Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8008,2,Mod(1,8008)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8008, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("8008.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8008 = 2^{3} \cdot 7 \cdot 11 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8008.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(63.9442019386\) |
Analytic rank: | \(1\) |
Dimension: | \(11\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{11} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{11} - 2 x^{10} - 19 x^{9} + 33 x^{8} + 120 x^{7} - 178 x^{6} - 296 x^{5} + 380 x^{4} + 280 x^{3} - 295 x^{2} - 87 x + 64 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{17}]\) |
Coefficient ring index: | \( 2^{4} \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.6 | ||
Root | \(0.447939\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8008.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −0.447939 | −0.258618 | −0.129309 | − | 0.991604i | \(-0.541276\pi\) | ||||
−0.129309 | + | 0.991604i | \(0.541276\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 3.28103 | 1.46732 | 0.733661 | − | 0.679515i | \(-0.237810\pi\) | ||||
0.733661 | + | 0.679515i | \(0.237810\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.79935 | −0.933117 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.00000 | 0.301511 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.00000 | −0.277350 | ||||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.46970 | −0.379476 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 4.02477 | 0.976150 | 0.488075 | − | 0.872802i | \(-0.337699\pi\) | ||||
0.488075 | + | 0.872802i | \(0.337699\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.40652 | 0.322678 | 0.161339 | − | 0.986899i | \(-0.448419\pi\) | ||||
0.161339 | + | 0.986899i | \(0.448419\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.447939 | 0.0977484 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −4.52401 | −0.943320 | −0.471660 | − | 0.881780i | \(-0.656345\pi\) | ||||
−0.471660 | + | 0.881780i | \(0.656345\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 5.76518 | 1.15304 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 2.59776 | 0.499939 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −1.61567 | −0.300022 | −0.150011 | − | 0.988684i | \(-0.547931\pi\) | ||||
−0.150011 | + | 0.988684i | \(0.547931\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.93017 | −0.526274 | −0.263137 | − | 0.964758i | \(-0.584757\pi\) | ||||
−0.263137 | + | 0.964758i | \(0.584757\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −0.447939 | −0.0779762 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −3.28103 | −0.554596 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −11.8490 | −1.94796 | −0.973982 | − | 0.226623i | \(-0.927231\pi\) | ||||
−0.973982 | + | 0.226623i | \(0.927231\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0.447939 | 0.0717277 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −6.65896 | −1.03995 | −0.519977 | − | 0.854180i | \(-0.674060\pi\) | ||||
−0.519977 | + | 0.854180i | \(0.674060\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −3.31326 | −0.505268 | −0.252634 | − | 0.967562i | \(-0.581297\pi\) | ||||
−0.252634 | + | 0.967562i | \(0.581297\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −9.18476 | −1.36918 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −4.52401 | −0.659894 | −0.329947 | − | 0.943999i | \(-0.607031\pi\) | ||||
−0.329947 | + | 0.943999i | \(0.607031\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −1.80285 | −0.252450 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 10.5741 | 1.45247 | 0.726233 | − | 0.687448i | \(-0.241269\pi\) | ||||
0.726233 | + | 0.687448i | \(0.241269\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 3.28103 | 0.442415 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −0.630036 | −0.0834503 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −5.53810 | −0.720999 | −0.360499 | − | 0.932759i | \(-0.617394\pi\) | ||||
−0.360499 | + | 0.932759i | \(0.617394\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 10.3262 | 1.32213 | 0.661065 | − | 0.750329i | \(-0.270105\pi\) | ||||
0.661065 | + | 0.750329i | \(0.270105\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 2.79935 | 0.352685 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −3.28103 | −0.406962 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 4.73986 | 0.579066 | 0.289533 | − | 0.957168i | \(-0.406500\pi\) | ||||
0.289533 | + | 0.957168i | \(0.406500\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 2.02648 | 0.243960 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −9.78183 | −1.16089 | −0.580445 | − | 0.814300i | \(-0.697121\pi\) | ||||
−0.580445 | + | 0.814300i | \(0.697121\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −4.97428 | −0.582196 | −0.291098 | − | 0.956693i | \(-0.594021\pi\) | ||||
−0.291098 | + | 0.956693i | \(0.594021\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −2.58245 | −0.298196 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −1.00000 | −0.113961 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −0.859419 | −0.0966922 | −0.0483461 | − | 0.998831i | \(-0.515395\pi\) | ||||
−0.0483461 | + | 0.998831i | \(0.515395\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 7.23441 | 0.803824 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −17.7747 | −1.95103 | −0.975513 | − | 0.219942i | \(-0.929413\pi\) | ||||
−0.975513 | + | 0.219942i | \(0.929413\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 13.2054 | 1.43233 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0.723722 | 0.0775911 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 3.79972 | 0.402769 | 0.201385 | − | 0.979512i | \(-0.435456\pi\) | ||||
0.201385 | + | 0.979512i | \(0.435456\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.00000 | 0.104828 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 1.31254 | 0.136104 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 4.61484 | 0.473473 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −18.7636 | −1.90516 | −0.952578 | − | 0.304294i | \(-0.901579\pi\) | ||||
−0.952578 | + | 0.304294i | \(0.901579\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −2.79935 | −0.281345 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 13.4588 | 1.33920 | 0.669599 | − | 0.742722i | \(-0.266466\pi\) | ||||
0.669599 | + | 0.742722i | \(0.266466\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 5.80963 | 0.572440 | 0.286220 | − | 0.958164i | \(-0.407601\pi\) | ||||
0.286220 | + | 0.958164i | \(0.407601\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 1.46970 | 0.143428 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 4.92441 | 0.476061 | 0.238031 | − | 0.971258i | \(-0.423498\pi\) | ||||
0.238031 | + | 0.971258i | \(0.423498\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −7.40719 | −0.709480 | −0.354740 | − | 0.934965i | \(-0.615431\pi\) | ||||
−0.354740 | + | 0.934965i | \(0.615431\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 5.30764 | 0.503779 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 11.9253 | 1.12184 | 0.560921 | − | 0.827869i | \(-0.310447\pi\) | ||||
0.560921 | + | 0.827869i | \(0.310447\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −14.8434 | −1.38416 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 2.79935 | 0.258800 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −4.02477 | −0.368950 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 2.98281 | 0.268951 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 2.51059 | 0.224554 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −6.98619 | −0.619925 | −0.309962 | − | 0.950749i | \(-0.600316\pi\) | ||||
−0.309962 | + | 0.950749i | \(0.600316\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 1.48414 | 0.130671 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −5.64597 | −0.493291 | −0.246645 | − | 0.969106i | \(-0.579328\pi\) | ||||
−0.246645 | + | 0.969106i | \(0.579328\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1.40652 | −0.121961 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 8.52333 | 0.733571 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −7.78732 | −0.665315 | −0.332658 | − | 0.943048i | \(-0.607945\pi\) | ||||
−0.332658 | + | 0.943048i | \(0.607945\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −10.3891 | −0.881191 | −0.440596 | − | 0.897706i | \(-0.645233\pi\) | ||||
−0.440596 | + | 0.897706i | \(0.645233\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 2.02648 | 0.170660 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −1.00000 | −0.0836242 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −5.30107 | −0.440230 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −0.447939 | −0.0369454 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 4.17537 | 0.342060 | 0.171030 | − | 0.985266i | \(-0.445291\pi\) | ||||
0.171030 | + | 0.985266i | \(0.445291\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 14.5117 | 1.18095 | 0.590474 | − | 0.807057i | \(-0.298941\pi\) | ||||
0.590474 | + | 0.807057i | \(0.298941\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −11.2667 | −0.910862 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −9.61399 | −0.772214 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −0.900121 | −0.0718375 | −0.0359187 | − | 0.999355i | \(-0.511436\pi\) | ||||
−0.0359187 | + | 0.999355i | \(0.511436\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −4.73656 | −0.375634 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 4.52401 | 0.356542 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −11.2253 | −0.879237 | −0.439618 | − | 0.898185i | \(-0.644886\pi\) | ||||
−0.439618 | + | 0.898185i | \(0.644886\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −1.46970 | −0.114416 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −19.0047 | −1.47062 | −0.735312 | − | 0.677729i | \(-0.762964\pi\) | ||||
−0.735312 | + | 0.677729i | \(0.762964\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −3.93734 | −0.301096 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −2.55089 | −0.193940 | −0.0969702 | − | 0.995287i | \(-0.530915\pi\) | ||||
−0.0969702 | + | 0.995287i | \(0.530915\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −5.76518 | −0.435807 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 2.48073 | 0.186463 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 10.4286 | 0.779472 | 0.389736 | − | 0.920927i | \(-0.372566\pi\) | ||||
0.389736 | + | 0.920927i | \(0.372566\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 18.6854 | 1.38887 | 0.694436 | − | 0.719554i | \(-0.255654\pi\) | ||||
0.694436 | + | 0.719554i | \(0.255654\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −4.62549 | −0.341926 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −38.8770 | −2.85829 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 4.02477 | 0.294320 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −2.59776 | −0.188959 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −10.4631 | −0.757080 | −0.378540 | − | 0.925585i | \(-0.623574\pi\) | ||||
−0.378540 | + | 0.925585i | \(0.623574\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −14.8324 | −1.06766 | −0.533828 | − | 0.845593i | \(-0.679247\pi\) | ||||
−0.533828 | + | 0.845593i | \(0.679247\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 1.46970 | 0.105248 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 5.00417 | 0.356532 | 0.178266 | − | 0.983982i | \(-0.442951\pi\) | ||||
0.178266 | + | 0.983982i | \(0.442951\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −21.8705 | −1.55036 | −0.775178 | − | 0.631742i | \(-0.782340\pi\) | ||||
−0.775178 | + | 0.631742i | \(0.782340\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −2.12317 | −0.149757 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 1.61567 | 0.113398 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −21.8483 | −1.52595 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 12.6643 | 0.880228 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 1.40652 | 0.0972911 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −21.2994 | −1.46631 | −0.733156 | − | 0.680061i | \(-0.761953\pi\) | ||||
−0.733156 | + | 0.680061i | \(0.761953\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 4.38167 | 0.300227 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −10.8709 | −0.741392 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 2.93017 | 0.198913 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 2.22818 | 0.150566 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −4.02477 | −0.270735 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 14.0607 | 0.941577 | 0.470788 | − | 0.882246i | \(-0.343970\pi\) | ||||
0.470788 | + | 0.882246i | \(0.343970\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −16.1388 | −1.07592 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 16.6931 | 1.10796 | 0.553980 | − | 0.832530i | \(-0.313108\pi\) | ||||
0.553980 | + | 0.832530i | \(0.313108\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −20.4263 | −1.34981 | −0.674905 | − | 0.737905i | \(-0.735815\pi\) | ||||
−0.674905 | + | 0.737905i | \(0.735815\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0.447939 | 0.0294722 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 10.3057 | 0.675150 | 0.337575 | − | 0.941299i | \(-0.390393\pi\) | ||||
0.337575 | + | 0.941299i | \(0.390393\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −14.8434 | −0.968278 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0.384968 | 0.0250063 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 5.58873 | 0.361505 | 0.180752 | − | 0.983529i | \(-0.442147\pi\) | ||||
0.180752 | + | 0.983529i | \(0.442147\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −11.2193 | −0.722701 | −0.361350 | − | 0.932430i | \(-0.617684\pi\) | ||||
−0.361350 | + | 0.932430i | \(0.617684\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −11.0339 | −0.707822 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 3.28103 | 0.209618 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1.40652 | −0.0894948 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 7.96198 | 0.504570 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −1.01675 | −0.0641770 | −0.0320885 | − | 0.999485i | \(-0.510216\pi\) | ||||
−0.0320885 | + | 0.999485i | \(0.510216\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −4.52401 | −0.284422 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −5.91522 | −0.370426 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −5.19821 | −0.324256 | −0.162128 | − | 0.986770i | \(-0.551836\pi\) | ||||
−0.162128 | + | 0.986770i | \(0.551836\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 11.8490 | 0.736262 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 4.52283 | 0.279956 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −19.0413 | −1.17413 | −0.587067 | − | 0.809538i | \(-0.699718\pi\) | ||||
−0.587067 | + | 0.809538i | \(0.699718\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 34.6940 | 2.13124 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −1.70204 | −0.104163 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 25.7218 | 1.56829 | 0.784143 | − | 0.620580i | \(-0.213103\pi\) | ||||
0.784143 | + | 0.620580i | \(0.213103\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −15.5256 | −0.943113 | −0.471557 | − | 0.881836i | \(-0.656308\pi\) | ||||
−0.471557 | + | 0.881836i | \(0.656308\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −0.447939 | −0.0271105 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 5.76518 | 0.347654 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 0.194004 | 0.0116566 | 0.00582829 | − | 0.999983i | \(-0.498145\pi\) | ||||
0.00582829 | + | 0.999983i | \(0.498145\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 8.20257 | 0.491075 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 16.7248 | 0.997719 | 0.498859 | − | 0.866683i | \(-0.333752\pi\) | ||||
0.498859 | + | 0.866683i | \(0.333752\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −8.74211 | −0.519665 | −0.259832 | − | 0.965654i | \(-0.583667\pi\) | ||||
−0.259832 | + | 0.965654i | \(0.583667\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −2.06717 | −0.122449 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 6.65896 | 0.393066 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −0.801224 | −0.0471308 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 8.40496 | 0.492708 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 0.773173 | 0.0451693 | 0.0225846 | − | 0.999745i | \(-0.492810\pi\) | ||||
0.0225846 | + | 0.999745i | \(0.492810\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −18.1707 | −1.05794 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 2.59776 | 0.150737 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 4.52401 | 0.261630 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 3.31326 | 0.190973 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −6.02872 | −0.346341 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 33.8805 | 1.93999 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 13.9348 | 0.795299 | 0.397650 | − | 0.917537i | \(-0.369826\pi\) | ||||
0.397650 | + | 0.917537i | \(0.369826\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −2.60236 | −0.148043 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −8.59928 | −0.487620 | −0.243810 | − | 0.969823i | \(-0.578397\pi\) | ||||
−0.243810 | + | 0.969823i | \(0.578397\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 16.8743 | 0.953792 | 0.476896 | − | 0.878960i | \(-0.341762\pi\) | ||||
0.476896 | + | 0.878960i | \(0.341762\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 9.18476 | 0.517503 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 10.8781 | 0.610976 | 0.305488 | − | 0.952196i | \(-0.401180\pi\) | ||||
0.305488 | + | 0.952196i | \(0.401180\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −1.61567 | −0.0904601 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −2.20584 | −0.123118 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 5.66092 | 0.314982 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −5.76518 | −0.319795 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 3.31797 | 0.183484 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 4.52401 | 0.249416 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −0.857840 | −0.0471511 | −0.0235756 | − | 0.999722i | \(-0.507505\pi\) | ||||
−0.0235756 | + | 0.999722i | \(0.507505\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 33.1695 | 1.81768 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 15.5517 | 0.849677 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 20.4394 | 1.11340 | 0.556701 | − | 0.830713i | \(-0.312067\pi\) | ||||
0.556701 | + | 0.830713i | \(0.312067\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −5.34183 | −0.290129 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −2.93017 | −0.158678 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 6.64895 | 0.357967 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −23.0289 | −1.23626 | −0.618129 | − | 0.786077i | \(-0.712109\pi\) | ||||
−0.618129 | + | 0.786077i | \(0.712109\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −22.0666 | −1.18120 | −0.590598 | − | 0.806966i | \(-0.701108\pi\) | ||||
−0.590598 | + | 0.806966i | \(0.701108\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −2.59776 | −0.138658 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −13.7935 | −0.734153 | −0.367076 | − | 0.930191i | \(-0.619641\pi\) | ||||
−0.367076 | + | 0.930191i | \(0.619641\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −32.0945 | −1.70340 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 1.80285 | 0.0954171 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 0.247233 | 0.0130484 | 0.00652422 | − | 0.999979i | \(-0.497923\pi\) | ||||
0.00652422 | + | 0.999979i | \(0.497923\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −17.0217 | −0.895879 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −0.447939 | −0.0235107 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −16.3208 | −0.854270 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −13.5596 | −0.707806 | −0.353903 | − | 0.935282i | \(-0.615146\pi\) | ||||
−0.353903 | + | 0.935282i | \(0.615146\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 18.6408 | 0.970399 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −10.5741 | −0.548981 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 38.4069 | 1.98864 | 0.994318 | − | 0.106455i | \(-0.0339499\pi\) | ||||
0.994318 | + | 0.106455i | \(0.0339499\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −1.12459 | −0.0580738 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 1.61567 | 0.0832112 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 20.1382 | 1.03443 | 0.517215 | − | 0.855855i | \(-0.326969\pi\) | ||||
0.517215 | + | 0.855855i | \(0.326969\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 3.12939 | 0.160324 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 9.70876 | 0.496094 | 0.248047 | − | 0.968748i | \(-0.420211\pi\) | ||||
0.248047 | + | 0.968748i | \(0.420211\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −3.28103 | −0.167217 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 9.27499 | 0.471474 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 13.9463 | 0.707104 | 0.353552 | − | 0.935415i | \(-0.384974\pi\) | ||||
0.353552 | + | 0.935415i | \(0.384974\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −18.2081 | −0.920822 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 2.52905 | 0.127574 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −2.81978 | −0.141879 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −14.1889 | −0.712121 | −0.356060 | − | 0.934463i | \(-0.615880\pi\) | ||||
−0.356060 | + | 0.934463i | \(0.615880\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0.630036 | 0.0315412 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −27.7777 | −1.38715 | −0.693576 | − | 0.720384i | \(-0.743966\pi\) | ||||
−0.693576 | + | 0.720384i | \(0.743966\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 2.93017 | 0.145962 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 23.7364 | 1.17947 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −11.8490 | −0.587334 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −35.7851 | −1.76946 | −0.884729 | − | 0.466106i | \(-0.845656\pi\) | ||||
−0.884729 | + | 0.466106i | \(0.845656\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 3.48825 | 0.172062 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 5.53810 | 0.272512 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −58.3194 | −2.86279 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 4.65368 | 0.227892 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −2.62309 | −0.128146 | −0.0640731 | − | 0.997945i | \(-0.520409\pi\) | ||||
−0.0640731 | + | 0.997945i | \(0.520409\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −0.181796 | −0.00886017 | −0.00443009 | − | 0.999990i | \(-0.501410\pi\) | ||||
−0.00443009 | + | 0.999990i | \(0.501410\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 12.6643 | 0.615758 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 23.2035 | 1.12554 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −10.3262 | −0.499718 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0.447939 | 0.0216267 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −36.7451 | −1.76995 | −0.884974 | − | 0.465641i | \(-0.845824\pi\) | ||||
−0.884974 | + | 0.465641i | \(0.845824\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 3.97484 | 0.191019 | 0.0955093 | − | 0.995429i | \(-0.469552\pi\) | ||||
0.0955093 | + | 0.995429i | \(0.469552\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 2.37456 | 0.113851 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −6.36311 | −0.304389 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 1.86289 | 0.0889107 | 0.0444554 | − | 0.999011i | \(-0.485845\pi\) | ||||
0.0444554 | + | 0.999011i | \(0.485845\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −2.79935 | −0.133302 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 8.71373 | 0.414002 | 0.207001 | − | 0.978341i | \(-0.433630\pi\) | ||||
0.207001 | + | 0.978341i | \(0.433630\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 12.4670 | 0.590993 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −1.87031 | −0.0884628 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 21.7433 | 1.02613 | 0.513064 | − | 0.858350i | \(-0.328510\pi\) | ||||
0.513064 | + | 0.858350i | \(0.328510\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −6.65896 | −0.313558 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −6.50038 | −0.305414 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 3.28103 | 0.153817 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −14.7921 | −0.691947 | −0.345974 | − | 0.938244i | \(-0.612451\pi\) | ||||
−0.345974 | + | 0.938244i | \(0.612451\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 10.4554 | 0.488015 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 15.1545 | 0.705817 | 0.352908 | − | 0.935658i | \(-0.385193\pi\) | ||||
0.352908 | + | 0.935658i | \(0.385193\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −20.1333 | −0.935675 | −0.467837 | − | 0.883815i | \(-0.654967\pi\) | ||||
−0.467837 | + | 0.883815i | \(0.654967\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 4.30648 | 0.199708 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 20.9108 | 0.967635 | 0.483817 | − | 0.875169i | \(-0.339250\pi\) | ||||
0.483817 | + | 0.875169i | \(0.339250\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −4.73986 | −0.218867 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0.403200 | 0.0185785 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −3.31326 | −0.152344 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 8.10885 | 0.372060 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −29.6007 | −1.35532 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −19.4194 | −0.887294 | −0.443647 | − | 0.896202i | \(-0.646316\pi\) | ||||
−0.443647 | + | 0.896202i | \(0.646316\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 11.8490 | 0.540268 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −2.02648 | −0.0922080 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −61.5641 | −2.79548 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −28.6495 | −1.29823 | −0.649116 | − | 0.760689i | \(-0.724861\pi\) | ||||
−0.649116 | + | 0.760689i | \(0.724861\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 5.02827 | 0.227386 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 20.7493 | 0.936403 | 0.468201 | − | 0.883622i | \(-0.344902\pi\) | ||||
0.468201 | + | 0.883622i | \(0.344902\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −6.50270 | −0.292867 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −9.18476 | −0.412824 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 9.78183 | 0.438775 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 8.45028 | 0.378287 | 0.189143 | − | 0.981950i | \(-0.439429\pi\) | ||||
0.189143 | + | 0.981950i | \(0.439429\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 8.51293 | 0.380330 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 4.15294 | 0.185170 | 0.0925851 | − | 0.995705i | \(-0.470487\pi\) | ||||
0.0925851 | + | 0.995705i | \(0.470487\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 44.1587 | 1.96504 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −0.447939 | −0.0198937 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 29.4711 | 1.30628 | 0.653142 | − | 0.757236i | \(-0.273451\pi\) | ||||
0.653142 | + | 0.757236i | \(0.273451\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 4.97428 | 0.220049 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 3.65380 | 0.161319 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 19.0616 | 0.839954 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −4.52401 | −0.198966 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 1.14264 | 0.0501565 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −13.7754 | −0.603510 | −0.301755 | − | 0.953386i | \(-0.597572\pi\) | ||||
−0.301755 | + | 0.953386i | \(0.597572\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 12.7796 | 0.558814 | 0.279407 | − | 0.960173i | \(-0.409862\pi\) | ||||
0.279407 | + | 0.960173i | \(0.409862\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 2.58245 | 0.112707 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −11.7933 | −0.513723 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −2.53338 | −0.110147 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 15.5031 | 0.672776 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 6.65896 | 0.288431 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 16.1572 | 0.698535 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −4.67139 | −0.201586 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 1.00000 | 0.0430730 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 3.21818 | 0.138360 | 0.0691801 | − | 0.997604i | \(-0.477962\pi\) | ||||
0.0691801 | + | 0.997604i | \(0.477962\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −8.36991 | −0.359187 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −24.3033 | −1.04104 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −5.59881 | −0.239388 | −0.119694 | − | 0.992811i | \(-0.538191\pi\) | ||||
−0.119694 | + | 0.992811i | \(0.538191\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −28.9065 | −1.23370 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −2.27247 | −0.0968106 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0.859419 | 0.0365462 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 17.4145 | 0.739206 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −34.1662 | −1.44767 | −0.723835 | − | 0.689973i | \(-0.757622\pi\) | ||||
−0.723835 | + | 0.689973i | \(0.757622\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 3.31326 | 0.140136 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −1.80285 | −0.0761165 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 12.0881 | 0.509453 | 0.254726 | − | 0.967013i | \(-0.418015\pi\) | ||||
0.254726 | + | 0.967013i | \(0.418015\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 39.1275 | 1.64611 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −7.23441 | −0.303817 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −17.7546 | −0.744312 | −0.372156 | − | 0.928170i | \(-0.621381\pi\) | ||||
−0.372156 | + | 0.928170i | \(0.621381\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 30.4778 | 1.27546 | 0.637728 | − | 0.770261i | \(-0.279874\pi\) | ||||
0.637728 | + | 0.770261i | \(0.279874\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 4.68681 | 0.195794 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −26.0817 | −1.08768 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −18.5397 | −0.771819 | −0.385909 | − | 0.922537i | \(-0.626112\pi\) | ||||
−0.385909 | + | 0.922537i | \(0.626112\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 6.64400 | 0.276115 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 17.7747 | 0.737418 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 10.5741 | 0.437935 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 9.18476 | 0.379743 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 12.1426 | 0.501180 | 0.250590 | − | 0.968093i | \(-0.419375\pi\) | ||||
0.250590 | + | 0.968093i | \(0.419375\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −4.12134 | −0.169817 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −2.24157 | −0.0922057 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 0.323537 | 0.0132861 | 0.00664304 | − | 0.999978i | \(-0.497885\pi\) | ||||
0.00664304 | + | 0.999978i | \(0.497885\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −13.2054 | −0.541369 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 9.79665 | 0.400950 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −10.6184 | −0.433854 | −0.216927 | − | 0.976188i | \(-0.569603\pi\) | ||||
−0.216927 | + | 0.976188i | \(0.569603\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −4.61907 | −0.188416 | −0.0942078 | − | 0.995553i | \(-0.530032\pi\) | ||||
−0.0942078 | + | 0.995553i | \(0.530032\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −13.2685 | −0.540337 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 3.28103 | 0.133393 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 1.96513 | 0.0797622 | 0.0398811 | − | 0.999204i | \(-0.487302\pi\) | ||||
0.0398811 | + | 0.999204i | \(0.487302\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −0.723722 | −0.0293267 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 4.52401 | 0.183022 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −1.23085 | −0.0497136 | −0.0248568 | − | 0.999691i | \(-0.507913\pi\) | ||||
−0.0248568 | + | 0.999691i | \(0.507913\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 9.78670 | 0.394638 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 21.4707 | 0.864377 | 0.432188 | − | 0.901783i | \(-0.357742\pi\) | ||||
0.432188 | + | 0.901783i | \(0.357742\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −7.78189 | −0.312780 | −0.156390 | − | 0.987695i | \(-0.549986\pi\) | ||||
−0.156390 | + | 0.987695i | \(0.549986\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −11.7523 | −0.471602 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −3.79972 | −0.152232 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −20.5886 | −0.823543 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −0.630036 | −0.0251612 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −47.6895 | −1.90151 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 40.4400 | 1.60989 | 0.804945 | − | 0.593350i | \(-0.202195\pi\) | ||||
0.804945 | + | 0.593350i | \(0.202195\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 9.54084 | 0.379214 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −22.9219 | −0.909630 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1.00000 | −0.0396214 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 27.3828 | 1.08325 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 4.68498 | 0.185045 | 0.0925227 | − | 0.995711i | \(-0.470507\pi\) | ||||
0.0925227 | + | 0.995711i | \(0.470507\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 9.04913 | 0.356863 | 0.178431 | − | 0.983952i | \(-0.442898\pi\) | ||||
0.178431 | + | 0.983952i | \(0.442898\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 4.86952 | 0.191737 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −22.4978 | −0.884478 | −0.442239 | − | 0.896897i | \(-0.645816\pi\) | ||||
−0.442239 | + | 0.896897i | \(0.645816\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −5.53810 | −0.217389 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −1.31254 | −0.0514424 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 30.9847 | 1.21253 | 0.606263 | − | 0.795264i | \(-0.292668\pi\) | ||||
0.606263 | + | 0.795264i | \(0.292668\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −18.5246 | −0.723817 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 13.9248 | 0.543257 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −33.4325 | −1.30235 | −0.651173 | − | 0.758929i | \(-0.725723\pi\) | ||||
−0.651173 | + | 0.758929i | \(0.725723\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −24.9115 | −0.968945 | −0.484472 | − | 0.874807i | \(-0.660988\pi\) | ||||
−0.484472 | + | 0.874807i | \(0.660988\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 1.80285 | 0.0700170 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −4.61484 | −0.178956 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 7.30930 | 0.283017 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −6.29836 | −0.243509 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 10.3262 | 0.398637 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −19.4048 | −0.747999 | −0.373999 | − | 0.927429i | \(-0.622014\pi\) | ||||
−0.373999 | + | 0.927429i | \(0.622014\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 14.9765 | 0.576448 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −21.8427 | −0.839481 | −0.419741 | − | 0.907644i | \(-0.637879\pi\) | ||||
−0.419741 | + | 0.907644i | \(0.637879\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 18.7636 | 0.720081 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −7.47750 | −0.286538 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −49.4004 | −1.89025 | −0.945126 | − | 0.326706i | \(-0.894061\pi\) | ||||
−0.945126 | + | 0.326706i | \(0.894061\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −25.5504 | −0.976232 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 9.14976 | 0.349085 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −10.5741 | −0.402842 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −2.77894 | −0.105716 | −0.0528580 | − | 0.998602i | \(-0.516833\pi\) | ||||
−0.0528580 | + | 0.998602i | \(0.516833\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 2.79935 | 0.106339 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −34.0870 | −1.29299 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −26.8008 | −1.01515 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −4.61634 | −0.174606 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −23.2999 | −0.880023 | −0.440012 | − | 0.897992i | \(-0.645026\pi\) | ||||
−0.440012 | + | 0.897992i | \(0.645026\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −16.6659 | −0.628565 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 6.64895 | 0.250414 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −13.4588 | −0.506170 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 16.6855 | 0.626639 | 0.313319 | − | 0.949648i | \(-0.398559\pi\) | ||||
0.313319 | + | 0.949648i | \(0.398559\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 2.40582 | 0.0902251 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 13.2561 | 0.496445 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −3.28103 | −0.122704 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −2.50341 | −0.0934917 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 32.3650 | 1.20701 | 0.603506 | − | 0.797359i | \(-0.293770\pi\) | ||||
0.603506 | + | 0.797359i | \(0.293770\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −5.80963 | −0.216362 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 5.02558 | 0.186903 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −9.31463 | −0.345937 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 13.4062 | 0.497208 | 0.248604 | − | 0.968605i | \(-0.420028\pi\) | ||||
0.248604 | + | 0.968605i | \(0.420028\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −16.7607 | −0.620768 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −13.3351 | −0.493218 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −40.1158 | −1.48171 | −0.740856 | − | 0.671664i | \(-0.765580\pi\) | ||||
−0.740856 | + | 0.671664i | \(0.765580\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −1.46970 | −0.0542109 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 4.73986 | 0.174595 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −11.5972 | −0.426609 | −0.213304 | − | 0.976986i | \(-0.568423\pi\) | ||||
−0.213304 | + | 0.976986i | \(0.568423\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0.630036 | 0.0231449 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −19.8775 | −0.729235 | −0.364618 | − | 0.931157i | \(-0.618800\pi\) | ||||
−0.364618 | + | 0.931157i | \(0.618800\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 13.6995 | 0.501912 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 49.7576 | 1.82053 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −4.92441 | −0.179934 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 42.4212 | 1.54797 | 0.773986 | − | 0.633203i | \(-0.218260\pi\) | ||||
0.773986 | + | 0.633203i | \(0.218260\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0.455444 | 0.0165973 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 47.6135 | 1.73283 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 1.25244 | 0.0455207 | 0.0227603 | − | 0.999741i | \(-0.492755\pi\) | ||||
0.0227603 | + | 0.999741i | \(0.492755\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 2.02648 | 0.0735566 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 3.53131 | 0.128010 | 0.0640050 | − | 0.997950i | \(-0.479613\pi\) | ||||
0.0640050 | + | 0.997950i | \(0.479613\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 7.40719 | 0.268158 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −36.9666 | −1.33653 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 5.53810 | 0.199969 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −4.82723 | −0.174075 | −0.0870373 | − | 0.996205i | \(-0.527740\pi\) | ||||
−0.0870373 | + | 0.996205i | \(0.527740\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 2.32848 | 0.0838583 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 2.30903 | 0.0830502 | 0.0415251 | − | 0.999137i | \(-0.486778\pi\) | ||||
0.0415251 | + | 0.999137i | \(0.486778\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −16.8930 | −0.606813 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −5.30764 | −0.190410 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −9.36596 | −0.335570 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −9.78183 | −0.350021 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −4.19712 | −0.149993 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −2.95333 | −0.105409 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −45.8744 | −1.63524 | −0.817622 | − | 0.575755i | \(-0.804708\pi\) | ||||
−0.817622 | + | 0.575755i | \(0.804708\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 8.52933 | 0.303652 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −11.9253 | −0.424017 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −10.3262 | −0.366693 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −15.5408 | −0.551176 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −41.1585 | −1.45791 | −0.728954 | − | 0.684563i | \(-0.759993\pi\) | ||||
−0.728954 | + | 0.684563i | \(0.759993\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −18.2081 | −0.644156 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −10.6367 | −0.375831 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −4.97428 | −0.175539 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 14.8434 | 0.523162 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −11.5218 | −0.405587 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 11.2111 | 0.394163 | 0.197081 | − | 0.980387i | \(-0.436854\pi\) | ||||
0.197081 | + | 0.980387i | \(0.436854\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −18.2886 | −0.642201 | −0.321100 | − | 0.947045i | \(-0.604053\pi\) | ||||
−0.321100 | + | 0.947045i | \(0.604053\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 6.95453 | 0.243906 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −36.8307 | −1.29012 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −4.66018 | −0.163039 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −2.79935 | −0.0978172 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −5.66576 | −0.197736 | −0.0988682 | − | 0.995101i | \(-0.531522\pi\) | ||||
−0.0988682 | + | 0.995101i | \(0.531522\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 6.89165 | 0.240228 | 0.120114 | − | 0.992760i | \(-0.461674\pi\) | ||||
0.120114 | + | 0.992760i | \(0.461674\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −2.58245 | −0.0899095 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 25.2955 | 0.879609 | 0.439804 | − | 0.898094i | \(-0.355048\pi\) | ||||
0.439804 | + | 0.898094i | \(0.355048\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −46.2104 | −1.60495 | −0.802477 | − | 0.596683i | \(-0.796485\pi\) | ||||
−0.802477 | + | 0.596683i | \(0.796485\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −0.0869020 | −0.00301460 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 4.02477 | 0.139450 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −62.3549 | −2.15788 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −7.61187 | −0.263105 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 46.6446 | 1.61035 | 0.805175 | − | 0.593037i | \(-0.202071\pi\) | ||||
0.805175 | + | 0.593037i | \(0.202071\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −26.3896 | −0.909987 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −7.49170 | −0.258028 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 3.28103 | 0.112871 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −1.00000 | −0.0343604 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 3.91594 | 0.134395 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 53.6050 | 1.83755 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 22.1666 | 0.758970 | 0.379485 | − | 0.925198i | \(-0.376101\pi\) | ||||
0.379485 | + | 0.925198i | \(0.376101\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −12.9186 | −0.441805 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 18.9996 | 0.649015 | 0.324507 | − | 0.945883i | \(-0.394802\pi\) | ||||
0.324507 | + | 0.945883i | \(0.394802\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 0.272422 | 0.00929493 | 0.00464746 | − | 0.999989i | \(-0.498521\pi\) | ||||
0.00464746 | + | 0.999989i | \(0.498521\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −2.98281 | −0.101654 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 26.5519 | 0.903836 | 0.451918 | − | 0.892059i | \(-0.350740\pi\) | ||||
0.451918 | + | 0.892059i | \(0.350740\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −8.36955 | −0.284573 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0.358900 | 0.0121889 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −0.859419 | −0.0291538 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −4.73986 | −0.160604 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 52.5259 | 1.77773 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −2.51059 | −0.0848736 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 32.6734 | 1.10330 | 0.551650 | − | 0.834075i | \(-0.313998\pi\) | ||||
0.551650 | + | 0.834075i | \(0.313998\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −0.346335 | −0.0116816 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 38.8204 | 1.30789 | 0.653946 | − | 0.756541i | \(-0.273112\pi\) | ||||
0.653946 | + | 0.756541i | \(0.273112\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 17.6060 | 0.592488 | 0.296244 | − | 0.955112i | \(-0.404266\pi\) | ||||
0.296244 | + | 0.955112i | \(0.404266\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 8.13937 | 0.273602 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −23.5297 | −0.790050 | −0.395025 | − | 0.918670i | \(-0.629264\pi\) | ||||
−0.395025 | + | 0.918670i | \(0.629264\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 6.98619 | 0.234309 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 7.23441 | 0.242362 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −6.36311 | −0.212933 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 34.2167 | 1.14374 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −2.02648 | −0.0676622 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 4.73419 | 0.157894 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 42.5584 | 1.41783 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −1.48414 | −0.0493891 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 61.3073 | 2.03792 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −40.7665 | −1.35363 | −0.676815 | − | 0.736153i | \(-0.736640\pi\) | ||||
−0.676815 | + | 0.736153i | \(0.736640\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −37.6758 | −1.24963 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 5.29899 | 0.175563 | 0.0877817 | − | 0.996140i | \(-0.472022\pi\) | ||||
0.0877817 | + | 0.996140i | \(0.472022\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −17.7747 | −0.588256 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −15.1764 | −0.501716 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 5.64597 | 0.186446 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −50.9761 | −1.68155 | −0.840773 | − | 0.541388i | \(-0.817899\pi\) | ||||
−0.840773 | + | 0.541388i | \(0.817899\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −6.24193 | −0.205679 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 9.78183 | 0.321973 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −68.3117 | −2.24608 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −16.2632 | −0.534153 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −0.932456 | −0.0305929 | −0.0152964 | − | 0.999883i | \(-0.504869\pi\) | ||||
−0.0152964 | + | 0.999883i | \(0.504869\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1.40652 | 0.0460969 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 3.85196 | 0.126107 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 13.2054 | 0.431863 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −19.1283 | −0.624893 | −0.312447 | − | 0.949935i | \(-0.601149\pi\) | ||||
−0.312447 | + | 0.949935i | \(0.601149\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −7.55867 | −0.246668 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 16.2679 | 0.530318 | 0.265159 | − | 0.964205i | \(-0.414576\pi\) | ||||
0.265159 | + | 0.964205i | \(0.414576\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 30.1252 | 0.981010 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −8.52333 | −0.277264 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −50.7920 | −1.65052 | −0.825259 | − | 0.564754i | \(-0.808971\pi\) | ||||
−0.825259 | + | 0.564754i | \(0.808971\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 4.97428 | 0.161472 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −4.87274 | −0.158009 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −29.3455 | −0.950594 | −0.475297 | − | 0.879825i | \(-0.657659\pi\) | ||||
−0.475297 | + | 0.879825i | \(0.657659\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −34.3296 | −1.11088 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0.723722 | 0.0233946 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 7.78732 | 0.251466 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −22.4141 | −0.723036 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −13.7852 | −0.444221 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −48.6655 | −1.56660 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −4.30901 | −0.138568 | −0.0692841 | − | 0.997597i | \(-0.522072\pi\) | ||||
−0.0692841 | + | 0.997597i | \(0.522072\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −2.53575 | −0.0814600 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 19.4778 | 0.625074 | 0.312537 | − | 0.949906i | \(-0.398821\pi\) | ||||
0.312537 | + | 0.949906i | \(0.398821\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 10.3891 | 0.333059 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 2.58245 | 0.0827047 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 38.5692 | 1.23394 | 0.616968 | − | 0.786988i | \(-0.288361\pi\) | ||||
0.616968 | + | 0.786988i | \(0.288361\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 3.79972 | 0.121439 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 20.7353 | 0.662028 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 13.8737 | 0.442502 | 0.221251 | − | 0.975217i | \(-0.428986\pi\) | ||||
0.221251 | + | 0.975217i | \(0.428986\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 16.4189 | 0.523148 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −2.02648 | −0.0645036 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 14.9892 | 0.476630 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 46.2789 | 1.47010 | 0.735048 | − | 0.678015i | \(-0.237159\pi\) | ||||
0.735048 | + | 0.678015i | \(0.237159\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0.384260 | 0.0121941 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −71.7578 | −2.27487 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 44.6421 | 1.41383 | 0.706915 | − | 0.707298i | \(-0.250086\pi\) | ||||
0.706915 | + | 0.707298i | \(0.250086\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −30.7808 | −0.973863 |
(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 | 8008.2.a.v.1.6 | ✓ | 11 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8008.2.a.v.1.6 | ✓ | 11 | 1.1 | even | 1 | trivial |