Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [9075,2,Mod(1,9075)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(9075, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("9075.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 9075 = 3 \cdot 5^{2} \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 9075.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: | \(72.4642398343\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{8})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - 2 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 165) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(1.41421\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 9075.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.414214 | 0.292893 | 0.146447 | − | 0.989219i | \(-0.453216\pi\) | ||||
0.146447 | + | 0.989219i | \(0.453216\pi\) | |||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | −1.82843 | −0.914214 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0.414214 | 0.169102 | ||||||||
\(7\) | −4.82843 | −1.82497 | −0.912487 | − | 0.409106i | \(-0.865841\pi\) | ||||
−0.912487 | + | 0.409106i | \(0.865841\pi\) | |||||||
\(8\) | −1.58579 | −0.560660 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | −1.82843 | −0.527821 | ||||||||
\(13\) | 5.65685 | 1.56893 | 0.784465 | − | 0.620174i | \(-0.212938\pi\) | ||||
0.784465 | + | 0.620174i | \(0.212938\pi\) | |||||||
\(14\) | −2.00000 | −0.534522 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 3.00000 | 0.750000 | ||||||||
\(17\) | −6.82843 | −1.65614 | −0.828068 | − | 0.560627i | \(-0.810560\pi\) | ||||
−0.828068 | + | 0.560627i | \(0.810560\pi\) | |||||||
\(18\) | 0.414214 | 0.0976311 | ||||||||
\(19\) | 1.17157 | 0.268777 | 0.134389 | − | 0.990929i | \(-0.457093\pi\) | ||||
0.134389 | + | 0.990929i | \(0.457093\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −4.82843 | −1.05365 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 4.00000 | 0.834058 | 0.417029 | − | 0.908893i | \(-0.363071\pi\) | ||||
0.417029 | + | 0.908893i | \(0.363071\pi\) | |||||||
\(24\) | −1.58579 | −0.323697 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 2.34315 | 0.459529 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 8.82843 | 1.66842 | ||||||||
\(29\) | −0.828427 | −0.153835 | −0.0769175 | − | 0.997037i | \(-0.524508\pi\) | ||||
−0.0769175 | + | 0.997037i | \(0.524508\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(32\) | 4.41421 | 0.780330 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −2.82843 | −0.485071 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −1.82843 | −0.304738 | ||||||||
\(37\) | −0.343146 | −0.0564128 | −0.0282064 | − | 0.999602i | \(-0.508980\pi\) | ||||
−0.0282064 | + | 0.999602i | \(0.508980\pi\) | |||||||
\(38\) | 0.485281 | 0.0787230 | ||||||||
\(39\) | 5.65685 | 0.905822 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0.828427 | 0.129379 | 0.0646893 | − | 0.997905i | \(-0.479394\pi\) | ||||
0.0646893 | + | 0.997905i | \(0.479394\pi\) | |||||||
\(42\) | −2.00000 | −0.308607 | ||||||||
\(43\) | −3.17157 | −0.483660 | −0.241830 | − | 0.970319i | \(-0.577748\pi\) | ||||
−0.241830 | + | 0.970319i | \(0.577748\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 1.65685 | 0.244290 | ||||||||
\(47\) | 4.00000 | 0.583460 | 0.291730 | − | 0.956501i | \(-0.405769\pi\) | ||||
0.291730 | + | 0.956501i | \(0.405769\pi\) | |||||||
\(48\) | 3.00000 | 0.433013 | ||||||||
\(49\) | 16.3137 | 2.33053 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −6.82843 | −0.956171 | ||||||||
\(52\) | −10.3431 | −1.43434 | ||||||||
\(53\) | 13.3137 | 1.82878 | 0.914389 | − | 0.404836i | \(-0.132671\pi\) | ||||
0.914389 | + | 0.404836i | \(0.132671\pi\) | |||||||
\(54\) | 0.414214 | 0.0563673 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 7.65685 | 1.02319 | ||||||||
\(57\) | 1.17157 | 0.155179 | ||||||||
\(58\) | −0.343146 | −0.0450572 | ||||||||
\(59\) | −4.00000 | −0.520756 | −0.260378 | − | 0.965507i | \(-0.583847\pi\) | ||||
−0.260378 | + | 0.965507i | \(0.583847\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0.343146 | 0.0439353 | 0.0219677 | − | 0.999759i | \(-0.493007\pi\) | ||||
0.0219677 | + | 0.999759i | \(0.493007\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −4.82843 | −0.608325 | ||||||||
\(64\) | −4.17157 | −0.521447 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −5.65685 | −0.691095 | −0.345547 | − | 0.938401i | \(-0.612307\pi\) | ||||
−0.345547 | + | 0.938401i | \(0.612307\pi\) | |||||||
\(68\) | 12.4853 | 1.51406 | ||||||||
\(69\) | 4.00000 | 0.481543 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 13.6569 | 1.62077 | 0.810385 | − | 0.585897i | \(-0.199258\pi\) | ||||
0.810385 | + | 0.585897i | \(0.199258\pi\) | |||||||
\(72\) | −1.58579 | −0.186887 | ||||||||
\(73\) | −11.3137 | −1.32417 | −0.662085 | − | 0.749429i | \(-0.730328\pi\) | ||||
−0.662085 | + | 0.749429i | \(0.730328\pi\) | |||||||
\(74\) | −0.142136 | −0.0165229 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −2.14214 | −0.245720 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 2.34315 | 0.265309 | ||||||||
\(79\) | 8.48528 | 0.954669 | 0.477334 | − | 0.878722i | \(-0.341603\pi\) | ||||
0.477334 | + | 0.878722i | \(0.341603\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0.343146 | 0.0378941 | ||||||||
\(83\) | −10.0000 | −1.09764 | −0.548821 | − | 0.835940i | \(-0.684923\pi\) | ||||
−0.548821 | + | 0.835940i | \(0.684923\pi\) | |||||||
\(84\) | 8.82843 | 0.963260 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −1.31371 | −0.141661 | ||||||||
\(87\) | −0.828427 | −0.0888167 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −7.65685 | −0.811625 | −0.405812 | − | 0.913956i | \(-0.633011\pi\) | ||||
−0.405812 | + | 0.913956i | \(0.633011\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −27.3137 | −2.86325 | ||||||||
\(92\) | −7.31371 | −0.762507 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 1.65685 | 0.170891 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 4.41421 | 0.450524 | ||||||||
\(97\) | −0.343146 | −0.0348412 | −0.0174206 | − | 0.999848i | \(-0.505545\pi\) | ||||
−0.0174206 | + | 0.999848i | \(0.505545\pi\) | |||||||
\(98\) | 6.75736 | 0.682596 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −4.82843 | −0.480446 | −0.240223 | − | 0.970718i | \(-0.577221\pi\) | ||||
−0.240223 | + | 0.970718i | \(0.577221\pi\) | |||||||
\(102\) | −2.82843 | −0.280056 | ||||||||
\(103\) | −19.3137 | −1.90304 | −0.951518 | − | 0.307593i | \(-0.900477\pi\) | ||||
−0.951518 | + | 0.307593i | \(0.900477\pi\) | |||||||
\(104\) | −8.97056 | −0.879636 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 5.51472 | 0.535637 | ||||||||
\(107\) | −5.31371 | −0.513696 | −0.256848 | − | 0.966452i | \(-0.582684\pi\) | ||||
−0.256848 | + | 0.966452i | \(0.582684\pi\) | |||||||
\(108\) | −1.82843 | −0.175940 | ||||||||
\(109\) | 5.31371 | 0.508961 | 0.254480 | − | 0.967078i | \(-0.418096\pi\) | ||||
0.254480 | + | 0.967078i | \(0.418096\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −0.343146 | −0.0325700 | ||||||||
\(112\) | −14.4853 | −1.36873 | ||||||||
\(113\) | −14.9706 | −1.40831 | −0.704156 | − | 0.710045i | \(-0.748674\pi\) | ||||
−0.704156 | + | 0.710045i | \(0.748674\pi\) | |||||||
\(114\) | 0.485281 | 0.0454508 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 1.51472 | 0.140638 | ||||||||
\(117\) | 5.65685 | 0.522976 | ||||||||
\(118\) | −1.65685 | −0.152526 | ||||||||
\(119\) | 32.9706 | 3.02241 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | 0.142136 | 0.0128684 | ||||||||
\(123\) | 0.828427 | 0.0746968 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −2.00000 | −0.178174 | ||||||||
\(127\) | 2.48528 | 0.220533 | 0.110267 | − | 0.993902i | \(-0.464830\pi\) | ||||
0.110267 | + | 0.993902i | \(0.464830\pi\) | |||||||
\(128\) | −10.5563 | −0.933058 | ||||||||
\(129\) | −3.17157 | −0.279241 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 19.3137 | 1.68745 | 0.843723 | − | 0.536778i | \(-0.180359\pi\) | ||||
0.843723 | + | 0.536778i | \(0.180359\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −5.65685 | −0.490511 | ||||||||
\(134\) | −2.34315 | −0.202417 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 10.8284 | 0.928530 | ||||||||
\(137\) | −9.31371 | −0.795724 | −0.397862 | − | 0.917445i | \(-0.630248\pi\) | ||||
−0.397862 | + | 0.917445i | \(0.630248\pi\) | |||||||
\(138\) | 1.65685 | 0.141041 | ||||||||
\(139\) | 16.4853 | 1.39826 | 0.699132 | − | 0.714993i | \(-0.253570\pi\) | ||||
0.699132 | + | 0.714993i | \(0.253570\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 4.00000 | 0.336861 | ||||||||
\(142\) | 5.65685 | 0.474713 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 3.00000 | 0.250000 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −4.68629 | −0.387840 | ||||||||
\(147\) | 16.3137 | 1.34553 | ||||||||
\(148\) | 0.627417 | 0.0515734 | ||||||||
\(149\) | −18.4853 | −1.51437 | −0.757187 | − | 0.653199i | \(-0.773427\pi\) | ||||
−0.757187 | + | 0.653199i | \(0.773427\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 0.485281 | 0.0394916 | 0.0197458 | − | 0.999805i | \(-0.493714\pi\) | ||||
0.0197458 | + | 0.999805i | \(0.493714\pi\) | |||||||
\(152\) | −1.85786 | −0.150693 | ||||||||
\(153\) | −6.82843 | −0.552046 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −10.3431 | −0.828114 | ||||||||
\(157\) | −18.0000 | −1.43656 | −0.718278 | − | 0.695756i | \(-0.755069\pi\) | ||||
−0.718278 | + | 0.695756i | \(0.755069\pi\) | |||||||
\(158\) | 3.51472 | 0.279616 | ||||||||
\(159\) | 13.3137 | 1.05585 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −19.3137 | −1.52213 | ||||||||
\(162\) | 0.414214 | 0.0325437 | ||||||||
\(163\) | −15.3137 | −1.19946 | −0.599731 | − | 0.800202i | \(-0.704726\pi\) | ||||
−0.599731 | + | 0.800202i | \(0.704726\pi\) | |||||||
\(164\) | −1.51472 | −0.118280 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −4.14214 | −0.321492 | ||||||||
\(167\) | 9.31371 | 0.720716 | 0.360358 | − | 0.932814i | \(-0.382654\pi\) | ||||
0.360358 | + | 0.932814i | \(0.382654\pi\) | |||||||
\(168\) | 7.65685 | 0.590739 | ||||||||
\(169\) | 19.0000 | 1.46154 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1.17157 | 0.0895924 | ||||||||
\(172\) | 5.79899 | 0.442169 | ||||||||
\(173\) | −2.82843 | −0.215041 | −0.107521 | − | 0.994203i | \(-0.534291\pi\) | ||||
−0.107521 | + | 0.994203i | \(0.534291\pi\) | |||||||
\(174\) | −0.343146 | −0.0260138 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −4.00000 | −0.300658 | ||||||||
\(178\) | −3.17157 | −0.237719 | ||||||||
\(179\) | −6.34315 | −0.474109 | −0.237054 | − | 0.971496i | \(-0.576182\pi\) | ||||
−0.237054 | + | 0.971496i | \(0.576182\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −14.0000 | −1.04061 | −0.520306 | − | 0.853980i | \(-0.674182\pi\) | ||||
−0.520306 | + | 0.853980i | \(0.674182\pi\) | |||||||
\(182\) | −11.3137 | −0.838628 | ||||||||
\(183\) | 0.343146 | 0.0253661 | ||||||||
\(184\) | −6.34315 | −0.467623 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | −7.31371 | −0.533407 | ||||||||
\(189\) | −4.82843 | −0.351216 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −5.65685 | −0.409316 | −0.204658 | − | 0.978834i | \(-0.565608\pi\) | ||||
−0.204658 | + | 0.978834i | \(0.565608\pi\) | |||||||
\(192\) | −4.17157 | −0.301057 | ||||||||
\(193\) | 2.34315 | 0.168663 | 0.0843317 | − | 0.996438i | \(-0.473124\pi\) | ||||
0.0843317 | + | 0.996438i | \(0.473124\pi\) | |||||||
\(194\) | −0.142136 | −0.0102047 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −29.8284 | −2.13060 | ||||||||
\(197\) | 8.48528 | 0.604551 | 0.302276 | − | 0.953221i | \(-0.402254\pi\) | ||||
0.302276 | + | 0.953221i | \(0.402254\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −10.3431 | −0.733206 | −0.366603 | − | 0.930377i | \(-0.619479\pi\) | ||||
−0.366603 | + | 0.930377i | \(0.619479\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −5.65685 | −0.399004 | ||||||||
\(202\) | −2.00000 | −0.140720 | ||||||||
\(203\) | 4.00000 | 0.280745 | ||||||||
\(204\) | 12.4853 | 0.874145 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −8.00000 | −0.557386 | ||||||||
\(207\) | 4.00000 | 0.278019 | ||||||||
\(208\) | 16.9706 | 1.17670 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −6.82843 | −0.470088 | −0.235044 | − | 0.971985i | \(-0.575523\pi\) | ||||
−0.235044 | + | 0.971985i | \(0.575523\pi\) | |||||||
\(212\) | −24.3431 | −1.67189 | ||||||||
\(213\) | 13.6569 | 0.935752 | ||||||||
\(214\) | −2.20101 | −0.150458 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −1.58579 | −0.107899 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 2.20101 | 0.149071 | ||||||||
\(219\) | −11.3137 | −0.764510 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −38.6274 | −2.59836 | ||||||||
\(222\) | −0.142136 | −0.00953952 | ||||||||
\(223\) | 17.6569 | 1.18239 | 0.591195 | − | 0.806529i | \(-0.298656\pi\) | ||||
0.591195 | + | 0.806529i | \(0.298656\pi\) | |||||||
\(224\) | −21.3137 | −1.42408 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −6.20101 | −0.412485 | ||||||||
\(227\) | −14.0000 | −0.929213 | −0.464606 | − | 0.885517i | \(-0.653804\pi\) | ||||
−0.464606 | + | 0.885517i | \(0.653804\pi\) | |||||||
\(228\) | −2.14214 | −0.141866 | ||||||||
\(229\) | −2.00000 | −0.132164 | −0.0660819 | − | 0.997814i | \(-0.521050\pi\) | ||||
−0.0660819 | + | 0.997814i | \(0.521050\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 1.31371 | 0.0862492 | ||||||||
\(233\) | −13.1716 | −0.862898 | −0.431449 | − | 0.902137i | \(-0.641998\pi\) | ||||
−0.431449 | + | 0.902137i | \(0.641998\pi\) | |||||||
\(234\) | 2.34315 | 0.153176 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 7.31371 | 0.476082 | ||||||||
\(237\) | 8.48528 | 0.551178 | ||||||||
\(238\) | 13.6569 | 0.885242 | ||||||||
\(239\) | −6.34315 | −0.410304 | −0.205152 | − | 0.978730i | \(-0.565769\pi\) | ||||
−0.205152 | + | 0.978730i | \(0.565769\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 23.6569 | 1.52387 | 0.761936 | − | 0.647652i | \(-0.224249\pi\) | ||||
0.761936 | + | 0.647652i | \(0.224249\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | −0.627417 | −0.0401663 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0.343146 | 0.0218782 | ||||||||
\(247\) | 6.62742 | 0.421692 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −10.0000 | −0.633724 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −12.9706 | −0.818695 | −0.409347 | − | 0.912379i | \(-0.634244\pi\) | ||||
−0.409347 | + | 0.912379i | \(0.634244\pi\) | |||||||
\(252\) | 8.82843 | 0.556139 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 1.02944 | 0.0645926 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 3.97056 | 0.248160 | ||||||||
\(257\) | 27.6569 | 1.72519 | 0.862594 | − | 0.505898i | \(-0.168839\pi\) | ||||
0.862594 | + | 0.505898i | \(0.168839\pi\) | |||||||
\(258\) | −1.31371 | −0.0817879 | ||||||||
\(259\) | 1.65685 | 0.102952 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −0.828427 | −0.0512784 | ||||||||
\(262\) | 8.00000 | 0.494242 | ||||||||
\(263\) | 18.0000 | 1.10993 | 0.554964 | − | 0.831875i | \(-0.312732\pi\) | ||||
0.554964 | + | 0.831875i | \(0.312732\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −2.34315 | −0.143667 | ||||||||
\(267\) | −7.65685 | −0.468592 | ||||||||
\(268\) | 10.3431 | 0.631808 | ||||||||
\(269\) | −24.6274 | −1.50156 | −0.750780 | − | 0.660552i | \(-0.770322\pi\) | ||||
−0.750780 | + | 0.660552i | \(0.770322\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −27.7990 | −1.68867 | −0.844334 | − | 0.535817i | \(-0.820004\pi\) | ||||
−0.844334 | + | 0.535817i | \(0.820004\pi\) | |||||||
\(272\) | −20.4853 | −1.24210 | ||||||||
\(273\) | −27.3137 | −1.65310 | ||||||||
\(274\) | −3.85786 | −0.233062 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −7.31371 | −0.440234 | ||||||||
\(277\) | −13.6569 | −0.820561 | −0.410280 | − | 0.911959i | \(-0.634569\pi\) | ||||
−0.410280 | + | 0.911959i | \(0.634569\pi\) | |||||||
\(278\) | 6.82843 | 0.409542 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 16.8284 | 1.00390 | 0.501950 | − | 0.864897i | \(-0.332616\pi\) | ||||
0.501950 | + | 0.864897i | \(0.332616\pi\) | |||||||
\(282\) | 1.65685 | 0.0986642 | ||||||||
\(283\) | −3.17157 | −0.188530 | −0.0942652 | − | 0.995547i | \(-0.530050\pi\) | ||||
−0.0942652 | + | 0.995547i | \(0.530050\pi\) | |||||||
\(284\) | −24.9706 | −1.48173 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −4.00000 | −0.236113 | ||||||||
\(288\) | 4.41421 | 0.260110 | ||||||||
\(289\) | 29.6274 | 1.74279 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −0.343146 | −0.0201156 | ||||||||
\(292\) | 20.6863 | 1.21057 | ||||||||
\(293\) | −1.17157 | −0.0684440 | −0.0342220 | − | 0.999414i | \(-0.510895\pi\) | ||||
−0.0342220 | + | 0.999414i | \(0.510895\pi\) | |||||||
\(294\) | 6.75736 | 0.394097 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0.544156 | 0.0316284 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −7.65685 | −0.443550 | ||||||||
\(299\) | 22.6274 | 1.30858 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 15.3137 | 0.882667 | ||||||||
\(302\) | 0.201010 | 0.0115668 | ||||||||
\(303\) | −4.82843 | −0.277386 | ||||||||
\(304\) | 3.51472 | 0.201583 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −2.82843 | −0.161690 | ||||||||
\(307\) | −8.82843 | −0.503865 | −0.251932 | − | 0.967745i | \(-0.581066\pi\) | ||||
−0.251932 | + | 0.967745i | \(0.581066\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −19.3137 | −1.09872 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 19.3137 | 1.09518 | 0.547590 | − | 0.836747i | \(-0.315545\pi\) | ||||
0.547590 | + | 0.836747i | \(0.315545\pi\) | |||||||
\(312\) | −8.97056 | −0.507858 | ||||||||
\(313\) | −4.34315 | −0.245489 | −0.122745 | − | 0.992438i | \(-0.539170\pi\) | ||||
−0.122745 | + | 0.992438i | \(0.539170\pi\) | |||||||
\(314\) | −7.45584 | −0.420758 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −15.5147 | −0.872771 | ||||||||
\(317\) | −30.2843 | −1.70093 | −0.850467 | − | 0.526028i | \(-0.823681\pi\) | ||||
−0.850467 | + | 0.526028i | \(0.823681\pi\) | |||||||
\(318\) | 5.51472 | 0.309250 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −5.31371 | −0.296582 | ||||||||
\(322\) | −8.00000 | −0.445823 | ||||||||
\(323\) | −8.00000 | −0.445132 | ||||||||
\(324\) | −1.82843 | −0.101579 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −6.34315 | −0.351314 | ||||||||
\(327\) | 5.31371 | 0.293849 | ||||||||
\(328\) | −1.31371 | −0.0725374 | ||||||||
\(329\) | −19.3137 | −1.06480 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 17.6569 | 0.970508 | 0.485254 | − | 0.874373i | \(-0.338727\pi\) | ||||
0.485254 | + | 0.874373i | \(0.338727\pi\) | |||||||
\(332\) | 18.2843 | 1.00348 | ||||||||
\(333\) | −0.343146 | −0.0188043 | ||||||||
\(334\) | 3.85786 | 0.211093 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −14.4853 | −0.790237 | ||||||||
\(337\) | −19.3137 | −1.05208 | −0.526042 | − | 0.850458i | \(-0.676325\pi\) | ||||
−0.526042 | + | 0.850458i | \(0.676325\pi\) | |||||||
\(338\) | 7.87006 | 0.428075 | ||||||||
\(339\) | −14.9706 | −0.813089 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0.485281 | 0.0262410 | ||||||||
\(343\) | −44.9706 | −2.42818 | ||||||||
\(344\) | 5.02944 | 0.271169 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −1.17157 | −0.0629841 | ||||||||
\(347\) | −6.68629 | −0.358939 | −0.179469 | − | 0.983764i | \(-0.557438\pi\) | ||||
−0.179469 | + | 0.983764i | \(0.557438\pi\) | |||||||
\(348\) | 1.51472 | 0.0811974 | ||||||||
\(349\) | 22.9706 | 1.22959 | 0.614793 | − | 0.788688i | \(-0.289240\pi\) | ||||
0.614793 | + | 0.788688i | \(0.289240\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 5.65685 | 0.301941 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −26.0000 | −1.38384 | −0.691920 | − | 0.721974i | \(-0.743235\pi\) | ||||
−0.691920 | + | 0.721974i | \(0.743235\pi\) | |||||||
\(354\) | −1.65685 | −0.0880608 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 14.0000 | 0.741999 | ||||||||
\(357\) | 32.9706 | 1.74499 | ||||||||
\(358\) | −2.62742 | −0.138863 | ||||||||
\(359\) | −12.0000 | −0.633336 | −0.316668 | − | 0.948536i | \(-0.602564\pi\) | ||||
−0.316668 | + | 0.948536i | \(0.602564\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −17.6274 | −0.927759 | ||||||||
\(362\) | −5.79899 | −0.304788 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 49.9411 | 2.61763 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0.142136 | 0.00742955 | ||||||||
\(367\) | 1.65685 | 0.0864871 | 0.0432435 | − | 0.999065i | \(-0.486231\pi\) | ||||
0.0432435 | + | 0.999065i | \(0.486231\pi\) | |||||||
\(368\) | 12.0000 | 0.625543 | ||||||||
\(369\) | 0.828427 | 0.0431262 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −64.2843 | −3.33747 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −34.6274 | −1.79294 | −0.896470 | − | 0.443105i | \(-0.853877\pi\) | ||||
−0.896470 | + | 0.443105i | \(0.853877\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −6.34315 | −0.327123 | ||||||||
\(377\) | −4.68629 | −0.241356 | ||||||||
\(378\) | −2.00000 | −0.102869 | ||||||||
\(379\) | −0.686292 | −0.0352524 | −0.0176262 | − | 0.999845i | \(-0.505611\pi\) | ||||
−0.0176262 | + | 0.999845i | \(0.505611\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 2.48528 | 0.127325 | ||||||||
\(382\) | −2.34315 | −0.119886 | ||||||||
\(383\) | 8.00000 | 0.408781 | 0.204390 | − | 0.978889i | \(-0.434479\pi\) | ||||
0.204390 | + | 0.978889i | \(0.434479\pi\) | |||||||
\(384\) | −10.5563 | −0.538701 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0.970563 | 0.0494003 | ||||||||
\(387\) | −3.17157 | −0.161220 | ||||||||
\(388\) | 0.627417 | 0.0318523 | ||||||||
\(389\) | −12.3431 | −0.625822 | −0.312911 | − | 0.949782i | \(-0.601304\pi\) | ||||
−0.312911 | + | 0.949782i | \(0.601304\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −27.3137 | −1.38131 | ||||||||
\(392\) | −25.8701 | −1.30664 | ||||||||
\(393\) | 19.3137 | 0.974248 | ||||||||
\(394\) | 3.51472 | 0.177069 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −18.9706 | −0.952105 | −0.476053 | − | 0.879417i | \(-0.657933\pi\) | ||||
−0.476053 | + | 0.879417i | \(0.657933\pi\) | |||||||
\(398\) | −4.28427 | −0.214751 | ||||||||
\(399\) | −5.65685 | −0.283197 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −29.3137 | −1.46386 | −0.731928 | − | 0.681382i | \(-0.761379\pi\) | ||||
−0.731928 | + | 0.681382i | \(0.761379\pi\) | |||||||
\(402\) | −2.34315 | −0.116865 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 8.82843 | 0.439231 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 1.65685 | 0.0822283 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 10.8284 | 0.536087 | ||||||||
\(409\) | 8.34315 | 0.412542 | 0.206271 | − | 0.978495i | \(-0.433867\pi\) | ||||
0.206271 | + | 0.978495i | \(0.433867\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −9.31371 | −0.459411 | ||||||||
\(412\) | 35.3137 | 1.73978 | ||||||||
\(413\) | 19.3137 | 0.950365 | ||||||||
\(414\) | 1.65685 | 0.0814299 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 24.9706 | 1.22428 | ||||||||
\(417\) | 16.4853 | 0.807288 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −3.02944 | −0.147998 | −0.0739988 | − | 0.997258i | \(-0.523576\pi\) | ||||
−0.0739988 | + | 0.997258i | \(0.523576\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −6.00000 | −0.292422 | −0.146211 | − | 0.989253i | \(-0.546708\pi\) | ||||
−0.146211 | + | 0.989253i | \(0.546708\pi\) | |||||||
\(422\) | −2.82843 | −0.137686 | ||||||||
\(423\) | 4.00000 | 0.194487 | ||||||||
\(424\) | −21.1127 | −1.02532 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 5.65685 | 0.274075 | ||||||||
\(427\) | −1.65685 | −0.0801808 | ||||||||
\(428\) | 9.71573 | 0.469627 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −10.3431 | −0.498212 | −0.249106 | − | 0.968476i | \(-0.580137\pi\) | ||||
−0.249106 | + | 0.968476i | \(0.580137\pi\) | |||||||
\(432\) | 3.00000 | 0.144338 | ||||||||
\(433\) | 4.34315 | 0.208718 | 0.104359 | − | 0.994540i | \(-0.466721\pi\) | ||||
0.104359 | + | 0.994540i | \(0.466721\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −9.71573 | −0.465299 | ||||||||
\(437\) | 4.68629 | 0.224176 | ||||||||
\(438\) | −4.68629 | −0.223920 | ||||||||
\(439\) | 3.51472 | 0.167748 | 0.0838742 | − | 0.996476i | \(-0.473271\pi\) | ||||
0.0838742 | + | 0.996476i | \(0.473271\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 16.3137 | 0.776843 | ||||||||
\(442\) | −16.0000 | −0.761042 | ||||||||
\(443\) | −12.0000 | −0.570137 | −0.285069 | − | 0.958507i | \(-0.592016\pi\) | ||||
−0.285069 | + | 0.958507i | \(0.592016\pi\) | |||||||
\(444\) | 0.627417 | 0.0297759 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 7.31371 | 0.346314 | ||||||||
\(447\) | −18.4853 | −0.874324 | ||||||||
\(448\) | 20.1421 | 0.951626 | ||||||||
\(449\) | −2.97056 | −0.140190 | −0.0700948 | − | 0.997540i | \(-0.522330\pi\) | ||||
−0.0700948 | + | 0.997540i | \(0.522330\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 27.3726 | 1.28750 | ||||||||
\(453\) | 0.485281 | 0.0228005 | ||||||||
\(454\) | −5.79899 | −0.272160 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −1.85786 | −0.0870025 | ||||||||
\(457\) | −0.686292 | −0.0321034 | −0.0160517 | − | 0.999871i | \(-0.505110\pi\) | ||||
−0.0160517 | + | 0.999871i | \(0.505110\pi\) | |||||||
\(458\) | −0.828427 | −0.0387099 | ||||||||
\(459\) | −6.82843 | −0.318724 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 28.1421 | 1.31071 | 0.655355 | − | 0.755321i | \(-0.272519\pi\) | ||||
0.655355 | + | 0.755321i | \(0.272519\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 28.9706 | 1.34638 | 0.673188 | − | 0.739471i | \(-0.264924\pi\) | ||||
0.673188 | + | 0.739471i | \(0.264924\pi\) | |||||||
\(464\) | −2.48528 | −0.115376 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −5.45584 | −0.252737 | ||||||||
\(467\) | −22.6274 | −1.04707 | −0.523536 | − | 0.852004i | \(-0.675387\pi\) | ||||
−0.523536 | + | 0.852004i | \(0.675387\pi\) | |||||||
\(468\) | −10.3431 | −0.478112 | ||||||||
\(469\) | 27.3137 | 1.26123 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −18.0000 | −0.829396 | ||||||||
\(472\) | 6.34315 | 0.291967 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 3.51472 | 0.161436 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −60.2843 | −2.76313 | ||||||||
\(477\) | 13.3137 | 0.609593 | ||||||||
\(478\) | −2.62742 | −0.120175 | ||||||||
\(479\) | −3.02944 | −0.138419 | −0.0692093 | − | 0.997602i | \(-0.522048\pi\) | ||||
−0.0692093 | + | 0.997602i | \(0.522048\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1.94113 | −0.0885077 | ||||||||
\(482\) | 9.79899 | 0.446332 | ||||||||
\(483\) | −19.3137 | −0.878804 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0.414214 | 0.0187891 | ||||||||
\(487\) | −20.9706 | −0.950267 | −0.475133 | − | 0.879914i | \(-0.657600\pi\) | ||||
−0.475133 | + | 0.879914i | \(0.657600\pi\) | |||||||
\(488\) | −0.544156 | −0.0246328 | ||||||||
\(489\) | −15.3137 | −0.692510 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −25.6569 | −1.15788 | −0.578939 | − | 0.815371i | \(-0.696533\pi\) | ||||
−0.578939 | + | 0.815371i | \(0.696533\pi\) | |||||||
\(492\) | −1.51472 | −0.0682888 | ||||||||
\(493\) | 5.65685 | 0.254772 | ||||||||
\(494\) | 2.74517 | 0.123511 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −65.9411 | −2.95786 | ||||||||
\(498\) | −4.14214 | −0.185614 | ||||||||
\(499\) | −33.6569 | −1.50669 | −0.753344 | − | 0.657627i | \(-0.771560\pi\) | ||||
−0.753344 | + | 0.657627i | \(0.771560\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 9.31371 | 0.416106 | ||||||||
\(502\) | −5.37258 | −0.239790 | ||||||||
\(503\) | −5.31371 | −0.236927 | −0.118463 | − | 0.992958i | \(-0.537797\pi\) | ||||
−0.118463 | + | 0.992958i | \(0.537797\pi\) | |||||||
\(504\) | 7.65685 | 0.341063 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 19.0000 | 0.843820 | ||||||||
\(508\) | −4.54416 | −0.201614 | ||||||||
\(509\) | 41.3137 | 1.83120 | 0.915599 | − | 0.402093i | \(-0.131717\pi\) | ||||
0.915599 | + | 0.402093i | \(0.131717\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 54.6274 | 2.41657 | ||||||||
\(512\) | 22.7574 | 1.00574 | ||||||||
\(513\) | 1.17157 | 0.0517262 | ||||||||
\(514\) | 11.4558 | 0.505296 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 5.79899 | 0.255286 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0.686292 | 0.0301539 | ||||||||
\(519\) | −2.82843 | −0.124154 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 12.6274 | 0.553217 | 0.276609 | − | 0.960983i | \(-0.410789\pi\) | ||||
0.276609 | + | 0.960983i | \(0.410789\pi\) | |||||||
\(522\) | −0.343146 | −0.0150191 | ||||||||
\(523\) | −26.4853 | −1.15812 | −0.579060 | − | 0.815285i | \(-0.696580\pi\) | ||||
−0.579060 | + | 0.815285i | \(0.696580\pi\) | |||||||
\(524\) | −35.3137 | −1.54269 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 7.45584 | 0.325090 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −7.00000 | −0.304348 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −4.00000 | −0.173585 | ||||||||
\(532\) | 10.3431 | 0.448432 | ||||||||
\(533\) | 4.68629 | 0.202986 | ||||||||
\(534\) | −3.17157 | −0.137247 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 8.97056 | 0.387469 | ||||||||
\(537\) | −6.34315 | −0.273727 | ||||||||
\(538\) | −10.2010 | −0.439797 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 5.31371 | 0.228454 | 0.114227 | − | 0.993455i | \(-0.463561\pi\) | ||||
0.114227 | + | 0.993455i | \(0.463561\pi\) | |||||||
\(542\) | −11.5147 | −0.494600 | ||||||||
\(543\) | −14.0000 | −0.600798 | ||||||||
\(544\) | −30.1421 | −1.29233 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −11.3137 | −0.484182 | ||||||||
\(547\) | 20.1421 | 0.861216 | 0.430608 | − | 0.902539i | \(-0.358299\pi\) | ||||
0.430608 | + | 0.902539i | \(0.358299\pi\) | |||||||
\(548\) | 17.0294 | 0.727462 | ||||||||
\(549\) | 0.343146 | 0.0146451 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −0.970563 | −0.0413474 | ||||||||
\(552\) | −6.34315 | −0.269982 | ||||||||
\(553\) | −40.9706 | −1.74225 | ||||||||
\(554\) | −5.65685 | −0.240337 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −30.1421 | −1.27831 | ||||||||
\(557\) | 10.8284 | 0.458815 | 0.229408 | − | 0.973330i | \(-0.426321\pi\) | ||||
0.229408 | + | 0.973330i | \(0.426321\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −17.9411 | −0.758829 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 6.97056 | 0.294035 | ||||||||
\(563\) | 20.3431 | 0.857361 | 0.428681 | − | 0.903456i | \(-0.358979\pi\) | ||||
0.428681 | + | 0.903456i | \(0.358979\pi\) | |||||||
\(564\) | −7.31371 | −0.307963 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −1.31371 | −0.0552193 | ||||||||
\(567\) | −4.82843 | −0.202775 | ||||||||
\(568\) | −21.6569 | −0.908701 | ||||||||
\(569\) | −15.4558 | −0.647943 | −0.323971 | − | 0.946067i | \(-0.605018\pi\) | ||||
−0.323971 | + | 0.946067i | \(0.605018\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −0.485281 | −0.0203084 | −0.0101542 | − | 0.999948i | \(-0.503232\pi\) | ||||
−0.0101542 | + | 0.999948i | \(0.503232\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −5.65685 | −0.236318 | ||||||||
\(574\) | −1.65685 | −0.0691558 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −4.17157 | −0.173816 | ||||||||
\(577\) | −14.0000 | −0.582828 | −0.291414 | − | 0.956597i | \(-0.594126\pi\) | ||||
−0.291414 | + | 0.956597i | \(0.594126\pi\) | |||||||
\(578\) | 12.2721 | 0.510451 | ||||||||
\(579\) | 2.34315 | 0.0973778 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 48.2843 | 2.00317 | ||||||||
\(582\) | −0.142136 | −0.00589171 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 17.9411 | 0.742409 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −0.485281 | −0.0200468 | ||||||||
\(587\) | 30.6274 | 1.26413 | 0.632064 | − | 0.774916i | \(-0.282208\pi\) | ||||
0.632064 | + | 0.774916i | \(0.282208\pi\) | |||||||
\(588\) | −29.8284 | −1.23010 | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 8.48528 | 0.349038 | ||||||||
\(592\) | −1.02944 | −0.0423096 | ||||||||
\(593\) | −17.1716 | −0.705152 | −0.352576 | − | 0.935783i | \(-0.614694\pi\) | ||||
−0.352576 | + | 0.935783i | \(0.614694\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 33.7990 | 1.38446 | ||||||||
\(597\) | −10.3431 | −0.423317 | ||||||||
\(598\) | 9.37258 | 0.383273 | ||||||||
\(599\) | 4.68629 | 0.191477 | 0.0957383 | − | 0.995407i | \(-0.469479\pi\) | ||||
0.0957383 | + | 0.995407i | \(0.469479\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −17.3137 | −0.706241 | −0.353120 | − | 0.935578i | \(-0.614879\pi\) | ||||
−0.353120 | + | 0.935578i | \(0.614879\pi\) | |||||||
\(602\) | 6.34315 | 0.258527 | ||||||||
\(603\) | −5.65685 | −0.230365 | ||||||||
\(604\) | −0.887302 | −0.0361038 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −2.00000 | −0.0812444 | ||||||||
\(607\) | 18.4853 | 0.750294 | 0.375147 | − | 0.926965i | \(-0.377592\pi\) | ||||
0.375147 | + | 0.926965i | \(0.377592\pi\) | |||||||
\(608\) | 5.17157 | 0.209735 | ||||||||
\(609\) | 4.00000 | 0.162088 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 22.6274 | 0.915407 | ||||||||
\(612\) | 12.4853 | 0.504688 | ||||||||
\(613\) | 21.9411 | 0.886194 | 0.443097 | − | 0.896474i | \(-0.353880\pi\) | ||||
0.443097 | + | 0.896474i | \(0.353880\pi\) | |||||||
\(614\) | −3.65685 | −0.147579 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −11.6569 | −0.469287 | −0.234644 | − | 0.972081i | \(-0.575392\pi\) | ||||
−0.234644 | + | 0.972081i | \(0.575392\pi\) | |||||||
\(618\) | −8.00000 | −0.321807 | ||||||||
\(619\) | −25.6569 | −1.03124 | −0.515618 | − | 0.856819i | \(-0.672438\pi\) | ||||
−0.515618 | + | 0.856819i | \(0.672438\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 4.00000 | 0.160514 | ||||||||
\(622\) | 8.00000 | 0.320771 | ||||||||
\(623\) | 36.9706 | 1.48119 | ||||||||
\(624\) | 16.9706 | 0.679366 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −1.79899 | −0.0719021 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 32.9117 | 1.31332 | ||||||||
\(629\) | 2.34315 | 0.0934273 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 34.3431 | 1.36718 | 0.683590 | − | 0.729867i | \(-0.260418\pi\) | ||||
0.683590 | + | 0.729867i | \(0.260418\pi\) | |||||||
\(632\) | −13.4558 | −0.535245 | ||||||||
\(633\) | −6.82843 | −0.271406 | ||||||||
\(634\) | −12.5442 | −0.498192 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −24.3431 | −0.965269 | ||||||||
\(637\) | 92.2843 | 3.65644 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 13.6569 | 0.540257 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −26.9706 | −1.06527 | −0.532637 | − | 0.846344i | \(-0.678799\pi\) | ||||
−0.532637 | + | 0.846344i | \(0.678799\pi\) | |||||||
\(642\) | −2.20101 | −0.0868669 | ||||||||
\(643\) | 29.9411 | 1.18076 | 0.590381 | − | 0.807124i | \(-0.298977\pi\) | ||||
0.590381 | + | 0.807124i | \(0.298977\pi\) | |||||||
\(644\) | 35.3137 | 1.39156 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −3.31371 | −0.130376 | ||||||||
\(647\) | −27.3137 | −1.07381 | −0.536906 | − | 0.843642i | \(-0.680407\pi\) | ||||
−0.536906 | + | 0.843642i | \(0.680407\pi\) | |||||||
\(648\) | −1.58579 | −0.0622956 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 28.0000 | 1.09656 | ||||||||
\(653\) | 26.9706 | 1.05544 | 0.527720 | − | 0.849418i | \(-0.323047\pi\) | ||||
0.527720 | + | 0.849418i | \(0.323047\pi\) | |||||||
\(654\) | 2.20101 | 0.0860663 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 2.48528 | 0.0970339 | ||||||||
\(657\) | −11.3137 | −0.441390 | ||||||||
\(658\) | −8.00000 | −0.311872 | ||||||||
\(659\) | −7.31371 | −0.284902 | −0.142451 | − | 0.989802i | \(-0.545498\pi\) | ||||
−0.142451 | + | 0.989802i | \(0.545498\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −13.3137 | −0.517843 | −0.258922 | − | 0.965898i | \(-0.583367\pi\) | ||||
−0.258922 | + | 0.965898i | \(0.583367\pi\) | |||||||
\(662\) | 7.31371 | 0.284255 | ||||||||
\(663\) | −38.6274 | −1.50016 | ||||||||
\(664\) | 15.8579 | 0.615404 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −0.142136 | −0.00550764 | ||||||||
\(667\) | −3.31371 | −0.128307 | ||||||||
\(668\) | −17.0294 | −0.658889 | ||||||||
\(669\) | 17.6569 | 0.682653 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | −21.3137 | −0.822194 | ||||||||
\(673\) | 29.6569 | 1.14319 | 0.571594 | − | 0.820537i | \(-0.306325\pi\) | ||||
0.571594 | + | 0.820537i | \(0.306325\pi\) | |||||||
\(674\) | −8.00000 | −0.308148 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −34.7401 | −1.33616 | ||||||||
\(677\) | −21.4558 | −0.824615 | −0.412308 | − | 0.911045i | \(-0.635277\pi\) | ||||
−0.412308 | + | 0.911045i | \(0.635277\pi\) | |||||||
\(678\) | −6.20101 | −0.238148 | ||||||||
\(679\) | 1.65685 | 0.0635842 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −14.0000 | −0.536481 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −24.0000 | −0.918334 | −0.459167 | − | 0.888350i | \(-0.651852\pi\) | ||||
−0.459167 | + | 0.888350i | \(0.651852\pi\) | |||||||
\(684\) | −2.14214 | −0.0819066 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −18.6274 | −0.711198 | ||||||||
\(687\) | −2.00000 | −0.0763048 | ||||||||
\(688\) | −9.51472 | −0.362745 | ||||||||
\(689\) | 75.3137 | 2.86922 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 20.0000 | 0.760836 | 0.380418 | − | 0.924815i | \(-0.375780\pi\) | ||||
0.380418 | + | 0.924815i | \(0.375780\pi\) | |||||||
\(692\) | 5.17157 | 0.196594 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −2.76955 | −0.105131 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 1.31371 | 0.0497960 | ||||||||
\(697\) | −5.65685 | −0.214269 | ||||||||
\(698\) | 9.51472 | 0.360137 | ||||||||
\(699\) | −13.1716 | −0.498195 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −7.85786 | −0.296787 | −0.148394 | − | 0.988928i | \(-0.547410\pi\) | ||||
−0.148394 | + | 0.988928i | \(0.547410\pi\) | |||||||
\(702\) | 2.34315 | 0.0884363 | ||||||||
\(703\) | −0.402020 | −0.0151625 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −10.7696 | −0.405317 | ||||||||
\(707\) | 23.3137 | 0.876802 | ||||||||
\(708\) | 7.31371 | 0.274866 | ||||||||
\(709\) | 29.3137 | 1.10090 | 0.550450 | − | 0.834868i | \(-0.314456\pi\) | ||||
0.550450 | + | 0.834868i | \(0.314456\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 8.48528 | 0.318223 | ||||||||
\(712\) | 12.1421 | 0.455046 | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 13.6569 | 0.511095 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 11.5980 | 0.433437 | ||||||||
\(717\) | −6.34315 | −0.236889 | ||||||||
\(718\) | −4.97056 | −0.185500 | ||||||||
\(719\) | 31.5980 | 1.17841 | 0.589203 | − | 0.807985i | \(-0.299442\pi\) | ||||
0.589203 | + | 0.807985i | \(0.299442\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 93.2548 | 3.47299 | ||||||||
\(722\) | −7.30152 | −0.271734 | ||||||||
\(723\) | 23.6569 | 0.879808 | ||||||||
\(724\) | 25.5980 | 0.951341 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 33.9411 | 1.25881 | 0.629403 | − | 0.777079i | \(-0.283299\pi\) | ||||
0.629403 | + | 0.777079i | \(0.283299\pi\) | |||||||
\(728\) | 43.3137 | 1.60531 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 21.6569 | 0.801008 | ||||||||
\(732\) | −0.627417 | −0.0231900 | ||||||||
\(733\) | −17.6569 | −0.652171 | −0.326085 | − | 0.945340i | \(-0.605730\pi\) | ||||
−0.326085 | + | 0.945340i | \(0.605730\pi\) | |||||||
\(734\) | 0.686292 | 0.0253315 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 17.6569 | 0.650840 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0.343146 | 0.0126314 | ||||||||
\(739\) | −47.1127 | −1.73307 | −0.866534 | − | 0.499118i | \(-0.833658\pi\) | ||||
−0.866534 | + | 0.499118i | \(0.833658\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 6.62742 | 0.243464 | ||||||||
\(742\) | −26.6274 | −0.977523 | ||||||||
\(743\) | 47.6569 | 1.74836 | 0.874180 | − | 0.485602i | \(-0.161399\pi\) | ||||
0.874180 | + | 0.485602i | \(0.161399\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −14.3431 | −0.525140 | ||||||||
\(747\) | −10.0000 | −0.365881 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 25.6569 | 0.937481 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −36.2843 | −1.32403 | −0.662016 | − | 0.749490i | \(-0.730299\pi\) | ||||
−0.662016 | + | 0.749490i | \(0.730299\pi\) | |||||||
\(752\) | 12.0000 | 0.437595 | ||||||||
\(753\) | −12.9706 | −0.472674 | ||||||||
\(754\) | −1.94113 | −0.0706916 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 8.82843 | 0.321087 | ||||||||
\(757\) | −8.62742 | −0.313569 | −0.156784 | − | 0.987633i | \(-0.550113\pi\) | ||||
−0.156784 | + | 0.987633i | \(0.550113\pi\) | |||||||
\(758\) | −0.284271 | −0.0103252 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 23.1716 | 0.839969 | 0.419984 | − | 0.907531i | \(-0.362036\pi\) | ||||
0.419984 | + | 0.907531i | \(0.362036\pi\) | |||||||
\(762\) | 1.02944 | 0.0372926 | ||||||||
\(763\) | −25.6569 | −0.928840 | ||||||||
\(764\) | 10.3431 | 0.374202 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 3.31371 | 0.119729 | ||||||||
\(767\) | −22.6274 | −0.817029 | ||||||||
\(768\) | 3.97056 | 0.143275 | ||||||||
\(769\) | −33.3137 | −1.20132 | −0.600662 | − | 0.799503i | \(-0.705096\pi\) | ||||
−0.600662 | + | 0.799503i | \(0.705096\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 27.6569 | 0.996037 | ||||||||
\(772\) | −4.28427 | −0.154194 | ||||||||
\(773\) | 7.65685 | 0.275398 | 0.137699 | − | 0.990474i | \(-0.456029\pi\) | ||||
0.137699 | + | 0.990474i | \(0.456029\pi\) | |||||||
\(774\) | −1.31371 | −0.0472203 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0.544156 | 0.0195341 | ||||||||
\(777\) | 1.65685 | 0.0594393 | ||||||||
\(778\) | −5.11270 | −0.183299 | ||||||||
\(779\) | 0.970563 | 0.0347740 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | −11.3137 | −0.404577 | ||||||||
\(783\) | −0.828427 | −0.0296056 | ||||||||
\(784\) | 48.9411 | 1.74790 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 8.00000 | 0.285351 | ||||||||
\(787\) | 8.14214 | 0.290236 | 0.145118 | − | 0.989414i | \(-0.453644\pi\) | ||||
0.145118 | + | 0.989414i | \(0.453644\pi\) | |||||||
\(788\) | −15.5147 | −0.552689 | ||||||||
\(789\) | 18.0000 | 0.640817 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 72.2843 | 2.57013 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1.94113 | 0.0689314 | ||||||||
\(794\) | −7.85786 | −0.278865 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 18.9117 | 0.670307 | ||||||||
\(797\) | −1.02944 | −0.0364645 | −0.0182323 | − | 0.999834i | \(-0.505804\pi\) | ||||
−0.0182323 | + | 0.999834i | \(0.505804\pi\) | |||||||
\(798\) | −2.34315 | −0.0829465 | ||||||||
\(799\) | −27.3137 | −0.966290 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −7.65685 | −0.270542 | ||||||||
\(802\) | −12.1421 | −0.428754 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 10.3431 | 0.364775 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −24.6274 | −0.866926 | ||||||||
\(808\) | 7.65685 | 0.269367 | ||||||||
\(809\) | 56.4264 | 1.98385 | 0.991923 | − | 0.126838i | \(-0.0404829\pi\) | ||||
0.991923 | + | 0.126838i | \(0.0404829\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 16.4853 | 0.578877 | 0.289438 | − | 0.957197i | \(-0.406532\pi\) | ||||
0.289438 | + | 0.957197i | \(0.406532\pi\) | |||||||
\(812\) | −7.31371 | −0.256661 | ||||||||
\(813\) | −27.7990 | −0.974953 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −20.4853 | −0.717128 | ||||||||
\(817\) | −3.71573 | −0.129997 | ||||||||
\(818\) | 3.45584 | 0.120831 | ||||||||
\(819\) | −27.3137 | −0.954418 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 7.17157 | 0.250290 | 0.125145 | − | 0.992138i | \(-0.460060\pi\) | ||||
0.125145 | + | 0.992138i | \(0.460060\pi\) | |||||||
\(822\) | −3.85786 | −0.134558 | ||||||||
\(823\) | −16.0000 | −0.557725 | −0.278862 | − | 0.960331i | \(-0.589957\pi\) | ||||
−0.278862 | + | 0.960331i | \(0.589957\pi\) | |||||||
\(824\) | 30.6274 | 1.06696 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 8.00000 | 0.278356 | ||||||||
\(827\) | 18.6863 | 0.649786 | 0.324893 | − | 0.945751i | \(-0.394672\pi\) | ||||
0.324893 | + | 0.945751i | \(0.394672\pi\) | |||||||
\(828\) | −7.31371 | −0.254169 | ||||||||
\(829\) | −38.0000 | −1.31979 | −0.659897 | − | 0.751356i | \(-0.729400\pi\) | ||||
−0.659897 | + | 0.751356i | \(0.729400\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −13.6569 | −0.473751 | ||||||||
\(832\) | −23.5980 | −0.818113 | ||||||||
\(833\) | −111.397 | −3.85968 | ||||||||
\(834\) | 6.82843 | 0.236449 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −1.25483 | −0.0433475 | ||||||||
\(839\) | 22.6274 | 0.781185 | 0.390593 | − | 0.920564i | \(-0.372270\pi\) | ||||
0.390593 | + | 0.920564i | \(0.372270\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −28.3137 | −0.976335 | ||||||||
\(842\) | −2.48528 | −0.0856485 | ||||||||
\(843\) | 16.8284 | 0.579602 | ||||||||
\(844\) | 12.4853 | 0.429761 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 1.65685 | 0.0569638 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 39.9411 | 1.37158 | ||||||||
\(849\) | −3.17157 | −0.108848 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −1.37258 | −0.0470515 | ||||||||
\(852\) | −24.9706 | −0.855477 | ||||||||
\(853\) | −31.3137 | −1.07216 | −0.536080 | − | 0.844167i | \(-0.680096\pi\) | ||||
−0.536080 | + | 0.844167i | \(0.680096\pi\) | |||||||
\(854\) | −0.686292 | −0.0234844 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 8.42641 | 0.288009 | ||||||||
\(857\) | −11.5147 | −0.393335 | −0.196668 | − | 0.980470i | \(-0.563012\pi\) | ||||
−0.196668 | + | 0.980470i | \(0.563012\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −19.0294 | −0.649276 | −0.324638 | − | 0.945838i | \(-0.605242\pi\) | ||||
−0.324638 | + | 0.945838i | \(0.605242\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −4.00000 | −0.136320 | ||||||||
\(862\) | −4.28427 | −0.145923 | ||||||||
\(863\) | 43.3137 | 1.47442 | 0.737208 | − | 0.675666i | \(-0.236144\pi\) | ||||
0.737208 | + | 0.675666i | \(0.236144\pi\) | |||||||
\(864\) | 4.41421 | 0.150175 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 1.79899 | 0.0611322 | ||||||||
\(867\) | 29.6274 | 1.00620 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −32.0000 | −1.08428 | ||||||||
\(872\) | −8.42641 | −0.285354 | ||||||||
\(873\) | −0.343146 | −0.0116137 | ||||||||
\(874\) | 1.94113 | 0.0656595 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 20.6863 | 0.698925 | ||||||||
\(877\) | −42.6274 | −1.43943 | −0.719713 | − | 0.694272i | \(-0.755727\pi\) | ||||
−0.719713 | + | 0.694272i | \(0.755727\pi\) | |||||||
\(878\) | 1.45584 | 0.0491324 | ||||||||
\(879\) | −1.17157 | −0.0395162 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −13.0294 | −0.438973 | −0.219486 | − | 0.975616i | \(-0.570438\pi\) | ||||
−0.219486 | + | 0.975616i | \(0.570438\pi\) | |||||||
\(882\) | 6.75736 | 0.227532 | ||||||||
\(883\) | 50.6274 | 1.70375 | 0.851874 | − | 0.523747i | \(-0.175466\pi\) | ||||
0.851874 | + | 0.523747i | \(0.175466\pi\) | |||||||
\(884\) | 70.6274 | 2.37546 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −4.97056 | −0.166989 | ||||||||
\(887\) | −4.34315 | −0.145829 | −0.0729143 | − | 0.997338i | \(-0.523230\pi\) | ||||
−0.0729143 | + | 0.997338i | \(0.523230\pi\) | |||||||
\(888\) | 0.544156 | 0.0182607 | ||||||||
\(889\) | −12.0000 | −0.402467 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −32.2843 | −1.08096 | ||||||||
\(893\) | 4.68629 | 0.156821 | ||||||||
\(894\) | −7.65685 | −0.256084 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 50.9706 | 1.70281 | ||||||||
\(897\) | 22.6274 | 0.755507 | ||||||||
\(898\) | −1.23045 | −0.0410606 | ||||||||
\(899\) | 0 | 0 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −90.9117 | −3.02871 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 15.3137 | 0.509608 | ||||||||
\(904\) | 23.7401 | 0.789584 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0.201010 | 0.00667811 | ||||||||
\(907\) | −7.02944 | −0.233409 | −0.116704 | − | 0.993167i | \(-0.537233\pi\) | ||||
−0.116704 | + | 0.993167i | \(0.537233\pi\) | |||||||
\(908\) | 25.5980 | 0.849499 | ||||||||
\(909\) | −4.82843 | −0.160149 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −15.0294 | −0.497947 | −0.248974 | − | 0.968510i | \(-0.580093\pi\) | ||||
−0.248974 | + | 0.968510i | \(0.580093\pi\) | |||||||
\(912\) | 3.51472 | 0.116384 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | −0.284271 | −0.00940286 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 3.65685 | 0.120826 | ||||||||
\(917\) | −93.2548 | −3.07955 | ||||||||
\(918\) | −2.82843 | −0.0933520 | ||||||||
\(919\) | −28.4853 | −0.939643 | −0.469821 | − | 0.882762i | \(-0.655682\pi\) | ||||
−0.469821 | + | 0.882762i | \(0.655682\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −8.82843 | −0.290907 | ||||||||
\(922\) | 11.6569 | 0.383898 | ||||||||
\(923\) | 77.2548 | 2.54287 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 12.0000 | 0.394344 | ||||||||
\(927\) | −19.3137 | −0.634345 | ||||||||
\(928\) | −3.65685 | −0.120042 | ||||||||
\(929\) | 33.5980 | 1.10231 | 0.551157 | − | 0.834402i | \(-0.314187\pi\) | ||||
0.551157 | + | 0.834402i | \(0.314187\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 19.1127 | 0.626393 | ||||||||
\(932\) | 24.0833 | 0.788873 | ||||||||
\(933\) | 19.3137 | 0.632302 | ||||||||
\(934\) | −9.37258 | −0.306680 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −8.97056 | −0.293212 | ||||||||
\(937\) | 44.9706 | 1.46912 | 0.734562 | − | 0.678541i | \(-0.237388\pi\) | ||||
0.734562 | + | 0.678541i | \(0.237388\pi\) | |||||||
\(938\) | 11.3137 | 0.369406 | ||||||||
\(939\) | −4.34315 | −0.141733 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −38.7696 | −1.26385 | −0.631926 | − | 0.775029i | \(-0.717735\pi\) | ||||
−0.631926 | + | 0.775029i | \(0.717735\pi\) | |||||||
\(942\) | −7.45584 | −0.242925 | ||||||||
\(943\) | 3.31371 | 0.107909 | ||||||||
\(944\) | −12.0000 | −0.390567 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 38.6274 | 1.25522 | 0.627611 | − | 0.778527i | \(-0.284033\pi\) | ||||
0.627611 | + | 0.778527i | \(0.284033\pi\) | |||||||
\(948\) | −15.5147 | −0.503895 | ||||||||
\(949\) | −64.0000 | −2.07753 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −30.2843 | −0.982035 | ||||||||
\(952\) | −52.2843 | −1.69454 | ||||||||
\(953\) | 27.7990 | 0.900498 | 0.450249 | − | 0.892903i | \(-0.351335\pi\) | ||||
0.450249 | + | 0.892903i | \(0.351335\pi\) | |||||||
\(954\) | 5.51472 | 0.178546 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 11.5980 | 0.375105 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −1.25483 | −0.0405418 | ||||||||
\(959\) | 44.9706 | 1.45218 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −31.0000 | −1.00000 | ||||||||
\(962\) | −0.804041 | −0.0259233 | ||||||||
\(963\) | −5.31371 | −0.171232 | ||||||||
\(964\) | −43.2548 | −1.39314 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −8.00000 | −0.257396 | ||||||||
\(967\) | −39.4558 | −1.26881 | −0.634407 | − | 0.772999i | \(-0.718756\pi\) | ||||
−0.634407 | + | 0.772999i | \(0.718756\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −8.00000 | −0.256997 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 10.6274 | 0.341050 | 0.170525 | − | 0.985353i | \(-0.445454\pi\) | ||||
0.170525 | + | 0.985353i | \(0.445454\pi\) | |||||||
\(972\) | −1.82843 | −0.0586468 | ||||||||
\(973\) | −79.5980 | −2.55179 | ||||||||
\(974\) | −8.68629 | −0.278327 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 1.02944 | 0.0329515 | ||||||||
\(977\) | −25.3137 | −0.809857 | −0.404929 | − | 0.914348i | \(-0.632704\pi\) | ||||
−0.404929 | + | 0.914348i | \(0.632704\pi\) | |||||||
\(978\) | −6.34315 | −0.202831 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 5.31371 | 0.169654 | ||||||||
\(982\) | −10.6274 | −0.339135 | ||||||||
\(983\) | −14.6274 | −0.466542 | −0.233271 | − | 0.972412i | \(-0.574943\pi\) | ||||
−0.233271 | + | 0.972412i | \(0.574943\pi\) | |||||||
\(984\) | −1.31371 | −0.0418795 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 2.34315 | 0.0746210 | ||||||||
\(987\) | −19.3137 | −0.614762 | ||||||||
\(988\) | −12.1177 | −0.385517 | ||||||||
\(989\) | −12.6863 | −0.403401 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 14.6274 | 0.464655 | 0.232328 | − | 0.972638i | \(-0.425366\pi\) | ||||
0.232328 | + | 0.972638i | \(0.425366\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 17.6569 | 0.560323 | ||||||||
\(994\) | −27.3137 | −0.866338 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 18.2843 | 0.579359 | ||||||||
\(997\) | −16.6863 | −0.528460 | −0.264230 | − | 0.964460i | \(-0.585118\pi\) | ||||
−0.264230 | + | 0.964460i | \(0.585118\pi\) | |||||||
\(998\) | −13.9411 | −0.441299 | ||||||||
\(999\) | −0.343146 | −0.0108567 |
(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 | 9075.2.a.v.1.2 | 2 | ||
5.4 | even | 2 | 1815.2.a.k.1.1 | 2 | |||
11.10 | odd | 2 | 825.2.a.g.1.1 | 2 | |||
15.14 | odd | 2 | 5445.2.a.m.1.2 | 2 | |||
33.32 | even | 2 | 2475.2.a.m.1.2 | 2 | |||
55.32 | even | 4 | 825.2.c.e.199.2 | 4 | |||
55.43 | even | 4 | 825.2.c.e.199.3 | 4 | |||
55.54 | odd | 2 | 165.2.a.a.1.2 | ✓ | 2 | ||
165.32 | odd | 4 | 2475.2.c.m.199.3 | 4 | |||
165.98 | odd | 4 | 2475.2.c.m.199.2 | 4 | |||
165.164 | even | 2 | 495.2.a.d.1.1 | 2 | |||
220.219 | even | 2 | 2640.2.a.bb.1.2 | 2 | |||
385.384 | even | 2 | 8085.2.a.ba.1.2 | 2 | |||
660.659 | odd | 2 | 7920.2.a.cg.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
165.2.a.a.1.2 | ✓ | 2 | 55.54 | odd | 2 | ||
495.2.a.d.1.1 | 2 | 165.164 | even | 2 | |||
825.2.a.g.1.1 | 2 | 11.10 | odd | 2 | |||
825.2.c.e.199.2 | 4 | 55.32 | even | 4 | |||
825.2.c.e.199.3 | 4 | 55.43 | even | 4 | |||
1815.2.a.k.1.1 | 2 | 5.4 | even | 2 | |||
2475.2.a.m.1.2 | 2 | 33.32 | even | 2 | |||
2475.2.c.m.199.2 | 4 | 165.98 | odd | 4 | |||
2475.2.c.m.199.3 | 4 | 165.32 | odd | 4 | |||
2640.2.a.bb.1.2 | 2 | 220.219 | even | 2 | |||
5445.2.a.m.1.2 | 2 | 15.14 | odd | 2 | |||
7920.2.a.cg.1.2 | 2 | 660.659 | odd | 2 | |||
8085.2.a.ba.1.2 | 2 | 385.384 | even | 2 | |||
9075.2.a.v.1.2 | 2 | 1.1 | even | 1 | trivial |