Properties

Label 54.9.f.a.5.8
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 5.8
Character \(\chi\) \(=\) 54.5
Dual form 54.9.f.a.11.8

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-7.27231 - 8.66680i) q^{2} +(24.6435 - 77.1602i) q^{3} +(-22.2270 + 126.055i) q^{4} +(-216.760 - 595.543i) q^{5} +(-847.948 + 347.553i) q^{6} +(-99.0312 - 561.634i) q^{7} +(1254.14 - 724.077i) q^{8} +(-5346.40 - 3802.99i) q^{9} +O(q^{10})\) \(q+(-7.27231 - 8.66680i) q^{2} +(24.6435 - 77.1602i) q^{3} +(-22.2270 + 126.055i) q^{4} +(-216.760 - 595.543i) q^{5} +(-847.948 + 347.553i) q^{6} +(-99.0312 - 561.634i) q^{7} +(1254.14 - 724.077i) q^{8} +(-5346.40 - 3802.99i) q^{9} +(-3585.11 + 6209.59i) q^{10} +(-1455.85 + 3999.90i) q^{11} +(9178.71 + 4821.48i) q^{12} +(-21377.8 - 17938.1i) q^{13} +(-4147.38 + 4942.66i) q^{14} +(-51293.9 + 2048.98i) q^{15} +(-15395.9 - 5603.66i) q^{16} +(19756.1 + 11406.2i) q^{17} +(5920.85 + 73992.7i) q^{18} +(-55972.8 - 96947.7i) q^{19} +(79889.3 - 14086.6i) q^{20} +(-45776.2 - 6199.35i) q^{21} +(45253.7 - 16471.0i) q^{22} +(-11818.7 - 2083.95i) q^{23} +(-24963.6 - 114613. i) q^{24} +(-8450.42 + 7090.75i) q^{25} +315729. i q^{26} +(-425194. + 318810. i) q^{27} +72998.1 q^{28} +(809328. + 964520. i) q^{29} +(390784. + 429654. i) q^{30} +(-124217. + 704467. i) q^{31} +(63398.2 + 174185. i) q^{32} +(272756. + 210905. i) q^{33} +(-44817.3 - 254171. i) q^{34} +(-313011. + 180717. i) q^{35} +(598222. - 589413. i) q^{36} +(-918855. + 1.59150e6i) q^{37} +(-433175. + 1.19014e6i) q^{38} +(-1.91093e6 + 1.20746e6i) q^{39} +(-703066. - 589943. i) q^{40} +(-1.67572e6 + 1.99705e6i) q^{41} +(279171. + 441817. i) q^{42} +(-1364.61 - 496.678i) q^{43} +(-471850. - 272423. i) q^{44} +(-1.10596e6 + 4.00835e6i) q^{45} +(67887.9 + 117585. i) q^{46} +(380970. - 67175.3i) q^{47} +(-811789. + 1.04986e6i) q^{48} +(5.11152e6 - 1.86044e6i) q^{49} +(122908. + 21672.0i) q^{50} +(1.36696e6 - 1.24330e6i) q^{51} +(2.73636e6 - 2.29608e6i) q^{52} -6.04899e6i q^{53} +(5.85520e6 + 1.36659e6i) q^{54} +2.69768e6 q^{55} +(-530865. - 632660. i) q^{56} +(-8.85987e6 + 1.92974e6i) q^{57} +(2.47362e6 - 1.40286e7i) q^{58} +(3.78438e6 + 1.03975e7i) q^{59} +(881824. - 6.51142e6i) q^{60} +(-2.21405e6 - 1.25565e7i) q^{61} +(7.00882e6 - 4.04654e6i) q^{62} +(-1.60643e6 + 3.37933e6i) q^{63} +(1.04858e6 - 1.81619e6i) q^{64} +(-6.04907e6 + 1.66197e7i) q^{65} +(-155697. - 3.89769e6i) q^{66} +(-2.83577e7 - 2.37949e7i) q^{67} +(-1.87693e6 + 2.23684e6i) q^{68} +(-452052. + 860576. i) q^{69} +(3.84255e6 + 1.39857e6i) q^{70} +(-2.36177e7 - 1.36357e7i) q^{71} +(-9.45878e6 - 898279. i) q^{72} +(-1.48352e7 - 2.56954e7i) q^{73} +(2.04754e7 - 3.61037e6i) q^{74} +(338876. + 826777. i) q^{75} +(1.34649e7 - 4.90082e6i) q^{76} +(2.39065e6 + 421537. i) q^{77} +(2.43617e7 + 7.78067e6i) q^{78} +(1.47037e7 - 1.23379e7i) q^{79} +1.03836e7i q^{80} +(1.41212e7 + 4.06646e7i) q^{81} +2.94944e7 q^{82} +(-4.69687e6 - 5.59752e6i) q^{83} +(1.79893e6 - 5.63255e6i) q^{84} +(2.51054e6 - 1.42380e7i) q^{85} +(5619.27 + 15438.8i) q^{86} +(9.43673e7 - 3.86788e7i) q^{87} +(1.07041e6 + 6.07058e6i) q^{88} +(-4.34519e7 + 2.50870e7i) q^{89} +(4.27824e7 - 1.95648e7i) q^{90} +(-7.95758e6 + 1.37829e7i) q^{91} +(525387. - 1.44349e6i) q^{92} +(5.12957e7 + 2.69451e7i) q^{93} +(-3.35273e6 - 2.81327e6i) q^{94} +(-4.56038e7 + 5.43485e7i) q^{95} +(1.50025e7 - 599288. i) q^{96} +(-6.10107e7 - 2.22061e7i) q^{97} +(-5.32966e7 - 3.07708e7i) q^{98} +(2.29951e7 - 1.58485e7i) 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
\(3\) 24.6435 77.1602i 0.304241 0.952595i
\(4\) −22.2270 + 126.055i −0.0868241 + 0.492404i
\(5\) −216.760 595.543i −0.346816 0.952869i −0.983366 0.181634i \(-0.941862\pi\)
0.636550 0.771235i \(-0.280361\pi\)
\(6\) −847.948 + 347.553i −0.654281 + 0.268173i
\(7\) −99.0312 561.634i −0.0412458 0.233917i 0.957215 0.289377i \(-0.0934483\pi\)
−0.998461 + 0.0554609i \(0.982337\pi\)
\(8\) 1254.14 724.077i 0.306186 0.176777i
\(9\) −5346.40 3802.99i −0.814875 0.579636i
\(10\) −3585.11 + 6209.59i −0.358511 + 0.620959i
\(11\) −1455.85 + 3999.90i −0.0994362 + 0.273199i −0.979429 0.201788i \(-0.935325\pi\)
0.879993 + 0.474987i \(0.157547\pi\)
\(12\) 9178.71 + 4821.48i 0.442646 + 0.232518i
\(13\) −21377.8 17938.1i −0.748497 0.628064i 0.186608 0.982434i \(-0.440251\pi\)
−0.935105 + 0.354371i \(0.884695\pi\)
\(14\) −4147.38 + 4942.66i −0.107960 + 0.128661i
\(15\) −51293.9 + 2048.98i −1.01321 + 0.0404737i
\(16\) −15395.9 5603.66i −0.234923 0.0855050i
\(17\) 19756.1 + 11406.2i 0.236540 + 0.136567i 0.613586 0.789628i \(-0.289727\pi\)
−0.377045 + 0.926195i \(0.623060\pi\)
\(18\) 5920.85 + 73992.7i 0.0564019 + 0.704854i
\(19\) −55972.8 96947.7i −0.429499 0.743914i 0.567330 0.823491i \(-0.307977\pi\)
−0.996829 + 0.0795765i \(0.974643\pi\)
\(20\) 79889.3 14086.6i 0.499308 0.0880415i
\(21\) −45776.2 6199.35i −0.235376 0.0318764i
\(22\) 45253.7 16471.0i 0.193181 0.0703120i
\(23\) −11818.7 2083.95i −0.0422335 0.00744691i 0.152491 0.988305i \(-0.451270\pi\)
−0.194725 + 0.980858i \(0.562381\pi\)
\(24\) −24963.6 114613.i −0.0752423 0.345454i
\(25\) −8450.42 + 7090.75i −0.0216331 + 0.0181523i
\(26\) 315729.i 0.690910i
\(27\) −425194. + 318810.i −0.800077 + 0.599897i
\(28\) 72998.1 0.118763
\(29\) 809328. + 964520.i 1.14428 + 1.36370i 0.921288 + 0.388882i \(0.127138\pi\)
0.222994 + 0.974820i \(0.428417\pi\)
\(30\) 390784. + 429654.i 0.482449 + 0.530437i
\(31\) −124217. + 704467.i −0.134503 + 0.762806i 0.840701 + 0.541499i \(0.182143\pi\)
−0.975204 + 0.221306i \(0.928968\pi\)
\(32\) 63398.2 + 174185.i 0.0604612 + 0.166116i
\(33\) 272756. + 210905.i 0.229995 + 0.177841i
\(34\) −44817.3 254171.i −0.0335374 0.190200i
\(35\) −313011. + 180717.i −0.208587 + 0.120428i
\(36\) 598222. 589413.i 0.356166 0.350921i
\(37\) −918855. + 1.59150e6i −0.490275 + 0.849182i −0.999937 0.0111931i \(-0.996437\pi\)
0.509662 + 0.860375i \(0.329770\pi\)
\(38\) −433175. + 1.19014e6i −0.207744 + 0.570773i
\(39\) −1.91093e6 + 1.20746e6i −0.826014 + 0.521932i
\(40\) −703066. 589943.i −0.274635 0.230446i
\(41\) −1.67572e6 + 1.99705e6i −0.593016 + 0.706729i −0.976183 0.216950i \(-0.930389\pi\)
0.383166 + 0.923679i \(0.374834\pi\)
\(42\) 279171. + 441817.i 0.0897165 + 0.141986i
\(43\) −1364.61 496.678i −0.000399149 0.000145278i 0.341821 0.939765i \(-0.388956\pi\)
−0.342220 + 0.939620i \(0.611179\pi\)
\(44\) −471850. 272423.i −0.125891 0.0726830i
\(45\) −1.10596e6 + 4.00835e6i −0.269706 + 0.977496i
\(46\) 67887.9 + 117585.i 0.0151622 + 0.0262616i
\(47\) 380970. 67175.3i 0.0780727 0.0137663i −0.134475 0.990917i \(-0.542935\pi\)
0.212548 + 0.977151i \(0.431824\pi\)
\(48\) −811789. + 1.04986e6i −0.152925 + 0.197773i
\(49\) 5.11152e6 1.86044e6i 0.886677 0.322724i
\(50\) 122908. + 21672.0i 0.0196653 + 0.00346753i
\(51\) 1.36696e6 1.24330e6i 0.202058 0.183778i
\(52\) 2.73636e6 2.29608e6i 0.374249 0.314032i
\(53\) 6.04899e6i 0.766619i −0.923620 0.383309i \(-0.874784\pi\)
0.923620 0.383309i \(-0.125216\pi\)
\(54\) 5.85520e6 + 1.36659e6i 0.688600 + 0.160717i
\(55\) 2.69768e6 0.294809
\(56\) −530865. 632660.i −0.0539799 0.0643307i
\(57\) −8.85987e6 + 1.92974e6i −0.839320 + 0.182810i
\(58\) 2.47362e6 1.40286e7i 0.218585 1.23966i
\(59\) 3.78438e6 + 1.03975e7i 0.312311 + 0.858067i 0.992189 + 0.124742i \(0.0398103\pi\)
−0.679879 + 0.733325i \(0.737968\pi\)
\(60\) 881824. 6.51142e6i 0.0680420 0.502424i
\(61\) −2.21405e6 1.25565e7i −0.159907 0.906879i −0.954161 0.299293i \(-0.903249\pi\)
0.794254 0.607586i \(-0.207862\pi\)
\(62\) 7.00882e6 4.04654e6i 0.474327 0.273853i
\(63\) −1.60643e6 + 3.37933e6i −0.101976 + 0.214520i
\(64\) 1.04858e6 1.81619e6i 0.0625000 0.108253i
\(65\) −6.04907e6 + 1.66197e7i −0.338872 + 0.931042i
\(66\) −155697. 3.89769e6i −0.00820546 0.205415i
\(67\) −2.83577e7 2.37949e7i −1.40725 1.18083i −0.957770 0.287536i \(-0.907164\pi\)
−0.449483 0.893289i \(-0.648392\pi\)
\(68\) −1.87693e6 + 2.23684e6i −0.0877833 + 0.104616i
\(69\) −452052. + 860576.i −0.0199431 + 0.0379658i
\(70\) 3.84255e6 + 1.39857e6i 0.160040 + 0.0582497i
\(71\) −2.36177e7 1.36357e7i −0.929402 0.536590i −0.0427795 0.999085i \(-0.513621\pi\)
−0.886622 + 0.462494i \(0.846955\pi\)
\(72\) −9.45878e6 898279.i −0.351970 0.0334257i
\(73\) −1.48352e7 2.56954e7i −0.522400 0.904823i −0.999660 0.0260609i \(-0.991704\pi\)
0.477261 0.878762i \(-0.341630\pi\)
\(74\) 2.04754e7 3.61037e6i 0.682820 0.120400i
\(75\) 338876. + 826777.i 0.0107101 + 0.0261302i
\(76\) 1.34649e7 4.90082e6i 0.403597 0.146897i
\(77\) 2.39065e6 + 421537.i 0.0680070 + 0.0119915i
\(78\) 2.43617e7 + 7.78067e6i 0.658157 + 0.210203i
\(79\) 1.47037e7 1.23379e7i 0.377501 0.316761i −0.434220 0.900807i \(-0.642976\pi\)
0.811720 + 0.584046i \(0.198531\pi\)
\(80\) 1.03836e7i 0.253505i
\(81\) 1.41212e7 + 4.06646e7i 0.328043 + 0.944663i
\(82\) 2.94944e7 0.652355
\(83\) −4.69687e6 5.59752e6i −0.0989684 0.117946i 0.714287 0.699853i \(-0.246751\pi\)
−0.813255 + 0.581907i \(0.802307\pi\)
\(84\) 1.79893e6 5.63255e6i 0.0361324 0.113133i
\(85\) 2.51054e6 1.42380e7i 0.0480941 0.272755i
\(86\) 5619.27 + 15438.8i 0.000102727 + 0.000282241i
\(87\) 9.43673e7 3.86788e7i 1.64719 0.675143i
\(88\) 1.07041e6 + 6.07058e6i 0.0178492 + 0.101228i
\(89\) −4.34519e7 + 2.50870e7i −0.692546 + 0.399842i −0.804565 0.593864i \(-0.797602\pi\)
0.112019 + 0.993706i \(0.464268\pi\)
\(90\) 4.27824e7 1.95648e7i 0.652072 0.298198i
\(91\) −7.95758e6 + 1.37829e7i −0.116042 + 0.200991i
\(92\) 525387. 1.44349e6i 0.00733378 0.0201494i
\(93\) 5.12957e7 + 2.69451e7i 0.685724 + 0.360204i
\(94\) −3.35273e6 2.81327e6i −0.0429425 0.0360330i
\(95\) −4.56038e7 + 5.43485e7i −0.559896 + 0.667258i
\(96\) 1.50025e7 599288.i 0.176636 0.00705587i
\(97\) −6.10107e7 2.22061e7i −0.689159 0.250833i −0.0263837 0.999652i \(-0.508399\pi\)
−0.662775 + 0.748819i \(0.730621\pi\)
\(98\) −5.32966e7 3.07708e7i −0.577824 0.333607i
\(99\) 2.29951e7 1.58485e7i 0.239384 0.164986i
\(100\) −706000. 1.22283e6i −0.00706000 0.0122283i
\(101\) −1.81255e8 + 3.19601e7i −1.74182 + 0.307131i −0.951976 0.306172i \(-0.900952\pi\)
−0.789848 + 0.613302i \(0.789841\pi\)
\(102\) −2.07164e7 2.80556e6i −0.191387 0.0259190i
\(103\) 4.03940e7 1.47022e7i 0.358896 0.130627i −0.156278 0.987713i \(-0.549950\pi\)
0.515174 + 0.857086i \(0.327727\pi\)
\(104\) −3.97994e7 7.01770e6i −0.340207 0.0599876i
\(105\) 6.23047e6 + 2.86055e7i 0.0512583 + 0.235338i
\(106\) −5.24254e7 + 4.39901e7i −0.415258 + 0.348443i
\(107\) 5.04609e7i 0.384964i 0.981301 + 0.192482i \(0.0616537\pi\)
−0.981301 + 0.192482i \(0.938346\pi\)
\(108\) −3.07369e7 6.06841e7i −0.225926 0.446047i
\(109\) −5.57423e7 −0.394893 −0.197446 0.980314i \(-0.563265\pi\)
−0.197446 + 0.980314i \(0.563265\pi\)
\(110\) −1.96184e7 2.33803e7i −0.133996 0.159690i
\(111\) 1.00157e8 + 1.10119e8i 0.659765 + 0.725389i
\(112\) −1.62253e6 + 9.20181e6i −0.0103114 + 0.0584791i
\(113\) 8.65996e6 + 2.37930e7i 0.0531132 + 0.145927i 0.963412 0.268024i \(-0.0863706\pi\)
−0.910299 + 0.413951i \(0.864148\pi\)
\(114\) 8.11564e7 + 6.27530e7i 0.480511 + 0.371548i
\(115\) 1.32073e6 + 7.49025e6i 0.00755133 + 0.0428257i
\(116\) −1.39572e8 + 8.05819e7i −0.770843 + 0.445046i
\(117\) 4.60757e7 + 1.77204e8i 0.245883 + 0.945650i
\(118\) 6.25919e7 1.08412e8i 0.322842 0.559179i
\(119\) 4.44963e6 1.22252e7i 0.0221889 0.0609635i
\(120\) −6.28461e7 + 3.97105e7i −0.303077 + 0.191505i
\(121\) 1.50329e8 + 1.26141e8i 0.701294 + 0.588456i
\(122\) −9.27234e7 + 1.10503e8i −0.418553 + 0.498812i
\(123\) 1.12797e8 + 1.78513e8i 0.492807 + 0.779920i
\(124\) −8.60409e7 3.13163e7i −0.363930 0.132460i
\(125\) −2.08342e8 1.20286e8i −0.853369 0.492693i
\(126\) 4.09705e7 1.06529e7i 0.162551 0.0422656i
\(127\) −2.36850e8 4.10236e8i −0.910455 1.57695i −0.813422 0.581674i \(-0.802398\pi\)
−0.0970330 0.995281i \(-0.530935\pi\)
\(128\) −2.33661e7 + 4.12008e6i −0.0870455 + 0.0153485i
\(129\) −71952.5 + 93053.8i −0.000259829 + 0.000336028i
\(130\) 1.88030e8 6.84374e7i 0.658346 0.239618i
\(131\) 4.31057e8 + 7.60070e7i 1.46369 + 0.258089i 0.848041 0.529930i \(-0.177782\pi\)
0.615651 + 0.788019i \(0.288893\pi\)
\(132\) −3.26482e7 + 2.96946e7i −0.107539 + 0.0978097i
\(133\) −4.89060e7 + 4.10370e7i −0.156299 + 0.131150i
\(134\) 4.18815e8i 1.29898i
\(135\) 2.82030e8 + 1.84116e8i 0.849103 + 0.554315i
\(136\) 3.30358e7 0.0965672
\(137\) −1.73674e8 2.06976e8i −0.493006 0.587542i 0.460973 0.887414i \(-0.347500\pi\)
−0.953979 + 0.299872i \(0.903056\pi\)
\(138\) 1.07459e7 2.34053e6i 0.0296297 0.00645354i
\(139\) −1.12790e7 + 6.39666e7i −0.0302143 + 0.171354i −0.996181 0.0873129i \(-0.972172\pi\)
0.965967 + 0.258667i \(0.0832831\pi\)
\(140\) −1.58231e7 4.34735e7i −0.0411887 0.113165i
\(141\) 4.20517e6 3.10512e7i 0.0106392 0.0785600i
\(142\) 5.35774e7 + 3.03852e8i 0.131774 + 0.747325i
\(143\) 1.02874e8 5.93941e7i 0.246014 0.142036i
\(144\) 6.10020e7 + 8.85100e7i 0.141871 + 0.205846i
\(145\) 3.98983e8 6.91059e8i 0.902573 1.56330i
\(146\) −1.14810e8 + 3.15439e8i −0.252679 + 0.694230i
\(147\) −1.75863e7 4.40253e8i −0.0376621 0.942830i
\(148\) −1.80194e8 1.51201e8i −0.375573 0.315143i
\(149\) 2.45054e8 2.92044e8i 0.497183 0.592520i −0.457846 0.889031i \(-0.651379\pi\)
0.955029 + 0.296512i \(0.0958234\pi\)
\(150\) 4.70111e6 8.94955e6i 0.00928614 0.0176781i
\(151\) −1.80606e7 6.57351e6i −0.0347395 0.0126441i 0.324592 0.945854i \(-0.394773\pi\)
−0.359331 + 0.933210i \(0.616995\pi\)
\(152\) −1.40395e8 8.10572e7i −0.263013 0.151851i
\(153\) −6.22462e7 1.36114e8i −0.113592 0.248392i
\(154\) −1.37322e7 2.37849e7i −0.0244150 0.0422881i
\(155\) 4.46466e8 7.87239e7i 0.773501 0.136389i
\(156\) −1.09733e8 2.67722e8i −0.185284 0.452049i
\(157\) −8.14030e7 + 2.96283e7i −0.133981 + 0.0487650i −0.408140 0.912919i \(-0.633823\pi\)
0.274160 + 0.961684i \(0.411600\pi\)
\(158\) −2.13860e8 3.77092e7i −0.343163 0.0605089i
\(159\) −4.66741e8 1.49068e8i −0.730277 0.233237i
\(160\) 8.99925e7 7.55126e7i 0.137318 0.115223i
\(161\) 6.84414e6i 0.0101863i
\(162\) 2.49739e8 4.18111e8i 0.362598 0.607060i
\(163\) −4.86256e8 −0.688834 −0.344417 0.938817i \(-0.611923\pi\)
−0.344417 + 0.938817i \(0.611923\pi\)
\(164\) −2.14493e8 2.55622e8i −0.296508 0.353365i
\(165\) 6.64803e7 2.08154e8i 0.0896928 0.280833i
\(166\) −1.43554e7 + 8.14138e7i −0.0189053 + 0.107217i
\(167\) 2.20727e8 + 6.06441e8i 0.283785 + 0.779692i 0.996902 + 0.0786475i \(0.0250602\pi\)
−0.713118 + 0.701044i \(0.752718\pi\)
\(168\) −6.18986e7 + 2.53707e7i −0.0777040 + 0.0318490i
\(169\) −6.41506e6 3.63816e7i −0.00786418 0.0446000i
\(170\) −1.41655e8 + 8.17848e7i −0.169604 + 0.0979212i
\(171\) −6.94389e7 + 7.31185e8i −0.0812117 + 0.855151i
\(172\) 92940.1 160977.i 0.000106191 0.000183929i
\(173\) 3.74716e8 1.02952e9i 0.418329 1.14935i −0.534322 0.845281i \(-0.679433\pi\)
0.952651 0.304067i \(-0.0983447\pi\)
\(174\) −1.02149e9 5.36578e8i −1.11439 0.585377i
\(175\) 4.81926e6 + 4.04384e6i 0.00513840 + 0.00431163i
\(176\) 4.48282e7 5.34241e7i 0.0467197 0.0556784i
\(177\) 8.95534e8 3.57729e7i 0.912408 0.0364469i
\(178\) 5.33419e8 + 1.94149e8i 0.531360 + 0.193399i
\(179\) −1.09873e9 6.34351e8i −1.07023 0.617899i −0.141987 0.989868i \(-0.545349\pi\)
−0.928245 + 0.371970i \(0.878683\pi\)
\(180\) −4.80691e8 2.28506e8i −0.457906 0.217674i
\(181\) −6.86282e8 1.18868e9i −0.639423 1.10751i −0.985560 0.169329i \(-0.945840\pi\)
0.346136 0.938184i \(-0.387493\pi\)
\(182\) 1.77324e8 3.12670e7i 0.161615 0.0284971i
\(183\) −1.02342e9 1.38599e8i −0.912539 0.123583i
\(184\) −1.63312e7 + 5.94407e6i −0.0142478 + 0.00518576i
\(185\) 1.14698e9 + 2.02243e8i 0.979194 + 0.172658i
\(186\) −1.39510e8 6.40523e8i −0.116561 0.535159i
\(187\) −7.43854e7 + 6.24168e7i −0.0608305 + 0.0510428i
\(188\) 4.95164e7i 0.0396386i
\(189\) 2.21162e8 + 2.07231e8i 0.173326 + 0.162408i
\(190\) 8.02674e8 0.615920
\(191\) 1.14809e9 + 1.36824e9i 0.862668 + 1.02809i 0.999298 + 0.0374652i \(0.0119284\pi\)
−0.136630 + 0.990622i \(0.543627\pi\)
\(192\) −1.14297e8 1.25666e8i −0.0841064 0.0924722i
\(193\) −4.04067e7 + 2.29158e8i −0.0291222 + 0.165160i −0.995900 0.0904566i \(-0.971167\pi\)
0.966778 + 0.255617i \(0.0822785\pi\)
\(194\) 2.51233e8 + 6.90257e8i 0.177366 + 0.487309i
\(195\) 1.13331e9 + 8.76314e8i 0.783808 + 0.606068i
\(196\) 1.20905e8 + 6.85686e8i 0.0819256 + 0.464623i
\(197\) 1.79227e9 1.03477e9i 1.18998 0.687035i 0.231678 0.972793i \(-0.425578\pi\)
0.958302 + 0.285757i \(0.0922452\pi\)
\(198\) −3.04584e8 8.40392e7i −0.198174 0.0546790i
\(199\) −1.00793e9 + 1.74578e9i −0.642711 + 1.11321i 0.342114 + 0.939659i \(0.388857\pi\)
−0.984825 + 0.173550i \(0.944476\pi\)
\(200\) −5.46375e6 + 1.50115e7i −0.00341485 + 0.00938221i
\(201\) −2.53486e9 + 1.60170e9i −1.55299 + 0.981287i
\(202\) 1.59513e9 + 1.33848e9i 0.958058 + 0.803906i
\(203\) 4.61558e8 5.50064e8i 0.271796 0.323913i
\(204\) 1.26341e8 + 1.99948e8i 0.0729495 + 0.115450i
\(205\) 1.55256e9 + 5.65085e8i 0.879088 + 0.319962i
\(206\) −4.21179e8 2.43168e8i −0.233883 0.135032i
\(207\) 5.52621e7 + 5.60880e7i 0.0300986 + 0.0305484i
\(208\) 2.28612e8 + 3.95968e8i 0.122137 + 0.211547i
\(209\) 4.69269e8 8.27448e7i 0.245944 0.0433666i
\(210\) 2.02608e8 2.62026e8i 0.104179 0.134731i
\(211\) −3.07345e9 + 1.11865e9i −1.55059 + 0.564368i −0.968556 0.248796i \(-0.919965\pi\)
−0.582034 + 0.813165i \(0.697743\pi\)
\(212\) 7.62508e8 + 1.34451e8i 0.377486 + 0.0665610i
\(213\) −1.63415e9 + 1.48631e9i −0.793915 + 0.722091i
\(214\) 4.37335e8 3.66967e8i 0.208525 0.174974i
\(215\) 920344.i 0.000430721i
\(216\) −3.02409e8 + 7.07705e8i −0.138925 + 0.325115i
\(217\) 4.07954e8 0.183981
\(218\) 4.05376e8 + 4.83108e8i 0.179486 + 0.213904i
\(219\) −2.34825e9 + 5.11466e8i −1.02086 + 0.222351i
\(220\) −5.99613e7 + 3.40057e8i −0.0255965 + 0.145165i
\(221\) −2.17737e8 5.98226e8i −0.0912772 0.250782i
\(222\) 2.26009e8 1.66886e9i 0.0930496 0.687082i
\(223\) 6.90071e8 + 3.91359e9i 0.279045 + 1.58254i 0.725812 + 0.687893i \(0.241464\pi\)
−0.446767 + 0.894650i \(0.647425\pi\)
\(224\) 9.15498e7 5.28563e7i 0.0363635 0.0209944i
\(225\) 7.21454e7 5.77303e6i 0.0281500 0.00225255i
\(226\) 1.43232e8 2.48085e8i 0.0549042 0.0950968i
\(227\) −4.20769e8 + 1.15605e9i −0.158468 + 0.435386i −0.993363 0.115023i \(-0.963306\pi\)
0.834895 + 0.550409i \(0.185528\pi\)
\(228\) −4.63262e7 1.15973e9i −0.0171430 0.429157i
\(229\) −1.59179e9 1.33567e9i −0.578820 0.485688i 0.305739 0.952115i \(-0.401096\pi\)
−0.884559 + 0.466428i \(0.845541\pi\)
\(230\) 5.53117e7 6.59179e7i 0.0197654 0.0235555i
\(231\) 9.14399e7 1.74075e8i 0.0321135 0.0611349i
\(232\) 1.71340e9 + 6.23626e8i 0.591434 + 0.215264i
\(233\) −3.92097e9 2.26377e9i −1.33036 0.768084i −0.345006 0.938600i \(-0.612123\pi\)
−0.985355 + 0.170516i \(0.945457\pi\)
\(234\) 1.20072e9 1.68801e9i 0.400476 0.563005i
\(235\) −1.22585e8 2.12323e8i −0.0401944 0.0696187i
\(236\) −1.39478e9 + 2.45937e8i −0.449631 + 0.0792822i
\(237\) −5.89641e8 1.43859e9i −0.186894 0.455977i
\(238\) −1.38313e8 + 5.03418e7i −0.0431077 + 0.0156899i
\(239\) 2.27069e9 + 4.00383e8i 0.695930 + 0.122711i 0.510412 0.859930i \(-0.329493\pi\)
0.185518 + 0.982641i \(0.440604\pi\)
\(240\) 8.01199e8 + 2.55888e8i 0.241488 + 0.0771267i
\(241\) −4.31644e9 + 3.62192e9i −1.27955 + 1.07367i −0.286244 + 0.958157i \(0.592407\pi\)
−0.993306 + 0.115513i \(0.963149\pi\)
\(242\) 2.22020e9i 0.647339i
\(243\) 3.48569e9 8.74747e7i 0.999685 0.0250875i
\(244\) 1.63203e9 0.460434
\(245\) −2.21594e9 2.64086e9i −0.615027 0.732961i
\(246\) 7.26845e8 2.27579e9i 0.198473 0.621431i
\(247\) −5.42483e8 + 3.07658e9i −0.145747 + 0.826571i
\(248\) 3.54304e8 + 9.73442e8i 0.0936632 + 0.257338i
\(249\) −5.47653e8 + 2.24469e8i −0.142465 + 0.0583929i
\(250\) 4.72630e8 + 2.68042e9i 0.120993 + 0.686187i
\(251\) 2.60292e9 1.50280e9i 0.655791 0.378621i −0.134880 0.990862i \(-0.543065\pi\)
0.790672 + 0.612241i \(0.209732\pi\)
\(252\) −3.90277e8 2.77611e8i −0.0967766 0.0688391i
\(253\) 2.55418e7 4.42396e7i 0.00623403 0.0107977i
\(254\) −1.83299e9 + 5.03610e9i −0.440378 + 1.20993i
\(255\) −1.03674e9 5.44588e8i −0.245193 0.128797i
\(256\) 2.05633e8 + 1.72547e8i 0.0478778 + 0.0401742i
\(257\) 4.32196e9 5.15071e9i 0.990714 1.18069i 0.00717862 0.999974i \(-0.497715\pi\)
0.983536 0.180713i \(-0.0578406\pi\)
\(258\) 1.32974e6 53117.6i 0.000300115 1.19884e-5i
\(259\) 9.84837e8 + 3.58451e8i 0.218859 + 0.0796583i
\(260\) −1.96055e9 1.13192e9i −0.429026 0.247699i
\(261\) −6.58926e8 8.23458e9i −0.141995 1.77451i
\(262\) −2.47605e9 4.28864e9i −0.525477 0.910152i
\(263\) 3.20583e9 5.65274e8i 0.670066 0.118151i 0.171742 0.985142i \(-0.445060\pi\)
0.498323 + 0.866991i \(0.333949\pi\)
\(264\) 4.94786e8 + 6.70075e7i 0.101859 + 0.0137945i
\(265\) −3.60243e9 + 1.31118e9i −0.730487 + 0.265875i
\(266\) 7.11320e8 + 1.25425e8i 0.142082 + 0.0250528i
\(267\) 8.64909e8 + 3.97099e9i 0.170187 + 0.781364i
\(268\) 3.62979e9 3.04575e9i 0.703626 0.590413i
\(269\) 6.10781e9i 1.16648i −0.812301 0.583239i \(-0.801785\pi\)
0.812301 0.583239i \(-0.198215\pi\)
\(270\) −4.55313e8 3.78325e9i −0.0856752 0.711885i
\(271\) 6.65460e9 1.23380 0.616900 0.787042i \(-0.288388\pi\)
0.616900 + 0.787042i \(0.288388\pi\)
\(272\) −2.40247e8 2.86315e8i −0.0438917 0.0523080i
\(273\) 8.67392e8 + 9.53669e8i 0.156158 + 0.171691i
\(274\) −5.30814e8 + 3.01039e9i −0.0941759 + 0.534098i
\(275\) −1.60598e7 4.41239e7i −0.00280808 0.00771513i
\(276\) −9.84325e7 7.61115e7i −0.0169630 0.0131164i
\(277\) −1.11019e9 6.29620e9i −0.188572 1.06945i −0.921279 0.388902i \(-0.872854\pi\)
0.732707 0.680545i \(-0.238257\pi\)
\(278\) 6.36410e8 3.67432e8i 0.106551 0.0615173i
\(279\) 3.34320e9 3.29397e9i 0.551753 0.543628i
\(280\) −2.61706e8 + 4.53288e8i −0.0425777 + 0.0737467i
\(281\) −3.56756e9 + 9.80179e9i −0.572197 + 1.57210i 0.228827 + 0.973467i \(0.426511\pi\)
−0.801024 + 0.598632i \(0.795711\pi\)
\(282\) −2.99696e8 + 1.89368e8i −0.0473897 + 0.0299441i
\(283\) −3.55072e9 2.97941e9i −0.553568 0.464499i 0.322579 0.946543i \(-0.395450\pi\)
−0.876147 + 0.482044i \(0.839895\pi\)
\(284\) 2.24380e9 2.67405e9i 0.344914 0.411052i
\(285\) 3.06971e9 + 4.85814e9i 0.465283 + 0.736361i
\(286\) −1.26289e9 4.59653e8i −0.188756 0.0687014i
\(287\) 1.28756e9 + 7.43372e8i 0.189775 + 0.109567i
\(288\) 3.23473e8 1.17236e9i 0.0470184 0.170409i
\(289\) −3.22768e9 5.59050e9i −0.462699 0.801418i
\(290\) −8.89080e9 + 1.56769e9i −1.25704 + 0.221650i
\(291\) −3.21694e9 + 4.16036e9i −0.448613 + 0.580175i
\(292\) 3.56878e9 1.29893e9i 0.490895 0.178671i
\(293\) 7.69714e9 + 1.35721e9i 1.04438 + 0.184153i 0.669417 0.742887i \(-0.266544\pi\)
0.374964 + 0.927039i \(0.377655\pi\)
\(294\) −3.68770e9 + 3.35408e9i −0.493589 + 0.448935i
\(295\) 5.37186e9 4.50752e9i 0.709311 0.595182i
\(296\) 2.66129e9i 0.346677i
\(297\) −6.56192e8 2.16487e9i −0.0843345 0.278232i
\(298\) −4.31319e9 −0.546932
\(299\) 2.15275e8 + 2.56555e8i 0.0269346 + 0.0320993i
\(300\) −1.11752e8 + 2.43403e7i −0.0137965 + 0.00300498i
\(301\) −143812. + 815598.i −1.75198e−5 + 9.93597e-5i
\(302\) 7.43708e7 + 2.04332e8i 0.00894076 + 0.0245645i
\(303\) −2.00070e9 + 1.47733e10i −0.237363 + 1.75270i
\(304\) 3.18491e8 + 1.80625e9i 0.0372909 + 0.211487i
\(305\) −6.99802e9 + 4.04031e9i −0.808678 + 0.466890i
\(306\) −7.27001e8 + 1.52934e9i −0.0829181 + 0.174429i
\(307\) 7.79523e9 1.35017e10i 0.877557 1.51997i 0.0235432 0.999723i \(-0.492505\pi\)
0.854014 0.520250i \(-0.174161\pi\)
\(308\) −1.06274e8 + 2.91985e8i −0.0118093 + 0.0324458i
\(309\) −1.38977e8 3.47913e9i −0.0152443 0.381625i
\(310\) −3.92912e9 3.29692e9i −0.425450 0.356995i
\(311\) 8.12810e8 9.68669e8i 0.0868856 0.103546i −0.720850 0.693091i \(-0.756248\pi\)
0.807736 + 0.589545i \(0.200693\pi\)
\(312\) −1.52228e9 + 2.89799e9i −0.160649 + 0.305828i
\(313\) 9.81955e9 + 3.57402e9i 1.02309 + 0.372375i 0.798446 0.602066i \(-0.205656\pi\)
0.224645 + 0.974441i \(0.427878\pi\)
\(314\) 8.48771e8 + 4.90038e8i 0.0873116 + 0.0504094i
\(315\) 2.36075e9 + 2.24195e8i 0.239777 + 0.0227710i
\(316\) 1.22844e9 + 2.12771e9i 0.123198 + 0.213385i
\(317\) −3.61163e9 + 6.36828e8i −0.357657 + 0.0630645i −0.349590 0.936903i \(-0.613679\pi\)
−0.00806710 + 0.999967i \(0.502568\pi\)
\(318\) 2.10234e9 + 5.12923e9i 0.205587 + 0.501584i
\(319\) −5.03624e9 + 1.83304e9i −0.486344 + 0.177015i
\(320\) −1.30891e9 2.30796e8i −0.124827 0.0220104i
\(321\) 3.89357e9 + 1.24353e9i 0.366715 + 0.117122i
\(322\) 5.93168e7 4.97727e7i 0.00551765 0.00462986i
\(323\) 2.55374e9i 0.234621i
\(324\) −5.43987e9 + 8.76200e8i −0.493638 + 0.0795102i
\(325\) 3.07846e8 0.0275931
\(326\) 3.53620e9 + 4.21428e9i 0.313088 + 0.373124i
\(327\) −1.37369e9 + 4.30109e9i −0.120142 + 0.376173i
\(328\) −6.55571e8 + 3.71793e9i −0.0566402 + 0.321222i
\(329\) −7.54558e7 2.07313e8i −0.00644034 0.0176947i
\(330\) −2.28749e9 + 9.37587e8i −0.192888 + 0.0790598i
\(331\) −1.11585e9 6.32831e9i −0.0929597 0.527201i −0.995353 0.0962883i \(-0.969303\pi\)
0.902394 0.430912i \(-0.141808\pi\)
\(332\) 8.09994e8 4.67650e8i 0.0666699 0.0384919i
\(333\) 1.09650e10 5.01441e9i 0.891730 0.407796i
\(334\) 3.65071e9 6.32322e9i 0.293354 0.508104i
\(335\) −8.02410e9 + 2.20460e10i −0.637114 + 1.75046i
\(336\) 6.70029e8 + 3.51959e8i 0.0525698 + 0.0276144i
\(337\) −1.76551e10 1.48144e10i −1.36884 1.14859i −0.973141 0.230209i \(-0.926059\pi\)
−0.395696 0.918382i \(-0.629497\pi\)
\(338\) −2.68660e8 + 3.20176e8i −0.0205843 + 0.0245314i
\(339\) 2.04929e9 8.18605e7i 0.155169 0.00619835i
\(340\) 1.73897e9 + 6.32935e8i 0.130130 + 0.0473635i
\(341\) −2.63696e9 1.52245e9i −0.195023 0.112597i
\(342\) 6.84202e9 4.71559e9i 0.500126 0.344692i
\(343\) −3.19491e9 5.53375e9i −0.230825 0.399800i
\(344\) −2.07104e6 + 365181.i −0.000147896 + 2.60780e-5i
\(345\) 6.10496e8 + 8.26779e7i 0.0430930 + 0.00583597i
\(346\) −1.16477e10 + 4.23942e9i −0.812712 + 0.295803i
\(347\) −6.20720e9 1.09450e9i −0.428132 0.0754913i −0.0445700 0.999006i \(-0.514192\pi\)
−0.383562 + 0.923515i \(0.625303\pi\)
\(348\) 2.77817e9 + 1.27552e10i 0.189427 + 0.869703i
\(349\) 9.77165e9 8.19939e9i 0.658667 0.552688i −0.251020 0.967982i \(-0.580766\pi\)
0.909687 + 0.415294i \(0.136321\pi\)
\(350\) 7.11756e7i 0.00474306i
\(351\) 1.48086e10 + 8.11716e8i 0.975629 + 0.0534780i
\(352\) −7.89021e8 −0.0513946
\(353\) 3.91985e9 + 4.67150e9i 0.252448 + 0.300855i 0.877353 0.479845i \(-0.159307\pi\)
−0.624906 + 0.780700i \(0.714863\pi\)
\(354\) −6.82264e9 7.50127e9i −0.434449 0.477663i
\(355\) −3.00126e9 + 1.70210e10i −0.188969 + 1.07170i
\(356\) −2.19654e9 6.03495e9i −0.136754 0.375728i
\(357\) −8.33648e8 6.44607e8i −0.0513228 0.0396846i
\(358\) 2.49250e9 + 1.41357e10i 0.151741 + 0.860565i
\(359\) −1.38714e10 + 8.00868e9i −0.835110 + 0.482151i −0.855599 0.517639i \(-0.826811\pi\)
0.0204888 + 0.999790i \(0.493478\pi\)
\(360\) 1.51532e9 + 5.82782e9i 0.0902183 + 0.346974i
\(361\) 2.22588e9 3.85534e9i 0.131061 0.227004i
\(362\) −5.31116e9 + 1.45923e10i −0.309282 + 0.849746i
\(363\) 1.34377e10 8.49084e9i 0.773923 0.489017i
\(364\) −1.56054e9 1.30945e9i −0.0888934 0.0745904i
\(365\) −1.20870e10 + 1.44047e10i −0.681001 + 0.811585i
\(366\) 6.24144e9 + 9.87775e9i 0.347825 + 0.550470i
\(367\) 3.38320e10 + 1.23139e10i 1.86494 + 0.678781i 0.974797 + 0.223092i \(0.0716150\pi\)
0.890139 + 0.455689i \(0.150607\pi\)
\(368\) 1.70282e8 + 9.83122e7i 0.00928489 + 0.00536063i
\(369\) 1.65538e10 4.30425e9i 0.892881 0.232162i
\(370\) −6.58839e9 1.14114e10i −0.351538 0.608882i
\(371\) −3.39732e9 + 5.99038e8i −0.179325 + 0.0316198i
\(372\) −4.53672e9 + 5.86719e9i −0.236903 + 0.306379i
\(373\) −2.03071e10 + 7.39118e9i −1.04909 + 0.381837i −0.808319 0.588745i \(-0.799622\pi\)
−0.240771 + 0.970582i \(0.577400\pi\)
\(374\) 1.08191e9 + 1.90769e8i 0.0552973 + 0.00975040i
\(375\) −1.44156e10 + 1.31114e10i −0.728966 + 0.663018i
\(376\) 4.29149e8 3.60099e8i 0.0214712 0.0180165i
\(377\) 3.51372e10i 1.73941i
\(378\) 1.87673e8 3.42381e9i 0.00919250 0.167704i
\(379\) −2.48531e9 −0.120455 −0.0602273 0.998185i \(-0.519183\pi\)
−0.0602273 + 0.998185i \(0.519183\pi\)
\(380\) −5.83729e9 6.95661e9i −0.279948 0.333629i
\(381\) −3.74907e10 + 8.16574e9i −1.77920 + 0.387521i
\(382\) 3.50901e9 1.99006e10i 0.164790 0.934571i
\(383\) 4.98464e9 + 1.36952e10i 0.231653 + 0.636462i 0.999994 0.00357932i \(-0.00113934\pi\)
−0.768340 + 0.640042i \(0.778917\pi\)
\(384\) −2.57917e8 + 1.90447e9i −0.0118619 + 0.0875888i
\(385\) −2.67155e8 1.51511e9i −0.0121596 0.0689606i
\(386\) 2.27991e9 1.31631e9i 0.102700 0.0592937i
\(387\) 5.40689e6 + 7.84504e6i 0.000241048 + 0.000349745i
\(388\) 4.15528e9 7.19716e9i 0.183347 0.317566i
\(389\) −7.41248e9 + 2.03656e10i −0.323717 + 0.889405i 0.665947 + 0.745999i \(0.268028\pi\)
−0.989664 + 0.143406i \(0.954195\pi\)
\(390\) −6.46922e8 1.61950e10i −0.0279636 0.700039i
\(391\) −2.09721e8 1.75977e8i −0.00897293 0.00752919i
\(392\) 5.06345e9 6.03438e9i 0.214438 0.255557i
\(393\) 1.64875e10 3.13874e10i 0.691169 1.31579i
\(394\) −2.20021e10 8.00812e9i −0.913019 0.332312i
\(395\) −1.05349e10 6.08232e9i −0.432755 0.249851i
\(396\) 1.48668e9 + 3.25092e9i 0.0604555 + 0.132198i
\(397\) 8.47217e9 + 1.46742e10i 0.341061 + 0.590736i 0.984630 0.174653i \(-0.0558803\pi\)
−0.643569 + 0.765388i \(0.722547\pi\)
\(398\) 2.24603e10 3.96035e9i 0.895122 0.157834i
\(399\) 1.96121e9 + 4.78489e9i 0.0773807 + 0.188791i
\(400\) 1.69836e8 6.18153e7i 0.00663423 0.00241466i
\(401\) 1.98526e10 + 3.50055e9i 0.767785 + 0.135381i 0.543804 0.839212i \(-0.316983\pi\)
0.223981 + 0.974593i \(0.428095\pi\)
\(402\) 3.23159e10 + 1.03211e10i 1.23740 + 0.395203i
\(403\) 1.52923e10 1.28318e10i 0.579766 0.486481i
\(404\) 2.35585e10i 0.884347i
\(405\) 2.11566e10 1.72242e10i 0.786369 0.640206i
\(406\) −8.12389e9 −0.298992
\(407\) −5.02815e9 5.99231e9i −0.183244 0.218382i
\(408\) 8.14118e8 2.54905e9i 0.0293797 0.0919894i
\(409\) −1.15917e9 + 6.57401e9i −0.0414244 + 0.234929i −0.998489 0.0549439i \(-0.982502\pi\)
0.957065 + 0.289873i \(0.0936131\pi\)
\(410\) −6.39320e9 1.75652e10i −0.226247 0.621609i
\(411\) −2.02503e10 + 8.30009e9i −0.709682 + 0.290881i
\(412\) 9.55458e8 + 5.41867e9i 0.0331606 + 0.188063i
\(413\) 5.46482e9 3.15511e9i 0.187834 0.108446i
\(414\) 8.42206e7 8.86835e8i 0.00286693 0.0301885i
\(415\) −2.31547e9 + 4.01051e9i −0.0780632 + 0.135209i
\(416\) 1.76924e9 4.86094e9i 0.0590762 0.162311i
\(417\) 4.65772e9 + 2.44665e9i 0.154038 + 0.0809148i
\(418\) −4.12980e9 3.46532e9i −0.135277 0.113511i
\(419\) 3.23959e9 3.86079e9i 0.105107 0.125262i −0.710926 0.703267i \(-0.751724\pi\)
0.816034 + 0.578005i \(0.196168\pi\)
\(420\) −3.74436e9 + 1.49572e8i −0.120332 + 0.00480676i
\(421\) 1.09090e10 + 3.97055e9i 0.347262 + 0.126393i 0.509762 0.860316i \(-0.329734\pi\)
−0.162500 + 0.986709i \(0.551956\pi\)
\(422\) 3.20462e10 + 1.85019e10i 1.01048 + 0.583399i
\(423\) −2.29228e9 1.08968e9i −0.0715990 0.0340360i
\(424\) −4.37994e9 7.58627e9i −0.135520 0.234728i
\(425\) −2.47826e8 + 4.36983e7i −0.00759609 + 0.00133940i
\(426\) 2.47657e10 + 3.35394e9i 0.751989 + 0.101840i
\(427\) −6.83289e9 + 2.48697e9i −0.205538 + 0.0748099i
\(428\) −6.36087e9 1.12159e9i −0.189558 0.0334241i
\(429\) −2.04770e9 9.40142e9i −0.0604556 0.277565i
\(430\) 7.97644e6 6.69303e6i 0.000233311 0.000195771i
\(431\) 2.29309e10i 0.664527i −0.943187 0.332264i \(-0.892188\pi\)
0.943187 0.332264i \(-0.107812\pi\)
\(432\) 8.33275e9 2.52573e9i 0.239251 0.0725191i
\(433\) 1.82602e10 0.519461 0.259730 0.965681i \(-0.416366\pi\)
0.259730 + 0.965681i \(0.416366\pi\)
\(434\) −2.96677e9 3.53565e9i −0.0836227 0.0996577i
\(435\) −4.34899e10 4.78157e10i −1.21460 1.33541i
\(436\) 1.23898e9 7.02662e9i 0.0342862 0.194447i
\(437\) 4.59490e8 + 1.26244e9i 0.0125994 + 0.0346166i
\(438\) 2.15100e10 + 1.66323e10i 0.584445 + 0.451914i
\(439\) 5.70903e8 + 3.23775e9i 0.0153711 + 0.0871736i 0.991528 0.129891i \(-0.0414628\pi\)
−0.976157 + 0.217065i \(0.930352\pi\)
\(440\) 3.38327e9 1.95333e9i 0.0902663 0.0521153i
\(441\) −3.44034e10 9.49242e9i −0.909594 0.250970i
\(442\) −3.60126e9 + 6.23757e9i −0.0943552 + 0.163428i
\(443\) 3.24469e9 8.91472e9i 0.0842478 0.231469i −0.890414 0.455151i \(-0.849585\pi\)
0.974662 + 0.223682i \(0.0718076\pi\)
\(444\) −1.61073e10 + 1.01777e10i −0.414468 + 0.261889i
\(445\) 2.43590e10 + 2.04396e10i 0.621183 + 0.521234i
\(446\) 2.88999e10 3.44415e10i 0.730393 0.870448i
\(447\) −1.64952e10 2.61054e10i −0.413168 0.653883i
\(448\) −1.12387e9 4.09056e8i −0.0279001 0.0101548i
\(449\) −6.08671e10 3.51416e10i −1.49760 0.864642i −0.497608 0.867402i \(-0.665788\pi\)
−0.999996 + 0.00275951i \(0.999122\pi\)
\(450\) −5.74697e8 5.83287e8i −0.0140149 0.0142243i
\(451\) −5.54841e9 9.61012e9i −0.134110 0.232286i
\(452\) −3.19173e9 + 5.62788e8i −0.0764666 + 0.0134831i
\(453\) −9.52289e8 + 1.23156e9i −0.0226139 + 0.0292458i
\(454\) 1.30793e10 4.76046e9i 0.307864 0.112053i
\(455\) 9.93322e9 + 1.75149e9i 0.231763 + 0.0408661i
\(456\) −9.71422e9 + 8.83539e9i −0.224672 + 0.204346i
\(457\) −3.91291e10 + 3.28332e10i −0.897087 + 0.752746i −0.969619 0.244621i \(-0.921337\pi\)
0.0725317 + 0.997366i \(0.476892\pi\)
\(458\) 2.35091e10i 0.534287i
\(459\) −1.20366e10 + 1.44860e9i −0.271176 + 0.0326360i
\(460\) −9.73542e8 −0.0217432
\(461\) −2.42735e10 2.89280e10i −0.537438 0.640494i 0.427173 0.904170i \(-0.359509\pi\)
−0.964611 + 0.263676i \(0.915065\pi\)
\(462\) −2.17366e9 + 4.73437e8i −0.0477115 + 0.0103919i
\(463\) −1.05458e10 + 5.98085e10i −0.229487 + 1.30148i 0.624433 + 0.781078i \(0.285330\pi\)
−0.853920 + 0.520405i \(0.825781\pi\)
\(464\) −7.05552e9 1.93849e10i −0.152215 0.418207i
\(465\) 4.92812e9 3.63894e10i 0.105407 0.778329i
\(466\) 8.89483e9 + 5.04451e10i 0.188623 + 1.06973i
\(467\) −5.99210e10 + 3.45954e10i −1.25983 + 0.727362i −0.973041 0.230632i \(-0.925921\pi\)
−0.286787 + 0.957994i \(0.592587\pi\)
\(468\) −2.33617e10 + 1.86938e9i −0.486990 + 0.0389686i
\(469\) −1.05557e10 + 1.82831e10i −0.218171 + 0.377884i
\(470\) −9.48688e8 + 2.60650e9i −0.0194416 + 0.0534153i
\(471\) 2.80069e8 + 7.01122e9i 0.00569091 + 0.142466i
\(472\) 1.22747e10 + 1.02997e10i 0.247311 + 0.207519i
\(473\) 3.97332e6 4.73522e6i 7.93797e−5 9.46010e-5i
\(474\) −8.17990e9 + 1.55722e10i −0.162045 + 0.308486i
\(475\) 1.16042e9 + 4.22360e8i 0.0227952 + 0.00829676i
\(476\) 1.44216e9 + 8.32629e8i 0.0280921 + 0.0162190i
\(477\) −2.30043e10 + 3.23403e10i −0.444360 + 0.624699i
\(478\) −1.30431e10 2.25913e10i −0.249844 0.432743i
\(479\) 7.61704e10 1.34309e10i 1.44692 0.255131i 0.605643 0.795737i \(-0.292916\pi\)
0.841276 + 0.540606i \(0.181805\pi\)
\(480\) −3.60884e9 8.80473e9i −0.0679834 0.165864i
\(481\) 4.81917e10 1.75403e10i 0.900310 0.327686i
\(482\) 6.27809e10 + 1.10700e10i 1.16316 + 0.205097i
\(483\) 5.28095e8 + 1.68664e8i 0.00970340 + 0.00309908i
\(484\) −1.92421e10 + 1.61460e10i −0.350647 + 0.294228i
\(485\) 4.11479e10i 0.743671i
\(486\) −2.61071e10 2.95736e10i −0.467966 0.530102i
\(487\) 4.64052e8 0.00824994 0.00412497 0.999991i \(-0.498687\pi\)
0.00412497 + 0.999991i \(0.498687\pi\)
\(488\) −1.18686e10 1.41444e10i −0.209276 0.249406i
\(489\) −1.19830e10 + 3.75196e10i −0.209571 + 0.656180i
\(490\) −6.77277e9 + 3.84103e10i −0.117485 + 0.666290i
\(491\) 3.28490e10 + 9.02519e10i 0.565192 + 1.55285i 0.811920 + 0.583769i \(0.198422\pi\)
−0.246728 + 0.969085i \(0.579355\pi\)
\(492\) −2.50097e10 + 1.02509e10i −0.426823 + 0.174944i
\(493\) 4.98767e9 + 2.82865e10i 0.0844326 + 0.478841i
\(494\) 3.06092e10 1.76722e10i 0.513978 0.296745i
\(495\) −1.44229e10 1.02593e10i −0.240232 0.170882i
\(496\) 5.86002e9 1.01499e10i 0.0968216 0.167700i
\(497\) −5.31936e9 + 1.46148e10i −0.0871834 + 0.239535i
\(498\) 5.92813e9 + 3.11399e9i 0.0963830 + 0.0506290i
\(499\) −1.09641e10 9.19998e9i −0.176836 0.148383i 0.550074 0.835116i \(-0.314600\pi\)
−0.726910 + 0.686733i \(0.759044\pi\)
\(500\) 1.97936e10 2.35890e10i 0.316697 0.377425i
\(501\) 5.22326e10 2.08648e9i 0.829069 0.0331179i
\(502\) −3.19537e10 1.16302e10i −0.503160 0.183135i
\(503\) 9.40236e10 + 5.42846e10i 1.46881 + 0.848017i 0.999389 0.0349587i \(-0.0111300\pi\)
0.469419 + 0.882975i \(0.344463\pi\)
\(504\) 4.32211e8 + 5.40133e9i 0.00669844 + 0.0837102i
\(505\) 5.83224e10 + 1.01017e11i 0.896747 + 1.55321i
\(506\) −5.69164e8 + 1.00359e8i −0.00868231 + 0.00153093i
\(507\) −2.96530e9 4.01583e8i −0.0448783 0.00607775i
\(508\) 5.69770e10 2.07379e10i 0.855548 0.311394i
\(509\) 7.92730e10 + 1.39780e10i 1.18101 + 0.208244i 0.729474 0.684008i \(-0.239765\pi\)
0.451537 + 0.892252i \(0.350876\pi\)
\(510\) 2.81965e9 + 1.29456e10i 0.0416787 + 0.191356i
\(511\) −1.29622e10 + 1.08766e10i −0.190106 + 0.159518i
\(512\) 3.03700e9i 0.0441942i
\(513\) 5.47071e10 + 2.33769e10i 0.789905 + 0.337533i
\(514\) −7.60709e10 −1.08985
\(515\) −1.75116e10 2.08695e10i −0.248942 0.296677i
\(516\) −1.01306e7 1.11383e7i −0.000142902 0.000157116i
\(517\) −2.85939e8 + 1.62164e9i −0.00400231 + 0.0226982i
\(518\) −4.05541e9 1.11422e10i −0.0563269 0.154757i
\(519\) −7.02039e10 5.42842e10i −0.967591 0.748176i
\(520\) 4.44756e9 + 2.52234e10i 0.0608287 + 0.344977i
\(521\) 3.36431e10 1.94239e10i 0.456610 0.263624i −0.254008 0.967202i \(-0.581749\pi\)
0.710618 + 0.703578i \(0.248416\pi\)
\(522\) −6.65756e10 + 6.55952e10i −0.896670 + 0.883466i
\(523\) 5.20790e10 9.02035e10i 0.696075 1.20564i −0.273742 0.961803i \(-0.588261\pi\)
0.969817 0.243834i \(-0.0784052\pi\)
\(524\) −1.91622e10 + 5.26477e10i −0.254168 + 0.698320i
\(525\) 4.30787e8 2.72201e8i 0.00567055 0.00358304i
\(526\) −2.82129e10 2.36734e10i −0.368557 0.309256i
\(527\) −1.04893e10 + 1.25007e10i −0.135989 + 0.162066i
\(528\) −3.01749e9 4.77551e9i −0.0388249 0.0614446i
\(529\) −7.34529e10 2.67347e10i −0.937964 0.341391i
\(530\) 3.75617e10 + 2.16863e10i 0.476039 + 0.274841i
\(531\) 1.93088e10 6.99812e10i 0.242872 0.880244i
\(532\) −4.08591e9 7.07700e9i −0.0510084 0.0883492i
\(533\) 7.16466e10 1.26332e10i 0.887742 0.156533i
\(534\) 2.81259e10 3.63743e10i 0.345893 0.447331i
\(535\) 3.00516e10 1.09379e10i 0.366820 0.133512i
\(536\) −5.27939e10 9.30899e9i −0.639624 0.112783i
\(537\) −7.60231e10 + 6.91454e10i −0.914216 + 0.831508i
\(538\) −5.29352e10 + 4.44179e10i −0.631852 + 0.530187i
\(539\) 2.31541e10i 0.274329i
\(540\) −2.94775e10 + 3.14591e10i −0.346669 + 0.369974i
\(541\) 1.67734e10 0.195808 0.0979041 0.995196i \(-0.468786\pi\)
0.0979041 + 0.995196i \(0.468786\pi\)
\(542\) −4.83943e10 5.76741e10i −0.560786 0.668318i
\(543\) −1.08631e11 + 2.36606e10i −1.24955 + 0.272161i
\(544\) −7.34286e8 + 4.16434e9i −0.00838436 + 0.0475500i
\(545\) 1.20827e10 + 3.31970e10i 0.136955 + 0.376281i
\(546\) 1.95732e9 1.44529e10i 0.0220237 0.162624i
\(547\) −2.15713e10 1.22337e11i −0.240950 1.36650i −0.829713 0.558190i \(-0.811496\pi\)
0.588763 0.808306i \(-0.299615\pi\)
\(548\) 2.99507e10 1.72921e10i 0.332113 0.191745i
\(549\) −3.59151e10 + 7.55520e10i −0.395356 + 0.831681i
\(550\) −2.65621e8 + 4.60070e8i −0.00290277 + 0.00502774i
\(551\) 4.82076e10 1.32449e11i 0.523009 1.43696i
\(552\) 5.61879e7 + 1.40660e9i 0.000605183 + 0.0151501i
\(553\) −8.38548e9 7.03625e9i −0.0896659 0.0752386i
\(554\) −4.64943e10 + 5.54097e10i −0.493583 + 0.588230i
\(555\) 4.38707e10 8.35172e10i 0.462384 0.880246i
\(556\) −7.81263e9 2.84356e9i −0.0817519 0.0297553i
\(557\) −1.18293e11 6.82964e10i −1.22896 0.709540i −0.262147 0.965028i \(-0.584431\pi\)
−0.966812 + 0.255488i \(0.917764\pi\)
\(558\) −5.28609e10 5.02008e9i −0.545253 0.0517814i
\(559\) 2.02629e7 + 3.50964e7i 0.000207518 + 0.000359431i
\(560\) 5.83177e9 1.02830e9i 0.0592991 0.0104560i
\(561\) 2.98297e9 + 7.27776e9i 0.0301160 + 0.0734761i
\(562\) 1.10895e11 4.03623e10i 1.11164 0.404605i
\(563\) −1.35414e11 2.38771e10i −1.34781 0.237656i −0.547283 0.836947i \(-0.684338\pi\)
−0.800531 + 0.599291i \(0.795449\pi\)
\(564\) 3.82070e9 + 1.22026e9i 0.0377595 + 0.0120597i
\(565\) 1.22926e10 1.03148e10i 0.120629 0.101220i
\(566\) 5.24406e10i 0.510978i
\(567\) 2.14402e10 1.19580e10i 0.207442 0.115698i
\(568\) −3.94931e10 −0.379427
\(569\) −5.75180e10 6.85472e10i −0.548725 0.653945i 0.418395 0.908265i \(-0.362593\pi\)
−0.967120 + 0.254320i \(0.918148\pi\)
\(570\) 1.97807e10 6.19345e10i 0.187388 0.586723i
\(571\) 1.04381e10 5.91975e10i 0.0981923 0.556876i −0.895530 0.445001i \(-0.853203\pi\)
0.993722 0.111875i \(-0.0356856\pi\)
\(572\) 5.20038e9 + 1.42879e10i 0.0485792 + 0.133470i
\(573\) 1.33867e11 5.48688e10i 1.24181 0.508987i
\(574\) −2.92087e9 1.65650e10i −0.0269069 0.152597i
\(575\) 1.14650e8 6.61930e7i 0.00104882 0.000605537i
\(576\) −1.25131e10 + 5.72233e9i −0.113677 + 0.0519855i
\(577\) −4.15908e10 + 7.20373e10i −0.375227 + 0.649912i −0.990361 0.138511i \(-0.955768\pi\)
0.615134 + 0.788422i \(0.289102\pi\)
\(578\) −2.49791e10 + 6.86295e10i −0.223803 + 0.614893i
\(579\) 1.66861e10 + 8.76503e9i 0.148470 + 0.0779900i
\(580\) 7.82435e10 + 6.56541e10i 0.691411 + 0.580163i
\(581\) −2.67862e9 + 3.19225e9i −0.0235075 + 0.0280151i
\(582\) 5.94517e10 2.37485e9i 0.518170 0.0206987i
\(583\) 2.41954e10 + 8.80639e9i 0.209439 + 0.0762296i
\(584\) −3.72109e10 2.14837e10i −0.319903 0.184696i
\(585\) 9.55453e10 6.58508e10i 0.815804 0.562261i
\(586\) −4.42133e10 7.65797e10i −0.374941 0.649416i
\(587\) 2.10516e11 3.71197e10i 1.77310 0.312645i 0.810940 0.585129i \(-0.198956\pi\)
0.962160 + 0.272484i \(0.0878452\pi\)
\(588\) 5.58872e10 + 7.56865e9i 0.467523 + 0.0633154i
\(589\) 7.52492e10 2.73885e10i 0.625231 0.227566i
\(590\) −7.81316e10 1.37767e10i −0.644791 0.113694i
\(591\) −3.56752e10 1.63793e11i −0.292426 1.34259i
\(592\) 2.30649e10 1.93537e10i 0.187786 0.157571i
\(593\) 8.86022e10i 0.716516i 0.933623 + 0.358258i \(0.116629\pi\)
−0.933623 + 0.358258i \(0.883371\pi\)
\(594\) −1.39905e10 + 2.14307e10i −0.112379 + 0.172144i
\(595\) −8.24516e9 −0.0657856
\(596\) 3.13669e10 + 3.73816e10i 0.248591 + 0.296260i
\(597\) 1.09866e11 + 1.20794e11i 0.864898 + 0.950927i
\(598\) 6.57964e8 3.73150e9i 0.00514514 0.0291796i
\(599\) −4.88605e10 1.34243e11i −0.379534 1.04276i −0.971550 0.236834i \(-0.923890\pi\)
0.592016 0.805926i \(-0.298332\pi\)
\(600\) 1.02365e9 + 7.91521e8i 0.00789852 + 0.00610742i
\(601\) −1.06177e10 6.02162e10i −0.0813831 0.461546i −0.998079 0.0619600i \(-0.980265\pi\)
0.916696 0.399586i \(-0.130846\pi\)
\(602\) 8.11447e6 4.68489e6i 6.17837e−5 3.56709e-5i
\(603\) 6.11195e10 + 2.35061e11i 0.462286 + 1.77792i
\(604\) 1.23006e9 2.13052e9i 0.00924225 0.0160081i
\(605\) 4.25370e10 1.16869e11i 0.317501 0.872327i
\(606\) 1.42587e11 9.00962e10i 1.05728 0.668061i
\(607\) −1.87939e11 1.57700e11i −1.38440 1.16165i −0.967550 0.252679i \(-0.918688\pi\)
−0.416854 0.908974i \(-0.636867\pi\)
\(608\) 1.33383e10 1.58959e10i 0.0976079 0.116325i
\(609\) −3.10686e10 4.91694e10i −0.225867 0.357459i
\(610\) 8.59083e10 + 3.12681e10i 0.620463 + 0.225830i
\(611\) −9.34931e9 5.39783e9i −0.0670834 0.0387306i
\(612\) 1.85415e10 4.82106e9i 0.132172 0.0343666i
\(613\) 1.05581e11 + 1.82871e11i 0.747727 + 1.29510i 0.948910 + 0.315548i \(0.102188\pi\)
−0.201182 + 0.979554i \(0.564478\pi\)
\(614\) −1.73706e11 + 3.06291e10i −1.22220 + 0.215507i
\(615\) 8.18625e10 1.05870e11i 0.572248 0.740069i
\(616\) 3.30344e9 1.20235e9i 0.0229426 0.00835043i
\(617\) −2.61436e11 4.60982e10i −1.80395 0.318085i −0.832268 0.554374i \(-0.812958\pi\)
−0.971683 + 0.236289i \(0.924069\pi\)
\(618\) −2.91422e10 + 2.65058e10i −0.199788 + 0.181713i
\(619\) 1.29618e11 1.08763e11i 0.882884 0.740828i −0.0838860 0.996475i \(-0.526733\pi\)
0.966770 + 0.255648i \(0.0822887\pi\)
\(620\) 5.80292e10i 0.392717i
\(621\) 5.68961e9 2.88183e9i 0.0382575 0.0193777i
\(622\) −1.43063e10 −0.0955796
\(623\) 1.83928e10 + 2.19197e10i 0.122094 + 0.145506i
\(624\) 3.61868e10 7.88173e9i 0.238678 0.0519856i
\(625\) −2.72237e10 + 1.54394e11i −0.178414 + 1.01183i
\(626\) −4.04355e10 1.11096e11i −0.263309 0.723435i
\(627\) 5.17982e9 3.82480e10i 0.0335154 0.247479i
\(628\) −1.92546e9 1.09198e10i −0.0123793 0.0702066i
\(629\) −3.63059e10 + 2.09612e10i −0.231940 + 0.133910i
\(630\) −1.52250e10 2.20905e10i −0.0966487 0.140231i
\(631\) −1.06645e11 + 1.84715e11i −0.672705 + 1.16516i 0.304430 + 0.952535i \(0.401534\pi\)
−0.977134 + 0.212624i \(0.931799\pi\)
\(632\) 9.50690e9 2.61200e10i 0.0595896 0.163721i
\(633\) 1.05743e10 + 2.64716e11i 0.0658622 + 1.64879i
\(634\) 3.17842e10 + 2.66701e10i 0.196722 + 0.165070i
\(635\) −1.92974e11 + 2.29977e11i −1.18687 + 1.41446i
\(636\) 2.91651e10 5.55219e10i 0.178252 0.339341i
\(637\) −1.42646e11 5.19189e10i −0.866366 0.315332i
\(638\) 5.25118e10 + 3.03177e10i 0.316938 + 0.182984i
\(639\) 7.44130e10 + 1.62720e11i 0.446319 + 0.975969i
\(640\) 7.51852e9 + 1.30225e10i 0.0448139 + 0.0776199i
\(641\) 1.01812e11 1.79523e10i 0.603071 0.106338i 0.136227 0.990678i \(-0.456502\pi\)
0.466843 + 0.884340i \(0.345391\pi\)
\(642\) −1.75378e10 4.27882e10i −0.103237 0.251874i
\(643\) 1.21899e11 4.43675e10i 0.713107 0.259550i 0.0401106 0.999195i \(-0.487229\pi\)
0.672997 + 0.739645i \(0.265007\pi\)
\(644\) −8.62741e8 1.52125e8i −0.00501576 0.000884414i
\(645\) 7.10139e7 + 2.26805e7i 0.000410303 + 0.000131043i
\(646\) −2.21328e10 + 1.85716e10i −0.127088 + 0.106640i
\(647\) 1.34435e11i 0.767178i 0.923504 + 0.383589i \(0.125312\pi\)
−0.923504 + 0.383589i \(0.874688\pi\)
\(648\) 4.71543e10 + 4.07743e10i 0.267437 + 0.231252i
\(649\) −4.70985e10 −0.265478
\(650\) −2.23875e9 2.66804e9i −0.0125416 0.0149465i
\(651\) 1.00534e10 3.14778e10i 0.0559744 0.175259i
\(652\) 1.08080e10 6.12952e10i 0.0598074 0.339184i
\(653\) 4.39363e10 + 1.20714e11i 0.241641 + 0.663903i 0.999928 + 0.0119825i \(0.00381423\pi\)
−0.758287 + 0.651921i \(0.773964\pi\)
\(654\) 4.72666e10 1.93734e10i 0.258371 0.105900i
\(655\) −4.81705e10 2.73188e11i −0.261707 1.48422i
\(656\) 3.69901e10 2.13562e10i 0.199742 0.115321i
\(657\) −1.84043e10 + 1.93796e11i −0.0987777 + 1.04012i
\(658\) −1.24800e9 + 2.16161e9i −0.00665752 + 0.0115312i
\(659\) −2.41219e10 + 6.62743e10i −0.127900 + 0.351402i −0.987070 0.160288i \(-0.948758\pi\)
0.859171 + 0.511689i \(0.170980\pi\)
\(660\) 2.47612e10 + 1.30068e10i 0.130496 + 0.0685482i
\(661\) −2.36228e11 1.98219e11i −1.23744 1.03834i −0.997720 0.0674961i \(-0.978499\pi\)
−0.239723 0.970841i \(-0.577057\pi\)
\(662\) −4.67314e10 + 5.56923e10i −0.243320 + 0.289977i
\(663\) −5.15251e10 + 2.05821e9i −0.266664 + 0.0106521i
\(664\) −9.94356e9 3.61916e9i −0.0511528 0.0186181i
\(665\) 3.50402e10 + 2.02305e10i 0.179176 + 0.103447i
\(666\) −1.23200e11 5.85655e10i −0.626201 0.297677i
\(667\) −7.55518e9 1.30860e10i −0.0381717 0.0661153i
\(668\) −8.13513e10 + 1.43444e10i −0.408562 + 0.0720406i
\(669\) 3.18979e11 + 4.31984e10i 1.59242 + 0.215657i
\(670\) 2.49422e11 9.07823e10i 1.23776 0.450507i
\(671\) 5.34481e10 + 9.42434e9i 0.263659 + 0.0464901i
\(672\) −1.82230e9 8.36656e9i −0.00893597 0.0410270i
\(673\) −8.54704e10 + 7.17182e10i −0.416635 + 0.349598i −0.826881 0.562377i \(-0.809887\pi\)
0.410246 + 0.911975i \(0.365443\pi\)
\(674\) 2.60749e11i 1.26352i
\(675\) 1.33247e9 5.70902e9i 0.00641861 0.0275009i
\(676\) 4.72868e9 0.0226440
\(677\) −9.41592e10 1.12215e11i −0.448238 0.534189i 0.493854 0.869545i \(-0.335588\pi\)
−0.942091 + 0.335356i \(0.891143\pi\)
\(678\) −1.56125e10 1.71655e10i −0.0738847 0.0812338i
\(679\) −6.42972e9 + 3.64648e10i −0.0302491 + 0.171551i
\(680\) −7.16084e9 1.96742e10i −0.0334910 0.0920158i
\(681\) 7.88321e10 + 6.09558e10i 0.366534 + 0.283418i
\(682\) 5.98202e9 + 3.39257e10i 0.0276510 + 0.156817i
\(683\) 2.33083e10 1.34570e10i 0.107109 0.0618395i −0.445488 0.895288i \(-0.646970\pi\)
0.552598 + 0.833448i \(0.313637\pi\)
\(684\) −9.06264e10 2.50052e10i −0.414028 0.114237i
\(685\) −8.56178e10 + 1.48294e11i −0.388868 + 0.673539i
\(686\) −2.47255e10 + 6.79328e10i −0.111647 + 0.306749i
\(687\) −1.42288e11 + 8.99072e10i −0.638764 + 0.403615i
\(688\) 1.82262e7 + 1.52936e7i 8.13473e−5 + 6.82585e-5i
\(689\) −1.08508e11 + 1.29314e11i −0.481485 + 0.573812i
\(690\) −3.72317e9 5.89231e9i −0.0164254 0.0259950i
\(691\) −3.17072e11 1.15405e11i −1.39074 0.506188i −0.465324 0.885140i \(-0.654062\pi\)
−0.925416 + 0.378952i \(0.876284\pi\)
\(692\) 1.21448e11 + 7.01181e10i 0.529623 + 0.305778i
\(693\) −1.11783e10 1.13453e10i −0.0484665 0.0491909i
\(694\) 3.56549e10 + 6.17561e10i 0.153703 + 0.266221i
\(695\) 4.05397e10 7.14824e9i 0.173756 0.0306380i
\(696\) 9.03432e10 1.16838e11i 0.384998 0.497905i
\(697\) −5.58844e10 + 2.03403e10i −0.236788 + 0.0861837i
\(698\) −1.42125e11 2.50605e10i −0.598754 0.105577i
\(699\) −2.71299e11 + 2.46755e11i −1.13642 + 1.03361i
\(700\) −6.16865e8 + 5.17611e8i −0.00256920 + 0.00215581i
\(701\) 9.79000e10i 0.405425i −0.979238 0.202712i \(-0.935024\pi\)
0.979238 0.202712i \(-0.0649757\pi\)
\(702\) −1.00658e11 1.34246e11i −0.414475 0.552781i
\(703\) 2.05723e11 0.842291
\(704\) 5.73801e9 + 6.83829e9i 0.0233599 + 0.0278392i
\(705\) −1.94038e10 + 4.22629e9i −0.0785472 + 0.0171081i
\(706\) 1.19806e10 6.79452e10i 0.0482235 0.273489i
\(707\) 3.58998e10 + 9.86338e10i 0.143686 + 0.394774i
\(708\) −1.53956e10 + 1.13682e11i −0.0612724 + 0.452438i
\(709\) −2.55572e10 1.44942e11i −0.101141 0.573602i −0.992692 0.120679i \(-0.961493\pi\)
0.891550 0.452922i \(-0.149618\pi\)
\(710\) 1.69344e11 9.77707e10i 0.666401 0.384747i
\(711\) −1.25533e11 + 1.00450e10i −0.491222 + 0.0393073i
\(712\) −3.63298e10 + 6.29251e10i −0.141365 + 0.244852i
\(713\) 2.93615e9 8.06701e9i 0.0113611 0.0312144i
\(714\) 4.75869e8 + 1.19128e10i 0.00183102 + 0.0458377i
\(715\) −5.76706e10 4.83914e10i −0.220663 0.185159i
\(716\) 1.04385e11 1.24401e11i 0.397178 0.473338i
\(717\) 8.68513e10 1.65340e11i 0.328624 0.625606i
\(718\) 1.70287e11 + 6.19794e10i 0.640743 + 0.233211i
\(719\) 3.97304e10 + 2.29384e10i 0.148665 + 0.0858315i 0.572487 0.819914i \(-0.305979\pi\)
−0.423823 + 0.905745i \(0.639312\pi\)
\(720\) 3.94887e10 5.55147e10i 0.146941 0.206575i
\(721\) −1.22575e10 2.12307e10i −0.0453589 0.0785639i
\(722\) −4.96008e10 + 8.74596e9i −0.182532 + 0.0321854i
\(723\) 1.73096e11 + 4.22314e11i 0.633482 + 1.54555i
\(724\) 1.65093e11 6.00889e10i 0.600861 0.218696i
\(725\) −1.36783e10 2.41186e9i −0.0495087 0.00872971i
\(726\) −1.71311e11 5.47136e10i −0.616652 0.196947i
\(727\) 2.57974e11 2.16466e11i 0.923504 0.774912i −0.0511354 0.998692i \(-0.516284\pi\)
0.974640 + 0.223780i \(0.0718396\pi\)
\(728\) 2.30476e10i 0.0820542i
\(729\) 7.91500e10 2.71112e11i 0.280247 0.959928i
\(730\) 2.12744e11 0.749144
\(731\) −2.12942e7 2.53774e7i −7.45746e−5 8.88746e-5i
\(732\) 4.02188e10 1.25927e11i 0.140083 0.438608i
\(733\) −3.98252e10 + 2.25860e11i −0.137956 + 0.782390i 0.834799 + 0.550555i \(0.185584\pi\)
−0.972755 + 0.231835i \(0.925527\pi\)
\(734\) −1.39315e11 3.82766e11i −0.479971 1.31871i
\(735\) −2.58378e11 + 1.05903e11i −0.885331 + 0.362875i
\(736\) −3.86289e8 2.19075e9i −0.00131644 0.00746591i
\(737\) 1.36462e11 7.87863e10i 0.462532 0.267043i
\(738\) −1.57689e11 1.12167e11i −0.531588 0.378129i
\(739\) −4.34101e10 + 7.51885e10i −0.145550 + 0.252101i −0.929578 0.368625i \(-0.879829\pi\)
0.784028 + 0.620726i \(0.213162\pi\)
\(740\) −5.09877e10 + 1.40088e11i −0.170035 + 0.467168i
\(741\) 2.24021e11 + 1.17676e11i 0.743045 + 0.390314i
\(742\) 2.98981e10 + 2.50875e10i 0.0986343 + 0.0827640i
\(743\) −1.85979e9 + 2.21641e9i −0.00610252 + 0.00727270i −0.769087 0.639144i \(-0.779289\pi\)
0.762985 + 0.646417i \(0.223733\pi\)
\(744\) 8.38423e10 3.34915e9i 0.273635 0.0109306i
\(745\) −2.27042e11 8.26367e10i −0.737024 0.268255i
\(746\) 2.11738e11 + 1.22247e11i 0.683664 + 0.394713i
\(747\) 3.82402e9 + 4.77887e10i 0.0122811 + 0.153477i
\(748\) −6.21461e9 1.07640e10i −0.0198521 0.0343849i
\(749\) 2.83405e10 4.99720e9i 0.0900494 0.0158781i
\(750\) 2.18469e11 + 2.95867e10i 0.690470 + 0.0935084i
\(751\) 2.12013e11 7.71666e10i 0.666505 0.242588i 0.0134628 0.999909i \(-0.495715\pi\)
0.653042 + 0.757321i \(0.273492\pi\)
\(752\) −6.24181e9 1.10060e9i −0.0195182 0.00344158i
\(753\) −5.18110e10 2.37876e11i −0.161154 0.739896i
\(754\) −3.04527e11 + 2.55529e11i −0.942194 + 0.790595i
\(755\) 1.21807e10i 0.0374874i