Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1694,2,Mod(1,1694)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1694, 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("1694.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1694 = 2 \cdot 7 \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1694.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: | \(13.5266581024\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{10})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 154) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-0.618034\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1694.1 |
$q$-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 | ||||||||
\(3\) | 1.23607 | 0.713644 | 0.356822 | − | 0.934172i | \(-0.383860\pi\) | ||||
0.356822 | + | 0.934172i | \(0.383860\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −1.23607 | −0.552786 | −0.276393 | − | 0.961045i | \(-0.589139\pi\) | ||||
−0.276393 | + | 0.961045i | \(0.589139\pi\) | |||||||
\(6\) | −1.23607 | −0.504623 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | −1.47214 | −0.490712 | ||||||||
\(10\) | 1.23607 | 0.390879 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | 1.23607 | 0.356822 | ||||||||
\(13\) | 3.23607 | 0.897524 | 0.448762 | − | 0.893651i | \(-0.351865\pi\) | ||||
0.448762 | + | 0.893651i | \(0.351865\pi\) | |||||||
\(14\) | 1.00000 | 0.267261 | ||||||||
\(15\) | −1.52786 | −0.394493 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −2.47214 | −0.599581 | −0.299791 | − | 0.954005i | \(-0.596917\pi\) | ||||
−0.299791 | + | 0.954005i | \(0.596917\pi\) | |||||||
\(18\) | 1.47214 | 0.346986 | ||||||||
\(19\) | 7.23607 | 1.66007 | 0.830034 | − | 0.557713i | \(-0.188321\pi\) | ||||
0.830034 | + | 0.557713i | \(0.188321\pi\) | |||||||
\(20\) | −1.23607 | −0.276393 | ||||||||
\(21\) | −1.23607 | −0.269732 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 4.00000 | 0.834058 | 0.417029 | − | 0.908893i | \(-0.363071\pi\) | ||||
0.417029 | + | 0.908893i | \(0.363071\pi\) | |||||||
\(24\) | −1.23607 | −0.252311 | ||||||||
\(25\) | −3.47214 | −0.694427 | ||||||||
\(26\) | −3.23607 | −0.634645 | ||||||||
\(27\) | −5.52786 | −1.06384 | ||||||||
\(28\) | −1.00000 | −0.188982 | ||||||||
\(29\) | −4.47214 | −0.830455 | −0.415227 | − | 0.909718i | \(-0.636298\pi\) | ||||
−0.415227 | + | 0.909718i | \(0.636298\pi\) | |||||||
\(30\) | 1.52786 | 0.278949 | ||||||||
\(31\) | 2.00000 | 0.359211 | 0.179605 | − | 0.983739i | \(-0.442518\pi\) | ||||
0.179605 | + | 0.983739i | \(0.442518\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 2.47214 | 0.423968 | ||||||||
\(35\) | 1.23607 | 0.208934 | ||||||||
\(36\) | −1.47214 | −0.245356 | ||||||||
\(37\) | 6.94427 | 1.14163 | 0.570816 | − | 0.821078i | \(-0.306627\pi\) | ||||
0.570816 | + | 0.821078i | \(0.306627\pi\) | |||||||
\(38\) | −7.23607 | −1.17385 | ||||||||
\(39\) | 4.00000 | 0.640513 | ||||||||
\(40\) | 1.23607 | 0.195440 | ||||||||
\(41\) | 2.47214 | 0.386083 | 0.193041 | − | 0.981191i | \(-0.438165\pi\) | ||||
0.193041 | + | 0.981191i | \(0.438165\pi\) | |||||||
\(42\) | 1.23607 | 0.190729 | ||||||||
\(43\) | 10.4721 | 1.59699 | 0.798493 | − | 0.602004i | \(-0.205631\pi\) | ||||
0.798493 | + | 0.602004i | \(0.205631\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 1.81966 | 0.271259 | ||||||||
\(46\) | −4.00000 | −0.589768 | ||||||||
\(47\) | −2.00000 | −0.291730 | −0.145865 | − | 0.989305i | \(-0.546597\pi\) | ||||
−0.145865 | + | 0.989305i | \(0.546597\pi\) | |||||||
\(48\) | 1.23607 | 0.178411 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 3.47214 | 0.491034 | ||||||||
\(51\) | −3.05573 | −0.427888 | ||||||||
\(52\) | 3.23607 | 0.448762 | ||||||||
\(53\) | 8.47214 | 1.16374 | 0.581869 | − | 0.813283i | \(-0.302322\pi\) | ||||
0.581869 | + | 0.813283i | \(0.302322\pi\) | |||||||
\(54\) | 5.52786 | 0.752247 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 1.00000 | 0.133631 | ||||||||
\(57\) | 8.94427 | 1.18470 | ||||||||
\(58\) | 4.47214 | 0.587220 | ||||||||
\(59\) | 2.76393 | 0.359833 | 0.179917 | − | 0.983682i | \(-0.442417\pi\) | ||||
0.179917 | + | 0.983682i | \(0.442417\pi\) | |||||||
\(60\) | −1.52786 | −0.197246 | ||||||||
\(61\) | 0.763932 | 0.0978115 | 0.0489057 | − | 0.998803i | \(-0.484427\pi\) | ||||
0.0489057 | + | 0.998803i | \(0.484427\pi\) | |||||||
\(62\) | −2.00000 | −0.254000 | ||||||||
\(63\) | 1.47214 | 0.185472 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −4.00000 | −0.496139 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 11.4164 | 1.39474 | 0.697368 | − | 0.716713i | \(-0.254354\pi\) | ||||
0.697368 | + | 0.716713i | \(0.254354\pi\) | |||||||
\(68\) | −2.47214 | −0.299791 | ||||||||
\(69\) | 4.94427 | 0.595220 | ||||||||
\(70\) | −1.23607 | −0.147738 | ||||||||
\(71\) | 6.47214 | 0.768101 | 0.384051 | − | 0.923312i | \(-0.374529\pi\) | ||||
0.384051 | + | 0.923312i | \(0.374529\pi\) | |||||||
\(72\) | 1.47214 | 0.173493 | ||||||||
\(73\) | −12.9443 | −1.51501 | −0.757506 | − | 0.652828i | \(-0.773582\pi\) | ||||
−0.757506 | + | 0.652828i | \(0.773582\pi\) | |||||||
\(74\) | −6.94427 | −0.807255 | ||||||||
\(75\) | −4.29180 | −0.495574 | ||||||||
\(76\) | 7.23607 | 0.830034 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −4.00000 | −0.452911 | ||||||||
\(79\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(80\) | −1.23607 | −0.138197 | ||||||||
\(81\) | −2.41641 | −0.268490 | ||||||||
\(82\) | −2.47214 | −0.273002 | ||||||||
\(83\) | 12.1803 | 1.33697 | 0.668483 | − | 0.743727i | \(-0.266944\pi\) | ||||
0.668483 | + | 0.743727i | \(0.266944\pi\) | |||||||
\(84\) | −1.23607 | −0.134866 | ||||||||
\(85\) | 3.05573 | 0.331440 | ||||||||
\(86\) | −10.4721 | −1.12924 | ||||||||
\(87\) | −5.52786 | −0.592649 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 10.0000 | 1.06000 | 0.529999 | − | 0.847998i | \(-0.322192\pi\) | ||||
0.529999 | + | 0.847998i | \(0.322192\pi\) | |||||||
\(90\) | −1.81966 | −0.191809 | ||||||||
\(91\) | −3.23607 | −0.339232 | ||||||||
\(92\) | 4.00000 | 0.417029 | ||||||||
\(93\) | 2.47214 | 0.256349 | ||||||||
\(94\) | 2.00000 | 0.206284 | ||||||||
\(95\) | −8.94427 | −0.917663 | ||||||||
\(96\) | −1.23607 | −0.126156 | ||||||||
\(97\) | 12.4721 | 1.26635 | 0.633177 | − | 0.774007i | \(-0.281751\pi\) | ||||
0.633177 | + | 0.774007i | \(0.281751\pi\) | |||||||
\(98\) | −1.00000 | −0.101015 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −3.47214 | −0.347214 | ||||||||
\(101\) | −8.18034 | −0.813974 | −0.406987 | − | 0.913434i | \(-0.633421\pi\) | ||||
−0.406987 | + | 0.913434i | \(0.633421\pi\) | |||||||
\(102\) | 3.05573 | 0.302562 | ||||||||
\(103\) | −14.9443 | −1.47250 | −0.736251 | − | 0.676708i | \(-0.763406\pi\) | ||||
−0.736251 | + | 0.676708i | \(0.763406\pi\) | |||||||
\(104\) | −3.23607 | −0.317323 | ||||||||
\(105\) | 1.52786 | 0.149104 | ||||||||
\(106\) | −8.47214 | −0.822887 | ||||||||
\(107\) | −2.47214 | −0.238990 | −0.119495 | − | 0.992835i | \(-0.538128\pi\) | ||||
−0.119495 | + | 0.992835i | \(0.538128\pi\) | |||||||
\(108\) | −5.52786 | −0.531919 | ||||||||
\(109\) | 10.0000 | 0.957826 | 0.478913 | − | 0.877862i | \(-0.341031\pi\) | ||||
0.478913 | + | 0.877862i | \(0.341031\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 8.58359 | 0.814719 | ||||||||
\(112\) | −1.00000 | −0.0944911 | ||||||||
\(113\) | −0.472136 | −0.0444148 | −0.0222074 | − | 0.999753i | \(-0.507069\pi\) | ||||
−0.0222074 | + | 0.999753i | \(0.507069\pi\) | |||||||
\(114\) | −8.94427 | −0.837708 | ||||||||
\(115\) | −4.94427 | −0.461056 | ||||||||
\(116\) | −4.47214 | −0.415227 | ||||||||
\(117\) | −4.76393 | −0.440426 | ||||||||
\(118\) | −2.76393 | −0.254441 | ||||||||
\(119\) | 2.47214 | 0.226620 | ||||||||
\(120\) | 1.52786 | 0.139474 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | −0.763932 | −0.0691632 | ||||||||
\(123\) | 3.05573 | 0.275526 | ||||||||
\(124\) | 2.00000 | 0.179605 | ||||||||
\(125\) | 10.4721 | 0.936656 | ||||||||
\(126\) | −1.47214 | −0.131148 | ||||||||
\(127\) | 12.0000 | 1.06483 | 0.532414 | − | 0.846484i | \(-0.321285\pi\) | ||||
0.532414 | + | 0.846484i | \(0.321285\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | 12.9443 | 1.13968 | ||||||||
\(130\) | 4.00000 | 0.350823 | ||||||||
\(131\) | −4.76393 | −0.416227 | −0.208113 | − | 0.978105i | \(-0.566732\pi\) | ||||
−0.208113 | + | 0.978105i | \(0.566732\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −7.23607 | −0.627447 | ||||||||
\(134\) | −11.4164 | −0.986227 | ||||||||
\(135\) | 6.83282 | 0.588075 | ||||||||
\(136\) | 2.47214 | 0.211984 | ||||||||
\(137\) | −19.8885 | −1.69919 | −0.849596 | − | 0.527433i | \(-0.823154\pi\) | ||||
−0.849596 | + | 0.527433i | \(0.823154\pi\) | |||||||
\(138\) | −4.94427 | −0.420884 | ||||||||
\(139\) | 21.7082 | 1.84127 | 0.920633 | − | 0.390429i | \(-0.127673\pi\) | ||||
0.920633 | + | 0.390429i | \(0.127673\pi\) | |||||||
\(140\) | 1.23607 | 0.104467 | ||||||||
\(141\) | −2.47214 | −0.208191 | ||||||||
\(142\) | −6.47214 | −0.543130 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −1.47214 | −0.122678 | ||||||||
\(145\) | 5.52786 | 0.459064 | ||||||||
\(146\) | 12.9443 | 1.07128 | ||||||||
\(147\) | 1.23607 | 0.101949 | ||||||||
\(148\) | 6.94427 | 0.570816 | ||||||||
\(149\) | 22.3607 | 1.83186 | 0.915929 | − | 0.401340i | \(-0.131455\pi\) | ||||
0.915929 | + | 0.401340i | \(0.131455\pi\) | |||||||
\(150\) | 4.29180 | 0.350424 | ||||||||
\(151\) | −12.0000 | −0.976546 | −0.488273 | − | 0.872691i | \(-0.662373\pi\) | ||||
−0.488273 | + | 0.872691i | \(0.662373\pi\) | |||||||
\(152\) | −7.23607 | −0.586923 | ||||||||
\(153\) | 3.63932 | 0.294222 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −2.47214 | −0.198567 | ||||||||
\(156\) | 4.00000 | 0.320256 | ||||||||
\(157\) | −12.6525 | −1.00978 | −0.504889 | − | 0.863184i | \(-0.668466\pi\) | ||||
−0.504889 | + | 0.863184i | \(0.668466\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 10.4721 | 0.830494 | ||||||||
\(160\) | 1.23607 | 0.0977198 | ||||||||
\(161\) | −4.00000 | −0.315244 | ||||||||
\(162\) | 2.41641 | 0.189851 | ||||||||
\(163\) | −19.4164 | −1.52081 | −0.760405 | − | 0.649449i | \(-0.775000\pi\) | ||||
−0.760405 | + | 0.649449i | \(0.775000\pi\) | |||||||
\(164\) | 2.47214 | 0.193041 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −12.1803 | −0.945378 | ||||||||
\(167\) | −11.4164 | −0.883428 | −0.441714 | − | 0.897156i | \(-0.645629\pi\) | ||||
−0.441714 | + | 0.897156i | \(0.645629\pi\) | |||||||
\(168\) | 1.23607 | 0.0953647 | ||||||||
\(169\) | −2.52786 | −0.194451 | ||||||||
\(170\) | −3.05573 | −0.234364 | ||||||||
\(171\) | −10.6525 | −0.814615 | ||||||||
\(172\) | 10.4721 | 0.798493 | ||||||||
\(173\) | 3.23607 | 0.246034 | 0.123017 | − | 0.992405i | \(-0.460743\pi\) | ||||
0.123017 | + | 0.992405i | \(0.460743\pi\) | |||||||
\(174\) | 5.52786 | 0.419066 | ||||||||
\(175\) | 3.47214 | 0.262469 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 3.41641 | 0.256793 | ||||||||
\(178\) | −10.0000 | −0.749532 | ||||||||
\(179\) | −8.94427 | −0.668526 | −0.334263 | − | 0.942480i | \(-0.608487\pi\) | ||||
−0.334263 | + | 0.942480i | \(0.608487\pi\) | |||||||
\(180\) | 1.81966 | 0.135629 | ||||||||
\(181\) | 9.23607 | 0.686512 | 0.343256 | − | 0.939242i | \(-0.388470\pi\) | ||||
0.343256 | + | 0.939242i | \(0.388470\pi\) | |||||||
\(182\) | 3.23607 | 0.239873 | ||||||||
\(183\) | 0.944272 | 0.0698026 | ||||||||
\(184\) | −4.00000 | −0.294884 | ||||||||
\(185\) | −8.58359 | −0.631078 | ||||||||
\(186\) | −2.47214 | −0.181266 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | −2.00000 | −0.145865 | ||||||||
\(189\) | 5.52786 | 0.402093 | ||||||||
\(190\) | 8.94427 | 0.648886 | ||||||||
\(191\) | −2.47214 | −0.178877 | −0.0894387 | − | 0.995992i | \(-0.528507\pi\) | ||||
−0.0894387 | + | 0.995992i | \(0.528507\pi\) | |||||||
\(192\) | 1.23607 | 0.0892055 | ||||||||
\(193\) | 14.9443 | 1.07571 | 0.537856 | − | 0.843037i | \(-0.319234\pi\) | ||||
0.537856 | + | 0.843037i | \(0.319234\pi\) | |||||||
\(194\) | −12.4721 | −0.895447 | ||||||||
\(195\) | −4.94427 | −0.354067 | ||||||||
\(196\) | 1.00000 | 0.0714286 | ||||||||
\(197\) | −18.0000 | −1.28245 | −0.641223 | − | 0.767354i | \(-0.721573\pi\) | ||||
−0.641223 | + | 0.767354i | \(0.721573\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 18.9443 | 1.34292 | 0.671462 | − | 0.741039i | \(-0.265667\pi\) | ||||
0.671462 | + | 0.741039i | \(0.265667\pi\) | |||||||
\(200\) | 3.47214 | 0.245517 | ||||||||
\(201\) | 14.1115 | 0.995345 | ||||||||
\(202\) | 8.18034 | 0.575567 | ||||||||
\(203\) | 4.47214 | 0.313882 | ||||||||
\(204\) | −3.05573 | −0.213944 | ||||||||
\(205\) | −3.05573 | −0.213421 | ||||||||
\(206\) | 14.9443 | 1.04122 | ||||||||
\(207\) | −5.88854 | −0.409282 | ||||||||
\(208\) | 3.23607 | 0.224381 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | −1.52786 | −0.105433 | ||||||||
\(211\) | 13.5279 | 0.931297 | 0.465648 | − | 0.884970i | \(-0.345821\pi\) | ||||
0.465648 | + | 0.884970i | \(0.345821\pi\) | |||||||
\(212\) | 8.47214 | 0.581869 | ||||||||
\(213\) | 8.00000 | 0.548151 | ||||||||
\(214\) | 2.47214 | 0.168992 | ||||||||
\(215\) | −12.9443 | −0.882792 | ||||||||
\(216\) | 5.52786 | 0.376124 | ||||||||
\(217\) | −2.00000 | −0.135769 | ||||||||
\(218\) | −10.0000 | −0.677285 | ||||||||
\(219\) | −16.0000 | −1.08118 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −8.00000 | −0.538138 | ||||||||
\(222\) | −8.58359 | −0.576093 | ||||||||
\(223\) | −0.472136 | −0.0316166 | −0.0158083 | − | 0.999875i | \(-0.505032\pi\) | ||||
−0.0158083 | + | 0.999875i | \(0.505032\pi\) | |||||||
\(224\) | 1.00000 | 0.0668153 | ||||||||
\(225\) | 5.11146 | 0.340764 | ||||||||
\(226\) | 0.472136 | 0.0314060 | ||||||||
\(227\) | 19.2361 | 1.27674 | 0.638371 | − | 0.769729i | \(-0.279608\pi\) | ||||
0.638371 | + | 0.769729i | \(0.279608\pi\) | |||||||
\(228\) | 8.94427 | 0.592349 | ||||||||
\(229\) | 17.2361 | 1.13899 | 0.569496 | − | 0.821994i | \(-0.307139\pi\) | ||||
0.569496 | + | 0.821994i | \(0.307139\pi\) | |||||||
\(230\) | 4.94427 | 0.326016 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 4.47214 | 0.293610 | ||||||||
\(233\) | 14.9443 | 0.979032 | 0.489516 | − | 0.871994i | \(-0.337174\pi\) | ||||
0.489516 | + | 0.871994i | \(0.337174\pi\) | |||||||
\(234\) | 4.76393 | 0.311428 | ||||||||
\(235\) | 2.47214 | 0.161264 | ||||||||
\(236\) | 2.76393 | 0.179917 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −2.47214 | −0.160245 | ||||||||
\(239\) | −20.0000 | −1.29369 | −0.646846 | − | 0.762620i | \(-0.723912\pi\) | ||||
−0.646846 | + | 0.762620i | \(0.723912\pi\) | |||||||
\(240\) | −1.52786 | −0.0986232 | ||||||||
\(241\) | −15.4164 | −0.993058 | −0.496529 | − | 0.868020i | \(-0.665392\pi\) | ||||
−0.496529 | + | 0.868020i | \(0.665392\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 13.5967 | 0.872232 | ||||||||
\(244\) | 0.763932 | 0.0489057 | ||||||||
\(245\) | −1.23607 | −0.0789695 | ||||||||
\(246\) | −3.05573 | −0.194826 | ||||||||
\(247\) | 23.4164 | 1.48995 | ||||||||
\(248\) | −2.00000 | −0.127000 | ||||||||
\(249\) | 15.0557 | 0.954118 | ||||||||
\(250\) | −10.4721 | −0.662316 | ||||||||
\(251\) | 29.2361 | 1.84536 | 0.922682 | − | 0.385562i | \(-0.125992\pi\) | ||||
0.922682 | + | 0.385562i | \(0.125992\pi\) | |||||||
\(252\) | 1.47214 | 0.0927358 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | −12.0000 | −0.752947 | ||||||||
\(255\) | 3.77709 | 0.236530 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 6.94427 | 0.433172 | 0.216586 | − | 0.976264i | \(-0.430508\pi\) | ||||
0.216586 | + | 0.976264i | \(0.430508\pi\) | |||||||
\(258\) | −12.9443 | −0.805875 | ||||||||
\(259\) | −6.94427 | −0.431496 | ||||||||
\(260\) | −4.00000 | −0.248069 | ||||||||
\(261\) | 6.58359 | 0.407514 | ||||||||
\(262\) | 4.76393 | 0.294317 | ||||||||
\(263\) | 4.94427 | 0.304877 | 0.152438 | − | 0.988313i | \(-0.451287\pi\) | ||||
0.152438 | + | 0.988313i | \(0.451287\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −10.4721 | −0.643298 | ||||||||
\(266\) | 7.23607 | 0.443672 | ||||||||
\(267\) | 12.3607 | 0.756461 | ||||||||
\(268\) | 11.4164 | 0.697368 | ||||||||
\(269\) | −22.7639 | −1.38794 | −0.693971 | − | 0.720003i | \(-0.744140\pi\) | ||||
−0.693971 | + | 0.720003i | \(0.744140\pi\) | |||||||
\(270\) | −6.83282 | −0.415832 | ||||||||
\(271\) | −0.944272 | −0.0573604 | −0.0286802 | − | 0.999589i | \(-0.509130\pi\) | ||||
−0.0286802 | + | 0.999589i | \(0.509130\pi\) | |||||||
\(272\) | −2.47214 | −0.149895 | ||||||||
\(273\) | −4.00000 | −0.242091 | ||||||||
\(274\) | 19.8885 | 1.20151 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 4.94427 | 0.297610 | ||||||||
\(277\) | −3.52786 | −0.211969 | −0.105984 | − | 0.994368i | \(-0.533799\pi\) | ||||
−0.105984 | + | 0.994368i | \(0.533799\pi\) | |||||||
\(278\) | −21.7082 | −1.30197 | ||||||||
\(279\) | −2.94427 | −0.176269 | ||||||||
\(280\) | −1.23607 | −0.0738692 | ||||||||
\(281\) | −28.8328 | −1.72002 | −0.860011 | − | 0.510276i | \(-0.829543\pi\) | ||||
−0.860011 | + | 0.510276i | \(0.829543\pi\) | |||||||
\(282\) | 2.47214 | 0.147214 | ||||||||
\(283\) | −14.6525 | −0.870999 | −0.435500 | − | 0.900189i | \(-0.643428\pi\) | ||||
−0.435500 | + | 0.900189i | \(0.643428\pi\) | |||||||
\(284\) | 6.47214 | 0.384051 | ||||||||
\(285\) | −11.0557 | −0.654885 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −2.47214 | −0.145926 | ||||||||
\(288\) | 1.47214 | 0.0867464 | ||||||||
\(289\) | −10.8885 | −0.640503 | ||||||||
\(290\) | −5.52786 | −0.324607 | ||||||||
\(291\) | 15.4164 | 0.903726 | ||||||||
\(292\) | −12.9443 | −0.757506 | ||||||||
\(293\) | 26.6525 | 1.55705 | 0.778527 | − | 0.627611i | \(-0.215967\pi\) | ||||
0.778527 | + | 0.627611i | \(0.215967\pi\) | |||||||
\(294\) | −1.23607 | −0.0720889 | ||||||||
\(295\) | −3.41641 | −0.198911 | ||||||||
\(296\) | −6.94427 | −0.403628 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −22.3607 | −1.29532 | ||||||||
\(299\) | 12.9443 | 0.748587 | ||||||||
\(300\) | −4.29180 | −0.247787 | ||||||||
\(301\) | −10.4721 | −0.603604 | ||||||||
\(302\) | 12.0000 | 0.690522 | ||||||||
\(303\) | −10.1115 | −0.580888 | ||||||||
\(304\) | 7.23607 | 0.415017 | ||||||||
\(305\) | −0.944272 | −0.0540689 | ||||||||
\(306\) | −3.63932 | −0.208046 | ||||||||
\(307\) | 26.0689 | 1.48783 | 0.743915 | − | 0.668274i | \(-0.232967\pi\) | ||||
0.743915 | + | 0.668274i | \(0.232967\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −18.4721 | −1.05084 | ||||||||
\(310\) | 2.47214 | 0.140408 | ||||||||
\(311\) | −21.4164 | −1.21441 | −0.607207 | − | 0.794544i | \(-0.707710\pi\) | ||||
−0.607207 | + | 0.794544i | \(0.707710\pi\) | |||||||
\(312\) | −4.00000 | −0.226455 | ||||||||
\(313\) | 19.5279 | 1.10378 | 0.551890 | − | 0.833917i | \(-0.313907\pi\) | ||||
0.551890 | + | 0.833917i | \(0.313907\pi\) | |||||||
\(314\) | 12.6525 | 0.714021 | ||||||||
\(315\) | −1.81966 | −0.102526 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −30.9443 | −1.73800 | −0.869002 | − | 0.494809i | \(-0.835238\pi\) | ||||
−0.869002 | + | 0.494809i | \(0.835238\pi\) | |||||||
\(318\) | −10.4721 | −0.587248 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | −1.23607 | −0.0690983 | ||||||||
\(321\) | −3.05573 | −0.170554 | ||||||||
\(322\) | 4.00000 | 0.222911 | ||||||||
\(323\) | −17.8885 | −0.995345 | ||||||||
\(324\) | −2.41641 | −0.134245 | ||||||||
\(325\) | −11.2361 | −0.623265 | ||||||||
\(326\) | 19.4164 | 1.07538 | ||||||||
\(327\) | 12.3607 | 0.683547 | ||||||||
\(328\) | −2.47214 | −0.136501 | ||||||||
\(329\) | 2.00000 | 0.110264 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −16.9443 | −0.931341 | −0.465671 | − | 0.884958i | \(-0.654187\pi\) | ||||
−0.465671 | + | 0.884958i | \(0.654187\pi\) | |||||||
\(332\) | 12.1803 | 0.668483 | ||||||||
\(333\) | −10.2229 | −0.560212 | ||||||||
\(334\) | 11.4164 | 0.624678 | ||||||||
\(335\) | −14.1115 | −0.770991 | ||||||||
\(336\) | −1.23607 | −0.0674330 | ||||||||
\(337\) | −18.0000 | −0.980522 | −0.490261 | − | 0.871576i | \(-0.663099\pi\) | ||||
−0.490261 | + | 0.871576i | \(0.663099\pi\) | |||||||
\(338\) | 2.52786 | 0.137498 | ||||||||
\(339\) | −0.583592 | −0.0316964 | ||||||||
\(340\) | 3.05573 | 0.165720 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 10.6525 | 0.576020 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | −10.4721 | −0.564620 | ||||||||
\(345\) | −6.11146 | −0.329030 | ||||||||
\(346\) | −3.23607 | −0.173972 | ||||||||
\(347\) | −2.47214 | −0.132711 | −0.0663556 | − | 0.997796i | \(-0.521137\pi\) | ||||
−0.0663556 | + | 0.997796i | \(0.521137\pi\) | |||||||
\(348\) | −5.52786 | −0.296325 | ||||||||
\(349\) | −21.7082 | −1.16201 | −0.581007 | − | 0.813899i | \(-0.697341\pi\) | ||||
−0.581007 | + | 0.813899i | \(0.697341\pi\) | |||||||
\(350\) | −3.47214 | −0.185593 | ||||||||
\(351\) | −17.8885 | −0.954820 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −17.0557 | −0.907785 | −0.453892 | − | 0.891056i | \(-0.649965\pi\) | ||||
−0.453892 | + | 0.891056i | \(0.649965\pi\) | |||||||
\(354\) | −3.41641 | −0.181580 | ||||||||
\(355\) | −8.00000 | −0.424596 | ||||||||
\(356\) | 10.0000 | 0.529999 | ||||||||
\(357\) | 3.05573 | 0.161726 | ||||||||
\(358\) | 8.94427 | 0.472719 | ||||||||
\(359\) | −26.8328 | −1.41618 | −0.708091 | − | 0.706121i | \(-0.750443\pi\) | ||||
−0.708091 | + | 0.706121i | \(0.750443\pi\) | |||||||
\(360\) | −1.81966 | −0.0959045 | ||||||||
\(361\) | 33.3607 | 1.75583 | ||||||||
\(362\) | −9.23607 | −0.485437 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −3.23607 | −0.169616 | ||||||||
\(365\) | 16.0000 | 0.837478 | ||||||||
\(366\) | −0.944272 | −0.0493579 | ||||||||
\(367\) | −5.41641 | −0.282734 | −0.141367 | − | 0.989957i | \(-0.545150\pi\) | ||||
−0.141367 | + | 0.989957i | \(0.545150\pi\) | |||||||
\(368\) | 4.00000 | 0.208514 | ||||||||
\(369\) | −3.63932 | −0.189455 | ||||||||
\(370\) | 8.58359 | 0.446240 | ||||||||
\(371\) | −8.47214 | −0.439851 | ||||||||
\(372\) | 2.47214 | 0.128174 | ||||||||
\(373\) | 6.00000 | 0.310668 | 0.155334 | − | 0.987862i | \(-0.450355\pi\) | ||||
0.155334 | + | 0.987862i | \(0.450355\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 12.9443 | 0.668439 | ||||||||
\(376\) | 2.00000 | 0.103142 | ||||||||
\(377\) | −14.4721 | −0.745353 | ||||||||
\(378\) | −5.52786 | −0.284323 | ||||||||
\(379\) | 14.4721 | 0.743384 | 0.371692 | − | 0.928356i | \(-0.378778\pi\) | ||||
0.371692 | + | 0.928356i | \(0.378778\pi\) | |||||||
\(380\) | −8.94427 | −0.458831 | ||||||||
\(381\) | 14.8328 | 0.759908 | ||||||||
\(382\) | 2.47214 | 0.126485 | ||||||||
\(383\) | −23.8885 | −1.22065 | −0.610324 | − | 0.792152i | \(-0.708961\pi\) | ||||
−0.610324 | + | 0.792152i | \(0.708961\pi\) | |||||||
\(384\) | −1.23607 | −0.0630778 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −14.9443 | −0.760643 | ||||||||
\(387\) | −15.4164 | −0.783660 | ||||||||
\(388\) | 12.4721 | 0.633177 | ||||||||
\(389\) | 33.4164 | 1.69428 | 0.847140 | − | 0.531370i | \(-0.178323\pi\) | ||||
0.847140 | + | 0.531370i | \(0.178323\pi\) | |||||||
\(390\) | 4.94427 | 0.250363 | ||||||||
\(391\) | −9.88854 | −0.500085 | ||||||||
\(392\) | −1.00000 | −0.0505076 | ||||||||
\(393\) | −5.88854 | −0.297038 | ||||||||
\(394\) | 18.0000 | 0.906827 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −23.7082 | −1.18988 | −0.594940 | − | 0.803770i | \(-0.702824\pi\) | ||||
−0.594940 | + | 0.803770i | \(0.702824\pi\) | |||||||
\(398\) | −18.9443 | −0.949591 | ||||||||
\(399\) | −8.94427 | −0.447774 | ||||||||
\(400\) | −3.47214 | −0.173607 | ||||||||
\(401\) | 14.3607 | 0.717138 | 0.358569 | − | 0.933503i | \(-0.383265\pi\) | ||||
0.358569 | + | 0.933503i | \(0.383265\pi\) | |||||||
\(402\) | −14.1115 | −0.703815 | ||||||||
\(403\) | 6.47214 | 0.322400 | ||||||||
\(404\) | −8.18034 | −0.406987 | ||||||||
\(405\) | 2.98684 | 0.148417 | ||||||||
\(406\) | −4.47214 | −0.221948 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 3.05573 | 0.151281 | ||||||||
\(409\) | −3.41641 | −0.168930 | −0.0844652 | − | 0.996426i | \(-0.526918\pi\) | ||||
−0.0844652 | + | 0.996426i | \(0.526918\pi\) | |||||||
\(410\) | 3.05573 | 0.150912 | ||||||||
\(411\) | −24.5836 | −1.21262 | ||||||||
\(412\) | −14.9443 | −0.736251 | ||||||||
\(413\) | −2.76393 | −0.136004 | ||||||||
\(414\) | 5.88854 | 0.289406 | ||||||||
\(415\) | −15.0557 | −0.739057 | ||||||||
\(416\) | −3.23607 | −0.158661 | ||||||||
\(417\) | 26.8328 | 1.31401 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 17.2361 | 0.842037 | 0.421019 | − | 0.907052i | \(-0.361673\pi\) | ||||
0.421019 | + | 0.907052i | \(0.361673\pi\) | |||||||
\(420\) | 1.52786 | 0.0745521 | ||||||||
\(421\) | 16.4721 | 0.802803 | 0.401401 | − | 0.915902i | \(-0.368523\pi\) | ||||
0.401401 | + | 0.915902i | \(0.368523\pi\) | |||||||
\(422\) | −13.5279 | −0.658526 | ||||||||
\(423\) | 2.94427 | 0.143155 | ||||||||
\(424\) | −8.47214 | −0.411443 | ||||||||
\(425\) | 8.58359 | 0.416365 | ||||||||
\(426\) | −8.00000 | −0.387601 | ||||||||
\(427\) | −0.763932 | −0.0369693 | ||||||||
\(428\) | −2.47214 | −0.119495 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 12.9443 | 0.624228 | ||||||||
\(431\) | −23.0557 | −1.11056 | −0.555278 | − | 0.831665i | \(-0.687388\pi\) | ||||
−0.555278 | + | 0.831665i | \(0.687388\pi\) | |||||||
\(432\) | −5.52786 | −0.265959 | ||||||||
\(433\) | 28.4721 | 1.36828 | 0.684142 | − | 0.729349i | \(-0.260177\pi\) | ||||
0.684142 | + | 0.729349i | \(0.260177\pi\) | |||||||
\(434\) | 2.00000 | 0.0960031 | ||||||||
\(435\) | 6.83282 | 0.327608 | ||||||||
\(436\) | 10.0000 | 0.478913 | ||||||||
\(437\) | 28.9443 | 1.38459 | ||||||||
\(438\) | 16.0000 | 0.764510 | ||||||||
\(439\) | −8.94427 | −0.426887 | −0.213443 | − | 0.976955i | \(-0.568468\pi\) | ||||
−0.213443 | + | 0.976955i | \(0.568468\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −1.47214 | −0.0701017 | ||||||||
\(442\) | 8.00000 | 0.380521 | ||||||||
\(443\) | −24.9443 | −1.18514 | −0.592569 | − | 0.805520i | \(-0.701886\pi\) | ||||
−0.592569 | + | 0.805520i | \(0.701886\pi\) | |||||||
\(444\) | 8.58359 | 0.407359 | ||||||||
\(445\) | −12.3607 | −0.585952 | ||||||||
\(446\) | 0.472136 | 0.0223563 | ||||||||
\(447\) | 27.6393 | 1.30729 | ||||||||
\(448\) | −1.00000 | −0.0472456 | ||||||||
\(449\) | 18.9443 | 0.894035 | 0.447018 | − | 0.894525i | \(-0.352486\pi\) | ||||
0.447018 | + | 0.894525i | \(0.352486\pi\) | |||||||
\(450\) | −5.11146 | −0.240956 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | −0.472136 | −0.0222074 | ||||||||
\(453\) | −14.8328 | −0.696906 | ||||||||
\(454\) | −19.2361 | −0.902793 | ||||||||
\(455\) | 4.00000 | 0.187523 | ||||||||
\(456\) | −8.94427 | −0.418854 | ||||||||
\(457\) | −26.9443 | −1.26040 | −0.630200 | − | 0.776433i | \(-0.717027\pi\) | ||||
−0.630200 | + | 0.776433i | \(0.717027\pi\) | |||||||
\(458\) | −17.2361 | −0.805389 | ||||||||
\(459\) | 13.6656 | 0.637857 | ||||||||
\(460\) | −4.94427 | −0.230528 | ||||||||
\(461\) | −24.7639 | −1.15337 | −0.576686 | − | 0.816966i | \(-0.695654\pi\) | ||||
−0.576686 | + | 0.816966i | \(0.695654\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −30.4721 | −1.41616 | −0.708080 | − | 0.706132i | \(-0.750438\pi\) | ||||
−0.708080 | + | 0.706132i | \(0.750438\pi\) | |||||||
\(464\) | −4.47214 | −0.207614 | ||||||||
\(465\) | −3.05573 | −0.141706 | ||||||||
\(466\) | −14.9443 | −0.692280 | ||||||||
\(467\) | −27.1246 | −1.25518 | −0.627589 | − | 0.778545i | \(-0.715958\pi\) | ||||
−0.627589 | + | 0.778545i | \(0.715958\pi\) | |||||||
\(468\) | −4.76393 | −0.220213 | ||||||||
\(469\) | −11.4164 | −0.527161 | ||||||||
\(470\) | −2.47214 | −0.114031 | ||||||||
\(471\) | −15.6393 | −0.720622 | ||||||||
\(472\) | −2.76393 | −0.127220 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −25.1246 | −1.15280 | ||||||||
\(476\) | 2.47214 | 0.113310 | ||||||||
\(477\) | −12.4721 | −0.571060 | ||||||||
\(478\) | 20.0000 | 0.914779 | ||||||||
\(479\) | −12.3607 | −0.564774 | −0.282387 | − | 0.959301i | \(-0.591126\pi\) | ||||
−0.282387 | + | 0.959301i | \(0.591126\pi\) | |||||||
\(480\) | 1.52786 | 0.0697371 | ||||||||
\(481\) | 22.4721 | 1.02464 | ||||||||
\(482\) | 15.4164 | 0.702198 | ||||||||
\(483\) | −4.94427 | −0.224972 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −15.4164 | −0.700023 | ||||||||
\(486\) | −13.5967 | −0.616761 | ||||||||
\(487\) | 16.9443 | 0.767818 | 0.383909 | − | 0.923371i | \(-0.374578\pi\) | ||||
0.383909 | + | 0.923371i | \(0.374578\pi\) | |||||||
\(488\) | −0.763932 | −0.0345816 | ||||||||
\(489\) | −24.0000 | −1.08532 | ||||||||
\(490\) | 1.23607 | 0.0558399 | ||||||||
\(491\) | 16.9443 | 0.764684 | 0.382342 | − | 0.924021i | \(-0.375118\pi\) | ||||
0.382342 | + | 0.924021i | \(0.375118\pi\) | |||||||
\(492\) | 3.05573 | 0.137763 | ||||||||
\(493\) | 11.0557 | 0.497925 | ||||||||
\(494\) | −23.4164 | −1.05355 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 2.00000 | 0.0898027 | ||||||||
\(497\) | −6.47214 | −0.290315 | ||||||||
\(498\) | −15.0557 | −0.674663 | ||||||||
\(499\) | −32.3607 | −1.44866 | −0.724331 | − | 0.689452i | \(-0.757851\pi\) | ||||
−0.724331 | + | 0.689452i | \(0.757851\pi\) | |||||||
\(500\) | 10.4721 | 0.468328 | ||||||||
\(501\) | −14.1115 | −0.630453 | ||||||||
\(502\) | −29.2361 | −1.30487 | ||||||||
\(503\) | −4.00000 | −0.178351 | −0.0891756 | − | 0.996016i | \(-0.528423\pi\) | ||||
−0.0891756 | + | 0.996016i | \(0.528423\pi\) | |||||||
\(504\) | −1.47214 | −0.0655741 | ||||||||
\(505\) | 10.1115 | 0.449954 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −3.12461 | −0.138769 | ||||||||
\(508\) | 12.0000 | 0.532414 | ||||||||
\(509\) | 24.0689 | 1.06683 | 0.533417 | − | 0.845852i | \(-0.320908\pi\) | ||||
0.533417 | + | 0.845852i | \(0.320908\pi\) | |||||||
\(510\) | −3.77709 | −0.167252 | ||||||||
\(511\) | 12.9443 | 0.572621 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | −40.0000 | −1.76604 | ||||||||
\(514\) | −6.94427 | −0.306299 | ||||||||
\(515\) | 18.4721 | 0.813980 | ||||||||
\(516\) | 12.9443 | 0.569840 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 6.94427 | 0.305114 | ||||||||
\(519\) | 4.00000 | 0.175581 | ||||||||
\(520\) | 4.00000 | 0.175412 | ||||||||
\(521\) | −10.3607 | −0.453910 | −0.226955 | − | 0.973905i | \(-0.572877\pi\) | ||||
−0.226955 | + | 0.973905i | \(0.572877\pi\) | |||||||
\(522\) | −6.58359 | −0.288156 | ||||||||
\(523\) | 14.2918 | 0.624937 | 0.312468 | − | 0.949928i | \(-0.398844\pi\) | ||||
0.312468 | + | 0.949928i | \(0.398844\pi\) | |||||||
\(524\) | −4.76393 | −0.208113 | ||||||||
\(525\) | 4.29180 | 0.187309 | ||||||||
\(526\) | −4.94427 | −0.215580 | ||||||||
\(527\) | −4.94427 | −0.215376 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −7.00000 | −0.304348 | ||||||||
\(530\) | 10.4721 | 0.454881 | ||||||||
\(531\) | −4.06888 | −0.176575 | ||||||||
\(532\) | −7.23607 | −0.313723 | ||||||||
\(533\) | 8.00000 | 0.346518 | ||||||||
\(534\) | −12.3607 | −0.534899 | ||||||||
\(535\) | 3.05573 | 0.132111 | ||||||||
\(536\) | −11.4164 | −0.493114 | ||||||||
\(537\) | −11.0557 | −0.477090 | ||||||||
\(538\) | 22.7639 | 0.981423 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 6.83282 | 0.294038 | ||||||||
\(541\) | 26.9443 | 1.15842 | 0.579212 | − | 0.815177i | \(-0.303360\pi\) | ||||
0.579212 | + | 0.815177i | \(0.303360\pi\) | |||||||
\(542\) | 0.944272 | 0.0405600 | ||||||||
\(543\) | 11.4164 | 0.489925 | ||||||||
\(544\) | 2.47214 | 0.105992 | ||||||||
\(545\) | −12.3607 | −0.529473 | ||||||||
\(546\) | 4.00000 | 0.171184 | ||||||||
\(547\) | 0.944272 | 0.0403742 | 0.0201871 | − | 0.999796i | \(-0.493574\pi\) | ||||
0.0201871 | + | 0.999796i | \(0.493574\pi\) | |||||||
\(548\) | −19.8885 | −0.849596 | ||||||||
\(549\) | −1.12461 | −0.0479973 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −32.3607 | −1.37861 | ||||||||
\(552\) | −4.94427 | −0.210442 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 3.52786 | 0.149885 | ||||||||
\(555\) | −10.6099 | −0.450365 | ||||||||
\(556\) | 21.7082 | 0.920633 | ||||||||
\(557\) | −24.8328 | −1.05220 | −0.526100 | − | 0.850423i | \(-0.676346\pi\) | ||||
−0.526100 | + | 0.850423i | \(0.676346\pi\) | |||||||
\(558\) | 2.94427 | 0.124641 | ||||||||
\(559\) | 33.8885 | 1.43333 | ||||||||
\(560\) | 1.23607 | 0.0522334 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 28.8328 | 1.21624 | ||||||||
\(563\) | −31.2361 | −1.31644 | −0.658222 | − | 0.752824i | \(-0.728691\pi\) | ||||
−0.658222 | + | 0.752824i | \(0.728691\pi\) | |||||||
\(564\) | −2.47214 | −0.104096 | ||||||||
\(565\) | 0.583592 | 0.0245519 | ||||||||
\(566\) | 14.6525 | 0.615889 | ||||||||
\(567\) | 2.41641 | 0.101480 | ||||||||
\(568\) | −6.47214 | −0.271565 | ||||||||
\(569\) | 36.8328 | 1.54411 | 0.772056 | − | 0.635555i | \(-0.219228\pi\) | ||||
0.772056 | + | 0.635555i | \(0.219228\pi\) | |||||||
\(570\) | 11.0557 | 0.463073 | ||||||||
\(571\) | 10.1115 | 0.423151 | 0.211576 | − | 0.977362i | \(-0.432141\pi\) | ||||
0.211576 | + | 0.977362i | \(0.432141\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −3.05573 | −0.127655 | ||||||||
\(574\) | 2.47214 | 0.103185 | ||||||||
\(575\) | −13.8885 | −0.579192 | ||||||||
\(576\) | −1.47214 | −0.0613390 | ||||||||
\(577\) | 26.9443 | 1.12170 | 0.560852 | − | 0.827916i | \(-0.310474\pi\) | ||||
0.560852 | + | 0.827916i | \(0.310474\pi\) | |||||||
\(578\) | 10.8885 | 0.452904 | ||||||||
\(579\) | 18.4721 | 0.767676 | ||||||||
\(580\) | 5.52786 | 0.229532 | ||||||||
\(581\) | −12.1803 | −0.505326 | ||||||||
\(582\) | −15.4164 | −0.639031 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 12.9443 | 0.535638 | ||||||||
\(585\) | 5.88854 | 0.243461 | ||||||||
\(586\) | −26.6525 | −1.10100 | ||||||||
\(587\) | −5.81966 | −0.240203 | −0.120102 | − | 0.992762i | \(-0.538322\pi\) | ||||
−0.120102 | + | 0.992762i | \(0.538322\pi\) | |||||||
\(588\) | 1.23607 | 0.0509746 | ||||||||
\(589\) | 14.4721 | 0.596314 | ||||||||
\(590\) | 3.41641 | 0.140651 | ||||||||
\(591\) | −22.2492 | −0.915211 | ||||||||
\(592\) | 6.94427 | 0.285408 | ||||||||
\(593\) | −24.0000 | −0.985562 | −0.492781 | − | 0.870153i | \(-0.664020\pi\) | ||||
−0.492781 | + | 0.870153i | \(0.664020\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −3.05573 | −0.125273 | ||||||||
\(596\) | 22.3607 | 0.915929 | ||||||||
\(597\) | 23.4164 | 0.958370 | ||||||||
\(598\) | −12.9443 | −0.529331 | ||||||||
\(599\) | −32.3607 | −1.32222 | −0.661111 | − | 0.750288i | \(-0.729915\pi\) | ||||
−0.661111 | + | 0.750288i | \(0.729915\pi\) | |||||||
\(600\) | 4.29180 | 0.175212 | ||||||||
\(601\) | 34.8328 | 1.42086 | 0.710430 | − | 0.703768i | \(-0.248500\pi\) | ||||
0.710430 | + | 0.703768i | \(0.248500\pi\) | |||||||
\(602\) | 10.4721 | 0.426812 | ||||||||
\(603\) | −16.8065 | −0.684414 | ||||||||
\(604\) | −12.0000 | −0.488273 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 10.1115 | 0.410750 | ||||||||
\(607\) | 32.0000 | 1.29884 | 0.649420 | − | 0.760430i | \(-0.275012\pi\) | ||||
0.649420 | + | 0.760430i | \(0.275012\pi\) | |||||||
\(608\) | −7.23607 | −0.293461 | ||||||||
\(609\) | 5.52786 | 0.224000 | ||||||||
\(610\) | 0.944272 | 0.0382325 | ||||||||
\(611\) | −6.47214 | −0.261835 | ||||||||
\(612\) | 3.63932 | 0.147111 | ||||||||
\(613\) | −28.4721 | −1.14998 | −0.574989 | − | 0.818161i | \(-0.694994\pi\) | ||||
−0.574989 | + | 0.818161i | \(0.694994\pi\) | |||||||
\(614\) | −26.0689 | −1.05205 | ||||||||
\(615\) | −3.77709 | −0.152307 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 21.4164 | 0.862192 | 0.431096 | − | 0.902306i | \(-0.358127\pi\) | ||||
0.431096 | + | 0.902306i | \(0.358127\pi\) | |||||||
\(618\) | 18.4721 | 0.743058 | ||||||||
\(619\) | 18.5410 | 0.745227 | 0.372613 | − | 0.927987i | \(-0.378462\pi\) | ||||
0.372613 | + | 0.927987i | \(0.378462\pi\) | |||||||
\(620\) | −2.47214 | −0.0992834 | ||||||||
\(621\) | −22.1115 | −0.887302 | ||||||||
\(622\) | 21.4164 | 0.858720 | ||||||||
\(623\) | −10.0000 | −0.400642 | ||||||||
\(624\) | 4.00000 | 0.160128 | ||||||||
\(625\) | 4.41641 | 0.176656 | ||||||||
\(626\) | −19.5279 | −0.780490 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −12.6525 | −0.504889 | ||||||||
\(629\) | −17.1672 | −0.684500 | ||||||||
\(630\) | 1.81966 | 0.0724970 | ||||||||
\(631\) | −31.4164 | −1.25067 | −0.625334 | − | 0.780357i | \(-0.715037\pi\) | ||||
−0.625334 | + | 0.780357i | \(0.715037\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 16.7214 | 0.664614 | ||||||||
\(634\) | 30.9443 | 1.22895 | ||||||||
\(635\) | −14.8328 | −0.588622 | ||||||||
\(636\) | 10.4721 | 0.415247 | ||||||||
\(637\) | 3.23607 | 0.128218 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −9.52786 | −0.376916 | ||||||||
\(640\) | 1.23607 | 0.0488599 | ||||||||
\(641\) | 27.5279 | 1.08729 | 0.543643 | − | 0.839317i | \(-0.317045\pi\) | ||||
0.543643 | + | 0.839317i | \(0.317045\pi\) | |||||||
\(642\) | 3.05573 | 0.120600 | ||||||||
\(643\) | −18.7639 | −0.739977 | −0.369989 | − | 0.929036i | \(-0.620638\pi\) | ||||
−0.369989 | + | 0.929036i | \(0.620638\pi\) | |||||||
\(644\) | −4.00000 | −0.157622 | ||||||||
\(645\) | −16.0000 | −0.629999 | ||||||||
\(646\) | 17.8885 | 0.703815 | ||||||||
\(647\) | −28.8328 | −1.13353 | −0.566767 | − | 0.823878i | \(-0.691806\pi\) | ||||
−0.566767 | + | 0.823878i | \(0.691806\pi\) | |||||||
\(648\) | 2.41641 | 0.0949255 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 11.2361 | 0.440715 | ||||||||
\(651\) | −2.47214 | −0.0968906 | ||||||||
\(652\) | −19.4164 | −0.760405 | ||||||||
\(653\) | 46.3607 | 1.81423 | 0.907117 | − | 0.420879i | \(-0.138278\pi\) | ||||
0.907117 | + | 0.420879i | \(0.138278\pi\) | |||||||
\(654\) | −12.3607 | −0.483341 | ||||||||
\(655\) | 5.88854 | 0.230084 | ||||||||
\(656\) | 2.47214 | 0.0965207 | ||||||||
\(657\) | 19.0557 | 0.743435 | ||||||||
\(658\) | −2.00000 | −0.0779681 | ||||||||
\(659\) | −16.5836 | −0.646005 | −0.323003 | − | 0.946398i | \(-0.604692\pi\) | ||||
−0.323003 | + | 0.946398i | \(0.604692\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −3.12461 | −0.121533 | −0.0607667 | − | 0.998152i | \(-0.519355\pi\) | ||||
−0.0607667 | + | 0.998152i | \(0.519355\pi\) | |||||||
\(662\) | 16.9443 | 0.658558 | ||||||||
\(663\) | −9.88854 | −0.384039 | ||||||||
\(664\) | −12.1803 | −0.472689 | ||||||||
\(665\) | 8.94427 | 0.346844 | ||||||||
\(666\) | 10.2229 | 0.396130 | ||||||||
\(667\) | −17.8885 | −0.692647 | ||||||||
\(668\) | −11.4164 | −0.441714 | ||||||||
\(669\) | −0.583592 | −0.0225630 | ||||||||
\(670\) | 14.1115 | 0.545173 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 1.23607 | 0.0476824 | ||||||||
\(673\) | 3.88854 | 0.149892 | 0.0749462 | − | 0.997188i | \(-0.476122\pi\) | ||||
0.0749462 | + | 0.997188i | \(0.476122\pi\) | |||||||
\(674\) | 18.0000 | 0.693334 | ||||||||
\(675\) | 19.1935 | 0.738758 | ||||||||
\(676\) | −2.52786 | −0.0972255 | ||||||||
\(677\) | 26.0689 | 1.00191 | 0.500954 | − | 0.865474i | \(-0.332982\pi\) | ||||
0.500954 | + | 0.865474i | \(0.332982\pi\) | |||||||
\(678\) | 0.583592 | 0.0224127 | ||||||||
\(679\) | −12.4721 | −0.478637 | ||||||||
\(680\) | −3.05573 | −0.117182 | ||||||||
\(681\) | 23.7771 | 0.911140 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 32.9443 | 1.26058 | 0.630289 | − | 0.776361i | \(-0.282936\pi\) | ||||
0.630289 | + | 0.776361i | \(0.282936\pi\) | |||||||
\(684\) | −10.6525 | −0.407308 | ||||||||
\(685\) | 24.5836 | 0.939291 | ||||||||
\(686\) | 1.00000 | 0.0381802 | ||||||||
\(687\) | 21.3050 | 0.812835 | ||||||||
\(688\) | 10.4721 | 0.399246 | ||||||||
\(689\) | 27.4164 | 1.04448 | ||||||||
\(690\) | 6.11146 | 0.232659 | ||||||||
\(691\) | 12.6525 | 0.481323 | 0.240661 | − | 0.970609i | \(-0.422636\pi\) | ||||
0.240661 | + | 0.970609i | \(0.422636\pi\) | |||||||
\(692\) | 3.23607 | 0.123017 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 2.47214 | 0.0938410 | ||||||||
\(695\) | −26.8328 | −1.01783 | ||||||||
\(696\) | 5.52786 | 0.209533 | ||||||||
\(697\) | −6.11146 | −0.231488 | ||||||||
\(698\) | 21.7082 | 0.821668 | ||||||||
\(699\) | 18.4721 | 0.698680 | ||||||||
\(700\) | 3.47214 | 0.131234 | ||||||||
\(701\) | 42.7214 | 1.61356 | 0.806782 | − | 0.590850i | \(-0.201207\pi\) | ||||
0.806782 | + | 0.590850i | \(0.201207\pi\) | |||||||
\(702\) | 17.8885 | 0.675160 | ||||||||
\(703\) | 50.2492 | 1.89519 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 3.05573 | 0.115085 | ||||||||
\(706\) | 17.0557 | 0.641901 | ||||||||
\(707\) | 8.18034 | 0.307653 | ||||||||
\(708\) | 3.41641 | 0.128396 | ||||||||
\(709\) | 4.47214 | 0.167955 | 0.0839773 | − | 0.996468i | \(-0.473238\pi\) | ||||
0.0839773 | + | 0.996468i | \(0.473238\pi\) | |||||||
\(710\) | 8.00000 | 0.300235 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −10.0000 | −0.374766 | ||||||||
\(713\) | 8.00000 | 0.299602 | ||||||||
\(714\) | −3.05573 | −0.114358 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −8.94427 | −0.334263 | ||||||||
\(717\) | −24.7214 | −0.923236 | ||||||||
\(718\) | 26.8328 | 1.00139 | ||||||||
\(719\) | 16.8328 | 0.627758 | 0.313879 | − | 0.949463i | \(-0.398371\pi\) | ||||
0.313879 | + | 0.949463i | \(0.398371\pi\) | |||||||
\(720\) | 1.81966 | 0.0678147 | ||||||||
\(721\) | 14.9443 | 0.556554 | ||||||||
\(722\) | −33.3607 | −1.24156 | ||||||||
\(723\) | −19.0557 | −0.708690 | ||||||||
\(724\) | 9.23607 | 0.343256 | ||||||||
\(725\) | 15.5279 | 0.576690 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 18.0000 | 0.667583 | 0.333792 | − | 0.942647i | \(-0.391672\pi\) | ||||
0.333792 | + | 0.942647i | \(0.391672\pi\) | |||||||
\(728\) | 3.23607 | 0.119937 | ||||||||
\(729\) | 24.0557 | 0.890953 | ||||||||
\(730\) | −16.0000 | −0.592187 | ||||||||
\(731\) | −25.8885 | −0.957522 | ||||||||
\(732\) | 0.944272 | 0.0349013 | ||||||||
\(733\) | −49.1246 | −1.81446 | −0.907229 | − | 0.420636i | \(-0.861807\pi\) | ||||
−0.907229 | + | 0.420636i | \(0.861807\pi\) | |||||||
\(734\) | 5.41641 | 0.199923 | ||||||||
\(735\) | −1.52786 | −0.0563561 | ||||||||
\(736\) | −4.00000 | −0.147442 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 3.63932 | 0.133965 | ||||||||
\(739\) | −20.0000 | −0.735712 | −0.367856 | − | 0.929883i | \(-0.619908\pi\) | ||||
−0.367856 | + | 0.929883i | \(0.619908\pi\) | |||||||
\(740\) | −8.58359 | −0.315539 | ||||||||
\(741\) | 28.9443 | 1.06329 | ||||||||
\(742\) | 8.47214 | 0.311022 | ||||||||
\(743\) | −21.8885 | −0.803013 | −0.401506 | − | 0.915856i | \(-0.631513\pi\) | ||||
−0.401506 | + | 0.915856i | \(0.631513\pi\) | |||||||
\(744\) | −2.47214 | −0.0906329 | ||||||||
\(745\) | −27.6393 | −1.01263 | ||||||||
\(746\) | −6.00000 | −0.219676 | ||||||||
\(747\) | −17.9311 | −0.656065 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 2.47214 | 0.0903299 | ||||||||
\(750\) | −12.9443 | −0.472658 | ||||||||
\(751\) | −16.9443 | −0.618305 | −0.309153 | − | 0.951012i | \(-0.600045\pi\) | ||||
−0.309153 | + | 0.951012i | \(0.600045\pi\) | |||||||
\(752\) | −2.00000 | −0.0729325 | ||||||||
\(753\) | 36.1378 | 1.31693 | ||||||||
\(754\) | 14.4721 | 0.527044 | ||||||||
\(755\) | 14.8328 | 0.539821 | ||||||||
\(756\) | 5.52786 | 0.201046 | ||||||||
\(757\) | −23.3050 | −0.847033 | −0.423516 | − | 0.905888i | \(-0.639204\pi\) | ||||
−0.423516 | + | 0.905888i | \(0.639204\pi\) | |||||||
\(758\) | −14.4721 | −0.525652 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 8.94427 | 0.324443 | ||||||||
\(761\) | 11.4164 | 0.413844 | 0.206922 | − | 0.978357i | \(-0.433655\pi\) | ||||
0.206922 | + | 0.978357i | \(0.433655\pi\) | |||||||
\(762\) | −14.8328 | −0.537336 | ||||||||
\(763\) | −10.0000 | −0.362024 | ||||||||
\(764\) | −2.47214 | −0.0894387 | ||||||||
\(765\) | −4.49845 | −0.162642 | ||||||||
\(766\) | 23.8885 | 0.863128 | ||||||||
\(767\) | 8.94427 | 0.322959 | ||||||||
\(768\) | 1.23607 | 0.0446028 | ||||||||
\(769\) | 43.4164 | 1.56564 | 0.782818 | − | 0.622251i | \(-0.213782\pi\) | ||||
0.782818 | + | 0.622251i | \(0.213782\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 8.58359 | 0.309131 | ||||||||
\(772\) | 14.9443 | 0.537856 | ||||||||
\(773\) | 15.7082 | 0.564985 | 0.282492 | − | 0.959270i | \(-0.408839\pi\) | ||||
0.282492 | + | 0.959270i | \(0.408839\pi\) | |||||||
\(774\) | 15.4164 | 0.554131 | ||||||||
\(775\) | −6.94427 | −0.249446 | ||||||||
\(776\) | −12.4721 | −0.447724 | ||||||||
\(777\) | −8.58359 | −0.307935 | ||||||||
\(778\) | −33.4164 | −1.19804 | ||||||||
\(779\) | 17.8885 | 0.640924 | ||||||||
\(780\) | −4.94427 | −0.177033 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 9.88854 | 0.353614 | ||||||||
\(783\) | 24.7214 | 0.883469 | ||||||||
\(784\) | 1.00000 | 0.0357143 | ||||||||
\(785\) | 15.6393 | 0.558191 | ||||||||
\(786\) | 5.88854 | 0.210037 | ||||||||
\(787\) | 28.1803 | 1.00452 | 0.502260 | − | 0.864716i | \(-0.332502\pi\) | ||||
0.502260 | + | 0.864716i | \(0.332502\pi\) | |||||||
\(788\) | −18.0000 | −0.641223 | ||||||||
\(789\) | 6.11146 | 0.217574 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0.472136 | 0.0167872 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 2.47214 | 0.0877881 | ||||||||
\(794\) | 23.7082 | 0.841373 | ||||||||
\(795\) | −12.9443 | −0.459086 | ||||||||
\(796\) | 18.9443 | 0.671462 | ||||||||
\(797\) | −41.5967 | −1.47343 | −0.736716 | − | 0.676202i | \(-0.763625\pi\) | ||||
−0.736716 | + | 0.676202i | \(0.763625\pi\) | |||||||
\(798\) | 8.94427 | 0.316624 | ||||||||
\(799\) | 4.94427 | 0.174916 | ||||||||
\(800\) | 3.47214 | 0.122759 | ||||||||
\(801\) | −14.7214 | −0.520154 | ||||||||
\(802\) | −14.3607 | −0.507093 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 14.1115 | 0.497673 | ||||||||
\(805\) | 4.94427 | 0.174263 | ||||||||
\(806\) | −6.47214 | −0.227971 | ||||||||
\(807\) | −28.1378 | −0.990496 | ||||||||
\(808\) | 8.18034 | 0.287783 | ||||||||
\(809\) | 21.0557 | 0.740280 | 0.370140 | − | 0.928976i | \(-0.379310\pi\) | ||||
0.370140 | + | 0.928976i | \(0.379310\pi\) | |||||||
\(810\) | −2.98684 | −0.104947 | ||||||||
\(811\) | −4.76393 | −0.167284 | −0.0836421 | − | 0.996496i | \(-0.526655\pi\) | ||||
−0.0836421 | + | 0.996496i | \(0.526655\pi\) | |||||||
\(812\) | 4.47214 | 0.156941 | ||||||||
\(813\) | −1.16718 | −0.0409349 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 24.0000 | 0.840683 | ||||||||
\(816\) | −3.05573 | −0.106972 | ||||||||
\(817\) | 75.7771 | 2.65110 | ||||||||
\(818\) | 3.41641 | 0.119452 | ||||||||
\(819\) | 4.76393 | 0.166465 | ||||||||
\(820\) | −3.05573 | −0.106711 | ||||||||
\(821\) | 1.41641 | 0.0494330 | 0.0247165 | − | 0.999695i | \(-0.492132\pi\) | ||||
0.0247165 | + | 0.999695i | \(0.492132\pi\) | |||||||
\(822\) | 24.5836 | 0.857451 | ||||||||
\(823\) | −46.2492 | −1.61215 | −0.806073 | − | 0.591816i | \(-0.798411\pi\) | ||||
−0.806073 | + | 0.591816i | \(0.798411\pi\) | |||||||
\(824\) | 14.9443 | 0.520608 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 2.76393 | 0.0961695 | ||||||||
\(827\) | −16.9443 | −0.589210 | −0.294605 | − | 0.955619i | \(-0.595188\pi\) | ||||
−0.294605 | + | 0.955619i | \(0.595188\pi\) | |||||||
\(828\) | −5.88854 | −0.204641 | ||||||||
\(829\) | 11.7082 | 0.406643 | 0.203321 | − | 0.979112i | \(-0.434826\pi\) | ||||
0.203321 | + | 0.979112i | \(0.434826\pi\) | |||||||
\(830\) | 15.0557 | 0.522592 | ||||||||
\(831\) | −4.36068 | −0.151270 | ||||||||
\(832\) | 3.23607 | 0.112190 | ||||||||
\(833\) | −2.47214 | −0.0856544 | ||||||||
\(834\) | −26.8328 | −0.929144 | ||||||||
\(835\) | 14.1115 | 0.488347 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −11.0557 | −0.382142 | ||||||||
\(838\) | −17.2361 | −0.595410 | ||||||||
\(839\) | 16.8328 | 0.581133 | 0.290567 | − | 0.956855i | \(-0.406156\pi\) | ||||
0.290567 | + | 0.956855i | \(0.406156\pi\) | |||||||
\(840\) | −1.52786 | −0.0527163 | ||||||||
\(841\) | −9.00000 | −0.310345 | ||||||||
\(842\) | −16.4721 | −0.567667 | ||||||||
\(843\) | −35.6393 | −1.22748 | ||||||||
\(844\) | 13.5279 | 0.465648 | ||||||||
\(845\) | 3.12461 | 0.107490 | ||||||||
\(846\) | −2.94427 | −0.101226 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 8.47214 | 0.290934 | ||||||||
\(849\) | −18.1115 | −0.621584 | ||||||||
\(850\) | −8.58359 | −0.294415 | ||||||||
\(851\) | 27.7771 | 0.952186 | ||||||||
\(852\) | 8.00000 | 0.274075 | ||||||||
\(853\) | −32.5410 | −1.11418 | −0.557092 | − | 0.830451i | \(-0.688083\pi\) | ||||
−0.557092 | + | 0.830451i | \(0.688083\pi\) | |||||||
\(854\) | 0.763932 | 0.0261412 | ||||||||
\(855\) | 13.1672 | 0.450308 | ||||||||
\(856\) | 2.47214 | 0.0844959 | ||||||||
\(857\) | 46.4721 | 1.58746 | 0.793729 | − | 0.608272i | \(-0.208137\pi\) | ||||
0.793729 | + | 0.608272i | \(0.208137\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 15.1246 | 0.516045 | 0.258023 | − | 0.966139i | \(-0.416929\pi\) | ||||
0.258023 | + | 0.966139i | \(0.416929\pi\) | |||||||
\(860\) | −12.9443 | −0.441396 | ||||||||
\(861\) | −3.05573 | −0.104139 | ||||||||
\(862\) | 23.0557 | 0.785281 | ||||||||
\(863\) | 0.583592 | 0.0198657 | 0.00993285 | − | 0.999951i | \(-0.496838\pi\) | ||||
0.00993285 | + | 0.999951i | \(0.496838\pi\) | |||||||
\(864\) | 5.52786 | 0.188062 | ||||||||
\(865\) | −4.00000 | −0.136004 | ||||||||
\(866\) | −28.4721 | −0.967523 | ||||||||
\(867\) | −13.4590 | −0.457091 | ||||||||
\(868\) | −2.00000 | −0.0678844 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | −6.83282 | −0.231654 | ||||||||
\(871\) | 36.9443 | 1.25181 | ||||||||
\(872\) | −10.0000 | −0.338643 | ||||||||
\(873\) | −18.3607 | −0.621415 | ||||||||
\(874\) | −28.9443 | −0.979055 | ||||||||
\(875\) | −10.4721 | −0.354023 | ||||||||
\(876\) | −16.0000 | −0.540590 | ||||||||
\(877\) | −9.05573 | −0.305790 | −0.152895 | − | 0.988242i | \(-0.548860\pi\) | ||||
−0.152895 | + | 0.988242i | \(0.548860\pi\) | |||||||
\(878\) | 8.94427 | 0.301855 | ||||||||
\(879\) | 32.9443 | 1.11118 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 28.8328 | 0.971402 | 0.485701 | − | 0.874125i | \(-0.338564\pi\) | ||||
0.485701 | + | 0.874125i | \(0.338564\pi\) | |||||||
\(882\) | 1.47214 | 0.0495694 | ||||||||
\(883\) | −2.83282 | −0.0953318 | −0.0476659 | − | 0.998863i | \(-0.515178\pi\) | ||||
−0.0476659 | + | 0.998863i | \(0.515178\pi\) | |||||||
\(884\) | −8.00000 | −0.269069 | ||||||||
\(885\) | −4.22291 | −0.141952 | ||||||||
\(886\) | 24.9443 | 0.838019 | ||||||||
\(887\) | 44.3607 | 1.48949 | 0.744743 | − | 0.667351i | \(-0.232572\pi\) | ||||
0.744743 | + | 0.667351i | \(0.232572\pi\) | |||||||
\(888\) | −8.58359 | −0.288046 | ||||||||
\(889\) | −12.0000 | −0.402467 | ||||||||
\(890\) | 12.3607 | 0.414331 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −0.472136 | −0.0158083 | ||||||||
\(893\) | −14.4721 | −0.484292 | ||||||||
\(894\) | −27.6393 | −0.924397 | ||||||||
\(895\) | 11.0557 | 0.369552 | ||||||||
\(896\) | 1.00000 | 0.0334077 | ||||||||
\(897\) | 16.0000 | 0.534224 | ||||||||
\(898\) | −18.9443 | −0.632179 | ||||||||
\(899\) | −8.94427 | −0.298308 | ||||||||
\(900\) | 5.11146 | 0.170382 | ||||||||
\(901\) | −20.9443 | −0.697755 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −12.9443 | −0.430758 | ||||||||
\(904\) | 0.472136 | 0.0157030 | ||||||||
\(905\) | −11.4164 | −0.379494 | ||||||||
\(906\) | 14.8328 | 0.492787 | ||||||||
\(907\) | −24.3607 | −0.808883 | −0.404442 | − | 0.914564i | \(-0.632534\pi\) | ||||
−0.404442 | + | 0.914564i | \(0.632534\pi\) | |||||||
\(908\) | 19.2361 | 0.638371 | ||||||||
\(909\) | 12.0426 | 0.399427 | ||||||||
\(910\) | −4.00000 | −0.132599 | ||||||||
\(911\) | −28.0000 | −0.927681 | −0.463841 | − | 0.885919i | \(-0.653529\pi\) | ||||
−0.463841 | + | 0.885919i | \(0.653529\pi\) | |||||||
\(912\) | 8.94427 | 0.296174 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 26.9443 | 0.891237 | ||||||||
\(915\) | −1.16718 | −0.0385859 | ||||||||
\(916\) | 17.2361 | 0.569496 | ||||||||
\(917\) | 4.76393 | 0.157319 | ||||||||
\(918\) | −13.6656 | −0.451033 | ||||||||
\(919\) | 22.1115 | 0.729390 | 0.364695 | − | 0.931127i | \(-0.381173\pi\) | ||||
0.364695 | + | 0.931127i | \(0.381173\pi\) | |||||||
\(920\) | 4.94427 | 0.163008 | ||||||||
\(921\) | 32.2229 | 1.06178 | ||||||||
\(922\) | 24.7639 | 0.815557 | ||||||||
\(923\) | 20.9443 | 0.689389 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −24.1115 | −0.792780 | ||||||||
\(926\) | 30.4721 | 1.00138 | ||||||||
\(927\) | 22.0000 | 0.722575 | ||||||||
\(928\) | 4.47214 | 0.146805 | ||||||||
\(929\) | 40.2492 | 1.32053 | 0.660267 | − | 0.751031i | \(-0.270443\pi\) | ||||
0.660267 | + | 0.751031i | \(0.270443\pi\) | |||||||
\(930\) | 3.05573 | 0.100201 | ||||||||
\(931\) | 7.23607 | 0.237153 | ||||||||
\(932\) | 14.9443 | 0.489516 | ||||||||
\(933\) | −26.4721 | −0.866659 | ||||||||
\(934\) | 27.1246 | 0.887544 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 4.76393 | 0.155714 | ||||||||
\(937\) | 3.05573 | 0.0998263 | 0.0499131 | − | 0.998754i | \(-0.484106\pi\) | ||||
0.0499131 | + | 0.998754i | \(0.484106\pi\) | |||||||
\(938\) | 11.4164 | 0.372759 | ||||||||
\(939\) | 24.1378 | 0.787706 | ||||||||
\(940\) | 2.47214 | 0.0806322 | ||||||||
\(941\) | 11.8197 | 0.385310 | 0.192655 | − | 0.981267i | \(-0.438290\pi\) | ||||
0.192655 | + | 0.981267i | \(0.438290\pi\) | |||||||
\(942\) | 15.6393 | 0.509557 | ||||||||
\(943\) | 9.88854 | 0.322015 | ||||||||
\(944\) | 2.76393 | 0.0899583 | ||||||||
\(945\) | −6.83282 | −0.222272 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 16.9443 | 0.550615 | 0.275307 | − | 0.961356i | \(-0.411220\pi\) | ||||
0.275307 | + | 0.961356i | \(0.411220\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −41.8885 | −1.35976 | ||||||||
\(950\) | 25.1246 | 0.815150 | ||||||||
\(951\) | −38.2492 | −1.24032 | ||||||||
\(952\) | −2.47214 | −0.0801224 | ||||||||
\(953\) | −22.9443 | −0.743238 | −0.371619 | − | 0.928385i | \(-0.621197\pi\) | ||||
−0.371619 | + | 0.928385i | \(0.621197\pi\) | |||||||
\(954\) | 12.4721 | 0.403800 | ||||||||
\(955\) | 3.05573 | 0.0988810 | ||||||||
\(956\) | −20.0000 | −0.646846 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 12.3607 | 0.399355 | ||||||||
\(959\) | 19.8885 | 0.642235 | ||||||||
\(960\) | −1.52786 | −0.0493116 | ||||||||
\(961\) | −27.0000 | −0.870968 | ||||||||
\(962\) | −22.4721 | −0.724531 | ||||||||
\(963\) | 3.63932 | 0.117275 | ||||||||
\(964\) | −15.4164 | −0.496529 | ||||||||
\(965\) | −18.4721 | −0.594639 | ||||||||
\(966\) | 4.94427 | 0.159079 | ||||||||
\(967\) | −45.8885 | −1.47568 | −0.737838 | − | 0.674978i | \(-0.764153\pi\) | ||||
−0.737838 | + | 0.674978i | \(0.764153\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −22.1115 | −0.710322 | ||||||||
\(970\) | 15.4164 | 0.494991 | ||||||||
\(971\) | 50.5410 | 1.62194 | 0.810969 | − | 0.585089i | \(-0.198940\pi\) | ||||
0.810969 | + | 0.585089i | \(0.198940\pi\) | |||||||
\(972\) | 13.5967 | 0.436116 | ||||||||
\(973\) | −21.7082 | −0.695933 | ||||||||
\(974\) | −16.9443 | −0.542929 | ||||||||
\(975\) | −13.8885 | −0.444789 | ||||||||
\(976\) | 0.763932 | 0.0244529 | ||||||||
\(977\) | −28.8328 | −0.922443 | −0.461222 | − | 0.887285i | \(-0.652589\pi\) | ||||
−0.461222 | + | 0.887285i | \(0.652589\pi\) | |||||||
\(978\) | 24.0000 | 0.767435 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | −1.23607 | −0.0394847 | ||||||||
\(981\) | −14.7214 | −0.470017 | ||||||||
\(982\) | −16.9443 | −0.540713 | ||||||||
\(983\) | 14.0000 | 0.446531 | 0.223265 | − | 0.974758i | \(-0.428328\pi\) | ||||
0.223265 | + | 0.974758i | \(0.428328\pi\) | |||||||
\(984\) | −3.05573 | −0.0974131 | ||||||||
\(985\) | 22.2492 | 0.708919 | ||||||||
\(986\) | −11.0557 | −0.352086 | ||||||||
\(987\) | 2.47214 | 0.0786890 | ||||||||
\(988\) | 23.4164 | 0.744975 | ||||||||
\(989\) | 41.8885 | 1.33198 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −0.360680 | −0.0114574 | −0.00572869 | − | 0.999984i | \(-0.501824\pi\) | ||||
−0.00572869 | + | 0.999984i | \(0.501824\pi\) | |||||||
\(992\) | −2.00000 | −0.0635001 | ||||||||
\(993\) | −20.9443 | −0.664646 | ||||||||
\(994\) | 6.47214 | 0.205284 | ||||||||
\(995\) | −23.4164 | −0.742350 | ||||||||
\(996\) | 15.0557 | 0.477059 | ||||||||
\(997\) | −24.1803 | −0.765799 | −0.382900 | − | 0.923790i | \(-0.625074\pi\) | ||||
−0.382900 | + | 0.923790i | \(0.625074\pi\) | |||||||
\(998\) | 32.3607 | 1.02436 | ||||||||
\(999\) | −38.3870 | −1.21451 |
(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 | 1694.2.a.l.1.2 | 2 | ||
11.10 | odd | 2 | 154.2.a.d.1.2 | ✓ | 2 | ||
33.32 | even | 2 | 1386.2.a.m.1.2 | 2 | |||
44.43 | even | 2 | 1232.2.a.p.1.1 | 2 | |||
55.32 | even | 4 | 3850.2.c.q.1849.3 | 4 | |||
55.43 | even | 4 | 3850.2.c.q.1849.2 | 4 | |||
55.54 | odd | 2 | 3850.2.a.bj.1.1 | 2 | |||
77.10 | even | 6 | 1078.2.e.n.177.2 | 4 | |||
77.32 | odd | 6 | 1078.2.e.q.177.1 | 4 | |||
77.54 | even | 6 | 1078.2.e.n.67.2 | 4 | |||
77.65 | odd | 6 | 1078.2.e.q.67.1 | 4 | |||
77.76 | even | 2 | 1078.2.a.w.1.1 | 2 | |||
88.21 | odd | 2 | 4928.2.a.bt.1.1 | 2 | |||
88.43 | even | 2 | 4928.2.a.bk.1.2 | 2 | |||
231.230 | odd | 2 | 9702.2.a.cu.1.1 | 2 | |||
308.307 | odd | 2 | 8624.2.a.bf.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
154.2.a.d.1.2 | ✓ | 2 | 11.10 | odd | 2 | ||
1078.2.a.w.1.1 | 2 | 77.76 | even | 2 | |||
1078.2.e.n.67.2 | 4 | 77.54 | even | 6 | |||
1078.2.e.n.177.2 | 4 | 77.10 | even | 6 | |||
1078.2.e.q.67.1 | 4 | 77.65 | odd | 6 | |||
1078.2.e.q.177.1 | 4 | 77.32 | odd | 6 | |||
1232.2.a.p.1.1 | 2 | 44.43 | even | 2 | |||
1386.2.a.m.1.2 | 2 | 33.32 | even | 2 | |||
1694.2.a.l.1.2 | 2 | 1.1 | even | 1 | trivial | ||
3850.2.a.bj.1.1 | 2 | 55.54 | odd | 2 | |||
3850.2.c.q.1849.2 | 4 | 55.43 | even | 4 | |||
3850.2.c.q.1849.3 | 4 | 55.32 | even | 4 | |||
4928.2.a.bk.1.2 | 2 | 88.43 | even | 2 | |||
4928.2.a.bt.1.1 | 2 | 88.21 | odd | 2 | |||
8624.2.a.bf.1.2 | 2 | 308.307 | odd | 2 | |||
9702.2.a.cu.1.1 | 2 | 231.230 | odd | 2 |