Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4008,2,Mod(1,4008)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4008, 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("4008.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4008 = 2^{3} \cdot 3 \cdot 167 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4008.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: | \(32.0040411301\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 4 x^{11} - 31 x^{10} + 131 x^{9} + 309 x^{8} - 1453 x^{7} - 1072 x^{6} + 6350 x^{5} + \cdots + 3008 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-3.64003\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4008.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −3.64003 | −1.62787 | −0.813935 | − | 0.580957i | \(-0.802679\pi\) | ||||
−0.813935 | + | 0.580957i | \(0.802679\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.45249 | −0.548991 | −0.274496 | − | 0.961588i | \(-0.588511\pi\) | ||||
−0.274496 | + | 0.961588i | \(0.588511\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −6.42846 | −1.93825 | −0.969127 | − | 0.246561i | \(-0.920699\pi\) | ||||
−0.969127 | + | 0.246561i | \(0.920699\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −4.46811 | −1.23923 | −0.619615 | − | 0.784906i | \(-0.712711\pi\) | ||||
−0.619615 | + | 0.784906i | \(0.712711\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −3.64003 | −0.939851 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −3.08793 | −0.748932 | −0.374466 | − | 0.927241i | \(-0.622174\pi\) | ||||
−0.374466 | + | 0.927241i | \(0.622174\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.23264 | −0.282787 | −0.141393 | − | 0.989954i | \(-0.545158\pi\) | ||||
−0.141393 | + | 0.989954i | \(0.545158\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.45249 | −0.316960 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.06502 | 0.222071 | 0.111036 | − | 0.993816i | \(-0.464583\pi\) | ||||
0.111036 | + | 0.993816i | \(0.464583\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 8.24979 | 1.64996 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1.27384 | 0.236546 | 0.118273 | − | 0.992981i | \(-0.462264\pi\) | ||||
0.118273 | + | 0.992981i | \(0.462264\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.58373 | 0.823262 | 0.411631 | − | 0.911351i | \(-0.364959\pi\) | ||||
0.411631 | + | 0.911351i | \(0.364959\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −6.42846 | −1.11905 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 5.28712 | 0.893686 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 3.59595 | 0.591171 | 0.295586 | − | 0.955316i | \(-0.404485\pi\) | ||||
0.295586 | + | 0.955316i | \(0.404485\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −4.46811 | −0.715470 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −9.41085 | −1.46973 | −0.734864 | − | 0.678214i | \(-0.762754\pi\) | ||||
−0.734864 | + | 0.678214i | \(0.762754\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.44738 | 0.220724 | 0.110362 | − | 0.993891i | \(-0.464799\pi\) | ||||
0.110362 | + | 0.993891i | \(0.464799\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −3.64003 | −0.542623 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −3.82478 | −0.557901 | −0.278951 | − | 0.960305i | \(-0.589987\pi\) | ||||
−0.278951 | + | 0.960305i | \(0.589987\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −4.89026 | −0.698609 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −3.08793 | −0.432396 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 9.67640 | 1.32916 | 0.664578 | − | 0.747219i | \(-0.268611\pi\) | ||||
0.664578 | + | 0.747219i | \(0.268611\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 23.3998 | 3.15522 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −1.23264 | −0.163267 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 7.68527 | 1.00054 | 0.500269 | − | 0.865870i | \(-0.333235\pi\) | ||||
0.500269 | + | 0.865870i | \(0.333235\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 6.50606 | 0.833016 | 0.416508 | − | 0.909132i | \(-0.363254\pi\) | ||||
0.416508 | + | 0.909132i | \(0.363254\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −1.45249 | −0.182997 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 16.2640 | 2.01731 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −7.73227 | −0.944647 | −0.472324 | − | 0.881425i | \(-0.656585\pi\) | ||||
−0.472324 | + | 0.881425i | \(0.656585\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 1.06502 | 0.128213 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −10.4166 | −1.23622 | −0.618109 | − | 0.786092i | \(-0.712101\pi\) | ||||
−0.618109 | + | 0.786092i | \(0.712101\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 2.25213 | 0.263591 | 0.131796 | − | 0.991277i | \(-0.457926\pi\) | ||||
0.131796 | + | 0.991277i | \(0.457926\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 8.24979 | 0.952604 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 9.33730 | 1.06408 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 15.3378 | 1.72564 | 0.862818 | − | 0.505515i | \(-0.168698\pi\) | ||||
0.862818 | + | 0.505515i | \(0.168698\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 2.64462 | 0.290285 | 0.145142 | − | 0.989411i | \(-0.453636\pi\) | ||||
0.145142 | + | 0.989411i | \(0.453636\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 11.2401 | 1.21916 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 1.27384 | 0.136570 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 3.71818 | 0.394126 | 0.197063 | − | 0.980391i | \(-0.436860\pi\) | ||||
0.197063 | + | 0.980391i | \(0.436860\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 6.48990 | 0.680327 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 4.58373 | 0.475311 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 4.48683 | 0.460340 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 5.92298 | 0.601388 | 0.300694 | − | 0.953721i | \(-0.402782\pi\) | ||||
0.300694 | + | 0.953721i | \(0.402782\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −6.42846 | −0.646085 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 13.6005 | 1.35330 | 0.676648 | − | 0.736307i | \(-0.263432\pi\) | ||||
0.676648 | + | 0.736307i | \(0.263432\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 7.45117 | 0.734186 | 0.367093 | − | 0.930184i | \(-0.380353\pi\) | ||||
0.367093 | + | 0.930184i | \(0.380353\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 5.28712 | 0.515970 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −16.0477 | −1.55139 | −0.775695 | − | 0.631108i | \(-0.782601\pi\) | ||||
−0.775695 | + | 0.631108i | \(0.782601\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −17.8483 | −1.70956 | −0.854778 | − | 0.518994i | \(-0.826307\pi\) | ||||
−0.854778 | + | 0.518994i | \(0.826307\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 3.59595 | 0.341313 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 6.77367 | 0.637213 | 0.318607 | − | 0.947887i | \(-0.396785\pi\) | ||||
0.318607 | + | 0.947887i | \(0.396785\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −3.87669 | −0.361503 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −4.46811 | −0.413077 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 4.48520 | 0.411157 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 30.3251 | 2.75683 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −9.41085 | −0.848548 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −11.8293 | −1.05805 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 6.35044 | 0.563511 | 0.281755 | − | 0.959486i | \(-0.409083\pi\) | ||||
0.281755 | + | 0.959486i | \(0.409083\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 1.44738 | 0.127435 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −6.51198 | −0.568954 | −0.284477 | − | 0.958683i | \(-0.591820\pi\) | ||||
−0.284477 | + | 0.958683i | \(0.591820\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1.79040 | 0.155247 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −3.64003 | −0.313284 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −16.8446 | −1.43914 | −0.719568 | − | 0.694422i | \(-0.755660\pi\) | ||||
−0.719568 | + | 0.694422i | \(0.755660\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −18.0810 | −1.53361 | −0.766806 | − | 0.641879i | \(-0.778155\pi\) | ||||
−0.766806 | + | 0.641879i | \(0.778155\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −3.82478 | −0.322104 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 28.7231 | 2.40194 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −4.63680 | −0.385065 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −4.89026 | −0.403342 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −17.4067 | −1.42602 | −0.713008 | − | 0.701156i | \(-0.752667\pi\) | ||||
−0.713008 | + | 0.701156i | \(0.752667\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 12.0142 | 0.977702 | 0.488851 | − | 0.872367i | \(-0.337416\pi\) | ||||
0.488851 | + | 0.872367i | \(0.337416\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −3.08793 | −0.249644 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −16.6849 | −1.34016 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −5.05762 | −0.403642 | −0.201821 | − | 0.979422i | \(-0.564686\pi\) | ||||
−0.201821 | + | 0.979422i | \(0.564686\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 9.67640 | 0.767388 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −1.54693 | −0.121915 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −11.8323 | −0.926780 | −0.463390 | − | 0.886155i | \(-0.653367\pi\) | ||||
−0.463390 | + | 0.886155i | \(0.653367\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 23.3998 | 1.82167 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 1.00000 | 0.0773823 | ||||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 6.96400 | 0.535692 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −1.23264 | −0.0942622 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −1.55262 | −0.118043 | −0.0590216 | − | 0.998257i | \(-0.518798\pi\) | ||||
−0.0590216 | + | 0.998257i | \(0.518798\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −11.9828 | −0.905812 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 7.68527 | 0.577660 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −12.2516 | −0.915726 | −0.457863 | − | 0.889023i | \(-0.651385\pi\) | ||||
−0.457863 | + | 0.889023i | \(0.651385\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 2.63499 | 0.195857 | 0.0979286 | − | 0.995193i | \(-0.468778\pi\) | ||||
0.0979286 | + | 0.995193i | \(0.468778\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 6.50606 | 0.480942 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −13.0894 | −0.962349 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 19.8506 | 1.45162 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −1.45249 | −0.105653 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 10.3171 | 0.746519 | 0.373260 | − | 0.927727i | \(-0.378240\pi\) | ||||
0.373260 | + | 0.927727i | \(0.378240\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −5.69351 | −0.409828 | −0.204914 | − | 0.978780i | \(-0.565691\pi\) | ||||
−0.204914 | + | 0.978780i | \(0.565691\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 16.2640 | 1.16469 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 2.61257 | 0.186138 | 0.0930690 | − | 0.995660i | \(-0.470332\pi\) | ||||
0.0930690 | + | 0.995660i | \(0.470332\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 26.1850 | 1.85620 | 0.928102 | − | 0.372325i | \(-0.121439\pi\) | ||||
0.928102 | + | 0.372325i | \(0.121439\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −7.73227 | −0.545392 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −1.85024 | −0.129861 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 34.2557 | 2.39253 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 1.06502 | 0.0740237 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 7.92397 | 0.548112 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 17.2397 | 1.18683 | 0.593416 | − | 0.804896i | \(-0.297779\pi\) | ||||
0.593416 | + | 0.804896i | \(0.297779\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −10.4166 | −0.713731 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −5.26851 | −0.359309 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −6.65784 | −0.451964 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 2.25213 | 0.152185 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 13.7972 | 0.928100 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −15.2142 | −1.01882 | −0.509408 | − | 0.860525i | \(-0.670135\pi\) | ||||
−0.509408 | + | 0.860525i | \(0.670135\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 8.24979 | 0.549986 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 27.6521 | 1.83533 | 0.917666 | − | 0.397353i | \(-0.130071\pi\) | ||||
0.917666 | + | 0.397353i | \(0.130071\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −17.6115 | −1.16380 | −0.581900 | − | 0.813261i | \(-0.697690\pi\) | ||||
−0.581900 | + | 0.813261i | \(0.697690\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 9.33730 | 0.614350 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −5.06669 | −0.331930 | −0.165965 | − | 0.986132i | \(-0.553074\pi\) | ||||
−0.165965 | + | 0.986132i | \(0.553074\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 13.9223 | 0.908190 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 15.3378 | 0.996296 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 14.5435 | 0.940741 | 0.470371 | − | 0.882469i | \(-0.344120\pi\) | ||||
0.470371 | + | 0.882469i | \(0.344120\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 14.4271 | 0.929328 | 0.464664 | − | 0.885487i | \(-0.346175\pi\) | ||||
0.464664 | + | 0.885487i | \(0.346175\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 17.8007 | 1.13724 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 5.50756 | 0.350438 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 2.64462 | 0.167596 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −18.0066 | −1.13657 | −0.568283 | − | 0.822833i | \(-0.692392\pi\) | ||||
−0.568283 | + | 0.822833i | \(0.692392\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −6.84641 | −0.430430 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 11.2401 | 0.703885 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 3.82924 | 0.238861 | 0.119431 | − | 0.992843i | \(-0.461893\pi\) | ||||
0.119431 | + | 0.992843i | \(0.461893\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −5.22310 | −0.324548 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 1.27384 | 0.0788485 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −20.9906 | −1.29434 | −0.647168 | − | 0.762348i | \(-0.724047\pi\) | ||||
−0.647168 | + | 0.762348i | \(0.724047\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −35.2223 | −2.16369 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 3.71818 | 0.227549 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −22.2290 | −1.35533 | −0.677664 | − | 0.735371i | \(-0.737008\pi\) | ||||
−0.677664 | + | 0.735371i | \(0.737008\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 12.1552 | 0.738377 | 0.369189 | − | 0.929355i | \(-0.379636\pi\) | ||||
0.369189 | + | 0.929355i | \(0.379636\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 6.48990 | 0.392787 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −53.0335 | −3.19804 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −7.50659 | −0.451027 | −0.225514 | − | 0.974240i | \(-0.572406\pi\) | ||||
−0.225514 | + | 0.974240i | \(0.572406\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 4.58373 | 0.274421 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 3.74128 | 0.223186 | 0.111593 | − | 0.993754i | \(-0.464405\pi\) | ||||
0.111593 | + | 0.993754i | \(0.464405\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 2.47396 | 0.147062 | 0.0735309 | − | 0.997293i | \(-0.476573\pi\) | ||||
0.0735309 | + | 0.997293i | \(0.476573\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 4.48683 | 0.265777 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 13.6692 | 0.806868 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −7.46471 | −0.439100 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 5.92298 | 0.347212 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 26.1746 | 1.52914 | 0.764568 | − | 0.644543i | \(-0.222952\pi\) | ||||
0.764568 | + | 0.644543i | \(0.222952\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −27.9746 | −1.62874 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −6.42846 | −0.373017 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −4.75861 | −0.275197 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −2.10231 | −0.121175 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 13.6005 | 0.781326 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −23.6822 | −1.35604 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 28.4693 | 1.62483 | 0.812413 | − | 0.583082i | \(-0.198154\pi\) | ||||
0.812413 | + | 0.583082i | \(0.198154\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 7.45117 | 0.423882 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −0.793105 | −0.0449728 | −0.0224864 | − | 0.999747i | \(-0.507158\pi\) | ||||
−0.0224864 | + | 0.999747i | \(0.507158\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 11.1869 | 0.632319 | 0.316160 | − | 0.948706i | \(-0.397606\pi\) | ||||
0.316160 | + | 0.948706i | \(0.397606\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 5.28712 | 0.297895 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −12.2513 | −0.688103 | −0.344052 | − | 0.938951i | \(-0.611800\pi\) | ||||
−0.344052 | + | 0.938951i | \(0.611800\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −8.18881 | −0.458485 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −16.0477 | −0.895696 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 3.80630 | 0.211788 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −36.8610 | −2.04468 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −17.8483 | −0.987012 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 5.55547 | 0.306283 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 7.48597 | 0.411466 | 0.205733 | − | 0.978608i | \(-0.434042\pi\) | ||||
0.205733 | + | 0.978608i | \(0.434042\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 3.59595 | 0.197057 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 28.1457 | 1.53776 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 24.8638 | 1.35442 | 0.677208 | − | 0.735792i | \(-0.263190\pi\) | ||||
0.677208 | + | 0.735792i | \(0.263190\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 6.77367 | 0.367895 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −29.4663 | −1.59569 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 17.2705 | 0.932521 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −3.87669 | −0.208714 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −11.7194 | −0.629132 | −0.314566 | − | 0.949236i | \(-0.601859\pi\) | ||||
−0.314566 | + | 0.949236i | \(0.601859\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −20.1366 | −1.07789 | −0.538945 | − | 0.842341i | \(-0.681177\pi\) | ||||
−0.538945 | + | 0.842341i | \(0.681177\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −4.46811 | −0.238490 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 25.7845 | 1.37237 | 0.686184 | − | 0.727428i | \(-0.259284\pi\) | ||||
0.686184 | + | 0.727428i | \(0.259284\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 37.9165 | 2.01240 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 4.48520 | 0.237382 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 27.1422 | 1.43251 | 0.716256 | − | 0.697838i | \(-0.245854\pi\) | ||||
0.716256 | + | 0.697838i | \(0.245854\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −17.4806 | −0.920032 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 30.3251 | 1.59166 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −8.19779 | −0.429092 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 26.6657 | 1.39194 | 0.695969 | − | 0.718072i | \(-0.254975\pi\) | ||||
0.695969 | + | 0.718072i | \(0.254975\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −9.41085 | −0.489909 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −14.0549 | −0.729695 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −23.4526 | −1.21433 | −0.607165 | − | 0.794576i | \(-0.707693\pi\) | ||||
−0.607165 | + | 0.794576i | \(0.707693\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −11.8293 | −0.610863 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −5.69164 | −0.293134 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 6.29453 | 0.323328 | 0.161664 | − | 0.986846i | \(-0.448314\pi\) | ||||
0.161664 | + | 0.986846i | \(0.448314\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 6.35044 | 0.325343 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 17.7486 | 0.906913 | 0.453456 | − | 0.891278i | \(-0.350191\pi\) | ||||
0.453456 | + | 0.891278i | \(0.350191\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −33.9880 | −1.73219 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 1.44738 | 0.0735746 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 23.1572 | 1.17412 | 0.587058 | − | 0.809545i | \(-0.300286\pi\) | ||||
0.587058 | + | 0.809545i | \(0.300286\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −3.28869 | −0.166316 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −6.51198 | −0.328486 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −55.8299 | −2.80911 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −24.1170 | −1.21040 | −0.605198 | − | 0.796075i | \(-0.706906\pi\) | ||||
−0.605198 | + | 0.796075i | \(0.706906\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 1.79040 | 0.0896321 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −5.17511 | −0.258433 | −0.129216 | − | 0.991616i | \(-0.541246\pi\) | ||||
−0.129216 | + | 0.991616i | \(0.541246\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −20.4806 | −1.02021 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −3.64003 | −0.180874 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −23.1165 | −1.14584 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −4.19365 | −0.207363 | −0.103681 | − | 0.994611i | \(-0.533062\pi\) | ||||
−0.103681 | + | 0.994611i | \(0.533062\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −16.8446 | −0.830885 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −11.1628 | −0.549286 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −9.62649 | −0.472546 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −18.0810 | −0.885431 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −5.34361 | −0.261053 | −0.130526 | − | 0.991445i | \(-0.541667\pi\) | ||||
−0.130526 | + | 0.991445i | \(0.541667\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −19.8415 | −0.967017 | −0.483509 | − | 0.875340i | \(-0.660638\pi\) | ||||
−0.483509 | + | 0.875340i | \(0.660638\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −3.82478 | −0.185967 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −25.4747 | −1.23571 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −9.45002 | −0.457318 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 28.7231 | 1.38676 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 36.1172 | 1.73970 | 0.869852 | − | 0.493313i | \(-0.164214\pi\) | ||||
0.869852 | + | 0.493313i | \(0.164214\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 22.4261 | 1.07773 | 0.538866 | − | 0.842392i | \(-0.318853\pi\) | ||||
0.538866 | + | 0.842392i | \(0.318853\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −4.63680 | −0.222318 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −1.31278 | −0.0627987 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 31.0932 | 1.48400 | 0.741999 | − | 0.670401i | \(-0.233878\pi\) | ||||
0.741999 | + | 0.670401i | \(0.233878\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −4.89026 | −0.232870 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −21.4614 | −1.01966 | −0.509830 | − | 0.860275i | \(-0.670292\pi\) | ||||
−0.509830 | + | 0.860275i | \(0.670292\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −13.5343 | −0.641586 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −17.4067 | −0.823310 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −34.3531 | −1.62122 | −0.810611 | − | 0.585585i | \(-0.800865\pi\) | ||||
−0.810611 | + | 0.585585i | \(0.800865\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 60.4973 | 2.84871 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 12.0142 | 0.564476 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −23.6234 | −1.10748 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −21.6954 | −1.01487 | −0.507434 | − | 0.861691i | \(-0.669406\pi\) | ||||
−0.507434 | + | 0.861691i | \(0.669406\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −3.08793 | −0.144132 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 9.58945 | 0.446625 | 0.223313 | − | 0.974747i | \(-0.428313\pi\) | ||||
0.223313 | + | 0.974747i | \(0.428313\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 2.30946 | 0.107330 | 0.0536648 | − | 0.998559i | \(-0.482910\pi\) | ||||
0.0536648 | + | 0.998559i | \(0.482910\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −16.6849 | −0.773744 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 13.5368 | 0.626408 | 0.313204 | − | 0.949686i | \(-0.398598\pi\) | ||||
0.313204 | + | 0.949686i | \(0.398598\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 11.2311 | 0.518603 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −5.05762 | −0.233043 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −9.30444 | −0.427819 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −10.1690 | −0.466586 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 9.67640 | 0.443052 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 2.42006 | 0.110575 | 0.0552876 | − | 0.998470i | \(-0.482392\pi\) | ||||
0.0552876 | + | 0.998470i | \(0.482392\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −16.0671 | −0.732597 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −1.54693 | −0.0703877 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −21.5598 | −0.978981 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −24.3709 | −1.10435 | −0.552174 | − | 0.833729i | \(-0.686202\pi\) | ||||
−0.552174 | + | 0.833729i | \(0.686202\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −11.8323 | −0.535076 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −9.19207 | −0.414832 | −0.207416 | − | 0.978253i | \(-0.566505\pi\) | ||||
−0.207416 | + | 0.978253i | \(0.566505\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −3.93352 | −0.177157 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 23.3998 | 1.05174 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 15.1300 | 0.678673 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 42.8570 | 1.91854 | 0.959272 | − | 0.282483i | \(-0.0911580\pi\) | ||||
0.959272 | + | 0.282483i | \(0.0911580\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 1.00000 | 0.0446767 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 19.5868 | 0.873332 | 0.436666 | − | 0.899624i | \(-0.356159\pi\) | ||||
0.436666 | + | 0.899624i | \(0.356159\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −49.5060 | −2.20299 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 6.96400 | 0.309282 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 6.59346 | 0.292250 | 0.146125 | − | 0.989266i | \(-0.453320\pi\) | ||||
0.146125 | + | 0.989266i | \(0.453320\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −3.27120 | −0.144709 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −1.23264 | −0.0544223 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −27.1225 | −1.19516 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 24.5874 | 1.08135 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −1.55262 | −0.0681523 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −32.7504 | −1.43482 | −0.717410 | − | 0.696652i | \(-0.754672\pi\) | ||||
−0.717410 | + | 0.696652i | \(0.754672\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 7.97133 | 0.348562 | 0.174281 | − | 0.984696i | \(-0.444240\pi\) | ||||
0.174281 | + | 0.984696i | \(0.444240\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −11.9828 | −0.522971 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −14.1542 | −0.616568 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −21.8657 | −0.950684 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 7.68527 | 0.333512 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 42.0487 | 1.82133 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 58.4141 | 2.52546 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −12.2516 | −0.528695 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 31.4369 | 1.35408 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −21.8235 | −0.938267 | −0.469134 | − | 0.883127i | \(-0.655434\pi\) | ||||
−0.469134 | + | 0.883127i | \(0.655434\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 2.63499 | 0.113078 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 64.9682 | 2.78293 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 19.2970 | 0.825080 | 0.412540 | − | 0.910939i | \(-0.364642\pi\) | ||||
0.412540 | + | 0.910939i | \(0.364642\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 6.50606 | 0.277672 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −1.57018 | −0.0668919 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −22.2780 | −0.947359 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −13.0894 | −0.555613 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 7.31531 | 0.309959 | 0.154980 | − | 0.987918i | \(-0.450469\pi\) | ||||
0.154980 | + | 0.987918i | \(0.450469\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −6.46706 | −0.273528 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 19.8506 | 0.838094 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 20.8755 | 0.879795 | 0.439898 | − | 0.898048i | \(-0.355015\pi\) | ||||
0.439898 | + | 0.898048i | \(0.355015\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −24.6563 | −1.03730 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −1.45249 | −0.0609990 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 7.99366 | 0.335112 | 0.167556 | − | 0.985863i | \(-0.446413\pi\) | ||||
0.167556 | + | 0.985863i | \(0.446413\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −2.10566 | −0.0881193 | −0.0440596 | − | 0.999029i | \(-0.514029\pi\) | ||||
−0.0440596 | + | 0.999029i | \(0.514029\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 10.3171 | 0.431003 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 8.78616 | 0.366408 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −27.1596 | −1.13067 | −0.565334 | − | 0.824862i | \(-0.691253\pi\) | ||||
−0.565334 | + | 0.824862i | \(0.691253\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −5.69351 | −0.236614 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −3.84130 | −0.159364 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −62.2043 | −2.57624 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 16.2640 | 0.672435 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −18.0687 | −0.745773 | −0.372887 | − | 0.927877i | \(-0.621632\pi\) | ||||
−0.372887 | + | 0.927877i | \(0.621632\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −5.65008 | −0.232808 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 2.61257 | 0.107467 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −9.55608 | −0.392421 | −0.196211 | − | 0.980562i | \(-0.562864\pi\) | ||||
−0.196211 | + | 0.980562i | \(0.562864\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −16.3262 | −0.669310 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 26.1850 | 1.07168 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −24.3175 | −0.993586 | −0.496793 | − | 0.867869i | \(-0.665489\pi\) | ||||
−0.496793 | + | 0.867869i | \(0.665489\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 37.5779 | 1.53284 | 0.766418 | − | 0.642343i | \(-0.222037\pi\) | ||||
0.766418 | + | 0.642343i | \(0.222037\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −7.73227 | −0.314882 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −110.384 | −4.48776 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 28.2208 | 1.14545 | 0.572723 | − | 0.819749i | \(-0.305887\pi\) | ||||
0.572723 | + | 0.819749i | \(0.305887\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −1.85024 | −0.0749755 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 17.0895 | 0.691368 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 27.0371 | 1.09202 | 0.546009 | − | 0.837779i | \(-0.316146\pi\) | ||||
0.546009 | + | 0.837779i | \(0.316146\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 34.2557 | 1.38133 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 13.1293 | 0.528565 | 0.264282 | − | 0.964445i | \(-0.414865\pi\) | ||||
0.264282 | + | 0.964445i | \(0.414865\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −11.7358 | −0.471702 | −0.235851 | − | 0.971789i | \(-0.575788\pi\) | ||||
−0.235851 | + | 0.971789i | \(0.575788\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1.06502 | 0.0427376 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −5.40063 | −0.216372 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.81008 | 0.0724031 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 7.92397 | 0.316453 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −11.1040 | −0.442747 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −4.55833 | −0.181464 | −0.0907321 | − | 0.995875i | \(-0.528921\pi\) | ||||
−0.0907321 | + | 0.995875i | \(0.528921\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 17.2397 | 0.685218 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −23.1158 | −0.917322 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 21.8502 | 0.865737 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −10.4166 | −0.412073 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −42.0838 | −1.66221 | −0.831105 | − | 0.556116i | \(-0.812291\pi\) | ||||
−0.831105 | + | 0.556116i | \(0.812291\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −10.8426 | −0.427590 | −0.213795 | − | 0.976879i | \(-0.568582\pi\) | ||||
−0.213795 | + | 0.976879i | \(0.568582\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −5.26851 | −0.207447 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 29.1805 | 1.14721 | 0.573603 | − | 0.819134i | \(-0.305545\pi\) | ||||
0.573603 | + | 0.819134i | \(0.305545\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −49.4045 | −1.93930 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −6.65784 | −0.260941 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 24.1983 | 0.946953 | 0.473477 | − | 0.880806i | \(-0.342999\pi\) | ||||
0.473477 | + | 0.880806i | \(0.342999\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 23.7038 | 0.926183 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 2.25213 | 0.0878638 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 4.14327 | 0.161399 | 0.0806995 | − | 0.996738i | \(-0.474285\pi\) | ||||
0.0806995 | + | 0.996738i | \(0.474285\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −16.6852 | −0.648980 | −0.324490 | − | 0.945889i | \(-0.605193\pi\) | ||||
−0.324490 | + | 0.945889i | \(0.605193\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 13.7972 | 0.535839 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −6.51710 | −0.252722 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1.35666 | 0.0525299 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −15.2142 | −0.588213 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −41.8240 | −1.61460 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 35.7946 | 1.37978 | 0.689891 | − | 0.723914i | \(-0.257659\pi\) | ||||
0.689891 | + | 0.723914i | \(0.257659\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 8.24979 | 0.317535 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −18.4624 | −0.709567 | −0.354783 | − | 0.934949i | \(-0.615445\pi\) | ||||
−0.354783 | + | 0.934949i | \(0.615445\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −8.60310 | −0.330157 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 27.6521 | 1.05963 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 2.16551 | 0.0828610 | 0.0414305 | − | 0.999141i | \(-0.486808\pi\) | ||||
0.0414305 | + | 0.999141i | \(0.486808\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 61.3150 | 2.34272 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −17.6115 | −0.671920 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −43.2352 | −1.64713 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −15.9965 | −0.608535 | −0.304268 | − | 0.952587i | \(-0.598412\pi\) | ||||
−0.304268 | + | 0.952587i | \(0.598412\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 9.33730 | 0.354695 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 65.8153 | 2.49652 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 29.0600 | 1.10073 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −5.06669 | −0.191640 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 32.8720 | 1.24156 | 0.620779 | − | 0.783986i | \(-0.286817\pi\) | ||||
0.620779 | + | 0.783986i | \(0.286817\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −4.43251 | −0.167175 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 13.9223 | 0.524344 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −19.7546 | −0.742948 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 36.9184 | 1.38650 | 0.693249 | − | 0.720698i | \(-0.256178\pi\) | ||||
0.693249 | + | 0.720698i | \(0.256178\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 15.3378 | 0.575212 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 4.88175 | 0.182823 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −104.553 | −3.91005 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 14.5435 | 0.543137 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −11.5566 | −0.430989 | −0.215494 | − | 0.976505i | \(-0.569136\pi\) | ||||
−0.215494 | + | 0.976505i | \(0.569136\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −10.8228 | −0.403062 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 14.4271 | 0.536548 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 10.5089 | 0.390290 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 15.0101 | 0.556696 | 0.278348 | − | 0.960480i | \(-0.410213\pi\) | ||||
0.278348 | + | 0.960480i | \(0.410213\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −4.46941 | −0.165307 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 44.7907 | 1.65438 | 0.827191 | − | 0.561921i | \(-0.189937\pi\) | ||||
0.827191 | + | 0.561921i | \(0.189937\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 17.8007 | 0.656588 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 49.7066 | 1.83097 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 7.53470 | 0.277168 | 0.138584 | − | 0.990351i | \(-0.455745\pi\) | ||||
0.138584 | + | 0.990351i | \(0.455745\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 5.50756 | 0.202325 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −31.7204 | −1.16371 | −0.581855 | − | 0.813293i | \(-0.697673\pi\) | ||||
−0.581855 | + | 0.813293i | \(0.697673\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 63.3610 | 2.32137 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 2.64462 | 0.0967616 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 23.3092 | 0.851700 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 42.8785 | 1.56466 | 0.782329 | − | 0.622866i | \(-0.214032\pi\) | ||||
0.782329 | + | 0.622866i | \(0.214032\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −18.0066 | −0.656196 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −43.7320 | −1.59157 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −29.9811 | −1.08968 | −0.544841 | − | 0.838539i | \(-0.683410\pi\) | ||||
−0.544841 | + | 0.838539i | \(0.683410\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −6.84641 | −0.248509 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 37.2320 | 1.34966 | 0.674829 | − | 0.737974i | \(-0.264217\pi\) | ||||
0.674829 | + | 0.737974i | \(0.264217\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 25.9245 | 0.938531 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 11.2401 | 0.406388 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −34.3386 | −1.23990 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −14.3416 | −0.517171 | −0.258585 | − | 0.965988i | \(-0.583256\pi\) | ||||
−0.258585 | + | 0.965988i | \(0.583256\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 3.82924 | 0.137907 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 19.2550 | 0.692553 | 0.346277 | − | 0.938132i | \(-0.387446\pi\) | ||||
0.346277 | + | 0.938132i | \(0.387446\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 37.8148 | 1.35835 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −5.22310 | −0.187378 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 11.6002 | 0.415619 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 66.9625 | 2.39611 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 1.27384 | 0.0455232 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 18.4099 | 0.657077 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −41.2670 | −1.47101 | −0.735504 | − | 0.677520i | \(-0.763055\pi\) | ||||
−0.735504 | + | 0.677520i | \(0.763055\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −20.9906 | −0.747285 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −9.83872 | −0.349824 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −29.0698 | −1.03230 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −35.2223 | −1.24921 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −25.6409 | −0.908248 | −0.454124 | − | 0.890938i | \(-0.650048\pi\) | ||||
−0.454124 | + | 0.890938i | \(0.650048\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 11.8106 | 0.417830 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 3.71818 | 0.131375 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −14.4777 | −0.510907 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 5.63086 | 0.198462 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −22.2290 | −0.782499 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 9.07049 | 0.318901 | 0.159451 | − | 0.987206i | \(-0.449028\pi\) | ||||
0.159451 | + | 0.987206i | \(0.449028\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 26.9376 | 0.945906 | 0.472953 | − | 0.881088i | \(-0.343188\pi\) | ||||
0.472953 | + | 0.881088i | \(0.343188\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 12.1552 | 0.426302 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 43.0700 | 1.50868 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −1.78410 | −0.0624177 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 6.48990 | 0.226776 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −48.6191 | −1.69682 | −0.848410 | − | 0.529340i | \(-0.822440\pi\) | ||||
−0.848410 | + | 0.529340i | \(0.822440\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −50.5500 | −1.76206 | −0.881032 | − | 0.473057i | \(-0.843150\pi\) | ||||
−0.881032 | + | 0.473057i | \(0.843150\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −53.0335 | −1.84639 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −7.92496 | −0.275578 | −0.137789 | − | 0.990462i | \(-0.544000\pi\) | ||||
−0.137789 | + | 0.990462i | \(0.544000\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −3.81681 | −0.132563 | −0.0662816 | − | 0.997801i | \(-0.521114\pi\) | ||||
−0.0662816 | + | 0.997801i | \(0.521114\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −7.50659 | −0.260401 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 15.1008 | 0.523211 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −3.64003 | −0.125968 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 4.58373 | 0.158437 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 19.7601 | 0.682193 | 0.341096 | − | 0.940028i | \(-0.389202\pi\) | ||||
0.341096 | + | 0.940028i | \(0.389202\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −27.3773 | −0.944046 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 3.74128 | 0.128857 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −25.3491 | −0.872037 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −44.0471 | −1.51348 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 2.47396 | 0.0849062 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 3.82975 | 0.131282 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −15.9023 | −0.544485 | −0.272242 | − | 0.962229i | \(-0.587765\pi\) | ||||
−0.272242 | + | 0.962229i | \(0.587765\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 4.48683 | 0.153447 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 48.5947 | 1.65996 | 0.829981 | − | 0.557792i | \(-0.188351\pi\) | ||||
0.829981 | + | 0.557792i | \(0.188351\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 17.4581 | 0.595662 | 0.297831 | − | 0.954619i | \(-0.403737\pi\) | ||||
0.297831 | + | 0.954619i | \(0.403737\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 13.6692 | 0.465845 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 6.80517 | 0.231651 | 0.115825 | − | 0.993270i | \(-0.463049\pi\) | ||||
0.115825 | + | 0.993270i | \(0.463049\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 5.65156 | 0.192159 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −7.46471 | −0.253515 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −98.5984 | −3.34472 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 34.5486 | 1.17064 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 5.92298 | 0.200463 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 17.1820 | 0.580858 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −13.6188 | −0.459875 | −0.229937 | − | 0.973205i | \(-0.573852\pi\) | ||||
−0.229937 | + | 0.973205i | \(0.573852\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 26.1746 | 0.882847 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 25.7736 | 0.868336 | 0.434168 | − | 0.900832i | \(-0.357042\pi\) | ||||
0.434168 | + | 0.900832i | \(0.357042\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 24.1106 | 0.811386 | 0.405693 | − | 0.914009i | \(-0.367030\pi\) | ||||
0.405693 | + | 0.914009i | \(0.367030\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −27.9746 | −0.940355 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −17.4973 | −0.587503 | −0.293751 | − | 0.955882i | \(-0.594904\pi\) | ||||
−0.293751 | + | 0.955882i | \(0.594904\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −9.22398 | −0.309362 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −6.42846 | −0.215362 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 4.71457 | 0.157767 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 44.5961 | 1.49068 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −4.75861 | −0.158885 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 5.83892 | 0.194739 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −29.8800 | −0.995447 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −2.10231 | −0.0699607 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −9.59143 | −0.318830 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −41.0307 | −1.36240 | −0.681201 | − | 0.732097i | \(-0.738542\pi\) | ||||
−0.681201 | + | 0.732097i | \(0.738542\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 13.6005 | 0.451099 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 21.4782 | 0.711606 | 0.355803 | − | 0.934561i | \(-0.384207\pi\) | ||||
0.355803 | + | 0.934561i | \(0.384207\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −17.0008 | −0.562646 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −23.6822 | −0.782911 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 9.45861 | 0.312351 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −32.3806 | −1.06814 | −0.534068 | − | 0.845441i | \(-0.679337\pi\) | ||||
−0.534068 | + | 0.845441i | \(0.679337\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 28.4693 | 0.938094 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 46.5423 | 1.53196 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 29.6659 | 0.975408 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 7.45117 | 0.244729 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −0.577842 | −0.0189584 | −0.00947918 | − | 0.999955i | \(-0.503017\pi\) | ||||
−0.00947918 | + | 0.999955i | \(0.503017\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 6.02792 | 0.197557 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −0.793105 | −0.0259651 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −72.2568 | −2.36305 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −29.2764 | −0.956417 | −0.478209 | − | 0.878246i | \(-0.658714\pi\) | ||||
−0.478209 | + | 0.878246i | \(0.658714\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 11.1869 | 0.365070 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 3.37113 | 0.109896 | 0.0549479 | − | 0.998489i | \(-0.482501\pi\) | ||||
0.0549479 | + | 0.998489i | \(0.482501\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −10.0227 | −0.326384 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 5.28712 | 0.171990 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 0.805786 | 0.0261845 | 0.0130923 | − | 0.999914i | \(-0.495832\pi\) | ||||
0.0130923 | + | 0.999914i | \(0.495832\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −10.0627 | −0.326650 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −12.2513 | −0.397277 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −16.1015 | −0.521580 | −0.260790 | − | 0.965396i | \(-0.583983\pi\) | ||||
−0.260790 | + | 0.965396i | \(0.583983\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −37.5545 | −1.21524 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −8.18881 | −0.264707 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 24.4668 | 0.790073 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −9.98941 | −0.322239 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −16.0477 | −0.517130 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 20.7245 | 0.667147 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −7.26784 | −0.233718 | −0.116859 | − | 0.993149i | \(-0.537283\pi\) | ||||
−0.116859 | + | 0.993149i | \(0.537283\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 3.80630 | 0.122276 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −49.9617 | −1.60335 | −0.801674 | − | 0.597761i | \(-0.796057\pi\) | ||||
−0.801674 | + | 0.597761i | \(0.796057\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 26.2626 | 0.841939 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −36.8610 | −1.18050 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 15.2258 | 0.487117 | 0.243558 | − | 0.969886i | \(-0.421685\pi\) | ||||
0.243558 | + | 0.969886i | \(0.421685\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −23.9022 | −0.763917 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −17.8483 | −0.569852 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 31.1238 | 0.992695 | 0.496348 | − | 0.868124i | \(-0.334674\pi\) | ||||
0.496348 | + | 0.868124i | \(0.334674\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −9.50982 | −0.303008 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 5.55547 | 0.176832 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 1.54149 | 0.0490164 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −54.9753 | −1.74635 | −0.873174 | − | 0.487409i | \(-0.837942\pi\) | ||||
−0.873174 | + | 0.487409i | \(0.837942\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 7.48597 | 0.237560 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −95.3140 | −3.02166 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −39.2882 | −1.24427 | −0.622135 | − | 0.782910i | \(-0.713734\pi\) | ||||
−0.622135 | + | 0.782910i | \(0.713734\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 3.59595 | 0.113771 |
(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 | 4008.2.a.l.1.1 | ✓ | 12 | |
4.3 | odd | 2 | 8016.2.a.bf.1.1 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4008.2.a.l.1.1 | ✓ | 12 | 1.1 | even | 1 | trivial | |
8016.2.a.bf.1.1 | 12 | 4.3 | odd | 2 |