Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6014,2,Mod(1,6014)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6014, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("6014.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6014 = 2 \cdot 31 \cdot 97 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6014.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: | \(48.0220317756\) |
Analytic rank: | \(0\) |
Dimension: | \(38\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.15 | ||
Character | \(\chi\) | \(=\) | 6014.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | −1.26563 | −0.730715 | −0.365357 | − | 0.930867i | \(-0.619053\pi\) | ||||
−0.365357 | + | 0.930867i | \(0.619053\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 1.94989 | 0.872019 | 0.436009 | − | 0.899942i | \(-0.356391\pi\) | ||||
0.436009 | + | 0.899942i | \(0.356391\pi\) | |||||||
\(6\) | 1.26563 | 0.516693 | ||||||||
\(7\) | −2.66768 | −1.00829 | −0.504145 | − | 0.863619i | \(-0.668192\pi\) | ||||
−0.504145 | + | 0.863619i | \(0.668192\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | −1.39817 | −0.466056 | ||||||||
\(10\) | −1.94989 | −0.616610 | ||||||||
\(11\) | −5.22737 | −1.57611 | −0.788056 | − | 0.615603i | \(-0.788912\pi\) | ||||
−0.788056 | + | 0.615603i | \(0.788912\pi\) | |||||||
\(12\) | −1.26563 | −0.365357 | ||||||||
\(13\) | −3.09749 | −0.859089 | −0.429545 | − | 0.903046i | \(-0.641326\pi\) | ||||
−0.429545 | + | 0.903046i | \(0.641326\pi\) | |||||||
\(14\) | 2.66768 | 0.712968 | ||||||||
\(15\) | −2.46785 | −0.637197 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 2.37272 | 0.575469 | 0.287735 | − | 0.957710i | \(-0.407098\pi\) | ||||
0.287735 | + | 0.957710i | \(0.407098\pi\) | |||||||
\(18\) | 1.39817 | 0.329552 | ||||||||
\(19\) | 5.22260 | 1.19815 | 0.599074 | − | 0.800694i | \(-0.295536\pi\) | ||||
0.599074 | + | 0.800694i | \(0.295536\pi\) | |||||||
\(20\) | 1.94989 | 0.436009 | ||||||||
\(21\) | 3.37631 | 0.736772 | ||||||||
\(22\) | 5.22737 | 1.11448 | ||||||||
\(23\) | −6.75349 | −1.40820 | −0.704100 | − | 0.710101i | \(-0.748649\pi\) | ||||
−0.704100 | + | 0.710101i | \(0.748649\pi\) | |||||||
\(24\) | 1.26563 | 0.258347 | ||||||||
\(25\) | −1.19791 | −0.239583 | ||||||||
\(26\) | 3.09749 | 0.607468 | ||||||||
\(27\) | 5.56648 | 1.07127 | ||||||||
\(28\) | −2.66768 | −0.504145 | ||||||||
\(29\) | 9.08445 | 1.68694 | 0.843470 | − | 0.537176i | \(-0.180509\pi\) | ||||
0.843470 | + | 0.537176i | \(0.180509\pi\) | |||||||
\(30\) | 2.46785 | 0.450566 | ||||||||
\(31\) | 1.00000 | 0.179605 | ||||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 6.61594 | 1.15169 | ||||||||
\(34\) | −2.37272 | −0.406918 | ||||||||
\(35\) | −5.20170 | −0.879248 | ||||||||
\(36\) | −1.39817 | −0.233028 | ||||||||
\(37\) | −4.41612 | −0.726006 | −0.363003 | − | 0.931788i | \(-0.618248\pi\) | ||||
−0.363003 | + | 0.931788i | \(0.618248\pi\) | |||||||
\(38\) | −5.22260 | −0.847218 | ||||||||
\(39\) | 3.92029 | 0.627749 | ||||||||
\(40\) | −1.94989 | −0.308305 | ||||||||
\(41\) | 7.40463 | 1.15641 | 0.578204 | − | 0.815892i | \(-0.303754\pi\) | ||||
0.578204 | + | 0.815892i | \(0.303754\pi\) | |||||||
\(42\) | −3.37631 | −0.520976 | ||||||||
\(43\) | −11.3820 | −1.73574 | −0.867869 | − | 0.496794i | \(-0.834511\pi\) | ||||
−0.867869 | + | 0.496794i | \(0.834511\pi\) | |||||||
\(44\) | −5.22737 | −0.788056 | ||||||||
\(45\) | −2.72628 | −0.406410 | ||||||||
\(46\) | 6.75349 | 0.995748 | ||||||||
\(47\) | −10.4992 | −1.53146 | −0.765729 | − | 0.643163i | \(-0.777622\pi\) | ||||
−0.765729 | + | 0.643163i | \(0.777622\pi\) | |||||||
\(48\) | −1.26563 | −0.182679 | ||||||||
\(49\) | 0.116534 | 0.0166477 | ||||||||
\(50\) | 1.19791 | 0.169411 | ||||||||
\(51\) | −3.00300 | −0.420504 | ||||||||
\(52\) | −3.09749 | −0.429545 | ||||||||
\(53\) | −9.41301 | −1.29298 | −0.646488 | − | 0.762924i | \(-0.723763\pi\) | ||||
−0.646488 | + | 0.762924i | \(0.723763\pi\) | |||||||
\(54\) | −5.56648 | −0.757501 | ||||||||
\(55\) | −10.1928 | −1.37440 | ||||||||
\(56\) | 2.66768 | 0.356484 | ||||||||
\(57\) | −6.60991 | −0.875504 | ||||||||
\(58\) | −9.08445 | −1.19285 | ||||||||
\(59\) | −14.1437 | −1.84135 | −0.920675 | − | 0.390330i | \(-0.872361\pi\) | ||||
−0.920675 | + | 0.390330i | \(0.872361\pi\) | |||||||
\(60\) | −2.46785 | −0.318598 | ||||||||
\(61\) | 1.37878 | 0.176535 | 0.0882674 | − | 0.996097i | \(-0.471867\pi\) | ||||
0.0882674 | + | 0.996097i | \(0.471867\pi\) | |||||||
\(62\) | −1.00000 | −0.127000 | ||||||||
\(63\) | 3.72987 | 0.469920 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −6.03978 | −0.749142 | ||||||||
\(66\) | −6.61594 | −0.814366 | ||||||||
\(67\) | −5.35993 | −0.654819 | −0.327410 | − | 0.944883i | \(-0.606176\pi\) | ||||
−0.327410 | + | 0.944883i | \(0.606176\pi\) | |||||||
\(68\) | 2.37272 | 0.287735 | ||||||||
\(69\) | 8.54745 | 1.02899 | ||||||||
\(70\) | 5.20170 | 0.621722 | ||||||||
\(71\) | −5.76766 | −0.684495 | −0.342248 | − | 0.939610i | \(-0.611188\pi\) | ||||
−0.342248 | + | 0.939610i | \(0.611188\pi\) | |||||||
\(72\) | 1.39817 | 0.164776 | ||||||||
\(73\) | −3.88527 | −0.454737 | −0.227368 | − | 0.973809i | \(-0.573012\pi\) | ||||
−0.227368 | + | 0.973809i | \(0.573012\pi\) | |||||||
\(74\) | 4.41612 | 0.513363 | ||||||||
\(75\) | 1.51612 | 0.175067 | ||||||||
\(76\) | 5.22260 | 0.599074 | ||||||||
\(77\) | 13.9450 | 1.58918 | ||||||||
\(78\) | −3.92029 | −0.443886 | ||||||||
\(79\) | 7.72257 | 0.868857 | 0.434429 | − | 0.900706i | \(-0.356950\pi\) | ||||
0.434429 | + | 0.900706i | \(0.356950\pi\) | |||||||
\(80\) | 1.94989 | 0.218005 | ||||||||
\(81\) | −2.85062 | −0.316735 | ||||||||
\(82\) | −7.40463 | −0.817704 | ||||||||
\(83\) | 10.7802 | 1.18329 | 0.591643 | − | 0.806200i | \(-0.298480\pi\) | ||||
0.591643 | + | 0.806200i | \(0.298480\pi\) | |||||||
\(84\) | 3.37631 | 0.368386 | ||||||||
\(85\) | 4.62655 | 0.501820 | ||||||||
\(86\) | 11.3820 | 1.22735 | ||||||||
\(87\) | −11.4976 | −1.23267 | ||||||||
\(88\) | 5.22737 | 0.557240 | ||||||||
\(89\) | −10.1291 | −1.07369 | −0.536843 | − | 0.843682i | \(-0.680383\pi\) | ||||
−0.536843 | + | 0.843682i | \(0.680383\pi\) | |||||||
\(90\) | 2.72628 | 0.287375 | ||||||||
\(91\) | 8.26312 | 0.866211 | ||||||||
\(92\) | −6.75349 | −0.704100 | ||||||||
\(93\) | −1.26563 | −0.131240 | ||||||||
\(94\) | 10.4992 | 1.08290 | ||||||||
\(95\) | 10.1835 | 1.04481 | ||||||||
\(96\) | 1.26563 | 0.129173 | ||||||||
\(97\) | −1.00000 | −0.101535 | ||||||||
\(98\) | −0.116534 | −0.0117717 | ||||||||
\(99\) | 7.30875 | 0.734557 | ||||||||
\(100\) | −1.19791 | −0.119791 | ||||||||
\(101\) | 13.1008 | 1.30358 | 0.651789 | − | 0.758401i | \(-0.274019\pi\) | ||||
0.651789 | + | 0.758401i | \(0.274019\pi\) | |||||||
\(102\) | 3.00300 | 0.297341 | ||||||||
\(103\) | 5.85042 | 0.576459 | 0.288229 | − | 0.957561i | \(-0.406933\pi\) | ||||
0.288229 | + | 0.957561i | \(0.406933\pi\) | |||||||
\(104\) | 3.09749 | 0.303734 | ||||||||
\(105\) | 6.58345 | 0.642479 | ||||||||
\(106\) | 9.41301 | 0.914273 | ||||||||
\(107\) | 5.93015 | 0.573289 | 0.286645 | − | 0.958037i | \(-0.407460\pi\) | ||||
0.286645 | + | 0.958037i | \(0.407460\pi\) | |||||||
\(108\) | 5.56648 | 0.535634 | ||||||||
\(109\) | 14.7868 | 1.41632 | 0.708160 | − | 0.706052i | \(-0.249526\pi\) | ||||
0.708160 | + | 0.706052i | \(0.249526\pi\) | |||||||
\(110\) | 10.1928 | 0.971847 | ||||||||
\(111\) | 5.58919 | 0.530503 | ||||||||
\(112\) | −2.66768 | −0.252072 | ||||||||
\(113\) | 5.76413 | 0.542244 | 0.271122 | − | 0.962545i | \(-0.412605\pi\) | ||||
0.271122 | + | 0.962545i | \(0.412605\pi\) | |||||||
\(114\) | 6.60991 | 0.619075 | ||||||||
\(115\) | −13.1686 | −1.22798 | ||||||||
\(116\) | 9.08445 | 0.843470 | ||||||||
\(117\) | 4.33082 | 0.400384 | ||||||||
\(118\) | 14.1437 | 1.30203 | ||||||||
\(119\) | −6.32967 | −0.580240 | ||||||||
\(120\) | 2.46785 | 0.225283 | ||||||||
\(121\) | 16.3254 | 1.48413 | ||||||||
\(122\) | −1.37878 | −0.124829 | ||||||||
\(123\) | −9.37155 | −0.845005 | ||||||||
\(124\) | 1.00000 | 0.0898027 | ||||||||
\(125\) | −12.0853 | −1.08094 | ||||||||
\(126\) | −3.72987 | −0.332283 | ||||||||
\(127\) | −9.18792 | −0.815296 | −0.407648 | − | 0.913139i | \(-0.633651\pi\) | ||||
−0.407648 | + | 0.913139i | \(0.633651\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | 14.4054 | 1.26833 | ||||||||
\(130\) | 6.03978 | 0.529724 | ||||||||
\(131\) | −5.96717 | −0.521354 | −0.260677 | − | 0.965426i | \(-0.583946\pi\) | ||||
−0.260677 | + | 0.965426i | \(0.583946\pi\) | |||||||
\(132\) | 6.61594 | 0.575844 | ||||||||
\(133\) | −13.9323 | −1.20808 | ||||||||
\(134\) | 5.35993 | 0.463027 | ||||||||
\(135\) | 10.8540 | 0.934167 | ||||||||
\(136\) | −2.37272 | −0.203459 | ||||||||
\(137\) | −8.95303 | −0.764909 | −0.382454 | − | 0.923974i | \(-0.624921\pi\) | ||||
−0.382454 | + | 0.923974i | \(0.624921\pi\) | |||||||
\(138\) | −8.54745 | −0.727608 | ||||||||
\(139\) | −11.4499 | −0.971166 | −0.485583 | − | 0.874191i | \(-0.661393\pi\) | ||||
−0.485583 | + | 0.874191i | \(0.661393\pi\) | |||||||
\(140\) | −5.20170 | −0.439624 | ||||||||
\(141\) | 13.2881 | 1.11906 | ||||||||
\(142\) | 5.76766 | 0.484011 | ||||||||
\(143\) | 16.1917 | 1.35402 | ||||||||
\(144\) | −1.39817 | −0.116514 | ||||||||
\(145\) | 17.7137 | 1.47104 | ||||||||
\(146\) | 3.88527 | 0.321547 | ||||||||
\(147\) | −0.147489 | −0.0121647 | ||||||||
\(148\) | −4.41612 | −0.363003 | ||||||||
\(149\) | −1.83408 | −0.150254 | −0.0751269 | − | 0.997174i | \(-0.523936\pi\) | ||||
−0.0751269 | + | 0.997174i | \(0.523936\pi\) | |||||||
\(150\) | −1.51612 | −0.123791 | ||||||||
\(151\) | −11.0204 | −0.896824 | −0.448412 | − | 0.893827i | \(-0.648010\pi\) | ||||
−0.448412 | + | 0.893827i | \(0.648010\pi\) | |||||||
\(152\) | −5.22260 | −0.423609 | ||||||||
\(153\) | −3.31747 | −0.268201 | ||||||||
\(154\) | −13.9450 | −1.12372 | ||||||||
\(155\) | 1.94989 | 0.156619 | ||||||||
\(156\) | 3.92029 | 0.313875 | ||||||||
\(157\) | −7.85364 | −0.626789 | −0.313395 | − | 0.949623i | \(-0.601466\pi\) | ||||
−0.313395 | + | 0.949623i | \(0.601466\pi\) | |||||||
\(158\) | −7.72257 | −0.614375 | ||||||||
\(159\) | 11.9134 | 0.944797 | ||||||||
\(160\) | −1.94989 | −0.154153 | ||||||||
\(161\) | 18.0162 | 1.41987 | ||||||||
\(162\) | 2.85062 | 0.223966 | ||||||||
\(163\) | 13.4381 | 1.05255 | 0.526275 | − | 0.850314i | \(-0.323588\pi\) | ||||
0.526275 | + | 0.850314i | \(0.323588\pi\) | |||||||
\(164\) | 7.40463 | 0.578204 | ||||||||
\(165\) | 12.9004 | 1.00429 | ||||||||
\(166\) | −10.7802 | −0.836709 | ||||||||
\(167\) | 7.11664 | 0.550702 | 0.275351 | − | 0.961344i | \(-0.411206\pi\) | ||||
0.275351 | + | 0.961344i | \(0.411206\pi\) | |||||||
\(168\) | −3.37631 | −0.260488 | ||||||||
\(169\) | −3.40555 | −0.261965 | ||||||||
\(170\) | −4.62655 | −0.354841 | ||||||||
\(171\) | −7.30208 | −0.558404 | ||||||||
\(172\) | −11.3820 | −0.867869 | ||||||||
\(173\) | −3.03986 | −0.231116 | −0.115558 | − | 0.993301i | \(-0.536866\pi\) | ||||
−0.115558 | + | 0.993301i | \(0.536866\pi\) | |||||||
\(174\) | 11.4976 | 0.871630 | ||||||||
\(175\) | 3.19566 | 0.241569 | ||||||||
\(176\) | −5.22737 | −0.394028 | ||||||||
\(177\) | 17.9007 | 1.34550 | ||||||||
\(178\) | 10.1291 | 0.759211 | ||||||||
\(179\) | −11.6031 | −0.867255 | −0.433627 | − | 0.901092i | \(-0.642767\pi\) | ||||
−0.433627 | + | 0.901092i | \(0.642767\pi\) | |||||||
\(180\) | −2.72628 | −0.203205 | ||||||||
\(181\) | 9.58979 | 0.712804 | 0.356402 | − | 0.934333i | \(-0.384003\pi\) | ||||
0.356402 | + | 0.934333i | \(0.384003\pi\) | |||||||
\(182\) | −8.26312 | −0.612504 | ||||||||
\(183\) | −1.74503 | −0.128997 | ||||||||
\(184\) | 6.75349 | 0.497874 | ||||||||
\(185\) | −8.61096 | −0.633091 | ||||||||
\(186\) | 1.26563 | 0.0928008 | ||||||||
\(187\) | −12.4031 | −0.907004 | ||||||||
\(188\) | −10.4992 | −0.765729 | ||||||||
\(189\) | −14.8496 | −1.08015 | ||||||||
\(190\) | −10.1835 | −0.738790 | ||||||||
\(191\) | 12.0863 | 0.874532 | 0.437266 | − | 0.899332i | \(-0.355947\pi\) | ||||
0.437266 | + | 0.899332i | \(0.355947\pi\) | |||||||
\(192\) | −1.26563 | −0.0913393 | ||||||||
\(193\) | 5.49083 | 0.395239 | 0.197619 | − | 0.980279i | \(-0.436679\pi\) | ||||
0.197619 | + | 0.980279i | \(0.436679\pi\) | |||||||
\(194\) | 1.00000 | 0.0717958 | ||||||||
\(195\) | 7.64415 | 0.547409 | ||||||||
\(196\) | 0.116534 | 0.00832383 | ||||||||
\(197\) | 24.2500 | 1.72774 | 0.863869 | − | 0.503716i | \(-0.168034\pi\) | ||||
0.863869 | + | 0.503716i | \(0.168034\pi\) | |||||||
\(198\) | −7.30875 | −0.519410 | ||||||||
\(199\) | 14.0168 | 0.993626 | 0.496813 | − | 0.867857i | \(-0.334503\pi\) | ||||
0.496813 | + | 0.867857i | \(0.334503\pi\) | |||||||
\(200\) | 1.19791 | 0.0847054 | ||||||||
\(201\) | 6.78371 | 0.478486 | ||||||||
\(202\) | −13.1008 | −0.921768 | ||||||||
\(203\) | −24.2344 | −1.70092 | ||||||||
\(204\) | −3.00300 | −0.210252 | ||||||||
\(205\) | 14.4382 | 1.00841 | ||||||||
\(206\) | −5.85042 | −0.407618 | ||||||||
\(207\) | 9.44252 | 0.656301 | ||||||||
\(208\) | −3.09749 | −0.214772 | ||||||||
\(209\) | −27.3005 | −1.88841 | ||||||||
\(210\) | −6.58345 | −0.454301 | ||||||||
\(211\) | 13.2954 | 0.915290 | 0.457645 | − | 0.889135i | \(-0.348693\pi\) | ||||
0.457645 | + | 0.889135i | \(0.348693\pi\) | |||||||
\(212\) | −9.41301 | −0.646488 | ||||||||
\(213\) | 7.29975 | 0.500171 | ||||||||
\(214\) | −5.93015 | −0.405377 | ||||||||
\(215\) | −22.1937 | −1.51360 | ||||||||
\(216\) | −5.56648 | −0.378751 | ||||||||
\(217\) | −2.66768 | −0.181094 | ||||||||
\(218\) | −14.7868 | −1.00149 | ||||||||
\(219\) | 4.91734 | 0.332283 | ||||||||
\(220\) | −10.1928 | −0.687200 | ||||||||
\(221\) | −7.34948 | −0.494380 | ||||||||
\(222\) | −5.58919 | −0.375122 | ||||||||
\(223\) | 11.5547 | 0.773757 | 0.386879 | − | 0.922131i | \(-0.373553\pi\) | ||||
0.386879 | + | 0.922131i | \(0.373553\pi\) | |||||||
\(224\) | 2.66768 | 0.178242 | ||||||||
\(225\) | 1.67489 | 0.111659 | ||||||||
\(226\) | −5.76413 | −0.383424 | ||||||||
\(227\) | 27.7500 | 1.84183 | 0.920915 | − | 0.389764i | \(-0.127443\pi\) | ||||
0.920915 | + | 0.389764i | \(0.127443\pi\) | |||||||
\(228\) | −6.60991 | −0.437752 | ||||||||
\(229\) | −10.3009 | −0.680703 | −0.340351 | − | 0.940298i | \(-0.610546\pi\) | ||||
−0.340351 | + | 0.940298i | \(0.610546\pi\) | |||||||
\(230\) | 13.1686 | 0.868311 | ||||||||
\(231\) | −17.6492 | −1.16123 | ||||||||
\(232\) | −9.08445 | −0.596423 | ||||||||
\(233\) | 11.2048 | 0.734049 | 0.367024 | − | 0.930211i | \(-0.380377\pi\) | ||||
0.367024 | + | 0.930211i | \(0.380377\pi\) | |||||||
\(234\) | −4.33082 | −0.283114 | ||||||||
\(235\) | −20.4722 | −1.33546 | ||||||||
\(236\) | −14.1437 | −0.920675 | ||||||||
\(237\) | −9.77396 | −0.634887 | ||||||||
\(238\) | 6.32967 | 0.410292 | ||||||||
\(239\) | 27.4050 | 1.77268 | 0.886342 | − | 0.463032i | \(-0.153238\pi\) | ||||
0.886342 | + | 0.463032i | \(0.153238\pi\) | |||||||
\(240\) | −2.46785 | −0.159299 | ||||||||
\(241\) | 28.8657 | 1.85940 | 0.929700 | − | 0.368317i | \(-0.120066\pi\) | ||||
0.929700 | + | 0.368317i | \(0.120066\pi\) | |||||||
\(242\) | −16.3254 | −1.04944 | ||||||||
\(243\) | −13.0916 | −0.839826 | ||||||||
\(244\) | 1.37878 | 0.0882674 | ||||||||
\(245\) | 0.227228 | 0.0145171 | ||||||||
\(246\) | 9.37155 | 0.597508 | ||||||||
\(247\) | −16.1770 | −1.02932 | ||||||||
\(248\) | −1.00000 | −0.0635001 | ||||||||
\(249\) | −13.6438 | −0.864644 | ||||||||
\(250\) | 12.0853 | 0.764340 | ||||||||
\(251\) | 18.0563 | 1.13970 | 0.569851 | − | 0.821748i | \(-0.307001\pi\) | ||||
0.569851 | + | 0.821748i | \(0.307001\pi\) | |||||||
\(252\) | 3.72987 | 0.234960 | ||||||||
\(253\) | 35.3030 | 2.21948 | ||||||||
\(254\) | 9.18792 | 0.576501 | ||||||||
\(255\) | −5.85553 | −0.366687 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 20.4236 | 1.27399 | 0.636995 | − | 0.770868i | \(-0.280177\pi\) | ||||
0.636995 | + | 0.770868i | \(0.280177\pi\) | |||||||
\(258\) | −14.4054 | −0.896844 | ||||||||
\(259\) | 11.7808 | 0.732024 | ||||||||
\(260\) | −6.03978 | −0.374571 | ||||||||
\(261\) | −12.7016 | −0.786209 | ||||||||
\(262\) | 5.96717 | 0.368653 | ||||||||
\(263\) | −5.85635 | −0.361118 | −0.180559 | − | 0.983564i | \(-0.557791\pi\) | ||||
−0.180559 | + | 0.983564i | \(0.557791\pi\) | |||||||
\(264\) | −6.61594 | −0.407183 | ||||||||
\(265\) | −18.3544 | −1.12750 | ||||||||
\(266\) | 13.9323 | 0.854241 | ||||||||
\(267\) | 12.8198 | 0.784558 | ||||||||
\(268\) | −5.35993 | −0.327410 | ||||||||
\(269\) | 26.9843 | 1.64526 | 0.822630 | − | 0.568577i | \(-0.192506\pi\) | ||||
0.822630 | + | 0.568577i | \(0.192506\pi\) | |||||||
\(270\) | −10.8540 | −0.660555 | ||||||||
\(271\) | −14.8981 | −0.904992 | −0.452496 | − | 0.891766i | \(-0.649466\pi\) | ||||
−0.452496 | + | 0.891766i | \(0.649466\pi\) | |||||||
\(272\) | 2.37272 | 0.143867 | ||||||||
\(273\) | −10.4581 | −0.632953 | ||||||||
\(274\) | 8.95303 | 0.540872 | ||||||||
\(275\) | 6.26195 | 0.377610 | ||||||||
\(276\) | 8.54745 | 0.514496 | ||||||||
\(277\) | −23.4010 | −1.40603 | −0.703014 | − | 0.711176i | \(-0.748163\pi\) | ||||
−0.703014 | + | 0.711176i | \(0.748163\pi\) | |||||||
\(278\) | 11.4499 | 0.686718 | ||||||||
\(279\) | −1.39817 | −0.0837062 | ||||||||
\(280\) | 5.20170 | 0.310861 | ||||||||
\(281\) | −26.8670 | −1.60275 | −0.801376 | − | 0.598160i | \(-0.795899\pi\) | ||||
−0.801376 | + | 0.598160i | \(0.795899\pi\) | |||||||
\(282\) | −13.2881 | −0.791294 | ||||||||
\(283\) | 19.8041 | 1.17723 | 0.588617 | − | 0.808412i | \(-0.299673\pi\) | ||||
0.588617 | + | 0.808412i | \(0.299673\pi\) | |||||||
\(284\) | −5.76766 | −0.342248 | ||||||||
\(285\) | −12.8886 | −0.763456 | ||||||||
\(286\) | −16.1917 | −0.957438 | ||||||||
\(287\) | −19.7532 | −1.16599 | ||||||||
\(288\) | 1.39817 | 0.0823879 | ||||||||
\(289\) | −11.3702 | −0.668835 | ||||||||
\(290\) | −17.7137 | −1.04018 | ||||||||
\(291\) | 1.26563 | 0.0741928 | ||||||||
\(292\) | −3.88527 | −0.227368 | ||||||||
\(293\) | −0.812185 | −0.0474484 | −0.0237242 | − | 0.999719i | \(-0.507552\pi\) | ||||
−0.0237242 | + | 0.999719i | \(0.507552\pi\) | |||||||
\(294\) | 0.147489 | 0.00860173 | ||||||||
\(295\) | −27.5787 | −1.60569 | ||||||||
\(296\) | 4.41612 | 0.256682 | ||||||||
\(297\) | −29.0980 | −1.68844 | ||||||||
\(298\) | 1.83408 | 0.106246 | ||||||||
\(299\) | 20.9189 | 1.20977 | ||||||||
\(300\) | 1.51612 | 0.0875334 | ||||||||
\(301\) | 30.3635 | 1.75013 | ||||||||
\(302\) | 11.0204 | 0.634150 | ||||||||
\(303\) | −16.5808 | −0.952543 | ||||||||
\(304\) | 5.22260 | 0.299537 | ||||||||
\(305\) | 2.68848 | 0.153942 | ||||||||
\(306\) | 3.31747 | 0.189647 | ||||||||
\(307\) | 25.4624 | 1.45322 | 0.726608 | − | 0.687052i | \(-0.241095\pi\) | ||||
0.726608 | + | 0.687052i | \(0.241095\pi\) | |||||||
\(308\) | 13.9450 | 0.794589 | ||||||||
\(309\) | −7.40449 | −0.421227 | ||||||||
\(310\) | −1.94989 | −0.110747 | ||||||||
\(311\) | −14.3767 | −0.815227 | −0.407614 | − | 0.913154i | \(-0.633639\pi\) | ||||
−0.407614 | + | 0.913154i | \(0.633639\pi\) | |||||||
\(312\) | −3.92029 | −0.221943 | ||||||||
\(313\) | 8.18376 | 0.462573 | 0.231287 | − | 0.972886i | \(-0.425706\pi\) | ||||
0.231287 | + | 0.972886i | \(0.425706\pi\) | |||||||
\(314\) | 7.85364 | 0.443207 | ||||||||
\(315\) | 7.27285 | 0.409779 | ||||||||
\(316\) | 7.72257 | 0.434429 | ||||||||
\(317\) | −28.2390 | −1.58606 | −0.793029 | − | 0.609184i | \(-0.791497\pi\) | ||||
−0.793029 | + | 0.609184i | \(0.791497\pi\) | |||||||
\(318\) | −11.9134 | −0.668072 | ||||||||
\(319\) | −47.4878 | −2.65881 | ||||||||
\(320\) | 1.94989 | 0.109002 | ||||||||
\(321\) | −7.50540 | −0.418911 | ||||||||
\(322\) | −18.0162 | −1.00400 | ||||||||
\(323\) | 12.3918 | 0.689497 | ||||||||
\(324\) | −2.85062 | −0.158368 | ||||||||
\(325\) | 3.71053 | 0.205823 | ||||||||
\(326\) | −13.4381 | −0.744265 | ||||||||
\(327\) | −18.7147 | −1.03493 | ||||||||
\(328\) | −7.40463 | −0.408852 | ||||||||
\(329\) | 28.0084 | 1.54415 | ||||||||
\(330\) | −12.9004 | −0.710143 | ||||||||
\(331\) | 31.6846 | 1.74154 | 0.870772 | − | 0.491686i | \(-0.163619\pi\) | ||||
0.870772 | + | 0.491686i | \(0.163619\pi\) | |||||||
\(332\) | 10.7802 | 0.591643 | ||||||||
\(333\) | 6.17448 | 0.338359 | ||||||||
\(334\) | −7.11664 | −0.389405 | ||||||||
\(335\) | −10.4513 | −0.571015 | ||||||||
\(336\) | 3.37631 | 0.184193 | ||||||||
\(337\) | 15.5577 | 0.847481 | 0.423741 | − | 0.905784i | \(-0.360717\pi\) | ||||
0.423741 | + | 0.905784i | \(0.360717\pi\) | |||||||
\(338\) | 3.40555 | 0.185237 | ||||||||
\(339\) | −7.29529 | −0.396226 | ||||||||
\(340\) | 4.62655 | 0.250910 | ||||||||
\(341\) | −5.22737 | −0.283078 | ||||||||
\(342\) | 7.30208 | 0.394851 | ||||||||
\(343\) | 18.3629 | 0.991504 | ||||||||
\(344\) | 11.3820 | 0.613676 | ||||||||
\(345\) | 16.6666 | 0.897301 | ||||||||
\(346\) | 3.03986 | 0.163424 | ||||||||
\(347\) | −17.8940 | −0.960599 | −0.480300 | − | 0.877104i | \(-0.659472\pi\) | ||||
−0.480300 | + | 0.877104i | \(0.659472\pi\) | |||||||
\(348\) | −11.4976 | −0.616336 | ||||||||
\(349\) | −25.4040 | −1.35984 | −0.679921 | − | 0.733285i | \(-0.737986\pi\) | ||||
−0.679921 | + | 0.733285i | \(0.737986\pi\) | |||||||
\(350\) | −3.19566 | −0.170815 | ||||||||
\(351\) | −17.2421 | −0.920316 | ||||||||
\(352\) | 5.22737 | 0.278620 | ||||||||
\(353\) | 0.0373432 | 0.00198758 | 0.000993789 | − | 1.00000i | \(-0.499684\pi\) | ||||
0.000993789 | 1.00000i | \(0.499684\pi\) | ||||||||
\(354\) | −17.9007 | −0.951413 | ||||||||
\(355\) | −11.2463 | −0.596893 | ||||||||
\(356\) | −10.1291 | −0.536843 | ||||||||
\(357\) | 8.01105 | 0.423990 | ||||||||
\(358\) | 11.6031 | 0.613242 | ||||||||
\(359\) | 7.83321 | 0.413421 | 0.206711 | − | 0.978402i | \(-0.433724\pi\) | ||||
0.206711 | + | 0.978402i | \(0.433724\pi\) | |||||||
\(360\) | 2.72628 | 0.143688 | ||||||||
\(361\) | 8.27559 | 0.435557 | ||||||||
\(362\) | −9.58979 | −0.504028 | ||||||||
\(363\) | −20.6620 | −1.08447 | ||||||||
\(364\) | 8.26312 | 0.433105 | ||||||||
\(365\) | −7.57587 | −0.396539 | ||||||||
\(366\) | 1.74503 | 0.0912143 | ||||||||
\(367\) | −26.3646 | −1.37622 | −0.688109 | − | 0.725607i | \(-0.741559\pi\) | ||||
−0.688109 | + | 0.725607i | \(0.741559\pi\) | |||||||
\(368\) | −6.75349 | −0.352050 | ||||||||
\(369\) | −10.3529 | −0.538951 | ||||||||
\(370\) | 8.61096 | 0.447663 | ||||||||
\(371\) | 25.1109 | 1.30370 | ||||||||
\(372\) | −1.26563 | −0.0656201 | ||||||||
\(373\) | 27.5033 | 1.42407 | 0.712035 | − | 0.702144i | \(-0.247774\pi\) | ||||
0.712035 | + | 0.702144i | \(0.247774\pi\) | |||||||
\(374\) | 12.4031 | 0.641349 | ||||||||
\(375\) | 15.2955 | 0.789858 | ||||||||
\(376\) | 10.4992 | 0.541452 | ||||||||
\(377\) | −28.1390 | −1.44923 | ||||||||
\(378\) | 14.8496 | 0.763781 | ||||||||
\(379\) | 17.1114 | 0.878952 | 0.439476 | − | 0.898254i | \(-0.355164\pi\) | ||||
0.439476 | + | 0.898254i | \(0.355164\pi\) | |||||||
\(380\) | 10.1835 | 0.522404 | ||||||||
\(381\) | 11.6285 | 0.595749 | ||||||||
\(382\) | −12.0863 | −0.618388 | ||||||||
\(383\) | −24.0296 | −1.22786 | −0.613928 | − | 0.789362i | \(-0.710411\pi\) | ||||
−0.613928 | + | 0.789362i | \(0.710411\pi\) | |||||||
\(384\) | 1.26563 | 0.0645867 | ||||||||
\(385\) | 27.1912 | 1.38579 | ||||||||
\(386\) | −5.49083 | −0.279476 | ||||||||
\(387\) | 15.9139 | 0.808951 | ||||||||
\(388\) | −1.00000 | −0.0507673 | ||||||||
\(389\) | −25.9380 | −1.31511 | −0.657554 | − | 0.753407i | \(-0.728409\pi\) | ||||
−0.657554 | + | 0.753407i | \(0.728409\pi\) | |||||||
\(390\) | −7.64415 | −0.387077 | ||||||||
\(391\) | −16.0242 | −0.810376 | ||||||||
\(392\) | −0.116534 | −0.00588584 | ||||||||
\(393\) | 7.55226 | 0.380961 | ||||||||
\(394\) | −24.2500 | −1.22170 | ||||||||
\(395\) | 15.0582 | 0.757660 | ||||||||
\(396\) | 7.30875 | 0.367278 | ||||||||
\(397\) | 19.8959 | 0.998548 | 0.499274 | − | 0.866444i | \(-0.333600\pi\) | ||||
0.499274 | + | 0.866444i | \(0.333600\pi\) | |||||||
\(398\) | −14.0168 | −0.702600 | ||||||||
\(399\) | 17.6331 | 0.882761 | ||||||||
\(400\) | −1.19791 | −0.0598957 | ||||||||
\(401\) | 13.3050 | 0.664418 | 0.332209 | − | 0.943206i | \(-0.392206\pi\) | ||||
0.332209 | + | 0.943206i | \(0.392206\pi\) | |||||||
\(402\) | −6.78371 | −0.338341 | ||||||||
\(403\) | −3.09749 | −0.154297 | ||||||||
\(404\) | 13.1008 | 0.651789 | ||||||||
\(405\) | −5.55840 | −0.276199 | ||||||||
\(406\) | 24.2344 | 1.20273 | ||||||||
\(407\) | 23.0847 | 1.14427 | ||||||||
\(408\) | 3.00300 | 0.148671 | ||||||||
\(409\) | −2.21626 | −0.109587 | −0.0547936 | − | 0.998498i | \(-0.517450\pi\) | ||||
−0.0547936 | + | 0.998498i | \(0.517450\pi\) | |||||||
\(410\) | −14.4382 | −0.713054 | ||||||||
\(411\) | 11.3313 | 0.558930 | ||||||||
\(412\) | 5.85042 | 0.288229 | ||||||||
\(413\) | 37.7308 | 1.85661 | ||||||||
\(414\) | −9.44252 | −0.464075 | ||||||||
\(415\) | 21.0203 | 1.03185 | ||||||||
\(416\) | 3.09749 | 0.151867 | ||||||||
\(417\) | 14.4914 | 0.709645 | ||||||||
\(418\) | 27.3005 | 1.33531 | ||||||||
\(419\) | 0.277866 | 0.0135746 | 0.00678732 | − | 0.999977i | \(-0.497840\pi\) | ||||
0.00678732 | + | 0.999977i | \(0.497840\pi\) | |||||||
\(420\) | 6.58345 | 0.321239 | ||||||||
\(421\) | 31.4285 | 1.53173 | 0.765865 | − | 0.643001i | \(-0.222311\pi\) | ||||
0.765865 | + | 0.643001i | \(0.222311\pi\) | |||||||
\(422\) | −13.2954 | −0.647208 | ||||||||
\(423\) | 14.6796 | 0.713746 | ||||||||
\(424\) | 9.41301 | 0.457136 | ||||||||
\(425\) | −2.84232 | −0.137873 | ||||||||
\(426\) | −7.29975 | −0.353674 | ||||||||
\(427\) | −3.67815 | −0.177998 | ||||||||
\(428\) | 5.93015 | 0.286645 | ||||||||
\(429\) | −20.4928 | −0.989403 | ||||||||
\(430\) | 22.1937 | 1.07027 | ||||||||
\(431\) | 34.0903 | 1.64207 | 0.821035 | − | 0.570877i | \(-0.193397\pi\) | ||||
0.821035 | + | 0.570877i | \(0.193397\pi\) | |||||||
\(432\) | 5.56648 | 0.267817 | ||||||||
\(433\) | 36.9809 | 1.77719 | 0.888594 | − | 0.458695i | \(-0.151683\pi\) | ||||
0.888594 | + | 0.458695i | \(0.151683\pi\) | |||||||
\(434\) | 2.66768 | 0.128053 | ||||||||
\(435\) | −22.4191 | −1.07491 | ||||||||
\(436\) | 14.7868 | 0.708160 | ||||||||
\(437\) | −35.2708 | −1.68723 | ||||||||
\(438\) | −4.91734 | −0.234959 | ||||||||
\(439\) | −1.85530 | −0.0885488 | −0.0442744 | − | 0.999019i | \(-0.514098\pi\) | ||||
−0.0442744 | + | 0.999019i | \(0.514098\pi\) | |||||||
\(440\) | 10.1928 | 0.485924 | ||||||||
\(441\) | −0.162934 | −0.00775875 | ||||||||
\(442\) | 7.34948 | 0.349579 | ||||||||
\(443\) | −3.87605 | −0.184157 | −0.0920783 | − | 0.995752i | \(-0.529351\pi\) | ||||
−0.0920783 | + | 0.995752i | \(0.529351\pi\) | |||||||
\(444\) | 5.58919 | 0.265251 | ||||||||
\(445\) | −19.7507 | −0.936275 | ||||||||
\(446\) | −11.5547 | −0.547129 | ||||||||
\(447\) | 2.32128 | 0.109793 | ||||||||
\(448\) | −2.66768 | −0.126036 | ||||||||
\(449\) | 1.92416 | 0.0908069 | 0.0454034 | − | 0.998969i | \(-0.485543\pi\) | ||||
0.0454034 | + | 0.998969i | \(0.485543\pi\) | |||||||
\(450\) | −1.67489 | −0.0789549 | ||||||||
\(451\) | −38.7067 | −1.82263 | ||||||||
\(452\) | 5.76413 | 0.271122 | ||||||||
\(453\) | 13.9477 | 0.655322 | ||||||||
\(454\) | −27.7500 | −1.30237 | ||||||||
\(455\) | 16.1122 | 0.755352 | ||||||||
\(456\) | 6.60991 | 0.309537 | ||||||||
\(457\) | −35.4478 | −1.65818 | −0.829089 | − | 0.559116i | \(-0.811141\pi\) | ||||
−0.829089 | + | 0.559116i | \(0.811141\pi\) | |||||||
\(458\) | 10.3009 | 0.481330 | ||||||||
\(459\) | 13.2077 | 0.616482 | ||||||||
\(460\) | −13.1686 | −0.613989 | ||||||||
\(461\) | 0.839413 | 0.0390954 | 0.0195477 | − | 0.999809i | \(-0.493777\pi\) | ||||
0.0195477 | + | 0.999809i | \(0.493777\pi\) | |||||||
\(462\) | 17.6492 | 0.821117 | ||||||||
\(463\) | −17.4738 | −0.812078 | −0.406039 | − | 0.913856i | \(-0.633090\pi\) | ||||
−0.406039 | + | 0.913856i | \(0.633090\pi\) | |||||||
\(464\) | 9.08445 | 0.421735 | ||||||||
\(465\) | −2.46785 | −0.114444 | ||||||||
\(466\) | −11.2048 | −0.519051 | ||||||||
\(467\) | −17.2684 | −0.799086 | −0.399543 | − | 0.916714i | \(-0.630831\pi\) | ||||
−0.399543 | + | 0.916714i | \(0.630831\pi\) | |||||||
\(468\) | 4.33082 | 0.200192 | ||||||||
\(469\) | 14.2986 | 0.660247 | ||||||||
\(470\) | 20.4722 | 0.944314 | ||||||||
\(471\) | 9.93985 | 0.458004 | ||||||||
\(472\) | 14.1437 | 0.651016 | ||||||||
\(473\) | 59.4979 | 2.73572 | ||||||||
\(474\) | 9.77396 | 0.448933 | ||||||||
\(475\) | −6.25623 | −0.287056 | ||||||||
\(476\) | −6.32967 | −0.290120 | ||||||||
\(477\) | 13.1610 | 0.602600 | ||||||||
\(478\) | −27.4050 | −1.25348 | ||||||||
\(479\) | −38.5054 | −1.75936 | −0.879678 | − | 0.475569i | \(-0.842242\pi\) | ||||
−0.879678 | + | 0.475569i | \(0.842242\pi\) | |||||||
\(480\) | 2.46785 | 0.112642 | ||||||||
\(481\) | 13.6789 | 0.623704 | ||||||||
\(482\) | −28.8657 | −1.31479 | ||||||||
\(483\) | −22.8019 | −1.03752 | ||||||||
\(484\) | 16.3254 | 0.742065 | ||||||||
\(485\) | −1.94989 | −0.0885401 | ||||||||
\(486\) | 13.0916 | 0.593846 | ||||||||
\(487\) | 18.3889 | 0.833282 | 0.416641 | − | 0.909071i | \(-0.363207\pi\) | ||||
0.416641 | + | 0.909071i | \(0.363207\pi\) | |||||||
\(488\) | −1.37878 | −0.0624145 | ||||||||
\(489\) | −17.0077 | −0.769114 | ||||||||
\(490\) | −0.227228 | −0.0102651 | ||||||||
\(491\) | −0.591152 | −0.0266783 | −0.0133392 | − | 0.999911i | \(-0.504246\pi\) | ||||
−0.0133392 | + | 0.999911i | \(0.504246\pi\) | |||||||
\(492\) | −9.37155 | −0.422502 | ||||||||
\(493\) | 21.5549 | 0.970783 | ||||||||
\(494\) | 16.1770 | 0.727836 | ||||||||
\(495\) | 14.2513 | 0.640548 | ||||||||
\(496\) | 1.00000 | 0.0449013 | ||||||||
\(497\) | 15.3863 | 0.690170 | ||||||||
\(498\) | 13.6438 | 0.611396 | ||||||||
\(499\) | −25.9442 | −1.16142 | −0.580710 | − | 0.814110i | \(-0.697225\pi\) | ||||
−0.580710 | + | 0.814110i | \(0.697225\pi\) | |||||||
\(500\) | −12.0853 | −0.540470 | ||||||||
\(501\) | −9.00706 | −0.402406 | ||||||||
\(502\) | −18.0563 | −0.805891 | ||||||||
\(503\) | −34.4315 | −1.53523 | −0.767613 | − | 0.640914i | \(-0.778555\pi\) | ||||
−0.767613 | + | 0.640914i | \(0.778555\pi\) | |||||||
\(504\) | −3.72987 | −0.166142 | ||||||||
\(505\) | 25.5451 | 1.13674 | ||||||||
\(506\) | −35.3030 | −1.56941 | ||||||||
\(507\) | 4.31018 | 0.191422 | ||||||||
\(508\) | −9.18792 | −0.407648 | ||||||||
\(509\) | 20.7445 | 0.919486 | 0.459743 | − | 0.888052i | \(-0.347942\pi\) | ||||
0.459743 | + | 0.888052i | \(0.347942\pi\) | |||||||
\(510\) | 5.85553 | 0.259287 | ||||||||
\(511\) | 10.3647 | 0.458506 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 29.0715 | 1.28354 | ||||||||
\(514\) | −20.4236 | −0.900846 | ||||||||
\(515\) | 11.4077 | 0.502683 | ||||||||
\(516\) | 14.4054 | 0.634164 | ||||||||
\(517\) | 54.8830 | 2.41375 | ||||||||
\(518\) | −11.7808 | −0.517619 | ||||||||
\(519\) | 3.84735 | 0.168880 | ||||||||
\(520\) | 6.03978 | 0.264862 | ||||||||
\(521\) | −31.0547 | −1.36053 | −0.680265 | − | 0.732966i | \(-0.738135\pi\) | ||||
−0.680265 | + | 0.732966i | \(0.738135\pi\) | |||||||
\(522\) | 12.7016 | 0.555934 | ||||||||
\(523\) | −36.8872 | −1.61297 | −0.806483 | − | 0.591257i | \(-0.798632\pi\) | ||||
−0.806483 | + | 0.591257i | \(0.798632\pi\) | |||||||
\(524\) | −5.96717 | −0.260677 | ||||||||
\(525\) | −4.04454 | −0.176518 | ||||||||
\(526\) | 5.85635 | 0.255349 | ||||||||
\(527\) | 2.37272 | 0.103357 | ||||||||
\(528\) | 6.61594 | 0.287922 | ||||||||
\(529\) | 22.6097 | 0.983028 | ||||||||
\(530\) | 18.3544 | 0.797263 | ||||||||
\(531\) | 19.7752 | 0.858173 | ||||||||
\(532\) | −13.9323 | −0.604040 | ||||||||
\(533\) | −22.9358 | −0.993458 | ||||||||
\(534\) | −12.8198 | −0.554767 | ||||||||
\(535\) | 11.5632 | 0.499919 | ||||||||
\(536\) | 5.35993 | 0.231514 | ||||||||
\(537\) | 14.6853 | 0.633716 | ||||||||
\(538\) | −26.9843 | −1.16337 | ||||||||
\(539\) | −0.609165 | −0.0262386 | ||||||||
\(540\) | 10.8540 | 0.467083 | ||||||||
\(541\) | 43.9010 | 1.88745 | 0.943725 | − | 0.330731i | \(-0.107295\pi\) | ||||
0.943725 | + | 0.330731i | \(0.107295\pi\) | |||||||
\(542\) | 14.8981 | 0.639926 | ||||||||
\(543\) | −12.1372 | −0.520856 | ||||||||
\(544\) | −2.37272 | −0.101730 | ||||||||
\(545\) | 28.8327 | 1.23506 | ||||||||
\(546\) | 10.4581 | 0.447565 | ||||||||
\(547\) | −0.00902360 | −0.000385821 0 | −0.000192911 | − | 1.00000i | \(-0.500061\pi\) | ||||
−0.000192911 | 1.00000i | \(0.500061\pi\) | ||||||||
\(548\) | −8.95303 | −0.382454 | ||||||||
\(549\) | −1.92777 | −0.0822751 | ||||||||
\(550\) | −6.26195 | −0.267010 | ||||||||
\(551\) | 47.4445 | 2.02120 | ||||||||
\(552\) | −8.54745 | −0.363804 | ||||||||
\(553\) | −20.6014 | −0.876060 | ||||||||
\(554\) | 23.4010 | 0.994213 | ||||||||
\(555\) | 10.8983 | 0.462608 | ||||||||
\(556\) | −11.4499 | −0.485583 | ||||||||
\(557\) | 22.5672 | 0.956201 | 0.478101 | − | 0.878305i | \(-0.341325\pi\) | ||||
0.478101 | + | 0.878305i | \(0.341325\pi\) | |||||||
\(558\) | 1.39817 | 0.0591892 | ||||||||
\(559\) | 35.2556 | 1.49115 | ||||||||
\(560\) | −5.20170 | −0.219812 | ||||||||
\(561\) | 15.6978 | 0.662761 | ||||||||
\(562\) | 26.8670 | 1.13332 | ||||||||
\(563\) | 5.08080 | 0.214130 | 0.107065 | − | 0.994252i | \(-0.465855\pi\) | ||||
0.107065 | + | 0.994252i | \(0.465855\pi\) | |||||||
\(564\) | 13.2881 | 0.559530 | ||||||||
\(565\) | 11.2394 | 0.472847 | ||||||||
\(566\) | −19.8041 | −0.832430 | ||||||||
\(567\) | 7.60454 | 0.319361 | ||||||||
\(568\) | 5.76766 | 0.242006 | ||||||||
\(569\) | 7.61121 | 0.319079 | 0.159539 | − | 0.987192i | \(-0.448999\pi\) | ||||
0.159539 | + | 0.987192i | \(0.448999\pi\) | |||||||
\(570\) | 12.8886 | 0.539845 | ||||||||
\(571\) | −25.1865 | −1.05402 | −0.527012 | − | 0.849858i | \(-0.676688\pi\) | ||||
−0.527012 | + | 0.849858i | \(0.676688\pi\) | |||||||
\(572\) | 16.1917 | 0.677011 | ||||||||
\(573\) | −15.2968 | −0.639033 | ||||||||
\(574\) | 19.7532 | 0.824483 | ||||||||
\(575\) | 8.09011 | 0.337381 | ||||||||
\(576\) | −1.39817 | −0.0582570 | ||||||||
\(577\) | −35.0060 | −1.45732 | −0.728660 | − | 0.684876i | \(-0.759856\pi\) | ||||
−0.728660 | + | 0.684876i | \(0.759856\pi\) | |||||||
\(578\) | 11.3702 | 0.472938 | ||||||||
\(579\) | −6.94939 | −0.288807 | ||||||||
\(580\) | 17.7137 | 0.735522 | ||||||||
\(581\) | −28.7583 | −1.19309 | ||||||||
\(582\) | −1.26563 | −0.0524622 | ||||||||
\(583\) | 49.2053 | 2.03788 | ||||||||
\(584\) | 3.88527 | 0.160774 | ||||||||
\(585\) | 8.44463 | 0.349142 | ||||||||
\(586\) | 0.812185 | 0.0335511 | ||||||||
\(587\) | 23.2481 | 0.959550 | 0.479775 | − | 0.877392i | \(-0.340718\pi\) | ||||
0.479775 | + | 0.877392i | \(0.340718\pi\) | |||||||
\(588\) | −0.147489 | −0.00608234 | ||||||||
\(589\) | 5.22260 | 0.215194 | ||||||||
\(590\) | 27.5787 | 1.13540 | ||||||||
\(591\) | −30.6916 | −1.26248 | ||||||||
\(592\) | −4.41612 | −0.181501 | ||||||||
\(593\) | 13.3423 | 0.547902 | 0.273951 | − | 0.961744i | \(-0.411669\pi\) | ||||
0.273951 | + | 0.961744i | \(0.411669\pi\) | |||||||
\(594\) | 29.0980 | 1.19391 | ||||||||
\(595\) | −12.3422 | −0.505980 | ||||||||
\(596\) | −1.83408 | −0.0751269 | ||||||||
\(597\) | −17.7402 | −0.726057 | ||||||||
\(598\) | −20.9189 | −0.855437 | ||||||||
\(599\) | −19.0823 | −0.779682 | −0.389841 | − | 0.920882i | \(-0.627470\pi\) | ||||
−0.389841 | + | 0.920882i | \(0.627470\pi\) | |||||||
\(600\) | −1.51612 | −0.0618954 | ||||||||
\(601\) | 11.0751 | 0.451761 | 0.225881 | − | 0.974155i | \(-0.427474\pi\) | ||||
0.225881 | + | 0.974155i | \(0.427474\pi\) | |||||||
\(602\) | −30.3635 | −1.23753 | ||||||||
\(603\) | 7.49408 | 0.305183 | ||||||||
\(604\) | −11.0204 | −0.448412 | ||||||||
\(605\) | 31.8328 | 1.29419 | ||||||||
\(606\) | 16.5808 | 0.673550 | ||||||||
\(607\) | 19.7998 | 0.803649 | 0.401825 | − | 0.915717i | \(-0.368376\pi\) | ||||
0.401825 | + | 0.915717i | \(0.368376\pi\) | |||||||
\(608\) | −5.22260 | −0.211805 | ||||||||
\(609\) | 30.6719 | 1.24289 | ||||||||
\(610\) | −2.68848 | −0.108853 | ||||||||
\(611\) | 32.5210 | 1.31566 | ||||||||
\(612\) | −3.31747 | −0.134101 | ||||||||
\(613\) | −0.663095 | −0.0267821 | −0.0133911 | − | 0.999910i | \(-0.504263\pi\) | ||||
−0.0133911 | + | 0.999910i | \(0.504263\pi\) | |||||||
\(614\) | −25.4624 | −1.02758 | ||||||||
\(615\) | −18.2735 | −0.736860 | ||||||||
\(616\) | −13.9450 | −0.561859 | ||||||||
\(617\) | 20.8327 | 0.838695 | 0.419347 | − | 0.907826i | \(-0.362259\pi\) | ||||
0.419347 | + | 0.907826i | \(0.362259\pi\) | |||||||
\(618\) | 7.40449 | 0.297852 | ||||||||
\(619\) | −26.8026 | −1.07729 | −0.538644 | − | 0.842533i | \(-0.681063\pi\) | ||||
−0.538644 | + | 0.842533i | \(0.681063\pi\) | |||||||
\(620\) | 1.94989 | 0.0783096 | ||||||||
\(621\) | −37.5931 | −1.50856 | ||||||||
\(622\) | 14.3767 | 0.576453 | ||||||||
\(623\) | 27.0213 | 1.08259 | ||||||||
\(624\) | 3.92029 | 0.156937 | ||||||||
\(625\) | −17.5754 | −0.703017 | ||||||||
\(626\) | −8.18376 | −0.327089 | ||||||||
\(627\) | 34.5525 | 1.37989 | ||||||||
\(628\) | −7.85364 | −0.313395 | ||||||||
\(629\) | −10.4782 | −0.417794 | ||||||||
\(630\) | −7.27285 | −0.289757 | ||||||||
\(631\) | 22.5507 | 0.897728 | 0.448864 | − | 0.893600i | \(-0.351829\pi\) | ||||
0.448864 | + | 0.893600i | \(0.351829\pi\) | |||||||
\(632\) | −7.72257 | −0.307187 | ||||||||
\(633\) | −16.8271 | −0.668816 | ||||||||
\(634\) | 28.2390 | 1.12151 | ||||||||
\(635\) | −17.9155 | −0.710953 | ||||||||
\(636\) | 11.9134 | 0.472399 | ||||||||
\(637\) | −0.360962 | −0.0143018 | ||||||||
\(638\) | 47.4878 | 1.88006 | ||||||||
\(639\) | 8.06416 | 0.319013 | ||||||||
\(640\) | −1.94989 | −0.0770763 | ||||||||
\(641\) | 33.0314 | 1.30466 | 0.652330 | − | 0.757935i | \(-0.273791\pi\) | ||||
0.652330 | + | 0.757935i | \(0.273791\pi\) | |||||||
\(642\) | 7.50540 | 0.296215 | ||||||||
\(643\) | −24.6351 | −0.971514 | −0.485757 | − | 0.874094i | \(-0.661456\pi\) | ||||
−0.485757 | + | 0.874094i | \(0.661456\pi\) | |||||||
\(644\) | 18.0162 | 0.709937 | ||||||||
\(645\) | 28.0891 | 1.10601 | ||||||||
\(646\) | −12.3918 | −0.487548 | ||||||||
\(647\) | −18.5484 | −0.729213 | −0.364607 | − | 0.931162i | \(-0.618797\pi\) | ||||
−0.364607 | + | 0.931162i | \(0.618797\pi\) | |||||||
\(648\) | 2.85062 | 0.111983 | ||||||||
\(649\) | 73.9343 | 2.90217 | ||||||||
\(650\) | −3.71053 | −0.145539 | ||||||||
\(651\) | 3.37631 | 0.132328 | ||||||||
\(652\) | 13.4381 | 0.526275 | ||||||||
\(653\) | 47.3735 | 1.85387 | 0.926935 | − | 0.375222i | \(-0.122434\pi\) | ||||
0.926935 | + | 0.375222i | \(0.122434\pi\) | |||||||
\(654\) | 18.7147 | 0.731803 | ||||||||
\(655\) | −11.6353 | −0.454631 | ||||||||
\(656\) | 7.40463 | 0.289102 | ||||||||
\(657\) | 5.43227 | 0.211933 | ||||||||
\(658\) | −28.0084 | −1.09188 | ||||||||
\(659\) | 2.23952 | 0.0872395 | 0.0436197 | − | 0.999048i | \(-0.486111\pi\) | ||||
0.0436197 | + | 0.999048i | \(0.486111\pi\) | |||||||
\(660\) | 12.9004 | 0.502147 | ||||||||
\(661\) | 34.9675 | 1.36008 | 0.680038 | − | 0.733177i | \(-0.261963\pi\) | ||||
0.680038 | + | 0.733177i | \(0.261963\pi\) | |||||||
\(662\) | −31.6846 | −1.23146 | ||||||||
\(663\) | 9.30176 | 0.361250 | ||||||||
\(664\) | −10.7802 | −0.418355 | ||||||||
\(665\) | −27.1664 | −1.05347 | ||||||||
\(666\) | −6.17448 | −0.239256 | ||||||||
\(667\) | −61.3518 | −2.37555 | ||||||||
\(668\) | 7.11664 | 0.275351 | ||||||||
\(669\) | −14.6240 | −0.565396 | ||||||||
\(670\) | 10.4513 | 0.403768 | ||||||||
\(671\) | −7.20740 | −0.278239 | ||||||||
\(672\) | −3.37631 | −0.130244 | ||||||||
\(673\) | 6.69011 | 0.257885 | 0.128942 | − | 0.991652i | \(-0.458842\pi\) | ||||
0.128942 | + | 0.991652i | \(0.458842\pi\) | |||||||
\(674\) | −15.5577 | −0.599260 | ||||||||
\(675\) | −6.66816 | −0.256658 | ||||||||
\(676\) | −3.40555 | −0.130983 | ||||||||
\(677\) | −33.4012 | −1.28371 | −0.641857 | − | 0.766825i | \(-0.721836\pi\) | ||||
−0.641857 | + | 0.766825i | \(0.721836\pi\) | |||||||
\(678\) | 7.29529 | 0.280174 | ||||||||
\(679\) | 2.66768 | 0.102376 | ||||||||
\(680\) | −4.62655 | −0.177420 | ||||||||
\(681\) | −35.1213 | −1.34585 | ||||||||
\(682\) | 5.22737 | 0.200166 | ||||||||
\(683\) | −10.5090 | −0.402114 | −0.201057 | − | 0.979580i | \(-0.564438\pi\) | ||||
−0.201057 | + | 0.979580i | \(0.564438\pi\) | |||||||
\(684\) | −7.30208 | −0.279202 | ||||||||
\(685\) | −17.4575 | −0.667015 | ||||||||
\(686\) | −18.3629 | −0.701099 | ||||||||
\(687\) | 13.0372 | 0.497400 | ||||||||
\(688\) | −11.3820 | −0.433934 | ||||||||
\(689\) | 29.1567 | 1.11078 | ||||||||
\(690\) | −16.6666 | −0.634488 | ||||||||
\(691\) | −21.1228 | −0.803548 | −0.401774 | − | 0.915739i | \(-0.631606\pi\) | ||||
−0.401774 | + | 0.915739i | \(0.631606\pi\) | |||||||
\(692\) | −3.03986 | −0.115558 | ||||||||
\(693\) | −19.4974 | −0.740646 | ||||||||
\(694\) | 17.8940 | 0.679246 | ||||||||
\(695\) | −22.3260 | −0.846875 | ||||||||
\(696\) | 11.4976 | 0.435815 | ||||||||
\(697\) | 17.5691 | 0.665478 | ||||||||
\(698\) | 25.4040 | 0.961554 | ||||||||
\(699\) | −14.1811 | −0.536380 | ||||||||
\(700\) | 3.19566 | 0.120785 | ||||||||
\(701\) | −50.0893 | −1.89185 | −0.945924 | − | 0.324388i | \(-0.894842\pi\) | ||||
−0.945924 | + | 0.324388i | \(0.894842\pi\) | |||||||
\(702\) | 17.2421 | 0.650761 | ||||||||
\(703\) | −23.0636 | −0.869862 | ||||||||
\(704\) | −5.22737 | −0.197014 | ||||||||
\(705\) | 25.9104 | 0.975841 | ||||||||
\(706\) | −0.0373432 | −0.00140543 | ||||||||
\(707\) | −34.9488 | −1.31438 | ||||||||
\(708\) | 17.9007 | 0.672751 | ||||||||
\(709\) | 27.5526 | 1.03476 | 0.517380 | − | 0.855756i | \(-0.326908\pi\) | ||||
0.517380 | + | 0.855756i | \(0.326908\pi\) | |||||||
\(710\) | 11.2463 | 0.422067 | ||||||||
\(711\) | −10.7975 | −0.404936 | ||||||||
\(712\) | 10.1291 | 0.379606 | ||||||||
\(713\) | −6.75349 | −0.252920 | ||||||||
\(714\) | −8.01105 | −0.299806 | ||||||||
\(715\) | 31.5722 | 1.18073 | ||||||||
\(716\) | −11.6031 | −0.433627 | ||||||||
\(717\) | −34.6847 | −1.29533 | ||||||||
\(718\) | −7.83321 | −0.292333 | ||||||||
\(719\) | −5.20954 | −0.194283 | −0.0971416 | − | 0.995271i | \(-0.530970\pi\) | ||||
−0.0971416 | + | 0.995271i | \(0.530970\pi\) | |||||||
\(720\) | −2.72628 | −0.101602 | ||||||||
\(721\) | −15.6071 | −0.581237 | ||||||||
\(722\) | −8.27559 | −0.307985 | ||||||||
\(723\) | −36.5334 | −1.35869 | ||||||||
\(724\) | 9.58979 | 0.356402 | ||||||||
\(725\) | −10.8824 | −0.404162 | ||||||||
\(726\) | 20.6620 | 0.766840 | ||||||||
\(727\) | −10.4960 | −0.389274 | −0.194637 | − | 0.980875i | \(-0.562353\pi\) | ||||
−0.194637 | + | 0.980875i | \(0.562353\pi\) | |||||||
\(728\) | −8.26312 | −0.306252 | ||||||||
\(729\) | 25.1210 | 0.930408 | ||||||||
\(730\) | 7.57587 | 0.280395 | ||||||||
\(731\) | −27.0063 | −0.998864 | ||||||||
\(732\) | −1.74503 | −0.0644983 | ||||||||
\(733\) | 7.71136 | 0.284825 | 0.142413 | − | 0.989807i | \(-0.454514\pi\) | ||||
0.142413 | + | 0.989807i | \(0.454514\pi\) | |||||||
\(734\) | 26.3646 | 0.973133 | ||||||||
\(735\) | −0.287588 | −0.0106078 | ||||||||
\(736\) | 6.75349 | 0.248937 | ||||||||
\(737\) | 28.0183 | 1.03207 | ||||||||
\(738\) | 10.3529 | 0.381096 | ||||||||
\(739\) | 47.7675 | 1.75716 | 0.878579 | − | 0.477598i | \(-0.158492\pi\) | ||||
0.878579 | + | 0.477598i | \(0.158492\pi\) | |||||||
\(740\) | −8.61096 | −0.316545 | ||||||||
\(741\) | 20.4741 | 0.752136 | ||||||||
\(742\) | −25.1109 | −0.921852 | ||||||||
\(743\) | −2.18953 | −0.0803262 | −0.0401631 | − | 0.999193i | \(-0.512788\pi\) | ||||
−0.0401631 | + | 0.999193i | \(0.512788\pi\) | |||||||
\(744\) | 1.26563 | 0.0464004 | ||||||||
\(745\) | −3.57627 | −0.131024 | ||||||||
\(746\) | −27.5033 | −1.00697 | ||||||||
\(747\) | −15.0726 | −0.551478 | ||||||||
\(748\) | −12.4031 | −0.453502 | ||||||||
\(749\) | −15.8198 | −0.578042 | ||||||||
\(750\) | −15.2955 | −0.558514 | ||||||||
\(751\) | 13.6668 | 0.498708 | 0.249354 | − | 0.968412i | \(-0.419782\pi\) | ||||
0.249354 | + | 0.968412i | \(0.419782\pi\) | |||||||
\(752\) | −10.4992 | −0.382865 | ||||||||
\(753\) | −22.8526 | −0.832797 | ||||||||
\(754\) | 28.1390 | 1.02476 | ||||||||
\(755\) | −21.4885 | −0.782047 | ||||||||
\(756\) | −14.8496 | −0.540074 | ||||||||
\(757\) | 22.1752 | 0.805972 | 0.402986 | − | 0.915206i | \(-0.367972\pi\) | ||||
0.402986 | + | 0.915206i | \(0.367972\pi\) | |||||||
\(758\) | −17.1114 | −0.621513 | ||||||||
\(759\) | −44.6807 | −1.62181 | ||||||||
\(760\) | −10.1835 | −0.369395 | ||||||||
\(761\) | −3.24618 | −0.117674 | −0.0588370 | − | 0.998268i | \(-0.518739\pi\) | ||||
−0.0588370 | + | 0.998268i | \(0.518739\pi\) | |||||||
\(762\) | −11.6285 | −0.421258 | ||||||||
\(763\) | −39.4465 | −1.42806 | ||||||||
\(764\) | 12.0863 | 0.437266 | ||||||||
\(765\) | −6.46870 | −0.233876 | ||||||||
\(766\) | 24.0296 | 0.868225 | ||||||||
\(767\) | 43.8099 | 1.58188 | ||||||||
\(768\) | −1.26563 | −0.0456697 | ||||||||
\(769\) | −29.7308 | −1.07212 | −0.536060 | − | 0.844180i | \(-0.680088\pi\) | ||||
−0.536060 | + | 0.844180i | \(0.680088\pi\) | |||||||
\(770\) | −27.1912 | −0.979903 | ||||||||
\(771\) | −25.8488 | −0.930922 | ||||||||
\(772\) | 5.49083 | 0.197619 | ||||||||
\(773\) | −6.34496 | −0.228212 | −0.114106 | − | 0.993469i | \(-0.536400\pi\) | ||||
−0.114106 | + | 0.993469i | \(0.536400\pi\) | |||||||
\(774\) | −15.9139 | −0.572015 | ||||||||
\(775\) | −1.19791 | −0.0430304 | ||||||||
\(776\) | 1.00000 | 0.0358979 | ||||||||
\(777\) | −14.9102 | −0.534900 | ||||||||
\(778\) | 25.9380 | 0.929922 | ||||||||
\(779\) | 38.6714 | 1.38555 | ||||||||
\(780\) | 7.64415 | 0.273705 | ||||||||
\(781\) | 30.1497 | 1.07884 | ||||||||
\(782\) | 16.0242 | 0.573023 | ||||||||
\(783\) | 50.5684 | 1.80717 | ||||||||
\(784\) | 0.116534 | 0.00416192 | ||||||||
\(785\) | −15.3138 | −0.546572 | ||||||||
\(786\) | −7.55226 | −0.269380 | ||||||||
\(787\) | 54.1808 | 1.93134 | 0.965668 | − | 0.259778i | \(-0.0836495\pi\) | ||||
0.965668 | + | 0.259778i | \(0.0836495\pi\) | |||||||
\(788\) | 24.2500 | 0.863869 | ||||||||
\(789\) | 7.41201 | 0.263874 | ||||||||
\(790\) | −15.0582 | −0.535747 | ||||||||
\(791\) | −15.3769 | −0.546739 | ||||||||
\(792\) | −7.30875 | −0.259705 | ||||||||
\(793\) | −4.27076 | −0.151659 | ||||||||
\(794\) | −19.8959 | −0.706080 | ||||||||
\(795\) | 23.2299 | 0.823881 | ||||||||
\(796\) | 14.0168 | 0.496813 | ||||||||
\(797\) | −35.4082 | −1.25422 | −0.627111 | − | 0.778930i | \(-0.715763\pi\) | ||||
−0.627111 | + | 0.778930i | \(0.715763\pi\) | |||||||
\(798\) | −17.6331 | −0.624206 | ||||||||
\(799\) | −24.9116 | −0.881308 | ||||||||
\(800\) | 1.19791 | 0.0423527 | ||||||||
\(801\) | 14.1622 | 0.500398 | ||||||||
\(802\) | −13.3050 | −0.469814 | ||||||||
\(803\) | 20.3098 | 0.716716 | ||||||||
\(804\) | 6.78371 | 0.239243 | ||||||||
\(805\) | 35.1296 | 1.23816 | ||||||||
\(806\) | 3.09749 | 0.109104 | ||||||||
\(807\) | −34.1522 | −1.20222 | ||||||||
\(808\) | −13.1008 | −0.460884 | ||||||||
\(809\) | −16.4334 | −0.577767 | −0.288883 | − | 0.957364i | \(-0.593284\pi\) | ||||
−0.288883 | + | 0.957364i | \(0.593284\pi\) | |||||||
\(810\) | 5.55840 | 0.195302 | ||||||||
\(811\) | 18.0429 | 0.633572 | 0.316786 | − | 0.948497i | \(-0.397396\pi\) | ||||
0.316786 | + | 0.948497i | \(0.397396\pi\) | |||||||
\(812\) | −24.2344 | −0.850462 | ||||||||
\(813\) | 18.8555 | 0.661291 | ||||||||
\(814\) | −23.0847 | −0.809118 | ||||||||
\(815\) | 26.2028 | 0.917844 | ||||||||
\(816\) | −3.00300 | −0.105126 | ||||||||
\(817\) | −59.4436 | −2.07967 | ||||||||
\(818\) | 2.21626 | 0.0774898 | ||||||||
\(819\) | −11.5532 | −0.403703 | ||||||||
\(820\) | 14.4382 | 0.504205 | ||||||||
\(821\) | −27.1615 | −0.947944 | −0.473972 | − | 0.880540i | \(-0.657180\pi\) | ||||
−0.473972 | + | 0.880540i | \(0.657180\pi\) | |||||||
\(822\) | −11.3313 | −0.395223 | ||||||||
\(823\) | −48.5334 | −1.69177 | −0.845884 | − | 0.533367i | \(-0.820926\pi\) | ||||
−0.845884 | + | 0.533367i | \(0.820926\pi\) | |||||||
\(824\) | −5.85042 | −0.203809 | ||||||||
\(825\) | −7.92534 | −0.275925 | ||||||||
\(826\) | −37.7308 | −1.31282 | ||||||||
\(827\) | 27.8336 | 0.967869 | 0.483934 | − | 0.875104i | \(-0.339207\pi\) | ||||
0.483934 | + | 0.875104i | \(0.339207\pi\) | |||||||
\(828\) | 9.44252 | 0.328150 | ||||||||
\(829\) | −32.9579 | −1.14468 | −0.572338 | − | 0.820018i | \(-0.693963\pi\) | ||||
−0.572338 | + | 0.820018i | \(0.693963\pi\) | |||||||
\(830\) | −21.0203 | −0.729626 | ||||||||
\(831\) | 29.6171 | 1.02741 | ||||||||
\(832\) | −3.09749 | −0.107386 | ||||||||
\(833\) | 0.276502 | 0.00958022 | ||||||||
\(834\) | −14.4914 | −0.501795 | ||||||||
\(835\) | 13.8767 | 0.480222 | ||||||||
\(836\) | −27.3005 | −0.944207 | ||||||||
\(837\) | 5.56648 | 0.192406 | ||||||||
\(838\) | −0.277866 | −0.00959872 | ||||||||
\(839\) | −7.35979 | −0.254088 | −0.127044 | − | 0.991897i | \(-0.540549\pi\) | ||||
−0.127044 | + | 0.991897i | \(0.540549\pi\) | |||||||
\(840\) | −6.58345 | −0.227151 | ||||||||
\(841\) | 53.5272 | 1.84577 | ||||||||
\(842\) | −31.4285 | −1.08310 | ||||||||
\(843\) | 34.0039 | 1.17115 | ||||||||
\(844\) | 13.2954 | 0.457645 | ||||||||
\(845\) | −6.64046 | −0.228439 | ||||||||
\(846\) | −14.6796 | −0.504695 | ||||||||
\(847\) | −43.5511 | −1.49643 | ||||||||
\(848\) | −9.41301 | −0.323244 | ||||||||
\(849\) | −25.0648 | −0.860222 | ||||||||
\(850\) | 2.84232 | 0.0974907 | ||||||||
\(851\) | 29.8242 | 1.02236 | ||||||||
\(852\) | 7.29975 | 0.250085 | ||||||||
\(853\) | 35.5826 | 1.21833 | 0.609163 | − | 0.793045i | \(-0.291505\pi\) | ||||
0.609163 | + | 0.793045i | \(0.291505\pi\) | |||||||
\(854\) | 3.67815 | 0.125864 | ||||||||
\(855\) | −14.2383 | −0.486939 | ||||||||
\(856\) | −5.93015 | −0.202688 | ||||||||
\(857\) | 57.3253 | 1.95820 | 0.979098 | − | 0.203388i | \(-0.0651954\pi\) | ||||
0.979098 | + | 0.203388i | \(0.0651954\pi\) | |||||||
\(858\) | 20.4928 | 0.699614 | ||||||||
\(859\) | 18.0698 | 0.616534 | 0.308267 | − | 0.951300i | \(-0.400251\pi\) | ||||
0.308267 | + | 0.951300i | \(0.400251\pi\) | |||||||
\(860\) | −22.1937 | −0.756798 | ||||||||
\(861\) | 25.0003 | 0.852009 | ||||||||
\(862\) | −34.0903 | −1.16112 | ||||||||
\(863\) | 1.51201 | 0.0514695 | 0.0257347 | − | 0.999669i | \(-0.491807\pi\) | ||||
0.0257347 | + | 0.999669i | \(0.491807\pi\) | |||||||
\(864\) | −5.56648 | −0.189375 | ||||||||
\(865\) | −5.92740 | −0.201538 | ||||||||
\(866\) | −36.9809 | −1.25666 | ||||||||
\(867\) | 14.3905 | 0.488727 | ||||||||
\(868\) | −2.66768 | −0.0905471 | ||||||||
\(869\) | −40.3688 | −1.36942 | ||||||||
\(870\) | 22.4191 | 0.760078 | ||||||||
\(871\) | 16.6023 | 0.562548 | ||||||||
\(872\) | −14.7868 | −0.500745 | ||||||||
\(873\) | 1.39817 | 0.0473208 | ||||||||
\(874\) | 35.2708 | 1.19305 | ||||||||
\(875\) | 32.2397 | 1.08990 | ||||||||
\(876\) | 4.91734 | 0.166141 | ||||||||
\(877\) | −22.1574 | −0.748201 | −0.374101 | − | 0.927388i | \(-0.622049\pi\) | ||||
−0.374101 | + | 0.927388i | \(0.622049\pi\) | |||||||
\(878\) | 1.85530 | 0.0626134 | ||||||||
\(879\) | 1.02793 | 0.0346712 | ||||||||
\(880\) | −10.1928 | −0.343600 | ||||||||
\(881\) | −52.4572 | −1.76733 | −0.883663 | − | 0.468123i | \(-0.844930\pi\) | ||||
−0.883663 | + | 0.468123i | \(0.844930\pi\) | |||||||
\(882\) | 0.162934 | 0.00548626 | ||||||||
\(883\) | −34.1132 | −1.14800 | −0.574001 | − | 0.818855i | \(-0.694609\pi\) | ||||
−0.574001 | + | 0.818855i | \(0.694609\pi\) | |||||||
\(884\) | −7.34948 | −0.247190 | ||||||||
\(885\) | 34.9045 | 1.17330 | ||||||||
\(886\) | 3.87605 | 0.130218 | ||||||||
\(887\) | −29.7572 | −0.999149 | −0.499574 | − | 0.866271i | \(-0.666510\pi\) | ||||
−0.499574 | + | 0.866271i | \(0.666510\pi\) | |||||||
\(888\) | −5.58919 | −0.187561 | ||||||||
\(889\) | 24.5105 | 0.822054 | ||||||||
\(890\) | 19.7507 | 0.662047 | ||||||||
\(891\) | 14.9012 | 0.499210 | ||||||||
\(892\) | 11.5547 | 0.386879 | ||||||||
\(893\) | −54.8329 | −1.83491 | ||||||||
\(894\) | −2.32128 | −0.0776352 | ||||||||
\(895\) | −22.6248 | −0.756263 | ||||||||
\(896\) | 2.66768 | 0.0891210 | ||||||||
\(897\) | −26.4757 | −0.883997 | ||||||||
\(898\) | −1.92416 | −0.0642102 | ||||||||
\(899\) | 9.08445 | 0.302983 | ||||||||
\(900\) | 1.67489 | 0.0558296 | ||||||||
\(901\) | −22.3345 | −0.744069 | ||||||||
\(902\) | 38.7067 | 1.28879 | ||||||||
\(903\) | −38.4292 | −1.27884 | ||||||||
\(904\) | −5.76413 | −0.191712 | ||||||||
\(905\) | 18.6991 | 0.621578 | ||||||||
\(906\) | −13.9477 | −0.463383 | ||||||||
\(907\) | 23.5868 | 0.783185 | 0.391593 | − | 0.920139i | \(-0.371924\pi\) | ||||
0.391593 | + | 0.920139i | \(0.371924\pi\) | |||||||
\(908\) | 27.7500 | 0.920915 | ||||||||
\(909\) | −18.3171 | −0.607540 | ||||||||
\(910\) | −16.1122 | −0.534115 | ||||||||
\(911\) | 30.9659 | 1.02595 | 0.512973 | − | 0.858405i | \(-0.328544\pi\) | ||||
0.512973 | + | 0.858405i | \(0.328544\pi\) | |||||||
\(912\) | −6.60991 | −0.218876 | ||||||||
\(913\) | −56.3523 | −1.86499 | ||||||||
\(914\) | 35.4478 | 1.17251 | ||||||||
\(915\) | −3.40263 | −0.112487 | ||||||||
\(916\) | −10.3009 | −0.340351 | ||||||||
\(917\) | 15.9185 | 0.525676 | ||||||||
\(918\) | −13.2077 | −0.435919 | ||||||||
\(919\) | 32.3256 | 1.06632 | 0.533162 | − | 0.846013i | \(-0.321004\pi\) | ||||
0.533162 | + | 0.846013i | \(0.321004\pi\) | |||||||
\(920\) | 13.1686 | 0.434156 | ||||||||
\(921\) | −32.2261 | −1.06189 | ||||||||
\(922\) | −0.839413 | −0.0276446 | ||||||||
\(923\) | 17.8653 | 0.588043 | ||||||||
\(924\) | −17.6492 | −0.580617 | ||||||||
\(925\) | 5.29014 | 0.173939 | ||||||||
\(926\) | 17.4738 | 0.574226 | ||||||||
\(927\) | −8.17987 | −0.268662 | ||||||||
\(928\) | −9.08445 | −0.298212 | ||||||||
\(929\) | −2.46694 | −0.0809377 | −0.0404689 | − | 0.999181i | \(-0.512885\pi\) | ||||
−0.0404689 | + | 0.999181i | \(0.512885\pi\) | |||||||
\(930\) | 2.46785 | 0.0809241 | ||||||||
\(931\) | 0.608609 | 0.0199464 | ||||||||
\(932\) | 11.2048 | 0.367024 | ||||||||
\(933\) | 18.1956 | 0.595698 | ||||||||
\(934\) | 17.2684 | 0.565039 | ||||||||
\(935\) | −24.1847 | −0.790925 | ||||||||
\(936\) | −4.33082 | −0.141557 | ||||||||
\(937\) | 27.4222 | 0.895843 | 0.447922 | − | 0.894073i | \(-0.352164\pi\) | ||||
0.447922 | + | 0.894073i | \(0.352164\pi\) | |||||||
\(938\) | −14.2986 | −0.466865 | ||||||||
\(939\) | −10.3577 | −0.338009 | ||||||||
\(940\) | −20.4722 | −0.667731 | ||||||||
\(941\) | −47.1337 | −1.53651 | −0.768257 | − | 0.640141i | \(-0.778876\pi\) | ||||
−0.768257 | + | 0.640141i | \(0.778876\pi\) | |||||||
\(942\) | −9.93985 | −0.323858 | ||||||||
\(943\) | −50.0071 | −1.62845 | ||||||||
\(944\) | −14.1437 | −0.460337 | ||||||||
\(945\) | −28.9551 | −0.941910 | ||||||||
\(946\) | −59.4979 | −1.93444 | ||||||||
\(947\) | 12.9777 | 0.421719 | 0.210859 | − | 0.977516i | \(-0.432374\pi\) | ||||
0.210859 | + | 0.977516i | \(0.432374\pi\) | |||||||
\(948\) | −9.77396 | −0.317443 | ||||||||
\(949\) | 12.0346 | 0.390660 | ||||||||
\(950\) | 6.25623 | 0.202979 | ||||||||
\(951\) | 35.7402 | 1.15896 | ||||||||
\(952\) | 6.32967 | 0.205146 | ||||||||
\(953\) | 53.4647 | 1.73189 | 0.865946 | − | 0.500138i | \(-0.166717\pi\) | ||||
0.865946 | + | 0.500138i | \(0.166717\pi\) | |||||||
\(954\) | −13.1610 | −0.426103 | ||||||||
\(955\) | 23.5670 | 0.762609 | ||||||||
\(956\) | 27.4050 | 0.886342 | ||||||||
\(957\) | 60.1022 | 1.94283 | ||||||||
\(958\) | 38.5054 | 1.24405 | ||||||||
\(959\) | 23.8838 | 0.771250 | ||||||||
\(960\) | −2.46785 | −0.0796496 | ||||||||
\(961\) | 1.00000 | 0.0322581 | ||||||||
\(962\) | −13.6789 | −0.441025 | ||||||||
\(963\) | −8.29135 | −0.267185 | ||||||||
\(964\) | 28.8657 | 0.929700 | ||||||||
\(965\) | 10.7065 | 0.344656 | ||||||||
\(966\) | 22.8019 | 0.733639 | ||||||||
\(967\) | 8.44918 | 0.271707 | 0.135854 | − | 0.990729i | \(-0.456622\pi\) | ||||
0.135854 | + | 0.990729i | \(0.456622\pi\) | |||||||
\(968\) | −16.3254 | −0.524719 | ||||||||
\(969\) | −15.6835 | −0.503826 | ||||||||
\(970\) | 1.94989 | 0.0626073 | ||||||||
\(971\) | −36.1359 | −1.15966 | −0.579829 | − | 0.814738i | \(-0.696881\pi\) | ||||
−0.579829 | + | 0.814738i | \(0.696881\pi\) | |||||||
\(972\) | −13.0916 | −0.419913 | ||||||||
\(973\) | 30.5446 | 0.979216 | ||||||||
\(974\) | −18.3889 | −0.589219 | ||||||||
\(975\) | −4.69618 | −0.150398 | ||||||||
\(976\) | 1.37878 | 0.0441337 | ||||||||
\(977\) | 60.3113 | 1.92953 | 0.964765 | − | 0.263112i | \(-0.0847489\pi\) | ||||
0.964765 | + | 0.263112i | \(0.0847489\pi\) | |||||||
\(978\) | 17.0077 | 0.543846 | ||||||||
\(979\) | 52.9488 | 1.69225 | ||||||||
\(980\) | 0.227228 | 0.00725854 | ||||||||
\(981\) | −20.6745 | −0.660085 | ||||||||
\(982\) | 0.591152 | 0.0188644 | ||||||||
\(983\) | 22.9239 | 0.731158 | 0.365579 | − | 0.930780i | \(-0.380871\pi\) | ||||
0.365579 | + | 0.930780i | \(0.380871\pi\) | |||||||
\(984\) | 9.37155 | 0.298754 | ||||||||
\(985\) | 47.2848 | 1.50662 | ||||||||
\(986\) | −21.5549 | −0.686447 | ||||||||
\(987\) | −35.4484 | −1.12834 | ||||||||
\(988\) | −16.1770 | −0.514658 | ||||||||
\(989\) | 76.8682 | 2.44427 | ||||||||
\(990\) | −14.2513 | −0.452936 | ||||||||
\(991\) | −52.5822 | −1.67033 | −0.835164 | − | 0.550001i | \(-0.814627\pi\) | ||||
−0.835164 | + | 0.550001i | \(0.814627\pi\) | |||||||
\(992\) | −1.00000 | −0.0317500 | ||||||||
\(993\) | −40.1012 | −1.27257 | ||||||||
\(994\) | −15.3863 | −0.488024 | ||||||||
\(995\) | 27.3313 | 0.866461 | ||||||||
\(996\) | −13.6438 | −0.432322 | ||||||||
\(997\) | 13.4114 | 0.424745 | 0.212372 | − | 0.977189i | \(-0.431881\pi\) | ||||
0.212372 | + | 0.977189i | \(0.431881\pi\) | |||||||
\(998\) | 25.9442 | 0.821248 | ||||||||
\(999\) | −24.5822 | −0.777747 |
(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 | 6014.2.a.l.1.15 | ✓ | 38 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6014.2.a.l.1.15 | ✓ | 38 | 1.1 | even | 1 | trivial |