Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [128,4,Mod(33,128)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(128, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 3]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("128.33");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 128 = 2^{7} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 128.e (of order \(4\), degree \(2\), not 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: | \(7.55224448073\) |
Analytic rank: | \(0\) |
Dimension: | \(10\) |
Relative dimension: | \(5\) over \(\Q(i)\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{10} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{10} - 2x^{9} - x^{8} + 6x^{7} + 14x^{6} - 80x^{5} + 56x^{4} + 96x^{3} - 64x^{2} - 512x + 1024 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{9}]\) |
Coefficient ring index: | \( 2^{20} \) |
Twist minimal: | no (minimal twist has level 16) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 97.4 | ||
Root | \(-1.56339 + 1.24732i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 128.97 |
Dual form | 128.4.e.b.33.4 |
$q$-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 \(\left(\mathbb{Z}/128\mathbb{Z}\right)^\times\).
\(n\) | \(5\) | \(127\) |
\(\chi(n)\) | \(e\left(\frac{1}{4}\right)\) | \(1\) |
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 | ||||||||
\(3\) | 3.27139 | − | 3.27139i | 0.629578 | − | 0.629578i | −0.318384 | − | 0.947962i | \(-0.603140\pi\) |
0.947962 | + | 0.318384i | \(0.103140\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 12.6449 | + | 12.6449i | 1.13099 | + | 1.13099i | 0.990012 | + | 0.140981i | \(0.0450257\pi\) |
0.140981 | + | 0.990012i | \(0.454974\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 13.8754i | 0.749200i | 0.927187 | + | 0.374600i | \(0.122220\pi\) | ||||
−0.927187 | + | 0.374600i | \(0.877780\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 5.59607i | 0.207262i | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.54694 | − | 1.54694i | −0.0424019 | − | 0.0424019i | 0.685588 | − | 0.727990i | \(-0.259545\pi\) |
−0.727990 | + | 0.685588i | \(0.759545\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −32.7875 | + | 32.7875i | −0.699509 | + | 0.699509i | −0.964304 | − | 0.264796i | \(-0.914695\pi\) |
0.264796 | + | 0.964304i | \(0.414695\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 82.7326 | 1.42410 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 18.6531 | 0.266119 | 0.133060 | − | 0.991108i | \(-0.457520\pi\) | ||||
0.133060 | + | 0.991108i | \(0.457520\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 86.4042 | − | 86.4042i | 1.04329 | − | 1.04329i | 0.0442688 | − | 0.999020i | \(-0.485904\pi\) |
0.999020 | − | 0.0442688i | \(-0.0140958\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 45.3917 | + | 45.3917i | 0.471680 | + | 0.471680i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − | 134.006i | − | 1.21488i | −0.794367 | − | 0.607438i | \(-0.792197\pi\) | ||
0.794367 | − | 0.607438i | \(-0.207803\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 194.786i | 1.55829i | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 106.634 | + | 106.634i | 0.760066 | + | 0.760066i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 59.7949 | − | 59.7949i | 0.382884 | − | 0.382884i | −0.489256 | − | 0.872140i | \(-0.662732\pi\) |
0.872140 | + | 0.489256i | \(0.162732\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −31.5391 | −0.182729 | −0.0913645 | − | 0.995818i | \(-0.529123\pi\) | ||||
−0.0913645 | + | 0.995818i | \(0.529123\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −10.1213 | −0.0533906 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −175.453 | + | 175.453i | −0.847340 | + | 0.847340i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −89.1866 | − | 89.1866i | −0.396275 | − | 0.396275i | 0.480642 | − | 0.876917i | \(-0.340404\pi\) |
−0.876917 | + | 0.480642i | \(0.840404\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 214.521i | 0.880791i | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 210.504i | − | 0.801834i | −0.916114 | − | 0.400917i | \(-0.868692\pi\) | ||
0.916114 | − | 0.400917i | \(-0.131308\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −119.402 | − | 119.402i | −0.423456 | − | 0.423456i | 0.462936 | − | 0.886392i | \(-0.346796\pi\) |
−0.886392 | + | 0.462936i | \(0.846796\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −70.7617 | + | 70.7617i | −0.234412 | + | 0.234412i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −182.902 | −0.567638 | −0.283819 | − | 0.958878i | \(-0.591602\pi\) | ||||
−0.283819 | + | 0.958878i | \(0.591602\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 150.474 | 0.438699 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 61.0213 | − | 61.0213i | 0.167543 | − | 0.167543i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 26.1644 | + | 26.1644i | 0.0678104 | + | 0.0678104i | 0.740199 | − | 0.672388i | \(-0.234731\pi\) |
−0.672388 | + | 0.740199i | \(0.734731\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 39.1219i | − | 0.0959125i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − | 565.323i | − | 1.31366i | ||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −441.584 | − | 441.584i | −0.974395 | − | 0.974395i | 0.0252856 | − | 0.999680i | \(-0.491950\pi\) |
−0.999680 | + | 0.0252856i | \(0.991950\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 174.485 | − | 174.485i | 0.366238 | − | 0.366238i | −0.499865 | − | 0.866103i | \(-0.666617\pi\) |
0.866103 | + | 0.499865i | \(0.166617\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −77.6476 | −0.155281 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −829.188 | −1.58228 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −91.7562 | + | 91.7562i | −0.167311 | + | 0.167311i | −0.785796 | − | 0.618486i | \(-0.787747\pi\) |
0.618486 | + | 0.785796i | \(0.287747\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −438.385 | − | 438.385i | −0.764860 | − | 0.764860i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 348.360i | 0.582291i | 0.956679 | + | 0.291146i | \(0.0940364\pi\) | ||||
−0.956679 | + | 0.291146i | \(0.905964\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 299.436i | − | 0.480087i | −0.970762 | − | 0.240043i | \(-0.922838\pi\) | ||
0.970762 | − | 0.240043i | \(-0.0771617\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 637.222 | + | 637.222i | 0.981067 | + | 0.981067i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 21.4644 | − | 21.4644i | 0.0317675 | − | 0.0317675i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −943.487 | −1.34368 | −0.671839 | − | 0.740697i | \(-0.734495\pi\) | ||||
−0.671839 | + | 0.740697i | \(0.734495\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 546.590 | 0.749781 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −313.272 | + | 313.272i | −0.414290 | + | 0.414290i | −0.883230 | − | 0.468940i | \(-0.844636\pi\) |
0.468940 | + | 0.883230i | \(0.344636\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 235.866 | + | 235.866i | 0.300979 | + | 0.300979i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | − | 391.224i | − | 0.482111i | ||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 1412.35i | 1.68212i | 0.540942 | + | 0.841060i | \(0.318068\pi\) | ||||
−0.540942 | + | 0.841060i | \(0.681932\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −454.939 | − | 454.939i | −0.524072 | − | 0.524072i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −103.177 | + | 103.177i | −0.115042 | + | 0.115042i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 2185.14 | 2.35990 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1515.29 | 1.58613 | 0.793063 | − | 0.609140i | \(-0.208485\pi\) | ||||
0.793063 | + | 0.609140i | \(0.208485\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 8.65680 | − | 8.65680i | 0.00878830 | − | 0.00878830i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 573.202 | + | 573.202i | 0.564711 | + | 0.564711i | 0.930642 | − | 0.365931i | \(-0.119249\pi\) |
−0.365931 | + | 0.930642i | \(0.619249\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 1021.00i | − | 0.976717i | −0.872643 | − | 0.488359i | \(-0.837596\pi\) | ||
0.872643 | − | 0.488359i | \(-0.162404\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 1147.95i | 1.06693i | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 1240.79 | + | 1240.79i | 1.12105 | + | 1.12105i | 0.991584 | + | 0.129462i | \(0.0413251\pi\) |
0.129462 | + | 0.991584i | \(0.458675\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 108.629 | − | 108.629i | 0.0954565 | − | 0.0954565i | −0.657766 | − | 0.753222i | \(-0.728498\pi\) |
0.753222 | + | 0.657766i | \(0.228498\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −583.528 | −0.498973 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −1722.22 | −1.43374 | −0.716870 | − | 0.697207i | \(-0.754426\pi\) | ||||
−0.716870 | + | 0.697207i | \(0.754426\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1694.49 | − | 1694.49i | 1.37402 | − | 1.37402i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −183.481 | − | 183.481i | −0.144981 | − | 0.144981i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 258.818i | 0.199377i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | − | 1326.21i | − | 0.996404i | ||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −688.639 | − | 688.639i | −0.504817 | − | 0.504817i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −882.442 | + | 882.442i | −0.631424 | + | 0.631424i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 699.127 | 0.488484 | 0.244242 | − | 0.969714i | \(-0.421461\pi\) | ||||
0.244242 | + | 0.969714i | \(0.421461\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −781.219 | −0.533198 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −197.970 | + | 197.970i | −0.132036 | + | 0.132036i | −0.770036 | − | 0.638000i | \(-0.779762\pi\) |
0.638000 | + | 0.770036i | \(0.279762\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1198.89 | + | 1198.89i | 0.781632 | + | 0.781632i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 2696.76i | 1.71926i | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − | 271.386i | − | 0.169242i | −0.996413 | − | 0.0846209i | \(-0.973032\pi\) | ||
0.996413 | − | 0.0846209i | \(-0.0269679\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −459.937 | − | 459.937i | −0.280657 | − | 0.280657i | 0.552714 | − | 0.833371i | \(-0.313592\pi\) |
−0.833371 | + | 0.552714i | \(0.813592\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −598.343 | + | 598.343i | −0.357373 | + | 0.357373i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 101.441 | 0.0593210 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 1512.20 | 0.866079 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 492.258 | − | 492.258i | 0.276196 | − | 0.276196i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −605.772 | − | 605.772i | −0.333066 | − | 0.333066i | 0.520684 | − | 0.853750i | \(-0.325677\pi\) |
−0.853750 | + | 0.520684i | \(0.825677\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 3534.47i | − | 1.90484i | −0.304785 | − | 0.952421i | \(-0.598585\pi\) | ||
0.304785 | − | 0.952421i | \(-0.401415\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 104.384i | 0.0551564i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −398.809 | − | 398.809i | −0.206665 | − | 0.206665i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1233.54 | − | 1233.54i | 0.627051 | − | 0.627051i | −0.320274 | − | 0.947325i | \(-0.603775\pi\) |
0.947325 | + | 0.320274i | \(0.103775\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 171.187 | 0.0853839 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1859.38 | 0.910186 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −2569.36 | + | 2569.36i | −1.23465 | + | 1.23465i | −0.272494 | + | 0.962158i | \(0.587848\pi\) |
−0.962158 | + | 0.272494i | \(0.912152\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −127.983 | − | 127.983i | −0.0603845 | − | 0.0603845i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 3048.39i | 1.41252i | 0.707950 | + | 0.706262i | \(0.249620\pi\) | ||||
−0.707950 | + | 0.706262i | \(0.750380\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 46.9618i | 0.0213754i | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 483.524 | + | 483.524i | 0.216234 | + | 0.216234i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 1522.05 | − | 1522.05i | 0.668898 | − | 0.668898i | −0.288563 | − | 0.957461i | \(-0.593177\pi\) |
0.957461 | + | 0.288563i | \(0.0931773\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −2702.74 | −1.16747 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −2889.18 | −1.22692 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −302.258 | + | 302.258i | −0.126211 | + | 0.126211i | −0.767391 | − | 0.641180i | \(-0.778445\pi\) |
0.641180 | + | 0.767391i | \(0.278445\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −1696.94 | − | 1696.94i | −0.696865 | − | 0.696865i | 0.266868 | − | 0.963733i | \(-0.414011\pi\) |
−0.963733 | + | 0.266868i | \(0.914011\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − | 1141.62i | − | 0.461151i | ||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | − | 2255.51i | − | 0.896370i | ||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −28.8552 | − | 28.8552i | −0.0112840 | − | 0.0112840i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −1479.59 | + | 1479.59i | −0.569442 | + | 0.569442i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −4035.31 | −1.52872 | −0.764358 | − | 0.644792i | \(-0.776944\pi\) | ||||
−0.764358 | + | 0.644792i | \(0.776944\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −886.172 | −0.330508 | −0.165254 | − | 0.986251i | \(-0.552844\pi\) | ||||
−0.165254 | + | 0.986251i | \(0.552844\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −2712.59 | + | 2712.59i | −0.996169 | + | 0.996169i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −3270.12 | − | 3270.12i | −1.18267 | − | 1.18267i | −0.979049 | − | 0.203624i | \(-0.934728\pi\) |
−0.203624 | − | 0.979049i | \(-0.565272\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 222.513i | 0.0792639i | 0.999214 | + | 0.0396319i | \(0.0126185\pi\) | ||||
−0.999214 | + | 0.0396319i | \(0.987381\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 600.340i | 0.210670i | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 829.677 | + | 829.677i | 0.286857 | + | 0.286857i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 2661.80 | − | 2661.80i | 0.906868 | − | 0.906868i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 749.907 | 0.251798 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −267.325 | −0.0884748 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 3527.46 | − | 3527.46i | 1.15090 | − | 1.15090i | 0.164529 | − | 0.986372i | \(-0.447390\pi\) |
0.986372 | − | 0.164529i | \(-0.0526105\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 1139.62 | + | 1139.62i | 0.366598 | + | 0.366598i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | − | 3019.65i | − | 0.957852i | ||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 437.618i | − | 0.136901i | ||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −979.571 | − | 979.571i | −0.302252 | − | 0.302252i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −611.587 | + | 611.587i | −0.186153 | + | 0.186153i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 5841.90 | 1.75427 | 0.877136 | − | 0.480242i | \(-0.159451\pi\) | ||||
0.877136 | + | 0.480242i | \(0.159451\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −1090.04 | −0.322975 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 1129.54 | − | 1129.54i | 0.330265 | − | 0.330265i | −0.522422 | − | 0.852687i | \(-0.674971\pi\) |
0.852687 | + | 0.522422i | \(0.174971\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 2905.40 | + | 2905.40i | 0.838403 | + | 0.838403i | 0.988649 | − | 0.150246i | \(-0.0480065\pi\) |
−0.150246 | + | 0.988649i | \(0.548006\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | − | 140.437i | − | 0.0400003i | ||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 734.054i | − | 0.206393i | −0.994661 | − | 0.103196i | \(-0.967093\pi\) | ||
0.994661 | − | 0.103196i | \(-0.0329070\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −2312.78 | − | 2312.78i | −0.641995 | − | 0.641995i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −3086.51 | + | 3086.51i | −0.845951 | + | 0.845951i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −511.807 | −0.138519 | −0.0692595 | − | 0.997599i | \(-0.522064\pi\) | ||||
−0.0692595 | + | 0.997599i | \(0.522064\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 5920.31 | 1.58241 | 0.791204 | − | 0.611552i | \(-0.209455\pi\) | ||||
0.791204 | + | 0.611552i | \(0.209455\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −1091.02 | + | 1091.02i | −0.288020 | + | 0.288020i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 1902.73 | + | 1902.73i | 0.496166 | + | 0.496166i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 5665.95i | 1.45958i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 2049.67i | 0.521656i | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 309.332 | + | 309.332i | 0.0777883 | + | 0.0777883i | 0.744930 | − | 0.667142i | \(-0.232483\pi\) |
−0.667142 | + | 0.744930i | \(0.732483\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −207.300 | + | 207.300i | −0.0515131 | + | 0.0515131i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 1543.22 | 0.378980 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 323.723 | 0.0785730 | 0.0392865 | − | 0.999228i | \(-0.487491\pi\) | ||||
0.0392865 | + | 0.999228i | \(0.487491\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1237.50 | − | 1237.50i | 0.296890 | − | 0.296890i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 334.617 | + | 334.617i | 0.0793573 | + | 0.0793573i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 2689.15i | 0.630495i | 0.949009 | + | 0.315248i | \(0.102088\pi\) | ||||
−0.949009 | + | 0.315248i | \(0.897912\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 661.691i | 0.153386i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 4620.34 | + | 4620.34i | 1.05903 | + | 1.05903i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −4703.78 | + | 4703.78i | −1.06615 | + | 1.06615i | −0.0684995 | + | 0.997651i | \(0.521821\pi\) |
−0.997651 | + | 0.0684995i | \(0.978179\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −2018.97 | −0.452561 | −0.226280 | − | 0.974062i | \(-0.572657\pi\) | ||||
−0.226280 | + | 0.974062i | \(0.572657\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −2976.56 | −0.659889 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 301.324 | − | 301.324i | 0.0660745 | − | 0.0660745i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 3080.60 | + | 3080.60i | 0.668215 | + | 0.668215i | 0.957303 | − | 0.289088i | \(-0.0933519\pi\) |
−0.289088 | + | 0.957303i | \(0.593352\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | − | 176.495i | − | 0.0378728i | ||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 3893.51i | 0.826575i | 0.910601 | + | 0.413287i | \(0.135619\pi\) | ||||
−0.910601 | + | 0.413287i | \(0.864381\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −2026.38 | − | 2026.38i | −0.425639 | − | 0.425639i | 0.461501 | − | 0.887140i | \(-0.347311\pi\) |
−0.887140 | + | 0.461501i | \(0.847311\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 7148.45 | − | 7148.45i | 1.48575 | − | 1.48575i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 2920.82 | 0.600734 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −4565.06 | −0.929180 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 4957.09 | − | 4957.09i | 0.998591 | − | 0.998591i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 1001.68 | + | 1001.68i | 0.199724 | + | 0.199724i | 0.799882 | − | 0.600158i | \(-0.204896\pi\) |
−0.600158 | + | 0.799882i | \(0.704896\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − | 11167.6i | − | 2.20407i | ||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | − | 329.914i | − | 0.0644565i | ||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 4393.72 | + | 4393.72i | 0.849817 | + | 0.849817i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1656.75 | − | 1656.75i | 0.317253 | − | 0.317253i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 3750.33 | 0.711059 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 4412.69 | 0.828425 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −2966.54 | + | 2966.54i | −0.551497 | + | 0.551497i | −0.926873 | − | 0.375376i | \(-0.877514\pi\) |
0.375376 | + | 0.926873i | \(0.377514\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −3340.08 | − | 3340.08i | −0.614920 | − | 0.614920i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 2911.18i | − | 0.530797i | −0.964139 | − | 0.265399i | \(-0.914496\pi\) | ||
0.964139 | − | 0.265399i | \(-0.0855036\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 8287.74i | 1.49665i | 0.663333 | + | 0.748324i | \(0.269141\pi\) | ||||
−0.663333 | + | 0.748324i | \(0.730859\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −981.845 | − | 981.845i | −0.175621 | − | 0.175621i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −5742.18 | + | 5742.18i | −1.01739 | + | 1.01739i | −0.0175452 | + | 0.999846i | \(0.505585\pi\) |
−0.999846 | + | 0.0175452i | \(0.994415\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −184.999 | −0.0324700 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 8118.23 | 1.41157 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 1611.70 | − | 1611.70i | 0.277639 | − | 0.277639i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −6386.56 | − | 6386.56i | −1.09004 | − | 1.09004i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | − | 710.734i | − | 0.120195i | ||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | − | 2537.84i | − | 0.425275i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −4499.27 | − | 4499.27i | −0.747136 | − | 0.747136i | 0.226804 | − | 0.973940i | \(-0.427172\pi\) |
−0.973940 | + | 0.226804i | \(0.927172\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 499.095 | − | 499.095i | 0.0821328 | − | 0.0821328i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −2320.50 | −0.378454 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −5860.06 | −0.947234 | −0.473617 | − | 0.880731i | \(-0.657052\pi\) | ||||
−0.473617 | + | 0.880731i | \(0.657052\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −5634.04 | + | 5634.04i | −0.902652 | + | 0.902652i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 48.7893 | + | 48.7893i | 0.00774806 | + | 0.00774806i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 6847.14i | 1.07787i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | − | 11086.7i | − | 1.73010i | ||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 2029.11 | + | 2029.11i | 0.313915 | + | 0.313915i | 0.846424 | − | 0.532509i | \(-0.178751\pi\) |
−0.532509 | + | 0.846424i | \(0.678751\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 1943.26 | − | 1943.26i | 0.298053 | − | 0.298053i | −0.542198 | − | 0.840251i | \(-0.682408\pi\) |
0.840251 | + | 0.542198i | \(0.182408\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −6992.54 | −1.06335 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −7548.63 | −1.13817 | −0.569084 | − | 0.822280i | \(-0.692702\pi\) | ||||
−0.569084 | + | 0.822280i | \(0.692702\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −4404.97 | + | 4404.97i | −0.658568 | + | 0.658568i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 846.694 | + | 846.694i | 0.125523 | + | 0.125523i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 5554.15i | 0.816537i | 0.912862 | + | 0.408269i | \(0.133867\pi\) | ||||
−0.912862 | + | 0.408269i | \(0.866133\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | − | 8072.37i | − | 1.17690i | ||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −4338.56 | − | 4338.56i | −0.627315 | − | 0.627315i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 3786.34 | − | 3786.34i | 0.542975 | − | 0.542975i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −3610.98 | −0.513601 | −0.256800 | − | 0.966464i | \(-0.582668\pi\) | ||||
−0.256800 | + | 0.966464i | \(0.582668\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 1177.99 | 0.166190 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −363.040 | + | 363.040i | −0.0508035 | + | 0.0508035i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −1215.49 | − | 1215.49i | −0.168728 | − | 0.168728i | 0.617692 | − | 0.786420i | \(-0.288068\pi\) |
−0.786420 | + | 0.617692i | \(0.788068\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 5773.62i | 0.795062i | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 3921.05i | 0.535661i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 7347.81 | + | 7347.81i | 0.995861 | + | 0.995861i | 0.999991 | − | 0.00413018i | \(-0.00131468\pi\) |
−0.00413018 | + | 0.999991i | \(0.501315\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 2287.12 | − | 2287.12i | 0.307539 | − | 0.307539i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −7668.98 | −1.02315 | −0.511575 | − | 0.859238i | \(-0.670938\pi\) | ||||
−0.511575 | + | 0.859238i | \(0.670938\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 542.831 | 0.0718577 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 668.181 | − | 668.181i | 0.0877663 | − | 0.0877663i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 200.924 | + | 200.924i | 0.0261884 | + | 0.0261884i | 0.720080 | − | 0.693891i | \(-0.244105\pi\) |
−0.693891 | + | 0.720080i | \(0.744105\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 2499.62i | − | 0.323302i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 1295.27i | 0.166254i | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −11930.3 | − | 11930.3i | −1.51969 | − | 1.51969i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −6512.21 | + | 6512.21i | −0.823271 | + | 0.823271i | −0.986576 | − | 0.163305i | \(-0.947785\pi\) |
0.163305 | + | 0.986576i | \(0.447785\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 7844.07 | 0.984197 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 5565.10 | 0.693036 | 0.346518 | − | 0.938043i | \(-0.387364\pi\) | ||||
0.346518 | + | 0.938043i | \(0.387364\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1034.09 | − | 1034.09i | 0.127820 | − | 0.127820i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 6911.57 | + | 6911.57i | 0.847997 | + | 0.847997i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 275.933i | 0.0336057i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 12077.6i | − | 1.46014i | −0.683370 | − | 0.730072i | \(-0.739486\pi\) | ||
0.683370 | − | 0.730072i | \(-0.260514\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −887.810 | − | 887.810i | −0.106551 | − | 0.106551i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 6127.14 | − | 6127.14i | 0.730017 | − | 0.730017i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −7922.58 | −0.937119 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −3009.26 | −0.353391 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 1453.03 | − | 1453.03i | 0.169415 | − | 0.169415i | −0.617307 | − | 0.786722i | \(-0.711776\pi\) |
0.786722 | + | 0.617307i | \(0.211776\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 4822.25 | + | 4822.25i | 0.558247 | + | 0.558247i | 0.928808 | − | 0.370561i | \(-0.120835\pi\) |
−0.370561 | + | 0.928808i | \(0.620835\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | − | 1023.53i | − | 0.117650i | ||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 3633.36i | 0.414692i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 2421.04 | + | 2421.04i | 0.274385 | + | 0.274385i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 331.852 | − | 331.852i | 0.0373472 | − | 0.0373472i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 12519.2 | 1.39914 | 0.699571 | − | 0.714563i | \(-0.253374\pi\) | ||||
0.699571 | + | 0.714563i | \(0.253374\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −2921.40 | −0.324235 | −0.162117 | − | 0.986771i | \(-0.551832\pi\) | ||||
−0.162117 | + | 0.986771i | \(0.551832\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 4946.99 | − | 4946.99i | 0.545264 | − | 0.545264i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −11578.7 | − | 11578.7i | −1.26747 | − | 1.26747i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 1140.50i | 0.123993i | 0.998076 | + | 0.0619967i | \(0.0197468\pi\) | ||||
−0.998076 | + | 0.0619967i | \(0.980253\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 842.062i | 0.0909256i | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 1843.05 | + | 1843.05i | 0.197665 | + | 0.197665i | 0.798999 | − | 0.601333i | \(-0.205363\pi\) |
−0.601333 | + | 0.798999i | \(0.705363\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −17859.0 | + | 17859.0i | −1.90247 | + | 1.90247i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −3963.43 | −0.419382 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 1752.13 | 0.184161 | 0.0920805 | − | 0.995752i | \(-0.470648\pi\) | ||||
0.0920805 | + | 0.995752i | \(0.470648\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −325.637 | + | 325.637i | −0.0339993 | + | 0.0339993i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −11562.6 | − | 11562.6i | −1.19925 | − | 1.19925i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | − | 11505.3i | − | 1.18544i | ||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 12875.6i | 1.31794i | 0.752171 | + | 0.658968i | \(0.229007\pi\) | ||||
−0.752171 | + | 0.658968i | \(0.770993\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 1989.06 | + | 1989.06i | 0.202268 | + | 0.202268i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 13679.7 | − | 13679.7i | 1.38205 | − | 1.38205i | 0.541085 | − | 0.840968i | \(-0.318014\pi\) |
0.840968 | − | 0.541085i | \(-0.181986\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 15002.4 | 1.50588 | 0.752938 | − | 0.658091i | \(-0.228636\pi\) | ||||
0.752938 | + | 0.658091i | \(0.228636\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −2609.32 | −0.260224 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −9669.42 | + | 9669.42i | −0.958131 | + | 0.958131i | −0.999158 | − | 0.0410271i | \(-0.986937\pi\) |
0.0410271 | + | 0.999158i | \(0.486937\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −1273.15 | − | 1273.15i | −0.125349 | − | 0.125349i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | − | 8070.75i | − | 0.789555i | ||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 369.416i | 0.0359107i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 16830.4 | + | 16830.4i | 1.62575 | + | 1.62575i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −146.418 | + | 146.418i | −0.0140545 | + | 0.0140545i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −3072.68 | −0.293099 | −0.146550 | − | 0.989203i | \(-0.546817\pi\) | ||||
−0.146550 | + | 0.989203i | \(0.546817\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 5848.41 | 0.554396 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 6082.76 | − | 6082.76i | 0.573033 | − | 0.573033i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 19160.7 | + | 19160.7i | 1.79390 | + | 1.79390i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 8689.64i | 0.808553i | 0.914637 | + | 0.404276i | \(0.132477\pi\) | ||||
−0.914637 | + | 0.404276i | \(0.867523\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 16810.8i | 1.55462i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −11194.3 | − | 11194.3i | −1.02891 | − | 1.02891i | −0.999570 | − | 0.0293379i | \(-0.990660\pi\) |
−0.0293379 | − | 0.999570i | \(-0.509340\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 1115.36 | − | 1115.36i | 0.101893 | − | 0.101893i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 218.929 | 0.0198790 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −4833.62 | −0.436253 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 1632.72 | − | 1632.72i | 0.146474 | − | 0.146474i | −0.630067 | − | 0.776541i | \(-0.716973\pi\) |
0.776541 | + | 0.630067i | \(0.216973\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 9972.47 | + | 9972.47i | 0.889295 | + | 0.889295i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − | 6901.81i | − | 0.611802i | −0.952063 | − | 0.305901i | \(-0.901042\pi\) | ||
0.952063 | − | 0.305901i | \(-0.0989577\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 14496.2i | 1.27737i | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 153.630 | + | 153.630i | 0.0134575 | + | 0.0134575i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −92.9712 | + | 92.9712i | −0.00809603 | + | 0.00809603i | −0.711143 | − | 0.703047i | \(-0.751822\pi\) |
0.703047 | + | 0.711143i | \(0.251822\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 4154.79 | 0.359681 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 18427.3 | 1.58594 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 12910.4 | − | 12910.4i | 1.10466 | − | 1.10466i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 282.939 | + | 282.939i | 0.0240689 | + | 0.0240689i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | − | 9958.43i | − | 0.842248i | ||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 11931.3i | − | 1.00330i | −0.865071 | − | 0.501649i | \(-0.832727\pi\) | ||
0.865071 | − | 0.501649i | \(-0.167273\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 9702.46 | + | 9702.46i | 0.811203 | + | 0.811203i | 0.984814 | − | 0.173611i | \(-0.0555437\pi\) |
−0.173611 | + | 0.984814i | \(0.555544\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −8841.69 | + | 8841.69i | −0.735015 | + | 0.735015i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −588.301 | −0.0486277 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −5790.59 | −0.475926 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 2471.13 | − | 2471.13i | 0.201955 | − | 0.201955i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 6901.89 | + | 6901.89i | 0.560889 | + | 0.560889i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 31379.4i | 2.53579i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 1977.60i | 0.158920i | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −232.774 | − | 232.774i | −0.0186017 | − | 0.0186017i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 8556.67 | − | 8556.67i | 0.680000 | − | 0.680000i | −0.280000 | − | 0.960000i | \(-0.590334\pi\) |
0.960000 | + | 0.280000i | \(0.0903345\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −11102.7 | −0.877462 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 2747.20 | 0.215921 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 45.1953 | − | 45.1953i | 0.00353274 | − | 0.00353274i | −0.705338 | − | 0.708871i | \(-0.749205\pi\) |
0.708871 | + | 0.705338i | \(0.249205\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 976.430 | + | 976.430i | 0.0759071 | + | 0.0759071i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 10333.1i | − | 0.798917i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − | 13091.2i | − | 1.00668i | ||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −7378.64 | − | 7378.64i | −0.564335 | − | 0.564335i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −4279.60 | + | 4279.60i | −0.325552 | + | 0.325552i | −0.850892 | − | 0.525340i | \(-0.823938\pi\) |
0.525340 | + | 0.850892i | \(0.323938\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 7829.77 | 0.592422 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −188.793 | −0.0142083 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −14593.9 | + | 14593.9i | −1.09247 | + | 1.09247i | −0.0972023 | + | 0.995265i | \(0.530989\pi\) |
−0.995265 | + | 0.0972023i | \(0.969011\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −21777.3 | − | 21777.3i | −1.62155 | − | 1.62155i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 7584.14i | 0.561736i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 21728.1i | − | 1.60086i | −0.599425 | − | 0.800431i | \(-0.704604\pi\) | ||
0.599425 | − | 0.800431i | \(-0.295396\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −16078.0 | − | 16078.0i | −1.17836 | − | 1.17836i | −0.980161 | − | 0.198202i | \(-0.936490\pi\) |
−0.198202 | − | 0.980161i | \(-0.563510\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −13201.0 | + | 13201.0i | −0.962446 | + | 0.962446i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 26102.5 | 1.89313 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −26648.2 | −1.92267 | −0.961335 | − | 0.275383i | \(-0.911195\pi\) | ||||
−0.961335 | + | 0.275383i | \(0.911195\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −2899.01 | + | 2899.01i | −0.208081 | + | 0.208081i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −4346.77 | − | 4346.77i | −0.310386 | − | 0.310386i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 80.9495i | − | 0.00575058i | ||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | − | 4640.20i | − | 0.327946i | ||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −1342.62 | − | 1342.62i | −0.0944050 | − | 0.0944050i | 0.658327 | − | 0.752732i | \(-0.271264\pi\) |
−0.752732 | + | 0.658327i | \(0.771264\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −2725.11 | + | 2725.11i | −0.190639 | + | 0.190639i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −21395.7 | −1.48917 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 4474.79 | 0.309878 | 0.154939 | − | 0.987924i | \(-0.450482\pi\) | ||||
0.154939 | + | 0.987924i | \(0.450482\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −3272.73 | + | 3272.73i | −0.225494 | + | 0.225494i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 727.925 | + | 727.925i | 0.0499028 | + | 0.0499028i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 12603.8i | 0.859725i | 0.902894 | + | 0.429863i | \(0.141438\pi\) | ||||
−0.902894 | + | 0.429863i | \(0.858562\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 7220.64i | 0.490077i | 0.969513 | + | 0.245038i | \(0.0788006\pi\) | ||||
−0.969513 | + | 0.245038i | \(0.921199\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −513.474 | − | 513.474i | −0.0346771 | − | 0.0346771i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 16769.8 | − | 16769.8i | 1.12693 | − | 1.12693i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −13695.6 | −0.915796 | −0.457898 | − | 0.889005i | \(-0.651397\pi\) | ||||
−0.457898 | + | 0.889005i | \(0.651397\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 5428.39 | 0.361198 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 5996.90 | − | 5996.90i | 0.397068 | − | 0.397068i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 2358.34 | + | 2358.34i | 0.155387 | + | 0.155387i | 0.780519 | − | 0.625132i | \(-0.214955\pi\) |
−0.625132 | + | 0.780519i | \(0.714955\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | − | 17415.5i | − | 1.14189i | ||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 4186.39i | 0.273157i | 0.990629 | + | 0.136579i | \(0.0436106\pi\) | ||||
−0.990629 | + | 0.136579i | \(0.956389\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 4800.50 | + | 4800.50i | 0.311710 | + | 0.311710i | 0.845572 | − | 0.533862i | \(-0.179260\pi\) |
−0.533862 | + | 0.845572i | \(0.679260\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 14289.6 | − | 14289.6i | 0.923387 | − | 0.923387i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −19596.9 | −1.26024 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 2031.54 | 0.130018 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −874.522 | + | 874.522i | −0.0557018 | + | 0.0557018i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −1663.60 | − | 1663.60i | −0.105457 | − | 0.105457i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 16106.3i | − | 1.01614i | −0.861316 | − | 0.508069i | \(-0.830360\pi\) | ||
0.861316 | − | 0.508069i | \(-0.169640\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | − | 23079.3i | − | 1.44917i | ||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 8840.39 | + | 8840.39i | 0.552473 | + | 0.552473i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −4933.66 | + | 4933.66i | −0.306874 | + | 0.306874i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −1949.45 | −0.120687 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −6682.21 | −0.411749 | −0.205875 | − | 0.978578i | \(-0.566004\pi\) | ||||
−0.205875 | + | 0.978578i | \(0.566004\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 4983.47 | − | 4983.47i | 0.305644 | − | 0.305644i | −0.537573 | − | 0.843217i | \(-0.680659\pi\) |
0.843217 | + | 0.537573i | \(0.180659\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −9878.43 | − | 9878.43i | −0.603043 | − | 0.603043i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 5078.45i | 0.308585i | 0.988025 | + | 0.154292i | \(0.0493098\pi\) | ||||
−0.988025 | + | 0.154292i | \(0.950690\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 1366.21i | 0.0826324i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −1431.62 | − | 1431.62i | −0.0861896 | − | 0.0861896i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −6189.91 | + | 6189.91i | −0.370949 | + | 0.370949i | −0.867823 | − | 0.496874i | \(-0.834481\pi\) |
0.496874 | + | 0.867823i | \(0.334481\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −5006.62 | −0.298664 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 1675.67 | 0.0995037 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −5751.19 | + | 5751.19i | −0.339962 | + | 0.339962i | −0.856353 | − | 0.516391i | \(-0.827275\pi\) |
0.516391 | + | 0.856353i | \(0.327275\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 6305.38 | + | 6305.38i | 0.371030 | + | 0.371030i | 0.867852 | − | 0.496822i | \(-0.165500\pi\) |
−0.496822 | + | 0.867852i | \(0.665500\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 4001.47i | 0.234396i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 30319.7i | 1.76804i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −8012.87 | − | 8012.87i | −0.465157 | − | 0.465157i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 19111.1 | − | 19111.1i | 1.10445 | − | 1.10445i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −539.837 | −0.0310584 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 14664.4 | 0.839925 | 0.419963 | − | 0.907541i | \(-0.362043\pi\) | ||||
0.419963 | + | 0.907541i | \(0.362043\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −20770.9 | + | 20770.9i | −1.18440 | + | 1.18440i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −5795.16 | − | 5795.16i | −0.328990 | − | 0.328990i | 0.523212 | − | 0.852202i | \(-0.324733\pi\) |
−0.852202 | + | 0.523212i | \(0.824733\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 21025.2i | 1.18833i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | − | 7390.32i | − | 0.415855i | ||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 13134.1 | + | 13134.1i | 0.735816 | + | 0.735816i | 0.971765 | − | 0.235950i | \(-0.0758200\pi\) |
−0.235950 | + | 0.971765i | \(0.575820\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 3431.65 | − | 3431.65i | 0.191411 | − | 0.191411i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 19009.4 | 1.05568 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −1715.73 | −0.0948679 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −14324.0 | + | 14324.0i | −0.788583 | + | 0.788583i | −0.981262 | − | 0.192679i | \(-0.938282\pi\) |
0.192679 | + | 0.981262i | \(0.438282\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 120.116 | + | 120.116i | 0.00658419 | + | 0.00658419i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | − | 11631.7i | − | 0.634843i | ||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 3926.54i | − | 0.213383i | ||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −2401.37 | − | 2401.37i | −0.129940 | − | 0.129940i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −15987.2 | + | 15987.2i | −0.861382 | + | 0.861382i | −0.991499 | − | 0.130117i | \(-0.958465\pi\) |
0.130117 | + | 0.991499i | \(0.458465\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −15412.2 | −0.826859 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −15132.0 | −0.808373 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −7953.40 | + | 7953.40i | −0.423081 | + | 0.423081i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −19580.4 | − | 19580.4i | −1.03718 | − | 1.03718i | −0.999282 | − | 0.0378960i | \(-0.987934\pi\) |
−0.0378960 | − | 0.999282i | \(-0.512066\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | − | 5279.82i | − | 0.278493i | ||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 4226.43i | 0.221993i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1282.71 | + | 1282.71i | 0.0670916 | + | 0.0670916i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −1674.32 | + | 1674.32i | −0.0872085 | + | 0.0872085i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −2111.24 | −0.109507 | −0.0547537 | − | 0.998500i | \(-0.517437\pi\) | ||||
−0.0547537 | + | 0.998500i | \(0.517437\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 14166.7 | 0.731757 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 19367.6 | − | 19367.6i | 0.996250 | − | 0.996250i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 11647.2 | + | 11647.2i | 0.596645 | + | 0.596645i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 14763.6i | − | 0.753164i | −0.926383 | − | 0.376582i | \(-0.877099\pi\) | ||
0.926383 | − | 0.376582i | \(-0.122901\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 21896.2i | 1.11244i | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −2227.21 | − | 2227.21i | −0.112690 | − | 0.112690i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −3419.77 | + | 3419.77i | −0.172322 | + | 0.172322i | −0.787999 | − | 0.615677i | \(-0.788883\pi\) |
0.615677 | + | 0.787999i | \(0.288883\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 12449.1 | 0.624751 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 283.883 | 0.0141886 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 11324.8 | − | 11324.8i | 0.563723 | − | 0.563723i | −0.366640 | − | 0.930363i | \(-0.619492\pi\) |
0.930363 | + | 0.366640i | \(0.119492\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 18535.5 | + | 18535.5i | 0.918919 | + | 0.918919i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 20313.3i | 1.00299i | 0.865160 | + | 0.501495i | \(0.167217\pi\) | ||||
−0.865160 | + | 0.501495i | \(0.832783\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | − | 15319.9i | − | 0.753391i | ||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −1753.09 | − | 1753.09i | −0.0858665 | − | 0.0858665i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −17216.5 | + | 17216.5i | −0.839888 | + | 0.839888i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 28755.3 | 1.39720 | 0.698598 | − | 0.715514i | \(-0.253808\pi\) | ||||
0.698598 | + | 0.715514i | \(0.253808\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 2023.89 | 0.0979477 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 44693.0 | − | 44693.0i | 2.15436 | − | 2.15436i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 23006.0 | + | 23006.0i | 1.10458 | + | 1.10458i | 0.993850 | + | 0.110730i | \(0.0353190\pi\) |
0.110730 | + | 0.993850i | \(0.464681\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 1356.31i | 0.0648631i | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 9298.53i | − | 0.442932i | −0.975168 | − | 0.221466i | \(-0.928916\pi\) | ||
0.975168 | − | 0.221466i | \(-0.0710843\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 1507.27 | + | 1507.27i | 0.0715160 | + | 0.0715160i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −1319.92 | + | 1319.92i | −0.0623815 | + | 0.0623815i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 28956.8 | 1.36319 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −20402.0 | −0.956717 | −0.478358 | − | 0.878165i | \(-0.658768\pi\) | ||||
−0.478358 | + | 0.878165i | \(0.658768\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 1059.02 | − | 1059.02i | 0.0494679 | − | 0.0494679i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −7337.03 | − | 7337.03i | −0.341390 | − | 0.341390i | 0.515500 | − | 0.856890i | \(-0.327606\pi\) |
−0.856890 | + | 0.515500i | \(0.827606\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 6143.40i | − | 0.284745i | ||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | − | 8096.67i | − | 0.373831i | ||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −18188.4 | − | 18188.4i | −0.836544 | − | 0.836544i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 538.893 | − | 538.893i | 0.0246903 | − | 0.0246903i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 12752.4 | 0.582034 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 31195.9 | 1.41838 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 11928.6 | − | 11928.6i | 0.540292 | − | 0.540292i | −0.383323 | − | 0.923615i | \(-0.625220\pi\) |
0.923615 | + | 0.383323i | \(0.125220\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 8797.25 | + | 8797.25i | 0.396946 | + | 0.396946i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 23896.4i | − | 1.07416i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 11441.8i | 0.512373i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 2164.65 | + | 2164.65i | 0.0965686 | + | 0.0965686i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 6576.18 | − | 6576.18i | 0.292271 | − | 0.292271i | −0.545706 | − | 0.837977i | \(-0.683738\pi\) |
0.837977 | + | 0.545706i | \(0.183738\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −3411.68 | −0.151060 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −7903.61 | −0.348639 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −463.211 | + | 463.211i | −0.0203566 | + | 0.0203566i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 23511.7 | + | 23511.7i | 1.02941 | + | 1.02941i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 30775.8i | 1.34245i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 29320.9i | 1.27425i | 0.770760 | + | 0.637126i | \(0.219877\pi\) | ||||
−0.770760 | + | 0.637126i | \(0.780123\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 14487.9 | + | 14487.9i | 0.627297 | + | 0.627297i | 0.947387 | − | 0.320090i | \(-0.103713\pi\) |
−0.320090 | + | 0.947387i | \(0.603713\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −6604.84 | + | 6604.84i | −0.284922 | + | 0.284922i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −64978.7 | −2.79276 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −20633.6 | −0.883574 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 2545.87 | − | 2545.87i | 0.108620 | − | 0.108620i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −20259.2 | − | 20259.2i | −0.861208 | − | 0.861208i | 0.130270 | − | 0.991479i | \(-0.458415\pi\) |
−0.991479 | + | 0.130270i | \(0.958415\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 24605.9i | − | 1.04217i | −0.853504 | − | 0.521086i | \(-0.825527\pi\) | ||
0.853504 | − | 0.521086i | \(-0.174473\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | − | 1971.49i | − | 0.0831982i | ||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 24095.8 | + | 24095.8i | 1.01317 | + | 1.01317i | 0.999912 | + | 0.0132601i | \(0.00422096\pi\) |
0.0132601 | + | 0.999912i | \(0.495779\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 914.616 | − | 914.616i | 0.0383184 | − | 0.0383184i | −0.687688 | − | 0.726006i | \(-0.741374\pi\) |
0.726006 | + | 0.687688i | \(0.241374\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 20155.7 | 0.841388 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 2806.80 | 0.116746 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −38546.6 | + | 38546.6i | −1.59756 | + | 1.59756i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −3363.16 | − | 3363.16i | −0.138886 | − | 0.138886i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 28847.5i | 1.18704i | 0.804819 | + | 0.593521i | \(0.202263\pi\) | ||||
−0.804819 | + | 0.593521i | \(0.797737\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 17238.1i | 0.706800i | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 12737.2 | + | 12737.2i | 0.520394 | + | 0.520394i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −593.827 | + | 593.827i | −0.0241755 | + | 0.0241755i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 18401.7 | 0.746506 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −13258.2 | −0.535947 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −11951.5 | + | 11951.5i | −0.481426 | + | 0.481426i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −41.5562 | − | 41.5562i | −0.00166806 | − | 0.00166806i | 0.706272 | − | 0.707940i | \(-0.250375\pi\) |
−0.707940 | + | 0.706272i | \(0.750375\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 12228.2i | 0.489118i | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − | 20953.6i | − | 0.835194i | −0.908632 | − | 0.417597i | \(-0.862872\pi\) | ||
0.908632 | − | 0.417597i | \(-0.137128\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −29316.3 | − | 29316.3i | −1.16444 | − | 1.16444i | −0.983492 | − | 0.180953i | \(-0.942082\pi\) |
−0.180953 | − | 0.983492i | \(-0.557918\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 9555.13 | − | 9555.13i | 0.378209 | − | 0.378209i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −3389.59 | −0.133700 | −0.0668499 | − | 0.997763i | \(-0.521295\pi\) | ||||
−0.0668499 | + | 0.997763i | \(0.521295\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 38492.3 | 1.51304 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −14934.1 | + | 14934.1i | −0.584992 | + | 0.584992i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 1459.52 | + | 1459.52i | 0.0569745 | + | 0.0569745i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 6016.91i | − | 0.234070i | ||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 8479.66i | 0.328743i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −12244.2 | − | 12244.2i | −0.473063 | − | 0.473063i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 13912.5 | − | 13912.5i | 0.535681 | − | 0.535681i | −0.386576 | − | 0.922257i | \(-0.626342\pi\) |
0.922257 | + | 0.386576i | \(0.126342\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 6553.79 | 0.251484 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −1497.48 | −0.0572660 | −0.0286330 | − | 0.999590i | \(-0.509115\pi\) | ||||
−0.0286330 | + | 0.999590i | \(0.509115\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 4143.81 | − | 4143.81i | 0.157928 | − | 0.157928i | −0.623720 | − | 0.781648i | \(-0.714379\pi\) |
0.781648 | + | 0.623720i | \(0.214379\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −36533.4 | − | 36533.4i | −1.38763 | − | 1.38763i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − | 18058.0i | − | 0.683573i | −0.939778 | − | 0.341787i | \(-0.888968\pi\) | ||
0.939778 | − | 0.341787i | \(-0.111032\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 9700.66i | 0.365973i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −845.544 | − | 845.544i | −0.0317921 | − | 0.0317921i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −15803.5 | + | 15803.5i | −0.592211 | + | 0.592211i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −7644.03 | −0.285488 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 28747.1 | 1.07005 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −1885.88 | + | 1885.88i | −0.0699640 | + | 0.0699640i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 488.045 | + | 488.045i | 0.0180457 | + | 0.0180457i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | − | 10839.7i | − | 0.399472i | ||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | − | 42915.2i | − | 1.57630i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 21423.5 | + | 21423.5i | 0.784295 | + | 0.784295i | 0.980552 | − | 0.196257i | \(-0.0628788\pi\) |
−0.196257 | + | 0.980552i | \(0.562879\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −3207.68 | + | 3207.68i | −0.117043 | + | 0.117043i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −31977.7 | −1.16297 | −0.581487 | − | 0.813556i | \(-0.697529\pi\) | ||||
−0.581487 | + | 0.813556i | \(0.697529\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 969.228 | 0.0351334 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 14435.6 | − | 14435.6i | 0.521559 | − | 0.521559i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −2746.91 | − | 2746.91i | −0.0989215 | − | 0.0989215i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 40696.7i | − | 1.46078i | −0.683029 | − | 0.730391i | \(-0.739338\pi\) | ||
0.683029 | − | 0.730391i | \(-0.260662\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 19409.4i | 0.694421i | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −11421.8 | − | 11421.8i | −0.407318 | − | 0.407318i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 17372.4 | − | 17372.4i | 0.617513 | − | 0.617513i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 5713.57 | 0.202436 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −11467.5 | −0.404989 | −0.202495 | − | 0.979283i | \(-0.564905\pi\) | ||||
−0.202495 | + | 0.979283i | \(0.564905\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 13001.6 | − | 13001.6i | 0.457690 | − | 0.457690i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −9523.60 | − | 9523.60i | −0.334179 | − | 0.334179i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | − | 729.742i | − | 0.0255242i | ||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 14100.2i | − | 0.491603i | −0.969320 | − | 0.245802i | \(-0.920949\pi\) | ||
0.969320 | − | 0.245802i | \(-0.0790512\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 27112.4 | + | 27112.4i | 0.942257 | + | 0.942257i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 21058.7 | − | 21058.7i | 0.729538 | − | 0.729538i | −0.240989 | − | 0.970528i | \(-0.577472\pi\) |
0.970528 | + | 0.240989i | \(0.0774719\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −28208.8 | −0.974129 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −37418.5 | −1.28807 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −24998.9 | + | 24998.9i | −0.857820 | + | 0.857820i | −0.991081 | − | 0.133261i | \(-0.957455\pi\) |
0.133261 | + | 0.991081i | \(0.457455\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 9817.75 | + | 9817.75i | 0.335825 | + | 0.335825i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 37569.8i | 1.28106i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 6456.01i | 0.219445i | 0.993962 | + | 0.109722i | \(0.0349961\pi\) | ||||
−0.993962 | + | 0.109722i | \(0.965004\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −51026.0 | − | 51026.0i | −1.72897 | − | 1.72897i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −605.202 | + | 605.202i | −0.0204424 | + | 0.0204424i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 3765.59 | 0.126796 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −28796.3 | −0.966610 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −6943.57 | + | 6943.57i | −0.232350 | + | 0.232350i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −11205.5 | − | 11205.5i | −0.373802 | − | 0.373802i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 15099.9i | 0.502153i | 0.967967 | + | 0.251076i | \(0.0807845\pi\) | ||||
−0.967967 | + | 0.251076i | \(0.919215\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | − | 10545.0i | − | 0.349591i | ||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 6223.12 | + | 6223.12i | 0.205674 | + | 0.205674i | 0.802426 | − | 0.596752i | \(-0.203542\pi\) |
−0.596752 | + | 0.802426i | \(0.703542\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 6381.80 | − | 6381.80i | 0.210268 | − | 0.210268i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −41785.8 | −1.37253 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −34900.0 | −1.14284 | −0.571418 | − | 0.820659i | \(-0.693607\pi\) | ||||
−0.571418 | + | 0.820659i | \(0.693607\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 2184.82 | − | 2184.82i | 0.0713251 | − | 0.0713251i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 607.895 | + | 607.895i | 0.0197845 | + | 0.0197845i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 21221.5i | 0.688567i | 0.938866 | + | 0.344283i | \(0.111878\pi\) | ||||
−0.938866 | + | 0.344283i | \(0.888122\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | − | 82700.7i | − | 2.67519i | ||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −8302.24 | − | 8302.24i | −0.267744 | − | 0.267744i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −16000.6 | + | 16000.6i | −0.514447 | + | 0.514447i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 23985.3 | 0.768838 | 0.384419 | − | 0.923159i | \(-0.374402\pi\) | ||||
0.384419 | + | 0.923159i | \(0.374402\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −29437.7 | −0.940761 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −2813.65 | + | 2813.65i | −0.0896469 | + | 0.0896469i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −10763.8 | − | 10763.8i | −0.341919 | − | 0.341919i | 0.515169 | − | 0.857088i | \(-0.327729\pi\) |
−0.857088 | + | 0.515169i | \(0.827729\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | − | 19020.7i | − | 0.602391i |
(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 | 128.4.e.b.97.4 | 10 | ||
4.3 | odd | 2 | 128.4.e.a.97.2 | 10 | |||
8.3 | odd | 2 | 64.4.e.a.49.4 | 10 | |||
8.5 | even | 2 | 16.4.e.a.5.5 | ✓ | 10 | ||
16.3 | odd | 4 | 128.4.e.a.33.2 | 10 | |||
16.5 | even | 4 | 16.4.e.a.13.5 | yes | 10 | ||
16.11 | odd | 4 | 64.4.e.a.17.4 | 10 | |||
16.13 | even | 4 | inner | 128.4.e.b.33.4 | 10 | ||
24.5 | odd | 2 | 144.4.k.a.37.1 | 10 | |||
24.11 | even | 2 | 576.4.k.a.433.5 | 10 | |||
32.3 | odd | 8 | 1024.4.a.m.1.3 | 10 | |||
32.5 | even | 8 | 1024.4.b.j.513.8 | 10 | |||
32.11 | odd | 8 | 1024.4.b.k.513.8 | 10 | |||
32.13 | even | 8 | 1024.4.a.n.1.3 | 10 | |||
32.19 | odd | 8 | 1024.4.a.m.1.8 | 10 | |||
32.21 | even | 8 | 1024.4.b.j.513.3 | 10 | |||
32.27 | odd | 8 | 1024.4.b.k.513.3 | 10 | |||
32.29 | even | 8 | 1024.4.a.n.1.8 | 10 | |||
48.5 | odd | 4 | 144.4.k.a.109.1 | 10 | |||
48.11 | even | 4 | 576.4.k.a.145.5 | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
16.4.e.a.5.5 | ✓ | 10 | 8.5 | even | 2 | ||
16.4.e.a.13.5 | yes | 10 | 16.5 | even | 4 | ||
64.4.e.a.17.4 | 10 | 16.11 | odd | 4 | |||
64.4.e.a.49.4 | 10 | 8.3 | odd | 2 | |||
128.4.e.a.33.2 | 10 | 16.3 | odd | 4 | |||
128.4.e.a.97.2 | 10 | 4.3 | odd | 2 | |||
128.4.e.b.33.4 | 10 | 16.13 | even | 4 | inner | ||
128.4.e.b.97.4 | 10 | 1.1 | even | 1 | trivial | ||
144.4.k.a.37.1 | 10 | 24.5 | odd | 2 | |||
144.4.k.a.109.1 | 10 | 48.5 | odd | 4 | |||
576.4.k.a.145.5 | 10 | 48.11 | even | 4 | |||
576.4.k.a.433.5 | 10 | 24.11 | even | 2 | |||
1024.4.a.m.1.3 | 10 | 32.3 | odd | 8 | |||
1024.4.a.m.1.8 | 10 | 32.19 | odd | 8 | |||
1024.4.a.n.1.3 | 10 | 32.13 | even | 8 | |||
1024.4.a.n.1.8 | 10 | 32.29 | even | 8 | |||
1024.4.b.j.513.3 | 10 | 32.21 | even | 8 | |||
1024.4.b.j.513.8 | 10 | 32.5 | even | 8 | |||
1024.4.b.k.513.3 | 10 | 32.27 | odd | 8 | |||
1024.4.b.k.513.8 | 10 | 32.11 | odd | 8 |