Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8024,2,Mod(1,8024)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8024, 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("8024.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8024 = 2^{3} \cdot 17 \cdot 59 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8024.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: | \(64.0719625819\) |
Analytic rank: | \(1\) |
Dimension: | \(20\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} - 2 x^{19} - 29 x^{18} + 51 x^{17} + 341 x^{16} - 514 x^{15} - 2114 x^{14} + 2629 x^{13} + 7532 x^{12} - 7342 x^{11} - 15668 x^{10} + 11260 x^{9} + 18269 x^{8} - 9059 x^{7} + \cdots + 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{8} \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.11 | ||
Root | \(-0.126023\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8024.1 |
$q$-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 | ||||||||
\(3\) | 0.126023 | 0.0727596 | 0.0363798 | − | 0.999338i | \(-0.488417\pi\) | ||||
0.0363798 | + | 0.999338i | \(0.488417\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −3.00184 | −1.34246 | −0.671232 | − | 0.741247i | \(-0.734235\pi\) | ||||
−0.671232 | + | 0.741247i | \(0.734235\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.14075 | 0.431161 | 0.215581 | − | 0.976486i | \(-0.430836\pi\) | ||||
0.215581 | + | 0.976486i | \(0.430836\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.98412 | −0.994706 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −5.21479 | −1.57232 | −0.786159 | − | 0.618025i | \(-0.787933\pi\) | ||||
−0.786159 | + | 0.618025i | \(0.787933\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.40906 | 0.668153 | 0.334076 | − | 0.942546i | \(-0.391576\pi\) | ||||
0.334076 | + | 0.942546i | \(0.391576\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −0.378302 | −0.0976773 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1.00000 | 0.242536 | ||||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 6.00813 | 1.37836 | 0.689179 | − | 0.724591i | \(-0.257971\pi\) | ||||
0.689179 | + | 0.724591i | \(0.257971\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.143761 | 0.0313711 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 4.99584 | 1.04171 | 0.520853 | − | 0.853647i | \(-0.325614\pi\) | ||||
0.520853 | + | 0.853647i | \(0.325614\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 4.01106 | 0.802212 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −0.754139 | −0.145134 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 5.63999 | 1.04732 | 0.523660 | − | 0.851928i | \(-0.324566\pi\) | ||||
0.523660 | + | 0.851928i | \(0.324566\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −7.10972 | −1.27694 | −0.638471 | − | 0.769646i | \(-0.720433\pi\) | ||||
−0.638471 | + | 0.769646i | \(0.720433\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −0.657185 | −0.114401 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −3.42434 | −0.578819 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −10.3994 | −1.70965 | −0.854823 | − | 0.518920i | \(-0.826334\pi\) | ||||
−0.854823 | + | 0.518920i | \(0.826334\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0.303598 | 0.0486146 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 4.25539 | 0.664581 | 0.332290 | − | 0.943177i | \(-0.392179\pi\) | ||||
0.332290 | + | 0.943177i | \(0.392179\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 4.05492 | 0.618369 | 0.309184 | − | 0.951002i | \(-0.399944\pi\) | ||||
0.309184 | + | 0.951002i | \(0.399944\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 8.95785 | 1.33536 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 3.59029 | 0.523698 | 0.261849 | − | 0.965109i | \(-0.415668\pi\) | ||||
0.261849 | + | 0.965109i | \(0.415668\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −5.69870 | −0.814100 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0.126023 | 0.0176468 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 11.4309 | 1.57015 | 0.785077 | − | 0.619398i | \(-0.212623\pi\) | ||||
0.785077 | + | 0.619398i | \(0.212623\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 15.6540 | 2.11078 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0.757164 | 0.100289 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −1.00000 | −0.130189 | ||||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0.689168 | 0.0882389 | 0.0441194 | − | 0.999026i | \(-0.485952\pi\) | ||||
0.0441194 | + | 0.999026i | \(0.485952\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −3.40412 | −0.428879 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −7.23162 | −0.896972 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −0.334220 | −0.0408315 | −0.0204157 | − | 0.999792i | \(-0.506499\pi\) | ||||
−0.0204157 | + | 0.999792i | \(0.506499\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0.629593 | 0.0757941 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0.447166 | 0.0530689 | 0.0265344 | − | 0.999648i | \(-0.491553\pi\) | ||||
0.0265344 | + | 0.999648i | \(0.491553\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −6.96383 | −0.815054 | −0.407527 | − | 0.913193i | \(-0.633609\pi\) | ||||
−0.407527 | + | 0.913193i | \(0.633609\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0.505487 | 0.0583687 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −5.94874 | −0.677922 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −8.97581 | −1.00986 | −0.504929 | − | 0.863161i | \(-0.668481\pi\) | ||||
−0.504929 | + | 0.863161i | \(0.668481\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 8.85732 | 0.984146 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 3.58416 | 0.393413 | 0.196707 | − | 0.980462i | \(-0.436975\pi\) | ||||
0.196707 | + | 0.980462i | \(0.436975\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −3.00184 | −0.325596 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0.710770 | 0.0762026 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 13.2105 | 1.40031 | 0.700153 | − | 0.713993i | \(-0.253115\pi\) | ||||
0.700153 | + | 0.713993i | \(0.253115\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 2.74812 | 0.288082 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −0.895991 | −0.0929099 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −18.0354 | −1.85040 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 14.0084 | 1.42234 | 0.711170 | − | 0.703021i | \(-0.248166\pi\) | ||||
0.711170 | + | 0.703021i | \(0.248166\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 15.5615 | 1.56399 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 0.275049 | 0.0273684 | 0.0136842 | − | 0.999906i | \(-0.495644\pi\) | ||||
0.0136842 | + | 0.999906i | \(0.495644\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −12.4016 | −1.22196 | −0.610981 | − | 0.791646i | \(-0.709225\pi\) | ||||
−0.610981 | + | 0.791646i | \(0.709225\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −0.431547 | −0.0421147 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 5.37705 | 0.519819 | 0.259909 | − | 0.965633i | \(-0.416307\pi\) | ||||
0.259909 | + | 0.965633i | \(0.416307\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −6.90115 | −0.661010 | −0.330505 | − | 0.943804i | \(-0.607219\pi\) | ||||
−0.330505 | + | 0.943804i | \(0.607219\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −1.31056 | −0.124393 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −10.2548 | −0.964692 | −0.482346 | − | 0.875981i | \(-0.660215\pi\) | ||||
−0.482346 | + | 0.875981i | \(0.660215\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −14.9967 | −1.39845 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −7.18892 | −0.664616 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 1.14075 | 0.104572 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 16.1940 | 1.47218 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0.536279 | 0.0483547 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 2.96864 | 0.265523 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 10.4271 | 0.925254 | 0.462627 | − | 0.886553i | \(-0.346907\pi\) | ||||
0.462627 | + | 0.886553i | \(0.346907\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0.511014 | 0.0449923 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 7.42500 | 0.648725 | 0.324363 | − | 0.945933i | \(-0.394850\pi\) | ||||
0.324363 | + | 0.945933i | \(0.394850\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 6.85374 | 0.594295 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 2.26381 | 0.194837 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 1.38079 | 0.117969 | 0.0589844 | − | 0.998259i | \(-0.481214\pi\) | ||||
0.0589844 | + | 0.998259i | \(0.481214\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −11.7283 | −0.994784 | −0.497392 | − | 0.867526i | \(-0.665709\pi\) | ||||
−0.497392 | + | 0.867526i | \(0.665709\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0.452461 | 0.0381040 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −12.5627 | −1.05055 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −16.9303 | −1.40599 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −0.718170 | −0.0592336 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −15.8805 | −1.30098 | −0.650489 | − | 0.759515i | \(-0.725436\pi\) | ||||
−0.650489 | + | 0.759515i | \(0.725436\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 2.54563 | 0.207160 | 0.103580 | − | 0.994621i | \(-0.466970\pi\) | ||||
0.103580 | + | 0.994621i | \(0.466970\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −2.98412 | −0.241252 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 21.3422 | 1.71425 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −0.671821 | −0.0536172 | −0.0268086 | − | 0.999641i | \(-0.508534\pi\) | ||||
−0.0268086 | + | 0.999641i | \(0.508534\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 1.44056 | 0.114244 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 5.69899 | 0.449143 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −13.7045 | −1.07342 | −0.536711 | − | 0.843766i | \(-0.680333\pi\) | ||||
−0.536711 | + | 0.843766i | \(0.680333\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 1.97277 | 0.153580 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −16.1333 | −1.24843 | −0.624215 | − | 0.781253i | \(-0.714581\pi\) | ||||
−0.624215 | + | 0.781253i | \(0.714581\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −7.19643 | −0.553572 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −17.9290 | −1.37106 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 7.71861 | 0.586835 | 0.293417 | − | 0.955984i | \(-0.405207\pi\) | ||||
0.293417 | + | 0.955984i | \(0.405207\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 4.57560 | 0.345883 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −0.126023 | −0.00947250 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −8.46639 | −0.632808 | −0.316404 | − | 0.948625i | \(-0.602475\pi\) | ||||
−0.316404 | + | 0.948625i | \(0.602475\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 2.59899 | 0.193182 | 0.0965909 | − | 0.995324i | \(-0.469206\pi\) | ||||
0.0965909 | + | 0.995324i | \(0.469206\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0.0868513 | 0.00642023 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 31.2173 | 2.29514 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −5.21479 | −0.381343 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −0.860281 | −0.0625762 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −23.4647 | −1.69785 | −0.848924 | − | 0.528515i | \(-0.822749\pi\) | ||||
−0.848924 | + | 0.528515i | \(0.822749\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −21.2687 | −1.53095 | −0.765476 | − | 0.643464i | \(-0.777497\pi\) | ||||
−0.765476 | + | 0.643464i | \(0.777497\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −0.911353 | −0.0652634 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −1.99334 | −0.142019 | −0.0710096 | − | 0.997476i | \(-0.522622\pi\) | ||||
−0.0710096 | + | 0.997476i | \(0.522622\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −22.7503 | −1.61272 | −0.806362 | − | 0.591422i | \(-0.798567\pi\) | ||||
−0.806362 | + | 0.591422i | \(0.798567\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −0.0421195 | −0.00297088 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 6.43379 | 0.451563 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −12.7740 | −0.892176 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −14.9082 | −1.03619 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −31.3311 | −2.16722 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −7.07579 | −0.487118 | −0.243559 | − | 0.969886i | \(-0.578315\pi\) | ||||
−0.243559 | + | 0.969886i | \(0.578315\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0.0563534 | 0.00386127 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −12.1722 | −0.830139 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −8.11038 | −0.550568 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −0.877605 | −0.0593031 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 2.40906 | 0.162051 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 13.3477 | 0.893830 | 0.446915 | − | 0.894576i | \(-0.352523\pi\) | ||||
0.446915 | + | 0.894576i | \(0.352523\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −11.9695 | −0.797965 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 5.44827 | 0.361614 | 0.180807 | − | 0.983519i | \(-0.442129\pi\) | ||||
0.180807 | + | 0.983519i | \(0.442129\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −16.6875 | −1.10274 | −0.551370 | − | 0.834261i | \(-0.685895\pi\) | ||||
−0.551370 | + | 0.834261i | \(0.685895\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −0.749681 | −0.0493254 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −10.4889 | −0.687149 | −0.343574 | − | 0.939125i | \(-0.611638\pi\) | ||||
−0.343574 | + | 0.939125i | \(0.611638\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −10.7775 | −0.703046 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −1.13116 | −0.0734769 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 6.36138 | 0.411484 | 0.205742 | − | 0.978606i | \(-0.434039\pi\) | ||||
0.205742 | + | 0.978606i | \(0.434039\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −20.3695 | −1.31212 | −0.656058 | − | 0.754711i | \(-0.727777\pi\) | ||||
−0.656058 | + | 0.754711i | \(0.727777\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 3.37865 | 0.216740 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 17.1066 | 1.09290 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 14.4739 | 0.920954 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0.451688 | 0.0286246 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 0.481594 | 0.0303979 | 0.0151990 | − | 0.999884i | \(-0.495162\pi\) | ||||
0.0151990 | + | 0.999884i | \(0.495162\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −26.0523 | −1.63789 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −0.378302 | −0.0236902 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −24.4666 | −1.52618 | −0.763092 | − | 0.646290i | \(-0.776320\pi\) | ||||
−0.763092 | + | 0.646290i | \(0.776320\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −11.8630 | −0.737133 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −16.8304 | −1.04177 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −15.3833 | −0.948578 | −0.474289 | − | 0.880369i | \(-0.657295\pi\) | ||||
−0.474289 | + | 0.880369i | \(0.657295\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −34.3138 | −2.10788 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 1.66483 | 0.101886 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 9.73616 | 0.593624 | 0.296812 | − | 0.954936i | \(-0.404077\pi\) | ||||
0.296812 | + | 0.954936i | \(0.404077\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −2.06324 | −0.125333 | −0.0626665 | − | 0.998035i | \(-0.519960\pi\) | ||||
−0.0626665 | + | 0.998035i | \(0.519960\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0.346328 | 0.0209607 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −20.9168 | −1.26133 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −4.52104 | −0.271643 | −0.135821 | − | 0.990733i | \(-0.543367\pi\) | ||||
−0.135821 | + | 0.990733i | \(0.543367\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 21.2162 | 1.27018 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 26.1254 | 1.55851 | 0.779256 | − | 0.626706i | \(-0.215597\pi\) | ||||
0.779256 | + | 0.626706i | \(0.215597\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 16.5260 | 0.982368 | 0.491184 | − | 0.871056i | \(-0.336564\pi\) | ||||
0.491184 | + | 0.871056i | \(0.336564\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −2.27289 | −0.134634 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 4.85432 | 0.286541 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1.00000 | 0.0588235 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 1.76539 | 0.103489 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 8.10585 | 0.473549 | 0.236774 | − | 0.971565i | \(-0.423910\pi\) | ||||
0.236774 | + | 0.971565i | \(0.423910\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 3.00184 | 0.174774 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 3.93267 | 0.228197 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 12.0353 | 0.696019 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 4.62563 | 0.266617 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0.0346626 | 0.00199131 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −2.06877 | −0.118458 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −23.8670 | −1.36216 | −0.681081 | − | 0.732208i | \(-0.738490\pi\) | ||||
−0.681081 | + | 0.732208i | \(0.738490\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −1.56289 | −0.0889095 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 22.7334 | 1.28909 | 0.644547 | − | 0.764565i | \(-0.277046\pi\) | ||||
0.644547 | + | 0.764565i | \(0.277046\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −15.3489 | −0.867570 | −0.433785 | − | 0.901017i | \(-0.642822\pi\) | ||||
−0.433785 | + | 0.901017i | \(0.642822\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 10.2186 | 0.575755 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 15.1405 | 0.850378 | 0.425189 | − | 0.905105i | \(-0.360208\pi\) | ||||
0.425189 | + | 0.905105i | \(0.360208\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −29.4113 | −1.64672 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0.677634 | 0.0378218 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 6.00813 | 0.334301 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 9.66288 | 0.536000 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −0.869706 | −0.0480949 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 4.09561 | 0.225798 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 26.3595 | 1.44885 | 0.724426 | − | 0.689353i | \(-0.242105\pi\) | ||||
0.724426 | + | 0.689353i | \(0.242105\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 31.0329 | 1.70059 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 1.00328 | 0.0548148 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 6.14816 | 0.334912 | 0.167456 | − | 0.985880i | \(-0.446445\pi\) | ||||
0.167456 | + | 0.985880i | \(0.446445\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −1.29235 | −0.0701906 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 37.0756 | 2.00776 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −14.4860 | −0.782170 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −1.88994 | −0.101751 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −16.3568 | −0.878080 | −0.439040 | − | 0.898467i | \(-0.644681\pi\) | ||||
−0.439040 | + | 0.898467i | \(0.644681\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 13.0756 | 0.699920 | 0.349960 | − | 0.936765i | \(-0.386195\pi\) | ||||
0.349960 | + | 0.936765i | \(0.386195\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1.81677 | −0.0969718 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −20.5458 | −1.09354 | −0.546772 | − | 0.837282i | \(-0.684143\pi\) | ||||
−0.546772 | + | 0.837282i | \(0.684143\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −1.34232 | −0.0712431 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0.143761 | 0.00760862 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 16.8851 | 0.891162 | 0.445581 | − | 0.895242i | \(-0.352997\pi\) | ||||
0.445581 | + | 0.895242i | \(0.352997\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 17.0976 | 0.899872 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 2.04082 | 0.107115 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 20.9043 | 1.09418 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −7.49308 | −0.391136 | −0.195568 | − | 0.980690i | \(-0.562655\pi\) | ||||
−0.195568 | + | 0.980690i | \(0.562655\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −12.6986 | −0.661062 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 13.0397 | 0.676990 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −36.2372 | −1.87629 | −0.938147 | − | 0.346238i | \(-0.887459\pi\) | ||||
−0.938147 | + | 0.346238i | \(0.887459\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0.374118 | 0.0193194 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 13.5871 | 0.699769 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 19.1070 | 0.981462 | 0.490731 | − | 0.871311i | \(-0.336730\pi\) | ||||
0.490731 | + | 0.871311i | \(0.336730\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 1.31406 | 0.0673212 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 24.2104 | 1.23709 | 0.618547 | − | 0.785748i | \(-0.287722\pi\) | ||||
0.618547 | + | 0.785748i | \(0.287722\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 17.8572 | 0.910087 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −12.1003 | −0.615095 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −35.6273 | −1.80637 | −0.903187 | − | 0.429247i | \(-0.858779\pi\) | ||||
−0.903187 | + | 0.429247i | \(0.858779\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 4.99584 | 0.252651 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0.935724 | 0.0472010 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 26.9440 | 1.35570 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −4.47236 | −0.224461 | −0.112231 | − | 0.993682i | \(-0.535800\pi\) | ||||
−0.112231 | + | 0.993682i | \(0.535800\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0.863732 | 0.0432407 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 13.8281 | 0.690543 | 0.345271 | − | 0.938503i | \(-0.387787\pi\) | ||||
0.345271 | + | 0.938503i | \(0.387787\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −17.1277 | −0.853193 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −26.5883 | −1.32118 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 54.2305 | 2.68810 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −4.69046 | −0.231928 | −0.115964 | − | 0.993253i | \(-0.536996\pi\) | ||||
−0.115964 | + | 0.993253i | \(0.536996\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0.174012 | 0.00858337 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −1.14075 | −0.0561324 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −10.7591 | −0.528143 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −1.47804 | −0.0723801 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −20.9370 | −1.02284 | −0.511419 | − | 0.859332i | \(-0.670880\pi\) | ||||
−0.511419 | + | 0.859332i | \(0.670880\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 20.6293 | 1.00541 | 0.502706 | − | 0.864457i | \(-0.332338\pi\) | ||||
0.502706 | + | 0.864457i | \(0.332338\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −10.7138 | −0.520925 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 4.01106 | 0.194565 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0.786165 | 0.0380452 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −1.58320 | −0.0764375 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −9.83905 | −0.473930 | −0.236965 | − | 0.971518i | \(-0.576153\pi\) | ||||
−0.236965 | + | 0.971518i | \(0.576153\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −22.1984 | −1.06679 | −0.533393 | − | 0.845867i | \(-0.679083\pi\) | ||||
−0.533393 | + | 0.845867i | \(0.679083\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −2.13362 | −0.102299 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 30.0157 | 1.43584 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −23.0419 | −1.09973 | −0.549864 | − | 0.835254i | \(-0.685320\pi\) | ||||
−0.549864 | + | 0.835254i | \(0.685320\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 17.0056 | 0.809790 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −31.3020 | −1.48720 | −0.743601 | − | 0.668624i | \(-0.766884\pi\) | ||||
−0.743601 | + | 0.668624i | \(0.766884\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −39.6557 | −1.87986 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −2.00131 | −0.0946587 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −39.8384 | −1.88009 | −0.940046 | − | 0.341048i | \(-0.889218\pi\) | ||||
−0.940046 | + | 0.341048i | \(0.889218\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −22.1910 | −1.04493 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0.320808 | 0.0150729 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −8.24944 | −0.386740 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −37.8326 | −1.76973 | −0.884867 | − | 0.465844i | \(-0.845751\pi\) | ||||
−0.884867 | + | 0.465844i | \(0.845751\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −0.754139 | −0.0352002 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 17.4266 | 0.811636 | 0.405818 | − | 0.913954i | \(-0.366987\pi\) | ||||
0.405818 | + | 0.913954i | \(0.366987\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 16.3715 | 0.760848 | 0.380424 | − | 0.924812i | \(-0.375778\pi\) | ||||
0.380424 | + | 0.924812i | \(0.375778\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 2.68962 | 0.124728 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 24.3207 | 1.12543 | 0.562713 | − | 0.826652i | \(-0.309758\pi\) | ||||
0.562713 | + | 0.826652i | \(0.309758\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −0.381260 | −0.0176049 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −0.0846652 | −0.00390117 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −21.1455 | −0.972272 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 24.0990 | 1.10574 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −34.1112 | −1.56184 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −4.15815 | −0.189991 | −0.0949953 | − | 0.995478i | \(-0.530284\pi\) | ||||
−0.0949953 | + | 0.995478i | \(0.530284\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −25.0527 | −1.14230 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0.718206 | 0.0326795 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −42.0511 | −1.90944 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −27.9326 | −1.26575 | −0.632873 | − | 0.774255i | \(-0.718125\pi\) | ||||
−0.632873 | + | 0.774255i | \(0.718125\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −1.72709 | −0.0781017 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −16.0768 | −0.725535 | −0.362767 | − | 0.931880i | \(-0.618168\pi\) | ||||
−0.362767 | + | 0.931880i | \(0.618168\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 5.63999 | 0.254012 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −46.7133 | −2.09961 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0.510103 | 0.0228812 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 6.93251 | 0.310342 | 0.155171 | − | 0.987888i | \(-0.450407\pi\) | ||||
0.155171 | + | 0.987888i | \(0.450407\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −2.03317 | −0.0908353 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 26.7818 | 1.19414 | 0.597071 | − | 0.802189i | \(-0.296331\pi\) | ||||
0.597071 | + | 0.802189i | \(0.296331\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −0.825653 | −0.0367411 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −0.906919 | −0.0402777 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 13.6604 | 0.605488 | 0.302744 | − | 0.953072i | \(-0.402097\pi\) | ||||
0.302744 | + | 0.953072i | \(0.402097\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −7.94395 | −0.351420 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −4.53096 | −0.200047 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 37.2275 | 1.64044 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −18.7226 | −0.823419 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0.972725 | 0.0426979 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −1.64880 | −0.0722354 | −0.0361177 | − | 0.999348i | \(-0.511499\pi\) | ||||
−0.0361177 | + | 0.999348i | \(0.511499\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 10.3043 | 0.450573 | 0.225287 | − | 0.974293i | \(-0.427668\pi\) | ||||
0.225287 | + | 0.974293i | \(0.427668\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0.576633 | 0.0251663 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −7.10972 | −0.309704 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.95846 | 0.0851505 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 2.98412 | 0.129500 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 10.2515 | 0.444042 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −16.1411 | −0.697839 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −1.06696 | −0.0460429 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 29.7175 | 1.28002 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 30.7994 | 1.32417 | 0.662085 | − | 0.749429i | \(-0.269672\pi\) | ||||
0.662085 | + | 0.749429i | \(0.269672\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0.327534 | 0.0140558 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 20.7162 | 0.887383 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −12.3941 | −0.529933 | −0.264967 | − | 0.964258i | \(-0.585361\pi\) | ||||
−0.264967 | + | 0.964258i | \(0.585361\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −2.05656 | −0.0877717 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 33.8857 | 1.44358 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −10.2391 | −0.435412 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 3.93411 | 0.166993 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −41.9431 | −1.77718 | −0.888592 | − | 0.458698i | \(-0.848316\pi\) | ||||
−0.888592 | + | 0.458698i | \(0.848316\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 9.76853 | 0.413165 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −0.657185 | −0.0277464 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −32.4203 | −1.36635 | −0.683177 | − | 0.730253i | \(-0.739402\pi\) | ||||
−0.683177 | + | 0.730253i | \(0.739402\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 30.7833 | 1.29506 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 10.1039 | 0.424326 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 28.4154 | 1.19123 | 0.595617 | − | 0.803269i | \(-0.296908\pi\) | ||||
0.595617 | + | 0.803269i | \(0.296908\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 26.1767 | 1.09546 | 0.547731 | − | 0.836654i | \(-0.315492\pi\) | ||||
0.547731 | + | 0.836654i | \(0.315492\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −2.95710 | −0.123535 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 20.0386 | 0.835669 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −5.80115 | −0.241505 | −0.120752 | − | 0.992683i | \(-0.538531\pi\) | ||||
−0.120752 | + | 0.992683i | \(0.538531\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −2.68035 | −0.111392 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 4.08862 | 0.169624 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −59.6097 | −2.46878 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 21.5800 | 0.892223 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 41.6575 | 1.71939 | 0.859694 | − | 0.510809i | \(-0.170654\pi\) | ||||
0.859694 | + | 0.510809i | \(0.170654\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −42.7161 | −1.76008 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −0.251207 | −0.0103333 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −38.5296 | −1.58222 | −0.791111 | − | 0.611673i | \(-0.790497\pi\) | ||||
−0.791111 | + | 0.611673i | \(0.790497\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −3.42434 | −0.140384 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −2.86707 | −0.117341 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 28.7536 | 1.17484 | 0.587419 | − | 0.809283i | \(-0.300144\pi\) | ||||
0.587419 | + | 0.809283i | \(0.300144\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 26.2114 | 1.06919 | 0.534593 | − | 0.845110i | \(-0.320465\pi\) | ||||
0.534593 | + | 0.845110i | \(0.320465\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0.997352 | 0.0406153 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −48.6118 | −1.97635 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 12.0482 | 0.489020 | 0.244510 | − | 0.969647i | \(-0.421373\pi\) | ||||
0.244510 | + | 0.969647i | \(0.421373\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0.810808 | 0.0328556 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 8.64922 | 0.349910 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 24.5112 | 0.989999 | 0.495000 | − | 0.868893i | \(-0.335168\pi\) | ||||
0.495000 | + | 0.868893i | \(0.335168\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −1.60983 | −0.0649144 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −35.0974 | −1.41297 | −0.706484 | − | 0.707729i | \(-0.749720\pi\) | ||||
−0.706484 | + | 0.707729i | \(0.749720\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −25.5434 | −1.02667 | −0.513337 | − | 0.858187i | \(-0.671591\pi\) | ||||
−0.513337 | + | 0.858187i | \(0.671591\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −3.76756 | −0.151187 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 15.0698 | 0.603758 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −28.9667 | −1.15867 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −3.94845 | −0.157686 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −10.3994 | −0.414650 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −31.0208 | −1.23492 | −0.617459 | − | 0.786603i | \(-0.711838\pi\) | ||||
−0.617459 | + | 0.786603i | \(0.711838\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −0.891715 | −0.0354425 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −31.3005 | −1.24212 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −13.7285 | −0.543943 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −1.33440 | −0.0527879 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −4.31634 | −0.170485 | −0.0852425 | − | 0.996360i | \(-0.527166\pi\) | ||||
−0.0852425 | + | 0.996360i | \(0.527166\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 40.6051 | 1.60131 | 0.800654 | − | 0.599127i | \(-0.204486\pi\) | ||||
0.800654 | + | 0.599127i | \(0.204486\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −1.53398 | −0.0604006 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 33.0506 | 1.29935 | 0.649677 | − | 0.760210i | \(-0.274904\pi\) | ||||
0.649677 | + | 0.760210i | \(0.274904\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 5.21479 | 0.204698 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −1.02210 | −0.0400591 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −42.1162 | −1.64813 | −0.824067 | − | 0.566492i | \(-0.808300\pi\) | ||||
−0.824067 | + | 0.566492i | \(0.808300\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −22.2887 | −0.870891 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 20.7809 | 0.810739 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 24.7841 | 0.965453 | 0.482727 | − | 0.875771i | \(-0.339646\pi\) | ||||
0.482727 | + | 0.875771i | \(0.339646\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −41.9877 | −1.63313 | −0.816567 | − | 0.577251i | \(-0.804125\pi\) | ||||
−0.816567 | + | 0.577251i | \(0.804125\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0.303598 | 0.0117908 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −20.5739 | −0.797820 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 28.1765 | 1.09100 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 1.68213 | 0.0650347 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −3.59386 | −0.138740 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −23.2743 | −0.897159 | −0.448579 | − | 0.893743i | \(-0.648070\pi\) | ||||
−0.448579 | + | 0.893743i | \(0.648070\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −3.02490 | −0.116428 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −18.4973 | −0.710910 | −0.355455 | − | 0.934693i | \(-0.615674\pi\) | ||||
−0.355455 | + | 0.934693i | \(0.615674\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 15.9800 | 0.613258 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0.686609 | 0.0263109 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 35.3211 | 1.35153 | 0.675763 | − | 0.737119i | \(-0.263814\pi\) | ||||
0.675763 | + | 0.737119i | \(0.263814\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −4.14492 | −0.158369 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −2.10301 | −0.0802349 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 27.5377 | 1.04910 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 44.2119 | 1.68190 | 0.840950 | − | 0.541112i | \(-0.181997\pi\) | ||||
0.840950 | + | 0.541112i | \(0.181997\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 17.7518 | 0.674333 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 35.2066 | 1.33546 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 4.25539 | 0.161184 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −1.32184 | −0.0499967 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −12.1992 | −0.460756 | −0.230378 | − | 0.973101i | \(-0.573996\pi\) | ||||
−0.230378 | + | 0.973101i | \(0.573996\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −62.4807 | −2.35650 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −1.35822 | −0.0511533 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0.313761 | 0.0118002 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 28.4867 | 1.06984 | 0.534920 | − | 0.844903i | \(-0.320342\pi\) | ||||
0.534920 | + | 0.844903i | \(0.320342\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 26.7849 | 1.00451 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −35.5190 | −1.33020 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 37.7113 | 1.41032 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0.801683 | 0.0299394 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 10.4564 | 0.389956 | 0.194978 | − | 0.980808i | \(-0.437536\pi\) | ||||
0.194978 | + | 0.980808i | \(0.437536\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −14.1470 | −0.526862 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −2.56703 | −0.0954691 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 22.6223 | 0.840172 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −28.5216 | −1.05781 | −0.528904 | − | 0.848682i | \(-0.677397\pi\) | ||||
−0.528904 | + | 0.848682i | \(0.677397\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −26.1462 | −0.968376 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 4.05492 | 0.149976 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 45.5121 | 1.68103 | 0.840514 | − | 0.541789i | \(-0.182253\pi\) | ||||
0.840514 | + | 0.541789i | \(0.182253\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 2.15583 | 0.0795191 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 1.74289 | 0.0642000 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 10.3813 | 0.381880 | 0.190940 | − | 0.981602i | \(-0.438846\pi\) | ||||
0.190940 | + | 0.981602i | \(0.438846\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 1.82405 | 0.0670083 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −0.917458 | −0.0336583 | −0.0168291 | − | 0.999858i | \(-0.505357\pi\) | ||||
−0.0168291 | + | 0.999858i | \(0.505357\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 47.6707 | 1.74652 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −10.6956 | −0.391330 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 6.13384 | 0.224126 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −13.5297 | −0.493706 | −0.246853 | − | 0.969053i | \(-0.579396\pi\) | ||||
−0.246853 | + | 0.969053i | \(0.579396\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0.0606921 | 0.00221174 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −7.64157 | −0.278105 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −21.2041 | −0.770678 | −0.385339 | − | 0.922775i | \(-0.625915\pi\) | ||||
−0.385339 | + | 0.922775i | \(0.625915\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −3.28319 | −0.119172 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −32.4935 | −1.17789 | −0.588944 | − | 0.808174i | \(-0.700456\pi\) | ||||
−0.588944 | + | 0.808174i | \(0.700456\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −7.87246 | −0.285002 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 8.95785 | 0.323872 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −2.40906 | −0.0869861 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −33.6599 | −1.21381 | −0.606903 | − | 0.794776i | \(-0.707589\pi\) | ||||
−0.606903 | + | 0.794776i | \(0.707589\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −3.08336 | −0.111045 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 46.9565 | 1.68891 | 0.844454 | − | 0.535628i | \(-0.179925\pi\) | ||||
0.844454 | + | 0.535628i | \(0.179925\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −28.5175 | −1.02438 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −1.49502 | −0.0536335 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 25.5669 | 0.916030 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −2.33188 | −0.0834411 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −4.25333 | −0.152002 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 2.01670 | 0.0719792 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 22.6165 | 0.806191 | 0.403096 | − | 0.915158i | \(-0.367934\pi\) | ||||
0.403096 | + | 0.915158i | \(0.367934\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −1.93866 | −0.0690182 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −11.6981 | −0.415938 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1.66025 | 0.0589571 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −4.32434 | −0.153368 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −33.1861 | −1.17551 | −0.587757 | − | 0.809038i | \(-0.699989\pi\) | ||||
−0.587757 | + | 0.809038i | \(0.699989\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 3.59029 | 0.127015 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −39.4216 | −1.39289 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 36.3149 | 1.28152 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −17.1075 | −0.602959 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 1.22698 | 0.0431919 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −26.8722 | −0.944777 | −0.472389 | − | 0.881390i | \(-0.656608\pi\) | ||||
−0.472389 | + | 0.881390i | \(0.656608\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 26.9582 | 0.946629 | 0.473315 | − | 0.880893i | \(-0.343057\pi\) | ||||
0.473315 | + | 0.880893i | \(0.343057\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −0.260017 | −0.00911918 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 41.1388 | 1.44103 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 24.3624 | 0.852334 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −8.20073 | −0.286557 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 5.41068 | 0.188834 | 0.0944169 | − | 0.995533i | \(-0.469901\pi\) | ||||
0.0944169 | + | 0.995533i | \(0.469901\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −5.67516 | −0.197824 | −0.0989119 | − | 0.995096i | \(-0.531536\pi\) | ||||
−0.0989119 | + | 0.995096i | \(0.531536\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −2.63601 | −0.0917740 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −12.9948 | −0.451874 | −0.225937 | − | 0.974142i | \(-0.572544\pi\) | ||||
−0.225937 | + | 0.974142i | \(0.572544\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −38.9845 | −1.35399 | −0.676995 | − | 0.735988i | \(-0.736718\pi\) | ||||
−0.676995 | + | 0.735988i | \(0.736718\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −0.569756 | −0.0197646 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −5.69870 | −0.197448 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 48.4295 | 1.67597 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 5.36171 | 0.185328 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 46.8082 | 1.61600 | 0.808000 | − | 0.589183i | \(-0.200550\pi\) | ||||
0.808000 | + | 0.589183i | \(0.200550\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 2.80944 | 0.0968771 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 3.29241 | 0.113397 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 21.6026 | 0.743151 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 18.4732 | 0.634747 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 2.08266 | 0.0714768 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −51.9536 | −1.78095 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −19.1224 | −0.654739 | −0.327369 | − | 0.944896i | \(-0.606162\pi\) | ||||
−0.327369 | + | 0.944896i | \(0.606162\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 53.8199 | 1.84060 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −23.7980 | −0.812923 | −0.406461 | − | 0.913668i | \(-0.633237\pi\) | ||||
−0.406461 | + | 0.913668i | \(0.633237\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 53.8438 | 1.83713 | 0.918564 | − | 0.395273i | \(-0.129350\pi\) | ||||
0.918564 | + | 0.395273i | \(0.129350\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0.611758 | 0.0208487 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 19.5791 | 0.666480 | 0.333240 | − | 0.942842i | \(-0.391858\pi\) | ||||
0.333240 | + | 0.942842i | \(0.391858\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −23.1700 | −0.787805 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0.126023 | 0.00427998 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 46.8069 | 1.58782 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −0.805156 | −0.0272817 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −41.8028 | −1.41481 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 3.38646 | 0.114483 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 2.61615 | 0.0883411 | 0.0441706 | − | 0.999024i | \(-0.485935\pi\) | ||||
0.0441706 | + | 0.999024i | \(0.485935\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 1.02153 | 0.0344553 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −56.2447 | −1.89493 | −0.947467 | − | 0.319854i | \(-0.896366\pi\) | ||||
−0.947467 | + | 0.319854i | \(0.896366\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −50.6355 | −1.70402 | −0.852011 | − | 0.523524i | \(-0.824617\pi\) | ||||
−0.852011 | + | 0.523524i | \(0.824617\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0.378302 | 0.0127165 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −8.80356 | −0.295595 | −0.147797 | − | 0.989018i | \(-0.547218\pi\) | ||||
−0.147797 | + | 0.989018i | \(0.547218\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 11.8947 | 0.398934 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −46.1890 | −1.54739 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 21.5709 | 0.721843 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 25.4148 | 0.849522 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 1.51673 | 0.0506421 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −40.0987 | −1.33737 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 11.4309 | 0.380819 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0.582937 | 0.0193989 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −7.80177 | −0.259340 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 2.08465 | 0.0692197 | 0.0346099 | − | 0.999401i | \(-0.488981\pi\) | ||||
0.0346099 | + | 0.999401i | \(0.488981\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −0.820778 | −0.0272235 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −38.1870 | −1.26519 | −0.632596 | − | 0.774482i | \(-0.718011\pi\) | ||||
−0.632596 | + | 0.774482i | \(0.718011\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −18.6906 | −0.618570 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −0.260714 | −0.00861893 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 8.47004 | 0.279705 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 20.2009 | 0.666367 | 0.333183 | − | 0.942862i | \(-0.391877\pi\) | ||||
0.333183 | + | 0.942862i | \(0.391877\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −3.00780 | −0.0991104 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 1.07725 | 0.0354581 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −41.7125 | −1.37150 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 37.0077 | 1.21549 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −5.30223 | −0.173961 | −0.0869803 | − | 0.996210i | \(-0.527722\pi\) | ||||
−0.0869803 | + | 0.996210i | \(0.527722\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −34.2385 | −1.12212 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 2.86494 | 0.0937940 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 15.6540 | 0.511939 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −20.4181 | −0.667030 | −0.333515 | − | 0.942745i | \(-0.608235\pi\) | ||||
−0.333515 | + | 0.942745i | \(0.608235\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −1.93432 | −0.0631240 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 8.26900 | 0.269562 | 0.134781 | − | 0.990875i | \(-0.456967\pi\) | ||||
0.134781 | + | 0.990875i | \(0.456967\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 21.2593 | 0.692297 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 2.58243 | 0.0840064 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −51.1722 | −1.66287 | −0.831436 | − | 0.555620i | \(-0.812481\pi\) | ||||
−0.831436 | + | 0.555620i | \(0.812481\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −16.7763 | −0.544581 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 1.90806 | 0.0618732 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 10.1308 | 0.328170 | 0.164085 | − | 0.986446i | \(-0.447533\pi\) | ||||
0.164085 | + | 0.986446i | \(0.447533\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 70.4374 | 2.27930 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −3.70651 | −0.119815 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 1.57513 | 0.0508636 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 19.5481 | 0.630582 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −16.0457 | −0.517067 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 63.8452 | 2.05525 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 49.6026 | 1.59511 | 0.797556 | − | 0.603245i | \(-0.206126\pi\) | ||||
0.797556 | + | 0.603245i | \(0.206126\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0.757164 | 0.0243236 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −33.3721 | −1.07096 | −0.535480 | − | 0.844548i | \(-0.679869\pi\) | ||||
−0.535480 | + | 0.844548i | \(0.679869\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −13.3790 | −0.428912 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 1.21775 | 0.0389992 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −5.87049 | −0.187814 | −0.0939069 | − | 0.995581i | \(-0.529936\pi\) | ||||
−0.0939069 | + | 0.995581i | \(0.529936\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −68.8897 | −2.20173 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 20.5938 | 0.657511 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 53.4357 | 1.70433 | 0.852167 | − | 0.523269i | \(-0.175288\pi\) | ||||
0.852167 | + | 0.523269i | \(0.175288\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 5.98368 | 0.190656 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0.516142 | 0.0164290 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 20.2577 | 0.644158 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 2.14776 | 0.0682260 | 0.0341130 | − | 0.999418i | \(-0.489139\pi\) | ||||
0.0341130 | + | 0.999418i | \(0.489139\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 3.32192 | 0.105418 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 68.2927 | 2.16503 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 30.5213 | 0.966618 | 0.483309 | − | 0.875450i | \(-0.339435\pi\) | ||||
0.483309 | + | 0.875450i | \(0.339435\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 7.84257 | 0.248128 |
(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 | 8024.2.a.w.1.11 | ✓ | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8024.2.a.w.1.11 | ✓ | 20 | 1.1 | even | 1 | trivial |