Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [10,18,Mod(9,10)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(10, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1]))
N = Newforms(chi, 18, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("10.9");
S:= CuspForms(chi, 18);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 10 = 2 \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 18 \) |
Character orbit: | \([\chi]\) | \(=\) | 10.b (of order \(2\), degree \(1\), 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: | \(18.3222087345\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 556201x^{6} + 76870744104x^{4} + 1868329791349729x^{2} + 78074963590050625 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{40}\cdot 3^{4}\cdot 5^{11} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 9.7 | ||
Root | \(-6.46999i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 10.9 |
Dual form | 10.18.b.a.9.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/10\mathbb{Z}\right)^\times\).
\(n\) | \(7\) |
\(\chi(n)\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 256.000i | 0.707107i | ||||||||
\(3\) | 2973.91i | 0.261696i | 0.991402 | + | 0.130848i | \(0.0417699\pi\) | ||||
−0.991402 | + | 0.130848i | \(0.958230\pi\) | |||||||
\(4\) | −65536.0 | −0.500000 | ||||||||
\(5\) | 855091. | + | 178210.i | 0.978965 | + | 0.204027i | ||||
\(6\) | −761320. | −0.185047 | ||||||||
\(7\) | − | 7.58343e6i | − | 0.497201i | −0.968606 | − | 0.248601i | \(-0.920029\pi\) | ||
0.968606 | − | 0.248601i | \(-0.0799707\pi\) | |||||||
\(8\) | − | 1.67772e7i | − | 0.353553i | ||||||
\(9\) | 1.20296e8 | 0.931515 | ||||||||
\(10\) | −4.56218e7 | + | 2.18903e8i | −0.144269 | + | 0.692233i | ||||
\(11\) | 6.04893e8 | 0.850825 | 0.425413 | − | 0.904999i | \(-0.360129\pi\) | ||||
0.425413 | + | 0.904999i | \(0.360129\pi\) | |||||||
\(12\) | − | 1.94898e8i | − | 0.130848i | ||||||
\(13\) | − | 1.32682e9i | − | 0.451120i | −0.974229 | − | 0.225560i | \(-0.927579\pi\) | ||
0.974229 | − | 0.225560i | \(-0.0724212\pi\) | |||||||
\(14\) | 1.94136e9 | 0.351575 | ||||||||
\(15\) | −5.29980e8 | + | 2.54296e9i | −0.0533929 | + | 0.256191i | ||||
\(16\) | 4.29497e9 | 0.250000 | ||||||||
\(17\) | 3.25122e10i | 1.13040i | 0.824955 | + | 0.565198i | \(0.191200\pi\) | ||||
−0.824955 | + | 0.565198i | \(0.808800\pi\) | |||||||
\(18\) | 3.07958e10i | 0.658681i | ||||||||
\(19\) | −1.67948e10 | −0.226865 | −0.113433 | − | 0.993546i | \(-0.536185\pi\) | ||||
−0.113433 | + | 0.993546i | \(0.536185\pi\) | |||||||
\(20\) | −5.60392e10 | − | 1.16792e10i | −0.489483 | − | 0.102013i | ||||
\(21\) | 2.25524e10 | 0.130115 | ||||||||
\(22\) | 1.54853e11i | 0.601624i | ||||||||
\(23\) | 7.14069e11i | 1.90131i | 0.310246 | + | 0.950656i | \(0.399589\pi\) | ||||
−0.310246 | + | 0.950656i | \(0.600411\pi\) | |||||||
\(24\) | 4.98939e10 | 0.0925234 | ||||||||
\(25\) | 6.99422e11 | + | 3.04772e11i | 0.916746 | + | 0.399470i | ||||
\(26\) | 3.39665e11 | 0.318990 | ||||||||
\(27\) | 7.41800e11i | 0.505469i | ||||||||
\(28\) | 4.96988e11i | 0.248601i | ||||||||
\(29\) | 1.25241e12 | 0.464904 | 0.232452 | − | 0.972608i | \(-0.425325\pi\) | ||||
0.232452 | + | 0.972608i | \(0.425325\pi\) | |||||||
\(30\) | −6.50998e11 | − | 1.35675e11i | −0.181154 | − | 0.0377545i | ||||
\(31\) | −1.26092e12 | −0.265529 | −0.132764 | − | 0.991148i | \(-0.542385\pi\) | ||||
−0.132764 | + | 0.991148i | \(0.542385\pi\) | |||||||
\(32\) | 1.09951e12i | 0.176777i | ||||||||
\(33\) | 1.79889e12i | 0.222657i | ||||||||
\(34\) | −8.32313e12 | −0.799311 | ||||||||
\(35\) | 1.35144e12 | − | 6.48452e12i | 0.101442 | − | 0.486743i | ||||
\(36\) | −7.88372e12 | −0.465758 | ||||||||
\(37\) | − | 3.37394e13i | − | 1.57915i | −0.613655 | − | 0.789575i | \(-0.710301\pi\) | ||
0.613655 | − | 0.789575i | \(-0.289699\pi\) | |||||||
\(38\) | − | 4.29946e12i | − | 0.160418i | ||||||
\(39\) | 3.94583e12 | 0.118056 | ||||||||
\(40\) | 2.98987e12 | − | 1.43460e13i | 0.0721344 | − | 0.346117i | ||||
\(41\) | 3.95012e13 | 0.772588 | 0.386294 | − | 0.922376i | \(-0.373755\pi\) | ||||
0.386294 | + | 0.922376i | \(0.373755\pi\) | |||||||
\(42\) | 5.77342e12i | 0.0920055i | ||||||||
\(43\) | − | 8.15984e13i | − | 1.06463i | −0.846546 | − | 0.532316i | \(-0.821322\pi\) | ||
0.846546 | − | 0.532316i | \(-0.178678\pi\) | |||||||
\(44\) | −3.96422e13 | −0.425413 | ||||||||
\(45\) | 1.02864e14 | + | 2.14380e13i | 0.911921 | + | 0.190054i | ||||
\(46\) | −1.82802e14 | −1.34443 | ||||||||
\(47\) | 1.28862e14i | 0.789392i | 0.918812 | + | 0.394696i | \(0.129150\pi\) | ||||
−0.918812 | + | 0.394696i | \(0.870850\pi\) | |||||||
\(48\) | 1.27728e13i | 0.0654239i | ||||||||
\(49\) | 1.75122e14 | 0.752791 | ||||||||
\(50\) | −7.80216e13 | + | 1.79052e14i | −0.282468 | + | 0.648237i | ||||
\(51\) | −9.66883e13 | −0.295820 | ||||||||
\(52\) | 8.69542e13i | 0.225560i | ||||||||
\(53\) | 4.11135e14i | 0.907067i | 0.891239 | + | 0.453533i | \(0.149837\pi\) | ||||
−0.891239 | + | 0.453533i | \(0.850163\pi\) | |||||||
\(54\) | −1.89901e14 | −0.357421 | ||||||||
\(55\) | 5.17238e14 | + | 1.07798e14i | 0.832929 | + | 0.173591i | ||||
\(56\) | −1.27229e14 | −0.175787 | ||||||||
\(57\) | − | 4.99461e13i | − | 0.0593697i | ||||||
\(58\) | 3.20617e14i | 0.328737i | ||||||||
\(59\) | 1.32582e15 | 1.17555 | 0.587777 | − | 0.809023i | \(-0.300003\pi\) | ||||
0.587777 | + | 0.809023i | \(0.300003\pi\) | |||||||
\(60\) | 3.47328e13 | − | 1.66655e14i | 0.0266965 | − | 0.128096i | ||||
\(61\) | −1.20106e15 | −0.802161 | −0.401080 | − | 0.916043i | \(-0.631365\pi\) | ||||
−0.401080 | + | 0.916043i | \(0.631365\pi\) | |||||||
\(62\) | − | 3.22795e14i | − | 0.187757i | ||||||
\(63\) | − | 9.12257e14i | − | 0.463151i | ||||||
\(64\) | −2.81475e14 | −0.125000 | ||||||||
\(65\) | 2.36452e14 | − | 1.13455e15i | 0.0920406 | − | 0.441631i | ||||
\(66\) | −4.60517e14 | −0.157443 | ||||||||
\(67\) | − | 2.90250e15i | − | 0.873246i | −0.899645 | − | 0.436623i | \(-0.856174\pi\) | ||
0.899645 | − | 0.436623i | \(-0.143826\pi\) | |||||||
\(68\) | − | 2.13072e15i | − | 0.565198i | ||||||
\(69\) | −2.12357e15 | −0.497565 | ||||||||
\(70\) | 1.66004e15 | + | 3.45970e14i | 0.344179 | + | 0.0717306i | ||||
\(71\) | −7.20936e15 | −1.32495 | −0.662477 | − | 0.749082i | \(-0.730495\pi\) | ||||
−0.662477 | + | 0.749082i | \(0.730495\pi\) | |||||||
\(72\) | − | 2.01823e15i | − | 0.329340i | ||||||
\(73\) | 4.16197e15i | 0.604024i | 0.953304 | + | 0.302012i | \(0.0976583\pi\) | ||||
−0.953304 | + | 0.302012i | \(0.902342\pi\) | |||||||
\(74\) | 8.63730e15 | 1.11663 | ||||||||
\(75\) | −9.06362e14 | + | 2.08001e15i | −0.104540 | + | 0.239909i | ||||
\(76\) | 1.10066e15 | 0.113433 | ||||||||
\(77\) | − | 4.58716e15i | − | 0.423032i | ||||||
\(78\) | 1.01013e15i | 0.0834783i | ||||||||
\(79\) | −4.74555e15 | −0.351930 | −0.175965 | − | 0.984396i | \(-0.556305\pi\) | ||||
−0.175965 | + | 0.984396i | \(0.556305\pi\) | |||||||
\(80\) | 3.67259e15 | + | 7.65407e14i | 0.244741 | + | 0.0510067i | ||||
\(81\) | 1.33290e16 | 0.799236 | ||||||||
\(82\) | 1.01123e16i | 0.546302i | ||||||||
\(83\) | 1.57327e16i | 0.766724i | 0.923598 | + | 0.383362i | \(0.125234\pi\) | ||||
−0.923598 | + | 0.383362i | \(0.874766\pi\) | |||||||
\(84\) | −1.47799e15 | −0.0650577 | ||||||||
\(85\) | −5.79401e15 | + | 2.78009e16i | −0.230631 | + | 1.10662i | ||||
\(86\) | 2.08892e16 | 0.752809 | ||||||||
\(87\) | 3.72455e15i | 0.121663i | ||||||||
\(88\) | − | 1.01484e16i | − | 0.300812i | ||||||
\(89\) | −2.48196e16 | −0.668312 | −0.334156 | − | 0.942518i | \(-0.608451\pi\) | ||||
−0.334156 | + | 0.942518i | \(0.608451\pi\) | |||||||
\(90\) | −5.48812e15 | + | 2.63332e16i | −0.134389 | + | 0.644826i | ||||
\(91\) | −1.00618e16 | −0.224298 | ||||||||
\(92\) | − | 4.67972e16i | − | 0.950656i | ||||||
\(93\) | − | 3.74985e15i | − | 0.0694878i | ||||||
\(94\) | −3.29887e16 | −0.558185 | ||||||||
\(95\) | −1.43611e16 | − | 2.99300e15i | −0.222093 | − | 0.0462866i | ||||
\(96\) | −3.26984e15 | −0.0462617 | ||||||||
\(97\) | − | 1.31140e17i | − | 1.69893i | −0.527645 | − | 0.849465i | \(-0.676925\pi\) | ||
0.527645 | − | 0.849465i | \(-0.323075\pi\) | |||||||
\(98\) | 4.48313e16i | 0.532303i | ||||||||
\(99\) | 7.27662e16 | 0.792557 | ||||||||
\(100\) | −4.58373e16 | − | 1.99735e16i | −0.458373 | − | 0.199735i | ||||
\(101\) | 1.40289e17 | 1.28912 | 0.644560 | − | 0.764554i | \(-0.277041\pi\) | ||||
0.644560 | + | 0.764554i | \(0.277041\pi\) | |||||||
\(102\) | − | 2.47522e16i | − | 0.209176i | ||||||
\(103\) | 2.25271e16i | 0.175222i | 0.996155 | + | 0.0876110i | \(0.0279233\pi\) | ||||
−0.996155 | + | 0.0876110i | \(0.972077\pi\) | |||||||
\(104\) | −2.22603e16 | −0.159495 | ||||||||
\(105\) | 1.92844e16 | + | 4.01907e15i | 0.127379 | + | 0.0265470i | ||||
\(106\) | −1.05250e17 | −0.641393 | ||||||||
\(107\) | − | 2.96635e17i | − | 1.66902i | −0.550995 | − | 0.834509i | \(-0.685752\pi\) | ||
0.550995 | − | 0.834509i | \(-0.314248\pi\) | |||||||
\(108\) | − | 4.86146e16i | − | 0.252735i | ||||||
\(109\) | −1.00693e17 | −0.484032 | −0.242016 | − | 0.970272i | \(-0.577809\pi\) | ||||
−0.242016 | + | 0.970272i | \(0.577809\pi\) | |||||||
\(110\) | −2.75963e16 | + | 1.32413e17i | −0.122748 | + | 0.588969i | ||||
\(111\) | 1.00338e17 | 0.413257 | ||||||||
\(112\) | − | 3.25706e16i | − | 0.124300i | ||||||
\(113\) | 2.91587e17i | 1.03181i | 0.856645 | + | 0.515906i | \(0.172545\pi\) | ||||
−0.856645 | + | 0.515906i | \(0.827455\pi\) | |||||||
\(114\) | 1.27862e16 | 0.0419807 | ||||||||
\(115\) | −1.27254e17 | + | 6.10594e17i | −0.387919 | + | 1.86132i | ||||
\(116\) | −8.20779e16 | −0.232452 | ||||||||
\(117\) | − | 1.59611e17i | − | 0.420225i | ||||||
\(118\) | 3.39410e17i | 0.831242i | ||||||||
\(119\) | 2.46554e17 | 0.562035 | ||||||||
\(120\) | 4.26638e16 | + | 8.89159e15i | 0.0905772 | + | 0.0188773i | ||||
\(121\) | −1.39552e17 | −0.276096 | ||||||||
\(122\) | − | 3.07472e17i | − | 0.567213i | ||||||
\(123\) | 1.17473e17i | 0.202183i | ||||||||
\(124\) | 8.26354e16 | 0.132764 | ||||||||
\(125\) | 5.43756e17 | + | 3.85252e17i | 0.815960 | + | 0.578108i | ||||
\(126\) | 2.33538e17 | 0.327497 | ||||||||
\(127\) | − | 6.72025e17i | − | 0.881158i | −0.897714 | − | 0.440579i | \(-0.854773\pi\) | ||
0.897714 | − | 0.440579i | \(-0.145227\pi\) | |||||||
\(128\) | − | 7.20576e16i | − | 0.0883883i | ||||||
\(129\) | 2.42666e17 | 0.278610 | ||||||||
\(130\) | 2.90444e17 | + | 6.05317e16i | 0.312280 | + | 0.0650825i | ||||
\(131\) | −1.65072e18 | −1.66290 | −0.831452 | − | 0.555596i | \(-0.812490\pi\) | ||||
−0.831452 | + | 0.555596i | \(0.812490\pi\) | |||||||
\(132\) | − | 1.17892e17i | − | 0.111329i | ||||||
\(133\) | 1.27362e17i | 0.112798i | ||||||||
\(134\) | 7.43040e17 | 0.617478 | ||||||||
\(135\) | −1.32196e17 | + | 6.34306e17i | −0.103129 | + | 0.494837i | ||||
\(136\) | 5.45465e17 | 0.399656 | ||||||||
\(137\) | − | 2.53057e18i | − | 1.74218i | −0.491123 | − | 0.871090i | \(-0.663414\pi\) | ||
0.491123 | − | 0.871090i | \(-0.336586\pi\) | |||||||
\(138\) | − | 5.43635e17i | − | 0.351832i | ||||||
\(139\) | −2.77639e18 | −1.68987 | −0.844937 | − | 0.534865i | \(-0.820362\pi\) | ||||
−0.844937 | + | 0.534865i | \(0.820362\pi\) | |||||||
\(140\) | −8.85682e16 | + | 4.24970e17i | −0.0507212 | + | 0.243371i | ||||
\(141\) | −3.83223e17 | −0.206581 | ||||||||
\(142\) | − | 1.84560e18i | − | 0.936884i | ||||||
\(143\) | − | 8.02581e17i | − | 0.383825i | ||||||
\(144\) | 5.16668e17 | 0.232879 | ||||||||
\(145\) | 1.07092e18 | + | 2.23192e17i | 0.455125 | + | 0.0948529i | ||||
\(146\) | −1.06546e18 | −0.427110 | ||||||||
\(147\) | 5.20797e17i | 0.197002i | ||||||||
\(148\) | 2.21115e18i | 0.789575i | ||||||||
\(149\) | 1.48993e18 | 0.502439 | 0.251220 | − | 0.967930i | \(-0.419168\pi\) | ||||
0.251220 | + | 0.967930i | \(0.419168\pi\) | |||||||
\(150\) | −5.32484e17 | − | 2.32029e17i | −0.169641 | − | 0.0739207i | ||||
\(151\) | 2.85975e18 | 0.861040 | 0.430520 | − | 0.902581i | \(-0.358330\pi\) | ||||
0.430520 | + | 0.902581i | \(0.358330\pi\) | |||||||
\(152\) | 2.81769e17i | 0.0802091i | ||||||||
\(153\) | 3.91109e18i | 1.05298i | ||||||||
\(154\) | 1.17431e18 | 0.299129 | ||||||||
\(155\) | −1.07820e18 | − | 2.24708e17i | −0.259944 | − | 0.0541750i | ||||
\(156\) | −2.58594e17 | −0.0590281 | ||||||||
\(157\) | 1.39051e18i | 0.300625i | 0.988638 | + | 0.150313i | \(0.0480281\pi\) | ||||
−0.988638 | + | 0.150313i | \(0.951972\pi\) | |||||||
\(158\) | − | 1.21486e18i | − | 0.248852i | ||||||
\(159\) | −1.22268e18 | −0.237375 | ||||||||
\(160\) | −1.95944e17 | + | 9.40182e17i | −0.0360672 | + | 0.173058i | ||||
\(161\) | 5.41509e18 | 0.945335 | ||||||||
\(162\) | 3.41223e18i | 0.565145i | ||||||||
\(163\) | 2.67461e18i | 0.420404i | 0.977658 | + | 0.210202i | \(0.0674121\pi\) | ||||
−0.977658 | + | 0.210202i | \(0.932588\pi\) | |||||||
\(164\) | −2.58875e18 | −0.386294 | ||||||||
\(165\) | −3.20581e17 | + | 1.53822e18i | −0.0454281 | + | 0.217974i | ||||
\(166\) | −4.02757e18 | −0.542155 | ||||||||
\(167\) | 2.09954e18i | 0.268555i | 0.990944 | + | 0.134278i | \(0.0428714\pi\) | ||||
−0.990944 | + | 0.134278i | \(0.957129\pi\) | |||||||
\(168\) | − | 3.78367e17i | − | 0.0460028i | ||||||
\(169\) | 6.88997e18 | 0.796491 | ||||||||
\(170\) | −7.11703e18 | − | 1.48327e18i | −0.782498 | − | 0.163081i | ||||
\(171\) | −2.02034e18 | −0.211329 | ||||||||
\(172\) | 5.34763e18i | 0.532316i | ||||||||
\(173\) | − | 1.79690e19i | − | 1.70268i | −0.524616 | − | 0.851339i | \(-0.675791\pi\) | ||
0.524616 | − | 0.851339i | \(-0.324209\pi\) | |||||||
\(174\) | −9.53484e17 | −0.0860290 | ||||||||
\(175\) | 2.31121e18 | − | 5.30402e18i | 0.198617 | − | 0.455807i | ||||
\(176\) | 2.59799e18 | 0.212706 | ||||||||
\(177\) | 3.94287e18i | 0.307638i | ||||||||
\(178\) | − | 6.35382e18i | − | 0.472568i | ||||||
\(179\) | −2.38231e19 | −1.68946 | −0.844731 | − | 0.535191i | \(-0.820240\pi\) | ||||
−0.844731 | + | 0.535191i | \(0.820240\pi\) | |||||||
\(180\) | −6.74130e18 | − | 1.40496e18i | −0.455961 | − | 0.0950271i | ||||
\(181\) | 2.36044e19 | 1.52309 | 0.761546 | − | 0.648111i | \(-0.224441\pi\) | ||||
0.761546 | + | 0.648111i | \(0.224441\pi\) | |||||||
\(182\) | − | 2.57583e18i | − | 0.158602i | ||||||
\(183\) | − | 3.57184e18i | − | 0.209922i | ||||||
\(184\) | 1.19801e19 | 0.672216 | ||||||||
\(185\) | 6.01271e18 | − | 2.88503e19i | 0.322189 | − | 1.54593i | ||||
\(186\) | 9.59961e17 | 0.0491353 | ||||||||
\(187\) | 1.96664e19i | 0.961770i | ||||||||
\(188\) | − | 8.44510e18i | − | 0.394696i | ||||||
\(189\) | 5.62539e18 | 0.251320 | ||||||||
\(190\) | 7.66207e17 | − | 3.67643e18i | 0.0327296 | − | 0.157044i | ||||
\(191\) | −3.29525e19 | −1.34619 | −0.673093 | − | 0.739558i | \(-0.735035\pi\) | ||||
−0.673093 | + | 0.739558i | \(0.735035\pi\) | |||||||
\(192\) | − | 8.37080e17i | − | 0.0327120i | ||||||
\(193\) | 1.54581e19i | 0.577989i | 0.957331 | + | 0.288995i | \(0.0933210\pi\) | ||||
−0.957331 | + | 0.288995i | \(0.906679\pi\) | |||||||
\(194\) | 3.35718e19 | 1.20133 | ||||||||
\(195\) | 3.37404e18 | + | 7.03186e17i | 0.115573 | + | 0.0240866i | ||||
\(196\) | −1.14768e19 | −0.376395 | ||||||||
\(197\) | 2.38607e19i | 0.749410i | 0.927144 | + | 0.374705i | \(0.122256\pi\) | ||||
−0.927144 | + | 0.374705i | \(0.877744\pi\) | |||||||
\(198\) | 1.86281e19i | 0.560422i | ||||||||
\(199\) | −5.01370e19 | −1.44513 | −0.722566 | − | 0.691302i | \(-0.757037\pi\) | ||||
−0.722566 | + | 0.691302i | \(0.757037\pi\) | |||||||
\(200\) | 5.11322e18 | − | 1.17344e19i | 0.141234 | − | 0.324119i | ||||
\(201\) | 8.63176e18 | 0.228525 | ||||||||
\(202\) | 3.59141e19i | 0.911546i | ||||||||
\(203\) | − | 9.49756e18i | − | 0.231151i | ||||||
\(204\) | 6.33656e18 | 0.147910 | ||||||||
\(205\) | 3.37771e19 | + | 7.03952e18i | 0.756336 | + | 0.157629i | ||||
\(206\) | −5.76694e18 | −0.123901 | ||||||||
\(207\) | 8.58997e19i | 1.77110i | ||||||||
\(208\) | − | 5.69863e18i | − | 0.112780i | ||||||
\(209\) | −1.01590e19 | −0.193023 | ||||||||
\(210\) | −1.02888e18 | + | 4.93680e18i | −0.0187716 | + | 0.0900702i | ||||
\(211\) | −3.95410e19 | −0.692862 | −0.346431 | − | 0.938075i | \(-0.612607\pi\) | ||||
−0.346431 | + | 0.938075i | \(0.612607\pi\) | |||||||
\(212\) | − | 2.69441e19i | − | 0.453533i | ||||||
\(213\) | − | 2.14400e19i | − | 0.346735i | ||||||
\(214\) | 7.59387e19 | 1.18017 | ||||||||
\(215\) | 1.45417e19 | − | 6.97740e19i | 0.217214 | − | 1.04224i | ||||
\(216\) | 1.24453e19 | 0.178710 | ||||||||
\(217\) | 9.56207e18i | 0.132021i | ||||||||
\(218\) | − | 2.57774e19i | − | 0.342263i | ||||||
\(219\) | −1.23773e19 | −0.158071 | ||||||||
\(220\) | −3.38977e19 | − | 7.06465e18i | −0.416464 | − | 0.0867956i | ||||
\(221\) | 4.31377e19 | 0.509945 | ||||||||
\(222\) | 2.56865e19i | 0.292217i | ||||||||
\(223\) | 1.28208e19i | 0.140386i | 0.997533 | + | 0.0701929i | \(0.0223615\pi\) | ||||
−0.997533 | + | 0.0701929i | \(0.977639\pi\) | |||||||
\(224\) | 8.33807e18 | 0.0878936 | ||||||||
\(225\) | 8.41377e19 | + | 3.66628e19i | 0.853963 | + | 0.372113i | ||||
\(226\) | −7.46462e19 | −0.729602 | ||||||||
\(227\) | − | 1.74756e20i | − | 1.64517i | −0.568639 | − | 0.822587i | \(-0.692530\pi\) | ||
0.568639 | − | 0.822587i | \(-0.307470\pi\) | |||||||
\(228\) | 3.27327e18i | 0.0296849i | ||||||||
\(229\) | −5.58613e19 | −0.488100 | −0.244050 | − | 0.969763i | \(-0.578476\pi\) | ||||
−0.244050 | + | 0.969763i | \(0.578476\pi\) | |||||||
\(230\) | −1.56312e20 | − | 3.25771e19i | −1.31615 | − | 0.274300i | ||||
\(231\) | 1.36418e19 | 0.110706 | ||||||||
\(232\) | − | 2.10119e19i | − | 0.164368i | ||||||
\(233\) | − | 1.93341e20i | − | 1.45814i | −0.684440 | − | 0.729069i | \(-0.739953\pi\) | ||
0.684440 | − | 0.729069i | \(-0.260047\pi\) | |||||||
\(234\) | 4.08603e19 | 0.297144 | ||||||||
\(235\) | −2.29645e19 | + | 1.10189e20i | −0.161057 | + | 0.772788i | ||||
\(236\) | −8.68890e19 | −0.587777 | ||||||||
\(237\) | − | 1.41128e19i | − | 0.0920986i | ||||||
\(238\) | 6.31179e19i | 0.397419i | ||||||||
\(239\) | −9.14253e19 | −0.555500 | −0.277750 | − | 0.960653i | \(-0.589589\pi\) | ||||
−0.277750 | + | 0.960653i | \(0.589589\pi\) | |||||||
\(240\) | −2.27625e18 | + | 1.09219e19i | −0.0133482 | + | 0.0640478i | ||||
\(241\) | 1.42371e20 | 0.805889 | 0.402945 | − | 0.915224i | \(-0.367987\pi\) | ||||
0.402945 | + | 0.915224i | \(0.367987\pi\) | |||||||
\(242\) | − | 3.57253e19i | − | 0.195229i | ||||||
\(243\) | 1.35435e20i | 0.714626i | ||||||||
\(244\) | 7.87127e19 | 0.401080 | ||||||||
\(245\) | 1.49745e20 | + | 3.12085e19i | 0.736956 | + | 0.153589i | ||||
\(246\) | −3.00731e19 | −0.142965 | ||||||||
\(247\) | 2.22836e19i | 0.102344i | ||||||||
\(248\) | 2.11547e19i | 0.0938786i | ||||||||
\(249\) | −4.67875e19 | −0.200648 | ||||||||
\(250\) | −9.86244e19 | + | 1.39202e20i | −0.408784 | + | 0.576971i | ||||
\(251\) | 3.37128e20 | 1.35073 | 0.675364 | − | 0.737484i | \(-0.263986\pi\) | ||||
0.675364 | + | 0.737484i | \(0.263986\pi\) | |||||||
\(252\) | 5.97857e19i | 0.231575i | ||||||||
\(253\) | 4.31935e20i | 1.61769i | ||||||||
\(254\) | 1.72038e20 | 0.623073 | ||||||||
\(255\) | −8.26773e19 | − | 1.72308e19i | −0.289597 | − | 0.0603552i | ||||
\(256\) | 1.84467e19 | 0.0625000 | ||||||||
\(257\) | − | 3.29126e20i | − | 1.07877i | −0.842058 | − | 0.539387i | \(-0.818656\pi\) | ||
0.842058 | − | 0.539387i | \(-0.181344\pi\) | |||||||
\(258\) | 6.21225e19i | 0.197007i | ||||||||
\(259\) | −2.55861e20 | −0.785155 | ||||||||
\(260\) | −1.54961e19 | + | 7.43538e19i | −0.0460203 | + | 0.220816i | ||||
\(261\) | 1.50660e20 | 0.433065 | ||||||||
\(262\) | − | 4.22584e20i | − | 1.17585i | ||||||
\(263\) | 1.11758e20i | 0.301062i | 0.988605 | + | 0.150531i | \(0.0480984\pi\) | ||||
−0.988605 | + | 0.150531i | \(0.951902\pi\) | |||||||
\(264\) | 3.01804e19 | 0.0787213 | ||||||||
\(265\) | −7.32684e19 | + | 3.51558e20i | −0.185066 | + | 0.887987i | ||||
\(266\) | −3.26047e19 | −0.0797601 | ||||||||
\(267\) | − | 7.38111e19i | − | 0.174894i | ||||||
\(268\) | 1.90218e20i | 0.436623i | ||||||||
\(269\) | −6.46127e20 | −1.43689 | −0.718445 | − | 0.695584i | \(-0.755146\pi\) | ||||
−0.718445 | + | 0.695584i | \(0.755146\pi\) | |||||||
\(270\) | −1.62382e20 | − | 3.38422e19i | −0.349902 | − | 0.0729234i | ||||
\(271\) | −1.97364e20 | −0.412125 | −0.206063 | − | 0.978539i | \(-0.566065\pi\) | ||||
−0.206063 | + | 0.978539i | \(0.566065\pi\) | |||||||
\(272\) | 1.39639e20i | 0.282599i | ||||||||
\(273\) | − | 2.99229e19i | − | 0.0586977i | ||||||
\(274\) | 6.47825e20 | 1.23191 | ||||||||
\(275\) | 4.23075e20 | + | 1.84354e20i | 0.779991 | + | 0.339880i | ||||
\(276\) | 1.39171e20 | 0.248783 | ||||||||
\(277\) | − | 8.57818e20i | − | 1.48702i | −0.668725 | − | 0.743510i | \(-0.733160\pi\) | ||
0.668725 | − | 0.743510i | \(-0.266840\pi\) | |||||||
\(278\) | − | 7.10756e20i | − | 1.19492i | ||||||
\(279\) | −1.51683e20 | −0.247344 | ||||||||
\(280\) | −1.08792e20 | − | 2.26735e19i | −0.172090 | − | 0.0358653i | ||||
\(281\) | −8.95650e20 | −1.37447 | −0.687234 | − | 0.726436i | \(-0.741175\pi\) | ||||
−0.687234 | + | 0.726436i | \(0.741175\pi\) | |||||||
\(282\) | − | 9.81052e19i | − | 0.146075i | ||||||
\(283\) | − | 7.82868e20i | − | 1.13111i | −0.824712 | − | 0.565553i | \(-0.808663\pi\) | ||
0.824712 | − | 0.565553i | \(-0.191337\pi\) | |||||||
\(284\) | 4.72473e20 | 0.662477 | ||||||||
\(285\) | 8.90089e18 | − | 4.27084e19i | 0.0121130 | − | 0.0581209i | ||||
\(286\) | 2.05461e20 | 0.271405 | ||||||||
\(287\) | − | 2.99555e20i | − | 0.384132i | ||||||
\(288\) | 1.32267e20i | 0.164670i | ||||||||
\(289\) | −2.29804e20 | −0.277796 | ||||||||
\(290\) | −5.71371e19 | + | 2.74157e20i | −0.0670711 | + | 0.321822i | ||||
\(291\) | 3.89998e20 | 0.444603 | ||||||||
\(292\) | − | 2.72759e20i | − | 0.302012i | ||||||
\(293\) | 7.78207e20i | 0.836991i | 0.908219 | + | 0.418495i | \(0.137442\pi\) | ||||
−0.908219 | + | 0.418495i | \(0.862558\pi\) | |||||||
\(294\) | −1.33324e20 | −0.139302 | ||||||||
\(295\) | 1.13370e21 | + | 2.36275e20i | 1.15083 | + | 0.239845i | ||||
\(296\) | −5.66054e20 | −0.558314 | ||||||||
\(297\) | 4.48709e20i | 0.430066i | ||||||||
\(298\) | 3.81423e20i | 0.355278i | ||||||||
\(299\) | 9.47438e20 | 0.857720 | ||||||||
\(300\) | 5.93994e19 | − | 1.36316e20i | 0.0522698 | − | 0.119954i | ||||
\(301\) | −6.18796e20 | −0.529337 | ||||||||
\(302\) | 7.32095e20i | 0.608847i | ||||||||
\(303\) | 4.17208e20i | 0.337357i | ||||||||
\(304\) | −7.21330e19 | −0.0567164 | ||||||||
\(305\) | −1.02702e21 | − | 2.14041e20i | −0.785288 | − | 0.163662i | ||||
\(306\) | −1.00124e21 | −0.744571 | ||||||||
\(307\) | 6.36763e20i | 0.460577i | 0.973122 | + | 0.230288i | \(0.0739669\pi\) | ||||
−0.973122 | + | 0.230288i | \(0.926033\pi\) | |||||||
\(308\) | 3.00624e20i | 0.211516i | ||||||||
\(309\) | −6.69935e19 | −0.0458548 | ||||||||
\(310\) | 5.75252e19 | − | 2.76019e20i | 0.0383075 | − | 0.183808i | ||||
\(311\) | 1.01872e21 | 0.660069 | 0.330035 | − | 0.943969i | \(-0.392940\pi\) | ||||
0.330035 | + | 0.943969i | \(0.392940\pi\) | |||||||
\(312\) | − | 6.62000e19i | − | 0.0417392i | ||||||
\(313\) | 2.74009e20i | 0.168127i | 0.996460 | + | 0.0840636i | \(0.0267899\pi\) | ||||
−0.996460 | + | 0.0840636i | \(0.973210\pi\) | |||||||
\(314\) | −3.55970e20 | −0.212574 | ||||||||
\(315\) | 1.62573e20 | − | 7.80063e20i | 0.0944952 | − | 0.453409i | ||||
\(316\) | 3.11004e20 | 0.175965 | ||||||||
\(317\) | 2.82884e21i | 1.55814i | 0.626939 | + | 0.779068i | \(0.284307\pi\) | ||||
−0.626939 | + | 0.779068i | \(0.715693\pi\) | |||||||
\(318\) | − | 3.13005e20i | − | 0.167850i | ||||||
\(319\) | 7.57573e20 | 0.395552 | ||||||||
\(320\) | −2.40687e20 | − | 5.01617e19i | −0.122371 | − | 0.0255034i | ||||
\(321\) | 8.82166e20 | 0.436775 | ||||||||
\(322\) | 1.38626e21i | 0.668453i | ||||||||
\(323\) | − | 5.46035e20i | − | 0.256448i | ||||||
\(324\) | −8.73530e20 | −0.399618 | ||||||||
\(325\) | 4.04376e20 | − | 9.28004e20i | 0.180209 | − | 0.413563i | ||||
\(326\) | −6.84701e20 | −0.297270 | ||||||||
\(327\) | − | 2.99452e20i | − | 0.126669i | ||||||
\(328\) | − | 6.62720e20i | − | 0.273151i | ||||||
\(329\) | 9.77216e20 | 0.392487 | ||||||||
\(330\) | −3.93784e20 | − | 8.20687e19i | −0.154131 | − | 0.0321225i | ||||
\(331\) | 4.45083e20 | 0.169786 | 0.0848931 | − | 0.996390i | \(-0.472945\pi\) | ||||
0.0848931 | + | 0.996390i | \(0.472945\pi\) | |||||||
\(332\) | − | 1.03106e21i | − | 0.383362i | ||||||
\(333\) | − | 4.05872e21i | − | 1.47100i | ||||||
\(334\) | −5.37481e20 | −0.189897 | ||||||||
\(335\) | 5.17255e20 | − | 2.48190e21i | 0.178166 | − | 0.854877i | ||||
\(336\) | 9.68619e19 | 0.0325289 | ||||||||
\(337\) | − | 8.92853e20i | − | 0.292365i | −0.989258 | − | 0.146183i | \(-0.953301\pi\) | ||
0.989258 | − | 0.146183i | \(-0.0466987\pi\) | |||||||
\(338\) | 1.76383e21i | 0.563204i | ||||||||
\(339\) | −8.67151e20 | −0.270021 | ||||||||
\(340\) | 3.79716e20 | − | 1.82196e21i | 0.115316 | − | 0.553310i | ||||
\(341\) | −7.62719e20 | −0.225919 | ||||||||
\(342\) | − | 5.17208e20i | − | 0.149432i | ||||||
\(343\) | − | 3.09216e21i | − | 0.871490i | ||||||
\(344\) | −1.36899e21 | −0.376404 | ||||||||
\(345\) | −1.81585e21 | − | 3.78442e20i | −0.487099 | − | 0.101517i | ||||
\(346\) | 4.60007e21 | 1.20397 | ||||||||
\(347\) | 6.64293e21i | 1.69652i | 0.529579 | + | 0.848261i | \(0.322350\pi\) | ||||
−0.529579 | + | 0.848261i | \(0.677650\pi\) | |||||||
\(348\) | − | 2.44092e20i | − | 0.0608317i | ||||||
\(349\) | −5.41147e21 | −1.31613 | −0.658066 | − | 0.752961i | \(-0.728625\pi\) | ||||
−0.658066 | + | 0.752961i | \(0.728625\pi\) | |||||||
\(350\) | 1.35783e21 | + | 5.91671e20i | 0.322305 | + | 0.140444i | ||||
\(351\) | 9.84232e20 | 0.228027 | ||||||||
\(352\) | 6.65086e20i | 0.150406i | ||||||||
\(353\) | 3.84234e21i | 0.848225i | 0.905609 | + | 0.424113i | \(0.139414\pi\) | ||||
−0.905609 | + | 0.424113i | \(0.860586\pi\) | |||||||
\(354\) | −1.00937e21 | −0.217533 | ||||||||
\(355\) | −6.16466e21 | − | 1.28478e21i | −1.29708 | − | 0.270326i | ||||
\(356\) | 1.62658e21 | 0.334156 | ||||||||
\(357\) | 7.33229e20i | 0.147082i | ||||||||
\(358\) | − | 6.09873e21i | − | 1.19463i | ||||||
\(359\) | 7.97571e21 | 1.52569 | 0.762845 | − | 0.646581i | \(-0.223802\pi\) | ||||
0.762845 | + | 0.646581i | \(0.223802\pi\) | |||||||
\(360\) | 3.59669e20 | − | 1.72577e21i | 0.0671943 | − | 0.322413i | ||||
\(361\) | −5.19832e21 | −0.948532 | ||||||||
\(362\) | 6.04274e21i | 1.07699i | ||||||||
\(363\) | − | 4.15014e20i | − | 0.0722532i | ||||||
\(364\) | 6.59411e20 | 0.112149 | ||||||||
\(365\) | −7.41705e20 | + | 3.55886e21i | −0.123237 | + | 0.591319i | ||||
\(366\) | 9.14392e20 | 0.148437 | ||||||||
\(367\) | 3.93242e21i | 0.623733i | 0.950126 | + | 0.311866i | \(0.100954\pi\) | ||||
−0.950126 | + | 0.311866i | \(0.899046\pi\) | |||||||
\(368\) | 3.06690e21i | 0.475328i | ||||||||
\(369\) | 4.75184e21 | 0.719677 | ||||||||
\(370\) | 7.38567e21 | + | 1.53925e21i | 1.09314 | + | 0.227822i | ||||
\(371\) | 3.11781e21 | 0.450995 | ||||||||
\(372\) | 2.45750e20i | 0.0347439i | ||||||||
\(373\) | 2.14982e21i | 0.297082i | 0.988906 | + | 0.148541i | \(0.0474577\pi\) | ||||
−0.988906 | + | 0.148541i | \(0.952542\pi\) | |||||||
\(374\) | −5.03460e21 | −0.680074 | ||||||||
\(375\) | −1.14570e21 | + | 1.61708e21i | −0.151288 | + | 0.213533i | ||||
\(376\) | 2.16194e21 | 0.279092 | ||||||||
\(377\) | − | 1.66172e21i | − | 0.209728i | ||||||
\(378\) | 1.44010e21i | 0.177710i | ||||||||
\(379\) | −2.31293e21 | −0.279080 | −0.139540 | − | 0.990216i | \(-0.544562\pi\) | ||||
−0.139540 | + | 0.990216i | \(0.544562\pi\) | |||||||
\(380\) | 9.41166e20 | + | 1.96149e20i | 0.111047 | + | 0.0231433i | ||||
\(381\) | 1.99854e21 | 0.230595 | ||||||||
\(382\) | − | 8.43585e21i | − | 0.951898i | ||||||
\(383\) | 7.24934e21i | 0.800034i | 0.916508 | + | 0.400017i | \(0.130996\pi\) | ||||
−0.916508 | + | 0.400017i | \(0.869004\pi\) | |||||||
\(384\) | 2.14293e20 | 0.0231308 | ||||||||
\(385\) | 8.17478e20 | − | 3.92244e21i | 0.0863098 | − | 0.414133i | ||||
\(386\) | −3.95728e21 | −0.408700 | ||||||||
\(387\) | − | 9.81596e21i | − | 0.991721i | ||||||
\(388\) | 8.59439e21i | 0.849465i | ||||||||
\(389\) | 1.22297e22 | 1.18261 | 0.591306 | − | 0.806447i | \(-0.298612\pi\) | ||||
0.591306 | + | 0.806447i | \(0.298612\pi\) | |||||||
\(390\) | −1.80016e20 | + | 8.63754e20i | −0.0170318 | + | 0.0817224i | ||||
\(391\) | −2.32160e22 | −2.14924 | ||||||||
\(392\) | − | 2.93806e21i | − | 0.266152i | ||||||
\(393\) | − | 4.90909e21i | − | 0.435175i | ||||||
\(394\) | −6.10833e21 | −0.529913 | ||||||||
\(395\) | −4.05788e21 | − | 8.45705e20i | −0.344527 | − | 0.0718032i | ||||
\(396\) | −4.76880e21 | −0.396278 | ||||||||
\(397\) | − | 7.39980e21i | − | 0.601867i | −0.953645 | − | 0.300934i | \(-0.902702\pi\) | ||
0.953645 | − | 0.300934i | \(-0.0972983\pi\) | |||||||
\(398\) | − | 1.28351e22i | − | 1.02186i | ||||||
\(399\) | −3.78763e20 | −0.0295187 | ||||||||
\(400\) | 3.00399e21 | + | 1.30898e21i | 0.229187 | + | 0.0998676i | ||||
\(401\) | 2.64241e21 | 0.197366 | 0.0986832 | − | 0.995119i | \(-0.468537\pi\) | ||||
0.0986832 | + | 0.995119i | \(0.468537\pi\) | |||||||
\(402\) | 2.20973e21i | 0.161591i | ||||||||
\(403\) | 1.67300e21i | 0.119785i | ||||||||
\(404\) | −9.19401e21 | −0.644560 | ||||||||
\(405\) | 1.13975e22 | + | 2.37536e21i | 0.782425 | + | 0.163066i | ||||
\(406\) | 2.43138e21 | 0.163448 | ||||||||
\(407\) | − | 2.04087e22i | − | 1.34358i | ||||||
\(408\) | 1.62216e21i | 0.104588i | ||||||||
\(409\) | 1.85381e22 | 1.17063 | 0.585313 | − | 0.810808i | \(-0.300972\pi\) | ||||
0.585313 | + | 0.810808i | \(0.300972\pi\) | |||||||
\(410\) | −1.80212e21 | + | 8.64695e21i | −0.111460 | + | 0.534811i | ||||
\(411\) | 7.52567e21 | 0.455921 | ||||||||
\(412\) | − | 1.47634e21i | − | 0.0876110i | ||||||
\(413\) | − | 1.00543e22i | − | 0.584487i | ||||||
\(414\) | −2.19903e22 | −1.25236 | ||||||||
\(415\) | −2.80372e21 | + | 1.34529e22i | −0.156432 | + | 0.750596i | ||||
\(416\) | 1.45885e21 | 0.0797475 | ||||||||
\(417\) | − | 8.25672e21i | − | 0.442233i | ||||||
\(418\) | − | 2.60071e21i | − | 0.136488i | ||||||
\(419\) | 1.33787e22 | 0.688010 | 0.344005 | − | 0.938968i | \(-0.388216\pi\) | ||||
0.344005 | + | 0.938968i | \(0.388216\pi\) | |||||||
\(420\) | −1.26382e21 | − | 2.63394e20i | −0.0636893 | − | 0.0132735i | ||||
\(421\) | 1.34296e22 | 0.663233 | 0.331616 | − | 0.943414i | \(-0.392406\pi\) | ||||
0.331616 | + | 0.943414i | \(0.392406\pi\) | |||||||
\(422\) | − | 1.01225e22i | − | 0.489928i | ||||||
\(423\) | 1.55016e22i | 0.735331i | ||||||||
\(424\) | 6.89770e21 | 0.320697 | ||||||||
\(425\) | −9.90881e21 | + | 2.27398e22i | −0.451560 | + | 1.03629i | ||||
\(426\) | 5.48863e21 | 0.245179 | ||||||||
\(427\) | 9.10816e21i | 0.398836i | ||||||||
\(428\) | 1.94403e22i | 0.834509i | ||||||||
\(429\) | 2.38680e21 | 0.100445 | ||||||||
\(430\) | 1.78622e22 | + | 3.72266e21i | 0.736974 | + | 0.153593i | ||||
\(431\) | −2.93523e22 | −1.18737 | −0.593685 | − | 0.804698i | \(-0.702327\pi\) | ||||
−0.593685 | + | 0.804698i | \(0.702327\pi\) | |||||||
\(432\) | 3.18601e21i | 0.126367i | ||||||||
\(433\) | 2.26238e22i | 0.879870i | 0.898030 | + | 0.439935i | \(0.144998\pi\) | ||||
−0.898030 | + | 0.439935i | \(0.855002\pi\) | |||||||
\(434\) | −2.44789e21 | −0.0933532 | ||||||||
\(435\) | −6.63752e20 | + | 3.18483e21i | −0.0248226 | + | 0.119104i | ||||
\(436\) | 6.59902e21 | 0.242016 | ||||||||
\(437\) | − | 1.19926e22i | − | 0.431342i | ||||||
\(438\) | − | 3.16859e21i | − | 0.111773i | ||||||
\(439\) | −4.27977e22 | −1.48072 | −0.740359 | − | 0.672211i | \(-0.765345\pi\) | ||||
−0.740359 | + | 0.672211i | \(0.765345\pi\) | |||||||
\(440\) | 1.80855e21 | − | 8.67782e21i | 0.0613738 | − | 0.294485i | ||||
\(441\) | 2.10665e22 | 0.701236 | ||||||||
\(442\) | 1.10433e22i | 0.360585i | ||||||||
\(443\) | − | 6.70939e20i | − | 0.0214908i | −0.999942 | − | 0.0107454i | \(-0.996580\pi\) | ||
0.999942 | − | 0.0107454i | \(-0.00342043\pi\) | |||||||
\(444\) | −6.57575e21 | −0.206628 | ||||||||
\(445\) | −2.12230e22 | − | 4.42310e21i | −0.654255 | − | 0.136354i | ||||
\(446\) | −3.28212e21 | −0.0992678 | ||||||||
\(447\) | 4.43092e21i | 0.131486i | ||||||||
\(448\) | 2.13455e21i | 0.0621502i | ||||||||
\(449\) | 1.57543e22 | 0.450096 | 0.225048 | − | 0.974348i | \(-0.427746\pi\) | ||||
0.225048 | + | 0.974348i | \(0.427746\pi\) | |||||||
\(450\) | −9.38568e21 | + | 2.15392e22i | −0.263123 | + | 0.603843i | ||||
\(451\) | 2.38940e22 | 0.657337 | ||||||||
\(452\) | − | 1.91094e22i | − | 0.515906i | ||||||
\(453\) | 8.50462e21i | 0.225331i | ||||||||
\(454\) | 4.47375e22 | 1.16331 | ||||||||
\(455\) | −8.60377e21 | − | 1.79312e21i | −0.219580 | − | 0.0457627i | ||||
\(456\) | −8.37956e20 | −0.0209904 | ||||||||
\(457\) | − | 7.49413e21i | − | 0.184261i | −0.995747 | − | 0.0921305i | \(-0.970632\pi\) | ||
0.995747 | − | 0.0921305i | \(-0.0293677\pi\) | |||||||
\(458\) | − | 1.43005e22i | − | 0.345139i | ||||||
\(459\) | −2.41176e22 | −0.571381 | ||||||||
\(460\) | 8.33974e21 | − | 4.00159e22i | 0.193959 | − | 0.930660i | ||||
\(461\) | −7.56013e21 | −0.172612 | −0.0863061 | − | 0.996269i | \(-0.527506\pi\) | ||||
−0.0863061 | + | 0.996269i | \(0.527506\pi\) | |||||||
\(462\) | 3.49230e21i | 0.0782806i | ||||||||
\(463\) | − | 3.41230e22i | − | 0.750946i | −0.926833 | − | 0.375473i | \(-0.877480\pi\) | ||
0.926833 | − | 0.375473i | \(-0.122520\pi\) | |||||||
\(464\) | 5.37906e21 | 0.116226 | ||||||||
\(465\) | 6.68260e20 | − | 3.20646e21i | 0.0141774 | − | 0.0680261i | ||||
\(466\) | 4.94953e22 | 1.03106 | ||||||||
\(467\) | − | 4.12036e22i | − | 0.842834i | −0.906867 | − | 0.421417i | \(-0.861533\pi\) | ||
0.906867 | − | 0.421417i | \(-0.138467\pi\) | |||||||
\(468\) | 1.04602e22i | 0.210113i | ||||||||
\(469\) | −2.20109e22 | −0.434179 | ||||||||
\(470\) | −2.82083e22 | − | 5.87891e21i | −0.546443 | − | 0.113885i | ||||
\(471\) | −4.13523e21 | −0.0786724 | ||||||||
\(472\) | − | 2.22436e22i | − | 0.415621i | ||||||
\(473\) | − | 4.93582e22i | − | 0.905816i | ||||||
\(474\) | 3.61288e21 | 0.0651235 | ||||||||
\(475\) | −1.17466e22 | − | 5.11857e21i | −0.207978 | − | 0.0906260i | ||||
\(476\) | −1.61582e22 | −0.281017 | ||||||||
\(477\) | 4.94579e22i | 0.844947i | ||||||||
\(478\) | − | 2.34049e22i | − | 0.392798i | ||||||
\(479\) | 1.24427e22 | 0.205146 | 0.102573 | − | 0.994725i | \(-0.467293\pi\) | ||||
0.102573 | + | 0.994725i | \(0.467293\pi\) | |||||||
\(480\) | −2.79601e21 | − | 5.82719e20i | −0.0452886 | − | 0.00943863i | ||||
\(481\) | −4.47660e22 | −0.712386 | ||||||||
\(482\) | 3.64469e22i | 0.569850i | ||||||||
\(483\) | 1.61040e22i | 0.247390i | ||||||||
\(484\) | 9.14568e21 | 0.138048 | ||||||||
\(485\) | 2.33705e22 | − | 1.12137e23i | 0.346627 | − | 1.66319i | ||||
\(486\) | −3.46715e22 | −0.505317 | ||||||||
\(487\) | 1.33157e23i | 1.90707i | 0.301281 | + | 0.953535i | \(0.402586\pi\) | ||||
−0.301281 | + | 0.953535i | \(0.597414\pi\) | |||||||
\(488\) | 2.01505e22i | 0.283607i | ||||||||
\(489\) | −7.95405e21 | −0.110018 | ||||||||
\(490\) | −7.98938e21 | + | 3.83348e22i | −0.108604 | + | 0.521107i | ||||
\(491\) | 4.18591e22 | 0.559238 | 0.279619 | − | 0.960111i | \(-0.409792\pi\) | ||||
0.279619 | + | 0.960111i | \(0.409792\pi\) | |||||||
\(492\) | − | 7.69870e21i | − | 0.101091i | ||||||
\(493\) | 4.07186e22i | 0.525526i | ||||||||
\(494\) | −5.70459e21 | −0.0723679 | ||||||||
\(495\) | 6.22217e22 | + | 1.29677e22i | 0.775886 | + | 0.161703i | ||||
\(496\) | −5.41559e21 | −0.0663822 | ||||||||
\(497\) | 5.46717e22i | 0.658769i | ||||||||
\(498\) | − | 1.19776e22i | − | 0.141880i | ||||||
\(499\) | −1.80695e22 | −0.210422 | −0.105211 | − | 0.994450i | \(-0.533552\pi\) | ||||
−0.105211 | + | 0.994450i | \(0.533552\pi\) | |||||||
\(500\) | −3.56356e22 | − | 2.52478e22i | −0.407980 | − | 0.289054i | ||||
\(501\) | −6.24383e21 | −0.0702797 | ||||||||
\(502\) | 8.63047e22i | 0.955109i | ||||||||
\(503\) | − | 9.01337e22i | − | 0.980752i | −0.871511 | − | 0.490376i | \(-0.836859\pi\) | ||
0.871511 | − | 0.490376i | \(-0.163141\pi\) | |||||||
\(504\) | −1.53051e22 | −0.163749 | ||||||||
\(505\) | 1.19960e23 | + | 2.50010e22i | 1.26200 | + | 0.263015i | ||||
\(506\) | −1.10575e23 | −1.14388 | ||||||||
\(507\) | 2.04901e22i | 0.208438i | ||||||||
\(508\) | 4.40418e22i | 0.440579i | ||||||||
\(509\) | 4.22002e22 | 0.415158 | 0.207579 | − | 0.978218i | \(-0.433442\pi\) | ||||
0.207579 | + | 0.978218i | \(0.433442\pi\) | |||||||
\(510\) | 4.41109e21 | − | 2.11654e22i | 0.0426776 | − | 0.204776i | ||||
\(511\) | 3.15620e22 | 0.300322 | ||||||||
\(512\) | 4.72237e21i | 0.0441942i | ||||||||
\(513\) | − | 1.24584e22i | − | 0.114674i | ||||||
\(514\) | 8.42563e22 | 0.762809 | ||||||||
\(515\) | −4.01455e21 | + | 1.92627e22i | −0.0357500 | + | 0.171536i | ||||
\(516\) | −1.59034e22 | −0.139305 | ||||||||
\(517\) | 7.79476e22i | 0.671635i | ||||||||
\(518\) | − | 6.55003e22i | − | 0.555189i | ||||||
\(519\) | 5.34382e22 | 0.445583 | ||||||||
\(520\) | −1.90346e22 | − | 3.96701e21i | −0.156140 | − | 0.0325413i | ||||
\(521\) | 8.04709e21 | 0.0649409 | 0.0324704 | − | 0.999473i | \(-0.489663\pi\) | ||||
0.0324704 | + | 0.999473i | \(0.489663\pi\) | |||||||
\(522\) | 3.85689e22i | 0.306223i | ||||||||
\(523\) | 3.43617e22i | 0.268417i | 0.990953 | + | 0.134209i | \(0.0428492\pi\) | ||||
−0.990953 | + | 0.134209i | \(0.957151\pi\) | |||||||
\(524\) | 1.08182e23 | 0.831452 | ||||||||
\(525\) | 1.57736e22 | + | 6.87334e21i | 0.119283 | + | 0.0519773i | ||||
\(526\) | −2.86101e22 | −0.212883 | ||||||||
\(527\) | − | 4.09952e22i | − | 0.300153i | ||||||
\(528\) | 7.72619e21i | 0.0556643i | ||||||||
\(529\) | −3.68844e23 | −2.61499 | ||||||||
\(530\) | −8.99987e22 | − | 1.87567e22i | −0.627902 | − | 0.130861i | ||||
\(531\) | 1.59491e23 | 1.09505 | ||||||||
\(532\) | − | 8.34679e21i | − | 0.0563989i | ||||||
\(533\) | − | 5.24109e22i | − | 0.348530i | ||||||
\(534\) | 1.88956e22 | 0.123669 | ||||||||
\(535\) | 5.28634e22 | − | 2.53650e23i | 0.340524 | − | 1.63391i | ||||
\(536\) | −4.86959e22 | −0.308739 | ||||||||
\(537\) | − | 7.08478e22i | − | 0.442125i | ||||||
\(538\) | − | 1.65408e23i | − | 1.01603i | ||||||
\(539\) | 1.05930e23 | 0.640493 | ||||||||
\(540\) | 8.66361e21 | − | 4.15699e22i | 0.0515646 | − | 0.247418i | ||||
\(541\) | −1.71006e23 | −1.00192 | −0.500961 | − | 0.865470i | \(-0.667020\pi\) | ||||
−0.500961 | + | 0.865470i | \(0.667020\pi\) | |||||||
\(542\) | − | 5.05252e22i | − | 0.291417i | ||||||
\(543\) | 7.01974e22i | 0.398586i | ||||||||
\(544\) | −3.57476e22 | −0.199828 | ||||||||
\(545\) | −8.61017e22 | − | 1.79445e22i | −0.473851 | − | 0.0987556i | ||||
\(546\) | 7.66026e21 | 0.0415056 | ||||||||
\(547\) | − | 1.89622e23i | − | 1.01157i | −0.862659 | − | 0.505787i | \(-0.831202\pi\) | ||
0.862659 | − | 0.505787i | \(-0.168798\pi\) | |||||||
\(548\) | 1.65843e23i | 0.871090i | ||||||||
\(549\) | −1.44483e23 | −0.747225 | ||||||||
\(550\) | −4.71947e22 | + | 1.08307e23i | −0.240331 | + | 0.551537i | ||||
\(551\) | −2.10339e22 | −0.105471 | ||||||||
\(552\) | 3.56277e22i | 0.175916i | ||||||||
\(553\) | 3.59875e22i | 0.174980i | ||||||||
\(554\) | 2.19601e23 | 1.05148 | ||||||||
\(555\) | 8.57981e22 | + | 1.78812e22i | 0.404564 | + | 0.0843154i | ||||
\(556\) | 1.81953e23 | 0.844937 | ||||||||
\(557\) | 2.07568e23i | 0.949274i | 0.880182 | + | 0.474637i | \(0.157421\pi\) | ||||
−0.880182 | + | 0.474637i | \(0.842579\pi\) | |||||||
\(558\) | − | 3.88309e22i | − | 0.174899i | ||||||
\(559\) | −1.08266e23 | −0.480277 | ||||||||
\(560\) | 5.80441e21 | − | 2.78508e22i | 0.0253606 | − | 0.121686i | ||||
\(561\) | −5.84860e22 | −0.251691 | ||||||||
\(562\) | − | 2.29286e23i | − | 0.971895i | ||||||
\(563\) | 2.04881e22i | 0.0855423i | 0.999085 | + | 0.0427712i | \(0.0136186\pi\) | ||||
−0.999085 | + | 0.0427712i | \(0.986381\pi\) | |||||||
\(564\) | 2.51149e22 | 0.103290 | ||||||||
\(565\) | −5.19637e22 | + | 2.49333e23i | −0.210517 | + | 1.01011i | ||||
\(566\) | 2.00414e23 | 0.799813 | ||||||||
\(567\) | − | 1.01080e23i | − | 0.397381i | ||||||
\(568\) | 1.20953e23i | 0.468442i | ||||||||
\(569\) | 9.64035e22 | 0.367823 | 0.183911 | − | 0.982943i | \(-0.441124\pi\) | ||||
0.183911 | + | 0.982943i | \(0.441124\pi\) | |||||||
\(570\) | 1.09334e22 | + | 2.27863e21i | 0.0410977 | + | 0.00856520i | ||||
\(571\) | 2.17004e23 | 0.803640 | 0.401820 | − | 0.915719i | \(-0.368378\pi\) | ||||
0.401820 | + | 0.915719i | \(0.368378\pi\) | |||||||
\(572\) | 5.25980e22i | 0.191912i | ||||||||
\(573\) | − | 9.79978e22i | − | 0.352291i | ||||||
\(574\) | 7.66860e22 | 0.271622 | ||||||||
\(575\) | −2.17628e23 | + | 4.99435e23i | −0.759518 | + | 1.74302i | ||||
\(576\) | −3.38603e22 | −0.116439 | ||||||||
\(577\) | − | 2.31188e23i | − | 0.783376i | −0.920098 | − | 0.391688i | \(-0.871891\pi\) | ||
0.920098 | − | 0.391688i | \(-0.128109\pi\) | |||||||
\(578\) | − | 5.88299e22i | − | 0.196432i | ||||||
\(579\) | −4.59710e22 | −0.151257 | ||||||||
\(580\) | −7.01841e22 | − | 1.46271e22i | −0.227562 | − | 0.0474264i | ||||
\(581\) | 1.19308e23 | 0.381216 | ||||||||
\(582\) | 9.98395e22i | 0.314382i | ||||||||
\(583\) | 2.48692e23i | 0.771755i | ||||||||
\(584\) | 6.98262e22 | 0.213555 | ||||||||
\(585\) | 2.84442e22 | − | 1.36482e23i | 0.0857372 | − | 0.411386i | ||||
\(586\) | −1.99221e23 | −0.591842 | ||||||||
\(587\) | 1.48857e23i | 0.435858i | 0.975965 | + | 0.217929i | \(0.0699301\pi\) | ||||
−0.975965 | + | 0.217929i | \(0.930070\pi\) | |||||||
\(588\) | − | 3.41309e22i | − | 0.0985010i | ||||||
\(589\) | 2.11768e22 | 0.0602393 | ||||||||
\(590\) | −6.04863e22 | + | 2.90227e23i | −0.169596 | + | 0.813758i | ||||
\(591\) | −7.09593e22 | −0.196117 | ||||||||
\(592\) | − | 1.44910e23i | − | 0.394787i | ||||||
\(593\) | 4.31467e23i | 1.15873i | 0.815068 | + | 0.579366i | \(0.196700\pi\) | ||||
−0.815068 | + | 0.579366i | \(0.803300\pi\) | |||||||
\(594\) | −1.14870e23 | −0.304103 | ||||||||
\(595\) | 2.10826e23 | + | 4.39384e22i | 0.550213 | + | 0.114670i | ||||
\(596\) | −9.76443e22 | −0.251220 | ||||||||
\(597\) | − | 1.49103e23i | − | 0.378185i | ||||||
\(598\) | 2.42544e23i | 0.606500i | ||||||||
\(599\) | −3.97221e23 | −0.979275 | −0.489637 | − | 0.871926i | \(-0.662871\pi\) | ||||
−0.489637 | + | 0.871926i | \(0.662871\pi\) | |||||||
\(600\) | 3.48969e22 | + | 1.52062e22i | 0.0848205 | + | 0.0369604i | ||||
\(601\) | 3.06679e23 | 0.734938 | 0.367469 | − | 0.930036i | \(-0.380224\pi\) | ||||
0.367469 | + | 0.930036i | \(0.380224\pi\) | |||||||
\(602\) | − | 1.58412e23i | − | 0.374298i | ||||||
\(603\) | − | 3.49159e23i | − | 0.813442i | ||||||
\(604\) | −1.87416e23 | −0.430520 | ||||||||
\(605\) | −1.19330e23 | − | 2.48696e22i | −0.270289 | − | 0.0563310i | ||||
\(606\) | −1.06805e23 | −0.238548 | ||||||||
\(607\) | − | 7.44484e23i | − | 1.63965i | −0.572614 | − | 0.819825i | \(-0.694070\pi\) | ||
0.572614 | − | 0.819825i | \(-0.305930\pi\) | |||||||
\(608\) | − | 1.84660e22i | − | 0.0401045i | ||||||
\(609\) | 2.82448e22 | 0.0604912 | ||||||||
\(610\) | 5.47946e22 | − | 2.62916e23i | 0.115727 | − | 0.555282i | ||||
\(611\) | 1.70976e23 | 0.356111 | ||||||||
\(612\) | − | 2.56317e23i | − | 0.526491i | ||||||
\(613\) | − | 4.11346e23i | − | 0.833285i | −0.909070 | − | 0.416642i | \(-0.863207\pi\) | ||
0.909070 | − | 0.416642i | \(-0.136793\pi\) | |||||||
\(614\) | −1.63011e23 | −0.325677 | ||||||||
\(615\) | −2.09349e22 | + | 1.00450e23i | −0.0412507 | + | 0.197930i | ||||
\(616\) | −7.69598e22 | −0.149564 | ||||||||
\(617\) | − | 4.85159e23i | − | 0.929951i | −0.885324 | − | 0.464975i | \(-0.846063\pi\) | ||
0.885324 | − | 0.464975i | \(-0.153937\pi\) | |||||||
\(618\) | − | 1.71503e22i | − | 0.0324243i | ||||||
\(619\) | 7.11624e23 | 1.32703 | 0.663514 | − | 0.748164i | \(-0.269064\pi\) | ||||
0.663514 | + | 0.748164i | \(0.269064\pi\) | |||||||
\(620\) | 7.06608e22 | + | 1.47265e22i | 0.129972 | + | 0.0270875i | ||||
\(621\) | −5.29696e23 | −0.961055 | ||||||||
\(622\) | 2.60791e23i | 0.466739i | ||||||||
\(623\) | 1.88218e23i | 0.332286i | ||||||||
\(624\) | 1.69472e22 | 0.0295141 | ||||||||
\(625\) | 3.96305e23 | + | 4.26328e23i | 0.680847 | + | 0.732426i | ||||
\(626\) | −7.01463e22 | −0.118884 | ||||||||
\(627\) | − | 3.02120e22i | − | 0.0505133i | ||||||
\(628\) | − | 9.11282e22i | − | 0.150313i | ||||||
\(629\) | 1.09694e24 | 1.78506 | ||||||||
\(630\) | 1.99696e23 | + | 4.16188e22i | 0.320608 | + | 0.0668182i | ||||
\(631\) | −1.18116e23 | −0.187093 | −0.0935467 | − | 0.995615i | \(-0.529820\pi\) | ||||
−0.0935467 | + | 0.995615i | \(0.529820\pi\) | |||||||
\(632\) | 7.96171e22i | 0.124426i | ||||||||
\(633\) | − | 1.17591e23i | − | 0.181319i | ||||||
\(634\) | −7.24184e23 | −1.10177 | ||||||||
\(635\) | 1.19762e23 | − | 5.74642e23i | 0.179780 | − | 0.862623i | ||||
\(636\) | 8.01293e22 | 0.118688 | ||||||||
\(637\) | − | 2.32355e23i | − | 0.339599i | ||||||
\(638\) | 1.93939e23i | 0.279698i | ||||||||
\(639\) | −8.67258e23 | −1.23422 | ||||||||
\(640\) | 1.28414e22 | − | 6.16158e22i | 0.0180336 | − | 0.0865291i | ||||
\(641\) | −1.00048e24 | −1.38648 | −0.693240 | − | 0.720707i | \(-0.743817\pi\) | ||||
−0.693240 | + | 0.720707i | \(0.743817\pi\) | |||||||
\(642\) | 2.25834e23i | 0.308846i | ||||||||
\(643\) | 1.69711e23i | 0.229043i | 0.993421 | + | 0.114521i | \(0.0365334\pi\) | ||||
−0.993421 | + | 0.114521i | \(0.963467\pi\) | |||||||
\(644\) | −3.54883e23 | −0.472668 | ||||||||
\(645\) | 2.07501e23 | + | 4.32455e22i | 0.272749 | + | 0.0568438i | ||||
\(646\) | 1.39785e23 | 0.181336 | ||||||||
\(647\) | 1.31645e24i | 1.68546i | 0.538338 | + | 0.842729i | \(0.319052\pi\) | ||||
−0.538338 | + | 0.842729i | \(0.680948\pi\) | |||||||
\(648\) | − | 2.23624e23i | − | 0.282573i | ||||||
\(649\) | 8.01979e23 | 1.00019 | ||||||||
\(650\) | 2.37569e23 | + | 1.03520e23i | 0.292433 | + | 0.127427i | ||||
\(651\) | −2.84367e22 | −0.0345494 | ||||||||
\(652\) | − | 1.75284e23i | − | 0.210202i | ||||||
\(653\) | 8.36567e23i | 0.990236i | 0.868826 | + | 0.495118i | \(0.164875\pi\) | ||||
−0.868826 | + | 0.495118i | \(0.835125\pi\) | |||||||
\(654\) | 7.66596e22 | 0.0895686 | ||||||||
\(655\) | −1.41152e24 | − | 2.94175e23i | −1.62793 | − | 0.339277i | ||||
\(656\) | 1.69656e23 | 0.193147 | ||||||||
\(657\) | 5.00668e23i | 0.562658i | ||||||||
\(658\) | 2.50167e23i | 0.277530i | ||||||||
\(659\) | 5.10849e23 | 0.559457 | 0.279728 | − | 0.960079i | \(-0.409756\pi\) | ||||
0.279728 | + | 0.960079i | \(0.409756\pi\) | |||||||
\(660\) | 2.10096e22 | − | 1.00809e23i | 0.0227140 | − | 0.108987i | ||||
\(661\) | 4.02261e23 | 0.429334 | 0.214667 | − | 0.976687i | \(-0.431133\pi\) | ||||
0.214667 | + | 0.976687i | \(0.431133\pi\) | |||||||
\(662\) | 1.13941e23i | 0.120057i | ||||||||
\(663\) | 1.28288e23i | 0.133450i | ||||||||
\(664\) | 2.63951e23 | 0.271078 | ||||||||
\(665\) | −2.26972e22 | + | 1.08906e23i | −0.0230138 | + | 0.110425i | ||||
\(666\) | 1.03903e24 | 1.04016 | ||||||||
\(667\) | 8.94307e23i | 0.883928i | ||||||||
\(668\) | − | 1.37595e23i | − | 0.134278i | ||||||
\(669\) | −3.81278e22 | −0.0367384 | ||||||||
\(670\) | 6.35367e23 | + | 1.32417e23i | 0.604489 | + | 0.125982i | ||||
\(671\) | −7.26513e23 | −0.682499 | ||||||||
\(672\) | 2.47966e22i | 0.0230014i | ||||||||
\(673\) | − | 7.03551e23i | − | 0.644418i | −0.946669 | − | 0.322209i | \(-0.895575\pi\) | ||
0.946669 | − | 0.322209i | \(-0.104425\pi\) | |||||||
\(674\) | 2.28570e23 | 0.206734 | ||||||||
\(675\) | −2.26080e23 | + | 5.18831e23i | −0.201920 | + | 0.463387i | ||||
\(676\) | −4.51541e23 | −0.398245 | ||||||||
\(677\) | 6.68647e23i | 0.582362i | 0.956668 | + | 0.291181i | \(0.0940482\pi\) | ||||
−0.956668 | + | 0.291181i | \(0.905952\pi\) | |||||||
\(678\) | − | 2.21991e23i | − | 0.190934i | ||||||
\(679\) | −9.94491e23 | −0.844711 | ||||||||
\(680\) | 4.66422e23 | + | 9.72073e22i | 0.391249 | + | 0.0815404i | ||||
\(681\) | 5.19707e23 | 0.430535 | ||||||||
\(682\) | − | 1.95256e23i | − | 0.159749i | ||||||
\(683\) | − | 1.48694e24i | − | 1.20148i | −0.799445 | − | 0.600740i | \(-0.794873\pi\) | ||
0.799445 | − | 0.600740i | \(-0.205127\pi\) | |||||||
\(684\) | 1.32405e23 | 0.105664 | ||||||||
\(685\) | 4.50973e23 | − | 2.16387e24i | 0.355451 | − | 1.70553i | ||||
\(686\) | 7.91594e23 | 0.616237 | ||||||||
\(687\) | − | 1.66126e23i | − | 0.127734i | ||||||
\(688\) | − | 3.50462e23i | − | 0.266158i | ||||||
\(689\) | 5.45500e23 | 0.409196 | ||||||||
\(690\) | 9.68812e22 | − | 4.64857e23i | 0.0717831 | − | 0.344431i | ||||
\(691\) | 5.53790e23 | 0.405304 | 0.202652 | − | 0.979251i | \(-0.435044\pi\) | ||||
0.202652 | + | 0.979251i | \(0.435044\pi\) | |||||||
\(692\) | 1.17762e24i | 0.851339i | ||||||||
\(693\) | − | 5.51817e23i | − | 0.394060i | ||||||
\(694\) | −1.70059e24 | −1.19962 | ||||||||
\(695\) | −2.37407e24 | − | 4.94781e23i | −1.65433 | − | 0.344780i | ||||
\(696\) | 6.24875e22 | 0.0430145 | ||||||||
\(697\) | 1.28427e24i | 0.873330i | ||||||||
\(698\) | − | 1.38534e24i | − | 0.930645i | ||||||
\(699\) | 5.74978e23 | 0.381588 | ||||||||
\(700\) | −1.51468e23 | + | 3.47604e23i | −0.0993086 | + | 0.227904i | ||||
\(701\) | −3.73720e23 | −0.242071 | −0.121036 | − | 0.992648i | \(-0.538622\pi\) | ||||
−0.121036 | + | 0.992648i | \(0.538622\pi\) | |||||||
\(702\) | 2.51963e23i | 0.161240i | ||||||||
\(703\) | 5.66646e23i | 0.358254i | ||||||||
\(704\) | −1.70262e23 | −0.106353 | ||||||||
\(705\) | −3.27691e23 | − | 6.82943e22i | −0.202235 | − | 0.0421480i | ||||
\(706\) | −9.83640e23 | −0.599786 | ||||||||
\(707\) | − | 1.06388e24i | − | 0.640953i | ||||||
\(708\) | − | 2.58400e23i | − | 0.153819i | ||||||
\(709\) | 4.91345e23 | 0.288997 | 0.144499 | − | 0.989505i | \(-0.453843\pi\) | ||||
0.144499 | + | 0.989505i | \(0.453843\pi\) | |||||||
\(710\) | 3.28904e23 | − | 1.57815e24i | 0.191150 | − | 0.917177i | ||||
\(711\) | −5.70871e23 | −0.327828 | ||||||||
\(712\) | 4.16404e23i | 0.236284i | ||||||||
\(713\) | − | 9.00381e23i | − | 0.504853i | ||||||
\(714\) | −1.87707e23 | −0.104003 | ||||||||
\(715\) | 1.43028e23 | − | 6.86280e23i | 0.0783105 | − | 0.375751i | ||||
\(716\) | 1.56127e24 | 0.844731 | ||||||||
\(717\) | − | 2.71890e23i | − | 0.145372i | ||||||
\(718\) | 2.04178e24i | 1.07883i | ||||||||
\(719\) | −1.07832e24 | −0.563059 | −0.281529 | − | 0.959553i | \(-0.590842\pi\) | ||||
−0.281529 | + | 0.959553i | \(0.590842\pi\) | |||||||
\(720\) | 4.41798e23 | + | 9.20754e22i | 0.227980 | + | 0.0475135i | ||||
\(721\) | 1.70833e23 | 0.0871206 | ||||||||
\(722\) | − | 1.33077e24i | − | 0.670713i | ||||||
\(723\) | 4.23397e23i | 0.210898i | ||||||||
\(724\) | −1.54694e24 | −0.761546 | ||||||||
\(725\) | 8.75962e23 | + | 3.81699e23i | 0.426199 | + | 0.185715i | ||||
\(726\) | 1.06244e23 | 0.0510907 | ||||||||
\(727\) | 2.32801e24i | 1.10648i | 0.833023 | + | 0.553239i | \(0.186608\pi\) | ||||
−0.833023 | + | 0.553239i | \(0.813392\pi\) | |||||||
\(728\) | 1.68809e23i | 0.0793012i | ||||||||
\(729\) | 1.31854e24 | 0.612222 | ||||||||
\(730\) | −9.11069e23 | − | 1.89876e23i | −0.418126 | − | 0.0871418i | ||||
\(731\) | 2.65294e24 | 1.20346 | ||||||||
\(732\) | 2.34084e23i | 0.104961i | ||||||||
\(733\) | 2.98796e24i | 1.32431i | 0.749365 | + | 0.662157i | \(0.230359\pi\) | ||||
−0.749365 | + | 0.662157i | \(0.769641\pi\) | |||||||
\(734\) | −1.00670e24 | −0.441045 | ||||||||
\(735\) | −9.28112e22 | + | 4.45329e23i | −0.0401937 | + | 0.192858i | ||||
\(736\) | −7.85127e23 | −0.336108 | ||||||||
\(737\) | − | 1.75570e24i | − | 0.742980i | ||||||
\(738\) | 1.21647e24i | 0.508889i | ||||||||
\(739\) | 3.82346e24 | 1.58117 | 0.790585 | − | 0.612352i | \(-0.209777\pi\) | ||||
0.790585 | + | 0.612352i | \(0.209777\pi\) | |||||||
\(740\) | −3.94049e23 | + | 1.89073e24i | −0.161094 | + | 0.772966i | ||||
\(741\) | −6.62692e22 | −0.0267829 | ||||||||
\(742\) | 7.98160e23i | 0.318902i | ||||||||
\(743\) | − | 1.76990e24i | − | 0.699107i | −0.936916 | − | 0.349553i | \(-0.886333\pi\) | ||
0.936916 | − | 0.349553i | \(-0.113667\pi\) | |||||||
\(744\) | −6.29120e22 | −0.0245676 | ||||||||
\(745\) | 1.27403e24 | + | 2.65521e23i | 0.491871 | + | 0.102511i | ||||
\(746\) | −5.50353e23 | −0.210069 | ||||||||
\(747\) | 1.89258e24i | 0.714215i | ||||||||
\(748\) | − | 1.28886e24i | − | 0.480885i | ||||||
\(749\) | −2.24951e24 | −0.829838 | ||||||||
\(750\) | −4.13972e23 | − | 2.93300e23i | −0.150991 | − | 0.106977i | ||||
\(751\) | 1.13869e24 | 0.410645 | 0.205323 | − | 0.978694i | \(-0.434176\pi\) | ||||
0.205323 | + | 0.978694i | \(0.434176\pi\) | |||||||
\(752\) | 5.53458e23i | 0.197348i | ||||||||
\(753\) | 1.00259e24i | 0.353480i | ||||||||
\(754\) | 4.25400e23 | 0.148300 | ||||||||
\(755\) | 2.44534e24 | + | 5.09636e23i | 0.842929 | + | 0.175675i | ||||
\(756\) | −3.68665e23 | −0.125660 | ||||||||
\(757\) | − | 1.41930e24i | − | 0.478365i | −0.970975 | − | 0.239183i | \(-0.923121\pi\) | ||
0.970975 | − | 0.239183i | \(-0.0768795\pi\) | |||||||
\(758\) | − | 5.92109e23i | − | 0.197339i | ||||||
\(759\) | −1.28453e24 | −0.423341 | ||||||||
\(760\) | −5.02142e22 | + | 2.40939e23i | −0.0163648 | + | 0.0785219i | ||||
\(761\) | −4.87450e24 | −1.57094 | −0.785471 | − | 0.618898i | \(-0.787579\pi\) | ||||
−0.785471 | + | 0.618898i | \(0.787579\pi\) | |||||||
\(762\) | 5.11626e23i | 0.163055i | ||||||||
\(763\) | 7.63599e23i | 0.240662i | ||||||||
\(764\) | 2.15958e24 | 0.673093 | ||||||||
\(765\) | −6.96996e23 | + | 3.34434e24i | −0.214837 | + | 1.03083i | ||||
\(766\) | −1.85583e24 | −0.565710 | ||||||||
\(767\) | − | 1.75912e24i | − | 0.530316i | ||||||
\(768\) | 5.48589e22i | 0.0163560i | ||||||||
\(769\) | 3.78215e23 | 0.111523 | 0.0557616 | − | 0.998444i | \(-0.482241\pi\) | ||||
0.0557616 | + | 0.998444i | \(0.482241\pi\) | |||||||
\(770\) | 1.00414e24 | + | 2.09274e23i | 0.292836 | + | 0.0610302i | ||||
\(771\) | 9.78790e23 | 0.282311 | ||||||||
\(772\) | − | 1.01306e24i | − | 0.288995i | ||||||
\(773\) | − | 4.68953e24i | − | 1.32313i | −0.749886 | − | 0.661567i | \(-0.769892\pi\) | ||
0.749886 | − | 0.661567i | \(-0.230108\pi\) | |||||||
\(774\) | 2.51289e24 | 0.701253 | ||||||||
\(775\) | −8.81912e23 | − | 3.84292e23i | −0.243423 | − | 0.106071i | ||||
\(776\) | −2.20016e24 | −0.600663 | ||||||||
\(777\) | − | 7.60906e23i | − | 0.205472i | ||||||
\(778\) | 3.13079e24i | 0.836233i | ||||||||
\(779\) | −6.63414e23 | −0.175273 | ||||||||
\(780\) | −2.21121e23 | − | 4.60840e22i | −0.0577865 | − | 0.0120433i | ||||
\(781\) | −4.36089e24 | −1.12731 | ||||||||
\(782\) | − | 5.94329e24i | − | 1.51974i | ||||||
\(783\) | 9.29037e23i | 0.234995i | ||||||||
\(784\) | 7.52144e23 | 0.188198 | ||||||||
\(785\) | −2.47802e23 | + | 1.18901e24i | −0.0613357 | + | 0.294302i | ||||
\(786\) | 1.25673e24 | 0.307715 | ||||||||
\(787\) | − | 7.53697e24i | − | 1.82563i | −0.408379 | − | 0.912813i | \(-0.633906\pi\) | ||
0.408379 | − | 0.912813i | \(-0.366094\pi\) | |||||||
\(788\) | − | 1.56373e24i | − | 0.374705i | ||||||
\(789\) | −3.32359e23 | −0.0787867 | ||||||||
\(790\) | 2.16500e23 | − | 1.03882e24i | 0.0507725 | − | 0.243618i | ||||
\(791\) | 2.21123e24 | 0.513019 | ||||||||
\(792\) | − | 1.22081e24i | − | 0.280211i | ||||||
\(793\) | 1.59359e24i | 0.361871i | ||||||||
\(794\) | 1.89435e24 | 0.425585 | ||||||||
\(795\) | −1.04550e24 | − | 2.17893e23i | −0.232382 | − | 0.0484310i | ||||
\(796\) | 3.28578e24 | 0.722566 | ||||||||
\(797\) | − | 1.17363e24i | − | 0.255349i | −0.991816 | − | 0.127674i | \(-0.959249\pi\) | ||
0.991816 | − | 0.127674i | \(-0.0407512\pi\) | |||||||
\(798\) | − | 9.69632e22i | − | 0.0208729i | ||||||
\(799\) | −4.18959e24 | −0.892326 | ||||||||
\(800\) | −3.35100e23 | + | 7.69022e23i | −0.0706170 | + | 0.162059i | ||||
\(801\) | −2.98570e24 | −0.622543 | ||||||||
\(802\) | 6.76457e23i | 0.139559i | ||||||||
\(803\) | 2.51754e24i | 0.513919i | ||||||||
\(804\) | −5.65691e23 | −0.114262 | ||||||||
\(805\) | 4.63040e24 | + | 9.65024e23i | 0.925451 | + | 0.192874i | ||||
\(806\) | −4.28289e23 | −0.0847011 | ||||||||
\(807\) | − | 1.92152e24i | − | 0.376028i | ||||||
\(808\) | − | 2.35367e24i | − | 0.455773i | ||||||
\(809\) | −1.76470e24 | −0.338149 | −0.169075 | − | 0.985603i | \(-0.554078\pi\) | ||||
−0.169075 | + | 0.985603i | \(0.554078\pi\) | |||||||
\(810\) | −6.08093e23 | + | 2.91776e24i | −0.115305 | + | 0.553258i | ||||
\(811\) | 8.84401e24 | 1.65948 | 0.829740 | − | 0.558151i | \(-0.188489\pi\) | ||||
0.829740 | + | 0.558151i | \(0.188489\pi\) | |||||||
\(812\) | 6.22432e23i | 0.115575i | ||||||||
\(813\) | − | 5.86943e23i | − | 0.107851i | ||||||
\(814\) | 5.22464e24 | 0.950055 | ||||||||
\(815\) | −4.76643e23 | + | 2.28704e24i | −0.0857736 | + | 0.411561i | ||||
\(816\) | −4.15273e23 | −0.0739550 | ||||||||
\(817\) | 1.37043e24i | 0.241528i | ||||||||
\(818\) | 4.74576e24i | 0.827757i | ||||||||
\(819\) | −1.21040e24 | −0.208937 | ||||||||
\(820\) | −2.21362e24 | − | 4.61342e23i | −0.378168 | − | 0.0788143i | ||||
\(821\) | −4.68909e24 | −0.792815 | −0.396408 | − | 0.918075i | \(-0.629743\pi\) | ||||
−0.396408 | + | 0.918075i | \(0.629743\pi\) | |||||||
\(822\) | 1.92657e24i | 0.322385i | ||||||||
\(823\) | 5.49318e24i | 0.909756i | 0.890554 | + | 0.454878i | \(0.150317\pi\) | ||||
−0.890554 | + | 0.454878i | \(0.849683\pi\) | |||||||
\(824\) | 3.77942e23 | 0.0619503 | ||||||||
\(825\) | −5.48252e23 | + | 1.25819e24i | −0.0889450 | + | 0.204120i | ||||
\(826\) | 2.57389e24 | 0.413295 | ||||||||
\(827\) | − | 8.88420e23i | − | 0.141196i | −0.997505 | − | 0.0705978i | \(-0.977509\pi\) | ||
0.997505 | − | 0.0705978i | \(-0.0224907\pi\) | |||||||
\(828\) | − | 5.62952e24i | − | 0.885551i | ||||||
\(829\) | −2.89244e24 | −0.450350 | −0.225175 | − | 0.974318i | \(-0.572295\pi\) | ||||
−0.225175 | + | 0.974318i | \(0.572295\pi\) | |||||||
\(830\) | −3.44394e24 | − | 7.17753e23i | −0.530751 | − | 0.110614i | ||||
\(831\) | 2.55107e24 | 0.389147 | ||||||||
\(832\) | 3.73466e23i | 0.0563900i | ||||||||
\(833\) | 5.69361e24i | 0.850952i | ||||||||
\(834\) | 2.11372e24 | 0.312706 | ||||||||
\(835\) | −3.74159e23 | + | 1.79530e24i | −0.0547925 | + | 0.262906i | ||||
\(836\) | 6.65782e23 | 0.0965115 | ||||||||
\(837\) | − | 9.35347e23i | − | 0.134217i | ||||||
\(838\) | 3.42495e24i | 0.486497i | ||||||||
\(839\) | −1.16441e25 | −1.63730 | −0.818650 | − | 0.574293i | \(-0.805277\pi\) | ||||
−0.818650 | + | 0.574293i | \(0.805277\pi\) | |||||||
\(840\) | 6.74288e22 | − | 3.23538e23i | 0.00938580 | − | 0.0450351i | ||||
\(841\) | −5.68862e24 | −0.783864 | ||||||||
\(842\) | 3.43798e24i | 0.468976i | ||||||||
\(843\) | − | 2.66358e24i | − | 0.359692i | ||||||
\(844\) | 2.59136e24 | 0.346431 | ||||||||
\(845\) | 5.89156e24 | + | 1.22786e24i | 0.779737 | + | 0.162505i | ||||
\(846\) | −3.96841e24 | −0.519958 | ||||||||
\(847\) | 1.05828e24i | 0.137275i | ||||||||
\(848\) | 1.76581e24i | 0.226767i | ||||||||
\(849\) | 2.32817e24 | 0.296006 | ||||||||
\(850\) | −5.82138e24 | − | 2.53665e24i | −0.732765 | − | 0.319301i | ||||
\(851\) | 2.40923e25 | 3.00246 | ||||||||
\(852\) | 1.40509e24i | 0.173367i | ||||||||
\(853\) | 6.33999e24i | 0.774501i | 0.921975 | + | 0.387250i | \(0.126575\pi\) | ||||
−0.921975 | + | 0.387250i | \(0.873425\pi\) | |||||||
\(854\) | −2.33169e24 | −0.282019 | ||||||||
\(855\) | −1.72758e24 | − | 3.60046e23i | −0.206883 | − | 0.0431167i | ||||
\(856\) | −4.97672e24 | −0.590087 | ||||||||
\(857\) | 6.31715e24i | 0.741625i | 0.928708 | + | 0.370813i | \(0.120921\pi\) | ||||
−0.928708 | + | 0.370813i | \(0.879079\pi\) | |||||||
\(858\) | 6.11021e23i | 0.0710255i | ||||||||
\(859\) | 8.91034e24 | 1.02554 | 0.512770 | − | 0.858526i | \(-0.328619\pi\) | ||||
0.512770 | + | 0.858526i | \(0.328619\pi\) | |||||||
\(860\) | −9.53002e23 | + | 4.57271e24i | −0.108607 | + | 0.521119i | ||||
\(861\) | 8.90848e23 | 0.100526 | ||||||||
\(862\) | − | 7.51420e24i | − | 0.839597i | ||||||
\(863\) | − | 1.00324e25i | − | 1.10997i | −0.831861 | − | 0.554985i | \(-0.812724\pi\) | ||
0.831861 | − | 0.554985i | \(-0.187276\pi\) | |||||||
\(864\) | −8.15618e23 | −0.0893552 | ||||||||
\(865\) | 3.20226e24 | − | 1.53651e25i | 0.347392 | − | 1.66686i | ||||
\(866\) | −5.79169e24 | −0.622162 | ||||||||
\(867\) | − | 6.83417e23i | − | 0.0726981i | ||||||
\(868\) | − | 6.26660e23i | − | 0.0660107i | ||||||
\(869\) | −2.87055e24 | −0.299431 | ||||||||
\(870\) | −8.15316e23 | − | 1.69920e23i | −0.0842194 | − | 0.0175522i | ||||
\(871\) | −3.85108e24 | −0.393939 | ||||||||
\(872\) | 1.68935e24i | 0.171131i | ||||||||
\(873\) | − | 1.57756e25i | − | 1.58258i | ||||||
\(874\) | 3.07011e24 | 0.305005 | ||||||||
\(875\) | 2.92153e24 | − | 4.12353e24i | 0.287436 | − | 0.405696i | ||||
\(876\) | 8.11159e23 | 0.0790353 | ||||||||
\(877\) | − | 1.88816e24i | − | 0.182197i | −0.995842 | − | 0.0910986i | \(-0.970962\pi\) | ||
0.995842 | − | 0.0910986i | \(-0.0290378\pi\) | |||||||
\(878\) | − | 1.09562e25i | − | 1.04703i | ||||||
\(879\) | −2.31432e24 | −0.219037 | ||||||||
\(880\) | 2.22152e24 | + | 4.62989e23i | 0.208232 | + | 0.0433978i | ||||
\(881\) | 1.45784e24 | 0.135336 | 0.0676680 | − | 0.997708i | \(-0.478444\pi\) | ||||
0.0676680 | + | 0.997708i | \(0.478444\pi\) | |||||||
\(882\) | 5.39302e24i | 0.495849i | ||||||||
\(883\) | − | 5.53794e24i | − | 0.504292i | −0.967689 | − | 0.252146i | \(-0.918864\pi\) | ||
0.967689 | − | 0.252146i | \(-0.0811363\pi\) | |||||||
\(884\) | −2.82708e24 | −0.254972 | ||||||||
\(885\) | −7.02659e23 | + | 3.37151e24i | −0.0627663 | + | 0.301166i | ||||
\(886\) | 1.71760e23 | 0.0151963 | ||||||||
\(887\) | 1.80604e25i | 1.58262i | 0.611417 | + | 0.791309i | \(0.290600\pi\) | ||||
−0.611417 | + | 0.791309i | \(0.709400\pi\) | |||||||
\(888\) | − | 1.68339e24i | − | 0.146108i | ||||||
\(889\) | −5.09625e24 | −0.438113 | ||||||||
\(890\) | 1.13231e24 | − | 5.43309e24i | 0.0964166 | − | 0.462628i | ||||
\(891\) | 8.06262e24 | 0.680010 | ||||||||
\(892\) | − | 8.40223e23i | − | 0.0701929i | ||||||
\(893\) | − | 2.16421e24i | − | 0.179086i | ||||||
\(894\) | −1.13432e24 | −0.0929748 | ||||||||
\(895\) | −2.03710e25 | − | 4.24553e24i | −1.65392 | − | 0.344695i | ||||
\(896\) | −5.46444e23 | −0.0439468 | ||||||||
\(897\) | 2.81759e24i | 0.224462i | ||||||||
\(898\) | 4.03310e24i | 0.318266i | ||||||||
\(899\) | −1.57918e24 | −0.123445 | ||||||||
\(900\) | −5.51405e24 | − | 2.40274e24i | −0.426982 | − | 0.186056i | ||||
\(901\) | −1.33669e25 | −1.02535 | ||||||||
\(902\) | 6.11686e24i | 0.464808i | ||||||||
\(903\) | − | 1.84024e24i | − | 0.138525i | ||||||
\(904\) | 4.89201e24 | 0.364801 | ||||||||
\(905\) | 2.01839e25 | + | 4.20655e24i | 1.49105 | + | 0.310751i | ||||
\(906\) | −2.17718e24 | −0.159333 | ||||||||
\(907\) | − | 1.19863e24i | − | 0.0869010i | −0.999056 | − | 0.0434505i | \(-0.986165\pi\) | ||
0.999056 | − | 0.0434505i | \(-0.0138351\pi\) | |||||||
\(908\) | 1.14528e25i | 0.822587i | ||||||||
\(909\) | 1.68763e25 | 1.20084 | ||||||||
\(910\) | 4.59038e23 | − | 2.20257e24i | 0.0323591 | − | 0.155266i | ||||
\(911\) | −2.15950e25 | −1.50816 | −0.754078 | − | 0.656785i | \(-0.771916\pi\) | ||||
−0.754078 | + | 0.656785i | \(0.771916\pi\) | |||||||
\(912\) | − | 2.14517e23i | − | 0.0148424i | ||||||
\(913\) | 9.51658e24i | 0.652348i | ||||||||
\(914\) | 1.91850e24 | 0.130292 | ||||||||
\(915\) | 6.36538e23 | − | 3.05425e24i | 0.0428297 | − | 0.205506i | ||||
\(916\) | 3.66092e24 | 0.244050 | ||||||||
\(917\) | 1.25181e25i | 0.826799i | ||||||||
\(918\) | − | 6.17410e24i | − | 0.404027i | ||||||
\(919\) | −9.95266e24 | −0.645294 | −0.322647 | − | 0.946519i | \(-0.604573\pi\) | ||||
−0.322647 | + | 0.946519i | \(0.604573\pi\) | |||||||
\(920\) | 1.02441e25 | + | 2.13497e24i | 0.658076 | + | 0.137150i | ||||
\(921\) | −1.89367e24 | −0.120531 | ||||||||
\(922\) | − | 1.93539e24i | − | 0.122055i | ||||||
\(923\) | 9.56550e24i | 0.597714i | ||||||||
\(924\) | −8.94028e23 | −0.0553528 | ||||||||
\(925\) | 1.02828e25 | − | 2.35981e25i | 0.630823 | − | 1.44768i | ||||
\(926\) | 8.73548e24 | 0.530999 | ||||||||
\(927\) | 2.70992e24i | 0.163222i | ||||||||
\(928\) | 1.37704e24i | 0.0821842i | ||||||||
\(929\) | 1.13092e25 | 0.668806 | 0.334403 | − | 0.942430i | \(-0.391465\pi\) | ||||
0.334403 | + | 0.942430i | \(0.391465\pi\) | |||||||
\(930\) | 8.20854e23 | + | 1.71075e23i | 0.0481017 | + | 0.0100249i | ||||
\(931\) | −2.94114e24 | −0.170782 | ||||||||
\(932\) | 1.26708e25i | 0.729069i | ||||||||
\(933\) | 3.02956e24i | 0.172737i | ||||||||
\(934\) | 1.05481e25 | 0.595973 | ||||||||
\(935\) | −3.50475e24 | + | 1.68166e25i | −0.196227 | + | 0.941540i | ||||
\(936\) | −2.67782e24 | −0.148572 | ||||||||
\(937\) | 9.71463e24i | 0.534121i | 0.963680 | + | 0.267061i | \(0.0860524\pi\) | ||||
−0.963680 | + | 0.267061i | \(0.913948\pi\) | |||||||
\(938\) | − | 5.63479e24i | − | 0.307011i | ||||||
\(939\) | −8.14877e23 | −0.0439982 | ||||||||
\(940\) | 1.50500e24 | − | 7.22133e24i | 0.0805286 | − | 0.386394i | ||||
\(941\) | 7.36745e23 | 0.0390666 | 0.0195333 | − | 0.999809i | \(-0.493782\pi\) | ||||
0.0195333 | + | 0.999809i | \(0.493782\pi\) | |||||||
\(942\) | − | 1.05862e24i | − | 0.0556298i | ||||||
\(943\) | 2.82066e25i | 1.46893i | ||||||||
\(944\) | 5.69436e24 | 0.293889 | ||||||||
\(945\) | 4.81022e24 | + | 1.00250e24i | 0.246034 | + | 0.0512760i | ||||
\(946\) | 1.26357e25 | 0.640509 | ||||||||
\(947\) | 2.10628e25i | 1.05814i | 0.848579 | + | 0.529069i | \(0.177459\pi\) | ||||
−0.848579 | + | 0.529069i | \(0.822541\pi\) | |||||||
\(948\) | 9.24898e23i | 0.0460493i | ||||||||
\(949\) | 5.52217e24 | 0.272488 | ||||||||
\(950\) | 1.31035e24 | − | 3.00714e24i | 0.0640823 | − | 0.147063i | ||||
\(951\) | −8.41272e24 | −0.407757 | ||||||||
\(952\) | − | 4.13649e24i | − | 0.198709i | ||||||
\(953\) | − | 3.64294e25i | − | 1.73445i | −0.497915 | − | 0.867226i | \(-0.665901\pi\) | ||
0.497915 | − | 0.867226i | \(-0.334099\pi\) | |||||||
\(954\) | −1.26612e25 | −0.597468 | ||||||||
\(955\) | −2.81774e25 | − | 5.87247e24i | −1.31787 | − | 0.274658i | ||||
\(956\) | 5.99165e24 | 0.277750 | ||||||||
\(957\) | 2.25295e24i | 0.103514i | ||||||||
\(958\) | 3.18533e24i | 0.145060i | ||||||||
\(959\) | −1.91904e25 | −0.866214 | ||||||||
\(960\) | 1.49176e23 | − | 7.15780e23i | 0.00667412 | − | 0.0320239i | ||||
\(961\) | −2.09602e25 | −0.929494 | ||||||||
\(962\) | − | 1.14601e25i | − | 0.503733i | ||||||
\(963\) | − | 3.56841e25i | − | 1.55472i | ||||||
\(964\) | −9.33040e24 | −0.402945 | ||||||||
\(965\) | −2.75479e24 | + | 1.32181e25i | −0.117925 | + | 0.565831i | ||||
\(966\) | −4.12262e24 | −0.174931 | ||||||||
\(967\) | − | 4.62502e25i | − | 1.94531i | −0.232255 | − | 0.972655i | \(-0.574610\pi\) | ||
0.232255 | − | 0.972655i | \(-0.425390\pi\) | |||||||
\(968\) | 2.34129e24i | 0.0976147i | ||||||||
\(969\) | 1.62386e24 | 0.0671113 | ||||||||
\(970\) | 2.87070e25 | + | 5.98284e24i | 1.17606 | + | 0.245103i | ||||
\(971\) | 3.90538e25 | 1.58599 | 0.792995 | − | 0.609229i | \(-0.208521\pi\) | ||||
0.792995 | + | 0.609229i | \(0.208521\pi\) | |||||||
\(972\) | − | 8.87589e24i | − | 0.357313i | ||||||
\(973\) | 2.10546e25i | 0.840208i | ||||||||
\(974\) | −3.40881e25 | −1.34850 | ||||||||
\(975\) | 2.75980e24 | + | 1.20258e24i | 0.108228 | + | 0.0471600i | ||||
\(976\) | −5.15852e24 | −0.200540 | ||||||||
\(977\) | − | 2.75744e25i | − | 1.06268i | −0.847159 | − | 0.531340i | \(-0.821689\pi\) | ||
0.847159 | − | 0.531340i | \(-0.178311\pi\) | |||||||
\(978\) | − | 2.03624e24i | − | 0.0777944i | ||||||
\(979\) | −1.50132e25 | −0.568617 | ||||||||
\(980\) | −9.81371e24 | − | 2.04528e24i | −0.368478 | − | 0.0767947i | ||||
\(981\) | −1.21130e25 | −0.450884 | ||||||||
\(982\) | 1.07159e25i | 0.395441i | ||||||||
\(983\) | − | 1.24713e25i | − | 0.456253i | −0.973631 | − | 0.228127i | \(-0.926740\pi\) | ||
0.973631 | − | 0.228127i | \(-0.0732601\pi\) | |||||||
\(984\) | 1.97087e24 | 0.0714824 | ||||||||
\(985\) | −4.25221e24 | + | 2.04030e25i | −0.152900 | + | 0.733646i | ||||
\(986\) | −1.04240e25 | −0.371603 | ||||||||
\(987\) | 2.90615e24i | 0.102712i | ||||||||
\(988\) | − | 1.46038e24i | − | 0.0511718i | ||||||
\(989\) | 5.82669e25 | 2.02420 | ||||||||
\(990\) | −3.31972e24 | + | 1.59288e25i | −0.114341 | + | 0.548634i | ||||
\(991\) | 4.73657e25 | 1.61748 | 0.808738 | − | 0.588168i | \(-0.200151\pi\) | ||||
0.808738 | + | 0.588168i | \(0.200151\pi\) | |||||||
\(992\) | − | 1.38639e24i | − | 0.0469393i | ||||||
\(993\) | 1.32363e24i | 0.0444323i | ||||||||
\(994\) | −1.39960e25 | −0.465820 | ||||||||
\(995\) | −4.28717e25 | − | 8.93492e24i | −1.41473 | − | 0.294846i | ||||
\(996\) | 3.06627e24 | 0.100324 | ||||||||
\(997\) | − | 4.03130e25i | − | 1.30778i | −0.756588 | − | 0.653892i | \(-0.773135\pi\) | ||
0.756588 | − | 0.653892i | \(-0.226865\pi\) | |||||||
\(998\) | − | 4.62579e24i | − | 0.148791i | ||||||
\(999\) | 2.50279e25 | 0.798211 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 10.18.b.a.9.7 | yes | 8 | |
3.2 | odd | 2 | 90.18.c.b.19.1 | 8 | |||
4.3 | odd | 2 | 80.18.c.a.49.4 | 8 | |||
5.2 | odd | 4 | 50.18.a.j.1.3 | 4 | |||
5.3 | odd | 4 | 50.18.a.k.1.2 | 4 | |||
5.4 | even | 2 | inner | 10.18.b.a.9.2 | ✓ | 8 | |
15.14 | odd | 2 | 90.18.c.b.19.5 | 8 | |||
20.19 | odd | 2 | 80.18.c.a.49.5 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
10.18.b.a.9.2 | ✓ | 8 | 5.4 | even | 2 | inner | |
10.18.b.a.9.7 | yes | 8 | 1.1 | even | 1 | trivial | |
50.18.a.j.1.3 | 4 | 5.2 | odd | 4 | |||
50.18.a.k.1.2 | 4 | 5.3 | odd | 4 | |||
80.18.c.a.49.4 | 8 | 4.3 | odd | 2 | |||
80.18.c.a.49.5 | 8 | 20.19 | odd | 2 | |||
90.18.c.b.19.1 | 8 | 3.2 | odd | 2 | |||
90.18.c.b.19.5 | 8 | 15.14 | odd | 2 |