Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2205,4,Mod(1,2205)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2205, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("2205.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2205 = 3^{2} \cdot 5 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 2205.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: | \(130.099211563\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{41}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 10 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 105) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-2.70156\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2205.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.70156 | 0.601593 | 0.300797 | − | 0.953688i | \(-0.402747\pi\) | ||||
0.300797 | + | 0.953688i | \(0.402747\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −5.10469 | −0.638086 | ||||||||
\(5\) | −5.00000 | −0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −22.2984 | −0.985461 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −8.50781 | −0.269041 | ||||||||
\(11\) | −37.4031 | −1.02522 | −0.512612 | − | 0.858620i | \(-0.671322\pi\) | ||||
−0.512612 | + | 0.858620i | \(0.671322\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −29.0156 | −0.619037 | −0.309519 | − | 0.950893i | \(-0.600168\pi\) | ||||
−0.309519 | + | 0.950893i | \(0.600168\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 2.89531 | 0.0452393 | ||||||||
\(17\) | 58.4187 | 0.833449 | 0.416724 | − | 0.909033i | \(-0.363178\pi\) | ||||
0.416724 | + | 0.909033i | \(0.363178\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 54.5969 | 0.659231 | 0.329615 | − | 0.944115i | \(-0.393081\pi\) | ||||
0.329615 | + | 0.944115i | \(0.393081\pi\) | |||||||
\(20\) | 25.5234 | 0.285361 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −63.6437 | −0.616768 | ||||||||
\(23\) | −161.675 | −1.46572 | −0.732860 | − | 0.680379i | \(-0.761815\pi\) | ||||
−0.732860 | + | 0.680379i | \(0.761815\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 25.0000 | 0.200000 | ||||||||
\(26\) | −49.3719 | −0.372409 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −137.581 | −0.880972 | −0.440486 | − | 0.897759i | \(-0.645194\pi\) | ||||
−0.440486 | + | 0.897759i | \(0.645194\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −154.659 | −0.896053 | −0.448026 | − | 0.894020i | \(-0.647873\pi\) | ||||
−0.448026 | + | 0.894020i | \(0.647873\pi\) | |||||||
\(32\) | 183.314 | 1.01268 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 99.4031 | 0.501397 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −350.125 | −1.55568 | −0.777840 | − | 0.628462i | \(-0.783685\pi\) | ||||
−0.777840 | + | 0.628462i | \(0.783685\pi\) | |||||||
\(38\) | 92.9000 | 0.396589 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 111.492 | 0.440712 | ||||||||
\(41\) | 353.769 | 1.34755 | 0.673773 | − | 0.738938i | \(-0.264673\pi\) | ||||
0.673773 | + | 0.738938i | \(0.264673\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −518.156 | −1.83763 | −0.918815 | − | 0.394689i | \(-0.870852\pi\) | ||||
−0.918815 | + | 0.394689i | \(0.870852\pi\) | |||||||
\(44\) | 190.931 | 0.654181 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −275.100 | −0.881767 | ||||||||
\(47\) | −542.219 | −1.68278 | −0.841391 | − | 0.540427i | \(-0.818263\pi\) | ||||
−0.841391 | + | 0.540427i | \(0.818263\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 42.5391 | 0.120319 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 148.116 | 0.394999 | ||||||||
\(53\) | −305.309 | −0.791273 | −0.395637 | − | 0.918407i | \(-0.629476\pi\) | ||||
−0.395637 | + | 0.918407i | \(0.629476\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 187.016 | 0.458494 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −234.103 | −0.529987 | ||||||||
\(59\) | 14.6813 | 0.0323956 | 0.0161978 | − | 0.999869i | \(-0.494844\pi\) | ||||
0.0161978 | + | 0.999869i | \(0.494844\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 171.069 | 0.359067 | 0.179534 | − | 0.983752i | \(-0.442541\pi\) | ||||
0.179534 | + | 0.983752i | \(0.442541\pi\) | |||||||
\(62\) | −263.163 | −0.539059 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 288.758 | 0.563980 | ||||||||
\(65\) | 145.078 | 0.276842 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 551.956 | 1.00645 | 0.503225 | − | 0.864155i | \(-0.332147\pi\) | ||||
0.503225 | + | 0.864155i | \(0.332147\pi\) | |||||||
\(68\) | −298.209 | −0.531812 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 120.334 | 0.201142 | 0.100571 | − | 0.994930i | \(-0.467933\pi\) | ||||
0.100571 | + | 0.994930i | \(0.467933\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −284.659 | −0.456395 | −0.228198 | − | 0.973615i | \(-0.573283\pi\) | ||||
−0.228198 | + | 0.973615i | \(0.573283\pi\) | |||||||
\(74\) | −595.759 | −0.935887 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −278.700 | −0.420646 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 941.612 | 1.34101 | 0.670504 | − | 0.741906i | \(-0.266078\pi\) | ||||
0.670504 | + | 0.741906i | \(0.266078\pi\) | |||||||
\(80\) | −14.4766 | −0.0202316 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 601.959 | 0.810674 | ||||||||
\(83\) | 377.150 | 0.498766 | 0.249383 | − | 0.968405i | \(-0.419772\pi\) | ||||
0.249383 | + | 0.968405i | \(0.419772\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −292.094 | −0.372730 | ||||||||
\(86\) | −881.675 | −1.10551 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 834.031 | 1.01032 | ||||||||
\(89\) | −677.725 | −0.807176 | −0.403588 | − | 0.914941i | \(-0.632237\pi\) | ||||
−0.403588 | + | 0.914941i | \(0.632237\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 825.300 | 0.935255 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −922.619 | −1.01235 | ||||||||
\(95\) | −272.984 | −0.294817 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1225.03 | 1.28230 | 0.641151 | − | 0.767414i | \(-0.278457\pi\) | ||||
0.641151 | + | 0.767414i | \(0.278457\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −127.617 | −0.127617 | ||||||||
\(101\) | −338.144 | −0.333134 | −0.166567 | − | 0.986030i | \(-0.553268\pi\) | ||||
−0.166567 | + | 0.986030i | \(0.553268\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 566.700 | 0.542122 | 0.271061 | − | 0.962562i | \(-0.412625\pi\) | ||||
0.271061 | + | 0.962562i | \(0.412625\pi\) | |||||||
\(104\) | 647.003 | 0.610037 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −519.503 | −0.476024 | ||||||||
\(107\) | 562.531 | 0.508242 | 0.254121 | − | 0.967172i | \(-0.418214\pi\) | ||||
0.254121 | + | 0.967172i | \(0.418214\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1830.79 | 1.60879 | 0.804396 | − | 0.594094i | \(-0.202489\pi\) | ||||
0.804396 | + | 0.594094i | \(0.202489\pi\) | |||||||
\(110\) | 318.219 | 0.275827 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 31.8032 | 0.0264761 | 0.0132380 | − | 0.999912i | \(-0.495786\pi\) | ||||
0.0132380 | + | 0.999912i | \(0.495786\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 808.375 | 0.655490 | ||||||||
\(116\) | 702.309 | 0.562136 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 24.9811 | 0.0194890 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 67.9937 | 0.0510847 | ||||||||
\(122\) | 291.084 | 0.216012 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 789.488 | 0.571759 | ||||||||
\(125\) | −125.000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 2220.81 | 1.55169 | 0.775847 | − | 0.630921i | \(-0.217323\pi\) | ||||
0.775847 | + | 0.630921i | \(0.217323\pi\) | |||||||
\(128\) | −975.173 | −0.673390 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 246.859 | 0.166546 | ||||||||
\(131\) | 646.512 | 0.431191 | 0.215596 | − | 0.976483i | \(-0.430831\pi\) | ||||
0.215596 | + | 0.976483i | \(0.430831\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 939.188 | 0.605474 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −1302.65 | −0.821331 | ||||||||
\(137\) | 896.009 | 0.558768 | 0.279384 | − | 0.960179i | \(-0.409870\pi\) | ||||
0.279384 | + | 0.960179i | \(0.409870\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 2313.61 | 1.41178 | 0.705891 | − | 0.708320i | \(-0.250547\pi\) | ||||
0.705891 | + | 0.708320i | \(0.250547\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 204.756 | 0.121005 | ||||||||
\(143\) | 1085.27 | 0.634652 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 687.906 | 0.393983 | ||||||||
\(146\) | −484.366 | −0.274564 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 1787.28 | 0.992658 | ||||||||
\(149\) | −819.337 | −0.450488 | −0.225244 | − | 0.974302i | \(-0.572318\pi\) | ||||
−0.225244 | + | 0.974302i | \(0.572318\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 534.744 | 0.288191 | 0.144095 | − | 0.989564i | \(-0.453973\pi\) | ||||
0.144095 | + | 0.989564i | \(0.453973\pi\) | |||||||
\(152\) | −1217.43 | −0.649646 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 773.297 | 0.400727 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −1564.76 | −0.795423 | −0.397711 | − | 0.917511i | \(-0.630195\pi\) | ||||
−0.397711 | + | 0.917511i | \(0.630195\pi\) | |||||||
\(158\) | 1602.21 | 0.806741 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −916.570 | −0.452883 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −1114.31 | −0.535455 | −0.267728 | − | 0.963495i | \(-0.586273\pi\) | ||||
−0.267728 | + | 0.963495i | \(0.586273\pi\) | |||||||
\(164\) | −1805.88 | −0.859850 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 641.744 | 0.300054 | ||||||||
\(167\) | −1774.47 | −0.822231 | −0.411115 | − | 0.911583i | \(-0.634861\pi\) | ||||
−0.411115 | + | 0.911583i | \(0.634861\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1355.09 | −0.616793 | ||||||||
\(170\) | −497.016 | −0.224232 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 2645.02 | 1.17257 | ||||||||
\(173\) | −4215.88 | −1.85276 | −0.926380 | − | 0.376590i | \(-0.877097\pi\) | ||||
−0.926380 | + | 0.376590i | \(0.877097\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −108.294 | −0.0463804 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −1153.19 | −0.485592 | ||||||||
\(179\) | 2430.70 | 1.01497 | 0.507483 | − | 0.861662i | \(-0.330576\pi\) | ||||
0.507483 | + | 0.861662i | \(0.330576\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 2700.91 | 1.10916 | 0.554578 | − | 0.832132i | \(-0.312880\pi\) | ||||
0.554578 | + | 0.832132i | \(0.312880\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 3605.10 | 1.44441 | ||||||||
\(185\) | 1750.62 | 0.695722 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −2185.04 | −0.854472 | ||||||||
\(188\) | 2767.86 | 1.07376 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −464.500 | −0.177360 | ||||||||
\(191\) | −3611.10 | −1.36801 | −0.684005 | − | 0.729478i | \(-0.739763\pi\) | ||||
−0.684005 | + | 0.729478i | \(0.739763\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −4468.33 | −1.66651 | −0.833257 | − | 0.552886i | \(-0.813526\pi\) | ||||
−0.833257 | + | 0.552886i | \(0.813526\pi\) | |||||||
\(194\) | 2084.47 | 0.771425 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 434.422 | 0.157113 | 0.0785566 | − | 0.996910i | \(-0.474969\pi\) | ||||
0.0785566 | + | 0.996910i | \(0.474969\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 468.915 | 0.167038 | 0.0835189 | − | 0.996506i | \(-0.473384\pi\) | ||||
0.0835189 | + | 0.996506i | \(0.473384\pi\) | |||||||
\(200\) | −557.461 | −0.197092 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −575.372 | −0.200411 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −1768.84 | −0.602641 | ||||||||
\(206\) | 964.275 | 0.326137 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −84.0093 | −0.0280048 | ||||||||
\(209\) | −2042.09 | −0.675859 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 3735.51 | 1.21878 | 0.609392 | − | 0.792869i | \(-0.291414\pi\) | ||||
0.609392 | + | 0.792869i | \(0.291414\pi\) | |||||||
\(212\) | 1558.51 | 0.504900 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 957.182 | 0.305755 | ||||||||
\(215\) | 2590.78 | 0.821813 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 3115.21 | 0.967838 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −954.656 | −0.292559 | ||||||||
\(221\) | −1695.06 | −0.515936 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −842.806 | −0.253087 | −0.126544 | − | 0.991961i | \(-0.540388\pi\) | ||||
−0.126544 | + | 0.991961i | \(0.540388\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 54.1152 | 0.0159278 | ||||||||
\(227\) | 992.150 | 0.290094 | 0.145047 | − | 0.989425i | \(-0.453667\pi\) | ||||
0.145047 | + | 0.989425i | \(0.453667\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 6411.39 | 1.85012 | 0.925059 | − | 0.379825i | \(-0.124016\pi\) | ||||
0.925059 | + | 0.379825i | \(0.124016\pi\) | |||||||
\(230\) | 1375.50 | 0.394338 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 3067.85 | 0.868164 | ||||||||
\(233\) | 2274.35 | 0.639476 | 0.319738 | − | 0.947506i | \(-0.396405\pi\) | ||||
0.319738 | + | 0.947506i | \(0.396405\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 2711.09 | 0.752563 | ||||||||
\(236\) | −74.9433 | −0.0206712 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −2863.12 | −0.774893 | −0.387447 | − | 0.921892i | \(-0.626643\pi\) | ||||
−0.387447 | + | 0.921892i | \(0.626643\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 5364.23 | 1.43378 | 0.716889 | − | 0.697187i | \(-0.245565\pi\) | ||||
0.716889 | + | 0.697187i | \(0.245565\pi\) | |||||||
\(242\) | 115.696 | 0.0307322 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −873.252 | −0.229116 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1584.16 | −0.408088 | ||||||||
\(248\) | 3448.66 | 0.883025 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −212.695 | −0.0538081 | ||||||||
\(251\) | 5569.81 | 1.40065 | 0.700325 | − | 0.713824i | \(-0.253039\pi\) | ||||
0.700325 | + | 0.713824i | \(0.253039\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 6047.15 | 1.50269 | ||||||||
\(254\) | 3778.85 | 0.933489 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −3969.38 | −0.969087 | ||||||||
\(257\) | 2095.36 | 0.508580 | 0.254290 | − | 0.967128i | \(-0.418158\pi\) | ||||
0.254290 | + | 0.967128i | \(0.418158\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −740.578 | −0.176649 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 1100.08 | 0.259402 | ||||||||
\(263\) | 7465.88 | 1.75044 | 0.875220 | − | 0.483724i | \(-0.160716\pi\) | ||||
0.875220 | + | 0.483724i | \(0.160716\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 1526.55 | 0.353868 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −2817.56 | −0.642202 | ||||||||
\(269\) | −6521.38 | −1.47812 | −0.739062 | − | 0.673637i | \(-0.764731\pi\) | ||||
−0.739062 | + | 0.673637i | \(0.764731\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −2409.70 | −0.540144 | −0.270072 | − | 0.962840i | \(-0.587048\pi\) | ||||
−0.270072 | + | 0.962840i | \(0.587048\pi\) | |||||||
\(272\) | 169.141 | 0.0377046 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 1524.62 | 0.336151 | ||||||||
\(275\) | −935.078 | −0.205045 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −2219.83 | −0.481503 | −0.240752 | − | 0.970587i | \(-0.577394\pi\) | ||||
−0.240752 | + | 0.970587i | \(0.577394\pi\) | |||||||
\(278\) | 3936.75 | 0.849319 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −5838.56 | −1.23950 | −0.619749 | − | 0.784800i | \(-0.712766\pi\) | ||||
−0.619749 | + | 0.784800i | \(0.712766\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 3645.04 | 0.765636 | 0.382818 | − | 0.923824i | \(-0.374954\pi\) | ||||
0.382818 | + | 0.923824i | \(0.374954\pi\) | |||||||
\(284\) | −614.269 | −0.128346 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 1846.66 | 0.381802 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −1500.25 | −0.305363 | ||||||||
\(290\) | 1170.52 | 0.237017 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 1453.10 | 0.291219 | ||||||||
\(293\) | 3777.91 | 0.753268 | 0.376634 | − | 0.926362i | \(-0.377081\pi\) | ||||
0.376634 | + | 0.926362i | \(0.377081\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −73.4064 | −0.0144877 | ||||||||
\(296\) | 7807.24 | 1.53306 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −1394.15 | −0.271011 | ||||||||
\(299\) | 4691.10 | 0.907336 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 909.900 | 0.173374 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 158.075 | 0.0298231 | ||||||||
\(305\) | −855.344 | −0.160580 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 4799.64 | 0.892281 | 0.446140 | − | 0.894963i | \(-0.352798\pi\) | ||||
0.446140 | + | 0.894963i | \(0.352798\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 1315.81 | 0.241075 | ||||||||
\(311\) | 580.113 | 0.105772 | 0.0528861 | − | 0.998601i | \(-0.483158\pi\) | ||||
0.0528861 | + | 0.998601i | \(0.483158\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 6114.78 | 1.10424 | 0.552121 | − | 0.833764i | \(-0.313818\pi\) | ||||
0.552121 | + | 0.833764i | \(0.313818\pi\) | |||||||
\(314\) | −2662.53 | −0.478521 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −4806.64 | −0.855679 | ||||||||
\(317\) | 4300.63 | 0.761979 | 0.380989 | − | 0.924579i | \(-0.375583\pi\) | ||||
0.380989 | + | 0.924579i | \(0.375583\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 5145.97 | 0.903194 | ||||||||
\(320\) | −1443.79 | −0.252220 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 3189.48 | 0.549435 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −725.391 | −0.123807 | ||||||||
\(326\) | −1896.06 | −0.322126 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −7888.49 | −1.32795 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −6687.54 | −1.11051 | −0.555257 | − | 0.831679i | \(-0.687380\pi\) | ||||
−0.555257 | + | 0.831679i | \(0.687380\pi\) | |||||||
\(332\) | −1925.23 | −0.318256 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −3019.37 | −0.494648 | ||||||||
\(335\) | −2759.78 | −0.450098 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 5869.28 | 0.948723 | 0.474362 | − | 0.880330i | \(-0.342679\pi\) | ||||
0.474362 | + | 0.880330i | \(0.342679\pi\) | |||||||
\(338\) | −2305.78 | −0.371058 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 1491.05 | 0.237833 | ||||||||
\(341\) | 5784.74 | 0.918655 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 11554.1 | 1.81091 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −7173.58 | −1.11461 | ||||||||
\(347\) | −1937.22 | −0.299699 | −0.149850 | − | 0.988709i | \(-0.547879\pi\) | ||||
−0.149850 | + | 0.988709i | \(0.547879\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 9748.82 | 1.49525 | 0.747625 | − | 0.664121i | \(-0.231194\pi\) | ||||
0.747625 | + | 0.664121i | \(0.231194\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −6856.52 | −1.03822 | ||||||||
\(353\) | −4576.61 | −0.690052 | −0.345026 | − | 0.938593i | \(-0.612130\pi\) | ||||
−0.345026 | + | 0.938593i | \(0.612130\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −601.672 | −0.0899533 | ||||||||
\(356\) | 3459.57 | 0.515048 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 4135.98 | 0.610596 | ||||||||
\(359\) | −10849.9 | −1.59509 | −0.797546 | − | 0.603258i | \(-0.793869\pi\) | ||||
−0.797546 | + | 0.603258i | \(0.793869\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −3878.18 | −0.565415 | ||||||||
\(362\) | 4595.77 | 0.667261 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 1423.30 | 0.204106 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −11467.7 | −1.63108 | −0.815541 | − | 0.578699i | \(-0.803561\pi\) | ||||
−0.815541 | + | 0.578699i | \(0.803561\pi\) | |||||||
\(368\) | −468.100 | −0.0663081 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 2978.80 | 0.418541 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 539.982 | 0.0749576 | 0.0374788 | − | 0.999297i | \(-0.488067\pi\) | ||||
0.0374788 | + | 0.999297i | \(0.488067\pi\) | |||||||
\(374\) | −3717.99 | −0.514044 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 12090.6 | 1.65832 | ||||||||
\(377\) | 3992.01 | 0.545355 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 8577.57 | 1.16253 | 0.581267 | − | 0.813713i | \(-0.302557\pi\) | ||||
0.581267 | + | 0.813713i | \(0.302557\pi\) | |||||||
\(380\) | 1393.50 | 0.188118 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −6144.51 | −0.822985 | ||||||||
\(383\) | 8627.96 | 1.15109 | 0.575546 | − | 0.817770i | \(-0.304790\pi\) | ||||
0.575546 | + | 0.817770i | \(0.304790\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −7603.13 | −1.00256 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −6253.42 | −0.818219 | ||||||||
\(389\) | −9234.06 | −1.20356 | −0.601781 | − | 0.798661i | \(-0.705542\pi\) | ||||
−0.601781 | + | 0.798661i | \(0.705542\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −9444.85 | −1.22160 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 739.196 | 0.0945182 | ||||||||
\(395\) | −4708.06 | −0.599717 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −11618.0 | −1.46874 | −0.734372 | − | 0.678747i | \(-0.762523\pi\) | ||||
−0.734372 | + | 0.678747i | \(0.762523\pi\) | |||||||
\(398\) | 797.889 | 0.100489 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 72.3828 | 0.00904786 | ||||||||
\(401\) | −11157.1 | −1.38942 | −0.694711 | − | 0.719289i | \(-0.744468\pi\) | ||||
−0.694711 | + | 0.719289i | \(0.744468\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 4487.54 | 0.554690 | ||||||||
\(404\) | 1726.12 | 0.212568 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 13095.8 | 1.59492 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 7428.08 | 0.898031 | 0.449015 | − | 0.893524i | \(-0.351775\pi\) | ||||
0.449015 | + | 0.893524i | \(0.351775\pi\) | |||||||
\(410\) | −3009.80 | −0.362545 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −2892.83 | −0.345921 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −1885.75 | −0.223055 | ||||||||
\(416\) | −5318.97 | −0.626885 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −3474.75 | −0.406592 | ||||||||
\(419\) | 9644.74 | 1.12453 | 0.562263 | − | 0.826959i | \(-0.309931\pi\) | ||||
0.562263 | + | 0.826959i | \(0.309931\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 9918.18 | 1.14818 | 0.574088 | − | 0.818793i | \(-0.305357\pi\) | ||||
0.574088 | + | 0.818793i | \(0.305357\pi\) | |||||||
\(422\) | 6356.21 | 0.733212 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 6807.92 | 0.779769 | ||||||||
\(425\) | 1460.47 | 0.166690 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −2871.54 | −0.324302 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 4408.37 | 0.494397 | ||||||||
\(431\) | 16324.1 | 1.82437 | 0.912185 | − | 0.409779i | \(-0.134394\pi\) | ||||
0.912185 | + | 0.409779i | \(0.134394\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 5168.75 | 0.573659 | 0.286829 | − | 0.957982i | \(-0.407399\pi\) | ||||
0.286829 | + | 0.957982i | \(0.407399\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −9345.63 | −1.02655 | ||||||||
\(437\) | −8826.95 | −0.966248 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −18339.0 | −1.99378 | −0.996892 | − | 0.0787782i | \(-0.974898\pi\) | ||||
−0.996892 | + | 0.0787782i | \(0.974898\pi\) | |||||||
\(440\) | −4170.16 | −0.451828 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −2884.24 | −0.310383 | ||||||||
\(443\) | 1613.28 | 0.173023 | 0.0865113 | − | 0.996251i | \(-0.472428\pi\) | ||||
0.0865113 | + | 0.996251i | \(0.472428\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 3388.62 | 0.360980 | ||||||||
\(446\) | −1434.09 | −0.152256 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 886.750 | 0.0932034 | 0.0466017 | − | 0.998914i | \(-0.485161\pi\) | ||||
0.0466017 | + | 0.998914i | \(0.485161\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −13232.1 | −1.38154 | ||||||||
\(452\) | −162.345 | −0.0168940 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 1688.21 | 0.174518 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 7391.22 | 0.756557 | 0.378279 | − | 0.925692i | \(-0.376516\pi\) | ||||
0.378279 | + | 0.925692i | \(0.376516\pi\) | |||||||
\(458\) | 10909.4 | 1.11302 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −4126.50 | −0.418259 | ||||||||
\(461\) | −7133.35 | −0.720679 | −0.360340 | − | 0.932821i | \(-0.617339\pi\) | ||||
−0.360340 | + | 0.932821i | \(0.617339\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 14461.8 | 1.45162 | 0.725808 | − | 0.687897i | \(-0.241466\pi\) | ||||
0.725808 | + | 0.687897i | \(0.241466\pi\) | |||||||
\(464\) | −398.341 | −0.0398546 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 3869.95 | 0.384704 | ||||||||
\(467\) | −16393.5 | −1.62441 | −0.812206 | − | 0.583370i | \(-0.801734\pi\) | ||||
−0.812206 | + | 0.583370i | \(0.801734\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 4613.09 | 0.452737 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −327.370 | −0.0319246 | ||||||||
\(473\) | 19380.7 | 1.88398 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1364.92 | 0.131846 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −4871.77 | −0.466171 | ||||||||
\(479\) | −12991.4 | −1.23923 | −0.619617 | − | 0.784904i | \(-0.712712\pi\) | ||||
−0.619617 | + | 0.784904i | \(0.712712\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 10159.1 | 0.963025 | ||||||||
\(482\) | 9127.57 | 0.862551 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −347.087 | −0.0325964 | ||||||||
\(485\) | −6125.17 | −0.573463 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −12863.5 | −1.19692 | −0.598461 | − | 0.801152i | \(-0.704221\pi\) | ||||
−0.598461 | + | 0.801152i | \(0.704221\pi\) | |||||||
\(488\) | −3814.57 | −0.353847 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 4898.10 | 0.450200 | 0.225100 | − | 0.974336i | \(-0.427729\pi\) | ||||
0.225100 | + | 0.974336i | \(0.427729\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −8037.32 | −0.734245 | ||||||||
\(494\) | −2695.55 | −0.245503 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −447.787 | −0.0405368 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 10308.0 | 0.924746 | 0.462373 | − | 0.886686i | \(-0.346998\pi\) | ||||
0.462373 | + | 0.886686i | \(0.346998\pi\) | |||||||
\(500\) | 638.086 | 0.0570721 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 9477.37 | 0.842621 | ||||||||
\(503\) | −15119.6 | −1.34026 | −0.670130 | − | 0.742244i | \(-0.733762\pi\) | ||||
−0.670130 | + | 0.742244i | \(0.733762\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 1690.72 | 0.148982 | ||||||||
\(506\) | 10289.6 | 0.904009 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −11336.6 | −0.990114 | ||||||||
\(509\) | 14183.8 | 1.23514 | 0.617571 | − | 0.786515i | \(-0.288117\pi\) | ||||
0.617571 | + | 0.786515i | \(0.288117\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 1047.24 | 0.0903943 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 3565.39 | 0.305958 | ||||||||
\(515\) | −2833.50 | −0.242444 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 20280.7 | 1.72523 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −3235.02 | −0.272817 | ||||||||
\(521\) | −7464.08 | −0.627653 | −0.313827 | − | 0.949480i | \(-0.601611\pi\) | ||||
−0.313827 | + | 0.949480i | \(0.601611\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 16642.9 | 1.39148 | 0.695739 | − | 0.718295i | \(-0.255077\pi\) | ||||
0.695739 | + | 0.718295i | \(0.255077\pi\) | |||||||
\(524\) | −3300.24 | −0.275137 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 12703.7 | 1.05305 | ||||||||
\(527\) | −9035.01 | −0.746814 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 13971.8 | 1.14834 | ||||||||
\(530\) | 2597.51 | 0.212885 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −10264.8 | −0.834181 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −2812.66 | −0.227293 | ||||||||
\(536\) | −12307.8 | −0.991818 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −11096.5 | −0.889230 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 67.8755 | 0.00539408 | 0.00269704 | − | 0.999996i | \(-0.499142\pi\) | ||||
0.00269704 | + | 0.999996i | \(0.499142\pi\) | |||||||
\(542\) | −4100.26 | −0.324947 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 10709.0 | 0.844014 | ||||||||
\(545\) | −9153.97 | −0.719473 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −9212.91 | −0.720138 | −0.360069 | − | 0.932926i | \(-0.617247\pi\) | ||||
−0.360069 | + | 0.932926i | \(0.617247\pi\) | |||||||
\(548\) | −4573.85 | −0.356542 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −1591.09 | −0.123354 | ||||||||
\(551\) | −7511.51 | −0.580764 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −3777.17 | −0.289669 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −11810.2 | −0.900838 | ||||||||
\(557\) | −16699.6 | −1.27035 | −0.635173 | − | 0.772370i | \(-0.719071\pi\) | ||||
−0.635173 | + | 0.772370i | \(0.719071\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 15034.6 | 1.13756 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −9934.67 | −0.745674 | ||||||||
\(563\) | 14772.8 | 1.10586 | 0.552931 | − | 0.833227i | \(-0.313509\pi\) | ||||
0.552931 | + | 0.833227i | \(0.313509\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −159.016 | −0.0118405 | ||||||||
\(566\) | 6202.26 | 0.460601 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −2683.27 | −0.198217 | ||||||||
\(569\) | −5663.76 | −0.417289 | −0.208644 | − | 0.977992i | \(-0.566905\pi\) | ||||
−0.208644 | + | 0.977992i | \(0.566905\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 5579.58 | 0.408929 | 0.204464 | − | 0.978874i | \(-0.434455\pi\) | ||||
0.204464 | + | 0.978874i | \(0.434455\pi\) | |||||||
\(572\) | −5539.99 | −0.404962 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −4041.87 | −0.293144 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 2301.23 | 0.166034 | 0.0830170 | − | 0.996548i | \(-0.473544\pi\) | ||||
0.0830170 | + | 0.996548i | \(0.473544\pi\) | |||||||
\(578\) | −2552.77 | −0.183704 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −3511.55 | −0.251395 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 11419.5 | 0.811232 | ||||||||
\(584\) | 6347.46 | 0.449760 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 6428.34 | 0.453161 | ||||||||
\(587\) | −16470.4 | −1.15810 | −0.579052 | − | 0.815291i | \(-0.696577\pi\) | ||||
−0.579052 | + | 0.815291i | \(0.696577\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −8443.92 | −0.590706 | ||||||||
\(590\) | −124.906 | −0.00871573 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −1013.72 | −0.0703779 | ||||||||
\(593\) | −13570.0 | −0.939715 | −0.469858 | − | 0.882742i | \(-0.655695\pi\) | ||||
−0.469858 | + | 0.882742i | \(0.655695\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 4182.46 | 0.287450 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 7982.20 | 0.545847 | ||||||||
\(599\) | −27814.1 | −1.89725 | −0.948625 | − | 0.316403i | \(-0.897525\pi\) | ||||
−0.948625 | + | 0.316403i | \(0.897525\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −20646.1 | −1.40128 | −0.700641 | − | 0.713514i | \(-0.747102\pi\) | ||||
−0.700641 | + | 0.713514i | \(0.747102\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −2729.70 | −0.183891 | ||||||||
\(605\) | −339.969 | −0.0228458 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −3315.28 | −0.221686 | −0.110843 | − | 0.993838i | \(-0.535355\pi\) | ||||
−0.110843 | + | 0.993838i | \(0.535355\pi\) | |||||||
\(608\) | 10008.4 | 0.667588 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −1455.42 | −0.0966037 | ||||||||
\(611\) | 15732.8 | 1.04170 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −11113.9 | −0.732278 | −0.366139 | − | 0.930560i | \(-0.619320\pi\) | ||||
−0.366139 | + | 0.930560i | \(0.619320\pi\) | |||||||
\(614\) | 8166.89 | 0.536790 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −7871.34 | −0.513595 | −0.256797 | − | 0.966465i | \(-0.582667\pi\) | ||||
−0.256797 | + | 0.966465i | \(0.582667\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 19107.1 | 1.24068 | 0.620339 | − | 0.784334i | \(-0.286995\pi\) | ||||
0.620339 | + | 0.784334i | \(0.286995\pi\) | |||||||
\(620\) | −3947.44 | −0.255698 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 987.098 | 0.0636319 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 625.000 | 0.0400000 | ||||||||
\(626\) | 10404.7 | 0.664305 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 7987.60 | 0.507548 | ||||||||
\(629\) | −20453.9 | −1.29658 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −25769.9 | −1.62580 | −0.812902 | − | 0.582401i | \(-0.802113\pi\) | ||||
−0.812902 | + | 0.582401i | \(0.802113\pi\) | |||||||
\(632\) | −20996.5 | −1.32151 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 7317.79 | 0.458401 | ||||||||
\(635\) | −11104.1 | −0.693939 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 8756.19 | 0.543355 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 4875.87 | 0.301149 | ||||||||
\(641\) | 1954.61 | 0.120440 | 0.0602202 | − | 0.998185i | \(-0.480820\pi\) | ||||
0.0602202 | + | 0.998185i | \(0.480820\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 19396.5 | 1.18961 | 0.594807 | − | 0.803868i | \(-0.297228\pi\) | ||||
0.594807 | + | 0.803868i | \(0.297228\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 5427.10 | 0.330536 | ||||||||
\(647\) | 31264.3 | 1.89973 | 0.949865 | − | 0.312661i | \(-0.101220\pi\) | ||||
0.949865 | + | 0.312661i | \(0.101220\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −549.126 | −0.0332127 | ||||||||
\(650\) | −1234.30 | −0.0744817 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 5688.18 | 0.341666 | ||||||||
\(653\) | −6442.75 | −0.386102 | −0.193051 | − | 0.981189i | \(-0.561838\pi\) | ||||
−0.193051 | + | 0.981189i | \(0.561838\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −3232.56 | −0.192835 | ||||||||
\(656\) | 1024.27 | 0.0609620 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 3584.70 | 0.211897 | 0.105949 | − | 0.994372i | \(-0.466212\pi\) | ||||
0.105949 | + | 0.994372i | \(0.466212\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −6294.43 | −0.370386 | −0.185193 | − | 0.982702i | \(-0.559291\pi\) | ||||
−0.185193 | + | 0.982702i | \(0.559291\pi\) | |||||||
\(662\) | −11379.3 | −0.668078 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −8409.85 | −0.491514 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 22243.4 | 1.29126 | ||||||||
\(668\) | 9058.11 | 0.524654 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −4695.94 | −0.270776 | ||||||||
\(671\) | −6398.51 | −0.368125 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −10233.9 | −0.586162 | −0.293081 | − | 0.956088i | \(-0.594681\pi\) | ||||
−0.293081 | + | 0.956088i | \(0.594681\pi\) | |||||||
\(674\) | 9986.94 | 0.570745 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 6917.33 | 0.393567 | ||||||||
\(677\) | −7100.75 | −0.403108 | −0.201554 | − | 0.979477i | \(-0.564599\pi\) | ||||
−0.201554 | + | 0.979477i | \(0.564599\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 6513.23 | 0.367310 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 9843.10 | 0.552657 | ||||||||
\(683\) | 35274.6 | 1.97620 | 0.988100 | − | 0.153813i | \(-0.0491554\pi\) | ||||
0.988100 | + | 0.153813i | \(0.0491554\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −4480.05 | −0.249889 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −1500.22 | −0.0831330 | ||||||||
\(689\) | 8858.74 | 0.489828 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −4945.12 | −0.272245 | −0.136122 | − | 0.990692i | \(-0.543464\pi\) | ||||
−0.136122 | + | 0.990692i | \(0.543464\pi\) | |||||||
\(692\) | 21520.8 | 1.18222 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −3296.31 | −0.180297 | ||||||||
\(695\) | −11568.0 | −0.631368 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 20666.7 | 1.12311 | ||||||||
\(698\) | 16588.2 | 0.899532 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 15300.4 | 0.824379 | 0.412190 | − | 0.911098i | \(-0.364764\pi\) | ||||
0.412190 | + | 0.911098i | \(0.364764\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −19115.7 | −1.02555 | ||||||||
\(704\) | −10800.4 | −0.578206 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −7787.38 | −0.415130 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −28297.4 | −1.49892 | −0.749458 | − | 0.662052i | \(-0.769686\pi\) | ||||
−0.749458 | + | 0.662052i | \(0.769686\pi\) | |||||||
\(710\) | −1023.78 | −0.0541153 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 15112.2 | 0.795441 | ||||||||
\(713\) | 25004.5 | 1.31336 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −5426.37 | −0.283825 | ||||||||
\(716\) | −12407.9 | −0.647635 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −18461.9 | −0.959597 | ||||||||
\(719\) | 8548.96 | 0.443425 | 0.221712 | − | 0.975112i | \(-0.428835\pi\) | ||||
0.221712 | + | 0.975112i | \(0.428835\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −6598.97 | −0.340150 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −13787.3 | −0.707737 | ||||||||
\(725\) | −3439.53 | −0.176194 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −14345.3 | −0.731827 | −0.365913 | − | 0.930649i | \(-0.619243\pi\) | ||||
−0.365913 | + | 0.930649i | \(0.619243\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 2421.83 | 0.122789 | ||||||||
\(731\) | −30270.0 | −1.53157 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 22624.0 | 1.14002 | 0.570012 | − | 0.821637i | \(-0.306939\pi\) | ||||
0.570012 | + | 0.821637i | \(0.306939\pi\) | |||||||
\(734\) | −19512.9 | −0.981248 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −29637.3 | −1.48430 | ||||||||
\(737\) | −20644.9 | −1.03184 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 14837.3 | 0.738566 | 0.369283 | − | 0.929317i | \(-0.379603\pi\) | ||||
0.369283 | + | 0.929317i | \(0.379603\pi\) | |||||||
\(740\) | −8936.39 | −0.443930 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −13073.1 | −0.645497 | −0.322749 | − | 0.946485i | \(-0.604607\pi\) | ||||
−0.322749 | + | 0.946485i | \(0.604607\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 4096.69 | 0.201464 | ||||||||
\(746\) | 918.813 | 0.0450940 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 11154.0 | 0.545226 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 16213.3 | 0.787791 | 0.393895 | − | 0.919155i | \(-0.371127\pi\) | ||||
0.393895 | + | 0.919155i | \(0.371127\pi\) | |||||||
\(752\) | −1569.89 | −0.0761278 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 6792.65 | 0.328082 | ||||||||
\(755\) | −2673.72 | −0.128883 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 19903.9 | 0.955642 | 0.477821 | − | 0.878457i | \(-0.341427\pi\) | ||||
0.477821 | + | 0.878457i | \(0.341427\pi\) | |||||||
\(758\) | 14595.3 | 0.699372 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 6087.13 | 0.290531 | ||||||||
\(761\) | −30125.5 | −1.43502 | −0.717509 | − | 0.696549i | \(-0.754718\pi\) | ||||
−0.717509 | + | 0.696549i | \(0.754718\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 18433.5 | 0.872907 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 14681.0 | 0.692489 | ||||||||
\(767\) | −425.986 | −0.0200541 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 36049.1 | 1.69046 | 0.845230 | − | 0.534402i | \(-0.179463\pi\) | ||||
0.845230 | + | 0.534402i | \(0.179463\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 22809.4 | 1.06338 | ||||||||
\(773\) | −9644.77 | −0.448769 | −0.224384 | − | 0.974501i | \(-0.572037\pi\) | ||||
−0.224384 | + | 0.974501i | \(0.572037\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −3866.48 | −0.179211 | ||||||||
\(776\) | −27316.4 | −1.26366 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −15712.3 | −0.724054 | ||||||||
\(779\) | 19314.7 | 0.888344 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −4500.88 | −0.206215 | ||||||||
\(782\) | −16071.0 | −0.734908 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 7823.80 | 0.355724 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 25218.6 | 1.14224 | 0.571122 | − | 0.820865i | \(-0.306508\pi\) | ||||
0.571122 | + | 0.820865i | \(0.306508\pi\) | |||||||
\(788\) | −2217.59 | −0.100252 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −8011.06 | −0.360786 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −4963.67 | −0.222276 | ||||||||
\(794\) | −19768.8 | −0.883586 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −2393.67 | −0.106584 | ||||||||
\(797\) | 32042.3 | 1.42409 | 0.712044 | − | 0.702135i | \(-0.247770\pi\) | ||||
0.712044 | + | 0.702135i | \(0.247770\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −31675.7 | −1.40251 | ||||||||
\(800\) | 4582.85 | 0.202535 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −18984.5 | −0.835867 | ||||||||
\(803\) | 10647.1 | 0.467908 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 7635.82 | 0.333698 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 7540.07 | 0.328291 | ||||||||
\(809\) | −3427.90 | −0.148972 | −0.0744860 | − | 0.997222i | \(-0.523732\pi\) | ||||
−0.0744860 | + | 0.997222i | \(0.523732\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −23094.4 | −0.999943 | −0.499972 | − | 0.866042i | \(-0.666656\pi\) | ||||
−0.499972 | + | 0.866042i | \(0.666656\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 22283.3 | 0.959494 | ||||||||
\(815\) | 5571.53 | 0.239463 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −28289.7 | −1.21142 | ||||||||
\(818\) | 12639.3 | 0.540249 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 9029.39 | 0.384537 | ||||||||
\(821\) | −474.741 | −0.0201810 | −0.0100905 | − | 0.999949i | \(-0.503212\pi\) | ||||
−0.0100905 | + | 0.999949i | \(0.503212\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 24159.8 | 1.02328 | 0.511638 | − | 0.859201i | \(-0.329039\pi\) | ||||
0.511638 | + | 0.859201i | \(0.329039\pi\) | |||||||
\(824\) | −12636.5 | −0.534240 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 7566.35 | 0.318147 | 0.159074 | − | 0.987267i | \(-0.449149\pi\) | ||||
0.159074 | + | 0.987267i | \(0.449149\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 10580.9 | 0.443295 | 0.221648 | − | 0.975127i | \(-0.428857\pi\) | ||||
0.221648 | + | 0.975127i | \(0.428857\pi\) | |||||||
\(830\) | −3208.72 | −0.134188 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −8378.49 | −0.349125 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 8872.34 | 0.367713 | ||||||||
\(836\) | 10424.2 | 0.431256 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 16411.1 | 0.676507 | ||||||||
\(839\) | 15315.6 | 0.630218 | 0.315109 | − | 0.949055i | \(-0.397959\pi\) | ||||
0.315109 | + | 0.949055i | \(0.397959\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −5460.40 | −0.223888 | ||||||||
\(842\) | 16876.4 | 0.690735 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −19068.6 | −0.777688 | ||||||||
\(845\) | 6775.47 | 0.275838 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −883.966 | −0.0357966 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 2485.08 | 0.100279 | ||||||||
\(851\) | 56606.4 | 2.28019 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −18598.2 | −0.746528 | −0.373264 | − | 0.927725i | \(-0.621761\pi\) | ||||
−0.373264 | + | 0.927725i | \(0.621761\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −12543.6 | −0.500853 | ||||||||
\(857\) | 41775.3 | 1.66513 | 0.832566 | − | 0.553926i | \(-0.186871\pi\) | ||||
0.832566 | + | 0.553926i | \(0.186871\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −32414.7 | −1.28752 | −0.643758 | − | 0.765229i | \(-0.722626\pi\) | ||||
−0.643758 | + | 0.765229i | \(0.722626\pi\) | |||||||
\(860\) | −13225.1 | −0.524387 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 27776.4 | 1.09753 | ||||||||
\(863\) | 31299.7 | 1.23459 | 0.617297 | − | 0.786730i | \(-0.288228\pi\) | ||||
0.617297 | + | 0.786730i | \(0.288228\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 21079.4 | 0.828580 | ||||||||
\(866\) | 8794.94 | 0.345109 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −35219.2 | −1.37483 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −16015.4 | −0.623030 | ||||||||
\(872\) | −40823.8 | −1.58540 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −15019.6 | −0.581288 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −19973.0 | −0.769031 | −0.384515 | − | 0.923119i | \(-0.625631\pi\) | ||||
−0.384515 | + | 0.923119i | \(0.625631\pi\) | |||||||
\(878\) | −31204.9 | −1.19945 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 541.469 | 0.0207419 | ||||||||
\(881\) | 17367.9 | 0.664176 | 0.332088 | − | 0.943248i | \(-0.392247\pi\) | ||||
0.332088 | + | 0.943248i | \(0.392247\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −14364.2 | −0.547446 | −0.273723 | − | 0.961809i | \(-0.588255\pi\) | ||||
−0.273723 | + | 0.961809i | \(0.588255\pi\) | |||||||
\(884\) | 8652.73 | 0.329211 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 2745.09 | 0.104089 | ||||||||
\(887\) | −33738.1 | −1.27713 | −0.638564 | − | 0.769568i | \(-0.720471\pi\) | ||||
−0.638564 | + | 0.769568i | \(0.720471\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 5765.95 | 0.217163 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 4302.26 | 0.161491 | ||||||||
\(893\) | −29603.4 | −1.10934 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −12153.5 | −0.453906 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 1508.86 | 0.0560705 | ||||||||
\(899\) | 21278.2 | 0.789398 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −17835.8 | −0.659485 | ||||||||
\(902\) | −22515.2 | −0.831123 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −709.162 | −0.0260911 | ||||||||
\(905\) | −13504.6 | −0.496030 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −32998.6 | −1.20805 | −0.604024 | − | 0.796966i | \(-0.706437\pi\) | ||||
−0.604024 | + | 0.796966i | \(0.706437\pi\) | |||||||
\(908\) | −5064.62 | −0.185105 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −33446.3 | −1.21638 | −0.608192 | − | 0.793790i | \(-0.708105\pi\) | ||||
−0.608192 | + | 0.793790i | \(0.708105\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −14106.6 | −0.511347 | ||||||||
\(914\) | 12576.6 | 0.455139 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −32728.2 | −1.18053 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 41708.7 | 1.49711 | 0.748554 | − | 0.663074i | \(-0.230748\pi\) | ||||
0.748554 | + | 0.663074i | \(0.230748\pi\) | |||||||
\(920\) | −18025.5 | −0.645960 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −12137.8 | −0.433556 | ||||||||
\(923\) | −3491.58 | −0.124514 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −8753.12 | −0.311136 | ||||||||
\(926\) | 24607.7 | 0.873283 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −25220.6 | −0.892140 | ||||||||
\(929\) | 49024.6 | 1.73137 | 0.865686 | − | 0.500587i | \(-0.166883\pi\) | ||||
0.865686 | + | 0.500587i | \(0.166883\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −11609.9 | −0.408040 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −27894.6 | −0.977235 | ||||||||
\(935\) | 10925.2 | 0.382131 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 5447.58 | 0.189930 | 0.0949651 | − | 0.995481i | \(-0.469726\pi\) | ||||
0.0949651 | + | 0.995481i | \(0.469726\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −13839.3 | −0.480200 | ||||||||
\(941\) | 4125.75 | 0.142928 | 0.0714642 | − | 0.997443i | \(-0.477233\pi\) | ||||
0.0714642 | + | 0.997443i | \(0.477233\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −57195.5 | −1.97513 | ||||||||
\(944\) | 42.5069 | 0.00146555 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 32977.4 | 1.13339 | ||||||||
\(947\) | −17332.3 | −0.594747 | −0.297374 | − | 0.954761i | \(-0.596111\pi\) | ||||
−0.297374 | + | 0.954761i | \(0.596111\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 8259.57 | 0.282526 | ||||||||
\(950\) | 2322.50 | 0.0793177 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −56839.4 | −1.93201 | −0.966007 | − | 0.258517i | \(-0.916766\pi\) | ||||
−0.966007 | + | 0.258517i | \(0.916766\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 18055.5 | 0.611792 | ||||||||
\(956\) | 14615.3 | 0.494449 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −22105.7 | −0.745515 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −5871.48 | −0.197089 | ||||||||
\(962\) | 17286.3 | 0.579349 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −27382.7 | −0.914873 | ||||||||
\(965\) | 22341.6 | 0.745287 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −13284.2 | −0.441769 | −0.220884 | − | 0.975300i | \(-0.570894\pi\) | ||||
−0.220884 | + | 0.975300i | \(0.570894\pi\) | |||||||
\(968\) | −1516.15 | −0.0503420 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −10422.4 | −0.344992 | ||||||||
\(971\) | 12153.0 | 0.401658 | 0.200829 | − | 0.979626i | \(-0.435636\pi\) | ||||
0.200829 | + | 0.979626i | \(0.435636\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −21888.1 | −0.720060 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 495.298 | 0.0162440 | ||||||||
\(977\) | 37999.3 | 1.24433 | 0.622163 | − | 0.782888i | \(-0.286254\pi\) | ||||
0.622163 | + | 0.782888i | \(0.286254\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 25349.0 | 0.827537 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 8334.42 | 0.270837 | ||||||||
\(983\) | 22375.0 | 0.725993 | 0.362996 | − | 0.931791i | \(-0.381754\pi\) | ||||
0.362996 | + | 0.931791i | \(0.381754\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −2172.11 | −0.0702631 | ||||||||
\(986\) | −13676.0 | −0.441717 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 8086.65 | 0.260395 | ||||||||
\(989\) | 83772.9 | 2.69345 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 18985.3 | 0.608564 | 0.304282 | − | 0.952582i | \(-0.401583\pi\) | ||||
0.304282 | + | 0.952582i | \(0.401583\pi\) | |||||||
\(992\) | −28351.2 | −0.907412 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −2344.58 | −0.0747016 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 56476.5 | 1.79401 | 0.897006 | − | 0.442019i | \(-0.145738\pi\) | ||||
0.897006 | + | 0.442019i | \(0.145738\pi\) | |||||||
\(998\) | 17539.6 | 0.556321 | ||||||||
\(999\) | 0 | 0 |
(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 | 2205.4.a.v.1.2 | 2 | ||
3.2 | odd | 2 | 735.4.a.q.1.1 | 2 | |||
7.6 | odd | 2 | 315.4.a.g.1.2 | 2 | |||
21.20 | even | 2 | 105.4.a.g.1.1 | ✓ | 2 | ||
35.34 | odd | 2 | 1575.4.a.y.1.1 | 2 | |||
84.83 | odd | 2 | 1680.4.a.y.1.1 | 2 | |||
105.62 | odd | 4 | 525.4.d.j.274.2 | 4 | |||
105.83 | odd | 4 | 525.4.d.j.274.3 | 4 | |||
105.104 | even | 2 | 525.4.a.i.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
105.4.a.g.1.1 | ✓ | 2 | 21.20 | even | 2 | ||
315.4.a.g.1.2 | 2 | 7.6 | odd | 2 | |||
525.4.a.i.1.2 | 2 | 105.104 | even | 2 | |||
525.4.d.j.274.2 | 4 | 105.62 | odd | 4 | |||
525.4.d.j.274.3 | 4 | 105.83 | odd | 4 | |||
735.4.a.q.1.1 | 2 | 3.2 | odd | 2 | |||
1575.4.a.y.1.1 | 2 | 35.34 | odd | 2 | |||
1680.4.a.y.1.1 | 2 | 84.83 | odd | 2 | |||
2205.4.a.v.1.2 | 2 | 1.1 | even | 1 | trivial |