LMFDB - Embedded newform 27.10.e.a.7.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [27,10,Mod(4,27)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(27, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([2]))

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

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

chi := DirichletCharacter("27.4");

S:= CuspForms(chi, 10);

N := Newforms(S);

Level:	$ N $	$=$	$ 27 = 3^{3} $
Weight:	$ k $	$=$	$ 10 $
Character orbit:	$[\chi]$	$=$	27.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:	$13.9059675764$
Analytic rank:	$0$
Dimension:	$156$
Relative dimension:	$26$ over $\Q(\zeta_{9})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			7.18
Character	$\chi$	$=$	27.7
Dual form			27.10.e.a.4.18

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(17.4636 - 6.35623i) q^{2} +(-17.1474 - 139.244i) q^{3} +(-127.639 + 107.102i) q^{4} +(280.318 + 1589.76i) q^{5} +(-1184.52 - 2322.71i) q^{6} +(610.601 + 512.355i) q^{7} +(-6305.87 + 10922.1i) q^{8} +(-19094.9 + 4775.35i) q^{9} +(15000.2 + 25981.2i) q^{10} +(-4495.09 + 25492.9i) q^{11} +(17102.0 + 15936.5i) q^{12} +(106141. + 38632.3i) q^{13} +(13919.9 + 5066.44i) q^{14} +(216558. - 66292.8i) q^{15} +(-25886.0 + 146807. i) q^{16} +(64251.1 + 111286. i) q^{17} +(-303113. + 204767. i) q^{18} +(-175832. + 304550. i) q^{19} +(-206046. - 172893. i) q^{20} +(60872.3 - 93808.2i) q^{21} +(83538.4 + 473770. i) q^{22} +(-1965.39 + 1649.15i) q^{23} +(1.62897e6 + 690772. i) q^{24} +(-613422. + 223267. i) q^{25} +2.09916e6 q^{26} +(992367. + 2.57698e6i) q^{27} -132811. q^{28} +(-3.90737e6 + 1.42216e6i) q^{29} +(3.36051e6 - 2.53421e6i) q^{30} +(-4.10711e6 + 3.44627e6i) q^{31} +(-640209. - 3.63081e6i) q^{32} +(3.62682e6 + 188779. i) q^{33} +(1.82942e6 + 1.53506e6i) q^{34} +(-643359. + 1.11433e6i) q^{35} +(1.92581e6 - 2.65463e6i) q^{36} +(1.52669e6 + 2.64430e6i) q^{37} +(-1.13487e6 + 6.43617e6i) q^{38} +(3.55928e6 - 1.54420e7i) q^{39} +(-1.91312e7 - 6.96317e6i) q^{40} +(-2.20476e7 - 8.02467e6i) q^{41} +(466783. - 2.02515e6i) q^{42} +(3.33783e6 - 1.89298e7i) q^{43} +(-2.15659e6 - 3.73533e6i) q^{44} +(-1.29443e7 - 2.90178e7i) q^{45} +(-23840.3 + 41292.6i) q^{46} +(1.67023e7 + 1.40149e7i) q^{47} +(2.08859e7 + 1.08713e6i) q^{48} +(-6.89700e6 - 3.91149e7i) q^{49} +(-9.29341e6 + 7.79810e6i) q^{50} +(1.43942e7 - 1.08549e7i) q^{51} +(-1.76854e7 + 6.43695e6i) q^{52} +8.11126e7 q^{53} +(3.37102e7 + 3.86956e7i) q^{54} -4.17877e7 q^{55} +(-9.44636e6 + 3.43819e6i) q^{56} +(4.54219e7 + 1.92614e7i) q^{57} +(-5.91971e7 + 4.96722e7i) q^{58} +(3.01060e7 + 1.70740e8i) q^{59} +(-2.05412e7 + 3.16554e7i) q^{60} +(-7.48377e7 - 6.27963e7i) q^{61} +(-4.98196e7 + 8.62901e7i) q^{62} +(-1.41061e7 - 6.86755e6i) q^{63} +(-7.24209e7 - 1.25437e8i) q^{64} +(-3.16628e7 + 1.79568e8i) q^{65} +(6.45373e7 - 1.97562e7i) q^{66} +(2.17705e8 + 7.92381e7i) q^{67} +(-2.01199e7 - 7.32305e6i) q^{68} +(263337. + 245390. i) q^{69} +(-4.15242e6 + 2.35496e7i) q^{70} +(1.41531e8 + 2.45140e8i) q^{71} +(6.82535e7 - 2.38669e8i) q^{72} +(2.29279e8 - 3.97123e8i) q^{73} +(4.34693e7 + 3.64750e7i) q^{74} +(4.16073e7 + 8.15870e7i) q^{75} +(-1.01749e7 - 5.77045e7i) q^{76} +(-1.58061e7 + 1.32629e7i) q^{77} +(-3.59951e7 - 2.92297e8i) q^{78} +(-5.29687e8 + 1.92790e8i) q^{79} -2.40644e8 q^{80} +(3.41813e8 - 1.82370e8i) q^{81} -4.36037e8 q^{82} +(6.29101e7 - 2.28974e7i) q^{83} +(2.27736e6 + 1.84931e7i) q^{84} +(-1.58908e8 + 1.33339e8i) q^{85} +(-6.20314e7 - 3.51798e8i) q^{86} +(2.65029e8 + 5.19692e8i) q^{87} +(-2.50091e8 - 2.09851e8i) q^{88} +(2.71094e8 - 4.69549e8i) q^{89} +(-4.10498e8 - 4.24477e8i) q^{90} +(4.50165e7 + 7.79709e7i) q^{91} +(74232.5 - 420994. i) q^{92} +(5.50300e8 + 5.12797e8i) q^{93} +(3.80764e8 + 1.38587e8i) q^{94} +(-5.33450e8 - 1.94160e8i) q^{95} +(-4.94591e8 + 1.51404e8i) q^{96} +(1.23991e7 - 7.03187e7i) q^{97} +(-3.69070e8 - 6.39247e8i) q^{98} +(-3.59041e7 - 5.08251e8i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 156 q - 6 q^{2} - 6 q^{3} - 6 q^{4} + 2382 q^{5} - 6822 q^{6} - 6 q^{7} + 36861 q^{8} + 2538 q^{9} - 3 q^{10} - 121767 q^{11} + 319935 q^{12} - 6 q^{13} - 720417 q^{14} - 706356 q^{15} + 1530 q^{16} + 1002249 q^{17}+ \cdots + 5248107342 q^{99}+O(q^{100}) $ 156 * q - 6 * q^2 - 6 * q^3 - 6 * q^4 + 2382 * q^5 - 6822 * q^6 - 6 * q^7 + 36861 * q^8 + 2538 * q^9 - 3 * q^10 - 121767 * q^11 + 319935 * q^12 - 6 * q^13 - 720417 * q^14 - 706356 * q^15 + 1530 * q^16 + 1002249 * q^17 + 922437 * q^18 - 3 * q^19 - 8448573 * q^20 - 3497394 * q^21 - 1585014 * q^22 + 9316482 * q^23 + 7959258 * q^24 + 2192178 * q^25 - 33129678 * q^26 - 3148155 * q^27 - 12 * q^28 + 19657236 * q^29 + 21174507 * q^30 - 4633692 * q^31 - 37550952 * q^32 - 19055889 * q^33 + 14341770 * q^34 + 34449663 * q^35 + 137733552 * q^36 - 3 * q^37 - 92022060 * q^38 - 89330160 * q^39 + 6645801 * q^40 - 33127221 * q^41 + 227141658 * q^42 + 2356203 * q^43 + 1001541 * q^44 - 78992532 * q^45 - 3 * q^46 - 33488952 * q^47 + 248865393 * q^48 - 93214644 * q^49 - 72027753 * q^50 - 101541537 * q^51 + 160531713 * q^52 + 4841352 * q^53 - 315431874 * q^54 - 12 * q^55 - 91770981 * q^56 - 103852992 * q^57 - 320682489 * q^58 + 538090854 * q^59 + 1127571210 * q^60 + 36683436 * q^61 - 55862958 * q^62 - 419972706 * q^63 - 956301315 * q^64 - 852347310 * q^65 + 472205277 * q^66 - 109026897 * q^67 - 508886217 * q^68 - 1234413090 * q^69 - 815297649 * q^70 + 940878639 * q^71 + 2831326452 * q^72 - 221849931 * q^73 + 838884579 * q^74 - 226667796 * q^75 + 908401146 * q^76 - 967811358 * q^77 - 1247881230 * q^78 - 1228059150 * q^79 - 2497115154 * q^80 - 392600970 * q^81 - 12 * q^82 - 297703284 * q^83 + 1027656618 * q^84 + 1535949369 * q^85 + 2930201574 * q^86 + 2687612040 * q^87 + 2837227002 * q^88 + 1774997208 * q^89 + 7127326206 * q^90 + 551343507 * q^91 - 6896645517 * q^92 - 7299151842 * q^93 + 414852915 * q^94 - 9000269169 * q^95 - 2644638174 * q^96 + 3371772333 * q^97 + 6901039926 * q^98 + 5248107342 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/27\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{8}{9}\right)$

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 $

$2$	17.4636	−	6.35623i	0.771789	−	0.280908i	0.0740446	−	0.997255i	$-0.476409\pi$
$2$	17.4636	−	6.35623i	0.771789	−	0.280908i	0.697745	+	0.716347i	$0.254187\pi$
$3$	−17.1474	−	139.244i	−0.122223	−	0.992503i
$3$	−17.1474	−	139.244i	−0.122223	−	0.992503i
$4$	−127.639	+	107.102i	−0.249295	+	0.209184i
$5$	280.318	+	1589.76i	0.200579	+	1.13754i	0.904247	+	0.427010i	$0.140433\pi$
$5$	280.318	+	1589.76i	0.200579	+	1.13754i	−0.703668	+	0.710529i	$0.748456\pi$
$6$	−1184.52	−	2322.71i	−0.373132	−	0.731670i
$7$	610.601	+	512.355i	0.0961205	+	0.0806547i	0.689582	−	0.724208i	$-0.257794\pi$
$7$	610.601	+	512.355i	0.0961205	+	0.0806547i	−0.593461	+	0.804863i	$0.702239\pi$
$8$	−6305.87	+	10922.1i	−0.544302	+	0.942760i
$9$	−19094.9	+	4775.35i	−0.970123	+	0.242613i
$10$	15000.2	+	25981.2i	0.474349	+	0.821597i
$11$	−4495.09	+	25492.9i	−0.0925702	+	0.524992i	0.902895	+	0.429862i	$0.141438\pi$
$11$	−4495.09	+	25492.9i	−0.0925702	+	0.524992i	−0.995465	+	0.0951300i	$0.969673\pi$
$12$	17102.0	+	15936.5i	0.238085	+	0.221859i
$13$	106141.	+	38632.3i	1.03072	+	0.375150i	0.801354	−	0.598191i	$-0.204114\pi$
$13$	106141.	+	38632.3i	1.03072	+	0.375150i	0.229363	+	0.973341i	$0.426336\pi$
$14$	13919.9	+	5066.44i	0.0968414	+	0.0352474i
$15$	216558.	−	66292.8i	1.10450	−	0.338108i
$16$	−25886.0	+	146807.i	−0.0987472	+	0.560023i
$17$	64251.1	+	111286.i	0.186578	+	0.323162i	0.944107	−	0.329639i	$-0.106927\pi$
$17$	64251.1	+	111286.i	0.186578	+	0.323162i	−0.757529	+	0.652801i	$0.773594\pi$
$18$	−303113.	+	204767.i	−0.680579	+	0.459762i
$19$	−175832.	+	304550.i	−0.309533	+	0.536127i	−0.978260	−	0.207381i	$-0.933506\pi$
$19$	−175832.	+	304550.i	−0.309533	+	0.536127i	0.668727	+	0.743508i	$0.266839\pi$
$20$	−206046.	−	172893.i	−0.287958	−	0.241625i
$21$	60872.3	−	93808.2i	0.0683019	−	0.105258i
$22$	83538.4	+	473770.i	0.0760299	+	0.431187i
$23$	−1965.39	+	1649.15i	−0.00146444	+	0.00122881i	−0.643520	−	0.765430i	$-0.722526\pi$
$23$	−1965.39	+	1649.15i	−0.00146444	+	0.00122881i	0.642055	+	0.766659i	$0.278082\pi$
$24$	1.62897e6	+	690772.i	1.00222	+	0.424995i
$25$	−613422.	+	223267.i	−0.314072	+	0.114313i
$26$	2.09916e6			0.900879
$27$	992367.	+	2.57698e6i	0.359365	+	0.933197i
$28$	−132811.			−0.0408340
$29$	−3.90737e6	+	1.42216e6i	−1.02587	+	0.373387i	−0.799508	−	0.600656i	$-0.794906\pi$
$29$	−3.90737e6	+	1.42216e6i	−1.02587	+	0.373387i	−0.226364	+	0.974043i	$0.572684\pi$
$30$	3.36051e6	−	2.53421e6i	0.757461	−	0.571210i
$31$	−4.10711e6	+	3.44627e6i	−0.798746	+	0.670227i	−0.947893	−	0.318588i	$-0.896792\pi$
$31$	−4.10711e6	+	3.44627e6i	−0.798746	+	0.670227i	0.149147	+	0.988815i	$0.452347\pi$
$32$	−640209.	−	3.63081e6i	−0.107931	−	0.612108i
$33$	3.62682e6	+	188779.i	0.532370	+	0.0277103i
$34$	1.82942e6	+	1.53506e6i	0.234778	+	0.197002i
$35$	−643359.	+	1.11433e6i	−0.0724682	+	0.125519i
$36$	1.92581e6	−	2.65463e6i	0.191097	−	0.263416i
$37$	1.52669e6	+	2.64430e6i	0.133919	+	0.231955i	0.925184	−	0.379519i	$-0.123910\pi$
$37$	1.52669e6	+	2.64430e6i	0.133919	+	0.231955i	−0.791265	+	0.611474i	$0.790577\pi$
$38$	−1.13487e6	+	6.43617e6i	−0.0882917	+	0.500727i
$39$	3.55928e6	−	1.54420e7i	0.246361	−	1.06884i
$40$	−1.91312e7	−	6.96317e6i	−1.18160	−	0.430068i
$41$	−2.20476e7	−	8.02467e6i	−1.21852	−	0.443507i	−0.348872	−	0.937171i	$-0.613435\pi$
$41$	−2.20476e7	−	8.02467e6i	−1.21852	−	0.443507i	−0.869653	+	0.493664i	$0.835657\pi$
$42$	466783.	−	2.02515e6i	0.0231469	−	0.100423i
$43$	3.33783e6	−	1.89298e7i	0.148887	−	0.844379i	−0.815277	−	0.579071i	$-0.803415\pi$
$43$	3.33783e6	−	1.89298e7i	0.148887	−	0.844379i	0.964164	−	0.265308i	$-0.0854735\pi$
$44$	−2.15659e6	−	3.73533e6i	−0.0867424	−	0.150242i
$45$	−1.29443e7	−	2.90178e7i	−0.470568	−	1.05489i
$46$	−23840.3	+	41292.6i	−0.000785058	+	0.00135976i
$47$	1.67023e7	+	1.40149e7i	0.499270	+	0.418937i	0.857335	−	0.514760i	$-0.172119\pi$
$47$	1.67023e7	+	1.40149e7i	0.499270	+	0.418937i	−0.358065	+	0.933697i	$0.616563\pi$
$48$	2.08859e7	+	1.08713e6i	0.567893	+	0.0295593i
$49$	−6.89700e6	−	3.91149e7i	−0.170914	−	0.969303i
$50$	−9.29341e6	+	7.79810e6i	−0.210286	+	0.176451i
$51$	1.43942e7	−	1.08549e7i	0.297936	−	0.224677i
$52$	−1.76854e7	+	6.43695e6i	−0.335428	+	0.122086i
$53$	8.11126e7			1.41204			0.706020	−	0.708192i	$-0.250489\pi$
$53$	8.11126e7			1.41204			0.706020	+	0.708192i	$0.250489\pi$
$54$	3.37102e7	+	3.86956e7i	0.539497	+	0.619283i
$55$	−4.17877e7			−0.615767
$56$	−9.44636e6	+	3.43819e6i	−0.128357	+	0.0467180i
$57$	4.54219e7	+	1.92614e7i	0.569939	+	0.241685i
$58$	−5.91971e7	+	4.96722e7i	−0.686869	+	0.576352i
$59$	3.01060e7	+	1.70740e8i	0.323459	+	1.83443i	0.520291	+	0.853989i	$0.325823\pi$
$59$	3.01060e7	+	1.70740e8i	0.323459	+	1.83443i	−0.196832	+	0.980437i	$0.563065\pi$
$60$	−2.05412e7	+	3.16554e7i	−0.204619	+	0.315331i
$61$	−7.48377e7	−	6.27963e7i	−0.692048	−	0.580697i	0.227451	−	0.973790i	$-0.426961\pi$
$61$	−7.48377e7	−	6.27963e7i	−0.692048	−	0.580697i	−0.919499	+	0.393092i	$0.871405\pi$
$62$	−4.98196e7	+	8.62901e7i	−0.428191	+	0.741649i
$63$	−1.41061e7	−	6.86755e6i	−0.112817	−	0.0549249i
$64$	−7.24209e7	−	1.25437e8i	−0.539577	−	0.934576i
$65$	−3.16628e7	+	1.79568e8i	−0.220008	+	1.24773i
$66$	6.45373e7	−	1.97562e7i	0.418662	−	0.128161i
$67$	2.17705e8	+	7.92381e7i	1.31987	+	0.480394i	0.903417	−	0.428763i	$-0.141051\pi$
$67$	2.17705e8	+	7.92381e7i	1.31987	+	0.480394i	0.416454	+	0.909157i	$0.363273\pi$
$68$	−2.01199e7	−	7.32305e6i	−0.114113	−	0.0415338i
$69$	263337.	+	245390.i	0.00139859	+	0.00130328i
$70$	−4.15242e6	+	2.35496e7i	−0.0206709	+	0.117231i
$71$	1.41531e8	+	2.45140e8i	0.660983	+	1.14486i	0.980358	+	0.197228i	$0.0631938\pi$
$71$	1.41531e8	+	2.45140e8i	0.660983	+	1.14486i	−0.319375	+	0.947629i	$0.603473\pi$
$72$	6.82535e7	−	2.38669e8i	0.299315	−	1.04665i
$73$	2.29279e8	−	3.97123e8i	0.944957	−	1.63671i	0.189119	−	0.981954i	$-0.439437\pi$
$73$	2.29279e8	−	3.97123e8i	0.944957	−	1.63671i	0.755837	−	0.654759i	$-0.227230\pi$
$74$	4.34693e7	+	3.64750e7i	0.168515	+	0.141401i
$75$	4.16073e7	+	8.15870e7i	0.151843	+	0.297746i
$76$	−1.01749e7	−	5.77045e7i	−0.0349838	−	0.198403i
$77$	−1.58061e7	+	1.32629e7i	−0.0512410	+	0.0429963i
$78$	−3.59951e7	−	2.92297e8i	−0.110108	−	0.894125i
$79$	−5.29687e8	+	1.92790e8i	−1.53002	+	0.556882i	−0.963627	−	0.267252i	$-0.913884\pi$
$79$	−5.29687e8	+	1.92790e8i	−1.53002	+	0.556882i	−0.566394	+	0.824134i	$0.691662\pi$
$80$	−2.40644e8			−0.656855
$81$	3.41813e8	−	1.82370e8i	0.882278	−	0.470728i
$82$	−4.36037e8			−1.06503
$83$	6.29101e7	−	2.28974e7i	0.145502	−	0.0529584i	−0.268243	−	0.963351i	$-0.586443\pi$
$83$	6.29101e7	−	2.28974e7i	0.145502	−	0.0529584i	0.413745	+	0.910393i	$0.364221\pi$
$84$	2.27736e6	+	1.84931e7i	0.00499085	+	0.0405279i
$85$	−1.58908e8	+	1.33339e8i	−0.330187	+	0.277059i
$86$	−6.20314e7	−	3.51798e8i	−0.122284	−	0.693506i
$87$	2.65029e8	+	5.19692e8i	0.495972	+	0.972544i
$88$	−2.50091e8	−	2.09851e8i	−0.444555	−	0.373026i
$89$	2.71094e8	−	4.69549e8i	0.458000	−	0.793279i	−0.540855	−	0.841116i	$-0.681899\pi$
$89$	2.71094e8	−	4.69549e8i	0.458000	−	0.793279i	0.998855	+	0.0478365i	$0.0152326\pi$
$90$	−4.10498e8	−	4.24477e8i	−0.659507	−	0.681967i
$91$	4.50165e7	+	7.79709e7i	0.0688154	+	0.119192i
$92$	74232.5	−	420994.i	0.000108031	−	0.000612675i
$93$	5.50300e8	+	5.12797e8i	0.762827	+	0.710841i
$94$	3.80764e8	+	1.38587e8i	0.503014	+	0.183082i
$95$	−5.33450e8	−	1.94160e8i	−0.671951	−	0.244570i
$96$	−4.94591e8	+	1.51404e8i	−0.594327	+	0.181935i
$97$	1.23991e7	−	7.03187e7i	0.0142206	−	0.0806488i	−0.976872	−	0.213827i	$-0.931407\pi$
$97$	1.23991e7	−	7.03187e7i	0.0142206	−	0.0806488i	0.991092	+	0.133178i	$0.0425182\pi$
$98$	−3.69070e8	−	6.39247e8i	−0.404195	−	0.700086i
$99$	−3.59041e7	−	5.08251e8i	−0.0375652	−	0.531766i
$100$	5.43843e7	−	9.41964e7i	0.0543843	−	0.0941964i
$101$	1.11072e8	+	9.32004e7i	0.106208	+	0.0891192i	0.694345	−	0.719642i	$-0.255694\pi$
$101$	1.11072e8	+	9.32004e7i	0.106208	+	0.0891192i	−0.588137	+	0.808761i	$0.700138\pi$
$102$	1.82379e8	−	2.81058e8i	0.166830	−	0.257096i
$103$	2.46300e8	+	1.39683e9i	0.215624	+	1.22286i	0.879821	+	0.475305i	$0.157662\pi$
$103$	2.46300e8	+	1.39683e9i	0.215624	+	1.22286i	−0.664198	+	0.747557i	$0.731227\pi$
$104$	−1.09126e9	+	9.15675e8i	−0.914698	+	0.767523i
$105$	1.66196e8	+	7.04762e7i	0.133435	+	0.0565836i
$106$	1.41652e9	−	5.15571e8i	1.08980	−	0.396654i
$107$	2.27609e9			1.67866			0.839328	−	0.543625i	$-0.182949\pi$
$107$	2.27609e9			1.67866			0.839328	+	0.543625i	$0.182949\pi$
$108$	−4.02664e8	−	2.22639e8i	−0.284797	−	0.157468i
$109$	−7.56560e8			−0.513362			−0.256681	−	0.966496i	$-0.582629\pi$
$109$	−7.56560e8			−0.513362			−0.256681	+	0.966496i	$0.582629\pi$
$110$	−7.29763e8	+	2.65612e8i	−0.475242	+	0.172974i
$111$	3.42025e8	−	2.57925e8i	0.213848	−	0.161265i
$112$	−9.10231e7	+	7.63774e7i	−0.0546601	+	0.0458653i
$113$	−3.43870e8	−	1.95018e9i	−0.198400	−	1.12518i	−0.907493	−	0.420067i	$-0.862007\pi$
$113$	−3.43870e8	−	1.95018e9i	−0.198400	−	1.12518i	0.709093	−	0.705115i	$-0.249105\pi$
$114$	9.15660e8	+	4.76608e7i	0.507764	+	0.0264295i
$115$	−3.17269e6	−	2.66221e6i	−0.00169156	−	0.00141939i
$116$	3.46416e8	−	6.00011e8i	0.177639	−	0.307679i
$117$	−2.21124e9	−	2.30819e8i	−1.09094	−	0.113877i
$118$	1.61102e9	+	2.79037e9i	0.764948	+	1.32493i
$119$	−1.77862e7	+	1.00871e8i	−0.00813060	+	0.0461109i
$120$	−6.41533e8	+	2.78330e9i	−0.282425	+	1.22531i
$121$	1.58606e9	+	5.77280e8i	0.672645	+	0.244823i
$122$	−1.70608e9	−	6.20964e8i	−0.697238	−	0.253774i
$123$	−7.39331e8	+	3.20761e9i	−0.291250	+	1.26360i
$124$	1.55125e8	−	8.79759e8i	0.0589230	−	0.334169i
$125$	1.04956e9	+	1.81788e9i	0.384512	+	0.665995i
$126$	−2.89994e8	−	3.02709e7i	−0.102500	−	0.0106994i
$127$	1.94110e9	−	3.36209e9i	0.662112	−	1.14681i	−0.317948	−	0.948108i	$-0.602994\pi$
$127$	1.94110e9	−	3.36209e9i	0.662112	−	1.14681i	0.980060	−	0.198703i	$-0.0636731\pi$
$128$	−6.16009e8	−	5.16893e8i	−0.202835	−	0.170198i
$129$	−2.69310e9	−	1.40178e8i	−0.856245	−	0.0445683i
$130$	5.88433e8	+	3.33717e9i	0.180697	+	1.02479i
$131$	8.75614e8	−	7.34727e8i	0.259772	−	0.217974i	−0.503595	−	0.863940i	$-0.667990\pi$
$131$	8.75614e8	−	7.34727e8i	0.259772	−	0.217974i	0.763366	+	0.645966i	$0.223545\pi$
$132$	−4.83143e8	+	3.64344e8i	−0.138514	+	0.104455i
$133$	−2.63401e8	+	9.58701e7i	−0.0729936	+	0.0265675i
$134$	4.30556e9			1.15361
$135$	−3.81860e9	+	2.30000e9i	−0.989468	+	0.595971i
$136$	−1.62064e9			−0.406219
$137$	2.92900e9	−	1.06607e9i	0.710356	−	0.258549i	0.0385301	−	0.999257i	$-0.487732\pi$
$137$	2.92900e9	−	1.06607e9i	0.710356	−	0.258549i	0.671826	+	0.740709i	$0.265510\pi$
$138$	6.15856e6	+	2.61157e6i	0.00144552	+	0.000612978i
$139$	1.22616e9	−	1.02887e9i	0.278599	−	0.233772i	−0.492771	−	0.870159i	$-0.664016\pi$
$139$	1.22616e9	−	1.02887e9i	0.278599	−	0.233772i	0.771370	+	0.636387i	$0.219572\pi$
$140$	−3.72292e7	−	2.11137e8i	−0.00819045	−	0.0464503i
$141$	1.66509e9	−	2.56601e9i	0.354774	−	0.546730i
$142$	4.02981e9	+	3.38141e9i	0.831739	+	0.697912i
$143$	−1.46196e9	+	2.53220e9i	−0.292364	+	0.506390i
$144$	−2.06762e8	−	2.92688e9i	−0.0400718	−	0.567249i
$145$	−3.35620e9	−	5.81312e9i	−0.630511	−	1.09208i
$146$	1.47983e9	−	8.39256e9i	0.269541	−	1.52864i
$147$	−5.32825e9	+	1.63109e9i	−0.941146	+	0.288104i
$148$	−4.78075e8	−	1.74005e8i	−0.0819065	−	0.0298115i
$149$	−4.49393e8	−	1.63566e8i	−0.0746945	−	0.0271866i	0.304403	−	0.952543i	$-0.401543\pi$
$149$	−4.49393e8	−	1.63566e8i	−0.0746945	−	0.0271866i	−0.379097	+	0.925357i	$0.623765\pi$
$150$	1.24520e9	+	1.16034e9i	0.200830	+	0.187143i
$151$	1.20387e9	−	6.82747e9i	0.188444	−	1.06872i	−0.733006	−	0.680222i	$-0.761883\pi$
$151$	1.20387e9	−	6.82747e9i	0.188444	−	1.06872i	0.921450	−	0.388497i	$-0.127006\pi$
$152$	−2.21755e9	−	3.84091e9i	−0.336959	−	0.583630i
$153$	−1.75830e9	−	1.81818e9i	−0.259407	−	0.268241i
$154$	−1.91730e8	+	3.32086e8i	−0.0274692	+	0.0475781i
$155$	−6.63004e9	−	5.56327e9i	−0.922622	−	0.774172i
$156$	1.19957e9	+	2.35221e9i	0.162167	+	0.317992i
$157$	1.25829e9	+	7.13614e9i	0.165285	+	0.937379i	0.948770	+	0.315968i	$0.102329\pi$
$157$	1.25829e9	+	7.13614e9i	0.165285	+	0.937379i	−0.783485	+	0.621411i	$0.786560\pi$
$158$	−8.02482e9	+	6.73362e9i	−1.02442	+	0.859591i
$159$	−1.39087e9	−	1.12945e10i	−0.172583	−	1.40145i
$160$	5.59265e9	−	2.03556e9i	0.674648	−	0.245552i
$161$	−2.04502e6			−0.000239873
$162$	4.81009e9	−	5.35747e9i	0.548701	−	0.611142i
$163$	−1.48150e10			−1.64383			−0.821915	−	0.569610i	$-0.807094\pi$
$163$	−1.48150e10			−1.64383			−0.821915	+	0.569610i	$0.807094\pi$
$164$	3.67360e9	−	1.33708e9i	0.396547	−	0.144331i
$165$	7.16549e8	+	5.81870e9i	0.0752607	+	0.611150i
$166$	9.53096e8	−	7.99743e8i	0.0974205	−	0.0817455i
$167$	3.07828e9	+	1.74578e10i	0.306256	+	1.73686i	0.617534	+	0.786544i	$0.288132\pi$
$167$	3.07828e9	+	1.74578e10i	0.306256	+	1.73686i	−0.311278	+	0.950319i	$0.600757\pi$
$168$	6.40729e8	+	1.25640e9i	0.0620558	+	0.121684i
$169$	1.65000e9	+	1.38451e9i	0.155594	+	0.130559i
$170$	−1.92756e9	+	3.33864e9i	−0.177006	+	0.306584i
$171$	1.90317e9	−	6.65502e9i	0.170214	−	0.595206i
$172$	1.60138e9	+	2.77367e9i	0.139513	+	0.241644i
$173$	2.08583e9	−	1.18294e10i	0.177040	−	1.00405i	−0.758722	−	0.651414i	$-0.774176\pi$
$173$	2.08583e9	−	1.18294e10i	0.177040	−	1.00405i	0.935762	−	0.352631i	$-0.114713\pi$
$174$	7.93165e9	+	7.39110e9i	0.655982	+	0.611276i
$175$	−4.88948e8	−	1.77962e8i	−0.0394086	−	0.0143436i
$176$	−3.62617e9	−	1.31982e9i	−0.284867	−	0.103683i
$177$	2.32583e10	−	7.11982e9i	1.78114	−	0.545242i
$178$	1.74972e9	−	9.92316e9i	0.130641	−	0.740900i
$179$	1.07814e10	+	1.86739e10i	0.784939	+	1.35955i	0.929036	+	0.369990i	$0.120639\pi$
$179$	1.07814e10	+	1.86739e10i	0.784939	+	1.35955i	−0.144097	+	0.989564i	$0.546028\pi$
$180$	4.76006e9	+	2.31744e9i	0.337976	+	0.164544i
$181$	−1.09960e10	+	1.90457e10i	−0.761522	+	1.31900i	0.180543	+	0.983567i	$0.442214\pi$
$181$	−1.09960e10	+	1.90457e10i	−0.761522	+	1.31900i	−0.942066	+	0.335428i	$0.891119\pi$
$182$	1.28175e9	+	1.07552e9i	0.0865929	+	0.0726601i
$183$	−7.46075e9	+	1.14975e10i	−0.491760	+	0.757834i
$184$	−5.61875e6	−	3.18655e7i	−0.000361376	−	0.00204946i
$185$	−3.77585e9	+	3.16831e9i	−0.236996	+	0.198864i
$186$	1.28697e10	+	5.45745e9i	0.788423	+	0.334335i
$187$	−3.12582e9	+	1.13771e9i	−0.186929	+	0.0680367i
$188$	−3.63289e9			−0.212100
$189$	−7.14386e8	+	2.08195e9i	−0.0407244	+	0.118684i
$190$	−1.05501e10			−0.587307
$191$	4.20187e9	−	1.52936e9i	0.228451	−	0.0831493i	−0.225259	−	0.974299i	$-0.572323\pi$
$191$	4.20187e9	−	1.52936e9i	0.228451	−	0.0831493i	0.453709	+	0.891150i	$0.350100\pi$
$192$	−1.62245e10	+	1.22351e10i	−0.861620	+	0.649758i
$193$	−2.16606e10	+	1.81754e10i	−1.12373	+	0.942921i	−0.998787	−	0.0492430i	$-0.984319\pi$
$193$	−2.16606e10	+	1.81754e10i	−1.12373	+	0.942921i	−0.124943	+	0.992164i	$0.539875\pi$
$194$	−2.30429e8	−	1.30683e9i	−0.0116797	−	0.0662386i
$195$	2.55468e10	+	1.32973e9i	1.26526	+	0.0658580i
$196$	5.06961e9	+	4.25391e9i	0.245370	+	0.205890i
$197$	−8.39382e9	+	1.45385e10i	−0.397065	+	0.687737i	−0.993362	−	0.115027i	$-0.963305\pi$
$197$	−8.39382e9	+	1.45385e10i	−0.397065	+	0.687737i	0.596297	+	0.802764i	$0.296638\pi$
$198$	−3.85758e9	−	8.64768e9i	−0.178370	−	0.399859i
$199$	−1.43606e10	−	2.48733e10i	−0.649134	−	1.12433i	−0.983330	−	0.181830i	$-0.941798\pi$
$199$	−1.43606e10	−	2.48733e10i	−0.649134	−	1.12433i	0.334196	−	0.942504i	$-0.391535\pi$
$200$	1.42961e9	−	8.10775e9i	0.0631806	−	0.358315i
$201$	7.30038e9	−	3.16729e10i	0.315474	−	1.36869i
$202$	2.53212e9	+	9.21615e8i	0.107005	+	0.0389465i
$203$	−3.11449e9	−	1.13358e9i	−0.128723	−	0.0468512i
$204$	−6.74689e8	+	2.92716e9i	−0.0272752	+	0.118334i
$205$	6.57697e9	−	3.72999e10i	0.260096	−	1.47508i
$206$	1.31799e10	+	2.28282e10i	0.509928	+	0.883221i
$207$	2.96536e7	−	4.08759e7i	0.00112256	−	0.00154739i
$208$	−8.41904e9	+	1.45822e10i	−0.311873	+	0.540180i
$209$	−6.97349e9	−	5.85145e9i	−0.252809	−	0.212132i
$210$	3.35034e9	+	1.74388e8i	0.118878	+	0.00618771i
$211$	−1.83777e9	−	1.04225e10i	−0.0638294	−	0.361995i	−0.999947	−	0.0103071i	$-0.996719\pi$
$211$	−1.83777e9	−	1.04225e10i	−0.0638294	−	0.361995i	0.936117	−	0.351687i	$-0.114392\pi$
$212$	−1.03532e10	+	8.68732e9i	−0.352015	+	0.295376i
$213$	3.17074e10	−	2.39109e10i	1.05549	−	0.795955i
$214$	3.97487e10	−	1.44673e10i	1.29557	−	0.471548i
$215$	3.10294e10			0.990378
$216$	−3.44037e10	−	5.41135e9i	−1.07538	−	0.169147i
$217$	−4.27352e9			−0.130833
$218$	−1.32123e10	+	4.80887e9i	−0.396208	+	0.144208i
$219$	−5.92287e10	−	2.51162e10i	−1.73994	−	0.737829i
$220$	5.33375e9	−	4.47555e9i	0.153508	−	0.128808i
$221$	2.52046e9	+	1.42942e10i	0.0710745	+	0.403084i
$222$	4.33356e9	−	6.67830e9i	0.119745	−	0.184534i
$223$	4.93800e9	+	4.14348e9i	0.133715	+	0.112200i	0.707192	−	0.707021i	$-0.249962\pi$
$223$	4.93800e9	+	4.14348e9i	0.133715	+	0.112200i	−0.573477	+	0.819221i	$0.694406\pi$
$224$	1.46935e9	−	2.54499e9i	0.0389950	−	0.0675413i
$225$	1.06471e10	−	7.19258e9i	0.276955	−	0.187095i
$226$	−1.84010e10	−	3.18715e10i	−0.469196	−	0.812671i
$227$	5.28046e8	−	2.99470e9i	0.0131994	−	0.0748578i	−0.977497	−	0.210952i	$-0.932344\pi$
$227$	5.28046e8	−	2.99470e9i	0.0131994	−	0.0748578i	0.990696	+	0.136094i	$0.0434549\pi$
$228$	−7.86055e9	+	2.40627e9i	−0.192640	+	0.0589709i
$229$	1.65307e10	+	6.01668e9i	0.397220	+	0.144576i	0.532904	−	0.846176i	$-0.321101\pi$
$229$	1.65307e10	+	6.01668e9i	0.397220	+	0.144576i	−0.135684	+	0.990752i	$0.543323\pi$
$230$	−7.23282e7	−	2.63253e7i	−0.00170425	−	0.000620295i
$231$	2.11782e9	+	1.97349e9i	0.0489367	+	0.0456017i
$232$	9.10634e9	−	5.16446e10i	0.206371	−	1.17039i
$233$	2.16335e9	+	3.74704e9i	0.0480868	+	0.0832887i	0.889067	−	0.457777i	$-0.151354\pi$
$233$	2.16335e9	+	3.74704e9i	0.0480868	+	0.0832887i	−0.840980	+	0.541066i	$0.818021\pi$
$234$	−4.00834e10	+	1.00242e10i	−0.873963	+	0.218565i
$235$	−1.75983e10	+	3.04812e10i	−0.376415	+	0.651969i
$236$	−2.21293e10	−	1.85687e10i	−0.464369	−	0.389651i
$237$	3.59277e10	+	7.04500e10i	0.739710	+	1.45049i
$238$	3.30546e8	+	1.87462e9i	0.00667783	+	0.0378719i
$239$	−5.29871e10	+	4.44615e10i	−1.05046	+	0.881442i	−0.993142	−	0.116914i	$-0.962700\pi$
$239$	−5.29871e10	+	4.44615e10i	−1.05046	+	0.881442i	−0.0573191	+	0.998356i	$0.518255\pi$
$240$	4.12641e9	+	3.35083e10i	0.0802826	+	0.651930i
$241$	−3.12649e10	+	1.13795e10i	−0.597007	+	0.217293i	−0.622809	−	0.782374i	$-0.714008\pi$
$241$	−3.12649e10	+	1.13795e10i	−0.597007	+	0.217293i	0.0258013	+	0.999667i	$0.491786\pi$
$242$	3.13677e10			0.587913
$243$	−3.12551e10	−	4.44683e10i	−0.575034	−	0.818130i
$244$	1.62778e10			0.293997
$245$	6.02499e10	−	2.19292e10i	1.06834	−	0.388843i
$246$	7.47689e9	+	6.07157e10i	0.130171	+	1.05704i
$247$	−3.04285e10	+	2.55325e10i	−0.520169	+	0.436473i
$248$	−1.17416e10	−	6.65900e10i	−0.197104	−	1.11783i
$249$	−4.26708e9	−	8.36725e9i	−0.0703450	−	0.137939i
$250$	2.98839e10	+	2.50756e10i	0.483846	+	0.405995i
$251$	1.43058e10	−	2.47784e10i	0.227500	−	0.394042i	−0.729566	−	0.683910i	$-0.760278\pi$
$251$	1.43058e10	−	2.47784e10i	0.227500	−	0.394042i	0.957067	+	0.289868i	$0.0936114\pi$
$252$	2.53601e9	−	6.34218e8i	0.0396140	−	0.00990686i
$253$	−3.32072e7	−	5.75166e7i	−0.000509554	−	0.000882573i
$254$	1.25284e10	−	7.10522e10i	0.188862	−	1.07109i
$255$	2.12916e10	+	1.98405e10i	0.315338	+	0.293848i
$256$	5.56434e10	+	2.02525e10i	0.809718	+	0.294713i
$257$	1.28810e10	+	4.68831e9i	0.184184	+	0.0670374i	0.432466	−	0.901650i	$-0.357644\pi$
$257$	1.28810e10	+	4.68831e9i	0.184184	+	0.0670374i	−0.248282	+	0.968688i	$0.579866\pi$
$258$	−4.79222e10	+	1.46699e10i	−0.673361	+	0.206129i
$259$	−4.22624e8	+	2.39682e9i	−0.00583586	+	0.0330968i
$260$	−1.51907e10	−	2.63111e10i	−0.206157	−	0.357075i
$261$	6.78196e10	−	4.58152e10i	0.904634	−	0.611121i
$262$	1.06213e10	−	1.83966e10i	0.139258	−	0.241202i
$263$	1.54430e10	+	1.29582e10i	0.199036	+	0.167011i	0.736858	−	0.676047i	$-0.236308\pi$
$263$	1.54430e10	+	1.29582e10i	0.199036	+	0.167011i	−0.537822	+	0.843058i	$0.680753\pi$
$264$	−2.49322e10	+	3.84221e10i	−0.315895	+	0.486814i
$265$	2.27373e10	+	1.28950e11i	0.283226	+	1.60625i
$266$	−3.99055e9	+	3.34847e9i	−0.0488726	+	0.0410090i
$267$	−7.00306e10	−	2.96968e10i	−0.843310	−	0.357609i
$268$	−3.62742e10	+	1.32027e10i	−0.429528	+	0.156335i
$269$	−1.53806e10			−0.179096			−0.0895481	−	0.995982i	$-0.528542\pi$
$269$	−1.53806e10			−0.179096			−0.0895481	+	0.995982i	$0.528542\pi$
$270$	−5.20671e10	+	6.44381e10i	−0.596247	+	0.737914i
$271$	5.60281e10			0.631022			0.315511	−	0.948922i	$-0.397824\pi$
$271$	5.60281e10			0.631022			0.315511	+	0.948922i	$0.397824\pi$
$272$	−1.80007e10	+	6.55174e9i	−0.199402	+	0.0725766i
$273$	1.00851e10	−	7.60529e9i	0.109887	−	0.0828674i
$274$	4.43746e10	−	3.72347e10i	0.475617	−	0.399090i
$275$	−2.93435e9	−	1.66415e10i	−0.0309396	−	0.175467i
$276$	−5.98938e7	−	3.11752e6i	−0.000621286	−	3.23384e-5i
$277$	1.30917e11	+	1.09852e11i	1.33609	+	1.12111i	0.982612	+	0.185670i	$0.0594456\pi$
$277$	1.30917e11	+	1.09852e11i	1.33609	+	1.12111i	0.353478	+	0.935443i	$0.384999\pi$
$278$	1.48734e10	−	2.57615e10i	0.149351	−	0.258684i
$279$	6.19678e10	−	8.54193e10i	0.612276	−	0.843989i
$280$	−8.11388e9	−	1.40537e10i	−0.0788892	−	0.136640i
$281$	−9.07283e9	+	5.14545e10i	−0.0868089	+	0.492318i	0.910143	+	0.414295i	$0.135972\pi$
$281$	−9.07283e9	+	5.14545e10i	−0.0868089	+	0.492318i	−0.996952	+	0.0780227i	$0.975139\pi$
$282$	1.27683e10	−	5.53955e10i	0.120230	−	0.521620i
$283$	6.89819e10	+	2.51073e10i	0.639287	+	0.232681i	0.641268	−	0.767317i	$-0.278408\pi$
$283$	6.89819e10	+	2.51073e10i	0.639287	+	0.232681i	−0.00198143	+	0.999998i	$0.500631\pi$
$284$	−4.43199e10	−	1.61311e10i	−0.404265	−	0.147140i
$285$	−1.78884e10	+	7.76092e10i	−0.160609	+	0.696805i
$286$	−9.43593e9	+	5.35138e10i	−0.0833946	+	0.472954i
$287$	−9.35081e9	−	1.61961e10i	−0.0813543	−	0.140910i
$288$	2.95631e10	+	6.62728e10i	0.253212	+	0.567635i
$289$	5.10375e10	−	8.83996e10i	0.430377	−	0.745435i
$290$	−9.55609e10	−	8.01851e10i	−0.793395	−	0.665737i
$291$	−1.00041e10	−	5.20721e8i	−0.0817823	−	0.00425683i
$292$	1.32677e10	+	7.52448e10i	0.106800	+	0.605694i
$293$	−1.75418e10	+	1.47193e10i	−0.139050	+	0.116676i	−0.709660	−	0.704545i	$-0.751151\pi$
$293$	−1.75418e10	+	1.47193e10i	−0.139050	+	0.116676i	0.570610	+	0.821221i	$0.306707\pi$
$294$	−8.26829e10	+	6.23522e10i	−0.645436	+	0.486731i
$295$	−2.62996e11	+	9.57226e10i	−2.02185	+	0.735894i
$296$	−3.85084e10			−0.291570
$297$	−7.01554e10	+	1.37146e10i	−0.523188	+	0.102277i
$298$	−8.88769e9			−0.0652853
$299$	−2.72319e8	+	9.91161e7i	−0.00197042	+	0.000717173i
$300$	−1.40489e10	−	5.95748e9i	−0.100137	−	0.0424636i
$301$	1.17368e10	−	9.84838e9i	0.0824142	−	0.0691537i
$302$	−2.23731e10	−	1.26884e11i	−0.154773	−	0.877761i
$303$	1.10730e10	−	1.70643e10i	0.0754700	−	0.116304i
$304$	−4.01584e10	−	3.36969e10i	−0.269678	−	0.226287i
$305$	7.88527e10	−	1.36577e11i	0.521756	−	0.903708i
$306$	−4.22630e10	−	2.05758e10i	−0.275559	−	0.134156i
$307$	−2.68079e9	−	4.64326e9i	−0.0172242	−	0.0298333i	0.857285	−	0.514842i	$-0.172150\pi$
$307$	−2.68079e9	−	4.64326e9i	−0.0172242	−	0.0298333i	−0.874509	+	0.485009i	$0.838816\pi$
$308$	5.96997e8	−	3.38574e9i	0.00378002	−	0.0214375i
$309$	1.90278e11	−	5.82478e10i	1.18734	−	0.363468i
$310$	−1.51146e11	−	5.50126e10i	−0.929541	−	0.338325i
$311$	6.13619e9	+	2.23339e9i	0.0371944	+	0.0135376i	0.360550	−	0.932740i	$-0.382589\pi$
$311$	6.13619e9	+	2.23339e9i	0.0371944	+	0.0135376i	−0.323356	+	0.946277i	$0.604811\pi$
$312$	1.46215e11	+	1.36250e11i	0.873565	+	0.814031i
$313$	4.11967e10	−	2.33638e11i	0.242612	−	1.37592i	−0.583361	−	0.812213i	$-0.698263\pi$
$313$	4.11967e10	−	2.33638e11i	0.242612	−	1.37592i	0.825973	−	0.563709i	$-0.190626\pi$
$314$	6.73333e10	+	1.16625e11i	0.390883	+	0.677029i
$315$	6.96359e9	−	2.43503e10i	0.0398507	−	0.139350i
$316$	4.69606e10	−	8.13381e10i	0.264936	−	0.458883i
$317$	2.09537e11	+	1.75822e11i	1.16545	+	0.977929i	0.999966	−	0.00828314i	$-0.00263663\pi$
$317$	2.09537e11	+	1.75822e11i	1.16545	+	0.977929i	0.165485	+	0.986212i	$0.447081\pi$
$318$	−9.60798e10	−	1.88401e11i	−0.526878	−	1.03315i
$319$	−1.86912e10	−	1.06003e11i	−0.101060	−	0.573139i
$320$	1.79113e11	−	1.50294e11i	0.954889	−	0.801247i
$321$	−3.90289e10	−	3.16932e11i	−0.205170	−	1.66607i
$322$	−3.57134e7	+	1.29986e7i	−0.000185131	+	6.73822e-5i
$323$	−4.51896e10			−0.231008
$324$	−2.40965e10	+	5.98864e10i	−0.121479	+	0.301908i
$325$	−7.37347e10			−0.366604
$326$	−2.58723e11	+	9.41674e10i	−1.26869	+	0.461765i
$327$	1.29730e10	+	1.05347e11i	0.0627445	+	0.509514i
$328$	2.26676e11	−	1.90204e11i	1.08137	−	0.907374i
$329$	3.01783e9	+	1.71150e10i	0.0142008	+	0.0805369i
$330$	4.94985e10	+	9.70608e10i	0.229763	+	0.450538i
$331$	−1.45802e11	−	1.22342e11i	−0.667631	−	0.560209i	0.244732	−	0.969591i	$-0.421300\pi$
$331$	−1.45802e11	−	1.22342e11i	−0.667631	−	0.560209i	−0.912363	+	0.409382i	$0.865744\pi$
$332$	−5.57744e9	+	9.66041e9i	−0.0251950	+	0.0436389i
$333$	−4.17795e10	−	4.32023e10i	−0.186193	−	0.192534i
$334$	1.64724e11	+	2.85310e11i	0.724264	+	1.25446i
$335$	−6.49430e10	+	3.68310e11i	−0.281729	+	1.59776i
$336$	1.21959e10	+	1.13648e10i	0.0522021	+	0.0486445i
$337$	−2.47427e11	−	9.00562e10i	−1.04499	−	0.380346i	−0.238221	−	0.971211i	$-0.576564\pi$
$337$	−2.47427e11	−	9.00562e10i	−1.04499	−	0.380346i	−0.806771	+	0.590865i	$0.798787\pi$
$338$	3.76152e10	+	1.36908e10i	0.156761	+	0.0570564i
$339$	−2.65656e11	+	8.13225e10i	−1.09250	+	0.334435i
$340$	6.00193e9	−	3.40386e10i	0.0243577	−	0.138139i
$341$	−6.93938e10	−	1.20194e11i	−0.277924	−	0.481378i
$342$	−9.06466e9	−	1.28318e11i	−0.0358289	−	0.507188i
$343$	3.19120e10	−	5.52731e10i	0.124489	−	0.215621i
$344$	1.85705e11	+	1.55825e11i	0.715007	+	0.599962i
$345$	−3.16294e8	+	4.87429e8i	−0.00120200	+	0.00185236i
$346$	−3.87639e10	−	2.19841e11i	−0.145407	−	0.824644i
$347$	−1.87218e11	+	1.57095e11i	−0.693210	+	0.581673i	−0.919833	−	0.392310i	$-0.871676\pi$
$347$	−1.87218e11	+	1.57095e11i	−0.693210	+	0.581673i	0.226623	+	0.973983i	$0.427232\pi$
$348$	−8.94882e10	−	3.79479e10i	−0.327084	−	0.138701i
$349$	−1.11185e11	+	4.04679e10i	−0.401172	+	0.146015i	−0.534723	−	0.845027i	$-0.679584\pi$
$349$	−1.11185e11	+	4.04679e10i	−0.401172	+	0.146015i	0.133551	+	0.991042i	$0.457362\pi$
$350$	−9.66996e9			−0.0344444
$351$	5.77674e9	+	3.11861e11i	0.0203142	+	1.09668i
$352$	9.54377e10			0.331343
$353$	8.80596e10	−	3.20511e10i	0.301850	−	0.109864i	−0.186655	−	0.982425i	$-0.559765\pi$
$353$	8.80596e10	−	3.20511e10i	0.301850	−	0.109864i	0.488505	+	0.872561i	$0.337542\pi$
$354$	3.60918e11	−	2.72173e11i	1.22150	−	0.921149i
$355$	−3.50039e11	+	2.93718e11i	−1.16974	+	0.981528i
$356$	1.56874e10	+	8.89676e10i	0.0517638	+	0.293567i
$357$	1.43507e10	+	7.46963e8i	0.0467590	+	0.00243384i
$358$	3.06977e11	+	2.57584e11i	0.987717	+	0.828793i
$359$	−8.91130e10	+	1.54348e11i	−0.283150	+	0.490430i	−0.972159	−	0.234323i	$-0.924713\pi$
$359$	−8.91130e10	+	1.54348e11i	−0.283150	+	0.490430i	0.689009	+	0.724753i	$0.258046\pi$
$360$	3.98560e11	+	4.16034e10i	1.25064	+	0.130547i
$361$	9.95100e10	+	1.72356e11i	0.308379	+	0.534128i
$362$	−7.09716e10	+	4.02500e11i	−0.217218	+	1.23190i
$363$	5.31861e10	−	2.30749e11i	0.160775	−	0.697525i
$364$	−1.40967e10	−	5.13078e9i	−0.0420883	−	0.0153189i
$365$	6.95602e11	+	2.53178e11i	2.05136	+	0.746636i
$366$	−5.72108e10	+	2.48210e11i	−0.166653	+	0.723027i
$367$	−2.64512e10	+	1.50012e11i	−0.0761111	+	0.431647i	0.922812	+	0.385251i	$0.125885\pi$
$367$	−2.64512e10	+	1.50012e11i	−0.0761111	+	0.431647i	−0.998923	+	0.0463968i	$0.985226\pi$
$368$	−1.91231e8	−	3.31222e8i	−0.000543554	−	0.000941464i
$369$	4.59318e11	+	4.79457e10i	1.28972	+	0.134627i
$370$	−4.58014e10	+	7.93303e10i	−0.127049	+	0.220055i
$371$	4.95274e10	+	4.15585e10i	0.135726	+	0.113888i
$372$	−1.25161e11	−	6.51475e9i	−0.338865	−	0.0176382i
$373$	−1.18121e11	−	6.69899e11i	−0.315965	−	1.79193i	−0.566758	−	0.823884i	$-0.691802\pi$
$373$	−1.18121e11	−	6.69899e11i	−0.315965	−	1.79193i	0.250793	−	0.968041i	$-0.419309\pi$
$374$	−4.73566e10	+	3.97369e10i	−0.125158	+	0.105020i
$375$	2.35133e11	−	1.77317e11i	0.614006	−	0.463029i
$376$	−2.58394e11	+	9.40478e10i	−0.666711	+	0.242663i
$377$	−4.69674e11			−1.19746
$378$	7.57592e8	+	4.08991e10i	0.00190863	+	0.103039i
$379$	−1.34945e11			−0.335954			−0.167977	−	0.985791i	$-0.553723\pi$
$379$	−1.34945e11			−0.335954			−0.167977	+	0.985791i	$0.553723\pi$
$380$	8.88841e10	−	3.23512e10i	0.218674	−	0.0795910i
$381$	−5.01436e11	−	2.12636e11i	−1.21914	−	0.516982i
$382$	6.36589e10	−	5.34161e10i	0.152959	−	0.128347i
$383$	−6.63858e10	−	3.76492e11i	−0.157645	−	0.894050i	−0.956328	−	0.292297i	$-0.905580\pi$
$383$	−6.63858e10	−	3.76492e11i	−0.157645	−	0.894050i	0.798683	−	0.601753i	$-0.205531\pi$
$384$	−6.14114e10	+	9.46390e10i	−0.144131	+	0.222116i
$385$	−2.55156e10	−	2.14101e10i	−0.0591878	−	0.0496645i
$386$	−2.62744e11	+	4.55087e11i	−0.602408	+	1.04340i
$387$	2.66606e10	+	3.77402e11i	0.0604185	+	0.855273i
$388$	5.94867e9	+	1.03034e10i	0.0133253	+	0.0230801i
$389$	7.26294e10	−	4.11902e11i	0.160820	−	0.912054i	−0.792451	−	0.609936i	$-0.791195\pi$
$389$	7.26294e10	−	4.11902e11i	0.160820	−	0.912054i	0.953270	−	0.302118i	$-0.0976937\pi$
$390$	4.54591e11	−	1.39160e11i	0.995017	−	0.304595i
$391$	−3.09806e8	−	1.12760e8i	−0.000670339	−	0.000243984i
$392$	4.70708e11	+	1.71324e11i	1.00685	+	0.366463i
$393$	−1.17321e11	−	1.09326e11i	−0.248090	−	0.231183i
$394$	−5.41761e10	+	3.07248e11i	−0.113260	+	0.642327i
$395$	−4.54971e11	−	7.88033e11i	−0.940365	−	1.62876i
$396$	5.90175e10	+	6.10274e10i	0.120601	+	0.124709i
$397$	2.77084e11	−	4.79923e11i	0.559827	−	0.969649i	−0.437683	−	0.899129i	$-0.644201\pi$
$397$	2.77084e11	−	4.79923e11i	0.559827	−	0.969649i	0.997510	−	0.0705199i	$-0.0224658\pi$
$398$	−4.08889e11	−	3.43099e11i	−0.816830	−	0.685401i
$399$	1.78660e10	+	3.50331e10i	0.0352898	+	0.0691992i
$400$	−1.68981e10	−	9.58339e10i	−0.0330041	−	0.187176i
$401$	7.45020e10	−	6.25146e10i	0.143886	−	0.120735i	−0.568004	−	0.823026i	$-0.692284\pi$
$401$	7.45020e10	−	6.25146e10i	0.143886	−	0.120735i	0.711890	+	0.702291i	$0.247840\pi$
$402$	−7.38291e10	−	5.99525e11i	−0.140997	−	1.14496i
$403$	−5.69071e11	+	2.07125e11i	−1.07472	+	0.391165i
$404$	−2.41591e10			−0.0451195
$405$	3.85740e11	+	4.92279e11i	0.712439	+	0.909208i
$406$	−6.15956e10			−0.112508
$407$	−7.42736e10	+	2.70334e10i	−0.134171	+	0.0488344i
$408$	2.77897e10	+	2.25664e11i	0.0496492	+	0.403174i
$409$	2.35442e11	−	1.97559e11i	0.416033	−	0.349093i	−0.410618	−	0.911807i	$-0.634687\pi$
$409$	2.35442e11	−	1.97559e11i	0.416033	−	0.349093i	0.826652	+	0.562714i	$0.190243\pi$
$410$	−1.22229e11	−	6.93195e11i	−0.213622	−	1.21151i
$411$	−1.98668e11	−	3.89566e11i	−0.343432	−	0.673430i
$412$	−1.81041e11	−	1.51912e11i	−0.309556	−	0.259749i
$413$	−6.90965e10	+	1.19679e11i	−0.116864	+	0.202414i
$414$	2.58043e8	−	9.02326e8i	0.000431708	−	0.00150960i
$415$	5.40362e10	+	9.35935e10i	0.0894270	+	0.154892i
$416$	7.23136e10	−	4.10111e11i	0.118386	−	0.671400i
$417$	−1.64289e11	−	1.53093e11i	−0.266071	−	0.247938i
$418$	−1.58975e11	−	5.78623e10i	−0.254705	−	0.0927049i
$419$	7.46444e11	+	2.71683e11i	1.18313	+	0.430626i	0.857308	−	0.514804i	$-0.172135\pi$
$419$	7.46444e11	+	2.71683e11i	1.18313	+	0.430626i	0.325827	+	0.945430i	$0.394357\pi$
$420$	−2.87613e10	+	8.80440e9i	−0.0451010	+	0.0138063i
$421$	−6.14953e10	+	3.48757e11i	−0.0954053	+	0.541070i	0.899217	+	0.437503i	$0.144137\pi$
$421$	−6.14953e10	+	3.48757e11i	−0.0954053	+	0.541070i	−0.994622	+	0.103568i	$0.966974\pi$
$422$	−9.83421e10	−	1.70334e11i	−0.150950	−	0.261453i
$423$	−3.85855e11	−	1.87854e11i	−0.585993	−	0.285291i
$424$	−5.11486e11	+	8.85920e11i	−0.768577	+	1.33121i
$425$	−6.42596e10	−	5.39202e10i	−0.0955405	−	0.0801680i
$426$	4.01742e11	−	6.19111e11i	0.591022	−	0.910804i
$427$	−1.35220e10	−	7.66869e10i	−0.0196841	−	0.111634i
$428$	−2.90518e11	+	2.43773e11i	−0.418481	+	0.351147i
$429$	3.77663e11	+	1.60150e11i	0.538327	+	0.228280i
$430$	5.41886e11	−	1.97230e11i	0.764363	−	0.278205i
$431$	−4.28096e11			−0.597576			−0.298788	−	0.954319i	$-0.596582\pi$
$431$	−4.28096e11			−0.597576			−0.298788	+	0.954319i	$0.596582\pi$
$432$	−4.04006e11	+	7.89786e10i	−0.558098	+	0.109102i
$433$	1.26300e12			1.72666			0.863330	−	0.504639i	$-0.168375\pi$
$433$	1.26300e12			1.72666			0.863330	+	0.504639i	$0.168375\pi$
$434$	−7.46310e10	+	2.71635e10i	−0.100975	+	0.0367520i
$435$	−7.51893e11	+	5.67012e11i	−1.00683	+	0.759260i
$436$	9.65667e10	−	8.10291e10i	0.127979	−	0.107387i
$437$	−1.56672e8	−	8.88533e8i	−0.000205507	−	0.00116549i
$438$	−1.19399e12	−	6.21482e10i	−1.55013	−	0.0806854i
$439$	6.80449e11	+	5.70965e11i	0.874390	+	0.733701i	0.965018	−	0.262184i	$-0.0844428\pi$
$439$	6.80449e11	+	5.70965e11i	0.874390	+	0.733701i	−0.0906275	+	0.995885i	$0.528887\pi$
$440$	2.63508e11	−	4.56409e11i	0.335163	−	0.580520i
$441$	3.18485e11	+	7.13960e11i	0.400973	+	0.898877i
$442$	1.34874e11	+	2.33608e11i	0.168084	+	0.291130i
$443$	−4.14262e9	+	2.34940e10i	−0.00511044	+	0.0289827i	−0.987256	−	0.159138i	$-0.949129\pi$
$443$	−4.14262e9	+	2.34940e10i	−0.00511044	+	0.0289827i	0.982146	+	0.188121i	$0.0602396\pi$
$444$	−1.60315e10	+	6.95530e10i	−0.0195772	+	0.0849361i
$445$	8.22463e11	+	2.99352e11i	0.994252	+	0.361878i
$446$	1.12572e11	+	4.09729e10i	0.134718	+	0.0490332i
$447$	−1.50697e10	+	6.53802e10i	−0.0178534	+	0.0774573i
$448$	2.00478e10	−	1.13697e11i	0.0235134	−	0.133351i
$449$	2.17348e11	+	3.76458e11i	0.252375	+	0.437127i	0.964179	−	0.265251i	$-0.0854549\pi$
$449$	2.17348e11	+	3.76458e11i	0.252375	+	0.437127i	−0.711804	+	0.702378i	$0.752122\pi$
$450$	1.40219e11	−	1.93283e11i	0.161194	−	0.222197i
$451$	3.03679e11	−	5.25987e11i	0.345637	−	0.598660i
$452$	2.52760e11	+	2.12091e11i	0.284830	+	0.239001i
$453$	−9.71329e11	−	5.05584e10i	−1.08374	−	0.0564094i
$454$	−9.81341e9	−	5.56546e10i	−0.0108410	−	0.0614823i
$455$	−1.11336e11	+	9.34221e10i	−0.121782	+	0.102188i
$456$	−4.96799e11	+	3.74643e11i	−0.538071	+	0.405766i
$457$	1.03488e12	−	3.76664e11i	1.10985	−	0.403954i	0.278914	−	0.960316i	$-0.410026\pi$
$457$	1.03488e12	−	3.76664e11i	1.10985	−	0.403954i	0.830940	+	0.556362i	$0.187803\pi$
$458$	3.26929e11			0.347183
$459$	−2.23021e11	+	2.76010e11i	−0.234525	+	0.290247i
$460$	6.90087e8			0.000718611
$461$	−6.56893e10	+	2.39090e10i	−0.0677393	+	0.0246551i	−0.375668	−	0.926754i	$-0.622587\pi$
$461$	−6.56893e10	+	2.39090e10i	−0.0677393	+	0.0246551i	0.307928	+	0.951410i	$0.400364\pi$
$462$	4.95287e10	+	2.10029e10i	0.0505787	+	0.0214482i
$463$	−4.84959e11	+	4.06929e11i	−0.490445	+	0.411532i	−0.854186	−	0.519968i	$-0.825944\pi$
$463$	−4.84959e11	+	4.06929e11i	−0.490445	+	0.411532i	0.363741	+	0.931500i	$0.381499\pi$
$464$	−1.07637e11	−	6.10441e11i	−0.107803	−	0.611383i
$465$	−6.60965e11	+	1.01859e12i	−0.655602	+	1.01033i
$466$	6.15969e10	+	5.16860e10i	0.0605094	+	0.0507734i
$467$	5.33198e11	−	9.23527e11i	0.518756	−	0.898511i	−0.481007	−	0.876717i	$-0.659729\pi$
$467$	5.33198e11	−	9.23527e11i	0.518756	−	0.898511i	0.999762	−	0.0217944i	$-0.00693792\pi$
$468$	3.06962e11	−	2.07367e11i	0.295787	−	0.199817i
$469$	9.23327e10	+	1.59925e11i	0.0881207	+	0.152629i
$470$	−1.13585e11	+	6.44171e11i	−0.107369	+	0.608921i
$471$	9.72091e11	−	2.97576e11i	0.910150	−	0.278615i
$472$	−2.05468e12	−	7.47842e11i	−1.90548	−	0.693539i
$473$	4.67571e11	+	1.70182e11i	0.429509	+	0.156329i
$474$	1.07522e12	+	1.00195e12i	0.978354	+	0.911679i
$475$	3.98632e10	−	2.26075e11i	0.0359294	−	0.203766i
$476$	−8.53324e9	−	1.47800e10i	−0.00761873	−	0.0131960i
$477$	−1.54884e12	+	3.87341e11i	−1.36985	+	0.342579i
$478$	−6.42739e11	+	1.11326e12i	−0.563130	+	0.975370i
$479$	5.72842e11	+	4.80671e11i	0.497193	+	0.417194i	0.856596	−	0.515988i	$-0.172575\pi$
$479$	5.72842e11	+	4.80671e11i	0.497193	+	0.417194i	−0.359403	+	0.933182i	$0.617020\pi$
$480$	−3.79339e11	−	7.43840e11i	−0.326168	−	0.639578i
$481$	5.98893e10	+	3.39649e11i	0.0510148	+	0.289319i
$482$	−4.73666e11	+	3.97453e11i	−0.399724	+	0.335409i
$483$	3.50667e7	+	2.84757e8i	2.93179e−5	+	0.000238074i
$484$	−2.64271e11	+	9.61870e10i	−0.218900	+	0.0796732i
$485$	1.15266e11			0.0945936
$486$	−8.28478e11	−	5.77911e11i	−0.673624	−	0.469892i
$487$	6.87914e11			0.554184			0.277092	−	0.960843i	$-0.410629\pi$
$487$	6.87914e11			0.554184			0.277092	+	0.960843i	$0.410629\pi$
$488$	1.15778e12	−	4.21399e11i	0.924141	−	0.336360i
$489$	2.54038e11	+	2.06290e12i	0.200913	+	1.63151i
$490$	9.12793e11	−	7.65924e11i	0.715303	−	0.600210i
$491$	−3.57819e11	−	2.02929e12i	−0.277841	−	1.57572i	−0.729789	−	0.683672i	$-0.760382\pi$
$491$	−3.57819e11	−	2.02929e12i	−0.277841	−	1.57572i	0.451948	−	0.892045i	$-0.350729\pi$
$492$	−2.49173e11	−	4.88600e11i	−0.191716	−	0.375933i
$493$	−4.09320e11	−	3.43460e11i	−0.312070	−	0.261858i
$494$	−3.69100e11	+	6.39300e11i	−0.278852	+	0.482985i
$495$	7.97933e11	−	1.99551e11i	0.597370	−	0.149393i
$496$	−3.99619e11	−	6.92161e11i	−0.296469	−	0.513499i
$497$	−3.91793e10	+	2.22197e11i	−0.0288040	+	0.163356i
$498$	−1.27703e11	−	1.19000e11i	−0.0930396	−	0.0866989i
$499$	2.01988e12	+	7.35175e11i	1.45839	+	0.530809i	0.944920	−	0.327300i	$-0.106139\pi$
$499$	2.01988e12	+	7.35175e11i	1.45839	+	0.530809i	0.513466	+	0.858110i	$0.328361\pi$
$500$	−3.28663e11	−	1.19624e11i	−0.235172	−	0.0855957i
$501$	2.37812e12	−	7.27989e11i	1.68641	−	0.516244i
$502$	9.23340e10	−	5.23652e11i	0.0648925	−	0.368024i
$503$	−7.52953e10	−	1.30415e11i	−0.0524460	−	0.0908391i	0.838611	−	0.544731i	$-0.183368\pi$
$503$	−7.52953e10	−	1.30415e11i	−0.0524460	−	0.0908391i	−0.891057	+	0.453892i	$0.850035\pi$
$504$	1.63959e11	−	1.10762e11i	0.113187	−	0.0764632i
$505$	−1.17031e11	+	2.02703e11i	−0.0800735	+	0.138691i
$506$	−9.45506e8	−	7.93373e8i	−0.000641190	−	0.000538022i
$507$	1.64493e11	−	2.53494e11i	0.110563	−	0.170385i
$508$	1.12326e11	+	6.37030e11i	0.0748328	+	0.424398i
$509$	−1.00277e12	+	8.41426e11i	−0.662174	+	0.555630i	−0.910738	−	0.412985i	$-0.864486\pi$
$509$	−1.00277e12	+	8.41426e11i	−0.662174	+	0.555630i	0.248563	+	0.968616i	$0.420042\pi$
$510$	4.97939e11	+	2.11153e11i	0.325919	+	0.138208i
$511$	3.43466e11	−	1.25011e11i	0.222838	−	0.0811065i
$512$	1.51218e12			0.972501
$513$	−9.59308e11	−	1.50889e11i	−0.611547	−	0.0961901i
$514$	2.54749e11			0.160982
$515$	−2.15159e12	+	7.83114e11i	−1.34780	+	0.490561i
$516$	3.58758e11	−	2.70544e11i	0.222781	−	0.168002i
$517$	−4.32358e11	+	3.62792e11i	−0.266156	+	0.223332i
$518$	7.85420e9	+	4.45434e10i	0.00479312	+	0.0271831i
$519$	−1.68294e12	−	8.75982e10i	−1.01816	−	0.0529958i
$520$	−1.76160e12	−	1.47816e12i	−1.05656	−	0.886556i
$521$	−5.73452e10	+	9.93248e10i	−0.0340979	+	0.0590593i	−0.882571	−	0.470180i	$-0.844189\pi$
$521$	−5.73452e10	+	9.93248e10i	−0.0340979	+	0.0590593i	0.848473	+	0.529239i	$0.177522\pi$
$522$	8.93162e11	−	1.23117e12i	0.526518	−	0.725775i
$523$	−1.53405e12	−	2.65706e12i	−0.896566	−	1.55290i	−0.831854	−	0.554995i	$-0.812720\pi$
$523$	−1.53405e12	−	2.65706e12i	−0.896566	−	1.55290i	−0.0647127	−	0.997904i	$-0.520613\pi$
$524$	−3.30719e10	+	1.87560e11i	−0.0191632	+	0.108680i
$525$	−1.63961e10	+	7.11348e10i	−0.00941940	+	0.0408663i
$526$	3.52056e11	+	1.28138e11i	0.200529	+	0.0729865i
$527$	−6.47409e11	−	2.35638e11i	−0.365621	−	0.133075i
$528$	−1.21598e11	+	5.27555e11i	−0.0680884	+	0.295403i
$529$	−3.12766e11	+	1.77378e12i	−0.173648	+	0.984804i
$530$	1.21671e12	+	2.10740e12i	0.669800	+	1.16013i
$531$	−1.39021e12	−	3.11650e12i	−0.758850	−	1.70114i
$532$	2.33524e10	−	4.04475e10i	0.0126395	−	0.0218922i
$533$	−2.03015e12	−	1.70350e12i	−1.08957	−	0.914259i
$534$	−1.41175e12	−	7.34825e10i	−0.751313	−	0.0391064i
$535$	6.38027e11	+	3.61843e12i	0.336703	+	1.90954i
$536$	−2.23826e12	+	1.87813e12i	−1.17130	+	0.982841i
$537$	2.41536e12	−	1.82145e12i	1.25342	−	0.945222i
$538$	−2.68600e11	+	9.77623e10i	−0.138225	+	0.0503096i
$539$	1.02815e12			0.524698
$540$	2.41068e11	−	7.02549e11i	0.122002	−	0.355553i
$541$	−2.16618e12			−1.08719			−0.543597	−	0.839346i	$-0.682938\pi$
$541$	−2.16618e12			−1.08719			−0.543597	+	0.839346i	$0.682938\pi$
$542$	9.78453e11	−	3.56128e11i	0.487016	−	0.177259i
$543$	2.84056e12	+	1.20455e12i	1.40218	+	0.594602i
$544$	3.62924e11	−	3.04530e11i	0.177673	−	0.149085i
$545$	−2.12077e11	−	1.20275e12i	−0.102970	−	0.583970i
$546$	1.27781e11	−	1.96919e11i	0.0615317	−	0.0948244i
$547$	−2.55652e12	−	2.14518e12i	−1.22098	−	1.02452i	−0.998773	−	0.0495193i	$-0.984231\pi$
$547$	−2.55652e12	−	2.14518e12i	−1.22098	−	1.02452i	−0.222202	−	0.975001i	$-0.571324\pi$
$548$	−2.59677e11	+	4.49773e11i	−0.123004	+	0.213050i
$549$	1.72890e12	+	8.41715e11i	0.812256	+	0.395448i
$550$	−1.57022e11	−	2.71970e11i	−0.0731691	−	0.126733i
$551$	2.53920e11	−	1.44005e12i	0.117358	−	0.665573i
$552$	−4.34074e9	+	1.32879e9i	−0.00198993	+	0.000609158i
$553$	−4.22204e11	−	1.53670e11i	−0.191982	−	0.0698756i
$554$	2.98452e12	+	1.08628e12i	1.34611	+	0.489944i
$555$	5.05915e11	+	4.71437e11i	0.226339	+	0.210914i
$556$	−4.63118e10	+	2.62648e11i	−0.0205521	+	0.116557i
$557$	−1.36006e12	−	2.35570e12i	−0.598702	−	1.03698i	−0.993013	−	0.118006i	$-0.962350\pi$
$557$	−1.36006e12	−	2.35570e12i	−0.598702	−	1.03698i	0.394311	−	0.918977i	$-0.370983\pi$
$558$	5.39237e11	−	1.88561e12i	0.235465	−	0.823375i
$559$	1.08558e12	−	1.88028e12i	0.470229	−	0.814460i
$560$	−1.46937e11	−	1.23295e11i	−0.0631372	−	0.0529784i
$561$	2.12019e11	+	4.15744e11i	0.0903736	+	0.177212i
$562$	1.68613e11	+	9.56250e11i	0.0712979	+	0.404351i
$563$	−2.02498e12	+	1.69916e12i	−0.849441	+	0.712766i	−0.959667	−	0.281141i	$-0.909287\pi$
$563$	−2.02498e12	+	1.69916e12i	−0.849441	+	0.712766i	0.110225	+	0.993907i	$0.464843\pi$
$564$	6.22944e10	+	5.05859e11i	0.0259235	+	0.210510i
$565$	3.00393e12	−	1.09334e12i	1.24014	−	0.451376i
$566$	1.36426e12			0.558757
$567$	3.02149e11	+	6.37742e10i	0.122771	+	0.0259132i
$568$	−3.56992e12			−1.43910
$569$	1.25065e12	−	4.55200e11i	0.500186	−	0.182053i	−0.0795917	−	0.996828i	$-0.525362\pi$
$569$	1.25065e12	−	4.55200e11i	0.500186	−	0.182053i	0.579778	+	0.814775i	$0.303139\pi$
$570$	1.80906e11	+	1.46904e12i	0.0717822	+	0.582903i
$571$	−1.49100e12	+	1.25110e12i	−0.586969	+	0.492526i	−0.887227	−	0.461332i	$-0.847372\pi$
$571$	−1.49100e12	+	1.25110e12i	−0.586969	+	0.492526i	0.300258	+	0.953858i	$0.402927\pi$
$572$	−8.45994e10	−	4.79787e11i	−0.0330434	−	0.187399i
$573$	−2.85005e11	−	5.58862e11i	−0.110448	−	0.216575i
$574$	−2.66245e11	−	2.23406e11i	−0.102371	−	0.0858996i
$575$	8.37409e8	−	1.45043e9i	0.000319471	−	0.000553341i
$576$	1.98187e12	+	2.04937e12i	0.750197	+	0.775745i
$577$	−8.98161e11	−	1.55566e12i	−0.337336	−	0.584283i	0.646595	−	0.762834i	$-0.276193\pi$
$577$	−8.98161e11	−	1.55566e12i	−0.337336	−	0.584283i	−0.983931	+	0.178550i	$0.942859\pi$
$578$	3.29411e11	−	1.86818e12i	0.122762	−	0.696216i
$579$	2.90224e12	+	2.70445e12i	1.07320	+	1.00006i
$580$	1.05098e12	+	3.82525e11i	0.385628	+	0.140357i
$581$	5.01446e10	+	1.82511e10i	0.0182571	+	0.00664504i
$582$	−1.78017e11	+	5.44946e10i	−0.0643145	+	0.0196879i
$583$	−3.64609e11	+	2.06780e12i	−0.130713	+	0.741310i
$584$	2.89161e12	+	5.00842e12i	1.02868	+	1.78173i
$585$	−2.52903e11	−	3.58005e12i	−0.0892797	−	1.26383i
$586$	−2.12783e11	+	3.68552e11i	−0.0745416	+	0.129110i
$587$	3.44036e12	+	2.88680e12i	1.19600	+	1.00357i	0.999735	+	0.0230158i	$0.00732681\pi$
$587$	3.44036e12	+	2.88680e12i	1.19600	+	1.00357i	0.196268	+	0.980550i	$0.437118\pi$
$588$	5.05402e11	−	7.78857e11i	0.174357	−	0.268695i
$589$	−3.27401e11	−	1.85679e12i	−0.112089	−	0.635687i
$590$	−3.98442e12	+	3.34332e12i	−1.35373	+	1.13591i
$591$	2.16834e12	+	9.19494e11i	0.731111	+	0.310031i
$592$	−4.27721e11	+	1.55678e11i	−0.143124	+	0.0520929i
$593$	−2.68424e12			−0.891407			−0.445703	−	0.895181i	$-0.647046\pi$
$593$	−2.68424e12			−0.891407			−0.445703	+	0.895181i	$0.647046\pi$
$594$	−1.13799e12	+	6.85431e11i	−0.375060	+	0.225904i
$595$	−1.65346e11			−0.0540838
$596$	7.48784e10	−	2.72535e10i	0.0243080	−	0.00884738i
$597$	−3.21722e12	+	2.42615e12i	−1.03657	+	0.781687i
$598$	−4.12567e9	+	3.46185e9i	−0.00131929	+	0.00110701i
$599$	8.87977e10	+	5.03597e11i	0.0281826	+	0.159832i	0.995651	−	0.0931597i	$-0.0296967\pi$
$599$	8.87977e10	+	5.03597e11i	0.0281826	+	0.159832i	−0.967469	+	0.252991i	$0.918586\pi$
$600$	−1.15347e12	−	6.00391e10i	−0.363351	−	0.0189127i
$601$	2.07245e12	+	1.73900e12i	0.647962	+	0.543705i	0.906452	−	0.422309i	$-0.138780\pi$
$601$	2.07245e12	+	1.73900e12i	0.647962	+	0.543705i	−0.258490	+	0.966014i	$0.583225\pi$
$602$	1.42369e11	−	2.46590e11i	0.0441805	−	0.0765229i
$603$	−4.53545e12	−	4.73430e11i	−1.39699	−	0.145824i
$604$	5.77575e11	+	1.00039e12i	0.176580	+	0.305846i
$605$	−4.73135e11	+	2.68328e12i	−0.143577	+	0.814267i
$606$	8.49105e10	−	3.68386e11i	0.0255761	−	0.110963i
$607$	−4.72762e10	−	1.72071e10i	−0.0141349	−	0.00514470i	0.334943	−	0.942238i	$-0.391283\pi$
$607$	−4.72762e10	−	1.72071e10i	−0.0141349	−	0.00514470i	−0.349078	+	0.937094i	$0.613505\pi$
$608$	1.21833e12	+	4.43436e11i	0.361576	+	0.131603i
$609$	−1.04440e11	+	4.53113e11i	−0.0307671	+	0.133484i
$610$	5.08938e11	−	2.88633e12i	0.148827	−	0.844038i
$611$	1.23137e12	+	2.13280e12i	0.357441	+	0.619107i
$612$	4.19159e11	+	4.37536e10i	0.120781	+	0.0126076i
$613$	6.02886e9	−	1.04423e10i	0.00172450	−	0.00298692i	−0.865162	−	0.501493i	$-0.832784\pi$
$613$	6.02886e9	−	1.04423e10i	0.00172450	−	0.00298692i	0.866886	+	0.498506i	$0.166118\pi$
$614$	−7.63299e10	−	6.40484e10i	−0.0216739	−	0.0181866i
$615$	−5.30657e12	−	2.76211e11i	−1.49581	−	0.0778580i
$616$	−4.51874e10	−	2.56270e11i	−0.0126446	−	0.0717109i
$617$	−3.43937e12	+	2.88597e12i	−0.955422	+	0.801694i	−0.980202	−	0.197999i	$-0.936556\pi$
$617$	−3.43937e12	+	2.88597e12i	−0.955422	+	0.801694i	0.0247802	+	0.999693i	$0.492111\pi$
$618$	2.95270e12	−	2.22667e12i	0.814275	−	0.614054i
$619$	6.52254e12	−	2.37401e12i	1.78570	−	0.649942i	0.786214	−	0.617954i	$-0.212038\pi$
$619$	6.52254e12	−	2.37401e12i	1.78570	−	0.649942i	0.999488	−	0.0319882i	$-0.0101839\pi$
$620$	1.44209e12			0.391949
$621$	−6.20022e9	−	3.42819e9i	−0.00167300	−	0.000925022i
$622$	1.21356e11			0.0325091
$623$	4.06106e11	−	1.47811e11i	0.108005	−	0.0393106i
$624$	2.17485e12	+	9.22257e11i	0.574248	+	0.243513i
$625$	−3.57248e12	+	2.99767e12i	−0.936504	+	0.785821i
$626$	−7.65614e11	−	4.34201e12i	−0.199262	−	1.13007i
$627$	−6.95204e11	+	1.07136e12i	−0.179642	+	0.276841i
$628$	−9.24903e11	−	7.76086e11i	−0.237289	−	0.199109i
$629$	−1.96183e11	+	3.39799e11i	−0.0499727	+	0.0865553i
$630$	−3.31671e10	−	4.69507e11i	−0.00838831	−	0.118743i
$631$	2.17006e12	+	3.75865e12i	0.544928	+	0.943843i	0.998611	+	0.0526798i	$0.0167763\pi$
$631$	2.17006e12	+	3.75865e12i	0.544928	+	0.943843i	−0.453684	+	0.891163i	$0.649890\pi$
$632$	1.23447e12	−	7.00100e12i	0.307788	−	1.74555i
$633$	−1.41976e12	+	4.34618e11i	−0.351479	+	0.107595i
$634$	4.77684e12	+	1.73863e12i	1.17419	+	0.427370i
$635$	5.88904e12	+	2.14343e12i	1.43735	+	0.523152i
$636$	1.38719e12	+	1.29265e12i	0.336185	+	0.313274i
$637$	7.79039e11	−	4.41815e12i	0.187470	−	1.06319i
$638$	−1.00019e12	−	1.73239e12i	−0.238996	−	0.413954i
$639$	−3.87316e12	−	4.00506e12i	−0.918992	−	0.950289i
$640$	6.49057e11	−	1.12420e12i	0.152923	−	0.264871i
$641$	−6.22809e12	−	5.22599e12i	−1.45712	−	1.22267i	−0.927174	−	0.374631i	$-0.877769\pi$
$641$	−6.22809e12	−	5.22599e12i	−1.45712	−	1.22267i	−0.529942	−	0.848034i	$-0.677786\pi$
$642$	−2.69608e12	−	5.28670e12i	−0.626361	−	1.22822i
$643$	−7.54498e11	−	4.27897e12i	−0.174064	−	0.987165i	−0.939219	−	0.343319i	$-0.888449\pi$
$643$	−7.54498e11	−	4.27897e12i	−0.174064	−	0.987165i	0.765155	−	0.643846i	$-0.222662\pi$
$644$	2.61025e8	−	2.19026e8i	5.97991e−5	−	5.01774e-5i
$645$	−5.32073e11	−	4.32067e12i	−0.121047	−	0.982953i
$646$	−7.89173e11	+	2.87235e11i	−0.178290	+	0.0648921i
$647$	5.86334e12			1.31545			0.657727	−	0.753256i	$-0.271518\pi$
$647$	5.86334e12			1.31545			0.657727	+	0.753256i	$0.271518\pi$
$648$	−1.63567e11	+	4.88331e12i	−0.0364424	+	1.08799i
$649$	−4.48798e12			−0.993002
$650$	−1.28767e12	+	4.68675e11i	−0.282941	+	0.102982i
$651$	7.32796e10	+	5.95063e11i	0.0159907	+	0.129852i
$652$	1.89097e12	−	1.58671e12i	0.409799	−	0.343862i
$653$	−1.16333e12	−	6.59756e12i	−0.250376	−	1.41995i	−0.807669	−	0.589636i	$-0.799271\pi$
$653$	−1.16333e12	−	6.59756e12i	−0.250376	−	1.41995i	0.557293	−	0.830316i	$-0.311840\pi$
$654$	8.96163e11	+	1.75727e12i	0.191552	+	0.375612i
$655$	1.41349e12	+	1.18606e12i	0.300059	+	0.251780i
$656$	1.74880e12	−	3.02901e12i	0.368700	−	0.638607i
$657$	−2.48167e12	+	8.67793e12i	−0.519637	+	1.81707i
$658$	1.61489e11	+	2.79707e11i	0.0335835	+	0.0581684i
$659$	−4.47489e10	+	2.53783e11i	−0.00924267	+	0.0524178i	−0.989080	−	0.147378i	$-0.952917\pi$
$659$	−4.47489e10	+	2.53783e11i	−0.00924267	+	0.0524178i	0.979838	+	0.199796i	$0.0640278\pi$
$660$	−7.14654e11	−	6.65950e11i	−0.146605	−	0.136614i
$661$	−4.08951e12	−	1.48846e12i	−0.833229	−	0.303271i	−0.110046	−	0.993927i	$-0.535100\pi$
$661$	−4.08951e12	−	1.48846e12i	−0.833229	−	0.303271i	−0.723184	+	0.690656i	$0.757322\pi$
$662$	−3.32386e12	−	1.20978e12i	−0.672638	−	0.244820i
$663$	1.94717e12	−	5.96067e11i	0.391375	−	0.119808i
$664$	−1.46616e11	+	8.31499e11i	−0.0292701	+	0.165999i
$665$	−2.26246e11	−	3.91870e11i	−0.0448626	−	0.0777042i
$666$	−1.00422e12	−	4.88908e11i	−0.197786	−	0.0962926i
$667$	5.33411e9	−	9.23895e9i	0.00104351	−	0.00180741i
$668$	−2.26268e12	−	1.89861e12i	−0.439671	−	0.368928i
$669$	4.92282e11	−	7.58639e11i	0.0950159	−	0.146426i
$670$	1.20693e12	+	6.84481e12i	0.231390	+	1.31228i
$671$	1.93726e12	−	1.62556e12i	0.368924	−	0.309564i
$672$	−3.79570e11	−	1.60959e11i	−0.0718010	−	0.0304476i
$673$	4.63098e12	−	1.68554e12i	0.870173	−	0.316717i	0.131936	−	0.991258i	$-0.457881\pi$
$673$	4.63098e12	−	1.68554e12i	0.870173	−	0.316717i	0.738237	+	0.674541i	$0.235659\pi$
$674$	−4.89339e12			−0.913356
$675$	−1.18409e12	−	1.35921e12i	−0.219543	−	0.252011i
$676$	−3.58889e11			−0.0660998
$677$	8.07971e11	−	2.94078e11i	0.147825	−	0.0538038i	−0.267048	−	0.963683i	$-0.586048\pi$
$677$	8.07971e11	−	2.94078e11i	0.147825	−	0.0538038i	0.414873	+	0.909879i	$0.363826\pi$
$678$	−4.12240e12	+	3.10875e12i	−0.749232	+	0.565005i
$679$	4.35990e10	−	3.65839e10i	0.00787160	−	0.00660505i
$680$	−4.54293e11	−	2.57642e12i	−0.0814790	−	0.462091i
$681$	−4.26049e11	−	2.21762e10i	−0.0759098	−	0.00395117i
$682$	−1.97584e12	−	1.65793e12i	−0.349722	−	0.293451i
$683$	2.19930e12	−	3.80931e12i	0.386716	−	0.669812i	−0.605290	−	0.796005i	$-0.706943\pi$
$683$	2.19930e12	−	3.80931e12i	0.386716	−	0.669812i	0.992006	+	0.126194i	$0.0402761\pi$
$684$	4.69847e11	+	1.05327e12i	0.0820737	+	0.183988i
$685$	2.51584e12	+	4.35756e12i	0.436592	+	0.756199i
$686$	2.05969e11	−	1.16811e12i	0.0355094	−	0.201384i
$687$	5.54330e11	−	2.40497e12i	0.0949431	−	0.411913i
$688$	2.69261e12	+	9.80031e11i	0.458169	+	0.166760i
$689$	8.60940e12	+	3.13356e12i	1.45541	+	0.529727i
$690$	−2.42541e9	+	1.05227e10i	−0.000407347	+	0.00176728i
$691$	−1.08407e12	+	6.14808e12i	−0.180887	+	1.02586i	0.750240	+	0.661166i	$0.229938\pi$
$691$	−1.08407e12	+	6.14808e12i	−0.180887	+	1.02586i	−0.931127	+	0.364695i	$0.881173\pi$
$692$	1.00071e12	+	1.73329e12i	0.165895	+	0.287338i
$693$	2.38482e11	−	3.28734e11i	0.0392786	−	0.0541434i
$694$	−2.27097e12	+	3.93344e12i	−0.371616	+	0.643657i
$695$	1.97937e12	+	1.66088e12i	0.321806	+	0.270027i
$696$	−7.34736e12	−	3.82436e11i	−1.18683	−	0.0617757i
$697$	−5.23548e11	−	2.96919e12i	−0.0840251	−	0.476530i
$698$	−1.68446e12	+	1.41343e12i	−0.268603	+	0.225385i
$699$	4.84658e11	−	3.65486e11i	0.0767870	−	0.0579060i
$700$	8.14691e10	−	2.96523e10i	0.0128248	−	0.00466785i
$701$	−1.23156e13			−1.92630			−0.963150	−	0.268965i	$-0.913319\pi$
$701$	−1.23156e13			−1.92630			−0.963150	+	0.268965i	$0.913319\pi$
$702$	2.08314e12	+	5.40949e12i	0.323744	+	0.840697i
$703$	−1.07376e12			−0.165810
$704$	3.52329e12	−	1.28237e12i	0.540593	−	0.196760i
$705$	4.54610e12	+	1.92780e12i	0.693088	+	0.293907i
$706$	1.33411e12	−	1.11945e12i	0.202102	−	0.169584i
$707$	2.00689e10	+	1.13816e11i	0.00302090	+	0.0171324i
$708$	−2.20612e12	+	3.39978e12i	−0.329974	+	0.508511i
$709$	6.51478e12	+	5.46655e12i	0.968259	+	0.812466i	0.982277	−	0.187436i	$-0.0600178\pi$
$709$	6.51478e12	+	5.46655e12i	0.968259	+	0.812466i	−0.0140180	+	0.999902i	$0.504462\pi$
$710$	−4.24601e12	+	7.35430e12i	−0.627073	+	1.08612i
$711$	9.19370e12	−	6.21076e12i	1.34920	−	0.911447i
$712$	3.41897e12	+	5.92184e12i	0.498581	+	0.863568i
$713$	2.38862e9	−	1.35465e10i	0.000346133	−	0.00196302i
$714$	2.55362e11	−	7.81714e10i	0.0367718	−	0.0112566i
$715$	−4.43540e12	−	1.61435e12i	−0.634681	−	0.231005i
$716$	−3.37614e12	−	1.22881e12i	−0.480078	−	0.174734i
$717$	7.09960e12	+	6.61576e12i	1.00322	+	0.934853i
$718$	−5.75161e11	+	3.26190e12i	−0.0807661	+	0.458047i
$719$	−3.51879e12	−	6.09472e12i	−0.491036	−	0.850499i	0.508911	−	0.860819i	$-0.330048\pi$
$719$	−3.51879e12	−	6.09472e12i	−0.491036	−	0.850499i	−0.999947	+	0.0103202i	$0.996715\pi$
$720$	4.59508e12	−	1.14916e12i	0.637230	−	0.159361i
$721$	−5.65284e11	+	9.79101e11i	−0.0779037	+	0.134933i
$722$	2.83334e12	+	2.37745e12i	0.388044	+	0.325608i
$723$	2.12064e12	+	4.15832e12i	0.288632	+	0.565973i
$724$	−6.36307e11	−	3.60868e12i	−0.0860683	−	0.488117i
$725$	2.07934e12	−	1.74477e12i	0.279515	−	0.234541i
$726$	−5.37873e11	−	4.36777e12i	−0.0718563	−	0.583505i
$727$	−6.18464e12	+	2.25102e12i	−0.821125	+	0.298865i	−0.718211	−	0.695825i	$-0.755039\pi$
$727$	−6.18464e12	+	2.25102e12i	−0.821125	+	0.298865i	−0.102914	+	0.994690i	$0.532817\pi$
$728$	−1.13547e12			−0.149826
$729$	−5.65601e12	+	5.11461e12i	−0.741714	+	0.670716i
$730$	1.37570e13			1.79296
$731$	2.32108e12	−	8.44804e11i	0.300650	−	0.109428i
$732$	−2.79122e11	−	2.26660e12i	−0.0359331	−	0.291792i
$733$	3.20204e12	−	2.68683e12i	0.409693	−	0.343773i	−0.414533	−	0.910034i	$-0.636055\pi$
$733$	3.20204e12	−	2.68683e12i	0.409693	−	0.343773i	0.824226	+	0.566261i	$0.191611\pi$
$734$	4.91579e11	+	2.78788e12i	0.0625116	+	0.354521i
$735$	−4.08664e12	−	8.01342e12i	−0.516503	−	1.01280i
$736$	7.24602e9	+	6.08013e9i	0.000910226	+	0.000763770i
$737$	−2.99861e12	+	5.19375e12i	−0.374384	+	0.648451i
$738$	8.32610e12	−	2.08223e12i	1.03321	−	0.258389i
$739$	−3.48679e12	−	6.03931e12i	−0.430057	−	0.744881i	0.566820	−	0.823841i	$-0.308173\pi$
$739$	−3.48679e12	−	6.03931e12i	−0.430057	−	0.744881i	−0.996878	+	0.0789601i	$0.974840\pi$
$740$	1.42614e11	−	8.08802e11i	0.0174831	−	0.0991515i
$741$	4.07703e12	+	3.79918e12i	0.496777	+	0.462922i
$742$	1.12908e12	+	4.10952e11i	0.136744	+	0.0497707i
$743$	9.07412e12	+	3.30271e12i	1.09233	+	0.397577i	0.824484	−	0.565885i	$-0.191465\pi$
$743$	9.07412e12	+	3.30271e12i	1.09233	+	0.397577i	0.267848	+	0.963461i	$0.413687\pi$
$744$	−9.07094e12	+	2.77680e12i	−1.08536	+	0.332251i
$745$	1.34058e11	−	7.60278e11i	0.0159437	−	0.0904210i
$746$	−6.32086e12	−	1.09480e13i	−0.747225	−	1.29423i
$747$	−1.09192e12	+	7.37642e11i	−0.128307	+	0.0866769i
$748$	2.77127e11	−	4.79998e11i	0.0323684	−	0.0560638i
$749$	1.38978e12	+	1.16616e12i	0.161353	+	0.135392i
$750$	2.97920e12	−	4.59114e12i	0.343814	−	0.529840i
$751$	8.52907e11	+	4.83708e12i	0.0978413	+	0.554885i	0.993840	+	0.110828i	$0.0353503\pi$
$751$	8.52907e11	+	4.83708e12i	0.0978413	+	0.554885i	−0.895998	+	0.444057i	$0.853539\pi$
$752$	−2.48983e12	+	2.08922e12i	−0.283916	+	0.238234i
$753$	−3.69556e12	−	1.56712e12i	−0.418893	−	0.177634i
$754$	−8.20220e12	+	2.98536e12i	−0.924186	+	0.336376i
$755$	1.11915e13			1.25351
$756$	−1.31797e11	−	3.42250e11i	−0.0146743	−	0.0381062i
$757$	−4.59607e12			−0.508692			−0.254346	−	0.967113i	$-0.581860\pi$
$757$	−4.59607e12			−0.508692			−0.254346	+	0.967113i	$0.581860\pi$
$758$	−2.35662e12	+	8.57740e11i	−0.259286	+	0.0943723i
$759$	−7.43944e9	+	5.61017e9i	−0.000813677	+	0.000613604i
$760$	5.48450e12	−	4.60205e12i	0.596316	−	0.500368i
$761$	1.02595e12	+	5.81848e12i	0.110891	+	0.628895i	0.988703	+	0.149889i	$0.0478917\pi$
$761$	1.02595e12	+	5.81848e12i	0.110891	+	0.628895i	−0.877812	+	0.479006i	$0.840997\pi$
$762$	−1.01084e13	−	5.26152e11i	−1.08614	−	0.0565346i
$763$	−4.61956e11	−	3.87627e11i	−0.0493447	−	0.0414051i
$764$	−3.72526e11	+	6.45235e11i	−0.0395582	+	0.0685169i
$765$	2.39759e12	−	3.30494e12i	0.253103	−	0.348889i
$766$	−3.55241e12	−	6.15295e12i	−0.372815	−	0.645734i
$767$	−3.40057e12	+	1.92856e13i	−0.354791	+	2.01212i
$768$	1.86591e12	−	8.09530e12i	0.193538	−	0.839668i
$769$	−1.45061e13	−	5.27977e12i	−1.49583	−	0.544436i	−0.540849	−	0.841119i	$-0.681897\pi$
$769$	−1.45061e13	−	5.27977e12i	−1.49583	−	0.544436i	−0.954976	+	0.296684i	$0.904119\pi$
$770$	−5.81682e11	−	2.11715e11i	−0.0596317	−	0.0217042i
$771$	4.31945e11	−	1.87400e12i	0.0440234	−	0.190996i
$772$	8.18118e11	−	4.63978e12i	0.0828969	−	0.470132i
$773$	5.05669e11	+	8.75844e11i	0.0509400	+	0.0882306i	0.890371	−	0.455236i	$-0.150445\pi$
$773$	5.05669e11	+	8.75844e11i	0.0509400	+	0.0882306i	−0.839431	+	0.543466i	$0.817112\pi$
$774$	2.86444e12	+	6.42133e12i	0.286884	+	0.643118i
$775$	1.74995e12	−	3.03100e12i	0.174248	−	0.301807i
$776$	6.89841e11	+	5.78845e11i	0.0682922	+	0.0573039i
$777$	3.40990e11	+	1.77488e10i	0.0335620	+	0.00174693i
$778$	−1.34977e12	−	7.65494e12i	−0.132085	−	0.749089i
$779$	6.32059e12	−	5.30361e12i	0.614949	−	0.516004i
$780$	−3.40319e12	+	2.56639e12i	−0.329201	+	0.248254i
$781$	−6.88552e12	+	2.50613e12i	−0.662228	+	0.241031i
$782$	−6.12706e9			−0.000585898
$783$	−7.54243e12	−	8.65788e12i	−0.717106	−	0.823158i
$784$	5.92086e12			0.559709
$785$	−1.09920e13	+	4.00077e12i	−1.03315	+	0.376037i
$786$	−2.74375e12	−	1.16350e12i	−0.256414	−	0.108734i
$787$	−1.50781e12	+	1.26520e12i	−0.140107	+	0.117564i	−0.710148	−	0.704053i	$-0.751372\pi$
$787$	−1.50781e12	+	1.26520e12i	−0.140107	+	0.117564i	0.570041	+	0.821616i	$0.306927\pi$
$788$	−4.85725e11	−	2.75468e12i	−0.0448768	−	0.254509i
$789$	1.53955e12	−	2.37255e12i	0.141432	−	0.217956i
$790$	−1.29543e13	−	1.08700e13i	−1.18330	−	0.992903i
$791$	7.89219e11	−	1.36697e12i	0.0716809	−	0.124155i
$792$	5.77758e12	+	2.81282e12i	0.521774	+	0.254026i
$793$	−5.51741e12	−	9.55643e12i	−0.495457	−	0.858156i
$794$	1.78838e12	−	1.01424e13i	0.159686	−	0.905625i
$795$	1.75656e13	−	5.37719e12i	1.55959	−	0.477423i
$796$	4.49696e12	+	1.63676e12i	0.397018	+	0.144503i
$797$	1.89101e13	+	6.88272e12i	1.66009	+	0.604223i	0.990377	−	0.138396i	$-0.0441947\pi$
$797$	1.89101e13	+	6.88272e12i	1.66009	+	0.604223i	0.669713	+	0.742620i	$0.266417\pi$
$798$	5.34683e11	+	4.98244e11i	0.0466749	+	0.0434940i
$799$	−4.86522e11	+	2.75920e12i	−0.0422320	+	0.239510i
$800$	1.20336e12	+	2.08428e12i	0.103870	+	0.179908i
$801$	−2.93427e12	+	1.02606e13i	−0.251857	+	0.880695i
$802$	9.03715e11	−	1.56528e12i	0.0771342	−	0.133600i
$803$	9.09321e12	+	7.63011e12i	0.771786	+	0.647606i
$804$	2.46041e12	+	4.82459e12i	0.207661	+	0.407200i
$805$	−5.73255e8	−	3.25109e9i	−4.81134e−5	−	0.000272865i
$806$	−8.62150e12	+	7.23429e12i	−0.719573	+	0.603794i
$807$	2.63736e11	+	2.14165e12i	0.0218896	+	0.177754i
$808$	−1.71835e12	+	6.25428e11i	−0.141827	+	0.0516209i
$809$	−1.35819e12			−0.111479			−0.0557395	−	0.998445i	$-0.517752\pi$
$809$	−1.35819e12			−0.111479			−0.0557395	+	0.998445i	$0.517752\pi$
$810$	9.86545e12	+	6.14510e12i	0.805257	+	0.501587i
$811$	6.18683e12			0.502197			0.251099	−	0.967962i	$-0.419208\pi$
$811$	6.18683e12			0.502197			0.251099	+	0.967962i	$0.419208\pi$
$812$	5.18940e11	−	1.88879e11i	0.0418905	−	0.0152469i
$813$	−9.60735e11	−	7.80160e12i	−0.0771252	−	0.626291i
$814$	−1.12525e12	+	9.44200e11i	−0.0898340	+	0.0753797i
$815$	−4.15290e12	−	2.35523e13i	−0.329718	−	1.86992i
$816$	1.22096e12	+	2.39416e12i	0.0964039	+	0.189037i
$817$	5.17816e12	+	4.34500e12i	0.406609	+	0.341185i
$818$	2.85593e12	−	4.94661e12i	0.223027	−	0.386294i
$819$	−1.23193e12	−	1.27388e12i	−0.0956768	−	0.0989352i
$820$	3.15541e12	+	5.46533e12i	0.243721	+	0.422138i
$821$	−4.48393e12	+	2.54296e13i	−0.344441	+	1.95342i	−0.0461901	+	0.998933i	$0.514708\pi$
$821$	−4.48393e12	+	2.54296e13i	−0.344441	+	1.95342i	−0.298251	+	0.954488i	$0.596403\pi$
$822$	−5.94563e12	−	5.54044e12i	−0.454229	−	0.423273i
$823$	−6.41370e12	−	2.33440e12i	−0.487315	−	0.177368i	0.0866652	−	0.996237i	$-0.472379\pi$
$823$	−6.41370e12	−	2.33440e12i	−0.487315	−	0.177368i	−0.573980	+	0.818869i	$0.694601\pi$
$824$	−1.68095e13	−	6.11815e12i	−1.27023	−	0.462326i
$825$	−2.26692e12	+	6.93950e11i	−0.170370	+	0.0521537i
$826$	−4.45969e11	+	2.52921e12i	−0.0333345	+	0.189049i
$827$	6.35461e12	+	1.10065e13i	0.472404	+	0.818229i	0.999501	−	0.0315767i	$-0.0100528\pi$
$827$	6.35461e12	+	1.10065e13i	0.472404	+	0.818229i	−0.527097	+	0.849805i	$0.676719\pi$
$828$	5.92925e8	+	8.39333e9i	4.38392e−5	+	0.000620580i
$829$	8.41727e12	−	1.45791e13i	0.618979	−	1.07210i	−0.370694	−	0.928755i	$-0.620880\pi$
$829$	8.41727e12	−	1.45791e13i	0.618979	−	1.07210i	0.989672	−	0.143347i	$-0.0457866\pi$
$830$	1.53857e12	+	1.29101e12i	0.112529	+	0.0944232i
$831$	1.30514e13	−	2.01131e13i	0.949407	−	1.46310i
$832$	−2.84094e12	−	1.61118e13i	−0.205545	−	1.16570i
$833$	3.90980e12	−	3.28071e12i	0.281353	−	0.236084i
$834$	−3.84217e12	−	1.62929e12i	−0.274998	−	0.116614i
$835$	−2.68908e13	+	9.78746e12i	−1.91432	+	0.696756i
$836$	1.51679e12			0.107398
$837$	−1.29567e13	−	7.16395e12i	−0.912496	−	0.504531i
$838$	1.47625e13			1.03410
$839$	−2.09727e13	+	7.63342e12i	−1.46125	+	0.531852i	−0.945709	−	0.325013i	$-0.894631\pi$
$839$	−2.09727e13	+	7.63342e12i	−1.46125	+	0.531852i	−0.515541	+	0.856865i	$0.672409\pi$
$840$	−1.81776e12	+	1.37079e12i	−0.125974	+	0.0949983i
$841$	2.13183e12	−	1.78882e12i	0.146951	−	0.123306i
$842$	1.14285e12	+	6.48143e12i	0.0783584	+	0.444392i
$843$	7.32033e12	+	3.81029e11i	0.499237	+	0.0259857i
$844$	1.35085e12	+	1.13349e12i	0.0916357	+	0.0768915i
$845$	−1.73852e12	+	3.01121e12i	−0.117307	+	0.203182i
$846$	−7.93246e12	−	8.28025e11i	−0.532404	−	0.0555746i
$847$	6.72679e11	+	1.16511e12i	0.0449089	+	0.0777845i
$848$	−2.09968e12	+	1.19079e13i	−0.139435	+	0.790775i
$849$	2.31320e12	−	1.00359e13i	0.152802	−	0.662933i
$850$	−1.46493e12	−	5.33192e11i	−0.0962570	−	0.0350347i
$851$	−7.36140e9	−	2.67933e9i	−0.000481146	−	0.000175123i
$852$	−1.48620e12	+	6.44790e12i	−0.0966269	+	0.419218i
$853$	1.19454e12	−	6.77458e12i	0.0772556	−	0.438139i	−0.921505	−	0.388367i	$-0.873039\pi$
$853$	1.19454e12	−	6.77458e12i	0.0772556	−	0.438139i	0.998761	−	0.0497720i	$-0.0158495\pi$
$854$	−7.23582e11	−	1.25328e12i	−0.0465508	−	0.0806284i
$855$	1.11134e13	+	1.16006e12i	0.711211	+	0.0742394i
$856$	−1.43527e13	+	2.48596e13i	−0.913697	+	1.58257i
$857$	9.37934e12	+	7.87020e12i	0.593962	+	0.498393i	0.889498	−	0.456938i	$-0.151054\pi$
$857$	9.37934e12	+	7.87020e12i	0.593962	+	0.498393i	−0.295537	+	0.955331i	$0.595498\pi$
$858$	7.61330e12	+	3.96278e11i	0.479601	+	0.0249636i
$859$	7.76449e11	+	4.40346e12i	0.0486568	+	0.275946i	0.999423	−	0.0339623i	$-0.0108126\pi$
$859$	7.76449e11	+	4.40346e12i	0.0486568	+	0.275946i	−0.950766	+	0.309909i	$0.899702\pi$
$860$	−3.96057e12	+	3.32331e12i	−0.246896	+	0.207171i
$861$	−2.09487e12	+	1.57977e12i	−0.129910	+	0.0979667i
$862$	−7.47609e12	+	2.72107e12i	−0.461203	+	0.167864i
$863$	−1.77022e13			−1.08637			−0.543185	−	0.839613i	$-0.682782\pi$
$863$	−1.77022e13			−1.08637			−0.543185	+	0.839613i	$0.682782\pi$
$864$	8.72118e12	−	5.25290e12i	0.532431	−	0.320691i
$865$	1.93905e13			1.17765
$866$	2.20565e13	−	8.02790e12i	1.33262	−	0.485033i
$867$	−1.31843e13	−	5.59086e12i	−0.792449	−	0.336042i
$868$	5.45469e11	−	4.57702e11i	0.0326160	−	0.0273681i
$869$	−2.53380e12	−	1.43699e13i	−0.150724	−	0.854799i
$870$	−9.52670e12	+	1.46813e13i	−0.563775	+	0.868814i
$871$	2.00463e13	+	1.68209e13i	1.18019	+	0.990299i
$872$	4.77077e12	−	8.26322e12i	0.279424	−	0.483977i
$873$	9.90364e10	+	1.40194e12i	0.00577073	+	0.0816894i
$874$	−8.38378e9	−	1.45211e10i	−0.000486002	−	0.000841781i
$875$	−2.90542e11	+	1.64775e12i	−0.0167561	+	0.0950285i
$876$	1.02499e13	−	3.13770e12i	0.588100	−	0.180029i
$877$	1.81090e12	+	6.59112e11i	0.103370	+	0.0376237i	0.393187	−	0.919458i	$-0.371372\pi$
$877$	1.81090e12	+	6.59112e11i	0.103370	+	0.0376237i	−0.289817	+	0.957082i	$0.593595\pi$
$878$	1.55123e13	+	5.64601e12i	0.880948	+	0.320639i
$879$	2.35037e12	+	2.19020e12i	0.132797	+	0.123747i
$880$	1.08172e12	−	6.13471e12i	0.0608052	−	0.344844i
$881$	−1.42842e13	−	2.47410e13i	−0.798850	−	1.38365i	−0.920365	−	0.391059i	$-0.872109\pi$
$881$	−1.42842e13	−	2.47410e13i	−0.798850	−	1.38365i	0.121515	−	0.992590i	$-0.461225\pi$
$882$	1.01000e13	+	1.04439e13i	0.561969	+	0.581107i
$883$	−1.57308e11	+	2.72466e11i	−0.00870821	+	0.0150831i	−0.870347	−	0.492440i	$-0.836105\pi$
$883$	−1.57308e11	+	2.72466e11i	−0.00870821	+	0.0150831i	0.861638	+	0.507523i	$0.169439\pi$
$884$	−1.85265e12	−	1.55456e12i	−0.102037	−	0.0856192i
$885$	1.78385e13	+	3.49793e13i	0.977494	+	1.91675i
$886$	7.69880e10	+	4.36621e11i	0.00419731	+	0.0238041i
$887$	6.42115e12	−	5.38798e12i	0.348302	−	0.292260i	−0.451806	−	0.892116i	$-0.649220\pi$
$887$	6.42115e12	−	5.38798e12i	0.348302	−	0.292260i	0.800108	+	0.599856i	$0.204776\pi$
$888$	6.60318e11	+	5.36208e12i	0.0356365	+	0.289384i
$889$	2.90782e12	−	1.05836e12i	0.156138	−	0.0568297i
$890$	1.62659e13			0.869007
$891$	3.11266e12	+	9.53357e12i	0.165456	+	0.506764i
$892$	−1.07406e12			−0.0568049
$893$	−7.20503e12	+	2.62242e12i	−0.379144	+	0.137997i
$894$	1.52400e11	+	1.23756e12i	0.00797935	+	0.0647959i
$895$	−2.66648e13	+	2.23744e13i	−1.38910	+	1.16560i
$896$	−1.11303e11	−	6.31230e11i	−0.00576926	−	0.0327191i
$897$	1.84709e10	+	3.62193e10i	0.000952625	+	0.00186799i
$898$	6.18853e12	+	5.19279e12i	0.317573	+	0.266476i
$899$	1.11468e13	−	1.93068e13i	0.569157	−	0.985809i
$900$	−5.88644e11	+	2.05838e12i	−0.0299062	+	0.104576i
$901$	5.21157e12	+	9.02671e12i	0.263456	+	0.456318i
$902$	1.96003e12	−	1.11159e13i	0.0985900	−	0.559132i
$903$	−1.57259e12	−	1.46541e12i	−0.0787081	−	0.0733441i
$904$	2.34685e13	+	8.54184e12i	1.16877	+	0.425396i
$905$	−3.33605e13	−	1.21422e13i	−1.65316	−	0.601699i
$906$	−1.72843e13	+	5.29106e12i	−0.852263	+	0.260895i
$907$	−1.54084e12	+	8.73856e12i	−0.0756007	+	0.428753i	0.923391	+	0.383860i	$0.125406\pi$
$907$	−1.54084e12	+	8.73856e12i	−0.0756007	+	0.428753i	−0.998992	+	0.0448924i	$0.985705\pi$
$908$	2.53339e11	+	4.38796e11i	0.0123685	+	0.0214228i
$909$	−2.56597e12	−	1.24925e12i	−0.124656	−	0.0606892i
$910$	−1.35052e12	+	2.33916e12i	−0.0652850	+	0.113077i
$911$	−1.14696e13	−	9.62414e12i	−0.551716	−	0.462945i	0.323805	−	0.946124i	$-0.395038\pi$
$911$	−1.14696e13	−	9.62414e12i	−0.551716	−	0.462945i	−0.875522	+	0.483179i	$0.839482\pi$
$912$	−4.00349e12	+	6.16964e12i	−0.191629	+	0.295313i
$913$	3.00935e11	+	1.70669e12i	0.0143336	+	0.0812898i
$914$	1.56785e13	−	1.31558e13i	0.743099	−	0.623534i
$915$	−2.03697e13	−	8.63785e12i	−0.960703	−	0.407391i
$916$	−2.75436e12	+	1.00251e12i	−0.129268	+	0.0470497i
$917$	9.11092e11			0.0425501
$918$	−2.14036e12	+	6.23770e12i	−0.0994708	+	0.289890i
$919$	−3.61739e13			−1.67292			−0.836461	−	0.548027i	$-0.815379\pi$
$919$	−3.61739e13			−1.67292			−0.836461	+	0.548027i	$0.815379\pi$
$920$	4.90835e10	−	1.78649e10i	0.00225886	−	0.000822159i
$921$	−6.00579e11	+	4.52904e11i	−0.0275044	+	0.0207414i
$922$	−9.95201e11	+	8.35073e11i	−0.0453546	+	0.0380570i
$923$	5.55203e12	+	3.14871e13i	0.251793	+	1.42799i
$924$	−4.81681e11	−	2.50719e10i	−0.0217388	−	0.00113152i
$925$	−1.52689e12	−	1.28121e12i	−0.0685757	−	0.0575418i
$926$	−5.88259e12	+	1.01889e13i	−0.262917	+	0.455386i
$927$	−1.13734e13	−	2.54963e13i	−0.505863	−	1.13401i
$928$	7.66513e12	+	1.32764e13i	0.339277	+	0.587644i
$929$	3.46775e12	−	1.96666e13i	0.152748	−	0.866280i	−0.808067	−	0.589091i	$-0.799486\pi$
$929$	3.46775e12	−	1.96666e13i	0.152748	−	0.866280i	0.960815	−	0.277189i	$-0.0894028\pi$
$930$	−5.06843e12	+	2.19895e13i	−0.222178	+	0.963923i
$931$	1.31251e13	+	4.77716e12i	0.572573	+	0.208399i
$932$	−6.77444e11	−	2.46569e11i	−0.0294104	−	0.0107045i
$933$	2.05767e11	−	8.92727e11i	0.00889015	−	0.0385701i
$934$	3.44141e12	−	1.95172e13i	0.147971	−	0.839184i
$935$	−2.68490e12	−	4.65039e12i	−0.114889	−	0.198993i
$936$	1.64649e13	−	2.26959e13i	0.701159	−	0.966509i
$937$	1.43376e13	−	2.48334e13i	0.607642	−	1.05247i	−0.383986	−	0.923339i	$-0.625449\pi$
$937$	1.43376e13	−	2.48334e13i	0.607642	−	1.05247i	0.991628	−	0.129127i	$-0.0412176\pi$
$938$	2.62898e12	+	2.20598e12i	0.110885	+	0.0930440i
$939$	−3.32392e13	−	1.73012e12i	−1.39526	−	0.0726243i
$940$	−1.01836e12	−	5.77542e12i	−0.0425429	−	0.241273i
$941$	2.00326e13	−	1.68093e13i	0.832881	−	0.698870i	−0.123069	−	0.992398i	$-0.539274\pi$
$941$	2.00326e13	−	1.68093e13i	0.832881	−	0.698870i	0.955951	+	0.293528i	$0.0948293\pi$
$942$	1.50847e13	−	1.13756e13i	0.624178	−	0.470701i
$943$	5.65660e10	−	2.05883e10i	0.00232945	−	0.000847850i
$944$	−2.58450e13			−1.05926
$945$	−3.51005e12	−	5.52095e11i	−0.143176	−	0.0225201i
$946$	9.24719e12			0.375405
$947$	1.42502e13	−	5.18665e12i	0.575766	−	0.209562i	−0.0376913	−	0.999289i	$-0.512000\pi$
$947$	1.42502e13	−	5.18665e12i	0.575766	−	0.209562i	0.613458	+	0.789728i	$0.289778\pi$
$948$	−1.21311e13	−	5.14426e12i	−0.487824	−	0.206864i
$949$	3.96778e13	−	3.32936e13i	1.58800	−	1.33249i
$950$	−7.40832e11	−	4.20147e12i	−0.0295096	−	0.167357i
$951$	2.08892e13	−	3.21917e13i	0.828153	−	1.27624i
$952$	−9.89562e11	−	8.30341e11i	−0.0390460	−	0.0327635i
$953$	−4.99811e12	+	8.65697e12i	−0.196285	+	0.339976i	−0.947321	−	0.320286i	$-0.896221\pi$
$953$	−4.99811e12	+	8.65697e12i	−0.196285	+	0.339976i	0.751036	+	0.660261i	$0.229554\pi$
$954$	−2.45863e13	+	1.66092e13i	−0.961005	+	0.649202i
$955$	3.60917e12	+	6.25126e12i	0.140408	+	0.243194i
$956$	2.00132e12	−	1.13501e13i	0.0774919	−	0.439478i
$957$	−1.44398e13	+	4.42031e12i	−0.556490	+	0.170353i
$958$	1.30591e13	+	4.75314e12i	0.500921	+	0.182320i
$959$	2.33465e12	+	8.49744e11i	0.0891330	+	0.0324417i
$960$	−2.39989e13	−	2.23634e13i	−0.911949	−	0.849799i
$961$	4.00352e11	−	2.27051e12i	0.0151421	−	0.0858752i
$962$	3.20477e12	+	5.55082e12i	0.120645	+	0.208963i
$963$	−4.34617e13	+	1.08691e13i	−1.62850	+	0.407263i
$964$	2.77186e12	−	4.80099e12i	0.103377	−	0.179054i
$965$	−3.49663e13	−	2.93402e13i	−1.29801	−	1.08916i
$966$	2.42237e9	+	4.74999e9i	8.95043e−5	+	0.000175508i
$967$	2.08182e12	+	1.18066e13i	0.0765638	+	0.434215i	0.998860	+	0.0477315i	$0.0151992\pi$
$967$	2.08182e12	+	1.18066e13i	0.0765638	+	0.434215i	−0.922296	+	0.386483i	$0.873690\pi$
$968$	−1.63066e13	+	1.36829e13i	−0.596932	+	0.500885i
$969$	7.74883e11	+	6.29239e12i	0.0282344	+	0.229276i
$970$	2.01295e12	−	7.32654e11i	0.0730063	−	0.0265721i
$971$	−1.18164e13			−0.426577			−0.213289	−	0.976989i	$-0.568417\pi$
$971$	−1.18164e13			−0.426577			−0.213289	+	0.976989i	$0.568417\pi$
$972$	8.75202e12	+	2.32841e12i	0.314492	+	0.0836683i
$973$	1.27584e12			0.0456339
$974$	1.20135e13	−	4.37254e12i	0.427713	−	0.155675i
$975$	1.26436e12	+	1.02671e13i	0.0448073	+	0.363855i
$976$	1.11562e13	−	9.36113e12i	0.393542	−	0.330221i
$977$	7.51419e12	+	4.26151e13i	0.263850	+	1.49637i	0.772291	+	0.635269i	$0.219111\pi$
$977$	7.51419e12	+	4.26151e13i	0.263850	+	1.49637i	−0.508441	+	0.861097i	$0.669778\pi$
$978$	1.75487e13	+	3.44109e13i	0.613366	+	1.20274i
$979$	1.07516e13	+	9.02166e12i	0.374068	+	0.313880i
$980$	−5.34159e12	+	9.25190e12i	−0.184992	+	0.320416i
$981$	1.44465e13	−	3.61284e12i	0.498025	−	0.124548i
$982$	−1.91475e13	−	3.31644e13i	−0.657067	−	1.13807i
$983$	5.72807e12	−	3.24855e13i	0.195667	−	1.10968i	−0.715799	−	0.698306i	$-0.753937\pi$
$983$	5.72807e12	−	3.24855e13i	0.195667	−	1.10968i	0.911466	−	0.411375i	$-0.134951\pi$
$984$	−3.03716e13	−	2.83018e13i	−1.03274	−	0.962357i
$985$	−2.54657e13	−	9.26876e12i	−0.861971	−	0.313732i
$986$	−9.33130e12	−	3.39632e12i	−0.314410	−	0.114436i
$987$	2.33142e12	−	7.13693e11i	0.0781974	−	0.0239378i
$988$	1.14928e12	−	6.51790e12i	0.0383725	−	0.217621i
$989$	2.46580e10	+	4.27089e10i	0.000819548	+	0.00141950i
$990$	1.26664e13	−	8.55672e12i	0.419078	−	0.283106i
$991$	1.35439e12	−	2.34588e12i	0.0446080	−	0.0772634i	−0.842859	−	0.538134i	$-0.819129\pi$
$991$	1.35439e12	−	2.34588e12i	0.0446080	−	0.0772634i	0.887467	+	0.460871i	$0.152463\pi$
$992$	1.51422e13	+	1.27058e13i	0.496461	+	0.416580i
$993$	−1.45353e13	+	2.23999e13i	−0.474409	+	0.731096i
$994$	7.28122e11	+	4.12939e12i	0.0236573	+	0.134167i
$995$	3.55171e13	−	2.98024e13i	1.14877	−	0.963934i
$996$	1.44080e12	+	6.10976e11i	0.0463912	+	0.0196724i
$997$	3.57905e13	−	1.30267e13i	1.14720	−	0.417547i	0.302692	−	0.953088i	$-0.402115\pi$
$997$	3.57905e13	−	1.30267e13i	1.14720	−	0.417547i	0.844509	+	0.535541i	$0.179892\pi$
$998$	3.99473e13			1.27468
$999$	−5.29927e12	+	6.55836e12i	−0.168334	+	0.208329i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	27.10.e.a.7.18	yes	156
3.2	odd	2		81.10.e.a.19.9		156
27.4	even	9	inner	27.10.e.a.4.18	✓	156
27.23	odd	18		81.10.e.a.64.9		156

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
27.10.e.a.4.18	✓	156	27.4	even	9	inner
27.10.e.a.7.18	yes	156	1.1	even	1	trivial
81.10.e.a.19.9		156	3.2	odd	2
81.10.e.a.64.9		156	27.23	odd	18

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:	\( N \)	\(=\)	\( 27 = 3^{3} \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	27.e (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(17.4636 - 6.35623i) q^{2} +(-17.1474 - 139.244i) q^{3} +(-127.639 + 107.102i) q^{4} +(280.318 + 1589.76i) q^{5} +(-1184.52 - 2322.71i) q^{6} +(610.601 + 512.355i) q^{7} +(-6305.87 + 10922.1i) q^{8} +(-19094.9 + 4775.35i) q^{9} +(15000.2 + 25981.2i) q^{10} +(-4495.09 + 25492.9i) q^{11} +(17102.0 + 15936.5i) q^{12} +(106141. + 38632.3i) q^{13} +(13919.9 + 5066.44i) q^{14} +(216558. - 66292.8i) q^{15} +(-25886.0 + 146807. i) q^{16} +(64251.1 + 111286. i) q^{17} +(-303113. + 204767. i) q^{18} +(-175832. + 304550. i) q^{19} +(-206046. - 172893. i) q^{20} +(60872.3 - 93808.2i) q^{21} +(83538.4 + 473770. i) q^{22} +(-1965.39 + 1649.15i) q^{23} +(1.62897e6 + 690772. i) q^{24} +(-613422. + 223267. i) q^{25} +2.09916e6 q^{26} +(992367. + 2.57698e6i) q^{27} -132811. q^{28} +(-3.90737e6 + 1.42216e6i) q^{29} +(3.36051e6 - 2.53421e6i) q^{30} +(-4.10711e6 + 3.44627e6i) q^{31} +(-640209. - 3.63081e6i) q^{32} +(3.62682e6 + 188779. i) q^{33} +(1.82942e6 + 1.53506e6i) q^{34} +(-643359. + 1.11433e6i) q^{35} +(1.92581e6 - 2.65463e6i) q^{36} +(1.52669e6 + 2.64430e6i) q^{37} +(-1.13487e6 + 6.43617e6i) q^{38} +(3.55928e6 - 1.54420e7i) q^{39} +(-1.91312e7 - 6.96317e6i) q^{40} +(-2.20476e7 - 8.02467e6i) q^{41} +(466783. - 2.02515e6i) q^{42} +(3.33783e6 - 1.89298e7i) q^{43} +(-2.15659e6 - 3.73533e6i) q^{44} +(-1.29443e7 - 2.90178e7i) q^{45} +(-23840.3 + 41292.6i) q^{46} +(1.67023e7 + 1.40149e7i) q^{47} +(2.08859e7 + 1.08713e6i) q^{48} +(-6.89700e6 - 3.91149e7i) q^{49} +(-9.29341e6 + 7.79810e6i) q^{50} +(1.43942e7 - 1.08549e7i) q^{51} +(-1.76854e7 + 6.43695e6i) q^{52} +8.11126e7 q^{53} +(3.37102e7 + 3.86956e7i) q^{54} -4.17877e7 q^{55} +(-9.44636e6 + 3.43819e6i) q^{56} +(4.54219e7 + 1.92614e7i) q^{57} +(-5.91971e7 + 4.96722e7i) q^{58} +(3.01060e7 + 1.70740e8i) q^{59} +(-2.05412e7 + 3.16554e7i) q^{60} +(-7.48377e7 - 6.27963e7i) q^{61} +(-4.98196e7 + 8.62901e7i) q^{62} +(-1.41061e7 - 6.86755e6i) q^{63} +(-7.24209e7 - 1.25437e8i) q^{64} +(-3.16628e7 + 1.79568e8i) q^{65} +(6.45373e7 - 1.97562e7i) q^{66} +(2.17705e8 + 7.92381e7i) q^{67} +(-2.01199e7 - 7.32305e6i) q^{68} +(263337. + 245390. i) q^{69} +(-4.15242e6 + 2.35496e7i) q^{70} +(1.41531e8 + 2.45140e8i) q^{71} +(6.82535e7 - 2.38669e8i) q^{72} +(2.29279e8 - 3.97123e8i) q^{73} +(4.34693e7 + 3.64750e7i) q^{74} +(4.16073e7 + 8.15870e7i) q^{75} +(-1.01749e7 - 5.77045e7i) q^{76} +(-1.58061e7 + 1.32629e7i) q^{77} +(-3.59951e7 - 2.92297e8i) q^{78} +(-5.29687e8 + 1.92790e8i) q^{79} -2.40644e8 q^{80} +(3.41813e8 - 1.82370e8i) q^{81} -4.36037e8 q^{82} +(6.29101e7 - 2.28974e7i) q^{83} +(2.27736e6 + 1.84931e7i) q^{84} +(-1.58908e8 + 1.33339e8i) q^{85} +(-6.20314e7 - 3.51798e8i) q^{86} +(2.65029e8 + 5.19692e8i) q^{87} +(-2.50091e8 - 2.09851e8i) q^{88} +(2.71094e8 - 4.69549e8i) q^{89} +(-4.10498e8 - 4.24477e8i) q^{90} +(4.50165e7 + 7.79709e7i) q^{91} +(74232.5 - 420994. i) q^{92} +(5.50300e8 + 5.12797e8i) q^{93} +(3.80764e8 + 1.38587e8i) q^{94} +(-5.33450e8 - 1.94160e8i) q^{95} +(-4.94591e8 + 1.51404e8i) q^{96} +(1.23991e7 - 7.03187e7i) q^{97} +(-3.69070e8 - 6.39247e8i) q^{98} +(-3.59041e7 - 5.08251e8i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 156 q - 6 q^{2} - 6 q^{3} - 6 q^{4} + 2382 q^{5} - 6822 q^{6} - 6 q^{7} + 36861 q^{8} + 2538 q^{9} - 3 q^{10} - 121767 q^{11} + 319935 q^{12} - 6 q^{13} - 720417 q^{14} - 706356 q^{15} + 1530 q^{16} + 1002249 q^{17}+ \cdots + 5248107342 q^{99}+O(q^{100}) \) 156 * q - 6 * q^2 - 6 * q^3 - 6 * q^4 + 2382 * q^5 - 6822 * q^6 - 6 * q^7 + 36861 * q^8 + 2538 * q^9 - 3 * q^10 - 121767 * q^11 + 319935 * q^12 - 6 * q^13 - 720417 * q^14 - 706356 * q^15 + 1530 * q^16 + 1002249 * q^17 + 922437 * q^18 - 3 * q^19 - 8448573 * q^20 - 3497394 * q^21 - 1585014 * q^22 + 9316482 * q^23 + 7959258 * q^24 + 2192178 * q^25 - 33129678 * q^26 - 3148155 * q^27 - 12 * q^28 + 19657236 * q^29 + 21174507 * q^30 - 4633692 * q^31 - 37550952 * q^32 - 19055889 * q^33 + 14341770 * q^34 + 34449663 * q^35 + 137733552 * q^36 - 3 * q^37 - 92022060 * q^38 - 89330160 * q^39 + 6645801 * q^40 - 33127221 * q^41 + 227141658 * q^42 + 2356203 * q^43 + 1001541 * q^44 - 78992532 * q^45 - 3 * q^46 - 33488952 * q^47 + 248865393 * q^48 - 93214644 * q^49 - 72027753 * q^50 - 101541537 * q^51 + 160531713 * q^52 + 4841352 * q^53 - 315431874 * q^54 - 12 * q^55 - 91770981 * q^56 - 103852992 * q^57 - 320682489 * q^58 + 538090854 * q^59 + 1127571210 * q^60 + 36683436 * q^61 - 55862958 * q^62 - 419972706 * q^63 - 956301315 * q^64 - 852347310 * q^65 + 472205277 * q^66 - 109026897 * q^67 - 508886217 * q^68 - 1234413090 * q^69 - 815297649 * q^70 + 940878639 * q^71 + 2831326452 * q^72 - 221849931 * q^73 + 838884579 * q^74 - 226667796 * q^75 + 908401146 * q^76 - 967811358 * q^77 - 1247881230 * q^78 - 1228059150 * q^79 - 2497115154 * q^80 - 392600970 * q^81 - 12 * q^82 - 297703284 * q^83 + 1027656618 * q^84 + 1535949369 * q^85 + 2930201574 * q^86 + 2687612040 * q^87 + 2837227002 * q^88 + 1774997208 * q^89 + 7127326206 * q^90 + 551343507 * q^91 - 6896645517 * q^92 - 7299151842 * q^93 + 414852915 * q^94 - 9000269169 * q^95 - 2644638174 * q^96 + 3371772333 * q^97 + 6901039926 * q^98 + 5248107342 * q^99

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