Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1875,4,Mod(1,1875)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1875, 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("1875.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1875 = 3 \cdot 5^{4} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1875.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: | \(110.628581261\) |
Analytic rank: | \(1\) |
Dimension: | \(14\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{14} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{14} - 81 x^{12} - 7 x^{11} + 2512 x^{10} + 517 x^{9} - 36970 x^{8} - 12987 x^{7} + 257291 x^{6} + \cdots + 42064 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{2}\cdot 5^{3} \) |
Twist minimal: | no (minimal twist has level 75) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-4.95189\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1875.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −4.95189 | −1.75076 | −0.875379 | − | 0.483437i | \(-0.839388\pi\) | ||||
−0.875379 | + | 0.483437i | \(0.839388\pi\) | |||||||
\(3\) | 3.00000 | 0.577350 | ||||||||
\(4\) | 16.5212 | 2.06515 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −14.8557 | −1.01080 | ||||||||
\(7\) | 28.2766 | 1.52679 | 0.763396 | − | 0.645931i | \(-0.223531\pi\) | ||||
0.763396 | + | 0.645931i | \(0.223531\pi\) | |||||||
\(8\) | −42.1962 | −1.86483 | ||||||||
\(9\) | 9.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −9.92047 | −0.271921 | −0.135961 | − | 0.990714i | \(-0.543412\pi\) | ||||
−0.135961 | + | 0.990714i | \(0.543412\pi\) | |||||||
\(12\) | 49.5637 | 1.19232 | ||||||||
\(13\) | −92.2599 | −1.96833 | −0.984165 | − | 0.177253i | \(-0.943279\pi\) | ||||
−0.984165 | + | 0.177253i | \(0.943279\pi\) | |||||||
\(14\) | −140.023 | −2.67304 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 76.7811 | 1.19970 | ||||||||
\(17\) | −19.6128 | −0.279812 | −0.139906 | − | 0.990165i | \(-0.544680\pi\) | ||||
−0.139906 | + | 0.990165i | \(0.544680\pi\) | |||||||
\(18\) | −44.5670 | −0.583586 | ||||||||
\(19\) | −76.9153 | −0.928715 | −0.464357 | − | 0.885648i | \(-0.653715\pi\) | ||||
−0.464357 | + | 0.885648i | \(0.653715\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 84.8297 | 0.881494 | ||||||||
\(22\) | 49.1251 | 0.476068 | ||||||||
\(23\) | 101.305 | 0.918416 | 0.459208 | − | 0.888329i | \(-0.348133\pi\) | ||||
0.459208 | + | 0.888329i | \(0.348133\pi\) | |||||||
\(24\) | −126.589 | −1.07666 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 456.861 | 3.44607 | ||||||||
\(27\) | 27.0000 | 0.192450 | ||||||||
\(28\) | 467.164 | 3.15306 | ||||||||
\(29\) | 216.896 | 1.38885 | 0.694424 | − | 0.719566i | \(-0.255659\pi\) | ||||
0.694424 | + | 0.719566i | \(0.255659\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 105.058 | 0.608675 | 0.304337 | − | 0.952564i | \(-0.401565\pi\) | ||||
0.304337 | + | 0.952564i | \(0.401565\pi\) | |||||||
\(32\) | −42.6422 | −0.235567 | ||||||||
\(33\) | −29.7614 | −0.156994 | ||||||||
\(34\) | 97.1204 | 0.489883 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 148.691 | 0.688384 | ||||||||
\(37\) | −331.223 | −1.47169 | −0.735847 | − | 0.677148i | \(-0.763216\pi\) | ||||
−0.735847 | + | 0.677148i | \(0.763216\pi\) | |||||||
\(38\) | 380.876 | 1.62595 | ||||||||
\(39\) | −276.780 | −1.13642 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 95.1262 | 0.362347 | 0.181173 | − | 0.983451i | \(-0.442010\pi\) | ||||
0.181173 | + | 0.983451i | \(0.442010\pi\) | |||||||
\(42\) | −420.068 | −1.54328 | ||||||||
\(43\) | −67.8112 | −0.240491 | −0.120245 | − | 0.992744i | \(-0.538368\pi\) | ||||
−0.120245 | + | 0.992744i | \(0.538368\pi\) | |||||||
\(44\) | −163.898 | −0.561559 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −501.652 | −1.60792 | ||||||||
\(47\) | 117.427 | 0.364437 | 0.182219 | − | 0.983258i | \(-0.441672\pi\) | ||||
0.182219 | + | 0.983258i | \(0.441672\pi\) | |||||||
\(48\) | 230.343 | 0.692650 | ||||||||
\(49\) | 456.565 | 1.33109 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −58.8384 | −0.161549 | ||||||||
\(52\) | −1524.25 | −4.06490 | ||||||||
\(53\) | −222.826 | −0.577499 | −0.288750 | − | 0.957405i | \(-0.593240\pi\) | ||||
−0.288750 | + | 0.957405i | \(0.593240\pi\) | |||||||
\(54\) | −133.701 | −0.336934 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −1193.16 | −2.84720 | ||||||||
\(57\) | −230.746 | −0.536194 | ||||||||
\(58\) | −1074.05 | −2.43154 | ||||||||
\(59\) | 174.679 | 0.385446 | 0.192723 | − | 0.981253i | \(-0.438268\pi\) | ||||
0.192723 | + | 0.981253i | \(0.438268\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −472.301 | −0.991344 | −0.495672 | − | 0.868510i | \(-0.665078\pi\) | ||||
−0.495672 | + | 0.868510i | \(0.665078\pi\) | |||||||
\(62\) | −520.234 | −1.06564 | ||||||||
\(63\) | 254.489 | 0.508931 | ||||||||
\(64\) | −403.089 | −0.787284 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 147.375 | 0.274858 | ||||||||
\(67\) | −125.684 | −0.229175 | −0.114587 | − | 0.993413i | \(-0.536555\pi\) | ||||
−0.114587 | + | 0.993413i | \(0.536555\pi\) | |||||||
\(68\) | −324.027 | −0.577854 | ||||||||
\(69\) | 303.915 | 0.530248 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 927.678 | 1.55063 | 0.775317 | − | 0.631572i | \(-0.217590\pi\) | ||||
0.775317 | + | 0.631572i | \(0.217590\pi\) | |||||||
\(72\) | −379.766 | −0.621609 | ||||||||
\(73\) | 101.255 | 0.162342 | 0.0811709 | − | 0.996700i | \(-0.474134\pi\) | ||||
0.0811709 | + | 0.996700i | \(0.474134\pi\) | |||||||
\(74\) | 1640.18 | 2.57658 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −1270.73 | −1.91794 | ||||||||
\(77\) | −280.517 | −0.415167 | ||||||||
\(78\) | 1370.58 | 1.98959 | ||||||||
\(79\) | 295.407 | 0.420707 | 0.210353 | − | 0.977625i | \(-0.432539\pi\) | ||||
0.210353 | + | 0.977625i | \(0.432539\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 81.0000 | 0.111111 | ||||||||
\(82\) | −471.055 | −0.634381 | ||||||||
\(83\) | −1112.32 | −1.47100 | −0.735500 | − | 0.677525i | \(-0.763053\pi\) | ||||
−0.735500 | + | 0.677525i | \(0.763053\pi\) | |||||||
\(84\) | 1401.49 | 1.82042 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 335.794 | 0.421041 | ||||||||
\(87\) | 650.688 | 0.801851 | ||||||||
\(88\) | 418.606 | 0.507086 | ||||||||
\(89\) | 127.735 | 0.152133 | 0.0760666 | − | 0.997103i | \(-0.475764\pi\) | ||||
0.0760666 | + | 0.997103i | \(0.475764\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −2608.80 | −3.00523 | ||||||||
\(92\) | 1673.68 | 1.89667 | ||||||||
\(93\) | 315.173 | 0.351419 | ||||||||
\(94\) | −581.488 | −0.638042 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −127.927 | −0.136005 | ||||||||
\(97\) | −1520.97 | −1.59207 | −0.796035 | − | 0.605250i | \(-0.793073\pi\) | ||||
−0.796035 | + | 0.605250i | \(0.793073\pi\) | |||||||
\(98\) | −2260.86 | −2.33042 | ||||||||
\(99\) | −89.2842 | −0.0906404 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 441.976 | 0.435428 | 0.217714 | − | 0.976013i | \(-0.430140\pi\) | ||||
0.217714 | + | 0.976013i | \(0.430140\pi\) | |||||||
\(102\) | 291.361 | 0.282834 | ||||||||
\(103\) | −1555.99 | −1.48851 | −0.744255 | − | 0.667896i | \(-0.767195\pi\) | ||||
−0.744255 | + | 0.667896i | \(0.767195\pi\) | |||||||
\(104\) | 3893.02 | 3.67059 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 1103.41 | 1.01106 | ||||||||
\(107\) | −1108.54 | −1.00156 | −0.500779 | − | 0.865575i | \(-0.666953\pi\) | ||||
−0.500779 | + | 0.865575i | \(0.666953\pi\) | |||||||
\(108\) | 446.073 | 0.397439 | ||||||||
\(109\) | 1105.86 | 0.971767 | 0.485884 | − | 0.874024i | \(-0.338498\pi\) | ||||
0.485884 | + | 0.874024i | \(0.338498\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −993.668 | −0.849683 | ||||||||
\(112\) | 2171.11 | 1.83170 | ||||||||
\(113\) | 219.414 | 0.182662 | 0.0913308 | − | 0.995821i | \(-0.470888\pi\) | ||||
0.0913308 | + | 0.995821i | \(0.470888\pi\) | |||||||
\(114\) | 1142.63 | 0.938745 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 3583.39 | 2.86818 | ||||||||
\(117\) | −830.339 | −0.656110 | ||||||||
\(118\) | −864.992 | −0.674822 | ||||||||
\(119\) | −554.583 | −0.427214 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1232.58 | −0.926059 | ||||||||
\(122\) | 2338.78 | 1.73560 | ||||||||
\(123\) | 285.379 | 0.209201 | ||||||||
\(124\) | 1735.68 | 1.25701 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −1260.20 | −0.891014 | ||||||||
\(127\) | 1254.78 | 0.876720 | 0.438360 | − | 0.898800i | \(-0.355560\pi\) | ||||
0.438360 | + | 0.898800i | \(0.355560\pi\) | |||||||
\(128\) | 2337.19 | 1.61391 | ||||||||
\(129\) | −203.434 | −0.138847 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −1360.84 | −0.907609 | −0.453805 | − | 0.891101i | \(-0.649934\pi\) | ||||
−0.453805 | + | 0.891101i | \(0.649934\pi\) | |||||||
\(132\) | −491.695 | −0.324216 | ||||||||
\(133\) | −2174.90 | −1.41795 | ||||||||
\(134\) | 622.372 | 0.401230 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 827.585 | 0.521800 | ||||||||
\(137\) | −2290.71 | −1.42853 | −0.714264 | − | 0.699876i | \(-0.753239\pi\) | ||||
−0.714264 | + | 0.699876i | \(0.753239\pi\) | |||||||
\(138\) | −1504.95 | −0.928335 | ||||||||
\(139\) | 1947.64 | 1.18847 | 0.594233 | − | 0.804293i | \(-0.297456\pi\) | ||||
0.594233 | + | 0.804293i | \(0.297456\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 352.282 | 0.210408 | ||||||||
\(142\) | −4593.76 | −2.71479 | ||||||||
\(143\) | 915.262 | 0.535231 | ||||||||
\(144\) | 691.030 | 0.399902 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −501.402 | −0.284221 | ||||||||
\(147\) | 1369.69 | 0.768507 | ||||||||
\(148\) | −5472.21 | −3.03927 | ||||||||
\(149\) | −998.135 | −0.548795 | −0.274397 | − | 0.961616i | \(-0.588478\pi\) | ||||
−0.274397 | + | 0.961616i | \(0.588478\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −2961.42 | −1.59601 | −0.798003 | − | 0.602654i | \(-0.794110\pi\) | ||||
−0.798003 | + | 0.602654i | \(0.794110\pi\) | |||||||
\(152\) | 3245.53 | 1.73189 | ||||||||
\(153\) | −176.515 | −0.0932706 | ||||||||
\(154\) | 1389.09 | 0.726857 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −4572.74 | −2.34687 | ||||||||
\(157\) | −924.225 | −0.469816 | −0.234908 | − | 0.972018i | \(-0.575479\pi\) | ||||
−0.234908 | + | 0.972018i | \(0.575479\pi\) | |||||||
\(158\) | −1462.82 | −0.736556 | ||||||||
\(159\) | −668.477 | −0.333419 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 2864.56 | 1.40223 | ||||||||
\(162\) | −401.103 | −0.194529 | ||||||||
\(163\) | 796.093 | 0.382545 | 0.191273 | − | 0.981537i | \(-0.438739\pi\) | ||||
0.191273 | + | 0.981537i | \(0.438739\pi\) | |||||||
\(164\) | 1571.60 | 0.748302 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 5508.09 | 2.57537 | ||||||||
\(167\) | 1631.50 | 0.755983 | 0.377992 | − | 0.925809i | \(-0.376615\pi\) | ||||
0.377992 | + | 0.925809i | \(0.376615\pi\) | |||||||
\(168\) | −3579.49 | −1.64383 | ||||||||
\(169\) | 6314.89 | 2.87433 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −692.238 | −0.309572 | ||||||||
\(172\) | −1120.32 | −0.496651 | ||||||||
\(173\) | 277.716 | 0.122048 | 0.0610241 | − | 0.998136i | \(-0.480563\pi\) | ||||
0.0610241 | + | 0.998136i | \(0.480563\pi\) | |||||||
\(174\) | −3222.14 | −1.40385 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −761.705 | −0.326225 | ||||||||
\(177\) | 524.038 | 0.222537 | ||||||||
\(178\) | −632.529 | −0.266348 | ||||||||
\(179\) | −3218.41 | −1.34389 | −0.671943 | − | 0.740603i | \(-0.734540\pi\) | ||||
−0.671943 | + | 0.740603i | \(0.734540\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −145.382 | −0.0597027 | −0.0298514 | − | 0.999554i | \(-0.509503\pi\) | ||||
−0.0298514 | + | 0.999554i | \(0.509503\pi\) | |||||||
\(182\) | 12918.5 | 5.26143 | ||||||||
\(183\) | −1416.90 | −0.572352 | ||||||||
\(184\) | −4274.69 | −1.71269 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −1560.70 | −0.615249 | ||||||||
\(187\) | 194.568 | 0.0760868 | ||||||||
\(188\) | 1940.05 | 0.752619 | ||||||||
\(189\) | 763.468 | 0.293831 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −1216.19 | −0.460734 | −0.230367 | − | 0.973104i | \(-0.573993\pi\) | ||||
−0.230367 | + | 0.973104i | \(0.573993\pi\) | |||||||
\(192\) | −1209.27 | −0.454538 | ||||||||
\(193\) | −94.8613 | −0.0353796 | −0.0176898 | − | 0.999844i | \(-0.505631\pi\) | ||||
−0.0176898 | + | 0.999844i | \(0.505631\pi\) | |||||||
\(194\) | 7531.67 | 2.78733 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 7543.01 | 2.74891 | ||||||||
\(197\) | −3329.68 | −1.20421 | −0.602107 | − | 0.798415i | \(-0.705672\pi\) | ||||
−0.602107 | + | 0.798415i | \(0.705672\pi\) | |||||||
\(198\) | 442.126 | 0.158689 | ||||||||
\(199\) | 1975.34 | 0.703658 | 0.351829 | − | 0.936064i | \(-0.385560\pi\) | ||||
0.351829 | + | 0.936064i | \(0.385560\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −377.051 | −0.132314 | ||||||||
\(202\) | −2188.62 | −0.762329 | ||||||||
\(203\) | 6133.08 | 2.12048 | ||||||||
\(204\) | −972.082 | −0.333624 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 7705.10 | 2.60602 | ||||||||
\(207\) | 911.745 | 0.306139 | ||||||||
\(208\) | −7083.82 | −2.36142 | ||||||||
\(209\) | 763.036 | 0.252537 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1915.23 | −0.624880 | −0.312440 | − | 0.949937i | \(-0.601146\pi\) | ||||
−0.312440 | + | 0.949937i | \(0.601146\pi\) | |||||||
\(212\) | −3681.35 | −1.19262 | ||||||||
\(213\) | 2783.03 | 0.895260 | ||||||||
\(214\) | 5489.37 | 1.75349 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −1139.30 | −0.358886 | ||||||||
\(217\) | 2970.67 | 0.929320 | ||||||||
\(218\) | −5476.12 | −1.70133 | ||||||||
\(219\) | 303.764 | 0.0937281 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1809.47 | 0.550762 | ||||||||
\(222\) | 4920.54 | 1.48759 | ||||||||
\(223\) | 2286.67 | 0.686668 | 0.343334 | − | 0.939213i | \(-0.388444\pi\) | ||||
0.343334 | + | 0.939213i | \(0.388444\pi\) | |||||||
\(224\) | −1205.78 | −0.359662 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −1086.52 | −0.319796 | ||||||||
\(227\) | −4443.67 | −1.29928 | −0.649640 | − | 0.760242i | \(-0.725081\pi\) | ||||
−0.649640 | + | 0.760242i | \(0.725081\pi\) | |||||||
\(228\) | −3812.20 | −1.10732 | ||||||||
\(229\) | −445.935 | −0.128682 | −0.0643411 | − | 0.997928i | \(-0.520495\pi\) | ||||
−0.0643411 | + | 0.997928i | \(0.520495\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −841.551 | −0.239697 | ||||||||
\(232\) | −9152.18 | −2.58996 | ||||||||
\(233\) | −1989.69 | −0.559438 | −0.279719 | − | 0.960082i | \(-0.590241\pi\) | ||||
−0.279719 | + | 0.960082i | \(0.590241\pi\) | |||||||
\(234\) | 4111.75 | 1.14869 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 2885.91 | 0.796004 | ||||||||
\(237\) | 886.220 | 0.242895 | ||||||||
\(238\) | 2746.23 | 0.747949 | ||||||||
\(239\) | 270.159 | 0.0731178 | 0.0365589 | − | 0.999331i | \(-0.488360\pi\) | ||||
0.0365589 | + | 0.999331i | \(0.488360\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1719.33 | 0.459551 | 0.229775 | − | 0.973244i | \(-0.426201\pi\) | ||||
0.229775 | + | 0.973244i | \(0.426201\pi\) | |||||||
\(242\) | 6103.62 | 1.62130 | ||||||||
\(243\) | 243.000 | 0.0641500 | ||||||||
\(244\) | −7802.99 | −2.04728 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −1413.16 | −0.366260 | ||||||||
\(247\) | 7096.20 | 1.82802 | ||||||||
\(248\) | −4433.03 | −1.13507 | ||||||||
\(249\) | −3336.96 | −0.849282 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −1294.19 | −0.325453 | −0.162727 | − | 0.986671i | \(-0.552029\pi\) | ||||
−0.162727 | + | 0.986671i | \(0.552029\pi\) | |||||||
\(252\) | 4204.47 | 1.05102 | ||||||||
\(253\) | −1004.99 | −0.249737 | ||||||||
\(254\) | −6213.52 | −1.53492 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −8348.81 | −2.03828 | ||||||||
\(257\) | 5290.69 | 1.28414 | 0.642070 | − | 0.766646i | \(-0.278076\pi\) | ||||
0.642070 | + | 0.766646i | \(0.278076\pi\) | |||||||
\(258\) | 1007.38 | 0.243088 | ||||||||
\(259\) | −9365.85 | −2.24697 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 1952.06 | 0.462949 | ||||||||
\(262\) | 6738.71 | 1.58900 | ||||||||
\(263\) | −2364.44 | −0.554363 | −0.277182 | − | 0.960818i | \(-0.589400\pi\) | ||||
−0.277182 | + | 0.960818i | \(0.589400\pi\) | |||||||
\(264\) | 1255.82 | 0.292766 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 10769.9 | 2.48249 | ||||||||
\(267\) | 383.204 | 0.0878341 | ||||||||
\(268\) | −2076.45 | −0.473281 | ||||||||
\(269\) | −3891.67 | −0.882080 | −0.441040 | − | 0.897487i | \(-0.645390\pi\) | ||||
−0.441040 | + | 0.897487i | \(0.645390\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −2343.65 | −0.525337 | −0.262669 | − | 0.964886i | \(-0.584603\pi\) | ||||
−0.262669 | + | 0.964886i | \(0.584603\pi\) | |||||||
\(272\) | −1505.89 | −0.335692 | ||||||||
\(273\) | −7826.39 | −1.73507 | ||||||||
\(274\) | 11343.3 | 2.50101 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 5021.05 | 1.09504 | ||||||||
\(277\) | −4216.10 | −0.914516 | −0.457258 | − | 0.889334i | \(-0.651168\pi\) | ||||
−0.457258 | + | 0.889334i | \(0.651168\pi\) | |||||||
\(278\) | −9644.51 | −2.08072 | ||||||||
\(279\) | 945.519 | 0.202892 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −7235.84 | −1.53613 | −0.768067 | − | 0.640369i | \(-0.778781\pi\) | ||||
−0.768067 | + | 0.640369i | \(0.778781\pi\) | |||||||
\(282\) | −1744.46 | −0.368374 | ||||||||
\(283\) | 5145.49 | 1.08080 | 0.540402 | − | 0.841407i | \(-0.318272\pi\) | ||||
0.540402 | + | 0.841407i | \(0.318272\pi\) | |||||||
\(284\) | 15326.4 | 3.20230 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −4532.28 | −0.937060 | ||||||||
\(287\) | 2689.84 | 0.553228 | ||||||||
\(288\) | −383.780 | −0.0785224 | ||||||||
\(289\) | −4528.34 | −0.921705 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −4562.90 | −0.919183 | ||||||||
\(292\) | 1672.85 | 0.335261 | ||||||||
\(293\) | 1230.73 | 0.245392 | 0.122696 | − | 0.992444i | \(-0.460846\pi\) | ||||
0.122696 | + | 0.992444i | \(0.460846\pi\) | |||||||
\(294\) | −6782.58 | −1.34547 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 13976.3 | 2.74445 | ||||||||
\(297\) | −267.853 | −0.0523313 | ||||||||
\(298\) | 4942.66 | 0.960807 | ||||||||
\(299\) | −9346.40 | −1.80775 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1917.47 | −0.367179 | ||||||||
\(302\) | 14664.6 | 2.79422 | ||||||||
\(303\) | 1325.93 | 0.251395 | ||||||||
\(304\) | −5905.64 | −1.11418 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 874.084 | 0.163294 | ||||||||
\(307\) | −4082.53 | −0.758964 | −0.379482 | − | 0.925199i | \(-0.623898\pi\) | ||||
−0.379482 | + | 0.925199i | \(0.623898\pi\) | |||||||
\(308\) | −4634.48 | −0.857384 | ||||||||
\(309\) | −4667.98 | −0.859391 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 1112.65 | 0.202870 | 0.101435 | − | 0.994842i | \(-0.467657\pi\) | ||||
0.101435 | + | 0.994842i | \(0.467657\pi\) | |||||||
\(312\) | 11679.1 | 2.11922 | ||||||||
\(313\) | 5842.44 | 1.05506 | 0.527531 | − | 0.849536i | \(-0.323118\pi\) | ||||
0.527531 | + | 0.849536i | \(0.323118\pi\) | |||||||
\(314\) | 4576.66 | 0.822535 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 4880.48 | 0.868824 | ||||||||
\(317\) | 9629.18 | 1.70608 | 0.853042 | − | 0.521842i | \(-0.174755\pi\) | ||||
0.853042 | + | 0.521842i | \(0.174755\pi\) | |||||||
\(318\) | 3310.23 | 0.583737 | ||||||||
\(319\) | −2151.71 | −0.377657 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −3325.62 | −0.578250 | ||||||||
\(322\) | −14185.0 | −2.45496 | ||||||||
\(323\) | 1508.52 | 0.259865 | ||||||||
\(324\) | 1338.22 | 0.229461 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −3942.17 | −0.669744 | ||||||||
\(327\) | 3317.59 | 0.561050 | ||||||||
\(328\) | −4013.96 | −0.675714 | ||||||||
\(329\) | 3320.45 | 0.556420 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −5464.07 | −0.907349 | −0.453674 | − | 0.891168i | \(-0.649887\pi\) | ||||
−0.453674 | + | 0.891168i | \(0.649887\pi\) | |||||||
\(332\) | −18376.9 | −3.03784 | ||||||||
\(333\) | −2981.00 | −0.490565 | ||||||||
\(334\) | −8079.01 | −1.32354 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 6513.32 | 1.05753 | ||||||||
\(337\) | −10638.7 | −1.71966 | −0.859831 | − | 0.510579i | \(-0.829431\pi\) | ||||
−0.859831 | + | 0.510579i | \(0.829431\pi\) | |||||||
\(338\) | −31270.7 | −5.03225 | ||||||||
\(339\) | 658.243 | 0.105460 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −1042.22 | −0.165512 | ||||||||
\(342\) | 3427.89 | 0.541985 | ||||||||
\(343\) | 3211.23 | 0.505510 | ||||||||
\(344\) | 2861.37 | 0.448474 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −1375.22 | −0.213677 | ||||||||
\(347\) | −12036.4 | −1.86210 | −0.931051 | − | 0.364888i | \(-0.881107\pi\) | ||||
−0.931051 | + | 0.364888i | \(0.881107\pi\) | |||||||
\(348\) | 10750.2 | 1.65595 | ||||||||
\(349\) | −1475.05 | −0.226239 | −0.113120 | − | 0.993581i | \(-0.536084\pi\) | ||||
−0.113120 | + | 0.993581i | \(0.536084\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −2491.02 | −0.378805 | ||||||||
\(352\) | 423.031 | 0.0640557 | ||||||||
\(353\) | 5537.88 | 0.834990 | 0.417495 | − | 0.908679i | \(-0.362908\pi\) | ||||
0.417495 | + | 0.908679i | \(0.362908\pi\) | |||||||
\(354\) | −2594.98 | −0.389609 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 2110.33 | 0.314178 | ||||||||
\(357\) | −1663.75 | −0.246652 | ||||||||
\(358\) | 15937.2 | 2.35282 | ||||||||
\(359\) | 4764.83 | 0.700496 | 0.350248 | − | 0.936657i | \(-0.386097\pi\) | ||||
0.350248 | + | 0.936657i | \(0.386097\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −943.038 | −0.137489 | ||||||||
\(362\) | 719.918 | 0.104525 | ||||||||
\(363\) | −3697.75 | −0.534660 | ||||||||
\(364\) | −43100.5 | −6.20626 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 7016.35 | 1.00205 | ||||||||
\(367\) | −13284.0 | −1.88942 | −0.944712 | − | 0.327900i | \(-0.893659\pi\) | ||||
−0.944712 | + | 0.327900i | \(0.893659\pi\) | |||||||
\(368\) | 7778.31 | 1.10183 | ||||||||
\(369\) | 856.136 | 0.120782 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −6300.75 | −0.881721 | ||||||||
\(372\) | 5207.05 | 0.725733 | ||||||||
\(373\) | 9594.38 | 1.33184 | 0.665922 | − | 0.746021i | \(-0.268038\pi\) | ||||
0.665922 | + | 0.746021i | \(0.268038\pi\) | |||||||
\(374\) | −963.480 | −0.133210 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −4954.99 | −0.679612 | ||||||||
\(377\) | −20010.8 | −2.73371 | ||||||||
\(378\) | −3780.61 | −0.514427 | ||||||||
\(379\) | 3308.43 | 0.448397 | 0.224199 | − | 0.974543i | \(-0.428024\pi\) | ||||
0.224199 | + | 0.974543i | \(0.428024\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 3764.33 | 0.506174 | ||||||||
\(382\) | 6022.42 | 0.806633 | ||||||||
\(383\) | 10418.6 | 1.38998 | 0.694991 | − | 0.719019i | \(-0.255408\pi\) | ||||
0.694991 | + | 0.719019i | \(0.255408\pi\) | |||||||
\(384\) | 7011.58 | 0.931792 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 469.743 | 0.0619411 | ||||||||
\(387\) | −610.301 | −0.0801636 | ||||||||
\(388\) | −25128.3 | −3.28787 | ||||||||
\(389\) | 5369.28 | 0.699828 | 0.349914 | − | 0.936782i | \(-0.386211\pi\) | ||||
0.349914 | + | 0.936782i | \(0.386211\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −1986.87 | −0.256984 | ||||||||
\(392\) | −19265.3 | −2.48226 | ||||||||
\(393\) | −4082.51 | −0.524009 | ||||||||
\(394\) | 16488.2 | 2.10829 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −1475.08 | −0.187186 | ||||||||
\(397\) | −3634.27 | −0.459442 | −0.229721 | − | 0.973256i | \(-0.573781\pi\) | ||||
−0.229721 | + | 0.973256i | \(0.573781\pi\) | |||||||
\(398\) | −9781.66 | −1.23194 | ||||||||
\(399\) | −6524.70 | −0.818656 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 13921.2 | 1.73364 | 0.866820 | − | 0.498621i | \(-0.166160\pi\) | ||||
0.866820 | + | 0.498621i | \(0.166160\pi\) | |||||||
\(402\) | 1867.12 | 0.231650 | ||||||||
\(403\) | −9692.61 | −1.19807 | ||||||||
\(404\) | 7301.98 | 0.899226 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −30370.3 | −3.71245 | ||||||||
\(407\) | 3285.88 | 0.400185 | ||||||||
\(408\) | 2482.76 | 0.301261 | ||||||||
\(409\) | −77.4049 | −0.00935801 | −0.00467901 | − | 0.999989i | \(-0.501489\pi\) | ||||
−0.00467901 | + | 0.999989i | \(0.501489\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −6872.13 | −0.824761 | ||||||||
\(412\) | −25706.9 | −3.07400 | ||||||||
\(413\) | 4939.33 | 0.588495 | ||||||||
\(414\) | −4514.86 | −0.535975 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 3934.17 | 0.463674 | ||||||||
\(417\) | 5842.93 | 0.686161 | ||||||||
\(418\) | −3778.47 | −0.442132 | ||||||||
\(419\) | −9731.89 | −1.13469 | −0.567344 | − | 0.823481i | \(-0.692029\pi\) | ||||
−0.567344 | + | 0.823481i | \(0.692029\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −2067.95 | −0.239396 | −0.119698 | − | 0.992810i | \(-0.538193\pi\) | ||||
−0.119698 | + | 0.992810i | \(0.538193\pi\) | |||||||
\(422\) | 9484.00 | 1.09401 | ||||||||
\(423\) | 1056.85 | 0.121479 | ||||||||
\(424\) | 9402.40 | 1.07694 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −13781.3 | −1.56738 | ||||||||
\(427\) | −13355.1 | −1.51358 | ||||||||
\(428\) | −18314.5 | −2.06837 | ||||||||
\(429\) | 2745.78 | 0.309016 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −7910.22 | −0.884041 | −0.442021 | − | 0.897005i | \(-0.645738\pi\) | ||||
−0.442021 | + | 0.897005i | \(0.645738\pi\) | |||||||
\(432\) | 2073.09 | 0.230883 | ||||||||
\(433\) | −8190.70 | −0.909053 | −0.454526 | − | 0.890733i | \(-0.650192\pi\) | ||||
−0.454526 | + | 0.890733i | \(0.650192\pi\) | |||||||
\(434\) | −14710.4 | −1.62701 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 18270.2 | 2.00685 | ||||||||
\(437\) | −7791.91 | −0.852946 | ||||||||
\(438\) | −1504.21 | −0.164095 | ||||||||
\(439\) | 1420.57 | 0.154442 | 0.0772210 | − | 0.997014i | \(-0.475395\pi\) | ||||
0.0772210 | + | 0.997014i | \(0.475395\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 4109.08 | 0.443698 | ||||||||
\(442\) | −8960.32 | −0.964251 | ||||||||
\(443\) | −12966.5 | −1.39064 | −0.695322 | − | 0.718698i | \(-0.744738\pi\) | ||||
−0.695322 | + | 0.718698i | \(0.744738\pi\) | |||||||
\(444\) | −16416.6 | −1.75473 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −11323.4 | −1.20219 | ||||||||
\(447\) | −2994.40 | −0.316847 | ||||||||
\(448\) | −11398.0 | −1.20202 | ||||||||
\(449\) | 3893.44 | 0.409227 | 0.204613 | − | 0.978843i | \(-0.434406\pi\) | ||||
0.204613 | + | 0.978843i | \(0.434406\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −943.696 | −0.0985298 | ||||||||
\(452\) | 3624.99 | 0.377224 | ||||||||
\(453\) | −8884.25 | −0.921454 | ||||||||
\(454\) | 22004.6 | 2.27473 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 9736.60 | 0.999908 | ||||||||
\(457\) | 13592.6 | 1.39133 | 0.695663 | − | 0.718369i | \(-0.255111\pi\) | ||||
0.695663 | + | 0.718369i | \(0.255111\pi\) | |||||||
\(458\) | 2208.22 | 0.225291 | ||||||||
\(459\) | −529.545 | −0.0538498 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −10079.2 | −1.01829 | −0.509147 | − | 0.860680i | \(-0.670039\pi\) | ||||
−0.509147 | + | 0.860680i | \(0.670039\pi\) | |||||||
\(462\) | 4167.27 | 0.419651 | ||||||||
\(463\) | −11345.9 | −1.13885 | −0.569424 | − | 0.822044i | \(-0.692834\pi\) | ||||
−0.569424 | + | 0.822044i | \(0.692834\pi\) | |||||||
\(464\) | 16653.5 | 1.66621 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 9852.73 | 0.979440 | ||||||||
\(467\) | −780.833 | −0.0773718 | −0.0386859 | − | 0.999251i | \(-0.512317\pi\) | ||||
−0.0386859 | + | 0.999251i | \(0.512317\pi\) | |||||||
\(468\) | −13718.2 | −1.35497 | ||||||||
\(469\) | −3553.91 | −0.349902 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −2772.67 | −0.271249 | ||||||||
\(472\) | −7370.79 | −0.718789 | ||||||||
\(473\) | 672.719 | 0.0653946 | ||||||||
\(474\) | −4388.46 | −0.425251 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −9162.39 | −0.882263 | ||||||||
\(477\) | −2005.43 | −0.192500 | ||||||||
\(478\) | −1337.80 | −0.128012 | ||||||||
\(479\) | −15318.7 | −1.46123 | −0.730617 | − | 0.682788i | \(-0.760767\pi\) | ||||
−0.730617 | + | 0.682788i | \(0.760767\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 30558.6 | 2.89678 | ||||||||
\(482\) | −8513.93 | −0.804562 | ||||||||
\(483\) | 8593.68 | 0.809578 | ||||||||
\(484\) | −20363.8 | −1.91245 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −1203.31 | −0.112311 | ||||||||
\(487\) | −9262.14 | −0.861823 | −0.430911 | − | 0.902394i | \(-0.641808\pi\) | ||||
−0.430911 | + | 0.902394i | \(0.641808\pi\) | |||||||
\(488\) | 19929.3 | 1.84868 | ||||||||
\(489\) | 2388.28 | 0.220862 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 3196.74 | 0.293823 | 0.146911 | − | 0.989150i | \(-0.453067\pi\) | ||||
0.146911 | + | 0.989150i | \(0.453067\pi\) | |||||||
\(492\) | 4714.80 | 0.432032 | ||||||||
\(493\) | −4253.94 | −0.388616 | ||||||||
\(494\) | −35139.6 | −3.20042 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 8066.45 | 0.730230 | ||||||||
\(497\) | 26231.6 | 2.36750 | ||||||||
\(498\) | 16524.3 | 1.48689 | ||||||||
\(499\) | 7859.90 | 0.705125 | 0.352563 | − | 0.935788i | \(-0.385310\pi\) | ||||
0.352563 | + | 0.935788i | \(0.385310\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 4894.50 | 0.436467 | ||||||||
\(502\) | 6408.70 | 0.569789 | ||||||||
\(503\) | −14779.3 | −1.31009 | −0.655045 | − | 0.755590i | \(-0.727350\pi\) | ||||
−0.655045 | + | 0.755590i | \(0.727350\pi\) | |||||||
\(504\) | −10738.5 | −0.949067 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 4976.62 | 0.437229 | ||||||||
\(507\) | 18944.7 | 1.65949 | ||||||||
\(508\) | 20730.4 | 1.81056 | ||||||||
\(509\) | 8543.83 | 0.744006 | 0.372003 | − | 0.928232i | \(-0.378671\pi\) | ||||
0.372003 | + | 0.928232i | \(0.378671\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 2863.13 | 0.247862 | ||||||||
\(512\) | 22644.8 | 1.95463 | ||||||||
\(513\) | −2076.71 | −0.178731 | ||||||||
\(514\) | −26198.9 | −2.24822 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −3360.97 | −0.286741 | ||||||||
\(517\) | −1164.94 | −0.0990983 | ||||||||
\(518\) | 46378.7 | 3.93390 | ||||||||
\(519\) | 833.147 | 0.0704645 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 7402.74 | 0.622495 | 0.311248 | − | 0.950329i | \(-0.399253\pi\) | ||||
0.311248 | + | 0.950329i | \(0.399253\pi\) | |||||||
\(522\) | −9666.41 | −0.810512 | ||||||||
\(523\) | −732.790 | −0.0612670 | −0.0306335 | − | 0.999531i | \(-0.509752\pi\) | ||||
−0.0306335 | + | 0.999531i | \(0.509752\pi\) | |||||||
\(524\) | −22482.7 | −1.87435 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 11708.4 | 0.970556 | ||||||||
\(527\) | −2060.47 | −0.170314 | ||||||||
\(528\) | −2285.11 | −0.188346 | ||||||||
\(529\) | −1904.29 | −0.156513 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 1572.11 | 0.128482 | ||||||||
\(532\) | −35932.0 | −2.92829 | ||||||||
\(533\) | −8776.34 | −0.713218 | ||||||||
\(534\) | −1897.59 | −0.153776 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 5303.38 | 0.427371 | ||||||||
\(537\) | −9655.24 | −0.775893 | ||||||||
\(538\) | 19271.1 | 1.54431 | ||||||||
\(539\) | −4529.34 | −0.361953 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −11205.0 | −0.890467 | −0.445234 | − | 0.895414i | \(-0.646879\pi\) | ||||
−0.445234 | + | 0.895414i | \(0.646879\pi\) | |||||||
\(542\) | 11605.5 | 0.919738 | ||||||||
\(543\) | −436.147 | −0.0344694 | ||||||||
\(544\) | 836.333 | 0.0659145 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 38755.4 | 3.03769 | ||||||||
\(547\) | 7504.96 | 0.586634 | 0.293317 | − | 0.956015i | \(-0.405241\pi\) | ||||
0.293317 | + | 0.956015i | \(0.405241\pi\) | |||||||
\(548\) | −37845.3 | −2.95013 | ||||||||
\(549\) | −4250.71 | −0.330448 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −16682.6 | −1.28984 | ||||||||
\(552\) | −12824.1 | −0.988819 | ||||||||
\(553\) | 8353.09 | 0.642332 | ||||||||
\(554\) | 20877.7 | 1.60110 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 32177.4 | 2.45437 | ||||||||
\(557\) | 12871.1 | 0.979112 | 0.489556 | − | 0.871972i | \(-0.337159\pi\) | ||||
0.489556 | + | 0.871972i | \(0.337159\pi\) | |||||||
\(558\) | −4682.11 | −0.355214 | ||||||||
\(559\) | 6256.25 | 0.473366 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 583.704 | 0.0439287 | ||||||||
\(562\) | 35831.1 | 2.68940 | ||||||||
\(563\) | 525.300 | 0.0393228 | 0.0196614 | − | 0.999807i | \(-0.493741\pi\) | ||||
0.0196614 | + | 0.999807i | \(0.493741\pi\) | |||||||
\(564\) | 5820.14 | 0.434525 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −25479.9 | −1.89223 | ||||||||
\(567\) | 2290.40 | 0.169644 | ||||||||
\(568\) | −39144.5 | −2.89166 | ||||||||
\(569\) | 12768.5 | 0.940747 | 0.470374 | − | 0.882467i | \(-0.344119\pi\) | ||||
0.470374 | + | 0.882467i | \(0.344119\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −24.0985 | −0.00176619 | −0.000883093 | − | 1.00000i | \(-0.500281\pi\) | ||||
−0.000883093 | 1.00000i | \(0.500281\pi\) | ||||||||
\(572\) | 15121.2 | 1.10533 | ||||||||
\(573\) | −3648.56 | −0.266005 | ||||||||
\(574\) | −13319.8 | −0.968568 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −3627.80 | −0.262428 | ||||||||
\(577\) | −1831.98 | −0.132177 | −0.0660885 | − | 0.997814i | \(-0.521052\pi\) | ||||
−0.0660885 | + | 0.997814i | \(0.521052\pi\) | |||||||
\(578\) | 22423.8 | 1.61368 | ||||||||
\(579\) | −284.584 | −0.0204264 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −31452.6 | −2.24591 | ||||||||
\(582\) | 22595.0 | 1.60927 | ||||||||
\(583\) | 2210.54 | 0.157034 | ||||||||
\(584\) | −4272.56 | −0.302739 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −6094.42 | −0.429621 | ||||||||
\(587\) | 11952.2 | 0.840410 | 0.420205 | − | 0.907429i | \(-0.361958\pi\) | ||||
0.420205 | + | 0.907429i | \(0.361958\pi\) | |||||||
\(588\) | 22629.0 | 1.58708 | ||||||||
\(589\) | −8080.54 | −0.565285 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −9989.05 | −0.695253 | ||||||||
\(592\) | −25431.6 | −1.76560 | ||||||||
\(593\) | 6599.09 | 0.456985 | 0.228493 | − | 0.973546i | \(-0.426620\pi\) | ||||
0.228493 | + | 0.973546i | \(0.426620\pi\) | |||||||
\(594\) | 1326.38 | 0.0916194 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −16490.4 | −1.13335 | ||||||||
\(597\) | 5926.01 | 0.406257 | ||||||||
\(598\) | 46282.3 | 3.16493 | ||||||||
\(599\) | 5436.04 | 0.370802 | 0.185401 | − | 0.982663i | \(-0.440642\pi\) | ||||
0.185401 | + | 0.982663i | \(0.440642\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −20520.7 | −1.39277 | −0.696385 | − | 0.717668i | \(-0.745209\pi\) | ||||
−0.696385 | + | 0.717668i | \(0.745209\pi\) | |||||||
\(602\) | 9495.09 | 0.642842 | ||||||||
\(603\) | −1131.15 | −0.0763916 | ||||||||
\(604\) | −48926.3 | −3.29600 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −6565.85 | −0.440131 | ||||||||
\(607\) | 7627.67 | 0.510045 | 0.255023 | − | 0.966935i | \(-0.417917\pi\) | ||||
0.255023 | + | 0.966935i | \(0.417917\pi\) | |||||||
\(608\) | 3279.84 | 0.218775 | ||||||||
\(609\) | 18399.2 | 1.22426 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −10833.8 | −0.717333 | ||||||||
\(612\) | −2916.25 | −0.192618 | ||||||||
\(613\) | −7610.43 | −0.501439 | −0.250720 | − | 0.968060i | \(-0.580667\pi\) | ||||
−0.250720 | + | 0.968060i | \(0.580667\pi\) | |||||||
\(614\) | 20216.2 | 1.32876 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 11836.7 | 0.774214 | ||||||||
\(617\) | −14502.4 | −0.946267 | −0.473133 | − | 0.880991i | \(-0.656877\pi\) | ||||
−0.473133 | + | 0.880991i | \(0.656877\pi\) | |||||||
\(618\) | 23115.3 | 1.50459 | ||||||||
\(619\) | −22021.3 | −1.42991 | −0.714954 | − | 0.699172i | \(-0.753552\pi\) | ||||
−0.714954 | + | 0.699172i | \(0.753552\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 2735.24 | 0.176749 | ||||||||
\(622\) | −5509.73 | −0.355177 | ||||||||
\(623\) | 3611.90 | 0.232276 | ||||||||
\(624\) | −21251.5 | −1.36336 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −28931.1 | −1.84716 | ||||||||
\(627\) | 2289.11 | 0.145802 | ||||||||
\(628\) | −15269.3 | −0.970243 | ||||||||
\(629\) | 6496.20 | 0.411797 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 13701.4 | 0.864413 | 0.432206 | − | 0.901775i | \(-0.357735\pi\) | ||||
0.432206 | + | 0.901775i | \(0.357735\pi\) | |||||||
\(632\) | −12465.0 | −0.784545 | ||||||||
\(633\) | −5745.68 | −0.360775 | ||||||||
\(634\) | −47682.6 | −2.98694 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −11044.1 | −0.688562 | ||||||||
\(637\) | −42122.6 | −2.62003 | ||||||||
\(638\) | 10655.0 | 0.661186 | ||||||||
\(639\) | 8349.10 | 0.516878 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −2309.45 | −0.142306 | −0.0711528 | − | 0.997465i | \(-0.522668\pi\) | ||||
−0.0711528 | + | 0.997465i | \(0.522668\pi\) | |||||||
\(642\) | 16468.1 | 1.01238 | ||||||||
\(643\) | 2768.05 | 0.169768 | 0.0848842 | − | 0.996391i | \(-0.472948\pi\) | ||||
0.0848842 | + | 0.996391i | \(0.472948\pi\) | |||||||
\(644\) | 47326.0 | 2.89582 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −7470.05 | −0.454961 | ||||||||
\(647\) | −10901.1 | −0.662393 | −0.331197 | − | 0.943562i | \(-0.607452\pi\) | ||||
−0.331197 | + | 0.943562i | \(0.607452\pi\) | |||||||
\(648\) | −3417.89 | −0.207203 | ||||||||
\(649\) | −1732.90 | −0.104811 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 8912.02 | 0.536543 | ||||||||
\(652\) | 13152.4 | 0.790014 | ||||||||
\(653\) | 9894.06 | 0.592932 | 0.296466 | − | 0.955043i | \(-0.404192\pi\) | ||||
0.296466 | + | 0.955043i | \(0.404192\pi\) | |||||||
\(654\) | −16428.4 | −0.982263 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 7303.90 | 0.434709 | ||||||||
\(657\) | 911.292 | 0.0541140 | ||||||||
\(658\) | −16442.5 | −0.974157 | ||||||||
\(659\) | −13651.5 | −0.806958 | −0.403479 | − | 0.914989i | \(-0.632199\pi\) | ||||
−0.403479 | + | 0.914989i | \(0.632199\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −5867.49 | −0.345263 | −0.172632 | − | 0.984986i | \(-0.555227\pi\) | ||||
−0.172632 | + | 0.984986i | \(0.555227\pi\) | |||||||
\(662\) | 27057.5 | 1.58855 | ||||||||
\(663\) | 5428.42 | 0.317983 | ||||||||
\(664\) | 46935.7 | 2.74316 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 14761.6 | 0.858860 | ||||||||
\(667\) | 21972.7 | 1.27554 | ||||||||
\(668\) | 26954.4 | 1.56122 | ||||||||
\(669\) | 6860.02 | 0.396448 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 4685.45 | 0.269567 | ||||||||
\(672\) | −3617.33 | −0.207651 | ||||||||
\(673\) | −27053.1 | −1.54951 | −0.774754 | − | 0.632262i | \(-0.782126\pi\) | ||||
−0.774754 | + | 0.632262i | \(0.782126\pi\) | |||||||
\(674\) | 52681.6 | 3.01071 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 104330. | 5.93592 | ||||||||
\(677\) | 33037.9 | 1.87555 | 0.937777 | − | 0.347239i | \(-0.112881\pi\) | ||||
0.937777 | + | 0.347239i | \(0.112881\pi\) | |||||||
\(678\) | −3259.55 | −0.184634 | ||||||||
\(679\) | −43007.8 | −2.43076 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −13331.0 | −0.750140 | ||||||||
\(682\) | 5160.97 | 0.289771 | ||||||||
\(683\) | 21098.2 | 1.18199 | 0.590996 | − | 0.806674i | \(-0.298735\pi\) | ||||
0.590996 | + | 0.806674i | \(0.298735\pi\) | |||||||
\(684\) | −11436.6 | −0.639313 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −15901.7 | −0.885027 | ||||||||
\(687\) | −1337.80 | −0.0742947 | ||||||||
\(688\) | −5206.62 | −0.288518 | ||||||||
\(689\) | 20557.9 | 1.13671 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −15304.3 | −0.842553 | −0.421276 | − | 0.906932i | \(-0.638418\pi\) | ||||
−0.421276 | + | 0.906932i | \(0.638418\pi\) | |||||||
\(692\) | 4588.20 | 0.252048 | ||||||||
\(693\) | −2524.65 | −0.138389 | ||||||||
\(694\) | 59603.1 | 3.26009 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −27456.5 | −1.49531 | ||||||||
\(697\) | −1865.69 | −0.101389 | ||||||||
\(698\) | 7304.27 | 0.396090 | ||||||||
\(699\) | −5969.07 | −0.322992 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −1568.71 | −0.0845213 | −0.0422607 | − | 0.999107i | \(-0.513456\pi\) | ||||
−0.0422607 | + | 0.999107i | \(0.513456\pi\) | |||||||
\(702\) | 12335.2 | 0.663197 | ||||||||
\(703\) | 25476.1 | 1.36678 | ||||||||
\(704\) | 3998.83 | 0.214079 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −27423.0 | −1.46186 | ||||||||
\(707\) | 12497.6 | 0.664808 | ||||||||
\(708\) | 8657.74 | 0.459573 | ||||||||
\(709\) | 24085.5 | 1.27581 | 0.637906 | − | 0.770114i | \(-0.279801\pi\) | ||||
0.637906 | + | 0.770114i | \(0.279801\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 2658.66 | 0.140236 | ||||||||
\(712\) | −5389.92 | −0.283702 | ||||||||
\(713\) | 10642.9 | 0.559017 | ||||||||
\(714\) | 8238.70 | 0.431829 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −53172.2 | −2.77533 | ||||||||
\(717\) | 810.478 | 0.0422146 | ||||||||
\(718\) | −23594.9 | −1.22640 | ||||||||
\(719\) | 17170.7 | 0.890627 | 0.445313 | − | 0.895375i | \(-0.353092\pi\) | ||||
0.445313 | + | 0.895375i | \(0.353092\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −43998.1 | −2.27264 | ||||||||
\(722\) | 4669.82 | 0.240710 | ||||||||
\(723\) | 5157.99 | 0.265322 | ||||||||
\(724\) | −2401.90 | −0.123295 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 18310.9 | 0.936061 | ||||||||
\(727\) | 19404.9 | 0.989943 | 0.494971 | − | 0.868909i | \(-0.335179\pi\) | ||||
0.494971 | + | 0.868909i | \(0.335179\pi\) | |||||||
\(728\) | 110081. | 5.60423 | ||||||||
\(729\) | 729.000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 1329.97 | 0.0672922 | ||||||||
\(732\) | −23409.0 | −1.18200 | ||||||||
\(733\) | −22558.7 | −1.13673 | −0.568367 | − | 0.822775i | \(-0.692424\pi\) | ||||
−0.568367 | + | 0.822775i | \(0.692424\pi\) | |||||||
\(734\) | 65780.9 | 3.30793 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −4319.87 | −0.216349 | ||||||||
\(737\) | 1246.84 | 0.0623175 | ||||||||
\(738\) | −4239.49 | −0.211460 | ||||||||
\(739\) | 5378.11 | 0.267709 | 0.133855 | − | 0.991001i | \(-0.457264\pi\) | ||||
0.133855 | + | 0.991001i | \(0.457264\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 21288.6 | 1.05541 | ||||||||
\(742\) | 31200.6 | 1.54368 | ||||||||
\(743\) | −6218.08 | −0.307025 | −0.153512 | − | 0.988147i | \(-0.549058\pi\) | ||||
−0.153512 | + | 0.988147i | \(0.549058\pi\) | |||||||
\(744\) | −13299.1 | −0.655334 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −47510.3 | −2.33174 | ||||||||
\(747\) | −10010.9 | −0.490333 | ||||||||
\(748\) | 3214.50 | 0.157131 | ||||||||
\(749\) | −31345.7 | −1.52917 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −28975.1 | −1.40788 | −0.703939 | − | 0.710261i | \(-0.748577\pi\) | ||||
−0.703939 | + | 0.710261i | \(0.748577\pi\) | |||||||
\(752\) | 9016.21 | 0.437217 | ||||||||
\(753\) | −3882.58 | −0.187900 | ||||||||
\(754\) | 99091.3 | 4.78606 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 12613.4 | 0.606807 | ||||||||
\(757\) | 433.605 | 0.0208185 | 0.0104093 | − | 0.999946i | \(-0.496687\pi\) | ||||
0.0104093 | + | 0.999946i | \(0.496687\pi\) | |||||||
\(758\) | −16383.0 | −0.785035 | ||||||||
\(759\) | −3014.98 | −0.144186 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −32201.6 | −1.53391 | −0.766956 | − | 0.641699i | \(-0.778230\pi\) | ||||
−0.766956 | + | 0.641699i | \(0.778230\pi\) | |||||||
\(762\) | −18640.6 | −0.886189 | ||||||||
\(763\) | 31270.1 | 1.48369 | ||||||||
\(764\) | −20092.9 | −0.951486 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −51591.5 | −2.43352 | ||||||||
\(767\) | −16115.9 | −0.758684 | ||||||||
\(768\) | −25046.4 | −1.17680 | ||||||||
\(769\) | 17728.8 | 0.831361 | 0.415681 | − | 0.909511i | \(-0.363543\pi\) | ||||
0.415681 | + | 0.909511i | \(0.363543\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 15872.1 | 0.741399 | ||||||||
\(772\) | −1567.22 | −0.0730643 | ||||||||
\(773\) | 37345.9 | 1.73769 | 0.868847 | − | 0.495080i | \(-0.164861\pi\) | ||||
0.868847 | + | 0.495080i | \(0.164861\pi\) | |||||||
\(774\) | 3022.14 | 0.140347 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 64179.0 | 2.96893 | ||||||||
\(777\) | −28097.5 | −1.29729 | ||||||||
\(778\) | −26588.1 | −1.22523 | ||||||||
\(779\) | −7316.66 | −0.336517 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −9203.00 | −0.421651 | ||||||||
\(782\) | 9838.79 | 0.449916 | ||||||||
\(783\) | 5856.19 | 0.267284 | ||||||||
\(784\) | 35055.6 | 1.59692 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 20216.1 | 0.917412 | ||||||||
\(787\) | −29752.6 | −1.34761 | −0.673803 | − | 0.738911i | \(-0.735340\pi\) | ||||
−0.673803 | + | 0.738911i | \(0.735340\pi\) | |||||||
\(788\) | −55010.5 | −2.48689 | ||||||||
\(789\) | −7093.32 | −0.320062 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 6204.28 | 0.278886 | ||||||||
\(792\) | 3767.45 | 0.169029 | ||||||||
\(793\) | 43574.5 | 1.95129 | ||||||||
\(794\) | 17996.5 | 0.804372 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 32635.0 | 1.45316 | ||||||||
\(797\) | 38068.9 | 1.69193 | 0.845965 | − | 0.533238i | \(-0.179025\pi\) | ||||
0.845965 | + | 0.533238i | \(0.179025\pi\) | |||||||
\(798\) | 32309.6 | 1.43327 | ||||||||
\(799\) | −2303.08 | −0.101974 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 1149.61 | 0.0507111 | ||||||||
\(802\) | −68936.1 | −3.03519 | ||||||||
\(803\) | −1004.49 | −0.0441442 | ||||||||
\(804\) | −6229.35 | −0.273249 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 47996.8 | 2.09754 | ||||||||
\(807\) | −11675.0 | −0.509269 | ||||||||
\(808\) | −18649.7 | −0.811997 | ||||||||
\(809\) | 38246.4 | 1.66214 | 0.831070 | − | 0.556168i | \(-0.187729\pi\) | ||||
0.831070 | + | 0.556168i | \(0.187729\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 14312.9 | 0.619721 | 0.309861 | − | 0.950782i | \(-0.399718\pi\) | ||||
0.309861 | + | 0.950782i | \(0.399718\pi\) | |||||||
\(812\) | 101326. | 4.37912 | ||||||||
\(813\) | −7030.94 | −0.303304 | ||||||||
\(814\) | −16271.3 | −0.700627 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −4517.68 | −0.193812 | ||||||||
\(817\) | 5215.72 | 0.223347 | ||||||||
\(818\) | 383.301 | 0.0163836 | ||||||||
\(819\) | −23479.2 | −1.00174 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 3187.21 | 0.135486 | 0.0677431 | − | 0.997703i | \(-0.478420\pi\) | ||||
0.0677431 | + | 0.997703i | \(0.478420\pi\) | |||||||
\(822\) | 34030.0 | 1.44396 | ||||||||
\(823\) | 1125.25 | 0.0476595 | 0.0238298 | − | 0.999716i | \(-0.492414\pi\) | ||||
0.0238298 | + | 0.999716i | \(0.492414\pi\) | |||||||
\(824\) | 65656.9 | 2.77581 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −24459.0 | −1.03031 | ||||||||
\(827\) | −18498.6 | −0.777824 | −0.388912 | − | 0.921275i | \(-0.627149\pi\) | ||||
−0.388912 | + | 0.921275i | \(0.627149\pi\) | |||||||
\(828\) | 15063.2 | 0.632223 | ||||||||
\(829\) | −21867.6 | −0.916156 | −0.458078 | − | 0.888912i | \(-0.651462\pi\) | ||||
−0.458078 | + | 0.888912i | \(0.651462\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −12648.3 | −0.527996 | ||||||||
\(832\) | 37189.0 | 1.54963 | ||||||||
\(833\) | −8954.51 | −0.372456 | ||||||||
\(834\) | −28933.5 | −1.20130 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 12606.3 | 0.521528 | ||||||||
\(837\) | 2836.56 | 0.117140 | ||||||||
\(838\) | 48191.3 | 1.98656 | ||||||||
\(839\) | 15634.6 | 0.643345 | 0.321672 | − | 0.946851i | \(-0.395755\pi\) | ||||
0.321672 | + | 0.946851i | \(0.395755\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 22654.9 | 0.928896 | ||||||||
\(842\) | 10240.3 | 0.419124 | ||||||||
\(843\) | −21707.5 | −0.886888 | ||||||||
\(844\) | −31641.9 | −1.29047 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −5233.39 | −0.212681 | ||||||||
\(847\) | −34853.3 | −1.41390 | ||||||||
\(848\) | −17108.8 | −0.692829 | ||||||||
\(849\) | 15436.5 | 0.624002 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −33554.5 | −1.35163 | ||||||||
\(852\) | 45979.1 | 1.84885 | ||||||||
\(853\) | 43860.1 | 1.76054 | 0.880270 | − | 0.474474i | \(-0.157362\pi\) | ||||
0.880270 | + | 0.474474i | \(0.157362\pi\) | |||||||
\(854\) | 66132.8 | 2.64990 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 46776.2 | 1.86773 | ||||||||
\(857\) | −32206.5 | −1.28373 | −0.641863 | − | 0.766819i | \(-0.721838\pi\) | ||||
−0.641863 | + | 0.766819i | \(0.721838\pi\) | |||||||
\(858\) | −13596.8 | −0.541012 | ||||||||
\(859\) | 11852.2 | 0.470772 | 0.235386 | − | 0.971902i | \(-0.424365\pi\) | ||||
0.235386 | + | 0.971902i | \(0.424365\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 8069.53 | 0.319406 | ||||||||
\(862\) | 39170.5 | 1.54774 | ||||||||
\(863\) | −11179.3 | −0.440961 | −0.220481 | − | 0.975391i | \(-0.570763\pi\) | ||||
−0.220481 | + | 0.975391i | \(0.570763\pi\) | |||||||
\(864\) | −1151.34 | −0.0453349 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 40559.5 | 1.59153 | ||||||||
\(867\) | −13585.0 | −0.532147 | ||||||||
\(868\) | 49079.2 | 1.91919 | ||||||||
\(869\) | −2930.57 | −0.114399 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 11595.6 | 0.451092 | ||||||||
\(872\) | −46663.3 | −1.81218 | ||||||||
\(873\) | −13688.7 | −0.530690 | ||||||||
\(874\) | 38584.7 | 1.49330 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 5018.55 | 0.193563 | ||||||||
\(877\) | −9836.83 | −0.378753 | −0.189376 | − | 0.981905i | \(-0.560647\pi\) | ||||
−0.189376 | + | 0.981905i | \(0.560647\pi\) | |||||||
\(878\) | −7034.50 | −0.270391 | ||||||||
\(879\) | 3692.18 | 0.141677 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 26039.3 | 0.995783 | 0.497892 | − | 0.867239i | \(-0.334108\pi\) | ||||
0.497892 | + | 0.867239i | \(0.334108\pi\) | |||||||
\(882\) | −20347.7 | −0.776807 | ||||||||
\(883\) | 1238.88 | 0.0472159 | 0.0236079 | − | 0.999721i | \(-0.492485\pi\) | ||||
0.0236079 | + | 0.999721i | \(0.492485\pi\) | |||||||
\(884\) | 29894.7 | 1.13741 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 64208.5 | 2.43468 | ||||||||
\(887\) | −27114.3 | −1.02639 | −0.513195 | − | 0.858272i | \(-0.671538\pi\) | ||||
−0.513195 | + | 0.858272i | \(0.671538\pi\) | |||||||
\(888\) | 41929.0 | 1.58451 | ||||||||
\(889\) | 35480.8 | 1.33857 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −803.558 | −0.0302135 | ||||||||
\(892\) | 37778.7 | 1.41808 | ||||||||
\(893\) | −9031.97 | −0.338458 | ||||||||
\(894\) | 14828.0 | 0.554722 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 66087.8 | 2.46411 | ||||||||
\(897\) | −28039.2 | −1.04370 | ||||||||
\(898\) | −19279.9 | −0.716457 | ||||||||
\(899\) | 22786.6 | 0.845356 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 4370.23 | 0.161591 | ||||||||
\(902\) | 4673.08 | 0.172502 | ||||||||
\(903\) | −5752.40 | −0.211991 | ||||||||
\(904\) | −9258.44 | −0.340632 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 43993.9 | 1.61324 | ||||||||
\(907\) | 10290.2 | 0.376716 | 0.188358 | − | 0.982100i | \(-0.439684\pi\) | ||||
0.188358 | + | 0.982100i | \(0.439684\pi\) | |||||||
\(908\) | −73414.9 | −2.68321 | ||||||||
\(909\) | 3977.78 | 0.145143 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 31269.5 | 1.13722 | 0.568609 | − | 0.822608i | \(-0.307482\pi\) | ||||
0.568609 | + | 0.822608i | \(0.307482\pi\) | |||||||
\(912\) | −17716.9 | −0.643274 | ||||||||
\(913\) | 11034.7 | 0.399996 | ||||||||
\(914\) | −67309.1 | −2.43587 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −7367.39 | −0.265748 | ||||||||
\(917\) | −38479.8 | −1.38573 | ||||||||
\(918\) | 2622.25 | 0.0942780 | ||||||||
\(919\) | −17466.0 | −0.626932 | −0.313466 | − | 0.949599i | \(-0.601490\pi\) | ||||
−0.313466 | + | 0.949599i | \(0.601490\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −12247.6 | −0.438188 | ||||||||
\(922\) | 49910.9 | 1.78279 | ||||||||
\(923\) | −85587.5 | −3.05216 | ||||||||
\(924\) | −13903.4 | −0.495011 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 56183.4 | 1.99385 | ||||||||
\(927\) | −14003.9 | −0.496170 | ||||||||
\(928\) | −9248.92 | −0.327167 | ||||||||
\(929\) | −16800.8 | −0.593345 | −0.296672 | − | 0.954979i | \(-0.595877\pi\) | ||||
−0.296672 | + | 0.954979i | \(0.595877\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −35116.8 | −1.23621 | ||||||||
\(932\) | −32872.1 | −1.15532 | ||||||||
\(933\) | 3337.96 | 0.117127 | ||||||||
\(934\) | 3866.60 | 0.135459 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 35037.2 | 1.22353 | ||||||||
\(937\) | 1905.93 | 0.0664505 | 0.0332252 | − | 0.999448i | \(-0.489422\pi\) | ||||
0.0332252 | + | 0.999448i | \(0.489422\pi\) | |||||||
\(938\) | 17598.6 | 0.612594 | ||||||||
\(939\) | 17527.3 | 0.609140 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 8426.95 | 0.291935 | 0.145968 | − | 0.989289i | \(-0.453371\pi\) | ||||
0.145968 | + | 0.989289i | \(0.453371\pi\) | |||||||
\(942\) | 13730.0 | 0.474891 | ||||||||
\(943\) | 9636.76 | 0.332785 | ||||||||
\(944\) | 13412.1 | 0.462421 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −3331.23 | −0.114490 | ||||||||
\(947\) | −42729.0 | −1.46622 | −0.733108 | − | 0.680113i | \(-0.761931\pi\) | ||||
−0.733108 | + | 0.680113i | \(0.761931\pi\) | |||||||
\(948\) | 14641.4 | 0.501616 | ||||||||
\(949\) | −9341.74 | −0.319542 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 28887.5 | 0.985008 | ||||||||
\(952\) | 23401.3 | 0.796680 | ||||||||
\(953\) | −2854.92 | −0.0970408 | −0.0485204 | − | 0.998822i | \(-0.515451\pi\) | ||||
−0.0485204 | + | 0.998822i | \(0.515451\pi\) | |||||||
\(954\) | 9930.68 | 0.337021 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 4463.37 | 0.151000 | ||||||||
\(957\) | −6455.13 | −0.218040 | ||||||||
\(958\) | 75856.7 | 2.55827 | ||||||||
\(959\) | −64773.4 | −2.18107 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −18753.9 | −0.629515 | ||||||||
\(962\) | −151323. | −5.07156 | ||||||||
\(963\) | −9976.87 | −0.333853 | ||||||||
\(964\) | 28405.4 | 0.949043 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −42555.0 | −1.41737 | ||||||||
\(967\) | −11899.1 | −0.395709 | −0.197854 | − | 0.980231i | \(-0.563397\pi\) | ||||
−0.197854 | + | 0.980231i | \(0.563397\pi\) | |||||||
\(968\) | 52010.4 | 1.72694 | ||||||||
\(969\) | 4525.57 | 0.150033 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −1616.24 | −0.0534166 | −0.0267083 | − | 0.999643i | \(-0.508503\pi\) | ||||
−0.0267083 | + | 0.999643i | \(0.508503\pi\) | |||||||
\(972\) | 4014.66 | 0.132480 | ||||||||
\(973\) | 55072.6 | 1.81454 | ||||||||
\(974\) | 45865.1 | 1.50884 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −36263.8 | −1.18932 | ||||||||
\(977\) | −42150.9 | −1.38027 | −0.690136 | − | 0.723680i | \(-0.742449\pi\) | ||||
−0.690136 | + | 0.723680i | \(0.742449\pi\) | |||||||
\(978\) | −11826.5 | −0.386677 | ||||||||
\(979\) | −1267.19 | −0.0413683 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 9952.78 | 0.323922 | ||||||||
\(982\) | −15829.9 | −0.514412 | ||||||||
\(983\) | −109.496 | −0.00355276 | −0.00177638 | − | 0.999998i | \(-0.500565\pi\) | ||||
−0.00177638 | + | 0.999998i | \(0.500565\pi\) | |||||||
\(984\) | −12041.9 | −0.390123 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 21065.0 | 0.680372 | ||||||||
\(987\) | 9961.34 | 0.321249 | ||||||||
\(988\) | 117238. | 3.77514 | ||||||||
\(989\) | −6869.61 | −0.220871 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −24448.0 | −0.783671 | −0.391835 | − | 0.920035i | \(-0.628160\pi\) | ||||
−0.391835 | + | 0.920035i | \(0.628160\pi\) | |||||||
\(992\) | −4479.89 | −0.143384 | ||||||||
\(993\) | −16392.2 | −0.523858 | ||||||||
\(994\) | −129896. | −4.14491 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −55130.7 | −1.75390 | ||||||||
\(997\) | 5350.04 | 0.169947 | 0.0849737 | − | 0.996383i | \(-0.472919\pi\) | ||||
0.0849737 | + | 0.996383i | \(0.472919\pi\) | |||||||
\(998\) | −38921.4 | −1.23450 | ||||||||
\(999\) | −8943.01 | −0.283228 |
(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 | 1875.4.a.g.1.1 | 14 | ||
5.4 | even | 2 | 1875.4.a.f.1.14 | 14 | |||
25.11 | even | 5 | 75.4.g.b.46.1 | yes | 28 | ||
25.16 | even | 5 | 75.4.g.b.31.1 | ✓ | 28 | ||
75.11 | odd | 10 | 225.4.h.a.46.7 | 28 | |||
75.41 | odd | 10 | 225.4.h.a.181.7 | 28 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
75.4.g.b.31.1 | ✓ | 28 | 25.16 | even | 5 | ||
75.4.g.b.46.1 | yes | 28 | 25.11 | even | 5 | ||
225.4.h.a.46.7 | 28 | 75.11 | odd | 10 | |||
225.4.h.a.181.7 | 28 | 75.41 | odd | 10 | |||
1875.4.a.f.1.14 | 14 | 5.4 | even | 2 | |||
1875.4.a.g.1.1 | 14 | 1.1 | even | 1 | trivial |