Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [162,3,Mod(161,162)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(162, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("162.161");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 162 = 2 \cdot 3^{4} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 162.b (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(4.41418028264\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\sqrt{-2}, \sqrt{-3})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 2x^{2} + 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{2}\cdot 3^{2} \) |
Twist minimal: | no (minimal twist has level 18) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 161.1 | ||
Root | \(-1.22474 + 0.707107i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 162.161 |
Dual form | 162.3.b.a.161.4 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/162\mathbb{Z}\right)^\times\).
\(n\) | \(83\) |
\(\chi(n)\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − 1.41421i | − 0.707107i | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −2.00000 | −0.500000 | ||||||||
\(5\) | − 5.19615i | − 1.03923i | −0.854400 | − | 0.519615i | \(-0.826075\pi\) | ||||
0.854400 | − | 0.519615i | \(-0.173925\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −8.34847 | −1.19264 | −0.596319 | − | 0.802747i | \(-0.703371\pi\) | ||||
−0.596319 | + | 0.802747i | \(0.703371\pi\) | |||||||
\(8\) | 2.82843i | 0.353553i | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −7.34847 | −0.734847 | ||||||||
\(11\) | − 0.953512i | − 0.0866829i | −0.999060 | − | 0.0433414i | \(-0.986200\pi\) | ||||
0.999060 | − | 0.0433414i | \(-0.0138003\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −9.69694 | −0.745918 | −0.372959 | − | 0.927848i | \(-0.621657\pi\) | ||||
−0.372959 | + | 0.927848i | \(0.621657\pi\) | |||||||
\(14\) | 11.8065i | 0.843323i | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 4.00000 | 0.250000 | ||||||||
\(17\) | − 18.8776i | − 1.11045i | −0.831701 | − | 0.555223i | \(-0.812633\pi\) | ||||
0.831701 | − | 0.555223i | \(-0.187367\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −24.6969 | −1.29984 | −0.649919 | − | 0.760003i | \(-0.725197\pi\) | ||||
−0.649919 | + | 0.760003i | \(0.725197\pi\) | |||||||
\(20\) | 10.3923i | 0.519615i | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −1.34847 | −0.0612941 | ||||||||
\(23\) | 0.953512i | 0.0414570i | 0.999785 | + | 0.0207285i | \(0.00659856\pi\) | ||||
−0.999785 | + | 0.0207285i | \(0.993401\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2.00000 | −0.0800000 | ||||||||
\(26\) | 13.7135i | 0.527444i | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 16.6969 | 0.596319 | ||||||||
\(29\) | − 13.6814i | − 0.471774i | −0.971781 | − | 0.235887i | \(-0.924201\pi\) | ||||
0.971781 | − | 0.235887i | \(-0.0757995\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3.04541 | 0.0982390 | 0.0491195 | − | 0.998793i | \(-0.484358\pi\) | ||||
0.0491195 | + | 0.998793i | \(0.484358\pi\) | |||||||
\(32\) | − 5.65685i | − 0.176777i | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −26.6969 | −0.785204 | ||||||||
\(35\) | 43.3799i | 1.23943i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 46.6969 | 1.26208 | 0.631040 | − | 0.775751i | \(-0.282628\pi\) | ||||
0.631040 | + | 0.775751i | \(0.282628\pi\) | |||||||
\(38\) | 34.9267i | 0.919125i | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 14.6969 | 0.367423 | ||||||||
\(41\) | − 10.9172i | − 0.266274i | −0.991098 | − | 0.133137i | \(-0.957495\pi\) | ||||
0.991098 | − | 0.133137i | \(-0.0425050\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 45.0454 | 1.04757 | 0.523784 | − | 0.851851i | \(-0.324520\pi\) | ||||
0.523784 | + | 0.851851i | \(0.324520\pi\) | |||||||
\(44\) | 1.90702i | 0.0433414i | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 1.34847 | 0.0293145 | ||||||||
\(47\) | − 45.2869i | − 0.963552i | −0.876294 | − | 0.481776i | \(-0.839992\pi\) | ||||
0.876294 | − | 0.481776i | \(-0.160008\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 20.6969 | 0.422386 | ||||||||
\(50\) | 2.82843i | 0.0565685i | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 19.3939 | 0.372959 | ||||||||
\(53\) | − 94.3879i | − 1.78090i | −0.455077 | − | 0.890452i | \(-0.650388\pi\) | ||||
0.455077 | − | 0.890452i | \(-0.349612\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −4.95459 | −0.0900835 | ||||||||
\(56\) | − 23.6130i | − 0.421661i | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −19.3485 | −0.333594 | ||||||||
\(59\) | − 18.7813i | − 0.318326i | −0.987252 | − | 0.159163i | \(-0.949120\pi\) | ||||
0.987252 | − | 0.159163i | \(-0.0508796\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 13.0908 | 0.214604 | 0.107302 | − | 0.994226i | \(-0.465779\pi\) | ||||
0.107302 | + | 0.994226i | \(0.465779\pi\) | |||||||
\(62\) | − 4.30686i | − 0.0694654i | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −8.00000 | −0.125000 | ||||||||
\(65\) | 50.3868i | 0.775181i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 75.0454 | 1.12008 | 0.560040 | − | 0.828465i | \(-0.310786\pi\) | ||||
0.560040 | + | 0.828465i | \(0.310786\pi\) | |||||||
\(68\) | 37.7552i | 0.555223i | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 61.3485 | 0.876407 | ||||||||
\(71\) | 18.0204i | 0.253808i | 0.991915 | + | 0.126904i | \(0.0405041\pi\) | ||||
−0.991915 | + | 0.126904i | \(0.959496\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −7.90918 | −0.108345 | −0.0541725 | − | 0.998532i | \(-0.517252\pi\) | ||||
−0.0541725 | + | 0.998532i | \(0.517252\pi\) | |||||||
\(74\) | − 66.0394i | − 0.892425i | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 49.3939 | 0.649919 | ||||||||
\(77\) | 7.96036i | 0.103381i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −43.7423 | −0.553701 | −0.276850 | − | 0.960913i | \(-0.589291\pi\) | ||||
−0.276850 | + | 0.960913i | \(0.589291\pi\) | |||||||
\(80\) | − 20.7846i | − 0.259808i | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −15.4393 | −0.188284 | ||||||||
\(83\) | 130.332i | 1.57027i | 0.619325 | + | 0.785135i | \(0.287406\pi\) | ||||
−0.619325 | + | 0.785135i | \(0.712594\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −98.0908 | −1.15401 | ||||||||
\(86\) | − 63.7038i | − 0.740742i | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 2.69694 | 0.0306470 | ||||||||
\(89\) | 145.300i | 1.63258i | 0.577642 | + | 0.816290i | \(0.303973\pi\) | ||||
−0.577642 | + | 0.816290i | \(0.696027\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 80.9546 | 0.889611 | ||||||||
\(92\) | − 1.90702i | − 0.0207285i | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −64.0454 | −0.681334 | ||||||||
\(95\) | 128.329i | 1.35083i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −109.879 | −1.13277 | −0.566384 | − | 0.824141i | \(-0.691658\pi\) | ||||
−0.566384 | + | 0.824141i | \(0.691658\pi\) | |||||||
\(98\) | − 29.2699i | − 0.298672i | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 4.00000 | 0.0400000 | ||||||||
\(101\) | − 147.539i | − 1.46078i | −0.683030 | − | 0.730391i | \(-0.739338\pi\) | ||||
0.683030 | − | 0.730391i | \(-0.260662\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −103.136 | −1.00132 | −0.500661 | − | 0.865643i | \(-0.666910\pi\) | ||||
−0.500661 | + | 0.865643i | \(0.666910\pi\) | |||||||
\(104\) | − 27.4271i | − 0.263722i | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −133.485 | −1.25929 | ||||||||
\(107\) | 36.0408i | 0.336830i | 0.985716 | + | 0.168415i | \(0.0538649\pi\) | ||||
−0.985716 | + | 0.168415i | \(0.946135\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −148.272 | −1.36030 | −0.680149 | − | 0.733074i | \(-0.738085\pi\) | ||||
−0.680149 | + | 0.733074i | \(0.738085\pi\) | |||||||
\(110\) | 7.00685i | 0.0636987i | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −33.3939 | −0.298160 | ||||||||
\(113\) | − 171.088i | − 1.51405i | −0.653385 | − | 0.757025i | \(-0.726652\pi\) | ||||
0.653385 | − | 0.757025i | \(-0.273348\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 4.95459 | 0.0430834 | ||||||||
\(116\) | 27.3629i | 0.235887i | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −26.5607 | −0.225091 | ||||||||
\(119\) | 157.599i | 1.32436i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 120.091 | 0.992486 | ||||||||
\(122\) | − 18.5132i | − 0.151748i | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −6.09082 | −0.0491195 | ||||||||
\(125\) | − 119.512i | − 0.956092i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −78.0908 | −0.614888 | −0.307444 | − | 0.951566i | \(-0.599474\pi\) | ||||
−0.307444 | + | 0.951566i | \(0.599474\pi\) | |||||||
\(128\) | 11.3137i | 0.0883883i | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 71.2577 | 0.548136 | ||||||||
\(131\) | 234.063i | 1.78674i | 0.449323 | + | 0.893369i | \(0.351665\pi\) | ||||
−0.449323 | + | 0.893369i | \(0.648335\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 206.182 | 1.55024 | ||||||||
\(134\) | − 106.130i | − 0.792017i | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 53.3939 | 0.392602 | ||||||||
\(137\) | − 149.831i | − 1.09366i | −0.837244 | − | 0.546829i | \(-0.815835\pi\) | ||||
0.837244 | − | 0.546829i | \(-0.184165\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −84.5301 | −0.608130 | −0.304065 | − | 0.952651i | \(-0.598344\pi\) | ||||
−0.304065 | + | 0.952651i | \(0.598344\pi\) | |||||||
\(140\) | − 86.7598i | − 0.619713i | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 25.4847 | 0.179470 | ||||||||
\(143\) | 9.24614i | 0.0646584i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −71.0908 | −0.490281 | ||||||||
\(146\) | 11.1853i | 0.0766115i | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −93.3939 | −0.631040 | ||||||||
\(149\) | 115.505i | 0.775200i | 0.921828 | + | 0.387600i | \(0.126696\pi\) | ||||
−0.921828 | + | 0.387600i | \(0.873304\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −64.7730 | −0.428960 | −0.214480 | − | 0.976728i | \(-0.568806\pi\) | ||||
−0.214480 | + | 0.976728i | \(0.568806\pi\) | |||||||
\(152\) | − 69.8535i | − 0.459562i | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 11.2577 | 0.0731016 | ||||||||
\(155\) | − 15.8244i | − 0.102093i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −20.8184 | −0.132601 | −0.0663005 | − | 0.997800i | \(-0.521120\pi\) | ||||
−0.0663005 | + | 0.997800i | \(0.521120\pi\) | |||||||
\(158\) | 61.8610i | 0.391525i | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −29.3939 | −0.183712 | ||||||||
\(161\) | − 7.96036i | − 0.0494433i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 133.060 | 0.816320 | 0.408160 | − | 0.912910i | \(-0.366171\pi\) | ||||
0.408160 | + | 0.912910i | \(0.366171\pi\) | |||||||
\(164\) | 21.8344i | 0.133137i | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 184.318 | 1.11035 | ||||||||
\(167\) | − 294.510i | − 1.76353i | −0.471688 | − | 0.881765i | \(-0.656355\pi\) | ||||
0.471688 | − | 0.881765i | \(-0.343645\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −74.9694 | −0.443606 | ||||||||
\(170\) | 138.721i | 0.816008i | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −90.0908 | −0.523784 | ||||||||
\(173\) | 69.2644i | 0.400372i | 0.979758 | + | 0.200186i | \(0.0641546\pi\) | ||||
−0.979758 | + | 0.200186i | \(0.935845\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 16.6969 | 0.0954111 | ||||||||
\(176\) | − 3.81405i | − 0.0216707i | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 205.485 | 1.15441 | ||||||||
\(179\) | 47.4829i | 0.265268i | 0.991165 | + | 0.132634i | \(0.0423435\pi\) | ||||
−0.991165 | + | 0.132634i | \(0.957657\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 242.879 | 1.34187 | 0.670935 | − | 0.741516i | \(-0.265893\pi\) | ||||
0.670935 | + | 0.741516i | \(0.265893\pi\) | |||||||
\(182\) | − 114.487i | − 0.629050i | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −2.69694 | −0.0146573 | ||||||||
\(185\) | − 242.644i | − 1.31159i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −18.0000 | −0.0962567 | ||||||||
\(188\) | 90.5739i | 0.481776i | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 181.485 | 0.955183 | ||||||||
\(191\) | − 7.53177i | − 0.0394333i | −0.999806 | − | 0.0197167i | \(-0.993724\pi\) | ||||
0.999806 | − | 0.0197167i | \(-0.00627642\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 345.454 | 1.78992 | 0.894959 | − | 0.446149i | \(-0.147205\pi\) | ||||
0.894959 | + | 0.446149i | \(0.147205\pi\) | |||||||
\(194\) | 155.392i | 0.800988i | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −41.3939 | −0.211193 | ||||||||
\(197\) | 77.2247i | 0.392004i | 0.980604 | + | 0.196002i | \(0.0627959\pi\) | ||||
−0.980604 | + | 0.196002i | \(0.937204\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 153.485 | 0.771280 | 0.385640 | − | 0.922649i | \(-0.373981\pi\) | ||||
0.385640 | + | 0.922649i | \(0.373981\pi\) | |||||||
\(200\) | − 5.65685i | − 0.0282843i | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −208.652 | −1.03293 | ||||||||
\(203\) | 114.219i | 0.562655i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −56.7276 | −0.276720 | ||||||||
\(206\) | 145.857i | 0.708042i | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −38.7878 | −0.186480 | ||||||||
\(209\) | 23.5488i | 0.112674i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −51.5607 | −0.244364 | −0.122182 | − | 0.992508i | \(-0.538989\pi\) | ||||
−0.122182 | + | 0.992508i | \(0.538989\pi\) | |||||||
\(212\) | 188.776i | 0.890452i | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 50.9694 | 0.238175 | ||||||||
\(215\) | − 234.063i | − 1.08866i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −25.4245 | −0.117164 | ||||||||
\(218\) | 209.689i | 0.961876i | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 9.90918 | 0.0450417 | ||||||||
\(221\) | 183.055i | 0.828302i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 313.227 | 1.40461 | 0.702303 | − | 0.711878i | \(-0.252155\pi\) | ||||
0.702303 | + | 0.711878i | \(0.252155\pi\) | |||||||
\(224\) | 47.2261i | 0.210831i | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −241.955 | −1.07060 | ||||||||
\(227\) | 76.2712i | 0.335997i | 0.985787 | + | 0.167998i | \(0.0537303\pi\) | ||||
−0.985787 | + | 0.167998i | \(0.946270\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −121.545 | −0.530764 | −0.265382 | − | 0.964143i | \(-0.585498\pi\) | ||||
−0.265382 | + | 0.964143i | \(0.585498\pi\) | |||||||
\(230\) | − 7.00685i | − 0.0304646i | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 38.6969 | 0.166797 | ||||||||
\(233\) | − 151.021i | − 0.648157i | −0.946030 | − | 0.324079i | \(-0.894946\pi\) | ||||
0.946030 | − | 0.324079i | \(-0.105054\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −235.318 | −1.00135 | ||||||||
\(236\) | 37.5625i | 0.159163i | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 222.879 | 0.936465 | ||||||||
\(239\) | − 87.7133i | − 0.367001i | −0.983020 | − | 0.183501i | \(-0.941257\pi\) | ||||
0.983020 | − | 0.183501i | \(-0.0587430\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 201.788 | 0.837294 | 0.418647 | − | 0.908149i | \(-0.362505\pi\) | ||||
0.418647 | + | 0.908149i | \(0.362505\pi\) | |||||||
\(242\) | − 169.834i | − 0.701794i | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −26.1816 | −0.107302 | ||||||||
\(245\) | − 107.544i | − 0.438957i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 239.485 | 0.969574 | ||||||||
\(248\) | 8.61371i | 0.0347327i | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −169.015 | −0.676059 | ||||||||
\(251\) | 52.6261i | 0.209666i | 0.994490 | + | 0.104833i | \(0.0334307\pi\) | ||||
−0.994490 | + | 0.104833i | \(0.966569\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0.909185 | 0.00359362 | ||||||||
\(254\) | 110.437i | 0.434792i | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 16.0000 | 0.0625000 | ||||||||
\(257\) | − 80.7065i | − 0.314033i | −0.987596 | − | 0.157017i | \(-0.949812\pi\) | ||||
0.987596 | − | 0.157017i | \(-0.0501876\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −389.848 | −1.50520 | ||||||||
\(260\) | − 100.774i | − 0.387591i | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 331.015 | 1.26342 | ||||||||
\(263\) | − 463.743i | − 1.76328i | −0.471920 | − | 0.881641i | \(-0.656439\pi\) | ||||
0.471920 | − | 0.881641i | \(-0.343561\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −490.454 | −1.85077 | ||||||||
\(266\) | − 291.585i | − 1.09618i | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −150.091 | −0.560040 | ||||||||
\(269\) | − 43.4762i | − 0.161622i | −0.996729 | − | 0.0808109i | \(-0.974249\pi\) | ||||
0.996729 | − | 0.0808109i | \(-0.0257510\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −342.636 | −1.26434 | −0.632169 | − | 0.774830i | \(-0.717835\pi\) | ||||
−0.632169 | + | 0.774830i | \(0.717835\pi\) | |||||||
\(272\) | − 75.5103i | − 0.277612i | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −211.893 | −0.773333 | ||||||||
\(275\) | 1.90702i | 0.00693463i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −49.0000 | −0.176895 | −0.0884477 | − | 0.996081i | \(-0.528191\pi\) | ||||
−0.0884477 | + | 0.996081i | \(0.528191\pi\) | |||||||
\(278\) | 119.544i | 0.430013i | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −122.697 | −0.438203 | ||||||||
\(281\) | 20.6450i | 0.0734697i | 0.999325 | + | 0.0367349i | \(0.0116957\pi\) | ||||
−0.999325 | + | 0.0367349i | \(0.988304\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 53.4087 | 0.188723 | 0.0943616 | − | 0.995538i | \(-0.469919\pi\) | ||||
0.0943616 | + | 0.995538i | \(0.469919\pi\) | |||||||
\(284\) | − 36.0408i | − 0.126904i | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 13.0760 | 0.0457204 | ||||||||
\(287\) | 91.1421i | 0.317568i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −67.3633 | −0.233091 | ||||||||
\(290\) | 100.538i | 0.346681i | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 15.8184 | 0.0541725 | ||||||||
\(293\) | − 14.9239i | − 0.0509349i | −0.999676 | − | 0.0254674i | \(-0.991893\pi\) | ||||
0.999676 | − | 0.0254674i | \(-0.00810741\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −97.5903 | −0.330815 | ||||||||
\(296\) | 132.079i | 0.446212i | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 163.348 | 0.548149 | ||||||||
\(299\) | − 9.24614i | − 0.0309236i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −376.060 | −1.24937 | ||||||||
\(302\) | 91.6028i | 0.303321i | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −98.7878 | −0.324960 | ||||||||
\(305\) | − 68.0219i | − 0.223023i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 65.9092 | 0.214688 | 0.107344 | − | 0.994222i | \(-0.465765\pi\) | ||||
0.107344 | + | 0.994222i | \(0.465765\pi\) | |||||||
\(308\) | − 15.9207i | − 0.0516907i | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −22.3791 | −0.0721906 | ||||||||
\(311\) | − 250.176i | − 0.804425i | −0.915546 | − | 0.402213i | \(-0.868241\pi\) | ||||
0.915546 | − | 0.402213i | \(-0.131759\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −426.394 | −1.36228 | −0.681140 | − | 0.732153i | \(-0.738516\pi\) | ||||
−0.681140 | + | 0.732153i | \(0.738516\pi\) | |||||||
\(314\) | 29.4416i | 0.0937631i | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 87.4847 | 0.276850 | ||||||||
\(317\) | 463.979i | 1.46366i | 0.681489 | + | 0.731829i | \(0.261333\pi\) | ||||
−0.681489 | + | 0.731829i | \(0.738667\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −13.0454 | −0.0408947 | ||||||||
\(320\) | 41.5692i | 0.129904i | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −11.2577 | −0.0349617 | ||||||||
\(323\) | 466.219i | 1.44340i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 19.3939 | 0.0596735 | ||||||||
\(326\) | − 188.176i | − 0.577226i | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 30.8786 | 0.0941420 | ||||||||
\(329\) | 378.077i | 1.14917i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 472.803 | 1.42841 | 0.714203 | − | 0.699938i | \(-0.246789\pi\) | ||||
0.714203 | + | 0.699938i | \(0.246789\pi\) | |||||||
\(332\) | − 260.665i | − 0.785135i | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −416.499 | −1.24700 | ||||||||
\(335\) | − 389.947i | − 1.16402i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 305.606 | 0.906843 | 0.453422 | − | 0.891296i | \(-0.350203\pi\) | ||||
0.453422 | + | 0.891296i | \(0.350203\pi\) | |||||||
\(338\) | 106.023i | 0.313677i | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 196.182 | 0.577005 | ||||||||
\(341\) | − 2.90383i | − 0.00851564i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 236.287 | 0.688884 | ||||||||
\(344\) | 127.408i | 0.370371i | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 97.9546 | 0.283106 | ||||||||
\(347\) | 133.675i | 0.385229i | 0.981274 | + | 0.192615i | \(0.0616967\pi\) | ||||
−0.981274 | + | 0.192615i | \(0.938303\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −98.7571 | −0.282972 | −0.141486 | − | 0.989940i | \(-0.545188\pi\) | ||||
−0.141486 | + | 0.989940i | \(0.545188\pi\) | |||||||
\(350\) | − 23.6130i | − 0.0674658i | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −5.39388 | −0.0153235 | ||||||||
\(353\) | 326.115i | 0.923839i | 0.886922 | + | 0.461919i | \(0.152839\pi\) | ||||
−0.886922 | + | 0.461919i | \(0.847161\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 93.6367 | 0.263765 | ||||||||
\(356\) | − 290.599i | − 0.816290i | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 67.1510 | 0.187573 | ||||||||
\(359\) | − 418.736i | − 1.16639i | −0.812331 | − | 0.583197i | \(-0.801801\pi\) | ||||
0.812331 | − | 0.583197i | \(-0.198199\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 248.939 | 0.689581 | ||||||||
\(362\) | − 343.482i | − 0.948846i | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −161.909 | −0.444805 | ||||||||
\(365\) | 41.0973i | 0.112595i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 187.227 | 0.510155 | 0.255078 | − | 0.966921i | \(-0.417899\pi\) | ||||
0.255078 | + | 0.966921i | \(0.417899\pi\) | |||||||
\(368\) | 3.81405i | 0.0103643i | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −343.151 | −0.927435 | ||||||||
\(371\) | 787.995i | 2.12398i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 451.030 | 1.20919 | 0.604597 | − | 0.796531i | \(-0.293334\pi\) | ||||
0.604597 | + | 0.796531i | \(0.293334\pi\) | |||||||
\(374\) | 25.4558i | 0.0680638i | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 128.091 | 0.340667 | ||||||||
\(377\) | 132.668i | 0.351905i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −489.666 | −1.29200 | −0.645998 | − | 0.763339i | \(-0.723558\pi\) | ||||
−0.645998 | + | 0.763339i | \(0.723558\pi\) | |||||||
\(380\) | − 256.658i | − 0.675416i | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −10.6515 | −0.0278836 | ||||||||
\(383\) | 103.056i | 0.269076i | 0.990908 | + | 0.134538i | \(0.0429550\pi\) | ||||
−0.990908 | + | 0.134538i | \(0.957045\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 41.3633 | 0.107437 | ||||||||
\(386\) | − 488.546i | − 1.26566i | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 219.757 | 0.566384 | ||||||||
\(389\) | − 34.2734i | − 0.0881064i | −0.999029 | − | 0.0440532i | \(-0.985973\pi\) | ||||
0.999029 | − | 0.0440532i | \(-0.0140271\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 18.0000 | 0.0460358 | ||||||||
\(392\) | 58.5398i | 0.149336i | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 109.212 | 0.277188 | ||||||||
\(395\) | 227.292i | 0.575423i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 8.27245 | 0.0208374 | 0.0104187 | − | 0.999946i | \(-0.496684\pi\) | ||||
0.0104187 | + | 0.999946i | \(0.496684\pi\) | |||||||
\(398\) | − 217.060i | − 0.545377i | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −8.00000 | −0.0200000 | ||||||||
\(401\) | 414.117i | 1.03271i | 0.856374 | + | 0.516356i | \(0.172712\pi\) | ||||
−0.856374 | + | 0.516356i | \(0.827288\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −29.5311 | −0.0732782 | ||||||||
\(404\) | 295.078i | 0.730391i | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 161.530 | 0.397857 | ||||||||
\(407\) | − 44.5261i | − 0.109401i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −326.212 | −0.797585 | −0.398792 | − | 0.917041i | \(-0.630571\pi\) | ||||
−0.398792 | + | 0.917041i | \(0.630571\pi\) | |||||||
\(410\) | 80.2249i | 0.195670i | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 206.272 | 0.500661 | ||||||||
\(413\) | 156.795i | 0.379648i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 677.227 | 1.63187 | ||||||||
\(416\) | 54.8542i | 0.131861i | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 33.3031 | 0.0796724 | ||||||||
\(419\) | − 540.775i | − 1.29063i | −0.763915 | − | 0.645317i | \(-0.776725\pi\) | ||||
0.763915 | − | 0.645317i | \(-0.223275\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 283.697 | 0.673864 | 0.336932 | − | 0.941529i | \(-0.390611\pi\) | ||||
0.336932 | + | 0.941529i | \(0.390611\pi\) | |||||||
\(422\) | 72.9179i | 0.172791i | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 266.969 | 0.629645 | ||||||||
\(425\) | 37.7552i | 0.0888357i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −109.288 | −0.255944 | ||||||||
\(428\) | − 72.0816i | − 0.168415i | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −331.015 | −0.769802 | ||||||||
\(431\) | − 257.429i | − 0.597282i | −0.954365 | − | 0.298641i | \(-0.903467\pi\) | ||||
0.954365 | − | 0.298641i | \(-0.0965334\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 476.272 | 1.09994 | 0.549968 | − | 0.835186i | \(-0.314640\pi\) | ||||
0.549968 | + | 0.835186i | \(0.314640\pi\) | |||||||
\(434\) | 35.9557i | 0.0828471i | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 296.545 | 0.680149 | ||||||||
\(437\) | − 23.5488i | − 0.0538875i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −557.863 | −1.27076 | −0.635379 | − | 0.772200i | \(-0.719156\pi\) | ||||
−0.635379 | + | 0.772200i | \(0.719156\pi\) | |||||||
\(440\) | − 14.0137i | − 0.0318493i | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 258.879 | 0.585698 | ||||||||
\(443\) | − 831.847i | − 1.87776i | −0.344248 | − | 0.938879i | \(-0.611866\pi\) | ||||
0.344248 | − | 0.938879i | \(-0.388134\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 754.999 | 1.69663 | ||||||||
\(446\) | − 442.970i | − 0.993206i | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 66.7878 | 0.149080 | ||||||||
\(449\) | 729.927i | 1.62567i | 0.582492 | + | 0.812836i | \(0.302078\pi\) | ||||
−0.582492 | + | 0.812836i | \(0.697922\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −10.4097 | −0.0230814 | ||||||||
\(452\) | 342.175i | 0.757025i | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 107.864 | 0.237585 | ||||||||
\(455\) | − 420.652i | − 0.924511i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 709.636 | 1.55281 | 0.776407 | − | 0.630232i | \(-0.217040\pi\) | ||||
0.776407 | + | 0.630232i | \(0.217040\pi\) | |||||||
\(458\) | 171.890i | 0.375307i | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −9.90918 | −0.0215417 | ||||||||
\(461\) | 9.20285i | 0.0199628i | 0.999950 | + | 0.00998140i | \(0.00317723\pi\) | ||||
−0.999950 | + | 0.00998140i | \(0.996823\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −55.1975 | −0.119217 | −0.0596085 | − | 0.998222i | \(-0.518985\pi\) | ||||
−0.0596085 | + | 0.998222i | \(0.518985\pi\) | |||||||
\(464\) | − 54.7257i | − 0.117943i | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −213.576 | −0.458317 | ||||||||
\(467\) | − 625.811i | − 1.34007i | −0.742331 | − | 0.670033i | \(-0.766280\pi\) | ||||
0.742331 | − | 0.670033i | \(-0.233720\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −626.514 | −1.33585 | ||||||||
\(470\) | 332.790i | 0.708063i | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 53.1214 | 0.112545 | ||||||||
\(473\) | − 42.9513i | − 0.0908062i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 49.3939 | 0.103987 | ||||||||
\(476\) | − 315.198i | − 0.662180i | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −124.045 | −0.259509 | ||||||||
\(479\) | − 309.294i | − 0.645708i | −0.946449 | − | 0.322854i | \(-0.895358\pi\) | ||||
0.946449 | − | 0.322854i | \(-0.104642\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −452.817 | −0.941408 | ||||||||
\(482\) | − 285.371i | − 0.592056i | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −240.182 | −0.496243 | ||||||||
\(485\) | 570.946i | 1.17721i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −28.3337 | −0.0581800 | −0.0290900 | − | 0.999577i | \(-0.509261\pi\) | ||||
−0.0290900 | + | 0.999577i | \(0.509261\pi\) | |||||||
\(488\) | 37.0264i | 0.0758738i | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −152.091 | −0.310389 | ||||||||
\(491\) | 949.697i | 1.93421i | 0.254379 | + | 0.967105i | \(0.418129\pi\) | ||||
−0.254379 | + | 0.967105i | \(0.581871\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −258.272 | −0.523879 | ||||||||
\(494\) | − 338.682i | − 0.685592i | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 12.1816 | 0.0245597 | ||||||||
\(497\) | − 150.443i | − 0.302702i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −560.226 | −1.12270 | −0.561349 | − | 0.827579i | \(-0.689717\pi\) | ||||
−0.561349 | + | 0.827579i | \(0.689717\pi\) | |||||||
\(500\) | 239.023i | 0.478046i | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 74.4245 | 0.148256 | ||||||||
\(503\) | − 897.832i | − 1.78495i | −0.451094 | − | 0.892477i | \(-0.648966\pi\) | ||||
0.451094 | − | 0.892477i | \(-0.351034\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −766.635 | −1.51809 | ||||||||
\(506\) | − 1.28578i | − 0.00254107i | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 156.182 | 0.307444 | ||||||||
\(509\) | − 196.823i | − 0.386685i | −0.981131 | − | 0.193343i | \(-0.938067\pi\) | ||||
0.981131 | − | 0.193343i | \(-0.0619329\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 66.0296 | 0.129216 | ||||||||
\(512\) | − 22.6274i | − 0.0441942i | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −114.136 | −0.222055 | ||||||||
\(515\) | 535.912i | 1.04060i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −43.1816 | −0.0835235 | ||||||||
\(518\) | 551.328i | 1.06434i | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −142.515 | −0.274068 | ||||||||
\(521\) | − 375.837i | − 0.721377i | −0.932686 | − | 0.360688i | \(-0.882542\pi\) | ||||
0.932686 | − | 0.360688i | \(-0.117458\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 91.1827 | 0.174345 | 0.0871727 | − | 0.996193i | \(-0.472217\pi\) | ||||
0.0871727 | + | 0.996193i | \(0.472217\pi\) | |||||||
\(524\) | − 468.126i | − 0.893369i | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −655.832 | −1.24683 | ||||||||
\(527\) | − 57.4899i | − 0.109089i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 528.091 | 0.998281 | ||||||||
\(530\) | 693.607i | 1.30869i | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −412.363 | −0.775119 | ||||||||
\(533\) | 105.864i | 0.198618i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 187.273 | 0.350044 | ||||||||
\(536\) | 212.260i | 0.396008i | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −61.4847 | −0.114284 | ||||||||
\(539\) | − 19.7348i | − 0.0366137i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −38.8490 | −0.0718096 | −0.0359048 | − | 0.999355i | \(-0.511431\pi\) | ||||
−0.0359048 | + | 0.999355i | \(0.511431\pi\) | |||||||
\(542\) | 484.560i | 0.894022i | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −106.788 | −0.196301 | ||||||||
\(545\) | 770.446i | 1.41366i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −466.044 | −0.852001 | −0.426000 | − | 0.904723i | \(-0.640078\pi\) | ||||
−0.426000 | + | 0.904723i | \(0.640078\pi\) | |||||||
\(548\) | 299.662i | 0.546829i | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 2.69694 | 0.00490352 | ||||||||
\(551\) | 337.890i | 0.613230i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 365.182 | 0.660365 | ||||||||
\(554\) | 69.2965i | 0.125084i | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 169.060 | 0.304065 | ||||||||
\(557\) | 695.042i | 1.24783i | 0.781492 | + | 0.623916i | \(0.214459\pi\) | ||||
−0.781492 | + | 0.623916i | \(0.785541\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −436.803 | −0.781400 | ||||||||
\(560\) | 173.520i | 0.309857i | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 29.1964 | 0.0519509 | ||||||||
\(563\) | − 547.074i | − 0.971713i | −0.874039 | − | 0.485857i | \(-0.838508\pi\) | ||||
0.874039 | − | 0.485857i | \(-0.161492\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −888.998 | −1.57345 | ||||||||
\(566\) | − 75.5313i | − 0.133447i | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −50.9694 | −0.0897348 | ||||||||
\(569\) | − 249.362i | − 0.438247i | −0.975697 | − | 0.219123i | \(-0.929680\pi\) | ||||
0.975697 | − | 0.219123i | \(-0.0703197\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 73.8332 | 0.129305 | 0.0646525 | − | 0.997908i | \(-0.479406\pi\) | ||||
0.0646525 | + | 0.997908i | \(0.479406\pi\) | |||||||
\(572\) | − 18.4923i | − 0.0323292i | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 128.894 | 0.224555 | ||||||||
\(575\) | − 1.90702i | − 0.00331656i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −43.9092 | −0.0760991 | −0.0380496 | − | 0.999276i | \(-0.512114\pi\) | ||||
−0.0380496 | + | 0.999276i | \(0.512114\pi\) | |||||||
\(578\) | 95.2660i | 0.164820i | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 142.182 | 0.245141 | ||||||||
\(581\) | − 1088.08i | − 1.87276i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −90.0000 | −0.154374 | ||||||||
\(584\) | − 22.3706i | − 0.0383057i | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −21.1056 | −0.0360164 | ||||||||
\(587\) | 440.387i | 0.750234i | 0.926978 | + | 0.375117i | \(0.122397\pi\) | ||||
−0.926978 | + | 0.375117i | \(0.877603\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −75.2122 | −0.127695 | ||||||||
\(590\) | 138.014i | 0.233921i | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 186.788 | 0.315520 | ||||||||
\(593\) | − 347.232i | − 0.585551i | −0.956181 | − | 0.292776i | \(-0.905421\pi\) | ||||
0.956181 | − | 0.292776i | \(-0.0945789\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 818.908 | 1.37632 | ||||||||
\(596\) | − 231.010i | − 0.387600i | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −13.0760 | −0.0218663 | ||||||||
\(599\) | − 789.911i | − 1.31872i | −0.751829 | − | 0.659359i | \(-0.770828\pi\) | ||||
0.751829 | − | 0.659359i | \(-0.229172\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −706.909 | −1.17622 | −0.588111 | − | 0.808780i | \(-0.700128\pi\) | ||||
−0.588111 | + | 0.808780i | \(0.700128\pi\) | |||||||
\(602\) | 531.829i | 0.883438i | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 129.546 | 0.214480 | ||||||||
\(605\) | − 624.010i | − 1.03142i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −1193.26 | −1.96583 | −0.982913 | − | 0.184070i | \(-0.941073\pi\) | ||||
−0.982913 | + | 0.184070i | \(0.941073\pi\) | |||||||
\(608\) | 139.707i | 0.229781i | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −96.1975 | −0.157701 | ||||||||
\(611\) | 439.145i | 0.718731i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 629.181 | 1.02640 | 0.513198 | − | 0.858270i | \(-0.328461\pi\) | ||||
0.513198 | + | 0.858270i | \(0.328461\pi\) | |||||||
\(614\) | − 93.2097i | − 0.151807i | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −22.5153 | −0.0365508 | ||||||||
\(617\) | 192.730i | 0.312366i | 0.987728 | + | 0.156183i | \(0.0499189\pi\) | ||||
−0.987728 | + | 0.156183i | \(0.950081\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −152.955 | −0.247100 | −0.123550 | − | 0.992338i | \(-0.539428\pi\) | ||||
−0.123550 | + | 0.992338i | \(0.539428\pi\) | |||||||
\(620\) | 31.6488i | 0.0510465i | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −353.803 | −0.568814 | ||||||||
\(623\) | − 1213.03i | − 1.94708i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −671.000 | −1.07360 | ||||||||
\(626\) | 603.012i | 0.963278i | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 41.6367 | 0.0663005 | ||||||||
\(629\) | − 881.525i | − 1.40147i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 44.8786 | 0.0711229 | 0.0355615 | − | 0.999367i | \(-0.488678\pi\) | ||||
0.0355615 | + | 0.999367i | \(0.488678\pi\) | |||||||
\(632\) | − 123.722i | − 0.195763i | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 656.166 | 1.03496 | ||||||||
\(635\) | 405.772i | 0.639011i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −200.697 | −0.315066 | ||||||||
\(638\) | 18.4490i | 0.0289169i | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 58.7878 | 0.0918559 | ||||||||
\(641\) | 241.455i | 0.376685i | 0.982103 | + | 0.188342i | \(0.0603115\pi\) | ||||
−0.982103 | + | 0.188342i | \(0.939689\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 791.409 | 1.23081 | 0.615403 | − | 0.788212i | \(-0.288993\pi\) | ||||
0.615403 | + | 0.788212i | \(0.288993\pi\) | |||||||
\(644\) | 15.9207i | 0.0247216i | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 659.333 | 1.02064 | ||||||||
\(647\) | 294.028i | 0.454448i | 0.973842 | + | 0.227224i | \(0.0729650\pi\) | ||||
−0.973842 | + | 0.227224i | \(0.927035\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −17.9082 | −0.0275935 | ||||||||
\(650\) | − 27.4271i | − 0.0421955i | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −266.120 | −0.408160 | ||||||||
\(653\) | − 768.313i | − 1.17659i | −0.808647 | − | 0.588295i | \(-0.799799\pi\) | ||||
0.808647 | − | 0.588295i | \(-0.200201\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 1216.23 | 1.85683 | ||||||||
\(656\) | − 43.6689i | − 0.0665684i | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 534.681 | 0.812585 | ||||||||
\(659\) | 430.939i | 0.653928i | 0.945037 | + | 0.326964i | \(0.106026\pi\) | ||||
−0.945037 | + | 0.326964i | \(0.893974\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 1012.27 | 1.53142 | 0.765712 | − | 0.643183i | \(-0.222387\pi\) | ||||
0.765712 | + | 0.643183i | \(0.222387\pi\) | |||||||
\(662\) | − 668.644i | − 1.01004i | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −368.636 | −0.555174 | ||||||||
\(665\) | − 1071.35i | − 1.61105i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 13.0454 | 0.0195583 | ||||||||
\(668\) | 589.019i | 0.881765i | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −551.469 | −0.823088 | ||||||||
\(671\) | − 12.4822i | − 0.0186025i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 563.211 | 0.836867 | 0.418433 | − | 0.908248i | \(-0.362579\pi\) | ||||
0.418433 | + | 0.908248i | \(0.362579\pi\) | |||||||
\(674\) | − 432.192i | − 0.641235i | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 149.939 | 0.221803 | ||||||||
\(677\) | 350.136i | 0.517187i | 0.965986 | + | 0.258594i | \(0.0832591\pi\) | ||||
−0.965986 | + | 0.258594i | \(0.916741\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 917.318 | 1.35098 | ||||||||
\(680\) | − 277.443i | − 0.408004i | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −4.10664 | −0.00602146 | ||||||||
\(683\) | 502.818i | 0.736190i | 0.929788 | + | 0.368095i | \(0.119990\pi\) | ||||
−0.929788 | + | 0.368095i | \(0.880010\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −778.546 | −1.13656 | ||||||||
\(686\) | − 334.161i | − 0.487115i | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 180.182 | 0.261892 | ||||||||
\(689\) | 915.274i | 1.32841i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 376.319 | 0.544600 | 0.272300 | − | 0.962212i | \(-0.412216\pi\) | ||||
0.272300 | + | 0.962212i | \(0.412216\pi\) | |||||||
\(692\) | − 138.529i | − 0.200186i | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 189.044 | 0.272398 | ||||||||
\(695\) | 439.231i | 0.631987i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −206.091 | −0.295683 | ||||||||
\(698\) | 139.664i | 0.200091i | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −33.3939 | −0.0477055 | ||||||||
\(701\) | 489.681i | 0.698546i | 0.937021 | + | 0.349273i | \(0.113571\pi\) | ||||
−0.937021 | + | 0.349273i | \(0.886429\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −1153.27 | −1.64050 | ||||||||
\(704\) | 7.62809i | 0.0108354i | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 461.196 | 0.653253 | ||||||||
\(707\) | 1231.72i | 1.74218i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 474.029 | 0.668588 | 0.334294 | − | 0.942469i | \(-0.391502\pi\) | ||||
0.334294 | + | 0.942469i | \(0.391502\pi\) | |||||||
\(710\) | − 132.422i | − 0.186510i | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −410.969 | −0.577204 | ||||||||
\(713\) | 2.90383i | 0.00407270i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 48.0444 | 0.0671949 | ||||||||
\(716\) | − 94.9659i | − 0.132634i | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −592.182 | −0.824766 | ||||||||
\(719\) | − 108.122i | − 0.150379i | −0.997169 | − | 0.0751894i | \(-0.976044\pi\) | ||||
0.997169 | − | 0.0751894i | \(-0.0239561\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 861.030 | 1.19422 | ||||||||
\(722\) | − 352.053i | − 0.487607i | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −485.757 | −0.670935 | ||||||||
\(725\) | 27.3629i | 0.0377419i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −444.591 | −0.611542 | −0.305771 | − | 0.952105i | \(-0.598914\pi\) | ||||
−0.305771 | + | 0.952105i | \(0.598914\pi\) | |||||||
\(728\) | 228.974i | 0.314525i | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 58.1204 | 0.0796170 | ||||||||
\(731\) | − 850.349i | − 1.16327i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −716.362 | −0.977302 | −0.488651 | − | 0.872479i | \(-0.662511\pi\) | ||||
−0.488651 | + | 0.872479i | \(0.662511\pi\) | |||||||
\(734\) | − 264.779i | − 0.360734i | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 5.39388 | 0.00732864 | ||||||||
\(737\) | − 71.5567i | − 0.0970918i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 933.362 | 1.26301 | 0.631504 | − | 0.775373i | \(-0.282438\pi\) | ||||
0.631504 | + | 0.775373i | \(0.282438\pi\) | |||||||
\(740\) | 485.289i | 0.655796i | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 1114.39 | 1.50188 | ||||||||
\(743\) | − 15.9110i | − 0.0214145i | −0.999943 | − | 0.0107073i | \(-0.996592\pi\) | ||||
0.999943 | − | 0.0107073i | \(-0.00340829\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 600.181 | 0.805612 | ||||||||
\(746\) | − 637.852i | − 0.855030i | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 36.0000 | 0.0481283 | ||||||||
\(749\) | − 300.885i | − 0.401716i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 809.831 | 1.07834 | 0.539169 | − | 0.842198i | \(-0.318739\pi\) | ||||
0.539169 | + | 0.842198i | \(0.318739\pi\) | |||||||
\(752\) | − 181.148i | − 0.240888i | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 187.621 | 0.248834 | ||||||||
\(755\) | 336.570i | 0.445788i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 689.637 | 0.911013 | 0.455506 | − | 0.890232i | \(-0.349458\pi\) | ||||
0.455506 | + | 0.890232i | \(0.349458\pi\) | |||||||
\(758\) | 692.493i | 0.913579i | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −362.969 | −0.477591 | ||||||||
\(761\) | − 953.082i | − 1.25241i | −0.779659 | − | 0.626204i | \(-0.784608\pi\) | ||||
0.779659 | − | 0.626204i | \(-0.215392\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 1237.85 | 1.62234 | ||||||||
\(764\) | 15.0635i | 0.0197167i | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 145.743 | 0.190266 | ||||||||
\(767\) | 182.121i | 0.237446i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −656.696 | −0.853961 | −0.426980 | − | 0.904261i | \(-0.640423\pi\) | ||||
−0.426980 | + | 0.904261i | \(0.640423\pi\) | |||||||
\(770\) | − 58.4965i | − 0.0759695i | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −690.908 | −0.894959 | ||||||||
\(773\) | − 278.021i | − 0.359665i | −0.983697 | − | 0.179832i | \(-0.942445\pi\) | ||||
0.983697 | − | 0.179832i | \(-0.0575555\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −6.09082 | −0.00785912 | ||||||||
\(776\) | − 310.784i | − 0.400494i | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −48.4699 | −0.0623006 | ||||||||
\(779\) | 269.622i | 0.346113i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 17.1827 | 0.0220008 | ||||||||
\(782\) | − 25.4558i | − 0.0325522i | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 82.7878 | 0.105597 | ||||||||
\(785\) | 108.175i | 0.137803i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 821.954 | 1.04441 | 0.522207 | − | 0.852819i | \(-0.325109\pi\) | ||||
0.522207 | + | 0.852819i | \(0.325109\pi\) | |||||||
\(788\) | − 154.449i | − 0.196002i | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 321.439 | 0.406885 | ||||||||
\(791\) | 1428.32i | 1.80572i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −126.941 | −0.160077 | ||||||||
\(794\) | − 11.6990i | − 0.0147343i | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −306.969 | −0.385640 | ||||||||
\(797\) | 1322.51i | 1.65937i | 0.558235 | + | 0.829683i | \(0.311479\pi\) | ||||
−0.558235 | + | 0.829683i | \(0.688521\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −854.908 | −1.06997 | ||||||||
\(800\) | 11.3137i | 0.0141421i | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 585.650 | 0.730238 | ||||||||
\(803\) | 7.54150i | 0.00939166i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −41.3633 | −0.0513829 | ||||||||
\(806\) | 41.7633i | 0.0518155i | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 417.303 | 0.516464 | ||||||||
\(809\) | 235.681i | 0.291324i | 0.989334 | + | 0.145662i | \(0.0465311\pi\) | ||||
−0.989334 | + | 0.145662i | \(0.953469\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −587.362 | −0.724244 | −0.362122 | − | 0.932131i | \(-0.617948\pi\) | ||||
−0.362122 | + | 0.932131i | \(0.617948\pi\) | |||||||
\(812\) | − 228.438i | − 0.281328i | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −62.9694 | −0.0773580 | ||||||||
\(815\) | − 691.401i | − 0.848345i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −1112.48 | −1.36167 | ||||||||
\(818\) | 461.334i | 0.563978i | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 113.455 | 0.138360 | ||||||||
\(821\) | 943.913i | 1.14971i | 0.818255 | + | 0.574856i | \(0.194942\pi\) | ||||
−0.818255 | + | 0.574856i | \(0.805058\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −1615.74 | −1.96323 | −0.981617 | − | 0.190859i | \(-0.938873\pi\) | ||||
−0.981617 | + | 0.190859i | \(0.938873\pi\) | |||||||
\(824\) | − 291.713i | − 0.354021i | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 221.741 | 0.268452 | ||||||||
\(827\) | 582.354i | 0.704177i | 0.935967 | + | 0.352088i | \(0.114528\pi\) | ||||
−0.935967 | + | 0.352088i | \(0.885472\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 877.121 | 1.05805 | 0.529024 | − | 0.848607i | \(-0.322558\pi\) | ||||
0.529024 | + | 0.848607i | \(0.322558\pi\) | |||||||
\(830\) | − 957.744i | − 1.15391i | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 77.5755 | 0.0932398 | ||||||||
\(833\) | − 390.708i | − 0.469038i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −1530.32 | −1.83271 | ||||||||
\(836\) | − 47.0976i | − 0.0563369i | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −764.772 | −0.912616 | ||||||||
\(839\) | 1137.12i | 1.35533i | 0.735370 | + | 0.677666i | \(0.237009\pi\) | ||||
−0.735370 | + | 0.677666i | \(0.762991\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 653.818 | 0.777430 | ||||||||
\(842\) | − 401.208i | − 0.476494i | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 103.121 | 0.122182 | ||||||||
\(845\) | 389.552i | 0.461009i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −1002.57 | −1.18368 | ||||||||
\(848\) | − 377.552i | − 0.445226i | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 53.3939 | 0.0628163 | ||||||||
\(851\) | 44.5261i | 0.0523221i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −319.817 | −0.374932 | −0.187466 | − | 0.982271i | \(-0.560028\pi\) | ||||
−0.187466 | + | 0.982271i | \(0.560028\pi\) | |||||||
\(854\) | 154.557i | 0.180980i | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −101.939 | −0.119087 | ||||||||
\(857\) | − 797.968i | − 0.931118i | −0.885017 | − | 0.465559i | \(-0.845853\pi\) | ||||
0.885017 | − | 0.465559i | \(-0.154147\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −467.802 | −0.544588 | −0.272294 | − | 0.962214i | \(-0.587782\pi\) | ||||
−0.272294 | + | 0.962214i | \(0.587782\pi\) | |||||||
\(860\) | 468.126i | 0.544332i | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −364.059 | −0.422342 | ||||||||
\(863\) | − 1304.85i | − 1.51199i | −0.654578 | − | 0.755994i | \(-0.727154\pi\) | ||||
0.654578 | − | 0.755994i | \(-0.272846\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 359.908 | 0.416079 | ||||||||
\(866\) | − 673.551i | − 0.777772i | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 50.8490 | 0.0585818 | ||||||||
\(869\) | 41.7088i | 0.0479964i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −727.711 | −0.835489 | ||||||||
\(872\) | − 419.378i | − 0.480938i | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −33.3031 | −0.0381042 | ||||||||
\(875\) | 997.738i | 1.14027i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −373.756 | −0.426176 | −0.213088 | − | 0.977033i | \(-0.568352\pi\) | ||||
−0.213088 | + | 0.977033i | \(0.568352\pi\) | |||||||
\(878\) | 788.937i | 0.898562i | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −19.8184 | −0.0225209 | ||||||||
\(881\) | 229.979i | 0.261043i | 0.991445 | + | 0.130522i | \(0.0416652\pi\) | ||||
−0.991445 | + | 0.130522i | \(0.958335\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −1381.79 | −1.56488 | −0.782439 | − | 0.622728i | \(-0.786024\pi\) | ||||
−0.782439 | + | 0.622728i | \(0.786024\pi\) | |||||||
\(884\) | − 366.110i | − 0.414151i | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −1176.41 | −1.32778 | ||||||||
\(887\) | 876.180i | 0.987802i | 0.869518 | + | 0.493901i | \(0.164429\pi\) | ||||
−0.869518 | + | 0.493901i | \(0.835571\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 651.939 | 0.733339 | ||||||||
\(890\) | − 1067.73i | − 1.19970i | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −626.454 | −0.702303 | ||||||||
\(893\) | 1118.45i | 1.25246i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 246.729 | 0.275674 | ||||||||
\(896\) | − 94.4521i | − 0.105415i | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 1032.27 | 1.14952 | ||||||||
\(899\) | − 41.6655i | − 0.0463465i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −1781.82 | −1.97760 | ||||||||
\(902\) | 14.7215i | 0.0163210i | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 483.909 | 0.535298 | ||||||||
\(905\) | − 1262.03i | − 1.39451i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 1180.07 | 1.30107 | 0.650537 | − | 0.759475i | \(-0.274544\pi\) | ||||
0.650537 | + | 0.759475i | \(0.274544\pi\) | |||||||
\(908\) | − 152.542i | − 0.167998i | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −594.892 | −0.653728 | ||||||||
\(911\) | − 1270.32i | − 1.39442i | −0.716867 | − | 0.697210i | \(-0.754424\pi\) | ||||
0.716867 | − | 0.697210i | \(-0.245576\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 124.273 | 0.136116 | ||||||||
\(914\) | − 1003.58i | − 1.09800i | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 243.090 | 0.265382 | ||||||||
\(917\) | − 1954.07i | − 2.13093i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 1316.63 | 1.43268 | 0.716340 | − | 0.697751i | \(-0.245816\pi\) | ||||
0.716340 | + | 0.697751i | \(0.245816\pi\) | |||||||
\(920\) | 14.0137i | 0.0152323i | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 13.0148 | 0.0141158 | ||||||||
\(923\) | − 174.743i | − 0.189320i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −93.3939 | −0.100966 | ||||||||
\(926\) | 78.0610i | 0.0842991i | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −77.3939 | −0.0833986 | ||||||||
\(929\) | − 627.492i | − 0.675449i | −0.941245 | − | 0.337724i | \(-0.890343\pi\) | ||||
0.941245 | − | 0.337724i | \(-0.109657\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −511.151 | −0.549034 | ||||||||
\(932\) | 302.041i | 0.324079i | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −885.031 | −0.947570 | ||||||||
\(935\) | 93.5307i | 0.100033i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 469.789 | 0.501375 | 0.250688 | − | 0.968068i | \(-0.419343\pi\) | ||||
0.250688 | + | 0.968068i | \(0.419343\pi\) | |||||||
\(938\) | 886.025i | 0.944590i | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 470.636 | 0.500676 | ||||||||
\(941\) | 930.670i | 0.989022i | 0.869171 | + | 0.494511i | \(0.164653\pi\) | ||||
−0.869171 | + | 0.494511i | \(0.835347\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 10.4097 | 0.0110389 | ||||||||
\(944\) | − 75.1250i | − 0.0795816i | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −60.7423 | −0.0642097 | ||||||||
\(947\) | 3.63113i | 0.00383435i | 0.999998 | + | 0.00191717i | \(0.000610256\pi\) | ||||
−0.999998 | + | 0.00191717i | \(0.999390\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 76.6949 | 0.0808165 | ||||||||
\(950\) | − 69.8535i | − 0.0735300i | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −445.757 | −0.468232 | ||||||||
\(953\) | − 719.641i | − 0.755132i | −0.925983 | − | 0.377566i | \(-0.876761\pi\) | ||||
0.925983 | − | 0.377566i | \(-0.123239\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −39.1362 | −0.0409803 | ||||||||
\(956\) | 175.427i | 0.183501i | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −437.408 | −0.456584 | ||||||||
\(959\) | 1250.86i | 1.30434i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −951.725 | −0.990349 | ||||||||
\(962\) | 640.380i | 0.665676i | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −403.576 | −0.418647 | ||||||||
\(965\) | − 1795.03i | − 1.86014i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 33.7740 | 0.0349266 | 0.0174633 | − | 0.999848i | \(-0.494441\pi\) | ||||
0.0174633 | + | 0.999848i | \(0.494441\pi\) | |||||||
\(968\) | 339.668i | 0.350897i | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 807.439 | 0.832412 | ||||||||
\(971\) | 970.472i | 0.999456i | 0.866182 | + | 0.499728i | \(0.166567\pi\) | ||||
−0.866182 | + | 0.499728i | \(0.833433\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 705.697 | 0.725279 | ||||||||
\(974\) | 40.0699i | 0.0411395i | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 52.3633 | 0.0536509 | ||||||||
\(977\) | − 1570.30i | − 1.60727i | −0.595123 | − | 0.803635i | \(-0.702897\pi\) | ||||
0.595123 | − | 0.803635i | \(-0.297103\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 138.545 | 0.141517 | ||||||||
\(980\) | 215.089i | 0.219478i | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 1343.07 | 1.36769 | ||||||||
\(983\) | 775.878i | 0.789296i | 0.918832 | + | 0.394648i | \(0.129134\pi\) | ||||
−0.918832 | + | 0.394648i | \(0.870866\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 401.271 | 0.407382 | ||||||||
\(986\) | 365.252i | 0.370439i | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −478.969 | −0.484787 | ||||||||
\(989\) | 42.9513i | 0.0434290i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 870.454 | 0.878359 | 0.439180 | − | 0.898399i | \(-0.355269\pi\) | ||||
0.439180 | + | 0.898399i | \(0.355269\pi\) | |||||||
\(992\) | − 17.2274i | − 0.0173664i | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −212.758 | −0.214042 | ||||||||
\(995\) | − 797.530i | − 0.801538i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 1245.00 | 1.24874 | 0.624372 | − | 0.781127i | \(-0.285355\pi\) | ||||
0.624372 | + | 0.781127i | \(0.285355\pi\) | |||||||
\(998\) | 792.279i | 0.793867i | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))