Properties

Label 54.9.f.a.5.10
Level $54$
Weight $9$
Character 54.5
Analytic conductor $21.998$
Analytic rank $0$
Dimension $144$
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [54,9,Mod(5,54)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(54, base_ring=CyclotomicField(18))
 
chi = DirichletCharacter(H, H._module([5]))
 
N = Newforms(chi, 9, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("54.5");
 
S:= CuspForms(chi, 9);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 54 = 2 \cdot 3^{3} \)
Weight: \( k \) \(=\) \( 9 \)
Character orbit: \([\chi]\) \(=\) 54.f (of order \(18\), 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: \(21.9984449433\)
Analytic rank: \(0\)
Dimension: \(144\)
Relative dimension: \(24\) over \(\Q(\zeta_{18})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label 5.10
Character \(\chi\) \(=\) 54.5
Dual form 54.9.f.a.11.10

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-7.27231 - 8.66680i) q^{2} +(66.5510 - 46.1732i) q^{3} +(-22.2270 + 126.055i) q^{4} +(270.422 + 742.979i) q^{5} +(-884.154 - 240.999i) q^{6} +(-396.574 - 2249.09i) q^{7} +(1254.14 - 724.077i) q^{8} +(2297.08 - 6145.74i) q^{9} +O(q^{10})\) \(q+(-7.27231 - 8.66680i) q^{2} +(66.5510 - 46.1732i) q^{3} +(-22.2270 + 126.055i) q^{4} +(270.422 + 742.979i) q^{5} +(-884.154 - 240.999i) q^{6} +(-396.574 - 2249.09i) q^{7} +(1254.14 - 724.077i) q^{8} +(2297.08 - 6145.74i) q^{9} +(4472.66 - 7746.87i) q^{10} +(-6022.94 + 16547.9i) q^{11} +(4341.15 + 9415.41i) q^{12} +(33606.8 + 28199.5i) q^{13} +(-16608.4 + 19793.1i) q^{14} +(52302.5 + 36959.7i) q^{15} +(-15395.9 - 5603.66i) q^{16} +(-22028.9 - 12718.4i) q^{17} +(-69969.0 + 24785.4i) q^{18} +(37906.5 + 65655.9i) q^{19} +(-99667.1 + 17574.0i) q^{20} +(-130240. - 131368. i) q^{21} +(187218. - 68141.8i) q^{22} +(321952. + 56768.8i) q^{23} +(50031.3 - 106096. i) q^{24} +(-179653. + 150747. i) q^{25} -496339. i q^{26} +(-130895. - 515069. i) q^{27} +292324. q^{28} +(775325. + 923997. i) q^{29} +(-60037.5 - 722079. i) q^{30} +(62053.1 - 351921. i) q^{31} +(63398.2 + 174185. i) q^{32} +(363236. + 1.37938e6i) q^{33} +(49973.2 + 283412. i) q^{34} +(1.56378e6 - 902849. i) q^{35} +(723647. + 426160. i) q^{36} +(527182. - 913107. i) q^{37} +(293359. - 805998. i) q^{38} +(3.53863e6 + 324971. i) q^{39} +(877121. + 735992. i) q^{40} +(3.26989e6 - 3.89691e6i) q^{41} +(-191395. + 2.08411e6i) q^{42} +(-3.47988e6 - 1.26657e6i) q^{43} +(-1.95208e6 - 1.12703e6i) q^{44} +(5.18734e6 + 44736.2i) q^{45} +(-1.84933e6 - 3.20313e6i) q^{46} +(1.57619e6 - 277925. i) q^{47} +(-1.28335e6 + 337949. i) q^{48} +(516028. - 187819. i) q^{49} +(2.61298e6 + 460740. i) q^{50} +(-2.05329e6 + 170722. i) q^{51} +(-4.30167e6 + 3.60953e6i) q^{52} +1.47197e7i q^{53} +(-3.51209e6 + 4.88019e6i) q^{54} -1.39235e7 q^{55} +(-2.12587e6 - 2.53351e6i) q^{56} +(5.55425e6 + 2.61921e6i) q^{57} +(2.36969e6 - 1.34392e7i) q^{58} +(-4.66351e6 - 1.28129e7i) q^{59} +(-5.82150e6 + 5.77151e6i) q^{60} +(662358. + 3.75642e6i) q^{61} +(-3.50130e6 + 2.02148e6i) q^{62} +(-1.47333e7 - 2.72908e6i) q^{63} +(1.04858e6 - 1.81619e6i) q^{64} +(-1.18636e7 + 3.25949e7i) q^{65} +(9.31323e6 - 1.31794e7i) q^{66} +(3.80055e6 + 3.18904e6i) q^{67} +(2.09286e6 - 2.49417e6i) q^{68} +(2.40474e7 - 1.10875e7i) q^{69} +(-1.91971e7 - 6.98717e6i) q^{70} +(2.60783e7 + 1.50563e7i) q^{71} +(-1.56914e6 - 9.37088e6i) q^{72} +(4.30887e6 + 7.46319e6i) q^{73} +(-1.17475e7 + 2.07141e6i) q^{74} +(-4.99564e6 + 1.83275e7i) q^{75} +(-9.11883e6 + 3.31898e6i) q^{76} +(3.96062e7 + 6.98364e6i) q^{77} +(-2.29175e7 - 3.30319e7i) q^{78} +(-4.67634e7 + 3.92391e7i) q^{79} -1.29542e7i q^{80} +(-3.24936e7 - 2.82345e7i) q^{81} -5.75534e7 q^{82} +(-3.16948e7 - 3.77724e7i) q^{83} +(1.94545e7 - 1.34975e7i) q^{84} +(3.49239e6 - 1.98063e7i) q^{85} +(1.43296e7 + 3.93704e7i) q^{86} +(9.42625e7 + 2.56937e7i) q^{87} +(4.42835e6 + 2.51144e7i) q^{88} +(-3.06540e7 + 1.76981e7i) q^{89} +(-3.73362e7 - 4.52830e7i) q^{90} +(5.00954e7 - 8.67678e7i) q^{91} +(-1.43120e7 + 3.93220e7i) q^{92} +(-1.21196e7 - 2.62859e7i) q^{93} +(-1.38713e7 - 1.16394e7i) q^{94} +(-3.85302e7 + 4.59185e7i) q^{95} +(1.22619e7 + 8.66490e6i) q^{96} +(-4.65354e7 - 1.69375e7i) q^{97} +(-5.38051e6 - 3.10644e6i) q^{98} +(8.78639e7 + 7.50273e7i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 144 q + 882 q^{5} + 768 q^{6} + 25908 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 144 q + 882 q^{5} + 768 q^{6} + 25908 q^{9} - 45756 q^{11} - 21504 q^{12} + 94464 q^{14} - 70002 q^{15} - 182784 q^{18} - 225792 q^{20} - 2071668 q^{21} + 185472 q^{22} + 552996 q^{23} - 1015182 q^{25} - 4137588 q^{27} - 2856132 q^{29} - 861696 q^{30} - 1841490 q^{31} + 10547334 q^{33} - 661248 q^{34} - 12450834 q^{35} - 5104128 q^{36} + 14063616 q^{38} + 4239102 q^{39} - 15673536 q^{41} - 11028480 q^{42} - 4412520 q^{43} - 12558942 q^{45} + 15173838 q^{47} + 3440640 q^{48} - 11347488 q^{49} - 27744768 q^{50} - 3281850 q^{51} + 16379136 q^{54} + 12091392 q^{56} - 13553658 q^{57} - 86547168 q^{59} - 26125056 q^{60} - 34059456 q^{61} + 108329070 q^{63} + 150994944 q^{64} + 22190346 q^{65} + 152091648 q^{66} + 167100948 q^{67} + 13411584 q^{68} - 40190130 q^{69} - 118080000 q^{70} - 251437608 q^{71} - 60948480 q^{72} + 15265278 q^{73} + 41902848 q^{74} + 138868662 q^{75} + 67995648 q^{76} + 564911586 q^{77} + 201203712 q^{78} + 137535768 q^{79} - 23838948 q^{81} - 482857578 q^{83} - 128300544 q^{84} - 343215000 q^{85} - 46237824 q^{86} + 34353810 q^{87} + 47480832 q^{88} + 375969762 q^{89} + 452712960 q^{90} - 155093598 q^{91} + 97042176 q^{92} + 285095622 q^{93} - 70995456 q^{94} - 966996432 q^{95} - 88080384 q^{96} - 484917300 q^{97} - 234233856 q^{98} + 26756370 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/54\mathbb{Z}\right)^\times\).

\(n\) \(29\)
\(\chi(n)\) \(e\left(\frac{5}{18}\right)\)

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 \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −7.27231 8.66680i −0.454519 0.541675i
\(3\) 66.5510 46.1732i 0.821618 0.570039i
\(4\) −22.2270 + 126.055i −0.0868241 + 0.492404i
\(5\) 270.422 + 742.979i 0.432675 + 1.18877i 0.944164 + 0.329476i \(0.106872\pi\)
−0.511489 + 0.859290i \(0.670906\pi\)
\(6\) −884.154 240.999i −0.682217 0.185956i
\(7\) −396.574 2249.09i −0.165171 0.936728i −0.948888 0.315612i \(-0.897790\pi\)
0.783718 0.621117i \(-0.213321\pi\)
\(8\) 1254.14 724.077i 0.306186 0.176777i
\(9\) 2297.08 6145.74i 0.350111 0.936708i
\(10\) 4472.66 7746.87i 0.447266 0.774687i
\(11\) −6022.94 + 16547.9i −0.411375 + 1.13024i 0.545085 + 0.838381i \(0.316497\pi\)
−0.956460 + 0.291863i \(0.905725\pi\)
\(12\) 4341.15 + 9415.41i 0.209353 + 0.454061i
\(13\) 33606.8 + 28199.5i 1.17667 + 0.987342i 0.999995 + 0.00307193i \(0.000977827\pi\)
0.176673 + 0.984270i \(0.443467\pi\)
\(14\) −16608.4 + 19793.1i −0.432329 + 0.515230i
\(15\) 52302.5 + 36959.7i 1.03314 + 0.730069i
\(16\) −15395.9 5603.66i −0.234923 0.0855050i
\(17\) −22028.9 12718.4i −0.263753 0.152278i 0.362293 0.932064i \(-0.381994\pi\)
−0.626045 + 0.779787i \(0.715327\pi\)
\(18\) −69969.0 + 24785.4i −0.666524 + 0.236106i
\(19\) 37906.5 + 65655.9i 0.290870 + 0.503801i 0.974016 0.226481i \(-0.0727220\pi\)
−0.683146 + 0.730282i \(0.739389\pi\)
\(20\) −99667.1 + 17574.0i −0.622919 + 0.109838i
\(21\) −130240. 131368.i −0.669679 0.675479i
\(22\) 187218. 68141.8i 0.799203 0.290886i
\(23\) 321952. + 56768.8i 1.15048 + 0.202861i 0.716186 0.697910i \(-0.245886\pi\)
0.434295 + 0.900771i \(0.356997\pi\)
\(24\) 50031.3 106096.i 0.150798 0.319781i
\(25\) −179653. + 150747.i −0.459912 + 0.385912i
\(26\) 496339.i 1.08614i
\(27\) −130895. 515069.i −0.246303 0.969193i
\(28\) 292324. 0.475590
\(29\) 775325. + 923997.i 1.09621 + 1.30641i 0.948289 + 0.317407i \(0.102812\pi\)
0.147916 + 0.989000i \(0.452743\pi\)
\(30\) −60037.5 722079.i −0.0741203 0.891455i
\(31\) 62053.1 351921.i 0.0671919 0.381064i −0.932605 0.360899i \(-0.882470\pi\)
0.999797 0.0201649i \(-0.00641911\pi\)
\(32\) 63398.2 + 174185.i 0.0604612 + 0.166116i
\(33\) 363236. + 1.37938e6i 0.306290 + 1.16313i
\(34\) 49973.2 + 283412.i 0.0373957 + 0.212081i
\(35\) 1.56378e6 902849.i 1.04209 0.601648i
\(36\) 723647. + 426160.i 0.430841 + 0.253725i
\(37\) 527182. 913107.i 0.281290 0.487208i −0.690413 0.723416i \(-0.742571\pi\)
0.971703 + 0.236207i \(0.0759045\pi\)
\(38\) 293359. 805998.i 0.140691 0.386545i
\(39\) 3.53863e6 + 324971.i 1.52959 + 0.140471i
\(40\) 877121. + 735992.i 0.342625 + 0.287497i
\(41\) 3.26989e6 3.89691e6i 1.15717 1.37906i 0.244866 0.969557i \(-0.421256\pi\)
0.912307 0.409508i \(-0.134300\pi\)
\(42\) −191395. + 2.08411e6i −0.0615082 + 0.669767i
\(43\) −3.47988e6 1.26657e6i −1.01787 0.370473i −0.221417 0.975179i \(-0.571068\pi\)
−0.796449 + 0.604706i \(0.793291\pi\)
\(44\) −1.95208e6 1.12703e6i −0.520819 0.300695i
\(45\) 5.18734e6 + 44736.2i 1.26501 + 0.0109096i
\(46\) −1.84933e6 3.20313e6i −0.413031 0.715391i
\(47\) 1.57619e6 277925.i 0.323011 0.0569556i −0.00979147 0.999952i \(-0.503117\pi\)
0.332803 + 0.942996i \(0.392006\pi\)
\(48\) −1.28335e6 + 337949.i −0.241758 + 0.0636629i
\(49\) 516028. 187819.i 0.0895136 0.0325803i
\(50\) 2.61298e6 + 460740.i 0.418078 + 0.0737183i
\(51\) −2.05329e6 + 170722.i −0.303508 + 0.0252353i
\(52\) −4.30167e6 + 3.60953e6i −0.588334 + 0.493671i
\(53\) 1.47197e7i 1.86550i 0.360525 + 0.932750i \(0.382598\pi\)
−0.360525 + 0.932750i \(0.617402\pi\)
\(54\) −3.51209e6 + 4.88019e6i −0.413038 + 0.573933i
\(55\) −1.39235e7 −1.52159
\(56\) −2.12587e6 2.53351e6i −0.216165 0.257615i
\(57\) 5.55425e6 + 2.61921e6i 0.526170 + 0.248125i
\(58\) 2.36969e6 1.34392e7i 0.209401 1.18757i
\(59\) −4.66351e6 1.28129e7i −0.384861 1.05740i −0.969283 0.245948i \(-0.920901\pi\)
0.584422 0.811450i \(-0.301321\pi\)
\(60\) −5.82150e6 + 5.77151e6i −0.449190 + 0.445333i
\(61\) 662358. + 3.75642e6i 0.0478381 + 0.271303i 0.999339 0.0363413i \(-0.0115703\pi\)
−0.951501 + 0.307645i \(0.900459\pi\)
\(62\) −3.50130e6 + 2.02148e6i −0.236953 + 0.136805i
\(63\) −1.47333e7 2.72908e6i −0.935269 0.173243i
\(64\) 1.04858e6 1.81619e6i 0.0625000 0.108253i
\(65\) −1.18636e7 + 3.25949e7i −0.664603 + 1.82598i
\(66\) 9.31323e6 1.31794e7i 0.490823 0.694574i
\(67\) 3.80055e6 + 3.18904e6i 0.188602 + 0.158256i 0.732200 0.681090i \(-0.238494\pi\)
−0.543598 + 0.839346i \(0.682938\pi\)
\(68\) 2.09286e6 2.49417e6i 0.0978822 0.116651i
\(69\) 2.40474e7 1.10875e7i 1.06089 0.489145i
\(70\) −1.91971e7 6.98717e6i −0.799546 0.291011i
\(71\) 2.60783e7 + 1.50563e7i 1.02623 + 0.592495i 0.915903 0.401400i \(-0.131476\pi\)
0.110328 + 0.993895i \(0.464810\pi\)
\(72\) −1.56914e6 9.37088e6i −0.0583890 0.348699i
\(73\) 4.30887e6 + 7.46319e6i 0.151730 + 0.262805i 0.931864 0.362809i \(-0.118182\pi\)
−0.780133 + 0.625613i \(0.784849\pi\)
\(74\) −1.17475e7 + 2.07141e6i −0.391760 + 0.0690779i
\(75\) −4.99564e6 + 1.83275e7i −0.157887 + 0.579239i
\(76\) −9.11883e6 + 3.31898e6i −0.273328 + 0.0994834i
\(77\) 3.96062e7 + 6.98364e6i 1.12668 + 0.198664i
\(78\) −2.29175e7 3.30319e7i −0.619141 0.892390i
\(79\) −4.67634e7 + 3.92391e7i −1.20060 + 1.00742i −0.200985 + 0.979594i \(0.564414\pi\)
−0.999613 + 0.0278266i \(0.991141\pi\)
\(80\) 1.29542e7i 0.316265i
\(81\) −3.24936e7 2.82345e7i −0.754844 0.655904i
\(82\) −5.75534e7 −1.27296
\(83\) −3.16948e7 3.77724e7i −0.667845 0.795906i 0.320644 0.947200i \(-0.396101\pi\)
−0.988489 + 0.151294i \(0.951656\pi\)
\(84\) 1.94545e7 1.34975e7i 0.390753 0.271105i
\(85\) 3.49239e6 1.98063e7i 0.0669032 0.379427i
\(86\) 1.43296e7 + 3.93704e7i 0.261964 + 0.719740i
\(87\) 9.42625e7 + 2.56937e7i 1.64536 + 0.448487i
\(88\) 4.42835e6 + 2.51144e7i 0.0738434 + 0.418787i
\(89\) −3.06540e7 + 1.76981e7i −0.488571 + 0.282076i −0.723981 0.689820i \(-0.757690\pi\)
0.235411 + 0.971896i \(0.424356\pi\)
\(90\) −3.73362e7 4.52830e7i −0.569063 0.690184i
\(91\) 5.00954e7 8.67678e7i 0.730520 1.26530i
\(92\) −1.43120e7 + 3.93220e7i −0.199779 + 0.548888i
\(93\) −1.21196e7 2.62859e7i −0.162015 0.351391i
\(94\) −1.38713e7 1.16394e7i −0.177666 0.149080i
\(95\) −3.85302e7 + 4.59185e7i −0.473050 + 0.563759i
\(96\) 1.22619e7 + 8.66490e6i 0.144368 + 0.102018i
\(97\) −4.65354e7 1.69375e7i −0.525650 0.191321i 0.0655449 0.997850i \(-0.479121\pi\)
−0.591195 + 0.806529i \(0.701344\pi\)
\(98\) −5.38051e6 3.10644e6i −0.0583336 0.0336789i
\(99\) 8.78639e7 + 7.50273e7i 0.914681 + 0.781049i
\(100\) −1.50093e7 2.59969e7i −0.150093 0.259969i
\(101\) 9.41138e7 1.65948e7i 0.904415 0.159473i 0.297949 0.954582i \(-0.403698\pi\)
0.606467 + 0.795109i \(0.292586\pi\)
\(102\) 1.64118e7 + 1.65539e7i 0.151620 + 0.152933i
\(103\) −1.58943e8 + 5.78507e7i −1.41219 + 0.513996i −0.931772 0.363043i \(-0.881738\pi\)
−0.480420 + 0.877039i \(0.659516\pi\)
\(104\) 6.25662e7 + 1.10321e7i 0.534818 + 0.0943029i
\(105\) 6.23838e7 1.32290e8i 0.513233 1.08835i
\(106\) 1.27573e8 1.07046e8i 1.01049 0.847906i
\(107\) 7.89808e7i 0.602540i 0.953539 + 0.301270i \(0.0974106\pi\)
−0.953539 + 0.301270i \(0.902589\pi\)
\(108\) 6.78366e7 5.05164e6i 0.498619 0.0371311i
\(109\) 2.29035e7 0.162254 0.0811271 0.996704i \(-0.474148\pi\)
0.0811271 + 0.996704i \(0.474148\pi\)
\(110\) 1.01256e8 + 1.20672e8i 0.691591 + 0.824206i
\(111\) −7.07649e6 8.51099e7i −0.0466150 0.560645i
\(112\) −6.49747e6 + 3.68490e7i −0.0412926 + 0.234182i
\(113\) 5.69759e7 + 1.56540e8i 0.349444 + 0.960088i 0.982546 + 0.186020i \(0.0595590\pi\)
−0.633102 + 0.774068i \(0.718219\pi\)
\(114\) −1.76921e7 6.71853e7i −0.104752 0.397791i
\(115\) 4.48849e7 + 2.54555e8i 0.256631 + 1.45543i
\(116\) −1.33708e8 + 7.71963e7i −0.738457 + 0.426348i
\(117\) 2.50504e8 1.41762e8i 1.33682 0.756515i
\(118\) −7.71322e7 + 1.33597e8i −0.397839 + 0.689078i
\(119\) −1.98686e7 + 5.45886e7i −0.0990786 + 0.272216i
\(120\) 9.23564e7 + 8.48157e6i 0.445391 + 0.0409026i
\(121\) −7.33486e7 6.15468e7i −0.342177 0.287120i
\(122\) 2.77393e7 3.30584e7i 0.125215 0.149225i
\(123\) 3.76823e7 4.10325e8i 0.164633 1.79270i
\(124\) 4.29823e7 + 1.56443e7i 0.181804 + 0.0661711i
\(125\) 1.06890e8 + 6.17130e7i 0.437822 + 0.252776i
\(126\) 8.34924e7 + 1.47537e8i 0.331257 + 0.585354i
\(127\) −1.35865e8 2.35325e8i −0.522267 0.904593i −0.999664 0.0259058i \(-0.991753\pi\)
0.477397 0.878688i \(-0.341580\pi\)
\(128\) −2.33661e7 + 4.12008e6i −0.0870455 + 0.0153485i
\(129\) −2.90071e8 + 7.63854e7i −1.04748 + 0.275836i
\(130\) 3.68769e8 1.34221e8i 1.29116 0.469945i
\(131\) 1.24322e7 + 2.19213e6i 0.0422146 + 0.00744358i 0.194716 0.980860i \(-0.437622\pi\)
−0.152501 + 0.988303i \(0.548733\pi\)
\(132\) −1.81952e8 + 1.51284e7i −0.599322 + 0.0498308i
\(133\) 1.32633e8 1.11292e8i 0.423882 0.355679i
\(134\) 5.61302e7i 0.174092i
\(135\) 3.47288e8 2.36538e8i 1.04557 0.712142i
\(136\) −3.68364e7 −0.107677
\(137\) −1.28977e8 1.53709e8i −0.366126 0.436332i 0.551258 0.834335i \(-0.314148\pi\)
−0.917384 + 0.398003i \(0.869703\pi\)
\(138\) −2.70974e8 1.27782e8i −0.747155 0.352334i
\(139\) 7.60704e7 4.31417e8i 0.203778 1.15568i −0.695574 0.718454i \(-0.744850\pi\)
0.899352 0.437226i \(-0.144039\pi\)
\(140\) 7.90509e7 + 2.17190e8i 0.205776 + 0.565365i
\(141\) 9.20645e7 9.12740e7i 0.232925 0.230925i
\(142\) −5.91593e7 3.35509e8i −0.145502 0.825184i
\(143\) −6.69054e8 + 3.86278e8i −1.59999 + 0.923754i
\(144\) −6.98043e7 + 8.17473e7i −0.162342 + 0.190118i
\(145\) −4.76845e8 + 8.25919e8i −1.07871 + 1.86838i
\(146\) 3.33465e7 9.16188e7i 0.0733903 0.201638i
\(147\) 2.56700e7 3.63262e7i 0.0549739 0.0777948i
\(148\) 1.03384e8 + 8.67498e7i 0.215480 + 0.180810i
\(149\) −5.19947e7 + 6.19649e7i −0.105491 + 0.125719i −0.816206 0.577760i \(-0.803927\pi\)
0.710716 + 0.703479i \(0.248371\pi\)
\(150\) 1.95171e8 8.99870e7i 0.385522 0.177752i
\(151\) −5.69503e8 2.07282e8i −1.09544 0.398707i −0.269806 0.962915i \(-0.586960\pi\)
−0.825633 + 0.564208i \(0.809182\pi\)
\(152\) 9.50799e7 + 5.48944e7i 0.178121 + 0.102838i
\(153\) −1.28766e8 + 1.06169e8i −0.234982 + 0.193745i
\(154\) −2.27503e8 3.94046e8i −0.404486 0.700590i
\(155\) 2.78250e8 4.90630e7i 0.482068 0.0850017i
\(156\) −1.19617e8 + 4.38840e8i −0.201974 + 0.740982i
\(157\) −6.61477e8 + 2.40758e8i −1.08872 + 0.396262i −0.823147 0.567829i \(-0.807784\pi\)
−0.265573 + 0.964091i \(0.585561\pi\)
\(158\) 6.80156e8 + 1.19930e8i 1.09139 + 0.192441i
\(159\) 6.79654e8 + 9.79610e8i 1.06341 + 1.53273i
\(160\) −1.12271e8 + 9.42069e7i −0.171313 + 0.143748i
\(161\) 7.46610e8i 1.11119i
\(162\) −8.39957e6 + 4.86946e8i −0.0121954 + 0.707002i
\(163\) −5.08676e8 −0.720594 −0.360297 0.932838i \(-0.617325\pi\)
−0.360297 + 0.932838i \(0.617325\pi\)
\(164\) 4.18546e8 + 4.98804e8i 0.578586 + 0.689532i
\(165\) −9.26621e8 + 6.42891e8i −1.25016 + 0.867364i
\(166\) −9.68714e7 + 5.49385e8i −0.127574 + 0.723510i
\(167\) −3.97243e8 1.09141e9i −0.510728 1.40321i −0.880480 0.474084i \(-0.842779\pi\)
0.369752 0.929131i \(-0.379443\pi\)
\(168\) −2.58459e8 7.04498e7i −0.324455 0.0884388i
\(169\) 1.92558e8 + 1.09205e9i 0.236056 + 1.33874i
\(170\) −1.97055e8 + 1.13770e8i −0.235935 + 0.136217i
\(171\) 4.90578e8 8.21465e7i 0.573752 0.0960737i
\(172\) 2.37006e8 4.10506e8i 0.270798 0.469035i
\(173\) 4.20137e8 1.15432e9i 0.469037 1.28867i −0.449482 0.893289i \(-0.648391\pi\)
0.918518 0.395378i \(-0.129386\pi\)
\(174\) −4.62824e8 1.00381e9i −0.504916 1.09510i
\(175\) 4.10288e8 + 3.44272e8i 0.437458 + 0.367071i
\(176\) 1.85458e8 2.21020e8i 0.193283 0.230346i
\(177\) −9.01972e8 6.37381e8i −0.918967 0.649391i
\(178\) 3.76311e8 + 1.36966e8i 0.374859 + 0.136437i
\(179\) 2.20830e8 + 1.27497e8i 0.215103 + 0.124190i 0.603681 0.797226i \(-0.293700\pi\)
−0.388578 + 0.921416i \(0.627033\pi\)
\(180\) −1.20938e8 + 6.52897e8i −0.115205 + 0.621949i
\(181\) −8.60758e8 1.49088e9i −0.801986 1.38908i −0.918307 0.395869i \(-0.870444\pi\)
0.116321 0.993212i \(-0.462890\pi\)
\(182\) −1.11631e9 + 1.96835e8i −1.01742 + 0.179398i
\(183\) 2.17526e8 + 2.19411e8i 0.193958 + 0.195638i
\(184\) 4.44877e8 1.61922e8i 0.388122 0.141265i
\(185\) 8.20980e8 + 1.44761e8i 0.700884 + 0.123585i
\(186\) −1.39677e8 + 2.96197e8i −0.116701 + 0.247474i
\(187\) 3.43141e8 2.87930e8i 0.280612 0.235461i
\(188\) 2.04865e8i 0.163997i
\(189\) −1.10652e9 + 4.98658e8i −0.867189 + 0.390801i
\(190\) 6.78170e8 0.520384
\(191\) −8.60819e8 1.02588e9i −0.646812 0.770841i 0.338617 0.940924i \(-0.390041\pi\)
−0.985430 + 0.170083i \(0.945596\pi\)
\(192\) −1.40753e7 1.69285e8i −0.0103574 0.124570i
\(193\) −3.81751e8 + 2.16502e9i −0.275138 + 1.56039i 0.463385 + 0.886157i \(0.346635\pi\)
−0.738523 + 0.674228i \(0.764476\pi\)
\(194\) 1.91626e8 + 5.26488e8i 0.135284 + 0.371691i
\(195\) 7.15476e8 + 2.71700e9i 0.494831 + 1.87911i
\(196\) 1.22058e7 + 6.92228e7i 0.00827073 + 0.0469056i
\(197\) −1.78083e9 + 1.02816e9i −1.18238 + 0.682647i −0.956564 0.291523i \(-0.905838\pi\)
−0.225816 + 0.974170i \(0.572505\pi\)
\(198\) 1.12728e7 1.30712e9i 0.00733448 0.850462i
\(199\) 1.08212e9 1.87429e9i 0.690022 1.19515i −0.281808 0.959471i \(-0.590934\pi\)
0.971830 0.235682i \(-0.0757325\pi\)
\(200\) −1.16157e8 + 3.19140e8i −0.0725984 + 0.199462i
\(201\) 4.00178e8 + 3.67505e7i 0.245171 + 0.0225153i
\(202\) −8.28249e8 6.94983e8i −0.497457 0.417416i
\(203\) 1.77067e9 2.11021e9i 1.04269 1.24263i
\(204\) 2.41181e7 2.62623e8i 0.0139259 0.151640i
\(205\) 3.77957e9 + 1.37565e9i 2.14007 + 0.778920i
\(206\) 1.65727e9 + 9.56824e8i 0.920288 + 0.531328i
\(207\) 1.08843e9 1.84823e9i 0.592818 1.00664i
\(208\) −3.59388e8 6.22478e8i −0.192004 0.332560i
\(209\) −1.31478e9 + 2.31830e8i −0.689075 + 0.121503i
\(210\) −1.60021e9 + 4.21387e8i −0.822809 + 0.216673i
\(211\) 3.41335e9 1.24236e9i 1.72207 0.626782i 0.724053 0.689745i \(-0.242277\pi\)
0.998016 + 0.0629629i \(0.0200550\pi\)
\(212\) −1.85550e9 3.27174e8i −0.918579 0.161970i
\(213\) 2.43073e9 2.02104e8i 1.18091 0.0981875i
\(214\) 6.84511e8 5.74373e8i 0.326381 0.273866i
\(215\) 2.92799e9i 1.37030i
\(216\) −5.37111e8 5.51189e8i −0.246745 0.253213i
\(217\) −8.16109e8 −0.368052
\(218\) −1.66561e8 1.98500e8i −0.0737477 0.0878891i
\(219\) 6.31359e8 + 2.97728e8i 0.274473 + 0.129433i
\(220\) 3.09476e8 1.75513e9i 0.132110 0.749235i
\(221\) −3.81669e8 1.04863e9i −0.159999 0.439594i
\(222\) −6.86168e8 + 6.80276e8i −0.282500 + 0.280074i
\(223\) 5.19256e8 + 2.94484e9i 0.209972 + 1.19081i 0.889421 + 0.457089i \(0.151108\pi\)
−0.679449 + 0.733723i \(0.737781\pi\)
\(224\) 3.66615e8 2.11665e8i 0.145619 0.0840731i
\(225\) 5.13773e8 + 1.45038e9i 0.200466 + 0.565915i
\(226\) 9.42354e8 1.63221e9i 0.361227 0.625664i
\(227\) −9.02600e8 + 2.47987e9i −0.339932 + 0.933955i 0.645481 + 0.763776i \(0.276657\pi\)
−0.985413 + 0.170179i \(0.945565\pi\)
\(228\) −4.53619e8 + 6.41927e8i −0.167862 + 0.237545i
\(229\) 2.61657e9 + 2.19556e9i 0.951459 + 0.798369i 0.979543 0.201237i \(-0.0644961\pi\)
−0.0280839 + 0.999606i \(0.508941\pi\)
\(230\) 1.87976e9 2.24021e9i 0.671724 0.800530i
\(231\) 2.95829e9 1.36397e9i 1.03895 0.479025i
\(232\) 1.64141e9 + 5.97425e8i 0.566585 + 0.206220i
\(233\) −3.05123e9 1.76163e9i −1.03526 0.597710i −0.116776 0.993158i \(-0.537256\pi\)
−0.918488 + 0.395449i \(0.870589\pi\)
\(234\) −3.05037e9 1.14013e9i −1.01739 0.380269i
\(235\) 6.32730e8 + 1.09592e9i 0.207466 + 0.359341i
\(236\) 1.71879e9 3.03069e8i 0.554082 0.0976996i
\(237\) −1.30036e9 + 4.77062e9i −0.412163 + 1.51210i
\(238\) 6.17600e8 2.24788e8i 0.192486 0.0700592i
\(239\) 2.85244e9 + 5.02962e8i 0.874229 + 0.154150i 0.592720 0.805409i \(-0.298054\pi\)
0.281509 + 0.959559i \(0.409165\pi\)
\(240\) −5.98136e8 8.62115e8i −0.180283 0.259849i
\(241\) 2.06336e8 1.73137e8i 0.0611657 0.0513241i −0.611692 0.791096i \(-0.709511\pi\)
0.672858 + 0.739772i \(0.265066\pi\)
\(242\) 1.08329e9i 0.315851i
\(243\) −3.46616e9 3.78705e8i −0.994084 0.108612i
\(244\) −4.88239e8 −0.137744
\(245\) 2.79091e8 + 3.32608e8i 0.0774607 + 0.0923141i
\(246\) −3.83024e9 + 2.65742e9i −1.04589 + 0.725638i
\(247\) −5.77546e8 + 3.27543e9i −0.155167 + 0.879995i
\(248\) −1.76995e8 4.86289e8i −0.0467900 0.128555i
\(249\) −3.85339e9 1.05034e9i −1.00241 0.273233i
\(250\) −2.42483e8 1.37519e9i −0.0620757 0.352049i
\(251\) −2.28978e9 + 1.32201e9i −0.576898 + 0.333072i −0.759900 0.650040i \(-0.774752\pi\)
0.183002 + 0.983113i \(0.441419\pi\)
\(252\) 6.71491e8 1.79655e9i 0.166509 0.445489i
\(253\) −2.87850e9 + 4.98571e9i −0.702561 + 1.21687i
\(254\) −1.05146e9 + 2.88887e9i −0.252615 + 0.694055i
\(255\) −6.82098e8 1.47939e9i −0.161319 0.349881i
\(256\) 2.05633e8 + 1.72547e8i 0.0478778 + 0.0401742i
\(257\) 8.71954e8 1.03915e9i 0.199876 0.238203i −0.656791 0.754073i \(-0.728087\pi\)
0.856667 + 0.515869i \(0.172531\pi\)
\(258\) 2.77151e9 + 1.95849e9i 0.625514 + 0.442021i
\(259\) −2.26272e9 8.23563e8i −0.502843 0.183020i
\(260\) −3.84507e9 2.21995e9i −0.841417 0.485792i
\(261\) 7.45963e9 2.64246e9i 1.60752 0.569437i
\(262\) −7.14121e7 1.23689e8i −0.0151554 0.0262499i
\(263\) 4.10081e9 7.23084e8i 0.857130 0.151135i 0.272222 0.962235i \(-0.412242\pi\)
0.584908 + 0.811099i \(0.301130\pi\)
\(264\) 1.45432e9 + 1.46692e9i 0.299396 + 0.301989i
\(265\) −1.09364e10 + 3.98053e9i −2.21764 + 0.807155i
\(266\) −1.92910e9 3.40152e8i −0.385325 0.0679432i
\(267\) −1.22288e9 + 2.59322e9i −0.240624 + 0.510263i
\(268\) −4.86470e8 + 4.08197e8i −0.0943011 + 0.0791280i
\(269\) 6.19925e9i 1.18394i −0.805960 0.591970i \(-0.798350\pi\)
0.805960 0.591970i \(-0.201650\pi\)
\(270\) −4.57562e9 1.28970e9i −0.860984 0.242679i
\(271\) 4.98702e9 0.924622 0.462311 0.886718i \(-0.347020\pi\)
0.462311 + 0.886718i \(0.347020\pi\)
\(272\) 2.67885e8 + 3.19253e8i 0.0489411 + 0.0583257i
\(273\) −6.72442e8 8.08755e9i −0.121061 1.45602i
\(274\) −3.94203e8 + 2.23564e9i −0.0699388 + 0.396642i
\(275\) −1.41250e9 3.88082e9i −0.246978 0.678567i
\(276\) 8.63139e8 + 3.27775e9i 0.148746 + 0.564858i
\(277\) −1.72744e9 9.79680e9i −0.293416 1.66405i −0.673570 0.739123i \(-0.735240\pi\)
0.380154 0.924923i \(-0.375871\pi\)
\(278\) −4.29221e9 + 2.47811e9i −0.718624 + 0.414898i
\(279\) −2.02027e9 1.18975e9i −0.333421 0.196354i
\(280\) 1.30746e9 2.26459e9i 0.212715 0.368433i
\(281\) −3.86968e9 + 1.06319e10i −0.620654 + 1.70523i 0.0847258 + 0.996404i \(0.472999\pi\)
−0.705380 + 0.708829i \(0.749224\pi\)
\(282\) −1.46058e9 1.34132e8i −0.230955 0.0212098i
\(283\) −2.26961e9 1.90443e9i −0.353839 0.296906i 0.448490 0.893788i \(-0.351962\pi\)
−0.802330 + 0.596881i \(0.796406\pi\)
\(284\) −2.47757e9 + 2.95265e9i −0.380848 + 0.453877i
\(285\) −4.44022e8 + 4.83498e9i −0.0673016 + 0.732851i
\(286\) 8.21337e9 + 2.98942e9i 1.22760 + 0.446810i
\(287\) −1.00612e10 5.80886e9i −1.48294 0.856176i
\(288\) 1.21613e9 + 1.04880e7i 0.176770 + 0.00152449i
\(289\) −3.16436e9 5.48084e9i −0.453623 0.785698i
\(290\) 1.06258e10 1.87362e9i 1.50235 0.264905i
\(291\) −3.87904e9 + 1.02148e9i −0.540944 + 0.142448i
\(292\) −1.03655e9 + 3.77273e8i −0.142580 + 0.0518948i
\(293\) 2.81888e9 + 4.97044e8i 0.382477 + 0.0674410i 0.361581 0.932341i \(-0.382237\pi\)
0.0208960 + 0.999782i \(0.493348\pi\)
\(294\) −5.01512e8 + 4.16984e7i −0.0671263 + 0.00558123i
\(295\) 8.25858e9 6.92977e9i 1.09048 0.915020i
\(296\) 1.52688e9i 0.198902i
\(297\) 9.31168e9 + 9.36187e8i 1.19675 + 0.120320i
\(298\) 9.15159e8 0.116046
\(299\) 9.21892e9 + 1.09867e10i 1.15344 + 1.37462i
\(300\) −2.19924e9 1.03709e9i −0.271511 0.128036i
\(301\) −1.46860e9 + 8.32884e9i −0.178911 + 1.01466i
\(302\) 2.34513e9 + 6.44319e9i 0.281929 + 0.774592i
\(303\) 5.49714e9 5.44993e9i 0.652178 0.646578i
\(304\) −2.15692e8 1.22325e9i −0.0252545 0.143225i
\(305\) −2.61182e9 + 1.50794e9i −0.301818 + 0.174254i
\(306\) 1.85657e9 + 3.43897e8i 0.211751 + 0.0392232i
\(307\) 1.79427e9 3.10777e9i 0.201992 0.349861i −0.747178 0.664624i \(-0.768592\pi\)
0.949170 + 0.314763i \(0.101925\pi\)
\(308\) −1.76065e9 + 4.83735e9i −0.195646 + 0.537532i
\(309\) −7.90670e9 + 1.11889e10i −0.867284 + 1.22731i
\(310\) −2.44874e9 2.05474e9i −0.265153 0.222490i
\(311\) 3.48863e9 4.15759e9i 0.372918 0.444427i −0.546647 0.837363i \(-0.684096\pi\)
0.919566 + 0.392936i \(0.128541\pi\)
\(312\) 4.67323e9 2.15468e9i 0.493173 0.227386i
\(313\) 5.47380e9 + 1.99230e9i 0.570311 + 0.207576i 0.611048 0.791594i \(-0.290748\pi\)
−0.0407367 + 0.999170i \(0.512970\pi\)
\(314\) 6.89707e9 + 3.98203e9i 0.709490 + 0.409624i
\(315\) −1.95655e9 1.16845e10i −0.198723 1.18677i
\(316\) −3.90690e9 6.76694e9i −0.391817 0.678647i
\(317\) −5.60327e9 + 9.88007e8i −0.554887 + 0.0978415i −0.444058 0.895998i \(-0.646462\pi\)
−0.110829 + 0.993840i \(0.535350\pi\)
\(318\) 3.54743e9 1.30145e10i 0.346901 1.27268i
\(319\) −1.99599e10 + 7.26482e9i −1.92751 + 0.701556i
\(320\) 1.63295e9 + 2.87932e8i 0.155730 + 0.0274594i
\(321\) 3.64679e9 + 5.25625e9i 0.343471 + 0.495058i
\(322\) −6.47072e9 + 5.42958e9i −0.601907 + 0.505060i
\(323\) 1.92843e9i 0.177172i
\(324\) 4.28135e9 3.46842e9i 0.388508 0.314740i
\(325\) −1.02885e10 −0.922190
\(326\) 3.69925e9 + 4.40860e9i 0.327524 + 0.390328i
\(327\) 1.52425e9 1.05753e9i 0.133311 0.0924912i
\(328\) 1.27924e9 7.25492e9i 0.110524 0.626812i
\(329\) −1.25015e9 3.43477e9i −0.106704 0.293167i
\(330\) 1.23105e10 + 3.35554e9i 1.03805 + 0.282948i
\(331\) −9.68749e8 5.49405e9i −0.0807048 0.457700i −0.998201 0.0599552i \(-0.980904\pi\)
0.917496 0.397744i \(-0.130207\pi\)
\(332\) 5.46589e9 3.15573e9i 0.449892 0.259745i
\(333\) −4.40074e9 5.33740e9i −0.357889 0.434063i
\(334\) −6.57021e9 + 1.13799e10i −0.527950 + 0.914437i
\(335\) −1.34163e9 + 3.68611e9i −0.106526 + 0.292677i
\(336\) 1.26902e9 + 2.75235e9i 0.0995662 + 0.215947i
\(337\) −4.83231e9 4.05479e9i −0.374658 0.314375i 0.435943 0.899974i \(-0.356415\pi\)
−0.810601 + 0.585599i \(0.800859\pi\)
\(338\) 8.06424e9 9.61059e9i 0.617870 0.736348i
\(339\) 1.10197e10 + 7.78714e9i 0.834397 + 0.589629i
\(340\) 2.41907e9 + 8.80469e8i 0.181022 + 0.0658868i
\(341\) 5.44981e9 + 3.14645e9i 0.403054 + 0.232704i
\(342\) −4.27959e9 3.65435e9i −0.312822 0.267120i
\(343\) −7.20984e9 1.24878e10i −0.520893 0.902214i
\(344\) −5.28135e9 + 9.31245e8i −0.377148 + 0.0665013i
\(345\) 1.47407e10 + 1.48684e10i 1.04050 + 1.04951i
\(346\) −1.30596e10 + 4.75331e9i −0.911226 + 0.331659i
\(347\) 1.41947e10 + 2.50290e9i 0.979055 + 0.172634i 0.640203 0.768206i \(-0.278850\pi\)
0.338852 + 0.940840i \(0.389961\pi\)
\(348\) −5.33400e9 + 1.13112e10i −0.363694 + 0.771244i
\(349\) 1.37250e10 1.15166e10i 0.925144 0.776288i −0.0497954 0.998759i \(-0.515857\pi\)
0.974939 + 0.222472i \(0.0714125\pi\)
\(350\) 6.05954e9i 0.403801i
\(351\) 1.01257e10 2.10010e10i 0.667108 1.38360i
\(352\) −3.26424e9 −0.212624
\(353\) −1.84976e9 2.20446e9i −0.119129 0.141972i 0.703184 0.711008i \(-0.251761\pi\)
−0.822313 + 0.569036i \(0.807317\pi\)
\(354\) 1.03536e9 + 1.24524e10i 0.0659295 + 0.792943i
\(355\) −4.13436e9 + 2.34471e10i −0.260313 + 1.47631i
\(356\) −1.54960e9 4.25748e9i −0.0964758 0.265065i
\(357\) 1.19825e9 + 4.55033e9i 0.0737692 + 0.280136i
\(358\) −5.00960e8 2.84109e9i −0.0304980 0.172963i
\(359\) 1.26000e10 7.27461e9i 0.758565 0.437958i −0.0702154 0.997532i \(-0.522369\pi\)
0.828780 + 0.559574i \(0.189035\pi\)
\(360\) 6.53803e9 3.69993e9i 0.389258 0.220284i
\(361\) 5.61798e9 9.73063e9i 0.330789 0.572944i
\(362\) −6.66143e9 + 1.83021e10i −0.387912 + 1.06578i
\(363\) −7.72324e9 7.09266e8i −0.444808 0.0408491i
\(364\) 9.82408e9 + 8.24338e9i 0.559611 + 0.469569i
\(365\) −4.37977e9 + 5.21961e9i −0.246763 + 0.294081i
\(366\) 3.19668e8 3.48088e9i 0.0178145 0.193984i
\(367\) −1.73864e10 6.32814e9i −0.958397 0.348828i −0.184992 0.982740i \(-0.559226\pi\)
−0.773405 + 0.633912i \(0.781448\pi\)
\(368\) −4.63863e9 2.67812e9i −0.252929 0.146029i
\(369\) −1.64382e10 2.90474e10i −0.886642 1.56676i
\(370\) −4.71581e9 8.16802e9i −0.251622 0.435823i
\(371\) 3.31058e10 5.83745e9i 1.74747 0.308125i
\(372\) 3.58286e9 9.43485e8i 0.187093 0.0492678i
\(373\) 2.16131e10 7.86651e9i 1.11656 0.406394i 0.283163 0.959072i \(-0.408616\pi\)
0.833395 + 0.552678i \(0.186394\pi\)
\(374\) −4.99086e9 8.80023e8i −0.255087 0.0449788i
\(375\) 9.96312e9 8.28387e8i 0.503814 0.0418898i
\(376\) 1.77552e9 1.48984e9i 0.0888332 0.0745399i
\(377\) 5.29163e10i 2.61954i
\(378\) 1.23688e10 + 5.96363e9i 0.605841 + 0.292108i
\(379\) 5.00231e9 0.242445 0.121223 0.992625i \(-0.461319\pi\)
0.121223 + 0.992625i \(0.461319\pi\)
\(380\) −4.93186e9 5.87757e9i −0.236525 0.281879i
\(381\) −1.99077e10 9.38781e9i −0.944758 0.445517i
\(382\) −2.63099e9 + 1.49211e10i −0.123557 + 0.700725i
\(383\) 1.76902e9 + 4.86033e9i 0.0822123 + 0.225877i 0.973987 0.226603i \(-0.0727619\pi\)
−0.891775 + 0.452479i \(0.850540\pi\)
\(384\) −1.36480e9 + 1.35308e9i −0.0627689 + 0.0622299i
\(385\) 5.52169e9 + 3.13151e10i 0.251321 + 1.42531i
\(386\) 2.15400e10 1.24361e10i 0.970278 0.560190i
\(387\) −1.57776e10 + 1.84770e10i −0.703391 + 0.823737i
\(388\) 3.16941e9 5.48957e9i 0.139846 0.242221i
\(389\) −5.87665e9 + 1.61460e10i −0.256644 + 0.705124i 0.742725 + 0.669597i \(0.233533\pi\)
−0.999369 + 0.0355267i \(0.988689\pi\)
\(390\) 1.83446e10 2.59598e10i 0.792956 1.12213i
\(391\) −6.37023e9 5.34526e9i −0.272551 0.228698i
\(392\) 5.11176e8 6.09195e8i 0.0216484 0.0257996i
\(393\) 9.28594e8 4.28145e8i 0.0389274 0.0179482i
\(394\) 2.18616e10 + 7.95697e9i 0.907188 + 0.330189i
\(395\) −4.17997e10 2.41331e10i −1.71706 0.991343i
\(396\) −1.14105e10 + 9.40809e9i −0.464008 + 0.382579i
\(397\) −1.47040e10 2.54681e10i −0.591935 1.02526i −0.993972 0.109638i \(-0.965031\pi\)
0.402036 0.915624i \(-0.368303\pi\)
\(398\) −2.41136e10 + 4.25187e9i −0.961013 + 0.169453i
\(399\) 3.68815e9 1.35307e10i 0.145518 0.533862i
\(400\) 3.61066e9 1.31417e9i 0.141041 0.0513348i
\(401\) −1.17871e10 2.07839e9i −0.455859 0.0803802i −0.0589962 0.998258i \(-0.518790\pi\)
−0.396863 + 0.917878i \(0.629901\pi\)
\(402\) −2.59171e9 3.73553e9i −0.0992390 0.143037i
\(403\) 1.20094e10 1.00771e10i 0.455303 0.382045i
\(404\) 1.22324e10i 0.459184i
\(405\) 1.21907e10 3.17773e10i 0.453114 1.18113i
\(406\) −3.11656e10 −1.14702
\(407\) 1.19348e10 + 1.42233e10i 0.434948 + 0.518351i
\(408\) −2.45150e9 + 1.70085e9i −0.0884689 + 0.0613798i
\(409\) −6.42468e9 + 3.64362e10i −0.229593 + 1.30209i 0.624115 + 0.781333i \(0.285460\pi\)
−0.853708 + 0.520753i \(0.825651\pi\)
\(410\) −1.55637e10 4.27610e10i −0.550780 1.51325i
\(411\) −1.56808e10 4.27421e9i −0.549541 0.149792i
\(412\) −3.75956e9 2.13215e10i −0.130481 0.739996i
\(413\) −2.69678e10 + 1.55699e10i −0.926927 + 0.535162i
\(414\) −2.39337e10 + 4.00765e9i −0.814720 + 0.136423i
\(415\) 1.94931e10 3.37630e10i 0.657186 1.13828i
\(416\) −2.78131e9 + 7.64160e9i −0.0928703 + 0.255159i
\(417\) −1.48573e10 3.22236e10i −0.491355 1.06569i
\(418\) 1.15707e10 + 9.70896e9i 0.379013 + 0.318030i
\(419\) −6.08725e9 + 7.25450e9i −0.197499 + 0.235370i −0.855700 0.517472i \(-0.826873\pi\)
0.658201 + 0.752842i \(0.271318\pi\)
\(420\) 1.52893e10 + 1.08042e10i 0.491349 + 0.347213i
\(421\) 2.52986e9 + 9.20794e8i 0.0805319 + 0.0293112i 0.381972 0.924174i \(-0.375245\pi\)
−0.301440 + 0.953485i \(0.597467\pi\)
\(422\) −3.55902e10 2.05480e10i −1.12223 0.647917i
\(423\) 1.91258e9 1.03253e10i 0.0597391 0.322508i
\(424\) 1.06582e10 + 1.84605e10i 0.329777 + 0.571190i
\(425\) 5.87481e9 1.03589e9i 0.180069 0.0317509i
\(426\) −1.94286e10 1.95969e10i −0.589934 0.595044i
\(427\) 8.18584e9 2.97940e9i 0.246236 0.0896226i
\(428\) −9.95595e9 1.75550e9i −0.296693 0.0523150i
\(429\) −2.66905e10 + 5.65995e10i −0.788003 + 1.67103i
\(430\) −2.53763e10 + 2.12932e10i −0.742257 + 0.622828i
\(431\) 4.60537e9i 0.133461i −0.997771 0.0667307i \(-0.978743\pi\)
0.997771 0.0667307i \(-0.0212568\pi\)
\(432\) −8.71015e8 + 8.66345e9i −0.0250087 + 0.248746i
\(433\) 7.93589e9 0.225759 0.112879 0.993609i \(-0.463993\pi\)
0.112879 + 0.993609i \(0.463993\pi\)
\(434\) 5.93500e9 + 7.07305e9i 0.167287 + 0.199365i
\(435\) 6.40079e9 + 7.69832e10i 0.178763 + 2.15000i
\(436\) −5.09075e8 + 2.88711e9i −0.0140876 + 0.0798946i
\(437\) 8.47684e9 + 2.32899e10i 0.232439 + 0.638620i
\(438\) −2.01108e9 7.63704e9i −0.0546429 0.207505i
\(439\) 5.79736e9 + 3.28785e10i 0.156089 + 0.885225i 0.957783 + 0.287491i \(0.0928211\pi\)
−0.801694 + 0.597734i \(0.796068\pi\)
\(440\) −1.74620e10 + 1.00817e10i −0.465889 + 0.268981i
\(441\) 3.10711e7 3.60281e9i 0.000821489 0.0952549i
\(442\) −6.31263e9 + 1.09338e10i −0.165394 + 0.286472i
\(443\) −8.10918e9 + 2.22798e10i −0.210553 + 0.578490i −0.999346 0.0361693i \(-0.988484\pi\)
0.788792 + 0.614660i \(0.210707\pi\)
\(444\) 1.08858e10 + 9.99705e8i 0.280111 + 0.0257241i
\(445\) −2.14388e10 1.79893e10i −0.546715 0.458748i
\(446\) 2.17462e10 2.59161e10i 0.549597 0.654984i
\(447\) −5.99187e8 + 6.52458e9i −0.0150083 + 0.163427i
\(448\) −4.50060e9 1.63808e9i −0.111727 0.0406653i
\(449\) 1.43161e10 + 8.26538e9i 0.352240 + 0.203366i 0.665671 0.746245i \(-0.268145\pi\)
−0.313432 + 0.949611i \(0.601479\pi\)
\(450\) 8.83382e9 1.50004e10i 0.215426 0.365807i
\(451\) 4.47912e10 + 7.75807e10i 1.08265 + 1.87520i
\(452\) −2.09991e10 + 3.70271e9i −0.503091 + 0.0887086i
\(453\) −4.74719e10 + 1.25009e10i −1.12731 + 0.296858i
\(454\) 2.80566e10 1.02118e10i 0.660406 0.240368i
\(455\) 7.80135e10 + 1.37559e10i 1.82022 + 0.320954i
\(456\) 8.86232e9 7.36860e8i 0.204969 0.0170422i
\(457\) 4.83900e10 4.06040e10i 1.10941 0.930902i 0.111385 0.993777i \(-0.464471\pi\)
0.998021 + 0.0628751i \(0.0200270\pi\)
\(458\) 3.86441e10i 0.878256i
\(459\) −3.66736e9 + 1.30112e10i −0.0826234 + 0.293134i
\(460\) −3.30857e10 −0.738939
\(461\) −4.80073e10 5.72128e10i −1.06293 1.26675i −0.962349 0.271818i \(-0.912375\pi\)
−0.100578 0.994929i \(-0.532069\pi\)
\(462\) −3.33349e10 1.57197e10i −0.731697 0.345045i
\(463\) 8.72881e9 4.95036e10i 0.189946 1.07724i −0.729487 0.683995i \(-0.760241\pi\)
0.919434 0.393245i \(-0.128648\pi\)
\(464\) −6.75909e9 1.85704e10i −0.145820 0.400636i
\(465\) 1.62524e10 1.61129e10i 0.347622 0.344637i
\(466\) 6.92180e9 + 3.92555e10i 0.146783 + 0.832447i
\(467\) 1.55160e10 8.95817e9i 0.326222 0.188344i −0.327941 0.944698i \(-0.606355\pi\)
0.654162 + 0.756354i \(0.273021\pi\)
\(468\) 1.23020e10 + 3.47283e10i 0.256443 + 0.723937i
\(469\) 5.66522e9 9.81244e9i 0.117091 0.202808i
\(470\) 4.89672e9 1.34536e10i 0.100349 0.275707i
\(471\) −3.29054e10 + 4.65652e10i −0.668627 + 0.946188i
\(472\) −1.51262e10 1.26924e10i −0.304763 0.255726i
\(473\) 4.19183e10 4.99562e10i 0.837449 0.998033i
\(474\) 5.08026e10 2.34235e10i 1.00640 0.464021i
\(475\) −1.67074e10 6.08100e9i −0.328197 0.119454i
\(476\) −6.43957e9 3.71789e9i −0.125438 0.0724216i
\(477\) 9.04634e10 + 3.38123e10i 1.74743 + 0.653132i
\(478\) −1.63848e10 2.83792e10i −0.313855 0.543612i
\(479\) 2.63628e10 4.64848e9i 0.500784 0.0883017i 0.0824501 0.996595i \(-0.473725\pi\)
0.418333 + 0.908294i \(0.362614\pi\)
\(480\) −3.12195e9 + 1.14535e10i −0.0588113 + 0.215761i
\(481\) 4.34660e10 1.58203e10i 0.812026 0.295553i
\(482\) −3.00109e9 5.29172e8i −0.0556020 0.00980413i
\(483\) −3.44733e10 4.96877e10i −0.633424 0.912977i
\(484\) 9.38863e9 7.87799e9i 0.171088 0.143560i
\(485\) 3.91551e10i 0.707655i
\(486\) 2.19248e10 + 3.27946e10i 0.392998 + 0.587837i
\(487\) 3.61122e10 0.642004 0.321002 0.947079i \(-0.395980\pi\)
0.321002 + 0.947079i \(0.395980\pi\)
\(488\) 3.55063e9 + 4.23147e9i 0.0626074 + 0.0746127i
\(489\) −3.38529e10 + 2.34872e10i −0.592053 + 0.410767i
\(490\) 8.53009e8 4.83765e9i 0.0147968 0.0839171i
\(491\) 1.36964e10 + 3.76306e10i 0.235657 + 0.647463i 0.999996 + 0.00264862i \(0.000843081\pi\)
−0.764339 + 0.644814i \(0.776935\pi\)
\(492\) 5.08861e10 + 1.38703e10i 0.868437 + 0.236715i
\(493\) −5.32781e9 3.02155e10i −0.0901905 0.511496i
\(494\) 3.25876e10 1.88145e10i 0.547198 0.315925i
\(495\) −3.19833e10 + 8.55701e10i −0.532724 + 1.42528i
\(496\) −2.92741e9 + 5.07042e9i −0.0483678 + 0.0837756i
\(497\) 2.35209e10 6.46232e10i 0.385504 1.05916i
\(498\) 1.89199e10 + 4.10350e10i 0.307611 + 0.667171i
\(499\) −1.01781e10 8.54044e9i −0.164159 0.137746i 0.557008 0.830507i \(-0.311949\pi\)
−0.721167 + 0.692762i \(0.756394\pi\)
\(500\) −1.01551e10 + 1.21024e10i −0.162482 + 0.193638i
\(501\) −7.68310e10 5.42928e10i −1.21951 0.861771i
\(502\) 2.81096e10 + 1.02310e10i 0.442628 + 0.161104i
\(503\) −6.44972e10 3.72375e10i −1.00756 0.581712i −0.0970804 0.995277i \(-0.530950\pi\)
−0.910475 + 0.413564i \(0.864284\pi\)
\(504\) −2.04536e10 + 7.24537e9i −0.316992 + 0.112289i
\(505\) 3.77800e10 + 6.54370e10i 0.580894 + 1.00614i
\(506\) 6.41435e10 1.13102e10i 0.978477 0.172532i
\(507\) 6.32383e10 + 6.37861e10i 0.957081 + 0.965370i
\(508\) 3.26839e10 1.18960e10i 0.490771 0.178626i
\(509\) −5.39558e10 9.51386e9i −0.803835 0.141738i −0.243389 0.969929i \(-0.578259\pi\)
−0.560446 + 0.828191i \(0.689370\pi\)
\(510\) −7.86111e9 + 1.66702e10i −0.116199 + 0.246410i
\(511\) 1.50766e10 1.26507e10i 0.221115 0.185538i
\(512\) 3.03700e9i 0.0441942i
\(513\) 2.88555e10 2.81185e10i 0.416639 0.405997i
\(514\) −1.53473e10 −0.219876
\(515\) −8.59636e10 1.02447e11i −1.22204 1.45637i
\(516\) −3.18138e9 3.82629e10i −0.0448763 0.539733i
\(517\) −4.89424e9 + 2.77566e10i −0.0685051 + 0.388512i
\(518\) 9.31755e9 + 2.55998e10i 0.129414 + 0.355563i
\(519\) −2.53379e10 9.62201e10i −0.349222 1.32616i
\(520\) 8.72266e9 + 4.94687e10i 0.119299 + 0.676576i
\(521\) −8.41264e10 + 4.85704e10i −1.14178 + 0.659205i −0.946870 0.321617i \(-0.895774\pi\)
−0.194907 + 0.980822i \(0.562440\pi\)
\(522\) −7.71504e10 4.54344e10i −1.03910 0.611931i
\(523\) 2.69988e10 4.67633e10i 0.360859 0.625027i −0.627243 0.778823i \(-0.715817\pi\)
0.988102 + 0.153797i \(0.0491501\pi\)
\(524\) −5.52660e8 + 1.51842e9i −0.00733049 + 0.0201404i
\(525\) 4.32012e10 + 3.96740e9i 0.568668 + 0.0522238i
\(526\) −3.60892e10 3.02824e10i −0.471448 0.395592i
\(527\) −5.84282e9 + 6.96321e9i −0.0757496 + 0.0902748i
\(528\) 2.13721e9 2.32722e10i 0.0274987 0.299435i
\(529\) 2.68420e10 + 9.76967e9i 0.342761 + 0.124755i
\(530\) 1.14031e11 + 6.58361e10i 1.44518 + 0.834374i
\(531\) −8.94571e10 7.71488e8i −1.12522 0.00970400i
\(532\) 1.10810e10 + 1.91928e10i 0.138335 + 0.239603i
\(533\) 2.19781e11 3.87534e10i 2.72322 0.480176i
\(534\) 3.13681e10 8.26025e9i 0.385765 0.101585i
\(535\) −5.86810e10 + 2.13581e10i −0.716279 + 0.260704i
\(536\) 7.07552e9 + 1.24761e9i 0.0857234 + 0.0151153i
\(537\) 2.05834e10 1.71141e9i 0.247526 0.0205806i
\(538\) −5.37277e10 + 4.50829e10i −0.641311 + 0.538124i
\(539\) 9.67041e9i 0.114575i
\(540\) 2.20978e10 + 4.90351e10i 0.259880 + 0.576676i
\(541\) 1.33209e10 0.155505 0.0777525 0.996973i \(-0.475226\pi\)
0.0777525 + 0.996973i \(0.475226\pi\)
\(542\) −3.62672e10 4.32215e10i −0.420259 0.500845i
\(543\) −1.26123e11 5.94754e10i −1.45076 0.684130i
\(544\) 8.18761e8 4.64342e9i 0.00934892 0.0530203i
\(545\) 6.19361e9 + 1.70168e10i 0.0702034 + 0.192882i
\(546\) −6.52030e10 + 6.46431e10i −0.733663 + 0.727363i
\(547\) −1.30489e10 7.40040e10i −0.145755 0.826620i −0.966758 0.255695i \(-0.917696\pi\)
0.821002 0.570925i \(-0.193415\pi\)
\(548\) 2.22426e10 1.28418e10i 0.246640 0.142398i
\(549\) 2.46075e10 + 4.55811e9i 0.270881 + 0.0501760i
\(550\) −2.33621e10 + 4.04644e10i −0.255306 + 0.442204i
\(551\) −3.12760e10 + 8.59301e10i −0.339316 + 0.932264i
\(552\) 2.21306e10 3.13175e10i 0.238362 0.337311i
\(553\) 1.06797e11 + 8.96136e10i 1.14198 + 0.958238i
\(554\) −7.23445e10 + 8.62168e10i −0.768009 + 0.915278i
\(555\) 6.13212e10 2.82733e10i 0.646306 0.297992i
\(556\) 5.26916e10 + 1.91782e10i 0.551369 + 0.200682i
\(557\) 1.25014e11 + 7.21771e10i 1.29879 + 0.749857i 0.980195 0.198033i \(-0.0634554\pi\)
0.318596 + 0.947891i \(0.396789\pi\)
\(558\) 4.38071e9 + 2.61616e10i 0.0451864 + 0.269853i
\(559\) −8.12310e10 1.40696e11i −0.831907 1.44091i
\(560\) −2.91351e10 + 5.13730e9i −0.296254 + 0.0522376i
\(561\) 9.54178e9 3.50059e10i 0.0963336 0.353419i
\(562\) 1.20286e11 4.37804e10i 1.20578 0.438869i
\(563\) −1.01447e10 1.78878e9i −0.100973 0.0178042i 0.122933 0.992415i \(-0.460770\pi\)
−0.223906 + 0.974611i \(0.571881\pi\)
\(564\) 9.45926e9 + 1.36340e10i 0.0934848 + 0.134743i
\(565\) −1.00898e11 + 8.46637e10i −0.990125 + 0.830813i
\(566\) 3.35199e10i 0.326616i
\(567\) −5.06157e10 + 8.42779e10i −0.489726 + 0.815420i
\(568\) 4.36077e10 0.418957
\(569\) −1.06247e11 1.26620e11i −1.01360 1.20797i −0.978001 0.208600i \(-0.933109\pi\)
−0.0356030 0.999366i \(-0.511335\pi\)
\(570\) 4.51329e10 3.13133e10i 0.427557 0.296639i
\(571\) −3.27395e8 + 1.85675e9i −0.00307984 + 0.0174666i −0.986309 0.164908i \(-0.947267\pi\)
0.983229 + 0.182375i \(0.0583784\pi\)
\(572\) −3.38214e10 9.29236e10i −0.315942 0.868045i
\(573\) −1.04657e11 2.85269e10i −0.970842 0.264628i
\(574\) 2.28242e10 + 1.29443e11i 0.210256 + 1.19242i
\(575\) −6.63973e10 + 3.83345e10i −0.607406 + 0.350686i
\(576\) −8.75315e9 1.06162e10i −0.0795197 0.0964449i
\(577\) −5.73771e10 + 9.93801e10i −0.517649 + 0.896594i 0.482141 + 0.876094i \(0.339859\pi\)
−0.999790 + 0.0205007i \(0.993474\pi\)
\(578\) −2.44891e10 + 6.72833e10i −0.219413 + 0.602831i
\(579\) 7.45597e10 + 1.61711e11i 0.663422 + 1.43888i
\(580\) −9.35128e10 7.84665e10i −0.826340 0.693382i
\(581\) −7.23839e10 + 8.62638e10i −0.635240 + 0.757049i
\(582\) 3.70625e10 + 2.61904e10i 0.323030 + 0.228270i
\(583\) −2.43580e11 8.86558e10i −2.10847 0.767420i
\(584\) 1.08078e10 + 6.23991e9i 0.0929154 + 0.0536447i
\(585\) 1.73068e11 + 1.47784e11i 1.47773 + 1.26183i
\(586\) −1.61920e10 2.80453e10i −0.137312 0.237832i
\(587\) −1.69611e11 + 2.99069e10i −1.42857 + 0.251895i −0.833828 0.552024i \(-0.813856\pi\)
−0.594739 + 0.803919i \(0.702745\pi\)
\(588\) 4.00855e9 + 4.04327e9i 0.0335334 + 0.0338238i
\(589\) 2.54579e10 9.26592e9i 0.211525 0.0769887i
\(590\) −1.20118e11 2.11800e10i −0.991288 0.174791i
\(591\) −7.10425e10 + 1.50652e11i −0.582328 + 1.23488i
\(592\) −1.32332e10 + 1.11040e10i −0.107740 + 0.0904048i
\(593\) 9.12916e10i 0.738264i −0.929377 0.369132i \(-0.879655\pi\)
0.929377 0.369132i \(-0.120345\pi\)
\(594\) −5.96037e10 8.75108e10i −0.478771 0.702936i
\(595\) −4.59311e10 −0.366470
\(596\) −6.65532e9 7.93150e9i −0.0527453 0.0628594i
\(597\) −1.45255e10 1.74701e11i −0.114350 1.37530i
\(598\) 2.81766e10 1.59797e11i 0.220335 1.24958i
\(599\) 6.99336e10 + 1.92141e11i 0.543223 + 1.49249i 0.842696 + 0.538389i \(0.180967\pi\)
−0.299473 + 0.954105i \(0.596811\pi\)
\(600\) 7.00530e9 + 2.66024e10i 0.0540533 + 0.205266i
\(601\) −3.19264e10 1.81063e11i −0.244710 1.38782i −0.821165 0.570690i \(-0.806676\pi\)
0.576456 0.817129i \(-0.304435\pi\)
\(602\) 8.28645e10 4.78419e10i 0.630932 0.364269i
\(603\) 2.83291e10 1.60317e10i 0.214271 0.121258i
\(604\) 3.87874e10 6.71817e10i 0.291435 0.504781i
\(605\) 2.58929e10 7.11401e10i 0.193267 0.530998i
\(606\) −8.72104e10 8.00899e9i −0.646663 0.0593865i
\(607\) −1.25292e11 1.05133e11i −0.922930 0.774430i 0.0516044 0.998668i \(-0.483567\pi\)
−0.974535 + 0.224237i \(0.928011\pi\)
\(608\) −9.03308e9 + 1.07652e10i −0.0661030 + 0.0787785i
\(609\) 2.04052e10 2.22194e11i 0.148345 1.61534i
\(610\) 3.20630e10 + 1.16700e10i 0.231571 + 0.0842851i
\(611\) 6.08081e10 + 3.51076e10i 0.436312 + 0.251905i
\(612\) −1.05211e10 1.85915e10i −0.0749987 0.132528i
\(613\) 4.63682e10 + 8.03121e10i 0.328381 + 0.568773i 0.982191 0.187886i \(-0.0601636\pi\)
−0.653810 + 0.756659i \(0.726830\pi\)
\(614\) −3.99829e10 + 7.05007e9i −0.281320 + 0.0496044i
\(615\) 3.15052e11 8.29637e10i 2.20233 0.579946i
\(616\) 5.47283e10 1.99195e10i 0.380093 0.138342i
\(617\) 3.17421e10 + 5.59699e9i 0.219026 + 0.0386202i 0.282084 0.959390i \(-0.408974\pi\)
−0.0630583 + 0.998010i \(0.520085\pi\)
\(618\) 1.54472e11 1.28437e10i 1.05900 0.0880511i
\(619\) −2.08849e11 + 1.75245e11i −1.42256 + 1.19367i −0.472605 + 0.881274i \(0.656686\pi\)
−0.949953 + 0.312394i \(0.898869\pi\)
\(620\) 3.61655e10i 0.244753i
\(621\) −1.29021e10 1.73258e11i −0.0867552 1.16500i
\(622\) −6.14035e10 −0.410234
\(623\) 5.19611e10 + 6.19249e10i 0.344926 + 0.411067i
\(624\) −5.26594e10 2.48325e10i −0.347326 0.163788i
\(625\) −3.28538e10 + 1.86323e11i −0.215311 + 1.22109i
\(626\) −2.25403e10 6.19290e10i −0.146779 0.403271i
\(627\) −7.67953e10 + 7.61359e10i −0.496895 + 0.492628i
\(628\) −1.56462e10 8.87341e10i −0.100594 0.570495i
\(629\) −2.32265e10 + 1.34098e10i −0.148382 + 0.0856683i
\(630\) −8.70386e10 + 1.01930e11i −0.552522 + 0.647055i
\(631\) −1.08132e11 + 1.87290e11i −0.682083 + 1.18140i 0.292261 + 0.956339i \(0.405593\pi\)
−0.974344 + 0.225064i \(0.927741\pi\)
\(632\) −3.02356e10 + 8.30716e10i −0.189518 + 0.520696i
\(633\) 1.69798e11 2.40285e11i 1.05759 1.49662i
\(634\) 4.93116e10 + 4.13773e10i 0.305205 + 0.256097i
\(635\) 1.38101e11 1.64582e11i 0.849378 1.01225i
\(636\) −1.38592e11 + 6.39003e10i −0.847050 + 0.390548i
\(637\) 2.26385e10 + 8.23973e9i 0.137496 + 0.0500443i
\(638\) 2.08118e11 + 1.20157e11i 1.25611 + 0.725213i
\(639\) 1.52436e11 1.25685e11i 0.914290 0.753840i
\(640\) −9.37984e9 1.62464e10i −0.0559082 0.0968358i
\(641\) −2.27808e11 + 4.01687e10i −1.34939 + 0.237933i −0.801187 0.598414i \(-0.795798\pi\)
−0.548200 + 0.836347i \(0.684687\pi\)
\(642\) 1.90343e10 6.98311e10i 0.112046 0.411063i
\(643\) 2.77165e11 1.00880e11i 1.62142 0.590148i 0.637766 0.770230i \(-0.279859\pi\)
0.983652 + 0.180082i \(0.0576364\pi\)
\(644\) 9.41142e10 + 1.65949e10i 0.547157 + 0.0964785i
\(645\) −1.35194e11 1.94861e11i −0.781124 1.12586i
\(646\) −1.67134e10 + 1.40242e10i −0.0959696 + 0.0805281i
\(647\) 2.97676e11i 1.69874i 0.527798 + 0.849370i \(0.323018\pi\)
−0.527798 + 0.849370i \(0.676982\pi\)
\(648\) −6.11954e10 1.18821e10i −0.347071 0.0673898i
\(649\) 2.40114e11 1.35344
\(650\) 7.48215e10 + 8.91688e10i 0.419153 + 0.499527i
\(651\) −5.43129e10 + 3.76823e10i −0.302398 + 0.209804i
\(652\) 1.13063e10 6.41214e10i 0.0625649 0.354823i
\(653\) 3.67971e10 + 1.01099e11i 0.202377 + 0.556025i 0.998814 0.0486962i \(-0.0155066\pi\)
−0.796437 + 0.604722i \(0.793284\pi\)
\(654\) −2.02502e10 5.51972e9i −0.110693 0.0301722i
\(655\) 1.73323e9 + 9.82966e9i 0.00941656 + 0.0534040i
\(656\) −7.21800e10 + 4.16731e10i −0.389764 + 0.225030i
\(657\) 5.57646e10 9.33769e9i 0.299294 0.0501162i
\(658\) −2.06770e10 + 3.58136e10i −0.110302 + 0.191049i
\(659\) 1.23926e11 3.40484e11i 0.657084 1.80532i 0.0673423 0.997730i \(-0.478548\pi\)
0.589741 0.807592i \(-0.299230\pi\)
\(660\) −6.04438e10 1.31095e11i −0.318549 0.690893i
\(661\) −7.79933e10 6.54442e10i −0.408556 0.342819i 0.415234 0.909715i \(-0.363700\pi\)
−0.823790 + 0.566896i \(0.808144\pi\)
\(662\) −4.05708e10 + 4.83504e10i −0.211243 + 0.251749i
\(663\) −7.38189e10 5.21643e10i −0.382044 0.269972i
\(664\) −6.70998e10 2.44223e10i −0.345182 0.125636i
\(665\) 1.18555e11 + 6.84476e10i 0.606223 + 0.350003i
\(666\) −1.42547e10 + 7.69556e10i −0.0724538 + 0.391150i
\(667\) 1.97163e11 + 3.41497e11i 0.996145 + 1.72537i
\(668\) 1.46408e11 2.58157e10i 0.735292 0.129652i
\(669\) 1.70530e11 + 1.72007e11i 0.851326 + 0.858699i
\(670\) 4.17036e10 1.51789e10i 0.206954 0.0753251i
\(671\) −6.61502e10 1.16641e10i −0.326318 0.0575387i
\(672\) 1.46253e10 3.10143e10i 0.0717181 0.152084i
\(673\) 1.39564e11 1.17108e11i 0.680322 0.570858i −0.235779 0.971807i \(-0.575764\pi\)
0.916100 + 0.400949i \(0.131320\pi\)
\(674\) 7.13684e10i 0.345833i
\(675\) 1.01161e11 + 7.28016e10i 0.487300 + 0.350692i
\(676\) −1.41939e11 −0.679695
\(677\) −5.18761e9 6.18235e9i −0.0246952 0.0294306i 0.753555 0.657384i \(-0.228337\pi\)
−0.778251 + 0.627954i \(0.783893\pi\)
\(678\) −1.26494e10 1.52136e11i −0.0598621 0.719970i
\(679\) −1.96391e10 + 1.11379e11i −0.0923939 + 0.523992i
\(680\) −9.96137e9 2.73686e10i −0.0465890 0.128002i
\(681\) 5.44346e10 + 2.06714e11i 0.253097 + 0.961129i
\(682\) −1.23631e10 7.01144e10i −0.0571463 0.324093i
\(683\) 9.32768e10 5.38534e10i 0.428638 0.247474i −0.270128 0.962824i \(-0.587066\pi\)
0.698766 + 0.715350i \(0.253733\pi\)
\(684\) −5.49062e8 + 6.36659e10i −0.00250840 + 0.290859i
\(685\) 7.93242e10 1.37393e11i 0.360283 0.624028i
\(686\) −5.57972e10 + 1.53301e11i −0.251951 + 0.692229i
\(687\) 2.75511e11 + 2.53016e10i 1.23684 + 0.113585i
\(688\) 4.64786e10 + 3.90001e10i 0.207443 + 0.174065i
\(689\) −4.15087e11 + 4.94682e11i −1.84188 + 2.19507i
\(690\) 2.16624e10 2.35883e11i 0.0955673 1.04064i
\(691\) −1.16587e11 4.24341e10i −0.511372 0.186124i 0.0734296 0.997300i \(-0.476606\pi\)
−0.584802 + 0.811176i \(0.698828\pi\)
\(692\) 1.36170e11 + 7.86175e10i 0.593821 + 0.342843i
\(693\) 1.33898e11 2.27367e11i 0.580553 0.985815i
\(694\) −8.15359e10 1.41224e11i −0.351488 0.608796i
\(695\) 3.41104e11 6.01459e10i 1.46200 0.257790i
\(696\) 1.36823e11 3.60299e10i 0.583070 0.153542i
\(697\) −1.21594e11 + 4.42568e10i −0.515208 + 0.187520i
\(698\) −1.99624e11 3.51991e10i −0.840992 0.148290i
\(699\) −2.84402e11 + 2.36467e10i −1.19131 + 0.0990518i
\(700\) −5.25169e10 + 4.40669e10i −0.218729 + 0.183536i
\(701\) 3.36834e11i 1.39490i −0.716631 0.697452i \(-0.754317\pi\)
0.716631 0.697452i \(-0.245683\pi\)
\(702\) −2.55649e11 + 6.49685e10i −1.05268 + 0.267519i
\(703\) 7.99345e10 0.327275
\(704\) 2.37386e10 + 2.82905e10i 0.0966415 + 0.115173i
\(705\) 9.27109e10 + 4.37195e10i 0.375296 + 0.176978i
\(706\) −5.65359e9 + 3.20631e10i −0.0227565 + 0.129059i
\(707\) −7.46463e10 2.05089e11i −0.298766 0.820851i
\(708\) 1.00393e11 9.95314e10i 0.399551 0.396120i
\(709\) −4.02053e10 2.28016e11i −0.159110 0.902360i −0.954931 0.296828i \(-0.904071\pi\)
0.795821 0.605532i \(-0.207040\pi\)
\(710\) 2.33278e11 1.34683e11i 0.917996 0.530005i
\(711\) 1.33734e11 + 3.77531e11i 0.523317 + 1.47732i
\(712\) −2.56296e10 + 4.43917e10i −0.0997290 + 0.172736i
\(713\) 3.99562e10 1.09779e11i 0.154606 0.424777i
\(714\) 3.07227e10 4.34764e10i 0.118213 0.167286i
\(715\) −4.67923e11 3.92634e11i −1.79040 1.50233i
\(716\) −2.09800e10 + 2.50030e10i −0.0798277 + 0.0951350i
\(717\) 2.13056e11 9.82335e10i 0.806153 0.371692i
\(718\) −1.54679e11 5.62985e10i −0.582013 0.211835i
\(719\) 1.51076e11 + 8.72235e10i 0.565300 + 0.326376i 0.755270 0.655414i \(-0.227506\pi\)
−0.189970 + 0.981790i \(0.560839\pi\)
\(720\) −7.96131e10 2.97568e10i −0.296248 0.110728i
\(721\) 1.93144e11 + 3.34535e11i 0.714727 + 1.23794i
\(722\) −1.25189e11 + 2.20742e10i −0.460700 + 0.0812338i
\(723\) 5.73763e9 2.10496e10i 0.0209981 0.0770356i
\(724\) 2.07065e11 7.53655e10i 0.753620 0.274295i
\(725\) −2.78579e11 4.91210e10i −1.00832 0.177793i
\(726\) 5.00187e10 + 7.20938e10i 0.180047 + 0.259508i
\(727\) −1.37090e11 + 1.15032e11i −0.490757 + 0.411794i −0.854298 0.519784i \(-0.826012\pi\)
0.363540 + 0.931579i \(0.381568\pi\)
\(728\) 1.45092e11i 0.516556i
\(729\) −2.48162e11 + 1.34840e11i −0.878670 + 0.477430i
\(730\) 7.70884e10 0.271455
\(731\) 6.05491e10 + 7.21596e10i 0.212050 + 0.252711i
\(732\) −3.24928e10 + 2.25436e10i −0.113173 + 0.0785196i
\(733\) −4.63064e10 + 2.62617e11i −0.160408 + 0.909718i 0.793266 + 0.608875i \(0.208379\pi\)
−0.953674 + 0.300842i \(0.902732\pi\)
\(734\) 7.15947e10 + 1.96705e11i 0.246659 + 0.677689i
\(735\) 3.39313e10 + 9.24887e9i 0.116266 + 0.0316912i
\(736\) 1.05229e10 + 5.96782e10i 0.0358611 + 0.203378i
\(737\) −7.56623e10 + 4.36837e10i −0.256454 + 0.148064i
\(738\) −1.32205e11 + 3.53708e11i −0.445678 + 1.19239i
\(739\) 3.73697e10 6.47263e10i 0.125297 0.217022i −0.796552 0.604570i \(-0.793345\pi\)
0.921849 + 0.387549i \(0.126678\pi\)
\(740\) −3.64958e10 + 1.00271e11i −0.121707 + 0.334388i
\(741\) 1.12801e11 + 2.44650e11i 0.374144 + 0.811471i
\(742\) −2.91348e11 2.44470e11i −0.961161 0.806510i
\(743\) −4.07582e10 + 4.85737e10i −0.133739 + 0.159384i −0.828758 0.559608i \(-0.810952\pi\)
0.695018 + 0.718992i \(0.255396\pi\)
\(744\) −3.42327e10 2.41906e10i −0.111725 0.0789506i
\(745\) −6.00991e10 2.18743e10i −0.195093 0.0710082i
\(746\) −2.25355e11 1.30108e11i −0.727631 0.420098i
\(747\) −3.04945e11 + 1.08022e11i −0.979352 + 0.346920i
\(748\) 2.86681e10 + 4.96546e10i 0.0915782 + 0.158618i
\(749\) 1.77634e11 3.13217e10i 0.564417 0.0995219i
\(750\) −7.96344e10 8.03241e10i −0.251684 0.253864i
\(751\) −9.76751e10 + 3.55508e10i −0.307061 + 0.111761i −0.490955 0.871185i \(-0.663352\pi\)
0.183894 + 0.982946i \(0.441130\pi\)
\(752\) −2.58243e10 4.55353e9i −0.0807528 0.0142389i
\(753\) −9.13461e10 + 1.93707e11i −0.284126 + 0.602513i
\(754\) 4.58616e11 3.84824e11i 1.41894 1.19063i
\(755\) 4.79182e11i 1.47473i