Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8015,2,Mod(1,8015)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8015, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8015.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8015 = 5 \cdot 7 \cdot 229 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8015.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(64.0000972201\) |
Analytic rank: | \(0\) |
Dimension: | \(62\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.51 | ||
Character | \(\chi\) | \(=\) | 8015.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.00507 | 1.41780 | 0.708898 | − | 0.705311i | \(-0.249193\pi\) | ||||
0.708898 | + | 0.705311i | \(0.249193\pi\) | |||||||
\(3\) | −2.97462 | −1.71740 | −0.858700 | − | 0.512478i | \(-0.828727\pi\) | ||||
−0.858700 | + | 0.512478i | \(0.828727\pi\) | |||||||
\(4\) | 2.02029 | 1.01015 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | −5.96432 | −2.43492 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | 0.0406892 | 0.0143858 | ||||||||
\(9\) | 5.84839 | 1.94946 | ||||||||
\(10\) | −2.00507 | −0.634058 | ||||||||
\(11\) | −4.21808 | −1.27180 | −0.635900 | − | 0.771772i | \(-0.719371\pi\) | ||||
−0.635900 | + | 0.771772i | \(0.719371\pi\) | |||||||
\(12\) | −6.00961 | −1.73483 | ||||||||
\(13\) | 0.537768 | 0.149150 | 0.0745750 | − | 0.997215i | \(-0.476240\pi\) | ||||
0.0745750 | + | 0.997215i | \(0.476240\pi\) | |||||||
\(14\) | −2.00507 | −0.535877 | ||||||||
\(15\) | 2.97462 | 0.768045 | ||||||||
\(16\) | −3.95900 | −0.989750 | ||||||||
\(17\) | 5.04173 | 1.22280 | 0.611400 | − | 0.791322i | \(-0.290607\pi\) | ||||
0.611400 | + | 0.791322i | \(0.290607\pi\) | |||||||
\(18\) | 11.7264 | 2.76394 | ||||||||
\(19\) | −1.80467 | −0.414020 | −0.207010 | − | 0.978339i | \(-0.566373\pi\) | ||||
−0.207010 | + | 0.978339i | \(0.566373\pi\) | |||||||
\(20\) | −2.02029 | −0.451751 | ||||||||
\(21\) | 2.97462 | 0.649116 | ||||||||
\(22\) | −8.45753 | −1.80315 | ||||||||
\(23\) | 0.0595591 | 0.0124189 | 0.00620946 | − | 0.999981i | \(-0.498023\pi\) | ||||
0.00620946 | + | 0.999981i | \(0.498023\pi\) | |||||||
\(24\) | −0.121035 | −0.0247062 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 1.07826 | 0.211464 | ||||||||
\(27\) | −8.47289 | −1.63061 | ||||||||
\(28\) | −2.02029 | −0.381800 | ||||||||
\(29\) | 3.07069 | 0.570212 | 0.285106 | − | 0.958496i | \(-0.407971\pi\) | ||||
0.285106 | + | 0.958496i | \(0.407971\pi\) | |||||||
\(30\) | 5.96432 | 1.08893 | ||||||||
\(31\) | −3.60353 | −0.647214 | −0.323607 | − | 0.946192i | \(-0.604896\pi\) | ||||
−0.323607 | + | 0.946192i | \(0.604896\pi\) | |||||||
\(32\) | −8.01944 | −1.41765 | ||||||||
\(33\) | 12.5472 | 2.18419 | ||||||||
\(34\) | 10.1090 | 1.73368 | ||||||||
\(35\) | 1.00000 | 0.169031 | ||||||||
\(36\) | 11.8155 | 1.96924 | ||||||||
\(37\) | −10.8597 | −1.78533 | −0.892666 | − | 0.450719i | \(-0.851168\pi\) | ||||
−0.892666 | + | 0.450719i | \(0.851168\pi\) | |||||||
\(38\) | −3.61849 | −0.586997 | ||||||||
\(39\) | −1.59966 | −0.256150 | ||||||||
\(40\) | −0.0406892 | −0.00643352 | ||||||||
\(41\) | −4.34933 | −0.679250 | −0.339625 | − | 0.940561i | \(-0.610300\pi\) | ||||
−0.339625 | + | 0.940561i | \(0.610300\pi\) | |||||||
\(42\) | 5.96432 | 0.920315 | ||||||||
\(43\) | −7.91072 | −1.20637 | −0.603187 | − | 0.797600i | \(-0.706103\pi\) | ||||
−0.603187 | + | 0.797600i | \(0.706103\pi\) | |||||||
\(44\) | −8.52176 | −1.28470 | ||||||||
\(45\) | −5.84839 | −0.871826 | ||||||||
\(46\) | 0.119420 | 0.0176075 | ||||||||
\(47\) | −2.71923 | −0.396640 | −0.198320 | − | 0.980137i | \(-0.563549\pi\) | ||||
−0.198320 | + | 0.980137i | \(0.563549\pi\) | |||||||
\(48\) | 11.7765 | 1.69980 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 2.00507 | 0.283559 | ||||||||
\(51\) | −14.9973 | −2.10004 | ||||||||
\(52\) | 1.08645 | 0.150663 | ||||||||
\(53\) | −6.21568 | −0.853789 | −0.426895 | − | 0.904301i | \(-0.640392\pi\) | ||||
−0.426895 | + | 0.904301i | \(0.640392\pi\) | |||||||
\(54\) | −16.9887 | −2.31187 | ||||||||
\(55\) | 4.21808 | 0.568766 | ||||||||
\(56\) | −0.0406892 | −0.00543732 | ||||||||
\(57\) | 5.36822 | 0.711039 | ||||||||
\(58\) | 6.15693 | 0.808445 | ||||||||
\(59\) | −3.72905 | −0.485482 | −0.242741 | − | 0.970091i | \(-0.578046\pi\) | ||||
−0.242741 | + | 0.970091i | \(0.578046\pi\) | |||||||
\(60\) | 6.00961 | 0.775838 | ||||||||
\(61\) | −2.31653 | −0.296602 | −0.148301 | − | 0.988942i | \(-0.547380\pi\) | ||||
−0.148301 | + | 0.988942i | \(0.547380\pi\) | |||||||
\(62\) | −7.22533 | −0.917618 | ||||||||
\(63\) | −5.84839 | −0.736828 | ||||||||
\(64\) | −8.16151 | −1.02019 | ||||||||
\(65\) | −0.537768 | −0.0667019 | ||||||||
\(66\) | 25.1580 | 3.09673 | ||||||||
\(67\) | 1.76203 | 0.215266 | 0.107633 | − | 0.994191i | \(-0.465673\pi\) | ||||
0.107633 | + | 0.994191i | \(0.465673\pi\) | |||||||
\(68\) | 10.1858 | 1.23521 | ||||||||
\(69\) | −0.177166 | −0.0213283 | ||||||||
\(70\) | 2.00507 | 0.239651 | ||||||||
\(71\) | −6.64223 | −0.788287 | −0.394144 | − | 0.919049i | \(-0.628959\pi\) | ||||
−0.394144 | + | 0.919049i | \(0.628959\pi\) | |||||||
\(72\) | 0.237966 | 0.0280446 | ||||||||
\(73\) | 3.46914 | 0.406033 | 0.203016 | − | 0.979175i | \(-0.434926\pi\) | ||||
0.203016 | + | 0.979175i | \(0.434926\pi\) | |||||||
\(74\) | −21.7745 | −2.53124 | ||||||||
\(75\) | −2.97462 | −0.343480 | ||||||||
\(76\) | −3.64597 | −0.418221 | ||||||||
\(77\) | 4.21808 | 0.480695 | ||||||||
\(78\) | −3.20742 | −0.363169 | ||||||||
\(79\) | 16.1254 | 1.81425 | 0.907126 | − | 0.420859i | \(-0.138271\pi\) | ||||
0.907126 | + | 0.420859i | \(0.138271\pi\) | |||||||
\(80\) | 3.95900 | 0.442630 | ||||||||
\(81\) | 7.65849 | 0.850943 | ||||||||
\(82\) | −8.72069 | −0.963039 | ||||||||
\(83\) | 9.34281 | 1.02551 | 0.512754 | − | 0.858536i | \(-0.328625\pi\) | ||||
0.512754 | + | 0.858536i | \(0.328625\pi\) | |||||||
\(84\) | 6.00961 | 0.655703 | ||||||||
\(85\) | −5.04173 | −0.546853 | ||||||||
\(86\) | −15.8615 | −1.71039 | ||||||||
\(87\) | −9.13414 | −0.979282 | ||||||||
\(88\) | −0.171630 | −0.0182958 | ||||||||
\(89\) | 12.1526 | 1.28817 | 0.644087 | − | 0.764952i | \(-0.277238\pi\) | ||||
0.644087 | + | 0.764952i | \(0.277238\pi\) | |||||||
\(90\) | −11.7264 | −1.23607 | ||||||||
\(91\) | −0.537768 | −0.0563734 | ||||||||
\(92\) | 0.120327 | 0.0125449 | ||||||||
\(93\) | 10.7192 | 1.11153 | ||||||||
\(94\) | −5.45224 | −0.562355 | ||||||||
\(95\) | 1.80467 | 0.185156 | ||||||||
\(96\) | 23.8548 | 2.43467 | ||||||||
\(97\) | 4.40673 | 0.447436 | 0.223718 | − | 0.974654i | \(-0.428181\pi\) | ||||
0.223718 | + | 0.974654i | \(0.428181\pi\) | |||||||
\(98\) | 2.00507 | 0.202542 | ||||||||
\(99\) | −24.6690 | −2.47933 | ||||||||
\(100\) | 2.02029 | 0.202029 | ||||||||
\(101\) | 3.68268 | 0.366440 | 0.183220 | − | 0.983072i | \(-0.441348\pi\) | ||||
0.183220 | + | 0.983072i | \(0.441348\pi\) | |||||||
\(102\) | −30.0705 | −2.97742 | ||||||||
\(103\) | 12.9844 | 1.27939 | 0.639694 | − | 0.768630i | \(-0.279061\pi\) | ||||
0.639694 | + | 0.768630i | \(0.279061\pi\) | |||||||
\(104\) | 0.0218813 | 0.00214564 | ||||||||
\(105\) | −2.97462 | −0.290294 | ||||||||
\(106\) | −12.4628 | −1.21050 | ||||||||
\(107\) | −17.6012 | −1.70157 | −0.850785 | − | 0.525513i | \(-0.823873\pi\) | ||||
−0.850785 | + | 0.525513i | \(0.823873\pi\) | |||||||
\(108\) | −17.1177 | −1.64715 | ||||||||
\(109\) | −5.15431 | −0.493693 | −0.246846 | − | 0.969055i | \(-0.579394\pi\) | ||||
−0.246846 | + | 0.969055i | \(0.579394\pi\) | |||||||
\(110\) | 8.45753 | 0.806394 | ||||||||
\(111\) | 32.3037 | 3.06613 | ||||||||
\(112\) | 3.95900 | 0.374091 | ||||||||
\(113\) | −1.23862 | −0.116520 | −0.0582599 | − | 0.998301i | \(-0.518555\pi\) | ||||
−0.0582599 | + | 0.998301i | \(0.518555\pi\) | |||||||
\(114\) | 10.7636 | 1.00811 | ||||||||
\(115\) | −0.0595591 | −0.00555391 | ||||||||
\(116\) | 6.20369 | 0.575998 | ||||||||
\(117\) | 3.14508 | 0.290762 | ||||||||
\(118\) | −7.47700 | −0.688314 | ||||||||
\(119\) | −5.04173 | −0.462175 | ||||||||
\(120\) | 0.121035 | 0.0110489 | ||||||||
\(121\) | 6.79220 | 0.617473 | ||||||||
\(122\) | −4.64481 | −0.420521 | ||||||||
\(123\) | 12.9376 | 1.16654 | ||||||||
\(124\) | −7.28020 | −0.653781 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | −11.7264 | −1.04467 | ||||||||
\(127\) | 18.8785 | 1.67520 | 0.837598 | − | 0.546287i | \(-0.183959\pi\) | ||||
0.837598 | + | 0.546287i | \(0.183959\pi\) | |||||||
\(128\) | −0.325496 | −0.0287701 | ||||||||
\(129\) | 23.5314 | 2.07183 | ||||||||
\(130\) | −1.07826 | −0.0945697 | ||||||||
\(131\) | −5.27999 | −0.461315 | −0.230658 | − | 0.973035i | \(-0.574088\pi\) | ||||
−0.230658 | + | 0.973035i | \(0.574088\pi\) | |||||||
\(132\) | 25.3490 | 2.20635 | ||||||||
\(133\) | 1.80467 | 0.156485 | ||||||||
\(134\) | 3.53298 | 0.305203 | ||||||||
\(135\) | 8.47289 | 0.729230 | ||||||||
\(136\) | 0.205144 | 0.0175909 | ||||||||
\(137\) | −0.940881 | −0.0803849 | −0.0401924 | − | 0.999192i | \(-0.512797\pi\) | ||||
−0.0401924 | + | 0.999192i | \(0.512797\pi\) | |||||||
\(138\) | −0.355229 | −0.0302391 | ||||||||
\(139\) | −10.5016 | −0.890731 | −0.445365 | − | 0.895349i | \(-0.646926\pi\) | ||||
−0.445365 | + | 0.895349i | \(0.646926\pi\) | |||||||
\(140\) | 2.02029 | 0.170746 | ||||||||
\(141\) | 8.08869 | 0.681190 | ||||||||
\(142\) | −13.3181 | −1.11763 | ||||||||
\(143\) | −2.26835 | −0.189689 | ||||||||
\(144\) | −23.1538 | −1.92948 | ||||||||
\(145\) | −3.07069 | −0.255007 | ||||||||
\(146\) | 6.95587 | 0.575672 | ||||||||
\(147\) | −2.97462 | −0.245343 | ||||||||
\(148\) | −21.9399 | −1.80345 | ||||||||
\(149\) | 4.02623 | 0.329842 | 0.164921 | − | 0.986307i | \(-0.447263\pi\) | ||||
0.164921 | + | 0.986307i | \(0.447263\pi\) | |||||||
\(150\) | −5.96432 | −0.486985 | ||||||||
\(151\) | 10.9291 | 0.889397 | 0.444698 | − | 0.895680i | \(-0.353311\pi\) | ||||
0.444698 | + | 0.895680i | \(0.353311\pi\) | |||||||
\(152\) | −0.0734306 | −0.00595601 | ||||||||
\(153\) | 29.4860 | 2.38380 | ||||||||
\(154\) | 8.45753 | 0.681527 | ||||||||
\(155\) | 3.60353 | 0.289443 | ||||||||
\(156\) | −3.23178 | −0.258749 | ||||||||
\(157\) | 8.20693 | 0.654985 | 0.327492 | − | 0.944854i | \(-0.393796\pi\) | ||||
0.327492 | + | 0.944854i | \(0.393796\pi\) | |||||||
\(158\) | 32.3326 | 2.57224 | ||||||||
\(159\) | 18.4893 | 1.46630 | ||||||||
\(160\) | 8.01944 | 0.633993 | ||||||||
\(161\) | −0.0595591 | −0.00469391 | ||||||||
\(162\) | 15.3558 | 1.20646 | ||||||||
\(163\) | 3.61002 | 0.282758 | 0.141379 | − | 0.989956i | \(-0.454846\pi\) | ||||
0.141379 | + | 0.989956i | \(0.454846\pi\) | |||||||
\(164\) | −8.78691 | −0.686143 | ||||||||
\(165\) | −12.5472 | −0.976799 | ||||||||
\(166\) | 18.7330 | 1.45396 | ||||||||
\(167\) | 16.5517 | 1.28081 | 0.640405 | − | 0.768038i | \(-0.278767\pi\) | ||||
0.640405 | + | 0.768038i | \(0.278767\pi\) | |||||||
\(168\) | 0.121035 | 0.00933805 | ||||||||
\(169\) | −12.7108 | −0.977754 | ||||||||
\(170\) | −10.1090 | −0.775326 | ||||||||
\(171\) | −10.5544 | −0.807117 | ||||||||
\(172\) | −15.9820 | −1.21861 | ||||||||
\(173\) | 20.0193 | 1.52204 | 0.761018 | − | 0.648731i | \(-0.224700\pi\) | ||||
0.761018 | + | 0.648731i | \(0.224700\pi\) | |||||||
\(174\) | −18.3146 | −1.38842 | ||||||||
\(175\) | −1.00000 | −0.0755929 | ||||||||
\(176\) | 16.6994 | 1.25876 | ||||||||
\(177\) | 11.0925 | 0.833766 | ||||||||
\(178\) | 24.3668 | 1.82637 | ||||||||
\(179\) | −9.85328 | −0.736469 | −0.368234 | − | 0.929733i | \(-0.620038\pi\) | ||||
−0.368234 | + | 0.929733i | \(0.620038\pi\) | |||||||
\(180\) | −11.8155 | −0.880672 | ||||||||
\(181\) | 19.1524 | 1.42359 | 0.711794 | − | 0.702389i | \(-0.247883\pi\) | ||||
0.711794 | + | 0.702389i | \(0.247883\pi\) | |||||||
\(182\) | −1.07826 | −0.0799260 | ||||||||
\(183\) | 6.89082 | 0.509384 | ||||||||
\(184\) | 0.00242341 | 0.000178656 0 | ||||||||
\(185\) | 10.8597 | 0.798425 | ||||||||
\(186\) | 21.4926 | 1.57592 | ||||||||
\(187\) | −21.2664 | −1.55516 | ||||||||
\(188\) | −5.49364 | −0.400665 | ||||||||
\(189\) | 8.47289 | 0.616312 | ||||||||
\(190\) | 3.61849 | 0.262513 | ||||||||
\(191\) | 4.78905 | 0.346524 | 0.173262 | − | 0.984876i | \(-0.444569\pi\) | ||||
0.173262 | + | 0.984876i | \(0.444569\pi\) | |||||||
\(192\) | 24.2774 | 1.75207 | ||||||||
\(193\) | −6.03763 | −0.434598 | −0.217299 | − | 0.976105i | \(-0.569725\pi\) | ||||
−0.217299 | + | 0.976105i | \(0.569725\pi\) | |||||||
\(194\) | 8.83580 | 0.634373 | ||||||||
\(195\) | 1.59966 | 0.114554 | ||||||||
\(196\) | 2.02029 | 0.144307 | ||||||||
\(197\) | 10.1442 | 0.722741 | 0.361371 | − | 0.932422i | \(-0.382309\pi\) | ||||
0.361371 | + | 0.932422i | \(0.382309\pi\) | |||||||
\(198\) | −49.4630 | −3.51518 | ||||||||
\(199\) | 6.70984 | 0.475648 | 0.237824 | − | 0.971308i | \(-0.423566\pi\) | ||||
0.237824 | + | 0.971308i | \(0.423566\pi\) | |||||||
\(200\) | 0.0406892 | 0.00287716 | ||||||||
\(201\) | −5.24137 | −0.369698 | ||||||||
\(202\) | 7.38402 | 0.519538 | ||||||||
\(203\) | −3.07069 | −0.215520 | ||||||||
\(204\) | −30.2989 | −2.12134 | ||||||||
\(205\) | 4.34933 | 0.303770 | ||||||||
\(206\) | 26.0345 | 1.81391 | ||||||||
\(207\) | 0.348325 | 0.0242102 | ||||||||
\(208\) | −2.12902 | −0.147621 | ||||||||
\(209\) | 7.61226 | 0.526551 | ||||||||
\(210\) | −5.96432 | −0.411577 | ||||||||
\(211\) | −20.0259 | −1.37864 | −0.689321 | − | 0.724456i | \(-0.742091\pi\) | ||||
−0.689321 | + | 0.724456i | \(0.742091\pi\) | |||||||
\(212\) | −12.5575 | −0.862452 | ||||||||
\(213\) | 19.7581 | 1.35380 | ||||||||
\(214\) | −35.2916 | −2.41248 | ||||||||
\(215\) | 7.91072 | 0.539507 | ||||||||
\(216\) | −0.344755 | −0.0234576 | ||||||||
\(217\) | 3.60353 | 0.244624 | ||||||||
\(218\) | −10.3347 | −0.699956 | ||||||||
\(219\) | −10.3194 | −0.697320 | ||||||||
\(220\) | 8.52176 | 0.574537 | ||||||||
\(221\) | 2.71128 | 0.182381 | ||||||||
\(222\) | 64.7710 | 4.34715 | ||||||||
\(223\) | 4.60789 | 0.308567 | 0.154284 | − | 0.988027i | \(-0.450693\pi\) | ||||
0.154284 | + | 0.988027i | \(0.450693\pi\) | |||||||
\(224\) | 8.01944 | 0.535821 | ||||||||
\(225\) | 5.84839 | 0.389893 | ||||||||
\(226\) | −2.48352 | −0.165201 | ||||||||
\(227\) | −9.82621 | −0.652189 | −0.326094 | − | 0.945337i | \(-0.605733\pi\) | ||||
−0.326094 | + | 0.945337i | \(0.605733\pi\) | |||||||
\(228\) | 10.8454 | 0.718253 | ||||||||
\(229\) | 1.00000 | 0.0660819 | ||||||||
\(230\) | −0.119420 | −0.00787431 | ||||||||
\(231\) | −12.5472 | −0.825545 | ||||||||
\(232\) | 0.124944 | 0.00820295 | ||||||||
\(233\) | 26.5562 | 1.73975 | 0.869876 | − | 0.493271i | \(-0.164199\pi\) | ||||
0.869876 | + | 0.493271i | \(0.164199\pi\) | |||||||
\(234\) | 6.30609 | 0.412242 | ||||||||
\(235\) | 2.71923 | 0.177383 | ||||||||
\(236\) | −7.53378 | −0.490408 | ||||||||
\(237\) | −47.9671 | −3.11580 | ||||||||
\(238\) | −10.1090 | −0.655270 | ||||||||
\(239\) | 0.0705261 | 0.00456196 | 0.00228098 | − | 0.999997i | \(-0.499274\pi\) | ||||
0.00228098 | + | 0.999997i | \(0.499274\pi\) | |||||||
\(240\) | −11.7765 | −0.760173 | ||||||||
\(241\) | 6.36305 | 0.409880 | 0.204940 | − | 0.978774i | \(-0.434300\pi\) | ||||
0.204940 | + | 0.978774i | \(0.434300\pi\) | |||||||
\(242\) | 13.6188 | 0.875451 | ||||||||
\(243\) | 2.63753 | 0.169198 | ||||||||
\(244\) | −4.68008 | −0.299611 | ||||||||
\(245\) | −1.00000 | −0.0638877 | ||||||||
\(246\) | 25.9408 | 1.65392 | ||||||||
\(247\) | −0.970495 | −0.0617511 | ||||||||
\(248\) | −0.146625 | −0.00931068 | ||||||||
\(249\) | −27.7914 | −1.76121 | ||||||||
\(250\) | −2.00507 | −0.126812 | ||||||||
\(251\) | −26.6127 | −1.67978 | −0.839888 | − | 0.542759i | \(-0.817380\pi\) | ||||
−0.839888 | + | 0.542759i | \(0.817380\pi\) | |||||||
\(252\) | −11.8155 | −0.744304 | ||||||||
\(253\) | −0.251225 | −0.0157944 | ||||||||
\(254\) | 37.8527 | 2.37509 | ||||||||
\(255\) | 14.9973 | 0.939165 | ||||||||
\(256\) | 15.6704 | 0.979399 | ||||||||
\(257\) | 27.4541 | 1.71254 | 0.856271 | − | 0.516526i | \(-0.172775\pi\) | ||||
0.856271 | + | 0.516526i | \(0.172775\pi\) | |||||||
\(258\) | 47.1821 | 2.93743 | ||||||||
\(259\) | 10.8597 | 0.674792 | ||||||||
\(260\) | −1.08645 | −0.0673787 | ||||||||
\(261\) | 17.9586 | 1.11161 | ||||||||
\(262\) | −10.5867 | −0.654051 | ||||||||
\(263\) | −16.0791 | −0.991478 | −0.495739 | − | 0.868471i | \(-0.665103\pi\) | ||||
−0.495739 | + | 0.868471i | \(0.665103\pi\) | |||||||
\(264\) | 0.510535 | 0.0314213 | ||||||||
\(265\) | 6.21568 | 0.381826 | ||||||||
\(266\) | 3.61849 | 0.221864 | ||||||||
\(267\) | −36.1494 | −2.21231 | ||||||||
\(268\) | 3.55981 | 0.217450 | ||||||||
\(269\) | 25.4706 | 1.55297 | 0.776486 | − | 0.630135i | \(-0.217000\pi\) | ||||
0.776486 | + | 0.630135i | \(0.217000\pi\) | |||||||
\(270\) | 16.9887 | 1.03390 | ||||||||
\(271\) | 19.4672 | 1.18255 | 0.591274 | − | 0.806471i | \(-0.298625\pi\) | ||||
0.591274 | + | 0.806471i | \(0.298625\pi\) | |||||||
\(272\) | −19.9602 | −1.21027 | ||||||||
\(273\) | 1.59966 | 0.0968157 | ||||||||
\(274\) | −1.88653 | −0.113969 | ||||||||
\(275\) | −4.21808 | −0.254360 | ||||||||
\(276\) | −0.357927 | −0.0215447 | ||||||||
\(277\) | −1.94385 | −0.116794 | −0.0583972 | − | 0.998293i | \(-0.518599\pi\) | ||||
−0.0583972 | + | 0.998293i | \(0.518599\pi\) | |||||||
\(278\) | −21.0563 | −1.26287 | ||||||||
\(279\) | −21.0749 | −1.26172 | ||||||||
\(280\) | 0.0406892 | 0.00243164 | ||||||||
\(281\) | 0.724470 | 0.0432182 | 0.0216091 | − | 0.999766i | \(-0.493121\pi\) | ||||
0.0216091 | + | 0.999766i | \(0.493121\pi\) | |||||||
\(282\) | 16.2184 | 0.965789 | ||||||||
\(283\) | −15.5685 | −0.925449 | −0.462724 | − | 0.886502i | \(-0.653128\pi\) | ||||
−0.462724 | + | 0.886502i | \(0.653128\pi\) | |||||||
\(284\) | −13.4192 | −0.796286 | ||||||||
\(285\) | −5.36822 | −0.317986 | ||||||||
\(286\) | −4.54819 | −0.268940 | ||||||||
\(287\) | 4.34933 | 0.256733 | ||||||||
\(288\) | −46.9008 | −2.76366 | ||||||||
\(289\) | 8.41906 | 0.495239 | ||||||||
\(290\) | −6.15693 | −0.361547 | ||||||||
\(291\) | −13.1084 | −0.768427 | ||||||||
\(292\) | 7.00869 | 0.410152 | ||||||||
\(293\) | −3.24922 | −0.189822 | −0.0949108 | − | 0.995486i | \(-0.530257\pi\) | ||||
−0.0949108 | + | 0.995486i | \(0.530257\pi\) | |||||||
\(294\) | −5.96432 | −0.347846 | ||||||||
\(295\) | 3.72905 | 0.217114 | ||||||||
\(296\) | −0.441874 | −0.0256834 | ||||||||
\(297\) | 35.7393 | 2.07381 | ||||||||
\(298\) | 8.07287 | 0.467649 | ||||||||
\(299\) | 0.0320290 | 0.00185228 | ||||||||
\(300\) | −6.00961 | −0.346965 | ||||||||
\(301\) | 7.91072 | 0.455966 | ||||||||
\(302\) | 21.9136 | 1.26098 | ||||||||
\(303\) | −10.9546 | −0.629325 | ||||||||
\(304\) | 7.14470 | 0.409777 | ||||||||
\(305\) | 2.31653 | 0.132644 | ||||||||
\(306\) | 59.1214 | 3.37975 | ||||||||
\(307\) | −25.7115 | −1.46743 | −0.733717 | − | 0.679455i | \(-0.762216\pi\) | ||||
−0.733717 | + | 0.679455i | \(0.762216\pi\) | |||||||
\(308\) | 8.52176 | 0.485572 | ||||||||
\(309\) | −38.6236 | −2.19722 | ||||||||
\(310\) | 7.22533 | 0.410371 | ||||||||
\(311\) | −13.4262 | −0.761330 | −0.380665 | − | 0.924713i | \(-0.624305\pi\) | ||||
−0.380665 | + | 0.924713i | \(0.624305\pi\) | |||||||
\(312\) | −0.0650887 | −0.00368492 | ||||||||
\(313\) | −10.9285 | −0.617718 | −0.308859 | − | 0.951108i | \(-0.599947\pi\) | ||||
−0.308859 | + | 0.951108i | \(0.599947\pi\) | |||||||
\(314\) | 16.4555 | 0.928635 | ||||||||
\(315\) | 5.84839 | 0.329519 | ||||||||
\(316\) | 32.5781 | 1.83266 | ||||||||
\(317\) | 34.2758 | 1.92512 | 0.962560 | − | 0.271068i | \(-0.0873767\pi\) | ||||
0.962560 | + | 0.271068i | \(0.0873767\pi\) | |||||||
\(318\) | 37.0723 | 2.07891 | ||||||||
\(319\) | −12.9524 | −0.725195 | ||||||||
\(320\) | 8.16151 | 0.456242 | ||||||||
\(321\) | 52.3569 | 2.92228 | ||||||||
\(322\) | −0.119420 | −0.00665501 | ||||||||
\(323\) | −9.09868 | −0.506264 | ||||||||
\(324\) | 15.4724 | 0.859578 | ||||||||
\(325\) | 0.537768 | 0.0298300 | ||||||||
\(326\) | 7.23832 | 0.400894 | ||||||||
\(327\) | 15.3321 | 0.847868 | ||||||||
\(328\) | −0.176970 | −0.00977155 | ||||||||
\(329\) | 2.71923 | 0.149916 | ||||||||
\(330\) | −25.1580 | −1.38490 | ||||||||
\(331\) | 31.2613 | 1.71828 | 0.859138 | − | 0.511744i | \(-0.171000\pi\) | ||||
0.859138 | + | 0.511744i | \(0.171000\pi\) | |||||||
\(332\) | 18.8752 | 1.03591 | ||||||||
\(333\) | −63.5120 | −3.48044 | ||||||||
\(334\) | 33.1873 | 1.81593 | ||||||||
\(335\) | −1.76203 | −0.0962699 | ||||||||
\(336\) | −11.7765 | −0.642463 | ||||||||
\(337\) | −19.7364 | −1.07511 | −0.537554 | − | 0.843229i | \(-0.680652\pi\) | ||||
−0.537554 | + | 0.843229i | \(0.680652\pi\) | |||||||
\(338\) | −25.4860 | −1.38626 | ||||||||
\(339\) | 3.68444 | 0.200111 | ||||||||
\(340\) | −10.1858 | −0.552401 | ||||||||
\(341\) | 15.2000 | 0.823126 | ||||||||
\(342\) | −21.1623 | −1.14433 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | −0.321880 | −0.0173546 | ||||||||
\(345\) | 0.177166 | 0.00953829 | ||||||||
\(346\) | 40.1400 | 2.15794 | ||||||||
\(347\) | 14.2612 | 0.765581 | 0.382790 | − | 0.923835i | \(-0.374963\pi\) | ||||
0.382790 | + | 0.923835i | \(0.374963\pi\) | |||||||
\(348\) | −18.4536 | −0.989219 | ||||||||
\(349\) | 26.0146 | 1.39253 | 0.696266 | − | 0.717784i | \(-0.254843\pi\) | ||||
0.696266 | + | 0.717784i | \(0.254843\pi\) | |||||||
\(350\) | −2.00507 | −0.107175 | ||||||||
\(351\) | −4.55645 | −0.243205 | ||||||||
\(352\) | 33.8267 | 1.80297 | ||||||||
\(353\) | 25.7693 | 1.37156 | 0.685781 | − | 0.727808i | \(-0.259461\pi\) | ||||
0.685781 | + | 0.727808i | \(0.259461\pi\) | |||||||
\(354\) | 22.2413 | 1.18211 | ||||||||
\(355\) | 6.64223 | 0.352533 | ||||||||
\(356\) | 24.5518 | 1.30124 | ||||||||
\(357\) | 14.9973 | 0.793739 | ||||||||
\(358\) | −19.7565 | −1.04416 | ||||||||
\(359\) | 3.32748 | 0.175618 | 0.0878089 | − | 0.996137i | \(-0.472014\pi\) | ||||
0.0878089 | + | 0.996137i | \(0.472014\pi\) | |||||||
\(360\) | −0.237966 | −0.0125419 | ||||||||
\(361\) | −15.7432 | −0.828587 | ||||||||
\(362\) | 38.4019 | 2.01836 | ||||||||
\(363\) | −20.2043 | −1.06045 | ||||||||
\(364\) | −1.08645 | −0.0569454 | ||||||||
\(365\) | −3.46914 | −0.181583 | ||||||||
\(366\) | 13.8166 | 0.722203 | ||||||||
\(367\) | 25.1398 | 1.31229 | 0.656144 | − | 0.754635i | \(-0.272186\pi\) | ||||
0.656144 | + | 0.754635i | \(0.272186\pi\) | |||||||
\(368\) | −0.235794 | −0.0122916 | ||||||||
\(369\) | −25.4365 | −1.32417 | ||||||||
\(370\) | 21.7745 | 1.13200 | ||||||||
\(371\) | 6.21568 | 0.322702 | ||||||||
\(372\) | 21.6558 | 1.12280 | ||||||||
\(373\) | 6.46116 | 0.334546 | 0.167273 | − | 0.985911i | \(-0.446504\pi\) | ||||
0.167273 | + | 0.985911i | \(0.446504\pi\) | |||||||
\(374\) | −42.6406 | −2.20489 | ||||||||
\(375\) | 2.97462 | 0.153609 | ||||||||
\(376\) | −0.110643 | −0.00570599 | ||||||||
\(377\) | 1.65132 | 0.0850471 | ||||||||
\(378\) | 16.9887 | 0.873805 | ||||||||
\(379\) | −34.4818 | −1.77121 | −0.885604 | − | 0.464440i | \(-0.846256\pi\) | ||||
−0.885604 | + | 0.464440i | \(0.846256\pi\) | |||||||
\(380\) | 3.64597 | 0.187034 | ||||||||
\(381\) | −56.1565 | −2.87698 | ||||||||
\(382\) | 9.60237 | 0.491300 | ||||||||
\(383\) | −34.4404 | −1.75982 | −0.879911 | − | 0.475139i | \(-0.842398\pi\) | ||||
−0.879911 | + | 0.475139i | \(0.842398\pi\) | |||||||
\(384\) | 0.968230 | 0.0494098 | ||||||||
\(385\) | −4.21808 | −0.214973 | ||||||||
\(386\) | −12.1059 | −0.616172 | ||||||||
\(387\) | −46.2650 | −2.35178 | ||||||||
\(388\) | 8.90290 | 0.451976 | ||||||||
\(389\) | −8.42958 | −0.427397 | −0.213698 | − | 0.976900i | \(-0.568551\pi\) | ||||
−0.213698 | + | 0.976900i | \(0.568551\pi\) | |||||||
\(390\) | 3.20742 | 0.162414 | ||||||||
\(391\) | 0.300281 | 0.0151859 | ||||||||
\(392\) | 0.0406892 | 0.00205511 | ||||||||
\(393\) | 15.7060 | 0.792263 | ||||||||
\(394\) | 20.3397 | 1.02470 | ||||||||
\(395\) | −16.1254 | −0.811358 | ||||||||
\(396\) | −49.8386 | −2.50448 | ||||||||
\(397\) | −2.36237 | −0.118564 | −0.0592820 | − | 0.998241i | \(-0.518881\pi\) | ||||
−0.0592820 | + | 0.998241i | \(0.518881\pi\) | |||||||
\(398\) | 13.4537 | 0.674372 | ||||||||
\(399\) | −5.36822 | −0.268747 | ||||||||
\(400\) | −3.95900 | −0.197950 | ||||||||
\(401\) | −4.92460 | −0.245923 | −0.122961 | − | 0.992411i | \(-0.539239\pi\) | ||||
−0.122961 | + | 0.992411i | \(0.539239\pi\) | |||||||
\(402\) | −10.5093 | −0.524156 | ||||||||
\(403\) | −1.93787 | −0.0965320 | ||||||||
\(404\) | 7.44009 | 0.370158 | ||||||||
\(405\) | −7.65849 | −0.380553 | ||||||||
\(406\) | −6.15693 | −0.305563 | ||||||||
\(407\) | 45.8073 | 2.27058 | ||||||||
\(408\) | −0.610226 | −0.0302107 | ||||||||
\(409\) | −13.7940 | −0.682067 | −0.341034 | − | 0.940051i | \(-0.610777\pi\) | ||||
−0.341034 | + | 0.940051i | \(0.610777\pi\) | |||||||
\(410\) | 8.72069 | 0.430684 | ||||||||
\(411\) | 2.79877 | 0.138053 | ||||||||
\(412\) | 26.2322 | 1.29237 | ||||||||
\(413\) | 3.72905 | 0.183495 | ||||||||
\(414\) | 0.698414 | 0.0343252 | ||||||||
\(415\) | −9.34281 | −0.458621 | ||||||||
\(416\) | −4.31260 | −0.211443 | ||||||||
\(417\) | 31.2382 | 1.52974 | ||||||||
\(418\) | 15.2631 | 0.746542 | ||||||||
\(419\) | −5.80673 | −0.283678 | −0.141839 | − | 0.989890i | \(-0.545301\pi\) | ||||
−0.141839 | + | 0.989890i | \(0.545301\pi\) | |||||||
\(420\) | −6.00961 | −0.293239 | ||||||||
\(421\) | 12.5564 | 0.611959 | 0.305980 | − | 0.952038i | \(-0.401016\pi\) | ||||
0.305980 | + | 0.952038i | \(0.401016\pi\) | |||||||
\(422\) | −40.1533 | −1.95463 | ||||||||
\(423\) | −15.9031 | −0.773236 | ||||||||
\(424\) | −0.252911 | −0.0122824 | ||||||||
\(425\) | 5.04173 | 0.244560 | ||||||||
\(426\) | 39.6164 | 1.91942 | ||||||||
\(427\) | 2.31653 | 0.112105 | ||||||||
\(428\) | −35.5596 | −1.71884 | ||||||||
\(429\) | 6.74748 | 0.325772 | ||||||||
\(430\) | 15.8615 | 0.764910 | ||||||||
\(431\) | 1.04885 | 0.0505211 | 0.0252606 | − | 0.999681i | \(-0.491958\pi\) | ||||
0.0252606 | + | 0.999681i | \(0.491958\pi\) | |||||||
\(432\) | 33.5442 | 1.61390 | ||||||||
\(433\) | −20.8286 | −1.00096 | −0.500480 | − | 0.865748i | \(-0.666843\pi\) | ||||
−0.500480 | + | 0.865748i | \(0.666843\pi\) | |||||||
\(434\) | 7.22533 | 0.346827 | ||||||||
\(435\) | 9.13414 | 0.437948 | ||||||||
\(436\) | −10.4132 | −0.498702 | ||||||||
\(437\) | −0.107485 | −0.00514169 | ||||||||
\(438\) | −20.6911 | −0.988658 | ||||||||
\(439\) | −30.8376 | −1.47180 | −0.735899 | − | 0.677091i | \(-0.763240\pi\) | ||||
−0.735899 | + | 0.677091i | \(0.763240\pi\) | |||||||
\(440\) | 0.171630 | 0.00818214 | ||||||||
\(441\) | 5.84839 | 0.278495 | ||||||||
\(442\) | 5.43630 | 0.258578 | ||||||||
\(443\) | 5.46977 | 0.259877 | 0.129938 | − | 0.991522i | \(-0.458522\pi\) | ||||
0.129938 | + | 0.991522i | \(0.458522\pi\) | |||||||
\(444\) | 65.2629 | 3.09724 | ||||||||
\(445\) | −12.1526 | −0.576089 | ||||||||
\(446\) | 9.23913 | 0.437485 | ||||||||
\(447\) | −11.9765 | −0.566470 | ||||||||
\(448\) | 8.16151 | 0.385595 | ||||||||
\(449\) | 5.27563 | 0.248972 | 0.124486 | − | 0.992221i | \(-0.460272\pi\) | ||||
0.124486 | + | 0.992221i | \(0.460272\pi\) | |||||||
\(450\) | 11.7264 | 0.552788 | ||||||||
\(451\) | 18.3458 | 0.863870 | ||||||||
\(452\) | −2.50238 | −0.117702 | ||||||||
\(453\) | −32.5099 | −1.52745 | ||||||||
\(454\) | −19.7022 | −0.924671 | ||||||||
\(455\) | 0.537768 | 0.0252109 | ||||||||
\(456\) | 0.218428 | 0.0102289 | ||||||||
\(457\) | −10.2876 | −0.481235 | −0.240617 | − | 0.970620i | \(-0.577350\pi\) | ||||
−0.240617 | + | 0.970620i | \(0.577350\pi\) | |||||||
\(458\) | 2.00507 | 0.0936906 | ||||||||
\(459\) | −42.7180 | −1.99391 | ||||||||
\(460\) | −0.120327 | −0.00561026 | ||||||||
\(461\) | 21.4763 | 1.00025 | 0.500126 | − | 0.865953i | \(-0.333287\pi\) | ||||
0.500126 | + | 0.865953i | \(0.333287\pi\) | |||||||
\(462\) | −25.1580 | −1.17046 | ||||||||
\(463\) | −0.554878 | −0.0257874 | −0.0128937 | − | 0.999917i | \(-0.504104\pi\) | ||||
−0.0128937 | + | 0.999917i | \(0.504104\pi\) | |||||||
\(464\) | −12.1569 | −0.564368 | ||||||||
\(465\) | −10.7192 | −0.497089 | ||||||||
\(466\) | 53.2469 | 2.46661 | ||||||||
\(467\) | 13.4722 | 0.623418 | 0.311709 | − | 0.950178i | \(-0.399099\pi\) | ||||
0.311709 | + | 0.950178i | \(0.399099\pi\) | |||||||
\(468\) | 6.35398 | 0.293713 | ||||||||
\(469\) | −1.76203 | −0.0813629 | ||||||||
\(470\) | 5.45224 | 0.251493 | ||||||||
\(471\) | −24.4125 | −1.12487 | ||||||||
\(472\) | −0.151732 | −0.00698403 | ||||||||
\(473\) | 33.3681 | 1.53426 | ||||||||
\(474\) | −96.1772 | −4.41757 | ||||||||
\(475\) | −1.80467 | −0.0828041 | ||||||||
\(476\) | −10.1858 | −0.466864 | ||||||||
\(477\) | −36.3517 | −1.66443 | ||||||||
\(478\) | 0.141410 | 0.00646792 | ||||||||
\(479\) | −3.22190 | −0.147212 | −0.0736062 | − | 0.997287i | \(-0.523451\pi\) | ||||
−0.0736062 | + | 0.997287i | \(0.523451\pi\) | |||||||
\(480\) | −23.8548 | −1.08882 | ||||||||
\(481\) | −5.84002 | −0.266282 | ||||||||
\(482\) | 12.7584 | 0.581127 | ||||||||
\(483\) | 0.177166 | 0.00806132 | ||||||||
\(484\) | 13.7222 | 0.623738 | ||||||||
\(485\) | −4.40673 | −0.200100 | ||||||||
\(486\) | 5.28843 | 0.239888 | ||||||||
\(487\) | −15.6127 | −0.707481 | −0.353740 | − | 0.935344i | \(-0.615090\pi\) | ||||
−0.353740 | + | 0.935344i | \(0.615090\pi\) | |||||||
\(488\) | −0.0942578 | −0.00426685 | ||||||||
\(489\) | −10.7384 | −0.485609 | ||||||||
\(490\) | −2.00507 | −0.0905797 | ||||||||
\(491\) | 39.8739 | 1.79948 | 0.899742 | − | 0.436422i | \(-0.143755\pi\) | ||||
0.899742 | + | 0.436422i | \(0.143755\pi\) | |||||||
\(492\) | 26.1378 | 1.17838 | ||||||||
\(493\) | 15.4816 | 0.697255 | ||||||||
\(494\) | −1.94591 | −0.0875505 | ||||||||
\(495\) | 24.6690 | 1.10879 | ||||||||
\(496\) | 14.2664 | 0.640580 | ||||||||
\(497\) | 6.64223 | 0.297945 | ||||||||
\(498\) | −55.7235 | −2.49703 | ||||||||
\(499\) | 36.1402 | 1.61786 | 0.808929 | − | 0.587906i | \(-0.200048\pi\) | ||||
0.808929 | + | 0.587906i | \(0.200048\pi\) | |||||||
\(500\) | −2.02029 | −0.0903503 | ||||||||
\(501\) | −49.2351 | −2.19966 | ||||||||
\(502\) | −53.3602 | −2.38158 | ||||||||
\(503\) | −29.1419 | −1.29937 | −0.649686 | − | 0.760203i | \(-0.725100\pi\) | ||||
−0.649686 | + | 0.760203i | \(0.725100\pi\) | |||||||
\(504\) | −0.237966 | −0.0105998 | ||||||||
\(505\) | −3.68268 | −0.163877 | ||||||||
\(506\) | −0.503723 | −0.0223932 | ||||||||
\(507\) | 37.8099 | 1.67920 | ||||||||
\(508\) | 38.1401 | 1.69219 | ||||||||
\(509\) | −5.02226 | −0.222608 | −0.111304 | − | 0.993786i | \(-0.535503\pi\) | ||||
−0.111304 | + | 0.993786i | \(0.535503\pi\) | |||||||
\(510\) | 30.0705 | 1.33154 | ||||||||
\(511\) | −3.46914 | −0.153466 | ||||||||
\(512\) | 32.0712 | 1.41736 | ||||||||
\(513\) | 15.2908 | 0.675105 | ||||||||
\(514\) | 55.0474 | 2.42804 | ||||||||
\(515\) | −12.9844 | −0.572160 | ||||||||
\(516\) | 47.5404 | 2.09285 | ||||||||
\(517\) | 11.4699 | 0.504447 | ||||||||
\(518\) | 21.7745 | 0.956718 | ||||||||
\(519\) | −59.5498 | −2.61394 | ||||||||
\(520\) | −0.0218813 | −0.000959559 0 | ||||||||
\(521\) | −25.1235 | −1.10068 | −0.550341 | − | 0.834940i | \(-0.685502\pi\) | ||||
−0.550341 | + | 0.834940i | \(0.685502\pi\) | |||||||
\(522\) | 36.0081 | 1.57603 | ||||||||
\(523\) | 38.1779 | 1.66940 | 0.834702 | − | 0.550702i | \(-0.185640\pi\) | ||||
0.834702 | + | 0.550702i | \(0.185640\pi\) | |||||||
\(524\) | −10.6671 | −0.465996 | ||||||||
\(525\) | 2.97462 | 0.129823 | ||||||||
\(526\) | −32.2396 | −1.40571 | ||||||||
\(527\) | −18.1681 | −0.791413 | ||||||||
\(528\) | −49.6744 | −2.16180 | ||||||||
\(529\) | −22.9965 | −0.999846 | ||||||||
\(530\) | 12.4628 | 0.541352 | ||||||||
\(531\) | −21.8090 | −0.946428 | ||||||||
\(532\) | 3.64597 | 0.158073 | ||||||||
\(533\) | −2.33893 | −0.101310 | ||||||||
\(534\) | −72.4820 | −3.13660 | ||||||||
\(535\) | 17.6012 | 0.760966 | ||||||||
\(536\) | 0.0716954 | 0.00309677 | ||||||||
\(537\) | 29.3098 | 1.26481 | ||||||||
\(538\) | 51.0703 | 2.20180 | ||||||||
\(539\) | −4.21808 | −0.181686 | ||||||||
\(540\) | 17.1177 | 0.736629 | ||||||||
\(541\) | 35.4011 | 1.52201 | 0.761007 | − | 0.648744i | \(-0.224705\pi\) | ||||
0.761007 | + | 0.648744i | \(0.224705\pi\) | |||||||
\(542\) | 39.0330 | 1.67661 | ||||||||
\(543\) | −56.9712 | −2.44487 | ||||||||
\(544\) | −40.4319 | −1.73350 | ||||||||
\(545\) | 5.15431 | 0.220786 | ||||||||
\(546\) | 3.20742 | 0.137265 | ||||||||
\(547\) | −28.2855 | −1.20940 | −0.604699 | − | 0.796454i | \(-0.706707\pi\) | ||||
−0.604699 | + | 0.796454i | \(0.706707\pi\) | |||||||
\(548\) | −1.90086 | −0.0812005 | ||||||||
\(549\) | −13.5480 | −0.578214 | ||||||||
\(550\) | −8.45753 | −0.360630 | ||||||||
\(551\) | −5.54159 | −0.236079 | ||||||||
\(552\) | −0.00720873 | −0.000306824 0 | ||||||||
\(553\) | −16.1254 | −0.685723 | ||||||||
\(554\) | −3.89754 | −0.165591 | ||||||||
\(555\) | −32.3037 | −1.37121 | ||||||||
\(556\) | −21.2162 | −0.899768 | ||||||||
\(557\) | 2.45585 | 0.104058 | 0.0520288 | − | 0.998646i | \(-0.483431\pi\) | ||||
0.0520288 | + | 0.998646i | \(0.483431\pi\) | |||||||
\(558\) | −42.2565 | −1.78886 | ||||||||
\(559\) | −4.25413 | −0.179931 | ||||||||
\(560\) | −3.95900 | −0.167298 | ||||||||
\(561\) | 63.2596 | 2.67082 | ||||||||
\(562\) | 1.45261 | 0.0612746 | ||||||||
\(563\) | 30.2286 | 1.27399 | 0.636993 | − | 0.770870i | \(-0.280178\pi\) | ||||
0.636993 | + | 0.770870i | \(0.280178\pi\) | |||||||
\(564\) | 16.3415 | 0.688102 | ||||||||
\(565\) | 1.23862 | 0.0521093 | ||||||||
\(566\) | −31.2158 | −1.31210 | ||||||||
\(567\) | −7.65849 | −0.321626 | ||||||||
\(568\) | −0.270266 | −0.0113401 | ||||||||
\(569\) | −13.8470 | −0.580495 | −0.290248 | − | 0.956952i | \(-0.593738\pi\) | ||||
−0.290248 | + | 0.956952i | \(0.593738\pi\) | |||||||
\(570\) | −10.7636 | −0.450840 | ||||||||
\(571\) | −26.0706 | −1.09102 | −0.545511 | − | 0.838104i | \(-0.683664\pi\) | ||||
−0.545511 | + | 0.838104i | \(0.683664\pi\) | |||||||
\(572\) | −4.58273 | −0.191614 | ||||||||
\(573\) | −14.2456 | −0.595120 | ||||||||
\(574\) | 8.72069 | 0.363994 | ||||||||
\(575\) | 0.0595591 | 0.00248378 | ||||||||
\(576\) | −47.7317 | −1.98882 | ||||||||
\(577\) | 43.7245 | 1.82027 | 0.910137 | − | 0.414308i | \(-0.135976\pi\) | ||||
0.910137 | + | 0.414308i | \(0.135976\pi\) | |||||||
\(578\) | 16.8808 | 0.702148 | ||||||||
\(579\) | 17.9597 | 0.746379 | ||||||||
\(580\) | −6.20369 | −0.257594 | ||||||||
\(581\) | −9.34281 | −0.387605 | ||||||||
\(582\) | −26.2832 | −1.08947 | ||||||||
\(583\) | 26.2182 | 1.08585 | ||||||||
\(584\) | 0.141157 | 0.00584110 | ||||||||
\(585\) | −3.14508 | −0.130033 | ||||||||
\(586\) | −6.51491 | −0.269129 | ||||||||
\(587\) | 33.4838 | 1.38202 | 0.691012 | − | 0.722844i | \(-0.257165\pi\) | ||||
0.691012 | + | 0.722844i | \(0.257165\pi\) | |||||||
\(588\) | −6.00961 | −0.247832 | ||||||||
\(589\) | 6.50320 | 0.267960 | ||||||||
\(590\) | 7.47700 | 0.307823 | ||||||||
\(591\) | −30.1751 | −1.24124 | ||||||||
\(592\) | 42.9938 | 1.76703 | ||||||||
\(593\) | 23.6782 | 0.972345 | 0.486173 | − | 0.873863i | \(-0.338393\pi\) | ||||
0.486173 | + | 0.873863i | \(0.338393\pi\) | |||||||
\(594\) | 71.6597 | 2.94023 | ||||||||
\(595\) | 5.04173 | 0.206691 | ||||||||
\(596\) | 8.13417 | 0.333189 | ||||||||
\(597\) | −19.9593 | −0.816878 | ||||||||
\(598\) | 0.0642202 | 0.00262616 | ||||||||
\(599\) | 1.85993 | 0.0759946 | 0.0379973 | − | 0.999278i | \(-0.487902\pi\) | ||||
0.0379973 | + | 0.999278i | \(0.487902\pi\) | |||||||
\(600\) | −0.121035 | −0.00494123 | ||||||||
\(601\) | −9.18487 | −0.374659 | −0.187329 | − | 0.982297i | \(-0.559983\pi\) | ||||
−0.187329 | + | 0.982297i | \(0.559983\pi\) | |||||||
\(602\) | 15.8615 | 0.646467 | ||||||||
\(603\) | 10.3050 | 0.419653 | ||||||||
\(604\) | 22.0800 | 0.898421 | ||||||||
\(605\) | −6.79220 | −0.276142 | ||||||||
\(606\) | −21.9647 | −0.892254 | ||||||||
\(607\) | 28.5474 | 1.15870 | 0.579351 | − | 0.815078i | \(-0.303306\pi\) | ||||
0.579351 | + | 0.815078i | \(0.303306\pi\) | |||||||
\(608\) | 14.4725 | 0.586936 | ||||||||
\(609\) | 9.13414 | 0.370134 | ||||||||
\(610\) | 4.64481 | 0.188063 | ||||||||
\(611\) | −1.46231 | −0.0591589 | ||||||||
\(612\) | 59.5704 | 2.40799 | ||||||||
\(613\) | −13.3492 | −0.539168 | −0.269584 | − | 0.962977i | \(-0.586886\pi\) | ||||
−0.269584 | + | 0.962977i | \(0.586886\pi\) | |||||||
\(614\) | −51.5533 | −2.08052 | ||||||||
\(615\) | −12.9376 | −0.521695 | ||||||||
\(616\) | 0.171630 | 0.00691517 | ||||||||
\(617\) | −5.06353 | −0.203850 | −0.101925 | − | 0.994792i | \(-0.532500\pi\) | ||||
−0.101925 | + | 0.994792i | \(0.532500\pi\) | |||||||
\(618\) | −77.4430 | −3.11521 | ||||||||
\(619\) | 16.9850 | 0.682683 | 0.341342 | − | 0.939939i | \(-0.389119\pi\) | ||||
0.341342 | + | 0.939939i | \(0.389119\pi\) | |||||||
\(620\) | 7.28020 | 0.292380 | ||||||||
\(621\) | −0.504637 | −0.0202504 | ||||||||
\(622\) | −26.9204 | −1.07941 | ||||||||
\(623\) | −12.1526 | −0.486884 | ||||||||
\(624\) | 6.33305 | 0.253525 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | −21.9125 | −0.875798 | ||||||||
\(627\) | −22.6436 | −0.904298 | ||||||||
\(628\) | 16.5804 | 0.661630 | ||||||||
\(629\) | −54.7519 | −2.18310 | ||||||||
\(630\) | 11.7264 | 0.467191 | ||||||||
\(631\) | 11.2203 | 0.446673 | 0.223336 | − | 0.974741i | \(-0.428305\pi\) | ||||
0.223336 | + | 0.974741i | \(0.428305\pi\) | |||||||
\(632\) | 0.656130 | 0.0260994 | ||||||||
\(633\) | 59.5696 | 2.36768 | ||||||||
\(634\) | 68.7253 | 2.72943 | ||||||||
\(635\) | −18.8785 | −0.749171 | ||||||||
\(636\) | 37.3538 | 1.48118 | ||||||||
\(637\) | 0.537768 | 0.0213071 | ||||||||
\(638\) | −25.9704 | −1.02818 | ||||||||
\(639\) | −38.8463 | −1.53674 | ||||||||
\(640\) | 0.325496 | 0.0128664 | ||||||||
\(641\) | −3.24683 | −0.128242 | −0.0641210 | − | 0.997942i | \(-0.520424\pi\) | ||||
−0.0641210 | + | 0.997942i | \(0.520424\pi\) | |||||||
\(642\) | 104.979 | 4.14320 | ||||||||
\(643\) | 27.5358 | 1.08590 | 0.542952 | − | 0.839763i | \(-0.317306\pi\) | ||||
0.542952 | + | 0.839763i | \(0.317306\pi\) | |||||||
\(644\) | −0.120327 | −0.00474154 | ||||||||
\(645\) | −23.5314 | −0.926549 | ||||||||
\(646\) | −18.2435 | −0.717779 | ||||||||
\(647\) | −2.70474 | −0.106334 | −0.0531671 | − | 0.998586i | \(-0.516932\pi\) | ||||
−0.0531671 | + | 0.998586i | \(0.516932\pi\) | |||||||
\(648\) | 0.311618 | 0.0122415 | ||||||||
\(649\) | 15.7295 | 0.617435 | ||||||||
\(650\) | 1.07826 | 0.0422929 | ||||||||
\(651\) | −10.7192 | −0.420117 | ||||||||
\(652\) | 7.29329 | 0.285627 | ||||||||
\(653\) | 3.77151 | 0.147591 | 0.0737954 | − | 0.997273i | \(-0.476489\pi\) | ||||
0.0737954 | + | 0.997273i | \(0.476489\pi\) | |||||||
\(654\) | 30.7419 | 1.20210 | ||||||||
\(655\) | 5.27999 | 0.206306 | ||||||||
\(656\) | 17.2190 | 0.672288 | ||||||||
\(657\) | 20.2889 | 0.791546 | ||||||||
\(658\) | 5.45224 | 0.212550 | ||||||||
\(659\) | 32.0382 | 1.24803 | 0.624015 | − | 0.781412i | \(-0.285500\pi\) | ||||
0.624015 | + | 0.781412i | \(0.285500\pi\) | |||||||
\(660\) | −25.3490 | −0.986710 | ||||||||
\(661\) | 14.5424 | 0.565634 | 0.282817 | − | 0.959174i | \(-0.408731\pi\) | ||||
0.282817 | + | 0.959174i | \(0.408731\pi\) | |||||||
\(662\) | 62.6810 | 2.43617 | ||||||||
\(663\) | −8.06504 | −0.313220 | ||||||||
\(664\) | 0.380151 | 0.0147527 | ||||||||
\(665\) | −1.80467 | −0.0699822 | ||||||||
\(666\) | −127.346 | −4.93455 | ||||||||
\(667\) | 0.182887 | 0.00708142 | ||||||||
\(668\) | 33.4393 | 1.29380 | ||||||||
\(669\) | −13.7067 | −0.529933 | ||||||||
\(670\) | −3.53298 | −0.136491 | ||||||||
\(671\) | 9.77133 | 0.377218 | ||||||||
\(672\) | −23.8548 | −0.920220 | ||||||||
\(673\) | 30.4908 | 1.17533 | 0.587667 | − | 0.809103i | \(-0.300046\pi\) | ||||
0.587667 | + | 0.809103i | \(0.300046\pi\) | |||||||
\(674\) | −39.5728 | −1.52429 | ||||||||
\(675\) | −8.47289 | −0.326122 | ||||||||
\(676\) | −25.6796 | −0.987675 | ||||||||
\(677\) | 5.48274 | 0.210719 | 0.105359 | − | 0.994434i | \(-0.466401\pi\) | ||||
0.105359 | + | 0.994434i | \(0.466401\pi\) | |||||||
\(678\) | 7.38755 | 0.283717 | ||||||||
\(679\) | −4.40673 | −0.169115 | ||||||||
\(680\) | −0.205144 | −0.00786691 | ||||||||
\(681\) | 29.2293 | 1.12007 | ||||||||
\(682\) | 30.4770 | 1.16703 | ||||||||
\(683\) | 39.2025 | 1.50004 | 0.750022 | − | 0.661413i | \(-0.230043\pi\) | ||||
0.750022 | + | 0.661413i | \(0.230043\pi\) | |||||||
\(684\) | −21.3230 | −0.815307 | ||||||||
\(685\) | 0.940881 | 0.0359492 | ||||||||
\(686\) | −2.00507 | −0.0765538 | ||||||||
\(687\) | −2.97462 | −0.113489 | ||||||||
\(688\) | 31.3186 | 1.19401 | ||||||||
\(689\) | −3.34259 | −0.127343 | ||||||||
\(690\) | 0.355229 | 0.0135233 | ||||||||
\(691\) | −10.6839 | −0.406434 | −0.203217 | − | 0.979134i | \(-0.565140\pi\) | ||||
−0.203217 | + | 0.979134i | \(0.565140\pi\) | |||||||
\(692\) | 40.4448 | 1.53748 | ||||||||
\(693\) | 24.6690 | 0.937097 | ||||||||
\(694\) | 28.5946 | 1.08544 | ||||||||
\(695\) | 10.5016 | 0.398347 | ||||||||
\(696\) | −0.371660 | −0.0140877 | ||||||||
\(697\) | −21.9281 | −0.830587 | ||||||||
\(698\) | 52.1611 | 1.97433 | ||||||||
\(699\) | −78.9946 | −2.98785 | ||||||||
\(700\) | −2.02029 | −0.0763599 | ||||||||
\(701\) | 0.208068 | 0.00785862 | 0.00392931 | − | 0.999992i | \(-0.498749\pi\) | ||||
0.00392931 | + | 0.999992i | \(0.498749\pi\) | |||||||
\(702\) | −9.13598 | −0.344815 | ||||||||
\(703\) | 19.5983 | 0.739164 | ||||||||
\(704\) | 34.4259 | 1.29748 | ||||||||
\(705\) | −8.08869 | −0.304638 | ||||||||
\(706\) | 51.6692 | 1.94460 | ||||||||
\(707\) | −3.68268 | −0.138501 | ||||||||
\(708\) | 22.4102 | 0.842226 | ||||||||
\(709\) | −18.6005 | −0.698557 | −0.349278 | − | 0.937019i | \(-0.613573\pi\) | ||||
−0.349278 | + | 0.937019i | \(0.613573\pi\) | |||||||
\(710\) | 13.3181 | 0.499820 | ||||||||
\(711\) | 94.3078 | 3.53682 | ||||||||
\(712\) | 0.494479 | 0.0185314 | ||||||||
\(713\) | −0.214623 | −0.00803770 | ||||||||
\(714\) | 30.0705 | 1.12536 | ||||||||
\(715\) | 2.26835 | 0.0848314 | ||||||||
\(716\) | −19.9065 | −0.743941 | ||||||||
\(717\) | −0.209789 | −0.00783470 | ||||||||
\(718\) | 6.67182 | 0.248990 | ||||||||
\(719\) | −30.8939 | −1.15215 | −0.576074 | − | 0.817398i | \(-0.695416\pi\) | ||||
−0.576074 | + | 0.817398i | \(0.695416\pi\) | |||||||
\(720\) | 23.1538 | 0.862891 | ||||||||
\(721\) | −12.9844 | −0.483563 | ||||||||
\(722\) | −31.5661 | −1.17477 | ||||||||
\(723\) | −18.9277 | −0.703929 | ||||||||
\(724\) | 38.6935 | 1.43803 | ||||||||
\(725\) | 3.07069 | 0.114042 | ||||||||
\(726\) | −40.5109 | −1.50350 | ||||||||
\(727\) | −33.1830 | −1.23069 | −0.615344 | − | 0.788259i | \(-0.710983\pi\) | ||||
−0.615344 | + | 0.788259i | \(0.710983\pi\) | |||||||
\(728\) | −0.0218813 | −0.000810976 0 | ||||||||
\(729\) | −30.8211 | −1.14152 | ||||||||
\(730\) | −6.95587 | −0.257448 | ||||||||
\(731\) | −39.8837 | −1.47515 | ||||||||
\(732\) | 13.9215 | 0.514553 | ||||||||
\(733\) | 31.8446 | 1.17621 | 0.588104 | − | 0.808785i | \(-0.299874\pi\) | ||||
0.588104 | + | 0.808785i | \(0.299874\pi\) | |||||||
\(734\) | 50.4070 | 1.86056 | ||||||||
\(735\) | 2.97462 | 0.109721 | ||||||||
\(736\) | −0.477630 | −0.0176057 | ||||||||
\(737\) | −7.43238 | −0.273775 | ||||||||
\(738\) | −51.0020 | −1.87741 | ||||||||
\(739\) | 12.2176 | 0.449433 | 0.224716 | − | 0.974424i | \(-0.427854\pi\) | ||||
0.224716 | + | 0.974424i | \(0.427854\pi\) | |||||||
\(740\) | 21.9399 | 0.806526 | ||||||||
\(741\) | 2.88686 | 0.106051 | ||||||||
\(742\) | 12.4628 | 0.457526 | ||||||||
\(743\) | 10.8666 | 0.398658 | 0.199329 | − | 0.979933i | \(-0.436124\pi\) | ||||
0.199329 | + | 0.979933i | \(0.436124\pi\) | |||||||
\(744\) | 0.436154 | 0.0159902 | ||||||||
\(745\) | −4.02623 | −0.147510 | ||||||||
\(746\) | 12.9551 | 0.474318 | ||||||||
\(747\) | 54.6404 | 1.99919 | ||||||||
\(748\) | −42.9644 | −1.57094 | ||||||||
\(749\) | 17.6012 | 0.643133 | ||||||||
\(750\) | 5.96432 | 0.217786 | ||||||||
\(751\) | 11.8906 | 0.433893 | 0.216946 | − | 0.976184i | \(-0.430390\pi\) | ||||
0.216946 | + | 0.976184i | \(0.430390\pi\) | |||||||
\(752\) | 10.7654 | 0.392575 | ||||||||
\(753\) | 79.1627 | 2.88485 | ||||||||
\(754\) | 3.31100 | 0.120580 | ||||||||
\(755\) | −10.9291 | −0.397750 | ||||||||
\(756\) | 17.1177 | 0.622565 | ||||||||
\(757\) | 29.1979 | 1.06122 | 0.530608 | − | 0.847618i | \(-0.321964\pi\) | ||||
0.530608 | + | 0.847618i | \(0.321964\pi\) | |||||||
\(758\) | −69.1382 | −2.51121 | ||||||||
\(759\) | 0.747300 | 0.0271253 | ||||||||
\(760\) | 0.0734306 | 0.00266361 | ||||||||
\(761\) | −27.7343 | −1.00537 | −0.502684 | − | 0.864470i | \(-0.667654\pi\) | ||||
−0.502684 | + | 0.864470i | \(0.667654\pi\) | |||||||
\(762\) | −112.597 | −4.07898 | ||||||||
\(763\) | 5.15431 | 0.186598 | ||||||||
\(764\) | 9.67529 | 0.350040 | ||||||||
\(765\) | −29.4860 | −1.06607 | ||||||||
\(766\) | −69.0553 | −2.49507 | ||||||||
\(767\) | −2.00537 | −0.0724096 | ||||||||
\(768\) | −46.6135 | −1.68202 | ||||||||
\(769\) | 4.91549 | 0.177257 | 0.0886285 | − | 0.996065i | \(-0.471752\pi\) | ||||
0.0886285 | + | 0.996065i | \(0.471752\pi\) | |||||||
\(770\) | −8.45753 | −0.304788 | ||||||||
\(771\) | −81.6658 | −2.94112 | ||||||||
\(772\) | −12.1978 | −0.439008 | ||||||||
\(773\) | −28.3561 | −1.01990 | −0.509949 | − | 0.860205i | \(-0.670336\pi\) | ||||
−0.509949 | + | 0.860205i | \(0.670336\pi\) | |||||||
\(774\) | −92.7644 | −3.33435 | ||||||||
\(775\) | −3.60353 | −0.129443 | ||||||||
\(776\) | 0.179306 | 0.00643672 | ||||||||
\(777\) | −32.3037 | −1.15889 | ||||||||
\(778\) | −16.9019 | −0.605961 | ||||||||
\(779\) | 7.84911 | 0.281224 | ||||||||
\(780\) | 3.23178 | 0.115716 | ||||||||
\(781\) | 28.0174 | 1.00254 | ||||||||
\(782\) | 0.602083 | 0.0215304 | ||||||||
\(783\) | −26.0176 | −0.929793 | ||||||||
\(784\) | −3.95900 | −0.141393 | ||||||||
\(785\) | −8.20693 | −0.292918 | ||||||||
\(786\) | 31.4916 | 1.12327 | ||||||||
\(787\) | −1.92615 | −0.0686598 | −0.0343299 | − | 0.999411i | \(-0.510930\pi\) | ||||
−0.0343299 | + | 0.999411i | \(0.510930\pi\) | |||||||
\(788\) | 20.4942 | 0.730075 | ||||||||
\(789\) | 47.8292 | 1.70276 | ||||||||
\(790\) | −32.3326 | −1.15034 | ||||||||
\(791\) | 1.23862 | 0.0440404 | ||||||||
\(792\) | −1.00376 | −0.0356671 | ||||||||
\(793\) | −1.24576 | −0.0442382 | ||||||||
\(794\) | −4.73671 | −0.168100 | ||||||||
\(795\) | −18.4893 | −0.655748 | ||||||||
\(796\) | 13.5558 | 0.480474 | ||||||||
\(797\) | −10.7617 | −0.381197 | −0.190599 | − | 0.981668i | \(-0.561043\pi\) | ||||
−0.190599 | + | 0.981668i | \(0.561043\pi\) | |||||||
\(798\) | −10.7636 | −0.381029 | ||||||||
\(799\) | −13.7096 | −0.485012 | ||||||||
\(800\) | −8.01944 | −0.283530 | ||||||||
\(801\) | 71.0732 | 2.51125 | ||||||||
\(802\) | −9.87415 | −0.348668 | ||||||||
\(803\) | −14.6331 | −0.516392 | ||||||||
\(804\) | −10.5891 | −0.373449 | ||||||||
\(805\) | 0.0595591 | 0.00209918 | ||||||||
\(806\) | −3.88555 | −0.136863 | ||||||||
\(807\) | −75.7655 | −2.66707 | ||||||||
\(808\) | 0.149845 | 0.00527153 | ||||||||
\(809\) | −6.30481 | −0.221665 | −0.110833 | − | 0.993839i | \(-0.535352\pi\) | ||||
−0.110833 | + | 0.993839i | \(0.535352\pi\) | |||||||
\(810\) | −15.3558 | −0.539547 | ||||||||
\(811\) | −7.36136 | −0.258492 | −0.129246 | − | 0.991613i | \(-0.541256\pi\) | ||||
−0.129246 | + | 0.991613i | \(0.541256\pi\) | |||||||
\(812\) | −6.20369 | −0.217707 | ||||||||
\(813\) | −57.9076 | −2.03091 | ||||||||
\(814\) | 91.8467 | 3.21922 | ||||||||
\(815\) | −3.61002 | −0.126453 | ||||||||
\(816\) | 59.3742 | 2.07851 | ||||||||
\(817\) | 14.2763 | 0.499463 | ||||||||
\(818\) | −27.6578 | −0.967032 | ||||||||
\(819\) | −3.14508 | −0.109898 | ||||||||
\(820\) | 8.78691 | 0.306852 | ||||||||
\(821\) | −16.1155 | −0.562435 | −0.281218 | − | 0.959644i | \(-0.590738\pi\) | ||||
−0.281218 | + | 0.959644i | \(0.590738\pi\) | |||||||
\(822\) | 5.61172 | 0.195731 | ||||||||
\(823\) | 30.9022 | 1.07718 | 0.538592 | − | 0.842567i | \(-0.318957\pi\) | ||||
0.538592 | + | 0.842567i | \(0.318957\pi\) | |||||||
\(824\) | 0.528323 | 0.0184050 | ||||||||
\(825\) | 12.5472 | 0.436838 | ||||||||
\(826\) | 7.47700 | 0.260158 | ||||||||
\(827\) | −19.2827 | −0.670527 | −0.335263 | − | 0.942124i | \(-0.608825\pi\) | ||||
−0.335263 | + | 0.942124i | \(0.608825\pi\) | |||||||
\(828\) | 0.703718 | 0.0244559 | ||||||||
\(829\) | −31.4656 | −1.09284 | −0.546422 | − | 0.837510i | \(-0.684010\pi\) | ||||
−0.546422 | + | 0.837510i | \(0.684010\pi\) | |||||||
\(830\) | −18.7330 | −0.650231 | ||||||||
\(831\) | 5.78221 | 0.200583 | ||||||||
\(832\) | −4.38900 | −0.152161 | ||||||||
\(833\) | 5.04173 | 0.174686 | ||||||||
\(834\) | 62.6347 | 2.16886 | ||||||||
\(835\) | −16.5517 | −0.572795 | ||||||||
\(836\) | 15.3790 | 0.531893 | ||||||||
\(837\) | 30.5323 | 1.05535 | ||||||||
\(838\) | −11.6429 | −0.402197 | ||||||||
\(839\) | −39.9857 | −1.38046 | −0.690230 | − | 0.723590i | \(-0.742491\pi\) | ||||
−0.690230 | + | 0.723590i | \(0.742491\pi\) | |||||||
\(840\) | −0.121035 | −0.00417610 | ||||||||
\(841\) | −19.5709 | −0.674858 | ||||||||
\(842\) | 25.1763 | 0.867634 | ||||||||
\(843\) | −2.15502 | −0.0742230 | ||||||||
\(844\) | −40.4582 | −1.39263 | ||||||||
\(845\) | 12.7108 | 0.437265 | ||||||||
\(846\) | −31.8868 | −1.09629 | ||||||||
\(847\) | −6.79220 | −0.233383 | ||||||||
\(848\) | 24.6079 | 0.845038 | ||||||||
\(849\) | 46.3103 | 1.58937 | ||||||||
\(850\) | 10.1090 | 0.346736 | ||||||||
\(851\) | −0.646796 | −0.0221719 | ||||||||
\(852\) | 39.9172 | 1.36754 | ||||||||
\(853\) | −4.62619 | −0.158398 | −0.0791988 | − | 0.996859i | \(-0.525236\pi\) | ||||
−0.0791988 | + | 0.996859i | \(0.525236\pi\) | |||||||
\(854\) | 4.64481 | 0.158942 | ||||||||
\(855\) | 10.5544 | 0.360954 | ||||||||
\(856\) | −0.716177 | −0.0244784 | ||||||||
\(857\) | −19.2967 | −0.659161 | −0.329581 | − | 0.944127i | \(-0.606907\pi\) | ||||
−0.329581 | + | 0.944127i | \(0.606907\pi\) | |||||||
\(858\) | 13.5292 | 0.461878 | ||||||||
\(859\) | −28.1006 | −0.958781 | −0.479391 | − | 0.877602i | \(-0.659142\pi\) | ||||
−0.479391 | + | 0.877602i | \(0.659142\pi\) | |||||||
\(860\) | 15.9820 | 0.544981 | ||||||||
\(861\) | −12.9376 | −0.440913 | ||||||||
\(862\) | 2.10301 | 0.0716287 | ||||||||
\(863\) | −3.26753 | −0.111228 | −0.0556140 | − | 0.998452i | \(-0.517712\pi\) | ||||
−0.0556140 | + | 0.998452i | \(0.517712\pi\) | |||||||
\(864\) | 67.9478 | 2.31163 | ||||||||
\(865\) | −20.0193 | −0.680675 | ||||||||
\(866\) | −41.7628 | −1.41916 | ||||||||
\(867\) | −25.0435 | −0.850523 | ||||||||
\(868\) | 7.28020 | 0.247106 | ||||||||
\(869\) | −68.0183 | −2.30736 | ||||||||
\(870\) | 18.3146 | 0.620922 | ||||||||
\(871\) | 0.947562 | 0.0321069 | ||||||||
\(872\) | −0.209724 | −0.00710216 | ||||||||
\(873\) | 25.7723 | 0.872260 | ||||||||
\(874\) | −0.215514 | −0.00728987 | ||||||||
\(875\) | 1.00000 | 0.0338062 | ||||||||
\(876\) | −20.8482 | −0.704396 | ||||||||
\(877\) | −2.03846 | −0.0688339 | −0.0344169 | − | 0.999408i | \(-0.510957\pi\) | ||||
−0.0344169 | + | 0.999408i | \(0.510957\pi\) | |||||||
\(878\) | −61.8314 | −2.08671 | ||||||||
\(879\) | 9.66522 | 0.326000 | ||||||||
\(880\) | −16.6994 | −0.562936 | ||||||||
\(881\) | −59.1070 | −1.99137 | −0.995684 | − | 0.0928132i | \(-0.970414\pi\) | ||||
−0.995684 | + | 0.0928132i | \(0.970414\pi\) | |||||||
\(882\) | 11.7264 | 0.394849 | ||||||||
\(883\) | −10.8542 | −0.365274 | −0.182637 | − | 0.983180i | \(-0.558463\pi\) | ||||
−0.182637 | + | 0.983180i | \(0.558463\pi\) | |||||||
\(884\) | 5.47758 | 0.184231 | ||||||||
\(885\) | −11.0925 | −0.372872 | ||||||||
\(886\) | 10.9673 | 0.368452 | ||||||||
\(887\) | 23.0551 | 0.774114 | 0.387057 | − | 0.922056i | \(-0.373492\pi\) | ||||
0.387057 | + | 0.922056i | \(0.373492\pi\) | |||||||
\(888\) | 1.31441 | 0.0441087 | ||||||||
\(889\) | −18.8785 | −0.633165 | ||||||||
\(890\) | −24.3668 | −0.816776 | ||||||||
\(891\) | −32.3041 | −1.08223 | ||||||||
\(892\) | 9.30929 | 0.311698 | ||||||||
\(893\) | 4.90732 | 0.164217 | ||||||||
\(894\) | −24.0137 | −0.803140 | ||||||||
\(895\) | 9.85328 | 0.329359 | ||||||||
\(896\) | 0.325496 | 0.0108741 | ||||||||
\(897\) | −0.0952741 | −0.00318111 | ||||||||
\(898\) | 10.5780 | 0.352992 | ||||||||
\(899\) | −11.0653 | −0.369049 | ||||||||
\(900\) | 11.8155 | 0.393849 | ||||||||
\(901\) | −31.3378 | −1.04401 | ||||||||
\(902\) | 36.7846 | 1.22479 | ||||||||
\(903\) | −23.5314 | −0.783077 | ||||||||
\(904\) | −0.0503985 | −0.00167623 | ||||||||
\(905\) | −19.1524 | −0.636648 | ||||||||
\(906\) | −65.1846 | −2.16561 | ||||||||
\(907\) | 19.7985 | 0.657398 | 0.328699 | − | 0.944435i | \(-0.393390\pi\) | ||||
0.328699 | + | 0.944435i | \(0.393390\pi\) | |||||||
\(908\) | −19.8518 | −0.658806 | ||||||||
\(909\) | 21.5377 | 0.714362 | ||||||||
\(910\) | 1.07826 | 0.0357440 | ||||||||
\(911\) | −20.7775 | −0.688388 | −0.344194 | − | 0.938899i | \(-0.611848\pi\) | ||||
−0.344194 | + | 0.938899i | \(0.611848\pi\) | |||||||
\(912\) | −21.2528 | −0.703751 | ||||||||
\(913\) | −39.4087 | −1.30424 | ||||||||
\(914\) | −20.6274 | −0.682293 | ||||||||
\(915\) | −6.89082 | −0.227803 | ||||||||
\(916\) | 2.02029 | 0.0667524 | ||||||||
\(917\) | 5.27999 | 0.174361 | ||||||||
\(918\) | −85.6525 | −2.82695 | ||||||||
\(919\) | −17.1507 | −0.565750 | −0.282875 | − | 0.959157i | \(-0.591288\pi\) | ||||
−0.282875 | + | 0.959157i | \(0.591288\pi\) | |||||||
\(920\) | −0.00242341 | −7.98974e−5 0 | ||||||||
\(921\) | 76.4821 | 2.52017 | ||||||||
\(922\) | 43.0615 | 1.41815 | ||||||||
\(923\) | −3.57198 | −0.117573 | ||||||||
\(924\) | −25.3490 | −0.833922 | ||||||||
\(925\) | −10.8597 | −0.357066 | ||||||||
\(926\) | −1.11257 | −0.0365613 | ||||||||
\(927\) | 75.9377 | 2.49412 | ||||||||
\(928\) | −24.6252 | −0.808362 | ||||||||
\(929\) | −18.8004 | −0.616821 | −0.308411 | − | 0.951253i | \(-0.599797\pi\) | ||||
−0.308411 | + | 0.951253i | \(0.599797\pi\) | |||||||
\(930\) | −21.4926 | −0.704771 | ||||||||
\(931\) | −1.80467 | −0.0591458 | ||||||||
\(932\) | 53.6512 | 1.75740 | ||||||||
\(933\) | 39.9379 | 1.30751 | ||||||||
\(934\) | 27.0126 | 0.883879 | ||||||||
\(935\) | 21.2664 | 0.695487 | ||||||||
\(936\) | 0.127970 | 0.00418285 | ||||||||
\(937\) | 4.31292 | 0.140897 | 0.0704485 | − | 0.997515i | \(-0.477557\pi\) | ||||
0.0704485 | + | 0.997515i | \(0.477557\pi\) | |||||||
\(938\) | −3.53298 | −0.115356 | ||||||||
\(939\) | 32.5083 | 1.06087 | ||||||||
\(940\) | 5.49364 | 0.179183 | ||||||||
\(941\) | −35.2484 | −1.14906 | −0.574532 | − | 0.818482i | \(-0.694816\pi\) | ||||
−0.574532 | + | 0.818482i | \(0.694816\pi\) | |||||||
\(942\) | −48.9488 | −1.59484 | ||||||||
\(943\) | −0.259042 | −0.00843556 | ||||||||
\(944\) | 14.7633 | 0.480506 | ||||||||
\(945\) | −8.47289 | −0.275623 | ||||||||
\(946\) | 66.9052 | 2.17527 | ||||||||
\(947\) | 20.6912 | 0.672373 | 0.336187 | − | 0.941795i | \(-0.390863\pi\) | ||||
0.336187 | + | 0.941795i | \(0.390863\pi\) | |||||||
\(948\) | −96.9076 | −3.14741 | ||||||||
\(949\) | 1.86559 | 0.0605598 | ||||||||
\(950\) | −3.61849 | −0.117399 | ||||||||
\(951\) | −101.958 | −3.30620 | ||||||||
\(952\) | −0.205144 | −0.00664875 | ||||||||
\(953\) | −61.0154 | −1.97648 | −0.988241 | − | 0.152904i | \(-0.951138\pi\) | ||||
−0.988241 | + | 0.152904i | \(0.951138\pi\) | |||||||
\(954\) | −72.8876 | −2.35982 | ||||||||
\(955\) | −4.78905 | −0.154970 | ||||||||
\(956\) | 0.142483 | 0.00460824 | ||||||||
\(957\) | 38.5285 | 1.24545 | ||||||||
\(958\) | −6.46013 | −0.208717 | ||||||||
\(959\) | 0.940881 | 0.0303826 | ||||||||
\(960\) | −24.2774 | −0.783551 | ||||||||
\(961\) | −18.0145 | −0.581114 | ||||||||
\(962\) | −11.7096 | −0.377534 | ||||||||
\(963\) | −102.939 | −3.31715 | ||||||||
\(964\) | 12.8552 | 0.414039 | ||||||||
\(965\) | 6.03763 | 0.194358 | ||||||||
\(966\) | 0.355229 | 0.0114293 | ||||||||
\(967\) | 24.9242 | 0.801508 | 0.400754 | − | 0.916186i | \(-0.368748\pi\) | ||||
0.400754 | + | 0.916186i | \(0.368748\pi\) | |||||||
\(968\) | 0.276369 | 0.00888284 | ||||||||
\(969\) | 27.0651 | 0.869458 | ||||||||
\(970\) | −8.83580 | −0.283700 | ||||||||
\(971\) | 13.9355 | 0.447210 | 0.223605 | − | 0.974680i | \(-0.428217\pi\) | ||||
0.223605 | + | 0.974680i | \(0.428217\pi\) | |||||||
\(972\) | 5.32859 | 0.170915 | ||||||||
\(973\) | 10.5016 | 0.336664 | ||||||||
\(974\) | −31.3046 | −1.00306 | ||||||||
\(975\) | −1.59966 | −0.0512300 | ||||||||
\(976\) | 9.17116 | 0.293562 | ||||||||
\(977\) | 55.6211 | 1.77948 | 0.889738 | − | 0.456471i | \(-0.150887\pi\) | ||||
0.889738 | + | 0.456471i | \(0.150887\pi\) | |||||||
\(978\) | −21.5313 | −0.688495 | ||||||||
\(979\) | −51.2607 | −1.63830 | ||||||||
\(980\) | −2.02029 | −0.0645359 | ||||||||
\(981\) | −30.1444 | −0.962436 | ||||||||
\(982\) | 79.9498 | 2.55130 | ||||||||
\(983\) | −33.3702 | −1.06435 | −0.532173 | − | 0.846636i | \(-0.678624\pi\) | ||||
−0.532173 | + | 0.846636i | \(0.678624\pi\) | |||||||
\(984\) | 0.526420 | 0.0167817 | ||||||||
\(985\) | −10.1442 | −0.323220 | ||||||||
\(986\) | 31.0416 | 0.988566 | ||||||||
\(987\) | −8.08869 | −0.257466 | ||||||||
\(988\) | −1.96068 | −0.0623777 | ||||||||
\(989\) | −0.471155 | −0.0149819 | ||||||||
\(990\) | 49.4630 | 1.57204 | ||||||||
\(991\) | 17.7506 | 0.563867 | 0.281934 | − | 0.959434i | \(-0.409024\pi\) | ||||
0.281934 | + | 0.959434i | \(0.409024\pi\) | |||||||
\(992\) | 28.8983 | 0.917523 | ||||||||
\(993\) | −92.9906 | −2.95097 | ||||||||
\(994\) | 13.3181 | 0.422425 | ||||||||
\(995\) | −6.70984 | −0.212716 | ||||||||
\(996\) | −56.1467 | −1.77908 | ||||||||
\(997\) | −61.4602 | −1.94647 | −0.973233 | − | 0.229822i | \(-0.926186\pi\) | ||||
−0.973233 | + | 0.229822i | \(0.926186\pi\) | |||||||
\(998\) | 72.4635 | 2.29379 | ||||||||
\(999\) | 92.0134 | 2.91118 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 8015.2.a.l.1.51 | ✓ | 62 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8015.2.a.l.1.51 | ✓ | 62 | 1.1 | even | 1 | trivial |