LMFDB - Embedded newform 27.10.e.a.4.1

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			4.1
Character	$\chi$	$=$	27.4
Dual form			27.10.e.a.7.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-40.0613 - 14.5811i) q^{2} +(-125.031 + 63.6419i) q^{3} +(1000.08 + 839.170i) q^{4} +(-306.059 + 1735.74i) q^{5} +(5936.87 - 726.489i) q^{6} +(764.835 - 641.773i) q^{7} +(-16914.7 - 29297.2i) q^{8} +(11582.4 - 15914.4i) q^{9} +O(q^{10})$	\(q+(-40.0613 - 14.5811i) q^{2} +(-125.031 + 63.6419i) q^{3} +(1000.08 + 839.170i) q^{4} +(-306.059 + 1735.74i) q^{5} +(5936.87 - 726.489i) q^{6} +(764.835 - 641.773i) q^{7} +(-16914.7 - 29297.2i) q^{8} +(11582.4 - 15914.4i) q^{9} +(37570.2 - 65073.5i) q^{10} +(14169.6 + 80359.9i) q^{11} +(-178448. - 41274.8i) q^{12} +(142043. - 51699.4i) q^{13} +(-39998.1 + 14558.1i) q^{14} +(-72199.4 - 236500. i) q^{15} +(134370. + 762050. i) q^{16} +(-1161.53 + 2011.82i) q^{17} +(-696056. + 468667. i) q^{18} +(423226. + 733050. i) q^{19} +(-1.76267e6 + 1.47905e6i) q^{20} +(-54784.3 + 128917. i) q^{21} +(604084. - 3.42593e6i) q^{22} +(512754. + 430252. i) q^{23} +(3.97939e6 + 2.58656e6i) q^{24} +(-1.08380e6 - 394471. i) q^{25} -6.44426e6 q^{26} +(-435335. + 2.72692e6i) q^{27} +1.30346e6 q^{28} +(564405. + 205427. i) q^{29} +(-556030. + 1.05272e7i) q^{30} +(-1.38890e6 - 1.16542e6i) q^{31} +(2.72080e6 - 1.54304e7i) q^{32} +(-6.88590e6 - 9.14568e6i) q^{33} +(75866.9 - 63659.9i) q^{34} +(879869. + 1.52398e6i) q^{35} +(2.49383e7 - 6.19613e6i) q^{36} +(-900563. + 1.55982e6i) q^{37} +(-6.26631e6 - 3.55380e7i) q^{38} +(-1.44695e7 + 1.55039e7i) q^{39} +(5.60293e7 - 2.03930e7i) q^{40} +(-1.19014e7 + 4.33175e6i) q^{41} +(4.07448e6 - 4.36577e6i) q^{42} +(1.34805e6 + 7.64517e6i) q^{43} +(-5.32648e7 + 9.22574e7i) q^{44} +(2.40784e7 + 2.49748e7i) q^{45} +(-1.42680e7 - 2.47130e7i) q^{46} +(-6.26487e6 + 5.25685e6i) q^{47} +(-6.52987e7 - 8.67281e7i) q^{48} +(-6.83423e6 + 3.87588e7i) q^{49} +(3.76666e7 + 3.16060e7i) q^{50} +(17190.3 - 325462. i) q^{51} +(1.85439e8 + 6.74944e7i) q^{52} -1.05094e7 q^{53} +(5.72016e7 - 1.02896e8i) q^{54} -1.43821e8 q^{55} +(-3.17391e7 - 1.15521e7i) q^{56} +(-9.95690e7 - 6.47188e7i) q^{57} +(-1.96155e7 - 1.64593e7i) q^{58} +(2.49733e7 - 1.41631e8i) q^{59} +(1.26258e8 - 2.97107e8i) q^{60} +(-1.32541e8 + 1.11215e8i) q^{61} +(3.86478e7 + 6.69400e7i) q^{62} +(-1.35480e6 - 1.96052e7i) q^{63} +(-1.35897e8 + 2.35381e8i) q^{64} +(4.62635e7 + 2.62373e8i) q^{65} +(1.42504e8 + 4.66792e8i) q^{66} +(2.06709e8 - 7.52358e7i) q^{67} +(-2.84989e6 + 1.03727e6i) q^{68} +(-9.14921e7 - 2.11621e7i) q^{69} +(-1.30274e7 - 7.38820e7i) q^{70} +(6.86282e7 - 1.18868e8i) q^{71} +(-6.62161e8 - 7.01440e7i) q^{72} +(-6.59416e7 - 1.14214e8i) q^{73} +(5.88216e7 - 4.93572e7i) q^{74} +(1.60613e8 - 1.96541e7i) q^{75} +(-1.91891e8 + 1.08827e9i) q^{76} +(6.24102e7 + 5.23684e7i) q^{77} +(8.05731e8 - 4.10125e8i) q^{78} +(-1.41188e8 - 5.13881e7i) q^{79} -1.36385e9 q^{80} +(-1.19116e8 - 3.68654e8i) q^{81} +5.39946e8 q^{82} +(4.18517e8 + 1.52328e8i) q^{83} +(-1.62972e8 + 8.29544e7i) q^{84} +(-3.13652e6 - 2.63185e6i) q^{85} +(5.74705e7 - 3.25932e8i) q^{86} +(-8.36418e7 + 1.02352e7i) q^{87} +(2.11464e9 - 1.77440e9i) q^{88} +(1.97851e8 + 3.42687e8i) q^{89} +(-6.00453e8 - 1.35162e9i) q^{90} +(7.54601e7 - 1.30701e8i) q^{91} +(1.51743e8 + 8.60576e8i) q^{92} +(2.47825e8 + 5.73217e7i) q^{93} +(3.27630e8 - 1.19247e8i) q^{94} +(-1.40192e9 + 5.10257e8i) q^{95} +(6.41837e8 + 2.10243e9i) q^{96} +(-2.41831e8 - 1.37149e9i) q^{97} +(8.38935e8 - 1.45308e9i) q^{98} +(1.44300e9 + 7.05260e8i) 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}+O(q^{10}) $ 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	\( 156 q - 6 q^{2} - 6 q^{3} - 6 q^{4} + 2382 q^{5} - 6822 q^{6} - 6 q^{7} + 36861 q^{8} + 2538 q^{9} - 3 q^{10} - 121767 q^{11} + 319935 q^{12} - 6 q^{13} - 720417 q^{14} - 706356 q^{15} + 1530 q^{16} + 1002249 q^{17} + 922437 q^{18} - 3 q^{19} - 8448573 q^{20} - 3497394 q^{21} - 1585014 q^{22} + 9316482 q^{23} + 7959258 q^{24} + 2192178 q^{25} - 33129678 q^{26} - 3148155 q^{27} - 12 q^{28} + 19657236 q^{29} + 21174507 q^{30} - 4633692 q^{31} - 37550952 q^{32} - 19055889 q^{33} + 14341770 q^{34} + 34449663 q^{35} + 137733552 q^{36} - 3 q^{37} - 92022060 q^{38} - 89330160 q^{39} + 6645801 q^{40} - 33127221 q^{41} + 227141658 q^{42} + 2356203 q^{43} + 1001541 q^{44} - 78992532 q^{45} - 3 q^{46} - 33488952 q^{47} + 248865393 q^{48} - 93214644 q^{49} - 72027753 q^{50} - 101541537 q^{51} + 160531713 q^{52} + 4841352 q^{53} - 315431874 q^{54} - 12 q^{55} - 91770981 q^{56} - 103852992 q^{57} - 320682489 q^{58} + 538090854 q^{59} + 1127571210 q^{60} + 36683436 q^{61} - 55862958 q^{62} - 419972706 q^{63} - 956301315 q^{64} - 852347310 q^{65} + 472205277 q^{66} - 109026897 q^{67} - 508886217 q^{68} - 1234413090 q^{69} - 815297649 q^{70} + 940878639 q^{71} + 2831326452 q^{72} - 221849931 q^{73} + 838884579 q^{74} - 226667796 q^{75} + 908401146 q^{76} - 967811358 q^{77} - 1247881230 q^{78} - 1228059150 q^{79} - 2497115154 q^{80} - 392600970 q^{81} - 12 q^{82} - 297703284 q^{83} + 1027656618 q^{84} + 1535949369 q^{85} + 2930201574 q^{86} + 2687612040 q^{87} + 2837227002 q^{88} + 1774997208 q^{89} + 7127326206 q^{90} + 551343507 q^{91} - 6896645517 q^{92} - 7299151842 q^{93} + 414852915 q^{94} - 9000269169 q^{95} - 2644638174 q^{96} + 3371772333 q^{97} + 6901039926 q^{98} + 5248107342 q^{99}+O(q^{100}) \) 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

Display 100 coefficients 10 coefficients

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 $

$2$	−40.0613	−	14.5811i	−1.77048	−	0.644401i	−0.999976	−	0.00696084i	$-0.997784\pi$
$2$	−40.0613	−	14.5811i	−1.77048	−	0.644401i	−0.770500	−	0.637440i	$-0.779994\pi$
$3$	−125.031	+	63.6419i	−0.891192	+	0.453626i
$3$	−125.031	+	63.6419i	−0.891192	+	0.453626i
$4$	1000.08	+	839.170i	1.95329	+	1.63900i
$5$	−306.059	+	1735.74i	−0.218998	+	1.24200i	0.654835	+	0.755772i	$0.272738\pi$
$5$	−306.059	+	1735.74i	−0.218998	+	1.24200i	−0.873833	+	0.486226i	$0.838373\pi$
$6$	5936.87	−	726.489i	1.87015	−	0.228849i
$7$	764.835	−	641.773i	0.120400	−	0.101028i	−0.580600	−	0.814189i	$-0.697182\pi$
$7$	764.835	−	641.773i	0.120400	−	0.101028i	0.701000	+	0.713162i	$0.252737\pi$
$8$	−16914.7	−	29297.2i	−1.46003	−	2.52884i
$9$	11582.4	−	15914.4i	0.588447	−	0.808535i
$10$	37570.2	−	65073.5i	1.18807	−	2.05780i
$11$	14169.6	+	80359.9i	0.291804	+	1.65490i	0.679916	+	0.733290i	$0.262016\pi$
$11$	14169.6	+	80359.9i	0.291804	+	1.65490i	−0.388112	+	0.921612i	$0.626873\pi$
$12$	−178448.	−	41274.8i	−2.48425	−	0.574606i
$13$	142043.	−	51699.4i	1.37935	−	0.502042i	0.457368	−	0.889277i	$-0.348792\pi$
$13$	142043.	−	51699.4i	1.37935	−	0.502042i	0.921981	+	0.387235i	$0.126570\pi$
$14$	−39998.1	+	14558.1i	−0.278268	+	0.101281i
$15$	−72199.4	−	236500.i	−0.368233	−	1.20620i
$16$	134370.	+	762050.i	0.512580	+	2.90699i
$17$	−1161.53	+	2011.82i	−0.00337295	+	0.00584211i	−0.867707	−	0.497076i	$-0.834407\pi$
$17$	−1161.53	+	2011.82i	−0.00337295	+	0.00584211i	0.864334	+	0.502918i	$0.167740\pi$
$18$	−696056.	+	468667.i	−1.56285	+	1.05230i
$19$	423226.	+	733050.i	0.745043	+	1.29045i	0.950175	+	0.311718i	$0.100905\pi$
$19$	423226.	+	733050.i	0.745043	+	1.29045i	−0.205131	+	0.978734i	$0.565762\pi$
$20$	−1.76267e6	+	1.47905e6i	−2.46340	+	2.06704i
$21$	−54784.3	+	128917.i	−0.0614709	+	0.144652i
$22$	604084.	−	3.42593e6i	0.549788	−	3.11800i
$23$	512754.	+	430252.i	0.382062	+	0.320588i	0.813511	−	0.581549i	$-0.197553\pi$
$23$	512754.	+	430252.i	0.382062	+	0.320588i	−0.431449	+	0.902137i	$0.641998\pi$
$24$	3.97939e6	+	2.58656e6i	2.44831	+	1.59138i
$25$	−1.08380e6	−	394471.i	−0.554906	−	0.201969i
$26$	−6.44426e6			−2.76562
$27$	−435335.	+	2.72692e6i	−0.157647	+	0.987495i
$28$	1.30346e6			0.400761
$29$	564405.	+	205427.i	0.148184	+	0.0539344i	0.415047	−	0.909800i	$-0.363765\pi$
$29$	564405.	+	205427.i	0.148184	+	0.0539344i	−0.266864	+	0.963734i	$0.585987\pi$
$30$	−556030.	+	1.05272e7i	−0.125329	+	2.37284i
$31$	−1.38890e6	−	1.16542e6i	−0.270111	−	0.226650i	0.497663	−	0.867370i	$-0.334191\pi$
$31$	−1.38890e6	−	1.16542e6i	−0.270111	−	0.226650i	−0.767775	+	0.640720i	$0.778636\pi$
$32$	2.72080e6	−	1.54304e7i	0.458692	−	2.60137i
$33$	−6.88590e6	−	9.14568e6i	−1.01076	−	1.34247i
$34$	75866.9	−	63659.9i	0.00973638	−	0.00816979i
$35$	879869.	+	1.52398e6i	0.0991088	+	0.171661i
$36$	2.49383e7	−	6.19613e6i	2.47460	−	0.614836i
$37$	−900563.	+	1.55982e6i	−0.0789962	+	0.136825i	−0.902817	−	0.430025i	$-0.858505\pi$
$37$	−900563.	+	1.55982e6i	−0.0789962	+	0.136825i	0.823821	+	0.566850i	$0.191838\pi$
$38$	−6.26631e6	−	3.55380e7i	−0.487513	−	2.76482i
$39$	−1.44695e7	+	1.55039e7i	−1.00153	+	1.07312i
$40$	5.60293e7	−	2.03930e7i	3.46055	−	1.25954i
$41$	−1.19014e7	+	4.33175e6i	−0.657763	+	0.239406i	−0.649270	−	0.760558i	$-0.724926\pi$
$41$	−1.19014e7	+	4.33175e6i	−0.657763	+	0.239406i	−0.00849298	+	0.999964i	$0.502703\pi$
$42$	4.07448e6	−	4.36577e6i	0.202046	−	0.216490i
$43$	1.34805e6	+	7.64517e6i	0.0601310	+	0.341020i	1.00000		0.000515817i	$-0.000164190\pi$
$43$	1.34805e6	+	7.64517e6i	0.0601310	+	0.341020i	−0.939869	+	0.341535i	$0.889053\pi$
$44$	−5.32648e7	+	9.22574e7i	−2.14241	+	3.71077i
$45$	2.40784e7	+	2.49748e7i	0.875331	+	0.907918i
$46$	−1.42680e7	−	2.47130e7i	−0.469845	−	0.813795i
$47$	−6.26487e6	+	5.25685e6i	−0.187271	+	0.157139i	−0.731603	−	0.681731i	$-0.761228\pi$
$47$	−6.26487e6	+	5.25685e6i	−0.187271	+	0.157139i	0.544332	+	0.838870i	$0.316783\pi$
$48$	−6.52987e7	−	8.67281e7i	−1.77549	−	2.35817i
$49$	−6.83423e6	+	3.87588e7i	−0.169359	+	0.960480i
$50$	3.76666e7	+	3.16060e7i	0.852298	+	0.715163i
$51$	17190.3	−	325462.i	0.000355810	−	0.00673650i
$52$	1.85439e8	+	6.74944e7i	3.51712	+	1.28013i
$53$	−1.05094e7			−0.182952			−0.0914760	−	0.995807i	$-0.529158\pi$
$53$	−1.05094e7			−0.182952			−0.0914760	+	0.995807i	$0.529158\pi$
$54$	5.72016e7	−	1.02896e8i	0.915453	−	1.64675i
$55$	−1.43821e8			−2.11929
$56$	−3.17391e7	−	1.15521e7i	−0.431270	−	0.156969i
$57$	−9.95690e7	−	6.47188e7i	−1.24936	−	0.812071i
$58$	−1.96155e7	−	1.64593e7i	−0.227600	−	0.190979i
$59$	2.49733e7	−	1.41631e8i	0.268313	−	1.52168i	−0.491118	−	0.871093i	$-0.663412\pi$
$59$	2.49733e7	−	1.41631e8i	0.268313	−	1.52168i	0.759431	−	0.650587i	$-0.225477\pi$
$60$	1.26258e8	−	2.97107e8i	1.25770	−	2.95960i
$61$	−1.32541e8	+	1.11215e8i	−1.22565	+	1.02844i	−0.227137	+	0.973863i	$0.572937\pi$
$61$	−1.32541e8	+	1.11215e8i	−1.22565	+	1.02844i	−0.998510	+	0.0545769i	$0.982619\pi$
$62$	3.86478e7	+	6.69400e7i	0.332172	+	0.575338i
$63$	−1.35480e6	−	1.96052e7i	−0.0108353	−	0.156797i
$64$	−1.35897e8	+	2.35381e8i	−1.01251	+	1.75372i
$65$	4.62635e7	+	2.62373e8i	0.321461	+	1.82309i
$66$	1.42504e8	+	4.66792e8i	0.924440	+	3.02814i
$67$	2.06709e8	−	7.52358e7i	1.25320	−	0.456129i	0.371721	−	0.928344i	$-0.378768\pi$
$67$	2.06709e8	−	7.52358e7i	1.25320	−	0.456129i	0.881483	+	0.472215i	$0.156546\pi$
$68$	−2.84989e6	+	1.03727e6i	−0.0161636	+	0.00588306i
$69$	−9.14921e7	−	2.11621e7i	−0.485918	−	0.112393i
$70$	−1.30274e7	−	7.38820e7i	−0.0648510	−	0.367788i
$71$	6.86282e7	−	1.18868e8i	0.320509	−	0.555138i	−0.660084	−	0.751192i	$-0.729479\pi$
$71$	6.86282e7	−	1.18868e8i	0.320509	−	0.555138i	0.980593	+	0.196054i	$0.0628128\pi$
$72$	−6.62161e8	−	7.01440e7i	−2.90380	−	0.307606i
$73$	−6.59416e7	−	1.14214e8i	−0.271773	−	0.470725i	0.697543	−	0.716543i	$-0.254277\pi$
$73$	−6.59416e7	−	1.14214e8i	−0.271773	−	0.470725i	−0.969316	+	0.245818i	$0.920943\pi$
$74$	5.88216e7	−	4.93572e7i	0.228031	−	0.191341i
$75$	1.60613e8	−	1.96541e7i	0.586146	−	0.0717261i
$76$	−1.91891e8	+	1.08827e9i	−0.659772	+	3.74176i
$77$	6.24102e7	+	5.23684e7i	0.202324	+	0.169770i
$78$	8.05731e8	−	4.10125e8i	2.46470	−	1.25456i
$79$	−1.41188e8	−	5.13881e7i	−0.407826	−	0.148437i	0.129957	−	0.991520i	$-0.458516\pi$
$79$	−1.41188e8	−	5.13881e7i	−0.407826	−	0.148437i	−0.537783	+	0.843083i	$0.680738\pi$
$80$	−1.36385e9			−3.72273
$81$	−1.19116e8	−	3.68654e8i	−0.307459	−	0.951561i
$82$	5.39946e8			1.31883
$83$	4.18517e8	+	1.52328e8i	0.967970	+	0.352312i	0.777152	−	0.629313i	$-0.216664\pi$
$83$	4.18517e8	+	1.52328e8i	0.967970	+	0.352312i	0.190818	+	0.981625i	$0.438886\pi$
$84$	−1.62972e8	+	8.29544e7i	−0.357155	+	0.181795i
$85$	−3.13652e6	−	2.63185e6i	−0.00651722	−	0.00546860i
$86$	5.74705e7	−	3.25932e8i	0.113293	−	0.642515i
$87$	−8.36418e7	+	1.02352e7i	−0.156526	+	0.0191540i
$88$	2.11464e9	−	1.77440e9i	3.75894	−	3.15412i
$89$	1.97851e8	+	3.42687e8i	0.334258	+	0.578952i	0.983342	−	0.181765i	$-0.0581809\pi$
$89$	1.97851e8	+	3.42687e8i	0.334258	+	0.578952i	−0.649084	+	0.760717i	$0.724848\pi$
$90$	−6.00453e8	−	1.35162e9i	−0.964689	−	2.17151i
$91$	7.54601e7	−	1.30701e8i	0.115354	−	0.199798i
$92$	1.51743e8	+	8.60576e8i	0.220832	+	1.25240i
$93$	2.47825e8	+	5.73217e7i	0.343535	+	0.0794595i
$94$	3.27630e8	−	1.19247e8i	0.432820	−	0.157534i
$95$	−1.40192e9	+	5.10257e8i	−1.76590	+	0.642736i
$96$	6.41837e8	+	2.10243e9i	0.771266	+	2.52640i
$97$	−2.41831e8	−	1.37149e9i	−0.277357	−	1.57297i	−0.731372	−	0.681978i	$-0.761120\pi$
$97$	−2.41831e8	−	1.37149e9i	−0.277357	−	1.57297i	0.454015	−	0.890994i	$-0.349991\pi$
$98$	8.38935e8	−	1.45308e9i	0.918779	−	1.59137i
$99$	1.44300e9	+	7.05260e8i	1.50976	+	0.737889i
$100$	−7.52863e8	−	1.30400e9i	−0.752863	−	1.30400i
$101$	1.38550e6	−	1.16257e6i	0.00132483	−	0.00111166i	−0.642125	−	0.766600i	$-0.721947\pi$
$101$	1.38550e6	−	1.16257e6i	0.00132483	−	0.00111166i	0.643450	+	0.765488i	$0.277503\pi$
$102$	−5.43427e6	+	1.27878e7i	−0.00497096	+	0.0116975i
$103$	−3.01900e8	+	1.71216e9i	−0.264299	+	1.49891i	0.506726	+	0.862107i	$0.330856\pi$
$103$	−3.01900e8	+	1.71216e9i	−0.264299	+	1.49891i	−0.771024	+	0.636806i	$0.780255\pi$
$104$	−3.91726e9	−	3.28697e9i	−3.28347	−	2.75516i
$105$	−2.07000e8	−	1.34548e8i	−0.166195	−	0.108025i
$106$	4.21021e8	+	1.53239e8i	0.323912	+	0.117894i
$107$	−9.60585e8			−0.708449			−0.354225	−	0.935160i	$-0.615255\pi$
$107$	−9.60585e8			−0.708449			−0.354225	+	0.935160i	$0.615255\pi$
$108$	−2.72372e9	+	2.36183e9i	−1.92644	+	1.67048i
$109$	−1.53798e9			−1.04360			−0.521798	−	0.853069i	$-0.674738\pi$
$109$	−1.53798e9			−1.04360			−0.521798	+	0.853069i	$0.674738\pi$
$110$	5.76166e9	+	2.09707e9i	3.75215	+	1.36567i
$111$	1.33281e7	−	2.52339e8i	0.00833327	−	0.157772i
$112$	5.91834e8	+	4.96607e8i	0.355401	+	0.298217i
$113$	4.90269e7	−	2.78045e8i	0.0282866	−	0.160421i	−0.967392	−	0.253282i	$-0.918490\pi$
$113$	4.90269e7	−	2.78045e8i	0.0282866	−	0.160421i	0.995679	+	0.0928605i	$0.0296011\pi$
$114$	3.04519e9	+	4.04455e9i	1.68866	+	2.24284i
$115$	−9.03740e8	+	7.58328e8i	−0.481841	+	0.404312i
$116$	3.92065e8	+	6.79076e8i	0.201047	+	0.348223i
$117$	8.22434e8	−	2.85933e9i	0.405756	−	1.41068i
$118$	−3.06560e9	+	5.30977e9i	−1.45561	+	2.52120i
$119$	402757.	+	2.28415e6i	0.000184112	+	0.00104415i
$120$	−5.70754e9	+	6.11557e9i	−2.51266	+	2.69229i
$121$	−4.04119e9	+	1.47087e9i	−1.71386	+	0.623794i
$122$	6.93139e9	−	2.52282e9i	2.83271	−	1.03102i
$123$	1.21236e9	−	1.29903e9i	0.477593	−	0.511735i
$124$	−4.11025e8	−	2.33104e9i	−0.156125	−	0.885426i
$125$	−7.04805e8	+	1.22076e9i	−0.258210	+	0.447234i
$126$	−2.31590e8	+	8.05163e8i	−0.0818565	+	0.284588i
$127$	−7.69286e8	−	1.33244e9i	−0.262404	−	0.454498i	0.704476	−	0.709728i	$-0.251182\pi$
$127$	−7.69286e8	−	1.33244e9i	−0.262404	−	0.454498i	−0.966880	+	0.255230i	$0.917849\pi$
$128$	2.73093e9	−	2.29152e9i	0.899220	−	0.754535i
$129$	−6.55101e8	−	8.70090e8i	−0.208283	−	0.276637i
$130$	1.97232e9	−	1.11856e10i	0.605665	−	3.43490i
$131$	4.39027e9	+	3.68387e9i	1.30248	+	1.09291i	0.989711	+	0.143077i	$0.0456998\pi$
$131$	4.39027e9	+	3.68387e9i	1.30248	+	1.09291i	0.312765	+	0.949830i	$0.398745\pi$
$132$	7.88307e8	−	1.49249e10i	0.226002	−	4.27886i
$133$	7.94150e8	+	2.89047e8i	0.220075	+	0.0801006i
$134$	−9.37804e9			−2.51270
$135$	−4.59999e9	−	1.59023e9i	−1.19194	−	0.412057i
$136$	7.85877e7			0.0196983
$137$	−3.08044e9	−	1.12119e9i	−0.747084	−	0.271916i	−0.0597061	−	0.998216i	$-0.519016\pi$
$137$	−3.08044e9	−	1.12119e9i	−0.747084	−	0.271916i	−0.687378	+	0.726300i	$0.741239\pi$
$138$	3.35673e9	+	2.18184e9i	0.787880	+	0.512114i
$139$	2.24656e9	+	1.88509e9i	0.510448	+	0.428316i	0.861287	−	0.508119i	$-0.169659\pi$
$139$	2.24656e9	+	1.88509e9i	0.510448	+	0.428316i	−0.350839	+	0.936436i	$0.614104\pi$
$140$	−3.98934e8	+	2.26247e9i	−0.0877657	+	0.497744i
$141$	4.48746e8	−	1.05598e9i	0.0956124	−	0.224993i
$142$	−4.48256e9	+	3.76131e9i	−0.925184	+	0.776322i
$143$	6.16725e9	+	1.06820e10i	1.23333	+	2.13619i
$144$	1.36839e10	+	6.68795e9i	2.65203	+	1.29617i
$145$	−5.29309e8	+	9.16791e8i	−0.0994383	+	0.172232i
$146$	9.76336e8	+	5.53707e9i	0.177833	+	1.00854i
$147$	−1.61220e9	−	5.28099e9i	−0.284767	−	0.932798i
$148$	−2.20959e9	+	8.04226e8i	−0.378560	+	0.137784i
$149$	−5.34439e8	+	1.94520e8i	−0.0888301	+	0.0323315i	−0.386053	−	0.922477i	$-0.626162\pi$
$149$	−5.34439e8	+	1.94520e8i	−0.0888301	+	0.0323315i	0.297223	+	0.954808i	$0.403940\pi$
$150$	−6.72096e9	−	1.55455e9i	−1.08398	−	0.250723i
$151$	1.15596e9	+	6.55579e9i	0.180945	+	1.02619i	0.931055	+	0.364879i	$0.118890\pi$
$151$	1.15596e9	+	6.55579e9i	0.180945	+	1.02619i	−0.750110	+	0.661314i	$0.769999\pi$
$152$	1.43175e10	−	2.47987e10i	2.17556	−	3.76819i
$153$	1.85637e7	+	4.17868e7i	0.00273875	+	0.00616492i
$154$	−1.73665e9	−	3.00796e9i	−0.248810	−	0.430952i
$155$	2.44796e9	−	2.05408e9i	0.340653	−	0.285842i
$156$	−2.74811e10	+	3.36284e9i	−3.71513	+	0.454616i
$157$	5.55288e8	−	3.14919e9i	0.0729406	−	0.413667i	−0.926372	−	0.376609i	$-0.877090\pi$
$157$	5.55288e8	−	3.14919e9i	0.0729406	−	0.413667i	0.999313	−	0.0370583i	$-0.0117987\pi$
$158$	4.90687e9	+	4.11735e9i	0.626394	+	0.525607i
$159$	1.31400e9	−	6.68839e8i	0.163045	−	0.0829917i
$160$	2.59505e10	+	9.44522e9i	3.13045	+	1.13939i
$161$	6.68297e8			0.0783886
$162$	−6.03450e8	+	1.65056e10i	−0.0688373	+	1.88284i
$163$	−1.21348e10			−1.34644			−0.673222	−	0.739440i	$-0.735090\pi$
$163$	−1.21348e10			−1.34644			−0.673222	+	0.739440i	$0.735090\pi$
$164$	−1.55374e10	−	5.65517e9i	−1.67719	−	0.610447i
$165$	1.79821e10	−	9.15305e9i	1.88869	−	0.961364i
$166$	−1.45452e10	−	1.22049e10i	−1.48674	−	1.24752i
$167$	3.99194e8	−	2.26394e9i	0.0397155	−	0.225238i	−0.958489	−	0.285128i	$-0.907964\pi$
$167$	3.99194e8	−	2.26394e9i	0.0397155	−	0.225238i	0.998205	+	0.0598901i	$0.0190750\pi$
$168$	4.70357e9	−	5.75571e8i	0.455549	−	0.0557452i
$169$	9.37983e9	−	7.87061e9i	0.884514	−	0.742196i
$170$	8.72776e7	+	1.51169e8i	0.00801462	+	0.0138817i
$171$	1.65680e10	+	1.75509e9i	1.48180	+	0.156970i
$172$	−5.06744e9	+	8.77706e9i	−0.441479	+	0.764665i
$173$	−3.14934e9	−	1.78608e10i	−0.267308	−	1.51598i	−0.762381	−	0.647128i	$-0.775970\pi$
$173$	−3.14934e9	−	1.78608e10i	−0.267308	−	1.51598i	0.495073	−	0.868851i	$-0.335141\pi$
$174$	3.50004e9	+	8.09557e8i	0.289469	+	0.0669539i
$175$	−1.08209e9	+	3.93848e8i	−0.0872151	+	0.0317437i
$176$	−5.93343e10	+	2.15959e10i	−4.66121	+	1.69654i
$177$	5.89122e9	+	1.92976e10i	0.451155	+	1.47782i
$178$	−2.92939e9	−	1.66134e10i	−0.218719	−	1.24042i
$179$	4.27926e9	−	7.41190e9i	0.311552	−	0.539624i	−0.667147	−	0.744926i	$-0.732485\pi$
$179$	4.27926e9	−	7.41190e9i	0.311552	−	0.539624i	0.978699	+	0.205303i	$0.0658179\pi$
$180$	3.12232e9	+	4.51828e10i	0.221693	+	3.20810i
$181$	9.02073e9	+	1.56244e10i	0.624724	+	1.08205i	0.988594	+	0.150604i	$0.0481219\pi$
$181$	9.02073e9	+	1.56244e10i	0.624724	+	1.08205i	−0.363870	+	0.931450i	$0.618545\pi$
$182$	−4.92879e9	+	4.13575e9i	−0.332981	+	0.279404i
$183$	9.49375e9	−	2.23404e10i	0.625760	−	1.47252i
$184$	3.93207e9	−	2.22999e10i	0.252895	−	1.43424i
$185$	−2.43182e9	−	2.04054e9i	−0.152637	−	0.128078i
$186$	−9.09236e9	−	5.90994e9i	−0.557017	−	0.362055i
$187$	−1.78128e8	−	6.48334e7i	−0.0106524	−	0.00387714i
$188$	−1.06768e10			−0.623347
$189$	1.41710e9	+	2.36503e9i	0.0807836	+	0.134821i
$190$	6.36028e10			3.54067
$191$	2.22149e10	+	8.08556e9i	1.20780	+	0.439602i	0.865939	−	0.500150i	$-0.166722\pi$
$191$	2.22149e10	+	8.08556e9i	1.20780	+	0.439602i	0.341858	+	0.939752i	$0.388944\pi$
$192$	2.01124e9	−	3.80786e10i	0.106809	−	2.02221i
$193$	6.55309e9	+	5.49869e9i	0.339968	+	0.285267i	0.796747	−	0.604313i	$-0.206552\pi$
$193$	6.55309e9	+	5.49869e9i	0.339968	+	0.285267i	−0.456779	+	0.889580i	$0.650997\pi$
$194$	−1.03098e10	+	5.84700e10i	−0.522570	+	2.96364i
$195$	−2.24823e10	−	2.98604e10i	−1.11349	−	1.47891i
$196$	−3.93601e10	+	3.30270e10i	−1.90504	+	1.59852i
$197$	−1.23748e10	−	2.14337e10i	−0.585382	−	1.01391i	−0.994828	−	0.101577i	$-0.967611\pi$
$197$	−1.23748e10	−	2.14337e10i	−0.585382	−	1.01391i	0.409446	−	0.912334i	$-0.365722\pi$
$198$	−4.75249e10	−	4.92942e10i	−2.19750	−	2.27930i
$199$	1.06946e10	−	1.85236e10i	0.483421	−	0.837310i	−0.516398	−	0.856349i	$-0.672727\pi$
$199$	1.06946e10	−	1.85236e10i	0.483421	−	0.837310i	0.999819	+	0.0190389i	$0.00606063\pi$
$200$	6.77531e9	+	3.84247e10i	0.299429	+	1.69815i
$201$	−2.10568e10	+	2.25621e10i	−0.909934	+	0.974985i
$202$	−7.24563e7	+	2.63719e7i	−0.00306193	+	0.00111445i
$203$	5.63514e8	−	2.05102e8i	0.0232902	−	0.00847693i
$204$	2.90310e8	−	3.11064e8i	0.0117362	−	0.0125752i
$205$	−3.87629e9	−	2.19835e10i	−0.153293	−	0.869370i
$206$	3.70597e10	−	6.41893e10i	1.43384	−	2.48348i
$207$	1.27861e10	−	3.17682e9i	0.484030	−	0.120262i
$208$	5.84838e10	+	1.01297e11i	2.16646	+	3.75242i
$209$	−5.29108e10	+	4.43975e10i	−1.91817	+	1.60953i
$210$	6.33082e9	+	8.40844e9i	0.224633	+	0.298352i
$211$	−7.27307e9	+	4.12476e10i	−0.252608	+	1.43261i	0.549532	+	0.835473i	$0.314806\pi$
$211$	−7.27307e9	+	4.12476e10i	−0.252608	+	1.43261i	−0.802139	+	0.597137i	$0.796305\pi$
$212$	−1.05103e10	−	8.81918e9i	−0.357358	−	0.299859i
$213$	−1.01568e9	+	1.92297e10i	−0.0338103	+	0.640125i
$214$	3.84823e10	+	1.40064e10i	1.25429	+	0.456525i
$215$	−1.36827e10			−0.436714
$216$	8.72546e10	−	3.33710e10i	2.72738	−	1.04310i
$217$	−1.81021e9			−0.0554193
$218$	6.16136e10	+	2.24255e10i	1.84766	+	0.672493i
$219$	1.55136e10	+	1.00836e10i	0.455735	+	0.296223i
$220$	−1.43833e11	−	1.20690e11i	−4.13958	−	3.47352i
$221$	−6.09766e7	+	3.45816e8i	−0.00171948	+	0.00975168i
$222$	−4.21333e9	+	9.91470e9i	−0.116423	+	0.273962i
$223$	−2.62380e10	+	2.20163e10i	−0.710493	+	0.596174i	−0.924737	−	0.380606i	$-0.875715\pi$
$223$	−2.62380e10	+	2.20163e10i	−0.710493	+	0.596174i	0.214245	+	0.976780i	$0.431271\pi$
$224$	−7.82185e9	−	1.35478e10i	−0.207584	−	0.359546i
$225$	−1.88308e10	+	1.26791e10i	−0.489832	+	0.329813i
$226$	−6.01829e9	+	1.04240e10i	−0.153456	+	0.265794i
$227$	−2.23809e9	−	1.26928e10i	−0.0559449	−	0.317279i	0.943974	−	0.330020i	$-0.107055\pi$
$227$	−2.23809e9	−	1.26928e10i	−0.0559449	−	0.317279i	−0.999919	+	0.0127408i	$0.995944\pi$
$228$	−4.52673e10	−	1.48280e11i	−1.10937	−	3.63391i
$229$	4.45170e10	−	1.62029e10i	1.06971	−	0.389343i	0.253642	−	0.967298i	$-0.418372\pi$
$229$	4.45170e10	−	1.62029e10i	1.06971	−	0.389343i	0.816068	+	0.577956i	$0.196149\pi$
$230$	4.72623e10	−	1.72021e10i	1.11363	−	0.405327i
$231$	−1.11360e10	−	2.57576e9i	−0.257322	−	0.0595184i
$232$	−3.52834e9	−	2.00102e10i	−0.0799604	−	0.453478i
$233$	−7.99493e8	+	1.38476e9i	−0.0177710	+	0.0307803i	−0.874774	−	0.484531i	$-0.838990\pi$
$233$	−7.99493e8	+	1.38476e9i	−0.0177710	+	0.0307803i	0.857003	+	0.515311i	$0.172324\pi$
$234$	−7.46400e10	+	1.02556e11i	−1.62742	+	2.23610i
$235$	−7.20713e9	−	1.24831e10i	−0.154155	−	0.267004i
$236$	1.43828e11	−	1.20686e11i	3.01813	−	2.53251i
$237$	2.09233e10	−	2.56036e9i	0.430786	−	0.0527149i
$238$	1.71705e7	−	9.73787e7i	0.000346886	−	0.00196729i
$239$	−4.63942e10	−	3.89294e10i	−0.919758	−	0.771769i	0.0541922	−	0.998531i	$-0.482742\pi$
$239$	−4.63942e10	−	3.89294e10i	−0.919758	−	0.771769i	−0.973950	+	0.226762i	$0.927186\pi$
$240$	1.70523e11	−	8.67979e10i	3.31767	−	1.68872i
$241$	1.08729e10	+	3.95741e9i	0.207619	+	0.0755673i	0.443736	−	0.896157i	$-0.353653\pi$
$241$	1.08729e10	+	3.95741e9i	0.207619	+	0.0755673i	−0.236117	+	0.971725i	$0.575875\pi$
$242$	1.83342e11			3.43632
$243$	3.83550e10	+	3.85124e10i	0.705658	+	0.708553i
$244$	−2.25880e11			−4.07966
$245$	−6.51838e10	−	2.37250e10i	−1.15583	−	0.420686i
$246$	−6.75099e10	+	3.43632e10i	−1.17533	+	0.598254i
$247$	9.80145e10	+	8.22439e10i	1.67554	+	1.40594i
$248$	−1.06508e10	+	6.04036e10i	−0.178792	+	1.01398i
$249$	−6.20220e10	+	7.58957e9i	−1.02247	+	0.125118i
$250$	4.60354e10	−	3.86283e10i	0.745353	−	0.625425i
$251$	−3.03010e10	−	5.24829e10i	−0.481865	−	0.834615i	0.517918	−	0.855430i	$-0.326707\pi$
$251$	−3.03010e10	−	5.24829e10i	−0.481865	−	0.834615i	−0.999783	+	0.0208153i	$0.993374\pi$
$252$	1.50972e10	−	2.07437e10i	0.235827	−	0.324029i
$253$	−2.73095e10	+	4.73014e10i	−0.419055	+	0.725824i
$254$	1.13901e10	+	6.45964e10i	0.171702	+	0.973771i
$255$	5.59657e8	+	1.29448e8i	0.00828880	+	0.00191719i
$256$	−1.20513e10	+	4.38632e9i	−0.175370	+	0.0638294i
$257$	1.60778e9	−	5.85185e8i	0.0229894	−	0.00836746i	−0.330500	−	0.943806i	$-0.607217\pi$
$257$	1.60778e9	−	5.85185e8i	0.0229894	−	0.00836746i	0.353489	+	0.935439i	$0.384995\pi$
$258$	1.35573e10	+	4.44090e10i	0.190496	+	0.623997i
$259$	3.12268e8	+	1.77096e9i	0.00431200	+	0.0244546i
$260$	−1.73908e11	+	3.01218e11i	−2.36015	+	4.08791i
$261$	9.80642e9	−	6.60284e9i	0.130806	−	0.0880741i
$262$	−1.22165e11	−	2.11596e11i	−1.60173	−	2.77428i
$263$	−6.87309e10	+	5.76721e10i	−0.885832	+	0.743301i	−0.967370	−	0.253369i	$-0.918461\pi$
$263$	−6.87309e10	+	5.76721e10i	−0.885832	+	0.743301i	0.0815380	+	0.996670i	$0.474017\pi$
$264$	−1.51470e11	+	3.56434e11i	−1.91915	+	4.51608i
$265$	3.21650e9	−	1.82417e10i	0.0400661	−	0.227226i
$266$	−2.76000e10	−	2.31592e10i	−0.338020	−	0.283632i
$267$	−4.65467e10	−	3.02549e10i	−0.560516	−	0.364330i
$268$	2.69862e11	+	9.82216e10i	3.19547	+	1.16306i
$269$	−8.91050e10			−1.03757			−0.518785	−	0.854905i	$-0.673615\pi$
$269$	−8.91050e10			−1.03757			−0.518785	+	0.854905i	$0.673615\pi$
$270$	1.61094e11	+	1.30780e11i	1.84478	+	1.49763i
$271$	6.02821e9			0.0678933			0.0339466	−	0.999424i	$-0.489192\pi$
$271$	6.02821e9			0.0678933			0.0339466	+	0.999424i	$0.489192\pi$
$272$	−1.68918e9	−	6.14813e8i	−0.0187119	−	0.00681056i
$273$	−1.11679e9	+	2.11440e10i	−0.0121686	+	0.230386i
$274$	1.07058e11	+	8.98324e10i	1.14747	+	0.962843i
$275$	1.63426e10	−	9.26836e10i	0.172316	−	0.977250i
$276$	−7.37412e10	−	9.79413e10i	−0.764926	−	1.01596i
$277$	−1.80353e10	+	1.51334e10i	−0.184062	+	0.154446i	−0.730163	−	0.683273i	$-0.760556\pi$
$277$	−1.80353e10	+	1.51334e10i	−0.184062	+	0.154446i	0.546101	+	0.837719i	$0.316111\pi$
$278$	−6.25134e10	−	1.08276e11i	−0.627728	−	1.08726i
$279$	−3.46338e10	+	8.60506e9i	−0.342201	+	0.0850227i
$280$	2.97655e10	−	5.15554e10i	0.289403	−	0.501260i
$281$	−2.54330e10	−	1.44238e11i	−0.243344	−	1.38007i	−0.824308	−	0.566141i	$-0.808436\pi$
$281$	−2.54330e10	−	1.44238e11i	−0.243344	−	1.38007i	0.580964	−	0.813929i	$-0.302676\pi$
$282$	−3.33747e10	+	3.57606e10i	−0.314265	+	0.336731i
$283$	−8.02665e10	+	2.92146e10i	−0.743867	+	0.270746i	−0.686023	−	0.727580i	$-0.740645\pi$
$283$	−8.02665e10	+	2.92146e10i	−0.743867	+	0.270746i	−0.0578445	+	0.998326i	$0.518423\pi$
$284$	1.68384e11	−	6.12868e10i	1.53592	−	0.559029i
$285$	1.42809e11	−	1.53019e11i	1.28220	−	1.37386i
$286$	−9.13127e10	−	5.17860e11i	−0.807019	−	4.57683i
$287$	−6.32259e9	+	1.09511e10i	−0.0550081	+	0.0952768i
$288$	−2.14052e11	−	2.22021e11i	−1.83339	−	1.90164i
$289$	5.92912e10	+	1.02695e11i	0.499977	+	0.865986i
$290$	3.45727e10	−	2.90099e10i	0.287040	−	0.240855i
$291$	1.17521e11	+	1.56088e11i	0.960720	+	1.27600i
$292$	2.98980e10	−	1.69560e11i	0.240669	−	1.36490i
$293$	1.62983e11	+	1.36759e11i	1.29193	+	1.08406i	0.991480	+	0.130259i	$0.0415807\pi$
$293$	1.62983e11	+	1.36759e11i	1.29193	+	1.08406i	0.300448	+	0.953798i	$0.402864\pi$
$294$	−1.24160e10	+	2.35071e11i	−0.0969216	+	1.83500i
$295$	2.38192e11	+	8.66946e10i	1.83116	+	0.666489i
$296$	6.09311e10			0.461346
$297$	−2.25303e11	+	3.65592e9i	−1.68021	+	0.0272642i
$298$	2.42466e10			0.178106
$299$	9.50768e10	+	3.46051e10i	0.687946	+	0.250392i
$300$	1.77120e11	+	1.15126e11i	1.26247	+	0.820594i
$301$	5.93750e9	+	4.98216e9i	0.0416922	+	0.0349839i
$302$	4.92814e10	−	2.79489e11i	0.340920	−	1.93345i
$303$	−9.92415e7	+	2.33532e8i	−0.000676397	+	0.00159168i
$304$	−5.01751e11	+	4.21019e11i	−3.36944	+	2.82729i
$305$	−1.52475e11	−	2.64095e11i	−1.00891	−	1.74748i
$306$	−1.34388e8	−	1.94471e9i	−0.000876220	−	0.0126797i
$307$	−1.08380e10	+	1.87720e10i	−0.0696348	+	0.120611i	−0.898741	−	0.438481i	$-0.855517\pi$
$307$	−1.08380e10	+	1.87720e10i	−0.0696348	+	0.120611i	0.829106	+	0.559092i	$0.188850\pi$
$308$	1.84695e10	+	1.04746e11i	0.116944	+	0.663220i
$309$	−7.12183e10	−	2.33286e11i	−0.444404	−	1.45571i
$310$	−1.28019e11	+	4.65952e10i	−0.787314	+	0.286559i
$311$	1.04569e11	−	3.80599e10i	0.633841	−	0.230699i	−0.00506132	−	0.999987i	$-0.501611\pi$
$311$	1.04569e11	−	3.80599e10i	0.633841	−	0.230699i	0.638902	+	0.769288i	$0.279389\pi$
$312$	6.98968e11	+	1.61671e11i	4.17601	+	0.965909i
$313$	−2.97901e10	−	1.68948e11i	−0.175438	−	0.994956i	−0.937637	−	0.347615i	$-0.886992\pi$
$313$	−2.97901e10	−	1.68948e11i	−0.175438	−	0.994956i	0.762200	−	0.647342i	$-0.224119\pi$
$314$	−6.81643e10	+	1.18064e11i	−0.395707	+	0.685384i
$315$	3.44442e10	+	3.64875e9i	0.197115	+	0.0208808i
$316$	−9.80762e10	−	1.69873e11i	−0.553314	−	0.958368i
$317$	−1.57795e11	+	1.32406e11i	−0.877663	+	0.736447i	−0.965697	−	0.259671i	$-0.916386\pi$
$317$	−1.57795e11	+	1.32406e11i	−0.877663	+	0.736447i	0.0880341	+	0.996117i	$0.471942\pi$
$318$	−6.23930e10	+	7.63497e9i	−0.342148	+	0.0418683i
$319$	−8.51066e9	+	4.82664e10i	−0.0460156	+	0.260968i
$320$	−3.66968e11	−	3.07923e11i	−1.95638	−	1.64160i
$321$	1.20103e11	−	6.11335e10i	0.631364	−	0.321371i
$322$	−2.67728e10	−	9.74451e9i	−0.138785	−	0.0505136i
$323$	−1.96636e9			−0.0100520
$324$	1.90238e11	−	4.68644e11i	0.959056	−	2.36260i
$325$	−1.74340e11			−0.866806
$326$	4.86136e11	+	1.76939e11i	2.38385	+	0.867650i
$327$	1.92295e11	−	9.78802e10i	0.930044	−	0.473402i
$328$	3.28217e11	+	2.75406e11i	1.56577	+	1.31384i
$329$	−1.41789e9	+	8.04125e9i	−0.00667207	+	0.0378392i
$330$	−8.53846e11	+	1.04484e11i	−3.96339	+	0.484996i
$331$	2.39457e11	−	2.00929e11i	1.09648	−	0.920060i	0.0993006	−	0.995057i	$-0.468339\pi$
$331$	2.39457e11	−	2.00929e11i	1.09648	−	0.920060i	0.997184	+	0.0749980i	$0.0238950\pi$
$332$	2.90723e11	+	5.03548e11i	1.31328	+	2.27467i
$333$	1.43929e10	+	3.23984e10i	0.0641431	+	0.144386i
$334$	−4.90031e10	+	8.48758e10i	−0.215459	+	0.373185i
$335$	6.73251e10	+	3.81820e11i	0.292062	+	1.65637i
$336$	−1.05602e11	−	2.44258e10i	−0.452009	−	0.104549i
$337$	−5.06360e10	+	1.84300e10i	−0.213858	+	0.0778379i	−0.446728	−	0.894670i	$-0.647411\pi$
$337$	−5.06360e10	+	1.84300e10i	−0.213858	+	0.0778379i	0.232870	+	0.972508i	$0.425188\pi$
$338$	−4.90531e11	+	1.78539e11i	−2.04428	+	0.744058i
$339$	1.15655e10	+	3.78844e10i	0.0475625	+	0.155798i
$340$	−9.28211e8	−	5.26414e9i	−0.00376696	−	0.0213635i
$341$	7.39731e10	−	1.28125e11i	0.296264	−	0.513145i
$342$	−6.38146e11	−	3.11891e11i	−2.52233	−	1.23278i
$343$	3.97923e10	+	6.89222e10i	0.155230	+	0.268866i
$344$	2.01180e11	−	1.68810e11i	0.774590	−	0.649959i
$345$	6.47339e10	−	1.52330e11i	0.246006	−	0.578895i
$346$	−1.34264e11	+	7.61448e11i	−0.503636	+	2.85626i
$347$	5.54056e10	+	4.64908e10i	0.205150	+	0.172141i	0.739574	−	0.673075i	$-0.235027\pi$
$347$	5.54056e10	+	4.64908e10i	0.205150	+	0.172141i	−0.534424	+	0.845216i	$0.679471\pi$
$348$	−9.22379e10	−	5.99537e10i	−0.337134	−	0.219134i
$349$	−3.57222e11	−	1.30018e11i	−1.28891	−	0.469126i	−0.395543	−	0.918447i	$-0.629444\pi$
$349$	−3.57222e11	−	1.30018e11i	−1.28891	−	0.469126i	−0.893370	+	0.449321i	$0.851666\pi$
$350$	4.90927e10			0.174868
$351$	7.91437e10	+	4.09846e11i	0.278314	+	1.44125i
$352$	1.27854e12			4.43886
$353$	−3.20853e11	−	1.16781e11i	−1.09982	−	0.400300i	−0.272567	−	0.962137i	$-0.587873\pi$
$353$	−3.20853e11	−	1.16781e11i	−1.09982	−	0.400300i	−0.827248	+	0.561836i	$0.810095\pi$
$354$	4.53701e10	−	8.58986e11i	0.153552	−	2.90718i
$355$	1.85319e11	+	1.55501e11i	0.619289	+	0.519645i
$356$	−8.97057e10	+	5.08746e11i	−0.296002	+	1.67871i
$357$	−1.95725e8	−	2.59957e8i	−0.000637733	−	0.000847022i
$358$	−2.79507e11	+	2.34534e11i	−0.899329	+	0.754626i
$359$	6.98481e10	+	1.20980e11i	0.221937	+	0.384406i	0.955396	−	0.295328i	$-0.0954288\pi$
$359$	6.98481e10	+	1.20980e11i	0.221937	+	0.384406i	−0.733459	+	0.679733i	$0.762095\pi$
$360$	3.24412e11	−	1.12787e12i	1.01797	−	3.53915i
$361$	−1.96897e11	+	3.41036e11i	−0.610179	+	1.05686i
$362$	−1.33561e11	−	7.57465e11i	−0.408783	−	2.31832i
$363$	4.11664e11	−	4.41094e11i	1.24441	−	1.33337i
$364$	1.85147e11	−	6.73878e10i	0.552789	−	0.201199i
$365$	2.18429e11	−	7.95016e10i	0.644157	−	0.234454i
$366$	−7.06081e11	+	7.56558e11i	−2.05679	+	2.20383i
$367$	−3.15129e10	−	1.78719e11i	−0.0906758	−	0.514248i	−0.995987	−	0.0894991i	$-0.971473\pi$
$367$	−3.15129e10	−	1.78719e11i	−0.0906758	−	0.514248i	0.905311	−	0.424749i	$-0.139638\pi$
$368$	−2.58975e11	+	4.48557e11i	−0.736109	+	1.27498i
$369$	−6.89094e10	+	2.39575e11i	−0.193491	+	0.672703i
$370$	6.76687e10	+	1.17206e11i	0.187707	+	0.325118i
$371$	−8.03797e9	+	6.74466e9i	−0.0220274	+	0.0184832i
$372$	1.99743e11	+	2.65294e11i	0.540789	+	0.718263i
$373$	1.97145e9	−	1.11806e10i	0.00527346	−	0.0299073i	−0.982057	−	0.188582i	$-0.939611\pi$
$373$	1.97145e9	−	1.11806e10i	0.00527346	−	0.0299073i	0.987331	+	0.158675i	$0.0507220\pi$
$374$	6.19071e9	+	5.19462e9i	0.0163613	+	0.0137288i
$375$	1.04309e10	−	1.97487e11i	0.0272385	−	0.515702i
$376$	2.59980e11	+	9.46248e10i	0.670801	+	0.244152i
$377$	9.07902e10			0.231474
$378$	−2.22862e10	−	1.15409e11i	−0.0561465	−	0.290755i
$379$	−2.31369e11			−0.576009			−0.288005	−	0.957629i	$-0.592992\pi$
$379$	−2.31369e11			−0.576009			−0.288005	+	0.957629i	$0.592992\pi$
$380$	−1.83023e12	−	6.66149e11i	−4.50276	−	1.63887i
$381$	1.80984e11	+	1.17638e11i	0.440025	+	0.286012i
$382$	−7.72061e11	−	6.47836e11i	−1.85510	−	1.55661i
$383$	−2.86847e10	+	1.62679e11i	−0.0681170	+	0.386310i	0.931621	+	0.363431i	$0.118395\pi$
$383$	−2.86847e10	+	1.62679e11i	−0.0681170	+	0.386310i	−0.999738	+	0.0228798i	$0.992716\pi$
$384$	−1.95614e11	+	4.60313e11i	−0.459101	+	1.08035i
$385$	−1.09999e11	+	9.23004e10i	−0.255163	+	0.214107i
$386$	−1.82348e11	−	3.15836e11i	−0.418079	−	0.724134i
$387$	1.37282e11	+	6.70961e10i	0.311110	+	0.152054i
$388$	9.09065e11	−	1.57455e12i	2.03635	−	3.52706i
$389$	1.27432e11	+	7.22702e11i	0.282166	+	1.60024i	0.715236	+	0.698883i	$0.246319\pi$
$389$	1.27432e11	+	7.22702e11i	0.282166	+	1.60024i	−0.433069	+	0.901361i	$0.642569\pi$
$390$	4.65271e11	+	1.52406e12i	1.01839	+	3.33590i
$391$	−1.46117e9	+	5.31822e8i	−0.00316159	+	0.00115072i
$392$	1.25112e12	−	4.55372e11i	2.67617	−	0.974045i
$393$	−7.83367e11	−	1.81192e11i	−1.65653	−	0.383154i
$394$	1.83222e11	+	1.03910e12i	0.383040	+	2.17233i
$395$	1.32408e11	−	2.29338e11i	0.273671	−	0.474012i
$396$	8.51286e11	+	1.91624e12i	1.73959	+	3.91581i
$397$	−3.38008e11	−	5.85447e11i	−0.682920	−	1.18285i	−0.974086	−	0.226179i	$-0.927377\pi$
$397$	−3.38008e11	−	5.85447e11i	−0.682920	−	1.18285i	0.291166	−	0.956673i	$-0.405957\pi$
$398$	−6.98534e11	+	5.86140e11i	−1.39545	+	1.17092i
$399$	−1.17689e11	+	1.44015e10i	−0.232465	+	0.0284465i
$400$	1.54976e11	−	8.78915e11i	0.302688	−	1.71663i
$401$	3.73280e11	+	3.13219e11i	0.720917	+	0.604921i	0.927639	−	0.373479i	$-0.121835\pi$
$401$	3.73280e11	+	3.13219e11i	0.720917	+	0.604921i	−0.206722	+	0.978400i	$0.566280\pi$
$402$	1.17254e12	−	5.96836e11i	2.23930	−	1.13982i
$403$	−2.57535e11	−	9.37349e10i	−0.486366	−	0.177023i
$404$	2.36120e9			0.00440978
$405$	6.76346e11	−	9.39252e10i	1.24917	−	0.173474i
$406$	−2.55657e10			−0.0466972
$407$	−1.38108e11	−	5.02671e10i	−0.249484	−	0.0908048i
$408$	−9.82589e9	+	5.00147e9i	−0.0175550	+	0.00893567i
$409$	2.10060e11	+	1.76262e11i	0.371184	+	0.311461i	0.809230	−	0.587492i	$-0.199885\pi$
$409$	2.10060e11	+	1.76262e11i	0.371184	+	0.311461i	−0.438046	+	0.898953i	$0.644329\pi$
$410$	−1.65255e11	+	9.37209e11i	−0.288820	+	1.63798i
$411$	4.56504e11	−	5.58620e10i	0.789144	−	0.0965668i
$412$	−1.73872e12	+	1.45896e12i	−2.97298	+	2.49462i
$413$	−7.17943e10	−	1.24351e11i	−0.121427	−	0.210317i
$414$	−5.58551e11	−	5.91684e10i	−0.934461	−	0.0989894i
$415$	−3.92493e11	+	6.79818e11i	−0.649554	+	1.12506i
$416$	−4.11272e11	−	2.33244e12i	−0.673302	−	3.81848i
$417$	−4.00860e11	−	9.27186e10i	−0.649202	−	0.150160i
$418$	2.76704e12	−	1.00712e12i	4.43325	−	1.61357i
$419$	8.32453e11	−	3.02988e11i	1.31946	−	0.480244i	0.416175	−	0.909285i	$-0.363370\pi$
$419$	8.32453e11	−	3.02988e11i	1.31946	−	0.480244i	0.903285	+	0.429040i	$0.141148\pi$
$420$	−9.41087e10	−	3.08267e11i	−0.147573	−	0.483398i
$421$	−9.22583e10	−	5.23223e11i	−0.143132	−	0.811741i	−0.968848	−	0.247655i	$-0.920340\pi$
$421$	−9.22583e10	−	5.23223e11i	−0.143132	−	0.811741i	0.825716	−	0.564085i	$-0.190771\pi$
$422$	8.92805e11	−	1.54638e12i	1.37041	−	2.37362i
$423$	1.10973e10	+	1.60589e11i	0.0168534	+	0.243884i
$424$	1.77764e11	+	3.07896e11i	0.267114	+	0.462656i
$425$	2.05247e9	−	1.72223e9i	0.00305159	−	0.00256059i
$426$	3.21081e11	−	7.55558e11i	0.472357	−	1.11154i
$427$	−2.99971e10	+	1.70122e11i	−0.0436671	+	0.247648i
$428$	−9.60665e11	−	8.06094e11i	−1.38381	−	1.16115i
$429$	−1.45092e12	−	9.43082e11i	−2.06817	−	1.34429i
$430$	5.48145e11	+	1.99508e11i	0.773192	+	0.281419i
$431$	−8.61984e11			−1.20324			−0.601619	−	0.798783i	$-0.705477\pi$
$431$	−8.61984e11			−1.20324			−0.601619	+	0.798783i	$0.705477\pi$
$432$	−2.13654e12	+	3.46689e10i	−2.95144	+	0.0478921i
$433$	2.19871e11			0.300589			0.150294	−	0.988641i	$-0.451978\pi$
$433$	2.19871e11			0.300589			0.150294	+	0.988641i	$0.451978\pi$
$434$	7.25195e10	+	2.63950e10i	0.0981186	+	0.0357122i
$435$	7.83366e9	−	1.48313e11i	0.0104897	−	0.198600i
$436$	−1.53811e12	−	1.29063e12i	−2.03844	−	1.71046i
$437$	−9.83848e10	+	5.57968e11i	−0.129051	+	0.731885i
$438$	−4.74462e11	−	6.30169e11i	−0.615982	−	0.818132i
$439$	8.51495e11	−	7.14489e11i	1.09419	−	0.918132i	0.0971668	−	0.995268i	$-0.469022\pi$
$439$	8.51495e11	−	7.14489e11i	1.09419	−	0.918132i	0.997021	+	0.0771358i	$0.0245775\pi$
$440$	2.43269e12	+	4.21355e12i	3.09422	+	5.35934i
$441$	5.37667e11	+	5.57684e11i	0.676924	+	0.702125i
$442$	7.48518e9	−	1.29647e10i	0.00932829	−	0.0161571i
$443$	2.33387e10	+	1.32360e11i	0.0287911	+	0.163283i	0.995813	−	0.0914091i	$-0.0291371\pi$
$443$	2.33387e10	+	1.32360e11i	0.0287911	+	0.163283i	−0.967022	+	0.254692i	$0.918026\pi$
$444$	2.25085e11	−	2.41176e11i	0.274867	−	0.294517i
$445$	−6.55371e11	+	2.38536e11i	−0.792259	+	0.288359i
$446$	1.37215e12	−	4.99423e11i	1.64208	−	0.597670i
$447$	5.44417e10	−	5.83337e10i	0.0644983	−	0.0691092i
$448$	4.71220e10	+	2.67242e11i	0.0552679	+	0.313440i
$449$	3.17493e11	−	5.49914e11i	0.368660	−	0.638537i	−0.620697	−	0.784051i	$-0.713150\pi$
$449$	3.17493e11	−	5.49914e11i	0.368660	−	0.638537i	0.989356	+	0.145514i	$0.0464834\pi$
$450$	9.39262e11	−	2.33368e11i	1.07977	−	0.268277i
$451$	−5.16737e11	−	8.95014e11i	−0.588132	−	1.01867i
$452$	2.82358e11	−	2.36927e11i	0.318183	−	0.266988i
$453$	−5.61754e11	−	7.46108e11i	−0.626765	−	0.832453i
$454$	−9.54148e10	+	5.41124e11i	−0.105406	+	0.597786i
$455$	2.03768e11	+	1.70982e11i	0.222887	+	0.187024i
$456$	−2.11896e11	+	4.01179e12i	−0.229499	+	4.34507i
$457$	6.05693e11	+	2.20454e11i	0.649575	+	0.236426i	0.645729	−	0.763567i	$-0.276554\pi$
$457$	6.05693e11	+	2.20454e11i	0.649575	+	0.236426i	0.00384599	+	0.999993i	$0.498776\pi$
$458$	−2.01966e12			−2.14479
$459$	−4.98043e9	−	4.04321e9i	−0.00523732	−	0.00425176i
$460$	−1.54018e12			−1.60384
$461$	1.04273e10	+	3.79522e9i	0.0107527	+	0.00391366i	0.347391	−	0.937720i	$-0.387068\pi$
$461$	1.04273e10	+	3.79522e9i	0.0107527	+	0.00391366i	−0.336638	+	0.941634i	$0.609290\pi$
$462$	4.08566e11	+	2.65564e11i	0.417228	+	0.271194i
$463$	1.23850e12	+	1.03922e12i	1.25251	+	1.05098i	0.996439	+	0.0843199i	$0.0268718\pi$
$463$	1.23850e12	+	1.03922e12i	1.25251	+	1.05098i	0.256069	+	0.966659i	$0.417573\pi$
$464$	−8.07063e10	+	4.57708e11i	−0.0808307	+	0.458414i
$465$	−1.75345e11	+	4.12617e11i	−0.173922	+	0.409269i
$466$	5.22201e10	−	4.38179e10i	0.0512981	−	0.0430442i
$467$	3.91652e11	+	6.78361e11i	0.381044	+	0.659987i	0.991212	−	0.132285i	$-0.0422315\pi$
$467$	3.91652e11	+	6.78361e11i	0.381044	+	0.659987i	−0.610168	+	0.792272i	$0.708898\pi$
$468$	3.22197e12	−	2.16941e12i	3.10467	−	2.09043i
$469$	1.09814e11	−	1.90203e11i	0.104804	−	0.181526i
$470$	1.06709e11	+	6.05178e11i	0.100870	+	0.572061i
$471$	1.30993e11	+	4.29086e11i	0.122646	+	0.401745i
$472$	−4.57180e12	+	1.66400e12i	−4.23983	+	1.54317i
$473$	−5.95264e11	+	2.16658e11i	−0.546808	+	0.199022i
$474$	−8.75546e11	−	2.02513e11i	−0.796666	−	0.184268i
$475$	−1.69526e11	−	9.61430e11i	−0.152797	−	0.866555i
$476$	−1.51400e9	+	2.62232e9i	−0.00135174	+	0.00234129i
$477$	−1.21724e11	+	1.67251e11i	−0.107658	+	0.147923i
$478$	1.29098e12	+	2.23604e12i	1.13108	+	1.95909i
$479$	2.45539e11	−	2.06032e11i	0.213114	−	0.178824i	−0.529982	−	0.848009i	$-0.677801\pi$
$479$	2.45539e11	−	2.06032e11i	0.213114	−	0.178824i	0.743095	+	0.669185i	$0.233357\pi$
$480$	−3.84573e12	+	4.70598e11i	−3.30668	+	0.404636i
$481$	−4.72768e10	+	2.68120e11i	−0.0402712	+	0.228390i
$482$	−3.77878e11	−	3.17078e11i	−0.318890	−	0.267580i
$483$	−8.35577e10	+	4.25317e10i	−0.0698593	+	0.0355591i
$484$	−5.27584e12	−	1.92025e12i	−4.37006	−	1.59057i
$485$	2.45458e12			2.01437
$486$	−9.74999e11	−	2.10212e12i	−0.792759	−	1.70920i
$487$	−4.23287e11			−0.341000			−0.170500	−	0.985358i	$-0.554538\pi$
$487$	−4.23287e11			−0.341000			−0.170500	+	0.985358i	$0.554538\pi$
$488$	5.50018e12	+	2.00190e12i	4.39023	+	1.59791i
$489$	1.51722e12	−	7.72282e11i	1.19994	−	0.610782i
$490$	2.26541e12	+	1.90091e12i	1.77527	+	1.48963i
$491$	2.31973e11	−	1.31559e12i	0.180124	−	1.02153i	−0.751938	−	0.659234i	$-0.770881\pi$
$491$	2.31973e11	−	1.31559e12i	0.180124	−	1.02153i	0.932062	−	0.362300i	$-0.118008\pi$
$492$	2.30256e12	−	2.81763e11i	1.77161	−	0.216791i
$493$	−1.06885e9	+	8.96876e8i	−0.000814906	+	0.000683787i
$494$	−2.72738e12	−	4.72396e12i	−2.06051	−	3.56890i
$495$	−1.66579e12	+	2.28883e12i	−1.24709	+	1.71352i
$496$	7.01484e11	−	1.21501e12i	0.520416	−	0.901386i
$497$	−2.37967e10	−	1.34958e11i	−0.0174950	−	0.0992188i
$498$	2.59535e12	+	6.00302e11i	1.89088	+	0.437359i
$499$	−1.23408e12	+	4.49167e11i	−0.891024	+	0.324306i	−0.746650	−	0.665217i	$-0.768339\pi$
$499$	−1.23408e12	+	4.49167e11i	−0.891024	+	0.324306i	−0.144374	+	0.989523i	$0.546117\pi$
$500$	−1.72929e12	+	6.29409e11i	−1.23738	+	0.450368i
$501$	9.41701e10	+	3.08468e11i	0.0667795	+	0.218746i
$502$	4.48639e11	+	2.54436e12i	0.315304	+	1.78818i
$503$	2.42146e11	−	4.19410e11i	0.168664	−	0.292134i	−0.769286	−	0.638904i	$-0.779388\pi$
$503$	2.42146e11	−	4.19410e11i	0.168664	−	0.292134i	0.937950	+	0.346770i	$0.112721\pi$
$504$	−5.51460e11	+	3.71308e11i	−0.380695	+	0.256329i
$505$	1.59388e9	+	2.76068e9i	0.00109055	+	0.00188888i
$506$	1.78376e12	−	1.49675e12i	1.20965	−	1.01502i
$507$	−6.71867e11	+	1.58102e12i	−0.451593	+	1.06268i
$508$	3.48795e11	−	1.97812e12i	0.232372	−	1.31785i
$509$	−3.98331e11	−	3.34239e11i	−0.263035	−	0.220713i	0.501726	−	0.865027i	$-0.332699\pi$
$509$	−3.98331e11	−	3.34239e11i	−0.263035	−	0.220713i	−0.764761	+	0.644314i	$0.777143\pi$
$510$	−2.05331e10	−	1.33463e10i	−0.0134397	−	0.00873565i
$511$	−1.23734e11	−	4.50355e10i	−0.0802778	−	0.0292187i
$512$	−1.27852e12			−0.822228
$513$	−2.18321e12	+	8.34981e11i	−1.39177	+	0.532290i
$514$	−7.29425e10			−0.0460942
$515$	−2.87947e12	−	1.04804e12i	−1.80377	−	0.656517i
$516$	7.49969e10	−	1.41990e12i	0.0465714	−	0.881730i
$517$	−5.11211e11	−	4.28957e11i	−0.314697	−	0.264062i
$518$	1.33127e10	−	7.55003e10i	0.00812425	−	0.0460749i
$519$	1.53046e12	+	2.03272e12i	0.925910	+	1.22977i
$520$	6.90426e12	−	5.79336e12i	4.14097	−	3.47469i
$521$	1.53654e11	+	2.66136e11i	0.0913635	+	0.158246i	0.908085	−	0.418786i	$-0.137544\pi$
$521$	1.53654e11	+	2.66136e11i	0.0913635	+	0.158246i	−0.816722	+	0.577032i	$0.804211\pi$
$522$	−4.89135e11	+	1.21530e11i	−0.288344	+	0.0716416i
$523$	−2.84528e11	+	4.92818e11i	−0.166291	+	0.288024i	−0.937113	−	0.349026i	$-0.886512\pi$
$523$	−2.84528e11	+	4.92818e11i	−0.166291	+	0.288024i	0.770822	+	0.637050i	$0.219846\pi$
$524$	1.29924e12	+	7.36836e12i	0.752833	+	4.26953i
$525$	1.10229e11	−	1.18109e11i	0.0633257	−	0.0678528i
$526$	3.59437e12	−	1.30824e12i	2.04733	−	0.745166i
$527$	3.95787e9	−	1.44055e9i	0.00223519	−	0.000813541i
$528$	6.04421e12	−	6.47630e12i	3.38444	−	3.62639i
$529$	−2.34967e11	−	1.33256e12i	−0.130453	−	0.739839i
$530$	−3.94841e11	+	6.83884e11i	−0.217360	+	0.376479i
$531$	−1.96472e12	−	2.03786e12i	−1.07244	−	1.11237i
$532$	5.51657e11	+	9.55498e11i	0.298584	+	0.517163i
$533$	−1.46656e12	+	1.23059e12i	−0.787094	+	0.660450i
$534$	1.42357e12	+	1.89075e12i	0.757606	+	1.00623i
$535$	2.93995e11	−	1.66733e12i	0.155149	−	0.879892i
$536$	−5.70062e12	−	4.78339e12i	−2.98319	−	2.50319i
$537$	−6.33321e10	+	1.19906e12i	−0.0328654	+	0.622236i
$538$	3.56966e12	+	1.29925e12i	1.83699	+	0.668610i
$539$	−3.21150e12			−1.63892
$540$	−3.26591e12	−	5.45054e12i	−1.65285	−	2.75846i
$541$	1.15323e12			0.578798			0.289399	−	0.957209i	$-0.406545\pi$
$541$	1.15323e12			0.578798			0.289399	+	0.957209i	$0.406545\pi$
$542$	−2.41498e11	−	8.78981e10i	−0.120203	−	0.0437505i
$543$	−2.12223e12	−	1.37943e12i	−1.04760	−	0.680927i
$544$	2.78830e10	+	2.33966e10i	0.0136504	+	0.0114540i
$545$	4.70713e11	−	2.66954e12i	0.228545	−	1.29614i
$546$	3.53044e11	−	8.30774e11i	0.170005	−	0.400052i
$547$	2.48400e12	−	2.08432e12i	1.18634	−	0.995457i	0.186424	−	0.982469i	$-0.440310\pi$
$547$	2.48400e12	−	2.08432e12i	1.18634	−	0.995457i	0.999916	−	0.0129874i	$-0.00413413\pi$
$548$	−2.13983e12	−	3.70629e12i	−1.01360	−	1.75561i
$549$	2.34778e11	+	3.39744e12i	0.110301	+	1.59616i
$550$	−2.00614e12	+	3.47473e12i	−0.934821	+	1.61916i
$551$	8.82832e10	+	5.00679e11i	0.0408034	+	0.231407i
$552$	9.27576e11	+	3.03841e12i	0.425230	+	1.39290i
$553$	−1.40965e11	+	5.13070e10i	−0.0640985	+	0.0233299i
$554$	9.43179e11	−	3.43289e11i	0.425403	−	0.154834i
$555$	4.33917e11	+	1.00365e11i	0.194128	+	0.0449017i
$556$	6.64839e11	+	3.77049e12i	0.295039	+	1.67325i
$557$	−1.72217e12	+	2.98288e12i	−0.758101	+	1.31307i	0.185717	+	0.982603i	$0.440539\pi$
$557$	−1.72217e12	+	2.98288e12i	−0.758101	+	1.31307i	−0.943818	+	0.330466i	$0.892794\pi$
$558$	1.51295e12	+	1.60269e11i	0.660647	+	0.0699837i
$559$	5.86732e11	+	1.01625e12i	0.254148	+	0.440197i
$560$	−1.04312e12	+	8.75281e11i	−0.448216	+	0.376098i
$561$	2.63977e10	−	3.23026e9i	0.0112521	−	0.00137691i
$562$	−1.08427e12	+	6.14920e12i	−0.458484	+	2.60019i
$563$	3.09504e12	+	2.59705e12i	1.29831	+	1.08941i	0.990434	+	0.137985i	$0.0440627\pi$
$563$	3.09504e12	+	2.59705e12i	1.29831	+	1.08941i	0.307876	+	0.951426i	$0.400382\pi$
$564$	1.33493e12	−	6.79491e11i	0.555522	−	0.282766i
$565$	4.67610e11	+	1.70196e11i	0.193048	+	0.0702639i
$566$	3.64156e12			1.49147
$567$	−3.27696e11	−	2.05514e11i	−0.133152	−	0.0835061i
$568$	−4.64331e12			−1.87180
$569$	2.19892e12	+	8.00340e11i	0.879434	+	0.320088i	0.741981	−	0.670421i	$-0.233886\pi$
$569$	2.19892e12	+	8.00340e11i	0.879434	+	0.320088i	0.137453	+	0.990508i	$0.456108\pi$
$570$	−7.95231e12	+	4.04780e12i	−3.15541	+	1.60614i
$571$	1.90431e12	+	1.59791e12i	0.749679	+	0.629055i	0.935418	−	0.353544i	$-0.115023\pi$
$571$	1.90431e12	+	1.59791e12i	0.749679	+	0.629055i	−0.185739	+	0.982599i	$0.559468\pi$
$572$	−2.79624e12	+	1.58583e13i	−1.09217	+	6.19403i
$573$	−3.29213e12	+	4.02854e11i	−1.27579	+	0.156118i
$574$	4.12970e11	−	3.46523e11i	0.158787	−	0.133238i
$575$	−3.86001e11	−	6.68574e11i	−0.147260	−	0.255061i
$576$	2.17193e12	+	4.88900e12i	0.822137	+	1.85063i
$577$	1.65924e12	−	2.87388e12i	0.623185	−	1.07939i	−0.365704	−	0.930731i	$-0.619172\pi$
$577$	1.65924e12	−	2.87388e12i	0.623185	−	1.07939i	0.988889	−	0.148657i	$-0.0474949\pi$
$578$	−8.77870e11	−	4.97865e12i	−0.327156	−	1.85539i
$579$	−1.16928e12	−	2.70455e11i	−0.432381	−	0.100010i
$580$	−1.29870e12	+	4.72687e11i	−0.476521	+	0.173439i
$581$	4.17857e11	−	1.52087e11i	0.152137	−	0.0553733i
$582$	−2.43210e12	−	7.96669e12i	−0.878673	−	2.87822i
$583$	−1.48914e11	−	8.44535e11i	−0.0533861	−	0.302768i
$584$	−2.23077e12	+	3.86381e12i	−0.793592	+	1.37454i
$585$	4.71135e12	+	2.30266e12i	1.66320	+	0.812883i
$586$	−4.53522e12	−	7.85522e12i	−1.58876	−	2.75182i
$587$	2.03967e12	−	1.71149e12i	0.709068	−	0.594979i	−0.215269	−	0.976555i	$-0.569063\pi$
$587$	2.03967e12	−	1.71149e12i	0.709068	−	0.594979i	0.924338	+	0.381576i	$0.124618\pi$
$588$	2.81932e12	−	6.63434e12i	0.972626	−	2.28876i
$589$	2.66495e11	−	1.51137e12i	0.0912368	−	0.517430i
$590$	−8.27816e12	−	6.94620e12i	−2.81255	−	2.36001i
$591$	2.91131e12	+	1.89232e12i	0.981624	+	0.638046i
$592$	−1.30967e12	−	4.76680e11i	−0.438242	−	0.159507i
$593$	1.89596e12			0.629627			0.314813	−	0.949154i	$-0.398058\pi$
$593$	1.89596e12			0.629627			0.314813	+	0.949154i	$0.398058\pi$
$594$	9.07925e12	+	3.13872e12i	2.99234	+	1.03446i
$595$	−4.08797e9			−0.00133715
$596$	−6.97719e11	−	2.53949e11i	−0.226502	−	0.0824401i
$597$	−1.58278e11	+	2.99664e12i	−0.0509959	+	0.965497i
$598$	−3.30432e12	−	2.77265e12i	−1.05664	−	0.886626i
$599$	9.71267e11	−	5.50833e12i	0.308260	−	1.74823i	−0.299486	−	0.954101i	$-0.596815\pi$
$599$	9.71267e11	−	5.50833e12i	0.308260	−	1.74823i	0.607746	−	0.794131i	$-0.292074\pi$
$600$	−3.29254e12	−	4.37307e12i	−1.03717	−	1.37755i
$601$	2.05421e12	−	1.72368e12i	0.642258	−	0.538918i	−0.262453	−	0.964945i	$-0.584531\pi$
$601$	2.05421e12	−	1.72368e12i	0.642258	−	0.538918i	0.904711	+	0.426027i	$0.140087\pi$
$602$	−1.65219e11	−	2.86167e11i	−0.0512714	−	0.0888046i
$603$	1.19685e12	−	4.16106e12i	0.368648	−	1.28167i
$604$	−4.34536e12	+	7.52639e12i	−1.32849	+	2.30102i
$605$	−1.31622e12	−	7.46465e12i	−0.399419	−	2.26522i
$606$	7.38091e9	−	7.90856e9i	0.00222322	−	0.00238216i
$607$	−9.48426e11	+	3.45199e11i	−0.283566	+	0.103210i	−0.479888	−	0.877330i	$-0.659323\pi$
$607$	−9.48426e11	+	3.45199e11i	−0.283566	+	0.103210i	0.196321	+	0.980540i	$0.437100\pi$
$608$	1.24628e13	−	4.53607e12i	3.69869	−	1.34621i
$609$	−5.74035e10	+	6.15073e10i	−0.0169107	+	0.0181196i
$610$	2.25756e12	+	1.28033e13i	0.660169	+	3.74400i
$611$	−6.18104e11	+	1.07059e12i	−0.179422	+	0.310768i
$612$	−1.65010e10	+	5.73684e10i	−0.00475475	+	0.0165307i
$613$	1.49765e12	+	2.59401e12i	0.428389	+	0.741992i	0.996730	−	0.0808013i	$-0.0257479\pi$
$613$	1.49765e12	+	2.59401e12i	0.428389	+	0.741992i	−0.568341	+	0.822793i	$0.692415\pi$
$614$	7.07900e11	−	5.93999e11i	0.201008	−	0.168666i
$615$	1.88373e12	+	2.50192e12i	0.530983	+	0.705238i
$616$	4.78594e11	−	2.71424e12i	0.133923	−	0.759513i
$617$	4.11582e12	+	3.45359e12i	1.14334	+	0.959372i	0.999543	−	0.0302359i	$-0.00962586\pi$
$617$	4.11582e12	+	3.45359e12i	1.14334	+	0.959372i	0.143792	+	0.989608i	$0.454070\pi$
$618$	−5.48475e11	+	1.03842e13i	−0.151255	+	2.86368i
$619$	−5.17915e12	−	1.88506e12i	−1.41792	−	0.516079i	−0.484474	−	0.874806i	$-0.660989\pi$
$619$	−5.17915e12	−	1.88506e12i	−1.41792	−	0.516079i	−0.933443	+	0.358727i	$0.883211\pi$
$620$	4.17189e12			1.13389
$621$	−1.39648e12	+	1.21094e12i	−0.376810	+	0.326745i
$622$	−4.74412e12			−1.27086
$623$	3.71250e11	+	1.35124e11i	0.0987349	+	0.0359366i
$624$	−1.37590e13	−	8.94321e12i	−3.63292	−	2.36136i
$625$	−3.62884e12	−	3.04496e12i	−0.951279	−	0.798218i
$626$	−1.27002e12	+	7.20266e12i	−0.330542	+	1.87460i
$627$	3.78995e12	−	8.91840e12i	0.979330	−	2.30453i
$628$	3.19804e12	−	2.68348e12i	0.820476	−	0.688461i
$629$	−2.09206e9	−	3.62355e9i	−0.000532900	−	0.000923009i
$630$	−1.32668e12	−	6.48409e11i	−0.335531	−	0.163990i
$631$	−1.86766e12	+	3.23488e12i	−0.468992	+	0.812318i	−0.999372	−	0.0354419i	$-0.988716\pi$
$631$	−1.86766e12	+	3.23488e12i	−0.468992	+	0.812318i	0.530379	+	0.847760i	$0.322049\pi$
$632$	8.82626e11	+	5.00562e12i	0.220064	+	1.24805i
$633$	−1.71572e12	−	5.62010e12i	−0.424747	−	1.39132i
$634$	8.25212e12	−	3.00353e12i	2.02845	−	0.738295i
$635$	2.54823e12	−	9.27479e11i	0.621951	−	0.226372i
$636$	1.87538e12	+	4.33774e11i	0.454498	+	0.105125i
$637$	1.03305e12	+	5.85874e12i	0.248597	+	1.40986i
$638$	1.04473e12	−	1.80952e12i	0.249637	−	0.432384i
$639$	−1.09683e12	−	2.46895e12i	−0.260246	−	0.585812i
$640$	3.14167e12	+	5.44154e12i	0.740204	+	1.28207i
$641$	−2.83409e12	+	2.37809e12i	−0.663060	+	0.556374i	−0.911002	−	0.412401i	$-0.864690\pi$
$641$	−2.83409e12	+	2.37809e12i	−0.663060	+	0.556374i	0.247942	+	0.968775i	$0.420246\pi$
$642$	−5.70286e12	+	6.97854e11i	−1.32491	+	0.162128i
$643$	−7.86248e11	+	4.45903e12i	−0.181389	+	1.02871i	0.749119	+	0.662435i	$0.230477\pi$
$643$	−7.86248e11	+	4.45903e12i	−0.181389	+	1.02871i	−0.930508	+	0.366271i	$0.880634\pi$
$644$	6.68353e11	+	5.60814e11i	0.153116	+	0.128479i
$645$	1.71075e12	−	8.70790e11i	0.389196	−	0.198105i
$646$	7.87748e10	+	2.86717e10i	0.0177968	+	0.00647749i
$647$	7.61507e12			1.70846			0.854230	−	0.519896i	$-0.174029\pi$
$647$	7.61507e12			1.70846			0.854230	+	0.519896i	$0.174029\pi$
$648$	−8.78572e12	+	9.72546e12i	−1.95745	+	2.16682i
$649$	1.17353e13			2.59653
$650$	6.98429e12	+	2.54207e12i	1.53466	+	0.558570i
$651$	2.26333e11	−	1.15206e11i	0.0493893	−	0.0251396i
$652$	−1.21358e13	−	1.01832e13i	−2.62999	−	2.20683i
$653$	−5.58299e11	+	3.16627e12i	−0.120159	+	0.681457i	0.863906	+	0.503652i	$0.168011\pi$
$653$	−5.58299e11	+	3.16627e12i	−0.120159	+	0.681457i	−0.984066	+	0.177805i	$0.943100\pi$
$654$	−9.13080e12	+	1.11733e12i	−1.95168	+	0.238825i
$655$	−7.73794e12	+	6.49290e12i	−1.64263	+	1.37833i
$656$	−4.90019e12	−	8.48738e12i	−1.03311	−	1.78940i
$657$	−2.58141e12	−	2.73455e11i	−0.540522	−	0.0572586i
$658$	1.74053e11	−	3.01468e11i	0.0361963	−	0.0626939i
$659$	1.38988e12	+	7.88243e12i	0.287074	+	1.62808i	0.697780	+	0.716312i	$0.254171\pi$
$659$	1.38988e12	+	7.88243e12i	0.287074	+	1.62808i	−0.410706	+	0.911768i	$0.634718\pi$
$660$	2.56645e13	+	5.93619e12i	5.26484	+	1.21776i
$661$	5.79096e12	−	2.10774e12i	1.17990	−	0.429447i	0.323731	−	0.946149i	$-0.395063\pi$
$661$	5.79096e12	−	2.10774e12i	1.17990	−	0.429447i	0.856165	+	0.516702i	$0.172840\pi$
$662$	−1.25227e13	+	4.55791e12i	−2.53419	+	0.922368i
$663$	−1.43844e10	−	4.71183e10i	−0.00289122	−	0.00947062i
$664$	−2.61633e12	−	1.48380e13i	−0.522320	−	2.96222i
$665$	−7.44768e11	+	1.28998e12i	−0.147681	+	0.255790i
$666$	−1.04194e11	−	1.50779e12i	−0.0205215	−	0.296965i
$667$	2.01016e11	+	3.48170e11i	0.0393246	+	0.0681122i
$668$	2.29906e12	−	1.92914e12i	0.446742	−	0.374861i
$669$	1.87940e12	−	4.42256e12i	0.362746	−	0.853603i
$670$	2.87023e12	−	1.62779e13i	0.550275	−	3.12077i
$671$	−1.08153e13	−	9.07509e12i	−2.05962	−	1.72822i
$672$	1.84018e12	+	1.19610e12i	0.348096	+	0.226259i
$673$	−6.23701e12	−	2.27009e12i	−1.17195	−	0.426555i	−0.318597	−	0.947890i	$-0.603212\pi$
$673$	−6.23701e12	−	2.27009e12i	−1.17195	−	0.426555i	−0.853352	+	0.521336i	$0.825434\pi$
$674$	2.29728e12			0.428789
$675$	1.54751e12	−	2.78371e12i	0.286923	−	0.516127i
$676$	1.59854e13			2.94417
$677$	−1.99676e12	−	7.26760e11i	−0.365322	−	0.132966i	0.152835	−	0.988252i	$-0.451160\pi$
$677$	−1.99676e12	−	7.26760e11i	−0.365322	−	0.132966i	−0.518157	+	0.855285i	$0.673382\pi$
$678$	8.90693e10	−	1.68634e12i	0.0161880	−	0.306486i
$679$	−1.06515e12	−	8.93766e11i	−0.192308	−	0.161365i
$680$	−2.40525e10	+	1.36408e11i	−0.00431389	+	0.0244653i
$681$	1.08762e12	+	1.44456e12i	0.193784	+	0.257379i
$682$	−4.83167e12	+	4.05425e12i	−0.855200	+	0.717598i
$683$	1.76336e12	+	3.05423e12i	0.310062	+	0.537043i	0.978375	−	0.206837i	$-0.0663169\pi$
$683$	1.76336e12	+	3.05423e12i	0.310062	+	0.537043i	−0.668314	+	0.743880i	$0.732984\pi$
$684$	1.50966e13	+	1.56586e13i	2.63710	+	2.73528i
$685$	2.88889e12	−	5.00370e12i	0.501329	−	0.868328i
$686$	−5.89167e11	−	3.34133e12i	−0.101573	−	0.576051i
$687$	−4.53481e12	+	4.85900e12i	−0.776701	+	0.832227i
$688$	−5.64486e12	+	2.05456e12i	−0.960518	+	0.349600i
$689$	−1.49279e12	+	5.43330e11i	−0.252355	+	0.0918496i
$690$	−4.81447e12	+	5.15865e12i	−0.808588	+	0.866394i
$691$	−1.33168e11	−	7.55235e11i	−0.0222203	−	0.126017i	0.971680	−	0.236301i	$-0.0759352\pi$
$691$	−1.33168e11	−	7.55235e11i	−0.0222203	−	0.126017i	−0.993900	+	0.110284i	$0.964824\pi$
$692$	1.18386e13	−	2.05051e13i	1.96257	−	3.39927i
$693$	1.55627e12	−	3.86669e11i	0.256322	−	0.0636855i
$694$	−1.54173e12	−	2.67036e12i	−0.252285	−	0.436971i
$695$	−3.95961e12	+	3.32250e12i	−0.643755	+	0.540174i
$696$	1.71464e12	+	2.27734e12i	0.276969	+	0.367864i
$697$	5.10906e9	−	2.89749e10i	0.000819961	−	0.00465023i
$698$	1.24150e13	+	1.04174e13i	1.97968	+	1.66115i
$699$	1.18323e10	−	2.24019e11i	0.00187466	−	0.0354926i
$700$	−1.41269e12	−	5.14176e11i	−0.222384	−	0.0809413i
$701$	−3.18769e11			−0.0498592			−0.0249296	−	0.999689i	$-0.507936\pi$
$701$	−3.18769e11			−0.0498592			−0.0249296	+	0.999689i	$0.507936\pi$
$702$	2.80541e12	−	1.75730e13i	0.435993	−	2.73104i
$703$	−1.52457e12			−0.235422
$704$	−2.08408e13	−	7.58542e12i	−3.19769	−	1.16387i
$705$	1.69556e12	+	1.10210e12i	0.258501	+	0.168023i
$706$	1.11510e13	+	9.35679e12i	1.68924	+	1.41744i
$707$	3.13570e8	−	1.77835e9i	4.72006e−5	−	0.000267688i
$708$	−1.03022e13	+	2.42429e13i	−1.54092	+	3.62606i
$709$	−1.72238e12	+	1.44525e12i	−0.255989	+	0.214800i	−0.761746	−	0.647876i	$-0.775658\pi$
$709$	−1.72238e12	+	1.44525e12i	−0.255989	+	0.214800i	0.505757	+	0.862676i	$0.331213\pi$
$710$	−5.15675e12	−	8.93175e12i	−0.761576	−	1.31909i
$711$	−2.45311e12	+	1.65172e12i	−0.360000	+	0.242395i
$712$	6.69318e12	−	1.15929e13i	0.976051	−	1.69057i
$713$	−2.10737e11	−	1.19515e12i	−0.0305379	−	0.173189i
$714$	4.05053e9	+	1.32681e10i	0.000583270	+	0.00191059i
$715$	−2.04287e13	+	7.43546e12i	−2.92324	+	1.06397i
$716$	1.04995e13	−	3.82149e12i	1.49300	−	0.543406i
$717$	8.27825e12	+	1.91475e12i	1.16978	+	0.270568i
$718$	−1.03417e12	−	5.86510e12i	−0.145223	−	0.823598i
$719$	−1.90680e12	+	3.30267e12i	−0.266088	+	0.460878i	−0.967848	−	0.251536i	$-0.919064\pi$
$719$	−1.90680e12	+	3.30267e12i	−0.266088	+	0.460878i	0.701760	+	0.712413i	$0.252398\pi$
$720$	−1.57967e13	+	2.17048e13i	−2.19063	+	3.00996i
$721$	8.67913e11	+	1.50327e12i	0.119610	+	0.207171i
$722$	1.28606e13	−	1.07914e13i	1.76135	−	1.47795i
$723$	−1.61130e12	+	1.97174e11i	−0.219308	+	0.0268365i
$724$	−4.09001e12	+	2.31956e13i	−0.553224	+	3.13749i
$725$	−5.30668e11	−	4.45283e11i	−0.0713348	−	0.0598570i
$726$	−2.29234e13	+	1.16683e13i	−3.06242	+	1.55880i
$727$	6.62748e12	+	2.41221e12i	0.879921	+	0.320265i	0.742178	−	0.670203i	$-0.233793\pi$
$727$	6.62748e12	+	2.41221e12i	0.879921	+	0.320265i	0.137743	+	0.990468i	$0.456015\pi$
$728$	−5.10555e12			−0.673677
$729$	−7.24656e12	−	2.37424e12i	−0.950295	−	0.311352i
$730$	−9.90976e12			−1.29155
$731$	−1.69465e10	−	6.16804e9i	−0.00219509	−	0.000798949i
$732$	2.82420e13	−	1.43754e13i	3.63576	−	1.85064i
$733$	−9.21470e12	−	7.73205e12i	−1.17900	−	0.989298i	−0.999985	−	0.00545120i	$-0.998265\pi$
$733$	−9.21470e12	−	7.73205e12i	−1.17900	−	0.989298i	−0.179014	−	0.983847i	$-0.557291\pi$
$734$	−1.34347e12	+	7.61920e12i	−0.170842	+	0.968896i
$735$	9.65988e12	−	1.18207e12i	1.22090	−	0.149400i
$736$	8.03406e12	−	6.74138e12i	1.00922	−	0.846834i
$737$	8.97492e12	+	1.55450e13i	1.12054	+	1.94083i
$738$	6.25388e12	−	8.59292e12i	0.776061	−	1.06632i
$739$	−4.91227e11	+	8.50831e11i	−0.0605874	+	0.104941i	−0.894728	−	0.446611i	$-0.852631\pi$
$739$	−4.91227e11	+	8.50831e11i	−0.0605874	+	0.104941i	0.834141	+	0.551552i	$0.185964\pi$
$740$	−7.19666e11	−	4.08143e12i	−0.0882243	−	0.500345i
$741$	−1.74890e13	−	4.04519e12i	−2.13100	−	0.492898i
$742$	4.20356e11	−	1.52997e11i	0.0509096	−	0.0185296i
$743$	−1.24981e13	+	4.54895e12i	−1.50451	+	0.547598i	−0.957224	−	0.289347i	$-0.906562\pi$
$743$	−1.24981e13	+	4.54895e12i	−1.50451	+	0.547598i	−0.547288	+	0.836945i	$0.684340\pi$
$744$	−2.51253e12	−	8.23015e12i	−0.300630	−	0.984758i
$745$	−1.74067e11	−	9.87184e11i	−0.0207021	−	0.117407i
$746$	−2.42005e11	+	4.19165e11i	−0.0286088	+	0.0495519i
$747$	7.27164e12	−	4.89613e12i	0.854456	−	0.575321i
$748$	−1.23737e11	−	2.14319e11i	−0.0144525	−	0.0250324i
$749$	−7.34689e11	+	6.16477e11i	−0.0852973	+	0.0715729i
$750$	−3.29747e12	+	7.75951e12i	−0.380544	+	0.895486i
$751$	7.31937e11	−	4.15102e12i	0.0839641	−	0.476184i	−0.913611	−	0.406589i	$-0.866718\pi$
$751$	7.31937e11	−	4.15102e12i	0.0839641	−	0.476184i	0.997575	−	0.0695953i	$-0.0221708\pi$
$752$	−4.84779e12	−	4.06778e12i	−0.552794	−	0.463849i
$753$	7.12867e12	+	4.63356e12i	0.808037	+	0.525216i
$754$	−3.63717e12	−	1.32382e12i	−0.409820	−	0.149162i
$755$	−1.17330e13			−1.31416
$756$	−5.67440e11	+	3.55442e12i	−0.0631788	+	0.395749i
$757$	6.86528e12			0.759848			0.379924	−	0.925018i	$-0.375950\pi$
$757$	6.86528e12			0.759848			0.379924	+	0.925018i	$0.375950\pi$
$758$	9.26896e12	+	3.37362e12i	1.01981	+	0.371181i
$759$	4.04174e11	−	7.65216e12i	0.0442059	−	0.836943i
$760$	3.86622e13	+	3.24414e13i	4.20364	+	3.52727i
$761$	−2.54144e12	+	1.44132e13i	−0.274694	+	1.55787i	0.465238	+	0.885185i	$0.345969\pi$
$761$	−2.54144e12	+	1.44132e13i	−0.274694	+	1.55787i	−0.739932	+	0.672681i	$0.765142\pi$
$762$	−5.53515e12	−	7.35166e12i	−0.594747	−	0.789929i
$763$	−1.17630e12	+	9.87035e11i	−0.125649	+	0.105432i
$764$	1.54316e13	+	2.67283e13i	1.63867	+	2.83825i
$765$	−7.82128e10	+	1.94326e10i	−0.00825660	+	0.00205142i
$766$	3.52118e12	−	6.09887e12i	0.369538	−	0.640059i
$767$	−3.77494e12	−	2.14087e13i	−0.393850	−	2.23363i
$768$	1.22763e12	−	1.31539e12i	0.127334	−	0.136437i
$769$	−8.13618e12	+	2.96133e12i	−0.838981	+	0.305364i	−0.725539	−	0.688181i	$-0.758410\pi$
$769$	−8.13618e12	+	2.96133e12i	−0.838981	+	0.305364i	−0.113442	+	0.993545i	$0.536187\pi$
$770$	5.75256e12	−	2.09376e12i	0.589730	−	0.214644i
$771$	−1.63780e11	+	1.75488e11i	−0.0166923	+	0.0178856i
$772$	1.93930e12	+	1.09983e13i	0.196502	+	1.11442i
$773$	−8.24454e11	+	1.42800e12i	−0.0830536	+	0.143853i	−0.904560	−	0.426346i	$-0.859801\pi$
$773$	−8.24454e11	+	1.42800e12i	−0.0830536	+	0.143853i	0.821507	+	0.570199i	$0.193134\pi$
$774$	−4.52136e12	−	4.68968e12i	−0.452830	−	0.469688i
$775$	1.04556e12	+	1.81097e12i	0.104110	+	0.180324i
$776$	−3.60904e13	+	3.02834e13i	−3.57284	+	2.99797i
$777$	−1.51751e11	−	2.01551e11i	−0.0149361	−	0.0198377i
$778$	5.43272e12	−	3.08105e13i	0.531630	−	3.01502i
$779$	−8.21236e12	−	6.89099e12i	−0.799005	−	0.670445i
$780$	2.57380e12	−	4.87294e13i	0.248971	−	4.71374i
$781$	1.05246e13	+	3.83065e12i	1.01222	+	0.368419i
$782$	6.62909e10			0.00633904
$783$	−8.05887e11	+	1.44966e12i	−0.0766207	+	0.137828i
$784$	−3.04545e13			−2.87891
$785$	5.29624e12	+	1.92767e12i	0.497800	+	0.181184i
$786$	2.87407e13	+	1.86812e13i	2.68594	+	1.74583i
$787$	−8.82485e11	−	7.40493e11i	−0.0820013	−	0.0688073i	0.600866	−	0.799350i	$-0.294823\pi$
$787$	−8.82485e11	−	7.40493e11i	−0.0820013	−	0.0688073i	−0.682867	+	0.730543i	$0.739267\pi$
$788$	5.61074e12	−	3.18201e13i	0.518385	−	2.93990i
$789$	4.92312e12	−	1.15850e13i	0.452266	−	1.06426i
$790$	−8.64846e12	+	7.25692e12i	−0.789981	+	0.662873i
$791$	−1.40944e11	−	2.44123e11i	−0.0128013	−	0.0221725i
$792$	−3.74580e12	−	5.42051e13i	−0.338284	−	4.89527i
$793$	−1.30767e13	+	2.26496e13i	−1.17428	+	2.03390i
$794$	5.00457e12	+	2.83823e13i	0.446863	+	2.53428i
$795$	7.58773e11	+	2.48547e12i	0.0673690	+	0.220677i
$796$	2.62399e13	−	9.55056e12i	2.31662	−	0.843179i
$797$	2.00303e13	−	7.29044e12i	1.75843	−	0.640017i	0.758500	−	0.651673i	$-0.225933\pi$
$797$	2.00303e13	−	7.29044e12i	1.75843	−	0.640017i	0.999932	+	0.0116562i	$0.00371036\pi$
$798$	4.92475e12	+	1.13909e12i	0.429904	+	0.0994365i
$799$	−3.29904e9	−	1.87098e10i	−0.000286370	−	0.00162408i
$800$	−9.03565e12	+	1.56502e13i	−0.779928	+	1.35087i
$801$	7.74525e12	+	8.20470e11i	0.664797	+	0.0704233i
$802$	−1.03870e13	−	1.79908e13i	−0.886554	−	1.53556i
$803$	8.24388e12	−	6.91744e12i	0.699700	−	0.587118i
$804$	−3.99920e13	+	4.89379e12i	−3.37537	+	0.413041i
$805$	−2.04538e11	+	1.15999e12i	−0.0171669	+	0.0973584i
$806$	8.95041e12	+	7.51028e12i	0.747025	+	0.626828i
$807$	1.11409e13	−	5.67082e12i	0.924674	−	0.470668i
$808$	−5.74953e10	−	2.09266e10i	−0.00474549	−	0.00172722i
$809$	1.03932e13			0.853059			0.426530	−	0.904474i	$-0.359736\pi$
$809$	1.03932e13			0.853059			0.426530	+	0.904474i	$0.359736\pi$
$810$	−2.84648e13	−	6.09912e12i	−2.32341	−	0.497834i
$811$	1.57077e13			1.27503			0.637515	−	0.770438i	$-0.279963\pi$
$811$	1.57077e13			1.27503			0.637515	+	0.770438i	$0.279963\pi$
$812$	7.35677e11	+	2.67765e11i	0.0593862	+	0.0216148i
$813$	−7.53712e11	+	3.83647e11i	−0.0605059	+	0.0307981i
$814$	4.79982e12	+	4.02753e12i	0.383191	+	0.321535i
$815$	3.71396e12	−	2.10629e13i	0.294868	−	1.67228i
$816$	2.50328e11	−	3.06324e10i	0.0197653	−	0.00241866i
$817$	−5.03376e12	+	4.22383e12i	−0.395269	+	0.331670i
$818$	−5.84520e12	−	1.01242e13i	−0.456467	−	0.790625i
$819$	−1.20601e12	−	2.71473e12i	−0.0936645	−	0.210838i
$820$	1.45713e13	−	2.52382e13i	1.12547	−	1.94938i
$821$	−2.68395e12	−	1.52215e13i	−0.206173	−	1.16926i	−0.895584	−	0.444893i	$-0.853242\pi$
$821$	−2.68395e12	−	1.52215e13i	−0.206173	−	1.16926i	0.689411	−	0.724370i	$-0.257869\pi$
$822$	−1.91027e13	−	4.41844e12i	−1.45939	−	0.337556i
$823$	7.70324e12	−	2.80375e12i	0.585294	−	0.213030i	−0.0323644	−	0.999476i	$-0.510304\pi$
$823$	7.70324e12	−	2.80375e12i	0.585294	−	0.213030i	0.617658	+	0.786447i	$0.288081\pi$
$824$	5.52680e13	−	2.01159e13i	4.17639	−	1.52008i
$825$	3.85523e12	+	1.26284e13i	0.289740	+	0.949085i
$826$	1.06299e12	+	6.02852e12i	0.0794546	+	0.450610i
$827$	−9.10905e12	+	1.57773e13i	−0.677171	+	1.17289i	0.298658	+	0.954360i	$0.403461\pi$
$827$	−9.10905e12	+	1.57773e13i	−0.677171	+	1.17289i	−0.975829	+	0.218534i	$0.929872\pi$
$828$	1.54531e13	+	7.55265e12i	1.14256	+	0.558422i
$829$	2.04567e12	+	3.54320e12i	0.150432	+	0.260555i	0.931386	−	0.364033i	$-0.118600\pi$
$829$	2.04567e12	+	3.54320e12i	0.150432	+	0.260555i	−0.780955	+	0.624588i	$0.785267\pi$
$830$	2.56363e13	−	2.15114e13i	1.87501	−	1.57332i
$831$	1.29185e12	−	3.03994e12i	0.0939738	−	0.221137i
$832$	−7.13418e12	+	4.04599e13i	−0.516165	+	2.92732i
$833$	−7.00378e10	−	5.87687e10i	−0.00504000	−	0.00422906i
$834$	1.47070e13	+	9.55941e12i	1.05263	+	0.684201i
$835$	3.80745e12	+	1.38580e12i	0.271047	+	0.0986531i
$836$	−9.01723e13			−6.38476
$837$	3.78265e12	−	3.28006e12i	0.266398	−	0.231003i
$838$	−3.77670e13			−2.64554
$839$	−1.20843e13	−	4.39833e12i	−0.841964	−	0.306450i	−0.115205	−	0.993342i	$-0.536752\pi$
$839$	−1.20843e13	−	4.39833e12i	−0.841964	−	0.306450i	−0.726760	+	0.686892i	$0.758975\pi$
$840$	−4.40523e11	+	8.34035e12i	−0.0305289	+	0.577999i
$841$	−1.08368e13	−	9.09313e12i	−0.746995	−	0.626803i
$842$	−3.93319e12	+	2.23062e13i	−0.269675	+	1.52940i
$843$	1.23595e13	+	1.64156e13i	0.842901	+	1.11952i
$844$	−4.18874e13	+	3.51477e13i	−2.84147	+	2.38428i
$845$	1.07906e13	+	1.86899e13i	0.728099	+	1.26110i
$846$	1.89699e12	−	6.59520e12i	0.127320	−	0.442651i
$847$	−2.14688e12	+	3.71850e12i	−0.143328	+	0.248252i
$848$	−1.41215e12	−	8.00869e12i	−0.0937776	−	0.531839i
$849$	8.17651e12	−	8.76104e12i	0.540112	−	0.578724i
$850$	−1.07337e11	+	3.90673e10i	−0.00705282	+	0.00256702i
$851$	−1.13288e12	+	4.12336e11i	−0.0740461	+	0.0269506i
$852$	−1.71528e13	+	1.83790e13i	−1.11521	+	1.19493i
$853$	−3.58621e12	−	2.03384e13i	−0.231935	−	1.31537i	−0.848974	−	0.528434i	$-0.822779\pi$
$853$	−3.58621e12	−	2.03384e13i	−0.231935	−	1.31537i	0.617040	−	0.786932i	$-0.288332\pi$
$854$	3.68230e12	−	6.37792e12i	0.236896	−	0.410316i
$855$	−8.11717e12	+	2.82207e13i	−0.519466	+	1.80601i
$856$	1.62480e13	+	2.81424e13i	1.03435	+	1.79155i
$857$	−7.69826e12	+	6.45960e12i	−0.487505	+	0.409065i	−0.853131	−	0.521697i	$-0.825299\pi$
$857$	−7.69826e12	+	6.45960e12i	−0.487505	+	0.409065i	0.365626	+	0.930762i	$0.380855\pi$
$858$	4.43745e13	+	5.89371e13i	2.79538	+	3.71275i
$859$	−3.48683e12	+	1.97748e13i	−0.218505	+	1.23920i	0.656214	+	0.754575i	$0.272157\pi$
$859$	−3.48683e12	+	1.97748e13i	−0.218505	+	1.23920i	−0.874719	+	0.484630i	$0.838954\pi$
$860$	−1.36838e13	−	1.14821e13i	−0.853029	−	0.715776i
$861$	9.35729e10	−	1.77160e12i	0.00580278	−	0.109863i
$862$	3.45322e13	+	1.25687e13i	2.13030	+	0.775367i
$863$	−1.22213e13			−0.750013			−0.375006	−	0.927022i	$-0.622359\pi$
$863$	−1.22213e13			−0.750013			−0.375006	+	0.927022i	$0.622359\pi$
$864$	4.08930e13	+	1.41368e13i	2.49653	+	0.863055i
$865$	3.19657e13			1.94138
$866$	−8.80832e12	−	3.20597e12i	−0.532185	−	0.193699i
$867$	−1.39490e13	−	9.06669e12i	−0.838409	−	0.544958i
$868$	−1.81037e12	−	1.51908e12i	−0.108250	−	0.0908325i
$869$	2.12897e12	−	1.20740e13i	0.126643	−	0.718227i
$870$	−2.47640e12	+	5.82740e12i	−0.146550	+	0.344857i
$871$	2.54718e13	−	2.13734e13i	1.49961	−	1.25832i
$872$	2.60146e13	+	4.50586e13i	1.52368	+	2.63908i
$873$	−2.46275e13	−	1.20366e13i	−1.43501	−	0.701358i
$874$	1.20772e13	−	2.09184e13i	0.700109	−	1.21262i
$875$	2.44390e11	+	1.38600e12i	0.0140944	+	0.0799333i
$876$	7.05296e12	+	2.31030e13i	0.404672	+	1.32556i
$877$	2.78801e13	−	1.01475e13i	1.59146	−	0.579244i	0.613804	−	0.789459i	$-0.289639\pi$
$877$	2.78801e13	−	1.01475e13i	1.59146	−	0.579244i	0.977655	+	0.210215i	$0.0674164\pi$
$878$	−4.45300e13	+	1.62076e13i	−2.52888	+	0.920436i
$879$	−2.90815e13	−	6.72654e12i	−1.64311	−	0.380051i
$880$	−1.93252e13	−	1.09599e14i	−1.08631	−	6.16075i
$881$	7.06961e12	−	1.22449e13i	0.395370	−	0.684801i	−0.597778	−	0.801662i	$-0.703950\pi$
$881$	7.06961e12	−	1.22449e13i	0.395370	−	0.684801i	0.993148	+	0.116860i	$0.0372830\pi$
$882$	−1.34080e13	−	3.01813e13i	−0.746028	−	1.67930i
$883$	−1.68209e13	−	2.91347e13i	−0.931164	−	1.61282i	−0.781336	−	0.624111i	$-0.785461\pi$
$883$	−1.68209e13	−	2.91347e13i	−0.931164	−	1.61282i	−0.149828	−	0.988712i	$-0.547872\pi$
$884$	−3.51180e11	+	2.94675e11i	−0.0193417	+	0.0162296i
$885$	−3.52987e13	+	4.31947e12i	−1.93426	+	0.236693i
$886$	9.94981e11	−	5.64282e12i	0.0542454	−	0.307641i
$887$	−9.46668e12	−	7.94348e12i	−0.513501	−	0.430878i	0.348858	−	0.937176i	$-0.386569\pi$
$887$	−9.46668e12	−	7.94348e12i	−0.513501	−	0.430878i	−0.862359	+	0.506297i	$0.831014\pi$
$888$	−7.61827e12	+	3.87777e12i	−0.411148	+	0.209278i
$889$	−1.44350e12	−	5.25392e11i	−0.0775103	−	0.0282115i
$890$	2.97331e13			1.58849
$891$	2.79372e13	−	1.47958e13i	1.48502	−	0.786484i
$892$	−4.47157e13			−2.36493
$893$	−6.50499e12	−	2.36762e12i	−0.342306	−	0.124589i
$894$	−3.03158e12	+	1.54310e12i	−0.158727	+	0.0807934i
$895$	1.15555e13	+	9.69618e12i	0.601982	+	0.505123i
$896$	6.18075e11	−	3.50528e12i	0.0320372	−	0.181692i
$897$	−1.40899e13	+	1.72416e12i	−0.726676	+	0.0889227i
$898$	−2.07375e13	+	1.74009e13i	−1.06418	+	0.892951i
$899$	−5.44492e11	−	9.43087e11i	−0.0278018	−	0.0481541i
$900$	−2.94723e13	−	3.12206e12i	−1.49735	−	0.158617i
$901$	1.22070e10	−	2.11431e10i	0.000617087	−	0.00106883i
$902$	7.65083e12	+	4.33900e13i	0.384839	+	2.18253i
$903$	−1.05944e12	−	2.45049e11i	−0.0530253	−	0.0122647i
$904$	−8.97522e12	+	3.26671e12i	−0.446979	+	0.162687i
$905$	−2.98808e13	+	1.08757e13i	−1.48072	+	0.538939i
$906$	1.16255e13	+	3.80811e13i	0.573238	+	1.87773i
$907$	4.04140e12	+	2.29199e13i	0.198289	+	1.12455i	0.907656	+	0.419714i	$0.137870\pi$
$907$	4.04140e12	+	2.29199e13i	0.198289	+	1.12455i	−0.709367	+	0.704839i	$0.751019\pi$
$908$	8.41316e12	−	1.45720e13i	0.410745	−	0.711432i
$909$	−2.45421e9	−	3.55147e10i	−0.000119227	−	0.00172532i
$910$	−5.67010e12	−	9.82091e12i	−0.274097	−	0.474750i
$911$	2.29368e13	−	1.92462e13i	1.10332	−	0.925791i	0.105672	−	0.994401i	$-0.466301\pi$
$911$	2.29368e13	−	1.92462e13i	1.10332	−	0.925791i	0.997644	+	0.0686098i	$0.0218564\pi$
$912$	3.59399e13	−	8.45728e13i	1.72028	−	4.04812i
$913$	−6.31082e12	+	3.57904e13i	−0.300585	+	1.70470i
$914$	−2.10504e13	−	1.76634e13i	−0.997704	−	0.837173i
$915$	3.58717e13	+	2.33162e13i	1.69183	+	1.09967i
$916$	5.81177e13	+	2.11531e13i	2.72759	+	0.992760i
$917$	5.72204e12			0.267232
$918$	1.40568e11	+	2.34596e11i	0.00653272	+	0.0109026i
$919$	4.28637e13			1.98230			0.991152	−	0.132734i	$-0.0423758\pi$
$919$	4.28637e13			1.98230			0.991152	+	0.132734i	$0.0423758\pi$
$920$	3.75034e13	+	1.36501e13i	1.72594	+	0.628191i
$921$	1.60400e11	−	3.03682e12i	0.00734574	−	0.139076i
$922$	−3.62392e11	−	3.04083e11i	−0.0165154	−	0.0138581i
$923$	3.60277e12	−	2.04323e13i	0.163391	−	0.926638i
$924$	−8.97547e12	−	1.19210e13i	−0.405073	−	0.538008i
$925$	1.59133e12	−	1.33529e12i	0.0714700	−	0.0599704i
$926$	−3.44628e13	−	5.96912e13i	−1.54028	−	2.66785i
$927$	2.37513e13	+	2.46355e13i	1.05640	+	1.09573i
$928$	4.70545e12	−	8.15008e12i	0.208274	−	0.360741i
$929$	5.85871e12	+	3.32264e13i	0.258066	+	1.46357i	0.788078	+	0.615576i	$0.211076\pi$
$929$	5.85871e12	+	3.32264e13i	0.258066	+	1.46357i	−0.530012	+	0.847990i	$0.677812\pi$
$930$	1.30409e13	−	1.39732e13i	0.571658	−	0.612525i
$931$	−3.13046e13	+	1.13939e13i	−1.36563	+	0.497050i
$932$	−1.96161e12	+	7.13968e11i	−0.0851611	+	0.0309961i
$933$	−1.06521e13	+	1.14136e13i	−0.460223	+	0.493124i
$934$	−5.79882e12	−	3.28868e13i	−0.249333	−	1.41404i
$935$	1.67052e11	−	2.89343e11i	0.00714825	−	0.0123811i
$936$	−9.76816e13	+	2.42698e13i	−4.15979	+	1.03354i
$937$	−6.14862e12	−	1.06497e13i	−0.260585	−	0.451346i	0.705813	−	0.708399i	$-0.250582\pi$
$937$	−6.14862e12	−	1.06497e13i	−0.260585	−	0.451346i	−0.966398	+	0.257052i	$0.917249\pi$
$938$	−7.17265e12	+	6.01857e12i	−0.302529	+	0.253852i
$939$	1.44769e13	+	1.92278e13i	0.607687	+	0.807115i
$940$	3.26772e12	−	1.85322e13i	0.136512	−	0.774196i
$941$	5.56222e12	+	4.66725e12i	0.231257	+	0.194048i	0.751051	−	0.660244i	$-0.229547\pi$
$941$	5.56222e12	+	4.66725e12i	0.231257	+	0.194048i	−0.519794	+	0.854291i	$0.673991\pi$
$942$	1.00882e12	−	1.90997e13i	0.0417429	−	0.790312i
$943$	−7.96622e12	−	2.89947e12i	−0.328057	−	0.119403i
$944$	1.11285e14			4.56104
$945$	−4.53880e12	+	1.73589e12i	−0.185139	+	0.0708075i
$946$	2.70062e13			1.09636
$947$	−1.42198e13	−	5.17559e12i	−0.574538	−	0.209115i	0.0383772	−	0.999263i	$-0.487781\pi$
$947$	−1.42198e13	−	5.17559e12i	−0.574538	−	0.209115i	−0.612915	+	0.790148i	$0.710003\pi$
$948$	2.30736e13	+	1.49976e13i	0.927850	+	0.603093i
$949$	−1.52713e13	−	1.28142e13i	−0.611194	−	0.512853i
$950$	−7.22729e12	+	4.09880e13i	−0.287885	+	1.63268i
$951$	1.13027e13	−	2.65973e13i	0.448095	−	1.05445i
$952$	6.01067e10	−	5.04355e10i	0.00237168	−	0.00199008i
$953$	−1.45515e13	−	2.52039e13i	−0.571463	−	0.989803i	−0.996416	−	0.0845877i	$-0.973043\pi$
$953$	−1.45515e13	−	2.52039e13i	−0.571463	−	0.989803i	0.424953	−	0.905215i	$-0.360291\pi$
$954$	7.31514e12	−	4.92542e12i	0.285927	−	0.192520i
$955$	−2.08335e13	+	3.60847e13i	−0.810490	+	1.40381i
$956$	−1.37298e13	−	7.78653e13i	−0.531621	−	3.01497i
$957$	−2.00767e12	−	6.57642e12i	−0.0773729	−	0.253446i
$958$	−1.28408e13	+	4.67367e12i	−0.492547	+	0.179272i
$959$	−3.07557e12	+	1.11942e12i	−0.117420	+	0.0427374i
$960$	6.54791e13	+	1.51453e13i	2.48818	+	0.575515i
$961$	−4.02037e12	−	2.28006e13i	−0.152058	−	0.862366i
$962$	5.80346e12	−	1.00519e13i	0.218474	−	0.378407i
$963$	−1.11259e13	+	1.52871e13i	−0.416885	+	0.572806i
$964$	7.55286e12	+	1.30819e13i	0.281686	+	0.487894i
$965$	−1.15500e13	+	9.69156e12i	−0.428753	+	0.359767i
$966$	3.96759e12	−	4.85510e11i	0.146598	−	0.0179391i
$967$	2.21207e12	−	1.25453e13i	0.0813541	−	0.461382i	−0.916730	−	0.399508i	$-0.869181\pi$
$967$	2.21207e12	−	1.25453e13i	0.0813541	−	0.461382i	0.998084	−	0.0618744i	$-0.0197078\pi$
$968$	1.11448e14	+	9.35161e13i	4.07975	+	3.42332i
$969$	2.45855e11	−	1.25143e11i	0.00895823	−	0.00455983i
$970$	−9.83336e13	−	3.57905e13i	−3.56639	−	1.29806i
$971$	2.01914e13			0.728920			0.364460	−	0.931219i	$-0.381254\pi$
$971$	2.01914e13			0.728920			0.364460	+	0.931219i	$0.381254\pi$
$972$	6.03983e12	+	7.07020e13i	0.217033	+	2.54058i
$973$	2.92804e12			0.104730
$974$	1.69574e13	+	6.17200e12i	0.603733	+	0.219741i
$975$	2.17979e13	−	1.10953e13i	0.772491	−	0.393205i
$976$	−1.02561e14	−	8.60587e13i	−3.61790	−	3.03578i
$977$	1.70449e12	−	9.66662e12i	0.0598505	−	0.339429i	−0.940149	−	0.340765i	$-0.889314\pi$
$977$	1.70449e12	−	9.66662e12i	0.0598505	−	0.339429i	0.999999	+	0.00133561i	$0.000425139\pi$
$978$	−7.20427e13	+	8.81580e12i	−2.51805	+	0.308132i
$979$	−2.47348e13	+	2.07550e13i	−0.860572	+	0.722106i
$980$	−4.52800e13	−	7.84272e13i	−1.56815	−	2.71612i
$981$	−1.78135e13	+	2.44761e13i	−0.614101	+	0.843784i
$982$	−2.84759e13	+	4.93217e13i	−0.977182	+	1.69253i
$983$	−1.32916e12	−	7.53805e12i	−0.0454032	−	0.257495i	0.953654	−	0.300905i	$-0.0972887\pi$
$983$	−1.32916e12	−	7.53805e12i	−0.0454032	−	0.257495i	−0.999057	+	0.0434106i	$0.986178\pi$
$984$	−5.85646e13	−	1.35460e13i	−1.99139	−	0.460608i
$985$	4.09909e13	−	1.49195e13i	1.38747	−	0.504999i
$986$	5.58972e10	−	2.03449e10i	0.00188340	−	0.000685503i
$987$	−3.34481e11	−	1.09564e12i	−0.0112187	−	0.0367486i
$988$	2.90061e13	+	1.64502e14i	0.968462	+	5.49242i
$989$	−2.59813e12	+	4.50010e12i	−0.0863531	+	0.149568i
$990$	1.00108e14	−	6.74042e13i	3.31214	−	2.23012i
$991$	2.11872e13	+	3.66972e13i	0.697816	+	1.20865i	0.969222	+	0.246188i	$0.0791782\pi$
$991$	2.11872e13	+	3.66972e13i	0.697816	+	1.20865i	−0.271405	+	0.962465i	$0.587488\pi$
$992$	−2.17619e13	+	1.82604e13i	−0.713499	+	0.598697i
$993$	−1.71521e13	+	4.03618e13i	−0.559816	+	1.31734i
$994$	−1.01451e12	+	5.75357e12i	−0.0329623	+	0.186938i
$995$	2.88790e13	+	2.42324e13i	0.934069	+	0.783777i
$996$	−6.83961e13	−	4.44568e13i	−2.20224	−	1.43143i
$997$	−2.09231e13	−	7.61537e12i	−0.670652	−	0.244097i	−0.0158234	−	0.999875i	$-0.505037\pi$
$997$	−2.09231e13	−	7.61537e12i	−0.670652	−	0.244097i	−0.654829	+	0.755777i	$0.727259\pi$
$998$	5.59880e13			1.78652
$999$	−3.86146e12	−	3.13480e12i	−0.122661	−	0.0995785i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	27.10.e.a.4.1	✓	156
3.2	odd	2		81.10.e.a.64.26		156
27.7	even	9	inner	27.10.e.a.7.1	yes	156
27.20	odd	18		81.10.e.a.19.26		156

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
27.10.e.a.4.1	✓	156	1.1	even	1	trivial
27.10.e.a.7.1	yes	156	27.7	even	9	inner
81.10.e.a.19.26		156	27.20	odd	18
81.10.e.a.64.26		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)

\(f(q)\)	\(=\)	\(q+(-40.0613 - 14.5811i) q^{2} +(-125.031 + 63.6419i) q^{3} +(1000.08 + 839.170i) q^{4} +(-306.059 + 1735.74i) q^{5} +(5936.87 - 726.489i) q^{6} +(764.835 - 641.773i) q^{7} +(-16914.7 - 29297.2i) q^{8} +(11582.4 - 15914.4i) q^{9} +O(q^{10})\)	\(q+(-40.0613 - 14.5811i) q^{2} +(-125.031 + 63.6419i) q^{3} +(1000.08 + 839.170i) q^{4} +(-306.059 + 1735.74i) q^{5} +(5936.87 - 726.489i) q^{6} +(764.835 - 641.773i) q^{7} +(-16914.7 - 29297.2i) q^{8} +(11582.4 - 15914.4i) q^{9} +(37570.2 - 65073.5i) q^{10} +(14169.6 + 80359.9i) q^{11} +(-178448. - 41274.8i) q^{12} +(142043. - 51699.4i) q^{13} +(-39998.1 + 14558.1i) q^{14} +(-72199.4 - 236500. i) q^{15} +(134370. + 762050. i) q^{16} +(-1161.53 + 2011.82i) q^{17} +(-696056. + 468667. i) q^{18} +(423226. + 733050. i) q^{19} +(-1.76267e6 + 1.47905e6i) q^{20} +(-54784.3 + 128917. i) q^{21} +(604084. - 3.42593e6i) q^{22} +(512754. + 430252. i) q^{23} +(3.97939e6 + 2.58656e6i) q^{24} +(-1.08380e6 - 394471. i) q^{25} -6.44426e6 q^{26} +(-435335. + 2.72692e6i) q^{27} +1.30346e6 q^{28} +(564405. + 205427. i) q^{29} +(-556030. + 1.05272e7i) q^{30} +(-1.38890e6 - 1.16542e6i) q^{31} +(2.72080e6 - 1.54304e7i) q^{32} +(-6.88590e6 - 9.14568e6i) q^{33} +(75866.9 - 63659.9i) q^{34} +(879869. + 1.52398e6i) q^{35} +(2.49383e7 - 6.19613e6i) q^{36} +(-900563. + 1.55982e6i) q^{37} +(-6.26631e6 - 3.55380e7i) q^{38} +(-1.44695e7 + 1.55039e7i) q^{39} +(5.60293e7 - 2.03930e7i) q^{40} +(-1.19014e7 + 4.33175e6i) q^{41} +(4.07448e6 - 4.36577e6i) q^{42} +(1.34805e6 + 7.64517e6i) q^{43} +(-5.32648e7 + 9.22574e7i) q^{44} +(2.40784e7 + 2.49748e7i) q^{45} +(-1.42680e7 - 2.47130e7i) q^{46} +(-6.26487e6 + 5.25685e6i) q^{47} +(-6.52987e7 - 8.67281e7i) q^{48} +(-6.83423e6 + 3.87588e7i) q^{49} +(3.76666e7 + 3.16060e7i) q^{50} +(17190.3 - 325462. i) q^{51} +(1.85439e8 + 6.74944e7i) q^{52} -1.05094e7 q^{53} +(5.72016e7 - 1.02896e8i) q^{54} -1.43821e8 q^{55} +(-3.17391e7 - 1.15521e7i) q^{56} +(-9.95690e7 - 6.47188e7i) q^{57} +(-1.96155e7 - 1.64593e7i) q^{58} +(2.49733e7 - 1.41631e8i) q^{59} +(1.26258e8 - 2.97107e8i) q^{60} +(-1.32541e8 + 1.11215e8i) q^{61} +(3.86478e7 + 6.69400e7i) q^{62} +(-1.35480e6 - 1.96052e7i) q^{63} +(-1.35897e8 + 2.35381e8i) q^{64} +(4.62635e7 + 2.62373e8i) q^{65} +(1.42504e8 + 4.66792e8i) q^{66} +(2.06709e8 - 7.52358e7i) q^{67} +(-2.84989e6 + 1.03727e6i) q^{68} +(-9.14921e7 - 2.11621e7i) q^{69} +(-1.30274e7 - 7.38820e7i) q^{70} +(6.86282e7 - 1.18868e8i) q^{71} +(-6.62161e8 - 7.01440e7i) q^{72} +(-6.59416e7 - 1.14214e8i) q^{73} +(5.88216e7 - 4.93572e7i) q^{74} +(1.60613e8 - 1.96541e7i) q^{75} +(-1.91891e8 + 1.08827e9i) q^{76} +(6.24102e7 + 5.23684e7i) q^{77} +(8.05731e8 - 4.10125e8i) q^{78} +(-1.41188e8 - 5.13881e7i) q^{79} -1.36385e9 q^{80} +(-1.19116e8 - 3.68654e8i) q^{81} +5.39946e8 q^{82} +(4.18517e8 + 1.52328e8i) q^{83} +(-1.62972e8 + 8.29544e7i) q^{84} +(-3.13652e6 - 2.63185e6i) q^{85} +(5.74705e7 - 3.25932e8i) q^{86} +(-8.36418e7 + 1.02352e7i) q^{87} +(2.11464e9 - 1.77440e9i) q^{88} +(1.97851e8 + 3.42687e8i) q^{89} +(-6.00453e8 - 1.35162e9i) q^{90} +(7.54601e7 - 1.30701e8i) q^{91} +(1.51743e8 + 8.60576e8i) q^{92} +(2.47825e8 + 5.73217e7i) q^{93} +(3.27630e8 - 1.19247e8i) q^{94} +(-1.40192e9 + 5.10257e8i) q^{95} +(6.41837e8 + 2.10243e9i) q^{96} +(-2.41831e8 - 1.37149e9i) q^{97} +(8.38935e8 - 1.45308e9i) q^{98} +(1.44300e9 + 7.05260e8i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 156 q - 6 q^{2} - 6 q^{3} - 6 q^{4} + 2382 q^{5} - 6822 q^{6} - 6 q^{7} + 36861 q^{8} + 2538 q^{9}+O(q^{10}) \) 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	\( 156 q - 6 q^{2} - 6 q^{3} - 6 q^{4} + 2382 q^{5} - 6822 q^{6} - 6 q^{7} + 36861 q^{8} + 2538 q^{9} - 3 q^{10} - 121767 q^{11} + 319935 q^{12} - 6 q^{13} - 720417 q^{14} - 706356 q^{15} + 1530 q^{16} + 1002249 q^{17} + 922437 q^{18} - 3 q^{19} - 8448573 q^{20} - 3497394 q^{21} - 1585014 q^{22} + 9316482 q^{23} + 7959258 q^{24} + 2192178 q^{25} - 33129678 q^{26} - 3148155 q^{27} - 12 q^{28} + 19657236 q^{29} + 21174507 q^{30} - 4633692 q^{31} - 37550952 q^{32} - 19055889 q^{33} + 14341770 q^{34} + 34449663 q^{35} + 137733552 q^{36} - 3 q^{37} - 92022060 q^{38} - 89330160 q^{39} + 6645801 q^{40} - 33127221 q^{41} + 227141658 q^{42} + 2356203 q^{43} + 1001541 q^{44} - 78992532 q^{45} - 3 q^{46} - 33488952 q^{47} + 248865393 q^{48} - 93214644 q^{49} - 72027753 q^{50} - 101541537 q^{51} + 160531713 q^{52} + 4841352 q^{53} - 315431874 q^{54} - 12 q^{55} - 91770981 q^{56} - 103852992 q^{57} - 320682489 q^{58} + 538090854 q^{59} + 1127571210 q^{60} + 36683436 q^{61} - 55862958 q^{62} - 419972706 q^{63} - 956301315 q^{64} - 852347310 q^{65} + 472205277 q^{66} - 109026897 q^{67} - 508886217 q^{68} - 1234413090 q^{69} - 815297649 q^{70} + 940878639 q^{71} + 2831326452 q^{72} - 221849931 q^{73} + 838884579 q^{74} - 226667796 q^{75} + 908401146 q^{76} - 967811358 q^{77} - 1247881230 q^{78} - 1228059150 q^{79} - 2497115154 q^{80} - 392600970 q^{81} - 12 q^{82} - 297703284 q^{83} + 1027656618 q^{84} + 1535949369 q^{85} + 2930201574 q^{86} + 2687612040 q^{87} + 2837227002 q^{88} + 1774997208 q^{89} + 7127326206 q^{90} + 551343507 q^{91} - 6896645517 q^{92} - 7299151842 q^{93} + 414852915 q^{94} - 9000269169 q^{95} - 2644638174 q^{96} + 3371772333 q^{97} + 6901039926 q^{98} + 5248107342 q^{99}+O(q^{100}) \) 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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