Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2541,2,Mod(1,2541)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2541, 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("2541.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2541 = 3 \cdot 7 \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2541.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: | \(20.2899871536\) |
Analytic rank: | \(0\) |
Dimension: | \(10\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{10} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{10} - 19x^{8} - x^{7} + 124x^{6} + 6x^{5} - 316x^{4} + 17x^{3} + 253x^{2} - 70x - 11 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 231) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.8 | ||
Root | \(-2.09767\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2541.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.09767 | 1.48327 | 0.741637 | − | 0.670801i | \(-0.234050\pi\) | ||||
0.741637 | + | 0.670801i | \(0.234050\pi\) | |||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 2.40021 | 1.20010 | ||||||||
\(5\) | 3.15947 | 1.41296 | 0.706479 | − | 0.707734i | \(-0.250283\pi\) | ||||
0.706479 | + | 0.707734i | \(0.250283\pi\) | |||||||
\(6\) | 2.09767 | 0.856369 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | 0.839503 | 0.296809 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 6.62751 | 2.09580 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | 2.40021 | 0.692880 | ||||||||
\(13\) | −2.12862 | −0.590374 | −0.295187 | − | 0.955440i | \(-0.595382\pi\) | ||||
−0.295187 | + | 0.955440i | \(0.595382\pi\) | |||||||
\(14\) | 2.09767 | 0.560625 | ||||||||
\(15\) | 3.15947 | 0.815771 | ||||||||
\(16\) | −3.03942 | −0.759855 | ||||||||
\(17\) | 4.79430 | 1.16279 | 0.581395 | − | 0.813622i | \(-0.302507\pi\) | ||||
0.581395 | + | 0.813622i | \(0.302507\pi\) | |||||||
\(18\) | 2.09767 | 0.494425 | ||||||||
\(19\) | −1.53847 | −0.352949 | −0.176475 | − | 0.984305i | \(-0.556469\pi\) | ||||
−0.176475 | + | 0.984305i | \(0.556469\pi\) | |||||||
\(20\) | 7.58338 | 1.69570 | ||||||||
\(21\) | 1.00000 | 0.218218 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 5.11509 | 1.06657 | 0.533285 | − | 0.845935i | \(-0.320957\pi\) | ||||
0.533285 | + | 0.845935i | \(0.320957\pi\) | |||||||
\(24\) | 0.839503 | 0.171363 | ||||||||
\(25\) | 4.98224 | 0.996449 | ||||||||
\(26\) | −4.46514 | −0.875687 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 2.40021 | 0.453597 | ||||||||
\(29\) | 0.958246 | 0.177942 | 0.0889709 | − | 0.996034i | \(-0.471642\pi\) | ||||
0.0889709 | + | 0.996034i | \(0.471642\pi\) | |||||||
\(30\) | 6.62751 | 1.21001 | ||||||||
\(31\) | −7.22037 | −1.29682 | −0.648409 | − | 0.761292i | \(-0.724565\pi\) | ||||
−0.648409 | + | 0.761292i | \(0.724565\pi\) | |||||||
\(32\) | −8.05469 | −1.42388 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 10.0569 | 1.72474 | ||||||||
\(35\) | 3.15947 | 0.534048 | ||||||||
\(36\) | 2.40021 | 0.400035 | ||||||||
\(37\) | 2.39901 | 0.394394 | 0.197197 | − | 0.980364i | \(-0.436816\pi\) | ||||
0.197197 | + | 0.980364i | \(0.436816\pi\) | |||||||
\(38\) | −3.22720 | −0.523521 | ||||||||
\(39\) | −2.12862 | −0.340852 | ||||||||
\(40\) | 2.65238 | 0.419378 | ||||||||
\(41\) | −0.266914 | −0.0416850 | −0.0208425 | − | 0.999783i | \(-0.506635\pi\) | ||||
−0.0208425 | + | 0.999783i | \(0.506635\pi\) | |||||||
\(42\) | 2.09767 | 0.323677 | ||||||||
\(43\) | −9.28678 | −1.41622 | −0.708110 | − | 0.706102i | \(-0.750452\pi\) | ||||
−0.708110 | + | 0.706102i | \(0.750452\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 3.15947 | 0.470986 | ||||||||
\(46\) | 10.7298 | 1.58202 | ||||||||
\(47\) | 10.3245 | 1.50599 | 0.752993 | − | 0.658029i | \(-0.228609\pi\) | ||||
0.752993 | + | 0.658029i | \(0.228609\pi\) | |||||||
\(48\) | −3.03942 | −0.438702 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 10.4511 | 1.47801 | ||||||||
\(51\) | 4.79430 | 0.671337 | ||||||||
\(52\) | −5.10914 | −0.708510 | ||||||||
\(53\) | −0.945600 | −0.129888 | −0.0649441 | − | 0.997889i | \(-0.520687\pi\) | ||||
−0.0649441 | + | 0.997889i | \(0.520687\pi\) | |||||||
\(54\) | 2.09767 | 0.285456 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0.839503 | 0.112183 | ||||||||
\(57\) | −1.53847 | −0.203775 | ||||||||
\(58\) | 2.01008 | 0.263937 | ||||||||
\(59\) | −9.55077 | −1.24340 | −0.621702 | − | 0.783254i | \(-0.713558\pi\) | ||||
−0.621702 | + | 0.783254i | \(0.713558\pi\) | |||||||
\(60\) | 7.58338 | 0.979010 | ||||||||
\(61\) | −8.55756 | −1.09568 | −0.547841 | − | 0.836582i | \(-0.684550\pi\) | ||||
−0.547841 | + | 0.836582i | \(0.684550\pi\) | |||||||
\(62\) | −15.1459 | −1.92354 | ||||||||
\(63\) | 1.00000 | 0.125988 | ||||||||
\(64\) | −10.8172 | −1.35215 | ||||||||
\(65\) | −6.72532 | −0.834173 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 13.2710 | 1.62131 | 0.810657 | − | 0.585521i | \(-0.199110\pi\) | ||||
0.810657 | + | 0.585521i | \(0.199110\pi\) | |||||||
\(68\) | 11.5073 | 1.39547 | ||||||||
\(69\) | 5.11509 | 0.615785 | ||||||||
\(70\) | 6.62751 | 0.792139 | ||||||||
\(71\) | 14.1564 | 1.68006 | 0.840030 | − | 0.542540i | \(-0.182537\pi\) | ||||
0.840030 | + | 0.542540i | \(0.182537\pi\) | |||||||
\(72\) | 0.839503 | 0.0989363 | ||||||||
\(73\) | −7.72198 | −0.903789 | −0.451895 | − | 0.892071i | \(-0.649252\pi\) | ||||
−0.451895 | + | 0.892071i | \(0.649252\pi\) | |||||||
\(74\) | 5.03232 | 0.584995 | ||||||||
\(75\) | 4.98224 | 0.575300 | ||||||||
\(76\) | −3.69265 | −0.423576 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −4.46514 | −0.505578 | ||||||||
\(79\) | −9.31226 | −1.04771 | −0.523856 | − | 0.851807i | \(-0.675507\pi\) | ||||
−0.523856 | + | 0.851807i | \(0.675507\pi\) | |||||||
\(80\) | −9.60295 | −1.07364 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −0.559897 | −0.0618302 | ||||||||
\(83\) | 16.8536 | 1.84992 | 0.924961 | − | 0.380061i | \(-0.124097\pi\) | ||||
0.924961 | + | 0.380061i | \(0.124097\pi\) | |||||||
\(84\) | 2.40021 | 0.261884 | ||||||||
\(85\) | 15.1475 | 1.64297 | ||||||||
\(86\) | −19.4806 | −2.10064 | ||||||||
\(87\) | 0.958246 | 0.102735 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −11.2670 | −1.19430 | −0.597150 | − | 0.802130i | \(-0.703700\pi\) | ||||
−0.597150 | + | 0.802130i | \(0.703700\pi\) | |||||||
\(90\) | 6.62751 | 0.698601 | ||||||||
\(91\) | −2.12862 | −0.223140 | ||||||||
\(92\) | 12.2773 | 1.28000 | ||||||||
\(93\) | −7.22037 | −0.748718 | ||||||||
\(94\) | 21.6574 | 2.23379 | ||||||||
\(95\) | −4.86075 | −0.498702 | ||||||||
\(96\) | −8.05469 | −0.822079 | ||||||||
\(97\) | 7.08789 | 0.719666 | 0.359833 | − | 0.933017i | \(-0.382834\pi\) | ||||
0.359833 | + | 0.933017i | \(0.382834\pi\) | |||||||
\(98\) | 2.09767 | 0.211896 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 11.9584 | 1.19584 | ||||||||
\(101\) | −8.34609 | −0.830467 | −0.415234 | − | 0.909715i | \(-0.636300\pi\) | ||||
−0.415234 | + | 0.909715i | \(0.636300\pi\) | |||||||
\(102\) | 10.0569 | 0.995777 | ||||||||
\(103\) | −7.53555 | −0.742500 | −0.371250 | − | 0.928533i | \(-0.621071\pi\) | ||||
−0.371250 | + | 0.928533i | \(0.621071\pi\) | |||||||
\(104\) | −1.78698 | −0.175228 | ||||||||
\(105\) | 3.15947 | 0.308333 | ||||||||
\(106\) | −1.98355 | −0.192660 | ||||||||
\(107\) | −15.3887 | −1.48768 | −0.743841 | − | 0.668357i | \(-0.766998\pi\) | ||||
−0.743841 | + | 0.668357i | \(0.766998\pi\) | |||||||
\(108\) | 2.40021 | 0.230960 | ||||||||
\(109\) | −20.2581 | −1.94038 | −0.970188 | − | 0.242353i | \(-0.922081\pi\) | ||||
−0.970188 | + | 0.242353i | \(0.922081\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 2.39901 | 0.227704 | ||||||||
\(112\) | −3.03942 | −0.287198 | ||||||||
\(113\) | −18.1019 | −1.70288 | −0.851440 | − | 0.524452i | \(-0.824270\pi\) | ||||
−0.851440 | + | 0.524452i | \(0.824270\pi\) | |||||||
\(114\) | −3.22720 | −0.302255 | ||||||||
\(115\) | 16.1610 | 1.50702 | ||||||||
\(116\) | 2.29999 | 0.213549 | ||||||||
\(117\) | −2.12862 | −0.196791 | ||||||||
\(118\) | −20.0343 | −1.84431 | ||||||||
\(119\) | 4.79430 | 0.439493 | ||||||||
\(120\) | 2.65238 | 0.242128 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | −17.9509 | −1.62520 | ||||||||
\(123\) | −0.266914 | −0.0240668 | ||||||||
\(124\) | −17.3304 | −1.55632 | ||||||||
\(125\) | −0.0560984 | −0.00501759 | ||||||||
\(126\) | 2.09767 | 0.186875 | ||||||||
\(127\) | 15.3711 | 1.36396 | 0.681981 | − | 0.731369i | \(-0.261118\pi\) | ||||
0.681981 | + | 0.731369i | \(0.261118\pi\) | |||||||
\(128\) | −6.58156 | −0.581733 | ||||||||
\(129\) | −9.28678 | −0.817655 | ||||||||
\(130\) | −14.1075 | −1.23731 | ||||||||
\(131\) | 10.7418 | 0.938516 | 0.469258 | − | 0.883061i | \(-0.344522\pi\) | ||||
0.469258 | + | 0.883061i | \(0.344522\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1.53847 | −0.133402 | ||||||||
\(134\) | 27.8382 | 2.40485 | ||||||||
\(135\) | 3.15947 | 0.271924 | ||||||||
\(136\) | 4.02483 | 0.345126 | ||||||||
\(137\) | −4.42612 | −0.378149 | −0.189075 | − | 0.981963i | \(-0.560549\pi\) | ||||
−0.189075 | + | 0.981963i | \(0.560549\pi\) | |||||||
\(138\) | 10.7298 | 0.913378 | ||||||||
\(139\) | −4.52505 | −0.383810 | −0.191905 | − | 0.981414i | \(-0.561467\pi\) | ||||
−0.191905 | + | 0.981414i | \(0.561467\pi\) | |||||||
\(140\) | 7.58338 | 0.640913 | ||||||||
\(141\) | 10.3245 | 0.869481 | ||||||||
\(142\) | 29.6955 | 2.49199 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −3.03942 | −0.253285 | ||||||||
\(145\) | 3.02755 | 0.251424 | ||||||||
\(146\) | −16.1981 | −1.34057 | ||||||||
\(147\) | 1.00000 | 0.0824786 | ||||||||
\(148\) | 5.75812 | 0.473314 | ||||||||
\(149\) | −2.99471 | −0.245336 | −0.122668 | − | 0.992448i | \(-0.539145\pi\) | ||||
−0.122668 | + | 0.992448i | \(0.539145\pi\) | |||||||
\(150\) | 10.4511 | 0.853328 | ||||||||
\(151\) | −8.81260 | −0.717159 | −0.358579 | − | 0.933499i | \(-0.616739\pi\) | ||||
−0.358579 | + | 0.933499i | \(0.616739\pi\) | |||||||
\(152\) | −1.29155 | −0.104759 | ||||||||
\(153\) | 4.79430 | 0.387597 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −22.8125 | −1.83235 | ||||||||
\(156\) | −5.10914 | −0.409058 | ||||||||
\(157\) | 1.56655 | 0.125024 | 0.0625122 | − | 0.998044i | \(-0.480089\pi\) | ||||
0.0625122 | + | 0.998044i | \(0.480089\pi\) | |||||||
\(158\) | −19.5340 | −1.55404 | ||||||||
\(159\) | −0.945600 | −0.0749909 | ||||||||
\(160\) | −25.4486 | −2.01188 | ||||||||
\(161\) | 5.11509 | 0.403126 | ||||||||
\(162\) | 2.09767 | 0.164808 | ||||||||
\(163\) | −6.80568 | −0.533062 | −0.266531 | − | 0.963826i | \(-0.585877\pi\) | ||||
−0.266531 | + | 0.963826i | \(0.585877\pi\) | |||||||
\(164\) | −0.640649 | −0.0500263 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 35.3532 | 2.74394 | ||||||||
\(167\) | 12.2497 | 0.947913 | 0.473957 | − | 0.880548i | \(-0.342825\pi\) | ||||
0.473957 | + | 0.880548i | \(0.342825\pi\) | |||||||
\(168\) | 0.839503 | 0.0647690 | ||||||||
\(169\) | −8.46896 | −0.651459 | ||||||||
\(170\) | 31.7743 | 2.43698 | ||||||||
\(171\) | −1.53847 | −0.117650 | ||||||||
\(172\) | −22.2902 | −1.69961 | ||||||||
\(173\) | 19.8500 | 1.50917 | 0.754583 | − | 0.656204i | \(-0.227839\pi\) | ||||
0.754583 | + | 0.656204i | \(0.227839\pi\) | |||||||
\(174\) | 2.01008 | 0.152384 | ||||||||
\(175\) | 4.98224 | 0.376622 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −9.55077 | −0.717880 | ||||||||
\(178\) | −23.6344 | −1.77147 | ||||||||
\(179\) | 8.22231 | 0.614564 | 0.307282 | − | 0.951618i | \(-0.400580\pi\) | ||||
0.307282 | + | 0.951618i | \(0.400580\pi\) | |||||||
\(180\) | 7.58338 | 0.565232 | ||||||||
\(181\) | 10.4317 | 0.775381 | 0.387691 | − | 0.921790i | \(-0.373273\pi\) | ||||
0.387691 | + | 0.921790i | \(0.373273\pi\) | |||||||
\(182\) | −4.46514 | −0.330978 | ||||||||
\(183\) | −8.55756 | −0.632593 | ||||||||
\(184\) | 4.29413 | 0.316568 | ||||||||
\(185\) | 7.57959 | 0.557263 | ||||||||
\(186\) | −15.1459 | −1.11055 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 24.7810 | 1.80734 | ||||||||
\(189\) | 1.00000 | 0.0727393 | ||||||||
\(190\) | −10.1962 | −0.739713 | ||||||||
\(191\) | 14.2162 | 1.02865 | 0.514325 | − | 0.857595i | \(-0.328043\pi\) | ||||
0.514325 | + | 0.857595i | \(0.328043\pi\) | |||||||
\(192\) | −10.8172 | −0.780666 | ||||||||
\(193\) | 7.01633 | 0.505046 | 0.252523 | − | 0.967591i | \(-0.418740\pi\) | ||||
0.252523 | + | 0.967591i | \(0.418740\pi\) | |||||||
\(194\) | 14.8680 | 1.06746 | ||||||||
\(195\) | −6.72532 | −0.481610 | ||||||||
\(196\) | 2.40021 | 0.171443 | ||||||||
\(197\) | 3.60302 | 0.256705 | 0.128352 | − | 0.991729i | \(-0.459031\pi\) | ||||
0.128352 | + | 0.991729i | \(0.459031\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −3.85136 | −0.273015 | −0.136508 | − | 0.990639i | \(-0.543588\pi\) | ||||
−0.136508 | + | 0.990639i | \(0.543588\pi\) | |||||||
\(200\) | 4.18261 | 0.295755 | ||||||||
\(201\) | 13.2710 | 0.936066 | ||||||||
\(202\) | −17.5073 | −1.23181 | ||||||||
\(203\) | 0.958246 | 0.0672557 | ||||||||
\(204\) | 11.5073 | 0.805674 | ||||||||
\(205\) | −0.843306 | −0.0588991 | ||||||||
\(206\) | −15.8071 | −1.10133 | ||||||||
\(207\) | 5.11509 | 0.355524 | ||||||||
\(208\) | 6.46978 | 0.448598 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 6.62751 | 0.457342 | ||||||||
\(211\) | −11.1325 | −0.766391 | −0.383196 | − | 0.923667i | \(-0.625176\pi\) | ||||
−0.383196 | + | 0.923667i | \(0.625176\pi\) | |||||||
\(212\) | −2.26964 | −0.155879 | ||||||||
\(213\) | 14.1564 | 0.969983 | ||||||||
\(214\) | −32.2804 | −2.20664 | ||||||||
\(215\) | −29.3413 | −2.00106 | ||||||||
\(216\) | 0.839503 | 0.0571209 | ||||||||
\(217\) | −7.22037 | −0.490151 | ||||||||
\(218\) | −42.4948 | −2.87811 | ||||||||
\(219\) | −7.72198 | −0.521803 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −10.2053 | −0.686481 | ||||||||
\(222\) | 5.03232 | 0.337747 | ||||||||
\(223\) | −5.27119 | −0.352985 | −0.176493 | − | 0.984302i | \(-0.556475\pi\) | ||||
−0.176493 | + | 0.984302i | \(0.556475\pi\) | |||||||
\(224\) | −8.05469 | −0.538177 | ||||||||
\(225\) | 4.98224 | 0.332150 | ||||||||
\(226\) | −37.9717 | −2.52584 | ||||||||
\(227\) | 14.8204 | 0.983661 | 0.491831 | − | 0.870691i | \(-0.336328\pi\) | ||||
0.491831 | + | 0.870691i | \(0.336328\pi\) | |||||||
\(228\) | −3.69265 | −0.244552 | ||||||||
\(229\) | 7.60478 | 0.502538 | 0.251269 | − | 0.967917i | \(-0.419152\pi\) | ||||
0.251269 | + | 0.967917i | \(0.419152\pi\) | |||||||
\(230\) | 33.9004 | 2.23532 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0.804450 | 0.0528147 | ||||||||
\(233\) | 1.50544 | 0.0986248 | 0.0493124 | − | 0.998783i | \(-0.484297\pi\) | ||||
0.0493124 | + | 0.998783i | \(0.484297\pi\) | |||||||
\(234\) | −4.46514 | −0.291896 | ||||||||
\(235\) | 32.6200 | 2.12789 | ||||||||
\(236\) | −22.9238 | −1.49221 | ||||||||
\(237\) | −9.31226 | −0.604896 | ||||||||
\(238\) | 10.0569 | 0.651889 | ||||||||
\(239\) | 5.02336 | 0.324934 | 0.162467 | − | 0.986714i | \(-0.448055\pi\) | ||||
0.162467 | + | 0.986714i | \(0.448055\pi\) | |||||||
\(240\) | −9.60295 | −0.619868 | ||||||||
\(241\) | −16.1502 | −1.04033 | −0.520164 | − | 0.854066i | \(-0.674129\pi\) | ||||
−0.520164 | + | 0.854066i | \(0.674129\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | −20.5399 | −1.31493 | ||||||||
\(245\) | 3.15947 | 0.201851 | ||||||||
\(246\) | −0.559897 | −0.0356977 | ||||||||
\(247\) | 3.27482 | 0.208372 | ||||||||
\(248\) | −6.06152 | −0.384907 | ||||||||
\(249\) | 16.8536 | 1.06805 | ||||||||
\(250\) | −0.117676 | −0.00744246 | ||||||||
\(251\) | 25.7765 | 1.62700 | 0.813500 | − | 0.581565i | \(-0.197560\pi\) | ||||
0.813500 | + | 0.581565i | \(0.197560\pi\) | |||||||
\(252\) | 2.40021 | 0.151199 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 32.2434 | 2.02313 | ||||||||
\(255\) | 15.1475 | 0.948571 | ||||||||
\(256\) | 7.82853 | 0.489283 | ||||||||
\(257\) | 17.6678 | 1.10208 | 0.551042 | − | 0.834477i | \(-0.314230\pi\) | ||||
0.551042 | + | 0.834477i | \(0.314230\pi\) | |||||||
\(258\) | −19.4806 | −1.21281 | ||||||||
\(259\) | 2.39901 | 0.149067 | ||||||||
\(260\) | −16.1422 | −1.00109 | ||||||||
\(261\) | 0.958246 | 0.0593139 | ||||||||
\(262\) | 22.5327 | 1.39208 | ||||||||
\(263\) | −18.6325 | −1.14893 | −0.574465 | − | 0.818529i | \(-0.694790\pi\) | ||||
−0.574465 | + | 0.818529i | \(0.694790\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −2.98759 | −0.183526 | ||||||||
\(266\) | −3.22720 | −0.197872 | ||||||||
\(267\) | −11.2670 | −0.689529 | ||||||||
\(268\) | 31.8532 | 1.94575 | ||||||||
\(269\) | −20.7126 | −1.26287 | −0.631435 | − | 0.775429i | \(-0.717534\pi\) | ||||
−0.631435 | + | 0.775429i | \(0.717534\pi\) | |||||||
\(270\) | 6.62751 | 0.403338 | ||||||||
\(271\) | −14.8438 | −0.901694 | −0.450847 | − | 0.892601i | \(-0.648878\pi\) | ||||
−0.450847 | + | 0.892601i | \(0.648878\pi\) | |||||||
\(272\) | −14.5719 | −0.883551 | ||||||||
\(273\) | −2.12862 | −0.128830 | ||||||||
\(274\) | −9.28453 | −0.560899 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 12.2773 | 0.739006 | ||||||||
\(277\) | 3.07309 | 0.184644 | 0.0923221 | − | 0.995729i | \(-0.470571\pi\) | ||||
0.0923221 | + | 0.995729i | \(0.470571\pi\) | |||||||
\(278\) | −9.49206 | −0.569296 | ||||||||
\(279\) | −7.22037 | −0.432272 | ||||||||
\(280\) | 2.65238 | 0.158510 | ||||||||
\(281\) | −4.09698 | −0.244405 | −0.122203 | − | 0.992505i | \(-0.538996\pi\) | ||||
−0.122203 | + | 0.992505i | \(0.538996\pi\) | |||||||
\(282\) | 21.6574 | 1.28968 | ||||||||
\(283\) | 7.39800 | 0.439766 | 0.219883 | − | 0.975526i | \(-0.429432\pi\) | ||||
0.219883 | + | 0.975526i | \(0.429432\pi\) | |||||||
\(284\) | 33.9784 | 2.01625 | ||||||||
\(285\) | −4.86075 | −0.287926 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −0.266914 | −0.0157554 | ||||||||
\(288\) | −8.05469 | −0.474627 | ||||||||
\(289\) | 5.98536 | 0.352080 | ||||||||
\(290\) | 6.35079 | 0.372931 | ||||||||
\(291\) | 7.08789 | 0.415499 | ||||||||
\(292\) | −18.5344 | −1.08464 | ||||||||
\(293\) | 10.5489 | 0.616273 | 0.308137 | − | 0.951342i | \(-0.400295\pi\) | ||||
0.308137 | + | 0.951342i | \(0.400295\pi\) | |||||||
\(294\) | 2.09767 | 0.122338 | ||||||||
\(295\) | −30.1754 | −1.75688 | ||||||||
\(296\) | 2.01397 | 0.117060 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −6.28190 | −0.363901 | ||||||||
\(299\) | −10.8881 | −0.629675 | ||||||||
\(300\) | 11.9584 | 0.690420 | ||||||||
\(301\) | −9.28678 | −0.535281 | ||||||||
\(302\) | −18.4859 | −1.06374 | ||||||||
\(303\) | −8.34609 | −0.479471 | ||||||||
\(304\) | 4.67605 | 0.268190 | ||||||||
\(305\) | −27.0373 | −1.54815 | ||||||||
\(306\) | 10.0569 | 0.574912 | ||||||||
\(307\) | −1.74955 | −0.0998522 | −0.0499261 | − | 0.998753i | \(-0.515899\pi\) | ||||
−0.0499261 | + | 0.998753i | \(0.515899\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −7.53555 | −0.428683 | ||||||||
\(310\) | −47.8531 | −2.71788 | ||||||||
\(311\) | −23.0075 | −1.30463 | −0.652317 | − | 0.757946i | \(-0.726203\pi\) | ||||
−0.652317 | + | 0.757946i | \(0.726203\pi\) | |||||||
\(312\) | −1.78698 | −0.101168 | ||||||||
\(313\) | 18.2568 | 1.03193 | 0.515967 | − | 0.856608i | \(-0.327433\pi\) | ||||
0.515967 | + | 0.856608i | \(0.327433\pi\) | |||||||
\(314\) | 3.28610 | 0.185446 | ||||||||
\(315\) | 3.15947 | 0.178016 | ||||||||
\(316\) | −22.3514 | −1.25736 | ||||||||
\(317\) | 32.6206 | 1.83216 | 0.916079 | − | 0.400999i | \(-0.131337\pi\) | ||||
0.916079 | + | 0.400999i | \(0.131337\pi\) | |||||||
\(318\) | −1.98355 | −0.111232 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | −34.1767 | −1.91054 | ||||||||
\(321\) | −15.3887 | −0.858914 | ||||||||
\(322\) | 10.7298 | 0.597946 | ||||||||
\(323\) | −7.37589 | −0.410406 | ||||||||
\(324\) | 2.40021 | 0.133345 | ||||||||
\(325\) | −10.6053 | −0.588277 | ||||||||
\(326\) | −14.2760 | −0.790677 | ||||||||
\(327\) | −20.2581 | −1.12028 | ||||||||
\(328\) | −0.224075 | −0.0123725 | ||||||||
\(329\) | 10.3245 | 0.569209 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 6.80537 | 0.374057 | 0.187029 | − | 0.982354i | \(-0.440114\pi\) | ||||
0.187029 | + | 0.982354i | \(0.440114\pi\) | |||||||
\(332\) | 40.4521 | 2.22010 | ||||||||
\(333\) | 2.39901 | 0.131465 | ||||||||
\(334\) | 25.6959 | 1.40602 | ||||||||
\(335\) | 41.9294 | 2.29085 | ||||||||
\(336\) | −3.03942 | −0.165814 | ||||||||
\(337\) | −0.372041 | −0.0202664 | −0.0101332 | − | 0.999949i | \(-0.503226\pi\) | ||||
−0.0101332 | + | 0.999949i | \(0.503226\pi\) | |||||||
\(338\) | −17.7651 | −0.966292 | ||||||||
\(339\) | −18.1019 | −0.983158 | ||||||||
\(340\) | 36.3570 | 1.97174 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | −3.22720 | −0.174507 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | −7.79627 | −0.420347 | ||||||||
\(345\) | 16.1610 | 0.870078 | ||||||||
\(346\) | 41.6387 | 2.23851 | ||||||||
\(347\) | −5.75075 | −0.308716 | −0.154358 | − | 0.988015i | \(-0.549331\pi\) | ||||
−0.154358 | + | 0.988015i | \(0.549331\pi\) | |||||||
\(348\) | 2.29999 | 0.123292 | ||||||||
\(349\) | 0.646523 | 0.0346076 | 0.0173038 | − | 0.999850i | \(-0.494492\pi\) | ||||
0.0173038 | + | 0.999850i | \(0.494492\pi\) | |||||||
\(350\) | 10.4511 | 0.558634 | ||||||||
\(351\) | −2.12862 | −0.113617 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −18.3601 | −0.977209 | −0.488604 | − | 0.872505i | \(-0.662494\pi\) | ||||
−0.488604 | + | 0.872505i | \(0.662494\pi\) | |||||||
\(354\) | −20.0343 | −1.06481 | ||||||||
\(355\) | 44.7268 | 2.37385 | ||||||||
\(356\) | −27.0431 | −1.43328 | ||||||||
\(357\) | 4.79430 | 0.253742 | ||||||||
\(358\) | 17.2477 | 0.911567 | ||||||||
\(359\) | −26.9753 | −1.42370 | −0.711852 | − | 0.702330i | \(-0.752143\pi\) | ||||
−0.711852 | + | 0.702330i | \(0.752143\pi\) | |||||||
\(360\) | 2.65238 | 0.139793 | ||||||||
\(361\) | −16.6331 | −0.875427 | ||||||||
\(362\) | 21.8822 | 1.15010 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −5.10914 | −0.267792 | ||||||||
\(365\) | −24.3974 | −1.27702 | ||||||||
\(366\) | −17.9509 | −0.938309 | ||||||||
\(367\) | 28.3215 | 1.47837 | 0.739186 | − | 0.673501i | \(-0.235210\pi\) | ||||
0.739186 | + | 0.673501i | \(0.235210\pi\) | |||||||
\(368\) | −15.5469 | −0.810439 | ||||||||
\(369\) | −0.266914 | −0.0138950 | ||||||||
\(370\) | 15.8995 | 0.826574 | ||||||||
\(371\) | −0.945600 | −0.0490931 | ||||||||
\(372\) | −17.3304 | −0.898539 | ||||||||
\(373\) | 12.9215 | 0.669050 | 0.334525 | − | 0.942387i | \(-0.391424\pi\) | ||||
0.334525 | + | 0.942387i | \(0.391424\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −0.0560984 | −0.00289691 | ||||||||
\(376\) | 8.66746 | 0.446990 | ||||||||
\(377\) | −2.03974 | −0.105052 | ||||||||
\(378\) | 2.09767 | 0.107892 | ||||||||
\(379\) | 20.9480 | 1.07603 | 0.538014 | − | 0.842936i | \(-0.319175\pi\) | ||||
0.538014 | + | 0.842936i | \(0.319175\pi\) | |||||||
\(380\) | −11.6668 | −0.598495 | ||||||||
\(381\) | 15.3711 | 0.787484 | ||||||||
\(382\) | 29.8209 | 1.52577 | ||||||||
\(383\) | 24.9764 | 1.27623 | 0.638117 | − | 0.769939i | \(-0.279714\pi\) | ||||
0.638117 | + | 0.769939i | \(0.279714\pi\) | |||||||
\(384\) | −6.58156 | −0.335864 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 14.7179 | 0.749123 | ||||||||
\(387\) | −9.28678 | −0.472073 | ||||||||
\(388\) | 17.0124 | 0.863674 | ||||||||
\(389\) | −13.5780 | −0.688430 | −0.344215 | − | 0.938891i | \(-0.611855\pi\) | ||||
−0.344215 | + | 0.938891i | \(0.611855\pi\) | |||||||
\(390\) | −14.1075 | −0.714360 | ||||||||
\(391\) | 24.5233 | 1.24020 | ||||||||
\(392\) | 0.839503 | 0.0424013 | ||||||||
\(393\) | 10.7418 | 0.541852 | ||||||||
\(394\) | 7.55794 | 0.380763 | ||||||||
\(395\) | −29.4218 | −1.48037 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −4.26450 | −0.214029 | −0.107014 | − | 0.994257i | \(-0.534129\pi\) | ||||
−0.107014 | + | 0.994257i | \(0.534129\pi\) | |||||||
\(398\) | −8.07886 | −0.404957 | ||||||||
\(399\) | −1.53847 | −0.0770198 | ||||||||
\(400\) | −15.1431 | −0.757156 | ||||||||
\(401\) | −32.4423 | −1.62009 | −0.810045 | − | 0.586367i | \(-0.800558\pi\) | ||||
−0.810045 | + | 0.586367i | \(0.800558\pi\) | |||||||
\(402\) | 27.8382 | 1.38844 | ||||||||
\(403\) | 15.3695 | 0.765607 | ||||||||
\(404\) | −20.0324 | −0.996647 | ||||||||
\(405\) | 3.15947 | 0.156995 | ||||||||
\(406\) | 2.01008 | 0.0997587 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 4.02483 | 0.199259 | ||||||||
\(409\) | 24.8877 | 1.23062 | 0.615308 | − | 0.788287i | \(-0.289032\pi\) | ||||
0.615308 | + | 0.788287i | \(0.289032\pi\) | |||||||
\(410\) | −1.76898 | −0.0873635 | ||||||||
\(411\) | −4.42612 | −0.218325 | ||||||||
\(412\) | −18.0869 | −0.891077 | ||||||||
\(413\) | −9.55077 | −0.469963 | ||||||||
\(414\) | 10.7298 | 0.527339 | ||||||||
\(415\) | 53.2484 | 2.61386 | ||||||||
\(416\) | 17.1454 | 0.840623 | ||||||||
\(417\) | −4.52505 | −0.221593 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 10.5948 | 0.517588 | 0.258794 | − | 0.965933i | \(-0.416675\pi\) | ||||
0.258794 | + | 0.965933i | \(0.416675\pi\) | |||||||
\(420\) | 7.58338 | 0.370031 | ||||||||
\(421\) | −37.8632 | −1.84534 | −0.922670 | − | 0.385591i | \(-0.873998\pi\) | ||||
−0.922670 | + | 0.385591i | \(0.873998\pi\) | |||||||
\(422\) | −23.3522 | −1.13677 | ||||||||
\(423\) | 10.3245 | 0.501995 | ||||||||
\(424\) | −0.793833 | −0.0385520 | ||||||||
\(425\) | 23.8864 | 1.15866 | ||||||||
\(426\) | 29.6955 | 1.43875 | ||||||||
\(427\) | −8.55756 | −0.414129 | ||||||||
\(428\) | −36.9361 | −1.78537 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −61.5483 | −2.96812 | ||||||||
\(431\) | −5.64489 | −0.271905 | −0.135952 | − | 0.990715i | \(-0.543409\pi\) | ||||
−0.135952 | + | 0.990715i | \(0.543409\pi\) | |||||||
\(432\) | −3.03942 | −0.146234 | ||||||||
\(433\) | −2.69528 | −0.129527 | −0.0647635 | − | 0.997901i | \(-0.520629\pi\) | ||||
−0.0647635 | + | 0.997901i | \(0.520629\pi\) | |||||||
\(434\) | −15.1459 | −0.727028 | ||||||||
\(435\) | 3.02755 | 0.145160 | ||||||||
\(436\) | −48.6237 | −2.32865 | ||||||||
\(437\) | −7.86942 | −0.376445 | ||||||||
\(438\) | −16.1981 | −0.773977 | ||||||||
\(439\) | −30.5668 | −1.45888 | −0.729438 | − | 0.684047i | \(-0.760218\pi\) | ||||
−0.729438 | + | 0.684047i | \(0.760218\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1.00000 | 0.0476190 | ||||||||
\(442\) | −21.4073 | −1.01824 | ||||||||
\(443\) | −24.6371 | −1.17054 | −0.585272 | − | 0.810837i | \(-0.699012\pi\) | ||||
−0.585272 | + | 0.810837i | \(0.699012\pi\) | |||||||
\(444\) | 5.75812 | 0.273268 | ||||||||
\(445\) | −35.5977 | −1.68749 | ||||||||
\(446\) | −11.0572 | −0.523574 | ||||||||
\(447\) | −2.99471 | −0.141645 | ||||||||
\(448\) | −10.8172 | −0.511066 | ||||||||
\(449\) | −15.3755 | −0.725617 | −0.362808 | − | 0.931864i | \(-0.618182\pi\) | ||||
−0.362808 | + | 0.931864i | \(0.618182\pi\) | |||||||
\(450\) | 10.4511 | 0.492669 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | −43.4482 | −2.04363 | ||||||||
\(453\) | −8.81260 | −0.414052 | ||||||||
\(454\) | 31.0882 | 1.45904 | ||||||||
\(455\) | −6.72532 | −0.315288 | ||||||||
\(456\) | −1.29155 | −0.0604824 | ||||||||
\(457\) | −14.2362 | −0.665943 | −0.332972 | − | 0.942937i | \(-0.608051\pi\) | ||||
−0.332972 | + | 0.942937i | \(0.608051\pi\) | |||||||
\(458\) | 15.9523 | 0.745402 | ||||||||
\(459\) | 4.79430 | 0.223779 | ||||||||
\(460\) | 38.7897 | 1.80858 | ||||||||
\(461\) | 36.7148 | 1.70998 | 0.854990 | − | 0.518645i | \(-0.173563\pi\) | ||||
0.854990 | + | 0.518645i | \(0.173563\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −34.7682 | −1.61582 | −0.807908 | − | 0.589308i | \(-0.799400\pi\) | ||||
−0.807908 | + | 0.589308i | \(0.799400\pi\) | |||||||
\(464\) | −2.91251 | −0.135210 | ||||||||
\(465\) | −22.8125 | −1.05791 | ||||||||
\(466\) | 3.15792 | 0.146288 | ||||||||
\(467\) | 13.5536 | 0.627184 | 0.313592 | − | 0.949558i | \(-0.398468\pi\) | ||||
0.313592 | + | 0.949558i | \(0.398468\pi\) | |||||||
\(468\) | −5.10914 | −0.236170 | ||||||||
\(469\) | 13.2710 | 0.612799 | ||||||||
\(470\) | 68.4259 | 3.15625 | ||||||||
\(471\) | 1.56655 | 0.0721829 | ||||||||
\(472\) | −8.01789 | −0.369053 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | −19.5340 | −0.897227 | ||||||||
\(475\) | −7.66503 | −0.351696 | ||||||||
\(476\) | 11.5073 | 0.527437 | ||||||||
\(477\) | −0.945600 | −0.0432960 | ||||||||
\(478\) | 10.5373 | 0.481967 | ||||||||
\(479\) | −27.5973 | −1.26095 | −0.630476 | − | 0.776208i | \(-0.717140\pi\) | ||||
−0.630476 | + | 0.776208i | \(0.717140\pi\) | |||||||
\(480\) | −25.4486 | −1.16156 | ||||||||
\(481\) | −5.10658 | −0.232840 | ||||||||
\(482\) | −33.8778 | −1.54309 | ||||||||
\(483\) | 5.11509 | 0.232745 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 22.3940 | 1.01686 | ||||||||
\(486\) | 2.09767 | 0.0951521 | ||||||||
\(487\) | −20.4778 | −0.927936 | −0.463968 | − | 0.885852i | \(-0.653575\pi\) | ||||
−0.463968 | + | 0.885852i | \(0.653575\pi\) | |||||||
\(488\) | −7.18409 | −0.325208 | ||||||||
\(489\) | −6.80568 | −0.307763 | ||||||||
\(490\) | 6.62751 | 0.299401 | ||||||||
\(491\) | −28.8664 | −1.30272 | −0.651361 | − | 0.758768i | \(-0.725802\pi\) | ||||
−0.651361 | + | 0.758768i | \(0.725802\pi\) | |||||||
\(492\) | −0.640649 | −0.0288827 | ||||||||
\(493\) | 4.59412 | 0.206909 | ||||||||
\(494\) | 6.86949 | 0.309073 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 21.9457 | 0.985393 | ||||||||
\(497\) | 14.1564 | 0.635003 | ||||||||
\(498\) | 35.3532 | 1.58422 | ||||||||
\(499\) | −21.4940 | −0.962202 | −0.481101 | − | 0.876665i | \(-0.659763\pi\) | ||||
−0.481101 | + | 0.876665i | \(0.659763\pi\) | |||||||
\(500\) | −0.134648 | −0.00602163 | ||||||||
\(501\) | 12.2497 | 0.547278 | ||||||||
\(502\) | 54.0706 | 2.41329 | ||||||||
\(503\) | 8.60198 | 0.383543 | 0.191772 | − | 0.981440i | \(-0.438577\pi\) | ||||
0.191772 | + | 0.981440i | \(0.438577\pi\) | |||||||
\(504\) | 0.839503 | 0.0373944 | ||||||||
\(505\) | −26.3692 | −1.17342 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −8.46896 | −0.376120 | ||||||||
\(508\) | 36.8938 | 1.63690 | ||||||||
\(509\) | 11.0437 | 0.489505 | 0.244752 | − | 0.969586i | \(-0.421293\pi\) | ||||
0.244752 | + | 0.969586i | \(0.421293\pi\) | |||||||
\(510\) | 31.7743 | 1.40699 | ||||||||
\(511\) | −7.72198 | −0.341600 | ||||||||
\(512\) | 29.5848 | 1.30748 | ||||||||
\(513\) | −1.53847 | −0.0679251 | ||||||||
\(514\) | 37.0611 | 1.63469 | ||||||||
\(515\) | −23.8083 | −1.04912 | ||||||||
\(516\) | −22.2902 | −0.981271 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 5.03232 | 0.221107 | ||||||||
\(519\) | 19.8500 | 0.871318 | ||||||||
\(520\) | −5.64592 | −0.247590 | ||||||||
\(521\) | −12.6215 | −0.552960 | −0.276480 | − | 0.961020i | \(-0.589168\pi\) | ||||
−0.276480 | + | 0.961020i | \(0.589168\pi\) | |||||||
\(522\) | 2.01008 | 0.0879789 | ||||||||
\(523\) | 43.9100 | 1.92005 | 0.960025 | − | 0.279913i | \(-0.0903055\pi\) | ||||
0.960025 | + | 0.279913i | \(0.0903055\pi\) | |||||||
\(524\) | 25.7826 | 1.12632 | ||||||||
\(525\) | 4.98224 | 0.217443 | ||||||||
\(526\) | −39.0848 | −1.70418 | ||||||||
\(527\) | −34.6167 | −1.50793 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 3.16418 | 0.137573 | ||||||||
\(530\) | −6.26698 | −0.272220 | ||||||||
\(531\) | −9.55077 | −0.414468 | ||||||||
\(532\) | −3.69265 | −0.160097 | ||||||||
\(533\) | 0.568159 | 0.0246097 | ||||||||
\(534\) | −23.6344 | −1.02276 | ||||||||
\(535\) | −48.6201 | −2.10203 | ||||||||
\(536\) | 11.1411 | 0.481221 | ||||||||
\(537\) | 8.22231 | 0.354819 | ||||||||
\(538\) | −43.4482 | −1.87318 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 7.58338 | 0.326337 | ||||||||
\(541\) | 27.3128 | 1.17427 | 0.587134 | − | 0.809490i | \(-0.300256\pi\) | ||||
0.587134 | + | 0.809490i | \(0.300256\pi\) | |||||||
\(542\) | −31.1373 | −1.33746 | ||||||||
\(543\) | 10.4317 | 0.447667 | ||||||||
\(544\) | −38.6167 | −1.65568 | ||||||||
\(545\) | −64.0049 | −2.74167 | ||||||||
\(546\) | −4.46514 | −0.191090 | ||||||||
\(547\) | −18.3092 | −0.782845 | −0.391423 | − | 0.920211i | \(-0.628017\pi\) | ||||
−0.391423 | + | 0.920211i | \(0.628017\pi\) | |||||||
\(548\) | −10.6236 | −0.453818 | ||||||||
\(549\) | −8.55756 | −0.365228 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −1.47423 | −0.0628044 | ||||||||
\(552\) | 4.29413 | 0.182770 | ||||||||
\(553\) | −9.31226 | −0.395998 | ||||||||
\(554\) | 6.44632 | 0.273878 | ||||||||
\(555\) | 7.57959 | 0.321736 | ||||||||
\(556\) | −10.8611 | −0.460612 | ||||||||
\(557\) | 3.82733 | 0.162169 | 0.0810845 | − | 0.996707i | \(-0.474162\pi\) | ||||
0.0810845 | + | 0.996707i | \(0.474162\pi\) | |||||||
\(558\) | −15.1459 | −0.641179 | ||||||||
\(559\) | 19.7681 | 0.836099 | ||||||||
\(560\) | −9.60295 | −0.405799 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −8.59411 | −0.362520 | ||||||||
\(563\) | 36.1468 | 1.52340 | 0.761702 | − | 0.647927i | \(-0.224364\pi\) | ||||
0.761702 | + | 0.647927i | \(0.224364\pi\) | |||||||
\(564\) | 24.7810 | 1.04347 | ||||||||
\(565\) | −57.1923 | −2.40610 | ||||||||
\(566\) | 15.5186 | 0.652293 | ||||||||
\(567\) | 1.00000 | 0.0419961 | ||||||||
\(568\) | 11.8844 | 0.498657 | ||||||||
\(569\) | 9.55602 | 0.400609 | 0.200305 | − | 0.979734i | \(-0.435807\pi\) | ||||
0.200305 | + | 0.979734i | \(0.435807\pi\) | |||||||
\(570\) | −10.1962 | −0.427073 | ||||||||
\(571\) | 31.8446 | 1.33265 | 0.666327 | − | 0.745659i | \(-0.267865\pi\) | ||||
0.666327 | + | 0.745659i | \(0.267865\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 14.2162 | 0.593891 | ||||||||
\(574\) | −0.559897 | −0.0233696 | ||||||||
\(575\) | 25.4846 | 1.06278 | ||||||||
\(576\) | −10.8172 | −0.450718 | ||||||||
\(577\) | 8.65987 | 0.360515 | 0.180258 | − | 0.983619i | \(-0.442307\pi\) | ||||
0.180258 | + | 0.983619i | \(0.442307\pi\) | |||||||
\(578\) | 12.5553 | 0.522231 | ||||||||
\(579\) | 7.01633 | 0.291589 | ||||||||
\(580\) | 7.26674 | 0.301735 | ||||||||
\(581\) | 16.8536 | 0.699205 | ||||||||
\(582\) | 14.8680 | 0.616300 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | −6.48262 | −0.268253 | ||||||||
\(585\) | −6.72532 | −0.278058 | ||||||||
\(586\) | 22.1281 | 0.914103 | ||||||||
\(587\) | −5.32917 | −0.219959 | −0.109979 | − | 0.993934i | \(-0.535078\pi\) | ||||
−0.109979 | + | 0.993934i | \(0.535078\pi\) | |||||||
\(588\) | 2.40021 | 0.0989829 | ||||||||
\(589\) | 11.1083 | 0.457711 | ||||||||
\(590\) | −63.2978 | −2.60593 | ||||||||
\(591\) | 3.60302 | 0.148208 | ||||||||
\(592\) | −7.29159 | −0.299682 | ||||||||
\(593\) | −11.0464 | −0.453622 | −0.226811 | − | 0.973939i | \(-0.572830\pi\) | ||||
−0.226811 | + | 0.973939i | \(0.572830\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 15.1475 | 0.620985 | ||||||||
\(596\) | −7.18792 | −0.294429 | ||||||||
\(597\) | −3.85136 | −0.157626 | ||||||||
\(598\) | −22.8396 | −0.933982 | ||||||||
\(599\) | 26.2832 | 1.07390 | 0.536951 | − | 0.843614i | \(-0.319576\pi\) | ||||
0.536951 | + | 0.843614i | \(0.319576\pi\) | |||||||
\(600\) | 4.18261 | 0.170754 | ||||||||
\(601\) | −12.9669 | −0.528929 | −0.264465 | − | 0.964395i | \(-0.585195\pi\) | ||||
−0.264465 | + | 0.964395i | \(0.585195\pi\) | |||||||
\(602\) | −19.4806 | −0.793969 | ||||||||
\(603\) | 13.2710 | 0.540438 | ||||||||
\(604\) | −21.1521 | −0.860665 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −17.5073 | −0.711187 | ||||||||
\(607\) | 22.6090 | 0.917672 | 0.458836 | − | 0.888521i | \(-0.348266\pi\) | ||||
0.458836 | + | 0.888521i | \(0.348266\pi\) | |||||||
\(608\) | 12.3919 | 0.502558 | ||||||||
\(609\) | 0.958246 | 0.0388301 | ||||||||
\(610\) | −56.7153 | −2.29634 | ||||||||
\(611\) | −21.9770 | −0.889095 | ||||||||
\(612\) | 11.5073 | 0.465156 | ||||||||
\(613\) | 22.1412 | 0.894276 | 0.447138 | − | 0.894465i | \(-0.352443\pi\) | ||||
0.447138 | + | 0.894465i | \(0.352443\pi\) | |||||||
\(614\) | −3.66998 | −0.148108 | ||||||||
\(615\) | −0.843306 | −0.0340054 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −20.4747 | −0.824281 | −0.412140 | − | 0.911120i | \(-0.635219\pi\) | ||||
−0.412140 | + | 0.911120i | \(0.635219\pi\) | |||||||
\(618\) | −15.8071 | −0.635854 | ||||||||
\(619\) | 40.1013 | 1.61181 | 0.805903 | − | 0.592047i | \(-0.201680\pi\) | ||||
0.805903 | + | 0.592047i | \(0.201680\pi\) | |||||||
\(620\) | −54.7549 | −2.19901 | ||||||||
\(621\) | 5.11509 | 0.205262 | ||||||||
\(622\) | −48.2620 | −1.93513 | ||||||||
\(623\) | −11.2670 | −0.451403 | ||||||||
\(624\) | 6.46978 | 0.258998 | ||||||||
\(625\) | −25.0885 | −1.00354 | ||||||||
\(626\) | 38.2967 | 1.53064 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 3.76005 | 0.150042 | ||||||||
\(629\) | 11.5016 | 0.458598 | ||||||||
\(630\) | 6.62751 | 0.264046 | ||||||||
\(631\) | 29.1072 | 1.15874 | 0.579370 | − | 0.815064i | \(-0.303298\pi\) | ||||
0.579370 | + | 0.815064i | \(0.303298\pi\) | |||||||
\(632\) | −7.81767 | −0.310970 | ||||||||
\(633\) | −11.1325 | −0.442476 | ||||||||
\(634\) | 68.4272 | 2.71759 | ||||||||
\(635\) | 48.5645 | 1.92722 | ||||||||
\(636\) | −2.26964 | −0.0899969 | ||||||||
\(637\) | −2.12862 | −0.0843391 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 14.1564 | 0.560020 | ||||||||
\(640\) | −20.7942 | −0.821964 | ||||||||
\(641\) | 3.75720 | 0.148400 | 0.0742001 | − | 0.997243i | \(-0.476360\pi\) | ||||
0.0742001 | + | 0.997243i | \(0.476360\pi\) | |||||||
\(642\) | −32.2804 | −1.27400 | ||||||||
\(643\) | −9.96068 | −0.392811 | −0.196405 | − | 0.980523i | \(-0.562927\pi\) | ||||
−0.196405 | + | 0.980523i | \(0.562927\pi\) | |||||||
\(644\) | 12.2773 | 0.483793 | ||||||||
\(645\) | −29.3413 | −1.15531 | ||||||||
\(646\) | −15.4722 | −0.608744 | ||||||||
\(647\) | −11.5017 | −0.452180 | −0.226090 | − | 0.974106i | \(-0.572594\pi\) | ||||
−0.226090 | + | 0.974106i | \(0.572594\pi\) | |||||||
\(648\) | 0.839503 | 0.0329788 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | −22.2464 | −0.872577 | ||||||||
\(651\) | −7.22037 | −0.282989 | ||||||||
\(652\) | −16.3350 | −0.639729 | ||||||||
\(653\) | −5.08048 | −0.198815 | −0.0994073 | − | 0.995047i | \(-0.531695\pi\) | ||||
−0.0994073 | + | 0.995047i | \(0.531695\pi\) | |||||||
\(654\) | −42.4948 | −1.66168 | ||||||||
\(655\) | 33.9384 | 1.32608 | ||||||||
\(656\) | 0.811263 | 0.0316745 | ||||||||
\(657\) | −7.72198 | −0.301263 | ||||||||
\(658\) | 21.6574 | 0.844293 | ||||||||
\(659\) | 42.3777 | 1.65080 | 0.825401 | − | 0.564547i | \(-0.190949\pi\) | ||||
0.825401 | + | 0.564547i | \(0.190949\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −12.7151 | −0.494559 | −0.247280 | − | 0.968944i | \(-0.579537\pi\) | ||||
−0.247280 | + | 0.968944i | \(0.579537\pi\) | |||||||
\(662\) | 14.2754 | 0.554829 | ||||||||
\(663\) | −10.2053 | −0.396340 | ||||||||
\(664\) | 14.1486 | 0.549074 | ||||||||
\(665\) | −4.86075 | −0.188492 | ||||||||
\(666\) | 5.03232 | 0.194998 | ||||||||
\(667\) | 4.90152 | 0.189788 | ||||||||
\(668\) | 29.4019 | 1.13759 | ||||||||
\(669\) | −5.27119 | −0.203796 | ||||||||
\(670\) | 87.9539 | 3.39796 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | −8.05469 | −0.310717 | ||||||||
\(673\) | 28.0236 | 1.08023 | 0.540115 | − | 0.841591i | \(-0.318381\pi\) | ||||
0.540115 | + | 0.841591i | \(0.318381\pi\) | |||||||
\(674\) | −0.780419 | −0.0300606 | ||||||||
\(675\) | 4.98224 | 0.191767 | ||||||||
\(676\) | −20.3273 | −0.781818 | ||||||||
\(677\) | −12.3532 | −0.474773 | −0.237387 | − | 0.971415i | \(-0.576291\pi\) | ||||
−0.237387 | + | 0.971415i | \(0.576291\pi\) | |||||||
\(678\) | −37.9717 | −1.45829 | ||||||||
\(679\) | 7.08789 | 0.272008 | ||||||||
\(680\) | 12.7163 | 0.487649 | ||||||||
\(681\) | 14.8204 | 0.567917 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 4.43874 | 0.169844 | 0.0849219 | − | 0.996388i | \(-0.472936\pi\) | ||||
0.0849219 | + | 0.996388i | \(0.472936\pi\) | |||||||
\(684\) | −3.69265 | −0.141192 | ||||||||
\(685\) | −13.9842 | −0.534309 | ||||||||
\(686\) | 2.09767 | 0.0800893 | ||||||||
\(687\) | 7.60478 | 0.290141 | ||||||||
\(688\) | 28.2264 | 1.07612 | ||||||||
\(689\) | 2.01283 | 0.0766825 | ||||||||
\(690\) | 33.9004 | 1.29056 | ||||||||
\(691\) | 33.1423 | 1.26079 | 0.630395 | − | 0.776274i | \(-0.282893\pi\) | ||||
0.630395 | + | 0.776274i | \(0.282893\pi\) | |||||||
\(692\) | 47.6441 | 1.81116 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −12.0632 | −0.457911 | ||||||||
\(695\) | −14.2968 | −0.542307 | ||||||||
\(696\) | 0.804450 | 0.0304926 | ||||||||
\(697\) | −1.27967 | −0.0484708 | ||||||||
\(698\) | 1.35619 | 0.0513325 | ||||||||
\(699\) | 1.50544 | 0.0569411 | ||||||||
\(700\) | 11.9584 | 0.451986 | ||||||||
\(701\) | −4.62594 | −0.174719 | −0.0873596 | − | 0.996177i | \(-0.527843\pi\) | ||||
−0.0873596 | + | 0.996177i | \(0.527843\pi\) | |||||||
\(702\) | −4.46514 | −0.168526 | ||||||||
\(703\) | −3.69080 | −0.139201 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 32.6200 | 1.22854 | ||||||||
\(706\) | −38.5133 | −1.44947 | ||||||||
\(707\) | −8.34609 | −0.313887 | ||||||||
\(708\) | −22.9238 | −0.861530 | ||||||||
\(709\) | 14.9159 | 0.560178 | 0.280089 | − | 0.959974i | \(-0.409636\pi\) | ||||
0.280089 | + | 0.959974i | \(0.409636\pi\) | |||||||
\(710\) | 93.8220 | 3.52108 | ||||||||
\(711\) | −9.31226 | −0.349237 | ||||||||
\(712\) | −9.45868 | −0.354479 | ||||||||
\(713\) | −36.9329 | −1.38315 | ||||||||
\(714\) | 10.0569 | 0.376368 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 19.7352 | 0.737541 | ||||||||
\(717\) | 5.02336 | 0.187601 | ||||||||
\(718\) | −56.5852 | −2.11174 | ||||||||
\(719\) | 33.0569 | 1.23282 | 0.616408 | − | 0.787427i | \(-0.288587\pi\) | ||||
0.616408 | + | 0.787427i | \(0.288587\pi\) | |||||||
\(720\) | −9.60295 | −0.357881 | ||||||||
\(721\) | −7.53555 | −0.280639 | ||||||||
\(722\) | −34.8907 | −1.29850 | ||||||||
\(723\) | −16.1502 | −0.600634 | ||||||||
\(724\) | 25.0382 | 0.930538 | ||||||||
\(725\) | 4.77422 | 0.177310 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 6.06384 | 0.224895 | 0.112448 | − | 0.993658i | \(-0.464131\pi\) | ||||
0.112448 | + | 0.993658i | \(0.464131\pi\) | |||||||
\(728\) | −1.78698 | −0.0662301 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −51.1775 | −1.89417 | ||||||||
\(731\) | −44.5236 | −1.64677 | ||||||||
\(732\) | −20.5399 | −0.759177 | ||||||||
\(733\) | 0.926026 | 0.0342035 | 0.0171018 | − | 0.999854i | \(-0.494556\pi\) | ||||
0.0171018 | + | 0.999854i | \(0.494556\pi\) | |||||||
\(734\) | 59.4092 | 2.19283 | ||||||||
\(735\) | 3.15947 | 0.116539 | ||||||||
\(736\) | −41.2005 | −1.51867 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | −0.559897 | −0.0206101 | ||||||||
\(739\) | 30.4962 | 1.12182 | 0.560910 | − | 0.827877i | \(-0.310451\pi\) | ||||
0.560910 | + | 0.827877i | \(0.310451\pi\) | |||||||
\(740\) | 18.1926 | 0.668773 | ||||||||
\(741\) | 3.27482 | 0.120304 | ||||||||
\(742\) | −1.98355 | −0.0728185 | ||||||||
\(743\) | −17.8520 | −0.654925 | −0.327463 | − | 0.944864i | \(-0.606194\pi\) | ||||
−0.327463 | + | 0.944864i | \(0.606194\pi\) | |||||||
\(744\) | −6.06152 | −0.222226 | ||||||||
\(745\) | −9.46169 | −0.346649 | ||||||||
\(746\) | 27.1050 | 0.992386 | ||||||||
\(747\) | 16.8536 | 0.616641 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −15.3887 | −0.562291 | ||||||||
\(750\) | −0.117676 | −0.00429691 | ||||||||
\(751\) | 35.7837 | 1.30577 | 0.652884 | − | 0.757458i | \(-0.273559\pi\) | ||||
0.652884 | + | 0.757458i | \(0.273559\pi\) | |||||||
\(752\) | −31.3805 | −1.14433 | ||||||||
\(753\) | 25.7765 | 0.939348 | ||||||||
\(754\) | −4.27870 | −0.155821 | ||||||||
\(755\) | −27.8431 | −1.01332 | ||||||||
\(756\) | 2.40021 | 0.0872947 | ||||||||
\(757\) | 42.5125 | 1.54514 | 0.772571 | − | 0.634928i | \(-0.218970\pi\) | ||||
0.772571 | + | 0.634928i | \(0.218970\pi\) | |||||||
\(758\) | 43.9420 | 1.59605 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −4.08061 | −0.148019 | ||||||||
\(761\) | −9.10570 | −0.330081 | −0.165041 | − | 0.986287i | \(-0.552776\pi\) | ||||
−0.165041 | + | 0.986287i | \(0.552776\pi\) | |||||||
\(762\) | 32.2434 | 1.16806 | ||||||||
\(763\) | −20.2581 | −0.733393 | ||||||||
\(764\) | 34.1219 | 1.23449 | ||||||||
\(765\) | 15.1475 | 0.547657 | ||||||||
\(766\) | 52.3922 | 1.89301 | ||||||||
\(767\) | 20.3300 | 0.734073 | ||||||||
\(768\) | 7.82853 | 0.282488 | ||||||||
\(769\) | 6.93312 | 0.250015 | 0.125007 | − | 0.992156i | \(-0.460105\pi\) | ||||
0.125007 | + | 0.992156i | \(0.460105\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 17.6678 | 0.636289 | ||||||||
\(772\) | 16.8406 | 0.606108 | ||||||||
\(773\) | −18.2629 | −0.656872 | −0.328436 | − | 0.944526i | \(-0.606522\pi\) | ||||
−0.328436 | + | 0.944526i | \(0.606522\pi\) | |||||||
\(774\) | −19.4806 | −0.700215 | ||||||||
\(775\) | −35.9737 | −1.29221 | ||||||||
\(776\) | 5.95030 | 0.213603 | ||||||||
\(777\) | 2.39901 | 0.0860639 | ||||||||
\(778\) | −28.4820 | −1.02113 | ||||||||
\(779\) | 0.410639 | 0.0147127 | ||||||||
\(780\) | −16.1422 | −0.577982 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 51.4418 | 1.83955 | ||||||||
\(783\) | 0.958246 | 0.0342449 | ||||||||
\(784\) | −3.03942 | −0.108551 | ||||||||
\(785\) | 4.94947 | 0.176654 | ||||||||
\(786\) | 22.5327 | 0.803716 | ||||||||
\(787\) | 12.2571 | 0.436918 | 0.218459 | − | 0.975846i | \(-0.429897\pi\) | ||||
0.218459 | + | 0.975846i | \(0.429897\pi\) | |||||||
\(788\) | 8.64800 | 0.308072 | ||||||||
\(789\) | −18.6325 | −0.663335 | ||||||||
\(790\) | −61.7171 | −2.19580 | ||||||||
\(791\) | −18.1019 | −0.643628 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 18.2158 | 0.646862 | ||||||||
\(794\) | −8.94549 | −0.317464 | ||||||||
\(795\) | −2.98759 | −0.105959 | ||||||||
\(796\) | −9.24405 | −0.327647 | ||||||||
\(797\) | −22.8561 | −0.809606 | −0.404803 | − | 0.914404i | \(-0.632660\pi\) | ||||
−0.404803 | + | 0.914404i | \(0.632660\pi\) | |||||||
\(798\) | −3.22720 | −0.114242 | ||||||||
\(799\) | 49.4989 | 1.75114 | ||||||||
\(800\) | −40.1305 | −1.41883 | ||||||||
\(801\) | −11.2670 | −0.398100 | ||||||||
\(802\) | −68.0531 | −2.40304 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 31.8532 | 1.12338 | ||||||||
\(805\) | 16.1610 | 0.569600 | ||||||||
\(806\) | 32.2400 | 1.13561 | ||||||||
\(807\) | −20.7126 | −0.729119 | ||||||||
\(808\) | −7.00657 | −0.246490 | ||||||||
\(809\) | 43.6342 | 1.53410 | 0.767048 | − | 0.641589i | \(-0.221725\pi\) | ||||
0.767048 | + | 0.641589i | \(0.221725\pi\) | |||||||
\(810\) | 6.62751 | 0.232867 | ||||||||
\(811\) | 13.8319 | 0.485705 | 0.242853 | − | 0.970063i | \(-0.421917\pi\) | ||||
0.242853 | + | 0.970063i | \(0.421917\pi\) | |||||||
\(812\) | 2.29999 | 0.0807138 | ||||||||
\(813\) | −14.8438 | −0.520593 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −21.5023 | −0.753194 | ||||||||
\(816\) | −14.5719 | −0.510118 | ||||||||
\(817\) | 14.2874 | 0.499854 | ||||||||
\(818\) | 52.2060 | 1.82534 | ||||||||
\(819\) | −2.12862 | −0.0743801 | ||||||||
\(820\) | −2.02411 | −0.0706850 | ||||||||
\(821\) | 19.5987 | 0.684000 | 0.342000 | − | 0.939700i | \(-0.388896\pi\) | ||||
0.342000 | + | 0.939700i | \(0.388896\pi\) | |||||||
\(822\) | −9.28453 | −0.323835 | ||||||||
\(823\) | 38.0461 | 1.32620 | 0.663101 | − | 0.748530i | \(-0.269240\pi\) | ||||
0.663101 | + | 0.748530i | \(0.269240\pi\) | |||||||
\(824\) | −6.32612 | −0.220381 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −20.0343 | −0.697084 | ||||||||
\(827\) | 2.70341 | 0.0940068 | 0.0470034 | − | 0.998895i | \(-0.485033\pi\) | ||||
0.0470034 | + | 0.998895i | \(0.485033\pi\) | |||||||
\(828\) | 12.2773 | 0.426665 | ||||||||
\(829\) | −17.6913 | −0.614444 | −0.307222 | − | 0.951638i | \(-0.599399\pi\) | ||||
−0.307222 | + | 0.951638i | \(0.599399\pi\) | |||||||
\(830\) | 111.697 | 3.87708 | ||||||||
\(831\) | 3.07309 | 0.106604 | ||||||||
\(832\) | 23.0258 | 0.798276 | ||||||||
\(833\) | 4.79430 | 0.166113 | ||||||||
\(834\) | −9.49206 | −0.328683 | ||||||||
\(835\) | 38.7027 | 1.33936 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −7.22037 | −0.249573 | ||||||||
\(838\) | 22.2243 | 0.767725 | ||||||||
\(839\) | 0.168659 | 0.00582276 | 0.00291138 | − | 0.999996i | \(-0.499073\pi\) | ||||
0.00291138 | + | 0.999996i | \(0.499073\pi\) | |||||||
\(840\) | 2.65238 | 0.0915159 | ||||||||
\(841\) | −28.0818 | −0.968337 | ||||||||
\(842\) | −79.4244 | −2.73715 | ||||||||
\(843\) | −4.09698 | −0.141108 | ||||||||
\(844\) | −26.7203 | −0.919749 | ||||||||
\(845\) | −26.7574 | −0.920484 | ||||||||
\(846\) | 21.6574 | 0.744597 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 2.87407 | 0.0986961 | ||||||||
\(849\) | 7.39800 | 0.253899 | ||||||||
\(850\) | 50.1057 | 1.71861 | ||||||||
\(851\) | 12.2711 | 0.420650 | ||||||||
\(852\) | 33.9784 | 1.16408 | ||||||||
\(853\) | 42.9770 | 1.47151 | 0.735753 | − | 0.677250i | \(-0.236829\pi\) | ||||
0.735753 | + | 0.677250i | \(0.236829\pi\) | |||||||
\(854\) | −17.9509 | −0.614267 | ||||||||
\(855\) | −4.86075 | −0.166234 | ||||||||
\(856\) | −12.9189 | −0.441557 | ||||||||
\(857\) | 3.31550 | 0.113255 | 0.0566276 | − | 0.998395i | \(-0.481965\pi\) | ||||
0.0566276 | + | 0.998395i | \(0.481965\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 12.5924 | 0.429646 | 0.214823 | − | 0.976653i | \(-0.431083\pi\) | ||||
0.214823 | + | 0.976653i | \(0.431083\pi\) | |||||||
\(860\) | −70.4252 | −2.40148 | ||||||||
\(861\) | −0.266914 | −0.00909640 | ||||||||
\(862\) | −11.8411 | −0.403309 | ||||||||
\(863\) | −55.8374 | −1.90073 | −0.950363 | − | 0.311143i | \(-0.899288\pi\) | ||||
−0.950363 | + | 0.311143i | \(0.899288\pi\) | |||||||
\(864\) | −8.05469 | −0.274026 | ||||||||
\(865\) | 62.7154 | 2.13239 | ||||||||
\(866\) | −5.65381 | −0.192124 | ||||||||
\(867\) | 5.98536 | 0.203273 | ||||||||
\(868\) | −17.3304 | −0.588232 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 6.35079 | 0.215312 | ||||||||
\(871\) | −28.2490 | −0.957182 | ||||||||
\(872\) | −17.0067 | −0.575921 | ||||||||
\(873\) | 7.08789 | 0.239889 | ||||||||
\(874\) | −16.5074 | −0.558372 | ||||||||
\(875\) | −0.0560984 | −0.00189647 | ||||||||
\(876\) | −18.5344 | −0.626218 | ||||||||
\(877\) | −8.26736 | −0.279169 | −0.139584 | − | 0.990210i | \(-0.544577\pi\) | ||||
−0.139584 | + | 0.990210i | \(0.544577\pi\) | |||||||
\(878\) | −64.1191 | −2.16391 | ||||||||
\(879\) | 10.5489 | 0.355806 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 26.0843 | 0.878803 | 0.439401 | − | 0.898291i | \(-0.355191\pi\) | ||||
0.439401 | + | 0.898291i | \(0.355191\pi\) | |||||||
\(882\) | 2.09767 | 0.0706321 | ||||||||
\(883\) | 0.915087 | 0.0307951 | 0.0153976 | − | 0.999881i | \(-0.495099\pi\) | ||||
0.0153976 | + | 0.999881i | \(0.495099\pi\) | |||||||
\(884\) | −24.4948 | −0.823848 | ||||||||
\(885\) | −30.1754 | −1.01433 | ||||||||
\(886\) | −51.6804 | −1.73624 | ||||||||
\(887\) | 56.0572 | 1.88222 | 0.941108 | − | 0.338107i | \(-0.109786\pi\) | ||||
0.941108 | + | 0.338107i | \(0.109786\pi\) | |||||||
\(888\) | 2.01397 | 0.0675845 | ||||||||
\(889\) | 15.3711 | 0.515530 | ||||||||
\(890\) | −74.6722 | −2.50302 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −12.6520 | −0.423619 | ||||||||
\(893\) | −15.8840 | −0.531537 | ||||||||
\(894\) | −6.28190 | −0.210098 | ||||||||
\(895\) | 25.9781 | 0.868353 | ||||||||
\(896\) | −6.58156 | −0.219875 | ||||||||
\(897\) | −10.8881 | −0.363543 | ||||||||
\(898\) | −32.2528 | −1.07629 | ||||||||
\(899\) | −6.91889 | −0.230758 | ||||||||
\(900\) | 11.9584 | 0.398614 | ||||||||
\(901\) | −4.53349 | −0.151033 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −9.28678 | −0.309045 | ||||||||
\(904\) | −15.1966 | −0.505430 | ||||||||
\(905\) | 32.9586 | 1.09558 | ||||||||
\(906\) | −18.4859 | −0.614153 | ||||||||
\(907\) | 9.24637 | 0.307021 | 0.153510 | − | 0.988147i | \(-0.450942\pi\) | ||||
0.153510 | + | 0.988147i | \(0.450942\pi\) | |||||||
\(908\) | 35.5719 | 1.18050 | ||||||||
\(909\) | −8.34609 | −0.276822 | ||||||||
\(910\) | −14.1075 | −0.467658 | ||||||||
\(911\) | −37.2957 | −1.23566 | −0.617831 | − | 0.786311i | \(-0.711989\pi\) | ||||
−0.617831 | + | 0.786311i | \(0.711989\pi\) | |||||||
\(912\) | 4.67605 | 0.154840 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | −29.8629 | −0.987777 | ||||||||
\(915\) | −27.0373 | −0.893827 | ||||||||
\(916\) | 18.2531 | 0.603098 | ||||||||
\(917\) | 10.7418 | 0.354726 | ||||||||
\(918\) | 10.0569 | 0.331926 | ||||||||
\(919\) | 14.6385 | 0.482880 | 0.241440 | − | 0.970416i | \(-0.422380\pi\) | ||||
0.241440 | + | 0.970416i | \(0.422380\pi\) | |||||||
\(920\) | 13.5672 | 0.447297 | ||||||||
\(921\) | −1.74955 | −0.0576497 | ||||||||
\(922\) | 77.0155 | 2.53637 | ||||||||
\(923\) | −30.1337 | −0.991864 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 11.9524 | 0.392994 | ||||||||
\(926\) | −72.9322 | −2.39670 | ||||||||
\(927\) | −7.53555 | −0.247500 | ||||||||
\(928\) | −7.71838 | −0.253368 | ||||||||
\(929\) | −7.80689 | −0.256136 | −0.128068 | − | 0.991765i | \(-0.540878\pi\) | ||||
−0.128068 | + | 0.991765i | \(0.540878\pi\) | |||||||
\(930\) | −47.8531 | −1.56917 | ||||||||
\(931\) | −1.53847 | −0.0504213 | ||||||||
\(932\) | 3.61337 | 0.118360 | ||||||||
\(933\) | −23.0075 | −0.753231 | ||||||||
\(934\) | 28.4309 | 0.930287 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −1.78698 | −0.0584094 | ||||||||
\(937\) | 53.1013 | 1.73474 | 0.867372 | − | 0.497661i | \(-0.165808\pi\) | ||||
0.867372 | + | 0.497661i | \(0.165808\pi\) | |||||||
\(938\) | 27.8382 | 0.908950 | ||||||||
\(939\) | 18.2568 | 0.595788 | ||||||||
\(940\) | 78.2948 | 2.55369 | ||||||||
\(941\) | 13.0587 | 0.425702 | 0.212851 | − | 0.977085i | \(-0.431725\pi\) | ||||
0.212851 | + | 0.977085i | \(0.431725\pi\) | |||||||
\(942\) | 3.28610 | 0.107067 | ||||||||
\(943\) | −1.36529 | −0.0444599 | ||||||||
\(944\) | 29.0288 | 0.944806 | ||||||||
\(945\) | 3.15947 | 0.102778 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −39.8291 | −1.29427 | −0.647136 | − | 0.762375i | \(-0.724033\pi\) | ||||
−0.647136 | + | 0.762375i | \(0.724033\pi\) | |||||||
\(948\) | −22.3514 | −0.725938 | ||||||||
\(949\) | 16.4372 | 0.533574 | ||||||||
\(950\) | −16.0787 | −0.521662 | ||||||||
\(951\) | 32.6206 | 1.05780 | ||||||||
\(952\) | 4.02483 | 0.130446 | ||||||||
\(953\) | −3.79128 | −0.122812 | −0.0614058 | − | 0.998113i | \(-0.519558\pi\) | ||||
−0.0614058 | + | 0.998113i | \(0.519558\pi\) | |||||||
\(954\) | −1.98355 | −0.0642199 | ||||||||
\(955\) | 44.9157 | 1.45344 | ||||||||
\(956\) | 12.0571 | 0.389955 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −57.8899 | −1.87034 | ||||||||
\(959\) | −4.42612 | −0.142927 | ||||||||
\(960\) | −34.1767 | −1.10305 | ||||||||
\(961\) | 21.1338 | 0.681735 | ||||||||
\(962\) | −10.7119 | −0.345366 | ||||||||
\(963\) | −15.3887 | −0.495894 | ||||||||
\(964\) | −38.7639 | −1.24850 | ||||||||
\(965\) | 22.1679 | 0.713609 | ||||||||
\(966\) | 10.7298 | 0.345224 | ||||||||
\(967\) | −5.63563 | −0.181230 | −0.0906149 | − | 0.995886i | \(-0.528883\pi\) | ||||
−0.0906149 | + | 0.995886i | \(0.528883\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −7.37589 | −0.236948 | ||||||||
\(970\) | 46.9751 | 1.50828 | ||||||||
\(971\) | −2.41724 | −0.0775729 | −0.0387865 | − | 0.999248i | \(-0.512349\pi\) | ||||
−0.0387865 | + | 0.999248i | \(0.512349\pi\) | |||||||
\(972\) | 2.40021 | 0.0769867 | ||||||||
\(973\) | −4.52505 | −0.145067 | ||||||||
\(974\) | −42.9555 | −1.37638 | ||||||||
\(975\) | −10.6053 | −0.339642 | ||||||||
\(976\) | 26.0100 | 0.832560 | ||||||||
\(977\) | 46.6426 | 1.49223 | 0.746114 | − | 0.665818i | \(-0.231917\pi\) | ||||
0.746114 | + | 0.665818i | \(0.231917\pi\) | |||||||
\(978\) | −14.2760 | −0.456498 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 7.58338 | 0.242242 | ||||||||
\(981\) | −20.2581 | −0.646792 | ||||||||
\(982\) | −60.5521 | −1.93230 | ||||||||
\(983\) | 21.6905 | 0.691821 | 0.345910 | − | 0.938268i | \(-0.387570\pi\) | ||||
0.345910 | + | 0.938268i | \(0.387570\pi\) | |||||||
\(984\) | −0.224075 | −0.00714325 | ||||||||
\(985\) | 11.3836 | 0.362713 | ||||||||
\(986\) | 9.63694 | 0.306903 | ||||||||
\(987\) | 10.3245 | 0.328633 | ||||||||
\(988\) | 7.86026 | 0.250068 | ||||||||
\(989\) | −47.5027 | −1.51050 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 33.7715 | 1.07279 | 0.536394 | − | 0.843968i | \(-0.319786\pi\) | ||||
0.536394 | + | 0.843968i | \(0.319786\pi\) | |||||||
\(992\) | 58.1579 | 1.84652 | ||||||||
\(993\) | 6.80537 | 0.215962 | ||||||||
\(994\) | 29.6955 | 0.941884 | ||||||||
\(995\) | −12.1682 | −0.385759 | ||||||||
\(996\) | 40.4521 | 1.28178 | ||||||||
\(997\) | −0.624922 | −0.0197915 | −0.00989575 | − | 0.999951i | \(-0.503150\pi\) | ||||
−0.00989575 | + | 0.999951i | \(0.503150\pi\) | |||||||
\(998\) | −45.0872 | −1.42721 | ||||||||
\(999\) | 2.39901 | 0.0759013 |
(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 | 2541.2.a.br.1.8 | 10 | ||
3.2 | odd | 2 | 7623.2.a.cy.1.3 | 10 | |||
11.7 | odd | 10 | 231.2.j.g.148.2 | yes | 20 | ||
11.8 | odd | 10 | 231.2.j.g.64.2 | ✓ | 20 | ||
11.10 | odd | 2 | 2541.2.a.bq.1.3 | 10 | |||
33.8 | even | 10 | 693.2.m.j.64.4 | 20 | |||
33.29 | even | 10 | 693.2.m.j.379.4 | 20 | |||
33.32 | even | 2 | 7623.2.a.cx.1.8 | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
231.2.j.g.64.2 | ✓ | 20 | 11.8 | odd | 10 | ||
231.2.j.g.148.2 | yes | 20 | 11.7 | odd | 10 | ||
693.2.m.j.64.4 | 20 | 33.8 | even | 10 | |||
693.2.m.j.379.4 | 20 | 33.29 | even | 10 | |||
2541.2.a.bq.1.3 | 10 | 11.10 | odd | 2 | |||
2541.2.a.br.1.8 | 10 | 1.1 | even | 1 | trivial | ||
7623.2.a.cx.1.8 | 10 | 33.32 | even | 2 | |||
7623.2.a.cy.1.3 | 10 | 3.2 | odd | 2 |