Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3969,2,Mod(1,3969)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3969, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("3969.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3969 = 3^{4} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3969.a (trivial) |
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: | yes |
Analytic conductor: | \(31.6926245622\) |
Analytic rank: | \(0\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.321.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 4x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 63) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(0.239123\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3969.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.239123 | −0.169086 | −0.0845428 | − | 0.996420i | \(-0.526943\pi\) | ||||
−0.0845428 | + | 0.996420i | \(0.526943\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −1.94282 | −0.971410 | ||||||||
\(5\) | −1.18194 | −0.528581 | −0.264291 | − | 0.964443i | \(-0.585138\pi\) | ||||
−0.264291 | + | 0.964443i | \(0.585138\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0.942820 | 0.333337 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0.282630 | 0.0893755 | ||||||||
\(11\) | −3.70370 | −1.11671 | −0.558353 | − | 0.829603i | \(-0.688567\pi\) | ||||
−0.558353 | + | 0.829603i | \(0.688567\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.00000 | −0.277350 | −0.138675 | − | 0.990338i | \(-0.544284\pi\) | ||||
−0.138675 | + | 0.990338i | \(0.544284\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 3.66019 | 0.915047 | ||||||||
\(17\) | 6.94282 | 1.68388 | 0.841941 | − | 0.539570i | \(-0.181413\pi\) | ||||
0.841941 | + | 0.539570i | \(0.181413\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.94282 | −0.445713 | −0.222857 | − | 0.974851i | \(-0.571538\pi\) | ||||
−0.222857 | + | 0.974851i | \(0.571538\pi\) | |||||||
\(20\) | 2.29630 | 0.513469 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0.885640 | 0.188819 | ||||||||
\(23\) | −5.60301 | −1.16831 | −0.584154 | − | 0.811643i | \(-0.698574\pi\) | ||||
−0.584154 | + | 0.811643i | \(0.698574\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −3.60301 | −0.720602 | ||||||||
\(26\) | 0.239123 | 0.0468959 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0.239123 | 0.0444041 | 0.0222020 | − | 0.999754i | \(-0.492932\pi\) | ||||
0.0222020 | + | 0.999754i | \(0.492932\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.66019 | −0.298179 | −0.149089 | − | 0.988824i | \(-0.547634\pi\) | ||||
−0.149089 | + | 0.988824i | \(0.547634\pi\) | |||||||
\(32\) | −2.76088 | −0.488059 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −1.66019 | −0.284720 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −9.54583 | −1.56932 | −0.784662 | − | 0.619923i | \(-0.787164\pi\) | ||||
−0.784662 | + | 0.619923i | \(0.787164\pi\) | |||||||
\(38\) | 0.464574 | 0.0753638 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −1.11436 | −0.176196 | ||||||||
\(41\) | 10.1819 | 1.59015 | 0.795076 | − | 0.606510i | \(-0.207431\pi\) | ||||
0.795076 | + | 0.606510i | \(0.207431\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2.22545 | 0.339378 | 0.169689 | − | 0.985498i | \(-0.445724\pi\) | ||||
0.169689 | + | 0.985498i | \(0.445724\pi\) | |||||||
\(44\) | 7.19562 | 1.08478 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 1.33981 | 0.197544 | ||||||||
\(47\) | −5.82846 | −0.850168 | −0.425084 | − | 0.905154i | \(-0.639755\pi\) | ||||
−0.425084 | + | 0.905154i | \(0.639755\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0.861564 | 0.121843 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 1.94282 | 0.269421 | ||||||||
\(53\) | −11.6030 | −1.59380 | −0.796898 | − | 0.604114i | \(-0.793527\pi\) | ||||
−0.796898 | + | 0.604114i | \(0.793527\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 4.37756 | 0.590270 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −0.0571799 | −0.00750809 | ||||||||
\(59\) | −2.60301 | −0.338883 | −0.169442 | − | 0.985540i | \(-0.554196\pi\) | ||||
−0.169442 | + | 0.985540i | \(0.554196\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 7.60301 | 0.973466 | 0.486733 | − | 0.873551i | \(-0.338189\pi\) | ||||
0.486733 | + | 0.873551i | \(0.338189\pi\) | |||||||
\(62\) | 0.396990 | 0.0504178 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −6.66019 | −0.832524 | ||||||||
\(65\) | 1.18194 | 0.146602 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 3.50808 | 0.428580 | 0.214290 | − | 0.976770i | \(-0.431256\pi\) | ||||
0.214290 | + | 0.976770i | \(0.431256\pi\) | |||||||
\(68\) | −13.4887 | −1.63574 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 8.60301 | 1.02099 | 0.510495 | − | 0.859881i | \(-0.329462\pi\) | ||||
0.510495 | + | 0.859881i | \(0.329462\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −15.1488 | −1.77304 | −0.886519 | − | 0.462693i | \(-0.846883\pi\) | ||||
−0.886519 | + | 0.462693i | \(0.846883\pi\) | |||||||
\(74\) | 2.28263 | 0.265350 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 3.77455 | 0.432971 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 7.37756 | 0.830040 | 0.415020 | − | 0.909812i | \(-0.363775\pi\) | ||||
0.415020 | + | 0.909812i | \(0.363775\pi\) | |||||||
\(80\) | −4.32614 | −0.483677 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −2.43474 | −0.268872 | ||||||||
\(83\) | 6.94282 | 0.762074 | 0.381037 | − | 0.924560i | \(-0.375567\pi\) | ||||
0.381037 | + | 0.924560i | \(0.375567\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −8.20602 | −0.890068 | ||||||||
\(86\) | −0.532157 | −0.0573840 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −3.49192 | −0.372240 | ||||||||
\(89\) | −2.74720 | −0.291203 | −0.145602 | − | 0.989343i | \(-0.546512\pi\) | ||||
−0.145602 | + | 0.989343i | \(0.546512\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 10.8856 | 1.13491 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 1.39372 | 0.143751 | ||||||||
\(95\) | 2.29630 | 0.235596 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −7.16827 | −0.727828 | −0.363914 | − | 0.931433i | \(-0.618560\pi\) | ||||
−0.363914 | + | 0.931433i | \(0.618560\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 7.00000 | 0.700000 | ||||||||
\(101\) | 12.7850 | 1.27215 | 0.636075 | − | 0.771627i | \(-0.280557\pi\) | ||||
0.636075 | + | 0.771627i | \(0.280557\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 4.39699 | 0.433248 | 0.216624 | − | 0.976255i | \(-0.430495\pi\) | ||||
0.216624 | + | 0.976255i | \(0.430495\pi\) | |||||||
\(104\) | −0.942820 | −0.0924511 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 2.77455 | 0.269488 | ||||||||
\(107\) | 13.7278 | 1.32711 | 0.663557 | − | 0.748126i | \(-0.269046\pi\) | ||||
0.663557 | + | 0.748126i | \(0.269046\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1.26320 | 0.120993 | 0.0604963 | − | 0.998168i | \(-0.480732\pi\) | ||||
0.0604963 | + | 0.998168i | \(0.480732\pi\) | |||||||
\(110\) | −1.04678 | −0.0998062 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 12.1625 | 1.14415 | 0.572076 | − | 0.820200i | \(-0.306138\pi\) | ||||
0.572076 | + | 0.820200i | \(0.306138\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 6.62244 | 0.617546 | ||||||||
\(116\) | −0.464574 | −0.0431346 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0.622440 | 0.0573003 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 2.71737 | 0.247034 | ||||||||
\(122\) | −1.81806 | −0.164599 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 3.22545 | 0.289654 | ||||||||
\(125\) | 10.1683 | 0.909478 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1.33981 | 0.118889 | 0.0594445 | − | 0.998232i | \(-0.481067\pi\) | ||||
0.0594445 | + | 0.998232i | \(0.481067\pi\) | |||||||
\(128\) | 7.11436 | 0.628827 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −0.282630 | −0.0247883 | ||||||||
\(131\) | 4.96690 | 0.433960 | 0.216980 | − | 0.976176i | \(-0.430379\pi\) | ||||
0.216980 | + | 0.976176i | \(0.430379\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −0.838864 | −0.0724668 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 6.54583 | 0.561300 | ||||||||
\(137\) | −4.33981 | −0.370775 | −0.185387 | − | 0.982665i | \(-0.559354\pi\) | ||||
−0.185387 | + | 0.982665i | \(0.559354\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −3.94282 | −0.334426 | −0.167213 | − | 0.985921i | \(-0.553477\pi\) | ||||
−0.167213 | + | 0.985921i | \(0.553477\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −2.05718 | −0.172635 | ||||||||
\(143\) | 3.70370 | 0.309719 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −0.282630 | −0.0234712 | ||||||||
\(146\) | 3.62244 | 0.299795 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 18.5458 | 1.52446 | ||||||||
\(149\) | 11.1111 | 0.910256 | 0.455128 | − | 0.890426i | \(-0.349594\pi\) | ||||
0.455128 | + | 0.890426i | \(0.349594\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 13.9234 | 1.13307 | 0.566535 | − | 0.824038i | \(-0.308284\pi\) | ||||
0.566535 | + | 0.824038i | \(0.308284\pi\) | |||||||
\(152\) | −1.83173 | −0.148573 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 1.96225 | 0.157612 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −0.0571799 | −0.00456346 | −0.00228173 | − | 0.999997i | \(-0.500726\pi\) | ||||
−0.00228173 | + | 0.999997i | \(0.500726\pi\) | |||||||
\(158\) | −1.76415 | −0.140348 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 3.26320 | 0.257979 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −1.50808 | −0.118122 | −0.0590610 | − | 0.998254i | \(-0.518811\pi\) | ||||
−0.0590610 | + | 0.998254i | \(0.518811\pi\) | |||||||
\(164\) | −19.7817 | −1.54469 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −1.66019 | −0.128856 | ||||||||
\(167\) | 14.6843 | 1.13630 | 0.568151 | − | 0.822924i | \(-0.307659\pi\) | ||||
0.568151 | + | 0.822924i | \(0.307659\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.0000 | −0.923077 | ||||||||
\(170\) | 1.96225 | 0.150498 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −4.32365 | −0.329675 | ||||||||
\(173\) | −0.252796 | −0.0192197 | −0.00960987 | − | 0.999954i | \(-0.503059\pi\) | ||||
−0.00960987 | + | 0.999954i | \(0.503059\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −13.5562 | −1.02184 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0.656920 | 0.0492383 | ||||||||
\(179\) | 14.1923 | 1.06079 | 0.530393 | − | 0.847752i | \(-0.322044\pi\) | ||||
0.530393 | + | 0.847752i | \(0.322044\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1.43147 | 0.106400 | 0.0532002 | − | 0.998584i | \(-0.483058\pi\) | ||||
0.0532002 | + | 0.998584i | \(0.483058\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −5.28263 | −0.389441 | ||||||||
\(185\) | 11.2826 | 0.829515 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −25.7141 | −1.88040 | ||||||||
\(188\) | 11.3236 | 0.825862 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −0.549100 | −0.0398359 | ||||||||
\(191\) | 15.0676 | 1.09025 | 0.545126 | − | 0.838354i | \(-0.316482\pi\) | ||||
0.545126 | + | 0.838354i | \(0.316482\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −7.84789 | −0.564904 | −0.282452 | − | 0.959282i | \(-0.591148\pi\) | ||||
−0.282452 | + | 0.959282i | \(0.591148\pi\) | |||||||
\(194\) | 1.71410 | 0.123065 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 6.69002 | 0.476644 | 0.238322 | − | 0.971186i | \(-0.423403\pi\) | ||||
0.238322 | + | 0.971186i | \(0.423403\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 19.9396 | 1.41348 | 0.706739 | − | 0.707475i | \(-0.250166\pi\) | ||||
0.706739 | + | 0.707475i | \(0.250166\pi\) | |||||||
\(200\) | −3.39699 | −0.240203 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −3.05718 | −0.215102 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −12.0345 | −0.840525 | ||||||||
\(206\) | −1.05142 | −0.0732561 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −3.66019 | −0.253789 | ||||||||
\(209\) | 7.19562 | 0.497731 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −18.0917 | −1.24548 | −0.622741 | − | 0.782428i | \(-0.713981\pi\) | ||||
−0.622741 | + | 0.782428i | \(0.713981\pi\) | |||||||
\(212\) | 22.5426 | 1.54823 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −3.28263 | −0.224396 | ||||||||
\(215\) | −2.63036 | −0.179389 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −0.302060 | −0.0204581 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −8.50481 | −0.573394 | ||||||||
\(221\) | −6.94282 | −0.467025 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 22.6569 | 1.51722 | 0.758610 | − | 0.651545i | \(-0.225879\pi\) | ||||
0.758610 | + | 0.651545i | \(0.225879\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −2.90834 | −0.193460 | ||||||||
\(227\) | 5.28263 | 0.350620 | 0.175310 | − | 0.984513i | \(-0.443907\pi\) | ||||
0.175310 | + | 0.984513i | \(0.443907\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −19.3365 | −1.27779 | −0.638897 | − | 0.769292i | \(-0.720609\pi\) | ||||
−0.638897 | + | 0.769292i | \(0.720609\pi\) | |||||||
\(230\) | −1.58358 | −0.104418 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0.225450 | 0.0148015 | ||||||||
\(233\) | −16.9806 | −1.11243 | −0.556217 | − | 0.831037i | \(-0.687748\pi\) | ||||
−0.556217 | + | 0.831037i | \(0.687748\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 6.88891 | 0.449383 | ||||||||
\(236\) | 5.05718 | 0.329194 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 16.8856 | 1.09224 | 0.546121 | − | 0.837707i | \(-0.316104\pi\) | ||||
0.546121 | + | 0.837707i | \(0.316104\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −27.1456 | −1.74860 | −0.874300 | − | 0.485386i | \(-0.838679\pi\) | ||||
−0.874300 | + | 0.485386i | \(0.838679\pi\) | |||||||
\(242\) | −0.649786 | −0.0417699 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −14.7713 | −0.945634 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1.94282 | 0.123619 | ||||||||
\(248\) | −1.56526 | −0.0993941 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −2.43147 | −0.153780 | ||||||||
\(251\) | 19.0780 | 1.20419 | 0.602096 | − | 0.798424i | \(-0.294332\pi\) | ||||
0.602096 | + | 0.798424i | \(0.294332\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 20.7518 | 1.30466 | ||||||||
\(254\) | −0.320380 | −0.0201024 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 11.6192 | 0.726198 | ||||||||
\(257\) | 14.8421 | 0.925827 | 0.462913 | − | 0.886404i | \(-0.346804\pi\) | ||||
0.462913 | + | 0.886404i | \(0.346804\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −2.29630 | −0.142411 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −1.18770 | −0.0733764 | ||||||||
\(263\) | −7.74145 | −0.477358 | −0.238679 | − | 0.971099i | \(-0.576714\pi\) | ||||
−0.238679 | + | 0.971099i | \(0.576714\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 13.7141 | 0.842450 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −6.81557 | −0.416327 | ||||||||
\(269\) | 1.51135 | 0.0921486 | 0.0460743 | − | 0.998938i | \(-0.485329\pi\) | ||||
0.0460743 | + | 0.998938i | \(0.485329\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 21.9806 | 1.33522 | 0.667612 | − | 0.744509i | \(-0.267316\pi\) | ||||
0.667612 | + | 0.744509i | \(0.267316\pi\) | |||||||
\(272\) | 25.4120 | 1.54083 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 1.03775 | 0.0626927 | ||||||||
\(275\) | 13.3445 | 0.804701 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −10.8285 | −0.650619 | −0.325310 | − | 0.945608i | \(-0.605469\pi\) | ||||
−0.325310 | + | 0.945608i | \(0.605469\pi\) | |||||||
\(278\) | 0.942820 | 0.0565466 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −16.8766 | −1.00677 | −0.503387 | − | 0.864061i | \(-0.667913\pi\) | ||||
−0.503387 | + | 0.864061i | \(0.667913\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 15.3171 | 0.910508 | 0.455254 | − | 0.890362i | \(-0.349549\pi\) | ||||
0.455254 | + | 0.890362i | \(0.349549\pi\) | |||||||
\(284\) | −16.7141 | −0.991799 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −0.885640 | −0.0523690 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 31.2028 | 1.83546 | ||||||||
\(290\) | 0.0675835 | 0.00396864 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 29.4315 | 1.72235 | ||||||||
\(293\) | 9.36964 | 0.547380 | 0.273690 | − | 0.961818i | \(-0.411756\pi\) | ||||
0.273690 | + | 0.961818i | \(0.411756\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 3.07661 | 0.179127 | ||||||||
\(296\) | −9.00000 | −0.523114 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −2.65692 | −0.153911 | ||||||||
\(299\) | 5.60301 | 0.324030 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −3.32941 | −0.191586 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −7.11109 | −0.407849 | ||||||||
\(305\) | −8.98633 | −0.514556 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −2.71410 | −0.154902 | −0.0774509 | − | 0.996996i | \(-0.524678\pi\) | ||||
−0.0774509 | + | 0.996996i | \(0.524678\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −0.469220 | −0.0266499 | ||||||||
\(311\) | 13.9806 | 0.792765 | 0.396383 | − | 0.918085i | \(-0.370265\pi\) | ||||
0.396383 | + | 0.918085i | \(0.370265\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 19.0539 | 1.07699 | 0.538495 | − | 0.842628i | \(-0.318993\pi\) | ||||
0.538495 | + | 0.842628i | \(0.318993\pi\) | |||||||
\(314\) | 0.0136731 | 0.000771615 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −14.3333 | −0.806309 | ||||||||
\(317\) | −4.01943 | −0.225754 | −0.112877 | − | 0.993609i | \(-0.536007\pi\) | ||||
−0.112877 | + | 0.993609i | \(0.536007\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −0.885640 | −0.0495863 | ||||||||
\(320\) | 7.87197 | 0.440056 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −13.4887 | −0.750529 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 3.60301 | 0.199859 | ||||||||
\(326\) | 0.360617 | 0.0199727 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 9.59974 | 0.530057 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −12.3776 | −0.680332 | −0.340166 | − | 0.940365i | \(-0.610483\pi\) | ||||
−0.340166 | + | 0.940365i | \(0.610483\pi\) | |||||||
\(332\) | −13.4887 | −0.740286 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −3.51135 | −0.192133 | ||||||||
\(335\) | −4.14635 | −0.226539 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 12.2599 | 0.667841 | 0.333920 | − | 0.942601i | \(-0.391628\pi\) | ||||
0.333920 | + | 0.942601i | \(0.391628\pi\) | |||||||
\(338\) | 2.86948 | 0.156079 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 15.9428 | 0.864621 | ||||||||
\(341\) | 6.14884 | 0.332978 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 2.09820 | 0.113127 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0.0604495 | 0.00324978 | ||||||||
\(347\) | 6.64979 | 0.356979 | 0.178490 | − | 0.983942i | \(-0.442879\pi\) | ||||
0.178490 | + | 0.983942i | \(0.442879\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −11.4347 | −0.612088 | −0.306044 | − | 0.952017i | \(-0.599005\pi\) | ||||
−0.306044 | + | 0.952017i | \(0.599005\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 10.2255 | 0.545018 | ||||||||
\(353\) | 22.1956 | 1.18135 | 0.590677 | − | 0.806908i | \(-0.298861\pi\) | ||||
0.590677 | + | 0.806908i | \(0.298861\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −10.1683 | −0.539676 | ||||||||
\(356\) | 5.33732 | 0.282878 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −3.39372 | −0.179364 | ||||||||
\(359\) | −7.55623 | −0.398803 | −0.199401 | − | 0.979918i | \(-0.563900\pi\) | ||||
−0.199401 | + | 0.979918i | \(0.563900\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −15.2255 | −0.801339 | ||||||||
\(362\) | −0.342298 | −0.0179908 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 17.9051 | 0.937194 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 18.5231 | 0.966900 | 0.483450 | − | 0.875372i | \(-0.339384\pi\) | ||||
0.483450 | + | 0.875372i | \(0.339384\pi\) | |||||||
\(368\) | −20.5081 | −1.06906 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −2.69794 | −0.140259 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 15.6602 | 0.810854 | 0.405427 | − | 0.914127i | \(-0.367123\pi\) | ||||
0.405427 | + | 0.914127i | \(0.367123\pi\) | |||||||
\(374\) | 6.14884 | 0.317949 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −5.49519 | −0.283393 | ||||||||
\(377\) | −0.239123 | −0.0123155 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 4.03775 | 0.207405 | 0.103703 | − | 0.994608i | \(-0.466931\pi\) | ||||
0.103703 | + | 0.994608i | \(0.466931\pi\) | |||||||
\(380\) | −4.46130 | −0.228860 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −3.60301 | −0.184346 | ||||||||
\(383\) | −0.225450 | −0.0115200 | −0.00575998 | − | 0.999983i | \(-0.501833\pi\) | ||||
−0.00575998 | + | 0.999983i | \(0.501833\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 1.87661 | 0.0955171 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 13.9267 | 0.707019 | ||||||||
\(389\) | 25.2632 | 1.28090 | 0.640448 | − | 0.768002i | \(-0.278749\pi\) | ||||
0.640448 | + | 0.768002i | \(0.278749\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −38.9007 | −1.96729 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −1.59974 | −0.0805938 | ||||||||
\(395\) | −8.71986 | −0.438744 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 20.3009 | 1.01888 | 0.509438 | − | 0.860508i | \(-0.329853\pi\) | ||||
0.509438 | + | 0.860508i | \(0.329853\pi\) | |||||||
\(398\) | −4.76801 | −0.238999 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −13.1877 | −0.659385 | ||||||||
\(401\) | −15.2255 | −0.760323 | −0.380161 | − | 0.924920i | \(-0.624132\pi\) | ||||
−0.380161 | + | 0.924920i | \(0.624132\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1.66019 | 0.0826999 | ||||||||
\(404\) | −24.8389 | −1.23578 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 35.3549 | 1.75248 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −1.65692 | −0.0819294 | −0.0409647 | − | 0.999161i | \(-0.513043\pi\) | ||||
−0.0409647 | + | 0.999161i | \(0.513043\pi\) | |||||||
\(410\) | 2.87772 | 0.142121 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −8.54256 | −0.420862 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −8.20602 | −0.402818 | ||||||||
\(416\) | 2.76088 | 0.135363 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −1.72064 | −0.0841592 | ||||||||
\(419\) | −33.3743 | −1.63044 | −0.815220 | − | 0.579151i | \(-0.803384\pi\) | ||||
−0.815220 | + | 0.579151i | \(0.803384\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 18.2405 | 0.888988 | 0.444494 | − | 0.895782i | \(-0.353384\pi\) | ||||
0.444494 | + | 0.895782i | \(0.353384\pi\) | |||||||
\(422\) | 4.32614 | 0.210593 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −10.9396 | −0.531272 | ||||||||
\(425\) | −25.0150 | −1.21341 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −26.6706 | −1.28917 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0.628979 | 0.0303321 | ||||||||
\(431\) | 29.2826 | 1.41049 | 0.705247 | − | 0.708961i | \(-0.250836\pi\) | ||||
0.705247 | + | 0.708961i | \(0.250836\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 12.2449 | 0.588451 | 0.294226 | − | 0.955736i | \(-0.404938\pi\) | ||||
0.294226 | + | 0.955736i | \(0.404938\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −2.45417 | −0.117533 | ||||||||
\(437\) | 10.8856 | 0.520731 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 4.83173 | 0.230606 | 0.115303 | − | 0.993330i | \(-0.463216\pi\) | ||||
0.115303 | + | 0.993330i | \(0.463216\pi\) | |||||||
\(440\) | 4.12725 | 0.196759 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 1.66019 | 0.0789672 | ||||||||
\(443\) | 1.24488 | 0.0591461 | 0.0295730 | − | 0.999563i | \(-0.490585\pi\) | ||||
0.0295730 | + | 0.999563i | \(0.490585\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 3.24704 | 0.153924 | ||||||||
\(446\) | −5.41780 | −0.256540 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 8.82846 | 0.416641 | 0.208320 | − | 0.978061i | \(-0.433200\pi\) | ||||
0.208320 | + | 0.978061i | \(0.433200\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −37.7108 | −1.77573 | ||||||||
\(452\) | −23.6296 | −1.11144 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −1.26320 | −0.0592849 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −10.5081 | −0.491547 | −0.245774 | − | 0.969327i | \(-0.579042\pi\) | ||||
−0.245774 | + | 0.969327i | \(0.579042\pi\) | |||||||
\(458\) | 4.62382 | 0.216057 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −12.8662 | −0.599890 | ||||||||
\(461\) | −22.5516 | −1.05033 | −0.525166 | − | 0.851000i | \(-0.675997\pi\) | ||||
−0.525166 | + | 0.851000i | \(0.675997\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 10.3970 | 0.483189 | 0.241595 | − | 0.970377i | \(-0.422330\pi\) | ||||
0.241595 | + | 0.970377i | \(0.422330\pi\) | |||||||
\(464\) | 0.875237 | 0.0406318 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 4.06045 | 0.188097 | ||||||||
\(467\) | −13.3171 | −0.616242 | −0.308121 | − | 0.951347i | \(-0.599700\pi\) | ||||
−0.308121 | + | 0.951347i | \(0.599700\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −1.64730 | −0.0759842 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −2.45417 | −0.112962 | ||||||||
\(473\) | −8.24239 | −0.378986 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 7.00000 | 0.321182 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −4.03775 | −0.184682 | ||||||||
\(479\) | −14.5354 | −0.664141 | −0.332070 | − | 0.943255i | \(-0.607747\pi\) | ||||
−0.332070 | + | 0.943255i | \(0.607747\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 9.54583 | 0.435252 | ||||||||
\(482\) | 6.49114 | 0.295663 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −5.27936 | −0.239971 | ||||||||
\(485\) | 8.47249 | 0.384716 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 13.0539 | 0.591529 | 0.295765 | − | 0.955261i | \(-0.404426\pi\) | ||||
0.295765 | + | 0.955261i | \(0.404426\pi\) | |||||||
\(488\) | 7.16827 | 0.324492 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 19.3445 | 0.873003 | 0.436502 | − | 0.899704i | \(-0.356217\pi\) | ||||
0.436502 | + | 0.899704i | \(0.356217\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 1.66019 | 0.0747712 | ||||||||
\(494\) | −0.464574 | −0.0209022 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −6.07661 | −0.272848 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −36.2222 | −1.62153 | −0.810764 | − | 0.585374i | \(-0.800948\pi\) | ||||
−0.810764 | + | 0.585374i | \(0.800948\pi\) | |||||||
\(500\) | −19.7551 | −0.883476 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −4.56199 | −0.203612 | ||||||||
\(503\) | −15.6764 | −0.698974 | −0.349487 | − | 0.936941i | \(-0.613644\pi\) | ||||
−0.349487 | + | 0.936941i | \(0.613644\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −15.1111 | −0.672435 | ||||||||
\(506\) | −4.96225 | −0.220599 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −2.60301 | −0.115490 | ||||||||
\(509\) | −34.3034 | −1.52047 | −0.760237 | − | 0.649646i | \(-0.774917\pi\) | ||||
−0.760237 | + | 0.649646i | \(0.774917\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −17.0071 | −0.751616 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −3.54910 | −0.156544 | ||||||||
\(515\) | −5.19699 | −0.229007 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 21.5868 | 0.949389 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 1.11436 | 0.0488679 | ||||||||
\(521\) | 10.2449 | 0.448836 | 0.224418 | − | 0.974493i | \(-0.427952\pi\) | ||||
0.224418 | + | 0.974493i | \(0.427952\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −30.6030 | −1.33818 | −0.669088 | − | 0.743183i | \(-0.733315\pi\) | ||||
−0.669088 | + | 0.743183i | \(0.733315\pi\) | |||||||
\(524\) | −9.64979 | −0.421553 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 1.85116 | 0.0807144 | ||||||||
\(527\) | −11.5264 | −0.502098 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 8.39372 | 0.364944 | ||||||||
\(530\) | −3.27936 | −0.142446 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −10.1819 | −0.441029 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −16.2255 | −0.701487 | ||||||||
\(536\) | 3.30749 | 0.142862 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −0.361399 | −0.0155810 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −26.0917 | −1.12177 | −0.560884 | − | 0.827894i | \(-0.689539\pi\) | ||||
−0.560884 | + | 0.827894i | \(0.689539\pi\) | |||||||
\(542\) | −5.25607 | −0.225767 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −19.1683 | −0.821833 | ||||||||
\(545\) | −1.49303 | −0.0639544 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −10.9234 | −0.467050 | −0.233525 | − | 0.972351i | \(-0.575026\pi\) | ||||
−0.233525 | + | 0.972351i | \(0.575026\pi\) | |||||||
\(548\) | 8.43147 | 0.360175 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −3.19097 | −0.136063 | ||||||||
\(551\) | −0.464574 | −0.0197915 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 2.58934 | 0.110010 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 7.66019 | 0.324864 | ||||||||
\(557\) | −13.9442 | −0.590835 | −0.295417 | − | 0.955368i | \(-0.595459\pi\) | ||||
−0.295417 | + | 0.955368i | \(0.595459\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −2.22545 | −0.0941265 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 4.03559 | 0.170231 | ||||||||
\(563\) | −30.2574 | −1.27520 | −0.637600 | − | 0.770368i | \(-0.720073\pi\) | ||||
−0.637600 | + | 0.770368i | \(0.720073\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −14.3754 | −0.604778 | ||||||||
\(566\) | −3.66268 | −0.153954 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 8.11109 | 0.340334 | ||||||||
\(569\) | −21.1352 | −0.886032 | −0.443016 | − | 0.896514i | \(-0.646092\pi\) | ||||
−0.443016 | + | 0.896514i | \(0.646092\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −32.7863 | −1.37207 | −0.686033 | − | 0.727571i | \(-0.740649\pi\) | ||||
−0.686033 | + | 0.727571i | \(0.740649\pi\) | |||||||
\(572\) | −7.19562 | −0.300864 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 20.1877 | 0.841885 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 17.3743 | 0.723301 | 0.361651 | − | 0.932314i | \(-0.382213\pi\) | ||||
0.361651 | + | 0.932314i | \(0.382213\pi\) | |||||||
\(578\) | −7.46130 | −0.310349 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0.549100 | 0.0228001 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 42.9740 | 1.77980 | ||||||||
\(584\) | −14.2826 | −0.591019 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −2.24050 | −0.0925542 | ||||||||
\(587\) | −16.9759 | −0.700671 | −0.350336 | − | 0.936624i | \(-0.613932\pi\) | ||||
−0.350336 | + | 0.936624i | \(0.613932\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 3.22545 | 0.132902 | ||||||||
\(590\) | −0.735689 | −0.0302878 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −34.9396 | −1.43601 | ||||||||
\(593\) | 13.0733 | 0.536858 | 0.268429 | − | 0.963300i | \(-0.413496\pi\) | ||||
0.268429 | + | 0.963300i | \(0.413496\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −21.5868 | −0.884232 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −1.33981 | −0.0547889 | ||||||||
\(599\) | 29.2060 | 1.19333 | 0.596663 | − | 0.802492i | \(-0.296493\pi\) | ||||
0.596663 | + | 0.802492i | \(0.296493\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −7.79071 | −0.317790 | −0.158895 | − | 0.987296i | \(-0.550793\pi\) | ||||
−0.158895 | + | 0.987296i | \(0.550793\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −27.0506 | −1.10067 | ||||||||
\(605\) | −3.21178 | −0.130577 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 19.6408 | 0.797194 | 0.398597 | − | 0.917126i | \(-0.369497\pi\) | ||||
0.398597 | + | 0.917126i | \(0.369497\pi\) | |||||||
\(608\) | 5.36389 | 0.217534 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 2.14884 | 0.0870040 | ||||||||
\(611\) | 5.82846 | 0.235794 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 23.5653 | 0.951792 | 0.475896 | − | 0.879502i | \(-0.342124\pi\) | ||||
0.475896 | + | 0.879502i | \(0.342124\pi\) | |||||||
\(614\) | 0.649005 | 0.0261917 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −10.6602 | −0.429163 | −0.214582 | − | 0.976706i | \(-0.568839\pi\) | ||||
−0.214582 | + | 0.976706i | \(0.568839\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 18.0150 | 0.724086 | 0.362043 | − | 0.932161i | \(-0.382079\pi\) | ||||
0.362043 | + | 0.932161i | \(0.382079\pi\) | |||||||
\(620\) | −3.81230 | −0.153106 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −3.34308 | −0.134045 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 5.99673 | 0.239869 | ||||||||
\(626\) | −4.55623 | −0.182104 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0.111090 | 0.00443299 | ||||||||
\(629\) | −66.2750 | −2.64256 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 12.4703 | 0.496436 | 0.248218 | − | 0.968704i | \(-0.420155\pi\) | ||||
0.248218 | + | 0.968704i | \(0.420155\pi\) | |||||||
\(632\) | 6.95571 | 0.276683 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0.961139 | 0.0381717 | ||||||||
\(635\) | −1.58358 | −0.0628424 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0.211777 | 0.00838434 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −8.40877 | −0.332386 | ||||||||
\(641\) | 19.1456 | 0.756205 | 0.378102 | − | 0.925764i | \(-0.376577\pi\) | ||||
0.378102 | + | 0.925764i | \(0.376577\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −6.48865 | −0.255887 | −0.127944 | − | 0.991781i | \(-0.540838\pi\) | ||||
−0.127944 | + | 0.991781i | \(0.540838\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 3.22545 | 0.126904 | ||||||||
\(647\) | 48.0988 | 1.89096 | 0.945479 | − | 0.325682i | \(-0.105594\pi\) | ||||
0.945479 | + | 0.325682i | \(0.105594\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 9.64076 | 0.378433 | ||||||||
\(650\) | −0.861564 | −0.0337933 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 2.92993 | 0.114745 | ||||||||
\(653\) | −43.2405 | −1.69213 | −0.846066 | − | 0.533079i | \(-0.821035\pi\) | ||||
−0.846066 | + | 0.533079i | \(0.821035\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −5.87059 | −0.229383 | ||||||||
\(656\) | 37.2678 | 1.45506 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −2.50808 | −0.0977009 | −0.0488505 | − | 0.998806i | \(-0.515556\pi\) | ||||
−0.0488505 | + | 0.998806i | \(0.515556\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 42.3354 | 1.64666 | 0.823329 | − | 0.567565i | \(-0.192114\pi\) | ||||
0.823329 | + | 0.567565i | \(0.192114\pi\) | |||||||
\(662\) | 2.95976 | 0.115034 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 6.54583 | 0.254027 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −1.33981 | −0.0518777 | ||||||||
\(668\) | −28.5289 | −1.10382 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0.991489 | 0.0383046 | ||||||||
\(671\) | −28.1592 | −1.08708 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 13.4153 | 0.517122 | 0.258561 | − | 0.965995i | \(-0.416752\pi\) | ||||
0.258561 | + | 0.965995i | \(0.416752\pi\) | |||||||
\(674\) | −2.93163 | −0.112922 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 23.3138 | 0.896686 | ||||||||
\(677\) | −1.96225 | −0.0754154 | −0.0377077 | − | 0.999289i | \(-0.512006\pi\) | ||||
−0.0377077 | + | 0.999289i | \(0.512006\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −7.73680 | −0.296693 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −1.47033 | −0.0563019 | ||||||||
\(683\) | 27.1672 | 1.03952 | 0.519761 | − | 0.854312i | \(-0.326021\pi\) | ||||
0.519761 | + | 0.854312i | \(0.326021\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 5.12941 | 0.195985 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 8.14557 | 0.310547 | ||||||||
\(689\) | 11.6030 | 0.442039 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 50.3171 | 1.91415 | 0.957077 | − | 0.289835i | \(-0.0936005\pi\) | ||||
0.957077 | + | 0.289835i | \(0.0936005\pi\) | |||||||
\(692\) | 0.491138 | 0.0186703 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −1.59012 | −0.0603601 | ||||||||
\(695\) | 4.66019 | 0.176771 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 70.6914 | 2.67763 | ||||||||
\(698\) | 2.73431 | 0.103495 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 45.1672 | 1.70594 | 0.852970 | − | 0.521960i | \(-0.174799\pi\) | ||||
0.852970 | + | 0.521960i | \(0.174799\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 18.5458 | 0.699469 | ||||||||
\(704\) | 24.6673 | 0.929685 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −5.30749 | −0.199750 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 39.6181 | 1.48789 | 0.743944 | − | 0.668242i | \(-0.232953\pi\) | ||||
0.743944 | + | 0.668242i | \(0.232953\pi\) | |||||||
\(710\) | 2.43147 | 0.0912514 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −2.59012 | −0.0970688 | ||||||||
\(713\) | 9.30206 | 0.348365 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −4.37756 | −0.163711 | ||||||||
\(716\) | −27.5732 | −1.03046 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 1.80687 | 0.0674318 | ||||||||
\(719\) | 22.0377 | 0.821869 | 0.410935 | − | 0.911665i | \(-0.365202\pi\) | ||||
0.410935 | + | 0.911665i | \(0.365202\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 3.64076 | 0.135495 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −2.78109 | −0.103358 | ||||||||
\(725\) | −0.861564 | −0.0319977 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −28.1111 | −1.04258 | −0.521291 | − | 0.853379i | \(-0.674550\pi\) | ||||
−0.521291 | + | 0.853379i | \(0.674550\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −4.28152 | −0.158466 | ||||||||
\(731\) | 15.4509 | 0.571472 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −11.8695 | −0.438409 | −0.219205 | − | 0.975679i | \(-0.570346\pi\) | ||||
−0.219205 | + | 0.975679i | \(0.570346\pi\) | |||||||
\(734\) | −4.42931 | −0.163489 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 15.4692 | 0.570203 | ||||||||
\(737\) | −12.9929 | −0.478598 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −12.1844 | −0.448212 | −0.224106 | − | 0.974565i | \(-0.571946\pi\) | ||||
−0.224106 | + | 0.974565i | \(0.571946\pi\) | |||||||
\(740\) | −21.9201 | −0.805800 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −44.4854 | −1.63201 | −0.816005 | − | 0.578045i | \(-0.803816\pi\) | ||||
−0.816005 | + | 0.578045i | \(0.803816\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −13.1327 | −0.481144 | ||||||||
\(746\) | −3.74472 | −0.137104 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 49.9579 | 1.82664 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 42.8058 | 1.56200 | 0.781002 | − | 0.624528i | \(-0.214709\pi\) | ||||
0.781002 | + | 0.624528i | \(0.214709\pi\) | |||||||
\(752\) | −21.3333 | −0.777944 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0.0571799 | 0.00208237 | ||||||||
\(755\) | −16.4567 | −0.598919 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −22.4919 | −0.817483 | −0.408741 | − | 0.912650i | \(-0.634032\pi\) | ||||
−0.408741 | + | 0.912650i | \(0.634032\pi\) | |||||||
\(758\) | −0.965520 | −0.0350693 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 2.16500 | 0.0785328 | ||||||||
\(761\) | 14.3365 | 0.519699 | 0.259850 | − | 0.965649i | \(-0.416327\pi\) | ||||
0.259850 | + | 0.965649i | \(0.416327\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −29.2736 | −1.05908 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0.0539104 | 0.00194786 | ||||||||
\(767\) | 2.60301 | 0.0939892 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 31.2211 | 1.12586 | 0.562930 | − | 0.826504i | \(-0.309674\pi\) | ||||
0.562930 | + | 0.826504i | \(0.309674\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 15.2470 | 0.548753 | ||||||||
\(773\) | −4.38005 | −0.157539 | −0.0787697 | − | 0.996893i | \(-0.525099\pi\) | ||||
−0.0787697 | + | 0.996893i | \(0.525099\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 5.98168 | 0.214868 | ||||||||
\(776\) | −6.75839 | −0.242612 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −6.04102 | −0.216581 | ||||||||
\(779\) | −19.7817 | −0.708752 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −31.8629 | −1.14015 | ||||||||
\(782\) | 9.30206 | 0.332641 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0.0675835 | 0.00241216 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −27.6213 | −0.984594 | −0.492297 | − | 0.870427i | \(-0.663843\pi\) | ||||
−0.492297 | + | 0.870427i | \(0.663843\pi\) | |||||||
\(788\) | −12.9975 | −0.463017 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 2.08512 | 0.0741853 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −7.60301 | −0.269991 | ||||||||
\(794\) | −4.85443 | −0.172277 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −38.7390 | −1.37307 | ||||||||
\(797\) | 2.96363 | 0.104977 | 0.0524885 | − | 0.998622i | \(-0.483285\pi\) | ||||
0.0524885 | + | 0.998622i | \(0.483285\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −40.4660 | −1.43158 | ||||||||
\(800\) | 9.94747 | 0.351696 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 3.64076 | 0.128560 | ||||||||
\(803\) | 56.1067 | 1.97996 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −0.396990 | −0.0139834 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 12.0539 | 0.424055 | ||||||||
\(809\) | −24.7896 | −0.871556 | −0.435778 | − | 0.900054i | \(-0.643527\pi\) | ||||
−0.435778 | + | 0.900054i | \(0.643527\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −8.24377 | −0.289478 | −0.144739 | − | 0.989470i | \(-0.546234\pi\) | ||||
−0.144739 | + | 0.989470i | \(0.546234\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −8.45417 | −0.296319 | ||||||||
\(815\) | 1.78247 | 0.0624370 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −4.32365 | −0.151265 | ||||||||
\(818\) | 0.396208 | 0.0138531 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 23.3808 | 0.816494 | ||||||||
\(821\) | −28.8993 | −1.00859 | −0.504296 | − | 0.863531i | \(-0.668248\pi\) | ||||
−0.504296 | + | 0.863531i | \(0.668248\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −36.0000 | −1.25488 | −0.627441 | − | 0.778664i | \(-0.715897\pi\) | ||||
−0.627441 | + | 0.778664i | \(0.715897\pi\) | |||||||
\(824\) | 4.14557 | 0.144418 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −50.7108 | −1.76339 | −0.881694 | − | 0.471821i | \(-0.843597\pi\) | ||||
−0.881694 | + | 0.471821i | \(0.843597\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −14.8123 | −0.514452 | −0.257226 | − | 0.966351i | \(-0.582809\pi\) | ||||
−0.257226 | + | 0.966351i | \(0.582809\pi\) | |||||||
\(830\) | 1.96225 | 0.0681107 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 6.66019 | 0.230901 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −17.3560 | −0.600628 | ||||||||
\(836\) | −13.9798 | −0.483501 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 7.98057 | 0.275684 | ||||||||
\(839\) | −33.7212 | −1.16419 | −0.582093 | − | 0.813122i | \(-0.697766\pi\) | ||||
−0.582093 | + | 0.813122i | \(0.697766\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −28.9428 | −0.998028 | ||||||||
\(842\) | −4.36173 | −0.150315 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 35.1488 | 1.20987 | ||||||||
\(845\) | 14.1833 | 0.487921 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −42.4692 | −1.45840 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 5.98168 | 0.205170 | ||||||||
\(851\) | 53.4854 | 1.83346 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −11.7896 | −0.403668 | −0.201834 | − | 0.979420i | \(-0.564690\pi\) | ||||
−0.201834 | + | 0.979420i | \(0.564690\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 12.9428 | 0.442376 | ||||||||
\(857\) | 31.3261 | 1.07008 | 0.535040 | − | 0.844827i | \(-0.320296\pi\) | ||||
0.535040 | + | 0.844827i | \(0.320296\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 50.3893 | 1.71926 | 0.859631 | − | 0.510915i | \(-0.170693\pi\) | ||||
0.859631 | + | 0.510915i | \(0.170693\pi\) | |||||||
\(860\) | 5.11031 | 0.174260 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −7.00216 | −0.238494 | ||||||||
\(863\) | 1.13268 | 0.0385568 | 0.0192784 | − | 0.999814i | \(-0.493863\pi\) | ||||
0.0192784 | + | 0.999814i | \(0.493863\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0.298791 | 0.0101592 | ||||||||
\(866\) | −2.92804 | −0.0994987 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −27.3242 | −0.926911 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −3.50808 | −0.118867 | ||||||||
\(872\) | 1.19097 | 0.0403313 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −2.60301 | −0.0880481 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −27.3937 | −0.925020 | −0.462510 | − | 0.886614i | \(-0.653051\pi\) | ||||
−0.462510 | + | 0.886614i | \(0.653051\pi\) | |||||||
\(878\) | −1.15538 | −0.0389922 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 16.0227 | 0.540125 | ||||||||
\(881\) | −1.20929 | −0.0407420 | −0.0203710 | − | 0.999792i | \(-0.506485\pi\) | ||||
−0.0203710 | + | 0.999792i | \(0.506485\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −51.0884 | −1.71926 | −0.859631 | − | 0.510916i | \(-0.829306\pi\) | ||||
−0.859631 | + | 0.510916i | \(0.829306\pi\) | |||||||
\(884\) | 13.4887 | 0.453672 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −0.297680 | −0.0100008 | ||||||||
\(887\) | 41.5757 | 1.39597 | 0.697987 | − | 0.716110i | \(-0.254079\pi\) | ||||
0.697987 | + | 0.716110i | \(0.254079\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −0.776443 | −0.0260264 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −44.0183 | −1.47384 | ||||||||
\(893\) | 11.3236 | 0.378931 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −16.7745 | −0.560711 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −2.11109 | −0.0704480 | ||||||||
\(899\) | −0.396990 | −0.0132404 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −80.5576 | −2.68376 | ||||||||
\(902\) | 9.01754 | 0.300251 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 11.4671 | 0.381389 | ||||||||
\(905\) | −1.69192 | −0.0562412 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 35.4509 | 1.17713 | 0.588564 | − | 0.808451i | \(-0.299694\pi\) | ||||
0.588564 | + | 0.808451i | \(0.299694\pi\) | |||||||
\(908\) | −10.2632 | −0.340596 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −20.7108 | −0.686180 | −0.343090 | − | 0.939302i | \(-0.611474\pi\) | ||||
−0.343090 | + | 0.939302i | \(0.611474\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −25.7141 | −0.851013 | ||||||||
\(914\) | 2.51273 | 0.0831136 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 37.5674 | 1.24126 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 14.3926 | 0.474768 | 0.237384 | − | 0.971416i | \(-0.423710\pi\) | ||||
0.237384 | + | 0.971416i | \(0.423710\pi\) | |||||||
\(920\) | 6.24377 | 0.205851 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 5.39261 | 0.177596 | ||||||||
\(923\) | −8.60301 | −0.283172 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 34.3937 | 1.13086 | ||||||||
\(926\) | −2.48616 | −0.0817004 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −0.660190 | −0.0216718 | ||||||||
\(929\) | 41.7428 | 1.36954 | 0.684769 | − | 0.728760i | \(-0.259903\pi\) | ||||
0.684769 | + | 0.728760i | \(0.259903\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 32.9902 | 1.08063 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 3.18443 | 0.104198 | ||||||||
\(935\) | 30.3926 | 0.993945 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −3.17154 | −0.103610 | −0.0518048 | − | 0.998657i | \(-0.516497\pi\) | ||||
−0.0518048 | + | 0.998657i | \(0.516497\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −13.3839 | −0.436535 | ||||||||
\(941\) | 3.22080 | 0.104995 | 0.0524976 | − | 0.998621i | \(-0.483282\pi\) | ||||
0.0524976 | + | 0.998621i | \(0.483282\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −57.0495 | −1.85779 | ||||||||
\(944\) | −9.52751 | −0.310094 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 1.97095 | 0.0640810 | ||||||||
\(947\) | −45.3469 | −1.47358 | −0.736789 | − | 0.676123i | \(-0.763659\pi\) | ||||
−0.736789 | + | 0.676123i | \(0.763659\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 15.1488 | 0.491752 | ||||||||
\(950\) | −1.67386 | −0.0543073 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −54.2703 | −1.75799 | −0.878994 | − | 0.476832i | \(-0.841785\pi\) | ||||
−0.878994 | + | 0.476832i | \(0.841785\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −17.8090 | −0.576287 | ||||||||
\(956\) | −32.8058 | −1.06101 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 3.47576 | 0.112297 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −28.2438 | −0.911089 | ||||||||
\(962\) | −2.28263 | −0.0735950 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 52.7390 | 1.69861 | ||||||||
\(965\) | 9.27576 | 0.298597 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 25.6591 | 0.825140 | 0.412570 | − | 0.910926i | \(-0.364631\pi\) | ||||
0.412570 | + | 0.910926i | \(0.364631\pi\) | |||||||
\(968\) | 2.56199 | 0.0823455 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −2.02597 | −0.0650500 | ||||||||
\(971\) | 21.0183 | 0.674510 | 0.337255 | − | 0.941413i | \(-0.390502\pi\) | ||||
0.337255 | + | 0.941413i | \(0.390502\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −3.12149 | −0.100019 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 27.8285 | 0.890767 | ||||||||
\(977\) | −2.09820 | −0.0671273 | −0.0335637 | − | 0.999437i | \(-0.510686\pi\) | ||||
−0.0335637 | + | 0.999437i | \(0.510686\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 10.1748 | 0.325188 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −4.62571 | −0.147612 | ||||||||
\(983\) | −42.9923 | −1.37124 | −0.685622 | − | 0.727958i | \(-0.740469\pi\) | ||||
−0.685622 | + | 0.727958i | \(0.740469\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −7.90723 | −0.251945 | ||||||||
\(986\) | −0.396990 | −0.0126427 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −3.77455 | −0.120084 | ||||||||
\(989\) | −12.4692 | −0.396498 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −17.2632 | −0.548384 | −0.274192 | − | 0.961675i | \(-0.588410\pi\) | ||||
−0.274192 | + | 0.961675i | \(0.588410\pi\) | |||||||
\(992\) | 4.58358 | 0.145529 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −23.5674 | −0.747137 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 38.9018 | 1.23203 | 0.616016 | − | 0.787733i | \(-0.288746\pi\) | ||||
0.616016 | + | 0.787733i | \(0.288746\pi\) | |||||||
\(998\) | 8.66157 | 0.274177 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))