Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2008,2,Mod(1,2008)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2008, 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("2008.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2008 = 2^{3} \cdot 251 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2008.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: | \(16.0339607259\) |
Analytic rank: | \(0\) |
Dimension: | \(23\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.15 | ||
Character | \(\chi\) | \(=\) | 2008.1 |
$q$-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 | ||||||||
\(3\) | 1.39383 | 0.804729 | 0.402364 | − | 0.915480i | \(-0.368189\pi\) | ||||
0.402364 | + | 0.915480i | \(0.368189\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −3.54571 | −1.58569 | −0.792845 | − | 0.609423i | \(-0.791401\pi\) | ||||
−0.792845 | + | 0.609423i | \(0.791401\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −3.34862 | −1.26566 | −0.632829 | − | 0.774291i | \(-0.718107\pi\) | ||||
−0.632829 | + | 0.774291i | \(0.718107\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −1.05724 | −0.352412 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.30546 | −0.393612 | −0.196806 | − | 0.980442i | \(-0.563057\pi\) | ||||
−0.196806 | + | 0.980442i | \(0.563057\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.98436 | −0.550362 | −0.275181 | − | 0.961392i | \(-0.588738\pi\) | ||||
−0.275181 | + | 0.961392i | \(0.588738\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −4.94212 | −1.27605 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 7.91610 | 1.91994 | 0.959968 | − | 0.280110i | \(-0.0903710\pi\) | ||||
0.959968 | + | 0.280110i | \(0.0903710\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 4.46220 | 1.02370 | 0.511850 | − | 0.859075i | \(-0.328960\pi\) | ||||
0.511850 | + | 0.859075i | \(0.328960\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −4.66741 | −1.01851 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −1.70505 | −0.355527 | −0.177764 | − | 0.984073i | \(-0.556886\pi\) | ||||
−0.177764 | + | 0.984073i | \(0.556886\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 7.57207 | 1.51441 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −5.65510 | −1.08832 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0.208137 | 0.0386501 | 0.0193251 | − | 0.999813i | \(-0.493848\pi\) | ||||
0.0193251 | + | 0.999813i | \(0.493848\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 9.03679 | 1.62306 | 0.811528 | − | 0.584314i | \(-0.198636\pi\) | ||||
0.811528 | + | 0.584314i | \(0.198636\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −1.81960 | −0.316751 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 11.8732 | 2.00694 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −2.45973 | −0.404377 | −0.202189 | − | 0.979347i | \(-0.564805\pi\) | ||||
−0.202189 | + | 0.979347i | \(0.564805\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −2.76586 | −0.442892 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −3.96457 | −0.619161 | −0.309581 | − | 0.950873i | \(-0.600189\pi\) | ||||
−0.309581 | + | 0.950873i | \(0.600189\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0.799495 | 0.121922 | 0.0609609 | − | 0.998140i | \(-0.480584\pi\) | ||||
0.0609609 | + | 0.998140i | \(0.480584\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 3.74865 | 0.558816 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 10.8016 | 1.57558 | 0.787790 | − | 0.615943i | \(-0.211225\pi\) | ||||
0.787790 | + | 0.615943i | \(0.211225\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 4.21324 | 0.601892 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 11.0337 | 1.54503 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 0.665446 | 0.0914060 | 0.0457030 | − | 0.998955i | \(-0.485447\pi\) | ||||
0.0457030 | + | 0.998955i | \(0.485447\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 4.62880 | 0.624147 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 6.21956 | 0.823801 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 12.7607 | 1.66130 | 0.830648 | − | 0.556798i | \(-0.187970\pi\) | ||||
0.830648 | + | 0.556798i | \(0.187970\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.09665 | −0.140411 | −0.0702056 | − | 0.997533i | \(-0.522366\pi\) | ||||
−0.0702056 | + | 0.997533i | \(0.522366\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 3.54028 | 0.446033 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 7.03597 | 0.872704 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −14.2147 | −1.73660 | −0.868301 | − | 0.496037i | \(-0.834788\pi\) | ||||
−0.868301 | + | 0.496037i | \(0.834788\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −2.37655 | −0.286103 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −3.44150 | −0.408431 | −0.204216 | − | 0.978926i | \(-0.565464\pi\) | ||||
−0.204216 | + | 0.978926i | \(0.565464\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 15.8322 | 1.85302 | 0.926509 | − | 0.376273i | \(-0.122795\pi\) | ||||
0.926509 | + | 0.376273i | \(0.122795\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 10.5542 | 1.21869 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 4.37150 | 0.498179 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −8.66181 | −0.974529 | −0.487265 | − | 0.873254i | \(-0.662005\pi\) | ||||
−0.487265 | + | 0.873254i | \(0.662005\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −4.71055 | −0.523394 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 13.1306 | 1.44128 | 0.720638 | − | 0.693312i | \(-0.243849\pi\) | ||||
0.720638 | + | 0.693312i | \(0.243849\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −28.0682 | −3.04442 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0.290108 | 0.0311029 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −1.71867 | −0.182178 | −0.0910892 | − | 0.995843i | \(-0.529035\pi\) | ||||
−0.0910892 | + | 0.995843i | \(0.529035\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 6.64486 | 0.696571 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 12.5958 | 1.30612 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −15.8217 | −1.62327 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 17.1470 | 1.74102 | 0.870508 | − | 0.492154i | \(-0.163790\pi\) | ||||
0.870508 | + | 0.492154i | \(0.163790\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 1.38018 | 0.138714 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 11.2421 | 1.11864 | 0.559318 | − | 0.828953i | \(-0.311063\pi\) | ||||
0.559318 | + | 0.828953i | \(0.311063\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −4.36024 | −0.429627 | −0.214814 | − | 0.976655i | \(-0.568914\pi\) | ||||
−0.214814 | + | 0.976655i | \(0.568914\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 16.5493 | 1.61504 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −3.64445 | −0.352322 | −0.176161 | − | 0.984361i | \(-0.556368\pi\) | ||||
−0.176161 | + | 0.984361i | \(0.556368\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 7.47130 | 0.715621 | 0.357810 | − | 0.933794i | \(-0.383523\pi\) | ||||
0.357810 | + | 0.933794i | \(0.383523\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −3.42845 | −0.325414 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −0.345864 | −0.0325361 | −0.0162681 | − | 0.999868i | \(-0.505179\pi\) | ||||
−0.0162681 | + | 0.999868i | \(0.505179\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 6.04561 | 0.563756 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 2.09794 | 0.193954 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −26.5080 | −2.42998 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −9.29576 | −0.845069 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −5.52594 | −0.498257 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −9.11981 | −0.815700 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −2.67106 | −0.237019 | −0.118509 | − | 0.992953i | \(-0.537812\pi\) | ||||
−0.118509 | + | 0.992953i | \(0.537812\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 1.11436 | 0.0981140 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −2.76355 | −0.241453 | −0.120726 | − | 0.992686i | \(-0.538522\pi\) | ||||
−0.120726 | + | 0.992686i | \(0.538522\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −14.9422 | −1.29565 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 20.0514 | 1.72575 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 0.0385432 | 0.00329297 | 0.00164648 | − | 0.999999i | \(-0.499476\pi\) | ||||
0.00164648 | + | 0.999999i | \(0.499476\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −0.628671 | −0.0533232 | −0.0266616 | − | 0.999645i | \(-0.508488\pi\) | ||||
−0.0266616 | + | 0.999645i | \(0.508488\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 15.0557 | 1.26791 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 2.59051 | 0.216630 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −0.737995 | −0.0612871 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 5.87255 | 0.484360 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −11.3639 | −0.930968 | −0.465484 | − | 0.885056i | \(-0.654120\pi\) | ||||
−0.465484 | + | 0.885056i | \(0.654120\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 14.5798 | 1.18649 | 0.593245 | − | 0.805022i | \(-0.297846\pi\) | ||||
0.593245 | + | 0.805022i | \(0.297846\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −8.36918 | −0.676608 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −32.0418 | −2.57366 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 10.7179 | 0.855385 | 0.427693 | − | 0.903924i | \(-0.359327\pi\) | ||||
0.427693 | + | 0.903924i | \(0.359327\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0.927519 | 0.0735570 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 5.70955 | 0.449976 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −12.0147 | −0.941067 | −0.470534 | − | 0.882382i | \(-0.655939\pi\) | ||||
−0.470534 | + | 0.882382i | \(0.655939\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 6.45177 | 0.502269 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −5.47233 | −0.423462 | −0.211731 | − | 0.977328i | \(-0.567910\pi\) | ||||
−0.211731 | + | 0.977328i | \(0.567910\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −9.06232 | −0.697101 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −4.71760 | −0.360764 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −2.60501 | −0.198055 | −0.0990277 | − | 0.995085i | \(-0.531573\pi\) | ||||
−0.0990277 | + | 0.995085i | \(0.531573\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −25.3560 | −1.91673 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 17.7862 | 1.33689 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 9.95712 | 0.744230 | 0.372115 | − | 0.928187i | \(-0.378633\pi\) | ||||
0.372115 | + | 0.928187i | \(0.378633\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −10.4862 | −0.779431 | −0.389716 | − | 0.920935i | \(-0.627427\pi\) | ||||
−0.389716 | + | 0.920935i | \(0.627427\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −1.52854 | −0.112993 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 8.72149 | 0.641217 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −10.3342 | −0.755711 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 18.9368 | 1.37745 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 4.51146 | 0.326437 | 0.163219 | − | 0.986590i | \(-0.447812\pi\) | ||||
0.163219 | + | 0.986590i | \(0.447812\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 22.8795 | 1.64690 | 0.823451 | − | 0.567387i | \(-0.192046\pi\) | ||||
0.823451 | + | 0.567387i | \(0.192046\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 9.80695 | 0.702290 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 23.6017 | 1.68155 | 0.840775 | − | 0.541384i | \(-0.182099\pi\) | ||||
0.840775 | + | 0.541384i | \(0.182099\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −9.74219 | −0.690606 | −0.345303 | − | 0.938491i | \(-0.612224\pi\) | ||||
−0.345303 | + | 0.938491i | \(0.612224\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −19.8129 | −1.39749 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −0.696972 | −0.0489179 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 14.0572 | 0.981798 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 1.80264 | 0.125292 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −5.82525 | −0.402941 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −16.0568 | −1.10540 | −0.552699 | − | 0.833381i | \(-0.686402\pi\) | ||||
−0.552699 | + | 0.833381i | \(0.686402\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −4.79687 | −0.328676 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −2.83478 | −0.193330 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −30.2608 | −2.05423 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 22.0674 | 1.49118 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −15.7084 | −1.05666 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −23.7488 | −1.59034 | −0.795169 | − | 0.606388i | \(-0.792618\pi\) | ||||
−0.795169 | + | 0.606388i | \(0.792618\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −8.00546 | −0.533697 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −5.58879 | −0.370941 | −0.185471 | − | 0.982650i | \(-0.559381\pi\) | ||||
−0.185471 | + | 0.982650i | \(0.559381\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 2.15354 | 0.142310 | 0.0711549 | − | 0.997465i | \(-0.477332\pi\) | ||||
0.0711549 | + | 0.997465i | \(0.477332\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 6.09314 | 0.400899 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 7.54167 | 0.494071 | 0.247035 | − | 0.969006i | \(-0.420544\pi\) | ||||
0.247035 | + | 0.969006i | \(0.420544\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −38.2995 | −2.49838 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −12.0731 | −0.784232 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −2.69180 | −0.174118 | −0.0870590 | − | 0.996203i | \(-0.527747\pi\) | ||||
−0.0870590 | + | 0.996203i | \(0.527747\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −7.52116 | −0.484481 | −0.242240 | − | 0.970216i | \(-0.577882\pi\) | ||||
−0.242240 | + | 0.970216i | \(0.577882\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 10.3996 | 0.667134 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −14.9389 | −0.954414 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −8.85462 | −0.563406 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 18.3019 | 1.15984 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −1.00000 | −0.0631194 | ||||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 2.22588 | 0.139940 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −39.1223 | −2.44993 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −2.05695 | −0.128309 | −0.0641545 | − | 0.997940i | \(-0.520435\pi\) | ||||
−0.0641545 | + | 0.997940i | \(0.520435\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 8.23669 | 0.511803 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −0.220050 | −0.0136208 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 12.9847 | 0.800670 | 0.400335 | − | 0.916369i | \(-0.368894\pi\) | ||||
0.400335 | + | 0.916369i | \(0.368894\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −2.35948 | −0.144942 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −2.39553 | −0.146604 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 25.6995 | 1.56693 | 0.783463 | − | 0.621438i | \(-0.213451\pi\) | ||||
0.783463 | + | 0.621438i | \(0.213451\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 12.7065 | 0.771863 | 0.385931 | − | 0.922527i | \(-0.373880\pi\) | ||||
0.385931 | + | 0.922527i | \(0.373880\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 9.26182 | 0.560551 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −9.88507 | −0.596092 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 19.8677 | 1.19374 | 0.596868 | − | 0.802340i | \(-0.296412\pi\) | ||||
0.596868 | + | 0.802340i | \(0.296412\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −9.55401 | −0.571984 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 30.8497 | 1.84034 | 0.920171 | − | 0.391518i | \(-0.128050\pi\) | ||||
0.920171 | + | 0.391518i | \(0.128050\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −11.9389 | −0.709695 | −0.354848 | − | 0.934924i | \(-0.615467\pi\) | ||||
−0.354848 | + | 0.934924i | \(0.615467\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −22.0528 | −1.30629 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 13.2758 | 0.783647 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 45.6646 | 2.68615 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 23.9001 | 1.40105 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −10.0471 | −0.586961 | −0.293480 | − | 0.955965i | \(-0.594814\pi\) | ||||
−0.293480 | + | 0.955965i | \(0.594814\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −45.2456 | −2.63430 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 7.38253 | 0.428378 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 3.38343 | 0.195669 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −2.67720 | −0.154311 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 15.6696 | 0.900198 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 3.88839 | 0.222649 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −25.1331 | −1.43442 | −0.717210 | − | 0.696858i | \(-0.754581\pi\) | ||||
−0.717210 | + | 0.696858i | \(0.754581\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −6.07744 | −0.345733 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 23.3800 | 1.32576 | 0.662880 | − | 0.748725i | \(-0.269334\pi\) | ||||
0.662880 | + | 0.748725i | \(0.269334\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 32.8535 | 1.85699 | 0.928495 | − | 0.371344i | \(-0.121103\pi\) | ||||
0.928495 | + | 0.371344i | \(0.121103\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −12.5528 | −0.707270 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 7.68671 | 0.431729 | 0.215864 | − | 0.976423i | \(-0.430743\pi\) | ||||
0.215864 | + | 0.976423i | \(0.430743\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −0.271716 | −0.0152132 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −5.07974 | −0.283524 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 35.3233 | 1.96544 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −15.0257 | −0.833476 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 10.4137 | 0.575881 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −36.1706 | −1.99415 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −3.62040 | −0.198995 | −0.0994976 | − | 0.995038i | \(-0.531724\pi\) | ||||
−0.0994976 | + | 0.995038i | \(0.531724\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 2.60051 | 0.142507 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 50.4012 | 2.75371 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −7.27600 | −0.396349 | −0.198174 | − | 0.980167i | \(-0.563501\pi\) | ||||
−0.198174 | + | 0.980167i | \(0.563501\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −0.482076 | −0.0261828 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −11.7972 | −0.638855 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 9.33179 | 0.503869 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 8.42656 | 0.453670 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −10.7648 | −0.577887 | −0.288943 | − | 0.957346i | \(-0.593304\pi\) | ||||
−0.288943 | + | 0.957346i | \(0.593304\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 19.7330 | 1.05628 | 0.528142 | − | 0.849156i | \(-0.322889\pi\) | ||||
0.528142 | + | 0.849156i | \(0.322889\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 11.2218 | 0.598973 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 29.8869 | 1.59072 | 0.795360 | − | 0.606137i | \(-0.207282\pi\) | ||||
0.795360 | + | 0.606137i | \(0.207282\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 12.2026 | 0.647646 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −36.9477 | −1.95548 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 4.41597 | 0.233066 | 0.116533 | − | 0.993187i | \(-0.462822\pi\) | ||||
0.116533 | + | 0.993187i | \(0.462822\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 0.911272 | 0.0479617 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −12.9567 | −0.680051 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −56.1364 | −2.93831 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −10.3648 | −0.541038 | −0.270519 | − | 0.962715i | \(-0.587195\pi\) | ||||
−0.270519 | + | 0.962715i | \(0.587195\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 4.19148 | 0.218200 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −2.22832 | −0.115689 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 27.5539 | 1.42669 | 0.713344 | − | 0.700814i | \(-0.247180\pi\) | ||||
0.713344 | + | 0.700814i | \(0.247180\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −12.7115 | −0.656418 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −0.413019 | −0.0212716 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 0.503584 | 0.0258674 | 0.0129337 | − | 0.999916i | \(-0.495883\pi\) | ||||
0.0129337 | + | 0.999916i | \(0.495883\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −3.72301 | −0.190736 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 23.3960 | 1.19548 | 0.597741 | − | 0.801689i | \(-0.296065\pi\) | ||||
0.597741 | + | 0.801689i | \(0.296065\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −15.5001 | −0.789958 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −0.845254 | −0.0429667 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 35.0778 | 1.77852 | 0.889258 | − | 0.457407i | \(-0.151222\pi\) | ||||
0.889258 | + | 0.457407i | \(0.151222\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −13.4973 | −0.682589 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −3.85192 | −0.194304 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 30.7123 | 1.54530 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −30.3735 | −1.52440 | −0.762201 | − | 0.647341i | \(-0.775881\pi\) | ||||
−0.762201 | + | 0.647341i | \(0.775881\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −20.8269 | −1.04265 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 11.5805 | 0.578302 | 0.289151 | − | 0.957283i | \(-0.406627\pi\) | ||||
0.289151 | + | 0.957283i | \(0.406627\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −17.9322 | −0.893269 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 16.7022 | 0.829941 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 3.21109 | 0.159168 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 10.0559 | 0.497234 | 0.248617 | − | 0.968602i | \(-0.420024\pi\) | ||||
0.248617 | + | 0.968602i | \(0.420024\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0.0537227 | 0.00264995 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −42.7306 | −2.10263 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −46.5575 | −2.28542 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −0.876262 | −0.0429107 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −19.0038 | −0.928397 | −0.464198 | − | 0.885731i | \(-0.653658\pi\) | ||||
−0.464198 | + | 0.885731i | \(0.653658\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −22.8047 | −1.11143 | −0.555717 | − | 0.831371i | \(-0.687556\pi\) | ||||
−0.555717 | + | 0.831371i | \(0.687556\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −11.4199 | −0.555253 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 59.9412 | 2.90758 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 3.67225 | 0.177713 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 3.61074 | 0.174328 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −22.2844 | −1.07340 | −0.536702 | − | 0.843772i | \(-0.680330\pi\) | ||||
−0.536702 | + | 0.843772i | \(0.680330\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −26.4647 | −1.27181 | −0.635906 | − | 0.771766i | \(-0.719373\pi\) | ||||
−0.635906 | + | 0.771766i | \(0.719373\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −1.02864 | −0.0493195 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −7.60827 | −0.363953 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 10.9841 | 0.524245 | 0.262122 | − | 0.965035i | \(-0.415578\pi\) | ||||
0.262122 | + | 0.965035i | \(0.415578\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −4.45439 | −0.212114 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −16.1484 | −0.767235 | −0.383618 | − | 0.923492i | \(-0.625322\pi\) | ||||
−0.383618 | + | 0.923492i | \(0.625322\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 6.09390 | 0.288878 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −15.8394 | −0.749176 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 26.6912 | 1.25963 | 0.629817 | − | 0.776743i | \(-0.283130\pi\) | ||||
0.629817 | + | 0.776743i | \(0.283130\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 5.17560 | 0.243710 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 20.3218 | 0.954803 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −23.5608 | −1.10455 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 11.3731 | 0.532013 | 0.266006 | − | 0.963971i | \(-0.414296\pi\) | ||||
0.266006 | + | 0.963971i | \(0.414296\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −44.7663 | −2.08951 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −37.7563 | −1.75848 | −0.879242 | − | 0.476375i | \(-0.841950\pi\) | ||||
−0.879242 | + | 0.476375i | \(0.841950\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 24.4504 | 1.13631 | 0.568154 | − | 0.822922i | \(-0.307658\pi\) | ||||
0.568154 | + | 0.822922i | \(0.307658\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −44.6609 | −2.07110 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 13.3351 | 0.617073 | 0.308536 | − | 0.951213i | \(-0.400161\pi\) | ||||
0.308536 | + | 0.951213i | \(0.400161\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 47.5996 | 2.19795 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 14.9390 | 0.688353 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −1.04371 | −0.0479899 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 33.7881 | 1.55031 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −0.703533 | −0.0322126 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 16.5168 | 0.754672 | 0.377336 | − | 0.926076i | \(-0.376840\pi\) | ||||
0.377336 | + | 0.926076i | \(0.376840\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 4.88099 | 0.222554 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 7.95815 | 0.362109 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −60.7984 | −2.76071 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −29.5815 | −1.34047 | −0.670233 | − | 0.742151i | \(-0.733806\pi\) | ||||
−0.670233 | + | 0.742151i | \(0.733806\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −16.7465 | −0.757304 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 31.0452 | 1.40105 | 0.700525 | − | 0.713628i | \(-0.252949\pi\) | ||||
0.700525 | + | 0.713628i | \(0.252949\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 1.64764 | 0.0742058 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −4.89373 | −0.219957 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 11.5243 | 0.516935 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 12.5466 | 0.561661 | 0.280831 | − | 0.959757i | \(-0.409390\pi\) | ||||
0.280831 | + | 0.959757i | \(0.409390\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −7.62750 | −0.340772 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 35.8802 | 1.59982 | 0.799910 | − | 0.600119i | \(-0.204880\pi\) | ||||
0.799910 | + | 0.600119i | \(0.204880\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −39.8614 | −1.77381 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −12.6313 | −0.560977 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −25.7570 | −1.14166 | −0.570830 | − | 0.821068i | \(-0.693378\pi\) | ||||
−0.570830 | + | 0.821068i | \(0.693378\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −53.0159 | −2.34529 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −25.2342 | −1.11412 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 15.4602 | 0.681256 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −14.1012 | −0.620168 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −3.63095 | −0.159381 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −23.6115 | −1.03444 | −0.517219 | − | 0.855853i | \(-0.673033\pi\) | ||||
−0.517219 | + | 0.855853i | \(0.673033\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −43.6381 | −1.90816 | −0.954080 | − | 0.299551i | \(-0.903163\pi\) | ||||
−0.954080 | + | 0.299551i | \(0.903163\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −35.3419 | −1.54245 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 71.5361 | 3.11616 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −20.0928 | −0.873600 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −13.4910 | −0.585460 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 7.86713 | 0.340763 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 12.9222 | 0.558674 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 13.8785 | 0.598904 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −5.50024 | −0.236912 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −30.1373 | −1.29570 | −0.647852 | − | 0.761766i | \(-0.724332\pi\) | ||||
−0.647852 | + | 0.761766i | \(0.724332\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −14.6160 | −0.627231 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −26.4911 | −1.13475 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 22.9197 | 0.979974 | 0.489987 | − | 0.871730i | \(-0.337002\pi\) | ||||
0.489987 | + | 0.871730i | \(0.337002\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 1.15941 | 0.0494825 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0.928751 | 0.0395661 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 29.0051 | 1.23342 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 12.1563 | 0.516005 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 31.8431 | 1.34923 | 0.674617 | − | 0.738168i | \(-0.264309\pi\) | ||||
0.674617 | + | 0.738168i | \(0.264309\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −1.58649 | −0.0671012 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −14.4041 | −0.608142 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 7.47665 | 0.315103 | 0.157552 | − | 0.987511i | \(-0.449640\pi\) | ||||
0.157552 | + | 0.987511i | \(0.449640\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 1.22633 | 0.0515922 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 15.7738 | 0.662438 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 1.33344 | 0.0559005 | 0.0279503 | − | 0.999609i | \(-0.491102\pi\) | ||||
0.0279503 | + | 0.999609i | \(0.491102\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −38.2509 | −1.60075 | −0.800375 | − | 0.599500i | \(-0.795366\pi\) | ||||
−0.800375 | + | 0.599500i | \(0.795366\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 6.28821 | 0.262694 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −12.9107 | −0.538415 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 6.83043 | 0.284354 | 0.142177 | − | 0.989841i | \(-0.454590\pi\) | ||||
0.142177 | + | 0.989841i | \(0.454590\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 31.8901 | 1.32531 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −43.9695 | −1.82416 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −0.868716 | −0.0359786 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −7.43867 | −0.307551 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 28.2880 | 1.16757 | 0.583784 | − | 0.811909i | \(-0.301571\pi\) | ||||
0.583784 | + | 0.811909i | \(0.301571\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 40.3240 | 1.66152 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 32.8968 | 1.35319 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −7.03794 | −0.289014 | −0.144507 | − | 0.989504i | \(-0.546160\pi\) | ||||
−0.144507 | + | 0.989504i | \(0.546160\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 93.9897 | 3.85320 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −13.5790 | −0.555750 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −30.4870 | −1.24567 | −0.622833 | − | 0.782355i | \(-0.714018\pi\) | ||||
−0.622833 | + | 0.782355i | \(0.714018\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 7.23286 | 0.295035 | 0.147517 | − | 0.989059i | \(-0.452872\pi\) | ||||
0.147517 | + | 0.989059i | \(0.452872\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 15.0283 | 0.611999 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 32.9601 | 1.34002 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −22.0128 | −0.893471 | −0.446736 | − | 0.894666i | \(-0.647414\pi\) | ||||
−0.446736 | + | 0.894666i | \(0.647414\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −0.971462 | −0.0393656 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −21.4343 | −0.867141 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −14.1465 | −0.571372 | −0.285686 | − | 0.958323i | \(-0.592221\pi\) | ||||
−0.285686 | + | 0.958323i | \(0.592221\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 19.5934 | 0.790081 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −36.2883 | −1.46091 | −0.730456 | − | 0.682960i | \(-0.760692\pi\) | ||||
−0.730456 | + | 0.682960i | \(0.760692\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 2.67210 | 0.107401 | 0.0537005 | − | 0.998557i | \(-0.482898\pi\) | ||||
0.0537005 | + | 0.998557i | \(0.482898\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 9.64222 | 0.386929 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 5.75516 | 0.230576 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −5.52413 | −0.220965 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −8.11942 | −0.324258 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −19.4715 | −0.776378 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 41.5356 | 1.65351 | 0.826753 | − | 0.562565i | \(-0.190185\pi\) | ||||
0.826753 | + | 0.562565i | \(0.190185\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −22.3805 | −0.889546 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 9.47082 | 0.375838 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −8.36059 | −0.331259 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 3.63848 | 0.143936 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −38.6560 | −1.52682 | −0.763410 | − | 0.645914i | \(-0.776476\pi\) | ||||
−0.763410 | + | 0.645914i | \(0.776476\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 27.1319 | 1.06998 | 0.534989 | − | 0.844859i | \(-0.320316\pi\) | ||||
0.534989 | + | 0.844859i | \(0.320316\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −3.95120 | −0.155578 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 1.46110 | 0.0574419 | 0.0287209 | − | 0.999587i | \(-0.490857\pi\) | ||||
0.0287209 | + | 0.999587i | \(0.490857\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −16.6586 | −0.653907 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −42.1784 | −1.65310 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −22.2501 | −0.870714 | −0.435357 | − | 0.900258i | \(-0.643378\pi\) | ||||
−0.435357 | + | 0.900258i | \(0.643378\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 9.79876 | 0.382869 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −16.7383 | −0.653025 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −32.1491 | −1.25235 | −0.626176 | − | 0.779682i | \(-0.715381\pi\) | ||||
−0.626176 | + | 0.779682i | \(0.715381\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −43.9293 | −1.70865 | −0.854326 | − | 0.519738i | \(-0.826030\pi\) | ||||
−0.854326 | + | 0.519738i | \(0.826030\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −21.8948 | −0.850325 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 52.9808 | 2.05451 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −0.354884 | −0.0137412 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −33.1018 | −1.27979 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 1.43163 | 0.0552676 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 38.8748 | 1.49851 | 0.749257 | − | 0.662279i | \(-0.230411\pi\) | ||||
0.749257 | + | 0.662279i | \(0.230411\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −42.8208 | −1.64817 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 0.347985 | 0.0133742 | 0.00668708 | − | 0.999978i | \(-0.497871\pi\) | ||||
0.00668708 | + | 0.999978i | \(0.497871\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −57.4188 | −2.20353 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −7.78983 | −0.298507 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 1.74287 | 0.0666891 | 0.0333445 | − | 0.999444i | \(-0.489384\pi\) | ||||
0.0333445 | + | 0.999444i | \(0.489384\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −0.136663 | −0.00522163 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 3.00167 | 0.114521 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −1.32048 | −0.0503064 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −11.7853 | −0.448335 | −0.224168 | − | 0.974551i | \(-0.571966\pi\) | ||||
−0.224168 | + | 0.974551i | \(0.571966\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −4.62171 | −0.175564 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 2.22909 | 0.0845541 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −31.3839 | −1.18875 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 10.5118 | 0.397593 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 33.1814 | 1.25325 | 0.626623 | − | 0.779323i | \(-0.284437\pi\) | ||||
0.626623 | + | 0.779323i | \(0.284437\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −10.9758 | −0.413961 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −53.3830 | −2.01052 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −37.6456 | −1.41581 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 45.6003 | 1.71255 | 0.856277 | − | 0.516516i | \(-0.172771\pi\) | ||||
0.856277 | + | 0.516516i | \(0.172771\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 9.15757 | 0.343436 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −15.4082 | −0.577040 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −9.18521 | −0.343507 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −3.75191 | −0.140118 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 22.6657 | 0.845288 | 0.422644 | − | 0.906296i | \(-0.361102\pi\) | ||||
0.422644 | + | 0.906296i | \(0.361102\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 14.6008 | 0.543762 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −10.4832 | −0.389875 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 1.57603 | 0.0585323 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −11.2007 | −0.415410 | −0.207705 | − | 0.978191i | \(-0.566599\pi\) | ||||
−0.207705 | + | 0.978191i | \(0.566599\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 28.6269 | 1.06026 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 6.32888 | 0.234082 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 43.9473 | 1.62323 | 0.811615 | − | 0.584193i | \(-0.198589\pi\) | ||||
0.811615 | + | 0.584193i | \(0.198589\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −20.8224 | −0.768044 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 18.5568 | 0.683549 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 37.1650 | 1.36714 | 0.683569 | − | 0.729886i | \(-0.260427\pi\) | ||||
0.683569 | + | 0.729886i | \(0.260427\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −12.3418 | −0.453389 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 3.57194 | 0.131042 | 0.0655208 | − | 0.997851i | \(-0.479129\pi\) | ||||
0.0655208 | + | 0.997851i | \(0.479129\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 40.2931 | 1.47623 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −13.8822 | −0.507923 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 12.2039 | 0.445919 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −49.2531 | −1.79727 | −0.898636 | − | 0.438695i | \(-0.855441\pi\) | ||||
−0.898636 | + | 0.438695i | \(0.855441\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −1.39383 | −0.0507940 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −51.6959 | −1.88141 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 5.68995 | 0.206805 | 0.103402 | − | 0.994640i | \(-0.467027\pi\) | ||||
0.103402 | + | 0.994640i | \(0.467027\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 3.10250 | 0.112614 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −13.0205 | −0.471993 | −0.235997 | − | 0.971754i | \(-0.575835\pi\) | ||||
−0.235997 | + | 0.971754i | \(0.575835\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −25.0185 | −0.905732 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 29.6747 | 1.07289 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −25.3217 | −0.914315 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 52.3974 | 1.88950 | 0.944749 | − | 0.327793i | \(-0.106305\pi\) | ||||
0.944749 | + | 0.327793i | \(0.106305\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −2.86704 | −0.103254 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 35.0533 | 1.26078 | 0.630389 | − | 0.776279i | \(-0.282895\pi\) | ||||
0.630389 | + | 0.776279i | \(0.282895\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 68.4272 | 2.45798 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 11.4806 | 0.411863 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −17.6907 | −0.633835 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 4.49276 | 0.160764 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −1.17704 | −0.0420639 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −38.0027 | −1.35638 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −29.7824 | −1.06163 | −0.530814 | − | 0.847489i | \(-0.678114\pi\) | ||||
−0.530814 | + | 0.847489i | \(0.678114\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 18.0984 | 0.644322 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 1.15817 | 0.0411796 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 2.17614 | 0.0772770 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −3.28871 | −0.116639 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 17.9195 | 0.634742 | 0.317371 | − | 0.948301i | \(-0.397200\pi\) | ||||
0.317371 | + | 0.948301i | \(0.397200\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 85.5068 | 3.02501 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 1.81704 | 0.0642018 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −20.6684 | −0.729371 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −20.2444 | −0.713522 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 35.8208 | 1.26095 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 19.1408 | 0.672954 | 0.336477 | − | 0.941692i | \(-0.390765\pi\) | ||||
0.336477 | + | 0.941692i | \(0.390765\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −40.8997 | −1.43618 | −0.718091 | − | 0.695949i | \(-0.754984\pi\) | ||||
−0.718091 | + | 0.695949i | \(0.754984\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 17.7107 | 0.621140 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 42.6008 | 1.49224 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 3.56751 | 0.124811 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −7.02519 | −0.245480 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 10.4630 | 0.365160 | 0.182580 | − | 0.983191i | \(-0.441555\pi\) | ||||
0.182580 | + | 0.983191i | \(0.441555\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −41.3018 | −1.43969 | −0.719846 | − | 0.694134i | \(-0.755787\pi\) | ||||
−0.719846 | + | 0.694134i | \(0.755787\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −13.7781 | −0.479692 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 29.3280 | 1.01983 | 0.509917 | − | 0.860224i | \(-0.329676\pi\) | ||||
0.509917 | + | 0.860224i | \(0.329676\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 30.6086 | 1.06308 | 0.531540 | − | 0.847033i | \(-0.321614\pi\) | ||||
0.531540 | + | 0.847033i | \(0.321614\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 27.6922 | 0.960633 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 33.3524 | 1.15559 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 19.4033 | 0.671479 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −51.1039 | −1.76641 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 1.83313 | 0.0632867 | 0.0316434 | − | 0.999499i | \(-0.489926\pi\) | ||||
0.0316434 | + | 0.999499i | \(0.489926\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −28.9567 | −0.998506 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 42.9993 | 1.48098 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 32.1324 | 1.10539 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 31.1280 | 1.06957 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −16.6408 | −0.571112 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 4.19396 | 0.143767 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 11.8480 | 0.405669 | 0.202835 | − | 0.979213i | \(-0.434985\pi\) | ||||
0.202835 | + | 0.979213i | \(0.434985\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 16.7273 | 0.572060 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 17.1219 | 0.584873 | 0.292436 | − | 0.956285i | \(-0.405534\pi\) | ||||
0.292436 | + | 0.956285i | \(0.405534\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −24.0843 | −0.821745 | −0.410873 | − | 0.911693i | \(-0.634776\pi\) | ||||
−0.410873 | + | 0.911693i | \(0.634776\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 18.5042 | 0.630623 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 27.6792 | 0.942211 | 0.471106 | − | 0.882077i | \(-0.343855\pi\) | ||||
0.471106 | + | 0.882077i | \(0.343855\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 9.23662 | 0.314054 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 63.6487 | 2.16162 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 11.3077 | 0.383587 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 28.2071 | 0.955761 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −18.1284 | −0.613555 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 30.5388 | 1.03240 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −6.95777 | −0.234947 | −0.117474 | − | 0.993076i | \(-0.537480\pi\) | ||||
−0.117474 | + | 0.993076i | \(0.537480\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −14.0040 | −0.472344 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 8.74633 | 0.294671 | 0.147336 | − | 0.989087i | \(-0.452930\pi\) | ||||
0.147336 | + | 0.989087i | \(0.452930\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 12.9680 | 0.436407 | 0.218203 | − | 0.975903i | \(-0.429980\pi\) | ||||
0.218203 | + | 0.975903i | \(0.429980\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −63.0647 | −2.11990 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 42.5491 | 1.42866 | 0.714330 | − | 0.699810i | \(-0.246732\pi\) | ||||
0.714330 | + | 0.699810i | \(0.246732\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 8.94437 | 0.299985 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 6.14945 | 0.206014 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 48.1991 | 1.61292 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −35.3051 | −1.18012 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 4.71593 | 0.157460 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 1.88089 | 0.0627313 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 5.26774 | 0.175494 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −3.73157 | −0.124179 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 37.1810 | 1.23594 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −12.5298 | −0.416044 | −0.208022 | − | 0.978124i | \(-0.566703\pi\) | ||||
−0.208022 | + | 0.978124i | \(0.566703\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −11.8856 | −0.394220 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 6.34964 | 0.210373 | 0.105187 | − | 0.994453i | \(-0.466456\pi\) | ||||
0.105187 | + | 0.994453i | \(0.466456\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −17.1416 | −0.567304 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 5.41976 | 0.179172 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 9.25408 | 0.305597 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 2.92243 | 0.0964020 | 0.0482010 | − | 0.998838i | \(-0.484651\pi\) | ||||
0.0482010 | + | 0.998838i | \(0.484651\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −35.0312 | −1.15432 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 6.82918 | 0.224785 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −18.6252 | −0.612394 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 4.60980 | 0.151406 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 28.8491 | 0.946509 | 0.473254 | − | 0.880926i | \(-0.343079\pi\) | ||||
0.473254 | + | 0.880926i | \(0.343079\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 18.8004 | 0.616157 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 32.5878 | 1.06688 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 36.6420 | 1.19832 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 21.5329 | 0.703448 | 0.351724 | − | 0.936104i | \(-0.385595\pi\) | ||||
0.351724 | + | 0.936104i | \(0.385595\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 45.7922 | 1.49437 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −34.9091 | −1.13800 | −0.569001 | − | 0.822337i | \(-0.692670\pi\) | ||||
−0.569001 | + | 0.822337i | \(0.692670\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 6.75978 | 0.220129 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −67.1443 | −2.18420 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 16.5194 | 0.536807 | 0.268404 | − | 0.963307i | \(-0.413504\pi\) | ||||
0.268404 | + | 0.963307i | \(0.413504\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −31.4168 | −1.01983 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 10.7140 | 0.347425 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 14.2567 | 0.461820 | 0.230910 | − | 0.972975i | \(-0.425830\pi\) | ||||
0.230910 | + | 0.972975i | \(0.425830\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −15.9963 | −0.517629 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −0.378726 | −0.0122425 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −0.129066 | −0.00416777 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 50.6636 | 1.63431 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 3.85304 | 0.124162 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −81.1241 | −2.61148 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −0.743063 | −0.0238953 | −0.0119476 | − | 0.999929i | \(-0.503803\pi\) | ||||
−0.0119476 | + | 0.999929i | \(0.503803\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 49.2346 | 1.58164 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −57.8801 | −1.85746 | −0.928730 | − | 0.370757i | \(-0.879098\pi\) | ||||
−0.928730 | + | 0.370757i | \(0.879098\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 2.10518 | 0.0674890 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −20.9433 | −0.670722 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 34.4797 | 1.10310 | 0.551552 | − | 0.834140i | \(-0.314036\pi\) | ||||
0.551552 | + | 0.834140i | \(0.314036\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 2.24366 | 0.0717077 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −7.89892 | −0.252193 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −24.6634 | −0.786641 | −0.393320 | − | 0.919401i | \(-0.628674\pi\) | ||||
−0.393320 | + | 0.919401i | \(0.628674\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −83.6848 | −2.66642 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −50.4156 | −1.60475 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −1.36318 | −0.0433465 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 40.7214 | 1.29356 | 0.646779 | − | 0.762677i | \(-0.276115\pi\) | ||||
0.646779 | + | 0.762677i | \(0.276115\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −5.04623 | −0.160137 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 34.5430 | 1.09509 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −29.7702 | −0.942833 | −0.471417 | − | 0.881911i | \(-0.656257\pi\) | ||||
−0.471417 | + | 0.881911i | \(0.656257\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 13.9100 | 0.440093 |
(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 | 2008.2.a.d.1.15 | ✓ | 23 | |
4.3 | odd | 2 | 4016.2.a.m.1.9 | 23 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2008.2.a.d.1.15 | ✓ | 23 | 1.1 | even | 1 | trivial | |
4016.2.a.m.1.9 | 23 | 4.3 | odd | 2 |