Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2880,3,Mod(2431,2880)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2880, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 0, 0]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2880.2431");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2880 = 2^{6} \cdot 3^{2} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 2880.e (of order \(2\), degree \(1\), 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: | \(78.4743161358\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | 8.0.85100625.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - x^{7} - 2x^{6} + x^{5} + 3x^{4} + 2x^{3} - 8x^{2} - 8x + 16 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{19}]\) |
Coefficient ring index: | \( 2^{19} \) |
Twist minimal: | no (minimal twist has level 60) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 2431.2 | ||
Root | \(1.04064 - 0.957636i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2880.2431 |
Dual form | 2880.3.e.j.2431.3 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/2880\mathbb{Z}\right)^\times\).
\(n\) | \(577\) | \(641\) | \(901\) | \(2431\) |
\(\chi(n)\) | \(1\) | \(1\) | \(1\) | \(-1\) |
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 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −2.23607 | −0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − 5.46770i | − 0.781100i | −0.920582 | − | 0.390550i | \(-0.872285\pi\) | ||||
0.920582 | − | 0.390550i | \(-0.127715\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − 11.0403i | − 1.00366i | −0.864965 | − | 0.501832i | \(-0.832659\pi\) | ||||
0.864965 | − | 0.501832i | \(-0.167341\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −10.1242 | −0.778784 | −0.389392 | − | 0.921072i | \(-0.627315\pi\) | ||||
−0.389392 | + | 0.921072i | \(0.627315\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 24.4146 | 1.43615 | 0.718077 | − | 0.695964i | \(-0.245023\pi\) | ||||
0.718077 | + | 0.695964i | \(0.245023\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 23.7757i | 1.25135i | 0.780082 | + | 0.625677i | \(0.215177\pi\) | ||||
−0.780082 | + | 0.625677i | \(0.784823\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − 37.2526i | − 1.61968i | −0.586653 | − | 0.809838i | \(-0.699555\pi\) | ||||
0.586653 | − | 0.809838i | \(-0.300445\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 5.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −25.7726 | −0.888712 | −0.444356 | − | 0.895850i | \(-0.646567\pi\) | ||||
−0.444356 | + | 0.895850i | \(0.646567\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.83647i | 0.156015i | 0.996953 | + | 0.0780076i | \(0.0248558\pi\) | ||||
−0.996953 | + | 0.0780076i | \(0.975144\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 12.2261i | 0.349319i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −35.6493 | −0.963495 | −0.481747 | − | 0.876310i | \(-0.659998\pi\) | ||||
−0.481747 | + | 0.876310i | \(0.659998\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 9.30410 | 0.226929 | 0.113465 | − | 0.993542i | \(-0.463805\pi\) | ||||
0.113465 | + | 0.993542i | \(0.463805\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − 70.0287i | − 1.62857i | −0.580462 | − | 0.814287i | \(-0.697128\pi\) | ||||
0.580462 | − | 0.814287i | \(-0.302872\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − 38.0223i | − 0.808984i | −0.914542 | − | 0.404492i | \(-0.867448\pi\) | ||||
0.914542 | − | 0.404492i | \(-0.132552\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 19.1043 | 0.389883 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 55.7762 | 1.05238 | 0.526191 | − | 0.850366i | \(-0.323620\pi\) | ||||
0.526191 | + | 0.850366i | \(0.323620\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 24.6869i | 0.448853i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − 55.5411i | − 0.941374i | −0.882300 | − | 0.470687i | \(-0.844006\pi\) | ||||
0.882300 | − | 0.470687i | \(-0.155994\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 82.2412 | 1.34822 | 0.674108 | − | 0.738633i | \(-0.264528\pi\) | ||||
0.674108 | + | 0.738633i | \(0.264528\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 22.6384 | 0.348283 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 104.493i | 1.55960i | 0.626026 | + | 0.779802i | \(0.284680\pi\) | ||||
−0.626026 | + | 0.779802i | \(0.715320\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 76.7471i | 1.08094i | 0.841362 | + | 0.540472i | \(0.181754\pi\) | ||||
−0.841362 | + | 0.540472i | \(0.818246\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −93.5215 | −1.28112 | −0.640558 | − | 0.767910i | \(-0.721297\pi\) | ||||
−0.640558 | + | 0.767910i | \(0.721297\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −60.3651 | −0.783963 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 49.3762i | 0.625016i | 0.949915 | + | 0.312508i | \(0.101169\pi\) | ||||
−0.949915 | + | 0.312508i | \(0.898831\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − 72.3768i | − 0.872010i | −0.899944 | − | 0.436005i | \(-0.856393\pi\) | ||||
0.899944 | − | 0.436005i | \(-0.143607\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −54.5927 | −0.642267 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −115.691 | −1.29990 | −0.649950 | − | 0.759977i | \(-0.725210\pi\) | ||||
−0.649950 | + | 0.759977i | \(0.725210\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 55.3560i | 0.608308i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | − 53.1641i | − 0.559623i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −72.9589 | −0.752154 | −0.376077 | − | 0.926588i | \(-0.622727\pi\) | ||||
−0.376077 | + | 0.926588i | \(0.622727\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 29.4092 | 0.291180 | 0.145590 | − | 0.989345i | \(-0.453492\pi\) | ||||
0.145590 | + | 0.989345i | \(0.453492\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 28.1884i | 0.273673i | 0.990594 | + | 0.136837i | \(0.0436935\pi\) | ||||
−0.990594 | + | 0.136837i | \(0.956306\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 4.50700i | 0.0421215i | 0.999778 | + | 0.0210607i | \(0.00670434\pi\) | ||||
−0.999778 | + | 0.0210607i | \(0.993296\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −193.315 | −1.77353 | −0.886767 | − | 0.462217i | \(-0.847054\pi\) | ||||
−0.886767 | + | 0.462217i | \(0.847054\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −75.5727 | −0.668785 | −0.334392 | − | 0.942434i | \(-0.608531\pi\) | ||||
−0.334392 | + | 0.942434i | \(0.608531\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 83.2992i | 0.724341i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | − 133.492i | − 1.12178i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −0.888544 | −0.00734334 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −11.1803 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 131.306i | 1.03390i | 0.856015 | + | 0.516951i | \(0.172933\pi\) | ||||
−0.856015 | + | 0.516951i | \(0.827067\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 75.7533i | 0.578270i | 0.957288 | + | 0.289135i | \(0.0933676\pi\) | ||||
−0.957288 | + | 0.289135i | \(0.906632\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 129.999 | 0.977433 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −66.7927 | −0.487538 | −0.243769 | − | 0.969833i | \(-0.578384\pi\) | ||||
−0.243769 | + | 0.969833i | \(0.578384\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 38.1214i | 0.274255i | 0.990553 | + | 0.137127i | \(0.0437869\pi\) | ||||
−0.990553 | + | 0.137127i | \(0.956213\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 111.774i | 0.781638i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 57.6294 | 0.397444 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −126.717 | −0.850449 | −0.425225 | − | 0.905088i | \(-0.639805\pi\) | ||||
−0.425225 | + | 0.905088i | \(0.639805\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 68.4403i | 0.453247i | 0.973982 | + | 0.226623i | \(0.0727687\pi\) | ||||
−0.973982 | + | 0.226623i | \(0.927231\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − 10.8147i | − 0.0697721i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −25.5777 | −0.162915 | −0.0814577 | − | 0.996677i | \(-0.525958\pi\) | ||||
−0.0814577 | + | 0.996677i | \(0.525958\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −203.686 | −1.26513 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 63.4771i | 0.389430i | 0.980860 | + | 0.194715i | \(0.0623782\pi\) | ||||
−0.980860 | + | 0.194715i | \(0.937622\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 12.3771i | 0.0741144i | 0.999313 | + | 0.0370572i | \(0.0117984\pi\) | ||||
−0.999313 | + | 0.0370572i | \(0.988202\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −66.5008 | −0.393496 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 59.3729 | 0.343196 | 0.171598 | − | 0.985167i | \(-0.445107\pi\) | ||||
0.171598 | + | 0.985167i | \(0.445107\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − 27.3385i | − 0.156220i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − 252.782i | − 1.41219i | −0.708118 | − | 0.706094i | \(-0.750455\pi\) | ||||
0.708118 | − | 0.706094i | \(-0.249545\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −125.373 | −0.692670 | −0.346335 | − | 0.938111i | \(-0.612574\pi\) | ||||
−0.346335 | + | 0.938111i | \(0.612574\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 79.7143 | 0.430888 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − 269.545i | − 1.44142i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − 97.4640i | − 0.510283i | −0.966904 | − | 0.255141i | \(-0.917878\pi\) | ||||
0.966904 | − | 0.255141i | \(-0.0821220\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −342.376 | −1.77397 | −0.886985 | − | 0.461798i | \(-0.847204\pi\) | ||||
−0.886985 | + | 0.461798i | \(0.847204\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 74.4829 | 0.378086 | 0.189043 | − | 0.981969i | \(-0.439461\pi\) | ||||
0.189043 | + | 0.981969i | \(0.439461\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − 178.027i | − 0.894606i | −0.894382 | − | 0.447303i | \(-0.852385\pi\) | ||||
0.894382 | − | 0.447303i | \(-0.147615\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 140.917i | 0.694173i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −20.8046 | −0.101486 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 262.491 | 1.25594 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − 185.893i | − 0.881008i | −0.897751 | − | 0.440504i | \(-0.854800\pi\) | ||||
0.897751 | − | 0.440504i | \(-0.145200\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 156.589i | 0.728321i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 26.4444 | 0.121863 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −247.178 | −1.11845 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − 202.724i | − 0.909074i | −0.890728 | − | 0.454537i | \(-0.849805\pi\) | ||||
0.890728 | − | 0.454537i | \(-0.150195\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − 51.2708i | − 0.225863i | −0.993603 | − | 0.112931i | \(-0.963976\pi\) | ||||
0.993603 | − | 0.112931i | \(-0.0360240\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −337.056 | −1.47186 | −0.735930 | − | 0.677058i | \(-0.763255\pi\) | ||||
−0.735930 | + | 0.677058i | \(0.763255\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 80.2851 | 0.344571 | 0.172286 | − | 0.985047i | \(-0.444885\pi\) | ||||
0.172286 | + | 0.985047i | \(0.444885\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 85.0203i | 0.361789i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − 330.808i | − 1.38413i | −0.721834 | − | 0.692066i | \(-0.756701\pi\) | ||||
0.721834 | − | 0.692066i | \(-0.243299\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −359.914 | −1.49342 | −0.746710 | − | 0.665150i | \(-0.768368\pi\) | ||||
−0.746710 | + | 0.665150i | \(0.768368\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −42.7184 | −0.174361 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − 240.710i | − 0.974534i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 312.213i | 1.24388i | 0.783067 | + | 0.621938i | \(0.213654\pi\) | ||||
−0.783067 | + | 0.621938i | \(0.786346\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −411.280 | −1.62561 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −80.2592 | −0.312293 | −0.156146 | − | 0.987734i | \(-0.549907\pi\) | ||||
−0.156146 | + | 0.987734i | \(0.549907\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 194.920i | 0.752586i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 487.967i | 1.85539i | 0.373342 | + | 0.927694i | \(0.378212\pi\) | ||||
−0.373342 | + | 0.927694i | \(0.621788\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −124.719 | −0.470639 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −309.553 | −1.15076 | −0.575378 | − | 0.817888i | \(-0.695145\pi\) | ||||
−0.575378 | + | 0.817888i | \(0.695145\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 48.9693i | 0.180698i | 0.995910 | + | 0.0903492i | \(0.0287983\pi\) | ||||
−0.995910 | + | 0.0903492i | \(0.971202\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | − 55.2016i | − 0.200733i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 199.644 | 0.720736 | 0.360368 | − | 0.932810i | \(-0.382651\pi\) | ||||
0.360368 | + | 0.932810i | \(0.382651\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −61.1598 | −0.217650 | −0.108825 | − | 0.994061i | \(-0.534709\pi\) | ||||
−0.108825 | + | 0.994061i | \(0.534709\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − 432.506i | − 1.52829i | −0.645044 | − | 0.764145i | \(-0.723161\pi\) | ||||
0.645044 | − | 0.764145i | \(-0.276839\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − 50.8720i | − 0.177254i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 307.073 | 1.06254 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −283.234 | −0.966668 | −0.483334 | − | 0.875436i | \(-0.660574\pi\) | ||||
−0.483334 | + | 0.875436i | \(0.660574\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 124.194i | 0.420995i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 377.152i | 1.26138i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −382.896 | −1.27208 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −183.897 | −0.602940 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 100.077i | 0.325983i | 0.986627 | + | 0.162992i | \(0.0521144\pi\) | ||||
−0.986627 | + | 0.162992i | \(0.947886\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 404.185i | 1.29963i | 0.760092 | + | 0.649815i | \(0.225154\pi\) | ||||
−0.760092 | + | 0.649815i | \(0.774846\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −128.579 | −0.410795 | −0.205398 | − | 0.978679i | \(-0.565849\pi\) | ||||
−0.205398 | + | 0.978679i | \(0.565849\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 85.9315 | 0.271077 | 0.135539 | − | 0.990772i | \(-0.456724\pi\) | ||||
0.135539 | + | 0.990772i | \(0.456724\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 284.538i | 0.891969i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 580.475i | 1.79714i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −50.6209 | −0.155757 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −207.894 | −0.631898 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − 183.391i | − 0.554052i | −0.960862 | − | 0.277026i | \(-0.910651\pi\) | ||||
0.960862 | − | 0.277026i | \(-0.0893488\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | − 233.654i | − 0.697476i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 168.130 | 0.498901 | 0.249451 | − | 0.968388i | \(-0.419750\pi\) | ||||
0.249451 | + | 0.968388i | \(0.419750\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 53.3962 | 0.156587 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − 372.374i | − 1.08564i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − 137.414i | − 0.396006i | −0.980201 | − | 0.198003i | \(-0.936554\pi\) | ||||
0.980201 | − | 0.198003i | \(-0.0634455\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 13.4893 | 0.0386513 | 0.0193256 | − | 0.999813i | \(-0.493848\pi\) | ||||
0.0193256 | + | 0.999813i | \(0.493848\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −243.547 | −0.689935 | −0.344968 | − | 0.938615i | \(-0.612110\pi\) | ||||
−0.344968 | + | 0.938615i | \(0.612110\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − 171.612i | − 0.483413i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − 17.9166i | − 0.0499068i | −0.999689 | − | 0.0249534i | \(-0.992056\pi\) | ||||
0.999689 | − | 0.0249534i | \(-0.00794374\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −204.285 | −0.565887 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 209.120 | 0.572933 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − 238.417i | − 0.649637i | −0.945776 | − | 0.324818i | \(-0.894697\pi\) | ||||
0.945776 | − | 0.324818i | \(-0.105303\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − 304.968i | − 0.822016i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 181.271 | 0.485981 | 0.242990 | − | 0.970029i | \(-0.421872\pi\) | ||||
0.242990 | + | 0.970029i | \(0.421872\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 260.927 | 0.692114 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 306.206i | 0.807931i | 0.914774 | + | 0.403965i | \(0.132368\pi\) | ||||
−0.914774 | + | 0.403965i | \(0.867632\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − 144.027i | − 0.376050i | −0.982164 | − | 0.188025i | \(-0.939791\pi\) | ||||
0.982164 | − | 0.188025i | \(-0.0602086\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 134.981 | 0.350599 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 14.0099 | 0.0360152 | 0.0180076 | − | 0.999838i | \(-0.494268\pi\) | ||||
0.0180076 | + | 0.999838i | \(0.494268\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − 909.506i | − 2.32610i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | − 110.409i | − 0.279515i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −39.1084 | −0.0985098 | −0.0492549 | − | 0.998786i | \(-0.515685\pi\) | ||||
−0.0492549 | + | 0.998786i | \(0.515685\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 121.067 | 0.301913 | 0.150957 | − | 0.988540i | \(-0.451765\pi\) | ||||
0.150957 | + | 0.988540i | \(0.451765\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − 48.9653i | − 0.121502i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 393.579i | 0.967026i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −541.795 | −1.32468 | −0.662342 | − | 0.749202i | \(-0.730437\pi\) | ||||
−0.662342 | + | 0.749202i | \(0.730437\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −303.682 | −0.735307 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 161.839i | 0.389975i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − 687.825i | − 1.64159i | −0.571224 | − | 0.820794i | \(-0.693531\pi\) | ||||
0.571224 | − | 0.820794i | \(-0.306469\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 454.396 | 1.07932 | 0.539662 | − | 0.841882i | \(-0.318552\pi\) | ||||
0.539662 | + | 0.841882i | \(0.318552\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 122.073 | 0.287231 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − 449.670i | − 1.05309i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 466.145i | 1.08154i | 0.841169 | + | 0.540772i | \(0.181868\pi\) | ||||
−0.841169 | + | 0.540772i | \(0.818132\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 457.094 | 1.05565 | 0.527823 | − | 0.849355i | \(-0.323009\pi\) | ||||
0.527823 | + | 0.849355i | \(0.323009\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 885.706 | 2.02679 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 777.467i | 1.77100i | 0.464644 | + | 0.885498i | \(0.346182\pi\) | ||||
−0.464644 | + | 0.885498i | \(0.653818\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 247.484i | 0.558654i | 0.960196 | + | 0.279327i | \(0.0901114\pi\) | ||||
−0.960196 | + | 0.279327i | \(0.909889\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 258.693 | 0.581333 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −412.508 | −0.918726 | −0.459363 | − | 0.888249i | \(-0.651922\pi\) | ||||
−0.459363 | + | 0.888249i | \(0.651922\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − 102.720i | − 0.227761i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | − 123.780i | − 0.272044i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −745.400 | −1.63107 | −0.815537 | − | 0.578706i | \(-0.803558\pi\) | ||||
−0.815537 | + | 0.578706i | \(0.803558\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 81.6151 | 0.177039 | 0.0885196 | − | 0.996074i | \(-0.471786\pi\) | ||||
0.0885196 | + | 0.996074i | \(0.471786\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 292.248i | 0.631205i | 0.948891 | + | 0.315603i | \(0.102207\pi\) | ||||
−0.948891 | + | 0.315603i | \(0.897793\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − 51.4163i | − 0.110099i | −0.998484 | − | 0.0550495i | \(-0.982468\pi\) | ||||
0.998484 | − | 0.0550495i | \(-0.0175317\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 571.339 | 1.21821 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −773.139 | −1.63454 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 118.879i | 0.250271i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | − 122.593i | − 0.255935i | −0.991778 | − | 0.127967i | \(-0.959155\pi\) | ||||
0.991778 | − | 0.127967i | \(-0.0408453\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 360.920 | 0.750354 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 163.141 | 0.336373 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 65.9859i | 0.135495i | 0.997703 | + | 0.0677474i | \(0.0215812\pi\) | ||||
−0.997703 | + | 0.0677474i | \(0.978419\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 361.163i | 0.735567i | 0.929911 | + | 0.367783i | \(0.119883\pi\) | ||||
−0.929911 | + | 0.367783i | \(0.880117\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −629.229 | −1.27633 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 419.630 | 0.844326 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 711.138i | 1.42513i | 0.701608 | + | 0.712564i | \(0.252466\pi\) | ||||
−0.701608 | + | 0.712564i | \(0.747534\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − 353.756i | − 0.703292i | −0.936133 | − | 0.351646i | \(-0.885622\pi\) | ||||
0.936133 | − | 0.351646i | \(-0.114378\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −65.7610 | −0.130220 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 478.049 | 0.939192 | 0.469596 | − | 0.882881i | \(-0.344400\pi\) | ||||
0.469596 | + | 0.882881i | \(0.344400\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 511.348i | 1.00068i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | − 63.0311i | − 0.122390i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −419.778 | −0.811949 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 35.7365 | 0.0685921 | 0.0342960 | − | 0.999412i | \(-0.489081\pi\) | ||||
0.0342960 | + | 0.999412i | \(0.489081\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − 733.562i | − 1.40260i | −0.712864 | − | 0.701302i | \(-0.752602\pi\) | ||||
0.712864 | − | 0.701302i | \(-0.247398\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 118.081i | 0.224062i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −858.753 | −1.62335 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −94.1965 | −0.176729 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − 10.0780i | − 0.0188373i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − 210.917i | − 0.391312i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −608.939 | −1.12558 | −0.562790 | − | 0.826600i | \(-0.690272\pi\) | ||||
−0.562790 | + | 0.826600i | \(0.690272\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 432.266 | 0.793148 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 78.5868i | 0.143669i | 0.997417 | + | 0.0718344i | \(0.0228853\pi\) | ||||
−0.997417 | + | 0.0718344i | \(0.977115\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − 612.763i | − 1.11209i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 269.974 | 0.488200 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −928.488 | −1.66694 | −0.833472 | − | 0.552561i | \(-0.813651\pi\) | ||||
−0.833472 | + | 0.552561i | \(0.813651\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 708.984i | 1.26831i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − 447.978i | − 0.795697i | −0.917451 | − | 0.397849i | \(-0.869757\pi\) | ||||
0.917451 | − | 0.397849i | \(-0.130243\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 168.986 | 0.299090 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −571.441 | −1.00429 | −0.502145 | − | 0.864783i | \(-0.667456\pi\) | ||||
−0.502145 | + | 0.864783i | \(0.667456\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 990.801i | 1.73520i | 0.497260 | + | 0.867602i | \(0.334340\pi\) | ||||
−0.497260 | + | 0.867602i | \(0.665660\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − 186.263i | − 0.323935i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 826.638 | 1.43265 | 0.716324 | − | 0.697768i | \(-0.245823\pi\) | ||||
0.716324 | + | 0.697768i | \(0.245823\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −395.735 | −0.681127 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − 615.787i | − 1.05624i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 900.009i | 1.53323i | 0.642104 | + | 0.766617i | \(0.278062\pi\) | ||||
−0.642104 | + | 0.766617i | \(0.721938\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −114.991 | −0.195230 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 704.088 | 1.18733 | 0.593666 | − | 0.804711i | \(-0.297680\pi\) | ||||
0.593666 | + | 0.804711i | \(0.297680\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 298.497i | 0.501675i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 376.098i | 0.627876i | 0.949444 | + | 0.313938i | \(0.101648\pi\) | ||||
−0.949444 | + | 0.313938i | \(0.898352\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 430.191 | 0.715791 | 0.357896 | − | 0.933762i | \(-0.383494\pi\) | ||||
0.357896 | + | 0.933762i | \(0.383494\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 1.98684 | 0.00328404 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − 93.4019i | − 0.153875i | −0.997036 | − | 0.0769373i | \(-0.975486\pi\) | ||||
0.997036 | − | 0.0769373i | \(-0.0245141\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 384.944i | 0.630024i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 156.506 | 0.255312 | 0.127656 | − | 0.991818i | \(-0.459255\pi\) | ||||
0.127656 | + | 0.991818i | \(0.459255\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 553.493 | 0.897072 | 0.448536 | − | 0.893765i | \(-0.351946\pi\) | ||||
0.448536 | + | 0.893765i | \(0.351946\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 14.4398i | 0.0233276i | 0.999932 | + | 0.0116638i | \(0.00371278\pi\) | ||||
−0.999932 | + | 0.0116638i | \(0.996287\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 632.564i | 1.01535i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 25.0000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −870.364 | −1.38373 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − 352.389i | − 0.558460i | −0.960224 | − | 0.279230i | \(-0.909921\pi\) | ||||
0.960224 | − | 0.279230i | \(-0.0900793\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | − 293.608i | − 0.462375i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −193.415 | −0.303634 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 545.742 | 0.851391 | 0.425696 | − | 0.904866i | \(-0.360029\pi\) | ||||
0.425696 | + | 0.904866i | \(0.360029\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 757.447i | 1.17799i | 0.808137 | + | 0.588995i | \(0.200476\pi\) | ||||
−0.808137 | + | 0.588995i | \(0.799524\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − 1161.36i | − 1.79500i | −0.441016 | − | 0.897499i | \(-0.645382\pi\) | ||||
0.441016 | − | 0.897499i | \(-0.354618\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −613.191 | −0.944824 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −621.231 | −0.951348 | −0.475674 | − | 0.879622i | \(-0.657796\pi\) | ||||
−0.475674 | + | 0.879622i | \(0.657796\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − 169.390i | − 0.258610i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − 736.047i | − 1.11692i | −0.829533 | − | 0.558458i | \(-0.811393\pi\) | ||||
0.829533 | − | 0.558458i | \(-0.188607\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −383.845 | −0.580704 | −0.290352 | − | 0.956920i | \(-0.593772\pi\) | ||||
−0.290352 | + | 0.956920i | \(0.593772\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −290.686 | −0.437121 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 960.096i | 1.43942i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − 907.968i | − 1.35316i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 984.464 | 1.46280 | 0.731400 | − | 0.681949i | \(-0.238867\pi\) | ||||
0.731400 | + | 0.681949i | \(0.238867\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 673.154 | 0.994319 | 0.497160 | − | 0.867659i | \(-0.334376\pi\) | ||||
0.497160 | + | 0.867659i | \(0.334376\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 398.918i | 0.587507i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − 291.192i | − 0.426343i | −0.977015 | − | 0.213171i | \(-0.931621\pi\) | ||||
0.977015 | − | 0.213171i | \(-0.0683793\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 149.353 | 0.218034 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −564.689 | −0.819578 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − 943.693i | − 1.36569i | −0.730563 | − | 0.682846i | \(-0.760742\pi\) | ||||
0.730563 | − | 0.682846i | \(-0.239258\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | − 85.2420i | − 0.122650i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 227.156 | 0.325905 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 885.681 | 1.26345 | 0.631727 | − | 0.775191i | \(-0.282346\pi\) | ||||
0.631727 | + | 0.775191i | \(0.282346\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − 847.588i | − 1.20567i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − 160.801i | − 0.227441i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 286.183 | 0.403644 | 0.201822 | − | 0.979422i | \(-0.435314\pi\) | ||||
0.201822 | + | 0.979422i | \(0.435314\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 180.171 | 0.252694 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − 249.935i | − 0.349559i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | − 666.163i | − 0.926513i | −0.886224 | − | 0.463257i | \(-0.846681\pi\) | ||||
0.886224 | − | 0.463257i | \(-0.153319\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 154.125 | 0.213766 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −128.863 | −0.177742 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 856.270i | 1.17781i | 0.808201 | + | 0.588907i | \(0.200441\pi\) | ||||
−0.808201 | + | 0.588907i | \(0.799559\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − 1709.72i | − 2.33888i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 769.487 | 1.04978 | 0.524889 | − | 0.851171i | \(-0.324107\pi\) | ||||
0.524889 | + | 0.851171i | \(0.324107\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 1153.64 | 1.56532 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − 1156.70i | − 1.56522i | −0.622511 | − | 0.782611i | \(-0.713887\pi\) | ||||
0.622511 | − | 0.782611i | \(-0.286113\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 426.794i | 0.574421i | 0.957868 | + | 0.287210i | \(0.0927278\pi\) | ||||
−0.957868 | + | 0.287210i | \(0.907272\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 283.348 | 0.380332 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 24.6429 | 0.0329011 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1222.03i | 1.62721i | 0.581420 | + | 0.813604i | \(0.302497\pi\) | ||||
−0.581420 | + | 0.813604i | \(0.697503\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − 153.037i | − 0.202698i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 1312.95 | 1.73442 | 0.867209 | − | 0.497945i | \(-0.165912\pi\) | ||||
0.867209 | + | 0.497945i | \(0.165912\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 189.584 | 0.249124 | 0.124562 | − | 0.992212i | \(-0.460247\pi\) | ||||
0.124562 | + | 0.992212i | \(0.460247\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 1056.99i | 1.38531i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 562.308i | 0.733127i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 254.995 | 0.331594 | 0.165797 | − | 0.986160i | \(-0.446980\pi\) | ||||
0.165797 | + | 0.986160i | \(0.446980\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 23.2536 | 0.0300823 | 0.0150411 | − | 0.999887i | \(-0.495212\pi\) | ||||
0.0150411 | + | 0.999887i | \(0.495212\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 24.1824i | 0.0312030i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 221.212i | 0.283969i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 847.312 | 1.08491 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 57.1935 | 0.0728580 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 220.593i | 0.280296i | 0.990131 | + | 0.140148i | \(0.0447579\pi\) | ||||
−0.990131 | + | 0.140148i | \(0.955242\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 413.209i | 0.522388i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −832.625 | −1.04997 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 1010.38 | 1.26773 | 0.633867 | − | 0.773442i | \(-0.281467\pi\) | ||||
0.633867 | + | 0.773442i | \(0.281467\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − 928.298i | − 1.16183i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 1032.51i | 1.28581i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 455.455 | 0.565783 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −1410.37 | −1.74335 | −0.871674 | − | 0.490086i | \(-0.836965\pi\) | ||||
−0.871674 | + | 0.490086i | \(0.836965\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − 950.157i | − 1.17159i | −0.810460 | − | 0.585793i | \(-0.800783\pi\) | ||||
0.810460 | − | 0.585793i | \(-0.199217\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | − 141.939i | − 0.174158i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1664.98 | 2.03792 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 77.3347 | 0.0941957 | 0.0470979 | − | 0.998890i | \(-0.485003\pi\) | ||||
0.0470979 | + | 0.998890i | \(0.485003\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 1260.16i | 1.53118i | 0.643328 | + | 0.765591i | \(0.277553\pi\) | ||||
−0.643328 | + | 0.765591i | \(0.722447\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 438.047i | 0.529681i | 0.964292 | + | 0.264841i | \(0.0853194\pi\) | ||||
−0.964292 | + | 0.264841i | \(0.914681\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −361.388 | −0.435933 | −0.217966 | − | 0.975956i | \(-0.569942\pi\) | ||||
−0.217966 | + | 0.975956i | \(0.569942\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 466.423 | 0.559931 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − 27.6760i | − 0.0331450i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − 785.017i | − 0.935658i | −0.883819 | − | 0.467829i | \(-0.845036\pi\) | ||||
0.883819 | − | 0.467829i | \(-0.154964\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −176.771 | −0.210192 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 148.700 | 0.175977 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 4.85829i | 0.00573588i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 1328.03i | 1.56055i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −1113.79 | −1.30573 | −0.652865 | − | 0.757474i | \(-0.726433\pi\) | ||||
−0.652865 | + | 0.757474i | \(0.726433\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 306.591 | 0.357749 | 0.178875 | − | 0.983872i | \(-0.442754\pi\) | ||||
0.178875 | + | 0.983872i | \(0.442754\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − 204.542i | − 0.238116i | −0.992887 | − | 0.119058i | \(-0.962013\pi\) | ||||
0.992887 | − | 0.119058i | \(-0.0379875\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 654.384i | 0.758266i | 0.925342 | + | 0.379133i | \(0.123778\pi\) | ||||
−0.925342 | + | 0.379133i | \(0.876222\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −132.762 | −0.153482 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 545.129 | 0.627306 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − 1057.91i | − 1.21459i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 61.1307i | 0.0698637i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 604.453 | 0.689228 | 0.344614 | − | 0.938744i | \(-0.388010\pi\) | ||||
0.344614 | + | 0.938744i | \(0.388010\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −1436.81 | −1.63089 | −0.815445 | − | 0.578834i | \(-0.803508\pi\) | ||||
−0.815445 | + | 0.578834i | \(0.803508\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − 120.993i | − 0.137025i | −0.997650 | − | 0.0685123i | \(-0.978175\pi\) | ||||
0.997650 | − | 0.0685123i | \(-0.0218252\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 286.448i | 0.322941i | 0.986878 | + | 0.161470i | \(0.0516236\pi\) | ||||
−0.986878 | + | 0.161470i | \(0.948376\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 717.940 | 0.807582 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 904.007 | 1.01233 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 565.237i | 0.631550i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − 124.649i | − 0.138652i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1361.75 | 1.51138 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 280.343 | 0.309771 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − 234.706i | − 0.258772i | −0.991594 | − | 0.129386i | \(-0.958699\pi\) | ||||
0.991594 | − | 0.129386i | \(-0.0413006\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − 491.244i | − 0.539236i | −0.962967 | − | 0.269618i | \(-0.913103\pi\) | ||||
0.962967 | − | 0.269618i | \(-0.0868974\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −799.063 | −0.875206 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 414.197 | 0.451687 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − 356.091i | − 0.387477i | −0.981053 | − | 0.193738i | \(-0.937939\pi\) | ||||
0.981053 | − | 0.193738i | \(-0.0620613\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − 777.002i | − 0.841822i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −178.246 | −0.192699 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 916.019 | 0.986027 | 0.493014 | − | 0.870022i | \(-0.335895\pi\) | ||||
0.493014 | + | 0.870022i | \(0.335895\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 454.217i | 0.487881i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 602.721i | 0.644621i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 143.818 | 0.153488 | 0.0767440 | − | 0.997051i | \(-0.475548\pi\) | ||||
0.0767440 | + | 0.997051i | \(0.475548\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −1488.04 | −1.58133 | −0.790667 | − | 0.612246i | \(-0.790266\pi\) | ||||
−0.790667 | + | 0.612246i | \(0.790266\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − 346.602i | − 0.367552i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − 1095.51i | − 1.15682i | −0.815745 | − | 0.578411i | \(-0.803673\pi\) | ||||
0.815745 | − | 0.578411i | \(-0.196327\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 946.829 | 0.997713 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −1277.86 | −1.34089 | −0.670443 | − | 0.741961i | \(-0.733896\pi\) | ||||
−0.670443 | + | 0.741961i | \(0.733896\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 217.936i | 0.228205i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 365.202i | 0.380816i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 937.609 | 0.975659 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 765.576 | 0.793343 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − 237.958i | − 0.246079i | −0.992402 | − | 0.123039i | \(-0.960736\pi\) | ||||
0.992402 | − | 0.123039i | \(-0.0392641\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − 1602.10i | − 1.64995i | −0.565169 | − | 0.824975i | \(-0.691189\pi\) | ||||
0.565169 | − | 0.824975i | \(-0.308811\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 208.436 | 0.214220 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −918.977 | −0.940611 | −0.470305 | − | 0.882504i | \(-0.655856\pi\) | ||||
−0.470305 | + | 0.882504i | \(0.655856\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 1277.27i | 1.30466i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − 1162.30i | − 1.18240i | −0.806525 | − | 0.591200i | \(-0.798654\pi\) | ||||
0.806525 | − | 0.591200i | \(-0.201346\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −166.549 | −0.169085 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −2608.75 | −2.63776 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − 491.614i | − 0.496079i | −0.968750 | − | 0.248040i | \(-0.920214\pi\) | ||||
0.968750 | − | 0.248040i | \(-0.0797863\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 398.080i | 0.400080i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 1262.51 | 1.26630 | 0.633152 | − | 0.774027i | \(-0.281761\pi\) | ||||
0.633152 | + | 0.774027i | \(0.281761\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(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 | 2880.3.e.j.2431.2 | 8 | ||
3.2 | odd | 2 | 960.3.e.c.511.3 | 8 | |||
4.3 | odd | 2 | inner | 2880.3.e.j.2431.3 | 8 | ||
8.3 | odd | 2 | 180.3.c.b.91.2 | 8 | |||
8.5 | even | 2 | 180.3.c.b.91.1 | 8 | |||
12.11 | even | 2 | 960.3.e.c.511.8 | 8 | |||
24.5 | odd | 2 | 60.3.c.a.31.8 | yes | 8 | ||
24.11 | even | 2 | 60.3.c.a.31.7 | ✓ | 8 | ||
40.3 | even | 4 | 900.3.f.f.199.12 | 16 | |||
40.13 | odd | 4 | 900.3.f.f.199.6 | 16 | |||
40.19 | odd | 2 | 900.3.c.u.451.7 | 8 | |||
40.27 | even | 4 | 900.3.f.f.199.5 | 16 | |||
40.29 | even | 2 | 900.3.c.u.451.8 | 8 | |||
40.37 | odd | 4 | 900.3.f.f.199.11 | 16 | |||
120.29 | odd | 2 | 300.3.c.d.151.1 | 8 | |||
120.53 | even | 4 | 300.3.f.b.199.11 | 16 | |||
120.59 | even | 2 | 300.3.c.d.151.2 | 8 | |||
120.77 | even | 4 | 300.3.f.b.199.6 | 16 | |||
120.83 | odd | 4 | 300.3.f.b.199.5 | 16 | |||
120.107 | odd | 4 | 300.3.f.b.199.12 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
60.3.c.a.31.7 | ✓ | 8 | 24.11 | even | 2 | ||
60.3.c.a.31.8 | yes | 8 | 24.5 | odd | 2 | ||
180.3.c.b.91.1 | 8 | 8.5 | even | 2 | |||
180.3.c.b.91.2 | 8 | 8.3 | odd | 2 | |||
300.3.c.d.151.1 | 8 | 120.29 | odd | 2 | |||
300.3.c.d.151.2 | 8 | 120.59 | even | 2 | |||
300.3.f.b.199.5 | 16 | 120.83 | odd | 4 | |||
300.3.f.b.199.6 | 16 | 120.77 | even | 4 | |||
300.3.f.b.199.11 | 16 | 120.53 | even | 4 | |||
300.3.f.b.199.12 | 16 | 120.107 | odd | 4 | |||
900.3.c.u.451.7 | 8 | 40.19 | odd | 2 | |||
900.3.c.u.451.8 | 8 | 40.29 | even | 2 | |||
900.3.f.f.199.5 | 16 | 40.27 | even | 4 | |||
900.3.f.f.199.6 | 16 | 40.13 | odd | 4 | |||
900.3.f.f.199.11 | 16 | 40.37 | odd | 4 | |||
900.3.f.f.199.12 | 16 | 40.3 | even | 4 | |||
960.3.e.c.511.3 | 8 | 3.2 | odd | 2 | |||
960.3.e.c.511.8 | 8 | 12.11 | even | 2 | |||
2880.3.e.j.2431.2 | 8 | 1.1 | even | 1 | trivial | ||
2880.3.e.j.2431.3 | 8 | 4.3 | odd | 2 | inner |