Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4016,2,Mod(1,4016)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4016, 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("4016.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4016 = 2^{4} \cdot 251 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4016.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(32.0679214517\) |
Analytic rank: | \(0\) |
Dimension: | \(7\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{7} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{7} - 3x^{6} - 6x^{5} + 18x^{4} + 8x^{3} - 17x^{2} - 9x - 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 1004) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.6 | ||
Root | \(2.29157\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4016.1 |
$q$-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 | 0 | ||||||||
\(3\) | 2.29157 | 1.32304 | 0.661520 | − | 0.749928i | \(-0.269912\pi\) | ||||
0.661520 | + | 0.749928i | \(0.269912\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.78468 | −0.798133 | −0.399067 | − | 0.916922i | \(-0.630666\pi\) | ||||
−0.399067 | + | 0.916922i | \(0.630666\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.671050 | −0.253633 | −0.126817 | − | 0.991926i | \(-0.540476\pi\) | ||||
−0.126817 | + | 0.991926i | \(0.540476\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 2.25130 | 0.750433 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2.23015 | −0.672416 | −0.336208 | − | 0.941788i | \(-0.609145\pi\) | ||||
−0.336208 | + | 0.941788i | \(0.609145\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.0525243 | 0.0145676 | 0.00728381 | − | 0.999973i | \(-0.497681\pi\) | ||||
0.00728381 | + | 0.999973i | \(0.497681\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −4.08972 | −1.05596 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 5.52610 | 1.34028 | 0.670138 | − | 0.742236i | \(-0.266235\pi\) | ||||
0.670138 | + | 0.742236i | \(0.266235\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.49944 | −0.343995 | −0.171997 | − | 0.985097i | \(-0.555022\pi\) | ||||
−0.171997 | + | 0.985097i | \(0.555022\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.53776 | −0.335567 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 7.13437 | 1.48762 | 0.743810 | − | 0.668391i | \(-0.233017\pi\) | ||||
0.743810 | + | 0.668391i | \(0.233017\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.81492 | −0.362984 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.71570 | −0.330187 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 2.08515 | 0.387202 | 0.193601 | − | 0.981080i | \(-0.437983\pi\) | ||||
0.193601 | + | 0.981080i | \(0.437983\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 9.61596 | 1.72708 | 0.863539 | − | 0.504282i | \(-0.168243\pi\) | ||||
0.863539 | + | 0.504282i | \(0.168243\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −5.11055 | −0.889633 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 1.19761 | 0.202433 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 5.33025 | 0.876288 | 0.438144 | − | 0.898905i | \(-0.355636\pi\) | ||||
0.438144 | + | 0.898905i | \(0.355636\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0.120363 | 0.0192735 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −11.8708 | −1.85391 | −0.926956 | − | 0.375170i | \(-0.877584\pi\) | ||||
−0.926956 | + | 0.375170i | \(0.877584\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 9.09066 | 1.38631 | 0.693157 | − | 0.720787i | \(-0.256219\pi\) | ||||
0.693157 | + | 0.720787i | \(0.256219\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −4.01785 | −0.598946 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −5.21388 | −0.760523 | −0.380261 | − | 0.924879i | \(-0.624166\pi\) | ||||
−0.380261 | + | 0.924879i | \(0.624166\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.54969 | −0.935670 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 12.6635 | 1.77324 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 4.27480 | 0.587189 | 0.293595 | − | 0.955930i | \(-0.405148\pi\) | ||||
0.293595 | + | 0.955930i | \(0.405148\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 3.98011 | 0.536678 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −3.43607 | −0.455118 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 0.163804 | 0.0213254 | 0.0106627 | − | 0.999943i | \(-0.496606\pi\) | ||||
0.0106627 | + | 0.999943i | \(0.496606\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 11.4800 | 1.46987 | 0.734934 | − | 0.678138i | \(-0.237213\pi\) | ||||
0.734934 | + | 0.678138i | \(0.237213\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −1.51073 | −0.190335 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −0.0937391 | −0.0116269 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 10.6984 | 1.30702 | 0.653509 | − | 0.756918i | \(-0.273296\pi\) | ||||
0.653509 | + | 0.756918i | \(0.273296\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 16.3489 | 1.96818 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 8.24538 | 0.978546 | 0.489273 | − | 0.872131i | \(-0.337262\pi\) | ||||
0.489273 | + | 0.872131i | \(0.337262\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −12.8635 | −1.50556 | −0.752779 | − | 0.658273i | \(-0.771287\pi\) | ||||
−0.752779 | + | 0.658273i | \(0.771287\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −4.15901 | −0.480241 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 1.49654 | 0.170547 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 7.86983 | 0.885425 | 0.442712 | − | 0.896664i | \(-0.354016\pi\) | ||||
0.442712 | + | 0.896664i | \(0.354016\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −10.6855 | −1.18728 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 5.22811 | 0.573860 | 0.286930 | − | 0.957952i | \(-0.407365\pi\) | ||||
0.286930 | + | 0.957952i | \(0.407365\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −9.86233 | −1.06972 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 4.77826 | 0.512283 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −2.70075 | −0.286279 | −0.143140 | − | 0.989703i | \(-0.545720\pi\) | ||||
−0.143140 | + | 0.989703i | \(0.545720\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −0.0352465 | −0.00369483 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 22.0357 | 2.28499 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 2.67602 | 0.274554 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 16.2733 | 1.65230 | 0.826150 | − | 0.563450i | \(-0.190526\pi\) | ||||
0.826150 | + | 0.563450i | \(0.190526\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −5.02074 | −0.504604 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 7.31471 | 0.727841 | 0.363920 | − | 0.931430i | \(-0.381438\pi\) | ||||
0.363920 | + | 0.931430i | \(0.381438\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 8.43476 | 0.831102 | 0.415551 | − | 0.909570i | \(-0.363589\pi\) | ||||
0.415551 | + | 0.909570i | \(0.363589\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 2.74441 | 0.267827 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 13.4235 | 1.29770 | 0.648851 | − | 0.760915i | \(-0.275250\pi\) | ||||
0.648851 | + | 0.760915i | \(0.275250\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −10.8033 | −1.03477 | −0.517386 | − | 0.855752i | \(-0.673095\pi\) | ||||
−0.517386 | + | 0.855752i | \(0.673095\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 12.2147 | 1.15936 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 6.62110 | 0.622861 | 0.311431 | − | 0.950269i | \(-0.399192\pi\) | ||||
0.311431 | + | 0.950269i | \(0.399192\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −12.7326 | −1.18732 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0.118248 | 0.0109320 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −3.70829 | −0.339939 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −6.02642 | −0.547856 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −27.2029 | −2.45280 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 12.1624 | 1.08784 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1.34857 | 0.119666 | 0.0598329 | − | 0.998208i | \(-0.480943\pi\) | ||||
0.0598329 | + | 0.998208i | \(0.480943\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 20.8319 | 1.83415 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −14.5213 | −1.26873 | −0.634365 | − | 0.773034i | \(-0.718738\pi\) | ||||
−0.634365 | + | 0.773034i | \(0.718738\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1.00620 | 0.0872484 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 3.06198 | 0.263533 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 4.81237 | 0.411148 | 0.205574 | − | 0.978642i | \(-0.434094\pi\) | ||||
0.205574 | + | 0.978642i | \(0.434094\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 17.6736 | 1.49905 | 0.749527 | − | 0.661974i | \(-0.230281\pi\) | ||||
0.749527 | + | 0.661974i | \(0.230281\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −11.9480 | −1.00620 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −0.117137 | −0.00979551 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −3.72132 | −0.309039 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −15.0091 | −1.23793 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 3.49560 | 0.286371 | 0.143185 | − | 0.989696i | \(-0.454265\pi\) | ||||
0.143185 | + | 0.989696i | \(0.454265\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 3.05261 | 0.248418 | 0.124209 | − | 0.992256i | \(-0.460361\pi\) | ||||
0.124209 | + | 0.992256i | \(0.460361\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 12.4409 | 1.00579 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −17.1614 | −1.37844 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −2.92795 | −0.233676 | −0.116838 | − | 0.993151i | \(-0.537276\pi\) | ||||
−0.116838 | + | 0.993151i | \(0.537276\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 9.79602 | 0.776875 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −4.78752 | −0.377310 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −11.1100 | −0.870200 | −0.435100 | − | 0.900382i | \(-0.643287\pi\) | ||||
−0.435100 | + | 0.900382i | \(0.643287\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 9.12070 | 0.710046 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −6.79223 | −0.525599 | −0.262799 | − | 0.964851i | \(-0.584646\pi\) | ||||
−0.262799 | + | 0.964851i | \(0.584646\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.9972 | −0.999788 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −3.37568 | −0.258145 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 19.7703 | 1.50311 | 0.751553 | − | 0.659673i | \(-0.229305\pi\) | ||||
0.751553 | + | 0.659673i | \(0.229305\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1.21790 | 0.0920646 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0.375368 | 0.0282144 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 17.5575 | 1.31231 | 0.656154 | − | 0.754627i | \(-0.272182\pi\) | ||||
0.656154 | + | 0.754627i | \(0.272182\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −3.21551 | −0.239007 | −0.119503 | − | 0.992834i | \(-0.538130\pi\) | ||||
−0.119503 | + | 0.992834i | \(0.538130\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 26.3073 | 1.94469 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −9.51280 | −0.699395 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −12.3241 | −0.901224 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 1.15132 | 0.0837463 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 12.1389 | 0.878342 | 0.439171 | − | 0.898404i | \(-0.355272\pi\) | ||||
0.439171 | + | 0.898404i | \(0.355272\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 11.5502 | 0.831399 | 0.415700 | − | 0.909502i | \(-0.363537\pi\) | ||||
0.415700 | + | 0.909502i | \(0.363537\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −0.214810 | −0.0153829 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −0.556439 | −0.0396447 | −0.0198223 | − | 0.999804i | \(-0.506310\pi\) | ||||
−0.0198223 | + | 0.999804i | \(0.506310\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −15.8849 | −1.12605 | −0.563025 | − | 0.826440i | \(-0.690363\pi\) | ||||
−0.563025 | + | 0.826440i | \(0.690363\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 24.5162 | 1.72924 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −1.39924 | −0.0982072 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 21.1856 | 1.47967 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 16.0616 | 1.11636 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 3.34398 | 0.231308 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 23.8560 | 1.64231 | 0.821156 | − | 0.570703i | \(-0.193329\pi\) | ||||
0.821156 | + | 0.570703i | \(0.193329\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 18.8949 | 1.29466 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −16.2239 | −1.10646 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −6.45279 | −0.438044 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −29.4776 | −1.99191 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0.290255 | 0.0195247 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −6.27008 | −0.419876 | −0.209938 | − | 0.977715i | \(-0.567326\pi\) | ||||
−0.209938 | + | 0.977715i | \(0.567326\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −4.08592 | −0.272395 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −5.69103 | −0.377727 | −0.188863 | − | 0.982003i | \(-0.560480\pi\) | ||||
−0.188863 | + | 0.982003i | \(0.560480\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −21.9135 | −1.44808 | −0.724042 | − | 0.689756i | \(-0.757718\pi\) | ||||
−0.724042 | + | 0.689756i | \(0.757718\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 3.42944 | 0.225640 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 11.6290 | 0.761841 | 0.380921 | − | 0.924608i | \(-0.375607\pi\) | ||||
0.380921 | + | 0.924608i | \(0.375607\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 9.30511 | 0.606999 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 18.0343 | 1.17145 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −17.3971 | −1.12533 | −0.562664 | − | 0.826686i | \(-0.690223\pi\) | ||||
−0.562664 | + | 0.826686i | \(0.690223\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −2.35929 | −0.151975 | −0.0759875 | − | 0.997109i | \(-0.524211\pi\) | ||||
−0.0759875 | + | 0.997109i | \(0.524211\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −19.3396 | −1.24064 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 11.6891 | 0.746789 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −0.0787570 | −0.00501119 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 11.9806 | 0.759239 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −1.00000 | −0.0631194 | ||||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −15.9107 | −1.00030 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −22.6002 | −1.41528 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −18.2850 | −1.14059 | −0.570293 | − | 0.821442i | \(-0.693170\pi\) | ||||
−0.570293 | + | 0.821442i | \(0.693170\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −3.57687 | −0.222256 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 4.69429 | 0.290569 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 1.62067 | 0.0999350 | 0.0499675 | − | 0.998751i | \(-0.484088\pi\) | ||||
0.0499675 | + | 0.998751i | \(0.484088\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −7.62916 | −0.468655 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −6.18896 | −0.378758 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −26.9395 | −1.64253 | −0.821265 | − | 0.570547i | \(-0.806731\pi\) | ||||
−0.821265 | + | 0.570547i | \(0.806731\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −1.70433 | −0.103531 | −0.0517653 | − | 0.998659i | \(-0.516485\pi\) | ||||
−0.0517653 | + | 0.998659i | \(0.516485\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −0.0807698 | −0.00488841 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 4.04754 | 0.244076 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 0.720069 | 0.0432648 | 0.0216324 | − | 0.999766i | \(-0.493114\pi\) | ||||
0.0216324 | + | 0.999766i | \(0.493114\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 21.6484 | 1.29606 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −9.07112 | −0.541138 | −0.270569 | − | 0.962701i | \(-0.587212\pi\) | ||||
−0.270569 | + | 0.962701i | \(0.587212\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 10.0455 | 0.597140 | 0.298570 | − | 0.954388i | \(-0.403490\pi\) | ||||
0.298570 | + | 0.954388i | \(0.403490\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 6.13228 | 0.363245 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 7.96592 | 0.470213 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 13.5378 | 0.796342 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 37.2914 | 2.18606 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −9.10277 | −0.531790 | −0.265895 | − | 0.964002i | \(-0.585667\pi\) | ||||
−0.265895 | + | 0.964002i | \(0.585667\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −0.292337 | −0.0170205 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 3.82628 | 0.222023 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0.374728 | 0.0216711 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −6.10029 | −0.351615 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 16.7622 | 0.962962 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −20.4882 | −1.17315 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 9.11554 | 0.520251 | 0.260126 | − | 0.965575i | \(-0.416236\pi\) | ||||
0.260126 | + | 0.965575i | \(0.416236\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 19.3289 | 1.09958 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −29.5389 | −1.67500 | −0.837498 | − | 0.546440i | \(-0.815982\pi\) | ||||
−0.837498 | + | 0.546440i | \(0.815982\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −1.02555 | −0.0579676 | −0.0289838 | − | 0.999580i | \(-0.509227\pi\) | ||||
−0.0289838 | + | 0.999580i | \(0.509227\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 2.69618 | 0.151912 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −3.25854 | −0.183018 | −0.0915089 | − | 0.995804i | \(-0.529169\pi\) | ||||
−0.0915089 | + | 0.995804i | \(0.529169\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −4.65019 | −0.260361 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 30.7610 | 1.71691 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −8.28605 | −0.461048 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −0.0953273 | −0.00528781 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −24.7566 | −1.36904 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 3.49878 | 0.192894 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −1.22129 | −0.0671281 | −0.0335640 | − | 0.999437i | \(-0.510686\pi\) | ||||
−0.0335640 | + | 0.999437i | \(0.510686\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 12.0000 | 0.657596 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −19.0932 | −1.04318 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 28.7954 | 1.56859 | 0.784293 | − | 0.620391i | \(-0.213026\pi\) | ||||
0.784293 | + | 0.620391i | \(0.213026\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 15.1727 | 0.824070 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −21.4451 | −1.16132 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 9.09252 | 0.490950 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −29.1776 | −1.57087 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 13.0949 | 0.702970 | 0.351485 | − | 0.936194i | \(-0.385677\pi\) | ||||
0.351485 | + | 0.936194i | \(0.385677\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −14.8887 | −0.796974 | −0.398487 | − | 0.917174i | \(-0.630465\pi\) | ||||
−0.398487 | + | 0.917174i | \(0.630465\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −0.0901160 | −0.00481004 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −29.2068 | −1.55452 | −0.777260 | − | 0.629179i | \(-0.783391\pi\) | ||||
−0.777260 | + | 0.629179i | \(0.783391\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −14.7154 | −0.781010 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −8.49782 | −0.449752 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −27.4180 | −1.44707 | −0.723534 | − | 0.690288i | \(-0.757484\pi\) | ||||
−0.723534 | + | 0.690288i | \(0.757484\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −16.7517 | −0.881668 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −13.8100 | −0.724835 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 22.9572 | 1.20164 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 31.9200 | 1.66621 | 0.833105 | − | 0.553115i | \(-0.186561\pi\) | ||||
0.833105 | + | 0.553115i | \(0.186561\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −26.7248 | −1.39124 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −2.86861 | −0.148931 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 16.2376 | 0.840753 | 0.420376 | − | 0.907350i | \(-0.361898\pi\) | ||||
0.420376 | + | 0.907350i | \(0.361898\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 27.8711 | 1.43926 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0.109521 | 0.00564061 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −21.8277 | −1.12121 | −0.560607 | − | 0.828082i | \(-0.689432\pi\) | ||||
−0.560607 | + | 0.828082i | \(0.689432\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 3.09033 | 0.158323 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −5.38270 | −0.275043 | −0.137521 | − | 0.990499i | \(-0.543914\pi\) | ||||
−0.137521 | + | 0.990499i | \(0.543914\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −2.67085 | −0.136119 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 20.4658 | 1.04034 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −30.3894 | −1.54080 | −0.770401 | − | 0.637560i | \(-0.779944\pi\) | ||||
−0.770401 | + | 0.637560i | \(0.779944\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 39.4253 | 1.99382 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −33.2766 | −1.67858 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −14.0451 | −0.706687 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 13.3900 | 0.672023 | 0.336011 | − | 0.941858i | \(-0.390922\pi\) | ||||
0.336011 | + | 0.941858i | \(0.390922\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 2.30577 | 0.115433 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −34.2511 | −1.71042 | −0.855209 | − | 0.518284i | \(-0.826571\pi\) | ||||
−0.855209 | + | 0.518284i | \(0.826571\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0.505072 | 0.0251594 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 19.0703 | 0.947610 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −11.8873 | −0.589231 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 13.3152 | 0.658394 | 0.329197 | − | 0.944261i | \(-0.393222\pi\) | ||||
0.329197 | + | 0.944261i | \(0.393222\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 11.0279 | 0.543965 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −0.109920 | −0.00540883 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −9.33050 | −0.458016 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 40.5003 | 1.98331 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −3.62652 | −0.177167 | −0.0885836 | − | 0.996069i | \(-0.528234\pi\) | ||||
−0.0885836 | + | 0.996069i | \(0.528234\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −9.05916 | −0.441516 | −0.220758 | − | 0.975329i | \(-0.570853\pi\) | ||||
−0.220758 | + | 0.975329i | \(0.570853\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −11.7380 | −0.570722 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −10.0294 | −0.486498 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −7.70368 | −0.372807 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −0.268428 | −0.0129598 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −1.80929 | −0.0871506 | −0.0435753 | − | 0.999050i | \(-0.513875\pi\) | ||||
−0.0435753 | + | 0.999050i | \(0.513875\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 6.34504 | 0.304923 | 0.152462 | − | 0.988309i | \(-0.451280\pi\) | ||||
0.152462 | + | 0.988309i | \(0.451280\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −8.52766 | −0.408870 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −10.6975 | −0.511733 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −30.1384 | −1.43843 | −0.719214 | − | 0.694788i | \(-0.755498\pi\) | ||||
−0.719214 | + | 0.694788i | \(0.755498\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −14.7453 | −0.702158 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 11.1274 | 0.528679 | 0.264339 | − | 0.964430i | \(-0.414846\pi\) | ||||
0.264339 | + | 0.964430i | \(0.414846\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 4.81998 | 0.228489 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 8.01042 | 0.378880 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 35.6616 | 1.68297 | 0.841487 | − | 0.540277i | \(-0.181680\pi\) | ||||
0.841487 | + | 0.540277i | \(0.181680\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 26.4738 | 1.24660 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 6.99527 | 0.328666 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0.0629036 | 0.00294897 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −31.2226 | −1.46053 | −0.730266 | − | 0.683163i | \(-0.760604\pi\) | ||||
−0.730266 | + | 0.683163i | \(0.760604\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −9.48114 | −0.442542 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 10.3296 | 0.481097 | 0.240549 | − | 0.970637i | \(-0.422673\pi\) | ||||
0.240549 | + | 0.970637i | \(0.422673\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 24.1578 | 1.12271 | 0.561355 | − | 0.827575i | \(-0.310280\pi\) | ||||
0.561355 | + | 0.827575i | \(0.310280\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −39.3266 | −1.82373 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −35.6761 | −1.65089 | −0.825447 | − | 0.564479i | \(-0.809077\pi\) | ||||
−0.825447 | + | 0.564479i | \(0.809077\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −7.17917 | −0.331503 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −6.70960 | −0.309162 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −20.2736 | −0.932180 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 2.72136 | 0.124864 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 9.62386 | 0.440646 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 4.37843 | 0.200055 | 0.100028 | − | 0.994985i | \(-0.468107\pi\) | ||||
0.100028 | + | 0.994985i | \(0.468107\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0.279968 | 0.0127654 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −10.9709 | −0.499195 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −29.0426 | −1.31876 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 32.4930 | 1.47240 | 0.736198 | − | 0.676766i | \(-0.236619\pi\) | ||||
0.736198 | + | 0.676766i | \(0.236619\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −25.4593 | −1.15131 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −12.9926 | −0.586348 | −0.293174 | − | 0.956059i | \(-0.594711\pi\) | ||||
−0.293174 | + | 0.956059i | \(0.594711\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 11.5227 | 0.518958 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 8.96042 | 0.402741 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −5.53306 | −0.248192 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −2.12523 | −0.0951383 | −0.0475691 | − | 0.998868i | \(-0.515147\pi\) | ||||
−0.0475691 | + | 0.998868i | \(0.515147\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −15.5649 | −0.695388 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −28.1675 | −1.25593 | −0.627964 | − | 0.778243i | \(-0.716111\pi\) | ||||
−0.627964 | + | 0.778243i | \(0.716111\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −13.0544 | −0.580914 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −29.7841 | −1.32276 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −3.65358 | −0.161942 | −0.0809710 | − | 0.996716i | \(-0.525802\pi\) | ||||
−0.0809710 | + | 0.996716i | \(0.525802\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 8.63205 | 0.381859 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 2.57259 | 0.113582 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −15.0533 | −0.663330 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 11.6278 | 0.511388 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 45.3050 | 1.98867 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −30.7443 | −1.34693 | −0.673465 | − | 0.739219i | \(-0.735195\pi\) | ||||
−0.673465 | + | 0.739219i | \(0.735195\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −25.0146 | −1.09381 | −0.546906 | − | 0.837194i | \(-0.684194\pi\) | ||||
−0.546906 | + | 0.837194i | \(0.684194\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 2.79091 | 0.121805 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 53.1388 | 2.31476 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 27.8993 | 1.21301 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0.368771 | 0.0160033 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −0.623507 | −0.0270071 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −23.9567 | −1.03574 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 40.2342 | 1.73623 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 14.6068 | 0.629160 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 19.3510 | 0.831964 | 0.415982 | − | 0.909373i | \(-0.363438\pi\) | ||||
0.415982 | + | 0.909373i | \(0.363438\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −7.36856 | −0.316215 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 19.2805 | 0.825886 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 2.14537 | 0.0917294 | 0.0458647 | − | 0.998948i | \(-0.485396\pi\) | ||||
0.0458647 | + | 0.998948i | \(0.485396\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 25.8450 | 1.10304 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −3.12655 | −0.133195 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −5.28105 | −0.224573 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −21.7993 | −0.925327 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 42.7554 | 1.81160 | 0.905802 | − | 0.423702i | \(-0.139270\pi\) | ||||
0.905802 | + | 0.423702i | \(0.139270\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0.477481 | 0.0201953 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −28.2415 | −1.19236 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −17.4443 | −0.735191 | −0.367596 | − | 0.929986i | \(-0.619819\pi\) | ||||
−0.367596 | + | 0.929986i | \(0.619819\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −11.8166 | −0.497126 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 7.17054 | 0.301134 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −36.4900 | −1.52974 | −0.764871 | − | 0.644184i | \(-0.777197\pi\) | ||||
−0.764871 | + | 0.644184i | \(0.777197\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 41.9707 | 1.75642 | 0.878210 | − | 0.478275i | \(-0.158738\pi\) | ||||
0.878210 | + | 0.478275i | \(0.158738\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 27.8172 | 1.16208 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −12.9483 | −0.539981 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 12.3140 | 0.512639 | 0.256320 | − | 0.966592i | \(-0.417490\pi\) | ||||
0.256320 | + | 0.966592i | \(0.417490\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 26.4680 | 1.09997 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −3.50832 | −0.145550 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −9.53347 | −0.394836 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −0.211035 | −0.00872522 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −13.8231 | −0.570540 | −0.285270 | − | 0.958447i | \(-0.592083\pi\) | ||||
−0.285270 | + | 0.958447i | \(0.592083\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −14.4185 | −0.594105 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −1.27512 | −0.0524515 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 15.5625 | 0.639075 | 0.319538 | − | 0.947574i | \(-0.396472\pi\) | ||||
0.319538 | + | 0.947574i | \(0.396472\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 6.61811 | 0.271316 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −36.4014 | −1.48981 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −6.86070 | −0.280321 | −0.140160 | − | 0.990129i | \(-0.544762\pi\) | ||||
−0.140160 | + | 0.990129i | \(0.544762\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 3.73347 | 0.152292 | 0.0761458 | − | 0.997097i | \(-0.475739\pi\) | ||||
0.0761458 | + | 0.997097i | \(0.475739\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 24.0853 | 0.980830 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 10.7552 | 0.437262 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −40.4537 | −1.64197 | −0.820983 | − | 0.570953i | \(-0.806574\pi\) | ||||
−0.820983 | + | 0.570953i | \(0.806574\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −3.20645 | −0.129932 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −0.273856 | −0.0110790 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −18.2453 | −0.736921 | −0.368460 | − | 0.929643i | \(-0.620115\pi\) | ||||
−0.368460 | + | 0.929643i | \(0.620115\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 48.5484 | 1.95766 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 20.5886 | 0.828864 | 0.414432 | − | 0.910080i | \(-0.363980\pi\) | ||||
0.414432 | + | 0.910080i | \(0.363980\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 11.8400 | 0.475890 | 0.237945 | − | 0.971279i | \(-0.423526\pi\) | ||||
0.237945 | + | 0.971279i | \(0.423526\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −12.2404 | −0.491192 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 1.81234 | 0.0726098 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −12.6315 | −0.505259 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 7.66296 | 0.306029 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 29.4555 | 1.17447 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 24.3224 | 0.968258 | 0.484129 | − | 0.874997i | \(-0.339137\pi\) | ||||
0.484129 | + | 0.874997i | \(0.339137\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 54.6677 | 2.17284 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −2.40676 | −0.0955093 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −0.344018 | −0.0136305 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 18.5628 | 0.734333 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 14.8821 | 0.587808 | 0.293904 | − | 0.955835i | \(-0.405045\pi\) | ||||
0.293904 | + | 0.955835i | \(0.405045\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 9.38851 | 0.370247 | 0.185123 | − | 0.982715i | \(-0.440732\pi\) | ||||
0.185123 | + | 0.982715i | \(0.440732\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −37.1783 | −1.46389 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 24.9638 | 0.981430 | 0.490715 | − | 0.871320i | \(-0.336736\pi\) | ||||
0.490715 | + | 0.871320i | \(0.336736\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −0.365307 | −0.0143396 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −14.7870 | −0.579550 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 34.0819 | 1.33373 | 0.666865 | − | 0.745179i | \(-0.267636\pi\) | ||||
0.666865 | + | 0.745179i | \(0.267636\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 25.9158 | 1.01262 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −28.9596 | −1.12982 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −19.7009 | −0.767440 | −0.383720 | − | 0.923450i | \(-0.625357\pi\) | ||||
−0.383720 | + | 0.923450i | \(0.625357\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 17.9804 | 0.699358 | 0.349679 | − | 0.936870i | \(-0.386291\pi\) | ||||
0.349679 | + | 0.936870i | \(0.386291\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0.665140 | 0.0258319 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −1.79574 | −0.0696359 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 14.8762 | 0.576009 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −14.3683 | −0.555512 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −25.6022 | −0.988364 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −10.6371 | −0.410029 | −0.205015 | − | 0.978759i | \(-0.565724\pi\) | ||||
−0.205015 | + | 0.978759i | \(0.565724\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 3.11386 | 0.119852 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −11.0551 | −0.424883 | −0.212441 | − | 0.977174i | \(-0.568141\pi\) | ||||
−0.212441 | + | 0.977174i | \(0.568141\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −10.9202 | −0.419078 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −13.0414 | −0.499748 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 26.2786 | 1.00552 | 0.502762 | − | 0.864425i | \(-0.332317\pi\) | ||||
0.502762 | + | 0.864425i | \(0.332317\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −8.58853 | −0.328151 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −50.2163 | −1.91587 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 0.224531 | 0.00855396 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 29.0629 | 1.10561 | 0.552803 | − | 0.833312i | \(-0.313558\pi\) | ||||
0.552803 | + | 0.833312i | \(0.313558\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 3.36917 | 0.127984 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −31.5417 | −1.19644 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −65.5994 | −2.48476 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 26.6487 | 1.00795 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −29.7473 | −1.12354 | −0.561771 | − | 0.827293i | \(-0.689880\pi\) | ||||
−0.561771 | + | 0.827293i | \(0.689880\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −7.99238 | −0.301438 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 21.3233 | 0.803083 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −4.90854 | −0.184605 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 30.8047 | 1.15689 | 0.578447 | − | 0.815720i | \(-0.303659\pi\) | ||||
0.578447 | + | 0.815720i | \(0.303659\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 17.7173 | 0.664452 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 68.6038 | 2.56923 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0.209053 | 0.00781812 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −39.8668 | −1.48885 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −29.2904 | −1.09235 | −0.546175 | − | 0.837671i | \(-0.683917\pi\) | ||||
−0.546175 | + | 0.837671i | \(0.683917\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −5.66015 | −0.210795 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −5.40647 | −0.201069 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −3.78437 | −0.140548 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 37.9357 | 1.40696 | 0.703479 | − | 0.710716i | \(-0.251629\pi\) | ||||
0.703479 | + | 0.710716i | \(0.251629\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −12.2614 | −0.454127 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 50.2359 | 1.85804 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 15.8326 | 0.584792 | 0.292396 | − | 0.956297i | \(-0.405547\pi\) | ||||
0.292396 | + | 0.956297i | \(0.405547\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 26.7864 | 0.988032 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −23.8591 | −0.878861 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −9.06045 | −0.333294 | −0.166647 | − | 0.986017i | \(-0.553294\pi\) | ||||
−0.166647 | + | 0.986017i | \(0.553294\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −0.180477 | −0.00663000 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 8.42135 | 0.308949 | 0.154475 | − | 0.987997i | \(-0.450631\pi\) | ||||
0.154475 | + | 0.987997i | \(0.450631\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −6.23853 | −0.228562 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 11.7700 | 0.430643 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −9.00787 | −0.329140 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 19.2016 | 0.700677 | 0.350338 | − | 0.936623i | \(-0.386067\pi\) | ||||
0.350338 | + | 0.936623i | \(0.386067\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −2.29157 | −0.0835095 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −5.44793 | −0.198270 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −9.32193 | −0.338811 | −0.169406 | − | 0.985546i | \(-0.554185\pi\) | ||||
−0.169406 | + | 0.985546i | \(0.554185\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −36.4606 | −1.32344 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 51.3651 | 1.86198 | 0.930992 | − | 0.365041i | \(-0.118945\pi\) | ||||
0.930992 | + | 0.365041i | \(0.118945\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 7.24958 | 0.262452 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −22.2030 | −0.802753 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0.00860367 | 0.000310661 0 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 43.2738 | 1.56049 | 0.780246 | − | 0.625473i | \(-0.215094\pi\) | ||||
0.780246 | + | 0.625473i | \(0.215094\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −41.9013 | −1.50904 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −6.59292 | −0.237131 | −0.118565 | − | 0.992946i | \(-0.537830\pi\) | ||||
−0.118565 | + | 0.992946i | \(0.537830\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −17.4522 | −0.626901 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −8.19665 | −0.294053 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 17.7996 | 0.637736 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −18.3885 | −0.657991 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −3.57749 | −0.127849 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 5.22545 | 0.186504 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 51.1075 | 1.82179 | 0.910893 | − | 0.412642i | \(-0.135394\pi\) | ||||
0.910893 | + | 0.412642i | \(0.135394\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 3.71389 | 0.132218 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −4.44309 | −0.157978 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0.602981 | 0.0214125 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −17.4828 | −0.620049 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 37.6794 | 1.33467 | 0.667337 | − | 0.744756i | \(-0.267434\pi\) | ||||
0.667337 | + | 0.744756i | \(0.267434\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −28.8125 | −1.01931 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −6.08020 | −0.214833 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 28.6876 | 1.01236 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 8.54419 | 0.301143 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −61.7338 | −2.17313 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −38.0342 | −1.33721 | −0.668605 | − | 0.743618i | \(-0.733108\pi\) | ||||
−0.668605 | + | 0.743618i | \(0.733108\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −13.6164 | −0.478138 | −0.239069 | − | 0.971003i | \(-0.576842\pi\) | ||||
−0.239069 | + | 0.971003i | \(0.576842\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −3.90559 | −0.136975 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 19.8277 | 0.694535 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −13.6309 | −0.476884 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −0.0793503 | −0.00277272 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 30.5818 | 1.06731 | 0.533656 | − | 0.845702i | \(-0.320818\pi\) | ||||
0.533656 | + | 0.845702i | \(0.320818\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 18.4303 | 0.642439 | 0.321220 | − | 0.947005i | \(-0.395907\pi\) | ||||
0.321220 | + | 0.947005i | \(0.395907\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 9.27524 | 0.322922 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 2.06070 | 0.0716577 | 0.0358288 | − | 0.999358i | \(-0.488593\pi\) | ||||
0.0358288 | + | 0.999358i | \(0.488593\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 53.5915 | 1.86131 | 0.930655 | − | 0.365897i | \(-0.119238\pi\) | ||||
0.930655 | + | 0.365897i | \(0.119238\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 1.65009 | 0.0572410 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −36.1943 | −1.25406 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 12.1220 | 0.419498 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −16.4981 | −0.570258 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 9.37280 | 0.323585 | 0.161792 | − | 0.986825i | \(-0.448272\pi\) | ||||
0.161792 | + | 0.986825i | \(0.448272\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −24.6522 | −0.850075 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −20.7871 | −0.715946 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 23.1959 | 0.797964 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 4.04403 | 0.138954 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 23.0199 | 0.790040 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 38.0280 | 1.30358 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −8.69000 | −0.297540 | −0.148770 | − | 0.988872i | \(-0.547531\pi\) | ||||
−0.148770 | + | 0.988872i | \(0.547531\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 6.02451 | 0.206034 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −17.4197 | −0.595045 | −0.297522 | − | 0.954715i | \(-0.596160\pi\) | ||||
−0.297522 | + | 0.954715i | \(0.596160\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −38.0839 | −1.29941 | −0.649703 | − | 0.760188i | \(-0.725107\pi\) | ||||
−0.649703 | + | 0.760188i | \(0.725107\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 18.2545 | 0.622111 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −1.47779 | −0.0503046 | −0.0251523 | − | 0.999684i | \(-0.508007\pi\) | ||||
−0.0251523 | + | 0.999684i | \(0.508007\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −35.2836 | −1.19968 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 31.0229 | 1.05359 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −17.5509 | −0.595374 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0.561927 | 0.0190402 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 36.6360 | 1.23994 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −8.16161 | −0.275913 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 16.1183 | 0.544278 | 0.272139 | − | 0.962258i | \(-0.412269\pi\) | ||||
0.272139 | + | 0.962258i | \(0.412269\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −20.8597 | −0.703579 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −25.7458 | −0.867399 | −0.433699 | − | 0.901058i | \(-0.642792\pi\) | ||||
−0.433699 | + | 0.901058i | \(0.642792\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −51.3112 | −1.72676 | −0.863380 | − | 0.504554i | \(-0.831657\pi\) | ||||
−0.863380 | + | 0.504554i | \(0.831657\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −0.669911 | −0.0225188 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −26.4272 | −0.887339 | −0.443670 | − | 0.896190i | \(-0.646324\pi\) | ||||
−0.443670 | + | 0.896190i | \(0.646324\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −0.904955 | −0.0303512 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 23.8304 | 0.798349 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 7.81789 | 0.261616 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −31.3345 | −1.04740 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0.858716 | 0.0286717 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 20.0507 | 0.668727 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 23.6230 | 0.786996 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −13.9793 | −0.465200 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 5.73865 | 0.190759 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −41.6133 | −1.38175 | −0.690873 | − | 0.722976i | \(-0.742774\pi\) | ||||
−0.690873 | + | 0.722976i | \(0.742774\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 16.4676 | 0.546196 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −48.6569 | −1.61208 | −0.806038 | − | 0.591864i | \(-0.798392\pi\) | ||||
−0.806038 | + | 0.591864i | \(0.798392\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −11.6595 | −0.385873 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −46.9502 | −1.55212 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 9.74451 | 0.321792 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −32.6597 | −1.07734 | −0.538672 | − | 0.842515i | \(-0.681074\pi\) | ||||
−0.538672 | + | 0.842515i | \(0.681074\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 20.8889 | 0.688313 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0.433083 | 0.0142551 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −9.67397 | −0.318078 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 18.9892 | 0.623686 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −29.0898 | −0.954406 | −0.477203 | − | 0.878793i | \(-0.658349\pi\) | ||||
−0.477203 | + | 0.878793i | \(0.658349\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 9.82086 | 0.321866 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −67.6904 | −2.21609 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 21.9945 | 0.719297 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 39.3014 | 1.28392 | 0.641960 | − | 0.766738i | \(-0.278122\pi\) | ||||
0.641960 | + | 0.766738i | \(0.278122\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −2.35013 | −0.0766934 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 17.7356 | 0.578163 | 0.289082 | − | 0.957304i | \(-0.406650\pi\) | ||||
0.289082 | + | 0.957304i | \(0.406650\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −84.6909 | −2.75792 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −2.05474 | −0.0668407 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −41.3091 | −1.34237 | −0.671183 | − | 0.741292i | \(-0.734213\pi\) | ||||
−0.671183 | + | 0.741292i | \(0.734213\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −0.675646 | −0.0219324 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −7.46717 | −0.242140 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 19.6289 | 0.635842 | 0.317921 | − | 0.948117i | \(-0.397015\pi\) | ||||
0.317921 | + | 0.948117i | \(0.397015\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −21.6641 | −0.701033 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −10.6562 | −0.344468 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −3.22934 | −0.104281 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 61.4667 | 1.98280 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 30.2204 | 0.973839 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −20.6134 | −0.663567 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −44.3193 | −1.42521 | −0.712606 | − | 0.701565i | \(-0.752485\pi\) | ||||
−0.712606 | + | 0.701565i | \(0.752485\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −18.9881 | −0.609985 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 4.22052 | 0.135443 | 0.0677214 | − | 0.997704i | \(-0.478427\pi\) | ||||
0.0677214 | + | 0.997704i | \(0.478427\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −11.8599 | −0.380210 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −0.218449 | −0.00699598 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −29.3344 | −0.938492 | −0.469246 | − | 0.883068i | \(-0.655474\pi\) | ||||
−0.469246 | + | 0.883068i | \(0.655474\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 6.02309 | 0.192499 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −24.3215 | −0.776527 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −55.0110 | −1.75458 | −0.877290 | − | 0.479961i | \(-0.840651\pi\) | ||||
−0.877290 | + | 0.479961i | \(0.840651\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0.993066 | 0.0316417 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 8.01770 | 0.255206 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 64.8562 | 2.06231 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 8.39630 | 0.266717 | 0.133359 | − | 0.991068i | \(-0.457424\pi\) | ||||
0.133359 | + | 0.991068i | \(0.457424\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −2.79867 | −0.0888131 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 28.3495 | 0.898738 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 15.7423 | 0.498564 | 0.249282 | − | 0.968431i | \(-0.419805\pi\) | ||||
0.249282 | + | 0.968431i | \(0.419805\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −9.14512 | −0.289339 |
(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 | 4016.2.a.g.1.6 | 7 | ||
4.3 | odd | 2 | 1004.2.a.a.1.2 | ✓ | 7 | ||
12.11 | even | 2 | 9036.2.a.i.1.6 | 7 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1004.2.a.a.1.2 | ✓ | 7 | 4.3 | odd | 2 | ||
4016.2.a.g.1.6 | 7 | 1.1 | even | 1 | trivial | ||
9036.2.a.i.1.6 | 7 | 12.11 | even | 2 |