LMFDB - Embedded newform 27.10.e.a.7.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("27.4");

S:= CuspForms(chi, 10);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$13.9059675764$
Analytic rank:	$0$
Dimension:	$156$
Relative dimension:	$26$ over $\Q(\zeta_{9})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			7.15
Character	$\chi$	$=$	27.7
Dual form			27.10.e.a.4.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(4.82322 - 1.75551i) q^{2} +(-137.543 - 27.6597i) q^{3} +(-372.033 + 312.173i) q^{4} +(203.603 + 1154.69i) q^{5} +(-711.954 + 108.048i) q^{6} +(-440.948 - 369.999i) q^{7} +(-2560.36 + 4434.68i) q^{8} +(18152.9 + 7608.76i) q^{9} +(3009.09 + 5211.90i) q^{10} +(12328.1 - 69916.4i) q^{11} +(59805.0 - 32646.7i) q^{12} +(-143827. - 52348.7i) q^{13} +(-2776.32 - 1010.50i) q^{14} +(3934.29 - 164451. i) q^{15} +(38614.5 - 218993. i) q^{16} +(164482. + 284892. i) q^{17} +(100913. + 4831.19i) q^{18} +(140625. - 243570. i) q^{19} +(-436210. - 366024. i) q^{20} +(50415.0 + 63087.1i) q^{21} +(-63277.4 - 358864. i) q^{22} +(821687. - 689477. i) q^{23} +(474820. - 539138. i) q^{24} +(543480. - 197811. i) q^{25} -785607. q^{26} +(-2.28634e6 - 1.54863e6i) q^{27} +279551. q^{28} +(1.62591e6 - 591785. i) q^{29} +(-269718. - 800088. i) q^{30} +(4.00947e6 - 3.36434e6i) q^{31} +(-653471. - 3.70602e6i) q^{32} +(-3.62951e6 + 9.27548e6i) q^{33} +(1.29346e6 + 1.08535e6i) q^{34} +(337456. - 584492. i) q^{35} +(-9.12872e6 + 2.83613e6i) q^{36} +(3.24063e6 + 5.61294e6i) q^{37} +(250677. - 1.42166e6i) q^{38} +(1.83344e7 + 1.11784e7i) q^{39} +(-5.64198e6 - 2.05351e6i) q^{40} +(-1.80717e7 - 6.57754e6i) q^{41} +(353913. + 215779. i) q^{42} +(-5.74575e6 + 3.25858e7i) q^{43} +(1.72395e7 + 2.98597e7i) q^{44} +(-5.08979e6 + 2.25101e7i) q^{45} +(2.75279e6 - 4.76797e6i) q^{46} +(-2.17446e7 - 1.82459e7i) q^{47} +(-1.13684e7 + 2.90528e7i) q^{48} +(-6.94979e6 - 3.94142e7i) q^{49} +(2.27407e6 - 1.90817e6i) q^{50} +(-1.47433e7 - 4.37343e7i) q^{51} +(6.98503e7 - 2.54234e7i) q^{52} -5.03334e7 q^{53} +(-1.37461e7 - 3.45570e6i) q^{54} +8.32418e7 q^{55} +(2.76981e6 - 1.00813e6i) q^{56} +(-2.60790e7 + 2.96116e7i) q^{57} +(6.80326e6 - 5.70861e6i) q^{58} +(-1.89454e7 - 1.07445e8i) q^{59} +(4.98734e7 + 6.24093e7i) q^{60} +(-3.81453e7 - 3.20077e7i) q^{61} +(1.34324e7 - 2.32656e7i) q^{62} +(-5.18924e6 - 1.00716e7i) q^{63} +(4.72694e7 + 8.18730e7i) q^{64} +(3.11630e7 - 1.76734e8i) q^{65} +(-1.22273e6 + 5.11093e7i) q^{66} +(1.99585e8 + 7.26431e7i) q^{67} +(-1.50128e8 - 5.46423e7i) q^{68} +(-1.32088e8 + 7.21048e7i) q^{69} +(601546. - 3.41154e6i) q^{70} +(-1.75242e8 - 3.03528e8i) q^{71} +(-8.02204e7 + 6.10210e7i) q^{72} +(1.92455e8 - 3.33341e8i) q^{73} +(2.54838e7 + 2.13835e7i) q^{74} +(-8.02230e7 + 1.21749e7i) q^{75} +(2.37187e7 + 1.34516e8i) q^{76} +(-3.13051e7 + 2.62681e7i) q^{77} +(1.08054e8 + 2.17296e7i) q^{78} +(4.56193e7 - 1.66041e7i) q^{79} +2.60732e8 q^{80} +(2.71634e8 + 2.76242e8i) q^{81} -9.87104e7 q^{82} +(-1.67411e8 + 6.09326e7i) q^{83} +(-3.84502e7 - 7.73229e6i) q^{84} +(-2.95473e8 + 2.47931e8i) q^{85} +(2.94916e7 + 1.67255e8i) q^{86} +(-2.40001e8 + 3.64233e7i) q^{87} +(2.78492e8 + 2.33682e8i) q^{88} +(-3.40131e8 + 5.89124e8i) q^{89} +(1.49676e7 + 1.17506e8i) q^{90} +(4.40512e7 + 7.62990e7i) q^{91} +(-9.04587e7 + 5.13017e8i) q^{92} +(-6.44529e8 + 3.51839e8i) q^{93} +(-1.36910e8 - 4.98311e7i) q^{94} +(3.09880e8 + 1.12787e8i) q^{95} +(-1.26272e7 + 5.27810e8i) q^{96} +(2.16877e8 - 1.22997e9i) q^{97} +(-1.02712e8 - 1.77903e8i) q^{98} +(7.55768e8 - 1.17538e9i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 156 q - 6 q^{2} - 6 q^{3} - 6 q^{4} + 2382 q^{5} - 6822 q^{6} - 6 q^{7} + 36861 q^{8} + 2538 q^{9} - 3 q^{10} - 121767 q^{11} + 319935 q^{12} - 6 q^{13} - 720417 q^{14} - 706356 q^{15} + 1530 q^{16} + 1002249 q^{17}+ \cdots + 5248107342 q^{99}+O(q^{100}) $ 156 * q - 6 * q^2 - 6 * q^3 - 6 * q^4 + 2382 * q^5 - 6822 * q^6 - 6 * q^7 + 36861 * q^8 + 2538 * q^9 - 3 * q^10 - 121767 * q^11 + 319935 * q^12 - 6 * q^13 - 720417 * q^14 - 706356 * q^15 + 1530 * q^16 + 1002249 * q^17 + 922437 * q^18 - 3 * q^19 - 8448573 * q^20 - 3497394 * q^21 - 1585014 * q^22 + 9316482 * q^23 + 7959258 * q^24 + 2192178 * q^25 - 33129678 * q^26 - 3148155 * q^27 - 12 * q^28 + 19657236 * q^29 + 21174507 * q^30 - 4633692 * q^31 - 37550952 * q^32 - 19055889 * q^33 + 14341770 * q^34 + 34449663 * q^35 + 137733552 * q^36 - 3 * q^37 - 92022060 * q^38 - 89330160 * q^39 + 6645801 * q^40 - 33127221 * q^41 + 227141658 * q^42 + 2356203 * q^43 + 1001541 * q^44 - 78992532 * q^45 - 3 * q^46 - 33488952 * q^47 + 248865393 * q^48 - 93214644 * q^49 - 72027753 * q^50 - 101541537 * q^51 + 160531713 * q^52 + 4841352 * q^53 - 315431874 * q^54 - 12 * q^55 - 91770981 * q^56 - 103852992 * q^57 - 320682489 * q^58 + 538090854 * q^59 + 1127571210 * q^60 + 36683436 * q^61 - 55862958 * q^62 - 419972706 * q^63 - 956301315 * q^64 - 852347310 * q^65 + 472205277 * q^66 - 109026897 * q^67 - 508886217 * q^68 - 1234413090 * q^69 - 815297649 * q^70 + 940878639 * q^71 + 2831326452 * q^72 - 221849931 * q^73 + 838884579 * q^74 - 226667796 * q^75 + 908401146 * q^76 - 967811358 * q^77 - 1247881230 * q^78 - 1228059150 * q^79 - 2497115154 * q^80 - 392600970 * q^81 - 12 * q^82 - 297703284 * q^83 + 1027656618 * q^84 + 1535949369 * q^85 + 2930201574 * q^86 + 2687612040 * q^87 + 2837227002 * q^88 + 1774997208 * q^89 + 7127326206 * q^90 + 551343507 * q^91 - 6896645517 * q^92 - 7299151842 * q^93 + 414852915 * q^94 - 9000269169 * q^95 - 2644638174 * q^96 + 3371772333 * q^97 + 6901039926 * q^98 + 5248107342 * q^99

Character values

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

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

Coefficient data

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

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

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

$2$	4.82322	−	1.75551i	0.213158	−	0.0775832i	−0.233234	−	0.972421i	$-0.574931\pi$
$2$	4.82322	−	1.75551i	0.213158	−	0.0775832i	0.446392	+	0.894837i	$0.352709\pi$
$3$	−137.543	−	27.6597i	−0.980373	−	0.197152i
$3$	−137.543	−	27.6597i	−0.980373	−	0.197152i
$4$	−372.033	+	312.173i	−0.726627	+	0.609713i
$5$	203.603	+	1154.69i	0.145687	+	0.826230i	0.966813	+	0.255484i	$0.0822347\pi$
$5$	203.603	+	1154.69i	0.145687	+	0.826230i	−0.821127	+	0.570746i	$0.806654\pi$
$6$	−711.954	+	108.048i	−0.224270	+	0.0340359i
$7$	−440.948	−	369.999i	−0.0694139	−	0.0582452i	0.607421	−	0.794380i	$-0.292204\pi$
$7$	−440.948	−	369.999i	−0.0694139	−	0.0582452i	−0.676834	+	0.736135i	$0.736649\pi$
$8$	−2560.36	+	4434.68i	−0.221002	+	0.382787i
$9$	18152.9	+	7608.76i	0.922262	+	0.386565i
$10$	3009.09	+	5211.90i	0.0951558	+	0.164815i
$11$	12328.1	−	69916.4i	0.253881	−	1.43983i	−0.545047	−	0.838405i	$-0.683488\pi$
$11$	12328.1	−	69916.4i	0.253881	−	1.43983i	0.798928	−	0.601426i	$-0.205401\pi$
$12$	59805.0	−	32646.7i	0.832572	−	0.454490i
$13$	−143827.	−	52348.7i	−1.39667	−	0.508348i	−0.469485	−	0.882940i	$-0.655560\pi$
$13$	−143827.	−	52348.7i	−1.39667	−	0.508348i	−0.927190	+	0.374592i	$0.877783\pi$
$14$	−2776.32	−	1010.50i	−0.0193150	−	0.00703008i
$15$	3934.29	−	164451.i	0.0200658	−	0.838735i
$16$	38614.5	−	218993.i	0.147302	−	0.835394i
$17$	164482.	+	284892.i	0.477639	+	0.827294i	0.999671	−	0.0256311i	$-0.00815951\pi$
$17$	164482.	+	284892.i	0.477639	+	0.827294i	−0.522033	+	0.852925i	$0.674826\pi$
$18$	100913.	+	4831.19i	0.226579	+	0.0108475i
$19$	140625.	−	243570.i	0.247555	−	0.428779i	−0.715292	−	0.698826i	$-0.753706\pi$
$19$	140625.	−	243570.i	0.247555	−	0.428779i	0.962847	+	0.270048i	$0.0870394\pi$
$20$	−436210.	−	366024.i	−0.609622	−	0.511534i
$21$	50415.0	+	63087.1i	0.0565683	+	0.0707871i
$22$	−63277.4	−	358864.i	−0.0575899	−	0.326609i
$23$	821687.	−	689477.i	0.612253	−	0.513741i	−0.283105	−	0.959089i	$-0.591364\pi$
$23$	821687.	−	689477.i	0.612253	−	0.513741i	0.895358	+	0.445348i	$0.146920\pi$
$24$	474820.	−	539138.i	0.292132	−	0.331703i
$25$	543480.	−	197811.i	0.278262	−	0.101279i
$26$	−785607.			−0.337152
$27$	−2.28634e6	−	1.54863e6i	−0.827949	−	0.560804i
$28$	279551.			0.0859508
$29$	1.62591e6	−	591785.i	0.426881	−	0.155372i	−0.119640	−	0.992817i	$-0.538174\pi$
$29$	1.62591e6	−	591785.i	0.426881	−	0.155372i	0.546521	+	0.837445i	$0.315952\pi$
$30$	−269718.	−	800088.i	−0.0607946	−	0.180340i
$31$	4.00947e6	−	3.36434e6i	0.779756	−	0.654293i	−0.163431	−	0.986555i	$-0.552256\pi$
$31$	4.00947e6	−	3.36434e6i	0.779756	−	0.654293i	0.943187	+	0.332262i	$0.107812\pi$
$32$	−653471.	−	3.70602e6i	−0.110167	−	0.624788i
$33$	−3.62951e6	+	9.27548e6i	−0.532764	+	1.36152i
$34$	1.29346e6	+	1.08535e6i	0.165997	+	0.139288i
$35$	337456.	−	584492.i	0.0380112	−	0.0658373i
$36$	−9.12872e6	+	2.83613e6i	−0.905834	+	0.281426i
$37$	3.24063e6	+	5.61294e6i	0.284264	+	0.492360i	0.972430	−	0.233193i	$-0.0749175\pi$
$37$	3.24063e6	+	5.61294e6i	0.284264	+	0.492360i	−0.688167	+	0.725553i	$0.741584\pi$
$38$	250677.	−	1.42166e6i	0.0195024	−	0.110604i
$39$	1.83344e7	+	1.11784e7i	1.26904	+	0.773728i
$40$	−5.64198e6	−	2.05351e6i	−0.348467	−	0.126832i
$41$	−1.80717e7	−	6.57754e6i	−0.998781	−	0.363527i	−0.209667	−	0.977773i	$-0.567238\pi$
$41$	−1.80717e7	−	6.57754e6i	−0.998781	−	0.363527i	−0.789114	+	0.614246i	$0.789460\pi$
$42$	353913.	+	215779.i	0.0175499	+	0.0107001i
$43$	−5.74575e6	+	3.25858e7i	−0.256294	+	1.45352i	0.536434	+	0.843942i	$0.319771\pi$
$43$	−5.74575e6	+	3.25858e7i	−0.256294	+	1.45352i	−0.792728	+	0.609575i	$0.791340\pi$
$44$	1.72395e7	+	2.98597e7i	0.693407	+	1.20102i
$45$	−5.08979e6	+	2.25101e7i	−0.185030	+	0.818317i
$46$	2.75279e6	−	4.76797e6i	0.0906490	−	0.157009i
$47$	−2.17446e7	−	1.82459e7i	−0.649996	−	0.545412i	0.257073	−	0.966392i	$-0.417242\pi$
$47$	−2.17446e7	−	1.82459e7i	−0.649996	−	0.545412i	−0.907070	+	0.420980i	$0.861686\pi$
$48$	−1.13684e7	+	2.90528e7i	−0.309111	+	0.789956i
$49$	−6.94979e6	−	3.94142e7i	−0.172222	−	0.976722i
$50$	2.27407e6	−	1.90817e6i	0.0514562	−	0.0431769i
$51$	−1.47433e7	−	4.37343e7i	−0.305161	−	0.905224i
$52$	6.98503e7	−	2.54234e7i	1.32481	−	0.482191i
$53$	−5.03334e7			−0.876223			−0.438112	−	0.898921i	$-0.644353\pi$
$53$	−5.03334e7			−0.876223			−0.438112	+	0.898921i	$0.644353\pi$
$54$	−1.37461e7	−	3.45570e6i	−0.219993	−	0.0553050i
$55$	8.32418e7			1.22662
$56$	2.76981e6	−	1.00813e6i	0.0376361	−	0.0136984i
$57$	−2.60790e7	+	2.96116e7i	−0.327231	+	0.371557i
$58$	6.80326e6	−	5.70861e6i	0.0789389	−	0.0662376i
$59$	−1.89454e7	−	1.07445e8i	−0.203549	−	1.15438i	−0.899707	−	0.436495i	$-0.856220\pi$
$59$	−1.89454e7	−	1.07445e8i	−0.203549	−	1.15438i	0.696158	−	0.717889i	$-0.254891\pi$
$60$	4.98734e7	+	6.24093e7i	0.496807	+	0.621682i
$61$	−3.81453e7	−	3.20077e7i	−0.352742	−	0.295985i	0.449148	−	0.893457i	$-0.351728\pi$
$61$	−3.81453e7	−	3.20077e7i	−0.352742	−	0.295985i	−0.801890	+	0.597472i	$0.796172\pi$
$62$	1.34324e7	−	2.32656e7i	0.115449	−	0.199964i
$63$	−5.18924e6	−	1.00716e7i	−0.0415022	−	0.0805503i
$64$	4.72694e7	+	8.18730e7i	0.352184	+	0.610001i
$65$	3.11630e7	−	1.76734e8i	0.216535	−	1.22803i
$66$	−1.22273e6	+	5.11093e7i	−0.00793200	+	0.331552i
$67$	1.99585e8	+	7.26431e7i	1.21002	+	0.440411i	0.866710	−	0.498812i	$-0.166230\pi$
$67$	1.99585e8	+	7.26431e7i	1.21002	+	0.440411i	0.343308	+	0.939223i	$0.388453\pi$
$68$	−1.50128e8	−	5.46423e7i	−0.851477	−	0.309912i
$69$	−1.32088e8	+	7.21048e7i	−0.701521	+	0.382951i
$70$	601546.	−	3.41154e6i	0.00299452	−	0.0169828i
$71$	−1.75242e8	−	3.03528e8i	−0.818419	−	1.41754i	−0.906847	−	0.421461i	$-0.861518\pi$
$71$	−1.75242e8	−	3.03528e8i	−0.818419	−	1.41754i	0.0884276	−	0.996083i	$-0.471816\pi$
$72$	−8.02204e7	+	6.10210e7i	−0.351794	+	0.267598i
$73$	1.92455e8	−	3.33341e8i	0.793186	−	1.37384i	−0.130798	−	0.991409i	$-0.541754\pi$
$73$	1.92455e8	−	3.33341e8i	0.793186	−	1.37384i	0.923984	−	0.382430i	$-0.124913\pi$
$74$	2.54838e7	+	2.13835e7i	0.0987920	+	0.0828963i
$75$	−8.02230e7	+	1.21749e7i	−0.292768	+	0.0444313i
$76$	2.37187e7	+	1.34516e8i	0.0815512	+	0.462500i
$77$	−3.13051e7	+	2.62681e7i	−0.101486	+	0.0851569i
$78$	1.08054e8	+	2.17296e7i	0.330535	+	0.0664702i
$79$	4.56193e7	−	1.66041e7i	0.131773	−	0.0479615i	−0.275292	−	0.961361i	$-0.588774\pi$
$79$	4.56193e7	−	1.66041e7i	0.131773	−	0.0479615i	0.407065	+	0.913399i	$0.366552\pi$
$80$	2.60732e8			0.711687
$81$	2.71634e8	+	2.76242e8i	0.701135	+	0.713029i
$82$	−9.87104e7			−0.241102
$83$	−1.67411e8	+	6.09326e7i	−0.387197	+	0.140928i	−0.528281	−	0.849069i	$-0.677163\pi$
$83$	−1.67411e8	+	6.09326e7i	−0.387197	+	0.140928i	0.141084	+	0.989998i	$0.454941\pi$
$84$	−3.84502e7	−	7.73229e6i	−0.0842638	−	0.0169454i
$85$	−2.95473e8	+	2.47931e8i	−0.613949	+	0.515165i
$86$	2.94916e7	+	1.67255e8i	0.0581373	+	0.329713i
$87$	−2.40001e8	+	3.64233e7i	−0.449134	+	0.0681620i
$88$	2.78492e8	+	2.33682e8i	0.495040	+	0.415388i
$89$	−3.40131e8	+	5.89124e8i	−0.574634	+	0.995295i	0.421448	+	0.906853i	$0.361522\pi$
$89$	−3.40131e8	+	5.89124e8i	−0.574634	+	0.995295i	−0.996081	+	0.0884419i	$0.971811\pi$
$90$	1.49676e7	+	1.17506e8i	0.0240470	+	0.188786i
$91$	4.40512e7	+	7.62990e7i	0.0673398	+	0.116636i
$92$	−9.04587e7	+	5.13017e8i	−0.131645	+	0.746597i
$93$	−6.44529e8	+	3.51839e8i	−0.893447	+	0.487721i
$94$	−1.36910e8	−	4.98311e7i	−0.180867	−	0.0658301i
$95$	3.09880e8	+	1.12787e8i	0.390335	+	0.142070i
$96$	−1.26272e7	+	5.27810e8i	−0.0151736	+	0.634245i
$97$	2.16877e8	−	1.22997e9i	0.248737	−	1.41066i	−0.562913	−	0.826516i	$-0.690319\pi$
$97$	2.16877e8	−	1.22997e9i	0.248737	−	1.41066i	0.811650	−	0.584144i	$-0.198569\pi$
$98$	−1.02712e8	−	1.77903e8i	−0.112488	−	0.194835i
$99$	7.55768e8	−	1.17538e9i	0.790734	−	1.22976i
$100$	−1.40442e8	+	2.43252e8i	−0.140442	+	0.243252i
$101$	−1.70877e8	−	1.43383e8i	−0.163395	−	0.137104i	0.557424	−	0.830228i	$-0.311790\pi$
$101$	−1.70877e8	−	1.43383e8i	−0.163395	−	0.137104i	−0.720819	+	0.693123i	$0.756234\pi$
$102$	−1.47886e8	−	1.85058e8i	−0.135278	−	0.169281i
$103$	1.03428e8	+	5.86567e8i	0.0905460	+	0.513512i	0.996021	+	0.0891133i	$0.0284033\pi$
$103$	1.03428e8	+	5.86567e8i	0.0905460	+	0.513512i	−0.905476	+	0.424399i	$0.860486\pi$
$104$	6.00399e8	−	5.03794e8i	0.503257	−	0.422283i
$105$	−6.25815e7	+	7.10585e7i	−0.0502451	+	0.0570511i
$106$	−2.42769e8	+	8.83606e7i	−0.186774	+	0.0679802i
$107$	1.08574e9			0.800754			0.400377	−	0.916351i	$-0.368879\pi$
$107$	1.08574e9			0.800754			0.400377	+	0.916351i	$0.368879\pi$
$108$	1.33403e9	−	1.37590e8i	0.943539	−	0.0973152i
$109$	−1.86453e9			−1.26517			−0.632587	−	0.774489i	$-0.718007\pi$
$109$	−1.86453e9			−1.26517			−0.632587	+	0.774489i	$0.718007\pi$
$110$	4.01493e8	−	1.46132e8i	0.261464	−	0.0951650i
$111$	−2.90472e8	−	8.61652e8i	−0.181615	−	0.538739i
$112$	−9.80544e7	+	8.22774e7i	−0.0588825	+	0.0494083i
$113$	−2.47881e8	−	1.40580e9i	−0.143018	−	0.811095i	−0.968937	−	0.247307i	$-0.920454\pi$
$113$	−2.47881e8	−	1.40580e9i	−0.143018	−	0.811095i	0.825919	−	0.563788i	$-0.190657\pi$
$114$	−7.38015e7	+	1.88605e8i	−0.0409254	+	0.104588i
$115$	9.63431e8	+	8.08414e8i	0.513665	+	0.431016i
$116$	−4.20155e8	+	7.27730e8i	−0.215451	+	0.373172i
$117$	−2.21257e9	−	2.04463e9i	−1.09159	−	1.00874i
$118$	−2.79997e8	−	4.84970e8i	−0.132949	−	0.230274i
$119$	3.28816e7	−	1.86481e8i	0.0150311	−	0.0852458i
$120$	7.19212e8	+	4.38501e8i	0.316622	+	0.193043i
$121$	−2.52057e9	−	9.17412e8i	−1.06897	−	0.389072i
$122$	−2.40173e8	−	8.74158e7i	−0.0981532	−	0.0357249i
$123$	2.30369e9	+	1.40455e9i	0.907508	+	0.553304i
$124$	−4.41398e8	+	2.50329e9i	−0.167661	+	0.950855i
$125$	1.48409e9	+	2.57052e9i	0.543707	+	0.941727i
$126$	−4.27097e7	−	3.94679e7i	−0.0150959	−	0.0139501i
$127$	2.21753e9	−	3.84088e9i	0.756402	−	1.31013i	−0.188272	−	0.982117i	$-0.560289\pi$
$127$	2.21753e9	−	3.84088e9i	0.756402	−	1.31013i	0.944674	−	0.328010i	$-0.106378\pi$
$128$	1.84770e9	+	1.55040e9i	0.608396	+	0.510505i
$129$	1.69160e9	−	4.32301e9i	0.537828	−	1.37446i
$130$	−1.59952e8	−	9.07134e8i	−0.0491185	−	0.278565i
$131$	−1.64912e9	+	1.38378e9i	−0.489251	+	0.410530i	−0.853758	−	0.520671i	$-0.825682\pi$
$131$	−1.64912e9	+	1.38378e9i	−0.489251	+	0.410530i	0.364507	+	0.931201i	$0.381237\pi$
$132$	−1.54526e9	−	4.58382e9i	−0.443014	−	1.31415i
$133$	−1.52129e8	+	5.53705e7i	−0.0421580	+	0.0153443i
$134$	1.09017e9			0.292094
$135$	1.32269e9	−	2.95532e9i	0.342732	−	0.765777i
$136$	−1.68454e9			−0.422236
$137$	3.56983e9	−	1.29931e9i	0.865775	−	0.315116i	0.129320	−	0.991603i	$-0.458721\pi$
$137$	3.56983e9	−	1.29931e9i	0.865775	−	0.315116i	0.736455	+	0.676487i	$0.236498\pi$
$138$	−5.10506e8	+	5.79658e8i	−0.119824	+	0.136055i
$139$	−4.78102e9	+	4.01175e9i	−1.08631	+	0.911523i	−0.996429	−	0.0844297i	$-0.973093\pi$
$139$	−4.78102e9	+	4.01175e9i	−1.08631	+	0.911523i	−0.0898811	+	0.995953i	$0.528649\pi$
$140$	5.69175e7	+	3.22795e8i	0.0125219	+	0.0710151i
$141$	2.48613e9	+	3.11103e9i	0.529710	+	0.662855i
$142$	−1.37808e9	−	1.15634e9i	−0.284430	−	0.238665i
$143$	−5.43315e9	+	9.41050e9i	−1.08653	+	1.88192i
$144$	2.36723e9	−	3.68155e9i	0.458786	−	0.713510i
$145$	1.01437e9	+	1.75694e9i	0.190564	+	0.330066i
$146$	3.43067e8	−	1.94563e9i	0.0624873	−	0.354383i
$147$	−1.34293e8	+	5.61336e9i	−0.0237206	+	0.991506i
$148$	−2.95783e9	−	1.07656e9i	−0.506752	−	0.184443i
$149$	−4.70352e9	−	1.71194e9i	−0.781780	−	0.284545i	−0.0798651	−	0.996806i	$-0.525449\pi$
$149$	−4.70352e9	−	1.71194e9i	−0.781780	−	0.284545i	−0.701915	+	0.712261i	$0.747671\pi$
$150$	−3.65560e8	+	1.99554e8i	−0.0589587	+	0.0321848i
$151$	−5.60010e8	+	3.17597e9i	−0.0876595	+	0.497142i	0.909091	+	0.416597i	$0.136777\pi$
$151$	−5.60010e8	+	3.17597e9i	−0.0876595	+	0.497142i	−0.996751	+	0.0805453i	$0.974334\pi$
$152$	7.20103e8	+	1.24726e9i	0.109421	+	0.189522i
$153$	8.18155e8	+	6.42312e9i	0.120705	+	0.947621i
$154$	−1.04877e8	+	1.81653e8i	−0.0150258	+	0.0260255i
$155$	4.70111e9	+	3.94470e9i	0.654196	+	0.548936i
$156$	−1.03106e10	+	1.56476e9i	−1.39387	+	0.211538i
$157$	8.02176e8	+	4.54936e9i	0.105371	+	0.597589i	0.991071	+	0.133332i	$0.0425675\pi$
$157$	8.02176e8	+	4.54936e9i	0.105371	+	0.597589i	−0.885701	+	0.464257i	$0.846321\pi$
$158$	1.90883e8	−	1.60170e8i	0.0243675	−	0.0204468i
$159$	6.92298e9	+	1.39221e9i	0.859025	+	0.172749i
$160$	4.14626e9	−	1.50911e9i	0.500169	−	0.182047i
$161$	−6.17427e8			−0.0724218
$162$	1.79509e9	+	8.55520e8i	0.204772	+	0.0975916i
$163$	4.02954e9			0.447107			0.223553	−	0.974692i	$-0.428234\pi$
$163$	4.02954e9			0.447107			0.223553	+	0.974692i	$0.428234\pi$
$164$	8.77658e9	−	3.19442e9i	0.947389	−	0.344821i
$165$	−1.14493e10	−	2.30244e9i	−1.20254	−	0.241830i
$166$	−7.00491e8	+	5.87782e8i	−0.0716006	+	0.0600800i
$167$	−1.78494e9	−	1.01229e10i	−0.177583	−	1.00712i	−0.935120	−	0.354330i	$-0.884709\pi$
$167$	−1.78494e9	−	1.01229e10i	−0.177583	−	1.00712i	0.757538	−	0.652791i	$-0.226402\pi$
$168$	−4.08852e8	+	6.20485e7i	−0.0395981	+	0.00600952i
$169$	9.82229e9	+	8.24188e9i	0.926238	+	0.777206i
$170$	−9.89885e8	+	1.71453e9i	−0.0909002	+	0.157444i
$171$	4.40602e9	−	3.35152e9i	0.394062	−	0.299750i
$172$	−8.03479e9	−	1.39167e10i	−0.699997	−	1.21243i
$173$	1.57684e9	−	8.94273e9i	0.133839	−	0.759037i	−0.841823	−	0.539754i	$-0.818517\pi$
$173$	1.57684e9	−	8.94273e9i	0.133839	−	0.759037i	0.975661	−	0.219283i	$-0.0703716\pi$
$174$	−1.09364e9	+	5.97001e8i	−0.0904484	+	0.0493746i
$175$	−3.12836e8	−	1.13863e8i	−0.0252143	−	0.00917724i
$176$	−1.48352e10	−	5.39956e9i	−1.16543	−	0.424182i
$177$	−3.66088e8	+	1.53022e10i	−0.0280353	+	1.17186i
$178$	−6.06314e8	+	3.43857e9i	−0.0452697	+	0.256737i
$179$	−9.77182e9	−	1.69253e10i	−0.711438	−	1.23225i	−0.964318	−	0.264748i	$-0.914711\pi$
$179$	−9.77182e9	−	1.69253e10i	−0.711438	−	1.23225i	0.252880	−	0.967498i	$-0.418622\pi$
$180$	−5.13349e9	−	9.96341e9i	−0.364490	−	0.707427i
$181$	1.29853e10	−	2.24912e10i	0.899289	−	1.55761i	0.0708832	−	0.997485i	$-0.477418\pi$
$181$	1.29853e10	−	2.24912e10i	0.899289	−	1.55761i	0.828405	−	0.560129i	$-0.189248\pi$
$182$	3.46412e8	+	2.90674e8i	0.0234030	+	0.0196375i
$183$	4.36128e9	+	5.45751e9i	0.287464	+	0.359720i
$184$	9.53792e8	+	5.40922e9i	0.0613442	+	0.347900i
$185$	−5.82140e9	+	4.88474e9i	−0.365389	+	0.306597i
$186$	−2.49104e9	+	2.82847e9i	−0.152607	+	0.173278i
$187$	2.19464e10	−	7.98783e9i	1.31243	−	0.477685i
$188$	1.37856e10			0.804850
$189$	4.35163e8	+	1.52881e9i	0.0248070	+	0.0871516i
$190$	1.69262e9			0.0942253
$191$	1.30602e10	−	4.75351e9i	0.710065	−	0.258443i	0.0383631	−	0.999264i	$-0.487786\pi$
$191$	1.30602e10	−	4.75351e9i	0.710065	−	0.258443i	0.671702	+	0.740821i	$0.265563\pi$
$192$	−4.23697e9	−	1.25685e10i	−0.225009	−	0.667463i
$193$	−3.44582e8	+	2.89139e8i	−0.0178766	+	0.0150002i	−0.651682	−	0.758492i	$-0.725936\pi$
$193$	−3.44582e8	+	2.89139e8i	−0.0178766	+	0.0150002i	0.633806	+	0.773492i	$0.281492\pi$
$194$	−1.11318e9	−	6.31315e9i	−0.0564231	−	0.319991i
$195$	−9.17464e9	+	2.34465e10i	−0.454395	+	1.16124i
$196$	1.48896e10	+	1.24939e10i	0.720661	+	0.604706i
$197$	−1.48978e10	+	2.58038e10i	−0.704734	+	1.22063i	0.262054	+	0.965053i	$0.415600\pi$
$197$	−1.48978e10	+	2.58038e10i	−0.704734	+	1.22063i	−0.966788	+	0.255581i	$0.917733\pi$
$198$	1.58184e9	−	6.99588e9i	0.0731426	−	0.323481i
$199$	−1.10366e10	−	1.91160e10i	−0.498881	−	0.864086i	0.501119	−	0.865379i	$-0.332922\pi$
$199$	−1.10366e10	−	1.91160e10i	−0.498881	−	0.864086i	−0.999999	+	0.00129214i	$0.999589\pi$
$200$	−5.14280e8	+	2.91663e9i	−0.0227282	+	0.128898i
$201$	−2.54422e10	−	1.55120e10i	−1.09944	−	0.670324i
$202$	−1.07589e9	−	3.91591e8i	−0.0454659	−	0.0165482i
$203$	−9.35904e8	−	3.40641e8i	−0.0386811	−	0.0140788i
$204$	1.91377e10	+	1.16681e10i	0.773665	+	0.471700i
$205$	3.91558e9	−	2.22064e10i	0.154847	−	0.878184i
$206$	1.52858e9	+	2.64757e9i	0.0591405	+	0.102434i
$207$	2.01620e10	−	6.26398e9i	0.763252	−	0.237128i
$208$	−1.70178e10	+	2.94758e10i	−0.630404	+	1.09189i
$209$	−1.52959e10	−	1.28348e10i	−0.554519	−	0.465297i
$210$	−1.77100e8	+	4.52593e8i	−0.00628394	+	0.0160591i
$211$	1.04654e9	+	5.93525e9i	0.0363485	+	0.206143i	0.997573	−	0.0696232i	$-0.0221797\pi$
$211$	1.04654e9	+	5.93525e9i	0.0363485	+	0.206143i	−0.961225	+	0.275766i	$0.911069\pi$
$212$	1.87257e10	−	1.57127e10i	0.636688	−	0.534244i
$213$	1.57077e10	+	4.65952e10i	0.522884	+	1.55107i
$214$	5.23676e9	−	1.90602e9i	0.170687	−	0.0621250i
$215$	−3.87964e10			−1.23828
$216$	1.27215e10	−	6.17411e9i	0.397647	−	0.192989i
$217$	−3.01277e9			−0.0922353
$218$	−8.99303e9	+	3.27320e9i	−0.269682	+	0.0981562i
$219$	−3.56908e10	+	4.05253e10i	−1.04847	+	1.19050i
$220$	−3.09687e10	+	2.59858e10i	−0.891294	+	0.747885i
$221$	−8.74328e9	−	4.95856e10i	−0.246552	−	1.39827i
$222$	−2.91365e9	−	3.64601e9i	−0.0805098	−	0.100746i
$223$	4.79845e10	+	4.02638e10i	1.29936	+	1.09029i	0.990255	+	0.139264i	$0.0444736\pi$
$223$	4.79845e10	+	4.02638e10i	1.29936	+	1.09029i	0.309104	+	0.951028i	$0.399971\pi$
$224$	−1.08308e9	+	1.87595e9i	−0.0287438	+	0.0497857i
$225$	1.13708e10	+	5.44379e8i	0.295781	+	0.0141606i
$226$	−3.66348e9	−	6.34534e9i	−0.0934128	−	0.161796i
$227$	2.56021e9	−	1.45197e10i	0.0639969	−	0.362944i	−0.935945	−	0.352147i	$-0.885452\pi$
$227$	2.56021e9	−	1.45197e10i	0.0639969	−	0.362944i	0.999942	−	0.0107977i	$-0.00343709\pi$
$228$	4.58325e8	−	1.91577e10i	0.0112322	−	0.469500i
$229$	4.91315e9	+	1.78824e9i	0.118059	+	0.0429701i	0.400374	−	0.916352i	$-0.368880\pi$
$229$	4.91315e9	+	1.78824e9i	0.118059	+	0.0429701i	−0.282315	+	0.959322i	$0.591102\pi$
$230$	6.06601e9	+	2.20785e9i	0.142932	+	0.0520228i
$231$	5.03235e9	−	2.74709e9i	0.116283	−	0.0634774i
$232$	−1.53856e9	+	8.72559e9i	−0.0348672	+	0.197742i
$233$	3.50624e10	+	6.07298e10i	0.779363	+	1.34990i	0.932310	+	0.361661i	$0.117790\pi$
$233$	3.50624e10	+	6.07298e10i	0.779363	+	1.34990i	−0.152947	+	0.988234i	$0.548876\pi$
$234$	−1.42610e10	−	5.97750e9i	−0.310942	−	0.130331i
$235$	1.66411e10	−	2.88232e10i	0.355940	−	0.616505i
$236$	4.05896e10	+	3.40587e10i	0.851747	+	0.714700i
$237$	−6.73386e9	+	1.02195e9i	−0.138642	+	0.0210408i
$238$	−1.68774e8	−	9.57162e8i	−0.00340964	−	0.0193370i
$239$	−4.76010e10	+	3.99420e10i	−0.943681	+	0.791842i	−0.978222	−	0.207561i	$-0.933448\pi$
$239$	−4.76010e10	+	3.99420e10i	−0.943681	+	0.791842i	0.0345410	+	0.999403i	$0.489003\pi$
$240$	−3.58617e10	−	7.21176e9i	−0.697719	−	0.140311i
$241$	−1.98105e10	+	7.21044e9i	−0.378285	+	0.137684i	−0.524163	−	0.851618i	$-0.675622\pi$
$241$	−1.98105e10	+	7.21044e9i	−0.378285	+	0.137684i	0.145878	+	0.989303i	$0.453399\pi$
$242$	−1.37678e10			−0.258045
$243$	−2.97204e10	−	4.55083e10i	−0.546798	−	0.837264i
$244$	2.41832e10			0.436778
$245$	4.40963e10	−	1.60497e10i	0.781906	−	0.284590i
$246$	1.35769e10	+	2.73030e9i	0.236370	+	0.0475338i
$247$	−3.29763e10	+	2.76704e10i	−0.563723	+	0.473020i
$248$	4.65408e9	+	2.63946e10i	0.0781271	+	0.443081i
$249$	2.47115e10	−	3.75029e9i	0.407382	−	0.0618255i
$250$	1.16706e10	+	9.79283e9i	0.188958	+	0.158554i
$251$	2.25558e10	−	3.90679e10i	0.358697	−	0.621281i	−0.629047	−	0.777368i	$-0.716555\pi$
$251$	2.25558e10	−	3.90679e10i	0.358697	−	0.621281i	0.987743	+	0.156087i	$0.0498879\pi$
$252$	5.07466e9	+	2.12704e9i	0.0792692	+	0.0332256i
$253$	−3.80758e10	−	6.59493e10i	−0.584261	−	1.01197i
$254$	3.95295e9	−	2.24183e10i	0.0595894	−	0.337948i
$255$	4.74978e10	−	2.59284e10i	0.703465	−	0.384012i
$256$	−3.38512e10	−	1.23208e10i	−0.492599	−	0.179291i
$257$	−7.93532e10	−	2.88822e10i	−1.13466	−	0.412982i	−0.294678	−	0.955597i	$-0.595212\pi$
$257$	−7.93532e10	−	2.88822e10i	−1.13466	−	0.412982i	−0.839982	+	0.542614i	$0.817435\pi$
$258$	5.69875e8	−	2.38204e10i	0.00800739	−	0.334704i
$259$	6.47833e8	−	3.67404e9i	0.00894570	−	0.0507336i
$260$	4.35779e10	+	7.54792e10i	0.591407	+	1.02435i
$261$	3.40178e10	+	1.62860e9i	0.453757	+	0.0217237i
$262$	−5.52483e9	+	9.56929e9i	−0.0724375	+	0.125465i
$263$	4.66786e10	+	3.91680e10i	0.601612	+	0.504812i	0.891963	−	0.452108i	$-0.149328\pi$
$263$	4.66786e10	+	3.91680e10i	0.601612	+	0.504812i	−0.290351	+	0.956920i	$0.593772\pi$
$264$	−3.18409e10	−	3.98443e10i	−0.403429	−	0.504834i
$265$	−1.02480e10	−	5.81195e10i	−0.127654	−	0.723961i
$266$	−6.36549e8	+	5.34128e8i	−0.00779587	+	0.00654151i
$267$	6.30774e10	−	7.16217e10i	0.759580	−	0.862470i
$268$	−9.69295e10	+	3.52795e10i	−1.14776	+	0.417749i
$269$	−1.46201e10			−0.170242			−0.0851209	−	0.996371i	$-0.527128\pi$
$269$	−1.46201e10			−0.170242			−0.0851209	+	0.996371i	$0.527128\pi$
$270$	1.19151e9	−	1.65761e10i	0.0136446	−	0.189822i
$271$	2.22347e10			0.250420			0.125210	−	0.992130i	$-0.460039\pi$
$271$	2.22347e10			0.250420			0.125210	+	0.992130i	$0.460039\pi$
$272$	6.87409e10	−	2.50196e10i	0.761474	−	0.277154i
$273$	−3.94851e9	−	1.17128e10i	−0.0430231	−	0.127623i
$274$	1.49371e10	−	1.25337e10i	0.160099	−	0.134339i
$275$	−7.13010e9	−	4.04368e10i	−0.0751794	−	0.426363i
$276$	2.66318e10	−	6.80595e10i	0.276254	−	0.705989i
$277$	−1.16713e11	−	9.79335e10i	−1.19113	−	0.999476i	−0.999839	−	0.0179427i	$-0.994288\pi$
$277$	−1.16713e11	−	9.79335e10i	−1.19113	−	0.999476i	−0.191290	−	0.981534i	$-0.561267\pi$
$278$	−1.60172e10	+	2.77427e10i	−0.160837	+	0.278578i
$279$	9.83818e10	−	3.05654e10i	0.972067	−	0.302003i
$280$	1.72802e9	+	2.99302e9i	0.0168011	+	0.0291004i
$281$	−8.09146e9	+	4.58890e10i	−0.0774192	+	0.439066i	0.921317	+	0.388812i	$0.127114\pi$
$281$	−8.09146e9	+	4.58890e10i	−0.0774192	+	0.439066i	−0.998736	+	0.0502543i	$0.983997\pi$
$282$	1.74526e10	+	1.06408e10i	0.164338	+	0.100196i
$283$	−1.08318e11	−	3.94245e10i	−1.00383	−	0.365365i	−0.212771	−	0.977102i	$-0.568249\pi$
$283$	−1.08318e11	−	3.94245e10i	−1.00383	−	0.365365i	−0.791061	+	0.611737i	$0.790471\pi$
$284$	1.59949e11	+	5.82167e10i	1.45898	+	0.531025i
$285$	−3.95020e10	−	2.40842e10i	−0.354664	−	0.216237i
$286$	−9.68508e9	+	5.49268e10i	−0.0855965	+	0.485442i
$287$	5.53497e9	+	9.58685e9i	0.0481556	+	0.0834080i
$288$	1.63358e10	−	7.22471e10i	0.139919	−	0.618805i
$289$	5.18499e9	−	8.98066e9i	0.0437227	−	0.0757300i
$290$	7.97685e9	+	6.69337e9i	0.0662278	+	0.0555717i
$291$	−6.38504e10	+	1.63175e11i	−0.521970	+	1.33393i
$292$	3.24606e10	+	1.84093e11i	0.261296	+	1.48188i
$293$	1.29042e10	−	1.08279e10i	0.102288	−	0.0858299i	−0.590209	−	0.807250i	$-0.700955\pi$
$293$	1.29042e10	−	1.08279e10i	0.102288	−	0.0858299i	0.692497	+	0.721420i	$0.256510\pi$
$294$	9.20658e9	+	2.73102e10i	0.0718679	+	0.213188i
$295$	1.20208e11	−	4.37521e10i	0.924132	−	0.336356i
$296$	−3.31887e10			−0.251292
$297$	−1.36461e11	+	1.40761e11i	−1.01766	+	1.04973i
$298$	−2.56914e10			−0.188719
$299$	−1.54274e11	+	5.61511e10i	−1.11628	+	0.406292i
$300$	2.60450e10	−	2.95729e10i	0.185643	−	0.210789i
$301$	1.45903e10	−	1.22427e10i	0.102451	−	0.0859664i
$302$	2.87440e9	+	1.63015e10i	0.0198845	+	0.112771i
$303$	1.95369e10	+	2.44476e10i	0.133157	+	0.166627i
$304$	−4.79101e10	−	4.02014e10i	−0.321733	−	0.269966i
$305$	2.91925e10	−	5.05629e10i	0.193162	−	0.334567i
$306$	1.52220e10	+	2.95438e10i	0.0992486	+	0.192628i
$307$	1.28073e11	+	2.21829e11i	0.822878	+	1.42527i	0.903531	+	0.428524i	$0.140966\pi$
$307$	1.28073e11	+	2.21829e11i	0.822878	+	1.42527i	−0.0806528	+	0.996742i	$0.525701\pi$
$308$	3.44634e9	−	1.95452e10i	0.0218213	−	0.123755i
$309$	1.99857e9	−	8.35387e10i	0.0124711	−	0.521284i
$310$	2.95995e10	+	1.07733e10i	0.182035	+	0.0662555i
$311$	6.65416e10	+	2.42192e10i	0.403340	+	0.146804i	0.535721	−	0.844395i	$-0.320040\pi$
$311$	6.65416e10	+	2.42192e10i	0.403340	+	0.146804i	−0.132381	+	0.991199i	$0.542262\pi$
$312$	−9.65151e10	+	5.26863e10i	−0.576633	+	0.314776i
$313$	3.00272e9	−	1.70293e10i	0.0176834	−	0.100287i	−0.974689	−	0.223567i	$-0.928230\pi$
$313$	3.00272e9	−	1.70293e10i	0.0176834	−	0.100287i	0.992372	+	0.123279i	$0.0393411\pi$
$314$	1.18555e10	+	2.05343e10i	0.0688235	+	0.119206i
$315$	1.05731e10	−	8.04258e9i	0.0605067	−	0.0460255i
$316$	−1.17886e10	+	2.04184e10i	−0.0665072	+	0.115194i
$317$	−1.80799e11	−	1.51709e11i	−1.00561	−	0.843807i	−0.0178587	−	0.999841i	$-0.505685\pi$
$317$	−1.80799e11	−	1.51709e11i	−1.00561	−	0.843807i	−0.987752	+	0.156033i	$0.950129\pi$
$318$	3.58351e10	−	5.43843e9i	0.196511	−	0.0298230i
$319$	−2.13309e10	−	1.20974e11i	−0.115332	−	0.654083i
$320$	−8.49138e10	+	7.12511e10i	−0.452693	+	0.379854i
$321$	−1.49335e11	−	3.00312e10i	−0.785037	−	0.157870i
$322$	−2.97799e9	+	1.08390e9i	−0.0154373	+	0.00561871i
$323$	9.25216e10			0.472968
$324$	−1.87292e11	−	1.79744e10i	−0.944206	−	0.0906156i
$325$	−8.85223e10			−0.440127
$326$	1.94353e10	−	7.07389e9i	0.0953044	−	0.0346880i
$327$	2.56452e11	+	5.15723e10i	1.24034	+	0.249432i
$328$	7.54392e10	−	6.33010e10i	0.359886	−	0.301980i
$329$	2.83727e9	+	1.60910e10i	0.0133512	+	0.0757183i
$330$	−5.92644e10	+	8.99414e9i	−0.275094	+	0.0417491i
$331$	1.82248e11	+	1.52924e11i	0.834519	+	0.700244i	0.956324	−	0.292310i	$-0.0944238\pi$
$331$	1.82248e11	+	1.52924e11i	0.834519	+	0.700244i	−0.121805	+	0.992554i	$0.538868\pi$
$332$	4.32609e10	−	7.49301e10i	0.195422	−	0.338481i
$333$	1.61193e10	+	1.26548e11i	0.0718367	+	0.563971i
$334$	−2.63800e10	−	4.56916e10i	−0.115989	−	0.200899i
$335$	−4.32441e10	+	2.45250e11i	−0.187597	+	1.06391i
$336$	1.57624e10	−	8.60449e9i	0.0674677	−	0.0368297i
$337$	3.87477e11	+	1.41030e11i	1.63648	+	0.595631i	0.986419	−	0.164248i	$-0.0525197\pi$
$337$	3.87477e11	+	1.41030e11i	1.63648	+	0.595631i	0.650064	+	0.759879i	$0.274742\pi$
$338$	6.18437e10	+	2.25093e10i	0.257733	+	0.0938072i
$339$	−4.78989e9	+	2.00214e11i	−0.0196982	+	0.823372i
$340$	3.25283e10	−	1.84477e11i	0.132010	−	0.748665i
$341$	−1.85793e11	−	3.21803e11i	−0.744107	−	1.28883i
$342$	1.53676e10	−	2.38999e10i	0.0607419	−	0.0944667i
$343$	−2.31329e10	+	4.00673e10i	−0.0902414	+	0.156303i
$344$	−1.29796e11	−	1.08912e11i	−0.499746	−	0.419336i
$345$	−1.10152e11	−	1.37840e11i	−0.418608	−	0.523827i
$346$	−8.09357e9	−	4.59009e10i	−0.0303597	−	0.172178i
$347$	−8.58760e8	+	7.20585e8i	−0.00317972	+	0.00266810i	−0.644376	−	0.764709i	$-0.722883\pi$
$347$	−8.58760e8	+	7.20585e8i	−0.00317972	+	0.00266810i	0.641196	+	0.767377i	$0.278438\pi$
$348$	7.79180e10	−	8.84724e10i	0.284794	−	0.323371i
$349$	−2.74997e11	+	1.00091e11i	−0.992231	+	0.361143i	−0.786584	−	0.617484i	$-0.788152\pi$
$349$	−2.74997e11	+	1.00091e11i	−0.992231	+	0.361143i	−0.205647	+	0.978626i	$0.565930\pi$
$350$	−1.70877e9			−0.00608662
$351$	2.47768e11	+	3.42422e11i	0.871291	+	1.20415i
$352$	−2.67168e11			−0.927559
$353$	−4.45541e11	+	1.62164e11i	−1.52722	+	0.555862i	−0.962939	−	0.269721i	$-0.913069\pi$
$353$	−4.45541e11	+	1.62164e11i	−1.52722	+	0.555862i	−0.564281	+	0.825583i	$0.690846\pi$
$354$	2.50974e10	+	7.44486e10i	0.0849405	+	0.251966i
$355$	3.14801e11	−	2.64150e11i	1.05198	−	0.882719i
$356$	−5.73686e10	−	3.25353e11i	−0.189299	−	1.07357i
$357$	−9.68062e9	+	2.47396e10i	−0.0315425	+	0.0806093i
$358$	−7.68441e10	−	6.44798e10i	−0.247250	−	0.207468i
$359$	2.51241e11	−	4.35163e11i	0.798300	−	1.38270i	−0.122422	−	0.992478i	$-0.539066\pi$
$359$	2.51241e11	−	4.35163e11i	0.798300	−	1.38270i	0.920722	−	0.390218i	$-0.127600\pi$
$360$	−8.67935e10	−	8.02056e10i	−0.272349	−	0.251677i
$361$	1.21793e11	+	2.10951e11i	0.377433	+	0.653733i
$362$	2.31475e10	−	1.31276e11i	0.0708460	−	0.401788i
$363$	3.21310e11	+	1.95901e11i	0.971280	+	0.592185i
$364$	−4.02070e10	−	1.46341e10i	−0.120045	−	0.0436929i
$365$	4.24090e11	+	1.54356e11i	1.25066	+	0.455204i
$366$	3.06161e10	+	1.86665e10i	0.0891835	+	0.0543748i
$367$	8.92505e10	−	5.06165e11i	0.256811	−	1.45645i	−0.534571	−	0.845124i	$-0.679527\pi$
$367$	8.92505e10	−	5.06165e11i	0.256811	−	1.45645i	0.791382	−	0.611323i	$-0.209362\pi$
$368$	−1.19262e11	−	2.06568e11i	−0.338990	−	0.587148i
$369$	−2.78006e11	−	2.56904e11i	−0.780611	−	0.721361i
$370$	−1.95027e10	+	3.37797e10i	−0.0540987	+	0.0937017i
$371$	2.21944e10	+	1.86233e10i	0.0608220	+	0.0510357i
$372$	1.29951e11	−	3.32100e11i	0.351834	−	0.899137i
$373$	−3.61006e10	−	2.04737e11i	−0.0965661	−	0.547653i	−0.994256	−	0.107026i	$-0.965867\pi$
$373$	−3.61006e10	−	2.04737e11i	−0.0965661	−	0.547653i	0.897690	−	0.440627i	$-0.145244\pi$
$374$	9.18294e10	−	7.70540e10i	0.242694	−	0.203645i
$375$	−1.33026e11	−	3.94605e11i	−0.347372	−	1.03044i
$376$	1.36589e11	−	4.97142e10i	0.352427	−	0.128273i
$377$	−2.64830e11			−0.675197
$378$	4.78272e9	+	6.60985e9i	0.0120493	+	0.0166525i
$379$	5.11931e11			1.27449			0.637243	−	0.770663i	$-0.280075\pi$
$379$	5.11931e11			1.27449			0.637243	+	0.770663i	$0.280075\pi$
$380$	−1.50495e11	+	5.47756e10i	−0.370250	+	0.134760i
$381$	−4.11242e11	+	4.66947e11i	−0.999851	+	1.13529i
$382$	5.46472e10	−	4.58544e10i	0.131305	−	0.110178i
$383$	6.18978e10	+	3.51040e11i	0.146988	+	0.833608i	0.965750	+	0.259475i	$0.0835496\pi$
$383$	6.18978e10	+	3.51040e11i	0.146988	+	0.833608i	−0.818762	+	0.574133i	$0.805339\pi$
$384$	−2.11253e11	−	2.64353e11i	−0.495808	−	0.620432i
$385$	−3.67053e10	−	3.07994e10i	−0.0851443	−	0.0714446i
$386$	−1.15441e9	+	1.99950e9i	−0.00264677	+	0.00458435i
$387$	−3.52240e11	+	5.47808e11i	−0.798250	+	1.24145i
$388$	3.03278e11	+	5.25293e11i	0.679358	+	1.17668i
$389$	6.84736e10	−	3.88333e11i	0.151618	−	0.859866i	−0.810196	−	0.586160i	$-0.800639\pi$
$389$	6.84736e10	−	3.88333e11i	0.151618	−	0.859866i	0.961813	−	0.273707i	$-0.0882498\pi$
$390$	−3.09081e9	+	1.29194e11i	−0.00676521	+	0.282781i
$391$	3.31579e11	+	1.20685e11i	0.717451	+	0.261131i
$392$	1.92583e11	+	7.00946e10i	0.411938	+	0.149933i
$393$	2.65099e11	−	1.44714e11i	0.560585	−	0.306016i
$394$	−2.65567e10	+	1.50611e11i	−0.0555190	+	0.314864i
$395$	2.84608e10	+	4.92955e10i	0.0588248	+	0.101887i
$396$	8.57514e10	+	6.73211e11i	0.175232	+	1.37570i
$397$	−6.50349e10	+	1.12644e11i	−0.131398	+	0.227588i	−0.924216	−	0.381871i	$-0.875280\pi$
$397$	−6.50349e10	+	1.12644e11i	−0.131398	+	0.227588i	0.792818	+	0.609459i	$0.208613\pi$
$398$	−8.67901e10	−	7.28256e10i	−0.173379	−	0.145482i
$399$	2.24558e10	−	3.40795e9i	0.0443558	−	0.00673156i
$400$	−2.23331e10	−	1.26657e11i	−0.0436192	−	0.247377i
$401$	−7.62899e11	+	6.40148e11i	−1.47339	+	1.23632i	−0.560471	+	0.828174i	$0.689380\pi$
$401$	−7.62899e11	+	6.40148e11i	−1.47339	+	1.23632i	−0.912917	+	0.408145i	$0.866176\pi$
$402$	−1.49945e11	−	3.01537e10i	−0.286361	−	0.0575869i
$403$	−7.52788e11	+	2.73993e11i	−1.42167	+	0.517447i
$404$	1.08332e11			0.202321
$405$	−2.63669e11	+	3.69897e11i	−0.486980	+	0.683177i
$406$	−5.11207e9			−0.00933747
$407$	4.32387e11	−	1.57376e11i	0.781084	−	0.284291i
$408$	2.31696e11	+	4.65938e10i	0.413949	+	0.0832448i
$409$	−1.81185e11	+	1.52032e11i	−0.320160	+	0.268646i	−0.788676	−	0.614809i	$-0.789233\pi$
$409$	−1.81185e11	+	1.52032e11i	−0.320160	+	0.268646i	0.468516	+	0.883455i	$0.344789\pi$
$410$	−2.00978e10	−	1.13980e11i	−0.0351253	−	0.199206i
$411$	−5.26942e11	+	7.99703e10i	−0.910908	+	0.138242i
$412$	−2.21589e11	−	1.85935e11i	−0.378888	−	0.317925i
$413$	−3.14005e10	+	5.43872e10i	−0.0531081	+	0.0919860i
$414$	8.62495e10	−	6.56071e10i	0.144296	−	0.109761i
$415$	−1.04444e11	−	1.80902e11i	−0.172849	−	0.299382i
$416$	−1.00019e11	+	5.67234e11i	−0.163742	+	0.928629i
$417$	7.68557e11	−	4.19545e11i	1.24470	−	0.679464i
$418$	−9.63070e10	−	3.50529e10i	−0.154300	−	0.0561604i
$419$	5.69703e11	+	2.07355e11i	0.902995	+	0.328663i	0.751452	−	0.659787i	$-0.229354\pi$
$419$	5.69703e11	+	2.07355e11i	0.902995	+	0.328663i	0.151543	+	0.988451i	$0.451576\pi$
$420$	1.09983e9	−	4.59724e10i	0.00172467	−	0.0720900i
$421$	−1.59940e11	+	9.07063e11i	−0.248134	+	1.40724i	0.564966	+	0.825114i	$0.308889\pi$
$421$	−1.59940e11	+	9.07063e11i	−0.248134	+	1.40724i	−0.813100	+	0.582124i	$0.802222\pi$
$422$	1.54671e10	+	2.67898e10i	0.0237412	+	0.0411209i
$423$	−2.55899e11	−	4.96665e11i	−0.388630	−	0.754279i
$424$	1.28872e11	−	2.23212e11i	0.193647	−	0.335407i
$425$	1.45748e11	+	1.22297e11i	0.216696	+	0.181830i
$426$	1.57560e11	+	1.97164e11i	0.231794	+	0.290057i
$427$	4.97726e9	+	2.82275e10i	0.00724545	+	0.0410910i
$428$	−4.03931e11	+	3.38939e11i	−0.581849	+	0.488230i
$429$	1.00758e12	−	1.14406e12i	1.43622	−	1.63077i
$430$	−1.87123e11	+	6.81073e10i	−0.263949	+	0.0960695i
$431$	1.12321e12			1.56788			0.783941	−	0.620836i	$-0.213207\pi$
$431$	1.12321e12			1.56788			0.783941	+	0.620836i	$0.213207\pi$
$432$	−4.27426e11	+	4.40893e11i	−0.590451	+	0.609055i
$433$	−2.33971e11			−0.319864			−0.159932	−	0.987128i	$-0.551128\pi$
$433$	−2.33971e11			−0.319864			−0.159932	+	0.987128i	$0.551128\pi$
$434$	−1.45312e10	+	5.28894e9i	−0.0196607	+	0.00715591i
$435$	−9.09225e10	−	2.69711e11i	−0.121750	−	0.361158i
$436$	6.93667e11	−	5.82056e11i	0.919310	−	0.771392i
$437$	−5.23861e10	−	2.97096e11i	−0.0687147	−	0.389700i
$438$	−1.01002e11	+	2.58118e11i	−0.131128	+	0.335108i
$439$	−9.14258e11	−	7.67153e11i	−1.17484	−	0.985807i	−0.999999	−	0.00120975i	$-0.999615\pi$
$439$	−9.14258e11	−	7.67153e11i	−1.17484	−	0.985807i	−0.174839	−	0.984597i	$-0.555941\pi$
$440$	−2.13129e11	+	3.69151e11i	−0.271085	+	0.469533i
$441$	1.73735e11	−	7.68362e11i	0.218732	−	0.967369i
$442$	−1.29219e11	−	2.23813e11i	−0.161037	−	0.278924i
$443$	−6.46091e10	+	3.66417e11i	−0.0797035	+	0.452021i	0.918671	+	0.395024i	$0.129264\pi$
$443$	−6.46091e10	+	3.66417e11i	−0.0797035	+	0.452021i	−0.998374	+	0.0569970i	$0.981847\pi$
$444$	3.77050e11	+	2.29886e11i	0.460442	+	0.280730i
$445$	−7.49508e11	−	2.72798e11i	−0.906058	−	0.329778i
$446$	3.02123e11	+	1.09964e11i	0.361557	+	0.131596i
$447$	5.99582e11	+	3.65562e11i	0.710337	+	0.433089i
$448$	9.44961e9	−	5.35914e10i	0.0110831	−	0.0628556i
$449$	−5.94911e11	−	1.03042e12i	−0.690786	−	1.19648i	−0.971581	−	0.236709i	$-0.923931\pi$
$449$	−5.94911e11	−	1.03042e12i	−0.690786	−	1.19648i	0.280794	−	0.959768i	$-0.409402\pi$
$450$	5.57997e10	−	1.73359e10i	0.0641468	−	0.0199292i
$451$	−6.82668e11	+	1.18242e12i	−0.776989	+	1.34578i
$452$	5.31074e11	+	4.45624e11i	0.598456	+	0.502164i
$453$	1.64872e11	−	4.21342e11i	0.183952	−	0.470102i
$454$	−1.31409e10	−	7.45260e10i	−0.0145169	−	0.0823296i
$455$	−7.91327e10	+	6.64003e10i	−0.0865575	+	0.0726304i
$456$	−6.45461e10	−	1.91469e11i	−0.0699083	−	0.207375i
$457$	4.38390e11	−	1.59561e11i	0.470151	−	0.171121i	−0.0960696	−	0.995375i	$-0.530627\pi$
$457$	4.38390e11	−	1.59561e11i	0.470151	−	0.171121i	0.566221	+	0.824254i	$0.308405\pi$
$458$	2.68365e10			0.0284991
$459$	6.51303e10	−	9.06082e11i	0.0684898	−	0.952819i
$460$	−6.10793e11			−0.636039
$461$	−4.28880e11	+	1.56100e11i	−0.442264	+	0.160971i	−0.553547	−	0.832818i	$-0.686726\pi$
$461$	−4.28880e11	+	1.56100e11i	−0.442264	+	0.160971i	0.111283	+	0.993789i	$0.464504\pi$
$462$	1.94496e10	−	2.20841e10i	0.0198619	−	0.0225523i
$463$	−6.66831e11	+	5.59538e11i	−0.674375	+	0.565868i	−0.914357	−	0.404909i	$-0.867303\pi$
$463$	−6.66831e11	+	5.59538e11i	−0.674375	+	0.565868i	0.239982	+	0.970777i	$0.422859\pi$
$464$	−6.68131e10	−	3.78916e11i	−0.0669161	−	0.379500i
$465$	−5.37494e11	−	6.72596e11i	−0.533133	−	0.667138i
$466$	2.75725e11	+	2.31361e11i	0.270857	+	0.227276i
$467$	−6.42551e11	+	1.11293e12i	−0.625146	+	1.08279i	0.363366	+	0.931646i	$0.381627\pi$
$467$	−6.42551e11	+	1.11293e12i	−0.625146	+	1.08279i	−0.988513	+	0.151139i	$0.951706\pi$
$468$	1.46142e12	+	6.99658e10i	1.40822	+	0.0674185i
$469$	−6.11288e10	−	1.05878e11i	−0.0583403	−	0.101048i
$470$	2.96642e10	−	1.68234e11i	0.0280409	−	0.159028i
$471$	1.55007e10	−	6.47919e11i	0.0145130	−	0.606634i
$472$	5.24989e11	+	1.91080e11i	0.486868	+	0.177205i
$473$	2.20745e12	+	8.03444e11i	2.02775	+	0.738041i
$474$	−3.06848e10	+	1.67504e10i	−0.0279204	+	0.0152413i
$475$	2.82463e10	−	1.60193e11i	0.0254590	−	0.144385i
$476$	4.59812e10	+	7.96418e10i	0.0410534	+	0.0711066i
$477$	−9.13696e11	−	3.82975e11i	−0.808107	−	0.338717i
$478$	−1.59471e11	+	2.76213e11i	−0.139720	+	0.242001i
$479$	−9.49325e11	−	7.96578e11i	−0.823958	−	0.691383i	0.129937	−	0.991522i	$-0.458522\pi$
$479$	−9.49325e11	−	7.96578e11i	−0.823958	−	0.691383i	−0.953895	+	0.300139i	$0.902967\pi$
$480$	−6.12028e11	+	9.28832e10i	−0.526243	+	0.0798641i
$481$	−1.72260e11	−	9.76935e11i	−0.146734	−	0.832171i
$482$	−8.28924e10	+	6.95550e10i	−0.0699525	+	0.0586971i
$483$	8.49225e10	+	1.70778e10i	0.0710004	+	0.0142781i
$484$	1.22413e12	−	4.45546e11i	1.01396	−	0.369052i
$485$	1.46439e12			1.20177
$486$	−2.23238e11	−	1.67322e11i	−0.181512	−	0.136047i
$487$	1.32515e12			1.06754			0.533769	−	0.845630i	$-0.320775\pi$
$487$	1.32515e12			1.06754			0.533769	+	0.845630i	$0.320775\pi$
$488$	2.39610e11	−	8.72107e10i	0.191256	−	0.0696115i
$489$	−5.54233e11	−	1.11456e11i	−0.438331	−	0.0881481i
$490$	1.84510e11	−	1.54823e11i	0.144590	−	0.121326i
$491$	−3.50397e11	−	1.98720e12i	−0.272078	−	1.54303i	−0.748093	−	0.663594i	$-0.769030\pi$
$491$	−3.50397e11	−	1.98720e12i	−0.272078	−	1.54303i	0.476015	−	0.879437i	$-0.342081\pi$
$492$	−1.29551e12	+	1.96610e11i	−0.996776	+	0.151274i
$493$	4.36029e11	+	3.65872e11i	0.332433	+	0.278945i
$494$	−1.10476e11	+	1.91351e11i	−0.0834637	+	0.144563i
$495$	1.51108e12	+	6.33367e11i	1.13126	+	0.474168i
$496$	−5.81945e11	−	1.00796e12i	−0.431732	−	0.747783i
$497$	−3.50326e10	+	1.98680e11i	−0.0257554	+	0.146066i
$498$	1.12605e11	−	6.14697e10i	0.0820402	−	0.0447846i
$499$	−4.82759e11	−	1.75710e11i	−0.348560	−	0.126865i	0.161806	−	0.986823i	$-0.448268\pi$
$499$	−4.82759e11	−	1.75710e11i	−0.348560	−	0.126865i	−0.510366	+	0.859957i	$0.670490\pi$
$500$	−1.35458e12	−	4.93025e11i	−0.969255	−	0.352780i
$501$	−3.44911e10	+	1.44170e12i	−0.0244589	+	1.02237i
$502$	4.02078e10	−	2.28030e11i	0.0282581	−	0.160260i
$503$	7.16695e11	+	1.24135e12i	0.499204	+	0.864647i	1.00000		0.000918437i	$-0.000292348\pi$
$503$	7.16695e11	+	1.24135e12i	0.499204	+	0.864647i	−0.500795	+	0.865566i	$0.666959\pi$
$504$	5.79507e10	+	2.77439e9i	0.0400057	+	0.00191527i
$505$	1.30772e11	−	2.26503e11i	0.0894753	−	0.154976i
$506$	−2.99423e11	−	2.51245e11i	−0.203052	−	0.170381i
$507$	−1.12301e12	−	1.40529e12i	−0.754831	−	0.944562i
$508$	3.74022e11	+	2.12119e12i	0.249179	+	1.41316i
$509$	−7.35298e11	+	6.16988e11i	−0.485549	+	0.407424i	−0.852428	−	0.522845i	$-0.824871\pi$
$509$	−7.35298e11	+	6.16988e11i	−0.485549	+	0.407424i	0.366879	+	0.930269i	$0.380426\pi$
$510$	1.83575e11	−	2.08441e11i	0.120156	−	0.136432i
$511$	−2.08198e11	+	7.57780e10i	−0.135078	+	0.0491642i
$512$	−1.41984e12			−0.913116
$513$	−6.98717e11	+	3.39107e11i	−0.445424	+	0.216176i
$514$	−4.33441e11			−0.273902
$515$	−6.56246e11	+	2.38854e11i	−0.411087	+	0.149624i
$516$	7.20195e11	+	2.13637e12i	0.447225	+	1.32664i
$517$	−1.54376e12	+	1.29537e12i	−0.950323	+	0.797416i
$518$	−3.32517e9	−	1.88580e10i	−0.00202923	−	0.0115083i
$519$	−4.64236e11	+	1.18639e12i	−0.280857	+	0.717752i
$520$	7.03970e11	+	5.90701e11i	0.422220	+	0.354285i
$521$	1.14586e12	−	1.98469e12i	0.681336	−	1.18011i	−0.293238	−	0.956040i	$-0.594733\pi$
$521$	1.14586e12	−	1.98469e12i	0.681336	−	1.18011i	0.974573	−	0.224069i	$-0.0719340\pi$
$522$	1.66934e11	−	5.18634e10i	0.0984075	−	0.0305734i
$523$	−4.98633e11	−	8.63657e11i	−0.291422	−	0.504759i	0.682724	−	0.730677i	$-0.260795\pi$
$523$	−4.98633e11	−	8.63657e11i	−0.291422	−	0.504759i	−0.974146	+	0.225918i	$0.927462\pi$
$524$	1.81550e11	−	1.02962e12i	0.105197	−	0.596604i
$525$	3.98789e10	+	2.43140e10i	0.0229101	+	0.0139682i
$526$	2.93900e11	+	1.06971e11i	0.167403	+	0.0609299i
$527$	1.61796e12	+	5.88889e11i	0.913735	+	0.332572i
$528$	1.89112e12	+	1.15301e12i	1.05893	+	0.645623i
$529$	−1.12976e11	+	6.40721e11i	−0.0627245	+	0.355728i
$530$	−1.51458e11	−	2.62332e11i	−0.0833777	−	0.144414i
$531$	4.73607e11	−	2.09458e12i	0.258519	−	1.14333i
$532$	3.93120e10	−	6.80903e10i	0.0212776	−	0.0368539i
$533$	2.25486e12	+	1.89206e12i	1.21017	+	1.01546i
$534$	1.78504e11	−	4.56180e11i	0.0949974	−	0.242773i
$535$	2.21060e11	+	1.25369e12i	0.116659	+	0.661606i
$536$	−8.33159e11	+	6.99103e11i	−0.436000	+	0.365847i
$537$	8.75892e11	+	2.59823e12i	0.454534	+	1.34832i
$538$	−7.05161e10	+	2.56658e10i	−0.0362884	+	0.0132079i
$539$	−2.84138e12			−1.45004
$540$	4.30488e11	+	1.51238e12i	0.217866	+	0.765402i
$541$	2.03546e11			0.102159			0.0510794	−	0.998695i	$-0.483734\pi$
$541$	2.03546e11			0.102159			0.0510794	+	0.998695i	$0.483734\pi$
$542$	1.07243e11	−	3.90332e10i	0.0533791	−	0.0194284i
$543$	−2.40813e12	+	2.73433e12i	−1.18873	+	1.34975i
$544$	9.48331e11	−	7.95744e11i	0.464264	−	0.389564i
$545$	−3.79624e11	−	2.15296e12i	−0.184319	−	1.04532i
$546$	−3.96064e10	−	4.95617e10i	−0.0190721	−	0.0238660i
$547$	5.09924e11	+	4.27877e11i	0.243536	+	0.204351i	0.756383	−	0.654129i	$-0.226965\pi$
$547$	5.09924e11	+	4.27877e11i	0.243536	+	0.204351i	−0.512847	+	0.858480i	$0.671409\pi$
$548$	−9.22485e11	+	1.59779e12i	−0.436965	+	0.756846i
$549$	−4.48908e11	−	8.71271e11i	−0.210903	−	0.409334i
$550$	−1.05377e11	−	1.82519e11i	−0.0491037	−	0.0850501i
$551$	8.45037e10	−	4.79244e11i	0.0390565	−	0.221501i
$552$	1.84304e10	−	7.70380e11i	0.00844909	−	0.353166i
$553$	−2.62592e10	−	9.55758e9i	−0.0119404	−	0.00434595i
$554$	−7.34853e11	−	2.67465e11i	−0.331441	−	0.120635i
$555$	9.35801e11	−	5.10841e11i	0.418663	−	0.228543i
$556$	5.26338e11	−	2.98501e12i	0.233576	−	1.32467i
$557$	4.51240e11	+	7.81571e11i	0.198637	+	0.344049i	0.948087	−	0.318012i	$-0.103015\pi$
$557$	4.51240e11	+	7.81571e11i	0.198637	+	0.344049i	−0.749450	+	0.662061i	$0.769682\pi$
$558$	4.20859e11	−	3.20134e11i	0.183774	−	0.139790i
$559$	2.53222e12	−	4.38593e12i	1.09685	−	1.89980i
$560$	−1.14969e11	−	9.64706e10i	−0.0494009	−	0.0414523i
$561$	−3.23950e12	+	4.91636e11i	−1.38085	+	0.209561i
$562$	4.15315e10	+	2.35537e11i	0.0175616	+	0.0995969i
$563$	−3.00202e12	+	2.51899e12i	−1.25929	+	1.05667i	−0.263532	+	0.964651i	$0.584887\pi$
$563$	−3.00202e12	+	2.51899e12i	−1.25929	+	1.05667i	−0.995757	+	0.0920186i	$0.970668\pi$
$564$	−1.89610e12	−	3.81305e11i	−0.789053	−	0.158678i
$565$	1.57280e12	−	5.72452e11i	0.649315	−	0.236331i
$566$	−5.91651e11			−0.242321
$567$	−1.75671e10	−	2.22313e11i	−0.00713799	−	0.0903318i
$568$	1.79473e12			0.723489
$569$	3.73460e12	−	1.35928e12i	1.49361	−	0.543631i	0.539216	−	0.842168i	$-0.318721\pi$
$569$	3.73460e12	−	1.35928e12i	1.49361	−	0.543631i	0.954398	+	0.298536i	$0.0964984\pi$
$570$	−2.32807e11	−	4.68173e10i	−0.0923760	−	0.0185767i
$571$	−7.88821e11	+	6.61899e11i	−0.310539	+	0.260573i	−0.784715	−	0.619857i	$-0.787191\pi$
$571$	−7.88821e11	+	6.61899e11i	−0.310539	+	0.260573i	0.474176	+	0.880430i	$0.342746\pi$
$572$	−9.16389e11	−	5.19710e12i	−0.357930	−	2.02992i
$573$	−1.92781e12	+	2.92570e11i	−0.747081	+	0.113379i
$574$	4.35262e10	+	3.65228e10i	0.0167358	+	0.0140430i
$575$	3.10185e11	−	5.37256e11i	0.118335	−	0.204963i
$576$	2.35124e11	+	1.84589e12i	0.0890010	+	0.698723i
$577$	8.29829e11	+	1.43731e12i	0.311672	+	0.539832i	0.978724	−	0.205179i	$-0.0657777\pi$
$577$	8.29829e11	+	1.43731e12i	0.311672	+	0.539832i	−0.667053	+	0.745011i	$0.732444\pi$
$578$	9.24270e9	−	5.24180e10i	0.00344448	−	0.0195346i
$579$	5.53922e10	−	3.02378e10i	0.0204831	−	0.0111814i
$580$	−9.25848e11	−	3.36981e11i	−0.339714	−	0.123646i
$581$	9.63645e10	+	3.50738e10i	0.0350852	+	0.0127700i
$582$	−2.15103e10	+	8.99117e11i	−0.00777129	+	0.324835i
$583$	−6.20517e11	+	3.51913e12i	−0.222457	+	1.26161i
$584$	9.85506e11	+	1.70695e12i	0.350592	+	0.607243i
$585$	1.91043e12	−	2.97112e12i	0.674417	−	1.04886i
$586$	4.32311e10	−	7.48785e10i	0.0151446	−	0.0262312i
$587$	−2.56726e12	−	2.15418e12i	−0.892478	−	0.748878i	0.0762274	−	0.997090i	$-0.475713\pi$
$587$	−2.56726e12	−	2.15418e12i	−0.892478	−	0.748878i	−0.968706	+	0.248212i	$0.920157\pi$
$588$	−1.70238e12	−	2.13028e12i	−0.587297	−	0.734918i
$589$	−2.55621e11	−	1.44970e12i	−0.0875140	−	0.496317i
$590$	5.02982e11	−	4.22052e11i	0.170891	−	0.143394i
$591$	2.76281e12	−	3.13705e12i	0.931552	−	1.05774i
$592$	1.35433e12	−	4.92936e11i	0.453187	−	0.164947i
$593$	1.51807e11			0.0504135			0.0252067	−	0.999682i	$-0.491976\pi$
$593$	1.51807e11			0.0504135			0.0252067	+	0.999682i	$0.491976\pi$
$594$	−4.11075e11	+	9.18477e11i	−0.135482	+	0.302712i
$595$	2.22023e11			0.0726225
$596$	2.28428e12	−	8.31412e11i	0.741553	−	0.269903i
$597$	9.89261e11	+	2.93453e12i	0.318732	+	0.945482i
$598$	−6.45523e11	+	5.41658e11i	−0.206422	+	0.173209i
$599$	−9.76595e11	−	5.53854e12i	−0.309951	−	1.75782i	−0.599230	−	0.800577i	$-0.704526\pi$
$599$	−9.76595e11	−	5.53854e12i	−0.309951	−	1.75782i	0.289278	−	0.957245i	$-0.406585\pi$
$600$	1.51408e11	−	3.86935e11i	0.0476946	−	0.121887i
$601$	3.63412e12	+	3.04939e12i	1.13622	+	0.953405i	0.999309	−	0.0371781i	$-0.0118369\pi$
$601$	3.63412e12	+	3.04939e12i	1.13622	+	0.953405i	0.136915	+	0.990583i	$0.456281\pi$
$602$	4.88800e10	−	8.46627e10i	0.0151687	−	0.0262729i
$603$	3.07032e12	+	2.83728e12i	0.945706	+	0.873925i
$604$	−7.83110e11	−	1.35639e12i	−0.239418	−	0.414684i
$605$	5.46131e11	−	3.09727e12i	0.165729	−	0.939895i
$606$	1.37149e11	+	8.36191e10i	0.0413110	+	0.0251871i
$607$	−1.67977e12	−	6.11388e11i	−0.502229	−	0.182796i	0.0784673	−	0.996917i	$-0.474997\pi$
$607$	−1.67977e12	−	6.11388e11i	−0.502229	−	0.182796i	−0.580696	+	0.814120i	$0.697220\pi$
$608$	−9.94571e11	−	3.61994e11i	−0.295168	−	0.107432i
$609$	1.19305e11	+	7.27394e10i	0.0351463	+	0.0214285i
$610$	5.20382e10	−	2.95123e11i	0.0152173	−	0.0863017i
$611$	2.17231e12	+	3.76255e12i	0.630575	+	1.09219i
$612$	−2.30950e12	−	2.13421e12i	−0.665484	−	0.614972i
$613$	8.97771e11	−	1.55498e12i	0.256799	−	0.444789i	−0.708584	−	0.705627i	$-0.750665\pi$
$613$	8.97771e11	−	1.55498e12i	0.256799	−	0.444789i	0.965383	+	0.260838i	$0.0839988\pi$
$614$	1.00715e12	+	8.45097e11i	0.285980	+	0.239966i
$615$	−1.15278e12	+	2.94602e12i	−0.324944	+	0.830419i
$616$	−3.63381e10	−	2.06084e11i	−0.0101683	−	0.0576674i
$617$	−4.09727e12	+	3.43802e12i	−1.13818	+	0.955048i	−0.999378	−	0.0352723i	$-0.988770\pi$
$617$	−4.09727e12	+	3.43802e12i	−1.13818	+	0.955048i	−0.138804	+	0.990320i	$0.544326\pi$
$618$	−1.37013e11	−	4.06434e11i	−0.0377846	−	0.112084i
$619$	4.64841e11	−	1.69188e11i	0.127261	−	0.0463193i	−0.277604	−	0.960695i	$-0.589540\pi$
$619$	4.64841e11	−	1.69188e11i	0.127261	−	0.0463193i	0.404866	+	0.914376i	$0.367318\pi$
$620$	−2.98040e12			−0.810050
$621$	−2.94640e12	+	3.03887e11i	−0.795022	+	0.0819974i
$622$	3.63461e11			0.0973647
$623$	3.67955e11	−	1.33925e11i	0.0978586	−	0.0356176i
$624$	3.15597e12	−	3.58346e12i	0.833300	−	0.946176i
$625$	−1.80065e12	+	1.51093e12i	−0.472031	+	0.396081i
$626$	−1.54122e10	−	8.74072e10i	−0.00401126	−	0.0227490i
$627$	1.74883e12	+	2.18841e12i	0.451901	+	0.565489i
$628$	−1.71862e12	−	1.44210e12i	−0.440923	−	0.369978i
$629$	−1.06605e12	+	1.84646e12i	−0.271551	+	0.470340i
$630$	3.68774e10	−	5.73522e10i	0.00932669	−	0.0145050i
$631$	−6.83547e11	−	1.18394e12i	−0.171647	−	0.297301i	0.767349	−	0.641230i	$-0.221575\pi$
$631$	−6.83547e11	−	1.18394e12i	−0.171647	−	0.297301i	−0.938996	+	0.343929i	$0.888242\pi$
$632$	−4.31682e10	+	2.44819e11i	−0.0107631	+	0.0610406i
$633$	2.02227e10	−	8.45296e11i	0.00500637	−	0.209263i
$634$	−1.13836e12	−	4.14329e11i	−0.279819	−	0.101846i
$635$	4.88652e12	+	1.77855e12i	1.19266	+	0.434094i
$636$	−3.01019e12	+	1.64322e12i	−0.729519	+	0.398234i
$637$	−1.06372e12	+	6.03264e12i	−0.255976	+	1.45171i
$638$	−3.15254e11	−	5.46036e11i	−0.0753299	−	0.130475i
$639$	−8.71675e11	−	6.84329e12i	−0.206824	−	1.62372i
$640$	−1.41404e12	+	2.44919e12i	−0.333159	+	0.577048i
$641$	3.06971e12	+	2.57580e12i	0.718186	+	0.602630i	0.926883	−	0.375351i	$-0.122478\pi$
$641$	3.06971e12	+	2.57580e12i	0.718186	+	0.602630i	−0.208697	+	0.977980i	$0.566922\pi$
$642$	−7.72997e11	+	1.17312e11i	−0.179585	+	0.0272544i
$643$	−1.68695e11	−	9.56716e11i	−0.0389182	−	0.220716i	0.959146	−	0.282912i	$-0.0913006\pi$
$643$	−1.68695e11	−	9.56716e11i	−0.0389182	−	0.220716i	−0.998064	+	0.0621965i	$0.980189\pi$
$644$	2.29703e11	−	1.92744e11i	0.0526236	−	0.0441565i
$645$	5.33615e12	+	1.07309e12i	1.21397	+	0.244129i
$646$	4.46252e11	−	1.62422e11i	0.100817	−	0.0366944i
$647$	2.07885e12			0.466395			0.233198	−	0.972429i	$-0.425081\pi$
$647$	2.07885e12			0.466395			0.233198	+	0.972429i	$0.425081\pi$
$648$	−1.92052e12	+	4.97329e11i	−0.427890	+	0.110804i
$649$	−7.74569e12			−1.71380
$650$	−4.26962e11	+	1.55402e11i	−0.0938165	+	0.0341464i
$651$	4.14384e11	+	8.33323e10i	0.0904250	+	0.0181844i
$652$	−1.49912e12	+	1.25791e12i	−0.324880	+	0.272607i
$653$	3.38608e11	+	1.92034e12i	0.0728766	+	0.413304i	0.999320	+	0.0368699i	$0.0117387\pi$
$653$	3.38608e11	+	1.92034e12i	0.0728766	+	0.413304i	−0.926443	+	0.376434i	$0.877150\pi$
$654$	1.32746e12	−	2.01459e11i	0.283741	−	0.0430613i
$655$	−1.93360e12	−	1.62248e12i	−0.410469	−	0.344425i
$656$	−2.13827e12	+	3.70359e12i	−0.450811	+	0.780827i
$657$	6.02992e12	−	4.58676e12i	1.26260	−	0.960421i
$658$	4.19326e10	+	7.26294e10i	0.00872038	+	0.0151041i
$659$	−1.07304e12	+	6.08551e12i	−0.221631	+	1.25693i	0.647390	+	0.762159i	$0.275861\pi$
$659$	−1.07304e12	+	6.08551e12i	−0.221631	+	1.25693i	−0.869021	+	0.494775i	$0.835250\pi$
$660$	4.97828e12	−	2.71757e12i	1.02125	−	0.557485i
$661$	1.19594e12	+	4.35288e11i	0.243671	+	0.0886891i	0.460969	−	0.887416i	$-0.347502\pi$
$661$	1.19594e12	+	4.35288e11i	0.243671	+	0.0886891i	−0.217298	+	0.976105i	$0.569724\pi$
$662$	1.14748e12	+	4.17648e11i	0.232212	+	0.0845181i
$663$	−1.68949e11	+	7.06196e12i	−0.0339583	+	1.41943i
$664$	1.58416e11	−	8.98422e11i	0.0316259	−	0.179359i
$665$	−9.49099e10	−	1.64389e11i	−0.0188198	−	0.0325968i
$666$	2.99903e11	+	5.82072e11i	0.0590673	+	0.114642i
$667$	9.27970e11	−	1.60729e12i	0.181538	−	0.314433i
$668$	3.82416e12	+	3.20885e12i	0.743091	+	0.623527i
$669$	−5.48623e12	−	6.86522e12i	−1.05890	−	1.32506i
$670$	2.21962e11	+	1.25881e12i	0.0425541	+	0.241336i
$671$	−2.70812e12	+	2.27238e12i	−0.515724	+	0.432743i
$672$	2.00857e11	−	2.28065e11i	0.0379950	−	0.0431416i
$673$	2.80815e11	−	1.02208e11i	0.0527658	−	0.0192052i	−0.315502	−	0.948925i	$-0.602173\pi$
$673$	2.80815e11	−	1.02208e11i	0.0527658	−	0.0192052i	0.368268	+	0.929720i	$0.379951\pi$
$674$	2.11647e12			0.395041
$675$	−1.54892e12	−	3.89389e11i	−0.287184	−	0.0721966i
$676$	−6.22711e12			−1.14690
$677$	−4.73930e12	+	1.72497e12i	−0.867093	+	0.315596i	−0.736989	−	0.675905i	$-0.763753\pi$
$677$	−4.73930e12	+	1.72497e12i	−0.867093	+	0.315596i	−0.130103	+	0.991500i	$0.541531\pi$
$678$	3.28375e11	+	9.74085e11i	0.0596810	+	0.177037i
$679$	−5.50720e11	+	4.62109e11i	−0.0994299	+	0.0834316i
$680$	−3.42977e11	−	1.94512e12i	−0.0615142	−	0.348864i
$681$	−7.53747e11	+	1.92626e12i	−0.134296	+	0.343204i
$682$	−1.46105e12	−	1.22597e12i	−0.258604	−	0.216995i
$683$	1.13832e12	−	1.97163e12i	0.200158	−	0.346683i	−0.748422	−	0.663223i	$-0.769188\pi$
$683$	1.13832e12	−	1.97163e12i	0.200158	−	0.346683i	0.948579	+	0.316540i	$0.102521\pi$
$684$	−5.92934e11	+	2.62232e12i	−0.103575	+	0.458071i
$685$	2.22713e12	+	3.85751e12i	0.386490	+	0.669421i
$686$	−4.12364e10	+	2.33863e11i	−0.00710922	+	0.0403184i
$687$	−6.26305e11	−	3.81855e11i	−0.107271	−	0.0654024i
$688$	6.91421e12	+	2.51656e12i	1.17651	+	0.428213i
$689$	7.23930e12	+	2.63489e12i	1.22380	+	0.445426i
$690$	−7.73266e11	−	4.71457e11i	−0.129870	−	0.0791810i
$691$	2.12817e11	−	1.20695e12i	0.0355104	−	0.201389i	−0.961891	−	0.273433i	$-0.911841\pi$
$691$	2.12817e11	−	1.20695e12i	0.0355104	−	0.201389i	0.997401	+	0.0720434i	$0.0229520\pi$
$692$	2.20504e12	+	3.81924e12i	0.365543	+	0.633140i
$693$	−7.68145e11	+	2.38648e11i	−0.126515	+	0.0393060i
$694$	−2.87699e9	+	4.98310e9i	−0.000470783	+	0.000815421i
$695$	−5.60576e12	−	4.70379e12i	−0.911388	−	0.764745i
$696$	4.52964e11	−	1.15758e12i	0.0731681	−	0.186987i
$697$	−1.09858e12	−	6.23036e12i	−0.176313	−	0.999921i
$698$	−1.15066e12	+	9.65517e11i	−0.183484	+	0.153961i
$699$	−3.14280e12	−	9.32274e12i	−0.497931	−	1.47705i
$700$	1.51931e11	−	5.52982e10i	0.0239168	−	0.00870502i
$701$	1.15369e12			0.180450			0.0902252	−	0.995921i	$-0.471241\pi$
$701$	1.15369e12			0.180450			0.0902252	+	0.995921i	$0.471241\pi$
$702$	1.79616e12	+	1.21662e12i	0.279144	+	0.189076i
$703$	1.82286e12			0.281484
$704$	6.30701e12	−	2.29556e12i	0.967712	−	0.352218i
$705$	−3.08610e12	+	3.50413e12i	−0.470499	+	0.534231i
$706$	−1.86426e12	+	1.56430e12i	−0.282414	+	0.236973i
$707$	2.22963e10	+	1.26449e11i	0.00335619	+	0.0190339i
$708$	−4.64074e12	−	5.80721e12i	−0.694125	−	0.868597i
$709$	4.61341e11	+	3.87111e11i	0.0685669	+	0.0575344i	0.676427	−	0.736510i	$-0.263527\pi$
$709$	4.61341e11	+	3.87111e11i	0.0685669	+	0.0575344i	−0.607860	+	0.794044i	$0.707972\pi$
$710$	1.05464e12	−	1.82669e12i	0.155755	−	0.269775i
$711$	9.54458e11	+	4.56947e10i	0.140070	+	0.00670584i
$712$	−1.74172e12	−	3.01674e12i	−0.253990	−	0.439924i
$713$	9.74889e11	−	5.52887e12i	0.141271	−	0.801186i
$714$	−3.26127e9	+	1.36319e11i	−0.000469617	+	0.0196297i
$715$	−1.19724e13	−	4.35760e12i	−1.71319	−	0.623549i
$716$	8.91906e12	+	3.24627e12i	1.26827	+	0.461611i
$717$	7.65194e12	−	4.17709e12i	1.08127	−	0.590252i
$718$	4.47860e11	−	2.53994e12i	0.0628901	−	0.356668i
$719$	−6.43613e12	−	1.11477e13i	−0.898141	−	1.55563i	−0.829868	−	0.557959i	$-0.811585\pi$
$719$	−6.43613e12	−	1.11477e13i	−0.898141	−	1.55563i	−0.0682726	−	0.997667i	$-0.521749\pi$
$720$	4.73303e12	+	1.98385e12i	0.656362	+	0.275113i
$721$	1.71423e11	−	2.96914e11i	0.0236244	−	0.0409187i
$722$	9.57760e11	+	8.03656e11i	0.131172	+	0.110066i
$723$	2.92423e12	−	4.43789e11i	0.398005	−	0.0604024i
$724$	2.19018e12	+	1.24211e13i	0.296249	+	1.68011i
$725$	7.66592e11	−	6.43247e11i	0.103049	−	0.0864682i
$726$	1.89365e12	+	3.80812e11i	0.252980	+	0.0508740i
$727$	−1.65453e11	+	6.02198e10i	−0.0219669	+	0.00799530i	−0.352980	−	0.935631i	$-0.614832\pi$
$727$	−1.65453e11	+	6.02198e10i	−0.0219669	+	0.00799530i	0.331013	+	0.943626i	$0.392609\pi$
$728$	−4.51148e11			−0.0595289
$729$	2.82908e12	+	7.08139e12i	0.370998	+	0.928634i
$730$	2.31645e12			0.301905
$731$	−1.02285e13	+	3.72287e12i	−1.32490	+	0.482225i
$732$	−3.32622e12	−	6.68901e11i	−0.428205	−	0.0861117i
$733$	1.10709e13	−	9.28958e12i	1.41649	−	1.18858i	0.463306	−	0.886198i	$-0.346663\pi$
$733$	1.10709e13	−	9.28958e12i	1.41649	−	1.18858i	0.953187	−	0.302381i	$-0.0977814\pi$
$734$	−4.58101e11	−	2.59802e12i	−0.0582545	−	0.330378i
$735$	−6.50904e12	+	9.87831e11i	−0.822667	+	0.124850i
$736$	−3.09216e12	−	2.59463e12i	−0.388430	−	0.325931i
$737$	7.53946e12	−	1.30587e13i	0.941318	−	1.63041i
$738$	−1.79188e12	−	7.51064e11i	−0.222359	−	0.0932016i
$739$	−3.65737e11	−	6.33476e11i	−0.0451096	−	0.0781322i	0.842589	−	0.538557i	$-0.181030\pi$
$739$	−3.65737e11	−	6.33476e11i	−0.0451096	−	0.0781322i	−0.887699	+	0.460425i	$0.847697\pi$
$740$	6.40872e11	−	3.63457e12i	0.0785650	−	0.445564i
$741$	5.30100e12	−	2.89374e12i	0.645916	−	0.352597i
$742$	1.39742e11	+	5.08619e10i	0.0169242	+	0.00615991i
$743$	−3.62672e12	−	1.32002e12i	−0.436581	−	0.158902i	0.114374	−	0.993438i	$-0.463514\pi$
$743$	−3.62672e12	−	1.32002e12i	−0.436581	−	0.158902i	−0.550954	+	0.834535i	$0.685736\pi$
$744$	8.99324e10	−	3.75911e12i	0.0107606	−	0.449787i
$745$	1.01911e12	−	5.77966e12i	0.121204	−	0.687384i
$746$	−5.33538e11	−	9.24114e11i	−0.0630725	−	0.109245i
$747$	−3.50261e12	−	1.67688e11i	−0.411575	−	0.0197042i
$748$	−5.67120e12	+	9.82280e12i	−0.662396	+	1.14730i
$749$	−4.78755e11	−	4.01723e11i	−0.0555834	−	0.0466400i
$750$	−1.33434e12	−	1.66974e12i	−0.153990	−	0.192696i
$751$	−4.82128e11	−	2.73429e12i	−0.0553074	−	0.313664i	0.944586	−	0.328264i	$-0.106464\pi$
$751$	−4.82128e11	−	2.73429e12i	−0.0553074	−	0.313664i	−0.999893	+	0.0146003i	$0.995352\pi$
$752$	−4.83538e12	+	4.05737e12i	−0.551380	+	0.462662i
$753$	−4.18299e12	+	4.74961e12i	−0.474143	+	0.538369i
$754$	−1.27733e12	+	4.64910e11i	−0.143924	+	0.0523839i
$755$	−3.78129e12			−0.423524
$756$	−6.39148e11	−	4.32922e11i	−0.0711629	−	0.0482016i
$757$	1.43220e13			1.58516			0.792581	−	0.609767i	$-0.208737\pi$
$757$	1.43220e13			1.58516			0.792581	+	0.609767i	$0.208737\pi$
$758$	2.46916e12	−	8.98699e11i	0.271667	−	0.0988787i
$759$	3.41291e12	+	1.01240e13i	0.373282	+	1.10730i
$760$	−1.29358e12	+	1.08544e12i	−0.140647	+	0.118017i
$761$	1.37154e12	+	7.77841e12i	0.148244	+	0.840736i	0.964705	+	0.263334i	$0.0848222\pi$
$761$	1.37154e12	+	7.77841e12i	0.148244	+	0.840736i	−0.816460	+	0.577402i	$0.804067\pi$
$762$	−1.16378e12	+	2.97413e12i	−0.125047	+	0.319567i
$763$	8.22161e11	+	6.89875e11i	0.0878206	+	0.0736902i
$764$	−3.37490e12	+	5.84549e12i	−0.358377	+	0.620727i
$765$	−7.25014e12	+	2.25248e12i	−0.765367	+	0.237785i
$766$	9.14800e11	+	1.58448e12i	0.0960056	+	0.166287i
$767$	−2.89973e12	+	1.64452e13i	−0.302537	+	1.71577i
$768$	4.31518e12	+	2.63095e12i	0.447583	+	0.272889i
$769$	1.36410e13	+	4.96493e12i	1.40663	+	0.511970i	0.930138	−	0.367210i	$-0.119687\pi$
$769$	1.36410e13	+	4.96493e12i	1.40663	+	0.511970i	0.476489	+	0.879180i	$0.341909\pi$
$770$	−2.31106e11	−	8.41158e10i	−0.0236921	−	0.00862322i
$771$	1.01156e13	+	6.16742e12i	1.03097	+	0.628577i
$772$	3.79347e10	−	2.15138e11i	0.00384378	−	0.0217992i
$773$	−1.96630e12	−	3.40574e12i	−0.198081	−	0.343086i	0.749825	−	0.661636i	$-0.230138\pi$
$773$	−1.96630e12	−	3.40574e12i	−0.198081	−	0.343086i	−0.947906	+	0.318550i	$0.896804\pi$
$774$	−7.37247e11	+	3.26056e12i	−0.0738378	+	0.326556i
$775$	1.51356e12	−	2.62157e12i	0.150710	−	0.261038i
$776$	4.89924e12	+	4.11095e12i	0.485010	+	0.406972i
$777$	−1.90727e11	+	4.87418e11i	−0.0187724	+	0.0479742i
$778$	−3.51458e11	−	1.99322e12i	−0.0343927	−	0.195050i
$779$	−4.14343e12	+	3.47675e12i	−0.403126	+	0.338263i
$780$	−3.90609e12	−	1.15869e13i	−0.377847	−	1.12084i
$781$	−2.33820e13	+	8.51035e12i	−2.24881	+	0.818498i
$782$	1.81114e12			0.173190
$783$	−4.63385e12	−	1.16492e12i	−0.440569	−	0.110757i
$784$	−8.89982e12			−0.841316
$785$	−5.08978e12	+	1.85253e12i	−0.478394	+	0.174121i
$786$	1.02458e12	−	1.16337e12i	0.0957515	−	0.108722i
$787$	1.19610e13	−	1.00364e13i	1.11143	−	0.932596i	0.113285	−	0.993562i	$-0.463863\pi$
$787$	1.19610e13	−	1.00364e13i	1.11143	−	0.932596i	0.998140	+	0.0609660i	$0.0194181\pi$
$788$	−2.51276e12	−	1.42506e13i	−0.232158	−	1.31663i
$789$	−5.33691e12	−	6.67837e12i	−0.490279	−	0.613514i
$790$	2.23811e11	+	1.87800e11i	0.0204437	+	0.0171543i
$791$	−4.10844e11	+	7.11602e11i	−0.0373149	+	0.0646313i
$792$	3.27740e12	+	6.36099e12i	0.295982	+	0.574462i
$793$	3.81076e12	+	6.60043e12i	0.342202	+	0.592711i
$794$	−1.15931e11	+	6.57475e11i	−0.0103516	+	0.0587066i
$795$	−1.98026e11	+	8.27736e12i	−0.0175821	+	0.734919i
$796$	1.00735e13	+	3.66644e12i	0.889345	+	0.323695i
$797$	6.32997e12	+	2.30392e12i	0.555698	+	0.202258i	0.604576	−	0.796547i	$-0.293342\pi$
$797$	6.32997e12	+	2.30392e12i	0.555698	+	0.202258i	−0.0488781	+	0.998805i	$0.515565\pi$
$798$	1.02326e11	−	5.58586e10i	0.00893253	−	0.00487615i
$799$	1.62150e12	−	9.19599e12i	0.140753	−	0.798248i
$800$	−1.08824e12	−	1.88489e12i	−0.0939333	−	0.162697i
$801$	−1.06569e13	+	8.10632e12i	−0.914709	+	0.695789i
$802$	−2.55584e12	+	4.42685e12i	−0.218147	+	0.377842i
$803$	−2.09334e13	−	1.75652e13i	−1.77672	−	1.49085i
$804$	1.43078e13	−	2.17139e12i	1.20759	−	0.183267i
$805$	−1.25710e11	−	7.12937e11i	−0.0105509	−	0.0598370i
$806$	−3.14987e12	+	2.64305e12i	−0.262896	+	0.220596i
$807$	2.01089e12	+	4.04388e11i	0.166900	+	0.0335635i
$808$	1.07336e12	−	3.90673e11i	0.0885923	−	0.0322450i
$809$	8.17110e12			0.670675			0.335338	−	0.942098i	$-0.391150\pi$
$809$	8.17110e12			0.670675			0.335338	+	0.942098i	$0.391150\pi$
$810$	−6.22374e11	+	2.24697e12i	−0.0508006	+	0.183406i
$811$	2.07621e13			1.68530			0.842651	−	0.538460i	$-0.180994\pi$
$811$	2.07621e13			1.68530			0.842651	+	0.538460i	$0.180994\pi$
$812$	4.54526e11	−	1.65434e11i	0.0366908	−	0.0133543i
$813$	−3.05822e12	−	6.15005e11i	−0.245505	−	0.0493709i
$814$	1.80922e12	−	1.51812e12i	0.144438	−	0.121198i
$815$	8.20427e11	+	4.65287e12i	0.0651375	+	0.369413i
$816$	−1.01468e13	+	1.53991e12i	−0.801170	+	0.121588i
$817$	7.12893e12	+	5.98188e12i	0.559790	+	0.469719i
$818$	−6.07001e11	+	1.05136e12i	−0.0474023	+	0.0821032i
$819$	2.19116e11	+	1.72022e12i	0.0170175	+	0.133600i
$820$	5.47550e12	+	9.48385e12i	0.422923	+	0.732525i
$821$	3.56272e12	−	2.02052e13i	0.273676	−	1.55210i	−0.469458	−	0.882955i	$-0.655551\pi$
$821$	3.56272e12	−	2.02052e13i	0.273676	−	1.55210i	0.743135	−	0.669142i	$-0.233338\pi$
$822$	−2.40117e12	+	1.31076e12i	−0.183442	+	0.100139i
$823$	−1.30605e13	−	4.75362e12i	−0.992336	−	0.361181i	−0.205712	−	0.978613i	$-0.565951\pi$
$823$	−1.30605e13	−	4.75362e12i	−0.992336	−	0.361181i	−0.786625	+	0.617432i	$0.788173\pi$
$824$	−2.86605e12	−	1.04316e12i	−0.216576	−	0.0788274i
$825$	−1.37777e11	+	5.75900e12i	−0.0103546	+	0.432817i
$826$	−5.59742e10	+	3.17445e11i	−0.00418386	+	0.0237279i
$827$	−7.13700e12	−	1.23617e13i	−0.530568	−	0.918971i	−0.999364	−	0.0356643i	$-0.988645\pi$
$827$	−7.13700e12	−	1.23617e13i	−0.530568	−	0.918971i	0.468796	−	0.883307i	$-0.344688\pi$
$828$	−5.54551e12	+	8.62445e12i	−0.410020	+	0.637668i
$829$	−3.70442e12	+	6.41625e12i	−0.272411	+	0.471830i	−0.969479	−	0.245175i	$-0.921154\pi$
$829$	−3.70442e12	+	6.41625e12i	−0.272411	+	0.471830i	0.697067	+	0.717006i	$0.254488\pi$
$830$	−8.21329e11	−	6.89177e11i	−0.0600711	−	0.0504056i
$831$	1.33441e13	+	1.66983e13i	0.970702	+	1.21469i
$832$	−2.51267e12	−	1.42500e13i	−0.181794	−	1.03101i
$833$	1.00857e13	−	8.46289e12i	0.725776	−	0.608999i
$834$	2.97040e12	−	3.37276e12i	0.212603	−	0.241401i
$835$	1.13254e13	−	4.12212e12i	0.806242	−	0.293448i
$836$	9.69725e12			0.686626
$837$	−1.43771e13	+	1.48283e12i	−1.01253	+	0.104431i
$838$	3.11181e12			0.217979
$839$	−1.28307e13	+	4.67001e12i	−0.893970	+	0.325378i	−0.747834	−	0.663886i	$-0.768906\pi$
$839$	−1.28307e13	+	4.67001e12i	−0.893970	+	0.325378i	−0.146136	+	0.989264i	$0.546684\pi$
$840$	−1.54890e11	−	4.59464e11i	−0.0107341	−	0.0318416i
$841$	−8.81973e12	+	7.40063e12i	−0.607958	+	0.510137i
$842$	8.20932e11	+	4.65573e12i	0.0562863	+	0.319215i
$843$	2.38219e12	−	6.08788e12i	0.162462	−	0.415185i
$844$	−2.24217e12	−	1.88141e12i	−0.152100	−	0.127627i
$845$	−7.51697e12	+	1.30198e13i	−0.507210	+	0.878514i
$846$	−2.10615e12	−	1.94629e12i	−0.141359	−	0.130629i
$847$	7.71998e11	+	1.33714e12i	0.0515396	+	0.0892692i
$848$	−1.94360e12	+	1.10227e13i	−0.129070	+	0.731991i
$849$	1.38078e13	+	8.41858e12i	0.912097	+	0.556102i
$850$	9.17666e11	+	3.34003e11i	0.0602975	+	0.0219465i
$851$	6.53277e12	+	2.37773e12i	0.426987	+	0.155410i
$852$	−2.03895e13	−	1.24314e13i	−1.32565	−	0.808244i
$853$	−3.48320e12	+	1.97542e13i	−0.225272	+	1.27758i	0.636892	+	0.770953i	$0.280220\pi$
$853$	−3.48320e12	+	1.97542e13i	−0.225272	+	1.27758i	−0.862164	+	0.506628i	$0.830892\pi$
$854$	7.35600e10	+	1.27410e11i	0.00473240	+	0.00819675i
$855$	4.76705e12	+	4.40522e12i	0.305072	+	0.281916i
$856$	−2.77989e12	+	4.81491e12i	−0.176968	+	0.306518i
$857$	−1.19917e13	−	1.00623e13i	−0.759396	−	0.637209i	0.178574	−	0.983927i	$-0.442852\pi$
$857$	−1.19917e13	−	1.00623e13i	−0.759396	−	0.637209i	−0.937970	+	0.346718i	$0.887296\pi$
$858$	2.85137e12	−	7.28689e12i	0.179622	−	0.459039i
$859$	−1.80369e12	−	1.02293e13i	−0.113030	−	0.641025i	−0.987707	−	0.156318i	$-0.950037\pi$
$859$	−1.80369e12	−	1.02293e13i	−0.113030	−	0.641025i	0.874677	−	0.484707i	$-0.161074\pi$
$860$	1.44335e13	−	1.21112e13i	0.899766	−	0.754993i
$861$	−4.96125e11	−	1.47170e12i	−0.0307664	−	0.0912649i
$862$	5.41749e12	−	1.97180e12i	0.334207	−	0.121641i
$863$	1.57454e13			0.966288			0.483144	−	0.875541i	$-0.339495\pi$
$863$	1.57454e13			0.966288			0.483144	+	0.875541i	$0.339495\pi$
$864$	−4.24520e12	+	9.48520e12i	−0.259171	+	0.579075i
$865$	1.06471e13			0.646637
$866$	−1.12849e12	+	4.10737e11i	−0.0681817	+	0.0248161i
$867$	−9.61559e11	+	1.09181e12i	−0.0577949	+	0.0656236i
$868$	1.12085e12	−	9.40505e11i	0.0670207	−	0.0562370i
$869$	−5.98495e11	−	3.39423e12i	−0.0356018	−	0.201908i
$870$	−9.12019e11	−	1.14126e12i	−0.0539718	−	0.0675379i
$871$	−2.49030e13	−	2.08961e13i	−1.46612	−	1.23022i
$872$	4.77387e12	−	8.26859e12i	0.279606	−	0.484292i
$873$	1.32955e13	−	2.06774e13i	0.774713	−	1.20484i
$874$	−7.74224e11	−	1.34100e12i	−0.0448813	−	0.0777367i
$875$	2.96683e11	−	1.68258e12i	0.0171103	−	0.0970372i
$876$	6.27246e11	−	2.62185e13i	0.0359890	−	1.50431i
$877$	1.03678e13	+	3.77357e12i	0.591818	+	0.215404i	0.620529	−	0.784184i	$-0.286918\pi$
$877$	1.03678e13	+	3.77357e12i	0.591818	+	0.215404i	−0.0287108	+	0.999588i	$0.509140\pi$
$878$	−5.75641e12	−	2.09516e12i	−0.326908	−	0.118985i
$879$	−2.07437e12	+	1.13237e12i	−0.117202	+	0.0639790i
$880$	3.21434e12	−	1.82294e13i	0.180684	−	1.02471i
$881$	−6.34675e12	−	1.09929e13i	−0.354944	−	0.614781i	0.632164	−	0.774834i	$-0.282167\pi$
$881$	−6.34675e12	−	1.09929e13i	−0.354944	−	0.614781i	−0.987108	+	0.160053i	$0.948833\pi$
$882$	−5.10904e11	−	4.01097e12i	−0.0284270	−	0.223172i
$883$	−6.78125e11	+	1.17455e12i	−0.0375394	+	0.0650201i	−0.884185	−	0.467138i	$-0.845285\pi$
$883$	−6.78125e11	+	1.17455e12i	−0.0375394	+	0.0650201i	0.846645	+	0.532158i	$0.178619\pi$
$884$	1.87321e13	+	1.57181e13i	1.03169	+	0.865693i
$885$	−1.77439e13	+	2.69286e12i	−0.972307	+	0.147560i
$886$	3.31623e11	+	1.88073e12i	0.0180798	+	0.102536i
$887$	−1.03849e13	+	8.71394e12i	−0.563306	+	0.472670i	−0.879417	−	0.476052i	$-0.842067\pi$
$887$	−1.03849e13	+	8.71394e12i	−0.563306	+	0.472670i	0.316111	+	0.948722i	$0.397623\pi$
$888$	4.56486e12	+	9.17990e11i	0.246360	+	0.0495427i
$889$	−2.39894e12	+	8.73142e11i	−0.128813	+	0.0468842i
$890$	−4.09394e12			−0.218719
$891$	2.26626e13	−	1.55861e13i	1.20465	−	0.828491i
$892$	−3.04211e13			−1.60891
$893$	−7.50199e12	+	2.73050e12i	−0.394771	+	0.143685i
$894$	3.53366e12	+	7.10616e11i	0.185015	+	0.0372063i
$895$	1.75539e13	−	1.47295e13i	0.914471	−	0.767332i
$896$	−2.41091e11	−	1.36729e12i	−0.0124967	−	0.0708722i
$897$	2.27723e13	−	3.45600e12i	1.17447	−	0.178241i
$898$	−4.67829e12	−	3.92555e12i	−0.240073	−	0.201445i
$899$	4.52808e12	−	7.84287e12i	0.231204	−	0.400458i
$900$	−4.40027e12	+	3.34714e12i	−0.223557	+	0.170052i
$901$	−8.27896e12	−	1.43396e13i	−0.418518	−	0.724894i
$902$	−1.21692e12	+	6.90147e12i	−0.0612112	+	0.347146i
$903$	−2.34542e12	+	1.28033e12i	−0.117388	+	0.0640807i
$904$	6.86895e12	+	2.50009e12i	0.342084	+	0.124508i
$905$	2.86143e13	+	1.04147e13i	1.41796	+	0.516095i
$906$	5.55429e10	−	2.32165e12i	0.00273874	−	0.114478i
$907$	−4.77134e11	+	2.70596e12i	−0.0234103	+	0.132766i	−0.994273	−	0.106870i	$-0.965917\pi$
$907$	−4.77134e11	+	2.70596e12i	−0.0234103	+	0.132766i	0.970863	+	0.239636i	$0.0770282\pi$
$908$	3.58016e12	+	6.20102e12i	0.174790	+	0.302745i
$909$	−2.01095e12	−	3.90298e12i	−0.0976929	−	0.189609i
$910$	−2.65108e11	+	4.59181e11i	−0.0128155	+	0.0221972i
$911$	1.61221e13	+	1.35280e13i	0.775512	+	0.650732i	0.942114	−	0.335292i	$-0.108835\pi$
$911$	1.61221e13	+	1.35280e13i	0.775512	+	0.650732i	−0.166602	+	0.986024i	$0.553280\pi$
$912$	5.47772e12	+	6.85457e12i	0.262194	+	0.328098i
$913$	2.19632e12	+	1.24559e13i	0.104611	+	0.593278i
$914$	1.83434e12	−	1.53919e12i	0.0869404	−	0.0729517i
$915$	−5.41376e12	+	6.14709e12i	−0.255331	+	0.289918i
$916$	−2.38610e12	+	8.68468e11i	−0.111985	+	0.0407590i
$917$	1.23917e12			0.0578721
$918$	−1.27650e12	−	4.48457e12i	−0.0593236	−	0.208415i
$919$	−2.55574e13			−1.18194			−0.590972	−	0.806692i	$-0.701256\pi$
$919$	−2.55574e13			−1.18194			−0.590972	+	0.806692i	$0.701256\pi$
$920$	−6.05179e12	+	2.20267e12i	−0.278508	+	0.101369i
$921$	−1.14798e13	−	3.40534e13i	−0.525733	−	1.55952i
$922$	−1.79455e12	+	1.50581e12i	−0.0817836	+	0.0686246i
$923$	9.31522e12	+	5.28292e13i	0.422460	+	2.39589i
$924$	−1.01463e12	+	2.59297e12i	−0.0457915	+	0.117024i
$925$	2.87152e12	+	2.40949e12i	0.128966	+	0.108215i
$926$	−2.23400e12	+	3.86940e12i	−0.0998467	+	0.172940i
$927$	−2.58554e12	+	1.14348e13i	−0.114999	+	0.508594i
$928$	−3.25565e12	−	5.63896e12i	−0.144103	−	0.249593i
$929$	−6.29727e12	+	3.57136e13i	−0.277384	+	1.57312i	0.453901	+	0.891052i	$0.350032\pi$
$929$	−6.29727e12	+	3.57136e13i	−0.277384	+	1.57312i	−0.731285	+	0.682072i	$0.761079\pi$
$930$	−3.77320e12	−	2.30050e12i	−0.165400	−	0.100844i
$931$	−1.05775e13	−	3.84988e12i	−0.461432	−	0.167947i
$932$	−3.20026e13	−	1.16480e13i	−1.38935	−	0.505684i
$933$	−8.48240e12	−	5.17168e12i	−0.366481	−	0.223442i
$934$	−1.14540e12	+	6.49591e12i	−0.0492491	+	0.279305i
$935$	1.36918e13	+	2.37149e13i	0.585880	+	1.01477i
$936$	1.47322e13	−	4.57703e12i	0.627375	−	0.194914i
$937$	−2.55461e12	+	4.42471e12i	−0.108267	+	0.187524i	−0.915068	−	0.403299i	$-0.867863\pi$
$937$	−2.55461e12	+	4.42471e12i	−0.108267	+	0.187524i	0.806801	+	0.590823i	$0.201197\pi$
$938$	−4.80708e11	−	4.03362e11i	−0.0202753	−	0.0170130i
$939$	−8.84026e11	+	2.25919e12i	−0.0371082	+	0.0948328i
$940$	2.80679e12	+	1.59181e13i	0.117256	+	0.664990i
$941$	−3.82223e12	+	3.20723e12i	−0.158914	+	0.133345i	−0.718778	−	0.695240i	$-0.755298\pi$
$941$	−3.82223e12	+	3.20723e12i	−0.158914	+	0.133345i	0.559863	+	0.828585i	$0.310854\pi$
$942$	−1.06266e12	−	3.15227e12i	−0.0439710	−	0.130435i
$943$	−1.93843e13	+	7.05531e12i	−0.798266	+	0.290545i
$944$	−2.42612e13			−0.994348
$945$	−1.67670e12	+	8.13750e11i	−0.0683931	+	0.0331931i
$946$	1.20574e13			0.489491
$947$	2.70313e13	−	9.83859e12i	1.09217	−	0.397519i	0.267749	−	0.963489i	$-0.413720\pi$
$947$	2.70313e13	−	9.83859e12i	1.09217	−	0.397519i	0.824426	+	0.565970i	$0.191498\pi$
$948$	2.18619e12	−	2.48233e12i	0.0879125	−	0.0998209i
$949$	−4.51301e13	+	3.78687e13i	−1.80621	+	1.51559i
$950$	−1.44982e11	−	8.22232e11i	−0.00577506	−	0.0327520i
$951$	2.06714e13	+	2.58672e13i	0.819515	+	1.02550i
$952$	7.42794e11	+	6.23278e11i	0.0293091	+	0.0245932i
$953$	2.07896e13	−	3.60087e13i	0.816448	−	1.41413i	−0.0918357	−	0.995774i	$-0.529273\pi$
$953$	2.07896e13	−	3.60087e13i	0.816448	−	1.41413i	0.908284	−	0.418355i	$-0.137393\pi$
$954$	−5.07927e12	−	2.43170e11i	−0.198533	−	0.00950480i
$955$	8.14792e12	+	1.41126e13i	0.316980	+	0.549025i
$956$	5.24034e12	−	2.97195e13i	0.202908	−	1.15075i
$957$	−4.12184e11	+	1.72290e13i	−0.0158850	+	0.663983i
$958$	−5.97720e12	−	2.17552e12i	−0.229273	−	0.0834486i
$959$	−2.05485e12	−	7.47906e11i	−0.0784508	−	0.0285537i
$960$	1.36500e13	−	7.45137e12i	0.518697	−	0.283149i
$961$	1.65832e11	−	9.40478e11i	0.00627209	−	0.0355708i
$962$	−2.54586e12	−	4.40956e12i	−0.0958401	−	0.166000i
$963$	1.97093e13	+	8.26114e12i	0.738505	+	0.309543i
$964$	5.11926e12	−	8.86683e12i	0.190924	−	0.330690i
$965$	−4.04024e11	−	3.39016e11i	−0.0149980	−	0.0125848i
$966$	4.39580e11	−	6.67119e10i	0.0162420	−	0.00246494i
$967$	3.55453e12	+	2.01588e13i	0.130726	+	0.741386i	0.977741	+	0.209816i	$0.0672866\pi$
$967$	3.55453e12	+	2.01588e13i	0.130726	+	0.741386i	−0.847014	+	0.531570i	$0.821602\pi$
$968$	1.05220e13	−	8.82900e12i	0.385176	−	0.323201i
$969$	−1.27257e13	−	2.55912e12i	−0.463685	−	0.0932467i
$970$	7.06309e12	−	2.57075e12i	0.256166	−	0.0932369i
$971$	−2.70481e13			−0.976451			−0.488225	−	0.872718i	$-0.662356\pi$
$971$	−2.70481e13			−0.976451			−0.488225	+	0.872718i	$0.662356\pi$
$972$	2.52635e13	+	7.65269e12i	0.907809	+	0.274989i
$973$	3.59253e12			0.128497
$974$	6.39147e12	−	2.32630e12i	0.227554	−	0.0828230i
$975$	1.21756e13	+	2.44850e12i	0.431488	+	0.0867719i
$976$	−8.48244e12	+	7.11761e12i	−0.299224	+	0.251079i
$977$	−8.79943e11	−	4.99040e12i	−0.0308979	−	0.175231i	0.965454	−	0.260575i	$-0.0839121\pi$
$977$	−8.79943e11	−	4.99040e12i	−0.0308979	−	0.175231i	−0.996352	+	0.0853443i	$0.972801\pi$
$978$	−2.86885e12	+	4.35385e11i	−0.100273	+	0.0152177i
$979$	3.69962e13	+	3.10435e13i	1.28717	+	1.08006i
$980$	−1.13950e13	+	1.97367e13i	−0.394636	+	0.683529i
$981$	−3.38466e13	−	1.41868e13i	−1.16682	−	0.489072i
$982$	−5.17858e12	−	8.96957e12i	−0.177709	−	0.307801i
$983$	1.60186e12	−	9.08461e12i	0.0547185	−	0.310324i	−0.945148	−	0.326641i	$-0.894083\pi$
$983$	1.60186e12	−	9.08461e12i	0.0547185	−	0.310324i	0.999867	+	0.0163173i	$0.00519418\pi$
$984$	−1.21270e13	+	6.61996e12i	−0.412359	+	0.225101i
$985$	−3.28287e13	−	1.19487e13i	−1.11119	−	0.404442i
$986$	2.74535e12	+	9.99227e11i	0.0925022	+	0.0336681i
$987$	5.48255e10	−	2.29167e12i	0.00183889	−	0.0768644i
$988$	3.63033e12	−	2.05886e13i	0.121210	−	0.687418i
$989$	1.77459e13	+	3.07369e13i	0.589815	+	1.02159i
$990$	8.40015e12	+	4.02158e11i	0.277926	+	0.0133057i
$991$	2.01024e13	−	3.48184e13i	0.662090	−	1.14677i	−0.317975	−	0.948099i	$-0.603003\pi$
$991$	2.01024e13	−	3.48184e13i	0.662090	−	1.14677i	0.980065	−	0.198675i	$-0.0636638\pi$
$992$	−1.50884e13	−	1.26607e13i	−0.494698	−	0.415101i
$993$	−2.08370e13	−	2.60745e13i	−0.680085	−	0.851028i
$994$	1.79814e11	+	1.01977e12i	0.00584231	+	0.0331334i
$995$	1.98259e13	−	1.66359e13i	0.641254	−	0.538076i
$996$	−8.02275e12	+	9.10949e12i	−0.258319	+	0.293310i
$997$	−1.53940e13	+	5.60295e12i	−0.493427	+	0.179593i	−0.576735	−	0.816931i	$-0.695674\pi$
$997$	−1.53940e13	+	5.60295e12i	−0.493427	+	0.179593i	0.0833084	+	0.996524i	$0.473451\pi$
$998$	−2.63691e12			−0.0841410
$999$	1.28320e12	−	1.78516e13i	0.0407613	−	0.567065i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	27.10.e.a.7.15	yes	156
3.2	odd	2		81.10.e.a.19.12		156
27.4	even	9	inner	27.10.e.a.4.15	✓	156
27.23	odd	18		81.10.e.a.64.12		156

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
27.10.e.a.4.15	✓	156	27.4	even	9	inner
27.10.e.a.7.15	yes	156	1.1	even	1	trivial
81.10.e.a.19.12		156	3.2	odd	2
81.10.e.a.64.12		156	27.23	odd	18

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(4.82322 - 1.75551i) q^{2} +(-137.543 - 27.6597i) q^{3} +(-372.033 + 312.173i) q^{4} +(203.603 + 1154.69i) q^{5} +(-711.954 + 108.048i) q^{6} +(-440.948 - 369.999i) q^{7} +(-2560.36 + 4434.68i) q^{8} +(18152.9 + 7608.76i) q^{9} +(3009.09 + 5211.90i) q^{10} +(12328.1 - 69916.4i) q^{11} +(59805.0 - 32646.7i) q^{12} +(-143827. - 52348.7i) q^{13} +(-2776.32 - 1010.50i) q^{14} +(3934.29 - 164451. i) q^{15} +(38614.5 - 218993. i) q^{16} +(164482. + 284892. i) q^{17} +(100913. + 4831.19i) q^{18} +(140625. - 243570. i) q^{19} +(-436210. - 366024. i) q^{20} +(50415.0 + 63087.1i) q^{21} +(-63277.4 - 358864. i) q^{22} +(821687. - 689477. i) q^{23} +(474820. - 539138. i) q^{24} +(543480. - 197811. i) q^{25} -785607. q^{26} +(-2.28634e6 - 1.54863e6i) q^{27} +279551. q^{28} +(1.62591e6 - 591785. i) q^{29} +(-269718. - 800088. i) q^{30} +(4.00947e6 - 3.36434e6i) q^{31} +(-653471. - 3.70602e6i) q^{32} +(-3.62951e6 + 9.27548e6i) q^{33} +(1.29346e6 + 1.08535e6i) q^{34} +(337456. - 584492. i) q^{35} +(-9.12872e6 + 2.83613e6i) q^{36} +(3.24063e6 + 5.61294e6i) q^{37} +(250677. - 1.42166e6i) q^{38} +(1.83344e7 + 1.11784e7i) q^{39} +(-5.64198e6 - 2.05351e6i) q^{40} +(-1.80717e7 - 6.57754e6i) q^{41} +(353913. + 215779. i) q^{42} +(-5.74575e6 + 3.25858e7i) q^{43} +(1.72395e7 + 2.98597e7i) q^{44} +(-5.08979e6 + 2.25101e7i) q^{45} +(2.75279e6 - 4.76797e6i) q^{46} +(-2.17446e7 - 1.82459e7i) q^{47} +(-1.13684e7 + 2.90528e7i) q^{48} +(-6.94979e6 - 3.94142e7i) q^{49} +(2.27407e6 - 1.90817e6i) q^{50} +(-1.47433e7 - 4.37343e7i) q^{51} +(6.98503e7 - 2.54234e7i) q^{52} -5.03334e7 q^{53} +(-1.37461e7 - 3.45570e6i) q^{54} +8.32418e7 q^{55} +(2.76981e6 - 1.00813e6i) q^{56} +(-2.60790e7 + 2.96116e7i) q^{57} +(6.80326e6 - 5.70861e6i) q^{58} +(-1.89454e7 - 1.07445e8i) q^{59} +(4.98734e7 + 6.24093e7i) q^{60} +(-3.81453e7 - 3.20077e7i) q^{61} +(1.34324e7 - 2.32656e7i) q^{62} +(-5.18924e6 - 1.00716e7i) q^{63} +(4.72694e7 + 8.18730e7i) q^{64} +(3.11630e7 - 1.76734e8i) q^{65} +(-1.22273e6 + 5.11093e7i) q^{66} +(1.99585e8 + 7.26431e7i) q^{67} +(-1.50128e8 - 5.46423e7i) q^{68} +(-1.32088e8 + 7.21048e7i) q^{69} +(601546. - 3.41154e6i) q^{70} +(-1.75242e8 - 3.03528e8i) q^{71} +(-8.02204e7 + 6.10210e7i) q^{72} +(1.92455e8 - 3.33341e8i) q^{73} +(2.54838e7 + 2.13835e7i) q^{74} +(-8.02230e7 + 1.21749e7i) q^{75} +(2.37187e7 + 1.34516e8i) q^{76} +(-3.13051e7 + 2.62681e7i) q^{77} +(1.08054e8 + 2.17296e7i) q^{78} +(4.56193e7 - 1.66041e7i) q^{79} +2.60732e8 q^{80} +(2.71634e8 + 2.76242e8i) q^{81} -9.87104e7 q^{82} +(-1.67411e8 + 6.09326e7i) q^{83} +(-3.84502e7 - 7.73229e6i) q^{84} +(-2.95473e8 + 2.47931e8i) q^{85} +(2.94916e7 + 1.67255e8i) q^{86} +(-2.40001e8 + 3.64233e7i) q^{87} +(2.78492e8 + 2.33682e8i) q^{88} +(-3.40131e8 + 5.89124e8i) q^{89} +(1.49676e7 + 1.17506e8i) q^{90} +(4.40512e7 + 7.62990e7i) q^{91} +(-9.04587e7 + 5.13017e8i) q^{92} +(-6.44529e8 + 3.51839e8i) q^{93} +(-1.36910e8 - 4.98311e7i) q^{94} +(3.09880e8 + 1.12787e8i) q^{95} +(-1.26272e7 + 5.27810e8i) q^{96} +(2.16877e8 - 1.22997e9i) q^{97} +(-1.02712e8 - 1.77903e8i) q^{98} +(7.55768e8 - 1.17538e9i) 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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