Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [9800,2,Mod(1,9800)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(9800, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("9800.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 9800 = 2^{3} \cdot 5^{2} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 9800.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: | \(78.2533939809\) |
Analytic rank: | \(1\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.568.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 6x - 2 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 280) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(3.12489\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 9800.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −3.12489 | −1.80415 | −0.902077 | − | 0.431576i | \(-0.857958\pi\) | ||||
−0.902077 | + | 0.431576i | \(0.857958\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 6.76491 | 2.25497 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.48486 | 0.749214 | 0.374607 | − | 0.927184i | \(-0.377778\pi\) | ||||
0.374607 | + | 0.927184i | \(0.377778\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 4.15516 | 1.15243 | 0.576217 | − | 0.817297i | \(-0.304528\pi\) | ||||
0.576217 | + | 0.817297i | \(0.304528\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −5.76491 | −1.39820 | −0.699098 | − | 0.715026i | \(-0.746415\pi\) | ||||
−0.699098 | + | 0.715026i | \(0.746415\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.60975 | 0.369301 | 0.184651 | − | 0.982804i | \(-0.440885\pi\) | ||||
0.184651 | + | 0.982804i | \(0.440885\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 7.28005 | 1.51799 | 0.758997 | − | 0.651094i | \(-0.225690\pi\) | ||||
0.758997 | + | 0.651094i | \(0.225690\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −11.7649 | −2.26416 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1.45459 | 0.270110 | 0.135055 | − | 0.990838i | \(-0.456879\pi\) | ||||
0.135055 | + | 0.990838i | \(0.456879\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.24977 | 0.404071 | 0.202035 | − | 0.979378i | \(-0.435244\pi\) | ||||
0.202035 | + | 0.979378i | \(0.435244\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −7.76491 | −1.35170 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −6.00000 | −0.986394 | −0.493197 | − | 0.869918i | \(-0.664172\pi\) | ||||
−0.493197 | + | 0.869918i | \(0.664172\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −12.9844 | −2.07917 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −11.2800 | −1.76165 | −0.880824 | − | 0.473444i | \(-0.843010\pi\) | ||||
−0.880824 | + | 0.473444i | \(0.843010\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −5.28005 | −0.805200 | −0.402600 | − | 0.915376i | \(-0.631893\pi\) | ||||
−0.402600 | + | 0.915376i | \(0.631893\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −3.45459 | −0.503903 | −0.251952 | − | 0.967740i | \(-0.581072\pi\) | ||||
−0.251952 | + | 0.967740i | \(0.581072\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 18.0147 | 2.52256 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −9.21949 | −1.26639 | −0.633197 | − | 0.773990i | \(-0.718258\pi\) | ||||
−0.633197 | + | 0.773990i | \(0.718258\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −5.03028 | −0.666276 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 5.92007 | 0.770728 | 0.385364 | − | 0.922765i | \(-0.374076\pi\) | ||||
0.385364 | + | 0.922765i | \(0.374076\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −5.35998 | −0.686275 | −0.343137 | − | 0.939285i | \(-0.611490\pi\) | ||||
−0.343137 | + | 0.939285i | \(0.611490\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −7.52982 | −0.919914 | −0.459957 | − | 0.887941i | \(-0.652135\pi\) | ||||
−0.459957 | + | 0.887941i | \(0.652135\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −22.7493 | −2.73870 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −4.24977 | −0.504355 | −0.252178 | − | 0.967681i | \(-0.581147\pi\) | ||||
−0.252178 | + | 0.967681i | \(0.581147\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −7.28005 | −0.852065 | −0.426033 | − | 0.904708i | \(-0.640089\pi\) | ||||
−0.426033 | + | 0.904708i | \(0.640089\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 16.9844 | 1.91089 | 0.955447 | − | 0.295162i | \(-0.0953735\pi\) | ||||
0.955447 | + | 0.295162i | \(0.0953735\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 16.4693 | 1.82992 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 10.1093 | 1.10964 | 0.554819 | − | 0.831971i | \(-0.312787\pi\) | ||||
0.554819 | + | 0.831971i | \(0.312787\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −4.54541 | −0.487320 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 11.4693 | 1.21574 | 0.607870 | − | 0.794037i | \(-0.292024\pi\) | ||||
0.607870 | + | 0.794037i | \(0.292024\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −7.03028 | −0.729006 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 2.73463 | 0.277660 | 0.138830 | − | 0.990316i | \(-0.455666\pi\) | ||||
0.138830 | + | 0.990316i | \(0.455666\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 16.8099 | 1.68945 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 4.57947 | 0.455674 | 0.227837 | − | 0.973699i | \(-0.426835\pi\) | ||||
0.227837 | + | 0.973699i | \(0.426835\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 2.48486 | 0.244841 | 0.122420 | − | 0.992478i | \(-0.460934\pi\) | ||||
0.122420 | + | 0.992478i | \(0.460934\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −9.95413 | −0.953433 | −0.476716 | − | 0.879057i | \(-0.658173\pi\) | ||||
−0.476716 | + | 0.879057i | \(0.658173\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 18.7493 | 1.77961 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −18.4995 | −1.74029 | −0.870145 | − | 0.492795i | \(-0.835975\pi\) | ||||
−0.870145 | + | 0.492795i | \(0.835975\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 28.1093 | 2.59870 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −4.82546 | −0.438678 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 35.2489 | 3.17828 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −7.15894 | −0.635253 | −0.317627 | − | 0.948216i | \(-0.602886\pi\) | ||||
−0.317627 | + | 0.948216i | \(0.602886\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 16.4995 | 1.45270 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −7.85952 | −0.686689 | −0.343345 | − | 0.939209i | \(-0.611560\pi\) | ||||
−0.343345 | + | 0.939209i | \(0.611560\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −10.5601 | −0.902210 | −0.451105 | − | 0.892471i | \(-0.648970\pi\) | ||||
−0.451105 | + | 0.892471i | \(0.648970\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −9.79897 | −0.831137 | −0.415569 | − | 0.909562i | \(-0.636417\pi\) | ||||
−0.415569 | + | 0.909562i | \(0.636417\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 10.7952 | 0.909119 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 10.3250 | 0.863420 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 2.49954 | 0.204770 | 0.102385 | − | 0.994745i | \(-0.467353\pi\) | ||||
0.102385 | + | 0.994745i | \(0.467353\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −3.76491 | −0.306384 | −0.153192 | − | 0.988196i | \(-0.548955\pi\) | ||||
−0.153192 | + | 0.988196i | \(0.548955\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −38.9991 | −3.15289 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 5.67030 | 0.452539 | 0.226270 | − | 0.974065i | \(-0.427347\pi\) | ||||
0.226270 | + | 0.974065i | \(0.427347\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 28.8099 | 2.28477 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −10.2498 | −0.802824 | −0.401412 | − | 0.915898i | \(-0.631480\pi\) | ||||
−0.401412 | + | 0.915898i | \(0.631480\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −2.95504 | −0.228668 | −0.114334 | − | 0.993442i | \(-0.536473\pi\) | ||||
−0.114334 | + | 0.993442i | \(0.536473\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 4.26537 | 0.328105 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 10.8898 | 0.832763 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 22.4049 | 1.70342 | 0.851708 | − | 0.524017i | \(-0.175567\pi\) | ||||
0.851708 | + | 0.524017i | \(0.175567\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −18.4995 | −1.39051 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 14.5601 | 1.08827 | 0.544136 | − | 0.838997i | \(-0.316857\pi\) | ||||
0.544136 | + | 0.838997i | \(0.316857\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 9.67030 | 0.718788 | 0.359394 | − | 0.933186i | \(-0.382983\pi\) | ||||
0.359394 | + | 0.933186i | \(0.382983\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 16.7493 | 1.23814 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −14.3250 | −1.04755 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 8.01468 | 0.579922 | 0.289961 | − | 0.957038i | \(-0.406358\pi\) | ||||
0.289961 | + | 0.957038i | \(0.406358\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −3.46927 | −0.249723 | −0.124862 | − | 0.992174i | \(-0.539849\pi\) | ||||
−0.124862 | + | 0.992174i | \(0.539849\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 16.2791 | 1.15984 | 0.579920 | − | 0.814673i | \(-0.303084\pi\) | ||||
0.579920 | + | 0.814673i | \(0.303084\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −26.8704 | −1.90479 | −0.952397 | − | 0.304862i | \(-0.901390\pi\) | ||||
−0.952397 | + | 0.304862i | \(0.901390\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 23.5298 | 1.65967 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 49.2489 | 3.42303 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 4.00000 | 0.276686 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 17.2342 | 1.18645 | 0.593225 | − | 0.805037i | \(-0.297855\pi\) | ||||
0.593225 | + | 0.805037i | \(0.297855\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 13.2800 | 0.909934 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 22.7493 | 1.53726 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −23.9541 | −1.61133 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −0.235091 | −0.0157429 | −0.00787143 | − | 0.999969i | \(-0.502506\pi\) | ||||
−0.00787143 | + | 0.999969i | \(0.502506\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −0.564792 | −0.0374865 | −0.0187433 | − | 0.999824i | \(-0.505967\pi\) | ||||
−0.0187433 | + | 0.999824i | \(0.505967\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −7.11021 | −0.469856 | −0.234928 | − | 0.972013i | \(-0.575485\pi\) | ||||
−0.234928 | + | 0.972013i | \(0.575485\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −8.49954 | −0.556823 | −0.278412 | − | 0.960462i | \(-0.589808\pi\) | ||||
−0.278412 | + | 0.960462i | \(0.589808\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −53.0743 | −3.44755 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −7.26537 | −0.469958 | −0.234979 | − | 0.972001i | \(-0.575502\pi\) | ||||
−0.234979 | + | 0.972001i | \(0.575502\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −7.28005 | −0.468949 | −0.234475 | − | 0.972122i | \(-0.575337\pi\) | ||||
−0.234475 | + | 0.972122i | \(0.575337\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −16.1698 | −1.03730 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 6.68876 | 0.425596 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −31.5904 | −2.00196 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −22.9192 | −1.44664 | −0.723322 | − | 0.690511i | \(-0.757386\pi\) | ||||
−0.723322 | + | 0.690511i | \(0.757386\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 18.0899 | 1.13730 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 0.719953 | 0.0449094 | 0.0224547 | − | 0.999748i | \(-0.492852\pi\) | ||||
0.0224547 | + | 0.999748i | \(0.492852\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 9.84014 | 0.609089 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 18.5601 | 1.14446 | 0.572232 | − | 0.820092i | \(-0.306078\pi\) | ||||
0.572232 | + | 0.820092i | \(0.306078\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −35.8401 | −2.19338 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 22.1698 | 1.35172 | 0.675860 | − | 0.737030i | \(-0.263773\pi\) | ||||
0.675860 | + | 0.737030i | \(0.263773\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 7.87890 | 0.478609 | 0.239304 | − | 0.970945i | \(-0.423081\pi\) | ||||
0.239304 | + | 0.970945i | \(0.423081\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 2.78051 | 0.167064 | 0.0835322 | − | 0.996505i | \(-0.473380\pi\) | ||||
0.0835322 | + | 0.996505i | \(0.473380\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 15.2195 | 0.911167 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −23.7044 | −1.41408 | −0.707042 | − | 0.707172i | \(-0.749971\pi\) | ||||
−0.707042 | + | 0.707172i | \(0.749971\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 26.8439 | 1.59571 | 0.797853 | − | 0.602852i | \(-0.205969\pi\) | ||||
0.797853 | + | 0.602852i | \(0.205969\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 16.2342 | 0.954951 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −8.54541 | −0.500941 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −9.93475 | −0.580394 | −0.290197 | − | 0.956967i | \(-0.593721\pi\) | ||||
−0.290197 | + | 0.956967i | \(0.593721\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −29.2342 | −1.69634 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 30.2498 | 1.74939 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −14.3103 | −0.822107 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −32.0946 | −1.83174 | −0.915868 | − | 0.401479i | \(-0.868496\pi\) | ||||
−0.915868 | + | 0.401479i | \(0.868496\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −7.76491 | −0.441730 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 10.0606 | 0.570482 | 0.285241 | − | 0.958456i | \(-0.407926\pi\) | ||||
0.285241 | + | 0.958456i | \(0.407926\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 20.8245 | 1.17707 | 0.588536 | − | 0.808471i | \(-0.299704\pi\) | ||||
0.588536 | + | 0.808471i | \(0.299704\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −15.7502 | −0.884621 | −0.442311 | − | 0.896862i | \(-0.645841\pi\) | ||||
−0.442311 | + | 0.896862i | \(0.645841\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 3.61445 | 0.202370 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −9.28005 | −0.516356 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 31.1055 | 1.72014 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −25.7796 | −1.41697 | −0.708487 | − | 0.705724i | \(-0.750622\pi\) | ||||
−0.708487 | + | 0.705724i | \(0.750622\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −40.5895 | −2.22429 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −0.0605522 | −0.00329849 | −0.00164924 | − | 0.999999i | \(-0.500525\pi\) | ||||
−0.00164924 | + | 0.999999i | \(0.500525\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 57.8089 | 3.13975 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 5.59037 | 0.302736 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 20.9310 | 1.12363 | 0.561817 | − | 0.827262i | \(-0.310103\pi\) | ||||
0.561817 | + | 0.827262i | \(0.310103\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −5.48108 | −0.293396 | −0.146698 | − | 0.989181i | \(-0.546864\pi\) | ||||
−0.146698 | + | 0.989181i | \(0.546864\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −48.8851 | −2.60929 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −26.9239 | −1.43301 | −0.716506 | − | 0.697581i | \(-0.754260\pi\) | ||||
−0.716506 | + | 0.697581i | \(0.754260\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 6.06055 | 0.319864 | 0.159932 | − | 0.987128i | \(-0.448873\pi\) | ||||
0.159932 | + | 0.987128i | \(0.448873\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −16.4087 | −0.863616 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 15.0790 | 0.791443 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 30.7034 | 1.60271 | 0.801353 | − | 0.598191i | \(-0.204114\pi\) | ||||
0.801353 | + | 0.598191i | \(0.204114\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −76.3085 | −3.97246 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 10.8099 | 0.559714 | 0.279857 | − | 0.960042i | \(-0.409713\pi\) | ||||
0.279857 | + | 0.960042i | \(0.409713\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 6.04404 | 0.311284 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −9.28005 | −0.476684 | −0.238342 | − | 0.971181i | \(-0.576604\pi\) | ||||
−0.238342 | + | 0.971181i | \(0.576604\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 22.3709 | 1.14609 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −5.28005 | −0.269798 | −0.134899 | − | 0.990859i | \(-0.543071\pi\) | ||||
−0.134899 | + | 0.990859i | \(0.543071\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −35.7190 | −1.81570 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 5.48395 | 0.278047 | 0.139024 | − | 0.990289i | \(-0.455604\pi\) | ||||
0.139024 | + | 0.990289i | \(0.455604\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −41.9688 | −2.12245 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 24.5601 | 1.23889 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 6.40493 | 0.321454 | 0.160727 | − | 0.986999i | \(-0.448616\pi\) | ||||
0.160727 | + | 0.986999i | \(0.448616\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −1.20482 | −0.0601656 | −0.0300828 | − | 0.999547i | \(-0.509577\pi\) | ||||
−0.0300828 | + | 0.999547i | \(0.509577\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 9.34816 | 0.465665 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −14.9092 | −0.739020 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 2.31032 | 0.114238 | 0.0571191 | − | 0.998367i | \(-0.481809\pi\) | ||||
0.0571191 | + | 0.998367i | \(0.481809\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 32.9991 | 1.62772 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 30.6206 | 1.49950 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 19.7384 | 0.964285 | 0.482142 | − | 0.876093i | \(-0.339859\pi\) | ||||
0.482142 | + | 0.876093i | \(0.339859\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 30.1433 | 1.46910 | 0.734548 | − | 0.678556i | \(-0.237394\pi\) | ||||
0.734548 | + | 0.678556i | \(0.237394\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −23.3700 | −1.13629 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −32.2645 | −1.55774 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −4.61353 | −0.222226 | −0.111113 | − | 0.993808i | \(-0.535442\pi\) | ||||
−0.111113 | + | 0.993808i | \(0.535442\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −11.4399 | −0.549767 | −0.274883 | − | 0.961478i | \(-0.588639\pi\) | ||||
−0.274883 | + | 0.961478i | \(0.588639\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 11.7190 | 0.560598 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −12.0294 | −0.574130 | −0.287065 | − | 0.957911i | \(-0.592680\pi\) | ||||
−0.287065 | + | 0.957911i | \(0.592680\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 14.4390 | 0.686017 | 0.343009 | − | 0.939332i | \(-0.388554\pi\) | ||||
0.343009 | + | 0.939332i | \(0.388554\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −7.81078 | −0.369437 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 19.2342 | 0.907717 | 0.453858 | − | 0.891074i | \(-0.350047\pi\) | ||||
0.453858 | + | 0.891074i | \(0.350047\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −28.0294 | −1.31985 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 11.7649 | 0.552764 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −34.8780 | −1.63152 | −0.815762 | − | 0.578388i | \(-0.803682\pi\) | ||||
−0.815762 | + | 0.578388i | \(0.803682\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 67.8236 | 3.16574 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 15.2607 | 0.710760 | 0.355380 | − | 0.934722i | \(-0.384351\pi\) | ||||
0.355380 | + | 0.934722i | \(0.384351\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −24.9991 | −1.16181 | −0.580903 | − | 0.813973i | \(-0.697300\pi\) | ||||
−0.580903 | + | 0.813973i | \(0.697300\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 5.06433 | 0.234349 | 0.117175 | − | 0.993111i | \(-0.462616\pi\) | ||||
0.117175 | + | 0.993111i | \(0.462616\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −17.7190 | −0.816450 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −13.1202 | −0.603267 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −62.3690 | −2.85568 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −41.8089 | −1.91030 | −0.955150 | − | 0.296123i | \(-0.904306\pi\) | ||||
−0.955150 | + | 0.296123i | \(0.904306\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −24.9310 | −1.13675 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −21.3406 | −0.967035 | −0.483517 | − | 0.875335i | \(-0.660641\pi\) | ||||
−0.483517 | + | 0.875335i | \(0.660641\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 32.0294 | 1.44842 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 8.35620 | 0.377110 | 0.188555 | − | 0.982063i | \(-0.439620\pi\) | ||||
0.188555 | + | 0.982063i | \(0.439620\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −8.38555 | −0.377666 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −38.8539 | −1.73934 | −0.869670 | − | 0.493634i | \(-0.835668\pi\) | ||||
−0.869670 | + | 0.493634i | \(0.835668\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 9.23417 | 0.412552 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −17.7044 | −0.789398 | −0.394699 | − | 0.918810i | \(-0.629151\pi\) | ||||
−0.394699 | + | 0.918810i | \(0.629151\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −13.3288 | −0.591952 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −7.11021 | −0.315154 | −0.157577 | − | 0.987507i | \(-0.550368\pi\) | ||||
−0.157577 | + | 0.987507i | \(0.550368\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −18.9385 | −0.836157 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −8.58417 | −0.377531 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −70.0128 | −3.07322 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −18.1892 | −0.796884 | −0.398442 | − | 0.917194i | \(-0.630449\pi\) | ||||
−0.398442 | + | 0.917194i | \(0.630449\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −13.9882 | −0.611661 | −0.305830 | − | 0.952086i | \(-0.598934\pi\) | ||||
−0.305830 | + | 0.952086i | \(0.598934\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −12.9697 | −0.564970 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 29.9991 | 1.30431 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 40.0487 | 1.73797 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −46.8704 | −2.03018 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −45.4986 | −1.96341 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −20.8245 | −0.895317 | −0.447659 | − | 0.894205i | \(-0.647742\pi\) | ||||
−0.447659 | + | 0.894205i | \(0.647742\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −30.2186 | −1.29680 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 3.09839 | 0.132478 | 0.0662388 | − | 0.997804i | \(-0.478900\pi\) | ||||
0.0662388 | + | 0.997804i | \(0.478900\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −36.2598 | −1.54753 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 2.34152 | 0.0997519 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −18.8099 | −0.797000 | −0.398500 | − | 0.917168i | \(-0.630469\pi\) | ||||
−0.398500 | + | 0.917168i | \(0.630469\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −21.9394 | −0.927940 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 44.7640 | 1.88994 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −28.9503 | −1.22011 | −0.610056 | − | 0.792358i | \(-0.708853\pi\) | ||||
−0.610056 | + | 0.792358i | \(0.708853\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −29.9688 | −1.25636 | −0.628179 | − | 0.778069i | \(-0.716199\pi\) | ||||
−0.628179 | + | 0.778069i | \(0.716199\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 0.280964 | 0.0117580 | 0.00587898 | − | 0.999983i | \(-0.498129\pi\) | ||||
0.00587898 | + | 0.999983i | \(0.498129\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −25.0450 | −1.04627 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −25.9541 | −1.08048 | −0.540242 | − | 0.841510i | \(-0.681667\pi\) | ||||
−0.540242 | + | 0.841510i | \(0.681667\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 10.8411 | 0.450539 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −22.9092 | −0.948801 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 22.2304 | 0.917547 | 0.458773 | − | 0.888553i | \(-0.348289\pi\) | ||||
0.458773 | + | 0.888553i | \(0.348289\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 3.62156 | 0.149224 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −50.8704 | −2.09253 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −35.0743 | −1.44033 | −0.720165 | − | 0.693803i | \(-0.755934\pi\) | ||||
−0.720165 | + | 0.693803i | \(0.755934\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 83.9670 | 3.43654 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −21.7262 | −0.887707 | −0.443853 | − | 0.896099i | \(-0.646389\pi\) | ||||
−0.443853 | + | 0.896099i | \(0.646389\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 23.9688 | 0.977708 | 0.488854 | − | 0.872366i | \(-0.337415\pi\) | ||||
0.488854 | + | 0.872366i | \(0.337415\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −50.9385 | −2.07438 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −43.3241 | −1.75847 | −0.879235 | − | 0.476388i | \(-0.841946\pi\) | ||||
−0.879235 | + | 0.476388i | \(0.841946\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −14.3544 | −0.580715 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −8.90917 | −0.359838 | −0.179919 | − | 0.983681i | \(-0.557584\pi\) | ||||
−0.179919 | + | 0.983681i | \(0.557584\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 27.2413 | 1.09669 | 0.548347 | − | 0.836251i | \(-0.315257\pi\) | ||||
0.548347 | + | 0.836251i | \(0.315257\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −24.1405 | −0.970288 | −0.485144 | − | 0.874434i | \(-0.661233\pi\) | ||||
−0.485144 | + | 0.874434i | \(0.661233\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −85.6491 | −3.43698 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −12.4995 | −0.499184 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 34.5895 | 1.37917 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 8.01468 | 0.319059 | 0.159530 | − | 0.987193i | \(-0.449002\pi\) | ||||
0.159530 | + | 0.987193i | \(0.449002\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −53.8548 | −2.14054 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −28.7493 | −1.13731 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −49.1495 | −1.94129 | −0.970645 | − | 0.240516i | \(-0.922683\pi\) | ||||
−0.970645 | + | 0.240516i | \(0.922683\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −7.24599 | −0.285754 | −0.142877 | − | 0.989740i | \(-0.545635\pi\) | ||||
−0.142877 | + | 0.989740i | \(0.545635\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −30.2791 | −1.19040 | −0.595198 | − | 0.803579i | \(-0.702926\pi\) | ||||
−0.595198 | + | 0.803579i | \(0.702926\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 14.7106 | 0.577440 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 7.96881 | 0.311844 | 0.155922 | − | 0.987769i | \(-0.450165\pi\) | ||||
0.155922 | + | 0.987769i | \(0.450165\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −49.2489 | −1.92138 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 20.9239 | 0.815078 | 0.407539 | − | 0.913188i | \(-0.366387\pi\) | ||||
0.407539 | + | 0.913188i | \(0.366387\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −46.1992 | −1.79694 | −0.898470 | − | 0.439034i | \(-0.855321\pi\) | ||||
−0.898470 | + | 0.439034i | \(0.855321\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 74.8539 | 2.90708 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 10.5895 | 0.410025 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0.734633 | 0.0284025 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −13.3188 | −0.514167 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 40.3784 | 1.55647 | 0.778237 | − | 0.627970i | \(-0.216114\pi\) | ||||
0.778237 | + | 0.627970i | \(0.216114\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 44.3737 | 1.70542 | 0.852711 | − | 0.522383i | \(-0.174957\pi\) | ||||
0.852711 | + | 0.522383i | \(0.174957\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 1.76491 | 0.0676315 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 17.9394 | 0.686434 | 0.343217 | − | 0.939256i | \(-0.388483\pi\) | ||||
0.343217 | + | 0.939256i | \(0.388483\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 22.2186 | 0.847692 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −38.3085 | −1.45944 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 12.7905 | 0.486573 | 0.243287 | − | 0.969954i | \(-0.421774\pi\) | ||||
0.243287 | + | 0.969954i | \(0.421774\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 65.0284 | 2.46313 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 26.5601 | 1.00460 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −19.4234 | −0.733611 | −0.366806 | − | 0.930298i | \(-0.619549\pi\) | ||||
−0.366806 | + | 0.930298i | \(0.619549\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −9.65848 | −0.364277 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −13.4839 | −0.506400 | −0.253200 | − | 0.967414i | \(-0.581483\pi\) | ||||
−0.253200 | + | 0.967414i | \(0.581483\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 114.898 | 4.30901 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 16.3784 | 0.613377 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 22.7034 | 0.847876 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −15.3700 | −0.573203 | −0.286601 | − | 0.958050i | \(-0.592526\pi\) | ||||
−0.286601 | + | 0.958050i | \(0.592526\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 22.7493 | 0.846056 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 13.1589 | 0.488038 | 0.244019 | − | 0.969770i | \(-0.421534\pi\) | ||||
0.244019 | + | 0.969770i | \(0.421534\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.12110 | 0.0415224 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 30.4390 | 1.12583 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −10.0265 | −0.370337 | −0.185169 | − | 0.982707i | \(-0.559283\pi\) | ||||
−0.185169 | + | 0.982707i | \(0.559283\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −18.7106 | −0.689212 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 19.2266 | 0.707262 | 0.353631 | − | 0.935385i | \(-0.384947\pi\) | ||||
0.353631 | + | 0.935385i | \(0.384947\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −20.9016 | −0.767840 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 5.21949 | 0.191485 | 0.0957423 | − | 0.995406i | \(-0.469478\pi\) | ||||
0.0957423 | + | 0.995406i | \(0.469478\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 68.3884 | 2.50220 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 29.8548 | 1.08942 | 0.544709 | − | 0.838625i | \(-0.316640\pi\) | ||||
0.544709 | + | 0.838625i | \(0.316640\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 71.6197 | 2.60997 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 18.0294 | 0.655288 | 0.327644 | − | 0.944801i | \(-0.393745\pi\) | ||||
0.327644 | + | 0.944801i | \(0.393745\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −56.5289 | −2.05187 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −8.22041 | −0.297990 | −0.148995 | − | 0.988838i | \(-0.547604\pi\) | ||||
−0.148995 | + | 0.988838i | \(0.547604\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 24.5988 | 0.888213 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −50.6888 | −1.82788 | −0.913942 | − | 0.405845i | \(-0.866977\pi\) | ||||
−0.913942 | + | 0.405845i | \(0.866977\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −2.24977 | −0.0810235 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 6.99622 | 0.251637 | 0.125818 | − | 0.992053i | \(-0.459844\pi\) | ||||
0.125818 | + | 0.992053i | \(0.459844\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −18.1580 | −0.650579 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −10.5601 | −0.377870 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −17.1131 | −0.611571 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −14.3444 | −0.511322 | −0.255661 | − | 0.966767i | \(-0.582293\pi\) | ||||
−0.255661 | + | 0.966767i | \(0.582293\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −57.9982 | −2.06479 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −22.2716 | −0.790887 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −13.9348 | −0.493594 | −0.246797 | − | 0.969067i | \(-0.579378\pi\) | ||||
−0.246797 | + | 0.969067i | \(0.579378\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 19.9154 | 0.704555 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 77.5885 | 2.74146 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −18.0899 | −0.638379 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −69.2782 | −2.43871 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −5.58325 | −0.196297 | −0.0981483 | − | 0.995172i | \(-0.531292\pi\) | ||||
−0.0981483 | + | 0.995172i | \(0.531292\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 6.57947 | 0.231036 | 0.115518 | − | 0.993305i | \(-0.463147\pi\) | ||||
0.115518 | + | 0.993305i | \(0.463147\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −24.6206 | −0.863484 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −8.49954 | −0.297361 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 16.3250 | 0.569747 | 0.284873 | − | 0.958565i | \(-0.408048\pi\) | ||||
0.284873 | + | 0.958565i | \(0.408048\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −12.3491 | −0.430462 | −0.215231 | − | 0.976563i | \(-0.569050\pi\) | ||||
−0.215231 | + | 0.976563i | \(0.569050\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −6.40963 | −0.222885 | −0.111442 | − | 0.993771i | \(-0.535547\pi\) | ||||
−0.111442 | + | 0.993771i | \(0.535547\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 26.1698 | 0.908916 | 0.454458 | − | 0.890768i | \(-0.349833\pi\) | ||||
0.454458 | + | 0.890768i | \(0.349833\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −8.68876 | −0.301410 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −26.4683 | −0.914880 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 1.12958 | 0.0389975 | 0.0194988 | − | 0.999810i | \(-0.493793\pi\) | ||||
0.0194988 | + | 0.999810i | \(0.493793\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −26.8842 | −0.927041 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 74.0734 | 2.55122 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −83.8842 | −2.87890 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −43.6803 | −1.49734 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 6.29095 | 0.215398 | 0.107699 | − | 0.994184i | \(-0.465652\pi\) | ||||
0.107699 | + | 0.994184i | \(0.465652\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −25.0596 | −0.856021 | −0.428010 | − | 0.903774i | \(-0.640785\pi\) | ||||
−0.428010 | + | 0.903774i | \(0.640785\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −53.7896 | −1.83528 | −0.917638 | − | 0.397417i | \(-0.869907\pi\) | ||||
−0.917638 | + | 0.397417i | \(0.869907\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 58.0899 | 1.97740 | 0.988702 | − | 0.149896i | \(-0.0478938\pi\) | ||||
0.988702 | + | 0.149896i | \(0.0478938\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −50.7299 | −1.72288 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 42.2039 | 1.43167 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −31.2876 | −1.06014 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 18.4995 | 0.626115 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 24.0899 | 0.813459 | 0.406729 | − | 0.913549i | \(-0.366669\pi\) | ||||
0.406729 | + | 0.913549i | \(0.366669\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 31.0450 | 1.04712 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −40.9679 | −1.38024 | −0.690122 | − | 0.723693i | \(-0.742443\pi\) | ||||
−0.690122 | + | 0.723693i | \(0.742443\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 43.8014 | 1.47403 | 0.737017 | − | 0.675874i | \(-0.236234\pi\) | ||||
0.737017 | + | 0.675874i | \(0.236234\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −1.77959 | −0.0597527 | −0.0298764 | − | 0.999554i | \(-0.509511\pi\) | ||||
−0.0298764 | + | 0.999554i | \(0.509511\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 40.9239 | 1.37100 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −5.56101 | −0.186092 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −94.5271 | −3.15617 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 3.27248 | 0.109143 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 53.1495 | 1.77067 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −53.0284 | −1.76078 | −0.880390 | − | 0.474250i | \(-0.842719\pi\) | ||||
−0.880390 | + | 0.474250i | \(0.842719\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 30.9797 | 1.02753 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 28.1798 | 0.933639 | 0.466820 | − | 0.884353i | \(-0.345400\pi\) | ||||
0.466820 | + | 0.884353i | \(0.345400\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 25.1202 | 0.831357 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 38.4243 | 1.26750 | 0.633751 | − | 0.773538i | \(-0.281515\pi\) | ||||
0.633751 | + | 0.773538i | \(0.281515\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 100.292 | 3.30473 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −17.6585 | −0.581236 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 16.8099 | 0.552108 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 36.6576 | 1.20270 | 0.601348 | − | 0.798987i | \(-0.294631\pi\) | ||||
0.601348 | + | 0.798987i | \(0.294631\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −31.4381 | −1.02924 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 5.83302 | 0.190557 | 0.0952783 | − | 0.995451i | \(-0.469626\pi\) | ||||
0.0952783 | + | 0.995451i | \(0.469626\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −65.0743 | −2.12362 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 2.23796 | 0.0729553 | 0.0364776 | − | 0.999334i | \(-0.488386\pi\) | ||||
0.0364776 | + | 0.999334i | \(0.488386\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −82.1193 | −2.67417 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 17.7502 | 0.576805 | 0.288402 | − | 0.957509i | \(-0.406876\pi\) | ||||
0.288402 | + | 0.957509i | \(0.406876\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −30.2498 | −0.981949 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 49.2177 | 1.59599 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 32.0294 | 1.03753 | 0.518766 | − | 0.854916i | \(-0.326391\pi\) | ||||
0.518766 | + | 0.854916i | \(0.326391\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −11.2947 | −0.365107 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −25.9385 | −0.836727 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −43.4305 | −1.39663 | −0.698316 | − | 0.715790i | \(-0.746067\pi\) | ||||
−0.698316 | + | 0.715790i | \(0.746067\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 28.9991 | 0.931585 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 1.79897 | 0.0577316 | 0.0288658 | − | 0.999583i | \(-0.490810\pi\) | ||||
0.0288658 | + | 0.999583i | \(0.490810\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 22.4390 | 0.717887 | 0.358943 | − | 0.933359i | \(-0.383137\pi\) | ||||
0.358943 | + | 0.933359i | \(0.383137\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 28.4995 | 0.910849 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −67.3388 | −2.14996 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 37.6950 | 1.20228 | 0.601141 | − | 0.799143i | \(-0.294713\pi\) | ||||
0.601141 | + | 0.799143i | \(0.294713\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −38.4390 | −1.22229 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 13.5686 | 0.431020 | 0.215510 | − | 0.976502i | \(-0.430859\pi\) | ||||
0.215510 | + | 0.976502i | \(0.430859\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 80.5583 | 2.55644 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 14.2838 | 0.452373 | 0.226187 | − | 0.974084i | \(-0.427374\pi\) | ||||
0.226187 | + | 0.974084i | \(0.427374\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 70.5895 | 2.23335 |
(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 | 9800.2.a.cd.1.1 | 3 | ||
5.2 | odd | 4 | 1960.2.g.c.1569.6 | 6 | |||
5.3 | odd | 4 | 1960.2.g.c.1569.1 | 6 | |||
5.4 | even | 2 | 9800.2.a.cg.1.3 | 3 | |||
7.6 | odd | 2 | 1400.2.a.t.1.3 | 3 | |||
28.27 | even | 2 | 2800.2.a.bq.1.1 | 3 | |||
35.13 | even | 4 | 280.2.g.b.169.6 | yes | 6 | ||
35.27 | even | 4 | 280.2.g.b.169.1 | ✓ | 6 | ||
35.34 | odd | 2 | 1400.2.a.s.1.1 | 3 | |||
105.62 | odd | 4 | 2520.2.t.g.1009.2 | 6 | |||
105.83 | odd | 4 | 2520.2.t.g.1009.1 | 6 | |||
140.27 | odd | 4 | 560.2.g.f.449.6 | 6 | |||
140.83 | odd | 4 | 560.2.g.f.449.1 | 6 | |||
140.139 | even | 2 | 2800.2.a.br.1.3 | 3 | |||
280.13 | even | 4 | 2240.2.g.l.449.1 | 6 | |||
280.27 | odd | 4 | 2240.2.g.m.449.1 | 6 | |||
280.83 | odd | 4 | 2240.2.g.m.449.6 | 6 | |||
280.237 | even | 4 | 2240.2.g.l.449.6 | 6 | |||
420.83 | even | 4 | 5040.2.t.y.1009.1 | 6 | |||
420.167 | even | 4 | 5040.2.t.y.1009.2 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
280.2.g.b.169.1 | ✓ | 6 | 35.27 | even | 4 | ||
280.2.g.b.169.6 | yes | 6 | 35.13 | even | 4 | ||
560.2.g.f.449.1 | 6 | 140.83 | odd | 4 | |||
560.2.g.f.449.6 | 6 | 140.27 | odd | 4 | |||
1400.2.a.s.1.1 | 3 | 35.34 | odd | 2 | |||
1400.2.a.t.1.3 | 3 | 7.6 | odd | 2 | |||
1960.2.g.c.1569.1 | 6 | 5.3 | odd | 4 | |||
1960.2.g.c.1569.6 | 6 | 5.2 | odd | 4 | |||
2240.2.g.l.449.1 | 6 | 280.13 | even | 4 | |||
2240.2.g.l.449.6 | 6 | 280.237 | even | 4 | |||
2240.2.g.m.449.1 | 6 | 280.27 | odd | 4 | |||
2240.2.g.m.449.6 | 6 | 280.83 | odd | 4 | |||
2520.2.t.g.1009.1 | 6 | 105.83 | odd | 4 | |||
2520.2.t.g.1009.2 | 6 | 105.62 | odd | 4 | |||
2800.2.a.bq.1.1 | 3 | 28.27 | even | 2 | |||
2800.2.a.br.1.3 | 3 | 140.139 | even | 2 | |||
5040.2.t.y.1009.1 | 6 | 420.83 | even | 4 | |||
5040.2.t.y.1009.2 | 6 | 420.167 | even | 4 | |||
9800.2.a.cd.1.1 | 3 | 1.1 | even | 1 | trivial | ||
9800.2.a.cg.1.3 | 3 | 5.4 | even | 2 |