Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3200,2,Mod(1,3200)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3200, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("3200.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3200 = 2^{7} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3200.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: | \(25.5521286468\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{8})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - 2 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-1.41421\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3200.1 |
$q$-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 | ||||||||
\(3\) | −0.414214 | −0.239146 | −0.119573 | − | 0.992825i | \(-0.538153\pi\) | ||||
−0.119573 | + | 0.992825i | \(0.538153\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 4.82843 | 1.82497 | 0.912487 | − | 0.409106i | \(-0.134159\pi\) | ||||
0.912487 | + | 0.409106i | \(0.134159\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.82843 | −0.942809 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 3.24264 | 0.977693 | 0.488846 | − | 0.872370i | \(-0.337418\pi\) | ||||
0.488846 | + | 0.872370i | \(0.337418\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −5.65685 | −1.56893 | −0.784465 | − | 0.620174i | \(-0.787062\pi\) | ||||
−0.784465 | + | 0.620174i | \(0.787062\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 5.82843 | 1.41360 | 0.706801 | − | 0.707413i | \(-0.250138\pi\) | ||||
0.706801 | + | 0.707413i | \(0.250138\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −4.41421 | −1.01269 | −0.506345 | − | 0.862331i | \(-0.669004\pi\) | ||||
−0.506345 | + | 0.862331i | \(0.669004\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −2.00000 | −0.436436 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −0.828427 | −0.172739 | −0.0863695 | − | 0.996263i | \(-0.527527\pi\) | ||||
−0.0863695 | + | 0.996263i | \(0.527527\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 2.41421 | 0.464616 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 8.00000 | 1.48556 | 0.742781 | − | 0.669534i | \(-0.233506\pi\) | ||||
0.742781 | + | 0.669534i | \(0.233506\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.82843 | 0.867211 | 0.433606 | − | 0.901103i | \(-0.357241\pi\) | ||||
0.433606 | + | 0.901103i | \(0.357241\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −1.34315 | −0.233812 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −3.65685 | −0.601183 | −0.300592 | − | 0.953753i | \(-0.597184\pi\) | ||||
−0.300592 | + | 0.953753i | \(0.597184\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 2.34315 | 0.375204 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −0.656854 | −0.102583 | −0.0512917 | − | 0.998684i | \(-0.516334\pi\) | ||||
−0.0512917 | + | 0.998684i | \(0.516334\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 10.0000 | 1.52499 | 0.762493 | − | 0.646997i | \(-0.223975\pi\) | ||||
0.762493 | + | 0.646997i | \(0.223975\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −1.65685 | −0.241677 | −0.120839 | − | 0.992672i | \(-0.538558\pi\) | ||||
−0.120839 | + | 0.992672i | \(0.538558\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 16.3137 | 2.33053 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −2.41421 | −0.338058 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 3.65685 | 0.502308 | 0.251154 | − | 0.967947i | \(-0.419190\pi\) | ||||
0.251154 | + | 0.967947i | \(0.419190\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 1.82843 | 0.242181 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −7.65685 | −0.996838 | −0.498419 | − | 0.866936i | \(-0.666086\pi\) | ||||
−0.498419 | + | 0.866936i | \(0.666086\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 6.00000 | 0.768221 | 0.384111 | − | 0.923287i | \(-0.374508\pi\) | ||||
0.384111 | + | 0.923287i | \(0.374508\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −13.6569 | −1.72060 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −11.2426 | −1.37351 | −0.686754 | − | 0.726890i | \(-0.740965\pi\) | ||||
−0.686754 | + | 0.726890i | \(0.740965\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0.343146 | 0.0413099 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 1.65685 | 0.196632 | 0.0983162 | − | 0.995155i | \(-0.468654\pi\) | ||||
0.0983162 | + | 0.995155i | \(0.468654\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −0.171573 | −0.0200811 | −0.0100405 | − | 0.999950i | \(-0.503196\pi\) | ||||
−0.0100405 | + | 0.999950i | \(0.503196\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 15.6569 | 1.78426 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 7.17157 | 0.806865 | 0.403432 | − | 0.915009i | \(-0.367817\pi\) | ||||
0.403432 | + | 0.915009i | \(0.367817\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 7.48528 | 0.831698 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −7.24264 | −0.794983 | −0.397492 | − | 0.917606i | \(-0.630119\pi\) | ||||
−0.397492 | + | 0.917606i | \(0.630119\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −3.31371 | −0.355267 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 11.8284 | 1.25381 | 0.626905 | − | 0.779095i | \(-0.284321\pi\) | ||||
0.626905 | + | 0.779095i | \(0.284321\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −27.3137 | −2.86325 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −2.00000 | −0.207390 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −5.31371 | −0.539525 | −0.269763 | − | 0.962927i | \(-0.586945\pi\) | ||||
−0.269763 | + | 0.962927i | \(0.586945\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −9.17157 | −0.921778 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 14.9706 | 1.48963 | 0.744813 | − | 0.667273i | \(-0.232539\pi\) | ||||
0.744813 | + | 0.667273i | \(0.232539\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 9.65685 | 0.951518 | 0.475759 | − | 0.879576i | \(-0.342173\pi\) | ||||
0.475759 | + | 0.879576i | \(0.342173\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −16.0711 | −1.55365 | −0.776824 | − | 0.629717i | \(-0.783171\pi\) | ||||
−0.776824 | + | 0.629717i | \(0.783171\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 0.343146 | 0.0328674 | 0.0164337 | − | 0.999865i | \(-0.494769\pi\) | ||||
0.0164337 | + | 0.999865i | \(0.494769\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 1.51472 | 0.143771 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −14.6569 | −1.37880 | −0.689400 | − | 0.724380i | \(-0.742126\pi\) | ||||
−0.689400 | + | 0.724380i | \(0.742126\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 16.0000 | 1.47920 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 28.1421 | 2.57979 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −0.485281 | −0.0441165 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0.272078 | 0.0245324 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 8.14214 | 0.722498 | 0.361249 | − | 0.932469i | \(-0.382350\pi\) | ||||
0.361249 | + | 0.932469i | \(0.382350\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −4.14214 | −0.364695 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 17.3137 | 1.51271 | 0.756353 | − | 0.654164i | \(-0.226979\pi\) | ||||
0.756353 | + | 0.654164i | \(0.226979\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −21.3137 | −1.84813 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 5.00000 | 0.427179 | 0.213589 | − | 0.976924i | \(-0.431485\pi\) | ||||
0.213589 | + | 0.976924i | \(0.431485\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 8.89949 | 0.754845 | 0.377423 | − | 0.926041i | \(-0.376810\pi\) | ||||
0.377423 | + | 0.926041i | \(0.376810\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0.686292 | 0.0577962 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −18.3431 | −1.53393 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −6.75736 | −0.557338 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 19.3137 | 1.58224 | 0.791120 | − | 0.611661i | \(-0.209498\pi\) | ||||
0.791120 | + | 0.611661i | \(0.209498\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −10.4853 | −0.853280 | −0.426640 | − | 0.904422i | \(-0.640303\pi\) | ||||
−0.426640 | + | 0.904422i | \(0.640303\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −16.4853 | −1.33276 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −8.34315 | −0.665856 | −0.332928 | − | 0.942952i | \(-0.608037\pi\) | ||||
−0.332928 | + | 0.942952i | \(0.608037\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −1.51472 | −0.120125 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −4.00000 | −0.315244 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 5.72792 | 0.448645 | 0.224323 | − | 0.974515i | \(-0.427983\pi\) | ||||
0.224323 | + | 0.974515i | \(0.427983\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 13.6569 | 1.05680 | 0.528400 | − | 0.848996i | \(-0.322792\pi\) | ||||
0.528400 | + | 0.848996i | \(0.322792\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 19.0000 | 1.46154 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 12.4853 | 0.954773 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 1.65685 | 0.125968 | 0.0629841 | − | 0.998015i | \(-0.479938\pi\) | ||||
0.0629841 | + | 0.998015i | \(0.479938\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 3.17157 | 0.238390 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −24.4142 | −1.82480 | −0.912402 | − | 0.409295i | \(-0.865775\pi\) | ||||
−0.912402 | + | 0.409295i | \(0.865775\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 4.34315 | 0.322823 | 0.161412 | − | 0.986887i | \(-0.448395\pi\) | ||||
0.161412 | + | 0.986887i | \(0.448395\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −2.48528 | −0.183717 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 18.8995 | 1.38207 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 11.6569 | 0.847911 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 18.4853 | 1.33755 | 0.668774 | − | 0.743466i | \(-0.266819\pi\) | ||||
0.668774 | + | 0.743466i | \(0.266819\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 13.8284 | 0.995392 | 0.497696 | − | 0.867352i | \(-0.334180\pi\) | ||||
0.497696 | + | 0.867352i | \(0.334180\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 3.65685 | 0.260540 | 0.130270 | − | 0.991479i | \(-0.458416\pi\) | ||||
0.130270 | + | 0.991479i | \(0.458416\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 14.3431 | 1.01676 | 0.508379 | − | 0.861133i | \(-0.330245\pi\) | ||||
0.508379 | + | 0.861133i | \(0.330245\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 4.65685 | 0.328469 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 38.6274 | 2.71111 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 2.34315 | 0.162860 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −14.3137 | −0.990100 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −8.89949 | −0.612666 | −0.306333 | − | 0.951924i | \(-0.599102\pi\) | ||||
−0.306333 | + | 0.951924i | \(0.599102\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −0.686292 | −0.0470239 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 23.3137 | 1.58264 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0.0710678 | 0.00480232 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −32.9706 | −2.21784 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −2.34315 | −0.156909 | −0.0784543 | − | 0.996918i | \(-0.524998\pi\) | ||||
−0.0784543 | + | 0.996918i | \(0.524998\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 1.31371 | 0.0871939 | 0.0435969 | − | 0.999049i | \(-0.486118\pi\) | ||||
0.0435969 | + | 0.999049i | \(0.486118\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 23.3137 | 1.54061 | 0.770307 | − | 0.637674i | \(-0.220103\pi\) | ||||
0.770307 | + | 0.637674i | \(0.220103\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −6.48528 | −0.426700 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −9.31371 | −0.610161 | −0.305081 | − | 0.952327i | \(-0.598683\pi\) | ||||
−0.305081 | + | 0.952327i | \(0.598683\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −2.97056 | −0.192959 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −26.6274 | −1.72238 | −0.861192 | − | 0.508279i | \(-0.830282\pi\) | ||||
−0.861192 | + | 0.508279i | \(0.830282\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 4.17157 | 0.268715 | 0.134357 | − | 0.990933i | \(-0.457103\pi\) | ||||
0.134357 | + | 0.990933i | \(0.457103\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −10.3431 | −0.663513 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 24.9706 | 1.58884 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 3.00000 | 0.190117 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −17.2426 | −1.08835 | −0.544173 | − | 0.838973i | \(-0.683156\pi\) | ||||
−0.544173 | + | 0.838973i | \(0.683156\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −2.68629 | −0.168886 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 17.3137 | 1.08000 | 0.540000 | − | 0.841665i | \(-0.318424\pi\) | ||||
0.540000 | + | 0.841665i | \(0.318424\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −17.6569 | −1.09714 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −22.6274 | −1.40060 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 6.48528 | 0.399900 | 0.199950 | − | 0.979806i | \(-0.435922\pi\) | ||||
0.199950 | + | 0.979806i | \(0.435922\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −4.89949 | −0.299844 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −17.6569 | −1.07656 | −0.538279 | − | 0.842767i | \(-0.680925\pi\) | ||||
−0.538279 | + | 0.842767i | \(0.680925\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 24.8284 | 1.50822 | 0.754110 | − | 0.656748i | \(-0.228069\pi\) | ||||
0.754110 | + | 0.656748i | \(0.228069\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 11.3137 | 0.684737 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1.65685 | 0.0995507 | 0.0497754 | − | 0.998760i | \(-0.484149\pi\) | ||||
0.0497754 | + | 0.998760i | \(0.484149\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −13.6569 | −0.817614 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 24.6274 | 1.46915 | 0.734574 | − | 0.678528i | \(-0.237382\pi\) | ||||
0.734574 | + | 0.678528i | \(0.237382\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 15.7279 | 0.934928 | 0.467464 | − | 0.884012i | \(-0.345168\pi\) | ||||
0.467464 | + | 0.884012i | \(0.345168\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −3.17157 | −0.187212 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 16.9706 | 0.998268 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 2.20101 | 0.129025 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 5.31371 | 0.310430 | 0.155215 | − | 0.987881i | \(-0.450393\pi\) | ||||
0.155215 | + | 0.987881i | \(0.450393\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 7.82843 | 0.454251 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 4.68629 | 0.271015 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 48.2843 | 2.78306 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −6.20101 | −0.356239 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 5.24264 | 0.299213 | 0.149607 | − | 0.988746i | \(-0.452199\pi\) | ||||
0.149607 | + | 0.988746i | \(0.452199\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −4.00000 | −0.227552 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −5.51472 | −0.312711 | −0.156356 | − | 0.987701i | \(-0.549975\pi\) | ||||
−0.156356 | + | 0.987701i | \(0.549975\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 10.0000 | 0.565233 | 0.282617 | − | 0.959233i | \(-0.408798\pi\) | ||||
0.282617 | + | 0.959233i | \(0.408798\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −13.6569 | −0.767045 | −0.383523 | − | 0.923531i | \(-0.625289\pi\) | ||||
−0.383523 | + | 0.923531i | \(0.625289\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 25.9411 | 1.45242 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 6.65685 | 0.371549 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −25.7279 | −1.43154 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −0.142136 | −0.00786012 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −8.00000 | −0.441054 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −3.10051 | −0.170419 | −0.0852096 | − | 0.996363i | \(-0.527156\pi\) | ||||
−0.0852096 | + | 0.996363i | \(0.527156\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 10.3431 | 0.566801 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −18.6569 | −1.01630 | −0.508152 | − | 0.861268i | \(-0.669671\pi\) | ||||
−0.508152 | + | 0.861268i | \(0.669671\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 6.07107 | 0.329735 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 15.6569 | 0.847866 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 44.9706 | 2.42818 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 0.899495 | 0.0482874 | 0.0241437 | − | 0.999708i | \(-0.492314\pi\) | ||||
0.0241437 | + | 0.999708i | \(0.492314\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 6.68629 | 0.357909 | 0.178954 | − | 0.983857i | \(-0.442729\pi\) | ||||
0.178954 | + | 0.983857i | \(0.442729\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −13.6569 | −0.728949 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −32.6274 | −1.73658 | −0.868291 | − | 0.496055i | \(-0.834781\pi\) | ||||
−0.868291 | + | 0.496055i | \(0.834781\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −11.6569 | −0.616946 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 3.17157 | 0.167389 | 0.0836946 | − | 0.996491i | \(-0.473328\pi\) | ||||
0.0836946 | + | 0.996491i | \(0.473328\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 0.485281 | 0.0255411 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0.201010 | 0.0105503 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −32.9706 | −1.72105 | −0.860525 | − | 0.509409i | \(-0.829864\pi\) | ||||
−0.860525 | + | 0.509409i | \(0.829864\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 1.85786 | 0.0967166 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 17.6569 | 0.916698 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 10.6863 | 0.553315 | 0.276658 | − | 0.960969i | \(-0.410773\pi\) | ||||
0.276658 | + | 0.960969i | \(0.410773\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −45.2548 | −2.33074 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −2.89949 | −0.148937 | −0.0744685 | − | 0.997223i | \(-0.523726\pi\) | ||||
−0.0744685 | + | 0.997223i | \(0.523726\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −3.37258 | −0.172783 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −23.4558 | −1.19854 | −0.599269 | − | 0.800548i | \(-0.704542\pi\) | ||||
−0.599269 | + | 0.800548i | \(0.704542\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −28.2843 | −1.43777 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −17.3137 | −0.877840 | −0.438920 | − | 0.898526i | \(-0.644639\pi\) | ||||
−0.438920 | + | 0.898526i | \(0.644639\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −4.82843 | −0.244184 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −7.17157 | −0.361758 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 31.3137 | 1.57159 | 0.785795 | − | 0.618487i | \(-0.212254\pi\) | ||||
0.785795 | + | 0.618487i | \(0.212254\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 8.82843 | 0.441974 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −30.4558 | −1.52089 | −0.760446 | − | 0.649401i | \(-0.775020\pi\) | ||||
−0.760446 | + | 0.649401i | \(0.775020\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −27.3137 | −1.36059 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −11.8579 | −0.587773 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −27.9706 | −1.38306 | −0.691528 | − | 0.722350i | \(-0.743062\pi\) | ||||
−0.691528 | + | 0.722350i | \(0.743062\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −2.07107 | −0.102158 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −36.9706 | −1.81920 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −3.68629 | −0.180518 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 24.5563 | 1.19966 | 0.599828 | − | 0.800129i | \(-0.295236\pi\) | ||||
0.599828 | + | 0.800129i | \(0.295236\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −4.00000 | −0.194948 | −0.0974740 | − | 0.995238i | \(-0.531076\pi\) | ||||
−0.0974740 | + | 0.995238i | \(0.531076\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 4.68629 | 0.227855 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 28.9706 | 1.40198 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 7.59798 | 0.366834 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −16.1421 | −0.777539 | −0.388770 | − | 0.921335i | \(-0.627100\pi\) | ||||
−0.388770 | + | 0.921335i | \(0.627100\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 16.1716 | 0.777156 | 0.388578 | − | 0.921416i | \(-0.372966\pi\) | ||||
0.388578 | + | 0.921416i | \(0.372966\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 3.65685 | 0.174931 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 23.3137 | 1.11270 | 0.556351 | − | 0.830947i | \(-0.312201\pi\) | ||||
0.556351 | + | 0.830947i | \(0.312201\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −46.1421 | −2.19724 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −8.55635 | −0.406524 | −0.203262 | − | 0.979124i | \(-0.565154\pi\) | ||||
−0.203262 | + | 0.979124i | \(0.565154\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −8.00000 | −0.378387 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 16.4558 | 0.776599 | 0.388300 | − | 0.921533i | \(-0.373063\pi\) | ||||
0.388300 | + | 0.921533i | \(0.373063\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −2.12994 | −0.100295 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 4.34315 | 0.204059 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −28.6569 | −1.34051 | −0.670256 | − | 0.742130i | \(-0.733816\pi\) | ||||
−0.670256 | + | 0.742130i | \(0.733816\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 14.0711 | 0.656781 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −5.65685 | −0.263466 | −0.131733 | − | 0.991285i | \(-0.542054\pi\) | ||||
−0.131733 | + | 0.991285i | \(0.542054\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −20.9706 | −0.974585 | −0.487292 | − | 0.873239i | \(-0.662015\pi\) | ||||
−0.487292 | + | 0.873239i | \(0.662015\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −13.3137 | −0.616085 | −0.308042 | − | 0.951373i | \(-0.599674\pi\) | ||||
−0.308042 | + | 0.951373i | \(0.599674\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −54.2843 | −2.50661 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 3.45584 | 0.159237 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 32.4264 | 1.49097 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −10.3431 | −0.473580 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −40.8284 | −1.86550 | −0.932749 | − | 0.360526i | \(-0.882597\pi\) | ||||
−0.932749 | + | 0.360526i | \(0.882597\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 20.6863 | 0.943214 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 1.65685 | 0.0753895 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −37.1127 | −1.68174 | −0.840868 | − | 0.541240i | \(-0.817955\pi\) | ||||
−0.840868 | + | 0.541240i | \(0.817955\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −2.37258 | −0.107292 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −28.6274 | −1.29194 | −0.645969 | − | 0.763364i | \(-0.723546\pi\) | ||||
−0.645969 | + | 0.763364i | \(0.723546\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 46.6274 | 2.09999 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 8.00000 | 0.358849 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 14.0000 | 0.626726 | 0.313363 | − | 0.949633i | \(-0.398544\pi\) | ||||
0.313363 | + | 0.949633i | \(0.398544\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −5.65685 | −0.252730 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −16.9706 | −0.756680 | −0.378340 | − | 0.925667i | \(-0.623505\pi\) | ||||
−0.378340 | + | 0.925667i | \(0.623505\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −7.87006 | −0.349522 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 14.0000 | 0.620539 | 0.310270 | − | 0.950649i | \(-0.399581\pi\) | ||||
0.310270 | + | 0.950649i | \(0.399581\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −0.828427 | −0.0366475 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −10.6569 | −0.470512 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −5.37258 | −0.236286 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −0.686292 | −0.0301249 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −6.31371 | −0.276609 | −0.138304 | − | 0.990390i | \(-0.544165\pi\) | ||||
−0.138304 | + | 0.990390i | \(0.544165\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −22.4142 | −0.980105 | −0.490053 | − | 0.871693i | \(-0.663022\pi\) | ||||
−0.490053 | + | 0.871693i | \(0.663022\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 28.1421 | 1.22589 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −22.3137 | −0.970161 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 21.6569 | 0.939827 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 3.71573 | 0.160946 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 10.1127 | 0.436395 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 52.8995 | 2.27854 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −6.34315 | −0.272713 | −0.136357 | − | 0.990660i | \(-0.543539\pi\) | ||||
−0.136357 | + | 0.990660i | \(0.543539\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −1.79899 | −0.0772020 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 16.5563 | 0.707898 | 0.353949 | − | 0.935265i | \(-0.384839\pi\) | ||||
0.353949 | + | 0.935265i | \(0.384839\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −16.9706 | −0.724286 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −35.3137 | −1.50441 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 34.6274 | 1.47251 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 37.6569 | 1.59557 | 0.797786 | − | 0.602941i | \(-0.206004\pi\) | ||||
0.797786 | + | 0.602941i | \(0.206004\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −56.5685 | −2.39259 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −7.82843 | −0.330516 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 26.9706 | 1.13667 | 0.568337 | − | 0.822796i | \(-0.307587\pi\) | ||||
0.568337 | + | 0.822796i | \(0.307587\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 36.1421 | 1.51783 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −3.68629 | −0.154537 | −0.0772687 | − | 0.997010i | \(-0.524620\pi\) | ||||
−0.0772687 | + | 0.997010i | \(0.524620\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 35.9411 | 1.50409 | 0.752045 | − | 0.659112i | \(-0.229068\pi\) | ||||
0.752045 | + | 0.659112i | \(0.229068\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −7.65685 | −0.319870 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 15.2843 | 0.636293 | 0.318146 | − | 0.948042i | \(-0.396940\pi\) | ||||
0.318146 | + | 0.948042i | \(0.396940\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −5.72792 | −0.238044 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −34.9706 | −1.45082 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 11.8579 | 0.491103 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 14.0711 | 0.580775 | 0.290388 | − | 0.956909i | \(-0.406216\pi\) | ||||
0.290388 | + | 0.956909i | \(0.406216\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −21.3137 | −0.878216 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −1.51472 | −0.0623072 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 7.00000 | 0.287456 | 0.143728 | − | 0.989617i | \(-0.454091\pi\) | ||||
0.143728 | + | 0.989617i | \(0.454091\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −5.94113 | −0.243154 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −46.7696 | −1.91095 | −0.955476 | − | 0.295069i | \(-0.904657\pi\) | ||||
−0.955476 | + | 0.295069i | \(0.904657\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 6.85786 | 0.279738 | 0.139869 | − | 0.990170i | \(-0.455332\pi\) | ||||
0.139869 | + | 0.990170i | \(0.455332\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 31.7990 | 1.29495 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −36.0000 | −1.46119 | −0.730597 | − | 0.682808i | \(-0.760758\pi\) | ||||
−0.730597 | + | 0.682808i | \(0.760758\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −16.0000 | −0.648353 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 9.37258 | 0.379174 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 29.3137 | 1.18397 | 0.591985 | − | 0.805949i | \(-0.298345\pi\) | ||||
0.591985 | + | 0.805949i | \(0.298345\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 18.0000 | 0.724653 | 0.362326 | − | 0.932051i | \(-0.381983\pi\) | ||||
0.362326 | + | 0.932051i | \(0.381983\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −9.31371 | −0.374350 | −0.187175 | − | 0.982327i | \(-0.559933\pi\) | ||||
−0.187175 | + | 0.982327i | \(0.559933\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −2.00000 | −0.0802572 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 57.1127 | 2.28817 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 5.92893 | 0.236779 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −21.3137 | −0.849833 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 44.1421 | 1.75727 | 0.878635 | − | 0.477493i | \(-0.158455\pi\) | ||||
0.878635 | + | 0.477493i | \(0.158455\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 3.68629 | 0.146517 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −92.2843 | −3.65644 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −4.68629 | −0.185387 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −22.6863 | −0.896055 | −0.448027 | − | 0.894020i | \(-0.647873\pi\) | ||||
−0.448027 | + | 0.894020i | \(0.647873\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −37.3137 | −1.47151 | −0.735755 | − | 0.677248i | \(-0.763172\pi\) | ||||
−0.735755 | + | 0.677248i | \(0.763172\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −5.65685 | −0.222394 | −0.111197 | − | 0.993798i | \(-0.535468\pi\) | ||||
−0.111197 | + | 0.993798i | \(0.535468\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −24.8284 | −0.974601 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −9.65685 | −0.378482 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −6.00000 | −0.234798 | −0.117399 | − | 0.993085i | \(-0.537456\pi\) | ||||
−0.117399 | + | 0.993085i | \(0.537456\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0.485281 | 0.0189326 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −25.1838 | −0.981020 | −0.490510 | − | 0.871435i | \(-0.663190\pi\) | ||||
−0.490510 | + | 0.871435i | \(0.663190\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 17.6569 | 0.686772 | 0.343386 | − | 0.939194i | \(-0.388426\pi\) | ||||
0.343386 | + | 0.939194i | \(0.388426\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 13.6569 | 0.530388 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −6.62742 | −0.256615 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0.970563 | 0.0375241 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 19.4558 | 0.751085 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 2.68629 | 0.103549 | 0.0517745 | − | 0.998659i | \(-0.483512\pi\) | ||||
0.0517745 | + | 0.998659i | \(0.483512\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −51.3137 | −1.97215 | −0.986073 | − | 0.166313i | \(-0.946814\pi\) | ||||
−0.986073 | + | 0.166313i | \(0.946814\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −25.6569 | −0.984620 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −0.544156 | −0.0208521 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −42.6985 | −1.63381 | −0.816906 | − | 0.576771i | \(-0.804313\pi\) | ||||
−0.816906 | + | 0.576771i | \(0.804313\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −9.65685 | −0.368432 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −20.6863 | −0.788085 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 6.21320 | 0.236361 | 0.118181 | − | 0.992992i | \(-0.462294\pi\) | ||||
0.118181 | + | 0.992992i | \(0.462294\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −44.2843 | −1.68222 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −3.82843 | −0.145012 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 3.85786 | 0.145918 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −24.6863 | −0.932388 | −0.466194 | − | 0.884682i | \(-0.654375\pi\) | ||||
−0.466194 | + | 0.884682i | \(0.654375\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 16.1421 | 0.608812 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 72.2843 | 2.71853 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 45.9411 | 1.72536 | 0.862678 | − | 0.505754i | \(-0.168786\pi\) | ||||
0.862678 | + | 0.505754i | \(0.168786\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −20.2843 | −0.760720 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −4.00000 | −0.149801 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 11.0294 | 0.411902 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 27.4558 | 1.02393 | 0.511965 | − | 0.859006i | \(-0.328918\pi\) | ||||
0.511965 | + | 0.859006i | \(0.328918\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 46.6274 | 1.73650 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −1.72792 | −0.0642621 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −32.0000 | −1.18681 | −0.593407 | − | 0.804902i | \(-0.702218\pi\) | ||||
−0.593407 | + | 0.804902i | \(0.702218\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −18.1716 | −0.673021 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 58.2843 | 2.15572 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 37.6569 | 1.39089 | 0.695444 | − | 0.718580i | \(-0.255208\pi\) | ||||
0.695444 | + | 0.718580i | \(0.255208\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −36.4558 | −1.34287 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −16.6274 | −0.611649 | −0.305825 | − | 0.952088i | \(-0.598932\pi\) | ||||
−0.305825 | + | 0.952088i | \(0.598932\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −10.3431 | −0.379965 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 13.7990 | 0.506236 | 0.253118 | − | 0.967435i | \(-0.418544\pi\) | ||||
0.253118 | + | 0.967435i | \(0.418544\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 20.4853 | 0.749517 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −77.5980 | −2.83537 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 10.6274 | 0.387800 | 0.193900 | − | 0.981021i | \(-0.437886\pi\) | ||||
0.193900 | + | 0.981021i | \(0.437886\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 7.14214 | 0.260274 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −14.3431 | −0.521310 | −0.260655 | − | 0.965432i | \(-0.583939\pi\) | ||||
−0.260655 | + | 0.965432i | \(0.583939\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 1.11270 | 0.0403884 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 17.2843 | 0.626554 | 0.313277 | − | 0.949662i | \(-0.398573\pi\) | ||||
0.313277 | + | 0.949662i | \(0.398573\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 1.65685 | 0.0599822 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 43.3137 | 1.56397 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −28.1127 | −1.01377 | −0.506885 | − | 0.862014i | \(-0.669203\pi\) | ||||
−0.506885 | + | 0.862014i | \(0.669203\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −7.17157 | −0.258278 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 3.31371 | 0.119186 | 0.0595929 | − | 0.998223i | \(-0.481020\pi\) | ||||
0.0595929 | + | 0.998223i | \(0.481020\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 7.31371 | 0.262378 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 2.89949 | 0.103885 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 5.37258 | 0.192246 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 19.3137 | 0.690216 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 28.6274 | 1.02046 | 0.510229 | − | 0.860039i | \(-0.329561\pi\) | ||||
0.510229 | + | 0.860039i | \(0.329561\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −2.68629 | −0.0956345 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −70.7696 | −2.51628 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −33.9411 | −1.20528 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −42.0000 | −1.48772 | −0.743858 | − | 0.668338i | \(-0.767006\pi\) | ||||
−0.743858 | + | 0.668338i | \(0.767006\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −9.65685 | −0.341635 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −33.4558 | −1.18210 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −0.556349 | −0.0196331 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 7.31371 | 0.257455 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −4.62742 | −0.162691 | −0.0813457 | − | 0.996686i | \(-0.525922\pi\) | ||||
−0.0813457 | + | 0.996686i | \(0.525922\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −31.9411 | −1.12160 | −0.560802 | − | 0.827950i | \(-0.689507\pi\) | ||||
−0.560802 | + | 0.827950i | \(0.689507\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −10.2843 | −0.360685 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −44.1421 | −1.54434 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 77.2548 | 2.69950 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 4.62742 | 0.161498 | 0.0807490 | − | 0.996734i | \(-0.474269\pi\) | ||||
0.0807490 | + | 0.996734i | \(0.474269\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −20.9706 | −0.730988 | −0.365494 | − | 0.930814i | \(-0.619100\pi\) | ||||
−0.365494 | + | 0.930814i | \(0.619100\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −33.9289 | −1.17982 | −0.589912 | − | 0.807467i | \(-0.700838\pi\) | ||||
−0.589912 | + | 0.807467i | \(0.700838\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 20.0000 | 0.694629 | 0.347314 | − | 0.937749i | \(-0.387094\pi\) | ||||
0.347314 | + | 0.937749i | \(0.387094\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −0.686292 | −0.0238072 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 95.0833 | 3.29444 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 11.6569 | 0.402920 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 4.00000 | 0.138095 | 0.0690477 | − | 0.997613i | \(-0.478004\pi\) | ||||
0.0690477 | + | 0.997613i | \(0.478004\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 35.0000 | 1.20690 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −10.2010 | −0.351341 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −2.34315 | −0.0805114 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −6.51472 | −0.223585 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 3.02944 | 0.103848 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 28.6274 | 0.980184 | 0.490092 | − | 0.871671i | \(-0.336963\pi\) | ||||
0.490092 | + | 0.871671i | \(0.336963\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −11.0000 | −0.375753 | −0.187876 | − | 0.982193i | \(-0.560160\pi\) | ||||
−0.187876 | + | 0.982193i | \(0.560160\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −11.7868 | −0.402160 | −0.201080 | − | 0.979575i | \(-0.564445\pi\) | ||||
−0.201080 | + | 0.979575i | \(0.564445\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 1.31371 | 0.0447711 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 4.00000 | 0.136162 | 0.0680808 | − | 0.997680i | \(-0.478312\pi\) | ||||
0.0680808 | + | 0.997680i | \(0.478312\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −7.02944 | −0.238732 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 23.2548 | 0.788866 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 63.5980 | 2.15494 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 15.0294 | 0.508669 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 37.6569 | 1.27158 | 0.635791 | − | 0.771861i | \(-0.280674\pi\) | ||||
0.635791 | + | 0.771861i | \(0.280674\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −2.20101 | −0.0742382 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −37.3137 | −1.25713 | −0.628565 | − | 0.777757i | \(-0.716358\pi\) | ||||
−0.628565 | + | 0.777757i | \(0.716358\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −34.7574 | −1.16968 | −0.584839 | − | 0.811149i | \(-0.698842\pi\) | ||||
−0.584839 | + | 0.811149i | \(0.698842\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −33.6569 | −1.13009 | −0.565043 | − | 0.825061i | \(-0.691141\pi\) | ||||
−0.565043 | + | 0.825061i | \(0.691141\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 39.3137 | 1.31854 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 24.2721 | 0.813145 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 7.31371 | 0.244744 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −1.94113 | −0.0648123 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 38.6274 | 1.28830 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 21.3137 | 0.710063 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −20.0000 | −0.665558 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 22.6863 | 0.753286 | 0.376643 | − | 0.926359i | \(-0.377078\pi\) | ||||
0.376643 | + | 0.926359i | \(0.377078\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −42.3431 | −1.40443 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −20.2843 | −0.672048 | −0.336024 | − | 0.941853i | \(-0.609082\pi\) | ||||
−0.336024 | + | 0.941853i | \(0.609082\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −23.4853 | −0.777249 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 83.5980 | 2.76065 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −44.8284 | −1.47875 | −0.739377 | − | 0.673292i | \(-0.764880\pi\) | ||||
−0.739377 | + | 0.673292i | \(0.764880\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −2.17157 | −0.0715558 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −9.37258 | −0.308502 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −27.3137 | −0.897100 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −44.6274 | −1.46418 | −0.732089 | − | 0.681209i | \(-0.761455\pi\) | ||||
−0.732089 | + | 0.681209i | \(0.761455\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −72.0122 | −2.36010 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 2.28427 | 0.0747837 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −42.1127 | −1.37576 | −0.687881 | − | 0.725824i | \(-0.741459\pi\) | ||||
−0.687881 | + | 0.725824i | \(0.741459\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −4.14214 | −0.135173 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 7.02944 | 0.229153 | 0.114577 | − | 0.993414i | \(-0.463449\pi\) | ||||
0.114577 | + | 0.993414i | \(0.463449\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0.544156 | 0.0177202 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −45.5980 | −1.48174 | −0.740868 | − | 0.671651i | \(-0.765585\pi\) | ||||
−0.740868 | + | 0.671651i | \(0.765585\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0.970563 | 0.0315058 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 5.65685 | 0.183436 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −10.3137 | −0.334094 | −0.167047 | − | 0.985949i | \(-0.553423\pi\) | ||||
−0.167047 | + | 0.985949i | \(0.553423\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −10.7452 | −0.347342 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 24.1421 | 0.779590 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −7.68629 | −0.247945 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 45.4558 | 1.46479 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 2.62742 | 0.0844920 | 0.0422460 | − | 0.999107i | \(-0.486549\pi\) | ||||
0.0422460 | + | 0.999107i | \(0.486549\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 10.6569 | 0.342347 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −23.1005 | −0.741330 | −0.370665 | − | 0.928767i | \(-0.620870\pi\) | ||||
−0.370665 | + | 0.928767i | \(0.620870\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 42.9706 | 1.37757 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 38.1127 | 1.21933 | 0.609667 | − | 0.792658i | \(-0.291303\pi\) | ||||
0.609667 | + | 0.792658i | \(0.291303\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 38.3553 | 1.22584 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −0.970563 | −0.0309877 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 5.79899 | 0.184959 | 0.0924795 | − | 0.995715i | \(-0.470521\pi\) | ||||
0.0924795 | + | 0.995715i | \(0.470521\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 3.31371 | 0.105477 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −8.28427 | −0.263425 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −34.0833 | −1.08269 | −0.541345 | − | 0.840800i | \(-0.682085\pi\) | ||||
−0.541345 | + | 0.840800i | \(0.682085\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 1.28427 | 0.0407551 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 16.9706 | 0.537463 | 0.268732 | − | 0.963215i | \(-0.413396\pi\) | ||||
0.268732 | + | 0.963215i | \(0.413396\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −8.82843 | −0.279319 |
(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 | 3200.2.a.bm.1.1 | yes | 2 | |
4.3 | odd | 2 | 3200.2.a.bd.1.2 | yes | 2 | ||
5.2 | odd | 4 | 3200.2.c.y.2049.3 | 4 | |||
5.3 | odd | 4 | 3200.2.c.y.2049.2 | 4 | |||
5.4 | even | 2 | 3200.2.a.bc.1.2 | ✓ | 2 | ||
8.3 | odd | 2 | 3200.2.a.bi.1.1 | yes | 2 | ||
8.5 | even | 2 | 3200.2.a.bh.1.2 | yes | 2 | ||
20.3 | even | 4 | 3200.2.c.ba.2049.3 | 4 | |||
20.7 | even | 4 | 3200.2.c.ba.2049.2 | 4 | |||
20.19 | odd | 2 | 3200.2.a.bn.1.1 | yes | 2 | ||
40.3 | even | 4 | 3200.2.c.z.2049.2 | 4 | |||
40.13 | odd | 4 | 3200.2.c.bb.2049.3 | 4 | |||
40.19 | odd | 2 | 3200.2.a.bg.1.2 | yes | 2 | ||
40.27 | even | 4 | 3200.2.c.z.2049.3 | 4 | |||
40.29 | even | 2 | 3200.2.a.bj.1.1 | yes | 2 | ||
40.37 | odd | 4 | 3200.2.c.bb.2049.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
3200.2.a.bc.1.2 | ✓ | 2 | 5.4 | even | 2 | ||
3200.2.a.bd.1.2 | yes | 2 | 4.3 | odd | 2 | ||
3200.2.a.bg.1.2 | yes | 2 | 40.19 | odd | 2 | ||
3200.2.a.bh.1.2 | yes | 2 | 8.5 | even | 2 | ||
3200.2.a.bi.1.1 | yes | 2 | 8.3 | odd | 2 | ||
3200.2.a.bj.1.1 | yes | 2 | 40.29 | even | 2 | ||
3200.2.a.bm.1.1 | yes | 2 | 1.1 | even | 1 | trivial | |
3200.2.a.bn.1.1 | yes | 2 | 20.19 | odd | 2 | ||
3200.2.c.y.2049.2 | 4 | 5.3 | odd | 4 | |||
3200.2.c.y.2049.3 | 4 | 5.2 | odd | 4 | |||
3200.2.c.z.2049.2 | 4 | 40.3 | even | 4 | |||
3200.2.c.z.2049.3 | 4 | 40.27 | even | 4 | |||
3200.2.c.ba.2049.2 | 4 | 20.7 | even | 4 | |||
3200.2.c.ba.2049.3 | 4 | 20.3 | even | 4 | |||
3200.2.c.bb.2049.2 | 4 | 40.37 | odd | 4 | |||
3200.2.c.bb.2049.3 | 4 | 40.13 | odd | 4 |