Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1088,4,Mod(1,1088)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1088, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1088.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1088 = 2^{6} \cdot 17 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1088.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: | \(64.1940780862\) |
Analytic rank: | \(0\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.8396.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 20x + 8 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 136) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-4.20657\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1088.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −2.95089 | −0.567900 | −0.283950 | − | 0.958839i | \(-0.591645\pi\) | ||||
−0.283950 | + | 0.958839i | \(0.591645\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 20.3149 | 1.81702 | 0.908511 | − | 0.417861i | \(-0.137220\pi\) | ||||
0.908511 | + | 0.417861i | \(0.137220\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 22.2885 | 1.20347 | 0.601733 | − | 0.798697i | \(-0.294477\pi\) | ||||
0.601733 | + | 0.798697i | \(0.294477\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −18.2922 | −0.677490 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 41.8754 | 1.14781 | 0.573905 | − | 0.818922i | \(-0.305428\pi\) | ||||
0.573905 | + | 0.818922i | \(0.305428\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 35.3376 | 0.753915 | 0.376957 | − | 0.926231i | \(-0.376970\pi\) | ||||
0.376957 | + | 0.926231i | \(0.376970\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −59.9472 | −1.03189 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −17.0000 | −0.242536 | ||||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 67.1209 | 0.810452 | 0.405226 | − | 0.914216i | \(-0.367193\pi\) | ||||
0.405226 | + | 0.914216i | \(0.367193\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −65.7710 | −0.683449 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −64.6360 | −0.585980 | −0.292990 | − | 0.956116i | \(-0.594650\pi\) | ||||
−0.292990 | + | 0.956116i | \(0.594650\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 287.696 | 2.30157 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 133.653 | 0.952646 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 83.0810 | 0.531991 | 0.265996 | − | 0.963974i | \(-0.414299\pi\) | ||||
0.265996 | + | 0.963974i | \(0.414299\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 239.181 | 1.38575 | 0.692874 | − | 0.721059i | \(-0.256344\pi\) | ||||
0.692874 | + | 0.721059i | \(0.256344\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −123.570 | −0.651841 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 452.790 | 2.18673 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 49.0207 | 0.217810 | 0.108905 | − | 0.994052i | \(-0.465266\pi\) | ||||
0.108905 | + | 0.994052i | \(0.465266\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −104.278 | −0.428148 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −225.820 | −0.860173 | −0.430087 | − | 0.902788i | \(-0.641517\pi\) | ||||
−0.430087 | + | 0.902788i | \(0.641517\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 83.4282 | 0.295876 | 0.147938 | − | 0.988997i | \(-0.452736\pi\) | ||||
0.147938 | + | 0.988997i | \(0.452736\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −371.605 | −1.23101 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −54.9476 | −0.170531 | −0.0852653 | − | 0.996358i | \(-0.527174\pi\) | ||||
−0.0852653 | + | 0.996358i | \(0.527174\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 153.778 | 0.448332 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 50.1652 | 0.137736 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −641.241 | −1.66191 | −0.830955 | − | 0.556339i | \(-0.812206\pi\) | ||||
−0.830955 | + | 0.556339i | \(0.812206\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 850.695 | 2.08559 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −198.067 | −0.460256 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −727.129 | −1.60448 | −0.802238 | − | 0.597004i | \(-0.796358\pi\) | ||||
−0.802238 | + | 0.597004i | \(0.796358\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −868.730 | −1.82343 | −0.911717 | − | 0.410818i | \(-0.865243\pi\) | ||||
−0.911717 | + | 0.410818i | \(0.865243\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −407.707 | −0.815337 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 717.881 | 1.36988 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1005.09 | 1.83270 | 0.916350 | − | 0.400379i | \(-0.131122\pi\) | ||||
0.916350 | + | 0.400379i | \(0.131122\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 190.734 | 0.332778 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 382.967 | 0.640139 | 0.320069 | − | 0.947394i | \(-0.396294\pi\) | ||||
0.320069 | + | 0.947394i | \(0.396294\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −640.421 | −1.02679 | −0.513395 | − | 0.858152i | \(-0.671612\pi\) | ||||
−0.513395 | + | 0.858152i | \(0.671612\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −848.961 | −1.30706 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 933.340 | 1.38135 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 19.6094 | 0.0279270 | 0.0139635 | − | 0.999903i | \(-0.495555\pi\) | ||||
0.0139635 | + | 0.999903i | \(0.495555\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 99.4956 | 0.136482 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 619.902 | 0.819796 | 0.409898 | − | 0.912131i | \(-0.365564\pi\) | ||||
0.409898 | + | 0.912131i | \(0.365564\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −345.354 | −0.440693 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −245.163 | −0.302118 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −1302.88 | −1.55174 | −0.775871 | − | 0.630891i | \(-0.782689\pi\) | ||||
−0.775871 | + | 0.630891i | \(0.782689\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 787.623 | 0.907312 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −705.798 | −0.786966 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 1363.56 | 1.47261 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1685.31 | 1.76410 | 0.882050 | − | 0.471155i | \(-0.156163\pi\) | ||||
0.882050 | + | 0.471155i | \(0.156163\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −765.994 | −0.777629 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 880.978 | 0.867927 | 0.433963 | − | 0.900931i | \(-0.357115\pi\) | ||||
0.433963 | + | 0.900931i | \(0.357115\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1305.59 | −1.24897 | −0.624484 | − | 0.781037i | \(-0.714691\pi\) | ||||
−0.624484 | + | 0.781037i | \(0.714691\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −1336.13 | −1.24184 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −1123.58 | −1.01514 | −0.507572 | − | 0.861609i | \(-0.669457\pi\) | ||||
−0.507572 | + | 0.861609i | \(0.669457\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1876.51 | 1.64896 | 0.824481 | − | 0.565890i | \(-0.191467\pi\) | ||||
0.824481 | + | 0.565890i | \(0.191467\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −144.655 | −0.123694 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −652.720 | −0.543387 | −0.271693 | − | 0.962384i | \(-0.587584\pi\) | ||||
−0.271693 | + | 0.962384i | \(0.587584\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1313.07 | −1.06474 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −646.404 | −0.510770 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −378.905 | −0.291884 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 422.547 | 0.317466 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 666.370 | 0.488492 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 3305.16 | 2.36498 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1500.95 | −1.04872 | −0.524362 | − | 0.851495i | \(-0.675696\pi\) | ||||
−0.524362 | + | 0.851495i | \(0.675696\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −246.188 | −0.168028 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1608.92 | 1.07307 | 0.536533 | − | 0.843879i | \(-0.319734\pi\) | ||||
0.536533 | + | 0.843879i | \(0.319734\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1496.03 | 0.975352 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 2715.14 | 1.73098 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −452.630 | −0.282269 | −0.141134 | − | 0.989990i | \(-0.545075\pi\) | ||||
−0.141134 | + | 0.989990i | \(0.545075\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −416.188 | −0.253961 | −0.126981 | − | 0.991905i | \(-0.540529\pi\) | ||||
−0.126981 | + | 0.991905i | \(0.540529\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 162.145 | 0.0968443 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 1479.78 | 0.865351 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 1687.78 | 0.966640 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −453.783 | −0.254608 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −2758.63 | −1.51675 | −0.758376 | − | 0.651817i | \(-0.774007\pi\) | ||||
−0.758376 | + | 0.651817i | \(0.774007\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −14.1640 | −0.00763344 | −0.00381672 | − | 0.999993i | \(-0.501215\pi\) | ||||
−0.00381672 | + | 0.999993i | \(0.501215\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 310.968 | 0.164315 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 4858.95 | 2.51794 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −1150.42 | −0.584802 | −0.292401 | − | 0.956296i | \(-0.594454\pi\) | ||||
−0.292401 | + | 0.956296i | \(0.594454\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 1892.24 | 0.943799 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −1440.64 | −0.705207 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 3172.29 | 1.52437 | 0.762187 | − | 0.647357i | \(-0.224126\pi\) | ||||
0.762187 | + | 0.647357i | \(0.224126\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −2510.31 | −1.18441 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 1037.92 | 0.480936 | 0.240468 | − | 0.970657i | \(-0.422699\pi\) | ||||
0.240468 | + | 0.970657i | \(0.422699\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −948.252 | −0.431612 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −1227.79 | −0.549073 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 1253.09 | 0.550695 | 0.275348 | − | 0.961345i | \(-0.411207\pi\) | ||||
0.275348 | + | 0.961345i | \(0.411207\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 6412.32 | 2.76986 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 2145.68 | 0.911182 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 4287.22 | 1.79018 | 0.895090 | − | 0.445886i | \(-0.147111\pi\) | ||||
0.895090 | + | 0.445886i | \(0.147111\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 321.513 | 0.132032 | 0.0660162 | − | 0.997819i | \(-0.478971\pi\) | ||||
0.0660162 | + | 0.997819i | \(0.478971\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 2563.53 | 1.03553 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 995.853 | 0.395765 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −711.881 | −0.278385 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 2978.92 | 1.14648 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −1202.62 | −0.455594 | −0.227797 | − | 0.973709i | \(-0.573152\pi\) | ||||
−0.227797 | + | 0.973709i | \(0.573152\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 2423.56 | 0.903895 | 0.451948 | − | 0.892045i | \(-0.350729\pi\) | ||||
0.451948 | + | 0.892045i | \(0.350729\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −2118.39 | −0.777955 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 3049.26 | 1.10280 | 0.551398 | − | 0.834243i | \(-0.314095\pi\) | ||||
0.551398 | + | 0.834243i | \(0.314095\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1722.08 | 0.613444 | 0.306722 | − | 0.951799i | \(-0.400768\pi\) | ||||
0.306722 | + | 0.951799i | \(0.400768\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −2965.90 | −1.04079 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 1851.75 | 0.640234 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −4587.51 | −1.56295 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 1182.34 | 0.396995 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 2810.71 | 0.930245 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1259.46 | 0.410924 | 0.205462 | − | 0.978665i | \(-0.434130\pi\) | ||||
0.205462 | + | 0.978665i | \(0.434130\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −1130.10 | −0.363535 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 1694.84 | 0.537613 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 5330.99 | 1.66770 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 1889.82 | 0.583114 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −600.740 | −0.182851 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −3632.09 | −1.09069 | −0.545343 | − | 0.838213i | \(-0.683600\pi\) | ||||
−0.545343 | + | 0.838213i | \(0.683600\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −5262.60 | −1.55929 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −1304.97 | −0.381558 | −0.190779 | − | 0.981633i | \(-0.561101\pi\) | ||||
−0.190779 | + | 0.981633i | \(0.561101\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −2633.32 | −0.759889 | −0.379944 | − | 0.925009i | \(-0.624057\pi\) | ||||
−0.379944 | + | 0.925009i | \(0.624057\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −2754.19 | −0.784469 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 554.016 | 0.155772 | 0.0778858 | − | 0.996962i | \(-0.475183\pi\) | ||||
0.0778858 | + | 0.996962i | \(0.475183\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −1116.26 | −0.309858 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −57.8653 | −0.0158597 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 1655.66 | 0.448099 | 0.224049 | − | 0.974578i | \(-0.428072\pi\) | ||||
0.224049 | + | 0.974578i | \(0.428072\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 5367.63 | 1.43469 | 0.717343 | − | 0.696720i | \(-0.245358\pi\) | ||||
0.717343 | + | 0.696720i | \(0.245358\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −3902.22 | −1.03015 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 3123.99 | 0.814630 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 2371.89 | 0.611012 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −1829.27 | −0.465562 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 5880.71 | 1.47883 | 0.739417 | − | 0.673248i | \(-0.235101\pi\) | ||||
0.739417 | + | 0.673248i | \(0.235101\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −2706.66 | −0.672593 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 1019.10 | 0.250269 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 4933.74 | 1.19750 | 0.598751 | − | 0.800935i | \(-0.295664\pi\) | ||||
0.598751 | + | 0.800935i | \(0.295664\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1092.60 | 0.262127 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −1519.74 | −0.360419 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −3159.19 | −0.740700 | −0.370350 | − | 0.928892i | \(-0.620762\pi\) | ||||
−0.370350 | + | 0.928892i | \(0.620762\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −13026.8 | −3.01973 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 3844.66 | 0.881234 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −5575.92 | −1.26383 | −0.631914 | − | 0.775038i | \(-0.717731\pi\) | ||||
−0.631914 | + | 0.775038i | \(0.717731\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −5176.42 | −1.16031 | −0.580157 | − | 0.814504i | \(-0.697009\pi\) | ||||
−0.580157 | + | 0.814504i | \(0.697009\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −2324.19 | −0.515262 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 12047.4 | 2.64176 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −495.895 | −0.107565 | −0.0537823 | − | 0.998553i | \(-0.517128\pi\) | ||||
−0.0537823 | + | 0.998553i | \(0.517128\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −4375.15 | −0.938830 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 153.597 | 0.0326080 | 0.0163040 | − | 0.999867i | \(-0.494810\pi\) | ||||
0.0163040 | + | 0.999867i | \(0.494810\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −838.842 | −0.176198 | −0.0880990 | − | 0.996112i | \(-0.528079\pi\) | ||||
−0.0880990 | + | 0.996112i | \(0.528079\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −4023.71 | −0.836295 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −5033.19 | −1.03519 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 289.000 | 0.0588235 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −4973.18 | −1.00183 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 719.532 | 0.143466 | 0.0717330 | − | 0.997424i | \(-0.477147\pi\) | ||||
0.0717330 | + | 0.997424i | \(0.477147\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −14771.6 | −2.91537 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 5596.75 | 1.09346 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −2284.08 | −0.441779 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1859.49 | 0.356077 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −2599.67 | −0.492895 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −17648.2 | −3.31322 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −5805.49 | −1.07927 | −0.539637 | − | 0.841898i | \(-0.681438\pi\) | ||||
−0.539637 | + | 0.841898i | \(0.681438\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 3852.66 | 0.709289 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 8382.25 | 1.52834 | 0.764170 | − | 0.645015i | \(-0.223149\pi\) | ||||
0.764170 | + | 0.645015i | \(0.223149\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 9017.59 | 1.62845 | 0.814224 | − | 0.580551i | \(-0.197163\pi\) | ||||
0.814224 | + | 0.580551i | \(0.197163\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −8282.53 | −1.48148 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −3387.27 | −0.600152 | −0.300076 | − | 0.953915i | \(-0.597012\pi\) | ||||
−0.300076 | + | 0.953915i | \(0.597012\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 3479.05 | 0.610625 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 3315.56 | 0.576500 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −1141.06 | −0.196564 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 10166.5 | 1.73519 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −5537.37 | −0.936445 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −1224.70 | −0.205228 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −7034.50 | −1.16813 | −0.584065 | − | 0.811707i | \(-0.698539\pi\) | ||||
−0.584065 | + | 0.811707i | \(0.698539\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −896.698 | −0.147564 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 20418.3 | 3.33005 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 726.807 | 0.117483 | 0.0587414 | − | 0.998273i | \(-0.481291\pi\) | ||||
0.0587414 | + | 0.998273i | \(0.481291\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 1926.11 | 0.308589 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 10015.8 | 1.59057 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −4217.48 | −0.663914 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 3874.74 | 0.604664 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −12717.6 | −1.96748 | −0.983740 | − | 0.179599i | \(-0.942520\pi\) | ||||
−0.983740 | + | 0.179599i | \(0.942520\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 5731.11 | 0.879024 | 0.439512 | − | 0.898237i | \(-0.355151\pi\) | ||||
0.439512 | + | 0.898237i | \(0.355151\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 4722.96 | 0.718214 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −10421.7 | −1.57136 | −0.785679 | − | 0.618634i | \(-0.787686\pi\) | ||||
−0.785679 | + | 0.618634i | \(0.787686\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 7779.95 | 1.16315 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 1118.11 | 0.165761 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 2695.18 | 0.396229 | 0.198115 | − | 0.980179i | \(-0.436518\pi\) | ||||
0.198115 | + | 0.980179i | \(0.436518\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −2353.78 | −0.343167 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −1246.89 | −0.180289 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −13010.1 | −1.86570 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 4415.83 | 0.628078 | 0.314039 | − | 0.949410i | \(-0.398318\pi\) | ||||
0.314039 | + | 0.949410i | \(0.398318\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 4130.74 | 0.582759 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −14292.3 | −2.00005 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 1279.95 | 0.177676 | 0.0888381 | − | 0.996046i | \(-0.471685\pi\) | ||||
0.0888381 | + | 0.996046i | \(0.471685\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −9753.18 | −1.34307 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 2935.88 | 0.401076 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 11875.3 | 1.60948 | 0.804742 | − | 0.593625i | \(-0.202304\pi\) | ||||
0.804742 | + | 0.593625i | \(0.202304\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 4429.15 | 0.595571 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −7769.82 | −1.03660 | −0.518302 | − | 0.855198i | \(-0.673436\pi\) | ||||
−0.518302 | + | 0.855198i | \(0.673436\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 18960.7 | 2.50994 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −1526.09 | −0.200453 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 8585.82 | 1.11907 | 0.559535 | − | 0.828807i | \(-0.310980\pi\) | ||||
0.559535 | + | 0.828807i | \(0.310980\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1098.81 | 0.142121 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −4747.74 | −0.609394 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 398.364 | 0.0507439 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 4189.66 | 0.529655 | 0.264827 | − | 0.964296i | \(-0.414685\pi\) | ||||
0.264827 | + | 0.964296i | \(0.414685\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −4414.61 | −0.553902 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 2385.57 | 0.297082 | 0.148541 | − | 0.988906i | \(-0.452542\pi\) | ||||
0.148541 | + | 0.988906i | \(0.452542\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 8452.09 | 1.04474 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 2021.25 | 0.247991 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 2052.76 | 0.250004 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −8595.38 | −1.03916 | −0.519578 | − | 0.854423i | \(-0.673911\pi\) | ||||
−0.519578 | + | 0.854423i | \(0.673911\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 1335.66 | 0.160300 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −16206.6 | −1.93093 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 12593.3 | 1.48959 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 1228.13 | 0.144224 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −7594.80 | −0.885513 | −0.442757 | − | 0.896642i | \(-0.645999\pi\) | ||||
−0.442757 | + | 0.896642i | \(0.645999\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −13228.6 | −1.53141 | −0.765703 | − | 0.643194i | \(-0.777609\pi\) | ||||
−0.765703 | + | 0.643194i | \(0.777609\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 1005.11 | 0.115533 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −4890.83 | −0.558213 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −19362.7 | −2.19444 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −4366.66 | −0.491432 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −11945.2 | −1.33498 | −0.667492 | − | 0.744617i | \(-0.732632\pi\) | ||||
−0.667492 | + | 0.744617i | \(0.732632\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −1088.93 | −0.120856 | −0.0604282 | − | 0.998173i | \(-0.519247\pi\) | ||||
−0.0604282 | + | 0.998173i | \(0.519247\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −4980.47 | −0.548955 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −4338.43 | −0.474909 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −4884.36 | −0.531020 | −0.265510 | − | 0.964108i | \(-0.585540\pi\) | ||||
−0.265510 | + | 0.964108i | \(0.585540\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −2812.94 | −0.303741 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 3063.27 | 0.328534 | 0.164267 | − | 0.986416i | \(-0.447474\pi\) | ||||
0.164267 | + | 0.986416i | \(0.447474\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −26467.9 | −2.81955 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 8140.44 | 0.861364 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −7269.92 | −0.764117 | −0.382058 | − | 0.924138i | \(-0.624785\pi\) | ||||
−0.382058 | + | 0.924138i | \(0.624785\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −9456.28 | −0.987315 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 41.7964 | 0.00433503 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 16000.5 | 1.64861 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −3660.30 | −0.374664 | −0.187332 | − | 0.982297i | \(-0.559984\pi\) | ||||
−0.187332 | + | 0.982297i | \(0.559984\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −2272.09 | −0.231051 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 2683.39 | 0.271102 | 0.135551 | − | 0.990770i | \(-0.456720\pi\) | ||||
0.135551 | + | 0.990770i | \(0.456720\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −16455.5 | −1.65173 | −0.825865 | − | 0.563868i | \(-0.809313\pi\) | ||||
−0.825865 | + | 0.563868i | \(0.809313\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −14338.2 | −1.42993 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −4902.37 | −0.485770 | −0.242885 | − | 0.970055i | \(-0.578094\pi\) | ||||
−0.242885 | + | 0.970055i | \(0.578094\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 22401.9 | 2.20559 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 3394.78 | 0.332109 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 3493.59 | 0.339609 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 19310.4 | 1.86531 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 11729.7 | 1.12593 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −8325.55 | −0.794163 | −0.397081 | − | 0.917783i | \(-0.629977\pi\) | ||||
−0.397081 | + | 0.917783i | \(0.629977\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1732.28 | 0.164210 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 4251.18 | 0.400487 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 34237.0 | 3.20541 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 5436.03 | 0.505811 | 0.252905 | − | 0.967491i | \(-0.418614\pi\) | ||||
0.252905 | + | 0.967491i | \(0.418614\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −9361.09 | −0.865692 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 7108.10 | 0.653328 | 0.326664 | − | 0.945141i | \(-0.394075\pi\) | ||||
0.326664 | + | 0.945141i | \(0.394075\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −1412.38 | −0.129027 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −15561.1 | −1.41297 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 8535.77 | 0.770386 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 7795.04 | 0.699306 | 0.349653 | − | 0.936879i | \(-0.386299\pi\) | ||||
0.349653 | + | 0.936879i | \(0.386299\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −3062.78 | −0.273124 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 20257.3 | 1.79568 | 0.897840 | − | 0.440323i | \(-0.145136\pi\) | ||||
0.897840 | + | 0.440323i | \(0.145136\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 17897.0 | 1.57704 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 2798.19 | 0.245113 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −1940.28 | −0.168961 | −0.0844806 | − | 0.996425i | \(-0.526923\pi\) | ||||
−0.0844806 | + | 0.996425i | \(0.526923\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −14274.0 | −1.23571 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 8970.88 | 0.772074 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −26523.0 | −2.26940 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −2300.95 | −0.195737 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −3697.72 | −0.312740 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −10297.8 | −0.865943 | −0.432971 | − | 0.901408i | \(-0.642535\pi\) | ||||
−0.432971 | + | 0.901408i | \(0.642535\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −1895.90 | −0.158512 | −0.0792560 | − | 0.996854i | \(-0.525254\pi\) | ||||
−0.0792560 | + | 0.996854i | \(0.525254\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −18922.1 | −1.57300 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −4066.08 | −0.336093 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −7989.19 | −0.656628 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 13300.8 | 1.08702 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −7979.93 | −0.648497 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −22825.4 | −1.84454 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −12651.1 | −1.01664 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 6439.51 | 0.514600 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −2926.34 | −0.232557 | −0.116278 | − | 0.993217i | \(-0.537096\pi\) | ||||
−0.116278 | + | 0.993217i | \(0.537096\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −948.750 | −0.0749811 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 38121.1 | 2.99620 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 16514.5 | 1.29088 | 0.645440 | − | 0.763811i | \(-0.276674\pi\) | ||||
0.645440 | + | 0.763811i | \(0.276674\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 15891.0 | 1.23536 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 5576.47 | 0.431154 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 437.065 | 0.0336092 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −2938.66 | −0.224755 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 2601.51 | 0.197899 | 0.0989494 | − | 0.995092i | \(-0.468452\pi\) | ||||
0.0989494 | + | 0.995092i | \(0.468452\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 2948.15 | 0.223065 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 2100.69 | 0.158095 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 15095.3 | 1.13000 | 0.565001 | − | 0.825090i | \(-0.308876\pi\) | ||||
0.565001 | + | 0.825090i | \(0.308876\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −13260.0 | −0.987346 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 2217.61 | 0.164252 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 10564.9 | 0.778391 | 0.389195 | − | 0.921155i | \(-0.372753\pi\) | ||||
0.389195 | + | 0.921155i | \(0.372753\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −2783.27 | −0.203987 | −0.101993 | − | 0.994785i | \(-0.532522\pi\) | ||||
−0.101993 | + | 0.994785i | \(0.532522\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 3548.80 | 0.258732 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −18595.5 | −1.34867 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 2965.98 | 0.213995 | 0.106998 | − | 0.994259i | \(-0.465876\pi\) | ||||
0.106998 | + | 0.994259i | \(0.465876\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −7151.67 | −0.513322 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 13816.7 | 0.986598 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −26852.2 | −1.90756 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −13131.6 | −0.928080 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −17710.3 | −1.24528 | −0.622642 | − | 0.782507i | \(-0.713941\pi\) | ||||
−0.622642 | + | 0.782507i | \(0.713941\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 16054.1 | 1.12308 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −8998.04 | −0.626277 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 10029.3 | 0.694527 | 0.347264 | − | 0.937768i | \(-0.387111\pi\) | ||||
0.347264 | + | 0.937768i | \(0.387111\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −7697.42 | −0.530359 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −5081.69 | −0.348375 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −7889.70 | −0.538171 | −0.269086 | − | 0.963116i | \(-0.586721\pi\) | ||||
−0.269086 | + | 0.963116i | \(0.586721\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 4972.07 | 0.337463 | 0.168731 | − | 0.985662i | \(-0.446033\pi\) | ||||
0.168731 | + | 0.985662i | \(0.446033\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −18385.3 | −1.24164 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 8584.02 | 0.576843 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 6455.66 | 0.431676 | 0.215838 | − | 0.976429i | \(-0.430752\pi\) | ||||
0.215838 | + | 0.976429i | \(0.430752\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −5464.32 | −0.363589 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −1941.72 | −0.128566 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −9457.73 | −0.623155 | −0.311577 | − | 0.950221i | \(-0.600857\pi\) | ||||
−0.311577 | + | 0.950221i | \(0.600857\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 13537.3 | 0.887601 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −96.7142 | −0.00631048 | −0.00315524 | − | 0.999995i | \(-0.501004\pi\) | ||||
−0.00315524 | + | 0.999995i | \(0.501004\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 14409.5 | 0.935649 | 0.467824 | − | 0.883821i | \(-0.345038\pi\) | ||||
0.467824 | + | 0.883821i | \(0.345038\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −8638.76 | −0.558231 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −29039.3 | −1.86747 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 31182.1 | 1.99565 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −8294.12 | −0.528286 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −833.353 | −0.0528266 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −13888.8 | −0.876236 | −0.438118 | − | 0.898918i | \(-0.644355\pi\) | ||||
−0.438118 | + | 0.898918i | \(0.644355\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −3716.54 | −0.233364 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −30491.7 | −1.90556 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 5434.15 | 0.338004 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −7005.32 | −0.433688 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 14430.5 | 0.889190 | 0.444595 | − | 0.895732i | \(-0.353348\pi\) | ||||
0.444595 | + | 0.895732i | \(0.353348\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −29147.1 | −1.78763 | −0.893816 | − | 0.448433i | \(-0.851982\pi\) | ||||
−0.893816 | + | 0.448433i | \(0.851982\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −5001.28 | −0.305311 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 19933.0 | 1.21120 | 0.605602 | − | 0.795768i | \(-0.292932\pi\) | ||||
0.605602 | + | 0.795768i | \(0.292932\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −30448.8 | −1.84163 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −15731.2 | −0.947088 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −10675.7 | −0.639774 | −0.319887 | − | 0.947456i | \(-0.603645\pi\) | ||||
−0.319887 | + | 0.947456i | \(0.603645\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 32685.0 | 1.94979 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 11714.7 | 0.695640 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −16145.1 | −0.954363 | −0.477181 | − | 0.878805i | \(-0.658342\pi\) | ||||
−0.477181 | + | 0.878805i | \(0.658342\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −600.194 | −0.0353175 | −0.0176587 | − | 0.999844i | \(-0.505621\pi\) | ||||
−0.0176587 | + | 0.999844i | \(0.505621\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 1772.72 | 0.103841 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 30391.6 | 1.77224 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −5370.02 | −0.311736 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 10717.9 | 0.619400 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −36378.4 | −2.09296 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −18470.6 | −1.05793 | −0.528966 | − | 0.848643i | \(-0.677420\pi\) | ||||
−0.528966 | + | 0.848643i | \(0.677420\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 38451.3 | 2.19258 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −22195.9 | −1.26006 | −0.630028 | − | 0.776572i | \(-0.716957\pi\) | ||||
−0.630028 | + | 0.776572i | \(0.716957\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 37563.2 | 2.12304 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 3850.81 | 0.216686 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 6407.71 | 0.358982 | 0.179491 | − | 0.983760i | \(-0.442555\pi\) | ||||
0.179491 | + | 0.983760i | \(0.442555\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −9195.15 | −0.512888 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 7770.64 | 0.431541 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −22659.9 | −1.25294 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 8163.28 | 0.449415 | 0.224708 | − | 0.974426i | \(-0.427857\pi\) | ||||
0.224708 | + | 0.974426i | \(0.427857\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −17072.9 | −0.935851 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −8454.82 | −0.461453 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 3838.93 | 0.208623 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −1634.84 | −0.0884627 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −20637.0 | −1.11191 | −0.555956 | − | 0.831212i | \(-0.687648\pi\) | ||||
−0.555956 | + | 0.831212i | \(0.687648\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 3290.32 | 0.176524 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 3293.96 | 0.175968 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 19635.7 | 1.04452 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 13995.2 | 0.741326 | 0.370663 | − | 0.928767i | \(-0.379131\pi\) | ||||
0.370663 | + | 0.928767i | \(0.379131\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −358.700 | −0.0189202 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −15459.7 | −0.812020 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 30061.5 | 1.57236 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −4885.67 | −0.254475 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 31872.3 | 1.65318 | 0.826590 | − | 0.562804i | \(-0.190278\pi\) | ||||
0.826590 | + | 0.562804i | \(0.190278\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −29099.7 | −1.50309 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −15839.3 | −0.814758 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 23902.1 | 1.22441 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −18002.0 | −0.918371 | −0.459186 | − | 0.888340i | \(-0.651859\pi\) | ||||
−0.459186 | + | 0.888340i | \(0.651859\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 8828.65 | 0.448542 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −1418.28 | −0.0717605 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 11807.6 | 0.594983 | 0.297491 | − | 0.954725i | \(-0.403850\pi\) | ||||
0.297491 | + | 0.954725i | \(0.403850\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −9218.56 | −0.462628 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 42088.4 | 2.10359 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −26955.2 | −1.34176 | −0.670882 | − | 0.741564i | \(-0.734084\pi\) | ||||
−0.670882 | + | 0.741564i | \(0.734084\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −6999.21 | −0.346994 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −34852.2 | −1.72087 | −0.860433 | − | 0.509564i | \(-0.829807\pi\) | ||||
−0.860433 | + | 0.509564i | \(0.829807\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −56041.5 | −2.75597 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −11339.4 | −0.555404 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −25042.9 | −1.22169 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 15904.0 | 0.772764 | 0.386382 | − | 0.922339i | \(-0.373725\pi\) | ||||
0.386382 | + | 0.922339i | \(0.373725\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −17353.4 | −0.839830 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −287.740 | −0.0138701 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −9077.01 | −0.435812 | −0.217906 | − | 0.975970i | \(-0.569923\pi\) | ||||
−0.217906 | + | 0.975970i | \(0.569923\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 7987.05 | 0.381965 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −15418.6 | −0.734458 | −0.367229 | − | 0.930130i | \(-0.619694\pi\) | ||||
−0.367229 | + | 0.930130i | \(0.619694\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 41824.6 | 1.98447 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 6317.29 | 0.298565 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −25695.0 | −1.20964 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 7493.32 | 0.351386 | 0.175693 | − | 0.984445i | \(-0.443783\pi\) | ||||
0.175693 | + | 0.984445i | \(0.443783\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −14558.9 | −0.680061 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 3589.28 | 0.167008 | 0.0835041 | − | 0.996507i | \(-0.473389\pi\) | ||||
0.0835041 | + | 0.996507i | \(0.473389\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 68811.5 | 3.18940 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −3224.15 | −0.148862 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −15157.2 | −0.697129 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 16036.9 | 0.734757 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 11104.0 | 0.506799 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −23370.8 | −1.06260 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 23754.7 | 1.07594 | 0.537970 | − | 0.842964i | \(-0.319191\pi\) | ||||
0.537970 | + | 0.842964i | \(0.319191\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 9322.44 | 0.420644 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −14548.2 | −0.653948 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −30698.9 | −1.37471 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 38440.6 | 1.71490 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −9472.15 | −0.420980 | −0.210490 | − | 0.977596i | \(-0.567506\pi\) | ||||
−0.210490 | + | 0.977596i | \(0.567506\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 934.110 | 0.0413597 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 23832.6 | 1.05129 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −26817.9 | −1.17856 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −29266.5 | −1.28138 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 16454.0 | 0.717728 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 5852.20 | 0.254329 | 0.127165 | − | 0.991882i | \(-0.459412\pi\) | ||||
0.127165 | + | 0.991882i | \(0.459412\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 27780.9 | 1.20286 | 0.601430 | − | 0.798925i | \(-0.294598\pi\) | ||||
0.601430 | + | 0.798925i | \(0.294598\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 15275.1 | 0.658942 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 64444.9 | 2.76982 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 5599.77 | 0.239793 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −14407.4 | −0.614694 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 31092.6 | 1.32173 | 0.660865 | − | 0.750505i | \(-0.270190\pi\) | ||||
0.660865 | + | 0.750505i | \(0.270190\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 21769.4 | 0.922032 | 0.461016 | − | 0.887392i | \(-0.347485\pi\) | ||||
0.461016 | + | 0.887392i | \(0.347485\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −35550.6 | −1.50026 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −22163.7 | −0.931931 | −0.465966 | − | 0.884803i | \(-0.654293\pi\) | ||||
−0.465966 | + | 0.884803i | \(0.654293\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 28760.0 | 1.20492 | 0.602459 | − | 0.798150i | \(-0.294188\pi\) | ||||
0.602459 | + | 0.798150i | \(0.294188\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 1463.33 | 0.0610860 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −2614.23 | −0.108737 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 21085.2 | 0.873872 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 31967.2 | 1.32013 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −44987.0 | −1.85116 | −0.925580 | − | 0.378551i | \(-0.876422\pi\) | ||||
−0.925580 | + | 0.378551i | \(0.876422\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −17486.6 | −0.716985 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −453.249 | −0.0185181 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −19263.7 | −0.784249 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 9417.96 | 0.382060 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 2475.34 | 0.100063 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −3168.50 | −0.127632 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −39205.2 | −1.57369 | −0.786846 | − | 0.617150i | \(-0.788287\pi\) | ||||
−0.786846 | + | 0.617150i | \(0.788287\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −24942.5 | −0.997678 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 2604.07 | 0.103796 | 0.0518981 | − | 0.998652i | \(-0.483473\pi\) | ||||
0.0518981 | + | 0.998652i | \(0.483473\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 6875.54 | 0.273097 | 0.136549 | − | 0.990633i | \(-0.456399\pi\) | ||||
0.136549 | + | 0.990633i | \(0.456399\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 14852.4 | 0.587884 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 16188.0 | 0.638524 | 0.319262 | − | 0.947666i | \(-0.396565\pi\) | ||||
0.319262 | + | 0.947666i | \(0.396565\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 25456.3 | 1.00063 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −852.808 | −0.0334059 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 821.152 | 0.0320548 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 35517.4 | 1.38170 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −30828.2 | −1.19516 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 73667.1 | 2.84618 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 4950.76 | 0.190622 | 0.0953110 | − | 0.995448i | \(-0.469615\pi\) | ||||
0.0953110 | + | 0.995448i | \(0.469615\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −2123.26 | −0.0814743 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 37393.6 | 1.42999 | 0.714995 | − | 0.699129i | \(-0.246429\pi\) | ||||
0.714995 | + | 0.699129i | \(0.246429\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 15390.9 | 0.586574 | 0.293287 | − | 0.956024i | \(-0.405251\pi\) | ||||
0.293287 | + | 0.956024i | \(0.405251\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 43589.3 | 1.65564 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 7165.69 | 0.271252 | 0.135626 | − | 0.990760i | \(-0.456695\pi\) | ||||
0.135626 | + | 0.990760i | \(0.456695\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −33454.0 | −1.26211 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 4166.42 | 0.156656 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −3688.14 | −0.138207 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 87094.6 | 3.25280 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 6740.08 | 0.250886 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 19871.4 | 0.737206 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 10901.1 | 0.403073 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −5487.16 | −0.202216 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 6531.51 | 0.239906 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 23524.1 | 0.861196 | 0.430598 | − | 0.902544i | \(-0.358303\pi\) | ||||
0.430598 | + | 0.902544i | \(0.358303\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −16115.0 | −0.588011 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −14148.4 | −0.514553 | −0.257276 | − | 0.966338i | \(-0.582825\pi\) | ||||
−0.257276 | + | 0.966338i | \(0.582825\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 25958.6 | 0.940970 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 52077.9 | 1.88158 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 35860.4 | 1.29140 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −30972.7 | −1.11175 | −0.555874 | − | 0.831267i | \(-0.687616\pi\) | ||||
−0.555874 | + | 0.831267i | \(0.687616\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 17131.4 | 0.612919 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 13533.2 | 0.482610 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 14103.1 | 0.501304 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 23882.2 | 0.846164 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −38998.3 | −1.37728 | −0.688640 | − | 0.725103i | \(-0.741792\pi\) | ||||
−0.688640 | + | 0.725103i | \(0.741792\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 10321.7 | 0.363352 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −24735.1 | −0.867944 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −14461.8 | −0.505831 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 42772.3 | 1.49126 | 0.745629 | − | 0.666361i | \(-0.232149\pi\) | ||||
0.745629 | + | 0.666361i | \(0.232149\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −26609.9 | −0.924795 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −14143.3 | −0.489967 | −0.244983 | − | 0.969527i | \(-0.578783\pi\) | ||||
−0.244983 | + | 0.969527i | \(0.578783\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 14596.1 | 0.504044 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 60516.5 | 2.08318 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −2085.11 | −0.0715491 | −0.0357746 | − | 0.999360i | \(-0.511390\pi\) | ||||
−0.0357746 | + | 0.999360i | \(0.511390\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −22631.0 | −0.774112 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 9995.48 | 0.340826 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −26684.3 | −0.907018 | −0.453509 | − | 0.891252i | \(-0.649828\pi\) | ||||
−0.453509 | + | 0.891252i | \(0.649828\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −24431.1 | −0.827825 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −10266.3 | −0.346774 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −10088.5 | −0.339701 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 27416.6 | 0.920298 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 20552.8 | 0.687750 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 49234.5 | 1.64240 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 11405.5 | 0.379292 | 0.189646 | − | 0.981852i | \(-0.439266\pi\) | ||||
0.189646 | + | 0.981852i | \(0.439266\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 3367.13 | 0.111628 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −58306.3 | −1.92702 | −0.963510 | − | 0.267672i | \(-0.913746\pi\) | ||||
−0.963510 | + | 0.267672i | \(0.913746\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −9276.21 | −0.305634 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −30000.3 | −0.985413 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −3492.44 | −0.114363 | −0.0571817 | − | 0.998364i | \(-0.518211\pi\) | ||||
−0.0571817 | + | 0.998364i | \(0.518211\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −54558.6 | −1.78110 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −34325.5 | −1.11715 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 13554.6 | 0.439800 | 0.219900 | − | 0.975522i | \(-0.429427\pi\) | ||||
0.219900 | + | 0.975522i | \(0.429427\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 61945.4 | 2.00380 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 3613.96 | 0.116549 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −5392.46 | −0.173377 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −18929.4 | −0.606772 | −0.303386 | − | 0.952868i | \(-0.598117\pi\) | ||||
−0.303386 | + | 0.952868i | \(0.598117\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 20758.1 | 0.663381 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 34984.0 | 1.11464 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −47042.8 | −1.49434 | −0.747171 | − | 0.664632i | \(-0.768588\pi\) | ||||
−0.747171 | + | 0.664632i | \(0.768588\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 6551.75 | 0.207496 |
(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 | 1088.4.a.y.1.1 | 3 | ||
4.3 | odd | 2 | 1088.4.a.u.1.3 | 3 | |||
8.3 | odd | 2 | 272.4.a.j.1.1 | 3 | |||
8.5 | even | 2 | 136.4.a.b.1.3 | ✓ | 3 | ||
24.5 | odd | 2 | 1224.4.a.i.1.3 | 3 | |||
24.11 | even | 2 | 2448.4.a.bj.1.3 | 3 | |||
136.101 | even | 2 | 2312.4.a.d.1.1 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
136.4.a.b.1.3 | ✓ | 3 | 8.5 | even | 2 | ||
272.4.a.j.1.1 | 3 | 8.3 | odd | 2 | |||
1088.4.a.u.1.3 | 3 | 4.3 | odd | 2 | |||
1088.4.a.y.1.1 | 3 | 1.1 | even | 1 | trivial | ||
1224.4.a.i.1.3 | 3 | 24.5 | odd | 2 | |||
2312.4.a.d.1.1 | 3 | 136.101 | even | 2 | |||
2448.4.a.bj.1.3 | 3 | 24.11 | even | 2 |