Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [288,3,Mod(17,288)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(288, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("288.17");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 288 = 2^{5} \cdot 3^{2} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 288.h (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: | \(7.84743161358\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | 8.0.33808912384.2 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 2x^{7} + 11x^{6} - 18x^{5} + 47x^{4} - 28x^{3} - 44x^{2} + 48x + 36 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{17}]\) |
Coefficient ring index: | \( 2^{14}\cdot 3^{2} \) |
Twist minimal: | no (minimal twist has level 72) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 17.4 | ||
Root | \(-0.651388 + 2.66948i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 288.17 |
Dual form | 288.3.h.a.17.3 |
$q$-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 \(\left(\mathbb{Z}/288\mathbb{Z}\right)^\times\).
\(n\) | \(37\) | \(65\) | \(127\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(1\) |
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 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.07498 | −0.214997 | −0.107498 | − | 0.994205i | \(-0.534284\pi\) | ||||
−0.107498 | + | 0.994205i | \(0.534284\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −7.21110 | −1.03016 | −0.515079 | − | 0.857143i | \(-0.672237\pi\) | ||||
−0.515079 | + | 0.857143i | \(0.672237\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 16.3517 | 1.48652 | 0.743258 | − | 0.669004i | \(-0.233279\pi\) | ||||
0.743258 | + | 0.669004i | \(0.233279\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 21.6045i | 1.66189i | 0.556357 | + | 0.830943i | \(0.312199\pi\) | ||||
−0.556357 | + | 0.830943i | \(0.687801\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 18.9819i | 1.11658i | 0.829646 | + | 0.558290i | \(0.188542\pi\) | ||||
−0.829646 | + | 0.558290i | \(0.811458\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 17.0438i | 0.897040i | 0.893773 | + | 0.448520i | \(0.148049\pi\) | ||||
−0.893773 | + | 0.448520i | \(0.851951\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − 1.11567i | − 0.0485074i | −0.999706 | − | 0.0242537i | \(-0.992279\pi\) | ||||
0.999706 | − | 0.0242537i | \(-0.00772094\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −23.8444 | −0.953776 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 29.4784 | 1.01650 | 0.508249 | − | 0.861210i | \(-0.330293\pi\) | ||||
0.508249 | + | 0.861210i | \(0.330293\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −5.63331 | −0.181720 | −0.0908598 | − | 0.995864i | \(-0.528962\pi\) | ||||
−0.0908598 | + | 0.995864i | \(0.528962\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 7.75182 | 0.221480 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 17.0438i | 0.460642i | 0.973115 | + | 0.230321i | \(0.0739776\pi\) | ||||
−0.973115 | + | 0.230321i | \(0.926022\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − 27.4671i | − 0.669930i | −0.942231 | − | 0.334965i | \(-0.891275\pi\) | ||||
0.942231 | − | 0.334965i | \(-0.108725\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 52.3306i | 1.21699i | 0.793558 | + | 0.608495i | \(0.208226\pi\) | ||||
−0.793558 | + | 0.608495i | \(0.791774\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 64.5352i | 1.37309i | 0.727087 | + | 0.686545i | \(0.240874\pi\) | ||||
−0.727087 | + | 0.686545i | \(0.759126\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 3.00000 | 0.0612245 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 35.9283 | 0.677893 | 0.338946 | − | 0.940806i | \(-0.389929\pi\) | ||||
0.338946 | + | 0.940806i | \(0.389929\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −17.5778 | −0.319596 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −56.8069 | −0.962828 | −0.481414 | − | 0.876493i | \(-0.659877\pi\) | ||||
−0.481414 | + | 0.876493i | \(0.659877\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − 69.3743i | − 1.13728i | −0.822585 | − | 0.568642i | \(-0.807469\pi\) | ||||
0.822585 | − | 0.568642i | \(-0.192531\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | − 23.2245i | − 0.357300i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − 69.3743i | − 1.03544i | −0.855551 | − | 0.517719i | \(-0.826781\pi\) | ||||
0.855551 | − | 0.517719i | \(-0.173219\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − 98.4764i | − 1.38699i | −0.720461 | − | 0.693496i | \(-0.756070\pi\) | ||||
0.720461 | − | 0.693496i | \(-0.243930\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 37.6888 | 0.516285 | 0.258143 | − | 0.966107i | \(-0.416890\pi\) | ||||
0.258143 | + | 0.966107i | \(0.416890\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −117.914 | −1.53135 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 127.322 | 1.61167 | 0.805836 | − | 0.592138i | \(-0.201716\pi\) | ||||
0.805836 | + | 0.592138i | \(0.201716\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −7.75182 | −0.0933954 | −0.0466977 | − | 0.998909i | \(-0.514870\pi\) | ||||
−0.0466977 | + | 0.998909i | \(0.514870\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | − 20.4052i | − 0.240061i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 76.1475i | 0.855590i | 0.903876 | + | 0.427795i | \(0.140709\pi\) | ||||
−0.903876 | + | 0.427795i | \(0.859291\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − 155.792i | − 1.71200i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | − 18.3218i | − 0.192861i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 4.84441 | 0.0499424 | 0.0249712 | − | 0.999688i | \(-0.492051\pi\) | ||||
0.0249712 | + | 0.999688i | \(0.492051\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −105.635 | −1.04589 | −0.522946 | − | 0.852366i | \(-0.675167\pi\) | ||||
−0.522946 | + | 0.852366i | \(0.675167\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −104.789 | −1.01737 | −0.508684 | − | 0.860953i | \(-0.669868\pi\) | ||||
−0.508684 | + | 0.860953i | \(0.669868\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 65.4067 | 0.611278 | 0.305639 | − | 0.952147i | \(-0.401130\pi\) | ||||
0.305639 | + | 0.952147i | \(0.401130\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − 3.36144i | − 0.0308389i | −0.999881 | − | 0.0154195i | \(-0.995092\pi\) | ||||
0.999881 | − | 0.0154195i | \(-0.00490836\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − 84.1927i | − 0.745068i | −0.928019 | − | 0.372534i | \(-0.878489\pi\) | ||||
0.928019 | − | 0.372534i | \(-0.121511\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1.19933i | 0.0104289i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | − 136.880i | − 1.15025i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 146.378 | 1.20973 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 52.5069 | 0.420056 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 45.5223 | 0.358443 | 0.179222 | − | 0.983809i | \(-0.442642\pi\) | ||||
0.179222 | + | 0.983809i | \(0.442642\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −129.117 | −0.985629 | −0.492814 | − | 0.870134i | \(-0.664032\pi\) | ||||
−0.492814 | + | 0.870134i | \(0.664032\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − 122.904i | − 0.924092i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − 10.9367i | − 0.0798296i | −0.999203 | − | 0.0399148i | \(-0.987291\pi\) | ||||
0.999203 | − | 0.0399148i | \(-0.0127087\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − 1.19933i | − 0.00862825i | −0.999991 | − | 0.00431412i | \(-0.998627\pi\) | ||||
0.999991 | − | 0.00431412i | \(-0.00137323\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 353.270i | 2.47042i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −31.6888 | −0.218544 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −29.9323 | −0.200888 | −0.100444 | − | 0.994943i | \(-0.532026\pi\) | ||||
−0.100444 | + | 0.994943i | \(0.532026\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −61.5223 | −0.407432 | −0.203716 | − | 0.979030i | \(-0.565302\pi\) | ||||
−0.203716 | + | 0.979030i | \(0.565302\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 6.05571 | 0.0390691 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 137.549i | 0.876110i | 0.898948 | + | 0.438055i | \(0.144333\pi\) | ||||
−0.898948 | + | 0.438055i | \(0.855667\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 8.04521i | 0.0499702i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 191.079i | 1.17227i | 0.810215 | + | 0.586133i | \(0.199350\pi\) | ||||
−0.810215 | + | 0.586133i | \(0.800650\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − 233.125i | − 1.39596i | −0.716118 | − | 0.697980i | \(-0.754083\pi\) | ||||
0.716118 | − | 0.697980i | \(-0.245917\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −297.755 | −1.76187 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 323.809 | 1.87173 | 0.935864 | − | 0.352363i | \(-0.114622\pi\) | ||||
0.935864 | + | 0.352363i | \(0.114622\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 171.944 | 0.982540 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 185.924 | 1.03868 | 0.519342 | − | 0.854567i | \(-0.326177\pi\) | ||||
0.519342 | + | 0.854567i | \(0.326177\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 126.266i | 0.697600i | 0.937197 | + | 0.348800i | \(0.113411\pi\) | ||||
−0.937197 | + | 0.348800i | \(0.886589\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | − 18.3218i | − 0.0990365i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 310.385i | 1.65982i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 233.125i | 1.22055i | 0.792189 | + | 0.610275i | \(0.208941\pi\) | ||||
−0.792189 | + | 0.610275i | \(0.791059\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −117.378 | −0.608174 | −0.304087 | − | 0.952644i | \(-0.598351\pi\) | ||||
−0.304087 | + | 0.952644i | \(0.598351\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 296.313 | 1.50413 | 0.752064 | − | 0.659091i | \(-0.229059\pi\) | ||||
0.752064 | + | 0.659091i | \(0.229059\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −233.011 | −1.17091 | −0.585455 | − | 0.810705i | \(-0.699084\pi\) | ||||
−0.585455 | + | 0.810705i | \(0.699084\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −212.572 | −1.04715 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 29.5267i | 0.144033i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 278.694i | 1.33346i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − 35.2868i | − 0.167236i | −0.996498 | − | 0.0836181i | \(-0.973352\pi\) | ||||
0.996498 | − | 0.0836181i | \(-0.0266476\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | − 56.2545i | − 0.261649i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 40.6224 | 0.187200 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −410.094 | −1.85563 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 51.8335 | 0.232437 | 0.116219 | − | 0.993224i | \(-0.462923\pi\) | ||||
0.116219 | + | 0.993224i | \(0.462923\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 334.786 | 1.47483 | 0.737413 | − | 0.675442i | \(-0.236047\pi\) | ||||
0.737413 | + | 0.675442i | \(0.236047\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 219.407i | 0.958108i | 0.877786 | + | 0.479054i | \(0.159020\pi\) | ||||
−0.877786 | + | 0.479054i | \(0.840980\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − 203.867i | − 0.874965i | −0.899227 | − | 0.437482i | \(-0.855870\pi\) | ||||
0.899227 | − | 0.437482i | \(-0.144130\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − 69.3743i | − 0.295210i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 54.0232i | 0.226038i | 0.993593 | + | 0.113019i | \(0.0360522\pi\) | ||||
−0.993593 | + | 0.113019i | \(0.963948\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 327.600 | 1.35933 | 0.679667 | − | 0.733520i | \(-0.262124\pi\) | ||||
0.679667 | + | 0.733520i | \(0.262124\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −3.22495 | −0.0131631 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −368.222 | −1.49078 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 362.281 | 1.44335 | 0.721676 | − | 0.692231i | \(-0.243372\pi\) | ||||
0.721676 | + | 0.692231i | \(0.243372\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − 18.2431i | − 0.0721070i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − 21.2132i | − 0.0825416i | −0.999148 | − | 0.0412708i | \(-0.986859\pi\) | ||||
0.999148 | − | 0.0412708i | \(-0.0131406\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − 122.904i | − 0.474534i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − 205.878i | − 0.782806i | −0.920219 | − | 0.391403i | \(-0.871990\pi\) | ||||
0.920219 | − | 0.391403i | \(-0.128010\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −38.6224 | −0.145745 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −2.77109 | −0.0103014 | −0.00515072 | − | 0.999987i | \(-0.501640\pi\) | ||||
−0.00515072 | + | 0.999987i | \(0.501640\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 125.744 | 0.464001 | 0.232001 | − | 0.972716i | \(-0.425473\pi\) | ||||
0.232001 | + | 0.972716i | \(0.425473\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −389.896 | −1.41780 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 162.752i | 0.587552i | 0.955874 | + | 0.293776i | \(0.0949119\pi\) | ||||
−0.955874 | + | 0.293776i | \(0.905088\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 301.227i | 1.07198i | 0.844223 | + | 0.535992i | \(0.180062\pi\) | ||||
−0.844223 | + | 0.535992i | \(0.819938\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − 31.6888i | − 0.111975i | −0.998431 | − | 0.0559874i | \(-0.982169\pi\) | ||||
0.998431 | − | 0.0559874i | \(-0.0178307\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 198.068i | 0.690134i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −71.3112 | −0.246751 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −304.913 | −1.04066 | −0.520329 | − | 0.853966i | \(-0.674191\pi\) | ||||
−0.520329 | + | 0.853966i | \(0.674191\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 61.0665 | 0.207005 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 24.1035 | 0.0806137 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | − 377.361i | − 1.25369i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 74.5763i | 0.244512i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − 105.860i | − 0.344822i | −0.985025 | − | 0.172411i | \(-0.944844\pi\) | ||||
0.985025 | − | 0.172411i | \(-0.0551558\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − 555.157i | − 1.78507i | −0.450978 | − | 0.892535i | \(-0.648925\pi\) | ||||
0.450978 | − | 0.892535i | \(-0.351075\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 158.000 | 0.504792 | 0.252396 | − | 0.967624i | \(-0.418781\pi\) | ||||
0.252396 | + | 0.967624i | \(0.418781\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 97.0351 | 0.306105 | 0.153052 | − | 0.988218i | \(-0.451090\pi\) | ||||
0.153052 | + | 0.988218i | \(0.451090\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 482.022 | 1.51104 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −323.522 | −1.00162 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − 515.147i | − 1.58507i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | − 465.370i | − 1.41450i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − 619.572i | − 1.87182i | −0.352242 | − | 0.935909i | \(-0.614581\pi\) | ||||
0.352242 | − | 0.935909i | \(-0.385419\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 74.5763i | 0.222616i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −170.755 | −0.506692 | −0.253346 | − | 0.967376i | \(-0.581531\pi\) | ||||
−0.253346 | + | 0.967376i | \(0.581531\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −92.1141 | −0.270129 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 331.711 | 0.967087 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −300.386 | −0.865666 | −0.432833 | − | 0.901474i | \(-0.642486\pi\) | ||||
−0.432833 | + | 0.901474i | \(0.642486\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 53.5299i | 0.153381i | 0.997055 | + | 0.0766904i | \(0.0244353\pi\) | ||||
−0.997055 | + | 0.0766904i | \(0.975565\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − 600.475i | − 1.70106i | −0.525925 | − | 0.850531i | \(-0.676281\pi\) | ||||
0.525925 | − | 0.850531i | \(-0.323719\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 105.860i | 0.298199i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 148.508i | 0.413671i | 0.978376 | + | 0.206836i | \(0.0663165\pi\) | ||||
−0.978376 | + | 0.206836i | \(0.933683\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 70.5106 | 0.195320 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −40.5149 | −0.111000 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −316.389 | −0.862094 | −0.431047 | − | 0.902329i | \(-0.641856\pi\) | ||||
−0.431047 | + | 0.902329i | \(0.641856\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −259.083 | −0.698336 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − 626.768i | − 1.68034i | −0.542321 | − | 0.840171i | \(-0.682455\pi\) | ||||
0.542321 | − | 0.840171i | \(-0.317545\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 636.867i | 1.68930i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 331.027i | 0.873423i | 0.899602 | + | 0.436711i | \(0.143857\pi\) | ||||
−0.899602 | + | 0.436711i | \(0.856143\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 407.765i | 1.06466i | 0.846537 | + | 0.532330i | \(0.178683\pi\) | ||||
−0.846537 | + | 0.532330i | \(0.821317\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 126.755 | 0.329234 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 53.5819 | 0.137743 | 0.0688714 | − | 0.997626i | \(-0.478060\pi\) | ||||
0.0688714 | + | 0.997626i | \(0.478060\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 21.1775 | 0.0541624 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −136.869 | −0.346504 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 289.744i | 0.729833i | 0.931040 | + | 0.364917i | \(0.118902\pi\) | ||||
−0.931040 | + | 0.364917i | \(0.881098\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − 203.458i | − 0.507376i | −0.967286 | − | 0.253688i | \(-0.918356\pi\) | ||||
0.967286 | − | 0.253688i | \(-0.0816436\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − 121.705i | − 0.301997i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 278.694i | 0.684752i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 412.844 | 1.00940 | 0.504700 | − | 0.863295i | \(-0.331603\pi\) | ||||
0.504700 | + | 0.863295i | \(0.331603\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 409.640 | 0.991865 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 8.33308 | 0.0200797 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 336.482 | 0.803059 | 0.401529 | − | 0.915846i | \(-0.368479\pi\) | ||||
0.401529 | + | 0.915846i | \(0.368479\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 217.481i | 0.516582i | 0.966067 | + | 0.258291i | \(0.0831594\pi\) | ||||
−0.966067 | + | 0.258291i | \(0.916841\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | − 452.611i | − 1.06497i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 500.265i | 1.17158i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − 750.994i | − 1.74245i | −0.490888 | − | 0.871223i | \(-0.663328\pi\) | ||||
0.490888 | − | 0.871223i | \(-0.336672\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −176.133 | −0.406773 | −0.203387 | − | 0.979098i | \(-0.565195\pi\) | ||||
−0.203387 | + | 0.979098i | \(0.565195\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 19.0152 | 0.0435130 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −417.788 | −0.951681 | −0.475841 | − | 0.879531i | \(-0.657856\pi\) | ||||
−0.475841 | + | 0.879531i | \(0.657856\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −61.0471 | −0.137804 | −0.0689020 | − | 0.997623i | \(-0.521950\pi\) | ||||
−0.0689020 | + | 0.997623i | \(0.521950\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | − 81.8573i | − 0.183949i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 182.905i | 0.407360i | 0.979038 | + | 0.203680i | \(0.0652902\pi\) | ||||
−0.979038 | + | 0.203680i | \(0.934710\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − 449.134i | − 0.995863i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 167.474i | 0.368075i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −443.600 | −0.970678 | −0.485339 | − | 0.874326i | \(-0.661304\pi\) | ||||
−0.485339 | + | 0.874326i | \(0.661304\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −728.241 | −1.57970 | −0.789850 | − | 0.613301i | \(-0.789841\pi\) | ||||
−0.789850 | + | 0.613301i | \(0.789841\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 107.722 | 0.232662 | 0.116331 | − | 0.993211i | \(-0.462887\pi\) | ||||
0.116331 | + | 0.993211i | \(0.462887\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 820.248 | 1.75642 | 0.878210 | − | 0.478276i | \(-0.158738\pi\) | ||||
0.878210 | + | 0.478276i | \(0.158738\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 500.265i | 1.06666i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 855.693i | 1.80908i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − 406.398i | − 0.855575i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | − 120.790i | − 0.252171i | −0.992019 | − | 0.126085i | \(-0.959759\pi\) | ||||
0.992019 | − | 0.126085i | \(-0.0402413\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −368.222 | −0.765534 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −5.20766 | −0.0107374 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 128.234 | 0.263314 | 0.131657 | − | 0.991295i | \(-0.457970\pi\) | ||||
0.131657 | + | 0.991295i | \(0.457970\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 382.144 | 0.778298 | 0.389149 | − | 0.921175i | \(-0.372769\pi\) | ||||
0.389149 | + | 0.921175i | \(0.372769\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 559.555i | 1.13500i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 710.123i | 1.42882i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 554.995i | 1.11221i | 0.831111 | + | 0.556107i | \(0.187705\pi\) | ||||
−0.831111 | + | 0.556107i | \(0.812295\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − 78.3943i | − 0.155854i | −0.996959 | − | 0.0779268i | \(-0.975170\pi\) | ||||
0.996959 | − | 0.0779268i | \(-0.0248300\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 113.556 | 0.224863 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 514.941 | 1.01167 | 0.505836 | − | 0.862630i | \(-0.331184\pi\) | ||||
0.505836 | + | 0.862630i | \(0.331184\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −271.778 | −0.531855 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 112.646 | 0.218731 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1055.26i | 2.04112i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − 489.695i | − 0.939914i | −0.882689 | − | 0.469957i | \(-0.844270\pi\) | ||||
0.882689 | − | 0.469957i | \(-0.155730\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 774.165i | 1.48024i | 0.672476 | + | 0.740119i | \(0.265231\pi\) | ||||
−0.672476 | + | 0.740119i | \(0.734769\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − 106.931i | − 0.202905i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 527.755 | 0.997647 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 593.415 | 1.11335 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −70.3112 | −0.131423 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 49.0551 | 0.0910112 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − 590.045i | − 1.09066i | −0.838223 | − | 0.545328i | \(-0.816405\pi\) | ||||
0.838223 | − | 0.545328i | \(-0.183595\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 3.61350i | 0.00663027i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 707.189i | 1.29285i | 0.762977 | + | 0.646425i | \(0.223737\pi\) | ||||
−0.762977 | + | 0.646425i | \(0.776263\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 502.423i | 0.911838i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −918.133 | −1.66028 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −75.0816 | −0.134796 | −0.0673982 | − | 0.997726i | \(-0.521470\pi\) | ||||
−0.0673982 | + | 0.997726i | \(0.521470\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −1130.58 | −2.02250 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 114.462 | 0.203307 | 0.101653 | − | 0.994820i | \(-0.467587\pi\) | ||||
0.101653 | + | 0.994820i | \(0.467587\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 90.5058i | 0.160187i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − 45.8199i | − 0.0805270i | −0.999189 | − | 0.0402635i | \(-0.987180\pi\) | ||||
0.999189 | − | 0.0402635i | \(-0.0128197\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − 830.093i | − 1.45375i | −0.686768 | − | 0.726877i | \(-0.740971\pi\) | ||||
0.686768 | − | 0.726877i | \(-0.259029\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 26.6025i | 0.0462652i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −69.3776 | −0.120239 | −0.0601193 | − | 0.998191i | \(-0.519148\pi\) | ||||
−0.0601193 | + | 0.998191i | \(0.519148\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 55.8991 | 0.0962120 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 587.489 | 1.00770 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 428.655 | 0.730248 | 0.365124 | − | 0.930959i | \(-0.381027\pi\) | ||||
0.365124 | + | 0.930959i | \(0.381027\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − 96.0127i | − 0.163010i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 77.0276i | 0.129895i | 0.997889 | + | 0.0649474i | \(0.0206880\pi\) | ||||
−0.997889 | + | 0.0649474i | \(0.979312\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 147.144i | 0.247301i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 963.566i | 1.60862i | 0.594207 | + | 0.804312i | \(0.297466\pi\) | ||||
−0.594207 | + | 0.804312i | \(0.702534\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 840.133 | 1.39789 | 0.698946 | − | 0.715175i | \(-0.253653\pi\) | ||||
0.698946 | + | 0.715175i | \(0.253653\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −157.354 | −0.260089 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −156.611 | −0.258008 | −0.129004 | − | 0.991644i | \(-0.541178\pi\) | ||||
−0.129004 | + | 0.991644i | \(0.541178\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −1394.25 | −2.28192 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − 426.094i | − 0.695096i | −0.937662 | − | 0.347548i | \(-0.887014\pi\) | ||||
0.937662 | − | 0.347548i | \(-0.112986\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − 963.520i | − 1.56162i | −0.624769 | − | 0.780810i | \(-0.714807\pi\) | ||||
0.624769 | − | 0.780810i | \(-0.285193\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 175.235i | 0.283093i | 0.989932 | + | 0.141547i | \(0.0452075\pi\) | ||||
−0.989932 | + | 0.141547i | \(0.954792\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − 549.107i | − 0.881392i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 539.666 | 0.863466 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −323.522 | −0.514344 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 1140.72 | 1.80780 | 0.903900 | − | 0.427744i | \(-0.140692\pi\) | ||||
0.903900 | + | 0.427744i | \(0.140692\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −48.9357 | −0.0770641 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 64.8136i | 0.101748i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − 351.730i | − 0.548721i | −0.961627 | − | 0.274360i | \(-0.911534\pi\) | ||||
0.961627 | − | 0.274360i | \(-0.0884661\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − 86.4181i | − 0.134398i | −0.997740 | − | 0.0671991i | \(-0.978594\pi\) | ||||
0.997740 | − | 0.0671991i | \(-0.0214063\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 430.723i | 0.665723i | 0.942976 | + | 0.332861i | \(0.108014\pi\) | ||||
−0.942976 | + | 0.332861i | \(0.891986\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −928.888 | −1.43126 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 886.670 | 1.35784 | 0.678920 | − | 0.734212i | \(-0.262448\pi\) | ||||
0.678920 | + | 0.734212i | \(0.262448\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 138.799 | 0.211907 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −352.833 | −0.535407 | −0.267704 | − | 0.963501i | \(-0.586265\pi\) | ||||
−0.267704 | + | 0.963501i | \(0.586265\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − 1206.26i | − 1.82489i | −0.409195 | − | 0.912447i | \(-0.634190\pi\) | ||||
0.409195 | − | 0.912447i | \(-0.365810\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 132.120i | 0.198677i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − 32.8882i | − 0.0493076i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − 1134.39i | − 1.69059i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −956.133 | −1.42070 | −0.710351 | − | 0.703847i | \(-0.751464\pi\) | ||||
−0.710351 | + | 0.703847i | \(0.751464\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 420.557 | 0.621207 | 0.310604 | − | 0.950540i | \(-0.399469\pi\) | ||||
0.310604 | + | 0.950540i | \(0.399469\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −34.9335 | −0.0514485 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −539.725 | −0.790227 | −0.395113 | − | 0.918632i | \(-0.629295\pi\) | ||||
−0.395113 | + | 0.918632i | \(0.629295\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 11.7567i | 0.0171631i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 776.214i | 1.12658i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − 432.090i | − 0.625312i | −0.949866 | − | 0.312656i | \(-0.898781\pi\) | ||||
0.949866 | − | 0.312656i | \(-0.101219\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 1.28926i | 0.00185504i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 521.378 | 0.748031 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −880.339 | −1.25583 | −0.627917 | − | 0.778280i | \(-0.716092\pi\) | ||||
−0.627917 | + | 0.778280i | \(0.716092\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −290.489 | −0.413214 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 761.745 | 1.07743 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − 799.367i | − 1.12746i | −0.825960 | − | 0.563729i | \(-0.809366\pi\) | ||||
0.825960 | − | 0.563729i | \(-0.190634\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 6.28491i | 0.00881474i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − 379.760i | − 0.531133i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | − 258.786i | − 0.359924i | −0.983674 | − | 0.179962i | \(-0.942402\pi\) | ||||
0.983674 | − | 0.179962i | \(-0.0575975\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 755.643 | 1.04805 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −702.896 | −0.969511 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 663.211 | 0.912257 | 0.456129 | − | 0.889914i | \(-0.349236\pi\) | ||||
0.456129 | + | 0.889914i | \(0.349236\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −993.332 | −1.35887 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 908.826i | 1.23987i | 0.784653 | + | 0.619936i | \(0.212841\pi\) | ||||
−0.784653 | + | 0.619936i | \(0.787159\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − 1134.39i | − 1.53920i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − 1112.39i | − 1.50526i | −0.658443 | − | 0.752631i | \(-0.728785\pi\) | ||||
0.658443 | − | 0.752631i | \(-0.271215\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 541.298i | 0.728530i | 0.931295 | + | 0.364265i | \(0.118680\pi\) | ||||
−0.931295 | + | 0.364265i | \(0.881320\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 32.1767 | 0.0431902 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −471.655 | −0.629713 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 763.699 | 1.01691 | 0.508455 | − | 0.861089i | \(-0.330217\pi\) | ||||
0.508455 | + | 0.861089i | \(0.330217\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 66.1354 | 0.0875966 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 419.134i | 0.553678i | 0.960916 | + | 0.276839i | \(0.0892869\pi\) | ||||
−0.960916 | + | 0.276839i | \(0.910713\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 1330.24i | 1.74802i | 0.485912 | + | 0.874008i | \(0.338488\pi\) | ||||
−0.485912 | + | 0.874008i | \(0.661512\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 24.2397i | 0.0317690i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − 1227.29i | − 1.60011i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 671.511 | 0.873226 | 0.436613 | − | 0.899649i | \(-0.356178\pi\) | ||||
0.436613 | + | 0.899649i | \(0.356178\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −1421.13 | −1.83846 | −0.919229 | − | 0.393724i | \(-0.871187\pi\) | ||||
−0.919229 | + | 0.393724i | \(0.871187\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 134.323 | 0.173320 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 468.143 | 0.600954 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − 1610.25i | − 2.06179i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − 147.863i | − 0.188361i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − 649.808i | − 0.825677i | −0.910804 | − | 0.412839i | \(-0.864537\pi\) | ||||
0.910804 | − | 0.412839i | \(-0.135463\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 607.122i | 0.767538i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1498.80 | 1.89004 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 422.946 | 0.530672 | 0.265336 | − | 0.964156i | \(-0.414517\pi\) | ||||
0.265336 | + | 0.964156i | \(0.414517\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −1225.00 | −1.53317 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 616.276 | 0.767467 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | − 8.64847i | − 0.0107434i | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − 1353.87i | − 1.67351i | −0.547574 | − | 0.836757i | \(-0.684448\pi\) | ||||
0.547574 | − | 0.836757i | \(-0.315552\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − 842.340i | − 1.03864i | −0.854579 | − | 0.519322i | \(-0.826185\pi\) | ||||
0.854579 | − | 0.519322i | \(-0.173815\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | − 205.407i | − 0.252033i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −891.909 | −1.09169 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −616.897 | −0.751397 | −0.375698 | − | 0.926742i | \(-0.622597\pi\) | ||||
−0.375698 | + | 0.926742i | \(0.622597\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −980.500 | −1.19137 | −0.595686 | − | 0.803217i | \(-0.703120\pi\) | ||||
−0.595686 | + | 0.803217i | \(0.703120\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 70.4951 | 0.0852419 | 0.0426210 | − | 0.999091i | \(-0.486429\pi\) | ||||
0.0426210 | + | 0.999091i | \(0.486429\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 515.147i | 0.621408i | 0.950507 | + | 0.310704i | \(0.100565\pi\) | ||||
−0.950507 | + | 0.310704i | \(0.899435\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 56.9456i | 0.0683621i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 250.606i | 0.300127i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − 47.1556i | − 0.0562045i | −0.999605 | − | 0.0281022i | \(-0.991054\pi\) | ||||
0.999605 | − | 0.0281022i | \(-0.00894640\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 27.9773 | 0.0332667 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 320.082 | 0.378795 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −1055.54 | −1.24622 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 19.0152 | 0.0223445 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 763.118i | 0.894628i | 0.894377 | + | 0.447314i | \(0.147619\pi\) | ||||
−0.894377 | + | 0.447314i | \(0.852381\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 1641.05i | 1.91488i | 0.288631 | + | 0.957440i | \(0.406800\pi\) | ||||
−0.288631 | + | 0.957440i | \(0.593200\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 1366.84i | 1.59120i | 0.605819 | + | 0.795602i | \(0.292845\pi\) | ||||
−0.605819 | + | 0.795602i | \(0.707155\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − 836.082i | − 0.968809i | −0.874844 | − | 0.484405i | \(-0.839036\pi\) | ||||
0.874844 | − | 0.484405i | \(-0.160964\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −348.089 | −0.402415 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 2081.93 | 2.39578 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1498.80 | 1.72078 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −378.633 | −0.432723 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 158.191i | 0.180377i | 0.995925 | + | 0.0901887i | \(0.0287470\pi\) | ||||
−0.995925 | + | 0.0901887i | \(0.971253\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − 237.430i | − 0.269500i | −0.990880 | − | 0.134750i | \(-0.956977\pi\) | ||||
0.990880 | − | 0.134750i | \(-0.0430232\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 592.933i | 0.671499i | 0.941951 | + | 0.335749i | \(0.108989\pi\) | ||||
−0.941951 | + | 0.335749i | \(0.891011\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 1420.72i | 1.60171i | 0.598858 | + | 0.800855i | \(0.295621\pi\) | ||||
−0.598858 | + | 0.800855i | \(0.704379\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −328.266 | −0.369253 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −1099.92 | −1.23172 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −199.866 | −0.223313 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −166.061 | −0.184717 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 681.987i | 0.756922i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | − 135.734i | − 0.149982i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 816.648i | 0.900383i | 0.892932 | + | 0.450192i | \(0.148644\pi\) | ||||
−0.892932 | + | 0.450192i | \(0.851356\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 469.895i | 0.515801i | 0.966171 | + | 0.257901i | \(0.0830307\pi\) | ||||
−0.966171 | + | 0.257901i | \(0.916969\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −126.755 | −0.138834 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 931.079 | 1.01535 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 1648.21 | 1.79348 | 0.896741 | − | 0.442555i | \(-0.145928\pi\) | ||||
0.896741 | + | 0.442555i | \(0.145928\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 2127.53 | 2.30502 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − 406.398i | − 0.439349i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − 421.311i | − 0.453510i | −0.973952 | − | 0.226755i | \(-0.927188\pi\) | ||||
0.973952 | − | 0.226755i | \(-0.0728116\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 51.1313i | 0.0549208i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | − 333.659i | − 0.356855i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −1434.27 | −1.53070 | −0.765350 | − | 0.643614i | \(-0.777434\pi\) | ||||
−0.765350 | + | 0.643614i | \(0.777434\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 732.876 | 0.778827 | 0.389413 | − | 0.921063i | \(-0.372678\pi\) | ||||
0.389413 | + | 0.921063i | \(0.372678\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −30.6443 | −0.0324966 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −1385.53 | −1.46308 | −0.731538 | − | 0.681800i | \(-0.761197\pi\) | ||||
−0.731538 | + | 0.681800i | \(0.761197\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 814.249i | 0.858007i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 957.328i | 1.00454i | 0.864711 | + | 0.502270i | \(0.167502\pi\) | ||||
−0.864711 | + | 0.502270i | \(0.832498\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − 250.606i | − 0.262414i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 78.8654i | 0.0822371i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −929.266 | −0.966978 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 126.179 | 0.130755 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −1225.90 | −1.26773 | −0.633867 | − | 0.773442i | \(-0.718533\pi\) | ||||
−0.633867 | + | 0.773442i | \(0.718533\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −752.906 | −0.775393 | −0.387696 | − | 0.921787i | \(-0.626729\pi\) | ||||
−0.387696 | + | 0.921787i | \(0.626729\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 8.64847i | 0.00888845i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 642.932i | 0.658068i | 0.944318 | + | 0.329034i | \(0.106723\pi\) | ||||
−0.944318 | + | 0.329034i | \(0.893277\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 1245.14i | 1.27185i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 161.251i | 0.164040i | 0.996631 | + | 0.0820200i | \(0.0261371\pi\) | ||||
−0.996631 | + | 0.0820200i | \(0.973863\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −318.532 | −0.323382 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 58.3836 | 0.0590330 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −811.500 | −0.818870 | −0.409435 | − | 0.912339i | \(-0.634274\pi\) | ||||
−0.409435 | + | 0.912339i | \(0.634274\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 250.483 | 0.251742 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − 390.554i | − 0.391729i | −0.980631 | − | 0.195864i | \(-0.937249\pi\) | ||||
0.980631 | − | 0.195864i | \(-0.0627513\pi\) | |||||||
\(998\) | 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 | 288.3.h.a.17.4 | 8 | ||
3.2 | odd | 2 | inner | 288.3.h.a.17.6 | 8 | ||
4.3 | odd | 2 | 72.3.h.a.53.7 | yes | 8 | ||
8.3 | odd | 2 | 72.3.h.a.53.1 | ✓ | 8 | ||
8.5 | even | 2 | inner | 288.3.h.a.17.5 | 8 | ||
12.11 | even | 2 | 72.3.h.a.53.2 | yes | 8 | ||
16.3 | odd | 4 | 2304.3.e.n.1025.5 | 8 | |||
16.5 | even | 4 | 2304.3.e.o.1025.4 | 8 | |||
16.11 | odd | 4 | 2304.3.e.n.1025.4 | 8 | |||
16.13 | even | 4 | 2304.3.e.o.1025.5 | 8 | |||
24.5 | odd | 2 | inner | 288.3.h.a.17.3 | 8 | ||
24.11 | even | 2 | 72.3.h.a.53.8 | yes | 8 | ||
48.5 | odd | 4 | 2304.3.e.o.1025.6 | 8 | |||
48.11 | even | 4 | 2304.3.e.n.1025.6 | 8 | |||
48.29 | odd | 4 | 2304.3.e.o.1025.3 | 8 | |||
48.35 | even | 4 | 2304.3.e.n.1025.3 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
72.3.h.a.53.1 | ✓ | 8 | 8.3 | odd | 2 | ||
72.3.h.a.53.2 | yes | 8 | 12.11 | even | 2 | ||
72.3.h.a.53.7 | yes | 8 | 4.3 | odd | 2 | ||
72.3.h.a.53.8 | yes | 8 | 24.11 | even | 2 | ||
288.3.h.a.17.3 | 8 | 24.5 | odd | 2 | inner | ||
288.3.h.a.17.4 | 8 | 1.1 | even | 1 | trivial | ||
288.3.h.a.17.5 | 8 | 8.5 | even | 2 | inner | ||
288.3.h.a.17.6 | 8 | 3.2 | odd | 2 | inner | ||
2304.3.e.n.1025.3 | 8 | 48.35 | even | 4 | |||
2304.3.e.n.1025.4 | 8 | 16.11 | odd | 4 | |||
2304.3.e.n.1025.5 | 8 | 16.3 | odd | 4 | |||
2304.3.e.n.1025.6 | 8 | 48.11 | even | 4 | |||
2304.3.e.o.1025.3 | 8 | 48.29 | odd | 4 | |||
2304.3.e.o.1025.4 | 8 | 16.5 | even | 4 | |||
2304.3.e.o.1025.5 | 8 | 16.13 | even | 4 | |||
2304.3.e.o.1025.6 | 8 | 48.5 | odd | 4 |