Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1300,2,Mod(649,1300)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1300, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1300.649");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1300 = 2^{2} \cdot 5^{2} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1300.d (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: | \(10.3805522628\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | 6.0.9144576.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} + 12x^{4} + 36x^{2} + 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 260) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 649.1 | ||
Root | \(-2.60168i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1300.649 |
Dual form | 1300.2.d.d.649.6 |
$q$-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 \(\left(\mathbb{Z}/1300\mathbb{Z}\right)^\times\).
\(n\) | \(301\) | \(651\) | \(677\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(-1\) |
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 | ||||||||
\(3\) | − | 2.60168i | − | 1.50208i | −0.660257 | − | 0.751040i | \(-0.729552\pi\) | ||
0.660257 | − | 0.751040i | \(-0.270448\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.76873 | 1.04648 | 0.523242 | − | 0.852184i | \(-0.324723\pi\) | ||||
0.523242 | + | 0.852184i | \(0.324723\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −3.76873 | −1.25624 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − | 2.16706i | − | 0.653392i | −0.945130 | − | 0.326696i | \(-0.894065\pi\) | ||
0.945130 | − | 0.326696i | \(-0.105935\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.60168 | + | 0.167055i | 0.998926 | + | 0.0463328i | ||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 5.03630i | − | 1.15541i | −0.816247 | − | 0.577704i | \(-0.803949\pi\) | ||
0.816247 | − | 0.577704i | \(-0.196051\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | − | 7.20336i | − | 1.57190i | ||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 4.93579i | 1.02918i | 0.857435 | + | 0.514592i | \(0.172056\pi\) | ||||
−0.857435 | + | 0.514592i | \(0.827944\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 2.00000i | 0.384900i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 4.43462 | 0.823489 | 0.411744 | − | 0.911299i | \(-0.364920\pi\) | ||||
0.411744 | + | 0.911299i | \(0.364920\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 3.37041i | − | 0.605344i | −0.953095 | − | 0.302672i | \(-0.902121\pi\) | ||
0.953095 | − | 0.302672i | \(-0.0978787\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −5.63798 | −0.981447 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −3.97209 | −0.653008 | −0.326504 | − | 0.945196i | \(-0.605871\pi\) | ||||
−0.326504 | + | 0.945196i | \(0.605871\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0.434624 | − | 9.37041i | 0.0695955 | − | 1.50047i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 1.66589i | − | 0.260168i | −0.991503 | − | 0.130084i | \(-0.958475\pi\) | ||
0.991503 | − | 0.130084i | \(-0.0415247\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 9.80504i | − | 1.49525i | −0.664119 | − | 0.747627i | \(-0.731193\pi\) | ||
0.664119 | − | 0.747627i | \(-0.268807\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 11.6380 | 1.69757 | 0.848787 | − | 0.528735i | \(-0.177333\pi\) | ||||
0.848787 | + | 0.528735i | \(0.177333\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0.665890 | 0.0951271 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 12.7408i | 1.75009i | 0.484044 | + | 0.875044i | \(0.339167\pi\) | ||||
−0.484044 | + | 0.875044i | \(0.660833\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −13.1028 | −1.73551 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − | 8.16706i | − | 1.06326i | −0.846977 | − | 0.531630i | \(-0.821580\pi\) | ||
0.846977 | − | 0.531630i | \(-0.178420\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −10.3062 | −1.31957 | −0.659787 | − | 0.751453i | \(-0.729354\pi\) | ||||
−0.659787 | + | 0.751453i | \(0.729354\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −10.4346 | −1.31464 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 7.10284 | 0.867751 | 0.433875 | − | 0.900973i | \(-0.357146\pi\) | ||||
0.433875 | + | 0.900973i | \(0.357146\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 12.8413 | 1.54592 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 16.1112i | 1.91205i | 0.293281 | + | 0.956026i | \(0.405253\pi\) | ||||
−0.293281 | + | 0.956026i | \(0.594747\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −15.9721 | −1.86939 | −0.934696 | − | 0.355448i | \(-0.884328\pi\) | ||||
−0.934696 | + | 0.355448i | \(0.884328\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − | 6.00000i | − | 0.683763i | ||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −11.9442 | −1.34383 | −0.671913 | − | 0.740630i | \(-0.734527\pi\) | ||||
−0.671913 | + | 0.740630i | \(0.734527\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −6.10284 | −0.678094 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −3.97209 | −0.435994 | −0.217997 | − | 0.975949i | \(-0.569952\pi\) | ||||
−0.217997 | + | 0.975949i | \(0.569952\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | − | 11.5375i | − | 1.23695i | ||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 7.94419i | − | 0.842082i | −0.907042 | − | 0.421041i | \(-0.861665\pi\) | ||
0.907042 | − | 0.421041i | \(-0.138335\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 9.97209 | + | 0.462531i | 1.04536 | + | 0.0484865i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −8.76873 | −0.909275 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −0.462531 | −0.0469629 | −0.0234815 | − | 0.999724i | \(-0.507475\pi\) | ||||
−0.0234815 | + | 0.999724i | \(0.507475\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 8.16706i | 0.820820i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 12.7408 | 1.26776 | 0.633880 | − | 0.773432i | \(-0.281461\pi\) | ||||
0.633880 | + | 0.773432i | \(0.281461\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 4.13915i | 0.407842i | 0.978987 | + | 0.203921i | \(0.0653686\pi\) | ||||
−0.978987 | + | 0.203921i | \(0.934631\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 7.06421i | 0.682923i | 0.939896 | + | 0.341462i | \(0.110922\pi\) | ||||
−0.939896 | + | 0.341462i | \(0.889078\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 14.8692i | − | 1.42422i | −0.702070 | − | 0.712108i | \(-0.747741\pi\) | ||
0.702070 | − | 0.712108i | \(-0.252259\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 10.3341i | 0.980870i | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 3.13075i | − | 0.294516i | −0.989098 | − | 0.147258i | \(-0.952955\pi\) | ||
0.989098 | − | 0.147258i | \(-0.0470448\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −13.5738 | − | 0.629587i | −1.25490 | − | 0.0582053i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 6.30387 | 0.573079 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −4.33411 | −0.390794 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 16.1391i | 1.43212i | 0.698040 | + | 0.716059i | \(0.254056\pi\) | ||||
−0.698040 | + | 0.716059i | \(0.745944\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −25.5096 | −2.24599 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −8.86925 | −0.774910 | −0.387455 | − | 0.921889i | \(-0.626646\pi\) | ||||
−0.387455 | + | 0.921889i | \(0.626646\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − | 13.9442i | − | 1.20911i | ||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −1.66589 | −0.142327 | −0.0711633 | − | 0.997465i | \(-0.522671\pi\) | ||||
−0.0711633 | + | 0.997465i | \(0.522671\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −19.2760 | −1.63497 | −0.817483 | − | 0.575953i | \(-0.804631\pi\) | ||||
−0.817483 | + | 0.575953i | \(0.804631\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | − | 30.2783i | − | 2.54989i | ||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0.362018 | − | 7.80504i | 0.0302734 | − | 0.652690i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | − | 1.73243i | − | 0.142889i | ||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 13.9442i | 1.14235i | 0.820828 | + | 0.571176i | \(0.193513\pi\) | ||||
−0.820828 | + | 0.571176i | \(0.806487\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 6.96370i | − | 0.566698i | −0.959017 | − | 0.283349i | \(-0.908555\pi\) | ||
0.959017 | − | 0.283349i | \(-0.0914454\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 12.3341i | 0.984369i | 0.870491 | + | 0.492185i | \(0.163801\pi\) | ||||
−0.870491 | + | 0.492185i | \(0.836199\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 33.1475 | 2.62877 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 13.6659i | 1.07702i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 20.5072 | 1.60625 | 0.803125 | − | 0.595810i | \(-0.203169\pi\) | ||||
0.803125 | + | 0.595810i | \(0.203169\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 19.3039 | 1.49378 | 0.746889 | − | 0.664948i | \(-0.231547\pi\) | ||||
0.746889 | + | 0.664948i | \(0.231547\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 12.9442 | + | 1.20336i | 0.995707 | + | 0.0925660i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 18.9805i | 1.45147i | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − | 9.61007i | − | 0.730640i | −0.930882 | − | 0.365320i | \(-0.880959\pi\) | ||
0.930882 | − | 0.365320i | \(-0.119041\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −21.2481 | −1.59710 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 9.87158 | 0.737836 | 0.368918 | − | 0.929462i | \(-0.379728\pi\) | ||||
0.368918 | + | 0.929462i | \(0.379728\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −1.97209 | −0.146584 | −0.0732922 | − | 0.997311i | \(-0.523351\pi\) | ||||
−0.0732922 | + | 0.997311i | \(0.523351\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 26.8134i | 1.98211i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 5.53747i | 0.402792i | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −5.73850 | −0.415223 | −0.207611 | − | 0.978211i | \(-0.566569\pi\) | ||||
−0.207611 | + | 0.978211i | \(0.566569\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 4.07261 | 0.293153 | 0.146576 | − | 0.989199i | \(-0.453175\pi\) | ||||
0.146576 | + | 0.989199i | \(0.453175\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 21.6101 | 1.53965 | 0.769827 | − | 0.638253i | \(-0.220342\pi\) | ||||
0.769827 | + | 0.638253i | \(0.220342\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 11.6101 | 0.823016 | 0.411508 | − | 0.911406i | \(-0.365002\pi\) | ||||
0.411508 | + | 0.911406i | \(0.365002\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | − | 18.4793i | − | 1.30343i | ||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 12.2783 | 0.861767 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | − | 18.6017i | − | 1.29291i | ||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −10.9139 | −0.754933 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 16.2783 | 1.12064 | 0.560322 | − | 0.828275i | \(-0.310677\pi\) | ||||
0.560322 | + | 0.828275i | \(0.310677\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 41.9163 | 2.87206 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 9.33178i | − | 0.633482i | ||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 41.5543i | 2.80798i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 11.4370 | 0.765875 | 0.382938 | − | 0.923774i | \(-0.374912\pi\) | ||||
0.382938 | + | 0.923774i | \(0.374912\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 15.9721 | 1.06011 | 0.530053 | − | 0.847965i | \(-0.322172\pi\) | ||||
0.530053 | + | 0.847965i | \(0.322172\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 2.12842i | 0.140650i | 0.997524 | + | 0.0703250i | \(0.0224036\pi\) | ||||
−0.997524 | + | 0.0703250i | \(0.977596\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −15.6101 | −1.02707 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 2.86925i | 0.187971i | 0.995574 | + | 0.0939853i | \(0.0299607\pi\) | ||||
−0.995574 | + | 0.0939853i | \(0.970039\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 31.0749i | 2.01853i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 3.16939i | − | 0.205011i | −0.994732 | − | 0.102505i | \(-0.967314\pi\) | ||
0.994732 | − | 0.102505i | \(-0.0326859\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 4.79664i | − | 0.308979i | −0.987994 | − | 0.154489i | \(-0.950627\pi\) | ||
0.987994 | − | 0.154489i | \(-0.0493733\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 21.8776i | 1.40345i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0.841340 | − | 18.1391i | 0.0535332 | − | 1.15417i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 10.3341i | 0.654898i | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 1.00233 | 0.0632666 | 0.0316333 | − | 0.999500i | \(-0.489929\pi\) | ||||
0.0316333 | + | 0.999500i | \(0.489929\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 10.6961 | 0.672460 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − | 19.4817i | − | 1.21523i | −0.794231 | − | 0.607616i | \(-0.792126\pi\) | ||
0.794231 | − | 0.607616i | \(-0.207874\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −10.9977 | −0.683362 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −16.7129 | −1.03450 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 4.19496i | 0.258672i | 0.991601 | + | 0.129336i | \(0.0412847\pi\) | ||||
−0.991601 | + | 0.129336i | \(0.958715\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −20.6682 | −1.26487 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −30.4793 | −1.85836 | −0.929179 | − | 0.369631i | \(-0.879484\pi\) | ||||
−0.929179 | + | 0.369631i | \(0.879484\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 4.83528i | 0.293722i | 0.989157 | + | 0.146861i | \(0.0469170\pi\) | ||||
−0.989157 | + | 0.146861i | \(0.953083\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 1.20336 | − | 25.9442i | 0.0728306 | − | 1.57021i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 3.00233i | 0.180393i | 0.995924 | + | 0.0901963i | \(0.0287494\pi\) | ||||
−0.995924 | + | 0.0901963i | \(0.971251\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 12.7022i | 0.760460i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 21.6101i | 1.28915i | 0.764542 | + | 0.644574i | \(0.222965\pi\) | ||||
−0.764542 | + | 0.644574i | \(0.777035\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 2.47326i | − | 0.147020i | −0.997294 | − | 0.0735100i | \(-0.976580\pi\) | ||
0.997294 | − | 0.0735100i | \(-0.0234201\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − | 4.61241i | − | 0.272262i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 17.0000 | 1.00000 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 1.20336i | 0.0705421i | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 23.9163 | 1.39720 | 0.698602 | − | 0.715511i | \(-0.253806\pi\) | ||||
0.698602 | + | 0.715511i | \(0.253806\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 4.33411 | 0.251491 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −0.824549 | + | 17.7771i | −0.0476849 | + | 1.02808i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | − | 27.1475i | − | 1.56476i | ||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | − | 33.1475i | − | 1.90428i | ||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 13.5654 | 0.774217 | 0.387108 | − | 0.922034i | \(-0.373474\pi\) | ||||
0.387108 | + | 0.922034i | \(0.373474\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 10.7687 | 0.612612 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −2.12842 | −0.120692 | −0.0603458 | − | 0.998178i | \(-0.519220\pi\) | ||||
−0.0603458 | + | 0.998178i | \(0.519220\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 22.6077i | 1.27787i | 0.769263 | + | 0.638933i | \(0.220624\pi\) | ||||
−0.769263 | + | 0.638933i | \(0.779376\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −10.6357 | −0.597358 | −0.298679 | − | 0.954354i | \(-0.596546\pi\) | ||||
−0.298679 | + | 0.954354i | \(0.596546\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 9.61007i | − | 0.538061i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 18.3788 | 1.02581 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −38.6850 | −2.13929 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 32.2225 | 1.77648 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 1.16472i | 0.0640190i | 0.999488 | + | 0.0320095i | \(0.0101907\pi\) | ||||
−0.999488 | + | 0.0320095i | \(0.989809\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 14.9698 | 0.820338 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 20.0000i | − | 1.08947i | −0.838608 | − | 0.544735i | \(-0.816630\pi\) | ||
0.838608 | − | 0.544735i | \(-0.183370\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −8.14521 | −0.442387 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −7.30387 | −0.395527 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −17.5375 | −0.946934 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 4.67429i | 0.250929i | 0.992098 | + | 0.125464i | \(0.0400421\pi\) | ||||
−0.992098 | + | 0.125464i | \(0.959958\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 4.33411i | − | 0.232000i | −0.993249 | − | 0.116000i | \(-0.962993\pi\) | ||
0.993249 | − | 0.116000i | \(-0.0370072\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −0.334110 | + | 7.20336i | −0.0178335 | + | 0.384487i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −21.3085 | −1.13414 | −0.567069 | − | 0.823670i | \(-0.691923\pi\) | ||||
−0.567069 | + | 0.823670i | \(0.691923\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 12.7795i | 0.674474i | 0.941420 | + | 0.337237i | \(0.109492\pi\) | ||||
−0.941420 | + | 0.337237i | \(0.890508\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −6.36435 | −0.334966 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − | 16.4007i | − | 0.860811i | ||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 12.1950i | 0.636572i | 0.947995 | + | 0.318286i | \(0.103107\pi\) | ||||
−0.947995 | + | 0.318286i | \(0.896893\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 6.27830i | 0.326835i | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 35.2760i | 1.83144i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 28.2225i | 1.46130i | 0.682750 | + | 0.730652i | \(0.260784\pi\) | ||||
−0.682750 | + | 0.730652i | \(0.739216\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 15.9721 | + | 0.740827i | 0.822605 | + | 0.0381545i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 23.3146i | 1.19759i | 0.800902 | + | 0.598795i | \(0.204354\pi\) | ||||
−0.800902 | + | 0.598795i | \(0.795646\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 41.9889 | 2.15116 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −8.02791 | −0.410207 | −0.205103 | − | 0.978740i | \(-0.565753\pi\) | ||||
−0.205103 | + | 0.978740i | \(0.565753\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 36.9526i | 1.87841i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −23.7385 | −1.20359 | −0.601795 | − | 0.798651i | \(-0.705547\pi\) | ||||
−0.601795 | + | 0.798651i | \(0.705547\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 23.0749i | 1.16398i | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −3.04703 | −0.152926 | −0.0764630 | − | 0.997072i | \(-0.524363\pi\) | ||||
−0.0764630 | + | 0.997072i | \(0.524363\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −36.2783 | −1.81619 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 31.2201i | 1.55906i | 0.626365 | + | 0.779530i | \(0.284542\pi\) | ||||
−0.626365 | + | 0.779530i | \(0.715458\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0.563045 | − | 12.1391i | 0.0280473 | − | 0.604694i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 8.60774i | 0.426670i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 33.4090i | − | 1.65197i | −0.563691 | − | 0.825986i | \(-0.690619\pi\) | ||
0.563691 | − | 0.825986i | \(-0.309381\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 4.33411i | 0.213786i | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − | 22.6124i | − | 1.11268i | ||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 50.1499i | 2.45585i | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 30.7408 | 1.50179 | 0.750894 | − | 0.660423i | \(-0.229623\pi\) | ||||
0.750894 | + | 0.660423i | \(0.229623\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 19.2806i | 0.939680i | 0.882752 | + | 0.469840i | \(0.155688\pi\) | ||||
−0.882752 | + | 0.469840i | \(0.844312\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −43.8605 | −2.13257 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −28.5351 | −1.38091 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −20.3062 | − | 0.941854i | −0.980393 | − | 0.0454731i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 2.44535i | − | 0.117788i | −0.998264 | − | 0.0588942i | \(-0.981243\pi\) | ||
0.998264 | − | 0.0588942i | \(-0.0187575\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 2.00000i | 0.0961139i | 0.998845 | + | 0.0480569i | \(0.0153029\pi\) | ||||
−0.998845 | + | 0.0480569i | \(0.984697\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 24.8581 | 1.18913 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 11.6659 | 0.556783 | 0.278391 | − | 0.960468i | \(-0.410199\pi\) | ||||
0.278391 | + | 0.960468i | \(0.410199\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −2.50956 | −0.119503 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − | 20.8074i | − | 0.988588i | −0.869295 | − | 0.494294i | \(-0.835427\pi\) | ||
0.869295 | − | 0.494294i | \(-0.164573\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 36.2783 | 1.71590 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 30.2783i | 1.42892i | 0.699676 | + | 0.714461i | \(0.253328\pi\) | ||||
−0.699676 | + | 0.714461i | \(0.746672\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −3.61007 | −0.169992 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −18.1173 | −0.851225 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −22.6124 | −1.05776 | −0.528882 | − | 0.848695i | \(-0.677389\pi\) | ||||
−0.528882 | + | 0.848695i | \(0.677389\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 18.9419i | 0.882210i | 0.897455 | + | 0.441105i | \(0.145413\pi\) | ||||
−0.897455 | + | 0.441105i | \(0.854587\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −11.6380 | −0.540863 | −0.270431 | − | 0.962739i | \(-0.587166\pi\) | ||||
−0.270431 | + | 0.962739i | \(0.587166\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − | 25.0642i | − | 1.15983i | −0.814676 | − | 0.579917i | \(-0.803085\pi\) | ||
0.814676 | − | 0.579917i | \(-0.196915\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 19.6659 | 0.908086 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 32.0894 | 1.47860 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −21.2481 | −0.976987 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | − | 48.0168i | − | 2.19854i | ||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | − | 18.4407i | − | 0.842577i | −0.906927 | − | 0.421288i | \(-0.861578\pi\) | ||
0.906927 | − | 0.421288i | \(-0.138422\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −14.3062 | − | 0.663559i | −0.652307 | − | 0.0302557i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 35.5543 | 1.61777 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −25.1196 | −1.13828 | −0.569140 | − | 0.822241i | \(-0.692724\pi\) | ||||
−0.569140 | + | 0.822241i | \(0.692724\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | − | 53.3532i | − | 2.41272i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −5.73850 | −0.258975 | −0.129487 | − | 0.991581i | \(-0.541333\pi\) | ||||
−0.129487 | + | 0.991581i | \(0.541333\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 44.6077i | 2.00093i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 33.3704i | 1.49386i | 0.664900 | + | 0.746932i | \(0.268474\pi\) | ||||
−0.664900 | + | 0.746932i | \(0.731526\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | − | 50.2225i | − | 2.24377i | ||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 12.6789i | 0.565326i | 0.959219 | + | 0.282663i | \(0.0912179\pi\) | ||||
−0.959219 | + | 0.282663i | \(0.908782\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 3.13075 | − | 33.6766i | 0.139042 | − | 1.49563i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − | 17.6147i | − | 0.780759i | −0.920654 | − | 0.390380i | \(-0.872344\pi\) | ||
0.920654 | − | 0.390380i | \(-0.127656\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −44.2225 | −1.95629 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 10.0726 | 0.444716 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 25.2201i | − | 1.10918i | ||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −25.0023 | −1.09748 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −16.4346 | −0.720014 | −0.360007 | − | 0.932950i | \(-0.617226\pi\) | ||||
−0.360007 | + | 0.932950i | \(0.617226\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 20.4733i | 0.895233i | 0.894226 | + | 0.447617i | \(0.147727\pi\) | ||||
−0.894226 | + | 0.447617i | \(0.852273\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −1.36202 | −0.0592182 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 30.7795i | 1.33571i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0.278295 | − | 6.00000i | 0.0120543 | − | 0.259889i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | − | 25.6827i | − | 1.10829i | ||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − | 1.44302i | − | 0.0621553i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − | 41.2928i | − | 1.77531i | −0.460505 | − | 0.887657i | \(-0.652332\pi\) | ||
0.460505 | − | 0.887657i | \(-0.347668\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 5.13075i | 0.220182i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 10.4174i | − | 0.445418i | −0.974885 | − | 0.222709i | \(-0.928510\pi\) | ||
0.974885 | − | 0.222709i | \(-0.0714899\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 38.8413 | 1.65771 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 22.3341i | − | 0.951465i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −33.0703 | −1.40629 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 20.5845 | 0.872193 | 0.436097 | − | 0.899900i | \(-0.356361\pi\) | ||||
0.436097 | + | 0.899900i | \(0.356361\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 1.63798 | − | 35.3146i | 0.0692793 | − | 1.49365i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 23.6766i | 0.997850i | 0.866645 | + | 0.498925i | \(0.166272\pi\) | ||||
−0.866645 | + | 0.498925i | \(0.833728\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −16.8972 | −0.709614 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −5.43695 | −0.227929 | −0.113965 | − | 0.993485i | \(-0.536355\pi\) | ||||
−0.113965 | + | 0.993485i | \(0.536355\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 15.2760 | 0.639279 | 0.319640 | − | 0.947539i | \(-0.396438\pi\) | ||||
0.319640 | + | 0.947539i | \(0.396438\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 14.9297i | 0.623698i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 1.76640 | 0.0735363 | 0.0367682 | − | 0.999324i | \(-0.488294\pi\) | ||||
0.0367682 | + | 0.999324i | \(0.488294\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | − | 10.5956i | − | 0.440339i | ||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −10.9977 | −0.456260 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 27.6101 | 1.14349 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 22.9139 | 0.945760 | 0.472880 | − | 0.881127i | \(-0.343214\pi\) | ||||
0.472880 | + | 0.881127i | \(0.343214\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −16.9744 | −0.699419 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | − | 56.2225i | − | 2.31268i | ||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 6.72404 | 0.276123 | 0.138062 | − | 0.990424i | \(-0.455913\pi\) | ||||
0.138062 | + | 0.990424i | \(0.455913\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | − | 30.2057i | − | 1.23624i | ||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 19.8669 | 0.811740 | 0.405870 | − | 0.913931i | \(-0.366969\pi\) | ||||
0.405870 | + | 0.913931i | \(0.366969\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −33.2201 | −1.35508 | −0.677539 | − | 0.735487i | \(-0.736954\pi\) | ||||
−0.677539 | + | 0.735487i | \(0.736954\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −26.7687 | −1.09011 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 14.4174i | 0.585186i | 0.956237 | + | 0.292593i | \(0.0945181\pi\) | ||||
−0.956237 | + | 0.292593i | \(0.905482\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | − | 31.9442i | − | 1.29444i | ||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 41.9163 | + | 1.94419i | 1.69575 | + | 0.0786533i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 11.3364 | 0.457875 | 0.228937 | − | 0.973441i | \(-0.426475\pi\) | ||||
0.228937 | + | 0.973441i | \(0.426475\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −34.8907 | −1.40465 | −0.702323 | − | 0.711858i | \(-0.747854\pi\) | ||||
−0.702323 | + | 0.711858i | \(0.747854\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 32.6464i | 1.31217i | 0.754688 | + | 0.656084i | \(0.227788\pi\) | ||||
−0.754688 | + | 0.656084i | \(0.772212\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −9.87158 | −0.396133 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − | 21.9953i | − | 0.881225i | ||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 28.3946i | 1.13397i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 47.3146i | − | 1.88356i | −0.336224 | − | 0.941782i | \(-0.609150\pi\) | ||
0.336224 | − | 0.941782i | \(-0.390850\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | − | 42.3509i | − | 1.68330i | ||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 2.39832 | + | 0.111240i | 0.0950249 | + | 0.00440750i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | − | 60.7190i | − | 2.40201i | ||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 43.4817 | 1.71742 | 0.858711 | − | 0.512460i | \(-0.171266\pi\) | ||||
0.858711 | + | 0.512460i | \(0.171266\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 20.3062 | 0.800798 | 0.400399 | − | 0.916341i | \(-0.368871\pi\) | ||||
0.400399 | + | 0.916341i | \(0.368871\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 30.8027i | 1.21098i | 0.795853 | + | 0.605490i | \(0.207023\pi\) | ||||
−0.795853 | + | 0.605490i | \(0.792977\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −17.6985 | −0.694725 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −24.2783 | −0.951541 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − | 3.61007i | − | 0.141273i | −0.997502 | − | 0.0706366i | \(-0.977497\pi\) | ||
0.997502 | − | 0.0706366i | \(-0.0225031\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 60.1946 | 2.34841 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 6.74083 | 0.262585 | 0.131293 | − | 0.991344i | \(-0.458087\pi\) | ||||
0.131293 | + | 0.991344i | \(0.458087\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 26.6682i | 1.03727i | 0.854995 | + | 0.518637i | \(0.173560\pi\) | ||||
−0.854995 | + | 0.518637i | \(0.826440\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 21.8884i | 0.847521i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | − | 29.7553i | − | 1.15041i | ||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 22.3341i | 0.862199i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 8.61241i | 0.331984i | 0.986127 | + | 0.165992i | \(0.0530826\pi\) | ||||
−0.986127 | + | 0.165992i | \(0.946917\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 8.12842i | 0.312401i | 0.987725 | + | 0.156200i | \(0.0499245\pi\) | ||||
−0.987725 | + | 0.156200i | \(0.950075\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −1.28063 | −0.0491459 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | − | 41.5543i | − | 1.59236i | ||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 8.02791 | 0.307179 | 0.153590 | − | 0.988135i | \(-0.450917\pi\) | ||||
0.153590 | + | 0.988135i | \(0.450917\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 5.53747 | 0.211268 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −2.12842 | + | 45.8884i | −0.0810864 | + | 1.74821i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 22.1112i | − | 0.841151i | −0.907257 | − | 0.420576i | \(-0.861828\pi\) | ||
0.907257 | − | 0.420576i | \(-0.138172\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 22.6124i | 0.858974i | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 7.46486 | 0.282347 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −6.47932 | −0.244721 | −0.122360 | − | 0.992486i | \(-0.539046\pi\) | ||||
−0.122360 | + | 0.992486i | \(0.539046\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 20.0047i | 0.754490i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 35.2760 | 1.32669 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 2.85246i | 0.107126i | 0.998564 | + | 0.0535631i | \(0.0170578\pi\) | ||||
−0.998564 | + | 0.0535631i | \(0.982942\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 45.0145 | 1.68817 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 16.6357 | 0.623010 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −8.24573 | −0.307942 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −42.0941 | −1.56984 | −0.784922 | − | 0.619595i | \(-0.787297\pi\) | ||||
−0.784922 | + | 0.619595i | \(0.787297\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 11.4602i | 0.426800i | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −12.4793 | −0.464111 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 32.8027i | − | 1.21659i | −0.793713 | − | 0.608293i | \(-0.791855\pi\) | ||
0.793713 | − | 0.608293i | \(-0.208145\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 38.6101 | 1.43000 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −2.38993 | −0.0882739 | −0.0441370 | − | 0.999025i | \(-0.514054\pi\) | ||||
−0.0441370 | + | 0.999025i | \(0.514054\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − | 15.3923i | − | 0.566981i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 41.4988i | − | 1.52656i | −0.646068 | − | 0.763280i | \(-0.723588\pi\) | ||
0.646068 | − | 0.763280i | \(-0.276412\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −47.1922 | − | 2.18890i | −1.73365 | − | 0.0804112i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −39.8046 | −1.46029 | −0.730145 | − | 0.683292i | \(-0.760548\pi\) | ||||
−0.730145 | + | 0.683292i | \(0.760548\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 14.9698 | 0.547715 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 19.5589i | 0.714667i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 15.6659 | 0.571656 | 0.285828 | − | 0.958281i | \(-0.407731\pi\) | ||||
0.285828 | + | 0.958281i | \(0.407731\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | − | 2.60774i | − | 0.0950315i | ||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 32.2736i | 1.17301i | 0.809947 | + | 0.586503i | \(0.199496\pi\) | ||||
−0.809947 | + | 0.586503i | \(0.800504\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | − | 27.8279i | − | 1.01009i | ||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 13.2806i | 0.481422i | 0.970597 | + | 0.240711i | \(0.0773807\pi\) | ||||
−0.970597 | + | 0.240711i | \(0.922619\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − | 41.1690i | − | 1.49042i | ||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 1.36435 | − | 29.4151i | 0.0492638 | − | 1.06212i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 12.2010i | − | 0.439980i | −0.975502 | − | 0.219990i | \(-0.929397\pi\) | ||
0.975502 | − | 0.219990i | \(-0.0706025\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −50.6850 | −1.82538 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −27.9721 | −1.00609 | −0.503043 | − | 0.864261i | \(-0.667786\pi\) | ||||
−0.503043 | + | 0.864261i | \(0.667786\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 28.6124i | 1.02646i | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −8.38993 | −0.300600 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 34.9139 | 1.24932 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 8.86925i | 0.316961i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 10.2336 | 0.364788 | 0.182394 | − | 0.983225i | \(-0.441615\pi\) | ||||
0.182394 | + | 0.983225i | \(0.441615\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 10.9139 | 0.388547 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 8.66822i | − | 0.308206i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −37.1196 | − | 1.72170i | −1.31816 | − | 0.0611395i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − | 23.3532i | − | 0.827214i | −0.910456 | − | 0.413607i | \(-0.864269\pi\) | ||
0.910456 | − | 0.413607i | \(-0.135731\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 29.9395i | 1.05786i | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 34.6124i | 1.22145i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 79.2974i | 2.79140i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −37.1364 | −1.30565 | −0.652824 | − | 0.757510i | \(-0.726416\pi\) | ||||
−0.652824 | + | 0.757510i | \(0.726416\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 20.6296i | − | 0.724403i | −0.932100 | − | 0.362201i | \(-0.882025\pi\) | ||
0.932100 | − | 0.362201i | \(-0.117975\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 12.5798 | 0.441194 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −49.3811 | −1.72763 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −37.5822 | − | 1.74316i | −1.31323 | − | 0.0609109i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 20.6077i | 0.719215i | 0.933104 | + | 0.359608i | \(0.117089\pi\) | ||||
−0.933104 | + | 0.359608i | \(0.882911\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 39.8050i | − | 1.38752i | −0.720208 | − | 0.693758i | \(-0.755954\pi\) | ||
0.720208 | − | 0.693758i | \(-0.244046\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −55.8605 | −1.94246 | −0.971229 | − | 0.238146i | \(-0.923460\pi\) | ||||
−0.971229 | + | 0.238146i | \(0.923460\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 33.5822 | 1.16636 | 0.583178 | − | 0.812344i | \(-0.301809\pi\) | ||||
0.583178 | + | 0.812344i | \(0.301809\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 7.81110 | 0.270964 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 6.74083 | 0.232997 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − | 26.4454i | − | 0.912995i | −0.889725 | − | 0.456497i | \(-0.849104\pi\) | ||
0.889725 | − | 0.456497i | \(-0.150896\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −9.33411 | −0.321866 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 56.2225 | 1.93641 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 17.4537 | 0.599718 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −6.43462 | −0.220836 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − | 19.6054i | − | 0.672065i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −35.7153 | −1.22287 | −0.611433 | − | 0.791296i | \(-0.709407\pi\) | ||||
−0.611433 | + | 0.791296i | \(0.709407\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 22.0894i | 0.754559i | 0.926099 | + | 0.377280i | \(0.123140\pi\) | ||||
−0.926099 | + | 0.377280i | \(0.876860\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 39.2201 | 1.33817 | 0.669087 | − | 0.743184i | \(-0.266685\pi\) | ||||
0.669087 | + | 0.743184i | \(0.266685\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −12.0000 | −0.408959 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −28.9744 | −0.986301 | −0.493150 | − | 0.869944i | \(-0.664155\pi\) | ||||
−0.493150 | + | 0.869944i | \(0.664155\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | − | 44.2285i | − | 1.50208i | ||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 25.8837i | 0.878045i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 25.5822 | + | 1.18657i | 0.866819 | + | 0.0402053i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 1.74316 | 0.0589970 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −30.9251 | −1.04427 | −0.522133 | − | 0.852864i | \(-0.674863\pi\) | ||||
−0.522133 | + | 0.852864i | \(0.674863\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | − | 62.2225i | − | 2.09871i | ||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 41.2695 | 1.39041 | 0.695203 | − | 0.718814i | \(-0.255315\pi\) | ||||
0.695203 | + | 0.718814i | \(0.255315\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 15.1973i | − | 0.511430i | −0.966752 | − | 0.255715i | \(-0.917689\pi\) | ||
0.966752 | − | 0.255715i | \(-0.0823108\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − | 12.4174i | − | 0.416937i | −0.978029 | − | 0.208468i | \(-0.933152\pi\) | ||
0.978029 | − | 0.208468i | \(-0.0668479\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 44.6850i | 1.49869i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 13.2252i | 0.443061i | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − | 58.6124i | − | 1.96139i | ||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 46.2504 | + | 2.14521i | 1.54426 | + | 0.0716266i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − | 14.9465i | − | 0.498494i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −70.6292 | −2.35039 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 11.4709i | − | 0.380886i | −0.981698 | − | 0.190443i | \(-0.939008\pi\) | ||
0.981698 | − | 0.190443i | \(-0.0609924\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −48.0168 | −1.59262 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 54.5734 | 1.80810 | 0.904048 | − | 0.427430i | \(-0.140581\pi\) | ||||
0.904048 | + | 0.427430i | \(0.140581\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 8.60774i | 0.284875i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −24.5566 | −0.810930 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −9.05815 | −0.298801 | −0.149400 | − | 0.988777i | \(-0.547734\pi\) | ||||
−0.149400 | + | 0.988777i | \(0.547734\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | − | 35.2928i | − | 1.16294i | ||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −2.69147 | + | 58.0275i | −0.0885907 | + | 1.91000i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | − | 15.5993i | − | 0.512350i | ||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 50.2225i | 1.64775i | 0.566774 | + | 0.823873i | \(0.308191\pi\) | ||||
−0.566774 | + | 0.823873i | \(0.691809\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − | 3.35362i | − | 0.109911i | ||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 5.53747i | 0.181289i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 5.38759i | 0.176005i | 0.996120 | + | 0.0880025i | \(0.0280484\pi\) | ||||
−0.996120 | + | 0.0880025i | \(0.971952\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 58.8181 | 1.91946 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 58.8302i | 1.91781i | 0.283726 | + | 0.958905i | \(0.408429\pi\) | ||||
−0.283726 | + | 0.958905i | \(0.591571\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 8.22248 | 0.267761 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −12.6403 | −0.410755 | −0.205377 | − | 0.978683i | \(-0.565842\pi\) | ||||
−0.205377 | + | 0.978683i | \(0.565842\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −57.5264 | − | 2.66822i | −1.86738 | − | 0.0866141i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 27.6706i | 0.897279i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 32.6077i | 1.05627i | 0.849161 | + | 0.528134i | \(0.177108\pi\) | ||||
−0.849161 | + | 0.528134i | \(0.822892\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −25.0023 | −0.808211 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −4.61241 | −0.148942 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 19.6403 | 0.633558 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | − | 26.6231i | − | 0.857918i | ||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −20.5845 | −0.661953 | −0.330976 | − | 0.943639i | \(-0.607378\pi\) | ||||
−0.330976 | + | 0.943639i | \(0.607378\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −60.8349 | −1.95228 | −0.976142 | − | 0.217132i | \(-0.930330\pi\) | ||||
−0.976142 | + | 0.217132i | \(0.930330\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −53.3700 | −1.71096 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −7.30387 | −0.233672 | −0.116836 | − | 0.993151i | \(-0.537275\pi\) | ||||
−0.116836 | + | 0.993151i | \(0.537275\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −17.2155 | −0.550209 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 56.0382i | 1.78916i | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 40.2504 | 1.28379 | 0.641894 | − | 0.766793i | \(-0.278149\pi\) | ||||
0.641894 | + | 0.766793i | \(0.278149\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | − | 83.8326i | − | 2.66842i | ||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 48.3956 | 1.53889 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −50.2271 | −1.59552 | −0.797759 | − | 0.602977i | \(-0.793981\pi\) | ||||
−0.797759 | + | 0.602977i | \(0.793981\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 3.03024 | 0.0961617 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 0.273633i | 0.00866606i | 0.999991 | + | 0.00433303i | \(0.00137925\pi\) | ||||
−0.999991 | + | 0.00433303i | \(0.998621\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | − | 7.94419i | − | 0.251343i |
(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 | 1300.2.d.d.649.1 | 6 | ||
5.2 | odd | 4 | 1300.2.f.e.701.2 | 6 | |||
5.3 | odd | 4 | 260.2.f.a.181.6 | yes | 6 | ||
5.4 | even | 2 | 1300.2.d.c.649.6 | 6 | |||
13.12 | even | 2 | 1300.2.d.c.649.1 | 6 | |||
15.8 | even | 4 | 2340.2.c.d.181.1 | 6 | |||
20.3 | even | 4 | 1040.2.k.c.961.2 | 6 | |||
65.8 | even | 4 | 3380.2.a.m.1.3 | 3 | |||
65.12 | odd | 4 | 1300.2.f.e.701.1 | 6 | |||
65.18 | even | 4 | 3380.2.a.n.1.3 | 3 | |||
65.38 | odd | 4 | 260.2.f.a.181.5 | ✓ | 6 | ||
65.64 | even | 2 | inner | 1300.2.d.d.649.6 | 6 | ||
195.38 | even | 4 | 2340.2.c.d.181.6 | 6 | |||
260.103 | even | 4 | 1040.2.k.c.961.1 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
260.2.f.a.181.5 | ✓ | 6 | 65.38 | odd | 4 | ||
260.2.f.a.181.6 | yes | 6 | 5.3 | odd | 4 | ||
1040.2.k.c.961.1 | 6 | 260.103 | even | 4 | |||
1040.2.k.c.961.2 | 6 | 20.3 | even | 4 | |||
1300.2.d.c.649.1 | 6 | 13.12 | even | 2 | |||
1300.2.d.c.649.6 | 6 | 5.4 | even | 2 | |||
1300.2.d.d.649.1 | 6 | 1.1 | even | 1 | trivial | ||
1300.2.d.d.649.6 | 6 | 65.64 | even | 2 | inner | ||
1300.2.f.e.701.1 | 6 | 65.12 | odd | 4 | |||
1300.2.f.e.701.2 | 6 | 5.2 | odd | 4 | |||
2340.2.c.d.181.1 | 6 | 15.8 | even | 4 | |||
2340.2.c.d.181.6 | 6 | 195.38 | even | 4 | |||
3380.2.a.m.1.3 | 3 | 65.8 | even | 4 | |||
3380.2.a.n.1.3 | 3 | 65.18 | even | 4 |