Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8001,2,Mod(1,8001)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8001, 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("8001.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8001 = 3^{2} \cdot 7 \cdot 127 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8001.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: | \(63.8883066572\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 2 x^{15} - 20 x^{14} + 38 x^{13} + 155 x^{12} - 275 x^{11} - 593 x^{10} + 957 x^{9} + 1177 x^{8} - 1655 x^{7} - 1150 x^{6} + 1279 x^{5} + 474 x^{4} - 280 x^{3} - 83 x^{2} + \cdots + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 889) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.6 | ||
Root | \(-0.532475\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8001.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.532475 | −0.376517 | −0.188258 | − | 0.982120i | \(-0.560284\pi\) | ||||
−0.188258 | + | 0.982120i | \(0.560284\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −1.71647 | −0.858235 | ||||||||
\(5\) | 0.118172 | 0.0528481 | 0.0264241 | − | 0.999651i | \(-0.491588\pi\) | ||||
0.0264241 | + | 0.999651i | \(0.491588\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | 1.97893 | 0.699657 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −0.0629236 | −0.0198982 | ||||||||
\(11\) | 5.22568 | 1.57560 | 0.787800 | − | 0.615931i | \(-0.211220\pi\) | ||||
0.787800 | + | 0.615931i | \(0.211220\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.19166 | −0.607856 | −0.303928 | − | 0.952695i | \(-0.598298\pi\) | ||||
−0.303928 | + | 0.952695i | \(0.598298\pi\) | |||||||
\(14\) | 0.532475 | 0.142310 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 2.37921 | 0.594803 | ||||||||
\(17\) | 1.28158 | 0.310829 | 0.155415 | − | 0.987849i | \(-0.450329\pi\) | ||||
0.155415 | + | 0.987849i | \(0.450329\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 8.34525 | 1.91453 | 0.957266 | − | 0.289210i | \(-0.0933925\pi\) | ||||
0.957266 | + | 0.289210i | \(0.0933925\pi\) | |||||||
\(20\) | −0.202839 | −0.0453561 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −2.78254 | −0.593240 | ||||||||
\(23\) | 9.05966 | 1.88907 | 0.944535 | − | 0.328412i | \(-0.106513\pi\) | ||||
0.944535 | + | 0.328412i | \(0.106513\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.98604 | −0.997207 | ||||||||
\(26\) | 1.16700 | 0.228868 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 1.71647 | 0.324382 | ||||||||
\(29\) | 9.26366 | 1.72022 | 0.860109 | − | 0.510111i | \(-0.170396\pi\) | ||||
0.860109 | + | 0.510111i | \(0.170396\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 6.76707 | 1.21540 | 0.607701 | − | 0.794166i | \(-0.292092\pi\) | ||||
0.607701 | + | 0.794166i | \(0.292092\pi\) | |||||||
\(32\) | −5.22473 | −0.923610 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −0.682411 | −0.117033 | ||||||||
\(35\) | −0.118172 | −0.0199747 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 6.01829 | 0.989401 | 0.494700 | − | 0.869064i | \(-0.335278\pi\) | ||||
0.494700 | + | 0.869064i | \(0.335278\pi\) | |||||||
\(38\) | −4.44364 | −0.720853 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0.233854 | 0.0369755 | ||||||||
\(41\) | 4.32714 | 0.675786 | 0.337893 | − | 0.941184i | \(-0.390286\pi\) | ||||
0.337893 | + | 0.941184i | \(0.390286\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2.14731 | 0.327461 | 0.163730 | − | 0.986505i | \(-0.447647\pi\) | ||||
0.163730 | + | 0.986505i | \(0.447647\pi\) | |||||||
\(44\) | −8.96972 | −1.35224 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −4.82404 | −0.711266 | ||||||||
\(47\) | −1.79425 | −0.261718 | −0.130859 | − | 0.991401i | \(-0.541773\pi\) | ||||
−0.130859 | + | 0.991401i | \(0.541773\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 2.65494 | 0.375465 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 3.76191 | 0.521683 | ||||||||
\(53\) | −4.27074 | −0.586631 | −0.293315 | − | 0.956016i | \(-0.594759\pi\) | ||||
−0.293315 | + | 0.956016i | \(0.594759\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0.617528 | 0.0832675 | ||||||||
\(56\) | −1.97893 | −0.264445 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −4.93267 | −0.647691 | ||||||||
\(59\) | −11.1673 | −1.45386 | −0.726931 | − | 0.686710i | \(-0.759054\pi\) | ||||
−0.726931 | + | 0.686710i | \(0.759054\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −10.4330 | −1.33581 | −0.667907 | − | 0.744245i | \(-0.732810\pi\) | ||||
−0.667907 | + | 0.744245i | \(0.732810\pi\) | |||||||
\(62\) | −3.60330 | −0.457619 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −1.97638 | −0.247048 | ||||||||
\(65\) | −0.258992 | −0.0321240 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −14.4350 | −1.76352 | −0.881760 | − | 0.471699i | \(-0.843641\pi\) | ||||
−0.881760 | + | 0.471699i | \(0.843641\pi\) | |||||||
\(68\) | −2.19980 | −0.266765 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0.0629236 | 0.00752081 | ||||||||
\(71\) | 4.12479 | 0.489523 | 0.244761 | − | 0.969583i | \(-0.421290\pi\) | ||||
0.244761 | + | 0.969583i | \(0.421290\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 16.5937 | 1.94215 | 0.971075 | − | 0.238774i | \(-0.0767454\pi\) | ||||
0.971075 | + | 0.238774i | \(0.0767454\pi\) | |||||||
\(74\) | −3.20459 | −0.372526 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −14.3244 | −1.64312 | ||||||||
\(77\) | −5.22568 | −0.595521 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −11.3780 | −1.28012 | −0.640060 | − | 0.768325i | \(-0.721091\pi\) | ||||
−0.640060 | + | 0.768325i | \(0.721091\pi\) | |||||||
\(80\) | 0.281156 | 0.0314342 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −2.30410 | −0.254445 | ||||||||
\(83\) | −6.41125 | −0.703727 | −0.351863 | − | 0.936051i | \(-0.614452\pi\) | ||||
−0.351863 | + | 0.936051i | \(0.614452\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0.151447 | 0.0164267 | ||||||||
\(86\) | −1.14339 | −0.123295 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 10.3412 | 1.10238 | ||||||||
\(89\) | 3.69932 | 0.392127 | 0.196064 | − | 0.980591i | \(-0.437184\pi\) | ||||
0.196064 | + | 0.980591i | \(0.437184\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 2.19166 | 0.229748 | ||||||||
\(92\) | −15.5506 | −1.62127 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0.955391 | 0.0985410 | ||||||||
\(95\) | 0.986174 | 0.101179 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 6.10975 | 0.620351 | 0.310176 | − | 0.950679i | \(-0.399612\pi\) | ||||
0.310176 | + | 0.950679i | \(0.399612\pi\) | |||||||
\(98\) | −0.532475 | −0.0537881 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 8.55838 | 0.855838 | ||||||||
\(101\) | −0.593672 | −0.0590726 | −0.0295363 | − | 0.999564i | \(-0.509403\pi\) | ||||
−0.0295363 | + | 0.999564i | \(0.509403\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 7.82074 | 0.770600 | 0.385300 | − | 0.922791i | \(-0.374098\pi\) | ||||
0.385300 | + | 0.922791i | \(0.374098\pi\) | |||||||
\(104\) | −4.33713 | −0.425290 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 2.27406 | 0.220876 | ||||||||
\(107\) | 11.0220 | 1.06553 | 0.532767 | − | 0.846262i | \(-0.321152\pi\) | ||||
0.532767 | + | 0.846262i | \(0.321152\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −0.329550 | −0.0315652 | −0.0157826 | − | 0.999875i | \(-0.505024\pi\) | ||||
−0.0157826 | + | 0.999875i | \(0.505024\pi\) | |||||||
\(110\) | −0.328818 | −0.0313516 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −2.37921 | −0.224814 | ||||||||
\(113\) | 1.82578 | 0.171755 | 0.0858777 | − | 0.996306i | \(-0.472631\pi\) | ||||
0.0858777 | + | 0.996306i | \(0.472631\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1.07060 | 0.0998337 | ||||||||
\(116\) | −15.9008 | −1.47635 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 5.94632 | 0.547404 | ||||||||
\(119\) | −1.28158 | −0.117482 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 16.3077 | 1.48252 | ||||||||
\(122\) | 5.55533 | 0.502956 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −11.6155 | −1.04310 | ||||||||
\(125\) | −1.18007 | −0.105549 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1.00000 | −0.0887357 | ||||||||
\(128\) | 11.5018 | 1.01663 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0.137907 | 0.0120952 | ||||||||
\(131\) | 8.23408 | 0.719415 | 0.359707 | − | 0.933065i | \(-0.382877\pi\) | ||||
0.359707 | + | 0.933065i | \(0.382877\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −8.34525 | −0.723625 | ||||||||
\(134\) | 7.68629 | 0.663994 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 2.53616 | 0.217474 | ||||||||
\(137\) | 3.79688 | 0.324390 | 0.162195 | − | 0.986759i | \(-0.448143\pi\) | ||||
0.162195 | + | 0.986759i | \(0.448143\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −4.53910 | −0.385001 | −0.192501 | − | 0.981297i | \(-0.561660\pi\) | ||||
−0.192501 | + | 0.981297i | \(0.561660\pi\) | |||||||
\(140\) | 0.202839 | 0.0171430 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −2.19635 | −0.184314 | ||||||||
\(143\) | −11.4529 | −0.957738 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 1.09470 | 0.0909102 | ||||||||
\(146\) | −8.83575 | −0.731252 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −10.3302 | −0.849138 | ||||||||
\(149\) | 4.89325 | 0.400871 | 0.200435 | − | 0.979707i | \(-0.435764\pi\) | ||||
0.200435 | + | 0.979707i | \(0.435764\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 11.1366 | 0.906286 | 0.453143 | − | 0.891438i | \(-0.350303\pi\) | ||||
0.453143 | + | 0.891438i | \(0.350303\pi\) | |||||||
\(152\) | 16.5146 | 1.33951 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 2.78254 | 0.224224 | ||||||||
\(155\) | 0.799678 | 0.0642317 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −15.9627 | −1.27397 | −0.636983 | − | 0.770878i | \(-0.719818\pi\) | ||||
−0.636983 | + | 0.770878i | \(0.719818\pi\) | |||||||
\(158\) | 6.05848 | 0.481987 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −0.617416 | −0.0488110 | ||||||||
\(161\) | −9.05966 | −0.714001 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −11.4892 | −0.899906 | −0.449953 | − | 0.893052i | \(-0.648559\pi\) | ||||
−0.449953 | + | 0.893052i | \(0.648559\pi\) | |||||||
\(164\) | −7.42741 | −0.579984 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 3.41383 | 0.264965 | ||||||||
\(167\) | 14.2726 | 1.10445 | 0.552223 | − | 0.833697i | \(-0.313780\pi\) | ||||
0.552223 | + | 0.833697i | \(0.313780\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −8.19665 | −0.630511 | ||||||||
\(170\) | −0.0806418 | −0.00618495 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −3.68579 | −0.281039 | ||||||||
\(173\) | −3.15204 | −0.239645 | −0.119823 | − | 0.992795i | \(-0.538233\pi\) | ||||
−0.119823 | + | 0.992795i | \(0.538233\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 4.98604 | 0.376909 | ||||||||
\(176\) | 12.4330 | 0.937171 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −1.96980 | −0.147642 | ||||||||
\(179\) | −22.0690 | −1.64951 | −0.824757 | − | 0.565488i | \(-0.808688\pi\) | ||||
−0.824757 | + | 0.565488i | \(0.808688\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 17.7881 | 1.32218 | 0.661089 | − | 0.750307i | \(-0.270094\pi\) | ||||
0.661089 | + | 0.750307i | \(0.270094\pi\) | |||||||
\(182\) | −1.16700 | −0.0865039 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 17.9284 | 1.32170 | ||||||||
\(185\) | 0.711193 | 0.0522879 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 6.69713 | 0.489743 | ||||||||
\(188\) | 3.07977 | 0.224615 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −0.525113 | −0.0380957 | ||||||||
\(191\) | −9.64651 | −0.697997 | −0.348999 | − | 0.937123i | \(-0.613478\pi\) | ||||
−0.348999 | + | 0.937123i | \(0.613478\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 12.1823 | 0.876901 | 0.438451 | − | 0.898755i | \(-0.355527\pi\) | ||||
0.438451 | + | 0.898755i | \(0.355527\pi\) | |||||||
\(194\) | −3.25329 | −0.233573 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −1.71647 | −0.122605 | ||||||||
\(197\) | −5.07522 | −0.361595 | −0.180797 | − | 0.983520i | \(-0.557868\pi\) | ||||
−0.180797 | + | 0.983520i | \(0.557868\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 3.43881 | 0.243771 | 0.121885 | − | 0.992544i | \(-0.461106\pi\) | ||||
0.121885 | + | 0.992544i | \(0.461106\pi\) | |||||||
\(200\) | −9.86700 | −0.697703 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0.316116 | 0.0222418 | ||||||||
\(203\) | −9.26366 | −0.650181 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0.511347 | 0.0357140 | ||||||||
\(206\) | −4.16435 | −0.290144 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −5.21441 | −0.361554 | ||||||||
\(209\) | 43.6096 | 3.01654 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −13.3818 | −0.921243 | −0.460621 | − | 0.887597i | \(-0.652373\pi\) | ||||
−0.460621 | + | 0.887597i | \(0.652373\pi\) | |||||||
\(212\) | 7.33059 | 0.503467 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −5.86892 | −0.401191 | ||||||||
\(215\) | 0.253751 | 0.0173057 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −6.76707 | −0.459379 | ||||||||
\(218\) | 0.175477 | 0.0118848 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −1.05997 | −0.0714631 | ||||||||
\(221\) | −2.80879 | −0.188940 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −3.72789 | −0.249638 | −0.124819 | − | 0.992180i | \(-0.539835\pi\) | ||||
−0.124819 | + | 0.992180i | \(0.539835\pi\) | |||||||
\(224\) | 5.22473 | 0.349092 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −0.972184 | −0.0646687 | ||||||||
\(227\) | −7.52598 | −0.499517 | −0.249759 | − | 0.968308i | \(-0.580351\pi\) | ||||
−0.249759 | + | 0.968308i | \(0.580351\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −0.811157 | −0.0536027 | −0.0268014 | − | 0.999641i | \(-0.508532\pi\) | ||||
−0.0268014 | + | 0.999641i | \(0.508532\pi\) | |||||||
\(230\) | −0.570066 | −0.0375891 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 18.3321 | 1.20356 | ||||||||
\(233\) | −21.7672 | −1.42602 | −0.713008 | − | 0.701156i | \(-0.752668\pi\) | ||||
−0.713008 | + | 0.701156i | \(0.752668\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −0.212029 | −0.0138313 | ||||||||
\(236\) | 19.1684 | 1.24776 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0.682411 | 0.0442341 | ||||||||
\(239\) | −10.2516 | −0.663119 | −0.331559 | − | 0.943434i | \(-0.607575\pi\) | ||||
−0.331559 | + | 0.943434i | \(0.607575\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 12.4960 | 0.804938 | 0.402469 | − | 0.915434i | \(-0.368152\pi\) | ||||
0.402469 | + | 0.915434i | \(0.368152\pi\) | |||||||
\(242\) | −8.68343 | −0.558192 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 17.9080 | 1.14644 | ||||||||
\(245\) | 0.118172 | 0.00754973 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −18.2899 | −1.16376 | ||||||||
\(248\) | 13.3915 | 0.850364 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0.628358 | 0.0397408 | ||||||||
\(251\) | 21.5708 | 1.36154 | 0.680769 | − | 0.732498i | \(-0.261646\pi\) | ||||
0.680769 | + | 0.732498i | \(0.261646\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 47.3428 | 2.97642 | ||||||||
\(254\) | 0.532475 | 0.0334105 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −2.17167 | −0.135729 | ||||||||
\(257\) | 19.5843 | 1.22163 | 0.610817 | − | 0.791772i | \(-0.290841\pi\) | ||||
0.610817 | + | 0.791772i | \(0.290841\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −6.01829 | −0.373958 | ||||||||
\(260\) | 0.444552 | 0.0275700 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −4.38444 | −0.270872 | ||||||||
\(263\) | 7.21804 | 0.445083 | 0.222542 | − | 0.974923i | \(-0.428565\pi\) | ||||
0.222542 | + | 0.974923i | \(0.428565\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −0.504681 | −0.0310023 | ||||||||
\(266\) | 4.44364 | 0.272457 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 24.7773 | 1.51351 | ||||||||
\(269\) | 14.4911 | 0.883538 | 0.441769 | − | 0.897129i | \(-0.354351\pi\) | ||||
0.441769 | + | 0.897129i | \(0.354351\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −17.3584 | −1.05445 | −0.527224 | − | 0.849726i | \(-0.676767\pi\) | ||||
−0.527224 | + | 0.849726i | \(0.676767\pi\) | |||||||
\(272\) | 3.04916 | 0.184882 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −2.02175 | −0.122138 | ||||||||
\(275\) | −26.0554 | −1.57120 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −25.4371 | −1.52836 | −0.764182 | − | 0.645000i | \(-0.776857\pi\) | ||||
−0.764182 | + | 0.645000i | \(0.776857\pi\) | |||||||
\(278\) | 2.41696 | 0.144959 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −0.233854 | −0.0139754 | ||||||||
\(281\) | −10.7927 | −0.643837 | −0.321918 | − | 0.946767i | \(-0.604328\pi\) | ||||
−0.321918 | + | 0.946767i | \(0.604328\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 1.47440 | 0.0876441 | 0.0438220 | − | 0.999039i | \(-0.486047\pi\) | ||||
0.0438220 | + | 0.999039i | \(0.486047\pi\) | |||||||
\(284\) | −7.08009 | −0.420126 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 6.09837 | 0.360604 | ||||||||
\(287\) | −4.32714 | −0.255423 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −15.3575 | −0.903385 | ||||||||
\(290\) | −0.582903 | −0.0342292 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −28.4827 | −1.66682 | ||||||||
\(293\) | −12.6888 | −0.741290 | −0.370645 | − | 0.928775i | \(-0.620863\pi\) | ||||
−0.370645 | + | 0.928775i | \(0.620863\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −1.31966 | −0.0768339 | ||||||||
\(296\) | 11.9098 | 0.692241 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −2.60553 | −0.150934 | ||||||||
\(299\) | −19.8557 | −1.14828 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −2.14731 | −0.123769 | ||||||||
\(302\) | −5.92998 | −0.341232 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 19.8551 | 1.13877 | ||||||||
\(305\) | −1.23289 | −0.0705952 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −7.60261 | −0.433904 | −0.216952 | − | 0.976182i | \(-0.569612\pi\) | ||||
−0.216952 | + | 0.976182i | \(0.569612\pi\) | |||||||
\(308\) | 8.96972 | 0.511097 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −0.425808 | −0.0241843 | ||||||||
\(311\) | 34.6469 | 1.96465 | 0.982324 | − | 0.187190i | \(-0.0599381\pi\) | ||||
0.982324 | + | 0.187190i | \(0.0599381\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −13.4142 | −0.758216 | −0.379108 | − | 0.925352i | \(-0.623769\pi\) | ||||
−0.379108 | + | 0.925352i | \(0.623769\pi\) | |||||||
\(314\) | 8.49977 | 0.479670 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 19.5299 | 1.09864 | ||||||||
\(317\) | 25.3786 | 1.42540 | 0.712702 | − | 0.701467i | \(-0.247471\pi\) | ||||
0.712702 | + | 0.701467i | \(0.247471\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 48.4089 | 2.71038 | ||||||||
\(320\) | −0.233553 | −0.0130560 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 4.82404 | 0.268833 | ||||||||
\(323\) | 10.6951 | 0.595093 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 10.9277 | 0.606158 | ||||||||
\(326\) | 6.11773 | 0.338830 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 8.56311 | 0.472818 | ||||||||
\(329\) | 1.79425 | 0.0989199 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 4.32910 | 0.237949 | 0.118974 | − | 0.992897i | \(-0.462039\pi\) | ||||
0.118974 | + | 0.992897i | \(0.462039\pi\) | |||||||
\(332\) | 11.0047 | 0.603963 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −7.59979 | −0.415842 | ||||||||
\(335\) | −1.70582 | −0.0931986 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −30.9193 | −1.68428 | −0.842141 | − | 0.539257i | \(-0.818705\pi\) | ||||
−0.842141 | + | 0.539257i | \(0.818705\pi\) | |||||||
\(338\) | 4.36451 | 0.237398 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −0.259954 | −0.0140980 | ||||||||
\(341\) | 35.3625 | 1.91499 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | 4.24936 | 0.229110 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 1.67838 | 0.0902304 | ||||||||
\(347\) | −11.4166 | −0.612873 | −0.306436 | − | 0.951891i | \(-0.599137\pi\) | ||||
−0.306436 | + | 0.951891i | \(0.599137\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −25.1259 | −1.34496 | −0.672479 | − | 0.740116i | \(-0.734771\pi\) | ||||
−0.672479 | + | 0.740116i | \(0.734771\pi\) | |||||||
\(350\) | −2.65494 | −0.141912 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −27.3027 | −1.45524 | ||||||||
\(353\) | −16.4066 | −0.873234 | −0.436617 | − | 0.899647i | \(-0.643824\pi\) | ||||
−0.436617 | + | 0.899647i | \(0.643824\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0.487435 | 0.0258704 | ||||||||
\(356\) | −6.34977 | −0.336537 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 11.7512 | 0.621069 | ||||||||
\(359\) | 17.7879 | 0.938809 | 0.469404 | − | 0.882983i | \(-0.344469\pi\) | ||||
0.469404 | + | 0.882983i | \(0.344469\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 50.6432 | 2.66543 | ||||||||
\(362\) | −9.47172 | −0.497822 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −3.76191 | −0.197178 | ||||||||
\(365\) | 1.96091 | 0.102639 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −23.9393 | −1.24962 | −0.624812 | − | 0.780776i | \(-0.714824\pi\) | ||||
−0.624812 | + | 0.780776i | \(0.714824\pi\) | |||||||
\(368\) | 21.5548 | 1.12362 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −0.378693 | −0.0196873 | ||||||||
\(371\) | 4.27074 | 0.221726 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 24.1062 | 1.24817 | 0.624085 | − | 0.781356i | \(-0.285472\pi\) | ||||
0.624085 | + | 0.781356i | \(0.285472\pi\) | |||||||
\(374\) | −3.56606 | −0.184396 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −3.55068 | −0.183112 | ||||||||
\(377\) | −20.3027 | −1.04564 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −9.74899 | −0.500772 | −0.250386 | − | 0.968146i | \(-0.580558\pi\) | ||||
−0.250386 | + | 0.968146i | \(0.580558\pi\) | |||||||
\(380\) | −1.69274 | −0.0868357 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 5.13653 | 0.262808 | ||||||||
\(383\) | −21.0940 | −1.07785 | −0.538925 | − | 0.842354i | \(-0.681169\pi\) | ||||
−0.538925 | + | 0.842354i | \(0.681169\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −0.617528 | −0.0314722 | ||||||||
\(386\) | −6.48677 | −0.330168 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −10.4872 | −0.532407 | ||||||||
\(389\) | −11.4795 | −0.582032 | −0.291016 | − | 0.956718i | \(-0.593993\pi\) | ||||
−0.291016 | + | 0.956718i | \(0.593993\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 11.6107 | 0.587178 | ||||||||
\(392\) | 1.97893 | 0.0999510 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 2.70243 | 0.136146 | ||||||||
\(395\) | −1.34456 | −0.0676520 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 33.4207 | 1.67734 | 0.838668 | − | 0.544643i | \(-0.183335\pi\) | ||||
0.838668 | + | 0.544643i | \(0.183335\pi\) | |||||||
\(398\) | −1.83108 | −0.0917838 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −11.8628 | −0.593141 | ||||||||
\(401\) | −0.506322 | −0.0252845 | −0.0126423 | − | 0.999920i | \(-0.504024\pi\) | ||||
−0.0126423 | + | 0.999920i | \(0.504024\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −14.8311 | −0.738789 | ||||||||
\(404\) | 1.01902 | 0.0506982 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 4.93267 | 0.244804 | ||||||||
\(407\) | 31.4496 | 1.55890 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 27.6889 | 1.36913 | 0.684563 | − | 0.728953i | \(-0.259993\pi\) | ||||
0.684563 | + | 0.728953i | \(0.259993\pi\) | |||||||
\(410\) | −0.272280 | −0.0134469 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −13.4241 | −0.661356 | ||||||||
\(413\) | 11.1673 | 0.549508 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −0.757631 | −0.0371906 | ||||||||
\(416\) | 11.4508 | 0.561422 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −23.2210 | −1.13578 | ||||||||
\(419\) | −5.22108 | −0.255067 | −0.127533 | − | 0.991834i | \(-0.540706\pi\) | ||||
−0.127533 | + | 0.991834i | \(0.540706\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −30.2687 | −1.47521 | −0.737603 | − | 0.675235i | \(-0.764042\pi\) | ||||
−0.737603 | + | 0.675235i | \(0.764042\pi\) | |||||||
\(422\) | 7.12549 | 0.346863 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −8.45148 | −0.410440 | ||||||||
\(425\) | −6.39002 | −0.309961 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 10.4330 | 0.504890 | ||||||||
\(428\) | −18.9189 | −0.914479 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −0.135116 | −0.00651588 | ||||||||
\(431\) | 12.4316 | 0.598807 | 0.299403 | − | 0.954127i | \(-0.403212\pi\) | ||||
0.299403 | + | 0.954127i | \(0.403212\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 27.6679 | 1.32964 | 0.664818 | − | 0.747006i | \(-0.268509\pi\) | ||||
0.664818 | + | 0.747006i | \(0.268509\pi\) | |||||||
\(434\) | 3.60330 | 0.172964 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0.565664 | 0.0270904 | ||||||||
\(437\) | 75.6051 | 3.61668 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 5.41016 | 0.258213 | 0.129106 | − | 0.991631i | \(-0.458789\pi\) | ||||
0.129106 | + | 0.991631i | \(0.458789\pi\) | |||||||
\(440\) | 1.22204 | 0.0582587 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 1.49561 | 0.0711389 | ||||||||
\(443\) | 11.5485 | 0.548686 | 0.274343 | − | 0.961632i | \(-0.411540\pi\) | ||||
0.274343 | + | 0.961632i | \(0.411540\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0.437156 | 0.0207232 | ||||||||
\(446\) | 1.98501 | 0.0939930 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 1.97638 | 0.0933754 | ||||||||
\(449\) | 37.7469 | 1.78138 | 0.890692 | − | 0.454607i | \(-0.150220\pi\) | ||||
0.890692 | + | 0.454607i | \(0.150220\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 22.6123 | 1.06477 | ||||||||
\(452\) | −3.13390 | −0.147406 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 4.00740 | 0.188077 | ||||||||
\(455\) | 0.258992 | 0.0121417 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −4.86171 | −0.227421 | −0.113711 | − | 0.993514i | \(-0.536274\pi\) | ||||
−0.113711 | + | 0.993514i | \(0.536274\pi\) | |||||||
\(458\) | 0.431921 | 0.0201823 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −1.83765 | −0.0856808 | ||||||||
\(461\) | 22.2371 | 1.03569 | 0.517843 | − | 0.855475i | \(-0.326735\pi\) | ||||
0.517843 | + | 0.855475i | \(0.326735\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −34.0919 | −1.58439 | −0.792193 | − | 0.610271i | \(-0.791061\pi\) | ||||
−0.792193 | + | 0.610271i | \(0.791061\pi\) | |||||||
\(464\) | 22.0402 | 1.02319 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 11.5905 | 0.536919 | ||||||||
\(467\) | 18.0906 | 0.837131 | 0.418566 | − | 0.908187i | \(-0.362533\pi\) | ||||
0.418566 | + | 0.908187i | \(0.362533\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 14.4350 | 0.666548 | ||||||||
\(470\) | 0.112900 | 0.00520771 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −22.0993 | −1.01720 | ||||||||
\(473\) | 11.2211 | 0.515948 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −41.6097 | −1.90918 | ||||||||
\(476\) | 2.19980 | 0.100828 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 5.45871 | 0.249675 | ||||||||
\(479\) | −13.8985 | −0.635037 | −0.317519 | − | 0.948252i | \(-0.602850\pi\) | ||||
−0.317519 | + | 0.948252i | \(0.602850\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −13.1900 | −0.601413 | ||||||||
\(482\) | −6.65380 | −0.303072 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −27.9916 | −1.27235 | ||||||||
\(485\) | 0.722001 | 0.0327844 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −1.46671 | −0.0664628 | −0.0332314 | − | 0.999448i | \(-0.510580\pi\) | ||||
−0.0332314 | + | 0.999448i | \(0.510580\pi\) | |||||||
\(488\) | −20.6462 | −0.934611 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −0.0629236 | −0.00284260 | ||||||||
\(491\) | −13.3834 | −0.603983 | −0.301992 | − | 0.953311i | \(-0.597651\pi\) | ||||
−0.301992 | + | 0.953311i | \(0.597651\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 11.8721 | 0.534694 | ||||||||
\(494\) | 9.73892 | 0.438175 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 16.1003 | 0.722924 | ||||||||
\(497\) | −4.12479 | −0.185022 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 21.8737 | 0.979201 | 0.489601 | − | 0.871947i | \(-0.337143\pi\) | ||||
0.489601 | + | 0.871947i | \(0.337143\pi\) | |||||||
\(500\) | 2.02555 | 0.0905855 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −11.4859 | −0.512642 | ||||||||
\(503\) | 41.4018 | 1.84601 | 0.923007 | − | 0.384784i | \(-0.125724\pi\) | ||||
0.923007 | + | 0.384784i | \(0.125724\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −0.0701554 | −0.00312187 | ||||||||
\(506\) | −25.2089 | −1.12067 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 1.71647 | 0.0761561 | ||||||||
\(509\) | −12.5384 | −0.555757 | −0.277878 | − | 0.960616i | \(-0.589631\pi\) | ||||
−0.277878 | + | 0.960616i | \(0.589631\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −16.5937 | −0.734064 | ||||||||
\(512\) | −21.8473 | −0.965523 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −10.4281 | −0.459965 | ||||||||
\(515\) | 0.924192 | 0.0407248 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −9.37614 | −0.412362 | ||||||||
\(518\) | 3.20459 | 0.140802 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −0.512527 | −0.0224758 | ||||||||
\(521\) | 25.5657 | 1.12006 | 0.560028 | − | 0.828474i | \(-0.310790\pi\) | ||||
0.560028 | + | 0.828474i | \(0.310790\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −0.965570 | −0.0422214 | −0.0211107 | − | 0.999777i | \(-0.506720\pi\) | ||||
−0.0211107 | + | 0.999777i | \(0.506720\pi\) | |||||||
\(524\) | −14.1335 | −0.617427 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −3.84343 | −0.167581 | ||||||||
\(527\) | 8.67256 | 0.377783 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 59.0774 | 2.56858 | ||||||||
\(530\) | 0.268730 | 0.0116729 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 14.3244 | 0.621040 | ||||||||
\(533\) | −9.48361 | −0.410781 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 1.30249 | 0.0563115 | ||||||||
\(536\) | −28.5659 | −1.23386 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −7.71615 | −0.332667 | ||||||||
\(539\) | 5.22568 | 0.225086 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −1.43271 | −0.0615970 | −0.0307985 | − | 0.999526i | \(-0.509805\pi\) | ||||
−0.0307985 | + | 0.999526i | \(0.509805\pi\) | |||||||
\(542\) | 9.24292 | 0.397017 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −6.69592 | −0.287085 | ||||||||
\(545\) | −0.0389436 | −0.00166816 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −13.4988 | −0.577167 | −0.288584 | − | 0.957455i | \(-0.593184\pi\) | ||||
−0.288584 | + | 0.957455i | \(0.593184\pi\) | |||||||
\(548\) | −6.51724 | −0.278403 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 13.8739 | 0.591583 | ||||||||
\(551\) | 77.3075 | 3.29341 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 11.3780 | 0.483840 | ||||||||
\(554\) | 13.5446 | 0.575455 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 7.79122 | 0.330421 | ||||||||
\(557\) | −29.6076 | −1.25451 | −0.627257 | − | 0.778812i | \(-0.715822\pi\) | ||||
−0.627257 | + | 0.778812i | \(0.715822\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −4.70615 | −0.199049 | ||||||||
\(560\) | −0.281156 | −0.0118810 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 5.74683 | 0.242415 | ||||||||
\(563\) | −18.3169 | −0.771963 | −0.385982 | − | 0.922506i | \(-0.626137\pi\) | ||||
−0.385982 | + | 0.922506i | \(0.626137\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0.215756 | 0.00907694 | ||||||||
\(566\) | −0.785082 | −0.0329995 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 8.16267 | 0.342498 | ||||||||
\(569\) | 35.3075 | 1.48017 | 0.740083 | − | 0.672516i | \(-0.234786\pi\) | ||||
0.740083 | + | 0.672516i | \(0.234786\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 3.93893 | 0.164839 | 0.0824196 | − | 0.996598i | \(-0.473735\pi\) | ||||
0.0824196 | + | 0.996598i | \(0.473735\pi\) | |||||||
\(572\) | 19.6585 | 0.821964 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 2.30410 | 0.0961711 | ||||||||
\(575\) | −45.1718 | −1.88379 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 33.2150 | 1.38276 | 0.691380 | − | 0.722492i | \(-0.257003\pi\) | ||||
0.691380 | + | 0.722492i | \(0.257003\pi\) | |||||||
\(578\) | 8.17751 | 0.340140 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −1.87903 | −0.0780224 | ||||||||
\(581\) | 6.41125 | 0.265984 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −22.3175 | −0.924296 | ||||||||
\(584\) | 32.8378 | 1.35884 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 6.75649 | 0.279108 | ||||||||
\(587\) | −24.6822 | −1.01874 | −0.509372 | − | 0.860546i | \(-0.670122\pi\) | ||||
−0.509372 | + | 0.860546i | \(0.670122\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 56.4729 | 2.32692 | ||||||||
\(590\) | 0.702689 | 0.0289292 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 14.3188 | 0.588498 | ||||||||
\(593\) | −6.61375 | −0.271594 | −0.135797 | − | 0.990737i | \(-0.543360\pi\) | ||||
−0.135797 | + | 0.990737i | \(0.543360\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −0.151447 | −0.00620873 | ||||||||
\(596\) | −8.39912 | −0.344041 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 10.5726 | 0.432347 | ||||||||
\(599\) | 25.3672 | 1.03648 | 0.518239 | − | 0.855236i | \(-0.326588\pi\) | ||||
0.518239 | + | 0.855236i | \(0.326588\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −10.2704 | −0.418940 | −0.209470 | − | 0.977815i | \(-0.567174\pi\) | ||||
−0.209470 | + | 0.977815i | \(0.567174\pi\) | |||||||
\(602\) | 1.14339 | 0.0466010 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −19.1157 | −0.777807 | ||||||||
\(605\) | 1.92711 | 0.0783482 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −0.280009 | −0.0113652 | −0.00568261 | − | 0.999984i | \(-0.501809\pi\) | ||||
−0.00568261 | + | 0.999984i | \(0.501809\pi\) | |||||||
\(608\) | −43.6016 | −1.76828 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0.656485 | 0.0265803 | ||||||||
\(611\) | 3.93237 | 0.159087 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −34.3249 | −1.38637 | −0.693185 | − | 0.720760i | \(-0.743793\pi\) | ||||
−0.693185 | + | 0.720760i | \(0.743793\pi\) | |||||||
\(614\) | 4.04820 | 0.163372 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −10.3412 | −0.416660 | ||||||||
\(617\) | 7.14920 | 0.287816 | 0.143908 | − | 0.989591i | \(-0.454033\pi\) | ||||
0.143908 | + | 0.989591i | \(0.454033\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 10.8686 | 0.436846 | 0.218423 | − | 0.975854i | \(-0.429909\pi\) | ||||
0.218423 | + | 0.975854i | \(0.429909\pi\) | |||||||
\(620\) | −1.37262 | −0.0551259 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −18.4486 | −0.739723 | ||||||||
\(623\) | −3.69932 | −0.148210 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 24.7907 | 0.991629 | ||||||||
\(626\) | 7.14273 | 0.285481 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 27.3996 | 1.09336 | ||||||||
\(629\) | 7.71293 | 0.307535 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −46.4839 | −1.85050 | −0.925248 | − | 0.379362i | \(-0.876143\pi\) | ||||
−0.925248 | + | 0.379362i | \(0.876143\pi\) | |||||||
\(632\) | −22.5162 | −0.895645 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −13.5135 | −0.536689 | ||||||||
\(635\) | −0.118172 | −0.00468951 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −2.19166 | −0.0868366 | ||||||||
\(638\) | −25.7765 | −1.02050 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 1.35919 | 0.0537268 | ||||||||
\(641\) | −13.4471 | −0.531127 | −0.265563 | − | 0.964093i | \(-0.585558\pi\) | ||||
−0.265563 | + | 0.964093i | \(0.585558\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −40.9464 | −1.61477 | −0.807383 | − | 0.590027i | \(-0.799117\pi\) | ||||
−0.807383 | + | 0.590027i | \(0.799117\pi\) | |||||||
\(644\) | 15.5506 | 0.612781 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −5.69489 | −0.224062 | ||||||||
\(647\) | 9.04141 | 0.355454 | 0.177727 | − | 0.984080i | \(-0.443126\pi\) | ||||
0.177727 | + | 0.984080i | \(0.443126\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −58.3568 | −2.29071 | ||||||||
\(650\) | −5.81871 | −0.228229 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 19.7209 | 0.772331 | ||||||||
\(653\) | 9.65099 | 0.377672 | 0.188836 | − | 0.982009i | \(-0.439528\pi\) | ||||
0.188836 | + | 0.982009i | \(0.439528\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0.973037 | 0.0380197 | ||||||||
\(656\) | 10.2952 | 0.401960 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −0.955391 | −0.0372450 | ||||||||
\(659\) | 25.6398 | 0.998786 | 0.499393 | − | 0.866376i | \(-0.333556\pi\) | ||||
0.499393 | + | 0.866376i | \(0.333556\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 5.36192 | 0.208555 | 0.104277 | − | 0.994548i | \(-0.466747\pi\) | ||||
0.104277 | + | 0.994548i | \(0.466747\pi\) | |||||||
\(662\) | −2.30514 | −0.0895918 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −12.6874 | −0.492367 | ||||||||
\(665\) | −0.986174 | −0.0382422 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 83.9256 | 3.24961 | ||||||||
\(668\) | −24.4985 | −0.947874 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0.908304 | 0.0350908 | ||||||||
\(671\) | −54.5197 | −2.10471 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 10.4649 | 0.403392 | 0.201696 | − | 0.979448i | \(-0.435355\pi\) | ||||
0.201696 | + | 0.979448i | \(0.435355\pi\) | |||||||
\(674\) | 16.4638 | 0.634161 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 14.0693 | 0.541127 | ||||||||
\(677\) | −9.28929 | −0.357017 | −0.178508 | − | 0.983938i | \(-0.557127\pi\) | ||||
−0.178508 | + | 0.983938i | \(0.557127\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −6.10975 | −0.234471 | ||||||||
\(680\) | 0.299703 | 0.0114931 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −18.8297 | −0.721025 | ||||||||
\(683\) | 16.7140 | 0.639544 | 0.319772 | − | 0.947494i | \(-0.396394\pi\) | ||||
0.319772 | + | 0.947494i | \(0.396394\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0.448685 | 0.0171434 | ||||||||
\(686\) | 0.532475 | 0.0203300 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 5.10889 | 0.194775 | ||||||||
\(689\) | 9.35998 | 0.356587 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 32.0986 | 1.22109 | 0.610544 | − | 0.791982i | \(-0.290951\pi\) | ||||
0.610544 | + | 0.791982i | \(0.290951\pi\) | |||||||
\(692\) | 5.41038 | 0.205672 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 6.07903 | 0.230757 | ||||||||
\(695\) | −0.536394 | −0.0203466 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 5.54559 | 0.210054 | ||||||||
\(698\) | 13.3789 | 0.506399 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −8.55838 | −0.323476 | ||||||||
\(701\) | −8.24121 | −0.311266 | −0.155633 | − | 0.987815i | \(-0.549742\pi\) | ||||
−0.155633 | + | 0.987815i | \(0.549742\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 50.2241 | 1.89424 | ||||||||
\(704\) | −10.3279 | −0.389249 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 8.73610 | 0.328787 | ||||||||
\(707\) | 0.593672 | 0.0223273 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 18.5251 | 0.695723 | 0.347862 | − | 0.937546i | \(-0.386908\pi\) | ||||
0.347862 | + | 0.937546i | \(0.386908\pi\) | |||||||
\(710\) | −0.259547 | −0.00974062 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 7.32069 | 0.274354 | ||||||||
\(713\) | 61.3073 | 2.29598 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −1.35341 | −0.0506146 | ||||||||
\(716\) | 37.8807 | 1.41567 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −9.47161 | −0.353477 | ||||||||
\(719\) | 29.8462 | 1.11308 | 0.556538 | − | 0.830822i | \(-0.312129\pi\) | ||||
0.556538 | + | 0.830822i | \(0.312129\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −7.82074 | −0.291260 | ||||||||
\(722\) | −26.9662 | −1.00358 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −30.5327 | −1.13474 | ||||||||
\(725\) | −46.1889 | −1.71541 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −42.7041 | −1.58381 | −0.791904 | − | 0.610645i | \(-0.790910\pi\) | ||||
−0.791904 | + | 0.610645i | \(0.790910\pi\) | |||||||
\(728\) | 4.33713 | 0.160745 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −1.04414 | −0.0386453 | ||||||||
\(731\) | 2.75195 | 0.101785 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 13.0748 | 0.482930 | 0.241465 | − | 0.970409i | \(-0.422372\pi\) | ||||
0.241465 | + | 0.970409i | \(0.422372\pi\) | |||||||
\(734\) | 12.7471 | 0.470504 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −47.3342 | −1.74476 | ||||||||
\(737\) | −75.4328 | −2.77860 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −11.8892 | −0.437351 | −0.218676 | − | 0.975798i | \(-0.570174\pi\) | ||||
−0.218676 | + | 0.975798i | \(0.570174\pi\) | |||||||
\(740\) | −1.22074 | −0.0448753 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −2.27406 | −0.0834834 | ||||||||
\(743\) | −24.3686 | −0.893998 | −0.446999 | − | 0.894534i | \(-0.647507\pi\) | ||||
−0.446999 | + | 0.894534i | \(0.647507\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0.578245 | 0.0211853 | ||||||||
\(746\) | −12.8359 | −0.469957 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −11.4954 | −0.420315 | ||||||||
\(749\) | −11.0220 | −0.402734 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 14.6876 | 0.535957 | 0.267978 | − | 0.963425i | \(-0.413644\pi\) | ||||
0.267978 | + | 0.963425i | \(0.413644\pi\) | |||||||
\(752\) | −4.26889 | −0.155670 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 10.8107 | 0.393703 | ||||||||
\(755\) | 1.31604 | 0.0478955 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −2.79722 | −0.101667 | −0.0508334 | − | 0.998707i | \(-0.516188\pi\) | ||||
−0.0508334 | + | 0.998707i | \(0.516188\pi\) | |||||||
\(758\) | 5.19110 | 0.188549 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 1.95157 | 0.0707908 | ||||||||
\(761\) | −36.1872 | −1.31179 | −0.655893 | − | 0.754854i | \(-0.727708\pi\) | ||||
−0.655893 | + | 0.754854i | \(0.727708\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0.329550 | 0.0119305 | ||||||||
\(764\) | 16.5580 | 0.599046 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 11.2320 | 0.405829 | ||||||||
\(767\) | 24.4749 | 0.883739 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −9.22886 | −0.332801 | −0.166401 | − | 0.986058i | \(-0.553214\pi\) | ||||
−0.166401 | + | 0.986058i | \(0.553214\pi\) | |||||||
\(770\) | 0.328818 | 0.0118498 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −20.9106 | −0.752588 | ||||||||
\(773\) | 4.09236 | 0.147192 | 0.0735959 | − | 0.997288i | \(-0.476552\pi\) | ||||
0.0735959 | + | 0.997288i | \(0.476552\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −33.7408 | −1.21201 | ||||||||
\(776\) | 12.0908 | 0.434033 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 6.11253 | 0.219145 | ||||||||
\(779\) | 36.1111 | 1.29381 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 21.5548 | 0.771293 | ||||||||
\(782\) | −6.18241 | −0.221083 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 2.37921 | 0.0849718 | ||||||||
\(785\) | −1.88635 | −0.0673267 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −10.3020 | −0.367225 | −0.183613 | − | 0.982999i | \(-0.558779\pi\) | ||||
−0.183613 | + | 0.982999i | \(0.558779\pi\) | |||||||
\(788\) | 8.71147 | 0.310333 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0.715943 | 0.0254721 | ||||||||
\(791\) | −1.82578 | −0.0649174 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 22.8656 | 0.811982 | ||||||||
\(794\) | −17.7957 | −0.631545 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −5.90262 | −0.209213 | ||||||||
\(797\) | −40.9311 | −1.44986 | −0.724928 | − | 0.688825i | \(-0.758127\pi\) | ||||
−0.724928 | + | 0.688825i | \(0.758127\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −2.29947 | −0.0813495 | ||||||||
\(800\) | 26.0507 | 0.921030 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0.269604 | 0.00952004 | ||||||||
\(803\) | 86.7135 | 3.06005 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −1.07060 | −0.0377336 | ||||||||
\(806\) | 7.89718 | 0.278166 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −1.17483 | −0.0413305 | ||||||||
\(809\) | −9.34786 | −0.328653 | −0.164327 | − | 0.986406i | \(-0.552545\pi\) | ||||
−0.164327 | + | 0.986406i | \(0.552545\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −10.7341 | −0.376925 | −0.188463 | − | 0.982080i | \(-0.560350\pi\) | ||||
−0.188463 | + | 0.982080i | \(0.560350\pi\) | |||||||
\(812\) | 15.9008 | 0.558008 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −16.7461 | −0.586952 | ||||||||
\(815\) | −1.35770 | −0.0475583 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 17.9198 | 0.626934 | ||||||||
\(818\) | −14.7436 | −0.515499 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −0.877712 | −0.0306510 | ||||||||
\(821\) | −13.9500 | −0.486859 | −0.243430 | − | 0.969919i | \(-0.578272\pi\) | ||||
−0.243430 | + | 0.969919i | \(0.578272\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −7.62995 | −0.265963 | −0.132982 | − | 0.991119i | \(-0.542455\pi\) | ||||
−0.132982 | + | 0.991119i | \(0.542455\pi\) | |||||||
\(824\) | 15.4767 | 0.539156 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −5.94632 | −0.206899 | ||||||||
\(827\) | 50.6423 | 1.76101 | 0.880503 | − | 0.474040i | \(-0.157205\pi\) | ||||
0.880503 | + | 0.474040i | \(0.157205\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 27.1635 | 0.943428 | 0.471714 | − | 0.881752i | \(-0.343635\pi\) | ||||
0.471714 | + | 0.881752i | \(0.343635\pi\) | |||||||
\(830\) | 0.403419 | 0.0140029 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 4.33155 | 0.150170 | ||||||||
\(833\) | 1.28158 | 0.0444042 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 1.68662 | 0.0583678 | ||||||||
\(836\) | −74.8545 | −2.58890 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 2.78010 | 0.0960368 | ||||||||
\(839\) | −18.7378 | −0.646900 | −0.323450 | − | 0.946245i | \(-0.604843\pi\) | ||||
−0.323450 | + | 0.946245i | \(0.604843\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 56.8153 | 1.95915 | ||||||||
\(842\) | 16.1173 | 0.555440 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 22.9695 | 0.790643 | ||||||||
\(845\) | −0.968614 | −0.0333213 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −16.3077 | −0.560339 | ||||||||
\(848\) | −10.1610 | −0.348930 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 3.40252 | 0.116706 | ||||||||
\(851\) | 54.5236 | 1.86905 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 49.8498 | 1.70682 | 0.853412 | − | 0.521238i | \(-0.174530\pi\) | ||||
0.853412 | + | 0.521238i | \(0.174530\pi\) | |||||||
\(854\) | −5.55533 | −0.190100 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 21.8117 | 0.745508 | ||||||||
\(857\) | −39.2898 | −1.34211 | −0.671057 | − | 0.741406i | \(-0.734159\pi\) | ||||
−0.671057 | + | 0.741406i | \(0.734159\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 37.3922 | 1.27581 | 0.637903 | − | 0.770117i | \(-0.279802\pi\) | ||||
0.637903 | + | 0.770117i | \(0.279802\pi\) | |||||||
\(860\) | −0.435556 | −0.0148524 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −6.61949 | −0.225461 | ||||||||
\(863\) | −41.1465 | −1.40064 | −0.700322 | − | 0.713827i | \(-0.746960\pi\) | ||||
−0.700322 | + | 0.713827i | \(0.746960\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −0.372483 | −0.0126648 | ||||||||
\(866\) | −14.7325 | −0.500630 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 11.6155 | 0.394255 | ||||||||
\(869\) | −59.4575 | −2.01696 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 31.6366 | 1.07197 | ||||||||
\(872\) | −0.652157 | −0.0220848 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −40.2578 | −1.36174 | ||||||||
\(875\) | 1.18007 | 0.0398936 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −40.2479 | −1.35907 | −0.679537 | − | 0.733641i | \(-0.737819\pi\) | ||||
−0.679537 | + | 0.733641i | \(0.737819\pi\) | |||||||
\(878\) | −2.88077 | −0.0972214 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 1.46923 | 0.0495277 | ||||||||
\(881\) | −45.5773 | −1.53554 | −0.767769 | − | 0.640727i | \(-0.778633\pi\) | ||||
−0.767769 | + | 0.640727i | \(0.778633\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 11.2401 | 0.378259 | 0.189130 | − | 0.981952i | \(-0.439433\pi\) | ||||
0.189130 | + | 0.981952i | \(0.439433\pi\) | |||||||
\(884\) | 4.82120 | 0.162155 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −6.14929 | −0.206589 | ||||||||
\(887\) | −18.7760 | −0.630437 | −0.315219 | − | 0.949019i | \(-0.602078\pi\) | ||||
−0.315219 | + | 0.949019i | \(0.602078\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1.00000 | 0.0335389 | ||||||||
\(890\) | −0.232775 | −0.00780262 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 6.39882 | 0.214248 | ||||||||
\(893\) | −14.9734 | −0.501066 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −2.60793 | −0.0871736 | ||||||||
\(896\) | −11.5018 | −0.384249 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −20.0993 | −0.670721 | ||||||||
\(899\) | 62.6878 | 2.09076 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −5.47330 | −0.182342 | ||||||||
\(902\) | −12.0405 | −0.400903 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 3.61309 | 0.120170 | ||||||||
\(905\) | 2.10205 | 0.0698746 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −28.0916 | −0.932767 | −0.466383 | − | 0.884583i | \(-0.654443\pi\) | ||||
−0.466383 | + | 0.884583i | \(0.654443\pi\) | |||||||
\(908\) | 12.9181 | 0.428703 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −0.137907 | −0.00457157 | ||||||||
\(911\) | 11.5012 | 0.381053 | 0.190526 | − | 0.981682i | \(-0.438981\pi\) | ||||
0.190526 | + | 0.981682i | \(0.438981\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −33.5031 | −1.10879 | ||||||||
\(914\) | 2.58874 | 0.0856279 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 1.39233 | 0.0460038 | ||||||||
\(917\) | −8.23408 | −0.271913 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −21.4575 | −0.707818 | −0.353909 | − | 0.935280i | \(-0.615148\pi\) | ||||
−0.353909 | + | 0.935280i | \(0.615148\pi\) | |||||||
\(920\) | 2.11864 | 0.0698493 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −11.8407 | −0.389953 | ||||||||
\(923\) | −9.04013 | −0.297559 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −30.0074 | −0.986637 | ||||||||
\(926\) | 18.1531 | 0.596548 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −48.4001 | −1.58881 | ||||||||
\(929\) | −58.5953 | −1.92245 | −0.961225 | − | 0.275766i | \(-0.911068\pi\) | ||||
−0.961225 | + | 0.275766i | \(0.911068\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 8.34525 | 0.273504 | ||||||||
\(932\) | 37.3628 | 1.22386 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −9.63277 | −0.315194 | ||||||||
\(935\) | 0.791413 | 0.0258820 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −37.4295 | −1.22277 | −0.611384 | − | 0.791334i | \(-0.709387\pi\) | ||||
−0.611384 | + | 0.791334i | \(0.709387\pi\) | |||||||
\(938\) | −7.68629 | −0.250966 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0.363942 | 0.0118705 | ||||||||
\(941\) | 44.8032 | 1.46054 | 0.730272 | − | 0.683157i | \(-0.239393\pi\) | ||||
0.730272 | + | 0.683157i | \(0.239393\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 39.2024 | 1.27661 | ||||||||
\(944\) | −26.5694 | −0.864761 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −5.97497 | −0.194263 | ||||||||
\(947\) | −30.9990 | −1.00733 | −0.503666 | − | 0.863898i | \(-0.668016\pi\) | ||||
−0.503666 | + | 0.863898i | \(0.668016\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −36.3678 | −1.18055 | ||||||||
\(950\) | 22.1561 | 0.718840 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −2.53616 | −0.0821974 | ||||||||
\(953\) | −45.1029 | −1.46103 | −0.730513 | − | 0.682899i | \(-0.760719\pi\) | ||||
−0.730513 | + | 0.682899i | \(0.760719\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −1.13995 | −0.0368878 | ||||||||
\(956\) | 17.5965 | 0.569112 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 7.40059 | 0.239102 | ||||||||
\(959\) | −3.79688 | −0.122608 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 14.7932 | 0.477201 | ||||||||
\(962\) | 7.02335 | 0.226442 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −21.4490 | −0.690826 | ||||||||
\(965\) | 1.43961 | 0.0463426 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 57.9650 | 1.86403 | 0.932015 | − | 0.362420i | \(-0.118049\pi\) | ||||
0.932015 | + | 0.362420i | \(0.118049\pi\) | |||||||
\(968\) | 32.2717 | 1.03725 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −0.384448 | −0.0123439 | ||||||||
\(971\) | −48.9510 | −1.57091 | −0.785457 | − | 0.618916i | \(-0.787572\pi\) | ||||
−0.785457 | + | 0.618916i | \(0.787572\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 4.53910 | 0.145517 | ||||||||
\(974\) | 0.780984 | 0.0250243 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −24.8224 | −0.794546 | ||||||||
\(977\) | −38.2915 | −1.22505 | −0.612526 | − | 0.790450i | \(-0.709847\pi\) | ||||
−0.612526 | + | 0.790450i | \(0.709847\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 19.3314 | 0.617836 | ||||||||
\(980\) | −0.202839 | −0.00647944 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 7.12632 | 0.227410 | ||||||||
\(983\) | 4.26394 | 0.135999 | 0.0679993 | − | 0.997685i | \(-0.478338\pi\) | ||||
0.0679993 | + | 0.997685i | \(0.478338\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −0.599749 | −0.0191096 | ||||||||
\(986\) | −6.32162 | −0.201321 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 31.3941 | 0.998779 | ||||||||
\(989\) | 19.4539 | 0.618596 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 8.67251 | 0.275491 | 0.137746 | − | 0.990468i | \(-0.456014\pi\) | ||||
0.137746 | + | 0.990468i | \(0.456014\pi\) | |||||||
\(992\) | −35.3561 | −1.12256 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 2.19635 | 0.0696640 | ||||||||
\(995\) | 0.406371 | 0.0128828 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 31.2119 | 0.988492 | 0.494246 | − | 0.869322i | \(-0.335444\pi\) | ||||
0.494246 | + | 0.869322i | \(0.335444\pi\) | |||||||
\(998\) | −11.6472 | −0.368686 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 8001.2.a.t.1.6 | 16 | ||
3.2 | odd | 2 | 889.2.a.c.1.11 | ✓ | 16 | ||
21.20 | even | 2 | 6223.2.a.k.1.11 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
889.2.a.c.1.11 | ✓ | 16 | 3.2 | odd | 2 | ||
6223.2.a.k.1.11 | 16 | 21.20 | even | 2 | |||
8001.2.a.t.1.6 | 16 | 1.1 | even | 1 | trivial |