Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1800,2,Mod(899,1800)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1800, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1, 1, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1800.899");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1800 = 2^{3} \cdot 3^{2} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1800.m (of order \(2\), degree \(1\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(14.3730723638\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Coefficient field: | 12.0.426337261060096.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 4x^{9} - 3x^{8} + 4x^{7} + 8x^{6} + 8x^{5} - 12x^{4} - 32x^{3} + 64 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{7} \) |
Twist minimal: | no (minimal twist has level 360) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 899.12 | ||
Root | \(-1.35818 - 0.394157i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1800.899 |
Dual form | 1800.2.m.d.899.11 |
$q$-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 \(\left(\mathbb{Z}/1800\mathbb{Z}\right)^\times\).
\(n\) | \(577\) | \(901\) | \(1001\) | \(1351\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(-1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.23909 | + | 0.681664i | 0.876166 | + | 0.482009i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.07067 | + | 1.68928i | 0.535334 | + | 0.844640i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.41421 | −0.534522 | −0.267261 | − | 0.963624i | \(-0.586119\pi\) | ||||
−0.267261 | + | 0.963624i | \(0.586119\pi\) | |||||||
\(8\) | 0.175128 | + | 2.82300i | 0.0619170 | + | 0.998081i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 6.37056i | 1.92080i | 0.278633 | + | 0.960398i | \(0.410119\pi\) | ||||
−0.278633 | + | 0.960398i | \(0.589881\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −3.54213 | −0.982410 | −0.491205 | − | 0.871044i | \(-0.663443\pi\) | ||||
−0.491205 | + | 0.871044i | \(0.663443\pi\) | |||||||
\(14\) | −1.75233 | − | 0.964019i | −0.468330 | − | 0.257645i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −1.70734 | + | 3.61732i | −0.426835 | + | 0.904330i | ||||
\(17\) | 3.92870 | 0.952849 | 0.476424 | − | 0.879215i | \(-0.341933\pi\) | ||||
0.476424 | + | 0.879215i | \(0.341933\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.27334 | −0.292125 | −0.146063 | − | 0.989275i | \(-0.546660\pi\) | ||||
−0.146063 | + | 0.989275i | \(0.546660\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −4.34258 | + | 7.89367i | −0.925841 | + | 1.68294i | ||||
\(23\) | − | 6.28267i | − | 1.31003i | −0.755617 | − | 0.655014i | \(-0.772663\pi\) | ||
0.755617 | − | 0.655014i | \(-0.227337\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −4.38900 | − | 2.41454i | −0.860754 | − | 0.473531i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −1.51415 | − | 2.38900i | −0.286148 | − | 0.451479i | ||||
\(29\) | −9.00933 | −1.67299 | −0.836495 | − | 0.547974i | \(-0.815399\pi\) | ||||
−0.836495 | + | 0.547974i | \(0.815399\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3.92870i | 0.705615i | 0.935696 | + | 0.352807i | \(0.114773\pi\) | ||||
−0.935696 | + | 0.352807i | \(0.885227\pi\) | |||||||
\(32\) | −4.58134 | + | 3.31834i | −0.809874 | + | 0.586604i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 4.86799 | + | 2.67805i | 0.834854 | + | 0.459282i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 2.51448 | 0.413378 | 0.206689 | − | 0.978407i | \(-0.433731\pi\) | ||||
0.206689 | + | 0.978407i | \(0.433731\pi\) | |||||||
\(38\) | −1.57778 | − | 0.867993i | −0.255950 | − | 0.140807i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 5.27029i | − | 0.823081i | −0.911392 | − | 0.411540i | \(-0.864991\pi\) | ||
0.911392 | − | 0.411540i | \(-0.135009\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.55602i | 0.237290i | 0.992937 | + | 0.118645i | \(0.0378551\pi\) | ||||
−0.992937 | + | 0.118645i | \(0.962145\pi\) | |||||||
\(44\) | −10.7617 | + | 6.82075i | −1.62238 | + | 1.02827i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 4.28267 | − | 7.78477i | 0.631446 | − | 1.14780i | ||||
\(47\) | 9.73599i | 1.42014i | 0.704131 | + | 0.710070i | \(0.251337\pi\) | ||||
−0.704131 | + | 0.710070i | \(0.748663\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −5.00000 | −0.714286 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −3.79245 | − | 5.98365i | −0.525918 | − | 0.829783i | ||||
\(53\) | − | 5.55602i | − | 0.763177i | −0.924332 | − | 0.381589i | \(-0.875377\pi\) | ||
0.924332 | − | 0.381589i | \(-0.124623\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −0.247668 | − | 3.99233i | −0.0330960 | − | 0.533497i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −11.1633 | − | 6.14134i | −1.46582 | − | 0.806397i | ||||
\(59\) | − | 0.313944i | − | 0.0408721i | −0.999791 | − | 0.0204360i | \(-0.993495\pi\) | ||
0.999791 | − | 0.0204360i | \(-0.00650544\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 12.7411i | 1.63133i | 0.578523 | + | 0.815666i | \(0.303629\pi\) | ||||
−0.578523 | + | 0.815666i | \(0.696371\pi\) | |||||||
\(62\) | −2.67805 | + | 4.86799i | −0.340113 | + | 0.618236i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −7.93866 | + | 0.988770i | −0.992333 | + | 0.123596i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 7.00933i | 0.856326i | 0.903702 | + | 0.428163i | \(0.140839\pi\) | ||||
−0.903702 | + | 0.428163i | \(0.859161\pi\) | |||||||
\(68\) | 4.20633 | + | 6.63667i | 0.510092 | + | 0.804815i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0.990671 | 0.117571 | 0.0587855 | − | 0.998271i | \(-0.481277\pi\) | ||||
0.0587855 | + | 0.998271i | \(0.481277\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 12.0187i | 1.40668i | 0.710855 | + | 0.703339i | \(0.248308\pi\) | ||||
−0.710855 | + | 0.703339i | \(0.751692\pi\) | |||||||
\(74\) | 3.11566 | + | 1.71403i | 0.362188 | + | 0.199252i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −1.36333 | − | 2.15103i | −0.156384 | − | 0.246741i | ||||
\(77\) | − | 9.00933i | − | 1.02671i | ||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 8.18453i | 0.920832i | 0.887703 | + | 0.460416i | \(0.152300\pi\) | ||||
−0.887703 | + | 0.460416i | \(0.847700\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 3.59257 | − | 6.53034i | 0.396733 | − | 0.721155i | ||||
\(83\) | 5.02897 | 0.552001 | 0.276000 | − | 0.961158i | \(-0.410991\pi\) | ||||
0.276000 | + | 0.961158i | \(0.410991\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −1.06068 | + | 1.92804i | −0.114376 | + | 0.207906i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −17.9841 | + | 1.11566i | −1.91711 | + | 0.118930i | ||||
\(89\) | − | 0.386566i | − | 0.0409759i | −0.999790 | − | 0.0204880i | \(-0.993478\pi\) | ||
0.999790 | − | 0.0204880i | \(-0.00652198\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 5.00933 | 0.525120 | ||||||||
\(92\) | 10.6132 | − | 6.72666i | 1.10650 | − | 0.701302i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −6.63667 | + | 12.0637i | −0.684520 | + | 1.24428i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 10.4626i | − | 1.06232i | −0.847271 | − | 0.531160i | \(-0.821756\pi\) | ||
0.847271 | − | 0.531160i | \(-0.178244\pi\) | |||||||
\(98\) | −6.19543 | − | 3.40832i | −0.625833 | − | 0.344292i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 13.1120 | 1.30470 | 0.652348 | − | 0.757920i | \(-0.273784\pi\) | ||||
0.652348 | + | 0.757920i | \(0.273784\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 6.04342 | 0.595476 | 0.297738 | − | 0.954648i | \(-0.403768\pi\) | ||||
0.297738 | + | 0.954648i | \(0.403768\pi\) | |||||||
\(104\) | −0.620325 | − | 9.99943i | −0.0608278 | − | 0.980525i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 3.78734 | − | 6.88438i | 0.367859 | − | 0.668670i | ||||
\(107\) | 2.82843 | 0.273434 | 0.136717 | − | 0.990610i | \(-0.456345\pi\) | ||||
0.136717 | + | 0.990610i | \(0.456345\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 7.08426i | 0.678549i | 0.940687 | + | 0.339275i | \(0.110182\pi\) | ||||
−0.940687 | + | 0.339275i | \(0.889818\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 2.41454 | − | 5.11566i | 0.228153 | − | 0.483384i | ||||
\(113\) | 16.6698 | 1.56816 | 0.784082 | − | 0.620657i | \(-0.213134\pi\) | ||||
0.784082 | + | 0.620657i | \(0.213134\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −9.64600 | − | 15.2193i | −0.895609 | − | 1.41308i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0.214005 | − | 0.389004i | 0.0197007 | − | 0.0358107i | ||||
\(119\) | −5.55602 | −0.509319 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −29.5840 | −2.68945 | ||||||||
\(122\) | −8.68516 | + | 15.7873i | −0.786318 | + | 1.42932i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −6.63667 | + | 4.20633i | −0.595991 | + | 0.377740i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 16.5840 | 1.47159 | 0.735796 | − | 0.677203i | \(-0.236808\pi\) | ||||
0.735796 | + | 0.677203i | \(0.236808\pi\) | |||||||
\(128\) | −10.5107 | − | 4.18633i | −0.929023 | − | 0.370023i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 4.96954i | 0.434190i | 0.976150 | + | 0.217095i | \(0.0696582\pi\) | ||||
−0.976150 | + | 0.217095i | \(0.930342\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1.80078 | 0.156147 | ||||||||
\(134\) | −4.77801 | + | 8.68516i | −0.412757 | + | 0.750284i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0.688023 | + | 11.0907i | 0.0589975 | + | 0.951021i | ||||
\(137\) | −2.50129 | −0.213700 | −0.106850 | − | 0.994275i | \(-0.534076\pi\) | ||||
−0.106850 | + | 0.994275i | \(0.534076\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 18.8480 | 1.59867 | 0.799334 | − | 0.600887i | \(-0.205186\pi\) | ||||
0.799334 | + | 0.600887i | \(0.205186\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 1.22753 | + | 0.675305i | 0.103012 | + | 0.0566703i | ||||
\(143\) | − | 22.5653i | − | 1.88701i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −8.19269 | + | 14.8921i | −0.678032 | + | 1.23248i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 2.69218 | + | 4.24767i | 0.221296 | + | 0.349156i | ||||
\(149\) | −1.00933 | −0.0826874 | −0.0413437 | − | 0.999145i | \(-0.513164\pi\) | ||||
−0.0413437 | + | 0.999145i | \(0.513164\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 16.5246i | − | 1.34475i | −0.740211 | − | 0.672375i | \(-0.765274\pi\) | ||
0.740211 | − | 0.672375i | \(-0.234726\pi\) | |||||||
\(152\) | −0.222998 | − | 3.59465i | −0.0180875 | − | 0.291565i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 6.14134 | − | 11.1633i | 0.494883 | − | 0.899567i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −10.2266 | −0.816174 | −0.408087 | − | 0.912943i | \(-0.633804\pi\) | ||||
−0.408087 | + | 0.912943i | \(0.633804\pi\) | |||||||
\(158\) | −5.57910 | + | 10.1413i | −0.443849 | + | 0.806801i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 8.88504i | 0.700239i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 6.54669i | − | 0.512776i | −0.966574 | − | 0.256388i | \(-0.917468\pi\) | ||
0.966574 | − | 0.256388i | \(-0.0825325\pi\) | |||||||
\(164\) | 8.90300 | − | 5.64273i | 0.695207 | − | 0.440623i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 6.23132 | + | 3.42807i | 0.483644 | + | 0.266069i | ||||
\(167\) | − | 22.8480i | − | 1.76803i | −0.467456 | − | 0.884016i | \(-0.654829\pi\) | ||
0.467456 | − | 0.884016i | \(-0.345171\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −0.453313 | −0.0348702 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −2.62855 | + | 1.66598i | −0.200425 | + | 0.127030i | ||||
\(173\) | − | 17.5560i | − | 1.33476i | −0.744718 | − | 0.667380i | \(-0.767416\pi\) | ||
0.744718 | − | 0.667380i | \(-0.232584\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −23.0443 | − | 10.8767i | −1.73703 | − | 0.819863i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0.263508 | − | 0.478989i | 0.0197508 | − | 0.0359017i | ||||
\(179\) | − | 1.48684i | − | 0.111131i | −0.998455 | − | 0.0555656i | \(-0.982304\pi\) | ||
0.998455 | − | 0.0555656i | \(-0.0176962\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 16.1974i | 1.20395i | 0.798517 | + | 0.601973i | \(0.205618\pi\) | ||||
−0.798517 | + | 0.601973i | \(0.794382\pi\) | |||||||
\(182\) | 6.20699 | + | 3.41468i | 0.460093 | + | 0.253113i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 17.7360 | − | 1.10027i | 1.30751 | − | 0.0811129i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 25.0280i | 1.83023i | ||||||||
\(188\) | −16.4468 | + | 10.4240i | −1.19951 | + | 0.760249i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 24.0373 | 1.73928 | 0.869640 | − | 0.493687i | \(-0.164351\pi\) | ||||
0.869640 | + | 0.493687i | \(0.164351\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − | 18.4626i | − | 1.32897i | −0.747302 | − | 0.664485i | \(-0.768651\pi\) | ||
0.747302 | − | 0.664485i | \(-0.231349\pi\) | |||||||
\(194\) | 7.13201 | − | 12.9641i | 0.512048 | − | 0.930769i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −5.35334 | − | 8.44640i | −0.382381 | − | 0.603315i | ||||
\(197\) | − | 11.4533i | − | 0.816015i | −0.912979 | − | 0.408007i | \(-0.866224\pi\) | ||
0.912979 | − | 0.408007i | \(-0.133776\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 2.50129i | 0.177312i | 0.996062 | + | 0.0886559i | \(0.0282571\pi\) | ||||
−0.996062 | + | 0.0886559i | \(0.971743\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 16.2469 | + | 8.93800i | 1.14313 | + | 0.628876i | ||||
\(203\) | 12.7411 | 0.894251 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 7.48832 | + | 4.11958i | 0.521736 | + | 0.287025i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 6.04762 | − | 12.8130i | 0.419327 | − | 0.888423i | ||||
\(209\) | − | 8.11191i | − | 0.561112i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 17.1893 | 1.18336 | 0.591680 | − | 0.806173i | \(-0.298465\pi\) | ||||
0.591680 | + | 0.806173i | \(0.298465\pi\) | |||||||
\(212\) | 9.38567 | − | 5.94865i | 0.644611 | − | 0.408555i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 3.50466 | + | 1.92804i | 0.239574 | + | 0.131798i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 5.55602i | − | 0.377167i | ||||||
\(218\) | −4.82909 | + | 8.77801i | −0.327067 | + | 0.594522i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −13.9160 | −0.936088 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −2.04210 | −0.136749 | −0.0683746 | − | 0.997660i | \(-0.521781\pi\) | ||||
−0.0683746 | + | 0.997660i | \(0.521781\pi\) | |||||||
\(224\) | 6.47899 | − | 4.69284i | 0.432896 | − | 0.313553i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 20.6553 | + | 11.3632i | 1.37397 | + | 0.755870i | ||||
\(227\) | −21.2264 | −1.40885 | −0.704423 | − | 0.709781i | \(-0.748794\pi\) | ||||
−0.704423 | + | 0.709781i | \(0.748794\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 13.3690i | 0.883449i | 0.897151 | + | 0.441724i | \(0.145633\pi\) | ||||
−0.897151 | + | 0.441724i | \(0.854367\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −1.57778 | − | 25.4333i | −0.103586 | − | 1.66978i | ||||
\(233\) | −17.2977 | −1.13321 | −0.566605 | − | 0.823990i | \(-0.691743\pi\) | ||||
−0.566605 | + | 0.823990i | \(0.691743\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0.530340 | − | 0.336130i | 0.0345222 | − | 0.0218802i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −6.88438 | − | 3.78734i | −0.446248 | − | 0.245497i | ||||
\(239\) | 13.4533 | 0.870222 | 0.435111 | − | 0.900377i | \(-0.356709\pi\) | ||||
0.435111 | + | 0.900377i | \(0.356709\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −4.56534 | −0.294080 | −0.147040 | − | 0.989131i | \(-0.546975\pi\) | ||||
−0.147040 | + | 0.989131i | \(0.546975\pi\) | |||||||
\(242\) | −36.6571 | − | 20.1664i | −2.35641 | − | 1.29634i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −21.5233 | + | 13.6415i | −1.37789 | + | 0.873308i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 4.51035 | 0.286987 | ||||||||
\(248\) | −11.0907 | + | 0.688023i | −0.704261 | + | 0.0436895i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 25.9414i | 1.63741i | 0.574216 | + | 0.818704i | \(0.305307\pi\) | ||||
−0.574216 | + | 0.818704i | \(0.694693\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 40.0241 | 2.51630 | ||||||||
\(254\) | 20.5490 | + | 11.3047i | 1.28936 | + | 0.709321i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −10.1700 | − | 12.3520i | −0.635624 | − | 0.771999i | ||||
\(257\) | 24.3820 | 1.52090 | 0.760452 | − | 0.649394i | \(-0.224977\pi\) | ||||
0.760452 | + | 0.649394i | \(0.224977\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −3.55602 | −0.220960 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −3.38755 | + | 6.15768i | −0.209284 | + | 0.380423i | ||||
\(263\) | 11.7360i | 0.723672i | 0.932242 | + | 0.361836i | \(0.117850\pi\) | ||||
−0.932242 | + | 0.361836i | \(0.882150\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 2.23132 | + | 1.22753i | 0.136811 | + | 0.0752645i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −11.8407 | + | 7.50466i | −0.723287 | + | 0.458420i | ||||
\(269\) | 11.0280 | 0.672388 | 0.336194 | − | 0.941793i | \(-0.390860\pi\) | ||||
0.336194 | + | 0.941793i | \(0.390860\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 20.2714i | 1.23140i | 0.787981 | + | 0.615699i | \(0.211126\pi\) | ||||
−0.787981 | + | 0.615699i | \(0.788874\pi\) | |||||||
\(272\) | −6.70762 | + | 14.2113i | −0.406709 | + | 0.861689i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −3.09931 | − | 1.70504i | −0.187236 | − | 0.103005i | ||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 3.28762 | 0.197534 | 0.0987668 | − | 0.995111i | \(-0.468510\pi\) | ||||
0.0987668 | + | 0.995111i | \(0.468510\pi\) | |||||||
\(278\) | 23.3543 | + | 12.8480i | 1.40070 | + | 0.770573i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 23.4401i | − | 1.39832i | −0.714965 | − | 0.699160i | \(-0.753557\pi\) | ||
0.714965 | − | 0.699160i | \(-0.246443\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 27.0093i | 1.60554i | 0.596290 | + | 0.802769i | \(0.296641\pi\) | ||||
−0.596290 | + | 0.802769i | \(0.703359\pi\) | |||||||
\(284\) | 1.06068 | + | 1.67352i | 0.0629398 | + | 0.0993053i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 15.3820 | − | 27.9604i | 0.909556 | − | 1.65333i | ||||
\(287\) | 7.45331i | 0.439955i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −1.56534 | −0.0920791 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −20.3029 | + | 12.8680i | −1.18814 | + | 0.753042i | ||||
\(293\) | 6.00000i | 0.350524i | 0.984522 | + | 0.175262i | \(0.0560772\pi\) | ||||
−0.984522 | + | 0.175262i | \(0.943923\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0.440355 | + | 7.09839i | 0.0255951 | + | 0.412585i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −1.25065 | − | 0.688023i | −0.0724479 | − | 0.0398561i | ||||
\(299\) | 22.2540i | 1.28698i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | − | 2.20054i | − | 0.126837i | ||||||
\(302\) | 11.2642 | − | 20.4754i | 0.648182 | − | 1.17822i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 2.17403 | − | 4.60609i | 0.124689 | − | 0.264177i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 0.565344i | 0.0322659i | 0.999870 | + | 0.0161330i | \(0.00513550\pi\) | ||||
−0.999870 | + | 0.0161330i | \(0.994864\pi\) | |||||||
\(308\) | 15.2193 | − | 9.64600i | 0.867199 | − | 0.549632i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 25.4533 | 1.44332 | 0.721662 | − | 0.692245i | \(-0.243378\pi\) | ||||
0.721662 | + | 0.692245i | \(0.243378\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 29.5747i | 1.67166i | 0.548989 | + | 0.835830i | \(0.315013\pi\) | ||||
−0.548989 | + | 0.835830i | \(0.684987\pi\) | |||||||
\(314\) | −12.6717 | − | 6.97113i | −0.715104 | − | 0.393404i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −13.8260 | + | 8.76291i | −0.777772 | + | 0.492952i | ||||
\(317\) | 6.56534i | 0.368746i | 0.982856 | + | 0.184373i | \(0.0590255\pi\) | ||||
−0.982856 | + | 0.184373i | \(0.940974\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 57.3944i | − | 3.21347i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −6.05661 | + | 11.0093i | −0.337522 | + | 0.613526i | ||||
\(323\) | −5.00258 | −0.278351 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 4.46264 | − | 8.11191i | 0.247163 | − | 0.449277i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 14.8780 | − | 0.922973i | 0.821501 | − | 0.0509627i | ||||
\(329\) | − | 13.7688i | − | 0.759096i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 7.29200 | 0.400805 | 0.200402 | − | 0.979714i | \(-0.435775\pi\) | ||||
0.200402 | + | 0.979714i | \(0.435775\pi\) | |||||||
\(332\) | 5.38435 | + | 8.49534i | 0.295505 | + | 0.466242i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 15.5747 | − | 28.3107i | 0.852208 | − | 1.54909i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 19.1307i | − | 1.04212i | −0.853522 | − | 0.521058i | \(-0.825538\pi\) | ||
0.853522 | − | 0.521058i | \(-0.174462\pi\) | |||||||
\(338\) | −0.561694 | − | 0.309007i | −0.0305521 | − | 0.0168078i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −25.0280 | −1.35534 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 16.9706 | 0.916324 | ||||||||
\(344\) | −4.39263 | + | 0.272501i | −0.236835 | + | 0.0146923i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 11.9673 | − | 21.7534i | 0.643366 | − | 1.16947i | ||||
\(347\) | −21.8807 | −1.17462 | −0.587308 | − | 0.809364i | \(-0.699812\pi\) | ||||
−0.587308 | + | 0.809364i | \(0.699812\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 24.8543i | − | 1.33042i | −0.746655 | − | 0.665211i | \(-0.768342\pi\) | ||
0.746655 | − | 0.665211i | \(-0.231658\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −21.1396 | − | 29.1857i | −1.12675 | − | 1.55560i | ||||
\(353\) | 8.18453 | 0.435619 | 0.217809 | − | 0.975991i | \(-0.430109\pi\) | ||||
0.217809 | + | 0.975991i | \(0.430109\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0.653019 | − | 0.413884i | 0.0346099 | − | 0.0219358i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 1.01352 | − | 1.84232i | 0.0535663 | − | 0.0973695i | ||||
\(359\) | −11.8973 | −0.627915 | −0.313958 | − | 0.949437i | \(-0.601655\pi\) | ||||
−0.313958 | + | 0.949437i | \(0.601655\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −17.3786 | −0.914663 | ||||||||
\(362\) | −11.0412 | + | 20.0700i | −0.580313 | + | 1.05486i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 5.36333 | + | 8.46216i | 0.281115 | + | 0.443538i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 6.67131 | 0.348239 | 0.174120 | − | 0.984724i | \(-0.444292\pi\) | ||||
0.174120 | + | 0.984724i | \(0.444292\pi\) | |||||||
\(368\) | 22.7264 | + | 10.7267i | 1.18470 | + | 0.559166i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 7.85739i | 0.407936i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 0.340330 | 0.0176216 | 0.00881081 | − | 0.999961i | \(-0.497195\pi\) | ||||
0.00881081 | + | 0.999961i | \(0.497195\pi\) | |||||||
\(374\) | −17.0607 | + | 31.0118i | −0.882187 | + | 1.60358i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −27.4847 | + | 1.70504i | −1.41741 | + | 0.0879307i | ||||
\(377\) | 31.9122 | 1.64356 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −20.3013 | −1.04281 | −0.521405 | − | 0.853310i | \(-0.674592\pi\) | ||||
−0.521405 | + | 0.853310i | \(0.674592\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 29.7843 | + | 16.3854i | 1.52390 | + | 0.838349i | ||||
\(383\) | 10.3013i | 0.526373i | 0.964745 | + | 0.263187i | \(0.0847735\pi\) | ||||
−0.964745 | + | 0.263187i | \(0.915226\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 12.5853 | − | 22.8768i | 0.640576 | − | 1.16440i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 17.6743 | − | 11.2020i | 0.897279 | − | 0.568696i | ||||
\(389\) | 19.1307 | 0.969964 | 0.484982 | − | 0.874524i | \(-0.338826\pi\) | ||||
0.484982 | + | 0.874524i | \(0.338826\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 24.6827i | − | 1.24826i | ||||||
\(392\) | −0.875638 | − | 14.1150i | −0.0442264 | − | 0.712915i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 7.80731 | − | 14.1916i | 0.393327 | − | 0.714964i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −3.39689 | −0.170485 | −0.0852424 | − | 0.996360i | \(-0.527166\pi\) | ||||
−0.0852424 | + | 0.996360i | \(0.527166\pi\) | |||||||
\(398\) | −1.70504 | + | 3.09931i | −0.0854659 | + | 0.155355i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 10.2993i | − | 0.514320i | −0.966369 | − | 0.257160i | \(-0.917213\pi\) | ||
0.966369 | − | 0.257160i | \(-0.0827868\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − | 13.9160i | − | 0.693203i | ||||||
\(404\) | 14.0386 | + | 22.1499i | 0.698448 | + | 1.10200i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 15.7873 | + | 8.68516i | 0.783512 | + | 0.431037i | ||||
\(407\) | 16.0187i | 0.794015i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −9.11203 | −0.450561 | −0.225280 | − | 0.974294i | \(-0.572330\pi\) | ||||
−0.225280 | + | 0.974294i | \(0.572330\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 6.47050 | + | 10.2090i | 0.318779 | + | 0.502963i | ||||
\(413\) | 0.443984i | 0.0218470i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 16.2277 | − | 11.7540i | 0.795628 | − | 0.576286i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 5.52960 | − | 10.0514i | 0.270461 | − | 0.491628i | ||||
\(419\) | 8.17134i | 0.399196i | 0.979878 | + | 0.199598i | \(0.0639636\pi\) | ||||
−0.979878 | + | 0.199598i | \(0.936036\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 3.60156i | − | 0.175529i | −0.996141 | − | 0.0877646i | \(-0.972028\pi\) | ||
0.996141 | − | 0.0877646i | \(-0.0279723\pi\) | |||||||
\(422\) | 21.2990 | + | 11.7173i | 1.03682 | + | 0.570391i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 15.6846 | − | 0.973012i | 0.761713 | − | 0.0472536i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − | 18.0187i | − | 0.871984i | ||||||
\(428\) | 3.02831 | + | 4.77801i | 0.146379 | + | 0.230954i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −8.10270 | −0.390293 | −0.195147 | − | 0.980774i | \(-0.562518\pi\) | ||||
−0.195147 | + | 0.980774i | \(0.562518\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 8.01866i | − | 0.385352i | −0.981262 | − | 0.192676i | \(-0.938283\pi\) | ||
0.981262 | − | 0.192676i | \(-0.0617166\pi\) | |||||||
\(434\) | 3.78734 | − | 6.88438i | 0.181798 | − | 0.330461i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −11.9673 | + | 7.58489i | −0.573130 | + | 0.363250i | ||||
\(437\) | 8.00000i | 0.382692i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 13.8150i | 0.659354i | 0.944094 | + | 0.329677i | \(0.106940\pi\) | ||||
−0.944094 | + | 0.329677i | \(0.893060\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −17.2431 | − | 9.48601i | −0.820169 | − | 0.451203i | ||||
\(443\) | 12.7147 | 0.604095 | 0.302048 | − | 0.953293i | \(-0.402330\pi\) | ||||
0.302048 | + | 0.953293i | \(0.402330\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −2.53034 | − | 1.39203i | −0.119815 | − | 0.0659144i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 11.2270 | − | 1.39833i | 0.530424 | − | 0.0660650i | ||||
\(449\) | − | 4.24264i | − | 0.200223i | −0.994976 | − | 0.100111i | \(-0.968080\pi\) | ||
0.994976 | − | 0.100111i | \(-0.0319199\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 33.5747 | 1.58097 | ||||||||
\(452\) | 17.8478 | + | 28.1600i | 0.839492 | + | 1.32453i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −26.3013 | − | 14.4693i | −1.23438 | − | 0.679077i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 3.35061i | − | 0.156735i | −0.996925 | − | 0.0783675i | \(-0.975029\pi\) | ||
0.996925 | − | 0.0783675i | \(-0.0249707\pi\) | |||||||
\(458\) | −9.11317 | + | 16.5653i | −0.425830 | + | 0.774048i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 18.1400 | 0.844865 | 0.422432 | − | 0.906394i | \(-0.361176\pi\) | ||||
0.422432 | + | 0.906394i | \(0.361176\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −32.9267 | −1.53023 | −0.765116 | − | 0.643892i | \(-0.777318\pi\) | ||||
−0.765116 | + | 0.643892i | \(0.777318\pi\) | |||||||
\(464\) | 15.3820 | − | 32.5896i | 0.714091 | − | 1.51293i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −21.4333 | − | 11.7912i | −0.992880 | − | 0.546218i | ||||
\(467\) | 6.42999 | 0.297544 | 0.148772 | − | 0.988872i | \(-0.452468\pi\) | ||||
0.148772 | + | 0.988872i | \(0.452468\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − | 9.91269i | − | 0.457725i | ||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0.886265 | − | 0.0549803i | 0.0407936 | − | 0.00253067i | ||||
\(473\) | −9.91269 | −0.455786 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −5.94865 | − | 9.38567i | −0.272656 | − | 0.430192i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 16.6698 | + | 9.17064i | 0.762459 | + | 0.419455i | ||||
\(479\) | 29.0280 | 1.32632 | 0.663161 | − | 0.748477i | \(-0.269214\pi\) | ||||
0.663161 | + | 0.748477i | \(0.269214\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −8.90663 | −0.406107 | ||||||||
\(482\) | −5.65685 | − | 3.11203i | −0.257663 | − | 0.141749i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −31.6746 | − | 49.9757i | −1.43976 | − | 2.27162i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 11.7267 | 0.531386 | 0.265693 | − | 0.964058i | \(-0.414399\pi\) | ||||
0.265693 | + | 0.964058i | \(0.414399\pi\) | |||||||
\(488\) | −35.9682 | + | 2.23132i | −1.62820 | + | 0.101007i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 8.02609i | 0.362213i | 0.983464 | + | 0.181106i | \(0.0579678\pi\) | ||||
−0.983464 | + | 0.181106i | \(0.942032\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −35.3949 | −1.59411 | ||||||||
\(494\) | 5.58871 | + | 3.07454i | 0.251448 | + | 0.138330i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −14.2113 | − | 6.70762i | −0.638108 | − | 0.301181i | ||||
\(497\) | −1.40102 | −0.0628444 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 26.4040 | 1.18201 | 0.591003 | − | 0.806669i | \(-0.298732\pi\) | ||||
0.591003 | + | 0.806669i | \(0.298732\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −17.6833 | + | 32.1436i | −0.789246 | + | 1.43464i | ||||
\(503\) | 31.3947i | 1.39982i | 0.714231 | + | 0.699910i | \(0.246777\pi\) | ||||
−0.714231 | + | 0.699910i | \(0.753223\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 49.5933 | + | 27.2830i | 2.20469 | + | 1.21288i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 17.7560 | + | 28.0150i | 0.787793 | + | 1.24297i | ||||
\(509\) | −26.9253 | −1.19344 | −0.596721 | − | 0.802449i | \(-0.703530\pi\) | ||||
−0.596721 | + | 0.802449i | \(0.703530\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − | 16.9969i | − | 0.751901i | ||||||
\(512\) | −4.18158 | − | 22.2377i | −0.184801 | − | 0.982776i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 30.2113 | + | 16.6203i | 1.33257 | + | 0.733090i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −62.0237 | −2.72780 | ||||||||
\(518\) | −4.40621 | − | 2.42401i | −0.193598 | − | 0.106505i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 0.641081i | − | 0.0280863i | −0.999901 | − | 0.0140431i | \(-0.995530\pi\) | ||
0.999901 | − | 0.0140431i | \(-0.00447022\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 13.1307i | − | 0.574165i | −0.957906 | − | 0.287082i | \(-0.907315\pi\) | ||
0.957906 | − | 0.287082i | \(-0.0926854\pi\) | |||||||
\(524\) | −8.39494 | + | 5.32072i | −0.366735 | + | 0.232437i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −8.00000 | + | 14.5419i | −0.348817 | + | 0.634057i | ||||
\(527\) | 15.4347i | 0.672344i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −16.4720 | −0.716173 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 1.92804 | + | 3.04202i | 0.0835910 | + | 0.131888i | ||||
\(533\) | 18.6680i | 0.808603i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −19.7873 | + | 1.22753i | −0.854683 | + | 0.0530211i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 13.6646 | + | 7.51738i | 0.589124 | + | 0.324097i | ||||
\(539\) | − | 31.8528i | − | 1.37200i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − | 12.8864i | − | 0.554028i | −0.960866 | − | 0.277014i | \(-0.910655\pi\) | ||
0.960866 | − | 0.277014i | \(-0.0893448\pi\) | |||||||
\(542\) | −13.8183 | + | 25.1180i | −0.593545 | + | 1.07891i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −17.9987 | + | 13.0367i | −0.771687 | + | 0.558945i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 30.4813i | 1.30329i | 0.758526 | + | 0.651643i | \(0.225920\pi\) | ||||
−0.758526 | + | 0.651643i | \(0.774080\pi\) | |||||||
\(548\) | −2.67805 | − | 4.22538i | −0.114401 | − | 0.180499i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 11.4720 | 0.488722 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − | 11.5747i | − | 0.492205i | ||||||
\(554\) | 4.07364 | + | 2.24105i | 0.173072 | + | 0.0952131i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 20.1800 | + | 31.8396i | 0.855821 | + | 1.35030i | ||||
\(557\) | − | 0.462642i | − | 0.0196028i | −0.999952 | − | 0.00980138i | \(-0.996880\pi\) | ||
0.999952 | − | 0.00980138i | \(-0.00311993\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 5.51161i | − | 0.233116i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 15.9783 | − | 29.0443i | 0.674004 | − | 1.22516i | ||||
\(563\) | −36.7959 | −1.55076 | −0.775382 | − | 0.631493i | \(-0.782443\pi\) | ||||
−0.775382 | + | 0.631493i | \(0.782443\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −18.4113 | + | 33.4669i | −0.773884 | + | 1.40672i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0.173494 | + | 2.79667i | 0.00727964 | + | 0.117345i | ||||
\(569\) | 7.44444i | 0.312087i | 0.987750 | + | 0.156044i | \(0.0498740\pi\) | ||||
−0.987750 | + | 0.156044i | \(0.950126\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 10.1986 | 0.426799 | 0.213400 | − | 0.976965i | \(-0.431546\pi\) | ||||
0.213400 | + | 0.976965i | \(0.431546\pi\) | |||||||
\(572\) | 38.1192 | − | 24.1600i | 1.59384 | − | 1.01018i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −5.08066 | + | 9.23530i | −0.212062 | + | 0.385474i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 0.443984i | − | 0.0184833i | −0.999957 | − | 0.00924165i | \(-0.997058\pi\) | ||
0.999957 | − | 0.00924165i | \(-0.00294175\pi\) | |||||||
\(578\) | −1.93960 | − | 1.06704i | −0.0806766 | − | 0.0443830i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −7.11203 | −0.295057 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 35.3949 | 1.46591 | ||||||||
\(584\) | −33.9287 | + | 2.10480i | −1.40398 | + | 0.0870972i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −4.08998 | + | 7.43452i | −0.168956 | + | 0.307117i | ||||
\(587\) | 30.3660 | 1.25334 | 0.626668 | − | 0.779286i | \(-0.284418\pi\) | ||||
0.626668 | + | 0.779286i | \(0.284418\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 5.00258i | − | 0.206128i | ||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −4.29308 | + | 9.09568i | −0.176444 | + | 0.373830i | ||||
\(593\) | −23.1262 | −0.949679 | −0.474839 | − | 0.880073i | \(-0.657494\pi\) | ||||
−0.474839 | + | 0.880073i | \(0.657494\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −1.08066 | − | 1.70504i | −0.0442654 | − | 0.0698411i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −15.1698 | + | 27.5747i | −0.620339 | + | 1.12761i | ||||
\(599\) | −16.1027 | −0.657939 | −0.328969 | − | 0.944341i | \(-0.606701\pi\) | ||||
−0.328969 | + | 0.944341i | \(0.606701\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −8.20541 | −0.334705 | −0.167353 | − | 0.985897i | \(-0.553522\pi\) | ||||
−0.167353 | + | 0.985897i | \(0.553522\pi\) | |||||||
\(602\) | 1.50003 | − | 2.72666i | 0.0611366 | − | 0.111130i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 27.9146 | − | 17.6923i | 1.13583 | − | 0.719891i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −5.81529 | −0.236035 | −0.118018 | − | 0.993011i | \(-0.537654\pi\) | ||||
−0.118018 | + | 0.993011i | \(0.537654\pi\) | |||||||
\(608\) | 5.83362 | − | 4.22538i | 0.236584 | − | 0.171362i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 34.4861i | − | 1.39516i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −0.0858146 | −0.00346602 | −0.00173301 | − | 0.999998i | \(-0.500552\pi\) | ||||
−0.00173301 | + | 0.999998i | \(0.500552\pi\) | |||||||
\(614\) | −0.385375 | + | 0.700510i | −0.0155525 | + | 0.0282703i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 25.4333 | − | 1.57778i | 1.02474 | − | 0.0635707i | ||||
\(617\) | −39.3236 | −1.58311 | −0.791555 | − | 0.611099i | \(-0.790728\pi\) | ||||
−0.791555 | + | 0.611099i | \(0.790728\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 28.0959 | 1.12927 | 0.564635 | − | 0.825341i | \(-0.309017\pi\) | ||||
0.564635 | + | 0.825341i | \(0.309017\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 31.5388 | + | 17.3506i | 1.26459 | + | 0.695696i | ||||
\(623\) | 0.546687i | 0.0219026i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −20.1600 | + | 36.6456i | −0.805755 | + | 1.46465i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −10.9493 | − | 17.2757i | −0.436926 | − | 0.689374i | ||||
\(629\) | 9.87864 | 0.393887 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 18.8440i | − | 0.750166i | −0.926991 | − | 0.375083i | \(-0.877614\pi\) | ||
0.926991 | − | 0.375083i | \(-0.122386\pi\) | |||||||
\(632\) | −23.1049 | + | 1.43334i | −0.919065 | + | 0.0570151i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −4.47536 | + | 8.13503i | −0.177739 | + | 0.323083i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 17.7107 | 0.701722 | ||||||||
\(638\) | 39.1237 | − | 71.1167i | 1.54892 | − | 2.81554i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 14.1817i | − | 0.560144i | −0.959979 | − | 0.280072i | \(-0.909642\pi\) | ||
0.959979 | − | 0.280072i | \(-0.0903583\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 18.5467i | − | 0.731410i | −0.930731 | − | 0.365705i | \(-0.880828\pi\) | ||
0.930731 | − | 0.365705i | \(-0.119172\pi\) | |||||||
\(644\) | −15.0093 | + | 9.51293i | −0.591450 | + | 0.374862i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −6.19863 | − | 3.41008i | −0.243882 | − | 0.134168i | ||||
\(647\) | 7.75464i | 0.304866i | 0.988314 | + | 0.152433i | \(0.0487109\pi\) | ||||
−0.988314 | + | 0.152433i | \(0.951289\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 2.00000 | 0.0785069 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 11.0592 | − | 7.00933i | 0.433111 | − | 0.274506i | ||||
\(653\) | 27.6960i | 1.08383i | 0.840433 | + | 0.541915i | \(0.182300\pi\) | ||||
−0.840433 | + | 0.541915i | \(0.817700\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 19.0643 | + | 8.99817i | 0.744336 | + | 0.351320i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 9.38567 | − | 17.0607i | 0.365892 | − | 0.665095i | ||||
\(659\) | 28.1420i | 1.09625i | 0.836395 | + | 0.548127i | \(0.184659\pi\) | ||||
−0.836395 | + | 0.548127i | \(0.815341\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 19.7990i | 0.770091i | 0.922897 | + | 0.385046i | \(0.125814\pi\) | ||||
−0.922897 | + | 0.385046i | \(0.874186\pi\) | |||||||
\(662\) | 9.03542 | + | 4.97070i | 0.351171 | + | 0.193192i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0.880711 | + | 14.1968i | 0.0341782 | + | 0.550942i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 56.6027i | 2.19166i | ||||||||
\(668\) | 38.5967 | − | 24.4626i | 1.49335 | − | 0.946488i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −81.1680 | −3.13346 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 11.8133i | 0.455367i | 0.973735 | + | 0.227684i | \(0.0731152\pi\) | ||||
−0.973735 | + | 0.227684i | \(0.926885\pi\) | |||||||
\(674\) | 13.0407 | − | 23.7046i | 0.502309 | − | 0.913066i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −0.485348 | − | 0.765773i | −0.0186672 | − | 0.0294528i | ||||
\(677\) | − | 11.4533i | − | 0.440187i | −0.975479 | − | 0.220093i | \(-0.929364\pi\) | ||
0.975479 | − | 0.220093i | \(-0.0706362\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 14.7964i | 0.567834i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −31.0118 | − | 17.0607i | −1.18750 | − | 0.653287i | ||||
\(683\) | 41.0254 | 1.56979 | 0.784896 | − | 0.619627i | \(-0.212716\pi\) | ||||
0.784896 | + | 0.619627i | \(0.212716\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 21.0280 | + | 11.5682i | 0.802852 | + | 0.441677i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −5.62860 | − | 2.65665i | −0.214589 | − | 0.101284i | ||||
\(689\) | 19.6801i | 0.749753i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 4.38538 | 0.166828 | 0.0834138 | − | 0.996515i | \(-0.473418\pi\) | ||||
0.0834138 | + | 0.996515i | \(0.473418\pi\) | |||||||
\(692\) | 29.6570 | − | 18.7967i | 1.12739 | − | 0.714542i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −27.1120 | − | 14.9153i | −1.02916 | − | 0.566176i | ||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 20.7054i | − | 0.784272i | ||||||
\(698\) | 16.9423 | − | 30.7967i | 0.641276 | − | 1.16567i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −5.11203 | −0.193079 | −0.0965394 | − | 0.995329i | \(-0.530777\pi\) | ||||
−0.0965394 | + | 0.995329i | \(0.530777\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −3.20180 | −0.120758 | ||||||||
\(704\) | −6.29902 | − | 50.5737i | −0.237403 | − | 1.90607i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 10.1413 | + | 5.57910i | 0.381674 | + | 0.209972i | ||||
\(707\) | −18.5432 | −0.697389 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 32.6853i | 1.22752i | 0.789491 | + | 0.613762i | \(0.210345\pi\) | ||||
−0.789491 | + | 0.613762i | \(0.789655\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 1.09128 | − | 0.0676984i | 0.0408973 | − | 0.00253710i | ||||
\(713\) | 24.6827 | 0.924375 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 2.51168 | − | 1.59191i | 0.0938660 | − | 0.0594924i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −14.7418 | − | 8.10996i | −0.550158 | − | 0.302661i | ||||
\(719\) | −10.4813 | −0.390886 | −0.195443 | − | 0.980715i | \(-0.562615\pi\) | ||||
−0.195443 | + | 0.980715i | \(0.562615\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −8.54669 | −0.318295 | ||||||||
\(722\) | −21.5336 | − | 11.8464i | −0.801397 | − | 0.440876i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −27.3620 | + | 17.3421i | −1.01690 | + | 0.644513i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −48.5226 | −1.79960 | −0.899802 | − | 0.436299i | \(-0.856289\pi\) | ||||
−0.899802 | + | 0.436299i | \(0.856289\pi\) | |||||||
\(728\) | 0.877272 | + | 14.1413i | 0.0325139 | + | 0.524113i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 6.11311i | 0.226102i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −8.94447 | −0.330372 | −0.165186 | − | 0.986262i | \(-0.552822\pi\) | ||||
−0.165186 | + | 0.986262i | \(0.552822\pi\) | |||||||
\(734\) | 8.26633 | + | 4.54759i | 0.305116 | + | 0.167855i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 20.8480 | + | 28.7830i | 0.768468 | + | 1.06096i | ||||
\(737\) | −44.6533 | −1.64483 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −4.17997 | −0.153763 | −0.0768813 | − | 0.997040i | \(-0.524496\pi\) | ||||
−0.0768813 | + | 0.997040i | \(0.524496\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −5.35610 | + | 9.73599i | −0.196629 | + | 0.357419i | ||||
\(743\) | 0.245357i | 0.00900129i | 0.999990 | + | 0.00450065i | \(0.00143260\pi\) | ||||
−0.999990 | + | 0.00450065i | \(0.998567\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0.421698 | + | 0.231991i | 0.0154395 | + | 0.00849378i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −42.2793 | + | 26.7967i | −1.54588 | + | 0.979783i | ||||
\(749\) | −4.00000 | −0.146157 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 8.78603i | 0.320607i | 0.987068 | + | 0.160303i | \(0.0512473\pi\) | ||||
−0.987068 | + | 0.160303i | \(0.948753\pi\) | |||||||
\(752\) | −35.2182 | − | 16.6226i | −1.28427 | − | 0.606165i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 39.5420 | + | 21.7534i | 1.44003 | + | 0.792213i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 41.3393 | 1.50250 | 0.751252 | − | 0.660016i | \(-0.229450\pi\) | ||||
0.751252 | + | 0.660016i | \(0.229450\pi\) | |||||||
\(758\) | −25.1551 | − | 13.8387i | −0.913674 | − | 0.502644i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 10.6726i | − | 0.386882i | −0.981112 | − | 0.193441i | \(-0.938035\pi\) | ||
0.981112 | − | 0.193441i | \(-0.0619649\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − | 10.0187i | − | 0.362700i | ||||||
\(764\) | 25.7360 | + | 40.6058i | 0.931095 | + | 1.46907i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −7.02205 | + | 12.7642i | −0.253717 | + | 0.461190i | ||||
\(767\) | 1.11203i | 0.0401531i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 28.2427 | 1.01846 | 0.509229 | − | 0.860631i | \(-0.329931\pi\) | ||||
0.509229 | + | 0.860631i | \(0.329931\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 31.1886 | − | 19.7674i | 1.12250 | − | 0.711443i | ||||
\(773\) | 41.4720i | 1.49164i | 0.666146 | + | 0.745822i | \(0.267943\pi\) | ||||
−0.666146 | + | 0.745822i | \(0.732057\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 29.5360 | − | 1.83230i | 1.06028 | − | 0.0657756i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 23.7046 | + | 13.0407i | 0.849850 | + | 0.467532i | ||||
\(779\) | 6.71089i | 0.240442i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 6.31113i | 0.225830i | ||||||||
\(782\) | 16.8253 | − | 30.5840i | 0.601672 | − | 1.09368i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 8.53670 | − | 18.0866i | 0.304882 | − | 0.645950i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 45.1680i | − | 1.61007i | −0.593230 | − | 0.805033i | \(-0.702148\pi\) | ||
0.593230 | − | 0.805033i | \(-0.297852\pi\) | |||||||
\(788\) | 19.3479 | − | 12.2627i | 0.689239 | − | 0.436840i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −23.5747 | −0.838219 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 45.1307i | − | 1.60264i | ||||||
\(794\) | −4.20903 | − | 2.31554i | −0.149373 | − | 0.0821753i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −4.22538 | + | 2.67805i | −0.149765 | + | 0.0949210i | ||||
\(797\) | − | 12.4626i | − | 0.441449i | −0.975336 | − | 0.220725i | \(-0.929158\pi\) | ||
0.975336 | − | 0.220725i | \(-0.0708422\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 38.2497i | 1.35318i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 7.02063 | − | 12.7617i | 0.247907 | − | 0.450630i | ||||
\(803\) | −76.5655 | −2.70194 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 9.48601 | − | 17.2431i | 0.334130 | − | 0.607361i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 2.29628 | + | 37.0153i | 0.0807828 | + | 1.30219i | ||||
\(809\) | 34.7802i | 1.22281i | 0.791319 | + | 0.611404i | \(0.209395\pi\) | ||||
−0.791319 | + | 0.611404i | \(0.790605\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −31.7360 | −1.11440 | −0.557201 | − | 0.830378i | \(-0.688125\pi\) | ||||
−0.557201 | + | 0.830378i | \(0.688125\pi\) | |||||||
\(812\) | 13.6415 | + | 21.5233i | 0.478723 | + | 0.755321i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −10.9193 | + | 19.8485i | −0.382723 | + | 0.695689i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 1.98134i | − | 0.0693184i | ||||||
\(818\) | −11.2906 | − | 6.21134i | −0.394766 | − | 0.217175i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −4.97201 | −0.173524 | −0.0867622 | − | 0.996229i | \(-0.527652\pi\) | ||||
−0.0867622 | + | 0.996229i | \(0.527652\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −44.0386 | −1.53509 | −0.767545 | − | 0.640995i | \(-0.778522\pi\) | ||||
−0.767545 | + | 0.640995i | \(0.778522\pi\) | |||||||
\(824\) | 1.05837 | + | 17.0606i | 0.0368701 | + | 0.594333i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −0.302648 | + | 0.550135i | −0.0105305 | + | 0.0191416i | ||||
\(827\) | −32.0838 | −1.11566 | −0.557832 | − | 0.829954i | \(-0.688367\pi\) | ||||
−0.557832 | + | 0.829954i | \(0.688367\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 41.1706i | 1.42992i | 0.699168 | + | 0.714958i | \(0.253554\pi\) | ||||
−0.699168 | + | 0.714958i | \(0.746446\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 28.1198 | − | 3.50235i | 0.974878 | − | 0.121422i | ||||
\(833\) | −19.6435 | −0.680606 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 13.7033 | − | 8.68516i | 0.473938 | − | 0.300383i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −5.57011 | + | 10.1250i | −0.192416 | + | 0.349762i | ||||
\(839\) | 39.9346 | 1.37870 | 0.689348 | − | 0.724430i | \(-0.257897\pi\) | ||||
0.689348 | + | 0.724430i | \(0.257897\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 52.1680 | 1.79890 | ||||||||
\(842\) | 2.45505 | − | 4.46264i | 0.0846067 | − | 0.153793i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 18.4040 | + | 29.0376i | 0.633493 | + | 0.999514i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 41.8381 | 1.43757 | ||||||||
\(848\) | 20.0979 | + | 9.48601i | 0.690164 | + | 0.325751i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − | 15.7977i | − | 0.541537i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −36.0822 | −1.23543 | −0.617716 | − | 0.786401i | \(-0.711942\pi\) | ||||
−0.617716 | + | 0.786401i | \(0.711942\pi\) | |||||||
\(854\) | 12.2827 | − | 22.3267i | 0.420304 | − | 0.764003i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0.495336 | + | 7.98465i | 0.0169302 | + | 0.272910i | ||||
\(857\) | 23.0998 | 0.789074 | 0.394537 | − | 0.918880i | \(-0.370905\pi\) | ||||
0.394537 | + | 0.918880i | \(0.370905\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −44.3013 | −1.51154 | −0.755771 | − | 0.654836i | \(-0.772738\pi\) | ||||
−0.755771 | + | 0.654836i | \(0.772738\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −10.0399 | − | 5.52332i | −0.341962 | − | 0.188125i | ||||
\(863\) | − | 25.5492i | − | 0.869706i | −0.900501 | − | 0.434853i | \(-0.856800\pi\) | ||
0.900501 | − | 0.434853i | \(-0.143200\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 5.46603 | − | 9.93581i | 0.185743 | − | 0.337632i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 9.38567 | − | 5.94865i | 0.318570 | − | 0.201910i | ||||
\(869\) | −52.1400 | −1.76873 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 24.8280i | − | 0.841263i | ||||||
\(872\) | −19.9989 | + | 1.24065i | −0.677247 | + | 0.0420137i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −5.45331 | + | 9.91269i | −0.184461 | + | 0.335302i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 0.168701 | 0.00569661 | 0.00284831 | − | 0.999996i | \(-0.499093\pi\) | ||||
0.00284831 | + | 0.999996i | \(0.499093\pi\) | |||||||
\(878\) | −9.41719 | + | 17.1180i | −0.317815 | + | 0.577704i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 29.4704i | − | 0.992881i | −0.868071 | − | 0.496441i | \(-0.834640\pi\) | ||
0.868071 | − | 0.496441i | \(-0.165360\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 3.43466i | − | 0.115585i | −0.998329 | − | 0.0577927i | \(-0.981594\pi\) | ||
0.998329 | − | 0.0577927i | \(-0.0184062\pi\) | |||||||
\(884\) | −14.8994 | − | 23.5080i | −0.501120 | − | 0.790658i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 15.7546 | + | 8.66717i | 0.529288 | + | 0.291179i | ||||
\(887\) | − | 16.6240i | − | 0.558178i | −0.960265 | − | 0.279089i | \(-0.909968\pi\) | ||
0.960265 | − | 0.279089i | \(-0.0900324\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −23.4533 | −0.786599 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −2.18641 | − | 3.44968i | −0.0732065 | − | 0.115504i | ||||
\(893\) | − | 12.3973i | − | 0.414858i | ||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 14.8644 | + | 5.92036i | 0.496584 | + | 0.197785i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 2.89206 | − | 5.25700i | 0.0965092 | − | 0.175428i | ||||
\(899\) | − | 35.3949i | − | 1.18049i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 21.8279i | − | 0.727193i | ||||||
\(902\) | 41.6019 | + | 22.8867i | 1.38519 | + | 0.762042i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 2.91934 | + | 47.0589i | 0.0970959 | + | 1.56516i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 50.1587i | − | 1.66549i | −0.553656 | − | 0.832746i | \(-0.686768\pi\) | ||
0.553656 | − | 0.832746i | \(-0.313232\pi\) | |||||||
\(908\) | −22.7264 | − | 35.8573i | −0.754203 | − | 1.18997i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 26.5467 | 0.879531 | 0.439765 | − | 0.898113i | \(-0.355062\pi\) | ||||
0.439765 | + | 0.898113i | \(0.355062\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 32.0373i | 1.06028i | ||||||||
\(914\) | 2.28399 | − | 4.15169i | 0.0755477 | − | 0.137326i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −22.5840 | + | 14.3138i | −0.746196 | + | 0.472940i | ||||
\(917\) | − | 7.02799i | − | 0.232085i | ||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 39.3236i | 1.29717i | 0.761144 | + | 0.648583i | \(0.224638\pi\) | ||||
−0.761144 | + | 0.648583i | \(0.775362\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 22.4770 | + | 12.3654i | 0.740242 | + | 0.407233i | ||||
\(923\) | −3.50909 | −0.115503 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −40.7990 | − | 22.4449i | −1.34074 | − | 0.737586i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 41.2748 | − | 29.8960i | 1.35491 | − | 0.981384i | ||||
\(929\) | − | 38.9833i | − | 1.27900i | −0.768791 | − | 0.639500i | \(-0.779141\pi\) | ||
0.768791 | − | 0.639500i | \(-0.220859\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 6.36672 | 0.208661 | ||||||||
\(932\) | −18.5201 | − | 29.2207i | −0.606646 | − | 0.957155i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 7.96731 | + | 4.38309i | 0.260698 | + | 0.143419i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 11.1307i | 0.363624i | 0.983333 | + | 0.181812i | \(0.0581962\pi\) | ||||
−0.983333 | + | 0.181812i | \(0.941804\pi\) | |||||||
\(938\) | 6.75712 | − | 12.2827i | 0.220628 | − | 0.401043i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −46.2427 | −1.50747 | −0.753735 | − | 0.657179i | \(-0.771750\pi\) | ||||
−0.753735 | + | 0.657179i | \(0.771750\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −33.1115 | −1.07826 | ||||||||
\(944\) | 1.13564 | + | 0.536010i | 0.0369618 | + | 0.0174456i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −12.2827 | − | 6.75712i | −0.399344 | − | 0.219693i | ||||
\(947\) | −16.3163 | −0.530208 | −0.265104 | − | 0.964220i | \(-0.585406\pi\) | ||||
−0.265104 | + | 0.964220i | \(0.585406\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − | 42.5717i | − | 1.38193i | ||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −0.973012 | − | 15.6846i | −0.0315355 | − | 0.508342i | ||||
\(953\) | 8.01290 | 0.259563 | 0.129782 | − | 0.991543i | \(-0.458572\pi\) | ||||
0.129782 | + | 0.991543i | \(0.458572\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 14.4040 | + | 22.7264i | 0.465860 | + | 0.735025i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 35.9682 | + | 19.7873i | 1.16208 | + | 0.639300i | ||||
\(959\) | 3.53736 | 0.114227 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 15.5653 | 0.502108 | ||||||||
\(962\) | −11.0361 | − | 6.07133i | −0.355817 | − | 0.195747i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −4.88797 | − | 7.71215i | −0.157431 | − | 0.248392i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −61.0092 | −1.96192 | −0.980962 | − | 0.194201i | \(-0.937789\pi\) | ||||
−0.980962 | + | 0.194201i | \(0.937789\pi\) | |||||||
\(968\) | −5.18098 | − | 83.5156i | −0.166523 | − | 2.68429i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 16.0023i | 0.513540i | 0.966473 | + | 0.256770i | \(0.0826582\pi\) | ||||
−0.966473 | + | 0.256770i | \(0.917342\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −26.6551 | −0.854524 | ||||||||
\(974\) | 14.5303 | + | 7.99364i | 0.465582 | + | 0.256133i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −46.0887 | − | 21.7534i | −1.47526 | − | 0.696310i | ||||
\(977\) | 34.2683 | 1.09634 | 0.548169 | − | 0.836367i | \(-0.315325\pi\) | ||||
0.548169 | + | 0.836367i | \(0.315325\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 2.46264 | 0.0787064 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −5.47110 | + | 9.94502i | −0.174590 | + | 0.317358i | ||||
\(983\) | − | 15.3947i | − | 0.491015i | −0.969395 | − | 0.245507i | \(-0.921045\pi\) | ||
0.969395 | − | 0.245507i | \(-0.0789546\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −43.8573 | − | 24.1274i | −1.39670 | − | 0.768374i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 4.82909 | + | 7.61925i | 0.153634 | + | 0.242401i | ||||
\(989\) | 9.77594 | 0.310857 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 14.6145i | − | 0.464245i | −0.972687 | − | 0.232123i | \(-0.925433\pi\) | ||
0.972687 | − | 0.232123i | \(-0.0745671\pi\) | |||||||
\(992\) | −13.0367 | − | 17.9987i | −0.413917 | − | 0.571459i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −1.73599 | − | 0.955026i | −0.0550621 | − | 0.0302916i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 44.7655 | 1.41774 | 0.708869 | − | 0.705340i | \(-0.249206\pi\) | ||||
0.708869 | + | 0.705340i | \(0.249206\pi\) | |||||||
\(998\) | 32.7169 | + | 17.9987i | 1.03563 | + | 0.569738i | ||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))