Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [825,2,Mod(1,825)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(825, 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("825.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 825 = 3 \cdot 5^{2} \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 825.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: | \(6.58765816676\) |
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: | no (minimal twist has level 165) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(1.41421\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 825.1 |
$q$-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 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 2.41421 | 0.985599 | ||||||||
\(7\) | −0.828427 | −0.313116 | −0.156558 | − | 0.987669i | \(-0.550040\pi\) | ||||
−0.156558 | + | 0.987669i | \(0.550040\pi\) | |||||||
\(8\) | 4.41421 | 1.56066 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.00000 | −0.301511 | ||||||||
\(12\) | 3.82843 | 1.10517 | ||||||||
\(13\) | 5.65685 | 1.56893 | 0.784465 | − | 0.620174i | \(-0.212938\pi\) | ||||
0.784465 | + | 0.620174i | \(0.212938\pi\) | |||||||
\(14\) | −2.00000 | −0.534522 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 3.00000 | 0.750000 | ||||||||
\(17\) | 1.17157 | 0.284148 | 0.142074 | − | 0.989856i | \(-0.454623\pi\) | ||||
0.142074 | + | 0.989856i | \(0.454623\pi\) | |||||||
\(18\) | 2.41421 | 0.569036 | ||||||||
\(19\) | −6.82843 | −1.56655 | −0.783274 | − | 0.621676i | \(-0.786452\pi\) | ||||
−0.783274 | + | 0.621676i | \(0.786452\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −0.828427 | −0.180778 | ||||||||
\(22\) | −2.41421 | −0.514712 | ||||||||
\(23\) | 4.00000 | 0.834058 | 0.417029 | − | 0.908893i | \(-0.363071\pi\) | ||||
0.417029 | + | 0.908893i | \(0.363071\pi\) | |||||||
\(24\) | 4.41421 | 0.901048 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 13.6569 | 2.67833 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | −3.17157 | −0.599371 | ||||||||
\(29\) | −4.82843 | −0.896616 | −0.448308 | − | 0.893879i | \(-0.647973\pi\) | ||||
−0.448308 | + | 0.893879i | \(0.647973\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(32\) | −1.58579 | −0.280330 | ||||||||
\(33\) | −1.00000 | −0.174078 | ||||||||
\(34\) | 2.82843 | 0.485071 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 3.82843 | 0.638071 | ||||||||
\(37\) | −11.6569 | −1.91638 | −0.958188 | − | 0.286141i | \(-0.907627\pi\) | ||||
−0.958188 | + | 0.286141i | \(0.907627\pi\) | |||||||
\(38\) | −16.4853 | −2.67427 | ||||||||
\(39\) | 5.65685 | 0.905822 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 4.82843 | 0.754074 | 0.377037 | − | 0.926198i | \(-0.376943\pi\) | ||||
0.377037 | + | 0.926198i | \(0.376943\pi\) | |||||||
\(42\) | −2.00000 | −0.308607 | ||||||||
\(43\) | 8.82843 | 1.34632 | 0.673161 | − | 0.739496i | \(-0.264936\pi\) | ||||
0.673161 | + | 0.739496i | \(0.264936\pi\) | |||||||
\(44\) | −3.82843 | −0.577157 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 9.65685 | 1.42383 | ||||||||
\(47\) | 4.00000 | 0.583460 | 0.291730 | − | 0.956501i | \(-0.405769\pi\) | ||||
0.291730 | + | 0.956501i | \(0.405769\pi\) | |||||||
\(48\) | 3.00000 | 0.433013 | ||||||||
\(49\) | −6.31371 | −0.901958 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 1.17157 | 0.164053 | ||||||||
\(52\) | 21.6569 | 3.00327 | ||||||||
\(53\) | −9.31371 | −1.27934 | −0.639668 | − | 0.768651i | \(-0.720928\pi\) | ||||
−0.639668 | + | 0.768651i | \(0.720928\pi\) | |||||||
\(54\) | 2.41421 | 0.328533 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −3.65685 | −0.488668 | ||||||||
\(57\) | −6.82843 | −0.904447 | ||||||||
\(58\) | −11.6569 | −1.53062 | ||||||||
\(59\) | −4.00000 | −0.520756 | −0.260378 | − | 0.965507i | \(-0.583847\pi\) | ||||
−0.260378 | + | 0.965507i | \(0.583847\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −11.6569 | −1.49251 | −0.746254 | − | 0.665662i | \(-0.768149\pi\) | ||||
−0.746254 | + | 0.665662i | \(0.768149\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −0.828427 | −0.104372 | ||||||||
\(64\) | −9.82843 | −1.22855 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −2.41421 | −0.297169 | ||||||||
\(67\) | 5.65685 | 0.691095 | 0.345547 | − | 0.938401i | \(-0.387693\pi\) | ||||
0.345547 | + | 0.938401i | \(0.387693\pi\) | |||||||
\(68\) | 4.48528 | 0.543920 | ||||||||
\(69\) | 4.00000 | 0.481543 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 2.34315 | 0.278080 | 0.139040 | − | 0.990287i | \(-0.455598\pi\) | ||||
0.139040 | + | 0.990287i | \(0.455598\pi\) | |||||||
\(72\) | 4.41421 | 0.520220 | ||||||||
\(73\) | −11.3137 | −1.32417 | −0.662085 | − | 0.749429i | \(-0.730328\pi\) | ||||
−0.662085 | + | 0.749429i | \(0.730328\pi\) | |||||||
\(74\) | −28.1421 | −3.27146 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −26.1421 | −2.99871 | ||||||||
\(77\) | 0.828427 | 0.0944080 | ||||||||
\(78\) | 13.6569 | 1.54633 | ||||||||
\(79\) | 8.48528 | 0.954669 | 0.477334 | − | 0.878722i | \(-0.341603\pi\) | ||||
0.477334 | + | 0.878722i | \(0.341603\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 11.6569 | 1.28728 | ||||||||
\(83\) | 10.0000 | 1.09764 | 0.548821 | − | 0.835940i | \(-0.315077\pi\) | ||||
0.548821 | + | 0.835940i | \(0.315077\pi\) | |||||||
\(84\) | −3.17157 | −0.346047 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 21.3137 | 2.29832 | ||||||||
\(87\) | −4.82843 | −0.517662 | ||||||||
\(88\) | −4.41421 | −0.470557 | ||||||||
\(89\) | 3.65685 | 0.387626 | 0.193813 | − | 0.981039i | \(-0.437915\pi\) | ||||
0.193813 | + | 0.981039i | \(0.437915\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −4.68629 | −0.491257 | ||||||||
\(92\) | 15.3137 | 1.59656 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 9.65685 | 0.996028 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −1.58579 | −0.161849 | ||||||||
\(97\) | −11.6569 | −1.18357 | −0.591787 | − | 0.806094i | \(-0.701577\pi\) | ||||
−0.591787 | + | 0.806094i | \(0.701577\pi\) | |||||||
\(98\) | −15.2426 | −1.53974 | ||||||||
\(99\) | −1.00000 | −0.100504 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −0.828427 | −0.0824316 | −0.0412158 | − | 0.999150i | \(-0.513123\pi\) | ||||
−0.0412158 | + | 0.999150i | \(0.513123\pi\) | |||||||
\(102\) | 2.82843 | 0.280056 | ||||||||
\(103\) | 3.31371 | 0.326509 | 0.163255 | − | 0.986584i | \(-0.447801\pi\) | ||||
0.163255 | + | 0.986584i | \(0.447801\pi\) | |||||||
\(104\) | 24.9706 | 2.44857 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −22.4853 | −2.18396 | ||||||||
\(107\) | −17.3137 | −1.67378 | −0.836890 | − | 0.547372i | \(-0.815628\pi\) | ||||
−0.836890 | + | 0.547372i | \(0.815628\pi\) | |||||||
\(108\) | 3.82843 | 0.368391 | ||||||||
\(109\) | 17.3137 | 1.65835 | 0.829176 | − | 0.558987i | \(-0.188810\pi\) | ||||
0.829176 | + | 0.558987i | \(0.188810\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −11.6569 | −1.10642 | ||||||||
\(112\) | −2.48528 | −0.234837 | ||||||||
\(113\) | 18.9706 | 1.78460 | 0.892300 | − | 0.451442i | \(-0.149090\pi\) | ||||
0.892300 | + | 0.451442i | \(0.149090\pi\) | |||||||
\(114\) | −16.4853 | −1.54399 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −18.4853 | −1.71632 | ||||||||
\(117\) | 5.65685 | 0.522976 | ||||||||
\(118\) | −9.65685 | −0.888985 | ||||||||
\(119\) | −0.970563 | −0.0889713 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | −28.1421 | −2.54787 | ||||||||
\(123\) | 4.82843 | 0.435365 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −2.00000 | −0.178174 | ||||||||
\(127\) | 14.4853 | 1.28536 | 0.642680 | − | 0.766134i | \(-0.277822\pi\) | ||||
0.642680 | + | 0.766134i | \(0.277822\pi\) | |||||||
\(128\) | −20.5563 | −1.81694 | ||||||||
\(129\) | 8.82843 | 0.777300 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 3.31371 | 0.289520 | 0.144760 | − | 0.989467i | \(-0.453759\pi\) | ||||
0.144760 | + | 0.989467i | \(0.453759\pi\) | |||||||
\(132\) | −3.82843 | −0.333222 | ||||||||
\(133\) | 5.65685 | 0.490511 | ||||||||
\(134\) | 13.6569 | 1.17977 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 5.17157 | 0.443459 | ||||||||
\(137\) | 13.3137 | 1.13747 | 0.568733 | − | 0.822522i | \(-0.307434\pi\) | ||||
0.568733 | + | 0.822522i | \(0.307434\pi\) | |||||||
\(138\) | 9.65685 | 0.822046 | ||||||||
\(139\) | 0.485281 | 0.0411610 | 0.0205805 | − | 0.999788i | \(-0.493449\pi\) | ||||
0.0205805 | + | 0.999788i | \(0.493449\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 4.00000 | 0.336861 | ||||||||
\(142\) | 5.65685 | 0.474713 | ||||||||
\(143\) | −5.65685 | −0.473050 | ||||||||
\(144\) | 3.00000 | 0.250000 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −27.3137 | −2.26050 | ||||||||
\(147\) | −6.31371 | −0.520746 | ||||||||
\(148\) | −44.6274 | −3.66835 | ||||||||
\(149\) | 1.51472 | 0.124091 | 0.0620453 | − | 0.998073i | \(-0.480238\pi\) | ||||
0.0620453 | + | 0.998073i | \(0.480238\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 16.4853 | 1.34155 | 0.670777 | − | 0.741659i | \(-0.265961\pi\) | ||||
0.670777 | + | 0.741659i | \(0.265961\pi\) | |||||||
\(152\) | −30.1421 | −2.44485 | ||||||||
\(153\) | 1.17157 | 0.0947161 | ||||||||
\(154\) | 2.00000 | 0.161165 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 21.6569 | 1.73394 | ||||||||
\(157\) | −18.0000 | −1.43656 | −0.718278 | − | 0.695756i | \(-0.755069\pi\) | ||||
−0.718278 | + | 0.695756i | \(0.755069\pi\) | |||||||
\(158\) | 20.4853 | 1.62972 | ||||||||
\(159\) | −9.31371 | −0.738625 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −3.31371 | −0.261157 | ||||||||
\(162\) | 2.41421 | 0.189679 | ||||||||
\(163\) | 7.31371 | 0.572854 | 0.286427 | − | 0.958102i | \(-0.407532\pi\) | ||||
0.286427 | + | 0.958102i | \(0.407532\pi\) | |||||||
\(164\) | 18.4853 | 1.44346 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 24.1421 | 1.87379 | ||||||||
\(167\) | 13.3137 | 1.03025 | 0.515123 | − | 0.857116i | \(-0.327746\pi\) | ||||
0.515123 | + | 0.857116i | \(0.327746\pi\) | |||||||
\(168\) | −3.65685 | −0.282132 | ||||||||
\(169\) | 19.0000 | 1.46154 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −6.82843 | −0.522183 | ||||||||
\(172\) | 33.7990 | 2.57715 | ||||||||
\(173\) | −2.82843 | −0.215041 | −0.107521 | − | 0.994203i | \(-0.534291\pi\) | ||||
−0.107521 | + | 0.994203i | \(0.534291\pi\) | |||||||
\(174\) | −11.6569 | −0.883704 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −3.00000 | −0.226134 | ||||||||
\(177\) | −4.00000 | −0.300658 | ||||||||
\(178\) | 8.82843 | 0.661719 | ||||||||
\(179\) | −17.6569 | −1.31974 | −0.659868 | − | 0.751382i | \(-0.729388\pi\) | ||||
−0.659868 | + | 0.751382i | \(0.729388\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −14.0000 | −1.04061 | −0.520306 | − | 0.853980i | \(-0.674182\pi\) | ||||
−0.520306 | + | 0.853980i | \(0.674182\pi\) | |||||||
\(182\) | −11.3137 | −0.838628 | ||||||||
\(183\) | −11.6569 | −0.861699 | ||||||||
\(184\) | 17.6569 | 1.30168 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −1.17157 | −0.0856739 | ||||||||
\(188\) | 15.3137 | 1.11687 | ||||||||
\(189\) | −0.828427 | −0.0602592 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 5.65685 | 0.409316 | 0.204658 | − | 0.978834i | \(-0.434392\pi\) | ||||
0.204658 | + | 0.978834i | \(0.434392\pi\) | |||||||
\(192\) | −9.82843 | −0.709306 | ||||||||
\(193\) | −13.6569 | −0.983042 | −0.491521 | − | 0.870866i | \(-0.663559\pi\) | ||||
−0.491521 | + | 0.870866i | \(0.663559\pi\) | |||||||
\(194\) | −28.1421 | −2.02049 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −24.1716 | −1.72654 | ||||||||
\(197\) | 8.48528 | 0.604551 | 0.302276 | − | 0.953221i | \(-0.402254\pi\) | ||||
0.302276 | + | 0.953221i | \(0.402254\pi\) | |||||||
\(198\) | −2.41421 | −0.171571 | ||||||||
\(199\) | −21.6569 | −1.53521 | −0.767607 | − | 0.640921i | \(-0.778553\pi\) | ||||
−0.767607 | + | 0.640921i | \(0.778553\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 5.65685 | 0.399004 | ||||||||
\(202\) | −2.00000 | −0.140720 | ||||||||
\(203\) | 4.00000 | 0.280745 | ||||||||
\(204\) | 4.48528 | 0.314033 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 8.00000 | 0.557386 | ||||||||
\(207\) | 4.00000 | 0.278019 | ||||||||
\(208\) | 16.9706 | 1.17670 | ||||||||
\(209\) | 6.82843 | 0.472332 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1.17157 | 0.0806544 | 0.0403272 | − | 0.999187i | \(-0.487160\pi\) | ||||
0.0403272 | + | 0.999187i | \(0.487160\pi\) | |||||||
\(212\) | −35.6569 | −2.44892 | ||||||||
\(213\) | 2.34315 | 0.160550 | ||||||||
\(214\) | −41.7990 | −2.85732 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 4.41421 | 0.300349 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 41.7990 | 2.83098 | ||||||||
\(219\) | −11.3137 | −0.764510 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 6.62742 | 0.445808 | ||||||||
\(222\) | −28.1421 | −1.88878 | ||||||||
\(223\) | 6.34315 | 0.424768 | 0.212384 | − | 0.977186i | \(-0.431877\pi\) | ||||
0.212384 | + | 0.977186i | \(0.431877\pi\) | |||||||
\(224\) | 1.31371 | 0.0877758 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 45.7990 | 3.04650 | ||||||||
\(227\) | 14.0000 | 0.929213 | 0.464606 | − | 0.885517i | \(-0.346196\pi\) | ||||
0.464606 | + | 0.885517i | \(0.346196\pi\) | |||||||
\(228\) | −26.1421 | −1.73131 | ||||||||
\(229\) | −2.00000 | −0.132164 | −0.0660819 | − | 0.997814i | \(-0.521050\pi\) | ||||
−0.0660819 | + | 0.997814i | \(0.521050\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0.828427 | 0.0545065 | ||||||||
\(232\) | −21.3137 | −1.39931 | ||||||||
\(233\) | 18.8284 | 1.23349 | 0.616746 | − | 0.787163i | \(-0.288451\pi\) | ||||
0.616746 | + | 0.787163i | \(0.288451\pi\) | |||||||
\(234\) | 13.6569 | 0.892776 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −15.3137 | −0.996838 | ||||||||
\(237\) | 8.48528 | 0.551178 | ||||||||
\(238\) | −2.34315 | −0.151884 | ||||||||
\(239\) | 17.6569 | 1.14213 | 0.571063 | − | 0.820906i | \(-0.306531\pi\) | ||||
0.571063 | + | 0.820906i | \(0.306531\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −12.3431 | −0.795092 | −0.397546 | − | 0.917582i | \(-0.630138\pi\) | ||||
−0.397546 | + | 0.917582i | \(0.630138\pi\) | |||||||
\(242\) | 2.41421 | 0.155192 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | −44.6274 | −2.85698 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 11.6569 | 0.743214 | ||||||||
\(247\) | −38.6274 | −2.45780 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 10.0000 | 0.633724 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 20.9706 | 1.32365 | 0.661825 | − | 0.749658i | \(-0.269782\pi\) | ||||
0.661825 | + | 0.749658i | \(0.269782\pi\) | |||||||
\(252\) | −3.17157 | −0.199790 | ||||||||
\(253\) | −4.00000 | −0.251478 | ||||||||
\(254\) | 34.9706 | 2.19425 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −29.9706 | −1.87316 | ||||||||
\(257\) | 16.3431 | 1.01946 | 0.509729 | − | 0.860335i | \(-0.329746\pi\) | ||||
0.509729 | + | 0.860335i | \(0.329746\pi\) | |||||||
\(258\) | 21.3137 | 1.32693 | ||||||||
\(259\) | 9.65685 | 0.600048 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −4.82843 | −0.298872 | ||||||||
\(262\) | 8.00000 | 0.494242 | ||||||||
\(263\) | −18.0000 | −1.10993 | −0.554964 | − | 0.831875i | \(-0.687268\pi\) | ||||
−0.554964 | + | 0.831875i | \(0.687268\pi\) | |||||||
\(264\) | −4.41421 | −0.271676 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 13.6569 | 0.837355 | ||||||||
\(267\) | 3.65685 | 0.223796 | ||||||||
\(268\) | 21.6569 | 1.32290 | ||||||||
\(269\) | 20.6274 | 1.25768 | 0.628838 | − | 0.777536i | \(-0.283531\pi\) | ||||
0.628838 | + | 0.777536i | \(0.283531\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −11.7990 | −0.716738 | −0.358369 | − | 0.933580i | \(-0.616667\pi\) | ||||
−0.358369 | + | 0.933580i | \(0.616667\pi\) | |||||||
\(272\) | 3.51472 | 0.213111 | ||||||||
\(273\) | −4.68629 | −0.283627 | ||||||||
\(274\) | 32.1421 | 1.94178 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 15.3137 | 0.921777 | ||||||||
\(277\) | 2.34315 | 0.140786 | 0.0703930 | − | 0.997519i | \(-0.477575\pi\) | ||||
0.0703930 | + | 0.997519i | \(0.477575\pi\) | |||||||
\(278\) | 1.17157 | 0.0702663 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −11.1716 | −0.666440 | −0.333220 | − | 0.942849i | \(-0.608135\pi\) | ||||
−0.333220 | + | 0.942849i | \(0.608135\pi\) | |||||||
\(282\) | 9.65685 | 0.575057 | ||||||||
\(283\) | 8.82843 | 0.524796 | 0.262398 | − | 0.964960i | \(-0.415487\pi\) | ||||
0.262398 | + | 0.964960i | \(0.415487\pi\) | |||||||
\(284\) | 8.97056 | 0.532305 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −13.6569 | −0.807547 | ||||||||
\(287\) | −4.00000 | −0.236113 | ||||||||
\(288\) | −1.58579 | −0.0934434 | ||||||||
\(289\) | −15.6274 | −0.919260 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −11.6569 | −0.683337 | ||||||||
\(292\) | −43.3137 | −2.53474 | ||||||||
\(293\) | 6.82843 | 0.398921 | 0.199460 | − | 0.979906i | \(-0.436081\pi\) | ||||
0.199460 | + | 0.979906i | \(0.436081\pi\) | |||||||
\(294\) | −15.2426 | −0.888969 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −51.4558 | −2.99081 | ||||||||
\(297\) | −1.00000 | −0.0580259 | ||||||||
\(298\) | 3.65685 | 0.211836 | ||||||||
\(299\) | 22.6274 | 1.30858 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −7.31371 | −0.421555 | ||||||||
\(302\) | 39.7990 | 2.29017 | ||||||||
\(303\) | −0.828427 | −0.0475919 | ||||||||
\(304\) | −20.4853 | −1.17491 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 2.82843 | 0.161690 | ||||||||
\(307\) | 3.17157 | 0.181011 | 0.0905056 | − | 0.995896i | \(-0.471152\pi\) | ||||
0.0905056 | + | 0.995896i | \(0.471152\pi\) | |||||||
\(308\) | 3.17157 | 0.180717 | ||||||||
\(309\) | 3.31371 | 0.188510 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −3.31371 | −0.187903 | −0.0939516 | − | 0.995577i | \(-0.529950\pi\) | ||||
−0.0939516 | + | 0.995577i | \(0.529950\pi\) | |||||||
\(312\) | 24.9706 | 1.41368 | ||||||||
\(313\) | −15.6569 | −0.884978 | −0.442489 | − | 0.896774i | \(-0.645904\pi\) | ||||
−0.442489 | + | 0.896774i | \(0.645904\pi\) | |||||||
\(314\) | −43.4558 | −2.45236 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 32.4853 | 1.82744 | ||||||||
\(317\) | 26.2843 | 1.47627 | 0.738136 | − | 0.674652i | \(-0.235706\pi\) | ||||
0.738136 | + | 0.674652i | \(0.235706\pi\) | |||||||
\(318\) | −22.4853 | −1.26091 | ||||||||
\(319\) | 4.82843 | 0.270340 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −17.3137 | −0.966357 | ||||||||
\(322\) | −8.00000 | −0.445823 | ||||||||
\(323\) | −8.00000 | −0.445132 | ||||||||
\(324\) | 3.82843 | 0.212690 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 17.6569 | 0.977923 | ||||||||
\(327\) | 17.3137 | 0.957450 | ||||||||
\(328\) | 21.3137 | 1.17685 | ||||||||
\(329\) | −3.31371 | −0.182691 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 6.34315 | 0.348651 | 0.174325 | − | 0.984688i | \(-0.444226\pi\) | ||||
0.174325 | + | 0.984688i | \(0.444226\pi\) | |||||||
\(332\) | 38.2843 | 2.10112 | ||||||||
\(333\) | −11.6569 | −0.638792 | ||||||||
\(334\) | 32.1421 | 1.75874 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −2.48528 | −0.135583 | ||||||||
\(337\) | −3.31371 | −0.180509 | −0.0902546 | − | 0.995919i | \(-0.528768\pi\) | ||||
−0.0902546 | + | 0.995919i | \(0.528768\pi\) | |||||||
\(338\) | 45.8701 | 2.49500 | ||||||||
\(339\) | 18.9706 | 1.03034 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | −16.4853 | −0.891422 | ||||||||
\(343\) | 11.0294 | 0.595534 | ||||||||
\(344\) | 38.9706 | 2.10115 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −6.82843 | −0.367099 | ||||||||
\(347\) | 29.3137 | 1.57364 | 0.786821 | − | 0.617181i | \(-0.211725\pi\) | ||||
0.786821 | + | 0.617181i | \(0.211725\pi\) | |||||||
\(348\) | −18.4853 | −0.990915 | ||||||||
\(349\) | 10.9706 | 0.587241 | 0.293620 | − | 0.955922i | \(-0.405140\pi\) | ||||
0.293620 | + | 0.955922i | \(0.405140\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 5.65685 | 0.301941 | ||||||||
\(352\) | 1.58579 | 0.0845227 | ||||||||
\(353\) | −26.0000 | −1.38384 | −0.691920 | − | 0.721974i | \(-0.743235\pi\) | ||||
−0.691920 | + | 0.721974i | \(0.743235\pi\) | |||||||
\(354\) | −9.65685 | −0.513256 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 14.0000 | 0.741999 | ||||||||
\(357\) | −0.970563 | −0.0513676 | ||||||||
\(358\) | −42.6274 | −2.25293 | ||||||||
\(359\) | 12.0000 | 0.633336 | 0.316668 | − | 0.948536i | \(-0.397436\pi\) | ||||
0.316668 | + | 0.948536i | \(0.397436\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 27.6274 | 1.45407 | ||||||||
\(362\) | −33.7990 | −1.77644 | ||||||||
\(363\) | 1.00000 | 0.0524864 | ||||||||
\(364\) | −17.9411 | −0.940370 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −28.1421 | −1.47101 | ||||||||
\(367\) | −9.65685 | −0.504084 | −0.252042 | − | 0.967716i | \(-0.581102\pi\) | ||||
−0.252042 | + | 0.967716i | \(0.581102\pi\) | |||||||
\(368\) | 12.0000 | 0.625543 | ||||||||
\(369\) | 4.82843 | 0.251358 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 7.71573 | 0.400581 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −10.6274 | −0.550267 | −0.275133 | − | 0.961406i | \(-0.588722\pi\) | ||||
−0.275133 | + | 0.961406i | \(0.588722\pi\) | |||||||
\(374\) | −2.82843 | −0.146254 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 17.6569 | 0.910583 | ||||||||
\(377\) | −27.3137 | −1.40673 | ||||||||
\(378\) | −2.00000 | −0.102869 | ||||||||
\(379\) | −23.3137 | −1.19754 | −0.598772 | − | 0.800919i | \(-0.704345\pi\) | ||||
−0.598772 | + | 0.800919i | \(0.704345\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 14.4853 | 0.742103 | ||||||||
\(382\) | 13.6569 | 0.698745 | ||||||||
\(383\) | 8.00000 | 0.408781 | 0.204390 | − | 0.978889i | \(-0.434479\pi\) | ||||
0.204390 | + | 0.978889i | \(0.434479\pi\) | |||||||
\(384\) | −20.5563 | −1.04901 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −32.9706 | −1.67816 | ||||||||
\(387\) | 8.82843 | 0.448774 | ||||||||
\(388\) | −44.6274 | −2.26561 | ||||||||
\(389\) | −23.6569 | −1.19945 | −0.599725 | − | 0.800206i | \(-0.704723\pi\) | ||||
−0.599725 | + | 0.800206i | \(0.704723\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 4.68629 | 0.236996 | ||||||||
\(392\) | −27.8701 | −1.40765 | ||||||||
\(393\) | 3.31371 | 0.167154 | ||||||||
\(394\) | 20.4853 | 1.03203 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −3.82843 | −0.192386 | ||||||||
\(397\) | 14.9706 | 0.751351 | 0.375676 | − | 0.926751i | \(-0.377411\pi\) | ||||
0.375676 | + | 0.926751i | \(0.377411\pi\) | |||||||
\(398\) | −52.2843 | −2.62077 | ||||||||
\(399\) | 5.65685 | 0.283197 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −6.68629 | −0.333897 | −0.166949 | − | 0.985966i | \(-0.553391\pi\) | ||||
−0.166949 | + | 0.985966i | \(0.553391\pi\) | |||||||
\(402\) | 13.6569 | 0.681142 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | −3.17157 | −0.157792 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 9.65685 | 0.479262 | ||||||||
\(407\) | 11.6569 | 0.577809 | ||||||||
\(408\) | 5.17157 | 0.256031 | ||||||||
\(409\) | −19.6569 | −0.971969 | −0.485984 | − | 0.873967i | \(-0.661539\pi\) | ||||
−0.485984 | + | 0.873967i | \(0.661539\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 13.3137 | 0.656717 | ||||||||
\(412\) | 12.6863 | 0.625009 | ||||||||
\(413\) | 3.31371 | 0.163057 | ||||||||
\(414\) | 9.65685 | 0.474608 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −8.97056 | −0.439818 | ||||||||
\(417\) | 0.485281 | 0.0237643 | ||||||||
\(418\) | 16.4853 | 0.806321 | ||||||||
\(419\) | −36.9706 | −1.80613 | −0.903065 | − | 0.429504i | \(-0.858689\pi\) | ||||
−0.903065 | + | 0.429504i | \(0.858689\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −6.00000 | −0.292422 | −0.146211 | − | 0.989253i | \(-0.546708\pi\) | ||||
−0.146211 | + | 0.989253i | \(0.546708\pi\) | |||||||
\(422\) | 2.82843 | 0.137686 | ||||||||
\(423\) | 4.00000 | 0.194487 | ||||||||
\(424\) | −41.1127 | −1.99661 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 5.65685 | 0.274075 | ||||||||
\(427\) | 9.65685 | 0.467328 | ||||||||
\(428\) | −66.2843 | −3.20397 | ||||||||
\(429\) | −5.65685 | −0.273115 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 21.6569 | 1.04317 | 0.521587 | − | 0.853198i | \(-0.325340\pi\) | ||||
0.521587 | + | 0.853198i | \(0.325340\pi\) | |||||||
\(432\) | 3.00000 | 0.144338 | ||||||||
\(433\) | 15.6569 | 0.752420 | 0.376210 | − | 0.926534i | \(-0.377227\pi\) | ||||
0.376210 | + | 0.926534i | \(0.377227\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 66.2843 | 3.17444 | ||||||||
\(437\) | −27.3137 | −1.30659 | ||||||||
\(438\) | −27.3137 | −1.30510 | ||||||||
\(439\) | −20.4853 | −0.977709 | −0.488855 | − | 0.872365i | \(-0.662585\pi\) | ||||
−0.488855 | + | 0.872365i | \(0.662585\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −6.31371 | −0.300653 | ||||||||
\(442\) | 16.0000 | 0.761042 | ||||||||
\(443\) | −12.0000 | −0.570137 | −0.285069 | − | 0.958507i | \(-0.592016\pi\) | ||||
−0.285069 | + | 0.958507i | \(0.592016\pi\) | |||||||
\(444\) | −44.6274 | −2.11792 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 15.3137 | 0.725125 | ||||||||
\(447\) | 1.51472 | 0.0716437 | ||||||||
\(448\) | 8.14214 | 0.384680 | ||||||||
\(449\) | 30.9706 | 1.46159 | 0.730796 | − | 0.682596i | \(-0.239149\pi\) | ||||
0.730796 | + | 0.682596i | \(0.239149\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −4.82843 | −0.227362 | ||||||||
\(452\) | 72.6274 | 3.41611 | ||||||||
\(453\) | 16.4853 | 0.774546 | ||||||||
\(454\) | 33.7990 | 1.58627 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −30.1421 | −1.41153 | ||||||||
\(457\) | 23.3137 | 1.09057 | 0.545285 | − | 0.838251i | \(-0.316422\pi\) | ||||
0.545285 | + | 0.838251i | \(0.316422\pi\) | |||||||
\(458\) | −4.82843 | −0.225618 | ||||||||
\(459\) | 1.17157 | 0.0546843 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 0.142136 | 0.00661992 | 0.00330996 | − | 0.999995i | \(-0.498946\pi\) | ||||
0.00330996 | + | 0.999995i | \(0.498946\pi\) | |||||||
\(462\) | 2.00000 | 0.0930484 | ||||||||
\(463\) | −4.97056 | −0.231002 | −0.115501 | − | 0.993307i | \(-0.536847\pi\) | ||||
−0.115501 | + | 0.993307i | \(0.536847\pi\) | |||||||
\(464\) | −14.4853 | −0.672462 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 45.4558 | 2.10570 | ||||||||
\(467\) | 22.6274 | 1.04707 | 0.523536 | − | 0.852004i | \(-0.324613\pi\) | ||||
0.523536 | + | 0.852004i | \(0.324613\pi\) | |||||||
\(468\) | 21.6569 | 1.00109 | ||||||||
\(469\) | −4.68629 | −0.216393 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −18.0000 | −0.829396 | ||||||||
\(472\) | −17.6569 | −0.812723 | ||||||||
\(473\) | −8.82843 | −0.405932 | ||||||||
\(474\) | 20.4853 | 0.940920 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −3.71573 | −0.170310 | ||||||||
\(477\) | −9.31371 | −0.426445 | ||||||||
\(478\) | 42.6274 | 1.94973 | ||||||||
\(479\) | 36.9706 | 1.68923 | 0.844614 | − | 0.535376i | \(-0.179830\pi\) | ||||
0.844614 | + | 0.535376i | \(0.179830\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −65.9411 | −3.00666 | ||||||||
\(482\) | −29.7990 | −1.35731 | ||||||||
\(483\) | −3.31371 | −0.150779 | ||||||||
\(484\) | 3.82843 | 0.174019 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 2.41421 | 0.109511 | ||||||||
\(487\) | 12.9706 | 0.587752 | 0.293876 | − | 0.955844i | \(-0.405055\pi\) | ||||
0.293876 | + | 0.955844i | \(0.405055\pi\) | |||||||
\(488\) | −51.4558 | −2.32930 | ||||||||
\(489\) | 7.31371 | 0.330737 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 14.3431 | 0.647297 | 0.323649 | − | 0.946177i | \(-0.395090\pi\) | ||||
0.323649 | + | 0.946177i | \(0.395090\pi\) | |||||||
\(492\) | 18.4853 | 0.833381 | ||||||||
\(493\) | −5.65685 | −0.254772 | ||||||||
\(494\) | −93.2548 | −4.19573 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −1.94113 | −0.0870714 | ||||||||
\(498\) | 24.1421 | 1.08183 | ||||||||
\(499\) | −22.3431 | −1.00022 | −0.500108 | − | 0.865963i | \(-0.666706\pi\) | ||||
−0.500108 | + | 0.865963i | \(0.666706\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 13.3137 | 0.594813 | ||||||||
\(502\) | 50.6274 | 2.25961 | ||||||||
\(503\) | −17.3137 | −0.771980 | −0.385990 | − | 0.922503i | \(-0.626140\pi\) | ||||
−0.385990 | + | 0.922503i | \(0.626140\pi\) | |||||||
\(504\) | −3.65685 | −0.162889 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −9.65685 | −0.429300 | ||||||||
\(507\) | 19.0000 | 0.843820 | ||||||||
\(508\) | 55.4558 | 2.46046 | ||||||||
\(509\) | 18.6863 | 0.828255 | 0.414128 | − | 0.910219i | \(-0.364087\pi\) | ||||
0.414128 | + | 0.910219i | \(0.364087\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 9.37258 | 0.414619 | ||||||||
\(512\) | −31.2426 | −1.38074 | ||||||||
\(513\) | −6.82843 | −0.301482 | ||||||||
\(514\) | 39.4558 | 1.74032 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 33.7990 | 1.48792 | ||||||||
\(517\) | −4.00000 | −0.175920 | ||||||||
\(518\) | 23.3137 | 1.02435 | ||||||||
\(519\) | −2.82843 | −0.124154 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −32.6274 | −1.42943 | −0.714717 | − | 0.699414i | \(-0.753444\pi\) | ||||
−0.714717 | + | 0.699414i | \(0.753444\pi\) | |||||||
\(522\) | −11.6569 | −0.510207 | ||||||||
\(523\) | 9.51472 | 0.416050 | 0.208025 | − | 0.978124i | \(-0.433297\pi\) | ||||
0.208025 | + | 0.978124i | \(0.433297\pi\) | |||||||
\(524\) | 12.6863 | 0.554203 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −43.4558 | −1.89476 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | −3.00000 | −0.130558 | ||||||||
\(529\) | −7.00000 | −0.304348 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −4.00000 | −0.173585 | ||||||||
\(532\) | 21.6569 | 0.938944 | ||||||||
\(533\) | 27.3137 | 1.18309 | ||||||||
\(534\) | 8.82843 | 0.382043 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 24.9706 | 1.07856 | ||||||||
\(537\) | −17.6569 | −0.761950 | ||||||||
\(538\) | 49.7990 | 2.14699 | ||||||||
\(539\) | 6.31371 | 0.271951 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 17.3137 | 0.744374 | 0.372187 | − | 0.928158i | \(-0.378608\pi\) | ||||
0.372187 | + | 0.928158i | \(0.378608\pi\) | |||||||
\(542\) | −28.4853 | −1.22355 | ||||||||
\(543\) | −14.0000 | −0.600798 | ||||||||
\(544\) | −1.85786 | −0.0796553 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −11.3137 | −0.484182 | ||||||||
\(547\) | 8.14214 | 0.348133 | 0.174066 | − | 0.984734i | \(-0.444309\pi\) | ||||
0.174066 | + | 0.984734i | \(0.444309\pi\) | |||||||
\(548\) | 50.9706 | 2.17735 | ||||||||
\(549\) | −11.6569 | −0.497502 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 32.9706 | 1.40459 | ||||||||
\(552\) | 17.6569 | 0.751526 | ||||||||
\(553\) | −7.02944 | −0.298922 | ||||||||
\(554\) | 5.65685 | 0.240337 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 1.85786 | 0.0787910 | ||||||||
\(557\) | −5.17157 | −0.219127 | −0.109563 | − | 0.993980i | \(-0.534945\pi\) | ||||
−0.109563 | + | 0.993980i | \(0.534945\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 49.9411 | 2.11228 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −1.17157 | −0.0494638 | ||||||||
\(562\) | −26.9706 | −1.13768 | ||||||||
\(563\) | −31.6569 | −1.33418 | −0.667089 | − | 0.744978i | \(-0.732460\pi\) | ||||
−0.667089 | + | 0.744978i | \(0.732460\pi\) | |||||||
\(564\) | 15.3137 | 0.644823 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 21.3137 | 0.895882 | ||||||||
\(567\) | −0.828427 | −0.0347907 | ||||||||
\(568\) | 10.3431 | 0.433989 | ||||||||
\(569\) | −35.4558 | −1.48639 | −0.743193 | − | 0.669077i | \(-0.766690\pi\) | ||||
−0.743193 | + | 0.669077i | \(0.766690\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −16.4853 | −0.689888 | −0.344944 | − | 0.938623i | \(-0.612102\pi\) | ||||
−0.344944 | + | 0.938623i | \(0.612102\pi\) | |||||||
\(572\) | −21.6569 | −0.905519 | ||||||||
\(573\) | 5.65685 | 0.236318 | ||||||||
\(574\) | −9.65685 | −0.403069 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −9.82843 | −0.409518 | ||||||||
\(577\) | −14.0000 | −0.582828 | −0.291414 | − | 0.956597i | \(-0.594126\pi\) | ||||
−0.291414 | + | 0.956597i | \(0.594126\pi\) | |||||||
\(578\) | −37.7279 | −1.56927 | ||||||||
\(579\) | −13.6569 | −0.567559 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −8.28427 | −0.343689 | ||||||||
\(582\) | −28.1421 | −1.16653 | ||||||||
\(583\) | 9.31371 | 0.385734 | ||||||||
\(584\) | −49.9411 | −2.06658 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 16.4853 | 0.681001 | ||||||||
\(587\) | −14.6274 | −0.603738 | −0.301869 | − | 0.953349i | \(-0.597611\pi\) | ||||
−0.301869 | + | 0.953349i | \(0.597611\pi\) | |||||||
\(588\) | −24.1716 | −0.996819 | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 8.48528 | 0.349038 | ||||||||
\(592\) | −34.9706 | −1.43728 | ||||||||
\(593\) | 22.8284 | 0.937451 | 0.468726 | − | 0.883344i | \(-0.344713\pi\) | ||||
0.468726 | + | 0.883344i | \(0.344713\pi\) | |||||||
\(594\) | −2.41421 | −0.0990564 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 5.79899 | 0.237536 | ||||||||
\(597\) | −21.6569 | −0.886356 | ||||||||
\(598\) | 54.6274 | 2.23388 | ||||||||
\(599\) | 27.3137 | 1.11601 | 0.558004 | − | 0.829838i | \(-0.311567\pi\) | ||||
0.558004 | + | 0.829838i | \(0.311567\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −5.31371 | −0.216751 | −0.108375 | − | 0.994110i | \(-0.534565\pi\) | ||||
−0.108375 | + | 0.994110i | \(0.534565\pi\) | |||||||
\(602\) | −17.6569 | −0.719640 | ||||||||
\(603\) | 5.65685 | 0.230365 | ||||||||
\(604\) | 63.1127 | 2.56802 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −2.00000 | −0.0812444 | ||||||||
\(607\) | −1.51472 | −0.0614805 | −0.0307403 | − | 0.999527i | \(-0.509786\pi\) | ||||
−0.0307403 | + | 0.999527i | \(0.509786\pi\) | |||||||
\(608\) | 10.8284 | 0.439151 | ||||||||
\(609\) | 4.00000 | 0.162088 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 22.6274 | 0.915407 | ||||||||
\(612\) | 4.48528 | 0.181307 | ||||||||
\(613\) | 45.9411 | 1.85554 | 0.927772 | − | 0.373147i | \(-0.121721\pi\) | ||||
0.927772 | + | 0.373147i | \(0.121721\pi\) | |||||||
\(614\) | 7.65685 | 0.309005 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 3.65685 | 0.147339 | ||||||||
\(617\) | −0.343146 | −0.0138145 | −0.00690726 | − | 0.999976i | \(-0.502199\pi\) | ||||
−0.00690726 | + | 0.999976i | \(0.502199\pi\) | |||||||
\(618\) | 8.00000 | 0.321807 | ||||||||
\(619\) | −14.3431 | −0.576500 | −0.288250 | − | 0.957555i | \(-0.593073\pi\) | ||||
−0.288250 | + | 0.957555i | \(0.593073\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 4.00000 | 0.160514 | ||||||||
\(622\) | −8.00000 | −0.320771 | ||||||||
\(623\) | −3.02944 | −0.121372 | ||||||||
\(624\) | 16.9706 | 0.679366 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −37.7990 | −1.51075 | ||||||||
\(627\) | 6.82843 | 0.272701 | ||||||||
\(628\) | −68.9117 | −2.74988 | ||||||||
\(629\) | −13.6569 | −0.544534 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 45.6569 | 1.81757 | 0.908785 | − | 0.417264i | \(-0.137011\pi\) | ||||
0.908785 | + | 0.417264i | \(0.137011\pi\) | |||||||
\(632\) | 37.4558 | 1.48991 | ||||||||
\(633\) | 1.17157 | 0.0465658 | ||||||||
\(634\) | 63.4558 | 2.52015 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −35.6569 | −1.41389 | ||||||||
\(637\) | −35.7157 | −1.41511 | ||||||||
\(638\) | 11.6569 | 0.461499 | ||||||||
\(639\) | 2.34315 | 0.0926934 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 6.97056 | 0.275321 | 0.137660 | − | 0.990479i | \(-0.456042\pi\) | ||||
0.137660 | + | 0.990479i | \(0.456042\pi\) | |||||||
\(642\) | −41.7990 | −1.64967 | ||||||||
\(643\) | −37.9411 | −1.49625 | −0.748126 | − | 0.663557i | \(-0.769046\pi\) | ||||
−0.748126 | + | 0.663557i | \(0.769046\pi\) | |||||||
\(644\) | −12.6863 | −0.499910 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −19.3137 | −0.759888 | ||||||||
\(647\) | −4.68629 | −0.184237 | −0.0921186 | − | 0.995748i | \(-0.529364\pi\) | ||||
−0.0921186 | + | 0.995748i | \(0.529364\pi\) | |||||||
\(648\) | 4.41421 | 0.173407 | ||||||||
\(649\) | 4.00000 | 0.157014 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 28.0000 | 1.09656 | ||||||||
\(653\) | −6.97056 | −0.272779 | −0.136390 | − | 0.990655i | \(-0.543550\pi\) | ||||
−0.136390 | + | 0.990655i | \(0.543550\pi\) | |||||||
\(654\) | 41.7990 | 1.63447 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 14.4853 | 0.565555 | ||||||||
\(657\) | −11.3137 | −0.441390 | ||||||||
\(658\) | −8.00000 | −0.311872 | ||||||||
\(659\) | −15.3137 | −0.596537 | −0.298269 | − | 0.954482i | \(-0.596409\pi\) | ||||
−0.298269 | + | 0.954482i | \(0.596409\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 9.31371 | 0.362261 | 0.181131 | − | 0.983459i | \(-0.442024\pi\) | ||||
0.181131 | + | 0.983459i | \(0.442024\pi\) | |||||||
\(662\) | 15.3137 | 0.595184 | ||||||||
\(663\) | 6.62742 | 0.257388 | ||||||||
\(664\) | 44.1421 | 1.71305 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −28.1421 | −1.09049 | ||||||||
\(667\) | −19.3137 | −0.747830 | ||||||||
\(668\) | 50.9706 | 1.97211 | ||||||||
\(669\) | 6.34315 | 0.245240 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 11.6569 | 0.450008 | ||||||||
\(672\) | 1.31371 | 0.0506774 | ||||||||
\(673\) | −18.3431 | −0.707076 | −0.353538 | − | 0.935420i | \(-0.615022\pi\) | ||||
−0.353538 | + | 0.935420i | \(0.615022\pi\) | |||||||
\(674\) | −8.00000 | −0.308148 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 72.7401 | 2.79770 | ||||||||
\(677\) | −29.4558 | −1.13208 | −0.566040 | − | 0.824378i | \(-0.691525\pi\) | ||||
−0.566040 | + | 0.824378i | \(0.691525\pi\) | |||||||
\(678\) | 45.7990 | 1.75890 | ||||||||
\(679\) | 9.65685 | 0.370596 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 14.0000 | 0.536481 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −24.0000 | −0.918334 | −0.459167 | − | 0.888350i | \(-0.651852\pi\) | ||||
−0.459167 | + | 0.888350i | \(0.651852\pi\) | |||||||
\(684\) | −26.1421 | −0.999570 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 26.6274 | 1.01664 | ||||||||
\(687\) | −2.00000 | −0.0763048 | ||||||||
\(688\) | 26.4853 | 1.00974 | ||||||||
\(689\) | −52.6863 | −2.00719 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 20.0000 | 0.760836 | 0.380418 | − | 0.924815i | \(-0.375780\pi\) | ||||
0.380418 | + | 0.924815i | \(0.375780\pi\) | |||||||
\(692\) | −10.8284 | −0.411635 | ||||||||
\(693\) | 0.828427 | 0.0314693 | ||||||||
\(694\) | 70.7696 | 2.68638 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −21.3137 | −0.807894 | ||||||||
\(697\) | 5.65685 | 0.214269 | ||||||||
\(698\) | 26.4853 | 1.00248 | ||||||||
\(699\) | 18.8284 | 0.712157 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 36.1421 | 1.36507 | 0.682535 | − | 0.730853i | \(-0.260878\pi\) | ||||
0.682535 | + | 0.730853i | \(0.260878\pi\) | |||||||
\(702\) | 13.6569 | 0.515445 | ||||||||
\(703\) | 79.5980 | 3.00209 | ||||||||
\(704\) | 9.82843 | 0.370423 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −62.7696 | −2.36236 | ||||||||
\(707\) | 0.686292 | 0.0258106 | ||||||||
\(708\) | −15.3137 | −0.575524 | ||||||||
\(709\) | 6.68629 | 0.251109 | 0.125554 | − | 0.992087i | \(-0.459929\pi\) | ||||
0.125554 | + | 0.992087i | \(0.459929\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 8.48528 | 0.318223 | ||||||||
\(712\) | 16.1421 | 0.604952 | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | −2.34315 | −0.0876900 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −67.5980 | −2.52626 | ||||||||
\(717\) | 17.6569 | 0.659407 | ||||||||
\(718\) | 28.9706 | 1.08117 | ||||||||
\(719\) | −47.5980 | −1.77511 | −0.887553 | − | 0.460706i | \(-0.847596\pi\) | ||||
−0.887553 | + | 0.460706i | \(0.847596\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −2.74517 | −0.102235 | ||||||||
\(722\) | 66.6985 | 2.48226 | ||||||||
\(723\) | −12.3431 | −0.459047 | ||||||||
\(724\) | −53.5980 | −1.99195 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 2.41421 | 0.0895999 | ||||||||
\(727\) | −33.9411 | −1.25881 | −0.629403 | − | 0.777079i | \(-0.716701\pi\) | ||||
−0.629403 | + | 0.777079i | \(0.716701\pi\) | |||||||
\(728\) | −20.6863 | −0.766685 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 10.3431 | 0.382555 | ||||||||
\(732\) | −44.6274 | −1.64948 | ||||||||
\(733\) | 6.34315 | 0.234289 | 0.117145 | − | 0.993115i | \(-0.462626\pi\) | ||||
0.117145 | + | 0.993115i | \(0.462626\pi\) | |||||||
\(734\) | −23.3137 | −0.860525 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −6.34315 | −0.233811 | ||||||||
\(737\) | −5.65685 | −0.208373 | ||||||||
\(738\) | 11.6569 | 0.429095 | ||||||||
\(739\) | −15.1127 | −0.555930 | −0.277965 | − | 0.960591i | \(-0.589660\pi\) | ||||
−0.277965 | + | 0.960591i | \(0.589660\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −38.6274 | −1.41901 | ||||||||
\(742\) | 18.6274 | 0.683834 | ||||||||
\(743\) | −36.3431 | −1.33330 | −0.666650 | − | 0.745371i | \(-0.732273\pi\) | ||||
−0.666650 | + | 0.745371i | \(0.732273\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −25.6569 | −0.939364 | ||||||||
\(747\) | 10.0000 | 0.365881 | ||||||||
\(748\) | −4.48528 | −0.163998 | ||||||||
\(749\) | 14.3431 | 0.524087 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 20.2843 | 0.740184 | 0.370092 | − | 0.928995i | \(-0.379326\pi\) | ||||
0.370092 | + | 0.928995i | \(0.379326\pi\) | |||||||
\(752\) | 12.0000 | 0.437595 | ||||||||
\(753\) | 20.9706 | 0.764210 | ||||||||
\(754\) | −65.9411 | −2.40143 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −3.17157 | −0.115349 | ||||||||
\(757\) | 36.6274 | 1.33125 | 0.665623 | − | 0.746288i | \(-0.268166\pi\) | ||||
0.665623 | + | 0.746288i | \(0.268166\pi\) | |||||||
\(758\) | −56.2843 | −2.04434 | ||||||||
\(759\) | −4.00000 | −0.145191 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −28.8284 | −1.04503 | −0.522515 | − | 0.852630i | \(-0.675006\pi\) | ||||
−0.522515 | + | 0.852630i | \(0.675006\pi\) | |||||||
\(762\) | 34.9706 | 1.26685 | ||||||||
\(763\) | −14.3431 | −0.519257 | ||||||||
\(764\) | 21.6569 | 0.783517 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 19.3137 | 0.697833 | ||||||||
\(767\) | −22.6274 | −0.817029 | ||||||||
\(768\) | −29.9706 | −1.08147 | ||||||||
\(769\) | 10.6863 | 0.385358 | 0.192679 | − | 0.981262i | \(-0.438282\pi\) | ||||
0.192679 | + | 0.981262i | \(0.438282\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 16.3431 | 0.588584 | ||||||||
\(772\) | −52.2843 | −1.88175 | ||||||||
\(773\) | −3.65685 | −0.131528 | −0.0657640 | − | 0.997835i | \(-0.520948\pi\) | ||||
−0.0657640 | + | 0.997835i | \(0.520948\pi\) | |||||||
\(774\) | 21.3137 | 0.766105 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −51.4558 | −1.84716 | ||||||||
\(777\) | 9.65685 | 0.346438 | ||||||||
\(778\) | −57.1127 | −2.04759 | ||||||||
\(779\) | −32.9706 | −1.18129 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −2.34315 | −0.0838443 | ||||||||
\(782\) | 11.3137 | 0.404577 | ||||||||
\(783\) | −4.82843 | −0.172554 | ||||||||
\(784\) | −18.9411 | −0.676469 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 8.00000 | 0.285351 | ||||||||
\(787\) | 20.1421 | 0.717990 | 0.358995 | − | 0.933340i | \(-0.383120\pi\) | ||||
0.358995 | + | 0.933340i | \(0.383120\pi\) | |||||||
\(788\) | 32.4853 | 1.15724 | ||||||||
\(789\) | −18.0000 | −0.640817 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −15.7157 | −0.558787 | ||||||||
\(792\) | −4.41421 | −0.156852 | ||||||||
\(793\) | −65.9411 | −2.34164 | ||||||||
\(794\) | 36.1421 | 1.28264 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −82.9117 | −2.93873 | ||||||||
\(797\) | −34.9706 | −1.23872 | −0.619360 | − | 0.785107i | \(-0.712608\pi\) | ||||
−0.619360 | + | 0.785107i | \(0.712608\pi\) | |||||||
\(798\) | 13.6569 | 0.483447 | ||||||||
\(799\) | 4.68629 | 0.165789 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 3.65685 | 0.129209 | ||||||||
\(802\) | −16.1421 | −0.569999 | ||||||||
\(803\) | 11.3137 | 0.399252 | ||||||||
\(804\) | 21.6569 | 0.763778 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 20.6274 | 0.726119 | ||||||||
\(808\) | −3.65685 | −0.128648 | ||||||||
\(809\) | 28.4264 | 0.999419 | 0.499710 | − | 0.866193i | \(-0.333440\pi\) | ||||
0.499710 | + | 0.866193i | \(0.333440\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 0.485281 | 0.0170405 | 0.00852027 | − | 0.999964i | \(-0.497288\pi\) | ||||
0.00852027 | + | 0.999964i | \(0.497288\pi\) | |||||||
\(812\) | 15.3137 | 0.537406 | ||||||||
\(813\) | −11.7990 | −0.413809 | ||||||||
\(814\) | 28.1421 | 0.986381 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 3.51472 | 0.123040 | ||||||||
\(817\) | −60.2843 | −2.10908 | ||||||||
\(818\) | −47.4558 | −1.65925 | ||||||||
\(819\) | −4.68629 | −0.163752 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −12.8284 | −0.447715 | −0.223858 | − | 0.974622i | \(-0.571865\pi\) | ||||
−0.223858 | + | 0.974622i | \(0.571865\pi\) | |||||||
\(822\) | 32.1421 | 1.12109 | ||||||||
\(823\) | −16.0000 | −0.557725 | −0.278862 | − | 0.960331i | \(-0.589957\pi\) | ||||
−0.278862 | + | 0.960331i | \(0.589957\pi\) | |||||||
\(824\) | 14.6274 | 0.509570 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 8.00000 | 0.278356 | ||||||||
\(827\) | −41.3137 | −1.43662 | −0.718309 | − | 0.695724i | \(-0.755084\pi\) | ||||
−0.718309 | + | 0.695724i | \(0.755084\pi\) | |||||||
\(828\) | 15.3137 | 0.532188 | ||||||||
\(829\) | −38.0000 | −1.31979 | −0.659897 | − | 0.751356i | \(-0.729400\pi\) | ||||
−0.659897 | + | 0.751356i | \(0.729400\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 2.34315 | 0.0812828 | ||||||||
\(832\) | −55.5980 | −1.92751 | ||||||||
\(833\) | −7.39697 | −0.256290 | ||||||||
\(834\) | 1.17157 | 0.0405683 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 26.1421 | 0.904145 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −89.2548 | −3.08326 | ||||||||
\(839\) | −22.6274 | −0.781185 | −0.390593 | − | 0.920564i | \(-0.627730\pi\) | ||||
−0.390593 | + | 0.920564i | \(0.627730\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −5.68629 | −0.196079 | ||||||||
\(842\) | −14.4853 | −0.499196 | ||||||||
\(843\) | −11.1716 | −0.384769 | ||||||||
\(844\) | 4.48528 | 0.154390 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 9.65685 | 0.332009 | ||||||||
\(847\) | −0.828427 | −0.0284651 | ||||||||
\(848\) | −27.9411 | −0.959502 | ||||||||
\(849\) | 8.82843 | 0.302991 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −46.6274 | −1.59837 | ||||||||
\(852\) | 8.97056 | 0.307326 | ||||||||
\(853\) | 8.68629 | 0.297413 | 0.148706 | − | 0.988881i | \(-0.452489\pi\) | ||||
0.148706 | + | 0.988881i | \(0.452489\pi\) | |||||||
\(854\) | 23.3137 | 0.797779 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −76.4264 | −2.61220 | ||||||||
\(857\) | 28.4853 | 0.973039 | 0.486519 | − | 0.873670i | \(-0.338266\pi\) | ||||
0.486519 | + | 0.873670i | \(0.338266\pi\) | |||||||
\(858\) | −13.6569 | −0.466237 | ||||||||
\(859\) | −52.9706 | −1.80733 | −0.903666 | − | 0.428238i | \(-0.859135\pi\) | ||||
−0.903666 | + | 0.428238i | \(0.859135\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −4.00000 | −0.136320 | ||||||||
\(862\) | 52.2843 | 1.78081 | ||||||||
\(863\) | 20.6863 | 0.704170 | 0.352085 | − | 0.935968i | \(-0.385473\pi\) | ||||
0.352085 | + | 0.935968i | \(0.385473\pi\) | |||||||
\(864\) | −1.58579 | −0.0539496 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 37.7990 | 1.28446 | ||||||||
\(867\) | −15.6274 | −0.530735 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −8.48528 | −0.287843 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 32.0000 | 1.08428 | ||||||||
\(872\) | 76.4264 | 2.58812 | ||||||||
\(873\) | −11.6569 | −0.394525 | ||||||||
\(874\) | −65.9411 | −2.23049 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −43.3137 | −1.46343 | ||||||||
\(877\) | −2.62742 | −0.0887216 | −0.0443608 | − | 0.999016i | \(-0.514125\pi\) | ||||
−0.0443608 | + | 0.999016i | \(0.514125\pi\) | |||||||
\(878\) | −49.4558 | −1.66905 | ||||||||
\(879\) | 6.82843 | 0.230317 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −46.9706 | −1.58248 | −0.791239 | − | 0.611507i | \(-0.790564\pi\) | ||||
−0.791239 | + | 0.611507i | \(0.790564\pi\) | |||||||
\(882\) | −15.2426 | −0.513246 | ||||||||
\(883\) | 5.37258 | 0.180802 | 0.0904009 | − | 0.995905i | \(-0.471185\pi\) | ||||
0.0904009 | + | 0.995905i | \(0.471185\pi\) | |||||||
\(884\) | 25.3726 | 0.853372 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −28.9706 | −0.973285 | ||||||||
\(887\) | 15.6569 | 0.525706 | 0.262853 | − | 0.964836i | \(-0.415337\pi\) | ||||
0.262853 | + | 0.964836i | \(0.415337\pi\) | |||||||
\(888\) | −51.4558 | −1.72675 | ||||||||
\(889\) | −12.0000 | −0.402467 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −1.00000 | −0.0335013 | ||||||||
\(892\) | 24.2843 | 0.813098 | ||||||||
\(893\) | −27.3137 | −0.914018 | ||||||||
\(894\) | 3.65685 | 0.122304 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 17.0294 | 0.568914 | ||||||||
\(897\) | 22.6274 | 0.755507 | ||||||||
\(898\) | 74.7696 | 2.49509 | ||||||||
\(899\) | 0 | 0 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −10.9117 | −0.363521 | ||||||||
\(902\) | −11.6569 | −0.388131 | ||||||||
\(903\) | −7.31371 | −0.243385 | ||||||||
\(904\) | 83.7401 | 2.78515 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 39.7990 | 1.32223 | ||||||||
\(907\) | −40.9706 | −1.36041 | −0.680203 | − | 0.733024i | \(-0.738108\pi\) | ||||
−0.680203 | + | 0.733024i | \(0.738108\pi\) | |||||||
\(908\) | 53.5980 | 1.77871 | ||||||||
\(909\) | −0.828427 | −0.0274772 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −48.9706 | −1.62247 | −0.811234 | − | 0.584722i | \(-0.801203\pi\) | ||||
−0.811234 | + | 0.584722i | \(0.801203\pi\) | |||||||
\(912\) | −20.4853 | −0.678335 | ||||||||
\(913\) | −10.0000 | −0.330952 | ||||||||
\(914\) | 56.2843 | 1.86172 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −7.65685 | −0.252990 | ||||||||
\(917\) | −2.74517 | −0.0906534 | ||||||||
\(918\) | 2.82843 | 0.0933520 | ||||||||
\(919\) | 11.5147 | 0.379836 | 0.189918 | − | 0.981800i | \(-0.439178\pi\) | ||||
0.189918 | + | 0.981800i | \(0.439178\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 3.17157 | 0.104507 | ||||||||
\(922\) | 0.343146 | 0.0113009 | ||||||||
\(923\) | 13.2548 | 0.436288 | ||||||||
\(924\) | 3.17157 | 0.104337 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −12.0000 | −0.394344 | ||||||||
\(927\) | 3.31371 | 0.108836 | ||||||||
\(928\) | 7.65685 | 0.251349 | ||||||||
\(929\) | −45.5980 | −1.49602 | −0.748011 | − | 0.663687i | \(-0.768991\pi\) | ||||
−0.748011 | + | 0.663687i | \(0.768991\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 43.1127 | 1.41296 | ||||||||
\(932\) | 72.0833 | 2.36117 | ||||||||
\(933\) | −3.31371 | −0.108486 | ||||||||
\(934\) | 54.6274 | 1.78746 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 24.9706 | 0.816188 | ||||||||
\(937\) | −11.0294 | −0.360316 | −0.180158 | − | 0.983638i | \(-0.557661\pi\) | ||||
−0.180158 | + | 0.983638i | \(0.557661\pi\) | |||||||
\(938\) | −11.3137 | −0.369406 | ||||||||
\(939\) | −15.6569 | −0.510942 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −34.7696 | −1.13346 | −0.566728 | − | 0.823905i | \(-0.691791\pi\) | ||||
−0.566728 | + | 0.823905i | \(0.691791\pi\) | |||||||
\(942\) | −43.4558 | −1.41587 | ||||||||
\(943\) | 19.3137 | 0.628941 | ||||||||
\(944\) | −12.0000 | −0.390567 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −21.3137 | −0.692968 | ||||||||
\(947\) | −6.62742 | −0.215362 | −0.107681 | − | 0.994185i | \(-0.534343\pi\) | ||||
−0.107681 | + | 0.994185i | \(0.534343\pi\) | |||||||
\(948\) | 32.4853 | 1.05507 | ||||||||
\(949\) | −64.0000 | −2.07753 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 26.2843 | 0.852326 | ||||||||
\(952\) | −4.28427 | −0.138854 | ||||||||
\(953\) | 11.7990 | 0.382207 | 0.191103 | − | 0.981570i | \(-0.438793\pi\) | ||||
0.191103 | + | 0.981570i | \(0.438793\pi\) | |||||||
\(954\) | −22.4853 | −0.727988 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 67.5980 | 2.18627 | ||||||||
\(957\) | 4.82843 | 0.156081 | ||||||||
\(958\) | 89.2548 | 2.88369 | ||||||||
\(959\) | −11.0294 | −0.356159 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −31.0000 | −1.00000 | ||||||||
\(962\) | −159.196 | −5.13268 | ||||||||
\(963\) | −17.3137 | −0.557926 | ||||||||
\(964\) | −47.2548 | −1.52198 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −8.00000 | −0.257396 | ||||||||
\(967\) | −11.4558 | −0.368395 | −0.184198 | − | 0.982889i | \(-0.558969\pi\) | ||||
−0.184198 | + | 0.982889i | \(0.558969\pi\) | |||||||
\(968\) | 4.41421 | 0.141878 | ||||||||
\(969\) | −8.00000 | −0.256997 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −34.6274 | −1.11125 | −0.555623 | − | 0.831434i | \(-0.687520\pi\) | ||||
−0.555623 | + | 0.831434i | \(0.687520\pi\) | |||||||
\(972\) | 3.82843 | 0.122797 | ||||||||
\(973\) | −0.402020 | −0.0128882 | ||||||||
\(974\) | 31.3137 | 1.00336 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −34.9706 | −1.11938 | ||||||||
\(977\) | −2.68629 | −0.0859421 | −0.0429710 | − | 0.999076i | \(-0.513682\pi\) | ||||
−0.0429710 | + | 0.999076i | \(0.513682\pi\) | |||||||
\(978\) | 17.6569 | 0.564604 | ||||||||
\(979\) | −3.65685 | −0.116874 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 17.3137 | 0.552784 | ||||||||
\(982\) | 34.6274 | 1.10501 | ||||||||
\(983\) | 30.6274 | 0.976863 | 0.488431 | − | 0.872602i | \(-0.337569\pi\) | ||||
0.488431 | + | 0.872602i | \(0.337569\pi\) | |||||||
\(984\) | 21.3137 | 0.679456 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −13.6569 | −0.434923 | ||||||||
\(987\) | −3.31371 | −0.105477 | ||||||||
\(988\) | −147.882 | −4.70476 | ||||||||
\(989\) | 35.3137 | 1.12291 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −30.6274 | −0.972912 | −0.486456 | − | 0.873705i | \(-0.661711\pi\) | ||||
−0.486456 | + | 0.873705i | \(0.661711\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 6.34315 | 0.201294 | ||||||||
\(994\) | −4.68629 | −0.148640 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 38.2843 | 1.21308 | ||||||||
\(997\) | 39.3137 | 1.24508 | 0.622539 | − | 0.782589i | \(-0.286101\pi\) | ||||
0.622539 | + | 0.782589i | \(0.286101\pi\) | |||||||
\(998\) | −53.9411 | −1.70748 | ||||||||
\(999\) | −11.6569 | −0.368807 |
(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 | 825.2.a.g.1.2 | 2 | ||
3.2 | odd | 2 | 2475.2.a.m.1.1 | 2 | |||
5.2 | odd | 4 | 825.2.c.e.199.4 | 4 | |||
5.3 | odd | 4 | 825.2.c.e.199.1 | 4 | |||
5.4 | even | 2 | 165.2.a.a.1.1 | ✓ | 2 | ||
11.10 | odd | 2 | 9075.2.a.v.1.1 | 2 | |||
15.2 | even | 4 | 2475.2.c.m.199.1 | 4 | |||
15.8 | even | 4 | 2475.2.c.m.199.4 | 4 | |||
15.14 | odd | 2 | 495.2.a.d.1.2 | 2 | |||
20.19 | odd | 2 | 2640.2.a.bb.1.1 | 2 | |||
35.34 | odd | 2 | 8085.2.a.ba.1.1 | 2 | |||
55.54 | odd | 2 | 1815.2.a.k.1.2 | 2 | |||
60.59 | even | 2 | 7920.2.a.cg.1.1 | 2 | |||
165.164 | even | 2 | 5445.2.a.m.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
165.2.a.a.1.1 | ✓ | 2 | 5.4 | even | 2 | ||
495.2.a.d.1.2 | 2 | 15.14 | odd | 2 | |||
825.2.a.g.1.2 | 2 | 1.1 | even | 1 | trivial | ||
825.2.c.e.199.1 | 4 | 5.3 | odd | 4 | |||
825.2.c.e.199.4 | 4 | 5.2 | odd | 4 | |||
1815.2.a.k.1.2 | 2 | 55.54 | odd | 2 | |||
2475.2.a.m.1.1 | 2 | 3.2 | odd | 2 | |||
2475.2.c.m.199.1 | 4 | 15.2 | even | 4 | |||
2475.2.c.m.199.4 | 4 | 15.8 | even | 4 | |||
2640.2.a.bb.1.1 | 2 | 20.19 | odd | 2 | |||
5445.2.a.m.1.1 | 2 | 165.164 | even | 2 | |||
7920.2.a.cg.1.1 | 2 | 60.59 | even | 2 | |||
8085.2.a.ba.1.1 | 2 | 35.34 | odd | 2 | |||
9075.2.a.v.1.1 | 2 | 11.10 | odd | 2 |