.46495e11	+	2.03908e11i	−1.06028	+	0.484216i	−0.867712	−	0.497067i	$-0.834410\pi$
$383$	−4.46495e11	+	2.03908e11i	−1.06028	+	0.484216i	−0.192573	+	0.981283i	$0.561683\pi$
$384$	−4.26183e11	+	1.94631e11i	−1.00024	+	0.456796i
$385$	6.98150e10	+	1.08634e11i	0.161948	+	0.251996i
$386$	3.33240e10	+	4.79127e9i	0.0764038	+	0.0109852i
$387$	4.72576e10	−	1.60945e11i	0.107096	−	0.364735i
$388$	−3.59297e11	−	7.86750e11i	−0.804842	−	1.76236i
$389$	2.41950e11	+	1.10495e11i	0.535737	+	0.244663i	0.664863	−	0.746965i	$-0.268490\pi$
$389$	2.41950e11	+	1.10495e11i	0.535737	+	0.244663i	−0.129126	+	0.991628i	$0.541217\pi$
$390$	7.26541e10			0.159026
$391$	−6.85798e11	−	3.13193e11i	−1.48389	−	0.677668i
$392$	1.33409e11	+	9.27882e11i	0.285364	+	1.98475i
$393$		−	4.55741e11i		−	0.963722i
$394$	−2.88280e11	+	4.48572e11i	−0.602673	+	0.937777i
$395$	−1.90253e9	+	5.58633e8i	−0.00393228	+	0.00115462i
$396$	1.41408e11	−	3.09641e11i	0.288966	−	0.632747i
$397$	3.34098e11	+	4.80360e10i	0.675019	+	0.0970531i	0.471296	−	0.881975i	$-0.343787\pi$
$397$	3.34098e11	+	4.80360e10i	0.675019	+	0.0970531i	0.203724	+	0.979028i	$0.434696\pi$
$398$	2.91839e10	−	2.02979e11i	0.0583002	−	0.405486i
$399$	1.50849e11	−	2.34725e11i	0.297964	−	0.463641i
$400$	−1.63947e10	+	1.89204e10i	−0.0320208	+	0.0369540i
$401$	2.95661e11	−	3.41211e11i	0.571011	−	0.658982i	−0.394636	−	0.918837i	$-0.629129\pi$
$401$	2.95661e11	−	3.41211e11i	0.571011	−	0.658982i	0.965648	+	0.259855i	$0.0836748\pi$
$402$	4.44525e11	−	6.91694e11i	0.848944	−	1.32098i
$403$	−7.72778e10	+	5.37479e11i	−0.145943	+	1.01505i
$404$	8.63392e11	+	1.24137e11i	1.61247	+	0.231838i
$405$	1.00015e10	−	2.19002e10i	0.0184721	−	0.0404483i
$406$	−1.94157e12	+	5.70098e11i	−3.54639	+	1.04132i
$407$	−3.05487e10	+	4.75347e10i	−0.0551846	+	0.0858690i
$408$		−	6.11552e11i		−	1.09260i
$409$	−1.96002e10	−	1.36323e11i	−0.0346343	−	0.240887i	0.965149	−	0.261701i	$-0.0842833\pi$
$409$	−1.96002e10	−	1.36323e11i	−0.0346343	−	0.240887i	−0.999783	+	0.0208139i	$0.993374\pi$
$410$	−1.02736e11	−	4.69179e10i	−0.179554	−	0.0819996i
$411$	5.66648e11			0.979546
$412$	1.29260e12	+	5.90309e11i	2.21017	+	1.00935i
$413$	5.81417e9	+	1.27313e10i	0.00983360	+	0.0215326i
$414$	−1.39135e11	+	4.73851e11i	−0.232775	+	0.792758i
$415$	1.87824e11	+	2.70050e10i	0.310838	+	0.0446918i
$416$	2.42323e11	+	3.77062e11i	0.396711	+	0.617294i
$417$	6.99927e11	−	3.19646e11i	1.13355	−	0.517675i
$418$	−3.48822e11	+	1.59302e11i	−0.558869	+	0.255227i
$419$	−6.42202e11	−	5.56471e11i	−1.01791	−	0.882022i	−0.0248553	−	0.999691i	$-0.507912\pi$
$419$	−6.42202e11	−	5.56471e11i	−1.01791	−	0.882022i	−0.993053	+	0.117669i	$0.962458\pi$
$420$	1.04015e11	−	2.27761e11i	0.163108	−	0.357156i
$421$	2.58285e10	−	2.23806e10i	0.0400710	−	0.0347217i	−0.634595	−	0.772845i	$-0.718833\pi$
$421$	2.58285e10	−	2.23806e10i	0.0400710	−	0.0347217i	0.674666	+	0.738123i	$0.264288\pi$
$422$	−5.71131e11	−	1.94509e12i	−0.876656	−	2.98562i
$423$	−2.19498e10	−	1.52664e11i	−0.0333349	−	0.231849i
$424$	2.03203e11	+	2.34509e11i	0.305340	+	0.352381i
$425$	−4.38522e11	−	9.60229e11i	−0.651990	−	1.42766i
$426$	−1.60113e11	−	5.45295e11i	−0.235550	−	0.802210i
$427$	1.75865e12	+	1.13022e12i	2.56008	+	1.64526i
$428$	5.96092e11	−	6.87927e11i	0.858650	−	0.990935i
$429$	2.80593e11	+	8.23896e10i	0.399963	+	0.117440i
$430$	−1.28156e11	+	1.11048e11i	−0.180772	+	0.156640i
$431$	1.77209e11	−	6.03520e11i	0.247365	−	0.842449i	−0.738406	−	0.674357i	$-0.764421\pi$
$431$	1.77209e11	−	6.03520e11i	0.247365	−	0.842449i	0.985771	−	0.168093i	$-0.0537607\pi$
$432$	3.85312e10	−	5.53995e9i	0.0532274	−	0.00765295i
$433$		−	1.03624e12i		−	1.41665i	−0.705885	−	0.708326i	$-0.749451\pi$
$433$		−	1.03624e12i		−	1.41665i	0.705885	−	0.708326i	$-0.250549\pi$
$434$	2.56131e12	+	1.64605e12i	3.46543	+	2.22710i
$435$	1.30892e11	+	3.84334e10i	0.175272	+	0.0514644i
$436$	−2.18952e12	+	6.42902e11i	−2.90175	+	0.852031i
$437$	2.87671e11	−	1.84875e11i	0.377338	−	0.242500i
$438$	2.39880e11	+	3.73261e11i	0.311431	+	0.484595i
$439$	7.04133e11	+	6.10135e11i	0.904824	+	0.784035i	0.976974	−	0.213359i	$-0.0684404\pi$
$439$	7.04133e11	+	6.10135e11i	0.904824	+	0.784035i	−0.0721494	+	0.997394i	$0.522986\pi$
$440$	−1.07996e11	+	6.94047e10i	−0.137363	+	0.0882779i
$441$	1.21595e11	−	8.45712e11i	0.153088	−	1.06475i
$442$	−1.47556e12	+	2.12154e11i	−1.83890	+	0.264394i
$443$	4.12989e11	+	4.76614e11i	0.509473	+	0.587963i	0.950964	−	0.309302i	$-0.100096\pi$
$443$	4.12989e11	+	4.76614e11i	0.509473	+	0.587963i	−0.441490	+	0.897266i	$0.645550\pi$
$444$	1.09562e11			0.133794
$445$	−1.20927e11	+	1.13943e11i	−0.146185	+	0.137743i
$446$	−5.70910e11			−0.683221
$447$	−2.67705e10	−	3.08948e10i	−0.0317156	−	0.0366017i
$448$	2.41194e12	−	3.46784e11i	2.82888	−	0.406732i
$449$	7.60511e10	−	5.28947e11i	0.0883074	−	0.614192i	−0.896824	−	0.442388i	$-0.854131\pi$
$449$	7.60511e10	−	5.28947e11i	0.0883074	−	0.614192i	0.985131	−	0.171804i	$-0.0549595\pi$
$450$	−5.81709e11	+	3.73842e11i	−0.668728	+	0.429766i
$451$	−3.43566e11	−	2.97701e11i	−0.391035	−	0.338834i
$452$	4.36809e11	+	6.79689e11i	0.492231	+	0.765927i
$453$	−3.25900e10	+	2.09443e10i	−0.0363616	+	0.0233682i
$454$	9.81609e11	−	2.88226e11i	1.08439	−	0.318407i
$455$	−2.18466e11	−	6.41475e10i	−0.238964	−	0.0701663i
$456$	2.33346e11	+	1.49962e11i	0.252731	+	0.162420i
$457$		−	6.70520e11i		−	0.719099i	−0.933126	−	0.359550i	$-0.882930\pi$
$457$		−	6.70520e11i		−	0.719099i	0.933126	−	0.359550i	$-0.117070\pi$
$458$	8.90336e11	−	1.28011e11i	0.945495	−	0.135942i
$459$	−4.62432e11	+	1.57490e12i	−0.486285	+	1.65614i
$460$	2.31915e11	−	2.00956e11i	0.241501	−	0.209262i
$461$	−1.11607e12	−	3.27707e11i	−1.15090	−	0.337934i	−0.350008	−	0.936747i	$-0.613821\pi$
$461$	−1.11607e12	−	3.27707e11i	−1.15090	−	0.337934i	−0.800889	+	0.598813i	$0.795639\pi$
$462$	1.07378e12	−	1.23920e12i	1.09654	−	1.26548i
$463$	7.21015e11	+	4.63368e11i	0.729172	+	0.468610i	0.851816	−	0.523840i	$-0.175501\pi$
$463$	7.21015e11	+	4.63368e11i	0.729172	+	0.468610i	−0.122645	+	0.992451i	$0.539138\pi$
$464$	1.87022e10	+	6.36940e10i	0.0187311	+	0.0637922i
$465$	−8.52660e10	−	1.86706e11i	−0.0845741	−	0.185192i
$466$	−1.01025e12	−	1.16588e12i	−0.992408	−	1.14530i
$467$	−1.75440e11	−	1.22021e12i	−0.170688	−	1.18716i	−0.877435	−	0.479695i	$-0.840747\pi$
$467$	−1.75440e11	−	1.22021e12i	−0.170688	−	1.18716i	0.706747	−	0.707466i	$-0.250162\pi$
$468$	1.69096e11	+	5.75887e11i	0.162939	+	0.554921i
$469$	−1.94737e12	+	1.68740e12i	−1.85853	+	1.61043i
$470$	−6.47723e10	+	1.41831e11i	−0.0612278	+	0.134070i
$471$	6.62327e11	+	5.73910e11i	0.620124	+	0.537340i
$472$	−1.26564e10	+	5.78000e9i	−0.0117374	+	0.00536030i
$473$	−6.20872e11	+	2.83543e11i	−0.570331	+	0.260462i
$474$	1.36121e10	+	2.11808e10i	0.0123857	+	0.0192726i
$475$	4.73921e11	+	6.81395e10i	0.427154	+	0.0614154i
$476$	−1.44741e12	+	4.92943e12i	−1.29229	+	4.40115i
$477$	−1.17488e11	−	2.57263e11i	−0.103911	−	0.227533i
$478$	3.23064e11	+	1.47538e11i	0.283050	+	0.129265i
$479$	−1.37146e12			−1.19035			−0.595173	−	0.803597i	$-0.702917\pi$
$479$	−1.37146e12			−1.19035			−0.595173	+	0.803597i	$0.702917\pi$
$480$	−1.54113e11	−	7.03812e10i	−0.132512	−	0.0605161i
$481$	−1.41787e10	−	9.86152e10i	−0.0120777	−	0.0840023i
$482$		−	1.93383e12i		−	1.63195i
$483$	−7.90507e11	+	1.23005e12i	−0.660912	+	1.02840i
$484$	5.18572e11	−	1.52266e11i	0.429541	−	0.126125i
$485$	1.23501e11	−	2.70430e11i	0.101352	−	0.221930i
$486$	1.76707e12	+	2.54066e11i	1.43678	+	0.206578i
$487$	−4.90286e9	+	3.41002e10i	−0.00394975	+	0.0274711i	−0.991701	−	0.128566i	$-0.958963\pi$
$487$	−4.90286e9	+	3.41002e10i	−0.00394975	+	0.0274711i	0.987751	+	0.156037i	$0.0498718\pi$
$488$	−1.12357e12	+	1.74831e12i	−0.896834	+	1.39550i
$489$	−2.09166e10	+	2.41390e10i	−0.0165425	+	0.0190910i
$490$	−5.65641e11	+	6.52785e11i	−0.443260	+	0.511550i
$491$	9.59676e11	−	1.49328e12i	0.745174	−	1.15951i	−0.236994	−	0.971511i	$-0.576162\pi$
$491$	9.59676e11	−	1.49328e12i	0.745174	−	1.15951i	0.982169	−	0.188003i	$-0.0602013\pi$
$492$	−1.25446e11	+	8.72496e11i	−0.0965192	+	0.671306i
$493$	−2.77057e12	−	3.98348e11i	−2.11231	−	0.303705i
$494$	2.80881e11	−	6.15044e11i	0.212203	−	0.464660i
$495$	1.12267e11	−	3.29645e10i	0.0840482	−	0.0246788i
$496$	5.39992e10	−	8.40245e10i	0.0400608	−	0.0623359i
$497$			1.78103e12i			1.30939i
$498$	−3.42901e11	−	2.38493e12i	−0.249826	−	1.73758i
$499$	8.34608e11	+	3.81153e11i	0.602601	+	0.275199i	0.693265	−	0.720683i	$-0.256172\pi$
$499$	8.34608e11	+	3.81153e11i	0.602601	+	0.275199i	−0.0906638	+	0.995882i	$0.528899\pi$
$500$	8.77393e11			0.627811
$501$	−6.51696e11	−	2.97619e11i	−0.462142	−	0.211053i
$502$	6.86654e11	+	1.50356e12i	0.482582	+	1.05671i
$503$	−4.47606e11	+	1.52441e12i	−0.311774	+	1.06181i	0.643343	+	0.765578i	$0.277547\pi$
$503$	−4.47606e11	+	1.52441e12i	−0.311774	+	1.06181i	−0.955117	+	0.296228i	$0.904271\pi$
$504$	1.24263e12	+	1.78664e11i	0.857839	+	0.123339i
$505$	1.62098e11	+	2.52229e11i	0.110909	+	0.172577i
$506$	1.82796e12	−	8.34803e11i	1.23962	−	0.566118i
$507$	4.74218e11	−	2.16568e11i	0.318744	−	0.145565i
$508$	2.63674e12	+	2.28475e12i	1.75663	+	1.52213i
$509$	−1.39483e10	+	3.05426e10i	−0.00921069	+	0.0201686i	−0.914181	−	0.405305i	$-0.867165\pi$
$509$	−1.39483e10	+	3.05426e10i	−0.00921069	+	0.0201686i	0.904971	+	0.425474i	$0.139893\pi$
$510$	4.25861e11	−	3.69011e11i	0.278742	−	0.241531i
$511$	−3.91747e11	−	1.33417e12i	−0.254162	−	0.865598i
$512$	−2.25405e10	−	1.56773e11i	−0.0144960	−	0.100822i
$513$	−4.87528e11	−	5.62637e11i	−0.310793	−	0.358674i
$514$	−1.73686e12	−	3.80320e12i	−1.09757	−	2.40334i
$515$	1.37611e11	+	4.68659e11i	0.0862024	+	0.293578i
$516$	1.11337e12	+	7.15517e11i	0.691376	+	0.444320i
$517$	−4.10990e11	+	4.74308e11i	−0.253002	+	0.291980i
$518$	−5.35992e11	−	1.57382e11i	−0.327096	−	0.0960439i
$519$	−1.10089e11	+	9.53923e10i	−0.0666023	+	0.0577112i
$520$	6.37705e10	−	2.17182e11i	0.0382477	−	0.130260i
$521$	1.58581e12	−	2.28006e11i	0.942937	−	0.135574i	0.346335	−	0.938111i	$-0.387426\pi$
$521$	1.58581e12	−	2.28006e11i	0.942937	−	0.135574i	0.596602	+	0.802537i	$0.296517\pi$
$522$			1.83351e12i			1.08085i
$523$	−1.23389e12	−	7.92970e11i	−0.721136	−	0.463446i	0.127896	−	0.991788i	$-0.459178\pi$
$523$	−1.23389e12	−	7.92970e11i	−0.721136	−	0.463446i	−0.849032	+	0.528341i	$0.822814\pi$
$524$	−3.65193e12	−	1.07230e12i	−2.11608	−	0.621336i
$525$	−1.96435e12	+	5.76784e11i	−1.12850	+	0.331357i
$526$	−1.87344e12	+	1.20399e12i	−1.06710	+	0.685781i
$527$	2.27690e12	+	3.54292e12i	1.28587	+	2.00085i
$528$	−4.06525e10	−	3.52256e10i	−0.0227633	−	0.0197245i
$529$	7.71457e9	−	4.95785e9i	0.00428313	−	0.00275260i
$530$	−4.06900e10	+	2.83005e11i	−0.0223999	+	0.155795i
$531$	1.25526e10	−	1.80479e9i	0.00685184	−	0.000985146i
$532$	−1.52596e12	−	1.76105e12i	−0.825926	−	0.953170i
$533$	8.01558e11			0.430192
$534$	1.82081e12	+	1.06568e12i	0.969014	+	0.567143i
$535$	3.12883e11			0.165116
$536$	−1.67749e12	−	1.93592e12i	−0.877844	−	1.01309i
$537$	−2.63002e12	+	3.78140e11i	−1.36482	+	0.196231i
$538$	−2.20662e11	+	1.53474e12i	−0.113555	+	0.789794i
$539$	−2.92479e12	+	1.87965e12i	−1.49261	+	0.959239i
$540$	−5.04905e11	−	4.37503e11i	−0.255528	−	0.221416i
$541$	1.82691e12	+	2.84273e12i	0.916917	+	1.42675i	0.904332	+	0.426830i	$0.140370\pi$
$541$	1.82691e12	+	2.84273e12i	0.916917	+	1.42675i	0.0125847	+	0.999921i	$0.495994\pi$
$542$	1.83500e12	−	1.17928e12i	0.913352	−	0.586976i
$543$	−1.16295e11	+	3.41474e10i	−0.0574067	+	0.0168561i
$544$	3.33547e12	+	9.79383e11i	1.63291	+	0.479465i
$545$	−6.59860e11	−	4.24066e11i	−0.320382	−	0.205897i
$546$			2.89113e12i			1.39220i
$547$	−3.15168e12	+	4.53143e11i	−1.50522	+	0.216417i	−0.845044	−	0.534697i	$-0.820426\pi$
$547$	−3.15168e12	+	4.53143e11i	−1.50522	+	0.216417i	−0.660172	+	0.751114i	$0.729517\pi$
$548$	1.33325e12	−	4.54064e12i	0.631538	−	2.15082i
$549$	1.43153e12	−	1.24043e12i	0.672551	−	0.582768i
$550$	2.69975e12	+	7.92717e11i	1.25803	+	0.369391i
$551$	8.31383e11	−	9.59467e11i	0.384254	−	0.443453i
$552$	−1.22282e12	−	7.85862e11i	−0.560581	−	0.360263i
$553$	−2.22297e10	−	7.57076e10i	−0.0101081	−	0.0344252i
$554$	−4.79306e11	−	1.04953e12i	−0.216182	−	0.473372i
$555$	2.46618e10	+	2.84612e10i	0.0110333	+	0.0127331i
$556$	−9.14532e11	−	6.36071e12i	−0.405847	−	2.82273i
$557$	−4.91532e11	−	1.67400e12i	−0.216373	−	0.736899i	−0.994116	−	0.108317i	$-0.965454\pi$
$557$	−4.91532e11	−	1.67400e12i	−0.216373	−	0.736899i	0.777743	−	0.628582i	$-0.216364\pi$
$558$	2.08489e12	−	1.80657e12i	0.910393	−	0.788860i
$559$	4.99944e11	−	1.09473e12i	0.216555	−	0.474190i
$560$	3.16515e10	+	2.74262e10i	0.0136003	+	0.0117847i
$561$	2.06315e12	−	9.42210e11i	0.879424	−	0.401619i
$562$	1.03026e12	−	4.70502e11i	0.435644	−	0.198952i
$563$	6.36615e11	+	9.90592e11i	0.267048	+	0.415535i	0.948717	−	0.316126i	$-0.102382\pi$
$563$	6.36615e11	+	9.90592e11i	0.267048	+	0.415535i	−0.681669	+	0.731660i	$0.738746\pi$
$564$	1.20452e12	+	1.73184e11i	0.501254	+	0.0720694i
$565$	−7.82416e10	+	2.66466e11i	−0.0323013	+	0.110008i
$566$	1.64786e12	+	3.60830e12i	0.674909	+	1.47785i
$567$	8.71477e11	+	3.97990e11i	0.354105	+	0.161714i
$568$	−1.77057e12			−0.713748
$569$	−5.80244e10	−	2.64988e10i	−0.0232063	−	0.0105979i	0.403778	−	0.914857i	$-0.367697\pi$
$569$	−5.80244e10	−	2.64988e10i	−0.0232063	−	0.0105979i	−0.426984	+	0.904259i	$0.640424\pi$
$570$	3.63731e10	+	2.52980e11i	0.0144325	+	0.100381i
$571$		−	3.16579e12i		−	1.24629i	−0.782106	−	0.623145i	$-0.785854\pi$
$571$		−	3.16579e12i		−	1.24629i	0.782106	−	0.623145i	$-0.214146\pi$
$572$	1.32040e12	−	2.05459e12i	0.515732	−	0.802494i
$573$	−1.41847e12	+	4.16500e11i	−0.549697	+	0.161406i
$574$	1.86701e12	−	4.08818e12i	0.717866	−	1.57191i
$575$	−2.48353e12	−	3.57078e11i	−0.947468	−	0.136225i
$576$	3.14217e11	−	2.18543e12i	0.118940	−	0.827247i
$577$	2.21342e12	−	3.44415e12i	0.831329	−	1.29357i	−0.122271	−	0.992497i	$-0.539018\pi$
$577$	2.21342e12	−	3.44415e12i	0.831329	−	1.29357i	0.953600	−	0.301076i	$-0.0973459\pi$
$578$	−4.74077e12	+	5.47114e12i	−1.76674	+	2.03893i
$579$	5.91448e10	−	6.82568e10i	0.0218707	−	0.0252402i
$580$	6.15945e11	−	9.58430e11i	0.226004	−	0.351669i
$581$	−1.07461e12	+	7.47409e12i	−0.391254	+	2.72123i
$582$	−3.73655e12	−	5.37235e11i	−1.34995	−	0.194093i
$583$	−4.78074e11	+	1.04684e12i	−0.171390	+	0.375293i
$584$	1.32633e12	−	3.89445e11i	0.471838	−	0.138544i
$585$	−1.11538e11	+	1.73556e11i	−0.0393750	+	0.0612687i
$586$		−	2.14806e12i		−	0.752500i
$587$	5.18085e11	+	3.60336e12i	0.180107	+	1.25267i	0.856507	+	0.516135i	$0.172630\pi$
$587$	5.18085e11	+	3.60336e12i	0.180107	+	1.25267i	−0.676401	+	0.736534i	$0.736461\pi$
$588$	6.13208e12	+	2.80043e12i	2.11548	+	0.966109i
$589$	−1.91018e12			−0.653966
$590$	−1.16619e10	−	5.32580e9i	−0.00396218	−	0.00180947i
$591$	5.94230e11	+	1.30118e12i	0.200360	+	0.438727i
$592$	−5.16295e9	+	1.75834e10i	−0.00172763	+	0.00588376i
$593$	2.16250e12	+	3.10921e11i	0.718142	+	0.103253i	0.491692	−	0.870769i	$-0.336379\pi$
$593$	2.16250e12	+	3.10921e11i	0.718142	+	0.103253i	0.226450	+	0.974023i	$0.427288\pi$
$594$	−2.36533e12	−	3.68053e12i	−0.779566	−	1.21303i
$595$	−1.60634e12	+	7.33592e11i	−0.525427	+	0.239954i
$596$	−3.10553e11	+	1.41825e11i	−0.100815	+	0.0460409i
$597$	−4.15756e11	−	3.60254e11i	−0.133953	−	0.116071i
$598$	−1.47193e12	+	3.22308e12i	−0.470686	+	1.03066i
$599$	3.75221e10	−	3.25131e10i	0.0119088	−	0.0103190i	−0.648886	−	0.760886i	$-0.724765\pi$
$599$	3.75221e10	−	3.25131e10i	0.0119088	−	0.0103190i	0.660795	+	0.750567i	$0.270219\pi$
$600$	−5.73394e11	−	1.95280e12i	−0.180623	−	0.615145i
$601$	1.96960e11	+	1.36988e12i	0.0615804	+	0.428301i	0.997168	+	0.0752062i	$0.0239615\pi$
$601$	1.96960e11	+	1.36988e12i	0.0615804	+	0.428301i	−0.935588	+	0.353095i	$0.885129\pi$
$602$	−4.41894e12	−	5.09973e12i	−1.37130	−	1.58257i
$603$	9.69889e11	+	2.12376e12i	0.298741	+	0.654151i
$604$	9.11500e10	+	3.10428e11i	0.0278670	+	0.0949064i
$605$	1.56283e11	+	1.00437e11i	0.0474255	+	0.0304785i
$606$	2.49312e12	−	2.87721e12i	0.750958	−	0.866652i
$607$	−2.55110e12	−	7.49072e11i	−0.762744	−	0.223962i	−0.122850	−	0.992425i	$-0.539204\pi$
$607$	−2.55110e12	−	7.49072e11i	−0.762744	−	0.223962i	−0.639894	+	0.768463i	$0.721022\pi$
$608$	−1.19161e12	+	1.03253e12i	−0.353644	+	0.306434i
$609$	−1.52938e12	+	5.20860e12i	−0.450545	+	1.53442i
$610$	−1.89542e12	+	2.72521e11i	−0.554270	+	0.0796920i
$611$		−	1.10659e12i		−	0.321218i
$612$	3.91609e12	+	2.51672e12i	1.12842	+	0.725192i
$613$	2.39801e12	+	7.04118e11i	0.685928	+	0.201407i	0.606084	−	0.795401i	$-0.292740\pi$
$613$	2.39801e12	+	7.04118e11i	0.685928	+	0.201407i	0.0798439	+	0.996807i	$0.474558\pi$
$614$	−6.11969e12	+	1.79690e12i	−1.73769	+	0.510232i
$615$	−2.54889e11	+	1.63807e11i	−0.0718477	+	0.0461737i
$616$	−2.76183e12	−	4.29749e12i	−0.772829	−	1.20255i
$617$	3.24929e12	+	2.81553e12i	0.902622	+	0.782126i	0.976584	−	0.215135i	$-0.0690191\pi$
$617$	3.24929e12	+	2.81553e12i	0.902622	+	0.782126i	−0.0739627	+	0.997261i	$0.523565\pi$
$618$	5.21755e12	−	3.35312e12i	1.43886	−	0.924700i
$619$	6.62739e11	−	4.60945e12i	0.181441	−	1.26195i	−0.671919	−	0.740625i	$-0.734530\pi$
$619$	6.62739e11	−	4.60945e12i	0.181441	−	1.26195i	0.853359	−	0.521323i	$-0.174561\pi$
$620$	−1.69673e12	+	2.43953e11i	−0.461158	+	0.0663045i
$621$	2.55484e12	+	2.94844e12i	0.689369	+	0.795574i
$622$	8.99766e11			0.241031
$623$	−4.53416e12	−	4.81207e12i	−1.20587	−	1.27978i
$624$	9.48445e10			0.0250427
$625$	−2.19982e12	−	2.53872e12i	−0.576669	−	0.665511i
$626$	3.89064e12	−	5.59389e11i	1.01260	−	0.145589i
$627$	−1.46405e11	+	1.01827e12i	−0.0378313	+	0.263122i
$628$	6.15720e12	−	3.95699e12i	1.57967	−	1.01519i
$629$	−5.83976e11	−	5.06018e11i	−0.148753	−	0.128896i
$630$	6.25391e11	+	9.73127e11i	0.158168	+	0.246114i
$631$	−5.74600e12	+	3.69273e12i	−1.44289	+	0.927290i	−0.443370	+	0.896338i	$0.646217\pi$
$631$	−5.74600e12	+	3.69273e12i	−1.44289	+	0.927290i	−0.999521	+	0.0309515i	$0.990146\pi$
$632$	7.52627e10	−	2.20991e10i	0.0187652	−	0.00550995i
$633$	−5.21804e12	−	1.53215e12i	−1.29179	−	0.379303i
$634$	−4.36511e12	−	2.80529e12i	−1.07299	−	0.689566i
$635$			1.19924e12i			0.292701i
$636$	2.20874e12	−	3.17569e11i	0.535288	−	0.0769627i
$637$	1.72706e12	−	5.88183e12i	0.415604	−	1.41542i
$638$	5.63848e12	−	4.88577e12i	1.34731	−	1.16746i
$639$	1.54840e12	+	4.54652e11i	0.367392	+	0.107876i
$640$	−8.80762e11	+	1.01645e12i	−0.207515	+	0.239485i
$641$	−1.54114e12	−	9.90430e11i	−0.360563	−	0.231719i	0.347799	−	0.937569i	$-0.386929\pi$
$641$	−1.54114e12	−	9.90430e11i	−0.360563	−	0.231719i	−0.708362	+	0.705850i	$0.750565\pi$
$642$	−1.11929e12	−	3.81196e12i	−0.260038	−	0.885607i
$643$	2.56541e12	+	5.61747e12i	0.591844	+	1.29596i	0.934321	+	0.356432i	$0.116007\pi$
$643$	2.56541e12	+	5.61747e12i	0.591844	+	1.29596i	−0.342477	+	0.939526i	$0.611266\pi$
$644$	7.99664e12	+	9.22862e12i	1.83198	+	2.11422i
$645$	6.47409e10	+	4.50283e11i	0.0147285	+	0.102439i
$646$	−1.47743e12	−	5.03167e12i	−0.333781	−	1.13675i
$647$	6.53697e12	−	5.66432e12i	1.46659	−	1.27080i	0.574840	−	0.818266i	$-0.305064\pi$
$647$	6.53697e12	−	5.66432e12i	1.46659	−	1.27080i	0.891745	−	0.452537i	$-0.149481\pi$
$648$	−3.95651e11	+	8.66355e11i	−0.0881505	+	0.193023i
$649$	−3.89992e10	−	3.37930e10i	−0.00862888	−	0.00747696i
$650$	−4.51284e12	+	2.06094e12i	−0.991607	+	0.452852i
$651$	7.42963e12	−	3.39300e12i	1.62126	−	0.740405i
$652$	1.44215e11	+	2.24404e11i	0.0312534	+	0.0486313i
$653$	−6.36317e11	−	9.14886e10i	−0.136951	−	0.0196905i	0.0734985	−	0.997295i	$-0.476584\pi$
$653$	−6.36317e11	−	9.14886e10i	−0.136951	−	0.0196905i	−0.210449	+	0.977605i	$0.567493\pi$
$654$	−2.80600e12	+	9.55635e12i	−0.599773	+	2.04264i
$655$	−5.43475e11	−	1.19004e12i	−0.115370	−	0.252626i
$656$	−1.34114e11	−	6.12479e10i	−0.0282753	−	0.0129129i
$657$	−1.25991e12			−0.263812
$658$	−5.64392e12	−	2.57749e12i	−1.17372	−	0.536019i
$659$	2.77909e11	+	1.93290e12i	0.0574009	+	0.399232i	0.998185	+	0.0602251i	$0.0191818\pi$
$659$	2.77909e11	+	1.93290e12i	0.0574009	+	0.399232i	−0.940784	+	0.339007i	$0.889909\pi$
$660$			9.23180e11i			0.189382i
$661$	7.54576e11	−	1.17414e12i	0.153743	−	0.239229i	−0.755835	−	0.654763i	$-0.772769\pi$
$661$	7.54576e11	−	1.17414e12i	0.153743	−	0.239229i	0.909578	+	0.415533i	$0.136405\pi$
$662$	5.65016e12	−	1.65904e12i	1.14340	−	0.335734i
$663$	−1.66131e12	+	3.63776e12i	−0.333918	+	0.731178i
$664$	−7.43017e12	−	1.06830e12i	−1.48335	−	0.213273i
$665$	1.13989e11	−	7.92810e11i	0.0226029	−	0.157207i
$666$	−2.73650e11	+	4.25808e11i	−0.0538966	+	0.0838648i
$667$	−4.35677e12	+	5.02799e12i	−0.852312	+	0.983621i
$668$	−3.91823e12	+	4.52188e12i	−0.761370	+	0.878668i
$669$	−8.28026e11	+	1.28843e12i	−0.159818	+	0.248682i
$670$	3.35905e11	−	2.33627e12i	0.0643991	−	0.447906i
$671$	−7.62924e12	−	1.09692e12i	−1.45288	−	0.208893i
$672$	2.80069e12	−	6.13265e12i	0.529789	−	1.16008i
$673$	1.29940e12	−	3.81537e11i	0.244159	−	0.0716917i	−0.157363	−	0.987541i	$-0.550299\pi$
$673$	1.29940e12	−	3.81537e11i	0.244159	−	0.0716917i	0.401523	+	0.915849i	$0.368481\pi$
$674$	−4.89458e12	+	7.61612e12i	−0.913579	+	1.42156i
$675$			5.46253e12i			1.01281i
$676$	−6.19618e11	−	4.30954e12i	−0.114121	−	0.793726i
$677$	−2.26287e12	−	1.03342e12i	−0.414009	−	0.189072i	0.197511	−	0.980301i	$-0.436714\pi$
$677$	−2.26287e12	−	1.03342e12i	−0.414009	−	0.189072i	−0.611520	+	0.791229i	$0.709442\pi$
$678$	3.52635e12			0.640903
$679$	1.07612e13	+	4.91449e12i	1.94289	+	0.887288i
$680$	−7.29281e11	−	1.59690e12i	−0.130799	−	0.286410i
$681$	7.73216e11	−	2.63333e12i	0.137765	−	0.469184i
$682$	−1.11113e13	−	1.59756e12i	−1.96668	−	0.282766i
$683$	−3.52152e12	−	5.47959e12i	−0.619209	−	0.963508i	−0.999257	−	0.0385409i	$-0.987729\pi$
$683$	−3.52152e12	−	5.47959e12i	−0.619209	−	0.963508i	0.380048	−	0.924967i	$-0.375907\pi$
$684$	−1.92057e12	+	8.77096e11i	−0.335489	+	0.153213i
$685$	1.47965e12	−	6.75732e11i	0.256774	−	0.117265i
$686$	−1.35592e13	−	1.17491e13i	−2.33762	−	2.02556i
$687$	1.00241e12	−	2.19498e12i	0.171688	−	0.375945i
$688$	−1.67298e11	+	1.44965e11i	−0.0284671	+	0.0246669i
$689$	−5.71680e11	−	1.94696e12i	−0.0966421	−	0.329133i
$690$	−1.90609e11	−	1.32572e12i	−0.0320127	−	0.222654i
$691$	−8.92458e11	−	1.02995e12i	−0.148914	−	0.171856i	0.676392	−	0.736542i	$-0.263543\pi$
$691$	−8.92458e11	−	1.02995e12i	−0.148914	−	0.171856i	−0.825306	+	0.564686i	$0.808997\pi$
$692$	5.05369e11	+	1.10660e12i	0.0837782	+	0.183449i
$693$	1.31176e12	+	4.46745e12i	0.216051	+	0.735801i
$694$	−9.59529e11	−	6.16652e11i	−0.157015	−	0.100907i
$695$	1.44649e12	−	1.66934e12i	0.235171	−	0.271402i
$696$	−5.17799e12	−	1.52040e12i	−0.836411	−	0.245593i
$697$	4.69832e12	−	4.07112e12i	0.754041	−	0.653381i
$698$	3.66525e12	−	1.24827e13i	0.584459	−	1.99048i
$699$	−4.09639e12	+	5.88972e11i	−0.649014	+	0.0933142i
$700$			1.70977e13i			2.69151i
$701$	3.67292e12	+	2.36045e12i	0.574488	+	0.369201i	0.795393	−	0.606094i	$-0.207265\pi$
$701$	3.67292e12	+	2.36045e12i	0.574488	+	0.369201i	−0.220905	+	0.975295i	$0.570901\pi$
$702$	7.40163e12	+	2.17332e12i	1.15030	+	0.337758i
$703$	3.36278e11	−	9.87401e10i	0.0519277	−	0.0152474i
$704$	−7.55802e12	+	4.85725e12i	−1.15966	+	0.745269i
$705$	2.26143e11	+	3.51885e11i	0.0344772	+	0.0536475i
$706$	1.15300e13	+	9.99082e12i	1.74666	+	1.51349i
$707$	−1.00370e13	+	6.45037e12i	−1.51083	+	0.970952i
$708$	−1.42397e10	+	9.90396e10i	−0.00212987	+	0.0148135i
$709$	9.48255e12	−	1.36338e12i	1.40934	−	0.202633i	0.604730	−	0.796431i	$-0.293281\pi$
$709$	9.48255e12	−	1.36338e12i	1.40934	−	0.202633i	0.804615	+	0.593798i	$0.202372\pi$
$710$	−1.06836e12	−	1.23295e12i	−0.157781	−	0.182089i
$711$	−7.14937e10			−0.0104919
$712$	4.78379e12	−	4.50752e12i	0.697610	−	0.657321i
$713$	1.00101e13			1.45056
$714$	1.46841e13	+	1.69463e13i	2.11449	+	2.44025i
$715$	8.30943e11	−	1.19472e11i	0.118903	−	0.0170957i
$716$	−3.15802e12	+	2.19645e13i	−0.449061	+	3.12329i
$717$	8.01525e11	−	5.15109e11i	0.113261	−	0.0727885i
$718$	−1.13031e13	−	9.79416e12i	−1.58722	−	1.37533i
$719$	1.27459e11	+	1.98330e11i	0.0177865	+	0.0276764i	0.850033	−	0.526729i	$-0.176582\pi$
$719$	1.27459e11	+	1.98330e11i	0.0177865	+	0.0276764i	−0.832246	+	0.554406i	$0.812946\pi$
$720$	3.19237e10	−	2.05161e10i	0.00442708	−	0.00284511i
$721$	−1.86494e13	+	5.47595e12i	−2.57013	+	0.754659i
$722$	−9.00352e12	−	2.64367e12i	−1.23309	−	0.362068i
$723$	−4.36428e12	−	2.80476e12i	−0.594006	−	0.381744i
$724$			1.01224e12i			0.136917i
$725$	−9.22045e12	+	1.32570e12i	−1.23946	+	0.178207i
$726$	6.64579e11	−	2.26335e12i	0.0887834	−	0.302369i
$727$	−2.25629e12	+	1.95509e12i	−0.299565	+	0.259574i	−0.791653	−	0.610971i	$-0.790779\pi$
$727$	−2.25629e12	+	1.95509e12i	−0.299565	+	0.259574i	0.492088	+	0.870545i	$0.336234\pi$
$728$	8.64236e12	+	2.53763e12i	1.14036	+	0.334839i
$729$	4.24180e12	−	4.89530e12i	0.556258	−	0.641956i
$730$	1.07150e12	+	6.88611e11i	0.139649	+	0.0897472i
$731$	−2.62970e12	−	8.95594e12i	−0.340626	−	1.16007i
$732$	6.20842e12	+	1.35945e13i	0.799247	+	1.75011i
$733$	−1.49165e12	−	1.72145e12i	−0.190852	−	0.220256i	0.652256	−	0.757998i	$-0.273823\pi$
$733$	−1.49165e12	−	1.72145e12i	−0.190852	−	0.220256i	−0.843109	+	0.537743i	$0.819277\pi$
$734$	3.00494e12	+	2.08998e13i	0.382124	+	2.65773i
$735$	6.52824e11	+	2.22332e12i	0.0825094	+	0.281001i
$736$	6.24449e12	−	5.41088e12i	0.784416	−	0.679701i
$737$	3.94661e12	−	8.64187e12i	0.492743	−	1.07896i
$738$	−3.07760e12	−	2.66676e12i	−0.381908	−	0.330925i
$739$	−3.04004e12	+	1.38834e12i	−0.374956	+	0.171237i	−0.593974	−	0.804484i	$-0.702442\pi$
$739$	−3.04004e12	+	1.38834e12i	−0.374956	+	0.171237i	0.219018	+	0.975721i	$0.429715\pi$
$740$	2.86091e11	−	1.30653e11i	0.0350720	−	0.0160169i
$741$	−9.80655e11	−	1.52593e12i	−0.119491	−	0.185931i
$742$	−1.12617e13	−	1.61918e12i	−1.36391	−	0.196100i
$743$	3.89244e12	−	1.32564e13i	0.468567	−	1.59579i	−0.298622	−	0.954372i	$-0.596527\pi$
$743$	3.89244e12	−	1.32564e13i	0.468567	−	1.59579i	0.767189	−	0.641421i	$-0.221655\pi$
$744$	3.37306e12	+	7.38597e12i	0.403595	+	0.883750i
$745$	−1.06746e11	−	4.87494e10i	−0.0126955	−	0.00579783i
$746$	1.32937e13			1.57153
$747$	6.22354e12	+	2.84220e12i	0.731299	+	0.333973i
$748$	−2.69574e12	−	1.87493e13i	−0.314862	−	2.18991i
$749$			1.24506e13i			1.44551i
$750$	2.07036e12	−	3.22154e12i	0.238930	−	0.371782i
$751$	8.40353e12	−	2.46750e12i	0.964011	−	0.283059i	0.238402	−	0.971167i	$-0.423376\pi$
$751$	8.40353e12	−	2.46750e12i	0.964011	−	0.283059i	0.725609	+	0.688107i	$0.241558\pi$
$752$	−8.45554e10	+	1.85150e11i	−0.00964186	+	0.0211127i
$753$	4.38914e12	+	6.31063e11i	0.497510	+	0.0715312i
$754$	−1.87214e12	+	1.30210e13i	−0.210944	+	1.46714i
$755$	−6.01237e10	+	9.35543e10i	−0.00673418	+	0.0104786i
$756$	1.74096e13	−	2.00918e13i	1.93839	−	2.23702i
$757$	1.60657e12	−	1.85408e12i	0.177815	−	0.205209i	−0.659845	−	0.751402i	$-0.729378\pi$
$757$	1.60657e12	−	1.85408e12i	0.177815	−	0.205209i	0.837660	+	0.546193i	$0.183923\pi$
$758$	−6.61784e12	+	1.02976e13i	−0.728123	+	1.13298i
$759$	7.67219e11	−	5.33612e12i	0.0839134	−	0.583630i
$760$	7.88151e11	+	1.13319e11i	0.0856935	+	0.0123209i
$761$	2.09286e12	−	4.58273e12i	0.226209	−	0.495328i	−0.762163	−	0.647385i	$-0.775862\pi$
$761$	2.09286e12	−	4.58273e12i	0.226209	−	0.495328i	0.988372	+	0.152057i	$0.0485898\pi$
$762$	1.46108e13	−	4.29011e12i	1.56992	−	0.460969i
$763$	1.68749e13	−	2.62579e13i	1.80252	−	2.80478i
$764$			1.23464e13i			1.31105i
$765$	2.27716e11	+	1.58380e12i	0.0240390	+	0.167195i
$766$	1.62750e13	+	7.43255e12i	1.70802	+	0.780025i
$767$	9.09872e10			0.00949295
$768$	5.59984e12	+	2.55736e12i	0.580832	+	0.265257i
$769$	−2.40027e12	−	5.25587e12i	−0.247510	−	0.541971i	0.744575	−	0.667538i	$-0.232652\pi$
$769$	−2.40027e12	−	5.25587e12i	−0.247510	−	0.541971i	−0.992085	+	0.125568i	$0.959925\pi$
$770$	1.32612e12	−	4.51633e12i	0.135948	−	0.462997i
$771$	−1.11022e13	−	1.59625e12i	−1.13152	−	0.162688i
$772$	−4.07792e11	−	6.34536e11i	−0.0413200	−	0.0642952i
$773$	6.19426e12	−	2.82882e12i	0.623996	−	0.284969i	−0.0782171	−	0.996936i	$-0.524923\pi$
$773$	6.19426e12	−	2.82882e12i	0.623996	−	0.284969i	0.702213	+	0.711967i	$0.252195\pi$
$774$	−5.56167e12	+	2.53993e12i	−0.557020	+	0.254383i
$775$	1.05924e13	+	9.17838e12i	1.05472	+	0.913921i
$776$	−4.88561e12	+	1.06980e13i	−0.483661	+	1.05907i
$777$	−1.13256e12	+	9.81370e11i	−0.111472	+	0.0965913i
$778$	−2.73150e12	−	9.30262e12i	−0.267296	−	0.910327i
$779$	4.01286e11	+	2.79101e12i	0.0390423	+	0.271545i
$780$	−1.06595e12	−	1.23018e12i	−0.103113	−	0.118998i
$781$	−2.72789e12	−	5.97324e12i	−0.262359	−	0.574487i
$782$	7.74233e12	+	2.63680e13i	0.740357	+	2.52143i
$783$	1.21850e13	+	7.83080e12i	1.15850	+	0.744523i
$784$	−7.38403e11	+	8.52162e11i	−0.0698025	+	0.0805564i
$785$	2.41388e12	+	7.08779e11i	0.226883	+	0.0666189i
$786$	−1.25545e13	+	1.08786e13i	−1.17327	+	1.01665i
$787$	3.07592e12	−	1.04756e13i	0.285817	−	0.973405i	−0.683982	−	0.729499i	$-0.739753\pi$
$787$	3.07592e12	−	1.04756e13i	0.285817	−	0.973405i	0.969799	−	0.243905i	$-0.0784287\pi$
$788$	1.18247e13	−	1.70014e12i	1.09251	−	0.157079i
$789$			5.97420e12i			0.548824i
$790$	6.08025e10	+	3.90754e10i	0.00555392	+	0.00356928i
$791$	−1.06035e13	−	3.11348e12i	−0.963066	−	0.282782i
$792$	−4.44120e12	+	1.30405e12i	−0.401085	+	0.117769i
$793$	1.14328e13	−	7.34744e12i	1.02666	−	0.659791i
$794$	−6.65166e12	−	1.03502e13i	−0.593933	−	0.924178i
$795$	5.79672e11	+	5.02289e11i	0.0514672	+	0.0445966i
$796$	−3.86500e12	+	2.48388e12i	−0.341225	+	0.219292i
$797$	−2.71421e12	+	1.88777e13i	−0.238276	+	1.65725i	0.422275	+	0.906468i	$0.361232\pi$
$797$	−2.71421e12	+	1.88777e13i	−0.238276	+	1.65725i	−0.660552	+	0.750781i	$0.729677\pi$
$798$	−1.00669e13	+	1.44740e12i	−0.878782	+	0.126350i
$799$	−5.62036e12	−	6.48624e12i	−0.487869	−	0.563031i
$800$	1.15691e13			0.998603
$801$	−5.34100e12	+	2.71353e12i	−0.458433	+	0.232910i
$802$	−1.64570e13			−1.40464
$803$	3.35729e12	+	3.87452e12i	0.284950	+	0.328850i
$804$	−1.82336e13	+	2.62160e12i	−1.53894	+	0.221266i
$805$	−5.97347e11	+	4.15464e12i	−0.0501354	+	0.348700i
$806$	1.66508e13	−	1.07008e13i	1.38972	−	0.893121i
$807$	3.14356e12	+	2.72391e12i	0.260910	+	0.226080i
$808$	−6.41247e12	−	9.97800e12i	−0.529266	−	0.823554i
$809$	−1.31871e13	+	8.47485e12i	−1.08238	+	0.695606i	−0.955107	−	0.296261i	$-0.904260\pi$
$809$	−1.31871e13	+	8.47485e12i	−1.08238	+	0.695606i	−0.127277	+	0.991867i	$0.540624\pi$
$810$	−8.42032e11	+	2.47243e11i	−0.0687299	+	0.0201809i
$811$	9.04869e12	+	2.65693e12i	0.734500	+	0.215669i	0.627529	−	0.778594i	$-0.284067\pi$
$811$	9.04869e12	+	2.65693e12i	0.734500	+	0.215669i	0.106971	+	0.994262i	$0.465885\pi$
$812$	3.81389e13	+	2.45104e13i	3.07869	+	1.97855i
$813$		−	5.85161e12i		−	0.469751i
$814$	2.03866e12	−	2.93116e11i	0.162756	−	0.0234007i
$815$	−2.58320e10	+	8.79756e10i	−0.00205092	+	0.00698478i
$816$	5.55930e11	−	4.81716e11i	0.0438949	−	0.0380352i
$817$	4.06210e12	+	1.19274e12i	0.318971	+	0.0936584i
$818$	−3.28749e12	+	3.79397e12i	−0.256729	+	0.296281i
$819$	−6.90633e12	−	4.43843e12i	−0.536377	−	0.344708i
$820$	7.12890e11	+	2.42788e12i	0.0550631	+	0.187528i
$821$	−1.71465e12	−	3.75456e12i	−0.131714	−	0.288413i	0.832272	−	0.554368i	$-0.187040\pi$
$821$	−1.71465e12	−	3.75456e12i	−0.131714	−	0.288413i	−0.963985	+	0.265955i	$0.914313\pi$
$822$	−1.35259e13	−	1.56097e13i	−1.03334	−	1.19254i
$823$	2.26473e12	+	1.57516e13i	0.172075	+	1.19681i	0.874491	+	0.485041i	$0.161195\pi$
$823$	2.26473e12	+	1.57516e13i	0.172075	+	1.19681i	−0.702416	+	0.711766i	$0.747896\pi$
$824$	−5.44377e12	−	1.85398e13i	−0.411365	−	1.40098i
$825$	5.70461e12	−	4.94307e12i	0.428729	−	0.371496i
$826$	2.11930e11	−	4.64062e11i	0.0158410	−	0.0346869i
$827$	6.34517e12	+	5.49812e12i	0.471703	+	0.408733i	0.858007	−	0.513639i	$-0.171703\pi$
$827$	6.34517e12	+	5.49812e12i	0.471703	+	0.408733i	−0.386304	+	0.922372i	$0.626248\pi$
$828$	1.00646e13	−	4.59633e12i	0.744146	−	0.339840i
$829$	1.34091e13	−	6.12372e12i	0.986060	−	0.450319i	0.143927	−	0.989588i	$-0.454027\pi$
$829$	1.34091e13	−	6.12372e12i	0.986060	−	0.450319i	0.842133	+	0.539270i	$0.181300\pi$
$830$	−3.73944e12	−	5.81869e12i	−0.273499	−	0.425573i
$831$	−3.06376e12	−	4.40502e11i	−0.222869	−	0.0320437i
$832$	4.46294e12	−	1.51994e13i	0.322899	−	1.09969i
$833$	−1.97507e13	−	4.32480e13i	−1.42128	−	3.11217i
$834$	−2.55128e13	−	1.16513e13i	−1.82604	−	0.833924i
$835$	−2.05664e12			−0.146409
$836$	7.81506e12	+	3.56902e12i	0.553355	+	0.252709i
$837$	−3.10148e12	−	2.15713e13i	−0.218426	−	1.51919i
$838$			3.09741e13i			2.16970i
$839$	3.98135e12	−	6.19511e12i	0.277397	−	0.431638i	−0.674400	−	0.738366i	$-0.735598\pi$
$839$	3.98135e12	−	6.19511e12i	0.277397	−	0.431638i	0.951797	+	0.306728i	$0.0992341\pi$
$840$	−3.26679e12	+	9.59217e11i	−0.226394	+	0.0664752i
$841$	−4.23430e12	+	9.27183e12i	−0.291877	+	0.639121i
$842$	−1.23306e12	−	1.77287e11i	−0.0845432	−	0.0121555i
$843$	4.32411e11	−	3.00748e12i	0.0294898	−	0.205106i
$844$	−2.45548e13	+	3.82080e13i	−1.66569	+	2.59187i
$845$	9.80032e11	−	1.13102e12i	0.0661279	−	0.0763157i
$846$	−3.68158e12	+	4.24877e12i	−0.247097	+	0.285165i
$847$	−3.99669e12	+	6.21898e12i	−0.266824	+	0.415187i
$848$	−5.31178e10	+	3.69442e11i	−0.00352743	+	0.0245338i
$849$	1.05332e13	+	1.51445e12i	0.695787	+	0.100039i
$850$	−1.59844e13	+	3.50009e13i	−1.05029	+	2.29982i
$851$	−1.76223e12	+	5.17437e11i	−0.115181	+	0.0338201i
$852$	−6.88379e12	+	1.07114e13i	−0.447558	+	0.696414i
$853$			6.74949e12i			0.436516i	0.975891	+	0.218258i	$0.0700374\pi$
$853$			6.74949e12i			0.436516i	−0.975891	+	0.218258i	$0.929963\pi$
$854$	−1.08444e13	−	7.54247e13i	−0.697664	−	4.85236i
$855$	−6.60158e11	−	3.01484e11i	−0.0422474	−	0.0192938i
$856$	−1.23774e13			−0.787949
$857$	3.70596e12	+	1.69245e12i	0.234686	+	0.107177i	0.529287	−	0.848443i	$-0.322459\pi$
$857$	3.70596e12	+	1.69245e12i	0.234686	+	0.107177i	−0.294601	+	0.955620i	$0.595187\pi$
$858$	−4.42815e12	−	9.69629e12i	−0.278952	−	0.610819i
$859$	−6.50075e12	+	2.21395e13i	−0.407375	+	1.38739i	0.459195	+	0.888336i	$0.348138\pi$
$859$	−6.50075e12	+	2.21395e13i	−0.407375	+	1.38739i	−0.866570	+	0.499056i	$0.833680\pi$
$860$	3.76051e12	+	5.40680e11i	0.234425	+	0.0337052i
$861$	−6.51839e12	−	1.01428e13i	−0.404228	−	0.628991i
$862$	−2.08555e13	+	9.52437e12i	−1.28658	+	0.587562i
$863$	1.54797e13	−	7.06933e12i	0.949978	−	0.433840i	0.120707	−	0.992688i	$-0.461484\pi$
$863$	1.54797e13	−	7.06933e12i	0.949978	−	0.433840i	0.829270	+	0.558848i	$0.188756\pi$
$864$	−1.35950e13	−	1.17801e13i	−0.829977	−	0.719179i
$865$	−1.73710e11	+	3.80373e11i	−0.0105500	+	0.0231013i
$866$	−2.85457e13	+	2.47350e13i	−1.72469	+	1.49445i
$867$	5.47147e12	+	1.86341e13i	0.328865	+	1.12001i
$868$	−9.70764e12	−	6.75181e13i	−0.580463	−	4.03721i
$869$	1.90510e11	+	2.19861e11i	0.0113326	+	0.0130785i
$870$	−2.06566e12	−	4.52316e12i	−0.122242	−	0.267673i
$871$	4.71934e12	+	1.60726e13i	0.277843	+	0.946247i
$872$	2.61036e13	+	1.67757e13i	1.52889	+	0.982557i
$873$	7.01965e12	−	8.10111e12i	0.409026	−	0.472042i
$874$	−1.19596e13	−	3.51165e12i	−0.693289	−	0.203568i
$875$	−9.06979e12	+	7.85902e12i	−0.523071	+	0.453244i
$876$	2.80061e12	−	9.53798e12i	0.160688	−	0.547253i
$877$	−2.79968e13	+	4.02533e12i	−1.59812	+	0.229775i	−0.883051	−	0.469278i	$-0.844514\pi$
$877$	−2.79968e13	+	4.02533e12i	−1.59812	+	0.229775i	−0.715070	+	0.699053i	$0.753605\pi$
$878$		−	3.39611e13i		−	1.92866i
$879$	−4.84774e12	−	3.11545e12i	−0.273898	−	0.176024i
$880$	−1.48160e11	−	4.35037e10i	−0.00832834	−	0.00244542i
$881$	−3.39384e12	+	9.96522e11i	−0.189802	+	0.0557308i	−0.375252	−	0.926923i	$-0.622444\pi$
$881$	−3.39384e12	+	9.96522e11i	−0.189802	+	0.0557308i	0.185450	+	0.982654i	$0.440626\pi$
$882$	−2.61998e13	+	1.68376e13i	−1.45777	+	0.936851i
$883$	−2.86054e12	−	4.45109e12i	−0.158352	−	0.246401i	0.753007	−	0.658012i	$-0.228603\pi$
$883$	−2.86054e12	−	4.45109e12i	−0.158352	−	0.246401i	−0.911360	+	0.411611i	$0.864966\pi$
$884$	2.52411e13	+	2.18715e13i	1.39019	+	1.20460i
$885$	−2.89332e10	+	1.85942e10i	−0.00158545	+	0.00101890i
$886$	3.27148e12	−	2.27536e13i	0.178358	−	1.24051i
$887$	2.17856e13	−	3.13230e12i	1.18172	−	0.169905i	0.476682	−	0.879076i	$-0.341839\pi$
$887$	2.17856e13	−	3.13230e12i	1.18172	−	0.169905i	0.705037	+	0.709171i	$0.250930\pi$
$888$	−9.75603e11	−	1.12591e12i	−0.0526520	−	0.0607636i
$889$	−4.77215e13			−2.56246
$890$	6.02540e12	+	6.11409e11i	0.321907	+	0.0326646i
$891$	−3.53234e12			−0.187764
$892$	8.37617e12	+	9.66662e12i	0.443000	+	0.511249i
$893$	3.85311e12	−	5.53993e11i	0.202759	−	0.0291523i
$894$	−2.12062e11	+	1.47492e12i	−0.0111031	+	0.0772236i
$895$	−6.41665e12	+	4.12373e12i	−0.334276	+	0.214826i
$896$	−4.04478e13	−	3.50482e13i	−2.09657	−	1.81669i
$897$	5.13902e12	+	7.99648e12i	0.265042	+	0.412413i
$898$	−1.63865e13	+	1.05310e13i	−0.840898	+	0.540413i
$899$	3.56584e13	−	1.04703e13i	1.82072	−	0.534612i
$900$	1.48645e13	+	4.36461e12i	0.755194	+	0.221745i
$901$	−1.32395e13	−	8.50853e12i	−0.669285	−	0.430123i
$902$			1.65705e13i			0.833503i
$903$	−1.79181e13	+	2.57624e12i	−0.896805	+	0.128941i
$904$	3.09518e12	−	1.05412e13i	0.154144	−	0.524968i
$905$	−2.62953e11	+	2.27850e11i	−0.0130304	+	0.0112909i
$906$	1.35489e12	+	3.97832e11i	0.0668078	+	0.0196165i
$907$	1.01734e13	−	1.17407e13i	0.499153	−	0.576054i	−0.449135	−	0.893464i	$-0.648268\pi$
$907$	1.01734e13	−	1.17407e13i	0.499153	−	0.576054i	0.948288	+	0.317410i	$0.102813\pi$
$908$	−1.92820e13	−	1.23918e13i	−0.941382	−	0.604990i
$909$	3.04567e12	+	1.03726e13i	0.147961	+	0.503907i
$910$	3.44770e12	+	7.54941e12i	0.166664	+	0.364944i
$911$	−2.12772e13	−	2.45552e13i	−1.02349	−	1.18117i	−0.983304	−	0.181973i	$-0.941752\pi$
$911$	−2.12772e13	−	2.45552e13i	−1.02349	−	1.18117i	−0.0401818	−	0.999192i	$-0.512794\pi$
$912$	4.74823e10	+	3.30247e11i	0.00227277	+	0.0158074i
$913$	−7.84351e12	−	2.67125e13i	−0.373587	−	1.27232i
$914$	−1.84712e13	+	1.60054e13i	−0.875460	+	0.758591i
$915$	−2.13402e12	+	4.67285e12i	−0.100648	+	0.220387i
$916$	−1.52301e13	−	1.31970e13i	−0.714783	−	0.619363i
$917$	4.73556e13	−	2.16266e13i	2.21161	−	1.01001i
$918$	5.44229e13	−	2.48541e13i	2.52924	−	1.15506i
$919$	2.07090e12	+	3.22238e12i	0.0957721	+	0.149024i	0.885833	−	0.464004i	$-0.153588\pi$
$919$	2.07090e12	+	3.22238e12i	0.0957721	+	0.149024i	−0.790061	+	0.613028i	$0.789951\pi$
$920$	−4.13022e12	−	5.93836e11i	−0.190076	−	0.0273289i
$921$	−4.82050e12	+	1.64171e13i	−0.220762	+	0.751845i
$922$	1.76131e13	+	3.85673e13i	0.802687	+	1.75764i
$923$	1.05320e13	+	4.80982e12i	0.477645	+	0.218133i
$924$	−3.67362e13			−1.65795
$925$	−2.33919e12	−	1.06827e12i	−0.105058	−	0.0479782i
$926$	−4.44603e12	−	3.09228e13i	−0.198711	−	1.38207i
$927$			1.76114e13i			0.783311i
$928$	1.65848e13	−	2.58064e13i	0.734081	−	1.14225i
$929$	2.65735e13	−	7.80268e12i	1.17052	−	0.343695i	0.362007	−	0.932176i	$-0.382092\pi$
$929$	2.65735e13	−	7.80268e12i	1.17052	−	0.343695i	0.808511	+	0.588480i	$0.200274\pi$
$930$	−3.10800e12	+	6.80556e12i	−0.136241	+	0.298326i
$931$	2.13450e13	+	3.06895e12i	0.931157	+	0.133880i
$932$	−4.91877e12	+	3.42108e13i	−0.213543	+	1.48522i
$933$	1.30498e12	−	2.03060e12i	0.0563817	−	0.0877316i
$934$	−2.94261e13	+	3.39595e13i	−1.26524	+	1.46016i
$935$	4.26377e12	−	4.92065e12i	0.182449	−	0.210557i
$936$	4.41235e12	−	6.86575e12i	0.187901	−	0.292379i
$937$	−9.95115e11	+	6.92117e12i	−0.0421740	+	0.293327i	0.957808	+	0.287407i	$0.0927933\pi$
$937$	−9.95115e11	+	6.92117e12i	−0.0421740	+	0.293327i	−0.999982	+	0.00591943i	$0.998116\pi$
$938$	9.29675e13	+	1.33667e13i	3.92119	+	0.563783i
$939$	4.38039e12	−	9.59173e12i	0.183873	−	0.402626i
$940$	3.35180e12	−	9.84176e11i	0.140024	−	0.0411147i
$941$	7.68427e12	−	1.19570e13i	0.319484	−	0.497127i	−0.643952	−	0.765066i	$-0.722706\pi$
$941$	7.68427e12	−	1.19570e13i	0.319484	−	0.497127i	0.963436	+	0.267939i	$0.0863426\pi$
$942$		−	3.19447e13i		−	1.32181i
$943$	−2.10290e12	−	1.46260e13i	−0.0865996	−	0.602314i
$944$	−1.52237e10	−	6.95243e9i	−0.000623945	−	0.000284946i
$945$	9.13813e12			0.372747
$946$	2.26312e13	+	1.03353e13i	0.918749	+	0.419578i
$947$	1.38826e13	+	3.03987e13i	0.560914	+	1.22823i	0.951496	+	0.307661i	$0.0995464\pi$
$947$	1.38826e13	+	3.03987e13i	0.560914	+	1.22823i	−0.390582	+	0.920568i	$0.627726\pi$
$948$	1.58921e11	−	5.41235e11i	0.00639063	−	0.0217645i
$949$	−8.94747e12	−	1.28645e12i	−0.358098	−	0.0514867i
$950$	−9.43544e12	−	1.46818e13i	−0.375842	−	0.584822i
$951$	−1.26620e13	+	5.78253e12i	−0.501983	+	0.229248i
$952$	6.35457e13	−	2.90204e13i	2.50738	−	1.14508i
$953$	−2.63976e13	−	2.28736e13i	−1.03668	−	0.898291i	−0.0417798	−	0.999127i	$-0.513303\pi$
$953$	−2.63976e13	−	2.28736e13i	−1.03668	−	0.898291i	−0.994903	+	0.100836i	$0.967848\pi$
$954$	−4.28250e12	+	9.37738e12i	−0.167390	+	0.366533i
$955$	−3.20726e12	+	2.77911e12i	−0.124773	+	0.108116i
$956$	−2.24176e12	−	7.63473e12i	−0.0868017	−	0.295620i
$957$	−2.84840e12	−	1.98111e13i	−0.109774	−	0.763492i
$958$	3.27368e13	+	3.77803e13i	1.25572	+	1.44917i
$959$	2.68895e13	+	5.88797e13i	1.02659	+	2.24793i
$960$	1.68698e12	+	5.74533e12i	0.0641047	+	0.218320i
$961$	−2.47978e13	−	1.59366e13i	−0.937904	−	0.602754i
$962$	−2.37816e12	+	2.74454e12i	−0.0895267	+	0.103319i
$963$	1.08243e13	+	3.17831e12i	0.405586	+	0.119091i
$964$	−3.27436e13	+	2.83725e13i	−1.22118	+	1.05816i
$965$	7.30439e10	−	2.48765e11i	0.00271151	−	0.00923455i
$966$	5.27544e13	−	7.58493e12i	1.94922	−	0.280256i
$967$			3.43701e13i			1.26404i	0.774951	+	0.632022i	$0.217775\pi$
$967$			3.43701e13i			1.26404i	−0.774951	+	0.632022i	$0.782225\pi$
$968$	−6.18243e12	−	3.97321e12i	−0.226319	−	0.145446i
$969$	−1.34983e13	−	3.96346e12i	−0.491838	−	0.144417i
$970$	−1.03976e13	+	3.05302e12i	−0.377105	+	0.110728i
$971$	2.56842e13	−	1.65062e13i	0.927212	−	0.595883i	0.0124707	−	0.999922i	$-0.496030\pi$
$971$	2.56842e13	−	1.65062e13i	0.927212	−	0.595883i	0.914742	+	0.404039i	$0.132394\pi$
$972$	−2.16239e13	−	3.36475e13i	−0.777028	−	1.20908i
$973$	6.64281e13	+	5.75603e13i	2.37599	+	2.05881i
$974$	1.05641e12	−	6.78911e11i	0.0376111	−	0.0241712i
$975$	−1.89409e12	+	1.31737e13i	−0.0671244	+	0.466860i
$976$	−2.47433e12	+	3.55755e11i	−0.0872838	+	0.0125495i
$977$	3.56916e12	+	4.11903e12i	0.125326	+	0.144634i	0.814945	−	0.579539i	$-0.196767\pi$
$977$	3.56916e12	+	4.11903e12i	0.125326	+	0.144634i	−0.689619	+	0.724173i	$0.742222\pi$
$978$	1.16425e12			0.0406931
$979$	2.25770e13	+	9.19408e12i	0.785497	+	0.319879i
$980$	1.93518e13			0.670199
$981$	−1.85205e13	−	2.13738e13i	−0.638471	−	0.736835i
$982$	−6.40438e13	+	9.20811e12i	−2.19774	+	0.315987i
$983$	2.09053e12	−	1.45400e13i	0.0714112	−	0.496676i	−0.922457	−	0.386101i	$-0.873822\pi$
$983$	2.09053e12	−	1.45400e13i	0.0714112	−	0.496676i	0.993868	−	0.110575i	$-0.0352693\pi$
$984$	1.00832e13	−	6.48009e12i	0.342863	−	0.220345i
$985$	3.10334e12	+	2.68906e12i	0.105043	+	0.0910202i
$986$	5.51602e13	+	8.58310e13i	1.85857	+	2.89200i
$987$	−1.40026e13	+	8.99892e12i	−0.469658	+	0.301831i
$988$	−1.45349e13	+	4.26782e12i	−0.485294	+	0.142495i
$989$	−2.12870e13	−	6.25043e12i	−0.707508	−	0.207743i
$990$	−3.58791e12	−	2.30581e12i	−0.118709	−	0.0762895i
$991$			5.18761e12i			0.170858i	0.996344	+	0.0854291i	$0.0272261\pi$
$991$			5.18761e12i			0.170858i	−0.996344	+	0.0854291i	$0.972774\pi$
$992$	−4.56857e13	+	6.56861e12i	−1.49788	+	0.215363i
$993$	4.45064e12	−	1.51575e13i	0.145262	−	0.494716i
$994$	4.90630e13	−	4.25134e13i	1.59410	−	1.38130i
$995$	−1.51524e12	−	4.44915e11i	−0.0490092	−	0.0143904i
$996$	−3.53506e13	+	4.07968e13i	−1.13823	+	1.31359i
$997$	1.82170e13	+	1.17074e13i	0.583915	+	0.375259i	0.798995	−	0.601337i	$-0.205365\pi$
$997$	1.82170e13	+	1.17074e13i	0.583915	+	0.375259i	−0.215081	+	0.976596i	$0.569001\pi$
$998$	−9.42233e12	−	3.20895e13i	−0.300657	−	1.02394i
$999$	1.66105e12	+	3.63720e12i	0.0527642	+	0.115537i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	89.10.f.a.11.8	✓	660
89.81	even	22	inner	89.10.f.a.81.8	yes	660

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
89.10.f.a.11.8	✓	660	1.1	even	1	trivial
89.10.f.a.81.8	yes	660	89.81	even	22	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:	\( N \)	\(=\)	\( 89 \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	89.f (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-23.8701 - 27.5475i) q^{2} +(-96.7895 + 13.9162i) q^{3} +(-116.221 + 808.333i) q^{4} +(-236.144 + 151.761i) q^{5} +(2693.73 + 2334.13i) q^{6} +(-6039.03 - 9396.92i) q^{7} +(9341.70 - 6003.54i) q^{8} +(-9711.15 + 2851.45i) q^{9} +O(q^{10})\)	\(q+(-23.8701 - 27.5475i) q^{2} +(-96.7895 + 13.9162i) q^{3} +(-116.221 + 808.333i) q^{4} +(-236.144 + 151.761i) q^{5} +(2693.73 + 2334.13i) q^{6} +(-6039.03 - 9396.92i) q^{7} +(9341.70 - 6003.54i) q^{8} +(-9711.15 + 2851.45i) q^{9} +(9817.41 + 2882.65i) q^{10} +(34646.3 + 22265.9i) q^{11} -79855.5i q^{12} +(-71877.0 + 10334.4i) q^{13} +(-114710. + 390665. i) q^{14} +(20744.4 - 17975.1i) q^{15} +(12815.9 + 3763.09i) q^{16} +(-368818. + 425639. i) q^{17} +(310356. + 199454. i) q^{18} +(-71968.1 - 245101. i) q^{19} +(-95228.4 - 208521. i) q^{20} +(715285. + 825483. i) q^{21} +(-213641. - 1.48591e6i) q^{22} +(377141. + 1.28442e6i) q^{23} +(-820632. + 711081. i) q^{24} +(-778625. + 1.70495e6i) q^{25} +(2.00040e6 + 1.73335e6i) q^{26} +(2.65102e6 - 1.21068e6i) q^{27} +(8.29770e6 - 3.78943e6i) q^{28} +(2.68694e6 + 4.18096e6i) q^{29} +(-990338. - 142389. i) q^{30} +(2.10673e6 - 7.17486e6i) q^{31} +(-2.56410e6 - 5.61459e6i) q^{32} +(-3.66326e6 - 1.67295e6i) q^{33} +2.05290e7 q^{34} +(2.85217e6 + 1.30254e6i) q^{35} +(-1.17628e6 - 8.18124e6i) q^{36} +1.37200e6i q^{37} +(-5.03403e6 + 7.83311e6i) q^{38} +(6.81313e6 - 2.00052e6i) q^{39} +(-1.29489e6 + 2.83541e6i) q^{40} +(-1.09259e7 - 1.57091e6i) q^{41} +(5.66611e6 - 3.94086e7i) q^{42} +(-8.96014e6 + 1.39423e7i) q^{43} +(-2.20248e7 + 2.54180e7i) q^{44} +(1.86049e6 - 2.14713e6i) q^{45} +(2.63803e7 - 4.10486e7i) q^{46} +(-2.16871e6 + 1.50837e7i) q^{47} +(-1.29281e6 - 185879. i) q^{48} +(-3.50687e7 + 7.67897e7i) q^{49} +(6.55530e7 - 1.92481e7i) q^{50} +(2.97744e7 - 4.63299e7i) q^{51} -5.93016e7i q^{52} +(3.97679e6 + 2.76592e7i) q^{53} +(-9.66314e7 - 4.41301e7i) q^{54} -1.15606e7 q^{55} +(-1.12830e8 - 5.15276e7i) q^{56} +(1.03766e7 + 2.27217e7i) q^{57} +(5.10377e7 - 1.73818e8i) q^{58} +(-1.24023e6 - 178319. i) q^{59} +(1.21189e7 + 1.88574e7i) q^{60} +(-1.70239e8 + 7.77456e7i) q^{61} +(-2.47937e8 + 1.13229e8i) q^{62} +(8.54408e7 + 7.40349e7i) q^{63} +(-9.06219e7 + 1.98434e8i) q^{64} +(1.54050e7 - 1.33485e7i) q^{65} +(4.13565e7 + 1.40847e8i) q^{66} +(-3.28293e7 - 2.28333e8i) q^{67} +(-3.01194e8 - 3.47596e8i) q^{68} +(-5.43777e7 - 1.19070e8i) q^{69} +(-3.21996e7 - 1.09662e8i) q^{70} +(-1.34134e8 - 8.62030e7i) q^{71} +(-7.35998e7 + 8.49387e7i) q^{72} +(1.19441e8 + 3.50709e7i) q^{73} +(3.77951e7 - 3.27497e7i) q^{74} +(5.16362e7 - 1.75857e8i) q^{75} +(2.06487e8 - 2.96884e7i) q^{76} -4.60033e8i q^{77} +(-2.17739e8 - 1.39932e8i) q^{78} +(6.77768e6 + 1.99011e6i) q^{79} +(-3.59749e6 + 1.05632e6i) q^{80} +(-7.21537e7 + 4.63703e7i) q^{81} +(2.17528e8 + 3.38480e8i) q^{82} +(-5.10882e8 - 4.42682e8i) q^{83} +(-7.50396e8 + 4.82250e8i) q^{84} +(2.24991e7 - 1.56484e8i) q^{85} +(5.97954e8 - 8.59727e7i) q^{86} +(-3.18251e8 - 3.67281e8i) q^{87} +4.57330e8 q^{88} +(5.81866e8 - 1.08573e8i) q^{89} -1.03558e8 q^{90} +(5.31179e8 + 6.13013e8i) q^{91} +(-1.08207e9 + 1.55579e8i) q^{92} +(-1.04062e8 + 7.23769e8i) q^{93} +(4.67286e8 - 3.00307e8i) q^{94} +(5.41915e7 + 4.69572e7i) q^{95} +(3.26311e8 + 5.07751e8i) q^{96} +(-8.90973e8 + 5.72594e8i) q^{97} +(2.95246e9 - 8.66919e8i) q^{98} +(-3.99946e8 - 1.17435e8i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 660 q - 9 q^{2} - 825 q^{3} - 16393 q^{4} - 5127 q^{5} - 11 q^{6} - 11 q^{7} + 1015 q^{8} + 489535 q^{9}+O(q^{10}) \) 660 * q - 9 * q^2 - 825 * q^3 - 16393 * q^4 - 5127 * q^5 - 11 * q^6 - 11 * q^7 + 1015 * q^8 + 489535 * q^9	\( 660 q - 9 q^{2} - 825 q^{3} - 16393 q^{4} - 5127 q^{5} - 11 q^{6} - 11 q^{7} + 1015 q^{8} + 489535 q^{9} - 225841 q^{10} - 224944 q^{11} - 11 q^{13} + 1940664 q^{14} - 11 q^{15} - 5125641 q^{16} + 1457606 q^{17} + 2864796 q^{18} - 11 q^{19} - 5955661 q^{20} + 856653 q^{21} + 13531907 q^{22} - 11 q^{23} + 5621 q^{24} - 31973709 q^{25} - 4206763 q^{26} - 17737896 q^{27} - 11 q^{28} + 10200729 q^{29} - 81004858 q^{30} - 11 q^{31} - 44372422 q^{32} - 19516475 q^{33} + 35594328 q^{34} - 35970209 q^{35} + 71890930 q^{36} - 87132859 q^{38} + 42308203 q^{39} - 128175356 q^{40} + 60926635 q^{41} + 121333817 q^{42} + 296517661 q^{43} + 115664209 q^{44} + 48133749 q^{45} + 311125309 q^{46} - 46792325 q^{47} - 141127426 q^{48} + 164252871 q^{49} + 103838041 q^{50} - 427287971 q^{51} + 850769769 q^{53} - 329099771 q^{54} + 793594654 q^{55} - 2036185316 q^{56} - 154197519 q^{57} + 188920501 q^{58} + 405753711 q^{59} + 21484364 q^{60} + 344711653 q^{61} - 1167226764 q^{62} - 1320295229 q^{63} - 134364169 q^{64} + 1450391239 q^{65} + 863803105 q^{66} + 646170445 q^{67} + 1285178775 q^{68} - 221829309 q^{69} + 854155808 q^{70} - 1113621013 q^{71} - 2392386072 q^{72} - 314298299 q^{73} - 479039451 q^{74} - 3075936347 q^{75} - 6170784400 q^{76} - 2037231963 q^{78} - 79886655 q^{79} + 6302566534 q^{80} + 281226707 q^{81} + 5439310019 q^{82} + 1306521271 q^{83} + 1958614914 q^{84} + 4403895759 q^{85} - 3738814827 q^{86} - 4959185007 q^{87} + 2745817562 q^{88} + 3415767517 q^{89} - 10039266258 q^{90} + 1585238913 q^{91} + 8669558172 q^{92} + 1795690413 q^{93} - 8679076027 q^{94} + 10576695701 q^{95} + 12941524981 q^{96} - 2702894895 q^{97} + 1786224002 q^{98} - 9157402144 q^{99}+O(q^{100}) \) 660 * q - 9 * q^2 - 825 * q^3 - 16393 * q^4 - 5127 * q^5 - 11 * q^6 - 11 * q^7 + 1015 * q^8 + 489535 * q^9 - 225841 * q^10 - 224944 * q^11 - 11 * q^13 + 1940664 * q^14 - 11 * q^15 - 5125641 * q^16 + 1457606 * q^17 + 2864796 * q^18 - 11 * q^19 - 5955661 * q^20 + 856653 * q^21 + 13531907 * q^22 - 11 * q^23 + 5621 * q^24 - 31973709 * q^25 - 4206763 * q^26 - 17737896 * q^27 - 11 * q^28 + 10200729 * q^29 - 81004858 * q^30 - 11 * q^31 - 44372422 * q^32 - 19516475 * q^33 + 35594328 * q^34 - 35970209 * q^35 + 71890930 * q^36 - 87132859 * q^38 + 42308203 * q^39 - 128175356 * q^40 + 60926635 * q^41 + 121333817 * q^42 + 296517661 * q^43 + 115664209 * q^44 + 48133749 * q^45 + 311125309 * q^46 - 46792325 * q^47 - 141127426 * q^48 + 164252871 * q^49 + 103838041 * q^50 - 427287971 * q^51 + 850769769 * q^53 - 329099771 * q^54 + 793594654 * q^55 - 2036185316 * q^56 - 154197519 * q^57 + 188920501 * q^58 + 405753711 * q^59 + 21484364 * q^60 + 344711653 * q^61 - 1167226764 * q^62 - 1320295229 * q^63 - 134364169 * q^64 + 1450391239 * q^65 + 863803105 * q^66 + 646170445 * q^67 + 1285178775 * q^68 - 221829309 * q^69 + 854155808 * q^70 - 1113621013 * q^71 - 2392386072 * q^72 - 314298299 * q^73 - 479039451 * q^74 - 3075936347 * q^75 - 6170784400 * q^76 - 2037231963 * q^78 - 79886655 * q^79 + 6302566534 * q^80 + 281226707 * q^81 + 5439310019 * q^82 + 1306521271 * q^83 + 1958614914 * q^84 + 4403895759 * q^85 - 3738814827 * q^86 - 4959185007 * q^87 + 2745817562 * q^88 + 3415767517 * q^89 - 10039266258 * q^90 + 1585238913 * q^91 + 8669558172 * q^92 + 1795690413 * q^93 - 8679076027 * q^94 + 10576695701 * q^95 + 12941524981 * q^96 - 2702894895 * q^97 + 1786224002 * q^98 - 9157402144 * q^99

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