Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1859,4,Mod(1,1859)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1859, 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("1859.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1859 = 11 \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1859.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: | \(109.684550701\) |
Analytic rank: | \(0\) |
Dimension: | \(11\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{11} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{11} - 5 x^{10} - 64 x^{9} + 268 x^{8} + 1564 x^{7} - 4963 x^{6} - 16942 x^{5} + 37082 x^{4} + 68209 x^{3} - 90926 x^{2} - 1672 x + 16256 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 143) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.8 | ||
Root | \(3.58491\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1859.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.58491 | 0.913905 | 0.456953 | − | 0.889491i | \(-0.348941\pi\) | ||||
0.456953 | + | 0.889491i | \(0.348941\pi\) | |||||||
\(3\) | −2.54183 | −0.489175 | −0.244587 | − | 0.969627i | \(-0.578653\pi\) | ||||
−0.244587 | + | 0.969627i | \(0.578653\pi\) | |||||||
\(4\) | −1.31822 | −0.164777 | ||||||||
\(5\) | 20.1048 | 1.79823 | 0.899116 | − | 0.437710i | \(-0.144210\pi\) | ||||
0.899116 | + | 0.437710i | \(0.144210\pi\) | |||||||
\(6\) | −6.57040 | −0.447059 | ||||||||
\(7\) | 29.2165 | 1.57754 | 0.788771 | − | 0.614687i | \(-0.210718\pi\) | ||||
0.788771 | + | 0.614687i | \(0.210718\pi\) | |||||||
\(8\) | −24.0868 | −1.06450 | ||||||||
\(9\) | −20.5391 | −0.760708 | ||||||||
\(10\) | 51.9693 | 1.64341 | ||||||||
\(11\) | −11.0000 | −0.301511 | ||||||||
\(12\) | 3.35069 | 0.0806050 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | 75.5221 | 1.44172 | ||||||||
\(15\) | −51.1030 | −0.879650 | ||||||||
\(16\) | −51.7165 | −0.808071 | ||||||||
\(17\) | −127.832 | −1.82376 | −0.911878 | − | 0.410462i | \(-0.865367\pi\) | ||||
−0.911878 | + | 0.410462i | \(0.865367\pi\) | |||||||
\(18\) | −53.0918 | −0.695215 | ||||||||
\(19\) | 14.1385 | 0.170716 | 0.0853580 | − | 0.996350i | \(-0.472797\pi\) | ||||
0.0853580 | + | 0.996350i | \(0.472797\pi\) | |||||||
\(20\) | −26.5026 | −0.296308 | ||||||||
\(21\) | −74.2633 | −0.771694 | ||||||||
\(22\) | −28.4341 | −0.275553 | ||||||||
\(23\) | 93.3531 | 0.846324 | 0.423162 | − | 0.906054i | \(-0.360920\pi\) | ||||
0.423162 | + | 0.906054i | \(0.360920\pi\) | |||||||
\(24\) | 61.2245 | 0.520725 | ||||||||
\(25\) | 279.205 | 2.23364 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 120.836 | 0.861294 | ||||||||
\(28\) | −38.5137 | −0.259943 | ||||||||
\(29\) | −83.3385 | −0.533641 | −0.266820 | − | 0.963746i | \(-0.585973\pi\) | ||||
−0.266820 | + | 0.963746i | \(0.585973\pi\) | |||||||
\(30\) | −132.097 | −0.803917 | ||||||||
\(31\) | 211.118 | 1.22316 | 0.611579 | − | 0.791183i | \(-0.290534\pi\) | ||||
0.611579 | + | 0.791183i | \(0.290534\pi\) | |||||||
\(32\) | 59.0115 | 0.325996 | ||||||||
\(33\) | 27.9601 | 0.147492 | ||||||||
\(34\) | −330.435 | −1.66674 | ||||||||
\(35\) | 587.393 | 2.83679 | ||||||||
\(36\) | 27.0751 | 0.125347 | ||||||||
\(37\) | −125.862 | −0.559233 | −0.279616 | − | 0.960112i | \(-0.590207\pi\) | ||||
−0.279616 | + | 0.960112i | \(0.590207\pi\) | |||||||
\(38\) | 36.5469 | 0.156018 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −484.261 | −1.91421 | ||||||||
\(41\) | 250.303 | 0.953432 | 0.476716 | − | 0.879057i | \(-0.341827\pi\) | ||||
0.476716 | + | 0.879057i | \(0.341827\pi\) | |||||||
\(42\) | −191.964 | −0.705255 | ||||||||
\(43\) | 367.915 | 1.30480 | 0.652401 | − | 0.757874i | \(-0.273762\pi\) | ||||
0.652401 | + | 0.757874i | \(0.273762\pi\) | |||||||
\(44\) | 14.5004 | 0.0496823 | ||||||||
\(45\) | −412.936 | −1.36793 | ||||||||
\(46\) | 241.310 | 0.773460 | ||||||||
\(47\) | 477.490 | 1.48190 | 0.740948 | − | 0.671563i | \(-0.234377\pi\) | ||||
0.740948 | + | 0.671563i | \(0.234377\pi\) | |||||||
\(48\) | 131.455 | 0.395288 | ||||||||
\(49\) | 510.603 | 1.48864 | ||||||||
\(50\) | 721.720 | 2.04133 | ||||||||
\(51\) | 324.927 | 0.892135 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −297.083 | −0.769953 | −0.384976 | − | 0.922926i | \(-0.625790\pi\) | ||||
−0.384976 | + | 0.922926i | \(0.625790\pi\) | |||||||
\(54\) | 312.351 | 0.787141 | ||||||||
\(55\) | −221.153 | −0.542187 | ||||||||
\(56\) | −703.732 | −1.67929 | ||||||||
\(57\) | −35.9377 | −0.0835100 | ||||||||
\(58\) | −215.423 | −0.487697 | ||||||||
\(59\) | 578.993 | 1.27760 | 0.638800 | − | 0.769373i | \(-0.279431\pi\) | ||||
0.638800 | + | 0.769373i | \(0.279431\pi\) | |||||||
\(60\) | 67.3650 | 0.144946 | ||||||||
\(61\) | −305.672 | −0.641595 | −0.320798 | − | 0.947148i | \(-0.603951\pi\) | ||||
−0.320798 | + | 0.947148i | \(0.603951\pi\) | |||||||
\(62\) | 545.722 | 1.11785 | ||||||||
\(63\) | −600.081 | −1.20005 | ||||||||
\(64\) | 566.272 | 1.10600 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 72.2745 | 0.134793 | ||||||||
\(67\) | 330.902 | 0.603374 | 0.301687 | − | 0.953407i | \(-0.402450\pi\) | ||||
0.301687 | + | 0.953407i | \(0.402450\pi\) | |||||||
\(68\) | 168.511 | 0.300514 | ||||||||
\(69\) | −237.287 | −0.414001 | ||||||||
\(70\) | 1518.36 | 2.59255 | ||||||||
\(71\) | 123.873 | 0.207056 | 0.103528 | − | 0.994627i | \(-0.466987\pi\) | ||||
0.103528 | + | 0.994627i | \(0.466987\pi\) | |||||||
\(72\) | 494.721 | 0.809771 | ||||||||
\(73\) | 432.090 | 0.692771 | 0.346385 | − | 0.938092i | \(-0.387409\pi\) | ||||
0.346385 | + | 0.938092i | \(0.387409\pi\) | |||||||
\(74\) | −325.343 | −0.511086 | ||||||||
\(75\) | −709.690 | −1.09264 | ||||||||
\(76\) | −18.6377 | −0.0281301 | ||||||||
\(77\) | −321.381 | −0.475647 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 269.398 | 0.383666 | 0.191833 | − | 0.981428i | \(-0.438557\pi\) | ||||
0.191833 | + | 0.981428i | \(0.438557\pi\) | |||||||
\(80\) | −1039.75 | −1.45310 | ||||||||
\(81\) | 247.411 | 0.339385 | ||||||||
\(82\) | 647.011 | 0.871346 | ||||||||
\(83\) | −425.366 | −0.562530 | −0.281265 | − | 0.959630i | \(-0.590754\pi\) | ||||
−0.281265 | + | 0.959630i | \(0.590754\pi\) | |||||||
\(84\) | 97.8953 | 0.127158 | ||||||||
\(85\) | −2570.04 | −3.27954 | ||||||||
\(86\) | 951.028 | 1.19246 | ||||||||
\(87\) | 211.832 | 0.261044 | ||||||||
\(88\) | 264.955 | 0.320958 | ||||||||
\(89\) | 317.243 | 0.377840 | 0.188920 | − | 0.981993i | \(-0.439501\pi\) | ||||
0.188920 | + | 0.981993i | \(0.439501\pi\) | |||||||
\(90\) | −1067.40 | −1.25016 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −123.060 | −0.139455 | ||||||||
\(93\) | −536.626 | −0.598339 | ||||||||
\(94\) | 1234.27 | 1.35431 | ||||||||
\(95\) | 284.253 | 0.306987 | ||||||||
\(96\) | −149.997 | −0.159469 | ||||||||
\(97\) | −1562.33 | −1.63536 | −0.817682 | − | 0.575671i | \(-0.804741\pi\) | ||||
−0.817682 | + | 0.575671i | \(0.804741\pi\) | |||||||
\(98\) | 1319.87 | 1.36047 | ||||||||
\(99\) | 225.930 | 0.229362 | ||||||||
\(100\) | −368.053 | −0.368053 | ||||||||
\(101\) | 572.371 | 0.563891 | 0.281946 | − | 0.959430i | \(-0.409020\pi\) | ||||
0.281946 | + | 0.959430i | \(0.409020\pi\) | |||||||
\(102\) | 839.909 | 0.815327 | ||||||||
\(103\) | 64.9567 | 0.0621395 | 0.0310698 | − | 0.999517i | \(-0.490109\pi\) | ||||
0.0310698 | + | 0.999517i | \(0.490109\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −1493.05 | −1.38768 | ||||||||
\(106\) | −767.934 | −0.703664 | ||||||||
\(107\) | −324.100 | −0.292822 | −0.146411 | − | 0.989224i | \(-0.546772\pi\) | ||||
−0.146411 | + | 0.989224i | \(0.546772\pi\) | |||||||
\(108\) | −159.289 | −0.141922 | ||||||||
\(109\) | −49.2595 | −0.0432862 | −0.0216431 | − | 0.999766i | \(-0.506890\pi\) | ||||
−0.0216431 | + | 0.999766i | \(0.506890\pi\) | |||||||
\(110\) | −571.662 | −0.495508 | ||||||||
\(111\) | 319.920 | 0.273563 | ||||||||
\(112\) | −1510.98 | −1.27477 | ||||||||
\(113\) | −462.767 | −0.385252 | −0.192626 | − | 0.981272i | \(-0.561700\pi\) | ||||
−0.192626 | + | 0.981272i | \(0.561700\pi\) | |||||||
\(114\) | −92.8959 | −0.0763202 | ||||||||
\(115\) | 1876.85 | 1.52189 | ||||||||
\(116\) | 109.858 | 0.0879319 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 1496.65 | 1.16761 | ||||||||
\(119\) | −3734.81 | −2.87705 | ||||||||
\(120\) | 1230.91 | 0.936384 | ||||||||
\(121\) | 121.000 | 0.0909091 | ||||||||
\(122\) | −790.136 | −0.586357 | ||||||||
\(123\) | −636.226 | −0.466395 | ||||||||
\(124\) | −278.300 | −0.201549 | ||||||||
\(125\) | 3100.26 | 2.21837 | ||||||||
\(126\) | −1551.16 | −1.09673 | ||||||||
\(127\) | 1618.54 | 1.13088 | 0.565441 | − | 0.824789i | \(-0.308706\pi\) | ||||
0.565441 | + | 0.824789i | \(0.308706\pi\) | |||||||
\(128\) | 991.672 | 0.684783 | ||||||||
\(129\) | −935.175 | −0.638276 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1858.13 | 1.23928 | 0.619641 | − | 0.784885i | \(-0.287278\pi\) | ||||
0.619641 | + | 0.784885i | \(0.287278\pi\) | |||||||
\(132\) | −36.8575 | −0.0243033 | ||||||||
\(133\) | 413.079 | 0.269312 | ||||||||
\(134\) | 855.352 | 0.551427 | ||||||||
\(135\) | 2429.39 | 1.54881 | ||||||||
\(136\) | 3079.07 | 1.94138 | ||||||||
\(137\) | −1987.30 | −1.23932 | −0.619660 | − | 0.784871i | \(-0.712729\pi\) | ||||
−0.619660 | + | 0.784871i | \(0.712729\pi\) | |||||||
\(138\) | −613.367 | −0.378357 | ||||||||
\(139\) | 322.673 | 0.196898 | 0.0984488 | − | 0.995142i | \(-0.468612\pi\) | ||||
0.0984488 | + | 0.995142i | \(0.468612\pi\) | |||||||
\(140\) | −774.313 | −0.467438 | ||||||||
\(141\) | −1213.70 | −0.724906 | ||||||||
\(142\) | 320.200 | 0.189230 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 1062.21 | 0.614706 | ||||||||
\(145\) | −1675.51 | −0.959610 | ||||||||
\(146\) | 1116.91 | 0.633127 | ||||||||
\(147\) | −1297.86 | −0.728205 | ||||||||
\(148\) | 165.914 | 0.0921489 | ||||||||
\(149\) | 2965.54 | 1.63051 | 0.815257 | − | 0.579100i | \(-0.196596\pi\) | ||||
0.815257 | + | 0.579100i | \(0.196596\pi\) | |||||||
\(150\) | −1834.49 | −0.998569 | ||||||||
\(151\) | 1914.70 | 1.03190 | 0.515948 | − | 0.856620i | \(-0.327440\pi\) | ||||
0.515948 | + | 0.856620i | \(0.327440\pi\) | |||||||
\(152\) | −340.552 | −0.181726 | ||||||||
\(153\) | 2625.56 | 1.38735 | ||||||||
\(154\) | −830.743 | −0.434696 | ||||||||
\(155\) | 4244.50 | 2.19952 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −16.2680 | −0.00826960 | −0.00413480 | − | 0.999991i | \(-0.501316\pi\) | ||||
−0.00413480 | + | 0.999991i | \(0.501316\pi\) | |||||||
\(158\) | 696.370 | 0.350634 | ||||||||
\(159\) | 755.134 | 0.376641 | ||||||||
\(160\) | 1186.42 | 0.586216 | ||||||||
\(161\) | 2727.45 | 1.33511 | ||||||||
\(162\) | 639.537 | 0.310165 | ||||||||
\(163\) | 1584.56 | 0.761424 | 0.380712 | − | 0.924694i | \(-0.375679\pi\) | ||||
0.380712 | + | 0.924694i | \(0.375679\pi\) | |||||||
\(164\) | −329.954 | −0.157104 | ||||||||
\(165\) | 562.133 | 0.265224 | ||||||||
\(166\) | −1099.53 | −0.514099 | ||||||||
\(167\) | 600.706 | 0.278347 | 0.139174 | − | 0.990268i | \(-0.455555\pi\) | ||||
0.139174 | + | 0.990268i | \(0.455555\pi\) | |||||||
\(168\) | 1788.76 | 0.821465 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | −6643.35 | −2.99718 | ||||||||
\(171\) | −290.393 | −0.129865 | ||||||||
\(172\) | −484.992 | −0.215002 | ||||||||
\(173\) | 1707.02 | 0.750185 | 0.375093 | − | 0.926987i | \(-0.377611\pi\) | ||||
0.375093 | + | 0.926987i | \(0.377611\pi\) | |||||||
\(174\) | 547.568 | 0.238569 | ||||||||
\(175\) | 8157.38 | 3.52366 | ||||||||
\(176\) | 568.882 | 0.243643 | ||||||||
\(177\) | −1471.70 | −0.624970 | ||||||||
\(178\) | 820.047 | 0.345310 | ||||||||
\(179\) | −4568.66 | −1.90770 | −0.953849 | − | 0.300287i | \(-0.902917\pi\) | ||||
−0.953849 | + | 0.300287i | \(0.902917\pi\) | |||||||
\(180\) | 544.340 | 0.225404 | ||||||||
\(181\) | 1562.07 | 0.641477 | 0.320739 | − | 0.947168i | \(-0.396069\pi\) | ||||
0.320739 | + | 0.947168i | \(0.396069\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 776.966 | 0.313852 | ||||||||
\(184\) | −2248.58 | −0.900909 | ||||||||
\(185\) | −2530.44 | −1.00563 | ||||||||
\(186\) | −1387.13 | −0.546825 | ||||||||
\(187\) | 1406.15 | 0.549883 | ||||||||
\(188\) | −629.436 | −0.244183 | ||||||||
\(189\) | 3530.41 | 1.35873 | ||||||||
\(190\) | 734.770 | 0.280557 | ||||||||
\(191\) | −3288.63 | −1.24585 | −0.622923 | − | 0.782283i | \(-0.714055\pi\) | ||||
−0.622923 | + | 0.782283i | \(0.714055\pi\) | |||||||
\(192\) | −1439.37 | −0.541028 | ||||||||
\(193\) | −2159.36 | −0.805358 | −0.402679 | − | 0.915341i | \(-0.631921\pi\) | ||||
−0.402679 | + | 0.915341i | \(0.631921\pi\) | |||||||
\(194\) | −4038.48 | −1.49457 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −673.087 | −0.245294 | ||||||||
\(197\) | −5369.47 | −1.94192 | −0.970961 | − | 0.239237i | \(-0.923103\pi\) | ||||
−0.970961 | + | 0.239237i | \(0.923103\pi\) | |||||||
\(198\) | 584.010 | 0.209615 | ||||||||
\(199\) | 46.8723 | 0.0166969 | 0.00834846 | − | 0.999965i | \(-0.497343\pi\) | ||||
0.00834846 | + | 0.999965i | \(0.497343\pi\) | |||||||
\(200\) | −6725.15 | −2.37770 | ||||||||
\(201\) | −841.095 | −0.295155 | ||||||||
\(202\) | 1479.53 | 0.515343 | ||||||||
\(203\) | −2434.86 | −0.841840 | ||||||||
\(204\) | −428.325 | −0.147004 | ||||||||
\(205\) | 5032.30 | 1.71449 | ||||||||
\(206\) | 167.907 | 0.0567896 | ||||||||
\(207\) | −1917.39 | −0.643806 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −155.524 | −0.0514728 | ||||||||
\(210\) | −3859.41 | −1.26821 | ||||||||
\(211\) | 2336.92 | 0.762464 | 0.381232 | − | 0.924479i | \(-0.375500\pi\) | ||||
0.381232 | + | 0.924479i | \(0.375500\pi\) | |||||||
\(212\) | 391.620 | 0.126871 | ||||||||
\(213\) | −314.863 | −0.101287 | ||||||||
\(214\) | −837.770 | −0.267611 | ||||||||
\(215\) | 7396.87 | 2.34634 | ||||||||
\(216\) | −2910.56 | −0.916844 | ||||||||
\(217\) | 6168.13 | 1.92958 | ||||||||
\(218\) | −127.331 | −0.0395595 | ||||||||
\(219\) | −1098.30 | −0.338886 | ||||||||
\(220\) | 291.529 | 0.0893402 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 826.965 | 0.250010 | ||||||||
\(223\) | 1803.10 | 0.541454 | 0.270727 | − | 0.962656i | \(-0.412736\pi\) | ||||
0.270727 | + | 0.962656i | \(0.412736\pi\) | |||||||
\(224\) | 1724.11 | 0.514272 | ||||||||
\(225\) | −5734.62 | −1.69915 | ||||||||
\(226\) | −1196.21 | −0.352084 | ||||||||
\(227\) | −2123.99 | −0.621031 | −0.310516 | − | 0.950568i | \(-0.600502\pi\) | ||||
−0.310516 | + | 0.950568i | \(0.600502\pi\) | |||||||
\(228\) | 47.3738 | 0.0137606 | ||||||||
\(229\) | 5138.84 | 1.48290 | 0.741450 | − | 0.671008i | \(-0.234139\pi\) | ||||
0.741450 | + | 0.671008i | \(0.234139\pi\) | |||||||
\(230\) | 4851.49 | 1.39086 | ||||||||
\(231\) | 816.896 | 0.232674 | ||||||||
\(232\) | 2007.36 | 0.568058 | ||||||||
\(233\) | 3454.75 | 0.971366 | 0.485683 | − | 0.874135i | \(-0.338571\pi\) | ||||
0.485683 | + | 0.874135i | \(0.338571\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 9599.86 | 2.66479 | ||||||||
\(236\) | −763.239 | −0.210520 | ||||||||
\(237\) | −684.762 | −0.187680 | ||||||||
\(238\) | −9654.15 | −2.62935 | ||||||||
\(239\) | 5868.90 | 1.58840 | 0.794200 | − | 0.607656i | \(-0.207890\pi\) | ||||
0.794200 | + | 0.607656i | \(0.207890\pi\) | |||||||
\(240\) | 2642.87 | 0.710820 | ||||||||
\(241\) | −7025.67 | −1.87786 | −0.938928 | − | 0.344114i | \(-0.888179\pi\) | ||||
−0.938928 | + | 0.344114i | \(0.888179\pi\) | |||||||
\(242\) | 312.775 | 0.0830823 | ||||||||
\(243\) | −3891.45 | −1.02731 | ||||||||
\(244\) | 402.943 | 0.105720 | ||||||||
\(245\) | 10265.6 | 2.67692 | ||||||||
\(246\) | −1644.59 | −0.426241 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | −5085.16 | −1.30205 | ||||||||
\(249\) | 1081.21 | 0.275175 | ||||||||
\(250\) | 8013.91 | 2.02738 | ||||||||
\(251\) | −6384.82 | −1.60560 | −0.802801 | − | 0.596247i | \(-0.796658\pi\) | ||||
−0.802801 | + | 0.596247i | \(0.796658\pi\) | |||||||
\(252\) | 791.038 | 0.197741 | ||||||||
\(253\) | −1026.88 | −0.255176 | ||||||||
\(254\) | 4183.78 | 1.03352 | ||||||||
\(255\) | 6532.61 | 1.60427 | ||||||||
\(256\) | −1966.79 | −0.480173 | ||||||||
\(257\) | 71.1715 | 0.0172745 | 0.00863726 | − | 0.999963i | \(-0.497251\pi\) | ||||
0.00863726 | + | 0.999963i | \(0.497251\pi\) | |||||||
\(258\) | −2417.35 | −0.583324 | ||||||||
\(259\) | −3677.25 | −0.882213 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 1711.70 | 0.405945 | ||||||||
\(262\) | 4803.12 | 1.13259 | ||||||||
\(263\) | −795.011 | −0.186397 | −0.0931986 | − | 0.995648i | \(-0.529709\pi\) | ||||
−0.0931986 | + | 0.995648i | \(0.529709\pi\) | |||||||
\(264\) | −673.469 | −0.157004 | ||||||||
\(265\) | −5972.81 | −1.38455 | ||||||||
\(266\) | 1067.77 | 0.246125 | ||||||||
\(267\) | −806.378 | −0.184830 | ||||||||
\(268\) | −436.201 | −0.0994224 | ||||||||
\(269\) | 1886.71 | 0.427638 | 0.213819 | − | 0.976873i | \(-0.431410\pi\) | ||||
0.213819 | + | 0.976873i | \(0.431410\pi\) | |||||||
\(270\) | 6279.77 | 1.41546 | ||||||||
\(271\) | 1280.68 | 0.287070 | 0.143535 | − | 0.989645i | \(-0.454153\pi\) | ||||
0.143535 | + | 0.989645i | \(0.454153\pi\) | |||||||
\(272\) | 6611.04 | 1.47372 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −5137.01 | −1.13262 | ||||||||
\(275\) | −3071.25 | −0.673467 | ||||||||
\(276\) | 312.797 | 0.0682179 | ||||||||
\(277\) | −369.108 | −0.0800634 | −0.0400317 | − | 0.999198i | \(-0.512746\pi\) | ||||
−0.0400317 | + | 0.999198i | \(0.512746\pi\) | |||||||
\(278\) | 834.082 | 0.179946 | ||||||||
\(279\) | −4336.18 | −0.930467 | ||||||||
\(280\) | −14148.4 | −3.01975 | ||||||||
\(281\) | 1026.86 | 0.217997 | 0.108999 | − | 0.994042i | \(-0.465236\pi\) | ||||
0.108999 | + | 0.994042i | \(0.465236\pi\) | |||||||
\(282\) | −3137.30 | −0.662495 | ||||||||
\(283\) | 1815.31 | 0.381303 | 0.190652 | − | 0.981658i | \(-0.438940\pi\) | ||||
0.190652 | + | 0.981658i | \(0.438940\pi\) | |||||||
\(284\) | −163.291 | −0.0341182 | ||||||||
\(285\) | −722.522 | −0.150170 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 7312.96 | 1.50408 | ||||||||
\(288\) | −1212.04 | −0.247988 | ||||||||
\(289\) | 11428.1 | 2.32608 | ||||||||
\(290\) | −4331.04 | −0.876992 | ||||||||
\(291\) | 3971.16 | 0.799979 | ||||||||
\(292\) | −569.589 | −0.114153 | ||||||||
\(293\) | 6464.43 | 1.28893 | 0.644464 | − | 0.764635i | \(-0.277081\pi\) | ||||
0.644464 | + | 0.764635i | \(0.277081\pi\) | |||||||
\(294\) | −3354.87 | −0.665510 | ||||||||
\(295\) | 11640.6 | 2.29742 | ||||||||
\(296\) | 3031.62 | 0.595301 | ||||||||
\(297\) | −1329.20 | −0.259690 | ||||||||
\(298\) | 7665.67 | 1.49013 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 935.527 | 0.180042 | ||||||||
\(301\) | 10749.2 | 2.05838 | ||||||||
\(302\) | 4949.34 | 0.943054 | ||||||||
\(303\) | −1454.87 | −0.275841 | ||||||||
\(304\) | −731.196 | −0.137951 | ||||||||
\(305\) | −6145.49 | −1.15374 | ||||||||
\(306\) | 6786.84 | 1.26790 | ||||||||
\(307\) | 9616.30 | 1.78772 | 0.893862 | − | 0.448342i | \(-0.147985\pi\) | ||||
0.893862 | + | 0.448342i | \(0.147985\pi\) | |||||||
\(308\) | 423.651 | 0.0783758 | ||||||||
\(309\) | −165.109 | −0.0303971 | ||||||||
\(310\) | 10971.7 | 2.01016 | ||||||||
\(311\) | −4420.02 | −0.805904 | −0.402952 | − | 0.915221i | \(-0.632016\pi\) | ||||
−0.402952 | + | 0.915221i | \(0.632016\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 4656.56 | 0.840909 | 0.420454 | − | 0.907314i | \(-0.361871\pi\) | ||||
0.420454 | + | 0.907314i | \(0.361871\pi\) | |||||||
\(314\) | −42.0514 | −0.00755763 | ||||||||
\(315\) | −12064.5 | −2.15797 | ||||||||
\(316\) | −355.125 | −0.0632195 | ||||||||
\(317\) | −5986.49 | −1.06068 | −0.530339 | − | 0.847786i | \(-0.677935\pi\) | ||||
−0.530339 | + | 0.847786i | \(0.677935\pi\) | |||||||
\(318\) | 1951.96 | 0.344215 | ||||||||
\(319\) | 916.724 | 0.160899 | ||||||||
\(320\) | 11384.8 | 1.98885 | ||||||||
\(321\) | 823.806 | 0.143241 | ||||||||
\(322\) | 7050.22 | 1.22017 | ||||||||
\(323\) | −1807.36 | −0.311344 | ||||||||
\(324\) | −326.142 | −0.0559229 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 4095.95 | 0.695870 | ||||||||
\(327\) | 125.209 | 0.0211745 | ||||||||
\(328\) | −6028.99 | −1.01492 | ||||||||
\(329\) | 13950.6 | 2.33775 | ||||||||
\(330\) | 1453.07 | 0.242390 | ||||||||
\(331\) | −3685.65 | −0.612028 | −0.306014 | − | 0.952027i | \(-0.598996\pi\) | ||||
−0.306014 | + | 0.952027i | \(0.598996\pi\) | |||||||
\(332\) | 560.725 | 0.0926922 | ||||||||
\(333\) | 2585.10 | 0.425413 | ||||||||
\(334\) | 1552.77 | 0.254383 | ||||||||
\(335\) | 6652.72 | 1.08501 | ||||||||
\(336\) | 3840.64 | 0.623583 | ||||||||
\(337\) | −8580.79 | −1.38702 | −0.693509 | − | 0.720447i | \(-0.743936\pi\) | ||||
−0.693509 | + | 0.720447i | \(0.743936\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 1176.27 | 0.188456 | ||||||||
\(340\) | 3387.88 | 0.540393 | ||||||||
\(341\) | −2322.30 | −0.368796 | ||||||||
\(342\) | −750.641 | −0.118684 | ||||||||
\(343\) | 4896.77 | 0.770848 | ||||||||
\(344\) | −8861.88 | −1.38896 | ||||||||
\(345\) | −4770.63 | −0.744469 | ||||||||
\(346\) | 4412.49 | 0.685598 | ||||||||
\(347\) | 194.543 | 0.0300968 | 0.0150484 | − | 0.999887i | \(-0.495210\pi\) | ||||
0.0150484 | + | 0.999887i | \(0.495210\pi\) | |||||||
\(348\) | −279.241 | −0.0430141 | ||||||||
\(349\) | 10043.2 | 1.54040 | 0.770200 | − | 0.637802i | \(-0.220156\pi\) | ||||
0.770200 | + | 0.637802i | \(0.220156\pi\) | |||||||
\(350\) | 21086.1 | 3.22029 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −649.127 | −0.0982914 | ||||||||
\(353\) | −9089.71 | −1.37053 | −0.685264 | − | 0.728295i | \(-0.740313\pi\) | ||||
−0.685264 | + | 0.728295i | \(0.740313\pi\) | |||||||
\(354\) | −3804.22 | −0.571163 | ||||||||
\(355\) | 2490.44 | 0.372335 | ||||||||
\(356\) | −418.196 | −0.0622594 | ||||||||
\(357\) | 9493.23 | 1.40738 | ||||||||
\(358\) | −11809.6 | −1.74345 | ||||||||
\(359\) | −8571.96 | −1.26020 | −0.630098 | − | 0.776515i | \(-0.716985\pi\) | ||||
−0.630098 | + | 0.776515i | \(0.716985\pi\) | |||||||
\(360\) | 9946.30 | 1.45616 | ||||||||
\(361\) | −6659.10 | −0.970856 | ||||||||
\(362\) | 4037.80 | 0.586249 | ||||||||
\(363\) | −307.561 | −0.0444704 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 8687.10 | 1.24576 | ||||||||
\(366\) | 2008.39 | 0.286831 | ||||||||
\(367\) | −4128.93 | −0.587271 | −0.293636 | − | 0.955917i | \(-0.594865\pi\) | ||||
−0.293636 | + | 0.955917i | \(0.594865\pi\) | |||||||
\(368\) | −4827.90 | −0.683890 | ||||||||
\(369\) | −5140.99 | −0.725283 | ||||||||
\(370\) | −6540.97 | −0.919051 | ||||||||
\(371\) | −8679.72 | −1.21463 | ||||||||
\(372\) | 707.390 | 0.0985927 | ||||||||
\(373\) | −12786.4 | −1.77495 | −0.887474 | − | 0.460857i | \(-0.847542\pi\) | ||||
−0.887474 | + | 0.460857i | \(0.847542\pi\) | |||||||
\(374\) | 3634.79 | 0.502541 | ||||||||
\(375\) | −7880.33 | −1.08517 | ||||||||
\(376\) | −11501.2 | −1.57747 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 9125.81 | 1.24175 | ||||||||
\(379\) | 7006.18 | 0.949561 | 0.474780 | − | 0.880104i | \(-0.342527\pi\) | ||||
0.474780 | + | 0.880104i | \(0.342527\pi\) | |||||||
\(380\) | −374.708 | −0.0505845 | ||||||||
\(381\) | −4114.04 | −0.553199 | ||||||||
\(382\) | −8500.82 | −1.13859 | ||||||||
\(383\) | 5394.86 | 0.719750 | 0.359875 | − | 0.933000i | \(-0.382819\pi\) | ||||
0.359875 | + | 0.933000i | \(0.382819\pi\) | |||||||
\(384\) | −2520.66 | −0.334979 | ||||||||
\(385\) | −6461.32 | −0.855323 | ||||||||
\(386\) | −5581.76 | −0.736021 | ||||||||
\(387\) | −7556.64 | −0.992573 | ||||||||
\(388\) | 2059.49 | 0.269471 | ||||||||
\(389\) | 7762.65 | 1.01178 | 0.505889 | − | 0.862598i | \(-0.331164\pi\) | ||||
0.505889 | + | 0.862598i | \(0.331164\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −11933.5 | −1.54349 | ||||||||
\(392\) | −12298.8 | −1.58465 | ||||||||
\(393\) | −4723.06 | −0.606226 | ||||||||
\(394\) | −13879.6 | −1.77473 | ||||||||
\(395\) | 5416.20 | 0.689920 | ||||||||
\(396\) | −297.826 | −0.0377937 | ||||||||
\(397\) | 1736.65 | 0.219547 | 0.109773 | − | 0.993957i | \(-0.464988\pi\) | ||||
0.109773 | + | 0.993957i | \(0.464988\pi\) | |||||||
\(398\) | 121.161 | 0.0152594 | ||||||||
\(399\) | −1049.97 | −0.131740 | ||||||||
\(400\) | −14439.5 | −1.80494 | ||||||||
\(401\) | 8665.93 | 1.07919 | 0.539596 | − | 0.841924i | \(-0.318577\pi\) | ||||
0.539596 | + | 0.841924i | \(0.318577\pi\) | |||||||
\(402\) | −2174.16 | −0.269744 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | −754.510 | −0.0929165 | ||||||||
\(405\) | 4974.17 | 0.610292 | ||||||||
\(406\) | −6293.90 | −0.769362 | ||||||||
\(407\) | 1384.48 | 0.168615 | ||||||||
\(408\) | −7826.45 | −0.949675 | ||||||||
\(409\) | −12146.8 | −1.46851 | −0.734257 | − | 0.678871i | \(-0.762469\pi\) | ||||
−0.734257 | + | 0.678871i | \(0.762469\pi\) | |||||||
\(410\) | 13008.1 | 1.56688 | ||||||||
\(411\) | 5051.38 | 0.606244 | ||||||||
\(412\) | −85.6271 | −0.0102392 | ||||||||
\(413\) | 16916.1 | 2.01547 | ||||||||
\(414\) | −4956.29 | −0.588377 | ||||||||
\(415\) | −8551.91 | −1.01156 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −820.179 | −0.0963174 | ||||||||
\(418\) | −402.016 | −0.0470413 | ||||||||
\(419\) | −5363.15 | −0.625315 | −0.312658 | − | 0.949866i | \(-0.601219\pi\) | ||||
−0.312658 | + | 0.949866i | \(0.601219\pi\) | |||||||
\(420\) | 1968.17 | 0.228659 | ||||||||
\(421\) | 9460.90 | 1.09524 | 0.547620 | − | 0.836727i | \(-0.315534\pi\) | ||||
0.547620 | + | 0.836727i | \(0.315534\pi\) | |||||||
\(422\) | 6040.73 | 0.696820 | ||||||||
\(423\) | −9807.22 | −1.12729 | ||||||||
\(424\) | 7155.78 | 0.819611 | ||||||||
\(425\) | −35691.3 | −4.07361 | ||||||||
\(426\) | −813.894 | −0.0925664 | ||||||||
\(427\) | −8930.67 | −1.01214 | ||||||||
\(428\) | 427.235 | 0.0482504 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 19120.3 | 2.14433 | ||||||||
\(431\) | 1127.27 | 0.125983 | 0.0629915 | − | 0.998014i | \(-0.479936\pi\) | ||||
0.0629915 | + | 0.998014i | \(0.479936\pi\) | |||||||
\(432\) | −6249.23 | −0.695987 | ||||||||
\(433\) | 13819.1 | 1.53373 | 0.766865 | − | 0.641809i | \(-0.221816\pi\) | ||||
0.766865 | + | 0.641809i | \(0.221816\pi\) | |||||||
\(434\) | 15944.1 | 1.76346 | ||||||||
\(435\) | 4258.85 | 0.469417 | ||||||||
\(436\) | 64.9348 | 0.00713260 | ||||||||
\(437\) | 1319.88 | 0.144481 | ||||||||
\(438\) | −2839.00 | −0.309710 | ||||||||
\(439\) | 548.517 | 0.0596339 | 0.0298170 | − | 0.999555i | \(-0.490508\pi\) | ||||
0.0298170 | + | 0.999555i | \(0.490508\pi\) | |||||||
\(440\) | 5326.87 | 0.577156 | ||||||||
\(441\) | −10487.3 | −1.13242 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 7693.16 | 0.825086 | 0.412543 | − | 0.910938i | \(-0.364641\pi\) | ||||
0.412543 | + | 0.910938i | \(0.364641\pi\) | |||||||
\(444\) | −421.724 | −0.0450769 | ||||||||
\(445\) | 6378.13 | 0.679443 | ||||||||
\(446\) | 4660.85 | 0.494838 | ||||||||
\(447\) | −7537.89 | −0.797606 | ||||||||
\(448\) | 16544.5 | 1.74476 | ||||||||
\(449\) | 2843.93 | 0.298916 | 0.149458 | − | 0.988768i | \(-0.452247\pi\) | ||||
0.149458 | + | 0.988768i | \(0.452247\pi\) | |||||||
\(450\) | −14823.5 | −1.55286 | ||||||||
\(451\) | −2753.33 | −0.287471 | ||||||||
\(452\) | 610.029 | 0.0634808 | ||||||||
\(453\) | −4866.84 | −0.504777 | ||||||||
\(454\) | −5490.33 | −0.567564 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 865.625 | 0.0888960 | ||||||||
\(457\) | −3002.57 | −0.307340 | −0.153670 | − | 0.988122i | \(-0.549109\pi\) | ||||
−0.153670 | + | 0.988122i | \(0.549109\pi\) | |||||||
\(458\) | 13283.5 | 1.35523 | ||||||||
\(459\) | −15446.7 | −1.57079 | ||||||||
\(460\) | −2474.10 | −0.250773 | ||||||||
\(461\) | 5826.46 | 0.588645 | 0.294322 | − | 0.955706i | \(-0.404906\pi\) | ||||
0.294322 | + | 0.955706i | \(0.404906\pi\) | |||||||
\(462\) | 2111.61 | 0.212642 | ||||||||
\(463\) | −8250.98 | −0.828197 | −0.414099 | − | 0.910232i | \(-0.635903\pi\) | ||||
−0.414099 | + | 0.910232i | \(0.635903\pi\) | |||||||
\(464\) | 4309.98 | 0.431219 | ||||||||
\(465\) | −10788.8 | −1.07595 | ||||||||
\(466\) | 8930.24 | 0.887737 | ||||||||
\(467\) | −14425.6 | −1.42942 | −0.714709 | − | 0.699422i | \(-0.753441\pi\) | ||||
−0.714709 | + | 0.699422i | \(0.753441\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 9667.78 | 0.951848 | ||||||||
\(470\) | 24814.8 | 2.43537 | ||||||||
\(471\) | 41.3505 | 0.00404528 | ||||||||
\(472\) | −13946.1 | −1.36000 | ||||||||
\(473\) | −4047.06 | −0.393412 | ||||||||
\(474\) | −1770.05 | −0.171521 | ||||||||
\(475\) | 3947.55 | 0.381318 | ||||||||
\(476\) | 4923.29 | 0.474073 | ||||||||
\(477\) | 6101.82 | 0.585709 | ||||||||
\(478\) | 15170.6 | 1.45165 | ||||||||
\(479\) | −17012.9 | −1.62284 | −0.811419 | − | 0.584465i | \(-0.801305\pi\) | ||||
−0.811419 | + | 0.584465i | \(0.801305\pi\) | |||||||
\(480\) | −3015.67 | −0.286762 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | −18160.8 | −1.71618 | ||||||||
\(483\) | −6932.70 | −0.653103 | ||||||||
\(484\) | −159.505 | −0.0149798 | ||||||||
\(485\) | −31410.3 | −2.94076 | ||||||||
\(486\) | −10059.1 | −0.938866 | ||||||||
\(487\) | 8912.81 | 0.829318 | 0.414659 | − | 0.909977i | \(-0.363901\pi\) | ||||
0.414659 | + | 0.909977i | \(0.363901\pi\) | |||||||
\(488\) | 7362.66 | 0.682976 | ||||||||
\(489\) | −4027.67 | −0.372470 | ||||||||
\(490\) | 26535.7 | 2.44645 | ||||||||
\(491\) | 16340.6 | 1.50192 | 0.750959 | − | 0.660349i | \(-0.229592\pi\) | ||||
0.750959 | + | 0.660349i | \(0.229592\pi\) | |||||||
\(492\) | 838.685 | 0.0768513 | ||||||||
\(493\) | 10653.3 | 0.973230 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 4542.29 | 0.412446 | ||||||||
\(496\) | −10918.3 | −0.988399 | ||||||||
\(497\) | 3619.13 | 0.326640 | ||||||||
\(498\) | 2794.83 | 0.251484 | ||||||||
\(499\) | 1245.47 | 0.111733 | 0.0558665 | − | 0.998438i | \(-0.482208\pi\) | ||||
0.0558665 | + | 0.998438i | \(0.482208\pi\) | |||||||
\(500\) | −4086.83 | −0.365537 | ||||||||
\(501\) | −1526.89 | −0.136160 | ||||||||
\(502\) | −16504.2 | −1.46737 | ||||||||
\(503\) | 2095.58 | 0.185760 | 0.0928801 | − | 0.995677i | \(-0.470393\pi\) | ||||
0.0928801 | + | 0.995677i | \(0.470393\pi\) | |||||||
\(504\) | 14454.0 | 1.27745 | ||||||||
\(505\) | 11507.4 | 1.01401 | ||||||||
\(506\) | −2654.41 | −0.233207 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −2133.59 | −0.186344 | ||||||||
\(509\) | −17414.0 | −1.51643 | −0.758216 | − | 0.652004i | \(-0.773929\pi\) | ||||
−0.758216 | + | 0.652004i | \(0.773929\pi\) | |||||||
\(510\) | 16886.2 | 1.46615 | ||||||||
\(511\) | 12624.1 | 1.09288 | ||||||||
\(512\) | −13017.4 | −1.12362 | ||||||||
\(513\) | 1708.45 | 0.147037 | ||||||||
\(514\) | 183.972 | 0.0157873 | ||||||||
\(515\) | 1305.94 | 0.111741 | ||||||||
\(516\) | 1232.77 | 0.105173 | ||||||||
\(517\) | −5252.39 | −0.446808 | ||||||||
\(518\) | −9505.38 | −0.806259 | ||||||||
\(519\) | −4338.94 | −0.366972 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −14865.5 | −1.25004 | −0.625020 | − | 0.780609i | \(-0.714909\pi\) | ||||
−0.625020 | + | 0.780609i | \(0.714909\pi\) | |||||||
\(522\) | 4424.60 | 0.370995 | ||||||||
\(523\) | −4969.64 | −0.415501 | −0.207751 | − | 0.978182i | \(-0.566614\pi\) | ||||
−0.207751 | + | 0.978182i | \(0.566614\pi\) | |||||||
\(524\) | −2449.43 | −0.204206 | ||||||||
\(525\) | −20734.7 | −1.72369 | ||||||||
\(526\) | −2055.04 | −0.170349 | ||||||||
\(527\) | −26987.7 | −2.23074 | ||||||||
\(528\) | −1446.00 | −0.119184 | ||||||||
\(529\) | −3452.21 | −0.283735 | ||||||||
\(530\) | −15439.2 | −1.26535 | ||||||||
\(531\) | −11892.0 | −0.971881 | ||||||||
\(532\) | −544.528 | −0.0443765 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | −2084.42 | −0.168917 | ||||||||
\(535\) | −6515.98 | −0.526561 | ||||||||
\(536\) | −7970.36 | −0.642289 | ||||||||
\(537\) | 11612.8 | 0.933198 | ||||||||
\(538\) | 4876.97 | 0.390820 | ||||||||
\(539\) | −5616.63 | −0.448842 | ||||||||
\(540\) | −3202.47 | −0.255208 | ||||||||
\(541\) | −3278.56 | −0.260548 | −0.130274 | − | 0.991478i | \(-0.541586\pi\) | ||||
−0.130274 | + | 0.991478i | \(0.541586\pi\) | |||||||
\(542\) | 3310.46 | 0.262355 | ||||||||
\(543\) | −3970.50 | −0.313795 | ||||||||
\(544\) | −7543.57 | −0.594537 | ||||||||
\(545\) | −990.354 | −0.0778387 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −1923.63 | −0.150363 | −0.0751813 | − | 0.997170i | \(-0.523954\pi\) | ||||
−0.0751813 | + | 0.997170i | \(0.523954\pi\) | |||||||
\(548\) | 2619.70 | 0.204212 | ||||||||
\(549\) | 6278.23 | 0.488067 | ||||||||
\(550\) | −7938.92 | −0.615485 | ||||||||
\(551\) | −1178.29 | −0.0911010 | ||||||||
\(552\) | 5715.49 | 0.440702 | ||||||||
\(553\) | 7870.85 | 0.605249 | ||||||||
\(554\) | −954.113 | −0.0731703 | ||||||||
\(555\) | 6431.94 | 0.491929 | ||||||||
\(556\) | −425.354 | −0.0324443 | ||||||||
\(557\) | −4445.39 | −0.338163 | −0.169082 | − | 0.985602i | \(-0.554080\pi\) | ||||
−0.169082 | + | 0.985602i | \(0.554080\pi\) | |||||||
\(558\) | −11208.6 | −0.850358 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | −30377.9 | −2.29232 | ||||||||
\(561\) | −3574.20 | −0.268989 | ||||||||
\(562\) | 2654.34 | 0.199229 | ||||||||
\(563\) | 7326.15 | 0.548420 | 0.274210 | − | 0.961670i | \(-0.411584\pi\) | ||||
0.274210 | + | 0.961670i | \(0.411584\pi\) | |||||||
\(564\) | 1599.92 | 0.119448 | ||||||||
\(565\) | −9303.86 | −0.692772 | ||||||||
\(566\) | 4692.41 | 0.348475 | ||||||||
\(567\) | 7228.49 | 0.535393 | ||||||||
\(568\) | −2983.70 | −0.220410 | ||||||||
\(569\) | 20265.7 | 1.49311 | 0.746557 | − | 0.665322i | \(-0.231706\pi\) | ||||
0.746557 | + | 0.665322i | \(0.231706\pi\) | |||||||
\(570\) | −1867.66 | −0.137241 | ||||||||
\(571\) | 10664.6 | 0.781612 | 0.390806 | − | 0.920473i | \(-0.372196\pi\) | ||||
0.390806 | + | 0.920473i | \(0.372196\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 8359.12 | 0.609437 | ||||||||
\(574\) | 18903.4 | 1.37459 | ||||||||
\(575\) | 26064.6 | 1.89038 | ||||||||
\(576\) | −11630.7 | −0.841343 | ||||||||
\(577\) | −23415.6 | −1.68943 | −0.844717 | − | 0.535214i | \(-0.820231\pi\) | ||||
−0.844717 | + | 0.535214i | \(0.820231\pi\) | |||||||
\(578\) | 29540.5 | 2.12582 | ||||||||
\(579\) | 5488.72 | 0.393961 | ||||||||
\(580\) | 2208.69 | 0.158122 | ||||||||
\(581\) | −12427.7 | −0.887414 | ||||||||
\(582\) | 10265.1 | 0.731105 | ||||||||
\(583\) | 3267.91 | 0.232149 | ||||||||
\(584\) | −10407.7 | −0.737452 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 16710.0 | 1.17796 | ||||||||
\(587\) | −24346.6 | −1.71191 | −0.855954 | − | 0.517052i | \(-0.827030\pi\) | ||||
−0.855954 | + | 0.517052i | \(0.827030\pi\) | |||||||
\(588\) | 1710.87 | 0.119992 | ||||||||
\(589\) | 2984.90 | 0.208813 | ||||||||
\(590\) | 30089.8 | 2.09963 | ||||||||
\(591\) | 13648.3 | 0.949940 | ||||||||
\(592\) | 6509.16 | 0.451900 | ||||||||
\(593\) | −25082.6 | −1.73696 | −0.868480 | − | 0.495725i | \(-0.834903\pi\) | ||||
−0.868480 | + | 0.495725i | \(0.834903\pi\) | |||||||
\(594\) | −3435.86 | −0.237332 | ||||||||
\(595\) | −75087.7 | −5.17360 | ||||||||
\(596\) | −3909.23 | −0.268672 | ||||||||
\(597\) | −119.141 | −0.00816771 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −26412.5 | −1.80165 | −0.900823 | − | 0.434186i | \(-0.857036\pi\) | ||||
−0.900823 | + | 0.434186i | \(0.857036\pi\) | |||||||
\(600\) | 17094.2 | 1.16311 | ||||||||
\(601\) | −2941.50 | −0.199645 | −0.0998223 | − | 0.995005i | \(-0.531827\pi\) | ||||
−0.0998223 | + | 0.995005i | \(0.531827\pi\) | |||||||
\(602\) | 27785.7 | 1.88116 | ||||||||
\(603\) | −6796.43 | −0.458991 | ||||||||
\(604\) | −2524.00 | −0.170033 | ||||||||
\(605\) | 2432.69 | 0.163476 | ||||||||
\(606\) | −3760.71 | −0.252093 | ||||||||
\(607\) | 28694.7 | 1.91875 | 0.959377 | − | 0.282128i | \(-0.0910404\pi\) | ||||
0.959377 | + | 0.282128i | \(0.0910404\pi\) | |||||||
\(608\) | 834.337 | 0.0556527 | ||||||||
\(609\) | 6188.99 | 0.411807 | ||||||||
\(610\) | −15885.6 | −1.05441 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | −3461.06 | −0.228603 | ||||||||
\(613\) | −2153.88 | −0.141916 | −0.0709578 | − | 0.997479i | \(-0.522606\pi\) | ||||
−0.0709578 | + | 0.997479i | \(0.522606\pi\) | |||||||
\(614\) | 24857.3 | 1.63381 | ||||||||
\(615\) | −12791.2 | −0.838686 | ||||||||
\(616\) | 7741.05 | 0.506324 | ||||||||
\(617\) | −2450.26 | −0.159877 | −0.0799383 | − | 0.996800i | \(-0.525472\pi\) | ||||
−0.0799383 | + | 0.996800i | \(0.525472\pi\) | |||||||
\(618\) | −426.792 | −0.0277801 | ||||||||
\(619\) | −15715.2 | −1.02043 | −0.510216 | − | 0.860046i | \(-0.670435\pi\) | ||||
−0.510216 | + | 0.860046i | \(0.670435\pi\) | |||||||
\(620\) | −5595.18 | −0.362432 | ||||||||
\(621\) | 11280.4 | 0.728934 | ||||||||
\(622\) | −11425.4 | −0.736520 | ||||||||
\(623\) | 9268.73 | 0.596058 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 27429.7 | 1.75550 | ||||||||
\(626\) | 12036.8 | 0.768511 | ||||||||
\(627\) | 395.315 | 0.0251792 | ||||||||
\(628\) | 21.4448 | 0.00136264 | ||||||||
\(629\) | 16089.2 | 1.01990 | ||||||||
\(630\) | −31185.8 | −1.97218 | ||||||||
\(631\) | 8790.00 | 0.554555 | 0.277278 | − | 0.960790i | \(-0.410568\pi\) | ||||
0.277278 | + | 0.960790i | \(0.410568\pi\) | |||||||
\(632\) | −6488.93 | −0.408411 | ||||||||
\(633\) | −5940.04 | −0.372978 | ||||||||
\(634\) | −15474.6 | −0.969358 | ||||||||
\(635\) | 32540.4 | 2.03359 | ||||||||
\(636\) | −995.432 | −0.0620620 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 2369.65 | 0.147046 | ||||||||
\(639\) | −2544.24 | −0.157509 | ||||||||
\(640\) | 19937.4 | 1.23140 | ||||||||
\(641\) | 15059.9 | 0.927973 | 0.463987 | − | 0.885842i | \(-0.346419\pi\) | ||||
0.463987 | + | 0.885842i | \(0.346419\pi\) | |||||||
\(642\) | 2129.47 | 0.130909 | ||||||||
\(643\) | −4383.40 | −0.268841 | −0.134420 | − | 0.990924i | \(-0.542917\pi\) | ||||
−0.134420 | + | 0.990924i | \(0.542917\pi\) | |||||||
\(644\) | −3595.38 | −0.219996 | ||||||||
\(645\) | −18801.6 | −1.14777 | ||||||||
\(646\) | −4671.87 | −0.284539 | ||||||||
\(647\) | −7536.76 | −0.457961 | −0.228980 | − | 0.973431i | \(-0.573539\pi\) | ||||
−0.228980 | + | 0.973431i | \(0.573539\pi\) | |||||||
\(648\) | −5959.35 | −0.361273 | ||||||||
\(649\) | −6368.92 | −0.385211 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −15678.3 | −0.943904 | ||||||||
\(652\) | −2088.80 | −0.125466 | ||||||||
\(653\) | −13190.7 | −0.790493 | −0.395247 | − | 0.918575i | \(-0.629341\pi\) | ||||
−0.395247 | + | 0.918575i | \(0.629341\pi\) | |||||||
\(654\) | 323.655 | 0.0193515 | ||||||||
\(655\) | 37357.5 | 2.22852 | ||||||||
\(656\) | −12944.8 | −0.770441 | ||||||||
\(657\) | −8874.74 | −0.526996 | ||||||||
\(658\) | 36061.1 | 2.13648 | ||||||||
\(659\) | 7596.99 | 0.449069 | 0.224535 | − | 0.974466i | \(-0.427914\pi\) | ||||
0.224535 | + | 0.974466i | \(0.427914\pi\) | |||||||
\(660\) | −741.015 | −0.0437030 | ||||||||
\(661\) | 1252.96 | 0.0737285 | 0.0368642 | − | 0.999320i | \(-0.488263\pi\) | ||||
0.0368642 | + | 0.999320i | \(0.488263\pi\) | |||||||
\(662\) | −9527.08 | −0.559336 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 10245.7 | 0.598811 | ||||||||
\(665\) | 8304.88 | 0.484285 | ||||||||
\(666\) | 6682.25 | 0.388787 | ||||||||
\(667\) | −7779.91 | −0.451633 | ||||||||
\(668\) | −791.862 | −0.0458653 | ||||||||
\(669\) | −4583.16 | −0.264866 | ||||||||
\(670\) | 17196.7 | 0.991593 | ||||||||
\(671\) | 3362.39 | 0.193448 | ||||||||
\(672\) | −4382.39 | −0.251569 | ||||||||
\(673\) | 6436.84 | 0.368680 | 0.184340 | − | 0.982862i | \(-0.440985\pi\) | ||||
0.184340 | + | 0.982862i | \(0.440985\pi\) | |||||||
\(674\) | −22180.6 | −1.26760 | ||||||||
\(675\) | 33738.0 | 1.92382 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −19087.6 | −1.08360 | −0.541798 | − | 0.840509i | \(-0.682256\pi\) | ||||
−0.541798 | + | 0.840509i | \(0.682256\pi\) | |||||||
\(678\) | 3040.57 | 0.172231 | ||||||||
\(679\) | −45645.7 | −2.57985 | ||||||||
\(680\) | 61904.1 | 3.49105 | ||||||||
\(681\) | 5398.81 | 0.303793 | ||||||||
\(682\) | −6002.94 | −0.337045 | ||||||||
\(683\) | 22989.3 | 1.28794 | 0.643970 | − | 0.765051i | \(-0.277286\pi\) | ||||
0.643970 | + | 0.765051i | \(0.277286\pi\) | |||||||
\(684\) | 382.802 | 0.0213988 | ||||||||
\(685\) | −39954.4 | −2.22858 | ||||||||
\(686\) | 12657.7 | 0.704482 | ||||||||
\(687\) | −13062.0 | −0.725397 | ||||||||
\(688\) | −19027.3 | −1.05437 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | −12331.7 | −0.680374 | ||||||||
\(691\) | 22256.4 | 1.22529 | 0.612644 | − | 0.790359i | \(-0.290106\pi\) | ||||
0.612644 | + | 0.790359i | \(0.290106\pi\) | |||||||
\(692\) | −2250.22 | −0.123614 | ||||||||
\(693\) | 6600.89 | 0.361828 | ||||||||
\(694\) | 502.876 | 0.0275056 | ||||||||
\(695\) | 6487.29 | 0.354068 | ||||||||
\(696\) | −5102.36 | −0.277880 | ||||||||
\(697\) | −31996.7 | −1.73883 | ||||||||
\(698\) | 25960.8 | 1.40778 | ||||||||
\(699\) | −8781.38 | −0.475168 | ||||||||
\(700\) | −10753.2 | −0.580619 | ||||||||
\(701\) | 26090.6 | 1.40575 | 0.702874 | − | 0.711315i | \(-0.251900\pi\) | ||||
0.702874 | + | 0.711315i | \(0.251900\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −1779.51 | −0.0954700 | ||||||||
\(704\) | −6228.99 | −0.333472 | ||||||||
\(705\) | −24401.2 | −1.30355 | ||||||||
\(706\) | −23496.1 | −1.25253 | ||||||||
\(707\) | 16722.7 | 0.889562 | ||||||||
\(708\) | 1940.02 | 0.102981 | ||||||||
\(709\) | −15288.9 | −0.809855 | −0.404927 | − | 0.914349i | \(-0.632703\pi\) | ||||
−0.404927 | + | 0.914349i | \(0.632703\pi\) | |||||||
\(710\) | 6437.58 | 0.340279 | ||||||||
\(711\) | −5533.19 | −0.291858 | ||||||||
\(712\) | −7641.37 | −0.402209 | ||||||||
\(713\) | 19708.5 | 1.03519 | ||||||||
\(714\) | 24539.2 | 1.28621 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 6022.50 | 0.314345 | ||||||||
\(717\) | −14917.7 | −0.777006 | ||||||||
\(718\) | −22157.8 | −1.15170 | ||||||||
\(719\) | 7202.62 | 0.373592 | 0.186796 | − | 0.982399i | \(-0.440190\pi\) | ||||
0.186796 | + | 0.982399i | \(0.440190\pi\) | |||||||
\(720\) | 21355.6 | 1.10538 | ||||||||
\(721\) | 1897.81 | 0.0980277 | ||||||||
\(722\) | −17213.2 | −0.887270 | ||||||||
\(723\) | 17858.0 | 0.918600 | ||||||||
\(724\) | −2059.14 | −0.105701 | ||||||||
\(725\) | −23268.5 | −1.19196 | ||||||||
\(726\) | −795.019 | −0.0406418 | ||||||||
\(727\) | −8345.29 | −0.425736 | −0.212868 | − | 0.977081i | \(-0.568280\pi\) | ||||
−0.212868 | + | 0.977081i | \(0.568280\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 3211.30 | 0.163151 | ||||||||
\(730\) | 22455.4 | 1.13851 | ||||||||
\(731\) | −47031.3 | −2.37964 | ||||||||
\(732\) | −1024.21 | −0.0517158 | ||||||||
\(733\) | 6942.80 | 0.349847 | 0.174924 | − | 0.984582i | \(-0.444032\pi\) | ||||
0.174924 | + | 0.984582i | \(0.444032\pi\) | |||||||
\(734\) | −10672.9 | −0.536710 | ||||||||
\(735\) | −26093.4 | −1.30948 | ||||||||
\(736\) | 5508.91 | 0.275898 | ||||||||
\(737\) | −3639.92 | −0.181924 | ||||||||
\(738\) | −13289.0 | −0.662840 | ||||||||
\(739\) | −18054.1 | −0.898686 | −0.449343 | − | 0.893359i | \(-0.648342\pi\) | ||||
−0.449343 | + | 0.893359i | \(0.648342\pi\) | |||||||
\(740\) | 3335.67 | 0.165705 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −22436.3 | −1.11006 | ||||||||
\(743\) | 27215.4 | 1.34379 | 0.671895 | − | 0.740647i | \(-0.265481\pi\) | ||||
0.671895 | + | 0.740647i | \(0.265481\pi\) | |||||||
\(744\) | 12925.6 | 0.636929 | ||||||||
\(745\) | 59621.7 | 2.93204 | ||||||||
\(746\) | −33051.8 | −1.62213 | ||||||||
\(747\) | 8736.64 | 0.427921 | ||||||||
\(748\) | −1853.62 | −0.0906083 | ||||||||
\(749\) | −9469.06 | −0.461938 | ||||||||
\(750\) | −20370.0 | −0.991742 | ||||||||
\(751\) | 30044.8 | 1.45985 | 0.729927 | − | 0.683525i | \(-0.239554\pi\) | ||||
0.729927 | + | 0.683525i | \(0.239554\pi\) | |||||||
\(752\) | −24694.1 | −1.19748 | ||||||||
\(753\) | 16229.1 | 0.785420 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 38494.8 | 1.85559 | ||||||||
\(756\) | −4653.85 | −0.223888 | ||||||||
\(757\) | −32140.6 | −1.54316 | −0.771578 | − | 0.636135i | \(-0.780532\pi\) | ||||
−0.771578 | + | 0.636135i | \(0.780532\pi\) | |||||||
\(758\) | 18110.4 | 0.867808 | ||||||||
\(759\) | 2610.16 | 0.124826 | ||||||||
\(760\) | −6846.75 | −0.326786 | ||||||||
\(761\) | 5510.25 | 0.262479 | 0.131240 | − | 0.991351i | \(-0.458104\pi\) | ||||
0.131240 | + | 0.991351i | \(0.458104\pi\) | |||||||
\(762\) | −10634.4 | −0.505571 | ||||||||
\(763\) | −1439.19 | −0.0682859 | ||||||||
\(764\) | 4335.13 | 0.205287 | ||||||||
\(765\) | 52786.4 | 2.49477 | ||||||||
\(766\) | 13945.2 | 0.657784 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 4999.24 | 0.234889 | ||||||||
\(769\) | 4317.43 | 0.202459 | 0.101229 | − | 0.994863i | \(-0.467722\pi\) | ||||
0.101229 | + | 0.994863i | \(0.467722\pi\) | |||||||
\(770\) | −16702.0 | −0.781684 | ||||||||
\(771\) | −180.906 | −0.00845026 | ||||||||
\(772\) | 2846.51 | 0.132705 | ||||||||
\(773\) | 11644.8 | 0.541831 | 0.270916 | − | 0.962603i | \(-0.412674\pi\) | ||||
0.270916 | + | 0.962603i | \(0.412674\pi\) | |||||||
\(774\) | −19533.3 | −0.907117 | ||||||||
\(775\) | 58945.2 | 2.73209 | ||||||||
\(776\) | 37631.4 | 1.74084 | ||||||||
\(777\) | 9346.93 | 0.431556 | ||||||||
\(778\) | 20065.8 | 0.924670 | ||||||||
\(779\) | 3538.91 | 0.162766 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −1362.60 | −0.0624298 | ||||||||
\(782\) | −30847.1 | −1.41060 | ||||||||
\(783\) | −10070.3 | −0.459621 | ||||||||
\(784\) | −26406.6 | −1.20293 | ||||||||
\(785\) | −327.066 | −0.0148707 | ||||||||
\(786\) | −12208.7 | −0.554033 | ||||||||
\(787\) | −36525.7 | −1.65438 | −0.827191 | − | 0.561921i | \(-0.810063\pi\) | ||||
−0.827191 | + | 0.561921i | \(0.810063\pi\) | |||||||
\(788\) | 7078.14 | 0.319985 | ||||||||
\(789\) | 2020.78 | 0.0911809 | ||||||||
\(790\) | 14000.4 | 0.630522 | ||||||||
\(791\) | −13520.4 | −0.607751 | ||||||||
\(792\) | −5441.94 | −0.244155 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 4489.09 | 0.200645 | ||||||||
\(795\) | 15181.8 | 0.677289 | ||||||||
\(796\) | −61.7879 | −0.00275127 | ||||||||
\(797\) | −5661.21 | −0.251607 | −0.125803 | − | 0.992055i | \(-0.540151\pi\) | ||||
−0.125803 | + | 0.992055i | \(0.540151\pi\) | |||||||
\(798\) | −2714.09 | −0.120398 | ||||||||
\(799\) | −61038.6 | −2.70261 | ||||||||
\(800\) | 16476.3 | 0.728157 | ||||||||
\(801\) | −6515.90 | −0.287426 | ||||||||
\(802\) | 22400.7 | 0.986279 | ||||||||
\(803\) | −4752.99 | −0.208878 | ||||||||
\(804\) | 1108.75 | 0.0486349 | ||||||||
\(805\) | 54834.9 | 2.40084 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −4795.68 | −0.209190 | ||||||||
\(808\) | −13786.6 | −0.600260 | ||||||||
\(809\) | 13730.7 | 0.596719 | 0.298359 | − | 0.954454i | \(-0.403561\pi\) | ||||
0.298359 | + | 0.954454i | \(0.403561\pi\) | |||||||
\(810\) | 12857.8 | 0.557749 | ||||||||
\(811\) | −12954.7 | −0.560913 | −0.280456 | − | 0.959867i | \(-0.590486\pi\) | ||||
−0.280456 | + | 0.959867i | \(0.590486\pi\) | |||||||
\(812\) | 3209.68 | 0.138716 | ||||||||
\(813\) | −3255.28 | −0.140428 | ||||||||
\(814\) | 3578.77 | 0.154098 | ||||||||
\(815\) | 31857.3 | 1.36922 | ||||||||
\(816\) | −16804.1 | −0.720909 | ||||||||
\(817\) | 5201.78 | 0.222750 | ||||||||
\(818\) | −31398.5 | −1.34208 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −6633.67 | −0.282509 | ||||||||
\(821\) | −12151.3 | −0.516546 | −0.258273 | − | 0.966072i | \(-0.583153\pi\) | ||||
−0.258273 | + | 0.966072i | \(0.583153\pi\) | |||||||
\(822\) | 13057.4 | 0.554050 | ||||||||
\(823\) | −7267.59 | −0.307815 | −0.153908 | − | 0.988085i | \(-0.549186\pi\) | ||||
−0.153908 | + | 0.988085i | \(0.549186\pi\) | |||||||
\(824\) | −1564.60 | −0.0661473 | ||||||||
\(825\) | 7806.59 | 0.329443 | ||||||||
\(826\) | 43726.8 | 1.84195 | ||||||||
\(827\) | 16200.3 | 0.681183 | 0.340591 | − | 0.940211i | \(-0.389373\pi\) | ||||
0.340591 | + | 0.940211i | \(0.389373\pi\) | |||||||
\(828\) | 2527.54 | 0.106085 | ||||||||
\(829\) | 327.283 | 0.0137117 | 0.00685585 | − | 0.999976i | \(-0.497818\pi\) | ||||
0.00685585 | + | 0.999976i | \(0.497818\pi\) | |||||||
\(830\) | −22106.0 | −0.924469 | ||||||||
\(831\) | 938.209 | 0.0391650 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −65271.5 | −2.71491 | ||||||||
\(834\) | −2120.09 | −0.0880249 | ||||||||
\(835\) | 12077.1 | 0.500533 | ||||||||
\(836\) | 205.015 | 0.00848156 | ||||||||
\(837\) | 25510.7 | 1.05350 | ||||||||
\(838\) | −13863.3 | −0.571479 | ||||||||
\(839\) | 20762.4 | 0.854346 | 0.427173 | − | 0.904170i | \(-0.359510\pi\) | ||||
0.427173 | + | 0.904170i | \(0.359510\pi\) | |||||||
\(840\) | 35962.8 | 1.47718 | ||||||||
\(841\) | −17443.7 | −0.715228 | ||||||||
\(842\) | 24455.6 | 1.00095 | ||||||||
\(843\) | −2610.10 | −0.106639 | ||||||||
\(844\) | −3080.57 | −0.125637 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −25350.8 | −1.03024 | ||||||||
\(847\) | 3535.19 | 0.143413 | ||||||||
\(848\) | 15364.1 | 0.622176 | ||||||||
\(849\) | −4614.19 | −0.186524 | ||||||||
\(850\) | −92259.0 | −3.72289 | ||||||||
\(851\) | −11749.6 | −0.473292 | ||||||||
\(852\) | 415.058 | 0.0166898 | ||||||||
\(853\) | −5761.34 | −0.231260 | −0.115630 | − | 0.993292i | \(-0.536889\pi\) | ||||
−0.115630 | + | 0.993292i | \(0.536889\pi\) | |||||||
\(854\) | −23085.0 | −0.925003 | ||||||||
\(855\) | −5838.31 | −0.233527 | ||||||||
\(856\) | 7806.53 | 0.311707 | ||||||||
\(857\) | −29258.6 | −1.16623 | −0.583113 | − | 0.812391i | \(-0.698166\pi\) | ||||
−0.583113 | + | 0.812391i | \(0.698166\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −24016.1 | −0.953923 | −0.476961 | − | 0.878924i | \(-0.658262\pi\) | ||||
−0.476961 | + | 0.878924i | \(0.658262\pi\) | |||||||
\(860\) | −9750.69 | −0.386623 | ||||||||
\(861\) | −18588.3 | −0.735758 | ||||||||
\(862\) | 2913.89 | 0.115136 | ||||||||
\(863\) | −6376.10 | −0.251500 | −0.125750 | − | 0.992062i | \(-0.540134\pi\) | ||||
−0.125750 | + | 0.992062i | \(0.540134\pi\) | |||||||
\(864\) | 7130.73 | 0.280778 | ||||||||
\(865\) | 34319.3 | 1.34901 | ||||||||
\(866\) | 35721.3 | 1.40168 | ||||||||
\(867\) | −29048.1 | −1.13786 | ||||||||
\(868\) | −8130.95 | −0.317952 | ||||||||
\(869\) | −2963.37 | −0.115680 | ||||||||
\(870\) | 11008.8 | 0.429003 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 1186.50 | 0.0460780 | ||||||||
\(873\) | 32088.8 | 1.24403 | ||||||||
\(874\) | 3411.77 | 0.132042 | ||||||||
\(875\) | 90578.8 | 3.49957 | ||||||||
\(876\) | 1447.80 | 0.0558408 | ||||||||
\(877\) | 22771.4 | 0.876780 | 0.438390 | − | 0.898785i | \(-0.355549\pi\) | ||||
0.438390 | + | 0.898785i | \(0.355549\pi\) | |||||||
\(878\) | 1417.87 | 0.0544998 | ||||||||
\(879\) | −16431.5 | −0.630511 | ||||||||
\(880\) | 11437.3 | 0.438126 | ||||||||
\(881\) | 32496.4 | 1.24272 | 0.621358 | − | 0.783527i | \(-0.286581\pi\) | ||||
0.621358 | + | 0.783527i | \(0.286581\pi\) | |||||||
\(882\) | −27108.9 | −1.03492 | ||||||||
\(883\) | 23978.0 | 0.913843 | 0.456922 | − | 0.889507i | \(-0.348952\pi\) | ||||
0.456922 | + | 0.889507i | \(0.348952\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −29588.3 | −1.12384 | ||||||||
\(886\) | 19886.2 | 0.754050 | ||||||||
\(887\) | 20034.6 | 0.758396 | 0.379198 | − | 0.925315i | \(-0.376200\pi\) | ||||
0.379198 | + | 0.925315i | \(0.376200\pi\) | |||||||
\(888\) | −7705.84 | −0.291206 | ||||||||
\(889\) | 47288.0 | 1.78401 | ||||||||
\(890\) | 16486.9 | 0.620947 | ||||||||
\(891\) | −2721.52 | −0.102328 | ||||||||
\(892\) | −2376.88 | −0.0892194 | ||||||||
\(893\) | 6751.01 | 0.252983 | ||||||||
\(894\) | −19484.8 | −0.728936 | ||||||||
\(895\) | −91852.3 | −3.43048 | ||||||||
\(896\) | 28973.2 | 1.08027 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 7351.32 | 0.273181 | ||||||||
\(899\) | −17594.3 | −0.652727 | ||||||||
\(900\) | 7559.49 | 0.279981 | ||||||||
\(901\) | 37976.7 | 1.40421 | ||||||||
\(902\) | −7117.12 | −0.262721 | ||||||||
\(903\) | −27322.5 | −1.00691 | ||||||||
\(904\) | 11146.6 | 0.410099 | ||||||||
\(905\) | 31405.1 | 1.15353 | ||||||||
\(906\) | −12580.4 | −0.461318 | ||||||||
\(907\) | 9988.69 | 0.365677 | 0.182838 | − | 0.983143i | \(-0.441471\pi\) | ||||
0.182838 | + | 0.983143i | \(0.441471\pi\) | |||||||
\(908\) | 2799.88 | 0.102332 | ||||||||
\(909\) | −11756.0 | −0.428957 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 44710.0 | 1.62602 | 0.813012 | − | 0.582246i | \(-0.197826\pi\) | ||||
0.813012 | + | 0.582246i | \(0.197826\pi\) | |||||||
\(912\) | 1858.58 | 0.0674820 | ||||||||
\(913\) | 4679.02 | 0.169609 | ||||||||
\(914\) | −7761.39 | −0.280879 | ||||||||
\(915\) | 15620.8 | 0.564379 | ||||||||
\(916\) | −6774.12 | −0.244348 | ||||||||
\(917\) | 54288.2 | 1.95502 | ||||||||
\(918\) | −39928.5 | −1.43555 | ||||||||
\(919\) | −8616.15 | −0.309272 | −0.154636 | − | 0.987972i | \(-0.549420\pi\) | ||||
−0.154636 | + | 0.987972i | \(0.549420\pi\) | |||||||
\(920\) | −45207.3 | −1.62004 | ||||||||
\(921\) | −24443.0 | −0.874510 | ||||||||
\(922\) | 15060.9 | 0.537966 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | −1076.85 | −0.0383395 | ||||||||
\(925\) | −35141.3 | −1.24912 | ||||||||
\(926\) | −21328.1 | −0.756894 | ||||||||
\(927\) | −1334.15 | −0.0472700 | ||||||||
\(928\) | −4917.94 | −0.173965 | ||||||||
\(929\) | 38673.1 | 1.36579 | 0.682897 | − | 0.730515i | \(-0.260720\pi\) | ||||
0.682897 | + | 0.730515i | \(0.260720\pi\) | |||||||
\(930\) | −27888.1 | −0.983318 | ||||||||
\(931\) | 7219.18 | 0.254134 | ||||||||
\(932\) | −4554.12 | −0.160059 | ||||||||
\(933\) | 11234.9 | 0.394228 | ||||||||
\(934\) | −37289.0 | −1.30635 | ||||||||
\(935\) | 28270.5 | 0.988817 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −25983.5 | −0.905917 | −0.452959 | − | 0.891532i | \(-0.649631\pi\) | ||||
−0.452959 | + | 0.891532i | \(0.649631\pi\) | |||||||
\(938\) | 24990.4 | 0.869899 | ||||||||
\(939\) | −11836.2 | −0.411351 | ||||||||
\(940\) | −12654.7 | −0.439097 | ||||||||
\(941\) | −29657.7 | −1.02743 | −0.513716 | − | 0.857960i | \(-0.671731\pi\) | ||||
−0.513716 | + | 0.857960i | \(0.671731\pi\) | |||||||
\(942\) | 106.887 | 0.00369700 | ||||||||
\(943\) | 23366.5 | 0.806913 | ||||||||
\(944\) | −29943.5 | −1.03239 | ||||||||
\(945\) | 70978.3 | 2.44331 | ||||||||
\(946\) | −10461.3 | −0.359542 | ||||||||
\(947\) | 43620.2 | 1.49680 | 0.748399 | − | 0.663249i | \(-0.230823\pi\) | ||||
0.748399 | + | 0.663249i | \(0.230823\pi\) | |||||||
\(948\) | 902.667 | 0.0309254 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 10204.1 | 0.348488 | ||||||||
\(951\) | 15216.6 | 0.518857 | ||||||||
\(952\) | 89959.5 | 3.06261 | ||||||||
\(953\) | 42069.1 | 1.42996 | 0.714980 | − | 0.699145i | \(-0.246436\pi\) | ||||
0.714980 | + | 0.699145i | \(0.246436\pi\) | |||||||
\(954\) | 15772.7 | 0.535282 | ||||||||
\(955\) | −66117.3 | −2.24032 | ||||||||
\(956\) | −7736.50 | −0.261733 | ||||||||
\(957\) | −2330.15 | −0.0787076 | ||||||||
\(958\) | −43976.9 | −1.48312 | ||||||||
\(959\) | −58062.0 | −1.95508 | ||||||||
\(960\) | −28938.2 | −0.972893 | ||||||||
\(961\) | 14779.8 | 0.496118 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 6656.72 | 0.222752 | ||||||||
\(964\) | 9261.37 | 0.309428 | ||||||||
\(965\) | −43413.6 | −1.44822 | ||||||||
\(966\) | −17920.4 | −0.596874 | ||||||||
\(967\) | −7071.73 | −0.235172 | −0.117586 | − | 0.993063i | \(-0.537516\pi\) | ||||
−0.117586 | + | 0.993063i | \(0.537516\pi\) | |||||||
\(968\) | −2914.50 | −0.0967724 | ||||||||
\(969\) | 4594.00 | 0.152302 | ||||||||
\(970\) | −81193.0 | −2.68758 | ||||||||
\(971\) | −25984.5 | −0.858787 | −0.429394 | − | 0.903117i | \(-0.641273\pi\) | ||||
−0.429394 | + | 0.903117i | \(0.641273\pi\) | |||||||
\(972\) | 5129.79 | 0.169278 | ||||||||
\(973\) | 9427.37 | 0.310614 | ||||||||
\(974\) | 23038.8 | 0.757918 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 15808.3 | 0.518454 | ||||||||
\(977\) | 56338.0 | 1.84484 | 0.922421 | − | 0.386186i | \(-0.126208\pi\) | ||||
0.922421 | + | 0.386186i | \(0.126208\pi\) | |||||||
\(978\) | −10411.2 | −0.340402 | ||||||||
\(979\) | −3489.68 | −0.113923 | ||||||||
\(980\) | −13532.3 | −0.441096 | ||||||||
\(981\) | 1011.75 | 0.0329282 | ||||||||
\(982\) | 42239.1 | 1.37261 | ||||||||
\(983\) | −37200.9 | −1.20704 | −0.603522 | − | 0.797346i | \(-0.706237\pi\) | ||||
−0.603522 | + | 0.797346i | \(0.706237\pi\) | |||||||
\(984\) | 15324.6 | 0.496476 | ||||||||
\(985\) | −107952. | −3.49203 | ||||||||
\(986\) | 27538.0 | 0.889440 | ||||||||
\(987\) | −35460.0 | −1.14357 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 34346.0 | 1.10428 | ||||||||
\(990\) | 11741.4 | 0.376937 | ||||||||
\(991\) | −26813.7 | −0.859501 | −0.429751 | − | 0.902948i | \(-0.641399\pi\) | ||||
−0.429751 | + | 0.902948i | \(0.641399\pi\) | |||||||
\(992\) | 12458.4 | 0.398745 | ||||||||
\(993\) | 9368.27 | 0.299389 | ||||||||
\(994\) | 9355.13 | 0.298518 | ||||||||
\(995\) | 942.359 | 0.0300249 | ||||||||
\(996\) | −1425.27 | −0.0453427 | ||||||||
\(997\) | −18893.6 | −0.600165 | −0.300083 | − | 0.953913i | \(-0.597014\pi\) | ||||
−0.300083 | + | 0.953913i | \(0.597014\pi\) | |||||||
\(998\) | 3219.43 | 0.102113 | ||||||||
\(999\) | −15208.7 | −0.481664 |
(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 | 1859.4.a.e.1.8 | 11 | ||
13.12 | even | 2 | 143.4.a.d.1.4 | ✓ | 11 | ||
39.38 | odd | 2 | 1287.4.a.m.1.8 | 11 | |||
52.51 | odd | 2 | 2288.4.a.u.1.7 | 11 | |||
143.142 | odd | 2 | 1573.4.a.f.1.8 | 11 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
143.4.a.d.1.4 | ✓ | 11 | 13.12 | even | 2 | ||
1287.4.a.m.1.8 | 11 | 39.38 | odd | 2 | |||
1573.4.a.f.1.8 | 11 | 143.142 | odd | 2 | |||
1859.4.a.e.1.8 | 11 | 1.1 | even | 1 | trivial | ||
2288.4.a.u.1.7 | 11 | 52.51 | odd | 2 |