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: | \(10\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{10} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{10} - 3x^{9} - 15x^{8} + 43x^{7} + 66x^{6} - 173x^{5} - 127x^{4} + 246x^{3} + 99x^{2} - 82x + 8 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(2.46329\) 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 | ||||||||
\(3\) | −2.46329 | −1.42218 | −0.711089 | − | 0.703102i | \(-0.751798\pi\) | ||||
−0.711089 | + | 0.703102i | \(0.751798\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.35093 | −0.604156 | −0.302078 | − | 0.953283i | \(-0.597680\pi\) | ||||
−0.302078 | + | 0.953283i | \(0.597680\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 3.06778 | 1.02259 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.00000 | 0.301511 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.00000 | −0.277350 | ||||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 3.32773 | 0.859217 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 3.18596 | 0.772709 | 0.386355 | − | 0.922350i | \(-0.373734\pi\) | ||||
0.386355 | + | 0.922350i | \(0.373734\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 4.39961 | 1.00934 | 0.504670 | − | 0.863312i | \(-0.331614\pi\) | ||||
0.504670 | + | 0.863312i | \(0.331614\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −2.46329 | −0.537533 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −2.64117 | −0.550721 | −0.275361 | − | 0.961341i | \(-0.588797\pi\) | ||||
−0.275361 | + | 0.961341i | \(0.588797\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −3.17498 | −0.634996 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −0.166958 | −0.0321311 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −5.83924 | −1.08432 | −0.542160 | − | 0.840276i | \(-0.682393\pi\) | ||||
−0.542160 | + | 0.840276i | \(0.682393\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −8.29622 | −1.49005 | −0.745023 | − | 0.667039i | \(-0.767561\pi\) | ||||
−0.745023 | + | 0.667039i | \(0.767561\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −2.46329 | −0.428803 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −1.35093 | −0.228349 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 5.93067 | 0.974996 | 0.487498 | − | 0.873124i | \(-0.337910\pi\) | ||||
0.487498 | + | 0.873124i | \(0.337910\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 2.46329 | 0.394441 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0.838410 | 0.130938 | 0.0654688 | − | 0.997855i | \(-0.479146\pi\) | ||||
0.0654688 | + | 0.997855i | \(0.479146\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −4.98346 | −0.759970 | −0.379985 | − | 0.924993i | \(-0.624071\pi\) | ||||
−0.379985 | + | 0.924993i | \(0.624071\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −4.14436 | −0.617805 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −3.71058 | −0.541244 | −0.270622 | − | 0.962686i | \(-0.587229\pi\) | ||||
−0.270622 | + | 0.962686i | \(0.587229\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −7.84793 | −1.09893 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 11.1825 | 1.53603 | 0.768017 | − | 0.640430i | \(-0.221244\pi\) | ||||
0.768017 | + | 0.640430i | \(0.221244\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −1.35093 | −0.182160 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −10.8375 | −1.43546 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 11.1625 | 1.45323 | 0.726616 | − | 0.687044i | \(-0.241092\pi\) | ||||
0.726616 | + | 0.687044i | \(0.241092\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −12.9239 | −1.65474 | −0.827369 | − | 0.561659i | \(-0.810163\pi\) | ||||
−0.827369 | + | 0.561659i | \(0.810163\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 3.06778 | 0.386504 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 1.35093 | 0.167563 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 2.65052 | 0.323812 | 0.161906 | − | 0.986806i | \(-0.448236\pi\) | ||||
0.161906 | + | 0.986806i | \(0.448236\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 6.50595 | 0.783224 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 9.04103 | 1.07297 | 0.536486 | − | 0.843909i | \(-0.319751\pi\) | ||||
0.536486 | + | 0.843909i | \(0.319751\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −7.48913 | −0.876536 | −0.438268 | − | 0.898844i | \(-0.644408\pi\) | ||||
−0.438268 | + | 0.898844i | \(0.644408\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 7.82088 | 0.903078 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 1.00000 | 0.113961 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −5.13527 | −0.577763 | −0.288882 | − | 0.957365i | \(-0.593283\pi\) | ||||
−0.288882 | + | 0.957365i | \(0.593283\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −8.79207 | −0.976897 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −6.21047 | −0.681687 | −0.340844 | − | 0.940120i | \(-0.610713\pi\) | ||||
−0.340844 | + | 0.940120i | \(0.610713\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −4.30402 | −0.466837 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 14.3837 | 1.54210 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 16.5794 | 1.75742 | 0.878709 | − | 0.477358i | \(-0.158405\pi\) | ||||
0.878709 | + | 0.477358i | \(0.158405\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.00000 | −0.104828 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 20.4360 | 2.11911 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −5.94358 | −0.609798 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 4.42426 | 0.449215 | 0.224608 | − | 0.974449i | \(-0.427890\pi\) | ||||
0.224608 | + | 0.974449i | \(0.427890\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 3.06778 | 0.308323 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −15.9983 | −1.59190 | −0.795948 | − | 0.605366i | \(-0.793027\pi\) | ||||
−0.795948 | + | 0.605366i | \(0.793027\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 0.599693 | 0.0590895 | 0.0295447 | − | 0.999563i | \(-0.490594\pi\) | ||||
0.0295447 | + | 0.999563i | \(0.490594\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 3.32773 | 0.324754 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 18.3701 | 1.77590 | 0.887952 | − | 0.459936i | \(-0.152128\pi\) | ||||
0.887952 | + | 0.459936i | \(0.152128\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 9.37221 | 0.897695 | 0.448847 | − | 0.893608i | \(-0.351835\pi\) | ||||
0.448847 | + | 0.893608i | \(0.351835\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −14.6089 | −1.38662 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −8.62416 | −0.811293 | −0.405647 | − | 0.914030i | \(-0.632954\pi\) | ||||
−0.405647 | + | 0.914030i | \(0.632954\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 3.56804 | 0.332721 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −3.06778 | −0.283616 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 3.18596 | 0.292057 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −2.06524 | −0.186217 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 11.0438 | 0.987792 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 8.08723 | 0.717626 | 0.358813 | − | 0.933410i | \(-0.383182\pi\) | ||||
0.358813 | + | 0.933410i | \(0.383182\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 12.2757 | 1.08081 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −3.46938 | −0.303121 | −0.151560 | − | 0.988448i | \(-0.548430\pi\) | ||||
−0.151560 | + | 0.988448i | \(0.548430\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 4.39961 | 0.381495 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0.225549 | 0.0194122 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −4.59224 | −0.392342 | −0.196171 | − | 0.980570i | \(-0.562851\pi\) | ||||
−0.196171 | + | 0.980570i | \(0.562851\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 9.60157 | 0.814395 | 0.407197 | − | 0.913340i | \(-0.366506\pi\) | ||||
0.407197 | + | 0.913340i | \(0.366506\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 9.14023 | 0.769746 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −1.00000 | −0.0836242 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 7.88842 | 0.655097 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −2.46329 | −0.203168 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −12.0202 | −0.984733 | −0.492366 | − | 0.870388i | \(-0.663868\pi\) | ||||
−0.492366 | + | 0.870388i | \(0.663868\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 17.2257 | 1.40181 | 0.700906 | − | 0.713254i | \(-0.252779\pi\) | ||||
0.700906 | + | 0.713254i | \(0.252779\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 9.77382 | 0.790167 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 11.2076 | 0.900219 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1.54531 | 0.123329 | 0.0616647 | − | 0.998097i | \(-0.480359\pi\) | ||||
0.0616647 | + | 0.998097i | \(0.480359\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −27.5457 | −2.18451 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −2.64117 | −0.208153 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 12.7567 | 0.999183 | 0.499592 | − | 0.866261i | \(-0.333483\pi\) | ||||
0.499592 | + | 0.866261i | \(0.333483\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 3.32773 | 0.259064 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −10.5517 | −0.816513 | −0.408256 | − | 0.912867i | \(-0.633863\pi\) | ||||
−0.408256 | + | 0.912867i | \(0.633863\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 13.4970 | 1.03214 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −23.4206 | −1.78064 | −0.890318 | − | 0.455340i | \(-0.849518\pi\) | ||||
−0.890318 | + | 0.455340i | \(0.849518\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −3.17498 | −0.240006 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −27.4964 | −2.06676 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 24.8944 | 1.86069 | 0.930347 | − | 0.366682i | \(-0.119506\pi\) | ||||
0.930347 | + | 0.366682i | \(0.119506\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −20.4521 | −1.52019 | −0.760095 | − | 0.649812i | \(-0.774847\pi\) | ||||
−0.760095 | + | 0.649812i | \(0.774847\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 31.8353 | 2.35333 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −8.01193 | −0.589049 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 3.18596 | 0.232981 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −0.166958 | −0.0121444 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −5.62671 | −0.407134 | −0.203567 | − | 0.979061i | \(-0.565253\pi\) | ||||
−0.203567 | + | 0.979061i | \(0.565253\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −2.56450 | −0.184597 | −0.0922984 | − | 0.995731i | \(-0.529421\pi\) | ||||
−0.0922984 | + | 0.995731i | \(0.529421\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −3.32773 | −0.238304 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 10.1710 | 0.724656 | 0.362328 | − | 0.932051i | \(-0.381982\pi\) | ||||
0.362328 | + | 0.932051i | \(0.381982\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 12.3576 | 0.876010 | 0.438005 | − | 0.898973i | \(-0.355685\pi\) | ||||
0.438005 | + | 0.898973i | \(0.355685\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −6.52898 | −0.460519 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −5.83924 | −0.409834 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −1.13264 | −0.0791067 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −8.10251 | −0.563164 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 4.39961 | 0.304327 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 12.7165 | 0.875437 | 0.437718 | − | 0.899112i | \(-0.355787\pi\) | ||||
0.437718 | + | 0.899112i | \(0.355787\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −22.2706 | −1.52596 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 6.73232 | 0.459140 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −8.29622 | −0.563184 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 18.4479 | 1.24659 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −3.18596 | −0.214311 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −17.6861 | −1.18435 | −0.592175 | − | 0.805809i | \(-0.701731\pi\) | ||||
−0.592175 | + | 0.805809i | \(0.701731\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −9.74014 | −0.649342 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 12.5324 | 0.831804 | 0.415902 | − | 0.909409i | \(-0.363466\pi\) | ||||
0.415902 | + | 0.909409i | \(0.363466\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 3.68995 | 0.243839 | 0.121919 | − | 0.992540i | \(-0.461095\pi\) | ||||
0.121919 | + | 0.992540i | \(0.461095\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −2.46329 | −0.162072 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −15.6168 | −1.02309 | −0.511546 | − | 0.859256i | \(-0.670927\pi\) | ||||
−0.511546 | + | 0.859256i | \(0.670927\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 5.01275 | 0.326996 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 12.6496 | 0.821683 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −22.0562 | −1.42669 | −0.713347 | − | 0.700811i | \(-0.752822\pi\) | ||||
−0.713347 | + | 0.700811i | \(0.752822\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 8.92740 | 0.575065 | 0.287532 | − | 0.957771i | \(-0.407165\pi\) | ||||
0.287532 | + | 0.957771i | \(0.407165\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 22.1583 | 1.42145 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −1.35093 | −0.0863079 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −4.39961 | −0.279941 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 15.2982 | 0.969481 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −17.9062 | −1.13023 | −0.565116 | − | 0.825011i | \(-0.691169\pi\) | ||||
−0.565116 | + | 0.825011i | \(0.691169\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −2.64117 | −0.166049 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 10.6020 | 0.663925 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −26.9545 | −1.68138 | −0.840688 | − | 0.541519i | \(-0.817849\pi\) | ||||
−0.840688 | + | 0.541519i | \(0.817849\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 5.93067 | 0.368514 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −17.9135 | −1.10882 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −5.99043 | −0.369386 | −0.184693 | − | 0.982796i | \(-0.559129\pi\) | ||||
−0.184693 | + | 0.982796i | \(0.559129\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −15.1068 | −0.928003 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −40.8399 | −2.49936 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −29.4761 | −1.79719 | −0.898594 | − | 0.438782i | \(-0.855410\pi\) | ||||
−0.898594 | + | 0.438782i | \(0.855410\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −2.05759 | −0.124989 | −0.0624947 | − | 0.998045i | \(-0.519906\pi\) | ||||
−0.0624947 | + | 0.998045i | \(0.519906\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 2.46329 | 0.149085 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −3.17498 | −0.191459 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 10.1057 | 0.607195 | 0.303598 | − | 0.952800i | \(-0.401812\pi\) | ||||
0.303598 | + | 0.952800i | \(0.401812\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −25.4510 | −1.52371 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −11.0777 | −0.660841 | −0.330420 | − | 0.943834i | \(-0.607190\pi\) | ||||
−0.330420 | + | 0.943834i | \(0.607190\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 4.59180 | 0.272954 | 0.136477 | − | 0.990643i | \(-0.456422\pi\) | ||||
0.136477 | + | 0.990643i | \(0.456422\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 14.6407 | 0.867242 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0.838410 | 0.0494898 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −6.84965 | −0.402921 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −10.8982 | −0.638865 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −32.6070 | −1.90492 | −0.952461 | − | 0.304659i | \(-0.901457\pi\) | ||||
−0.952461 | + | 0.304659i | \(0.901457\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −15.0798 | −0.877978 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −0.166958 | −0.00968789 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 2.64117 | 0.152743 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −4.98346 | −0.287242 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 39.4085 | 2.26396 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 17.4593 | 0.999719 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 10.7352 | 0.612692 | 0.306346 | − | 0.951920i | \(-0.400894\pi\) | ||||
0.306346 | + | 0.951920i | \(0.400894\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −1.47721 | −0.0840358 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −14.1123 | −0.800233 | −0.400117 | − | 0.916464i | \(-0.631030\pi\) | ||||
−0.400117 | + | 0.916464i | \(0.631030\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 4.90962 | 0.277508 | 0.138754 | − | 0.990327i | \(-0.455690\pi\) | ||||
0.138754 | + | 0.990327i | \(0.455690\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −4.14436 | −0.233508 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 14.8092 | 0.831768 | 0.415884 | − | 0.909418i | \(-0.363472\pi\) | ||||
0.415884 | + | 0.909418i | \(0.363472\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −5.83924 | −0.326935 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −45.2508 | −2.52565 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 14.0170 | 0.779926 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 3.17498 | 0.176116 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −23.0864 | −1.27668 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −3.71058 | −0.204571 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 9.20520 | 0.505963 | 0.252982 | − | 0.967471i | \(-0.418589\pi\) | ||||
0.252982 | + | 0.967471i | \(0.418589\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 18.1940 | 0.997024 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −3.58067 | −0.195633 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −9.43834 | −0.514139 | −0.257070 | − | 0.966393i | \(-0.582757\pi\) | ||||
−0.257070 | + | 0.966393i | \(0.582757\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 21.2438 | 1.15380 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −8.29622 | −0.449266 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −8.78910 | −0.473189 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −26.8945 | −1.44377 | −0.721886 | − | 0.692012i | \(-0.756725\pi\) | ||||
−0.721886 | + | 0.692012i | \(0.756725\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 15.5615 | 0.832990 | 0.416495 | − | 0.909138i | \(-0.363258\pi\) | ||||
0.416495 | + | 0.909138i | \(0.363258\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0.166958 | 0.00891156 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −29.0537 | −1.54637 | −0.773186 | − | 0.634180i | \(-0.781338\pi\) | ||||
−0.773186 | + | 0.634180i | \(0.781338\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −12.2138 | −0.648242 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −7.84793 | −0.415357 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −35.5627 | −1.87693 | −0.938463 | − | 0.345380i | \(-0.887750\pi\) | ||||
−0.938463 | + | 0.345380i | \(0.887750\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 0.356572 | 0.0187669 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −2.46329 | −0.129289 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 10.1173 | 0.529564 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 28.0017 | 1.46168 | 0.730839 | − | 0.682550i | \(-0.239129\pi\) | ||||
0.730839 | + | 0.682550i | \(0.239129\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 2.57206 | 0.133896 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 11.1825 | 0.580566 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −8.59794 | −0.445185 | −0.222592 | − | 0.974912i | \(-0.571452\pi\) | ||||
−0.222592 | + | 0.974912i | \(0.571452\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −27.2042 | −1.40482 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 5.83924 | 0.300736 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 9.29924 | 0.477670 | 0.238835 | − | 0.971060i | \(-0.423235\pi\) | ||||
0.238835 | + | 0.971060i | \(0.423235\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −19.9212 | −1.02059 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −11.2423 | −0.574455 | −0.287227 | − | 0.957862i | \(-0.592734\pi\) | ||||
−0.287227 | + | 0.957862i | \(0.592734\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −1.35093 | −0.0688499 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −15.2881 | −0.777140 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 31.1249 | 1.57809 | 0.789046 | − | 0.614334i | \(-0.210575\pi\) | ||||
0.789046 | + | 0.614334i | \(0.210575\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −8.41465 | −0.425547 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 8.54606 | 0.431092 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 6.93741 | 0.349059 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 3.66752 | 0.184067 | 0.0920337 | − | 0.995756i | \(-0.470663\pi\) | ||||
0.0920337 | + | 0.995756i | \(0.470663\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −10.8375 | −0.542554 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −7.01974 | −0.350549 | −0.175275 | − | 0.984520i | \(-0.556081\pi\) | ||||
−0.175275 | + | 0.984520i | \(0.556081\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 8.29622 | 0.413264 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 11.8775 | 0.590198 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 5.93067 | 0.293972 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 17.8214 | 0.881212 | 0.440606 | − | 0.897701i | \(-0.354764\pi\) | ||||
0.440606 | + | 0.897701i | \(0.354764\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 11.3120 | 0.557980 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 11.1625 | 0.549270 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 8.38993 | 0.411845 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −23.6514 | −1.15821 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −14.1126 | −0.689444 | −0.344722 | − | 0.938705i | \(-0.612027\pi\) | ||||
−0.344722 | + | 0.938705i | \(0.612027\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 1.33945 | 0.0652808 | 0.0326404 | − | 0.999467i | \(-0.489608\pi\) | ||||
0.0326404 | + | 0.999467i | \(0.489608\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −11.3832 | −0.553473 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −10.1154 | −0.490667 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −12.9239 | −0.625432 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 2.46329 | 0.118929 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 12.8072 | 0.616902 | 0.308451 | − | 0.951240i | \(-0.400189\pi\) | ||||
0.308451 | + | 0.951240i | \(0.400189\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −14.3722 | −0.690683 | −0.345341 | − | 0.938477i | \(-0.612237\pi\) | ||||
−0.345341 | + | 0.938477i | \(0.612237\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −19.4314 | −0.931666 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −11.6201 | −0.555865 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −22.4871 | −1.07325 | −0.536625 | − | 0.843821i | \(-0.680301\pi\) | ||||
−0.536625 | + | 0.843821i | \(0.680301\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 3.06778 | 0.146085 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 10.5139 | 0.499528 | 0.249764 | − | 0.968307i | \(-0.419647\pi\) | ||||
0.249764 | + | 0.968307i | \(0.419647\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −22.3977 | −1.06175 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 29.6092 | 1.40047 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 21.5042 | 1.01484 | 0.507422 | − | 0.861698i | \(-0.330598\pi\) | ||||
0.507422 | + | 0.861698i | \(0.330598\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0.838410 | 0.0394792 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −42.4320 | −1.99363 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 1.35093 | 0.0633327 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −22.2943 | −1.04288 | −0.521442 | − | 0.853287i | \(-0.674606\pi\) | ||||
−0.521442 | + | 0.853287i | \(0.674606\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −0.531922 | −0.0248280 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 32.8453 | 1.52976 | 0.764880 | − | 0.644173i | \(-0.222798\pi\) | ||||
0.764880 | + | 0.644173i | \(0.222798\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −27.0927 | −1.25910 | −0.629552 | − | 0.776958i | \(-0.716762\pi\) | ||||
−0.629552 | + | 0.776958i | \(0.716762\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −27.6076 | −1.28027 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 0.0125807 | 0.000582167 0 | 0.000291083 | − | 1.00000i | \(-0.499907\pi\) | ||||
0.000291083 | 1.00000i | \(0.499907\pi\) | ||||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 2.65052 | 0.122389 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −3.80655 | −0.175396 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −4.98346 | −0.229140 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −13.9687 | −0.640927 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 34.3054 | 1.57074 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 6.92578 | 0.316447 | 0.158223 | − | 0.987403i | \(-0.449423\pi\) | ||||
0.158223 | + | 0.987403i | \(0.449423\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −5.93067 | −0.270415 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 6.50595 | 0.296031 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −5.97688 | −0.271396 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 25.7243 | 1.16568 | 0.582840 | − | 0.812587i | \(-0.301941\pi\) | ||||
0.582840 | + | 0.812587i | \(0.301941\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −31.4234 | −1.42102 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 35.1520 | 1.58639 | 0.793193 | − | 0.608970i | \(-0.208417\pi\) | ||||
0.793193 | + | 0.608970i | \(0.208417\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −18.6036 | −0.837863 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −4.14436 | −0.186275 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 9.04103 | 0.405545 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 10.0030 | 0.447797 | 0.223898 | − | 0.974612i | \(-0.428122\pi\) | ||||
0.223898 | + | 0.974612i | \(0.428122\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 25.9918 | 1.16123 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 1.72411 | 0.0768742 | 0.0384371 | − | 0.999261i | \(-0.487762\pi\) | ||||
0.0384371 | + | 0.999261i | \(0.487762\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 21.6127 | 0.961752 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −2.46329 | −0.109398 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −31.7114 | −1.40558 | −0.702792 | − | 0.711395i | \(-0.748064\pi\) | ||||
−0.702792 | + | 0.711395i | \(0.748064\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −7.48913 | −0.331300 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −0.734551 | −0.0324312 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −0.810145 | −0.0356992 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −3.71058 | −0.163191 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 57.6916 | 2.53238 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 13.5878 | 0.595294 | 0.297647 | − | 0.954676i | \(-0.403798\pi\) | ||||
0.297647 | + | 0.954676i | \(0.403798\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −22.2291 | −0.972010 | −0.486005 | − | 0.873956i | \(-0.661546\pi\) | ||||
−0.486005 | + | 0.873956i | \(0.661546\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 7.82088 | 0.341331 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −26.4314 | −1.15137 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −16.0242 | −0.696706 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 34.2440 | 1.48607 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −0.838410 | −0.0363156 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −24.8168 | −1.07292 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −61.3220 | −2.64624 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 1.00000 | 0.0430730 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 19.7593 | 0.849517 | 0.424759 | − | 0.905307i | \(-0.360359\pi\) | ||||
0.424759 | + | 0.905307i | \(0.360359\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 50.3793 | 2.16198 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −12.6612 | −0.542347 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −16.6384 | −0.711408 | −0.355704 | − | 0.934599i | \(-0.615759\pi\) | ||||
−0.355704 | + | 0.934599i | \(0.615759\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −39.6477 | −1.69212 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −25.6904 | −1.09445 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −5.13527 | −0.218374 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 19.7357 | 0.837733 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −29.5860 | −1.25360 | −0.626799 | − | 0.779181i | \(-0.715635\pi\) | ||||
−0.626799 | + | 0.779181i | \(0.715635\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 4.98346 | 0.210778 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −7.84793 | −0.331340 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −8.06054 | −0.339711 | −0.169856 | − | 0.985469i | \(-0.554330\pi\) | ||||
−0.169856 | + | 0.985469i | \(0.554330\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 11.6507 | 0.490147 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −8.79207 | −0.369232 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −28.1597 | −1.18052 | −0.590258 | − | 0.807215i | \(-0.700974\pi\) | ||||
−0.590258 | + | 0.807215i | \(0.700974\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −8.77328 | −0.367150 | −0.183575 | − | 0.983006i | \(-0.558767\pi\) | ||||
−0.183575 | + | 0.983006i | \(0.558767\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 13.8602 | 0.579018 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 8.38565 | 0.349706 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −46.3842 | −1.93100 | −0.965499 | − | 0.260405i | \(-0.916144\pi\) | ||||
−0.965499 | + | 0.260405i | \(0.916144\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 6.31710 | 0.262530 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −6.21047 | −0.257654 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 11.1825 | 0.463131 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 4.14436 | 0.171348 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 4.55730 | 0.188100 | 0.0940499 | − | 0.995567i | \(-0.470019\pi\) | ||||
0.0940499 | + | 0.995567i | \(0.470019\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −36.5001 | −1.50396 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −25.0542 | −1.03059 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 0.399117 | 0.0163898 | 0.00819489 | − | 0.999966i | \(-0.497391\pi\) | ||||
0.00819489 | + | 0.999966i | \(0.497391\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −4.30402 | −0.176448 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −30.4404 | −1.24584 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −15.5508 | −0.635388 | −0.317694 | − | 0.948193i | \(-0.602908\pi\) | ||||
−0.317694 | + | 0.948193i | \(0.602908\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 7.98613 | 0.325761 | 0.162881 | − | 0.986646i | \(-0.447921\pi\) | ||||
0.162881 | + | 0.986646i | \(0.447921\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 8.13120 | 0.331128 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −1.35093 | −0.0549232 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −40.6607 | −1.65037 | −0.825183 | − | 0.564865i | \(-0.808928\pi\) | ||||
−0.825183 | + | 0.564865i | \(0.808928\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 14.3837 | 0.582857 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 3.71058 | 0.150114 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −31.1689 | −1.25890 | −0.629451 | − | 0.777040i | \(-0.716720\pi\) | ||||
−0.629451 | + | 0.777040i | \(0.716720\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 2.79001 | 0.112504 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −28.3109 | −1.13975 | −0.569877 | − | 0.821730i | \(-0.693009\pi\) | ||||
−0.569877 | + | 0.821730i | \(0.693009\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −22.2838 | −0.895661 | −0.447831 | − | 0.894118i | \(-0.647803\pi\) | ||||
−0.447831 | + | 0.894118i | \(0.647803\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0.440964 | 0.0176953 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 16.5794 | 0.664242 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0.955401 | 0.0382160 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −10.8375 | −0.432808 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 18.8949 | 0.753388 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −34.9786 | −1.39248 | −0.696238 | − | 0.717811i | \(-0.745144\pi\) | ||||
−0.696238 | + | 0.717811i | \(0.745144\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −31.3243 | −1.24503 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −10.9253 | −0.433558 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1.00000 | −0.0396214 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 27.7359 | 1.09721 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 18.4872 | 0.730199 | 0.365099 | − | 0.930969i | \(-0.381035\pi\) | ||||
0.365099 | + | 0.930969i | \(0.381035\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −36.8122 | −1.45173 | −0.725866 | − | 0.687836i | \(-0.758561\pi\) | ||||
−0.725866 | + | 0.687836i | \(0.758561\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −16.5836 | −0.652980 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −28.5174 | −1.12114 | −0.560568 | − | 0.828108i | \(-0.689417\pi\) | ||||
−0.560568 | + | 0.828108i | \(0.689417\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 11.1625 | 0.438166 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 20.4360 | 0.800949 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 39.8728 | 1.56034 | 0.780171 | − | 0.625567i | \(-0.215132\pi\) | ||||
0.780171 | + | 0.625567i | \(0.215132\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 4.68689 | 0.183132 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −22.9750 | −0.896340 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −38.0278 | −1.48135 | −0.740677 | − | 0.671862i | \(-0.765495\pi\) | ||||
−0.740677 | + | 0.671862i | \(0.765495\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 47.7002 | 1.85532 | 0.927661 | − | 0.373424i | \(-0.121816\pi\) | ||||
0.927661 | + | 0.373424i | \(0.121816\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 7.84793 | 0.304789 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −5.94358 | −0.230482 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 15.4224 | 0.597158 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 43.5660 | 1.68436 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −12.9239 | −0.498922 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −19.9971 | −0.770831 | −0.385415 | − | 0.922743i | \(-0.625942\pi\) | ||||
−0.385415 | + | 0.922743i | \(0.625942\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0.530089 | 0.0204031 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −16.5933 | −0.637731 | −0.318865 | − | 0.947800i | \(-0.603302\pi\) | ||||
−0.318865 | + | 0.947800i | \(0.603302\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 4.42426 | 0.169787 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −30.8709 | −1.18297 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −3.36101 | −0.128605 | −0.0643027 | − | 0.997930i | \(-0.520482\pi\) | ||||
−0.0643027 | + | 0.997930i | \(0.520482\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 6.20381 | 0.237035 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −9.08940 | −0.346782 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −11.1825 | −0.426019 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 11.9872 | 0.456015 | 0.228008 | − | 0.973659i | \(-0.426779\pi\) | ||||
0.228008 | + | 0.973659i | \(0.426779\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 3.06778 | 0.116535 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −12.9711 | −0.492021 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 2.67114 | 0.101177 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 38.4687 | 1.45502 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −42.4807 | −1.60448 | −0.802238 | − | 0.597005i | \(-0.796357\pi\) | ||||
−0.802238 | + | 0.597005i | \(0.796357\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 26.0926 | 0.984102 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −12.3478 | −0.465046 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −15.9983 | −0.601680 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 11.6705 | 0.438293 | 0.219146 | − | 0.975692i | \(-0.429673\pi\) | ||||
0.219146 | + | 0.975692i | \(0.429673\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −15.7539 | −0.590817 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 21.9117 | 0.820600 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1.35093 | 0.0505220 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 54.3306 | 2.02901 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −17.1474 | −0.639491 | −0.319746 | − | 0.947503i | \(-0.603597\pi\) | ||||
−0.319746 | + | 0.947503i | \(0.603597\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0.599693 | 0.0223337 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −21.9908 | −0.817845 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 18.5395 | 0.688538 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −20.1774 | −0.748339 | −0.374170 | − | 0.927360i | \(-0.622072\pi\) | ||||
−0.374170 | + | 0.927360i | \(0.622072\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −28.2059 | −1.04466 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −15.8771 | −0.587236 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −28.2515 | −1.04349 | −0.521746 | − | 0.853101i | \(-0.674719\pi\) | ||||
−0.521746 | + | 0.853101i | \(0.674719\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 3.32773 | 0.122745 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 2.65052 | 0.0976330 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 22.9454 | 0.844061 | 0.422031 | − | 0.906582i | \(-0.361317\pi\) | ||||
0.422031 | + | 0.906582i | \(0.361317\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 10.8375 | 0.398125 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 28.2336 | 1.03579 | 0.517895 | − | 0.855444i | \(-0.326716\pi\) | ||||
0.517895 | + | 0.855444i | \(0.326716\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 16.2385 | 0.594932 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −19.0523 | −0.697089 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 18.3701 | 0.671229 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −3.83280 | −0.139861 | −0.0699304 | − | 0.997552i | \(-0.522278\pi\) | ||||
−0.0699304 | + | 0.997552i | \(0.522278\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 44.1082 | 1.60739 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −23.2708 | −0.846912 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −5.27925 | −0.191878 | −0.0959389 | − | 0.995387i | \(-0.530585\pi\) | ||||
−0.0959389 | + | 0.995387i | \(0.530585\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 6.50595 | 0.236151 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −36.3162 | −1.31646 | −0.658231 | − | 0.752816i | \(-0.728695\pi\) | ||||
−0.658231 | + | 0.752816i | \(0.728695\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 9.37221 | 0.339297 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −13.2038 | −0.477384 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −11.1625 | −0.403054 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −11.4002 | −0.411101 | −0.205550 | − | 0.978647i | \(-0.565898\pi\) | ||||
−0.205550 | + | 0.978647i | \(0.565898\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 66.3967 | 2.39122 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −10.1555 | −0.365268 | −0.182634 | − | 0.983181i | \(-0.558462\pi\) | ||||
−0.182634 | + | 0.983181i | \(0.558462\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 26.3403 | 0.946173 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −14.6089 | −0.524092 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 3.68868 | 0.132161 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 9.04103 | 0.323513 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0.974908 | 0.0348404 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −2.08761 | −0.0745102 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −9.57018 | −0.341140 | −0.170570 | − | 0.985346i | \(-0.554561\pi\) | ||||
−0.170570 | + | 0.985346i | \(0.554561\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 14.7561 | 0.525333 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −8.62416 | −0.306640 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 12.9239 | 0.458942 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 37.2124 | 1.31979 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −12.7480 | −0.451557 | −0.225779 | − | 0.974179i | \(-0.572493\pi\) | ||||
−0.225779 | + | 0.974179i | \(0.572493\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −11.8218 | −0.418224 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 50.8621 | 1.79712 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −7.48913 | −0.264286 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 3.56804 | 0.125757 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 72.6080 | 2.55592 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 12.8669 | 0.452377 | 0.226189 | − | 0.974084i | \(-0.427373\pi\) | ||||
0.226189 | + | 0.974084i | \(0.427373\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −15.4923 | −0.544010 | −0.272005 | − | 0.962296i | \(-0.587687\pi\) | ||||
−0.272005 | + | 0.962296i | \(0.587687\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 5.06842 | 0.177757 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −17.2335 | −0.603662 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −21.9253 | −0.767068 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −3.06778 | −0.107197 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 23.7513 | 0.828927 | 0.414463 | − | 0.910066i | \(-0.363969\pi\) | ||||
0.414463 | + | 0.910066i | \(0.363969\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 52.3347 | 1.82427 | 0.912137 | − | 0.409886i | \(-0.134432\pi\) | ||||
0.912137 | + | 0.409886i | \(0.134432\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 7.82088 | 0.272288 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 34.2952 | 1.19256 | 0.596280 | − | 0.802777i | \(-0.296645\pi\) | ||||
0.596280 | + | 0.802777i | \(0.296645\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −12.3995 | −0.430652 | −0.215326 | − | 0.976542i | \(-0.569081\pi\) | ||||
−0.215326 | + | 0.976542i | \(0.569081\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −24.8933 | −0.863540 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 3.18596 | 0.110387 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 14.2546 | 0.493301 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 1.38512 | 0.0478768 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −19.9994 | −0.690456 | −0.345228 | − | 0.938519i | \(-0.612198\pi\) | ||||
−0.345228 | + | 0.938519i | \(0.612198\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 5.09669 | 0.175748 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 27.2876 | 0.939834 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −1.35093 | −0.0464735 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 1.00000 | 0.0343604 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −11.3109 | −0.388190 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −15.6639 | −0.536951 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −27.2841 | −0.934190 | −0.467095 | − | 0.884207i | \(-0.654699\pi\) | ||||
−0.467095 | + | 0.884207i | \(0.654699\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −18.2336 | −0.623575 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −25.9605 | −0.886795 | −0.443397 | − | 0.896325i | \(-0.646227\pi\) | ||||
−0.443397 | + | 0.896325i | \(0.646227\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 16.5988 | 0.566345 | 0.283173 | − | 0.959069i | \(-0.408613\pi\) | ||||
0.283173 | + | 0.959069i | \(0.408613\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −2.06524 | −0.0703833 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −44.6487 | −1.51986 | −0.759929 | − | 0.650006i | \(-0.774767\pi\) | ||||
−0.759929 | + | 0.650006i | \(0.774767\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 31.6397 | 1.07578 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 16.8726 | 0.573025 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −5.13527 | −0.174202 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −2.65052 | −0.0898093 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 13.5726 | 0.459364 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 11.0438 | 0.373350 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −15.7613 | −0.532221 | −0.266110 | − | 0.963943i | \(-0.585739\pi\) | ||||
−0.266110 | + | 0.963943i | \(0.585739\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 80.3204 | 2.70914 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −42.9162 | −1.44588 | −0.722942 | − | 0.690909i | \(-0.757211\pi\) | ||||
−0.722942 | + | 0.690909i | \(0.757211\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −10.2080 | −0.343527 | −0.171764 | − | 0.985138i | \(-0.554946\pi\) | ||||
−0.171764 | + | 0.985138i | \(0.554946\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 37.1458 | 1.24864 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 32.4015 | 1.08794 | 0.543968 | − | 0.839106i | \(-0.316921\pi\) | ||||
0.543968 | + | 0.839106i | \(0.316921\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 8.08723 | 0.271237 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −8.79207 | −0.294545 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −16.3251 | −0.546299 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −33.6306 | −1.12415 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −6.50595 | −0.217227 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 48.4436 | 1.61568 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 35.6270 | 1.18691 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 12.2757 | 0.408509 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 27.6294 | 0.918431 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −37.2661 | −1.23740 | −0.618700 | − | 0.785628i | \(-0.712340\pi\) | ||||
−0.618700 | + | 0.785628i | \(0.712340\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −49.0794 | −1.62786 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −7.99443 | −0.264867 | −0.132434 | − | 0.991192i | \(-0.542279\pi\) | ||||
−0.132434 | + | 0.991192i | \(0.542279\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −6.21047 | −0.205536 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −43.0073 | −1.42178 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −3.46938 | −0.114569 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 42.4336 | 1.39976 | 0.699878 | − | 0.714262i | \(-0.253238\pi\) | ||||
0.699878 | + | 0.714262i | \(0.253238\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −26.4439 | −0.871357 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −9.04103 | −0.297589 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −18.8298 | −0.619118 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 1.83972 | 0.0604245 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −37.1310 | −1.21823 | −0.609114 | − | 0.793082i | \(-0.708475\pi\) | ||||
−0.609114 | + | 0.793082i | \(0.708475\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 4.39961 | 0.144191 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 34.7626 | 1.13807 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −4.30402 | −0.140757 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 44.7878 | 1.46315 | 0.731576 | − | 0.681760i | \(-0.238785\pi\) | ||||
0.731576 | + | 0.681760i | \(0.238785\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −12.0938 | −0.394666 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 24.4694 | 0.797679 | 0.398840 | − | 0.917021i | \(-0.369413\pi\) | ||||
0.398840 | + | 0.917021i | \(0.369413\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −2.21438 | −0.0721101 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0.225549 | 0.00733712 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −6.01950 | −0.195607 | −0.0978037 | − | 0.995206i | \(-0.531182\pi\) | ||||
−0.0978037 | + | 0.995206i | \(0.531182\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 7.48913 | 0.243107 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −36.4793 | −1.18292 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −11.4091 | −0.369577 | −0.184788 | − | 0.982778i | \(-0.559160\pi\) | ||||
−0.184788 | + | 0.982778i | \(0.559160\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 7.60130 | 0.245972 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 14.3837 | 0.464959 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −4.59224 | −0.148291 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 37.8273 | 1.22024 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 56.3554 | 1.81603 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 3.46447 | 0.111525 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 30.3666 | 0.976524 | 0.488262 | − | 0.872697i | \(-0.337631\pi\) | ||||
0.488262 | + | 0.872697i | \(0.337631\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −34.5279 | −1.10919 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −37.7717 | −1.21215 | −0.606075 | − | 0.795407i | \(-0.707257\pi\) | ||||
−0.606075 | + | 0.795407i | \(0.707257\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 9.60157 | 0.307812 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −7.82088 | −0.250469 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 31.3212 | 1.00205 | 0.501027 | − | 0.865432i | \(-0.332956\pi\) | ||||
0.501027 | + | 0.865432i | \(0.332956\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 16.5794 | 0.529881 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 28.7519 | 0.917976 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 46.9288 | 1.49679 | 0.748397 | − | 0.663250i | \(-0.230824\pi\) | ||||
0.748397 | + | 0.663250i | \(0.230824\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −13.7404 | −0.437805 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 9.14023 | 0.290937 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 13.1621 | 0.418532 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 40.3861 | 1.28291 | 0.641453 | − | 0.767163i | \(-0.278332\pi\) | ||||
0.641453 | + | 0.767163i | \(0.278332\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −22.6750 | −0.719570 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −16.6943 | −0.529246 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 53.2863 | 1.68759 | 0.843797 | − | 0.536662i | \(-0.180315\pi\) | ||||
0.843797 | + | 0.536662i | \(0.180315\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −0.990173 | −0.0313277 |
(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.s.1.2 | ✓ | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8008.2.a.s.1.2 | ✓ | 10 | 1.1 | even | 1 | trivial |