Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [177,4,Mod(1,177)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(177, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("177.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 177 = 3 \cdot 59 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 177.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: | \(10.4433380710\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 2x^{7} - 45x^{6} + 47x^{5} + 654x^{4} - 157x^{3} - 2898x^{2} + 96x + 2432 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(4.77847\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 177.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −3.77847 | −1.33589 | −0.667945 | − | 0.744211i | \(-0.732826\pi\) | ||||
−0.667945 | + | 0.744211i | \(0.732826\pi\) | |||||||
\(3\) | 3.00000 | 0.577350 | ||||||||
\(4\) | 6.27681 | 0.784601 | ||||||||
\(5\) | −5.74283 | −0.513655 | −0.256827 | − | 0.966457i | \(-0.582677\pi\) | ||||
−0.256827 | + | 0.966457i | \(0.582677\pi\) | |||||||
\(6\) | −11.3354 | −0.771276 | ||||||||
\(7\) | −24.4226 | −1.31870 | −0.659348 | − | 0.751838i | \(-0.729168\pi\) | ||||
−0.659348 | + | 0.751838i | \(0.729168\pi\) | |||||||
\(8\) | 6.51103 | 0.287749 | ||||||||
\(9\) | 9.00000 | 0.333333 | ||||||||
\(10\) | 21.6991 | 0.686186 | ||||||||
\(11\) | 9.31943 | 0.255447 | 0.127723 | − | 0.991810i | \(-0.459233\pi\) | ||||
0.127723 | + | 0.991810i | \(0.459233\pi\) | |||||||
\(12\) | 18.8304 | 0.452990 | ||||||||
\(13\) | 17.0721 | 0.364227 | 0.182114 | − | 0.983277i | \(-0.441706\pi\) | ||||
0.182114 | + | 0.983277i | \(0.441706\pi\) | |||||||
\(14\) | 92.2799 | 1.76163 | ||||||||
\(15\) | −17.2285 | −0.296559 | ||||||||
\(16\) | −74.8162 | −1.16900 | ||||||||
\(17\) | 19.6787 | 0.280752 | 0.140376 | − | 0.990098i | \(-0.455169\pi\) | ||||
0.140376 | + | 0.990098i | \(0.455169\pi\) | |||||||
\(18\) | −34.0062 | −0.445297 | ||||||||
\(19\) | −15.1270 | −0.182651 | −0.0913256 | − | 0.995821i | \(-0.529110\pi\) | ||||
−0.0913256 | + | 0.995821i | \(0.529110\pi\) | |||||||
\(20\) | −36.0466 | −0.403014 | ||||||||
\(21\) | −73.2678 | −0.761349 | ||||||||
\(22\) | −35.2132 | −0.341249 | ||||||||
\(23\) | 108.469 | 0.983367 | 0.491683 | − | 0.870774i | \(-0.336382\pi\) | ||||
0.491683 | + | 0.870774i | \(0.336382\pi\) | |||||||
\(24\) | 19.5331 | 0.166132 | ||||||||
\(25\) | −92.0199 | −0.736159 | ||||||||
\(26\) | −64.5065 | −0.486568 | ||||||||
\(27\) | 27.0000 | 0.192450 | ||||||||
\(28\) | −153.296 | −1.03465 | ||||||||
\(29\) | 237.137 | 1.51846 | 0.759228 | − | 0.650825i | \(-0.225577\pi\) | ||||
0.759228 | + | 0.650825i | \(0.225577\pi\) | |||||||
\(30\) | 65.0973 | 0.396169 | ||||||||
\(31\) | 184.628 | 1.06968 | 0.534841 | − | 0.844953i | \(-0.320372\pi\) | ||||
0.534841 | + | 0.844953i | \(0.320372\pi\) | |||||||
\(32\) | 230.602 | 1.27391 | ||||||||
\(33\) | 27.9583 | 0.147482 | ||||||||
\(34\) | −74.3553 | −0.375054 | ||||||||
\(35\) | 140.255 | 0.677354 | ||||||||
\(36\) | 56.4913 | 0.261534 | ||||||||
\(37\) | 155.472 | 0.690795 | 0.345398 | − | 0.938456i | \(-0.387744\pi\) | ||||
0.345398 | + | 0.938456i | \(0.387744\pi\) | |||||||
\(38\) | 57.1569 | 0.244002 | ||||||||
\(39\) | 51.2164 | 0.210287 | ||||||||
\(40\) | −37.3917 | −0.147804 | ||||||||
\(41\) | 261.745 | 0.997019 | 0.498509 | − | 0.866884i | \(-0.333881\pi\) | ||||
0.498509 | + | 0.866884i | \(0.333881\pi\) | |||||||
\(42\) | 276.840 | 1.01708 | ||||||||
\(43\) | 127.647 | 0.452697 | 0.226349 | − | 0.974046i | \(-0.427321\pi\) | ||||
0.226349 | + | 0.974046i | \(0.427321\pi\) | |||||||
\(44\) | 58.4963 | 0.200424 | ||||||||
\(45\) | −51.6855 | −0.171218 | ||||||||
\(46\) | −409.848 | −1.31367 | ||||||||
\(47\) | 555.816 | 1.72498 | 0.862490 | − | 0.506075i | \(-0.168904\pi\) | ||||
0.862490 | + | 0.506075i | \(0.168904\pi\) | |||||||
\(48\) | −224.448 | −0.674924 | ||||||||
\(49\) | 253.463 | 0.738959 | ||||||||
\(50\) | 347.694 | 0.983427 | ||||||||
\(51\) | 59.0361 | 0.162092 | ||||||||
\(52\) | 107.158 | 0.285773 | ||||||||
\(53\) | −220.668 | −0.571908 | −0.285954 | − | 0.958243i | \(-0.592311\pi\) | ||||
−0.285954 | + | 0.958243i | \(0.592311\pi\) | |||||||
\(54\) | −102.019 | −0.257092 | ||||||||
\(55\) | −53.5199 | −0.131211 | ||||||||
\(56\) | −159.016 | −0.379454 | ||||||||
\(57\) | −45.3810 | −0.105454 | ||||||||
\(58\) | −896.014 | −2.02849 | ||||||||
\(59\) | 59.0000 | 0.130189 | ||||||||
\(60\) | −108.140 | −0.232680 | ||||||||
\(61\) | −436.694 | −0.916606 | −0.458303 | − | 0.888796i | \(-0.651543\pi\) | ||||
−0.458303 | + | 0.888796i | \(0.651543\pi\) | |||||||
\(62\) | −697.610 | −1.42898 | ||||||||
\(63\) | −219.803 | −0.439565 | ||||||||
\(64\) | −272.793 | −0.532799 | ||||||||
\(65\) | −98.0424 | −0.187087 | ||||||||
\(66\) | −105.639 | −0.197020 | ||||||||
\(67\) | 924.006 | 1.68486 | 0.842428 | − | 0.538809i | \(-0.181126\pi\) | ||||
0.842428 | + | 0.538809i | \(0.181126\pi\) | |||||||
\(68\) | 123.519 | 0.220278 | ||||||||
\(69\) | 325.408 | 0.567747 | ||||||||
\(70\) | −529.948 | −0.904870 | ||||||||
\(71\) | −937.019 | −1.56625 | −0.783125 | − | 0.621865i | \(-0.786375\pi\) | ||||
−0.783125 | + | 0.621865i | \(0.786375\pi\) | |||||||
\(72\) | 58.5992 | 0.0959165 | ||||||||
\(73\) | 13.0348 | 0.0208988 | 0.0104494 | − | 0.999945i | \(-0.496674\pi\) | ||||
0.0104494 | + | 0.999945i | \(0.496674\pi\) | |||||||
\(74\) | −587.446 | −0.922826 | ||||||||
\(75\) | −276.060 | −0.425022 | ||||||||
\(76\) | −94.9493 | −0.143308 | ||||||||
\(77\) | −227.605 | −0.336857 | ||||||||
\(78\) | −193.519 | −0.280920 | ||||||||
\(79\) | 140.714 | 0.200400 | 0.100200 | − | 0.994967i | \(-0.468052\pi\) | ||||
0.100200 | + | 0.994967i | \(0.468052\pi\) | |||||||
\(80\) | 429.657 | 0.600463 | ||||||||
\(81\) | 81.0000 | 0.111111 | ||||||||
\(82\) | −988.996 | −1.33191 | ||||||||
\(83\) | −26.4265 | −0.0349480 | −0.0174740 | − | 0.999847i | \(-0.505562\pi\) | ||||
−0.0174740 | + | 0.999847i | \(0.505562\pi\) | |||||||
\(84\) | −459.888 | −0.597355 | ||||||||
\(85\) | −113.011 | −0.144210 | ||||||||
\(86\) | −482.310 | −0.604753 | ||||||||
\(87\) | 711.411 | 0.876681 | ||||||||
\(88\) | 60.6791 | 0.0735047 | ||||||||
\(89\) | −136.748 | −0.162869 | −0.0814343 | − | 0.996679i | \(-0.525950\pi\) | ||||
−0.0814343 | + | 0.996679i | \(0.525950\pi\) | |||||||
\(90\) | 195.292 | 0.228729 | ||||||||
\(91\) | −416.946 | −0.480305 | ||||||||
\(92\) | 680.842 | 0.771551 | ||||||||
\(93\) | 553.883 | 0.617581 | ||||||||
\(94\) | −2100.13 | −2.30438 | ||||||||
\(95\) | 86.8719 | 0.0938196 | ||||||||
\(96\) | 691.806 | 0.735491 | ||||||||
\(97\) | −360.785 | −0.377651 | −0.188826 | − | 0.982011i | \(-0.560468\pi\) | ||||
−0.188826 | + | 0.982011i | \(0.560468\pi\) | |||||||
\(98\) | −957.701 | −0.987168 | ||||||||
\(99\) | 83.8749 | 0.0851489 | ||||||||
\(100\) | −577.591 | −0.577591 | ||||||||
\(101\) | 421.340 | 0.415098 | 0.207549 | − | 0.978225i | \(-0.433451\pi\) | ||||
0.207549 | + | 0.978225i | \(0.433451\pi\) | |||||||
\(102\) | −223.066 | −0.216537 | ||||||||
\(103\) | −1389.28 | −1.32903 | −0.664515 | − | 0.747275i | \(-0.731362\pi\) | ||||
−0.664515 | + | 0.747275i | \(0.731362\pi\) | |||||||
\(104\) | 111.157 | 0.104806 | ||||||||
\(105\) | 420.765 | 0.391071 | ||||||||
\(106\) | 833.788 | 0.764006 | ||||||||
\(107\) | −339.530 | −0.306763 | −0.153382 | − | 0.988167i | \(-0.549016\pi\) | ||||
−0.153382 | + | 0.988167i | \(0.549016\pi\) | |||||||
\(108\) | 169.474 | 0.150997 | ||||||||
\(109\) | 297.022 | 0.261005 | 0.130503 | − | 0.991448i | \(-0.458341\pi\) | ||||
0.130503 | + | 0.991448i | \(0.458341\pi\) | |||||||
\(110\) | 202.223 | 0.175284 | ||||||||
\(111\) | 466.416 | 0.398831 | ||||||||
\(112\) | 1827.20 | 1.54156 | ||||||||
\(113\) | 1553.81 | 1.29354 | 0.646769 | − | 0.762686i | \(-0.276120\pi\) | ||||
0.646769 | + | 0.762686i | \(0.276120\pi\) | |||||||
\(114\) | 171.471 | 0.140875 | ||||||||
\(115\) | −622.922 | −0.505111 | ||||||||
\(116\) | 1488.46 | 1.19138 | ||||||||
\(117\) | 153.649 | 0.121409 | ||||||||
\(118\) | −222.930 | −0.173918 | ||||||||
\(119\) | −480.605 | −0.370227 | ||||||||
\(120\) | −112.175 | −0.0853346 | ||||||||
\(121\) | −1244.15 | −0.934747 | ||||||||
\(122\) | 1650.03 | 1.22448 | ||||||||
\(123\) | 785.236 | 0.575629 | ||||||||
\(124\) | 1158.87 | 0.839273 | ||||||||
\(125\) | 1246.31 | 0.891786 | ||||||||
\(126\) | 830.519 | 0.587211 | ||||||||
\(127\) | 1320.50 | 0.922642 | 0.461321 | − | 0.887233i | \(-0.347376\pi\) | ||||
0.461321 | + | 0.887233i | \(0.347376\pi\) | |||||||
\(128\) | −814.078 | −0.562148 | ||||||||
\(129\) | 382.941 | 0.261365 | ||||||||
\(130\) | 370.450 | 0.249928 | ||||||||
\(131\) | −1738.41 | −1.15943 | −0.579716 | − | 0.814819i | \(-0.696836\pi\) | ||||
−0.579716 | + | 0.814819i | \(0.696836\pi\) | |||||||
\(132\) | 175.489 | 0.115715 | ||||||||
\(133\) | 369.441 | 0.240861 | ||||||||
\(134\) | −3491.33 | −2.25078 | ||||||||
\(135\) | −155.056 | −0.0988529 | ||||||||
\(136\) | 128.129 | 0.0807863 | ||||||||
\(137\) | −776.721 | −0.484378 | −0.242189 | − | 0.970229i | \(-0.577865\pi\) | ||||
−0.242189 | + | 0.970229i | \(0.577865\pi\) | |||||||
\(138\) | −1229.54 | −0.758447 | ||||||||
\(139\) | 855.546 | 0.522061 | 0.261030 | − | 0.965331i | \(-0.415938\pi\) | ||||
0.261030 | + | 0.965331i | \(0.415938\pi\) | |||||||
\(140\) | 880.353 | 0.531453 | ||||||||
\(141\) | 1667.45 | 0.995917 | ||||||||
\(142\) | 3540.49 | 2.09234 | ||||||||
\(143\) | 159.103 | 0.0930407 | ||||||||
\(144\) | −673.345 | −0.389667 | ||||||||
\(145\) | −1361.84 | −0.779962 | ||||||||
\(146\) | −49.2517 | −0.0279185 | ||||||||
\(147\) | 760.389 | 0.426638 | ||||||||
\(148\) | 975.867 | 0.541999 | ||||||||
\(149\) | 2001.36 | 1.10039 | 0.550194 | − | 0.835037i | \(-0.314554\pi\) | ||||
0.550194 | + | 0.835037i | \(0.314554\pi\) | |||||||
\(150\) | 1043.08 | 0.567782 | ||||||||
\(151\) | 1656.52 | 0.892750 | 0.446375 | − | 0.894846i | \(-0.352715\pi\) | ||||
0.446375 | + | 0.894846i | \(0.352715\pi\) | |||||||
\(152\) | −98.4924 | −0.0525578 | ||||||||
\(153\) | 177.108 | 0.0935841 | ||||||||
\(154\) | 859.996 | 0.450003 | ||||||||
\(155\) | −1060.29 | −0.549447 | ||||||||
\(156\) | 321.475 | 0.164991 | ||||||||
\(157\) | 649.443 | 0.330135 | 0.165068 | − | 0.986282i | \(-0.447216\pi\) | ||||
0.165068 | + | 0.986282i | \(0.447216\pi\) | |||||||
\(158\) | −531.685 | −0.267713 | ||||||||
\(159\) | −662.005 | −0.330191 | ||||||||
\(160\) | −1324.31 | −0.654349 | ||||||||
\(161\) | −2649.10 | −1.29676 | ||||||||
\(162\) | −306.056 | −0.148432 | ||||||||
\(163\) | 508.548 | 0.244372 | 0.122186 | − | 0.992507i | \(-0.461010\pi\) | ||||
0.122186 | + | 0.992507i | \(0.461010\pi\) | |||||||
\(164\) | 1642.93 | 0.782262 | ||||||||
\(165\) | −160.560 | −0.0757549 | ||||||||
\(166\) | 99.8517 | 0.0466867 | ||||||||
\(167\) | 1419.46 | 0.657733 | 0.328867 | − | 0.944376i | \(-0.393333\pi\) | ||||
0.328867 | + | 0.944376i | \(0.393333\pi\) | |||||||
\(168\) | −477.048 | −0.219078 | ||||||||
\(169\) | −1905.54 | −0.867338 | ||||||||
\(170\) | 427.010 | 0.192648 | ||||||||
\(171\) | −136.143 | −0.0608837 | ||||||||
\(172\) | 801.215 | 0.355187 | ||||||||
\(173\) | −929.169 | −0.408343 | −0.204172 | − | 0.978935i | \(-0.565450\pi\) | ||||
−0.204172 | + | 0.978935i | \(0.565450\pi\) | |||||||
\(174\) | −2688.04 | −1.17115 | ||||||||
\(175\) | 2247.36 | 0.970770 | ||||||||
\(176\) | −697.244 | −0.298618 | ||||||||
\(177\) | 177.000 | 0.0751646 | ||||||||
\(178\) | 516.699 | 0.217574 | ||||||||
\(179\) | −2212.72 | −0.923948 | −0.461974 | − | 0.886893i | \(-0.652859\pi\) | ||||
−0.461974 | + | 0.886893i | \(0.652859\pi\) | |||||||
\(180\) | −324.420 | −0.134338 | ||||||||
\(181\) | −46.5937 | −0.0191342 | −0.00956709 | − | 0.999954i | \(-0.503045\pi\) | ||||
−0.00956709 | + | 0.999954i | \(0.503045\pi\) | |||||||
\(182\) | 1575.41 | 0.641635 | ||||||||
\(183\) | −1310.08 | −0.529203 | ||||||||
\(184\) | 706.247 | 0.282963 | ||||||||
\(185\) | −892.849 | −0.354830 | ||||||||
\(186\) | −2092.83 | −0.825020 | ||||||||
\(187\) | 183.394 | 0.0717172 | ||||||||
\(188\) | 3488.75 | 1.35342 | ||||||||
\(189\) | −659.410 | −0.253783 | ||||||||
\(190\) | −328.242 | −0.125333 | ||||||||
\(191\) | −2035.98 | −0.771302 | −0.385651 | − | 0.922645i | \(-0.626023\pi\) | ||||
−0.385651 | + | 0.922645i | \(0.626023\pi\) | |||||||
\(192\) | −818.379 | −0.307611 | ||||||||
\(193\) | −1530.18 | −0.570697 | −0.285349 | − | 0.958424i | \(-0.592109\pi\) | ||||
−0.285349 | + | 0.958424i | \(0.592109\pi\) | |||||||
\(194\) | 1363.21 | 0.504500 | ||||||||
\(195\) | −294.127 | −0.108015 | ||||||||
\(196\) | 1590.94 | 0.579788 | ||||||||
\(197\) | 2461.81 | 0.890337 | 0.445169 | − | 0.895447i | \(-0.353144\pi\) | ||||
0.445169 | + | 0.895447i | \(0.353144\pi\) | |||||||
\(198\) | −316.918 | −0.113750 | ||||||||
\(199\) | 1442.27 | 0.513768 | 0.256884 | − | 0.966442i | \(-0.417304\pi\) | ||||
0.256884 | + | 0.966442i | \(0.417304\pi\) | |||||||
\(200\) | −599.144 | −0.211829 | ||||||||
\(201\) | 2772.02 | 0.972752 | ||||||||
\(202\) | −1592.02 | −0.554525 | ||||||||
\(203\) | −5791.50 | −2.00238 | ||||||||
\(204\) | 370.558 | 0.127178 | ||||||||
\(205\) | −1503.16 | −0.512123 | ||||||||
\(206\) | 5249.36 | 1.77544 | ||||||||
\(207\) | 976.225 | 0.327789 | ||||||||
\(208\) | −1277.27 | −0.425783 | ||||||||
\(209\) | −140.975 | −0.0466577 | ||||||||
\(210\) | −1589.84 | −0.522427 | ||||||||
\(211\) | −732.346 | −0.238942 | −0.119471 | − | 0.992838i | \(-0.538120\pi\) | ||||
−0.119471 | + | 0.992838i | \(0.538120\pi\) | |||||||
\(212\) | −1385.09 | −0.448720 | ||||||||
\(213\) | −2811.06 | −0.904274 | ||||||||
\(214\) | 1282.90 | 0.409802 | ||||||||
\(215\) | −733.055 | −0.232530 | ||||||||
\(216\) | 175.798 | 0.0553774 | ||||||||
\(217\) | −4509.09 | −1.41058 | ||||||||
\(218\) | −1122.29 | −0.348674 | ||||||||
\(219\) | 39.1045 | 0.0120659 | ||||||||
\(220\) | −335.934 | −0.102949 | ||||||||
\(221\) | 335.957 | 0.102258 | ||||||||
\(222\) | −1762.34 | −0.532794 | ||||||||
\(223\) | 2928.26 | 0.879332 | 0.439666 | − | 0.898161i | \(-0.355097\pi\) | ||||
0.439666 | + | 0.898161i | \(0.355097\pi\) | |||||||
\(224\) | −5631.90 | −1.67990 | ||||||||
\(225\) | −828.179 | −0.245386 | ||||||||
\(226\) | −5871.00 | −1.72802 | ||||||||
\(227\) | 3909.72 | 1.14316 | 0.571580 | − | 0.820546i | \(-0.306331\pi\) | ||||
0.571580 | + | 0.820546i | \(0.306331\pi\) | |||||||
\(228\) | −284.848 | −0.0827391 | ||||||||
\(229\) | 5580.68 | 1.61040 | 0.805200 | − | 0.593003i | \(-0.202058\pi\) | ||||
0.805200 | + | 0.593003i | \(0.202058\pi\) | |||||||
\(230\) | 2353.69 | 0.674772 | ||||||||
\(231\) | −682.814 | −0.194484 | ||||||||
\(232\) | 1544.01 | 0.436935 | ||||||||
\(233\) | −3793.50 | −1.06661 | −0.533306 | − | 0.845923i | \(-0.679050\pi\) | ||||
−0.533306 | + | 0.845923i | \(0.679050\pi\) | |||||||
\(234\) | −580.558 | −0.162189 | ||||||||
\(235\) | −3191.96 | −0.886043 | ||||||||
\(236\) | 370.332 | 0.102146 | ||||||||
\(237\) | 422.143 | 0.115701 | ||||||||
\(238\) | 1815.95 | 0.494582 | ||||||||
\(239\) | 4995.54 | 1.35203 | 0.676013 | − | 0.736889i | \(-0.263706\pi\) | ||||
0.676013 | + | 0.736889i | \(0.263706\pi\) | |||||||
\(240\) | 1288.97 | 0.346678 | ||||||||
\(241\) | 1674.51 | 0.447572 | 0.223786 | − | 0.974638i | \(-0.428158\pi\) | ||||
0.223786 | + | 0.974638i | \(0.428158\pi\) | |||||||
\(242\) | 4700.97 | 1.24872 | ||||||||
\(243\) | 243.000 | 0.0641500 | ||||||||
\(244\) | −2741.05 | −0.719170 | ||||||||
\(245\) | −1455.60 | −0.379570 | ||||||||
\(246\) | −2966.99 | −0.768977 | ||||||||
\(247\) | −258.250 | −0.0665266 | ||||||||
\(248\) | 1202.12 | 0.307800 | ||||||||
\(249\) | −79.2795 | −0.0201773 | ||||||||
\(250\) | −4709.14 | −1.19133 | ||||||||
\(251\) | 4489.35 | 1.12895 | 0.564473 | − | 0.825452i | \(-0.309080\pi\) | ||||
0.564473 | + | 0.825452i | \(0.309080\pi\) | |||||||
\(252\) | −1379.66 | −0.344883 | ||||||||
\(253\) | 1010.87 | 0.251198 | ||||||||
\(254\) | −4989.47 | −1.23255 | ||||||||
\(255\) | −339.034 | −0.0832595 | ||||||||
\(256\) | 5258.31 | 1.28377 | ||||||||
\(257\) | 5099.27 | 1.23768 | 0.618840 | − | 0.785517i | \(-0.287603\pi\) | ||||
0.618840 | + | 0.785517i | \(0.287603\pi\) | |||||||
\(258\) | −1446.93 | −0.349154 | ||||||||
\(259\) | −3797.03 | −0.910949 | ||||||||
\(260\) | −615.393 | −0.146789 | ||||||||
\(261\) | 2134.23 | 0.506152 | ||||||||
\(262\) | 6568.52 | 1.54887 | ||||||||
\(263\) | 7949.30 | 1.86378 | 0.931892 | − | 0.362737i | \(-0.118158\pi\) | ||||
0.931892 | + | 0.362737i | \(0.118158\pi\) | |||||||
\(264\) | 182.037 | 0.0424379 | ||||||||
\(265\) | 1267.26 | 0.293763 | ||||||||
\(266\) | −1395.92 | −0.321764 | ||||||||
\(267\) | −410.245 | −0.0940322 | ||||||||
\(268\) | 5799.81 | 1.32194 | ||||||||
\(269\) | −3831.43 | −0.868426 | −0.434213 | − | 0.900810i | \(-0.642973\pi\) | ||||
−0.434213 | + | 0.900810i | \(0.642973\pi\) | |||||||
\(270\) | 585.876 | 0.132056 | ||||||||
\(271\) | −6824.86 | −1.52982 | −0.764909 | − | 0.644139i | \(-0.777216\pi\) | ||||
−0.764909 | + | 0.644139i | \(0.777216\pi\) | |||||||
\(272\) | −1472.28 | −0.328200 | ||||||||
\(273\) | −1250.84 | −0.277304 | ||||||||
\(274\) | 2934.82 | 0.647075 | ||||||||
\(275\) | −857.573 | −0.188049 | ||||||||
\(276\) | 2042.52 | 0.445455 | ||||||||
\(277\) | −40.1056 | −0.00869931 | −0.00434966 | − | 0.999991i | \(-0.501385\pi\) | ||||
−0.00434966 | + | 0.999991i | \(0.501385\pi\) | |||||||
\(278\) | −3232.65 | −0.697416 | ||||||||
\(279\) | 1661.65 | 0.356560 | ||||||||
\(280\) | 913.203 | 0.194908 | ||||||||
\(281\) | −2405.83 | −0.510746 | −0.255373 | − | 0.966843i | \(-0.582198\pi\) | ||||
−0.255373 | + | 0.966843i | \(0.582198\pi\) | |||||||
\(282\) | −6300.39 | −1.33044 | ||||||||
\(283\) | 8232.15 | 1.72915 | 0.864577 | − | 0.502501i | \(-0.167587\pi\) | ||||
0.864577 | + | 0.502501i | \(0.167587\pi\) | |||||||
\(284\) | −5881.49 | −1.22888 | ||||||||
\(285\) | 260.616 | 0.0541668 | ||||||||
\(286\) | −601.164 | −0.124292 | ||||||||
\(287\) | −6392.50 | −1.31476 | ||||||||
\(288\) | 2075.42 | 0.424636 | ||||||||
\(289\) | −4525.75 | −0.921178 | ||||||||
\(290\) | 5145.66 | 1.04194 | ||||||||
\(291\) | −1082.36 | −0.218037 | ||||||||
\(292\) | 81.8171 | 0.0163972 | ||||||||
\(293\) | 1902.22 | 0.379280 | 0.189640 | − | 0.981854i | \(-0.439268\pi\) | ||||
0.189640 | + | 0.981854i | \(0.439268\pi\) | |||||||
\(294\) | −2873.10 | −0.569941 | ||||||||
\(295\) | −338.827 | −0.0668721 | ||||||||
\(296\) | 1012.28 | 0.198776 | ||||||||
\(297\) | 251.625 | 0.0491608 | ||||||||
\(298\) | −7562.07 | −1.47000 | ||||||||
\(299\) | 1851.80 | 0.358169 | ||||||||
\(300\) | −1732.77 | −0.333472 | ||||||||
\(301\) | −3117.47 | −0.596970 | ||||||||
\(302\) | −6259.09 | −1.19262 | ||||||||
\(303\) | 1264.02 | 0.239657 | ||||||||
\(304\) | 1131.74 | 0.213520 | ||||||||
\(305\) | 2507.86 | 0.470819 | ||||||||
\(306\) | −669.198 | −0.125018 | ||||||||
\(307\) | 9226.20 | 1.71520 | 0.857601 | − | 0.514315i | \(-0.171954\pi\) | ||||
0.857601 | + | 0.514315i | \(0.171954\pi\) | |||||||
\(308\) | −1428.63 | −0.264298 | ||||||||
\(309\) | −4167.85 | −0.767316 | ||||||||
\(310\) | 4006.26 | 0.734000 | ||||||||
\(311\) | −2395.89 | −0.436844 | −0.218422 | − | 0.975854i | \(-0.570091\pi\) | ||||
−0.218422 | + | 0.975854i | \(0.570091\pi\) | |||||||
\(312\) | 333.471 | 0.0605099 | ||||||||
\(313\) | −10071.9 | −1.81884 | −0.909421 | − | 0.415878i | \(-0.863474\pi\) | ||||
−0.909421 | + | 0.415878i | \(0.863474\pi\) | |||||||
\(314\) | −2453.90 | −0.441024 | ||||||||
\(315\) | 1262.29 | 0.225785 | ||||||||
\(316\) | 883.238 | 0.157234 | ||||||||
\(317\) | 1068.39 | 0.189296 | 0.0946478 | − | 0.995511i | \(-0.469828\pi\) | ||||
0.0946478 | + | 0.995511i | \(0.469828\pi\) | |||||||
\(318\) | 2501.36 | 0.441099 | ||||||||
\(319\) | 2209.98 | 0.387885 | ||||||||
\(320\) | 1566.60 | 0.273674 | ||||||||
\(321\) | −1018.59 | −0.177110 | ||||||||
\(322\) | 10009.6 | 1.73233 | ||||||||
\(323\) | −297.680 | −0.0512797 | ||||||||
\(324\) | 508.421 | 0.0871779 | ||||||||
\(325\) | −1570.98 | −0.268129 | ||||||||
\(326\) | −1921.53 | −0.326454 | ||||||||
\(327\) | 891.066 | 0.150691 | ||||||||
\(328\) | 1704.23 | 0.286892 | ||||||||
\(329\) | −13574.5 | −2.27472 | ||||||||
\(330\) | 606.670 | 0.101200 | ||||||||
\(331\) | −9649.80 | −1.60242 | −0.801210 | − | 0.598384i | \(-0.795810\pi\) | ||||
−0.801210 | + | 0.598384i | \(0.795810\pi\) | |||||||
\(332\) | −165.874 | −0.0274203 | ||||||||
\(333\) | 1399.25 | 0.230265 | ||||||||
\(334\) | −5363.40 | −0.878659 | ||||||||
\(335\) | −5306.41 | −0.865434 | ||||||||
\(336\) | 5481.61 | 0.890019 | ||||||||
\(337\) | −6617.95 | −1.06974 | −0.534871 | − | 0.844934i | \(-0.679640\pi\) | ||||
−0.534871 | + | 0.844934i | \(0.679640\pi\) | |||||||
\(338\) | 7200.03 | 1.15867 | ||||||||
\(339\) | 4661.42 | 0.746824 | ||||||||
\(340\) | −709.351 | −0.113147 | ||||||||
\(341\) | 1720.63 | 0.273247 | ||||||||
\(342\) | 514.412 | 0.0813340 | ||||||||
\(343\) | 2186.73 | 0.344234 | ||||||||
\(344\) | 831.113 | 0.130263 | ||||||||
\(345\) | −1868.77 | −0.291626 | ||||||||
\(346\) | 3510.83 | 0.545502 | ||||||||
\(347\) | 3888.20 | 0.601525 | 0.300763 | − | 0.953699i | \(-0.402759\pi\) | ||||
0.300763 | + | 0.953699i | \(0.402759\pi\) | |||||||
\(348\) | 4465.39 | 0.687845 | ||||||||
\(349\) | −8651.21 | −1.32690 | −0.663451 | − | 0.748220i | \(-0.730909\pi\) | ||||
−0.663451 | + | 0.748220i | \(0.730909\pi\) | |||||||
\(350\) | −8491.59 | −1.29684 | ||||||||
\(351\) | 460.948 | 0.0700956 | ||||||||
\(352\) | 2149.08 | 0.325416 | ||||||||
\(353\) | 1996.55 | 0.301036 | 0.150518 | − | 0.988607i | \(-0.451906\pi\) | ||||
0.150518 | + | 0.988607i | \(0.451906\pi\) | |||||||
\(354\) | −668.789 | −0.100412 | ||||||||
\(355\) | 5381.14 | 0.804511 | ||||||||
\(356\) | −858.343 | −0.127787 | ||||||||
\(357\) | −1441.81 | −0.213751 | ||||||||
\(358\) | 8360.70 | 1.23429 | ||||||||
\(359\) | 11674.1 | 1.71626 | 0.858128 | − | 0.513436i | \(-0.171627\pi\) | ||||
0.858128 | + | 0.513436i | \(0.171627\pi\) | |||||||
\(360\) | −336.526 | −0.0492679 | ||||||||
\(361\) | −6630.17 | −0.966639 | ||||||||
\(362\) | 176.053 | 0.0255611 | ||||||||
\(363\) | −3732.44 | −0.539676 | ||||||||
\(364\) | −2617.09 | −0.376848 | ||||||||
\(365\) | −74.8569 | −0.0107348 | ||||||||
\(366\) | 4950.10 | 0.706956 | ||||||||
\(367\) | 11122.7 | 1.58201 | 0.791005 | − | 0.611810i | \(-0.209558\pi\) | ||||
0.791005 | + | 0.611810i | \(0.209558\pi\) | |||||||
\(368\) | −8115.27 | −1.14956 | ||||||||
\(369\) | 2355.71 | 0.332340 | ||||||||
\(370\) | 3373.60 | 0.474014 | ||||||||
\(371\) | 5389.30 | 0.754173 | ||||||||
\(372\) | 3476.62 | 0.484554 | ||||||||
\(373\) | 7447.39 | 1.03381 | 0.516905 | − | 0.856043i | \(-0.327084\pi\) | ||||
0.516905 | + | 0.856043i | \(0.327084\pi\) | |||||||
\(374\) | −692.949 | −0.0958063 | ||||||||
\(375\) | 3738.93 | 0.514873 | ||||||||
\(376\) | 3618.93 | 0.496362 | ||||||||
\(377\) | 4048.43 | 0.553063 | ||||||||
\(378\) | 2491.56 | 0.339026 | ||||||||
\(379\) | −2736.87 | −0.370933 | −0.185467 | − | 0.982651i | \(-0.559380\pi\) | ||||
−0.185467 | + | 0.982651i | \(0.559380\pi\) | |||||||
\(380\) | 545.278 | 0.0736110 | ||||||||
\(381\) | 3961.51 | 0.532688 | ||||||||
\(382\) | 7692.90 | 1.03037 | ||||||||
\(383\) | −3711.27 | −0.495136 | −0.247568 | − | 0.968871i | \(-0.579631\pi\) | ||||
−0.247568 | + | 0.968871i | \(0.579631\pi\) | |||||||
\(384\) | −2442.23 | −0.324556 | ||||||||
\(385\) | 1307.10 | 0.173028 | ||||||||
\(386\) | 5781.72 | 0.762388 | ||||||||
\(387\) | 1148.82 | 0.150899 | ||||||||
\(388\) | −2264.58 | −0.296306 | ||||||||
\(389\) | 68.7597 | 0.00896209 | 0.00448105 | − | 0.999990i | \(-0.498574\pi\) | ||||
0.00448105 | + | 0.999990i | \(0.498574\pi\) | |||||||
\(390\) | 1111.35 | 0.144296 | ||||||||
\(391\) | 2134.54 | 0.276082 | ||||||||
\(392\) | 1650.30 | 0.212635 | ||||||||
\(393\) | −5215.23 | −0.669398 | ||||||||
\(394\) | −9301.85 | −1.18939 | ||||||||
\(395\) | −808.100 | −0.102936 | ||||||||
\(396\) | 526.466 | 0.0668079 | ||||||||
\(397\) | −9361.13 | −1.18343 | −0.591715 | − | 0.806147i | \(-0.701549\pi\) | ||||
−0.591715 | + | 0.806147i | \(0.701549\pi\) | |||||||
\(398\) | −5449.57 | −0.686337 | ||||||||
\(399\) | 1108.32 | 0.139061 | ||||||||
\(400\) | 6884.57 | 0.860572 | ||||||||
\(401\) | −95.5960 | −0.0119048 | −0.00595241 | − | 0.999982i | \(-0.501895\pi\) | ||||
−0.00595241 | + | 0.999982i | \(0.501895\pi\) | |||||||
\(402\) | −10474.0 | −1.29949 | ||||||||
\(403\) | 3151.99 | 0.389607 | ||||||||
\(404\) | 2644.67 | 0.325686 | ||||||||
\(405\) | −465.169 | −0.0570727 | ||||||||
\(406\) | 21883.0 | 2.67496 | ||||||||
\(407\) | 1448.91 | 0.176461 | ||||||||
\(408\) | 384.386 | 0.0466420 | ||||||||
\(409\) | −11054.7 | −1.33648 | −0.668240 | − | 0.743946i | \(-0.732952\pi\) | ||||
−0.668240 | + | 0.743946i | \(0.732952\pi\) | |||||||
\(410\) | 5679.64 | 0.684140 | ||||||||
\(411\) | −2330.16 | −0.279656 | ||||||||
\(412\) | −8720.26 | −1.04276 | ||||||||
\(413\) | −1440.93 | −0.171680 | ||||||||
\(414\) | −3688.63 | −0.437890 | ||||||||
\(415\) | 151.763 | 0.0179512 | ||||||||
\(416\) | 3936.87 | 0.463992 | ||||||||
\(417\) | 2566.64 | 0.301412 | ||||||||
\(418\) | 532.670 | 0.0623295 | ||||||||
\(419\) | −4854.35 | −0.565992 | −0.282996 | − | 0.959121i | \(-0.591328\pi\) | ||||
−0.282996 | + | 0.959121i | \(0.591328\pi\) | |||||||
\(420\) | 2641.06 | 0.306834 | ||||||||
\(421\) | −5480.81 | −0.634485 | −0.317242 | − | 0.948344i | \(-0.602757\pi\) | ||||
−0.317242 | + | 0.948344i | \(0.602757\pi\) | |||||||
\(422\) | 2767.14 | 0.319200 | ||||||||
\(423\) | 5002.34 | 0.574993 | ||||||||
\(424\) | −1436.78 | −0.164566 | ||||||||
\(425\) | −1810.83 | −0.206678 | ||||||||
\(426\) | 10621.5 | 1.20801 | ||||||||
\(427\) | 10665.2 | 1.20872 | ||||||||
\(428\) | −2131.17 | −0.240687 | ||||||||
\(429\) | 477.308 | 0.0537171 | ||||||||
\(430\) | 2769.82 | 0.310634 | ||||||||
\(431\) | 7366.56 | 0.823282 | 0.411641 | − | 0.911346i | \(-0.364956\pi\) | ||||
0.411641 | + | 0.911346i | \(0.364956\pi\) | |||||||
\(432\) | −2020.04 | −0.224975 | ||||||||
\(433\) | 228.362 | 0.0253450 | 0.0126725 | − | 0.999920i | \(-0.495966\pi\) | ||||
0.0126725 | + | 0.999920i | \(0.495966\pi\) | |||||||
\(434\) | 17037.4 | 1.88439 | ||||||||
\(435\) | −4085.51 | −0.450311 | ||||||||
\(436\) | 1864.35 | 0.204785 | ||||||||
\(437\) | −1640.82 | −0.179613 | ||||||||
\(438\) | −147.755 | −0.0161187 | ||||||||
\(439\) | −16897.8 | −1.83710 | −0.918550 | − | 0.395305i | \(-0.870639\pi\) | ||||
−0.918550 | + | 0.395305i | \(0.870639\pi\) | |||||||
\(440\) | −348.470 | −0.0377560 | ||||||||
\(441\) | 2281.17 | 0.246320 | ||||||||
\(442\) | −1269.40 | −0.136605 | ||||||||
\(443\) | 8663.70 | 0.929176 | 0.464588 | − | 0.885527i | \(-0.346202\pi\) | ||||
0.464588 | + | 0.885527i | \(0.346202\pi\) | |||||||
\(444\) | 2927.60 | 0.312923 | ||||||||
\(445\) | 785.323 | 0.0836582 | ||||||||
\(446\) | −11064.3 | −1.17469 | ||||||||
\(447\) | 6004.08 | 0.635309 | ||||||||
\(448\) | 6662.31 | 0.702599 | ||||||||
\(449\) | −12014.8 | −1.26284 | −0.631418 | − | 0.775442i | \(-0.717527\pi\) | ||||
−0.631418 | + | 0.775442i | \(0.717527\pi\) | |||||||
\(450\) | 3129.25 | 0.327809 | ||||||||
\(451\) | 2439.32 | 0.254685 | ||||||||
\(452\) | 9752.94 | 1.01491 | ||||||||
\(453\) | 4969.55 | 0.515430 | ||||||||
\(454\) | −14772.8 | −1.52714 | ||||||||
\(455\) | 2394.45 | 0.246711 | ||||||||
\(456\) | −295.477 | −0.0303443 | ||||||||
\(457\) | 15590.7 | 1.59585 | 0.797925 | − | 0.602756i | \(-0.205931\pi\) | ||||
0.797925 | + | 0.602756i | \(0.205931\pi\) | |||||||
\(458\) | −21086.4 | −2.15132 | ||||||||
\(459\) | 531.325 | 0.0540308 | ||||||||
\(460\) | −3909.96 | −0.396310 | ||||||||
\(461\) | 1475.12 | 0.149031 | 0.0745155 | − | 0.997220i | \(-0.476259\pi\) | ||||
0.0745155 | + | 0.997220i | \(0.476259\pi\) | |||||||
\(462\) | 2579.99 | 0.259809 | ||||||||
\(463\) | 1335.14 | 0.134015 | 0.0670077 | − | 0.997752i | \(-0.478655\pi\) | ||||
0.0670077 | + | 0.997752i | \(0.478655\pi\) | |||||||
\(464\) | −17741.7 | −1.77508 | ||||||||
\(465\) | −3180.86 | −0.317223 | ||||||||
\(466\) | 14333.6 | 1.42488 | ||||||||
\(467\) | −13910.9 | −1.37841 | −0.689205 | − | 0.724566i | \(-0.742040\pi\) | ||||
−0.689205 | + | 0.724566i | \(0.742040\pi\) | |||||||
\(468\) | 964.426 | 0.0952577 | ||||||||
\(469\) | −22566.6 | −2.22181 | ||||||||
\(470\) | 12060.7 | 1.18366 | ||||||||
\(471\) | 1948.33 | 0.190604 | ||||||||
\(472\) | 384.151 | 0.0374618 | ||||||||
\(473\) | 1189.60 | 0.115640 | ||||||||
\(474\) | −1595.05 | −0.154564 | ||||||||
\(475\) | 1391.99 | 0.134460 | ||||||||
\(476\) | −3016.66 | −0.290480 | ||||||||
\(477\) | −1986.02 | −0.190636 | ||||||||
\(478\) | −18875.5 | −1.80616 | ||||||||
\(479\) | 15483.9 | 1.47699 | 0.738495 | − | 0.674259i | \(-0.235537\pi\) | ||||
0.738495 | + | 0.674259i | \(0.235537\pi\) | |||||||
\(480\) | −3972.93 | −0.377789 | ||||||||
\(481\) | 2654.24 | 0.251607 | ||||||||
\(482\) | −6327.09 | −0.597906 | ||||||||
\(483\) | −7947.31 | −0.748686 | ||||||||
\(484\) | −7809.28 | −0.733403 | ||||||||
\(485\) | 2071.93 | 0.193982 | ||||||||
\(486\) | −918.167 | −0.0856974 | ||||||||
\(487\) | −12901.8 | −1.20049 | −0.600243 | − | 0.799817i | \(-0.704930\pi\) | ||||
−0.600243 | + | 0.799817i | \(0.704930\pi\) | |||||||
\(488\) | −2843.33 | −0.263753 | ||||||||
\(489\) | 1525.65 | 0.141088 | ||||||||
\(490\) | 5499.92 | 0.507063 | ||||||||
\(491\) | −4348.11 | −0.399649 | −0.199824 | − | 0.979832i | \(-0.564037\pi\) | ||||
−0.199824 | + | 0.979832i | \(0.564037\pi\) | |||||||
\(492\) | 4928.78 | 0.451639 | ||||||||
\(493\) | 4666.55 | 0.426310 | ||||||||
\(494\) | 975.790 | 0.0888722 | ||||||||
\(495\) | −481.679 | −0.0437371 | ||||||||
\(496\) | −13813.1 | −1.25046 | ||||||||
\(497\) | 22884.4 | 2.06541 | ||||||||
\(498\) | 299.555 | 0.0269546 | ||||||||
\(499\) | −12051.7 | −1.08118 | −0.540589 | − | 0.841287i | \(-0.681798\pi\) | ||||
−0.540589 | + | 0.841287i | \(0.681798\pi\) | |||||||
\(500\) | 7822.84 | 0.699696 | ||||||||
\(501\) | 4258.39 | 0.379742 | ||||||||
\(502\) | −16962.9 | −1.50815 | ||||||||
\(503\) | 16522.2 | 1.46459 | 0.732293 | − | 0.680990i | \(-0.238450\pi\) | ||||
0.732293 | + | 0.680990i | \(0.238450\pi\) | |||||||
\(504\) | −1431.15 | −0.126485 | ||||||||
\(505\) | −2419.69 | −0.213217 | ||||||||
\(506\) | −3819.55 | −0.335573 | ||||||||
\(507\) | −5716.63 | −0.500758 | ||||||||
\(508\) | 8288.53 | 0.723906 | ||||||||
\(509\) | −15147.5 | −1.31906 | −0.659530 | − | 0.751678i | \(-0.729245\pi\) | ||||
−0.659530 | + | 0.751678i | \(0.729245\pi\) | |||||||
\(510\) | 1281.03 | 0.111225 | ||||||||
\(511\) | −318.344 | −0.0275592 | ||||||||
\(512\) | −13355.7 | −1.15282 | ||||||||
\(513\) | −408.429 | −0.0351512 | ||||||||
\(514\) | −19267.4 | −1.65340 | ||||||||
\(515\) | 7978.42 | 0.682662 | ||||||||
\(516\) | 2403.65 | 0.205067 | ||||||||
\(517\) | 5179.88 | 0.440640 | ||||||||
\(518\) | 14346.9 | 1.21693 | ||||||||
\(519\) | −2787.51 | −0.235757 | ||||||||
\(520\) | −638.357 | −0.0538342 | ||||||||
\(521\) | 14442.1 | 1.21443 | 0.607215 | − | 0.794538i | \(-0.292287\pi\) | ||||
0.607215 | + | 0.794538i | \(0.292287\pi\) | |||||||
\(522\) | −8064.13 | −0.676163 | ||||||||
\(523\) | −4796.97 | −0.401065 | −0.200532 | − | 0.979687i | \(-0.564267\pi\) | ||||
−0.200532 | + | 0.979687i | \(0.564267\pi\) | |||||||
\(524\) | −10911.7 | −0.909691 | ||||||||
\(525\) | 6742.09 | 0.560474 | ||||||||
\(526\) | −30036.2 | −2.48981 | ||||||||
\(527\) | 3633.24 | 0.300315 | ||||||||
\(528\) | −2091.73 | −0.172407 | ||||||||
\(529\) | −401.383 | −0.0329895 | ||||||||
\(530\) | −4788.31 | −0.392435 | ||||||||
\(531\) | 531.000 | 0.0433963 | ||||||||
\(532\) | 2318.91 | 0.188980 | ||||||||
\(533\) | 4468.55 | 0.363142 | ||||||||
\(534\) | 1550.10 | 0.125617 | ||||||||
\(535\) | 1949.87 | 0.157570 | ||||||||
\(536\) | 6016.23 | 0.484816 | ||||||||
\(537\) | −6638.17 | −0.533442 | ||||||||
\(538\) | 14476.9 | 1.16012 | ||||||||
\(539\) | 2362.13 | 0.188765 | ||||||||
\(540\) | −973.259 | −0.0775600 | ||||||||
\(541\) | −833.411 | −0.0662313 | −0.0331157 | − | 0.999452i | \(-0.510543\pi\) | ||||
−0.0331157 | + | 0.999452i | \(0.510543\pi\) | |||||||
\(542\) | 25787.5 | 2.04367 | ||||||||
\(543\) | −139.781 | −0.0110471 | ||||||||
\(544\) | 4537.95 | 0.357653 | ||||||||
\(545\) | −1705.75 | −0.134066 | ||||||||
\(546\) | 4726.24 | 0.370448 | ||||||||
\(547\) | −19682.1 | −1.53848 | −0.769239 | − | 0.638961i | \(-0.779365\pi\) | ||||
−0.769239 | + | 0.638961i | \(0.779365\pi\) | |||||||
\(548\) | −4875.33 | −0.380043 | ||||||||
\(549\) | −3930.25 | −0.305535 | ||||||||
\(550\) | 3240.31 | 0.251213 | ||||||||
\(551\) | −3587.17 | −0.277348 | ||||||||
\(552\) | 2118.74 | 0.163369 | ||||||||
\(553\) | −3436.61 | −0.264267 | ||||||||
\(554\) | 151.538 | 0.0116213 | ||||||||
\(555\) | −2678.55 | −0.204861 | ||||||||
\(556\) | 5370.10 | 0.409609 | ||||||||
\(557\) | −10287.7 | −0.782594 | −0.391297 | − | 0.920264i | \(-0.627974\pi\) | ||||
−0.391297 | + | 0.920264i | \(0.627974\pi\) | |||||||
\(558\) | −6278.49 | −0.476325 | ||||||||
\(559\) | 2179.21 | 0.164885 | ||||||||
\(560\) | −10493.3 | −0.791829 | ||||||||
\(561\) | 550.183 | 0.0414060 | ||||||||
\(562\) | 9090.34 | 0.682301 | ||||||||
\(563\) | −8172.20 | −0.611754 | −0.305877 | − | 0.952071i | \(-0.598950\pi\) | ||||
−0.305877 | + | 0.952071i | \(0.598950\pi\) | |||||||
\(564\) | 10466.2 | 0.781398 | ||||||||
\(565\) | −8923.25 | −0.664431 | ||||||||
\(566\) | −31104.9 | −2.30996 | ||||||||
\(567\) | −1978.23 | −0.146522 | ||||||||
\(568\) | −6100.96 | −0.450687 | ||||||||
\(569\) | 9993.92 | 0.736322 | 0.368161 | − | 0.929762i | \(-0.379988\pi\) | ||||
0.368161 | + | 0.929762i | \(0.379988\pi\) | |||||||
\(570\) | −984.727 | −0.0723608 | ||||||||
\(571\) | −8399.41 | −0.615594 | −0.307797 | − | 0.951452i | \(-0.599592\pi\) | ||||
−0.307797 | + | 0.951452i | \(0.599592\pi\) | |||||||
\(572\) | 998.656 | 0.0729998 | ||||||||
\(573\) | −6107.95 | −0.445311 | ||||||||
\(574\) | 24153.9 | 1.75638 | ||||||||
\(575\) | −9981.34 | −0.723914 | ||||||||
\(576\) | −2455.14 | −0.177600 | ||||||||
\(577\) | −9807.97 | −0.707645 | −0.353822 | − | 0.935313i | \(-0.615118\pi\) | ||||
−0.353822 | + | 0.935313i | \(0.615118\pi\) | |||||||
\(578\) | 17100.4 | 1.23059 | ||||||||
\(579\) | −4590.53 | −0.329492 | ||||||||
\(580\) | −8547.99 | −0.611959 | ||||||||
\(581\) | 645.404 | 0.0460858 | ||||||||
\(582\) | 4089.64 | 0.291273 | ||||||||
\(583\) | −2056.50 | −0.146092 | ||||||||
\(584\) | 84.8702 | 0.00601362 | ||||||||
\(585\) | −882.381 | −0.0623624 | ||||||||
\(586\) | −7187.48 | −0.506676 | ||||||||
\(587\) | −6955.54 | −0.489073 | −0.244537 | − | 0.969640i | \(-0.578636\pi\) | ||||
−0.244537 | + | 0.969640i | \(0.578636\pi\) | |||||||
\(588\) | 4772.81 | 0.334741 | ||||||||
\(589\) | −2792.87 | −0.195379 | ||||||||
\(590\) | 1280.25 | 0.0893338 | ||||||||
\(591\) | 7385.42 | 0.514036 | ||||||||
\(592\) | −11631.8 | −0.807542 | ||||||||
\(593\) | −13988.6 | −0.968710 | −0.484355 | − | 0.874872i | \(-0.660946\pi\) | ||||
−0.484355 | + | 0.874872i | \(0.660946\pi\) | |||||||
\(594\) | −950.755 | −0.0656733 | ||||||||
\(595\) | 2760.03 | 0.190169 | ||||||||
\(596\) | 12562.1 | 0.863365 | ||||||||
\(597\) | 4326.81 | 0.296624 | ||||||||
\(598\) | −6996.98 | −0.478475 | ||||||||
\(599\) | 26538.4 | 1.81023 | 0.905117 | − | 0.425163i | \(-0.139783\pi\) | ||||
0.905117 | + | 0.425163i | \(0.139783\pi\) | |||||||
\(600\) | −1797.43 | −0.122300 | ||||||||
\(601\) | −16540.3 | −1.12261 | −0.561307 | − | 0.827608i | \(-0.689701\pi\) | ||||
−0.561307 | + | 0.827608i | \(0.689701\pi\) | |||||||
\(602\) | 11779.3 | 0.797486 | ||||||||
\(603\) | 8316.06 | 0.561619 | ||||||||
\(604\) | 10397.6 | 0.700453 | ||||||||
\(605\) | 7144.93 | 0.480137 | ||||||||
\(606\) | −4776.06 | −0.320155 | ||||||||
\(607\) | 2733.68 | 0.182795 | 0.0913974 | − | 0.995814i | \(-0.470867\pi\) | ||||
0.0913974 | + | 0.995814i | \(0.470867\pi\) | |||||||
\(608\) | −3488.32 | −0.232681 | ||||||||
\(609\) | −17374.5 | −1.15608 | ||||||||
\(610\) | −9475.87 | −0.628962 | ||||||||
\(611\) | 9488.95 | 0.628285 | ||||||||
\(612\) | 1111.67 | 0.0734261 | ||||||||
\(613\) | 9935.81 | 0.654655 | 0.327328 | − | 0.944911i | \(-0.393852\pi\) | ||||
0.327328 | + | 0.944911i | \(0.393852\pi\) | |||||||
\(614\) | −34860.9 | −2.29132 | ||||||||
\(615\) | −4509.48 | −0.295674 | ||||||||
\(616\) | −1481.94 | −0.0969303 | ||||||||
\(617\) | 4126.63 | 0.269257 | 0.134629 | − | 0.990896i | \(-0.457016\pi\) | ||||
0.134629 | + | 0.990896i | \(0.457016\pi\) | |||||||
\(618\) | 15748.1 | 1.02505 | ||||||||
\(619\) | 13867.2 | 0.900436 | 0.450218 | − | 0.892919i | \(-0.351346\pi\) | ||||
0.450218 | + | 0.892919i | \(0.351346\pi\) | |||||||
\(620\) | −6655.21 | −0.431096 | ||||||||
\(621\) | 2928.67 | 0.189249 | ||||||||
\(622\) | 9052.79 | 0.583576 | ||||||||
\(623\) | 3339.75 | 0.214774 | ||||||||
\(624\) | −3831.81 | −0.245826 | ||||||||
\(625\) | 4345.14 | 0.278089 | ||||||||
\(626\) | 38056.3 | 2.42977 | ||||||||
\(627\) | −422.925 | −0.0269378 | ||||||||
\(628\) | 4076.43 | 0.259024 | ||||||||
\(629\) | 3059.49 | 0.193942 | ||||||||
\(630\) | −4769.53 | −0.301623 | ||||||||
\(631\) | 2950.74 | 0.186160 | 0.0930801 | − | 0.995659i | \(-0.470329\pi\) | ||||
0.0930801 | + | 0.995659i | \(0.470329\pi\) | |||||||
\(632\) | 916.196 | 0.0576651 | ||||||||
\(633\) | −2197.04 | −0.137953 | ||||||||
\(634\) | −4036.87 | −0.252878 | ||||||||
\(635\) | −7583.42 | −0.473919 | ||||||||
\(636\) | −4155.28 | −0.259068 | ||||||||
\(637\) | 4327.15 | 0.269149 | ||||||||
\(638\) | −8350.34 | −0.518171 | ||||||||
\(639\) | −8433.17 | −0.522083 | ||||||||
\(640\) | 4675.11 | 0.288750 | ||||||||
\(641\) | −11795.4 | −0.726820 | −0.363410 | − | 0.931629i | \(-0.618388\pi\) | ||||
−0.363410 | + | 0.931629i | \(0.618388\pi\) | |||||||
\(642\) | 3848.71 | 0.236599 | ||||||||
\(643\) | 19304.7 | 1.18398 | 0.591992 | − | 0.805944i | \(-0.298342\pi\) | ||||
0.591992 | + | 0.805944i | \(0.298342\pi\) | |||||||
\(644\) | −16627.9 | −1.01744 | ||||||||
\(645\) | −2199.16 | −0.134251 | ||||||||
\(646\) | 1124.77 | 0.0685041 | ||||||||
\(647\) | 21361.3 | 1.29799 | 0.648995 | − | 0.760793i | \(-0.275190\pi\) | ||||
0.648995 | + | 0.760793i | \(0.275190\pi\) | |||||||
\(648\) | 527.393 | 0.0319722 | ||||||||
\(649\) | 549.846 | 0.0332563 | ||||||||
\(650\) | 5935.88 | 0.358191 | ||||||||
\(651\) | −13527.3 | −0.814401 | ||||||||
\(652\) | 3192.06 | 0.191734 | ||||||||
\(653\) | 5795.08 | 0.347288 | 0.173644 | − | 0.984809i | \(-0.444446\pi\) | ||||
0.173644 | + | 0.984809i | \(0.444446\pi\) | |||||||
\(654\) | −3366.86 | −0.201307 | ||||||||
\(655\) | 9983.39 | 0.595547 | ||||||||
\(656\) | −19582.8 | −1.16552 | ||||||||
\(657\) | 117.313 | 0.00696626 | ||||||||
\(658\) | 51290.6 | 3.03878 | ||||||||
\(659\) | 11950.9 | 0.706434 | 0.353217 | − | 0.935542i | \(-0.385088\pi\) | ||||
0.353217 | + | 0.935542i | \(0.385088\pi\) | |||||||
\(660\) | −1007.80 | −0.0594374 | ||||||||
\(661\) | 17906.5 | 1.05368 | 0.526838 | − | 0.849965i | \(-0.323377\pi\) | ||||
0.526838 | + | 0.849965i | \(0.323377\pi\) | |||||||
\(662\) | 36461.4 | 2.14065 | ||||||||
\(663\) | 1007.87 | 0.0590385 | ||||||||
\(664\) | −172.064 | −0.0100563 | ||||||||
\(665\) | −2121.64 | −0.123720 | ||||||||
\(666\) | −5287.01 | −0.307609 | ||||||||
\(667\) | 25722.1 | 1.49320 | ||||||||
\(668\) | 8909.70 | 0.516058 | ||||||||
\(669\) | 8784.79 | 0.507683 | ||||||||
\(670\) | 20050.1 | 1.15612 | ||||||||
\(671\) | −4069.74 | −0.234144 | ||||||||
\(672\) | −16895.7 | −0.969890 | ||||||||
\(673\) | 12825.6 | 0.734608 | 0.367304 | − | 0.930101i | \(-0.380281\pi\) | ||||
0.367304 | + | 0.930101i | \(0.380281\pi\) | |||||||
\(674\) | 25005.7 | 1.42906 | ||||||||
\(675\) | −2484.54 | −0.141674 | ||||||||
\(676\) | −11960.7 | −0.680514 | ||||||||
\(677\) | 11752.0 | 0.667156 | 0.333578 | − | 0.942722i | \(-0.391744\pi\) | ||||
0.333578 | + | 0.942722i | \(0.391744\pi\) | |||||||
\(678\) | −17613.0 | −0.997675 | ||||||||
\(679\) | 8811.31 | 0.498007 | ||||||||
\(680\) | −735.821 | −0.0414962 | ||||||||
\(681\) | 11729.2 | 0.660004 | ||||||||
\(682\) | −6501.33 | −0.365027 | ||||||||
\(683\) | −10731.7 | −0.601223 | −0.300612 | − | 0.953747i | \(-0.597191\pi\) | ||||
−0.300612 | + | 0.953747i | \(0.597191\pi\) | |||||||
\(684\) | −854.544 | −0.0477694 | ||||||||
\(685\) | 4460.58 | 0.248803 | ||||||||
\(686\) | −8262.47 | −0.459858 | ||||||||
\(687\) | 16742.0 | 0.929765 | ||||||||
\(688\) | −9550.05 | −0.529204 | ||||||||
\(689\) | −3767.28 | −0.208305 | ||||||||
\(690\) | 7061.07 | 0.389580 | ||||||||
\(691\) | 28804.7 | 1.58579 | 0.792895 | − | 0.609358i | \(-0.208573\pi\) | ||||
0.792895 | + | 0.609358i | \(0.208573\pi\) | |||||||
\(692\) | −5832.21 | −0.320387 | ||||||||
\(693\) | −2048.44 | −0.112286 | ||||||||
\(694\) | −14691.4 | −0.803572 | ||||||||
\(695\) | −4913.26 | −0.268159 | ||||||||
\(696\) | 4632.02 | 0.252265 | ||||||||
\(697\) | 5150.81 | 0.279915 | ||||||||
\(698\) | 32688.3 | 1.77259 | ||||||||
\(699\) | −11380.5 | −0.615808 | ||||||||
\(700\) | 14106.3 | 0.761667 | ||||||||
\(701\) | −1663.10 | −0.0896070 | −0.0448035 | − | 0.998996i | \(-0.514266\pi\) | ||||
−0.0448035 | + | 0.998996i | \(0.514266\pi\) | |||||||
\(702\) | −1741.67 | −0.0936400 | ||||||||
\(703\) | −2351.83 | −0.126175 | ||||||||
\(704\) | −2542.28 | −0.136102 | ||||||||
\(705\) | −9575.87 | −0.511557 | ||||||||
\(706\) | −7543.90 | −0.402151 | ||||||||
\(707\) | −10290.2 | −0.547388 | ||||||||
\(708\) | 1110.99 | 0.0589742 | ||||||||
\(709\) | 32357.6 | 1.71399 | 0.856993 | − | 0.515328i | \(-0.172330\pi\) | ||||
0.856993 | + | 0.515328i | \(0.172330\pi\) | |||||||
\(710\) | −20332.5 | −1.07474 | ||||||||
\(711\) | 1266.43 | 0.0668001 | ||||||||
\(712\) | −890.372 | −0.0468653 | ||||||||
\(713\) | 20026.5 | 1.05189 | ||||||||
\(714\) | 5447.85 | 0.285547 | ||||||||
\(715\) | −913.699 | −0.0477908 | ||||||||
\(716\) | −13888.8 | −0.724931 | ||||||||
\(717\) | 14986.6 | 0.780593 | ||||||||
\(718\) | −44110.2 | −2.29273 | ||||||||
\(719\) | −9360.97 | −0.485543 | −0.242771 | − | 0.970084i | \(-0.578057\pi\) | ||||
−0.242771 | + | 0.970084i | \(0.578057\pi\) | |||||||
\(720\) | 3866.91 | 0.200154 | ||||||||
\(721\) | 33929.9 | 1.75259 | ||||||||
\(722\) | 25051.9 | 1.29132 | ||||||||
\(723\) | 5023.54 | 0.258406 | ||||||||
\(724\) | −292.460 | −0.0150127 | ||||||||
\(725\) | −21821.3 | −1.11783 | ||||||||
\(726\) | 14102.9 | 0.720948 | ||||||||
\(727\) | −18574.0 | −0.947556 | −0.473778 | − | 0.880644i | \(-0.657110\pi\) | ||||
−0.473778 | + | 0.880644i | \(0.657110\pi\) | |||||||
\(728\) | −2714.74 | −0.138208 | ||||||||
\(729\) | 729.000 | 0.0370370 | ||||||||
\(730\) | 282.844 | 0.0143405 | ||||||||
\(731\) | 2511.93 | 0.127096 | ||||||||
\(732\) | −8223.14 | −0.415213 | ||||||||
\(733\) | 26673.5 | 1.34408 | 0.672038 | − | 0.740516i | \(-0.265419\pi\) | ||||
0.672038 | + | 0.740516i | \(0.265419\pi\) | |||||||
\(734\) | −42026.6 | −2.11339 | ||||||||
\(735\) | −4366.79 | −0.219145 | ||||||||
\(736\) | 25013.3 | 1.25272 | ||||||||
\(737\) | 8611.21 | 0.430391 | ||||||||
\(738\) | −8900.97 | −0.443969 | ||||||||
\(739\) | 25484.9 | 1.26857 | 0.634287 | − | 0.773098i | \(-0.281294\pi\) | ||||
0.634287 | + | 0.773098i | \(0.281294\pi\) | |||||||
\(740\) | −5604.24 | −0.278400 | ||||||||
\(741\) | −774.751 | −0.0384091 | ||||||||
\(742\) | −20363.3 | −1.00749 | ||||||||
\(743\) | −14039.9 | −0.693237 | −0.346619 | − | 0.938006i | \(-0.612670\pi\) | ||||
−0.346619 | + | 0.938006i | \(0.612670\pi\) | |||||||
\(744\) | 3606.35 | 0.177709 | ||||||||
\(745\) | −11493.5 | −0.565219 | ||||||||
\(746\) | −28139.7 | −1.38106 | ||||||||
\(747\) | −237.839 | −0.0116493 | ||||||||
\(748\) | 1151.13 | 0.0562694 | ||||||||
\(749\) | 8292.21 | 0.404527 | ||||||||
\(750\) | −14127.4 | −0.687813 | ||||||||
\(751\) | 34000.2 | 1.65205 | 0.826023 | − | 0.563637i | \(-0.190598\pi\) | ||||
0.826023 | + | 0.563637i | \(0.190598\pi\) | |||||||
\(752\) | −41584.0 | −2.01650 | ||||||||
\(753\) | 13468.1 | 0.651797 | ||||||||
\(754\) | −15296.9 | −0.738832 | ||||||||
\(755\) | −9513.09 | −0.458565 | ||||||||
\(756\) | −4138.99 | −0.199118 | ||||||||
\(757\) | −37552.9 | −1.80302 | −0.901508 | − | 0.432763i | \(-0.857539\pi\) | ||||
−0.901508 | + | 0.432763i | \(0.857539\pi\) | |||||||
\(758\) | 10341.2 | 0.495526 | ||||||||
\(759\) | 3032.62 | 0.145029 | ||||||||
\(760\) | 565.625 | 0.0269966 | ||||||||
\(761\) | −18976.0 | −0.903917 | −0.451959 | − | 0.892039i | \(-0.649275\pi\) | ||||
−0.451959 | + | 0.892039i | \(0.649275\pi\) | |||||||
\(762\) | −14968.4 | −0.711612 | ||||||||
\(763\) | −7254.05 | −0.344186 | ||||||||
\(764\) | −12779.5 | −0.605164 | ||||||||
\(765\) | −1017.10 | −0.0480699 | ||||||||
\(766\) | 14022.9 | 0.661447 | ||||||||
\(767\) | 1007.26 | 0.0474184 | ||||||||
\(768\) | 15774.9 | 0.741183 | ||||||||
\(769\) | −14782.6 | −0.693206 | −0.346603 | − | 0.938012i | \(-0.612665\pi\) | ||||
−0.346603 | + | 0.938012i | \(0.612665\pi\) | |||||||
\(770\) | −4938.82 | −0.231146 | ||||||||
\(771\) | 15297.8 | 0.714575 | ||||||||
\(772\) | −9604.62 | −0.447769 | ||||||||
\(773\) | −32518.7 | −1.51309 | −0.756543 | − | 0.653944i | \(-0.773113\pi\) | ||||
−0.756543 | + | 0.653944i | \(0.773113\pi\) | |||||||
\(774\) | −4340.79 | −0.201584 | ||||||||
\(775\) | −16989.4 | −0.787456 | ||||||||
\(776\) | −2349.08 | −0.108669 | ||||||||
\(777\) | −11391.1 | −0.525937 | ||||||||
\(778\) | −259.806 | −0.0119724 | ||||||||
\(779\) | −3959.43 | −0.182107 | ||||||||
\(780\) | −1846.18 | −0.0847485 | ||||||||
\(781\) | −8732.48 | −0.400093 | ||||||||
\(782\) | −8065.28 | −0.368816 | ||||||||
\(783\) | 6402.70 | 0.292227 | ||||||||
\(784\) | −18963.1 | −0.863845 | ||||||||
\(785\) | −3729.64 | −0.169575 | ||||||||
\(786\) | 19705.6 | 0.894242 | ||||||||
\(787\) | −7602.30 | −0.344336 | −0.172168 | − | 0.985068i | \(-0.555077\pi\) | ||||
−0.172168 | + | 0.985068i | \(0.555077\pi\) | |||||||
\(788\) | 15452.3 | 0.698559 | ||||||||
\(789\) | 23847.9 | 1.07606 | ||||||||
\(790\) | 3053.38 | 0.137512 | ||||||||
\(791\) | −37948.0 | −1.70578 | ||||||||
\(792\) | 546.112 | 0.0245016 | ||||||||
\(793\) | −7455.30 | −0.333853 | ||||||||
\(794\) | 35370.7 | 1.58093 | ||||||||
\(795\) | 3801.79 | 0.169604 | ||||||||
\(796\) | 9052.85 | 0.403103 | ||||||||
\(797\) | −7713.91 | −0.342836 | −0.171418 | − | 0.985198i | \(-0.554835\pi\) | ||||
−0.171418 | + | 0.985198i | \(0.554835\pi\) | |||||||
\(798\) | −4187.76 | −0.185771 | ||||||||
\(799\) | 10937.7 | 0.484292 | ||||||||
\(800\) | −21220.0 | −0.937799 | ||||||||
\(801\) | −1230.74 | −0.0542895 | ||||||||
\(802\) | 361.206 | 0.0159035 | ||||||||
\(803\) | 121.477 | 0.00533853 | ||||||||
\(804\) | 17399.4 | 0.763222 | ||||||||
\(805\) | 15213.4 | 0.666088 | ||||||||
\(806\) | −11909.7 | −0.520472 | ||||||||
\(807\) | −11494.3 | −0.501386 | ||||||||
\(808\) | 2743.36 | 0.119444 | ||||||||
\(809\) | 25690.3 | 1.11647 | 0.558234 | − | 0.829683i | \(-0.311479\pi\) | ||||
0.558234 | + | 0.829683i | \(0.311479\pi\) | |||||||
\(810\) | 1757.63 | 0.0762429 | ||||||||
\(811\) | 28467.8 | 1.23260 | 0.616302 | − | 0.787510i | \(-0.288630\pi\) | ||||
0.616302 | + | 0.787510i | \(0.288630\pi\) | |||||||
\(812\) | −36352.1 | −1.57107 | ||||||||
\(813\) | −20474.6 | −0.883241 | ||||||||
\(814\) | −5474.66 | −0.235733 | ||||||||
\(815\) | −2920.51 | −0.125523 | ||||||||
\(816\) | −4416.85 | −0.189486 | ||||||||
\(817\) | −1930.92 | −0.0826857 | ||||||||
\(818\) | 41769.8 | 1.78539 | ||||||||
\(819\) | −3752.51 | −0.160102 | ||||||||
\(820\) | −9435.05 | −0.401812 | ||||||||
\(821\) | −38119.4 | −1.62043 | −0.810217 | − | 0.586130i | \(-0.800651\pi\) | ||||
−0.810217 | + | 0.586130i | \(0.800651\pi\) | |||||||
\(822\) | 8804.45 | 0.373589 | ||||||||
\(823\) | −26656.3 | −1.12902 | −0.564508 | − | 0.825427i | \(-0.690934\pi\) | ||||
−0.564508 | + | 0.825427i | \(0.690934\pi\) | |||||||
\(824\) | −9045.66 | −0.382428 | ||||||||
\(825\) | −2572.72 | −0.108570 | ||||||||
\(826\) | 5444.52 | 0.229345 | ||||||||
\(827\) | −19016.7 | −0.799606 | −0.399803 | − | 0.916601i | \(-0.630922\pi\) | ||||
−0.399803 | + | 0.916601i | \(0.630922\pi\) | |||||||
\(828\) | 6127.57 | 0.257184 | ||||||||
\(829\) | −36260.4 | −1.51915 | −0.759575 | − | 0.650420i | \(-0.774593\pi\) | ||||
−0.759575 | + | 0.650420i | \(0.774593\pi\) | |||||||
\(830\) | −573.432 | −0.0239808 | ||||||||
\(831\) | −120.317 | −0.00502255 | ||||||||
\(832\) | −4657.16 | −0.194060 | ||||||||
\(833\) | 4987.82 | 0.207464 | ||||||||
\(834\) | −9697.95 | −0.402653 | ||||||||
\(835\) | −8151.75 | −0.337848 | ||||||||
\(836\) | −884.873 | −0.0366076 | ||||||||
\(837\) | 4984.95 | 0.205860 | ||||||||
\(838\) | 18342.0 | 0.756102 | ||||||||
\(839\) | 18034.3 | 0.742088 | 0.371044 | − | 0.928615i | \(-0.379000\pi\) | ||||
0.371044 | + | 0.928615i | \(0.379000\pi\) | |||||||
\(840\) | 2739.61 | 0.112530 | ||||||||
\(841\) | 31845.0 | 1.30571 | ||||||||
\(842\) | 20709.0 | 0.847602 | ||||||||
\(843\) | −7217.49 | −0.294880 | ||||||||
\(844\) | −4596.79 | −0.187474 | ||||||||
\(845\) | 10943.2 | 0.445512 | ||||||||
\(846\) | −18901.2 | −0.768127 | ||||||||
\(847\) | 30385.3 | 1.23265 | ||||||||
\(848\) | 16509.6 | 0.668562 | ||||||||
\(849\) | 24696.4 | 0.998327 | ||||||||
\(850\) | 6842.17 | 0.276099 | ||||||||
\(851\) | 16864.0 | 0.679305 | ||||||||
\(852\) | −17644.5 | −0.709494 | ||||||||
\(853\) | −17485.1 | −0.701851 | −0.350926 | − | 0.936403i | \(-0.614133\pi\) | ||||
−0.350926 | + | 0.936403i | \(0.614133\pi\) | |||||||
\(854\) | −40298.1 | −1.61472 | ||||||||
\(855\) | 781.847 | 0.0312732 | ||||||||
\(856\) | −2210.69 | −0.0882709 | ||||||||
\(857\) | 3337.89 | 0.133046 | 0.0665228 | − | 0.997785i | \(-0.478809\pi\) | ||||
0.0665228 | + | 0.997785i | \(0.478809\pi\) | |||||||
\(858\) | −1803.49 | −0.0717601 | ||||||||
\(859\) | −41566.7 | −1.65103 | −0.825517 | − | 0.564377i | \(-0.809117\pi\) | ||||
−0.825517 | + | 0.564377i | \(0.809117\pi\) | |||||||
\(860\) | −4601.24 | −0.182443 | ||||||||
\(861\) | −19177.5 | −0.759080 | ||||||||
\(862\) | −27834.3 | −1.09981 | ||||||||
\(863\) | 21883.2 | 0.863165 | 0.431583 | − | 0.902073i | \(-0.357955\pi\) | ||||
0.431583 | + | 0.902073i | \(0.357955\pi\) | |||||||
\(864\) | 6226.26 | 0.245164 | ||||||||
\(865\) | 5336.06 | 0.209747 | ||||||||
\(866\) | −862.859 | −0.0338581 | ||||||||
\(867\) | −13577.2 | −0.531842 | ||||||||
\(868\) | −28302.7 | −1.10675 | ||||||||
\(869\) | 1311.38 | 0.0511916 | ||||||||
\(870\) | 15437.0 | 0.601566 | ||||||||
\(871\) | 15774.8 | 0.613671 | ||||||||
\(872\) | 1933.92 | 0.0751041 | ||||||||
\(873\) | −3247.07 | −0.125884 | ||||||||
\(874\) | 6199.77 | 0.239943 | ||||||||
\(875\) | −30438.1 | −1.17599 | ||||||||
\(876\) | 245.451 | 0.00946693 | ||||||||
\(877\) | −18985.8 | −0.731019 | −0.365509 | − | 0.930808i | \(-0.619105\pi\) | ||||
−0.365509 | + | 0.930808i | \(0.619105\pi\) | |||||||
\(878\) | 63847.7 | 2.45416 | ||||||||
\(879\) | 5706.66 | 0.218977 | ||||||||
\(880\) | 4004.16 | 0.153386 | ||||||||
\(881\) | −47938.8 | −1.83326 | −0.916628 | − | 0.399742i | \(-0.869100\pi\) | ||||
−0.916628 | + | 0.399742i | \(0.869100\pi\) | |||||||
\(882\) | −8619.31 | −0.329056 | ||||||||
\(883\) | 45963.2 | 1.75174 | 0.875868 | − | 0.482550i | \(-0.160290\pi\) | ||||
0.875868 | + | 0.482550i | \(0.160290\pi\) | |||||||
\(884\) | 2108.74 | 0.0802314 | ||||||||
\(885\) | −1016.48 | −0.0386086 | ||||||||
\(886\) | −32735.5 | −1.24128 | ||||||||
\(887\) | −25211.9 | −0.954378 | −0.477189 | − | 0.878801i | \(-0.658344\pi\) | ||||
−0.477189 | + | 0.878801i | \(0.658344\pi\) | |||||||
\(888\) | 3036.85 | 0.114763 | ||||||||
\(889\) | −32250.1 | −1.21668 | ||||||||
\(890\) | −2967.32 | −0.111758 | ||||||||
\(891\) | 754.874 | 0.0283830 | ||||||||
\(892\) | 18380.2 | 0.689925 | ||||||||
\(893\) | −8407.83 | −0.315070 | ||||||||
\(894\) | −22686.2 | −0.848703 | ||||||||
\(895\) | 12707.3 | 0.474590 | ||||||||
\(896\) | 19881.9 | 0.741303 | ||||||||
\(897\) | 5555.41 | 0.206789 | ||||||||
\(898\) | 45397.5 | 1.68701 | ||||||||
\(899\) | 43782.1 | 1.62426 | ||||||||
\(900\) | −5198.32 | −0.192530 | ||||||||
\(901\) | −4342.47 | −0.160565 | ||||||||
\(902\) | −9216.88 | −0.340231 | ||||||||
\(903\) | −9352.41 | −0.344661 | ||||||||
\(904\) | 10116.9 | 0.372215 | ||||||||
\(905\) | 267.580 | 0.00982836 | ||||||||
\(906\) | −18777.3 | −0.688557 | ||||||||
\(907\) | −9607.36 | −0.351717 | −0.175858 | − | 0.984415i | \(-0.556270\pi\) | ||||
−0.175858 | + | 0.984415i | \(0.556270\pi\) | |||||||
\(908\) | 24540.6 | 0.896924 | ||||||||
\(909\) | 3792.06 | 0.138366 | ||||||||
\(910\) | −9047.34 | −0.329579 | ||||||||
\(911\) | −44171.3 | −1.60643 | −0.803217 | − | 0.595686i | \(-0.796880\pi\) | ||||
−0.803217 | + | 0.595686i | \(0.796880\pi\) | |||||||
\(912\) | 3395.23 | 0.123276 | ||||||||
\(913\) | −246.280 | −0.00892736 | ||||||||
\(914\) | −58909.1 | −2.13188 | ||||||||
\(915\) | 7523.59 | 0.271827 | ||||||||
\(916\) | 35028.8 | 1.26352 | ||||||||
\(917\) | 42456.4 | 1.52894 | ||||||||
\(918\) | −2007.59 | −0.0721792 | ||||||||
\(919\) | 33636.3 | 1.20736 | 0.603678 | − | 0.797228i | \(-0.293701\pi\) | ||||
0.603678 | + | 0.797228i | \(0.293701\pi\) | |||||||
\(920\) | −4055.86 | −0.145345 | ||||||||
\(921\) | 27678.6 | 0.990273 | ||||||||
\(922\) | −5573.70 | −0.199089 | ||||||||
\(923\) | −15996.9 | −0.570471 | ||||||||
\(924\) | −4285.89 | −0.152593 | ||||||||
\(925\) | −14306.5 | −0.508535 | ||||||||
\(926\) | −5044.78 | −0.179030 | ||||||||
\(927\) | −12503.5 | −0.443010 | ||||||||
\(928\) | 54684.3 | 1.93437 | ||||||||
\(929\) | 11890.9 | 0.419945 | 0.209972 | − | 0.977707i | \(-0.432663\pi\) | ||||
0.209972 | + | 0.977707i | \(0.432663\pi\) | |||||||
\(930\) | 12018.8 | 0.423775 | ||||||||
\(931\) | −3834.14 | −0.134972 | ||||||||
\(932\) | −23811.1 | −0.836864 | ||||||||
\(933\) | −7187.67 | −0.252212 | ||||||||
\(934\) | 52561.7 | 1.84140 | ||||||||
\(935\) | −1053.20 | −0.0368379 | ||||||||
\(936\) | 1000.41 | 0.0349354 | ||||||||
\(937\) | −18281.5 | −0.637385 | −0.318692 | − | 0.947858i | \(-0.603244\pi\) | ||||
−0.318692 | + | 0.947858i | \(0.603244\pi\) | |||||||
\(938\) | 85267.2 | 2.96810 | ||||||||
\(939\) | −30215.7 | −1.05011 | ||||||||
\(940\) | −20035.3 | −0.695190 | ||||||||
\(941\) | 40341.0 | 1.39753 | 0.698767 | − | 0.715349i | \(-0.253732\pi\) | ||||
0.698767 | + | 0.715349i | \(0.253732\pi\) | |||||||
\(942\) | −7361.70 | −0.254625 | ||||||||
\(943\) | 28391.4 | 0.980435 | ||||||||
\(944\) | −4414.15 | −0.152191 | ||||||||
\(945\) | 3786.88 | 0.130357 | ||||||||
\(946\) | −4494.85 | −0.154482 | ||||||||
\(947\) | −44404.6 | −1.52371 | −0.761856 | − | 0.647746i | \(-0.775712\pi\) | ||||
−0.761856 | + | 0.647746i | \(0.775712\pi\) | |||||||
\(948\) | 2649.71 | 0.0907792 | ||||||||
\(949\) | 222.532 | 0.00761191 | ||||||||
\(950\) | −5259.57 | −0.179624 | ||||||||
\(951\) | 3205.17 | 0.109290 | ||||||||
\(952\) | −3129.23 | −0.106533 | ||||||||
\(953\) | 34851.1 | 1.18461 | 0.592307 | − | 0.805713i | \(-0.298217\pi\) | ||||
0.592307 | + | 0.805713i | \(0.298217\pi\) | |||||||
\(954\) | 7504.09 | 0.254669 | ||||||||
\(955\) | 11692.3 | 0.396183 | ||||||||
\(956\) | 31356.0 | 1.06080 | ||||||||
\(957\) | 6629.95 | 0.223945 | ||||||||
\(958\) | −58505.5 | −1.97310 | ||||||||
\(959\) | 18969.5 | 0.638747 | ||||||||
\(960\) | 4699.81 | 0.158006 | ||||||||
\(961\) | 4296.41 | 0.144218 | ||||||||
\(962\) | −10028.9 | −0.336119 | ||||||||
\(963\) | −3055.77 | −0.102254 | ||||||||
\(964\) | 10510.6 | 0.351165 | ||||||||
\(965\) | 8787.55 | 0.293141 | ||||||||
\(966\) | 30028.7 | 1.00016 | ||||||||
\(967\) | 2971.34 | 0.0988128 | 0.0494064 | − | 0.998779i | \(-0.484267\pi\) | ||||
0.0494064 | + | 0.998779i | \(0.484267\pi\) | |||||||
\(968\) | −8100.68 | −0.268973 | ||||||||
\(969\) | −893.040 | −0.0296064 | ||||||||
\(970\) | −7828.71 | −0.259139 | ||||||||
\(971\) | 34741.0 | 1.14819 | 0.574094 | − | 0.818789i | \(-0.305354\pi\) | ||||
0.574094 | + | 0.818789i | \(0.305354\pi\) | |||||||
\(972\) | 1525.26 | 0.0503322 | ||||||||
\(973\) | −20894.6 | −0.688440 | ||||||||
\(974\) | 48749.1 | 1.60372 | ||||||||
\(975\) | −4712.93 | −0.154805 | ||||||||
\(976\) | 32671.8 | 1.07151 | ||||||||
\(977\) | −31701.1 | −1.03808 | −0.519042 | − | 0.854749i | \(-0.673711\pi\) | ||||
−0.519042 | + | 0.854749i | \(0.673711\pi\) | |||||||
\(978\) | −5764.60 | −0.188478 | ||||||||
\(979\) | −1274.42 | −0.0416042 | ||||||||
\(980\) | −9136.49 | −0.297811 | ||||||||
\(981\) | 2673.20 | 0.0870017 | ||||||||
\(982\) | 16429.2 | 0.533887 | ||||||||
\(983\) | −47493.5 | −1.54100 | −0.770502 | − | 0.637437i | \(-0.779995\pi\) | ||||
−0.770502 | + | 0.637437i | \(0.779995\pi\) | |||||||
\(984\) | 5112.70 | 0.165637 | ||||||||
\(985\) | −14137.7 | −0.457326 | ||||||||
\(986\) | −17632.4 | −0.569503 | ||||||||
\(987\) | −40723.4 | −1.31331 | ||||||||
\(988\) | −1620.99 | −0.0521968 | ||||||||
\(989\) | 13845.8 | 0.445167 | ||||||||
\(990\) | 1820.01 | 0.0584280 | ||||||||
\(991\) | −48621.1 | −1.55853 | −0.779263 | − | 0.626697i | \(-0.784406\pi\) | ||||
−0.779263 | + | 0.626697i | \(0.784406\pi\) | |||||||
\(992\) | 42575.5 | 1.36268 | ||||||||
\(993\) | −28949.4 | −0.925157 | ||||||||
\(994\) | −86468.0 | −2.75915 | ||||||||
\(995\) | −8282.71 | −0.263899 | ||||||||
\(996\) | −497.622 | −0.0158311 | ||||||||
\(997\) | 37128.0 | 1.17939 | 0.589697 | − | 0.807625i | \(-0.299247\pi\) | ||||
0.589697 | + | 0.807625i | \(0.299247\pi\) | |||||||
\(998\) | 45536.9 | 1.44433 | ||||||||
\(999\) | 4197.74 | 0.132944 |
(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 | 177.4.a.d.1.2 | ✓ | 8 | |
3.2 | odd | 2 | 531.4.a.e.1.7 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
177.4.a.d.1.2 | ✓ | 8 | 1.1 | even | 1 | trivial | |
531.4.a.e.1.7 | 8 | 3.2 | odd | 2 |