Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6037,2,Mod(1,6037)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6037, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("6037.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6037 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6037.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: | \(48.2056877002\) |
Analytic rank: | \(0\) |
Dimension: | \(259\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Character | \(\chi\) | \(=\) | 6037.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.65823 | −1.87965 | −0.939827 | − | 0.341650i | \(-0.889014\pi\) | ||||
−0.939827 | + | 0.341650i | \(0.889014\pi\) | |||||||
\(3\) | −1.47107 | −0.849321 | −0.424661 | − | 0.905353i | \(-0.639607\pi\) | ||||
−0.424661 | + | 0.905353i | \(0.639607\pi\) | |||||||
\(4\) | 5.06620 | 2.53310 | ||||||||
\(5\) | −0.123247 | −0.0551179 | −0.0275589 | − | 0.999620i | \(-0.508773\pi\) | ||||
−0.0275589 | + | 0.999620i | \(0.508773\pi\) | |||||||
\(6\) | 3.91044 | 1.59643 | ||||||||
\(7\) | −2.04180 | −0.771726 | −0.385863 | − | 0.922556i | \(-0.626096\pi\) | ||||
−0.385863 | + | 0.922556i | \(0.626096\pi\) | |||||||
\(8\) | −8.15068 | −2.88170 | ||||||||
\(9\) | −0.835960 | −0.278653 | ||||||||
\(10\) | 0.327620 | 0.103603 | ||||||||
\(11\) | −1.27617 | −0.384779 | −0.192389 | − | 0.981319i | \(-0.561624\pi\) | ||||
−0.192389 | + | 0.981319i | \(0.561624\pi\) | |||||||
\(12\) | −7.45273 | −2.15142 | ||||||||
\(13\) | 1.33307 | 0.369727 | 0.184863 | − | 0.982764i | \(-0.440816\pi\) | ||||
0.184863 | + | 0.982764i | \(0.440816\pi\) | |||||||
\(14\) | 5.42757 | 1.45058 | ||||||||
\(15\) | 0.181305 | 0.0468128 | ||||||||
\(16\) | 11.5340 | 2.88350 | ||||||||
\(17\) | 2.50462 | 0.607459 | 0.303730 | − | 0.952758i | \(-0.401768\pi\) | ||||
0.303730 | + | 0.952758i | \(0.401768\pi\) | |||||||
\(18\) | 2.22218 | 0.523772 | ||||||||
\(19\) | −0.794015 | −0.182160 | −0.0910798 | − | 0.995844i | \(-0.529032\pi\) | ||||
−0.0910798 | + | 0.995844i | \(0.529032\pi\) | |||||||
\(20\) | −0.624396 | −0.139619 | ||||||||
\(21\) | 3.00362 | 0.655443 | ||||||||
\(22\) | 3.39235 | 0.723251 | ||||||||
\(23\) | 6.36334 | 1.32685 | 0.663424 | − | 0.748244i | \(-0.269103\pi\) | ||||
0.663424 | + | 0.748244i | \(0.269103\pi\) | |||||||
\(24\) | 11.9902 | 2.44749 | ||||||||
\(25\) | −4.98481 | −0.996962 | ||||||||
\(26\) | −3.54361 | −0.694959 | ||||||||
\(27\) | 5.64296 | 1.08599 | ||||||||
\(28\) | −10.3442 | −1.95486 | ||||||||
\(29\) | 5.26622 | 0.977912 | 0.488956 | − | 0.872309i | \(-0.337378\pi\) | ||||
0.488956 | + | 0.872309i | \(0.337378\pi\) | |||||||
\(30\) | −0.481951 | −0.0879918 | ||||||||
\(31\) | 4.00337 | 0.719026 | 0.359513 | − | 0.933140i | \(-0.382943\pi\) | ||||
0.359513 | + | 0.933140i | \(0.382943\pi\) | |||||||
\(32\) | −14.3587 | −2.53829 | ||||||||
\(33\) | 1.87733 | 0.326801 | ||||||||
\(34\) | −6.65786 | −1.14181 | ||||||||
\(35\) | 0.251646 | 0.0425359 | ||||||||
\(36\) | −4.23514 | −0.705857 | ||||||||
\(37\) | 6.53938 | 1.07507 | 0.537534 | − | 0.843242i | \(-0.319356\pi\) | ||||
0.537534 | + | 0.843242i | \(0.319356\pi\) | |||||||
\(38\) | 2.11068 | 0.342397 | ||||||||
\(39\) | −1.96103 | −0.314017 | ||||||||
\(40\) | 1.00455 | 0.158833 | ||||||||
\(41\) | 5.59187 | 0.873303 | 0.436652 | − | 0.899631i | \(-0.356164\pi\) | ||||
0.436652 | + | 0.899631i | \(0.356164\pi\) | |||||||
\(42\) | −7.98432 | −1.23201 | ||||||||
\(43\) | 9.30737 | 1.41936 | 0.709680 | − | 0.704524i | \(-0.248839\pi\) | ||||
0.709680 | + | 0.704524i | \(0.248839\pi\) | |||||||
\(44\) | −6.46532 | −0.974684 | ||||||||
\(45\) | 0.103030 | 0.0153588 | ||||||||
\(46\) | −16.9152 | −2.49402 | ||||||||
\(47\) | −1.09584 | −0.159845 | −0.0799224 | − | 0.996801i | \(-0.525467\pi\) | ||||
−0.0799224 | + | 0.996801i | \(0.525467\pi\) | |||||||
\(48\) | −16.9673 | −2.44902 | ||||||||
\(49\) | −2.83107 | −0.404439 | ||||||||
\(50\) | 13.2508 | 1.87394 | ||||||||
\(51\) | −3.68446 | −0.515928 | ||||||||
\(52\) | 6.75360 | 0.936556 | ||||||||
\(53\) | −3.14381 | −0.431836 | −0.215918 | − | 0.976412i | \(-0.569274\pi\) | ||||
−0.215918 | + | 0.976412i | \(0.569274\pi\) | |||||||
\(54\) | −15.0003 | −2.04128 | ||||||||
\(55\) | 0.157284 | 0.0212082 | ||||||||
\(56\) | 16.6420 | 2.22388 | ||||||||
\(57\) | 1.16805 | 0.154712 | ||||||||
\(58\) | −13.9988 | −1.83814 | ||||||||
\(59\) | −8.64986 | −1.12612 | −0.563058 | − | 0.826418i | \(-0.690375\pi\) | ||||
−0.563058 | + | 0.826418i | \(0.690375\pi\) | |||||||
\(60\) | 0.918528 | 0.118581 | ||||||||
\(61\) | −13.0794 | −1.67465 | −0.837325 | − | 0.546705i | \(-0.815882\pi\) | ||||
−0.837325 | + | 0.546705i | \(0.815882\pi\) | |||||||
\(62\) | −10.6419 | −1.35152 | ||||||||
\(63\) | 1.70686 | 0.215044 | ||||||||
\(64\) | 15.1008 | 1.88760 | ||||||||
\(65\) | −0.164297 | −0.0203786 | ||||||||
\(66\) | −4.99038 | −0.614273 | ||||||||
\(67\) | −7.37724 | −0.901274 | −0.450637 | − | 0.892707i | \(-0.648803\pi\) | ||||
−0.450637 | + | 0.892707i | \(0.648803\pi\) | |||||||
\(68\) | 12.6889 | 1.53876 | ||||||||
\(69\) | −9.36090 | −1.12692 | ||||||||
\(70\) | −0.668933 | −0.0799528 | ||||||||
\(71\) | 3.68520 | 0.437353 | 0.218677 | − | 0.975797i | \(-0.429826\pi\) | ||||
0.218677 | + | 0.975797i | \(0.429826\pi\) | |||||||
\(72\) | 6.81364 | 0.802996 | ||||||||
\(73\) | −12.4700 | −1.45950 | −0.729752 | − | 0.683712i | \(-0.760364\pi\) | ||||
−0.729752 | + | 0.683712i | \(0.760364\pi\) | |||||||
\(74\) | −17.3832 | −2.02076 | ||||||||
\(75\) | 7.33299 | 0.846741 | ||||||||
\(76\) | −4.02264 | −0.461429 | ||||||||
\(77\) | 2.60567 | 0.296944 | ||||||||
\(78\) | 5.21289 | 0.590243 | ||||||||
\(79\) | 10.4393 | 1.17451 | 0.587256 | − | 0.809401i | \(-0.300208\pi\) | ||||
0.587256 | + | 0.809401i | \(0.300208\pi\) | |||||||
\(80\) | −1.42154 | −0.158932 | ||||||||
\(81\) | −5.79329 | −0.643699 | ||||||||
\(82\) | −14.8645 | −1.64151 | ||||||||
\(83\) | −2.55002 | −0.279901 | −0.139950 | − | 0.990159i | \(-0.544694\pi\) | ||||
−0.139950 | + | 0.990159i | \(0.544694\pi\) | |||||||
\(84\) | 15.2169 | 1.66030 | ||||||||
\(85\) | −0.308687 | −0.0334818 | ||||||||
\(86\) | −24.7412 | −2.66791 | ||||||||
\(87\) | −7.74696 | −0.830561 | ||||||||
\(88\) | 10.4016 | 1.10882 | ||||||||
\(89\) | −4.05771 | −0.430117 | −0.215058 | − | 0.976601i | \(-0.568994\pi\) | ||||
−0.215058 | + | 0.976601i | \(0.568994\pi\) | |||||||
\(90\) | −0.273877 | −0.0288692 | ||||||||
\(91\) | −2.72185 | −0.285328 | ||||||||
\(92\) | 32.2380 | 3.36104 | ||||||||
\(93\) | −5.88923 | −0.610684 | ||||||||
\(94\) | 2.91300 | 0.300453 | ||||||||
\(95\) | 0.0978602 | 0.0100402 | ||||||||
\(96\) | 21.1226 | 2.15582 | ||||||||
\(97\) | 11.8973 | 1.20798 | 0.603992 | − | 0.796990i | \(-0.293576\pi\) | ||||
0.603992 | + | 0.796990i | \(0.293576\pi\) | |||||||
\(98\) | 7.52565 | 0.760205 | ||||||||
\(99\) | 1.06682 | 0.107220 | ||||||||
\(100\) | −25.2541 | −2.52541 | ||||||||
\(101\) | 14.0613 | 1.39915 | 0.699574 | − | 0.714560i | \(-0.253373\pi\) | ||||
0.699574 | + | 0.714560i | \(0.253373\pi\) | |||||||
\(102\) | 9.79416 | 0.969766 | ||||||||
\(103\) | −8.63753 | −0.851082 | −0.425541 | − | 0.904939i | \(-0.639916\pi\) | ||||
−0.425541 | + | 0.904939i | \(0.639916\pi\) | |||||||
\(104\) | −10.8654 | −1.06544 | ||||||||
\(105\) | −0.370188 | −0.0361266 | ||||||||
\(106\) | 8.35698 | 0.811702 | ||||||||
\(107\) | −7.53328 | −0.728270 | −0.364135 | − | 0.931346i | \(-0.618635\pi\) | ||||
−0.364135 | + | 0.931346i | \(0.618635\pi\) | |||||||
\(108\) | 28.5884 | 2.75092 | ||||||||
\(109\) | −10.7117 | −1.02599 | −0.512997 | − | 0.858391i | \(-0.671465\pi\) | ||||
−0.512997 | + | 0.858391i | \(0.671465\pi\) | |||||||
\(110\) | −0.418098 | −0.0398641 | ||||||||
\(111\) | −9.61987 | −0.913078 | ||||||||
\(112\) | −23.5501 | −2.22527 | ||||||||
\(113\) | 5.82344 | 0.547823 | 0.273911 | − | 0.961755i | \(-0.411682\pi\) | ||||
0.273911 | + | 0.961755i | \(0.411682\pi\) | |||||||
\(114\) | −3.10495 | −0.290805 | ||||||||
\(115\) | −0.784264 | −0.0731330 | ||||||||
\(116\) | 26.6797 | 2.47715 | ||||||||
\(117\) | −1.11439 | −0.103026 | ||||||||
\(118\) | 22.9933 | 2.11671 | ||||||||
\(119\) | −5.11392 | −0.468792 | ||||||||
\(120\) | −1.47776 | −0.134900 | ||||||||
\(121\) | −9.37140 | −0.851945 | ||||||||
\(122\) | 34.7682 | 3.14776 | ||||||||
\(123\) | −8.22602 | −0.741715 | ||||||||
\(124\) | 20.2819 | 1.82137 | ||||||||
\(125\) | 1.23060 | 0.110068 | ||||||||
\(126\) | −4.53723 | −0.404209 | ||||||||
\(127\) | 2.17453 | 0.192958 | 0.0964791 | − | 0.995335i | \(-0.469242\pi\) | ||||
0.0964791 | + | 0.995335i | \(0.469242\pi\) | |||||||
\(128\) | −11.4240 | −1.00975 | ||||||||
\(129\) | −13.6918 | −1.20549 | ||||||||
\(130\) | 0.436740 | 0.0383046 | ||||||||
\(131\) | −12.7862 | −1.11714 | −0.558568 | − | 0.829459i | \(-0.688649\pi\) | ||||
−0.558568 | + | 0.829459i | \(0.688649\pi\) | |||||||
\(132\) | 9.51093 | 0.827820 | ||||||||
\(133\) | 1.62122 | 0.140577 | ||||||||
\(134\) | 19.6104 | 1.69408 | ||||||||
\(135\) | −0.695479 | −0.0598573 | ||||||||
\(136\) | −20.4143 | −1.75052 | ||||||||
\(137\) | 2.25089 | 0.192307 | 0.0961534 | − | 0.995367i | \(-0.469346\pi\) | ||||
0.0961534 | + | 0.995367i | \(0.469346\pi\) | |||||||
\(138\) | 24.8835 | 2.11822 | ||||||||
\(139\) | −21.9323 | −1.86027 | −0.930135 | − | 0.367218i | \(-0.880310\pi\) | ||||
−0.930135 | + | 0.367218i | \(0.880310\pi\) | |||||||
\(140\) | 1.27489 | 0.107748 | ||||||||
\(141\) | 1.61206 | 0.135760 | ||||||||
\(142\) | −9.79613 | −0.822073 | ||||||||
\(143\) | −1.70122 | −0.142263 | ||||||||
\(144\) | −9.64197 | −0.803498 | ||||||||
\(145\) | −0.649047 | −0.0539004 | ||||||||
\(146\) | 33.1482 | 2.74336 | ||||||||
\(147\) | 4.16470 | 0.343498 | ||||||||
\(148\) | 33.1298 | 2.72326 | ||||||||
\(149\) | 17.5974 | 1.44163 | 0.720817 | − | 0.693125i | \(-0.243767\pi\) | ||||
0.720817 | + | 0.693125i | \(0.243767\pi\) | |||||||
\(150\) | −19.4928 | −1.59158 | ||||||||
\(151\) | −4.93173 | −0.401339 | −0.200669 | − | 0.979659i | \(-0.564312\pi\) | ||||
−0.200669 | + | 0.979659i | \(0.564312\pi\) | |||||||
\(152\) | 6.47177 | 0.524930 | ||||||||
\(153\) | −2.09376 | −0.169270 | ||||||||
\(154\) | −6.92648 | −0.558152 | ||||||||
\(155\) | −0.493404 | −0.0396312 | ||||||||
\(156\) | −9.93500 | −0.795437 | ||||||||
\(157\) | 14.2892 | 1.14040 | 0.570201 | − | 0.821505i | \(-0.306865\pi\) | ||||
0.570201 | + | 0.821505i | \(0.306865\pi\) | |||||||
\(158\) | −27.7501 | −2.20768 | ||||||||
\(159\) | 4.62476 | 0.366767 | ||||||||
\(160\) | 1.76967 | 0.139905 | ||||||||
\(161\) | −12.9926 | −1.02396 | ||||||||
\(162\) | 15.3999 | 1.20993 | ||||||||
\(163\) | 22.8863 | 1.79260 | 0.896298 | − | 0.443451i | \(-0.146246\pi\) | ||||
0.896298 | + | 0.443451i | \(0.146246\pi\) | |||||||
\(164\) | 28.3295 | 2.21217 | ||||||||
\(165\) | −0.231376 | −0.0180126 | ||||||||
\(166\) | 6.77854 | 0.526117 | ||||||||
\(167\) | −6.70468 | −0.518824 | −0.259412 | − | 0.965767i | \(-0.583529\pi\) | ||||
−0.259412 | + | 0.965767i | \(0.583529\pi\) | |||||||
\(168\) | −24.4815 | −1.88879 | ||||||||
\(169\) | −11.2229 | −0.863302 | ||||||||
\(170\) | 0.820563 | 0.0629343 | ||||||||
\(171\) | 0.663765 | 0.0507594 | ||||||||
\(172\) | 47.1530 | 3.59538 | ||||||||
\(173\) | 1.94342 | 0.147755 | 0.0738777 | − | 0.997267i | \(-0.476463\pi\) | ||||
0.0738777 | + | 0.997267i | \(0.476463\pi\) | |||||||
\(174\) | 20.5932 | 1.56117 | ||||||||
\(175\) | 10.1780 | 0.769382 | ||||||||
\(176\) | −14.7193 | −1.10951 | ||||||||
\(177\) | 12.7245 | 0.956434 | ||||||||
\(178\) | 10.7863 | 0.808471 | ||||||||
\(179\) | 21.5858 | 1.61340 | 0.806698 | − | 0.590965i | \(-0.201253\pi\) | ||||
0.806698 | + | 0.590965i | \(0.201253\pi\) | |||||||
\(180\) | 0.521970 | 0.0389053 | ||||||||
\(181\) | −4.25783 | −0.316482 | −0.158241 | − | 0.987400i | \(-0.550582\pi\) | ||||
−0.158241 | + | 0.987400i | \(0.550582\pi\) | |||||||
\(182\) | 7.23532 | 0.536318 | ||||||||
\(183\) | 19.2407 | 1.42232 | ||||||||
\(184\) | −51.8656 | −3.82358 | ||||||||
\(185\) | −0.805961 | −0.0592554 | ||||||||
\(186\) | 15.6549 | 1.14788 | ||||||||
\(187\) | −3.19631 | −0.233737 | ||||||||
\(188\) | −5.55175 | −0.404903 | ||||||||
\(189\) | −11.5218 | −0.838085 | ||||||||
\(190\) | −0.260135 | −0.0188722 | ||||||||
\(191\) | 13.2374 | 0.957824 | 0.478912 | − | 0.877863i | \(-0.341031\pi\) | ||||
0.478912 | + | 0.877863i | \(0.341031\pi\) | |||||||
\(192\) | −22.2143 | −1.60318 | ||||||||
\(193\) | 14.8525 | 1.06911 | 0.534554 | − | 0.845134i | \(-0.320480\pi\) | ||||
0.534554 | + | 0.845134i | \(0.320480\pi\) | |||||||
\(194\) | −31.6257 | −2.27059 | ||||||||
\(195\) | 0.241692 | 0.0173079 | ||||||||
\(196\) | −14.3428 | −1.02448 | ||||||||
\(197\) | 22.4429 | 1.59899 | 0.799494 | − | 0.600674i | \(-0.205101\pi\) | ||||
0.799494 | + | 0.600674i | \(0.205101\pi\) | |||||||
\(198\) | −2.83587 | −0.201536 | ||||||||
\(199\) | −10.4590 | −0.741422 | −0.370711 | − | 0.928748i | \(-0.620886\pi\) | ||||
−0.370711 | + | 0.928748i | \(0.620886\pi\) | |||||||
\(200\) | 40.6296 | 2.87295 | ||||||||
\(201\) | 10.8524 | 0.765471 | ||||||||
\(202\) | −37.3781 | −2.62992 | ||||||||
\(203\) | −10.7525 | −0.754680 | ||||||||
\(204\) | −18.6662 | −1.30690 | ||||||||
\(205\) | −0.689183 | −0.0481346 | ||||||||
\(206\) | 22.9606 | 1.59974 | ||||||||
\(207\) | −5.31950 | −0.369731 | ||||||||
\(208\) | 15.3756 | 1.06611 | ||||||||
\(209\) | 1.01330 | 0.0700912 | ||||||||
\(210\) | 0.984046 | 0.0679056 | ||||||||
\(211\) | −12.2074 | −0.840390 | −0.420195 | − | 0.907434i | \(-0.638038\pi\) | ||||
−0.420195 | + | 0.907434i | \(0.638038\pi\) | |||||||
\(212\) | −15.9272 | −1.09388 | ||||||||
\(213\) | −5.42118 | −0.371453 | ||||||||
\(214\) | 20.0252 | 1.36890 | ||||||||
\(215\) | −1.14711 | −0.0782321 | ||||||||
\(216\) | −45.9940 | −3.12949 | ||||||||
\(217\) | −8.17406 | −0.554891 | ||||||||
\(218\) | 28.4742 | 1.92851 | ||||||||
\(219\) | 18.3442 | 1.23959 | ||||||||
\(220\) | 0.796833 | 0.0537225 | ||||||||
\(221\) | 3.33883 | 0.224594 | ||||||||
\(222\) | 25.5719 | 1.71627 | ||||||||
\(223\) | 3.99085 | 0.267247 | 0.133624 | − | 0.991032i | \(-0.457339\pi\) | ||||
0.133624 | + | 0.991032i | \(0.457339\pi\) | |||||||
\(224\) | 29.3176 | 1.95886 | ||||||||
\(225\) | 4.16710 | 0.277807 | ||||||||
\(226\) | −15.4801 | −1.02972 | ||||||||
\(227\) | 23.1676 | 1.53769 | 0.768844 | − | 0.639437i | \(-0.220832\pi\) | ||||
0.768844 | + | 0.639437i | \(0.220832\pi\) | |||||||
\(228\) | 5.91758 | 0.391901 | ||||||||
\(229\) | −14.5876 | −0.963973 | −0.481986 | − | 0.876179i | \(-0.660085\pi\) | ||||
−0.481986 | + | 0.876179i | \(0.660085\pi\) | |||||||
\(230\) | 2.08476 | 0.137465 | ||||||||
\(231\) | −3.83312 | −0.252201 | ||||||||
\(232\) | −42.9233 | −2.81805 | ||||||||
\(233\) | −22.0413 | −1.44398 | −0.721988 | − | 0.691906i | \(-0.756771\pi\) | ||||
−0.721988 | + | 0.691906i | \(0.756771\pi\) | |||||||
\(234\) | 2.96232 | 0.193653 | ||||||||
\(235\) | 0.135059 | 0.00881030 | ||||||||
\(236\) | −43.8219 | −2.85256 | ||||||||
\(237\) | −15.3569 | −0.997538 | ||||||||
\(238\) | 13.5940 | 0.881167 | ||||||||
\(239\) | −2.97495 | −0.192433 | −0.0962167 | − | 0.995360i | \(-0.530674\pi\) | ||||
−0.0962167 | + | 0.995360i | \(0.530674\pi\) | |||||||
\(240\) | 2.09117 | 0.134985 | ||||||||
\(241\) | −6.97510 | −0.449306 | −0.224653 | − | 0.974439i | \(-0.572125\pi\) | ||||
−0.224653 | + | 0.974439i | \(0.572125\pi\) | |||||||
\(242\) | 24.9114 | 1.60136 | ||||||||
\(243\) | −8.40655 | −0.539280 | ||||||||
\(244\) | −66.2631 | −4.24206 | ||||||||
\(245\) | 0.348922 | 0.0222918 | ||||||||
\(246\) | 21.8667 | 1.39417 | ||||||||
\(247\) | −1.05848 | −0.0673493 | ||||||||
\(248\) | −32.6302 | −2.07202 | ||||||||
\(249\) | 3.75125 | 0.237726 | ||||||||
\(250\) | −3.27122 | −0.206890 | ||||||||
\(251\) | −13.5245 | −0.853658 | −0.426829 | − | 0.904332i | \(-0.640369\pi\) | ||||
−0.426829 | + | 0.904332i | \(0.640369\pi\) | |||||||
\(252\) | 8.64730 | 0.544728 | ||||||||
\(253\) | −8.12068 | −0.510543 | ||||||||
\(254\) | −5.78040 | −0.362695 | ||||||||
\(255\) | 0.454100 | 0.0284368 | ||||||||
\(256\) | 0.166096 | 0.0103810 | ||||||||
\(257\) | −7.74036 | −0.482830 | −0.241415 | − | 0.970422i | \(-0.577612\pi\) | ||||
−0.241415 | + | 0.970422i | \(0.577612\pi\) | |||||||
\(258\) | 36.3959 | 2.26591 | ||||||||
\(259\) | −13.3521 | −0.829658 | ||||||||
\(260\) | −0.832363 | −0.0516209 | ||||||||
\(261\) | −4.40235 | −0.272498 | ||||||||
\(262\) | 33.9887 | 2.09983 | ||||||||
\(263\) | −5.46077 | −0.336726 | −0.168363 | − | 0.985725i | \(-0.553848\pi\) | ||||
−0.168363 | + | 0.985725i | \(0.553848\pi\) | |||||||
\(264\) | −15.3015 | −0.941743 | ||||||||
\(265\) | 0.387466 | 0.0238019 | ||||||||
\(266\) | −4.30957 | −0.264237 | ||||||||
\(267\) | 5.96917 | 0.365307 | ||||||||
\(268\) | −37.3746 | −2.28302 | ||||||||
\(269\) | −5.03875 | −0.307218 | −0.153609 | − | 0.988132i | \(-0.549090\pi\) | ||||
−0.153609 | + | 0.988132i | \(0.549090\pi\) | |||||||
\(270\) | 1.84875 | 0.112511 | ||||||||
\(271\) | 28.3921 | 1.72470 | 0.862349 | − | 0.506314i | \(-0.168992\pi\) | ||||
0.862349 | + | 0.506314i | \(0.168992\pi\) | |||||||
\(272\) | 28.8883 | 1.75161 | ||||||||
\(273\) | 4.00403 | 0.242335 | ||||||||
\(274\) | −5.98340 | −0.361470 | ||||||||
\(275\) | 6.36145 | 0.383610 | ||||||||
\(276\) | −47.4242 | −2.85460 | ||||||||
\(277\) | −16.2218 | −0.974673 | −0.487337 | − | 0.873214i | \(-0.662032\pi\) | ||||
−0.487337 | + | 0.873214i | \(0.662032\pi\) | |||||||
\(278\) | 58.3011 | 3.49666 | ||||||||
\(279\) | −3.34666 | −0.200359 | ||||||||
\(280\) | −2.05108 | −0.122576 | ||||||||
\(281\) | −10.6618 | −0.636031 | −0.318016 | − | 0.948085i | \(-0.603016\pi\) | ||||
−0.318016 | + | 0.948085i | \(0.603016\pi\) | |||||||
\(282\) | −4.28522 | −0.255181 | ||||||||
\(283\) | −11.0767 | −0.658443 | −0.329222 | − | 0.944253i | \(-0.606786\pi\) | ||||
−0.329222 | + | 0.944253i | \(0.606786\pi\) | |||||||
\(284\) | 18.6700 | 1.10786 | ||||||||
\(285\) | −0.143959 | −0.00852740 | ||||||||
\(286\) | 4.52224 | 0.267406 | ||||||||
\(287\) | −11.4175 | −0.673951 | ||||||||
\(288\) | 12.0033 | 0.707302 | ||||||||
\(289\) | −10.7269 | −0.630993 | ||||||||
\(290\) | 1.72532 | 0.101314 | ||||||||
\(291\) | −17.5017 | −1.02597 | ||||||||
\(292\) | −63.1756 | −3.69707 | ||||||||
\(293\) | 16.2931 | 0.951853 | 0.475926 | − | 0.879485i | \(-0.342113\pi\) | ||||
0.475926 | + | 0.879485i | \(0.342113\pi\) | |||||||
\(294\) | −11.0707 | −0.645659 | ||||||||
\(295\) | 1.06607 | 0.0620691 | ||||||||
\(296\) | −53.3004 | −3.09802 | ||||||||
\(297\) | −7.20136 | −0.417865 | ||||||||
\(298\) | −46.7780 | −2.70977 | ||||||||
\(299\) | 8.48277 | 0.490571 | ||||||||
\(300\) | 37.1504 | 2.14488 | ||||||||
\(301\) | −19.0037 | −1.09536 | ||||||||
\(302\) | 13.1097 | 0.754378 | ||||||||
\(303\) | −20.6851 | −1.18833 | ||||||||
\(304\) | −9.15818 | −0.525258 | ||||||||
\(305\) | 1.61200 | 0.0923031 | ||||||||
\(306\) | 5.56570 | 0.318170 | ||||||||
\(307\) | −6.26009 | −0.357282 | −0.178641 | − | 0.983914i | \(-0.557170\pi\) | ||||
−0.178641 | + | 0.983914i | \(0.557170\pi\) | |||||||
\(308\) | 13.2009 | 0.752189 | ||||||||
\(309\) | 12.7064 | 0.722842 | ||||||||
\(310\) | 1.31158 | 0.0744929 | ||||||||
\(311\) | −6.34983 | −0.360066 | −0.180033 | − | 0.983661i | \(-0.557620\pi\) | ||||
−0.180033 | + | 0.983661i | \(0.557620\pi\) | |||||||
\(312\) | 15.9838 | 0.904903 | ||||||||
\(313\) | −12.4130 | −0.701624 | −0.350812 | − | 0.936446i | \(-0.614094\pi\) | ||||
−0.350812 | + | 0.936446i | \(0.614094\pi\) | |||||||
\(314\) | −37.9840 | −2.14356 | ||||||||
\(315\) | −0.210366 | −0.0118528 | ||||||||
\(316\) | 52.8876 | 2.97516 | ||||||||
\(317\) | −12.7675 | −0.717095 | −0.358548 | − | 0.933511i | \(-0.616728\pi\) | ||||
−0.358548 | + | 0.933511i | \(0.616728\pi\) | |||||||
\(318\) | −12.2937 | −0.689396 | ||||||||
\(319\) | −6.72057 | −0.376280 | ||||||||
\(320\) | −1.86113 | −0.104040 | ||||||||
\(321\) | 11.0820 | 0.618535 | ||||||||
\(322\) | 34.5375 | 1.92470 | ||||||||
\(323\) | −1.98871 | −0.110655 | ||||||||
\(324\) | −29.3500 | −1.63055 | ||||||||
\(325\) | −6.64510 | −0.368604 | ||||||||
\(326\) | −60.8372 | −3.36946 | ||||||||
\(327\) | 15.7576 | 0.871398 | ||||||||
\(328\) | −45.5776 | −2.51660 | ||||||||
\(329\) | 2.23748 | 0.123356 | ||||||||
\(330\) | 0.615050 | 0.0338574 | ||||||||
\(331\) | 12.9665 | 0.712705 | 0.356352 | − | 0.934352i | \(-0.384020\pi\) | ||||
0.356352 | + | 0.934352i | \(0.384020\pi\) | |||||||
\(332\) | −12.9189 | −0.709017 | ||||||||
\(333\) | −5.46666 | −0.299571 | ||||||||
\(334\) | 17.8226 | 0.975210 | ||||||||
\(335\) | 0.909225 | 0.0496763 | ||||||||
\(336\) | 34.6438 | 1.88997 | ||||||||
\(337\) | 30.2355 | 1.64703 | 0.823517 | − | 0.567292i | \(-0.192009\pi\) | ||||
0.823517 | + | 0.567292i | \(0.192009\pi\) | |||||||
\(338\) | 29.8332 | 1.62271 | ||||||||
\(339\) | −8.56667 | −0.465278 | ||||||||
\(340\) | −1.56387 | −0.0848129 | ||||||||
\(341\) | −5.10897 | −0.276666 | ||||||||
\(342\) | −1.76444 | −0.0954101 | ||||||||
\(343\) | 20.0730 | 1.08384 | ||||||||
\(344\) | −75.8614 | −4.09017 | ||||||||
\(345\) | 1.15371 | 0.0621134 | ||||||||
\(346\) | −5.16606 | −0.277729 | ||||||||
\(347\) | 7.18036 | 0.385462 | 0.192731 | − | 0.981252i | \(-0.438266\pi\) | ||||
0.192731 | + | 0.981252i | \(0.438266\pi\) | |||||||
\(348\) | −39.2477 | −2.10390 | ||||||||
\(349\) | 26.1025 | 1.39724 | 0.698618 | − | 0.715495i | \(-0.253799\pi\) | ||||
0.698618 | + | 0.715495i | \(0.253799\pi\) | |||||||
\(350\) | −27.0554 | −1.44617 | ||||||||
\(351\) | 7.52245 | 0.401519 | ||||||||
\(352\) | 18.3241 | 0.976679 | ||||||||
\(353\) | −3.78779 | −0.201604 | −0.100802 | − | 0.994907i | \(-0.532141\pi\) | ||||
−0.100802 | + | 0.994907i | \(0.532141\pi\) | |||||||
\(354\) | −33.8247 | −1.79776 | ||||||||
\(355\) | −0.454191 | −0.0241060 | ||||||||
\(356\) | −20.5572 | −1.08953 | ||||||||
\(357\) | 7.52292 | 0.398155 | ||||||||
\(358\) | −57.3800 | −3.03263 | ||||||||
\(359\) | 30.1551 | 1.59152 | 0.795762 | − | 0.605609i | \(-0.207070\pi\) | ||||
0.795762 | + | 0.605609i | \(0.207070\pi\) | |||||||
\(360\) | −0.839763 | −0.0442594 | ||||||||
\(361\) | −18.3695 | −0.966818 | ||||||||
\(362\) | 11.3183 | 0.594878 | ||||||||
\(363\) | 13.7860 | 0.723575 | ||||||||
\(364\) | −13.7895 | −0.722765 | ||||||||
\(365\) | 1.53689 | 0.0804447 | ||||||||
\(366\) | −51.1464 | −2.67346 | ||||||||
\(367\) | −2.14491 | −0.111963 | −0.0559817 | − | 0.998432i | \(-0.517829\pi\) | ||||
−0.0559817 | + | 0.998432i | \(0.517829\pi\) | |||||||
\(368\) | 73.3948 | 3.82597 | ||||||||
\(369\) | −4.67458 | −0.243349 | ||||||||
\(370\) | 2.14243 | 0.111380 | ||||||||
\(371\) | 6.41902 | 0.333259 | ||||||||
\(372\) | −29.8360 | −1.54693 | ||||||||
\(373\) | −17.4326 | −0.902628 | −0.451314 | − | 0.892365i | \(-0.649045\pi\) | ||||
−0.451314 | + | 0.892365i | \(0.649045\pi\) | |||||||
\(374\) | 8.49654 | 0.439346 | ||||||||
\(375\) | −1.81030 | −0.0934833 | ||||||||
\(376\) | 8.93185 | 0.460625 | ||||||||
\(377\) | 7.02023 | 0.361560 | ||||||||
\(378\) | 30.6275 | 1.57531 | ||||||||
\(379\) | 14.8171 | 0.761102 | 0.380551 | − | 0.924760i | \(-0.375734\pi\) | ||||
0.380551 | + | 0.924760i | \(0.375734\pi\) | |||||||
\(380\) | 0.495780 | 0.0254330 | ||||||||
\(381\) | −3.19888 | −0.163884 | ||||||||
\(382\) | −35.1881 | −1.80038 | ||||||||
\(383\) | 32.0701 | 1.63871 | 0.819353 | − | 0.573289i | \(-0.194333\pi\) | ||||
0.819353 | + | 0.573289i | \(0.194333\pi\) | |||||||
\(384\) | 16.8055 | 0.857602 | ||||||||
\(385\) | −0.321142 | −0.0163669 | ||||||||
\(386\) | −39.4815 | −2.00955 | ||||||||
\(387\) | −7.78059 | −0.395509 | ||||||||
\(388\) | 60.2740 | 3.05995 | ||||||||
\(389\) | −30.4168 | −1.54219 | −0.771097 | − | 0.636718i | \(-0.780292\pi\) | ||||
−0.771097 | + | 0.636718i | \(0.780292\pi\) | |||||||
\(390\) | −0.642474 | −0.0325329 | ||||||||
\(391\) | 15.9377 | 0.806006 | ||||||||
\(392\) | 23.0752 | 1.16547 | ||||||||
\(393\) | 18.8094 | 0.948808 | ||||||||
\(394\) | −59.6584 | −3.00554 | ||||||||
\(395\) | −1.28661 | −0.0647366 | ||||||||
\(396\) | 5.40475 | 0.271599 | ||||||||
\(397\) | 30.6312 | 1.53733 | 0.768667 | − | 0.639650i | \(-0.220920\pi\) | ||||
0.768667 | + | 0.639650i | \(0.220920\pi\) | |||||||
\(398\) | 27.8026 | 1.39362 | ||||||||
\(399\) | −2.38492 | −0.119395 | ||||||||
\(400\) | −57.4948 | −2.87474 | ||||||||
\(401\) | 12.8447 | 0.641433 | 0.320717 | − | 0.947175i | \(-0.396076\pi\) | ||||
0.320717 | + | 0.947175i | \(0.396076\pi\) | |||||||
\(402\) | −28.8483 | −1.43882 | ||||||||
\(403\) | 5.33677 | 0.265843 | ||||||||
\(404\) | 71.2372 | 3.54419 | ||||||||
\(405\) | 0.714007 | 0.0354793 | ||||||||
\(406\) | 28.5827 | 1.41854 | ||||||||
\(407\) | −8.34534 | −0.413663 | ||||||||
\(408\) | 30.0309 | 1.48675 | ||||||||
\(409\) | −35.3205 | −1.74648 | −0.873242 | − | 0.487287i | \(-0.837987\pi\) | ||||
−0.873242 | + | 0.487287i | \(0.837987\pi\) | |||||||
\(410\) | 1.83201 | 0.0904764 | ||||||||
\(411\) | −3.31122 | −0.163330 | ||||||||
\(412\) | −43.7595 | −2.15588 | ||||||||
\(413\) | 17.6612 | 0.869053 | ||||||||
\(414\) | 14.1405 | 0.694966 | ||||||||
\(415\) | 0.314283 | 0.0154275 | ||||||||
\(416\) | −19.1412 | −0.938473 | ||||||||
\(417\) | 32.2638 | 1.57997 | ||||||||
\(418\) | −2.69358 | −0.131747 | ||||||||
\(419\) | −13.0390 | −0.636995 | −0.318498 | − | 0.947924i | \(-0.603178\pi\) | ||||
−0.318498 | + | 0.947924i | \(0.603178\pi\) | |||||||
\(420\) | −1.87545 | −0.0915124 | ||||||||
\(421\) | −15.0702 | −0.734478 | −0.367239 | − | 0.930127i | \(-0.619697\pi\) | ||||
−0.367239 | + | 0.930127i | \(0.619697\pi\) | |||||||
\(422\) | 32.4500 | 1.57964 | ||||||||
\(423\) | 0.916079 | 0.0445413 | ||||||||
\(424\) | 25.6242 | 1.24442 | ||||||||
\(425\) | −12.4850 | −0.605614 | ||||||||
\(426\) | 14.4108 | 0.698204 | ||||||||
\(427\) | 26.7055 | 1.29237 | ||||||||
\(428\) | −38.1652 | −1.84478 | ||||||||
\(429\) | 2.50261 | 0.120827 | ||||||||
\(430\) | 3.04928 | 0.147049 | ||||||||
\(431\) | 35.3658 | 1.70351 | 0.851755 | − | 0.523940i | \(-0.175539\pi\) | ||||
0.851755 | + | 0.523940i | \(0.175539\pi\) | |||||||
\(432\) | 65.0859 | 3.13145 | ||||||||
\(433\) | −28.5793 | −1.37343 | −0.686716 | − | 0.726926i | \(-0.740948\pi\) | ||||
−0.686716 | + | 0.726926i | \(0.740948\pi\) | |||||||
\(434\) | 21.7286 | 1.04300 | ||||||||
\(435\) | 0.954792 | 0.0457788 | ||||||||
\(436\) | −54.2676 | −2.59895 | ||||||||
\(437\) | −5.05259 | −0.241698 | ||||||||
\(438\) | −48.7632 | −2.33000 | ||||||||
\(439\) | 38.1836 | 1.82240 | 0.911201 | − | 0.411962i | \(-0.135156\pi\) | ||||
0.911201 | + | 0.411962i | \(0.135156\pi\) | |||||||
\(440\) | −1.28197 | −0.0611157 | ||||||||
\(441\) | 2.36666 | 0.112698 | ||||||||
\(442\) | −8.87539 | −0.422159 | ||||||||
\(443\) | 39.1935 | 1.86214 | 0.931071 | − | 0.364838i | \(-0.118876\pi\) | ||||
0.931071 | + | 0.364838i | \(0.118876\pi\) | |||||||
\(444\) | −48.7362 | −2.31292 | ||||||||
\(445\) | 0.500102 | 0.0237071 | ||||||||
\(446\) | −10.6086 | −0.502332 | ||||||||
\(447\) | −25.8870 | −1.22441 | ||||||||
\(448\) | −30.8327 | −1.45671 | ||||||||
\(449\) | 14.4712 | 0.682940 | 0.341470 | − | 0.939893i | \(-0.389075\pi\) | ||||
0.341470 | + | 0.939893i | \(0.389075\pi\) | |||||||
\(450\) | −11.0771 | −0.522181 | ||||||||
\(451\) | −7.13616 | −0.336029 | ||||||||
\(452\) | 29.5027 | 1.38769 | ||||||||
\(453\) | 7.25491 | 0.340865 | ||||||||
\(454\) | −61.5849 | −2.89032 | ||||||||
\(455\) | 0.335461 | 0.0157267 | ||||||||
\(456\) | −9.52041 | −0.445834 | ||||||||
\(457\) | −2.23754 | −0.104668 | −0.0523338 | − | 0.998630i | \(-0.516666\pi\) | ||||
−0.0523338 | + | 0.998630i | \(0.516666\pi\) | |||||||
\(458\) | 38.7771 | 1.81194 | ||||||||
\(459\) | 14.1335 | 0.659693 | ||||||||
\(460\) | −3.97324 | −0.185253 | ||||||||
\(461\) | −4.76473 | −0.221916 | −0.110958 | − | 0.993825i | \(-0.535392\pi\) | ||||
−0.110958 | + | 0.993825i | \(0.535392\pi\) | |||||||
\(462\) | 10.1893 | 0.474050 | ||||||||
\(463\) | −20.1966 | −0.938617 | −0.469309 | − | 0.883034i | \(-0.655497\pi\) | ||||
−0.469309 | + | 0.883034i | \(0.655497\pi\) | |||||||
\(464\) | 60.7406 | 2.81981 | ||||||||
\(465\) | 0.725831 | 0.0336596 | ||||||||
\(466\) | 58.5910 | 2.71418 | ||||||||
\(467\) | 19.5488 | 0.904611 | 0.452306 | − | 0.891863i | \(-0.350602\pi\) | ||||
0.452306 | + | 0.891863i | \(0.350602\pi\) | |||||||
\(468\) | −5.64574 | −0.260974 | ||||||||
\(469\) | 15.0628 | 0.695537 | ||||||||
\(470\) | −0.359019 | −0.0165603 | ||||||||
\(471\) | −21.0204 | −0.968568 | ||||||||
\(472\) | 70.5022 | 3.24513 | ||||||||
\(473\) | −11.8778 | −0.546140 | ||||||||
\(474\) | 40.8222 | 1.87503 | ||||||||
\(475\) | 3.95802 | 0.181606 | ||||||||
\(476\) | −25.9081 | −1.18750 | ||||||||
\(477\) | 2.62810 | 0.120332 | ||||||||
\(478\) | 7.90810 | 0.361708 | ||||||||
\(479\) | −0.979237 | −0.0447425 | −0.0223712 | − | 0.999750i | \(-0.507122\pi\) | ||||
−0.0223712 | + | 0.999750i | \(0.507122\pi\) | |||||||
\(480\) | −2.60331 | −0.118824 | ||||||||
\(481\) | 8.71745 | 0.397481 | ||||||||
\(482\) | 18.5414 | 0.844540 | ||||||||
\(483\) | 19.1130 | 0.869674 | ||||||||
\(484\) | −47.4774 | −2.15806 | ||||||||
\(485\) | −1.46631 | −0.0665815 | ||||||||
\(486\) | 22.3466 | 1.01366 | ||||||||
\(487\) | 27.8793 | 1.26333 | 0.631666 | − | 0.775241i | \(-0.282371\pi\) | ||||
0.631666 | + | 0.775241i | \(0.282371\pi\) | |||||||
\(488\) | 106.606 | 4.82584 | ||||||||
\(489\) | −33.6674 | −1.52249 | ||||||||
\(490\) | −0.927516 | −0.0419009 | ||||||||
\(491\) | −3.72056 | −0.167907 | −0.0839534 | − | 0.996470i | \(-0.526755\pi\) | ||||
−0.0839534 | + | 0.996470i | \(0.526755\pi\) | |||||||
\(492\) | −41.6747 | −1.87884 | ||||||||
\(493\) | 13.1899 | 0.594041 | ||||||||
\(494\) | 2.81368 | 0.126593 | ||||||||
\(495\) | −0.131483 | −0.00590973 | ||||||||
\(496\) | 46.1749 | 2.07331 | ||||||||
\(497\) | −7.52443 | −0.337517 | ||||||||
\(498\) | −9.97169 | −0.446842 | ||||||||
\(499\) | 39.3383 | 1.76102 | 0.880511 | − | 0.474025i | \(-0.157199\pi\) | ||||
0.880511 | + | 0.474025i | \(0.157199\pi\) | |||||||
\(500\) | 6.23447 | 0.278814 | ||||||||
\(501\) | 9.86304 | 0.440648 | ||||||||
\(502\) | 35.9512 | 1.60458 | ||||||||
\(503\) | 35.8281 | 1.59749 | 0.798747 | − | 0.601667i | \(-0.205496\pi\) | ||||
0.798747 | + | 0.601667i | \(0.205496\pi\) | |||||||
\(504\) | −13.9121 | −0.619693 | ||||||||
\(505\) | −1.73301 | −0.0771181 | ||||||||
\(506\) | 21.5867 | 0.959645 | ||||||||
\(507\) | 16.5097 | 0.733221 | ||||||||
\(508\) | 11.0166 | 0.488783 | ||||||||
\(509\) | −0.332989 | −0.0147595 | −0.00737974 | − | 0.999973i | \(-0.502349\pi\) | ||||
−0.00737974 | + | 0.999973i | \(0.502349\pi\) | |||||||
\(510\) | −1.20710 | −0.0534514 | ||||||||
\(511\) | 25.4612 | 1.12634 | ||||||||
\(512\) | 22.4065 | 0.990237 | ||||||||
\(513\) | −4.48059 | −0.197823 | ||||||||
\(514\) | 20.5757 | 0.907554 | ||||||||
\(515\) | 1.06455 | 0.0469098 | ||||||||
\(516\) | −69.3653 | −3.05364 | ||||||||
\(517\) | 1.39848 | 0.0615049 | ||||||||
\(518\) | 35.4929 | 1.55947 | ||||||||
\(519\) | −2.85890 | −0.125492 | ||||||||
\(520\) | 1.33913 | 0.0587249 | ||||||||
\(521\) | 15.4969 | 0.678930 | 0.339465 | − | 0.940619i | \(-0.389754\pi\) | ||||
0.339465 | + | 0.940619i | \(0.389754\pi\) | |||||||
\(522\) | 11.7025 | 0.512203 | ||||||||
\(523\) | −15.5011 | −0.677816 | −0.338908 | − | 0.940820i | \(-0.610057\pi\) | ||||
−0.338908 | + | 0.940820i | \(0.610057\pi\) | |||||||
\(524\) | −64.7775 | −2.82982 | ||||||||
\(525\) | −14.9725 | −0.653452 | ||||||||
\(526\) | 14.5160 | 0.632928 | ||||||||
\(527\) | 10.0269 | 0.436779 | ||||||||
\(528\) | 21.6531 | 0.942331 | ||||||||
\(529\) | 17.4921 | 0.760525 | ||||||||
\(530\) | −1.02998 | −0.0447393 | ||||||||
\(531\) | 7.23093 | 0.313796 | ||||||||
\(532\) | 8.21341 | 0.356097 | ||||||||
\(533\) | 7.45435 | 0.322884 | ||||||||
\(534\) | −15.8674 | −0.686651 | ||||||||
\(535\) | 0.928457 | 0.0401407 | ||||||||
\(536\) | 60.1296 | 2.59720 | ||||||||
\(537\) | −31.7541 | −1.37029 | ||||||||
\(538\) | 13.3942 | 0.577463 | ||||||||
\(539\) | 3.61292 | 0.155620 | ||||||||
\(540\) | −3.52344 | −0.151625 | ||||||||
\(541\) | −26.0999 | −1.12212 | −0.561061 | − | 0.827774i | \(-0.689607\pi\) | ||||
−0.561061 | + | 0.827774i | \(0.689607\pi\) | |||||||
\(542\) | −75.4729 | −3.24184 | ||||||||
\(543\) | 6.26356 | 0.268795 | ||||||||
\(544\) | −35.9631 | −1.54191 | ||||||||
\(545\) | 1.32019 | 0.0565506 | ||||||||
\(546\) | −10.6437 | −0.455506 | ||||||||
\(547\) | −5.71922 | −0.244536 | −0.122268 | − | 0.992497i | \(-0.539017\pi\) | ||||
−0.122268 | + | 0.992497i | \(0.539017\pi\) | |||||||
\(548\) | 11.4035 | 0.487133 | ||||||||
\(549\) | 10.9339 | 0.466647 | ||||||||
\(550\) | −16.9102 | −0.721054 | ||||||||
\(551\) | −4.18146 | −0.178136 | ||||||||
\(552\) | 76.2977 | 3.24745 | ||||||||
\(553\) | −21.3149 | −0.906401 | ||||||||
\(554\) | 43.1213 | 1.83205 | ||||||||
\(555\) | 1.18562 | 0.0503269 | ||||||||
\(556\) | −111.113 | −4.71225 | ||||||||
\(557\) | 33.7544 | 1.43022 | 0.715110 | − | 0.699012i | \(-0.246377\pi\) | ||||
0.715110 | + | 0.699012i | \(0.246377\pi\) | |||||||
\(558\) | 8.89619 | 0.376606 | ||||||||
\(559\) | 12.4074 | 0.524776 | ||||||||
\(560\) | 2.90248 | 0.122652 | ||||||||
\(561\) | 4.70199 | 0.198518 | ||||||||
\(562\) | 28.3416 | 1.19552 | ||||||||
\(563\) | −33.3496 | −1.40552 | −0.702759 | − | 0.711428i | \(-0.748049\pi\) | ||||
−0.702759 | + | 0.711428i | \(0.748049\pi\) | |||||||
\(564\) | 8.16700 | 0.343893 | ||||||||
\(565\) | −0.717723 | −0.0301948 | ||||||||
\(566\) | 29.4445 | 1.23765 | ||||||||
\(567\) | 11.8287 | 0.496759 | ||||||||
\(568\) | −30.0369 | −1.26032 | ||||||||
\(569\) | 18.5066 | 0.775838 | 0.387919 | − | 0.921693i | \(-0.373194\pi\) | ||||
0.387919 | + | 0.921693i | \(0.373194\pi\) | |||||||
\(570\) | 0.382677 | 0.0160286 | ||||||||
\(571\) | −22.2615 | −0.931615 | −0.465808 | − | 0.884886i | \(-0.654236\pi\) | ||||
−0.465808 | + | 0.884886i | \(0.654236\pi\) | |||||||
\(572\) | −8.61872 | −0.360367 | ||||||||
\(573\) | −19.4731 | −0.813500 | ||||||||
\(574\) | 30.3503 | 1.26680 | ||||||||
\(575\) | −31.7200 | −1.32282 | ||||||||
\(576\) | −12.6237 | −0.525986 | ||||||||
\(577\) | −32.7314 | −1.36263 | −0.681313 | − | 0.731992i | \(-0.738591\pi\) | ||||
−0.681313 | + | 0.731992i | \(0.738591\pi\) | |||||||
\(578\) | 28.5146 | 1.18605 | ||||||||
\(579\) | −21.8491 | −0.908016 | ||||||||
\(580\) | −3.28820 | −0.136535 | ||||||||
\(581\) | 5.20661 | 0.216007 | ||||||||
\(582\) | 46.5236 | 1.92846 | ||||||||
\(583\) | 4.01203 | 0.166161 | ||||||||
\(584\) | 101.639 | 4.20585 | ||||||||
\(585\) | 0.137346 | 0.00567855 | ||||||||
\(586\) | −43.3108 | −1.78915 | ||||||||
\(587\) | −13.5519 | −0.559346 | −0.279673 | − | 0.960095i | \(-0.590226\pi\) | ||||
−0.279673 | + | 0.960095i | \(0.590226\pi\) | |||||||
\(588\) | 21.0992 | 0.870117 | ||||||||
\(589\) | −3.17874 | −0.130978 | ||||||||
\(590\) | −2.83387 | −0.116668 | ||||||||
\(591\) | −33.0150 | −1.35805 | ||||||||
\(592\) | 75.4253 | 3.09996 | ||||||||
\(593\) | −29.3196 | −1.20401 | −0.602006 | − | 0.798491i | \(-0.705632\pi\) | ||||
−0.602006 | + | 0.798491i | \(0.705632\pi\) | |||||||
\(594\) | 19.1429 | 0.785442 | ||||||||
\(595\) | 0.630276 | 0.0258388 | ||||||||
\(596\) | 89.1520 | 3.65181 | ||||||||
\(597\) | 15.3860 | 0.629705 | ||||||||
\(598\) | −22.5492 | −0.922105 | ||||||||
\(599\) | −33.1465 | −1.35433 | −0.677165 | − | 0.735831i | \(-0.736792\pi\) | ||||
−0.677165 | + | 0.735831i | \(0.736792\pi\) | |||||||
\(600\) | −59.7689 | −2.44006 | ||||||||
\(601\) | 0.0735303 | 0.00299936 | 0.00149968 | − | 0.999999i | \(-0.499523\pi\) | ||||
0.00149968 | + | 0.999999i | \(0.499523\pi\) | |||||||
\(602\) | 50.5164 | 2.05889 | ||||||||
\(603\) | 6.16708 | 0.251143 | ||||||||
\(604\) | −24.9852 | −1.01663 | ||||||||
\(605\) | 1.15500 | 0.0469574 | ||||||||
\(606\) | 54.9858 | 2.23364 | ||||||||
\(607\) | 19.8711 | 0.806542 | 0.403271 | − | 0.915081i | \(-0.367873\pi\) | ||||
0.403271 | + | 0.915081i | \(0.367873\pi\) | |||||||
\(608\) | 11.4010 | 0.462373 | ||||||||
\(609\) | 15.8177 | 0.640966 | ||||||||
\(610\) | −4.28509 | −0.173498 | ||||||||
\(611\) | −1.46083 | −0.0590989 | ||||||||
\(612\) | −10.6074 | −0.428779 | ||||||||
\(613\) | 21.7731 | 0.879409 | 0.439705 | − | 0.898142i | \(-0.355083\pi\) | ||||
0.439705 | + | 0.898142i | \(0.355083\pi\) | |||||||
\(614\) | 16.6408 | 0.671567 | ||||||||
\(615\) | 1.01383 | 0.0408817 | ||||||||
\(616\) | −21.2380 | −0.855704 | ||||||||
\(617\) | 18.1435 | 0.730430 | 0.365215 | − | 0.930923i | \(-0.380995\pi\) | ||||
0.365215 | + | 0.930923i | \(0.380995\pi\) | |||||||
\(618\) | −33.7766 | −1.35869 | ||||||||
\(619\) | 9.55638 | 0.384103 | 0.192052 | − | 0.981385i | \(-0.438486\pi\) | ||||
0.192052 | + | 0.981385i | \(0.438486\pi\) | |||||||
\(620\) | −2.49969 | −0.100390 | ||||||||
\(621\) | 35.9080 | 1.44094 | ||||||||
\(622\) | 16.8793 | 0.676799 | ||||||||
\(623\) | 8.28502 | 0.331932 | ||||||||
\(624\) | −22.6186 | −0.905468 | ||||||||
\(625\) | 24.7724 | 0.990895 | ||||||||
\(626\) | 32.9966 | 1.31881 | ||||||||
\(627\) | −1.49063 | −0.0595299 | ||||||||
\(628\) | 72.3920 | 2.88875 | ||||||||
\(629\) | 16.3786 | 0.653059 | ||||||||
\(630\) | 0.559201 | 0.0222791 | ||||||||
\(631\) | −5.80640 | −0.231149 | −0.115575 | − | 0.993299i | \(-0.536871\pi\) | ||||
−0.115575 | + | 0.993299i | \(0.536871\pi\) | |||||||
\(632\) | −85.0873 | −3.38459 | ||||||||
\(633\) | 17.9579 | 0.713761 | ||||||||
\(634\) | 33.9390 | 1.34789 | ||||||||
\(635\) | −0.268005 | −0.0106354 | ||||||||
\(636\) | 23.4300 | 0.929059 | ||||||||
\(637\) | −3.77401 | −0.149532 | ||||||||
\(638\) | 17.8648 | 0.707276 | ||||||||
\(639\) | −3.08068 | −0.121870 | ||||||||
\(640\) | 1.40798 | 0.0556553 | ||||||||
\(641\) | 21.8923 | 0.864694 | 0.432347 | − | 0.901707i | \(-0.357686\pi\) | ||||
0.432347 | + | 0.901707i | \(0.357686\pi\) | |||||||
\(642\) | −29.4585 | −1.16263 | ||||||||
\(643\) | 33.3216 | 1.31408 | 0.657038 | − | 0.753858i | \(-0.271809\pi\) | ||||
0.657038 | + | 0.753858i | \(0.271809\pi\) | |||||||
\(644\) | −65.8233 | −2.59380 | ||||||||
\(645\) | 1.68747 | 0.0664442 | ||||||||
\(646\) | 5.28644 | 0.207992 | ||||||||
\(647\) | −29.5283 | −1.16088 | −0.580438 | − | 0.814305i | \(-0.697119\pi\) | ||||
−0.580438 | + | 0.814305i | \(0.697119\pi\) | |||||||
\(648\) | 47.2193 | 1.85495 | ||||||||
\(649\) | 11.0387 | 0.433305 | ||||||||
\(650\) | 17.6642 | 0.692848 | ||||||||
\(651\) | 12.0246 | 0.471281 | ||||||||
\(652\) | 115.947 | 4.54083 | ||||||||
\(653\) | 38.6693 | 1.51325 | 0.756624 | − | 0.653850i | \(-0.226847\pi\) | ||||
0.756624 | + | 0.653850i | \(0.226847\pi\) | |||||||
\(654\) | −41.8874 | −1.63793 | ||||||||
\(655\) | 1.57587 | 0.0615742 | ||||||||
\(656\) | 64.4967 | 2.51817 | ||||||||
\(657\) | 10.4244 | 0.406695 | ||||||||
\(658\) | −5.94775 | −0.231867 | ||||||||
\(659\) | −14.2591 | −0.555456 | −0.277728 | − | 0.960660i | \(-0.589581\pi\) | ||||
−0.277728 | + | 0.960660i | \(0.589581\pi\) | |||||||
\(660\) | −1.17220 | −0.0456277 | ||||||||
\(661\) | −21.4216 | −0.833202 | −0.416601 | − | 0.909089i | \(-0.636779\pi\) | ||||
−0.416601 | + | 0.909089i | \(0.636779\pi\) | |||||||
\(662\) | −34.4681 | −1.33964 | ||||||||
\(663\) | −4.91164 | −0.190752 | ||||||||
\(664\) | 20.7844 | 0.806591 | ||||||||
\(665\) | −0.199811 | −0.00774832 | ||||||||
\(666\) | 14.5317 | 0.563090 | ||||||||
\(667\) | 33.5107 | 1.29754 | ||||||||
\(668\) | −33.9673 | −1.31423 | ||||||||
\(669\) | −5.87081 | −0.226979 | ||||||||
\(670\) | −2.41693 | −0.0933743 | ||||||||
\(671\) | 16.6916 | 0.644370 | ||||||||
\(672\) | −43.1281 | −1.66370 | ||||||||
\(673\) | 5.83221 | 0.224815 | 0.112408 | − | 0.993662i | \(-0.464144\pi\) | ||||
0.112408 | + | 0.993662i | \(0.464144\pi\) | |||||||
\(674\) | −80.3730 | −3.09585 | ||||||||
\(675\) | −28.1291 | −1.08269 | ||||||||
\(676\) | −56.8576 | −2.18683 | ||||||||
\(677\) | −2.33503 | −0.0897423 | −0.0448712 | − | 0.998993i | \(-0.514288\pi\) | ||||
−0.0448712 | + | 0.998993i | \(0.514288\pi\) | |||||||
\(678\) | 22.7722 | 0.874561 | ||||||||
\(679\) | −24.2918 | −0.932233 | ||||||||
\(680\) | 2.51601 | 0.0964847 | ||||||||
\(681\) | −34.0811 | −1.30599 | ||||||||
\(682\) | 13.5808 | 0.520037 | ||||||||
\(683\) | 17.6777 | 0.676419 | 0.338209 | − | 0.941071i | \(-0.390179\pi\) | ||||
0.338209 | + | 0.941071i | \(0.390179\pi\) | |||||||
\(684\) | 3.36277 | 0.128579 | ||||||||
\(685\) | −0.277416 | −0.0105995 | ||||||||
\(686\) | −53.3588 | −2.03725 | ||||||||
\(687\) | 21.4593 | 0.818723 | ||||||||
\(688\) | 107.351 | 4.09273 | ||||||||
\(689\) | −4.19092 | −0.159661 | ||||||||
\(690\) | −3.06682 | −0.116752 | ||||||||
\(691\) | 25.8715 | 0.984200 | 0.492100 | − | 0.870539i | \(-0.336229\pi\) | ||||
0.492100 | + | 0.870539i | \(0.336229\pi\) | |||||||
\(692\) | 9.84575 | 0.374279 | ||||||||
\(693\) | −2.17824 | −0.0827444 | ||||||||
\(694\) | −19.0871 | −0.724535 | ||||||||
\(695\) | 2.70309 | 0.102534 | ||||||||
\(696\) | 63.1430 | 2.39343 | ||||||||
\(697\) | 14.0055 | 0.530496 | ||||||||
\(698\) | −69.3866 | −2.62632 | ||||||||
\(699\) | 32.4243 | 1.22640 | ||||||||
\(700\) | 51.5636 | 1.94892 | ||||||||
\(701\) | −31.4019 | −1.18603 | −0.593017 | − | 0.805190i | \(-0.702063\pi\) | ||||
−0.593017 | + | 0.805190i | \(0.702063\pi\) | |||||||
\(702\) | −19.9964 | −0.754717 | ||||||||
\(703\) | −5.19237 | −0.195834 | ||||||||
\(704\) | −19.2712 | −0.726309 | ||||||||
\(705\) | −0.198681 | −0.00748277 | ||||||||
\(706\) | 10.0688 | 0.378946 | ||||||||
\(707\) | −28.7102 | −1.07976 | ||||||||
\(708\) | 64.4650 | 2.42274 | ||||||||
\(709\) | 4.68375 | 0.175902 | 0.0879509 | − | 0.996125i | \(-0.471968\pi\) | ||||
0.0879509 | + | 0.996125i | \(0.471968\pi\) | |||||||
\(710\) | 1.20735 | 0.0453109 | ||||||||
\(711\) | −8.72683 | −0.327282 | ||||||||
\(712\) | 33.0731 | 1.23947 | ||||||||
\(713\) | 25.4748 | 0.954038 | ||||||||
\(714\) | −19.9977 | −0.748394 | ||||||||
\(715\) | 0.209671 | 0.00784124 | ||||||||
\(716\) | 109.358 | 4.08689 | ||||||||
\(717\) | 4.37635 | 0.163438 | ||||||||
\(718\) | −80.1593 | −2.99152 | ||||||||
\(719\) | 40.1197 | 1.49621 | 0.748106 | − | 0.663580i | \(-0.230964\pi\) | ||||
0.748106 | + | 0.663580i | \(0.230964\pi\) | |||||||
\(720\) | 1.18835 | 0.0442871 | ||||||||
\(721\) | 17.6361 | 0.656802 | ||||||||
\(722\) | 48.8305 | 1.81728 | ||||||||
\(723\) | 10.2608 | 0.381605 | ||||||||
\(724\) | −21.5711 | −0.801682 | ||||||||
\(725\) | −26.2511 | −0.974941 | ||||||||
\(726\) | −36.6463 | −1.36007 | ||||||||
\(727\) | 19.5640 | 0.725589 | 0.362794 | − | 0.931869i | \(-0.381823\pi\) | ||||
0.362794 | + | 0.931869i | \(0.381823\pi\) | |||||||
\(728\) | 22.1850 | 0.822230 | ||||||||
\(729\) | 29.7465 | 1.10172 | ||||||||
\(730\) | −4.08542 | −0.151208 | ||||||||
\(731\) | 23.3114 | 0.862203 | ||||||||
\(732\) | 97.4775 | 3.60287 | ||||||||
\(733\) | −15.5232 | −0.573361 | −0.286681 | − | 0.958026i | \(-0.592552\pi\) | ||||
−0.286681 | + | 0.958026i | \(0.592552\pi\) | |||||||
\(734\) | 5.70167 | 0.210453 | ||||||||
\(735\) | −0.513288 | −0.0189329 | ||||||||
\(736\) | −91.3694 | −3.36792 | ||||||||
\(737\) | 9.41460 | 0.346791 | ||||||||
\(738\) | 12.4261 | 0.457412 | ||||||||
\(739\) | −36.0840 | −1.32737 | −0.663686 | − | 0.748012i | \(-0.731009\pi\) | ||||
−0.663686 | + | 0.748012i | \(0.731009\pi\) | |||||||
\(740\) | −4.08316 | −0.150100 | ||||||||
\(741\) | 1.55709 | 0.0572012 | ||||||||
\(742\) | −17.0633 | −0.626412 | ||||||||
\(743\) | 6.71066 | 0.246190 | 0.123095 | − | 0.992395i | \(-0.460718\pi\) | ||||
0.123095 | + | 0.992395i | \(0.460718\pi\) | |||||||
\(744\) | 48.0012 | 1.75981 | ||||||||
\(745\) | −2.16883 | −0.0794598 | ||||||||
\(746\) | 46.3400 | 1.69663 | ||||||||
\(747\) | 2.13171 | 0.0779953 | ||||||||
\(748\) | −16.1932 | −0.592081 | ||||||||
\(749\) | 15.3814 | 0.562025 | ||||||||
\(750\) | 4.81219 | 0.175716 | ||||||||
\(751\) | 46.0707 | 1.68114 | 0.840571 | − | 0.541701i | \(-0.182219\pi\) | ||||
0.840571 | + | 0.541701i | \(0.182219\pi\) | |||||||
\(752\) | −12.6394 | −0.460913 | ||||||||
\(753\) | 19.8954 | 0.725030 | ||||||||
\(754\) | −18.6614 | −0.679608 | ||||||||
\(755\) | 0.607823 | 0.0221209 | ||||||||
\(756\) | −58.3716 | −2.12295 | ||||||||
\(757\) | 2.24877 | 0.0817329 | 0.0408664 | − | 0.999165i | \(-0.486988\pi\) | ||||
0.0408664 | + | 0.999165i | \(0.486988\pi\) | |||||||
\(758\) | −39.3872 | −1.43061 | ||||||||
\(759\) | 11.9461 | 0.433615 | ||||||||
\(760\) | −0.797628 | −0.0289330 | ||||||||
\(761\) | 31.9562 | 1.15841 | 0.579206 | − | 0.815181i | \(-0.303363\pi\) | ||||
0.579206 | + | 0.815181i | \(0.303363\pi\) | |||||||
\(762\) | 8.50337 | 0.308044 | ||||||||
\(763\) | 21.8711 | 0.791786 | ||||||||
\(764\) | 67.0633 | 2.42626 | ||||||||
\(765\) | 0.258050 | 0.00932983 | ||||||||
\(766\) | −85.2498 | −3.08020 | ||||||||
\(767\) | −11.5309 | −0.416355 | ||||||||
\(768\) | −0.244338 | −0.00881679 | ||||||||
\(769\) | 2.48880 | 0.0897486 | 0.0448743 | − | 0.998993i | \(-0.485711\pi\) | ||||
0.0448743 | + | 0.998993i | \(0.485711\pi\) | |||||||
\(770\) | 0.853670 | 0.0307641 | ||||||||
\(771\) | 11.3866 | 0.410078 | ||||||||
\(772\) | 75.2459 | 2.70816 | ||||||||
\(773\) | −2.76538 | −0.0994638 | −0.0497319 | − | 0.998763i | \(-0.515837\pi\) | ||||
−0.0497319 | + | 0.998763i | \(0.515837\pi\) | |||||||
\(774\) | 20.6826 | 0.743421 | ||||||||
\(775\) | −19.9560 | −0.716842 | ||||||||
\(776\) | −96.9709 | −3.48105 | ||||||||
\(777\) | 19.6418 | 0.704646 | ||||||||
\(778\) | 80.8550 | 2.89879 | ||||||||
\(779\) | −4.44003 | −0.159081 | ||||||||
\(780\) | 1.22446 | 0.0438428 | ||||||||
\(781\) | −4.70293 | −0.168284 | ||||||||
\(782\) | −42.3662 | −1.51501 | ||||||||
\(783\) | 29.7170 | 1.06200 | ||||||||
\(784\) | −32.6536 | −1.16620 | ||||||||
\(785\) | −1.76110 | −0.0628565 | ||||||||
\(786\) | −49.9997 | −1.78343 | ||||||||
\(787\) | −21.0935 | −0.751900 | −0.375950 | − | 0.926640i | \(-0.622684\pi\) | ||||
−0.375950 | + | 0.926640i | \(0.622684\pi\) | |||||||
\(788\) | 113.700 | 4.05040 | ||||||||
\(789\) | 8.03316 | 0.285988 | ||||||||
\(790\) | 3.42012 | 0.121682 | ||||||||
\(791\) | −11.8903 | −0.422769 | ||||||||
\(792\) | −8.69535 | −0.308976 | ||||||||
\(793\) | −17.4358 | −0.619163 | ||||||||
\(794\) | −81.4247 | −2.88966 | ||||||||
\(795\) | −0.569989 | −0.0202154 | ||||||||
\(796\) | −52.9876 | −1.87810 | ||||||||
\(797\) | 33.5808 | 1.18949 | 0.594747 | − | 0.803913i | \(-0.297252\pi\) | ||||
0.594747 | + | 0.803913i | \(0.297252\pi\) | |||||||
\(798\) | 6.33967 | 0.224422 | ||||||||
\(799\) | −2.74466 | −0.0970991 | ||||||||
\(800\) | 71.5755 | 2.53058 | ||||||||
\(801\) | 3.39209 | 0.119853 | ||||||||
\(802\) | −34.1442 | −1.20567 | ||||||||
\(803\) | 15.9138 | 0.561586 | ||||||||
\(804\) | 54.9806 | 1.93902 | ||||||||
\(805\) | 1.60131 | 0.0564386 | ||||||||
\(806\) | −14.1864 | −0.499694 | ||||||||
\(807\) | 7.41234 | 0.260927 | ||||||||
\(808\) | −114.609 | −4.03193 | ||||||||
\(809\) | −17.8743 | −0.628429 | −0.314214 | − | 0.949352i | \(-0.601741\pi\) | ||||
−0.314214 | + | 0.949352i | \(0.601741\pi\) | |||||||
\(810\) | −1.89800 | −0.0666888 | ||||||||
\(811\) | 28.5801 | 1.00358 | 0.501791 | − | 0.864989i | \(-0.332674\pi\) | ||||
0.501791 | + | 0.864989i | \(0.332674\pi\) | |||||||
\(812\) | −54.4745 | −1.91168 | ||||||||
\(813\) | −41.7667 | −1.46482 | ||||||||
\(814\) | 22.1839 | 0.777544 | ||||||||
\(815\) | −2.82068 | −0.0988041 | ||||||||
\(816\) | −42.4966 | −1.48768 | ||||||||
\(817\) | −7.39019 | −0.258550 | ||||||||
\(818\) | 93.8900 | 3.28279 | ||||||||
\(819\) | 2.27536 | 0.0795076 | ||||||||
\(820\) | −3.49154 | −0.121930 | ||||||||
\(821\) | −47.7934 | −1.66800 | −0.834000 | − | 0.551764i | \(-0.813955\pi\) | ||||
−0.834000 | + | 0.551764i | \(0.813955\pi\) | |||||||
\(822\) | 8.80198 | 0.307004 | ||||||||
\(823\) | −24.8377 | −0.865788 | −0.432894 | − | 0.901445i | \(-0.642508\pi\) | ||||
−0.432894 | + | 0.901445i | \(0.642508\pi\) | |||||||
\(824\) | 70.4018 | 2.45256 | ||||||||
\(825\) | −9.35813 | −0.325808 | ||||||||
\(826\) | −46.9477 | −1.63352 | ||||||||
\(827\) | −4.72241 | −0.164214 | −0.0821072 | − | 0.996624i | \(-0.526165\pi\) | ||||
−0.0821072 | + | 0.996624i | \(0.526165\pi\) | |||||||
\(828\) | −26.9496 | −0.936565 | ||||||||
\(829\) | 2.58244 | 0.0896918 | 0.0448459 | − | 0.998994i | \(-0.485720\pi\) | ||||
0.0448459 | + | 0.998994i | \(0.485720\pi\) | |||||||
\(830\) | −0.835437 | −0.0289984 | ||||||||
\(831\) | 23.8634 | 0.827811 | ||||||||
\(832\) | 20.1304 | 0.697897 | ||||||||
\(833\) | −7.09075 | −0.245680 | ||||||||
\(834\) | −85.7648 | −2.96979 | ||||||||
\(835\) | 0.826334 | 0.0285965 | ||||||||
\(836\) | 5.13357 | 0.177548 | ||||||||
\(837\) | 22.5908 | 0.780853 | ||||||||
\(838\) | 34.6606 | 1.19733 | ||||||||
\(839\) | 27.9234 | 0.964024 | 0.482012 | − | 0.876165i | \(-0.339906\pi\) | ||||
0.482012 | + | 0.876165i | \(0.339906\pi\) | |||||||
\(840\) | 3.01728 | 0.104106 | ||||||||
\(841\) | −1.26698 | −0.0436888 | ||||||||
\(842\) | 40.0602 | 1.38056 | ||||||||
\(843\) | 15.6843 | 0.540195 | ||||||||
\(844\) | −61.8450 | −2.12879 | ||||||||
\(845\) | 1.38320 | 0.0475834 | ||||||||
\(846\) | −2.43515 | −0.0837222 | ||||||||
\(847\) | 19.1345 | 0.657468 | ||||||||
\(848\) | −36.2608 | −1.24520 | ||||||||
\(849\) | 16.2946 | 0.559230 | ||||||||
\(850\) | 33.1882 | 1.13834 | ||||||||
\(851\) | 41.6123 | 1.42645 | ||||||||
\(852\) | −27.4648 | −0.940929 | ||||||||
\(853\) | 51.7741 | 1.77271 | 0.886355 | − | 0.463006i | \(-0.153229\pi\) | ||||
0.886355 | + | 0.463006i | \(0.153229\pi\) | |||||||
\(854\) | −70.9895 | −2.42921 | ||||||||
\(855\) | −0.0818072 | −0.00279775 | ||||||||
\(856\) | 61.4014 | 2.09866 | ||||||||
\(857\) | 53.7137 | 1.83482 | 0.917412 | − | 0.397939i | \(-0.130275\pi\) | ||||
0.917412 | + | 0.397939i | \(0.130275\pi\) | |||||||
\(858\) | −6.65252 | −0.227113 | ||||||||
\(859\) | −1.73783 | −0.0592941 | −0.0296471 | − | 0.999560i | \(-0.509438\pi\) | ||||
−0.0296471 | + | 0.999560i | \(0.509438\pi\) | |||||||
\(860\) | −5.81148 | −0.198170 | ||||||||
\(861\) | 16.7958 | 0.572401 | ||||||||
\(862\) | −94.0105 | −3.20201 | ||||||||
\(863\) | −52.7174 | −1.79452 | −0.897260 | − | 0.441502i | \(-0.854446\pi\) | ||||
−0.897260 | + | 0.441502i | \(0.854446\pi\) | |||||||
\(864\) | −81.0256 | −2.75655 | ||||||||
\(865\) | −0.239521 | −0.00814396 | ||||||||
\(866\) | 75.9703 | 2.58158 | ||||||||
\(867\) | 15.7800 | 0.535916 | ||||||||
\(868\) | −41.4114 | −1.40560 | ||||||||
\(869\) | −13.3223 | −0.451927 | ||||||||
\(870\) | −2.53806 | −0.0860482 | ||||||||
\(871\) | −9.83438 | −0.333225 | ||||||||
\(872\) | 87.3075 | 2.95661 | ||||||||
\(873\) | −9.94564 | −0.336609 | ||||||||
\(874\) | 13.4310 | 0.454309 | ||||||||
\(875\) | −2.51263 | −0.0849426 | ||||||||
\(876\) | 92.9355 | 3.14000 | ||||||||
\(877\) | 40.5530 | 1.36938 | 0.684689 | − | 0.728836i | \(-0.259938\pi\) | ||||
0.684689 | + | 0.728836i | \(0.259938\pi\) | |||||||
\(878\) | −101.501 | −3.42549 | ||||||||
\(879\) | −23.9682 | −0.808429 | ||||||||
\(880\) | 1.81412 | 0.0611539 | ||||||||
\(881\) | −27.5684 | −0.928802 | −0.464401 | − | 0.885625i | \(-0.653730\pi\) | ||||
−0.464401 | + | 0.885625i | \(0.653730\pi\) | |||||||
\(882\) | −6.29114 | −0.211834 | ||||||||
\(883\) | 25.7517 | 0.866614 | 0.433307 | − | 0.901246i | \(-0.357347\pi\) | ||||
0.433307 | + | 0.901246i | \(0.357347\pi\) | |||||||
\(884\) | 16.9152 | 0.568919 | ||||||||
\(885\) | −1.56826 | −0.0527166 | ||||||||
\(886\) | −104.186 | −3.50018 | ||||||||
\(887\) | −24.6468 | −0.827560 | −0.413780 | − | 0.910377i | \(-0.635792\pi\) | ||||
−0.413780 | + | 0.910377i | \(0.635792\pi\) | |||||||
\(888\) | 78.4085 | 2.63122 | ||||||||
\(889\) | −4.43994 | −0.148911 | ||||||||
\(890\) | −1.32939 | −0.0445612 | ||||||||
\(891\) | 7.39321 | 0.247682 | ||||||||
\(892\) | 20.2185 | 0.676964 | ||||||||
\(893\) | 0.870114 | 0.0291173 | ||||||||
\(894\) | 68.8136 | 2.30147 | ||||||||
\(895\) | −2.66039 | −0.0889269 | ||||||||
\(896\) | 23.3255 | 0.779250 | ||||||||
\(897\) | −12.4787 | −0.416653 | ||||||||
\(898\) | −38.4679 | −1.28369 | ||||||||
\(899\) | 21.0826 | 0.703144 | ||||||||
\(900\) | 21.1114 | 0.703713 | ||||||||
\(901\) | −7.87405 | −0.262323 | ||||||||
\(902\) | 18.9696 | 0.631618 | ||||||||
\(903\) | 27.9558 | 0.930310 | ||||||||
\(904\) | −47.4650 | −1.57866 | ||||||||
\(905\) | 0.524767 | 0.0174438 | ||||||||
\(906\) | −19.2852 | −0.640709 | ||||||||
\(907\) | −44.2748 | −1.47012 | −0.735060 | − | 0.678002i | \(-0.762846\pi\) | ||||
−0.735060 | + | 0.678002i | \(0.762846\pi\) | |||||||
\(908\) | 117.372 | 3.89512 | ||||||||
\(909\) | −11.7547 | −0.389877 | ||||||||
\(910\) | −0.891734 | −0.0295607 | ||||||||
\(911\) | −22.9975 | −0.761941 | −0.380971 | − | 0.924587i | \(-0.624410\pi\) | ||||
−0.380971 | + | 0.924587i | \(0.624410\pi\) | |||||||
\(912\) | 13.4723 | 0.446113 | ||||||||
\(913\) | 3.25425 | 0.107700 | ||||||||
\(914\) | 5.94790 | 0.196739 | ||||||||
\(915\) | −2.37137 | −0.0783950 | ||||||||
\(916\) | −73.9035 | −2.44184 | ||||||||
\(917\) | 26.1068 | 0.862123 | ||||||||
\(918\) | −37.5700 | −1.23999 | ||||||||
\(919\) | 35.6080 | 1.17460 | 0.587300 | − | 0.809369i | \(-0.300191\pi\) | ||||
0.587300 | + | 0.809369i | \(0.300191\pi\) | |||||||
\(920\) | 6.39229 | 0.210747 | ||||||||
\(921\) | 9.20902 | 0.303447 | ||||||||
\(922\) | 12.6658 | 0.417125 | ||||||||
\(923\) | 4.91263 | 0.161701 | ||||||||
\(924\) | −19.4194 | −0.638850 | ||||||||
\(925\) | −32.5976 | −1.07180 | ||||||||
\(926\) | 53.6874 | 1.76428 | ||||||||
\(927\) | 7.22063 | 0.237157 | ||||||||
\(928\) | −75.6161 | −2.48222 | ||||||||
\(929\) | −36.3221 | −1.19169 | −0.595845 | − | 0.803099i | \(-0.703183\pi\) | ||||
−0.595845 | + | 0.803099i | \(0.703183\pi\) | |||||||
\(930\) | −1.92943 | −0.0632684 | ||||||||
\(931\) | 2.24791 | 0.0736724 | ||||||||
\(932\) | −111.666 | −3.65774 | ||||||||
\(933\) | 9.34103 | 0.305812 | ||||||||
\(934\) | −51.9653 | −1.70036 | ||||||||
\(935\) | 0.393937 | 0.0128831 | ||||||||
\(936\) | 9.08306 | 0.296889 | ||||||||
\(937\) | −3.50674 | −0.114560 | −0.0572801 | − | 0.998358i | \(-0.518243\pi\) | ||||
−0.0572801 | + | 0.998358i | \(0.518243\pi\) | |||||||
\(938\) | −40.0405 | −1.30737 | ||||||||
\(939\) | 18.2603 | 0.595904 | ||||||||
\(940\) | 0.684238 | 0.0223174 | ||||||||
\(941\) | 26.7201 | 0.871050 | 0.435525 | − | 0.900177i | \(-0.356563\pi\) | ||||
0.435525 | + | 0.900177i | \(0.356563\pi\) | |||||||
\(942\) | 55.8771 | 1.82057 | ||||||||
\(943\) | 35.5830 | 1.15874 | ||||||||
\(944\) | −99.7675 | −3.24716 | ||||||||
\(945\) | 1.42003 | 0.0461934 | ||||||||
\(946\) | 31.5738 | 1.02655 | ||||||||
\(947\) | −18.8544 | −0.612687 | −0.306344 | − | 0.951921i | \(-0.599106\pi\) | ||||
−0.306344 | + | 0.951921i | \(0.599106\pi\) | |||||||
\(948\) | −77.8012 | −2.52686 | ||||||||
\(949\) | −16.6234 | −0.539618 | ||||||||
\(950\) | −10.5213 | −0.341357 | ||||||||
\(951\) | 18.7819 | 0.609044 | ||||||||
\(952\) | 41.6819 | 1.35092 | ||||||||
\(953\) | −48.0782 | −1.55741 | −0.778703 | − | 0.627393i | \(-0.784122\pi\) | ||||
−0.778703 | + | 0.627393i | \(0.784122\pi\) | |||||||
\(954\) | −6.98610 | −0.226183 | ||||||||
\(955\) | −1.63147 | −0.0527932 | ||||||||
\(956\) | −15.0717 | −0.487453 | ||||||||
\(957\) | 9.88642 | 0.319582 | ||||||||
\(958\) | 2.60304 | 0.0841004 | ||||||||
\(959\) | −4.59586 | −0.148408 | ||||||||
\(960\) | 2.73785 | 0.0883638 | ||||||||
\(961\) | −14.9730 | −0.483001 | ||||||||
\(962\) | −23.1730 | −0.747128 | ||||||||
\(963\) | 6.29752 | 0.202935 | ||||||||
\(964\) | −35.3373 | −1.13814 | ||||||||
\(965\) | −1.83053 | −0.0589270 | ||||||||
\(966\) | −50.8069 | −1.63469 | ||||||||
\(967\) | 20.2183 | 0.650176 | 0.325088 | − | 0.945684i | \(-0.394606\pi\) | ||||
0.325088 | + | 0.945684i | \(0.394606\pi\) | |||||||
\(968\) | 76.3833 | 2.45505 | ||||||||
\(969\) | 2.92552 | 0.0939812 | ||||||||
\(970\) | 3.89778 | 0.125150 | ||||||||
\(971\) | −15.5725 | −0.499746 | −0.249873 | − | 0.968279i | \(-0.580389\pi\) | ||||
−0.249873 | + | 0.968279i | \(0.580389\pi\) | |||||||
\(972\) | −42.5893 | −1.36605 | ||||||||
\(973\) | 44.7812 | 1.43562 | ||||||||
\(974\) | −74.1097 | −2.37463 | ||||||||
\(975\) | 9.77539 | 0.313063 | ||||||||
\(976\) | −150.858 | −4.82886 | ||||||||
\(977\) | −19.1176 | −0.611626 | −0.305813 | − | 0.952092i | \(-0.598928\pi\) | ||||
−0.305813 | + | 0.952092i | \(0.598928\pi\) | |||||||
\(978\) | 89.4957 | 2.86176 | ||||||||
\(979\) | 5.17832 | 0.165500 | ||||||||
\(980\) | 1.76771 | 0.0564674 | ||||||||
\(981\) | 8.95454 | 0.285896 | ||||||||
\(982\) | 9.89013 | 0.315607 | ||||||||
\(983\) | −16.1669 | −0.515644 | −0.257822 | − | 0.966192i | \(-0.583005\pi\) | ||||
−0.257822 | + | 0.966192i | \(0.583005\pi\) | |||||||
\(984\) | 67.0477 | 2.13740 | ||||||||
\(985\) | −2.76602 | −0.0881328 | ||||||||
\(986\) | −35.0617 | −1.11659 | ||||||||
\(987\) | −3.29149 | −0.104769 | ||||||||
\(988\) | −5.36246 | −0.170603 | ||||||||
\(989\) | 59.2259 | 1.88327 | ||||||||
\(990\) | 0.349513 | 0.0111083 | ||||||||
\(991\) | −20.5614 | −0.653153 | −0.326576 | − | 0.945171i | \(-0.605895\pi\) | ||||
−0.326576 | + | 0.945171i | \(0.605895\pi\) | |||||||
\(992\) | −57.4832 | −1.82509 | ||||||||
\(993\) | −19.0746 | −0.605315 | ||||||||
\(994\) | 20.0017 | 0.634415 | ||||||||
\(995\) | 1.28905 | 0.0408656 | ||||||||
\(996\) | 19.0046 | 0.602183 | ||||||||
\(997\) | 4.38677 | 0.138930 | 0.0694652 | − | 0.997584i | \(-0.477871\pi\) | ||||
0.0694652 | + | 0.997584i | \(0.477871\pi\) | |||||||
\(998\) | −104.570 | −3.31011 | ||||||||
\(999\) | 36.9014 | 1.16751 |
(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 | 6037.2.a.b.1.3 | ✓ | 259 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6037.2.a.b.1.3 | ✓ | 259 | 1.1 | even | 1 | trivial |