Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8043,2,Mod(1,8043)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8043, 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("8043.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8043 = 3 \cdot 7 \cdot 383 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8043.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(64.2236783457\) |
Analytic rank: | \(0\) |
Dimension: | \(53\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.7 | ||
Character | \(\chi\) | \(=\) | 8043.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.15559 | −1.52423 | −0.762116 | − | 0.647440i | \(-0.775839\pi\) | ||||
−0.762116 | + | 0.647440i | \(0.775839\pi\) | |||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 2.64657 | 1.32328 | ||||||||
\(5\) | 3.65015 | 1.63240 | 0.816199 | − | 0.577771i | \(-0.196077\pi\) | ||||
0.816199 | + | 0.577771i | \(0.196077\pi\) | |||||||
\(6\) | −2.15559 | −0.880016 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | −1.39373 | −0.492759 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −7.86823 | −2.48815 | ||||||||
\(11\) | −2.40764 | −0.725930 | −0.362965 | − | 0.931803i | \(-0.618236\pi\) | ||||
−0.362965 | + | 0.931803i | \(0.618236\pi\) | |||||||
\(12\) | 2.64657 | 0.763998 | ||||||||
\(13\) | 5.41813 | 1.50272 | 0.751359 | − | 0.659893i | \(-0.229399\pi\) | ||||
0.751359 | + | 0.659893i | \(0.229399\pi\) | |||||||
\(14\) | −2.15559 | −0.576106 | ||||||||
\(15\) | 3.65015 | 0.942465 | ||||||||
\(16\) | −2.28882 | −0.572204 | ||||||||
\(17\) | 2.19164 | 0.531550 | 0.265775 | − | 0.964035i | \(-0.414372\pi\) | ||||
0.265775 | + | 0.964035i | \(0.414372\pi\) | |||||||
\(18\) | −2.15559 | −0.508077 | ||||||||
\(19\) | 3.14459 | 0.721419 | 0.360709 | − | 0.932678i | \(-0.382535\pi\) | ||||
0.360709 | + | 0.932678i | \(0.382535\pi\) | |||||||
\(20\) | 9.66037 | 2.16012 | ||||||||
\(21\) | 1.00000 | 0.218218 | ||||||||
\(22\) | 5.18988 | 1.10649 | ||||||||
\(23\) | −3.57444 | −0.745323 | −0.372661 | − | 0.927967i | \(-0.621555\pi\) | ||||
−0.372661 | + | 0.927967i | \(0.621555\pi\) | |||||||
\(24\) | −1.39373 | −0.284495 | ||||||||
\(25\) | 8.32361 | 1.66472 | ||||||||
\(26\) | −11.6793 | −2.29049 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 2.64657 | 0.500154 | ||||||||
\(29\) | 6.48940 | 1.20505 | 0.602526 | − | 0.798099i | \(-0.294161\pi\) | ||||
0.602526 | + | 0.798099i | \(0.294161\pi\) | |||||||
\(30\) | −7.86823 | −1.43654 | ||||||||
\(31\) | −9.56205 | −1.71740 | −0.858698 | − | 0.512482i | \(-0.828726\pi\) | ||||
−0.858698 | + | 0.512482i | \(0.828726\pi\) | |||||||
\(32\) | 7.72122 | 1.36493 | ||||||||
\(33\) | −2.40764 | −0.419116 | ||||||||
\(34\) | −4.72427 | −0.810206 | ||||||||
\(35\) | 3.65015 | 0.616988 | ||||||||
\(36\) | 2.64657 | 0.441094 | ||||||||
\(37\) | −6.05844 | −0.996002 | −0.498001 | − | 0.867177i | \(-0.665932\pi\) | ||||
−0.498001 | + | 0.867177i | \(0.665932\pi\) | |||||||
\(38\) | −6.77845 | −1.09961 | ||||||||
\(39\) | 5.41813 | 0.867595 | ||||||||
\(40\) | −5.08734 | −0.804379 | ||||||||
\(41\) | 10.1134 | 1.57945 | 0.789726 | − | 0.613460i | \(-0.210223\pi\) | ||||
0.789726 | + | 0.613460i | \(0.210223\pi\) | |||||||
\(42\) | −2.15559 | −0.332615 | ||||||||
\(43\) | 5.55063 | 0.846464 | 0.423232 | − | 0.906021i | \(-0.360896\pi\) | ||||
0.423232 | + | 0.906021i | \(0.360896\pi\) | |||||||
\(44\) | −6.37197 | −0.960611 | ||||||||
\(45\) | 3.65015 | 0.544133 | ||||||||
\(46\) | 7.70503 | 1.13604 | ||||||||
\(47\) | 4.65440 | 0.678913 | 0.339457 | − | 0.940622i | \(-0.389757\pi\) | ||||
0.339457 | + | 0.940622i | \(0.389757\pi\) | |||||||
\(48\) | −2.28882 | −0.330362 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | −17.9423 | −2.53742 | ||||||||
\(51\) | 2.19164 | 0.306891 | ||||||||
\(52\) | 14.3394 | 1.98852 | ||||||||
\(53\) | −4.77275 | −0.655587 | −0.327793 | − | 0.944749i | \(-0.606305\pi\) | ||||
−0.327793 | + | 0.944749i | \(0.606305\pi\) | |||||||
\(54\) | −2.15559 | −0.293339 | ||||||||
\(55\) | −8.78824 | −1.18501 | ||||||||
\(56\) | −1.39373 | −0.186245 | ||||||||
\(57\) | 3.14459 | 0.416511 | ||||||||
\(58\) | −13.9885 | −1.83678 | ||||||||
\(59\) | 2.92751 | 0.381129 | 0.190564 | − | 0.981675i | \(-0.438968\pi\) | ||||
0.190564 | + | 0.981675i | \(0.438968\pi\) | |||||||
\(60\) | 9.66037 | 1.24715 | ||||||||
\(61\) | −5.72176 | −0.732597 | −0.366298 | − | 0.930497i | \(-0.619375\pi\) | ||||
−0.366298 | + | 0.930497i | \(0.619375\pi\) | |||||||
\(62\) | 20.6119 | 2.61771 | ||||||||
\(63\) | 1.00000 | 0.125988 | ||||||||
\(64\) | −12.0661 | −1.50827 | ||||||||
\(65\) | 19.7770 | 2.45303 | ||||||||
\(66\) | 5.18988 | 0.638830 | ||||||||
\(67\) | 5.54279 | 0.677160 | 0.338580 | − | 0.940938i | \(-0.390053\pi\) | ||||
0.338580 | + | 0.940938i | \(0.390053\pi\) | |||||||
\(68\) | 5.80032 | 0.703392 | ||||||||
\(69\) | −3.57444 | −0.430312 | ||||||||
\(70\) | −7.86823 | −0.940433 | ||||||||
\(71\) | 0.0521291 | 0.00618658 | 0.00309329 | − | 0.999995i | \(-0.499015\pi\) | ||||
0.00309329 | + | 0.999995i | \(0.499015\pi\) | |||||||
\(72\) | −1.39373 | −0.164253 | ||||||||
\(73\) | 13.9762 | 1.63579 | 0.817895 | − | 0.575367i | \(-0.195141\pi\) | ||||
0.817895 | + | 0.575367i | \(0.195141\pi\) | |||||||
\(74\) | 13.0595 | 1.51814 | ||||||||
\(75\) | 8.32361 | 0.961128 | ||||||||
\(76\) | 8.32237 | 0.954641 | ||||||||
\(77\) | −2.40764 | −0.274376 | ||||||||
\(78\) | −11.6793 | −1.32242 | ||||||||
\(79\) | −7.64587 | −0.860228 | −0.430114 | − | 0.902775i | \(-0.641527\pi\) | ||||
−0.430114 | + | 0.902775i | \(0.641527\pi\) | |||||||
\(80\) | −8.35453 | −0.934065 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −21.8004 | −2.40745 | ||||||||
\(83\) | −8.88061 | −0.974774 | −0.487387 | − | 0.873186i | \(-0.662050\pi\) | ||||
−0.487387 | + | 0.873186i | \(0.662050\pi\) | |||||||
\(84\) | 2.64657 | 0.288764 | ||||||||
\(85\) | 7.99981 | 0.867702 | ||||||||
\(86\) | −11.9649 | −1.29021 | ||||||||
\(87\) | 6.48940 | 0.695737 | ||||||||
\(88\) | 3.35560 | 0.357708 | ||||||||
\(89\) | −5.52135 | −0.585262 | −0.292631 | − | 0.956225i | \(-0.594531\pi\) | ||||
−0.292631 | + | 0.956225i | \(0.594531\pi\) | |||||||
\(90\) | −7.86823 | −0.829384 | ||||||||
\(91\) | 5.41813 | 0.567974 | ||||||||
\(92\) | −9.46000 | −0.986273 | ||||||||
\(93\) | −9.56205 | −0.991539 | ||||||||
\(94\) | −10.0330 | −1.03482 | ||||||||
\(95\) | 11.4782 | 1.17764 | ||||||||
\(96\) | 7.72122 | 0.788043 | ||||||||
\(97\) | 0.287463 | 0.0291875 | 0.0145937 | − | 0.999894i | \(-0.495355\pi\) | ||||
0.0145937 | + | 0.999894i | \(0.495355\pi\) | |||||||
\(98\) | −2.15559 | −0.217747 | ||||||||
\(99\) | −2.40764 | −0.241977 | ||||||||
\(100\) | 22.0290 | 2.20290 | ||||||||
\(101\) | 4.34648 | 0.432491 | 0.216246 | − | 0.976339i | \(-0.430619\pi\) | ||||
0.216246 | + | 0.976339i | \(0.430619\pi\) | |||||||
\(102\) | −4.72427 | −0.467773 | ||||||||
\(103\) | −11.5843 | −1.14143 | −0.570716 | − | 0.821147i | \(-0.693334\pi\) | ||||
−0.570716 | + | 0.821147i | \(0.693334\pi\) | |||||||
\(104\) | −7.55142 | −0.740478 | ||||||||
\(105\) | 3.65015 | 0.356218 | ||||||||
\(106\) | 10.2881 | 0.999267 | ||||||||
\(107\) | −13.8875 | −1.34255 | −0.671276 | − | 0.741207i | \(-0.734254\pi\) | ||||
−0.671276 | + | 0.741207i | \(0.734254\pi\) | |||||||
\(108\) | 2.64657 | 0.254666 | ||||||||
\(109\) | 13.7979 | 1.32160 | 0.660802 | − | 0.750561i | \(-0.270216\pi\) | ||||
0.660802 | + | 0.750561i | \(0.270216\pi\) | |||||||
\(110\) | 18.9438 | 1.80622 | ||||||||
\(111\) | −6.05844 | −0.575042 | ||||||||
\(112\) | −2.28882 | −0.216273 | ||||||||
\(113\) | −3.49061 | −0.328369 | −0.164184 | − | 0.986430i | \(-0.552499\pi\) | ||||
−0.164184 | + | 0.986430i | \(0.552499\pi\) | |||||||
\(114\) | −6.77845 | −0.634860 | ||||||||
\(115\) | −13.0473 | −1.21666 | ||||||||
\(116\) | 17.1746 | 1.59463 | ||||||||
\(117\) | 5.41813 | 0.500906 | ||||||||
\(118\) | −6.31050 | −0.580929 | ||||||||
\(119\) | 2.19164 | 0.200907 | ||||||||
\(120\) | −5.08734 | −0.464408 | ||||||||
\(121\) | −5.20329 | −0.473026 | ||||||||
\(122\) | 12.3338 | 1.11665 | ||||||||
\(123\) | 10.1134 | 0.911897 | ||||||||
\(124\) | −25.3066 | −2.27260 | ||||||||
\(125\) | 12.1317 | 1.08509 | ||||||||
\(126\) | −2.15559 | −0.192035 | ||||||||
\(127\) | 1.66509 | 0.147753 | 0.0738764 | − | 0.997267i | \(-0.476463\pi\) | ||||
0.0738764 | + | 0.997267i | \(0.476463\pi\) | |||||||
\(128\) | 10.5672 | 0.934019 | ||||||||
\(129\) | 5.55063 | 0.488706 | ||||||||
\(130\) | −42.6311 | −3.73899 | ||||||||
\(131\) | −7.50074 | −0.655343 | −0.327672 | − | 0.944792i | \(-0.606264\pi\) | ||||
−0.327672 | + | 0.944792i | \(0.606264\pi\) | |||||||
\(132\) | −6.37197 | −0.554609 | ||||||||
\(133\) | 3.14459 | 0.272671 | ||||||||
\(134\) | −11.9480 | −1.03215 | ||||||||
\(135\) | 3.65015 | 0.314155 | ||||||||
\(136\) | −3.05456 | −0.261926 | ||||||||
\(137\) | 13.7101 | 1.17133 | 0.585664 | − | 0.810554i | \(-0.300834\pi\) | ||||
0.585664 | + | 0.810554i | \(0.300834\pi\) | |||||||
\(138\) | 7.70503 | 0.655896 | ||||||||
\(139\) | 16.8845 | 1.43213 | 0.716063 | − | 0.698036i | \(-0.245942\pi\) | ||||
0.716063 | + | 0.698036i | \(0.245942\pi\) | |||||||
\(140\) | 9.66037 | 0.816450 | ||||||||
\(141\) | 4.65440 | 0.391971 | ||||||||
\(142\) | −0.112369 | −0.00942979 | ||||||||
\(143\) | −13.0449 | −1.09087 | ||||||||
\(144\) | −2.28882 | −0.190735 | ||||||||
\(145\) | 23.6873 | 1.96712 | ||||||||
\(146\) | −30.1270 | −2.49332 | ||||||||
\(147\) | 1.00000 | 0.0824786 | ||||||||
\(148\) | −16.0341 | −1.31799 | ||||||||
\(149\) | 16.3997 | 1.34352 | 0.671759 | − | 0.740770i | \(-0.265539\pi\) | ||||
0.671759 | + | 0.740770i | \(0.265539\pi\) | |||||||
\(150\) | −17.9423 | −1.46498 | ||||||||
\(151\) | 18.5869 | 1.51258 | 0.756289 | − | 0.654238i | \(-0.227010\pi\) | ||||
0.756289 | + | 0.654238i | \(0.227010\pi\) | |||||||
\(152\) | −4.38272 | −0.355486 | ||||||||
\(153\) | 2.19164 | 0.177183 | ||||||||
\(154\) | 5.18988 | 0.418212 | ||||||||
\(155\) | −34.9030 | −2.80347 | ||||||||
\(156\) | 14.3394 | 1.14807 | ||||||||
\(157\) | −4.65606 | −0.371594 | −0.185797 | − | 0.982588i | \(-0.559487\pi\) | ||||
−0.185797 | + | 0.982588i | \(0.559487\pi\) | |||||||
\(158\) | 16.4814 | 1.31119 | ||||||||
\(159\) | −4.77275 | −0.378503 | ||||||||
\(160\) | 28.1836 | 2.22811 | ||||||||
\(161\) | −3.57444 | −0.281706 | ||||||||
\(162\) | −2.15559 | −0.169359 | ||||||||
\(163\) | −14.5124 | −1.13670 | −0.568351 | − | 0.822786i | \(-0.692418\pi\) | ||||
−0.568351 | + | 0.822786i | \(0.692418\pi\) | |||||||
\(164\) | 26.7659 | 2.09006 | ||||||||
\(165\) | −8.78824 | −0.684164 | ||||||||
\(166\) | 19.1430 | 1.48578 | ||||||||
\(167\) | 18.3195 | 1.41760 | 0.708801 | − | 0.705408i | \(-0.249236\pi\) | ||||
0.708801 | + | 0.705408i | \(0.249236\pi\) | |||||||
\(168\) | −1.39373 | −0.107529 | ||||||||
\(169\) | 16.3561 | 1.25816 | ||||||||
\(170\) | −17.2443 | −1.32258 | ||||||||
\(171\) | 3.14459 | 0.240473 | ||||||||
\(172\) | 14.6901 | 1.12011 | ||||||||
\(173\) | 19.0336 | 1.44710 | 0.723549 | − | 0.690273i | \(-0.242510\pi\) | ||||
0.723549 | + | 0.690273i | \(0.242510\pi\) | |||||||
\(174\) | −13.9885 | −1.06046 | ||||||||
\(175\) | 8.32361 | 0.629206 | ||||||||
\(176\) | 5.51064 | 0.415380 | ||||||||
\(177\) | 2.92751 | 0.220045 | ||||||||
\(178\) | 11.9018 | 0.892075 | ||||||||
\(179\) | 9.03796 | 0.675529 | 0.337764 | − | 0.941231i | \(-0.390329\pi\) | ||||
0.337764 | + | 0.941231i | \(0.390329\pi\) | |||||||
\(180\) | 9.66037 | 0.720042 | ||||||||
\(181\) | −26.3548 | −1.95894 | −0.979468 | − | 0.201599i | \(-0.935386\pi\) | ||||
−0.979468 | + | 0.201599i | \(0.935386\pi\) | |||||||
\(182\) | −11.6793 | −0.865724 | ||||||||
\(183\) | −5.72176 | −0.422965 | ||||||||
\(184\) | 4.98182 | 0.367264 | ||||||||
\(185\) | −22.1142 | −1.62587 | ||||||||
\(186\) | 20.6119 | 1.51134 | ||||||||
\(187\) | −5.27667 | −0.385868 | ||||||||
\(188\) | 12.3182 | 0.898395 | ||||||||
\(189\) | 1.00000 | 0.0727393 | ||||||||
\(190\) | −24.7424 | −1.79500 | ||||||||
\(191\) | 23.2967 | 1.68569 | 0.842844 | − | 0.538158i | \(-0.180880\pi\) | ||||
0.842844 | + | 0.538158i | \(0.180880\pi\) | |||||||
\(192\) | −12.0661 | −0.870799 | ||||||||
\(193\) | −7.71605 | −0.555413 | −0.277707 | − | 0.960666i | \(-0.589574\pi\) | ||||
−0.277707 | + | 0.960666i | \(0.589574\pi\) | |||||||
\(194\) | −0.619653 | −0.0444885 | ||||||||
\(195\) | 19.7770 | 1.41626 | ||||||||
\(196\) | 2.64657 | 0.189040 | ||||||||
\(197\) | 3.04912 | 0.217241 | 0.108620 | − | 0.994083i | \(-0.465357\pi\) | ||||
0.108620 | + | 0.994083i | \(0.465357\pi\) | |||||||
\(198\) | 5.18988 | 0.368828 | ||||||||
\(199\) | −7.35446 | −0.521344 | −0.260672 | − | 0.965427i | \(-0.583944\pi\) | ||||
−0.260672 | + | 0.965427i | \(0.583944\pi\) | |||||||
\(200\) | −11.6009 | −0.820307 | ||||||||
\(201\) | 5.54279 | 0.390958 | ||||||||
\(202\) | −9.36923 | −0.659217 | ||||||||
\(203\) | 6.48940 | 0.455467 | ||||||||
\(204\) | 5.80032 | 0.406103 | ||||||||
\(205\) | 36.9156 | 2.57829 | ||||||||
\(206\) | 24.9709 | 1.73981 | ||||||||
\(207\) | −3.57444 | −0.248441 | ||||||||
\(208\) | −12.4011 | −0.859862 | ||||||||
\(209\) | −7.57103 | −0.523699 | ||||||||
\(210\) | −7.86823 | −0.542959 | ||||||||
\(211\) | 3.36809 | 0.231869 | 0.115935 | − | 0.993257i | \(-0.463014\pi\) | ||||
0.115935 | + | 0.993257i | \(0.463014\pi\) | |||||||
\(212\) | −12.6314 | −0.867527 | ||||||||
\(213\) | 0.0521291 | 0.00357183 | ||||||||
\(214\) | 29.9357 | 2.04636 | ||||||||
\(215\) | 20.2607 | 1.38177 | ||||||||
\(216\) | −1.39373 | −0.0948315 | ||||||||
\(217\) | −9.56205 | −0.649115 | ||||||||
\(218\) | −29.7427 | −2.01443 | ||||||||
\(219\) | 13.9762 | 0.944424 | ||||||||
\(220\) | −23.2587 | −1.56810 | ||||||||
\(221\) | 11.8746 | 0.798770 | ||||||||
\(222\) | 13.0595 | 0.876497 | ||||||||
\(223\) | −2.37933 | −0.159332 | −0.0796660 | − | 0.996822i | \(-0.525385\pi\) | ||||
−0.0796660 | + | 0.996822i | \(0.525385\pi\) | |||||||
\(224\) | 7.72122 | 0.515896 | ||||||||
\(225\) | 8.32361 | 0.554907 | ||||||||
\(226\) | 7.52431 | 0.500510 | ||||||||
\(227\) | 14.8099 | 0.982967 | 0.491483 | − | 0.870887i | \(-0.336455\pi\) | ||||
0.491483 | + | 0.870887i | \(0.336455\pi\) | |||||||
\(228\) | 8.32237 | 0.551162 | ||||||||
\(229\) | 11.8892 | 0.785660 | 0.392830 | − | 0.919611i | \(-0.371496\pi\) | ||||
0.392830 | + | 0.919611i | \(0.371496\pi\) | |||||||
\(230\) | 28.1245 | 1.85448 | ||||||||
\(231\) | −2.40764 | −0.158411 | ||||||||
\(232\) | −9.04450 | −0.593800 | ||||||||
\(233\) | −21.2250 | −1.39050 | −0.695249 | − | 0.718769i | \(-0.744706\pi\) | ||||
−0.695249 | + | 0.718769i | \(0.744706\pi\) | |||||||
\(234\) | −11.6793 | −0.763497 | ||||||||
\(235\) | 16.9893 | 1.10826 | ||||||||
\(236\) | 7.74784 | 0.504342 | ||||||||
\(237\) | −7.64587 | −0.496653 | ||||||||
\(238\) | −4.72427 | −0.306229 | ||||||||
\(239\) | −25.1699 | −1.62810 | −0.814052 | − | 0.580792i | \(-0.802743\pi\) | ||||
−0.814052 | + | 0.580792i | \(0.802743\pi\) | |||||||
\(240\) | −8.35453 | −0.539283 | ||||||||
\(241\) | 13.8128 | 0.889761 | 0.444880 | − | 0.895590i | \(-0.353246\pi\) | ||||
0.444880 | + | 0.895590i | \(0.353246\pi\) | |||||||
\(242\) | 11.2161 | 0.721001 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | −15.1430 | −0.969433 | ||||||||
\(245\) | 3.65015 | 0.233200 | ||||||||
\(246\) | −21.8004 | −1.38994 | ||||||||
\(247\) | 17.0378 | 1.08409 | ||||||||
\(248\) | 13.3269 | 0.846262 | ||||||||
\(249\) | −8.88061 | −0.562786 | ||||||||
\(250\) | −26.1509 | −1.65393 | ||||||||
\(251\) | 20.4634 | 1.29164 | 0.645820 | − | 0.763490i | \(-0.276516\pi\) | ||||
0.645820 | + | 0.763490i | \(0.276516\pi\) | |||||||
\(252\) | 2.64657 | 0.166718 | ||||||||
\(253\) | 8.60596 | 0.541052 | ||||||||
\(254\) | −3.58925 | −0.225210 | ||||||||
\(255\) | 7.99981 | 0.500968 | ||||||||
\(256\) | 1.35370 | 0.0846065 | ||||||||
\(257\) | −0.0952126 | −0.00593920 | −0.00296960 | − | 0.999996i | \(-0.500945\pi\) | ||||
−0.00296960 | + | 0.999996i | \(0.500945\pi\) | |||||||
\(258\) | −11.9649 | −0.744901 | ||||||||
\(259\) | −6.05844 | −0.376453 | ||||||||
\(260\) | 52.3411 | 3.24606 | ||||||||
\(261\) | 6.48940 | 0.401684 | ||||||||
\(262\) | 16.1685 | 0.998895 | ||||||||
\(263\) | −8.14349 | −0.502149 | −0.251075 | − | 0.967968i | \(-0.580784\pi\) | ||||
−0.251075 | + | 0.967968i | \(0.580784\pi\) | |||||||
\(264\) | 3.35560 | 0.206523 | ||||||||
\(265\) | −17.4212 | −1.07018 | ||||||||
\(266\) | −6.77845 | −0.415613 | ||||||||
\(267\) | −5.52135 | −0.337901 | ||||||||
\(268\) | 14.6694 | 0.896074 | ||||||||
\(269\) | 16.7336 | 1.02027 | 0.510134 | − | 0.860095i | \(-0.329596\pi\) | ||||
0.510134 | + | 0.860095i | \(0.329596\pi\) | |||||||
\(270\) | −7.86823 | −0.478845 | ||||||||
\(271\) | −8.33824 | −0.506512 | −0.253256 | − | 0.967399i | \(-0.581502\pi\) | ||||
−0.253256 | + | 0.967399i | \(0.581502\pi\) | |||||||
\(272\) | −5.01626 | −0.304155 | ||||||||
\(273\) | 5.41813 | 0.327920 | ||||||||
\(274\) | −29.5532 | −1.78538 | ||||||||
\(275\) | −20.0402 | −1.20847 | ||||||||
\(276\) | −9.46000 | −0.569425 | ||||||||
\(277\) | −28.1966 | −1.69417 | −0.847083 | − | 0.531460i | \(-0.821644\pi\) | ||||
−0.847083 | + | 0.531460i | \(0.821644\pi\) | |||||||
\(278\) | −36.3961 | −2.18289 | ||||||||
\(279\) | −9.56205 | −0.572465 | ||||||||
\(280\) | −5.08734 | −0.304027 | ||||||||
\(281\) | 9.23440 | 0.550878 | 0.275439 | − | 0.961319i | \(-0.411177\pi\) | ||||
0.275439 | + | 0.961319i | \(0.411177\pi\) | |||||||
\(282\) | −10.0330 | −0.597454 | ||||||||
\(283\) | −17.9477 | −1.06688 | −0.533441 | − | 0.845837i | \(-0.679102\pi\) | ||||
−0.533441 | + | 0.845837i | \(0.679102\pi\) | |||||||
\(284\) | 0.137963 | 0.00818660 | ||||||||
\(285\) | 11.4782 | 0.679912 | ||||||||
\(286\) | 28.1194 | 1.66274 | ||||||||
\(287\) | 10.1134 | 0.596977 | ||||||||
\(288\) | 7.72122 | 0.454977 | ||||||||
\(289\) | −12.1967 | −0.717454 | ||||||||
\(290\) | −51.0601 | −2.99835 | ||||||||
\(291\) | 0.287463 | 0.0168514 | ||||||||
\(292\) | 36.9889 | 2.16461 | ||||||||
\(293\) | 5.88333 | 0.343708 | 0.171854 | − | 0.985122i | \(-0.445024\pi\) | ||||
0.171854 | + | 0.985122i | \(0.445024\pi\) | |||||||
\(294\) | −2.15559 | −0.125717 | ||||||||
\(295\) | 10.6858 | 0.622154 | ||||||||
\(296\) | 8.44385 | 0.490789 | ||||||||
\(297\) | −2.40764 | −0.139705 | ||||||||
\(298\) | −35.3511 | −2.04783 | ||||||||
\(299\) | −19.3668 | −1.12001 | ||||||||
\(300\) | 22.0290 | 1.27184 | ||||||||
\(301\) | 5.55063 | 0.319933 | ||||||||
\(302\) | −40.0657 | −2.30552 | ||||||||
\(303\) | 4.34648 | 0.249699 | ||||||||
\(304\) | −7.19740 | −0.412799 | ||||||||
\(305\) | −20.8853 | −1.19589 | ||||||||
\(306\) | −4.72427 | −0.270069 | ||||||||
\(307\) | −15.0865 | −0.861032 | −0.430516 | − | 0.902583i | \(-0.641668\pi\) | ||||
−0.430516 | + | 0.902583i | \(0.641668\pi\) | |||||||
\(308\) | −6.37197 | −0.363077 | ||||||||
\(309\) | −11.5843 | −0.659006 | ||||||||
\(310\) | 75.2364 | 4.27314 | ||||||||
\(311\) | 16.1821 | 0.917605 | 0.458803 | − | 0.888538i | \(-0.348278\pi\) | ||||
0.458803 | + | 0.888538i | \(0.348278\pi\) | |||||||
\(312\) | −7.55142 | −0.427515 | ||||||||
\(313\) | 2.62515 | 0.148382 | 0.0741912 | − | 0.997244i | \(-0.476363\pi\) | ||||
0.0741912 | + | 0.997244i | \(0.476363\pi\) | |||||||
\(314\) | 10.0366 | 0.566395 | ||||||||
\(315\) | 3.65015 | 0.205663 | ||||||||
\(316\) | −20.2353 | −1.13833 | ||||||||
\(317\) | 15.6924 | 0.881374 | 0.440687 | − | 0.897661i | \(-0.354735\pi\) | ||||
0.440687 | + | 0.897661i | \(0.354735\pi\) | |||||||
\(318\) | 10.2881 | 0.576927 | ||||||||
\(319\) | −15.6241 | −0.874783 | ||||||||
\(320\) | −44.0433 | −2.46209 | ||||||||
\(321\) | −13.8875 | −0.775123 | ||||||||
\(322\) | 7.70503 | 0.429385 | ||||||||
\(323\) | 6.89181 | 0.383470 | ||||||||
\(324\) | 2.64657 | 0.147031 | ||||||||
\(325\) | 45.0984 | 2.50161 | ||||||||
\(326\) | 31.2828 | 1.73260 | ||||||||
\(327\) | 13.7979 | 0.763028 | ||||||||
\(328\) | −14.0954 | −0.778289 | ||||||||
\(329\) | 4.65440 | 0.256605 | ||||||||
\(330\) | 18.9438 | 1.04282 | ||||||||
\(331\) | −14.3093 | −0.786510 | −0.393255 | − | 0.919430i | \(-0.628651\pi\) | ||||
−0.393255 | + | 0.919430i | \(0.628651\pi\) | |||||||
\(332\) | −23.5031 | −1.28990 | ||||||||
\(333\) | −6.05844 | −0.332001 | ||||||||
\(334\) | −39.4892 | −2.16075 | ||||||||
\(335\) | 20.2320 | 1.10539 | ||||||||
\(336\) | −2.28882 | −0.124865 | ||||||||
\(337\) | −10.5620 | −0.575350 | −0.287675 | − | 0.957728i | \(-0.592882\pi\) | ||||
−0.287675 | + | 0.957728i | \(0.592882\pi\) | |||||||
\(338\) | −35.2571 | −1.91773 | ||||||||
\(339\) | −3.49061 | −0.189584 | ||||||||
\(340\) | 21.1720 | 1.14822 | ||||||||
\(341\) | 23.0220 | 1.24671 | ||||||||
\(342\) | −6.77845 | −0.366536 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | −7.73610 | −0.417103 | ||||||||
\(345\) | −13.0473 | −0.702441 | ||||||||
\(346\) | −41.0286 | −2.20571 | ||||||||
\(347\) | 16.5244 | 0.887075 | 0.443537 | − | 0.896256i | \(-0.353723\pi\) | ||||
0.443537 | + | 0.896256i | \(0.353723\pi\) | |||||||
\(348\) | 17.1746 | 0.920658 | ||||||||
\(349\) | −10.8420 | −0.580360 | −0.290180 | − | 0.956972i | \(-0.593715\pi\) | ||||
−0.290180 | + | 0.956972i | \(0.593715\pi\) | |||||||
\(350\) | −17.9423 | −0.959056 | ||||||||
\(351\) | 5.41813 | 0.289198 | ||||||||
\(352\) | −18.5899 | −0.990844 | ||||||||
\(353\) | −22.4569 | −1.19526 | −0.597631 | − | 0.801771i | \(-0.703891\pi\) | ||||
−0.597631 | + | 0.801771i | \(0.703891\pi\) | |||||||
\(354\) | −6.31050 | −0.335399 | ||||||||
\(355\) | 0.190279 | 0.0100990 | ||||||||
\(356\) | −14.6126 | −0.774468 | ||||||||
\(357\) | 2.19164 | 0.115994 | ||||||||
\(358\) | −19.4821 | −1.02966 | ||||||||
\(359\) | −18.4578 | −0.974168 | −0.487084 | − | 0.873355i | \(-0.661939\pi\) | ||||
−0.487084 | + | 0.873355i | \(0.661939\pi\) | |||||||
\(360\) | −5.08734 | −0.268126 | ||||||||
\(361\) | −9.11155 | −0.479555 | ||||||||
\(362\) | 56.8101 | 2.98587 | ||||||||
\(363\) | −5.20329 | −0.273102 | ||||||||
\(364\) | 14.3394 | 0.751591 | ||||||||
\(365\) | 51.0153 | 2.67026 | ||||||||
\(366\) | 12.3338 | 0.644697 | ||||||||
\(367\) | 1.80127 | 0.0940257 | 0.0470128 | − | 0.998894i | \(-0.485030\pi\) | ||||
0.0470128 | + | 0.998894i | \(0.485030\pi\) | |||||||
\(368\) | 8.18125 | 0.426477 | ||||||||
\(369\) | 10.1134 | 0.526484 | ||||||||
\(370\) | 47.6692 | 2.47820 | ||||||||
\(371\) | −4.77275 | −0.247789 | ||||||||
\(372\) | −25.3066 | −1.31209 | ||||||||
\(373\) | 12.0176 | 0.622249 | 0.311125 | − | 0.950369i | \(-0.399294\pi\) | ||||
0.311125 | + | 0.950369i | \(0.399294\pi\) | |||||||
\(374\) | 11.3743 | 0.588153 | ||||||||
\(375\) | 12.1317 | 0.626478 | ||||||||
\(376\) | −6.48698 | −0.334541 | ||||||||
\(377\) | 35.1604 | 1.81085 | ||||||||
\(378\) | −2.15559 | −0.110872 | ||||||||
\(379\) | 2.38003 | 0.122254 | 0.0611270 | − | 0.998130i | \(-0.480531\pi\) | ||||
0.0611270 | + | 0.998130i | \(0.480531\pi\) | |||||||
\(380\) | 30.3779 | 1.55835 | ||||||||
\(381\) | 1.66509 | 0.0853052 | ||||||||
\(382\) | −50.2181 | −2.56938 | ||||||||
\(383\) | 1.00000 | 0.0510976 | ||||||||
\(384\) | 10.5672 | 0.539256 | ||||||||
\(385\) | −8.78824 | −0.447890 | ||||||||
\(386\) | 16.6326 | 0.846579 | ||||||||
\(387\) | 5.55063 | 0.282155 | ||||||||
\(388\) | 0.760791 | 0.0386233 | ||||||||
\(389\) | 19.4132 | 0.984288 | 0.492144 | − | 0.870514i | \(-0.336213\pi\) | ||||
0.492144 | + | 0.870514i | \(0.336213\pi\) | |||||||
\(390\) | −42.6311 | −2.15871 | ||||||||
\(391\) | −7.83388 | −0.396177 | ||||||||
\(392\) | −1.39373 | −0.0703941 | ||||||||
\(393\) | −7.50074 | −0.378362 | ||||||||
\(394\) | −6.57265 | −0.331125 | ||||||||
\(395\) | −27.9086 | −1.40423 | ||||||||
\(396\) | −6.37197 | −0.320204 | ||||||||
\(397\) | −21.1059 | −1.05928 | −0.529638 | − | 0.848224i | \(-0.677672\pi\) | ||||
−0.529638 | + | 0.848224i | \(0.677672\pi\) | |||||||
\(398\) | 15.8532 | 0.794649 | ||||||||
\(399\) | 3.14459 | 0.157426 | ||||||||
\(400\) | −19.0512 | −0.952561 | ||||||||
\(401\) | −25.6464 | −1.28072 | −0.640360 | − | 0.768075i | \(-0.721215\pi\) | ||||
−0.640360 | + | 0.768075i | \(0.721215\pi\) | |||||||
\(402\) | −11.9480 | −0.595911 | ||||||||
\(403\) | −51.8084 | −2.58076 | ||||||||
\(404\) | 11.5033 | 0.572308 | ||||||||
\(405\) | 3.65015 | 0.181378 | ||||||||
\(406\) | −13.9885 | −0.694237 | ||||||||
\(407\) | 14.5865 | 0.723027 | ||||||||
\(408\) | −3.05456 | −0.151223 | ||||||||
\(409\) | −11.3471 | −0.561080 | −0.280540 | − | 0.959842i | \(-0.590513\pi\) | ||||
−0.280540 | + | 0.959842i | \(0.590513\pi\) | |||||||
\(410\) | −79.5748 | −3.92992 | ||||||||
\(411\) | 13.7101 | 0.676267 | ||||||||
\(412\) | −30.6586 | −1.51044 | ||||||||
\(413\) | 2.92751 | 0.144053 | ||||||||
\(414\) | 7.70503 | 0.378682 | ||||||||
\(415\) | −32.4156 | −1.59122 | ||||||||
\(416\) | 41.8345 | 2.05111 | ||||||||
\(417\) | 16.8845 | 0.826838 | ||||||||
\(418\) | 16.3200 | 0.798239 | ||||||||
\(419\) | −14.5182 | −0.709259 | −0.354630 | − | 0.935007i | \(-0.615393\pi\) | ||||
−0.354630 | + | 0.935007i | \(0.615393\pi\) | |||||||
\(420\) | 9.66037 | 0.471378 | ||||||||
\(421\) | −21.7400 | −1.05954 | −0.529771 | − | 0.848141i | \(-0.677722\pi\) | ||||
−0.529771 | + | 0.848141i | \(0.677722\pi\) | |||||||
\(422\) | −7.26023 | −0.353422 | ||||||||
\(423\) | 4.65440 | 0.226304 | ||||||||
\(424\) | 6.65193 | 0.323046 | ||||||||
\(425\) | 18.2423 | 0.884884 | ||||||||
\(426\) | −0.112369 | −0.00544429 | ||||||||
\(427\) | −5.72176 | −0.276896 | ||||||||
\(428\) | −36.7541 | −1.77658 | ||||||||
\(429\) | −13.0449 | −0.629813 | ||||||||
\(430\) | −43.6737 | −2.10613 | ||||||||
\(431\) | −21.8362 | −1.05181 | −0.525907 | − | 0.850542i | \(-0.676274\pi\) | ||||
−0.525907 | + | 0.850542i | \(0.676274\pi\) | |||||||
\(432\) | −2.28882 | −0.110121 | ||||||||
\(433\) | 14.5073 | 0.697176 | 0.348588 | − | 0.937276i | \(-0.386661\pi\) | ||||
0.348588 | + | 0.937276i | \(0.386661\pi\) | |||||||
\(434\) | 20.6119 | 0.989401 | ||||||||
\(435\) | 23.6873 | 1.13572 | ||||||||
\(436\) | 36.5172 | 1.74886 | ||||||||
\(437\) | −11.2402 | −0.537690 | ||||||||
\(438\) | −30.1270 | −1.43952 | ||||||||
\(439\) | −24.3720 | −1.16321 | −0.581606 | − | 0.813471i | \(-0.697576\pi\) | ||||
−0.581606 | + | 0.813471i | \(0.697576\pi\) | |||||||
\(440\) | 12.2485 | 0.583922 | ||||||||
\(441\) | 1.00000 | 0.0476190 | ||||||||
\(442\) | −25.5967 | −1.21751 | ||||||||
\(443\) | −38.6261 | −1.83518 | −0.917591 | − | 0.397525i | \(-0.869869\pi\) | ||||
−0.917591 | + | 0.397525i | \(0.869869\pi\) | |||||||
\(444\) | −16.0341 | −0.760943 | ||||||||
\(445\) | −20.1538 | −0.955381 | ||||||||
\(446\) | 5.12887 | 0.242859 | ||||||||
\(447\) | 16.3997 | 0.775680 | ||||||||
\(448\) | −12.0661 | −0.570072 | ||||||||
\(449\) | −6.20044 | −0.292617 | −0.146308 | − | 0.989239i | \(-0.546739\pi\) | ||||
−0.146308 | + | 0.989239i | \(0.546739\pi\) | |||||||
\(450\) | −17.9423 | −0.845808 | ||||||||
\(451\) | −24.3495 | −1.14657 | ||||||||
\(452\) | −9.23812 | −0.434525 | ||||||||
\(453\) | 18.5869 | 0.873287 | ||||||||
\(454\) | −31.9240 | −1.49827 | ||||||||
\(455\) | 19.7770 | 0.927160 | ||||||||
\(456\) | −4.38272 | −0.205240 | ||||||||
\(457\) | 5.18910 | 0.242736 | 0.121368 | − | 0.992608i | \(-0.461272\pi\) | ||||
0.121368 | + | 0.992608i | \(0.461272\pi\) | |||||||
\(458\) | −25.6282 | −1.19753 | ||||||||
\(459\) | 2.19164 | 0.102297 | ||||||||
\(460\) | −34.5304 | −1.60999 | ||||||||
\(461\) | 34.6598 | 1.61427 | 0.807133 | − | 0.590370i | \(-0.201018\pi\) | ||||
0.807133 | + | 0.590370i | \(0.201018\pi\) | |||||||
\(462\) | 5.18988 | 0.241455 | ||||||||
\(463\) | 6.38523 | 0.296747 | 0.148373 | − | 0.988931i | \(-0.452596\pi\) | ||||
0.148373 | + | 0.988931i | \(0.452596\pi\) | |||||||
\(464\) | −14.8531 | −0.689536 | ||||||||
\(465\) | −34.9030 | −1.61859 | ||||||||
\(466\) | 45.7524 | 2.11944 | ||||||||
\(467\) | 34.4507 | 1.59419 | 0.797094 | − | 0.603855i | \(-0.206369\pi\) | ||||
0.797094 | + | 0.603855i | \(0.206369\pi\) | |||||||
\(468\) | 14.3394 | 0.662841 | ||||||||
\(469\) | 5.54279 | 0.255942 | ||||||||
\(470\) | −36.6219 | −1.68924 | ||||||||
\(471\) | −4.65606 | −0.214540 | ||||||||
\(472\) | −4.08016 | −0.187805 | ||||||||
\(473\) | −13.3639 | −0.614473 | ||||||||
\(474\) | 16.4814 | 0.757014 | ||||||||
\(475\) | 26.1744 | 1.20096 | ||||||||
\(476\) | 5.80032 | 0.265857 | ||||||||
\(477\) | −4.77275 | −0.218529 | ||||||||
\(478\) | 54.2559 | 2.48161 | ||||||||
\(479\) | −10.2961 | −0.470440 | −0.235220 | − | 0.971942i | \(-0.575581\pi\) | ||||
−0.235220 | + | 0.971942i | \(0.575581\pi\) | |||||||
\(480\) | 28.1836 | 1.28640 | ||||||||
\(481\) | −32.8254 | −1.49671 | ||||||||
\(482\) | −29.7747 | −1.35620 | ||||||||
\(483\) | −3.57444 | −0.162643 | ||||||||
\(484\) | −13.7708 | −0.625947 | ||||||||
\(485\) | 1.04929 | 0.0476456 | ||||||||
\(486\) | −2.15559 | −0.0977795 | ||||||||
\(487\) | −12.3741 | −0.560724 | −0.280362 | − | 0.959894i | \(-0.590455\pi\) | ||||
−0.280362 | + | 0.959894i | \(0.590455\pi\) | |||||||
\(488\) | 7.97461 | 0.360994 | ||||||||
\(489\) | −14.5124 | −0.656275 | ||||||||
\(490\) | −7.86823 | −0.355450 | ||||||||
\(491\) | −36.2982 | −1.63811 | −0.819057 | − | 0.573712i | \(-0.805503\pi\) | ||||
−0.819057 | + | 0.573712i | \(0.805503\pi\) | |||||||
\(492\) | 26.7659 | 1.20670 | ||||||||
\(493\) | 14.2224 | 0.640546 | ||||||||
\(494\) | −36.7265 | −1.65240 | ||||||||
\(495\) | −8.78824 | −0.395002 | ||||||||
\(496\) | 21.8858 | 0.982701 | ||||||||
\(497\) | 0.0521291 | 0.00233831 | ||||||||
\(498\) | 19.1430 | 0.857816 | ||||||||
\(499\) | −0.699596 | −0.0313182 | −0.0156591 | − | 0.999877i | \(-0.504985\pi\) | ||||
−0.0156591 | + | 0.999877i | \(0.504985\pi\) | |||||||
\(500\) | 32.1073 | 1.43588 | ||||||||
\(501\) | 18.3195 | 0.818453 | ||||||||
\(502\) | −44.1107 | −1.96876 | ||||||||
\(503\) | 6.22672 | 0.277636 | 0.138818 | − | 0.990318i | \(-0.455670\pi\) | ||||
0.138818 | + | 0.990318i | \(0.455670\pi\) | |||||||
\(504\) | −1.39373 | −0.0620818 | ||||||||
\(505\) | 15.8653 | 0.705998 | ||||||||
\(506\) | −18.5509 | −0.824689 | ||||||||
\(507\) | 16.3561 | 0.726401 | ||||||||
\(508\) | 4.40677 | 0.195519 | ||||||||
\(509\) | 20.8313 | 0.923332 | 0.461666 | − | 0.887054i | \(-0.347252\pi\) | ||||
0.461666 | + | 0.887054i | \(0.347252\pi\) | |||||||
\(510\) | −17.2443 | −0.763591 | ||||||||
\(511\) | 13.9762 | 0.618271 | ||||||||
\(512\) | −24.0525 | −1.06298 | ||||||||
\(513\) | 3.14459 | 0.138837 | ||||||||
\(514\) | 0.205239 | 0.00905272 | ||||||||
\(515\) | −42.2844 | −1.86327 | ||||||||
\(516\) | 14.6901 | 0.646697 | ||||||||
\(517\) | −11.2061 | −0.492843 | ||||||||
\(518\) | 13.0595 | 0.573802 | ||||||||
\(519\) | 19.0336 | 0.835483 | ||||||||
\(520\) | −27.5638 | −1.20875 | ||||||||
\(521\) | −4.12511 | −0.180724 | −0.0903622 | − | 0.995909i | \(-0.528802\pi\) | ||||
−0.0903622 | + | 0.995909i | \(0.528802\pi\) | |||||||
\(522\) | −13.9885 | −0.612260 | ||||||||
\(523\) | 15.9217 | 0.696206 | 0.348103 | − | 0.937456i | \(-0.386826\pi\) | ||||
0.348103 | + | 0.937456i | \(0.386826\pi\) | |||||||
\(524\) | −19.8512 | −0.867205 | ||||||||
\(525\) | 8.32361 | 0.363272 | ||||||||
\(526\) | 17.5540 | 0.765392 | ||||||||
\(527\) | −20.9566 | −0.912882 | ||||||||
\(528\) | 5.51064 | 0.239820 | ||||||||
\(529\) | −10.2234 | −0.444494 | ||||||||
\(530\) | 37.5531 | 1.63120 | ||||||||
\(531\) | 2.92751 | 0.127043 | ||||||||
\(532\) | 8.32237 | 0.360821 | ||||||||
\(533\) | 54.7959 | 2.37347 | ||||||||
\(534\) | 11.9018 | 0.515040 | ||||||||
\(535\) | −50.6914 | −2.19158 | ||||||||
\(536\) | −7.72517 | −0.333676 | ||||||||
\(537\) | 9.03796 | 0.390017 | ||||||||
\(538\) | −36.0709 | −1.55513 | ||||||||
\(539\) | −2.40764 | −0.103704 | ||||||||
\(540\) | 9.66037 | 0.415716 | ||||||||
\(541\) | 12.4358 | 0.534657 | 0.267328 | − | 0.963605i | \(-0.413859\pi\) | ||||
0.267328 | + | 0.963605i | \(0.413859\pi\) | |||||||
\(542\) | 17.9738 | 0.772042 | ||||||||
\(543\) | −26.3548 | −1.13099 | ||||||||
\(544\) | 16.9221 | 0.725530 | ||||||||
\(545\) | 50.3646 | 2.15738 | ||||||||
\(546\) | −11.6793 | −0.499826 | ||||||||
\(547\) | −29.2955 | −1.25258 | −0.626292 | − | 0.779589i | \(-0.715428\pi\) | ||||
−0.626292 | + | 0.779589i | \(0.715428\pi\) | |||||||
\(548\) | 36.2846 | 1.55000 | ||||||||
\(549\) | −5.72176 | −0.244199 | ||||||||
\(550\) | 43.1985 | 1.84199 | ||||||||
\(551\) | 20.4065 | 0.869347 | ||||||||
\(552\) | 4.98182 | 0.212040 | ||||||||
\(553\) | −7.64587 | −0.325136 | ||||||||
\(554\) | 60.7802 | 2.58230 | ||||||||
\(555\) | −22.1142 | −0.938697 | ||||||||
\(556\) | 44.6860 | 1.89511 | ||||||||
\(557\) | 10.9887 | 0.465606 | 0.232803 | − | 0.972524i | \(-0.425210\pi\) | ||||
0.232803 | + | 0.972524i | \(0.425210\pi\) | |||||||
\(558\) | 20.6119 | 0.872570 | ||||||||
\(559\) | 30.0740 | 1.27200 | ||||||||
\(560\) | −8.35453 | −0.353043 | ||||||||
\(561\) | −5.27667 | −0.222781 | ||||||||
\(562\) | −19.9056 | −0.839666 | ||||||||
\(563\) | −28.9692 | −1.22091 | −0.610454 | − | 0.792052i | \(-0.709013\pi\) | ||||
−0.610454 | + | 0.792052i | \(0.709013\pi\) | |||||||
\(564\) | 12.3182 | 0.518688 | ||||||||
\(565\) | −12.7412 | −0.536028 | ||||||||
\(566\) | 38.6880 | 1.62618 | ||||||||
\(567\) | 1.00000 | 0.0419961 | ||||||||
\(568\) | −0.0726540 | −0.00304849 | ||||||||
\(569\) | 22.0370 | 0.923838 | 0.461919 | − | 0.886922i | \(-0.347161\pi\) | ||||
0.461919 | + | 0.886922i | \(0.347161\pi\) | |||||||
\(570\) | −24.7424 | −1.03634 | ||||||||
\(571\) | 15.8466 | 0.663160 | 0.331580 | − | 0.943427i | \(-0.392418\pi\) | ||||
0.331580 | + | 0.943427i | \(0.392418\pi\) | |||||||
\(572\) | −34.5242 | −1.44353 | ||||||||
\(573\) | 23.2967 | 0.973233 | ||||||||
\(574\) | −21.8004 | −0.909931 | ||||||||
\(575\) | −29.7523 | −1.24076 | ||||||||
\(576\) | −12.0661 | −0.502756 | ||||||||
\(577\) | 17.8690 | 0.743898 | 0.371949 | − | 0.928253i | \(-0.378690\pi\) | ||||
0.371949 | + | 0.928253i | \(0.378690\pi\) | |||||||
\(578\) | 26.2911 | 1.09357 | ||||||||
\(579\) | −7.71605 | −0.320668 | ||||||||
\(580\) | 62.6901 | 2.60306 | ||||||||
\(581\) | −8.88061 | −0.368430 | ||||||||
\(582\) | −0.619653 | −0.0256855 | ||||||||
\(583\) | 11.4910 | 0.475910 | ||||||||
\(584\) | −19.4791 | −0.806050 | ||||||||
\(585\) | 19.7770 | 0.817678 | ||||||||
\(586\) | −12.6821 | −0.523891 | ||||||||
\(587\) | 22.4986 | 0.928617 | 0.464309 | − | 0.885674i | \(-0.346303\pi\) | ||||
0.464309 | + | 0.885674i | \(0.346303\pi\) | |||||||
\(588\) | 2.64657 | 0.109143 | ||||||||
\(589\) | −30.0687 | −1.23896 | ||||||||
\(590\) | −23.0343 | −0.948307 | ||||||||
\(591\) | 3.04912 | 0.125424 | ||||||||
\(592\) | 13.8667 | 0.569917 | ||||||||
\(593\) | 35.7329 | 1.46737 | 0.733687 | − | 0.679488i | \(-0.237798\pi\) | ||||
0.733687 | + | 0.679488i | \(0.237798\pi\) | |||||||
\(594\) | 5.18988 | 0.212943 | ||||||||
\(595\) | 7.99981 | 0.327960 | ||||||||
\(596\) | 43.4030 | 1.77785 | ||||||||
\(597\) | −7.35446 | −0.300998 | ||||||||
\(598\) | 41.7468 | 1.70716 | ||||||||
\(599\) | −18.8601 | −0.770602 | −0.385301 | − | 0.922791i | \(-0.625902\pi\) | ||||
−0.385301 | + | 0.922791i | \(0.625902\pi\) | |||||||
\(600\) | −11.6009 | −0.473604 | ||||||||
\(601\) | 4.74151 | 0.193410 | 0.0967051 | − | 0.995313i | \(-0.469170\pi\) | ||||
0.0967051 | + | 0.995313i | \(0.469170\pi\) | |||||||
\(602\) | −11.9649 | −0.487652 | ||||||||
\(603\) | 5.54279 | 0.225720 | ||||||||
\(604\) | 49.1914 | 2.00157 | ||||||||
\(605\) | −18.9928 | −0.772167 | ||||||||
\(606\) | −9.36923 | −0.380599 | ||||||||
\(607\) | 7.51614 | 0.305071 | 0.152535 | − | 0.988298i | \(-0.451256\pi\) | ||||
0.152535 | + | 0.988298i | \(0.451256\pi\) | |||||||
\(608\) | 24.2801 | 0.984687 | ||||||||
\(609\) | 6.48940 | 0.262964 | ||||||||
\(610\) | 45.0202 | 1.82281 | ||||||||
\(611\) | 25.2181 | 1.02022 | ||||||||
\(612\) | 5.80032 | 0.234464 | ||||||||
\(613\) | 26.3762 | 1.06533 | 0.532663 | − | 0.846327i | \(-0.321191\pi\) | ||||
0.532663 | + | 0.846327i | \(0.321191\pi\) | |||||||
\(614\) | 32.5203 | 1.31241 | ||||||||
\(615\) | 36.9156 | 1.48858 | ||||||||
\(616\) | 3.35560 | 0.135201 | ||||||||
\(617\) | −22.1997 | −0.893725 | −0.446862 | − | 0.894603i | \(-0.647459\pi\) | ||||
−0.446862 | + | 0.894603i | \(0.647459\pi\) | |||||||
\(618\) | 24.9709 | 1.00448 | ||||||||
\(619\) | 1.31859 | 0.0529984 | 0.0264992 | − | 0.999649i | \(-0.491564\pi\) | ||||
0.0264992 | + | 0.999649i | \(0.491564\pi\) | |||||||
\(620\) | −92.3730 | −3.70979 | ||||||||
\(621\) | −3.57444 | −0.143437 | ||||||||
\(622\) | −34.8821 | −1.39864 | ||||||||
\(623\) | −5.52135 | −0.221208 | ||||||||
\(624\) | −12.4011 | −0.496442 | ||||||||
\(625\) | 2.66445 | 0.106578 | ||||||||
\(626\) | −5.65875 | −0.226169 | ||||||||
\(627\) | −7.57103 | −0.302358 | ||||||||
\(628\) | −12.3226 | −0.491724 | ||||||||
\(629\) | −13.2779 | −0.529425 | ||||||||
\(630\) | −7.86823 | −0.313478 | ||||||||
\(631\) | −9.62948 | −0.383344 | −0.191672 | − | 0.981459i | \(-0.561391\pi\) | ||||
−0.191672 | + | 0.981459i | \(0.561391\pi\) | |||||||
\(632\) | 10.6563 | 0.423885 | ||||||||
\(633\) | 3.36809 | 0.133870 | ||||||||
\(634\) | −33.8264 | −1.34342 | ||||||||
\(635\) | 6.07783 | 0.241191 | ||||||||
\(636\) | −12.6314 | −0.500867 | ||||||||
\(637\) | 5.41813 | 0.214674 | ||||||||
\(638\) | 33.6792 | 1.33337 | ||||||||
\(639\) | 0.0521291 | 0.00206219 | ||||||||
\(640\) | 38.5719 | 1.52469 | ||||||||
\(641\) | 0.154604 | 0.00610648 | 0.00305324 | − | 0.999995i | \(-0.499028\pi\) | ||||
0.00305324 | + | 0.999995i | \(0.499028\pi\) | |||||||
\(642\) | 29.9357 | 1.18147 | ||||||||
\(643\) | −10.6917 | −0.421641 | −0.210821 | − | 0.977525i | \(-0.567614\pi\) | ||||
−0.210821 | + | 0.977525i | \(0.567614\pi\) | |||||||
\(644\) | −9.46000 | −0.372776 | ||||||||
\(645\) | 20.2607 | 0.797763 | ||||||||
\(646\) | −14.8559 | −0.584498 | ||||||||
\(647\) | 40.7766 | 1.60309 | 0.801547 | − | 0.597932i | \(-0.204011\pi\) | ||||
0.801547 | + | 0.597932i | \(0.204011\pi\) | |||||||
\(648\) | −1.39373 | −0.0547510 | ||||||||
\(649\) | −7.04837 | −0.276673 | ||||||||
\(650\) | −97.2136 | −3.81303 | ||||||||
\(651\) | −9.56205 | −0.374766 | ||||||||
\(652\) | −38.4081 | −1.50418 | ||||||||
\(653\) | 27.7113 | 1.08443 | 0.542214 | − | 0.840240i | \(-0.317586\pi\) | ||||
0.542214 | + | 0.840240i | \(0.317586\pi\) | |||||||
\(654\) | −29.7427 | −1.16303 | ||||||||
\(655\) | −27.3789 | −1.06978 | ||||||||
\(656\) | −23.1478 | −0.903770 | ||||||||
\(657\) | 13.9762 | 0.545263 | ||||||||
\(658\) | −10.0330 | −0.391126 | ||||||||
\(659\) | 22.9421 | 0.893696 | 0.446848 | − | 0.894610i | \(-0.352547\pi\) | ||||
0.446848 | + | 0.894610i | \(0.352547\pi\) | |||||||
\(660\) | −23.2587 | −0.905342 | ||||||||
\(661\) | 24.4034 | 0.949184 | 0.474592 | − | 0.880206i | \(-0.342596\pi\) | ||||
0.474592 | + | 0.880206i | \(0.342596\pi\) | |||||||
\(662\) | 30.8450 | 1.19882 | ||||||||
\(663\) | 11.8746 | 0.461170 | ||||||||
\(664\) | 12.3772 | 0.480328 | ||||||||
\(665\) | 11.4782 | 0.445107 | ||||||||
\(666\) | 13.0595 | 0.506046 | ||||||||
\(667\) | −23.1960 | −0.898153 | ||||||||
\(668\) | 48.4837 | 1.87589 | ||||||||
\(669\) | −2.37933 | −0.0919904 | ||||||||
\(670\) | −43.6120 | −1.68488 | ||||||||
\(671\) | 13.7759 | 0.531814 | ||||||||
\(672\) | 7.72122 | 0.297852 | ||||||||
\(673\) | 8.37386 | 0.322789 | 0.161394 | − | 0.986890i | \(-0.448401\pi\) | ||||
0.161394 | + | 0.986890i | \(0.448401\pi\) | |||||||
\(674\) | 22.7674 | 0.876966 | ||||||||
\(675\) | 8.32361 | 0.320376 | ||||||||
\(676\) | 43.2875 | 1.66491 | ||||||||
\(677\) | −40.2952 | −1.54867 | −0.774335 | − | 0.632775i | \(-0.781916\pi\) | ||||
−0.774335 | + | 0.632775i | \(0.781916\pi\) | |||||||
\(678\) | 7.52431 | 0.288970 | ||||||||
\(679\) | 0.287463 | 0.0110318 | ||||||||
\(680\) | −11.1496 | −0.427568 | ||||||||
\(681\) | 14.8099 | 0.567516 | ||||||||
\(682\) | −49.6259 | −1.90027 | ||||||||
\(683\) | −0.957326 | −0.0366311 | −0.0183155 | − | 0.999832i | \(-0.505830\pi\) | ||||
−0.0183155 | + | 0.999832i | \(0.505830\pi\) | |||||||
\(684\) | 8.32237 | 0.318214 | ||||||||
\(685\) | 50.0438 | 1.91207 | ||||||||
\(686\) | −2.15559 | −0.0823008 | ||||||||
\(687\) | 11.8892 | 0.453601 | ||||||||
\(688\) | −12.7044 | −0.484350 | ||||||||
\(689\) | −25.8593 | −0.985163 | ||||||||
\(690\) | 28.1245 | 1.07068 | ||||||||
\(691\) | −48.7993 | −1.85641 | −0.928206 | − | 0.372065i | \(-0.878650\pi\) | ||||
−0.928206 | + | 0.372065i | \(0.878650\pi\) | |||||||
\(692\) | 50.3737 | 1.91492 | ||||||||
\(693\) | −2.40764 | −0.0914586 | ||||||||
\(694\) | −35.6198 | −1.35211 | ||||||||
\(695\) | 61.6311 | 2.33780 | ||||||||
\(696\) | −9.04450 | −0.342831 | ||||||||
\(697\) | 22.1650 | 0.839558 | ||||||||
\(698\) | 23.3709 | 0.884603 | ||||||||
\(699\) | −21.2250 | −0.802804 | ||||||||
\(700\) | 22.0290 | 0.832618 | ||||||||
\(701\) | 15.4261 | 0.582637 | 0.291319 | − | 0.956626i | \(-0.405906\pi\) | ||||
0.291319 | + | 0.956626i | \(0.405906\pi\) | |||||||
\(702\) | −11.6793 | −0.440805 | ||||||||
\(703\) | −19.0513 | −0.718534 | ||||||||
\(704\) | 29.0509 | 1.09490 | ||||||||
\(705\) | 16.9893 | 0.639852 | ||||||||
\(706\) | 48.4079 | 1.82186 | ||||||||
\(707\) | 4.34648 | 0.163466 | ||||||||
\(708\) | 7.74784 | 0.291182 | ||||||||
\(709\) | −22.3176 | −0.838155 | −0.419077 | − | 0.907951i | \(-0.637646\pi\) | ||||
−0.419077 | + | 0.907951i | \(0.637646\pi\) | |||||||
\(710\) | −0.410164 | −0.0153932 | ||||||||
\(711\) | −7.64587 | −0.286743 | ||||||||
\(712\) | 7.69529 | 0.288393 | ||||||||
\(713\) | 34.1790 | 1.28001 | ||||||||
\(714\) | −4.72427 | −0.176801 | ||||||||
\(715\) | −47.6158 | −1.78073 | ||||||||
\(716\) | 23.9196 | 0.893916 | ||||||||
\(717\) | −25.1699 | −0.939987 | ||||||||
\(718\) | 39.7875 | 1.48486 | ||||||||
\(719\) | 21.2848 | 0.793791 | 0.396895 | − | 0.917864i | \(-0.370088\pi\) | ||||
0.396895 | + | 0.917864i | \(0.370088\pi\) | |||||||
\(720\) | −8.35453 | −0.311355 | ||||||||
\(721\) | −11.5843 | −0.431421 | ||||||||
\(722\) | 19.6408 | 0.730953 | ||||||||
\(723\) | 13.8128 | 0.513704 | ||||||||
\(724\) | −69.7497 | −2.59223 | ||||||||
\(725\) | 54.0153 | 2.00608 | ||||||||
\(726\) | 11.2161 | 0.416270 | ||||||||
\(727\) | 8.94927 | 0.331910 | 0.165955 | − | 0.986133i | \(-0.446929\pi\) | ||||
0.165955 | + | 0.986133i | \(0.446929\pi\) | |||||||
\(728\) | −7.55142 | −0.279874 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −109.968 | −4.07010 | ||||||||
\(731\) | 12.1650 | 0.449938 | ||||||||
\(732\) | −15.1430 | −0.559703 | ||||||||
\(733\) | −36.1281 | −1.33442 | −0.667211 | − | 0.744869i | \(-0.732512\pi\) | ||||
−0.667211 | + | 0.744869i | \(0.732512\pi\) | |||||||
\(734\) | −3.88281 | −0.143317 | ||||||||
\(735\) | 3.65015 | 0.134638 | ||||||||
\(736\) | −27.5990 | −1.01731 | ||||||||
\(737\) | −13.3450 | −0.491570 | ||||||||
\(738\) | −21.8004 | −0.802484 | ||||||||
\(739\) | 12.4900 | 0.459452 | 0.229726 | − | 0.973255i | \(-0.426217\pi\) | ||||
0.229726 | + | 0.973255i | \(0.426217\pi\) | |||||||
\(740\) | −58.5268 | −2.15149 | ||||||||
\(741\) | 17.0378 | 0.625899 | ||||||||
\(742\) | 10.2881 | 0.377687 | ||||||||
\(743\) | −35.2226 | −1.29219 | −0.646095 | − | 0.763257i | \(-0.723599\pi\) | ||||
−0.646095 | + | 0.763257i | \(0.723599\pi\) | |||||||
\(744\) | 13.3269 | 0.488590 | ||||||||
\(745\) | 59.8615 | 2.19315 | ||||||||
\(746\) | −25.9051 | −0.948453 | ||||||||
\(747\) | −8.88061 | −0.324925 | ||||||||
\(748\) | −13.9651 | −0.510613 | ||||||||
\(749\) | −13.8875 | −0.507437 | ||||||||
\(750\) | −26.1509 | −0.954897 | ||||||||
\(751\) | 34.9681 | 1.27600 | 0.638002 | − | 0.770034i | \(-0.279761\pi\) | ||||
0.638002 | + | 0.770034i | \(0.279761\pi\) | |||||||
\(752\) | −10.6531 | −0.388477 | ||||||||
\(753\) | 20.4634 | 0.745728 | ||||||||
\(754\) | −75.7915 | −2.76016 | ||||||||
\(755\) | 67.8449 | 2.46913 | ||||||||
\(756\) | 2.64657 | 0.0962547 | ||||||||
\(757\) | −29.2029 | −1.06140 | −0.530698 | − | 0.847561i | \(-0.678070\pi\) | ||||
−0.530698 | + | 0.847561i | \(0.678070\pi\) | |||||||
\(758\) | −5.13037 | −0.186344 | ||||||||
\(759\) | 8.60596 | 0.312376 | ||||||||
\(760\) | −15.9976 | −0.580294 | ||||||||
\(761\) | 3.63818 | 0.131884 | 0.0659419 | − | 0.997823i | \(-0.478995\pi\) | ||||
0.0659419 | + | 0.997823i | \(0.478995\pi\) | |||||||
\(762\) | −3.58925 | −0.130025 | ||||||||
\(763\) | 13.7979 | 0.499519 | ||||||||
\(764\) | 61.6562 | 2.23064 | ||||||||
\(765\) | 7.99981 | 0.289234 | ||||||||
\(766\) | −2.15559 | −0.0778846 | ||||||||
\(767\) | 15.8616 | 0.572729 | ||||||||
\(768\) | 1.35370 | 0.0488476 | ||||||||
\(769\) | −0.544551 | −0.0196370 | −0.00981851 | − | 0.999952i | \(-0.503125\pi\) | ||||
−0.00981851 | + | 0.999952i | \(0.503125\pi\) | |||||||
\(770\) | 18.9438 | 0.682689 | ||||||||
\(771\) | −0.0952126 | −0.00342900 | ||||||||
\(772\) | −20.4210 | −0.734969 | ||||||||
\(773\) | −24.3661 | −0.876389 | −0.438195 | − | 0.898880i | \(-0.644382\pi\) | ||||
−0.438195 | + | 0.898880i | \(0.644382\pi\) | |||||||
\(774\) | −11.9649 | −0.430069 | ||||||||
\(775\) | −79.5908 | −2.85899 | ||||||||
\(776\) | −0.400647 | −0.0143824 | ||||||||
\(777\) | −6.05844 | −0.217345 | ||||||||
\(778\) | −41.8469 | −1.50028 | ||||||||
\(779\) | 31.8026 | 1.13945 | ||||||||
\(780\) | 52.3411 | 1.87411 | ||||||||
\(781\) | −0.125508 | −0.00449102 | ||||||||
\(782\) | 16.8866 | 0.603865 | ||||||||
\(783\) | 6.48940 | 0.231912 | ||||||||
\(784\) | −2.28882 | −0.0817435 | ||||||||
\(785\) | −16.9953 | −0.606589 | ||||||||
\(786\) | 16.1685 | 0.576712 | ||||||||
\(787\) | −36.0913 | −1.28651 | −0.643257 | − | 0.765650i | \(-0.722417\pi\) | ||||
−0.643257 | + | 0.765650i | \(0.722417\pi\) | |||||||
\(788\) | 8.06970 | 0.287471 | ||||||||
\(789\) | −8.14349 | −0.289916 | ||||||||
\(790\) | 60.1595 | 2.14038 | ||||||||
\(791\) | −3.49061 | −0.124112 | ||||||||
\(792\) | 3.35560 | 0.119236 | ||||||||
\(793\) | −31.0013 | −1.10089 | ||||||||
\(794\) | 45.4957 | 1.61458 | ||||||||
\(795\) | −17.4212 | −0.617868 | ||||||||
\(796\) | −19.4641 | −0.689885 | ||||||||
\(797\) | −0.105685 | −0.00374354 | −0.00187177 | − | 0.999998i | \(-0.500596\pi\) | ||||
−0.00187177 | + | 0.999998i | \(0.500596\pi\) | |||||||
\(798\) | −6.77845 | −0.239954 | ||||||||
\(799\) | 10.2008 | 0.360877 | ||||||||
\(800\) | 64.2684 | 2.27223 | ||||||||
\(801\) | −5.52135 | −0.195087 | ||||||||
\(802\) | 55.2831 | 1.95211 | ||||||||
\(803\) | −33.6496 | −1.18747 | ||||||||
\(804\) | 14.6694 | 0.517349 | ||||||||
\(805\) | −13.0473 | −0.459855 | ||||||||
\(806\) | 111.678 | 3.93368 | ||||||||
\(807\) | 16.7336 | 0.589052 | ||||||||
\(808\) | −6.05783 | −0.213114 | ||||||||
\(809\) | 10.2779 | 0.361351 | 0.180675 | − | 0.983543i | \(-0.442172\pi\) | ||||
0.180675 | + | 0.983543i | \(0.442172\pi\) | |||||||
\(810\) | −7.86823 | −0.276461 | ||||||||
\(811\) | 28.8261 | 1.01222 | 0.506110 | − | 0.862469i | \(-0.331083\pi\) | ||||
0.506110 | + | 0.862469i | \(0.331083\pi\) | |||||||
\(812\) | 17.1746 | 0.602712 | ||||||||
\(813\) | −8.33824 | −0.292435 | ||||||||
\(814\) | −31.4426 | −1.10206 | ||||||||
\(815\) | −52.9726 | −1.85555 | ||||||||
\(816\) | −5.01626 | −0.175604 | ||||||||
\(817\) | 17.4545 | 0.610655 | ||||||||
\(818\) | 24.4598 | 0.855216 | ||||||||
\(819\) | 5.41813 | 0.189325 | ||||||||
\(820\) | 97.6995 | 3.41181 | ||||||||
\(821\) | −8.70278 | −0.303729 | −0.151865 | − | 0.988401i | \(-0.548528\pi\) | ||||
−0.151865 | + | 0.988401i | \(0.548528\pi\) | |||||||
\(822\) | −29.5532 | −1.03079 | ||||||||
\(823\) | 3.23833 | 0.112881 | 0.0564405 | − | 0.998406i | \(-0.482025\pi\) | ||||
0.0564405 | + | 0.998406i | \(0.482025\pi\) | |||||||
\(824\) | 16.1454 | 0.562451 | ||||||||
\(825\) | −20.0402 | −0.697711 | ||||||||
\(826\) | −6.31050 | −0.219571 | ||||||||
\(827\) | 34.5219 | 1.20044 | 0.600222 | − | 0.799834i | \(-0.295079\pi\) | ||||
0.600222 | + | 0.799834i | \(0.295079\pi\) | |||||||
\(828\) | −9.46000 | −0.328758 | ||||||||
\(829\) | −30.5484 | −1.06099 | −0.530495 | − | 0.847688i | \(-0.677994\pi\) | ||||
−0.530495 | + | 0.847688i | \(0.677994\pi\) | |||||||
\(830\) | 69.8747 | 2.42539 | ||||||||
\(831\) | −28.1966 | −0.978128 | ||||||||
\(832\) | −65.3759 | −2.26650 | ||||||||
\(833\) | 2.19164 | 0.0759358 | ||||||||
\(834\) | −36.3961 | −1.26029 | ||||||||
\(835\) | 66.8688 | 2.31409 | ||||||||
\(836\) | −20.0372 | −0.693003 | ||||||||
\(837\) | −9.56205 | −0.330513 | ||||||||
\(838\) | 31.2952 | 1.08108 | ||||||||
\(839\) | 15.9327 | 0.550058 | 0.275029 | − | 0.961436i | \(-0.411313\pi\) | ||||
0.275029 | + | 0.961436i | \(0.411313\pi\) | |||||||
\(840\) | −5.08734 | −0.175530 | ||||||||
\(841\) | 13.1124 | 0.452151 | ||||||||
\(842\) | 46.8624 | 1.61499 | ||||||||
\(843\) | 9.23440 | 0.318049 | ||||||||
\(844\) | 8.91389 | 0.306829 | ||||||||
\(845\) | 59.7023 | 2.05382 | ||||||||
\(846\) | −10.0330 | −0.344940 | ||||||||
\(847\) | −5.20329 | −0.178787 | ||||||||
\(848\) | 10.9239 | 0.375130 | ||||||||
\(849\) | −17.9477 | −0.615965 | ||||||||
\(850\) | −39.3230 | −1.34877 | ||||||||
\(851\) | 21.6556 | 0.742343 | ||||||||
\(852\) | 0.137963 | 0.00472654 | ||||||||
\(853\) | −32.2332 | −1.10364 | −0.551821 | − | 0.833962i | \(-0.686067\pi\) | ||||
−0.551821 | + | 0.833962i | \(0.686067\pi\) | |||||||
\(854\) | 12.3338 | 0.422053 | ||||||||
\(855\) | 11.4782 | 0.392547 | ||||||||
\(856\) | 19.3554 | 0.661555 | ||||||||
\(857\) | 25.4124 | 0.868072 | 0.434036 | − | 0.900896i | \(-0.357089\pi\) | ||||
0.434036 | + | 0.900896i | \(0.357089\pi\) | |||||||
\(858\) | 28.1194 | 0.959981 | ||||||||
\(859\) | 47.3247 | 1.61470 | 0.807348 | − | 0.590075i | \(-0.200902\pi\) | ||||
0.807348 | + | 0.590075i | \(0.200902\pi\) | |||||||
\(860\) | 53.6212 | 1.82847 | ||||||||
\(861\) | 10.1134 | 0.344665 | ||||||||
\(862\) | 47.0699 | 1.60321 | ||||||||
\(863\) | 37.9162 | 1.29068 | 0.645341 | − | 0.763894i | \(-0.276715\pi\) | ||||
0.645341 | + | 0.763894i | \(0.276715\pi\) | |||||||
\(864\) | 7.72122 | 0.262681 | ||||||||
\(865\) | 69.4756 | 2.36224 | ||||||||
\(866\) | −31.2718 | −1.06266 | ||||||||
\(867\) | −12.1967 | −0.414222 | ||||||||
\(868\) | −25.3066 | −0.858962 | ||||||||
\(869\) | 18.4085 | 0.624465 | ||||||||
\(870\) | −51.0601 | −1.73110 | ||||||||
\(871\) | 30.0315 | 1.01758 | ||||||||
\(872\) | −19.2306 | −0.651232 | ||||||||
\(873\) | 0.287463 | 0.00972917 | ||||||||
\(874\) | 24.2292 | 0.819564 | ||||||||
\(875\) | 12.1317 | 0.410126 | ||||||||
\(876\) | 36.9889 | 1.24974 | ||||||||
\(877\) | −34.5553 | −1.16685 | −0.583424 | − | 0.812168i | \(-0.698288\pi\) | ||||
−0.583424 | + | 0.812168i | \(0.698288\pi\) | |||||||
\(878\) | 52.5360 | 1.77301 | ||||||||
\(879\) | 5.88333 | 0.198440 | ||||||||
\(880\) | 20.1147 | 0.678066 | ||||||||
\(881\) | −24.9627 | −0.841015 | −0.420508 | − | 0.907289i | \(-0.638148\pi\) | ||||
−0.420508 | + | 0.907289i | \(0.638148\pi\) | |||||||
\(882\) | −2.15559 | −0.0725825 | ||||||||
\(883\) | −23.6177 | −0.794800 | −0.397400 | − | 0.917646i | \(-0.630087\pi\) | ||||
−0.397400 | + | 0.917646i | \(0.630087\pi\) | |||||||
\(884\) | 31.4269 | 1.05700 | ||||||||
\(885\) | 10.6858 | 0.359201 | ||||||||
\(886\) | 83.2621 | 2.79724 | ||||||||
\(887\) | −16.4447 | −0.552158 | −0.276079 | − | 0.961135i | \(-0.589035\pi\) | ||||
−0.276079 | + | 0.961135i | \(0.589035\pi\) | |||||||
\(888\) | 8.44385 | 0.283357 | ||||||||
\(889\) | 1.66509 | 0.0558453 | ||||||||
\(890\) | 43.4433 | 1.45622 | ||||||||
\(891\) | −2.40764 | −0.0806589 | ||||||||
\(892\) | −6.29707 | −0.210841 | ||||||||
\(893\) | 14.6362 | 0.489781 | ||||||||
\(894\) | −35.3511 | −1.18232 | ||||||||
\(895\) | 32.9899 | 1.10273 | ||||||||
\(896\) | 10.5672 | 0.353026 | ||||||||
\(897\) | −19.3668 | −0.646638 | ||||||||
\(898\) | 13.3656 | 0.446016 | ||||||||
\(899\) | −62.0520 | −2.06955 | ||||||||
\(900\) | 22.0290 | 0.734300 | ||||||||
\(901\) | −10.4601 | −0.348477 | ||||||||
\(902\) | 52.4875 | 1.74764 | ||||||||
\(903\) | 5.55063 | 0.184714 | ||||||||
\(904\) | 4.86497 | 0.161807 | ||||||||
\(905\) | −96.1990 | −3.19776 | ||||||||
\(906\) | −40.0657 | −1.33109 | ||||||||
\(907\) | −29.7229 | −0.986932 | −0.493466 | − | 0.869765i | \(-0.664270\pi\) | ||||
−0.493466 | + | 0.869765i | \(0.664270\pi\) | |||||||
\(908\) | 39.1954 | 1.30074 | ||||||||
\(909\) | 4.34648 | 0.144164 | ||||||||
\(910\) | −42.6311 | −1.41321 | ||||||||
\(911\) | −30.4629 | −1.00928 | −0.504641 | − | 0.863329i | \(-0.668375\pi\) | ||||
−0.504641 | + | 0.863329i | \(0.668375\pi\) | |||||||
\(912\) | −7.19740 | −0.238330 | ||||||||
\(913\) | 21.3813 | 0.707617 | ||||||||
\(914\) | −11.1856 | −0.369985 | ||||||||
\(915\) | −20.8853 | −0.690447 | ||||||||
\(916\) | 31.4655 | 1.03965 | ||||||||
\(917\) | −7.50074 | −0.247696 | ||||||||
\(918\) | −4.72427 | −0.155924 | ||||||||
\(919\) | 32.8179 | 1.08256 | 0.541282 | − | 0.840841i | \(-0.317939\pi\) | ||||
0.541282 | + | 0.840841i | \(0.317939\pi\) | |||||||
\(920\) | 18.1844 | 0.599522 | ||||||||
\(921\) | −15.0865 | −0.497117 | ||||||||
\(922\) | −74.7122 | −2.46052 | ||||||||
\(923\) | 0.282442 | 0.00929669 | ||||||||
\(924\) | −6.37197 | −0.209622 | ||||||||
\(925\) | −50.4281 | −1.65807 | ||||||||
\(926\) | −13.7639 | −0.452311 | ||||||||
\(927\) | −11.5843 | −0.380477 | ||||||||
\(928\) | 50.1061 | 1.64481 | ||||||||
\(929\) | −31.5384 | −1.03474 | −0.517371 | − | 0.855761i | \(-0.673089\pi\) | ||||
−0.517371 | + | 0.855761i | \(0.673089\pi\) | |||||||
\(930\) | 75.2364 | 2.46710 | ||||||||
\(931\) | 3.14459 | 0.103060 | ||||||||
\(932\) | −56.1735 | −1.84002 | ||||||||
\(933\) | 16.1821 | 0.529780 | ||||||||
\(934\) | −74.2616 | −2.42991 | ||||||||
\(935\) | −19.2606 | −0.629890 | ||||||||
\(936\) | −7.55142 | −0.246826 | ||||||||
\(937\) | 8.79735 | 0.287397 | 0.143698 | − | 0.989622i | \(-0.454100\pi\) | ||||
0.143698 | + | 0.989622i | \(0.454100\pi\) | |||||||
\(938\) | −11.9480 | −0.390115 | ||||||||
\(939\) | 2.62515 | 0.0856686 | ||||||||
\(940\) | 44.9632 | 1.46654 | ||||||||
\(941\) | −23.5639 | −0.768160 | −0.384080 | − | 0.923300i | \(-0.625481\pi\) | ||||
−0.384080 | + | 0.923300i | \(0.625481\pi\) | |||||||
\(942\) | 10.0366 | 0.327008 | ||||||||
\(943\) | −36.1499 | −1.17720 | ||||||||
\(944\) | −6.70053 | −0.218084 | ||||||||
\(945\) | 3.65015 | 0.118739 | ||||||||
\(946\) | 28.8071 | 0.936600 | ||||||||
\(947\) | −14.3560 | −0.466507 | −0.233253 | − | 0.972416i | \(-0.574937\pi\) | ||||
−0.233253 | + | 0.972416i | \(0.574937\pi\) | |||||||
\(948\) | −20.2353 | −0.657213 | ||||||||
\(949\) | 75.7248 | 2.45813 | ||||||||
\(950\) | −56.4212 | −1.83054 | ||||||||
\(951\) | 15.6924 | 0.508862 | ||||||||
\(952\) | −3.05456 | −0.0989988 | ||||||||
\(953\) | −40.7720 | −1.32073 | −0.660367 | − | 0.750943i | \(-0.729599\pi\) | ||||
−0.660367 | + | 0.750943i | \(0.729599\pi\) | |||||||
\(954\) | 10.2881 | 0.333089 | ||||||||
\(955\) | 85.0364 | 2.75171 | ||||||||
\(956\) | −66.6138 | −2.15444 | ||||||||
\(957\) | −15.6241 | −0.505056 | ||||||||
\(958\) | 22.1941 | 0.717059 | ||||||||
\(959\) | 13.7101 | 0.442721 | ||||||||
\(960\) | −44.0433 | −1.42149 | ||||||||
\(961\) | 60.4329 | 1.94945 | ||||||||
\(962\) | 70.7581 | 2.28133 | ||||||||
\(963\) | −13.8875 | −0.447518 | ||||||||
\(964\) | 36.5565 | 1.17741 | ||||||||
\(965\) | −28.1647 | −0.906655 | ||||||||
\(966\) | 7.70503 | 0.247905 | ||||||||
\(967\) | 28.5024 | 0.916576 | 0.458288 | − | 0.888804i | \(-0.348463\pi\) | ||||
0.458288 | + | 0.888804i | \(0.348463\pi\) | |||||||
\(968\) | 7.25199 | 0.233088 | ||||||||
\(969\) | 6.89181 | 0.221397 | ||||||||
\(970\) | −2.26183 | −0.0726230 | ||||||||
\(971\) | −25.6857 | −0.824292 | −0.412146 | − | 0.911118i | \(-0.635221\pi\) | ||||
−0.412146 | + | 0.911118i | \(0.635221\pi\) | |||||||
\(972\) | 2.64657 | 0.0848887 | ||||||||
\(973\) | 16.8845 | 0.541293 | ||||||||
\(974\) | 26.6735 | 0.854674 | ||||||||
\(975\) | 45.0984 | 1.44430 | ||||||||
\(976\) | 13.0961 | 0.419195 | ||||||||
\(977\) | 33.7704 | 1.08041 | 0.540205 | − | 0.841533i | \(-0.318347\pi\) | ||||
0.540205 | + | 0.841533i | \(0.318347\pi\) | |||||||
\(978\) | 31.2828 | 1.00032 | ||||||||
\(979\) | 13.2934 | 0.424859 | ||||||||
\(980\) | 9.66037 | 0.308589 | ||||||||
\(981\) | 13.7979 | 0.440534 | ||||||||
\(982\) | 78.2440 | 2.49687 | ||||||||
\(983\) | 53.2854 | 1.69954 | 0.849770 | − | 0.527154i | \(-0.176741\pi\) | ||||
0.849770 | + | 0.527154i | \(0.176741\pi\) | |||||||
\(984\) | −14.0954 | −0.449346 | ||||||||
\(985\) | 11.1298 | 0.354623 | ||||||||
\(986\) | −30.6577 | −0.976341 | ||||||||
\(987\) | 4.65440 | 0.148151 | ||||||||
\(988\) | 45.0917 | 1.43456 | ||||||||
\(989\) | −19.8404 | −0.630889 | ||||||||
\(990\) | 18.9438 | 0.602075 | ||||||||
\(991\) | 29.4983 | 0.937045 | 0.468523 | − | 0.883452i | \(-0.344786\pi\) | ||||
0.468523 | + | 0.883452i | \(0.344786\pi\) | |||||||
\(992\) | −73.8307 | −2.34413 | ||||||||
\(993\) | −14.3093 | −0.454091 | ||||||||
\(994\) | −0.112369 | −0.00356412 | ||||||||
\(995\) | −26.8449 | −0.851040 | ||||||||
\(996\) | −23.5031 | −0.744725 | ||||||||
\(997\) | −11.1138 | −0.351979 | −0.175990 | − | 0.984392i | \(-0.556313\pi\) | ||||
−0.175990 | + | 0.984392i | \(0.556313\pi\) | |||||||
\(998\) | 1.50804 | 0.0477362 | ||||||||
\(999\) | −6.05844 | −0.191681 |
(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 | 8043.2.a.u.1.7 | ✓ | 53 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8043.2.a.u.1.7 | ✓ | 53 | 1.1 | even | 1 | trivial |