Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1300,2,Mod(701,1300)]
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, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1300.701");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1300 = 2^{2} \cdot 5^{2} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1300.f (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(10.3805522628\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | 8.0.796594176.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 2x^{7} - 5x^{6} - 2x^{5} + 63x^{4} - 64x^{3} + 46x^{2} - 16x + 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{8} \) |
Twist minimal: | no (minimal twist has level 260) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 701.3 | ||
Root | \(0.170899 + 0.478682i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1300.701 |
Dual form | 1300.2.f.f.701.4 |
$q$-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 | ||||||||
\(3\) | −0.646084 | −0.373017 | −0.186508 | − | 0.982453i | \(-0.559717\pi\) | ||||
−0.186508 | + | 0.982453i | \(0.559717\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 0.913701i | − | 0.345346i | −0.984979 | − | 0.172673i | \(-0.944760\pi\) | ||
0.984979 | − | 0.172673i | \(-0.0552404\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.58258 | −0.860859 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 3.94748i | 1.19021i | 0.803648 | + | 0.595105i | \(0.202889\pi\) | ||||
−0.803648 | + | 0.595105i | \(0.797111\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.44949 | − | 2.64575i | −0.679366 | − | 0.733799i | ||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 6.19115 | 1.50157 | 0.750787 | − | 0.660545i | \(-0.229675\pi\) | ||||
0.750787 | + | 0.660545i | \(0.229675\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 1.11905i | − | 0.256728i | −0.991727 | − | 0.128364i | \(-0.959027\pi\) | ||
0.991727 | − | 0.128364i | \(-0.0409725\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.590327i | 0.128820i | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 5.54506 | 1.15623 | 0.578113 | − | 0.815957i | \(-0.303789\pi\) | ||||
0.578113 | + | 0.815957i | \(0.303789\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 3.60681 | 0.694131 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −1.58258 | −0.293877 | −0.146938 | − | 0.989146i | \(-0.546942\pi\) | ||||
−0.146938 | + | 0.989146i | \(0.546942\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 9.60433i | − | 1.72499i | −0.506067 | − | 0.862494i | \(-0.668901\pi\) | ||
0.506067 | − | 0.862494i | \(-0.331099\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | − | 2.55040i | − | 0.443968i | ||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 7.84190i | − | 1.28920i | −0.764520 | − | 0.644601i | \(-0.777024\pi\) | ||
0.764520 | − | 0.644601i | \(-0.222976\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 1.58258 | + | 1.70938i | 0.253415 | + | 0.273719i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 5.06653i | 0.791259i | 0.918410 | + | 0.395629i | \(0.129473\pi\) | ||||
−0.918410 | + | 0.395629i | \(0.870527\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 6.83723 | 1.04267 | 0.521334 | − | 0.853353i | \(-0.325435\pi\) | ||||
0.521334 | + | 0.853353i | \(0.325435\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − | 9.66930i | − | 1.41041i | −0.709002 | − | 0.705207i | \(-0.750854\pi\) | ||
0.709002 | − | 0.705207i | \(-0.249146\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 6.16515 | 0.880736 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −4.00000 | −0.560112 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −1.29217 | −0.177493 | −0.0887464 | − | 0.996054i | \(-0.528286\pi\) | ||||
−0.0887464 | + | 0.996054i | \(0.528286\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0.723000i | 0.0957637i | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 9.01400i | 1.17352i | 0.809760 | + | 0.586762i | \(0.199597\pi\) | ||||
−0.809760 | + | 0.586762i | \(0.800403\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −5.58258 | −0.714776 | −0.357388 | − | 0.933956i | \(-0.616333\pi\) | ||||
−0.357388 | + | 0.933956i | \(0.616333\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 2.35970i | 0.297294i | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 7.84190i | − | 0.958041i | −0.877804 | − | 0.479021i | \(-0.840992\pi\) | ||
0.877804 | − | 0.479021i | \(-0.159008\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −3.58258 | −0.431291 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 6.77590i | − | 0.804152i | −0.915606 | − | 0.402076i | \(-0.868289\pi\) | ||
0.915606 | − | 0.402076i | \(-0.131711\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 7.84190i | 0.917825i | 0.888481 | + | 0.458913i | \(0.151761\pi\) | ||||
−0.888481 | + | 0.458913i | \(0.848239\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 3.60681 | 0.411034 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 7.16515 | 0.806143 | 0.403071 | − | 0.915169i | \(-0.367943\pi\) | ||||
0.403071 | + | 0.915169i | \(0.367943\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 5.41742 | 0.601936 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − | 16.5975i | − | 1.82181i | −0.412613 | − | 0.910907i | \(-0.635384\pi\) | ||
0.412613 | − | 0.910907i | \(-0.364616\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 1.02248 | 0.109621 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 11.3137i | − | 1.19925i | −0.800281 | − | 0.599625i | \(-0.795316\pi\) | ||
0.800281 | − | 0.599625i | \(-0.204684\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −2.41742 | + | 2.23810i | −0.253415 | + | 0.234617i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 6.20520i | 0.643450i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 1.63670i | − | 0.166182i | −0.996542 | − | 0.0830909i | \(-0.973521\pi\) | ||
0.996542 | − | 0.0830909i | \(-0.0264792\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | − | 10.1947i | − | 1.02460i | ||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 9.16515 | 0.911967 | 0.455983 | − | 0.889988i | \(-0.349288\pi\) | ||||
0.455983 | + | 0.889988i | \(0.349288\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1.93825 | −0.190982 | −0.0954908 | − | 0.995430i | \(-0.530442\pi\) | ||||
−0.0954908 | + | 0.995430i | \(0.530442\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 8.12940 | 0.785899 | 0.392949 | − | 0.919560i | \(-0.371455\pi\) | ||||
0.392949 | + | 0.919560i | \(0.371455\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 8.48528i | 0.812743i | 0.913708 | + | 0.406371i | \(0.133206\pi\) | ||||
−0.913708 | + | 0.406371i | \(0.866794\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 5.06653i | 0.480893i | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 3.60681 | 0.339300 | 0.169650 | − | 0.985504i | \(-0.445736\pi\) | ||||
0.169650 | + | 0.985504i | \(0.445736\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 6.32599 | + | 6.83285i | 0.584838 | + | 0.631697i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | − | 5.65685i | − | 0.518563i | ||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −4.58258 | −0.416598 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | − | 3.27340i | − | 0.295153i | ||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 11.7362 | 1.04142 | 0.520710 | − | 0.853734i | \(-0.325667\pi\) | ||||
0.520710 | + | 0.853734i | \(0.325667\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −4.41742 | −0.388933 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 15.1652 | 1.32499 | 0.662493 | − | 0.749068i | \(-0.269499\pi\) | ||||
0.662493 | + | 0.749068i | \(0.269499\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1.02248 | −0.0886600 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 10.3923i | 0.887875i | 0.896058 | + | 0.443937i | \(0.146419\pi\) | ||||
−0.896058 | + | 0.443937i | \(0.853581\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −11.1652 | −0.947016 | −0.473508 | − | 0.880790i | \(-0.657012\pi\) | ||||
−0.473508 | + | 0.880790i | \(0.657012\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 6.24718i | 0.526108i | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 10.4440 | − | 9.66930i | 0.873375 | − | 0.808588i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −3.98320 | −0.328529 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − | 2.82843i | − | 0.231714i | −0.993266 | − | 0.115857i | \(-0.963039\pi\) | ||
0.993266 | − | 0.115857i | \(-0.0369614\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 3.35715i | 0.273201i | 0.990626 | + | 0.136600i | \(0.0436177\pi\) | ||||
−0.990626 | + | 0.136600i | \(0.956382\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −15.9891 | −1.29264 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −22.4499 | −1.79170 | −0.895850 | − | 0.444356i | \(-0.853433\pi\) | ||||
−0.895850 | + | 0.444356i | \(0.853433\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0.834849 | 0.0662078 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − | 5.06653i | − | 0.399298i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 6.01450i | − | 0.471092i | −0.971863 | − | 0.235546i | \(-0.924312\pi\) | ||
0.971863 | − | 0.235546i | \(-0.0756879\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − | 16.5975i | − | 1.28435i | −0.766557 | − | 0.642177i | \(-0.778031\pi\) | ||
0.766557 | − | 0.642177i | \(-0.221969\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1.00000 | + | 12.9615i | −0.0769231 | + | 0.997037i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 2.89003i | 0.221006i | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −11.0901 | −0.843167 | −0.421583 | − | 0.906790i | \(-0.638526\pi\) | ||||
−0.421583 | + | 0.906790i | \(0.638526\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | − | 5.82380i | − | 0.437744i | ||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −14.4174 | −1.07164 | −0.535819 | − | 0.844333i | \(-0.679997\pi\) | ||||
−0.535819 | + | 0.844333i | \(0.679997\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 3.60681 | 0.266623 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 24.4394i | 1.78719i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | − | 3.29555i | − | 0.239716i | ||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −12.0000 | −0.868290 | −0.434145 | − | 0.900843i | \(-0.642949\pi\) | ||||
−0.434145 | + | 0.900843i | \(0.642949\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 20.9753i | 1.50984i | 0.655819 | + | 0.754918i | \(0.272323\pi\) | ||||
−0.655819 | + | 0.754918i | \(0.727677\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 8.94630i | 0.637398i | 0.947856 | + | 0.318699i | \(0.103246\pi\) | ||||
−0.947856 | + | 0.318699i | \(0.896754\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 4.00000 | 0.283552 | 0.141776 | − | 0.989899i | \(-0.454719\pi\) | ||||
0.141776 | + | 0.989899i | \(0.454719\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 5.06653i | 0.357365i | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 1.44600i | 0.101489i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −14.3205 | −0.995347 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 4.41742 | 0.305560 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 20.0000 | 1.37686 | 0.688428 | − | 0.725304i | \(-0.258301\pi\) | ||||
0.688428 | + | 0.725304i | \(0.258301\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 4.37780i | 0.299962i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −8.77548 | −0.595719 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | − | 5.06653i | − | 0.342364i | ||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −15.1652 | − | 16.3802i | −1.02012 | − | 1.10185i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 7.84190i | 0.525133i | 0.964914 | + | 0.262566i | \(0.0845689\pi\) | ||||
−0.964914 | + | 0.262566i | \(0.915431\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 11.1153i | 0.737749i | 0.929479 | + | 0.368874i | \(0.120257\pi\) | ||||
−0.929479 | + | 0.368874i | \(0.879743\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 2.23810i | − | 0.147898i | −0.997262 | − | 0.0739489i | \(-0.976440\pi\) | ||
0.997262 | − | 0.0739489i | \(-0.0235602\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −2.33030 | −0.153323 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 2.58434 | 0.169305 | 0.0846527 | − | 0.996411i | \(-0.473022\pi\) | ||||
0.0846527 | + | 0.996411i | \(0.473022\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −4.62929 | −0.300705 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 10.7850i | 0.697623i | 0.937193 | + | 0.348811i | \(0.113415\pi\) | ||||
−0.937193 | + | 0.348811i | \(0.886585\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 27.6939i | − | 1.78392i | −0.452111 | − | 0.891962i | \(-0.649329\pi\) | ||
0.452111 | − | 0.891962i | \(-0.350671\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −14.3205 | −0.918663 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −2.96073 | + | 2.74110i | −0.188387 | + | 0.174412i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 10.7234i | 0.679567i | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 3.16515 | 0.199783 | 0.0998913 | − | 0.994998i | \(-0.468150\pi\) | ||||
0.0998913 | + | 0.994998i | \(0.468150\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 21.8890i | 1.37615i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −22.1803 | −1.38357 | −0.691783 | − | 0.722105i | \(-0.743175\pi\) | ||||
−0.691783 | + | 0.722105i | \(0.743175\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −7.16515 | −0.445221 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 4.08712 | 0.252986 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 20.2420 | 1.24818 | 0.624088 | − | 0.781354i | \(-0.285471\pi\) | ||||
0.624088 | + | 0.781354i | \(0.285471\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 7.30960i | 0.447341i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 9.16515 | 0.558809 | 0.279405 | − | 0.960173i | \(-0.409863\pi\) | ||||
0.279405 | + | 0.960173i | \(0.409863\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 15.8515i | 0.962911i | 0.876471 | + | 0.481455i | \(0.159892\pi\) | ||||
−0.876471 | + | 0.481455i | \(0.840108\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 1.56186 | − | 1.44600i | 0.0945280 | − | 0.0875159i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −5.92146 | −0.355786 | −0.177893 | − | 0.984050i | \(-0.556928\pi\) | ||||
−0.177893 | + | 0.984050i | \(0.556928\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 24.8039i | 1.48497i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 26.5133i | 1.58165i | 0.612042 | + | 0.790825i | \(0.290348\pi\) | ||||
−0.612042 | + | 0.790825i | \(0.709652\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 6.83723 | 0.406431 | 0.203216 | − | 0.979134i | \(-0.434861\pi\) | ||||
0.203216 | + | 0.979134i | \(0.434861\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 4.62929 | 0.273258 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 21.3303 | 1.25472 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 1.05745i | 0.0619886i | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − | 9.66930i | − | 0.564887i | −0.959284 | − | 0.282443i | \(-0.908855\pi\) | ||
0.959284 | − | 0.282443i | \(-0.0911449\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 14.2378i | 0.826161i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −13.5826 | − | 14.6709i | −0.785501 | − | 0.848438i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | − | 6.24718i | − | 0.360082i | ||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −5.92146 | −0.340179 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 18.4249i | 1.05157i | 0.850619 | + | 0.525783i | \(0.176227\pi\) | ||||
−0.850619 | + | 0.525783i | \(0.823773\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 1.25227 | 0.0712393 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −30.3303 | −1.71987 | −0.859937 | − | 0.510400i | \(-0.829497\pi\) | ||||
−0.859937 | + | 0.510400i | \(0.829497\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −18.5734 | −1.04983 | −0.524916 | − | 0.851154i | \(-0.675903\pi\) | ||||
−0.524916 | + | 0.851154i | \(0.675903\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − | 4.18710i | − | 0.235171i | −0.993063 | − | 0.117586i | \(-0.962485\pi\) | ||
0.993063 | − | 0.117586i | \(-0.0375154\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 6.24718i | − | 0.349775i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −5.25227 | −0.293153 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 6.92820i | − | 0.385496i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | − | 5.48220i | − | 0.303167i | ||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −8.83485 | −0.487081 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 5.12813i | 0.281868i | 0.990019 | + | 0.140934i | \(0.0450105\pi\) | ||||
−0.990019 | + | 0.140934i | \(0.954990\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 20.2523i | 1.10982i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −1.02248 | −0.0556978 | −0.0278489 | − | 0.999612i | \(-0.508866\pi\) | ||||
−0.0278489 | + | 0.999612i | \(0.508866\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −2.33030 | −0.126565 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 37.9129 | 2.05310 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 12.0290i | − | 0.649505i | ||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −24.1185 | −1.29475 | −0.647375 | − | 0.762172i | \(-0.724133\pi\) | ||||
−0.647375 | + | 0.762172i | \(0.724133\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 6.71430i | 0.359408i | 0.983721 | + | 0.179704i | \(0.0575140\pi\) | ||||
−0.983721 | + | 0.179704i | \(0.942486\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −8.83485 | − | 9.54273i | −0.471569 | − | 0.509353i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − | 9.66930i | − | 0.514645i | −0.966326 | − | 0.257323i | \(-0.917160\pi\) | ||
0.966326 | − | 0.257323i | \(-0.0828403\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 3.65480i | 0.193433i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 2.29970i | 0.121374i | 0.998157 | + | 0.0606869i | \(0.0193291\pi\) | ||||
−0.998157 | + | 0.0606869i | \(0.980671\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 17.7477 | 0.934091 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 2.96073 | 0.155398 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 1.93825 | 0.101176 | 0.0505880 | − | 0.998720i | \(-0.483890\pi\) | ||||
0.0505880 | + | 0.998720i | \(0.483890\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | − | 13.0847i | − | 0.681162i | ||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 1.18065i | 0.0612965i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −14.6969 | −0.760979 | −0.380489 | − | 0.924785i | \(-0.624244\pi\) | ||||
−0.380489 | + | 0.924785i | \(0.624244\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 3.87650 | + | 4.18710i | 0.199650 | + | 0.215647i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 31.0511i | − | 1.59499i | −0.603327 | − | 0.797494i | \(-0.706159\pi\) | ||
0.603327 | − | 0.797494i | \(-0.293841\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −7.58258 | −0.388467 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − | 29.0079i | − | 1.48224i | −0.671375 | − | 0.741118i | \(-0.734296\pi\) | ||
0.671375 | − | 0.741118i | \(-0.265704\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −17.6577 | −0.897590 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −18.0000 | −0.912636 | −0.456318 | − | 0.889817i | \(-0.650832\pi\) | ||||
−0.456318 | + | 0.889817i | \(0.650832\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 34.3303 | 1.73616 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −9.79796 | −0.494242 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 19.8709i | 0.997292i | 0.866806 | + | 0.498646i | \(0.166169\pi\) | ||||
−0.866806 | + | 0.498646i | \(0.833831\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0.660606 | 0.0330716 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 22.6274i | − | 1.12996i | −0.825105 | − | 0.564980i | \(-0.808884\pi\) | ||
0.825105 | − | 0.564980i | \(-0.191116\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −25.4107 | + | 23.5257i | −1.26580 | + | 1.17190i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 30.9557 | 1.53442 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 32.1701i | − | 1.59071i | −0.606143 | − | 0.795356i | \(-0.707284\pi\) | ||
0.606143 | − | 0.795356i | \(-0.292716\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | − | 6.71430i | − | 0.331192i | ||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 8.23610 | 0.405272 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 7.21362 | 0.353253 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 21.4955 | 1.05012 | 0.525061 | − | 0.851065i | \(-0.324043\pi\) | ||||
0.525061 | + | 0.851065i | \(0.324043\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 34.4082i | 1.67696i | 0.544936 | + | 0.838478i | \(0.316554\pi\) | ||||
−0.544936 | + | 0.838478i | \(0.683446\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 24.9717i | 1.21417i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 5.10080i | 0.246845i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −6.74773 | + | 6.24718i | −0.325783 | + | 0.301617i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 10.7850i | − | 0.519494i | −0.965677 | − | 0.259747i | \(-0.916361\pi\) | ||
0.965677 | − | 0.259747i | \(-0.0836392\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 9.79796 | 0.470860 | 0.235430 | − | 0.971891i | \(-0.424350\pi\) | ||||
0.235430 | + | 0.971891i | \(0.424350\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − | 6.20520i | − | 0.296835i | ||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −17.4955 | −0.835012 | −0.417506 | − | 0.908674i | \(-0.637096\pi\) | ||||
−0.417506 | + | 0.908674i | \(0.637096\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −15.9220 | −0.758189 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 6.56754 | 0.312033 | 0.156017 | − | 0.987754i | \(-0.450135\pi\) | ||||
0.156017 | + | 0.987754i | \(0.450135\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 1.82740i | 0.0864331i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 3.88587i | 0.183386i | 0.995787 | + | 0.0916928i | \(0.0292278\pi\) | ||||
−0.995787 | + | 0.0916928i | \(0.970772\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −20.0000 | −0.941763 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | − | 2.16900i | − | 0.101909i | ||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 12.2197i | 0.571614i | 0.958287 | + | 0.285807i | \(0.0922616\pi\) | ||||
−0.958287 | + | 0.285807i | \(0.907738\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 22.3303 | 1.04229 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 13.5518i | 0.631171i | 0.948897 | + | 0.315585i | \(0.102201\pi\) | ||||
−0.948897 | + | 0.315585i | \(0.897799\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 33.7273i | − | 1.56744i | −0.621113 | − | 0.783721i | \(-0.713319\pi\) | ||
0.621113 | − | 0.783721i | \(-0.286681\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 5.27537 | 0.244115 | 0.122058 | − | 0.992523i | \(-0.461051\pi\) | ||||
0.122058 | + | 0.992523i | \(0.461051\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −7.16515 | −0.330856 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 14.5045 | 0.668334 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 26.9898i | 1.24099i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 3.33712 | 0.152796 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 6.77590i | 0.309599i | 0.987946 | + | 0.154799i | \(0.0494732\pi\) | ||||
−0.987946 | + | 0.154799i | \(0.950527\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −20.7477 | + | 19.2087i | −0.946015 | + | 0.875840i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 3.27340i | 0.148945i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 14.7701i | − | 0.669297i | −0.942343 | − | 0.334649i | \(-0.891382\pi\) | ||
0.942343 | − | 0.334649i | \(-0.108618\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 3.88587i | 0.175725i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −6.33030 | −0.285683 | −0.142841 | − | 0.989746i | \(-0.545624\pi\) | ||||
−0.142841 | + | 0.989746i | \(0.545624\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −9.79796 | −0.441278 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −6.19115 | −0.277711 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 20.3277i | 0.909993i | 0.890493 | + | 0.454997i | \(0.150360\pi\) | ||||
−0.890493 | + | 0.454997i | \(0.849640\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 10.7234i | 0.479085i | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 42.6919 | 1.90354 | 0.951770 | − | 0.306813i | \(-0.0992625\pi\) | ||||
0.951770 | + | 0.306813i | \(0.0992625\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0.646084 | − | 8.37420i | 0.0286936 | − | 0.371911i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 24.8655i | 1.10214i | 0.834457 | + | 0.551072i | \(0.185781\pi\) | ||||
−0.834457 | + | 0.551072i | \(0.814219\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 7.16515 | 0.316968 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | − | 4.03620i | − | 0.178203i | ||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 38.1694 | 1.67869 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 7.16515 | 0.314515 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 22.4174 | 0.982125 | 0.491063 | − | 0.871124i | \(-0.336609\pi\) | ||||
0.491063 | + | 0.871124i | \(0.336609\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −35.2086 | −1.53957 | −0.769783 | − | 0.638306i | \(-0.779636\pi\) | ||||
−0.769783 | + | 0.638306i | \(0.779636\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − | 59.4618i | − | 2.59020i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 7.74773 | 0.336858 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − | 23.2793i | − | 1.01024i | ||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 13.4048 | − | 12.4104i | 0.580625 | − | 0.537554i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 24.3368i | 1.04826i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − | 45.1316i | − | 1.94036i | −0.242385 | − | 0.970180i | \(-0.577930\pi\) | ||
0.242385 | − | 0.970180i | \(-0.422070\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 9.31486 | 0.399739 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −26.4331 | −1.13020 | −0.565100 | − | 0.825022i | \(-0.691162\pi\) | ||||
−0.565100 | + | 0.825022i | \(0.691162\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 14.4174 | 0.615321 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1.77098i | 0.0754463i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − | 6.54680i | − | 0.278398i | ||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 23.5257i | 0.996816i | 0.866942 | + | 0.498408i | \(0.166082\pi\) | ||||
−0.866942 | + | 0.498408i | \(0.833918\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −16.7477 | − | 18.0896i | −0.708353 | − | 0.765109i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | − | 15.7899i | − | 0.666650i | ||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 46.5684 | 1.96263 | 0.981313 | − | 0.192418i | \(-0.0616329\pi\) | ||||
0.981313 | + | 0.192418i | \(0.0616329\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | − | 4.94990i | − | 0.207876i | ||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 10.4174 | 0.436721 | 0.218361 | − | 0.975868i | \(-0.429929\pi\) | ||||
0.218361 | + | 0.975868i | \(0.429929\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −37.4955 | −1.56914 | −0.784568 | − | 0.620043i | \(-0.787115\pi\) | ||||
−0.784568 | + | 0.620043i | \(0.787115\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 7.75301 | 0.323886 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 46.5191i | − | 1.93662i | −0.249758 | − | 0.968308i | \(-0.580351\pi\) | ||
0.249758 | − | 0.968308i | \(-0.419649\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | − | 13.5518i | − | 0.563194i | ||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −15.1652 | −0.629156 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 5.10080i | − | 0.211254i | ||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − | 11.1153i | − | 0.458778i | −0.973335 | − | 0.229389i | \(-0.926327\pi\) | ||
0.973335 | − | 0.229389i | \(-0.0736727\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −10.7477 | −0.442852 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | − | 5.78006i | − | 0.237760i | ||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 15.8745i | − | 0.651888i | −0.945389 | − | 0.325944i | \(-0.894318\pi\) | ||
0.945389 | − | 0.325944i | \(-0.105682\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −2.58434 | −0.105770 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 42.3303 | 1.72957 | 0.864785 | − | 0.502143i | \(-0.167455\pi\) | ||||
0.864785 | + | 0.502143i | \(0.167455\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 44.3303 | 1.80827 | 0.904135 | − | 0.427246i | \(-0.140516\pi\) | ||||
0.904135 | + | 0.427246i | \(0.140516\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 20.2523i | 0.824738i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 34.1862 | 1.38757 | 0.693787 | − | 0.720181i | \(-0.255941\pi\) | ||||
0.693787 | + | 0.720181i | \(0.255941\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | − | 0.934237i | − | 0.0378572i | ||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −25.5826 | + | 23.6849i | −1.03496 | + | 0.958187i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 24.6301i | − | 0.994801i | −0.867521 | − | 0.497400i | \(-0.834288\pi\) | ||
0.867521 | − | 0.497400i | \(-0.165712\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 28.2849i | − | 1.13871i | −0.822093 | − | 0.569354i | \(-0.807193\pi\) | ||
0.822093 | − | 0.569354i | \(-0.192807\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 32.8221i | 1.31923i | 0.751603 | + | 0.659615i | \(0.229281\pi\) | ||||
−0.751603 | + | 0.659615i | \(0.770719\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 20.0000 | 0.802572 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −10.3373 | −0.414157 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −2.85403 | −0.113979 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − | 48.5504i | − | 1.93583i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 24.3368i | 0.968832i | 0.874838 | + | 0.484416i | \(0.160968\pi\) | ||||
−0.874838 | + | 0.484416i | \(0.839032\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −12.9217 | −0.513591 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −15.1015 | − | 16.3115i | −0.598342 | − | 0.646283i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 17.4993i | 0.692261i | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −24.3303 | −0.960989 | −0.480495 | − | 0.876998i | \(-0.659543\pi\) | ||||
−0.480495 | + | 0.876998i | \(0.659543\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 9.28790i | 0.366279i | 0.983087 | + | 0.183140i | \(0.0586260\pi\) | ||||
−0.983087 | + | 0.183140i | \(0.941374\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 28.7478 | 1.13019 | 0.565096 | − | 0.825025i | \(-0.308839\pi\) | ||||
0.565096 | + | 0.825025i | \(0.308839\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −35.5826 | −1.39674 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 5.66970 | 0.222213 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 15.2363 | 0.596243 | 0.298122 | − | 0.954528i | \(-0.403640\pi\) | ||||
0.298122 | + | 0.954528i | \(0.403640\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | − | 20.2523i | − | 0.790118i | ||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −21.4955 | −0.837344 | −0.418672 | − | 0.908138i | \(-0.637504\pi\) | ||||
−0.418672 | + | 0.908138i | \(0.637504\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 8.48528i | 0.330039i | 0.986290 | + | 0.165020i | \(0.0527687\pi\) | ||||
−0.986290 | + | 0.165020i | \(0.947231\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 9.79796 | + | 10.5830i | 0.380521 | + | 0.411010i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −8.77548 | −0.339788 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | − | 5.06653i | − | 0.195883i | ||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 22.0371i | − | 0.850732i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 1.02248 | 0.0394136 | 0.0197068 | − | 0.999806i | \(-0.493727\pi\) | ||||
0.0197068 | + | 0.999806i | \(0.493727\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 28.6411 | 1.10077 | 0.550383 | − | 0.834912i | \(-0.314482\pi\) | ||||
0.550383 | + | 0.834912i | \(0.314482\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −1.49545 | −0.0573903 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | − | 7.18142i | − | 0.275193i | ||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 11.1153i | 0.425315i | 0.977127 | + | 0.212658i | \(0.0682119\pi\) | ||||
−0.977127 | + | 0.212658i | \(0.931788\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 1.44600i | 0.0551683i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 3.16515 | + | 3.41875i | 0.120583 | + | 0.130244i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 26.5749i | 1.01096i | 0.862839 | + | 0.505478i | \(0.168684\pi\) | ||||
−0.862839 | + | 0.505478i | \(0.831316\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −9.31486 | −0.353842 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 31.3676i | 1.18813i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −1.66970 | −0.0631537 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −33.1652 | −1.25263 | −0.626315 | − | 0.779570i | \(-0.715438\pi\) | ||||
−0.626315 | + | 0.779570i | \(0.715438\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −8.77548 | −0.330974 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − | 8.37420i | − | 0.314944i | ||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 23.6849i | 0.889504i | 0.895654 | + | 0.444752i | \(0.146708\pi\) | ||||
−0.895654 | + | 0.444752i | \(0.853292\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −18.5045 | −0.693975 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 53.2566i | − | 1.99448i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | − | 6.96800i | − | 0.260225i | ||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −21.4955 | −0.801645 | −0.400823 | − | 0.916156i | \(-0.631276\pi\) | ||||
−0.400823 | + | 0.916156i | \(0.631276\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 1.77098i | 0.0659548i | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 17.8926i | 0.665433i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 26.4331 | 0.980351 | 0.490176 | − | 0.871624i | \(-0.336933\pi\) | ||||
0.490176 | + | 0.871624i | \(0.336933\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −7.00000 | −0.259259 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 42.3303 | 1.56564 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 22.4213i | 0.828150i | 0.910243 | + | 0.414075i | \(0.135895\pi\) | ||||
−0.910243 | + | 0.414075i | \(0.864105\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 30.9557 | 1.14027 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 37.7654i | 1.38922i | 0.719385 | + | 0.694611i | \(0.244424\pi\) | ||||
−0.719385 | + | 0.694611i | \(0.755576\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 1.91288 | − | 1.77098i | 0.0702713 | − | 0.0650586i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 29.0079i | − | 1.06420i | −0.846682 | − | 0.532099i | \(-0.821404\pi\) | ||
0.846682 | − | 0.532099i | \(-0.178596\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 42.8643i | 1.56832i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − | 7.42784i | − | 0.271407i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 23.1652 | 0.845308 | 0.422654 | − | 0.906291i | \(-0.361098\pi\) | ||||
0.422654 | + | 0.906291i | \(0.361098\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −2.04495 | −0.0745222 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 41.0234 | 1.49102 | 0.745510 | − | 0.666494i | \(-0.232206\pi\) | ||||
0.745510 | + | 0.666494i | \(0.232206\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | − | 14.1421i | − | 0.513327i | ||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 11.3137i | 0.410122i | 0.978749 | + | 0.205061i | \(0.0657392\pi\) | ||||
−0.978749 | + | 0.205061i | \(0.934261\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 7.75301 | 0.280678 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 23.8488 | − | 22.0797i | 0.861131 | − | 0.797252i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 8.95240i | − | 0.322832i | −0.986886 | − | 0.161416i | \(-0.948394\pi\) | ||
0.986886 | − | 0.161416i | \(-0.0516061\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 14.3303 | 0.516093 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − | 9.66930i | − | 0.347781i | −0.984765 | − | 0.173890i | \(-0.944366\pi\) | ||
0.984765 | − | 0.173890i | \(-0.0556338\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 4.62929 | 0.166075 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 5.66970 | 0.203138 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 26.7477 | 0.957109 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −5.70805 | −0.203989 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 18.4249i | 0.656777i | 0.944543 | + | 0.328389i | \(0.106506\pi\) | ||||
−0.944543 | + | 0.328389i | \(0.893494\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −13.0780 | −0.465590 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 3.29555i | − | 0.117176i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 13.6745 | + | 14.7701i | 0.485594 | + | 0.524502i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −25.0343 | −0.886760 | −0.443380 | − | 0.896334i | \(-0.646221\pi\) | ||||
−0.443380 | + | 0.896334i | \(0.646221\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 59.8641i | − | 2.11784i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 29.2185i | 1.03239i | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −30.9557 | −1.09240 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −5.92146 | −0.208445 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −4.74773 | −0.166921 | −0.0834606 | − | 0.996511i | \(-0.526597\pi\) | ||||
−0.0834606 | + | 0.996511i | \(0.526597\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 33.2892i | − | 1.16894i | −0.811415 | − | 0.584471i | \(-0.801302\pi\) | ||
0.811415 | − | 0.584471i | \(-0.198698\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − | 10.2414i | − | 0.359182i | ||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 7.65120i | − | 0.267682i | ||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 6.24318 | − | 5.78006i | 0.218154 | − | 0.201972i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 19.7990i | 0.690990i | 0.938421 | + | 0.345495i | \(0.112289\pi\) | ||||
−0.938421 | + | 0.345495i | \(0.887711\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −50.9280 | −1.77524 | −0.887620 | − | 0.460576i | \(-0.847643\pi\) | ||||
−0.887620 | + | 0.460576i | \(0.847643\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 15.1515i | − | 0.526870i | −0.964677 | − | 0.263435i | \(-0.915145\pi\) | ||
0.964677 | − | 0.263435i | \(-0.0848554\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 42.2432 | 1.46717 | 0.733583 | − | 0.679600i | \(-0.237846\pi\) | ||||
0.733583 | + | 0.679600i | \(0.237846\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 3.82576 | 0.132714 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 38.1694 | 1.32249 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | − | 34.6410i | − | 1.19737i | ||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − | 44.6029i | − | 1.53986i | −0.638126 | − | 0.769932i | \(-0.720290\pi\) | ||
0.638126 | − | 0.769932i | \(-0.279710\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −26.4955 | −0.913636 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | − | 17.1298i | − | 0.589982i | ||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 4.18710i | 0.143871i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −4.41742 | −0.151606 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − | 43.4839i | − | 1.49061i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 33.7273i | − | 1.15480i | −0.816461 | − | 0.577401i | \(-0.804067\pi\) | ||
0.816461 | − | 0.577401i | \(-0.195933\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −14.4272 | −0.492825 | −0.246413 | − | 0.969165i | \(-0.579252\pi\) | ||||
−0.246413 | + | 0.969165i | \(0.579252\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 4.00000 | 0.136478 | 0.0682391 | − | 0.997669i | \(-0.478262\pi\) | ||||
0.0682391 | + | 0.997669i | \(0.478262\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −2.99091 | −0.101930 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 9.66930i | − | 0.329147i | −0.986365 | − | 0.164573i | \(-0.947375\pi\) | ||
0.986365 | − | 0.164573i | \(-0.0526248\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −13.7812 | −0.468033 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 28.2843i | 0.959478i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −20.7477 | + | 19.2087i | −0.703010 | + | 0.650861i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 4.22690i | 0.143059i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − | 41.7599i | − | 1.41013i | −0.709142 | − | 0.705066i | \(-0.750917\pi\) | ||
0.709142 | − | 0.705066i | \(-0.249083\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 6.24718i | 0.210712i | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 13.5826 | 0.457609 | 0.228804 | − | 0.973472i | \(-0.426518\pi\) | ||||
0.228804 | + | 0.973472i | \(0.426518\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 24.3882 | 0.820728 | 0.410364 | − | 0.911922i | \(-0.365402\pi\) | ||||
0.410364 | + | 0.911922i | \(0.365402\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −8.39909 | −0.282014 | −0.141007 | − | 0.990009i | \(-0.545034\pi\) | ||||
−0.141007 | + | 0.990009i | \(0.545034\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − | 10.7234i | − | 0.359651i | ||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 21.3852i | 0.716430i | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −10.8204 | −0.362092 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 8.77548 | + | 9.47860i | 0.293005 | + | 0.316481i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 15.1996i | 0.506934i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −8.00000 | −0.266519 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 4.03620i | 0.134316i | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −50.9280 | −1.69104 | −0.845519 | − | 0.533945i | \(-0.820709\pi\) | ||||
−0.845519 | + | 0.533945i | \(0.820709\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −23.6697 | −0.785074 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 54.3303 | 1.80004 | 0.900022 | − | 0.435845i | \(-0.143551\pi\) | ||||
0.900022 | + | 0.435845i | \(0.143551\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 65.5183 | 2.16834 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − | 13.8564i | − | 0.457579i | ||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −50.3303 | −1.66024 | −0.830122 | − | 0.557582i | \(-0.811729\pi\) | ||||
−0.830122 | + | 0.557582i | \(0.811729\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | − | 11.9040i | − | 0.392251i | ||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −17.9274 | + | 16.5975i | −0.590086 | + | 0.546314i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 5.00568 | 0.164408 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 46.7794i | 1.53478i | 0.641179 | + | 0.767391i | \(0.278445\pi\) | ||||
−0.641179 | + | 0.767391i | \(0.721555\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − | 6.89911i | − | 0.226109i | ||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 19.5959 | 0.641542 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 37.1469 | 1.21354 | 0.606768 | − | 0.794879i | \(-0.292466\pi\) | ||||
0.606768 | + | 0.794879i | \(0.292466\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 12.0000 | 0.391605 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 18.0280i | 0.587696i | 0.955852 | + | 0.293848i | \(0.0949360\pi\) | ||||
−0.955852 | + | 0.293848i | \(0.905064\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 28.0942i | 0.914873i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 51.2385i | 1.66503i | 0.554004 | + | 0.832514i | \(0.313099\pi\) | ||||
−0.554004 | + | 0.832514i | \(0.686901\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 20.7477 | − | 19.2087i | 0.673500 | − | 0.623540i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 2.70522i | 0.0877227i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −22.7196 | −0.735961 | −0.367981 | − | 0.929833i | \(-0.619951\pi\) | ||||
−0.367981 | + | 0.929833i | \(0.619951\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 4.03620i | 0.130472i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 9.49545 | 0.306624 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −61.2432 | −1.97559 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −20.9948 | −0.676548 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 7.46050i | 0.239914i | 0.992779 | + | 0.119957i | \(0.0382756\pi\) | ||||
−0.992779 | + | 0.119957i | \(0.961724\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 4.47620i | 0.143796i | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −24.6606 | −0.791396 | −0.395698 | − | 0.918381i | \(-0.629497\pi\) | ||||
−0.395698 | + | 0.918381i | \(0.629497\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 10.2016i | 0.327048i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 20.6337i | 0.660131i | 0.943958 | + | 0.330065i | \(0.107071\pi\) | ||||
−0.943958 | + | 0.330065i | \(0.892929\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 44.6606 | 1.42736 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | − | 21.9139i | − | 0.699656i | ||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − | 20.6337i | − | 0.658113i | −0.944310 | − | 0.329057i | \(-0.893269\pi\) | ||
0.944310 | − | 0.329057i | \(-0.106731\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 5.70805 | 0.181689 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 37.9129 | 1.20556 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 29.4955 | 0.936954 | 0.468477 | − | 0.883476i | \(-0.344803\pi\) | ||||
0.468477 | + | 0.883476i | \(0.344803\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | − | 3.31320i | − | 0.105141i | ||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −52.8663 | −1.67429 | −0.837146 | − | 0.546979i | \(-0.815778\pi\) | ||||
−0.837146 | + | 0.546979i | \(0.815778\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | − | 28.2843i | − | 0.894875i |
(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.f.f.701.3 | 8 | ||
5.2 | odd | 4 | 260.2.d.a.129.5 | yes | 8 | ||
5.3 | odd | 4 | 260.2.d.a.129.4 | yes | 8 | ||
5.4 | even | 2 | inner | 1300.2.f.f.701.6 | 8 | ||
13.12 | even | 2 | inner | 1300.2.f.f.701.4 | 8 | ||
15.2 | even | 4 | 2340.2.j.d.649.6 | 8 | |||
15.8 | even | 4 | 2340.2.j.d.649.1 | 8 | |||
20.3 | even | 4 | 1040.2.f.e.129.6 | 8 | |||
20.7 | even | 4 | 1040.2.f.e.129.3 | 8 | |||
65.8 | even | 4 | 3380.2.c.d.2029.3 | 8 | |||
65.12 | odd | 4 | 260.2.d.a.129.6 | yes | 8 | ||
65.18 | even | 4 | 3380.2.c.d.2029.4 | 8 | |||
65.38 | odd | 4 | 260.2.d.a.129.3 | ✓ | 8 | ||
65.47 | even | 4 | 3380.2.c.d.2029.5 | 8 | |||
65.57 | even | 4 | 3380.2.c.d.2029.6 | 8 | |||
65.64 | even | 2 | inner | 1300.2.f.f.701.5 | 8 | ||
195.38 | even | 4 | 2340.2.j.d.649.8 | 8 | |||
195.77 | even | 4 | 2340.2.j.d.649.3 | 8 | |||
260.103 | even | 4 | 1040.2.f.e.129.5 | 8 | |||
260.207 | even | 4 | 1040.2.f.e.129.4 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
260.2.d.a.129.3 | ✓ | 8 | 65.38 | odd | 4 | ||
260.2.d.a.129.4 | yes | 8 | 5.3 | odd | 4 | ||
260.2.d.a.129.5 | yes | 8 | 5.2 | odd | 4 | ||
260.2.d.a.129.6 | yes | 8 | 65.12 | odd | 4 | ||
1040.2.f.e.129.3 | 8 | 20.7 | even | 4 | |||
1040.2.f.e.129.4 | 8 | 260.207 | even | 4 | |||
1040.2.f.e.129.5 | 8 | 260.103 | even | 4 | |||
1040.2.f.e.129.6 | 8 | 20.3 | even | 4 | |||
1300.2.f.f.701.3 | 8 | 1.1 | even | 1 | trivial | ||
1300.2.f.f.701.4 | 8 | 13.12 | even | 2 | inner | ||
1300.2.f.f.701.5 | 8 | 65.64 | even | 2 | inner | ||
1300.2.f.f.701.6 | 8 | 5.4 | even | 2 | inner | ||
2340.2.j.d.649.1 | 8 | 15.8 | even | 4 | |||
2340.2.j.d.649.3 | 8 | 195.77 | even | 4 | |||
2340.2.j.d.649.6 | 8 | 15.2 | even | 4 | |||
2340.2.j.d.649.8 | 8 | 195.38 | even | 4 | |||
3380.2.c.d.2029.3 | 8 | 65.8 | even | 4 | |||
3380.2.c.d.2029.4 | 8 | 65.18 | even | 4 | |||
3380.2.c.d.2029.5 | 8 | 65.47 | even | 4 | |||
3380.2.c.d.2029.6 | 8 | 65.57 | even | 4 |