Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3072,2,Mod(1,3072)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3072, 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("3072.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3072 = 2^{10} \cdot 3 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3072.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: | \(24.5300435009\) |
Analytic rank: | \(1\) |
Dimension: | \(4\) |
Coefficient field: | 4.4.4352.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 6x^{2} - 4x + 2 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 48) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-1.74912\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3072.1 |
$q$-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 | ||||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −2.47363 | −1.10624 | −0.553120 | − | 0.833102i | \(-0.686563\pi\) | ||||
−0.553120 | + | 0.833102i | \(0.686563\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.55765 | −0.966700 | −0.483350 | − | 0.875427i | \(-0.660580\pi\) | ||||
−0.483350 | + | 0.875427i | \(0.660580\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.669808 | 0.201955 | 0.100977 | − | 0.994889i | \(-0.467803\pi\) | ||||
0.100977 | + | 0.994889i | \(0.467803\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −4.08402 | −1.13270 | −0.566352 | − | 0.824164i | \(-0.691646\pi\) | ||||
−0.566352 | + | 0.824164i | \(0.691646\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 2.47363 | 0.638687 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 6.44549 | 1.56326 | 0.781630 | − | 0.623742i | \(-0.214389\pi\) | ||||
0.781630 | + | 0.623742i | \(0.214389\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 6.44549 | 1.47870 | 0.739348 | − | 0.673323i | \(-0.235134\pi\) | ||||
0.739348 | + | 0.673323i | \(0.235134\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 2.55765 | 0.558124 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 2.82843 | 0.589768 | 0.294884 | − | 0.955533i | \(-0.404719\pi\) | ||||
0.294884 | + | 0.955533i | \(0.404719\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.11882 | 0.223765 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −4.35480 | −0.808666 | −0.404333 | − | 0.914612i | \(-0.632496\pi\) | ||||
−0.404333 | + | 0.914612i | \(0.632496\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 6.55765 | 1.17779 | 0.588894 | − | 0.808210i | \(-0.299563\pi\) | ||||
0.588894 | + | 0.808210i | \(0.299563\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −0.669808 | −0.116599 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 6.32666 | 1.06940 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 3.85970 | 0.634531 | 0.317265 | − | 0.948337i | \(-0.397235\pi\) | ||||
0.317265 | + | 0.948337i | \(0.397235\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 4.08402 | 0.653967 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0.788632 | 0.123164 | 0.0615818 | − | 0.998102i | \(-0.480385\pi\) | ||||
0.0615818 | + | 0.998102i | \(0.480385\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −0.550984 | −0.0840242 | −0.0420121 | − | 0.999117i | \(-0.513377\pi\) | ||||
−0.0420121 | + | 0.999117i | \(0.513377\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −2.47363 | −0.368746 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −2.82843 | −0.412568 | −0.206284 | − | 0.978492i | \(-0.566137\pi\) | ||||
−0.206284 | + | 0.978492i | \(0.566137\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −0.458440 | −0.0654915 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −6.44549 | −0.902549 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −3.64520 | −0.500707 | −0.250353 | − | 0.968155i | \(-0.580547\pi\) | ||||
−0.250353 | + | 0.968155i | \(0.580547\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −1.65685 | −0.223410 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −6.44549 | −0.853726 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −5.65685 | −0.736460 | −0.368230 | − | 0.929735i | \(-0.620036\pi\) | ||||
−0.368230 | + | 0.929735i | \(0.620036\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −6.20285 | −0.794193 | −0.397097 | − | 0.917777i | \(-0.629982\pi\) | ||||
−0.397097 | + | 0.917777i | \(0.629982\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −2.55765 | −0.322233 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 10.1023 | 1.25304 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −2.99647 | −0.366077 | −0.183039 | − | 0.983106i | \(-0.558593\pi\) | ||||
−0.183039 | + | 0.983106i | \(0.558593\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −2.82843 | −0.340503 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 5.11529 | 0.607074 | 0.303537 | − | 0.952820i | \(-0.401832\pi\) | ||||
0.303537 | + | 0.952820i | \(0.401832\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −14.7721 | −1.72895 | −0.864475 | − | 0.502676i | \(-0.832349\pi\) | ||||
−0.864475 | + | 0.502676i | \(0.832349\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −1.11882 | −0.129191 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −1.71313 | −0.195230 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 6.32000 | 0.711055 | 0.355528 | − | 0.934666i | \(-0.384301\pi\) | ||||
0.355528 | + | 0.934666i | \(0.384301\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −0.907457 | −0.0996063 | −0.0498032 | − | 0.998759i | \(-0.515859\pi\) | ||||
−0.0498032 | + | 0.998759i | \(0.515859\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −15.9437 | −1.72934 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 4.35480 | 0.466884 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −6.31724 | −0.669626 | −0.334813 | − | 0.942285i | \(-0.608673\pi\) | ||||
−0.334813 | + | 0.942285i | \(0.608673\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 10.4455 | 1.09498 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −6.55765 | −0.679996 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −15.9437 | −1.63579 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 12.6533 | 1.28475 | 0.642375 | − | 0.766390i | \(-0.277949\pi\) | ||||
0.642375 | + | 0.766390i | \(0.277949\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0.669808 | 0.0673182 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −10.6417 | −1.05889 | −0.529443 | − | 0.848346i | \(-0.677599\pi\) | ||||
−0.529443 | + | 0.848346i | \(0.677599\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 3.33686 | 0.328790 | 0.164395 | − | 0.986395i | \(-0.447433\pi\) | ||||
0.164395 | + | 0.986395i | \(0.447433\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −6.32666 | −0.617419 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −19.8874 | −1.92259 | −0.961296 | − | 0.275518i | \(-0.911151\pi\) | ||||
−0.961296 | + | 0.275518i | \(0.911151\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −3.91598 | −0.375083 | −0.187541 | − | 0.982257i | \(-0.560052\pi\) | ||||
−0.187541 | + | 0.982257i | \(0.560052\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −3.85970 | −0.366347 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −2.23765 | −0.210500 | −0.105250 | − | 0.994446i | \(-0.533564\pi\) | ||||
−0.105250 | + | 0.994446i | \(0.533564\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −6.99647 | −0.652424 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −4.08402 | −0.377568 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −16.4853 | −1.51120 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.5514 | −0.959214 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −0.788632 | −0.0711086 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 9.60058 | 0.858702 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 12.2145 | 1.08386 | 0.541931 | − | 0.840423i | \(-0.317693\pi\) | ||||
0.541931 | + | 0.840423i | \(0.317693\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0.550984 | 0.0485114 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −5.33962 | −0.466524 | −0.233262 | − | 0.972414i | \(-0.574940\pi\) | ||||
−0.233262 | + | 0.972414i | \(0.574940\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −16.4853 | −1.42946 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 2.47363 | 0.212896 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −5.10587 | −0.436224 | −0.218112 | − | 0.975924i | \(-0.569990\pi\) | ||||
−0.218112 | + | 0.975924i | \(0.569990\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 16.6533 | 1.41252 | 0.706258 | − | 0.707954i | \(-0.250382\pi\) | ||||
0.706258 | + | 0.707954i | \(0.250382\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 2.82843 | 0.238197 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −2.73551 | −0.228755 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 10.7721 | 0.894578 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0.458440 | 0.0378115 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −11.1832 | −0.916166 | −0.458083 | − | 0.888909i | \(-0.651464\pi\) | ||||
−0.458083 | + | 0.888909i | \(0.651464\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 14.6506 | 1.19225 | 0.596123 | − | 0.802893i | \(-0.296707\pi\) | ||||
0.596123 | + | 0.802893i | \(0.296707\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 6.44549 | 0.521087 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −16.2212 | −1.30292 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −4.45754 | −0.355750 | −0.177875 | − | 0.984053i | \(-0.556922\pi\) | ||||
−0.177875 | + | 0.984053i | \(0.556922\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 3.64520 | 0.289083 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −7.23412 | −0.570128 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 7.78510 | 0.609776 | 0.304888 | − | 0.952388i | \(-0.401381\pi\) | ||||
0.304888 | + | 0.952388i | \(0.401381\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 1.65685 | 0.128986 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −20.1814 | −1.56168 | −0.780841 | − | 0.624730i | \(-0.785209\pi\) | ||||
−0.780841 | + | 0.624730i | \(0.785209\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 3.67923 | 0.283018 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 6.44549 | 0.492899 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −6.15639 | −0.468061 | −0.234031 | − | 0.972229i | \(-0.575192\pi\) | ||||
−0.234031 | + | 0.972229i | \(0.575192\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −2.86156 | −0.216313 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 5.65685 | 0.425195 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 18.7855 | 1.40409 | 0.702046 | − | 0.712131i | \(-0.252270\pi\) | ||||
0.702046 | + | 0.712131i | \(0.252270\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 8.97499 | 0.667106 | 0.333553 | − | 0.942731i | \(-0.391752\pi\) | ||||
0.333553 | + | 0.942731i | \(0.391752\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 6.20285 | 0.458528 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −9.54745 | −0.701943 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 4.31724 | 0.315708 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 2.55765 | 0.186041 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 5.60058 | 0.405243 | 0.202622 | − | 0.979257i | \(-0.435054\pi\) | ||||
0.202622 | + | 0.979257i | \(0.435054\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −19.4514 | −1.40014 | −0.700071 | − | 0.714074i | \(-0.746848\pi\) | ||||
−0.700071 | + | 0.714074i | \(0.746848\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −10.1023 | −0.723444 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −1.75070 | −0.124732 | −0.0623659 | − | 0.998053i | \(-0.519865\pi\) | ||||
−0.0623659 | + | 0.998053i | \(0.519865\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −0.993710 | −0.0704422 | −0.0352211 | − | 0.999380i | \(-0.511214\pi\) | ||||
−0.0352211 | + | 0.999380i | \(0.511214\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 2.99647 | 0.211355 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 11.1380 | 0.781738 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −1.95078 | −0.136248 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 2.82843 | 0.196589 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 4.31724 | 0.298630 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −5.97409 | −0.411273 | −0.205637 | − | 0.978628i | \(-0.565927\pi\) | ||||
−0.205637 | + | 0.978628i | \(0.565927\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −5.11529 | −0.350494 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 1.36293 | 0.0929509 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −16.7721 | −1.13857 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 14.7721 | 0.998209 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −26.3235 | −1.77071 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −23.7659 | −1.59148 | −0.795740 | − | 0.605639i | \(-0.792918\pi\) | ||||
−0.795740 | + | 0.605639i | \(0.792918\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1.11882 | 0.0745883 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −0.907457 | −0.0602300 | −0.0301150 | − | 0.999546i | \(-0.509587\pi\) | ||||
−0.0301150 | + | 0.999546i | \(0.509587\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −7.55579 | −0.499301 | −0.249650 | − | 0.968336i | \(-0.580316\pi\) | ||||
−0.249650 | + | 0.968336i | \(0.580316\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 1.71313 | 0.112716 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −23.2271 | −1.52166 | −0.760828 | − | 0.648954i | \(-0.775207\pi\) | ||||
−0.760828 | + | 0.648954i | \(0.775207\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 6.99647 | 0.456399 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −6.32000 | −0.410528 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −26.9213 | −1.74140 | −0.870698 | − | 0.491817i | \(-0.836333\pi\) | ||||
−0.870698 | + | 0.491817i | \(0.836333\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 10.3494 | 0.666664 | 0.333332 | − | 0.942809i | \(-0.391827\pi\) | ||||
0.333332 | + | 0.942809i | \(0.391827\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 1.13401 | 0.0724492 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −26.3235 | −1.67492 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0.907457 | 0.0575077 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 13.7984 | 0.870949 | 0.435475 | − | 0.900201i | \(-0.356581\pi\) | ||||
0.435475 | + | 0.900201i | \(0.356581\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1.89450 | 0.119106 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 15.9437 | 0.998435 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 16.9965 | 1.06021 | 0.530105 | − | 0.847932i | \(-0.322152\pi\) | ||||
0.530105 | + | 0.847932i | \(0.322152\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −9.87175 | −0.613401 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −4.35480 | −0.269555 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −29.9929 | −1.84944 | −0.924722 | − | 0.380643i | \(-0.875703\pi\) | ||||
−0.924722 | + | 0.380643i | \(0.875703\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 9.01686 | 0.553901 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 6.31724 | 0.386609 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −29.1332 | −1.77628 | −0.888142 | − | 0.459569i | \(-0.848004\pi\) | ||||
−0.888142 | + | 0.459569i | \(0.848004\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 26.6506 | 1.61891 | 0.809453 | − | 0.587184i | \(-0.199764\pi\) | ||||
0.809453 | + | 0.587184i | \(0.199764\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −10.4455 | −0.632190 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0.749397 | 0.0451904 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 17.1430 | 1.03003 | 0.515013 | − | 0.857183i | \(-0.327787\pi\) | ||||
0.515013 | + | 0.857183i | \(0.327787\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 6.55765 | 0.392596 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 2.76588 | 0.164999 | 0.0824993 | − | 0.996591i | \(-0.473710\pi\) | ||||
0.0824993 | + | 0.996591i | \(0.473710\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −6.34315 | −0.377061 | −0.188530 | − | 0.982067i | \(-0.560372\pi\) | ||||
−0.188530 | + | 0.982067i | \(0.560372\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 15.9437 | 0.944425 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −2.01704 | −0.119062 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 24.5443 | 1.44378 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −12.6533 | −0.741751 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 11.6078 | 0.678133 | 0.339067 | − | 0.940762i | \(-0.389889\pi\) | ||||
0.339067 | + | 0.940762i | \(0.389889\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 13.9929 | 0.814700 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −0.669808 | −0.0388662 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −11.5514 | −0.668032 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1.40922 | 0.0812262 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 10.6417 | 0.611348 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 15.3435 | 0.878567 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −14.7855 | −0.843852 | −0.421926 | − | 0.906630i | \(-0.638646\pi\) | ||||
−0.421926 | + | 0.906630i | \(0.638646\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −3.33686 | −0.189827 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −15.0761 | −0.854885 | −0.427442 | − | 0.904043i | \(-0.640585\pi\) | ||||
−0.427442 | + | 0.904043i | \(0.640585\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 23.0027 | 1.30019 | 0.650096 | − | 0.759852i | \(-0.274729\pi\) | ||||
0.650096 | + | 0.759852i | \(0.274729\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 6.32666 | 0.356467 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −9.55855 | −0.536862 | −0.268431 | − | 0.963299i | \(-0.586505\pi\) | ||||
−0.268431 | + | 0.963299i | \(0.586505\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −2.91688 | −0.163314 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 19.8874 | 1.11001 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 41.5443 | 2.31159 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −4.56930 | −0.253459 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 3.91598 | 0.216554 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 7.23412 | 0.398830 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −27.8079 | −1.52846 | −0.764229 | − | 0.644945i | \(-0.776880\pi\) | ||||
−0.764229 | + | 0.644945i | \(0.776880\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 3.85970 | 0.211510 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 7.41215 | 0.404969 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −3.00980 | −0.163954 | −0.0819771 | − | 0.996634i | \(-0.526123\pi\) | ||||
−0.0819771 | + | 0.996634i | \(0.526123\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 2.23765 | 0.121532 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 4.39236 | 0.237860 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 19.0761 | 1.03001 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 6.99647 | 0.376677 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −8.87449 | −0.476408 | −0.238204 | − | 0.971215i | \(-0.576559\pi\) | ||||
−0.238204 | + | 0.971215i | \(0.576559\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −6.70698 | −0.359016 | −0.179508 | − | 0.983757i | \(-0.557451\pi\) | ||||
−0.179508 | + | 0.983757i | \(0.557451\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 4.08402 | 0.217989 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −8.75882 | −0.466185 | −0.233093 | − | 0.972455i | \(-0.574884\pi\) | ||||
−0.233093 | + | 0.972455i | \(0.574884\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −12.6533 | −0.671569 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 16.4853 | 0.872494 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 32.7917 | 1.73068 | 0.865341 | − | 0.501184i | \(-0.167102\pi\) | ||||
0.865341 | + | 0.501184i | \(0.167102\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 22.5443 | 1.18654 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 10.5514 | 0.553803 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 36.5408 | 1.91263 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −20.6435 | −1.07758 | −0.538791 | − | 0.842439i | \(-0.681119\pi\) | ||||
−0.538791 | + | 0.842439i | \(0.681119\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0.788632 | 0.0410546 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 9.32313 | 0.484033 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −23.4995 | −1.21676 | −0.608379 | − | 0.793646i | \(-0.708180\pi\) | ||||
−0.608379 | + | 0.793646i | \(0.708180\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −9.60058 | −0.495772 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 17.7851 | 0.915979 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −11.0004 | −0.565051 | −0.282526 | − | 0.959260i | \(-0.591172\pi\) | ||||
−0.282526 | + | 0.959260i | \(0.591172\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −12.2145 | −0.625768 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −17.2037 | −0.879070 | −0.439535 | − | 0.898225i | \(-0.644857\pi\) | ||||
−0.439535 | + | 0.898225i | \(0.644857\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 4.23765 | 0.215971 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −0.550984 | −0.0280081 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 33.7311 | 1.71023 | 0.855116 | − | 0.518436i | \(-0.173486\pi\) | ||||
0.855116 | + | 0.518436i | \(0.173486\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 18.2306 | 0.921961 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 5.33962 | 0.269348 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −15.6333 | −0.786597 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 14.5201 | 0.728742 | 0.364371 | − | 0.931254i | \(-0.381284\pi\) | ||||
0.364371 | + | 0.931254i | \(0.381284\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 16.4853 | 0.825296 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −32.2274 | −1.60936 | −0.804681 | − | 0.593708i | \(-0.797663\pi\) | ||||
−0.804681 | + | 0.593708i | \(0.797663\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −26.7816 | −1.33409 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −2.47363 | −0.122915 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 2.58526 | 0.128146 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −11.5702 | −0.572110 | −0.286055 | − | 0.958213i | \(-0.592344\pi\) | ||||
−0.286055 | + | 0.958213i | \(0.592344\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 5.10587 | 0.251854 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 14.4682 | 0.711935 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 2.24471 | 0.110188 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −16.6533 | −0.815517 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 9.54193 | 0.466154 | 0.233077 | − | 0.972458i | \(-0.425121\pi\) | ||||
0.233077 | + | 0.972458i | \(0.425121\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 24.3583 | 1.18715 | 0.593576 | − | 0.804778i | \(-0.297716\pi\) | ||||
0.593576 | + | 0.804778i | \(0.297716\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −2.82843 | −0.137523 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 7.21137 | 0.349803 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 15.8647 | 0.767746 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 2.73551 | 0.132072 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −40.7088 | −1.96087 | −0.980437 | − | 0.196832i | \(-0.936935\pi\) | ||||
−0.980437 | + | 0.196832i | \(0.936935\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −7.31371 | −0.351474 | −0.175737 | − | 0.984437i | \(-0.556231\pi\) | ||||
−0.175737 | + | 0.984437i | \(0.556231\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −10.7721 | −0.516485 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 18.2306 | 0.872087 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 17.7122 | 0.845356 | 0.422678 | − | 0.906280i | \(-0.361090\pi\) | ||||
0.422678 | + | 0.906280i | \(0.361090\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −0.458440 | −0.0218305 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −22.1953 | −1.05453 | −0.527264 | − | 0.849701i | \(-0.676782\pi\) | ||||
−0.527264 | + | 0.849701i | \(0.676782\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 15.6265 | 0.740766 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 11.1832 | 0.528949 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −28.3400 | −1.33745 | −0.668723 | − | 0.743511i | \(-0.733159\pi\) | ||||
−0.668723 | + | 0.743511i | \(0.733159\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0.528232 | 0.0248735 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −14.6506 | −0.688344 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −25.8382 | −1.21131 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −17.3396 | −0.811113 | −0.405557 | − | 0.914070i | \(-0.632922\pi\) | ||||
−0.405557 | + | 0.914070i | \(0.632922\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −6.44549 | −0.300850 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 2.39404 | 0.111501 | 0.0557507 | − | 0.998445i | \(-0.482245\pi\) | ||||
0.0557507 | + | 0.998445i | \(0.482245\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −2.70238 | −0.125590 | −0.0627951 | − | 0.998026i | \(-0.520001\pi\) | ||||
−0.0627951 | + | 0.998026i | \(0.520001\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 16.2212 | 0.752239 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 24.2023 | 1.11995 | 0.559975 | − | 0.828510i | \(-0.310811\pi\) | ||||
0.559975 | + | 0.828510i | \(0.310811\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 7.66391 | 0.353887 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 4.45754 | 0.205393 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −0.369053 | −0.0169691 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 7.21137 | 0.330880 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −3.64520 | −0.166902 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −22.2251 | −1.01549 | −0.507745 | − | 0.861508i | \(-0.669521\pi\) | ||||
−0.507745 | + | 0.861508i | \(0.669521\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −15.7631 | −0.718735 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 7.23412 | 0.329164 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −31.2996 | −1.42124 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 13.9839 | 0.633672 | 0.316836 | − | 0.948480i | \(-0.397380\pi\) | ||||
0.316836 | + | 0.948480i | \(0.397380\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −7.78510 | −0.352055 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 10.2306 | 0.461700 | 0.230850 | − | 0.972989i | \(-0.425849\pi\) | ||||
0.230850 | + | 0.972989i | \(0.425849\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −28.0688 | −1.26416 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −1.65685 | −0.0744701 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −13.0831 | −0.586858 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −3.66391 | −0.164019 | −0.0820097 | − | 0.996632i | \(-0.526134\pi\) | ||||
−0.0820097 | + | 0.996632i | \(0.526134\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 20.1814 | 0.901637 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −39.6443 | −1.76765 | −0.883825 | − | 0.467817i | \(-0.845041\pi\) | ||||
−0.883825 | + | 0.467817i | \(0.845041\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 26.3235 | 1.17138 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −3.67923 | −0.163400 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 28.6909 | 1.27170 | 0.635851 | − | 0.771812i | \(-0.280649\pi\) | ||||
0.635851 | + | 0.771812i | \(0.280649\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 37.7819 | 1.67137 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −6.44549 | −0.284575 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −8.25413 | −0.363721 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −1.89450 | −0.0833201 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 6.15639 | 0.270235 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 23.1784 | 1.01546 | 0.507732 | − | 0.861515i | \(-0.330484\pi\) | ||||
0.507732 | + | 0.861515i | \(0.330484\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −8.18193 | −0.357771 | −0.178885 | − | 0.983870i | \(-0.557249\pi\) | ||||
−0.178885 | + | 0.983870i | \(0.557249\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 2.86156 | 0.124889 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 42.2672 | 1.84119 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −15.0000 | −0.652174 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −5.65685 | −0.245487 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −3.22079 | −0.139508 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 49.1941 | 2.12685 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −18.7855 | −0.810653 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −0.307067 | −0.0132263 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 6.43715 | 0.276755 | 0.138377 | − | 0.990380i | \(-0.455811\pi\) | ||||
0.138377 | + | 0.990380i | \(0.455811\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −8.97499 | −0.385154 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 9.68667 | 0.414931 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −39.2239 | −1.67709 | −0.838546 | − | 0.544830i | \(-0.816594\pi\) | ||||
−0.838546 | + | 0.544830i | \(0.816594\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −6.20285 | −0.264731 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −28.0688 | −1.19577 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −16.1643 | −0.687377 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 9.54745 | 0.405267 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 1.66224 | 0.0704315 | 0.0352157 | − | 0.999380i | \(-0.488788\pi\) | ||||
0.0352157 | + | 0.999380i | \(0.488788\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 2.25023 | 0.0951745 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −4.31724 | −0.182274 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 40.6368 | 1.71264 | 0.856319 | − | 0.516447i | \(-0.172746\pi\) | ||||
0.856319 | + | 0.516447i | \(0.172746\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 5.53511 | 0.232864 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −2.55765 | −0.107411 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −27.0004 | −1.13191 | −0.565957 | − | 0.824435i | \(-0.691493\pi\) | ||||
−0.565957 | + | 0.824435i | \(0.691493\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 20.9706 | 0.877591 | 0.438795 | − | 0.898587i | \(-0.355405\pi\) | ||||
0.438795 | + | 0.898587i | \(0.355405\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −5.60058 | −0.233967 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 3.16451 | 0.131969 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −37.6372 | −1.56686 | −0.783429 | − | 0.621481i | \(-0.786531\pi\) | ||||
−0.783429 | + | 0.621481i | \(0.786531\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 19.4514 | 0.808372 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 2.32095 | 0.0962894 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −2.44158 | −0.101120 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 10.1023 | 0.417680 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −44.2047 | −1.82452 | −0.912261 | − | 0.409609i | \(-0.865665\pi\) | ||||
−0.912261 | + | 0.409609i | \(0.865665\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 42.2672 | 1.74159 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 1.75070 | 0.0720140 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 3.59611 | 0.147675 | 0.0738373 | − | 0.997270i | \(-0.476475\pi\) | ||||
0.0738373 | + | 0.997270i | \(0.476475\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 40.7784 | 1.67175 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0.993710 | 0.0406698 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 22.0296 | 0.900104 | 0.450052 | − | 0.893002i | \(-0.351405\pi\) | ||||
0.450052 | + | 0.893002i | \(0.351405\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 10.7721 | 0.439405 | 0.219703 | − | 0.975567i | \(-0.429491\pi\) | ||||
0.219703 | + | 0.975567i | \(0.429491\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −2.99647 | −0.122026 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 26.1001 | 1.06112 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 5.47453 | 0.222204 | 0.111102 | − | 0.993809i | \(-0.464562\pi\) | ||||
0.111102 | + | 0.993809i | \(0.464562\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −11.1380 | −0.451336 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 11.5514 | 0.467318 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 14.8562 | 0.600035 | 0.300018 | − | 0.953934i | \(-0.403007\pi\) | ||||
0.300018 | + | 0.953934i | \(0.403007\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 1.95078 | 0.0786631 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 22.2235 | 0.894686 | 0.447343 | − | 0.894363i | \(-0.352370\pi\) | ||||
0.447343 | + | 0.894363i | \(0.352370\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 16.4612 | 0.661631 | 0.330815 | − | 0.943696i | \(-0.392676\pi\) | ||||
0.330815 | + | 0.943696i | \(0.392676\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −2.82843 | −0.113501 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 16.1573 | 0.647327 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −29.3424 | −1.17369 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −4.31724 | −0.172414 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 24.8776 | 0.991937 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −4.06977 | −0.162015 | −0.0810075 | − | 0.996713i | \(-0.525814\pi\) | ||||
−0.0810075 | + | 0.996713i | \(0.525814\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 5.97409 | 0.237449 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −30.2141 | −1.19901 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1.87228 | 0.0741824 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 5.11529 | 0.202358 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −8.41958 | −0.332553 | −0.166277 | − | 0.986079i | \(-0.553174\pi\) | ||||
−0.166277 | + | 0.986079i | \(0.553174\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −10.4266 | −0.411186 | −0.205593 | − | 0.978638i | \(-0.565912\pi\) | ||||
−0.205593 | + | 0.978638i | \(0.565912\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −1.36293 | −0.0536652 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 11.6132 | 0.456560 | 0.228280 | − | 0.973595i | \(-0.426690\pi\) | ||||
0.228280 | + | 0.973595i | \(0.426690\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −3.78901 | −0.148731 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 16.7721 | 0.657352 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 2.73012 | 0.106838 | 0.0534190 | − | 0.998572i | \(-0.482988\pi\) | ||||
0.0534190 | + | 0.998572i | \(0.482988\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 13.2082 | 0.516088 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −14.7721 | −0.576316 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −31.5514 | −1.22907 | −0.614533 | − | 0.788891i | \(-0.710656\pi\) | ||||
−0.614533 | + | 0.788891i | \(0.710656\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 15.1368 | 0.588752 | 0.294376 | − | 0.955690i | \(-0.404888\pi\) | ||||
0.294376 | + | 0.955690i | \(0.404888\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 26.3235 | 1.02232 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 40.7784 | 1.58132 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −12.3172 | −0.476925 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 23.7659 | 0.918841 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −4.15472 | −0.160391 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −20.6345 | −0.795401 | −0.397700 | − | 0.917515i | \(-0.630192\pi\) | ||||
−0.397700 | + | 0.917515i | \(0.630192\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −1.11882 | −0.0430636 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −37.9357 | −1.45799 | −0.728994 | − | 0.684520i | \(-0.760012\pi\) | ||||
−0.728994 | + | 0.684520i | \(0.760012\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −32.3627 | −1.24197 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0.907457 | 0.0347738 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 18.2471 | 0.698205 | 0.349102 | − | 0.937085i | \(-0.386487\pi\) | ||||
0.349102 | + | 0.937085i | \(0.386487\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 12.6300 | 0.482568 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 7.55579 | 0.288271 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 14.8871 | 0.567152 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 30.2533 | 1.15089 | 0.575446 | − | 0.817840i | \(-0.304829\pi\) | ||||
0.575446 | + | 0.817840i | \(0.304829\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −1.71313 | −0.0650765 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −41.1941 | −1.56258 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 5.08312 | 0.192537 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 23.2271 | 0.878528 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 20.0875 | 0.758696 | 0.379348 | − | 0.925254i | \(-0.376148\pi\) | ||||
0.379348 | + | 0.925254i | \(0.376148\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 24.8776 | 0.938278 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −6.99647 | −0.263502 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 27.2176 | 1.02362 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 41.7864 | 1.56932 | 0.784660 | − | 0.619926i | \(-0.212837\pi\) | ||||
0.784660 | + | 0.619926i | \(0.212837\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 6.32000 | 0.237018 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 18.5478 | 0.694622 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 6.76663 | 0.253058 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 26.9213 | 1.00540 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −28.3683 | −1.05796 | −0.528979 | − | 0.848635i | \(-0.677425\pi\) | ||||
−0.528979 | + | 0.848635i | \(0.677425\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −8.53450 | −0.317841 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −10.3494 | −0.384899 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −4.87226 | −0.180951 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −20.4843 | −0.759722 | −0.379861 | − | 0.925044i | \(-0.624028\pi\) | ||||
−0.379861 | + | 0.925044i | \(0.624028\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −3.55136 | −0.131352 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 48.0777 | 1.77579 | 0.887895 | − | 0.460045i | \(-0.152167\pi\) | ||||
0.887895 | + | 0.460045i | \(0.152167\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −1.13401 | −0.0418286 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −2.00706 | −0.0739310 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 21.4459 | 0.788899 | 0.394449 | − | 0.918918i | \(-0.370935\pi\) | ||||
0.394449 | + | 0.918918i | \(0.370935\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 26.3235 | 0.967018 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 2.17431 | 0.0797677 | 0.0398839 | − | 0.999204i | \(-0.487301\pi\) | ||||
0.0398839 | + | 0.999204i | \(0.487301\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 27.6631 | 1.01350 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −0.907457 | −0.0332021 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 50.8651 | 1.85857 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −29.8980 | −1.09099 | −0.545497 | − | 0.838113i | \(-0.683659\pi\) | ||||
−0.545497 | + | 0.838113i | \(0.683659\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −13.7984 | −0.502843 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −36.2400 | −1.31891 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −21.6791 | −0.787939 | −0.393970 | − | 0.919123i | \(-0.628899\pi\) | ||||
−0.393970 | + | 0.919123i | \(0.628899\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −1.89450 | −0.0687661 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 4.29449 | 0.155675 | 0.0778375 | − | 0.996966i | \(-0.475198\pi\) | ||||
0.0778375 | + | 0.996966i | \(0.475198\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 10.0157 | 0.362592 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −15.9437 | −0.576446 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 23.1027 | 0.834191 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 33.8819 | 1.22181 | 0.610907 | − | 0.791703i | \(-0.290805\pi\) | ||||
0.610907 | + | 0.791703i | \(0.290805\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −16.9965 | −0.612113 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 49.5300 | 1.78147 | 0.890736 | − | 0.454521i | \(-0.150190\pi\) | ||||
0.890736 | + | 0.454521i | \(0.150190\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 7.33686 | 0.263548 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 9.87175 | 0.354147 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 5.08312 | 0.182122 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 3.42627 | 0.122601 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 4.35480 | 0.155628 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 11.0263 | 0.393545 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −34.0953 | −1.21537 | −0.607683 | − | 0.794180i | \(-0.707901\pi\) | ||||
−0.607683 | + | 0.794180i | \(0.707901\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 29.9929 | 1.06778 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 5.72312 | 0.203491 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 25.3326 | 0.899585 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −9.01686 | −0.319795 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −40.6901 | −1.44132 | −0.720659 | − | 0.693290i | \(-0.756160\pi\) | ||||
−0.720659 | + | 0.693290i | \(0.756160\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −18.2306 | −0.644952 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −6.31724 | −0.223209 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −9.89450 | −0.349169 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 17.8945 | 0.630698 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 29.1332 | 1.02554 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −10.9926 | −0.386478 | −0.193239 | − | 0.981152i | \(-0.561899\pi\) | ||||
−0.193239 | + | 0.981152i | \(0.561899\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −21.2498 | −0.746182 | −0.373091 | − | 0.927795i | \(-0.621702\pi\) | ||||
−0.373091 | + | 0.927795i | \(0.621702\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −26.6506 | −0.934676 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −19.2574 | −0.674558 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −3.55136 | −0.124246 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 10.4455 | 0.364995 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −30.0572 | −1.04900 | −0.524501 | − | 0.851410i | \(-0.675748\pi\) | ||||
−0.524501 | + | 0.851410i | \(0.675748\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −55.0851 | −1.92015 | −0.960073 | − | 0.279751i | \(-0.909748\pi\) | ||||
−0.960073 | + | 0.279751i | \(0.909748\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −0.749397 | −0.0260907 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 34.5478 | 1.20135 | 0.600673 | − | 0.799495i | \(-0.294899\pi\) | ||||
0.600673 | + | 0.799495i | \(0.294899\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −31.0046 | −1.07683 | −0.538417 | − | 0.842679i | \(-0.680977\pi\) | ||||
−0.538417 | + | 0.842679i | \(0.680977\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −17.1430 | −0.594685 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −2.95487 | −0.102380 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 49.9212 | 1.72759 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −6.55765 | −0.226665 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 5.14195 | 0.177520 | 0.0887599 | − | 0.996053i | \(-0.471710\pi\) | ||||
0.0887599 | + | 0.996053i | \(0.471710\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −10.0357 | −0.346059 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −2.76588 | −0.0952620 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −9.10104 | −0.313085 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 26.9867 | 0.927272 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 6.34315 | 0.217696 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 10.9169 | 0.374226 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 18.5060 | 0.633632 | 0.316816 | − | 0.948487i | \(-0.397386\pi\) | ||||
0.316816 | + | 0.948487i | \(0.397386\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −15.9437 | −0.545264 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 22.8878 | 0.781833 | 0.390916 | − | 0.920426i | \(-0.372158\pi\) | ||||
0.390916 | + | 0.920426i | \(0.372158\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 35.5286 | 1.21222 | 0.606110 | − | 0.795381i | \(-0.292729\pi\) | ||||
0.606110 | + | 0.795381i | \(0.292729\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 2.01704 | 0.0687407 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −43.9296 | −1.49538 | −0.747691 | − | 0.664047i | \(-0.768837\pi\) | ||||
−0.747691 | + | 0.664047i | \(0.768837\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 15.2286 | 0.517788 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −24.5443 | −0.833568 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 4.23319 | 0.143601 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 12.2376 | 0.414657 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 12.6533 | 0.428250 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −24.5549 | −0.830107 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −21.5773 | −0.728614 | −0.364307 | − | 0.931279i | \(-0.618694\pi\) | ||||
−0.364307 | + | 0.931279i | \(0.618694\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −11.6078 | −0.391520 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −21.6686 | −0.730035 | −0.365018 | − | 0.931001i | \(-0.618937\pi\) | ||||
−0.365018 | + | 0.931001i | \(0.618937\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 0.0834930 | 0.00280976 | 0.00140488 | − | 0.999999i | \(-0.499553\pi\) | ||||
0.00140488 | + | 0.999999i | \(0.499553\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −13.9929 | −0.470368 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 30.8043 | 1.03431 | 0.517154 | − | 0.855892i | \(-0.326991\pi\) | ||||
0.517154 | + | 0.855892i | \(0.326991\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −31.2404 | −1.04777 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0.669808 | 0.0224394 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −18.2306 | −0.610063 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −46.4682 | −1.55326 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 11.5514 | 0.385689 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −28.5573 | −0.952438 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −23.4951 | −0.782735 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −1.40922 | −0.0468960 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −22.2008 | −0.737979 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 49.5215 | 1.64434 | 0.822168 | − | 0.569245i | \(-0.192764\pi\) | ||||
0.822168 | + | 0.569245i | \(0.192764\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −10.6417 | −0.352962 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −0.0829331 | −0.00274770 | −0.00137385 | − | 0.999999i | \(-0.500437\pi\) | ||||
−0.00137385 | + | 0.999999i | \(0.500437\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −0.607822 | −0.0201160 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −15.3435 | −0.507241 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 13.6569 | 0.450989 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 20.1161 | 0.663568 | 0.331784 | − | 0.943355i | \(-0.392350\pi\) | ||||
0.331784 | + | 0.943355i | \(0.392350\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 14.7855 | 0.487198 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −20.8910 | −0.687635 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 4.31833 | 0.141986 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 3.33686 | 0.109597 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 8.55098 | 0.280549 | 0.140274 | − | 0.990113i | \(-0.455202\pi\) | ||||
0.140274 | + | 0.990113i | \(0.455202\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −2.95487 | −0.0968420 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 15.0761 | 0.493568 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −10.6792 | −0.349248 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 33.5780 | 1.09695 | 0.548473 | − | 0.836168i | \(-0.315209\pi\) | ||||
0.548473 | + | 0.836168i | \(0.315209\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −23.0027 | −0.750666 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 11.9991 | 0.391159 | 0.195579 | − | 0.980688i | \(-0.437341\pi\) | ||||
0.195579 | + | 0.980688i | \(0.437341\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 2.23059 | 0.0726380 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −6.32666 | −0.205806 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −25.2537 | −0.820635 | −0.410318 | − | 0.911943i | \(-0.634582\pi\) | ||||
−0.410318 | + | 0.911943i | \(0.634582\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 60.3298 | 1.95839 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 9.55855 | 0.309957 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 3.86469 | 0.125190 | 0.0625948 | − | 0.998039i | \(-0.480062\pi\) | ||||
0.0625948 | + | 0.998039i | \(0.480062\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −13.8537 | −0.448296 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 2.91688 | 0.0942894 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 13.0590 | 0.421698 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 12.0027 | 0.387185 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −19.8874 | −0.640864 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 48.1154 | 1.54889 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −37.8714 | −1.21786 | −0.608930 | − | 0.793224i | \(-0.708401\pi\) | ||||
−0.608930 | + | 0.793224i | \(0.708401\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −41.5443 | −1.33460 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 3.74587 | 0.120211 | 0.0601053 | − | 0.998192i | \(-0.480856\pi\) | ||||
0.0601053 | + | 0.998192i | \(0.480856\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −42.5933 | −1.36548 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 4.56930 | 0.146335 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −17.6530 | −0.564768 | −0.282384 | − | 0.959301i | \(-0.591125\pi\) | ||||
−0.282384 | + | 0.959301i | \(0.591125\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −4.23134 | −0.135234 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −3.91598 | −0.125028 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 22.3557 | 0.713035 | 0.356518 | − | 0.934289i | \(-0.383964\pi\) | ||||
0.356518 | + | 0.934289i | \(0.383964\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 4.33057 | 0.137983 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −7.23412 | −0.230265 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −1.55842 | −0.0495548 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 17.8769 | 0.567878 | 0.283939 | − | 0.958842i | \(-0.408359\pi\) | ||||
0.283939 | + | 0.958842i | \(0.408359\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 27.8079 | 0.882456 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 2.45807 | 0.0779260 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −6.06146 | −0.191968 | −0.0959841 | − | 0.995383i | \(-0.530600\pi\) | ||||
−0.0959841 | + | 0.995383i | \(0.530600\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −3.85970 | −0.122116 |
(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 | 3072.2.a.i.1.2 | 4 | ||
3.2 | odd | 2 | 9216.2.a.bo.1.3 | 4 | |||
4.3 | odd | 2 | 3072.2.a.o.1.2 | 4 | |||
8.3 | odd | 2 | 3072.2.a.n.1.3 | 4 | |||
8.5 | even | 2 | 3072.2.a.t.1.3 | 4 | |||
12.11 | even | 2 | 9216.2.a.bn.1.3 | 4 | |||
16.3 | odd | 4 | 3072.2.d.i.1537.7 | 8 | |||
16.5 | even | 4 | 3072.2.d.f.1537.6 | 8 | |||
16.11 | odd | 4 | 3072.2.d.i.1537.2 | 8 | |||
16.13 | even | 4 | 3072.2.d.f.1537.3 | 8 | |||
24.5 | odd | 2 | 9216.2.a.y.1.2 | 4 | |||
24.11 | even | 2 | 9216.2.a.x.1.2 | 4 | |||
32.3 | odd | 8 | 192.2.j.a.145.4 | 8 | |||
32.5 | even | 8 | 384.2.j.b.97.3 | 8 | |||
32.11 | odd | 8 | 192.2.j.a.49.4 | 8 | |||
32.13 | even | 8 | 384.2.j.b.289.3 | 8 | |||
32.19 | odd | 8 | 384.2.j.a.289.1 | 8 | |||
32.21 | even | 8 | 48.2.j.a.37.2 | yes | 8 | ||
32.27 | odd | 8 | 384.2.j.a.97.1 | 8 | |||
32.29 | even | 8 | 48.2.j.a.13.2 | ✓ | 8 | ||
96.5 | odd | 8 | 1152.2.k.c.865.4 | 8 | |||
96.11 | even | 8 | 576.2.k.b.433.1 | 8 | |||
96.29 | odd | 8 | 144.2.k.b.109.3 | 8 | |||
96.35 | even | 8 | 576.2.k.b.145.1 | 8 | |||
96.53 | odd | 8 | 144.2.k.b.37.3 | 8 | |||
96.59 | even | 8 | 1152.2.k.f.865.4 | 8 | |||
96.77 | odd | 8 | 1152.2.k.c.289.4 | 8 | |||
96.83 | even | 8 | 1152.2.k.f.289.4 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
48.2.j.a.13.2 | ✓ | 8 | 32.29 | even | 8 | ||
48.2.j.a.37.2 | yes | 8 | 32.21 | even | 8 | ||
144.2.k.b.37.3 | 8 | 96.53 | odd | 8 | |||
144.2.k.b.109.3 | 8 | 96.29 | odd | 8 | |||
192.2.j.a.49.4 | 8 | 32.11 | odd | 8 | |||
192.2.j.a.145.4 | 8 | 32.3 | odd | 8 | |||
384.2.j.a.97.1 | 8 | 32.27 | odd | 8 | |||
384.2.j.a.289.1 | 8 | 32.19 | odd | 8 | |||
384.2.j.b.97.3 | 8 | 32.5 | even | 8 | |||
384.2.j.b.289.3 | 8 | 32.13 | even | 8 | |||
576.2.k.b.145.1 | 8 | 96.35 | even | 8 | |||
576.2.k.b.433.1 | 8 | 96.11 | even | 8 | |||
1152.2.k.c.289.4 | 8 | 96.77 | odd | 8 | |||
1152.2.k.c.865.4 | 8 | 96.5 | odd | 8 | |||
1152.2.k.f.289.4 | 8 | 96.83 | even | 8 | |||
1152.2.k.f.865.4 | 8 | 96.59 | even | 8 | |||
3072.2.a.i.1.2 | 4 | 1.1 | even | 1 | trivial | ||
3072.2.a.n.1.3 | 4 | 8.3 | odd | 2 | |||
3072.2.a.o.1.2 | 4 | 4.3 | odd | 2 | |||
3072.2.a.t.1.3 | 4 | 8.5 | even | 2 | |||
3072.2.d.f.1537.3 | 8 | 16.13 | even | 4 | |||
3072.2.d.f.1537.6 | 8 | 16.5 | even | 4 | |||
3072.2.d.i.1537.2 | 8 | 16.11 | odd | 4 | |||
3072.2.d.i.1537.7 | 8 | 16.3 | odd | 4 | |||
9216.2.a.x.1.2 | 4 | 24.11 | even | 2 | |||
9216.2.a.y.1.2 | 4 | 24.5 | odd | 2 | |||
9216.2.a.bn.1.3 | 4 | 12.11 | even | 2 | |||
9216.2.a.bo.1.3 | 4 | 3.2 | odd | 2 |