Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [384,4,Mod(191,384)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(384, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1, 1]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("384.191");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 384 = 2^{7} \cdot 3 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 384.f (of order \(2\), degree \(1\), 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: | \(22.6567334422\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | 8.0.77720518656.6 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 12x^{6} + 119x^{4} - 300x^{2} + 625 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{17}]\) |
Coefficient ring index: | \( 2^{18}\cdot 3^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 191.7 | ||
Root | \(-1.41864 + 0.819051i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 384.191 |
Dual form | 384.4.f.i.191.5 |
$q$-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 \(\left(\mathbb{Z}/384\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(133\) | \(257\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(-1\) |
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 | ||||||||
\(3\) | 4.89898 | + | 1.73205i | 0.942809 | + | 0.333333i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −16.2481 | −1.45327 | −0.726636 | − | 0.687023i | \(-0.758917\pi\) | ||||
−0.726636 | + | 0.687023i | \(0.758917\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 28.1425i | − | 1.51955i | −0.650185 | − | 0.759776i | \(-0.725309\pi\) | ||
0.650185 | − | 0.759776i | \(-0.274691\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 21.0000 | + | 16.9706i | 0.777778 | + | 0.628539i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 24.2487i | 0.664660i | 0.943163 | + | 0.332330i | \(0.107835\pi\) | ||||
−0.943163 | + | 0.332330i | \(0.892165\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 45.9565i | 0.980465i | 0.871592 | + | 0.490232i | \(0.163088\pi\) | ||||
−0.871592 | + | 0.490232i | \(0.836912\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −79.5990 | − | 28.1425i | −1.37016 | − | 0.484424i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 79.1960i | 1.12987i | 0.825134 | + | 0.564937i | \(0.191099\pi\) | ||||
−0.825134 | + | 0.564937i | \(0.808901\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −9.79796 | −0.118306 | −0.0591528 | − | 0.998249i | \(-0.518840\pi\) | ||||
−0.0591528 | + | 0.998249i | \(0.518840\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 48.7442 | − | 137.870i | 0.506517 | − | 1.43265i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 159.198 | 1.44326 | 0.721632 | − | 0.692277i | \(-0.243392\pi\) | ||||
0.721632 | + | 0.692277i | \(0.243392\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 139.000 | 1.11200 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 73.4847 | + | 119.512i | 0.523783 | + | 0.851852i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 113.737 | 0.728288 | 0.364144 | − | 0.931343i | \(-0.381362\pi\) | ||||
0.364144 | + | 0.931343i | \(0.381362\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 196.997i | 1.14135i | 0.821177 | + | 0.570674i | \(0.193318\pi\) | ||||
−0.821177 | + | 0.570674i | \(0.806682\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −42.0000 | + | 118.794i | −0.221553 | + | 0.626648i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 457.261i | 2.20832i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 321.696i | 1.42936i | 0.699450 | + | 0.714681i | \(0.253428\pi\) | ||||
−0.699450 | + | 0.714681i | \(0.746572\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −79.5990 | + | 225.140i | −0.326822 | + | 0.924391i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 316.784i | − | 1.20667i | −0.797489 | − | 0.603333i | \(-0.793839\pi\) | ||
0.797489 | − | 0.603333i | \(-0.206161\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 480.100 | 1.70266 | 0.851332 | − | 0.524627i | \(-0.175795\pi\) | ||||
0.851332 | + | 0.524627i | \(0.175795\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −341.210 | − | 275.739i | −1.13032 | − | 0.913439i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −449.000 | −1.30904 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −137.171 | + | 387.979i | −0.376624 | + | 1.06525i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −341.210 | −0.884316 | −0.442158 | − | 0.896937i | \(-0.645787\pi\) | ||||
−0.442158 | + | 0.896937i | \(0.645787\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 393.995i | − | 0.965932i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −48.0000 | − | 16.9706i | −0.111540 | − | 0.0394352i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 682.428i | 1.50584i | 0.658112 | + | 0.752920i | \(0.271355\pi\) | ||||
−0.658112 | + | 0.752920i | \(0.728645\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 45.9565i | 0.0964611i | 0.998836 | + | 0.0482305i | \(0.0153582\pi\) | ||||
−0.998836 | + | 0.0482305i | \(0.984642\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 477.594 | − | 590.992i | 0.955098 | − | 1.18187i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | − | 746.705i | − | 1.42488i | ||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −342.929 | −0.625304 | −0.312652 | − | 0.949868i | \(-0.601217\pi\) | ||||
−0.312652 | + | 0.949868i | \(0.601217\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 779.908 | + | 275.739i | 1.36072 | + | 0.481088i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −1114.39 | −1.86272 | −0.931361 | − | 0.364097i | \(-0.881378\pi\) | ||||
−0.931361 | + | 0.364097i | \(0.881378\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −98.0000 | −0.157124 | −0.0785619 | − | 0.996909i | \(-0.525033\pi\) | ||||
−0.0785619 | + | 0.996909i | \(0.525033\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 680.958 | + | 240.755i | 1.04840 | + | 0.370667i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 682.419 | 1.00999 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 140.712i | − | 0.200397i | −0.994967 | − | 0.100199i | \(-0.968052\pi\) | ||
0.994967 | − | 0.100199i | \(-0.0319478\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 153.000 | + | 712.764i | 0.209877 | + | 0.977728i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 924.915i | 1.22316i | 0.791181 | + | 0.611582i | \(0.209467\pi\) | ||||
−0.791181 | + | 0.611582i | \(0.790533\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | − | 1286.78i | − | 1.64201i | ||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 557.193 | + | 196.997i | 0.686636 | + | 0.242763i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 395.980i | − | 0.471615i | −0.971800 | − | 0.235808i | \(-0.924226\pi\) | ||
0.971800 | − | 0.235808i | \(-0.0757736\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1293.33 | 1.48987 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −341.210 | + | 965.087i | −0.380449 | + | 1.07607i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 159.198 | 0.171930 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 994.000 | 1.04047 | 0.520234 | − | 0.854024i | \(-0.325845\pi\) | ||||
0.520234 | + | 0.854024i | \(0.325845\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −411.514 | + | 509.223i | −0.417765 | + | 0.516958i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −926.140 | −0.912420 | −0.456210 | − | 0.889872i | \(-0.650793\pi\) | ||||
−0.456210 | + | 0.889872i | \(0.650793\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 984.987i | 0.942269i | 0.882061 | + | 0.471134i | \(0.156155\pi\) | ||||
−0.882061 | + | 0.471134i | \(0.843845\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −792.000 | + | 2240.11i | −0.736107 | + | 2.08203i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − | 897.202i | − | 0.810615i | −0.914180 | − | 0.405308i | \(-0.867164\pi\) | ||
0.914180 | − | 0.405308i | \(-0.132836\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 321.696i | − | 0.282687i | −0.989961 | − | 0.141343i | \(-0.954858\pi\) | ||
0.989961 | − | 0.141343i | \(-0.0451421\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −557.193 | + | 1575.98i | −0.476454 | + | 1.34762i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 520.431i | − | 0.433257i | −0.976254 | − | 0.216628i | \(-0.930494\pi\) | ||
0.976254 | − | 0.216628i | \(-0.0695060\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −2586.66 | −2.09746 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −779.908 | + | 965.087i | −0.616261 | + | 0.762584i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 2228.77 | 1.71690 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 743.000 | 0.558227 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 548.686 | − | 1551.92i | 0.402222 | − | 1.13766i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −227.473 | −0.162766 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 196.997i | 0.137643i | 0.997629 | + | 0.0688216i | \(0.0219239\pi\) | ||||
−0.997629 | + | 0.0688216i | \(0.978076\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 2352.00 | + | 831.558i | 1.60529 | + | 0.567555i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − | 1215.90i | − | 0.810944i | −0.914107 | − | 0.405472i | \(-0.867107\pi\) | ||
0.914107 | − | 0.405472i | \(-0.132893\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 275.739i | 0.179771i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −1193.98 | − | 1941.83i | −0.761199 | − | 1.23797i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − | 791.960i | − | 0.493881i | −0.969031 | − | 0.246940i | \(-0.920575\pi\) | ||
0.969031 | − | 0.246940i | \(-0.0794252\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1518.68 | 0.926713 | 0.463356 | − | 0.886172i | \(-0.346645\pi\) | ||||
0.463356 | + | 0.886172i | \(0.346645\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −1114.39 | −0.651676 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −1848.00 | −1.05840 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −2199.64 | − | 777.691i | −1.23417 | − | 0.436346i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 2843.41 | 1.56337 | 0.781683 | − | 0.623676i | \(-0.214362\pi\) | ||||
0.781683 | + | 0.623676i | \(0.214362\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 590.992i | − | 0.318505i | −0.987238 | − | 0.159253i | \(-0.949092\pi\) | ||
0.987238 | − | 0.159253i | \(-0.0509084\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −1344.00 | + | 1663.12i | −0.710170 | + | 0.878790i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − | 3200.83i | − | 1.65869i | ||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 1976.13i | − | 1.00454i | −0.864712 | − | 0.502268i | \(-0.832499\pi\) | ||
0.864712 | − | 0.502268i | \(-0.167501\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −1671.58 | − | 590.992i | −0.833741 | − | 0.294772i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − | 4480.23i | − | 2.19311i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −205.757 | −0.0988720 | −0.0494360 | − | 0.998777i | \(-0.515742\pi\) | ||||
−0.0494360 | + | 0.998777i | \(0.515742\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 682.419 | − | 1930.17i | 0.321977 | − | 0.910690i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 1114.39 | 0.516370 | 0.258185 | − | 0.966096i | \(-0.416876\pi\) | ||||
0.258185 | + | 0.966096i | \(0.416876\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 85.0000 | 0.0386891 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −205.757 | − | 166.277i | −0.0920154 | − | 0.0743597i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −1576.06 | −0.692635 | −0.346318 | − | 0.938117i | \(-0.612568\pi\) | ||||
−0.346318 | + | 0.938117i | \(0.612568\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − | 3911.81i | − | 1.68974i | ||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −1182.00 | + | 3343.20i | −0.501947 | + | 1.41972i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − | 1964.15i | − | 0.820152i | −0.912051 | − | 0.410076i | \(-0.865502\pi\) | ||
0.912051 | − | 0.410076i | \(-0.134498\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 4549.69i | 1.86838i | 0.356781 | + | 0.934188i | \(0.383874\pi\) | ||||
−0.356781 | + | 0.934188i | \(0.616126\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −79.5990 | + | 225.140i | −0.0321537 | + | 0.0909444i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | − | 5226.93i | − | 2.07725i | ||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −1920.40 | −0.750982 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 3363.35 | − | 2068.04i | 1.29443 | − | 0.795915i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 2228.77 | 0.844337 | 0.422168 | − | 0.906517i | \(-0.361269\pi\) | ||||
0.422168 | + | 0.906517i | \(0.361269\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −2618.00 | −0.976413 | −0.488207 | − | 0.872728i | \(-0.662349\pi\) | ||||
−0.488207 | + | 0.872728i | \(0.662349\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 1293.33 | − | 3658.09i | 0.474961 | − | 1.34339i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −2160.99 | −0.781545 | −0.390773 | − | 0.920487i | \(-0.627792\pi\) | ||||
−0.390773 | + | 0.920487i | \(0.627792\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 2560.97i | 0.912272i | 0.889910 | + | 0.456136i | \(0.150767\pi\) | ||||
−0.889910 | + | 0.456136i | \(0.849233\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −1680.00 | − | 593.970i | −0.589543 | − | 0.208435i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − | 3200.83i | − | 1.10667i | ||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 5147.13i | 1.75361i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 3343.16 | + | 2701.68i | 1.12254 | + | 0.907148i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − | 237.588i | − | 0.0786330i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −3909.39 | −1.27551 | −0.637756 | − | 0.770238i | \(-0.720137\pi\) | ||||
−0.637756 | + | 0.770238i | \(0.720137\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −5459.35 | − | 1930.17i | −1.75619 | − | 0.620907i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −7800.70 | −2.47443 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 5544.00 | 1.73434 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −480.100 | − | 169.741i | −0.148138 | − | 0.0523746i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −3639.57 | −1.10780 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 5712.93i | 1.71554i | 0.514032 | + | 0.857771i | \(0.328151\pi\) | ||||
−0.514032 | + | 0.857771i | \(0.671849\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 2919.00 | + | 2358.91i | 0.864889 | + | 0.698936i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − | 1208.97i | − | 0.353490i | −0.984257 | − | 0.176745i | \(-0.943443\pi\) | ||
0.984257 | − | 0.176745i | \(-0.0565568\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 5193.08i | − | 1.49855i | −0.662257 | − | 0.749277i | \(-0.730401\pi\) | ||
0.662257 | − | 0.749277i | \(-0.269599\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 3343.16 | + | 1181.98i | 0.952224 | + | 0.336662i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 1346.33i | − | 0.378545i | −0.981925 | − | 0.189273i | \(-0.939387\pi\) | ||
0.981925 | − | 0.189273i | \(-0.0606130\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 243.721 | − | 689.348i | 0.0667991 | − | 0.188936i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 1273.58 | 0.344692 | 0.172346 | − | 0.985037i | \(-0.444865\pi\) | ||||
0.172346 | + | 0.985037i | \(0.444865\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −5642.00 | −1.50802 | −0.754011 | − | 0.656862i | \(-0.771883\pi\) | ||||
−0.754011 | + | 0.656862i | \(0.771883\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −484.999 | + | 3756.82i | −0.128036 | + | 0.991770i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 7295.39 | 1.90239 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 450.280i | − | 0.115994i | ||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −1602.00 | + | 4531.14i | −0.407721 | + | 1.15321i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 4264.31i | 1.07235i | 0.844106 | + | 0.536177i | \(0.180132\pi\) | ||||
−0.844106 | + | 0.536177i | \(0.819868\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 3860.35i | 0.959280i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 2228.77 | − | 6303.92i | 0.547338 | − | 1.54810i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 2059.09i | 0.499777i | 0.968275 | + | 0.249889i | \(0.0803940\pi\) | ||||
−0.968275 | + | 0.249889i | \(0.919606\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 9053.31 | 2.17199 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 2388.47 | + | 1930.17i | 0.566446 | + | 0.457758i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 3343.16 | 0.783832 | 0.391916 | − | 0.920001i | \(-0.371812\pi\) | ||||
0.391916 | + | 0.920001i | \(0.371812\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 5544.00 | 1.28515 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 685.857 | − | 1939.90i | 0.157205 | − | 0.444643i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 5248.13 | 1.18953 | 0.594766 | − | 0.803899i | \(-0.297245\pi\) | ||||
0.594766 | + | 0.803899i | \(0.297245\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 2166.97i | − | 0.485735i | −0.970059 | − | 0.242867i | \(-0.921912\pi\) | ||
0.970059 | − | 0.242867i | \(-0.0780880\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 6336.00 | + | 2240.11i | 1.40466 | + | 0.496622i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 3370.57i | 0.739102i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − | 965.087i | − | 0.209337i | −0.994507 | − | 0.104669i | \(-0.966622\pi\) | ||
0.994507 | − | 0.104669i | \(-0.0333782\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −3343.16 | + | 4136.95i | −0.717382 | + | 0.887715i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 1029.55i | 0.218568i | 0.994011 | + | 0.109284i | \(0.0348558\pi\) | ||||
−0.994011 | + | 0.109284i | \(0.965144\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −4791.20 | −1.00639 | −0.503193 | − | 0.864174i | \(-0.667842\pi\) | ||||
−0.503193 | + | 0.864174i | \(0.667842\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 779.908 | + | 275.739i | 0.162097 | + | 0.0573101i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −8915.09 | −1.83359 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −1359.00 | −0.276613 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 4869.59 | + | 1721.66i | 0.980963 | + | 0.346823i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −4760.69 | −0.949223 | −0.474611 | − | 0.880195i | \(-0.657411\pi\) | ||||
−0.474611 | + | 0.880195i | \(0.657411\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − | 11088.1i | − | 2.18840i | ||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −2898.00 | + | 1781.91i | −0.566192 | + | 0.348138i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 7316.18i | 1.41507i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | − | 13511.2i | − | 2.58729i | ||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −4537.14 | − | 1604.12i | −0.860238 | − | 0.304140i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | − | 746.705i | − | 0.140184i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 1773.43 | 0.329691 | 0.164845 | − | 0.986319i | \(-0.447288\pi\) | ||||
0.164845 | + | 0.986319i | \(0.447288\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −1706.05 | + | 4825.43i | −0.314090 | + | 0.888380i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 5571.93 | 1.01593 | 0.507966 | − | 0.861377i | \(-0.330397\pi\) | ||||
0.507966 | + | 0.861377i | \(0.330397\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 3374.00 | 0.609296 | 0.304648 | − | 0.952465i | \(-0.401461\pi\) | ||||
0.304648 | + | 0.952465i | \(0.401461\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −7759.98 | + | 9602.49i | −1.38802 | + | 1.71758i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −4890.67 | −0.866522 | −0.433261 | − | 0.901269i | \(-0.642637\pi\) | ||||
−0.433261 | + | 0.901269i | \(0.642637\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 2757.96i | 0.484064i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 1554.00 | − | 4395.38i | 0.270205 | − | 0.764255i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 775.959i | − | 0.133670i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 6387.95i | 1.09028i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 557.193 | − | 1575.98i | 0.0942289 | − | 0.266519i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 617.271 | 0.102502 | 0.0512512 | − | 0.998686i | \(-0.483679\pi\) | ||||
0.0512512 | + | 0.998686i | \(0.483679\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −5459.35 | + | 6755.61i | −0.898411 | + | 1.11173i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 5571.93 | 0.908737 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 1526.00 | 0.246666 | 0.123333 | − | 0.992365i | \(-0.460642\pi\) | ||||
0.123333 | + | 0.992365i | \(0.460642\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 901.412 | − | 2549.58i | 0.144419 | − | 0.408478i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −4776.93 | −0.758609 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 2983.10i | 0.469599i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −12672.0 | − | 4480.23i | −1.97750 | − | 0.699152i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 11081.7i | 1.71439i | 0.514989 | + | 0.857197i | \(0.327796\pi\) | ||||
−0.514989 | + | 0.857197i | \(0.672204\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 689.348i | − | 0.105730i | −0.998602 | − | 0.0528652i | \(-0.983165\pi\) | ||
0.998602 | − | 0.0528652i | \(-0.0168354\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −5492.33 | + | 3377.10i | −0.835211 | + | 0.513551i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − | 316.784i | − | 0.0477640i | −0.999715 | − | 0.0238820i | \(-0.992397\pi\) | ||
0.999715 | − | 0.0238820i | \(-0.00760260\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 18106.6 | 2.70704 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 10918.7 | + | 3860.35i | 1.61871 | + | 0.572300i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 6527.12 | 0.959577 | 0.479788 | − | 0.877384i | \(-0.340713\pi\) | ||||
0.479788 | + | 0.877384i | \(0.340713\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −6763.00 | −0.986004 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 3639.94 | + | 1286.91i | 0.526301 | + | 0.186076i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 1592.31 | 0.228344 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 9652.88i | 1.37296i | 0.727149 | + | 0.686480i | \(0.240845\pi\) | ||||
−0.727149 | + | 0.686480i | \(0.759155\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 5376.00 | − | 6652.46i | 0.758437 | − | 0.938518i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 9602.49i | 1.34376i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 12546.1i | − | 1.74159i | −0.491645 | − | 0.870796i | \(-0.663604\pi\) | ||
0.491645 | − | 0.870796i | \(-0.336396\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −1114.39 | − | 393.995i | −0.153458 | − | 0.0542555i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 5226.93i | 0.714060i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −11042.3 | −1.49658 | −0.748291 | − | 0.663370i | \(-0.769125\pi\) | ||||
−0.748291 | + | 0.663370i | \(0.769125\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −341.210 | + | 965.087i | −0.0458811 | + | 0.129771i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 6686.32 | 0.892049 | 0.446024 | − | 0.895021i | \(-0.352839\pi\) | ||||
0.446024 | + | 0.895021i | \(0.352839\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −11088.0 | −1.46778 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 10082.1 | + | 8147.57i | 1.32429 | + | 1.07019i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −341.210 | −0.0444730 | −0.0222365 | − | 0.999753i | \(-0.507079\pi\) | ||||
−0.0222365 | + | 0.999753i | \(0.507079\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 12607.8i | 1.63071i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 2106.00 | − | 5956.67i | 0.270315 | − | 0.764565i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 2286.31i | 0.291232i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 4457.78i | 0.563551i | 0.959480 | + | 0.281775i | \(0.0909233\pi\) | ||||
−0.959480 | + | 0.281775i | \(0.909077\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −477.594 | + | 1350.84i | −0.0599238 | + | 0.169490i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 11121.4i | − | 1.38498i | −0.721430 | − | 0.692488i | \(-0.756515\pi\) | ||
0.721430 | − | 0.692488i | \(-0.243485\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −9053.31 | −1.11905 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −2485.96 | − | 11581.0i | −0.305008 | − | 1.42090i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −7800.70 | −0.950040 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 2618.00 | 0.316508 | 0.158254 | − | 0.987398i | \(-0.449414\pi\) | ||||
0.158254 | + | 0.987398i | \(0.449414\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 1371.71 | − | 3879.79i | 0.164627 | − | 0.465635i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 19205.2 | 2.28820 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − | 15028.1i | − | 1.77759i | ||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 7440.00 | + | 2630.44i | 0.873713 | + | 0.308904i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − | 6640.68i | − | 0.774269i | −0.922023 | − | 0.387134i | \(-0.873465\pi\) | ||
0.922023 | − | 0.387134i | \(-0.126535\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 5468.82i | 0.633098i | 0.948576 | + | 0.316549i | \(0.102524\pi\) | ||||
−0.948576 | + | 0.316549i | \(0.897476\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 11008.2i | 1.25642i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 1293.33 | 0.146578 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −5459.35 | − | 1930.17i | −0.614406 | − | 0.217225i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −1273.58 | −0.142335 | −0.0711675 | − | 0.997464i | \(-0.522672\pi\) | ||||
−0.0711675 | + | 0.997464i | \(0.522672\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 2674.00 | 0.296777 | 0.148388 | − | 0.988929i | \(-0.452591\pi\) | ||||
0.148388 | + | 0.988929i | \(0.452591\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −9053.31 | − | 3200.83i | −0.997869 | − | 0.352800i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −1559.82 | −0.170746 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 6894.91i | − | 0.749604i | −0.927105 | − | 0.374802i | \(-0.877711\pi\) | ||
0.927105 | − | 0.374802i | \(-0.122289\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −9429.00 | − | 7619.78i | −1.01814 | − | 0.822782i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − | 11809.1i | − | 1.26652i | −0.773939 | − | 0.633260i | \(-0.781716\pi\) | ||
0.773939 | − | 0.633260i | \(-0.218284\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 6433.91i | 0.685386i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 13929.8 | + | 4924.94i | 1.47396 | + | 0.521122i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 18135.9i | 1.90620i | 0.302652 | + | 0.953101i | \(0.402128\pi\) | ||||
−0.302652 | + | 0.953101i | \(0.597872\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 7681.60 | 0.802023 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 1023.63 | − | 2895.26i | 0.106168 | − | 0.300290i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −21014.1 | −2.16518 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 15722.0 | 1.60929 | 0.804643 | − | 0.593758i | \(-0.202356\pi\) | ||||
0.804643 | + | 0.593758i | \(0.202356\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −9464.83 | + | 5819.69i | −0.962484 | + | 0.591808i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −3655.82 | −0.369346 | −0.184673 | − | 0.982800i | \(-0.559123\pi\) | ||||
−0.184673 | + | 0.982800i | \(0.559123\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 13536.5i | − | 1.35874i | −0.733796 | − | 0.679370i | \(-0.762253\pi\) | ||
0.733796 | − | 0.679370i | \(-0.237747\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 5544.00 | − | 15680.8i | 0.552896 | − | 1.56383i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 1700.87i | 0.168538i | 0.996443 | + | 0.0842688i | \(0.0268554\pi\) | ||||
−0.996443 | + | 0.0842688i | \(0.973145\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 9650.87i | 0.950182i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 3422.76 | − | 9681.02i | 0.334846 | − | 0.947087i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 11641.8i | 1.13169i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −1361.92 | −0.131556 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −7165.40 | − | 5790.52i | −0.687801 | − | 0.555827i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −4457.54 | −0.425199 | −0.212600 | − | 0.977139i | \(-0.568193\pi\) | ||||
−0.212600 | + | 0.977139i | \(0.568193\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −14784.0 | −1.40144 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 7759.98 | − | 21948.5i | 0.731038 | − | 2.06769i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −16150.6 | −1.51208 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 3348.96i | 0.311613i | 0.987788 | + | 0.155807i | \(0.0497977\pi\) | ||||
−0.987788 | + | 0.155807i | \(0.950202\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −1008.00 | − | 356.382i | −0.0932175 | − | 0.0329573i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 5940.93i | − | 0.546050i | −0.962007 | − | 0.273025i | \(-0.911976\pi\) | ||
0.962007 | − | 0.273025i | \(-0.0880242\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 9007.47i | 0.822873i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 6686.32 | − | 8273.89i | 0.607126 | − | 0.751281i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 31361.6i | 2.83050i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −13237.0 | −1.18752 | −0.593759 | − | 0.804643i | \(-0.702357\pi\) | ||||
−0.593759 | + | 0.804643i | \(0.702357\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 5459.35 | + | 1930.17i | 0.486838 | + | 0.172123i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 14487.0 | 1.28418 | 0.642092 | − | 0.766628i | \(-0.278067\pi\) | ||||
0.642092 | + | 0.766628i | \(0.278067\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 15048.0 | 1.32599 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 416.413 | + | 147.224i | 0.0364765 | + | 0.0128964i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −13404.7 | −1.16729 | −0.583646 | − | 0.812008i | \(-0.698374\pi\) | ||||
−0.583646 | + | 0.812008i | \(0.698374\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 2757.96i | 0.238758i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −720.000 | − | 1170.97i | −0.0619664 | − | 0.100779i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | − | 16004.1i | − | 1.36937i | ||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −7721.10 | − | 2729.82i | −0.653023 | − | 0.230878i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 13146.5i | − | 1.10549i | −0.833351 | − | 0.552745i | \(-0.813580\pi\) | ||
0.833351 | − | 0.552745i | \(-0.186420\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 2322.12 | 0.194147 | 0.0970737 | − | 0.995277i | \(-0.469052\pi\) | ||||
0.0970737 | + | 0.995277i | \(0.469052\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 6775.45 | − | 19163.9i | 0.563247 | − | 1.59310i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −15601.4 | −1.28958 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 13177.0 | 1.08301 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −11581.2 | + | 14331.0i | −0.946480 | + | 1.17121i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 14558.3 | 1.18309 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 14577.8i | 1.17804i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 3402.00 | − | 9622.31i | 0.273384 | − | 0.773246i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − | 10887.7i | − | 0.870065i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − | 5468.82i | − | 0.434608i | −0.976104 | − | 0.217304i | \(-0.930274\pi\) | ||
0.976104 | − | 0.217304i | \(-0.0697263\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −7880.30 | + | 22288.9i | −0.622792 | + | 1.76152i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 5226.93i | 0.410821i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 7750.19 | 0.605803 | 0.302901 | − | 0.953022i | \(-0.402045\pi\) | ||||
0.302901 | + | 0.953022i | \(0.402045\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −779.908 | + | 965.087i | −0.0606296 | + | 0.0750253i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −1114.39 | −0.0861605 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −3960.00 | −0.304514 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 9053.31 | − | 25606.6i | 0.692418 | − | 1.95845i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 6028.04 | 0.458557 | 0.229278 | − | 0.973361i | \(-0.426363\pi\) | ||||
0.229278 | + | 0.973361i | \(0.426363\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 22063.7i | 1.66940i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −9408.00 | − | 3326.23i | −0.708032 | − | 0.250327i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − | 15425.6i | − | 1.15473i | −0.816486 | − | 0.577365i | \(-0.804081\pi\) | ||
0.816486 | − | 0.577365i | \(-0.195919\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 8456.00i | 0.629640i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 20058.9 | − | 4305.80i | 1.48571 | − | 0.318918i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 15092.5i | 1.11197i | 0.831193 | + | 0.555984i | \(0.187658\pi\) | ||||
−0.831193 | + | 0.555984i | \(0.812342\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −1577.47 | −0.115613 | −0.0578066 | − | 0.998328i | \(-0.518411\pi\) | ||||
−0.0578066 | + | 0.998328i | \(0.518411\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 10918.7 | + | 3860.35i | 0.796048 | + | 0.281446i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 22128.5 | 1.60491 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −20314.0 | −1.46565 | −0.732827 | − | 0.680415i | \(-0.761800\pi\) | ||||
−0.732827 | + | 0.680415i | \(0.761800\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −12825.5 | − | 4534.51i | −0.920571 | − | 0.325471i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 26029.4 | 1.85866 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 8273.89i | − | 0.587770i | ||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 12672.0 | − | 15680.8i | 0.895594 | − | 1.10824i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − | 11206.4i | − | 0.787967i | −0.919118 | − | 0.393983i | \(-0.871097\pi\) | ||
0.919118 | − | 0.393983i | \(-0.128903\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 1930.17i | − | 0.135028i | ||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −10586.7 | − | 3742.95i | −0.736848 | − | 0.260515i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 11721.0i | − | 0.811676i | −0.913945 | − | 0.405838i | \(-0.866980\pi\) | ||
0.913945 | − | 0.405838i | \(-0.133020\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −36213.3 | −2.49512 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −4435.72 | + | 12546.1i | −0.304091 | + | 0.860098i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 21173.3 | 1.44427 | 0.722136 | − | 0.691751i | \(-0.243160\pi\) | ||||
0.722136 | + | 0.691751i | \(0.243160\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −5138.00 | −0.348724 | −0.174362 | − | 0.984682i | \(-0.555786\pi\) | ||||
−0.174362 | + | 0.984682i | \(0.555786\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −7201.50 | − | 5819.69i | −0.486348 | − | 0.393028i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −12072.3 | −0.811256 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 17138.8i | − | 1.14603i | −0.819544 | − | 0.573016i | \(-0.805773\pi\) | ||
0.819544 | − | 0.573016i | \(-0.194227\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 5544.00 | − | 15680.8i | 0.368890 | − | 1.04338i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 24127.2i | − | 1.58970i | −0.606805 | − | 0.794851i | \(-0.707549\pi\) | ||
0.606805 | − | 0.794851i | \(-0.292451\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −8915.09 | + | 25215.7i | −0.584538 | + | 1.65332i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 1301.08i | 0.0848936i | 0.999099 | + | 0.0424468i | \(0.0135153\pi\) | ||||
−0.999099 | + | 0.0424468i | \(0.986485\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 16999.5 | 1.10382 | 0.551911 | − | 0.833903i | \(-0.313899\pi\) | ||||
0.551911 | + | 0.833903i | \(0.313899\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 11698.6 | + | 19026.0i | 0.755957 | + | 1.22945i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −11143.9 | −0.716644 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −13679.0 | −0.875456 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 411.514 | − | 1163.94i | 0.0262110 | − | 0.0741359i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −25477.0 | −1.61500 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 10384.6i | − | 0.655156i | −0.944824 | − | 0.327578i | \(-0.893768\pi\) | ||
0.944824 | − | 0.327578i | \(-0.106232\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −19152.0 | − | 6771.25i | −1.20257 | − | 0.425171i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | − | 3200.83i | − | 0.200033i | ||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − | 20634.5i | − | 1.28347i | ||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −23402.1 | − | 18911.8i | −1.44878 | − | 1.17079i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 8428.71i | 0.519367i | 0.965694 | + | 0.259683i | \(0.0836182\pi\) | ||||
−0.965694 | + | 0.259683i | \(0.916382\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −14824.3 | −0.909197 | −0.454599 | − | 0.890696i | \(-0.650217\pi\) | ||||
−0.454599 | + | 0.890696i | \(0.650217\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −38215.5 | − | 13511.2i | −2.33292 | − | 0.824812i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 10029.5 | 0.609427 | 0.304714 | − | 0.952444i | \(-0.401439\pi\) | ||||
0.304714 | + | 0.952444i | \(0.401439\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −16548.0 | −1.00087 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 27159.9 | + | 9602.49i | 1.63515 | + | 0.578113i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −7165.40 | −0.429409 | −0.214704 | − | 0.976679i | \(-0.568879\pi\) | ||||
−0.214704 | + | 0.976679i | \(0.568879\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 19756.0i | 1.17852i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −2058.00 | − | 1663.12i | −0.122207 | − | 0.0987585i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 14331.0i | 0.847126i | 0.905867 | + | 0.423563i | \(0.139221\pi\) | ||||
−0.905867 | + | 0.423563i | \(0.860779\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 5836.48i | 0.343438i | 0.985146 | + | 0.171719i | \(0.0549321\pi\) | ||||
−0.985146 | + | 0.171719i | \(0.945068\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −17830.2 | − | 6303.92i | −1.04444 | − | 0.369267i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | − | 4480.23i | − | 0.261257i | ||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 18106.6 | 1.05111 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −9895.08 | + | 27987.5i | −0.571847 | + | 1.61743i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −1114.39 | −0.0641138 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 18562.0 | 1.06317 | 0.531584 | − | 0.847005i | \(-0.321597\pi\) | ||||
0.531584 | + | 0.847005i | \(0.321597\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 10214.4 | + | 16612.1i | 0.582446 | + | 0.947259i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 16621.8 | 0.943614 | 0.471807 | − | 0.881702i | \(-0.343602\pi\) | ||||
0.471807 | + | 0.881702i | \(0.343602\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − | 27973.6i | − | 1.58105i | ||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 2094.00 | − | 5922.73i | 0.117830 | − | 0.333274i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 15882.9i | − | 0.889813i | −0.895577 | − | 0.444907i | \(-0.853237\pi\) | ||
0.895577 | − | 0.444907i | \(-0.146763\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 12867.8i | 0.717743i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 8994.69 | − | 25440.8i | 0.499518 | − | 1.41285i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − | 15680.8i | − | 0.867040i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −7965.74 | −0.438540 | −0.219270 | − | 0.975664i | \(-0.570368\pi\) | ||||
−0.219270 | + | 0.975664i | \(0.570368\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 14330.8 | + | 11581.0i | 0.785544 | + | 0.634816i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −24675.7 | −1.34677 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 25088.0 | 1.36338 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 2331.91 | − | 6595.65i | 0.126182 | − | 0.356896i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 8757.71 | 0.471861 | 0.235930 | − | 0.971770i | \(-0.424186\pi\) | ||||
0.235930 | + | 0.971770i | \(0.424186\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 3151.96i | − | 0.169102i | ||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 26063.9i | 1.38647i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − | 15119.7i | − | 0.800891i | −0.916321 | − | 0.400446i | \(-0.868855\pi\) | ||
0.916321 | − | 0.400446i | \(-0.131145\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 2387.97 | − | 2954.96i | 0.125958 | − | 0.155865i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 31361.6i | 1.64727i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 18106.6 | 0.947062 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 6239.26 | + | 2205.91i | 0.324978 | + | 0.114897i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 33431.6 | 1.73406 | 0.867029 | − | 0.498258i | \(-0.166027\pi\) | ||||
0.867029 | + | 0.498258i | \(0.166027\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 27720.0 | 1.43183 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −27640.0 | − | 9772.23i | −1.42178 | − | 0.502674i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 15809.4 | 0.809856 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 2560.97i | 0.130648i | 0.997864 | + | 0.0653239i | \(0.0208081\pi\) | ||||
−0.997864 | + | 0.0653239i | \(0.979192\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −8883.00 | + | 17564.5i | −0.451303 | + | 0.892371i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 38022.0i | 1.92379i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 689.348i | − | 0.0347362i | −0.999849 | − | 0.0173681i | \(-0.994471\pi\) | ||
0.999849 | − | 0.0173681i | \(-0.00552872\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 35739.9 | + | 12636.0i | 1.79359 | + | 0.634129i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − | 8315.58i | − | 0.415615i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 18038.0 | 0.897889 | 0.448945 | − | 0.893560i | \(-0.351800\pi\) | ||||
0.448945 | + | 0.893560i | \(0.351800\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 779.908 | − | 2205.91i | 0.0386648 | − | 0.109361i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −10984.7 | −0.542380 | −0.271190 | − | 0.962526i | \(-0.587417\pi\) | ||||
−0.271190 | + | 0.962526i | \(0.587417\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −46200.0 | −2.27200 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −15696.3 | + | 19423.2i | −0.768807 | + | 0.951350i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −25249.5 | −1.23177 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 7288.91i | 0.354162i | 0.984196 | + | 0.177081i | \(0.0566655\pi\) | ||||
−0.984196 | + | 0.177081i | \(0.943334\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −7386.00 | + | 20890.8i | −0.357451 | + | 1.01102i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 9602.49i | 0.462875i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 24127.2i | − | 1.15841i | −0.815182 | − | 0.579205i | \(-0.803363\pi\) | ||
0.815182 | − | 0.579205i | \(-0.196637\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −6686.32 | + | 18911.8i | −0.319760 | + | 0.904418i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 20274.2i | − | 0.965753i | −0.875689 | − | 0.482876i | \(-0.839592\pi\) | ||
0.875689 | − | 0.482876i | \(-0.160408\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −9053.31 | −0.429557 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 21837.4 | − | 27022.4i | 1.03207 | − | 1.27712i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −31362.0 | −1.47642 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 26950.0 | 1.26377 | 0.631887 | − | 0.775061i | \(-0.282281\pi\) | ||||
0.631887 | + | 0.775061i | \(0.282281\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −3566.46 | + | 10087.5i | −0.166592 | + | 0.471195i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 2713.43 | 0.126255 | 0.0631276 | − | 0.998005i | \(-0.479892\pi\) | ||||
0.0631276 | + | 0.998005i | \(0.479892\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 27382.6i | 1.26918i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 44352.0 | + | 15680.8i | 2.04777 | + | 0.723997i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 3103.84i | 0.142755i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − | 27022.4i | − | 1.23808i | ||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 8357.89 | + | 13592.8i | 0.381465 | + | 0.620393i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 32108.3i | 1.45987i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −2322.12 | −0.105177 | −0.0525886 | − | 0.998616i | \(-0.516747\pi\) | ||||
−0.0525886 | + | 0.998616i | \(0.516747\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 16378.1 | + | 5790.52i | 0.739004 | + | 0.261277i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −14646.2 | −0.658356 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −2112.00 | −0.0945767 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 27159.9 | + | 9602.49i | 1.21165 | + | 0.428384i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 14997.0 | 0.666525 | 0.333262 | − | 0.942834i | \(-0.391851\pi\) | ||||
0.333262 | + | 0.942834i | \(0.391851\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 6720.00 | − | 8315.58i | 0.296429 | − | 0.366812i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − | 2376.37i | − | 0.104434i | ||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 72795.1i | 3.18719i | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 25710.5 | + | 9090.03i | 1.12150 | + | 0.396511i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 19369.1i | 0.841756i | 0.907117 | + | 0.420878i | \(0.138278\pi\) | ||||
−0.907117 | + | 0.420878i | \(0.861722\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 31559.2 | 1.36645 | 0.683227 | − | 0.730206i | \(-0.260576\pi\) | ||||
0.683227 | + | 0.730206i | \(0.260576\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 3753.31 | − | 10616.0i | 0.161912 | − | 0.457955i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 3343.16 | 0.143688 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −4704.00 | −0.201435 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 27159.9 | + | 21948.5i | 1.15879 | + | 0.936440i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −24453.4 | −1.03950 | −0.519749 | − | 0.854319i | \(-0.673975\pi\) | ||||
−0.519749 | + | 0.854319i | \(0.673975\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 18658.5i | 0.790272i | 0.918623 | + | 0.395136i | \(0.129302\pi\) | ||||
−0.918623 | + | 0.395136i | \(0.870698\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −5838.00 | + | 16512.4i | −0.246367 | + | 0.696832i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 29171.2i | 1.22658i | 0.789858 | + | 0.613290i | \(0.210154\pi\) | ||||
−0.789858 | + | 0.613290i | \(0.789846\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 6479.87i | 0.271478i | 0.990745 | + | 0.135739i | \(0.0433408\pi\) | ||||
−0.990745 | + | 0.135739i | \(0.956659\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 1671.58 | − | 4727.94i | 0.0697791 | − | 0.197365i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − | 35559.0i | − | 1.47905i | ||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −18106.6 | −0.750426 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −23543.5 | + | 14476.3i | −0.972259 | + | 0.597818i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 16715.8 | 0.687834 | 0.343917 | − | 0.939000i | \(-0.388246\pi\) | ||||
0.343917 | + | 0.939000i | \(0.388246\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −11453.0 | −0.469597 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −1783.23 | + | 5043.73i | −0.0728561 | + | 0.206068i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −1381.09 | −0.0562258 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 20909.9i | − | 0.848255i | ||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −23472.0 | − | 8298.61i | −0.948830 | − | 0.335462i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 51213.3i | 2.06295i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 5101.17i | 0.204761i | 0.994745 | + | 0.102380i | \(0.0326459\pi\) | ||||
−0.994745 | + | 0.102380i | \(0.967354\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 3343.16 | + | 2701.68i | 0.133723 | + | 0.108065i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − | 13146.5i | − | 0.524010i | −0.965066 | − | 0.262005i | \(-0.915616\pi\) | ||
0.965066 | − | 0.262005i | \(-0.0843838\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 19057.0 | 0.756947 | 0.378474 | − | 0.925612i | \(-0.376449\pi\) | ||||
0.378474 | + | 0.925612i | \(0.376449\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −43674.8 | − | 15441.4i | −1.72873 | − | 0.611197i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −2228.77 | −0.0879123 | −0.0439561 | − | 0.999033i | \(-0.513996\pi\) | ||||
−0.0439561 | + | 0.999033i | \(0.513996\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 25608.0 | 1.00659 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −6657.71 | − | 2353.86i | −0.260793 | − | 0.0922044i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 3412.10 | 0.133196 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 15759.8i | − | 0.613089i | ||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 20874.0 | + | 16868.7i | 0.809253 | + | 0.653975i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 6401.66i | 0.247332i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 44715.7i | 1.72171i | 0.508849 | + | 0.860856i | \(0.330071\pi\) | ||||
−0.508849 | + | 0.860856i | \(0.669929\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −23322.5 | − | 8245.75i | −0.894936 | − | 0.316408i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 16947.9i | − | 0.648116i | −0.946037 | − | 0.324058i | \(-0.894953\pi\) | ||
0.946037 | − | 0.324058i | \(-0.105047\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 32989.7 | 1.25730 | 0.628648 | − | 0.777690i | \(-0.283609\pi\) | ||||
0.628648 | + | 0.777690i | \(0.283609\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 19205.2 | − | 54320.6i | 0.729465 | − | 2.06324i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −25630.9 | −0.970237 | −0.485119 | − | 0.874448i | \(-0.661224\pi\) | ||||
−0.485119 | + | 0.874448i | \(0.661224\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 5544.00 | 0.209156 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −17283.6 | + | 3710.05i | −0.649857 | + | 0.139497i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 31913.6i | 1.19190i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −12672.0 | + | 35841.8i | −0.471690 | + | 1.33414i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 22405.8i | 0.831230i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 27022.4i | − | 0.999165i | ||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 23402.1 | − | 66191.1i | 0.862429 | − | 2.43932i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | − | 73923.8i | − | 2.71526i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −36281.8 | −1.32825 | −0.664123 | − | 0.747623i | \(-0.731195\pi\) | ||||
−0.664123 | + | 0.747623i | \(0.731195\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −19448.9 | − | 15717.1i | −0.709660 | − | 0.573492i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −5731.13 | −0.208431 | −0.104216 | − | 0.994555i | \(-0.533233\pi\) | ||||
−0.104216 | + | 0.994555i | \(0.533233\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −22428.0 | −0.812988 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 1293.33 | − | 3658.09i | 0.0467281 | − | 0.132167i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −34218.4 | −1.23227 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 30872.3i | − | 1.10814i | −0.832469 | − | 0.554072i | \(-0.813073\pi\) | ||
0.832469 | − | 0.554072i | \(-0.186927\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 8688.00 | + | 3071.67i | 0.310835 | + | 0.109897i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − | 51213.3i | − | 1.82633i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 44715.7i | 1.58945i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −16715.8 | + | 20684.7i | −0.592253 | + | 0.732876i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − | 8949.14i | − | 0.316052i | −0.987435 | − | 0.158026i | \(-0.949487\pi\) | ||
0.987435 | − | 0.158026i | \(-0.0505129\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 4399.28 | 0.154866 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 27296.8 | + | 9650.87i | 0.957831 | + | 0.338644i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 31202.8 | 1.09138 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −43862.0 | −1.52925 | −0.764626 | − | 0.644474i | \(-0.777076\pi\) | ||||
−0.764626 | + | 0.644474i | \(0.777076\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 16529.2 | + | 5843.94i | 0.574450 | + | 0.203099i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 24550.8 | 0.850515 | 0.425258 | − | 0.905072i | \(-0.360184\pi\) | ||||
0.425258 | + | 0.905072i | \(0.360184\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 50431.4i | − | 1.74154i | ||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −54648.0 | + | 33601.7i | −1.88116 | + | 1.15668i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − | 39986.1i | − | 1.37210i | −0.727557 | − | 0.686048i | \(-0.759344\pi\) | ||
0.727557 | − | 0.686048i | \(-0.240656\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − | 4503.74i | − | 0.154054i | ||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −23959.3 | − | 8470.89i | −0.816965 | − | 0.288841i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 46408.8i | − | 1.57747i | −0.614733 | − | 0.788735i | \(-0.710736\pi\) | ||
0.614733 | − | 0.788735i | \(-0.289264\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −36213.3 | −1.22705 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −4776.93 | + | 13511.2i | −0.161355 | + | 0.456380i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −22287.7 | −0.750478 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −9017.00 | −0.302675 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 15226.0 | − | 18841.2i | 0.509504 | − | 0.630478i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 42537.5 | 1.41899 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 8076.90i | 0.268599i | 0.990941 | + | 0.134300i | \(0.0428785\pi\) | ||||
−0.990941 | + | 0.134300i | \(0.957122\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 1344.00 | − | 3801.41i | 0.0445568 | − | 0.126026i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 41371.8i | 1.36734i | 0.729793 | + | 0.683668i | \(0.239616\pi\) | ||||
−0.729793 | + | 0.683668i | \(0.760384\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − | 42739.5i | − | 1.40819i | ||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −11064.3 | + | 31294.5i | −0.363426 | + | 1.02792i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − | 21778.9i | − | 0.713171i | −0.934263 | − | 0.356586i | \(-0.883941\pi\) | ||
0.934263 | − | 0.356586i | \(-0.116059\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 9602.00 | 0.313464 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 5459.35 | − | 6755.61i | 0.177680 | − | 0.219867i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 41232.3 | 1.33785 | 0.668924 | − | 0.743330i | \(-0.266755\pi\) | ||||
0.668924 | + | 0.743330i | \(0.266755\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 35112.0 | 1.13580 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 76431.0 | 2.45739 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 15225.1i | − | 0.488033i | −0.969771 | − | 0.244017i | \(-0.921535\pi\) | ||
0.969771 | − | 0.244017i | \(-0.0784651\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 3024.00 | + | 1069.15i | 0.0966402 | + | 0.0341675i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − | 41610.8i | − | 1.32578i | ||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − | 19899.2i | − | 0.632109i | −0.948741 | − | 0.316055i | \(-0.897642\pi\) | ||
0.948741 | − | 0.316055i | \(-0.102358\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −38446.3 | + | 23639.7i | −1.21761 | + | 0.748676i |
(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 | 384.4.f.i.191.7 | yes | 8 | |
3.2 | odd | 2 | inner | 384.4.f.i.191.6 | yes | 8 | |
4.3 | odd | 2 | inner | 384.4.f.i.191.1 | ✓ | 8 | |
8.3 | odd | 2 | inner | 384.4.f.i.191.8 | yes | 8 | |
8.5 | even | 2 | inner | 384.4.f.i.191.2 | yes | 8 | |
12.11 | even | 2 | inner | 384.4.f.i.191.4 | yes | 8 | |
16.3 | odd | 4 | 768.4.c.s.767.6 | 8 | |||
16.5 | even | 4 | 768.4.c.s.767.5 | 8 | |||
16.11 | odd | 4 | 768.4.c.s.767.3 | 8 | |||
16.13 | even | 4 | 768.4.c.s.767.4 | 8 | |||
24.5 | odd | 2 | inner | 384.4.f.i.191.3 | yes | 8 | |
24.11 | even | 2 | inner | 384.4.f.i.191.5 | yes | 8 | |
48.5 | odd | 4 | 768.4.c.s.767.2 | 8 | |||
48.11 | even | 4 | 768.4.c.s.767.8 | 8 | |||
48.29 | odd | 4 | 768.4.c.s.767.7 | 8 | |||
48.35 | even | 4 | 768.4.c.s.767.1 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
384.4.f.i.191.1 | ✓ | 8 | 4.3 | odd | 2 | inner | |
384.4.f.i.191.2 | yes | 8 | 8.5 | even | 2 | inner | |
384.4.f.i.191.3 | yes | 8 | 24.5 | odd | 2 | inner | |
384.4.f.i.191.4 | yes | 8 | 12.11 | even | 2 | inner | |
384.4.f.i.191.5 | yes | 8 | 24.11 | even | 2 | inner | |
384.4.f.i.191.6 | yes | 8 | 3.2 | odd | 2 | inner | |
384.4.f.i.191.7 | yes | 8 | 1.1 | even | 1 | trivial | |
384.4.f.i.191.8 | yes | 8 | 8.3 | odd | 2 | inner | |
768.4.c.s.767.1 | 8 | 48.35 | even | 4 | |||
768.4.c.s.767.2 | 8 | 48.5 | odd | 4 | |||
768.4.c.s.767.3 | 8 | 16.11 | odd | 4 | |||
768.4.c.s.767.4 | 8 | 16.13 | even | 4 | |||
768.4.c.s.767.5 | 8 | 16.5 | even | 4 | |||
768.4.c.s.767.6 | 8 | 16.3 | odd | 4 | |||
768.4.c.s.767.7 | 8 | 48.29 | odd | 4 | |||
768.4.c.s.767.8 | 8 | 48.11 | even | 4 |