Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [735,2,Mod(1,735)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(735, 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("735.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 735 = 3 \cdot 5 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 735.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: | \(5.86900454856\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{8})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - 2 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(1.41421\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 735.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.41421 | 1.70711 | 0.853553 | − | 0.521005i | \(-0.174443\pi\) | ||||
0.853553 | + | 0.521005i | \(0.174443\pi\) | |||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 3.82843 | 1.91421 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | 2.41421 | 0.985599 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 4.41421 | 1.56066 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 2.41421 | 0.763441 | ||||||||
\(11\) | 2.82843 | 0.852803 | 0.426401 | − | 0.904534i | \(-0.359781\pi\) | ||||
0.426401 | + | 0.904534i | \(0.359781\pi\) | |||||||
\(12\) | 3.82843 | 1.10517 | ||||||||
\(13\) | −4.82843 | −1.33916 | −0.669582 | − | 0.742738i | \(-0.733527\pi\) | ||||
−0.669582 | + | 0.742738i | \(0.733527\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.00000 | 0.258199 | ||||||||
\(16\) | 3.00000 | 0.750000 | ||||||||
\(17\) | −7.65685 | −1.85706 | −0.928530 | − | 0.371257i | \(-0.878927\pi\) | ||||
−0.928530 | + | 0.371257i | \(0.878927\pi\) | |||||||
\(18\) | 2.41421 | 0.569036 | ||||||||
\(19\) | −0.828427 | −0.190054 | −0.0950271 | − | 0.995475i | \(-0.530294\pi\) | ||||
−0.0950271 | + | 0.995475i | \(0.530294\pi\) | |||||||
\(20\) | 3.82843 | 0.856062 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 6.82843 | 1.45583 | ||||||||
\(23\) | −7.65685 | −1.59656 | −0.798282 | − | 0.602284i | \(-0.794258\pi\) | ||||
−0.798282 | + | 0.602284i | \(0.794258\pi\) | |||||||
\(24\) | 4.41421 | 0.901048 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | −11.6569 | −2.28610 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 6.00000 | 1.11417 | 0.557086 | − | 0.830455i | \(-0.311919\pi\) | ||||
0.557086 | + | 0.830455i | \(0.311919\pi\) | |||||||
\(30\) | 2.41421 | 0.440773 | ||||||||
\(31\) | 6.48528 | 1.16479 | 0.582395 | − | 0.812906i | \(-0.302116\pi\) | ||||
0.582395 | + | 0.812906i | \(0.302116\pi\) | |||||||
\(32\) | −1.58579 | −0.280330 | ||||||||
\(33\) | 2.82843 | 0.492366 | ||||||||
\(34\) | −18.4853 | −3.17020 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 3.82843 | 0.638071 | ||||||||
\(37\) | −3.65685 | −0.601183 | −0.300592 | − | 0.953753i | \(-0.597184\pi\) | ||||
−0.300592 | + | 0.953753i | \(0.597184\pi\) | |||||||
\(38\) | −2.00000 | −0.324443 | ||||||||
\(39\) | −4.82843 | −0.773167 | ||||||||
\(40\) | 4.41421 | 0.697948 | ||||||||
\(41\) | 11.6569 | 1.82049 | 0.910247 | − | 0.414065i | \(-0.135891\pi\) | ||||
0.910247 | + | 0.414065i | \(0.135891\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 8.00000 | 1.21999 | 0.609994 | − | 0.792406i | \(-0.291172\pi\) | ||||
0.609994 | + | 0.792406i | \(0.291172\pi\) | |||||||
\(44\) | 10.8284 | 1.63245 | ||||||||
\(45\) | 1.00000 | 0.149071 | ||||||||
\(46\) | −18.4853 | −2.72551 | ||||||||
\(47\) | 5.65685 | 0.825137 | 0.412568 | − | 0.910927i | \(-0.364632\pi\) | ||||
0.412568 | + | 0.910927i | \(0.364632\pi\) | |||||||
\(48\) | 3.00000 | 0.433013 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 2.41421 | 0.341421 | ||||||||
\(51\) | −7.65685 | −1.07217 | ||||||||
\(52\) | −18.4853 | −2.56345 | ||||||||
\(53\) | −8.48528 | −1.16554 | −0.582772 | − | 0.812636i | \(-0.698032\pi\) | ||||
−0.582772 | + | 0.812636i | \(0.698032\pi\) | |||||||
\(54\) | 2.41421 | 0.328533 | ||||||||
\(55\) | 2.82843 | 0.381385 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −0.828427 | −0.109728 | ||||||||
\(58\) | 14.4853 | 1.90201 | ||||||||
\(59\) | 2.34315 | 0.305052 | 0.152526 | − | 0.988299i | \(-0.451259\pi\) | ||||
0.152526 | + | 0.988299i | \(0.451259\pi\) | |||||||
\(60\) | 3.82843 | 0.494248 | ||||||||
\(61\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(62\) | 15.6569 | 1.98842 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −9.82843 | −1.22855 | ||||||||
\(65\) | −4.82843 | −0.598893 | ||||||||
\(66\) | 6.82843 | 0.840521 | ||||||||
\(67\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(68\) | −29.3137 | −3.55481 | ||||||||
\(69\) | −7.65685 | −0.921777 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −2.82843 | −0.335673 | −0.167836 | − | 0.985815i | \(-0.553678\pi\) | ||||
−0.167836 | + | 0.985815i | \(0.553678\pi\) | |||||||
\(72\) | 4.41421 | 0.520220 | ||||||||
\(73\) | −11.1716 | −1.30753 | −0.653767 | − | 0.756696i | \(-0.726812\pi\) | ||||
−0.653767 | + | 0.756696i | \(0.726812\pi\) | |||||||
\(74\) | −8.82843 | −1.02628 | ||||||||
\(75\) | 1.00000 | 0.115470 | ||||||||
\(76\) | −3.17157 | −0.363804 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −11.6569 | −1.31988 | ||||||||
\(79\) | −8.00000 | −0.900070 | −0.450035 | − | 0.893011i | \(-0.648589\pi\) | ||||
−0.450035 | + | 0.893011i | \(0.648589\pi\) | |||||||
\(80\) | 3.00000 | 0.335410 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 28.1421 | 3.10778 | ||||||||
\(83\) | −1.65685 | −0.181863 | −0.0909317 | − | 0.995857i | \(-0.528984\pi\) | ||||
−0.0909317 | + | 0.995857i | \(0.528984\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −7.65685 | −0.830502 | ||||||||
\(86\) | 19.3137 | 2.08265 | ||||||||
\(87\) | 6.00000 | 0.643268 | ||||||||
\(88\) | 12.4853 | 1.33094 | ||||||||
\(89\) | −5.31371 | −0.563252 | −0.281626 | − | 0.959524i | \(-0.590874\pi\) | ||||
−0.281626 | + | 0.959524i | \(0.590874\pi\) | |||||||
\(90\) | 2.41421 | 0.254480 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −29.3137 | −3.05617 | ||||||||
\(93\) | 6.48528 | 0.672492 | ||||||||
\(94\) | 13.6569 | 1.40860 | ||||||||
\(95\) | −0.828427 | −0.0849948 | ||||||||
\(96\) | −1.58579 | −0.161849 | ||||||||
\(97\) | 6.48528 | 0.658481 | 0.329240 | − | 0.944246i | \(-0.393207\pi\) | ||||
0.329240 | + | 0.944246i | \(0.393207\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 2.82843 | 0.284268 | ||||||||
\(100\) | 3.82843 | 0.382843 | ||||||||
\(101\) | 7.65685 | 0.761885 | 0.380943 | − | 0.924599i | \(-0.375599\pi\) | ||||
0.380943 | + | 0.924599i | \(0.375599\pi\) | |||||||
\(102\) | −18.4853 | −1.83032 | ||||||||
\(103\) | −12.0000 | −1.18240 | −0.591198 | − | 0.806527i | \(-0.701345\pi\) | ||||
−0.591198 | + | 0.806527i | \(0.701345\pi\) | |||||||
\(104\) | −21.3137 | −2.08998 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −20.4853 | −1.98971 | ||||||||
\(107\) | 5.31371 | 0.513696 | 0.256848 | − | 0.966452i | \(-0.417316\pi\) | ||||
0.256848 | + | 0.966452i | \(0.417316\pi\) | |||||||
\(108\) | 3.82843 | 0.368391 | ||||||||
\(109\) | 6.00000 | 0.574696 | 0.287348 | − | 0.957826i | \(-0.407226\pi\) | ||||
0.287348 | + | 0.957826i | \(0.407226\pi\) | |||||||
\(110\) | 6.82843 | 0.651065 | ||||||||
\(111\) | −3.65685 | −0.347093 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 2.82843 | 0.266076 | 0.133038 | − | 0.991111i | \(-0.457527\pi\) | ||||
0.133038 | + | 0.991111i | \(0.457527\pi\) | |||||||
\(114\) | −2.00000 | −0.187317 | ||||||||
\(115\) | −7.65685 | −0.714005 | ||||||||
\(116\) | 22.9706 | 2.13276 | ||||||||
\(117\) | −4.82843 | −0.446388 | ||||||||
\(118\) | 5.65685 | 0.520756 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 4.41421 | 0.402961 | ||||||||
\(121\) | −3.00000 | −0.272727 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 11.6569 | 1.05106 | ||||||||
\(124\) | 24.8284 | 2.22966 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 19.3137 | 1.71381 | 0.856907 | − | 0.515471i | \(-0.172383\pi\) | ||||
0.856907 | + | 0.515471i | \(0.172383\pi\) | |||||||
\(128\) | −20.5563 | −1.81694 | ||||||||
\(129\) | 8.00000 | 0.704361 | ||||||||
\(130\) | −11.6569 | −1.02237 | ||||||||
\(131\) | 5.65685 | 0.494242 | 0.247121 | − | 0.968985i | \(-0.420516\pi\) | ||||
0.247121 | + | 0.968985i | \(0.420516\pi\) | |||||||
\(132\) | 10.8284 | 0.942494 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 1.00000 | 0.0860663 | ||||||||
\(136\) | −33.7990 | −2.89824 | ||||||||
\(137\) | 13.1716 | 1.12532 | 0.562662 | − | 0.826687i | \(-0.309777\pi\) | ||||
0.562662 | + | 0.826687i | \(0.309777\pi\) | |||||||
\(138\) | −18.4853 | −1.57357 | ||||||||
\(139\) | −1.51472 | −0.128477 | −0.0642384 | − | 0.997935i | \(-0.520462\pi\) | ||||
−0.0642384 | + | 0.997935i | \(0.520462\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 5.65685 | 0.476393 | ||||||||
\(142\) | −6.82843 | −0.573029 | ||||||||
\(143\) | −13.6569 | −1.14204 | ||||||||
\(144\) | 3.00000 | 0.250000 | ||||||||
\(145\) | 6.00000 | 0.498273 | ||||||||
\(146\) | −26.9706 | −2.23210 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −14.0000 | −1.15079 | ||||||||
\(149\) | −7.65685 | −0.627274 | −0.313637 | − | 0.949543i | \(-0.601547\pi\) | ||||
−0.313637 | + | 0.949543i | \(0.601547\pi\) | |||||||
\(150\) | 2.41421 | 0.197120 | ||||||||
\(151\) | −16.9706 | −1.38104 | −0.690522 | − | 0.723311i | \(-0.742619\pi\) | ||||
−0.690522 | + | 0.723311i | \(0.742619\pi\) | |||||||
\(152\) | −3.65685 | −0.296610 | ||||||||
\(153\) | −7.65685 | −0.619020 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 6.48528 | 0.520910 | ||||||||
\(156\) | −18.4853 | −1.48001 | ||||||||
\(157\) | 12.1421 | 0.969048 | 0.484524 | − | 0.874778i | \(-0.338993\pi\) | ||||
0.484524 | + | 0.874778i | \(0.338993\pi\) | |||||||
\(158\) | −19.3137 | −1.53652 | ||||||||
\(159\) | −8.48528 | −0.672927 | ||||||||
\(160\) | −1.58579 | −0.125367 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 2.41421 | 0.189679 | ||||||||
\(163\) | −12.0000 | −0.939913 | −0.469956 | − | 0.882690i | \(-0.655730\pi\) | ||||
−0.469956 | + | 0.882690i | \(0.655730\pi\) | |||||||
\(164\) | 44.6274 | 3.48482 | ||||||||
\(165\) | 2.82843 | 0.220193 | ||||||||
\(166\) | −4.00000 | −0.310460 | ||||||||
\(167\) | 11.3137 | 0.875481 | 0.437741 | − | 0.899101i | \(-0.355779\pi\) | ||||
0.437741 | + | 0.899101i | \(0.355779\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 10.3137 | 0.793362 | ||||||||
\(170\) | −18.4853 | −1.41776 | ||||||||
\(171\) | −0.828427 | −0.0633514 | ||||||||
\(172\) | 30.6274 | 2.33532 | ||||||||
\(173\) | 24.6274 | 1.87239 | 0.936194 | − | 0.351484i | \(-0.114323\pi\) | ||||
0.936194 | + | 0.351484i | \(0.114323\pi\) | |||||||
\(174\) | 14.4853 | 1.09813 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 8.48528 | 0.639602 | ||||||||
\(177\) | 2.34315 | 0.176122 | ||||||||
\(178\) | −12.8284 | −0.961531 | ||||||||
\(179\) | −1.17157 | −0.0875675 | −0.0437837 | − | 0.999041i | \(-0.513941\pi\) | ||||
−0.0437837 | + | 0.999041i | \(0.513941\pi\) | |||||||
\(180\) | 3.82843 | 0.285354 | ||||||||
\(181\) | 2.34315 | 0.174165 | 0.0870823 | − | 0.996201i | \(-0.472246\pi\) | ||||
0.0870823 | + | 0.996201i | \(0.472246\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −33.7990 | −2.49169 | ||||||||
\(185\) | −3.65685 | −0.268857 | ||||||||
\(186\) | 15.6569 | 1.14802 | ||||||||
\(187\) | −21.6569 | −1.58371 | ||||||||
\(188\) | 21.6569 | 1.57949 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −2.00000 | −0.145095 | ||||||||
\(191\) | −9.17157 | −0.663632 | −0.331816 | − | 0.943344i | \(-0.607661\pi\) | ||||
−0.331816 | + | 0.943344i | \(0.607661\pi\) | |||||||
\(192\) | −9.82843 | −0.709306 | ||||||||
\(193\) | 15.6569 | 1.12701 | 0.563503 | − | 0.826114i | \(-0.309454\pi\) | ||||
0.563503 | + | 0.826114i | \(0.309454\pi\) | |||||||
\(194\) | 15.6569 | 1.12410 | ||||||||
\(195\) | −4.82843 | −0.345771 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −3.51472 | −0.250413 | −0.125207 | − | 0.992131i | \(-0.539959\pi\) | ||||
−0.125207 | + | 0.992131i | \(0.539959\pi\) | |||||||
\(198\) | 6.82843 | 0.485275 | ||||||||
\(199\) | −0.828427 | −0.0587256 | −0.0293628 | − | 0.999569i | \(-0.509348\pi\) | ||||
−0.0293628 | + | 0.999569i | \(0.509348\pi\) | |||||||
\(200\) | 4.41421 | 0.312132 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 18.4853 | 1.30062 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −29.3137 | −2.05237 | ||||||||
\(205\) | 11.6569 | 0.814150 | ||||||||
\(206\) | −28.9706 | −2.01847 | ||||||||
\(207\) | −7.65685 | −0.532188 | ||||||||
\(208\) | −14.4853 | −1.00437 | ||||||||
\(209\) | −2.34315 | −0.162079 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −9.65685 | −0.664805 | −0.332403 | − | 0.943138i | \(-0.607859\pi\) | ||||
−0.332403 | + | 0.943138i | \(0.607859\pi\) | |||||||
\(212\) | −32.4853 | −2.23110 | ||||||||
\(213\) | −2.82843 | −0.193801 | ||||||||
\(214\) | 12.8284 | 0.876933 | ||||||||
\(215\) | 8.00000 | 0.545595 | ||||||||
\(216\) | 4.41421 | 0.300349 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 14.4853 | 0.981067 | ||||||||
\(219\) | −11.1716 | −0.754905 | ||||||||
\(220\) | 10.8284 | 0.730052 | ||||||||
\(221\) | 36.9706 | 2.48691 | ||||||||
\(222\) | −8.82843 | −0.592525 | ||||||||
\(223\) | −20.9706 | −1.40429 | −0.702146 | − | 0.712033i | \(-0.747775\pi\) | ||||
−0.702146 | + | 0.712033i | \(0.747775\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1.00000 | 0.0666667 | ||||||||
\(226\) | 6.82843 | 0.454220 | ||||||||
\(227\) | 28.9706 | 1.92284 | 0.961422 | − | 0.275078i | \(-0.0887037\pi\) | ||||
0.961422 | + | 0.275078i | \(0.0887037\pi\) | |||||||
\(228\) | −3.17157 | −0.210043 | ||||||||
\(229\) | −15.3137 | −1.01196 | −0.505979 | − | 0.862546i | \(-0.668869\pi\) | ||||
−0.505979 | + | 0.862546i | \(0.668869\pi\) | |||||||
\(230\) | −18.4853 | −1.21888 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 26.4853 | 1.73884 | ||||||||
\(233\) | 14.8284 | 0.971443 | 0.485721 | − | 0.874114i | \(-0.338557\pi\) | ||||
0.485721 | + | 0.874114i | \(0.338557\pi\) | |||||||
\(234\) | −11.6569 | −0.762032 | ||||||||
\(235\) | 5.65685 | 0.369012 | ||||||||
\(236\) | 8.97056 | 0.583934 | ||||||||
\(237\) | −8.00000 | −0.519656 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −2.14214 | −0.138563 | −0.0692816 | − | 0.997597i | \(-0.522071\pi\) | ||||
−0.0692816 | + | 0.997597i | \(0.522071\pi\) | |||||||
\(240\) | 3.00000 | 0.193649 | ||||||||
\(241\) | −21.6569 | −1.39504 | −0.697520 | − | 0.716565i | \(-0.745713\pi\) | ||||
−0.697520 | + | 0.716565i | \(0.745713\pi\) | |||||||
\(242\) | −7.24264 | −0.465575 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 28.1421 | 1.79428 | ||||||||
\(247\) | 4.00000 | 0.254514 | ||||||||
\(248\) | 28.6274 | 1.81784 | ||||||||
\(249\) | −1.65685 | −0.104999 | ||||||||
\(250\) | 2.41421 | 0.152688 | ||||||||
\(251\) | 29.6569 | 1.87192 | 0.935962 | − | 0.352101i | \(-0.114533\pi\) | ||||
0.935962 | + | 0.352101i | \(0.114533\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −21.6569 | −1.36155 | ||||||||
\(254\) | 46.6274 | 2.92566 | ||||||||
\(255\) | −7.65685 | −0.479491 | ||||||||
\(256\) | −29.9706 | −1.87316 | ||||||||
\(257\) | −0.343146 | −0.0214048 | −0.0107024 | − | 0.999943i | \(-0.503407\pi\) | ||||
−0.0107024 | + | 0.999943i | \(0.503407\pi\) | |||||||
\(258\) | 19.3137 | 1.20242 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −18.4853 | −1.14641 | ||||||||
\(261\) | 6.00000 | 0.371391 | ||||||||
\(262\) | 13.6569 | 0.843723 | ||||||||
\(263\) | −2.68629 | −0.165644 | −0.0828219 | − | 0.996564i | \(-0.526393\pi\) | ||||
−0.0828219 | + | 0.996564i | \(0.526393\pi\) | |||||||
\(264\) | 12.4853 | 0.768416 | ||||||||
\(265\) | −8.48528 | −0.521247 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −5.31371 | −0.325194 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 0.343146 | 0.0209220 | 0.0104610 | − | 0.999945i | \(-0.496670\pi\) | ||||
0.0104610 | + | 0.999945i | \(0.496670\pi\) | |||||||
\(270\) | 2.41421 | 0.146924 | ||||||||
\(271\) | −22.4853 | −1.36588 | −0.682942 | − | 0.730473i | \(-0.739300\pi\) | ||||
−0.682942 | + | 0.730473i | \(0.739300\pi\) | |||||||
\(272\) | −22.9706 | −1.39279 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 31.7990 | 1.92105 | ||||||||
\(275\) | 2.82843 | 0.170561 | ||||||||
\(276\) | −29.3137 | −1.76448 | ||||||||
\(277\) | 21.3137 | 1.28062 | 0.640308 | − | 0.768118i | \(-0.278807\pi\) | ||||
0.640308 | + | 0.768118i | \(0.278807\pi\) | |||||||
\(278\) | −3.65685 | −0.219324 | ||||||||
\(279\) | 6.48528 | 0.388264 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 12.3431 | 0.736330 | 0.368165 | − | 0.929760i | \(-0.379986\pi\) | ||||
0.368165 | + | 0.929760i | \(0.379986\pi\) | |||||||
\(282\) | 13.6569 | 0.813254 | ||||||||
\(283\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(284\) | −10.8284 | −0.642549 | ||||||||
\(285\) | −0.828427 | −0.0490718 | ||||||||
\(286\) | −32.9706 | −1.94959 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −1.58579 | −0.0934434 | ||||||||
\(289\) | 41.6274 | 2.44867 | ||||||||
\(290\) | 14.4853 | 0.850605 | ||||||||
\(291\) | 6.48528 | 0.380174 | ||||||||
\(292\) | −42.7696 | −2.50290 | ||||||||
\(293\) | −12.3431 | −0.721094 | −0.360547 | − | 0.932741i | \(-0.617410\pi\) | ||||
−0.360547 | + | 0.932741i | \(0.617410\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 2.34315 | 0.136423 | ||||||||
\(296\) | −16.1421 | −0.938243 | ||||||||
\(297\) | 2.82843 | 0.164122 | ||||||||
\(298\) | −18.4853 | −1.07082 | ||||||||
\(299\) | 36.9706 | 2.13806 | ||||||||
\(300\) | 3.82843 | 0.221034 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −40.9706 | −2.35759 | ||||||||
\(303\) | 7.65685 | 0.439875 | ||||||||
\(304\) | −2.48528 | −0.142541 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −18.4853 | −1.05673 | ||||||||
\(307\) | −28.9706 | −1.65344 | −0.826719 | − | 0.562616i | \(-0.809795\pi\) | ||||
−0.826719 | + | 0.562616i | \(0.809795\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −12.0000 | −0.682656 | ||||||||
\(310\) | 15.6569 | 0.889250 | ||||||||
\(311\) | 9.65685 | 0.547590 | 0.273795 | − | 0.961788i | \(-0.411721\pi\) | ||||
0.273795 | + | 0.961788i | \(0.411721\pi\) | |||||||
\(312\) | −21.3137 | −1.20665 | ||||||||
\(313\) | 2.48528 | 0.140476 | 0.0702382 | − | 0.997530i | \(-0.477624\pi\) | ||||
0.0702382 | + | 0.997530i | \(0.477624\pi\) | |||||||
\(314\) | 29.3137 | 1.65427 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −30.6274 | −1.72293 | ||||||||
\(317\) | 22.1421 | 1.24363 | 0.621813 | − | 0.783166i | \(-0.286396\pi\) | ||||
0.621813 | + | 0.783166i | \(0.286396\pi\) | |||||||
\(318\) | −20.4853 | −1.14876 | ||||||||
\(319\) | 16.9706 | 0.950169 | ||||||||
\(320\) | −9.82843 | −0.549426 | ||||||||
\(321\) | 5.31371 | 0.296582 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 6.34315 | 0.352942 | ||||||||
\(324\) | 3.82843 | 0.212690 | ||||||||
\(325\) | −4.82843 | −0.267833 | ||||||||
\(326\) | −28.9706 | −1.60453 | ||||||||
\(327\) | 6.00000 | 0.331801 | ||||||||
\(328\) | 51.4558 | 2.84117 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 6.82843 | 0.375893 | ||||||||
\(331\) | 1.65685 | 0.0910689 | 0.0455345 | − | 0.998963i | \(-0.485501\pi\) | ||||
0.0455345 | + | 0.998963i | \(0.485501\pi\) | |||||||
\(332\) | −6.34315 | −0.348125 | ||||||||
\(333\) | −3.65685 | −0.200394 | ||||||||
\(334\) | 27.3137 | 1.49454 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −6.97056 | −0.379711 | −0.189855 | − | 0.981812i | \(-0.560802\pi\) | ||||
−0.189855 | + | 0.981812i | \(0.560802\pi\) | |||||||
\(338\) | 24.8995 | 1.35435 | ||||||||
\(339\) | 2.82843 | 0.153619 | ||||||||
\(340\) | −29.3137 | −1.58976 | ||||||||
\(341\) | 18.3431 | 0.993337 | ||||||||
\(342\) | −2.00000 | −0.108148 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 35.3137 | 1.90399 | ||||||||
\(345\) | −7.65685 | −0.412231 | ||||||||
\(346\) | 59.4558 | 3.19637 | ||||||||
\(347\) | −22.9706 | −1.23312 | −0.616562 | − | 0.787306i | \(-0.711475\pi\) | ||||
−0.616562 | + | 0.787306i | \(0.711475\pi\) | |||||||
\(348\) | 22.9706 | 1.23135 | ||||||||
\(349\) | 16.0000 | 0.856460 | 0.428230 | − | 0.903670i | \(-0.359137\pi\) | ||||
0.428230 | + | 0.903670i | \(0.359137\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −4.82843 | −0.257722 | ||||||||
\(352\) | −4.48528 | −0.239066 | ||||||||
\(353\) | −25.3137 | −1.34731 | −0.673656 | − | 0.739045i | \(-0.735277\pi\) | ||||
−0.673656 | + | 0.739045i | \(0.735277\pi\) | |||||||
\(354\) | 5.65685 | 0.300658 | ||||||||
\(355\) | −2.82843 | −0.150117 | ||||||||
\(356\) | −20.3431 | −1.07818 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −2.82843 | −0.149487 | ||||||||
\(359\) | −15.7990 | −0.833839 | −0.416919 | − | 0.908943i | \(-0.636890\pi\) | ||||
−0.416919 | + | 0.908943i | \(0.636890\pi\) | |||||||
\(360\) | 4.41421 | 0.232649 | ||||||||
\(361\) | −18.3137 | −0.963879 | ||||||||
\(362\) | 5.65685 | 0.297318 | ||||||||
\(363\) | −3.00000 | −0.157459 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −11.1716 | −0.584747 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −12.9706 | −0.677058 | −0.338529 | − | 0.940956i | \(-0.609929\pi\) | ||||
−0.338529 | + | 0.940956i | \(0.609929\pi\) | |||||||
\(368\) | −22.9706 | −1.19742 | ||||||||
\(369\) | 11.6569 | 0.606832 | ||||||||
\(370\) | −8.82843 | −0.458968 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 24.8284 | 1.28729 | ||||||||
\(373\) | −24.6274 | −1.27516 | −0.637580 | − | 0.770384i | \(-0.720064\pi\) | ||||
−0.637580 | + | 0.770384i | \(0.720064\pi\) | |||||||
\(374\) | −52.2843 | −2.70356 | ||||||||
\(375\) | 1.00000 | 0.0516398 | ||||||||
\(376\) | 24.9706 | 1.28776 | ||||||||
\(377\) | −28.9706 | −1.49206 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −20.9706 | −1.07719 | −0.538593 | − | 0.842566i | \(-0.681044\pi\) | ||||
−0.538593 | + | 0.842566i | \(0.681044\pi\) | |||||||
\(380\) | −3.17157 | −0.162698 | ||||||||
\(381\) | 19.3137 | 0.989471 | ||||||||
\(382\) | −22.1421 | −1.13289 | ||||||||
\(383\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(384\) | −20.5563 | −1.04901 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 37.7990 | 1.92392 | ||||||||
\(387\) | 8.00000 | 0.406663 | ||||||||
\(388\) | 24.8284 | 1.26047 | ||||||||
\(389\) | −11.6569 | −0.591026 | −0.295513 | − | 0.955339i | \(-0.595491\pi\) | ||||
−0.295513 | + | 0.955339i | \(0.595491\pi\) | |||||||
\(390\) | −11.6569 | −0.590268 | ||||||||
\(391\) | 58.6274 | 2.96492 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 5.65685 | 0.285351 | ||||||||
\(394\) | −8.48528 | −0.427482 | ||||||||
\(395\) | −8.00000 | −0.402524 | ||||||||
\(396\) | 10.8284 | 0.544149 | ||||||||
\(397\) | −24.8284 | −1.24610 | −0.623052 | − | 0.782181i | \(-0.714107\pi\) | ||||
−0.623052 | + | 0.782181i | \(0.714107\pi\) | |||||||
\(398\) | −2.00000 | −0.100251 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 3.00000 | 0.150000 | ||||||||
\(401\) | 30.0000 | 1.49813 | 0.749064 | − | 0.662497i | \(-0.230503\pi\) | ||||
0.749064 | + | 0.662497i | \(0.230503\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −31.3137 | −1.55985 | ||||||||
\(404\) | 29.3137 | 1.45841 | ||||||||
\(405\) | 1.00000 | 0.0496904 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −10.3431 | −0.512691 | ||||||||
\(408\) | −33.7990 | −1.67330 | ||||||||
\(409\) | 12.0000 | 0.593362 | 0.296681 | − | 0.954977i | \(-0.404120\pi\) | ||||
0.296681 | + | 0.954977i | \(0.404120\pi\) | |||||||
\(410\) | 28.1421 | 1.38984 | ||||||||
\(411\) | 13.1716 | 0.649706 | ||||||||
\(412\) | −45.9411 | −2.26336 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −18.4853 | −0.908502 | ||||||||
\(415\) | −1.65685 | −0.0813318 | ||||||||
\(416\) | 7.65685 | 0.375408 | ||||||||
\(417\) | −1.51472 | −0.0741761 | ||||||||
\(418\) | −5.65685 | −0.276686 | ||||||||
\(419\) | −0.686292 | −0.0335275 | −0.0167638 | − | 0.999859i | \(-0.505336\pi\) | ||||
−0.0167638 | + | 0.999859i | \(0.505336\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −6.00000 | −0.292422 | −0.146211 | − | 0.989253i | \(-0.546708\pi\) | ||||
−0.146211 | + | 0.989253i | \(0.546708\pi\) | |||||||
\(422\) | −23.3137 | −1.13489 | ||||||||
\(423\) | 5.65685 | 0.275046 | ||||||||
\(424\) | −37.4558 | −1.81902 | ||||||||
\(425\) | −7.65685 | −0.371412 | ||||||||
\(426\) | −6.82843 | −0.330838 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 20.3431 | 0.983323 | ||||||||
\(429\) | −13.6569 | −0.659359 | ||||||||
\(430\) | 19.3137 | 0.931390 | ||||||||
\(431\) | −10.8284 | −0.521587 | −0.260793 | − | 0.965395i | \(-0.583984\pi\) | ||||
−0.260793 | + | 0.965395i | \(0.583984\pi\) | |||||||
\(432\) | 3.00000 | 0.144338 | ||||||||
\(433\) | 7.17157 | 0.344644 | 0.172322 | − | 0.985041i | \(-0.444873\pi\) | ||||
0.172322 | + | 0.985041i | \(0.444873\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 6.00000 | 0.287678 | ||||||||
\(436\) | 22.9706 | 1.10009 | ||||||||
\(437\) | 6.34315 | 0.303434 | ||||||||
\(438\) | −26.9706 | −1.28870 | ||||||||
\(439\) | −13.5147 | −0.645022 | −0.322511 | − | 0.946566i | \(-0.604527\pi\) | ||||
−0.322511 | + | 0.946566i | \(0.604527\pi\) | |||||||
\(440\) | 12.4853 | 0.595212 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 89.2548 | 4.24542 | ||||||||
\(443\) | 23.6569 | 1.12397 | 0.561986 | − | 0.827147i | \(-0.310038\pi\) | ||||
0.561986 | + | 0.827147i | \(0.310038\pi\) | |||||||
\(444\) | −14.0000 | −0.664411 | ||||||||
\(445\) | −5.31371 | −0.251894 | ||||||||
\(446\) | −50.6274 | −2.39728 | ||||||||
\(447\) | −7.65685 | −0.362157 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −12.6274 | −0.595925 | −0.297962 | − | 0.954578i | \(-0.596307\pi\) | ||||
−0.297962 | + | 0.954578i | \(0.596307\pi\) | |||||||
\(450\) | 2.41421 | 0.113807 | ||||||||
\(451\) | 32.9706 | 1.55252 | ||||||||
\(452\) | 10.8284 | 0.509326 | ||||||||
\(453\) | −16.9706 | −0.797347 | ||||||||
\(454\) | 69.9411 | 3.28250 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −3.65685 | −0.171248 | ||||||||
\(457\) | 16.3431 | 0.764500 | 0.382250 | − | 0.924059i | \(-0.375149\pi\) | ||||
0.382250 | + | 0.924059i | \(0.375149\pi\) | |||||||
\(458\) | −36.9706 | −1.72752 | ||||||||
\(459\) | −7.65685 | −0.357391 | ||||||||
\(460\) | −29.3137 | −1.36676 | ||||||||
\(461\) | 13.3137 | 0.620081 | 0.310041 | − | 0.950723i | \(-0.399657\pi\) | ||||
0.310041 | + | 0.950723i | \(0.399657\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 38.6274 | 1.79517 | 0.897584 | − | 0.440843i | \(-0.145321\pi\) | ||||
0.897584 | + | 0.440843i | \(0.145321\pi\) | |||||||
\(464\) | 18.0000 | 0.835629 | ||||||||
\(465\) | 6.48528 | 0.300748 | ||||||||
\(466\) | 35.7990 | 1.65836 | ||||||||
\(467\) | −24.2843 | −1.12374 | −0.561871 | − | 0.827225i | \(-0.689918\pi\) | ||||
−0.561871 | + | 0.827225i | \(0.689918\pi\) | |||||||
\(468\) | −18.4853 | −0.854482 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 13.6569 | 0.629944 | ||||||||
\(471\) | 12.1421 | 0.559480 | ||||||||
\(472\) | 10.3431 | 0.476082 | ||||||||
\(473\) | 22.6274 | 1.04041 | ||||||||
\(474\) | −19.3137 | −0.887108 | ||||||||
\(475\) | −0.828427 | −0.0380108 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −8.48528 | −0.388514 | ||||||||
\(478\) | −5.17157 | −0.236542 | ||||||||
\(479\) | −14.3431 | −0.655355 | −0.327678 | − | 0.944790i | \(-0.606266\pi\) | ||||
−0.327678 | + | 0.944790i | \(0.606266\pi\) | |||||||
\(480\) | −1.58579 | −0.0723809 | ||||||||
\(481\) | 17.6569 | 0.805083 | ||||||||
\(482\) | −52.2843 | −2.38148 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −11.4853 | −0.522058 | ||||||||
\(485\) | 6.48528 | 0.294481 | ||||||||
\(486\) | 2.41421 | 0.109511 | ||||||||
\(487\) | 29.9411 | 1.35676 | 0.678381 | − | 0.734710i | \(-0.262682\pi\) | ||||
0.678381 | + | 0.734710i | \(0.262682\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −12.0000 | −0.542659 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 18.1421 | 0.818743 | 0.409372 | − | 0.912368i | \(-0.365748\pi\) | ||||
0.409372 | + | 0.912368i | \(0.365748\pi\) | |||||||
\(492\) | 44.6274 | 2.01196 | ||||||||
\(493\) | −45.9411 | −2.06908 | ||||||||
\(494\) | 9.65685 | 0.434482 | ||||||||
\(495\) | 2.82843 | 0.127128 | ||||||||
\(496\) | 19.4558 | 0.873593 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −4.00000 | −0.179244 | ||||||||
\(499\) | 4.97056 | 0.222513 | 0.111256 | − | 0.993792i | \(-0.464512\pi\) | ||||
0.111256 | + | 0.993792i | \(0.464512\pi\) | |||||||
\(500\) | 3.82843 | 0.171212 | ||||||||
\(501\) | 11.3137 | 0.505459 | ||||||||
\(502\) | 71.5980 | 3.19557 | ||||||||
\(503\) | 4.68629 | 0.208951 | 0.104476 | − | 0.994527i | \(-0.466684\pi\) | ||||
0.104476 | + | 0.994527i | \(0.466684\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 7.65685 | 0.340726 | ||||||||
\(506\) | −52.2843 | −2.32432 | ||||||||
\(507\) | 10.3137 | 0.458048 | ||||||||
\(508\) | 73.9411 | 3.28061 | ||||||||
\(509\) | −28.3431 | −1.25629 | −0.628144 | − | 0.778097i | \(-0.716185\pi\) | ||||
−0.628144 | + | 0.778097i | \(0.716185\pi\) | |||||||
\(510\) | −18.4853 | −0.818542 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −31.2426 | −1.38074 | ||||||||
\(513\) | −0.828427 | −0.0365760 | ||||||||
\(514\) | −0.828427 | −0.0365404 | ||||||||
\(515\) | −12.0000 | −0.528783 | ||||||||
\(516\) | 30.6274 | 1.34830 | ||||||||
\(517\) | 16.0000 | 0.703679 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 24.6274 | 1.08102 | ||||||||
\(520\) | −21.3137 | −0.934668 | ||||||||
\(521\) | 22.2843 | 0.976292 | 0.488146 | − | 0.872762i | \(-0.337673\pi\) | ||||
0.488146 | + | 0.872762i | \(0.337673\pi\) | |||||||
\(522\) | 14.4853 | 0.634004 | ||||||||
\(523\) | 36.2843 | 1.58660 | 0.793300 | − | 0.608831i | \(-0.208361\pi\) | ||||
0.793300 | + | 0.608831i | \(0.208361\pi\) | |||||||
\(524\) | 21.6569 | 0.946084 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −6.48528 | −0.282772 | ||||||||
\(527\) | −49.6569 | −2.16309 | ||||||||
\(528\) | 8.48528 | 0.369274 | ||||||||
\(529\) | 35.6274 | 1.54902 | ||||||||
\(530\) | −20.4853 | −0.889824 | ||||||||
\(531\) | 2.34315 | 0.101684 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −56.2843 | −2.43794 | ||||||||
\(534\) | −12.8284 | −0.555140 | ||||||||
\(535\) | 5.31371 | 0.229732 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −1.17157 | −0.0505571 | ||||||||
\(538\) | 0.828427 | 0.0357160 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 3.82843 | 0.164749 | ||||||||
\(541\) | 18.0000 | 0.773880 | 0.386940 | − | 0.922105i | \(-0.373532\pi\) | ||||
0.386940 | + | 0.922105i | \(0.373532\pi\) | |||||||
\(542\) | −54.2843 | −2.33171 | ||||||||
\(543\) | 2.34315 | 0.100554 | ||||||||
\(544\) | 12.1421 | 0.520590 | ||||||||
\(545\) | 6.00000 | 0.257012 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −27.3137 | −1.16785 | −0.583925 | − | 0.811808i | \(-0.698484\pi\) | ||||
−0.583925 | + | 0.811808i | \(0.698484\pi\) | |||||||
\(548\) | 50.4264 | 2.15411 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 6.82843 | 0.291165 | ||||||||
\(551\) | −4.97056 | −0.211753 | ||||||||
\(552\) | −33.7990 | −1.43858 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 51.4558 | 2.18615 | ||||||||
\(555\) | −3.65685 | −0.155225 | ||||||||
\(556\) | −5.79899 | −0.245932 | ||||||||
\(557\) | 26.8284 | 1.13676 | 0.568378 | − | 0.822767i | \(-0.307571\pi\) | ||||
0.568378 | + | 0.822767i | \(0.307571\pi\) | |||||||
\(558\) | 15.6569 | 0.662807 | ||||||||
\(559\) | −38.6274 | −1.63377 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −21.6569 | −0.914353 | ||||||||
\(562\) | 29.7990 | 1.25699 | ||||||||
\(563\) | 8.68629 | 0.366084 | 0.183042 | − | 0.983105i | \(-0.441406\pi\) | ||||
0.183042 | + | 0.983105i | \(0.441406\pi\) | |||||||
\(564\) | 21.6569 | 0.911918 | ||||||||
\(565\) | 2.82843 | 0.118993 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −12.4853 | −0.523871 | ||||||||
\(569\) | 10.6863 | 0.447993 | 0.223996 | − | 0.974590i | \(-0.428090\pi\) | ||||
0.223996 | + | 0.974590i | \(0.428090\pi\) | |||||||
\(570\) | −2.00000 | −0.0837708 | ||||||||
\(571\) | −16.6863 | −0.698300 | −0.349150 | − | 0.937067i | \(-0.613530\pi\) | ||||
−0.349150 | + | 0.937067i | \(0.613530\pi\) | |||||||
\(572\) | −52.2843 | −2.18612 | ||||||||
\(573\) | −9.17157 | −0.383148 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −7.65685 | −0.319313 | ||||||||
\(576\) | −9.82843 | −0.409518 | ||||||||
\(577\) | 18.4853 | 0.769552 | 0.384776 | − | 0.923010i | \(-0.374279\pi\) | ||||
0.384776 | + | 0.923010i | \(0.374279\pi\) | |||||||
\(578\) | 100.497 | 4.18014 | ||||||||
\(579\) | 15.6569 | 0.650677 | ||||||||
\(580\) | 22.9706 | 0.953801 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 15.6569 | 0.648997 | ||||||||
\(583\) | −24.0000 | −0.993978 | ||||||||
\(584\) | −49.3137 | −2.04062 | ||||||||
\(585\) | −4.82843 | −0.199631 | ||||||||
\(586\) | −29.7990 | −1.23098 | ||||||||
\(587\) | −8.68629 | −0.358522 | −0.179261 | − | 0.983802i | \(-0.557371\pi\) | ||||
−0.179261 | + | 0.983802i | \(0.557371\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −5.37258 | −0.221373 | ||||||||
\(590\) | 5.65685 | 0.232889 | ||||||||
\(591\) | −3.51472 | −0.144576 | ||||||||
\(592\) | −10.9706 | −0.450887 | ||||||||
\(593\) | −4.62742 | −0.190025 | −0.0950126 | − | 0.995476i | \(-0.530289\pi\) | ||||
−0.0950126 | + | 0.995476i | \(0.530289\pi\) | |||||||
\(594\) | 6.82843 | 0.280174 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −29.3137 | −1.20074 | ||||||||
\(597\) | −0.828427 | −0.0339053 | ||||||||
\(598\) | 89.2548 | 3.64990 | ||||||||
\(599\) | −44.4853 | −1.81762 | −0.908810 | − | 0.417211i | \(-0.863008\pi\) | ||||
−0.908810 | + | 0.417211i | \(0.863008\pi\) | |||||||
\(600\) | 4.41421 | 0.180210 | ||||||||
\(601\) | 33.6569 | 1.37289 | 0.686446 | − | 0.727181i | \(-0.259170\pi\) | ||||
0.686446 | + | 0.727181i | \(0.259170\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −64.9706 | −2.64361 | ||||||||
\(605\) | −3.00000 | −0.121967 | ||||||||
\(606\) | 18.4853 | 0.750913 | ||||||||
\(607\) | −3.02944 | −0.122961 | −0.0614805 | − | 0.998108i | \(-0.519582\pi\) | ||||
−0.0614805 | + | 0.998108i | \(0.519582\pi\) | |||||||
\(608\) | 1.31371 | 0.0532779 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −27.3137 | −1.10499 | ||||||||
\(612\) | −29.3137 | −1.18494 | ||||||||
\(613\) | −23.9411 | −0.966973 | −0.483486 | − | 0.875352i | \(-0.660630\pi\) | ||||
−0.483486 | + | 0.875352i | \(0.660630\pi\) | |||||||
\(614\) | −69.9411 | −2.82259 | ||||||||
\(615\) | 11.6569 | 0.470050 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 13.4558 | 0.541712 | 0.270856 | − | 0.962620i | \(-0.412693\pi\) | ||||
0.270856 | + | 0.962620i | \(0.412693\pi\) | |||||||
\(618\) | −28.9706 | −1.16537 | ||||||||
\(619\) | −48.1421 | −1.93500 | −0.967498 | − | 0.252879i | \(-0.918623\pi\) | ||||
−0.967498 | + | 0.252879i | \(0.918623\pi\) | |||||||
\(620\) | 24.8284 | 0.997134 | ||||||||
\(621\) | −7.65685 | −0.307259 | ||||||||
\(622\) | 23.3137 | 0.934795 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −14.4853 | −0.579875 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 6.00000 | 0.239808 | ||||||||
\(627\) | −2.34315 | −0.0935762 | ||||||||
\(628\) | 46.4853 | 1.85496 | ||||||||
\(629\) | 28.0000 | 1.11643 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 3.31371 | 0.131917 | 0.0659583 | − | 0.997822i | \(-0.478990\pi\) | ||||
0.0659583 | + | 0.997822i | \(0.478990\pi\) | |||||||
\(632\) | −35.3137 | −1.40470 | ||||||||
\(633\) | −9.65685 | −0.383825 | ||||||||
\(634\) | 53.4558 | 2.12300 | ||||||||
\(635\) | 19.3137 | 0.766441 | ||||||||
\(636\) | −32.4853 | −1.28813 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 40.9706 | 1.62204 | ||||||||
\(639\) | −2.82843 | −0.111891 | ||||||||
\(640\) | −20.5563 | −0.812561 | ||||||||
\(641\) | −34.2843 | −1.35415 | −0.677074 | − | 0.735915i | \(-0.736752\pi\) | ||||
−0.677074 | + | 0.735915i | \(0.736752\pi\) | |||||||
\(642\) | 12.8284 | 0.506298 | ||||||||
\(643\) | 4.97056 | 0.196020 | 0.0980099 | − | 0.995185i | \(-0.468752\pi\) | ||||
0.0980099 | + | 0.995185i | \(0.468752\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 8.00000 | 0.315000 | ||||||||
\(646\) | 15.3137 | 0.602510 | ||||||||
\(647\) | −19.3137 | −0.759300 | −0.379650 | − | 0.925130i | \(-0.623956\pi\) | ||||
−0.379650 | + | 0.925130i | \(0.623956\pi\) | |||||||
\(648\) | 4.41421 | 0.173407 | ||||||||
\(649\) | 6.62742 | 0.260149 | ||||||||
\(650\) | −11.6569 | −0.457219 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −45.9411 | −1.79919 | ||||||||
\(653\) | 19.7990 | 0.774794 | 0.387397 | − | 0.921913i | \(-0.373374\pi\) | ||||
0.387397 | + | 0.921913i | \(0.373374\pi\) | |||||||
\(654\) | 14.4853 | 0.566419 | ||||||||
\(655\) | 5.65685 | 0.221032 | ||||||||
\(656\) | 34.9706 | 1.36537 | ||||||||
\(657\) | −11.1716 | −0.435845 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 43.1127 | 1.67943 | 0.839716 | − | 0.543026i | \(-0.182721\pi\) | ||||
0.839716 | + | 0.543026i | \(0.182721\pi\) | |||||||
\(660\) | 10.8284 | 0.421496 | ||||||||
\(661\) | −19.3137 | −0.751216 | −0.375608 | − | 0.926779i | \(-0.622566\pi\) | ||||
−0.375608 | + | 0.926779i | \(0.622566\pi\) | |||||||
\(662\) | 4.00000 | 0.155464 | ||||||||
\(663\) | 36.9706 | 1.43582 | ||||||||
\(664\) | −7.31371 | −0.283827 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −8.82843 | −0.342095 | ||||||||
\(667\) | −45.9411 | −1.77885 | ||||||||
\(668\) | 43.3137 | 1.67586 | ||||||||
\(669\) | −20.9706 | −0.810769 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 22.9706 | 0.885450 | 0.442725 | − | 0.896657i | \(-0.354012\pi\) | ||||
0.442725 | + | 0.896657i | \(0.354012\pi\) | |||||||
\(674\) | −16.8284 | −0.648207 | ||||||||
\(675\) | 1.00000 | 0.0384900 | ||||||||
\(676\) | 39.4853 | 1.51866 | ||||||||
\(677\) | −15.6569 | −0.601742 | −0.300871 | − | 0.953665i | \(-0.597277\pi\) | ||||
−0.300871 | + | 0.953665i | \(0.597277\pi\) | |||||||
\(678\) | 6.82843 | 0.262244 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −33.7990 | −1.29613 | ||||||||
\(681\) | 28.9706 | 1.11015 | ||||||||
\(682\) | 44.2843 | 1.69573 | ||||||||
\(683\) | −16.3431 | −0.625353 | −0.312677 | − | 0.949860i | \(-0.601226\pi\) | ||||
−0.312677 | + | 0.949860i | \(0.601226\pi\) | |||||||
\(684\) | −3.17157 | −0.121268 | ||||||||
\(685\) | 13.1716 | 0.503260 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −15.3137 | −0.584254 | ||||||||
\(688\) | 24.0000 | 0.914991 | ||||||||
\(689\) | 40.9706 | 1.56085 | ||||||||
\(690\) | −18.4853 | −0.703723 | ||||||||
\(691\) | −6.48528 | −0.246712 | −0.123356 | − | 0.992362i | \(-0.539366\pi\) | ||||
−0.123356 | + | 0.992362i | \(0.539366\pi\) | |||||||
\(692\) | 94.2843 | 3.58415 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −55.4558 | −2.10508 | ||||||||
\(695\) | −1.51472 | −0.0574566 | ||||||||
\(696\) | 26.4853 | 1.00392 | ||||||||
\(697\) | −89.2548 | −3.38077 | ||||||||
\(698\) | 38.6274 | 1.46207 | ||||||||
\(699\) | 14.8284 | 0.560863 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 12.6274 | 0.476931 | 0.238465 | − | 0.971151i | \(-0.423356\pi\) | ||||
0.238465 | + | 0.971151i | \(0.423356\pi\) | |||||||
\(702\) | −11.6569 | −0.439960 | ||||||||
\(703\) | 3.02944 | 0.114257 | ||||||||
\(704\) | −27.7990 | −1.04771 | ||||||||
\(705\) | 5.65685 | 0.213049 | ||||||||
\(706\) | −61.1127 | −2.30001 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 8.97056 | 0.337134 | ||||||||
\(709\) | 2.00000 | 0.0751116 | 0.0375558 | − | 0.999295i | \(-0.488043\pi\) | ||||
0.0375558 | + | 0.999295i | \(0.488043\pi\) | |||||||
\(710\) | −6.82843 | −0.256266 | ||||||||
\(711\) | −8.00000 | −0.300023 | ||||||||
\(712\) | −23.4558 | −0.879045 | ||||||||
\(713\) | −49.6569 | −1.85966 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −13.6569 | −0.510737 | ||||||||
\(716\) | −4.48528 | −0.167623 | ||||||||
\(717\) | −2.14214 | −0.0799995 | ||||||||
\(718\) | −38.1421 | −1.42345 | ||||||||
\(719\) | −9.65685 | −0.360140 | −0.180070 | − | 0.983654i | \(-0.557632\pi\) | ||||
−0.180070 | + | 0.983654i | \(0.557632\pi\) | |||||||
\(720\) | 3.00000 | 0.111803 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −44.2132 | −1.64545 | ||||||||
\(723\) | −21.6569 | −0.805427 | ||||||||
\(724\) | 8.97056 | 0.333388 | ||||||||
\(725\) | 6.00000 | 0.222834 | ||||||||
\(726\) | −7.24264 | −0.268800 | ||||||||
\(727\) | −10.3431 | −0.383606 | −0.191803 | − | 0.981433i | \(-0.561433\pi\) | ||||
−0.191803 | + | 0.981433i | \(0.561433\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −26.9706 | −0.998225 | ||||||||
\(731\) | −61.2548 | −2.26559 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −3.45584 | −0.127645 | −0.0638223 | − | 0.997961i | \(-0.520329\pi\) | ||||
−0.0638223 | + | 0.997961i | \(0.520329\pi\) | |||||||
\(734\) | −31.3137 | −1.15581 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 12.1421 | 0.447565 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 28.1421 | 1.03593 | ||||||||
\(739\) | −29.9411 | −1.10140 | −0.550701 | − | 0.834703i | \(-0.685640\pi\) | ||||
−0.550701 | + | 0.834703i | \(0.685640\pi\) | |||||||
\(740\) | −14.0000 | −0.514650 | ||||||||
\(741\) | 4.00000 | 0.146944 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −29.3137 | −1.07542 | −0.537708 | − | 0.843131i | \(-0.680710\pi\) | ||||
−0.537708 | + | 0.843131i | \(0.680710\pi\) | |||||||
\(744\) | 28.6274 | 1.04953 | ||||||||
\(745\) | −7.65685 | −0.280525 | ||||||||
\(746\) | −59.4558 | −2.17683 | ||||||||
\(747\) | −1.65685 | −0.0606211 | ||||||||
\(748\) | −82.9117 | −3.03155 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 2.41421 | 0.0881546 | ||||||||
\(751\) | −37.6569 | −1.37412 | −0.687059 | − | 0.726602i | \(-0.741099\pi\) | ||||
−0.687059 | + | 0.726602i | \(0.741099\pi\) | |||||||
\(752\) | 16.9706 | 0.618853 | ||||||||
\(753\) | 29.6569 | 1.08076 | ||||||||
\(754\) | −69.9411 | −2.54711 | ||||||||
\(755\) | −16.9706 | −0.617622 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −4.34315 | −0.157854 | −0.0789272 | − | 0.996880i | \(-0.525149\pi\) | ||||
−0.0789272 | + | 0.996880i | \(0.525149\pi\) | |||||||
\(758\) | −50.6274 | −1.83887 | ||||||||
\(759\) | −21.6569 | −0.786094 | ||||||||
\(760\) | −3.65685 | −0.132648 | ||||||||
\(761\) | 9.31371 | 0.337622 | 0.168811 | − | 0.985648i | \(-0.446007\pi\) | ||||
0.168811 | + | 0.985648i | \(0.446007\pi\) | |||||||
\(762\) | 46.6274 | 1.68913 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −35.1127 | −1.27033 | ||||||||
\(765\) | −7.65685 | −0.276834 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −11.3137 | −0.408514 | ||||||||
\(768\) | −29.9706 | −1.08147 | ||||||||
\(769\) | 3.02944 | 0.109244 | 0.0546222 | − | 0.998507i | \(-0.482605\pi\) | ||||
0.0546222 | + | 0.998507i | \(0.482605\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −0.343146 | −0.0123581 | ||||||||
\(772\) | 59.9411 | 2.15733 | ||||||||
\(773\) | 32.6274 | 1.17353 | 0.586763 | − | 0.809758i | \(-0.300402\pi\) | ||||
0.586763 | + | 0.809758i | \(0.300402\pi\) | |||||||
\(774\) | 19.3137 | 0.694217 | ||||||||
\(775\) | 6.48528 | 0.232958 | ||||||||
\(776\) | 28.6274 | 1.02766 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −28.1421 | −1.00894 | ||||||||
\(779\) | −9.65685 | −0.345993 | ||||||||
\(780\) | −18.4853 | −0.661879 | ||||||||
\(781\) | −8.00000 | −0.286263 | ||||||||
\(782\) | 141.539 | 5.06143 | ||||||||
\(783\) | 6.00000 | 0.214423 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 12.1421 | 0.433371 | ||||||||
\(786\) | 13.6569 | 0.487124 | ||||||||
\(787\) | 13.6569 | 0.486814 | 0.243407 | − | 0.969924i | \(-0.421735\pi\) | ||||
0.243407 | + | 0.969924i | \(0.421735\pi\) | |||||||
\(788\) | −13.4558 | −0.479345 | ||||||||
\(789\) | −2.68629 | −0.0956345 | ||||||||
\(790\) | −19.3137 | −0.687151 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 12.4853 | 0.443645 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | −59.9411 | −2.12723 | ||||||||
\(795\) | −8.48528 | −0.300942 | ||||||||
\(796\) | −3.17157 | −0.112413 | ||||||||
\(797\) | −7.37258 | −0.261150 | −0.130575 | − | 0.991438i | \(-0.541682\pi\) | ||||
−0.130575 | + | 0.991438i | \(0.541682\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −43.3137 | −1.53233 | ||||||||
\(800\) | −1.58579 | −0.0560660 | ||||||||
\(801\) | −5.31371 | −0.187751 | ||||||||
\(802\) | 72.4264 | 2.55747 | ||||||||
\(803\) | −31.5980 | −1.11507 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −75.5980 | −2.66283 | ||||||||
\(807\) | 0.343146 | 0.0120793 | ||||||||
\(808\) | 33.7990 | 1.18904 | ||||||||
\(809\) | 3.65685 | 0.128568 | 0.0642841 | − | 0.997932i | \(-0.479524\pi\) | ||||
0.0642841 | + | 0.997932i | \(0.479524\pi\) | |||||||
\(810\) | 2.41421 | 0.0848268 | ||||||||
\(811\) | −43.4558 | −1.52594 | −0.762971 | − | 0.646433i | \(-0.776260\pi\) | ||||
−0.762971 | + | 0.646433i | \(0.776260\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −22.4853 | −0.788593 | ||||||||
\(814\) | −24.9706 | −0.875218 | ||||||||
\(815\) | −12.0000 | −0.420342 | ||||||||
\(816\) | −22.9706 | −0.804131 | ||||||||
\(817\) | −6.62742 | −0.231864 | ||||||||
\(818\) | 28.9706 | 1.01293 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 44.6274 | 1.55846 | ||||||||
\(821\) | −44.6274 | −1.55751 | −0.778754 | − | 0.627330i | \(-0.784148\pi\) | ||||
−0.778754 | + | 0.627330i | \(0.784148\pi\) | |||||||
\(822\) | 31.7990 | 1.10912 | ||||||||
\(823\) | −41.9411 | −1.46198 | −0.730988 | − | 0.682390i | \(-0.760940\pi\) | ||||
−0.730988 | + | 0.682390i | \(0.760940\pi\) | |||||||
\(824\) | −52.9706 | −1.84532 | ||||||||
\(825\) | 2.82843 | 0.0984732 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 5.31371 | 0.184776 | 0.0923879 | − | 0.995723i | \(-0.470550\pi\) | ||||
0.0923879 | + | 0.995723i | \(0.470550\pi\) | |||||||
\(828\) | −29.3137 | −1.01872 | ||||||||
\(829\) | 47.5980 | 1.65315 | 0.826573 | − | 0.562829i | \(-0.190287\pi\) | ||||
0.826573 | + | 0.562829i | \(0.190287\pi\) | |||||||
\(830\) | −4.00000 | −0.138842 | ||||||||
\(831\) | 21.3137 | 0.739364 | ||||||||
\(832\) | 47.4558 | 1.64524 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −3.65685 | −0.126627 | ||||||||
\(835\) | 11.3137 | 0.391527 | ||||||||
\(836\) | −8.97056 | −0.310253 | ||||||||
\(837\) | 6.48528 | 0.224164 | ||||||||
\(838\) | −1.65685 | −0.0572351 | ||||||||
\(839\) | −46.6274 | −1.60976 | −0.804879 | − | 0.593439i | \(-0.797770\pi\) | ||||
−0.804879 | + | 0.593439i | \(0.797770\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 7.00000 | 0.241379 | ||||||||
\(842\) | −14.4853 | −0.499196 | ||||||||
\(843\) | 12.3431 | 0.425121 | ||||||||
\(844\) | −36.9706 | −1.27258 | ||||||||
\(845\) | 10.3137 | 0.354802 | ||||||||
\(846\) | 13.6569 | 0.469532 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −25.4558 | −0.874157 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −18.4853 | −0.634040 | ||||||||
\(851\) | 28.0000 | 0.959828 | ||||||||
\(852\) | −10.8284 | −0.370976 | ||||||||
\(853\) | 10.4853 | 0.359009 | 0.179505 | − | 0.983757i | \(-0.442551\pi\) | ||||
0.179505 | + | 0.983757i | \(0.442551\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −0.828427 | −0.0283316 | ||||||||
\(856\) | 23.4558 | 0.801704 | ||||||||
\(857\) | 44.6274 | 1.52444 | 0.762222 | − | 0.647316i | \(-0.224109\pi\) | ||||
0.762222 | + | 0.647316i | \(0.224109\pi\) | |||||||
\(858\) | −32.9706 | −1.12560 | ||||||||
\(859\) | −45.7990 | −1.56264 | −0.781321 | − | 0.624130i | \(-0.785454\pi\) | ||||
−0.781321 | + | 0.624130i | \(0.785454\pi\) | |||||||
\(860\) | 30.6274 | 1.04439 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −26.1421 | −0.890405 | ||||||||
\(863\) | 46.9706 | 1.59890 | 0.799448 | − | 0.600735i | \(-0.205125\pi\) | ||||
0.799448 | + | 0.600735i | \(0.205125\pi\) | |||||||
\(864\) | −1.58579 | −0.0539496 | ||||||||
\(865\) | 24.6274 | 0.837357 | ||||||||
\(866\) | 17.3137 | 0.588344 | ||||||||
\(867\) | 41.6274 | 1.41374 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −22.6274 | −0.767583 | ||||||||
\(870\) | 14.4853 | 0.491097 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 26.4853 | 0.896905 | ||||||||
\(873\) | 6.48528 | 0.219494 | ||||||||
\(874\) | 15.3137 | 0.517994 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −42.7696 | −1.44505 | ||||||||
\(877\) | 27.9411 | 0.943505 | 0.471752 | − | 0.881731i | \(-0.343622\pi\) | ||||
0.471752 | + | 0.881731i | \(0.343622\pi\) | |||||||
\(878\) | −32.6274 | −1.10112 | ||||||||
\(879\) | −12.3431 | −0.416324 | ||||||||
\(880\) | 8.48528 | 0.286039 | ||||||||
\(881\) | −43.2548 | −1.45729 | −0.728646 | − | 0.684890i | \(-0.759850\pi\) | ||||
−0.728646 | + | 0.684890i | \(0.759850\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 28.0000 | 0.942275 | 0.471138 | − | 0.882060i | \(-0.343844\pi\) | ||||
0.471138 | + | 0.882060i | \(0.343844\pi\) | |||||||
\(884\) | 141.539 | 4.76048 | ||||||||
\(885\) | 2.34315 | 0.0787640 | ||||||||
\(886\) | 57.1127 | 1.91874 | ||||||||
\(887\) | −7.02944 | −0.236025 | −0.118013 | − | 0.993012i | \(-0.537652\pi\) | ||||
−0.118013 | + | 0.993012i | \(0.537652\pi\) | |||||||
\(888\) | −16.1421 | −0.541695 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −12.8284 | −0.430010 | ||||||||
\(891\) | 2.82843 | 0.0947559 | ||||||||
\(892\) | −80.2843 | −2.68812 | ||||||||
\(893\) | −4.68629 | −0.156821 | ||||||||
\(894\) | −18.4853 | −0.618240 | ||||||||
\(895\) | −1.17157 | −0.0391614 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 36.9706 | 1.23441 | ||||||||
\(898\) | −30.4853 | −1.01731 | ||||||||
\(899\) | 38.9117 | 1.29778 | ||||||||
\(900\) | 3.82843 | 0.127614 | ||||||||
\(901\) | 64.9706 | 2.16448 | ||||||||
\(902\) | 79.5980 | 2.65032 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 12.4853 | 0.415254 | ||||||||
\(905\) | 2.34315 | 0.0778888 | ||||||||
\(906\) | −40.9706 | −1.36116 | ||||||||
\(907\) | −39.3137 | −1.30539 | −0.652695 | − | 0.757621i | \(-0.726362\pi\) | ||||
−0.652695 | + | 0.757621i | \(0.726362\pi\) | |||||||
\(908\) | 110.912 | 3.68073 | ||||||||
\(909\) | 7.65685 | 0.253962 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −7.79899 | −0.258392 | −0.129196 | − | 0.991619i | \(-0.541240\pi\) | ||||
−0.129196 | + | 0.991619i | \(0.541240\pi\) | |||||||
\(912\) | −2.48528 | −0.0822959 | ||||||||
\(913\) | −4.68629 | −0.155094 | ||||||||
\(914\) | 39.4558 | 1.30508 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −58.6274 | −1.93710 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −18.4853 | −0.610105 | ||||||||
\(919\) | 44.2843 | 1.46080 | 0.730402 | − | 0.683018i | \(-0.239333\pi\) | ||||
0.730402 | + | 0.683018i | \(0.239333\pi\) | |||||||
\(920\) | −33.7990 | −1.11432 | ||||||||
\(921\) | −28.9706 | −0.954612 | ||||||||
\(922\) | 32.1421 | 1.05854 | ||||||||
\(923\) | 13.6569 | 0.449521 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −3.65685 | −0.120237 | ||||||||
\(926\) | 93.2548 | 3.06454 | ||||||||
\(927\) | −12.0000 | −0.394132 | ||||||||
\(928\) | −9.51472 | −0.312336 | ||||||||
\(929\) | −42.0000 | −1.37798 | −0.688988 | − | 0.724773i | \(-0.741945\pi\) | ||||
−0.688988 | + | 0.724773i | \(0.741945\pi\) | |||||||
\(930\) | 15.6569 | 0.513408 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 56.7696 | 1.85955 | ||||||||
\(933\) | 9.65685 | 0.316151 | ||||||||
\(934\) | −58.6274 | −1.91835 | ||||||||
\(935\) | −21.6569 | −0.708255 | ||||||||
\(936\) | −21.3137 | −0.696660 | ||||||||
\(937\) | 15.4558 | 0.504920 | 0.252460 | − | 0.967607i | \(-0.418760\pi\) | ||||
0.252460 | + | 0.967607i | \(0.418760\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 2.48528 | 0.0811041 | ||||||||
\(940\) | 21.6569 | 0.706369 | ||||||||
\(941\) | −0.627417 | −0.0204532 | −0.0102266 | − | 0.999948i | \(-0.503255\pi\) | ||||
−0.0102266 | + | 0.999948i | \(0.503255\pi\) | |||||||
\(942\) | 29.3137 | 0.955092 | ||||||||
\(943\) | −89.2548 | −2.90654 | ||||||||
\(944\) | 7.02944 | 0.228789 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 54.6274 | 1.77609 | ||||||||
\(947\) | −12.3431 | −0.401098 | −0.200549 | − | 0.979684i | \(-0.564273\pi\) | ||||
−0.200549 | + | 0.979684i | \(0.564273\pi\) | |||||||
\(948\) | −30.6274 | −0.994732 | ||||||||
\(949\) | 53.9411 | 1.75100 | ||||||||
\(950\) | −2.00000 | −0.0648886 | ||||||||
\(951\) | 22.1421 | 0.718008 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 6.14214 | 0.198963 | 0.0994816 | − | 0.995039i | \(-0.468282\pi\) | ||||
0.0994816 | + | 0.995039i | \(0.468282\pi\) | |||||||
\(954\) | −20.4853 | −0.663235 | ||||||||
\(955\) | −9.17157 | −0.296785 | ||||||||
\(956\) | −8.20101 | −0.265240 | ||||||||
\(957\) | 16.9706 | 0.548580 | ||||||||
\(958\) | −34.6274 | −1.11876 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −9.82843 | −0.317211 | ||||||||
\(961\) | 11.0589 | 0.356738 | ||||||||
\(962\) | 42.6274 | 1.37436 | ||||||||
\(963\) | 5.31371 | 0.171232 | ||||||||
\(964\) | −82.9117 | −2.67041 | ||||||||
\(965\) | 15.6569 | 0.504012 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 5.37258 | 0.172771 | 0.0863853 | − | 0.996262i | \(-0.472468\pi\) | ||||
0.0863853 | + | 0.996262i | \(0.472468\pi\) | |||||||
\(968\) | −13.2426 | −0.425635 | ||||||||
\(969\) | 6.34315 | 0.203771 | ||||||||
\(970\) | 15.6569 | 0.502711 | ||||||||
\(971\) | 39.3137 | 1.26164 | 0.630818 | − | 0.775930i | \(-0.282719\pi\) | ||||
0.630818 | + | 0.775930i | \(0.282719\pi\) | |||||||
\(972\) | 3.82843 | 0.122797 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 72.2843 | 2.31614 | ||||||||
\(975\) | −4.82843 | −0.154633 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −20.4853 | −0.655382 | −0.327691 | − | 0.944785i | \(-0.606271\pi\) | ||||
−0.327691 | + | 0.944785i | \(0.606271\pi\) | |||||||
\(978\) | −28.9706 | −0.926376 | ||||||||
\(979\) | −15.0294 | −0.480343 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 6.00000 | 0.191565 | ||||||||
\(982\) | 43.7990 | 1.39768 | ||||||||
\(983\) | 21.6569 | 0.690746 | 0.345373 | − | 0.938465i | \(-0.387752\pi\) | ||||
0.345373 | + | 0.938465i | \(0.387752\pi\) | |||||||
\(984\) | 51.4558 | 1.64035 | ||||||||
\(985\) | −3.51472 | −0.111988 | ||||||||
\(986\) | −110.912 | −3.53215 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 15.3137 | 0.487194 | ||||||||
\(989\) | −61.2548 | −1.94779 | ||||||||
\(990\) | 6.82843 | 0.217022 | ||||||||
\(991\) | 16.9706 | 0.539088 | 0.269544 | − | 0.962988i | \(-0.413127\pi\) | ||||
0.269544 | + | 0.962988i | \(0.413127\pi\) | |||||||
\(992\) | −10.2843 | −0.326526 | ||||||||
\(993\) | 1.65685 | 0.0525787 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −0.828427 | −0.0262629 | ||||||||
\(996\) | −6.34315 | −0.200990 | ||||||||
\(997\) | −55.4558 | −1.75630 | −0.878152 | − | 0.478382i | \(-0.841224\pi\) | ||||
−0.878152 | + | 0.478382i | \(0.841224\pi\) | |||||||
\(998\) | 12.0000 | 0.379853 | ||||||||
\(999\) | −3.65685 | −0.115698 |
(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 | 735.2.a.m.1.2 | yes | 2 | |
3.2 | odd | 2 | 2205.2.a.o.1.1 | 2 | |||
5.4 | even | 2 | 3675.2.a.s.1.1 | 2 | |||
7.2 | even | 3 | 735.2.i.g.361.1 | 4 | |||
7.3 | odd | 6 | 735.2.i.h.226.1 | 4 | |||
7.4 | even | 3 | 735.2.i.g.226.1 | 4 | |||
7.5 | odd | 6 | 735.2.i.h.361.1 | 4 | |||
7.6 | odd | 2 | 735.2.a.l.1.2 | ✓ | 2 | ||
21.20 | even | 2 | 2205.2.a.r.1.1 | 2 | |||
35.34 | odd | 2 | 3675.2.a.t.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
735.2.a.l.1.2 | ✓ | 2 | 7.6 | odd | 2 | ||
735.2.a.m.1.2 | yes | 2 | 1.1 | even | 1 | trivial | |
735.2.i.g.226.1 | 4 | 7.4 | even | 3 | |||
735.2.i.g.361.1 | 4 | 7.2 | even | 3 | |||
735.2.i.h.226.1 | 4 | 7.3 | odd | 6 | |||
735.2.i.h.361.1 | 4 | 7.5 | odd | 6 | |||
2205.2.a.o.1.1 | 2 | 3.2 | odd | 2 | |||
2205.2.a.r.1.1 | 2 | 21.20 | even | 2 | |||
3675.2.a.s.1.1 | 2 | 5.4 | even | 2 | |||
3675.2.a.t.1.1 | 2 | 35.34 | odd | 2 |