LMFDB - Embedded newform 27.10.e.a.4.18

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			4.18
Character	$\chi$	$=$	27.4
Dual form			27.10.e.a.7.18

$q$-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 $\left(\mathbb{Z}/27\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{1}{9}\right)$

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	0.697745	−	0.716347i	$-0.254187\pi$
$2$	17.4636	+	6.35623i	0.771789	+	0.280908i	0.0740446	+	0.997255i	$0.476409\pi$
$3$	−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	−0.703668	−	0.710529i	$-0.748456\pi$
$5$	280.318	−	1589.76i	0.200579	−	1.13754i	0.904247	−	0.427010i	$-0.140433\pi$
$6$	−1184.52	+	2322.71i	−0.373132	+	0.731670i
$7$	610.601	−	512.355i	0.0961205	−	0.0806547i	−0.593461	−	0.804863i	$-0.702239\pi$
$7$	610.601	−	512.355i	0.0961205	−	0.0806547i	0.689582	+	0.724208i	$0.257794\pi$
$8$	−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	−0.995465	−	0.0951300i	$-0.969673\pi$
$11$	−4495.09	−	25492.9i	−0.0925702	−	0.524992i	0.902895	−	0.429862i	$-0.141438\pi$
$12$	17102.0	−	15936.5i	0.238085	−	0.221859i
$13$	106141.	−	38632.3i	1.03072	−	0.375150i	0.229363	−	0.973341i	$-0.426336\pi$
$13$	106141.	−	38632.3i	1.03072	−	0.375150i	0.801354	+	0.598191i	$0.204114\pi$
$14$	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	−0.757529	−	0.652801i	$-0.773594\pi$
$17$	64251.1	−	111286.i	0.186578	−	0.323162i	0.944107	+	0.329639i	$0.106927\pi$
$18$	−303113.	−	204767.i	−0.680579	−	0.459762i
$19$	−175832.	−	304550.i	−0.309533	−	0.536127i	0.668727	−	0.743508i	$-0.266839\pi$
$19$	−175832.	−	304550.i	−0.309533	−	0.536127i	−0.978260	+	0.207381i	$0.933506\pi$
$20$	−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	0.642055	−	0.766659i	$-0.278082\pi$
$23$	−1965.39	−	1649.15i	−0.00146444	−	0.00122881i	−0.643520	+	0.765430i	$0.722526\pi$
$24$	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	−0.226364	−	0.974043i	$-0.572684\pi$
$29$	−3.90737e6	−	1.42216e6i	−1.02587	−	0.373387i	−0.799508	+	0.600656i	$0.794906\pi$
$30$	3.36051e6	+	2.53421e6i	0.757461	+	0.571210i
$31$	−4.10711e6	−	3.44627e6i	−0.798746	−	0.670227i	0.149147	−	0.988815i	$-0.452347\pi$
$31$	−4.10711e6	−	3.44627e6i	−0.798746	−	0.670227i	−0.947893	+	0.318588i	$0.896792\pi$
$32$	−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	−0.791265	−	0.611474i	$-0.790577\pi$
$37$	1.52669e6	−	2.64430e6i	0.133919	−	0.231955i	0.925184	+	0.379519i	$0.123910\pi$
$38$	−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	−0.869653	−	0.493664i	$-0.835657\pi$
$41$	−2.20476e7	+	8.02467e6i	−1.21852	+	0.443507i	−0.348872	+	0.937171i	$0.613435\pi$
$42$	466783.	+	2.02515e6i	0.0231469	+	0.100423i
$43$	3.33783e6	+	1.89298e7i	0.148887	+	0.844379i	0.964164	+	0.265308i	$0.0854735\pi$
$43$	3.33783e6	+	1.89298e7i	0.148887	+	0.844379i	−0.815277	+	0.579071i	$0.803415\pi$
$44$	−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	−0.358065	−	0.933697i	$-0.616563\pi$
$47$	1.67023e7	−	1.40149e7i	0.499270	−	0.418937i	0.857335	+	0.514760i	$0.172119\pi$
$48$	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	−0.196832	−	0.980437i	$-0.563065\pi$
$59$	3.01060e7	−	1.70740e8i	0.323459	−	1.83443i	0.520291	−	0.853989i	$-0.325823\pi$
$60$	−2.05412e7	−	3.16554e7i	−0.204619	−	0.315331i
$61$	−7.48377e7	+	6.27963e7i	−0.692048	+	0.580697i	−0.919499	−	0.393092i	$-0.871405\pi$
$61$	−7.48377e7	+	6.27963e7i	−0.692048	+	0.580697i	0.227451	+	0.973790i	$0.426961\pi$
$62$	−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	0.416454	−	0.909157i	$-0.363273\pi$
$67$	2.17705e8	−	7.92381e7i	1.31987	−	0.480394i	0.903417	+	0.428763i	$0.141051\pi$
$68$	−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	−0.319375	−	0.947629i	$-0.603473\pi$
$71$	1.41531e8	−	2.45140e8i	0.660983	−	1.14486i	0.980358	−	0.197228i	$-0.0631938\pi$
$72$	6.82535e7	+	2.38669e8i	0.299315	+	1.04665i
$73$	2.29279e8	+	3.97123e8i	0.944957	+	1.63671i	0.755837	+	0.654759i	$0.227230\pi$
$73$	2.29279e8	+	3.97123e8i	0.944957	+	1.63671i	0.189119	+	0.981954i	$0.439437\pi$
$74$	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	−0.566394	−	0.824134i	$-0.691662\pi$
$79$	−5.29687e8	−	1.92790e8i	−1.53002	−	0.556882i	−0.963627	+	0.267252i	$0.913884\pi$
$80$	−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	0.413745	−	0.910393i	$-0.364221\pi$
$83$	6.29101e7	+	2.28974e7i	0.145502	+	0.0529584i	−0.268243	+	0.963351i	$0.586443\pi$
$84$	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	0.998855	−	0.0478365i	$-0.0152326\pi$
$89$	2.71094e8	+	4.69549e8i	0.458000	+	0.793279i	−0.540855	+	0.841116i	$0.681899\pi$
$90$	−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	0.991092	−	0.133178i	$-0.0425182\pi$
$97$	1.23991e7	+	7.03187e7i	0.0142206	+	0.0806488i	−0.976872	+	0.213827i	$0.931407\pi$
$98$	−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	−0.588137	−	0.808761i	$-0.700138\pi$
$101$	1.11072e8	−	9.32004e7i	0.106208	−	0.0891192i	0.694345	+	0.719642i	$0.255694\pi$
$102$	1.82379e8	+	2.81058e8i	0.166830	+	0.257096i
$103$	2.46300e8	−	1.39683e9i	0.215624	−	1.22286i	−0.664198	−	0.747557i	$-0.731227\pi$
$103$	2.46300e8	−	1.39683e9i	0.215624	−	1.22286i	0.879821	−	0.475305i	$-0.157662\pi$
$104$	−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	0.709093	+	0.705115i	$0.249105\pi$
$113$	−3.43870e8	+	1.95018e9i	−0.198400	+	1.12518i	−0.907493	+	0.420067i	$0.862007\pi$
$114$	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	0.980060	+	0.198703i	$0.0636731\pi$
$127$	1.94110e9	+	3.36209e9i	0.662112	+	1.14681i	−0.317948	+	0.948108i	$0.602994\pi$
$128$	−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	0.763366	−	0.645966i	$-0.223545\pi$
$131$	8.75614e8	+	7.34727e8i	0.259772	+	0.217974i	−0.503595	+	0.863940i	$0.667990\pi$
$132$	−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	0.671826	−	0.740709i	$-0.265510\pi$
$137$	2.92900e9	+	1.06607e9i	0.710356	+	0.258549i	0.0385301	+	0.999257i	$0.487732\pi$
$138$	6.15856e6	−	2.61157e6i	0.00144552	−	0.000612978i
$139$	1.22616e9	+	1.02887e9i	0.278599	+	0.233772i	0.771370	−	0.636387i	$-0.219572\pi$
$139$	1.22616e9	+	1.02887e9i	0.278599	+	0.233772i	−0.492771	+	0.870159i	$0.664016\pi$
$140$	−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	−0.379097	−	0.925357i	$-0.623765\pi$
$149$	−4.49393e8	+	1.63566e8i	−0.0746945	+	0.0271866i	0.304403	+	0.952543i	$0.401543\pi$
$150$	1.24520e9	−	1.16034e9i	0.200830	−	0.187143i
$151$	1.20387e9	+	6.82747e9i	0.188444	+	1.06872i	0.921450	+	0.388497i	$0.127006\pi$
$151$	1.20387e9	+	6.82747e9i	0.188444	+	1.06872i	−0.733006	+	0.680222i	$0.761883\pi$
$152$	−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	−0.783485	−	0.621411i	$-0.786560\pi$
$157$	1.25829e9	−	7.13614e9i	0.165285	−	0.937379i	0.948770	−	0.315968i	$-0.102329\pi$
$158$	−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	−0.311278	−	0.950319i	$-0.600757\pi$
$167$	3.07828e9	−	1.74578e10i	0.306256	−	1.73686i	0.617534	−	0.786544i	$-0.288132\pi$
$168$	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	0.935762	+	0.352631i	$0.114713\pi$
$173$	2.08583e9	+	1.18294e10i	0.177040	+	1.00405i	−0.758722	+	0.651414i	$0.774176\pi$
$174$	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	−0.144097	−	0.989564i	$-0.546028\pi$
$179$	1.07814e10	−	1.86739e10i	0.784939	−	1.35955i	0.929036	−	0.369990i	$-0.120639\pi$
$180$	4.76006e9	−	2.31744e9i	0.337976	−	0.164544i
$181$	−1.09960e10	−	1.90457e10i	−0.761522	−	1.31900i	−0.942066	−	0.335428i	$-0.891119\pi$
$181$	−1.09960e10	−	1.90457e10i	−0.761522	−	1.31900i	0.180543	−	0.983567i	$-0.442214\pi$
$182$	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	0.453709	−	0.891150i	$-0.350100\pi$
$191$	4.20187e9	+	1.52936e9i	0.228451	+	0.0831493i	−0.225259	+	0.974299i	$0.572323\pi$
$192$	−1.62245e10	−	1.22351e10i	−0.861620	−	0.649758i
$193$	−2.16606e10	−	1.81754e10i	−1.12373	−	0.942921i	−0.124943	−	0.992164i	$-0.539875\pi$
$193$	−2.16606e10	−	1.81754e10i	−1.12373	−	0.942921i	−0.998787	+	0.0492430i	$0.984319\pi$
$194$	−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	0.596297	−	0.802764i	$-0.296638\pi$
$197$	−8.39382e9	−	1.45385e10i	−0.397065	−	0.687737i	−0.993362	+	0.115027i	$0.963305\pi$
$198$	−3.85758e9	+	8.64768e9i	−0.178370	+	0.399859i
$199$	−1.43606e10	+	2.48733e10i	−0.649134	+	1.12433i	0.334196	+	0.942504i	$0.391535\pi$
$199$	−1.43606e10	+	2.48733e10i	−0.649134	+	1.12433i	−0.983330	+	0.181830i	$0.941798\pi$
$200$	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	0.936117	+	0.351687i	$0.114392\pi$
$211$	−1.83777e9	+	1.04225e10i	−0.0638294	+	0.361995i	−0.999947	+	0.0103071i	$0.996719\pi$
$212$	−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	−0.573477	−	0.819221i	$-0.694406\pi$
$223$	4.93800e9	−	4.14348e9i	0.133715	−	0.112200i	0.707192	+	0.707021i	$0.249962\pi$
$224$	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	0.990696	−	0.136094i	$-0.0434549\pi$
$227$	5.28046e8	+	2.99470e9i	0.0131994	+	0.0748578i	−0.977497	+	0.210952i	$0.932344\pi$
$228$	−7.86055e9	−	2.40627e9i	−0.192640	−	0.0589709i
$229$	1.65307e10	−	6.01668e9i	0.397220	−	0.144576i	−0.135684	−	0.990752i	$-0.543323\pi$
$229$	1.65307e10	−	6.01668e9i	0.397220	−	0.144576i	0.532904	+	0.846176i	$0.321101\pi$
$230$	−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	−0.840980	−	0.541066i	$-0.818021\pi$
$233$	2.16335e9	−	3.74704e9i	0.0480868	−	0.0832887i	0.889067	+	0.457777i	$0.151354\pi$
$234$	−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	−0.0573191	−	0.998356i	$-0.518255\pi$
$239$	−5.29871e10	−	4.44615e10i	−1.05046	−	0.881442i	−0.993142	+	0.116914i	$0.962700\pi$
$240$	4.12641e9	−	3.35083e10i	0.0802826	−	0.651930i
$241$	−3.12649e10	−	1.13795e10i	−0.597007	−	0.217293i	0.0258013	−	0.999667i	$-0.491786\pi$
$241$	−3.12649e10	−	1.13795e10i	−0.597007	−	0.217293i	−0.622809	+	0.782374i	$0.714008\pi$
$242$	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	0.957067	−	0.289868i	$-0.0936114\pi$
$251$	1.43058e10	+	2.47784e10i	0.227500	+	0.394042i	−0.729566	+	0.683910i	$0.760278\pi$
$252$	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	−0.248282	−	0.968688i	$-0.579866\pi$
$257$	1.28810e10	−	4.68831e9i	0.184184	−	0.0670374i	0.432466	+	0.901650i	$0.357644\pi$
$258$	−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	−0.537822	−	0.843058i	$-0.680753\pi$
$263$	1.54430e10	−	1.29582e10i	0.199036	−	0.167011i	0.736858	+	0.676047i	$0.236308\pi$
$264$	−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	0.353478	−	0.935443i	$-0.384999\pi$
$277$	1.30917e11	−	1.09852e11i	1.33609	−	1.12111i	0.982612	−	0.185670i	$-0.0594456\pi$
$278$	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	−0.996952	−	0.0780227i	$-0.975139\pi$
$281$	−9.07283e9	−	5.14545e10i	−0.0868089	−	0.492318i	0.910143	−	0.414295i	$-0.135972\pi$
$282$	1.27683e10	+	5.53955e10i	0.120230	+	0.521620i
$283$	6.89819e10	−	2.51073e10i	0.639287	−	0.232681i	−0.00198143	−	0.999998i	$-0.500631\pi$
$283$	6.89819e10	−	2.51073e10i	0.639287	−	0.232681i	0.641268	+	0.767317i	$0.278408\pi$
$284$	−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	0.570610	−	0.821221i	$-0.306707\pi$
$293$	−1.75418e10	−	1.47193e10i	−0.139050	−	0.116676i	−0.709660	+	0.704545i	$0.751151\pi$
$294$	−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	−0.874509	−	0.485009i	$-0.838816\pi$
$307$	−2.68079e9	+	4.64326e9i	−0.0172242	+	0.0298333i	0.857285	+	0.514842i	$0.172150\pi$
$308$	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	−0.323356	−	0.946277i	$-0.604811\pi$
$311$	6.13619e9	−	2.23339e9i	0.0371944	−	0.0135376i	0.360550	+	0.932740i	$0.382589\pi$
$312$	1.46215e11	−	1.36250e11i	0.873565	−	0.814031i
$313$	4.11967e10	+	2.33638e11i	0.242612	+	1.37592i	0.825973	+	0.563709i	$0.190626\pi$
$313$	4.11967e10	+	2.33638e11i	0.242612	+	1.37592i	−0.583361	+	0.812213i	$0.698263\pi$
$314$	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	0.165485	−	0.986212i	$-0.447081\pi$
$317$	2.09537e11	−	1.75822e11i	1.16545	−	0.977929i	0.999966	+	0.00828314i	$0.00263663\pi$
$318$	−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	−0.912363	−	0.409382i	$-0.865744\pi$
$331$	−1.45802e11	+	1.22342e11i	−0.667631	+	0.560209i	0.244732	+	0.969591i	$0.421300\pi$
$332$	−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	−0.806771	−	0.590865i	$-0.798787\pi$
$337$	−2.47427e11	+	9.00562e10i	−1.04499	+	0.380346i	−0.238221	+	0.971211i	$0.576564\pi$
$338$	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	0.226623	−	0.973983i	$-0.427232\pi$
$347$	−1.87218e11	−	1.57095e11i	−0.693210	−	0.581673i	−0.919833	+	0.392310i	$0.871676\pi$
$348$	−8.94882e10	+	3.79479e10i	−0.327084	+	0.138701i
$349$	−1.11185e11	−	4.04679e10i	−0.401172	−	0.146015i	0.133551	−	0.991042i	$-0.457362\pi$
$349$	−1.11185e11	−	4.04679e10i	−0.401172	−	0.146015i	−0.534723	+	0.845027i	$0.679584\pi$
$350$	−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	0.488505	−	0.872561i	$-0.337542\pi$
$353$	8.80596e10	+	3.20511e10i	0.301850	+	0.109864i	−0.186655	+	0.982425i	$0.559765\pi$
$354$	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	0.689009	−	0.724753i	$-0.258046\pi$
$359$	−8.91130e10	−	1.54348e11i	−0.283150	−	0.490430i	−0.972159	+	0.234323i	$0.924713\pi$
$360$	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	−0.998923	−	0.0463968i	$-0.985226\pi$
$367$	−2.64512e10	−	1.50012e11i	−0.0761111	−	0.431647i	0.922812	−	0.385251i	$-0.125885\pi$
$368$	−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	0.250793	+	0.968041i	$0.419309\pi$
$373$	−1.18121e11	+	6.69899e11i	−0.315965	+	1.79193i	−0.566758	+	0.823884i	$0.691802\pi$
$374$	−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	0.798683	+	0.601753i	$0.205531\pi$
$383$	−6.63858e10	+	3.76492e11i	−0.157645	+	0.894050i	−0.956328	+	0.292297i	$0.905580\pi$
$384$	−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	0.953270	+	0.302118i	$0.0976937\pi$
$389$	7.26294e10	+	4.11902e11i	0.160820	+	0.912054i	−0.792451	+	0.609936i	$0.791195\pi$
$390$	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	0.997510	+	0.0705199i	$0.0224658\pi$
$397$	2.77084e11	+	4.79923e11i	0.559827	+	0.969649i	−0.437683	+	0.899129i	$0.644201\pi$
$398$	−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	0.711890	−	0.702291i	$-0.247840\pi$
$401$	7.45020e10	+	6.25146e10i	0.143886	+	0.120735i	−0.568004	+	0.823026i	$0.692284\pi$
$402$	−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	0.826652	−	0.562714i	$-0.190243\pi$
$409$	2.35442e11	+	1.97559e11i	0.416033	+	0.349093i	−0.410618	+	0.911807i	$0.634687\pi$
$410$	−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	0.325827	−	0.945430i	$-0.394357\pi$
$419$	7.46444e11	−	2.71683e11i	1.18313	−	0.430626i	0.857308	+	0.514804i	$0.172135\pi$
$420$	−2.87613e10	−	8.80440e9i	−0.0451010	−	0.0138063i
$421$	−6.14953e10	−	3.48757e11i	−0.0954053	−	0.541070i	−0.994622	−	0.103568i	$-0.966974\pi$
$421$	−6.14953e10	−	3.48757e11i	−0.0954053	−	0.541070i	0.899217	−	0.437503i	$-0.144137\pi$
$422$	−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	−0.0906275	−	0.995885i	$-0.528887\pi$
$439$	6.80449e11	−	5.70965e11i	0.874390	−	0.733701i	0.965018	+	0.262184i	$0.0844428\pi$
$440$	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	0.982146	−	0.188121i	$-0.0602396\pi$
$443$	−4.14262e9	−	2.34940e10i	−0.00511044	−	0.0289827i	−0.987256	+	0.159138i	$0.949129\pi$
$444$	−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	−0.711804	−	0.702378i	$-0.752122\pi$
$449$	2.17348e11	−	3.76458e11i	0.252375	−	0.437127i	0.964179	+	0.265251i	$0.0854549\pi$
$450$	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	0.830940	−	0.556362i	$-0.187803\pi$
$457$	1.03488e12	+	3.76664e11i	1.10985	+	0.403954i	0.278914	+	0.960316i	$0.410026\pi$
$458$	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	0.307928	−	0.951410i	$-0.400364\pi$
$461$	−6.56893e10	−	2.39090e10i	−0.0677393	−	0.0246551i	−0.375668	+	0.926754i	$0.622587\pi$
$462$	4.95287e10	−	2.10029e10i	0.0505787	−	0.0214482i
$463$	−4.84959e11	−	4.06929e11i	−0.490445	−	0.411532i	0.363741	−	0.931500i	$-0.381499\pi$
$463$	−4.84959e11	−	4.06929e11i	−0.490445	−	0.411532i	−0.854186	+	0.519968i	$0.825944\pi$
$464$	−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	0.999762	+	0.0217944i	$0.00693792\pi$
$467$	5.33198e11	+	9.23527e11i	0.518756	+	0.898511i	−0.481007	+	0.876717i	$0.659729\pi$
$468$	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	−0.359403	−	0.933182i	$-0.617020\pi$
$479$	5.72842e11	−	4.80671e11i	0.497193	−	0.417194i	0.856596	+	0.515988i	$0.172575\pi$
$480$	−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	0.451948	+	0.892045i	$0.350729\pi$
$491$	−3.57819e11	+	2.02929e12i	−0.277841	+	1.57572i	−0.729789	+	0.683672i	$0.760382\pi$
$492$	−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	0.513466	−	0.858110i	$-0.328361\pi$
$499$	2.01988e12	−	7.35175e11i	1.45839	−	0.530809i	0.944920	+	0.327300i	$0.106139\pi$
$500$	−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	−0.891057	−	0.453892i	$-0.850035\pi$
$503$	−7.52953e10	+	1.30415e11i	−0.0524460	+	0.0908391i	0.838611	+	0.544731i	$0.183368\pi$
$504$	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	0.248563	−	0.968616i	$-0.420042\pi$
$509$	−1.00277e12	−	8.41426e11i	−0.662174	−	0.555630i	−0.910738	+	0.412985i	$0.864486\pi$
$510$	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	0.848473	−	0.529239i	$-0.177522\pi$
$521$	−5.73452e10	−	9.93248e10i	−0.0340979	−	0.0590593i	−0.882571	+	0.470180i	$0.844189\pi$
$522$	8.93162e11	+	1.23117e12i	0.526518	+	0.725775i
$523$	−1.53405e12	+	2.65706e12i	−0.896566	+	1.55290i	−0.0647127	+	0.997904i	$0.520613\pi$
$523$	−1.53405e12	+	2.65706e12i	−0.896566	+	1.55290i	−0.831854	+	0.554995i	$0.812720\pi$
$524$	−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	−0.222202	+	0.975001i	$0.571324\pi$
$547$	−2.55652e12	+	2.14518e12i	−1.22098	+	1.02452i	−0.998773	+	0.0495193i	$0.984231\pi$
$548$	−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	0.394311	+	0.918977i	$0.370983\pi$
$557$	−1.36006e12	+	2.35570e12i	−0.598702	+	1.03698i	−0.993013	+	0.118006i	$0.962350\pi$
$558$	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	0.110225	−	0.993907i	$-0.464843\pi$
$563$	−2.02498e12	−	1.69916e12i	−0.849441	−	0.712766i	−0.959667	+	0.281141i	$0.909287\pi$
$564$	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	0.579778	−	0.814775i	$-0.303139\pi$
$569$	1.25065e12	+	4.55200e11i	0.500186	+	0.182053i	−0.0795917	+	0.996828i	$0.525362\pi$
$570$	1.80906e11	−	1.46904e12i	0.0717822	−	0.582903i
$571$	−1.49100e12	−	1.25110e12i	−0.586969	−	0.492526i	0.300258	−	0.953858i	$-0.402927\pi$
$571$	−1.49100e12	−	1.25110e12i	−0.586969	−	0.492526i	−0.887227	+	0.461332i	$0.847372\pi$
$572$	−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	−0.983931	−	0.178550i	$-0.942859\pi$
$577$	−8.98161e11	+	1.55566e12i	−0.337336	+	0.584283i	0.646595	+	0.762834i	$0.276193\pi$
$578$	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	0.196268	−	0.980550i	$-0.437118\pi$
$587$	3.44036e12	−	2.88680e12i	1.19600	−	1.00357i	0.999735	−	0.0230158i	$-0.00732681\pi$
$588$	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	−0.967469	−	0.252991i	$-0.918586\pi$
$599$	8.87977e10	−	5.03597e11i	0.0281826	−	0.159832i	0.995651	+	0.0931597i	$0.0296967\pi$
$600$	−1.15347e12	+	6.00391e10i	−0.363351	+	0.0189127i
$601$	2.07245e12	−	1.73900e12i	0.647962	−	0.543705i	−0.258490	−	0.966014i	$-0.583225\pi$
$601$	2.07245e12	−	1.73900e12i	0.647962	−	0.543705i	0.906452	+	0.422309i	$0.138780\pi$
$602$	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	−0.349078	−	0.937094i	$-0.613505\pi$
$607$	−4.72762e10	+	1.72071e10i	−0.0141349	+	0.00514470i	0.334943	+	0.942238i	$0.391283\pi$
$608$	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	0.866886	−	0.498506i	$-0.166118\pi$
$613$	6.02886e9	+	1.04423e10i	0.00172450	+	0.00298692i	−0.865162	+	0.501493i	$0.832784\pi$
$614$	−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	0.0247802	−	0.999693i	$-0.492111\pi$
$617$	−3.43937e12	−	2.88597e12i	−0.955422	−	0.801694i	−0.980202	+	0.197999i	$0.936556\pi$
$618$	2.95270e12	+	2.22667e12i	0.814275	+	0.614054i
$619$	6.52254e12	+	2.37401e12i	1.78570	+	0.649942i	0.999488	+	0.0319882i	$0.0101839\pi$
$619$	6.52254e12	+	2.37401e12i	1.78570	+	0.649942i	0.786214	+	0.617954i	$0.212038\pi$
$620$	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	−0.453684	−	0.891163i	$-0.649890\pi$
$631$	2.17006e12	−	3.75865e12i	0.544928	−	0.943843i	0.998611	−	0.0526798i	$-0.0167763\pi$
$632$	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	−0.529942	+	0.848034i	$0.677786\pi$
$641$	−6.22809e12	+	5.22599e12i	−1.45712	+	1.22267i	−0.927174	+	0.374631i	$0.877769\pi$
$642$	−2.69608e12	+	5.28670e12i	−0.626361	+	1.22822i
$643$	−7.54498e11	+	4.27897e12i	−0.174064	+	0.987165i	0.765155	+	0.643846i	$0.222662\pi$
$643$	−7.54498e11	+	4.27897e12i	−0.174064	+	0.987165i	−0.939219	+	0.343319i	$0.888449\pi$
$644$	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	0.557293	+	0.830316i	$0.311840\pi$
$653$	−1.16333e12	+	6.59756e12i	−0.250376	+	1.41995i	−0.807669	+	0.589636i	$0.799271\pi$
$654$	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	0.979838	−	0.199796i	$-0.0640278\pi$
$659$	−4.47489e10	−	2.53783e11i	−0.00924267	−	0.0524178i	−0.989080	+	0.147378i	$0.952917\pi$
$660$	−7.14654e11	+	6.65950e11i	−0.146605	+	0.136614i
$661$	−4.08951e12	+	1.48846e12i	−0.833229	+	0.303271i	−0.723184	−	0.690656i	$-0.757322\pi$
$661$	−4.08951e12	+	1.48846e12i	−0.833229	+	0.303271i	−0.110046	+	0.993927i	$0.535100\pi$
$662$	−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	0.738237	−	0.674541i	$-0.235659\pi$
$673$	4.63098e12	+	1.68554e12i	0.870173	+	0.316717i	0.131936	+	0.991258i	$0.457881\pi$
$674$	−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	0.414873	−	0.909879i	$-0.363826\pi$
$677$	8.07971e11	+	2.94078e11i	0.147825	+	0.0538038i	−0.267048	+	0.963683i	$0.586048\pi$
$678$	−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	0.992006	−	0.126194i	$-0.0402761\pi$
$683$	2.19930e12	+	3.80931e12i	0.386716	+	0.669812i	−0.605290	+	0.796005i	$0.706943\pi$
$684$	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	−0.931127	−	0.364695i	$-0.881173\pi$
$691$	−1.08407e12	−	6.14808e12i	−0.180887	−	1.02586i	0.750240	−	0.661166i	$-0.229938\pi$
$692$	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	−0.0140180	−	0.999902i	$-0.504462\pi$
$709$	6.51478e12	−	5.46655e12i	0.968259	−	0.812466i	0.982277	+	0.187436i	$0.0600178\pi$
$710$	−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	−0.999947	−	0.0103202i	$-0.996715\pi$
$719$	−3.51879e12	+	6.09472e12i	−0.491036	+	0.850499i	0.508911	+	0.860819i	$0.330048\pi$
$720$	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	−0.102914	−	0.994690i	$-0.532817\pi$
$727$	−6.18464e12	−	2.25102e12i	−0.821125	−	0.298865i	−0.718211	+	0.695825i	$0.755039\pi$
$728$	−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	0.824226	−	0.566261i	$-0.191611\pi$
$733$	3.20204e12	+	2.68683e12i	0.409693	+	0.343773i	−0.414533	+	0.910034i	$0.636055\pi$
$734$	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	−0.996878	−	0.0789601i	$-0.974840\pi$
$739$	−3.48679e12	+	6.03931e12i	−0.430057	+	0.744881i	0.566820	+	0.823841i	$0.308173\pi$
$740$	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	0.267848	−	0.963461i	$-0.413687\pi$
$743$	9.07412e12	−	3.30271e12i	1.09233	−	0.397577i	0.824484	+	0.565885i	$0.191465\pi$
$744$	−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	−0.895998	−	0.444057i	$-0.853539\pi$
$751$	8.52907e11	−	4.83708e12i	0.0978413	−	0.554885i	0.993840	−	0.110828i	$-0.0353503\pi$
$752$	−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	−0.877812	−	0.479006i	$-0.840997\pi$
$761$	1.02595e12	−	5.81848e12i	0.110891	−	0.628895i	0.988703	−	0.149889i	$-0.0478917\pi$
$762$	−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	−0.954976	−	0.296684i	$-0.904119\pi$
$769$	−1.45061e13	+	5.27977e12i	−1.49583	+	0.544436i	−0.540849	+	0.841119i	$0.681897\pi$
$770$	−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	−0.839431	−	0.543466i	$-0.817112\pi$
$773$	5.05669e11	−	8.75844e11i	0.0509400	−	0.0882306i	0.890371	+	0.455236i	$0.150445\pi$
$774$	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	0.570041	−	0.821616i	$-0.306927\pi$
$787$	−1.50781e12	−	1.26520e12i	−0.140107	−	0.117564i	−0.710148	+	0.704053i	$0.751372\pi$
$788$	−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	0.669713	−	0.742620i	$-0.266417\pi$
$797$	1.89101e13	−	6.88272e12i	1.66009	−	0.604223i	0.990377	+	0.138396i	$0.0441947\pi$
$798$	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	−0.298251	−	0.954488i	$-0.596403\pi$
$821$	−4.48393e12	−	2.54296e13i	−0.344441	−	1.95342i	−0.0461901	−	0.998933i	$-0.514708\pi$
$822$	−5.94563e12	+	5.54044e12i	−0.454229	+	0.423273i
$823$	−6.41370e12	+	2.33440e12i	−0.487315	+	0.177368i	−0.573980	−	0.818869i	$-0.694601\pi$
$823$	−6.41370e12	+	2.33440e12i	−0.487315	+	0.177368i	0.0866652	+	0.996237i	$0.472379\pi$
$824$	−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	−0.527097	−	0.849805i	$-0.676719\pi$
$827$	6.35461e12	−	1.10065e13i	0.472404	−	0.818229i	0.999501	+	0.0315767i	$0.0100528\pi$
$828$	5.92925e8	−	8.39333e9i	4.38392e−5	−	0.000620580i
$829$	8.41727e12	+	1.45791e13i	0.618979	+	1.07210i	0.989672	+	0.143347i	$0.0457866\pi$
$829$	8.41727e12	+	1.45791e13i	0.618979	+	1.07210i	−0.370694	+	0.928755i	$0.620880\pi$
$830$	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	−0.515541	−	0.856865i	$-0.672409\pi$
$839$	−2.09727e13	−	7.63342e12i	−1.46125	−	0.531852i	−0.945709	+	0.325013i	$0.894631\pi$
$840$	−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	0.998761	+	0.0497720i	$0.0158495\pi$
$853$	1.19454e12	+	6.77458e12i	0.0772556	+	0.438139i	−0.921505	+	0.388367i	$0.873039\pi$
$854$	−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	−0.295537	−	0.955331i	$-0.595498\pi$
$857$	9.37934e12	−	7.87020e12i	0.593962	−	0.498393i	0.889498	+	0.456938i	$0.151054\pi$
$858$	7.61330e12	−	3.96278e11i	0.479601	−	0.0249636i
$859$	7.76449e11	−	4.40346e12i	0.0486568	−	0.275946i	−0.950766	−	0.309909i	$-0.899702\pi$
$859$	7.76449e11	−	4.40346e12i	0.0486568	−	0.275946i	0.999423	+	0.0339623i	$0.0108126\pi$
$860$	−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	−0.289817	−	0.957082i	$-0.593595\pi$
$877$	1.81090e12	−	6.59112e11i	0.103370	−	0.0376237i	0.393187	+	0.919458i	$0.371372\pi$
$878$	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	0.121515	+	0.992590i	$0.461225\pi$
$881$	−1.42842e13	+	2.47410e13i	−0.798850	+	1.38365i	−0.920365	+	0.391059i	$0.872109\pi$
$882$	1.01000e13	−	1.04439e13i	0.561969	−	0.581107i
$883$	−1.57308e11	−	2.72466e11i	−0.00870821	−	0.0150831i	0.861638	−	0.507523i	$-0.169439\pi$
$883$	−1.57308e11	−	2.72466e11i	−0.00870821	−	0.0150831i	−0.870347	+	0.492440i	$0.836105\pi$
$884$	−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	0.800108	−	0.599856i	$-0.204776\pi$
$887$	6.42115e12	+	5.38798e12i	0.348302	+	0.292260i	−0.451806	+	0.892116i	$0.649220\pi$
$888$	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	−0.998992	−	0.0448924i	$-0.985705\pi$
$907$	−1.54084e12	−	8.73856e12i	−0.0756007	−	0.428753i	0.923391	−	0.383860i	$-0.125406\pi$
$908$	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	−0.875522	−	0.483179i	$-0.839482\pi$
$911$	−1.14696e13	+	9.62414e12i	−0.551716	+	0.462945i	0.323805	+	0.946124i	$0.395038\pi$
$912$	−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	0.960815	+	0.277189i	$0.0894028\pi$
$929$	3.46775e12	+	1.96666e13i	0.152748	+	0.866280i	−0.808067	+	0.589091i	$0.799486\pi$
$930$	−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	0.991628	+	0.129127i	$0.0412176\pi$
$937$	1.43376e13	+	2.48334e13i	0.607642	+	1.05247i	−0.383986	+	0.923339i	$0.625449\pi$
$938$	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	0.955951	−	0.293528i	$-0.0948293\pi$
$941$	2.00326e13	+	1.68093e13i	0.832881	+	0.698870i	−0.123069	+	0.992398i	$0.539274\pi$
$942$	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	0.613458	−	0.789728i	$-0.289778\pi$
$947$	1.42502e13	+	5.18665e12i	0.575766	+	0.209562i	−0.0376913	+	0.999289i	$0.512000\pi$
$948$	−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	0.751036	−	0.660261i	$-0.229554\pi$
$953$	−4.99811e12	−	8.65697e12i	−0.196285	−	0.339976i	−0.947321	+	0.320286i	$0.896221\pi$
$954$	−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	−0.922296	−	0.386483i	$-0.873690\pi$
$967$	2.08182e12	−	1.18066e13i	0.0765638	−	0.434215i	0.998860	−	0.0477315i	$-0.0151992\pi$
$968$	−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	−0.508441	−	0.861097i	$-0.669778\pi$
$977$	7.51419e12	−	4.26151e13i	0.263850	−	1.49637i	0.772291	−	0.635269i	$-0.219111\pi$
$978$	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	0.911466	+	0.411375i	$0.134951\pi$
$983$	5.72807e12	+	3.24855e13i	0.195667	+	1.10968i	−0.715799	+	0.698306i	$0.753937\pi$
$984$	−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	0.887467	−	0.460871i	$-0.152463\pi$
$991$	1.35439e12	+	2.34588e12i	0.0446080	+	0.0772634i	−0.842859	+	0.538134i	$0.819129\pi$
$992$	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	0.844509	−	0.535541i	$-0.179892\pi$
$997$	3.57905e13	+	1.30267e13i	1.14720	+	0.417547i	0.302692	+	0.953088i	$0.402115\pi$
$998$	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.4.18	✓	156
3.2	odd	2		81.10.e.a.64.9		156
27.7	even	9	inner	27.10.e.a.7.18	yes	156
27.20	odd	18		81.10.e.a.19.9		156

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
27.10.e.a.4.18	✓	156	1.1	even	1	trivial
27.10.e.a.7.18	yes	156	27.7	even	9	inner
81.10.e.a.19.9		156	27.20	odd	18
81.10.e.a.64.9		156	3.2	odd	2

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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