Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [136,4,Mod(81,136)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(136, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 0, 1]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("136.81");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 136 = 2^{3} \cdot 17 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 136.k (of order \(4\), degree \(2\), minimal) |
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: | no |
Analytic conductor: | \(8.02425976078\) |
Analytic rank: | \(0\) |
Dimension: | \(14\) |
Relative dimension: | \(7\) over \(\Q(i)\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{14} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{14} + 142x^{12} + 7785x^{10} + 208489x^{8} + 2822686x^{6} + 17977041x^{4} + 45020416x^{2} + 31719424 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{9}]\) |
Coefficient ring index: | \( 2^{17} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 89.3 | ||
Root | \(-1.84168i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 136.89 |
Dual form | 136.4.k.a.81.3 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/136\mathbb{Z}\right)^\times\).
\(n\) | \(69\) | \(103\) | \(105\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{3}{4}\right)\) |
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 | ||||||||
\(3\) | −1.84168 | + | 1.84168i | −0.354431 | + | 0.354431i | −0.861755 | − | 0.507324i | \(-0.830635\pi\) |
0.507324 | + | 0.861755i | \(0.330635\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 4.90158 | − | 4.90158i | 0.438410 | − | 0.438410i | −0.453066 | − | 0.891477i | \(-0.649670\pi\) |
0.891477 | + | 0.453066i | \(0.149670\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 6.14401 | + | 6.14401i | 0.331745 | + | 0.331745i | 0.853249 | − | 0.521504i | \(-0.174629\pi\) |
−0.521504 | + | 0.853249i | \(0.674629\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 20.2164i | 0.748757i | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −19.4554 | − | 19.4554i | −0.533275 | − | 0.533275i | 0.388270 | − | 0.921546i | \(-0.373073\pi\) |
−0.921546 | + | 0.388270i | \(0.873073\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 64.7611 | 1.38165 | 0.690827 | − | 0.723020i | \(-0.257247\pi\) | ||||
0.690827 | + | 0.723020i | \(0.257247\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 18.0543i | 0.310773i | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 69.5389 | − | 8.79432i | 0.992098 | − | 0.125467i | ||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 162.870i | 1.96658i | 0.182058 | + | 0.983288i | \(0.441724\pi\) | ||||
−0.182058 | + | 0.983288i | \(0.558276\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −22.6306 | −0.235162 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 114.732 | + | 114.732i | 1.04014 | + | 1.04014i | 0.999160 | + | 0.0409792i | \(0.0130478\pi\) |
0.0409792 | + | 0.999160i | \(0.486952\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 76.9491i | 0.615593i | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −86.9575 | − | 86.9575i | −0.619814 | − | 0.619814i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 21.2323 | − | 21.2323i | 0.135957 | − | 0.135957i | −0.635853 | − | 0.771810i | \(-0.719352\pi\) |
0.771810 | + | 0.635853i | \(0.219352\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −11.9156 | + | 11.9156i | −0.0690358 | + | 0.0690358i | −0.740782 | − | 0.671746i | \(-0.765545\pi\) |
0.671746 | + | 0.740782i | \(0.265545\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 71.6612 | 0.378019 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 60.2306 | 0.290881 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 206.020 | − | 206.020i | 0.915392 | − | 0.915392i | −0.0812980 | − | 0.996690i | \(-0.525907\pi\) |
0.996690 | + | 0.0812980i | \(0.0259065\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −119.269 | + | 119.269i | −0.489701 | + | 0.489701i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −164.183 | − | 164.183i | −0.625393 | − | 0.625393i | 0.321513 | − | 0.946905i | \(-0.395809\pi\) |
−0.946905 | + | 0.321513i | \(0.895809\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 150.537i | − | 0.533877i | −0.963714 | − | 0.266938i | \(-0.913988\pi\) | ||
0.963714 | − | 0.266938i | \(-0.0860120\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 99.0925 | + | 99.0925i | 0.328263 | + | 0.328263i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −371.156 | −1.15189 | −0.575944 | − | 0.817489i | \(-0.695365\pi\) | ||||
−0.575944 | + | 0.817489i | \(0.695365\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | − | 267.502i | − | 0.779890i | ||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −111.872 | + | 144.265i | −0.307161 | + | 0.396100i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − | 55.4454i | − | 0.143698i | −0.997416 | − | 0.0718492i | \(-0.977110\pi\) | ||
0.997416 | − | 0.0718492i | \(-0.0228900\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −190.724 | −0.467587 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −299.954 | − | 299.954i | −0.697015 | − | 0.697015i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − | 15.6670i | − | 0.0345706i | −0.999851 | − | 0.0172853i | \(-0.994498\pi\) | ||
0.999851 | − | 0.0172853i | \(-0.00550236\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 127.371 | + | 127.371i | 0.267348 | + | 0.267348i | 0.828031 | − | 0.560683i | \(-0.189461\pi\) |
−0.560683 | + | 0.828031i | \(0.689461\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −124.210 | + | 124.210i | −0.248397 | + | 0.248397i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 317.432 | − | 317.432i | 0.605731 | − | 0.605731i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 159.183 | 0.290258 | 0.145129 | − | 0.989413i | \(-0.453640\pi\) | ||||
0.145129 | + | 0.989413i | \(0.453640\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −422.597 | −0.737315 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 27.7245 | − | 27.7245i | 0.0463422 | − | 0.0463422i | −0.683556 | − | 0.729898i | \(-0.739567\pi\) |
0.729898 | + | 0.683556i | \(0.239567\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −525.063 | + | 525.063i | −0.841834 | + | 0.841834i | −0.989097 | − | 0.147263i | \(-0.952954\pi\) |
0.147263 | + | 0.989097i | \(0.452954\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −141.715 | − | 141.715i | −0.218185 | − | 0.218185i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − | 239.068i | − | 0.353823i | ||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −526.679 | − | 526.679i | −0.750076 | − | 0.750076i | 0.224417 | − | 0.974493i | \(-0.427952\pi\) |
−0.974493 | + | 0.224417i | \(0.927952\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −225.549 | −0.309395 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − | 768.177i | − | 1.01588i | −0.861391 | − | 0.507942i | \(-0.830406\pi\) | ||
0.861391 | − | 0.507942i | \(-0.169594\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 297.744 | − | 383.956i | 0.379940 | − | 0.489952i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 78.2062i | 0.0963745i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 1576.01 | 1.87704 | 0.938520 | − | 0.345224i | \(-0.112197\pi\) | ||||
0.938520 | + | 0.345224i | \(0.112197\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 397.893 | + | 397.893i | 0.458357 | + | 0.458357i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | − | 43.8895i | − | 0.0489368i | ||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 798.320 | + | 798.320i | 0.862167 | + | 0.862167i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −1259.75 | + | 1259.75i | −1.31864 | + | 1.31864i | −0.403782 | + | 0.914855i | \(0.632305\pi\) |
−0.914855 | + | 0.403782i | \(0.867695\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 393.319 | − | 393.319i | 0.399294 | − | 0.399294i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −661.687 | −0.651884 | −0.325942 | − | 0.945390i | \(-0.605681\pi\) | ||||
−0.325942 | + | 0.945390i | \(0.605681\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −930.870 | −0.890499 | −0.445249 | − | 0.895407i | \(-0.646885\pi\) | ||||
−0.445249 | + | 0.895407i | \(0.646885\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −110.925 | + | 110.925i | −0.103097 | + | 0.103097i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 993.949 | − | 993.949i | 0.898025 | − | 0.898025i | −0.0972362 | − | 0.995261i | \(-0.531000\pi\) |
0.995261 | + | 0.0972362i | \(0.0310002\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 459.889 | + | 459.889i | 0.404123 | + | 0.404123i | 0.879683 | − | 0.475560i | \(-0.157755\pi\) |
−0.475560 | + | 0.879683i | \(0.657755\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 758.845i | 0.648887i | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 46.1480 | + | 46.1480i | 0.0384181 | + | 0.0384181i | 0.726055 | − | 0.687637i | \(-0.241352\pi\) |
−0.687637 | + | 0.726055i | \(0.741352\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1124.73 | 0.912016 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 1309.24i | 1.03452i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 481.280 | + | 373.215i | 0.370747 | + | 0.287501i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | − | 573.973i | − | 0.431235i | ||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 604.745 | 0.443317 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 989.869 | + | 989.869i | 0.708293 | + | 0.708293i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1959.28i | 1.36896i | 0.729031 | + | 0.684480i | \(0.239971\pi\) | ||||
−0.729031 | + | 0.684480i | \(0.760029\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 277.241 | + | 277.241i | 0.189222 | + | 0.189222i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1104.58 | − | 1104.58i | 0.736697 | − | 0.736697i | −0.235240 | − | 0.971937i | \(-0.575588\pi\) |
0.971937 | + | 0.235240i | \(0.0755878\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1000.67 | + | 1000.67i | −0.652402 | + | 0.652402i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −852.458 | −0.543466 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −446.567 | −0.278487 | −0.139244 | − | 0.990258i | \(-0.544467\pi\) | ||||
−0.139244 | + | 0.990258i | \(0.544467\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1738.60 | − | 1738.60i | 1.06091 | − | 1.06091i | 0.0628879 | − | 0.998021i | \(-0.479969\pi\) |
0.998021 | − | 0.0628879i | \(-0.0200310\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 683.550 | − | 683.550i | 0.408265 | − | 0.408265i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −1259.95 | − | 1259.95i | −0.736802 | − | 0.736802i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − | 208.144i | − | 0.119210i | ||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 492.653 | + | 492.653i | 0.276417 | + | 0.276417i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −1504.06 | −0.826961 | −0.413481 | − | 0.910513i | \(-0.635687\pi\) | ||||
−0.413481 | + | 0.910513i | \(0.635687\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1081.49i | 0.582852i | 0.956593 | + | 0.291426i | \(0.0941297\pi\) | ||||
−0.956593 | + | 0.291426i | \(0.905870\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 177.790 | + | 1405.83i | 0.0939442 | + | 0.742840i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 116.811i | 0.0605320i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −3618.49 | −1.83941 | −0.919705 | − | 0.392611i | \(-0.871572\pi\) | ||||
−0.919705 | + | 0.392611i | \(0.871572\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 102.113 | + | 102.113i | 0.0509311 | + | 0.0509311i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1409.82i | 0.690122i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 641.962 | + | 641.962i | 0.308480 | + | 0.308480i | 0.844320 | − | 0.535839i | \(-0.180005\pi\) |
−0.535839 | + | 0.844320i | \(0.680005\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 351.253 | − | 351.253i | 0.165727 | − | 0.165727i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 2397.82 | − | 2397.82i | 1.11107 | − | 1.11107i | 0.118064 | − | 0.993006i | \(-0.462331\pi\) |
0.993006 | − | 0.118064i | \(-0.0376688\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1997.00 | 0.908967 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −3292.65 | −1.47249 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 2381.19 | − | 2381.19i | 1.04647 | − | 1.04647i | 0.0476001 | − | 0.998866i | \(-0.484843\pi\) |
0.998866 | − | 0.0476001i | \(-0.0151573\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −472.776 | + | 472.776i | −0.204220 | + | 0.204220i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 28.8535 | + | 28.8535i | 0.0122529 | + | 0.0122529i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − | 2021.08i | − | 0.843924i | −0.906613 | − | 0.421962i | \(-0.861341\pi\) | ||
0.906613 | − | 0.421962i | \(-0.138659\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −1828.47 | − | 1828.47i | −0.750878 | − | 0.750878i | 0.223765 | − | 0.974643i | \(-0.428165\pi\) |
−0.974643 | + | 0.223765i | \(0.928165\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −469.154 | −0.189513 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | − | 2019.65i | − | 0.802635i | ||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −1524.01 | − | 1181.81i | −0.595970 | − | 0.462153i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | − | 1068.53i | − | 0.411240i | ||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −3474.47 | −1.31625 | −0.658125 | − | 0.752909i | \(-0.728650\pi\) | ||||
−0.658125 | + | 0.752909i | \(0.728650\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −2144.34 | − | 2144.34i | −0.799755 | − | 0.799755i | 0.183302 | − | 0.983057i | \(-0.441321\pi\) |
−0.983057 | + | 0.183302i | \(0.941321\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 1169.21i | 0.429380i | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 1178.53 | + | 1178.53i | 0.426226 | + | 0.426226i | 0.887341 | − | 0.461114i | \(-0.152550\pi\) |
−0.461114 | + | 0.887341i | \(0.652550\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −1157.98 | + | 1157.98i | −0.412497 | + | 0.412497i | −0.882607 | − | 0.470111i | \(-0.844214\pi\) |
0.470111 | + | 0.882607i | \(0.344214\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −293.164 | + | 293.164i | −0.102877 | + | 0.102877i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 260.903 | 0.0902059 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −1609.51 | −0.548357 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −2319.47 | + | 2319.47i | −0.778812 | + | 0.778812i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 3168.70 | − | 3168.70i | 1.04873 | − | 1.04873i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 694.783 | + | 694.783i | 0.226687 | + | 0.226687i | 0.811307 | − | 0.584620i | \(-0.198757\pi\) |
−0.584620 | + | 0.811307i | \(0.698757\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 102.119i | 0.0328502i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −737.869 | − | 737.869i | −0.234057 | − | 0.234057i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −146.419 | −0.0458046 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | − | 1933.99i | − | 0.596745i | ||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 4503.42 | − | 569.530i | 1.37074 | − | 0.173352i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 665.828i | − | 0.199942i | −0.994990 | − | 0.0999712i | \(-0.968125\pi\) | ||
0.994990 | − | 0.0999712i | \(-0.0318751\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −1555.64 | −0.460929 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −1410.05 | − | 1410.05i | −0.412283 | − | 0.412283i | 0.470250 | − | 0.882533i | \(-0.344164\pi\) |
−0.882533 | + | 0.470250i | \(0.844164\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 4743.56i | 1.36884i | 0.729090 | + | 0.684418i | \(0.239944\pi\) | ||||
−0.729090 | + | 0.684418i | \(0.760056\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 440.287 | + | 440.287i | 0.125406 | + | 0.125406i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −2734.00 | + | 2734.00i | −0.768713 | + | 0.768713i | −0.977880 | − | 0.209167i | \(-0.932925\pi\) |
0.209167 | + | 0.977880i | \(0.432925\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −1819.25 | + | 1819.25i | −0.504999 | + | 0.504999i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 1939.95 | 0.531700 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −2739.49 | −0.741435 | −0.370718 | − | 0.928746i | \(-0.620888\pi\) | ||||
−0.370718 | + | 0.928746i | \(0.620888\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 3780.15 | − | 3780.15i | 1.01038 | − | 1.01038i | 0.0104308 | − | 0.999946i | \(-0.496680\pi\) |
0.999946 | − | 0.0104308i | \(-0.00332030\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 2763.24 | − | 2763.24i | 0.729473 | − | 0.729473i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −1311.18 | − | 1311.18i | −0.341912 | − | 0.341912i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 10547.6i | 2.71713i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 1414.73 | + | 1414.73i | 0.360061 | + | 0.360061i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 2741.32 | 0.689364 | 0.344682 | − | 0.938719i | \(-0.387987\pi\) | ||||
0.344682 | + | 0.938719i | \(0.387987\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 4464.30i | − | 1.10936i | ||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 158.775 | + | 1255.47i | 0.0389916 | + | 0.308317i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − | 1407.95i | − | 0.341733i | −0.985294 | − | 0.170866i | \(-0.945343\pi\) | ||
0.985294 | − | 0.170866i | \(-0.0546567\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 2531.58 | 0.607354 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 429.242 | + | 429.242i | 0.101799 | + | 0.101799i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − | 88.8255i | − | 0.0208259i | −0.999946 | − | 0.0104130i | \(-0.996685\pi\) | ||
0.999946 | − | 0.0104130i | \(-0.00331461\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −271.770 | − | 271.770i | −0.0629988 | − | 0.0629988i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −2902.50 | + | 2902.50i | −0.665281 | + | 0.665281i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −1308.48 | + | 1308.48i | −0.296578 | + | 0.296578i | −0.839672 | − | 0.543094i | \(-0.817253\pi\) |
0.543094 | + | 0.839672i | \(0.317253\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 3712.58 | 0.832190 | 0.416095 | − | 0.909321i | \(-0.363398\pi\) | ||||
0.416095 | + | 0.909321i | \(0.363398\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −1465.58 | −0.324912 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 1497.08 | − | 1497.08i | 0.328280 | − | 0.328280i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 660.849 | − | 660.849i | 0.143345 | − | 0.143345i | −0.631793 | − | 0.775138i | \(-0.717681\pi\) |
0.775138 | + | 0.631793i | \(0.217681\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −240.892 | − | 240.892i | −0.0516910 | − | 0.0516910i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 4243.00i | 0.900769i | 0.892835 | + | 0.450385i | \(0.148713\pi\) | ||||
−0.892835 | + | 0.450385i | \(0.851287\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 767.424 | + | 767.424i | 0.161197 | + | 0.161197i | 0.783097 | − | 0.621900i | \(-0.213639\pi\) |
−0.621900 | + | 0.783097i | \(0.713639\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −2940.50 | −0.611158 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − | 2017.48i | − | 0.414942i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 4758.32 | − | 1223.09i | 0.968516 | − | 0.248951i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | − | 4640.09i | − | 0.934732i | ||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 4696.58 | 0.936441 | 0.468220 | − | 0.883612i | \(-0.344895\pi\) | ||||
0.468220 | + | 0.883612i | \(0.344895\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −76.7929 | − | 76.7929i | −0.0151561 | − | 0.0151561i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 3383.59i | 0.661063i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 7430.15 | + | 7430.15i | 1.43711 | + | 1.43711i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 924.901 | − | 924.901i | 0.177111 | − | 0.177111i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 1218.61 | − | 1218.61i | 0.231048 | − | 0.231048i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 1248.64 | 0.234417 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −7273.04 | −1.35210 | −0.676050 | − | 0.736856i | \(-0.736310\pi\) | ||||
−0.676050 | + | 0.736856i | \(0.736310\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 1714.36 | − | 1714.36i | 0.315620 | − | 0.315620i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 546.061 | − | 546.061i | 0.0995635 | − | 0.0995635i | −0.655570 | − | 0.755134i | \(-0.727572\pi\) |
0.755134 | + | 0.655570i | \(0.227572\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −2165.60 | − | 2165.60i | −0.391076 | − | 0.391076i | 0.483995 | − | 0.875071i | \(-0.339185\pi\) |
−0.875071 | + | 0.483995i | \(0.839185\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 1217.65i | 0.217799i | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 1458.79 | + | 1458.79i | 0.258466 | + | 0.258466i | 0.824430 | − | 0.565964i | \(-0.191496\pi\) |
−0.565964 | + | 0.824430i | \(0.691496\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −826.167 | −0.145005 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 3661.07i | 0.636576i | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 1432.33 | + | 11325.8i | 0.246740 | + | 1.95104i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 4983.31i | 0.850536i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −1693.94 | −0.286468 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −2280.39 | − | 2280.39i | −0.382133 | − | 0.382133i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 1122.37i | − | 0.186378i | −0.995648 | − | 0.0931890i | \(-0.970294\pi\) | ||
0.995648 | − | 0.0931890i | \(-0.0297061\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 4164.99 | + | 4164.99i | 0.685406 | + | 0.685406i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 780.248 | − | 780.248i | 0.127252 | − | 0.127252i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −1267.19 | + | 1267.19i | −0.204832 | + | 0.204832i | −0.802067 | − | 0.597235i | \(-0.796266\pi\) |
0.597235 | + | 0.802067i | \(0.296266\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −169.980 | −0.0272331 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 463.647 | 0.0736302 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 3750.93 | − | 3750.93i | 0.590470 | − | 0.590470i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −2071.39 | + | 2071.39i | −0.323247 | + | 0.323247i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −7844.57 | − | 7844.57i | −1.21360 | − | 1.21360i | −0.969835 | − | 0.243763i | \(-0.921618\pi\) |
−0.243763 | − | 0.969835i | \(-0.578382\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 753.380i | − | 0.115552i | −0.998330 | − | 0.0577758i | \(-0.981599\pi\) | ||
0.998330 | − | 0.0577758i | \(-0.0184008\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −5631.46 | − | 5631.46i | −0.856368 | − | 0.856368i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 6089.17 | 0.918113 | 0.459057 | − | 0.888407i | \(-0.348187\pi\) | ||||
0.459057 | + | 0.888407i | \(0.348187\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − | 271.788i | − | 0.0406338i | ||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −1573.70 | + | 199.020i | −0.233303 | + | 0.0295050i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 10897.8i | − | 1.60213i | −0.598579 | − | 0.801064i | \(-0.704268\pi\) | ||
0.598579 | − | 0.801064i | \(-0.295732\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −19667.6 | −2.86742 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 1057.07 | + | 1057.07i | 0.152843 | + | 0.152843i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 5147.27i | 0.738138i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 7319.04 | + | 7319.04i | 1.04101 | + | 1.04101i | 0.999122 | + | 0.0418881i | \(0.0133373\pi\) |
0.0418881 | + | 0.999122i | \(0.486663\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 3319.20 | − | 3319.20i | 0.468267 | − | 0.468267i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 340.657 | − | 340.657i | 0.0476712 | − | 0.0476712i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −3532.25 | −0.490329 | −0.245164 | − | 0.969481i | \(-0.578842\pi\) | ||||
−0.245164 | + | 0.969481i | \(0.578842\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −3646.04 | −0.502082 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 1375.03 | − | 1375.03i | 0.187845 | − | 0.187845i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 7321.72 | − | 7321.72i | 0.992326 | − | 0.992326i | −0.00764499 | − | 0.999971i | \(-0.502433\pi\) |
0.999971 | + | 0.00764499i | \(0.00243350\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −3608.36 | − | 3608.36i | −0.485202 | − | 0.485202i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − | 8011.16i | − | 1.06880i | −0.845231 | − | 0.534401i | \(-0.820537\pi\) | ||
0.845231 | − | 0.534401i | \(-0.179463\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −1171.81 | − | 1171.81i | −0.155120 | − | 0.155120i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 3043.33 | 0.399744 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − | 10247.3i | − | 1.33563i | −0.744329 | − | 0.667814i | \(-0.767230\pi\) | ||
0.744329 | − | 0.667814i | \(-0.232770\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 8987.30 | + | 6969.33i | 1.16242 | + | 0.901417i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 4068.55i | 0.522216i | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −5163.12 | −0.657682 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −8066.34 | − | 8066.34i | −1.01974 | − | 1.01974i | −0.999801 | − | 0.0199422i | \(-0.993652\pi\) |
−0.0199422 | − | 0.999801i | \(-0.506348\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | − | 3685.84i | − | 0.462463i | ||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −4181.06 | − | 4181.06i | −0.520679 | − | 0.520679i | 0.397098 | − | 0.917776i | \(-0.370017\pi\) |
−0.917776 | + | 0.397098i | \(0.870017\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −771.669 | + | 771.669i | −0.0953835 | + | 0.0953835i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −1105.54 | + | 1105.54i | −0.135642 | + | 0.135642i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −8016.42 | −0.976312 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −335.990 | −0.0406201 | −0.0203100 | − | 0.999794i | \(-0.506465\pi\) | ||||
−0.0203100 | + | 0.999794i | \(0.506465\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 822.432 | − | 822.432i | 0.0987046 | − | 0.0987046i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 96.2580 | − | 96.2580i | 0.0114686 | − | 0.0114686i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −3765.28 | − | 3765.28i | −0.445374 | − | 0.445374i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 6403.89i | 0.752038i | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −5848.32 | − | 5848.32i | −0.681883 | − | 0.681883i | 0.278541 | − | 0.960424i | \(-0.410149\pi\) |
−0.960424 | + | 0.278541i | \(0.910149\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −2751.51 | −0.318528 | −0.159264 | − | 0.987236i | \(-0.550912\pi\) | ||||
−0.159264 | + | 0.987236i | \(0.550912\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | − | 7503.46i | − | 0.862484i | ||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 676.715 | + | 5350.95i | 0.0772364 | + | 0.610728i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 1565.14i | 0.177383i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 4640.86 | 0.522291 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 7731.11 | + | 7731.11i | 0.864025 | + | 0.864025i | 0.991803 | − | 0.127778i | \(-0.0407845\pi\) |
−0.127778 | + | 0.991803i | \(0.540784\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 4563.47i | 0.506481i | 0.967403 | + | 0.253240i | \(0.0814964\pi\) | ||||
−0.967403 | + | 0.253240i | \(0.918504\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 383.334 | + | 383.334i | 0.0422516 | + | 0.0422516i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −18686.3 | + | 18686.3i | −2.04551 | + | 2.04551i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 6386.15 | − | 6386.15i | 0.694292 | − | 0.694292i | −0.268881 | − | 0.963173i | \(-0.586654\pi\) |
0.963173 | + | 0.268881i | \(0.0866539\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 5407.95 | 0.583949 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −5568.83 | −0.597253 | −0.298626 | − | 0.954370i | \(-0.596528\pi\) | ||||
−0.298626 | + | 0.954370i | \(0.596528\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 7724.93 | − | 7724.93i | 0.822914 | − | 0.822914i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 2769.99 | − | 2769.99i | 0.293101 | − | 0.293101i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −2068.57 | − | 2068.57i | −0.217421 | − | 0.217421i | 0.589990 | − | 0.807411i | \(-0.299132\pi\) |
−0.807411 | + | 0.589990i | \(0.799132\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 6388.50i | 0.667013i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −1991.76 | − | 1991.76i | −0.206581 | − | 0.206581i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 3900.60 | 0.401897 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 7185.44i | − | 0.735494i | −0.929926 | − | 0.367747i | \(-0.880129\pi\) | ||
0.929926 | − | 0.367747i | \(-0.119871\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −6811.66 | − | 5282.20i | −0.692682 | − | 0.537150i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 3480.28i | 0.351612i | 0.984425 | + | 0.175806i | \(0.0562531\pi\) | ||||
−0.984425 | + | 0.175806i | \(0.943747\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 15913.5 | 1.59732 | 0.798662 | − | 0.601779i | \(-0.205541\pi\) | ||||
0.798662 | + | 0.601779i | \(0.205541\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −215.128 | − | 215.128i | −0.0214544 | − | 0.0214544i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 15651.4i | 1.55088i | 0.631422 | + | 0.775439i | \(0.282472\pi\) | ||||
−0.631422 | + | 0.775439i | \(0.717528\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 978.022 | + | 978.022i | 0.0962918 | + | 0.0962918i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 6664.10 | − | 6664.10i | 0.651944 | − | 0.651944i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −2928.76 | + | 2928.76i | −0.284703 | + | 0.284703i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −12532.7 | −1.21061 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 1120.91 | 0.107595 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 599.977 | − | 599.977i | 0.0572310 | − | 0.0572310i | −0.677912 | − | 0.735143i | \(-0.737115\pi\) |
0.735143 | + | 0.677912i | \(0.237115\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 13342.1 | − | 13342.1i | 1.26475 | − | 1.26475i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −2596.44 | − | 2596.44i | −0.244601 | − | 0.244601i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 12349.5i | 1.15621i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 7737.55 | + | 7737.55i | 0.719963 | + | 0.719963i | 0.968597 | − | 0.248635i | \(-0.0799819\pi\) |
−0.248635 | + | 0.968597i | \(0.579982\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −2364.57 | −0.218670 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 18450.4i | 1.69583i | 0.530130 | + | 0.847916i | \(0.322143\pi\) | ||||
−0.530130 | + | 0.847916i | \(0.677857\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 1289.75 | − | 1663.20i | 0.117824 | − | 0.151940i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | − | 3855.77i | − | 0.350109i | ||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 340.679 | 0.0307476 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −2322.23 | − | 2322.23i | −0.208331 | − | 0.208331i | 0.595227 | − | 0.803558i | \(-0.297062\pi\) |
−0.803558 | + | 0.595227i | \(0.797062\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 8832.01i | 0.787595i | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 518.275 | + | 518.275i | 0.0459418 | + | 0.0459418i | 0.729704 | − | 0.683763i | \(-0.239658\pi\) |
−0.683763 | + | 0.729704i | \(0.739658\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −3243.31 | + | 3243.31i | −0.285793 | + | 0.285793i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −3677.83 | + | 3677.83i | −0.322166 | + | 0.322166i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 22300.1 | 1.94192 | 0.970958 | − | 0.239248i | \(-0.0769010\pi\) | ||||
0.970958 | + | 0.239248i | \(0.0769010\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −6451.97 | −0.558549 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 14162.8 | − | 14162.8i | 1.21891 | − | 1.21891i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −4562.73 | + | 4562.73i | −0.390404 | + | 0.390404i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 7221.00 | + | 7221.00i | 0.614273 | + | 0.614273i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 8770.78i | 0.741800i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −2962.20 | − | 2962.20i | −0.249091 | − | 0.249091i | 0.571507 | − | 0.820598i | \(-0.306359\pi\) |
−0.820598 | + | 0.571507i | \(0.806359\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 6211.85 | 0.519360 | 0.259680 | − | 0.965695i | \(-0.416383\pi\) | ||||
0.259680 | + | 0.965695i | \(0.416383\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | − | 1741.40i | − | 0.144764i | ||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −723.810 | + | 933.389i | −0.0598285 | + | 0.0771519i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 14159.7i | 1.16378i | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 316.731 | 0.0258850 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −10632.7 | − | 10632.7i | −0.864076 | − | 0.864076i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − | 9743.84i | − | 0.787407i | ||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 3722.17 | + | 3722.17i | 0.299113 | + | 0.299113i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −5204.37 | + | 5204.37i | −0.415896 | + | 0.415896i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 11931.1 | − | 11931.1i | 0.948166 | − | 0.948166i | −0.0505554 | − | 0.998721i | \(-0.516099\pi\) |
0.998721 | + | 0.0505554i | \(0.0160991\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 6734.90 | 0.532269 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 4508.37 | 0.354344 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −15281.2 | + | 15281.2i | −1.19447 | + | 1.19447i | −0.218677 | + | 0.975797i | \(0.570174\pi\) |
−0.975797 | + | 0.218677i | \(0.929826\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −2575.00 | + | 2575.00i | −0.200179 | + | 0.200179i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 3458.11 | + | 3458.11i | 0.267369 | + | 0.267369i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − | 6471.84i | − | 0.497668i | ||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 3719.54 | + | 3719.54i | 0.284479 | + | 0.284479i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −15096.4 | −1.14839 | −0.574195 | − | 0.818718i | \(-0.694685\pi\) | ||||
−0.574195 | + | 0.818718i | \(0.694685\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 9748.95i | − | 0.737633i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 4983.24 | − | 630.212i | 0.375032 | − | 0.0474288i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − | 11050.9i | − | 0.827244i | −0.910449 | − | 0.413622i | \(-0.864264\pi\) | ||
0.910449 | − | 0.413622i | \(-0.135736\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 452.396 | 0.0336858 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −1385.77 | − | 1385.77i | −0.102640 | − | 0.102640i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 16142.9i | 1.18936i | 0.803963 | + | 0.594680i | \(0.202721\pi\) | ||||
−0.803963 | + | 0.594680i | \(0.797279\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 16389.9 | + | 16389.9i | 1.20122 | + | 1.20122i | 0.973796 | + | 0.227424i | \(0.0730304\pi\) |
0.227424 | + | 0.973796i | \(0.426970\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 6398.85 | − | 6398.85i | 0.466520 | − | 0.466520i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −8828.49 | + | 8828.49i | −0.640302 | + | 0.640302i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 15499.1 | 1.11826 | 0.559130 | − | 0.829080i | \(-0.311135\pi\) | ||||
0.559130 | + | 0.829080i | \(0.311135\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 7898.35 | 0.566916 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 4719.68 | − | 4719.68i | 0.337014 | − | 0.337014i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −1078.71 | + | 1078.71i | −0.0766308 | + | 0.0766308i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 6417.34 | + | 6417.34i | 0.453546 | + | 0.453546i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − | 11464.9i | − | 0.806145i | −0.915168 | − | 0.403072i | \(-0.867942\pi\) | ||
0.915168 | − | 0.403072i | \(-0.132058\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −1940.70 | − | 1940.70i | −0.135764 | − | 0.135764i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −4340.93 | −0.302136 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 10536.2i | − | 0.729632i | −0.931080 | − | 0.364816i | \(-0.881132\pi\) | ||
0.931080 | − | 0.364816i | \(-0.118868\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 4188.37 | − | 529.687i | 0.288582 | − | 0.0364959i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | − | 4265.24i | − | 0.292403i | ||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −19638.2 | −1.33956 | −0.669779 | − | 0.742561i | \(-0.733611\pi\) | ||||
−0.669779 | + | 0.742561i | \(0.733611\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −2479.04 | − | 2479.04i | −0.168257 | − | 0.168257i | 0.617956 | − | 0.786213i | \(-0.287961\pi\) |
−0.786213 | + | 0.617956i | \(0.787961\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 3218.12i | 0.217333i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −2813.37 | − | 2813.37i | −0.189058 | − | 0.189058i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −5773.82 | + | 5773.82i | −0.386083 | + | 0.386083i | −0.873288 | − | 0.487205i | \(-0.838016\pi\) |
0.487205 | + | 0.873288i | \(0.338016\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −480.499 | + | 480.499i | −0.0319718 | + | 0.0319718i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −24036.5 | −1.59151 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −23768.5 | −1.56607 | −0.783036 | − | 0.621976i | \(-0.786330\pi\) | ||||
−0.783036 | + | 0.621976i | \(0.786330\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 2964.20 | − | 2964.20i | 0.194355 | − | 0.194355i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −13670.6 | + | 13670.6i | −0.891990 | + | 0.891990i | −0.994710 | − | 0.102720i | \(-0.967245\pi\) |
0.102720 | + | 0.994710i | \(0.467245\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −7930.48 | − | 7930.48i | −0.514948 | − | 0.514948i | 0.401091 | − | 0.916038i | \(-0.368631\pi\) |
−0.916038 | + | 0.401091i | \(0.868631\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | − | 19953.5i | − | 1.28939i | ||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 9683.01 | + | 9683.01i | 0.622699 | + | 0.622699i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 85.2057 | 0.00545316 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 11671.5i | 0.743402i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 12514.6 | − | 16138.2i | 0.793307 | − | 1.02301i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 17029.3i | − | 1.07437i | −0.843465 | − | 0.537184i | \(-0.819488\pi\) | ||
0.843465 | − | 0.537184i | \(-0.180512\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −2559.13 | −0.160689 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 9603.56 | + | 9603.56i | 0.600166 | + | 0.600166i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − | 17323.8i | − | 1.07754i | ||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 560.491 | + | 560.491i | 0.0346990 | + | 0.0346990i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 8695.98 | − | 8695.98i | 0.535835 | − | 0.535835i | −0.386468 | − | 0.922303i | \(-0.626305\pi\) |
0.922303 | + | 0.386468i | \(0.126305\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 11119.5 | − | 11119.5i | 0.681973 | − | 0.681973i | −0.278472 | − | 0.960444i | \(-0.589828\pi\) |
0.960444 | + | 0.278472i | \(0.0898278\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 2717.84 | 0.165914 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −16389.0 | −0.995856 | −0.497928 | − | 0.867218i | \(-0.665906\pi\) | ||||
−0.497928 | + | 0.867218i | \(0.665906\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −304.808 | + | 304.808i | −0.0184357 | + | 0.0184357i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 269.657 | − | 269.657i | 0.0162346 | − | 0.0162346i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 16983.6 | + | 16983.6i | 1.01779 | + | 1.01779i | 0.999839 | + | 0.0179542i | \(0.00571530\pi\) |
0.0179542 | + | 0.999839i | \(0.494285\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − | 10828.3i | − | 0.645951i | ||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −10614.9 | − | 10614.9i | −0.630330 | − | 0.630330i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −10440.0 | −0.617122 | −0.308561 | − | 0.951205i | \(-0.599847\pi\) | ||||
−0.308561 | + | 0.951205i | \(0.599847\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 29766.6i | 1.75157i | 0.482702 | + | 0.875784i | \(0.339655\pi\) | ||||
−0.482702 | + | 0.875784i | \(0.660345\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −7244.95 | + | 9342.73i | −0.424390 | + | 0.547272i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 9809.76i | 0.572039i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 4872.04 | 0.282828 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 1226.24 | + | 1226.24i | 0.0708658 | + | 0.0708658i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 4956.13i | − | 0.285141i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −21398.0 | − | 21398.0i | −1.22560 | − | 1.22560i | −0.965611 | − | 0.259992i | \(-0.916280\pi\) |
−0.259992 | − | 0.965611i | \(-0.583720\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 6691.30 | − | 6691.30i | 0.381553 | − | 0.381553i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −22225.8 | + | 22225.8i | −1.26176 | + | 1.26176i | −0.311515 | + | 0.950241i | \(0.600836\pi\) |
−0.950241 | + | 0.311515i | \(0.899164\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −15479.8 | −0.874903 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 5193.72 | 0.292252 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −2456.51 | + | 2456.51i | −0.137622 | + | 0.137622i | −0.772562 | − | 0.634940i | \(-0.781025\pi\) |
0.634940 | + | 0.772562i | \(0.281025\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −2188.88 | + | 2188.88i | −0.122092 | + | 0.122092i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −8736.11 | − | 8736.11i | −0.485158 | − | 0.485158i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − | 3590.71i | − | 0.198541i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −12190.7 | − | 12190.7i | −0.671136 | − | 0.671136i | 0.286842 | − | 0.957978i | \(-0.407395\pi\) |
−0.957978 | + | 0.286842i | \(0.907395\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 4833.11 | 0.264928 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | − | 17043.8i | − | 0.930227i | ||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −12861.0 | − | 9973.24i | −0.698917 | − | 0.541985i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | − | 10070.3i | − | 0.544912i | ||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −14126.4 | −0.761121 | −0.380561 | − | 0.924756i | \(-0.624269\pi\) | ||||
−0.380561 | + | 0.924756i | \(0.624269\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 33554.5 | + | 33554.5i | 1.80019 | + | 1.80019i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | − | 6700.95i | − | 0.357975i | ||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −4065.41 | − | 4065.41i | −0.216259 | − | 0.216259i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 13811.0 | − | 13811.0i | 0.731570 | − | 0.731570i | −0.239361 | − | 0.970931i | \(-0.576938\pi\) |
0.970931 | + | 0.239361i | \(0.0769379\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 10647.6 | − | 10647.6i | 0.561625 | − | 0.561625i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −2734.20 | −0.143614 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −12351.5 | −0.646043 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 5045.26 | − | 5045.26i | 0.262788 | − | 0.262788i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 23222.3 | − | 23222.3i | 1.20451 | − | 1.20451i | 0.231732 | − | 0.972780i | \(-0.425561\pi\) |
0.972780 | − | 0.231732i | \(-0.0744394\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −5719.27 | − | 5719.27i | −0.295419 | − | 0.295419i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 13923.6i | 0.716218i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 1633.81 | + | 1633.81i | 0.0836939 | + | 0.0836939i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 11849.0 | 0.604479 | 0.302240 | − | 0.953232i | \(-0.402266\pi\) | ||||
0.302240 | + | 0.953232i | \(0.402266\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 4088.18i | 0.207701i | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −1323.87 | − | 10468.2i | −0.0669838 | − | 0.529658i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 6968.81i | 0.351158i | 0.984465 | + | 0.175579i | \(0.0561797\pi\) | ||||
−0.984465 | + | 0.175579i | \(0.943820\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 4829.56 | 0.242368 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −3096.97 | − | 3096.97i | −0.154788 | − | 0.154788i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 12473.0i | − | 0.620877i | −0.950593 | − | 0.310439i | \(-0.899524\pi\) | ||
0.950593 | − | 0.310439i | \(-0.100476\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −19425.4 | − | 19425.4i | −0.963034 | − | 0.963034i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −7331.57 | + | 7331.57i | −0.362004 | + | 0.362004i | −0.864550 | − | 0.502546i | \(-0.832397\pi\) |
0.502546 | + | 0.864550i | \(0.332397\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −7372.26 | + | 7372.26i | −0.362548 | + | 0.362548i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 15529.8 | 0.760650 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 12213.7 | 0.595831 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −14291.7 | + | 14291.7i | −0.694421 | + | 0.694421i | −0.963201 | − | 0.268780i | \(-0.913379\pi\) |
0.268780 | + | 0.963201i | \(0.413379\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −5048.62 | + | 5048.62i | −0.244332 | + | 0.244332i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 5301.02 | + | 5301.02i | 0.255528 | + | 0.255528i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 27310.5i | 1.31125i | 0.755087 | + | 0.655624i | \(0.227594\pi\) | ||||
−0.755087 | + | 0.655624i | \(0.772406\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 8221.81 | + | 8221.81i | 0.393192 | + | 0.393192i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −12317.3 | −0.586730 | −0.293365 | − | 0.956001i | \(-0.594775\pi\) | ||||
−0.293365 | + | 0.956001i | \(0.594775\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 5651.13i | 0.268132i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 7762.23 | + | 6019.33i | 0.366855 | + | 0.284483i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − | 1014.61i | − | 0.0477646i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 23448.3 | 1.09957 | 0.549784 | − | 0.835307i | \(-0.314710\pi\) | ||||
0.549784 | + | 0.835307i | \(0.314710\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 2592.99 | + | 2592.99i | 0.121121 | + | 0.121121i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − | 8920.95i | − | 0.415090i | −0.978225 | − | 0.207545i | \(-0.933453\pi\) | ||
0.978225 | − | 0.207545i | \(-0.0665473\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −916.896 | − | 916.896i | −0.0424979 | − | 0.0424979i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −4662.35 | + | 4662.35i | −0.215265 | + | 0.215265i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 26740.5 | − | 26740.5i | 1.22988 | − | 1.22988i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −1078.78 | −0.0494263 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −3692.62 | −0.168536 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −17736.3 | + | 17736.3i | −0.806416 | + | 0.806416i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −1469.14 | + | 1469.14i | −0.0665429 | + | 0.0665429i | −0.739595 | − | 0.673052i | \(-0.764983\pi\) |
0.673052 | + | 0.739595i | \(0.264983\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 163.588 | + | 163.588i | 0.00738135 | + | 0.00738135i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 567.067i | 0.0254900i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 8248.72 | + | 8248.72i | 0.369383 | + | 0.369383i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 1001.03 | 0.0446575 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 17841.0i | 0.792926i | 0.918051 | + | 0.396463i | \(0.129762\pi\) | ||||
−0.918051 | + | 0.396463i | \(0.870238\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −25809.8 | + | 3264.07i | −1.14279 | + | 0.144524i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 31861.3i | 1.40545i | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 20430.6 | 0.897859 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 6910.36 | + | 6910.36i | 0.302557 | + | 0.302557i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | − | 4819.60i | − | 0.210233i | ||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 16280.0 | + | 16280.0i | 0.707510 | + | 0.707510i | 0.966011 | − | 0.258501i | \(-0.0832287\pi\) |
−0.258501 | + | 0.966011i | \(0.583229\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 1081.03 | − | 1081.03i | 0.0468067 | − | 0.0468067i | −0.683316 | − | 0.730123i | \(-0.739463\pi\) |
0.730123 | + | 0.683316i | \(0.239463\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −6837.38 | + | 6837.38i | −0.294954 | + | 0.294954i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 6293.25 | 0.270482 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 24518.0 | 1.04991 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −8043.97 | + | 8043.97i | −0.343198 | + | 0.343198i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −20742.1 | + | 20742.1i | −0.881736 | + | 0.881736i | −0.993711 | − | 0.111975i | \(-0.964282\pi\) |
0.111975 | + | 0.993711i | \(0.464282\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 12843.2 | + | 12843.2i | 0.543969 | + | 0.543969i | 0.924690 | − | 0.380721i | \(-0.124324\pi\) |
−0.380721 | + | 0.924690i | \(0.624324\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 5514.26i | 0.232706i | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 15185.3 | + | 15185.3i | 0.638507 | + | 0.638507i | 0.950187 | − | 0.311680i | \(-0.100892\pi\) |
−0.311680 | + | 0.950187i | \(0.600892\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 16515.8 | 0.691938 | 0.345969 | − | 0.938246i | \(-0.387550\pi\) | ||||
0.345969 | + | 0.938246i | \(0.387550\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 2434.14i | 0.101612i | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −2352.50 | − | 18601.8i | −0.0978504 | − | 0.773728i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − | 23506.2i | − | 0.974209i | ||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 2072.30 | 0.0855787 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 17119.0 | + | 17119.0i | 0.704428 | + | 0.704428i | 0.965358 | − | 0.260930i | \(-0.0840292\pi\) |
−0.260930 | + | 0.965358i | \(0.584029\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 23487.4i | 0.963032i | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −7814.24 | − | 7814.24i | −0.319261 | − | 0.319261i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 9788.46 | − | 9788.46i | 0.398501 | − | 0.398501i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 3526.50 | − | 3526.50i | 0.143060 | − | 0.143060i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −2826.70 | −0.114266 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 47274.1 | 1.90427 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 2845.44 | − | 2845.44i | 0.114216 | − | 0.114216i | −0.647689 | − | 0.761905i | \(-0.724264\pi\) |
0.761905 | + | 0.647689i | \(0.224264\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −16139.2 | + | 16139.2i | −0.645554 | + | 0.645554i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 8967.32 | + | 8967.32i | 0.357430 | + | 0.357430i | 0.862865 | − | 0.505435i | \(-0.168668\pi\) |
−0.505435 | + | 0.862865i | \(0.668668\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 39576.5i | − | 1.57198i | −0.618238 | − | 0.785991i | \(-0.712153\pi\) | ||
0.618238 | − | 0.785991i | \(-0.287847\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 3715.55 | + | 3715.55i | 0.147068 | + | 0.147068i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 3357.47 | 0.132433 | 0.0662164 | − | 0.997805i | \(-0.478907\pi\) | ||||
0.0662164 | + | 0.997805i | \(0.478907\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | − | 23343.2i | − | 0.917564i | ||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −6510.74 | + | 11015.8i | −0.255036 | + | 0.431508i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 20493.5i | 0.799994i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 10308.9 | 0.401037 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −25467.6 | − | 25467.6i | −0.987339 | − | 0.987339i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 12163.5i | 0.469945i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 8148.69 | + | 8148.69i | 0.313754 | + | 0.313754i | 0.846362 | − | 0.532608i | \(-0.178788\pi\) |
−0.532608 | + | 0.846362i | \(0.678788\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −8649.59 | + | 8649.59i | −0.331904 | + | 0.331904i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 27477.3 | − | 27477.3i | 1.05078 | − | 1.05078i | 0.0521358 | − | 0.998640i | \(-0.483397\pi\) |
0.998640 | − | 0.0521358i | \(-0.0166029\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −27805.7 | −1.05972 | −0.529862 | − | 0.848084i | \(-0.677756\pi\) | ||||
−0.529862 | + | 0.848084i | \(0.677756\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 282.856 | 0.0107436 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −35707.9 | + | 35707.9i | −1.35169 | + | 1.35169i | −0.467927 | + | 0.883767i | \(0.654999\pi\) |
−0.883767 | + | 0.467927i | \(0.845001\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −12037.8 | + | 12037.8i | −0.454146 | + | 0.454146i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 4388.15 | + | 4388.15i | 0.164993 | + | 0.164993i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − | 60450.2i | − | 2.26527i | ||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −9906.47 | − | 9906.47i | −0.369985 | − | 0.369985i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −27367.9 | −1.01871 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 505.993i | 0.0187717i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −487.605 | − | 3855.61i | −0.0180294 | − | 0.142563i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 3406.74i | 0.125547i | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −17924.8 | −0.658386 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −11594.5 | − | 11594.5i | −0.424464 | − | 0.424464i | 0.462274 | − | 0.886737i | \(-0.347034\pi\) |
−0.886737 | + | 0.462274i | \(0.847034\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | − | 13377.0i | − | 0.488103i | ||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −11849.5 | − | 11849.5i | −0.430945 | − | 0.430945i | 0.458005 | − | 0.888950i | \(-0.348564\pi\) |
−0.888950 | + | 0.458005i | \(0.848564\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −14945.2 | + | 14945.2i | −0.541746 | + | 0.541746i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −2299.60 | + | 2299.60i | −0.0830845 | + | 0.0830845i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 13573.0 | 0.488791 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 34873.5 | 1.25176 | 0.625882 | − | 0.779918i | \(-0.284739\pi\) | ||||
0.625882 | + | 0.779918i | \(0.284739\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 13394.6 | − | 13394.6i | 0.479226 | − | 0.479226i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 1795.47 | − | 1795.47i | 0.0640288 | − | 0.0640288i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 15853.1 | + | 15853.1i | 0.563508 | + | 0.563508i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | − | 18818.9i | − | 0.666767i | ||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 20106.2 | + | 20106.2i | 0.710077 | + | 0.710077i | 0.966551 | − | 0.256474i | \(-0.0825608\pi\) |
−0.256474 | + | 0.966551i | \(0.582561\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 43568.1 | 1.53371 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 2011.34i | 0.0705768i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −13262.8 | + | 1677.29i | −0.463892 | + | 0.0586667i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 14175.0i | 0.494212i | 0.968988 | + | 0.247106i | \(0.0794796\pi\) | ||||
−0.968988 | + | 0.247106i | \(0.920520\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 7976.66 | 0.277219 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −33557.7 | − | 33557.7i | −1.16254 | − | 1.16254i | −0.983918 | − | 0.178620i | \(-0.942837\pi\) |
−0.178620 | − | 0.983918i | \(-0.557163\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 37674.0i | − | 1.30099i | ||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −5237.50 | − | 5237.50i | −0.180292 | − | 0.180292i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 37237.0 | − | 37237.0i | 1.27776 | − | 1.27776i | 0.335842 | − | 0.941918i | \(-0.390979\pi\) |
0.941918 | − | 0.335842i | \(-0.109021\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −34003.6 | + | 34003.6i | −1.16312 | + | 1.16312i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −5373.24 | −0.183217 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 15886.0 | 0.539978 | 0.269989 | − | 0.962863i | \(-0.412980\pi\) | ||||
0.269989 | + | 0.962863i | \(0.412980\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −17030.4 | + | 17030.4i | −0.577058 | + | 0.577058i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 1521.53 | − | 1521.53i | 0.0513942 | − | 0.0513942i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −2743.71 | − | 2743.71i | −0.0923869 | − | 0.0923869i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 29507.0i | 0.990468i | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 20094.1 | + | 20094.1i | 0.672403 | + | 0.672403i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −21021.3 | −0.701242 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 22253.3i | 0.740040i | 0.929024 | + | 0.370020i | \(0.120649\pi\) | ||||
−0.929024 | + | 0.370020i | \(0.879351\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −23496.4 | − | 18220.6i | −0.778960 | − | 0.604055i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 10677.3i | − | 0.352886i | −0.984311 | − | 0.176443i | \(-0.943541\pi\) | ||
0.984311 | − | 0.176443i | \(-0.0564591\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 21364.0 | 0.703902 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −9177.65 | − | 9177.65i | −0.301456 | − | 0.301456i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − | 41948.5i | − | 1.37364i | −0.726826 | − | 0.686822i | \(-0.759005\pi\) | ||
0.726826 | − | 0.686822i | \(-0.240995\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −30661.9 | − | 30661.9i | −1.00098 | − | 1.00098i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −9297.33 | + | 9297.33i | −0.302590 | + | 0.302590i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −30718.5 | + | 30718.5i | −0.996713 | + | 0.996713i | −0.999995 | − | 0.00328142i | \(-0.998955\pi\) |
0.00328142 | + | 0.999995i | \(0.498955\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 11553.3 | 0.373724 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 8399.47 | 0.270880 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 17271.4 | − | 17271.4i | 0.555306 | − | 0.555306i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −42517.1 | + | 42517.1i | −1.36287 | + | 1.36287i | −0.492622 | + | 0.870243i | \(0.663961\pi\) |
−0.870243 | + | 0.492622i | \(0.836039\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 2067.05 | + | 2067.05i | 0.0660582 | + | 0.0660582i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 11351.8i | 0.361686i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −42498.1 | − | 42498.1i | −1.34998 | − | 1.34998i | −0.885677 | − | 0.464301i | \(-0.846306\pi\) |
−0.464301 | − | 0.885677i | \(-0.653694\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −35830.0 | −1.13475 |
(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 | 136.4.k.a.89.3 | yes | 14 | |
4.3 | odd | 2 | 272.4.o.g.225.5 | 14 | |||
17.8 | even | 8 | 2312.4.a.m.1.9 | 14 | |||
17.9 | even | 8 | 2312.4.a.m.1.6 | 14 | |||
17.13 | even | 4 | inner | 136.4.k.a.81.3 | ✓ | 14 | |
68.47 | odd | 4 | 272.4.o.g.81.5 | 14 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
136.4.k.a.81.3 | ✓ | 14 | 17.13 | even | 4 | inner | |
136.4.k.a.89.3 | yes | 14 | 1.1 | even | 1 | trivial | |
272.4.o.g.81.5 | 14 | 68.47 | odd | 4 | |||
272.4.o.g.225.5 | 14 | 4.3 | odd | 2 | |||
2312.4.a.m.1.6 | 14 | 17.9 | even | 8 | |||
2312.4.a.m.1.9 | 14 | 17.8 | even | 8 |