Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1800,4,Mod(649,1800)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1800, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 1]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1800.649");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1800 = 2^{3} \cdot 3^{2} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1800.f (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: | \(106.203438010\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(i)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 72) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 649.2 | ||
Root | \(1.00000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1800.649 |
Dual form | 1800.4.f.x.649.1 |
$q$-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 \(\left(\mathbb{Z}/1800\mathbb{Z}\right)^\times\).
\(n\) | \(577\) | \(901\) | \(1001\) | \(1351\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 12.0000i | 0.647939i | 0.946068 | + | 0.323970i | \(0.105018\pi\) | ||||
−0.946068 | + | 0.323970i | \(0.894982\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 64.0000 | 1.75425 | 0.877124 | − | 0.480264i | \(-0.159459\pi\) | ||||
0.877124 | + | 0.480264i | \(0.159459\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 58.0000i | 1.23741i | 0.785624 | + | 0.618704i | \(0.212342\pi\) | ||||
−0.785624 | + | 0.618704i | \(0.787658\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − 32.0000i | − 0.456538i | −0.973598 | − | 0.228269i | \(-0.926693\pi\) | ||||
0.973598 | − | 0.228269i | \(-0.0733065\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 136.000 | 1.64213 | 0.821067 | − | 0.570832i | \(-0.193379\pi\) | ||||
0.821067 | + | 0.570832i | \(0.193379\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − 128.000i | − 1.16043i | −0.814464 | − | 0.580214i | \(-0.802969\pi\) | ||||
0.814464 | − | 0.580214i | \(-0.197031\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 144.000 | 0.922073 | 0.461037 | − | 0.887381i | \(-0.347478\pi\) | ||||
0.461037 | + | 0.887381i | \(0.347478\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 20.0000 | 0.115874 | 0.0579372 | − | 0.998320i | \(-0.481548\pi\) | ||||
0.0579372 | + | 0.998320i | \(0.481548\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 18.0000i | 0.0799779i | 0.999200 | + | 0.0399889i | \(0.0127323\pi\) | ||||
−0.999200 | + | 0.0399889i | \(0.987268\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −288.000 | −1.09703 | −0.548513 | − | 0.836142i | \(-0.684806\pi\) | ||||
−0.548513 | + | 0.836142i | \(0.684806\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − 200.000i | − 0.709296i | −0.935000 | − | 0.354648i | \(-0.884601\pi\) | ||||
0.935000 | − | 0.354648i | \(-0.115399\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − 384.000i | − 1.19175i | −0.803078 | − | 0.595874i | \(-0.796806\pi\) | ||||
0.803078 | − | 0.595874i | \(-0.203194\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 199.000 | 0.580175 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 496.000i | 1.28549i | 0.766081 | + | 0.642744i | \(0.222204\pi\) | ||||
−0.766081 | + | 0.642744i | \(0.777796\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 128.000 | 0.282444 | 0.141222 | − | 0.989978i | \(-0.454897\pi\) | ||||
0.141222 | + | 0.989978i | \(0.454897\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −458.000 | −0.961326 | −0.480663 | − | 0.876905i | \(-0.659604\pi\) | ||||
−0.480663 | + | 0.876905i | \(0.659604\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 496.000i | 0.904419i | 0.891912 | + | 0.452209i | \(0.149364\pi\) | ||||
−0.891912 | + | 0.452209i | \(0.850636\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 512.000 | 0.855820 | 0.427910 | − | 0.903821i | \(-0.359250\pi\) | ||||
0.427910 | + | 0.903821i | \(0.359250\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − 602.000i | − 0.965189i | −0.875844 | − | 0.482594i | \(-0.839695\pi\) | ||||
0.875844 | − | 0.482594i | \(-0.160305\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 768.000i | 1.13665i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −1108.00 | −1.57797 | −0.788986 | − | 0.614412i | \(-0.789393\pi\) | ||||
−0.788986 | + | 0.614412i | \(0.789393\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 704.000i | 0.931013i | 0.885045 | + | 0.465506i | \(0.154128\pi\) | ||||
−0.885045 | + | 0.465506i | \(0.845872\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 960.000 | 1.14337 | 0.571684 | − | 0.820474i | \(-0.306290\pi\) | ||||
0.571684 | + | 0.820474i | \(0.306290\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −696.000 | −0.801765 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − 206.000i | − 0.215630i | −0.994171 | − | 0.107815i | \(-0.965615\pi\) | ||||
0.994171 | − | 0.107815i | \(-0.0343855\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 432.000 | 0.425600 | 0.212800 | − | 0.977096i | \(-0.431742\pi\) | ||||
0.212800 | + | 0.977096i | \(0.431742\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − 68.0000i | − 0.0650509i | −0.999471 | − | 0.0325254i | \(-0.989645\pi\) | ||||
0.999471 | − | 0.0325254i | \(-0.0103550\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 384.000i | 0.346941i | 0.984839 | + | 0.173470i | \(0.0554981\pi\) | ||||
−0.984839 | + | 0.173470i | \(0.944502\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 518.000 | 0.455187 | 0.227594 | − | 0.973756i | \(-0.426914\pi\) | ||||
0.227594 | + | 0.973756i | \(0.426914\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − 960.000i | − 0.799196i | −0.916690 | − | 0.399598i | \(-0.869150\pi\) | ||||
0.916690 | − | 0.399598i | \(-0.130850\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 384.000 | 0.295809 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 2765.00 | 2.07739 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − 796.000i | − 0.556170i | −0.960556 | − | 0.278085i | \(-0.910300\pi\) | ||||
0.960556 | − | 0.278085i | \(-0.0896997\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 512.000 | 0.341478 | 0.170739 | − | 0.985316i | \(-0.445384\pi\) | ||||
0.170739 | + | 0.985316i | \(0.445384\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1632.00i | 1.06400i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − 1824.00i | − 1.13748i | −0.822517 | − | 0.568740i | \(-0.807431\pi\) | ||||
0.822517 | − | 0.568740i | \(-0.192569\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 2160.00 | 1.31805 | 0.659024 | − | 0.752121i | \(-0.270969\pi\) | ||||
0.659024 | + | 0.752121i | \(0.270969\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 3712.00i | 2.17072i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 688.000 | 0.378276 | 0.189138 | − | 0.981950i | \(-0.439431\pi\) | ||||
0.189138 | + | 0.981950i | \(0.439431\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −844.000 | −0.454859 | −0.227430 | − | 0.973795i | \(-0.573032\pi\) | ||||
−0.227430 | + | 0.973795i | \(0.573032\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − 118.000i | − 0.0599836i | −0.999550 | − | 0.0299918i | \(-0.990452\pi\) | ||||
0.999550 | − | 0.0299918i | \(-0.00954812\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1536.00 | 0.751887 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 3576.00i | 1.71837i | 0.511667 | + | 0.859184i | \(0.329028\pi\) | ||||
−0.511667 | + | 0.859184i | \(0.670972\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − 384.000i | − 0.177933i | −0.996035 | − | 0.0889665i | \(-0.971644\pi\) | ||||
0.996035 | − | 0.0889665i | \(-0.0283564\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1167.00 | −0.531179 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 2448.00i | 1.07583i | 0.843000 | + | 0.537913i | \(0.180787\pi\) | ||||
−0.843000 | + | 0.537913i | \(0.819213\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 4224.00 | 1.76378 | 0.881890 | − | 0.471455i | \(-0.156271\pi\) | ||||
0.881890 | + | 0.471455i | \(0.156271\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −510.000 | −0.209436 | −0.104718 | − | 0.994502i | \(-0.533394\pi\) | ||||
−0.104718 | + | 0.994502i | \(0.533394\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − 2048.00i | − 0.800880i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −384.000 | −0.145473 | −0.0727363 | − | 0.997351i | \(-0.523173\pi\) | ||||
−0.0727363 | + | 0.997351i | \(0.523173\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − 3454.00i | − 1.28821i | −0.764937 | − | 0.644105i | \(-0.777230\pi\) | ||||
0.764937 | − | 0.644105i | \(-0.222770\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 3216.00i | 1.16310i | 0.813511 | + | 0.581550i | \(0.197553\pi\) | ||||
−0.813511 | + | 0.581550i | \(0.802447\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −1708.00 | −0.608427 | −0.304213 | − | 0.952604i | \(-0.598394\pi\) | ||||
−0.304213 | + | 0.952604i | \(0.598394\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 1728.00i | 0.597447i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 8704.00 | 2.88071 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2320.00 | 0.756945 | 0.378472 | − | 0.925613i | \(-0.376449\pi\) | ||||
0.378472 | + | 0.925613i | \(0.376449\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 240.000i | 0.0750795i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1856.00 | 0.564923 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − 116.000i | − 0.0348338i | −0.999848 | − | 0.0174169i | \(-0.994456\pi\) | ||||
0.999848 | − | 0.0174169i | \(-0.00554425\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − 1344.00i | − 0.392971i | −0.980507 | − | 0.196485i | \(-0.937047\pi\) | ||||
0.980507 | − | 0.196485i | \(-0.0629529\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −4594.00 | −1.32568 | −0.662839 | − | 0.748762i | \(-0.730648\pi\) | ||||
−0.662839 | + | 0.748762i | \(0.730648\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 5056.00i | 1.42159i | 0.703401 | + | 0.710793i | \(0.251664\pi\) | ||||
−0.703401 | + | 0.710793i | \(0.748336\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 3712.00 | 1.00464 | 0.502321 | − | 0.864681i | \(-0.332480\pi\) | ||||
0.502321 | + | 0.864681i | \(0.332480\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −978.000 | −0.261405 | −0.130702 | − | 0.991422i | \(-0.541723\pi\) | ||||
−0.130702 | + | 0.991422i | \(0.541723\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 7888.00i | 2.03199i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 1856.00 | 0.466732 | 0.233366 | − | 0.972389i | \(-0.425026\pi\) | ||||
0.233366 | + | 0.972389i | \(0.425026\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − 8192.00i | − 2.03568i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − 7808.00i | − 1.89513i | −0.319556 | − | 0.947567i | \(-0.603534\pi\) | ||||
0.319556 | − | 0.947567i | \(-0.396466\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −216.000 | −0.0518208 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 1024.00i | 0.240086i | 0.992769 | + | 0.120043i | \(0.0383032\pi\) | ||||
−0.992769 | + | 0.120043i | \(0.961697\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −1328.00 | −0.301002 | −0.150501 | − | 0.988610i | \(-0.548089\pi\) | ||||
−0.150501 | + | 0.988610i | \(0.548089\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −5812.00 | −1.30278 | −0.651391 | − | 0.758742i | \(-0.725814\pi\) | ||||
−0.651391 | + | 0.758742i | \(0.725814\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − 8386.00i | − 1.81901i | −0.415692 | − | 0.909505i | \(-0.636461\pi\) | ||||
0.415692 | − | 0.909505i | \(-0.363539\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −640.000 | −0.135869 | −0.0679345 | − | 0.997690i | \(-0.521641\pi\) | ||||
−0.0679345 | + | 0.997690i | \(0.521641\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 4832.00i | 1.01496i | 0.861665 | + | 0.507478i | \(0.169422\pi\) | ||||
−0.861665 | + | 0.507478i | \(0.830578\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − 3456.00i | − 0.710806i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 3889.00 | 0.791573 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 6384.00i | 1.27289i | 0.771321 | + | 0.636446i | \(0.219596\pi\) | ||||
−0.771321 | + | 0.636446i | \(0.780404\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 7424.00 | 1.43592 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 2400.00 | 0.459580 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 3312.00i | 0.615719i | 0.951432 | + | 0.307860i | \(0.0996127\pi\) | ||||
−0.951432 | + | 0.307860i | \(0.900387\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 9984.00 | 1.82039 | 0.910194 | − | 0.414182i | \(-0.135932\pi\) | ||||
0.910194 | + | 0.414182i | \(0.135932\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 2586.00i | 0.466995i | 0.972357 | + | 0.233497i | \(0.0750170\pi\) | ||||
−0.972357 | + | 0.233497i | \(0.924983\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 2832.00i | 0.501770i | 0.968017 | + | 0.250885i | \(0.0807215\pi\) | ||||
−0.968017 | + | 0.250885i | \(0.919278\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 9216.00 | 1.61755 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − 4352.00i | − 0.749696i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 4608.00 | 0.772180 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −5920.00 | −0.983059 | −0.491530 | − | 0.870861i | \(-0.663562\pi\) | ||||
−0.491530 | + | 0.870861i | \(0.663562\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 4674.00i | 0.755516i | 0.925904 | + | 0.377758i | \(0.123305\pi\) | ||||
−0.925904 | + | 0.377758i | \(0.876695\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 1280.00 | 0.203272 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 6504.00i | 1.02386i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 9024.00i | 1.39606i | 0.716067 | + | 0.698031i | \(0.245940\pi\) | ||||
−0.716067 | + | 0.698031i | \(0.754060\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 4362.00 | 0.669033 | 0.334516 | − | 0.942390i | \(-0.391427\pi\) | ||||
0.334516 | + | 0.942390i | \(0.391427\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 8768.00i | 1.32202i | 0.750376 | + | 0.661011i | \(0.229872\pi\) | ||||
−0.750376 | + | 0.661011i | \(0.770128\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 6144.00 | 0.903253 | 0.451627 | − | 0.892207i | \(-0.350844\pi\) | ||||
0.451627 | + | 0.892207i | \(0.350844\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 11637.0 | 1.69660 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − 4564.00i | − 0.649152i | −0.945860 | − | 0.324576i | \(-0.894778\pi\) | ||||
0.945860 | − | 0.324576i | \(-0.105222\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −5952.00 | −0.832918 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − 8770.00i | − 1.21741i | −0.793397 | − | 0.608704i | \(-0.791690\pi\) | ||||
0.793397 | − | 0.608704i | \(-0.208310\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 8352.00i | 1.14098i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 1096.00 | 0.148543 | 0.0742714 | − | 0.997238i | \(-0.476337\pi\) | ||||
0.0742714 | + | 0.997238i | \(0.476337\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 10368.0i | 1.38324i | 0.722263 | + | 0.691619i | \(0.243102\pi\) | ||||
−0.722263 | + | 0.691619i | \(0.756898\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 3248.00 | 0.423342 | 0.211671 | − | 0.977341i | \(-0.432109\pi\) | ||||
0.211671 | + | 0.977341i | \(0.432109\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −4096.00 | −0.529779 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 6106.00i | 0.771918i | 0.922516 | + | 0.385959i | \(0.126129\pi\) | ||||
−0.922516 | + | 0.385959i | \(0.873871\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 7008.00 | 0.872725 | 0.436363 | − | 0.899771i | \(-0.356266\pi\) | ||||
0.436363 | + | 0.899771i | \(0.356266\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1160.00i | 0.143384i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 1152.00i | 0.140301i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −1590.00 | −0.192226 | −0.0961130 | − | 0.995370i | \(-0.530641\pi\) | ||||
−0.0961130 | + | 0.995370i | \(0.530641\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 1536.00i | 0.183006i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 192.000 | 0.0223862 | 0.0111931 | − | 0.999937i | \(-0.496437\pi\) | ||||
0.0111931 | + | 0.999937i | \(0.496437\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 9074.00 | 1.05045 | 0.525225 | − | 0.850963i | \(-0.323981\pi\) | ||||
0.525225 | + | 0.850963i | \(0.323981\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − 5496.00i | − 0.622881i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −5248.00 | −0.586513 | −0.293257 | − | 0.956034i | \(-0.594739\pi\) | ||||
−0.293257 | + | 0.956034i | \(0.594739\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − 8222.00i | − 0.912527i | −0.889845 | − | 0.456263i | \(-0.849187\pi\) | ||||
0.889845 | − | 0.456263i | \(-0.150813\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − 17408.0i | − 1.90558i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −16236.0 | −1.76515 | −0.882576 | − | 0.470169i | \(-0.844193\pi\) | ||||
−0.882576 | + | 0.470169i | \(0.844193\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 14528.0i | 1.55812i | 0.626951 | + | 0.779059i | \(0.284303\pi\) | ||||
−0.626951 | + | 0.779059i | \(0.715697\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −6304.00 | −0.662593 | −0.331296 | − | 0.943527i | \(-0.607486\pi\) | ||||
−0.331296 | + | 0.943527i | \(0.607486\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −18432.0 | −1.92445 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − 1958.00i | − 0.200419i | −0.994966 | − | 0.100209i | \(-0.968049\pi\) | ||||
0.994966 | − | 0.100209i | \(-0.0319513\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 4048.00 | 0.408968 | 0.204484 | − | 0.978870i | \(-0.434448\pi\) | ||||
0.204484 | + | 0.978870i | \(0.434448\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 16988.0i | 1.70518i | 0.522579 | + | 0.852591i | \(0.324970\pi\) | ||||
−0.522579 | + | 0.852591i | \(0.675030\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − 6720.00i | − 0.665877i | −0.942949 | − | 0.332938i | \(-0.891960\pi\) | ||||
0.942949 | − | 0.332938i | \(-0.108040\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −5952.00 | −0.586008 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − 12800.0i | − 1.24428i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −9728.00 | −0.927941 | −0.463970 | − | 0.885851i | \(-0.653576\pi\) | ||||
−0.463970 | + | 0.885851i | \(0.653576\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1044.00 | −0.0989653 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 8444.00i | 0.785696i | 0.919603 | + | 0.392848i | \(0.128510\pi\) | ||||
−0.919603 | + | 0.392848i | \(0.871490\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −15360.0 | −1.41179 | −0.705893 | − | 0.708318i | \(-0.749454\pi\) | ||||
−0.705893 | + | 0.708318i | \(0.749454\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − 4608.00i | − 0.420961i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 6144.00i | 0.554519i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −6624.00 | −0.594250 | −0.297125 | − | 0.954839i | \(-0.596028\pi\) | ||||
−0.297125 | + | 0.954839i | \(0.596028\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − 6912.00i | − 0.612705i | −0.951918 | − | 0.306353i | \(-0.900891\pi\) | ||||
0.951918 | − | 0.306353i | \(-0.0991087\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 19920.0 | 1.73465 | 0.867327 | − | 0.497739i | \(-0.165836\pi\) | ||||
0.867327 | + | 0.497739i | \(0.165836\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 7224.00 | 0.625383 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − 24576.0i | − 2.09062i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 3680.00 | 0.309451 | 0.154725 | − | 0.987958i | \(-0.450551\pi\) | ||||
0.154725 | + | 0.987958i | \(0.450551\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − 11720.0i | − 0.979885i | −0.871755 | − | 0.489942i | \(-0.837018\pi\) | ||||
0.871755 | − | 0.489942i | \(-0.162982\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − 640.000i | − 0.0529010i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −4217.00 | −0.346593 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − 16704.0i | − 1.35747i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 12736.0 | 1.01777 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 11754.0 | 0.934092 | 0.467046 | − | 0.884233i | \(-0.345318\pi\) | ||||
0.467046 | + | 0.884233i | \(0.345318\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 18904.0i | 1.47765i | 0.673895 | + | 0.738827i | \(0.264620\pi\) | ||||
−0.673895 | + | 0.738827i | \(0.735380\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 19584.0 | 1.51417 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − 13296.0i | − 1.02243i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − 3088.00i | − 0.234906i | −0.993078 | − | 0.117453i | \(-0.962527\pi\) | ||||
0.993078 | − | 0.117453i | \(-0.0374730\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 11600.0 | 0.877688 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − 21440.0i | − 1.60495i | −0.596684 | − | 0.802476i | \(-0.703515\pi\) | ||||
0.596684 | − | 0.802476i | \(-0.296485\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −22624.0 | −1.66687 | −0.833434 | − | 0.552620i | \(-0.813628\pi\) | ||||
−0.833434 | + | 0.552620i | \(0.813628\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −6000.00 | −0.439741 | −0.219871 | − | 0.975529i | \(-0.570564\pi\) | ||||
−0.219871 | + | 0.975529i | \(0.570564\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − 19922.0i | − 1.43737i | −0.695335 | − | 0.718686i | \(-0.744744\pi\) | ||||
0.695335 | − | 0.718686i | \(-0.255256\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −8448.00 | −0.603239 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 31744.0i | 2.25506i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 3584.00i | 0.252006i | 0.992030 | + | 0.126003i | \(0.0402149\pi\) | ||||
−0.992030 | + | 0.126003i | \(0.959785\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 2720.00 | 0.190281 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 1984.00i | 0.137391i | 0.997638 | + | 0.0686957i | \(0.0218838\pi\) | ||||
−0.997638 | + | 0.0686957i | \(0.978116\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −14976.0 | −1.02154 | −0.510770 | − | 0.859717i | \(-0.670640\pi\) | ||||
−0.510770 | + | 0.859717i | \(0.670640\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 25738.0 | 1.74688 | 0.873440 | − | 0.486932i | \(-0.161884\pi\) | ||||
0.873440 | + | 0.486932i | \(0.161884\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 8548.00i | 0.571586i | 0.958291 | + | 0.285793i | \(0.0922570\pi\) | ||||
−0.958291 | + | 0.285793i | \(0.907743\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 22272.0 | 1.47468 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 8558.00i | 0.563873i | 0.959433 | + | 0.281937i | \(0.0909768\pi\) | ||||
−0.959433 | + | 0.281937i | \(0.909023\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 10368.0i | 0.676499i | 0.941056 | + | 0.338250i | \(0.109835\pi\) | ||||
−0.941056 | + | 0.338250i | \(0.890165\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 13088.0 | 0.849840 | 0.424920 | − | 0.905231i | \(-0.360302\pi\) | ||||
0.424920 | + | 0.905231i | \(0.360302\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 11520.0i | 0.740833i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 576.000 | 0.0365129 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −4412.00 | −0.278350 | −0.139175 | − | 0.990268i | \(-0.544445\pi\) | ||||
−0.139175 | + | 0.990268i | \(0.544445\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 11542.0i | 0.717913i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −30176.0 | −1.85941 | −0.929704 | − | 0.368308i | \(-0.879937\pi\) | ||||
−0.929704 | + | 0.368308i | \(0.879937\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 21288.0i | 1.30562i | 0.757520 | + | 0.652812i | \(0.226411\pi\) | ||||
−0.757520 | + | 0.652812i | \(0.773589\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − 17024.0i | − 1.03444i | −0.855853 | − | 0.517220i | \(-0.826967\pi\) | ||||
0.855853 | − | 0.517220i | \(-0.173033\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 8192.00 | 0.495476 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 2256.00i | 0.135198i | 0.997713 | + | 0.0675989i | \(0.0215338\pi\) | ||||
−0.997713 | + | 0.0675989i | \(0.978466\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −23808.0 | −1.40733 | −0.703663 | − | 0.710534i | \(-0.748454\pi\) | ||||
−0.703663 | + | 0.710534i | \(0.748454\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −26242.0 | −1.54417 | −0.772084 | − | 0.635520i | \(-0.780786\pi\) | ||||
−0.772084 | + | 0.635520i | \(0.780786\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − 18432.0i | − 1.07000i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −29312.0 | −1.68640 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − 24590.0i | − 1.40843i | −0.709986 | − | 0.704216i | \(-0.751299\pi\) | ||||
0.709986 | − | 0.704216i | \(-0.248701\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 2864.00i | 0.162589i | 0.996690 | + | 0.0812943i | \(0.0259054\pi\) | ||||
−0.996690 | + | 0.0812943i | \(0.974095\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 2472.00 | 0.139715 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − 7616.00i | − 0.426674i | −0.976979 | − | 0.213337i | \(-0.931567\pi\) | ||||
0.976979 | − | 0.213337i | \(-0.0684332\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −28768.0 | −1.59067 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 2168.00 | 0.119355 | 0.0596777 | − | 0.998218i | \(-0.480993\pi\) | ||||
0.0596777 | + | 0.998218i | \(0.480993\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 9216.00i | 0.500833i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −18000.0 | −0.969830 | −0.484915 | − | 0.874561i | \(-0.661149\pi\) | ||||
−0.484915 | + | 0.874561i | \(0.661149\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 2448.00i | 0.131334i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 5184.00i | 0.275763i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −3506.00 | −0.185713 | −0.0928566 | − | 0.995679i | \(-0.529600\pi\) | ||||
−0.0928566 | + | 0.995679i | \(0.529600\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − 2560.00i | − 0.134464i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −15616.0 | −0.809984 | −0.404992 | − | 0.914320i | \(-0.632726\pi\) | ||||
−0.404992 | + | 0.914320i | \(0.632726\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 816.000 | 0.0421490 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 15036.0i | 0.767062i | 0.923528 | + | 0.383531i | \(0.125292\pi\) | ||||
−0.923528 | + | 0.383531i | \(0.874708\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −6400.00 | −0.323820 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − 19126.0i | − 0.963758i | −0.876238 | − | 0.481879i | \(-0.839954\pi\) | ||||
0.876238 | − | 0.481879i | \(-0.160046\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 31744.0i | 1.58657i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 17392.0 | 0.865731 | 0.432865 | − | 0.901459i | \(-0.357503\pi\) | ||||
0.432865 | + | 0.901459i | \(0.357503\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − 32384.0i | − 1.59900i | −0.600669 | − | 0.799498i | \(-0.705099\pi\) | ||||
0.600669 | − | 0.799498i | \(-0.294901\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −4608.00 | −0.224797 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −27708.0 | −1.34631 | −0.673155 | − | 0.739501i | \(-0.735061\pi\) | ||||
−0.673155 | + | 0.739501i | \(0.735061\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 37246.0i | 1.78828i | 0.447786 | + | 0.894141i | \(0.352213\pi\) | ||||
−0.447786 | + | 0.894141i | \(0.647787\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −4192.00 | −0.199684 | −0.0998422 | − | 0.995003i | \(-0.531834\pi\) | ||||
−0.0998422 | + | 0.995003i | \(0.531834\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 6216.00i | 0.294934i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 7424.00i | 0.349498i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −26882.0 | −1.26058 | −0.630292 | − | 0.776358i | \(-0.717065\pi\) | ||||
−0.630292 | + | 0.776358i | \(0.717065\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − 17232.0i | − 0.801801i | −0.916122 | − | 0.400900i | \(-0.868697\pi\) | ||||
0.916122 | − | 0.400900i | \(-0.131303\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −39168.0 | −1.80146 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 32768.0 | 1.50132 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − 31816.0i | − 1.44106i | −0.693421 | − | 0.720532i | \(-0.743898\pi\) | ||||
0.693421 | − | 0.720532i | \(-0.256102\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 11520.0 | 0.517831 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − 26564.0i | − 1.18955i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − 8272.00i | − 0.367640i | −0.982960 | − | 0.183820i | \(-0.941154\pi\) | ||||
0.982960 | − | 0.183820i | \(-0.0588464\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −12288.0 | −0.544078 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − 38528.0i | − 1.69318i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 9184.00 | 0.399125 | 0.199563 | − | 0.979885i | \(-0.436048\pi\) | ||||
0.199563 | + | 0.979885i | \(0.436048\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −19832.0 | −0.858688 | −0.429344 | − | 0.903141i | \(-0.641255\pi\) | ||||
−0.429344 | + | 0.903141i | \(0.641255\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − 27200.0i | − 1.16476i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 15216.0 | 0.646823 | 0.323412 | − | 0.946258i | \(-0.395170\pi\) | ||||
0.323412 | + | 0.946258i | \(0.395170\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − 39772.0i | − 1.68453i | −0.539067 | − | 0.842263i | \(-0.681223\pi\) | ||||
0.539067 | − | 0.842263i | \(-0.318777\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 18304.0i | 0.769640i | 0.922992 | + | 0.384820i | \(0.125737\pi\) | ||||
−0.922992 | + | 0.384820i | \(0.874263\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −4906.00 | −0.205540 | −0.102770 | − | 0.994705i | \(-0.532771\pi\) | ||||
−0.102770 | + | 0.994705i | \(0.532771\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − 6368.00i | − 0.264872i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −15360.0 | −0.632045 | −0.316023 | − | 0.948752i | \(-0.602348\pi\) | ||||
−0.316023 | + | 0.948752i | \(0.602348\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −3653.00 | −0.149781 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 33180.0i | 1.34602i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 2304.00 | 0.0928086 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − 24802.0i | − 0.995550i | −0.867306 | − | 0.497775i | \(-0.834150\pi\) | ||||
0.867306 | − | 0.497775i | \(-0.165850\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − 15072.0i | − 0.600758i | −0.953820 | − | 0.300379i | \(-0.902887\pi\) | ||||
0.953820 | − | 0.300379i | \(-0.0971132\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −1800.00 | −0.0714962 | −0.0357481 | − | 0.999361i | \(-0.511381\pi\) | ||||
−0.0357481 | + | 0.999361i | \(0.511381\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 7552.00i | 0.297883i | 0.988846 | + | 0.148942i | \(0.0475866\pi\) | ||||
−0.988846 | + | 0.148942i | \(0.952413\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −70912.0 | −2.76815 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −28768.0 | −1.11913 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − 20838.0i | − 0.802337i | −0.916004 | − | 0.401168i | \(-0.868604\pi\) | ||||
0.916004 | − | 0.401168i | \(-0.131396\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 47744.0 | 1.82581 | 0.912904 | − | 0.408175i | \(-0.133835\pi\) | ||||
0.912904 | + | 0.408175i | \(0.133835\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 28280.0i | 1.07780i | 0.842370 | + | 0.538900i | \(0.181160\pi\) | ||||
−0.842370 | + | 0.538900i | \(0.818840\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − 7424.00i | − 0.281030i | −0.990079 | − | 0.140515i | \(-0.955124\pi\) | ||||
0.990079 | − | 0.140515i | \(-0.0448758\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 9552.00 | 0.360364 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − 52224.0i | − 1.95701i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 2880.00 | 0.106845 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 15872.0 | 0.586873 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 5912.00i | 0.216433i | 0.994127 | + | 0.108217i | \(0.0345140\pi\) | ||||
−0.994127 | + | 0.108217i | \(0.965486\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −26240.0 | −0.954303 | −0.477151 | − | 0.878821i | \(-0.658331\pi\) | ||||
−0.477151 | + | 0.878821i | \(0.658331\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 45056.0i | 1.63323i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 6144.00i | 0.221257i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −35620.0 | −1.27856 | −0.639279 | − | 0.768975i | \(-0.720767\pi\) | ||||
−0.639279 | + | 0.768975i | \(0.720767\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 29696.0i | 1.05900i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 3232.00 | 0.114143 | 0.0570713 | − | 0.998370i | \(-0.481824\pi\) | ||||
0.0570713 | + | 0.998370i | \(0.481824\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 27064.0 | 0.952725 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 11478.0i | 0.400181i | 0.979777 | + | 0.200091i | \(0.0641237\pi\) | ||||
−0.979777 | + | 0.200091i | \(0.935876\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −39984.0 | −1.38517 | −0.692583 | − | 0.721338i | \(-0.743527\pi\) | ||||
−0.692583 | + | 0.721338i | \(0.743527\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 36864.0i | 1.27302i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − 24192.0i | − 0.830131i | −0.909791 | − | 0.415066i | \(-0.863759\pi\) | ||||
0.909791 | − | 0.415066i | \(-0.136241\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 34916.0 | 1.19433 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − 39456.0i | − 1.34114i | −0.741847 | − | 0.670569i | \(-0.766050\pi\) | ||||
0.741847 | − | 0.670569i | \(-0.233950\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 21888.0 | 0.737018 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −29391.0 | −0.986573 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 41668.0i | 1.38568i | 0.721091 | + | 0.692840i | \(0.243641\pi\) | ||||
−0.721091 | + | 0.692840i | \(0.756359\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −51648.0 | −1.70697 | −0.853483 | − | 0.521121i | \(-0.825514\pi\) | ||||
−0.853483 | + | 0.521121i | \(0.825514\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 25920.0i | 0.854015i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − 55776.0i | − 1.82644i | −0.407466 | − | 0.913220i | \(-0.633588\pi\) | ||||
0.407466 | − | 0.913220i | \(-0.366412\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 61440.0 | 2.00575 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − 36096.0i | − 1.17119i | −0.810602 | − | 0.585597i | \(-0.800860\pi\) | ||||
0.810602 | − | 0.585597i | \(-0.199140\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −25600.0 | −0.823087 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 42532.0 | 1.36334 | 0.681672 | − | 0.731658i | \(-0.261253\pi\) | ||||
0.681672 | + | 0.731658i | \(0.261253\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − 29806.0i | − 0.946806i | −0.880846 | − | 0.473403i | \(-0.843025\pi\) | ||||
0.880846 | − | 0.473403i | \(-0.156975\pi\) | |||||||
\(998\) | 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 | 1800.4.f.x.649.2 | 2 | ||
3.2 | odd | 2 | 1800.4.f.b.649.2 | 2 | |||
5.2 | odd | 4 | 72.4.a.d.1.1 | yes | 1 | ||
5.3 | odd | 4 | 1800.4.a.ba.1.1 | 1 | |||
5.4 | even | 2 | inner | 1800.4.f.x.649.1 | 2 | ||
15.2 | even | 4 | 72.4.a.a.1.1 | ✓ | 1 | ||
15.8 | even | 4 | 1800.4.a.z.1.1 | 1 | |||
15.14 | odd | 2 | 1800.4.f.b.649.1 | 2 | |||
20.7 | even | 4 | 144.4.a.f.1.1 | 1 | |||
40.27 | even | 4 | 576.4.a.d.1.1 | 1 | |||
40.37 | odd | 4 | 576.4.a.c.1.1 | 1 | |||
45.2 | even | 12 | 648.4.i.l.433.1 | 2 | |||
45.7 | odd | 12 | 648.4.i.a.433.1 | 2 | |||
45.22 | odd | 12 | 648.4.i.a.217.1 | 2 | |||
45.32 | even | 12 | 648.4.i.l.217.1 | 2 | |||
60.47 | odd | 4 | 144.4.a.a.1.1 | 1 | |||
120.77 | even | 4 | 576.4.a.w.1.1 | 1 | |||
120.107 | odd | 4 | 576.4.a.x.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
72.4.a.a.1.1 | ✓ | 1 | 15.2 | even | 4 | ||
72.4.a.d.1.1 | yes | 1 | 5.2 | odd | 4 | ||
144.4.a.a.1.1 | 1 | 60.47 | odd | 4 | |||
144.4.a.f.1.1 | 1 | 20.7 | even | 4 | |||
576.4.a.c.1.1 | 1 | 40.37 | odd | 4 | |||
576.4.a.d.1.1 | 1 | 40.27 | even | 4 | |||
576.4.a.w.1.1 | 1 | 120.77 | even | 4 | |||
576.4.a.x.1.1 | 1 | 120.107 | odd | 4 | |||
648.4.i.a.217.1 | 2 | 45.22 | odd | 12 | |||
648.4.i.a.433.1 | 2 | 45.7 | odd | 12 | |||
648.4.i.l.217.1 | 2 | 45.32 | even | 12 | |||
648.4.i.l.433.1 | 2 | 45.2 | even | 12 | |||
1800.4.a.z.1.1 | 1 | 15.8 | even | 4 | |||
1800.4.a.ba.1.1 | 1 | 5.3 | odd | 4 | |||
1800.4.f.b.649.1 | 2 | 15.14 | odd | 2 | |||
1800.4.f.b.649.2 | 2 | 3.2 | odd | 2 | |||
1800.4.f.x.649.1 | 2 | 5.4 | even | 2 | inner | ||
1800.4.f.x.649.2 | 2 | 1.1 | even | 1 | trivial |