Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8016,2,Mod(1,8016)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8016, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8016.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8016 = 2^{4} \cdot 3 \cdot 167 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8016.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: | \(64.0080822603\) |
Analytic rank: | \(1\) |
Dimension: | \(5\) |
Coefficient field: | 5.5.149169.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{5} - 6x^{3} - 3x^{2} + 4x + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 2004) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-0.228573\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8016.1 |
$q$-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 | ||||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −2.71918 | −1.21606 | −0.608028 | − | 0.793916i | \(-0.708039\pi\) | ||||
−0.608028 | + | 0.793916i | \(0.708039\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.29630 | 0.867919 | 0.433960 | − | 0.900932i | \(-0.357116\pi\) | ||||
0.433960 | + | 0.900932i | \(0.357116\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2.71918 | −0.819864 | −0.409932 | − | 0.912116i | \(-0.634448\pi\) | ||||
−0.409932 | + | 0.912116i | \(0.634448\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −0.130922 | −0.0363112 | −0.0181556 | − | 0.999835i | \(-0.505779\pi\) | ||||
−0.0181556 | + | 0.999835i | \(0.505779\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −2.71918 | −0.702090 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 5.29280 | 1.28369 | 0.641847 | − | 0.766833i | \(-0.278169\pi\) | ||||
0.641847 | + | 0.766833i | \(0.278169\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2.49495 | −0.572380 | −0.286190 | − | 0.958173i | \(-0.592389\pi\) | ||||
−0.286190 | + | 0.958173i | \(0.592389\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 2.29630 | 0.501093 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −2.05324 | −0.428129 | −0.214065 | − | 0.976819i | \(-0.568670\pi\) | ||||
−0.214065 | + | 0.976819i | \(0.568670\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 2.39395 | 0.478790 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −5.85977 | −1.08813 | −0.544066 | − | 0.839042i | \(-0.683116\pi\) | ||||
−0.544066 | + | 0.839042i | \(0.683116\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −0.277324 | −0.0498088 | −0.0249044 | − | 0.999690i | \(-0.507928\pi\) | ||||
−0.0249044 | + | 0.999690i | \(0.507928\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −2.71918 | −0.473349 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −6.24405 | −1.05544 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 9.10161 | 1.49630 | 0.748148 | − | 0.663532i | \(-0.230943\pi\) | ||||
0.748148 | + | 0.663532i | \(0.230943\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −0.130922 | −0.0209643 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −8.78322 | −1.37171 | −0.685854 | − | 0.727739i | \(-0.740571\pi\) | ||||
−0.685854 | + | 0.727739i | \(0.740571\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 7.14952 | 1.09029 | 0.545146 | − | 0.838341i | \(-0.316474\pi\) | ||||
0.545146 | + | 0.838341i | \(0.316474\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −2.71918 | −0.405352 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 1.16618 | 0.170104 | 0.0850521 | − | 0.996377i | \(-0.472894\pi\) | ||||
0.0850521 | + | 0.996377i | \(0.472894\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.72701 | −0.246716 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 5.29280 | 0.741141 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −1.51392 | −0.207953 | −0.103976 | − | 0.994580i | \(-0.533157\pi\) | ||||
−0.103976 | + | 0.994580i | \(0.533157\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 7.39395 | 0.997000 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −2.49495 | −0.330464 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −6.58556 | −0.857367 | −0.428684 | − | 0.903455i | \(-0.641023\pi\) | ||||
−0.428684 | + | 0.903455i | \(0.641023\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −3.25671 | −0.416979 | −0.208489 | − | 0.978025i | \(-0.566855\pi\) | ||||
−0.208489 | + | 0.978025i | \(0.566855\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 2.29630 | 0.289306 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0.356000 | 0.0441564 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 11.6688 | 1.42557 | 0.712784 | − | 0.701384i | \(-0.247434\pi\) | ||||
0.712784 | + | 0.701384i | \(0.247434\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −2.05324 | −0.247181 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 10.5813 | 1.25577 | 0.627883 | − | 0.778308i | \(-0.283922\pi\) | ||||
0.627883 | + | 0.778308i | \(0.283922\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −13.9938 | −1.63785 | −0.818926 | − | 0.573899i | \(-0.805430\pi\) | ||||
−0.818926 | + | 0.573899i | \(0.805430\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 2.39395 | 0.276429 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −6.24405 | −0.711576 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1.32793 | 0.149404 | 0.0747018 | − | 0.997206i | \(-0.476200\pi\) | ||||
0.0747018 | + | 0.997206i | \(0.476200\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −15.3931 | −1.68961 | −0.844805 | − | 0.535074i | \(-0.820284\pi\) | ||||
−0.844805 | + | 0.535074i | \(0.820284\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −14.3921 | −1.56104 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −5.85977 | −0.628233 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −0.650613 | −0.0689649 | −0.0344824 | − | 0.999405i | \(-0.510978\pi\) | ||||
−0.0344824 | + | 0.999405i | \(0.510978\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −0.300636 | −0.0315152 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −0.277324 | −0.0287571 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 6.78421 | 0.696045 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −16.5435 | −1.67973 | −0.839867 | − | 0.542792i | \(-0.817367\pi\) | ||||
−0.839867 | + | 0.542792i | \(0.817367\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −2.71918 | −0.273288 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −3.96140 | −0.394174 | −0.197087 | − | 0.980386i | \(-0.563148\pi\) | ||||
−0.197087 | + | 0.980386i | \(0.563148\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 3.85793 | 0.380134 | 0.190067 | − | 0.981771i | \(-0.439130\pi\) | ||||
0.190067 | + | 0.981771i | \(0.439130\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −6.24405 | −0.609357 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −13.1188 | −1.26824 | −0.634121 | − | 0.773234i | \(-0.718638\pi\) | ||||
−0.634121 | + | 0.773234i | \(0.718638\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 2.33140 | 0.223308 | 0.111654 | − | 0.993747i | \(-0.464385\pi\) | ||||
0.111654 | + | 0.993747i | \(0.464385\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 9.10161 | 0.863887 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 13.1549 | 1.23751 | 0.618754 | − | 0.785585i | \(-0.287638\pi\) | ||||
0.618754 | + | 0.785585i | \(0.287638\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 5.58312 | 0.520629 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −0.130922 | −0.0121037 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 12.1539 | 1.11414 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −3.60605 | −0.327823 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −8.78322 | −0.791956 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 7.08633 | 0.633820 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 3.91471 | 0.347374 | 0.173687 | − | 0.984801i | \(-0.444432\pi\) | ||||
0.173687 | + | 0.984801i | \(0.444432\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 7.14952 | 0.629480 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 8.22025 | 0.718207 | 0.359104 | − | 0.933298i | \(-0.383083\pi\) | ||||
0.359104 | + | 0.933298i | \(0.383083\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −5.72914 | −0.496780 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −2.71918 | −0.234030 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 9.47880 | 0.809828 | 0.404914 | − | 0.914355i | \(-0.367301\pi\) | ||||
0.404914 | + | 0.914355i | \(0.367301\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −5.15967 | −0.437638 | −0.218819 | − | 0.975765i | \(-0.570220\pi\) | ||||
−0.218819 | + | 0.975765i | \(0.570220\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 1.16618 | 0.0982097 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0.356000 | 0.0297702 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 15.9338 | 1.32323 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −1.72701 | −0.142442 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −13.5693 | −1.11164 | −0.555821 | − | 0.831302i | \(-0.687596\pi\) | ||||
−0.555821 | + | 0.831302i | \(0.687596\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 21.5430 | 1.75315 | 0.876573 | − | 0.481268i | \(-0.159824\pi\) | ||||
0.876573 | + | 0.481268i | \(0.159824\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 5.29280 | 0.427898 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0.754094 | 0.0605703 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −18.1301 | −1.44694 | −0.723470 | − | 0.690356i | \(-0.757454\pi\) | ||||
−0.723470 | + | 0.690356i | \(0.757454\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −1.51392 | −0.120062 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −4.71484 | −0.371582 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −9.67728 | −0.757983 | −0.378992 | − | 0.925400i | \(-0.623729\pi\) | ||||
−0.378992 | + | 0.925400i | \(0.623729\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 7.39395 | 0.575618 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −1.00000 | −0.0773823 | ||||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.9829 | −0.998681 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −2.49495 | −0.190793 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −14.3167 | −1.08848 | −0.544240 | − | 0.838929i | \(-0.683182\pi\) | ||||
−0.544240 | + | 0.838929i | \(0.683182\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 5.49722 | 0.415551 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −6.58556 | −0.495001 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −15.6388 | −1.16890 | −0.584449 | − | 0.811430i | \(-0.698689\pi\) | ||||
−0.584449 | + | 0.811430i | \(0.698689\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −2.20115 | −0.163610 | −0.0818051 | − | 0.996648i | \(-0.526069\pi\) | ||||
−0.0818051 | + | 0.996648i | \(0.526069\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −3.25671 | −0.240743 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −24.7489 | −1.81958 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −14.3921 | −1.05245 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 2.29630 | 0.167031 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −16.9130 | −1.22378 | −0.611891 | − | 0.790942i | \(-0.709591\pi\) | ||||
−0.611891 | + | 0.790942i | \(0.709591\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −0.243254 | −0.0175098 | −0.00875491 | − | 0.999962i | \(-0.502787\pi\) | ||||
−0.00875491 | + | 0.999962i | \(0.502787\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0.356000 | 0.0254937 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −8.16812 | −0.581954 | −0.290977 | − | 0.956730i | \(-0.593980\pi\) | ||||
−0.290977 | + | 0.956730i | \(0.593980\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −2.34023 | −0.165894 | −0.0829471 | − | 0.996554i | \(-0.526433\pi\) | ||||
−0.0829471 | + | 0.996554i | \(0.526433\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 11.6688 | 0.823052 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −13.4558 | −0.944411 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 23.8832 | 1.66807 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −2.05324 | −0.142710 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 6.78421 | 0.469274 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −8.03191 | −0.552939 | −0.276470 | − | 0.961023i | \(-0.589165\pi\) | ||||
−0.276470 | + | 0.961023i | \(0.589165\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 10.5813 | 0.725017 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −19.4408 | −1.32585 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −0.636818 | −0.0432301 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −13.9938 | −0.945614 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −0.692944 | −0.0466124 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 21.4275 | 1.43489 | 0.717447 | − | 0.696613i | \(-0.245310\pi\) | ||||
0.717447 | + | 0.696613i | \(0.245310\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 2.39395 | 0.159597 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 1.04560 | 0.0693988 | 0.0346994 | − | 0.999398i | \(-0.488953\pi\) | ||||
0.0346994 | + | 0.999398i | \(0.488953\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −14.0173 | −0.926287 | −0.463144 | − | 0.886283i | \(-0.653279\pi\) | ||||
−0.463144 | + | 0.886283i | \(0.653279\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −6.24405 | −0.410829 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 9.82759 | 0.643827 | 0.321913 | − | 0.946769i | \(-0.395674\pi\) | ||||
0.321913 | + | 0.946769i | \(0.395674\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −3.17104 | −0.206856 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 1.32793 | 0.0862582 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −2.39155 | −0.154696 | −0.0773482 | − | 0.997004i | \(-0.524645\pi\) | ||||
−0.0773482 | + | 0.997004i | \(0.524645\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 9.59329 | 0.617958 | 0.308979 | − | 0.951069i | \(-0.400013\pi\) | ||||
0.308979 | + | 0.951069i | \(0.400013\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 4.69606 | 0.300020 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0.326643 | 0.0207838 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −15.3931 | −0.975497 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 16.4626 | 1.03911 | 0.519555 | − | 0.854437i | \(-0.326098\pi\) | ||||
0.519555 | + | 0.854437i | \(0.326098\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 5.58312 | 0.351008 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −14.3921 | −0.901268 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −24.4004 | −1.52205 | −0.761027 | − | 0.648720i | \(-0.775305\pi\) | ||||
−0.761027 | + | 0.648720i | \(0.775305\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 20.9000 | 1.29866 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −5.85977 | −0.362711 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −9.24379 | −0.569997 | −0.284998 | − | 0.958528i | \(-0.591993\pi\) | ||||
−0.284998 | + | 0.958528i | \(0.591993\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 4.11663 | 0.252882 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −0.650613 | −0.0398169 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −26.6107 | −1.62248 | −0.811242 | − | 0.584710i | \(-0.801208\pi\) | ||||
−0.811242 | + | 0.584710i | \(0.801208\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 25.3880 | 1.54221 | 0.771104 | − | 0.636709i | \(-0.219705\pi\) | ||||
0.771104 | + | 0.636709i | \(0.219705\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −0.300636 | −0.0181953 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −6.50958 | −0.392543 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −2.72565 | −0.163768 | −0.0818842 | − | 0.996642i | \(-0.526094\pi\) | ||||
−0.0818842 | + | 0.996642i | \(0.526094\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −0.277324 | −0.0166029 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 7.66109 | 0.457022 | 0.228511 | − | 0.973541i | \(-0.426614\pi\) | ||||
0.228511 | + | 0.973541i | \(0.426614\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −27.5196 | −1.63587 | −0.817934 | − | 0.575312i | \(-0.804881\pi\) | ||||
−0.817934 | + | 0.575312i | \(0.804881\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 6.78421 | 0.401862 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −20.1689 | −1.19053 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 11.0138 | 0.647869 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −16.5435 | −0.969795 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −3.58746 | −0.209582 | −0.104791 | − | 0.994494i | \(-0.533417\pi\) | ||||
−0.104791 | + | 0.994494i | \(0.533417\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 17.9073 | 1.04261 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −2.71918 | −0.157783 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0.268814 | 0.0155459 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 16.4174 | 0.946285 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −3.96140 | −0.227577 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 8.85558 | 0.507069 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −3.27758 | −0.187062 | −0.0935308 | − | 0.995616i | \(-0.529815\pi\) | ||||
−0.0935308 | + | 0.995616i | \(0.529815\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 3.85793 | 0.219470 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 24.2430 | 1.37469 | 0.687347 | − | 0.726329i | \(-0.258775\pi\) | ||||
0.687347 | + | 0.726329i | \(0.258775\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −5.06956 | −0.286548 | −0.143274 | − | 0.989683i | \(-0.545763\pi\) | ||||
−0.143274 | + | 0.989683i | \(0.545763\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −6.24405 | −0.351813 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −19.5721 | −1.09928 | −0.549639 | − | 0.835403i | \(-0.685235\pi\) | ||||
−0.549639 | + | 0.835403i | \(0.685235\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 15.9338 | 0.892120 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −13.1188 | −0.732220 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −13.2053 | −0.734760 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −0.313420 | −0.0173854 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 2.33140 | 0.128927 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 2.67789 | 0.147637 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 21.8103 | 1.19880 | 0.599401 | − | 0.800449i | \(-0.295405\pi\) | ||||
0.599401 | + | 0.800449i | \(0.295405\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 9.10161 | 0.498765 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −31.7295 | −1.73357 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 12.4451 | 0.677930 | 0.338965 | − | 0.940799i | \(-0.389923\pi\) | ||||
0.338965 | + | 0.940799i | \(0.389923\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 13.1549 | 0.714476 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0.754094 | 0.0408365 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −20.0398 | −1.08205 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 5.58312 | 0.300585 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −24.4597 | −1.31306 | −0.656532 | − | 0.754298i | \(-0.727977\pi\) | ||||
−0.656532 | + | 0.754298i | \(0.727977\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −10.6692 | −0.571107 | −0.285553 | − | 0.958363i | \(-0.592177\pi\) | ||||
−0.285553 | + | 0.958363i | \(0.592177\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −0.130922 | −0.00698809 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −23.5466 | −1.25326 | −0.626629 | − | 0.779318i | \(-0.715566\pi\) | ||||
−0.626629 | + | 0.779318i | \(0.715566\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −28.7724 | −1.52708 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 12.1539 | 0.643250 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 16.1523 | 0.852484 | 0.426242 | − | 0.904609i | \(-0.359837\pi\) | ||||
0.426242 | + | 0.904609i | \(0.359837\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −12.7752 | −0.672381 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −3.60605 | −0.189269 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 38.0517 | 1.99172 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −3.80007 | −0.198362 | −0.0991810 | − | 0.995069i | \(-0.531622\pi\) | ||||
−0.0991810 | + | 0.995069i | \(0.531622\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −8.78322 | −0.457236 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −3.47641 | −0.180486 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 19.5124 | 1.01031 | 0.505156 | − | 0.863028i | \(-0.331435\pi\) | ||||
0.505156 | + | 0.863028i | \(0.331435\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 7.08633 | 0.365936 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0.767172 | 0.0395113 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 0.918888 | 0.0472001 | 0.0236000 | − | 0.999721i | \(-0.492487\pi\) | ||||
0.0236000 | + | 0.999721i | \(0.492487\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 3.91471 | 0.200557 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −17.2962 | −0.883792 | −0.441896 | − | 0.897066i | \(-0.645694\pi\) | ||||
−0.441896 | + | 0.897066i | \(0.645694\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 16.9787 | 0.865315 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 7.14952 | 0.363431 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −31.7218 | −1.60836 | −0.804181 | − | 0.594385i | \(-0.797396\pi\) | ||||
−0.804181 | + | 0.594385i | \(0.797396\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −10.8674 | −0.549587 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 8.22025 | 0.414657 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −3.61088 | −0.181683 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −4.53970 | −0.227841 | −0.113920 | − | 0.993490i | \(-0.536341\pi\) | ||||
−0.113920 | + | 0.993490i | \(0.536341\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −5.72914 | −0.286816 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −5.11757 | −0.255559 | −0.127780 | − | 0.991803i | \(-0.540785\pi\) | ||||
−0.127780 | + | 0.991803i | \(0.540785\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0.0363078 | 0.00180862 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −2.71918 | −0.135117 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −24.7489 | −1.22676 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −9.84326 | −0.486718 | −0.243359 | − | 0.969936i | \(-0.578249\pi\) | ||||
−0.243359 | + | 0.969936i | \(0.578249\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 9.47880 | 0.467555 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −15.1224 | −0.744126 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 41.8566 | 2.05466 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −5.15967 | −0.252670 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −22.5715 | −1.10269 | −0.551345 | − | 0.834277i | \(-0.685885\pi\) | ||||
−0.551345 | + | 0.834277i | \(0.685885\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 6.15702 | 0.300075 | 0.150037 | − | 0.988680i | \(-0.452061\pi\) | ||||
0.150037 | + | 0.988680i | \(0.452061\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 1.16618 | 0.0567014 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 12.6707 | 0.614619 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −7.47837 | −0.361904 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0.356000 | 0.0171879 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 0.521526 | 0.0251210 | 0.0125605 | − | 0.999921i | \(-0.496002\pi\) | ||||
0.0125605 | + | 0.999921i | \(0.496002\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 6.11364 | 0.293803 | 0.146901 | − | 0.989151i | \(-0.453070\pi\) | ||||
0.146901 | + | 0.989151i | \(0.453070\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 15.9338 | 0.763966 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 5.12272 | 0.245053 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 13.0116 | 0.621012 | 0.310506 | − | 0.950571i | \(-0.399502\pi\) | ||||
0.310506 | + | 0.950571i | \(0.399502\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −1.72701 | −0.0822387 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −4.28260 | −0.203473 | −0.101736 | − | 0.994811i | \(-0.532440\pi\) | ||||
−0.101736 | + | 0.994811i | \(0.532440\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 1.76914 | 0.0838651 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −13.5693 | −0.641807 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 24.3609 | 1.14966 | 0.574831 | − | 0.818272i | \(-0.305068\pi\) | ||||
0.574831 | + | 0.818272i | \(0.305068\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 23.8832 | 1.12461 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 21.5430 | 1.01218 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0.817483 | 0.0383242 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −6.69421 | −0.313142 | −0.156571 | − | 0.987667i | \(-0.550044\pi\) | ||||
−0.156571 | + | 0.987667i | \(0.550044\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 5.29280 | 0.247047 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −2.94810 | −0.137307 | −0.0686533 | − | 0.997641i | \(-0.521870\pi\) | ||||
−0.0686533 | + | 0.997641i | \(0.521870\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −42.4252 | −1.97167 | −0.985833 | − | 0.167730i | \(-0.946356\pi\) | ||||
−0.985833 | + | 0.167730i | \(0.946356\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0.754094 | 0.0349703 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −11.7744 | −0.544853 | −0.272427 | − | 0.962177i | \(-0.587826\pi\) | ||||
−0.272427 | + | 0.962177i | \(0.587826\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 26.7950 | 1.23728 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −18.1301 | −0.835391 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −19.4408 | −0.893891 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −5.97277 | −0.274050 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −1.51392 | −0.0693177 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −7.48528 | −0.342011 | −0.171006 | − | 0.985270i | \(-0.554702\pi\) | ||||
−0.171006 | + | 0.985270i | \(0.554702\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1.19160 | −0.0543323 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −4.71484 | −0.214533 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 44.9847 | 2.04265 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −32.7190 | −1.48264 | −0.741319 | − | 0.671153i | \(-0.765800\pi\) | ||||
−0.741319 | + | 0.671153i | \(0.765800\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −9.67728 | −0.437622 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 15.0119 | 0.677477 | 0.338738 | − | 0.940881i | \(-0.390000\pi\) | ||||
0.338738 | + | 0.940881i | \(0.390000\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −31.0146 | −1.39683 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 7.39395 | 0.332333 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 24.2978 | 1.08990 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −25.5908 | −1.14560 | −0.572801 | − | 0.819694i | \(-0.694143\pi\) | ||||
−0.572801 | + | 0.819694i | \(0.694143\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −1.00000 | −0.0446767 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 4.56804 | 0.203679 | 0.101840 | − | 0.994801i | \(-0.467527\pi\) | ||||
0.101840 | + | 0.994801i | \(0.467527\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 10.7718 | 0.479337 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −12.9829 | −0.576589 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −19.6850 | −0.872524 | −0.436262 | − | 0.899820i | \(-0.643698\pi\) | ||||
−0.436262 | + | 0.899820i | \(0.643698\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −32.1340 | −1.42152 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −2.49495 | −0.110155 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −10.4904 | −0.462263 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −3.17104 | −0.139462 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −14.3167 | −0.628435 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 25.8709 | 1.13343 | 0.566713 | − | 0.823915i | \(-0.308215\pi\) | ||||
0.566713 | + | 0.823915i | \(0.308215\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −9.33225 | −0.408071 | −0.204035 | − | 0.978964i | \(-0.565406\pi\) | ||||
−0.204035 | + | 0.978964i | \(0.565406\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 5.49722 | 0.239918 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −1.46782 | −0.0639393 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −18.7842 | −0.816705 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −6.58556 | −0.285789 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 1.14992 | 0.0498084 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 35.6724 | 1.54225 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −15.6388 | −0.674864 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 4.69606 | 0.202274 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 8.57617 | 0.368718 | 0.184359 | − | 0.982859i | \(-0.440979\pi\) | ||||
0.184359 | + | 0.982859i | \(0.440979\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −2.20115 | −0.0944604 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −6.33951 | −0.271555 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 15.3088 | 0.654556 | 0.327278 | − | 0.944928i | \(-0.393869\pi\) | ||||
0.327278 | + | 0.944928i | \(0.393869\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −3.25671 | −0.138993 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 14.6198 | 0.622825 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 3.04932 | 0.129670 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −24.7489 | −1.05053 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −8.22455 | −0.348486 | −0.174243 | − | 0.984703i | \(-0.555748\pi\) | ||||
−0.174243 | + | 0.984703i | \(0.555748\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −0.936028 | −0.0395898 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −14.3921 | −0.607635 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 21.3271 | 0.898830 | 0.449415 | − | 0.893323i | \(-0.351632\pi\) | ||||
0.449415 | + | 0.893323i | \(0.351632\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −35.7705 | −1.50488 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 2.29630 | 0.0964355 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 10.5531 | 0.442407 | 0.221204 | − | 0.975228i | \(-0.429001\pi\) | ||||
0.221204 | + | 0.975228i | \(0.429001\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −6.43677 | −0.269371 | −0.134685 | − | 0.990888i | \(-0.543002\pi\) | ||||
−0.134685 | + | 0.990888i | \(0.543002\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −16.9130 | −0.706551 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −4.91535 | −0.204984 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −37.1930 | −1.54836 | −0.774182 | − | 0.632963i | \(-0.781839\pi\) | ||||
−0.774182 | + | 0.632963i | \(0.781839\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −0.243254 | −0.0101093 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −35.3471 | −1.46645 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 4.11663 | 0.170493 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0.356000 | 0.0147188 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −43.7880 | −1.80733 | −0.903663 | − | 0.428245i | \(-0.859132\pi\) | ||||
−0.903663 | + | 0.428245i | \(0.859132\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0.691908 | 0.0285096 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −8.16812 | −0.335992 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −29.7756 | −1.22274 | −0.611369 | − | 0.791346i | \(-0.709381\pi\) | ||||
−0.611369 | + | 0.791346i | \(0.709381\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −33.0485 | −1.35486 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −2.34023 | −0.0957791 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 18.7131 | 0.764595 | 0.382298 | − | 0.924039i | \(-0.375133\pi\) | ||||
0.382298 | + | 0.924039i | \(0.375133\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 15.6102 | 0.636753 | 0.318376 | − | 0.947964i | \(-0.396862\pi\) | ||||
0.318376 | + | 0.947964i | \(0.396862\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 11.6688 | 0.475189 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 9.80551 | 0.398651 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 27.5079 | 1.11651 | 0.558256 | − | 0.829669i | \(-0.311471\pi\) | ||||
0.558256 | + | 0.829669i | \(0.311471\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −13.4558 | −0.545256 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −0.152678 | −0.00617668 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 29.9599 | 1.21007 | 0.605034 | − | 0.796199i | \(-0.293159\pi\) | ||||
0.605034 | + | 0.796199i | \(0.293159\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 23.8832 | 0.963062 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 25.1911 | 1.01416 | 0.507078 | − | 0.861900i | \(-0.330726\pi\) | ||||
0.507078 | + | 0.861900i | \(0.330726\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 12.6419 | 0.508120 | 0.254060 | − | 0.967188i | \(-0.418234\pi\) | ||||
0.254060 | + | 0.967188i | \(0.418234\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −2.05324 | −0.0823936 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −1.49400 | −0.0598559 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −31.2388 | −1.24955 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 6.78421 | 0.270935 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 48.1731 | 1.92079 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 46.9107 | 1.86749 | 0.933744 | − | 0.357942i | \(-0.116522\pi\) | ||||
0.933744 | + | 0.357942i | \(0.116522\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −8.03191 | −0.319240 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −10.6448 | −0.422426 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0.226104 | 0.00895856 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 10.5813 | 0.418589 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −7.50494 | −0.296427 | −0.148214 | − | 0.988955i | \(-0.547352\pi\) | ||||
−0.148214 | + | 0.988955i | \(0.547352\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −28.5667 | −1.12656 | −0.563281 | − | 0.826266i | \(-0.690461\pi\) | ||||
−0.563281 | + | 0.826266i | \(0.690461\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −19.4408 | −0.765483 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 12.0671 | 0.474405 | 0.237202 | − | 0.971460i | \(-0.423770\pi\) | ||||
0.237202 | + | 0.971460i | \(0.423770\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 17.9073 | 0.702925 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −0.636818 | −0.0249589 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 10.8332 | 0.423934 | 0.211967 | − | 0.977277i | \(-0.432013\pi\) | ||||
0.211967 | + | 0.977277i | \(0.432013\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −22.3524 | −0.873379 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −13.9938 | −0.545951 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −17.3077 | −0.674211 | −0.337106 | − | 0.941467i | \(-0.609448\pi\) | ||||
−0.337106 | + | 0.941467i | \(0.609448\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 9.65536 | 0.375550 | 0.187775 | − | 0.982212i | \(-0.439872\pi\) | ||||
0.187775 | + | 0.982212i | \(0.439872\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −0.692944 | −0.0269117 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 15.5786 | 0.604111 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 12.0315 | 0.465861 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 21.4275 | 0.828437 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 8.85558 | 0.341866 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −2.27136 | −0.0875546 | −0.0437773 | − | 0.999041i | \(-0.513939\pi\) | ||||
−0.0437773 | + | 0.999041i | \(0.513939\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 2.39395 | 0.0921432 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 42.4522 | 1.63157 | 0.815785 | − | 0.578356i | \(-0.196305\pi\) | ||||
0.815785 | + | 0.578356i | \(0.196305\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −37.9887 | −1.45787 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 1.04560 | 0.0400674 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −26.2727 | −1.00530 | −0.502649 | − | 0.864491i | \(-0.667641\pi\) | ||||
−0.502649 | + | 0.864491i | \(0.667641\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −25.7746 | −0.984796 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −14.0173 | −0.534792 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 0.198205 | 0.00755102 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −4.24914 | −0.161645 | −0.0808225 | − | 0.996729i | \(-0.525755\pi\) | ||||
−0.0808225 | + | 0.996729i | \(0.525755\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −6.24405 | −0.237192 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 14.0301 | 0.532192 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −46.4879 | −1.76085 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 9.82759 | 0.371714 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 15.8974 | 0.600437 | 0.300219 | − | 0.953870i | \(-0.402940\pi\) | ||||
0.300219 | + | 0.953870i | \(0.402940\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −22.7080 | −0.856450 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −3.17104 | −0.119428 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −9.09656 | −0.342111 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 38.6638 | 1.45205 | 0.726025 | − | 0.687668i | \(-0.241366\pi\) | ||||
0.726025 | + | 0.687668i | \(0.241366\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 1.32793 | 0.0498012 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 0.569412 | 0.0213246 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −0.968029 | −0.0362022 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −2.39155 | −0.0893140 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 22.7418 | 0.848126 | 0.424063 | − | 0.905633i | \(-0.360603\pi\) | ||||
0.424063 | + | 0.905633i | \(0.360603\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 8.85897 | 0.329925 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 9.59329 | 0.356778 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −14.0280 | −0.520986 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 37.0957 | 1.37580 | 0.687902 | − | 0.725803i | \(-0.258532\pi\) | ||||
0.687902 | + | 0.725803i | \(0.258532\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 37.8410 | 1.39960 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −28.6271 | −1.05737 | −0.528683 | − | 0.848819i | \(-0.677314\pi\) | ||||
−0.528683 | + | 0.848819i | \(0.677314\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 4.69606 | 0.173217 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −31.7295 | −1.16877 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −1.48706 | −0.0547024 | −0.0273512 | − | 0.999626i | \(-0.508707\pi\) | ||||
−0.0273512 | + | 0.999626i | \(0.508707\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0.326643 | 0.0119995 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 29.0313 | 1.06506 | 0.532528 | − | 0.846413i | \(-0.321242\pi\) | ||||
0.532528 | + | 0.846413i | \(0.321242\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 36.8975 | 1.35182 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −15.3931 | −0.563204 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −30.1247 | −1.10073 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 44.7534 | 1.63307 | 0.816537 | − | 0.577293i | \(-0.195891\pi\) | ||||
0.816537 | + | 0.577293i | \(0.195891\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 16.4626 | 0.599931 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −58.5794 | −2.13192 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 24.5663 | 0.892878 | 0.446439 | − | 0.894814i | \(-0.352692\pi\) | ||||
0.446439 | + | 0.894814i | \(0.352692\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 5.58312 | 0.202655 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −16.5622 | −0.600379 | −0.300189 | − | 0.953880i | \(-0.597050\pi\) | ||||
−0.300189 | + | 0.953880i | \(0.597050\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 5.35360 | 0.193813 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −14.3921 | −0.520347 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0.862194 | 0.0311320 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −13.4445 | −0.484820 | −0.242410 | − | 0.970174i | \(-0.577938\pi\) | ||||
−0.242410 | + | 0.970174i | \(0.577938\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −24.4004 | −0.878758 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 52.2257 | 1.87843 | 0.939214 | − | 0.343333i | \(-0.111556\pi\) | ||||
0.939214 | + | 0.343333i | \(0.111556\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −0.663899 | −0.0238480 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 20.9000 | 0.749784 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 21.9137 | 0.785138 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −28.7724 | −1.02956 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −5.85977 | −0.209411 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 49.2990 | 1.75956 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 12.8705 | 0.458782 | 0.229391 | − | 0.973334i | \(-0.426326\pi\) | ||||
0.229391 | + | 0.973334i | \(0.426326\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −9.24379 | −0.329088 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 30.2076 | 1.07406 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0.426374 | 0.0151410 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 4.11663 | 0.146002 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −6.46623 | −0.229046 | −0.114523 | − | 0.993421i | \(-0.536534\pi\) | ||||
−0.114523 | + | 0.993421i | \(0.536534\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 6.17234 | 0.218362 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −0.650613 | −0.0229883 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 38.0517 | 1.34282 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 12.8205 | 0.451864 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −26.6107 | −0.936742 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −15.0052 | −0.527554 | −0.263777 | − | 0.964584i | \(-0.584968\pi\) | ||||
−0.263777 | + | 0.964584i | \(0.584968\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −20.6709 | −0.725852 | −0.362926 | − | 0.931818i | \(-0.618222\pi\) | ||||
−0.362926 | + | 0.931818i | \(0.618222\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 25.3880 | 0.890394 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 26.3143 | 0.921749 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −17.8377 | −0.624061 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −0.300636 | −0.0105051 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −27.2144 | −0.949787 | −0.474894 | − | 0.880043i | \(-0.657514\pi\) | ||||
−0.474894 | + | 0.880043i | \(0.657514\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 38.5039 | 1.34216 | 0.671081 | − | 0.741384i | \(-0.265830\pi\) | ||||
0.671081 | + | 0.741384i | \(0.265830\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −6.50958 | −0.226635 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 38.3481 | 1.33349 | 0.666747 | − | 0.745284i | \(-0.267686\pi\) | ||||
0.666747 | + | 0.745284i | \(0.267686\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 0.845959 | 0.0293814 | 0.0146907 | − | 0.999892i | \(-0.495324\pi\) | ||||
0.0146907 | + | 0.999892i | \(0.495324\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −2.72565 | −0.0945518 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −9.14074 | −0.316708 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 2.71918 | 0.0941012 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −0.277324 | −0.00958572 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −21.2959 | −0.735215 | −0.367607 | − | 0.929981i | \(-0.619823\pi\) | ||||
−0.367607 | + | 0.929981i | \(0.619823\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 5.33689 | 0.184031 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 7.66109 | 0.263862 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 35.3028 | 1.21445 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −8.28057 | −0.284524 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −27.5196 | −0.944469 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −18.6878 | −0.640608 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −5.56671 | −0.190601 | −0.0953003 | − | 0.995449i | \(-0.530381\pi\) | ||||
−0.0953003 | + | 0.995449i | \(0.530381\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 6.78421 | 0.232015 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −8.55275 | −0.292156 | −0.146078 | − | 0.989273i | \(-0.546665\pi\) | ||||
−0.146078 | + | 0.989273i | \(0.546665\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −16.4240 | −0.560378 | −0.280189 | − | 0.959945i | \(-0.590397\pi\) | ||||
−0.280189 | + | 0.959945i | \(0.590397\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −20.1689 | −0.687354 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −33.2268 | −1.13105 | −0.565526 | − | 0.824730i | \(-0.691327\pi\) | ||||
−0.565526 | + | 0.824730i | \(0.691327\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 38.9298 | 1.32365 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 11.0138 | 0.374047 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −3.61088 | −0.122491 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −1.52770 | −0.0517640 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −16.5435 | −0.559912 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 16.2723 | 0.550105 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −4.82148 | −0.162810 | −0.0814049 | − | 0.996681i | \(-0.525941\pi\) | ||||
−0.0814049 | + | 0.996681i | \(0.525941\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −3.58746 | −0.121002 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −15.4398 | −0.520180 | −0.260090 | − | 0.965584i | \(-0.583752\pi\) | ||||
−0.260090 | + | 0.965584i | \(0.583752\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −7.82614 | −0.263371 | −0.131685 | − | 0.991292i | \(-0.542039\pi\) | ||||
−0.131685 | + | 0.991292i | \(0.542039\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 17.9073 | 0.601949 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 22.8275 | 0.766474 | 0.383237 | − | 0.923650i | \(-0.374809\pi\) | ||||
0.383237 | + | 0.923650i | \(0.374809\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 8.98934 | 0.301493 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −2.71918 | −0.0910960 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −2.90954 | −0.0973642 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 42.5247 | 1.42145 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0.268814 | 0.00897542 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 1.62505 | 0.0541986 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −8.01289 | −0.266948 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 16.4174 | 0.546338 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 5.98533 | 0.198959 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 35.9162 | 1.19258 | 0.596289 | − | 0.802770i | \(-0.296641\pi\) | ||||
0.596289 | + | 0.802770i | \(0.296641\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −3.96140 | −0.131391 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −16.2051 | −0.536899 | −0.268449 | − | 0.963294i | \(-0.586511\pi\) | ||||
−0.268449 | + | 0.963294i | \(0.586511\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 41.8566 | 1.38525 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 8.85558 | 0.292756 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 18.8762 | 0.623346 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −44.6831 | −1.47396 | −0.736979 | − | 0.675915i | \(-0.763749\pi\) | ||||
−0.736979 | + | 0.675915i | \(0.763749\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −3.27758 | −0.108000 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −1.38532 | −0.0455983 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 21.7888 | 0.716411 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 3.85793 | 0.126711 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −45.4092 | −1.48983 | −0.744914 | − | 0.667161i | \(-0.767509\pi\) | ||||
−0.744914 | + | 0.667161i | \(0.767509\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 4.30880 | 0.141215 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 24.2430 | 0.793680 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 39.1347 | 1.27984 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −47.6798 | −1.55763 | −0.778815 | − | 0.627253i | \(-0.784179\pi\) | ||||
−0.778815 | + | 0.627253i | \(0.784179\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −5.06956 | −0.165439 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −35.3734 | −1.15314 | −0.576570 | − | 0.817048i | \(-0.695609\pi\) | ||||
−0.576570 | + | 0.817048i | \(0.695609\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 18.0340 | 0.587269 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −6.24405 | −0.203119 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 50.4841 | 1.64051 | 0.820257 | − | 0.571995i | \(-0.193830\pi\) | ||||
0.820257 | + | 0.571995i | \(0.193830\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 1.83210 | 0.0594723 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −19.5721 | −0.634668 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 25.9394 | 0.840259 | 0.420130 | − | 0.907464i | \(-0.361985\pi\) | ||||
0.420130 | + | 0.907464i | \(0.361985\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 45.9896 | 1.48819 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 15.9338 | 0.515066 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 21.7661 | 0.702866 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −30.9231 | −0.997519 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −13.1188 | −0.422747 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0.661453 | 0.0212929 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −9.50298 | −0.305595 | −0.152798 | − | 0.988257i | \(-0.548828\pi\) | ||||
−0.152798 | + | 0.988257i | \(0.548828\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −13.2053 | −0.424214 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 22.0186 | 0.706609 | 0.353305 | − | 0.935508i | \(-0.385058\pi\) | ||||
0.353305 | + | 0.935508i | \(0.385058\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −11.8481 | −0.379834 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −0.313420 | −0.0100375 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −49.7763 | −1.59248 | −0.796242 | − | 0.604978i | \(-0.793182\pi\) | ||||
−0.796242 | + | 0.604978i | \(0.793182\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 1.76914 | 0.0565418 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 2.33140 | 0.0744360 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 31.4675 | 1.00366 | 0.501828 | − | 0.864967i | \(-0.332661\pi\) | ||||
0.501828 | + | 0.864967i | \(0.332661\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 22.2106 | 0.707689 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 2.67789 | 0.0852381 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −14.6797 | −0.466786 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −28.2915 | −0.898708 | −0.449354 | − | 0.893354i | \(-0.648346\pi\) | ||||
−0.449354 | + | 0.893354i | \(0.648346\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 21.8103 | 0.692129 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 6.36350 | 0.201737 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 48.7224 | 1.54305 | 0.771527 | − | 0.636197i | \(-0.219494\pi\) | ||||
0.771527 | + | 0.636197i | \(0.219494\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 9.10161 | 0.287962 |
(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 | 8016.2.a.t.1.2 | 5 | ||
4.3 | odd | 2 | 2004.2.a.a.1.2 | ✓ | 5 | ||
12.11 | even | 2 | 6012.2.a.e.1.4 | 5 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2004.2.a.a.1.2 | ✓ | 5 | 4.3 | odd | 2 | ||
6012.2.a.e.1.4 | 5 | 12.11 | even | 2 | |||
8016.2.a.t.1.2 | 5 | 1.1 | even | 1 | trivial |