Properties

Label 54.9.f.a.5.4
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 5.4
Character \(\chi\) \(=\) 54.5
Dual form 54.9.f.a.11.4

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-7.27231 - 8.66680i) q^{2} +(-56.2872 - 58.2473i) q^{3} +(-22.2270 + 126.055i) q^{4} +(-19.4013 - 53.3047i) q^{5} +(-95.4793 + 911.423i) q^{6} +(-121.493 - 689.020i) q^{7} +(1254.14 - 724.077i) q^{8} +(-224.491 + 6557.16i) q^{9} +O(q^{10})\) \(q+(-7.27231 - 8.66680i) q^{2} +(-56.2872 - 58.2473i) q^{3} +(-22.2270 + 126.055i) q^{4} +(-19.4013 - 53.3047i) q^{5} +(-95.4793 + 911.423i) q^{6} +(-121.493 - 689.020i) q^{7} +(1254.14 - 724.077i) q^{8} +(-224.491 + 6557.16i) q^{9} +(-320.889 + 555.796i) q^{10} +(-2443.91 + 6714.58i) q^{11} +(8593.48 - 5800.65i) q^{12} +(30060.6 + 25223.8i) q^{13} +(-5088.07 + 6063.72i) q^{14} +(-2012.81 + 4130.45i) q^{15} +(-15395.9 - 5603.66i) q^{16} +(92987.3 + 53686.2i) q^{17} +(58462.2 - 45740.1i) q^{18} +(-40997.1 - 71009.1i) q^{19} +(7150.57 - 1260.84i) q^{20} +(-33295.0 + 45859.7i) q^{21} +(75966.8 - 27649.7i) q^{22} +(-312625. - 55124.2i) q^{23} +(-112768. - 32293.8i) q^{24} +(296771. - 249021. i) q^{25} -443965. i q^{26} +(394573. - 356008. i) q^{27} +89555.1 q^{28} +(-493225. - 587803. i) q^{29} +(50435.5 - 12593.3i) q^{30} +(-27356.6 + 155147. i) q^{31} +(63398.2 + 174185. i) q^{32} +(528667. - 235594. i) q^{33} +(-210945. - 1.19633e6i) q^{34} +(-34370.9 + 19844.0i) q^{35} +(-821575. - 174044. i) q^{36} +(412293. - 714112. i) q^{37} +(-317278. + 871714. i) q^{38} +(-222809. - 3.17073e6i) q^{39} +(-62928.6 - 52803.4i) q^{40} +(1.94681e6 - 2.32011e6i) q^{41} +(639589. - 44944.2i) q^{42} +(2.54141e6 + 924996. i) q^{43} +(-792089. - 457313. i) q^{44} +(353883. - 115251. i) q^{45} +(1.79576e6 + 3.11034e6i) q^{46} +(-1.21500e6 + 214238. i) q^{47} +(540196. + 1.21219e6i) q^{48} +(4.95715e6 - 1.80426e6i) q^{49} +(-4.31642e6 - 761102. i) q^{50} +(-2.10692e6 - 8.43811e6i) q^{51} +(-3.84776e6 + 3.22865e6i) q^{52} -4.86034e6i q^{53} +(-5.95491e6 - 830679. i) q^{54} +405334. q^{55} +(-651273. - 776156. i) q^{56} +(-1.82847e6 + 6.38487e6i) q^{57} +(-1.50749e6 + 8.54938e6i) q^{58} +(3.01980e6 + 8.29683e6i) q^{59} +(-475927. - 345532. i) q^{60} +(1.59873e6 + 9.06682e6i) q^{61} +(1.54358e6 - 891184. i) q^{62} +(4.54529e6 - 641969. i) q^{63} +(1.04858e6 - 1.81619e6i) q^{64} +(761333. - 2.09175e6i) q^{65} +(-5.88648e6 - 2.86854e6i) q^{66} +(1.90253e7 + 1.59641e7i) q^{67} +(-8.83427e6 + 1.05283e7i) q^{68} +(1.43860e7 + 2.13124e7i) q^{69} +(421940. + 153574. i) q^{70} +(-9.54968e6 - 5.51351e6i) q^{71} +(4.46635e6 + 8.38614e6i) q^{72} +(1.90890e7 + 3.30631e7i) q^{73} +(-9.18739e6 + 1.61998e6i) q^{74} +(-3.12092e7 - 3.26943e6i) q^{75} +(9.86232e6 - 3.58959e6i) q^{76} +(4.92340e6 + 868128. i) q^{77} +(-2.58598e7 + 2.49896e7i) q^{78} +(2.51274e7 - 2.10844e7i) q^{79} +929393. i q^{80} +(-4.29459e7 - 2.94405e6i) q^{81} -3.42658e7 q^{82} +(-3.42560e7 - 4.08248e7i) q^{83} +(-5.04081e6 - 5.21634e6i) q^{84} +(1.05765e6 - 5.99824e6i) q^{85} +(-1.04651e7 - 2.87527e7i) q^{86} +(-6.47563e6 + 6.18149e7i) q^{87} +(1.79688e6 + 1.01906e7i) q^{88} +(4.97686e7 - 2.87339e7i) q^{89} +(-3.57240e6 - 2.22889e6i) q^{90} +(1.37276e7 - 2.37769e7i) q^{91} +(1.38974e7 - 3.81828e7i) q^{92} +(1.05767e7 - 7.13936e6i) q^{93} +(1.06926e7 + 8.97220e6i) q^{94} +(-2.98972e6 + 3.56301e6i) q^{95} +(6.57729e6 - 1.34972e7i) q^{96} +(-2.11200e7 - 7.68705e6i) q^{97} +(-5.16871e7 - 2.98416e7i) q^{98} +(-4.34800e7 - 1.75325e7i) 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
\(3\) −56.2872 58.2473i −0.694904 0.719102i
\(4\) −22.2270 + 126.055i −0.0868241 + 0.492404i
\(5\) −19.4013 53.3047i −0.0310421 0.0852875i 0.923203 0.384312i \(-0.125561\pi\)
−0.954246 + 0.299024i \(0.903339\pi\)
\(6\) −95.4793 + 911.423i −0.0736723 + 0.703258i
\(7\) −121.493 689.020i −0.0506009 0.286972i 0.948998 0.315281i \(-0.102099\pi\)
−0.999599 + 0.0283091i \(0.990988\pi\)
\(8\) 1254.14 724.077i 0.306186 0.176777i
\(9\) −224.491 + 6557.16i −0.0342160 + 0.999414i
\(10\) −320.889 + 555.796i −0.0320889 + 0.0555796i
\(11\) −2443.91 + 6714.58i −0.166922 + 0.458615i −0.994746 0.102373i \(-0.967356\pi\)
0.827824 + 0.560988i \(0.189579\pi\)
\(12\) 8593.48 5800.65i 0.414423 0.279738i
\(13\) 30060.6 + 25223.8i 1.05251 + 0.883157i 0.993355 0.115092i \(-0.0367163\pi\)
0.0591507 + 0.998249i \(0.481161\pi\)
\(14\) −5088.07 + 6063.72i −0.132447 + 0.157844i
\(15\) −2012.81 + 4130.45i −0.0397591 + 0.0815891i
\(16\) −15395.9 5603.66i −0.234923 0.0855050i
\(17\) 92987.3 + 53686.2i 1.11334 + 0.642787i 0.939693 0.342020i \(-0.111111\pi\)
0.173648 + 0.984808i \(0.444445\pi\)
\(18\) 58462.2 45740.1i 0.556910 0.435719i
\(19\) −40997.1 71009.1i −0.314586 0.544878i 0.664764 0.747054i \(-0.268532\pi\)
−0.979349 + 0.202176i \(0.935199\pi\)
\(20\) 7150.57 1260.84i 0.0446911 0.00788024i
\(21\) −33295.0 + 45859.7i −0.171199 + 0.235805i
\(22\) 75966.8 27649.7i 0.324290 0.118032i
\(23\) −312625. 55124.2i −1.11715 0.196984i −0.415562 0.909565i \(-0.636415\pi\)
−0.701590 + 0.712581i \(0.747526\pi\)
\(24\) −112768. 32293.8i −0.339891 0.0973363i
\(25\) 296771. 249021.i 0.759734 0.637493i
\(26\) 443965.i 0.971528i
\(27\) 394573. 356008.i 0.742458 0.669893i
\(28\) 89555.1 0.145700
\(29\) −493225. 587803.i −0.697354 0.831074i 0.294870 0.955537i \(-0.404724\pi\)
−0.992224 + 0.124463i \(0.960279\pi\)
\(30\) 50435.5 12593.3i 0.0622661 0.0155473i
\(31\) −27356.6 + 155147.i −0.0296221 + 0.167995i −0.996030 0.0890177i \(-0.971627\pi\)
0.966408 + 0.257013i \(0.0827383\pi\)
\(32\) 63398.2 + 174185.i 0.0604612 + 0.166116i
\(33\) 528667. 235594.i 0.445786 0.198659i
\(34\) −210945. 1.19633e6i −0.157853 0.895228i
\(35\) −34370.9 + 19844.0i −0.0229044 + 0.0132238i
\(36\) −821575. 174044.i −0.489145 0.103621i
\(37\) 412293. 714112.i 0.219988 0.381030i −0.734816 0.678266i \(-0.762732\pi\)
0.954804 + 0.297236i \(0.0960649\pi\)
\(38\) −317278. + 871714.i −0.152162 + 0.418061i
\(39\) −222809. 3.17073e6i −0.0963105 1.37057i
\(40\) −62928.6 52803.4i −0.0245815 0.0206263i
\(41\) 1.94681e6 2.32011e6i 0.688949 0.821058i −0.302279 0.953220i \(-0.597747\pi\)
0.991228 + 0.132162i \(0.0421918\pi\)
\(42\) 639589. 44944.2i 0.205543 0.0144436i
\(43\) 2.54141e6 + 924996.i 0.743362 + 0.270562i 0.685810 0.727781i \(-0.259448\pi\)
0.0575522 + 0.998342i \(0.481670\pi\)
\(44\) −792089. 457313.i −0.211331 0.122012i
\(45\) 353883. 115251.i 0.0862997 0.0281057i
\(46\) 1.79576e6 + 3.11034e6i 0.401066 + 0.694667i
\(47\) −1.21500e6 + 214238.i −0.248993 + 0.0439041i −0.296751 0.954955i \(-0.595903\pi\)
0.0477587 + 0.998859i \(0.484792\pi\)
\(48\) 540196. + 1.21219e6i 0.101762 + 0.228352i
\(49\) 4.95715e6 1.80426e6i 0.859900 0.312978i
\(50\) −4.31642e6 761102.i −0.690628 0.121776i
\(51\) −2.10692e6 8.43811e6i −0.311435 1.24728i
\(52\) −3.84776e6 + 3.22865e6i −0.526253 + 0.441578i
\(53\) 4.86034e6i 0.615975i −0.951390 0.307988i \(-0.900345\pi\)
0.951390 0.307988i \(-0.0996555\pi\)
\(54\) −5.95491e6 830679.i −0.700326 0.0976918i
\(55\) 405334. 0.0442957
\(56\) −651273. 776156.i −0.0662233 0.0789218i
\(57\) −1.82847e6 + 6.38487e6i −0.173216 + 0.604857i
\(58\) −1.50749e6 + 8.54938e6i −0.133211 + 0.755479i
\(59\) 3.01980e6 + 8.29683e6i 0.249213 + 0.684706i 0.999716 + 0.0238391i \(0.00758895\pi\)
−0.750503 + 0.660867i \(0.770189\pi\)
\(60\) −475927. 345532.i −0.0367227 0.0266614i
\(61\) 1.59873e6 + 9.06682e6i 0.115466 + 0.654841i 0.986518 + 0.163651i \(0.0523269\pi\)
−0.871052 + 0.491190i \(0.836562\pi\)
\(62\) 1.54358e6 891184.i 0.104463 0.0603116i
\(63\) 4.54529e6 641969.i 0.288535 0.0407523i
\(64\) 1.04858e6 1.81619e6i 0.0625000 0.108253i
\(65\) 761333. 2.09175e6i 0.0426502 0.117181i
\(66\) −5.88648e6 2.86854e6i −0.310227 0.151177i
\(67\) 1.90253e7 + 1.59641e7i 0.944130 + 0.792219i 0.978299 0.207197i \(-0.0664342\pi\)
−0.0341695 + 0.999416i \(0.510879\pi\)
\(68\) −8.83427e6 + 1.05283e7i −0.413176 + 0.492404i
\(69\) 1.43860e7 + 2.13124e7i 0.634662 + 0.940232i
\(70\) 421940. + 153574.i 0.0175735 + 0.00639623i
\(71\) −9.54968e6 5.51351e6i −0.375799 0.216968i 0.300190 0.953879i \(-0.402950\pi\)
−0.675989 + 0.736912i \(0.736283\pi\)
\(72\) 4.46635e6 + 8.38614e6i 0.166197 + 0.312056i
\(73\) 1.90890e7 + 3.30631e7i 0.672189 + 1.16427i 0.977282 + 0.211943i \(0.0679792\pi\)
−0.305093 + 0.952323i \(0.598688\pi\)
\(74\) −9.18739e6 + 1.61998e6i −0.306383 + 0.0540237i
\(75\) −3.12092e7 3.26943e6i −0.986365 0.103330i
\(76\) 9.86232e6 3.58959e6i 0.295614 0.107595i
\(77\) 4.92340e6 + 868128.i 0.140056 + 0.0246957i
\(78\) −2.58598e7 + 2.49896e7i −0.698628 + 0.675119i
\(79\) 2.51274e7 2.10844e7i 0.645119 0.541319i −0.260466 0.965483i \(-0.583876\pi\)
0.905586 + 0.424164i \(0.139432\pi\)
\(80\) 929393.i 0.0226903i
\(81\) −4.29459e7 2.94405e6i −0.997659 0.0683919i
\(82\) −3.42658e7 −0.757888
\(83\) −3.42560e7 4.08248e7i −0.721813 0.860223i 0.272993 0.962016i \(-0.411987\pi\)
−0.994806 + 0.101793i \(0.967542\pi\)
\(84\) −5.04081e6 5.21634e6i −0.101247 0.104773i
\(85\) 1.05765e6 5.99824e6i 0.0202613 0.114907i
\(86\) −1.04651e7 2.87527e7i −0.191316 0.525636i
\(87\) −6.47563e6 + 6.18149e7i −0.113033 + 1.07899i
\(88\) 1.79688e6 + 1.01906e7i 0.0299632 + 0.169930i
\(89\) 4.97686e7 2.87339e7i 0.793223 0.457968i −0.0478728 0.998853i \(-0.515244\pi\)
0.841096 + 0.540886i \(0.181911\pi\)
\(90\) −3.57240e6 2.22889e6i −0.0544491 0.0339718i
\(91\) 1.37276e7 2.37769e7i 0.200184 0.346728i
\(92\) 1.38974e7 3.81828e7i 0.193992 0.532987i
\(93\) 1.05767e7 7.13936e6i 0.141390 0.0954394i
\(94\) 1.06926e7 + 8.97220e6i 0.136954 + 0.114918i
\(95\) −2.98972e6 + 3.56301e6i −0.0367059 + 0.0437444i
\(96\) 6.57729e6 1.34972e7i 0.0774395 0.158912i
\(97\) −2.11200e7 7.68705e6i −0.238565 0.0868306i 0.219971 0.975506i \(-0.429404\pi\)
−0.458536 + 0.888676i \(0.651626\pi\)
\(98\) −5.16871e7 2.98416e7i −0.560374 0.323532i
\(99\) −4.34800e7 1.75325e7i −0.452635 0.182516i
\(100\) 2.47941e7 + 4.29446e7i 0.247941 + 0.429446i
\(101\) 1.45180e8 2.55992e7i 1.39515 0.246003i 0.575002 0.818152i \(-0.305001\pi\)
0.820150 + 0.572149i \(0.193890\pi\)
\(102\) −5.78092e7 + 7.96248e7i −0.534068 + 0.735610i
\(103\) 4.05070e7 1.47434e7i 0.359900 0.130993i −0.155740 0.987798i \(-0.549776\pi\)
0.515640 + 0.856805i \(0.327554\pi\)
\(104\) 5.59642e7 + 9.86800e6i 0.478384 + 0.0843521i
\(105\) 3.09050e6 + 885043.i 0.0254256 + 0.00728127i
\(106\) −4.21236e7 + 3.53459e7i −0.333658 + 0.279973i
\(107\) 1.91749e8i 1.46284i −0.681927 0.731420i \(-0.738858\pi\)
0.681927 0.731420i \(-0.261142\pi\)
\(108\) 3.61066e7 + 5.76510e7i 0.265394 + 0.423752i
\(109\) 2.31126e8 1.63735 0.818676 0.574256i \(-0.194709\pi\)
0.818676 + 0.574256i \(0.194709\pi\)
\(110\) −2.94771e6 3.51295e6i −0.0201333 0.0239939i
\(111\) −6.48019e7 + 1.61805e7i −0.426870 + 0.106586i
\(112\) −1.99054e6 + 1.12889e7i −0.0126502 + 0.0717430i
\(113\) −3.24123e7 8.90520e7i −0.198791 0.546172i 0.799741 0.600345i \(-0.204970\pi\)
−0.998532 + 0.0541726i \(0.982748\pi\)
\(114\) 6.86337e7 3.05858e7i 0.406366 0.181092i
\(115\) 3.12696e6 + 1.77339e7i 0.0178785 + 0.101394i
\(116\) 8.50587e7 4.91086e7i 0.469771 0.271223i
\(117\) −1.72145e8 + 1.91450e8i −0.918652 + 1.02167i
\(118\) 4.99461e7 8.65091e7i 0.257616 0.446204i
\(119\) 2.56936e7 7.05926e7i 0.128126 0.352023i
\(120\) 466426. + 6.63758e6i 0.00224935 + 0.0320099i
\(121\) 1.25095e8 + 1.04968e8i 0.583580 + 0.489681i
\(122\) 6.69539e7 7.97926e7i 0.302229 0.360183i
\(123\) −2.44721e8 + 1.71966e7i −1.06918 + 0.0751317i
\(124\) −1.89491e7 6.89691e6i −0.0801497 0.0291721i
\(125\) −3.82215e7 2.20672e7i −0.156555 0.0903872i
\(126\) −3.86186e7 3.47245e7i −0.153219 0.137770i
\(127\) −1.34988e8 2.33807e8i −0.518897 0.898757i −0.999759 0.0219601i \(-0.993009\pi\)
0.480861 0.876797i \(-0.340324\pi\)
\(128\) −2.33661e7 + 4.12008e6i −0.0870455 + 0.0153485i
\(129\) −8.91703e7 2.00096e8i −0.322004 0.722568i
\(130\) −2.36654e7 + 8.61350e6i −0.0828592 + 0.0301583i
\(131\) 1.83624e8 + 3.23779e7i 0.623512 + 0.109942i 0.476473 0.879189i \(-0.341915\pi\)
0.147038 + 0.989131i \(0.453026\pi\)
\(132\) 1.79473e7 + 7.18779e7i 0.0591157 + 0.236755i
\(133\) −4.39458e7 + 3.68749e7i −0.140446 + 0.117849i
\(134\) 2.80984e8i 0.871491i
\(135\) −2.66321e7 1.41255e7i −0.0801809 0.0425275i
\(136\) 1.55492e8 0.454519
\(137\) −8.28785e7 9.87707e7i −0.235266 0.280379i 0.635474 0.772122i \(-0.280805\pi\)
−0.870741 + 0.491743i \(0.836360\pi\)
\(138\) 8.00907e7 2.79670e8i 0.220834 0.771135i
\(139\) −4.74801e7 + 2.69273e8i −0.127190 + 0.721330i 0.852793 + 0.522249i \(0.174907\pi\)
−0.979983 + 0.199081i \(0.936204\pi\)
\(140\) −1.73749e6 4.77370e6i −0.00452282 0.0124263i
\(141\) 8.08680e7 + 5.87118e7i 0.204598 + 0.148542i
\(142\) 2.16637e7 + 1.22861e8i 0.0532819 + 0.302177i
\(143\) −2.42833e8 + 1.40200e8i −0.580716 + 0.335276i
\(144\) 4.02003e7 9.96955e7i 0.0934931 0.231860i
\(145\) −2.17634e7 + 3.76954e7i −0.0492329 + 0.0852739i
\(146\) 1.47730e8 4.05886e8i 0.325131 0.893290i
\(147\) −3.84118e8 1.87184e8i −0.822612 0.400866i
\(148\) 8.08536e7 + 6.78443e7i 0.168520 + 0.141405i
\(149\) −4.74245e8 + 5.65183e8i −0.962182 + 1.14668i 0.0269470 + 0.999637i \(0.491421\pi\)
−0.989129 + 0.147048i \(0.953023\pi\)
\(150\) 1.98628e8 + 2.94260e8i 0.392351 + 0.581255i
\(151\) −3.96057e6 1.44153e6i −0.00761815 0.00277278i 0.338208 0.941071i \(-0.390179\pi\)
−0.345826 + 0.938299i \(0.612401\pi\)
\(152\) −1.02832e8 5.93701e7i −0.192644 0.111223i
\(153\) −3.72904e8 + 5.97680e8i −0.680505 + 1.09069i
\(154\) −2.82806e7 4.89834e7i −0.0502812 0.0870896i
\(155\) 8.80083e6 1.55182e6i 0.0152474 0.00268853i
\(156\) 4.04640e8 + 4.23895e7i 0.683235 + 0.0715747i
\(157\) −4.40928e7 + 1.60485e7i −0.0725719 + 0.0264140i −0.378051 0.925785i \(-0.623406\pi\)
0.305479 + 0.952199i \(0.401183\pi\)
\(158\) −3.65469e8 6.44421e7i −0.586439 0.103405i
\(159\) −2.83102e8 + 2.73575e8i −0.442949 + 0.428044i
\(160\) 8.05487e6 6.75883e6i 0.0122907 0.0103132i
\(161\) 2.22102e8i 0.330559i
\(162\) 2.86801e8 + 3.93614e8i 0.416409 + 0.571492i
\(163\) 1.16339e9 1.64807 0.824037 0.566536i \(-0.191717\pi\)
0.824037 + 0.566536i \(0.191717\pi\)
\(164\) 2.49191e8 + 2.96975e8i 0.344475 + 0.410529i
\(165\) −2.28151e7 2.36096e7i −0.0307813 0.0318532i
\(166\) −1.04700e8 + 5.93781e8i −0.137884 + 0.781976i
\(167\) 3.61399e8 + 9.92936e8i 0.464645 + 1.27660i 0.921956 + 0.387295i \(0.126590\pi\)
−0.457311 + 0.889307i \(0.651187\pi\)
\(168\) −8.55066e6 + 8.16226e7i −0.0107340 + 0.102464i
\(169\) 1.25748e8 + 7.13150e8i 0.154153 + 0.874247i
\(170\) −5.96772e7 + 3.44546e7i −0.0714517 + 0.0412526i
\(171\) 4.74821e8 2.52884e8i 0.555323 0.295758i
\(172\) −1.73089e8 + 2.99798e8i −0.197767 + 0.342543i
\(173\) −4.12523e8 + 1.13340e9i −0.460536 + 1.26531i 0.464547 + 0.885548i \(0.346217\pi\)
−0.925083 + 0.379764i \(0.876005\pi\)
\(174\) 5.82830e8 3.93414e8i 0.635836 0.429193i
\(175\) −2.07636e8 1.74227e8i −0.221386 0.185765i
\(176\) 7.52525e7 8.96824e7i 0.0784278 0.0934666i
\(177\) 3.13292e8 6.42901e8i 0.319195 0.655014i
\(178\) −6.10964e8 2.22373e8i −0.608605 0.221514i
\(179\) −8.98656e8 5.18839e8i −0.875349 0.505383i −0.00622722 0.999981i \(-0.501982\pi\)
−0.869122 + 0.494597i \(0.835316\pi\)
\(180\) 6.66228e6 + 4.71705e7i 0.00634648 + 0.0449345i
\(181\) −3.56364e8 6.17240e8i −0.332032 0.575096i 0.650878 0.759182i \(-0.274401\pi\)
−0.982910 + 0.184086i \(0.941067\pi\)
\(182\) −3.05901e8 + 5.39386e7i −0.278801 + 0.0491602i
\(183\) 4.38130e8 6.03468e8i 0.390660 0.538084i
\(184\) −4.31990e8 + 1.57231e8i −0.376879 + 0.137173i
\(185\) −4.60645e7 8.12242e6i −0.0393260 0.00693423i
\(186\) −1.38793e8 3.97468e7i −0.115962 0.0332086i
\(187\) −5.87733e8 + 4.93167e8i −0.480633 + 0.403299i
\(188\) 1.57920e8i 0.126417i
\(189\) −2.93235e8 2.28616e8i −0.229810 0.179168i
\(190\) 5.26220e7 0.0403788
\(191\) 5.83103e8 + 6.94915e8i 0.438139 + 0.522154i 0.939252 0.343228i \(-0.111520\pi\)
−0.501113 + 0.865382i \(0.667076\pi\)
\(192\) −1.64809e8 + 4.11515e7i −0.121277 + 0.0302817i
\(193\) 2.48429e8 1.40891e9i 0.179049 1.01544i −0.754316 0.656511i \(-0.772031\pi\)
0.933365 0.358928i \(-0.116858\pi\)
\(194\) 8.69691e7 + 2.38946e8i 0.0613985 + 0.168691i
\(195\) −1.64692e8 + 7.33931e7i −0.113903 + 0.0507594i
\(196\) 1.17254e8 + 6.64979e8i 0.0794516 + 0.450592i
\(197\) 8.92050e8 5.15025e8i 0.592276 0.341951i −0.173721 0.984795i \(-0.555579\pi\)
0.765997 + 0.642844i \(0.222246\pi\)
\(198\) 1.64249e8 + 5.04334e8i 0.106867 + 0.328139i
\(199\) 1.37020e9 2.37326e9i 0.873721 1.51333i 0.0156023 0.999878i \(-0.495033\pi\)
0.858119 0.513451i \(-0.171633\pi\)
\(200\) 1.91882e8 5.27192e8i 0.119926 0.329495i
\(201\) −1.41015e8 2.00675e9i −0.0863935 1.22944i
\(202\) −1.27766e9 1.07208e9i −0.767377 0.643906i
\(203\) −3.45085e8 + 4.11256e8i −0.203208 + 0.242174i
\(204\) 1.11050e9 7.80353e7i 0.641206 0.0450579i
\(205\) −1.61443e8 5.87606e7i −0.0914124 0.0332714i
\(206\) −4.22357e8 2.43848e8i −0.234537 0.135410i
\(207\) 4.31640e8 2.03756e9i 0.235093 1.10976i
\(208\) −3.21465e8 5.56794e8i −0.171744 0.297469i
\(209\) 5.76989e8 1.01739e8i 0.302401 0.0533214i
\(210\) −1.48046e7 3.32211e7i −0.00761236 0.0170819i
\(211\) −1.01531e9 + 3.69543e8i −0.512235 + 0.186438i −0.585189 0.810897i \(-0.698980\pi\)
0.0729536 + 0.997335i \(0.476757\pi\)
\(212\) 6.12672e8 + 1.08031e8i 0.303308 + 0.0534815i
\(213\) 2.16378e8 + 8.66583e8i 0.105122 + 0.421009i
\(214\) −1.66185e9 + 1.39446e9i −0.792385 + 0.664890i
\(215\) 1.53415e8i 0.0717983i
\(216\) 2.37071e8 7.32185e8i 0.108909 0.336361i
\(217\) 1.10223e8 0.0497089
\(218\) −1.68082e9 2.00312e9i −0.744208 0.886913i
\(219\) 8.51369e8 2.97291e9i 0.370119 1.29243i
\(220\) −9.00934e6 + 5.10945e7i −0.00384594 + 0.0218114i
\(221\) 1.44108e9 + 3.95934e9i 0.604115 + 1.65979i
\(222\) 6.11493e8 + 4.43956e8i 0.251756 + 0.182780i
\(223\) −5.48684e8 3.11174e9i −0.221872 1.25830i −0.868575 0.495558i \(-0.834964\pi\)
0.646703 0.762742i \(-0.276147\pi\)
\(224\) 1.12315e8 6.48448e7i 0.0446112 0.0257563i
\(225\) 1.56624e9 + 2.00188e9i 0.611124 + 0.781102i
\(226\) −5.36084e8 + 9.28525e8i −0.205494 + 0.355926i
\(227\) −3.84834e8 + 1.05732e9i −0.144934 + 0.398202i −0.990825 0.135154i \(-0.956847\pi\)
0.845891 + 0.533356i \(0.179069\pi\)
\(228\) −7.64206e8 3.72405e8i −0.282795 0.137809i
\(229\) −1.30324e9 1.09355e9i −0.473895 0.397646i 0.374318 0.927301i \(-0.377877\pi\)
−0.848213 + 0.529655i \(0.822321\pi\)
\(230\) 1.30956e8 1.56067e8i 0.0467965 0.0557698i
\(231\) −2.26558e8 3.35639e8i −0.0795669 0.117876i
\(232\) −1.04419e9 3.80053e8i −0.360435 0.131188i
\(233\) 3.10411e9 + 1.79216e9i 1.05321 + 0.608069i 0.923545 0.383489i \(-0.125278\pi\)
0.129661 + 0.991558i \(0.458611\pi\)
\(234\) 2.91115e9 + 9.96662e7i 0.970959 + 0.0332418i
\(235\) 3.49926e7 + 6.06089e7i 0.0114737 + 0.0198731i
\(236\) −1.11298e9 + 1.96249e8i −0.358789 + 0.0632643i
\(237\) −2.64247e9 2.76821e8i −0.837560 0.0877416i
\(238\) −7.98664e8 + 2.90690e8i −0.248918 + 0.0905987i
\(239\) 2.51697e9 + 4.43810e8i 0.771412 + 0.136021i 0.545482 0.838123i \(-0.316347\pi\)
0.225930 + 0.974144i \(0.427458\pi\)
\(240\) 5.41346e7 5.23130e7i 0.0163166 0.0157676i
\(241\) −6.13702e7 + 5.14957e7i −0.0181924 + 0.0152652i −0.651838 0.758358i \(-0.726002\pi\)
0.633646 + 0.773623i \(0.281558\pi\)
\(242\) 1.84753e9i 0.538680i
\(243\) 2.24583e9 + 2.66720e9i 0.644096 + 0.764944i
\(244\) −1.17846e9 −0.332471
\(245\) −1.92351e8 2.29234e8i −0.0533862 0.0636232i
\(246\) 1.92873e9 + 1.99589e9i 0.526659 + 0.544999i
\(247\) 5.58724e8 3.16868e9i 0.150110 0.851316i
\(248\) 7.80296e7 + 2.14384e8i 0.0206278 + 0.0566744i
\(249\) −4.49753e8 + 4.29323e9i −0.116997 + 1.11683i
\(250\) 8.67066e7 + 4.91738e8i 0.0221969 + 0.125885i
\(251\) 3.17366e9 1.83231e9i 0.799587 0.461642i −0.0437395 0.999043i \(-0.513927\pi\)
0.843327 + 0.537401i \(0.180594\pi\)
\(252\) −2.01043e7 + 5.87227e8i −0.00498525 + 0.145614i
\(253\) 1.13416e9 1.96443e9i 0.276818 0.479462i
\(254\) −1.04468e9 + 2.87023e9i −0.250985 + 0.689576i
\(255\) −4.08914e8 + 2.76019e8i −0.0967099 + 0.0652798i
\(256\) 2.05633e8 + 1.72547e8i 0.0478778 + 0.0401742i
\(257\) −3.09023e9 + 3.68279e9i −0.708367 + 0.844199i −0.993446 0.114305i \(-0.963536\pi\)
0.285079 + 0.958504i \(0.407980\pi\)
\(258\) −1.08571e9 + 2.22798e9i −0.245040 + 0.502843i
\(259\) −5.42128e8 1.97318e8i −0.120477 0.0438499i
\(260\) 2.46754e8 + 1.42463e8i 0.0539971 + 0.0311752i
\(261\) 3.96504e9 3.10220e9i 0.854448 0.668510i
\(262\) −1.05476e9 1.82690e9i −0.223845 0.387712i
\(263\) −6.32692e9 + 1.11561e9i −1.32242 + 0.233178i −0.789898 0.613238i \(-0.789867\pi\)
−0.532522 + 0.846416i \(0.678756\pi\)
\(264\) 4.92433e8 6.78264e8i 0.101375 0.139631i
\(265\) −2.59079e8 + 9.42970e7i −0.0525349 + 0.0191212i
\(266\) 6.39175e8 + 1.12704e8i 0.127671 + 0.0225119i
\(267\) −4.47501e9 1.28153e9i −0.880540 0.252165i
\(268\) −2.43523e9 + 2.04340e9i −0.472065 + 0.396109i
\(269\) 3.13152e9i 0.598061i −0.954244 0.299031i \(-0.903337\pi\)
0.954244 0.299031i \(-0.0966633\pi\)
\(270\) 7.12540e7 + 3.33541e8i 0.0134077 + 0.0627616i
\(271\) 4.59465e9 0.851873 0.425937 0.904753i \(-0.359945\pi\)
0.425937 + 0.904753i \(0.359945\pi\)
\(272\) −1.13079e9 1.34762e9i −0.206588 0.246202i
\(273\) −2.15763e9 + 5.38740e8i −0.388441 + 0.0969904i
\(274\) −2.53308e8 + 1.43658e9i −0.0449415 + 0.254876i
\(275\) 9.46788e8 + 2.60128e9i 0.165547 + 0.454837i
\(276\) −3.00629e9 + 1.33972e9i −0.518078 + 0.230875i
\(277\) 1.92456e9 + 1.09147e10i 0.326898 + 1.85393i 0.495991 + 0.868328i \(0.334805\pi\)
−0.169093 + 0.985600i \(0.554084\pi\)
\(278\) 2.67903e9 1.54674e9i 0.448537 0.258963i
\(279\) −1.01118e9 2.14211e8i −0.166883 0.0353529i
\(280\) −2.87372e7 + 4.97743e7i −0.00467533 + 0.00809791i
\(281\) −2.60324e9 + 7.15235e9i −0.417531 + 1.14716i 0.535566 + 0.844494i \(0.320098\pi\)
−0.953097 + 0.302665i \(0.902124\pi\)
\(282\) −7.92537e7 1.12784e9i −0.0125321 0.178341i
\(283\) −8.72173e9 7.31840e9i −1.35974 1.14096i −0.976061 0.217495i \(-0.930211\pi\)
−0.383682 0.923465i \(-0.625344\pi\)
\(284\) 9.07268e8 1.08124e9i 0.139464 0.166207i
\(285\) 3.75818e8 2.64089e7i 0.0569637 0.00400287i
\(286\) 2.98104e9 + 1.08501e9i 0.445557 + 0.162170i
\(287\) −1.83513e9 1.05951e9i −0.270482 0.156163i
\(288\) −1.15639e9 + 3.76609e8i −0.168087 + 0.0547420i
\(289\) 2.27655e9 + 3.94310e9i 0.326351 + 0.565257i
\(290\) 4.84969e8 8.55131e7i 0.0685681 0.0120904i
\(291\) 7.41037e8 + 1.66287e9i 0.103340 + 0.231892i
\(292\) −4.59207e9 + 1.67138e9i −0.631651 + 0.229902i
\(293\) 8.79465e9 + 1.55073e9i 1.19330 + 0.210410i 0.734798 0.678286i \(-0.237277\pi\)
0.458497 + 0.888696i \(0.348388\pi\)
\(294\) 1.17113e9 + 4.69033e9i 0.156754 + 0.627790i
\(295\) 3.83672e8 3.21939e8i 0.0506607 0.0425094i
\(296\) 1.19413e9i 0.155555i
\(297\) 1.42615e9 + 3.51944e9i 0.183290 + 0.452322i
\(298\) 8.34718e9 1.05846
\(299\) −8.00726e9 9.54268e9i −1.00184 1.19395i
\(300\) 1.10582e9 3.86142e9i 0.136520 0.476718i
\(301\) 3.28578e8 1.86346e9i 0.0400288 0.227015i
\(302\) 1.63090e7 + 4.48087e7i 0.00196065 + 0.00538685i
\(303\) −9.66287e9 7.01544e9i −1.14640 0.832308i
\(304\) 2.33278e8 + 1.32298e9i 0.0273136 + 0.154903i
\(305\) 4.52287e8 2.61128e8i 0.0522654 0.0301754i
\(306\) 7.89185e9 1.11463e9i 0.900105 0.127129i
\(307\) −6.07643e9 + 1.05247e10i −0.684062 + 1.18483i 0.289669 + 0.957127i \(0.406455\pi\)
−0.973731 + 0.227703i \(0.926879\pi\)
\(308\) −2.18864e8 + 6.01325e8i −0.0243205 + 0.0668200i
\(309\) −3.13879e9 1.52956e9i −0.344293 0.167777i
\(310\) −7.74517e7 6.49897e7i −0.00838657 0.00703716i
\(311\) 3.94165e9 4.69747e9i 0.421344 0.502138i −0.513061 0.858352i \(-0.671488\pi\)
0.934404 + 0.356215i \(0.115933\pi\)
\(312\) −2.57529e9 3.81520e9i −0.271774 0.402624i
\(313\) 1.40907e10 + 5.12860e9i 1.46810 + 0.534345i 0.947584 0.319507i \(-0.103517\pi\)
0.520516 + 0.853852i \(0.325740\pi\)
\(314\) 4.59745e8 + 2.65434e8i 0.0472932 + 0.0273047i
\(315\) −1.22404e8 2.29830e8i −0.0124324 0.0233434i
\(316\) 2.09930e9 + 3.63609e9i 0.210536 + 0.364659i
\(317\) −7.13246e9 + 1.25764e9i −0.706321 + 0.124543i −0.515259 0.857034i \(-0.672304\pi\)
−0.191062 + 0.981578i \(0.561193\pi\)
\(318\) 4.42982e9 + 4.64062e8i 0.433190 + 0.0453803i
\(319\) 5.15225e9 1.87527e9i 0.497547 0.181092i
\(320\) −1.17155e8 2.06576e7i −0.0111728 0.00197006i
\(321\) −1.11688e10 + 1.07930e10i −1.05193 + 1.01653i
\(322\) 1.92492e9 1.61520e9i 0.179056 0.150246i
\(323\) 8.80392e9i 0.808846i
\(324\) 1.32567e9 5.34813e9i 0.120297 0.485313i
\(325\) 1.52024e10 1.36263
\(326\) −8.46057e9 1.00829e10i −0.749082 0.892721i
\(327\) −1.30094e10 1.34624e10i −1.13780 1.17742i
\(328\) 7.61624e8 4.31938e9i 0.0658029 0.373187i
\(329\) 2.95229e8 + 8.11134e8i 0.0251985 + 0.0692323i
\(330\) −3.87010e7 + 3.69430e8i −0.00326337 + 0.0311513i
\(331\) 1.97518e9 + 1.12018e10i 0.164549 + 0.933202i 0.949529 + 0.313681i \(0.101562\pi\)
−0.784980 + 0.619521i \(0.787327\pi\)
\(332\) 5.90759e9 3.41075e9i 0.486248 0.280735i
\(333\) 4.58999e9 + 2.86378e9i 0.373280 + 0.232896i
\(334\) 5.97738e9 1.03531e10i 0.480313 0.831927i
\(335\) 4.81846e8 1.32386e9i 0.0382586 0.105115i
\(336\) 7.69590e8 5.19478e8i 0.0603813 0.0407577i
\(337\) −7.38852e9 6.19970e9i −0.572846 0.480675i 0.309743 0.950820i \(-0.399757\pi\)
−0.882589 + 0.470146i \(0.844201\pi\)
\(338\) 5.26626e9 6.27608e9i 0.403492 0.480864i
\(339\) −3.36264e9 + 6.90042e9i −0.254613 + 0.522488i
\(340\) 7.32602e8 + 2.66645e8i 0.0548217 + 0.0199535i
\(341\) −9.74892e8 5.62854e8i −0.0721006 0.0416273i
\(342\) −5.64474e9 2.27613e9i −0.412610 0.166377i
\(343\) −3.86210e9 6.68935e9i −0.279027 0.483289i
\(344\) 3.85705e9 6.80101e8i 0.275436 0.0485668i
\(345\) 8.56941e8 1.18033e9i 0.0604888 0.0833155i
\(346\) 1.28229e10 4.66716e9i 0.894711 0.325648i
\(347\) −1.54361e10 2.72180e9i −1.06468 0.187732i −0.386249 0.922395i \(-0.626229\pi\)
−0.678433 + 0.734663i \(0.737340\pi\)
\(348\) −7.64816e9 2.19025e9i −0.521483 0.149340i
\(349\) −8.90937e9 + 7.47585e9i −0.600544 + 0.503917i −0.891621 0.452783i \(-0.850431\pi\)
0.291076 + 0.956700i \(0.405987\pi\)
\(350\) 3.06657e9i 0.204353i
\(351\) 2.08410e10 7.49191e8i 1.37306 0.0493587i
\(352\) −1.32452e9 −0.0862755
\(353\) −7.20302e9 8.58422e9i −0.463891 0.552844i 0.482488 0.875903i \(-0.339733\pi\)
−0.946379 + 0.323059i \(0.895289\pi\)
\(354\) −7.85025e9 + 1.96014e9i −0.499885 + 0.124817i
\(355\) −1.08620e8 + 6.16012e8i −0.00683903 + 0.0387861i
\(356\) 2.51586e9 + 6.91227e9i 0.156634 + 0.430349i
\(357\) −5.55805e9 + 2.47688e9i −0.342176 + 0.152487i
\(358\) 2.03863e9 + 1.15616e10i 0.124110 + 0.703862i
\(359\) 1.96268e10 1.13315e10i 1.18160 0.682198i 0.225217 0.974309i \(-0.427691\pi\)
0.956384 + 0.292111i \(0.0943576\pi\)
\(360\) 3.60367e8 4.00779e8i 0.0214553 0.0238614i
\(361\) 5.13026e9 8.88587e9i 0.302072 0.523204i
\(362\) −2.75791e9 + 7.57730e9i −0.160600 + 0.441245i
\(363\) −9.27205e8 1.31948e10i −0.0534010 0.759935i
\(364\) 2.69208e9 + 2.25892e9i 0.153350 + 0.128676i
\(365\) 1.39207e9 1.65900e9i 0.0784311 0.0934706i
\(366\) −8.41635e9 + 5.91421e8i −0.469029 + 0.0329589i
\(367\) 2.55507e10 + 9.29971e9i 1.40844 + 0.512631i 0.930673 0.365853i \(-0.119223\pi\)
0.477771 + 0.878485i \(0.341445\pi\)
\(368\) 4.50426e9 + 2.60053e9i 0.245602 + 0.141798i
\(369\) 1.47763e10 + 1.32864e10i 0.797004 + 0.716639i
\(370\) 2.64600e8 + 4.58301e8i 0.0141183 + 0.0244537i
\(371\) −3.34887e9 + 5.90496e8i −0.176768 + 0.0311689i
\(372\) 6.64866e8 + 1.49194e9i 0.0347186 + 0.0779076i
\(373\) −2.85597e10 + 1.03949e10i −1.47543 + 0.537012i −0.949569 0.313559i \(-0.898479\pi\)
−0.525860 + 0.850571i \(0.676256\pi\)
\(374\) 8.54836e9 + 1.50731e9i 0.436914 + 0.0770398i
\(375\) 8.66029e8 + 3.46840e9i 0.0437933 + 0.175390i
\(376\) −1.36866e9 + 1.14844e9i −0.0684769 + 0.0574589i
\(377\) 3.01108e10i 1.49058i
\(378\) 1.51124e8 + 4.20397e9i 0.00740230 + 0.205917i
\(379\) 2.08359e10 1.00985 0.504924 0.863164i \(-0.331521\pi\)
0.504924 + 0.863164i \(0.331521\pi\)
\(380\) −3.82684e8 4.56065e8i −0.0183529 0.0218722i
\(381\) −6.02048e9 + 2.10230e10i −0.285714 + 0.997690i
\(382\) 1.78219e9 1.01073e10i 0.0836950 0.474658i
\(383\) −4.78955e9 1.31592e10i −0.222587 0.611553i 0.777258 0.629183i \(-0.216610\pi\)
−0.999845 + 0.0176297i \(0.994388\pi\)
\(384\) 1.55520e9 + 1.12910e9i 0.0715254 + 0.0519289i
\(385\) −4.92451e7 2.79283e8i −0.00224140 0.0127116i
\(386\) −1.40174e10 + 8.09295e9i −0.631420 + 0.364550i
\(387\) −6.63587e9 + 1.64568e10i −0.295838 + 0.733669i
\(388\) 1.43843e9 2.49143e9i 0.0634689 0.109931i
\(389\) −2.00479e9 + 5.50812e9i −0.0875529 + 0.240550i −0.975740 0.218932i \(-0.929743\pi\)
0.888187 + 0.459482i \(0.151965\pi\)
\(390\) 1.83377e9 + 8.93615e8i 0.0792661 + 0.0386271i
\(391\) −2.61108e10 2.19095e10i −1.11715 0.937402i
\(392\) 4.91054e9 5.85215e9i 0.207962 0.247840i
\(393\) −8.44977e9 1.25181e10i −0.354221 0.524768i
\(394\) −1.09509e10 3.98580e9i −0.454427 0.165398i
\(395\) −1.61140e9 9.30345e8i −0.0661936 0.0382169i
\(396\) 3.17649e9 5.09119e9i 0.129171 0.207032i
\(397\) 1.12687e10 + 1.95180e10i 0.453642 + 0.785732i 0.998609 0.0527260i \(-0.0167910\pi\)
−0.544967 + 0.838458i \(0.683458\pi\)
\(398\) −3.05331e10 + 5.38382e9i −1.21686 + 0.214565i
\(399\) 4.62145e9 + 4.84136e8i 0.182342 + 0.0191019i
\(400\) −5.96449e9 + 2.17090e9i −0.232988 + 0.0848007i
\(401\) 3.10390e10 + 5.47301e9i 1.20041 + 0.211665i 0.737876 0.674936i \(-0.235829\pi\)
0.462535 + 0.886601i \(0.346940\pi\)
\(402\) −1.63666e10 + 1.58158e10i −0.626691 + 0.605603i
\(403\) −4.73577e9 + 3.97378e9i −0.179544 + 0.150655i
\(404\) 1.88697e10i 0.708337i
\(405\) 6.76276e8 + 2.34634e9i 0.0251364 + 0.0872108i
\(406\) 6.07384e9 0.223542
\(407\) 3.78736e9 + 4.51360e9i 0.138025 + 0.164492i
\(408\) −8.75222e9 9.05698e9i −0.315847 0.326846i
\(409\) 2.04591e9 1.16029e10i 0.0731129 0.414644i −0.926181 0.377078i \(-0.876929\pi\)
0.999294 0.0375652i \(-0.0119602\pi\)
\(410\) 6.64801e8 + 1.82652e9i 0.0235264 + 0.0646383i
\(411\) −1.08812e9 + 1.03870e10i −0.0381339 + 0.364017i
\(412\) 9.58131e8 + 5.43383e9i 0.0332534 + 0.188589i
\(413\) 5.34980e9 3.08871e9i 0.183881 0.106164i
\(414\) −2.07981e10 + 1.10768e10i −0.707983 + 0.377063i
\(415\) −1.51154e9 + 2.61806e9i −0.0509597 + 0.0882647i
\(416\) −2.48783e9 + 6.83525e9i −0.0830706 + 0.228234i
\(417\) 1.83570e10 1.23911e10i 0.607095 0.409793i
\(418\) −5.07780e9 4.26078e9i −0.166330 0.139567i
\(419\) −2.13151e10 + 2.54023e10i −0.691562 + 0.824172i −0.991544 0.129773i \(-0.958575\pi\)
0.299982 + 0.953945i \(0.403019\pi\)
\(420\) −1.80257e8 + 3.69903e8i −0.00579288 + 0.0118875i
\(421\) −3.72111e10 1.35437e10i −1.18453 0.431132i −0.326728 0.945118i \(-0.605946\pi\)
−0.857798 + 0.513986i \(0.828168\pi\)
\(422\) 1.05864e10 + 6.11207e9i 0.333810 + 0.192725i
\(423\) −1.13204e9 8.01507e9i −0.0353589 0.250349i
\(424\) −3.51926e9 6.09554e9i −0.108890 0.188603i
\(425\) 4.09649e10 7.22322e9i 1.25561 0.221399i
\(426\) 5.93694e9 8.17737e9i 0.180270 0.248299i
\(427\) 6.05299e9 2.20311e9i 0.182078 0.0662711i
\(428\) 2.41709e10 + 4.26199e9i 0.720309 + 0.127010i
\(429\) 2.18347e10 + 6.25291e9i 0.644640 + 0.184609i
\(430\) −1.32962e9 + 1.11568e9i −0.0388913 + 0.0326337i
\(431\) 2.27136e10i 0.658227i −0.944290 0.329114i \(-0.893250\pi\)
0.944290 0.329114i \(-0.106750\pi\)
\(432\) −8.06976e9 + 3.27003e9i −0.231700 + 0.0938894i
\(433\) −6.29805e10 −1.79166 −0.895828 0.444401i \(-0.853417\pi\)
−0.895828 + 0.444401i \(0.853417\pi\)
\(434\) −8.01577e8 9.55283e8i −0.0225937 0.0269261i
\(435\) 3.42066e9 8.54108e8i 0.0955328 0.0238537i
\(436\) −5.13722e9 + 2.91346e10i −0.142162 + 0.806238i
\(437\) 8.90240e9 + 2.44592e10i 0.244108 + 0.670680i
\(438\) −3.19571e10 + 1.42413e10i −0.868301 + 0.386949i
\(439\) 6.92308e9 + 3.92627e10i 0.186398 + 1.05712i 0.924146 + 0.382039i \(0.124778\pi\)
−0.737748 + 0.675076i \(0.764111\pi\)
\(440\) 5.08345e8 2.93493e8i 0.0135627 0.00783045i
\(441\) 1.07180e10 + 3.29099e10i 0.283372 + 0.870105i
\(442\) 2.38348e10 4.12831e10i 0.624486 1.08164i
\(443\) −1.79053e10 + 4.91945e10i −0.464909 + 1.27733i 0.456844 + 0.889547i \(0.348980\pi\)
−0.921752 + 0.387779i \(0.873242\pi\)
\(444\) −5.99286e8 8.52827e9i −0.0154206 0.219447i
\(445\) −2.49723e9 2.09542e9i −0.0636822 0.0534357i
\(446\) −2.29787e10 + 2.73849e10i −0.580745 + 0.692105i
\(447\) 5.96143e10 4.18912e9i 1.49321 0.104928i
\(448\) −1.37878e9 5.01836e8i −0.0342282 0.0124580i
\(449\) −2.11630e8 1.22185e8i −0.00520706 0.00300630i 0.497394 0.867525i \(-0.334290\pi\)
−0.502601 + 0.864518i \(0.667624\pi\)
\(450\) 5.95967e9 2.81326e10i 0.145336 0.686057i
\(451\) 1.08208e10 + 1.87421e10i 0.261549 + 0.453015i
\(452\) 1.19459e10 2.10639e9i 0.286197 0.0504643i
\(453\) 1.38964e8 + 3.11832e8i 0.00329997 + 0.00740505i
\(454\) 1.19622e10 4.35390e9i 0.281572 0.102484i
\(455\) −1.53375e9 2.70442e8i −0.0357857 0.00630998i
\(456\) 2.32999e9 + 9.33147e9i 0.0538883 + 0.215820i
\(457\) 6.96709e9 5.84609e9i 0.159730 0.134029i −0.559420 0.828885i \(-0.688976\pi\)
0.719150 + 0.694855i \(0.244532\pi\)
\(458\) 1.92476e10i 0.437435i
\(459\) 5.58030e10 1.19211e10i 1.25721 0.268576i
\(460\) −2.30495e9 −0.0514790
\(461\) −4.16816e10 4.96742e10i −0.922870 1.09983i −0.994741 0.102420i \(-0.967341\pi\)
0.0718711 0.997414i \(-0.477103\pi\)
\(462\) −1.26131e9 + 4.40441e9i −0.0276857 + 0.0966763i
\(463\) −6.08059e9 + 3.44847e10i −0.132319 + 0.750418i 0.844370 + 0.535760i \(0.179975\pi\)
−0.976689 + 0.214658i \(0.931136\pi\)
\(464\) 4.29981e9 + 1.18136e10i 0.0927636 + 0.254866i
\(465\) −5.85764e8 4.25276e8i −0.0125288 0.00909619i
\(466\) −7.04177e9 3.99359e10i −0.149327 0.846875i
\(467\) 2.50755e10 1.44774e10i 0.527208 0.304384i −0.212671 0.977124i \(-0.568216\pi\)
0.739879 + 0.672740i \(0.234883\pi\)
\(468\) −2.03070e10 2.59552e10i −0.423314 0.541054i
\(469\) 8.68815e9 1.50483e10i 0.179571 0.311026i
\(470\) 2.70809e8 7.44041e8i 0.00554972 0.0152477i
\(471\) 3.41664e9 + 1.66496e9i 0.0694249 + 0.0338314i
\(472\) 9.79479e9 + 8.21881e9i 0.197345 + 0.165593i
\(473\) −1.24219e10 + 1.48039e10i −0.248167 + 0.295754i
\(474\) 1.68177e10 + 2.49149e10i 0.333160 + 0.493566i
\(475\) −2.98495e10 1.08643e10i −0.586357 0.213417i
\(476\) 8.32749e9 + 4.80788e9i 0.162213 + 0.0936538i
\(477\) 3.18700e10 + 1.09110e9i 0.615614 + 0.0210762i
\(478\) −1.44578e10 2.50416e10i −0.276943 0.479679i
\(479\) 5.51231e10 9.71969e9i 1.04711 0.184633i 0.376478 0.926426i \(-0.377135\pi\)
0.670630 + 0.741792i \(0.266024\pi\)
\(480\) −8.47070e8 8.87378e7i −0.0159571 0.00167164i
\(481\) 3.04064e10 1.10670e10i 0.568048 0.206753i
\(482\) 8.92606e8 + 1.57391e8i 0.0165376 + 0.00291602i
\(483\) 1.29368e10 1.25015e10i 0.237706 0.229707i
\(484\) −1.60122e10 + 1.34358e10i −0.291790 + 0.244841i
\(485\) 1.27493e9i 0.0230420i
\(486\) 6.78372e9 3.88608e10i 0.121597 0.696573i
\(487\) −5.31502e10 −0.944907 −0.472453 0.881356i \(-0.656632\pi\)
−0.472453 + 0.881356i \(0.656632\pi\)
\(488\) 8.57010e9 + 1.02135e10i 0.151115 + 0.180092i
\(489\) −6.54843e10 6.77646e10i −1.14525 1.18513i
\(490\) −5.87897e8 + 3.33413e9i −0.0101980 + 0.0578360i
\(491\) 2.18870e10 + 6.01341e10i 0.376583 + 1.03465i 0.972763 + 0.231803i \(0.0744623\pi\)
−0.596180 + 0.802851i \(0.703315\pi\)
\(492\) 3.27167e9 3.12306e10i 0.0558353 0.532991i
\(493\) −1.43068e10 8.11377e10i −0.242189 1.37352i
\(494\) −3.15255e10 + 1.82013e10i −0.529364 + 0.305629i
\(495\) −9.09938e7 + 2.65784e9i −0.00151562 + 0.0442698i
\(496\) 1.29057e9 2.23534e9i 0.0213234 0.0369332i
\(497\) −2.63870e9 + 7.24977e9i −0.0432479 + 0.118823i
\(498\) 4.04794e10 2.73238e10i 0.658137 0.444246i
\(499\) −4.61946e10 3.87618e10i −0.745056 0.625176i 0.189135 0.981951i \(-0.439432\pi\)
−0.934190 + 0.356775i \(0.883876\pi\)
\(500\) 3.63124e9 4.32754e9i 0.0580998 0.0692406i
\(501\) 3.74937e10 7.69402e10i 0.595123 1.22124i
\(502\) −3.89602e10 1.41803e10i −0.613488 0.223291i
\(503\) −8.99469e10 5.19309e10i −1.40512 0.811248i −0.410211 0.911991i \(-0.634545\pi\)
−0.994913 + 0.100742i \(0.967878\pi\)
\(504\) 5.23558e9 4.09626e9i 0.0811415 0.0634841i
\(505\) −4.18124e9 7.24212e9i −0.0642894 0.111353i
\(506\) −2.52733e10 + 4.45637e9i −0.385532 + 0.0679796i
\(507\) 3.44611e10 4.74657e10i 0.521551 0.718370i
\(508\) 3.24730e10 1.18192e10i 0.487604 0.177473i
\(509\) −1.01690e11 1.79307e10i −1.51499 0.267133i −0.646525 0.762893i \(-0.723779\pi\)
−0.868460 + 0.495760i \(0.834890\pi\)
\(510\) 5.36595e9 + 1.53668e9i 0.0793169 + 0.0227144i
\(511\) 2.04620e10 1.71696e10i 0.300098 0.251812i
\(512\) 3.03700e9i 0.0441942i
\(513\) −4.14562e10 1.34229e10i −0.598576 0.193811i
\(514\) 5.43912e10 0.779248
\(515\) −1.57178e9 1.87317e9i −0.0223441 0.0266286i
\(516\) 2.72051e10 6.79288e9i 0.383753 0.0958197i
\(517\) 1.53084e9 8.68183e9i 0.0214273 0.121520i
\(518\) 2.23240e9 + 6.13348e9i 0.0310066 + 0.0851898i
\(519\) 8.92371e10 3.97675e10i 1.22992 0.548098i
\(520\) −5.59768e8 3.17460e9i −0.00765588 0.0434186i
\(521\) −4.50406e10 + 2.60042e10i −0.611299 + 0.352934i −0.773474 0.633828i \(-0.781483\pi\)
0.162175 + 0.986762i \(0.448149\pi\)
\(522\) −5.57212e10 1.18041e10i −0.750479 0.158983i
\(523\) 3.02980e9 5.24776e9i 0.0404955 0.0701403i −0.845067 0.534660i \(-0.820440\pi\)
0.885563 + 0.464520i \(0.153773\pi\)
\(524\) −8.16282e9 + 2.24272e10i −0.108272 + 0.297474i
\(525\) 1.53899e9 + 2.19010e10i 0.0202581 + 0.288288i
\(526\) 5.56801e10 + 4.67211e10i 0.727373 + 0.610338i
\(527\) −1.08731e10 + 1.29580e10i −0.140965 + 0.167995i
\(528\) −9.45951e9 + 6.64724e8i −0.121712 + 0.00855275i
\(529\) 2.11075e10 + 7.68251e9i 0.269535 + 0.0981026i
\(530\) 2.70135e9 + 1.55963e9i 0.0342356 + 0.0197659i
\(531\) −5.50815e10 + 1.79387e10i −0.692832 + 0.225639i
\(532\) −3.67150e9 6.35922e9i −0.0458350 0.0793885i
\(533\) 1.17044e11 2.06381e10i 1.45025 0.255718i
\(534\) 2.14369e10 + 4.81037e10i 0.263631 + 0.591580i
\(535\) −1.02211e10 + 3.72017e9i −0.124762 + 0.0454097i
\(536\) 3.54196e10 + 6.24543e9i 0.429125 + 0.0756664i
\(537\) 2.03619e10 + 8.15483e10i 0.244862 + 0.980659i
\(538\) −2.71402e10 + 2.27734e10i −0.323955 + 0.271830i
\(539\) 3.76947e10i 0.446606i
\(540\) 2.37255e9 3.04316e9i 0.0279023 0.0357890i
\(541\) 9.43879e9 0.110186 0.0550931 0.998481i \(-0.482454\pi\)
0.0550931 + 0.998481i \(0.482454\pi\)
\(542\) −3.34137e10 3.98209e10i −0.387193 0.461439i
\(543\) −1.58938e10 + 5.55000e10i −0.182822 + 0.638401i
\(544\) −3.45612e9 + 1.96006e10i −0.0394632 + 0.223807i
\(545\) −4.48414e9 1.23201e10i −0.0508268 0.139646i
\(546\) 2.03601e10 + 1.47818e10i 0.229092 + 0.166325i
\(547\) 3.39203e9 + 1.92372e10i 0.0378888 + 0.214878i 0.997874 0.0651728i \(-0.0207599\pi\)
−0.959985 + 0.280051i \(0.909649\pi\)
\(548\) 1.42927e10 8.25191e9i 0.158487 0.0915023i
\(549\) −5.98115e10 + 8.44768e9i −0.658408 + 0.0929925i
\(550\) 1.56594e10 2.71229e10i 0.171130 0.296405i
\(551\) −2.15185e10 + 5.91217e10i −0.233457 + 0.641417i
\(552\) 3.34738e10 + 1.63121e10i 0.360536 + 0.175693i
\(553\) −1.75804e10 1.47517e10i −0.187987 0.157740i
\(554\) 8.05996e10 9.60549e10i 0.855646 1.01972i
\(555\) 2.11974e9 + 3.14032e9i 0.0223414 + 0.0330980i
\(556\) −3.28880e10 1.19703e10i −0.344142 0.125258i
\(557\) 6.40097e10 + 3.69560e10i 0.665005 + 0.383941i 0.794181 0.607681i \(-0.207900\pi\)
−0.129176 + 0.991622i \(0.541233\pi\)
\(558\) 5.49712e9 + 1.03215e10i 0.0567020 + 0.106465i
\(559\) 5.30643e10 + 9.19100e10i 0.543444 + 0.941273i
\(560\) 6.40370e8 1.12915e8i 0.00651147 0.00114815i
\(561\) 6.18075e10 + 6.47486e9i 0.624008 + 0.0653701i
\(562\) 8.09196e10 2.94523e10i 0.811163 0.295239i
\(563\) −1.34902e11 2.37869e10i −1.34272 0.236758i −0.544317 0.838880i \(-0.683211\pi\)
−0.798404 + 0.602122i \(0.794322\pi\)
\(564\) −9.19839e9 + 8.88887e9i −0.0909066 + 0.0878476i
\(565\) −4.11805e9 + 3.45545e9i −0.0404108 + 0.0339087i
\(566\) 1.28811e11i 1.25513i
\(567\) 3.18911e9 + 2.99483e10i 0.0308559 + 0.289761i
\(568\) −1.59688e10 −0.153419
\(569\) 1.18276e11 + 1.40955e11i 1.12836 + 1.34472i 0.931267 + 0.364338i \(0.118705\pi\)
0.197090 + 0.980385i \(0.436851\pi\)
\(570\) −2.96195e9 3.06509e9i −0.0280594 0.0290365i
\(571\) −3.44395e10 + 1.95316e11i −0.323975 + 1.83735i 0.192805 + 0.981237i \(0.438241\pi\)
−0.516781 + 0.856118i \(0.672870\pi\)
\(572\) −1.22755e10 3.37266e10i −0.114671 0.315057i
\(573\) 7.65565e9 7.30790e10i 0.0710172 0.677913i
\(574\) 4.16304e9 + 2.36098e10i 0.0383498 + 0.217493i
\(575\) −1.06505e11 + 6.14908e10i −0.974315 + 0.562521i
\(576\) 1.16736e10 + 7.28340e9i 0.106051 + 0.0661674i
\(577\) −8.79316e10 + 1.52302e11i −0.793308 + 1.37405i 0.130600 + 0.991435i \(0.458310\pi\)
−0.923908 + 0.382614i \(0.875024\pi\)
\(578\) 1.76183e10 4.84058e10i 0.157853 0.433697i
\(579\) −9.60485e10 + 6.48334e10i −0.854627 + 0.576878i
\(580\) −4.26797e9 3.58125e9i −0.0377146 0.0316463i
\(581\) −2.39672e10 + 2.85630e10i −0.210336 + 0.250668i
\(582\) 9.02268e9 1.85153e10i 0.0786400 0.161376i
\(583\) 3.26352e10 + 1.18782e10i 0.282495 + 0.102820i
\(584\) 4.78805e10 + 2.76438e10i 0.411630 + 0.237655i
\(585\) 1.35450e10 + 5.46176e9i 0.115653 + 0.0466347i
\(586\) −5.05175e10 8.74989e10i −0.428402 0.742014i
\(587\) 1.17697e11 2.07532e10i 0.991318 0.174796i 0.345608 0.938379i \(-0.387673\pi\)
0.645710 + 0.763583i \(0.276562\pi\)
\(588\) 3.21333e10 4.42596e10i 0.268811 0.370252i
\(589\) 1.21384e10 4.41802e9i 0.100856 0.0367085i
\(590\) −5.58036e9 9.83968e8i −0.0460526 0.00812031i
\(591\) −8.02099e10 2.29701e10i −0.657473 0.188284i
\(592\) −1.03493e10 + 8.68407e9i −0.0842602 + 0.0707027i
\(593\) 2.06793e11i 1.67231i −0.548495 0.836154i \(-0.684799\pi\)
0.548495 0.836154i \(-0.315201\pi\)
\(594\) 2.01309e10 3.79546e10i 0.161703 0.304873i
\(595\) −4.26140e9 −0.0340005
\(596\) −6.07033e10 7.23434e10i −0.481091 0.573342i
\(597\) −2.15361e11 + 5.37738e10i −1.69539 + 0.423324i
\(598\) −2.44732e10 + 1.38795e11i −0.191376 + 1.08535i
\(599\) −2.75602e10 7.57210e10i −0.214080 0.588179i 0.785448 0.618928i \(-0.212433\pi\)
−0.999527 + 0.0307494i \(0.990211\pi\)
\(600\) −4.15080e10 + 1.84976e10i −0.320278 + 0.142728i
\(601\) −2.89057e10 1.63932e11i −0.221557 1.25651i −0.869159 0.494533i \(-0.835339\pi\)
0.647602 0.761979i \(-0.275772\pi\)
\(602\) −1.85398e10 + 1.07039e10i −0.141162 + 0.0815000i
\(603\) −1.08950e11 + 1.21168e11i −0.824059 + 0.916470i
\(604\) 2.69744e8 4.67210e8i 0.00202677 0.00351046i
\(605\) 3.16825e9 8.70468e9i 0.0236482 0.0649728i
\(606\) 9.46997e9 + 1.34765e11i 0.0702196 + 0.999276i
\(607\) 1.00226e11 + 8.40994e10i 0.738286 + 0.619496i 0.932377 0.361488i \(-0.117731\pi\)
−0.194090 + 0.980984i \(0.562176\pi\)
\(608\) 9.76957e9 1.16429e10i 0.0714926 0.0852016i
\(609\) 4.33784e10 3.04822e9i 0.315358 0.0221604i
\(610\) −5.55231e9 2.02088e9i −0.0401009 0.0145955i
\(611\) −4.19277e10 2.42070e10i −0.300840 0.173690i
\(612\) −6.70523e10 6.02912e10i −0.477978 0.429782i
\(613\) −8.58372e10 1.48674e11i −0.607902 1.05292i −0.991586 0.129453i \(-0.958678\pi\)
0.383683 0.923465i \(-0.374655\pi\)
\(614\) 1.35405e11 2.38756e10i 0.952712 0.167989i
\(615\) 5.66456e9 + 1.27111e10i 0.0395973 + 0.0888553i
\(616\) 6.80322e9 2.47617e9i 0.0472489 0.0171972i
\(617\) 9.64446e10 + 1.70058e10i 0.665483 + 0.117343i 0.496178 0.868221i \(-0.334736\pi\)
0.169306 + 0.985564i \(0.445848\pi\)
\(618\) 9.56985e9 + 3.83267e10i 0.0656071 + 0.262753i
\(619\) 1.51400e11 1.27040e11i 1.03125 0.865322i 0.0402511 0.999190i \(-0.487184\pi\)
0.990999 + 0.133868i \(0.0427398\pi\)
\(620\) 1.14388e9i 0.00774132i
\(621\) −1.42978e11 + 8.95467e10i −0.961397 + 0.602120i
\(622\) −6.93770e10 −0.463504
\(623\) −2.58448e10 3.08006e10i −0.171562 0.204459i
\(624\) −1.43373e10 + 5.00649e10i −0.0945650 + 0.330213i
\(625\) 2.58436e10 1.46566e11i 0.169369 0.960537i
\(626\) −5.80235e10 1.59418e11i −0.377839 1.03810i
\(627\) −3.84032e10 2.78815e10i −0.248483 0.180404i
\(628\) −1.04295e9 5.91484e9i −0.00670537 0.0380281i
\(629\) 7.66760e10 4.42689e10i 0.489843 0.282811i
\(630\) −1.10173e9 + 2.73225e9i −0.00699378 + 0.0173444i
\(631\) −6.20469e10 + 1.07468e11i −0.391383 + 0.677896i −0.992632 0.121166i \(-0.961337\pi\)
0.601249 + 0.799062i \(0.294670\pi\)
\(632\) 1.62465e10 4.46370e10i 0.101834 0.279787i
\(633\) 7.86740e10 + 3.83386e10i 0.490023 + 0.238793i
\(634\) 6.27692e10 + 5.26696e10i 0.388499 + 0.325989i
\(635\) −9.84404e9 + 1.17317e10i −0.0605450 + 0.0721547i
\(636\) −2.81931e10 4.17672e10i −0.172312 0.255274i
\(637\) 1.94525e11 + 7.08014e10i 1.18146 + 0.430016i
\(638\) −5.37213e10 3.10160e10i −0.324238 0.187199i
\(639\) 3.82968e10 6.13810e10i 0.229699 0.368155i
\(640\) 6.72952e8 + 1.16559e9i 0.00401111 + 0.00694744i
\(641\) 1.77604e11 3.13164e10i 1.05201 0.185498i 0.379203 0.925314i \(-0.376198\pi\)
0.672810 + 0.739815i \(0.265087\pi\)
\(642\) 1.74764e11 + 1.83080e10i 1.02876 + 0.107771i
\(643\) 2.93453e11 1.06808e11i 1.71670 0.624827i 0.719153 0.694852i \(-0.244530\pi\)
0.997545 + 0.0700245i \(0.0223077\pi\)
\(644\) −2.79972e10 4.93666e9i −0.162769 0.0287005i
\(645\) −8.93601e9 + 8.63531e9i −0.0516303 + 0.0498929i
\(646\) −7.63019e10 + 6.40249e10i −0.438132 + 0.367636i
\(647\) 2.83725e11i 1.61913i 0.587033 + 0.809563i \(0.300296\pi\)
−0.587033 + 0.809563i \(0.699704\pi\)
\(648\) −5.59919e10 + 2.74039e10i −0.317559 + 0.155422i
\(649\) −6.30899e10 −0.355616
\(650\) −1.10556e11 1.31756e11i −0.619342 0.738103i
\(651\) −6.20416e9 6.42020e9i −0.0345429 0.0357458i
\(652\) −2.58587e10 + 1.46652e11i −0.143092 + 0.811518i
\(653\) −1.03574e11 2.84568e11i −0.569639 1.56507i −0.805070 0.593180i \(-0.797872\pi\)
0.235431 0.971891i \(-0.424350\pi\)
\(654\) −2.20677e10 + 2.10653e11i −0.120627 + 1.15148i
\(655\) −1.83666e9 1.04162e10i −0.00997844 0.0565906i
\(656\) −4.29740e10 + 2.48111e10i −0.232055 + 0.133977i
\(657\) −2.21085e11 + 1.17747e11i −1.18658 + 0.631959i
\(658\) 4.88294e9 8.45751e9i 0.0260482 0.0451168i
\(659\) 7.07069e10 1.94266e11i 0.374904 1.03004i −0.598536 0.801096i \(-0.704251\pi\)
0.973440 0.228944i \(-0.0735272\pi\)
\(660\) 3.48323e9 2.35120e9i 0.0183572 0.0123912i
\(661\) −2.22783e11 1.86937e11i −1.16701 0.979240i −0.167036 0.985951i \(-0.553420\pi\)
−0.999977 + 0.00671051i \(0.997864\pi\)
\(662\) 8.27196e10 9.85814e10i 0.430702 0.513290i
\(663\) 1.49506e11 3.06799e11i 0.773758 1.58782i
\(664\) −7.25221e10 2.63959e10i −0.373077 0.135789i
\(665\) 2.81821e9 + 1.62709e9i 0.0144108 + 0.00832006i
\(666\) −8.56001e9 6.06068e10i −0.0435088 0.308052i
\(667\) 1.21792e11 + 2.10951e11i 0.615343 + 1.06580i
\(668\) −1.33198e11 + 2.34864e10i −0.668946 + 0.117953i
\(669\) −1.50367e11 + 2.07111e11i −0.750666 + 1.03395i
\(670\) −1.49778e10 + 5.45146e9i −0.0743272 + 0.0270529i
\(671\) −6.47871e10 1.14237e10i −0.319594 0.0563530i
\(672\) −1.00989e10 2.89208e9i −0.0495219 0.0141819i
\(673\) 2.73256e11 2.29289e11i 1.33202 1.11770i 0.348415 0.937340i \(-0.386720\pi\)
0.983602 0.180355i \(-0.0577246\pi\)
\(674\) 1.09121e11i 0.528772i
\(675\) 2.84444e10 2.03910e11i 0.137019 0.982252i
\(676\) −9.26914e10 −0.443867
\(677\) 1.34340e11 + 1.60100e11i 0.639515 + 0.762144i 0.984293 0.176540i \(-0.0564905\pi\)
−0.344779 + 0.938684i \(0.612046\pi\)
\(678\) 8.42587e10 2.10387e10i 0.398746 0.0995633i
\(679\) −2.73060e9 + 1.54860e10i −0.0128463 + 0.0728552i
\(680\) −3.01675e9 8.28845e9i −0.0141092 0.0387648i
\(681\) 8.32474e10 3.70982e10i 0.387063 0.172490i
\(682\) 2.21157e9 + 1.25424e10i 0.0102227 + 0.0579755i
\(683\) 1.50962e10 8.71582e9i 0.0693723 0.0400521i −0.464913 0.885357i \(-0.653914\pi\)
0.534285 + 0.845304i \(0.320581\pi\)
\(684\) 2.13235e10 + 6.54746e10i 0.0974169 + 0.299122i
\(685\) −3.65699e9 + 6.33409e9i −0.0166097 + 0.0287688i
\(686\) −2.98889e10 + 8.21190e10i −0.134963 + 0.370807i
\(687\) 9.65959e9 + 1.37463e11i 0.0433642 + 0.617105i
\(688\) −3.39439e10 2.84823e10i −0.151499 0.127122i
\(689\) 1.22596e11 1.46105e11i 0.544003 0.648317i
\(690\) −1.64616e10 + 1.15676e9i −0.0726233 + 0.00510327i
\(691\) 1.88593e11 + 6.86424e10i 0.827207 + 0.301079i 0.720712 0.693234i \(-0.243815\pi\)
0.106495 + 0.994313i \(0.466037\pi\)
\(692\) −1.33702e11 7.71927e10i −0.583059 0.336629i
\(693\) −6.79771e9 + 3.20886e10i −0.0294734 + 0.139129i
\(694\) 8.86668e10 + 1.53575e11i 0.382229 + 0.662039i
\(695\) 1.52747e10 2.69334e9i 0.0654686 0.0115439i
\(696\) 3.66374e10 + 8.22133e10i 0.156130 + 0.350352i
\(697\) 3.05587e11 1.11224e11i 1.29480 0.471269i
\(698\) 1.29583e11 + 2.28490e10i 0.545918 + 0.0962601i
\(699\) −7.03335e10 2.81682e11i −0.294614 1.17991i
\(700\) 2.65774e10 2.23011e10i 0.110693 0.0928824i
\(701\) 8.32730e9i 0.0344852i 0.999851 + 0.0172426i \(0.00548876\pi\)
−0.999851 + 0.0172426i \(0.994511\pi\)
\(702\) −1.58055e11 1.75176e11i −0.650820 0.721319i
\(703\) −6.76112e10 −0.276820
\(704\) 9.63231e9 + 1.14793e10i 0.0392139 + 0.0467333i
\(705\) 1.56067e9 5.44973e9i 0.00631763 0.0220607i
\(706\) −2.20152e10 + 1.24854e11i −0.0886142 + 0.502556i
\(707\) −3.52767e10 9.69218e10i −0.141192 0.387922i
\(708\) 7.40776e10 + 5.37818e10i 0.294818 + 0.214044i
\(709\) −6.05480e9 3.43385e10i −0.0239616 0.135893i 0.970480 0.241181i \(-0.0775347\pi\)
−0.994442 + 0.105288i \(0.966424\pi\)
\(710\) 6.12877e9 3.53845e9i 0.0241179 0.0139245i
\(711\) 1.32613e11 + 1.69498e11i 0.518929 + 0.663263i
\(712\) 4.16112e10 7.20726e10i 0.161916 0.280447i
\(713\) 1.71047e10 4.69949e10i 0.0661848 0.181841i
\(714\) 6.18865e10 + 3.01579e10i 0.238124 + 0.116040i
\(715\) 1.21846e10 + 1.02241e10i 0.0466215 + 0.0391201i
\(716\) 8.53769e10 1.01748e11i 0.324854 0.387146i
\(717\) −1.15823e11 1.71587e11i −0.438245 0.649245i
\(718\) −2.40940e11 8.76950e10i −0.906590 0.329972i
\(719\) −6.72400e9 3.88210e9i −0.0251601 0.0145262i 0.487367 0.873197i \(-0.337957\pi\)
−0.512527 + 0.858671i \(0.671291\pi\)
\(720\) −6.09418e9 2.08640e8i −0.0226770 0.000776369i
\(721\) −1.50798e10 2.61189e10i −0.0558025 0.0966528i
\(722\) −1.14321e11 + 2.01579e10i −0.420704 + 0.0741815i
\(723\) 6.45384e9 + 6.76095e8i 0.0236192 + 0.00247431i
\(724\) 8.57274e10 3.12022e10i 0.312008 0.113561i
\(725\) −2.92750e11 5.16197e10i −1.05961 0.186837i
\(726\) −1.07614e11 + 1.03993e11i −0.387366 + 0.374331i
\(727\) 8.02983e10 6.73783e10i 0.287454 0.241203i −0.487645 0.873042i \(-0.662144\pi\)
0.775100 + 0.631839i \(0.217700\pi\)
\(728\) 3.97593e10i 0.141551i
\(729\) 2.89456e10 2.80942e11i 0.102488 0.994734i
\(730\) −2.45018e10 −0.0862792
\(731\) 1.86659e11 + 2.22452e11i 0.653701 + 0.779051i
\(732\) 6.63321e10 + 6.86419e10i 0.231036 + 0.239081i
\(733\) −6.03338e10 + 3.42170e11i −0.208999 + 1.18529i 0.682022 + 0.731332i \(0.261101\pi\)
−0.891021 + 0.453962i \(0.850010\pi\)
\(734\) −1.05214e11 2.89074e11i −0.362485 0.995920i
\(735\) −2.52540e9 + 2.41069e10i −0.00865328 + 0.0826022i
\(736\) −1.02180e10 5.79494e10i −0.0348222 0.197487i
\(737\) −1.53688e11 + 8.87320e10i −0.520920 + 0.300753i
\(738\) 7.69235e9 2.24686e11i 0.0259319 0.757444i
\(739\) −2.01985e11 + 3.49848e11i −0.677237 + 1.17301i 0.298573 + 0.954387i \(0.403489\pi\)
−0.975810 + 0.218622i \(0.929844\pi\)
\(740\) 2.04775e9 5.62614e9i 0.00682889 0.0187622i
\(741\) −2.16016e11 + 1.45812e11i −0.716495 + 0.483639i
\(742\) 2.94717e10 + 2.47297e10i 0.0972277 + 0.0815838i
\(743\) −2.07882e11 + 2.47744e11i −0.682122 + 0.812922i −0.990379 0.138381i \(-0.955810\pi\)
0.308257 + 0.951303i \(0.400254\pi\)
\(744\) 8.09524e9 1.66121e10i 0.0264203 0.0542167i
\(745\) 3.93279e10 + 1.43142e10i 0.127666 + 0.0464666i
\(746\) 2.97785e11 + 1.71926e11i 0.961497 + 0.555121i
\(747\) 2.75385e11 2.15457e11i 0.884417 0.691957i
\(748\) −4.91028e10 8.50485e10i −0.156856 0.271682i
\(749\) −1.32119e11 + 2.32961e10i −0.419794 + 0.0740211i
\(750\) 2.37619e10 3.27290e10i 0.0750993 0.103440i
\(751\) 2.28216e11 8.30640e10i 0.717442 0.261128i 0.0426027 0.999092i \(-0.486435\pi\)
0.674840 + 0.737964i \(0.264213\pi\)
\(752\) 1.99066e10 + 3.51008e9i 0.0622481 + 0.0109760i
\(753\) −2.85364e11 8.17212e10i −0.887604 0.254188i
\(754\) −2.60964e11 + 2.18975e11i −0.807412 + 0.677499i
\(755\) 2.39084e8i 0.000735806i