Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2700,3,Mod(449,2700)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2700, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 5, 3]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2700.449");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2700 = 2^{2} \cdot 3^{3} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 2700.u (of order \(6\), degree \(2\), not 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: | \(73.5696713773\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{6})\) |
Coefficient field: | 8.0.303595776.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 5x^{6} + 16x^{4} + 45x^{2} + 81 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{17}]\) |
Coefficient ring index: | \( 3^{4} \) |
Twist minimal: | no (minimal twist has level 36) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 449.4 | ||
Root | \(0.396143 + 1.68614i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2700.449 |
Dual form | 2700.3.u.b.2249.4 |
$q$-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 \(\left(\mathbb{Z}/2700\mathbb{Z}\right)^\times\).
\(n\) | \(1001\) | \(1351\) | \(2377\) |
\(\chi(n)\) | \(e\left(\frac{5}{6}\right)\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 7.89542 | − | 4.55842i | 1.12792 | − | 0.651203i | 0.184507 | − | 0.982831i | \(-0.440931\pi\) |
0.943410 | + | 0.331628i | \(0.107598\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.383156 | − | 0.221215i | 0.0348324 | − | 0.0201105i | −0.482483 | − | 0.875906i | \(-0.660265\pi\) |
0.517315 | + | 0.855795i | \(0.326932\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −9.62747 | − | 5.55842i | −0.740575 | − | 0.427571i | 0.0817036 | − | 0.996657i | \(-0.473964\pi\) |
−0.822278 | + | 0.569086i | \(0.807297\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −8.01544 | −0.471497 | −0.235748 | − | 0.971814i | \(-0.575754\pi\) | ||||
−0.235748 | + | 0.971814i | \(0.575754\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 8.11684 | 0.427202 | 0.213601 | − | 0.976921i | \(-0.431481\pi\) | ||||
0.213601 | + | 0.976921i | \(0.431481\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −11.8020 | + | 20.4416i | −0.513128 | + | 0.888764i | 0.486756 | + | 0.873538i | \(0.338180\pi\) |
−0.999884 | + | 0.0152262i | \(0.995153\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −45.9090 | + | 26.5055i | −1.58307 | + | 0.913984i | −0.588659 | + | 0.808381i | \(0.700344\pi\) |
−0.994408 | + | 0.105603i | \(0.966323\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −14.6753 | + | 25.4183i | −0.473396 | + | 0.819945i | −0.999536 | − | 0.0304523i | \(-0.990305\pi\) |
0.526141 | + | 0.850398i | \(0.323639\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 18.4674i | 0.499118i | 0.968360 | + | 0.249559i | \(0.0802857\pi\) | ||||
−0.968360 | + | 0.249559i | \(0.919714\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 38.9674 | + | 22.4978i | 0.950424 | + | 0.548727i | 0.893213 | − | 0.449635i | \(-0.148446\pi\) |
0.0572112 | + | 0.998362i | \(0.481779\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −19.9186 | + | 11.5000i | −0.463223 | + | 0.267442i | −0.713398 | − | 0.700759i | \(-0.752845\pi\) |
0.250176 | + | 0.968200i | \(0.419512\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 4.22894 | + | 7.32473i | 0.0899774 | + | 0.155845i | 0.907501 | − | 0.420049i | \(-0.137987\pi\) |
−0.817524 | + | 0.575895i | \(0.804654\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 17.0584 | − | 29.5461i | 0.348131 | − | 0.602981i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −60.5841 | −1.14310 | −0.571548 | − | 0.820569i | \(-0.693657\pi\) | ||||
−0.571548 | + | 0.820569i | \(0.693657\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 65.9674 | + | 38.0863i | 1.11809 | + | 0.645530i | 0.940913 | − | 0.338649i | \(-0.109970\pi\) |
0.177178 | + | 0.984179i | \(0.443303\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −2.67527 | − | 4.63370i | −0.0438568 | − | 0.0759622i | 0.843264 | − | 0.537500i | \(-0.180631\pi\) |
−0.887121 | + | 0.461538i | \(0.847298\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 95.0039 | + | 54.8505i | 1.41797 | + | 0.818665i | 0.996120 | − | 0.0880017i | \(-0.0280481\pi\) |
0.421848 | + | 0.906666i | \(0.361381\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 16.0309i | − | 0.225787i | −0.993607 | − | 0.112894i | \(-0.963988\pi\) | ||
0.993607 | − | 0.112894i | \(-0.0360119\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 4.35053i | 0.0595963i | 0.999556 | + | 0.0297982i | \(0.00948645\pi\) | ||||
−0.999556 | + | 0.0297982i | \(0.990514\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 2.01678 | − | 3.49317i | 0.0261920 | − | 0.0453659i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0.792110 | + | 1.37197i | 0.0100267 | + | 0.0173668i | 0.870995 | − | 0.491291i | \(-0.163475\pi\) |
−0.860969 | + | 0.508658i | \(0.830142\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −4.22894 | − | 7.32473i | −0.0509511 | − | 0.0882498i | 0.839425 | − | 0.543475i | \(-0.182892\pi\) |
−0.890376 | + | 0.455226i | \(0.849559\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 64.1236i | 0.720489i | 0.932858 | + | 0.360245i | \(0.117307\pi\) | ||||
−0.932858 | + | 0.360245i | \(0.882693\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −101.351 | −1.11374 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 99.7953 | − | 57.6168i | 1.02882 | − | 0.593988i | 0.112172 | − | 0.993689i | \(-0.464219\pi\) |
0.916646 | + | 0.399701i | \(0.130886\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −114.558 | + | 66.1403i | −1.13424 | + | 0.654855i | −0.944998 | − | 0.327075i | \(-0.893937\pi\) |
−0.189244 | + | 0.981930i | \(0.560604\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 108.557 | + | 62.6753i | 1.05395 | + | 0.608498i | 0.923752 | − | 0.382990i | \(-0.125106\pi\) |
0.130197 | + | 0.991488i | \(0.458439\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 36.5378 | 0.341475 | 0.170737 | − | 0.985317i | \(-0.445385\pi\) | ||||
0.170737 | + | 0.985317i | \(0.445385\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −134.701 | −1.23579 | −0.617895 | − | 0.786261i | \(-0.712014\pi\) | ||||
−0.617895 | + | 0.786261i | \(0.712014\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 95.1051 | − | 164.727i | 0.841638 | − | 1.45776i | −0.0468711 | − | 0.998901i | \(-0.514925\pi\) |
0.888509 | − | 0.458859i | \(-0.151742\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −63.2853 | + | 36.5378i | −0.531809 | + | 0.307040i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −60.4021 | + | 104.620i | −0.499191 | + | 0.864624i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 184.103i | 1.44963i | 0.688943 | + | 0.724816i | \(0.258075\pi\) | ||||
−0.688943 | + | 0.724816i | \(0.741925\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 109.194 | + | 63.0433i | 0.833544 | + | 0.481247i | 0.855064 | − | 0.518522i | \(-0.173517\pi\) |
−0.0215207 | + | 0.999768i | \(0.506851\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 64.0859 | − | 37.0000i | 0.481849 | − | 0.278195i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −62.1326 | − | 107.617i | −0.453523 | − | 0.785524i | 0.545079 | − | 0.838385i | \(-0.316500\pi\) |
−0.998602 | + | 0.0528602i | \(0.983166\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 13.3832 | − | 23.1803i | 0.0962817 | − | 0.166765i | −0.813861 | − | 0.581059i | \(-0.802638\pi\) |
0.910143 | + | 0.414295i | \(0.135972\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −4.91843 | −0.0343946 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 69.8437 | + | 40.3243i | 0.468750 | + | 0.270633i | 0.715716 | − | 0.698391i | \(-0.246100\pi\) |
−0.246966 | + | 0.969024i | \(0.579434\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −49.9742 | − | 86.5579i | −0.330955 | − | 0.573231i | 0.651744 | − | 0.758439i | \(-0.274037\pi\) |
−0.982699 | + | 0.185208i | \(0.940704\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 60.1487 | + | 34.7269i | 0.383113 | + | 0.221190i | 0.679172 | − | 0.733979i | \(-0.262339\pi\) |
−0.296059 | + | 0.955170i | \(0.595673\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 215.193i | 1.33660i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 162.467i | − | 0.996732i | −0.866967 | − | 0.498366i | \(-0.833934\pi\) | ||
0.866967 | − | 0.498366i | \(-0.166066\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 48.3397 | − | 83.7269i | 0.289459 | − | 0.501358i | −0.684221 | − | 0.729274i | \(-0.739858\pi\) |
0.973681 | + | 0.227916i | \(0.0731911\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −22.7079 | − | 39.3312i | −0.134366 | − | 0.232729i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −14.0141 | − | 24.2731i | −0.0810064 | − | 0.140307i | 0.822676 | − | 0.568510i | \(-0.192480\pi\) |
−0.903682 | + | 0.428203i | \(0.859147\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − | 35.6012i | − | 0.198889i | −0.995043 | − | 0.0994447i | \(-0.968293\pi\) | ||
0.995043 | − | 0.0994447i | \(-0.0317067\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −19.6358 | −0.108485 | −0.0542426 | − | 0.998528i | \(-0.517274\pi\) | ||||
−0.0542426 | + | 0.998528i | \(0.517274\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −3.07117 | + | 1.77314i | −0.0164233 | + | 0.00948202i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −188.662 | + | 108.924i | −0.987757 | + | 0.570282i | −0.904603 | − | 0.426255i | \(-0.859833\pi\) |
−0.0831540 | + | 0.996537i | \(0.526499\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −42.4352 | − | 24.5000i | −0.219872 | − | 0.126943i | 0.386019 | − | 0.922491i | \(-0.373850\pi\) |
−0.605891 | + | 0.795548i | \(0.707183\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 359.965 | 1.82723 | 0.913617 | − | 0.406575i | \(-0.133277\pi\) | ||||
0.913617 | + | 0.406575i | \(0.133277\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 61.0652 | 0.306861 | 0.153430 | − | 0.988159i | \(-0.450968\pi\) | ||||
0.153430 | + | 0.988159i | \(0.450968\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −241.647 | + | 418.545i | −1.19038 | + | 2.06180i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 3.11002 | − | 1.79557i | 0.0148805 | − | 0.00859124i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −193.493 | + | 335.140i | −0.917029 | + | 1.58834i | −0.113126 | + | 0.993581i | \(0.536087\pi\) |
−0.803903 | + | 0.594761i | \(0.797247\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 267.584i | 1.23311i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 77.1684 | + | 44.5532i | 0.349178 | + | 0.201598i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −88.9864 | + | 51.3763i | −0.399042 | + | 0.230387i | −0.686071 | − | 0.727535i | \(-0.740666\pi\) |
0.287028 | + | 0.957922i | \(0.407333\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 169.482 | + | 293.552i | 0.746617 | + | 1.29318i | 0.949435 | + | 0.313962i | \(0.101657\pi\) |
−0.202818 | + | 0.979216i | \(0.565010\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −148.376 | + | 256.995i | −0.647932 | + | 1.12225i | 0.335685 | + | 0.941974i | \(0.391032\pi\) |
−0.983616 | + | 0.180276i | \(0.942301\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 346.537 | 1.48728 | 0.743642 | − | 0.668578i | \(-0.233097\pi\) | ||||
0.743642 | + | 0.668578i | \(0.233097\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −140.026 | − | 80.8439i | −0.585882 | − | 0.338259i | 0.177586 | − | 0.984105i | \(-0.443171\pi\) |
−0.763468 | + | 0.645846i | \(0.776505\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 162.370 | + | 281.232i | 0.673732 | + | 1.16694i | 0.976838 | + | 0.213982i | \(0.0686433\pi\) |
−0.303105 | + | 0.952957i | \(0.598023\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −78.1447 | − | 45.1168i | −0.316375 | − | 0.182659i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 384.012i | 1.52993i | 0.644074 | + | 0.764963i | \(0.277243\pi\) | ||||
−0.644074 | + | 0.764963i | \(0.722757\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 10.4431i | 0.0412770i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −6.46694 | + | 11.2011i | −0.0251632 | + | 0.0435839i | −0.878333 | − | 0.478050i | \(-0.841344\pi\) |
0.853170 | + | 0.521634i | \(0.174677\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 84.1821 | + | 145.808i | 0.325027 | + | 0.562964i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −24.7358 | − | 42.8437i | −0.0940526 | − | 0.162904i | 0.815160 | − | 0.579236i | \(-0.196649\pi\) |
−0.909213 | + | 0.416332i | \(0.863316\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 21.4434i | 0.0797154i | 0.999205 | + | 0.0398577i | \(0.0126905\pi\) | ||||
−0.999205 | + | 0.0398577i | \(0.987310\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −326.907 | −1.20630 | −0.603150 | − | 0.797628i | \(-0.706088\pi\) | ||||
−0.603150 | + | 0.797628i | \(0.706088\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −413.487 | + | 238.727i | −1.49273 | + | 0.861830i | −0.999965 | − | 0.00833105i | \(-0.997348\pi\) |
−0.492768 | + | 0.870161i | \(0.664015\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 103.064 | − | 59.5039i | 0.366775 | − | 0.211758i | −0.305274 | − | 0.952265i | \(-0.598748\pi\) |
0.672049 | + | 0.740507i | \(0.265415\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −338.920 | − | 195.675i | −1.19760 | − | 0.691432i | −0.237577 | − | 0.971369i | \(-0.576353\pi\) |
−0.960018 | + | 0.279937i | \(0.909687\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 410.218 | 1.42933 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −224.753 | −0.777691 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −35.8483 | + | 62.0910i | −0.122349 | + | 0.211915i | −0.920694 | − | 0.390286i | \(-0.872376\pi\) |
0.798345 | + | 0.602201i | \(0.205709\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 227.246 | − | 131.200i | 0.760020 | − | 0.438797i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −104.844 | + | 181.595i | −0.348318 | + | 0.603304i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 172.351i | − | 0.561402i | −0.959795 | − | 0.280701i | \(-0.909433\pi\) | ||
0.959795 | − | 0.280701i | \(-0.0905670\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 524.246 | + | 302.673i | 1.68568 | + | 0.973227i | 0.957763 | + | 0.287559i | \(0.0928438\pi\) |
0.727915 | + | 0.685667i | \(0.240489\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −283.595 | + | 163.734i | −0.906055 | + | 0.523111i | −0.879160 | − | 0.476527i | \(-0.841895\pi\) |
−0.0268949 | + | 0.999638i | \(0.508562\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 34.5210 | + | 59.7921i | 0.108899 | + | 0.188619i | 0.915325 | − | 0.402717i | \(-0.131934\pi\) |
−0.806425 | + | 0.591336i | \(0.798601\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −11.7269 | + | 20.3115i | −0.0367613 | + | 0.0636725i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −65.0601 | −0.201424 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 66.7785 | + | 38.5546i | 0.202974 | + | 0.117187i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −254.895 | − | 441.492i | −0.770076 | − | 1.33381i | −0.937521 | − | 0.347930i | \(-0.886885\pi\) |
0.167444 | − | 0.985882i | \(-0.446449\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 292.232 | + | 168.720i | 0.867156 | + | 0.500653i | 0.866402 | − | 0.499347i | \(-0.166427\pi\) |
0.000754096 | 1.00000i | \(0.499760\pi\) | ||||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 12.9856i | 0.0380808i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 135.687i | 0.395590i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 107.622 | − | 186.407i | 0.310151 | − | 0.537197i | −0.668244 | − | 0.743942i | \(-0.732954\pi\) |
0.978395 | + | 0.206745i | \(0.0662871\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 181.012 | + | 313.522i | 0.518659 | + | 0.898345i | 0.999765 | + | 0.0216818i | \(0.00690207\pi\) |
−0.481105 | + | 0.876663i | \(0.659765\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −292.420 | − | 506.486i | −0.828385 | − | 1.43481i | −0.899304 | − | 0.437323i | \(-0.855926\pi\) |
0.0709189 | − | 0.997482i | \(-0.477407\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 393.693i | 1.09664i | 0.836269 | + | 0.548319i | \(0.184732\pi\) | ||||
−0.836269 | + | 0.548319i | \(0.815268\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −295.117 | −0.817498 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 329.831 | − | 190.428i | 0.898722 | − | 0.518877i | 0.0219364 | − | 0.999759i | \(-0.493017\pi\) |
0.876785 | + | 0.480882i | \(0.159684\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −478.337 | + | 276.168i | −1.28932 | + | 0.744388i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 115.080 | + | 66.4416i | 0.308526 | + | 0.178128i | 0.646267 | − | 0.763112i | \(-0.276329\pi\) |
−0.337741 | + | 0.941239i | \(0.609663\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 589.316 | 1.56317 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −507.622 | −1.33937 | −0.669686 | − | 0.742644i | \(-0.733571\pi\) | ||||
−0.669686 | + | 0.742644i | \(0.733571\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −165.968 | + | 287.466i | −0.433338 | + | 0.750564i | −0.997158 | − | 0.0753339i | \(-0.975998\pi\) |
0.563820 | + | 0.825898i | \(0.309331\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 296.662 | − | 171.278i | 0.762626 | − | 0.440302i | −0.0676116 | − | 0.997712i | \(-0.521538\pi\) |
0.830238 | + | 0.557409i | \(0.188205\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 94.5979 | − | 163.848i | 0.241938 | − | 0.419049i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 24.8043i | − | 0.0624792i | −0.999512 | − | 0.0312396i | \(-0.990055\pi\) | ||
0.999512 | − | 0.0312396i | \(-0.00994550\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −52.0842 | − | 30.0708i | −0.129886 | − | 0.0749896i | 0.433649 | − | 0.901082i | \(-0.357226\pi\) |
−0.563535 | + | 0.826092i | \(0.690559\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 282.571 | − | 163.143i | 0.701170 | − | 0.404820i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 4.08526 | + | 7.07589i | 0.0100375 | + | 0.0173855i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −240.720 | + | 416.939i | −0.588558 | + | 1.01941i | 0.405864 | + | 0.913933i | \(0.366971\pi\) |
−0.994422 | + | 0.105478i | \(0.966363\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 694.453 | 1.68149 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −479.531 | − | 276.857i | −1.14447 | − | 0.660758i | −0.196933 | − | 0.980417i | \(-0.563098\pi\) |
−0.947533 | + | 0.319659i | \(0.896432\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 190.947 | + | 330.730i | 0.453556 | + | 0.785581i | 0.998604 | − | 0.0528233i | \(-0.0168220\pi\) |
−0.545048 | + | 0.838405i | \(0.683489\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −42.2447 | − | 24.3900i | −0.0989337 | − | 0.0571194i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 821.321i | − | 1.90562i | −0.303570 | − | 0.952809i | \(-0.598179\pi\) | ||
0.303570 | − | 0.952809i | \(-0.401821\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 199.155i | 0.459942i | 0.973198 | + | 0.229971i | \(0.0738631\pi\) | ||||
−0.973198 | + | 0.229971i | \(0.926137\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −95.7946 | + | 165.921i | −0.219210 | + | 0.379682i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −240.830 | − | 417.130i | −0.548588 | − | 0.950182i | −0.998372 | − | 0.0570445i | \(-0.981832\pi\) |
0.449784 | − | 0.893137i | \(-0.351501\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −270.143 | − | 467.902i | −0.609805 | − | 1.05621i | −0.991272 | − | 0.131830i | \(-0.957915\pi\) |
0.381468 | − | 0.924382i | \(-0.375419\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 300.318i | 0.668859i | 0.942421 | + | 0.334429i | \(0.108544\pi\) | ||||
−0.942421 | + | 0.334429i | \(0.891456\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 19.9074 | 0.0441407 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 134.841 | − | 77.8505i | 0.295057 | − | 0.170351i | −0.345163 | − | 0.938543i | \(-0.612176\pi\) |
0.640220 | + | 0.768191i | \(0.278843\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −261.143 | + | 150.771i | −0.566470 | + | 0.327052i | −0.755738 | − | 0.654874i | \(-0.772722\pi\) |
0.189268 | + | 0.981925i | \(0.439388\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 206.790 | + | 119.390i | 0.446630 | + | 0.257862i | 0.706406 | − | 0.707807i | \(-0.250315\pi\) |
−0.259776 | + | 0.965669i | \(0.583649\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −423.152 | −0.906107 | −0.453054 | − | 0.891483i | \(-0.649665\pi\) | ||||
−0.453054 | + | 0.891483i | \(0.649665\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 1000.13 | 2.13247 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −5.08795 | + | 8.81259i | −0.0107568 | + | 0.0186313i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −379.284 | + | 218.980i | −0.791824 | + | 0.457160i | −0.840604 | − | 0.541650i | \(-0.817800\pi\) |
0.0487802 | + | 0.998810i | \(0.484467\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 102.649 | − | 177.794i | 0.213408 | − | 0.369634i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 401.945i | 0.825350i | 0.910878 | + | 0.412675i | \(0.135405\pi\) | ||||
−0.910878 | + | 0.412675i | \(0.864595\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 241.084 | + | 139.190i | 0.491007 | + | 0.283483i | 0.724992 | − | 0.688757i | \(-0.241843\pi\) |
−0.233985 | + | 0.972240i | \(0.575177\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 367.981 | − | 212.454i | 0.746411 | − | 0.430941i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −73.0756 | − | 126.571i | −0.147033 | − | 0.254669i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 272.655 | − | 472.252i | 0.546402 | − | 0.946397i | −0.452115 | − | 0.891960i | \(-0.649330\pi\) |
0.998517 | − | 0.0544369i | \(-0.0173364\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 306.460 | 0.609264 | 0.304632 | − | 0.952470i | \(-0.401466\pi\) | ||||
0.304632 | + | 0.952470i | \(0.401466\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 480.208 | + | 277.248i | 0.943434 | + | 0.544692i | 0.891035 | − | 0.453934i | \(-0.149980\pi\) |
0.0523989 | + | 0.998626i | \(0.483313\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 19.8316 | + | 34.3493i | 0.0388093 | + | 0.0672197i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 3.24069 | + | 1.87101i | 0.00626825 | + | 0.00361898i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 154.167i | − | 0.295905i | −0.988994 | − | 0.147953i | \(-0.952732\pi\) | ||
0.988994 | − | 0.147953i | \(-0.0472683\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 480.598i | − | 0.918925i | −0.888197 | − | 0.459463i | \(-0.848042\pi\) | ||
0.888197 | − | 0.459463i | \(-0.151958\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 117.629 | − | 203.739i | 0.223204 | − | 0.386602i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −14.0721 | − | 24.3735i | −0.0266013 | − | 0.0460748i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −250.105 | − | 433.194i | −0.469240 | − | 0.812747i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − | 15.0943i | − | 0.0280043i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −300.543 | −0.555533 | −0.277766 | − | 0.960649i | \(-0.589594\pi\) | ||||
−0.277766 | + | 0.960649i | \(0.589594\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −87.6473 | + | 50.6032i | −0.160233 | + | 0.0925104i | −0.577972 | − | 0.816056i | \(-0.696156\pi\) |
0.417739 | + | 0.908567i | \(0.362822\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −372.636 | + | 215.141i | −0.676290 | + | 0.390456i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 12.5081 | + | 7.22154i | 0.0226186 | + | 0.0130588i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −433.041 | −0.777452 | −0.388726 | − | 0.921353i | \(-0.627085\pi\) | ||||
−0.388726 | + | 0.921353i | \(0.627085\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 255.687 | 0.457401 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −520.886 | + | 902.201i | −0.925197 | + | 1.60249i | −0.133954 | + | 0.990988i | \(0.542767\pi\) |
−0.791244 | + | 0.611501i | \(0.790566\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 257.445 | − | 148.636i | 0.452452 | − | 0.261223i | −0.256413 | − | 0.966567i | \(-0.582541\pi\) |
0.708865 | + | 0.705344i | \(0.249207\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 339.524 | − | 588.073i | 0.594613 | − | 1.02990i | −0.398988 | − | 0.916956i | \(-0.630638\pi\) |
0.993601 | − | 0.112945i | \(-0.0360282\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 148.351i | − | 0.257107i | −0.991703 | − | 0.128553i | \(-0.958967\pi\) | ||
0.991703 | − | 0.128553i | \(-0.0410333\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −66.7785 | − | 38.5546i | −0.114937 | − | 0.0663590i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −23.2132 | + | 13.4021i | −0.0398168 | + | 0.0229882i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −263.559 | − | 456.497i | −0.448993 | − | 0.777678i | 0.549328 | − | 0.835607i | \(-0.314884\pi\) |
−0.998321 | + | 0.0579287i | \(0.981550\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −119.117 | + | 206.316i | −0.202236 | + | 0.350283i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 473.848 | 0.799069 | 0.399534 | − | 0.916718i | \(-0.369172\pi\) | ||||
0.399534 | + | 0.916718i | \(0.369172\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −601.414 | − | 347.227i | −1.00403 | − | 0.579677i | −0.0945922 | − | 0.995516i | \(-0.530155\pi\) |
−0.909438 | + | 0.415839i | \(0.863488\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −93.3559 | − | 161.697i | −0.155334 | − | 0.269047i | 0.777846 | − | 0.628454i | \(-0.216312\pi\) |
−0.933181 | + | 0.359408i | \(0.882979\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 712.209 | + | 411.194i | 1.17333 | + | 0.677420i | 0.954461 | − | 0.298335i | \(-0.0964311\pi\) |
0.218865 | + | 0.975755i | \(0.429764\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 94.0249i | − | 0.153887i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 482.206i | 0.786634i | 0.919403 | + | 0.393317i | \(0.128672\pi\) | ||||
−0.919403 | + | 0.393317i | \(0.871328\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −344.052 | + | 595.916i | −0.557621 | + | 0.965828i | 0.440073 | + | 0.897962i | \(0.354952\pi\) |
−0.997694 | + | 0.0678661i | \(0.978381\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −380.253 | − | 658.617i | −0.614302 | − | 1.06400i | −0.990507 | − | 0.137465i | \(-0.956105\pi\) |
0.376205 | − | 0.926536i | \(-0.377229\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 292.302 | + | 506.282i | 0.469185 | + | 0.812652i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − | 148.024i | − | 0.235333i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 1008.08 | 1.59758 | 0.798792 | − | 0.601607i | \(-0.205473\pi\) | ||||
0.798792 | + | 0.601607i | \(0.205473\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −328.459 | + | 189.636i | −0.515634 | + | 0.297701i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 488.095 | − | 281.802i | 0.761458 | − | 0.439628i | −0.0683607 | − | 0.997661i | \(-0.521777\pi\) |
0.829819 | + | 0.558032i | \(0.188444\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −499.697 | − | 288.500i | −0.777133 | − | 0.448678i | 0.0582801 | − | 0.998300i | \(-0.481438\pi\) |
−0.835413 | + | 0.549622i | \(0.814772\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −1024.52 | −1.58349 | −0.791744 | − | 0.610853i | \(-0.790827\pi\) | ||||
−0.791744 | + | 0.610853i | \(0.790827\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 33.7011 | 0.0519277 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −199.697 | + | 345.885i | −0.305814 | + | 0.529686i | −0.977442 | − | 0.211203i | \(-0.932262\pi\) |
0.671628 | + | 0.740888i | \(0.265595\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −646.308 | + | 373.146i | −0.980741 | + | 0.566231i | −0.902494 | − | 0.430703i | \(-0.858266\pi\) |
−0.0782470 | + | 0.996934i | \(0.524932\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −475.624 | + | 823.804i | −0.719552 | + | 1.24630i | 0.241626 | + | 0.970369i | \(0.422319\pi\) |
−0.961178 | + | 0.275931i | \(0.911014\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 1251.27i | − | 1.87596i | ||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −2.05009 | − | 1.18362i | −0.00305527 | − | 0.00176396i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 298.113 | − | 172.115i | 0.442961 | − | 0.255743i | −0.261892 | − | 0.965097i | \(-0.584346\pi\) |
0.704853 | + | 0.709354i | \(0.251013\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −492.832 | − | 853.610i | −0.727965 | − | 1.26087i | −0.957742 | − | 0.287628i | \(-0.907133\pi\) |
0.229778 | − | 0.973243i | \(-0.426200\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 525.284 | − | 909.818i | 0.773614 | − | 1.33994i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −166.658 | −0.244009 | −0.122004 | − | 0.992530i | \(-0.538932\pi\) | ||||
−0.122004 | + | 0.992530i | \(0.538932\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 583.272 | + | 336.752i | 0.846548 | + | 0.488755i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 449.077 | + | 777.825i | 0.649895 | + | 1.12565i | 0.983148 | + | 0.182813i | \(0.0585204\pi\) |
−0.333253 | + | 0.942838i | \(0.608146\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −312.341 | − | 180.330i | −0.448122 | − | 0.258723i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 730.549i | − | 1.04215i | −0.853510 | − | 0.521076i | \(-0.825531\pi\) | ||
0.853510 | − | 0.521076i | \(-0.174469\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 149.897i | 0.213224i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −602.991 | + | 1044.41i | −0.852887 | + | 1.47724i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −114.961 | − | 199.118i | −0.162145 | − | 0.280843i | 0.773493 | − | 0.633805i | \(-0.218508\pi\) |
−0.935638 | + | 0.352962i | \(0.885174\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −346.394 | − | 599.971i | −0.485825 | − | 0.841474i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | − | 907.095i | − | 1.26161i | −0.775943 | − | 0.630803i | \(-0.782725\pi\) | ||
0.775943 | − | 0.630803i | \(-0.217275\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 1142.80 | 1.58502 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 186.838 | − | 107.871i | 0.256999 | − | 0.148378i | −0.365966 | − | 0.930628i | \(-0.619261\pi\) |
0.622965 | + | 0.782250i | \(0.285928\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 159.656 | − | 92.1776i | 0.218408 | − | 0.126098i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 544.963 | + | 314.634i | 0.743469 | + | 0.429242i | 0.823329 | − | 0.567564i | \(-0.192114\pi\) |
−0.0798604 | + | 0.996806i | \(0.525447\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 48.5351 | 0.0658549 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −547.649 | −0.741068 | −0.370534 | − | 0.928819i | \(-0.620825\pi\) | ||||
−0.370534 | + | 0.928819i | \(0.620825\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 267.072 | − | 462.583i | 0.359451 | − | 0.622588i | −0.628418 | − | 0.777876i | \(-0.716297\pi\) |
0.987869 | + | 0.155288i | \(0.0496306\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 288.481 | − | 166.555i | 0.385155 | − | 0.222369i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 225.545 | − | 390.655i | 0.300326 | − | 0.520180i | −0.675884 | − | 0.737008i | \(-0.736238\pi\) |
0.976210 | + | 0.216828i | \(0.0695712\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 352.391i | − | 0.465511i | −0.972535 | − | 0.232755i | \(-0.925226\pi\) | ||
0.972535 | − | 0.232755i | \(-0.0747741\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 929.923 | + | 536.891i | 1.22197 | + | 0.705507i | 0.965339 | − | 0.261001i | \(-0.0840525\pi\) |
0.256636 | + | 0.966508i | \(0.417386\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −1063.52 | + | 614.024i | −1.39387 | + | 0.804750i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −423.399 | − | 733.349i | −0.552020 | − | 0.956126i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 177.988 | − | 308.284i | 0.231454 | − | 0.400889i | −0.726782 | − | 0.686868i | \(-0.758985\pi\) |
0.958236 | + | 0.285978i | \(0.0923185\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −370.790 | −0.479677 | −0.239838 | − | 0.970813i | \(-0.577094\pi\) | ||||
−0.239838 | + | 0.970813i | \(0.577094\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 316.292 | + | 182.611i | 0.406023 | + | 0.234418i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −3.54628 | − | 6.14233i | −0.00454069 | − | 0.00786470i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −998.581 | − | 576.531i | −1.26885 | − | 0.732568i | −0.294076 | − | 0.955782i | \(-0.595012\pi\) |
−0.974769 | + | 0.223214i | \(0.928345\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 1734.12i | − | 2.19231i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 59.4810i | 0.0750076i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −439.873 | + | 761.882i | −0.551910 | + | 0.955937i | 0.446226 | + | 0.894920i | \(0.352768\pi\) |
−0.998137 | + | 0.0610167i | \(0.980566\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −33.8968 | − | 58.7110i | −0.0424240 | − | 0.0734806i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 0.962404 | + | 1.66693i | 0.00119851 | + | 0.00207588i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 884.508i | 1.09334i | 0.837350 | + | 0.546668i | \(0.184104\pi\) | ||||
−0.837350 | + | 0.546668i | \(0.815896\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −961.464 | −1.18553 | −0.592765 | − | 0.805376i | \(-0.701964\pi\) | ||||
−0.592765 | + | 0.805376i | \(0.701964\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −161.676 | + | 93.3437i | −0.197890 | + | 0.114252i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −778.064 | + | 449.215i | −0.947702 | + | 0.547156i | −0.892366 | − | 0.451312i | \(-0.850956\pi\) |
−0.0553360 | + | 0.998468i | \(0.517623\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 187.219 | + | 108.091i | 0.227484 | + | 0.131338i | 0.609411 | − | 0.792855i | \(-0.291406\pi\) |
−0.381927 | + | 0.924193i | \(0.624739\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 113.883 | 0.137706 | 0.0688528 | − | 0.997627i | \(-0.478066\pi\) | ||||
0.0688528 | + | 0.997627i | \(0.478066\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −101.326 | −0.122227 | −0.0611135 | − | 0.998131i | \(-0.519465\pi\) | ||||
−0.0611135 | + | 0.998131i | \(0.519465\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −136.731 | + | 236.825i | −0.164143 | + | 0.284303i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 60.4689 | − | 34.9117i | 0.0720726 | − | 0.0416111i | −0.463531 | − | 0.886081i | \(-0.653418\pi\) |
0.535603 | + | 0.844470i | \(0.320084\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 984.588 | − | 1705.36i | 1.17073 | − | 2.02777i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 1101.35i | 1.30030i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −377.502 | − | 217.951i | −0.443598 | − | 0.256112i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 993.028 | − | 573.325i | 1.16416 | − | 0.672127i | 0.211862 | − | 0.977300i | \(-0.432047\pi\) |
0.952297 | + | 0.305172i | \(0.0987140\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −125.788 | − | 217.871i | −0.146777 | − | 0.254225i | 0.783258 | − | 0.621697i | \(-0.213557\pi\) |
−0.930035 | + | 0.367472i | \(0.880223\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −244.266 | + | 423.082i | −0.284361 | + | 0.492528i | −0.972454 | − | 0.233095i | \(-0.925115\pi\) |
0.688093 | + | 0.725623i | \(0.258448\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 596.889 | 0.691644 | 0.345822 | − | 0.938300i | \(-0.387600\pi\) | ||||
0.345822 | + | 0.938300i | \(0.387600\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0.607003 | + | 0.350454i | 0.000698508 | + | 0.000403284i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −609.765 | − | 1056.14i | −0.700074 | − | 1.21256i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −620.434 | − | 358.208i | −0.707451 | − | 0.408447i | 0.102666 | − | 0.994716i | \(-0.467263\pi\) |
−0.810116 | + | 0.586269i | \(0.800596\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 1200.86i | − | 1.36306i | −0.731790 | − | 0.681531i | \(-0.761315\pi\) | ||
0.731790 | − | 0.681531i | \(-0.238685\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 22.8938i | − | 0.0259273i | −0.999916 | − | 0.0129636i | \(-0.995873\pi\) | ||
0.999916 | − | 0.0129636i | \(-0.00412657\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 301.294 | − | 521.857i | 0.339678 | − | 0.588340i | −0.644694 | − | 0.764441i | \(-0.723015\pi\) |
0.984372 | + | 0.176101i | \(0.0563485\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 839.220 | + | 1453.57i | 0.944005 | + | 1.63506i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 34.3256 | + | 59.4537i | 0.0384385 | + | 0.0665775i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − | 1555.90i | − | 1.73071i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 485.609 | 0.538966 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 366.281 | − | 211.473i | 0.403838 | − | 0.233156i | −0.284300 | − | 0.958735i | \(-0.591761\pi\) |
0.688139 | + | 0.725579i | \(0.258428\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −125.376 | + | 72.3861i | −0.137625 | + | 0.0794578i | −0.567232 | − | 0.823558i | \(-0.691986\pi\) |
0.429607 | + | 0.903016i | \(0.358652\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −3.24069 | − | 1.87101i | −0.00354949 | − | 0.00204930i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 1149.51 | 1.25356 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 869.093 | 0.945694 | 0.472847 | − | 0.881145i | \(-0.343226\pi\) | ||||
0.472847 | + | 0.881145i | \(0.343226\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −89.1064 | + | 154.337i | −0.0965400 | + | 0.167212i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 82.2838 | − | 47.5066i | 0.0885724 | − | 0.0511373i | −0.455060 | − | 0.890461i | \(-0.650382\pi\) |
0.543632 | + | 0.839324i | \(0.317049\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 138.461 | − | 239.821i | 0.148722 | − | 0.257595i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 1555.55i | − | 1.66014i | −0.557657 | − | 0.830071i | \(-0.688300\pi\) | ||
0.557657 | − | 0.830071i | \(-0.311700\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −335.246 | − | 193.554i | −0.356265 | − | 0.205690i | 0.311176 | − | 0.950352i | \(-0.399277\pi\) |
−0.667441 | + | 0.744662i | \(0.732611\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −919.782 | + | 531.036i | −0.975379 | + | 0.563135i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 484.894 | + | 839.861i | 0.512032 | + | 0.886865i | 0.999903 | + | 0.0139492i | \(0.00444033\pi\) |
−0.487871 | + | 0.872916i | \(0.662226\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 24.1821 | − | 41.8846i | 0.0254817 | − | 0.0441355i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 1294.65 | 1.35850 | 0.679248 | − | 0.733909i | \(-0.262306\pi\) | ||||
0.679248 | + | 0.733909i | \(0.262306\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −981.126 | − | 566.453i | −1.02307 | − | 0.590671i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 49.7731 | + | 86.2096i | 0.0517931 | + | 0.0897082i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −713.668 | − | 412.036i | −0.738023 | − | 0.426098i | 0.0833272 | − | 0.996522i | \(-0.473445\pi\) |
−0.821350 | + | 0.570425i | \(0.806779\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 1518.35i | − | 1.56370i | −0.623469 | − | 0.781848i | \(-0.714277\pi\) | ||
0.623469 | − | 0.781848i | \(-0.285723\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − | 244.024i | − | 0.250796i | ||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −185.616 | + | 321.497i | −0.189986 | + | 0.329065i | −0.945245 | − | 0.326361i | \(-0.894178\pi\) |
0.755259 | + | 0.655426i | \(0.227511\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 14.1851 | + | 24.5693i | 0.0144894 | + | 0.0250963i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −466.522 | − | 808.039i | −0.474590 | − | 0.822014i | 0.524987 | − | 0.851110i | \(-0.324070\pi\) |
−0.999577 | + | 0.0290967i | \(0.990737\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − | 542.890i | − | 0.548928i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1615.53 | 1.63020 | 0.815099 | − | 0.579321i | \(-0.196682\pi\) | ||||
0.815099 | + | 0.579321i | \(0.196682\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 899.586 | − | 519.376i | 0.902293 | − | 0.520939i | 0.0243496 | − | 0.999704i | \(-0.492249\pi\) |
0.877943 | + | 0.478764i | \(0.158915\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))