Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8002,2,Mod(1,8002)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8002, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8002.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8002 = 2 \cdot 4001 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8002.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: | \(63.8962916974\) |
Analytic rank: | \(0\) |
Dimension: | \(77\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.8 | ||
Character | \(\chi\) | \(=\) | 8002.1 |
$q$-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 | ||||||||
\(3\) | −2.61328 | −1.50878 | −0.754389 | − | 0.656427i | \(-0.772067\pi\) | ||||
−0.754389 | + | 0.656427i | \(0.772067\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −3.49569 | −1.56332 | −0.781661 | − | 0.623704i | \(-0.785627\pi\) | ||||
−0.781661 | + | 0.623704i | \(0.785627\pi\) | |||||||
\(6\) | 2.61328 | 1.06687 | ||||||||
\(7\) | −0.478818 | −0.180976 | −0.0904881 | − | 0.995898i | \(-0.528843\pi\) | ||||
−0.0904881 | + | 0.995898i | \(0.528843\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 3.82924 | 1.27641 | ||||||||
\(10\) | 3.49569 | 1.10544 | ||||||||
\(11\) | −0.518766 | −0.156414 | −0.0782068 | − | 0.996937i | \(-0.524919\pi\) | ||||
−0.0782068 | + | 0.996937i | \(0.524919\pi\) | |||||||
\(12\) | −2.61328 | −0.754389 | ||||||||
\(13\) | 0.394051 | 0.109290 | 0.0546451 | − | 0.998506i | \(-0.482597\pi\) | ||||
0.0546451 | + | 0.998506i | \(0.482597\pi\) | |||||||
\(14\) | 0.478818 | 0.127969 | ||||||||
\(15\) | 9.13523 | 2.35871 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −1.63145 | −0.395684 | −0.197842 | − | 0.980234i | \(-0.563393\pi\) | ||||
−0.197842 | + | 0.980234i | \(0.563393\pi\) | |||||||
\(18\) | −3.82924 | −0.902560 | ||||||||
\(19\) | −1.57912 | −0.362275 | −0.181138 | − | 0.983458i | \(-0.557978\pi\) | ||||
−0.181138 | + | 0.983458i | \(0.557978\pi\) | |||||||
\(20\) | −3.49569 | −0.781661 | ||||||||
\(21\) | 1.25129 | 0.273053 | ||||||||
\(22\) | 0.518766 | 0.110601 | ||||||||
\(23\) | −1.44805 | −0.301940 | −0.150970 | − | 0.988538i | \(-0.548240\pi\) | ||||
−0.150970 | + | 0.988538i | \(0.548240\pi\) | |||||||
\(24\) | 2.61328 | 0.533434 | ||||||||
\(25\) | 7.21987 | 1.44397 | ||||||||
\(26\) | −0.394051 | −0.0772799 | ||||||||
\(27\) | −2.16703 | −0.417046 | ||||||||
\(28\) | −0.478818 | −0.0904881 | ||||||||
\(29\) | 6.68629 | 1.24161 | 0.620806 | − | 0.783964i | \(-0.286805\pi\) | ||||
0.620806 | + | 0.783964i | \(0.286805\pi\) | |||||||
\(30\) | −9.13523 | −1.66786 | ||||||||
\(31\) | 0.0346656 | 0.00622613 | 0.00311307 | − | 0.999995i | \(-0.499009\pi\) | ||||
0.00311307 | + | 0.999995i | \(0.499009\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 1.35568 | 0.235994 | ||||||||
\(34\) | 1.63145 | 0.279791 | ||||||||
\(35\) | 1.67380 | 0.282924 | ||||||||
\(36\) | 3.82924 | 0.638206 | ||||||||
\(37\) | −0.471003 | −0.0774323 | −0.0387162 | − | 0.999250i | \(-0.512327\pi\) | ||||
−0.0387162 | + | 0.999250i | \(0.512327\pi\) | |||||||
\(38\) | 1.57912 | 0.256167 | ||||||||
\(39\) | −1.02977 | −0.164895 | ||||||||
\(40\) | 3.49569 | 0.552718 | ||||||||
\(41\) | −1.81254 | −0.283071 | −0.141536 | − | 0.989933i | \(-0.545204\pi\) | ||||
−0.141536 | + | 0.989933i | \(0.545204\pi\) | |||||||
\(42\) | −1.25129 | −0.193078 | ||||||||
\(43\) | 0.346409 | 0.0528268 | 0.0264134 | − | 0.999651i | \(-0.491591\pi\) | ||||
0.0264134 | + | 0.999651i | \(0.491591\pi\) | |||||||
\(44\) | −0.518766 | −0.0782068 | ||||||||
\(45\) | −13.3858 | −1.99544 | ||||||||
\(46\) | 1.44805 | 0.213504 | ||||||||
\(47\) | 13.5266 | 1.97305 | 0.986526 | − | 0.163606i | \(-0.0523125\pi\) | ||||
0.986526 | + | 0.163606i | \(0.0523125\pi\) | |||||||
\(48\) | −2.61328 | −0.377195 | ||||||||
\(49\) | −6.77073 | −0.967248 | ||||||||
\(50\) | −7.21987 | −1.02104 | ||||||||
\(51\) | 4.26343 | 0.597000 | ||||||||
\(52\) | 0.394051 | 0.0546451 | ||||||||
\(53\) | 0.660429 | 0.0907169 | 0.0453585 | − | 0.998971i | \(-0.485557\pi\) | ||||
0.0453585 | + | 0.998971i | \(0.485557\pi\) | |||||||
\(54\) | 2.16703 | 0.294896 | ||||||||
\(55\) | 1.81344 | 0.244525 | ||||||||
\(56\) | 0.478818 | 0.0639847 | ||||||||
\(57\) | 4.12669 | 0.546593 | ||||||||
\(58\) | −6.68629 | −0.877953 | ||||||||
\(59\) | 2.43140 | 0.316541 | 0.158271 | − | 0.987396i | \(-0.449408\pi\) | ||||
0.158271 | + | 0.987396i | \(0.449408\pi\) | |||||||
\(60\) | 9.13523 | 1.17935 | ||||||||
\(61\) | −6.58531 | −0.843163 | −0.421581 | − | 0.906791i | \(-0.638525\pi\) | ||||
−0.421581 | + | 0.906791i | \(0.638525\pi\) | |||||||
\(62\) | −0.0346656 | −0.00440254 | ||||||||
\(63\) | −1.83351 | −0.231000 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −1.37748 | −0.170856 | ||||||||
\(66\) | −1.35568 | −0.166873 | ||||||||
\(67\) | −15.0872 | −1.84320 | −0.921600 | − | 0.388142i | \(-0.873117\pi\) | ||||
−0.921600 | + | 0.388142i | \(0.873117\pi\) | |||||||
\(68\) | −1.63145 | −0.197842 | ||||||||
\(69\) | 3.78417 | 0.455561 | ||||||||
\(70\) | −1.67380 | −0.200057 | ||||||||
\(71\) | −3.80058 | −0.451046 | −0.225523 | − | 0.974238i | \(-0.572409\pi\) | ||||
−0.225523 | + | 0.974238i | \(0.572409\pi\) | |||||||
\(72\) | −3.82924 | −0.451280 | ||||||||
\(73\) | −4.71638 | −0.552011 | −0.276005 | − | 0.961156i | \(-0.589011\pi\) | ||||
−0.276005 | + | 0.961156i | \(0.589011\pi\) | |||||||
\(74\) | 0.471003 | 0.0547529 | ||||||||
\(75\) | −18.8675 | −2.17864 | ||||||||
\(76\) | −1.57912 | −0.181138 | ||||||||
\(77\) | 0.248394 | 0.0283071 | ||||||||
\(78\) | 1.02977 | 0.116598 | ||||||||
\(79\) | −7.31985 | −0.823548 | −0.411774 | − | 0.911286i | \(-0.635091\pi\) | ||||
−0.411774 | + | 0.911286i | \(0.635091\pi\) | |||||||
\(80\) | −3.49569 | −0.390830 | ||||||||
\(81\) | −5.82465 | −0.647183 | ||||||||
\(82\) | 1.81254 | 0.200162 | ||||||||
\(83\) | −1.54698 | −0.169803 | −0.0849017 | − | 0.996389i | \(-0.527058\pi\) | ||||
−0.0849017 | + | 0.996389i | \(0.527058\pi\) | |||||||
\(84\) | 1.25129 | 0.136526 | ||||||||
\(85\) | 5.70304 | 0.618582 | ||||||||
\(86\) | −0.346409 | −0.0373542 | ||||||||
\(87\) | −17.4732 | −1.87332 | ||||||||
\(88\) | 0.518766 | 0.0553006 | ||||||||
\(89\) | 15.2625 | 1.61782 | 0.808909 | − | 0.587934i | \(-0.200059\pi\) | ||||
0.808909 | + | 0.587934i | \(0.200059\pi\) | |||||||
\(90\) | 13.3858 | 1.41099 | ||||||||
\(91\) | −0.188679 | −0.0197789 | ||||||||
\(92\) | −1.44805 | −0.150970 | ||||||||
\(93\) | −0.0905911 | −0.00939386 | ||||||||
\(94\) | −13.5266 | −1.39516 | ||||||||
\(95\) | 5.52012 | 0.566352 | ||||||||
\(96\) | 2.61328 | 0.266717 | ||||||||
\(97\) | 6.19777 | 0.629288 | 0.314644 | − | 0.949210i | \(-0.398115\pi\) | ||||
0.314644 | + | 0.949210i | \(0.398115\pi\) | |||||||
\(98\) | 6.77073 | 0.683947 | ||||||||
\(99\) | −1.98648 | −0.199648 | ||||||||
\(100\) | 7.21987 | 0.721987 | ||||||||
\(101\) | −9.37856 | −0.933201 | −0.466601 | − | 0.884468i | \(-0.654521\pi\) | ||||
−0.466601 | + | 0.884468i | \(0.654521\pi\) | |||||||
\(102\) | −4.26343 | −0.422143 | ||||||||
\(103\) | 15.4375 | 1.52110 | 0.760552 | − | 0.649277i | \(-0.224928\pi\) | ||||
0.760552 | + | 0.649277i | \(0.224928\pi\) | |||||||
\(104\) | −0.394051 | −0.0386399 | ||||||||
\(105\) | −4.37411 | −0.426869 | ||||||||
\(106\) | −0.660429 | −0.0641465 | ||||||||
\(107\) | 15.5729 | 1.50549 | 0.752744 | − | 0.658313i | \(-0.228730\pi\) | ||||
0.752744 | + | 0.658313i | \(0.228730\pi\) | |||||||
\(108\) | −2.16703 | −0.208523 | ||||||||
\(109\) | −4.04637 | −0.387572 | −0.193786 | − | 0.981044i | \(-0.562077\pi\) | ||||
−0.193786 | + | 0.981044i | \(0.562077\pi\) | |||||||
\(110\) | −1.81344 | −0.172905 | ||||||||
\(111\) | 1.23086 | 0.116828 | ||||||||
\(112\) | −0.478818 | −0.0452440 | ||||||||
\(113\) | 16.3223 | 1.53547 | 0.767735 | − | 0.640768i | \(-0.221384\pi\) | ||||
0.767735 | + | 0.640768i | \(0.221384\pi\) | |||||||
\(114\) | −4.12669 | −0.386500 | ||||||||
\(115\) | 5.06195 | 0.472029 | ||||||||
\(116\) | 6.68629 | 0.620806 | ||||||||
\(117\) | 1.50892 | 0.139499 | ||||||||
\(118\) | −2.43140 | −0.223828 | ||||||||
\(119\) | 0.781167 | 0.0716094 | ||||||||
\(120\) | −9.13523 | −0.833928 | ||||||||
\(121\) | −10.7309 | −0.975535 | ||||||||
\(122\) | 6.58531 | 0.596206 | ||||||||
\(123\) | 4.73668 | 0.427092 | ||||||||
\(124\) | 0.0346656 | 0.00311307 | ||||||||
\(125\) | −7.75997 | −0.694073 | ||||||||
\(126\) | 1.83351 | 0.163342 | ||||||||
\(127\) | −0.835001 | −0.0740944 | −0.0370472 | − | 0.999314i | \(-0.511795\pi\) | ||||
−0.0370472 | + | 0.999314i | \(0.511795\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | −0.905263 | −0.0797039 | ||||||||
\(130\) | 1.37748 | 0.120813 | ||||||||
\(131\) | −16.8384 | −1.47118 | −0.735589 | − | 0.677428i | \(-0.763094\pi\) | ||||
−0.735589 | + | 0.677428i | \(0.763094\pi\) | |||||||
\(132\) | 1.35568 | 0.117997 | ||||||||
\(133\) | 0.756111 | 0.0655631 | ||||||||
\(134\) | 15.0872 | 1.30334 | ||||||||
\(135\) | 7.57528 | 0.651977 | ||||||||
\(136\) | 1.63145 | 0.139896 | ||||||||
\(137\) | −20.0997 | −1.71723 | −0.858615 | − | 0.512622i | \(-0.828674\pi\) | ||||
−0.858615 | + | 0.512622i | \(0.828674\pi\) | |||||||
\(138\) | −3.78417 | −0.322130 | ||||||||
\(139\) | −8.90098 | −0.754971 | −0.377486 | − | 0.926015i | \(-0.623211\pi\) | ||||
−0.377486 | + | 0.926015i | \(0.623211\pi\) | |||||||
\(140\) | 1.67380 | 0.141462 | ||||||||
\(141\) | −35.3487 | −2.97690 | ||||||||
\(142\) | 3.80058 | 0.318937 | ||||||||
\(143\) | −0.204420 | −0.0170945 | ||||||||
\(144\) | 3.82924 | 0.319103 | ||||||||
\(145\) | −23.3732 | −1.94104 | ||||||||
\(146\) | 4.71638 | 0.390331 | ||||||||
\(147\) | 17.6938 | 1.45936 | ||||||||
\(148\) | −0.471003 | −0.0387162 | ||||||||
\(149\) | −15.4223 | −1.26345 | −0.631724 | − | 0.775194i | \(-0.717652\pi\) | ||||
−0.631724 | + | 0.775194i | \(0.717652\pi\) | |||||||
\(150\) | 18.8675 | 1.54053 | ||||||||
\(151\) | −23.7803 | −1.93521 | −0.967607 | − | 0.252460i | \(-0.918760\pi\) | ||||
−0.967607 | + | 0.252460i | \(0.918760\pi\) | |||||||
\(152\) | 1.57912 | 0.128084 | ||||||||
\(153\) | −6.24721 | −0.505057 | ||||||||
\(154\) | −0.248394 | −0.0200162 | ||||||||
\(155\) | −0.121180 | −0.00973345 | ||||||||
\(156\) | −1.02977 | −0.0824474 | ||||||||
\(157\) | 7.41881 | 0.592085 | 0.296043 | − | 0.955175i | \(-0.404333\pi\) | ||||
0.296043 | + | 0.955175i | \(0.404333\pi\) | |||||||
\(158\) | 7.31985 | 0.582336 | ||||||||
\(159\) | −1.72589 | −0.136872 | ||||||||
\(160\) | 3.49569 | 0.276359 | ||||||||
\(161\) | 0.693354 | 0.0546439 | ||||||||
\(162\) | 5.82465 | 0.457627 | ||||||||
\(163\) | −19.8529 | −1.55500 | −0.777500 | − | 0.628883i | \(-0.783512\pi\) | ||||
−0.777500 | + | 0.628883i | \(0.783512\pi\) | |||||||
\(164\) | −1.81254 | −0.141536 | ||||||||
\(165\) | −4.73904 | −0.368934 | ||||||||
\(166\) | 1.54698 | 0.120069 | ||||||||
\(167\) | 2.89092 | 0.223706 | 0.111853 | − | 0.993725i | \(-0.464321\pi\) | ||||
0.111853 | + | 0.993725i | \(0.464321\pi\) | |||||||
\(168\) | −1.25129 | −0.0965388 | ||||||||
\(169\) | −12.8447 | −0.988056 | ||||||||
\(170\) | −5.70304 | −0.437403 | ||||||||
\(171\) | −6.04683 | −0.462413 | ||||||||
\(172\) | 0.346409 | 0.0264134 | ||||||||
\(173\) | −10.7517 | −0.817435 | −0.408718 | − | 0.912661i | \(-0.634024\pi\) | ||||
−0.408718 | + | 0.912661i | \(0.634024\pi\) | |||||||
\(174\) | 17.4732 | 1.32464 | ||||||||
\(175\) | −3.45700 | −0.261325 | ||||||||
\(176\) | −0.518766 | −0.0391034 | ||||||||
\(177\) | −6.35393 | −0.477590 | ||||||||
\(178\) | −15.2625 | −1.14397 | ||||||||
\(179\) | −1.79236 | −0.133967 | −0.0669836 | − | 0.997754i | \(-0.521338\pi\) | ||||
−0.0669836 | + | 0.997754i | \(0.521338\pi\) | |||||||
\(180\) | −13.3858 | −0.997722 | ||||||||
\(181\) | −9.37633 | −0.696937 | −0.348468 | − | 0.937320i | \(-0.613298\pi\) | ||||
−0.348468 | + | 0.937320i | \(0.613298\pi\) | |||||||
\(182\) | 0.188679 | 0.0139858 | ||||||||
\(183\) | 17.2093 | 1.27215 | ||||||||
\(184\) | 1.44805 | 0.106752 | ||||||||
\(185\) | 1.64648 | 0.121052 | ||||||||
\(186\) | 0.0905911 | 0.00664246 | ||||||||
\(187\) | 0.846339 | 0.0618905 | ||||||||
\(188\) | 13.5266 | 0.986526 | ||||||||
\(189\) | 1.03761 | 0.0754753 | ||||||||
\(190\) | −5.52012 | −0.400472 | ||||||||
\(191\) | −8.09957 | −0.586064 | −0.293032 | − | 0.956103i | \(-0.594664\pi\) | ||||
−0.293032 | + | 0.956103i | \(0.594664\pi\) | |||||||
\(192\) | −2.61328 | −0.188597 | ||||||||
\(193\) | −15.3567 | −1.10540 | −0.552700 | − | 0.833381i | \(-0.686402\pi\) | ||||
−0.552700 | + | 0.833381i | \(0.686402\pi\) | |||||||
\(194\) | −6.19777 | −0.444974 | ||||||||
\(195\) | 3.59975 | 0.257783 | ||||||||
\(196\) | −6.77073 | −0.483624 | ||||||||
\(197\) | 7.45842 | 0.531390 | 0.265695 | − | 0.964057i | \(-0.414399\pi\) | ||||
0.265695 | + | 0.964057i | \(0.414399\pi\) | |||||||
\(198\) | 1.98648 | 0.141173 | ||||||||
\(199\) | 1.82888 | 0.129646 | 0.0648230 | − | 0.997897i | \(-0.479352\pi\) | ||||
0.0648230 | + | 0.997897i | \(0.479352\pi\) | |||||||
\(200\) | −7.21987 | −0.510522 | ||||||||
\(201\) | 39.4272 | 2.78098 | ||||||||
\(202\) | 9.37856 | 0.659873 | ||||||||
\(203\) | −3.20151 | −0.224702 | ||||||||
\(204\) | 4.26343 | 0.298500 | ||||||||
\(205\) | 6.33609 | 0.442531 | ||||||||
\(206\) | −15.4375 | −1.07558 | ||||||||
\(207\) | −5.54494 | −0.385400 | ||||||||
\(208\) | 0.394051 | 0.0273226 | ||||||||
\(209\) | 0.819193 | 0.0566648 | ||||||||
\(210\) | 4.37411 | 0.301842 | ||||||||
\(211\) | 12.8834 | 0.886930 | 0.443465 | − | 0.896292i | \(-0.353749\pi\) | ||||
0.443465 | + | 0.896292i | \(0.353749\pi\) | |||||||
\(212\) | 0.660429 | 0.0453585 | ||||||||
\(213\) | 9.93198 | 0.680528 | ||||||||
\(214\) | −15.5729 | −1.06454 | ||||||||
\(215\) | −1.21094 | −0.0825853 | ||||||||
\(216\) | 2.16703 | 0.147448 | ||||||||
\(217\) | −0.0165985 | −0.00112678 | ||||||||
\(218\) | 4.04637 | 0.274055 | ||||||||
\(219\) | 12.3252 | 0.832862 | ||||||||
\(220\) | 1.81344 | 0.122262 | ||||||||
\(221\) | −0.642875 | −0.0432444 | ||||||||
\(222\) | −1.23086 | −0.0826101 | ||||||||
\(223\) | −14.3736 | −0.962527 | −0.481263 | − | 0.876576i | \(-0.659822\pi\) | ||||
−0.481263 | + | 0.876576i | \(0.659822\pi\) | |||||||
\(224\) | 0.478818 | 0.0319924 | ||||||||
\(225\) | 27.6466 | 1.84311 | ||||||||
\(226\) | −16.3223 | −1.08574 | ||||||||
\(227\) | 25.8048 | 1.71272 | 0.856362 | − | 0.516376i | \(-0.172719\pi\) | ||||
0.856362 | + | 0.516376i | \(0.172719\pi\) | |||||||
\(228\) | 4.12669 | 0.273296 | ||||||||
\(229\) | −9.81575 | −0.648643 | −0.324321 | − | 0.945947i | \(-0.605136\pi\) | ||||
−0.324321 | + | 0.945947i | \(0.605136\pi\) | |||||||
\(230\) | −5.06195 | −0.333775 | ||||||||
\(231\) | −0.649124 | −0.0427092 | ||||||||
\(232\) | −6.68629 | −0.438976 | ||||||||
\(233\) | 27.4265 | 1.79677 | 0.898384 | − | 0.439210i | \(-0.144742\pi\) | ||||
0.898384 | + | 0.439210i | \(0.144742\pi\) | |||||||
\(234\) | −1.50892 | −0.0986410 | ||||||||
\(235\) | −47.2847 | −3.08451 | ||||||||
\(236\) | 2.43140 | 0.158271 | ||||||||
\(237\) | 19.1288 | 1.24255 | ||||||||
\(238\) | −0.781167 | −0.0506355 | ||||||||
\(239\) | −11.9191 | −0.770985 | −0.385493 | − | 0.922711i | \(-0.625968\pi\) | ||||
−0.385493 | + | 0.922711i | \(0.625968\pi\) | |||||||
\(240\) | 9.13523 | 0.589676 | ||||||||
\(241\) | −3.75561 | −0.241920 | −0.120960 | − | 0.992657i | \(-0.538597\pi\) | ||||
−0.120960 | + | 0.992657i | \(0.538597\pi\) | |||||||
\(242\) | 10.7309 | 0.689807 | ||||||||
\(243\) | 21.7225 | 1.39350 | ||||||||
\(244\) | −6.58531 | −0.421581 | ||||||||
\(245\) | 23.6684 | 1.51212 | ||||||||
\(246\) | −4.73668 | −0.302000 | ||||||||
\(247\) | −0.622255 | −0.0395931 | ||||||||
\(248\) | −0.0346656 | −0.00220127 | ||||||||
\(249\) | 4.04270 | 0.256196 | ||||||||
\(250\) | 7.75997 | 0.490784 | ||||||||
\(251\) | −22.7390 | −1.43527 | −0.717636 | − | 0.696418i | \(-0.754776\pi\) | ||||
−0.717636 | + | 0.696418i | \(0.754776\pi\) | |||||||
\(252\) | −1.83351 | −0.115500 | ||||||||
\(253\) | 0.751200 | 0.0472275 | ||||||||
\(254\) | 0.835001 | 0.0523926 | ||||||||
\(255\) | −14.9037 | −0.933303 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 15.7572 | 0.982905 | 0.491452 | − | 0.870904i | \(-0.336466\pi\) | ||||
0.491452 | + | 0.870904i | \(0.336466\pi\) | |||||||
\(258\) | 0.905263 | 0.0563592 | ||||||||
\(259\) | 0.225524 | 0.0140134 | ||||||||
\(260\) | −1.37748 | −0.0854279 | ||||||||
\(261\) | 25.6034 | 1.58481 | ||||||||
\(262\) | 16.8384 | 1.04028 | ||||||||
\(263\) | −3.72559 | −0.229730 | −0.114865 | − | 0.993381i | \(-0.536644\pi\) | ||||
−0.114865 | + | 0.993381i | \(0.536644\pi\) | |||||||
\(264\) | −1.35568 | −0.0834363 | ||||||||
\(265\) | −2.30866 | −0.141820 | ||||||||
\(266\) | −0.756111 | −0.0463601 | ||||||||
\(267\) | −39.8851 | −2.44093 | ||||||||
\(268\) | −15.0872 | −0.921600 | ||||||||
\(269\) | −11.7094 | −0.713934 | −0.356967 | − | 0.934117i | \(-0.616189\pi\) | ||||
−0.356967 | + | 0.934117i | \(0.616189\pi\) | |||||||
\(270\) | −7.57528 | −0.461017 | ||||||||
\(271\) | 17.9900 | 1.09281 | 0.546407 | − | 0.837520i | \(-0.315995\pi\) | ||||
0.546407 | + | 0.837520i | \(0.315995\pi\) | |||||||
\(272\) | −1.63145 | −0.0989211 | ||||||||
\(273\) | 0.493071 | 0.0298420 | ||||||||
\(274\) | 20.0997 | 1.21426 | ||||||||
\(275\) | −3.74542 | −0.225857 | ||||||||
\(276\) | 3.78417 | 0.227780 | ||||||||
\(277\) | −20.7574 | −1.24719 | −0.623597 | − | 0.781746i | \(-0.714329\pi\) | ||||
−0.623597 | + | 0.781746i | \(0.714329\pi\) | |||||||
\(278\) | 8.90098 | 0.533845 | ||||||||
\(279\) | 0.132743 | 0.00794712 | ||||||||
\(280\) | −1.67380 | −0.100029 | ||||||||
\(281\) | 27.2542 | 1.62585 | 0.812924 | − | 0.582369i | \(-0.197874\pi\) | ||||
0.812924 | + | 0.582369i | \(0.197874\pi\) | |||||||
\(282\) | 35.3487 | 2.10498 | ||||||||
\(283\) | 17.5891 | 1.04556 | 0.522782 | − | 0.852466i | \(-0.324894\pi\) | ||||
0.522782 | + | 0.852466i | \(0.324894\pi\) | |||||||
\(284\) | −3.80058 | −0.225523 | ||||||||
\(285\) | −14.4256 | −0.854500 | ||||||||
\(286\) | 0.204420 | 0.0120876 | ||||||||
\(287\) | 0.867877 | 0.0512292 | ||||||||
\(288\) | −3.82924 | −0.225640 | ||||||||
\(289\) | −14.3384 | −0.843434 | ||||||||
\(290\) | 23.3732 | 1.37252 | ||||||||
\(291\) | −16.1965 | −0.949457 | ||||||||
\(292\) | −4.71638 | −0.276005 | ||||||||
\(293\) | −29.2878 | −1.71101 | −0.855505 | − | 0.517794i | \(-0.826753\pi\) | ||||
−0.855505 | + | 0.517794i | \(0.826753\pi\) | |||||||
\(294\) | −17.6938 | −1.03193 | ||||||||
\(295\) | −8.49942 | −0.494855 | ||||||||
\(296\) | 0.471003 | 0.0273765 | ||||||||
\(297\) | 1.12418 | 0.0652317 | ||||||||
\(298\) | 15.4223 | 0.893392 | ||||||||
\(299\) | −0.570608 | −0.0329991 | ||||||||
\(300\) | −18.8675 | −1.08932 | ||||||||
\(301\) | −0.165867 | −0.00956039 | ||||||||
\(302\) | 23.7803 | 1.36840 | ||||||||
\(303\) | 24.5088 | 1.40799 | ||||||||
\(304\) | −1.57912 | −0.0905688 | ||||||||
\(305\) | 23.0202 | 1.31813 | ||||||||
\(306\) | 6.24721 | 0.357129 | ||||||||
\(307\) | 1.91738 | 0.109431 | 0.0547154 | − | 0.998502i | \(-0.482575\pi\) | ||||
0.0547154 | + | 0.998502i | \(0.482575\pi\) | |||||||
\(308\) | 0.248394 | 0.0141536 | ||||||||
\(309\) | −40.3426 | −2.29501 | ||||||||
\(310\) | 0.121180 | 0.00688259 | ||||||||
\(311\) | −2.28986 | −0.129846 | −0.0649230 | − | 0.997890i | \(-0.520680\pi\) | ||||
−0.0649230 | + | 0.997890i | \(0.520680\pi\) | |||||||
\(312\) | 1.02977 | 0.0582991 | ||||||||
\(313\) | 12.8454 | 0.726067 | 0.363034 | − | 0.931776i | \(-0.381741\pi\) | ||||
0.363034 | + | 0.931776i | \(0.381741\pi\) | |||||||
\(314\) | −7.41881 | −0.418668 | ||||||||
\(315\) | 6.40938 | 0.361128 | ||||||||
\(316\) | −7.31985 | −0.411774 | ||||||||
\(317\) | 2.01283 | 0.113052 | 0.0565259 | − | 0.998401i | \(-0.481998\pi\) | ||||
0.0565259 | + | 0.998401i | \(0.481998\pi\) | |||||||
\(318\) | 1.72589 | 0.0967829 | ||||||||
\(319\) | −3.46862 | −0.194205 | ||||||||
\(320\) | −3.49569 | −0.195415 | ||||||||
\(321\) | −40.6964 | −2.27145 | ||||||||
\(322\) | −0.693354 | −0.0386391 | ||||||||
\(323\) | 2.57625 | 0.143347 | ||||||||
\(324\) | −5.82465 | −0.323592 | ||||||||
\(325\) | 2.84500 | 0.157812 | ||||||||
\(326\) | 19.8529 | 1.09955 | ||||||||
\(327\) | 10.5743 | 0.584761 | ||||||||
\(328\) | 1.81254 | 0.100081 | ||||||||
\(329\) | −6.47676 | −0.357075 | ||||||||
\(330\) | 4.73904 | 0.260876 | ||||||||
\(331\) | 23.5787 | 1.29600 | 0.648001 | − | 0.761640i | \(-0.275605\pi\) | ||||
0.648001 | + | 0.761640i | \(0.275605\pi\) | |||||||
\(332\) | −1.54698 | −0.0849017 | ||||||||
\(333\) | −1.80358 | −0.0988356 | ||||||||
\(334\) | −2.89092 | −0.158184 | ||||||||
\(335\) | 52.7403 | 2.88151 | ||||||||
\(336\) | 1.25129 | 0.0682632 | ||||||||
\(337\) | −26.4651 | −1.44164 | −0.720822 | − | 0.693120i | \(-0.756236\pi\) | ||||
−0.720822 | + | 0.693120i | \(0.756236\pi\) | |||||||
\(338\) | 12.8447 | 0.698661 | ||||||||
\(339\) | −42.6547 | −2.31668 | ||||||||
\(340\) | 5.70304 | 0.309291 | ||||||||
\(341\) | −0.0179833 | −0.000973852 0 | ||||||||
\(342\) | 6.04683 | 0.326975 | ||||||||
\(343\) | 6.59367 | 0.356025 | ||||||||
\(344\) | −0.346409 | −0.0186771 | ||||||||
\(345\) | −13.2283 | −0.712187 | ||||||||
\(346\) | 10.7517 | 0.578014 | ||||||||
\(347\) | −13.2596 | −0.711811 | −0.355905 | − | 0.934522i | \(-0.615827\pi\) | ||||
−0.355905 | + | 0.934522i | \(0.615827\pi\) | |||||||
\(348\) | −17.4732 | −0.936659 | ||||||||
\(349\) | 13.0888 | 0.700625 | 0.350313 | − | 0.936633i | \(-0.386075\pi\) | ||||
0.350313 | + | 0.936633i | \(0.386075\pi\) | |||||||
\(350\) | 3.45700 | 0.184784 | ||||||||
\(351\) | −0.853923 | −0.0455790 | ||||||||
\(352\) | 0.518766 | 0.0276503 | ||||||||
\(353\) | 13.9656 | 0.743316 | 0.371658 | − | 0.928370i | \(-0.378789\pi\) | ||||
0.371658 | + | 0.928370i | \(0.378789\pi\) | |||||||
\(354\) | 6.35393 | 0.337707 | ||||||||
\(355\) | 13.2856 | 0.705129 | ||||||||
\(356\) | 15.2625 | 0.808909 | ||||||||
\(357\) | −2.04141 | −0.108043 | ||||||||
\(358\) | 1.79236 | 0.0947291 | ||||||||
\(359\) | 26.5440 | 1.40094 | 0.700470 | − | 0.713681i | \(-0.252974\pi\) | ||||
0.700470 | + | 0.713681i | \(0.252974\pi\) | |||||||
\(360\) | 13.3858 | 0.705496 | ||||||||
\(361\) | −16.5064 | −0.868757 | ||||||||
\(362\) | 9.37633 | 0.492809 | ||||||||
\(363\) | 28.0428 | 1.47187 | ||||||||
\(364\) | −0.188679 | −0.00988946 | ||||||||
\(365\) | 16.4870 | 0.862970 | ||||||||
\(366\) | −17.2093 | −0.899543 | ||||||||
\(367\) | 16.0040 | 0.835400 | 0.417700 | − | 0.908585i | \(-0.362836\pi\) | ||||
0.417700 | + | 0.908585i | \(0.362836\pi\) | |||||||
\(368\) | −1.44805 | −0.0754850 | ||||||||
\(369\) | −6.94065 | −0.361316 | ||||||||
\(370\) | −1.64648 | −0.0855964 | ||||||||
\(371\) | −0.316225 | −0.0164176 | ||||||||
\(372\) | −0.0905911 | −0.00469693 | ||||||||
\(373\) | −28.3811 | −1.46952 | −0.734759 | − | 0.678328i | \(-0.762705\pi\) | ||||
−0.734759 | + | 0.678328i | \(0.762705\pi\) | |||||||
\(374\) | −0.846339 | −0.0437632 | ||||||||
\(375\) | 20.2790 | 1.04720 | ||||||||
\(376\) | −13.5266 | −0.697579 | ||||||||
\(377\) | 2.63474 | 0.135696 | ||||||||
\(378\) | −1.03761 | −0.0533691 | ||||||||
\(379\) | 36.9387 | 1.89741 | 0.948707 | − | 0.316158i | \(-0.102393\pi\) | ||||
0.948707 | + | 0.316158i | \(0.102393\pi\) | |||||||
\(380\) | 5.52012 | 0.283176 | ||||||||
\(381\) | 2.18209 | 0.111792 | ||||||||
\(382\) | 8.09957 | 0.414410 | ||||||||
\(383\) | 14.6807 | 0.750147 | 0.375073 | − | 0.926995i | \(-0.377618\pi\) | ||||
0.375073 | + | 0.926995i | \(0.377618\pi\) | |||||||
\(384\) | 2.61328 | 0.133358 | ||||||||
\(385\) | −0.868310 | −0.0442532 | ||||||||
\(386\) | 15.3567 | 0.781635 | ||||||||
\(387\) | 1.32648 | 0.0674288 | ||||||||
\(388\) | 6.19777 | 0.314644 | ||||||||
\(389\) | 8.06683 | 0.409005 | 0.204502 | − | 0.978866i | \(-0.434442\pi\) | ||||
0.204502 | + | 0.978866i | \(0.434442\pi\) | |||||||
\(390\) | −3.59975 | −0.182280 | ||||||||
\(391\) | 2.36242 | 0.119473 | ||||||||
\(392\) | 6.77073 | 0.341974 | ||||||||
\(393\) | 44.0035 | 2.21968 | ||||||||
\(394\) | −7.45842 | −0.375750 | ||||||||
\(395\) | 25.5879 | 1.28747 | ||||||||
\(396\) | −1.98648 | −0.0998242 | ||||||||
\(397\) | −31.6162 | −1.58677 | −0.793386 | − | 0.608719i | \(-0.791684\pi\) | ||||
−0.793386 | + | 0.608719i | \(0.791684\pi\) | |||||||
\(398\) | −1.82888 | −0.0916735 | ||||||||
\(399\) | −1.97593 | −0.0989203 | ||||||||
\(400\) | 7.21987 | 0.360993 | ||||||||
\(401\) | 2.91703 | 0.145669 | 0.0728347 | − | 0.997344i | \(-0.476795\pi\) | ||||
0.0728347 | + | 0.997344i | \(0.476795\pi\) | |||||||
\(402\) | −39.4272 | −1.96645 | ||||||||
\(403\) | 0.0136600 | 0.000680455 0 | ||||||||
\(404\) | −9.37856 | −0.466601 | ||||||||
\(405\) | 20.3612 | 1.01175 | ||||||||
\(406\) | 3.20151 | 0.158888 | ||||||||
\(407\) | 0.244340 | 0.0121115 | ||||||||
\(408\) | −4.26343 | −0.211071 | ||||||||
\(409\) | 28.1151 | 1.39020 | 0.695102 | − | 0.718911i | \(-0.255359\pi\) | ||||
0.695102 | + | 0.718911i | \(0.255359\pi\) | |||||||
\(410\) | −6.33609 | −0.312917 | ||||||||
\(411\) | 52.5260 | 2.59092 | ||||||||
\(412\) | 15.4375 | 0.760552 | ||||||||
\(413\) | −1.16420 | −0.0572864 | ||||||||
\(414\) | 5.54494 | 0.272519 | ||||||||
\(415\) | 5.40777 | 0.265457 | ||||||||
\(416\) | −0.394051 | −0.0193200 | ||||||||
\(417\) | 23.2608 | 1.13908 | ||||||||
\(418\) | −0.819193 | −0.0400681 | ||||||||
\(419\) | −34.8537 | −1.70271 | −0.851356 | − | 0.524588i | \(-0.824219\pi\) | ||||
−0.851356 | + | 0.524588i | \(0.824219\pi\) | |||||||
\(420\) | −4.37411 | −0.213435 | ||||||||
\(421\) | −25.8122 | −1.25801 | −0.629005 | − | 0.777401i | \(-0.716537\pi\) | ||||
−0.629005 | + | 0.777401i | \(0.716537\pi\) | |||||||
\(422\) | −12.8834 | −0.627154 | ||||||||
\(423\) | 51.7964 | 2.51843 | ||||||||
\(424\) | −0.660429 | −0.0320733 | ||||||||
\(425\) | −11.7788 | −0.571358 | ||||||||
\(426\) | −9.93198 | −0.481206 | ||||||||
\(427\) | 3.15317 | 0.152592 | ||||||||
\(428\) | 15.5729 | 0.752744 | ||||||||
\(429\) | 0.534208 | 0.0257918 | ||||||||
\(430\) | 1.21094 | 0.0583966 | ||||||||
\(431\) | 16.4844 | 0.794028 | 0.397014 | − | 0.917813i | \(-0.370046\pi\) | ||||
0.397014 | + | 0.917813i | \(0.370046\pi\) | |||||||
\(432\) | −2.16703 | −0.104261 | ||||||||
\(433\) | 36.0861 | 1.73419 | 0.867094 | − | 0.498145i | \(-0.165985\pi\) | ||||
0.867094 | + | 0.498145i | \(0.165985\pi\) | |||||||
\(434\) | 0.0165985 | 0.000796755 0 | ||||||||
\(435\) | 61.0808 | 2.92860 | ||||||||
\(436\) | −4.04637 | −0.193786 | ||||||||
\(437\) | 2.28665 | 0.109385 | ||||||||
\(438\) | −12.3252 | −0.588923 | ||||||||
\(439\) | 12.2932 | 0.586721 | 0.293361 | − | 0.956002i | \(-0.405226\pi\) | ||||
0.293361 | + | 0.956002i | \(0.405226\pi\) | |||||||
\(440\) | −1.81344 | −0.0864526 | ||||||||
\(441\) | −25.9268 | −1.23461 | ||||||||
\(442\) | 0.642875 | 0.0305784 | ||||||||
\(443\) | −10.7849 | −0.512405 | −0.256202 | − | 0.966623i | \(-0.582471\pi\) | ||||
−0.256202 | + | 0.966623i | \(0.582471\pi\) | |||||||
\(444\) | 1.23086 | 0.0584141 | ||||||||
\(445\) | −53.3529 | −2.52917 | ||||||||
\(446\) | 14.3736 | 0.680609 | ||||||||
\(447\) | 40.3029 | 1.90626 | ||||||||
\(448\) | −0.478818 | −0.0226220 | ||||||||
\(449\) | −34.6427 | −1.63489 | −0.817446 | − | 0.576006i | \(-0.804611\pi\) | ||||
−0.817446 | + | 0.576006i | \(0.804611\pi\) | |||||||
\(450\) | −27.6466 | −1.30327 | ||||||||
\(451\) | 0.940284 | 0.0442762 | ||||||||
\(452\) | 16.3223 | 0.767735 | ||||||||
\(453\) | 62.1447 | 2.91981 | ||||||||
\(454\) | −25.8048 | −1.21108 | ||||||||
\(455\) | 0.659563 | 0.0309208 | ||||||||
\(456\) | −4.12669 | −0.193250 | ||||||||
\(457\) | 10.9190 | 0.510770 | 0.255385 | − | 0.966839i | \(-0.417798\pi\) | ||||
0.255385 | + | 0.966839i | \(0.417798\pi\) | |||||||
\(458\) | 9.81575 | 0.458660 | ||||||||
\(459\) | 3.53540 | 0.165019 | ||||||||
\(460\) | 5.06195 | 0.236015 | ||||||||
\(461\) | −12.4177 | −0.578349 | −0.289175 | − | 0.957276i | \(-0.593381\pi\) | ||||
−0.289175 | + | 0.957276i | \(0.593381\pi\) | |||||||
\(462\) | 0.649124 | 0.0302000 | ||||||||
\(463\) | −10.9578 | −0.509251 | −0.254626 | − | 0.967040i | \(-0.581952\pi\) | ||||
−0.254626 | + | 0.967040i | \(0.581952\pi\) | |||||||
\(464\) | 6.68629 | 0.310403 | ||||||||
\(465\) | 0.316679 | 0.0146856 | ||||||||
\(466\) | −27.4265 | −1.27051 | ||||||||
\(467\) | 1.70410 | 0.0788561 | 0.0394281 | − | 0.999222i | \(-0.487446\pi\) | ||||
0.0394281 | + | 0.999222i | \(0.487446\pi\) | |||||||
\(468\) | 1.50892 | 0.0697497 | ||||||||
\(469\) | 7.22404 | 0.333575 | ||||||||
\(470\) | 47.2847 | 2.18108 | ||||||||
\(471\) | −19.3874 | −0.893326 | ||||||||
\(472\) | −2.43140 | −0.111914 | ||||||||
\(473\) | −0.179705 | −0.00826283 | ||||||||
\(474\) | −19.1288 | −0.878616 | ||||||||
\(475\) | −11.4010 | −0.523116 | ||||||||
\(476\) | 0.781167 | 0.0358047 | ||||||||
\(477\) | 2.52894 | 0.115792 | ||||||||
\(478\) | 11.9191 | 0.545169 | ||||||||
\(479\) | −12.8413 | −0.586736 | −0.293368 | − | 0.956000i | \(-0.594776\pi\) | ||||
−0.293368 | + | 0.956000i | \(0.594776\pi\) | |||||||
\(480\) | −9.13523 | −0.416964 | ||||||||
\(481\) | −0.185599 | −0.00846260 | ||||||||
\(482\) | 3.75561 | 0.171063 | ||||||||
\(483\) | −1.81193 | −0.0824456 | ||||||||
\(484\) | −10.7309 | −0.487767 | ||||||||
\(485\) | −21.6655 | −0.983780 | ||||||||
\(486\) | −21.7225 | −0.985355 | ||||||||
\(487\) | 12.2065 | 0.553127 | 0.276564 | − | 0.960996i | \(-0.410804\pi\) | ||||
0.276564 | + | 0.960996i | \(0.410804\pi\) | |||||||
\(488\) | 6.58531 | 0.298103 | ||||||||
\(489\) | 51.8812 | 2.34615 | ||||||||
\(490\) | −23.6684 | −1.06923 | ||||||||
\(491\) | −8.79930 | −0.397107 | −0.198554 | − | 0.980090i | \(-0.563624\pi\) | ||||
−0.198554 | + | 0.980090i | \(0.563624\pi\) | |||||||
\(492\) | 4.73668 | 0.213546 | ||||||||
\(493\) | −10.9083 | −0.491287 | ||||||||
\(494\) | 0.622255 | 0.0279966 | ||||||||
\(495\) | 6.94411 | 0.312115 | ||||||||
\(496\) | 0.0346656 | 0.00155653 | ||||||||
\(497\) | 1.81978 | 0.0816285 | ||||||||
\(498\) | −4.04270 | −0.181158 | ||||||||
\(499\) | 23.9035 | 1.07007 | 0.535033 | − | 0.844831i | \(-0.320299\pi\) | ||||
0.535033 | + | 0.844831i | \(0.320299\pi\) | |||||||
\(500\) | −7.75997 | −0.347036 | ||||||||
\(501\) | −7.55478 | −0.337523 | ||||||||
\(502\) | 22.7390 | 1.01489 | ||||||||
\(503\) | −3.64287 | −0.162428 | −0.0812138 | − | 0.996697i | \(-0.525880\pi\) | ||||
−0.0812138 | + | 0.996697i | \(0.525880\pi\) | |||||||
\(504\) | 1.83351 | 0.0816709 | ||||||||
\(505\) | 32.7845 | 1.45889 | ||||||||
\(506\) | −0.751200 | −0.0333949 | ||||||||
\(507\) | 33.5669 | 1.49076 | ||||||||
\(508\) | −0.835001 | −0.0370472 | ||||||||
\(509\) | 25.7731 | 1.14237 | 0.571186 | − | 0.820821i | \(-0.306484\pi\) | ||||
0.571186 | + | 0.820821i | \(0.306484\pi\) | |||||||
\(510\) | 14.9037 | 0.659945 | ||||||||
\(511\) | 2.25829 | 0.0999008 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 3.42201 | 0.151085 | ||||||||
\(514\) | −15.7572 | −0.695019 | ||||||||
\(515\) | −53.9649 | −2.37798 | ||||||||
\(516\) | −0.905263 | −0.0398520 | ||||||||
\(517\) | −7.01711 | −0.308612 | ||||||||
\(518\) | −0.225524 | −0.00990897 | ||||||||
\(519\) | 28.0972 | 1.23333 | ||||||||
\(520\) | 1.37748 | 0.0604066 | ||||||||
\(521\) | 10.9232 | 0.478554 | 0.239277 | − | 0.970951i | \(-0.423090\pi\) | ||||
0.239277 | + | 0.970951i | \(0.423090\pi\) | |||||||
\(522\) | −25.6034 | −1.12063 | ||||||||
\(523\) | 3.92120 | 0.171462 | 0.0857311 | − | 0.996318i | \(-0.472677\pi\) | ||||
0.0857311 | + | 0.996318i | \(0.472677\pi\) | |||||||
\(524\) | −16.8384 | −0.735589 | ||||||||
\(525\) | 9.03411 | 0.394281 | ||||||||
\(526\) | 3.72559 | 0.162444 | ||||||||
\(527\) | −0.0565552 | −0.00246358 | ||||||||
\(528\) | 1.35568 | 0.0589984 | ||||||||
\(529\) | −20.9031 | −0.908832 | ||||||||
\(530\) | 2.30866 | 0.100282 | ||||||||
\(531\) | 9.31040 | 0.404037 | ||||||||
\(532\) | 0.756111 | 0.0327816 | ||||||||
\(533\) | −0.714234 | −0.0309369 | ||||||||
\(534\) | 39.8851 | 1.72600 | ||||||||
\(535\) | −54.4381 | −2.35356 | ||||||||
\(536\) | 15.0872 | 0.651669 | ||||||||
\(537\) | 4.68394 | 0.202127 | ||||||||
\(538\) | 11.7094 | 0.504828 | ||||||||
\(539\) | 3.51242 | 0.151291 | ||||||||
\(540\) | 7.57528 | 0.325988 | ||||||||
\(541\) | 33.3609 | 1.43430 | 0.717149 | − | 0.696920i | \(-0.245447\pi\) | ||||
0.717149 | + | 0.696920i | \(0.245447\pi\) | |||||||
\(542\) | −17.9900 | −0.772736 | ||||||||
\(543\) | 24.5030 | 1.05152 | ||||||||
\(544\) | 1.63145 | 0.0699478 | ||||||||
\(545\) | 14.1449 | 0.605900 | ||||||||
\(546\) | −0.493071 | −0.0211015 | ||||||||
\(547\) | −17.5347 | −0.749729 | −0.374865 | − | 0.927080i | \(-0.622311\pi\) | ||||
−0.374865 | + | 0.927080i | \(0.622311\pi\) | |||||||
\(548\) | −20.0997 | −0.858615 | ||||||||
\(549\) | −25.2167 | −1.07622 | ||||||||
\(550\) | 3.74542 | 0.159705 | ||||||||
\(551\) | −10.5585 | −0.449805 | ||||||||
\(552\) | −3.78417 | −0.161065 | ||||||||
\(553\) | 3.50487 | 0.149042 | ||||||||
\(554\) | 20.7574 | 0.881899 | ||||||||
\(555\) | −4.30272 | −0.182640 | ||||||||
\(556\) | −8.90098 | −0.377486 | ||||||||
\(557\) | 14.0175 | 0.593940 | 0.296970 | − | 0.954887i | \(-0.404024\pi\) | ||||
0.296970 | + | 0.954887i | \(0.404024\pi\) | |||||||
\(558\) | −0.132743 | −0.00561946 | ||||||||
\(559\) | 0.136503 | 0.00577345 | ||||||||
\(560\) | 1.67380 | 0.0707310 | ||||||||
\(561\) | −2.21172 | −0.0933790 | ||||||||
\(562\) | −27.2542 | −1.14965 | ||||||||
\(563\) | −15.2895 | −0.644377 | −0.322188 | − | 0.946676i | \(-0.604418\pi\) | ||||
−0.322188 | + | 0.946676i | \(0.604418\pi\) | |||||||
\(564\) | −35.3487 | −1.48845 | ||||||||
\(565\) | −57.0576 | −2.40043 | ||||||||
\(566\) | −17.5891 | −0.739326 | ||||||||
\(567\) | 2.78894 | 0.117125 | ||||||||
\(568\) | 3.80058 | 0.159469 | ||||||||
\(569\) | 21.0722 | 0.883392 | 0.441696 | − | 0.897165i | \(-0.354377\pi\) | ||||
0.441696 | + | 0.897165i | \(0.354377\pi\) | |||||||
\(570\) | 14.4256 | 0.604223 | ||||||||
\(571\) | −13.4449 | −0.562650 | −0.281325 | − | 0.959613i | \(-0.590774\pi\) | ||||
−0.281325 | + | 0.959613i | \(0.590774\pi\) | |||||||
\(572\) | −0.204420 | −0.00854724 | ||||||||
\(573\) | 21.1664 | 0.884241 | ||||||||
\(574\) | −0.867877 | −0.0362245 | ||||||||
\(575\) | −10.4548 | −0.435993 | ||||||||
\(576\) | 3.82924 | 0.159552 | ||||||||
\(577\) | 33.8215 | 1.40801 | 0.704004 | − | 0.710196i | \(-0.251394\pi\) | ||||
0.704004 | + | 0.710196i | \(0.251394\pi\) | |||||||
\(578\) | 14.3384 | 0.596398 | ||||||||
\(579\) | 40.1314 | 1.66780 | ||||||||
\(580\) | −23.3732 | −0.970520 | ||||||||
\(581\) | 0.740723 | 0.0307304 | ||||||||
\(582\) | 16.1965 | 0.671367 | ||||||||
\(583\) | −0.342608 | −0.0141894 | ||||||||
\(584\) | 4.71638 | 0.195165 | ||||||||
\(585\) | −5.27471 | −0.218082 | ||||||||
\(586\) | 29.2878 | 1.20987 | ||||||||
\(587\) | −18.8414 | −0.777669 | −0.388835 | − | 0.921308i | \(-0.627122\pi\) | ||||
−0.388835 | + | 0.921308i | \(0.627122\pi\) | |||||||
\(588\) | 17.6938 | 0.729681 | ||||||||
\(589\) | −0.0547412 | −0.00225557 | ||||||||
\(590\) | 8.49942 | 0.349916 | ||||||||
\(591\) | −19.4909 | −0.801750 | ||||||||
\(592\) | −0.471003 | −0.0193581 | ||||||||
\(593\) | 7.62865 | 0.313271 | 0.156636 | − | 0.987656i | \(-0.449935\pi\) | ||||
0.156636 | + | 0.987656i | \(0.449935\pi\) | |||||||
\(594\) | −1.12418 | −0.0461258 | ||||||||
\(595\) | −2.73072 | −0.111949 | ||||||||
\(596\) | −15.4223 | −0.631724 | ||||||||
\(597\) | −4.77938 | −0.195607 | ||||||||
\(598\) | 0.570608 | 0.0233339 | ||||||||
\(599\) | −5.73731 | −0.234420 | −0.117210 | − | 0.993107i | \(-0.537395\pi\) | ||||
−0.117210 | + | 0.993107i | \(0.537395\pi\) | |||||||
\(600\) | 18.8675 | 0.770264 | ||||||||
\(601\) | 27.0126 | 1.10187 | 0.550933 | − | 0.834550i | \(-0.314272\pi\) | ||||
0.550933 | + | 0.834550i | \(0.314272\pi\) | |||||||
\(602\) | 0.165867 | 0.00676022 | ||||||||
\(603\) | −57.7726 | −2.35268 | ||||||||
\(604\) | −23.7803 | −0.967607 | ||||||||
\(605\) | 37.5119 | 1.52507 | ||||||||
\(606\) | −24.5088 | −0.995602 | ||||||||
\(607\) | 10.3655 | 0.420722 | 0.210361 | − | 0.977624i | \(-0.432536\pi\) | ||||
0.210361 | + | 0.977624i | \(0.432536\pi\) | |||||||
\(608\) | 1.57912 | 0.0640418 | ||||||||
\(609\) | 8.36646 | 0.339026 | ||||||||
\(610\) | −23.0202 | −0.932062 | ||||||||
\(611\) | 5.33016 | 0.215635 | ||||||||
\(612\) | −6.24721 | −0.252528 | ||||||||
\(613\) | 32.3862 | 1.30807 | 0.654034 | − | 0.756465i | \(-0.273075\pi\) | ||||
0.654034 | + | 0.756465i | \(0.273075\pi\) | |||||||
\(614\) | −1.91738 | −0.0773792 | ||||||||
\(615\) | −16.5580 | −0.667682 | ||||||||
\(616\) | −0.248394 | −0.0100081 | ||||||||
\(617\) | 40.2542 | 1.62057 | 0.810287 | − | 0.586034i | \(-0.199311\pi\) | ||||
0.810287 | + | 0.586034i | \(0.199311\pi\) | |||||||
\(618\) | 40.3426 | 1.62282 | ||||||||
\(619\) | 37.7354 | 1.51671 | 0.758357 | − | 0.651839i | \(-0.226002\pi\) | ||||
0.758357 | + | 0.651839i | \(0.226002\pi\) | |||||||
\(620\) | −0.121180 | −0.00486672 | ||||||||
\(621\) | 3.13798 | 0.125923 | ||||||||
\(622\) | 2.28986 | 0.0918149 | ||||||||
\(623\) | −7.30794 | −0.292786 | ||||||||
\(624\) | −1.02977 | −0.0412237 | ||||||||
\(625\) | −8.97286 | −0.358914 | ||||||||
\(626\) | −12.8454 | −0.513407 | ||||||||
\(627\) | −2.14078 | −0.0854946 | ||||||||
\(628\) | 7.41881 | 0.296043 | ||||||||
\(629\) | 0.768417 | 0.0306388 | ||||||||
\(630\) | −6.40938 | −0.255356 | ||||||||
\(631\) | −25.7914 | −1.02674 | −0.513369 | − | 0.858168i | \(-0.671603\pi\) | ||||
−0.513369 | + | 0.858168i | \(0.671603\pi\) | |||||||
\(632\) | 7.31985 | 0.291168 | ||||||||
\(633\) | −33.6680 | −1.33818 | ||||||||
\(634\) | −2.01283 | −0.0799397 | ||||||||
\(635\) | 2.91891 | 0.115833 | ||||||||
\(636\) | −1.72589 | −0.0684359 | ||||||||
\(637\) | −2.66802 | −0.105711 | ||||||||
\(638\) | 3.46862 | 0.137324 | ||||||||
\(639\) | −14.5533 | −0.575720 | ||||||||
\(640\) | 3.49569 | 0.138179 | ||||||||
\(641\) | −26.0187 | −1.02768 | −0.513838 | − | 0.857887i | \(-0.671777\pi\) | ||||
−0.513838 | + | 0.857887i | \(0.671777\pi\) | |||||||
\(642\) | 40.6964 | 1.60616 | ||||||||
\(643\) | −0.311293 | −0.0122762 | −0.00613810 | − | 0.999981i | \(-0.501954\pi\) | ||||
−0.00613810 | + | 0.999981i | \(0.501954\pi\) | |||||||
\(644\) | 0.693354 | 0.0273220 | ||||||||
\(645\) | 3.16452 | 0.124603 | ||||||||
\(646\) | −2.57625 | −0.101361 | ||||||||
\(647\) | 27.6951 | 1.08881 | 0.544403 | − | 0.838824i | \(-0.316756\pi\) | ||||
0.544403 | + | 0.838824i | \(0.316756\pi\) | |||||||
\(648\) | 5.82465 | 0.228814 | ||||||||
\(649\) | −1.26133 | −0.0495113 | ||||||||
\(650\) | −2.84500 | −0.111590 | ||||||||
\(651\) | 0.0433766 | 0.00170006 | ||||||||
\(652\) | −19.8529 | −0.777500 | ||||||||
\(653\) | −19.7464 | −0.772736 | −0.386368 | − | 0.922345i | \(-0.626271\pi\) | ||||
−0.386368 | + | 0.922345i | \(0.626271\pi\) | |||||||
\(654\) | −10.5743 | −0.413488 | ||||||||
\(655\) | 58.8619 | 2.29992 | ||||||||
\(656\) | −1.81254 | −0.0707678 | ||||||||
\(657\) | −18.0602 | −0.704594 | ||||||||
\(658\) | 6.47676 | 0.252490 | ||||||||
\(659\) | 10.9891 | 0.428075 | 0.214037 | − | 0.976825i | \(-0.431339\pi\) | ||||
0.214037 | + | 0.976825i | \(0.431339\pi\) | |||||||
\(660\) | −4.73904 | −0.184467 | ||||||||
\(661\) | 39.8747 | 1.55095 | 0.775473 | − | 0.631381i | \(-0.217512\pi\) | ||||
0.775473 | + | 0.631381i | \(0.217512\pi\) | |||||||
\(662\) | −23.5787 | −0.916412 | ||||||||
\(663\) | 1.68001 | 0.0652463 | ||||||||
\(664\) | 1.54698 | 0.0600346 | ||||||||
\(665\) | −2.64313 | −0.102496 | ||||||||
\(666\) | 1.80358 | 0.0698873 | ||||||||
\(667\) | −9.68210 | −0.374892 | ||||||||
\(668\) | 2.89092 | 0.111853 | ||||||||
\(669\) | 37.5622 | 1.45224 | ||||||||
\(670\) | −52.7403 | −2.03754 | ||||||||
\(671\) | 3.41623 | 0.131882 | ||||||||
\(672\) | −1.25129 | −0.0482694 | ||||||||
\(673\) | 1.84249 | 0.0710227 | 0.0355114 | − | 0.999369i | \(-0.488694\pi\) | ||||
0.0355114 | + | 0.999369i | \(0.488694\pi\) | |||||||
\(674\) | 26.4651 | 1.01940 | ||||||||
\(675\) | −15.6457 | −0.602203 | ||||||||
\(676\) | −12.8447 | −0.494028 | ||||||||
\(677\) | 5.72080 | 0.219868 | 0.109934 | − | 0.993939i | \(-0.464936\pi\) | ||||
0.109934 | + | 0.993939i | \(0.464936\pi\) | |||||||
\(678\) | 42.6547 | 1.63814 | ||||||||
\(679\) | −2.96760 | −0.113886 | ||||||||
\(680\) | −5.70304 | −0.218702 | ||||||||
\(681\) | −67.4352 | −2.58412 | ||||||||
\(682\) | 0.0179833 | 0.000688618 0 | ||||||||
\(683\) | −3.41671 | −0.130737 | −0.0653684 | − | 0.997861i | \(-0.520822\pi\) | ||||
−0.0653684 | + | 0.997861i | \(0.520822\pi\) | |||||||
\(684\) | −6.04683 | −0.231206 | ||||||||
\(685\) | 70.2622 | 2.68458 | ||||||||
\(686\) | −6.59367 | −0.251748 | ||||||||
\(687\) | 25.6513 | 0.978658 | ||||||||
\(688\) | 0.346409 | 0.0132067 | ||||||||
\(689\) | 0.260243 | 0.00991447 | ||||||||
\(690\) | 13.2283 | 0.503593 | ||||||||
\(691\) | 39.0725 | 1.48639 | 0.743194 | − | 0.669076i | \(-0.233310\pi\) | ||||
0.743194 | + | 0.669076i | \(0.233310\pi\) | |||||||
\(692\) | −10.7517 | −0.408718 | ||||||||
\(693\) | 0.951161 | 0.0361316 | ||||||||
\(694\) | 13.2596 | 0.503326 | ||||||||
\(695\) | 31.1151 | 1.18026 | ||||||||
\(696\) | 17.4732 | 0.662318 | ||||||||
\(697\) | 2.95707 | 0.112007 | ||||||||
\(698\) | −13.0888 | −0.495417 | ||||||||
\(699\) | −71.6731 | −2.71093 | ||||||||
\(700\) | −3.45700 | −0.130662 | ||||||||
\(701\) | 23.3894 | 0.883404 | 0.441702 | − | 0.897162i | \(-0.354375\pi\) | ||||
0.441702 | + | 0.897162i | \(0.354375\pi\) | |||||||
\(702\) | 0.853923 | 0.0322292 | ||||||||
\(703\) | 0.743770 | 0.0280518 | ||||||||
\(704\) | −0.518766 | −0.0195517 | ||||||||
\(705\) | 123.568 | 4.65385 | ||||||||
\(706\) | −13.9656 | −0.525604 | ||||||||
\(707\) | 4.49062 | 0.168887 | ||||||||
\(708\) | −6.35393 | −0.238795 | ||||||||
\(709\) | 2.90057 | 0.108933 | 0.0544665 | − | 0.998516i | \(-0.482654\pi\) | ||||
0.0544665 | + | 0.998516i | \(0.482654\pi\) | |||||||
\(710\) | −13.2856 | −0.498602 | ||||||||
\(711\) | −28.0295 | −1.05119 | ||||||||
\(712\) | −15.2625 | −0.571985 | ||||||||
\(713\) | −0.0501977 | −0.00187992 | ||||||||
\(714\) | 2.04141 | 0.0763978 | ||||||||
\(715\) | 0.714591 | 0.0267242 | ||||||||
\(716\) | −1.79236 | −0.0669836 | ||||||||
\(717\) | 31.1481 | 1.16325 | ||||||||
\(718\) | −26.5440 | −0.990615 | ||||||||
\(719\) | 48.8678 | 1.82246 | 0.911231 | − | 0.411896i | \(-0.135133\pi\) | ||||
0.911231 | + | 0.411896i | \(0.135133\pi\) | |||||||
\(720\) | −13.3858 | −0.498861 | ||||||||
\(721\) | −7.39176 | −0.275284 | ||||||||
\(722\) | 16.5064 | 0.614304 | ||||||||
\(723\) | 9.81446 | 0.365004 | ||||||||
\(724\) | −9.37633 | −0.348468 | ||||||||
\(725\) | 48.2741 | 1.79286 | ||||||||
\(726\) | −28.0428 | −1.04077 | ||||||||
\(727\) | −10.0723 | −0.373559 | −0.186780 | − | 0.982402i | \(-0.559805\pi\) | ||||
−0.186780 | + | 0.982402i | \(0.559805\pi\) | |||||||
\(728\) | 0.188679 | 0.00699290 | ||||||||
\(729\) | −39.2932 | −1.45530 | ||||||||
\(730\) | −16.4870 | −0.610212 | ||||||||
\(731\) | −0.565148 | −0.0209027 | ||||||||
\(732\) | 17.2093 | 0.636073 | ||||||||
\(733\) | −29.4406 | −1.08741 | −0.543706 | − | 0.839276i | \(-0.682979\pi\) | ||||
−0.543706 | + | 0.839276i | \(0.682979\pi\) | |||||||
\(734\) | −16.0040 | −0.590717 | ||||||||
\(735\) | −61.8522 | −2.28145 | ||||||||
\(736\) | 1.44805 | 0.0533759 | ||||||||
\(737\) | 7.82674 | 0.288302 | ||||||||
\(738\) | 6.94065 | 0.255489 | ||||||||
\(739\) | 8.37310 | 0.308009 | 0.154005 | − | 0.988070i | \(-0.450783\pi\) | ||||
0.154005 | + | 0.988070i | \(0.450783\pi\) | |||||||
\(740\) | 1.64648 | 0.0605258 | ||||||||
\(741\) | 1.62613 | 0.0597373 | ||||||||
\(742\) | 0.316225 | 0.0116090 | ||||||||
\(743\) | −6.24975 | −0.229281 | −0.114641 | − | 0.993407i | \(-0.536572\pi\) | ||||
−0.114641 | + | 0.993407i | \(0.536572\pi\) | |||||||
\(744\) | 0.0905911 | 0.00332123 | ||||||||
\(745\) | 53.9118 | 1.97517 | ||||||||
\(746\) | 28.3811 | 1.03911 | ||||||||
\(747\) | −5.92376 | −0.216739 | ||||||||
\(748\) | 0.846339 | 0.0309452 | ||||||||
\(749\) | −7.45658 | −0.272458 | ||||||||
\(750\) | −20.2790 | −0.740484 | ||||||||
\(751\) | 19.6809 | 0.718166 | 0.359083 | − | 0.933306i | \(-0.383089\pi\) | ||||
0.359083 | + | 0.933306i | \(0.383089\pi\) | |||||||
\(752\) | 13.5266 | 0.493263 | ||||||||
\(753\) | 59.4234 | 2.16551 | ||||||||
\(754\) | −2.63474 | −0.0959517 | ||||||||
\(755\) | 83.1287 | 3.02536 | ||||||||
\(756\) | 1.03761 | 0.0377377 | ||||||||
\(757\) | −43.2565 | −1.57219 | −0.786093 | − | 0.618109i | \(-0.787899\pi\) | ||||
−0.786093 | + | 0.618109i | \(0.787899\pi\) | |||||||
\(758\) | −36.9387 | −1.34167 | ||||||||
\(759\) | −1.96310 | −0.0712559 | ||||||||
\(760\) | −5.52012 | −0.200236 | ||||||||
\(761\) | −29.2839 | −1.06154 | −0.530771 | − | 0.847515i | \(-0.678098\pi\) | ||||
−0.530771 | + | 0.847515i | \(0.678098\pi\) | |||||||
\(762\) | −2.18209 | −0.0790489 | ||||||||
\(763\) | 1.93748 | 0.0701414 | ||||||||
\(764\) | −8.09957 | −0.293032 | ||||||||
\(765\) | 21.8383 | 0.789566 | ||||||||
\(766\) | −14.6807 | −0.530434 | ||||||||
\(767\) | 0.958096 | 0.0345948 | ||||||||
\(768\) | −2.61328 | −0.0942987 | ||||||||
\(769\) | −25.1196 | −0.905836 | −0.452918 | − | 0.891552i | \(-0.649617\pi\) | ||||
−0.452918 | + | 0.891552i | \(0.649617\pi\) | |||||||
\(770\) | 0.868310 | 0.0312917 | ||||||||
\(771\) | −41.1779 | −1.48299 | ||||||||
\(772\) | −15.3567 | −0.552700 | ||||||||
\(773\) | −26.1489 | −0.940511 | −0.470256 | − | 0.882530i | \(-0.655838\pi\) | ||||
−0.470256 | + | 0.882530i | \(0.655838\pi\) | |||||||
\(774\) | −1.32648 | −0.0476794 | ||||||||
\(775\) | 0.250281 | 0.00899037 | ||||||||
\(776\) | −6.19777 | −0.222487 | ||||||||
\(777\) | −0.589359 | −0.0211431 | ||||||||
\(778\) | −8.06683 | −0.289210 | ||||||||
\(779\) | 2.86222 | 0.102550 | ||||||||
\(780\) | 3.59975 | 0.128892 | ||||||||
\(781\) | 1.97161 | 0.0705497 | ||||||||
\(782\) | −2.36242 | −0.0844801 | ||||||||
\(783\) | −14.4894 | −0.517809 | ||||||||
\(784\) | −6.77073 | −0.241812 | ||||||||
\(785\) | −25.9339 | −0.925620 | ||||||||
\(786\) | −44.0035 | −1.56955 | ||||||||
\(787\) | 19.9910 | 0.712602 | 0.356301 | − | 0.934371i | \(-0.384038\pi\) | ||||
0.356301 | + | 0.934371i | \(0.384038\pi\) | |||||||
\(788\) | 7.45842 | 0.265695 | ||||||||
\(789\) | 9.73602 | 0.346612 | ||||||||
\(790\) | −25.5879 | −0.910378 | ||||||||
\(791\) | −7.81539 | −0.277883 | ||||||||
\(792\) | 1.98648 | 0.0705864 | ||||||||
\(793\) | −2.59495 | −0.0921495 | ||||||||
\(794\) | 31.6162 | 1.12202 | ||||||||
\(795\) | 6.03317 | 0.213974 | ||||||||
\(796\) | 1.82888 | 0.0648230 | ||||||||
\(797\) | −45.4739 | −1.61077 | −0.805385 | − | 0.592752i | \(-0.798041\pi\) | ||||
−0.805385 | + | 0.592752i | \(0.798041\pi\) | |||||||
\(798\) | 1.97593 | 0.0699472 | ||||||||
\(799\) | −22.0679 | −0.780706 | ||||||||
\(800\) | −7.21987 | −0.255261 | ||||||||
\(801\) | 58.4436 | 2.06500 | ||||||||
\(802\) | −2.91703 | −0.103004 | ||||||||
\(803\) | 2.44670 | 0.0863421 | ||||||||
\(804\) | 39.4272 | 1.39049 | ||||||||
\(805\) | −2.42375 | −0.0854260 | ||||||||
\(806\) | −0.0136600 | −0.000481155 0 | ||||||||
\(807\) | 30.5999 | 1.07717 | ||||||||
\(808\) | 9.37856 | 0.329936 | ||||||||
\(809\) | 5.29557 | 0.186182 | 0.0930912 | − | 0.995658i | \(-0.470325\pi\) | ||||
0.0930912 | + | 0.995658i | \(0.470325\pi\) | |||||||
\(810\) | −20.3612 | −0.715419 | ||||||||
\(811\) | 38.0242 | 1.33521 | 0.667605 | − | 0.744516i | \(-0.267320\pi\) | ||||
0.667605 | + | 0.744516i | \(0.267320\pi\) | |||||||
\(812\) | −3.20151 | −0.112351 | ||||||||
\(813\) | −47.0129 | −1.64881 | ||||||||
\(814\) | −0.244340 | −0.00856411 | ||||||||
\(815\) | 69.3997 | 2.43096 | ||||||||
\(816\) | 4.26343 | 0.149250 | ||||||||
\(817\) | −0.547021 | −0.0191378 | ||||||||
\(818\) | −28.1151 | −0.983023 | ||||||||
\(819\) | −0.722496 | −0.0252461 | ||||||||
\(820\) | 6.33609 | 0.221266 | ||||||||
\(821\) | −0.494361 | −0.0172533 | −0.00862665 | − | 0.999963i | \(-0.502746\pi\) | ||||
−0.00862665 | + | 0.999963i | \(0.502746\pi\) | |||||||
\(822\) | −52.5260 | −1.83206 | ||||||||
\(823\) | −20.8898 | −0.728171 | −0.364085 | − | 0.931366i | \(-0.618618\pi\) | ||||
−0.364085 | + | 0.931366i | \(0.618618\pi\) | |||||||
\(824\) | −15.4375 | −0.537792 | ||||||||
\(825\) | 9.78783 | 0.340768 | ||||||||
\(826\) | 1.16420 | 0.0405076 | ||||||||
\(827\) | −41.5104 | −1.44346 | −0.721728 | − | 0.692176i | \(-0.756652\pi\) | ||||
−0.721728 | + | 0.692176i | \(0.756652\pi\) | |||||||
\(828\) | −5.54494 | −0.192700 | ||||||||
\(829\) | −45.4324 | −1.57793 | −0.788967 | − | 0.614436i | \(-0.789384\pi\) | ||||
−0.788967 | + | 0.614436i | \(0.789384\pi\) | |||||||
\(830\) | −5.40777 | −0.187707 | ||||||||
\(831\) | 54.2450 | 1.88174 | ||||||||
\(832\) | 0.394051 | 0.0136613 | ||||||||
\(833\) | 11.0461 | 0.382725 | ||||||||
\(834\) | −23.2608 | −0.805454 | ||||||||
\(835\) | −10.1058 | −0.349724 | ||||||||
\(836\) | 0.819193 | 0.0283324 | ||||||||
\(837\) | −0.0751216 | −0.00259658 | ||||||||
\(838\) | 34.8537 | 1.20400 | ||||||||
\(839\) | 12.5944 | 0.434806 | 0.217403 | − | 0.976082i | \(-0.430241\pi\) | ||||
0.217403 | + | 0.976082i | \(0.430241\pi\) | |||||||
\(840\) | 4.37411 | 0.150921 | ||||||||
\(841\) | 15.7065 | 0.541602 | ||||||||
\(842\) | 25.8122 | 0.889547 | ||||||||
\(843\) | −71.2229 | −2.45305 | ||||||||
\(844\) | 12.8834 | 0.443465 | ||||||||
\(845\) | 44.9012 | 1.54465 | ||||||||
\(846\) | −51.7964 | −1.78080 | ||||||||
\(847\) | 5.13814 | 0.176548 | ||||||||
\(848\) | 0.660429 | 0.0226792 | ||||||||
\(849\) | −45.9653 | −1.57752 | ||||||||
\(850\) | 11.7788 | 0.404011 | ||||||||
\(851\) | 0.682037 | 0.0233799 | ||||||||
\(852\) | 9.93198 | 0.340264 | ||||||||
\(853\) | 13.0591 | 0.447135 | 0.223567 | − | 0.974688i | \(-0.428230\pi\) | ||||
0.223567 | + | 0.974688i | \(0.428230\pi\) | |||||||
\(854\) | −3.15317 | −0.107899 | ||||||||
\(855\) | 21.1379 | 0.722899 | ||||||||
\(856\) | −15.5729 | −0.532271 | ||||||||
\(857\) | −39.1314 | −1.33670 | −0.668352 | − | 0.743846i | \(-0.733000\pi\) | ||||
−0.668352 | + | 0.743846i | \(0.733000\pi\) | |||||||
\(858\) | −0.534208 | −0.0182376 | ||||||||
\(859\) | −38.4392 | −1.31153 | −0.655763 | − | 0.754966i | \(-0.727653\pi\) | ||||
−0.655763 | + | 0.754966i | \(0.727653\pi\) | |||||||
\(860\) | −1.21094 | −0.0412926 | ||||||||
\(861\) | −2.26801 | −0.0772934 | ||||||||
\(862\) | −16.4844 | −0.561463 | ||||||||
\(863\) | −4.04441 | −0.137673 | −0.0688367 | − | 0.997628i | \(-0.521929\pi\) | ||||
−0.0688367 | + | 0.997628i | \(0.521929\pi\) | |||||||
\(864\) | 2.16703 | 0.0737240 | ||||||||
\(865\) | 37.5846 | 1.27791 | ||||||||
\(866\) | −36.0861 | −1.22626 | ||||||||
\(867\) | 37.4702 | 1.27255 | ||||||||
\(868\) | −0.0165985 | −0.000563391 0 | ||||||||
\(869\) | 3.79729 | 0.128814 | ||||||||
\(870\) | −61.0808 | −2.07083 | ||||||||
\(871\) | −5.94515 | −0.201444 | ||||||||
\(872\) | 4.04637 | 0.137028 | ||||||||
\(873\) | 23.7327 | 0.803232 | ||||||||
\(874\) | −2.28665 | −0.0773471 | ||||||||
\(875\) | 3.71561 | 0.125611 | ||||||||
\(876\) | 12.3252 | 0.416431 | ||||||||
\(877\) | 39.3482 | 1.32870 | 0.664348 | − | 0.747424i | \(-0.268709\pi\) | ||||
0.664348 | + | 0.747424i | \(0.268709\pi\) | |||||||
\(878\) | −12.2932 | −0.414875 | ||||||||
\(879\) | 76.5372 | 2.58154 | ||||||||
\(880\) | 1.81344 | 0.0611312 | ||||||||
\(881\) | −28.2778 | −0.952703 | −0.476351 | − | 0.879255i | \(-0.658041\pi\) | ||||
−0.476351 | + | 0.879255i | \(0.658041\pi\) | |||||||
\(882\) | 25.9268 | 0.872999 | ||||||||
\(883\) | 18.9825 | 0.638813 | 0.319407 | − | 0.947618i | \(-0.396516\pi\) | ||||
0.319407 | + | 0.947618i | \(0.396516\pi\) | |||||||
\(884\) | −0.642875 | −0.0216222 | ||||||||
\(885\) | 22.2114 | 0.746627 | ||||||||
\(886\) | 10.7849 | 0.362325 | ||||||||
\(887\) | 16.8953 | 0.567289 | 0.283645 | − | 0.958929i | \(-0.408456\pi\) | ||||
0.283645 | + | 0.958929i | \(0.408456\pi\) | |||||||
\(888\) | −1.23086 | −0.0413050 | ||||||||
\(889\) | 0.399813 | 0.0134093 | ||||||||
\(890\) | 53.3529 | 1.78839 | ||||||||
\(891\) | 3.02163 | 0.101228 | ||||||||
\(892\) | −14.3736 | −0.481263 | ||||||||
\(893\) | −21.3601 | −0.714787 | ||||||||
\(894\) | −40.3029 | −1.34793 | ||||||||
\(895\) | 6.26554 | 0.209434 | ||||||||
\(896\) | 0.478818 | 0.0159962 | ||||||||
\(897\) | 1.49116 | 0.0497883 | ||||||||
\(898\) | 34.6427 | 1.15604 | ||||||||
\(899\) | 0.231785 | 0.00773045 | ||||||||
\(900\) | 27.6466 | 0.921553 | ||||||||
\(901\) | −1.07746 | −0.0358953 | ||||||||
\(902\) | −0.940284 | −0.0313080 | ||||||||
\(903\) | 0.433456 | 0.0144245 | ||||||||
\(904\) | −16.3223 | −0.542871 | ||||||||
\(905\) | 32.7768 | 1.08954 | ||||||||
\(906\) | −62.1447 | −2.06462 | ||||||||
\(907\) | 0.764870 | 0.0253971 | 0.0126986 | − | 0.999919i | \(-0.495958\pi\) | ||||
0.0126986 | + | 0.999919i | \(0.495958\pi\) | |||||||
\(908\) | 25.8048 | 0.856362 | ||||||||
\(909\) | −35.9127 | −1.19115 | ||||||||
\(910\) | −0.659563 | −0.0218643 | ||||||||
\(911\) | 10.3890 | 0.344202 | 0.172101 | − | 0.985079i | \(-0.444944\pi\) | ||||
0.172101 | + | 0.985079i | \(0.444944\pi\) | |||||||
\(912\) | 4.12669 | 0.136648 | ||||||||
\(913\) | 0.802521 | 0.0265596 | ||||||||
\(914\) | −10.9190 | −0.361169 | ||||||||
\(915\) | −60.1583 | −1.98877 | ||||||||
\(916\) | −9.81575 | −0.324321 | ||||||||
\(917\) | 8.06252 | 0.266248 | ||||||||
\(918\) | −3.53540 | −0.116686 | ||||||||
\(919\) | −31.8574 | −1.05088 | −0.525439 | − | 0.850831i | \(-0.676099\pi\) | ||||
−0.525439 | + | 0.850831i | \(0.676099\pi\) | |||||||
\(920\) | −5.06195 | −0.166888 | ||||||||
\(921\) | −5.01066 | −0.165107 | ||||||||
\(922\) | 12.4177 | 0.408955 | ||||||||
\(923\) | −1.49762 | −0.0492949 | ||||||||
\(924\) | −0.649124 | −0.0213546 | ||||||||
\(925\) | −3.40058 | −0.111810 | ||||||||
\(926\) | 10.9578 | 0.360095 | ||||||||
\(927\) | 59.1140 | 1.94156 | ||||||||
\(928\) | −6.68629 | −0.219488 | ||||||||
\(929\) | 35.6028 | 1.16809 | 0.584046 | − | 0.811721i | \(-0.301469\pi\) | ||||
0.584046 | + | 0.811721i | \(0.301469\pi\) | |||||||
\(930\) | −0.316679 | −0.0103843 | ||||||||
\(931\) | 10.6918 | 0.350410 | ||||||||
\(932\) | 27.4265 | 0.898384 | ||||||||
\(933\) | 5.98404 | 0.195909 | ||||||||
\(934\) | −1.70410 | −0.0557597 | ||||||||
\(935\) | −2.95854 | −0.0967547 | ||||||||
\(936\) | −1.50892 | −0.0493205 | ||||||||
\(937\) | −20.9413 | −0.684122 | −0.342061 | − | 0.939678i | \(-0.611125\pi\) | ||||
−0.342061 | + | 0.939678i | \(0.611125\pi\) | |||||||
\(938\) | −7.22404 | −0.235873 | ||||||||
\(939\) | −33.5688 | −1.09547 | ||||||||
\(940\) | −47.2847 | −1.54226 | ||||||||
\(941\) | −22.3639 | −0.729043 | −0.364522 | − | 0.931195i | \(-0.618767\pi\) | ||||
−0.364522 | + | 0.931195i | \(0.618767\pi\) | |||||||
\(942\) | 19.3874 | 0.631677 | ||||||||
\(943\) | 2.62466 | 0.0854705 | ||||||||
\(944\) | 2.43140 | 0.0791353 | ||||||||
\(945\) | −3.62718 | −0.117992 | ||||||||
\(946\) | 0.179705 | 0.00584271 | ||||||||
\(947\) | 36.8400 | 1.19714 | 0.598569 | − | 0.801071i | \(-0.295736\pi\) | ||||
0.598569 | + | 0.801071i | \(0.295736\pi\) | |||||||
\(948\) | 19.1288 | 0.621275 | ||||||||
\(949\) | −1.85850 | −0.0603294 | ||||||||
\(950\) | 11.4010 | 0.369899 | ||||||||
\(951\) | −5.26009 | −0.170570 | ||||||||
\(952\) | −0.781167 | −0.0253178 | ||||||||
\(953\) | 38.3828 | 1.24334 | 0.621671 | − | 0.783279i | \(-0.286454\pi\) | ||||
0.621671 | + | 0.783279i | \(0.286454\pi\) | |||||||
\(954\) | −2.52894 | −0.0818775 | ||||||||
\(955\) | 28.3136 | 0.916206 | ||||||||
\(956\) | −11.9191 | −0.385493 | ||||||||
\(957\) | 9.06447 | 0.293013 | ||||||||
\(958\) | 12.8413 | 0.414885 | ||||||||
\(959\) | 9.62407 | 0.310777 | ||||||||
\(960\) | 9.13523 | 0.294838 | ||||||||
\(961\) | −30.9988 | −0.999961 | ||||||||
\(962\) | 0.185599 | 0.00598396 | ||||||||
\(963\) | 59.6323 | 1.92163 | ||||||||
\(964\) | −3.75561 | −0.120960 | ||||||||
\(965\) | 53.6823 | 1.72809 | ||||||||
\(966\) | 1.81193 | 0.0582978 | ||||||||
\(967\) | 19.3292 | 0.621586 | 0.310793 | − | 0.950478i | \(-0.399405\pi\) | ||||
0.310793 | + | 0.950478i | \(0.399405\pi\) | |||||||
\(968\) | 10.7309 | 0.344904 | ||||||||
\(969\) | −6.73248 | −0.216278 | ||||||||
\(970\) | 21.6655 | 0.695637 | ||||||||
\(971\) | −18.8060 | −0.603512 | −0.301756 | − | 0.953385i | \(-0.597573\pi\) | ||||
−0.301756 | + | 0.953385i | \(0.597573\pi\) | |||||||
\(972\) | 21.7225 | 0.696751 | ||||||||
\(973\) | 4.26195 | 0.136632 | ||||||||
\(974\) | −12.2065 | −0.391120 | ||||||||
\(975\) | −7.43478 | −0.238104 | ||||||||
\(976\) | −6.58531 | −0.210791 | ||||||||
\(977\) | −25.7961 | −0.825290 | −0.412645 | − | 0.910892i | \(-0.635395\pi\) | ||||
−0.412645 | + | 0.910892i | \(0.635395\pi\) | |||||||
\(978\) | −51.8812 | −1.65898 | ||||||||
\(979\) | −7.91764 | −0.253049 | ||||||||
\(980\) | 23.6684 | 0.756059 | ||||||||
\(981\) | −15.4945 | −0.494702 | ||||||||
\(982\) | 8.79930 | 0.280797 | ||||||||
\(983\) | −32.5300 | −1.03755 | −0.518773 | − | 0.854912i | \(-0.673611\pi\) | ||||
−0.518773 | + | 0.854912i | \(0.673611\pi\) | |||||||
\(984\) | −4.73668 | −0.151000 | ||||||||
\(985\) | −26.0723 | −0.830734 | ||||||||
\(986\) | 10.9083 | 0.347392 | ||||||||
\(987\) | 16.9256 | 0.538747 | ||||||||
\(988\) | −0.622255 | −0.0197966 | ||||||||
\(989\) | −0.501618 | −0.0159505 | ||||||||
\(990\) | −6.94411 | −0.220698 | ||||||||
\(991\) | 44.3905 | 1.41011 | 0.705055 | − | 0.709153i | \(-0.250922\pi\) | ||||
0.705055 | + | 0.709153i | \(0.250922\pi\) | |||||||
\(992\) | −0.0346656 | −0.00110064 | ||||||||
\(993\) | −61.6177 | −1.95538 | ||||||||
\(994\) | −1.81978 | −0.0577200 | ||||||||
\(995\) | −6.39320 | −0.202678 | ||||||||
\(996\) | 4.04270 | 0.128098 | ||||||||
\(997\) | −49.4824 | −1.56712 | −0.783562 | − | 0.621314i | \(-0.786599\pi\) | ||||
−0.783562 | + | 0.621314i | \(0.786599\pi\) | |||||||
\(998\) | −23.9035 | −0.756651 | ||||||||
\(999\) | 1.02068 | 0.0322928 |
(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 | 8002.2.a.e.1.8 | ✓ | 77 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8002.2.a.e.1.8 | ✓ | 77 | 1.1 | even | 1 | trivial |