Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4851,2,Mod(1,4851)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4851, 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("4851.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4851 = 3^{2} \cdot 7^{2} \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4851.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: | \(38.7354300205\) |
Analytic rank: | \(1\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.229.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - 4x - 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 1617) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(-1.86081\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4851.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.86081 | 1.31579 | 0.657894 | − | 0.753110i | \(-0.271447\pi\) | ||||
0.657894 | + | 0.753110i | \(0.271447\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.46260 | 0.731299 | ||||||||
\(5\) | 1.32340 | 0.591844 | 0.295922 | − | 0.955212i | \(-0.404373\pi\) | ||||
0.295922 | + | 0.955212i | \(0.404373\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 2.46260 | 0.778742 | ||||||||
\(11\) | −1.00000 | −0.301511 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −0.398207 | −0.110443 | −0.0552214 | − | 0.998474i | \(-0.517586\pi\) | ||||
−0.0552214 | + | 0.998474i | \(0.517586\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −4.78600 | −1.19650 | ||||||||
\(17\) | −6.64681 | −1.61209 | −0.806044 | − | 0.591856i | \(-0.798396\pi\) | ||||
−0.806044 | + | 0.591856i | \(0.798396\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.32340 | −0.303610 | −0.151805 | − | 0.988410i | \(-0.548509\pi\) | ||||
−0.151805 | + | 0.988410i | \(0.548509\pi\) | |||||||
\(20\) | 1.93561 | 0.432815 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −1.86081 | −0.396725 | ||||||||
\(23\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −3.24860 | −0.649720 | ||||||||
\(26\) | −0.740987 | −0.145319 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −1.47301 | −0.273531 | −0.136766 | − | 0.990603i | \(-0.543671\pi\) | ||||
−0.136766 | + | 0.990603i | \(0.543671\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.79641 | 0.861462 | 0.430731 | − | 0.902480i | \(-0.358256\pi\) | ||||
0.430731 | + | 0.902480i | \(0.358256\pi\) | |||||||
\(32\) | −6.90582 | −1.22079 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −12.3684 | −2.12117 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −1.60179 | −0.263333 | −0.131667 | − | 0.991294i | \(-0.542033\pi\) | ||||
−0.131667 | + | 0.991294i | \(0.542033\pi\) | |||||||
\(38\) | −2.46260 | −0.399486 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −1.32340 | −0.209249 | ||||||||
\(41\) | 4.79641 | 0.749074 | 0.374537 | − | 0.927212i | \(-0.377802\pi\) | ||||
0.374537 | + | 0.927212i | \(0.377802\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −4.79641 | −0.731446 | −0.365723 | − | 0.930724i | \(-0.619178\pi\) | ||||
−0.365723 | + | 0.930724i | \(0.619178\pi\) | |||||||
\(44\) | −1.46260 | −0.220495 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 3.04502 | 0.444161 | 0.222081 | − | 0.975028i | \(-0.428715\pi\) | ||||
0.222081 | + | 0.975028i | \(0.428715\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −6.04502 | −0.854894 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −0.582418 | −0.0807668 | ||||||||
\(53\) | −8.64681 | −1.18773 | −0.593865 | − | 0.804565i | \(-0.702399\pi\) | ||||
−0.593865 | + | 0.804565i | \(0.702399\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −1.32340 | −0.178448 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −2.74099 | −0.359909 | ||||||||
\(59\) | −13.6918 | −1.78252 | −0.891262 | − | 0.453489i | \(-0.850179\pi\) | ||||
−0.891262 | + | 0.453489i | \(0.850179\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 3.20359 | 0.410177 | 0.205089 | − | 0.978743i | \(-0.434252\pi\) | ||||
0.205089 | + | 0.978743i | \(0.434252\pi\) | |||||||
\(62\) | 8.92520 | 1.13350 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −3.27839 | −0.409799 | ||||||||
\(65\) | −0.526989 | −0.0653650 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −10.6170 | −1.29708 | −0.648538 | − | 0.761182i | \(-0.724619\pi\) | ||||
−0.648538 | + | 0.761182i | \(0.724619\pi\) | |||||||
\(68\) | −9.72161 | −1.17892 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −15.9404 | −1.89178 | −0.945890 | − | 0.324487i | \(-0.894808\pi\) | ||||
−0.945890 | + | 0.324487i | \(0.894808\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −1.45219 | −0.169966 | −0.0849828 | − | 0.996382i | \(-0.527084\pi\) | ||||
−0.0849828 | + | 0.996382i | \(0.527084\pi\) | |||||||
\(74\) | −2.98062 | −0.346491 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −1.93561 | −0.222030 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 3.44322 | 0.387393 | 0.193696 | − | 0.981062i | \(-0.437952\pi\) | ||||
0.193696 | + | 0.981062i | \(0.437952\pi\) | |||||||
\(80\) | −6.33382 | −0.708142 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 8.92520 | 0.985623 | ||||||||
\(83\) | −0.796415 | −0.0874179 | −0.0437089 | − | 0.999044i | \(-0.513917\pi\) | ||||
−0.0437089 | + | 0.999044i | \(0.513917\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −8.79641 | −0.954105 | ||||||||
\(86\) | −8.92520 | −0.962429 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 1.00000 | 0.106600 | ||||||||
\(89\) | −10.6468 | −1.12856 | −0.564280 | − | 0.825584i | \(-0.690846\pi\) | ||||
−0.564280 | + | 0.825584i | \(0.690846\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 5.66618 | 0.584422 | ||||||||
\(95\) | −1.75140 | −0.179690 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 12.2396 | 1.24275 | 0.621373 | − | 0.783515i | \(-0.286575\pi\) | ||||
0.621373 | + | 0.783515i | \(0.286575\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −4.75140 | −0.475140 | ||||||||
\(101\) | 16.4972 | 1.64153 | 0.820766 | − | 0.571264i | \(-0.193547\pi\) | ||||
0.820766 | + | 0.571264i | \(0.193547\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 13.8504 | 1.36472 | 0.682360 | − | 0.731016i | \(-0.260954\pi\) | ||||
0.682360 | + | 0.731016i | \(0.260954\pi\) | |||||||
\(104\) | 0.398207 | 0.0390475 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −16.0900 | −1.56280 | ||||||||
\(107\) | 5.69182 | 0.550249 | 0.275125 | − | 0.961409i | \(-0.411281\pi\) | ||||
0.275125 | + | 0.961409i | \(0.411281\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −4.14961 | −0.397460 | −0.198730 | − | 0.980054i | \(-0.563682\pi\) | ||||
−0.198730 | + | 0.980054i | \(0.563682\pi\) | |||||||
\(110\) | −2.46260 | −0.234800 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −0.946021 | −0.0889942 | −0.0444971 | − | 0.999010i | \(-0.514169\pi\) | ||||
−0.0444971 | + | 0.999010i | \(0.514169\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −2.15442 | −0.200033 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −25.4778 | −2.34542 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 5.96125 | 0.539706 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 7.01523 | 0.629986 | ||||||||
\(125\) | −10.9162 | −0.976378 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −4.55678 | −0.404349 | −0.202174 | − | 0.979350i | \(-0.564801\pi\) | ||||
−0.202174 | + | 0.979350i | \(0.564801\pi\) | |||||||
\(128\) | 7.71120 | 0.681580 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −0.980625 | −0.0860065 | ||||||||
\(131\) | 1.05398 | 0.0920866 | 0.0460433 | − | 0.998939i | \(-0.485339\pi\) | ||||
0.0460433 | + | 0.998939i | \(0.485339\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −19.7562 | −1.70668 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 6.64681 | 0.569959 | ||||||||
\(137\) | −1.44322 | −0.123303 | −0.0616514 | − | 0.998098i | \(-0.519637\pi\) | ||||
−0.0616514 | + | 0.998098i | \(0.519637\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 18.5872 | 1.57655 | 0.788274 | − | 0.615324i | \(-0.210975\pi\) | ||||
0.788274 | + | 0.615324i | \(0.210975\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −29.6620 | −2.48918 | ||||||||
\(143\) | 0.398207 | 0.0332998 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −1.94939 | −0.161888 | ||||||||
\(146\) | −2.70224 | −0.223639 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −2.34278 | −0.192575 | ||||||||
\(149\) | −3.88018 | −0.317877 | −0.158938 | − | 0.987289i | \(-0.550807\pi\) | ||||
−0.158938 | + | 0.987289i | \(0.550807\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 10.6468 | 0.866425 | 0.433212 | − | 0.901292i | \(-0.357380\pi\) | ||||
0.433212 | + | 0.901292i | \(0.357380\pi\) | |||||||
\(152\) | 1.32340 | 0.107342 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 6.34760 | 0.509851 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 16.7368 | 1.33575 | 0.667873 | − | 0.744276i | \(-0.267205\pi\) | ||||
0.667873 | + | 0.744276i | \(0.267205\pi\) | |||||||
\(158\) | 6.40717 | 0.509727 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −9.13919 | −0.722517 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 2.67660 | 0.209647 | 0.104824 | − | 0.994491i | \(-0.466572\pi\) | ||||
0.104824 | + | 0.994491i | \(0.466572\pi\) | |||||||
\(164\) | 7.01523 | 0.547797 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −1.48197 | −0.115023 | ||||||||
\(167\) | −16.0000 | −1.23812 | −0.619059 | − | 0.785345i | \(-0.712486\pi\) | ||||
−0.619059 | + | 0.785345i | \(0.712486\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.8414 | −0.987802 | ||||||||
\(170\) | −16.3684 | −1.25540 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −7.01523 | −0.534906 | ||||||||
\(173\) | −12.7368 | −0.968364 | −0.484182 | − | 0.874967i | \(-0.660883\pi\) | ||||
−0.484182 | + | 0.874967i | \(0.660883\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 4.78600 | 0.360759 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −19.8116 | −1.48495 | ||||||||
\(179\) | −5.85039 | −0.437279 | −0.218639 | − | 0.975806i | \(-0.570162\pi\) | ||||
−0.218639 | + | 0.975806i | \(0.570162\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 16.7964 | 1.24847 | 0.624234 | − | 0.781238i | \(-0.285411\pi\) | ||||
0.624234 | + | 0.781238i | \(0.285411\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −2.11982 | −0.155852 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 6.64681 | 0.486063 | ||||||||
\(188\) | 4.45364 | 0.324815 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −3.25901 | −0.236434 | ||||||||
\(191\) | 16.7368 | 1.21104 | 0.605518 | − | 0.795832i | \(-0.292966\pi\) | ||||
0.605518 | + | 0.795832i | \(0.292966\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 9.94043 | 0.715527 | 0.357764 | − | 0.933812i | \(-0.383539\pi\) | ||||
0.357764 | + | 0.933812i | \(0.383539\pi\) | |||||||
\(194\) | 22.7756 | 1.63519 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −15.8504 | −1.12929 | −0.564647 | − | 0.825333i | \(-0.690988\pi\) | ||||
−0.564647 | + | 0.825333i | \(0.690988\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −6.38924 | −0.452922 | −0.226461 | − | 0.974020i | \(-0.572716\pi\) | ||||
−0.226461 | + | 0.974020i | \(0.572716\pi\) | |||||||
\(200\) | 3.24860 | 0.229711 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 30.6981 | 2.15991 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 6.34760 | 0.443335 | ||||||||
\(206\) | 25.7729 | 1.79568 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 1.90582 | 0.132145 | ||||||||
\(209\) | 1.32340 | 0.0915418 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −26.0900 | −1.79611 | −0.898056 | − | 0.439881i | \(-0.855021\pi\) | ||||
−0.898056 | + | 0.439881i | \(0.855021\pi\) | |||||||
\(212\) | −12.6468 | −0.868586 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 10.5914 | 0.724012 | ||||||||
\(215\) | −6.34760 | −0.432902 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −7.72161 | −0.522974 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −1.93561 | −0.130499 | ||||||||
\(221\) | 2.64681 | 0.178044 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 18.0900 | 1.21140 | 0.605699 | − | 0.795694i | \(-0.292894\pi\) | ||||
0.605699 | + | 0.795694i | \(0.292894\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −1.76036 | −0.117098 | ||||||||
\(227\) | −28.1801 | −1.87038 | −0.935188 | − | 0.354151i | \(-0.884770\pi\) | ||||
−0.935188 | + | 0.354151i | \(0.884770\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −8.00000 | −0.528655 | −0.264327 | − | 0.964433i | \(-0.585150\pi\) | ||||
−0.264327 | + | 0.964433i | \(0.585150\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 1.47301 | 0.0967079 | ||||||||
\(233\) | 21.4432 | 1.40479 | 0.702396 | − | 0.711786i | \(-0.252114\pi\) | ||||
0.702396 | + | 0.711786i | \(0.252114\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 4.02979 | 0.262874 | ||||||||
\(236\) | −20.0256 | −1.30356 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −11.5422 | −0.746604 | −0.373302 | − | 0.927710i | \(-0.621774\pi\) | ||||
−0.373302 | + | 0.927710i | \(0.621774\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −12.9550 | −0.834504 | −0.417252 | − | 0.908791i | \(-0.637007\pi\) | ||||
−0.417252 | + | 0.908791i | \(0.637007\pi\) | |||||||
\(242\) | 1.86081 | 0.119617 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 4.68556 | 0.299962 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0.526989 | 0.0335315 | ||||||||
\(248\) | −4.79641 | −0.304573 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −20.3130 | −1.28471 | ||||||||
\(251\) | −28.8954 | −1.82386 | −0.911931 | − | 0.410343i | \(-0.865409\pi\) | ||||
−0.911931 | + | 0.410343i | \(0.865409\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | −8.47928 | −0.532037 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 20.9058 | 1.30661 | ||||||||
\(257\) | −12.2278 | −0.762748 | −0.381374 | − | 0.924421i | \(-0.624549\pi\) | ||||
−0.381374 | + | 0.924421i | \(0.624549\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −0.770774 | −0.0478014 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 1.96125 | 0.121166 | ||||||||
\(263\) | 0.954984 | 0.0588868 | 0.0294434 | − | 0.999566i | \(-0.490627\pi\) | ||||
0.0294434 | + | 0.999566i | \(0.490627\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −11.4432 | −0.702952 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −15.5284 | −0.948550 | ||||||||
\(269\) | 20.2396 | 1.23403 | 0.617016 | − | 0.786950i | \(-0.288341\pi\) | ||||
0.617016 | + | 0.786950i | \(0.288341\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −16.4674 | −1.00032 | −0.500162 | − | 0.865932i | \(-0.666726\pi\) | ||||
−0.500162 | + | 0.865932i | \(0.666726\pi\) | |||||||
\(272\) | 31.8116 | 1.92886 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −2.68556 | −0.162241 | ||||||||
\(275\) | 3.24860 | 0.195898 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 18.1801 | 1.09233 | 0.546167 | − | 0.837676i | \(-0.316086\pi\) | ||||
0.546167 | + | 0.837676i | \(0.316086\pi\) | |||||||
\(278\) | 34.5872 | 2.07440 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −24.3178 | −1.45068 | −0.725339 | − | 0.688391i | \(-0.758317\pi\) | ||||
−0.725339 | + | 0.688391i | \(0.758317\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −21.5035 | −1.27825 | −0.639124 | − | 0.769103i | \(-0.720703\pi\) | ||||
−0.639124 | + | 0.769103i | \(0.720703\pi\) | |||||||
\(284\) | −23.3144 | −1.38346 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0.740987 | 0.0438155 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 27.1801 | 1.59883 | ||||||||
\(290\) | −3.62743 | −0.213010 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −2.12397 | −0.124296 | ||||||||
\(293\) | −5.59283 | −0.326737 | −0.163368 | − | 0.986565i | \(-0.552236\pi\) | ||||
−0.163368 | + | 0.986565i | \(0.552236\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −18.1198 | −1.05498 | ||||||||
\(296\) | 1.60179 | 0.0931023 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −7.22026 | −0.418259 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 19.8116 | 1.14003 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 6.33382 | 0.363269 | ||||||||
\(305\) | 4.23964 | 0.242761 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −10.5872 | −0.604245 | −0.302123 | − | 0.953269i | \(-0.597695\pi\) | ||||
−0.302123 | + | 0.953269i | \(0.597695\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 11.8116 | 0.670856 | ||||||||
\(311\) | −5.59283 | −0.317140 | −0.158570 | − | 0.987348i | \(-0.550688\pi\) | ||||
−0.158570 | + | 0.987348i | \(0.550688\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 1.90997 | 0.107958 | 0.0539789 | − | 0.998542i | \(-0.482810\pi\) | ||||
0.0539789 | + | 0.998542i | \(0.482810\pi\) | |||||||
\(314\) | 31.1440 | 1.75756 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 5.03605 | 0.283300 | ||||||||
\(317\) | −9.44322 | −0.530384 | −0.265192 | − | 0.964196i | \(-0.585435\pi\) | ||||
−0.265192 | + | 0.964196i | \(0.585435\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1.47301 | 0.0824728 | ||||||||
\(320\) | −4.33863 | −0.242537 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 8.79641 | 0.489446 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1.29362 | 0.0717570 | ||||||||
\(326\) | 4.98062 | 0.275851 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −4.79641 | −0.264838 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −20.4793 | −1.12564 | −0.562821 | − | 0.826579i | \(-0.690284\pi\) | ||||
−0.562821 | + | 0.826579i | \(0.690284\pi\) | |||||||
\(332\) | −1.16484 | −0.0639286 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −29.7729 | −1.62910 | ||||||||
\(335\) | −14.0506 | −0.767667 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 17.3836 | 0.946948 | 0.473474 | − | 0.880808i | \(-0.343000\pi\) | ||||
0.473474 | + | 0.880808i | \(0.343000\pi\) | |||||||
\(338\) | −23.8954 | −1.29974 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −12.8656 | −0.697736 | ||||||||
\(341\) | −4.79641 | −0.259740 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 4.79641 | 0.258605 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −23.7008 | −1.27416 | ||||||||
\(347\) | 30.5872 | 1.64201 | 0.821004 | − | 0.570922i | \(-0.193414\pi\) | ||||
0.821004 | + | 0.570922i | \(0.193414\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −32.8775 | −1.75989 | −0.879946 | − | 0.475074i | \(-0.842421\pi\) | ||||
−0.879946 | + | 0.475074i | \(0.842421\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 6.90582 | 0.368082 | ||||||||
\(353\) | 33.0063 | 1.75675 | 0.878373 | − | 0.477976i | \(-0.158629\pi\) | ||||
0.878373 | + | 0.477976i | \(0.158629\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −21.0956 | −1.11964 | ||||||||
\(356\) | −15.5720 | −0.825315 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −10.8864 | −0.575367 | ||||||||
\(359\) | 19.7008 | 1.03977 | 0.519884 | − | 0.854237i | \(-0.325975\pi\) | ||||
0.519884 | + | 0.854237i | \(0.325975\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −17.2486 | −0.907821 | ||||||||
\(362\) | 31.2549 | 1.64272 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −1.92183 | −0.100593 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 31.1261 | 1.62477 | 0.812384 | − | 0.583123i | \(-0.198169\pi\) | ||||
0.812384 | + | 0.583123i | \(0.198169\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −3.94457 | −0.205069 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −8.94602 | −0.463207 | −0.231604 | − | 0.972810i | \(-0.574397\pi\) | ||||
−0.231604 | + | 0.972810i | \(0.574397\pi\) | |||||||
\(374\) | 12.3684 | 0.639556 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −3.04502 | −0.157035 | ||||||||
\(377\) | 0.586564 | 0.0302096 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 4.20985 | 0.216246 | 0.108123 | − | 0.994138i | \(-0.465516\pi\) | ||||
0.108123 | + | 0.994138i | \(0.465516\pi\) | |||||||
\(380\) | −2.56159 | −0.131407 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 31.1440 | 1.59347 | ||||||||
\(383\) | 14.5872 | 0.745373 | 0.372686 | − | 0.927957i | \(-0.378437\pi\) | ||||
0.372686 | + | 0.927957i | \(0.378437\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 18.4972 | 0.941483 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 17.9017 | 0.908820 | ||||||||
\(389\) | 30.4793 | 1.54536 | 0.772680 | − | 0.634795i | \(-0.218916\pi\) | ||||
0.772680 | + | 0.634795i | \(0.218916\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −29.4945 | −1.48591 | ||||||||
\(395\) | 4.55678 | 0.229276 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 10.9044 | 0.547275 | 0.273637 | − | 0.961833i | \(-0.411773\pi\) | ||||
0.273637 | + | 0.961833i | \(0.411773\pi\) | |||||||
\(398\) | −11.8891 | −0.595949 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 15.5478 | 0.777391 | ||||||||
\(401\) | −12.4072 | −0.619585 | −0.309792 | − | 0.950804i | \(-0.600260\pi\) | ||||
−0.309792 | + | 0.950804i | \(0.600260\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −1.90997 | −0.0951423 | ||||||||
\(404\) | 24.1288 | 1.20045 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 1.60179 | 0.0793979 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −31.3836 | −1.55182 | −0.775911 | − | 0.630843i | \(-0.782709\pi\) | ||||
−0.775911 | + | 0.630843i | \(0.782709\pi\) | |||||||
\(410\) | 11.8116 | 0.583336 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 20.2576 | 0.998019 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −1.05398 | −0.0517378 | ||||||||
\(416\) | 2.74995 | 0.134827 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 2.46260 | 0.120450 | ||||||||
\(419\) | 30.1711 | 1.47395 | 0.736977 | − | 0.675917i | \(-0.236252\pi\) | ||||
0.736977 | + | 0.675917i | \(0.236252\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −21.2847 | −1.03735 | −0.518675 | − | 0.854971i | \(-0.673575\pi\) | ||||
−0.518675 | + | 0.854971i | \(0.673575\pi\) | |||||||
\(422\) | −48.5485 | −2.36330 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 8.64681 | 0.419926 | ||||||||
\(425\) | 21.5928 | 1.04741 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 8.32485 | 0.402397 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −11.8116 | −0.569608 | ||||||||
\(431\) | 14.7279 | 0.709417 | 0.354708 | − | 0.934977i | \(-0.384580\pi\) | ||||
0.354708 | + | 0.934977i | \(0.384580\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 14.1496 | 0.679987 | 0.339993 | − | 0.940428i | \(-0.389575\pi\) | ||||
0.339993 | + | 0.940428i | \(0.389575\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −6.06921 | −0.290662 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 26.0007 | 1.24094 | 0.620472 | − | 0.784228i | \(-0.286941\pi\) | ||||
0.620472 | + | 0.784228i | \(0.286941\pi\) | |||||||
\(440\) | 1.32340 | 0.0630908 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 4.92520 | 0.234268 | ||||||||
\(443\) | 32.9765 | 1.56676 | 0.783380 | − | 0.621543i | \(-0.213494\pi\) | ||||
0.783380 | + | 0.621543i | \(0.213494\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −14.0900 | −0.667932 | ||||||||
\(446\) | 33.6620 | 1.59394 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −4.96395 | −0.234263 | −0.117132 | − | 0.993116i | \(-0.537370\pi\) | ||||
−0.117132 | + | 0.993116i | \(0.537370\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −4.79641 | −0.225854 | ||||||||
\(452\) | −1.38365 | −0.0650814 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −52.4376 | −2.46102 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −22.1980 | −1.03838 | −0.519189 | − | 0.854659i | \(-0.673766\pi\) | ||||
−0.519189 | + | 0.854659i | \(0.673766\pi\) | |||||||
\(458\) | −14.8864 | −0.695598 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 12.5389 | 0.583993 | 0.291996 | − | 0.956419i | \(-0.405681\pi\) | ||||
0.291996 | + | 0.956419i | \(0.405681\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 17.5214 | 0.814288 | 0.407144 | − | 0.913364i | \(-0.366525\pi\) | ||||
0.407144 | + | 0.913364i | \(0.366525\pi\) | |||||||
\(464\) | 7.04983 | 0.327280 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 39.9017 | 1.84841 | ||||||||
\(467\) | 11.7819 | 0.545199 | 0.272600 | − | 0.962128i | \(-0.412117\pi\) | ||||
0.272600 | + | 0.962128i | \(0.412117\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 7.49865 | 0.345887 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 13.6918 | 0.630217 | ||||||||
\(473\) | 4.79641 | 0.220539 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 4.29921 | 0.197261 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −21.4778 | −0.982373 | ||||||||
\(479\) | 5.03605 | 0.230103 | 0.115052 | − | 0.993360i | \(-0.463297\pi\) | ||||
0.115052 | + | 0.993360i | \(0.463297\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0.637846 | 0.0290833 | ||||||||
\(482\) | −24.1067 | −1.09803 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 1.46260 | 0.0664817 | ||||||||
\(485\) | 16.1980 | 0.735513 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 20.1801 | 0.914446 | 0.457223 | − | 0.889352i | \(-0.348844\pi\) | ||||
0.457223 | + | 0.889352i | \(0.348844\pi\) | |||||||
\(488\) | −3.20359 | −0.145019 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 25.3926 | 1.14595 | 0.572976 | − | 0.819572i | \(-0.305789\pi\) | ||||
0.572976 | + | 0.819572i | \(0.305789\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 9.79082 | 0.440956 | ||||||||
\(494\) | 0.980625 | 0.0441204 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −22.9557 | −1.03074 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 14.9162 | 0.667742 | 0.333871 | − | 0.942619i | \(-0.391645\pi\) | ||||
0.333871 | + | 0.942619i | \(0.391645\pi\) | |||||||
\(500\) | −15.9661 | −0.714024 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −53.7687 | −2.39982 | ||||||||
\(503\) | 28.9765 | 1.29200 | 0.645999 | − | 0.763339i | \(-0.276441\pi\) | ||||
0.645999 | + | 0.763339i | \(0.276441\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 21.8325 | 0.971532 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −6.66473 | −0.295700 | ||||||||
\(509\) | −1.05398 | −0.0467168 | −0.0233584 | − | 0.999727i | \(-0.507436\pi\) | ||||
−0.0233584 | + | 0.999727i | \(0.507436\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 23.4793 | 1.03765 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −22.7535 | −1.00361 | ||||||||
\(515\) | 18.3297 | 0.807702 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −3.04502 | −0.133920 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0.526989 | 0.0231100 | ||||||||
\(521\) | −14.2999 | −0.626489 | −0.313245 | − | 0.949672i | \(-0.601416\pi\) | ||||
−0.313245 | + | 0.949672i | \(0.601416\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −34.8567 | −1.52418 | −0.762088 | − | 0.647474i | \(-0.775825\pi\) | ||||
−0.762088 | + | 0.647474i | \(0.775825\pi\) | |||||||
\(524\) | 1.54155 | 0.0673428 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 1.77704 | 0.0774826 | ||||||||
\(527\) | −31.8809 | −1.38875 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −23.0000 | −1.00000 | ||||||||
\(530\) | −21.2936 | −0.924936 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −1.90997 | −0.0827299 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 7.53258 | 0.325662 | ||||||||
\(536\) | 10.6170 | 0.458585 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 37.6620 | 1.62373 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 39.2161 | 1.68603 | 0.843016 | − | 0.537888i | \(-0.180778\pi\) | ||||
0.843016 | + | 0.537888i | \(0.180778\pi\) | |||||||
\(542\) | −30.6427 | −1.31622 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 45.9017 | 1.96802 | ||||||||
\(545\) | −5.49161 | −0.235235 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −38.5277 | −1.64732 | −0.823662 | − | 0.567081i | \(-0.808073\pi\) | ||||
−0.823662 | + | 0.567081i | \(0.808073\pi\) | |||||||
\(548\) | −2.11086 | −0.0901713 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 6.04502 | 0.257760 | ||||||||
\(551\) | 1.94939 | 0.0830467 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 33.8296 | 1.43728 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 27.1857 | 1.15293 | ||||||||
\(557\) | −43.7610 | −1.85421 | −0.927107 | − | 0.374796i | \(-0.877713\pi\) | ||||
−0.927107 | + | 0.374796i | \(0.877713\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 1.90997 | 0.0807830 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −45.2507 | −1.90879 | ||||||||
\(563\) | 19.9821 | 0.842144 | 0.421072 | − | 0.907027i | \(-0.361654\pi\) | ||||
0.421072 | + | 0.907027i | \(0.361654\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −1.25197 | −0.0526707 | ||||||||
\(566\) | −40.0138 | −1.68190 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 15.9404 | 0.668845 | ||||||||
\(569\) | −31.7312 | −1.33024 | −0.665121 | − | 0.746735i | \(-0.731620\pi\) | ||||
−0.665121 | + | 0.746735i | \(0.731620\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −10.9460 | −0.458077 | −0.229038 | − | 0.973417i | \(-0.573558\pi\) | ||||
−0.229038 | + | 0.973417i | \(0.573558\pi\) | |||||||
\(572\) | 0.582418 | 0.0243521 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −3.24523 | −0.135101 | −0.0675504 | − | 0.997716i | \(-0.521518\pi\) | ||||
−0.0675504 | + | 0.997716i | \(0.521518\pi\) | |||||||
\(578\) | 50.5768 | 2.10372 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −2.85117 | −0.118388 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 8.64681 | 0.358114 | ||||||||
\(584\) | 1.45219 | 0.0600919 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −10.4072 | −0.429916 | ||||||||
\(587\) | −26.7875 | −1.10564 | −0.552818 | − | 0.833302i | \(-0.686448\pi\) | ||||
−0.552818 | + | 0.833302i | \(0.686448\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −6.34760 | −0.261548 | ||||||||
\(590\) | −33.7175 | −1.38813 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 7.66618 | 0.315078 | ||||||||
\(593\) | −32.2396 | −1.32392 | −0.661962 | − | 0.749538i | \(-0.730276\pi\) | ||||
−0.661962 | + | 0.749538i | \(0.730276\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −5.67515 | −0.232463 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 7.14401 | 0.291896 | 0.145948 | − | 0.989292i | \(-0.453377\pi\) | ||||
0.145948 | + | 0.989292i | \(0.453377\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −21.7514 | −0.887258 | −0.443629 | − | 0.896211i | \(-0.646309\pi\) | ||||
−0.443629 | + | 0.896211i | \(0.646309\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 15.5720 | 0.633616 | ||||||||
\(605\) | 1.32340 | 0.0538040 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 39.4134 | 1.59974 | 0.799871 | − | 0.600172i | \(-0.204901\pi\) | ||||
0.799871 | + | 0.600172i | \(0.204901\pi\) | |||||||
\(608\) | 9.13919 | 0.370643 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 7.88914 | 0.319422 | ||||||||
\(611\) | −1.21255 | −0.0490544 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −22.1980 | −0.896568 | −0.448284 | − | 0.893891i | \(-0.647965\pi\) | ||||
−0.448284 | + | 0.893891i | \(0.647965\pi\) | |||||||
\(614\) | −19.7008 | −0.795059 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 37.4432 | 1.50741 | 0.753704 | − | 0.657214i | \(-0.228265\pi\) | ||||
0.753704 | + | 0.657214i | \(0.228265\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 15.7008 | 0.631068 | 0.315534 | − | 0.948914i | \(-0.397816\pi\) | ||||
0.315534 | + | 0.948914i | \(0.397816\pi\) | |||||||
\(620\) | 9.28398 | 0.372854 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −10.4072 | −0.417290 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.79641 | 0.0718566 | ||||||||
\(626\) | 3.55408 | 0.142050 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 24.4793 | 0.976829 | ||||||||
\(629\) | 10.6468 | 0.424516 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 35.0665 | 1.39598 | 0.697988 | − | 0.716110i | \(-0.254079\pi\) | ||||
0.697988 | + | 0.716110i | \(0.254079\pi\) | |||||||
\(632\) | −3.44322 | −0.136964 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −17.5720 | −0.697873 | ||||||||
\(635\) | −6.03046 | −0.239311 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 2.74099 | 0.108517 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 10.2050 | 0.403389 | ||||||||
\(641\) | 30.1801 | 1.19204 | 0.596020 | − | 0.802969i | \(-0.296748\pi\) | ||||
0.596020 | + | 0.802969i | \(0.296748\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 36.7964 | 1.45111 | 0.725554 | − | 0.688165i | \(-0.241583\pi\) | ||||
0.725554 | + | 0.688165i | \(0.241583\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 16.3684 | 0.644007 | ||||||||
\(647\) | −33.4522 | −1.31514 | −0.657571 | − | 0.753393i | \(-0.728416\pi\) | ||||
−0.657571 | + | 0.753393i | \(0.728416\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 13.6918 | 0.537451 | ||||||||
\(650\) | 2.40717 | 0.0944170 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 3.91478 | 0.153315 | ||||||||
\(653\) | −5.50280 | −0.215341 | −0.107671 | − | 0.994187i | \(-0.534339\pi\) | ||||
−0.107671 | + | 0.994187i | \(0.534339\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 1.39484 | 0.0545009 | ||||||||
\(656\) | −22.9557 | −0.896268 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −33.1946 | −1.29308 | −0.646539 | − | 0.762881i | \(-0.723784\pi\) | ||||
−0.646539 | + | 0.762881i | \(0.723784\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −43.3241 | −1.68511 | −0.842556 | − | 0.538609i | \(-0.818950\pi\) | ||||
−0.842556 | + | 0.538609i | \(0.818950\pi\) | |||||||
\(662\) | −38.1080 | −1.48111 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0.796415 | 0.0309069 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | −23.4016 | −0.905434 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −26.1455 | −1.01009 | ||||||||
\(671\) | −3.20359 | −0.123673 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −28.0721 | −1.08210 | −0.541050 | − | 0.840990i | \(-0.681973\pi\) | ||||
−0.541050 | + | 0.840990i | \(0.681973\pi\) | |||||||
\(674\) | 32.3476 | 1.24598 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −18.7819 | −0.722379 | ||||||||
\(677\) | 22.8448 | 0.877997 | 0.438998 | − | 0.898488i | \(-0.355333\pi\) | ||||
0.438998 | + | 0.898488i | \(0.355333\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 8.79641 | 0.337327 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −8.92520 | −0.341763 | ||||||||
\(683\) | −11.4016 | −0.436269 | −0.218135 | − | 0.975919i | \(-0.569997\pi\) | ||||
−0.218135 | + | 0.975919i | \(0.569997\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −1.90997 | −0.0729761 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 22.9557 | 0.875176 | ||||||||
\(689\) | 3.44322 | 0.131176 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 11.9404 | 0.454235 | 0.227118 | − | 0.973867i | \(-0.427070\pi\) | ||||
0.227118 | + | 0.973867i | \(0.427070\pi\) | |||||||
\(692\) | −18.6289 | −0.708164 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 56.9169 | 2.16054 | ||||||||
\(695\) | 24.5984 | 0.933071 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −31.8809 | −1.20757 | ||||||||
\(698\) | −61.1786 | −2.31564 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −17.1440 | −0.647520 | −0.323760 | − | 0.946139i | \(-0.604947\pi\) | ||||
−0.323760 | + | 0.946139i | \(0.604947\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 2.11982 | 0.0799505 | ||||||||
\(704\) | 3.27839 | 0.123559 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 61.4183 | 2.31151 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −50.7583 | −1.90627 | −0.953135 | − | 0.302546i | \(-0.902163\pi\) | ||||
−0.953135 | + | 0.302546i | \(0.902163\pi\) | |||||||
\(710\) | −39.2549 | −1.47321 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 10.6468 | 0.399006 | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0.526989 | 0.0197083 | ||||||||
\(716\) | −8.55678 | −0.319782 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 36.6593 | 1.36811 | ||||||||
\(719\) | 4.35656 | 0.162472 | 0.0812361 | − | 0.996695i | \(-0.474113\pi\) | ||||
0.0812361 | + | 0.996695i | \(0.474113\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −32.0963 | −1.19450 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 24.5664 | 0.913003 | ||||||||
\(725\) | 4.78522 | 0.177719 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 33.1745 | 1.23037 | 0.615186 | − | 0.788382i | \(-0.289081\pi\) | ||||
0.615186 | + | 0.788382i | \(0.289081\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −3.57615 | −0.132359 | ||||||||
\(731\) | 31.8809 | 1.17916 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 31.3836 | 1.15918 | 0.579591 | − | 0.814908i | \(-0.303212\pi\) | ||||
0.579591 | + | 0.814908i | \(0.303212\pi\) | |||||||
\(734\) | 57.9196 | 2.13785 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 10.6170 | 0.391083 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 29.4737 | 1.08421 | 0.542103 | − | 0.840312i | \(-0.317628\pi\) | ||||
0.542103 | + | 0.840312i | \(0.317628\pi\) | |||||||
\(740\) | −3.10044 | −0.113975 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 15.8414 | 0.581166 | 0.290583 | − | 0.956850i | \(-0.406151\pi\) | ||||
0.290583 | + | 0.956850i | \(0.406151\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −5.13505 | −0.188134 | ||||||||
\(746\) | −16.6468 | −0.609483 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 9.72161 | 0.355457 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 44.1919 | 1.61259 | 0.806293 | − | 0.591516i | \(-0.201470\pi\) | ||||
0.806293 | + | 0.591516i | \(0.201470\pi\) | |||||||
\(752\) | −14.5735 | −0.531439 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 1.09148 | 0.0397494 | ||||||||
\(755\) | 14.0900 | 0.512789 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 44.1711 | 1.60543 | 0.802713 | − | 0.596366i | \(-0.203389\pi\) | ||||
0.802713 | + | 0.596366i | \(0.203389\pi\) | |||||||
\(758\) | 7.83372 | 0.284533 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 1.75140 | 0.0635299 | ||||||||
\(761\) | −41.0361 | −1.48756 | −0.743778 | − | 0.668427i | \(-0.766968\pi\) | ||||
−0.743778 | + | 0.668427i | \(0.766968\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 24.4793 | 0.885629 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 27.1440 | 0.980753 | ||||||||
\(767\) | 5.45219 | 0.196867 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −52.8358 | −1.90531 | −0.952654 | − | 0.304055i | \(-0.901659\pi\) | ||||
−0.952654 | + | 0.304055i | \(0.901659\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 14.5389 | 0.523265 | ||||||||
\(773\) | 32.0907 | 1.15422 | 0.577111 | − | 0.816666i | \(-0.304180\pi\) | ||||
0.577111 | + | 0.816666i | \(0.304180\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −15.5816 | −0.559709 | ||||||||
\(776\) | −12.2396 | −0.439377 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 56.7160 | 2.03337 | ||||||||
\(779\) | −6.34760 | −0.227426 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 15.9404 | 0.570393 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 22.1496 | 0.790553 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −2.37738 | −0.0847446 | −0.0423723 | − | 0.999102i | \(-0.513492\pi\) | ||||
−0.0423723 | + | 0.999102i | \(0.513492\pi\) | |||||||
\(788\) | −23.1828 | −0.825852 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 8.47928 | 0.301679 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −1.27569 | −0.0453011 | ||||||||
\(794\) | 20.2909 | 0.720098 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −9.34490 | −0.331221 | ||||||||
\(797\) | −20.5091 | −0.726468 | −0.363234 | − | 0.931698i | \(-0.618327\pi\) | ||||
−0.363234 | + | 0.931698i | \(0.618327\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −20.2396 | −0.716027 | ||||||||
\(800\) | 22.4343 | 0.793171 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −23.0873 | −0.815242 | ||||||||
\(803\) | 1.45219 | 0.0512465 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −3.55408 | −0.125187 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −16.4972 | −0.580370 | ||||||||
\(809\) | 8.85666 | 0.311384 | 0.155692 | − | 0.987806i | \(-0.450239\pi\) | ||||
0.155692 | + | 0.987806i | \(0.450239\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −8.26943 | −0.290379 | −0.145189 | − | 0.989404i | \(-0.546379\pi\) | ||||
−0.145189 | + | 0.989404i | \(0.546379\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 2.98062 | 0.104471 | ||||||||
\(815\) | 3.54222 | 0.124078 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 6.34760 | 0.222074 | ||||||||
\(818\) | −58.3989 | −2.04187 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 9.28398 | 0.324211 | ||||||||
\(821\) | 32.3595 | 1.12935 | 0.564676 | − | 0.825312i | \(-0.309001\pi\) | ||||
0.564676 | + | 0.825312i | \(0.309001\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −45.2459 | −1.57717 | −0.788587 | − | 0.614924i | \(-0.789187\pi\) | ||||
−0.788587 | + | 0.614924i | \(0.789187\pi\) | |||||||
\(824\) | −13.8504 | −0.482501 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −20.8954 | −0.726605 | −0.363302 | − | 0.931671i | \(-0.618351\pi\) | ||||
−0.363302 | + | 0.931671i | \(0.618351\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −44.6952 | −1.55233 | −0.776164 | − | 0.630531i | \(-0.782837\pi\) | ||||
−0.776164 | + | 0.630531i | \(0.782837\pi\) | |||||||
\(830\) | −1.96125 | −0.0680760 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 1.30548 | 0.0452593 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −21.1745 | −0.732773 | ||||||||
\(836\) | 1.93561 | 0.0669444 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 56.1426 | 1.93941 | ||||||||
\(839\) | 0.457782 | 0.0158044 | 0.00790219 | − | 0.999969i | \(-0.497485\pi\) | ||||
0.00790219 | + | 0.999969i | \(0.497485\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −26.8302 | −0.925181 | ||||||||
\(842\) | −39.6066 | −1.36493 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −38.1592 | −1.31350 | ||||||||
\(845\) | −16.9944 | −0.584625 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 41.3836 | 1.42112 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 40.1801 | 1.37816 | ||||||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −26.0900 | −0.893306 | −0.446653 | − | 0.894707i | \(-0.647384\pi\) | ||||
−0.446653 | + | 0.894707i | \(0.647384\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −5.69182 | −0.194543 | ||||||||
\(857\) | −6.38924 | −0.218252 | −0.109126 | − | 0.994028i | \(-0.534805\pi\) | ||||
−0.109126 | + | 0.994028i | \(0.534805\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −3.26316 | −0.111338 | −0.0556688 | − | 0.998449i | \(-0.517729\pi\) | ||||
−0.0556688 | + | 0.998449i | \(0.517729\pi\) | |||||||
\(860\) | −9.28398 | −0.316581 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 27.4057 | 0.933443 | ||||||||
\(863\) | 12.6164 | 0.429466 | 0.214733 | − | 0.976673i | \(-0.431112\pi\) | ||||
0.214733 | + | 0.976673i | \(0.431112\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −16.8560 | −0.573121 | ||||||||
\(866\) | 26.3297 | 0.894719 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −3.44322 | −0.116803 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 4.22778 | 0.143253 | ||||||||
\(872\) | 4.14961 | 0.140523 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −22.7964 | −0.769780 | −0.384890 | − | 0.922962i | \(-0.625761\pi\) | ||||
−0.384890 | + | 0.922962i | \(0.625761\pi\) | |||||||
\(878\) | 48.3822 | 1.63282 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 6.33382 | 0.213513 | ||||||||
\(881\) | 15.9881 | 0.538654 | 0.269327 | − | 0.963049i | \(-0.413199\pi\) | ||||
0.269327 | + | 0.963049i | \(0.413199\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 30.9162 | 1.04041 | 0.520207 | − | 0.854040i | \(-0.325855\pi\) | ||||
0.520207 | + | 0.854040i | \(0.325855\pi\) | |||||||
\(884\) | 3.87122 | 0.130203 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 61.3628 | 2.06152 | ||||||||
\(887\) | −27.7008 | −0.930101 | −0.465051 | − | 0.885284i | \(-0.653964\pi\) | ||||
−0.465051 | + | 0.885284i | \(0.653964\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −26.2188 | −0.878857 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 26.4585 | 0.885895 | ||||||||
\(893\) | −4.02979 | −0.134852 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −7.74244 | −0.258801 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −9.23694 | −0.308241 | ||||||||
\(899\) | −7.06517 | −0.235637 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 57.4737 | 1.91473 | ||||||||
\(902\) | −8.92520 | −0.297177 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0.946021 | 0.0314642 | ||||||||
\(905\) | 22.2284 | 0.738899 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 17.2936 | 0.574225 | 0.287113 | − | 0.957897i | \(-0.407305\pi\) | ||||
0.287113 | + | 0.957897i | \(0.407305\pi\) | |||||||
\(908\) | −41.2161 | −1.36780 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −8.85599 | −0.293412 | −0.146706 | − | 0.989180i | \(-0.546867\pi\) | ||||
−0.146706 | + | 0.989180i | \(0.546867\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0.796415 | 0.0263575 | ||||||||
\(914\) | −41.3061 | −1.36629 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −11.7008 | −0.386605 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 54.0305 | 1.78230 | 0.891150 | − | 0.453708i | \(-0.149899\pi\) | ||||
0.891150 | + | 0.453708i | \(0.149899\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 23.3324 | 0.768411 | ||||||||
\(923\) | 6.34760 | 0.208934 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 5.20359 | 0.171093 | ||||||||
\(926\) | 32.6039 | 1.07143 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 10.1723 | 0.333924 | ||||||||
\(929\) | −20.7666 | −0.681331 | −0.340665 | − | 0.940185i | \(-0.610652\pi\) | ||||
−0.340665 | + | 0.940185i | \(0.610652\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 31.3628 | 1.02732 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 21.9237 | 0.717367 | ||||||||
\(935\) | 8.79641 | 0.287674 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −3.20359 | −0.104657 | −0.0523283 | − | 0.998630i | \(-0.516664\pi\) | ||||
−0.0523283 | + | 0.998630i | \(0.516664\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 5.89396 | 0.192240 | ||||||||
\(941\) | 43.0249 | 1.40257 | 0.701285 | − | 0.712881i | \(-0.252610\pi\) | ||||
0.701285 | + | 0.712881i | \(0.252610\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | 65.5291 | 2.13279 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 8.92520 | 0.290183 | ||||||||
\(947\) | −17.5749 | −0.571108 | −0.285554 | − | 0.958363i | \(-0.592178\pi\) | ||||
−0.285554 | + | 0.958363i | \(0.592178\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0.578271 | 0.0187715 | ||||||||
\(950\) | 8.00000 | 0.259554 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 14.7846 | 0.478919 | 0.239459 | − | 0.970906i | \(-0.423030\pi\) | ||||
0.239459 | + | 0.970906i | \(0.423030\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 22.1496 | 0.716744 | ||||||||
\(956\) | −16.8816 | −0.545991 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 9.37112 | 0.302767 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −7.99440 | −0.257884 | ||||||||
\(962\) | 1.18691 | 0.0382674 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −18.9479 | −0.610272 | ||||||||
\(965\) | 13.1552 | 0.423481 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −23.1440 | −0.744261 | −0.372131 | − | 0.928180i | \(-0.621373\pi\) | ||||
−0.372131 | + | 0.928180i | \(0.621373\pi\) | |||||||
\(968\) | −1.00000 | −0.0321412 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 30.1413 | 0.967779 | ||||||||
\(971\) | 36.5783 | 1.17385 | 0.586926 | − | 0.809640i | \(-0.300338\pi\) | ||||
0.586926 | + | 0.809640i | \(0.300338\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 37.5512 | 1.20322 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −15.3324 | −0.490777 | ||||||||
\(977\) | −54.1621 | −1.73280 | −0.866400 | − | 0.499350i | \(-0.833572\pi\) | ||||
−0.866400 | + | 0.499350i | \(0.833572\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 10.6468 | 0.340273 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 47.2507 | 1.50783 | ||||||||
\(983\) | 1.29362 | 0.0412600 | 0.0206300 | − | 0.999787i | \(-0.493433\pi\) | ||||
0.0206300 | + | 0.999787i | \(0.493433\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −20.9765 | −0.668366 | ||||||||
\(986\) | 18.2188 | 0.580205 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0.770774 | 0.0245216 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −15.9523 | −0.506741 | −0.253371 | − | 0.967369i | \(-0.581539\pi\) | ||||
−0.253371 | + | 0.967369i | \(0.581539\pi\) | |||||||
\(992\) | −33.1232 | −1.05166 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −8.45555 | −0.268059 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 23.3836 | 0.740568 | 0.370284 | − | 0.928919i | \(-0.379260\pi\) | ||||
0.370284 | + | 0.928919i | \(0.379260\pi\) | |||||||
\(998\) | 27.7562 | 0.878608 | ||||||||
\(999\) | 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 | 4851.2.a.bl.1.3 | 3 | ||
3.2 | odd | 2 | 1617.2.a.r.1.1 | yes | 3 | ||
7.6 | odd | 2 | 4851.2.a.bm.1.3 | 3 | |||
21.20 | even | 2 | 1617.2.a.q.1.1 | ✓ | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1617.2.a.q.1.1 | ✓ | 3 | 21.20 | even | 2 | ||
1617.2.a.r.1.1 | yes | 3 | 3.2 | odd | 2 | ||
4851.2.a.bl.1.3 | 3 | 1.1 | even | 1 | trivial | ||
4851.2.a.bm.1.3 | 3 | 7.6 | odd | 2 |