Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6032,2,Mod(1,6032)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6032, 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("6032.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6032 = 2^{4} \cdot 13 \cdot 29 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6032.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: | \(48.1657624992\) |
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: | \( x^{10} - 3x^{9} - 17x^{8} + 47x^{7} + 104x^{6} - 235x^{5} - 283x^{4} + 364x^{3} + 330x^{2} + 12x - 8 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 3016) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.5 | ||
Root | \(0.131336\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6032.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −0.131336 | −0.0758266 | −0.0379133 | − | 0.999281i | \(-0.512071\pi\) | ||||
−0.0379133 | + | 0.999281i | \(0.512071\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −0.686438 | −0.306984 | −0.153492 | − | 0.988150i | \(-0.549052\pi\) | ||||
−0.153492 | + | 0.988150i | \(0.549052\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 3.43967 | 1.30007 | 0.650036 | − | 0.759904i | \(-0.274754\pi\) | ||||
0.650036 | + | 0.759904i | \(0.274754\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.98275 | −0.994250 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 5.55935 | 1.67621 | 0.838104 | − | 0.545511i | \(-0.183664\pi\) | ||||
0.838104 | + | 0.545511i | \(0.183664\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.00000 | −0.277350 | ||||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0.0901537 | 0.0232776 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −2.53126 | −0.613920 | −0.306960 | − | 0.951722i | \(-0.599312\pi\) | ||||
−0.306960 | + | 0.951722i | \(0.599312\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.08516 | −0.248953 | −0.124477 | − | 0.992223i | \(-0.539725\pi\) | ||||
−0.124477 | + | 0.992223i | \(0.539725\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −0.451750 | −0.0985800 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −3.63335 | −0.757605 | −0.378803 | − | 0.925478i | \(-0.623664\pi\) | ||||
−0.378803 | + | 0.925478i | \(0.623664\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.52880 | −0.905761 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0.785748 | 0.151217 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −1.00000 | −0.185695 | ||||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −5.76606 | −1.03562 | −0.517808 | − | 0.855497i | \(-0.673252\pi\) | ||||
−0.517808 | + | 0.855497i | \(0.673252\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −0.730140 | −0.127101 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −2.36112 | −0.399101 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 3.06448 | 0.503797 | 0.251899 | − | 0.967754i | \(-0.418945\pi\) | ||||
0.251899 | + | 0.967754i | \(0.418945\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0.131336 | 0.0210305 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 5.52019 | 0.862108 | 0.431054 | − | 0.902326i | \(-0.358142\pi\) | ||||
0.431054 | + | 0.902326i | \(0.358142\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −10.6453 | −1.62340 | −0.811700 | − | 0.584075i | \(-0.801457\pi\) | ||||
−0.811700 | + | 0.584075i | \(0.801457\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 2.04747 | 0.305219 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −1.05741 | −0.154239 | −0.0771194 | − | 0.997022i | \(-0.524572\pi\) | ||||
−0.0771194 | + | 0.997022i | \(0.524572\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 4.83130 | 0.690185 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0.332444 | 0.0465515 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −0.809282 | −0.111163 | −0.0555817 | − | 0.998454i | \(-0.517701\pi\) | ||||
−0.0555817 | + | 0.998454i | \(0.517701\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −3.81615 | −0.514569 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0.142520 | 0.0188773 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −8.17579 | −1.06440 | −0.532198 | − | 0.846620i | \(-0.678634\pi\) | ||||
−0.532198 | + | 0.846620i | \(0.678634\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −4.04037 | −0.517316 | −0.258658 | − | 0.965969i | \(-0.583280\pi\) | ||||
−0.258658 | + | 0.965969i | \(0.583280\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −10.2597 | −1.29260 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0.686438 | 0.0851421 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 8.59220 | 1.04970 | 0.524852 | − | 0.851193i | \(-0.324121\pi\) | ||||
0.524852 | + | 0.851193i | \(0.324121\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0.477188 | 0.0574466 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −14.5698 | −1.72912 | −0.864561 | − | 0.502528i | \(-0.832403\pi\) | ||||
−0.864561 | + | 0.502528i | \(0.832403\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −14.0357 | −1.64275 | −0.821377 | − | 0.570386i | \(-0.806794\pi\) | ||||
−0.821377 | + | 0.570386i | \(0.806794\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0.594793 | 0.0686808 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 19.1223 | 2.17919 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 7.02545 | 0.790425 | 0.395213 | − | 0.918590i | \(-0.370671\pi\) | ||||
0.395213 | + | 0.918590i | \(0.370671\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 8.84506 | 0.982784 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −8.52803 | −0.936073 | −0.468037 | − | 0.883709i | \(-0.655038\pi\) | ||||
−0.468037 | + | 0.883709i | \(0.655038\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.73755 | 0.188464 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0.131336 | 0.0140807 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −1.84349 | −0.195409 | −0.0977047 | − | 0.995215i | \(-0.531150\pi\) | ||||
−0.0977047 | + | 0.995215i | \(0.531150\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −3.43967 | −0.360575 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0.757289 | 0.0785272 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0.744897 | 0.0764248 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 14.2896 | 1.45088 | 0.725442 | − | 0.688283i | \(-0.241635\pi\) | ||||
0.725442 | + | 0.688283i | \(0.241635\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −16.5822 | −1.66657 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −3.52214 | −0.350466 | −0.175233 | − | 0.984527i | \(-0.556068\pi\) | ||||
−0.175233 | + | 0.984527i | \(0.556068\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1.06761 | 0.105195 | 0.0525975 | − | 0.998616i | \(-0.483250\pi\) | ||||
0.0525975 | + | 0.998616i | \(0.483250\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0.310099 | 0.0302625 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −2.41480 | −0.233447 | −0.116724 | − | 0.993164i | \(-0.537239\pi\) | ||||
−0.116724 | + | 0.993164i | \(0.537239\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −4.72653 | −0.452719 | −0.226360 | − | 0.974044i | \(-0.572682\pi\) | ||||
−0.226360 | + | 0.974044i | \(0.572682\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −0.402475 | −0.0382013 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −9.98385 | −0.939202 | −0.469601 | − | 0.882879i | \(-0.655602\pi\) | ||||
−0.469601 | + | 0.882879i | \(0.655602\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 2.49407 | 0.232573 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 2.98275 | 0.275755 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −8.70668 | −0.798140 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 19.9064 | 1.80967 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −0.724997 | −0.0653708 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 6.54093 | 0.585039 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 10.0684 | 0.893422 | 0.446711 | − | 0.894678i | \(-0.352595\pi\) | ||||
0.446711 | + | 0.894678i | \(0.352595\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 1.39811 | 0.123097 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 9.64133 | 0.842367 | 0.421184 | − | 0.906975i | \(-0.361615\pi\) | ||||
0.421184 | + | 0.906975i | \(0.361615\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −3.73260 | −0.323657 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −0.539367 | −0.0464213 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 0.270066 | 0.0230733 | 0.0115366 | − | 0.999933i | \(-0.496328\pi\) | ||||
0.0115366 | + | 0.999933i | \(0.496328\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 11.6477 | 0.987947 | 0.493974 | − | 0.869477i | \(-0.335544\pi\) | ||||
0.493974 | + | 0.869477i | \(0.335544\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0.138875 | 0.0116954 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −5.55935 | −0.464896 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0.686438 | 0.0570056 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −0.634521 | −0.0523344 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −13.0255 | −1.06709 | −0.533543 | − | 0.845773i | \(-0.679140\pi\) | ||||
−0.533543 | + | 0.845773i | \(0.679140\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 4.79500 | 0.390211 | 0.195106 | − | 0.980782i | \(-0.437495\pi\) | ||||
0.195106 | + | 0.980782i | \(0.437495\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 7.55011 | 0.610390 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 3.95804 | 0.317918 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −8.66128 | −0.691246 | −0.345623 | − | 0.938374i | \(-0.612332\pi\) | ||||
−0.345623 | + | 0.938374i | \(0.612332\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0.106288 | 0.00842915 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −12.4975 | −0.984941 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −20.0406 | −1.56970 | −0.784851 | − | 0.619685i | \(-0.787260\pi\) | ||||
−0.784851 | + | 0.619685i | \(0.787260\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0.501196 | 0.0390181 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 21.7096 | 1.67994 | 0.839970 | − | 0.542632i | \(-0.182572\pi\) | ||||
0.839970 | + | 0.542632i | \(0.182572\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 3.23677 | 0.247522 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 18.1395 | 1.37912 | 0.689562 | − | 0.724226i | \(-0.257803\pi\) | ||||
0.689562 | + | 0.724226i | \(0.257803\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −15.5776 | −1.17755 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 1.07377 | 0.0807096 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 23.8752 | 1.78452 | 0.892259 | − | 0.451525i | \(-0.149120\pi\) | ||||
0.892259 | + | 0.451525i | \(0.149120\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 0.0264796 | 0.00196821 | 0.000984105 | − | 1.00000i | \(-0.499687\pi\) | ||||
0.000984105 | 1.00000i | \(0.499687\pi\) | ||||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0.530644 | 0.0392263 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −2.10357 | −0.154658 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −14.0721 | −1.02906 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 2.70271 | 0.196593 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −19.3928 | −1.40322 | −0.701608 | − | 0.712563i | \(-0.747534\pi\) | ||||
−0.701608 | + | 0.712563i | \(0.747534\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −4.47916 | −0.322417 | −0.161209 | − | 0.986920i | \(-0.551539\pi\) | ||||
−0.161209 | + | 0.986920i | \(0.551539\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −0.0901537 | −0.00645604 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −15.4136 | −1.09817 | −0.549086 | − | 0.835766i | \(-0.685024\pi\) | ||||
−0.549086 | + | 0.835766i | \(0.685024\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 2.79503 | 0.198134 | 0.0990672 | − | 0.995081i | \(-0.468414\pi\) | ||||
0.0990672 | + | 0.995081i | \(0.468414\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −1.12846 | −0.0795956 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −3.43967 | −0.241417 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −3.78927 | −0.264654 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 10.8374 | 0.753249 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −6.03280 | −0.417297 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −11.3167 | −0.779070 | −0.389535 | − | 0.921012i | \(-0.627364\pi\) | ||||
−0.389535 | + | 0.921012i | \(0.627364\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 1.91354 | 0.131113 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 7.30737 | 0.498358 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −19.8333 | −1.34637 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 1.84339 | 0.124565 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 2.53126 | 0.170271 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −22.2875 | −1.49248 | −0.746241 | − | 0.665675i | \(-0.768144\pi\) | ||||
−0.746241 | + | 0.665675i | \(0.768144\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 13.5083 | 0.900553 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −27.3103 | −1.81265 | −0.906325 | − | 0.422582i | \(-0.861124\pi\) | ||||
−0.906325 | + | 0.422582i | \(0.861124\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −7.75270 | −0.512313 | −0.256156 | − | 0.966635i | \(-0.582456\pi\) | ||||
−0.256156 | + | 0.966635i | \(0.582456\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −2.51144 | −0.165241 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −13.9292 | −0.912532 | −0.456266 | − | 0.889843i | \(-0.650813\pi\) | ||||
−0.456266 | + | 0.889843i | \(0.650813\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0.725845 | 0.0473489 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −0.922692 | −0.0599353 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −16.4918 | −1.06677 | −0.533384 | − | 0.845873i | \(-0.679080\pi\) | ||||
−0.533384 | + | 0.845873i | \(0.679080\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 7.44009 | 0.479258 | 0.239629 | − | 0.970865i | \(-0.422974\pi\) | ||||
0.239629 | + | 0.970865i | \(0.422974\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −3.51892 | −0.225739 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −3.31638 | −0.211876 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1.08516 | 0.0690473 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 1.12003 | 0.0709793 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −24.2320 | −1.52951 | −0.764754 | − | 0.644322i | \(-0.777140\pi\) | ||||
−0.764754 | + | 0.644322i | \(0.777140\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −20.1990 | −1.26990 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −0.228202 | −0.0142906 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 10.7838 | 0.672674 | 0.336337 | − | 0.941742i | \(-0.390812\pi\) | ||||
0.336337 | + | 0.941742i | \(0.390812\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 10.5408 | 0.654973 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 2.98275 | 0.184628 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 28.8496 | 1.77894 | 0.889470 | − | 0.456994i | \(-0.151074\pi\) | ||||
0.889470 | + | 0.456994i | \(0.151074\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0.555522 | 0.0341254 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0.242116 | 0.0148172 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −4.59148 | −0.279948 | −0.139974 | − | 0.990155i | \(-0.544702\pi\) | ||||
−0.139974 | + | 0.990155i | \(0.544702\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −0.423401 | −0.0257198 | −0.0128599 | − | 0.999917i | \(-0.504094\pi\) | ||||
−0.0128599 | + | 0.999917i | \(0.504094\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0.451750 | 0.0273412 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −25.1772 | −1.51824 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 8.11882 | 0.487812 | 0.243906 | − | 0.969799i | \(-0.421571\pi\) | ||||
0.243906 | + | 0.969799i | \(0.421571\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 17.1987 | 1.02966 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 30.3456 | 1.81027 | 0.905134 | − | 0.425127i | \(-0.139771\pi\) | ||||
0.905134 | + | 0.425127i | \(0.139771\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −16.3570 | −0.972322 | −0.486161 | − | 0.873869i | \(-0.661603\pi\) | ||||
−0.486161 | + | 0.873869i | \(0.661603\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −0.0978314 | −0.00579503 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 18.9876 | 1.12080 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −10.5927 | −0.623102 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −1.87673 | −0.110016 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 1.53200 | 0.0895002 | 0.0447501 | − | 0.998998i | \(-0.485751\pi\) | ||||
0.0447501 | + | 0.998998i | \(0.485751\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 5.61217 | 0.326753 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 4.36825 | 0.253471 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 3.63335 | 0.210122 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −36.6164 | −2.11054 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0.462582 | 0.0265747 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 2.77346 | 0.158808 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −22.5274 | −1.28571 | −0.642853 | − | 0.765989i | \(-0.722250\pi\) | ||||
−0.642853 | + | 0.765989i | \(0.722250\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −0.140215 | −0.00797658 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 9.58495 | 0.543512 | 0.271756 | − | 0.962366i | \(-0.412396\pi\) | ||||
0.271756 | + | 0.962366i | \(0.412396\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 10.2299 | 0.578230 | 0.289115 | − | 0.957294i | \(-0.406639\pi\) | ||||
0.289115 | + | 0.957294i | \(0.406639\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 7.04262 | 0.396807 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 13.5846 | 0.762985 | 0.381492 | − | 0.924372i | \(-0.375410\pi\) | ||||
0.381492 | + | 0.924372i | \(0.375410\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −5.55935 | −0.311264 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0.317149 | 0.0177015 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 2.74683 | 0.152837 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 4.52880 | 0.251213 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0.620761 | 0.0343282 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −3.63713 | −0.200521 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −4.15749 | −0.228516 | −0.114258 | − | 0.993451i | \(-0.536449\pi\) | ||||
−0.114258 | + | 0.993451i | \(0.536449\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −9.14058 | −0.500901 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −5.89801 | −0.322243 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −23.6977 | −1.29090 | −0.645449 | − | 0.763803i | \(-0.723330\pi\) | ||||
−0.645449 | + | 0.763803i | \(0.723330\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 1.31124 | 0.0712165 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −32.0556 | −1.73591 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −7.45962 | −0.402781 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −0.327560 | −0.0176352 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −30.5937 | −1.64236 | −0.821179 | − | 0.570671i | \(-0.806683\pi\) | ||||
−0.821179 | + | 0.570671i | \(0.806683\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 9.56661 | 0.512089 | 0.256044 | − | 0.966665i | \(-0.417581\pi\) | ||||
0.256044 | + | 0.966665i | \(0.417581\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −0.785748 | −0.0419401 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 25.2989 | 1.34653 | 0.673263 | − | 0.739403i | \(-0.264892\pi\) | ||||
0.673263 | + | 0.739403i | \(0.264892\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 10.0013 | 0.530813 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 1.14350 | 0.0605203 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −8.24933 | −0.435383 | −0.217691 | − | 0.976018i | \(-0.569853\pi\) | ||||
−0.217691 | + | 0.976018i | \(0.569853\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −17.8224 | −0.938022 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −2.61441 | −0.137221 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 9.63463 | 0.504300 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −31.5997 | −1.64949 | −0.824746 | − | 0.565504i | \(-0.808682\pi\) | ||||
−0.824746 | + | 0.565504i | \(0.808682\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −16.4653 | −0.857152 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −2.78366 | −0.144520 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −21.2294 | −1.09922 | −0.549609 | − | 0.835422i | \(-0.685223\pi\) | ||||
−0.549609 | + | 0.835422i | \(0.685223\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −0.859057 | −0.0443615 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 1.00000 | 0.0515026 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −5.74408 | −0.295053 | −0.147527 | − | 0.989058i | \(-0.547131\pi\) | ||||
−0.147527 | + | 0.989058i | \(0.547131\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −1.32233 | −0.0677452 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 1.05900 | 0.0541122 | 0.0270561 | − | 0.999634i | \(-0.491387\pi\) | ||||
0.0270561 | + | 0.999634i | \(0.491387\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −13.1263 | −0.668977 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 31.7524 | 1.61407 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 15.7816 | 0.800161 | 0.400080 | − | 0.916480i | \(-0.368982\pi\) | ||||
0.400080 | + | 0.916480i | \(0.368982\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 9.19693 | 0.465109 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −1.26625 | −0.0638739 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −4.82254 | −0.242648 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −31.3536 | −1.57359 | −0.786797 | − | 0.617212i | \(-0.788262\pi\) | ||||
−0.786797 | + | 0.617212i | \(0.788262\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0.490223 | 0.0245418 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 26.2074 | 1.30873 | 0.654367 | − | 0.756177i | \(-0.272935\pi\) | ||||
0.654367 | + | 0.756177i | \(0.272935\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 5.76606 | 0.287228 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −6.07158 | −0.301699 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 17.0365 | 0.844469 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 24.1192 | 1.19262 | 0.596309 | − | 0.802755i | \(-0.296633\pi\) | ||||
0.596309 | + | 0.802755i | \(0.296633\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −0.0354693 | −0.00174957 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −28.1220 | −1.38379 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 5.85396 | 0.287360 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −1.52976 | −0.0749127 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −29.8130 | −1.45646 | −0.728229 | − | 0.685334i | \(-0.759656\pi\) | ||||
−0.728229 | + | 0.685334i | \(0.759656\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −13.4782 | −0.656885 | −0.328443 | − | 0.944524i | \(-0.606524\pi\) | ||||
−0.328443 | + | 0.944524i | \(0.606524\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 3.15399 | 0.153352 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 11.4636 | 0.556065 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −13.8975 | −0.672547 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0.730140 | 0.0352515 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −3.98838 | −0.192114 | −0.0960568 | − | 0.995376i | \(-0.530623\pi\) | ||||
−0.0960568 | + | 0.995376i | \(0.530623\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 28.7223 | 1.38030 | 0.690152 | − | 0.723664i | \(-0.257544\pi\) | ||||
0.690152 | + | 0.723664i | \(0.257544\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −0.0901537 | −0.00432254 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 3.94277 | 0.188608 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 26.9165 | 1.28465 | 0.642327 | − | 0.766431i | \(-0.277969\pi\) | ||||
0.642327 | + | 0.766431i | \(0.277969\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −14.4106 | −0.686217 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −10.3369 | −0.491122 | −0.245561 | − | 0.969381i | \(-0.578972\pi\) | ||||
−0.245561 | + | 0.969381i | \(0.578972\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 1.26544 | 0.0599876 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 1.71071 | 0.0809136 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 1.37807 | 0.0650349 | 0.0325175 | − | 0.999471i | \(-0.489648\pi\) | ||||
0.0325175 | + | 0.999471i | \(0.489648\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 30.6887 | 1.44507 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −0.629754 | −0.0295884 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 2.36112 | 0.110691 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −10.4675 | −0.489648 | −0.244824 | − | 0.969568i | \(-0.578730\pi\) | ||||
−0.244824 | + | 0.969568i | \(0.578730\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −1.98893 | −0.0928353 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 10.3355 | 0.481373 | 0.240686 | − | 0.970603i | \(-0.422627\pi\) | ||||
0.240686 | + | 0.970603i | \(0.422627\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 22.7588 | 1.05769 | 0.528846 | − | 0.848718i | \(-0.322625\pi\) | ||||
0.528846 | + | 0.848718i | \(0.322625\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −0.519832 | −0.0241066 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 11.5363 | 0.533837 | 0.266918 | − | 0.963719i | \(-0.413995\pi\) | ||||
0.266918 | + | 0.963719i | \(0.413995\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 29.5543 | 1.36469 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 1.13753 | 0.0524148 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −59.1812 | −2.72115 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 4.91449 | 0.225492 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 2.41389 | 0.110524 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −17.3214 | −0.791433 | −0.395716 | − | 0.918373i | \(-0.629504\pi\) | ||||
−0.395716 | + | 0.918373i | \(0.629504\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −3.06448 | −0.139728 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 1.64137 | 0.0746847 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −9.80889 | −0.445399 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −23.1290 | −1.04808 | −0.524038 | − | 0.851695i | \(-0.675575\pi\) | ||||
−0.524038 | + | 0.851695i | \(0.675575\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 2.63205 | 0.119025 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −15.3238 | −0.691552 | −0.345776 | − | 0.938317i | \(-0.612384\pi\) | ||||
−0.345776 | + | 0.938317i | \(0.612384\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 2.53126 | 0.114002 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 11.3826 | 0.511611 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −50.1154 | −2.24798 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 20.0357 | 0.896922 | 0.448461 | − | 0.893802i | \(-0.351972\pi\) | ||||
0.448461 | + | 0.893802i | \(0.351972\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −2.85125 | −0.127384 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 10.1268 | 0.451530 | 0.225765 | − | 0.974182i | \(-0.427512\pi\) | ||||
0.225765 | + | 0.974182i | \(0.427512\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 2.41773 | 0.107588 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −0.131336 | −0.00583282 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 41.7942 | 1.85250 | 0.926248 | − | 0.376915i | \(-0.123015\pi\) | ||||
0.926248 | + | 0.376915i | \(0.123015\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −48.2781 | −2.13570 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −0.852665 | −0.0376461 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −0.732849 | −0.0322932 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −5.87850 | −0.258536 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −2.38237 | −0.104574 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −12.1787 | −0.533561 | −0.266780 | − | 0.963757i | \(-0.585960\pi\) | ||||
−0.266780 | + | 0.963757i | \(0.585960\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −11.3592 | −0.496703 | −0.248352 | − | 0.968670i | \(-0.579889\pi\) | ||||
−0.248352 | + | 0.968670i | \(0.579889\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 2.04589 | 0.0892899 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 14.5954 | 0.635785 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −9.79879 | −0.426035 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 24.3863 | 1.05828 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −5.52019 | −0.239106 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 1.65761 | 0.0716646 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −3.13567 | −0.135314 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 26.8589 | 1.15689 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −8.44789 | −0.363203 | −0.181602 | − | 0.983372i | \(-0.558128\pi\) | ||||
−0.181602 | + | 0.983372i | \(0.558128\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −0.00347771 | −0.000149243 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 3.24447 | 0.138978 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −22.4946 | −0.961801 | −0.480901 | − | 0.876775i | \(-0.659690\pi\) | ||||
−0.480901 | + | 0.876775i | \(0.659690\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 12.0514 | 0.514341 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1.08516 | 0.0462295 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 24.1652 | 1.02761 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0.276274 | 0.0117272 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 42.5787 | 1.80412 | 0.902058 | − | 0.431615i | \(-0.142056\pi\) | ||||
0.902058 | + | 0.431615i | \(0.142056\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 10.6453 | 0.450250 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 1.84817 | 0.0780299 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −4.63542 | −0.195360 | −0.0976799 | − | 0.995218i | \(-0.531142\pi\) | ||||
−0.0976799 | + | 0.995218i | \(0.531142\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 6.85329 | 0.288320 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 30.4240 | 1.27769 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −29.7859 | −1.24869 | −0.624344 | − | 0.781149i | \(-0.714634\pi\) | ||||
−0.624344 | + | 0.781149i | \(0.714634\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −46.6867 | −1.95378 | −0.976890 | − | 0.213744i | \(-0.931434\pi\) | ||||
−0.976890 | + | 0.213744i | \(0.931434\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 2.54697 | 0.106401 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 16.4547 | 0.686209 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −11.2276 | −0.467411 | −0.233705 | − | 0.972307i | \(-0.575085\pi\) | ||||
−0.233705 | + | 0.972307i | \(0.575085\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0.588274 | 0.0244478 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −29.3336 | −1.21696 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −4.49908 | −0.186333 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −2.04747 | −0.0846526 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 47.3001 | 1.95228 | 0.976142 | − | 0.217135i | \(-0.0696712\pi\) | ||||
0.976142 | + | 0.217135i | \(0.0696712\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 6.25712 | 0.257820 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 2.02435 | 0.0832707 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 1.92154 | 0.0789084 | 0.0394542 | − | 0.999221i | \(-0.487438\pi\) | ||||
0.0394542 | + | 0.999221i | \(0.487438\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 5.97659 | 0.245016 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −0.367087 | −0.0150239 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 42.2462 | 1.72613 | 0.863067 | − | 0.505089i | \(-0.168540\pi\) | ||||
0.863067 | + | 0.505089i | \(0.168540\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −29.7707 | −1.21437 | −0.607187 | − | 0.794559i | \(-0.707702\pi\) | ||||
−0.607187 | + | 0.794559i | \(0.707702\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −25.6284 | −1.04367 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −13.6645 | −0.555540 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 10.9173 | 0.443119 | 0.221560 | − | 0.975147i | \(-0.428885\pi\) | ||||
0.221560 | + | 0.975147i | \(0.428885\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0.451750 | 0.0183059 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 1.05741 | 0.0427782 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −35.5720 | −1.43674 | −0.718370 | − | 0.695661i | \(-0.755112\pi\) | ||||
−0.718370 | + | 0.695661i | \(0.755112\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0.497665 | 0.0200678 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −36.8015 | −1.48157 | −0.740786 | − | 0.671741i | \(-0.765547\pi\) | ||||
−0.740786 | + | 0.671741i | \(0.765547\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −16.4788 | −0.662341 | −0.331170 | − | 0.943571i | \(-0.607444\pi\) | ||||
−0.331170 | + | 0.943571i | \(0.607444\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −2.85490 | −0.114563 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −6.34098 | −0.254046 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 18.1541 | 0.726163 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0.792321 | 0.0316423 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −7.75699 | −0.309291 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −11.4821 | −0.457097 | −0.228548 | − | 0.973533i | \(-0.573398\pi\) | ||||
−0.228548 | + | 0.973533i | \(0.573398\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 1.48628 | 0.0590743 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −6.91130 | −0.274267 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −4.83130 | −0.191423 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 43.4582 | 1.71918 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 13.4324 | 0.530546 | 0.265273 | − | 0.964173i | \(-0.414538\pi\) | ||||
0.265273 | + | 0.964173i | \(0.414538\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −2.41377 | −0.0951899 | −0.0475949 | − | 0.998867i | \(-0.515156\pi\) | ||||
−0.0475949 | + | 0.998867i | \(0.515156\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −0.959717 | −0.0377888 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 3.71669 | 0.146118 | 0.0730590 | − | 0.997328i | \(-0.476724\pi\) | ||||
0.0730590 | + | 0.997328i | \(0.476724\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −45.4521 | −1.78415 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 2.60482 | 0.102091 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 38.7029 | 1.51456 | 0.757280 | − | 0.653091i | \(-0.226528\pi\) | ||||
0.757280 | + | 0.653091i | \(0.226528\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −6.61817 | −0.258593 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 41.8650 | 1.63331 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −7.39422 | −0.288038 | −0.144019 | − | 0.989575i | \(-0.546003\pi\) | ||||
−0.144019 | + | 0.989575i | \(0.546003\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −8.27897 | −0.322015 | −0.161007 | − | 0.986953i | \(-0.551474\pi\) | ||||
−0.161007 | + | 0.986953i | \(0.551474\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −0.332444 | −0.0129111 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 2.56220 | 0.0993577 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 3.63335 | 0.140684 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 2.92714 | 0.113170 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −22.4618 | −0.867128 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 33.0124 | 1.27254 | 0.636268 | − | 0.771468i | \(-0.280477\pi\) | ||||
0.636268 | + | 0.771468i | \(0.280477\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −3.55850 | −0.136967 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 41.5826 | 1.59815 | 0.799075 | − | 0.601231i | \(-0.205323\pi\) | ||||
0.799075 | + | 0.601231i | \(0.205323\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 49.1513 | 1.88625 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 3.58682 | 0.137447 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 9.49601 | 0.363355 | 0.181677 | − | 0.983358i | \(-0.441847\pi\) | ||||
0.181677 | + | 0.983358i | \(0.441847\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −0.185383 | −0.00708314 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 1.01820 | 0.0388469 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 0.809282 | 0.0308312 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −35.8653 | −1.36438 | −0.682189 | − | 0.731176i | \(-0.738972\pi\) | ||||
−0.682189 | + | 0.731176i | \(0.738972\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −57.0371 | −2.16666 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −7.99544 | −0.303284 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −13.9730 | −0.529266 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 1.82940 | 0.0691942 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 26.3423 | 0.994934 | 0.497467 | − | 0.867483i | \(-0.334264\pi\) | ||||
0.497467 | + | 0.867483i | \(0.334264\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −3.32546 | −0.125422 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −0.0953293 | −0.00359031 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −12.1150 | −0.455631 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 14.3348 | 0.538356 | 0.269178 | − | 0.963090i | \(-0.413248\pi\) | ||||
0.269178 | + | 0.963090i | \(0.413248\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −20.9552 | −0.785881 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 20.9501 | 0.784588 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 3.81615 | 0.142716 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 2.16596 | 0.0808894 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 10.5642 | 0.393979 | 0.196989 | − | 0.980406i | \(-0.436884\pi\) | ||||
0.196989 | + | 0.980406i | \(0.436884\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 3.67223 | 0.136761 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −0.977148 | −0.0363405 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 4.52880 | 0.168196 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 26.9021 | 0.997743 | 0.498872 | − | 0.866676i | \(-0.333748\pi\) | ||||
0.498872 | + | 0.866676i | \(0.333748\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −26.0730 | −0.965667 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 26.9461 | 0.996638 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 3.31499 | 0.122442 | 0.0612209 | − | 0.998124i | \(-0.480501\pi\) | ||||
0.0612209 | + | 0.998124i | \(0.480501\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0.435559 | 0.0160658 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 47.7671 | 1.75952 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −30.4617 | −1.12055 | −0.560277 | − | 0.828305i | \(-0.689305\pi\) | ||||
−0.560277 | + | 0.828305i | \(0.689305\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −0.142520 | −0.00523562 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 25.9403 | 0.951658 | 0.475829 | − | 0.879538i | \(-0.342148\pi\) | ||||
0.475829 | + | 0.879538i | \(0.342148\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 8.94116 | 0.327579 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 25.4370 | 0.930691 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −8.30609 | −0.303498 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 35.5404 | 1.29689 | 0.648443 | − | 0.761263i | \(-0.275420\pi\) | ||||
0.648443 | + | 0.761263i | \(0.275420\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 3.18252 | 0.115977 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −3.29147 | −0.119789 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −52.6251 | −1.91269 | −0.956346 | − | 0.292237i | \(-0.905600\pi\) | ||||
−0.956346 | + | 0.292237i | \(0.905600\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 2.65285 | 0.0962925 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −33.8953 | −1.22870 | −0.614352 | − | 0.789032i | \(-0.710583\pi\) | ||||
−0.614352 | + | 0.789032i | \(0.710583\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −16.2577 | −0.588567 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −5.18268 | −0.187380 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 8.17579 | 0.295211 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −9.69096 | −0.349465 | −0.174732 | − | 0.984616i | \(-0.555906\pi\) | ||||
−0.174732 | + | 0.984616i | \(0.555906\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −1.41629 | −0.0510066 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −29.7639 | −1.07053 | −0.535266 | − | 0.844684i | \(-0.679789\pi\) | ||||
−0.535266 | + | 0.844684i | \(0.679789\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 26.1134 | 0.938020 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −1.38438 | −0.0496644 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −5.99030 | −0.214625 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −80.9988 | −2.89837 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −0.785748 | −0.0280803 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 5.94543 | 0.212202 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 43.5261 | 1.55154 | 0.775768 | − | 0.631018i | \(-0.217363\pi\) | ||||
0.775768 | + | 0.631018i | \(0.217363\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −3.78897 | −0.134891 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −34.3411 | −1.22103 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 4.04037 | 0.143478 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −0.0729598 | −0.00258762 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 41.0512 | 1.45411 | 0.727054 | − | 0.686580i | \(-0.240889\pi\) | ||||
0.727054 | + | 0.686580i | \(0.240889\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 2.67657 | 0.0946903 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 5.49866 | 0.194286 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −78.0293 | −2.75360 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 8.57875 | 0.302361 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0.603025 | 0.0212275 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 45.5107 | 1.60007 | 0.800036 | − | 0.599952i | \(-0.204814\pi\) | ||||
0.800036 | + | 0.599952i | \(0.204814\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 8.08353 | 0.283851 | 0.141926 | − | 0.989877i | \(-0.454671\pi\) | ||||
0.141926 | + | 0.989877i | \(0.454671\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0.0556076 | 0.00195024 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 13.7566 | 0.481874 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 11.5519 | 0.404151 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 10.2597 | 0.358502 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 34.1451 | 1.19167 | 0.595836 | − | 0.803106i | \(-0.296821\pi\) | ||||
0.595836 | + | 0.803106i | \(0.296821\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 43.3908 | 1.51251 | 0.756255 | − | 0.654277i | \(-0.227027\pi\) | ||||
0.756255 | + | 0.654277i | \(0.227027\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 3.30666 | 0.115123 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −3.17503 | −0.110406 | −0.0552032 | − | 0.998475i | \(-0.517581\pi\) | ||||
−0.0552032 | + | 0.998475i | \(0.517581\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −37.6627 | −1.30808 | −0.654040 | − | 0.756460i | \(-0.726927\pi\) | ||||
−0.654040 | + | 0.756460i | \(0.726927\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −1.06629 | −0.0369892 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −12.2293 | −0.423718 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −14.9023 | −0.515715 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −4.53067 | −0.156603 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −1.80602 | −0.0623509 | −0.0311755 | − | 0.999514i | \(-0.509925\pi\) | ||||
−0.0311755 | + | 0.999514i | \(0.509925\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1.00000 | 0.0344828 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −3.98546 | −0.137266 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −0.686438 | −0.0236142 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 68.4712 | 2.35270 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 2.14826 | 0.0737279 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −11.1343 | −0.381679 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 2.85524 | 0.0977615 | 0.0488808 | − | 0.998805i | \(-0.484435\pi\) | ||||
0.0488808 | + | 0.998805i | \(0.484435\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −2.22184 | −0.0759854 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −56.8440 | −1.94175 | −0.970876 | − | 0.239581i | \(-0.922990\pi\) | ||||
−0.970876 | + | 0.239581i | \(0.922990\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −4.86844 | −0.166109 | −0.0830545 | − | 0.996545i | \(-0.526468\pi\) | ||||
−0.0830545 | + | 0.996545i | \(0.526468\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −2.49375 | −0.0849867 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −0.313010 | −0.0106550 | −0.00532749 | − | 0.999986i | \(-0.501696\pi\) | ||||
−0.00532749 | + | 0.999986i | \(0.501696\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −12.4517 | −0.423370 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 1.39120 | 0.0472477 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 39.0570 | 1.32492 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −8.59220 | −0.291136 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −42.6222 | −1.44254 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 22.4986 | 0.760592 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −26.9944 | −0.911534 | −0.455767 | − | 0.890099i | \(-0.650635\pi\) | ||||
−0.455767 | + | 0.890099i | \(0.650635\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −0.201206 | −0.00678650 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 31.7567 | 1.06991 | 0.534956 | − | 0.844880i | \(-0.320328\pi\) | ||||
0.534956 | + | 0.844880i | \(0.320328\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 33.1872 | 1.11684 | 0.558420 | − | 0.829558i | \(-0.311408\pi\) | ||||
0.558420 | + | 0.829558i | \(0.311408\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −0.737078 | −0.0247766 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 1.39174 | 0.0467302 | 0.0233651 | − | 0.999727i | \(-0.492562\pi\) | ||||
0.0233651 | + | 0.999727i | \(0.492562\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 34.6318 | 1.16151 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 49.1728 | 1.64735 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 1.14746 | 0.0383983 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −16.3888 | −0.547819 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −0.477188 | −0.0159328 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 5.76606 | 0.192309 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 2.04850 | 0.0682455 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 4.80904 | 0.160035 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −0.0181766 | −0.000604210 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 12.7666 | 0.423910 | 0.211955 | − | 0.977279i | \(-0.432017\pi\) | ||||
0.211955 | + | 0.977279i | \(0.432017\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 10.5057 | 0.348451 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −10.3509 | −0.342939 | −0.171470 | − | 0.985189i | \(-0.554852\pi\) | ||||
−0.171470 | + | 0.985189i | \(0.554852\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −47.4103 | −1.56905 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −0.364254 | −0.0120419 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 33.1630 | 1.09514 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −32.1403 | −1.06021 | −0.530106 | − | 0.847932i | \(-0.677848\pi\) | ||||
−0.530106 | + | 0.847932i | \(0.677848\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 2.95865 | 0.0974908 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 14.5698 | 0.479572 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −13.8784 | −0.456320 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −3.18442 | −0.104590 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −13.8195 | −0.453402 | −0.226701 | − | 0.973964i | \(-0.572794\pi\) | ||||
−0.226701 | + | 0.973964i | \(0.572794\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −5.24274 | −0.171824 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −1.25884 | −0.0412127 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 9.65965 | 0.315904 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 32.5613 | 1.06373 | 0.531865 | − | 0.846829i | \(-0.321491\pi\) | ||||
0.531865 | + | 0.846829i | \(0.321491\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −1.34355 | −0.0438452 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 15.5171 | 0.505844 | 0.252922 | − | 0.967487i | \(-0.418608\pi\) | ||||
0.252922 | + | 0.967487i | \(0.418608\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −20.0568 | −0.653138 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −1.85524 | −0.0603510 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −8.09564 | −0.263073 | −0.131536 | − | 0.991311i | \(-0.541991\pi\) | ||||
−0.131536 | + | 0.991311i | \(0.541991\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 14.0357 | 0.455618 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −1.78414 | −0.0578546 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 38.7797 | 1.25620 | 0.628098 | − | 0.778134i | \(-0.283834\pi\) | ||||
0.628098 | + | 0.778134i | \(0.283834\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 13.3120 | 0.430765 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0.730140 | 0.0236021 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0.928936 | 0.0299969 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 2.24748 | 0.0724994 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 7.20274 | 0.232105 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 3.07467 | 0.0989771 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 54.7054 | 1.75921 | 0.879603 | − | 0.475708i | \(-0.157808\pi\) | ||||
0.879603 | + | 0.475708i | \(0.157808\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −0.360756 | −0.0115892 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −9.37898 | −0.300986 | −0.150493 | − | 0.988611i | \(-0.548086\pi\) | ||||
−0.150493 | + | 0.988611i | \(0.548086\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 40.0643 | 1.28440 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −0.594793 | −0.0190486 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −38.4218 | −1.22922 | −0.614611 | − | 0.788830i | \(-0.710687\pi\) | ||||
−0.614611 | + | 0.788830i | \(0.710687\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −10.2486 | −0.327546 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 14.0980 | 0.450116 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −43.5714 | −1.38971 | −0.694856 | − | 0.719149i | \(-0.744532\pi\) | ||||
−0.694856 | + | 0.719149i | \(0.744532\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 10.5805 | 0.337122 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0.477685 | 0.0152049 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 38.6782 | 1.22990 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 5.06919 | 0.161028 | 0.0805141 | − | 0.996753i | \(-0.474344\pi\) | ||||
0.0805141 | + | 0.996753i | \(0.474344\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0.546026 | 0.0173276 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −1.91861 | −0.0608241 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 23.3887 | 0.740727 | 0.370363 | − | 0.928887i | \(-0.379233\pi\) | ||||
0.370363 | + | 0.928887i | \(0.379233\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 2.40791 | 0.0761829 |
(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 | 6032.2.a.z.1.5 | 10 | ||
4.3 | odd | 2 | 3016.2.a.h.1.6 | ✓ | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
3016.2.a.h.1.6 | ✓ | 10 | 4.3 | odd | 2 | ||
6032.2.a.z.1.5 | 10 | 1.1 | even | 1 | trivial |