Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3234,2,Mod(1,3234)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3234, 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("3234.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3234 = 2 \cdot 3 \cdot 7^{2} \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3234.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: | \(25.8236200137\) |
Analytic rank: | \(1\) |
Dimension: | \(4\) |
Coefficient field: | 4.4.14336.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 8x^{2} + 14 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Fricke sign: | \(+1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(2.32685\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3234.1 |
$q$-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 | ||||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 3.29066 | 1.47163 | 0.735813 | − | 0.677184i | \(-0.236800\pi\) | ||||
0.735813 | + | 0.677184i | \(0.236800\pi\) | |||||||
\(6\) | 1.00000 | 0.408248 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −3.29066 | −1.04060 | ||||||||
\(11\) | −1.00000 | −0.301511 | ||||||||
\(12\) | −1.00000 | −0.288675 | ||||||||
\(13\) | −6.06791 | −1.68293 | −0.841467 | − | 0.540308i | \(-0.818308\pi\) | ||||
−0.841467 | + | 0.540308i | \(0.818308\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −3.29066 | −0.849644 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 6.11908 | 1.48410 | 0.742048 | − | 0.670347i | \(-0.233855\pi\) | ||||
0.742048 | + | 0.670347i | \(0.233855\pi\) | |||||||
\(18\) | −1.00000 | −0.235702 | ||||||||
\(19\) | −0.0511786 | −0.0117412 | −0.00587059 | − | 0.999983i | \(-0.501869\pi\) | ||||
−0.00587059 | + | 0.999983i | \(0.501869\pi\) | |||||||
\(20\) | 3.29066 | 0.735813 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 1.00000 | 0.213201 | ||||||||
\(23\) | −6.75605 | −1.40873 | −0.704367 | − | 0.709836i | \(-0.748769\pi\) | ||||
−0.704367 | + | 0.709836i | \(0.748769\pi\) | |||||||
\(24\) | 1.00000 | 0.204124 | ||||||||
\(25\) | 5.82843 | 1.16569 | ||||||||
\(26\) | 6.06791 | 1.19001 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 2.82843 | 0.525226 | 0.262613 | − | 0.964901i | \(-0.415416\pi\) | ||||
0.262613 | + | 0.964901i | \(0.415416\pi\) | |||||||
\(30\) | 3.29066 | 0.600789 | ||||||||
\(31\) | −5.87644 | −1.05544 | −0.527720 | − | 0.849418i | \(-0.676953\pi\) | ||||
−0.527720 | + | 0.849418i | \(0.676953\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 1.00000 | 0.174078 | ||||||||
\(34\) | −6.11908 | −1.04941 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | −8.31055 | −1.36625 | −0.683123 | − | 0.730304i | \(-0.739379\pi\) | ||||
−0.683123 | + | 0.730304i | \(0.739379\pi\) | |||||||
\(38\) | 0.0511786 | 0.00830226 | ||||||||
\(39\) | 6.06791 | 0.971643 | ||||||||
\(40\) | −3.29066 | −0.520299 | ||||||||
\(41\) | −6.11908 | −0.955640 | −0.477820 | − | 0.878458i | \(-0.658573\pi\) | ||||
−0.477820 | + | 0.878458i | \(0.658573\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2.90080 | 0.442369 | 0.221184 | − | 0.975232i | \(-0.429008\pi\) | ||||
0.221184 | + | 0.975232i | \(0.429008\pi\) | |||||||
\(44\) | −1.00000 | −0.150756 | ||||||||
\(45\) | 3.29066 | 0.490542 | ||||||||
\(46\) | 6.75605 | 0.996125 | ||||||||
\(47\) | −1.22275 | −0.178357 | −0.0891783 | − | 0.996016i | \(-0.528424\pi\) | ||||
−0.0891783 | + | 0.996016i | \(0.528424\pi\) | |||||||
\(48\) | −1.00000 | −0.144338 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −5.82843 | −0.824264 | ||||||||
\(51\) | −6.11908 | −0.856843 | ||||||||
\(52\) | −6.06791 | −0.841467 | ||||||||
\(53\) | 3.00316 | 0.412516 | 0.206258 | − | 0.978498i | \(-0.433871\pi\) | ||||
0.206258 | + | 0.978498i | \(0.433871\pi\) | |||||||
\(54\) | 1.00000 | 0.136083 | ||||||||
\(55\) | −3.29066 | −0.443712 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0.0511786 | 0.00677877 | ||||||||
\(58\) | −2.82843 | −0.371391 | ||||||||
\(59\) | −10.8284 | −1.40974 | −0.704871 | − | 0.709336i | \(-0.748995\pi\) | ||||
−0.704871 | + | 0.709336i | \(0.748995\pi\) | |||||||
\(60\) | −3.29066 | −0.424822 | ||||||||
\(61\) | −7.23948 | −0.926920 | −0.463460 | − | 0.886118i | \(-0.653392\pi\) | ||||
−0.463460 | + | 0.886118i | \(0.653392\pi\) | |||||||
\(62\) | 5.87644 | 0.746309 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −19.9674 | −2.47665 | ||||||||
\(66\) | −1.00000 | −0.123091 | ||||||||
\(67\) | −1.68051 | −0.205307 | −0.102654 | − | 0.994717i | \(-0.532733\pi\) | ||||
−0.102654 | + | 0.994717i | \(0.532733\pi\) | |||||||
\(68\) | 6.11908 | 0.742048 | ||||||||
\(69\) | 6.75605 | 0.813333 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −6.47896 | −0.768911 | −0.384455 | − | 0.923144i | \(-0.625611\pi\) | ||||
−0.384455 | + | 0.923144i | \(0.625611\pi\) | |||||||
\(72\) | −1.00000 | −0.117851 | ||||||||
\(73\) | 11.6736 | 1.36629 | 0.683145 | − | 0.730283i | \(-0.260612\pi\) | ||||
0.683145 | + | 0.730283i | \(0.260612\pi\) | |||||||
\(74\) | 8.31055 | 0.966081 | ||||||||
\(75\) | −5.82843 | −0.673009 | ||||||||
\(76\) | −0.0511786 | −0.00587059 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −6.06791 | −0.687055 | ||||||||
\(79\) | −9.13897 | −1.02821 | −0.514107 | − | 0.857726i | \(-0.671877\pi\) | ||||
−0.514107 | + | 0.857726i | \(0.671877\pi\) | |||||||
\(80\) | 3.29066 | 0.367907 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 6.11908 | 0.675740 | ||||||||
\(83\) | −0.951983 | −0.104494 | −0.0522469 | − | 0.998634i | \(-0.516638\pi\) | ||||
−0.0522469 | + | 0.998634i | \(0.516638\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 20.1358 | 2.18404 | ||||||||
\(86\) | −2.90080 | −0.312802 | ||||||||
\(87\) | −2.82843 | −0.303239 | ||||||||
\(88\) | 1.00000 | 0.106600 | ||||||||
\(89\) | −16.5469 | −1.75396 | −0.876982 | − | 0.480523i | \(-0.840447\pi\) | ||||
−0.876982 | + | 0.480523i | \(0.840447\pi\) | |||||||
\(90\) | −3.29066 | −0.346866 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −6.75605 | −0.704367 | ||||||||
\(93\) | 5.87644 | 0.609359 | ||||||||
\(94\) | 1.22275 | 0.126117 | ||||||||
\(95\) | −0.168411 | −0.0172786 | ||||||||
\(96\) | 1.00000 | 0.102062 | ||||||||
\(97\) | 14.7216 | 1.49475 | 0.747376 | − | 0.664401i | \(-0.231313\pi\) | ||||
0.747376 | + | 0.664401i | \(0.231313\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −1.00000 | −0.100504 | ||||||||
\(100\) | 5.82843 | 0.582843 | ||||||||
\(101\) | −5.51657 | −0.548919 | −0.274460 | − | 0.961599i | \(-0.588499\pi\) | ||||
−0.274460 | + | 0.961599i | \(0.588499\pi\) | |||||||
\(102\) | 6.11908 | 0.605880 | ||||||||
\(103\) | −11.6781 | −1.15067 | −0.575336 | − | 0.817917i | \(-0.695129\pi\) | ||||
−0.575336 | + | 0.817917i | \(0.695129\pi\) | |||||||
\(104\) | 6.06791 | 0.595007 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −3.00316 | −0.291693 | ||||||||
\(107\) | 15.9611 | 1.54302 | 0.771508 | − | 0.636220i | \(-0.219503\pi\) | ||||
0.771508 | + | 0.636220i | \(0.219503\pi\) | |||||||
\(108\) | −1.00000 | −0.0962250 | ||||||||
\(109\) | −5.65053 | −0.541223 | −0.270611 | − | 0.962689i | \(-0.587226\pi\) | ||||
−0.270611 | + | 0.962689i | \(0.587226\pi\) | |||||||
\(110\) | 3.29066 | 0.313752 | ||||||||
\(111\) | 8.31055 | 0.788802 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −0.247112 | −0.0232463 | −0.0116232 | − | 0.999932i | \(-0.503700\pi\) | ||||
−0.0116232 | + | 0.999932i | \(0.503700\pi\) | |||||||
\(114\) | −0.0511786 | −0.00479331 | ||||||||
\(115\) | −22.2318 | −2.07313 | ||||||||
\(116\) | 2.82843 | 0.262613 | ||||||||
\(117\) | −6.06791 | −0.560978 | ||||||||
\(118\) | 10.8284 | 0.996838 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 3.29066 | 0.300395 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 7.23948 | 0.655432 | ||||||||
\(123\) | 6.11908 | 0.551739 | ||||||||
\(124\) | −5.87644 | −0.527720 | ||||||||
\(125\) | 2.72607 | 0.243827 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 13.3310 | 1.18294 | 0.591469 | − | 0.806328i | \(-0.298548\pi\) | ||||
0.591469 | + | 0.806328i | \(0.298548\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | −2.90080 | −0.255402 | ||||||||
\(130\) | 19.9674 | 1.75126 | ||||||||
\(131\) | −3.04802 | −0.266306 | −0.133153 | − | 0.991095i | \(-0.542510\pi\) | ||||
−0.133153 | + | 0.991095i | \(0.542510\pi\) | |||||||
\(132\) | 1.00000 | 0.0870388 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 1.68051 | 0.145174 | ||||||||
\(135\) | −3.29066 | −0.283215 | ||||||||
\(136\) | −6.11908 | −0.524707 | ||||||||
\(137\) | 8.47896 | 0.724406 | 0.362203 | − | 0.932099i | \(-0.382025\pi\) | ||||
0.362203 | + | 0.932099i | \(0.382025\pi\) | |||||||
\(138\) | −6.75605 | −0.575113 | ||||||||
\(139\) | 3.80407 | 0.322657 | 0.161328 | − | 0.986901i | \(-0.448422\pi\) | ||||
0.161328 | + | 0.986901i | \(0.448422\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 1.22275 | 0.102974 | ||||||||
\(142\) | 6.47896 | 0.543702 | ||||||||
\(143\) | 6.06791 | 0.507424 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | 9.30739 | 0.772936 | ||||||||
\(146\) | −11.6736 | −0.966113 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −8.31055 | −0.683123 | ||||||||
\(149\) | 24.1269 | 1.97655 | 0.988275 | − | 0.152684i | \(-0.0487916\pi\) | ||||
0.988275 | + | 0.152684i | \(0.0487916\pi\) | |||||||
\(150\) | 5.82843 | 0.475889 | ||||||||
\(151\) | 7.85525 | 0.639251 | 0.319625 | − | 0.947544i | \(-0.396443\pi\) | ||||
0.319625 | + | 0.947544i | \(0.396443\pi\) | |||||||
\(152\) | 0.0511786 | 0.00415113 | ||||||||
\(153\) | 6.11908 | 0.494699 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −19.3374 | −1.55321 | ||||||||
\(156\) | 6.06791 | 0.485821 | ||||||||
\(157\) | 18.2549 | 1.45690 | 0.728450 | − | 0.685099i | \(-0.240241\pi\) | ||||
0.728450 | + | 0.685099i | \(0.240241\pi\) | |||||||
\(158\) | 9.13897 | 0.727058 | ||||||||
\(159\) | −3.00316 | −0.238166 | ||||||||
\(160\) | −3.29066 | −0.260149 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −1.00000 | −0.0785674 | ||||||||
\(163\) | 2.34315 | 0.183529 | 0.0917647 | − | 0.995781i | \(-0.470749\pi\) | ||||
0.0917647 | + | 0.995781i | \(0.470749\pi\) | |||||||
\(164\) | −6.11908 | −0.477820 | ||||||||
\(165\) | 3.29066 | 0.256177 | ||||||||
\(166\) | 0.951983 | 0.0738882 | ||||||||
\(167\) | −19.7863 | −1.53111 | −0.765557 | − | 0.643369i | \(-0.777536\pi\) | ||||
−0.765557 | + | 0.643369i | \(0.777536\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 23.8195 | 1.83227 | ||||||||
\(170\) | −20.1358 | −1.54435 | ||||||||
\(171\) | −0.0511786 | −0.00391372 | ||||||||
\(172\) | 2.90080 | 0.221184 | ||||||||
\(173\) | −10.5768 | −0.804143 | −0.402071 | − | 0.915608i | \(-0.631710\pi\) | ||||
−0.402071 | + | 0.915608i | \(0.631710\pi\) | |||||||
\(174\) | 2.82843 | 0.214423 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −1.00000 | −0.0753778 | ||||||||
\(177\) | 10.8284 | 0.813914 | ||||||||
\(178\) | 16.5469 | 1.24024 | ||||||||
\(179\) | 18.3016 | 1.36793 | 0.683963 | − | 0.729517i | \(-0.260255\pi\) | ||||
0.683963 | + | 0.729517i | \(0.260255\pi\) | |||||||
\(180\) | 3.29066 | 0.245271 | ||||||||
\(181\) | −25.0499 | −1.86194 | −0.930971 | − | 0.365093i | \(-0.881037\pi\) | ||||
−0.930971 | + | 0.365093i | \(0.881037\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 7.23948 | 0.535158 | ||||||||
\(184\) | 6.75605 | 0.498063 | ||||||||
\(185\) | −27.3472 | −2.01060 | ||||||||
\(186\) | −5.87644 | −0.430882 | ||||||||
\(187\) | −6.11908 | −0.447472 | ||||||||
\(188\) | −1.22275 | −0.0891783 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0.168411 | 0.0122178 | ||||||||
\(191\) | −21.8650 | −1.58210 | −0.791050 | − | 0.611752i | \(-0.790465\pi\) | ||||
−0.791050 | + | 0.611752i | \(0.790465\pi\) | |||||||
\(192\) | −1.00000 | −0.0721688 | ||||||||
\(193\) | 20.8195 | 1.49862 | 0.749310 | − | 0.662220i | \(-0.230385\pi\) | ||||
0.749310 | + | 0.662220i | \(0.230385\pi\) | |||||||
\(194\) | −14.7216 | −1.05695 | ||||||||
\(195\) | 19.9674 | 1.42990 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −20.4790 | −1.45907 | −0.729533 | − | 0.683946i | \(-0.760262\pi\) | ||||
−0.729533 | + | 0.683946i | \(0.760262\pi\) | |||||||
\(198\) | 1.00000 | 0.0710669 | ||||||||
\(199\) | −15.5333 | −1.10113 | −0.550563 | − | 0.834794i | \(-0.685587\pi\) | ||||
−0.550563 | + | 0.834794i | \(0.685587\pi\) | |||||||
\(200\) | −5.82843 | −0.412132 | ||||||||
\(201\) | 1.68051 | 0.118534 | ||||||||
\(202\) | 5.51657 | 0.388145 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −6.11908 | −0.428422 | ||||||||
\(205\) | −20.1358 | −1.40635 | ||||||||
\(206\) | 11.6781 | 0.813649 | ||||||||
\(207\) | −6.75605 | −0.469578 | ||||||||
\(208\) | −6.06791 | −0.420734 | ||||||||
\(209\) | 0.0511786 | 0.00354010 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −6.40658 | −0.441047 | −0.220524 | − | 0.975382i | \(-0.570777\pi\) | ||||
−0.220524 | + | 0.975382i | \(0.570777\pi\) | |||||||
\(212\) | 3.00316 | 0.206258 | ||||||||
\(213\) | 6.47896 | 0.443931 | ||||||||
\(214\) | −15.9611 | −1.09108 | ||||||||
\(215\) | 9.54555 | 0.651001 | ||||||||
\(216\) | 1.00000 | 0.0680414 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 5.65053 | 0.382702 | ||||||||
\(219\) | −11.6736 | −0.788828 | ||||||||
\(220\) | −3.29066 | −0.221856 | ||||||||
\(221\) | −37.1300 | −2.49764 | ||||||||
\(222\) | −8.31055 | −0.557767 | ||||||||
\(223\) | −28.4912 | −1.90791 | −0.953956 | − | 0.299945i | \(-0.903032\pi\) | ||||
−0.953956 | + | 0.299945i | \(0.903032\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 5.82843 | 0.388562 | ||||||||
\(226\) | 0.247112 | 0.0164376 | ||||||||
\(227\) | 2.90326 | 0.192696 | 0.0963481 | − | 0.995348i | \(-0.469284\pi\) | ||||
0.0963481 | + | 0.995348i | \(0.469284\pi\) | |||||||
\(228\) | 0.0511786 | 0.00338938 | ||||||||
\(229\) | −6.11908 | −0.404360 | −0.202180 | − | 0.979348i | \(-0.564803\pi\) | ||||
−0.202180 | + | 0.979348i | \(0.564803\pi\) | |||||||
\(230\) | 22.2318 | 1.46592 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −2.82843 | −0.185695 | ||||||||
\(233\) | −11.6569 | −0.763666 | −0.381833 | − | 0.924231i | \(-0.624707\pi\) | ||||
−0.381833 | + | 0.924231i | \(0.624707\pi\) | |||||||
\(234\) | 6.06791 | 0.396671 | ||||||||
\(235\) | −4.02366 | −0.262474 | ||||||||
\(236\) | −10.8284 | −0.704871 | ||||||||
\(237\) | 9.13897 | 0.593640 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −21.3074 | −1.37826 | −0.689130 | − | 0.724638i | \(-0.742007\pi\) | ||||
−0.689130 | + | 0.724638i | \(0.742007\pi\) | |||||||
\(240\) | −3.29066 | −0.212411 | ||||||||
\(241\) | 11.8783 | 0.765148 | 0.382574 | − | 0.923925i | \(-0.375038\pi\) | ||||
0.382574 | + | 0.923925i | \(0.375038\pi\) | |||||||
\(242\) | −1.00000 | −0.0642824 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | −7.23948 | −0.463460 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −6.11908 | −0.390139 | ||||||||
\(247\) | 0.310547 | 0.0197596 | ||||||||
\(248\) | 5.87644 | 0.373155 | ||||||||
\(249\) | 0.951983 | 0.0603295 | ||||||||
\(250\) | −2.72607 | −0.172412 | ||||||||
\(251\) | 7.21135 | 0.455176 | 0.227588 | − | 0.973757i | \(-0.426916\pi\) | ||||
0.227588 | + | 0.973757i | \(0.426916\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 6.75605 | 0.424749 | ||||||||
\(254\) | −13.3310 | −0.836464 | ||||||||
\(255\) | −20.1358 | −1.26095 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −9.08840 | −0.566919 | −0.283459 | − | 0.958984i | \(-0.591482\pi\) | ||||
−0.283459 | + | 0.958984i | \(0.591482\pi\) | |||||||
\(258\) | 2.90080 | 0.180596 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −19.9674 | −1.23833 | ||||||||
\(261\) | 2.82843 | 0.175075 | ||||||||
\(262\) | 3.04802 | 0.188307 | ||||||||
\(263\) | 5.28373 | 0.325809 | 0.162904 | − | 0.986642i | \(-0.447914\pi\) | ||||
0.162904 | + | 0.986642i | \(0.447914\pi\) | |||||||
\(264\) | −1.00000 | −0.0615457 | ||||||||
\(265\) | 9.88238 | 0.607070 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 16.5469 | 1.01265 | ||||||||
\(268\) | −1.68051 | −0.102654 | ||||||||
\(269\) | −20.2151 | −1.23254 | −0.616269 | − | 0.787536i | \(-0.711356\pi\) | ||||
−0.616269 | + | 0.787536i | \(0.711356\pi\) | |||||||
\(270\) | 3.29066 | 0.200263 | ||||||||
\(271\) | −11.1779 | −0.679009 | −0.339504 | − | 0.940604i | \(-0.610259\pi\) | ||||
−0.339504 | + | 0.940604i | \(0.610259\pi\) | |||||||
\(272\) | 6.11908 | 0.371024 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −8.47896 | −0.512233 | ||||||||
\(275\) | −5.82843 | −0.351467 | ||||||||
\(276\) | 6.75605 | 0.406666 | ||||||||
\(277\) | 25.7376 | 1.54642 | 0.773212 | − | 0.634148i | \(-0.218649\pi\) | ||||
0.773212 | + | 0.634148i | \(0.218649\pi\) | |||||||
\(278\) | −3.80407 | −0.228153 | ||||||||
\(279\) | −5.87644 | −0.351813 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −12.0063 | −0.716237 | −0.358119 | − | 0.933676i | \(-0.616582\pi\) | ||||
−0.358119 | + | 0.933676i | \(0.616582\pi\) | |||||||
\(282\) | −1.22275 | −0.0728138 | ||||||||
\(283\) | 28.7746 | 1.71047 | 0.855237 | − | 0.518237i | \(-0.173411\pi\) | ||||
0.855237 | + | 0.518237i | \(0.173411\pi\) | |||||||
\(284\) | −6.47896 | −0.384455 | ||||||||
\(285\) | 0.168411 | 0.00997582 | ||||||||
\(286\) | −6.06791 | −0.358803 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −1.00000 | −0.0589256 | ||||||||
\(289\) | 20.4432 | 1.20254 | ||||||||
\(290\) | −9.30739 | −0.546548 | ||||||||
\(291\) | −14.7216 | −0.862995 | ||||||||
\(292\) | 11.6736 | 0.683145 | ||||||||
\(293\) | −20.2337 | −1.18207 | −0.591033 | − | 0.806648i | \(-0.701280\pi\) | ||||
−0.591033 | + | 0.806648i | \(0.701280\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −35.6326 | −2.07461 | ||||||||
\(296\) | 8.31055 | 0.483041 | ||||||||
\(297\) | 1.00000 | 0.0580259 | ||||||||
\(298\) | −24.1269 | −1.39763 | ||||||||
\(299\) | 40.9951 | 2.37081 | ||||||||
\(300\) | −5.82843 | −0.336504 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −7.85525 | −0.452019 | ||||||||
\(303\) | 5.51657 | 0.316919 | ||||||||
\(304\) | −0.0511786 | −0.00293529 | ||||||||
\(305\) | −23.8226 | −1.36408 | ||||||||
\(306\) | −6.11908 | −0.349805 | ||||||||
\(307\) | 17.5033 | 0.998967 | 0.499484 | − | 0.866323i | \(-0.333523\pi\) | ||||
0.499484 | + | 0.866323i | \(0.333523\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 11.6781 | 0.664341 | ||||||||
\(310\) | 19.3374 | 1.09829 | ||||||||
\(311\) | −30.0486 | −1.70390 | −0.851949 | − | 0.523625i | \(-0.824579\pi\) | ||||
−0.851949 | + | 0.523625i | \(0.824579\pi\) | |||||||
\(312\) | −6.06791 | −0.343528 | ||||||||
\(313\) | −24.6256 | −1.39192 | −0.695960 | − | 0.718081i | \(-0.745021\pi\) | ||||
−0.695960 | + | 0.718081i | \(0.745021\pi\) | |||||||
\(314\) | −18.2549 | −1.03018 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −9.13897 | −0.514107 | ||||||||
\(317\) | 11.1479 | 0.626129 | 0.313065 | − | 0.949732i | \(-0.398644\pi\) | ||||
0.313065 | + | 0.949732i | \(0.398644\pi\) | |||||||
\(318\) | 3.00316 | 0.168409 | ||||||||
\(319\) | −2.82843 | −0.158362 | ||||||||
\(320\) | 3.29066 | 0.183953 | ||||||||
\(321\) | −15.9611 | −0.890860 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −0.313166 | −0.0174250 | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | −35.3663 | −1.96177 | ||||||||
\(326\) | −2.34315 | −0.129775 | ||||||||
\(327\) | 5.65053 | 0.312475 | ||||||||
\(328\) | 6.11908 | 0.337870 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −3.29066 | −0.181145 | ||||||||
\(331\) | −4.16841 | −0.229117 | −0.114558 | − | 0.993417i | \(-0.536545\pi\) | ||||
−0.114558 | + | 0.993417i | \(0.536545\pi\) | |||||||
\(332\) | −0.951983 | −0.0522469 | ||||||||
\(333\) | −8.31055 | −0.455415 | ||||||||
\(334\) | 19.7863 | 1.08266 | ||||||||
\(335\) | −5.52998 | −0.302135 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −15.8163 | −0.861570 | −0.430785 | − | 0.902455i | \(-0.641763\pi\) | ||||
−0.430785 | + | 0.902455i | \(0.641763\pi\) | |||||||
\(338\) | −23.8195 | −1.29561 | ||||||||
\(339\) | 0.247112 | 0.0134213 | ||||||||
\(340\) | 20.1358 | 1.09202 | ||||||||
\(341\) | 5.87644 | 0.318227 | ||||||||
\(342\) | 0.0511786 | 0.00276742 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −2.90080 | −0.156401 | ||||||||
\(345\) | 22.2318 | 1.19692 | ||||||||
\(346\) | 10.5768 | 0.568615 | ||||||||
\(347\) | −16.1058 | −0.864606 | −0.432303 | − | 0.901728i | \(-0.642299\pi\) | ||||
−0.432303 | + | 0.901728i | \(0.642299\pi\) | |||||||
\(348\) | −2.82843 | −0.151620 | ||||||||
\(349\) | 9.19076 | 0.491970 | 0.245985 | − | 0.969274i | \(-0.420889\pi\) | ||||
0.245985 | + | 0.969274i | \(0.420889\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 6.06791 | 0.323881 | ||||||||
\(352\) | 1.00000 | 0.0533002 | ||||||||
\(353\) | −24.8874 | −1.32462 | −0.662311 | − | 0.749229i | \(-0.730424\pi\) | ||||
−0.662311 | + | 0.749229i | \(0.730424\pi\) | |||||||
\(354\) | −10.8284 | −0.575524 | ||||||||
\(355\) | −21.3200 | −1.13155 | ||||||||
\(356\) | −16.5469 | −0.876982 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −18.3016 | −0.967270 | ||||||||
\(359\) | −6.37945 | −0.336694 | −0.168347 | − | 0.985728i | \(-0.553843\pi\) | ||||
−0.168347 | + | 0.985728i | \(0.553843\pi\) | |||||||
\(360\) | −3.29066 | −0.173433 | ||||||||
\(361\) | −18.9974 | −0.999862 | ||||||||
\(362\) | 25.0499 | 1.31659 | ||||||||
\(363\) | −1.00000 | −0.0524864 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 38.4138 | 2.01067 | ||||||||
\(366\) | −7.23948 | −0.378414 | ||||||||
\(367\) | −6.26831 | −0.327203 | −0.163602 | − | 0.986526i | \(-0.552311\pi\) | ||||
−0.163602 | + | 0.986526i | \(0.552311\pi\) | |||||||
\(368\) | −6.75605 | −0.352183 | ||||||||
\(369\) | −6.11908 | −0.318547 | ||||||||
\(370\) | 27.3472 | 1.42171 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 5.87644 | 0.304679 | ||||||||
\(373\) | −10.8348 | −0.561002 | −0.280501 | − | 0.959854i | \(-0.590501\pi\) | ||||
−0.280501 | + | 0.959854i | \(0.590501\pi\) | |||||||
\(374\) | 6.11908 | 0.316410 | ||||||||
\(375\) | −2.72607 | −0.140774 | ||||||||
\(376\) | 1.22275 | 0.0630586 | ||||||||
\(377\) | −17.1626 | −0.883920 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 12.7658 | 0.655738 | 0.327869 | − | 0.944723i | \(-0.393670\pi\) | ||||
0.327869 | + | 0.944723i | \(0.393670\pi\) | |||||||
\(380\) | −0.168411 | −0.00863931 | ||||||||
\(381\) | −13.3310 | −0.682970 | ||||||||
\(382\) | 21.8650 | 1.11871 | ||||||||
\(383\) | 32.6633 | 1.66902 | 0.834509 | − | 0.550994i | \(-0.185751\pi\) | ||||
0.834509 | + | 0.550994i | \(0.185751\pi\) | |||||||
\(384\) | 1.00000 | 0.0510310 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −20.8195 | −1.05968 | ||||||||
\(387\) | 2.90080 | 0.147456 | ||||||||
\(388\) | 14.7216 | 0.747376 | ||||||||
\(389\) | 31.0179 | 1.57267 | 0.786334 | − | 0.617801i | \(-0.211976\pi\) | ||||
0.786334 | + | 0.617801i | \(0.211976\pi\) | |||||||
\(390\) | −19.9674 | −1.01109 | ||||||||
\(391\) | −41.3408 | −2.09070 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 3.04802 | 0.153752 | ||||||||
\(394\) | 20.4790 | 1.03171 | ||||||||
\(395\) | −30.0732 | −1.51315 | ||||||||
\(396\) | −1.00000 | −0.0502519 | ||||||||
\(397\) | 15.0986 | 0.757777 | 0.378888 | − | 0.925442i | \(-0.376306\pi\) | ||||
0.378888 | + | 0.925442i | \(0.376306\pi\) | |||||||
\(398\) | 15.5333 | 0.778614 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 5.82843 | 0.291421 | ||||||||
\(401\) | −9.16525 | −0.457691 | −0.228845 | − | 0.973463i | \(-0.573495\pi\) | ||||
−0.228845 | + | 0.973463i | \(0.573495\pi\) | |||||||
\(402\) | −1.68051 | −0.0838162 | ||||||||
\(403\) | 35.6577 | 1.77624 | ||||||||
\(404\) | −5.51657 | −0.274460 | ||||||||
\(405\) | 3.29066 | 0.163514 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 8.31055 | 0.411939 | ||||||||
\(408\) | 6.11908 | 0.302940 | ||||||||
\(409\) | 9.32149 | 0.460918 | 0.230459 | − | 0.973082i | \(-0.425977\pi\) | ||||
0.230459 | + | 0.973082i | \(0.425977\pi\) | |||||||
\(410\) | 20.1358 | 0.994437 | ||||||||
\(411\) | −8.47896 | −0.418236 | ||||||||
\(412\) | −11.6781 | −0.575336 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 6.75605 | 0.332042 | ||||||||
\(415\) | −3.13265 | −0.153776 | ||||||||
\(416\) | 6.06791 | 0.297504 | ||||||||
\(417\) | −3.80407 | −0.186286 | ||||||||
\(418\) | −0.0511786 | −0.00250323 | ||||||||
\(419\) | 13.5456 | 0.661744 | 0.330872 | − | 0.943676i | \(-0.392657\pi\) | ||||
0.330872 | + | 0.943676i | \(0.392657\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −9.10899 | −0.443945 | −0.221973 | − | 0.975053i | \(-0.571250\pi\) | ||||
−0.221973 | + | 0.975053i | \(0.571250\pi\) | |||||||
\(422\) | 6.40658 | 0.311867 | ||||||||
\(423\) | −1.22275 | −0.0594522 | ||||||||
\(424\) | −3.00316 | −0.145846 | ||||||||
\(425\) | 35.6646 | 1.72999 | ||||||||
\(426\) | −6.47896 | −0.313907 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 15.9611 | 0.771508 | ||||||||
\(429\) | −6.06791 | −0.292961 | ||||||||
\(430\) | −9.54555 | −0.460328 | ||||||||
\(431\) | 4.02366 | 0.193813 | 0.0969064 | − | 0.995294i | \(-0.469105\pi\) | ||||
0.0969064 | + | 0.995294i | \(0.469105\pi\) | |||||||
\(432\) | −1.00000 | −0.0481125 | ||||||||
\(433\) | 8.09789 | 0.389160 | 0.194580 | − | 0.980887i | \(-0.437666\pi\) | ||||
0.194580 | + | 0.980887i | \(0.437666\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −9.30739 | −0.446255 | ||||||||
\(436\) | −5.65053 | −0.270611 | ||||||||
\(437\) | 0.345765 | 0.0165402 | ||||||||
\(438\) | 11.6736 | 0.557785 | ||||||||
\(439\) | 6.82843 | 0.325903 | 0.162952 | − | 0.986634i | \(-0.447899\pi\) | ||||
0.162952 | + | 0.986634i | \(0.447899\pi\) | |||||||
\(440\) | 3.29066 | 0.156876 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 37.1300 | 1.76610 | ||||||||
\(443\) | −1.62055 | −0.0769947 | −0.0384974 | − | 0.999259i | \(-0.512257\pi\) | ||||
−0.0384974 | + | 0.999259i | \(0.512257\pi\) | |||||||
\(444\) | 8.31055 | 0.394401 | ||||||||
\(445\) | −54.4501 | −2.58118 | ||||||||
\(446\) | 28.4912 | 1.34910 | ||||||||
\(447\) | −24.1269 | −1.14116 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 30.1756 | 1.42407 | 0.712037 | − | 0.702142i | \(-0.247773\pi\) | ||||
0.712037 | + | 0.702142i | \(0.247773\pi\) | |||||||
\(450\) | −5.82843 | −0.274755 | ||||||||
\(451\) | 6.11908 | 0.288136 | ||||||||
\(452\) | −0.247112 | −0.0116232 | ||||||||
\(453\) | −7.85525 | −0.369072 | ||||||||
\(454\) | −2.90326 | −0.136257 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −0.0511786 | −0.00239666 | ||||||||
\(457\) | 11.3200 | 0.529529 | 0.264764 | − | 0.964313i | \(-0.414706\pi\) | ||||
0.264764 | + | 0.964313i | \(0.414706\pi\) | |||||||
\(458\) | 6.11908 | 0.285926 | ||||||||
\(459\) | −6.11908 | −0.285614 | ||||||||
\(460\) | −22.2318 | −1.03657 | ||||||||
\(461\) | 7.51025 | 0.349787 | 0.174894 | − | 0.984587i | \(-0.444042\pi\) | ||||
0.174894 | + | 0.984587i | \(0.444042\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −3.10899 | −0.144487 | −0.0722436 | − | 0.997387i | \(-0.523016\pi\) | ||||
−0.0722436 | + | 0.997387i | \(0.523016\pi\) | |||||||
\(464\) | 2.82843 | 0.131306 | ||||||||
\(465\) | 19.3374 | 0.896749 | ||||||||
\(466\) | 11.6569 | 0.539993 | ||||||||
\(467\) | −36.3189 | −1.68064 | −0.840320 | − | 0.542091i | \(-0.817633\pi\) | ||||
−0.840320 | + | 0.542091i | \(0.817633\pi\) | |||||||
\(468\) | −6.06791 | −0.280489 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 4.02366 | 0.185597 | ||||||||
\(471\) | −18.2549 | −0.841141 | ||||||||
\(472\) | 10.8284 | 0.498419 | ||||||||
\(473\) | −2.90080 | −0.133379 | ||||||||
\(474\) | −9.13897 | −0.419767 | ||||||||
\(475\) | −0.298291 | −0.0136865 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 3.00316 | 0.137505 | ||||||||
\(478\) | 21.3074 | 0.974577 | ||||||||
\(479\) | 30.5035 | 1.39374 | 0.696870 | − | 0.717198i | \(-0.254576\pi\) | ||||
0.696870 | + | 0.717198i | \(0.254576\pi\) | |||||||
\(480\) | 3.29066 | 0.150197 | ||||||||
\(481\) | 50.4276 | 2.29930 | ||||||||
\(482\) | −11.8783 | −0.541042 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 1.00000 | 0.0454545 | ||||||||
\(485\) | 48.4437 | 2.19972 | ||||||||
\(486\) | 1.00000 | 0.0453609 | ||||||||
\(487\) | −12.6001 | −0.570963 | −0.285482 | − | 0.958384i | \(-0.592154\pi\) | ||||
−0.285482 | + | 0.958384i | \(0.592154\pi\) | |||||||
\(488\) | 7.23948 | 0.327716 | ||||||||
\(489\) | −2.34315 | −0.105961 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −31.3137 | −1.41317 | −0.706584 | − | 0.707629i | \(-0.749765\pi\) | ||||
−0.706584 | + | 0.707629i | \(0.749765\pi\) | |||||||
\(492\) | 6.11908 | 0.275870 | ||||||||
\(493\) | 17.3074 | 0.779485 | ||||||||
\(494\) | −0.310547 | −0.0139722 | ||||||||
\(495\) | −3.29066 | −0.147904 | ||||||||
\(496\) | −5.87644 | −0.263860 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −0.951983 | −0.0426594 | ||||||||
\(499\) | −3.49477 | −0.156447 | −0.0782236 | − | 0.996936i | \(-0.524925\pi\) | ||||
−0.0782236 | + | 0.996936i | \(0.524925\pi\) | |||||||
\(500\) | 2.72607 | 0.121914 | ||||||||
\(501\) | 19.7863 | 0.883989 | ||||||||
\(502\) | −7.21135 | −0.321858 | ||||||||
\(503\) | −20.2627 | −0.903468 | −0.451734 | − | 0.892153i | \(-0.649194\pi\) | ||||
−0.451734 | + | 0.892153i | \(0.649194\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −18.1531 | −0.807804 | ||||||||
\(506\) | −6.75605 | −0.300343 | ||||||||
\(507\) | −23.8195 | −1.05786 | ||||||||
\(508\) | 13.3310 | 0.591469 | ||||||||
\(509\) | 18.4123 | 0.816111 | 0.408055 | − | 0.912957i | \(-0.366207\pi\) | ||||
0.408055 | + | 0.912957i | \(0.366207\pi\) | |||||||
\(510\) | 20.1358 | 0.891629 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 0.0511786 | 0.00225959 | ||||||||
\(514\) | 9.08840 | 0.400872 | ||||||||
\(515\) | −38.4285 | −1.69336 | ||||||||
\(516\) | −2.90080 | −0.127701 | ||||||||
\(517\) | 1.22275 | 0.0537765 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 10.5768 | 0.464272 | ||||||||
\(520\) | 19.9674 | 0.875628 | ||||||||
\(521\) | 24.0053 | 1.05169 | 0.525846 | − | 0.850580i | \(-0.323749\pi\) | ||||
0.525846 | + | 0.850580i | \(0.323749\pi\) | |||||||
\(522\) | −2.82843 | −0.123797 | ||||||||
\(523\) | −39.3894 | −1.72238 | −0.861189 | − | 0.508285i | \(-0.830280\pi\) | ||||
−0.861189 | + | 0.508285i | \(0.830280\pi\) | |||||||
\(524\) | −3.04802 | −0.133153 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −5.28373 | −0.230382 | ||||||||
\(527\) | −35.9585 | −1.56638 | ||||||||
\(528\) | 1.00000 | 0.0435194 | ||||||||
\(529\) | 22.6442 | 0.984531 | ||||||||
\(530\) | −9.88238 | −0.429263 | ||||||||
\(531\) | −10.8284 | −0.469914 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 37.1300 | 1.60828 | ||||||||
\(534\) | −16.5469 | −0.716053 | ||||||||
\(535\) | 52.5224 | 2.27074 | ||||||||
\(536\) | 1.68051 | 0.0725870 | ||||||||
\(537\) | −18.3016 | −0.789773 | ||||||||
\(538\) | 20.2151 | 0.871536 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −3.29066 | −0.141607 | ||||||||
\(541\) | 35.1064 | 1.50934 | 0.754670 | − | 0.656104i | \(-0.227797\pi\) | ||||
0.754670 | + | 0.656104i | \(0.227797\pi\) | |||||||
\(542\) | 11.1779 | 0.480132 | ||||||||
\(543\) | 25.0499 | 1.07499 | ||||||||
\(544\) | −6.11908 | −0.262354 | ||||||||
\(545\) | −18.5940 | −0.796478 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 30.3342 | 1.29700 | 0.648498 | − | 0.761216i | \(-0.275397\pi\) | ||||
0.648498 | + | 0.761216i | \(0.275397\pi\) | |||||||
\(548\) | 8.47896 | 0.362203 | ||||||||
\(549\) | −7.23948 | −0.308973 | ||||||||
\(550\) | 5.82843 | 0.248525 | ||||||||
\(551\) | −0.144755 | −0.00616676 | ||||||||
\(552\) | −6.75605 | −0.287557 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −25.7376 | −1.09349 | ||||||||
\(555\) | 27.3472 | 1.16082 | ||||||||
\(556\) | 3.80407 | 0.161328 | ||||||||
\(557\) | −36.0643 | −1.52809 | −0.764047 | − | 0.645161i | \(-0.776790\pi\) | ||||
−0.764047 | + | 0.645161i | \(0.776790\pi\) | |||||||
\(558\) | 5.87644 | 0.248770 | ||||||||
\(559\) | −17.6018 | −0.744477 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 6.11908 | 0.258348 | ||||||||
\(562\) | 12.0063 | 0.506456 | ||||||||
\(563\) | −38.7908 | −1.63484 | −0.817418 | − | 0.576046i | \(-0.804595\pi\) | ||||
−0.817418 | + | 0.576046i | \(0.804595\pi\) | |||||||
\(564\) | 1.22275 | 0.0514871 | ||||||||
\(565\) | −0.813161 | −0.0342099 | ||||||||
\(566\) | −28.7746 | −1.20949 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 6.47896 | 0.271851 | ||||||||
\(569\) | −12.4101 | −0.520257 | −0.260128 | − | 0.965574i | \(-0.583765\pi\) | ||||
−0.260128 | + | 0.965574i | \(0.583765\pi\) | |||||||
\(570\) | −0.168411 | −0.00705397 | ||||||||
\(571\) | −35.7863 | −1.49761 | −0.748806 | − | 0.662789i | \(-0.769372\pi\) | ||||
−0.748806 | + | 0.662789i | \(0.769372\pi\) | |||||||
\(572\) | 6.06791 | 0.253712 | ||||||||
\(573\) | 21.8650 | 0.913425 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −39.3771 | −1.64214 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | 24.1313 | 1.00460 | 0.502300 | − | 0.864693i | \(-0.332487\pi\) | ||||
0.502300 | + | 0.864693i | \(0.332487\pi\) | |||||||
\(578\) | −20.4432 | −0.850325 | ||||||||
\(579\) | −20.8195 | −0.865228 | ||||||||
\(580\) | 9.30739 | 0.386468 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 14.7216 | 0.610230 | ||||||||
\(583\) | −3.00316 | −0.124378 | ||||||||
\(584\) | −11.6736 | −0.483056 | ||||||||
\(585\) | −19.9674 | −0.825550 | ||||||||
\(586\) | 20.2337 | 0.835846 | ||||||||
\(587\) | 31.0539 | 1.28173 | 0.640867 | − | 0.767652i | \(-0.278575\pi\) | ||||
0.640867 | + | 0.767652i | \(0.278575\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0.300748 | 0.0123921 | ||||||||
\(590\) | 35.6326 | 1.46697 | ||||||||
\(591\) | 20.4790 | 0.842392 | ||||||||
\(592\) | −8.31055 | −0.341561 | ||||||||
\(593\) | 23.5378 | 0.966580 | 0.483290 | − | 0.875460i | \(-0.339442\pi\) | ||||
0.483290 | + | 0.875460i | \(0.339442\pi\) | |||||||
\(594\) | −1.00000 | −0.0410305 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 24.1269 | 0.988275 | ||||||||
\(597\) | 15.5333 | 0.635736 | ||||||||
\(598\) | −40.9951 | −1.67641 | ||||||||
\(599\) | −20.0037 | −0.817329 | −0.408665 | − | 0.912685i | \(-0.634005\pi\) | ||||
−0.408665 | + | 0.912685i | \(0.634005\pi\) | |||||||
\(600\) | 5.82843 | 0.237945 | ||||||||
\(601\) | 0.799053 | 0.0325940 | 0.0162970 | − | 0.999867i | \(-0.494812\pi\) | ||||
0.0162970 | + | 0.999867i | \(0.494812\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −1.68051 | −0.0684357 | ||||||||
\(604\) | 7.85525 | 0.319625 | ||||||||
\(605\) | 3.29066 | 0.133784 | ||||||||
\(606\) | −5.51657 | −0.224095 | ||||||||
\(607\) | −21.3200 | −0.865353 | −0.432677 | − | 0.901549i | \(-0.642431\pi\) | ||||
−0.432677 | + | 0.901549i | \(0.642431\pi\) | |||||||
\(608\) | 0.0511786 | 0.00207557 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 23.8226 | 0.964551 | ||||||||
\(611\) | 7.41954 | 0.300162 | ||||||||
\(612\) | 6.11908 | 0.247349 | ||||||||
\(613\) | −8.37398 | −0.338222 | −0.169111 | − | 0.985597i | \(-0.554090\pi\) | ||||
−0.169111 | + | 0.985597i | \(0.554090\pi\) | |||||||
\(614\) | −17.5033 | −0.706376 | ||||||||
\(615\) | 20.1358 | 0.811954 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 3.74395 | 0.150726 | 0.0753628 | − | 0.997156i | \(-0.475989\pi\) | ||||
0.0753628 | + | 0.997156i | \(0.475989\pi\) | |||||||
\(618\) | −11.6781 | −0.469760 | ||||||||
\(619\) | −0.924461 | −0.0371572 | −0.0185786 | − | 0.999827i | \(-0.505914\pi\) | ||||
−0.0185786 | + | 0.999827i | \(0.505914\pi\) | |||||||
\(620\) | −19.3374 | −0.776607 | ||||||||
\(621\) | 6.75605 | 0.271111 | ||||||||
\(622\) | 30.0486 | 1.20484 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 6.06791 | 0.242911 | ||||||||
\(625\) | −20.1716 | −0.806863 | ||||||||
\(626\) | 24.6256 | 0.984236 | ||||||||
\(627\) | −0.0511786 | −0.00204388 | ||||||||
\(628\) | 18.2549 | 0.728450 | ||||||||
\(629\) | −50.8529 | −2.02764 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 40.4374 | 1.60979 | 0.804894 | − | 0.593419i | \(-0.202222\pi\) | ||||
0.804894 | + | 0.593419i | \(0.202222\pi\) | |||||||
\(632\) | 9.13897 | 0.363529 | ||||||||
\(633\) | 6.40658 | 0.254639 | ||||||||
\(634\) | −11.1479 | −0.442740 | ||||||||
\(635\) | 43.8679 | 1.74084 | ||||||||
\(636\) | −3.00316 | −0.119083 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 2.82843 | 0.111979 | ||||||||
\(639\) | −6.47896 | −0.256304 | ||||||||
\(640\) | −3.29066 | −0.130075 | ||||||||
\(641\) | 13.6777 | 0.540235 | 0.270118 | − | 0.962827i | \(-0.412937\pi\) | ||||
0.270118 | + | 0.962827i | \(0.412937\pi\) | |||||||
\(642\) | 15.9611 | 0.629933 | ||||||||
\(643\) | 40.2627 | 1.58781 | 0.793903 | − | 0.608045i | \(-0.208046\pi\) | ||||
0.793903 | + | 0.608045i | \(0.208046\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −9.54555 | −0.375856 | ||||||||
\(646\) | 0.313166 | 0.0123214 | ||||||||
\(647\) | 6.61985 | 0.260253 | 0.130127 | − | 0.991497i | \(-0.458462\pi\) | ||||
0.130127 | + | 0.991497i | \(0.458462\pi\) | |||||||
\(648\) | −1.00000 | −0.0392837 | ||||||||
\(649\) | 10.8284 | 0.425053 | ||||||||
\(650\) | 35.3663 | 1.38718 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 2.34315 | 0.0917647 | ||||||||
\(653\) | −15.3200 | −0.599519 | −0.299760 | − | 0.954015i | \(-0.596906\pi\) | ||||
−0.299760 | + | 0.954015i | \(0.596906\pi\) | |||||||
\(654\) | −5.65053 | −0.220953 | ||||||||
\(655\) | −10.0300 | −0.391904 | ||||||||
\(656\) | −6.11908 | −0.238910 | ||||||||
\(657\) | 11.6736 | 0.455430 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 31.7690 | 1.23754 | 0.618772 | − | 0.785570i | \(-0.287630\pi\) | ||||
0.618772 | + | 0.785570i | \(0.287630\pi\) | |||||||
\(660\) | 3.29066 | 0.128089 | ||||||||
\(661\) | 29.8296 | 1.16024 | 0.580118 | − | 0.814532i | \(-0.303006\pi\) | ||||
0.580118 | + | 0.814532i | \(0.303006\pi\) | |||||||
\(662\) | 4.16841 | 0.162010 | ||||||||
\(663\) | 37.1300 | 1.44201 | ||||||||
\(664\) | 0.951983 | 0.0369441 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 8.31055 | 0.322027 | ||||||||
\(667\) | −19.1090 | −0.739903 | ||||||||
\(668\) | −19.7863 | −0.765557 | ||||||||
\(669\) | 28.4912 | 1.10153 | ||||||||
\(670\) | 5.52998 | 0.213642 | ||||||||
\(671\) | 7.23948 | 0.279477 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 23.7690 | 0.916228 | 0.458114 | − | 0.888893i | \(-0.348525\pi\) | ||||
0.458114 | + | 0.888893i | \(0.348525\pi\) | |||||||
\(674\) | 15.8163 | 0.609222 | ||||||||
\(675\) | −5.82843 | −0.224336 | ||||||||
\(676\) | 23.8195 | 0.916134 | ||||||||
\(677\) | 22.6368 | 0.870003 | 0.435002 | − | 0.900430i | \(-0.356748\pi\) | ||||
0.435002 | + | 0.900430i | \(0.356748\pi\) | |||||||
\(678\) | −0.247112 | −0.00949028 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −20.1358 | −0.772173 | ||||||||
\(681\) | −2.90326 | −0.111253 | ||||||||
\(682\) | −5.87644 | −0.225021 | ||||||||
\(683\) | 6.79583 | 0.260035 | 0.130018 | − | 0.991512i | \(-0.458497\pi\) | ||||
0.130018 | + | 0.991512i | \(0.458497\pi\) | |||||||
\(684\) | −0.0511786 | −0.00195686 | ||||||||
\(685\) | 27.9013 | 1.06606 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 6.11908 | 0.233458 | ||||||||
\(688\) | 2.90080 | 0.110592 | ||||||||
\(689\) | −18.2229 | −0.694237 | ||||||||
\(690\) | −22.2318 | −0.846352 | ||||||||
\(691\) | −16.2292 | −0.617389 | −0.308694 | − | 0.951161i | \(-0.599892\pi\) | ||||
−0.308694 | + | 0.951161i | \(0.599892\pi\) | |||||||
\(692\) | −10.5768 | −0.402071 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 16.1058 | 0.611369 | ||||||||
\(695\) | 12.5179 | 0.474830 | ||||||||
\(696\) | 2.82843 | 0.107211 | ||||||||
\(697\) | −37.4432 | −1.41826 | ||||||||
\(698\) | −9.19076 | −0.347875 | ||||||||
\(699\) | 11.6569 | 0.440903 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −32.3253 | −1.22091 | −0.610454 | − | 0.792052i | \(-0.709013\pi\) | ||||
−0.610454 | + | 0.792052i | \(0.709013\pi\) | |||||||
\(702\) | −6.06791 | −0.229018 | ||||||||
\(703\) | 0.425322 | 0.0160413 | ||||||||
\(704\) | −1.00000 | −0.0376889 | ||||||||
\(705\) | 4.02366 | 0.151540 | ||||||||
\(706\) | 24.8874 | 0.936649 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 10.8284 | 0.406957 | ||||||||
\(709\) | −10.8458 | −0.407321 | −0.203661 | − | 0.979042i | \(-0.565284\pi\) | ||||
−0.203661 | + | 0.979042i | \(0.565284\pi\) | |||||||
\(710\) | 21.3200 | 0.800127 | ||||||||
\(711\) | −9.13897 | −0.342738 | ||||||||
\(712\) | 16.5469 | 0.620120 | ||||||||
\(713\) | 39.7015 | 1.48683 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 19.9674 | 0.746738 | ||||||||
\(716\) | 18.3016 | 0.683963 | ||||||||
\(717\) | 21.3074 | 0.795739 | ||||||||
\(718\) | 6.37945 | 0.238079 | ||||||||
\(719\) | −3.69277 | −0.137717 | −0.0688585 | − | 0.997626i | \(-0.521936\pi\) | ||||
−0.0688585 | + | 0.997626i | \(0.521936\pi\) | |||||||
\(720\) | 3.29066 | 0.122636 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 18.9974 | 0.707009 | ||||||||
\(723\) | −11.8783 | −0.441759 | ||||||||
\(724\) | −25.0499 | −0.930971 | ||||||||
\(725\) | 16.4853 | 0.612248 | ||||||||
\(726\) | 1.00000 | 0.0371135 | ||||||||
\(727\) | −34.8470 | −1.29240 | −0.646202 | − | 0.763166i | \(-0.723644\pi\) | ||||
−0.646202 | + | 0.763166i | \(0.723644\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −38.4138 | −1.42176 | ||||||||
\(731\) | 17.7503 | 0.656517 | ||||||||
\(732\) | 7.23948 | 0.267579 | ||||||||
\(733\) | 39.9168 | 1.47436 | 0.737181 | − | 0.675696i | \(-0.236157\pi\) | ||||
0.737181 | + | 0.675696i | \(0.236157\pi\) | |||||||
\(734\) | 6.26831 | 0.231368 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 6.75605 | 0.249031 | ||||||||
\(737\) | 1.68051 | 0.0619024 | ||||||||
\(738\) | 6.11908 | 0.225247 | ||||||||
\(739\) | 4.77479 | 0.175644 | 0.0878218 | − | 0.996136i | \(-0.472009\pi\) | ||||
0.0878218 | + | 0.996136i | \(0.472009\pi\) | |||||||
\(740\) | −27.3472 | −1.00530 | ||||||||
\(741\) | −0.310547 | −0.0114082 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −25.1153 | −0.921392 | −0.460696 | − | 0.887558i | \(-0.652400\pi\) | ||||
−0.460696 | + | 0.887558i | \(0.652400\pi\) | |||||||
\(744\) | −5.87644 | −0.215441 | ||||||||
\(745\) | 79.3933 | 2.90874 | ||||||||
\(746\) | 10.8348 | 0.396688 | ||||||||
\(747\) | −0.951983 | −0.0348312 | ||||||||
\(748\) | −6.11908 | −0.223736 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 2.72607 | 0.0995420 | ||||||||
\(751\) | 54.7154 | 1.99659 | 0.998296 | − | 0.0583532i | \(-0.0185850\pi\) | ||||
0.998296 | + | 0.0583532i | \(0.0185850\pi\) | |||||||
\(752\) | −1.22275 | −0.0445892 | ||||||||
\(753\) | −7.21135 | −0.262796 | ||||||||
\(754\) | 17.1626 | 0.625026 | ||||||||
\(755\) | 25.8489 | 0.940739 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 16.9316 | 0.615391 | 0.307695 | − | 0.951485i | \(-0.400442\pi\) | ||||
0.307695 | + | 0.951485i | \(0.400442\pi\) | |||||||
\(758\) | −12.7658 | −0.463676 | ||||||||
\(759\) | −6.75605 | −0.245229 | ||||||||
\(760\) | 0.168411 | 0.00610892 | ||||||||
\(761\) | 4.16781 | 0.151083 | 0.0755414 | − | 0.997143i | \(-0.475931\pi\) | ||||
0.0755414 | + | 0.997143i | \(0.475931\pi\) | |||||||
\(762\) | 13.3310 | 0.482933 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −21.8650 | −0.791050 | ||||||||
\(765\) | 20.1358 | 0.728012 | ||||||||
\(766\) | −32.6633 | −1.18017 | ||||||||
\(767\) | 65.7059 | 2.37250 | ||||||||
\(768\) | −1.00000 | −0.0360844 | ||||||||
\(769\) | −16.8273 | −0.606807 | −0.303403 | − | 0.952862i | \(-0.598123\pi\) | ||||
−0.303403 | + | 0.952862i | \(0.598123\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 9.08840 | 0.327311 | ||||||||
\(772\) | 20.8195 | 0.749310 | ||||||||
\(773\) | 1.60929 | 0.0578822 | 0.0289411 | − | 0.999581i | \(-0.490786\pi\) | ||||
0.0289411 | + | 0.999581i | \(0.490786\pi\) | |||||||
\(774\) | −2.90080 | −0.104267 | ||||||||
\(775\) | −34.2504 | −1.23031 | ||||||||
\(776\) | −14.7216 | −0.528475 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −31.0179 | −1.11204 | ||||||||
\(779\) | 0.313166 | 0.0112203 | ||||||||
\(780\) | 19.9674 | 0.714948 | ||||||||
\(781\) | 6.47896 | 0.231835 | ||||||||
\(782\) | 41.3408 | 1.47835 | ||||||||
\(783\) | −2.82843 | −0.101080 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 60.0706 | 2.14401 | ||||||||
\(786\) | −3.04802 | −0.108719 | ||||||||
\(787\) | 32.6123 | 1.16250 | 0.581252 | − | 0.813724i | \(-0.302563\pi\) | ||||
0.581252 | + | 0.813724i | \(0.302563\pi\) | |||||||
\(788\) | −20.4790 | −0.729533 | ||||||||
\(789\) | −5.28373 | −0.188106 | ||||||||
\(790\) | 30.0732 | 1.06996 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 1.00000 | 0.0355335 | ||||||||
\(793\) | 43.9285 | 1.55995 | ||||||||
\(794\) | −15.0986 | −0.535829 | ||||||||
\(795\) | −9.88238 | −0.350492 | ||||||||
\(796\) | −15.5333 | −0.550563 | ||||||||
\(797\) | −35.4599 | −1.25605 | −0.628027 | − | 0.778191i | \(-0.716137\pi\) | ||||
−0.628027 | + | 0.778191i | \(0.716137\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −7.48212 | −0.264698 | ||||||||
\(800\) | −5.82843 | −0.206066 | ||||||||
\(801\) | −16.5469 | −0.584655 | ||||||||
\(802\) | 9.16525 | 0.323636 | ||||||||
\(803\) | −11.6736 | −0.411952 | ||||||||
\(804\) | 1.68051 | 0.0592670 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −35.6577 | −1.25599 | ||||||||
\(807\) | 20.2151 | 0.711606 | ||||||||
\(808\) | 5.51657 | 0.194072 | ||||||||
\(809\) | −53.3953 | −1.87728 | −0.938640 | − | 0.344899i | \(-0.887913\pi\) | ||||
−0.938640 | + | 0.344899i | \(0.887913\pi\) | |||||||
\(810\) | −3.29066 | −0.115622 | ||||||||
\(811\) | −0.178048 | −0.00625211 | −0.00312606 | − | 0.999995i | \(-0.500995\pi\) | ||||
−0.00312606 | + | 0.999995i | \(0.500995\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 11.1779 | 0.392026 | ||||||||
\(814\) | −8.31055 | −0.291285 | ||||||||
\(815\) | 7.71049 | 0.270087 | ||||||||
\(816\) | −6.11908 | −0.214211 | ||||||||
\(817\) | −0.148459 | −0.00519392 | ||||||||
\(818\) | −9.32149 | −0.325918 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −20.1358 | −0.703173 | ||||||||
\(821\) | 4.15740 | 0.145094 | 0.0725472 | − | 0.997365i | \(-0.476887\pi\) | ||||
0.0725472 | + | 0.997365i | \(0.476887\pi\) | |||||||
\(822\) | 8.47896 | 0.295738 | ||||||||
\(823\) | 0.0210370 | 0.000733305 0 | 0.000366653 | − | 1.00000i | \(-0.499883\pi\) | ||||
0.000366653 | 1.00000i | \(0.499883\pi\) | ||||||||
\(824\) | 11.6781 | 0.406824 | ||||||||
\(825\) | 5.82843 | 0.202920 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −43.7774 | −1.52229 | −0.761145 | − | 0.648582i | \(-0.775362\pi\) | ||||
−0.761145 | + | 0.648582i | \(0.775362\pi\) | |||||||
\(828\) | −6.75605 | −0.234789 | ||||||||
\(829\) | −32.0602 | −1.11350 | −0.556749 | − | 0.830681i | \(-0.687951\pi\) | ||||
−0.556749 | + | 0.830681i | \(0.687951\pi\) | |||||||
\(830\) | 3.13265 | 0.108736 | ||||||||
\(831\) | −25.7376 | −0.892828 | ||||||||
\(832\) | −6.06791 | −0.210367 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 3.80407 | 0.131724 | ||||||||
\(835\) | −65.1101 | −2.25323 | ||||||||
\(836\) | 0.0511786 | 0.00177005 | ||||||||
\(837\) | 5.87644 | 0.203120 | ||||||||
\(838\) | −13.5456 | −0.467923 | ||||||||
\(839\) | −6.92200 | −0.238974 | −0.119487 | − | 0.992836i | \(-0.538125\pi\) | ||||
−0.119487 | + | 0.992836i | \(0.538125\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −21.0000 | −0.724138 | ||||||||
\(842\) | 9.10899 | 0.313917 | ||||||||
\(843\) | 12.0063 | 0.413520 | ||||||||
\(844\) | −6.40658 | −0.220524 | ||||||||
\(845\) | 78.3818 | 2.69641 | ||||||||
\(846\) | 1.22275 | 0.0420391 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 3.00316 | 0.103129 | ||||||||
\(849\) | −28.7746 | −0.987543 | ||||||||
\(850\) | −35.6646 | −1.22329 | ||||||||
\(851\) | 56.1465 | 1.92468 | ||||||||
\(852\) | 6.47896 | 0.221965 | ||||||||
\(853\) | 27.4727 | 0.940648 | 0.470324 | − | 0.882494i | \(-0.344137\pi\) | ||||
0.470324 | + | 0.882494i | \(0.344137\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −0.168411 | −0.00575954 | ||||||||
\(856\) | −15.9611 | −0.545538 | ||||||||
\(857\) | 30.1949 | 1.03144 | 0.515720 | − | 0.856757i | \(-0.327525\pi\) | ||||
0.515720 | + | 0.856757i | \(0.327525\pi\) | |||||||
\(858\) | 6.06791 | 0.207155 | ||||||||
\(859\) | −42.2869 | −1.44281 | −0.721405 | − | 0.692513i | \(-0.756503\pi\) | ||||
−0.721405 | + | 0.692513i | \(0.756503\pi\) | |||||||
\(860\) | 9.54555 | 0.325501 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −4.02366 | −0.137046 | ||||||||
\(863\) | 45.0340 | 1.53298 | 0.766488 | − | 0.642259i | \(-0.222003\pi\) | ||||
0.766488 | + | 0.642259i | \(0.222003\pi\) | |||||||
\(864\) | 1.00000 | 0.0340207 | ||||||||
\(865\) | −34.8048 | −1.18340 | ||||||||
\(866\) | −8.09789 | −0.275177 | ||||||||
\(867\) | −20.4432 | −0.694287 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 9.13897 | 0.310018 | ||||||||
\(870\) | 9.30739 | 0.315550 | ||||||||
\(871\) | 10.1972 | 0.345518 | ||||||||
\(872\) | 5.65053 | 0.191351 | ||||||||
\(873\) | 14.7216 | 0.498251 | ||||||||
\(874\) | −0.345765 | −0.0116957 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −11.6736 | −0.394414 | ||||||||
\(877\) | −42.6684 | −1.44081 | −0.720405 | − | 0.693554i | \(-0.756044\pi\) | ||||
−0.720405 | + | 0.693554i | \(0.756044\pi\) | |||||||
\(878\) | −6.82843 | −0.230448 | ||||||||
\(879\) | 20.2337 | 0.682466 | ||||||||
\(880\) | −3.29066 | −0.110928 | ||||||||
\(881\) | −11.1844 | −0.376813 | −0.188407 | − | 0.982091i | \(-0.560332\pi\) | ||||
−0.188407 | + | 0.982091i | \(0.560332\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −24.2843 | −0.817231 | −0.408615 | − | 0.912707i | \(-0.633988\pi\) | ||||
−0.408615 | + | 0.912707i | \(0.633988\pi\) | |||||||
\(884\) | −37.1300 | −1.24882 | ||||||||
\(885\) | 35.6326 | 1.19778 | ||||||||
\(886\) | 1.62055 | 0.0544435 | ||||||||
\(887\) | 26.2779 | 0.882327 | 0.441164 | − | 0.897427i | \(-0.354566\pi\) | ||||
0.441164 | + | 0.897427i | \(0.354566\pi\) | |||||||
\(888\) | −8.31055 | −0.278884 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 54.4501 | 1.82517 | ||||||||
\(891\) | −1.00000 | −0.0335013 | ||||||||
\(892\) | −28.4912 | −0.953956 | ||||||||
\(893\) | 0.0625787 | 0.00209412 | ||||||||
\(894\) | 24.1269 | 0.806923 | ||||||||
\(895\) | 60.2243 | 2.01308 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −40.9951 | −1.36879 | ||||||||
\(898\) | −30.1756 | −1.00697 | ||||||||
\(899\) | −16.6211 | −0.554345 | ||||||||
\(900\) | 5.82843 | 0.194281 | ||||||||
\(901\) | 18.3766 | 0.612213 | ||||||||
\(902\) | −6.11908 | −0.203743 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0.247112 | 0.00821882 | ||||||||
\(905\) | −82.4305 | −2.74008 | ||||||||
\(906\) | 7.85525 | 0.260973 | ||||||||
\(907\) | −48.9164 | −1.62424 | −0.812121 | − | 0.583489i | \(-0.801687\pi\) | ||||
−0.812121 | + | 0.583489i | \(0.801687\pi\) | |||||||
\(908\) | 2.90326 | 0.0963481 | ||||||||
\(909\) | −5.51657 | −0.182973 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 8.95444 | 0.296674 | 0.148337 | − | 0.988937i | \(-0.452608\pi\) | ||||
0.148337 | + | 0.988937i | \(0.452608\pi\) | |||||||
\(912\) | 0.0511786 | 0.00169469 | ||||||||
\(913\) | 0.951983 | 0.0315060 | ||||||||
\(914\) | −11.3200 | −0.374433 | ||||||||
\(915\) | 23.8226 | 0.787552 | ||||||||
\(916\) | −6.11908 | −0.202180 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 6.11908 | 0.201960 | ||||||||
\(919\) | −11.9222 | −0.393276 | −0.196638 | − | 0.980476i | \(-0.563002\pi\) | ||||
−0.196638 | + | 0.980476i | \(0.563002\pi\) | |||||||
\(920\) | 22.2318 | 0.732962 | ||||||||
\(921\) | −17.5033 | −0.576754 | ||||||||
\(922\) | −7.51025 | −0.247337 | ||||||||
\(923\) | 39.3137 | 1.29403 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −48.4374 | −1.59261 | ||||||||
\(926\) | 3.10899 | 0.102168 | ||||||||
\(927\) | −11.6781 | −0.383558 | ||||||||
\(928\) | −2.82843 | −0.0928477 | ||||||||
\(929\) | 13.9105 | 0.456389 | 0.228194 | − | 0.973616i | \(-0.426718\pi\) | ||||
0.228194 | + | 0.973616i | \(0.426718\pi\) | |||||||
\(930\) | −19.3374 | −0.634097 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −11.6569 | −0.381833 | ||||||||
\(933\) | 30.0486 | 0.983746 | ||||||||
\(934\) | 36.3189 | 1.18839 | ||||||||
\(935\) | −20.1358 | −0.658511 | ||||||||
\(936\) | 6.06791 | 0.198336 | ||||||||
\(937\) | −20.0104 | −0.653711 | −0.326856 | − | 0.945074i | \(-0.605989\pi\) | ||||
−0.326856 | + | 0.945074i | \(0.605989\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 24.6256 | 0.803625 | ||||||||
\(940\) | −4.02366 | −0.131237 | ||||||||
\(941\) | 54.9084 | 1.78996 | 0.894982 | − | 0.446103i | \(-0.147188\pi\) | ||||
0.894982 | + | 0.446103i | \(0.147188\pi\) | |||||||
\(942\) | 18.2549 | 0.594777 | ||||||||
\(943\) | 41.3408 | 1.34624 | ||||||||
\(944\) | −10.8284 | −0.352435 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 2.90080 | 0.0943133 | ||||||||
\(947\) | −7.39850 | −0.240419 | −0.120210 | − | 0.992749i | \(-0.538357\pi\) | ||||
−0.120210 | + | 0.992749i | \(0.538357\pi\) | |||||||
\(948\) | 9.13897 | 0.296820 | ||||||||
\(949\) | −70.8342 | −2.29938 | ||||||||
\(950\) | 0.298291 | 0.00967782 | ||||||||
\(951\) | −11.1479 | −0.361496 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 21.1416 | 0.684843 | 0.342422 | − | 0.939546i | \(-0.388753\pi\) | ||||
0.342422 | + | 0.939546i | \(0.388753\pi\) | |||||||
\(954\) | −3.00316 | −0.0972310 | ||||||||
\(955\) | −71.9504 | −2.32826 | ||||||||
\(956\) | −21.3074 | −0.689130 | ||||||||
\(957\) | 2.82843 | 0.0914301 | ||||||||
\(958\) | −30.5035 | −0.985522 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −3.29066 | −0.106206 | ||||||||
\(961\) | 3.53259 | 0.113955 | ||||||||
\(962\) | −50.4276 | −1.62585 | ||||||||
\(963\) | 15.9611 | 0.514339 | ||||||||
\(964\) | 11.8783 | 0.382574 | ||||||||
\(965\) | 68.5098 | 2.20541 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 11.7174 | 0.376807 | 0.188404 | − | 0.982092i | \(-0.439669\pi\) | ||||
0.188404 | + | 0.982092i | \(0.439669\pi\) | |||||||
\(968\) | −1.00000 | −0.0321412 | ||||||||
\(969\) | 0.313166 | 0.0100603 | ||||||||
\(970\) | −48.4437 | −1.55543 | ||||||||
\(971\) | −35.9487 | −1.15365 | −0.576824 | − | 0.816869i | \(-0.695708\pi\) | ||||
−0.576824 | + | 0.816869i | \(0.695708\pi\) | |||||||
\(972\) | −1.00000 | −0.0320750 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 12.6001 | 0.403732 | ||||||||
\(975\) | 35.3663 | 1.13263 | ||||||||
\(976\) | −7.23948 | −0.231730 | ||||||||
\(977\) | −4.33561 | −0.138709 | −0.0693543 | − | 0.997592i | \(-0.522094\pi\) | ||||
−0.0693543 | + | 0.997592i | \(0.522094\pi\) | |||||||
\(978\) | 2.34315 | 0.0749255 | ||||||||
\(979\) | 16.5469 | 0.528840 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −5.65053 | −0.180408 | ||||||||
\(982\) | 31.3137 | 0.999261 | ||||||||
\(983\) | 16.3444 | 0.521305 | 0.260653 | − | 0.965433i | \(-0.416062\pi\) | ||||
0.260653 | + | 0.965433i | \(0.416062\pi\) | |||||||
\(984\) | −6.11908 | −0.195069 | ||||||||
\(985\) | −67.3892 | −2.14720 | ||||||||
\(986\) | −17.3074 | −0.551179 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0.310547 | 0.00987981 | ||||||||
\(989\) | −19.5980 | −0.623180 | ||||||||
\(990\) | 3.29066 | 0.104584 | ||||||||
\(991\) | 11.5657 | 0.367398 | 0.183699 | − | 0.982983i | \(-0.441193\pi\) | ||||
0.183699 | + | 0.982983i | \(0.441193\pi\) | |||||||
\(992\) | 5.87644 | 0.186577 | ||||||||
\(993\) | 4.16841 | 0.132281 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −51.1148 | −1.62045 | ||||||||
\(996\) | 0.951983 | 0.0301647 | ||||||||
\(997\) | −41.6956 | −1.32051 | −0.660257 | − | 0.751040i | \(-0.729553\pi\) | ||||
−0.660257 | + | 0.751040i | \(0.729553\pi\) | |||||||
\(998\) | 3.49477 | 0.110625 | ||||||||
\(999\) | 8.31055 | 0.262934 |
(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 | 3234.2.a.bj.1.4 | ✓ | 4 | |
3.2 | odd | 2 | 9702.2.a.eb.1.1 | 4 | |||
7.6 | odd | 2 | 3234.2.a.bk.1.1 | yes | 4 | ||
21.20 | even | 2 | 9702.2.a.ec.1.4 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
3234.2.a.bj.1.4 | ✓ | 4 | 1.1 | even | 1 | trivial | |
3234.2.a.bk.1.1 | yes | 4 | 7.6 | odd | 2 | ||
9702.2.a.eb.1.1 | 4 | 3.2 | odd | 2 | |||
9702.2.a.ec.1.4 | 4 | 21.20 | even | 2 |