Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8001,2,Mod(1,8001)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8001, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8001.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8001 = 3^{2} \cdot 7 \cdot 127 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8001.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(63.8883066572\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{6}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - 6 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 2667) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(2.44949\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8001.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.44949 | 1.73205 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 4.00000 | 2.00000 | ||||||||
\(5\) | 2.44949 | 1.09545 | 0.547723 | − | 0.836660i | \(-0.315495\pi\) | ||||
0.547723 | + | 0.836660i | \(0.315495\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | 4.89898 | 1.73205 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 6.00000 | 1.89737 | ||||||||
\(11\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 6.89898 | 1.91343 | 0.956716 | − | 0.291022i | \(-0.0939953\pi\) | ||||
0.956716 | + | 0.291022i | \(0.0939953\pi\) | |||||||
\(14\) | 2.44949 | 0.654654 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 4.00000 | 1.00000 | ||||||||
\(17\) | 0.550510 | 0.133518 | 0.0667592 | − | 0.997769i | \(-0.478734\pi\) | ||||
0.0667592 | + | 0.997769i | \(0.478734\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −0.449490 | −0.103120 | −0.0515600 | − | 0.998670i | \(-0.516419\pi\) | ||||
−0.0515600 | + | 0.998670i | \(0.516419\pi\) | |||||||
\(20\) | 9.79796 | 2.19089 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −6.00000 | −1.25109 | −0.625543 | − | 0.780189i | \(-0.715123\pi\) | ||||
−0.625543 | + | 0.780189i | \(0.715123\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 16.8990 | 3.31416 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 4.00000 | 0.755929 | ||||||||
\(29\) | −1.89898 | −0.352632 | −0.176316 | − | 0.984334i | \(-0.556418\pi\) | ||||
−0.176316 | + | 0.984334i | \(0.556418\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 8.00000 | 1.43684 | 0.718421 | − | 0.695608i | \(-0.244865\pi\) | ||||
0.718421 | + | 0.695608i | \(0.244865\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 1.34847 | 0.231261 | ||||||||
\(35\) | 2.44949 | 0.414039 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −7.00000 | −1.15079 | −0.575396 | − | 0.817875i | \(-0.695152\pi\) | ||||
−0.575396 | + | 0.817875i | \(0.695152\pi\) | |||||||
\(38\) | −1.10102 | −0.178609 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 12.0000 | 1.89737 | ||||||||
\(41\) | −0.550510 | −0.0859753 | −0.0429876 | − | 0.999076i | \(-0.513688\pi\) | ||||
−0.0429876 | + | 0.999076i | \(0.513688\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2.00000 | 0.304997 | 0.152499 | − | 0.988304i | \(-0.451268\pi\) | ||||
0.152499 | + | 0.988304i | \(0.451268\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −14.6969 | −2.16695 | ||||||||
\(47\) | 12.0000 | 1.75038 | 0.875190 | − | 0.483779i | \(-0.160736\pi\) | ||||
0.875190 | + | 0.483779i | \(0.160736\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 2.44949 | 0.346410 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 27.5959 | 3.82687 | ||||||||
\(53\) | 7.89898 | 1.08501 | 0.542504 | − | 0.840053i | \(-0.317476\pi\) | ||||
0.542504 | + | 0.840053i | \(0.317476\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 4.89898 | 0.654654 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −4.65153 | −0.610776 | ||||||||
\(59\) | −2.44949 | −0.318896 | −0.159448 | − | 0.987206i | \(-0.550971\pi\) | ||||
−0.159448 | + | 0.987206i | \(0.550971\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −0.449490 | −0.0575513 | −0.0287756 | − | 0.999586i | \(-0.509161\pi\) | ||||
−0.0287756 | + | 0.999586i | \(0.509161\pi\) | |||||||
\(62\) | 19.5959 | 2.48868 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −8.00000 | −1.00000 | ||||||||
\(65\) | 16.8990 | 2.09606 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 14.2474 | 1.74060 | 0.870301 | − | 0.492519i | \(-0.163924\pi\) | ||||
0.870301 | + | 0.492519i | \(0.163924\pi\) | |||||||
\(68\) | 2.20204 | 0.267037 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 6.00000 | 0.717137 | ||||||||
\(71\) | −8.44949 | −1.00277 | −0.501385 | − | 0.865224i | \(-0.667176\pi\) | ||||
−0.501385 | + | 0.865224i | \(0.667176\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −11.3485 | −1.32824 | −0.664119 | − | 0.747627i | \(-0.731193\pi\) | ||||
−0.664119 | + | 0.747627i | \(0.731193\pi\) | |||||||
\(74\) | −17.1464 | −1.99323 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −1.79796 | −0.206240 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −5.89898 | −0.663687 | −0.331844 | − | 0.943334i | \(-0.607671\pi\) | ||||
−0.331844 | + | 0.943334i | \(0.607671\pi\) | |||||||
\(80\) | 9.79796 | 1.09545 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −1.34847 | −0.148914 | ||||||||
\(83\) | −6.00000 | −0.658586 | −0.329293 | − | 0.944228i | \(-0.606810\pi\) | ||||
−0.329293 | + | 0.944228i | \(0.606810\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.34847 | 0.146262 | ||||||||
\(86\) | 4.89898 | 0.528271 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −9.79796 | −1.03858 | −0.519291 | − | 0.854598i | \(-0.673804\pi\) | ||||
−0.519291 | + | 0.854598i | \(0.673804\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 6.89898 | 0.723210 | ||||||||
\(92\) | −24.0000 | −2.50217 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 29.3939 | 3.03175 | ||||||||
\(95\) | −1.10102 | −0.112962 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 12.3485 | 1.25380 | 0.626899 | − | 0.779101i | \(-0.284324\pi\) | ||||
0.626899 | + | 0.779101i | \(0.284324\pi\) | |||||||
\(98\) | 2.44949 | 0.247436 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 4.00000 | 0.400000 | ||||||||
\(101\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −4.00000 | −0.394132 | −0.197066 | − | 0.980390i | \(-0.563141\pi\) | ||||
−0.197066 | + | 0.980390i | \(0.563141\pi\) | |||||||
\(104\) | 33.7980 | 3.31416 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 19.3485 | 1.87929 | ||||||||
\(107\) | 7.34847 | 0.710403 | 0.355202 | − | 0.934790i | \(-0.384412\pi\) | ||||
0.355202 | + | 0.934790i | \(0.384412\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 9.34847 | 0.895421 | 0.447710 | − | 0.894179i | \(-0.352240\pi\) | ||||
0.447710 | + | 0.894179i | \(0.352240\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 4.00000 | 0.377964 | ||||||||
\(113\) | 6.00000 | 0.564433 | 0.282216 | − | 0.959351i | \(-0.408930\pi\) | ||||
0.282216 | + | 0.959351i | \(0.408930\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −14.6969 | −1.37050 | ||||||||
\(116\) | −7.59592 | −0.705263 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −6.00000 | −0.552345 | ||||||||
\(119\) | 0.550510 | 0.0504652 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −11.0000 | −1.00000 | ||||||||
\(122\) | −1.10102 | −0.0996817 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 32.0000 | 2.87368 | ||||||||
\(125\) | −9.79796 | −0.876356 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1.00000 | 0.0887357 | ||||||||
\(128\) | −19.5959 | −1.73205 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 41.3939 | 3.63048 | ||||||||
\(131\) | −10.3485 | −0.904150 | −0.452075 | − | 0.891980i | \(-0.649316\pi\) | ||||
−0.452075 | + | 0.891980i | \(0.649316\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −0.449490 | −0.0389757 | ||||||||
\(134\) | 34.8990 | 3.01481 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 2.69694 | 0.231261 | ||||||||
\(137\) | −21.7980 | −1.86233 | −0.931163 | − | 0.364604i | \(-0.881204\pi\) | ||||
−0.931163 | + | 0.364604i | \(0.881204\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −20.3485 | −1.72593 | −0.862967 | − | 0.505260i | \(-0.831397\pi\) | ||||
−0.862967 | + | 0.505260i | \(0.831397\pi\) | |||||||
\(140\) | 9.79796 | 0.828079 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −20.6969 | −1.73685 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −4.65153 | −0.386289 | ||||||||
\(146\) | −27.7980 | −2.30058 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −28.0000 | −2.30159 | ||||||||
\(149\) | −8.69694 | −0.712481 | −0.356240 | − | 0.934394i | \(-0.615942\pi\) | ||||
−0.356240 | + | 0.934394i | \(0.615942\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −5.34847 | −0.435252 | −0.217626 | − | 0.976032i | \(-0.569831\pi\) | ||||
−0.217626 | + | 0.976032i | \(0.569831\pi\) | |||||||
\(152\) | −2.20204 | −0.178609 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 19.5959 | 1.57398 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −6.44949 | −0.514725 | −0.257363 | − | 0.966315i | \(-0.582853\pi\) | ||||
−0.257363 | + | 0.966315i | \(0.582853\pi\) | |||||||
\(158\) | −14.4495 | −1.14954 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −6.00000 | −0.472866 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 17.0000 | 1.33154 | 0.665771 | − | 0.746156i | \(-0.268103\pi\) | ||||
0.665771 | + | 0.746156i | \(0.268103\pi\) | |||||||
\(164\) | −2.20204 | −0.171951 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −14.6969 | −1.14070 | ||||||||
\(167\) | 11.1464 | 0.862537 | 0.431268 | − | 0.902224i | \(-0.358066\pi\) | ||||
0.431268 | + | 0.902224i | \(0.358066\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 34.5959 | 2.66122 | ||||||||
\(170\) | 3.30306 | 0.253333 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 8.00000 | 0.609994 | ||||||||
\(173\) | 6.24745 | 0.474985 | 0.237492 | − | 0.971389i | \(-0.423675\pi\) | ||||
0.237492 | + | 0.971389i | \(0.423675\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1.00000 | 0.0755929 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −24.0000 | −1.79888 | ||||||||
\(179\) | 3.79796 | 0.283873 | 0.141936 | − | 0.989876i | \(-0.454667\pi\) | ||||
0.141936 | + | 0.989876i | \(0.454667\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −24.1464 | −1.79479 | −0.897395 | − | 0.441228i | \(-0.854543\pi\) | ||||
−0.897395 | + | 0.441228i | \(0.854543\pi\) | |||||||
\(182\) | 16.8990 | 1.25264 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −29.3939 | −2.16695 | ||||||||
\(185\) | −17.1464 | −1.26063 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 48.0000 | 3.50076 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −2.69694 | −0.195656 | ||||||||
\(191\) | −1.34847 | −0.0975718 | −0.0487859 | − | 0.998809i | \(-0.515535\pi\) | ||||
−0.0487859 | + | 0.998809i | \(0.515535\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 10.4495 | 0.752171 | 0.376085 | − | 0.926585i | \(-0.377270\pi\) | ||||
0.376085 | + | 0.926585i | \(0.377270\pi\) | |||||||
\(194\) | 30.2474 | 2.17164 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 4.00000 | 0.285714 | ||||||||
\(197\) | −3.55051 | −0.252963 | −0.126482 | − | 0.991969i | \(-0.540368\pi\) | ||||
−0.126482 | + | 0.991969i | \(0.540368\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 20.0000 | 1.41776 | 0.708881 | − | 0.705328i | \(-0.249200\pi\) | ||||
0.708881 | + | 0.705328i | \(0.249200\pi\) | |||||||
\(200\) | 4.89898 | 0.346410 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −1.89898 | −0.133282 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −1.34847 | −0.0941812 | ||||||||
\(206\) | −9.79796 | −0.682656 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 27.5959 | 1.91343 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 4.69694 | 0.323351 | 0.161675 | − | 0.986844i | \(-0.448310\pi\) | ||||
0.161675 | + | 0.986844i | \(0.448310\pi\) | |||||||
\(212\) | 31.5959 | 2.17002 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 18.0000 | 1.23045 | ||||||||
\(215\) | 4.89898 | 0.334108 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 8.00000 | 0.543075 | ||||||||
\(218\) | 22.8990 | 1.55091 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 3.79796 | 0.255478 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 7.44949 | 0.498855 | 0.249427 | − | 0.968394i | \(-0.419758\pi\) | ||||
0.249427 | + | 0.968394i | \(0.419758\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 14.6969 | 0.977626 | ||||||||
\(227\) | −12.0000 | −0.796468 | −0.398234 | − | 0.917284i | \(-0.630377\pi\) | ||||
−0.398234 | + | 0.917284i | \(0.630377\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 2.55051 | 0.168542 | 0.0842712 | − | 0.996443i | \(-0.473144\pi\) | ||||
0.0842712 | + | 0.996443i | \(0.473144\pi\) | |||||||
\(230\) | −36.0000 | −2.37377 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −9.30306 | −0.610776 | ||||||||
\(233\) | −1.89898 | −0.124406 | −0.0622031 | − | 0.998064i | \(-0.519813\pi\) | ||||
−0.0622031 | + | 0.998064i | \(0.519813\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 29.3939 | 1.91745 | ||||||||
\(236\) | −9.79796 | −0.637793 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 1.34847 | 0.0874083 | ||||||||
\(239\) | −3.00000 | −0.194054 | −0.0970269 | − | 0.995282i | \(-0.530933\pi\) | ||||
−0.0970269 | + | 0.995282i | \(0.530933\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −19.2474 | −1.23984 | −0.619919 | − | 0.784666i | \(-0.712834\pi\) | ||||
−0.619919 | + | 0.784666i | \(0.712834\pi\) | |||||||
\(242\) | −26.9444 | −1.73205 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −1.79796 | −0.115103 | ||||||||
\(245\) | 2.44949 | 0.156492 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −3.10102 | −0.197313 | ||||||||
\(248\) | 39.1918 | 2.48868 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −24.0000 | −1.51789 | ||||||||
\(251\) | 10.3485 | 0.653190 | 0.326595 | − | 0.945164i | \(-0.394099\pi\) | ||||
0.326595 | + | 0.945164i | \(0.394099\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 2.44949 | 0.153695 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −32.0000 | −2.00000 | ||||||||
\(257\) | −23.1464 | −1.44383 | −0.721917 | − | 0.691979i | \(-0.756739\pi\) | ||||
−0.721917 | + | 0.691979i | \(0.756739\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −7.00000 | −0.434959 | ||||||||
\(260\) | 67.5959 | 4.19212 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −25.3485 | −1.56603 | ||||||||
\(263\) | −11.1464 | −0.687318 | −0.343659 | − | 0.939094i | \(-0.611666\pi\) | ||||
−0.343659 | + | 0.939094i | \(0.611666\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 19.3485 | 1.18857 | ||||||||
\(266\) | −1.10102 | −0.0675079 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 56.9898 | 3.48121 | ||||||||
\(269\) | −2.75255 | −0.167826 | −0.0839130 | − | 0.996473i | \(-0.526742\pi\) | ||||
−0.0839130 | + | 0.996473i | \(0.526742\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 22.9444 | 1.39377 | 0.696886 | − | 0.717182i | \(-0.254568\pi\) | ||||
0.696886 | + | 0.717182i | \(0.254568\pi\) | |||||||
\(272\) | 2.20204 | 0.133518 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −53.3939 | −3.22564 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 29.7980 | 1.79039 | 0.895193 | − | 0.445679i | \(-0.147038\pi\) | ||||
0.895193 | + | 0.445679i | \(0.147038\pi\) | |||||||
\(278\) | −49.8434 | −2.98941 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 12.0000 | 0.717137 | ||||||||
\(281\) | 24.7980 | 1.47932 | 0.739661 | − | 0.672980i | \(-0.234986\pi\) | ||||
0.739661 | + | 0.672980i | \(0.234986\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 9.65153 | 0.573724 | 0.286862 | − | 0.957972i | \(-0.407388\pi\) | ||||
0.286862 | + | 0.957972i | \(0.407388\pi\) | |||||||
\(284\) | −33.7980 | −2.00554 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −0.550510 | −0.0324956 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −16.6969 | −0.982173 | ||||||||
\(290\) | −11.3939 | −0.669071 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −45.3939 | −2.65648 | ||||||||
\(293\) | −21.5505 | −1.25899 | −0.629497 | − | 0.777003i | \(-0.716739\pi\) | ||||
−0.629497 | + | 0.777003i | \(0.716739\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −6.00000 | −0.349334 | ||||||||
\(296\) | −34.2929 | −1.99323 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −21.3031 | −1.23405 | ||||||||
\(299\) | −41.3939 | −2.39387 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 2.00000 | 0.115278 | ||||||||
\(302\) | −13.1010 | −0.753879 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −1.79796 | −0.103120 | ||||||||
\(305\) | −1.10102 | −0.0630443 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 25.4495 | 1.45248 | 0.726240 | − | 0.687442i | \(-0.241266\pi\) | ||||
0.726240 | + | 0.687442i | \(0.241266\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 48.0000 | 2.72622 | ||||||||
\(311\) | −17.1464 | −0.972285 | −0.486142 | − | 0.873880i | \(-0.661596\pi\) | ||||
−0.486142 | + | 0.873880i | \(0.661596\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 20.5505 | 1.16158 | 0.580792 | − | 0.814052i | \(-0.302743\pi\) | ||||
0.580792 | + | 0.814052i | \(0.302743\pi\) | |||||||
\(314\) | −15.7980 | −0.891530 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −23.5959 | −1.32737 | ||||||||
\(317\) | 28.8990 | 1.62313 | 0.811564 | − | 0.584263i | \(-0.198616\pi\) | ||||
0.811564 | + | 0.584263i | \(0.198616\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | −19.5959 | −1.09545 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −14.6969 | −0.819028 | ||||||||
\(323\) | −0.247449 | −0.0137684 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 6.89898 | 0.382687 | ||||||||
\(326\) | 41.6413 | 2.30630 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −2.69694 | −0.148914 | ||||||||
\(329\) | 12.0000 | 0.661581 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −13.5505 | −0.744803 | −0.372402 | − | 0.928072i | \(-0.621466\pi\) | ||||
−0.372402 | + | 0.928072i | \(0.621466\pi\) | |||||||
\(332\) | −24.0000 | −1.31717 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 27.3031 | 1.49396 | ||||||||
\(335\) | 34.8990 | 1.90673 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −8.65153 | −0.471279 | −0.235639 | − | 0.971841i | \(-0.575718\pi\) | ||||
−0.235639 | + | 0.971841i | \(0.575718\pi\) | |||||||
\(338\) | 84.7423 | 4.60938 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 5.39388 | 0.292524 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | 9.79796 | 0.528271 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 15.3031 | 0.822698 | ||||||||
\(347\) | −11.6969 | −0.627925 | −0.313962 | − | 0.949435i | \(-0.601657\pi\) | ||||
−0.313962 | + | 0.949435i | \(0.601657\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 27.0454 | 1.44771 | 0.723854 | − | 0.689953i | \(-0.242369\pi\) | ||||
0.723854 | + | 0.689953i | \(0.242369\pi\) | |||||||
\(350\) | 2.44949 | 0.130931 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −7.10102 | −0.377949 | −0.188975 | − | 0.981982i | \(-0.560516\pi\) | ||||
−0.188975 | + | 0.981982i | \(0.560516\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −20.6969 | −1.09848 | ||||||||
\(356\) | −39.1918 | −2.07716 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 9.30306 | 0.491682 | ||||||||
\(359\) | −15.0000 | −0.791670 | −0.395835 | − | 0.918322i | \(-0.629545\pi\) | ||||
−0.395835 | + | 0.918322i | \(0.629545\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −18.7980 | −0.989366 | ||||||||
\(362\) | −59.1464 | −3.10867 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 27.5959 | 1.44642 | ||||||||
\(365\) | −27.7980 | −1.45501 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 2.00000 | 0.104399 | 0.0521996 | − | 0.998637i | \(-0.483377\pi\) | ||||
0.0521996 | + | 0.998637i | \(0.483377\pi\) | |||||||
\(368\) | −24.0000 | −1.25109 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −42.0000 | −2.18348 | ||||||||
\(371\) | 7.89898 | 0.410095 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 24.8990 | 1.28922 | 0.644610 | − | 0.764511i | \(-0.277020\pi\) | ||||
0.644610 | + | 0.764511i | \(0.277020\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 58.7878 | 3.03175 | ||||||||
\(377\) | −13.1010 | −0.674737 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 20.0000 | 1.02733 | 0.513665 | − | 0.857991i | \(-0.328287\pi\) | ||||
0.513665 | + | 0.857991i | \(0.328287\pi\) | |||||||
\(380\) | −4.40408 | −0.225925 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −3.30306 | −0.168999 | ||||||||
\(383\) | −3.24745 | −0.165937 | −0.0829684 | − | 0.996552i | \(-0.526440\pi\) | ||||
−0.0829684 | + | 0.996552i | \(0.526440\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 25.5959 | 1.30280 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 49.3939 | 2.50759 | ||||||||
\(389\) | −10.0454 | −0.509322 | −0.254661 | − | 0.967030i | \(-0.581964\pi\) | ||||
−0.254661 | + | 0.967030i | \(0.581964\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −3.30306 | −0.167043 | ||||||||
\(392\) | 4.89898 | 0.247436 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −8.69694 | −0.438145 | ||||||||
\(395\) | −14.4495 | −0.727033 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 22.6969 | 1.13913 | 0.569563 | − | 0.821947i | \(-0.307112\pi\) | ||||
0.569563 | + | 0.821947i | \(0.307112\pi\) | |||||||
\(398\) | 48.9898 | 2.45564 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 4.00000 | 0.200000 | ||||||||
\(401\) | 29.6969 | 1.48299 | 0.741497 | − | 0.670956i | \(-0.234116\pi\) | ||||
0.741497 | + | 0.670956i | \(0.234116\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 55.1918 | 2.74930 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −4.65153 | −0.230852 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −12.6969 | −0.627823 | −0.313912 | − | 0.949452i | \(-0.601640\pi\) | ||||
−0.313912 | + | 0.949452i | \(0.601640\pi\) | |||||||
\(410\) | −3.30306 | −0.163127 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −16.0000 | −0.788263 | ||||||||
\(413\) | −2.44949 | −0.120532 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −14.6969 | −0.721444 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −7.59592 | −0.371085 | −0.185542 | − | 0.982636i | \(-0.559404\pi\) | ||||
−0.185542 | + | 0.982636i | \(0.559404\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −38.0454 | −1.85422 | −0.927110 | − | 0.374790i | \(-0.877715\pi\) | ||||
−0.927110 | + | 0.374790i | \(0.877715\pi\) | |||||||
\(422\) | 11.5051 | 0.560060 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 38.6969 | 1.87929 | ||||||||
\(425\) | 0.550510 | 0.0267037 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −0.449490 | −0.0217523 | ||||||||
\(428\) | 29.3939 | 1.42081 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 12.0000 | 0.578691 | ||||||||
\(431\) | 13.3485 | 0.642973 | 0.321487 | − | 0.946914i | \(-0.395817\pi\) | ||||
0.321487 | + | 0.946914i | \(0.395817\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 15.3485 | 0.737600 | 0.368800 | − | 0.929509i | \(-0.379769\pi\) | ||||
0.368800 | + | 0.929509i | \(0.379769\pi\) | |||||||
\(434\) | 19.5959 | 0.940634 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 37.3939 | 1.79084 | ||||||||
\(437\) | 2.69694 | 0.129012 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 0.348469 | 0.0166315 | 0.00831576 | − | 0.999965i | \(-0.497353\pi\) | ||||
0.00831576 | + | 0.999965i | \(0.497353\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 9.30306 | 0.442502 | ||||||||
\(443\) | −26.4495 | −1.25665 | −0.628327 | − | 0.777950i | \(-0.716260\pi\) | ||||
−0.628327 | + | 0.777950i | \(0.716260\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −24.0000 | −1.13771 | ||||||||
\(446\) | 18.2474 | 0.864042 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −8.00000 | −0.377964 | ||||||||
\(449\) | −28.8990 | −1.36383 | −0.681914 | − | 0.731433i | \(-0.738852\pi\) | ||||
−0.681914 | + | 0.731433i | \(0.738852\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 24.0000 | 1.12887 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −29.3939 | −1.37952 | ||||||||
\(455\) | 16.8990 | 0.792236 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −19.4949 | −0.911933 | −0.455966 | − | 0.889997i | \(-0.650706\pi\) | ||||
−0.455966 | + | 0.889997i | \(0.650706\pi\) | |||||||
\(458\) | 6.24745 | 0.291924 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −58.7878 | −2.74099 | ||||||||
\(461\) | −29.1464 | −1.35748 | −0.678742 | − | 0.734377i | \(-0.737475\pi\) | ||||
−0.678742 | + | 0.734377i | \(0.737475\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −19.7980 | −0.920089 | −0.460045 | − | 0.887896i | \(-0.652167\pi\) | ||||
−0.460045 | + | 0.887896i | \(0.652167\pi\) | |||||||
\(464\) | −7.59592 | −0.352632 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −4.65153 | −0.215478 | ||||||||
\(467\) | 7.59592 | 0.351497 | 0.175749 | − | 0.984435i | \(-0.443765\pi\) | ||||
0.175749 | + | 0.984435i | \(0.443765\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 14.2474 | 0.657886 | ||||||||
\(470\) | 72.0000 | 3.32111 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −12.0000 | −0.552345 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −0.449490 | −0.0206240 | ||||||||
\(476\) | 2.20204 | 0.100930 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −7.34847 | −0.336111 | ||||||||
\(479\) | 21.2474 | 0.970821 | 0.485410 | − | 0.874286i | \(-0.338670\pi\) | ||||
0.485410 | + | 0.874286i | \(0.338670\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −48.2929 | −2.20196 | ||||||||
\(482\) | −47.1464 | −2.14746 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −44.0000 | −2.00000 | ||||||||
\(485\) | 30.2474 | 1.37347 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 22.9444 | 1.03971 | 0.519855 | − | 0.854255i | \(-0.325986\pi\) | ||||
0.519855 | + | 0.854255i | \(0.325986\pi\) | |||||||
\(488\) | −2.20204 | −0.0996817 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 6.00000 | 0.271052 | ||||||||
\(491\) | 22.8990 | 1.03342 | 0.516708 | − | 0.856162i | \(-0.327157\pi\) | ||||
0.516708 | + | 0.856162i | \(0.327157\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −1.04541 | −0.0470828 | ||||||||
\(494\) | −7.59592 | −0.341757 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 32.0000 | 1.43684 | ||||||||
\(497\) | −8.44949 | −0.379011 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −38.0454 | −1.70315 | −0.851573 | − | 0.524236i | \(-0.824351\pi\) | ||||
−0.851573 | + | 0.524236i | \(0.824351\pi\) | |||||||
\(500\) | −39.1918 | −1.75271 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 25.3485 | 1.13136 | ||||||||
\(503\) | −24.5505 | −1.09465 | −0.547327 | − | 0.836919i | \(-0.684354\pi\) | ||||
−0.547327 | + | 0.836919i | \(0.684354\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 4.00000 | 0.177471 | ||||||||
\(509\) | −37.0454 | −1.64201 | −0.821004 | − | 0.570922i | \(-0.806586\pi\) | ||||
−0.821004 | + | 0.570922i | \(0.806586\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −11.3485 | −0.502027 | ||||||||
\(512\) | −39.1918 | −1.73205 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −56.6969 | −2.50079 | ||||||||
\(515\) | −9.79796 | −0.431750 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | −17.1464 | −0.753371 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 82.7878 | 3.63048 | ||||||||
\(521\) | 18.0000 | 0.788594 | 0.394297 | − | 0.918983i | \(-0.370988\pi\) | ||||
0.394297 | + | 0.918983i | \(0.370988\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −3.75255 | −0.164088 | −0.0820438 | − | 0.996629i | \(-0.526145\pi\) | ||||
−0.0820438 | + | 0.996629i | \(0.526145\pi\) | |||||||
\(524\) | −41.3939 | −1.80830 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −27.3031 | −1.19047 | ||||||||
\(527\) | 4.40408 | 0.191845 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 13.0000 | 0.565217 | ||||||||
\(530\) | 47.3939 | 2.05866 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −1.79796 | −0.0779514 | ||||||||
\(533\) | −3.79796 | −0.164508 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 18.0000 | 0.778208 | ||||||||
\(536\) | 69.7980 | 3.01481 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −6.74235 | −0.290683 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 0.898979 | 0.0386501 | 0.0193251 | − | 0.999813i | \(-0.493848\pi\) | ||||
0.0193251 | + | 0.999813i | \(0.493848\pi\) | |||||||
\(542\) | 56.2020 | 2.41408 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 22.8990 | 0.980885 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 17.7980 | 0.760986 | 0.380493 | − | 0.924784i | \(-0.375754\pi\) | ||||
0.380493 | + | 0.924784i | \(0.375754\pi\) | |||||||
\(548\) | −87.1918 | −3.72465 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0.853572 | 0.0363634 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −5.89898 | −0.250850 | ||||||||
\(554\) | 72.9898 | 3.10104 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −81.3939 | −3.45187 | ||||||||
\(557\) | −2.20204 | −0.0933035 | −0.0466517 | − | 0.998911i | \(-0.514855\pi\) | ||||
−0.0466517 | + | 0.998911i | \(0.514855\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 13.7980 | 0.583591 | ||||||||
\(560\) | 9.79796 | 0.414039 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 60.7423 | 2.56226 | ||||||||
\(563\) | 34.2929 | 1.44527 | 0.722636 | − | 0.691229i | \(-0.242930\pi\) | ||||
0.722636 | + | 0.691229i | \(0.242930\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 14.6969 | 0.618305 | ||||||||
\(566\) | 23.6413 | 0.993719 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −41.3939 | −1.73685 | ||||||||
\(569\) | −18.4949 | −0.775346 | −0.387673 | − | 0.921797i | \(-0.626721\pi\) | ||||
−0.387673 | + | 0.921797i | \(0.626721\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −10.8536 | −0.454208 | −0.227104 | − | 0.973871i | \(-0.572926\pi\) | ||||
−0.227104 | + | 0.973871i | \(0.572926\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −1.34847 | −0.0562840 | ||||||||
\(575\) | −6.00000 | −0.250217 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −35.3485 | −1.47158 | −0.735788 | − | 0.677212i | \(-0.763188\pi\) | ||||
−0.735788 | + | 0.677212i | \(0.763188\pi\) | |||||||
\(578\) | −40.8990 | −1.70117 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −18.6061 | −0.772577 | ||||||||
\(581\) | −6.00000 | −0.248922 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | −55.5959 | −2.30058 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −52.7878 | −2.18064 | ||||||||
\(587\) | 0.550510 | 0.0227220 | 0.0113610 | − | 0.999935i | \(-0.496384\pi\) | ||||
0.0113610 | + | 0.999935i | \(0.496384\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −3.59592 | −0.148167 | ||||||||
\(590\) | −14.6969 | −0.605063 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −28.0000 | −1.15079 | ||||||||
\(593\) | −9.79796 | −0.402354 | −0.201177 | − | 0.979555i | \(-0.564477\pi\) | ||||
−0.201177 | + | 0.979555i | \(0.564477\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 1.34847 | 0.0552818 | ||||||||
\(596\) | −34.7878 | −1.42496 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −101.394 | −4.14630 | ||||||||
\(599\) | 33.0000 | 1.34834 | 0.674172 | − | 0.738575i | \(-0.264501\pi\) | ||||
0.674172 | + | 0.738575i | \(0.264501\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −20.3485 | −0.830031 | −0.415016 | − | 0.909814i | \(-0.636224\pi\) | ||||
−0.415016 | + | 0.909814i | \(0.636224\pi\) | |||||||
\(602\) | 4.89898 | 0.199667 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −21.3939 | −0.870505 | ||||||||
\(605\) | −26.9444 | −1.09545 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −5.34847 | −0.217088 | −0.108544 | − | 0.994092i | \(-0.534619\pi\) | ||||
−0.108544 | + | 0.994092i | \(0.534619\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −2.69694 | −0.109196 | ||||||||
\(611\) | 82.7878 | 3.34923 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −10.4949 | −0.423885 | −0.211942 | − | 0.977282i | \(-0.567979\pi\) | ||||
−0.211942 | + | 0.977282i | \(0.567979\pi\) | |||||||
\(614\) | 62.3383 | 2.51577 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −27.0000 | −1.08698 | −0.543490 | − | 0.839416i | \(-0.682897\pi\) | ||||
−0.543490 | + | 0.839416i | \(0.682897\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 3.65153 | 0.146767 | 0.0733837 | − | 0.997304i | \(-0.476620\pi\) | ||||
0.0733837 | + | 0.997304i | \(0.476620\pi\) | |||||||
\(620\) | 78.3837 | 3.14796 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −42.0000 | −1.68405 | ||||||||
\(623\) | −9.79796 | −0.392547 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −29.0000 | −1.16000 | ||||||||
\(626\) | 50.3383 | 2.01192 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −25.7980 | −1.02945 | ||||||||
\(629\) | −3.85357 | −0.153652 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 28.2020 | 1.12271 | 0.561353 | − | 0.827577i | \(-0.310281\pi\) | ||||
0.561353 | + | 0.827577i | \(0.310281\pi\) | |||||||
\(632\) | −28.8990 | −1.14954 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 70.7878 | 2.81134 | ||||||||
\(635\) | 2.44949 | 0.0972050 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 6.89898 | 0.273348 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −48.0000 | −1.89737 | ||||||||
\(641\) | 7.89898 | 0.311991 | 0.155995 | − | 0.987758i | \(-0.450141\pi\) | ||||
0.155995 | + | 0.987758i | \(0.450141\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −5.34847 | −0.210923 | −0.105462 | − | 0.994423i | \(-0.533632\pi\) | ||||
−0.105462 | + | 0.994423i | \(0.533632\pi\) | |||||||
\(644\) | −24.0000 | −0.945732 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −0.606123 | −0.0238476 | ||||||||
\(647\) | −15.3031 | −0.601625 | −0.300813 | − | 0.953683i | \(-0.597258\pi\) | ||||
−0.300813 | + | 0.953683i | \(0.597258\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 16.8990 | 0.662833 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 68.0000 | 2.66309 | ||||||||
\(653\) | −21.5505 | −0.843337 | −0.421668 | − | 0.906750i | \(-0.638555\pi\) | ||||
−0.421668 | + | 0.906750i | \(0.638555\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −25.3485 | −0.990447 | ||||||||
\(656\) | −2.20204 | −0.0859753 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 29.3939 | 1.14589 | ||||||||
\(659\) | 22.8990 | 0.892018 | 0.446009 | − | 0.895029i | \(-0.352845\pi\) | ||||
0.446009 | + | 0.895029i | \(0.352845\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −35.3485 | −1.37490 | −0.687448 | − | 0.726234i | \(-0.741269\pi\) | ||||
−0.687448 | + | 0.726234i | \(0.741269\pi\) | |||||||
\(662\) | −33.1918 | −1.29004 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −29.3939 | −1.14070 | ||||||||
\(665\) | −1.10102 | −0.0426957 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 11.3939 | 0.441173 | ||||||||
\(668\) | 44.5857 | 1.72507 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 85.4847 | 3.30256 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 14.3031 | 0.551343 | 0.275671 | − | 0.961252i | \(-0.411100\pi\) | ||||
0.275671 | + | 0.961252i | \(0.411100\pi\) | |||||||
\(674\) | −21.1918 | −0.816279 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 138.384 | 5.32245 | ||||||||
\(677\) | 18.5505 | 0.712954 | 0.356477 | − | 0.934304i | \(-0.383978\pi\) | ||||
0.356477 | + | 0.934304i | \(0.383978\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 12.3485 | 0.473891 | ||||||||
\(680\) | 6.60612 | 0.253333 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −13.5959 | −0.520233 | −0.260117 | − | 0.965577i | \(-0.583761\pi\) | ||||
−0.260117 | + | 0.965577i | \(0.583761\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −53.3939 | −2.04008 | ||||||||
\(686\) | 2.44949 | 0.0935220 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 8.00000 | 0.304997 | ||||||||
\(689\) | 54.4949 | 2.07609 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 37.4495 | 1.42465 | 0.712323 | − | 0.701852i | \(-0.247643\pi\) | ||||
0.712323 | + | 0.701852i | \(0.247643\pi\) | |||||||
\(692\) | 24.9898 | 0.949969 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −28.6515 | −1.08760 | ||||||||
\(695\) | −49.8434 | −1.89067 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −0.303062 | −0.0114793 | ||||||||
\(698\) | 66.2474 | 2.50750 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 4.00000 | 0.151186 | ||||||||
\(701\) | −24.4949 | −0.925160 | −0.462580 | − | 0.886578i | \(-0.653076\pi\) | ||||
−0.462580 | + | 0.886578i | \(0.653076\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 3.14643 | 0.118670 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −17.3939 | −0.654627 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −42.3939 | −1.59214 | −0.796068 | − | 0.605208i | \(-0.793090\pi\) | ||||
−0.796068 | + | 0.605208i | \(0.793090\pi\) | |||||||
\(710\) | −50.6969 | −1.90262 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −48.0000 | −1.79888 | ||||||||
\(713\) | −48.0000 | −1.79761 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 15.1918 | 0.567746 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −36.7423 | −1.37121 | ||||||||
\(719\) | 3.85357 | 0.143714 | 0.0718570 | − | 0.997415i | \(-0.477107\pi\) | ||||
0.0718570 | + | 0.997415i | \(0.477107\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −4.00000 | −0.148968 | ||||||||
\(722\) | −46.0454 | −1.71363 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −96.5857 | −3.58958 | ||||||||
\(725\) | −1.89898 | −0.0705263 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −30.6413 | −1.13642 | −0.568212 | − | 0.822882i | \(-0.692365\pi\) | ||||
−0.568212 | + | 0.822882i | \(0.692365\pi\) | |||||||
\(728\) | 33.7980 | 1.25264 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −68.0908 | −2.52015 | ||||||||
\(731\) | 1.10102 | 0.0407227 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −14.6515 | −0.541167 | −0.270583 | − | 0.962697i | \(-0.587217\pi\) | ||||
−0.270583 | + | 0.962697i | \(0.587217\pi\) | |||||||
\(734\) | 4.89898 | 0.180825 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −33.6969 | −1.23956 | −0.619781 | − | 0.784775i | \(-0.712779\pi\) | ||||
−0.619781 | + | 0.784775i | \(0.712779\pi\) | |||||||
\(740\) | −68.5857 | −2.52126 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 19.3485 | 0.710305 | ||||||||
\(743\) | −5.69694 | −0.209000 | −0.104500 | − | 0.994525i | \(-0.533324\pi\) | ||||
−0.104500 | + | 0.994525i | \(0.533324\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −21.3031 | −0.780484 | ||||||||
\(746\) | 60.9898 | 2.23300 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 7.34847 | 0.268507 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −39.6413 | −1.44653 | −0.723266 | − | 0.690569i | \(-0.757360\pi\) | ||||
−0.723266 | + | 0.690569i | \(0.757360\pi\) | |||||||
\(752\) | 48.0000 | 1.75038 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −32.0908 | −1.16868 | ||||||||
\(755\) | −13.1010 | −0.476795 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −45.0908 | −1.63885 | −0.819427 | − | 0.573184i | \(-0.805708\pi\) | ||||
−0.819427 | + | 0.573184i | \(0.805708\pi\) | |||||||
\(758\) | 48.9898 | 1.77939 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −5.39388 | −0.195656 | ||||||||
\(761\) | −29.6413 | −1.07450 | −0.537249 | − | 0.843424i | \(-0.680536\pi\) | ||||
−0.537249 | + | 0.843424i | \(0.680536\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 9.34847 | 0.338437 | ||||||||
\(764\) | −5.39388 | −0.195144 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −7.95459 | −0.287411 | ||||||||
\(767\) | −16.8990 | −0.610187 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 37.4495 | 1.35046 | 0.675232 | − | 0.737606i | \(-0.264044\pi\) | ||||
0.675232 | + | 0.737606i | \(0.264044\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 41.7980 | 1.50434 | ||||||||
\(773\) | 26.7526 | 0.962222 | 0.481111 | − | 0.876660i | \(-0.340233\pi\) | ||||
0.481111 | + | 0.876660i | \(0.340233\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 8.00000 | 0.287368 | ||||||||
\(776\) | 60.4949 | 2.17164 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −24.6061 | −0.882172 | ||||||||
\(779\) | 0.247449 | 0.00886577 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | −8.09082 | −0.289327 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 4.00000 | 0.142857 | ||||||||
\(785\) | −15.7980 | −0.563853 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 20.8536 | 0.743350 | 0.371675 | − | 0.928363i | \(-0.378784\pi\) | ||||
0.371675 | + | 0.928363i | \(0.378784\pi\) | |||||||
\(788\) | −14.2020 | −0.505927 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −35.3939 | −1.25926 | ||||||||
\(791\) | 6.00000 | 0.213335 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −3.10102 | −0.110120 | ||||||||
\(794\) | 55.5959 | 1.97303 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 80.0000 | 2.83552 | ||||||||
\(797\) | −27.7980 | −0.984654 | −0.492327 | − | 0.870410i | \(-0.663854\pi\) | ||||
−0.492327 | + | 0.870410i | \(0.663854\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 6.60612 | 0.233708 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 72.7423 | 2.56862 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −14.6969 | −0.517999 | ||||||||
\(806\) | 135.192 | 4.76193 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 23.1464 | 0.813785 | 0.406893 | − | 0.913476i | \(-0.366612\pi\) | ||||
0.406893 | + | 0.913476i | \(0.366612\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −4.49490 | −0.157837 | −0.0789186 | − | 0.996881i | \(-0.525147\pi\) | ||||
−0.0789186 | + | 0.996881i | \(0.525147\pi\) | |||||||
\(812\) | −7.59592 | −0.266564 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 41.6413 | 1.45863 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −0.898979 | −0.0314513 | ||||||||
\(818\) | −31.1010 | −1.08742 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −5.39388 | −0.188362 | ||||||||
\(821\) | 12.7980 | 0.446652 | 0.223326 | − | 0.974744i | \(-0.428309\pi\) | ||||
0.223326 | + | 0.974744i | \(0.428309\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −19.0000 | −0.662298 | −0.331149 | − | 0.943578i | \(-0.607436\pi\) | ||||
−0.331149 | + | 0.943578i | \(0.607436\pi\) | |||||||
\(824\) | −19.5959 | −0.682656 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −6.00000 | −0.208767 | ||||||||
\(827\) | 5.20204 | 0.180893 | 0.0904463 | − | 0.995901i | \(-0.471171\pi\) | ||||
0.0904463 | + | 0.995901i | \(0.471171\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −16.4949 | −0.572891 | −0.286446 | − | 0.958096i | \(-0.592474\pi\) | ||||
−0.286446 | + | 0.958096i | \(0.592474\pi\) | |||||||
\(830\) | −36.0000 | −1.24958 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −55.1918 | −1.91343 | ||||||||
\(833\) | 0.550510 | 0.0190740 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 27.3031 | 0.944861 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −18.6061 | −0.642738 | ||||||||
\(839\) | −25.8434 | −0.892212 | −0.446106 | − | 0.894980i | \(-0.647190\pi\) | ||||
−0.446106 | + | 0.894980i | \(0.647190\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −25.3939 | −0.875651 | ||||||||
\(842\) | −93.1918 | −3.21160 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 18.7878 | 0.646701 | ||||||||
\(845\) | 84.7423 | 2.91523 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −11.0000 | −0.377964 | ||||||||
\(848\) | 31.5959 | 1.08501 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 1.34847 | 0.0462521 | ||||||||
\(851\) | 42.0000 | 1.43974 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −55.7423 | −1.90858 | −0.954291 | − | 0.298880i | \(-0.903387\pi\) | ||||
−0.954291 | + | 0.298880i | \(0.903387\pi\) | |||||||
\(854\) | −1.10102 | −0.0376761 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 36.0000 | 1.23045 | ||||||||
\(857\) | −3.30306 | −0.112830 | −0.0564152 | − | 0.998407i | \(-0.517967\pi\) | ||||
−0.0564152 | + | 0.998407i | \(0.517967\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −1.85357 | −0.0632431 | −0.0316215 | − | 0.999500i | \(-0.510067\pi\) | ||||
−0.0316215 | + | 0.999500i | \(0.510067\pi\) | |||||||
\(860\) | 19.5959 | 0.668215 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 32.6969 | 1.11366 | ||||||||
\(863\) | 28.1010 | 0.956570 | 0.478285 | − | 0.878205i | \(-0.341259\pi\) | ||||
0.478285 | + | 0.878205i | \(0.341259\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 15.3031 | 0.520320 | ||||||||
\(866\) | 37.5959 | 1.27756 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 32.0000 | 1.08615 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 98.2929 | 3.33053 | ||||||||
\(872\) | 45.7980 | 1.55091 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 6.60612 | 0.223455 | ||||||||
\(875\) | −9.79796 | −0.331231 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 43.6969 | 1.47554 | 0.737770 | − | 0.675052i | \(-0.235879\pi\) | ||||
0.737770 | + | 0.675052i | \(0.235879\pi\) | |||||||
\(878\) | 0.853572 | 0.0288067 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 42.2474 | 1.42335 | 0.711676 | − | 0.702507i | \(-0.247936\pi\) | ||||
0.711676 | + | 0.702507i | \(0.247936\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −19.7980 | −0.666254 | −0.333127 | − | 0.942882i | \(-0.608104\pi\) | ||||
−0.333127 | + | 0.942882i | \(0.608104\pi\) | |||||||
\(884\) | 15.1918 | 0.510957 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −64.7878 | −2.17659 | ||||||||
\(887\) | 4.89898 | 0.164492 | 0.0822458 | − | 0.996612i | \(-0.473791\pi\) | ||||
0.0822458 | + | 0.996612i | \(0.473791\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1.00000 | 0.0335389 | ||||||||
\(890\) | −58.7878 | −1.97057 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 29.7980 | 0.997709 | ||||||||
\(893\) | −5.39388 | −0.180499 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 9.30306 | 0.310967 | ||||||||
\(896\) | −19.5959 | −0.654654 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −70.7878 | −2.36222 | ||||||||
\(899\) | −15.1918 | −0.506676 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 4.34847 | 0.144869 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 29.3939 | 0.977626 | ||||||||
\(905\) | −59.1464 | −1.96609 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 13.2020 | 0.438367 | 0.219183 | − | 0.975684i | \(-0.429661\pi\) | ||||
0.219183 | + | 0.975684i | \(0.429661\pi\) | |||||||
\(908\) | −48.0000 | −1.59294 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 41.3939 | 1.37219 | ||||||||
\(911\) | −8.69694 | −0.288142 | −0.144071 | − | 0.989567i | \(-0.546019\pi\) | ||||
−0.144071 | + | 0.989567i | \(0.546019\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | −47.7526 | −1.57951 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 10.2020 | 0.337085 | ||||||||
\(917\) | −10.3485 | −0.341737 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −4.79796 | −0.158270 | −0.0791350 | − | 0.996864i | \(-0.525216\pi\) | ||||
−0.0791350 | + | 0.996864i | \(0.525216\pi\) | |||||||
\(920\) | −72.0000 | −2.37377 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −71.3939 | −2.35123 | ||||||||
\(923\) | −58.2929 | −1.91873 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −7.00000 | −0.230159 | ||||||||
\(926\) | −48.4949 | −1.59364 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 22.2929 | 0.731405 | 0.365702 | − | 0.930732i | \(-0.380829\pi\) | ||||
0.365702 | + | 0.930732i | \(0.380829\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −0.449490 | −0.0147314 | ||||||||
\(932\) | −7.59592 | −0.248813 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 18.6061 | 0.608811 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −42.6969 | −1.39485 | −0.697424 | − | 0.716659i | \(-0.745671\pi\) | ||||
−0.697424 | + | 0.716659i | \(0.745671\pi\) | |||||||
\(938\) | 34.8990 | 1.13949 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 117.576 | 3.83489 | ||||||||
\(941\) | 28.8434 | 0.940267 | 0.470133 | − | 0.882595i | \(-0.344206\pi\) | ||||
0.470133 | + | 0.882595i | \(0.344206\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 3.30306 | 0.107562 | ||||||||
\(944\) | −9.79796 | −0.318896 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 51.9898 | 1.68944 | 0.844721 | − | 0.535207i | \(-0.179767\pi\) | ||||
0.844721 | + | 0.535207i | \(0.179767\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −78.2929 | −2.54149 | ||||||||
\(950\) | −1.10102 | −0.0357218 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 2.69694 | 0.0874083 | ||||||||
\(953\) | −13.3485 | −0.432399 | −0.216200 | − | 0.976349i | \(-0.569366\pi\) | ||||
−0.216200 | + | 0.976349i | \(0.569366\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −3.30306 | −0.106885 | ||||||||
\(956\) | −12.0000 | −0.388108 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 52.0454 | 1.68151 | ||||||||
\(959\) | −21.7980 | −0.703893 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 33.0000 | 1.06452 | ||||||||
\(962\) | −118.293 | −3.81391 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −76.9898 | −2.47967 | ||||||||
\(965\) | 25.5959 | 0.823962 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −42.9444 | −1.38100 | −0.690499 | − | 0.723333i | \(-0.742609\pi\) | ||||
−0.690499 | + | 0.723333i | \(0.742609\pi\) | |||||||
\(968\) | −53.8888 | −1.73205 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 74.0908 | 2.37891 | ||||||||
\(971\) | 1.59592 | 0.0512154 | 0.0256077 | − | 0.999672i | \(-0.491848\pi\) | ||||
0.0256077 | + | 0.999672i | \(0.491848\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −20.3485 | −0.652342 | ||||||||
\(974\) | 56.2020 | 1.80083 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −1.79796 | −0.0575513 | ||||||||
\(977\) | 38.2020 | 1.22219 | 0.611096 | − | 0.791557i | \(-0.290729\pi\) | ||||
0.611096 | + | 0.791557i | \(0.290729\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 9.79796 | 0.312984 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 56.0908 | 1.78993 | ||||||||
\(983\) | 41.9444 | 1.33782 | 0.668909 | − | 0.743344i | \(-0.266762\pi\) | ||||
0.668909 | + | 0.743344i | \(0.266762\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −8.69694 | −0.277108 | ||||||||
\(986\) | −2.56072 | −0.0815498 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −12.4041 | −0.394626 | ||||||||
\(989\) | −12.0000 | −0.381578 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 5.55051 | 0.176318 | 0.0881589 | − | 0.996106i | \(-0.471902\pi\) | ||||
0.0881589 | + | 0.996106i | \(0.471902\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −20.6969 | −0.656467 | ||||||||
\(995\) | 48.9898 | 1.55308 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 56.4949 | 1.78921 | 0.894606 | − | 0.446856i | \(-0.147457\pi\) | ||||
0.894606 | + | 0.446856i | \(0.147457\pi\) | |||||||
\(998\) | −93.1918 | −2.94994 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 8001.2.a.k.1.2 | 2 | ||
3.2 | odd | 2 | 2667.2.a.h.1.1 | ✓ | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2667.2.a.h.1.1 | ✓ | 2 | 3.2 | odd | 2 | ||
8001.2.a.k.1.2 | 2 | 1.1 | even | 1 | trivial |