Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6014,2,Mod(1,6014)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6014, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("6014.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6014 = 2 \cdot 31 \cdot 97 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6014.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: | \(48.0220317756\) |
Analytic rank: | \(0\) |
Dimension: | \(28\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.11 | ||
Character | \(\chi\) | \(=\) | 6014.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | 0.707107 | ||||||||
\(3\) | −0.492368 | −0.284269 | −0.142135 | − | 0.989847i | \(-0.545397\pi\) | ||||
−0.142135 | + | 0.989847i | \(0.545397\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −0.547220 | −0.244724 | −0.122362 | − | 0.992486i | \(-0.539047\pi\) | ||||
−0.122362 | + | 0.992486i | \(0.539047\pi\) | |||||||
\(6\) | −0.492368 | −0.201009 | ||||||||
\(7\) | 4.87929 | 1.84420 | 0.922099 | − | 0.386953i | \(-0.126472\pi\) | ||||
0.922099 | + | 0.386953i | \(0.126472\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | −2.75757 | −0.919191 | ||||||||
\(10\) | −0.547220 | −0.173046 | ||||||||
\(11\) | −1.69298 | −0.510454 | −0.255227 | − | 0.966881i | \(-0.582150\pi\) | ||||
−0.255227 | + | 0.966881i | \(0.582150\pi\) | |||||||
\(12\) | −0.492368 | −0.142135 | ||||||||
\(13\) | −3.38537 | −0.938932 | −0.469466 | − | 0.882951i | \(-0.655553\pi\) | ||||
−0.469466 | + | 0.882951i | \(0.655553\pi\) | |||||||
\(14\) | 4.87929 | 1.30405 | ||||||||
\(15\) | 0.269434 | 0.0695676 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −3.46765 | −0.841030 | −0.420515 | − | 0.907286i | \(-0.638151\pi\) | ||||
−0.420515 | + | 0.907286i | \(0.638151\pi\) | |||||||
\(18\) | −2.75757 | −0.649966 | ||||||||
\(19\) | −3.29297 | −0.755459 | −0.377729 | − | 0.925916i | \(-0.623295\pi\) | ||||
−0.377729 | + | 0.925916i | \(0.623295\pi\) | |||||||
\(20\) | −0.547220 | −0.122362 | ||||||||
\(21\) | −2.40241 | −0.524249 | ||||||||
\(22\) | −1.69298 | −0.360945 | ||||||||
\(23\) | 6.12734 | 1.27764 | 0.638819 | − | 0.769357i | \(-0.279423\pi\) | ||||
0.638819 | + | 0.769357i | \(0.279423\pi\) | |||||||
\(24\) | −0.492368 | −0.100504 | ||||||||
\(25\) | −4.70055 | −0.940110 | ||||||||
\(26\) | −3.38537 | −0.663925 | ||||||||
\(27\) | 2.83485 | 0.545567 | ||||||||
\(28\) | 4.87929 | 0.922099 | ||||||||
\(29\) | 3.87968 | 0.720438 | 0.360219 | − | 0.932868i | \(-0.382702\pi\) | ||||
0.360219 | + | 0.932868i | \(0.382702\pi\) | |||||||
\(30\) | 0.269434 | 0.0491917 | ||||||||
\(31\) | −1.00000 | −0.179605 | ||||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 0.833572 | 0.145106 | ||||||||
\(34\) | −3.46765 | −0.594698 | ||||||||
\(35\) | −2.67005 | −0.451320 | ||||||||
\(36\) | −2.75757 | −0.459596 | ||||||||
\(37\) | 3.70114 | 0.608463 | 0.304231 | − | 0.952598i | \(-0.401600\pi\) | ||||
0.304231 | + | 0.952598i | \(0.401600\pi\) | |||||||
\(38\) | −3.29297 | −0.534190 | ||||||||
\(39\) | 1.66685 | 0.266909 | ||||||||
\(40\) | −0.547220 | −0.0865231 | ||||||||
\(41\) | 4.48593 | 0.700584 | 0.350292 | − | 0.936640i | \(-0.386082\pi\) | ||||
0.350292 | + | 0.936640i | \(0.386082\pi\) | |||||||
\(42\) | −2.40241 | −0.370700 | ||||||||
\(43\) | 5.13533 | 0.783130 | 0.391565 | − | 0.920150i | \(-0.371934\pi\) | ||||
0.391565 | + | 0.920150i | \(0.371934\pi\) | |||||||
\(44\) | −1.69298 | −0.255227 | ||||||||
\(45\) | 1.50900 | 0.224948 | ||||||||
\(46\) | 6.12734 | 0.903427 | ||||||||
\(47\) | 1.82777 | 0.266607 | 0.133303 | − | 0.991075i | \(-0.457441\pi\) | ||||
0.133303 | + | 0.991075i | \(0.457441\pi\) | |||||||
\(48\) | −0.492368 | −0.0710673 | ||||||||
\(49\) | 16.8075 | 2.40107 | ||||||||
\(50\) | −4.70055 | −0.664758 | ||||||||
\(51\) | 1.70736 | 0.239079 | ||||||||
\(52\) | −3.38537 | −0.469466 | ||||||||
\(53\) | 12.1557 | 1.66971 | 0.834857 | − | 0.550468i | \(-0.185551\pi\) | ||||
0.834857 | + | 0.550468i | \(0.185551\pi\) | |||||||
\(54\) | 2.83485 | 0.385774 | ||||||||
\(55\) | 0.926435 | 0.124920 | ||||||||
\(56\) | 4.87929 | 0.652023 | ||||||||
\(57\) | 1.62135 | 0.214754 | ||||||||
\(58\) | 3.87968 | 0.509426 | ||||||||
\(59\) | 2.18113 | 0.283959 | 0.141980 | − | 0.989870i | \(-0.454653\pi\) | ||||
0.141980 | + | 0.989870i | \(0.454653\pi\) | |||||||
\(60\) | 0.269434 | 0.0347838 | ||||||||
\(61\) | 9.59850 | 1.22896 | 0.614481 | − | 0.788931i | \(-0.289365\pi\) | ||||
0.614481 | + | 0.788931i | \(0.289365\pi\) | |||||||
\(62\) | −1.00000 | −0.127000 | ||||||||
\(63\) | −13.4550 | −1.69517 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 1.85254 | 0.229779 | ||||||||
\(66\) | 0.833572 | 0.102606 | ||||||||
\(67\) | 13.3781 | 1.63440 | 0.817198 | − | 0.576356i | \(-0.195526\pi\) | ||||
0.817198 | + | 0.576356i | \(0.195526\pi\) | |||||||
\(68\) | −3.46765 | −0.420515 | ||||||||
\(69\) | −3.01691 | −0.363193 | ||||||||
\(70\) | −2.67005 | −0.319132 | ||||||||
\(71\) | 6.24843 | 0.741552 | 0.370776 | − | 0.928722i | \(-0.379092\pi\) | ||||
0.370776 | + | 0.928722i | \(0.379092\pi\) | |||||||
\(72\) | −2.75757 | −0.324983 | ||||||||
\(73\) | 6.47204 | 0.757496 | 0.378748 | − | 0.925500i | \(-0.376355\pi\) | ||||
0.378748 | + | 0.925500i | \(0.376355\pi\) | |||||||
\(74\) | 3.70114 | 0.430248 | ||||||||
\(75\) | 2.31440 | 0.267244 | ||||||||
\(76\) | −3.29297 | −0.377729 | ||||||||
\(77\) | −8.26056 | −0.941378 | ||||||||
\(78\) | 1.66685 | 0.188733 | ||||||||
\(79\) | −4.26535 | −0.479889 | −0.239945 | − | 0.970787i | \(-0.577129\pi\) | ||||
−0.239945 | + | 0.970787i | \(0.577129\pi\) | |||||||
\(80\) | −0.547220 | −0.0611811 | ||||||||
\(81\) | 6.87693 | 0.764103 | ||||||||
\(82\) | 4.48593 | 0.495388 | ||||||||
\(83\) | −3.67643 | −0.403541 | −0.201770 | − | 0.979433i | \(-0.564670\pi\) | ||||
−0.201770 | + | 0.979433i | \(0.564670\pi\) | |||||||
\(84\) | −2.40241 | −0.262124 | ||||||||
\(85\) | 1.89757 | 0.205820 | ||||||||
\(86\) | 5.13533 | 0.553757 | ||||||||
\(87\) | −1.91023 | −0.204798 | ||||||||
\(88\) | −1.69298 | −0.180473 | ||||||||
\(89\) | 14.3678 | 1.52298 | 0.761490 | − | 0.648177i | \(-0.224468\pi\) | ||||
0.761490 | + | 0.648177i | \(0.224468\pi\) | |||||||
\(90\) | 1.50900 | 0.159063 | ||||||||
\(91\) | −16.5182 | −1.73158 | ||||||||
\(92\) | 6.12734 | 0.638819 | ||||||||
\(93\) | 0.492368 | 0.0510562 | ||||||||
\(94\) | 1.82777 | 0.188520 | ||||||||
\(95\) | 1.80198 | 0.184879 | ||||||||
\(96\) | −0.492368 | −0.0502521 | ||||||||
\(97\) | −1.00000 | −0.101535 | ||||||||
\(98\) | 16.8075 | 1.69781 | ||||||||
\(99\) | 4.66853 | 0.469205 | ||||||||
\(100\) | −4.70055 | −0.470055 | ||||||||
\(101\) | 1.89529 | 0.188589 | 0.0942944 | − | 0.995544i | \(-0.469941\pi\) | ||||
0.0942944 | + | 0.995544i | \(0.469941\pi\) | |||||||
\(102\) | 1.70736 | 0.169054 | ||||||||
\(103\) | 11.1729 | 1.10090 | 0.550448 | − | 0.834869i | \(-0.314457\pi\) | ||||
0.550448 | + | 0.834869i | \(0.314457\pi\) | |||||||
\(104\) | −3.38537 | −0.331962 | ||||||||
\(105\) | 1.31465 | 0.128296 | ||||||||
\(106\) | 12.1557 | 1.18067 | ||||||||
\(107\) | −12.0847 | −1.16828 | −0.584138 | − | 0.811655i | \(-0.698567\pi\) | ||||
−0.584138 | + | 0.811655i | \(0.698567\pi\) | |||||||
\(108\) | 2.83485 | 0.272783 | ||||||||
\(109\) | −10.3866 | −0.994854 | −0.497427 | − | 0.867506i | \(-0.665722\pi\) | ||||
−0.497427 | + | 0.867506i | \(0.665722\pi\) | |||||||
\(110\) | 0.926435 | 0.0883321 | ||||||||
\(111\) | −1.82232 | −0.172967 | ||||||||
\(112\) | 4.87929 | 0.461050 | ||||||||
\(113\) | −12.4005 | −1.16654 | −0.583269 | − | 0.812279i | \(-0.698227\pi\) | ||||
−0.583269 | + | 0.812279i | \(0.698227\pi\) | |||||||
\(114\) | 1.62135 | 0.151854 | ||||||||
\(115\) | −3.35300 | −0.312669 | ||||||||
\(116\) | 3.87968 | 0.360219 | ||||||||
\(117\) | 9.33540 | 0.863058 | ||||||||
\(118\) | 2.18113 | 0.200790 | ||||||||
\(119\) | −16.9197 | −1.55103 | ||||||||
\(120\) | 0.269434 | 0.0245958 | ||||||||
\(121\) | −8.13381 | −0.739437 | ||||||||
\(122\) | 9.59850 | 0.869008 | ||||||||
\(123\) | −2.20873 | −0.199154 | ||||||||
\(124\) | −1.00000 | −0.0898027 | ||||||||
\(125\) | 5.30834 | 0.474792 | ||||||||
\(126\) | −13.4550 | −1.19867 | ||||||||
\(127\) | 10.7595 | 0.954752 | 0.477376 | − | 0.878699i | \(-0.341588\pi\) | ||||
0.477376 | + | 0.878699i | \(0.341588\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | −2.52847 | −0.222620 | ||||||||
\(130\) | 1.85254 | 0.162479 | ||||||||
\(131\) | 2.16298 | 0.188981 | 0.0944904 | − | 0.995526i | \(-0.469878\pi\) | ||||
0.0944904 | + | 0.995526i | \(0.469878\pi\) | |||||||
\(132\) | 0.833572 | 0.0725531 | ||||||||
\(133\) | −16.0674 | −1.39322 | ||||||||
\(134\) | 13.3781 | 1.15569 | ||||||||
\(135\) | −1.55129 | −0.133513 | ||||||||
\(136\) | −3.46765 | −0.297349 | ||||||||
\(137\) | −21.6698 | −1.85138 | −0.925688 | − | 0.378287i | \(-0.876513\pi\) | ||||
−0.925688 | + | 0.378287i | \(0.876513\pi\) | |||||||
\(138\) | −3.01691 | −0.256816 | ||||||||
\(139\) | 14.8221 | 1.25719 | 0.628596 | − | 0.777732i | \(-0.283630\pi\) | ||||
0.628596 | + | 0.777732i | \(0.283630\pi\) | |||||||
\(140\) | −2.67005 | −0.225660 | ||||||||
\(141\) | −0.899934 | −0.0757881 | ||||||||
\(142\) | 6.24843 | 0.524356 | ||||||||
\(143\) | 5.73137 | 0.479281 | ||||||||
\(144\) | −2.75757 | −0.229798 | ||||||||
\(145\) | −2.12304 | −0.176309 | ||||||||
\(146\) | 6.47204 | 0.535630 | ||||||||
\(147\) | −8.27548 | −0.682550 | ||||||||
\(148\) | 3.70114 | 0.304231 | ||||||||
\(149\) | 4.82747 | 0.395482 | 0.197741 | − | 0.980254i | \(-0.436640\pi\) | ||||
0.197741 | + | 0.980254i | \(0.436640\pi\) | |||||||
\(150\) | 2.31440 | 0.188970 | ||||||||
\(151\) | −11.1519 | −0.907530 | −0.453765 | − | 0.891121i | \(-0.649919\pi\) | ||||
−0.453765 | + | 0.891121i | \(0.649919\pi\) | |||||||
\(152\) | −3.29297 | −0.267095 | ||||||||
\(153\) | 9.56231 | 0.773067 | ||||||||
\(154\) | −8.26056 | −0.665655 | ||||||||
\(155\) | 0.547220 | 0.0439538 | ||||||||
\(156\) | 1.66685 | 0.133455 | ||||||||
\(157\) | 23.1586 | 1.84826 | 0.924129 | − | 0.382080i | \(-0.124792\pi\) | ||||
0.924129 | + | 0.382080i | \(0.124792\pi\) | |||||||
\(158\) | −4.26535 | −0.339333 | ||||||||
\(159\) | −5.98508 | −0.474648 | ||||||||
\(160\) | −0.547220 | −0.0432616 | ||||||||
\(161\) | 29.8971 | 2.35622 | ||||||||
\(162\) | 6.87693 | 0.540303 | ||||||||
\(163\) | −5.17824 | −0.405591 | −0.202796 | − | 0.979221i | \(-0.565003\pi\) | ||||
−0.202796 | + | 0.979221i | \(0.565003\pi\) | |||||||
\(164\) | 4.48593 | 0.350292 | ||||||||
\(165\) | −0.456147 | −0.0355110 | ||||||||
\(166\) | −3.67643 | −0.285347 | ||||||||
\(167\) | −4.22756 | −0.327138 | −0.163569 | − | 0.986532i | \(-0.552301\pi\) | ||||
−0.163569 | + | 0.986532i | \(0.552301\pi\) | |||||||
\(168\) | −2.40241 | −0.185350 | ||||||||
\(169\) | −1.53930 | −0.118407 | ||||||||
\(170\) | 1.89757 | 0.145537 | ||||||||
\(171\) | 9.08060 | 0.694411 | ||||||||
\(172\) | 5.13533 | 0.391565 | ||||||||
\(173\) | 13.8562 | 1.05347 | 0.526735 | − | 0.850030i | \(-0.323416\pi\) | ||||
0.526735 | + | 0.850030i | \(0.323416\pi\) | |||||||
\(174\) | −1.91023 | −0.144814 | ||||||||
\(175\) | −22.9354 | −1.73375 | ||||||||
\(176\) | −1.69298 | −0.127613 | ||||||||
\(177\) | −1.07392 | −0.0807208 | ||||||||
\(178\) | 14.3678 | 1.07691 | ||||||||
\(179\) | −9.02751 | −0.674748 | −0.337374 | − | 0.941371i | \(-0.609539\pi\) | ||||
−0.337374 | + | 0.941371i | \(0.609539\pi\) | |||||||
\(180\) | 1.50900 | 0.112474 | ||||||||
\(181\) | 6.06735 | 0.450983 | 0.225491 | − | 0.974245i | \(-0.427601\pi\) | ||||
0.225491 | + | 0.974245i | \(0.427601\pi\) | |||||||
\(182\) | −16.5182 | −1.22441 | ||||||||
\(183\) | −4.72600 | −0.349356 | ||||||||
\(184\) | 6.12734 | 0.451713 | ||||||||
\(185\) | −2.02534 | −0.148906 | ||||||||
\(186\) | 0.492368 | 0.0361022 | ||||||||
\(187\) | 5.87068 | 0.429307 | ||||||||
\(188\) | 1.82777 | 0.133303 | ||||||||
\(189\) | 13.8320 | 1.00613 | ||||||||
\(190\) | 1.80198 | 0.130729 | ||||||||
\(191\) | −15.5144 | −1.12258 | −0.561290 | − | 0.827619i | \(-0.689695\pi\) | ||||
−0.561290 | + | 0.827619i | \(0.689695\pi\) | |||||||
\(192\) | −0.492368 | −0.0355336 | ||||||||
\(193\) | 20.3696 | 1.46624 | 0.733120 | − | 0.680100i | \(-0.238064\pi\) | ||||
0.733120 | + | 0.680100i | \(0.238064\pi\) | |||||||
\(194\) | −1.00000 | −0.0717958 | ||||||||
\(195\) | −0.912133 | −0.0653192 | ||||||||
\(196\) | 16.8075 | 1.20053 | ||||||||
\(197\) | −1.04076 | −0.0741509 | −0.0370755 | − | 0.999312i | \(-0.511804\pi\) | ||||
−0.0370755 | + | 0.999312i | \(0.511804\pi\) | |||||||
\(198\) | 4.66853 | 0.331778 | ||||||||
\(199\) | −13.3436 | −0.945903 | −0.472951 | − | 0.881089i | \(-0.656811\pi\) | ||||
−0.472951 | + | 0.881089i | \(0.656811\pi\) | |||||||
\(200\) | −4.70055 | −0.332379 | ||||||||
\(201\) | −6.58696 | −0.464608 | ||||||||
\(202\) | 1.89529 | 0.133352 | ||||||||
\(203\) | 18.9301 | 1.32863 | ||||||||
\(204\) | 1.70736 | 0.119539 | ||||||||
\(205\) | −2.45479 | −0.171450 | ||||||||
\(206\) | 11.1729 | 0.778451 | ||||||||
\(207\) | −16.8966 | −1.17439 | ||||||||
\(208\) | −3.38537 | −0.234733 | ||||||||
\(209\) | 5.57494 | 0.385627 | ||||||||
\(210\) | 1.31465 | 0.0907193 | ||||||||
\(211\) | −10.8417 | −0.746372 | −0.373186 | − | 0.927757i | \(-0.621735\pi\) | ||||
−0.373186 | + | 0.927757i | \(0.621735\pi\) | |||||||
\(212\) | 12.1557 | 0.834857 | ||||||||
\(213\) | −3.07653 | −0.210800 | ||||||||
\(214\) | −12.0847 | −0.826095 | ||||||||
\(215\) | −2.81016 | −0.191651 | ||||||||
\(216\) | 2.83485 | 0.192887 | ||||||||
\(217\) | −4.87929 | −0.331228 | ||||||||
\(218\) | −10.3866 | −0.703468 | ||||||||
\(219\) | −3.18663 | −0.215333 | ||||||||
\(220\) | 0.926435 | 0.0624602 | ||||||||
\(221\) | 11.7393 | 0.789669 | ||||||||
\(222\) | −1.82232 | −0.122306 | ||||||||
\(223\) | −9.29209 | −0.622244 | −0.311122 | − | 0.950370i | \(-0.600705\pi\) | ||||
−0.311122 | + | 0.950370i | \(0.600705\pi\) | |||||||
\(224\) | 4.87929 | 0.326011 | ||||||||
\(225\) | 12.9621 | 0.864141 | ||||||||
\(226\) | −12.4005 | −0.824867 | ||||||||
\(227\) | −5.03824 | −0.334400 | −0.167200 | − | 0.985923i | \(-0.553472\pi\) | ||||
−0.167200 | + | 0.985923i | \(0.553472\pi\) | |||||||
\(228\) | 1.62135 | 0.107377 | ||||||||
\(229\) | 12.8339 | 0.848089 | 0.424044 | − | 0.905641i | \(-0.360610\pi\) | ||||
0.424044 | + | 0.905641i | \(0.360610\pi\) | |||||||
\(230\) | −3.35300 | −0.221090 | ||||||||
\(231\) | 4.06724 | 0.267605 | ||||||||
\(232\) | 3.87968 | 0.254713 | ||||||||
\(233\) | −20.6255 | −1.35122 | −0.675611 | − | 0.737259i | \(-0.736120\pi\) | ||||
−0.675611 | + | 0.737259i | \(0.736120\pi\) | |||||||
\(234\) | 9.33540 | 0.610274 | ||||||||
\(235\) | −1.00019 | −0.0652452 | ||||||||
\(236\) | 2.18113 | 0.141980 | ||||||||
\(237\) | 2.10012 | 0.136418 | ||||||||
\(238\) | −16.9197 | −1.09674 | ||||||||
\(239\) | −10.7351 | −0.694397 | −0.347199 | − | 0.937792i | \(-0.612867\pi\) | ||||
−0.347199 | + | 0.937792i | \(0.612867\pi\) | |||||||
\(240\) | 0.269434 | 0.0173919 | ||||||||
\(241\) | −10.0980 | −0.650472 | −0.325236 | − | 0.945633i | \(-0.605444\pi\) | ||||
−0.325236 | + | 0.945633i | \(0.605444\pi\) | |||||||
\(242\) | −8.13381 | −0.522861 | ||||||||
\(243\) | −11.8905 | −0.762778 | ||||||||
\(244\) | 9.59850 | 0.614481 | ||||||||
\(245\) | −9.19740 | −0.587600 | ||||||||
\(246\) | −2.20873 | −0.140823 | ||||||||
\(247\) | 11.1479 | 0.709324 | ||||||||
\(248\) | −1.00000 | −0.0635001 | ||||||||
\(249\) | 1.81016 | 0.114714 | ||||||||
\(250\) | 5.30834 | 0.335729 | ||||||||
\(251\) | −13.4245 | −0.847350 | −0.423675 | − | 0.905814i | \(-0.639260\pi\) | ||||
−0.423675 | + | 0.905814i | \(0.639260\pi\) | |||||||
\(252\) | −13.4550 | −0.847586 | ||||||||
\(253\) | −10.3735 | −0.652175 | ||||||||
\(254\) | 10.7595 | 0.675111 | ||||||||
\(255\) | −0.934304 | −0.0585084 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 11.8995 | 0.742271 | 0.371136 | − | 0.928579i | \(-0.378969\pi\) | ||||
0.371136 | + | 0.928579i | \(0.378969\pi\) | |||||||
\(258\) | −2.52847 | −0.157416 | ||||||||
\(259\) | 18.0589 | 1.12213 | ||||||||
\(260\) | 1.85254 | 0.114890 | ||||||||
\(261\) | −10.6985 | −0.662220 | ||||||||
\(262\) | 2.16298 | 0.133630 | ||||||||
\(263\) | 18.3943 | 1.13424 | 0.567120 | − | 0.823635i | \(-0.308058\pi\) | ||||
0.567120 | + | 0.823635i | \(0.308058\pi\) | |||||||
\(264\) | 0.833572 | 0.0513028 | ||||||||
\(265\) | −6.65184 | −0.408619 | ||||||||
\(266\) | −16.0674 | −0.985153 | ||||||||
\(267\) | −7.07423 | −0.432936 | ||||||||
\(268\) | 13.3781 | 0.817198 | ||||||||
\(269\) | 27.6715 | 1.68716 | 0.843580 | − | 0.537004i | \(-0.180444\pi\) | ||||
0.843580 | + | 0.537004i | \(0.180444\pi\) | |||||||
\(270\) | −1.55129 | −0.0944083 | ||||||||
\(271\) | −31.8892 | −1.93713 | −0.968565 | − | 0.248760i | \(-0.919977\pi\) | ||||
−0.968565 | + | 0.248760i | \(0.919977\pi\) | |||||||
\(272\) | −3.46765 | −0.210257 | ||||||||
\(273\) | 8.13303 | 0.492234 | ||||||||
\(274\) | −21.6698 | −1.30912 | ||||||||
\(275\) | 7.95795 | 0.479883 | ||||||||
\(276\) | −3.01691 | −0.181597 | ||||||||
\(277\) | −8.16520 | −0.490599 | −0.245300 | − | 0.969447i | \(-0.578886\pi\) | ||||
−0.245300 | + | 0.969447i | \(0.578886\pi\) | |||||||
\(278\) | 14.8221 | 0.888969 | ||||||||
\(279\) | 2.75757 | 0.165092 | ||||||||
\(280\) | −2.67005 | −0.159566 | ||||||||
\(281\) | 22.0398 | 1.31479 | 0.657393 | − | 0.753548i | \(-0.271659\pi\) | ||||
0.657393 | + | 0.753548i | \(0.271659\pi\) | |||||||
\(282\) | −0.899934 | −0.0535903 | ||||||||
\(283\) | 22.4232 | 1.33292 | 0.666461 | − | 0.745540i | \(-0.267808\pi\) | ||||
0.666461 | + | 0.745540i | \(0.267808\pi\) | |||||||
\(284\) | 6.24843 | 0.370776 | ||||||||
\(285\) | −0.887238 | −0.0525554 | ||||||||
\(286\) | 5.73137 | 0.338903 | ||||||||
\(287\) | 21.8882 | 1.29202 | ||||||||
\(288\) | −2.75757 | −0.162492 | ||||||||
\(289\) | −4.97537 | −0.292669 | ||||||||
\(290\) | −2.12304 | −0.124669 | ||||||||
\(291\) | 0.492368 | 0.0288631 | ||||||||
\(292\) | 6.47204 | 0.378748 | ||||||||
\(293\) | −4.82842 | −0.282079 | −0.141040 | − | 0.990004i | \(-0.545045\pi\) | ||||
−0.141040 | + | 0.990004i | \(0.545045\pi\) | |||||||
\(294\) | −8.27548 | −0.482636 | ||||||||
\(295\) | −1.19356 | −0.0694917 | ||||||||
\(296\) | 3.70114 | 0.215124 | ||||||||
\(297\) | −4.79935 | −0.278487 | ||||||||
\(298\) | 4.82747 | 0.279648 | ||||||||
\(299\) | −20.7433 | −1.19961 | ||||||||
\(300\) | 2.31440 | 0.133622 | ||||||||
\(301\) | 25.0568 | 1.44425 | ||||||||
\(302\) | −11.1519 | −0.641721 | ||||||||
\(303\) | −0.933183 | −0.0536099 | ||||||||
\(304\) | −3.29297 | −0.188865 | ||||||||
\(305\) | −5.25250 | −0.300757 | ||||||||
\(306\) | 9.56231 | 0.546641 | ||||||||
\(307\) | 1.93106 | 0.110211 | 0.0551057 | − | 0.998481i | \(-0.482450\pi\) | ||||
0.0551057 | + | 0.998481i | \(0.482450\pi\) | |||||||
\(308\) | −8.26056 | −0.470689 | ||||||||
\(309\) | −5.50117 | −0.312951 | ||||||||
\(310\) | 0.547220 | 0.0310800 | ||||||||
\(311\) | 7.45672 | 0.422832 | 0.211416 | − | 0.977396i | \(-0.432193\pi\) | ||||
0.211416 | + | 0.977396i | \(0.432193\pi\) | |||||||
\(312\) | 1.66685 | 0.0943667 | ||||||||
\(313\) | 25.8462 | 1.46091 | 0.730457 | − | 0.682958i | \(-0.239307\pi\) | ||||
0.730457 | + | 0.682958i | \(0.239307\pi\) | |||||||
\(314\) | 23.1586 | 1.30692 | ||||||||
\(315\) | 7.36285 | 0.414850 | ||||||||
\(316\) | −4.26535 | −0.239945 | ||||||||
\(317\) | −12.3077 | −0.691267 | −0.345634 | − | 0.938370i | \(-0.612336\pi\) | ||||
−0.345634 | + | 0.938370i | \(0.612336\pi\) | |||||||
\(318\) | −5.98508 | −0.335627 | ||||||||
\(319\) | −6.56823 | −0.367750 | ||||||||
\(320\) | −0.547220 | −0.0305905 | ||||||||
\(321\) | 5.95014 | 0.332105 | ||||||||
\(322\) | 29.8971 | 1.66610 | ||||||||
\(323\) | 11.4189 | 0.635363 | ||||||||
\(324\) | 6.87693 | 0.382052 | ||||||||
\(325\) | 15.9131 | 0.882699 | ||||||||
\(326\) | −5.17824 | −0.286796 | ||||||||
\(327\) | 5.11402 | 0.282806 | ||||||||
\(328\) | 4.48593 | 0.247694 | ||||||||
\(329\) | 8.91820 | 0.491676 | ||||||||
\(330\) | −0.456147 | −0.0251101 | ||||||||
\(331\) | −5.39932 | −0.296774 | −0.148387 | − | 0.988929i | \(-0.547408\pi\) | ||||
−0.148387 | + | 0.988929i | \(0.547408\pi\) | |||||||
\(332\) | −3.67643 | −0.201770 | ||||||||
\(333\) | −10.2062 | −0.559294 | ||||||||
\(334\) | −4.22756 | −0.231322 | ||||||||
\(335\) | −7.32078 | −0.399977 | ||||||||
\(336\) | −2.40241 | −0.131062 | ||||||||
\(337\) | −6.99344 | −0.380957 | −0.190479 | − | 0.981691i | \(-0.561004\pi\) | ||||
−0.190479 | + | 0.981691i | \(0.561004\pi\) | |||||||
\(338\) | −1.53930 | −0.0837267 | ||||||||
\(339\) | 6.10560 | 0.331611 | ||||||||
\(340\) | 1.89757 | 0.102910 | ||||||||
\(341\) | 1.69298 | 0.0916802 | ||||||||
\(342\) | 9.08060 | 0.491023 | ||||||||
\(343\) | 47.8536 | 2.58385 | ||||||||
\(344\) | 5.13533 | 0.276878 | ||||||||
\(345\) | 1.65091 | 0.0888822 | ||||||||
\(346\) | 13.8562 | 0.744915 | ||||||||
\(347\) | −12.5591 | −0.674208 | −0.337104 | − | 0.941467i | \(-0.609447\pi\) | ||||
−0.337104 | + | 0.941467i | \(0.609447\pi\) | |||||||
\(348\) | −1.91023 | −0.102399 | ||||||||
\(349\) | 8.37399 | 0.448250 | 0.224125 | − | 0.974560i | \(-0.428048\pi\) | ||||
0.224125 | + | 0.974560i | \(0.428048\pi\) | |||||||
\(350\) | −22.9354 | −1.22595 | ||||||||
\(351\) | −9.59700 | −0.512250 | ||||||||
\(352\) | −1.69298 | −0.0902363 | ||||||||
\(353\) | −18.0438 | −0.960375 | −0.480187 | − | 0.877166i | \(-0.659431\pi\) | ||||
−0.480187 | + | 0.877166i | \(0.659431\pi\) | |||||||
\(354\) | −1.07392 | −0.0570783 | ||||||||
\(355\) | −3.41927 | −0.181476 | ||||||||
\(356\) | 14.3678 | 0.761490 | ||||||||
\(357\) | 8.33072 | 0.440909 | ||||||||
\(358\) | −9.02751 | −0.477119 | ||||||||
\(359\) | −28.9683 | −1.52889 | −0.764444 | − | 0.644691i | \(-0.776986\pi\) | ||||
−0.764444 | + | 0.644691i | \(0.776986\pi\) | |||||||
\(360\) | 1.50900 | 0.0795313 | ||||||||
\(361\) | −8.15636 | −0.429282 | ||||||||
\(362\) | 6.06735 | 0.318893 | ||||||||
\(363\) | 4.00483 | 0.210199 | ||||||||
\(364\) | −16.5182 | −0.865788 | ||||||||
\(365\) | −3.54163 | −0.185378 | ||||||||
\(366\) | −4.72600 | −0.247032 | ||||||||
\(367\) | 15.6555 | 0.817212 | 0.408606 | − | 0.912711i | \(-0.366015\pi\) | ||||
0.408606 | + | 0.912711i | \(0.366015\pi\) | |||||||
\(368\) | 6.12734 | 0.319410 | ||||||||
\(369\) | −12.3703 | −0.643971 | ||||||||
\(370\) | −2.02534 | −0.105292 | ||||||||
\(371\) | 59.3112 | 3.07928 | ||||||||
\(372\) | 0.492368 | 0.0255281 | ||||||||
\(373\) | −25.0761 | −1.29839 | −0.649196 | − | 0.760621i | \(-0.724895\pi\) | ||||
−0.649196 | + | 0.760621i | \(0.724895\pi\) | |||||||
\(374\) | 5.87068 | 0.303566 | ||||||||
\(375\) | −2.61366 | −0.134969 | ||||||||
\(376\) | 1.82777 | 0.0942598 | ||||||||
\(377\) | −13.1341 | −0.676442 | ||||||||
\(378\) | 13.8320 | 0.711444 | ||||||||
\(379\) | 22.0357 | 1.13190 | 0.565950 | − | 0.824439i | \(-0.308509\pi\) | ||||
0.565950 | + | 0.824439i | \(0.308509\pi\) | |||||||
\(380\) | 1.80198 | 0.0924396 | ||||||||
\(381\) | −5.29764 | −0.271406 | ||||||||
\(382\) | −15.5144 | −0.793784 | ||||||||
\(383\) | 25.9200 | 1.32445 | 0.662224 | − | 0.749306i | \(-0.269613\pi\) | ||||
0.662224 | + | 0.749306i | \(0.269613\pi\) | |||||||
\(384\) | −0.492368 | −0.0251261 | ||||||||
\(385\) | 4.52035 | 0.230378 | ||||||||
\(386\) | 20.3696 | 1.03679 | ||||||||
\(387\) | −14.1610 | −0.719846 | ||||||||
\(388\) | −1.00000 | −0.0507673 | ||||||||
\(389\) | −33.8834 | −1.71796 | −0.858978 | − | 0.512012i | \(-0.828900\pi\) | ||||
−0.858978 | + | 0.512012i | \(0.828900\pi\) | |||||||
\(390\) | −0.912133 | −0.0461876 | ||||||||
\(391\) | −21.2475 | −1.07453 | ||||||||
\(392\) | 16.8075 | 0.848906 | ||||||||
\(393\) | −1.06498 | −0.0537214 | ||||||||
\(394\) | −1.04076 | −0.0524326 | ||||||||
\(395\) | 2.33409 | 0.117441 | ||||||||
\(396\) | 4.66853 | 0.234602 | ||||||||
\(397\) | 1.42616 | 0.0715771 | 0.0357886 | − | 0.999359i | \(-0.488606\pi\) | ||||
0.0357886 | + | 0.999359i | \(0.488606\pi\) | |||||||
\(398\) | −13.3436 | −0.668854 | ||||||||
\(399\) | 7.91106 | 0.396048 | ||||||||
\(400\) | −4.70055 | −0.235028 | ||||||||
\(401\) | 17.0063 | 0.849257 | 0.424628 | − | 0.905368i | \(-0.360405\pi\) | ||||
0.424628 | + | 0.905368i | \(0.360405\pi\) | |||||||
\(402\) | −6.58696 | −0.328528 | ||||||||
\(403\) | 3.38537 | 0.168637 | ||||||||
\(404\) | 1.89529 | 0.0942944 | ||||||||
\(405\) | −3.76320 | −0.186995 | ||||||||
\(406\) | 18.9301 | 0.939483 | ||||||||
\(407\) | −6.26596 | −0.310592 | ||||||||
\(408\) | 1.70736 | 0.0845271 | ||||||||
\(409\) | 11.6724 | 0.577161 | 0.288581 | − | 0.957456i | \(-0.406817\pi\) | ||||
0.288581 | + | 0.957456i | \(0.406817\pi\) | |||||||
\(410\) | −2.45479 | −0.121233 | ||||||||
\(411\) | 10.6695 | 0.526289 | ||||||||
\(412\) | 11.1729 | 0.550448 | ||||||||
\(413\) | 10.6424 | 0.523677 | ||||||||
\(414\) | −16.8966 | −0.830422 | ||||||||
\(415\) | 2.01182 | 0.0987563 | ||||||||
\(416\) | −3.38537 | −0.165981 | ||||||||
\(417\) | −7.29792 | −0.357381 | ||||||||
\(418\) | 5.57494 | 0.272679 | ||||||||
\(419\) | 18.4560 | 0.901635 | 0.450818 | − | 0.892616i | \(-0.351132\pi\) | ||||
0.450818 | + | 0.892616i | \(0.351132\pi\) | |||||||
\(420\) | 1.31465 | 0.0641482 | ||||||||
\(421\) | −16.7262 | −0.815187 | −0.407594 | − | 0.913163i | \(-0.633632\pi\) | ||||
−0.407594 | + | 0.913163i | \(0.633632\pi\) | |||||||
\(422\) | −10.8417 | −0.527765 | ||||||||
\(423\) | −5.04020 | −0.245063 | ||||||||
\(424\) | 12.1557 | 0.590333 | ||||||||
\(425\) | 16.2999 | 0.790660 | ||||||||
\(426\) | −3.07653 | −0.149058 | ||||||||
\(427\) | 46.8339 | 2.26645 | ||||||||
\(428\) | −12.0847 | −0.584138 | ||||||||
\(429\) | −2.82195 | −0.136245 | ||||||||
\(430\) | −2.81016 | −0.135518 | ||||||||
\(431\) | −21.6759 | −1.04409 | −0.522045 | − | 0.852918i | \(-0.674831\pi\) | ||||
−0.522045 | + | 0.852918i | \(0.674831\pi\) | |||||||
\(432\) | 2.83485 | 0.136392 | ||||||||
\(433\) | 31.9479 | 1.53532 | 0.767659 | − | 0.640858i | \(-0.221421\pi\) | ||||
0.767659 | + | 0.640858i | \(0.221421\pi\) | |||||||
\(434\) | −4.87929 | −0.234213 | ||||||||
\(435\) | 1.04532 | 0.0501191 | ||||||||
\(436\) | −10.3866 | −0.497427 | ||||||||
\(437\) | −20.1771 | −0.965203 | ||||||||
\(438\) | −3.18663 | −0.152263 | ||||||||
\(439\) | −39.3101 | −1.87617 | −0.938085 | − | 0.346405i | \(-0.887402\pi\) | ||||
−0.938085 | + | 0.346405i | \(0.887402\pi\) | |||||||
\(440\) | 0.926435 | 0.0441661 | ||||||||
\(441\) | −46.3479 | −2.20704 | ||||||||
\(442\) | 11.7393 | 0.558381 | ||||||||
\(443\) | 4.44918 | 0.211387 | 0.105694 | − | 0.994399i | \(-0.466294\pi\) | ||||
0.105694 | + | 0.994399i | \(0.466294\pi\) | |||||||
\(444\) | −1.82232 | −0.0864836 | ||||||||
\(445\) | −7.86233 | −0.372710 | ||||||||
\(446\) | −9.29209 | −0.439993 | ||||||||
\(447\) | −2.37689 | −0.112423 | ||||||||
\(448\) | 4.87929 | 0.230525 | ||||||||
\(449\) | −22.2100 | −1.04815 | −0.524077 | − | 0.851671i | \(-0.675590\pi\) | ||||
−0.524077 | + | 0.851671i | \(0.675590\pi\) | |||||||
\(450\) | 12.9621 | 0.611040 | ||||||||
\(451\) | −7.59460 | −0.357616 | ||||||||
\(452\) | −12.4005 | −0.583269 | ||||||||
\(453\) | 5.49085 | 0.257983 | ||||||||
\(454\) | −5.03824 | −0.236456 | ||||||||
\(455\) | 9.03909 | 0.423759 | ||||||||
\(456\) | 1.62135 | 0.0759268 | ||||||||
\(457\) | 1.37570 | 0.0643527 | 0.0321763 | − | 0.999482i | \(-0.489756\pi\) | ||||
0.0321763 | + | 0.999482i | \(0.489756\pi\) | |||||||
\(458\) | 12.8339 | 0.599689 | ||||||||
\(459\) | −9.83027 | −0.458838 | ||||||||
\(460\) | −3.35300 | −0.156335 | ||||||||
\(461\) | 11.1892 | 0.521132 | 0.260566 | − | 0.965456i | \(-0.416091\pi\) | ||||
0.260566 | + | 0.965456i | \(0.416091\pi\) | |||||||
\(462\) | 4.06724 | 0.189225 | ||||||||
\(463\) | 37.2506 | 1.73118 | 0.865591 | − | 0.500752i | \(-0.166943\pi\) | ||||
0.865591 | + | 0.500752i | \(0.166943\pi\) | |||||||
\(464\) | 3.87968 | 0.180109 | ||||||||
\(465\) | −0.269434 | −0.0124947 | ||||||||
\(466\) | −20.6255 | −0.955458 | ||||||||
\(467\) | −35.7101 | −1.65247 | −0.826234 | − | 0.563327i | \(-0.809521\pi\) | ||||
−0.826234 | + | 0.563327i | \(0.809521\pi\) | |||||||
\(468\) | 9.33540 | 0.431529 | ||||||||
\(469\) | 65.2757 | 3.01415 | ||||||||
\(470\) | −1.00019 | −0.0461353 | ||||||||
\(471\) | −11.4026 | −0.525403 | ||||||||
\(472\) | 2.18113 | 0.100395 | ||||||||
\(473\) | −8.69403 | −0.399752 | ||||||||
\(474\) | 2.10012 | 0.0964618 | ||||||||
\(475\) | 15.4788 | 0.710214 | ||||||||
\(476\) | −16.9197 | −0.775513 | ||||||||
\(477\) | −33.5202 | −1.53479 | ||||||||
\(478\) | −10.7351 | −0.491013 | ||||||||
\(479\) | 3.85971 | 0.176355 | 0.0881773 | − | 0.996105i | \(-0.471896\pi\) | ||||
0.0881773 | + | 0.996105i | \(0.471896\pi\) | |||||||
\(480\) | 0.269434 | 0.0122979 | ||||||||
\(481\) | −12.5297 | −0.571305 | ||||||||
\(482\) | −10.0980 | −0.459953 | ||||||||
\(483\) | −14.7204 | −0.669800 | ||||||||
\(484\) | −8.13381 | −0.369718 | ||||||||
\(485\) | 0.547220 | 0.0248480 | ||||||||
\(486\) | −11.8905 | −0.539365 | ||||||||
\(487\) | 37.9468 | 1.71953 | 0.859767 | − | 0.510687i | \(-0.170609\pi\) | ||||
0.859767 | + | 0.510687i | \(0.170609\pi\) | |||||||
\(488\) | 9.59850 | 0.434504 | ||||||||
\(489\) | 2.54960 | 0.115297 | ||||||||
\(490\) | −9.19740 | −0.415496 | ||||||||
\(491\) | 29.7247 | 1.34146 | 0.670729 | − | 0.741703i | \(-0.265981\pi\) | ||||
0.670729 | + | 0.741703i | \(0.265981\pi\) | |||||||
\(492\) | −2.20873 | −0.0995772 | ||||||||
\(493\) | −13.4534 | −0.605909 | ||||||||
\(494\) | 11.1479 | 0.501568 | ||||||||
\(495\) | −2.55471 | −0.114826 | ||||||||
\(496\) | −1.00000 | −0.0449013 | ||||||||
\(497\) | 30.4879 | 1.36757 | ||||||||
\(498\) | 1.81016 | 0.0811152 | ||||||||
\(499\) | 21.6164 | 0.967684 | 0.483842 | − | 0.875155i | \(-0.339241\pi\) | ||||
0.483842 | + | 0.875155i | \(0.339241\pi\) | |||||||
\(500\) | 5.30834 | 0.237396 | ||||||||
\(501\) | 2.08152 | 0.0929952 | ||||||||
\(502\) | −13.4245 | −0.599167 | ||||||||
\(503\) | −35.4718 | −1.58161 | −0.790804 | − | 0.612069i | \(-0.790338\pi\) | ||||
−0.790804 | + | 0.612069i | \(0.790338\pi\) | |||||||
\(504\) | −13.4550 | −0.599334 | ||||||||
\(505\) | −1.03714 | −0.0461522 | ||||||||
\(506\) | −10.3735 | −0.461158 | ||||||||
\(507\) | 0.757901 | 0.0336596 | ||||||||
\(508\) | 10.7595 | 0.477376 | ||||||||
\(509\) | −37.0953 | −1.64422 | −0.822110 | − | 0.569329i | \(-0.807203\pi\) | ||||
−0.822110 | + | 0.569329i | \(0.807203\pi\) | |||||||
\(510\) | −0.934304 | −0.0413717 | ||||||||
\(511\) | 31.5790 | 1.39697 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | −9.33506 | −0.412153 | ||||||||
\(514\) | 11.8995 | 0.524865 | ||||||||
\(515\) | −6.11402 | −0.269416 | ||||||||
\(516\) | −2.52847 | −0.111310 | ||||||||
\(517\) | −3.09438 | −0.136091 | ||||||||
\(518\) | 18.0589 | 0.793463 | ||||||||
\(519\) | −6.82237 | −0.299469 | ||||||||
\(520\) | 1.85254 | 0.0812393 | ||||||||
\(521\) | 8.30166 | 0.363702 | 0.181851 | − | 0.983326i | \(-0.441791\pi\) | ||||
0.181851 | + | 0.983326i | \(0.441791\pi\) | |||||||
\(522\) | −10.6985 | −0.468260 | ||||||||
\(523\) | 24.6183 | 1.07648 | 0.538242 | − | 0.842791i | \(-0.319089\pi\) | ||||
0.538242 | + | 0.842791i | \(0.319089\pi\) | |||||||
\(524\) | 2.16298 | 0.0944904 | ||||||||
\(525\) | 11.2926 | 0.492851 | ||||||||
\(526\) | 18.3943 | 0.802029 | ||||||||
\(527\) | 3.46765 | 0.151053 | ||||||||
\(528\) | 0.833572 | 0.0362766 | ||||||||
\(529\) | 14.5443 | 0.632360 | ||||||||
\(530\) | −6.65184 | −0.288938 | ||||||||
\(531\) | −6.01463 | −0.261013 | ||||||||
\(532\) | −16.0674 | −0.696608 | ||||||||
\(533\) | −15.1865 | −0.657801 | ||||||||
\(534\) | −7.07423 | −0.306132 | ||||||||
\(535\) | 6.61301 | 0.285905 | ||||||||
\(536\) | 13.3781 | 0.577847 | ||||||||
\(537\) | 4.44486 | 0.191810 | ||||||||
\(538\) | 27.6715 | 1.19300 | ||||||||
\(539\) | −28.4548 | −1.22564 | ||||||||
\(540\) | −1.55129 | −0.0667567 | ||||||||
\(541\) | 0.373642 | 0.0160641 | 0.00803205 | − | 0.999968i | \(-0.497443\pi\) | ||||
0.00803205 | + | 0.999968i | \(0.497443\pi\) | |||||||
\(542\) | −31.8892 | −1.36976 | ||||||||
\(543\) | −2.98737 | −0.128200 | ||||||||
\(544\) | −3.46765 | −0.148674 | ||||||||
\(545\) | 5.68375 | 0.243465 | ||||||||
\(546\) | 8.13303 | 0.348062 | ||||||||
\(547\) | 7.28654 | 0.311550 | 0.155775 | − | 0.987793i | \(-0.450213\pi\) | ||||
0.155775 | + | 0.987793i | \(0.450213\pi\) | |||||||
\(548\) | −21.6698 | −0.925688 | ||||||||
\(549\) | −26.4686 | −1.12965 | ||||||||
\(550\) | 7.95795 | 0.339328 | ||||||||
\(551\) | −12.7756 | −0.544261 | ||||||||
\(552\) | −3.01691 | −0.128408 | ||||||||
\(553\) | −20.8119 | −0.885011 | ||||||||
\(554\) | −8.16520 | −0.346906 | ||||||||
\(555\) | 0.997212 | 0.0423293 | ||||||||
\(556\) | 14.8221 | 0.628596 | ||||||||
\(557\) | 15.4123 | 0.653041 | 0.326520 | − | 0.945190i | \(-0.394124\pi\) | ||||
0.326520 | + | 0.945190i | \(0.394124\pi\) | |||||||
\(558\) | 2.75757 | 0.116737 | ||||||||
\(559\) | −17.3850 | −0.735306 | ||||||||
\(560\) | −2.67005 | −0.112830 | ||||||||
\(561\) | −2.89054 | −0.122039 | ||||||||
\(562\) | 22.0398 | 0.929694 | ||||||||
\(563\) | −7.61341 | −0.320867 | −0.160434 | − | 0.987047i | \(-0.551289\pi\) | ||||
−0.160434 | + | 0.987047i | \(0.551289\pi\) | |||||||
\(564\) | −0.899934 | −0.0378941 | ||||||||
\(565\) | 6.78579 | 0.285480 | ||||||||
\(566\) | 22.4232 | 0.942518 | ||||||||
\(567\) | 33.5545 | 1.40916 | ||||||||
\(568\) | 6.24843 | 0.262178 | ||||||||
\(569\) | 14.1773 | 0.594345 | 0.297173 | − | 0.954824i | \(-0.403956\pi\) | ||||
0.297173 | + | 0.954824i | \(0.403956\pi\) | |||||||
\(570\) | −0.887238 | −0.0371623 | ||||||||
\(571\) | 26.2001 | 1.09644 | 0.548221 | − | 0.836334i | \(-0.315305\pi\) | ||||
0.548221 | + | 0.836334i | \(0.315305\pi\) | |||||||
\(572\) | 5.73137 | 0.239641 | ||||||||
\(573\) | 7.63879 | 0.319115 | ||||||||
\(574\) | 21.8882 | 0.913594 | ||||||||
\(575\) | −28.8019 | −1.20112 | ||||||||
\(576\) | −2.75757 | −0.114899 | ||||||||
\(577\) | 42.7653 | 1.78034 | 0.890172 | − | 0.455625i | \(-0.150584\pi\) | ||||
0.890172 | + | 0.455625i | \(0.150584\pi\) | |||||||
\(578\) | −4.97537 | −0.206948 | ||||||||
\(579\) | −10.0294 | −0.416806 | ||||||||
\(580\) | −2.12304 | −0.0881543 | ||||||||
\(581\) | −17.9384 | −0.744210 | ||||||||
\(582\) | 0.492368 | 0.0204093 | ||||||||
\(583\) | −20.5794 | −0.852311 | ||||||||
\(584\) | 6.47204 | 0.267815 | ||||||||
\(585\) | −5.10852 | −0.211211 | ||||||||
\(586\) | −4.82842 | −0.199460 | ||||||||
\(587\) | 19.4624 | 0.803299 | 0.401650 | − | 0.915793i | \(-0.368437\pi\) | ||||
0.401650 | + | 0.915793i | \(0.368437\pi\) | |||||||
\(588\) | −8.27548 | −0.341275 | ||||||||
\(589\) | 3.29297 | 0.135684 | ||||||||
\(590\) | −1.19356 | −0.0491381 | ||||||||
\(591\) | 0.512436 | 0.0210788 | ||||||||
\(592\) | 3.70114 | 0.152116 | ||||||||
\(593\) | −17.0492 | −0.700128 | −0.350064 | − | 0.936726i | \(-0.613840\pi\) | ||||
−0.350064 | + | 0.936726i | \(0.613840\pi\) | |||||||
\(594\) | −4.79935 | −0.196920 | ||||||||
\(595\) | 9.25880 | 0.379574 | ||||||||
\(596\) | 4.82747 | 0.197741 | ||||||||
\(597\) | 6.56997 | 0.268891 | ||||||||
\(598\) | −20.7433 | −0.848256 | ||||||||
\(599\) | −2.44361 | −0.0998430 | −0.0499215 | − | 0.998753i | \(-0.515897\pi\) | ||||
−0.0499215 | + | 0.998753i | \(0.515897\pi\) | |||||||
\(600\) | 2.31440 | 0.0944851 | ||||||||
\(601\) | 8.09623 | 0.330252 | 0.165126 | − | 0.986272i | \(-0.447197\pi\) | ||||
0.165126 | + | 0.986272i | \(0.447197\pi\) | |||||||
\(602\) | 25.0568 | 1.02124 | ||||||||
\(603\) | −36.8911 | −1.50232 | ||||||||
\(604\) | −11.1519 | −0.453765 | ||||||||
\(605\) | 4.45098 | 0.180958 | ||||||||
\(606\) | −0.933183 | −0.0379079 | ||||||||
\(607\) | −24.9190 | −1.01143 | −0.505715 | − | 0.862701i | \(-0.668771\pi\) | ||||
−0.505715 | + | 0.862701i | \(0.668771\pi\) | |||||||
\(608\) | −3.29297 | −0.133548 | ||||||||
\(609\) | −9.32057 | −0.377688 | ||||||||
\(610\) | −5.25250 | −0.212667 | ||||||||
\(611\) | −6.18766 | −0.250326 | ||||||||
\(612\) | 9.56231 | 0.386534 | ||||||||
\(613\) | 46.2394 | 1.86759 | 0.933796 | − | 0.357806i | \(-0.116475\pi\) | ||||
0.933796 | + | 0.357806i | \(0.116475\pi\) | |||||||
\(614\) | 1.93106 | 0.0779313 | ||||||||
\(615\) | 1.20866 | 0.0487379 | ||||||||
\(616\) | −8.26056 | −0.332828 | ||||||||
\(617\) | 3.89219 | 0.156694 | 0.0783469 | − | 0.996926i | \(-0.475036\pi\) | ||||
0.0783469 | + | 0.996926i | \(0.475036\pi\) | |||||||
\(618\) | −5.50117 | −0.221290 | ||||||||
\(619\) | 8.36100 | 0.336057 | 0.168028 | − | 0.985782i | \(-0.446260\pi\) | ||||
0.168028 | + | 0.985782i | \(0.446260\pi\) | |||||||
\(620\) | 0.547220 | 0.0219769 | ||||||||
\(621\) | 17.3701 | 0.697037 | ||||||||
\(622\) | 7.45672 | 0.298987 | ||||||||
\(623\) | 70.1045 | 2.80868 | ||||||||
\(624\) | 1.66685 | 0.0667273 | ||||||||
\(625\) | 20.5979 | 0.823917 | ||||||||
\(626\) | 25.8462 | 1.03302 | ||||||||
\(627\) | −2.74493 | −0.109622 | ||||||||
\(628\) | 23.1586 | 0.924129 | ||||||||
\(629\) | −12.8343 | −0.511735 | ||||||||
\(630\) | 7.36285 | 0.293343 | ||||||||
\(631\) | −12.3082 | −0.489981 | −0.244990 | − | 0.969525i | \(-0.578785\pi\) | ||||
−0.244990 | + | 0.969525i | \(0.578785\pi\) | |||||||
\(632\) | −4.26535 | −0.169666 | ||||||||
\(633\) | 5.33810 | 0.212170 | ||||||||
\(634\) | −12.3077 | −0.488800 | ||||||||
\(635\) | −5.88782 | −0.233651 | ||||||||
\(636\) | −5.98508 | −0.237324 | ||||||||
\(637\) | −56.8995 | −2.25444 | ||||||||
\(638\) | −6.56823 | −0.260039 | ||||||||
\(639\) | −17.2305 | −0.681628 | ||||||||
\(640\) | −0.547220 | −0.0216308 | ||||||||
\(641\) | −20.1961 | −0.797696 | −0.398848 | − | 0.917017i | \(-0.630590\pi\) | ||||
−0.398848 | + | 0.917017i | \(0.630590\pi\) | |||||||
\(642\) | 5.95014 | 0.234833 | ||||||||
\(643\) | 6.75292 | 0.266309 | 0.133155 | − | 0.991095i | \(-0.457489\pi\) | ||||
0.133155 | + | 0.991095i | \(0.457489\pi\) | |||||||
\(644\) | 29.8971 | 1.17811 | ||||||||
\(645\) | 1.38363 | 0.0544804 | ||||||||
\(646\) | 11.4189 | 0.449270 | ||||||||
\(647\) | 12.0709 | 0.474556 | 0.237278 | − | 0.971442i | \(-0.423745\pi\) | ||||
0.237278 | + | 0.971442i | \(0.423745\pi\) | |||||||
\(648\) | 6.87693 | 0.270151 | ||||||||
\(649\) | −3.69262 | −0.144948 | ||||||||
\(650\) | 15.9131 | 0.624162 | ||||||||
\(651\) | 2.40241 | 0.0941578 | ||||||||
\(652\) | −5.17824 | −0.202796 | ||||||||
\(653\) | 15.6983 | 0.614322 | 0.307161 | − | 0.951658i | \(-0.400621\pi\) | ||||
0.307161 | + | 0.951658i | \(0.400621\pi\) | |||||||
\(654\) | 5.11402 | 0.199974 | ||||||||
\(655\) | −1.18363 | −0.0462482 | ||||||||
\(656\) | 4.48593 | 0.175146 | ||||||||
\(657\) | −17.8471 | −0.696283 | ||||||||
\(658\) | 8.91820 | 0.347668 | ||||||||
\(659\) | −21.5338 | −0.838839 | −0.419420 | − | 0.907793i | \(-0.637766\pi\) | ||||
−0.419420 | + | 0.907793i | \(0.637766\pi\) | |||||||
\(660\) | −0.456147 | −0.0177555 | ||||||||
\(661\) | −46.2703 | −1.79971 | −0.899854 | − | 0.436191i | \(-0.856327\pi\) | ||||
−0.899854 | + | 0.436191i | \(0.856327\pi\) | |||||||
\(662\) | −5.39932 | −0.209851 | ||||||||
\(663\) | −5.78005 | −0.224479 | ||||||||
\(664\) | −3.67643 | −0.142673 | ||||||||
\(665\) | 8.79238 | 0.340954 | ||||||||
\(666\) | −10.2062 | −0.395480 | ||||||||
\(667\) | 23.7721 | 0.920459 | ||||||||
\(668\) | −4.22756 | −0.163569 | ||||||||
\(669\) | 4.57513 | 0.176885 | ||||||||
\(670\) | −7.32078 | −0.282826 | ||||||||
\(671\) | −16.2501 | −0.627329 | ||||||||
\(672\) | −2.40241 | −0.0926749 | ||||||||
\(673\) | 37.5931 | 1.44911 | 0.724555 | − | 0.689217i | \(-0.242045\pi\) | ||||
0.724555 | + | 0.689217i | \(0.242045\pi\) | |||||||
\(674\) | −6.99344 | −0.269377 | ||||||||
\(675\) | −13.3253 | −0.512893 | ||||||||
\(676\) | −1.53930 | −0.0592037 | ||||||||
\(677\) | −13.0532 | −0.501677 | −0.250838 | − | 0.968029i | \(-0.580706\pi\) | ||||
−0.250838 | + | 0.968029i | \(0.580706\pi\) | |||||||
\(678\) | 6.10560 | 0.234484 | ||||||||
\(679\) | −4.87929 | −0.187250 | ||||||||
\(680\) | 1.89757 | 0.0727685 | ||||||||
\(681\) | 2.48067 | 0.0950595 | ||||||||
\(682\) | 1.69298 | 0.0648277 | ||||||||
\(683\) | 39.8102 | 1.52329 | 0.761647 | − | 0.647992i | \(-0.224391\pi\) | ||||
0.761647 | + | 0.647992i | \(0.224391\pi\) | |||||||
\(684\) | 9.08060 | 0.347206 | ||||||||
\(685\) | 11.8582 | 0.453077 | ||||||||
\(686\) | 47.8536 | 1.82706 | ||||||||
\(687\) | −6.31901 | −0.241085 | ||||||||
\(688\) | 5.13533 | 0.195783 | ||||||||
\(689\) | −41.1515 | −1.56775 | ||||||||
\(690\) | 1.65091 | 0.0628492 | ||||||||
\(691\) | 39.2479 | 1.49306 | 0.746531 | − | 0.665351i | \(-0.231718\pi\) | ||||
0.746531 | + | 0.665351i | \(0.231718\pi\) | |||||||
\(692\) | 13.8562 | 0.526735 | ||||||||
\(693\) | 22.7791 | 0.865307 | ||||||||
\(694\) | −12.5591 | −0.476737 | ||||||||
\(695\) | −8.11094 | −0.307665 | ||||||||
\(696\) | −1.91023 | −0.0724071 | ||||||||
\(697\) | −15.5557 | −0.589212 | ||||||||
\(698\) | 8.37399 | 0.316960 | ||||||||
\(699\) | 10.1553 | 0.384110 | ||||||||
\(700\) | −22.9354 | −0.866875 | ||||||||
\(701\) | −51.5574 | −1.94730 | −0.973649 | − | 0.228053i | \(-0.926764\pi\) | ||||
−0.973649 | + | 0.228053i | \(0.926764\pi\) | |||||||
\(702\) | −9.59700 | −0.362215 | ||||||||
\(703\) | −12.1877 | −0.459669 | ||||||||
\(704\) | −1.69298 | −0.0638067 | ||||||||
\(705\) | 0.492462 | 0.0185472 | ||||||||
\(706\) | −18.0438 | −0.679087 | ||||||||
\(707\) | 9.24769 | 0.347795 | ||||||||
\(708\) | −1.07392 | −0.0403604 | ||||||||
\(709\) | −24.3644 | −0.915025 | −0.457513 | − | 0.889203i | \(-0.651260\pi\) | ||||
−0.457513 | + | 0.889203i | \(0.651260\pi\) | |||||||
\(710\) | −3.41927 | −0.128323 | ||||||||
\(711\) | 11.7620 | 0.441110 | ||||||||
\(712\) | 14.3678 | 0.538455 | ||||||||
\(713\) | −6.12734 | −0.229471 | ||||||||
\(714\) | 8.33072 | 0.311770 | ||||||||
\(715\) | −3.13632 | −0.117292 | ||||||||
\(716\) | −9.02751 | −0.337374 | ||||||||
\(717\) | 5.28563 | 0.197396 | ||||||||
\(718\) | −28.9683 | −1.08109 | ||||||||
\(719\) | −42.3959 | −1.58110 | −0.790551 | − | 0.612397i | \(-0.790205\pi\) | ||||
−0.790551 | + | 0.612397i | \(0.790205\pi\) | |||||||
\(720\) | 1.50900 | 0.0562371 | ||||||||
\(721\) | 54.5157 | 2.03027 | ||||||||
\(722\) | −8.15636 | −0.303548 | ||||||||
\(723\) | 4.97195 | 0.184909 | ||||||||
\(724\) | 6.06735 | 0.225491 | ||||||||
\(725\) | −18.2366 | −0.677291 | ||||||||
\(726\) | 4.00483 | 0.148633 | ||||||||
\(727\) | −0.663978 | −0.0246256 | −0.0123128 | − | 0.999924i | \(-0.503919\pi\) | ||||
−0.0123128 | + | 0.999924i | \(0.503919\pi\) | |||||||
\(728\) | −16.5182 | −0.612205 | ||||||||
\(729\) | −14.7763 | −0.547269 | ||||||||
\(730\) | −3.54163 | −0.131082 | ||||||||
\(731\) | −17.8075 | −0.658636 | ||||||||
\(732\) | −4.72600 | −0.174678 | ||||||||
\(733\) | −6.32870 | −0.233756 | −0.116878 | − | 0.993146i | \(-0.537289\pi\) | ||||
−0.116878 | + | 0.993146i | \(0.537289\pi\) | |||||||
\(734\) | 15.6555 | 0.577856 | ||||||||
\(735\) | 4.52851 | 0.167037 | ||||||||
\(736\) | 6.12734 | 0.225857 | ||||||||
\(737\) | −22.6489 | −0.834284 | ||||||||
\(738\) | −12.3703 | −0.455356 | ||||||||
\(739\) | −25.1731 | −0.926007 | −0.463004 | − | 0.886356i | \(-0.653228\pi\) | ||||
−0.463004 | + | 0.886356i | \(0.653228\pi\) | |||||||
\(740\) | −2.02534 | −0.0744528 | ||||||||
\(741\) | −5.48888 | −0.201639 | ||||||||
\(742\) | 59.3112 | 2.17738 | ||||||||
\(743\) | −6.96576 | −0.255549 | −0.127775 | − | 0.991803i | \(-0.540783\pi\) | ||||
−0.127775 | + | 0.991803i | \(0.540783\pi\) | |||||||
\(744\) | 0.492368 | 0.0180511 | ||||||||
\(745\) | −2.64169 | −0.0967840 | ||||||||
\(746\) | −25.0761 | −0.918102 | ||||||||
\(747\) | 10.1380 | 0.370931 | ||||||||
\(748\) | 5.87068 | 0.214653 | ||||||||
\(749\) | −58.9649 | −2.15453 | ||||||||
\(750\) | −2.61366 | −0.0954373 | ||||||||
\(751\) | 38.6055 | 1.40873 | 0.704367 | − | 0.709836i | \(-0.251231\pi\) | ||||
0.704367 | + | 0.709836i | \(0.251231\pi\) | |||||||
\(752\) | 1.82777 | 0.0666517 | ||||||||
\(753\) | 6.60982 | 0.240875 | ||||||||
\(754\) | −13.1341 | −0.478316 | ||||||||
\(755\) | 6.10255 | 0.222095 | ||||||||
\(756\) | 13.8320 | 0.503067 | ||||||||
\(757\) | −52.9200 | −1.92341 | −0.961705 | − | 0.274087i | \(-0.911624\pi\) | ||||
−0.961705 | + | 0.274087i | \(0.911624\pi\) | |||||||
\(758\) | 22.0357 | 0.800374 | ||||||||
\(759\) | 5.10758 | 0.185393 | ||||||||
\(760\) | 1.80198 | 0.0653647 | ||||||||
\(761\) | −11.3999 | −0.413248 | −0.206624 | − | 0.978420i | \(-0.566248\pi\) | ||||
−0.206624 | + | 0.978420i | \(0.566248\pi\) | |||||||
\(762\) | −5.29764 | −0.191913 | ||||||||
\(763\) | −50.6792 | −1.83471 | ||||||||
\(764\) | −15.5144 | −0.561290 | ||||||||
\(765\) | −5.23269 | −0.189188 | ||||||||
\(766\) | 25.9200 | 0.936527 | ||||||||
\(767\) | −7.38393 | −0.266618 | ||||||||
\(768\) | −0.492368 | −0.0177668 | ||||||||
\(769\) | −7.60468 | −0.274232 | −0.137116 | − | 0.990555i | \(-0.543783\pi\) | ||||
−0.137116 | + | 0.990555i | \(0.543783\pi\) | |||||||
\(770\) | 4.52035 | 0.162902 | ||||||||
\(771\) | −5.85894 | −0.211005 | ||||||||
\(772\) | 20.3696 | 0.733120 | ||||||||
\(773\) | −4.36699 | −0.157070 | −0.0785348 | − | 0.996911i | \(-0.525024\pi\) | ||||
−0.0785348 | + | 0.996911i | \(0.525024\pi\) | |||||||
\(774\) | −14.1610 | −0.509008 | ||||||||
\(775\) | 4.70055 | 0.168849 | ||||||||
\(776\) | −1.00000 | −0.0358979 | ||||||||
\(777\) | −8.89164 | −0.318986 | ||||||||
\(778\) | −33.8834 | −1.21478 | ||||||||
\(779\) | −14.7720 | −0.529263 | ||||||||
\(780\) | −0.912133 | −0.0326596 | ||||||||
\(781\) | −10.5785 | −0.378528 | ||||||||
\(782\) | −21.2475 | −0.759809 | ||||||||
\(783\) | 10.9983 | 0.393047 | ||||||||
\(784\) | 16.8075 | 0.600267 | ||||||||
\(785\) | −12.6729 | −0.452314 | ||||||||
\(786\) | −1.06498 | −0.0379868 | ||||||||
\(787\) | −10.6198 | −0.378555 | −0.189277 | − | 0.981924i | \(-0.560615\pi\) | ||||
−0.189277 | + | 0.981924i | \(0.560615\pi\) | |||||||
\(788\) | −1.04076 | −0.0370755 | ||||||||
\(789\) | −9.05676 | −0.322429 | ||||||||
\(790\) | 2.33409 | 0.0830430 | ||||||||
\(791\) | −60.5055 | −2.15133 | ||||||||
\(792\) | 4.66853 | 0.165889 | ||||||||
\(793\) | −32.4944 | −1.15391 | ||||||||
\(794\) | 1.42616 | 0.0506127 | ||||||||
\(795\) | 3.27516 | 0.116158 | ||||||||
\(796\) | −13.3436 | −0.472951 | ||||||||
\(797\) | 33.7283 | 1.19472 | 0.597358 | − | 0.801975i | \(-0.296217\pi\) | ||||
0.597358 | + | 0.801975i | \(0.296217\pi\) | |||||||
\(798\) | 7.91106 | 0.280048 | ||||||||
\(799\) | −6.33806 | −0.224224 | ||||||||
\(800\) | −4.70055 | −0.166190 | ||||||||
\(801\) | −39.6202 | −1.39991 | ||||||||
\(802\) | 17.0063 | 0.600515 | ||||||||
\(803\) | −10.9571 | −0.386666 | ||||||||
\(804\) | −6.58696 | −0.232304 | ||||||||
\(805\) | −16.3603 | −0.576624 | ||||||||
\(806\) | 3.38537 | 0.119244 | ||||||||
\(807\) | −13.6246 | −0.479607 | ||||||||
\(808\) | 1.89529 | 0.0666762 | ||||||||
\(809\) | −38.9582 | −1.36970 | −0.684849 | − | 0.728685i | \(-0.740132\pi\) | ||||
−0.684849 | + | 0.728685i | \(0.740132\pi\) | |||||||
\(810\) | −3.76320 | −0.132225 | ||||||||
\(811\) | 43.0000 | 1.50994 | 0.754968 | − | 0.655762i | \(-0.227653\pi\) | ||||
0.754968 | + | 0.655762i | \(0.227653\pi\) | |||||||
\(812\) | 18.9301 | 0.664315 | ||||||||
\(813\) | 15.7012 | 0.550666 | ||||||||
\(814\) | −6.26596 | −0.219622 | ||||||||
\(815\) | 2.83364 | 0.0992581 | ||||||||
\(816\) | 1.70736 | 0.0597697 | ||||||||
\(817\) | −16.9105 | −0.591623 | ||||||||
\(818\) | 11.6724 | 0.408115 | ||||||||
\(819\) | 45.5501 | 1.59165 | ||||||||
\(820\) | −2.45479 | −0.0857250 | ||||||||
\(821\) | −5.23412 | −0.182672 | −0.0913360 | − | 0.995820i | \(-0.529114\pi\) | ||||
−0.0913360 | + | 0.995820i | \(0.529114\pi\) | |||||||
\(822\) | 10.6695 | 0.372143 | ||||||||
\(823\) | −18.2220 | −0.635178 | −0.317589 | − | 0.948229i | \(-0.602873\pi\) | ||||
−0.317589 | + | 0.948229i | \(0.602873\pi\) | |||||||
\(824\) | 11.1729 | 0.389226 | ||||||||
\(825\) | −3.91825 | −0.136416 | ||||||||
\(826\) | 10.6424 | 0.370296 | ||||||||
\(827\) | 18.9358 | 0.658463 | 0.329231 | − | 0.944249i | \(-0.393210\pi\) | ||||
0.329231 | + | 0.944249i | \(0.393210\pi\) | |||||||
\(828\) | −16.8966 | −0.587197 | ||||||||
\(829\) | 13.2920 | 0.461649 | 0.230825 | − | 0.972995i | \(-0.425858\pi\) | ||||
0.230825 | + | 0.972995i | \(0.425858\pi\) | |||||||
\(830\) | 2.01182 | 0.0698312 | ||||||||
\(831\) | 4.02029 | 0.139462 | ||||||||
\(832\) | −3.38537 | −0.117366 | ||||||||
\(833\) | −58.2826 | −2.01937 | ||||||||
\(834\) | −7.29792 | −0.252706 | ||||||||
\(835\) | 2.31340 | 0.0800587 | ||||||||
\(836\) | 5.57494 | 0.192813 | ||||||||
\(837\) | −2.83485 | −0.0979867 | ||||||||
\(838\) | 18.4560 | 0.637552 | ||||||||
\(839\) | 21.9369 | 0.757348 | 0.378674 | − | 0.925530i | \(-0.376380\pi\) | ||||
0.378674 | + | 0.925530i | \(0.376380\pi\) | |||||||
\(840\) | 1.31465 | 0.0453596 | ||||||||
\(841\) | −13.9481 | −0.480970 | ||||||||
\(842\) | −16.7262 | −0.576424 | ||||||||
\(843\) | −10.8517 | −0.373753 | ||||||||
\(844\) | −10.8417 | −0.373186 | ||||||||
\(845\) | 0.842334 | 0.0289772 | ||||||||
\(846\) | −5.04020 | −0.173286 | ||||||||
\(847\) | −39.6872 | −1.36367 | ||||||||
\(848\) | 12.1557 | 0.417428 | ||||||||
\(849\) | −11.0405 | −0.378908 | ||||||||
\(850\) | 16.2999 | 0.559081 | ||||||||
\(851\) | 22.6781 | 0.777396 | ||||||||
\(852\) | −3.07653 | −0.105400 | ||||||||
\(853\) | 40.2841 | 1.37930 | 0.689650 | − | 0.724143i | \(-0.257764\pi\) | ||||
0.689650 | + | 0.724143i | \(0.257764\pi\) | |||||||
\(854\) | 46.8339 | 1.60262 | ||||||||
\(855\) | −4.96909 | −0.169939 | ||||||||
\(856\) | −12.0847 | −0.413048 | ||||||||
\(857\) | −55.4421 | −1.89387 | −0.946934 | − | 0.321429i | \(-0.895837\pi\) | ||||
−0.946934 | + | 0.321429i | \(0.895837\pi\) | |||||||
\(858\) | −2.82195 | −0.0963396 | ||||||||
\(859\) | 48.7949 | 1.66486 | 0.832431 | − | 0.554129i | \(-0.186949\pi\) | ||||
0.832431 | + | 0.554129i | \(0.186949\pi\) | |||||||
\(860\) | −2.81016 | −0.0958255 | ||||||||
\(861\) | −10.7770 | −0.367280 | ||||||||
\(862\) | −21.6759 | −0.738283 | ||||||||
\(863\) | −13.5015 | −0.459596 | −0.229798 | − | 0.973238i | \(-0.573806\pi\) | ||||
−0.229798 | + | 0.973238i | \(0.573806\pi\) | |||||||
\(864\) | 2.83485 | 0.0964435 | ||||||||
\(865\) | −7.58241 | −0.257810 | ||||||||
\(866\) | 31.9479 | 1.08563 | ||||||||
\(867\) | 2.44972 | 0.0831968 | ||||||||
\(868\) | −4.87929 | −0.165614 | ||||||||
\(869\) | 7.22117 | 0.244961 | ||||||||
\(870\) | 1.04532 | 0.0354395 | ||||||||
\(871\) | −45.2898 | −1.53459 | ||||||||
\(872\) | −10.3866 | −0.351734 | ||||||||
\(873\) | 2.75757 | 0.0933297 | ||||||||
\(874\) | −20.1771 | −0.682502 | ||||||||
\(875\) | 25.9009 | 0.875611 | ||||||||
\(876\) | −3.18663 | −0.107666 | ||||||||
\(877\) | −47.2392 | −1.59516 | −0.797578 | − | 0.603216i | \(-0.793886\pi\) | ||||
−0.797578 | + | 0.603216i | \(0.793886\pi\) | |||||||
\(878\) | −39.3101 | −1.32665 | ||||||||
\(879\) | 2.37736 | 0.0801865 | ||||||||
\(880\) | 0.926435 | 0.0312301 | ||||||||
\(881\) | 18.6818 | 0.629404 | 0.314702 | − | 0.949190i | \(-0.398095\pi\) | ||||
0.314702 | + | 0.949190i | \(0.398095\pi\) | |||||||
\(882\) | −46.3479 | −1.56061 | ||||||||
\(883\) | 24.2524 | 0.816157 | 0.408079 | − | 0.912947i | \(-0.366199\pi\) | ||||
0.408079 | + | 0.912947i | \(0.366199\pi\) | |||||||
\(884\) | 11.7393 | 0.394835 | ||||||||
\(885\) | 0.587671 | 0.0197544 | ||||||||
\(886\) | 4.44918 | 0.149473 | ||||||||
\(887\) | −41.9282 | −1.40781 | −0.703906 | − | 0.710293i | \(-0.748562\pi\) | ||||
−0.703906 | + | 0.710293i | \(0.748562\pi\) | |||||||
\(888\) | −1.82232 | −0.0611531 | ||||||||
\(889\) | 52.4988 | 1.76075 | ||||||||
\(890\) | −7.86233 | −0.263546 | ||||||||
\(891\) | −11.6425 | −0.390039 | ||||||||
\(892\) | −9.29209 | −0.311122 | ||||||||
\(893\) | −6.01877 | −0.201411 | ||||||||
\(894\) | −2.37689 | −0.0794952 | ||||||||
\(895\) | 4.94004 | 0.165127 | ||||||||
\(896\) | 4.87929 | 0.163006 | ||||||||
\(897\) | 10.2133 | 0.341013 | ||||||||
\(898\) | −22.2100 | −0.741157 | ||||||||
\(899\) | −3.87968 | −0.129394 | ||||||||
\(900\) | 12.9621 | 0.432070 | ||||||||
\(901\) | −42.1517 | −1.40428 | ||||||||
\(902\) | −7.59460 | −0.252873 | ||||||||
\(903\) | −12.3372 | −0.410555 | ||||||||
\(904\) | −12.4005 | −0.412433 | ||||||||
\(905\) | −3.32018 | −0.110366 | ||||||||
\(906\) | 5.49085 | 0.182421 | ||||||||
\(907\) | 10.2331 | 0.339786 | 0.169893 | − | 0.985463i | \(-0.445658\pi\) | ||||
0.169893 | + | 0.985463i | \(0.445658\pi\) | |||||||
\(908\) | −5.03824 | −0.167200 | ||||||||
\(909\) | −5.22641 | −0.173349 | ||||||||
\(910\) | 9.03909 | 0.299643 | ||||||||
\(911\) | 57.2366 | 1.89633 | 0.948166 | − | 0.317774i | \(-0.102935\pi\) | ||||
0.948166 | + | 0.317774i | \(0.102935\pi\) | |||||||
\(912\) | 1.62135 | 0.0536884 | ||||||||
\(913\) | 6.22414 | 0.205989 | ||||||||
\(914\) | 1.37570 | 0.0455042 | ||||||||
\(915\) | 2.58616 | 0.0854959 | ||||||||
\(916\) | 12.8339 | 0.424044 | ||||||||
\(917\) | 10.5538 | 0.348518 | ||||||||
\(918\) | −9.83027 | −0.324447 | ||||||||
\(919\) | −53.4502 | −1.76316 | −0.881579 | − | 0.472036i | \(-0.843519\pi\) | ||||
−0.881579 | + | 0.472036i | \(0.843519\pi\) | |||||||
\(920\) | −3.35300 | −0.110545 | ||||||||
\(921\) | −0.950793 | −0.0313297 | ||||||||
\(922\) | 11.1892 | 0.368496 | ||||||||
\(923\) | −21.1532 | −0.696266 | ||||||||
\(924\) | 4.06724 | 0.133802 | ||||||||
\(925\) | −17.3974 | −0.572022 | ||||||||
\(926\) | 37.2506 | 1.22413 | ||||||||
\(927\) | −30.8100 | −1.01193 | ||||||||
\(928\) | 3.87968 | 0.127357 | ||||||||
\(929\) | −35.7928 | −1.17432 | −0.587162 | − | 0.809469i | \(-0.699755\pi\) | ||||
−0.587162 | + | 0.809469i | \(0.699755\pi\) | |||||||
\(930\) | −0.269434 | −0.00883509 | ||||||||
\(931\) | −55.3465 | −1.81391 | ||||||||
\(932\) | −20.6255 | −0.675611 | ||||||||
\(933\) | −3.67145 | −0.120198 | ||||||||
\(934\) | −35.7101 | −1.16847 | ||||||||
\(935\) | −3.21256 | −0.105062 | ||||||||
\(936\) | 9.33540 | 0.305137 | ||||||||
\(937\) | −46.9515 | −1.53384 | −0.766920 | − | 0.641743i | \(-0.778212\pi\) | ||||
−0.766920 | + | 0.641743i | \(0.778212\pi\) | |||||||
\(938\) | 65.2757 | 2.13133 | ||||||||
\(939\) | −12.7259 | −0.415293 | ||||||||
\(940\) | −1.00019 | −0.0326226 | ||||||||
\(941\) | −11.5442 | −0.376329 | −0.188164 | − | 0.982138i | \(-0.560254\pi\) | ||||
−0.188164 | + | 0.982138i | \(0.560254\pi\) | |||||||
\(942\) | −11.4026 | −0.371516 | ||||||||
\(943\) | 27.4868 | 0.895093 | ||||||||
\(944\) | 2.18113 | 0.0709898 | ||||||||
\(945\) | −7.56918 | −0.246225 | ||||||||
\(946\) | −8.69403 | −0.282667 | ||||||||
\(947\) | 12.6232 | 0.410200 | 0.205100 | − | 0.978741i | \(-0.434248\pi\) | ||||
0.205100 | + | 0.978741i | \(0.434248\pi\) | |||||||
\(948\) | 2.10012 | 0.0682088 | ||||||||
\(949\) | −21.9102 | −0.711236 | ||||||||
\(950\) | 15.4788 | 0.502197 | ||||||||
\(951\) | 6.05991 | 0.196506 | ||||||||
\(952\) | −16.9197 | −0.548370 | ||||||||
\(953\) | 14.5446 | 0.471147 | 0.235574 | − | 0.971857i | \(-0.424303\pi\) | ||||
0.235574 | + | 0.971857i | \(0.424303\pi\) | |||||||
\(954\) | −33.5202 | −1.08526 | ||||||||
\(955\) | 8.48978 | 0.274723 | ||||||||
\(956\) | −10.7351 | −0.347199 | ||||||||
\(957\) | 3.23399 | 0.104540 | ||||||||
\(958\) | 3.85971 | 0.124702 | ||||||||
\(959\) | −105.733 | −3.41431 | ||||||||
\(960\) | 0.269434 | 0.00869594 | ||||||||
\(961\) | 1.00000 | 0.0322581 | ||||||||
\(962\) | −12.5297 | −0.403974 | ||||||||
\(963\) | 33.3245 | 1.07387 | ||||||||
\(964\) | −10.0980 | −0.325236 | ||||||||
\(965\) | −11.1467 | −0.358824 | ||||||||
\(966\) | −14.7204 | −0.473620 | ||||||||
\(967\) | −4.68434 | −0.150638 | −0.0753191 | − | 0.997159i | \(-0.523998\pi\) | ||||
−0.0753191 | + | 0.997159i | \(0.523998\pi\) | |||||||
\(968\) | −8.13381 | −0.261430 | ||||||||
\(969\) | −5.62229 | −0.180614 | ||||||||
\(970\) | 0.547220 | 0.0175702 | ||||||||
\(971\) | 16.1261 | 0.517512 | 0.258756 | − | 0.965943i | \(-0.416688\pi\) | ||||
0.258756 | + | 0.965943i | \(0.416688\pi\) | |||||||
\(972\) | −11.8905 | −0.381389 | ||||||||
\(973\) | 72.3212 | 2.31851 | ||||||||
\(974\) | 37.9468 | 1.21589 | ||||||||
\(975\) | −7.83510 | −0.250924 | ||||||||
\(976\) | 9.59850 | 0.307241 | ||||||||
\(977\) | 8.67755 | 0.277619 | 0.138810 | − | 0.990319i | \(-0.455672\pi\) | ||||
0.138810 | + | 0.990319i | \(0.455672\pi\) | |||||||
\(978\) | 2.54960 | 0.0815273 | ||||||||
\(979\) | −24.3244 | −0.777411 | ||||||||
\(980\) | −9.19740 | −0.293800 | ||||||||
\(981\) | 28.6418 | 0.914461 | ||||||||
\(982\) | 29.7247 | 0.948554 | ||||||||
\(983\) | −23.0280 | −0.734479 | −0.367239 | − | 0.930126i | \(-0.619697\pi\) | ||||
−0.367239 | + | 0.930126i | \(0.619697\pi\) | |||||||
\(984\) | −2.20873 | −0.0704117 | ||||||||
\(985\) | 0.569524 | 0.0181465 | ||||||||
\(986\) | −13.4534 | −0.428443 | ||||||||
\(987\) | −4.39104 | −0.139768 | ||||||||
\(988\) | 11.1479 | 0.354662 | ||||||||
\(989\) | 31.4659 | 1.00056 | ||||||||
\(990\) | −2.55471 | −0.0811941 | ||||||||
\(991\) | −11.0579 | −0.351266 | −0.175633 | − | 0.984456i | \(-0.556197\pi\) | ||||
−0.175633 | + | 0.984456i | \(0.556197\pi\) | |||||||
\(992\) | −1.00000 | −0.0317500 | ||||||||
\(993\) | 2.65846 | 0.0843636 | ||||||||
\(994\) | 30.4879 | 0.967017 | ||||||||
\(995\) | 7.30189 | 0.231485 | ||||||||
\(996\) | 1.81016 | 0.0573571 | ||||||||
\(997\) | −25.4366 | −0.805586 | −0.402793 | − | 0.915291i | \(-0.631961\pi\) | ||||
−0.402793 | + | 0.915291i | \(0.631961\pi\) | |||||||
\(998\) | 21.6164 | 0.684256 | ||||||||
\(999\) | 10.4922 | 0.331957 |
(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 | 6014.2.a.i.1.11 | ✓ | 28 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6014.2.a.i.1.11 | ✓ | 28 | 1.1 | even | 1 | trivial |