Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8015,2,Mod(1,8015)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8015, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8015.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8015 = 5 \cdot 7 \cdot 229 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8015.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: | \(64.0000972201\) |
Analytic rank: | \(1\) |
Dimension: | \(38\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Character | \(\chi\) | \(=\) | 8015.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.59504 | −1.83497 | −0.917484 | − | 0.397773i | \(-0.869783\pi\) | ||||
−0.917484 | + | 0.397773i | \(0.869783\pi\) | |||||||
\(3\) | 0.990389 | 0.571801 | 0.285901 | − | 0.958259i | \(-0.407707\pi\) | ||||
0.285901 | + | 0.958259i | \(0.407707\pi\) | |||||||
\(4\) | 4.73422 | 2.36711 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | −2.57010 | −1.04924 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | −7.09539 | −2.50860 | ||||||||
\(9\) | −2.01913 | −0.673043 | ||||||||
\(10\) | −2.59504 | −0.820623 | ||||||||
\(11\) | 2.69347 | 0.812113 | 0.406056 | − | 0.913848i | \(-0.366904\pi\) | ||||
0.406056 | + | 0.913848i | \(0.366904\pi\) | |||||||
\(12\) | 4.68871 | 1.35352 | ||||||||
\(13\) | −1.27929 | −0.354811 | −0.177405 | − | 0.984138i | \(-0.556770\pi\) | ||||
−0.177405 | + | 0.984138i | \(0.556770\pi\) | |||||||
\(14\) | −2.59504 | −0.693553 | ||||||||
\(15\) | 0.990389 | 0.255717 | ||||||||
\(16\) | 8.94437 | 2.23609 | ||||||||
\(17\) | 3.50266 | 0.849519 | 0.424759 | − | 0.905306i | \(-0.360359\pi\) | ||||
0.424759 | + | 0.905306i | \(0.360359\pi\) | |||||||
\(18\) | 5.23972 | 1.23501 | ||||||||
\(19\) | −2.44770 | −0.561542 | −0.280771 | − | 0.959775i | \(-0.590590\pi\) | ||||
−0.280771 | + | 0.959775i | \(0.590590\pi\) | |||||||
\(20\) | 4.73422 | 1.05860 | ||||||||
\(21\) | 0.990389 | 0.216121 | ||||||||
\(22\) | −6.98966 | −1.49020 | ||||||||
\(23\) | 2.80389 | 0.584652 | 0.292326 | − | 0.956319i | \(-0.405571\pi\) | ||||
0.292326 | + | 0.956319i | \(0.405571\pi\) | |||||||
\(24\) | −7.02720 | −1.43442 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 3.31980 | 0.651067 | ||||||||
\(27\) | −4.97089 | −0.956648 | ||||||||
\(28\) | 4.73422 | 0.894683 | ||||||||
\(29\) | −4.34420 | −0.806698 | −0.403349 | − | 0.915046i | \(-0.632154\pi\) | ||||
−0.403349 | + | 0.915046i | \(0.632154\pi\) | |||||||
\(30\) | −2.57010 | −0.469233 | ||||||||
\(31\) | 4.94069 | 0.887374 | 0.443687 | − | 0.896182i | \(-0.353670\pi\) | ||||
0.443687 | + | 0.896182i | \(0.353670\pi\) | |||||||
\(32\) | −9.02018 | −1.59456 | ||||||||
\(33\) | 2.66759 | 0.464367 | ||||||||
\(34\) | −9.08952 | −1.55884 | ||||||||
\(35\) | 1.00000 | 0.169031 | ||||||||
\(36\) | −9.55899 | −1.59317 | ||||||||
\(37\) | −7.74705 | −1.27361 | −0.636803 | − | 0.771026i | \(-0.719744\pi\) | ||||
−0.636803 | + | 0.771026i | \(0.719744\pi\) | |||||||
\(38\) | 6.35188 | 1.03041 | ||||||||
\(39\) | −1.26699 | −0.202881 | ||||||||
\(40\) | −7.09539 | −1.12188 | ||||||||
\(41\) | −10.0194 | −1.56476 | −0.782382 | − | 0.622799i | \(-0.785995\pi\) | ||||
−0.782382 | + | 0.622799i | \(0.785995\pi\) | |||||||
\(42\) | −2.57010 | −0.396574 | ||||||||
\(43\) | 9.00403 | 1.37310 | 0.686551 | − | 0.727082i | \(-0.259124\pi\) | ||||
0.686551 | + | 0.727082i | \(0.259124\pi\) | |||||||
\(44\) | 12.7515 | 1.92236 | ||||||||
\(45\) | −2.01913 | −0.300994 | ||||||||
\(46\) | −7.27620 | −1.07282 | ||||||||
\(47\) | −5.38153 | −0.784977 | −0.392489 | − | 0.919757i | \(-0.628386\pi\) | ||||
−0.392489 | + | 0.919757i | \(0.628386\pi\) | |||||||
\(48\) | 8.85840 | 1.27860 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | −2.59504 | −0.366994 | ||||||||
\(51\) | 3.46899 | 0.485756 | ||||||||
\(52\) | −6.05643 | −0.839876 | ||||||||
\(53\) | −2.10468 | −0.289101 | −0.144550 | − | 0.989497i | \(-0.546174\pi\) | ||||
−0.144550 | + | 0.989497i | \(0.546174\pi\) | |||||||
\(54\) | 12.8996 | 1.75542 | ||||||||
\(55\) | 2.69347 | 0.363188 | ||||||||
\(56\) | −7.09539 | −0.948161 | ||||||||
\(57\) | −2.42418 | −0.321090 | ||||||||
\(58\) | 11.2734 | 1.48026 | ||||||||
\(59\) | −0.734590 | −0.0956355 | −0.0478178 | − | 0.998856i | \(-0.515227\pi\) | ||||
−0.0478178 | + | 0.998856i | \(0.515227\pi\) | |||||||
\(60\) | 4.68871 | 0.605310 | ||||||||
\(61\) | −0.871332 | −0.111563 | −0.0557813 | − | 0.998443i | \(-0.517765\pi\) | ||||
−0.0557813 | + | 0.998443i | \(0.517765\pi\) | |||||||
\(62\) | −12.8213 | −1.62830 | ||||||||
\(63\) | −2.01913 | −0.254386 | ||||||||
\(64\) | 5.51896 | 0.689870 | ||||||||
\(65\) | −1.27929 | −0.158676 | ||||||||
\(66\) | −6.92249 | −0.852099 | ||||||||
\(67\) | −15.4637 | −1.88919 | −0.944595 | − | 0.328239i | \(-0.893545\pi\) | ||||
−0.944595 | + | 0.328239i | \(0.893545\pi\) | |||||||
\(68\) | 16.5823 | 2.01090 | ||||||||
\(69\) | 2.77694 | 0.334305 | ||||||||
\(70\) | −2.59504 | −0.310166 | ||||||||
\(71\) | −7.70039 | −0.913869 | −0.456934 | − | 0.889500i | \(-0.651053\pi\) | ||||
−0.456934 | + | 0.889500i | \(0.651053\pi\) | |||||||
\(72\) | 14.3265 | 1.68840 | ||||||||
\(73\) | −14.7551 | −1.72696 | −0.863478 | − | 0.504386i | \(-0.831719\pi\) | ||||
−0.863478 | + | 0.504386i | \(0.831719\pi\) | |||||||
\(74\) | 20.1039 | 2.33703 | ||||||||
\(75\) | 0.990389 | 0.114360 | ||||||||
\(76\) | −11.5880 | −1.32923 | ||||||||
\(77\) | 2.69347 | 0.306950 | ||||||||
\(78\) | 3.28790 | 0.372281 | ||||||||
\(79\) | −4.33339 | −0.487545 | −0.243772 | − | 0.969832i | \(-0.578385\pi\) | ||||
−0.243772 | + | 0.969832i | \(0.578385\pi\) | |||||||
\(80\) | 8.94437 | 1.00001 | ||||||||
\(81\) | 1.13427 | 0.126030 | ||||||||
\(82\) | 26.0007 | 2.87129 | ||||||||
\(83\) | −9.19097 | −1.00884 | −0.504420 | − | 0.863458i | \(-0.668294\pi\) | ||||
−0.504420 | + | 0.863458i | \(0.668294\pi\) | |||||||
\(84\) | 4.68871 | 0.511581 | ||||||||
\(85\) | 3.50266 | 0.379916 | ||||||||
\(86\) | −23.3658 | −2.51960 | ||||||||
\(87\) | −4.30245 | −0.461271 | ||||||||
\(88\) | −19.1112 | −2.03727 | ||||||||
\(89\) | 0.0533003 | 0.00564982 | 0.00282491 | − | 0.999996i | \(-0.499101\pi\) | ||||
0.00282491 | + | 0.999996i | \(0.499101\pi\) | |||||||
\(90\) | 5.23972 | 0.552315 | ||||||||
\(91\) | −1.27929 | −0.134106 | ||||||||
\(92\) | 13.2742 | 1.38393 | ||||||||
\(93\) | 4.89320 | 0.507401 | ||||||||
\(94\) | 13.9653 | 1.44041 | ||||||||
\(95\) | −2.44770 | −0.251129 | ||||||||
\(96\) | −8.93348 | −0.911770 | ||||||||
\(97\) | 4.71499 | 0.478735 | 0.239368 | − | 0.970929i | \(-0.423060\pi\) | ||||
0.239368 | + | 0.970929i | \(0.423060\pi\) | |||||||
\(98\) | −2.59504 | −0.262138 | ||||||||
\(99\) | −5.43847 | −0.546587 | ||||||||
\(100\) | 4.73422 | 0.473422 | ||||||||
\(101\) | 13.4649 | 1.33981 | 0.669906 | − | 0.742446i | \(-0.266335\pi\) | ||||
0.669906 | + | 0.742446i | \(0.266335\pi\) | |||||||
\(102\) | −9.00216 | −0.891347 | ||||||||
\(103\) | 6.68061 | 0.658260 | 0.329130 | − | 0.944285i | \(-0.393245\pi\) | ||||
0.329130 | + | 0.944285i | \(0.393245\pi\) | |||||||
\(104\) | 9.07706 | 0.890079 | ||||||||
\(105\) | 0.990389 | 0.0966521 | ||||||||
\(106\) | 5.46173 | 0.530491 | ||||||||
\(107\) | 13.6633 | 1.32088 | 0.660440 | − | 0.750878i | \(-0.270370\pi\) | ||||
0.660440 | + | 0.750878i | \(0.270370\pi\) | |||||||
\(108\) | −23.5333 | −2.26449 | ||||||||
\(109\) | 2.71867 | 0.260401 | 0.130201 | − | 0.991488i | \(-0.458438\pi\) | ||||
0.130201 | + | 0.991488i | \(0.458438\pi\) | |||||||
\(110\) | −6.98966 | −0.666438 | ||||||||
\(111\) | −7.67259 | −0.728250 | ||||||||
\(112\) | 8.94437 | 0.845163 | ||||||||
\(113\) | 9.85764 | 0.927329 | 0.463664 | − | 0.886011i | \(-0.346534\pi\) | ||||
0.463664 | + | 0.886011i | \(0.346534\pi\) | |||||||
\(114\) | 6.29083 | 0.589190 | ||||||||
\(115\) | 2.80389 | 0.261464 | ||||||||
\(116\) | −20.5664 | −1.90954 | ||||||||
\(117\) | 2.58305 | 0.238803 | ||||||||
\(118\) | 1.90629 | 0.175488 | ||||||||
\(119\) | 3.50266 | 0.321088 | ||||||||
\(120\) | −7.02720 | −0.641492 | ||||||||
\(121\) | −3.74520 | −0.340473 | ||||||||
\(122\) | 2.26114 | 0.204714 | ||||||||
\(123\) | −9.92308 | −0.894734 | ||||||||
\(124\) | 23.3903 | 2.10051 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 5.23972 | 0.466791 | ||||||||
\(127\) | 2.26909 | 0.201349 | 0.100674 | − | 0.994919i | \(-0.467900\pi\) | ||||
0.100674 | + | 0.994919i | \(0.467900\pi\) | |||||||
\(128\) | 3.71845 | 0.328668 | ||||||||
\(129\) | 8.91750 | 0.785142 | ||||||||
\(130\) | 3.31980 | 0.291166 | ||||||||
\(131\) | 2.95094 | 0.257825 | 0.128912 | − | 0.991656i | \(-0.458851\pi\) | ||||
0.128912 | + | 0.991656i | \(0.458851\pi\) | |||||||
\(132\) | 12.6289 | 1.09921 | ||||||||
\(133\) | −2.44770 | −0.212243 | ||||||||
\(134\) | 40.1288 | 3.46660 | ||||||||
\(135\) | −4.97089 | −0.427826 | ||||||||
\(136\) | −24.8527 | −2.13110 | ||||||||
\(137\) | 1.57986 | 0.134976 | 0.0674881 | − | 0.997720i | \(-0.478502\pi\) | ||||
0.0674881 | + | 0.997720i | \(0.478502\pi\) | |||||||
\(138\) | −7.20627 | −0.613438 | ||||||||
\(139\) | −14.5723 | −1.23601 | −0.618003 | − | 0.786175i | \(-0.712058\pi\) | ||||
−0.618003 | + | 0.786175i | \(0.712058\pi\) | |||||||
\(140\) | 4.73422 | 0.400114 | ||||||||
\(141\) | −5.32981 | −0.448851 | ||||||||
\(142\) | 19.9828 | 1.67692 | ||||||||
\(143\) | −3.44573 | −0.288147 | ||||||||
\(144\) | −18.0598 | −1.50499 | ||||||||
\(145\) | −4.34420 | −0.360766 | ||||||||
\(146\) | 38.2901 | 3.16891 | ||||||||
\(147\) | 0.990389 | 0.0816859 | ||||||||
\(148\) | −36.6762 | −3.01476 | ||||||||
\(149\) | −21.6462 | −1.77333 | −0.886663 | − | 0.462417i | \(-0.846982\pi\) | ||||
−0.886663 | + | 0.462417i | \(0.846982\pi\) | |||||||
\(150\) | −2.57010 | −0.209847 | ||||||||
\(151\) | −9.71070 | −0.790246 | −0.395123 | − | 0.918628i | \(-0.629298\pi\) | ||||
−0.395123 | + | 0.918628i | \(0.629298\pi\) | |||||||
\(152\) | 17.3674 | 1.40868 | ||||||||
\(153\) | −7.07232 | −0.571763 | ||||||||
\(154\) | −6.98966 | −0.563243 | ||||||||
\(155\) | 4.94069 | 0.396846 | ||||||||
\(156\) | −5.99822 | −0.480242 | ||||||||
\(157\) | 5.13219 | 0.409593 | 0.204797 | − | 0.978805i | \(-0.434347\pi\) | ||||
0.204797 | + | 0.978805i | \(0.434347\pi\) | |||||||
\(158\) | 11.2453 | 0.894629 | ||||||||
\(159\) | −2.08446 | −0.165308 | ||||||||
\(160\) | −9.02018 | −0.713108 | ||||||||
\(161\) | 2.80389 | 0.220978 | ||||||||
\(162\) | −2.94348 | −0.231262 | ||||||||
\(163\) | 1.57000 | 0.122972 | 0.0614861 | − | 0.998108i | \(-0.480416\pi\) | ||||
0.0614861 | + | 0.998108i | \(0.480416\pi\) | |||||||
\(164\) | −47.4339 | −3.70396 | ||||||||
\(165\) | 2.66759 | 0.207671 | ||||||||
\(166\) | 23.8509 | 1.85119 | ||||||||
\(167\) | −13.0052 | −1.00637 | −0.503185 | − | 0.864179i | \(-0.667838\pi\) | ||||
−0.503185 | + | 0.864179i | \(0.667838\pi\) | |||||||
\(168\) | −7.02720 | −0.542160 | ||||||||
\(169\) | −11.3634 | −0.874109 | ||||||||
\(170\) | −9.08952 | −0.697134 | ||||||||
\(171\) | 4.94223 | 0.377942 | ||||||||
\(172\) | 42.6270 | 3.25028 | ||||||||
\(173\) | 19.0672 | 1.44965 | 0.724826 | − | 0.688932i | \(-0.241920\pi\) | ||||
0.724826 | + | 0.688932i | \(0.241920\pi\) | |||||||
\(174\) | 11.1650 | 0.846417 | ||||||||
\(175\) | 1.00000 | 0.0755929 | ||||||||
\(176\) | 24.0914 | 1.81596 | ||||||||
\(177\) | −0.727530 | −0.0546845 | ||||||||
\(178\) | −0.138316 | −0.0103672 | ||||||||
\(179\) | −10.3762 | −0.775550 | −0.387775 | − | 0.921754i | \(-0.626756\pi\) | ||||
−0.387775 | + | 0.921754i | \(0.626756\pi\) | |||||||
\(180\) | −9.55899 | −0.712485 | ||||||||
\(181\) | −11.4462 | −0.850787 | −0.425393 | − | 0.905009i | \(-0.639864\pi\) | ||||
−0.425393 | + | 0.905009i | \(0.639864\pi\) | |||||||
\(182\) | 3.31980 | 0.246080 | ||||||||
\(183\) | −0.862957 | −0.0637916 | ||||||||
\(184\) | −19.8947 | −1.46666 | ||||||||
\(185\) | −7.74705 | −0.569574 | ||||||||
\(186\) | −12.6980 | −0.931065 | ||||||||
\(187\) | 9.43431 | 0.689905 | ||||||||
\(188\) | −25.4773 | −1.85813 | ||||||||
\(189\) | −4.97089 | −0.361579 | ||||||||
\(190\) | 6.35188 | 0.460814 | ||||||||
\(191\) | −1.08598 | −0.0785788 | −0.0392894 | − | 0.999228i | \(-0.512509\pi\) | ||||
−0.0392894 | + | 0.999228i | \(0.512509\pi\) | |||||||
\(192\) | 5.46592 | 0.394469 | ||||||||
\(193\) | 14.5804 | 1.04952 | 0.524759 | − | 0.851251i | \(-0.324155\pi\) | ||||
0.524759 | + | 0.851251i | \(0.324155\pi\) | |||||||
\(194\) | −12.2356 | −0.878464 | ||||||||
\(195\) | −1.26699 | −0.0907313 | ||||||||
\(196\) | 4.73422 | 0.338158 | ||||||||
\(197\) | 0.866434 | 0.0617309 | 0.0308654 | − | 0.999524i | \(-0.490174\pi\) | ||||
0.0308654 | + | 0.999524i | \(0.490174\pi\) | |||||||
\(198\) | 14.1130 | 1.00297 | ||||||||
\(199\) | −14.5659 | −1.03255 | −0.516273 | − | 0.856424i | \(-0.672681\pi\) | ||||
−0.516273 | + | 0.856424i | \(0.672681\pi\) | |||||||
\(200\) | −7.09539 | −0.501720 | ||||||||
\(201\) | −15.3151 | −1.08024 | ||||||||
\(202\) | −34.9420 | −2.45851 | ||||||||
\(203\) | −4.34420 | −0.304903 | ||||||||
\(204\) | 16.4230 | 1.14984 | ||||||||
\(205\) | −10.0194 | −0.699784 | ||||||||
\(206\) | −17.3364 | −1.20789 | ||||||||
\(207\) | −5.66142 | −0.393496 | ||||||||
\(208\) | −11.4424 | −0.793390 | ||||||||
\(209\) | −6.59282 | −0.456035 | ||||||||
\(210\) | −2.57010 | −0.177353 | ||||||||
\(211\) | −22.9950 | −1.58304 | −0.791519 | − | 0.611144i | \(-0.790710\pi\) | ||||
−0.791519 | + | 0.611144i | \(0.790710\pi\) | |||||||
\(212\) | −9.96403 | −0.684333 | ||||||||
\(213\) | −7.62639 | −0.522551 | ||||||||
\(214\) | −35.4568 | −2.42377 | ||||||||
\(215\) | 9.00403 | 0.614070 | ||||||||
\(216\) | 35.2704 | 2.39985 | ||||||||
\(217\) | 4.94069 | 0.335396 | ||||||||
\(218\) | −7.05505 | −0.477828 | ||||||||
\(219\) | −14.6133 | −0.987476 | ||||||||
\(220\) | 12.7515 | 0.859705 | ||||||||
\(221\) | −4.48091 | −0.301419 | ||||||||
\(222\) | 19.9107 | 1.33632 | ||||||||
\(223\) | −15.7215 | −1.05279 | −0.526396 | − | 0.850239i | \(-0.676457\pi\) | ||||
−0.526396 | + | 0.850239i | \(0.676457\pi\) | |||||||
\(224\) | −9.02018 | −0.602686 | ||||||||
\(225\) | −2.01913 | −0.134609 | ||||||||
\(226\) | −25.5809 | −1.70162 | ||||||||
\(227\) | −2.40794 | −0.159821 | −0.0799103 | − | 0.996802i | \(-0.525463\pi\) | ||||
−0.0799103 | + | 0.996802i | \(0.525463\pi\) | |||||||
\(228\) | −11.4766 | −0.760055 | ||||||||
\(229\) | −1.00000 | −0.0660819 | ||||||||
\(230\) | −7.27620 | −0.479778 | ||||||||
\(231\) | 2.66759 | 0.175514 | ||||||||
\(232\) | 30.8238 | 2.02368 | ||||||||
\(233\) | 16.1465 | 1.05779 | 0.528895 | − | 0.848687i | \(-0.322606\pi\) | ||||
0.528895 | + | 0.848687i | \(0.322606\pi\) | |||||||
\(234\) | −6.70311 | −0.438196 | ||||||||
\(235\) | −5.38153 | −0.351053 | ||||||||
\(236\) | −3.47771 | −0.226380 | ||||||||
\(237\) | −4.29174 | −0.278779 | ||||||||
\(238\) | −9.08952 | −0.589186 | ||||||||
\(239\) | 0.439911 | 0.0284555 | 0.0142277 | − | 0.999899i | \(-0.495471\pi\) | ||||
0.0142277 | + | 0.999899i | \(0.495471\pi\) | |||||||
\(240\) | 8.85840 | 0.571807 | ||||||||
\(241\) | 23.2685 | 1.49885 | 0.749427 | − | 0.662087i | \(-0.230329\pi\) | ||||
0.749427 | + | 0.662087i | \(0.230329\pi\) | |||||||
\(242\) | 9.71893 | 0.624757 | ||||||||
\(243\) | 16.0360 | 1.02871 | ||||||||
\(244\) | −4.12507 | −0.264081 | ||||||||
\(245\) | 1.00000 | 0.0638877 | ||||||||
\(246\) | 25.7508 | 1.64181 | ||||||||
\(247\) | 3.13132 | 0.199241 | ||||||||
\(248\) | −35.0561 | −2.22606 | ||||||||
\(249\) | −9.10264 | −0.576856 | ||||||||
\(250\) | −2.59504 | −0.164125 | ||||||||
\(251\) | −18.2483 | −1.15182 | −0.575911 | − | 0.817513i | \(-0.695352\pi\) | ||||
−0.575911 | + | 0.817513i | \(0.695352\pi\) | |||||||
\(252\) | −9.55899 | −0.602160 | ||||||||
\(253\) | 7.55221 | 0.474803 | ||||||||
\(254\) | −5.88836 | −0.369468 | ||||||||
\(255\) | 3.46899 | 0.217237 | ||||||||
\(256\) | −20.6874 | −1.29296 | ||||||||
\(257\) | 28.9291 | 1.80455 | 0.902273 | − | 0.431166i | \(-0.141898\pi\) | ||||
0.902273 | + | 0.431166i | \(0.141898\pi\) | |||||||
\(258\) | −23.1412 | −1.44071 | ||||||||
\(259\) | −7.74705 | −0.481378 | ||||||||
\(260\) | −6.05643 | −0.375604 | ||||||||
\(261\) | 8.77150 | 0.542942 | ||||||||
\(262\) | −7.65780 | −0.473101 | ||||||||
\(263\) | −5.98973 | −0.369342 | −0.184671 | − | 0.982800i | \(-0.559122\pi\) | ||||
−0.184671 | + | 0.982800i | \(0.559122\pi\) | |||||||
\(264\) | −18.9276 | −1.16491 | ||||||||
\(265\) | −2.10468 | −0.129290 | ||||||||
\(266\) | 6.35188 | 0.389459 | ||||||||
\(267\) | 0.0527880 | 0.00323057 | ||||||||
\(268\) | −73.2084 | −4.47191 | ||||||||
\(269\) | −20.6362 | −1.25821 | −0.629106 | − | 0.777319i | \(-0.716579\pi\) | ||||
−0.629106 | + | 0.777319i | \(0.716579\pi\) | |||||||
\(270\) | 12.8996 | 0.785047 | ||||||||
\(271\) | −22.5419 | −1.36933 | −0.684663 | − | 0.728860i | \(-0.740051\pi\) | ||||
−0.684663 | + | 0.728860i | \(0.740051\pi\) | |||||||
\(272\) | 31.3290 | 1.89960 | ||||||||
\(273\) | −1.26699 | −0.0766820 | ||||||||
\(274\) | −4.09979 | −0.247677 | ||||||||
\(275\) | 2.69347 | 0.162423 | ||||||||
\(276\) | 13.1466 | 0.791335 | ||||||||
\(277\) | 5.12409 | 0.307877 | 0.153938 | − | 0.988080i | \(-0.450804\pi\) | ||||
0.153938 | + | 0.988080i | \(0.450804\pi\) | |||||||
\(278\) | 37.8157 | 2.26803 | ||||||||
\(279\) | −9.97589 | −0.597241 | ||||||||
\(280\) | −7.09539 | −0.424031 | ||||||||
\(281\) | 16.5014 | 0.984390 | 0.492195 | − | 0.870485i | \(-0.336195\pi\) | ||||
0.492195 | + | 0.870485i | \(0.336195\pi\) | |||||||
\(282\) | 13.8311 | 0.823627 | ||||||||
\(283\) | −8.68452 | −0.516241 | −0.258121 | − | 0.966113i | \(-0.583103\pi\) | ||||
−0.258121 | + | 0.966113i | \(0.583103\pi\) | |||||||
\(284\) | −36.4553 | −2.16323 | ||||||||
\(285\) | −2.42418 | −0.143596 | ||||||||
\(286\) | 8.94180 | 0.528740 | ||||||||
\(287\) | −10.0194 | −0.591425 | ||||||||
\(288\) | 18.2129 | 1.07321 | ||||||||
\(289\) | −4.73140 | −0.278318 | ||||||||
\(290\) | 11.2734 | 0.661994 | ||||||||
\(291\) | 4.66968 | 0.273741 | ||||||||
\(292\) | −69.8539 | −4.08789 | ||||||||
\(293\) | −0.0280092 | −0.00163631 | −0.000818157 | − | 1.00000i | \(-0.500260\pi\) | ||||
−0.000818157 | 1.00000i | \(0.500260\pi\) | ||||||||
\(294\) | −2.57010 | −0.149891 | ||||||||
\(295\) | −0.734590 | −0.0427695 | ||||||||
\(296\) | 54.9683 | 3.19497 | ||||||||
\(297\) | −13.3890 | −0.776906 | ||||||||
\(298\) | 56.1727 | 3.25399 | ||||||||
\(299\) | −3.58699 | −0.207441 | ||||||||
\(300\) | 4.68871 | 0.270703 | ||||||||
\(301\) | 9.00403 | 0.518984 | ||||||||
\(302\) | 25.1996 | 1.45008 | ||||||||
\(303\) | 13.3355 | 0.766106 | ||||||||
\(304\) | −21.8932 | −1.25566 | ||||||||
\(305\) | −0.871332 | −0.0498923 | ||||||||
\(306\) | 18.3529 | 1.04917 | ||||||||
\(307\) | 11.4750 | 0.654910 | 0.327455 | − | 0.944867i | \(-0.393809\pi\) | ||||
0.327455 | + | 0.944867i | \(0.393809\pi\) | |||||||
\(308\) | 12.7515 | 0.726583 | ||||||||
\(309\) | 6.61640 | 0.376394 | ||||||||
\(310\) | −12.8213 | −0.728199 | ||||||||
\(311\) | 32.2145 | 1.82672 | 0.913358 | − | 0.407158i | \(-0.133480\pi\) | ||||
0.913358 | + | 0.407158i | \(0.133480\pi\) | |||||||
\(312\) | 8.98982 | 0.508948 | ||||||||
\(313\) | −5.59802 | −0.316419 | −0.158209 | − | 0.987406i | \(-0.550572\pi\) | ||||
−0.158209 | + | 0.987406i | \(0.550572\pi\) | |||||||
\(314\) | −13.3182 | −0.751591 | ||||||||
\(315\) | −2.01913 | −0.113765 | ||||||||
\(316\) | −20.5152 | −1.15407 | ||||||||
\(317\) | −25.2480 | −1.41807 | −0.709035 | − | 0.705173i | \(-0.750869\pi\) | ||||
−0.709035 | + | 0.705173i | \(0.750869\pi\) | |||||||
\(318\) | 5.40924 | 0.303335 | ||||||||
\(319\) | −11.7010 | −0.655129 | ||||||||
\(320\) | 5.51896 | 0.308519 | ||||||||
\(321\) | 13.5320 | 0.755281 | ||||||||
\(322\) | −7.27620 | −0.405487 | ||||||||
\(323\) | −8.57346 | −0.477040 | ||||||||
\(324\) | 5.36990 | 0.298328 | ||||||||
\(325\) | −1.27929 | −0.0709622 | ||||||||
\(326\) | −4.07422 | −0.225650 | ||||||||
\(327\) | 2.69254 | 0.148898 | ||||||||
\(328\) | 71.0914 | 3.92537 | ||||||||
\(329\) | −5.38153 | −0.296694 | ||||||||
\(330\) | −6.92249 | −0.381070 | ||||||||
\(331\) | −27.7811 | −1.52699 | −0.763495 | − | 0.645814i | \(-0.776518\pi\) | ||||
−0.763495 | + | 0.645814i | \(0.776518\pi\) | |||||||
\(332\) | −43.5121 | −2.38803 | ||||||||
\(333\) | 15.6423 | 0.857192 | ||||||||
\(334\) | 33.7489 | 1.84666 | ||||||||
\(335\) | −15.4637 | −0.844871 | ||||||||
\(336\) | 8.85840 | 0.483265 | ||||||||
\(337\) | −17.1041 | −0.931720 | −0.465860 | − | 0.884858i | \(-0.654255\pi\) | ||||
−0.465860 | + | 0.884858i | \(0.654255\pi\) | |||||||
\(338\) | 29.4885 | 1.60396 | ||||||||
\(339\) | 9.76290 | 0.530248 | ||||||||
\(340\) | 16.5823 | 0.899303 | ||||||||
\(341\) | 13.3076 | 0.720647 | ||||||||
\(342\) | −12.8253 | −0.693511 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | −63.8871 | −3.44456 | ||||||||
\(345\) | 2.77694 | 0.149506 | ||||||||
\(346\) | −49.4801 | −2.66006 | ||||||||
\(347\) | 21.6884 | 1.16429 | 0.582147 | − | 0.813084i | \(-0.302213\pi\) | ||||
0.582147 | + | 0.813084i | \(0.302213\pi\) | |||||||
\(348\) | −20.3687 | −1.09188 | ||||||||
\(349\) | 18.7174 | 1.00192 | 0.500960 | − | 0.865471i | \(-0.332980\pi\) | ||||
0.500960 | + | 0.865471i | \(0.332980\pi\) | |||||||
\(350\) | −2.59504 | −0.138711 | ||||||||
\(351\) | 6.35921 | 0.339429 | ||||||||
\(352\) | −24.2956 | −1.29496 | ||||||||
\(353\) | −11.6226 | −0.618610 | −0.309305 | − | 0.950963i | \(-0.600096\pi\) | ||||
−0.309305 | + | 0.950963i | \(0.600096\pi\) | |||||||
\(354\) | 1.88797 | 0.100344 | ||||||||
\(355\) | −7.70039 | −0.408695 | ||||||||
\(356\) | 0.252335 | 0.0133737 | ||||||||
\(357\) | 3.46899 | 0.183599 | ||||||||
\(358\) | 26.9265 | 1.42311 | ||||||||
\(359\) | 30.8335 | 1.62733 | 0.813665 | − | 0.581334i | \(-0.197469\pi\) | ||||
0.813665 | + | 0.581334i | \(0.197469\pi\) | |||||||
\(360\) | 14.3265 | 0.755073 | ||||||||
\(361\) | −13.0087 | −0.684671 | ||||||||
\(362\) | 29.7032 | 1.56117 | ||||||||
\(363\) | −3.70921 | −0.194683 | ||||||||
\(364\) | −6.05643 | −0.317443 | ||||||||
\(365\) | −14.7551 | −0.772319 | ||||||||
\(366\) | 2.23941 | 0.117056 | ||||||||
\(367\) | 10.4553 | 0.545760 | 0.272880 | − | 0.962048i | \(-0.412024\pi\) | ||||
0.272880 | + | 0.962048i | \(0.412024\pi\) | |||||||
\(368\) | 25.0790 | 1.30733 | ||||||||
\(369\) | 20.2304 | 1.05315 | ||||||||
\(370\) | 20.1039 | 1.04515 | ||||||||
\(371\) | −2.10468 | −0.109270 | ||||||||
\(372\) | 23.1655 | 1.20107 | ||||||||
\(373\) | −15.3002 | −0.792213 | −0.396106 | − | 0.918205i | \(-0.629639\pi\) | ||||
−0.396106 | + | 0.918205i | \(0.629639\pi\) | |||||||
\(374\) | −24.4824 | −1.26595 | ||||||||
\(375\) | 0.990389 | 0.0511435 | ||||||||
\(376\) | 38.1841 | 1.96919 | ||||||||
\(377\) | 5.55749 | 0.286225 | ||||||||
\(378\) | 12.8996 | 0.663486 | ||||||||
\(379\) | 30.9733 | 1.59099 | 0.795497 | − | 0.605958i | \(-0.207210\pi\) | ||||
0.795497 | + | 0.605958i | \(0.207210\pi\) | |||||||
\(380\) | −11.5880 | −0.594450 | ||||||||
\(381\) | 2.24728 | 0.115131 | ||||||||
\(382\) | 2.81816 | 0.144190 | ||||||||
\(383\) | 27.3605 | 1.39806 | 0.699029 | − | 0.715093i | \(-0.253616\pi\) | ||||
0.699029 | + | 0.715093i | \(0.253616\pi\) | |||||||
\(384\) | 3.68271 | 0.187933 | ||||||||
\(385\) | 2.69347 | 0.137272 | ||||||||
\(386\) | −37.8366 | −1.92583 | ||||||||
\(387\) | −18.1803 | −0.924157 | ||||||||
\(388\) | 22.3218 | 1.13322 | ||||||||
\(389\) | 22.6420 | 1.14799 | 0.573997 | − | 0.818858i | \(-0.305392\pi\) | ||||
0.573997 | + | 0.818858i | \(0.305392\pi\) | |||||||
\(390\) | 3.28790 | 0.166489 | ||||||||
\(391\) | 9.82107 | 0.496673 | ||||||||
\(392\) | −7.09539 | −0.358371 | ||||||||
\(393\) | 2.92258 | 0.147425 | ||||||||
\(394\) | −2.24843 | −0.113274 | ||||||||
\(395\) | −4.33339 | −0.218037 | ||||||||
\(396\) | −25.7469 | −1.29383 | ||||||||
\(397\) | −16.8989 | −0.848132 | −0.424066 | − | 0.905631i | \(-0.639398\pi\) | ||||
−0.424066 | + | 0.905631i | \(0.639398\pi\) | |||||||
\(398\) | 37.7989 | 1.89469 | ||||||||
\(399\) | −2.42418 | −0.121361 | ||||||||
\(400\) | 8.94437 | 0.447218 | ||||||||
\(401\) | −3.12680 | −0.156145 | −0.0780724 | − | 0.996948i | \(-0.524877\pi\) | ||||
−0.0780724 | + | 0.996948i | \(0.524877\pi\) | |||||||
\(402\) | 39.7431 | 1.98221 | ||||||||
\(403\) | −6.32057 | −0.314850 | ||||||||
\(404\) | 63.7459 | 3.17148 | ||||||||
\(405\) | 1.13427 | 0.0563625 | ||||||||
\(406\) | 11.2734 | 0.559487 | ||||||||
\(407\) | −20.8665 | −1.03431 | ||||||||
\(408\) | −24.6139 | −1.21857 | ||||||||
\(409\) | −20.2809 | −1.00283 | −0.501413 | − | 0.865208i | \(-0.667186\pi\) | ||||
−0.501413 | + | 0.865208i | \(0.667186\pi\) | |||||||
\(410\) | 26.0007 | 1.28408 | ||||||||
\(411\) | 1.56467 | 0.0771796 | ||||||||
\(412\) | 31.6274 | 1.55817 | ||||||||
\(413\) | −0.734590 | −0.0361468 | ||||||||
\(414\) | 14.6916 | 0.722052 | ||||||||
\(415\) | −9.19097 | −0.451167 | ||||||||
\(416\) | 11.5394 | 0.565766 | ||||||||
\(417\) | −14.4323 | −0.706750 | ||||||||
\(418\) | 17.1086 | 0.836810 | ||||||||
\(419\) | −26.0715 | −1.27368 | −0.636839 | − | 0.770997i | \(-0.719758\pi\) | ||||
−0.636839 | + | 0.770997i | \(0.719758\pi\) | |||||||
\(420\) | 4.68871 | 0.228786 | ||||||||
\(421\) | 17.9304 | 0.873874 | 0.436937 | − | 0.899492i | \(-0.356063\pi\) | ||||
0.436937 | + | 0.899492i | \(0.356063\pi\) | |||||||
\(422\) | 59.6728 | 2.90482 | ||||||||
\(423\) | 10.8660 | 0.528324 | ||||||||
\(424\) | 14.9336 | 0.725238 | ||||||||
\(425\) | 3.50266 | 0.169904 | ||||||||
\(426\) | 19.7908 | 0.958865 | ||||||||
\(427\) | −0.871332 | −0.0421667 | ||||||||
\(428\) | 64.6850 | 3.12667 | ||||||||
\(429\) | −3.41261 | −0.164763 | ||||||||
\(430\) | −23.3658 | −1.12680 | ||||||||
\(431\) | −19.9206 | −0.959542 | −0.479771 | − | 0.877394i | \(-0.659280\pi\) | ||||
−0.479771 | + | 0.877394i | \(0.659280\pi\) | |||||||
\(432\) | −44.4615 | −2.13915 | ||||||||
\(433\) | −30.9701 | −1.48833 | −0.744165 | − | 0.667996i | \(-0.767152\pi\) | ||||
−0.744165 | + | 0.667996i | \(0.767152\pi\) | |||||||
\(434\) | −12.8213 | −0.615440 | ||||||||
\(435\) | −4.30245 | −0.206287 | ||||||||
\(436\) | 12.8708 | 0.616398 | ||||||||
\(437\) | −6.86309 | −0.328306 | ||||||||
\(438\) | 37.9221 | 1.81199 | ||||||||
\(439\) | 12.8854 | 0.614987 | 0.307494 | − | 0.951550i | \(-0.400510\pi\) | ||||
0.307494 | + | 0.951550i | \(0.400510\pi\) | |||||||
\(440\) | −19.1112 | −0.911093 | ||||||||
\(441\) | −2.01913 | −0.0961490 | ||||||||
\(442\) | 11.6281 | 0.553094 | ||||||||
\(443\) | 34.6147 | 1.64460 | 0.822298 | − | 0.569057i | \(-0.192692\pi\) | ||||
0.822298 | + | 0.569057i | \(0.192692\pi\) | |||||||
\(444\) | −36.3237 | −1.72385 | ||||||||
\(445\) | 0.0533003 | 0.00252667 | ||||||||
\(446\) | 40.7980 | 1.93184 | ||||||||
\(447\) | −21.4382 | −1.01399 | ||||||||
\(448\) | 5.51896 | 0.260746 | ||||||||
\(449\) | −36.1360 | −1.70536 | −0.852682 | − | 0.522431i | \(-0.825025\pi\) | ||||
−0.852682 | + | 0.522431i | \(0.825025\pi\) | |||||||
\(450\) | 5.23972 | 0.247003 | ||||||||
\(451\) | −26.9869 | −1.27076 | ||||||||
\(452\) | 46.6682 | 2.19509 | ||||||||
\(453\) | −9.61737 | −0.451864 | ||||||||
\(454\) | 6.24869 | 0.293266 | ||||||||
\(455\) | −1.27929 | −0.0599740 | ||||||||
\(456\) | 17.2005 | 0.805487 | ||||||||
\(457\) | 3.02590 | 0.141546 | 0.0707729 | − | 0.997492i | \(-0.477453\pi\) | ||||
0.0707729 | + | 0.997492i | \(0.477453\pi\) | |||||||
\(458\) | 2.59504 | 0.121258 | ||||||||
\(459\) | −17.4113 | −0.812691 | ||||||||
\(460\) | 13.2742 | 0.618914 | ||||||||
\(461\) | 17.4608 | 0.813232 | 0.406616 | − | 0.913599i | \(-0.366709\pi\) | ||||
0.406616 | + | 0.913599i | \(0.366709\pi\) | |||||||
\(462\) | −6.92249 | −0.322063 | ||||||||
\(463\) | −18.8781 | −0.877340 | −0.438670 | − | 0.898648i | \(-0.644550\pi\) | ||||
−0.438670 | + | 0.898648i | \(0.644550\pi\) | |||||||
\(464\) | −38.8561 | −1.80385 | ||||||||
\(465\) | 4.89320 | 0.226917 | ||||||||
\(466\) | −41.9007 | −1.94101 | ||||||||
\(467\) | −19.9635 | −0.923799 | −0.461900 | − | 0.886932i | \(-0.652832\pi\) | ||||
−0.461900 | + | 0.886932i | \(0.652832\pi\) | |||||||
\(468\) | 12.2287 | 0.565273 | ||||||||
\(469\) | −15.4637 | −0.714046 | ||||||||
\(470\) | 13.9653 | 0.644170 | ||||||||
\(471\) | 5.08286 | 0.234206 | ||||||||
\(472\) | 5.21220 | 0.239911 | ||||||||
\(473\) | 24.2521 | 1.11511 | ||||||||
\(474\) | 11.1372 | 0.511550 | ||||||||
\(475\) | −2.44770 | −0.112308 | ||||||||
\(476\) | 16.5823 | 0.760050 | ||||||||
\(477\) | 4.24963 | 0.194577 | ||||||||
\(478\) | −1.14159 | −0.0522149 | ||||||||
\(479\) | −14.1639 | −0.647165 | −0.323583 | − | 0.946200i | \(-0.604887\pi\) | ||||
−0.323583 | + | 0.946200i | \(0.604887\pi\) | |||||||
\(480\) | −8.93348 | −0.407756 | ||||||||
\(481\) | 9.91071 | 0.451890 | ||||||||
\(482\) | −60.3825 | −2.75035 | ||||||||
\(483\) | 2.77694 | 0.126355 | ||||||||
\(484\) | −17.7306 | −0.805936 | ||||||||
\(485\) | 4.71499 | 0.214097 | ||||||||
\(486\) | −41.6141 | −1.88765 | ||||||||
\(487\) | −16.7022 | −0.756847 | −0.378424 | − | 0.925633i | \(-0.623534\pi\) | ||||
−0.378424 | + | 0.925633i | \(0.623534\pi\) | |||||||
\(488\) | 6.18244 | 0.279866 | ||||||||
\(489\) | 1.55491 | 0.0703156 | ||||||||
\(490\) | −2.59504 | −0.117232 | ||||||||
\(491\) | −0.998906 | −0.0450800 | −0.0225400 | − | 0.999746i | \(-0.507175\pi\) | ||||
−0.0225400 | + | 0.999746i | \(0.507175\pi\) | |||||||
\(492\) | −46.9780 | −2.11793 | ||||||||
\(493\) | −15.2162 | −0.685305 | ||||||||
\(494\) | −8.12589 | −0.365601 | ||||||||
\(495\) | −5.43847 | −0.244441 | ||||||||
\(496\) | 44.1913 | 1.98425 | ||||||||
\(497\) | −7.70039 | −0.345410 | ||||||||
\(498\) | 23.6217 | 1.05851 | ||||||||
\(499\) | −24.6197 | −1.10213 | −0.551064 | − | 0.834463i | \(-0.685778\pi\) | ||||
−0.551064 | + | 0.834463i | \(0.685778\pi\) | |||||||
\(500\) | 4.73422 | 0.211721 | ||||||||
\(501\) | −12.8802 | −0.575443 | ||||||||
\(502\) | 47.3550 | 2.11356 | ||||||||
\(503\) | 19.5548 | 0.871904 | 0.435952 | − | 0.899970i | \(-0.356412\pi\) | ||||
0.435952 | + | 0.899970i | \(0.356412\pi\) | |||||||
\(504\) | 14.3265 | 0.638154 | ||||||||
\(505\) | 13.4649 | 0.599182 | ||||||||
\(506\) | −19.5983 | −0.871249 | ||||||||
\(507\) | −11.2542 | −0.499817 | ||||||||
\(508\) | 10.7423 | 0.476614 | ||||||||
\(509\) | 30.1264 | 1.33533 | 0.667665 | − | 0.744462i | \(-0.267294\pi\) | ||||
0.667665 | + | 0.744462i | \(0.267294\pi\) | |||||||
\(510\) | −9.00216 | −0.398622 | ||||||||
\(511\) | −14.7551 | −0.652728 | ||||||||
\(512\) | 46.2478 | 2.04388 | ||||||||
\(513\) | 12.1673 | 0.537198 | ||||||||
\(514\) | −75.0720 | −3.31128 | ||||||||
\(515\) | 6.68061 | 0.294383 | ||||||||
\(516\) | 42.2173 | 1.85852 | ||||||||
\(517\) | −14.4950 | −0.637490 | ||||||||
\(518\) | 20.1039 | 0.883313 | ||||||||
\(519\) | 18.8839 | 0.828913 | ||||||||
\(520\) | 9.07706 | 0.398055 | ||||||||
\(521\) | 29.3534 | 1.28600 | 0.642998 | − | 0.765868i | \(-0.277690\pi\) | ||||
0.642998 | + | 0.765868i | \(0.277690\pi\) | |||||||
\(522\) | −22.7624 | −0.996282 | ||||||||
\(523\) | 29.8661 | 1.30595 | 0.652976 | − | 0.757378i | \(-0.273520\pi\) | ||||
0.652976 | + | 0.757378i | \(0.273520\pi\) | |||||||
\(524\) | 13.9704 | 0.610300 | ||||||||
\(525\) | 0.990389 | 0.0432241 | ||||||||
\(526\) | 15.5436 | 0.677731 | ||||||||
\(527\) | 17.3055 | 0.753841 | ||||||||
\(528\) | 23.8599 | 1.03837 | ||||||||
\(529\) | −15.1382 | −0.658182 | ||||||||
\(530\) | 5.46173 | 0.237243 | ||||||||
\(531\) | 1.48323 | 0.0643668 | ||||||||
\(532\) | −11.5880 | −0.502402 | ||||||||
\(533\) | 12.8177 | 0.555195 | ||||||||
\(534\) | −0.136987 | −0.00592800 | ||||||||
\(535\) | 13.6633 | 0.590716 | ||||||||
\(536\) | 109.721 | 4.73922 | ||||||||
\(537\) | −10.2764 | −0.443460 | ||||||||
\(538\) | 53.5517 | 2.30878 | ||||||||
\(539\) | 2.69347 | 0.116016 | ||||||||
\(540\) | −23.5333 | −1.01271 | ||||||||
\(541\) | −8.61854 | −0.370540 | −0.185270 | − | 0.982688i | \(-0.559316\pi\) | ||||
−0.185270 | + | 0.982688i | \(0.559316\pi\) | |||||||
\(542\) | 58.4972 | 2.51267 | ||||||||
\(543\) | −11.3362 | −0.486481 | ||||||||
\(544\) | −31.5946 | −1.35461 | ||||||||
\(545\) | 2.71867 | 0.116455 | ||||||||
\(546\) | 3.28790 | 0.140709 | ||||||||
\(547\) | −9.97991 | −0.426710 | −0.213355 | − | 0.976975i | \(-0.568439\pi\) | ||||
−0.213355 | + | 0.976975i | \(0.568439\pi\) | |||||||
\(548\) | 7.47938 | 0.319503 | ||||||||
\(549\) | 1.75933 | 0.0750864 | ||||||||
\(550\) | −6.98966 | −0.298040 | ||||||||
\(551\) | 10.6333 | 0.452994 | ||||||||
\(552\) | −19.7035 | −0.838636 | ||||||||
\(553\) | −4.33339 | −0.184275 | ||||||||
\(554\) | −13.2972 | −0.564944 | ||||||||
\(555\) | −7.67259 | −0.325683 | ||||||||
\(556\) | −68.9884 | −2.92576 | ||||||||
\(557\) | 25.6136 | 1.08528 | 0.542642 | − | 0.839964i | \(-0.317424\pi\) | ||||
0.542642 | + | 0.839964i | \(0.317424\pi\) | |||||||
\(558\) | 25.8878 | 1.09592 | ||||||||
\(559\) | −11.5188 | −0.487192 | ||||||||
\(560\) | 8.94437 | 0.377968 | ||||||||
\(561\) | 9.34364 | 0.394489 | ||||||||
\(562\) | −42.8217 | −1.80632 | ||||||||
\(563\) | −21.0959 | −0.889087 | −0.444544 | − | 0.895757i | \(-0.646634\pi\) | ||||
−0.444544 | + | 0.895757i | \(0.646634\pi\) | |||||||
\(564\) | −25.2325 | −1.06248 | ||||||||
\(565\) | 9.85764 | 0.414714 | ||||||||
\(566\) | 22.5367 | 0.947286 | ||||||||
\(567\) | 1.13427 | 0.0476350 | ||||||||
\(568\) | 54.6373 | 2.29253 | ||||||||
\(569\) | −19.9563 | −0.836610 | −0.418305 | − | 0.908307i | \(-0.637376\pi\) | ||||
−0.418305 | + | 0.908307i | \(0.637376\pi\) | |||||||
\(570\) | 6.29083 | 0.263494 | ||||||||
\(571\) | 17.6773 | 0.739773 | 0.369886 | − | 0.929077i | \(-0.379397\pi\) | ||||
0.369886 | + | 0.929077i | \(0.379397\pi\) | |||||||
\(572\) | −16.3128 | −0.682074 | ||||||||
\(573\) | −1.07554 | −0.0449315 | ||||||||
\(574\) | 26.0007 | 1.08525 | ||||||||
\(575\) | 2.80389 | 0.116930 | ||||||||
\(576\) | −11.1435 | −0.464312 | ||||||||
\(577\) | 30.0343 | 1.25034 | 0.625172 | − | 0.780487i | \(-0.285029\pi\) | ||||
0.625172 | + | 0.780487i | \(0.285029\pi\) | |||||||
\(578\) | 12.2782 | 0.510704 | ||||||||
\(579\) | 14.4402 | 0.600116 | ||||||||
\(580\) | −20.5664 | −0.853972 | ||||||||
\(581\) | −9.19097 | −0.381306 | ||||||||
\(582\) | −12.1180 | −0.502307 | ||||||||
\(583\) | −5.66891 | −0.234782 | ||||||||
\(584\) | 104.693 | 4.33224 | ||||||||
\(585\) | 2.58305 | 0.106796 | ||||||||
\(586\) | 0.0726849 | 0.00300258 | ||||||||
\(587\) | 24.6305 | 1.01661 | 0.508306 | − | 0.861177i | \(-0.330272\pi\) | ||||
0.508306 | + | 0.861177i | \(0.330272\pi\) | |||||||
\(588\) | 4.68871 | 0.193359 | ||||||||
\(589\) | −12.0933 | −0.498297 | ||||||||
\(590\) | 1.90629 | 0.0784807 | ||||||||
\(591\) | 0.858107 | 0.0352978 | ||||||||
\(592\) | −69.2924 | −2.84790 | ||||||||
\(593\) | −12.9044 | −0.529921 | −0.264960 | − | 0.964259i | \(-0.585359\pi\) | ||||
−0.264960 | + | 0.964259i | \(0.585359\pi\) | |||||||
\(594\) | 34.7448 | 1.42560 | ||||||||
\(595\) | 3.50266 | 0.143595 | ||||||||
\(596\) | −102.478 | −4.19765 | ||||||||
\(597\) | −14.4259 | −0.590411 | ||||||||
\(598\) | 9.30836 | 0.380647 | ||||||||
\(599\) | 13.1927 | 0.539041 | 0.269520 | − | 0.962995i | \(-0.413135\pi\) | ||||
0.269520 | + | 0.962995i | \(0.413135\pi\) | |||||||
\(600\) | −7.02720 | −0.286884 | ||||||||
\(601\) | 33.1806 | 1.35346 | 0.676732 | − | 0.736229i | \(-0.263396\pi\) | ||||
0.676732 | + | 0.736229i | \(0.263396\pi\) | |||||||
\(602\) | −23.3658 | −0.952319 | ||||||||
\(603\) | 31.2232 | 1.27151 | ||||||||
\(604\) | −45.9726 | −1.87060 | ||||||||
\(605\) | −3.74520 | −0.152264 | ||||||||
\(606\) | −34.6062 | −1.40578 | ||||||||
\(607\) | −40.1475 | −1.62954 | −0.814768 | − | 0.579788i | \(-0.803136\pi\) | ||||
−0.814768 | + | 0.579788i | \(0.803136\pi\) | |||||||
\(608\) | 22.0787 | 0.895410 | ||||||||
\(609\) | −4.30245 | −0.174344 | ||||||||
\(610\) | 2.26114 | 0.0915508 | ||||||||
\(611\) | 6.88454 | 0.278519 | ||||||||
\(612\) | −33.4819 | −1.35342 | ||||||||
\(613\) | −30.4976 | −1.23179 | −0.615894 | − | 0.787829i | \(-0.711205\pi\) | ||||
−0.615894 | + | 0.787829i | \(0.711205\pi\) | |||||||
\(614\) | −29.7779 | −1.20174 | ||||||||
\(615\) | −9.92308 | −0.400137 | ||||||||
\(616\) | −19.1112 | −0.770014 | ||||||||
\(617\) | 23.1289 | 0.931135 | 0.465567 | − | 0.885012i | \(-0.345850\pi\) | ||||
0.465567 | + | 0.885012i | \(0.345850\pi\) | |||||||
\(618\) | −17.1698 | −0.690671 | ||||||||
\(619\) | 18.9162 | 0.760307 | 0.380154 | − | 0.924923i | \(-0.375871\pi\) | ||||
0.380154 | + | 0.924923i | \(0.375871\pi\) | |||||||
\(620\) | 23.3903 | 0.939376 | ||||||||
\(621\) | −13.9378 | −0.559306 | ||||||||
\(622\) | −83.5978 | −3.35196 | ||||||||
\(623\) | 0.0533003 | 0.00213543 | ||||||||
\(624\) | −11.3325 | −0.453661 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 14.5271 | 0.580619 | ||||||||
\(627\) | −6.52946 | −0.260762 | ||||||||
\(628\) | 24.2969 | 0.969552 | ||||||||
\(629\) | −27.1352 | −1.08195 | ||||||||
\(630\) | 5.23972 | 0.208755 | ||||||||
\(631\) | 6.28127 | 0.250053 | 0.125027 | − | 0.992153i | \(-0.460098\pi\) | ||||
0.125027 | + | 0.992153i | \(0.460098\pi\) | |||||||
\(632\) | 30.7471 | 1.22305 | ||||||||
\(633\) | −22.7740 | −0.905184 | ||||||||
\(634\) | 65.5195 | 2.60211 | ||||||||
\(635\) | 2.26909 | 0.0900459 | ||||||||
\(636\) | −9.86827 | −0.391302 | ||||||||
\(637\) | −1.27929 | −0.0506873 | ||||||||
\(638\) | 30.3645 | 1.20214 | ||||||||
\(639\) | 15.5481 | 0.615073 | ||||||||
\(640\) | 3.71845 | 0.146985 | ||||||||
\(641\) | −13.2055 | −0.521584 | −0.260792 | − | 0.965395i | \(-0.583984\pi\) | ||||
−0.260792 | + | 0.965395i | \(0.583984\pi\) | |||||||
\(642\) | −35.1160 | −1.38592 | ||||||||
\(643\) | 20.4234 | 0.805420 | 0.402710 | − | 0.915328i | \(-0.368068\pi\) | ||||
0.402710 | + | 0.915328i | \(0.368068\pi\) | |||||||
\(644\) | 13.2742 | 0.523078 | ||||||||
\(645\) | 8.91750 | 0.351126 | ||||||||
\(646\) | 22.2485 | 0.875354 | ||||||||
\(647\) | −36.3831 | −1.43037 | −0.715183 | − | 0.698937i | \(-0.753657\pi\) | ||||
−0.715183 | + | 0.698937i | \(0.753657\pi\) | |||||||
\(648\) | −8.04811 | −0.316160 | ||||||||
\(649\) | −1.97860 | −0.0776668 | ||||||||
\(650\) | 3.31980 | 0.130213 | ||||||||
\(651\) | 4.89320 | 0.191780 | ||||||||
\(652\) | 7.43273 | 0.291088 | ||||||||
\(653\) | 34.5184 | 1.35081 | 0.675405 | − | 0.737447i | \(-0.263969\pi\) | ||||
0.675405 | + | 0.737447i | \(0.263969\pi\) | |||||||
\(654\) | −6.98724 | −0.273223 | ||||||||
\(655\) | 2.95094 | 0.115303 | ||||||||
\(656\) | −89.6170 | −3.49895 | ||||||||
\(657\) | 29.7925 | 1.16232 | ||||||||
\(658\) | 13.9653 | 0.544423 | ||||||||
\(659\) | 37.1315 | 1.44644 | 0.723220 | − | 0.690618i | \(-0.242661\pi\) | ||||
0.723220 | + | 0.690618i | \(0.242661\pi\) | |||||||
\(660\) | 12.6289 | 0.491580 | ||||||||
\(661\) | 14.0781 | 0.547573 | 0.273787 | − | 0.961790i | \(-0.411724\pi\) | ||||
0.273787 | + | 0.961790i | \(0.411724\pi\) | |||||||
\(662\) | 72.0931 | 2.80198 | ||||||||
\(663\) | −4.43784 | −0.172352 | ||||||||
\(664\) | 65.2135 | 2.53078 | ||||||||
\(665\) | −2.44770 | −0.0949179 | ||||||||
\(666\) | −40.5923 | −1.57292 | ||||||||
\(667\) | −12.1807 | −0.471637 | ||||||||
\(668\) | −61.5692 | −2.38218 | ||||||||
\(669\) | −15.5704 | −0.601988 | ||||||||
\(670\) | 40.1288 | 1.55031 | ||||||||
\(671\) | −2.34691 | −0.0906014 | ||||||||
\(672\) | −8.93348 | −0.344617 | ||||||||
\(673\) | −20.7242 | −0.798861 | −0.399430 | − | 0.916764i | \(-0.630792\pi\) | ||||
−0.399430 | + | 0.916764i | \(0.630792\pi\) | |||||||
\(674\) | 44.3858 | 1.70968 | ||||||||
\(675\) | −4.97089 | −0.191330 | ||||||||
\(676\) | −53.7969 | −2.06911 | ||||||||
\(677\) | −27.3335 | −1.05051 | −0.525255 | − | 0.850945i | \(-0.676030\pi\) | ||||
−0.525255 | + | 0.850945i | \(0.676030\pi\) | |||||||
\(678\) | −25.3351 | −0.972988 | ||||||||
\(679\) | 4.71499 | 0.180945 | ||||||||
\(680\) | −24.8527 | −0.953058 | ||||||||
\(681\) | −2.38480 | −0.0913856 | ||||||||
\(682\) | −34.5337 | −1.32237 | ||||||||
\(683\) | 21.3011 | 0.815065 | 0.407532 | − | 0.913191i | \(-0.366389\pi\) | ||||
0.407532 | + | 0.913191i | \(0.366389\pi\) | |||||||
\(684\) | 23.3976 | 0.894629 | ||||||||
\(685\) | 1.57986 | 0.0603632 | ||||||||
\(686\) | −2.59504 | −0.0990790 | ||||||||
\(687\) | −0.990389 | −0.0377857 | ||||||||
\(688\) | 80.5354 | 3.07038 | ||||||||
\(689\) | 2.69250 | 0.102576 | ||||||||
\(690\) | −7.20627 | −0.274338 | ||||||||
\(691\) | −36.4636 | −1.38714 | −0.693571 | − | 0.720388i | \(-0.743964\pi\) | ||||
−0.693571 | + | 0.720388i | \(0.743964\pi\) | |||||||
\(692\) | 90.2682 | 3.43148 | ||||||||
\(693\) | −5.43847 | −0.206590 | ||||||||
\(694\) | −56.2821 | −2.13644 | ||||||||
\(695\) | −14.5723 | −0.552759 | ||||||||
\(696\) | 30.5275 | 1.15714 | ||||||||
\(697\) | −35.0944 | −1.32930 | ||||||||
\(698\) | −48.5723 | −1.83849 | ||||||||
\(699\) | 15.9913 | 0.604846 | ||||||||
\(700\) | 4.73422 | 0.178937 | ||||||||
\(701\) | −30.5707 | −1.15464 | −0.577319 | − | 0.816519i | \(-0.695901\pi\) | ||||
−0.577319 | + | 0.816519i | \(0.695901\pi\) | |||||||
\(702\) | −16.5024 | −0.622842 | ||||||||
\(703\) | 18.9625 | 0.715183 | ||||||||
\(704\) | 14.8652 | 0.560252 | ||||||||
\(705\) | −5.32981 | −0.200732 | ||||||||
\(706\) | 30.1612 | 1.13513 | ||||||||
\(707\) | 13.4649 | 0.506401 | ||||||||
\(708\) | −3.44428 | −0.129444 | ||||||||
\(709\) | −26.2595 | −0.986197 | −0.493099 | − | 0.869973i | \(-0.664136\pi\) | ||||
−0.493099 | + | 0.869973i | \(0.664136\pi\) | |||||||
\(710\) | 19.9828 | 0.749941 | ||||||||
\(711\) | 8.74968 | 0.328139 | ||||||||
\(712\) | −0.378186 | −0.0141731 | ||||||||
\(713\) | 13.8531 | 0.518804 | ||||||||
\(714\) | −9.00216 | −0.336897 | ||||||||
\(715\) | −3.44573 | −0.128863 | ||||||||
\(716\) | −49.1229 | −1.83581 | ||||||||
\(717\) | 0.435683 | 0.0162709 | ||||||||
\(718\) | −80.0140 | −2.98610 | ||||||||
\(719\) | −26.3878 | −0.984098 | −0.492049 | − | 0.870567i | \(-0.663752\pi\) | ||||
−0.492049 | + | 0.870567i | \(0.663752\pi\) | |||||||
\(720\) | −18.0598 | −0.673050 | ||||||||
\(721\) | 6.68061 | 0.248799 | ||||||||
\(722\) | 33.7582 | 1.25635 | ||||||||
\(723\) | 23.0448 | 0.857047 | ||||||||
\(724\) | −54.1886 | −2.01390 | ||||||||
\(725\) | −4.34420 | −0.161340 | ||||||||
\(726\) | 9.62552 | 0.357237 | ||||||||
\(727\) | −0.973822 | −0.0361171 | −0.0180585 | − | 0.999837i | \(-0.505749\pi\) | ||||
−0.0180585 | + | 0.999837i | \(0.505749\pi\) | |||||||
\(728\) | 9.07706 | 0.336418 | ||||||||
\(729\) | 12.4791 | 0.462189 | ||||||||
\(730\) | 38.2901 | 1.41718 | ||||||||
\(731\) | 31.5380 | 1.16648 | ||||||||
\(732\) | −4.08543 | −0.151002 | ||||||||
\(733\) | 1.68221 | 0.0621337 | 0.0310668 | − | 0.999517i | \(-0.490110\pi\) | ||||
0.0310668 | + | 0.999517i | \(0.490110\pi\) | |||||||
\(734\) | −27.1318 | −1.00145 | ||||||||
\(735\) | 0.990389 | 0.0365310 | ||||||||
\(736\) | −25.2916 | −0.932261 | ||||||||
\(737\) | −41.6510 | −1.53423 | ||||||||
\(738\) | −52.4987 | −1.93250 | ||||||||
\(739\) | 40.6856 | 1.49665 | 0.748323 | − | 0.663335i | \(-0.230859\pi\) | ||||
0.748323 | + | 0.663335i | \(0.230859\pi\) | |||||||
\(740\) | −36.6762 | −1.34824 | ||||||||
\(741\) | 3.10123 | 0.113926 | ||||||||
\(742\) | 5.46173 | 0.200507 | ||||||||
\(743\) | 47.3864 | 1.73844 | 0.869219 | − | 0.494428i | \(-0.164622\pi\) | ||||
0.869219 | + | 0.494428i | \(0.164622\pi\) | |||||||
\(744\) | −34.7192 | −1.27287 | ||||||||
\(745\) | −21.6462 | −0.793055 | ||||||||
\(746\) | 39.7045 | 1.45369 | ||||||||
\(747\) | 18.5578 | 0.678993 | ||||||||
\(748\) | 44.6641 | 1.63308 | ||||||||
\(749\) | 13.6633 | 0.499246 | ||||||||
\(750\) | −2.57010 | −0.0938466 | ||||||||
\(751\) | −27.7022 | −1.01087 | −0.505433 | − | 0.862866i | \(-0.668667\pi\) | ||||
−0.505433 | + | 0.862866i | \(0.668667\pi\) | |||||||
\(752\) | −48.1344 | −1.75528 | ||||||||
\(753\) | −18.0729 | −0.658613 | ||||||||
\(754\) | −14.4219 | −0.525214 | ||||||||
\(755\) | −9.71070 | −0.353409 | ||||||||
\(756\) | −23.5333 | −0.855897 | ||||||||
\(757\) | 32.1679 | 1.16916 | 0.584582 | − | 0.811335i | \(-0.301259\pi\) | ||||
0.584582 | + | 0.811335i | \(0.301259\pi\) | |||||||
\(758\) | −80.3770 | −2.91942 | ||||||||
\(759\) | 7.47962 | 0.271493 | ||||||||
\(760\) | 17.3674 | 0.629982 | ||||||||
\(761\) | −40.7100 | −1.47574 | −0.737869 | − | 0.674944i | \(-0.764168\pi\) | ||||
−0.737869 | + | 0.674944i | \(0.764168\pi\) | |||||||
\(762\) | −5.83177 | −0.211263 | ||||||||
\(763\) | 2.71867 | 0.0984224 | ||||||||
\(764\) | −5.14127 | −0.186004 | ||||||||
\(765\) | −7.07232 | −0.255700 | ||||||||
\(766\) | −71.0016 | −2.56539 | ||||||||
\(767\) | 0.939753 | 0.0339325 | ||||||||
\(768\) | −20.4886 | −0.739319 | ||||||||
\(769\) | 0.978215 | 0.0352754 | 0.0176377 | − | 0.999844i | \(-0.494385\pi\) | ||||
0.0176377 | + | 0.999844i | \(0.494385\pi\) | |||||||
\(770\) | −6.98966 | −0.251890 | ||||||||
\(771\) | 28.6510 | 1.03184 | ||||||||
\(772\) | 69.0266 | 2.48432 | ||||||||
\(773\) | −23.2725 | −0.837055 | −0.418527 | − | 0.908204i | \(-0.637454\pi\) | ||||
−0.418527 | + | 0.908204i | \(0.637454\pi\) | |||||||
\(774\) | 47.1786 | 1.69580 | ||||||||
\(775\) | 4.94069 | 0.177475 | ||||||||
\(776\) | −33.4547 | −1.20095 | ||||||||
\(777\) | −7.67259 | −0.275253 | ||||||||
\(778\) | −58.7568 | −2.10653 | ||||||||
\(779\) | 24.5245 | 0.878680 | ||||||||
\(780\) | −5.99822 | −0.214771 | ||||||||
\(781\) | −20.7408 | −0.742165 | ||||||||
\(782\) | −25.4860 | −0.911378 | ||||||||
\(783\) | 21.5945 | 0.771726 | ||||||||
\(784\) | 8.94437 | 0.319442 | ||||||||
\(785\) | 5.13219 | 0.183176 | ||||||||
\(786\) | −7.58420 | −0.270520 | ||||||||
\(787\) | −32.8283 | −1.17020 | −0.585102 | − | 0.810960i | \(-0.698945\pi\) | ||||
−0.585102 | + | 0.810960i | \(0.698945\pi\) | |||||||
\(788\) | 4.10189 | 0.146124 | ||||||||
\(789\) | −5.93216 | −0.211190 | ||||||||
\(790\) | 11.2453 | 0.400090 | ||||||||
\(791\) | 9.85764 | 0.350497 | ||||||||
\(792\) | 38.5881 | 1.37117 | ||||||||
\(793\) | 1.11469 | 0.0395836 | ||||||||
\(794\) | 43.8533 | 1.55630 | ||||||||
\(795\) | −2.08446 | −0.0739281 | ||||||||
\(796\) | −68.9579 | −2.44415 | ||||||||
\(797\) | −10.1817 | −0.360656 | −0.180328 | − | 0.983607i | \(-0.557716\pi\) | ||||
−0.180328 | + | 0.983607i | \(0.557716\pi\) | |||||||
\(798\) | 6.29083 | 0.222693 | ||||||||
\(799\) | −18.8497 | −0.666853 | ||||||||
\(800\) | −9.02018 | −0.318911 | ||||||||
\(801\) | −0.107620 | −0.00380257 | ||||||||
\(802\) | 8.11416 | 0.286521 | ||||||||
\(803\) | −39.7425 | −1.40248 | ||||||||
\(804\) | −72.5048 | −2.55705 | ||||||||
\(805\) | 2.80389 | 0.0988242 | ||||||||
\(806\) | 16.4021 | 0.577739 | ||||||||
\(807\) | −20.4379 | −0.719448 | ||||||||
\(808\) | −95.5390 | −3.36105 | ||||||||
\(809\) | −30.5692 | −1.07475 | −0.537377 | − | 0.843342i | \(-0.680585\pi\) | ||||
−0.537377 | + | 0.843342i | \(0.680585\pi\) | |||||||
\(810\) | −2.94348 | −0.103423 | ||||||||
\(811\) | −6.04757 | −0.212359 | −0.106180 | − | 0.994347i | \(-0.533862\pi\) | ||||
−0.106180 | + | 0.994347i | \(0.533862\pi\) | |||||||
\(812\) | −20.5664 | −0.721738 | ||||||||
\(813\) | −22.3253 | −0.782982 | ||||||||
\(814\) | 54.1492 | 1.89793 | ||||||||
\(815\) | 1.57000 | 0.0549948 | ||||||||
\(816\) | 31.0279 | 1.08619 | ||||||||
\(817\) | −22.0392 | −0.771054 | ||||||||
\(818\) | 52.6296 | 1.84015 | ||||||||
\(819\) | 2.58305 | 0.0902591 | ||||||||
\(820\) | −47.4339 | −1.65646 | ||||||||
\(821\) | 29.0789 | 1.01486 | 0.507431 | − | 0.861692i | \(-0.330595\pi\) | ||||
0.507431 | + | 0.861692i | \(0.330595\pi\) | |||||||
\(822\) | −4.06038 | −0.141622 | ||||||||
\(823\) | −19.9138 | −0.694151 | −0.347075 | − | 0.937837i | \(-0.612825\pi\) | ||||
−0.347075 | + | 0.937837i | \(0.612825\pi\) | |||||||
\(824\) | −47.4015 | −1.65131 | ||||||||
\(825\) | 2.66759 | 0.0928734 | ||||||||
\(826\) | 1.90629 | 0.0663283 | ||||||||
\(827\) | −12.1688 | −0.423151 | −0.211576 | − | 0.977362i | \(-0.567859\pi\) | ||||
−0.211576 | + | 0.977362i | \(0.567859\pi\) | |||||||
\(828\) | −26.8024 | −0.931447 | ||||||||
\(829\) | −24.9627 | −0.866992 | −0.433496 | − | 0.901155i | \(-0.642720\pi\) | ||||
−0.433496 | + | 0.901155i | \(0.642720\pi\) | |||||||
\(830\) | 23.8509 | 0.827877 | ||||||||
\(831\) | 5.07484 | 0.176044 | ||||||||
\(832\) | −7.06035 | −0.244773 | ||||||||
\(833\) | 3.50266 | 0.121360 | ||||||||
\(834\) | 37.4522 | 1.29686 | ||||||||
\(835\) | −13.0052 | −0.450062 | ||||||||
\(836\) | −31.2119 | −1.07948 | ||||||||
\(837\) | −24.5596 | −0.848904 | ||||||||
\(838\) | 67.6566 | 2.33716 | ||||||||
\(839\) | −42.5503 | −1.46900 | −0.734499 | − | 0.678609i | \(-0.762583\pi\) | ||||
−0.734499 | + | 0.678609i | \(0.762583\pi\) | |||||||
\(840\) | −7.02720 | −0.242461 | ||||||||
\(841\) | −10.1279 | −0.349239 | ||||||||
\(842\) | −46.5300 | −1.60353 | ||||||||
\(843\) | 16.3428 | 0.562876 | ||||||||
\(844\) | −108.863 | −3.74722 | ||||||||
\(845\) | −11.3634 | −0.390914 | ||||||||
\(846\) | −28.1977 | −0.969457 | ||||||||
\(847\) | −3.74520 | −0.128687 | ||||||||
\(848\) | −18.8251 | −0.646456 | ||||||||
\(849\) | −8.60106 | −0.295188 | ||||||||
\(850\) | −9.08952 | −0.311768 | ||||||||
\(851\) | −21.7219 | −0.744616 | ||||||||
\(852\) | −36.1050 | −1.23694 | ||||||||
\(853\) | 37.1701 | 1.27268 | 0.636339 | − | 0.771409i | \(-0.280448\pi\) | ||||
0.636339 | + | 0.771409i | \(0.280448\pi\) | |||||||
\(854\) | 2.26114 | 0.0773745 | ||||||||
\(855\) | 4.94223 | 0.169021 | ||||||||
\(856\) | −96.9464 | −3.31356 | ||||||||
\(857\) | −12.8464 | −0.438825 | −0.219412 | − | 0.975632i | \(-0.570414\pi\) | ||||
−0.219412 | + | 0.975632i | \(0.570414\pi\) | |||||||
\(858\) | 8.85586 | 0.302334 | ||||||||
\(859\) | −16.5681 | −0.565296 | −0.282648 | − | 0.959224i | \(-0.591213\pi\) | ||||
−0.282648 | + | 0.959224i | \(0.591213\pi\) | |||||||
\(860\) | 42.6270 | 1.45357 | ||||||||
\(861\) | −9.92308 | −0.338178 | ||||||||
\(862\) | 51.6947 | 1.76073 | ||||||||
\(863\) | 1.76156 | 0.0599641 | 0.0299821 | − | 0.999550i | \(-0.490455\pi\) | ||||
0.0299821 | + | 0.999550i | \(0.490455\pi\) | |||||||
\(864\) | 44.8383 | 1.52543 | ||||||||
\(865\) | 19.0672 | 0.648304 | ||||||||
\(866\) | 80.3687 | 2.73104 | ||||||||
\(867\) | −4.68593 | −0.159142 | ||||||||
\(868\) | 23.3903 | 0.793918 | ||||||||
\(869\) | −11.6719 | −0.395941 | ||||||||
\(870\) | 11.1650 | 0.378529 | ||||||||
\(871\) | 19.7825 | 0.670305 | ||||||||
\(872\) | −19.2900 | −0.653242 | ||||||||
\(873\) | −9.52019 | −0.322209 | ||||||||
\(874\) | 17.8100 | 0.602432 | ||||||||
\(875\) | 1.00000 | 0.0338062 | ||||||||
\(876\) | −69.1826 | −2.33746 | ||||||||
\(877\) | −35.8668 | −1.21114 | −0.605568 | − | 0.795793i | \(-0.707054\pi\) | ||||
−0.605568 | + | 0.795793i | \(0.707054\pi\) | |||||||
\(878\) | −33.4381 | −1.12848 | ||||||||
\(879\) | −0.0277400 | −0.000935646 0 | ||||||||
\(880\) | 24.0914 | 0.812121 | ||||||||
\(881\) | 0.656615 | 0.0221219 | 0.0110610 | − | 0.999939i | \(-0.496479\pi\) | ||||
0.0110610 | + | 0.999939i | \(0.496479\pi\) | |||||||
\(882\) | 5.23972 | 0.176430 | ||||||||
\(883\) | 20.1607 | 0.678461 | 0.339231 | − | 0.940703i | \(-0.389833\pi\) | ||||
0.339231 | + | 0.940703i | \(0.389833\pi\) | |||||||
\(884\) | −21.2136 | −0.713490 | ||||||||
\(885\) | −0.727530 | −0.0244557 | ||||||||
\(886\) | −89.8265 | −3.01778 | ||||||||
\(887\) | −22.4538 | −0.753926 | −0.376963 | − | 0.926228i | \(-0.623032\pi\) | ||||
−0.376963 | + | 0.926228i | \(0.623032\pi\) | |||||||
\(888\) | 54.4400 | 1.82689 | ||||||||
\(889\) | 2.26909 | 0.0761027 | ||||||||
\(890\) | −0.138316 | −0.00463637 | ||||||||
\(891\) | 3.05514 | 0.102351 | ||||||||
\(892\) | −74.4292 | −2.49207 | ||||||||
\(893\) | 13.1724 | 0.440798 | ||||||||
\(894\) | 55.6328 | 1.86064 | ||||||||
\(895\) | −10.3762 | −0.346836 | ||||||||
\(896\) | 3.71845 | 0.124225 | ||||||||
\(897\) | −3.55251 | −0.118615 | ||||||||
\(898\) | 93.7743 | 3.12929 | ||||||||
\(899\) | −21.4633 | −0.715842 | ||||||||
\(900\) | −9.55899 | −0.318633 | ||||||||
\(901\) | −7.37199 | −0.245597 | ||||||||
\(902\) | 70.0321 | 2.33181 | ||||||||
\(903\) | 8.91750 | 0.296756 | ||||||||
\(904\) | −69.9438 | −2.32630 | ||||||||
\(905\) | −11.4462 | −0.380483 | ||||||||
\(906\) | 24.9574 | 0.829155 | ||||||||
\(907\) | −40.7443 | −1.35289 | −0.676447 | − | 0.736492i | \(-0.736481\pi\) | ||||
−0.676447 | + | 0.736492i | \(0.736481\pi\) | |||||||
\(908\) | −11.3997 | −0.378313 | ||||||||
\(909\) | −27.1875 | −0.901751 | ||||||||
\(910\) | 3.31980 | 0.110050 | ||||||||
\(911\) | −30.4871 | −1.01008 | −0.505042 | − | 0.863095i | \(-0.668523\pi\) | ||||
−0.505042 | + | 0.863095i | \(0.668523\pi\) | |||||||
\(912\) | −21.6827 | −0.717987 | ||||||||
\(913\) | −24.7556 | −0.819292 | ||||||||
\(914\) | −7.85233 | −0.259732 | ||||||||
\(915\) | −0.862957 | −0.0285285 | ||||||||
\(916\) | −4.73422 | −0.156423 | ||||||||
\(917\) | 2.95094 | 0.0974487 | ||||||||
\(918\) | 45.1830 | 1.49126 | ||||||||
\(919\) | −34.2060 | −1.12835 | −0.564175 | − | 0.825655i | \(-0.690806\pi\) | ||||
−0.564175 | + | 0.825655i | \(0.690806\pi\) | |||||||
\(920\) | −19.8947 | −0.655909 | ||||||||
\(921\) | 11.3647 | 0.374479 | ||||||||
\(922\) | −45.3115 | −1.49225 | ||||||||
\(923\) | 9.85103 | 0.324251 | ||||||||
\(924\) | 12.6289 | 0.415461 | ||||||||
\(925\) | −7.74705 | −0.254721 | ||||||||
\(926\) | 48.9894 | 1.60989 | ||||||||
\(927\) | −13.4890 | −0.443037 | ||||||||
\(928\) | 39.1854 | 1.28633 | ||||||||
\(929\) | −50.3737 | −1.65271 | −0.826353 | − | 0.563152i | \(-0.809589\pi\) | ||||
−0.826353 | + | 0.563152i | \(0.809589\pi\) | |||||||
\(930\) | −12.6980 | −0.416385 | ||||||||
\(931\) | −2.44770 | −0.0802202 | ||||||||
\(932\) | 76.4409 | 2.50390 | ||||||||
\(933\) | 31.9049 | 1.04452 | ||||||||
\(934\) | 51.8059 | 1.69514 | ||||||||
\(935\) | 9.43431 | 0.308535 | ||||||||
\(936\) | −18.3278 | −0.599061 | ||||||||
\(937\) | −15.2255 | −0.497395 | −0.248698 | − | 0.968581i | \(-0.580003\pi\) | ||||
−0.248698 | + | 0.968581i | \(0.580003\pi\) | |||||||
\(938\) | 40.1288 | 1.31025 | ||||||||
\(939\) | −5.54422 | −0.180929 | ||||||||
\(940\) | −25.4773 | −0.830979 | ||||||||
\(941\) | −30.8436 | −1.00547 | −0.502736 | − | 0.864440i | \(-0.667673\pi\) | ||||
−0.502736 | + | 0.864440i | \(0.667673\pi\) | |||||||
\(942\) | −13.1902 | −0.429761 | ||||||||
\(943\) | −28.0932 | −0.914842 | ||||||||
\(944\) | −6.57044 | −0.213850 | ||||||||
\(945\) | −4.97089 | −0.161703 | ||||||||
\(946\) | −62.9352 | −2.04620 | ||||||||
\(947\) | −16.7112 | −0.543042 | −0.271521 | − | 0.962433i | \(-0.587527\pi\) | ||||
−0.271521 | + | 0.962433i | \(0.587527\pi\) | |||||||
\(948\) | −20.3180 | −0.659899 | ||||||||
\(949\) | 18.8761 | 0.612743 | ||||||||
\(950\) | 6.35188 | 0.206082 | ||||||||
\(951\) | −25.0054 | −0.810854 | ||||||||
\(952\) | −24.8527 | −0.805481 | ||||||||
\(953\) | 35.2087 | 1.14052 | 0.570260 | − | 0.821464i | \(-0.306842\pi\) | ||||
0.570260 | + | 0.821464i | \(0.306842\pi\) | |||||||
\(954\) | −11.0280 | −0.357043 | ||||||||
\(955\) | −1.08598 | −0.0351415 | ||||||||
\(956\) | 2.08263 | 0.0673572 | ||||||||
\(957\) | −11.5885 | −0.374604 | ||||||||
\(958\) | 36.7558 | 1.18753 | ||||||||
\(959\) | 1.57986 | 0.0510162 | ||||||||
\(960\) | 5.46592 | 0.176412 | ||||||||
\(961\) | −6.58961 | −0.212568 | ||||||||
\(962\) | −25.7187 | −0.829203 | ||||||||
\(963\) | −27.5880 | −0.889010 | ||||||||
\(964\) | 110.158 | 3.54795 | ||||||||
\(965\) | 14.5804 | 0.469359 | ||||||||
\(966\) | −7.20627 | −0.231858 | ||||||||
\(967\) | −13.3997 | −0.430906 | −0.215453 | − | 0.976514i | \(-0.569123\pi\) | ||||
−0.215453 | + | 0.976514i | \(0.569123\pi\) | |||||||
\(968\) | 26.5737 | 0.854110 | ||||||||
\(969\) | −8.49106 | −0.272772 | ||||||||
\(970\) | −12.2356 | −0.392861 | ||||||||
\(971\) | −17.2830 | −0.554636 | −0.277318 | − | 0.960778i | \(-0.589446\pi\) | ||||
−0.277318 | + | 0.960778i | \(0.589446\pi\) | |||||||
\(972\) | 75.9181 | 2.43507 | ||||||||
\(973\) | −14.5723 | −0.467167 | ||||||||
\(974\) | 43.3427 | 1.38879 | ||||||||
\(975\) | −1.26699 | −0.0405763 | ||||||||
\(976\) | −7.79351 | −0.249464 | ||||||||
\(977\) | −53.1612 | −1.70078 | −0.850389 | − | 0.526155i | \(-0.823633\pi\) | ||||
−0.850389 | + | 0.526155i | \(0.823633\pi\) | |||||||
\(978\) | −4.03506 | −0.129027 | ||||||||
\(979\) | 0.143563 | 0.00458829 | ||||||||
\(980\) | 4.73422 | 0.151229 | ||||||||
\(981\) | −5.48935 | −0.175261 | ||||||||
\(982\) | 2.59220 | 0.0827203 | ||||||||
\(983\) | 29.4385 | 0.938941 | 0.469470 | − | 0.882948i | \(-0.344445\pi\) | ||||
0.469470 | + | 0.882948i | \(0.344445\pi\) | |||||||
\(984\) | 70.4081 | 2.24453 | ||||||||
\(985\) | 0.866434 | 0.0276069 | ||||||||
\(986\) | 39.4867 | 1.25751 | ||||||||
\(987\) | −5.32981 | −0.169650 | ||||||||
\(988\) | 14.8243 | 0.471625 | ||||||||
\(989\) | 25.2463 | 0.802787 | ||||||||
\(990\) | 14.1130 | 0.448542 | ||||||||
\(991\) | −41.0658 | −1.30450 | −0.652249 | − | 0.758005i | \(-0.726174\pi\) | ||||
−0.652249 | + | 0.758005i | \(0.726174\pi\) | |||||||
\(992\) | −44.5659 | −1.41497 | ||||||||
\(993\) | −27.5141 | −0.873134 | ||||||||
\(994\) | 19.9828 | 0.633816 | ||||||||
\(995\) | −14.5659 | −0.461769 | ||||||||
\(996\) | −43.0939 | −1.36548 | ||||||||
\(997\) | 3.32687 | 0.105363 | 0.0526816 | − | 0.998611i | \(-0.483223\pi\) | ||||
0.0526816 | + | 0.998611i | \(0.483223\pi\) | |||||||
\(998\) | 63.8890 | 2.02237 | ||||||||
\(999\) | 38.5097 | 1.21839 |
(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 | 8015.2.a.h.1.2 | ✓ | 38 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8015.2.a.h.1.2 | ✓ | 38 | 1.1 | even | 1 | trivial |