Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2400,2,Mod(49,2400)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2400, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2400.49");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2400 = 2^{5} \cdot 3 \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2400.d (of order \(2\), degree \(1\), 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: | \(19.1640964851\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | 6.0.399424.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - 2x^{5} + 3x^{4} - 6x^{3} + 6x^{2} - 8x + 8 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{19}]\) |
Coefficient ring index: | \( 2^{8} \) |
Twist minimal: | no (minimal twist has level 120) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 49.1 | ||
Root | \(-0.671462 - 1.24464i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2400.49 |
Dual form | 2400.2.d.e.49.6 |
$q$-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 \(\left(\mathbb{Z}/2400\mathbb{Z}\right)^\times\).
\(n\) | \(577\) | \(901\) | \(1601\) | \(1951\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(1\) | \(1\) |
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 | ||||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − 4.68585i | − 1.77108i | −0.464560 | − | 0.885542i | \(-0.653787\pi\) | ||||
0.464560 | − | 0.885542i | \(-0.346213\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.29273i | 0.691284i | 0.938366 | + | 0.345642i | \(0.112339\pi\) | ||||
−0.938366 | + | 0.345642i | \(0.887661\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 4.97858 | 1.38081 | 0.690404 | − | 0.723424i | \(-0.257433\pi\) | ||||
0.690404 | + | 0.723424i | \(0.257433\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − 2.97858i | − 0.722411i | −0.932486 | − | 0.361206i | \(-0.882365\pi\) | ||||
0.932486 | − | 0.361206i | \(-0.117635\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − 2.68585i | − 0.616175i | −0.951358 | − | 0.308088i | \(-0.900311\pi\) | ||||
0.951358 | − | 0.308088i | \(-0.0996890\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 4.68585i | 1.02254i | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 2.68585i | 0.560038i | 0.959995 | + | 0.280019i | \(0.0903407\pi\) | ||||
−0.959995 | + | 0.280019i | \(0.909659\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 2.00000i | 0.371391i | 0.982607 | + | 0.185695i | \(0.0594537\pi\) | ||||
−0.982607 | + | 0.185695i | \(0.940546\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 6.97858 | 1.25339 | 0.626695 | − | 0.779265i | \(-0.284407\pi\) | ||||
0.626695 | + | 0.779265i | \(0.284407\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | − 2.29273i | − 0.399113i | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 4.39312 | 0.722224 | 0.361112 | − | 0.932523i | \(-0.382397\pi\) | ||||
0.361112 | + | 0.932523i | \(0.382397\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −4.97858 | −0.797210 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −11.3717 | −1.77596 | −0.887980 | − | 0.459882i | \(-0.847892\pi\) | ||||
−0.887980 | + | 0.459882i | \(0.847892\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 9.37169 | 1.42917 | 0.714585 | − | 0.699549i | \(-0.246616\pi\) | ||||
0.714585 | + | 0.699549i | \(0.246616\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − 7.27131i | − 1.06063i | −0.847801 | − | 0.530315i | \(-0.822074\pi\) | ||||
0.847801 | − | 0.530315i | \(-0.177926\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −14.9572 | −2.13674 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 2.97858i | 0.417084i | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 2.00000 | 0.274721 | 0.137361 | − | 0.990521i | \(-0.456138\pi\) | ||||
0.137361 | + | 0.990521i | \(0.456138\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 2.68585i | 0.355749i | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − 1.70727i | − 0.222267i | −0.993805 | − | 0.111134i | \(-0.964552\pi\) | ||||
0.993805 | − | 0.111134i | \(-0.0354482\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − 4.58546i | − 0.587108i | −0.955942 | − | 0.293554i | \(-0.905162\pi\) | ||||
0.955942 | − | 0.293554i | \(-0.0948381\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | − 4.68585i | − 0.590361i | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −4.00000 | −0.488678 | −0.244339 | − | 0.969690i | \(-0.578571\pi\) | ||||
−0.244339 | + | 0.969690i | \(0.578571\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | − 2.68585i | − 0.323338i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −0.585462 | −0.0694816 | −0.0347408 | − | 0.999396i | \(-0.511061\pi\) | ||||
−0.0347408 | + | 0.999396i | \(0.511061\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 6.00000i | 0.702247i | 0.936329 | + | 0.351123i | \(0.114200\pi\) | ||||
−0.936329 | + | 0.351123i | \(0.885800\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 10.7434 | 1.22432 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1.02142 | 0.114919 | 0.0574595 | − | 0.998348i | \(-0.481700\pi\) | ||||
0.0574595 | + | 0.998348i | \(0.481700\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −13.3717 | −1.46773 | −0.733867 | − | 0.679293i | \(-0.762286\pi\) | ||||
−0.733867 | + | 0.679293i | \(0.762286\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | − 2.00000i | − 0.214423i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −3.37169 | −0.357399 | −0.178699 | − | 0.983904i | \(-0.557189\pi\) | ||||
−0.178699 | + | 0.983904i | \(0.557189\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − 23.3288i | − 2.44553i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −6.97858 | −0.723645 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − 3.95715i | − 0.401788i | −0.979613 | − | 0.200894i | \(-0.935615\pi\) | ||||
0.979613 | − | 0.200894i | \(-0.0643847\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 2.29273i | 0.230428i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 2.00000i | 0.199007i | 0.995037 | + | 0.0995037i | \(0.0317255\pi\) | ||||
−0.995037 | + | 0.0995037i | \(0.968274\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − 14.6430i | − 1.44282i | −0.692509 | − | 0.721409i | \(-0.743495\pi\) | ||||
0.692509 | − | 0.721409i | \(-0.256505\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 11.3288 | 1.09520 | 0.547600 | − | 0.836740i | \(-0.315541\pi\) | ||||
0.547600 | + | 0.836740i | \(0.315541\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − 9.37169i | − 0.897645i | −0.893621 | − | 0.448823i | \(-0.851843\pi\) | ||||
0.893621 | − | 0.448823i | \(-0.148157\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −4.39312 | −0.416976 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − 19.7648i | − 1.85932i | −0.368423 | − | 0.929658i | \(-0.620102\pi\) | ||||
0.368423 | − | 0.929658i | \(-0.379898\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 4.97858 | 0.460270 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −13.9572 | −1.27945 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 5.74338 | 0.522126 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 11.3717 | 1.02535 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − 6.64300i | − 0.589471i | −0.955579 | − | 0.294735i | \(-0.904768\pi\) | ||||
0.955579 | − | 0.294735i | \(-0.0952315\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −9.37169 | −0.825132 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 7.07896i | 0.618492i | 0.950982 | + | 0.309246i | \(0.100077\pi\) | ||||
−0.950982 | + | 0.309246i | \(0.899923\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −12.5855 | −1.09130 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − 14.9786i | − 1.27971i | −0.768497 | − | 0.639853i | \(-0.778995\pi\) | ||||
0.768497 | − | 0.639853i | \(-0.221005\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − 4.64300i | − 0.393814i | −0.980422 | − | 0.196907i | \(-0.936910\pi\) | ||||
0.980422 | − | 0.196907i | \(-0.0630897\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 7.27131i | 0.612355i | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 11.4145i | 0.954532i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 14.9572 | 1.23365 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 2.00000i | 0.163846i | 0.996639 | + | 0.0819232i | \(0.0261062\pi\) | ||||
−0.996639 | + | 0.0819232i | \(0.973894\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 8.35027 | 0.679535 | 0.339768 | − | 0.940509i | \(-0.389652\pi\) | ||||
0.339768 | + | 0.940509i | \(0.389652\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | − 2.97858i | − 0.240804i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −22.3503 | −1.78375 | −0.891873 | − | 0.452286i | \(-0.850609\pi\) | ||||
−0.891873 | + | 0.452286i | \(0.850609\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −2.00000 | −0.158610 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 12.5855 | 0.991873 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −1.37169 | −0.107439 | −0.0537196 | − | 0.998556i | \(-0.517108\pi\) | ||||
−0.0537196 | + | 0.998556i | \(0.517108\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − 11.2713i | − 0.872200i | −0.899898 | − | 0.436100i | \(-0.856359\pi\) | ||||
0.899898 | − | 0.436100i | \(-0.143641\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 11.7862 | 0.906633 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | − 2.68585i | − 0.205392i | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 10.7862 | 0.820062 | 0.410031 | − | 0.912072i | \(-0.365518\pi\) | ||||
0.410031 | + | 0.912072i | \(0.365518\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 1.70727i | 0.128326i | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − 3.66442i | − 0.273892i | −0.990579 | − | 0.136946i | \(-0.956271\pi\) | ||||
0.990579 | − | 0.136946i | \(-0.0437287\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 6.62831i | 0.492678i | 0.969184 | + | 0.246339i | \(0.0792277\pi\) | ||||
−0.969184 | + | 0.246339i | \(0.920772\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 4.58546i | 0.338967i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 6.82908 | 0.499392 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 4.68585i | 0.340845i | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 8.00000 | 0.578860 | 0.289430 | − | 0.957199i | \(-0.406534\pi\) | ||||
0.289430 | + | 0.957199i | \(0.406534\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − 1.21377i | − 0.0873690i | −0.999045 | − | 0.0436845i | \(-0.986090\pi\) | ||||
0.999045 | − | 0.0436845i | \(-0.0139096\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 23.9572 | 1.70688 | 0.853438 | − | 0.521194i | \(-0.174513\pi\) | ||||
0.853438 | + | 0.521194i | \(0.174513\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 0.350269 | 0.0248299 | 0.0124150 | − | 0.999923i | \(-0.496048\pi\) | ||||
0.0124150 | + | 0.999923i | \(0.496048\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 4.00000 | 0.282138 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 9.37169 | 0.657764 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 2.68585i | 0.186679i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 6.15792 | 0.425952 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 14.1004i | 0.970710i | 0.874317 | + | 0.485355i | \(0.161310\pi\) | ||||
−0.874317 | + | 0.485355i | \(0.838690\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0.585462 | 0.0401152 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − 32.7005i | − 2.21986i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | − 6.00000i | − 0.405442i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − 14.8291i | − 0.997512i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − 6.72869i | − 0.450587i | −0.974291 | − | 0.225293i | \(-0.927666\pi\) | ||||
0.974291 | − | 0.225293i | \(-0.0723340\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −9.95715 | −0.660880 | −0.330440 | − | 0.943827i | \(-0.607197\pi\) | ||||
−0.330440 | + | 0.943827i | \(0.607197\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − 11.3288i | − 0.748631i | −0.927301 | − | 0.374316i | \(-0.877878\pi\) | ||||
0.927301 | − | 0.374316i | \(-0.122122\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −10.7434 | −0.706863 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 18.9786i | 1.24333i | 0.783284 | + | 0.621664i | \(0.213543\pi\) | ||||
−0.783284 | + | 0.621664i | \(0.786457\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −1.02142 | −0.0663485 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 2.62831 | 0.170011 | 0.0850055 | − | 0.996380i | \(-0.472909\pi\) | ||||
0.0850055 | + | 0.996380i | \(0.472909\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 10.7862 | 0.694802 | 0.347401 | − | 0.937717i | \(-0.387064\pi\) | ||||
0.347401 | + | 0.937717i | \(0.387064\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − 13.3717i | − 0.850820i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 13.3717 | 0.847397 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 30.9933i | 1.95628i | 0.207952 | + | 0.978139i | \(0.433320\pi\) | ||||
−0.207952 | + | 0.978139i | \(0.566680\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −6.15792 | −0.387145 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 20.9357i | 1.30594i | 0.757386 | + | 0.652968i | \(0.226476\pi\) | ||||
−0.757386 | + | 0.652968i | \(0.773524\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − 20.5855i | − 1.27912i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 2.00000i | 0.123797i | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − 19.2713i | − 1.18832i | −0.804347 | − | 0.594160i | \(-0.797485\pi\) | ||||
0.804347 | − | 0.594160i | \(-0.202515\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 3.37169 | 0.206344 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − 24.7434i | − 1.50863i | −0.656512 | − | 0.754315i | \(-0.727969\pi\) | ||||
0.656512 | − | 0.754315i | \(-0.272031\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −27.5640 | −1.67440 | −0.837198 | − | 0.546900i | \(-0.815808\pi\) | ||||
−0.837198 | + | 0.546900i | \(0.815808\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 23.3288i | 1.41193i | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −20.3074 | −1.22015 | −0.610077 | − | 0.792342i | \(-0.708862\pi\) | ||||
−0.610077 | + | 0.792342i | \(0.708862\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 6.97858 | 0.417796 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −10.7862 | −0.643453 | −0.321726 | − | 0.946833i | \(-0.604263\pi\) | ||||
−0.321726 | + | 0.946833i | \(0.604263\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −20.0000 | −1.18888 | −0.594438 | − | 0.804141i | \(-0.702626\pi\) | ||||
−0.594438 | + | 0.804141i | \(0.702626\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 53.2860i | 3.14537i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 8.12808 | 0.478122 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 3.95715i | 0.231972i | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 21.9143 | 1.28025 | 0.640124 | − | 0.768272i | \(-0.278883\pi\) | ||||
0.640124 | + | 0.768272i | \(0.278883\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | − 2.29273i | − 0.133038i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 13.3717i | 0.773305i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | − 43.9143i | − 2.53118i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | − 2.00000i | − 0.114897i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −26.5426 | −1.51487 | −0.757434 | − | 0.652912i | \(-0.773547\pi\) | ||||
−0.757434 | + | 0.652912i | \(0.773547\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 14.6430i | 0.833011i | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −12.2008 | −0.691842 | −0.345921 | − | 0.938264i | \(-0.612434\pi\) | ||||
−0.345921 | + | 0.938264i | \(0.612434\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − 15.9572i | − 0.901952i | −0.892536 | − | 0.450976i | \(-0.851076\pi\) | ||||
0.892536 | − | 0.450976i | \(-0.148924\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −33.5296 | −1.88321 | −0.941605 | − | 0.336718i | \(-0.890683\pi\) | ||||
−0.941605 | + | 0.336718i | \(0.890683\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −4.58546 | −0.256737 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −11.3288 | −0.632315 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −8.00000 | −0.445132 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 9.37169i | 0.518256i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −34.0722 | −1.87846 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − 19.8568i | − 1.09143i | −0.837972 | − | 0.545713i | \(-0.816259\pi\) | ||||
0.837972 | − | 0.545713i | \(-0.183741\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 4.39312 | 0.240741 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 7.17092i | 0.390625i | 0.980741 | + | 0.195313i | \(0.0625721\pi\) | ||||
−0.980741 | + | 0.195313i | \(0.937428\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 19.7648i | 1.07348i | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 16.0000i | 0.866449i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 37.2860i | 2.01325i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −0.786230 | −0.0422071 | −0.0211035 | − | 0.999777i | \(-0.506718\pi\) | ||||
−0.0211035 | + | 0.999777i | \(0.506718\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 6.15792i | 0.329626i | 0.986325 | + | 0.164813i | \(0.0527021\pi\) | ||||
−0.986325 | + | 0.164813i | \(0.947298\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −4.97858 | −0.265737 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − 21.7220i | − 1.15614i | −0.815986 | − | 0.578072i | \(-0.803805\pi\) | ||||
0.815986 | − | 0.578072i | \(-0.196195\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 13.9572 | 0.738691 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 0.585462 | 0.0308995 | 0.0154498 | − | 0.999881i | \(-0.495082\pi\) | ||||
0.0154498 | + | 0.999881i | \(0.495082\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 11.7862 | 0.620328 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −5.74338 | −0.301450 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 0.485078i | 0.0253209i | 0.999920 | + | 0.0126604i | \(0.00403005\pi\) | ||||
−0.999920 | + | 0.0126604i | \(0.995970\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −11.3717 | −0.591987 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − 9.37169i | − 0.486554i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 12.3931 | 0.641691 | 0.320846 | − | 0.947132i | \(-0.396033\pi\) | ||||
0.320846 | + | 0.947132i | \(0.396033\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 9.95715i | 0.512820i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 26.0147i | 1.33629i | 0.744033 | + | 0.668143i | \(0.232910\pi\) | ||||
−0.744033 | + | 0.668143i | \(0.767090\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 6.64300i | 0.340331i | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 6.68585i | 0.341631i | 0.985303 | + | 0.170815i | \(0.0546402\pi\) | ||||
−0.985303 | + | 0.170815i | \(0.945360\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 9.37169 | 0.476390 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 29.9143i | 1.51672i | 0.651838 | + | 0.758358i | \(0.273998\pi\) | ||||
−0.651838 | + | 0.758358i | \(0.726002\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 8.00000 | 0.404577 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − 7.07896i | − 0.357086i | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 9.76481 | 0.490082 | 0.245041 | − | 0.969513i | \(-0.421199\pi\) | ||||
0.245041 | + | 0.969513i | \(0.421199\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 12.5855 | 0.630061 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −6.58546 | −0.328862 | −0.164431 | − | 0.986389i | \(-0.552579\pi\) | ||||
−0.164431 | + | 0.986389i | \(0.552579\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 34.7434 | 1.73069 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 10.0722i | 0.499262i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 25.9143 | 1.28138 | 0.640690 | − | 0.767800i | \(-0.278648\pi\) | ||||
0.640690 | + | 0.767800i | \(0.278648\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 14.9786i | 0.738839i | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −8.00000 | −0.393654 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 4.64300i | 0.227369i | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 12.2499i | 0.598446i | 0.954183 | + | 0.299223i | \(0.0967275\pi\) | ||||
−0.954183 | + | 0.299223i | \(0.903273\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 4.67115i | 0.227658i | 0.993500 | + | 0.113829i | \(0.0363116\pi\) | ||||
−0.993500 | + | 0.113829i | \(0.963688\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | − 7.27131i | − 0.353543i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −21.4868 | −1.03982 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | − 11.4145i | − 0.551099i | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −0.585462 | −0.0282007 | −0.0141004 | − | 0.999901i | \(-0.504488\pi\) | ||||
−0.0141004 | + | 0.999901i | \(0.504488\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 21.9143i | 1.05313i | 0.850133 | + | 0.526567i | \(0.176521\pi\) | ||||
−0.850133 | + | 0.526567i | \(0.823479\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 7.21377 | 0.345081 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −2.39312 | −0.114217 | −0.0571086 | − | 0.998368i | \(-0.518188\pi\) | ||||
−0.0571086 | + | 0.998368i | \(0.518188\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −14.9572 | −0.712245 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −20.7005 | −0.983512 | −0.491756 | − | 0.870733i | \(-0.663645\pi\) | ||||
−0.491756 | + | 0.870733i | \(0.663645\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | − 2.00000i | − 0.0945968i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 37.9143 | 1.78929 | 0.894643 | − | 0.446781i | \(-0.147430\pi\) | ||||
0.894643 | + | 0.446781i | \(0.147430\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − 26.0722i | − 1.22769i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −8.35027 | −0.392330 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 38.7005i | 1.81033i | 0.425055 | + | 0.905167i | \(0.360255\pi\) | ||||
−0.425055 | + | 0.905167i | \(0.639745\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 2.97858i | 0.139028i | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 4.74338i | 0.220921i | 0.993880 | + | 0.110461i | \(0.0352326\pi\) | ||||
−0.993880 | + | 0.110461i | \(0.964767\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 15.3142i | 0.711709i | 0.934541 | + | 0.355855i | \(0.115810\pi\) | ||||
−0.934541 | + | 0.355855i | \(0.884190\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 30.5426 | 1.41334 | 0.706672 | − | 0.707541i | \(-0.250196\pi\) | ||||
0.706672 | + | 0.707541i | \(0.250196\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 18.7434i | 0.865489i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 22.3503 | 1.02985 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 21.4868i | 0.987963i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 2.00000 | 0.0915737 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 3.32885 | 0.152099 | 0.0760494 | − | 0.997104i | \(-0.475769\pi\) | ||||
0.0760494 | + | 0.997104i | \(0.475769\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 21.8715 | 0.997253 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −12.5855 | −0.572658 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 12.1004i | 0.548321i | 0.961684 | + | 0.274160i | \(0.0883999\pi\) | ||||
−0.961684 | + | 0.274160i | \(0.911600\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 1.37169 | 0.0620301 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 14.2927i | 0.645022i | 0.946566 | + | 0.322511i | \(0.104527\pi\) | ||||
−0.946566 | + | 0.322511i | \(0.895473\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 5.95715 | 0.268297 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 2.74338i | 0.123058i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 9.22846i | 0.413123i | 0.978434 | + | 0.206561i | \(0.0662273\pi\) | ||||
−0.978434 | + | 0.206561i | \(0.933773\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 11.2713i | 0.503565i | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − 14.1004i | − 0.628705i | −0.949306 | − | 0.314353i | \(-0.898213\pi\) | ||||
0.949306 | − | 0.314353i | \(-0.101787\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −11.7862 | −0.523445 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 43.4011i | 1.92372i | 0.273544 | + | 0.961859i | \(0.411804\pi\) | ||||
−0.273544 | + | 0.961859i | \(0.588196\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 28.1151 | 1.24374 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 2.68585i | 0.118583i | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 16.6712 | 0.733196 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −10.7862 | −0.473463 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 10.0000 | 0.438108 | 0.219054 | − | 0.975713i | \(-0.429703\pi\) | ||||
0.219054 | + | 0.975713i | \(0.429703\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −13.5725 | −0.593482 | −0.296741 | − | 0.954958i | \(-0.595900\pi\) | ||||
−0.296741 | + | 0.954958i | \(0.595900\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − 20.7862i | − 0.905462i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 15.7862 | 0.686358 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − 1.70727i | − 0.0740892i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −56.6148 | −2.45226 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 3.66442i | 0.158132i | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − 34.2927i | − 1.47709i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − 37.2860i | − 1.60305i | −0.597961 | − | 0.801525i | \(-0.704022\pi\) | ||||
0.597961 | − | 0.801525i | \(-0.295978\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | − 6.62831i | − 0.284448i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −0.200768 | −0.00858424 | −0.00429212 | − | 0.999991i | \(-0.501366\pi\) | ||||
−0.00429212 | + | 0.999991i | \(0.501366\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | − 4.58546i | − 0.195703i | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 5.37169 | 0.228842 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − 4.78623i | − 0.203531i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −9.21377 | −0.390400 | −0.195200 | − | 0.980763i | \(-0.562536\pi\) | ||||
−0.195200 | + | 0.980763i | \(0.562536\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 46.6577 | 1.97341 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −6.82908 | −0.288324 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 36.7005 | 1.54674 | 0.773372 | − | 0.633953i | \(-0.218569\pi\) | ||||
0.773372 | + | 0.633953i | \(0.218569\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | − 4.68585i | − 0.196787i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −13.4145 | −0.562367 | −0.281183 | − | 0.959654i | \(-0.590727\pi\) | ||||
−0.281183 | + | 0.959654i | \(0.590727\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − 18.6858i | − 0.781978i | −0.920395 | − | 0.390989i | \(-0.872133\pi\) | ||||
0.920395 | − | 0.390989i | \(-0.127867\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −8.00000 | −0.334205 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − 2.78623i | − 0.115992i | −0.998317 | − | 0.0579961i | \(-0.981529\pi\) | ||||
0.998317 | − | 0.0579961i | \(-0.0184711\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 1.21377i | 0.0504425i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 62.6577i | 2.59948i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 4.58546i | 0.189910i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −27.3288 | −1.12798 | −0.563991 | − | 0.825781i | \(-0.690735\pi\) | ||||
−0.563991 | + | 0.825781i | \(0.690735\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − 18.7434i | − 0.772308i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −23.9572 | −0.985466 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 6.97858i | 0.286576i | 0.989681 | + | 0.143288i | \(0.0457675\pi\) | ||||
−0.989681 | + | 0.143288i | \(0.954233\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −0.350269 | −0.0143356 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 36.4998 | 1.49134 | 0.745670 | − | 0.666315i | \(-0.232130\pi\) | ||||
0.745670 | + | 0.666315i | \(0.232130\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −15.5725 | −0.635214 | −0.317607 | − | 0.948222i | \(-0.602879\pi\) | ||||
−0.317607 | + | 0.948222i | \(0.602879\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −4.00000 | −0.162893 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 31.2285i | 1.26752i | 0.773528 | + | 0.633762i | \(0.218490\pi\) | ||||
−0.773528 | + | 0.633762i | \(0.781510\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −9.37169 | −0.379760 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − 36.2008i | − 1.46453i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −0.978577 | −0.0395244 | −0.0197622 | − | 0.999805i | \(-0.506291\pi\) | ||||
−0.0197622 | + | 0.999805i | \(0.506291\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 32.9357i | 1.32594i | 0.748645 | + | 0.662971i | \(0.230705\pi\) | ||||
−0.748645 | + | 0.662971i | \(0.769295\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 3.35700i | 0.134929i | 0.997722 | + | 0.0674646i | \(0.0214910\pi\) | ||||
−0.997722 | + | 0.0674646i | \(0.978509\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | − 2.68585i | − 0.107779i | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 15.7992i | 0.632983i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −6.15792 | −0.245924 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − 13.0852i | − 0.521742i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 27.7648 | 1.10530 | 0.552650 | − | 0.833414i | \(-0.313617\pi\) | ||||
0.552650 | + | 0.833414i | \(0.313617\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | − 14.1004i | − 0.560440i | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −74.4653 | −2.95042 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −0.585462 | −0.0231605 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −21.1281 | −0.834509 | −0.417254 | − | 0.908790i | \(-0.637008\pi\) | ||||
−0.417254 | + | 0.908790i | \(0.637008\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 29.2860 | 1.15493 | 0.577464 | − | 0.816416i | \(-0.304043\pi\) | ||||
0.577464 | + | 0.816416i | \(0.304043\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − 15.6728i | − 0.616163i | −0.951360 | − | 0.308082i | \(-0.900313\pi\) | ||||
0.951360 | − | 0.308082i | \(-0.0996870\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 3.91431 | 0.153650 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 32.7005i | 1.28164i | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −17.5296 | −0.685987 | −0.342993 | − | 0.939338i | \(-0.611441\pi\) | ||||
−0.342993 | + | 0.939338i | \(0.611441\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 6.00000i | 0.234082i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 23.8652i | 0.929656i | 0.885401 | + | 0.464828i | \(0.153884\pi\) | ||||
−0.885401 | + | 0.464828i | \(0.846116\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 30.1579i | 1.17301i | 0.809947 | + | 0.586504i | \(0.199496\pi\) | ||||
−0.809947 | + | 0.586504i | \(0.800504\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 14.8291i | 0.575914i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −5.37169 | −0.207993 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 6.72869i | 0.260146i | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 10.5132 | 0.405859 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 18.0000i | 0.693849i | 0.937893 | + | 0.346925i | \(0.112774\pi\) | ||||
−0.937893 | + | 0.346925i | \(0.887226\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 9.61531 | 0.369546 | 0.184773 | − | 0.982781i | \(-0.440845\pi\) | ||||
0.184773 | + | 0.982781i | \(0.440845\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −18.5426 | −0.711600 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 9.95715 | 0.381559 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 18.6283 | 0.712792 | 0.356396 | − | 0.934335i | \(-0.384005\pi\) | ||||
0.356396 | + | 0.934335i | \(0.384005\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 11.3288i | 0.432222i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 9.95715 | 0.379337 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − 13.4292i | − 0.510872i | −0.966826 | − | 0.255436i | \(-0.917781\pi\) | ||||
0.966826 | − | 0.255436i | \(-0.0822190\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 10.7434 | 0.408107 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 33.8715i | 1.28297i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | − 18.9786i | − 0.717836i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − 19.1709i | − 0.724076i | −0.932163 | − | 0.362038i | \(-0.882081\pi\) | ||||
0.932163 | − | 0.362038i | \(-0.117919\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − 11.7992i | − 0.445016i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 9.37169 | 0.352459 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 15.4145i | 0.578905i | 0.957192 | + | 0.289453i | \(0.0934732\pi\) | ||||
−0.957192 | + | 0.289453i | \(0.906527\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 1.02142 | 0.0383063 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 18.7434i | 0.701945i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −2.62831 | −0.0981559 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 20.7862 | 0.775196 | 0.387598 | − | 0.921829i | \(-0.373305\pi\) | ||||
0.387598 | + | 0.921829i | \(0.373305\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −68.6148 | −2.55535 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −10.7862 | −0.401144 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − 12.3012i | − 0.456224i | −0.973635 | − | 0.228112i | \(-0.926745\pi\) | ||||
0.973635 | − | 0.228112i | \(-0.0732553\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − 27.9143i | − 1.03245i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 35.9227 | 1.32684 | 0.663418 | − | 0.748249i | \(-0.269105\pi\) | ||||
0.663418 | + | 0.748249i | \(0.269105\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − 9.17092i | − 0.337815i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − 29.0277i | − 1.06780i | −0.845547 | − | 0.533900i | \(-0.820726\pi\) | ||||
0.845547 | − | 0.533900i | \(-0.179274\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 13.3717i | 0.491221i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 2.60015i | 0.0953904i | 0.998862 | + | 0.0476952i | \(0.0151876\pi\) | ||||
−0.998862 | + | 0.0476952i | \(0.984812\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −13.3717 | −0.489245 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − 53.0852i | − 1.93969i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 10.8929 | 0.397487 | 0.198744 | − | 0.980052i | \(-0.436314\pi\) | ||||
0.198744 | + | 0.980052i | \(0.436314\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | − 30.9933i | − 1.12946i | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 34.3503 | 1.24848 | 0.624241 | − | 0.781232i | \(-0.285408\pi\) | ||||
0.624241 | + | 0.781232i | \(0.285408\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 6.15792 | 0.223518 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −19.0852 | −0.691839 | −0.345920 | − | 0.938264i | \(-0.612433\pi\) | ||||
−0.345920 | + | 0.938264i | \(0.612433\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −43.9143 | −1.58980 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − 8.49977i | − 0.306909i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −31.8715 | −1.14931 | −0.574657 | − | 0.818394i | \(-0.694865\pi\) | ||||
−0.574657 | + | 0.818394i | \(0.694865\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | − 20.9357i | − 0.753982i | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 11.9572 | 0.430069 | 0.215034 | − | 0.976606i | \(-0.431014\pi\) | ||||
0.215034 | + | 0.976606i | \(0.431014\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 20.5855i | 0.738499i | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 30.5426i | 1.09430i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − 1.34231i | − 0.0480315i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | − 2.00000i | − 0.0714742i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −33.0852 | −1.17936 | −0.589681 | − | 0.807637i | \(-0.700746\pi\) | ||||
−0.589681 | + | 0.807637i | \(0.700746\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 19.2713i | 0.686077i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −92.6148 | −3.29300 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − 22.8291i | − 0.810684i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −10.0000 | −0.354218 | −0.177109 | − | 0.984191i | \(-0.556675\pi\) | ||||
−0.177109 | + | 0.984191i | \(0.556675\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −21.6582 | −0.766210 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −3.37169 | −0.119133 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −13.7564 | −0.485452 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 24.7434i | 0.871008i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 30.6148 | 1.07636 | 0.538180 | − | 0.842830i | \(-0.319112\pi\) | ||||
0.538180 | + | 0.842830i | \(0.319112\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 53.9290i | 1.89370i | 0.321670 | + | 0.946852i | \(0.395756\pi\) | ||||
−0.321670 | + | 0.946852i | \(0.604244\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 27.5640 | 0.966713 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − 25.1709i | − 0.880619i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | − 23.3288i | − 0.815176i | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − 12.6577i | − 0.441757i | −0.975301 | − | 0.220878i | \(-0.929108\pi\) | ||||
0.975301 | − | 0.220878i | \(-0.0708924\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − 19.8139i | − 0.690670i | −0.938479 | − | 0.345335i | \(-0.887765\pi\) | ||||
0.938479 | − | 0.345335i | \(-0.112235\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −20.0000 | −0.695468 | −0.347734 | − | 0.937593i | \(-0.613049\pi\) | ||||
−0.347734 | + | 0.937593i | \(0.613049\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − 41.3717i | − 1.43690i | −0.695580 | − | 0.718449i | \(-0.744852\pi\) | ||||
0.695580 | − | 0.718449i | \(-0.255148\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 20.3074 | 0.704457 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 44.5510i | 1.54360i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −6.97858 | −0.241215 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 20.9013 | 0.721593 | 0.360797 | − | 0.932645i | \(-0.382505\pi\) | ||||
0.360797 | + | 0.932645i | \(0.382505\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 25.0000 | 0.862069 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 10.7862 | 0.371498 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − 26.9126i | − 0.924728i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 20.0000 | 0.686398 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 11.7992i | 0.404472i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −6.63673 | −0.227237 | −0.113619 | − | 0.993524i | \(-0.536244\pi\) | ||||
−0.113619 | + | 0.993524i | \(0.536244\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 9.80765i | 0.335023i | 0.985870 | + | 0.167512i | \(0.0535731\pi\) | ||||
−0.985870 | + | 0.167512i | \(0.946427\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − 39.3864i | − 1.34385i | −0.740621 | − | 0.671923i | \(-0.765469\pi\) | ||||
0.740621 | − | 0.671923i | \(-0.234531\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | − 53.2860i | − 1.81598i | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 7.07054i | 0.240684i | 0.992732 | + | 0.120342i | \(0.0383991\pi\) | ||||
−0.992732 | + | 0.120342i | \(0.961601\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −8.12808 | −0.276044 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 2.34185i | 0.0794417i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −19.9143 | −0.674771 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | − 3.95715i | − 0.133929i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 23.1365 | 0.781264 | 0.390632 | − | 0.920547i | \(-0.372256\pi\) | ||||
0.390632 | + | 0.920547i | \(0.372256\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −21.9143 | −0.739151 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 28.4569 | 0.958738 | 0.479369 | − | 0.877613i | \(-0.340866\pi\) | ||||
0.479369 | + | 0.877613i | \(0.340866\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −41.2003 | −1.38650 | −0.693250 | − | 0.720697i | \(-0.743822\pi\) | ||||
−0.693250 | + | 0.720697i | \(0.743822\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 3.55777i | 0.119458i | 0.998215 | + | 0.0597291i | \(0.0190237\pi\) | ||||
−0.998215 | + | 0.0597291i | \(0.980976\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −31.1281 | −1.04400 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 2.29273i | 0.0768094i | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −19.5296 | −0.653534 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | − 13.3717i | − 0.446468i | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 13.9572i | 0.465497i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − 5.95715i | − 0.198462i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 43.9143i | 1.46138i | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 50.6577 | 1.68206 | 0.841031 | − | 0.540988i | \(-0.181949\pi\) | ||||
0.841031 | + | 0.540988i | \(0.181949\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 2.00000i | 0.0663358i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 26.4569 | 0.876557 | 0.438279 | − | 0.898839i | \(-0.355588\pi\) | ||||
0.438279 | + | 0.898839i | \(0.355588\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − 30.6577i | − 1.01462i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 33.1709 | 1.09540 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 29.8077 | 0.983264 | 0.491632 | − | 0.870803i | \(-0.336401\pi\) | ||||
0.491632 | + | 0.870803i | \(0.336401\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 26.5426 | 0.874609 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −2.91477 | −0.0959407 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | − 14.6430i | − 0.480939i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 8.82908 | 0.289673 | 0.144836 | − | 0.989456i | \(-0.453734\pi\) | ||||
0.144836 | + | 0.989456i | \(0.453734\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 40.1726i | 1.31660i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 12.2008 | 0.399435 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − 42.2302i | − 1.37960i | −0.724000 | − | 0.689799i | \(-0.757699\pi\) | ||||
0.724000 | − | 0.689799i | \(-0.242301\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 15.9572i | 0.520742i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − 32.7434i | − 1.06740i | −0.845673 | − | 0.533702i | \(-0.820800\pi\) | ||||
0.845673 | − | 0.533702i | \(-0.179200\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − 30.5426i | − 0.994604i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 15.9143 | 0.517146 | 0.258573 | − | 0.965992i | \(-0.416748\pi\) | ||||
0.258573 | + | 0.965992i | \(0.416748\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 29.8715i | 0.969669i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 33.5296 | 1.08727 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − 55.6791i | − 1.80362i | −0.432129 | − | 0.901812i | \(-0.642238\pi\) | ||||
0.432129 | − | 0.901812i | \(-0.357762\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 4.58546 | 0.148227 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −70.1873 | −2.26647 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 17.7005 | 0.570985 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 11.3288 | 0.365067 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 54.7581i | 1.76090i | 0.474138 | + | 0.880451i | \(0.342760\pi\) | ||||
−0.474138 | + | 0.880451i | \(0.657240\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 8.00000 | 0.256997 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − 30.3221i | − 0.973083i | −0.873657 | − | 0.486542i | \(-0.838258\pi\) | ||||
0.873657 | − | 0.486542i | \(-0.161742\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −21.7564 | −0.697478 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − 29.7220i | − 0.950890i | −0.879746 | − | 0.475445i | \(-0.842287\pi\) | ||||
0.879746 | − | 0.475445i | \(-0.157713\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − 7.73038i | − 0.247064i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | − 9.37169i | − 0.299215i | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − 49.5443i | − 1.58022i | −0.612966 | − | 0.790109i | \(-0.710024\pi\) | ||||
0.612966 | − | 0.790109i | \(-0.289976\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 34.0722 | 1.08453 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 25.1709i | 0.800389i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −19.0937 | −0.606530 | −0.303265 | − | 0.952906i | \(-0.598077\pi\) | ||||
−0.303265 | + | 0.952906i | \(0.598077\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 19.8568i | 0.630136i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 38.8500 | 1.23039 | 0.615197 | − | 0.788374i | \(-0.289077\pi\) | ||||
0.615197 | + | 0.788374i | \(0.289077\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −4.39312 | −0.138992 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))