Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4014,2,Mod(1,4014)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4014, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4014.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4014 = 2 \cdot 3^{2} \cdot 223 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4014.a (trivial) |
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: | yes |
Analytic conductor: | \(32.0519513713\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{13}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 3 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-1.30278\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4014.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.60555 | 0.984806 | 0.492403 | − | 0.870367i | \(-0.336119\pi\) | ||||
0.492403 | + | 0.870367i | \(0.336119\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −6.30278 | −1.90036 | −0.950179 | − | 0.311704i | \(-0.899100\pi\) | ||||
−0.950179 | + | 0.311704i | \(0.899100\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 5.30278 | 1.47073 | 0.735363 | − | 0.677674i | \(-0.237012\pi\) | ||||
0.735363 | + | 0.677674i | \(0.237012\pi\) | |||||||
\(14\) | −2.60555 | −0.696363 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −4.60555 | −1.11701 | −0.558505 | − | 0.829501i | \(-0.688625\pi\) | ||||
−0.558505 | + | 0.829501i | \(0.688625\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.697224 | 0.159954 | 0.0799771 | − | 0.996797i | \(-0.474515\pi\) | ||||
0.0799771 | + | 0.996797i | \(0.474515\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 6.30278 | 1.34376 | ||||||||
\(23\) | 4.00000 | 0.834058 | 0.417029 | − | 0.908893i | \(-0.363071\pi\) | ||||
0.417029 | + | 0.908893i | \(0.363071\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −5.00000 | −1.00000 | ||||||||
\(26\) | −5.30278 | −1.03996 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 2.60555 | 0.492403 | ||||||||
\(29\) | −1.69722 | −0.315167 | −0.157583 | − | 0.987506i | \(-0.550370\pi\) | ||||
−0.157583 | + | 0.987506i | \(0.550370\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −0.605551 | −0.108760 | −0.0543801 | − | 0.998520i | \(-0.517318\pi\) | ||||
−0.0543801 | + | 0.998520i | \(0.517318\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 4.60555 | 0.789846 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −2.60555 | −0.428350 | −0.214175 | − | 0.976795i | \(-0.568706\pi\) | ||||
−0.214175 | + | 0.976795i | \(0.568706\pi\) | |||||||
\(38\) | −0.697224 | −0.113105 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 4.00000 | 0.624695 | 0.312348 | − | 0.949968i | \(-0.398885\pi\) | ||||
0.312348 | + | 0.949968i | \(0.398885\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −6.90833 | −1.05351 | −0.526755 | − | 0.850017i | \(-0.676591\pi\) | ||||
−0.526755 | + | 0.850017i | \(0.676591\pi\) | |||||||
\(44\) | −6.30278 | −0.950179 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −4.00000 | −0.589768 | ||||||||
\(47\) | −4.30278 | −0.627624 | −0.313812 | − | 0.949485i | \(-0.601606\pi\) | ||||
−0.313812 | + | 0.949485i | \(0.601606\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −0.211103 | −0.0301575 | ||||||||
\(50\) | 5.00000 | 0.707107 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 5.30278 | 0.735363 | ||||||||
\(53\) | 3.90833 | 0.536850 | 0.268425 | − | 0.963301i | \(-0.413497\pi\) | ||||
0.268425 | + | 0.963301i | \(0.413497\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −2.60555 | −0.348181 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 1.69722 | 0.222856 | ||||||||
\(59\) | 3.30278 | 0.429985 | 0.214992 | − | 0.976616i | \(-0.431027\pi\) | ||||
0.214992 | + | 0.976616i | \(0.431027\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −6.30278 | −0.806988 | −0.403494 | − | 0.914982i | \(-0.632204\pi\) | ||||
−0.403494 | + | 0.914982i | \(0.632204\pi\) | |||||||
\(62\) | 0.605551 | 0.0769051 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −2.60555 | −0.318319 | −0.159159 | − | 0.987253i | \(-0.550878\pi\) | ||||
−0.159159 | + | 0.987253i | \(0.550878\pi\) | |||||||
\(68\) | −4.60555 | −0.558505 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 3.21110 | 0.381088 | 0.190544 | − | 0.981679i | \(-0.438975\pi\) | ||||
0.190544 | + | 0.981679i | \(0.438975\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 1.90833 | 0.223353 | 0.111676 | − | 0.993745i | \(-0.464378\pi\) | ||||
0.111676 | + | 0.993745i | \(0.464378\pi\) | |||||||
\(74\) | 2.60555 | 0.302889 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0.697224 | 0.0799771 | ||||||||
\(77\) | −16.4222 | −1.87148 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −9.51388 | −1.07039 | −0.535197 | − | 0.844727i | \(-0.679763\pi\) | ||||
−0.535197 | + | 0.844727i | \(0.679763\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −4.00000 | −0.441726 | ||||||||
\(83\) | −9.21110 | −1.01105 | −0.505525 | − | 0.862812i | \(-0.668701\pi\) | ||||
−0.505525 | + | 0.862812i | \(0.668701\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 6.90833 | 0.744944 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 6.30278 | 0.671878 | ||||||||
\(89\) | −2.78890 | −0.295623 | −0.147811 | − | 0.989016i | \(-0.547223\pi\) | ||||
−0.147811 | + | 0.989016i | \(0.547223\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 13.8167 | 1.44838 | ||||||||
\(92\) | 4.00000 | 0.417029 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 4.30278 | 0.443797 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −15.2111 | −1.54445 | −0.772227 | − | 0.635347i | \(-0.780857\pi\) | ||||
−0.772227 | + | 0.635347i | \(0.780857\pi\) | |||||||
\(98\) | 0.211103 | 0.0213246 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −5.00000 | −0.500000 | ||||||||
\(101\) | −0.0916731 | −0.00912181 | −0.00456091 | − | 0.999990i | \(-0.501452\pi\) | ||||
−0.00456091 | + | 0.999990i | \(0.501452\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 7.90833 | 0.779231 | 0.389615 | − | 0.920978i | \(-0.372608\pi\) | ||||
0.389615 | + | 0.920978i | \(0.372608\pi\) | |||||||
\(104\) | −5.30278 | −0.519980 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −3.90833 | −0.379610 | ||||||||
\(107\) | 9.90833 | 0.957874 | 0.478937 | − | 0.877849i | \(-0.341022\pi\) | ||||
0.478937 | + | 0.877849i | \(0.341022\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −12.6056 | −1.20739 | −0.603696 | − | 0.797214i | \(-0.706306\pi\) | ||||
−0.603696 | + | 0.797214i | \(0.706306\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 2.60555 | 0.246201 | ||||||||
\(113\) | −19.3028 | −1.81585 | −0.907926 | − | 0.419130i | \(-0.862335\pi\) | ||||
−0.907926 | + | 0.419130i | \(0.862335\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −1.69722 | −0.157583 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −3.30278 | −0.304045 | ||||||||
\(119\) | −12.0000 | −1.10004 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 28.7250 | 2.61136 | ||||||||
\(122\) | 6.30278 | 0.570626 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −0.605551 | −0.0543801 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −7.21110 | −0.639882 | −0.319941 | − | 0.947437i | \(-0.603663\pi\) | ||||
−0.319941 | + | 0.947437i | \(0.603663\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 12.4222 | 1.08533 | 0.542667 | − | 0.839948i | \(-0.317415\pi\) | ||||
0.542667 | + | 0.839948i | \(0.317415\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1.81665 | 0.157524 | ||||||||
\(134\) | 2.60555 | 0.225085 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 4.60555 | 0.394923 | ||||||||
\(137\) | −3.69722 | −0.315875 | −0.157938 | − | 0.987449i | \(-0.550484\pi\) | ||||
−0.157938 | + | 0.987449i | \(0.550484\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −1.09167 | −0.0925945 | −0.0462973 | − | 0.998928i | \(-0.514742\pi\) | ||||
−0.0462973 | + | 0.998928i | \(0.514742\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −3.21110 | −0.269470 | ||||||||
\(143\) | −33.4222 | −2.79491 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −1.90833 | −0.157934 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −2.60555 | −0.214175 | ||||||||
\(149\) | 9.21110 | 0.754603 | 0.377301 | − | 0.926090i | \(-0.376852\pi\) | ||||
0.377301 | + | 0.926090i | \(0.376852\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 18.5139 | 1.50664 | 0.753319 | − | 0.657655i | \(-0.228452\pi\) | ||||
0.753319 | + | 0.657655i | \(0.228452\pi\) | |||||||
\(152\) | −0.697224 | −0.0565524 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 16.4222 | 1.32334 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 6.30278 | 0.503016 | 0.251508 | − | 0.967855i | \(-0.419073\pi\) | ||||
0.251508 | + | 0.967855i | \(0.419073\pi\) | |||||||
\(158\) | 9.51388 | 0.756884 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 10.4222 | 0.821385 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 1.39445 | 0.109222 | 0.0546108 | − | 0.998508i | \(-0.482608\pi\) | ||||
0.0546108 | + | 0.998508i | \(0.482608\pi\) | |||||||
\(164\) | 4.00000 | 0.312348 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 9.21110 | 0.714920 | ||||||||
\(167\) | 4.60555 | 0.356388 | 0.178194 | − | 0.983995i | \(-0.442974\pi\) | ||||
0.178194 | + | 0.983995i | \(0.442974\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 15.1194 | 1.16303 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −6.90833 | −0.526755 | ||||||||
\(173\) | −23.0278 | −1.75077 | −0.875384 | − | 0.483428i | \(-0.839391\pi\) | ||||
−0.875384 | + | 0.483428i | \(0.839391\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −13.0278 | −0.984806 | ||||||||
\(176\) | −6.30278 | −0.475090 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 2.78890 | 0.209037 | ||||||||
\(179\) | 1.21110 | 0.0905221 | 0.0452610 | − | 0.998975i | \(-0.485588\pi\) | ||||
0.0452610 | + | 0.998975i | \(0.485588\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 8.60555 | 0.639646 | 0.319823 | − | 0.947477i | \(-0.396377\pi\) | ||||
0.319823 | + | 0.947477i | \(0.396377\pi\) | |||||||
\(182\) | −13.8167 | −1.02416 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −4.00000 | −0.294884 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 29.0278 | 2.12272 | ||||||||
\(188\) | −4.30278 | −0.313812 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −13.8167 | −0.999738 | −0.499869 | − | 0.866101i | \(-0.666619\pi\) | ||||
−0.499869 | + | 0.866101i | \(0.666619\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −20.4222 | −1.47002 | −0.735011 | − | 0.678055i | \(-0.762823\pi\) | ||||
−0.735011 | + | 0.678055i | \(0.762823\pi\) | |||||||
\(194\) | 15.2111 | 1.09209 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −0.211103 | −0.0150788 | ||||||||
\(197\) | 1.69722 | 0.120922 | 0.0604611 | − | 0.998171i | \(-0.480743\pi\) | ||||
0.0604611 | + | 0.998171i | \(0.480743\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −18.4222 | −1.30592 | −0.652958 | − | 0.757394i | \(-0.726472\pi\) | ||||
−0.652958 | + | 0.757394i | \(0.726472\pi\) | |||||||
\(200\) | 5.00000 | 0.353553 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0.0916731 | 0.00645010 | ||||||||
\(203\) | −4.42221 | −0.310378 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −7.90833 | −0.550999 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 5.30278 | 0.367681 | ||||||||
\(209\) | −4.39445 | −0.303970 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1.69722 | 0.116842 | 0.0584209 | − | 0.998292i | \(-0.481393\pi\) | ||||
0.0584209 | + | 0.998292i | \(0.481393\pi\) | |||||||
\(212\) | 3.90833 | 0.268425 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −9.90833 | −0.677319 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1.57779 | −0.107108 | ||||||||
\(218\) | 12.6056 | 0.853756 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −24.4222 | −1.64282 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −1.00000 | −0.0669650 | ||||||||
\(224\) | −2.60555 | −0.174091 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 19.3028 | 1.28400 | ||||||||
\(227\) | 17.0278 | 1.13017 | 0.565086 | − | 0.825032i | \(-0.308843\pi\) | ||||
0.565086 | + | 0.825032i | \(0.308843\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −10.0000 | −0.660819 | −0.330409 | − | 0.943838i | \(-0.607187\pi\) | ||||
−0.330409 | + | 0.943838i | \(0.607187\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 1.69722 | 0.111428 | ||||||||
\(233\) | 8.30278 | 0.543933 | 0.271966 | − | 0.962307i | \(-0.412326\pi\) | ||||
0.271966 | + | 0.962307i | \(0.412326\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 3.30278 | 0.214992 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 12.0000 | 0.777844 | ||||||||
\(239\) | −23.7250 | −1.53464 | −0.767321 | − | 0.641264i | \(-0.778411\pi\) | ||||
−0.767321 | + | 0.641264i | \(0.778411\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 13.5139 | 0.870505 | 0.435253 | − | 0.900308i | \(-0.356659\pi\) | ||||
0.435253 | + | 0.900308i | \(0.356659\pi\) | |||||||
\(242\) | −28.7250 | −1.84651 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −6.30278 | −0.403494 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 3.69722 | 0.235249 | ||||||||
\(248\) | 0.605551 | 0.0384525 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −6.42221 | −0.405366 | −0.202683 | − | 0.979244i | \(-0.564966\pi\) | ||||
−0.202683 | + | 0.979244i | \(0.564966\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −25.2111 | −1.58501 | ||||||||
\(254\) | 7.21110 | 0.452465 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −6.00000 | −0.374270 | −0.187135 | − | 0.982334i | \(-0.559920\pi\) | ||||
−0.187135 | + | 0.982334i | \(0.559920\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −6.78890 | −0.421842 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −12.4222 | −0.767446 | ||||||||
\(263\) | 14.6056 | 0.900617 | 0.450308 | − | 0.892873i | \(-0.351314\pi\) | ||||
0.450308 | + | 0.892873i | \(0.351314\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −1.81665 | −0.111386 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −2.60555 | −0.159159 | ||||||||
\(269\) | 21.0278 | 1.28208 | 0.641042 | − | 0.767505i | \(-0.278502\pi\) | ||||
0.641042 | + | 0.767505i | \(0.278502\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −10.1194 | −0.614712 | −0.307356 | − | 0.951595i | \(-0.599444\pi\) | ||||
−0.307356 | + | 0.951595i | \(0.599444\pi\) | |||||||
\(272\) | −4.60555 | −0.279253 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 3.69722 | 0.223357 | ||||||||
\(275\) | 31.5139 | 1.90036 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −3.57779 | −0.214969 | −0.107484 | − | 0.994207i | \(-0.534280\pi\) | ||||
−0.107484 | + | 0.994207i | \(0.534280\pi\) | |||||||
\(278\) | 1.09167 | 0.0654742 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −7.39445 | −0.441116 | −0.220558 | − | 0.975374i | \(-0.570788\pi\) | ||||
−0.220558 | + | 0.975374i | \(0.570788\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −19.3028 | −1.14743 | −0.573715 | − | 0.819055i | \(-0.694498\pi\) | ||||
−0.573715 | + | 0.819055i | \(0.694498\pi\) | |||||||
\(284\) | 3.21110 | 0.190544 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 33.4222 | 1.97630 | ||||||||
\(287\) | 10.4222 | 0.615203 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 4.21110 | 0.247712 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 1.90833 | 0.111676 | ||||||||
\(293\) | −30.2389 | −1.76657 | −0.883287 | − | 0.468834i | \(-0.844674\pi\) | ||||
−0.883287 | + | 0.468834i | \(0.844674\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 2.60555 | 0.151445 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −9.21110 | −0.533585 | ||||||||
\(299\) | 21.2111 | 1.22667 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −18.0000 | −1.03750 | ||||||||
\(302\) | −18.5139 | −1.06535 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0.697224 | 0.0399886 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −3.02776 | −0.172803 | −0.0864016 | − | 0.996260i | \(-0.527537\pi\) | ||||
−0.0864016 | + | 0.996260i | \(0.527537\pi\) | |||||||
\(308\) | −16.4222 | −0.935742 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −3.39445 | −0.192482 | −0.0962408 | − | 0.995358i | \(-0.530682\pi\) | ||||
−0.0962408 | + | 0.995358i | \(0.530682\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −20.0000 | −1.13047 | −0.565233 | − | 0.824931i | \(-0.691214\pi\) | ||||
−0.565233 | + | 0.824931i | \(0.691214\pi\) | |||||||
\(314\) | −6.30278 | −0.355686 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −9.51388 | −0.535197 | ||||||||
\(317\) | 13.3028 | 0.747158 | 0.373579 | − | 0.927598i | \(-0.378130\pi\) | ||||
0.373579 | + | 0.927598i | \(0.378130\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 10.6972 | 0.598930 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −10.4222 | −0.580807 | ||||||||
\(323\) | −3.21110 | −0.178671 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −26.5139 | −1.47073 | ||||||||
\(326\) | −1.39445 | −0.0772314 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −4.00000 | −0.220863 | ||||||||
\(329\) | −11.2111 | −0.618088 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −4.78890 | −0.263222 | −0.131611 | − | 0.991301i | \(-0.542015\pi\) | ||||
−0.131611 | + | 0.991301i | \(0.542015\pi\) | |||||||
\(332\) | −9.21110 | −0.505525 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −4.60555 | −0.252005 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −9.21110 | −0.501761 | −0.250880 | − | 0.968018i | \(-0.580720\pi\) | ||||
−0.250880 | + | 0.968018i | \(0.580720\pi\) | |||||||
\(338\) | −15.1194 | −0.822389 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 3.81665 | 0.206683 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −18.7889 | −1.01451 | ||||||||
\(344\) | 6.90833 | 0.372472 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 23.0278 | 1.23798 | ||||||||
\(347\) | −18.4222 | −0.988956 | −0.494478 | − | 0.869190i | \(-0.664641\pi\) | ||||
−0.494478 | + | 0.869190i | \(0.664641\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −32.6056 | −1.74534 | −0.872668 | − | 0.488315i | \(-0.837612\pi\) | ||||
−0.872668 | + | 0.488315i | \(0.837612\pi\) | |||||||
\(350\) | 13.0278 | 0.696363 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 6.30278 | 0.335939 | ||||||||
\(353\) | −22.6056 | −1.20317 | −0.601586 | − | 0.798808i | \(-0.705464\pi\) | ||||
−0.601586 | + | 0.798808i | \(0.705464\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −2.78890 | −0.147811 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −1.21110 | −0.0640088 | ||||||||
\(359\) | −5.48612 | −0.289546 | −0.144773 | − | 0.989465i | \(-0.546245\pi\) | ||||
−0.144773 | + | 0.989465i | \(0.546245\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −18.5139 | −0.974415 | ||||||||
\(362\) | −8.60555 | −0.452298 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 13.8167 | 0.724189 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 8.00000 | 0.417597 | 0.208798 | − | 0.977959i | \(-0.433045\pi\) | ||||
0.208798 | + | 0.977959i | \(0.433045\pi\) | |||||||
\(368\) | 4.00000 | 0.208514 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 10.1833 | 0.528693 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 30.8444 | 1.59706 | 0.798532 | − | 0.601953i | \(-0.205611\pi\) | ||||
0.798532 | + | 0.601953i | \(0.205611\pi\) | |||||||
\(374\) | −29.0278 | −1.50099 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 4.30278 | 0.221899 | ||||||||
\(377\) | −9.00000 | −0.463524 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 36.3305 | 1.86617 | 0.933087 | − | 0.359651i | \(-0.117104\pi\) | ||||
0.933087 | + | 0.359651i | \(0.117104\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 13.8167 | 0.706922 | ||||||||
\(383\) | 11.8167 | 0.603803 | 0.301901 | − | 0.953339i | \(-0.402379\pi\) | ||||
0.301901 | + | 0.953339i | \(0.402379\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 20.4222 | 1.03946 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −15.2111 | −0.772227 | ||||||||
\(389\) | −21.9361 | −1.11220 | −0.556102 | − | 0.831114i | \(-0.687704\pi\) | ||||
−0.556102 | + | 0.831114i | \(0.687704\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −18.4222 | −0.931651 | ||||||||
\(392\) | 0.211103 | 0.0106623 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −1.69722 | −0.0855049 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −19.5139 | −0.979373 | −0.489687 | − | 0.871898i | \(-0.662889\pi\) | ||||
−0.489687 | + | 0.871898i | \(0.662889\pi\) | |||||||
\(398\) | 18.4222 | 0.923422 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −5.00000 | −0.250000 | ||||||||
\(401\) | 2.97224 | 0.148427 | 0.0742134 | − | 0.997242i | \(-0.476355\pi\) | ||||
0.0742134 | + | 0.997242i | \(0.476355\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −3.21110 | −0.159956 | ||||||||
\(404\) | −0.0916731 | −0.00456091 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 4.42221 | 0.219470 | ||||||||
\(407\) | 16.4222 | 0.814018 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 24.2389 | 1.19853 | 0.599267 | − | 0.800549i | \(-0.295459\pi\) | ||||
0.599267 | + | 0.800549i | \(0.295459\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 7.90833 | 0.389615 | ||||||||
\(413\) | 8.60555 | 0.423451 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −5.30278 | −0.259990 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 4.39445 | 0.214940 | ||||||||
\(419\) | −3.39445 | −0.165830 | −0.0829148 | − | 0.996557i | \(-0.526423\pi\) | ||||
−0.0829148 | + | 0.996557i | \(0.526423\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −19.7250 | −0.961337 | −0.480668 | − | 0.876902i | \(-0.659606\pi\) | ||||
−0.480668 | + | 0.876902i | \(0.659606\pi\) | |||||||
\(422\) | −1.69722 | −0.0826196 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −3.90833 | −0.189805 | ||||||||
\(425\) | 23.0278 | 1.11701 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −16.4222 | −0.794726 | ||||||||
\(428\) | 9.90833 | 0.478937 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −25.8167 | −1.24354 | −0.621772 | − | 0.783198i | \(-0.713587\pi\) | ||||
−0.621772 | + | 0.783198i | \(0.713587\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 21.5416 | 1.03522 | 0.517612 | − | 0.855615i | \(-0.326821\pi\) | ||||
0.517612 | + | 0.855615i | \(0.326821\pi\) | |||||||
\(434\) | 1.57779 | 0.0757366 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −12.6056 | −0.603696 | ||||||||
\(437\) | 2.78890 | 0.133411 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −15.6333 | −0.746137 | −0.373069 | − | 0.927804i | \(-0.621694\pi\) | ||||
−0.373069 | + | 0.927804i | \(0.621694\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 24.4222 | 1.16165 | ||||||||
\(443\) | 8.60555 | 0.408862 | 0.204431 | − | 0.978881i | \(-0.434466\pi\) | ||||
0.204431 | + | 0.978881i | \(0.434466\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 1.00000 | 0.0473514 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 2.60555 | 0.123101 | ||||||||
\(449\) | 0.788897 | 0.0372304 | 0.0186152 | − | 0.999827i | \(-0.494074\pi\) | ||||
0.0186152 | + | 0.999827i | \(0.494074\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −25.2111 | −1.18714 | ||||||||
\(452\) | −19.3028 | −0.907926 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −17.0278 | −0.799152 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 10.1833 | 0.476357 | 0.238178 | − | 0.971221i | \(-0.423450\pi\) | ||||
0.238178 | + | 0.971221i | \(0.423450\pi\) | |||||||
\(458\) | 10.0000 | 0.467269 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −27.7250 | −1.29128 | −0.645641 | − | 0.763641i | \(-0.723410\pi\) | ||||
−0.645641 | + | 0.763641i | \(0.723410\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 3.21110 | 0.149233 | 0.0746163 | − | 0.997212i | \(-0.476227\pi\) | ||||
0.0746163 | + | 0.997212i | \(0.476227\pi\) | |||||||
\(464\) | −1.69722 | −0.0787917 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −8.30278 | −0.384619 | ||||||||
\(467\) | 2.09167 | 0.0967911 | 0.0483955 | − | 0.998828i | \(-0.484589\pi\) | ||||
0.0483955 | + | 0.998828i | \(0.484589\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −6.78890 | −0.313482 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −3.30278 | −0.152023 | ||||||||
\(473\) | 43.5416 | 2.00205 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −3.48612 | −0.159954 | ||||||||
\(476\) | −12.0000 | −0.550019 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 23.7250 | 1.08516 | ||||||||
\(479\) | −36.9083 | −1.68638 | −0.843192 | − | 0.537612i | \(-0.819326\pi\) | ||||
−0.843192 | + | 0.537612i | \(0.819326\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −13.8167 | −0.629985 | ||||||||
\(482\) | −13.5139 | −0.615540 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 28.7250 | 1.30568 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −4.00000 | −0.181257 | −0.0906287 | − | 0.995885i | \(-0.528888\pi\) | ||||
−0.0906287 | + | 0.995885i | \(0.528888\pi\) | |||||||
\(488\) | 6.30278 | 0.285313 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 13.9361 | 0.628927 | 0.314463 | − | 0.949270i | \(-0.398175\pi\) | ||||
0.314463 | + | 0.949270i | \(0.398175\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 7.81665 | 0.352044 | ||||||||
\(494\) | −3.69722 | −0.166346 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −0.605551 | −0.0271901 | ||||||||
\(497\) | 8.36669 | 0.375297 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −6.30278 | −0.282151 | −0.141075 | − | 0.989999i | \(-0.545056\pi\) | ||||
−0.141075 | + | 0.989999i | \(0.545056\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 6.42221 | 0.286637 | ||||||||
\(503\) | 12.0000 | 0.535054 | 0.267527 | − | 0.963550i | \(-0.413794\pi\) | ||||
0.267527 | + | 0.963550i | \(0.413794\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 25.2111 | 1.12077 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −7.21110 | −0.319941 | ||||||||
\(509\) | 27.7527 | 1.23012 | 0.615059 | − | 0.788481i | \(-0.289132\pi\) | ||||
0.615059 | + | 0.788481i | \(0.289132\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 4.97224 | 0.219959 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 6.00000 | 0.264649 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 27.1194 | 1.19271 | ||||||||
\(518\) | 6.78890 | 0.298287 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −6.00000 | −0.262865 | −0.131432 | − | 0.991325i | \(-0.541958\pi\) | ||||
−0.131432 | + | 0.991325i | \(0.541958\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −5.57779 | −0.243900 | −0.121950 | − | 0.992536i | \(-0.538915\pi\) | ||||
−0.121950 | + | 0.992536i | \(0.538915\pi\) | |||||||
\(524\) | 12.4222 | 0.542667 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −14.6056 | −0.636832 | ||||||||
\(527\) | 2.78890 | 0.121486 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −7.00000 | −0.304348 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 1.81665 | 0.0787619 | ||||||||
\(533\) | 21.2111 | 0.918755 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 2.60555 | 0.112543 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −21.0278 | −0.906571 | ||||||||
\(539\) | 1.33053 | 0.0573101 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 8.27502 | 0.355771 | 0.177885 | − | 0.984051i | \(-0.443074\pi\) | ||||
0.177885 | + | 0.984051i | \(0.443074\pi\) | |||||||
\(542\) | 10.1194 | 0.434667 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 4.60555 | 0.197461 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 9.72498 | 0.415810 | 0.207905 | − | 0.978149i | \(-0.433335\pi\) | ||||
0.207905 | + | 0.978149i | \(0.433335\pi\) | |||||||
\(548\) | −3.69722 | −0.157938 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −31.5139 | −1.34376 | ||||||||
\(551\) | −1.18335 | −0.0504122 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −24.7889 | −1.05413 | ||||||||
\(554\) | 3.57779 | 0.152006 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −1.09167 | −0.0462973 | ||||||||
\(557\) | −38.4222 | −1.62800 | −0.814001 | − | 0.580864i | \(-0.802715\pi\) | ||||
−0.814001 | + | 0.580864i | \(0.802715\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −36.6333 | −1.54942 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 7.39445 | 0.311916 | ||||||||
\(563\) | −42.5416 | −1.79292 | −0.896458 | − | 0.443129i | \(-0.853869\pi\) | ||||
−0.896458 | + | 0.443129i | \(0.853869\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 19.3028 | 0.811356 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −3.21110 | −0.134735 | ||||||||
\(569\) | 33.5416 | 1.40614 | 0.703069 | − | 0.711121i | \(-0.251812\pi\) | ||||
0.703069 | + | 0.711121i | \(0.251812\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 8.00000 | 0.334790 | 0.167395 | − | 0.985890i | \(-0.446465\pi\) | ||||
0.167395 | + | 0.985890i | \(0.446465\pi\) | |||||||
\(572\) | −33.4222 | −1.39745 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −10.4222 | −0.435014 | ||||||||
\(575\) | −20.0000 | −0.834058 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −42.9638 | −1.78861 | −0.894304 | − | 0.447460i | \(-0.852329\pi\) | ||||
−0.894304 | + | 0.447460i | \(0.852329\pi\) | |||||||
\(578\) | −4.21110 | −0.175159 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −24.0000 | −0.995688 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −24.6333 | −1.02021 | ||||||||
\(584\) | −1.90833 | −0.0789671 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 30.2389 | 1.24916 | ||||||||
\(587\) | 14.9361 | 0.616478 | 0.308239 | − | 0.951309i | \(-0.400260\pi\) | ||||
0.308239 | + | 0.951309i | \(0.400260\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −0.422205 | −0.0173967 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −2.60555 | −0.107087 | ||||||||
\(593\) | 32.4222 | 1.33142 | 0.665710 | − | 0.746210i | \(-0.268129\pi\) | ||||
0.665710 | + | 0.746210i | \(0.268129\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 9.21110 | 0.377301 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −21.2111 | −0.867386 | ||||||||
\(599\) | −9.88057 | −0.403709 | −0.201855 | − | 0.979416i | \(-0.564697\pi\) | ||||
−0.201855 | + | 0.979416i | \(0.564697\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 21.8167 | 0.889920 | 0.444960 | − | 0.895550i | \(-0.353218\pi\) | ||||
0.444960 | + | 0.895550i | \(0.353218\pi\) | |||||||
\(602\) | 18.0000 | 0.733625 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 18.5139 | 0.753319 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 32.8444 | 1.33311 | 0.666557 | − | 0.745454i | \(-0.267767\pi\) | ||||
0.666557 | + | 0.745454i | \(0.267767\pi\) | |||||||
\(608\) | −0.697224 | −0.0282762 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −22.8167 | −0.923063 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 0.486122 | 0.0196343 | 0.00981714 | − | 0.999952i | \(-0.496875\pi\) | ||||
0.00981714 | + | 0.999952i | \(0.496875\pi\) | |||||||
\(614\) | 3.02776 | 0.122190 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 16.4222 | 0.661669 | ||||||||
\(617\) | −18.4222 | −0.741650 | −0.370825 | − | 0.928703i | \(-0.620925\pi\) | ||||
−0.370825 | + | 0.928703i | \(0.620925\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 10.4222 | 0.418904 | 0.209452 | − | 0.977819i | \(-0.432832\pi\) | ||||
0.209452 | + | 0.977819i | \(0.432832\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 3.39445 | 0.136105 | ||||||||
\(623\) | −7.26662 | −0.291131 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 25.0000 | 1.00000 | ||||||||
\(626\) | 20.0000 | 0.799361 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 6.30278 | 0.251508 | ||||||||
\(629\) | 12.0000 | 0.478471 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 34.1194 | 1.35827 | 0.679137 | − | 0.734012i | \(-0.262354\pi\) | ||||
0.679137 | + | 0.734012i | \(0.262354\pi\) | |||||||
\(632\) | 9.51388 | 0.378442 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −13.3028 | −0.528321 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1.11943 | −0.0443534 | ||||||||
\(638\) | −10.6972 | −0.423507 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 40.5139 | 1.60020 | 0.800101 | − | 0.599865i | \(-0.204779\pi\) | ||||
0.800101 | + | 0.599865i | \(0.204779\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 30.3028 | 1.19502 | 0.597512 | − | 0.801860i | \(-0.296156\pi\) | ||||
0.597512 | + | 0.801860i | \(0.296156\pi\) | |||||||
\(644\) | 10.4222 | 0.410692 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 3.21110 | 0.126339 | ||||||||
\(647\) | −24.0917 | −0.947141 | −0.473571 | − | 0.880756i | \(-0.657035\pi\) | ||||
−0.473571 | + | 0.880756i | \(0.657035\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −20.8167 | −0.817125 | ||||||||
\(650\) | 26.5139 | 1.03996 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 1.39445 | 0.0546108 | ||||||||
\(653\) | 7.63331 | 0.298714 | 0.149357 | − | 0.988783i | \(-0.452280\pi\) | ||||
0.149357 | + | 0.988783i | \(0.452280\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 4.00000 | 0.156174 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 11.2111 | 0.437054 | ||||||||
\(659\) | 21.6333 | 0.842714 | 0.421357 | − | 0.906895i | \(-0.361554\pi\) | ||||
0.421357 | + | 0.906895i | \(0.361554\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −37.9361 | −1.47554 | −0.737771 | − | 0.675051i | \(-0.764122\pi\) | ||||
−0.737771 | + | 0.675051i | \(0.764122\pi\) | |||||||
\(662\) | 4.78890 | 0.186126 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 9.21110 | 0.357460 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −6.78890 | −0.262867 | ||||||||
\(668\) | 4.60555 | 0.178194 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 39.7250 | 1.53357 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 11.1194 | 0.428623 | 0.214311 | − | 0.976765i | \(-0.431249\pi\) | ||||
0.214311 | + | 0.976765i | \(0.431249\pi\) | |||||||
\(674\) | 9.21110 | 0.354798 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 15.1194 | 0.581517 | ||||||||
\(677\) | 20.7889 | 0.798982 | 0.399491 | − | 0.916737i | \(-0.369187\pi\) | ||||
0.399491 | + | 0.916737i | \(0.369187\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −39.6333 | −1.52099 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −3.81665 | −0.146147 | ||||||||
\(683\) | 45.8167 | 1.75313 | 0.876563 | − | 0.481288i | \(-0.159831\pi\) | ||||
0.876563 | + | 0.481288i | \(0.159831\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 18.7889 | 0.717363 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −6.90833 | −0.263377 | ||||||||
\(689\) | 20.7250 | 0.789559 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −0.183346 | −0.00697482 | −0.00348741 | − | 0.999994i | \(-0.501110\pi\) | ||||
−0.00348741 | + | 0.999994i | \(0.501110\pi\) | |||||||
\(692\) | −23.0278 | −0.875384 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 18.4222 | 0.699297 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −18.4222 | −0.697791 | ||||||||
\(698\) | 32.6056 | 1.23414 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −13.0278 | −0.492403 | ||||||||
\(701\) | 6.00000 | 0.226617 | 0.113308 | − | 0.993560i | \(-0.463855\pi\) | ||||
0.113308 | + | 0.993560i | \(0.463855\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −1.81665 | −0.0685164 | ||||||||
\(704\) | −6.30278 | −0.237545 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 22.6056 | 0.850771 | ||||||||
\(707\) | −0.238859 | −0.00898321 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −3.57779 | −0.134367 | −0.0671835 | − | 0.997741i | \(-0.521401\pi\) | ||||
−0.0671835 | + | 0.997741i | \(0.521401\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 2.78890 | 0.104518 | ||||||||
\(713\) | −2.42221 | −0.0907123 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 1.21110 | 0.0452610 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 5.48612 | 0.204740 | ||||||||
\(719\) | −21.2111 | −0.791041 | −0.395520 | − | 0.918457i | \(-0.629436\pi\) | ||||
−0.395520 | + | 0.918457i | \(0.629436\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 20.6056 | 0.767391 | ||||||||
\(722\) | 18.5139 | 0.689015 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 8.60555 | 0.319823 | ||||||||
\(725\) | 8.48612 | 0.315167 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −14.1833 | −0.526031 | −0.263016 | − | 0.964792i | \(-0.584717\pi\) | ||||
−0.263016 | + | 0.964792i | \(0.584717\pi\) | |||||||
\(728\) | −13.8167 | −0.512079 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 31.8167 | 1.17678 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 20.4222 | 0.754311 | 0.377156 | − | 0.926150i | \(-0.376902\pi\) | ||||
0.377156 | + | 0.926150i | \(0.376902\pi\) | |||||||
\(734\) | −8.00000 | −0.295285 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −4.00000 | −0.147442 | ||||||||
\(737\) | 16.4222 | 0.604920 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 43.4500 | 1.59833 | 0.799166 | − | 0.601110i | \(-0.205275\pi\) | ||||
0.799166 | + | 0.601110i | \(0.205275\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −10.1833 | −0.373842 | ||||||||
\(743\) | −16.9361 | −0.621325 | −0.310662 | − | 0.950520i | \(-0.600551\pi\) | ||||
−0.310662 | + | 0.950520i | \(0.600551\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −30.8444 | −1.12929 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 29.0278 | 1.06136 | ||||||||
\(749\) | 25.8167 | 0.943320 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 43.4500 | 1.58551 | 0.792756 | − | 0.609539i | \(-0.208646\pi\) | ||||
0.792756 | + | 0.609539i | \(0.208646\pi\) | |||||||
\(752\) | −4.30278 | −0.156906 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 9.00000 | 0.327761 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −6.33053 | −0.230087 | −0.115044 | − | 0.993360i | \(-0.536701\pi\) | ||||
−0.115044 | + | 0.993360i | \(0.536701\pi\) | |||||||
\(758\) | −36.3305 | −1.31958 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 26.0917 | 0.945822 | 0.472911 | − | 0.881110i | \(-0.343203\pi\) | ||||
0.472911 | + | 0.881110i | \(0.343203\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −32.8444 | −1.18905 | ||||||||
\(764\) | −13.8167 | −0.499869 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −11.8167 | −0.426953 | ||||||||
\(767\) | 17.5139 | 0.632389 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −34.1194 | −1.23038 | −0.615189 | − | 0.788380i | \(-0.710920\pi\) | ||||
−0.615189 | + | 0.788380i | \(0.710920\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −20.4222 | −0.735011 | ||||||||
\(773\) | 28.2389 | 1.01568 | 0.507841 | − | 0.861451i | \(-0.330444\pi\) | ||||
0.507841 | + | 0.861451i | \(0.330444\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 3.02776 | 0.108760 | ||||||||
\(776\) | 15.2111 | 0.546047 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 21.9361 | 0.786447 | ||||||||
\(779\) | 2.78890 | 0.0999226 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −20.2389 | −0.724203 | ||||||||
\(782\) | 18.4222 | 0.658777 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −0.211103 | −0.00753938 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 29.2111 | 1.04126 | 0.520632 | − | 0.853781i | \(-0.325696\pi\) | ||||
0.520632 | + | 0.853781i | \(0.325696\pi\) | |||||||
\(788\) | 1.69722 | 0.0604611 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −50.2944 | −1.78826 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −33.4222 | −1.18686 | ||||||||
\(794\) | 19.5139 | 0.692522 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −18.4222 | −0.652958 | ||||||||
\(797\) | 12.4222 | 0.440017 | 0.220009 | − | 0.975498i | \(-0.429391\pi\) | ||||
0.220009 | + | 0.975498i | \(0.429391\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 19.8167 | 0.701063 | ||||||||
\(800\) | 5.00000 | 0.176777 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −2.97224 | −0.104954 | ||||||||
\(803\) | −12.0278 | −0.424450 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 3.21110 | 0.113106 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0.0916731 | 0.00322505 | ||||||||
\(809\) | −14.8444 | −0.521902 | −0.260951 | − | 0.965352i | \(-0.584036\pi\) | ||||
−0.260951 | + | 0.965352i | \(0.584036\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 4.23886 | 0.148846 | 0.0744232 | − | 0.997227i | \(-0.476288\pi\) | ||||
0.0744232 | + | 0.997227i | \(0.476288\pi\) | |||||||
\(812\) | −4.42221 | −0.155189 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −16.4222 | −0.575598 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −4.81665 | −0.168513 | ||||||||
\(818\) | −24.2389 | −0.847492 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 1.45837 | 0.0508973 | 0.0254487 | − | 0.999676i | \(-0.491899\pi\) | ||||
0.0254487 | + | 0.999676i | \(0.491899\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −51.2666 | −1.78704 | −0.893521 | − | 0.449022i | \(-0.851773\pi\) | ||||
−0.893521 | + | 0.449022i | \(0.851773\pi\) | |||||||
\(824\) | −7.90833 | −0.275500 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −8.60555 | −0.299425 | ||||||||
\(827\) | −46.9361 | −1.63213 | −0.816064 | − | 0.577962i | \(-0.803848\pi\) | ||||
−0.816064 | + | 0.577962i | \(0.803848\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −51.5139 | −1.78915 | −0.894575 | − | 0.446917i | \(-0.852522\pi\) | ||||
−0.894575 | + | 0.446917i | \(0.852522\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 5.30278 | 0.183841 | ||||||||
\(833\) | 0.972244 | 0.0336862 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −4.39445 | −0.151985 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 3.39445 | 0.117259 | ||||||||
\(839\) | 16.6056 | 0.573287 | 0.286644 | − | 0.958037i | \(-0.407460\pi\) | ||||
0.286644 | + | 0.958037i | \(0.407460\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −26.1194 | −0.900670 | ||||||||
\(842\) | 19.7250 | 0.679768 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 1.69722 | 0.0584209 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 74.8444 | 2.57168 | ||||||||
\(848\) | 3.90833 | 0.134212 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −23.0278 | −0.789846 | ||||||||
\(851\) | −10.4222 | −0.357269 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 28.1194 | 0.962791 | 0.481395 | − | 0.876504i | \(-0.340130\pi\) | ||||
0.481395 | + | 0.876504i | \(0.340130\pi\) | |||||||
\(854\) | 16.4222 | 0.561956 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −9.90833 | −0.338660 | ||||||||
\(857\) | 7.39445 | 0.252590 | 0.126295 | − | 0.991993i | \(-0.459691\pi\) | ||||
0.126295 | + | 0.991993i | \(0.459691\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −55.0278 | −1.87752 | −0.938761 | − | 0.344568i | \(-0.888025\pi\) | ||||
−0.938761 | + | 0.344568i | \(0.888025\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 25.8167 | 0.879319 | ||||||||
\(863\) | −35.2111 | −1.19860 | −0.599300 | − | 0.800525i | \(-0.704554\pi\) | ||||
−0.599300 | + | 0.800525i | \(0.704554\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −21.5416 | −0.732015 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −1.57779 | −0.0535538 | ||||||||
\(869\) | 59.9638 | 2.03413 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −13.8167 | −0.468159 | ||||||||
\(872\) | 12.6056 | 0.426878 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −2.78890 | −0.0943359 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 40.1194 | 1.35474 | 0.677368 | − | 0.735644i | \(-0.263120\pi\) | ||||
0.677368 | + | 0.735644i | \(0.263120\pi\) | |||||||
\(878\) | 15.6333 | 0.527599 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −18.7889 | −0.633014 | −0.316507 | − | 0.948590i | \(-0.602510\pi\) | ||||
−0.316507 | + | 0.948590i | \(0.602510\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 32.0555 | 1.07875 | 0.539377 | − | 0.842064i | \(-0.318660\pi\) | ||||
0.539377 | + | 0.842064i | \(0.318660\pi\) | |||||||
\(884\) | −24.4222 | −0.821408 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −8.60555 | −0.289109 | ||||||||
\(887\) | 0.275019 | 0.00923424 | 0.00461712 | − | 0.999989i | \(-0.498530\pi\) | ||||
0.00461712 | + | 0.999989i | \(0.498530\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −18.7889 | −0.630159 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −1.00000 | −0.0334825 | ||||||||
\(893\) | −3.00000 | −0.100391 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −2.60555 | −0.0870454 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −0.788897 | −0.0263258 | ||||||||
\(899\) | 1.02776 | 0.0342776 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −18.0000 | −0.599667 | ||||||||
\(902\) | 25.2111 | 0.839438 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 19.3028 | 0.642001 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 28.3305 | 0.940700 | 0.470350 | − | 0.882480i | \(-0.344128\pi\) | ||||
0.470350 | + | 0.882480i | \(0.344128\pi\) | |||||||
\(908\) | 17.0278 | 0.565086 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −9.57779 | −0.317327 | −0.158663 | − | 0.987333i | \(-0.550718\pi\) | ||||
−0.158663 | + | 0.987333i | \(0.550718\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 58.0555 | 1.92136 | ||||||||
\(914\) | −10.1833 | −0.336835 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −10.0000 | −0.330409 | ||||||||
\(917\) | 32.3667 | 1.06884 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −7.54163 | −0.248776 | −0.124388 | − | 0.992234i | \(-0.539697\pi\) | ||||
−0.124388 | + | 0.992234i | \(0.539697\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 27.7250 | 0.913074 | ||||||||
\(923\) | 17.0278 | 0.560475 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 13.0278 | 0.428350 | ||||||||
\(926\) | −3.21110 | −0.105523 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 1.69722 | 0.0557141 | ||||||||
\(929\) | 22.9722 | 0.753695 | 0.376847 | − | 0.926275i | \(-0.377008\pi\) | ||||
0.376847 | + | 0.926275i | \(0.377008\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −0.147186 | −0.00482382 | ||||||||
\(932\) | 8.30278 | 0.271966 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −2.09167 | −0.0684416 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −24.7889 | −0.809818 | −0.404909 | − | 0.914357i | \(-0.632697\pi\) | ||||
−0.404909 | + | 0.914357i | \(0.632697\pi\) | |||||||
\(938\) | 6.78890 | 0.221665 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −49.1194 | −1.60125 | −0.800624 | − | 0.599167i | \(-0.795498\pi\) | ||||
−0.800624 | + | 0.599167i | \(0.795498\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 16.0000 | 0.521032 | ||||||||
\(944\) | 3.30278 | 0.107496 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −43.5416 | −1.41566 | ||||||||
\(947\) | 25.8167 | 0.838929 | 0.419464 | − | 0.907772i | \(-0.362218\pi\) | ||||
0.419464 | + | 0.907772i | \(0.362218\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 10.1194 | 0.328491 | ||||||||
\(950\) | 3.48612 | 0.113105 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 12.0000 | 0.388922 | ||||||||
\(953\) | −44.0555 | −1.42710 | −0.713549 | − | 0.700605i | \(-0.752913\pi\) | ||||
−0.713549 | + | 0.700605i | \(0.752913\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −23.7250 | −0.767321 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 36.9083 | 1.19245 | ||||||||
\(959\) | −9.63331 | −0.311076 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −30.6333 | −0.988171 | ||||||||
\(962\) | 13.8167 | 0.445467 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 13.5139 | 0.435253 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 12.0917 | 0.388842 | 0.194421 | − | 0.980918i | \(-0.437717\pi\) | ||||
0.194421 | + | 0.980918i | \(0.437717\pi\) | |||||||
\(968\) | −28.7250 | −0.923256 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 36.7250 | 1.17856 | 0.589280 | − | 0.807929i | \(-0.299411\pi\) | ||||
0.589280 | + | 0.807929i | \(0.299411\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −2.84441 | −0.0911876 | ||||||||
\(974\) | 4.00000 | 0.128168 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −6.30278 | −0.201747 | ||||||||
\(977\) | 30.7250 | 0.982979 | 0.491490 | − | 0.870883i | \(-0.336453\pi\) | ||||
0.491490 | + | 0.870883i | \(0.336453\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 17.5778 | 0.561789 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −13.9361 | −0.444718 | ||||||||
\(983\) | 36.7889 | 1.17338 | 0.586692 | − | 0.809810i | \(-0.300430\pi\) | ||||
0.586692 | + | 0.809810i | \(0.300430\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −7.81665 | −0.248933 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 3.69722 | 0.117624 | ||||||||
\(989\) | −27.6333 | −0.878688 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 30.8806 | 0.980954 | 0.490477 | − | 0.871454i | \(-0.336823\pi\) | ||||
0.490477 | + | 0.871454i | \(0.336823\pi\) | |||||||
\(992\) | 0.605551 | 0.0192263 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −8.36669 | −0.265375 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 11.8167 | 0.374237 | 0.187119 | − | 0.982337i | \(-0.440085\pi\) | ||||
0.187119 | + | 0.982337i | \(0.440085\pi\) | |||||||
\(998\) | 6.30278 | 0.199511 | ||||||||
\(999\) | 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 | 4014.2.a.j.1.2 | ✓ | 2 | |
3.2 | odd | 2 | 4014.2.a.l.1.2 | yes | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4014.2.a.j.1.2 | ✓ | 2 | 1.1 | even | 1 | trivial | |
4014.2.a.l.1.2 | yes | 2 | 3.2 | odd | 2 |