Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4400,2,Mod(1,4400)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4400, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4400.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4400 = 2^{4} \cdot 5^{2} \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4400.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(35.1341768894\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | 4.4.54764.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} - 9x^{2} + 3x + 2 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 440) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(0.655762\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4400.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0.655762 | 0.378604 | 0.189302 | − | 0.981919i | \(-0.439377\pi\) | ||||
0.189302 | + | 0.981919i | \(0.439377\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.415806 | −0.157160 | −0.0785800 | − | 0.996908i | \(-0.525039\pi\) | ||||
−0.0785800 | + | 0.996908i | \(0.525039\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.56998 | −0.856659 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.00000 | −0.301511 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −4.00000 | −1.10940 | −0.554700 | − | 0.832050i | \(-0.687167\pi\) | ||||
−0.554700 | + | 0.832050i | \(0.687167\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 6.51558 | 1.58026 | 0.790130 | − | 0.612939i | \(-0.210013\pi\) | ||||
0.790130 | + | 0.612939i | \(0.210013\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −5.20406 | −1.19389 | −0.596946 | − | 0.802281i | \(-0.703619\pi\) | ||||
−0.596946 | + | 0.802281i | \(0.703619\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −0.272670 | −0.0595015 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 8.54830 | 1.78244 | 0.891221 | − | 0.453568i | \(-0.149849\pi\) | ||||
0.891221 | + | 0.453568i | \(0.149849\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −3.65258 | −0.702939 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0.895717 | 0.166331 | 0.0831653 | − | 0.996536i | \(-0.473497\pi\) | ||||
0.0831653 | + | 0.996536i | \(0.473497\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 6.73836 | 1.21025 | 0.605123 | − | 0.796132i | \(-0.293124\pi\) | ||||
0.605123 | + | 0.796132i | \(0.293124\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −0.655762 | −0.114153 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −8.96410 | −1.47369 | −0.736845 | − | 0.676062i | \(-0.763685\pi\) | ||||
−0.736845 | + | 0.676062i | \(0.763685\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −2.62305 | −0.420024 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 10.0998 | 1.57732 | 0.788660 | − | 0.614830i | \(-0.210775\pi\) | ||||
0.788660 | + | 0.614830i | \(0.210775\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −4.78825 | −0.730201 | −0.365101 | − | 0.930968i | \(-0.618965\pi\) | ||||
−0.365101 | + | 0.930968i | \(0.618965\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 5.61986 | 0.819741 | 0.409871 | − | 0.912144i | \(-0.365574\pi\) | ||||
0.409871 | + | 0.912144i | \(0.365574\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.82711 | −0.975301 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 4.27267 | 0.598293 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −10.0357 | −1.37851 | −0.689253 | − | 0.724521i | \(-0.742061\pi\) | ||||
−0.689253 | + | 0.724521i | \(0.742061\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −3.41262 | −0.452013 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 1.63408 | 0.212739 | 0.106370 | − | 0.994327i | \(-0.466077\pi\) | ||||
0.106370 | + | 0.994327i | \(0.466077\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 7.10428 | 0.909610 | 0.454805 | − | 0.890591i | \(-0.349709\pi\) | ||||
0.454805 | + | 0.890591i | \(0.349709\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 1.06861 | 0.134633 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 10.6914 | 1.30617 | 0.653083 | − | 0.757286i | \(-0.273475\pi\) | ||||
0.653083 | + | 0.757286i | \(0.273475\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 5.60565 | 0.674841 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 6.19302 | 0.734977 | 0.367488 | − | 0.930028i | \(-0.380218\pi\) | ||||
0.367488 | + | 0.930028i | \(0.380218\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −3.16839 | −0.370832 | −0.185416 | − | 0.982660i | \(-0.559363\pi\) | ||||
−0.185416 | + | 0.982660i | \(0.559363\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0.415806 | 0.0473855 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 11.2682 | 1.26777 | 0.633884 | − | 0.773428i | \(-0.281460\pi\) | ||||
0.633884 | + | 0.773428i | \(0.281460\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 5.31471 | 0.590523 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 16.2429 | 1.78289 | 0.891446 | − | 0.453128i | \(-0.149692\pi\) | ||||
0.891446 | + | 0.453128i | \(0.149692\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0.587377 | 0.0629735 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 9.56998 | 1.01442 | 0.507208 | − | 0.861824i | \(-0.330678\pi\) | ||||
0.507208 | + | 0.861824i | \(0.330678\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.66323 | 0.174353 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 4.41876 | 0.458204 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −0.591657 | −0.0600737 | −0.0300368 | − | 0.999549i | \(-0.509562\pi\) | ||||
−0.0300368 | + | 0.999549i | \(0.509562\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 2.56998 | 0.258292 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −4.62305 | −0.460010 | −0.230005 | − | 0.973189i | \(-0.573874\pi\) | ||||
−0.230005 | + | 0.973189i | \(0.573874\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −8.24291 | −0.812198 | −0.406099 | − | 0.913829i | \(-0.633111\pi\) | ||||
−0.406099 | + | 0.913829i | \(0.633111\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 17.6199 | 1.70338 | 0.851688 | − | 0.524049i | \(-0.175579\pi\) | ||||
0.851688 | + | 0.524049i | \(0.175579\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 3.66323 | 0.350873 | 0.175437 | − | 0.984491i | \(-0.443866\pi\) | ||||
0.175437 | + | 0.984491i | \(0.443866\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −5.87832 | −0.557945 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 11.4797 | 1.07992 | 0.539959 | − | 0.841691i | \(-0.318440\pi\) | ||||
0.539959 | + | 0.841691i | \(0.318440\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 10.2799 | 0.950378 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −2.70922 | −0.248354 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 6.62305 | 0.597180 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −9.13995 | −0.811040 | −0.405520 | − | 0.914086i | \(-0.632909\pi\) | ||||
−0.405520 | + | 0.914086i | \(0.632909\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −3.13995 | −0.276457 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 2.48123 | 0.216787 | 0.108393 | − | 0.994108i | \(-0.465429\pi\) | ||||
0.108393 | + | 0.994108i | \(0.465429\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 2.16388 | 0.187632 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −7.40834 | −0.632937 | −0.316469 | − | 0.948603i | \(-0.602497\pi\) | ||||
−0.316469 | + | 0.948603i | \(0.602497\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1.69166 | 0.143485 | 0.0717424 | − | 0.997423i | \(-0.477144\pi\) | ||||
0.0717424 | + | 0.997423i | \(0.477144\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 3.68529 | 0.310358 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 4.00000 | 0.334497 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −4.47696 | −0.369253 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 3.74940 | 0.307163 | 0.153581 | − | 0.988136i | \(-0.450919\pi\) | ||||
0.153581 | + | 0.988136i | \(0.450919\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 15.1400 | 1.23207 | 0.616036 | − | 0.787718i | \(-0.288738\pi\) | ||||
0.616036 | + | 0.787718i | \(0.288738\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −16.7449 | −1.35374 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −11.5871 | −0.924755 | −0.462378 | − | 0.886683i | \(-0.653004\pi\) | ||||
−0.462378 | + | 0.886683i | \(0.653004\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −6.58101 | −0.521908 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −3.55444 | −0.280129 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 6.82392 | 0.534491 | 0.267245 | − | 0.963629i | \(-0.413887\pi\) | ||||
0.267245 | + | 0.963629i | \(0.413887\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 7.10428 | 0.549746 | 0.274873 | − | 0.961481i | \(-0.411364\pi\) | ||||
0.274873 | + | 0.961481i | \(0.411364\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 3.00000 | 0.230769 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 13.3743 | 1.02276 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −9.31152 | −0.707942 | −0.353971 | − | 0.935256i | \(-0.615169\pi\) | ||||
−0.353971 | + | 0.935256i | \(0.615169\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 1.07157 | 0.0805440 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 26.6368 | 1.99093 | 0.995464 | − | 0.0951359i | \(-0.0303286\pi\) | ||||
0.995464 | + | 0.0951359i | \(0.0303286\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1.01103 | 0.0751495 | 0.0375748 | − | 0.999294i | \(-0.488037\pi\) | ||||
0.0375748 | + | 0.999294i | \(0.488037\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 4.65872 | 0.344382 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −6.51558 | −0.476466 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 1.51877 | 0.110474 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −10.5655 | −0.764490 | −0.382245 | − | 0.924061i | \(-0.624849\pi\) | ||||
−0.382245 | + | 0.924061i | \(0.624849\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −11.8271 | −0.851334 | −0.425667 | − | 0.904880i | \(-0.639960\pi\) | ||||
−0.425667 | + | 0.904880i | \(0.639960\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 1.31152 | 0.0934422 | 0.0467211 | − | 0.998908i | \(-0.485123\pi\) | ||||
0.0467211 | + | 0.998908i | \(0.485123\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 11.8271 | 0.838401 | 0.419201 | − | 0.907894i | \(-0.362310\pi\) | ||||
0.419201 | + | 0.907894i | \(0.362310\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 7.01103 | 0.494520 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −0.372445 | −0.0261405 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −21.9689 | −1.52695 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 5.20406 | 0.359972 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 8.37244 | 0.576383 | 0.288191 | − | 0.957573i | \(-0.406946\pi\) | ||||
0.288191 | + | 0.957573i | \(0.406946\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 4.06115 | 0.278265 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −2.80185 | −0.190202 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −2.07771 | −0.140398 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −26.0623 | −1.75314 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −22.1461 | −1.48301 | −0.741506 | − | 0.670946i | \(-0.765888\pi\) | ||||
−0.741506 | + | 0.670946i | \(0.765888\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −21.8194 | −1.44821 | −0.724103 | − | 0.689692i | \(-0.757746\pi\) | ||||
−0.724103 | + | 0.689692i | \(0.757746\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 2.80247 | 0.185192 | 0.0925962 | − | 0.995704i | \(-0.470483\pi\) | ||||
0.0925962 | + | 0.995704i | \(0.470483\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0.272670 | 0.0179404 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −8.24424 | −0.540098 | −0.270049 | − | 0.962847i | \(-0.587040\pi\) | ||||
−0.270049 | + | 0.962847i | \(0.587040\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 7.38923 | 0.479982 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 11.2682 | 0.728877 | 0.364438 | − | 0.931227i | \(-0.381261\pi\) | ||||
0.364438 | + | 0.931227i | \(0.381261\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 22.3860 | 1.44201 | 0.721006 | − | 0.692929i | \(-0.243680\pi\) | ||||
0.721006 | + | 0.692929i | \(0.243680\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 14.4429 | 0.926514 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 20.8162 | 1.32451 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 10.6515 | 0.675010 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −3.84265 | −0.242546 | −0.121273 | − | 0.992619i | \(-0.538698\pi\) | ||||
−0.121273 | + | 0.992619i | \(0.538698\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −8.54830 | −0.537427 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −10.6230 | −0.662648 | −0.331324 | − | 0.943517i | \(-0.607495\pi\) | ||||
−0.331324 | + | 0.943517i | \(0.607495\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 3.72733 | 0.231605 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −2.30197 | −0.142489 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 5.79276 | 0.357197 | 0.178598 | − | 0.983922i | \(-0.442844\pi\) | ||||
0.178598 | + | 0.983922i | \(0.442844\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 6.27563 | 0.384062 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −8.20857 | −0.500485 | −0.250243 | − | 0.968183i | \(-0.580510\pi\) | ||||
−0.250243 | + | 0.968183i | \(0.580510\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −27.3111 | −1.65903 | −0.829515 | − | 0.558485i | \(-0.811383\pi\) | ||||
−0.829515 | + | 0.558485i | \(0.811383\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 1.09068 | 0.0660109 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 14.4735 | 0.869631 | 0.434815 | − | 0.900520i | \(-0.356814\pi\) | ||||
0.434815 | + | 0.900520i | \(0.356814\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −17.3174 | −1.03677 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 16.2799 | 0.971178 | 0.485589 | − | 0.874187i | \(-0.338605\pi\) | ||||
0.485589 | + | 0.874187i | \(0.338605\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 10.5169 | 0.625165 | 0.312583 | − | 0.949891i | \(-0.398806\pi\) | ||||
0.312583 | + | 0.949891i | \(0.398806\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −4.19955 | −0.247892 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 25.4528 | 1.49722 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −0.387986 | −0.0227441 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 9.37695 | 0.547807 | 0.273904 | − | 0.961757i | \(-0.411685\pi\) | ||||
0.273904 | + | 0.961757i | \(0.411685\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 3.65258 | 0.211944 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −34.1932 | −1.97744 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1.99099 | 0.114758 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −3.03162 | −0.174162 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 2.09978 | 0.119840 | 0.0599202 | − | 0.998203i | \(-0.480915\pi\) | ||||
0.0599202 | + | 0.998203i | \(0.480915\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −5.40539 | −0.307502 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 20.3724 | 1.15522 | 0.577608 | − | 0.816314i | \(-0.303986\pi\) | ||||
0.577608 | + | 0.816314i | \(0.303986\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 23.8968 | 1.35073 | 0.675364 | − | 0.737485i | \(-0.263987\pi\) | ||||
0.675364 | + | 0.737485i | \(0.263987\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 5.86114 | 0.329195 | 0.164597 | − | 0.986361i | \(-0.447368\pi\) | ||||
0.164597 | + | 0.986361i | \(0.447368\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −0.895717 | −0.0501506 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 11.5544 | 0.644906 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −33.9075 | −1.88666 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 2.40220 | 0.132842 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −2.33677 | −0.128831 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 0.574484 | 0.0315765 | 0.0157882 | − | 0.999875i | \(-0.494974\pi\) | ||||
0.0157882 | + | 0.999875i | \(0.494974\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 23.0375 | 1.26245 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 4.10747 | 0.223748 | 0.111874 | − | 0.993722i | \(-0.464315\pi\) | ||||
0.111874 | + | 0.993722i | \(0.464315\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 7.52794 | 0.408862 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −6.73836 | −0.364903 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 5.74940 | 0.310438 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −8.30834 | −0.446015 | −0.223008 | − | 0.974817i | \(-0.571587\pi\) | ||||
−0.223008 | + | 0.974817i | \(0.571587\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −18.4858 | −0.989523 | −0.494762 | − | 0.869029i | \(-0.664745\pi\) | ||||
−0.494762 | + | 0.869029i | \(0.664745\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 14.6103 | 0.779841 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −26.5199 | −1.41151 | −0.705755 | − | 0.708456i | \(-0.749392\pi\) | ||||
−0.705755 | + | 0.708456i | \(0.749392\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −1.77660 | −0.0940278 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 18.8226 | 0.993419 | 0.496709 | − | 0.867917i | \(-0.334541\pi\) | ||||
0.496709 | + | 0.867917i | \(0.334541\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 8.08222 | 0.425380 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0.655762 | 0.0344186 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −10.2115 | −0.533037 | −0.266519 | − | 0.963830i | \(-0.585873\pi\) | ||||
−0.266519 | + | 0.963830i | \(0.585873\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −25.9562 | −1.35122 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 4.17289 | 0.216646 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 32.3363 | 1.67431 | 0.837156 | − | 0.546965i | \(-0.184217\pi\) | ||||
0.837156 | + | 0.546965i | \(0.184217\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −3.58287 | −0.184527 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −15.3686 | −0.789434 | −0.394717 | − | 0.918803i | \(-0.629157\pi\) | ||||
−0.394717 | + | 0.918803i | \(0.629157\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −5.99363 | −0.307063 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −13.6662 | −0.698309 | −0.349155 | − | 0.937065i | \(-0.613531\pi\) | ||||
−0.349155 | + | 0.937065i | \(0.613531\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 12.3057 | 0.625534 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −9.01103 | −0.456878 | −0.228439 | − | 0.973558i | \(-0.573362\pi\) | ||||
−0.228439 | + | 0.973558i | \(0.573362\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 55.6971 | 2.81672 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 1.62710 | 0.0820763 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 3.45466 | 0.173384 | 0.0866922 | − | 0.996235i | \(-0.472370\pi\) | ||||
0.0866922 | + | 0.996235i | \(0.472370\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 1.41899 | 0.0710384 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −1.62756 | −0.0812762 | −0.0406381 | − | 0.999174i | \(-0.512939\pi\) | ||||
−0.0406381 | + | 0.999174i | \(0.512939\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −26.9535 | −1.34265 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 8.96410 | 0.444334 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 6.54534 | 0.323646 | 0.161823 | − | 0.986820i | \(-0.448263\pi\) | ||||
0.161823 | + | 0.986820i | \(0.448263\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −4.85811 | −0.239633 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −0.679461 | −0.0334341 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 1.10933 | 0.0543239 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 34.4795 | 1.68443 | 0.842216 | − | 0.539141i | \(-0.181251\pi\) | ||||
0.842216 | + | 0.539141i | \(0.181251\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 6.54534 | 0.319000 | 0.159500 | − | 0.987198i | \(-0.449012\pi\) | ||||
0.159500 | + | 0.987198i | \(0.449012\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −14.4429 | −0.702239 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −2.95401 | −0.142954 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 2.62305 | 0.126642 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −36.1711 | −1.74230 | −0.871151 | − | 0.491016i | \(-0.836626\pi\) | ||||
−0.871151 | + | 0.491016i | \(0.836626\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 38.1027 | 1.83110 | 0.915550 | − | 0.402204i | \(-0.131756\pi\) | ||||
0.915550 | + | 0.402204i | \(0.131756\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −44.4858 | −2.12805 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −12.1282 | −0.578848 | −0.289424 | − | 0.957201i | \(-0.593464\pi\) | ||||
−0.289424 | + | 0.957201i | \(0.593464\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 17.5455 | 0.835500 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −16.5483 | −0.786233 | −0.393117 | − | 0.919489i | \(-0.628603\pi\) | ||||
−0.393117 | + | 0.919489i | \(0.628603\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 2.45871 | 0.116293 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 15.6056 | 0.736476 | 0.368238 | − | 0.929732i | \(-0.379961\pi\) | ||||
0.368238 | + | 0.929732i | \(0.379961\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −10.0998 | −0.475580 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 9.92820 | 0.466468 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 5.87761 | 0.274943 | 0.137471 | − | 0.990506i | \(-0.456102\pi\) | ||||
0.137471 | + | 0.990506i | \(0.456102\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −23.7987 | −1.11083 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 36.7495 | 1.71159 | 0.855797 | − | 0.517312i | \(-0.173067\pi\) | ||||
0.855797 | + | 0.517312i | \(0.173067\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −19.3081 | −0.897324 | −0.448662 | − | 0.893702i | \(-0.648099\pi\) | ||||
−0.448662 | + | 0.893702i | \(0.648099\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −11.4129 | −0.528127 | −0.264064 | − | 0.964505i | \(-0.585063\pi\) | ||||
−0.264064 | + | 0.964505i | \(0.585063\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −4.44556 | −0.205277 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −7.59841 | −0.350116 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 4.78825 | 0.220164 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 25.7914 | 1.18091 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −29.2307 | −1.33559 | −0.667793 | − | 0.744347i | \(-0.732761\pi\) | ||||
−0.667793 | + | 0.744347i | \(0.732761\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 35.8564 | 1.63491 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −2.33086 | −0.106058 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −33.2932 | −1.50866 | −0.754329 | − | 0.656496i | \(-0.772038\pi\) | ||||
−0.754329 | + | 0.656496i | \(0.772038\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 4.47487 | 0.202361 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 24.5151 | 1.10635 | 0.553176 | − | 0.833064i | \(-0.313416\pi\) | ||||
0.553176 | + | 0.833064i | \(0.313416\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 5.83612 | 0.262846 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −2.57510 | −0.115509 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 18.9093 | 0.846497 | 0.423249 | − | 0.906014i | \(-0.360890\pi\) | ||||
0.423249 | + | 0.906014i | \(0.360890\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 4.65872 | 0.208136 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 9.42031 | 0.420031 | 0.210016 | − | 0.977698i | \(-0.432649\pi\) | ||||
0.210016 | + | 0.977698i | \(0.432649\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 1.96729 | 0.0873702 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −16.7804 | −0.743778 | −0.371889 | − | 0.928277i | \(-0.621290\pi\) | ||||
−0.371889 | + | 0.928277i | \(0.621290\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1.31744 | 0.0582799 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 19.0082 | 0.839234 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −5.61986 | −0.247161 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −6.10614 | −0.268030 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −37.8273 | −1.65724 | −0.828621 | − | 0.559810i | \(-0.810874\pi\) | ||||
−0.828621 | + | 0.559810i | \(0.810874\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −10.0998 | −0.441632 | −0.220816 | − | 0.975315i | \(-0.570872\pi\) | ||||
−0.220816 | + | 0.975315i | \(0.570872\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 43.9044 | 1.91250 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 50.0734 | 2.17710 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −4.19955 | −0.182245 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −40.3991 | −1.74988 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 17.4674 | 0.753774 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 6.82711 | 0.294064 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −29.9269 | −1.28666 | −0.643329 | − | 0.765590i | \(-0.722447\pi\) | ||||
−0.643329 | + | 0.765590i | \(0.722447\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0.662997 | 0.0284519 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −23.7630 | −1.01603 | −0.508016 | − | 0.861347i | \(-0.669621\pi\) | ||||
−0.508016 | + | 0.861347i | \(0.669621\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −18.2578 | −0.779226 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −4.66137 | −0.198581 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −4.68537 | −0.199242 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −24.3363 | −1.03116 | −0.515581 | − | 0.856841i | \(-0.672424\pi\) | ||||
−0.515581 | + | 0.856841i | \(0.672424\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 19.1530 | 0.810086 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −4.27267 | −0.180392 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 8.85368 | 0.373138 | 0.186569 | − | 0.982442i | \(-0.440263\pi\) | ||||
0.186569 | + | 0.982442i | \(0.440263\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −2.20989 | −0.0928066 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 26.3860 | 1.10616 | 0.553080 | − | 0.833128i | \(-0.313452\pi\) | ||||
0.553080 | + | 0.833128i | \(0.313452\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −6.45280 | −0.270041 | −0.135021 | − | 0.990843i | \(-0.543110\pi\) | ||||
−0.135021 | + | 0.990843i | \(0.543110\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −6.92843 | −0.289439 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 12.1745 | 0.506832 | 0.253416 | − | 0.967357i | \(-0.418446\pi\) | ||||
0.253416 | + | 0.967357i | \(0.418446\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −7.75576 | −0.322319 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −6.75390 | −0.280199 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 10.0357 | 0.415635 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 22.9521 | 0.947336 | 0.473668 | − | 0.880704i | \(-0.342930\pi\) | ||||
0.473668 | + | 0.880704i | \(0.342930\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −35.0668 | −1.44490 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0.860047 | 0.0353776 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 10.4081 | 0.427410 | 0.213705 | − | 0.976898i | \(-0.431447\pi\) | ||||
0.213705 | + | 0.976898i | \(0.431447\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 7.75576 | 0.317422 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 8.98913 | 0.367286 | 0.183643 | − | 0.982993i | \(-0.441211\pi\) | ||||
0.183643 | + | 0.982993i | \(0.441211\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −3.57650 | −0.145889 | −0.0729443 | − | 0.997336i | \(-0.523240\pi\) | ||||
−0.0729443 | + | 0.997336i | \(0.523240\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −27.4767 | −1.11894 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −27.0235 | −1.09685 | −0.548424 | − | 0.836200i | \(-0.684772\pi\) | ||||
−0.548424 | + | 0.836200i | \(0.684772\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −0.244235 | −0.00989691 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −22.4795 | −0.909421 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −44.5572 | −1.79965 | −0.899823 | − | 0.436254i | \(-0.856305\pi\) | ||||
−0.899823 | + | 0.436254i | \(0.856305\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −15.2966 | −0.615818 | −0.307909 | − | 0.951416i | \(-0.599629\pi\) | ||||
−0.307909 | + | 0.951416i | \(0.599629\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −14.5655 | −0.585436 | −0.292718 | − | 0.956199i | \(-0.594560\pi\) | ||||
−0.292718 | + | 0.956199i | \(0.594560\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −31.2233 | −1.25295 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −3.97926 | −0.159426 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 3.41262 | 0.136287 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −58.4063 | −2.32881 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 22.0779 | 0.878906 | 0.439453 | − | 0.898266i | \(-0.355172\pi\) | ||||
0.439453 | + | 0.898266i | \(0.355172\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 5.49033 | 0.218221 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 27.3084 | 1.08200 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −15.9159 | −0.629624 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −31.2152 | −1.23293 | −0.616463 | − | 0.787384i | \(-0.711435\pi\) | ||||
−0.616463 | + | 0.787384i | \(0.711435\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 10.4498 | 0.412102 | 0.206051 | − | 0.978541i | \(-0.433939\pi\) | ||||
0.206051 | + | 0.978541i | \(0.433939\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −26.1307 | −1.02730 | −0.513652 | − | 0.857999i | \(-0.671708\pi\) | ||||
−0.513652 | + | 0.857999i | \(0.671708\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −1.63408 | −0.0641433 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −1.83735 | −0.0720114 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 44.2097 | 1.73006 | 0.865030 | − | 0.501719i | \(-0.167299\pi\) | ||||
0.865030 | + | 0.501719i | \(0.167299\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 8.14268 | 0.317676 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −6.96706 | −0.271398 | −0.135699 | − | 0.990750i | \(-0.543328\pi\) | ||||
−0.135699 | + | 0.990750i | \(0.543328\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −9.19753 | −0.357743 | −0.178871 | − | 0.983872i | \(-0.557245\pi\) | ||||
−0.178871 | + | 0.983872i | \(0.557245\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −17.0907 | −0.663747 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 7.65686 | 0.296475 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −14.5226 | −0.561475 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −7.10428 | −0.274258 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −8.72415 | −0.336291 | −0.168146 | − | 0.985762i | \(-0.553778\pi\) | ||||
−0.168146 | + | 0.985762i | \(0.553778\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 8.76618 | 0.336912 | 0.168456 | − | 0.985709i | \(-0.446122\pi\) | ||||
0.168456 | + | 0.985709i | \(0.446122\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0.246015 | 0.00944118 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −14.3083 | −0.548297 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 49.2320 | 1.88381 | 0.941906 | − | 0.335877i | \(-0.109033\pi\) | ||||
0.941906 | + | 0.335877i | \(0.109033\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 1.83775 | 0.0701146 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 40.1427 | 1.52931 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 18.1483 | 0.690395 | 0.345198 | − | 0.938530i | \(-0.387812\pi\) | ||||
0.345198 | + | 0.938530i | \(0.387812\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −1.06861 | −0.0405932 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 65.8059 | 2.49258 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −5.40626 | −0.204483 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 22.6587 | 0.855808 | 0.427904 | − | 0.903824i | \(-0.359252\pi\) | ||||
0.427904 | + | 0.903824i | \(0.359252\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 46.6497 | 1.75943 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 1.92229 | 0.0722952 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −36.7366 | −1.37967 | −0.689836 | − | 0.723966i | \(-0.742317\pi\) | ||||
−0.689836 | + | 0.723966i | \(0.742317\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −28.9589 | −1.08604 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 57.6015 | 2.15719 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 7.38923 | 0.275956 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −8.74738 | −0.326222 | −0.163111 | − | 0.986608i | \(-0.552153\pi\) | ||||
−0.163111 | + | 0.986608i | \(0.552153\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 3.42745 | 0.127645 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 14.6799 | 0.545952 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 2.20887 | 0.0819226 | 0.0409613 | − | 0.999161i | \(-0.486958\pi\) | ||||
0.0409613 | + | 0.999161i | \(0.486958\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −6.47301 | −0.239741 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −31.1982 | −1.15391 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 3.58552 | 0.132434 | 0.0662171 | − | 0.997805i | \(-0.478907\pi\) | ||||
0.0662171 | + | 0.997805i | \(0.478907\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −10.6914 | −0.393824 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 24.9314 | 0.917116 | 0.458558 | − | 0.888665i | \(-0.348366\pi\) | ||||
0.458558 | + | 0.888665i | \(0.348366\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 13.6505 | 0.501463 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −21.4257 | −0.786032 | −0.393016 | − | 0.919532i | \(-0.628568\pi\) | ||||
−0.393016 | + | 0.919532i | \(0.628568\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −41.7439 | −1.52733 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −7.32645 | −0.267703 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −28.1582 | −1.02751 | −0.513754 | − | 0.857938i | \(-0.671746\pi\) | ||||
−0.513754 | + | 0.857938i | \(0.671746\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −2.51986 | −0.0918288 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −10.7513 | −0.390761 | −0.195381 | − | 0.980728i | \(-0.562594\pi\) | ||||
−0.195381 | + | 0.980728i | \(0.562594\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −5.60565 | −0.203472 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −38.0429 | −1.37905 | −0.689527 | − | 0.724260i | \(-0.742182\pi\) | ||||
−0.689527 | + | 0.724260i | \(0.742182\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −1.52319 | −0.0551433 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −6.53632 | −0.236013 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 26.2280 | 0.945805 | 0.472903 | − | 0.881115i | \(-0.343206\pi\) | ||||
0.472903 | + | 0.881115i | \(0.343206\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −6.96619 | −0.250881 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −8.94499 | −0.321729 | −0.160864 | − | 0.986977i | \(-0.551428\pi\) | ||||
−0.160864 | + | 0.986977i | \(0.551428\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 2.44424 | 0.0876867 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −52.5598 | −1.88315 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −6.19302 | −0.221604 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −3.27168 | −0.116920 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 29.9716 | 1.06837 | 0.534185 | − | 0.845367i | \(-0.320618\pi\) | ||||
0.534185 | + | 0.845367i | \(0.320618\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 3.79867 | 0.135236 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −4.77332 | −0.169720 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −28.4171 | −1.00912 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −6.80022 | −0.240876 | −0.120438 | − | 0.992721i | \(-0.538430\pi\) | ||||
−0.120438 | + | 0.992721i | \(0.538430\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 36.6167 | 1.29541 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −24.5946 | −0.869008 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 3.16839 | 0.111810 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −5.38286 | −0.189486 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 53.1246 | 1.86776 | 0.933880 | − | 0.357586i | \(-0.116400\pi\) | ||||
0.933880 | + | 0.357586i | \(0.116400\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 30.0487 | 1.05515 | 0.527577 | − | 0.849507i | \(-0.323101\pi\) | ||||
0.527577 | + | 0.849507i | \(0.323101\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −17.9096 | −0.628116 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 24.9183 | 0.871782 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −4.27445 | −0.149361 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 19.9069 | 0.694756 | 0.347378 | − | 0.937725i | \(-0.387072\pi\) | ||||
0.347378 | + | 0.937725i | \(0.387072\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −33.2491 | −1.15899 | −0.579495 | − | 0.814976i | \(-0.696750\pi\) | ||||
−0.579495 | + | 0.814976i | \(0.696750\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 28.3770 | 0.986766 | 0.493383 | − | 0.869812i | \(-0.335760\pi\) | ||||
0.493383 | + | 0.869812i | \(0.335760\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 3.63143 | 0.126125 | 0.0630625 | − | 0.998010i | \(-0.479913\pi\) | ||||
0.0630625 | + | 0.998010i | \(0.479913\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 9.49120 | 0.329246 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −44.4826 | −1.54123 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −24.6124 | −0.850729 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 3.45660 | 0.119335 | 0.0596675 | − | 0.998218i | \(-0.480996\pi\) | ||||
0.0596675 | + | 0.998218i | \(0.480996\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −28.1977 | −0.972334 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 10.6757 | 0.367692 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −0.415806 | −0.0142873 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 6.89659 | 0.236690 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −76.6278 | −2.62677 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 47.4452 | 1.62449 | 0.812246 | − | 0.583315i | \(-0.198245\pi\) | ||||
0.812246 | + | 0.583315i | \(0.198245\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −35.8271 | −1.22383 | −0.611915 | − | 0.790923i | \(-0.709601\pi\) | ||||
−0.611915 | + | 0.790923i | \(0.709601\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 39.0539 | 1.33250 | 0.666252 | − | 0.745727i | \(-0.267898\pi\) | ||||
0.666252 | + | 0.745727i | \(0.267898\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −2.75390 | −0.0938528 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −5.75072 | −0.195757 | −0.0978784 | − | 0.995198i | \(-0.531206\pi\) | ||||
−0.0978784 | + | 0.995198i | \(0.531206\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 16.6910 | 0.566855 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −11.2682 | −0.382246 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −42.7657 | −1.44906 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 1.52054 | 0.0514626 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 8.32776 | 0.281208 | 0.140604 | − | 0.990066i | \(-0.455095\pi\) | ||||
0.140604 | + | 0.990066i | \(0.455095\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 6.14905 | 0.207402 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −49.0954 | −1.65407 | −0.827033 | − | 0.562153i | \(-0.809973\pi\) | ||||
−0.827033 | + | 0.562153i | \(0.809973\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 10.7526 | 0.361853 | 0.180927 | − | 0.983497i | \(-0.442090\pi\) | ||||
0.180927 | + | 0.983497i | \(0.442090\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 53.0591 | 1.78155 | 0.890776 | − | 0.454443i | \(-0.150162\pi\) | ||||
0.890776 | + | 0.454443i | \(0.150162\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 3.80045 | 0.127463 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −5.31471 | −0.178049 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −29.2461 | −0.978683 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −22.4226 | −0.748668 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 6.03567 | 0.201301 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −65.3882 | −2.17840 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 1.30561 | 0.0434481 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −7.03885 | −0.233721 | −0.116861 | − | 0.993148i | \(-0.537283\pi\) | ||||
−0.116861 | + | 0.993148i | \(0.537283\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 11.8811 | 0.394072 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −32.0980 | −1.06345 | −0.531727 | − | 0.846916i | \(-0.678457\pi\) | ||||
−0.531727 | + | 0.846916i | \(0.678457\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −16.2429 | −0.537562 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −1.03171 | −0.0340702 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 1.05960 | 0.0349529 | 0.0174764 | − | 0.999847i | \(-0.494437\pi\) | ||||
0.0174764 | + | 0.999847i | \(0.494437\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 1.37695 | 0.0453721 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −24.7721 | −0.815383 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 21.1841 | 0.695777 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −12.9981 | −0.426455 | −0.213228 | − | 0.977003i | \(-0.568398\pi\) | ||||
−0.213228 | + | 0.977003i | \(0.568398\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 35.5286 | 1.16440 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 13.3595 | 0.437370 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −39.9846 | −1.30624 | −0.653120 | − | 0.757254i | \(-0.726540\pi\) | ||||
−0.653120 | + | 0.757254i | \(0.726540\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 15.6706 | 0.511391 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 34.0267 | 1.10924 | 0.554619 | − | 0.832105i | \(-0.312864\pi\) | ||||
0.554619 | + | 0.832105i | \(0.312864\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 86.3359 | 2.81148 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 27.1506 | 0.882276 | 0.441138 | − | 0.897439i | \(-0.354575\pi\) | ||||
0.441138 | + | 0.897439i | \(0.354575\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 12.6735 | 0.411401 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 3.84351 | 0.124634 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 43.1169 | 1.39669 | 0.698346 | − | 0.715760i | \(-0.253920\pi\) | ||||
0.698346 | + | 0.715760i | \(0.253920\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −0.587377 | −0.0189872 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 3.08044 | 0.0994725 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 14.4055 | 0.464695 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −45.2826 | −1.45921 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −12.0641 | −0.387955 | −0.193978 | − | 0.981006i | \(-0.562139\pi\) | ||||
−0.193978 | + | 0.981006i | \(0.562139\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −22.2352 | −0.714298 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 3.81156 | 0.122319 | 0.0611595 | − | 0.998128i | \(-0.480520\pi\) | ||||
0.0611595 | + | 0.998128i | \(0.480520\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −0.703403 | −0.0225501 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −39.4202 | −1.26116 | −0.630581 | − | 0.776123i | \(-0.717184\pi\) | ||||
−0.630581 | + | 0.776123i | \(0.717184\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −9.56998 | −0.305858 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −9.41440 | −0.300579 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −8.67651 | −0.276738 | −0.138369 | − | 0.990381i | \(-0.544186\pi\) | ||||
−0.138369 | + | 0.990381i | \(0.544186\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −1.53237 | −0.0487758 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −40.9314 | −1.30154 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −35.7256 | −1.13486 | −0.567430 | − | 0.823422i | \(-0.692062\pi\) | ||||
−0.567430 | + | 0.823422i | \(0.692062\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0.376725 | 0.0119550 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 26.3453 | 0.834365 | 0.417183 | − | 0.908823i | \(-0.363018\pi\) | ||||
0.417183 | + | 0.908823i | \(0.363018\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 32.7421 | 1.03591 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 4400.2.a.ce.1.3 | 4 | ||
4.3 | odd | 2 | 2200.2.a.x.1.2 | 4 | |||
5.2 | odd | 4 | 880.2.b.j.529.3 | 8 | |||
5.3 | odd | 4 | 880.2.b.j.529.6 | 8 | |||
5.4 | even | 2 | 4400.2.a.cb.1.2 | 4 | |||
20.3 | even | 4 | 440.2.b.d.89.3 | ✓ | 8 | ||
20.7 | even | 4 | 440.2.b.d.89.6 | yes | 8 | ||
20.19 | odd | 2 | 2200.2.a.y.1.3 | 4 | |||
60.23 | odd | 4 | 3960.2.d.f.3169.8 | 8 | |||
60.47 | odd | 4 | 3960.2.d.f.3169.7 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
440.2.b.d.89.3 | ✓ | 8 | 20.3 | even | 4 | ||
440.2.b.d.89.6 | yes | 8 | 20.7 | even | 4 | ||
880.2.b.j.529.3 | 8 | 5.2 | odd | 4 | |||
880.2.b.j.529.6 | 8 | 5.3 | odd | 4 | |||
2200.2.a.x.1.2 | 4 | 4.3 | odd | 2 | |||
2200.2.a.y.1.3 | 4 | 20.19 | odd | 2 | |||
3960.2.d.f.3169.7 | 8 | 60.47 | odd | 4 | |||
3960.2.d.f.3169.8 | 8 | 60.23 | odd | 4 | |||
4400.2.a.cb.1.2 | 4 | 5.4 | even | 2 | |||
4400.2.a.ce.1.3 | 4 | 1.1 | even | 1 | trivial |