Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4140,2,Mod(1,4140)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4140, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("4140.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4140 = 2^{2} \cdot 3^{2} \cdot 5 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4140.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: | \(33.0580664368\) |
Analytic rank: | \(0\) |
Dimension: | \(5\) |
Coefficient field: | 5.5.14345904.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{5} - 2x^{4} - 13x^{3} + 34x^{2} - 11x - 12 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(1.23445\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4140.1 |
$q$-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 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.81459 | 1.06382 | 0.531908 | − | 0.846802i | \(-0.321475\pi\) | ||||
0.531908 | + | 0.846802i | \(0.321475\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −4.70892 | −1.41979 | −0.709897 | − | 0.704306i | \(-0.751258\pi\) | ||||
−0.709897 | + | 0.704306i | \(0.751258\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 4.24002 | 1.17597 | 0.587985 | − | 0.808872i | \(-0.299921\pi\) | ||||
0.587985 | + | 0.808872i | \(0.299921\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 3.85252 | 0.934374 | 0.467187 | − | 0.884159i | \(-0.345267\pi\) | ||||
0.467187 | + | 0.884159i | \(0.345267\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 6.70892 | 1.53913 | 0.769566 | − | 0.638567i | \(-0.220473\pi\) | ||||
0.769566 | + | 0.638567i | \(0.220473\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.00000 | 0.208514 | ||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −1.42543 | −0.264696 | −0.132348 | − | 0.991203i | \(-0.542252\pi\) | ||||
−0.132348 | + | 0.991203i | \(0.542252\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −9.03035 | −1.62190 | −0.810949 | − | 0.585117i | \(-0.801049\pi\) | ||||
−0.810949 | + | 0.585117i | \(0.801049\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 2.81459 | 0.475753 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 5.28349 | 0.868601 | 0.434300 | − | 0.900768i | \(-0.356996\pi\) | ||||
0.434300 | + | 0.900768i | \(0.356996\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −10.3777 | −1.62072 | −0.810362 | − | 0.585930i | \(-0.800730\pi\) | ||||
−0.810362 | + | 0.585930i | \(0.800730\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 12.1739 | 1.85651 | 0.928255 | − | 0.371945i | \(-0.121309\pi\) | ||||
0.928255 | + | 0.371945i | \(0.121309\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 10.0287 | 1.46283 | 0.731417 | − | 0.681930i | \(-0.238859\pi\) | ||||
0.731417 | + | 0.681930i | \(0.238859\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0.921920 | 0.131703 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −9.17229 | −1.25991 | −0.629955 | − | 0.776632i | \(-0.716927\pi\) | ||||
−0.629955 | + | 0.776632i | \(0.716927\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −4.70892 | −0.634951 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 6.36323 | 0.828422 | 0.414211 | − | 0.910181i | \(-0.364058\pi\) | ||||
0.414211 | + | 0.910181i | \(0.364058\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −10.4140 | −1.33337 | −0.666686 | − | 0.745339i | \(-0.732288\pi\) | ||||
−0.666686 | + | 0.745339i | \(0.732288\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 4.24002 | 0.525910 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 6.50517 | 0.794733 | 0.397367 | − | 0.917660i | \(-0.369924\pi\) | ||||
0.397367 | + | 0.917660i | \(0.369924\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 8.74852 | 1.03826 | 0.519129 | − | 0.854696i | \(-0.326256\pi\) | ||||
0.519129 | + | 0.854696i | \(0.326256\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −0.240022 | −0.0280924 | −0.0140462 | − | 0.999901i | \(-0.504471\pi\) | ||||
−0.0140462 | + | 0.999901i | \(0.504471\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −13.2537 | −1.51040 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −4.48337 | −0.504418 | −0.252209 | − | 0.967673i | \(-0.581157\pi\) | ||||
−0.252209 | + | 0.967673i | \(0.581157\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 13.1109 | 1.43911 | 0.719553 | − | 0.694437i | \(-0.244347\pi\) | ||||
0.719553 | + | 0.694437i | \(0.244347\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 3.85252 | 0.417865 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −7.62918 | −0.808692 | −0.404346 | − | 0.914606i | \(-0.632501\pi\) | ||||
−0.404346 | + | 0.914606i | \(0.632501\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 11.9339 | 1.25102 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 6.70892 | 0.688321 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −0.385284 | −0.0391196 | −0.0195598 | − | 0.999809i | \(-0.506226\pi\) | ||||
−0.0195598 | + | 0.999809i | \(0.506226\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 16.5372 | 1.64551 | 0.822755 | − | 0.568396i | \(-0.192436\pi\) | ||||
0.822755 | + | 0.568396i | \(0.192436\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −17.5918 | −1.73337 | −0.866685 | − | 0.498855i | \(-0.833754\pi\) | ||||
−0.866685 | + | 0.498855i | \(0.833754\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −13.9506 | −1.34866 | −0.674328 | − | 0.738432i | \(-0.735567\pi\) | ||||
−0.674328 | + | 0.738432i | \(0.735567\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 6.70892 | 0.642598 | 0.321299 | − | 0.946978i | \(-0.395881\pi\) | ||||
0.321299 | + | 0.946978i | \(0.395881\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 11.1756 | 1.05131 | 0.525656 | − | 0.850697i | \(-0.323820\pi\) | ||||
0.525656 | + | 0.850697i | \(0.323820\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1.00000 | 0.0932505 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 10.8433 | 0.994001 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 11.1739 | 1.01581 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 15.0942 | 1.33939 | 0.669697 | − | 0.742634i | \(-0.266424\pi\) | ||||
0.669697 | + | 0.742634i | \(0.266424\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −1.62918 | −0.142342 | −0.0711711 | − | 0.997464i | \(-0.522674\pi\) | ||||
−0.0711711 | + | 0.997464i | \(0.522674\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 18.8829 | 1.63735 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −5.61804 | −0.479981 | −0.239991 | − | 0.970775i | \(-0.577144\pi\) | ||||
−0.239991 | + | 0.970775i | \(0.577144\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 4.07808 | 0.345898 | 0.172949 | − | 0.984931i | \(-0.444670\pi\) | ||||
0.172949 | + | 0.984931i | \(0.444670\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −19.9659 | −1.66964 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −1.42543 | −0.118376 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −20.1268 | −1.64885 | −0.824424 | − | 0.565972i | \(-0.808501\pi\) | ||||
−0.824424 | + | 0.565972i | \(0.808501\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 18.1739 | 1.47897 | 0.739487 | − | 0.673170i | \(-0.235068\pi\) | ||||
0.739487 | + | 0.673170i | \(0.235068\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −9.03035 | −0.725335 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 15.0833 | 1.20378 | 0.601889 | − | 0.798580i | \(-0.294415\pi\) | ||||
0.601889 | + | 0.798580i | \(0.294415\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 2.81459 | 0.221821 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 0.294954 | 0.0231026 | 0.0115513 | − | 0.999933i | \(-0.496323\pi\) | ||||
0.0115513 | + | 0.999933i | \(0.496323\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 4.24334 | 0.328360 | 0.164180 | − | 0.986430i | \(-0.447502\pi\) | ||||
0.164180 | + | 0.986430i | \(0.447502\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 4.97778 | 0.382906 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 24.9116 | 1.89399 | 0.946995 | − | 0.321248i | \(-0.104102\pi\) | ||||
0.946995 | + | 0.321248i | \(0.104102\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 2.81459 | 0.212763 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −7.03256 | −0.525638 | −0.262819 | − | 0.964845i | \(-0.584652\pi\) | ||||
−0.262819 | + | 0.964845i | \(0.584652\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −15.5806 | −1.15810 | −0.579050 | − | 0.815292i | \(-0.696576\pi\) | ||||
−0.579050 | + | 0.815292i | \(0.696576\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 5.28349 | 0.388450 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −18.1412 | −1.32662 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −16.8940 | −1.22241 | −0.611204 | − | 0.791473i | \(-0.709314\pi\) | ||||
−0.611204 | + | 0.791473i | \(0.709314\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −1.22500 | −0.0881776 | −0.0440888 | − | 0.999028i | \(-0.514038\pi\) | ||||
−0.0440888 | + | 0.999028i | \(0.514038\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −18.1092 | −1.29023 | −0.645114 | − | 0.764086i | \(-0.723190\pi\) | ||||
−0.645114 | + | 0.764086i | \(0.723190\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 22.1962 | 1.57344 | 0.786722 | − | 0.617307i | \(-0.211776\pi\) | ||||
0.786722 | + | 0.617307i | \(0.211776\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −4.01200 | −0.281588 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −10.3777 | −0.724810 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −31.5918 | −2.18525 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −23.6843 | −1.63050 | −0.815248 | − | 0.579111i | \(-0.803400\pi\) | ||||
−0.815248 | + | 0.579111i | \(0.803400\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 12.1739 | 0.830256 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −25.4167 | −1.72540 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 16.3348 | 1.09880 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 15.7050 | 1.05169 | 0.525844 | − | 0.850581i | \(-0.323750\pi\) | ||||
0.525844 | + | 0.850581i | \(0.323750\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −10.3206 | −0.685000 | −0.342500 | − | 0.939518i | \(-0.611274\pi\) | ||||
−0.342500 | + | 0.939518i | \(0.611274\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 3.54556 | 0.234297 | 0.117149 | − | 0.993114i | \(-0.462625\pi\) | ||||
0.117149 | + | 0.993114i | \(0.462625\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −1.22168 | −0.0800350 | −0.0400175 | − | 0.999199i | \(-0.512741\pi\) | ||||
−0.0400175 | + | 0.999199i | \(0.512741\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 10.0287 | 0.654199 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −12.8211 | −0.829325 | −0.414663 | − | 0.909975i | \(-0.636100\pi\) | ||||
−0.414663 | + | 0.909975i | \(0.636100\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 17.6390 | 1.13623 | 0.568113 | − | 0.822951i | \(-0.307674\pi\) | ||||
0.568113 | + | 0.822951i | \(0.307674\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0.921920 | 0.0588993 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 28.4460 | 1.80997 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −19.1596 | −1.20934 | −0.604671 | − | 0.796476i | \(-0.706695\pi\) | ||||
−0.604671 | + | 0.796476i | \(0.706695\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −4.70892 | −0.296047 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 13.2034 | 0.823607 | 0.411804 | − | 0.911273i | \(-0.364899\pi\) | ||||
0.411804 | + | 0.911273i | \(0.364899\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 14.8709 | 0.924031 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 26.3029 | 1.62191 | 0.810954 | − | 0.585110i | \(-0.198949\pi\) | ||||
0.810954 | + | 0.585110i | \(0.198949\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −9.17229 | −0.563449 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 7.53466 | 0.459396 | 0.229698 | − | 0.973262i | \(-0.426226\pi\) | ||||
0.229698 | + | 0.973262i | \(0.426226\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 2.21355 | 0.134464 | 0.0672319 | − | 0.997737i | \(-0.478583\pi\) | ||||
0.0672319 | + | 0.997737i | \(0.478583\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −4.70892 | −0.283959 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 10.4867 | 0.630084 | 0.315042 | − | 0.949078i | \(-0.397981\pi\) | ||||
0.315042 | + | 0.949078i | \(0.397981\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 23.2682 | 1.38806 | 0.694031 | − | 0.719945i | \(-0.255833\pi\) | ||||
0.694031 | + | 0.719945i | \(0.255833\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 23.3297 | 1.38681 | 0.693404 | − | 0.720549i | \(-0.256110\pi\) | ||||
0.693404 | + | 0.720549i | \(0.256110\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −29.2090 | −1.72415 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −2.15807 | −0.126945 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −26.2371 | −1.53279 | −0.766394 | − | 0.642371i | \(-0.777951\pi\) | ||||
−0.766394 | + | 0.642371i | \(0.777951\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 6.36323 | 0.370482 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 4.24002 | 0.245207 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 34.2647 | 1.97498 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −10.4140 | −0.596302 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 13.3814 | 0.763717 | 0.381859 | − | 0.924221i | \(-0.375284\pi\) | ||||
0.381859 | + | 0.924221i | \(0.375284\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 19.3309 | 1.09616 | 0.548078 | − | 0.836428i | \(-0.315360\pi\) | ||||
0.548078 | + | 0.836428i | \(0.315360\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −8.90492 | −0.503336 | −0.251668 | − | 0.967814i | \(-0.580979\pi\) | ||||
−0.251668 | + | 0.967814i | \(0.580979\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 4.32696 | 0.243026 | 0.121513 | − | 0.992590i | \(-0.461225\pi\) | ||||
0.121513 | + | 0.992590i | \(0.461225\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 6.71224 | 0.375814 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 25.8463 | 1.43813 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 4.24002 | 0.235194 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 28.2266 | 1.55619 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 17.9681 | 0.987619 | 0.493809 | − | 0.869570i | \(-0.335604\pi\) | ||||
0.493809 | + | 0.869570i | \(0.335604\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 6.50517 | 0.355416 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 4.93448 | 0.268798 | 0.134399 | − | 0.990927i | \(-0.457090\pi\) | ||||
0.134399 | + | 0.990927i | \(0.457090\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 42.5232 | 2.30276 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −17.1073 | −0.923708 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −7.06220 | −0.379119 | −0.189559 | − | 0.981869i | \(-0.560706\pi\) | ||||
−0.189559 | + | 0.981869i | \(0.560706\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −36.3349 | −1.94496 | −0.972482 | − | 0.232977i | \(-0.925153\pi\) | ||||
−0.972482 | + | 0.232977i | \(0.925153\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −1.83252 | −0.0975353 | −0.0487676 | − | 0.998810i | \(-0.515529\pi\) | ||||
−0.0487676 | + | 0.998810i | \(0.515529\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 8.74852 | 0.464323 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 16.6587 | 0.879211 | 0.439605 | − | 0.898191i | \(-0.355118\pi\) | ||||
0.439605 | + | 0.898191i | \(0.355118\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 26.0096 | 1.36893 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −0.240022 | −0.0125633 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 14.9060 | 0.778088 | 0.389044 | − | 0.921219i | \(-0.372805\pi\) | ||||
0.389044 | + | 0.921219i | \(0.372805\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −25.8162 | −1.34031 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 9.99929 | 0.517744 | 0.258872 | − | 0.965912i | \(-0.416649\pi\) | ||||
0.258872 | + | 0.965912i | \(0.416649\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −6.04386 | −0.311275 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −25.7624 | −1.32333 | −0.661663 | − | 0.749801i | \(-0.730149\pi\) | ||||
−0.661663 | + | 0.749801i | \(0.730149\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 7.56089 | 0.386343 | 0.193172 | − | 0.981165i | \(-0.438123\pi\) | ||||
0.193172 | + | 0.981165i | \(0.438123\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −13.2537 | −0.675470 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −20.1884 | −1.02359 | −0.511797 | − | 0.859107i | \(-0.671020\pi\) | ||||
−0.511797 | + | 0.859107i | \(0.671020\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 3.85252 | 0.194830 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −4.48337 | −0.225583 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −15.3453 | −0.770159 | −0.385079 | − | 0.922883i | \(-0.625826\pi\) | ||||
−0.385079 | + | 0.922883i | \(0.625826\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 22.8542 | 1.14128 | 0.570642 | − | 0.821199i | \(-0.306695\pi\) | ||||
0.570642 | + | 0.821199i | \(0.306695\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −38.2889 | −1.90730 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −24.8795 | −1.23323 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −21.9793 | −1.08681 | −0.543403 | − | 0.839472i | \(-0.682864\pi\) | ||||
−0.543403 | + | 0.839472i | \(0.682864\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 17.9099 | 0.881288 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 13.1109 | 0.643588 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 25.8207 | 1.26143 | 0.630713 | − | 0.776016i | \(-0.282763\pi\) | ||||
0.630713 | + | 0.776016i | \(0.282763\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −24.0431 | −1.17179 | −0.585896 | − | 0.810386i | \(-0.699257\pi\) | ||||
−0.585896 | + | 0.810386i | \(0.699257\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 3.85252 | 0.186875 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −29.3111 | −1.41846 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 39.4060 | 1.89812 | 0.949060 | − | 0.315096i | \(-0.102037\pi\) | ||||
0.949060 | + | 0.315096i | \(0.102037\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 29.2717 | 1.40671 | 0.703354 | − | 0.710839i | \(-0.251685\pi\) | ||||
0.703354 | + | 0.710839i | \(0.251685\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 6.70892 | 0.320931 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 32.5296 | 1.55255 | 0.776276 | − | 0.630393i | \(-0.217106\pi\) | ||||
0.776276 | + | 0.630393i | \(0.217106\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 17.0909 | 0.812012 | 0.406006 | − | 0.913870i | \(-0.366921\pi\) | ||||
0.406006 | + | 0.913870i | \(0.366921\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −7.62918 | −0.361658 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −24.7630 | −1.16864 | −0.584319 | − | 0.811524i | \(-0.698638\pi\) | ||||
−0.584319 | + | 0.811524i | \(0.698638\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 48.8678 | 2.30109 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 11.9339 | 0.559471 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −30.4397 | −1.42391 | −0.711956 | − | 0.702225i | \(-0.752190\pi\) | ||||
−0.711956 | + | 0.702225i | \(0.752190\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −21.0241 | −0.979190 | −0.489595 | − | 0.871950i | \(-0.662855\pi\) | ||||
−0.489595 | + | 0.871950i | \(0.662855\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −6.73114 | −0.312823 | −0.156411 | − | 0.987692i | \(-0.549993\pi\) | ||||
−0.156411 | + | 0.987692i | \(0.549993\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −22.7256 | −1.05162 | −0.525808 | − | 0.850603i | \(-0.676237\pi\) | ||||
−0.525808 | + | 0.850603i | \(0.676237\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 18.3094 | 0.845449 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −57.3262 | −2.63586 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 6.70892 | 0.307826 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 23.2759 | 1.06350 | 0.531752 | − | 0.846900i | \(-0.321534\pi\) | ||||
0.531752 | + | 0.846900i | \(0.321534\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 22.4021 | 1.02145 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −0.385284 | −0.0174948 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 19.6579 | 0.890783 | 0.445391 | − | 0.895336i | \(-0.353065\pi\) | ||||
0.445391 | + | 0.895336i | \(0.353065\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 17.1494 | 0.773940 | 0.386970 | − | 0.922092i | \(-0.373522\pi\) | ||||
0.386970 | + | 0.922092i | \(0.373522\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −5.49151 | −0.247325 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 24.6235 | 1.10451 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −29.2265 | −1.30836 | −0.654179 | − | 0.756340i | \(-0.726986\pi\) | ||||
−0.654179 | + | 0.756340i | \(0.726986\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −37.9543 | −1.69230 | −0.846150 | − | 0.532945i | \(-0.821085\pi\) | ||||
−0.846150 | + | 0.532945i | \(0.821085\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 16.5372 | 0.735895 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 22.8502 | 1.01282 | 0.506408 | − | 0.862294i | \(-0.330973\pi\) | ||||
0.506408 | + | 0.862294i | \(0.330973\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −0.675563 | −0.0298851 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −17.5918 | −0.775187 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −47.2243 | −2.07692 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −2.08566 | −0.0913742 | −0.0456871 | − | 0.998956i | \(-0.514548\pi\) | ||||
−0.0456871 | + | 0.998956i | \(0.514548\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −32.4682 | −1.41973 | −0.709867 | − | 0.704335i | \(-0.751245\pi\) | ||||
−0.709867 | + | 0.704335i | \(0.751245\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −34.7896 | −1.51546 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −44.0017 | −1.90592 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −13.9506 | −0.603137 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −4.34125 | −0.186991 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −34.9746 | −1.50367 | −0.751837 | − | 0.659349i | \(-0.770832\pi\) | ||||
−0.751837 | + | 0.659349i | \(0.770832\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 6.70892 | 0.287379 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −15.2321 | −0.651278 | −0.325639 | − | 0.945494i | \(-0.605579\pi\) | ||||
−0.325639 | + | 0.945494i | \(0.605579\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −9.56311 | −0.407402 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −12.6188 | −0.536608 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −9.75112 | −0.413168 | −0.206584 | − | 0.978429i | \(-0.566235\pi\) | ||||
−0.206584 | + | 0.978429i | \(0.566235\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 51.6178 | 2.18320 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −13.1405 | −0.553807 | −0.276904 | − | 0.960898i | \(-0.589308\pi\) | ||||
−0.276904 | + | 0.960898i | \(0.589308\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 11.1756 | 0.470161 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −0.855292 | −0.0358557 | −0.0179279 | − | 0.999839i | \(-0.505707\pi\) | ||||
−0.0179279 | + | 0.999839i | \(0.505707\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −32.9699 | −1.37975 | −0.689873 | − | 0.723930i | \(-0.742334\pi\) | ||||
−0.689873 | + | 0.723930i | \(0.742334\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 1.00000 | 0.0417029 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 18.5943 | 0.774091 | 0.387046 | − | 0.922061i | \(-0.373496\pi\) | ||||
0.387046 | + | 0.922061i | \(0.373496\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 36.9018 | 1.53094 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 43.1916 | 1.78881 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −44.7002 | −1.84498 | −0.922488 | − | 0.386027i | \(-0.873847\pi\) | ||||
−0.922488 | + | 0.386027i | \(0.873847\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −60.5839 | −2.49632 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 15.0501 | 0.618034 | 0.309017 | − | 0.951057i | \(-0.400000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 10.8433 | 0.444531 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −17.4970 | −0.714909 | −0.357455 | − | 0.933930i | \(-0.616355\pi\) | ||||
−0.357455 | + | 0.933930i | \(0.616355\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −26.4515 | −1.07898 | −0.539490 | − | 0.841992i | \(-0.681383\pi\) | ||||
−0.539490 | + | 0.841992i | \(0.681383\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 11.1739 | 0.454286 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −35.0390 | −1.42219 | −0.711095 | − | 0.703096i | \(-0.751800\pi\) | ||||
−0.711095 | + | 0.703096i | \(0.751800\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 42.5218 | 1.72025 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −10.4911 | −0.423732 | −0.211866 | − | 0.977299i | \(-0.567954\pi\) | ||||
−0.211866 | + | 0.977299i | \(0.567954\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −11.1126 | −0.447377 | −0.223688 | − | 0.974661i | \(-0.571810\pi\) | ||||
−0.223688 | + | 0.974661i | \(0.571810\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 6.36307 | 0.255753 | 0.127877 | − | 0.991790i | \(-0.459184\pi\) | ||||
0.127877 | + | 0.991790i | \(0.459184\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −21.4730 | −0.860298 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 20.3548 | 0.811598 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −24.3955 | −0.971168 | −0.485584 | − | 0.874190i | \(-0.661393\pi\) | ||||
−0.485584 | + | 0.874190i | \(0.661393\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 15.0942 | 0.598995 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 3.90896 | 0.154879 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 35.2130 | 1.39083 | 0.695414 | − | 0.718609i | \(-0.255221\pi\) | ||||
0.695414 | + | 0.718609i | \(0.255221\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 21.4200 | 0.844724 | 0.422362 | − | 0.906427i | \(-0.361201\pi\) | ||||
0.422362 | + | 0.906427i | \(0.361201\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 0.795930 | 0.0312912 | 0.0156456 | − | 0.999878i | \(-0.495020\pi\) | ||||
0.0156456 | + | 0.999878i | \(0.495020\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −29.9640 | −1.17619 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −42.4936 | −1.66290 | −0.831451 | − | 0.555599i | \(-0.812489\pi\) | ||||
−0.831451 | + | 0.555599i | \(0.812489\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −1.62918 | −0.0636574 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −21.5631 | −0.839979 | −0.419990 | − | 0.907529i | \(-0.637966\pi\) | ||||
−0.419990 | + | 0.907529i | \(0.637966\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −21.8328 | −0.849196 | −0.424598 | − | 0.905382i | \(-0.639585\pi\) | ||||
−0.424598 | + | 0.905382i | \(0.639585\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 18.8829 | 0.732246 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −1.42543 | −0.0551929 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 49.0386 | 1.89311 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 6.32696 | 0.243886 | 0.121943 | − | 0.992537i | \(-0.461087\pi\) | ||||
0.121943 | + | 0.992537i | \(0.461087\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −6.40504 | −0.246166 | −0.123083 | − | 0.992396i | \(-0.539278\pi\) | ||||
−0.123083 | + | 0.992396i | \(0.539278\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −1.08442 | −0.0416161 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −3.19300 | −0.122177 | −0.0610883 | − | 0.998132i | \(-0.519457\pi\) | ||||
−0.0610883 | + | 0.998132i | \(0.519457\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −5.61804 | −0.214654 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −38.8907 | −1.48162 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 17.4257 | 0.662904 | 0.331452 | − | 0.943472i | \(-0.392462\pi\) | ||||
0.331452 | + | 0.943472i | \(0.392462\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 4.07808 | 0.154690 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −39.9803 | −1.51436 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 7.53418 | 0.284562 | 0.142281 | − | 0.989826i | \(-0.454556\pi\) | ||||
0.142281 | + | 0.989826i | \(0.454556\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 35.4465 | 1.33689 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 46.5454 | 1.75052 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −27.8803 | −1.04707 | −0.523534 | − | 0.852005i | \(-0.675387\pi\) | ||||
−0.523534 | + | 0.852005i | \(0.675387\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −9.03035 | −0.338189 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −19.9659 | −0.746683 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −4.22333 | −0.157504 | −0.0787518 | − | 0.996894i | \(-0.525093\pi\) | ||||
−0.0787518 | + | 0.996894i | \(0.525093\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −49.5137 | −1.84399 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −1.42543 | −0.0529392 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −7.65770 | −0.284008 | −0.142004 | − | 0.989866i | \(-0.545355\pi\) | ||||
−0.142004 | + | 0.989866i | \(0.545355\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 46.9004 | 1.73467 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −32.3457 | −1.19472 | −0.597358 | − | 0.801975i | \(-0.703783\pi\) | ||||
−0.597358 | + | 0.801975i | \(0.703783\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −30.6323 | −1.12836 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 8.58366 | 0.315755 | 0.157878 | − | 0.987459i | \(-0.449535\pi\) | ||||
0.157878 | + | 0.987459i | \(0.449535\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −32.9601 | −1.20919 | −0.604594 | − | 0.796534i | \(-0.706665\pi\) | ||||
−0.604594 | + | 0.796534i | \(0.706665\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −20.1268 | −0.737388 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −39.2652 | −1.43472 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 7.31841 | 0.267053 | 0.133526 | − | 0.991045i | \(-0.457370\pi\) | ||||
0.133526 | + | 0.991045i | \(0.457370\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 18.1739 | 0.661418 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 9.65028 | 0.350745 | 0.175373 | − | 0.984502i | \(-0.443887\pi\) | ||||
0.175373 | + | 0.984502i | \(0.443887\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −26.8784 | −0.974340 | −0.487170 | − | 0.873307i | \(-0.661971\pi\) | ||||
−0.487170 | + | 0.873307i | \(0.661971\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 18.8829 | 0.683606 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 26.9802 | 0.974200 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 2.03983 | 0.0735581 | 0.0367790 | − | 0.999323i | \(-0.488290\pi\) | ||||
0.0367790 | + | 0.999323i | \(0.488290\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 9.54889 | 0.343450 | 0.171725 | − | 0.985145i | \(-0.445066\pi\) | ||||
0.171725 | + | 0.985145i | \(0.445066\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −9.03035 | −0.324380 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −69.6232 | −2.49451 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −41.1961 | −1.47411 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 15.0833 | 0.538346 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 40.2557 | 1.43496 | 0.717481 | − | 0.696578i | \(-0.245295\pi\) | ||||
0.717481 | + | 0.696578i | \(0.245295\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 31.4548 | 1.11840 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −44.1555 | −1.56801 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 42.6875 | 1.51207 | 0.756034 | − | 0.654532i | \(-0.227134\pi\) | ||||
0.756034 | + | 0.654532i | \(0.227134\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 38.6357 | 1.36683 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 1.13024 | 0.0398854 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 2.81459 | 0.0992013 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −28.3699 | −0.997434 | −0.498717 | − | 0.866765i | \(-0.666195\pi\) | ||||
−0.498717 | + | 0.866765i | \(0.666195\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −23.0415 | −0.809096 | −0.404548 | − | 0.914517i | \(-0.632571\pi\) | ||||
−0.404548 | + | 0.914517i | \(0.632571\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0.294954 | 0.0103318 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 81.6741 | 2.85741 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −12.5296 | −0.437286 | −0.218643 | − | 0.975805i | \(-0.570163\pi\) | ||||
−0.218643 | + | 0.975805i | \(0.570163\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 7.53814 | 0.262763 | 0.131382 | − | 0.991332i | \(-0.458059\pi\) | ||||
0.131382 | + | 0.991332i | \(0.458059\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −22.5405 | −0.783810 | −0.391905 | − | 0.920006i | \(-0.628184\pi\) | ||||
−0.391905 | + | 0.920006i | \(0.628184\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −5.28862 | −0.183681 | −0.0918406 | − | 0.995774i | \(-0.529275\pi\) | ||||
−0.0918406 | + | 0.995774i | \(0.529275\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 3.55172 | 0.123060 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 4.24334 | 0.146847 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 45.8187 | 1.58184 | 0.790918 | − | 0.611922i | \(-0.209603\pi\) | ||||
0.790918 | + | 0.611922i | \(0.209603\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −26.9681 | −0.929936 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 4.97778 | 0.171241 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 31.4501 | 1.08064 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 5.28349 | 0.181116 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −24.5910 | −0.841980 | −0.420990 | − | 0.907065i | \(-0.638317\pi\) | ||||
−0.420990 | + | 0.907065i | \(0.638317\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 8.53965 | 0.291709 | 0.145854 | − | 0.989306i | \(-0.453407\pi\) | ||||
0.145854 | + | 0.989306i | \(0.453407\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −43.0704 | −1.46954 | −0.734772 | − | 0.678314i | \(-0.762711\pi\) | ||||
−0.734772 | + | 0.678314i | \(0.762711\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −0.952975 | −0.0324396 | −0.0162198 | − | 0.999868i | \(-0.505163\pi\) | ||||
−0.0162198 | + | 0.999868i | \(0.505163\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 24.9116 | 0.847018 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 21.1118 | 0.716169 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 27.5821 | 0.934583 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 2.81459 | 0.0951505 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −38.1895 | −1.28957 | −0.644784 | − | 0.764365i | \(-0.723053\pi\) | ||||
−0.644784 | + | 0.764365i | \(0.723053\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −28.4747 | −0.959336 | −0.479668 | − | 0.877450i | \(-0.659243\pi\) | ||||
−0.479668 | + | 0.877450i | \(0.659243\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −15.9768 | −0.537663 | −0.268832 | − | 0.963187i | \(-0.586637\pi\) | ||||
−0.268832 | + | 0.963187i | \(0.586637\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −8.16280 | −0.274080 | −0.137040 | − | 0.990566i | \(-0.543759\pi\) | ||||
−0.137040 | + | 0.990566i | \(0.543759\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 42.4840 | 1.42487 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 67.2817 | 2.25149 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −7.03256 | −0.235073 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 12.8721 | 0.429310 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −35.3364 | −1.17723 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −15.5806 | −0.517918 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 28.0245 | 0.930538 | 0.465269 | − | 0.885169i | \(-0.345958\pi\) | ||||
0.465269 | + | 0.885169i | \(0.345958\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 26.0367 | 0.862634 | 0.431317 | − | 0.902201i | \(-0.358049\pi\) | ||||
0.431317 | + | 0.902201i | \(0.358049\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −61.7381 | −2.04323 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −4.58548 | −0.151426 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −30.0044 | −0.989754 | −0.494877 | − | 0.868963i | \(-0.664787\pi\) | ||||
−0.494877 | + | 0.868963i | \(0.664787\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 37.0939 | 1.22096 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 5.28349 | 0.173720 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −36.2038 | −1.18781 | −0.593903 | − | 0.804536i | \(-0.702414\pi\) | ||||
−0.593903 | + | 0.804536i | \(0.702414\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 6.18509 | 0.202708 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −18.1412 | −0.593282 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −6.68356 | −0.218342 | −0.109171 | − | 0.994023i | \(-0.534820\pi\) | ||||
−0.109171 | + | 0.994023i | \(0.534820\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 60.6068 | 1.97573 | 0.987863 | − | 0.155329i | \(-0.0496438\pi\) | ||||
0.987863 | + | 0.155329i | \(0.0496438\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −10.3777 | −0.337944 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −22.2369 | −0.722604 | −0.361302 | − | 0.932449i | \(-0.617668\pi\) | ||||
−0.361302 | + | 0.932449i | \(0.617668\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −1.01770 | −0.0330358 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 22.3412 | 0.723704 | 0.361852 | − | 0.932236i | \(-0.382145\pi\) | ||||
0.361852 | + | 0.932236i | \(0.382145\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −16.8940 | −0.546677 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −15.8125 | −0.510612 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 50.5471 | 1.63055 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −1.22500 | −0.0394342 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −30.6654 | −0.986132 | −0.493066 | − | 0.869992i | \(-0.664124\pi\) | ||||
−0.493066 | + | 0.869992i | \(0.664124\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −19.2779 | −0.618659 | −0.309329 | − | 0.950955i | \(-0.600105\pi\) | ||||
−0.309329 | + | 0.950955i | \(0.600105\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 11.4781 | 0.367972 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 27.9499 | 0.894196 | 0.447098 | − | 0.894485i | \(-0.352457\pi\) | ||||
0.447098 | + | 0.894485i | \(0.352457\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 35.9252 | 1.14817 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −55.4140 | −1.76743 | −0.883717 | − | 0.468022i | \(-0.844967\pi\) | ||||
−0.883717 | + | 0.468022i | \(0.844967\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −18.1092 | −0.577008 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 12.1739 | 0.387109 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −2.89148 | −0.0918510 | −0.0459255 | − | 0.998945i | \(-0.514624\pi\) | ||||
−0.0459255 | + | 0.998945i | \(0.514624\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 22.1962 | 0.703666 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −49.7428 | −1.57537 | −0.787685 | − | 0.616078i | \(-0.788721\pi\) | ||||
−0.787685 | + | 0.616078i | \(0.788721\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 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 | 4140.2.a.u.1.4 | yes | 5 | |
3.2 | odd | 2 | 4140.2.a.t.1.4 | ✓ | 5 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4140.2.a.t.1.4 | ✓ | 5 | 3.2 | odd | 2 | ||
4140.2.a.u.1.4 | yes | 5 | 1.1 | even | 1 | trivial |