Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8006,2,Mod(1,8006)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8006, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8006.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8006 = 2 \cdot 4003 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8006.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(63.9282318582\) |
Analytic rank: | \(0\) |
Dimension: | \(92\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.13 | ||
Character | \(\chi\) | \(=\) | 8006.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | −2.53187 | −1.46177 | −0.730887 | − | 0.682499i | \(-0.760893\pi\) | ||||
−0.730887 | + | 0.682499i | \(0.760893\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 4.10502 | 1.83582 | 0.917910 | − | 0.396788i | \(-0.129875\pi\) | ||||
0.917910 | + | 0.396788i | \(0.129875\pi\) | |||||||
\(6\) | 2.53187 | 1.03363 | ||||||||
\(7\) | 0.894818 | 0.338210 | 0.169105 | − | 0.985598i | \(-0.445912\pi\) | ||||
0.169105 | + | 0.985598i | \(0.445912\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 3.41035 | 1.13678 | ||||||||
\(10\) | −4.10502 | −1.29812 | ||||||||
\(11\) | −2.27031 | −0.684525 | −0.342262 | − | 0.939604i | \(-0.611193\pi\) | ||||
−0.342262 | + | 0.939604i | \(0.611193\pi\) | |||||||
\(12\) | −2.53187 | −0.730887 | ||||||||
\(13\) | 3.39210 | 0.940799 | 0.470400 | − | 0.882453i | \(-0.344110\pi\) | ||||
0.470400 | + | 0.882453i | \(0.344110\pi\) | |||||||
\(14\) | −0.894818 | −0.239150 | ||||||||
\(15\) | −10.3934 | −2.68355 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 3.85364 | 0.934645 | 0.467323 | − | 0.884087i | \(-0.345219\pi\) | ||||
0.467323 | + | 0.884087i | \(0.345219\pi\) | |||||||
\(18\) | −3.41035 | −0.803827 | ||||||||
\(19\) | 4.23841 | 0.972358 | 0.486179 | − | 0.873859i | \(-0.338390\pi\) | ||||
0.486179 | + | 0.873859i | \(0.338390\pi\) | |||||||
\(20\) | 4.10502 | 0.917910 | ||||||||
\(21\) | −2.26556 | −0.494386 | ||||||||
\(22\) | 2.27031 | 0.484032 | ||||||||
\(23\) | 2.95247 | 0.615633 | 0.307817 | − | 0.951446i | \(-0.400402\pi\) | ||||
0.307817 | + | 0.951446i | \(0.400402\pi\) | |||||||
\(24\) | 2.53187 | 0.516815 | ||||||||
\(25\) | 11.8512 | 2.37024 | ||||||||
\(26\) | −3.39210 | −0.665246 | ||||||||
\(27\) | −1.03894 | −0.199945 | ||||||||
\(28\) | 0.894818 | 0.169105 | ||||||||
\(29\) | 9.91858 | 1.84183 | 0.920917 | − | 0.389758i | \(-0.127441\pi\) | ||||
0.920917 | + | 0.389758i | \(0.127441\pi\) | |||||||
\(30\) | 10.3934 | 1.89756 | ||||||||
\(31\) | 2.22724 | 0.400024 | 0.200012 | − | 0.979793i | \(-0.435902\pi\) | ||||
0.200012 | + | 0.979793i | \(0.435902\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 5.74813 | 1.00062 | ||||||||
\(34\) | −3.85364 | −0.660894 | ||||||||
\(35\) | 3.67325 | 0.620892 | ||||||||
\(36\) | 3.41035 | 0.568391 | ||||||||
\(37\) | −3.10590 | −0.510607 | −0.255303 | − | 0.966861i | \(-0.582175\pi\) | ||||
−0.255303 | + | 0.966861i | \(0.582175\pi\) | |||||||
\(38\) | −4.23841 | −0.687561 | ||||||||
\(39\) | −8.58834 | −1.37524 | ||||||||
\(40\) | −4.10502 | −0.649061 | ||||||||
\(41\) | 5.43943 | 0.849497 | 0.424748 | − | 0.905311i | \(-0.360363\pi\) | ||||
0.424748 | + | 0.905311i | \(0.360363\pi\) | |||||||
\(42\) | 2.26556 | 0.349584 | ||||||||
\(43\) | −1.49342 | −0.227744 | −0.113872 | − | 0.993495i | \(-0.536325\pi\) | ||||
−0.113872 | + | 0.993495i | \(0.536325\pi\) | |||||||
\(44\) | −2.27031 | −0.342262 | ||||||||
\(45\) | 13.9995 | 2.08693 | ||||||||
\(46\) | −2.95247 | −0.435319 | ||||||||
\(47\) | −3.23230 | −0.471480 | −0.235740 | − | 0.971816i | \(-0.575751\pi\) | ||||
−0.235740 | + | 0.971816i | \(0.575751\pi\) | |||||||
\(48\) | −2.53187 | −0.365443 | ||||||||
\(49\) | −6.19930 | −0.885614 | ||||||||
\(50\) | −11.8512 | −1.67601 | ||||||||
\(51\) | −9.75691 | −1.36624 | ||||||||
\(52\) | 3.39210 | 0.470400 | ||||||||
\(53\) | −2.12914 | −0.292461 | −0.146230 | − | 0.989251i | \(-0.546714\pi\) | ||||
−0.146230 | + | 0.989251i | \(0.546714\pi\) | |||||||
\(54\) | 1.03894 | 0.141382 | ||||||||
\(55\) | −9.31968 | −1.25666 | ||||||||
\(56\) | −0.894818 | −0.119575 | ||||||||
\(57\) | −10.7311 | −1.42137 | ||||||||
\(58\) | −9.91858 | −1.30237 | ||||||||
\(59\) | −4.16828 | −0.542664 | −0.271332 | − | 0.962486i | \(-0.587464\pi\) | ||||
−0.271332 | + | 0.962486i | \(0.587464\pi\) | |||||||
\(60\) | −10.3934 | −1.34178 | ||||||||
\(61\) | 5.43795 | 0.696258 | 0.348129 | − | 0.937447i | \(-0.386817\pi\) | ||||
0.348129 | + | 0.937447i | \(0.386817\pi\) | |||||||
\(62\) | −2.22724 | −0.282859 | ||||||||
\(63\) | 3.05164 | 0.384471 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 13.9246 | 1.72714 | ||||||||
\(66\) | −5.74813 | −0.707545 | ||||||||
\(67\) | 12.2668 | 1.49863 | 0.749314 | − | 0.662215i | \(-0.230383\pi\) | ||||
0.749314 | + | 0.662215i | \(0.230383\pi\) | |||||||
\(68\) | 3.85364 | 0.467323 | ||||||||
\(69\) | −7.47527 | −0.899917 | ||||||||
\(70\) | −3.67325 | −0.439037 | ||||||||
\(71\) | 10.3261 | 1.22548 | 0.612741 | − | 0.790284i | \(-0.290067\pi\) | ||||
0.612741 | + | 0.790284i | \(0.290067\pi\) | |||||||
\(72\) | −3.41035 | −0.401913 | ||||||||
\(73\) | 14.8291 | 1.73561 | 0.867807 | − | 0.496901i | \(-0.165529\pi\) | ||||
0.867807 | + | 0.496901i | \(0.165529\pi\) | |||||||
\(74\) | 3.10590 | 0.361053 | ||||||||
\(75\) | −30.0056 | −3.46475 | ||||||||
\(76\) | 4.23841 | 0.486179 | ||||||||
\(77\) | −2.03152 | −0.231513 | ||||||||
\(78\) | 8.58834 | 0.972439 | ||||||||
\(79\) | −8.34555 | −0.938947 | −0.469474 | − | 0.882946i | \(-0.655556\pi\) | ||||
−0.469474 | + | 0.882946i | \(0.655556\pi\) | |||||||
\(80\) | 4.10502 | 0.458955 | ||||||||
\(81\) | −7.60057 | −0.844508 | ||||||||
\(82\) | −5.43943 | −0.600685 | ||||||||
\(83\) | −10.1561 | −1.11478 | −0.557389 | − | 0.830252i | \(-0.688197\pi\) | ||||
−0.557389 | + | 0.830252i | \(0.688197\pi\) | |||||||
\(84\) | −2.26556 | −0.247193 | ||||||||
\(85\) | 15.8193 | 1.71584 | ||||||||
\(86\) | 1.49342 | 0.161040 | ||||||||
\(87\) | −25.1125 | −2.69235 | ||||||||
\(88\) | 2.27031 | 0.242016 | ||||||||
\(89\) | 11.3078 | 1.19862 | 0.599311 | − | 0.800516i | \(-0.295441\pi\) | ||||
0.599311 | + | 0.800516i | \(0.295441\pi\) | |||||||
\(90\) | −13.9995 | −1.47568 | ||||||||
\(91\) | 3.03531 | 0.318187 | ||||||||
\(92\) | 2.95247 | 0.307817 | ||||||||
\(93\) | −5.63907 | −0.584744 | ||||||||
\(94\) | 3.23230 | 0.333386 | ||||||||
\(95\) | 17.3988 | 1.78508 | ||||||||
\(96\) | 2.53187 | 0.258408 | ||||||||
\(97\) | −5.29986 | −0.538120 | −0.269060 | − | 0.963123i | \(-0.586713\pi\) | ||||
−0.269060 | + | 0.963123i | \(0.586713\pi\) | |||||||
\(98\) | 6.19930 | 0.626224 | ||||||||
\(99\) | −7.74255 | −0.778156 | ||||||||
\(100\) | 11.8512 | 1.18512 | ||||||||
\(101\) | 6.97368 | 0.693907 | 0.346953 | − | 0.937882i | \(-0.387216\pi\) | ||||
0.346953 | + | 0.937882i | \(0.387216\pi\) | |||||||
\(102\) | 9.75691 | 0.966078 | ||||||||
\(103\) | −1.47997 | −0.145826 | −0.0729131 | − | 0.997338i | \(-0.523230\pi\) | ||||
−0.0729131 | + | 0.997338i | \(0.523230\pi\) | |||||||
\(104\) | −3.39210 | −0.332623 | ||||||||
\(105\) | −9.30017 | −0.907604 | ||||||||
\(106\) | 2.12914 | 0.206801 | ||||||||
\(107\) | 0.181821 | 0.0175773 | 0.00878867 | − | 0.999961i | \(-0.497202\pi\) | ||||
0.00878867 | + | 0.999961i | \(0.497202\pi\) | |||||||
\(108\) | −1.03894 | −0.0999724 | ||||||||
\(109\) | −5.99043 | −0.573779 | −0.286889 | − | 0.957964i | \(-0.592621\pi\) | ||||
−0.286889 | + | 0.957964i | \(0.592621\pi\) | |||||||
\(110\) | 9.31968 | 0.888596 | ||||||||
\(111\) | 7.86372 | 0.746391 | ||||||||
\(112\) | 0.894818 | 0.0845524 | ||||||||
\(113\) | 2.98984 | 0.281260 | 0.140630 | − | 0.990062i | \(-0.455087\pi\) | ||||
0.140630 | + | 0.990062i | \(0.455087\pi\) | |||||||
\(114\) | 10.7311 | 1.00506 | ||||||||
\(115\) | 12.1200 | 1.13019 | ||||||||
\(116\) | 9.91858 | 0.920917 | ||||||||
\(117\) | 11.5682 | 1.06948 | ||||||||
\(118\) | 4.16828 | 0.383721 | ||||||||
\(119\) | 3.44831 | 0.316106 | ||||||||
\(120\) | 10.3934 | 0.948780 | ||||||||
\(121\) | −5.84568 | −0.531426 | ||||||||
\(122\) | −5.43795 | −0.492329 | ||||||||
\(123\) | −13.7719 | −1.24177 | ||||||||
\(124\) | 2.22724 | 0.200012 | ||||||||
\(125\) | 28.1243 | 2.51551 | ||||||||
\(126\) | −3.05164 | −0.271862 | ||||||||
\(127\) | −7.11183 | −0.631073 | −0.315536 | − | 0.948913i | \(-0.602184\pi\) | ||||
−0.315536 | + | 0.948913i | \(0.602184\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | 3.78114 | 0.332911 | ||||||||
\(130\) | −13.9246 | −1.22127 | ||||||||
\(131\) | −1.79604 | −0.156921 | −0.0784603 | − | 0.996917i | \(-0.525000\pi\) | ||||
−0.0784603 | + | 0.996917i | \(0.525000\pi\) | |||||||
\(132\) | 5.74813 | 0.500310 | ||||||||
\(133\) | 3.79261 | 0.328861 | ||||||||
\(134\) | −12.2668 | −1.05969 | ||||||||
\(135\) | −4.26489 | −0.367063 | ||||||||
\(136\) | −3.85364 | −0.330447 | ||||||||
\(137\) | −5.25548 | −0.449006 | −0.224503 | − | 0.974473i | \(-0.572076\pi\) | ||||
−0.224503 | + | 0.974473i | \(0.572076\pi\) | |||||||
\(138\) | 7.47527 | 0.636337 | ||||||||
\(139\) | 10.3165 | 0.875032 | 0.437516 | − | 0.899211i | \(-0.355858\pi\) | ||||
0.437516 | + | 0.899211i | \(0.355858\pi\) | |||||||
\(140\) | 3.67325 | 0.310446 | ||||||||
\(141\) | 8.18375 | 0.689196 | ||||||||
\(142\) | −10.3261 | −0.866546 | ||||||||
\(143\) | −7.70113 | −0.644000 | ||||||||
\(144\) | 3.41035 | 0.284196 | ||||||||
\(145\) | 40.7160 | 3.38128 | ||||||||
\(146\) | −14.8291 | −1.22727 | ||||||||
\(147\) | 15.6958 | 1.29457 | ||||||||
\(148\) | −3.10590 | −0.255303 | ||||||||
\(149\) | −9.63547 | −0.789368 | −0.394684 | − | 0.918817i | \(-0.629146\pi\) | ||||
−0.394684 | + | 0.918817i | \(0.629146\pi\) | |||||||
\(150\) | 30.0056 | 2.44995 | ||||||||
\(151\) | −2.50913 | −0.204190 | −0.102095 | − | 0.994775i | \(-0.532555\pi\) | ||||
−0.102095 | + | 0.994775i | \(0.532555\pi\) | |||||||
\(152\) | −4.23841 | −0.343781 | ||||||||
\(153\) | 13.1423 | 1.06249 | ||||||||
\(154\) | 2.03152 | 0.163704 | ||||||||
\(155\) | 9.14286 | 0.734372 | ||||||||
\(156\) | −8.58834 | −0.687618 | ||||||||
\(157\) | −4.24098 | −0.338467 | −0.169234 | − | 0.985576i | \(-0.554129\pi\) | ||||
−0.169234 | + | 0.985576i | \(0.554129\pi\) | |||||||
\(158\) | 8.34555 | 0.663936 | ||||||||
\(159\) | 5.39071 | 0.427511 | ||||||||
\(160\) | −4.10502 | −0.324530 | ||||||||
\(161\) | 2.64193 | 0.208213 | ||||||||
\(162\) | 7.60057 | 0.597157 | ||||||||
\(163\) | 13.4953 | 1.05703 | 0.528515 | − | 0.848924i | \(-0.322749\pi\) | ||||
0.528515 | + | 0.848924i | \(0.322749\pi\) | |||||||
\(164\) | 5.43943 | 0.424748 | ||||||||
\(165\) | 23.5962 | 1.83696 | ||||||||
\(166\) | 10.1561 | 0.788266 | ||||||||
\(167\) | −9.02394 | −0.698294 | −0.349147 | − | 0.937068i | \(-0.613529\pi\) | ||||
−0.349147 | + | 0.937068i | \(0.613529\pi\) | |||||||
\(168\) | 2.26556 | 0.174792 | ||||||||
\(169\) | −1.49365 | −0.114897 | ||||||||
\(170\) | −15.8193 | −1.21328 | ||||||||
\(171\) | 14.4545 | 1.10536 | ||||||||
\(172\) | −1.49342 | −0.113872 | ||||||||
\(173\) | −18.0592 | −1.37302 | −0.686508 | − | 0.727122i | \(-0.740857\pi\) | ||||
−0.686508 | + | 0.727122i | \(0.740857\pi\) | |||||||
\(174\) | 25.1125 | 1.90378 | ||||||||
\(175\) | 10.6047 | 0.801637 | ||||||||
\(176\) | −2.27031 | −0.171131 | ||||||||
\(177\) | 10.5535 | 0.793251 | ||||||||
\(178\) | −11.3078 | −0.847554 | ||||||||
\(179\) | −13.0145 | −0.972750 | −0.486375 | − | 0.873750i | \(-0.661681\pi\) | ||||
−0.486375 | + | 0.873750i | \(0.661681\pi\) | |||||||
\(180\) | 13.9995 | 1.04346 | ||||||||
\(181\) | 15.0458 | 1.11835 | 0.559173 | − | 0.829051i | \(-0.311119\pi\) | ||||
0.559173 | + | 0.829051i | \(0.311119\pi\) | |||||||
\(182\) | −3.03531 | −0.224992 | ||||||||
\(183\) | −13.7682 | −1.01777 | ||||||||
\(184\) | −2.95247 | −0.217659 | ||||||||
\(185\) | −12.7498 | −0.937382 | ||||||||
\(186\) | 5.63907 | 0.413477 | ||||||||
\(187\) | −8.74897 | −0.639788 | ||||||||
\(188\) | −3.23230 | −0.235740 | ||||||||
\(189\) | −0.929666 | −0.0676233 | ||||||||
\(190\) | −17.3988 | −1.26224 | ||||||||
\(191\) | −7.62970 | −0.552066 | −0.276033 | − | 0.961148i | \(-0.589020\pi\) | ||||
−0.276033 | + | 0.961148i | \(0.589020\pi\) | |||||||
\(192\) | −2.53187 | −0.182722 | ||||||||
\(193\) | 7.96623 | 0.573422 | 0.286711 | − | 0.958017i | \(-0.407438\pi\) | ||||
0.286711 | + | 0.958017i | \(0.407438\pi\) | |||||||
\(194\) | 5.29986 | 0.380508 | ||||||||
\(195\) | −35.2553 | −2.52469 | ||||||||
\(196\) | −6.19930 | −0.442807 | ||||||||
\(197\) | 0.887818 | 0.0632544 | 0.0316272 | − | 0.999500i | \(-0.489931\pi\) | ||||
0.0316272 | + | 0.999500i | \(0.489931\pi\) | |||||||
\(198\) | 7.74255 | 0.550239 | ||||||||
\(199\) | 5.87976 | 0.416805 | 0.208403 | − | 0.978043i | \(-0.433174\pi\) | ||||
0.208403 | + | 0.978043i | \(0.433174\pi\) | |||||||
\(200\) | −11.8512 | −0.838006 | ||||||||
\(201\) | −31.0579 | −2.19066 | ||||||||
\(202\) | −6.97368 | −0.490666 | ||||||||
\(203\) | 8.87533 | 0.622926 | ||||||||
\(204\) | −9.75691 | −0.683120 | ||||||||
\(205\) | 22.3290 | 1.55952 | ||||||||
\(206\) | 1.47997 | 0.103115 | ||||||||
\(207\) | 10.0690 | 0.699841 | ||||||||
\(208\) | 3.39210 | 0.235200 | ||||||||
\(209\) | −9.62252 | −0.665603 | ||||||||
\(210\) | 9.30017 | 0.641773 | ||||||||
\(211\) | 7.20309 | 0.495881 | 0.247941 | − | 0.968775i | \(-0.420246\pi\) | ||||
0.247941 | + | 0.968775i | \(0.420246\pi\) | |||||||
\(212\) | −2.12914 | −0.146230 | ||||||||
\(213\) | −26.1443 | −1.79138 | ||||||||
\(214\) | −0.181821 | −0.0124291 | ||||||||
\(215\) | −6.13052 | −0.418098 | ||||||||
\(216\) | 1.03894 | 0.0706912 | ||||||||
\(217\) | 1.99297 | 0.135292 | ||||||||
\(218\) | 5.99043 | 0.405723 | ||||||||
\(219\) | −37.5453 | −2.53708 | ||||||||
\(220\) | −9.31968 | −0.628332 | ||||||||
\(221\) | 13.0719 | 0.879314 | ||||||||
\(222\) | −7.86372 | −0.527778 | ||||||||
\(223\) | 3.71904 | 0.249046 | 0.124523 | − | 0.992217i | \(-0.460260\pi\) | ||||
0.124523 | + | 0.992217i | \(0.460260\pi\) | |||||||
\(224\) | −0.894818 | −0.0597876 | ||||||||
\(225\) | 40.4167 | 2.69445 | ||||||||
\(226\) | −2.98984 | −0.198881 | ||||||||
\(227\) | −5.32747 | −0.353597 | −0.176798 | − | 0.984247i | \(-0.556574\pi\) | ||||
−0.176798 | + | 0.984247i | \(0.556574\pi\) | |||||||
\(228\) | −10.7311 | −0.710684 | ||||||||
\(229\) | −15.1469 | −1.00094 | −0.500468 | − | 0.865755i | \(-0.666839\pi\) | ||||
−0.500468 | + | 0.865755i | \(0.666839\pi\) | |||||||
\(230\) | −12.1200 | −0.799167 | ||||||||
\(231\) | 5.14353 | 0.338419 | ||||||||
\(232\) | −9.91858 | −0.651187 | ||||||||
\(233\) | 5.21825 | 0.341859 | 0.170929 | − | 0.985283i | \(-0.445323\pi\) | ||||
0.170929 | + | 0.985283i | \(0.445323\pi\) | |||||||
\(234\) | −11.5682 | −0.756239 | ||||||||
\(235\) | −13.2687 | −0.865552 | ||||||||
\(236\) | −4.16828 | −0.271332 | ||||||||
\(237\) | 21.1298 | 1.37253 | ||||||||
\(238\) | −3.44831 | −0.223521 | ||||||||
\(239\) | −4.17713 | −0.270196 | −0.135098 | − | 0.990832i | \(-0.543135\pi\) | ||||
−0.135098 | + | 0.990832i | \(0.543135\pi\) | |||||||
\(240\) | −10.3934 | −0.670889 | ||||||||
\(241\) | −7.95191 | −0.512228 | −0.256114 | − | 0.966647i | \(-0.582442\pi\) | ||||
−0.256114 | + | 0.966647i | \(0.582442\pi\) | |||||||
\(242\) | 5.84568 | 0.375775 | ||||||||
\(243\) | 22.3605 | 1.43442 | ||||||||
\(244\) | 5.43795 | 0.348129 | ||||||||
\(245\) | −25.4483 | −1.62583 | ||||||||
\(246\) | 13.7719 | 0.878066 | ||||||||
\(247\) | 14.3771 | 0.914794 | ||||||||
\(248\) | −2.22724 | −0.141430 | ||||||||
\(249\) | 25.7139 | 1.62955 | ||||||||
\(250\) | −28.1243 | −1.77874 | ||||||||
\(251\) | −23.7604 | −1.49974 | −0.749871 | − | 0.661584i | \(-0.769884\pi\) | ||||
−0.749871 | + | 0.661584i | \(0.769884\pi\) | |||||||
\(252\) | 3.05164 | 0.192235 | ||||||||
\(253\) | −6.70304 | −0.421416 | ||||||||
\(254\) | 7.11183 | 0.446236 | ||||||||
\(255\) | −40.0523 | −2.50817 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −13.3494 | −0.832710 | −0.416355 | − | 0.909202i | \(-0.636693\pi\) | ||||
−0.416355 | + | 0.909202i | \(0.636693\pi\) | |||||||
\(258\) | −3.78114 | −0.235403 | ||||||||
\(259\) | −2.77922 | −0.172692 | ||||||||
\(260\) | 13.9246 | 0.863570 | ||||||||
\(261\) | 33.8258 | 2.09377 | ||||||||
\(262\) | 1.79604 | 0.110960 | ||||||||
\(263\) | 2.60232 | 0.160466 | 0.0802330 | − | 0.996776i | \(-0.474434\pi\) | ||||
0.0802330 | + | 0.996776i | \(0.474434\pi\) | |||||||
\(264\) | −5.74813 | −0.353773 | ||||||||
\(265\) | −8.74018 | −0.536905 | ||||||||
\(266\) | −3.79261 | −0.232540 | ||||||||
\(267\) | −28.6298 | −1.75211 | ||||||||
\(268\) | 12.2668 | 0.749314 | ||||||||
\(269\) | −0.264247 | −0.0161114 | −0.00805570 | − | 0.999968i | \(-0.502564\pi\) | ||||
−0.00805570 | + | 0.999968i | \(0.502564\pi\) | |||||||
\(270\) | 4.26489 | 0.259553 | ||||||||
\(271\) | −16.4146 | −0.997114 | −0.498557 | − | 0.866857i | \(-0.666136\pi\) | ||||
−0.498557 | + | 0.866857i | \(0.666136\pi\) | |||||||
\(272\) | 3.85364 | 0.233661 | ||||||||
\(273\) | −7.68501 | −0.465118 | ||||||||
\(274\) | 5.25548 | 0.317495 | ||||||||
\(275\) | −26.9059 | −1.62249 | ||||||||
\(276\) | −7.47527 | −0.449958 | ||||||||
\(277\) | −9.16478 | −0.550658 | −0.275329 | − | 0.961350i | \(-0.588787\pi\) | ||||
−0.275329 | + | 0.961350i | \(0.588787\pi\) | |||||||
\(278\) | −10.3165 | −0.618741 | ||||||||
\(279\) | 7.59565 | 0.454740 | ||||||||
\(280\) | −3.67325 | −0.219519 | ||||||||
\(281\) | −21.9696 | −1.31060 | −0.655299 | − | 0.755370i | \(-0.727457\pi\) | ||||
−0.655299 | + | 0.755370i | \(0.727457\pi\) | |||||||
\(282\) | −8.18375 | −0.487335 | ||||||||
\(283\) | −31.0821 | −1.84764 | −0.923820 | − | 0.382827i | \(-0.874950\pi\) | ||||
−0.923820 | + | 0.382827i | \(0.874950\pi\) | |||||||
\(284\) | 10.3261 | 0.612741 | ||||||||
\(285\) | −44.0514 | −2.60938 | ||||||||
\(286\) | 7.70113 | 0.455377 | ||||||||
\(287\) | 4.86731 | 0.287308 | ||||||||
\(288\) | −3.41035 | −0.200957 | ||||||||
\(289\) | −2.14945 | −0.126438 | ||||||||
\(290\) | −40.7160 | −2.39092 | ||||||||
\(291\) | 13.4185 | 0.786609 | ||||||||
\(292\) | 14.8291 | 0.867807 | ||||||||
\(293\) | −31.0314 | −1.81288 | −0.906438 | − | 0.422338i | \(-0.861209\pi\) | ||||
−0.906438 | + | 0.422338i | \(0.861209\pi\) | |||||||
\(294\) | −15.6958 | −0.915398 | ||||||||
\(295\) | −17.1109 | −0.996233 | ||||||||
\(296\) | 3.10590 | 0.180527 | ||||||||
\(297\) | 2.35873 | 0.136867 | ||||||||
\(298\) | 9.63547 | 0.558168 | ||||||||
\(299\) | 10.0151 | 0.579188 | ||||||||
\(300\) | −30.0056 | −1.73238 | ||||||||
\(301\) | −1.33634 | −0.0770253 | ||||||||
\(302\) | 2.50913 | 0.144384 | ||||||||
\(303\) | −17.6564 | −1.01433 | ||||||||
\(304\) | 4.23841 | 0.243090 | ||||||||
\(305\) | 22.3229 | 1.27820 | ||||||||
\(306\) | −13.1423 | −0.751293 | ||||||||
\(307\) | 8.81240 | 0.502951 | 0.251475 | − | 0.967864i | \(-0.419084\pi\) | ||||
0.251475 | + | 0.967864i | \(0.419084\pi\) | |||||||
\(308\) | −2.03152 | −0.115756 | ||||||||
\(309\) | 3.74710 | 0.213165 | ||||||||
\(310\) | −9.14286 | −0.519279 | ||||||||
\(311\) | 26.7512 | 1.51692 | 0.758462 | − | 0.651717i | \(-0.225951\pi\) | ||||
0.758462 | + | 0.651717i | \(0.225951\pi\) | |||||||
\(312\) | 8.58834 | 0.486219 | ||||||||
\(313\) | −19.5340 | −1.10413 | −0.552064 | − | 0.833802i | \(-0.686160\pi\) | ||||
−0.552064 | + | 0.833802i | \(0.686160\pi\) | |||||||
\(314\) | 4.24098 | 0.239332 | ||||||||
\(315\) | 12.5270 | 0.705819 | ||||||||
\(316\) | −8.34555 | −0.469474 | ||||||||
\(317\) | 13.9817 | 0.785291 | 0.392645 | − | 0.919690i | \(-0.371560\pi\) | ||||
0.392645 | + | 0.919690i | \(0.371560\pi\) | |||||||
\(318\) | −5.39071 | −0.302296 | ||||||||
\(319\) | −22.5183 | −1.26078 | ||||||||
\(320\) | 4.10502 | 0.229478 | ||||||||
\(321\) | −0.460347 | −0.0256941 | ||||||||
\(322\) | −2.64193 | −0.147229 | ||||||||
\(323\) | 16.3333 | 0.908810 | ||||||||
\(324\) | −7.60057 | −0.422254 | ||||||||
\(325\) | 40.2004 | 2.22992 | ||||||||
\(326\) | −13.4953 | −0.747434 | ||||||||
\(327\) | 15.1670 | 0.838735 | ||||||||
\(328\) | −5.43943 | −0.300343 | ||||||||
\(329\) | −2.89232 | −0.159459 | ||||||||
\(330\) | −23.5962 | −1.29893 | ||||||||
\(331\) | −16.2256 | −0.891837 | −0.445918 | − | 0.895074i | \(-0.647123\pi\) | ||||
−0.445918 | + | 0.895074i | \(0.647123\pi\) | |||||||
\(332\) | −10.1561 | −0.557389 | ||||||||
\(333\) | −10.5922 | −0.580449 | ||||||||
\(334\) | 9.02394 | 0.493768 | ||||||||
\(335\) | 50.3555 | 2.75121 | ||||||||
\(336\) | −2.26556 | −0.123596 | ||||||||
\(337\) | 14.0146 | 0.763423 | 0.381712 | − | 0.924281i | \(-0.375335\pi\) | ||||
0.381712 | + | 0.924281i | \(0.375335\pi\) | |||||||
\(338\) | 1.49365 | 0.0812441 | ||||||||
\(339\) | −7.56987 | −0.411139 | ||||||||
\(340\) | 15.8193 | 0.857921 | ||||||||
\(341\) | −5.05652 | −0.273826 | ||||||||
\(342\) | −14.4545 | −0.781607 | ||||||||
\(343\) | −11.8110 | −0.637733 | ||||||||
\(344\) | 1.49342 | 0.0805198 | ||||||||
\(345\) | −30.6861 | −1.65209 | ||||||||
\(346\) | 18.0592 | 0.970869 | ||||||||
\(347\) | −28.1431 | −1.51080 | −0.755402 | − | 0.655262i | \(-0.772558\pi\) | ||||
−0.755402 | + | 0.655262i | \(0.772558\pi\) | |||||||
\(348\) | −25.1125 | −1.34617 | ||||||||
\(349\) | 30.4236 | 1.62854 | 0.814270 | − | 0.580487i | \(-0.197138\pi\) | ||||
0.814270 | + | 0.580487i | \(0.197138\pi\) | |||||||
\(350\) | −10.6047 | −0.566843 | ||||||||
\(351\) | −3.52420 | −0.188108 | ||||||||
\(352\) | 2.27031 | 0.121008 | ||||||||
\(353\) | 17.6425 | 0.939015 | 0.469507 | − | 0.882929i | \(-0.344432\pi\) | ||||
0.469507 | + | 0.882929i | \(0.344432\pi\) | |||||||
\(354\) | −10.5535 | −0.560913 | ||||||||
\(355\) | 42.3888 | 2.24976 | ||||||||
\(356\) | 11.3078 | 0.599311 | ||||||||
\(357\) | −8.73066 | −0.462075 | ||||||||
\(358\) | 13.0145 | 0.687838 | ||||||||
\(359\) | 30.1434 | 1.59091 | 0.795455 | − | 0.606013i | \(-0.207232\pi\) | ||||
0.795455 | + | 0.606013i | \(0.207232\pi\) | |||||||
\(360\) | −13.9995 | −0.737841 | ||||||||
\(361\) | −1.03587 | −0.0545193 | ||||||||
\(362\) | −15.0458 | −0.790790 | ||||||||
\(363\) | 14.8005 | 0.776824 | ||||||||
\(364\) | 3.03531 | 0.159094 | ||||||||
\(365\) | 60.8738 | 3.18628 | ||||||||
\(366\) | 13.7682 | 0.719673 | ||||||||
\(367\) | 10.9556 | 0.571876 | 0.285938 | − | 0.958248i | \(-0.407695\pi\) | ||||
0.285938 | + | 0.958248i | \(0.407695\pi\) | |||||||
\(368\) | 2.95247 | 0.153908 | ||||||||
\(369\) | 18.5504 | 0.965693 | ||||||||
\(370\) | 12.7498 | 0.662829 | ||||||||
\(371\) | −1.90520 | −0.0989129 | ||||||||
\(372\) | −5.63907 | −0.292372 | ||||||||
\(373\) | −16.6269 | −0.860910 | −0.430455 | − | 0.902612i | \(-0.641647\pi\) | ||||
−0.430455 | + | 0.902612i | \(0.641647\pi\) | |||||||
\(374\) | 8.74897 | 0.452398 | ||||||||
\(375\) | −71.2069 | −3.67711 | ||||||||
\(376\) | 3.23230 | 0.166693 | ||||||||
\(377\) | 33.6448 | 1.73280 | ||||||||
\(378\) | 0.929666 | 0.0478169 | ||||||||
\(379\) | 4.80098 | 0.246610 | 0.123305 | − | 0.992369i | \(-0.460651\pi\) | ||||
0.123305 | + | 0.992369i | \(0.460651\pi\) | |||||||
\(380\) | 17.3988 | 0.892538 | ||||||||
\(381\) | 18.0062 | 0.922486 | ||||||||
\(382\) | 7.62970 | 0.390370 | ||||||||
\(383\) | 2.69820 | 0.137872 | 0.0689358 | − | 0.997621i | \(-0.478040\pi\) | ||||
0.0689358 | + | 0.997621i | \(0.478040\pi\) | |||||||
\(384\) | 2.53187 | 0.129204 | ||||||||
\(385\) | −8.33942 | −0.425016 | ||||||||
\(386\) | −7.96623 | −0.405471 | ||||||||
\(387\) | −5.09308 | −0.258896 | ||||||||
\(388\) | −5.29986 | −0.269060 | ||||||||
\(389\) | −10.2263 | −0.518495 | −0.259247 | − | 0.965811i | \(-0.583475\pi\) | ||||
−0.259247 | + | 0.965811i | \(0.583475\pi\) | |||||||
\(390\) | 35.2553 | 1.78522 | ||||||||
\(391\) | 11.3778 | 0.575399 | ||||||||
\(392\) | 6.19930 | 0.313112 | ||||||||
\(393\) | 4.54733 | 0.229382 | ||||||||
\(394\) | −0.887818 | −0.0447276 | ||||||||
\(395\) | −34.2586 | −1.72374 | ||||||||
\(396\) | −7.74255 | −0.389078 | ||||||||
\(397\) | −1.61933 | −0.0812719 | −0.0406360 | − | 0.999174i | \(-0.512938\pi\) | ||||
−0.0406360 | + | 0.999174i | \(0.512938\pi\) | |||||||
\(398\) | −5.87976 | −0.294726 | ||||||||
\(399\) | −9.60238 | −0.480720 | ||||||||
\(400\) | 11.8512 | 0.592560 | ||||||||
\(401\) | 9.85489 | 0.492130 | 0.246065 | − | 0.969253i | \(-0.420862\pi\) | ||||
0.246065 | + | 0.969253i | \(0.420862\pi\) | |||||||
\(402\) | 31.0579 | 1.54903 | ||||||||
\(403\) | 7.55501 | 0.376342 | ||||||||
\(404\) | 6.97368 | 0.346953 | ||||||||
\(405\) | −31.2005 | −1.55037 | ||||||||
\(406\) | −8.87533 | −0.440475 | ||||||||
\(407\) | 7.05136 | 0.349523 | ||||||||
\(408\) | 9.75691 | 0.483039 | ||||||||
\(409\) | −10.5522 | −0.521773 | −0.260886 | − | 0.965369i | \(-0.584015\pi\) | ||||
−0.260886 | + | 0.965369i | \(0.584015\pi\) | |||||||
\(410\) | −22.3290 | −1.10275 | ||||||||
\(411\) | 13.3062 | 0.656346 | ||||||||
\(412\) | −1.47997 | −0.0729131 | ||||||||
\(413\) | −3.72985 | −0.183534 | ||||||||
\(414\) | −10.0690 | −0.494862 | ||||||||
\(415\) | −41.6910 | −2.04653 | ||||||||
\(416\) | −3.39210 | −0.166311 | ||||||||
\(417\) | −26.1199 | −1.27910 | ||||||||
\(418\) | 9.62252 | 0.470653 | ||||||||
\(419\) | 19.6283 | 0.958904 | 0.479452 | − | 0.877568i | \(-0.340836\pi\) | ||||
0.479452 | + | 0.877568i | \(0.340836\pi\) | |||||||
\(420\) | −9.30017 | −0.453802 | ||||||||
\(421\) | −22.0430 | −1.07431 | −0.537155 | − | 0.843484i | \(-0.680501\pi\) | ||||
−0.537155 | + | 0.843484i | \(0.680501\pi\) | |||||||
\(422\) | −7.20309 | −0.350641 | ||||||||
\(423\) | −11.0233 | −0.535970 | ||||||||
\(424\) | 2.12914 | 0.103400 | ||||||||
\(425\) | 45.6702 | 2.21533 | ||||||||
\(426\) | 26.1443 | 1.26669 | ||||||||
\(427\) | 4.86598 | 0.235481 | ||||||||
\(428\) | 0.181821 | 0.00878867 | ||||||||
\(429\) | 19.4982 | 0.941383 | ||||||||
\(430\) | 6.13052 | 0.295640 | ||||||||
\(431\) | −25.5575 | −1.23106 | −0.615531 | − | 0.788113i | \(-0.711058\pi\) | ||||
−0.615531 | + | 0.788113i | \(0.711058\pi\) | |||||||
\(432\) | −1.03894 | −0.0499862 | ||||||||
\(433\) | 5.85717 | 0.281478 | 0.140739 | − | 0.990047i | \(-0.455052\pi\) | ||||
0.140739 | + | 0.990047i | \(0.455052\pi\) | |||||||
\(434\) | −1.99297 | −0.0956658 | ||||||||
\(435\) | −103.087 | −4.94266 | ||||||||
\(436\) | −5.99043 | −0.286889 | ||||||||
\(437\) | 12.5138 | 0.598616 | ||||||||
\(438\) | 37.5453 | 1.79398 | ||||||||
\(439\) | −16.8707 | −0.805193 | −0.402597 | − | 0.915377i | \(-0.631892\pi\) | ||||
−0.402597 | + | 0.915377i | \(0.631892\pi\) | |||||||
\(440\) | 9.31968 | 0.444298 | ||||||||
\(441\) | −21.1418 | −1.00675 | ||||||||
\(442\) | −13.0719 | −0.621769 | ||||||||
\(443\) | −7.90860 | −0.375749 | −0.187874 | − | 0.982193i | \(-0.560160\pi\) | ||||
−0.187874 | + | 0.982193i | \(0.560160\pi\) | |||||||
\(444\) | 7.86372 | 0.373196 | ||||||||
\(445\) | 46.4187 | 2.20046 | ||||||||
\(446\) | −3.71904 | −0.176102 | ||||||||
\(447\) | 24.3957 | 1.15388 | ||||||||
\(448\) | 0.894818 | 0.0422762 | ||||||||
\(449\) | −25.1035 | −1.18471 | −0.592355 | − | 0.805677i | \(-0.701802\pi\) | ||||
−0.592355 | + | 0.805677i | \(0.701802\pi\) | |||||||
\(450\) | −40.4167 | −1.90526 | ||||||||
\(451\) | −12.3492 | −0.581502 | ||||||||
\(452\) | 2.98984 | 0.140630 | ||||||||
\(453\) | 6.35277 | 0.298479 | ||||||||
\(454\) | 5.32747 | 0.250031 | ||||||||
\(455\) | 12.4600 | 0.584135 | ||||||||
\(456\) | 10.7311 | 0.502529 | ||||||||
\(457\) | 22.4161 | 1.04858 | 0.524291 | − | 0.851539i | \(-0.324330\pi\) | ||||
0.524291 | + | 0.851539i | \(0.324330\pi\) | |||||||
\(458\) | 15.1469 | 0.707768 | ||||||||
\(459\) | −4.00372 | −0.186878 | ||||||||
\(460\) | 12.1200 | 0.565096 | ||||||||
\(461\) | 24.7103 | 1.15087 | 0.575436 | − | 0.817847i | \(-0.304832\pi\) | ||||
0.575436 | + | 0.817847i | \(0.304832\pi\) | |||||||
\(462\) | −5.14353 | −0.239299 | ||||||||
\(463\) | −39.7700 | −1.84827 | −0.924135 | − | 0.382065i | \(-0.875213\pi\) | ||||
−0.924135 | + | 0.382065i | \(0.875213\pi\) | |||||||
\(464\) | 9.91858 | 0.460459 | ||||||||
\(465\) | −23.1485 | −1.07349 | ||||||||
\(466\) | −5.21825 | −0.241731 | ||||||||
\(467\) | 14.2231 | 0.658168 | 0.329084 | − | 0.944301i | \(-0.393260\pi\) | ||||
0.329084 | + | 0.944301i | \(0.393260\pi\) | |||||||
\(468\) | 11.5682 | 0.534742 | ||||||||
\(469\) | 10.9766 | 0.506850 | ||||||||
\(470\) | 13.2687 | 0.612038 | ||||||||
\(471\) | 10.7376 | 0.494763 | ||||||||
\(472\) | 4.16828 | 0.191861 | ||||||||
\(473\) | 3.39053 | 0.155897 | ||||||||
\(474\) | −21.1298 | −0.970524 | ||||||||
\(475\) | 50.2302 | 2.30472 | ||||||||
\(476\) | 3.44831 | 0.158053 | ||||||||
\(477\) | −7.26112 | −0.332464 | ||||||||
\(478\) | 4.17713 | 0.191058 | ||||||||
\(479\) | 35.2372 | 1.61003 | 0.805014 | − | 0.593256i | \(-0.202158\pi\) | ||||
0.805014 | + | 0.593256i | \(0.202158\pi\) | |||||||
\(480\) | 10.3934 | 0.474390 | ||||||||
\(481\) | −10.5355 | −0.480378 | ||||||||
\(482\) | 7.95191 | 0.362200 | ||||||||
\(483\) | −6.68901 | −0.304360 | ||||||||
\(484\) | −5.84568 | −0.265713 | ||||||||
\(485\) | −21.7560 | −0.987891 | ||||||||
\(486\) | −22.3605 | −1.01429 | ||||||||
\(487\) | −18.4206 | −0.834716 | −0.417358 | − | 0.908742i | \(-0.637044\pi\) | ||||
−0.417358 | + | 0.908742i | \(0.637044\pi\) | |||||||
\(488\) | −5.43795 | −0.246164 | ||||||||
\(489\) | −34.1682 | −1.54514 | ||||||||
\(490\) | 25.4483 | 1.14963 | ||||||||
\(491\) | −26.4977 | −1.19583 | −0.597913 | − | 0.801561i | \(-0.704003\pi\) | ||||
−0.597913 | + | 0.801561i | \(0.704003\pi\) | |||||||
\(492\) | −13.7719 | −0.620886 | ||||||||
\(493\) | 38.2227 | 1.72146 | ||||||||
\(494\) | −14.3771 | −0.646857 | ||||||||
\(495\) | −31.7833 | −1.42855 | ||||||||
\(496\) | 2.22724 | 0.100006 | ||||||||
\(497\) | 9.23997 | 0.414469 | ||||||||
\(498\) | −25.7139 | −1.15227 | ||||||||
\(499\) | 34.6603 | 1.55161 | 0.775803 | − | 0.630975i | \(-0.217345\pi\) | ||||
0.775803 | + | 0.630975i | \(0.217345\pi\) | |||||||
\(500\) | 28.1243 | 1.25776 | ||||||||
\(501\) | 22.8474 | 1.02075 | ||||||||
\(502\) | 23.7604 | 1.06048 | ||||||||
\(503\) | −11.3361 | −0.505452 | −0.252726 | − | 0.967538i | \(-0.581327\pi\) | ||||
−0.252726 | + | 0.967538i | \(0.581327\pi\) | |||||||
\(504\) | −3.05164 | −0.135931 | ||||||||
\(505\) | 28.6271 | 1.27389 | ||||||||
\(506\) | 6.70304 | 0.297986 | ||||||||
\(507\) | 3.78173 | 0.167953 | ||||||||
\(508\) | −7.11183 | −0.315536 | ||||||||
\(509\) | 24.9073 | 1.10400 | 0.551999 | − | 0.833845i | \(-0.313865\pi\) | ||||
0.551999 | + | 0.833845i | \(0.313865\pi\) | |||||||
\(510\) | 40.0523 | 1.77355 | ||||||||
\(511\) | 13.2694 | 0.587002 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | −4.40347 | −0.194418 | ||||||||
\(514\) | 13.3494 | 0.588815 | ||||||||
\(515\) | −6.07532 | −0.267711 | ||||||||
\(516\) | 3.78114 | 0.166455 | ||||||||
\(517\) | 7.33833 | 0.322739 | ||||||||
\(518\) | 2.77922 | 0.122112 | ||||||||
\(519\) | 45.7235 | 2.00704 | ||||||||
\(520\) | −13.9246 | −0.610636 | ||||||||
\(521\) | 37.8801 | 1.65956 | 0.829779 | − | 0.558092i | \(-0.188466\pi\) | ||||
0.829779 | + | 0.558092i | \(0.188466\pi\) | |||||||
\(522\) | −33.8258 | −1.48052 | ||||||||
\(523\) | −0.622115 | −0.0272032 | −0.0136016 | − | 0.999907i | \(-0.504330\pi\) | ||||
−0.0136016 | + | 0.999907i | \(0.504330\pi\) | |||||||
\(524\) | −1.79604 | −0.0784603 | ||||||||
\(525\) | −26.8496 | −1.17181 | ||||||||
\(526\) | −2.60232 | −0.113467 | ||||||||
\(527\) | 8.58298 | 0.373880 | ||||||||
\(528\) | 5.74813 | 0.250155 | ||||||||
\(529\) | −14.2829 | −0.620996 | ||||||||
\(530\) | 8.74018 | 0.379649 | ||||||||
\(531\) | −14.2153 | −0.616890 | ||||||||
\(532\) | 3.79261 | 0.164430 | ||||||||
\(533\) | 18.4511 | 0.799206 | ||||||||
\(534\) | 28.6298 | 1.23893 | ||||||||
\(535\) | 0.746380 | 0.0322688 | ||||||||
\(536\) | −12.2668 | −0.529845 | ||||||||
\(537\) | 32.9510 | 1.42194 | ||||||||
\(538\) | 0.264247 | 0.0113925 | ||||||||
\(539\) | 14.0743 | 0.606225 | ||||||||
\(540\) | −4.26489 | −0.183532 | ||||||||
\(541\) | 12.2986 | 0.528757 | 0.264378 | − | 0.964419i | \(-0.414833\pi\) | ||||
0.264378 | + | 0.964419i | \(0.414833\pi\) | |||||||
\(542\) | 16.4146 | 0.705066 | ||||||||
\(543\) | −38.0940 | −1.63477 | ||||||||
\(544\) | −3.85364 | −0.165224 | ||||||||
\(545\) | −24.5908 | −1.05336 | ||||||||
\(546\) | 7.68501 | 0.328888 | ||||||||
\(547\) | 32.0657 | 1.37103 | 0.685515 | − | 0.728058i | \(-0.259577\pi\) | ||||
0.685515 | + | 0.728058i | \(0.259577\pi\) | |||||||
\(548\) | −5.25548 | −0.224503 | ||||||||
\(549\) | 18.5453 | 0.791494 | ||||||||
\(550\) | 26.9059 | 1.14727 | ||||||||
\(551\) | 42.0390 | 1.79092 | ||||||||
\(552\) | 7.47527 | 0.318169 | ||||||||
\(553\) | −7.46775 | −0.317561 | ||||||||
\(554\) | 9.16478 | 0.389374 | ||||||||
\(555\) | 32.2807 | 1.37024 | ||||||||
\(556\) | 10.3165 | 0.437516 | ||||||||
\(557\) | −24.9196 | −1.05588 | −0.527939 | − | 0.849282i | \(-0.677035\pi\) | ||||
−0.527939 | + | 0.849282i | \(0.677035\pi\) | |||||||
\(558\) | −7.59565 | −0.321550 | ||||||||
\(559\) | −5.06583 | −0.214262 | ||||||||
\(560\) | 3.67325 | 0.155223 | ||||||||
\(561\) | 22.1512 | 0.935225 | ||||||||
\(562\) | 21.9696 | 0.926732 | ||||||||
\(563\) | 5.82462 | 0.245478 | 0.122739 | − | 0.992439i | \(-0.460832\pi\) | ||||
0.122739 | + | 0.992439i | \(0.460832\pi\) | |||||||
\(564\) | 8.18375 | 0.344598 | ||||||||
\(565\) | 12.2733 | 0.516343 | ||||||||
\(566\) | 31.0821 | 1.30648 | ||||||||
\(567\) | −6.80113 | −0.285621 | ||||||||
\(568\) | −10.3261 | −0.433273 | ||||||||
\(569\) | 10.1091 | 0.423796 | 0.211898 | − | 0.977292i | \(-0.432036\pi\) | ||||
0.211898 | + | 0.977292i | \(0.432036\pi\) | |||||||
\(570\) | 44.0514 | 1.84511 | ||||||||
\(571\) | −35.3855 | −1.48084 | −0.740418 | − | 0.672147i | \(-0.765372\pi\) | ||||
−0.740418 | + | 0.672147i | \(0.765372\pi\) | |||||||
\(572\) | −7.70113 | −0.322000 | ||||||||
\(573\) | 19.3174 | 0.806995 | ||||||||
\(574\) | −4.86731 | −0.203157 | ||||||||
\(575\) | 34.9903 | 1.45920 | ||||||||
\(576\) | 3.41035 | 0.142098 | ||||||||
\(577\) | −30.1450 | −1.25495 | −0.627476 | − | 0.778636i | \(-0.715912\pi\) | ||||
−0.627476 | + | 0.778636i | \(0.715912\pi\) | |||||||
\(578\) | 2.14945 | 0.0894052 | ||||||||
\(579\) | −20.1694 | −0.838213 | ||||||||
\(580\) | 40.7160 | 1.69064 | ||||||||
\(581\) | −9.08787 | −0.377028 | ||||||||
\(582\) | −13.4185 | −0.556217 | ||||||||
\(583\) | 4.83382 | 0.200196 | ||||||||
\(584\) | −14.8291 | −0.613633 | ||||||||
\(585\) | 47.4879 | 1.96338 | ||||||||
\(586\) | 31.0314 | 1.28190 | ||||||||
\(587\) | −2.26699 | −0.0935686 | −0.0467843 | − | 0.998905i | \(-0.514897\pi\) | ||||
−0.0467843 | + | 0.998905i | \(0.514897\pi\) | |||||||
\(588\) | 15.6958 | 0.647284 | ||||||||
\(589\) | 9.43995 | 0.388966 | ||||||||
\(590\) | 17.1109 | 0.704443 | ||||||||
\(591\) | −2.24784 | −0.0924636 | ||||||||
\(592\) | −3.10590 | −0.127652 | ||||||||
\(593\) | −35.1579 | −1.44376 | −0.721880 | − | 0.692018i | \(-0.756722\pi\) | ||||
−0.721880 | + | 0.692018i | \(0.756722\pi\) | |||||||
\(594\) | −2.35873 | −0.0967797 | ||||||||
\(595\) | 14.1554 | 0.580314 | ||||||||
\(596\) | −9.63547 | −0.394684 | ||||||||
\(597\) | −14.8868 | −0.609275 | ||||||||
\(598\) | −10.0151 | −0.409547 | ||||||||
\(599\) | 10.7476 | 0.439136 | 0.219568 | − | 0.975597i | \(-0.429535\pi\) | ||||
0.219568 | + | 0.975597i | \(0.429535\pi\) | |||||||
\(600\) | 30.0056 | 1.22497 | ||||||||
\(601\) | 14.8691 | 0.606524 | 0.303262 | − | 0.952907i | \(-0.401924\pi\) | ||||
0.303262 | + | 0.952907i | \(0.401924\pi\) | |||||||
\(602\) | 1.33634 | 0.0544651 | ||||||||
\(603\) | 41.8340 | 1.70361 | ||||||||
\(604\) | −2.50913 | −0.102095 | ||||||||
\(605\) | −23.9967 | −0.975603 | ||||||||
\(606\) | 17.6564 | 0.717243 | ||||||||
\(607\) | 40.1751 | 1.63066 | 0.815328 | − | 0.579000i | \(-0.196557\pi\) | ||||
0.815328 | + | 0.579000i | \(0.196557\pi\) | |||||||
\(608\) | −4.23841 | −0.171890 | ||||||||
\(609\) | −22.4711 | −0.910577 | ||||||||
\(610\) | −22.3229 | −0.903827 | ||||||||
\(611\) | −10.9643 | −0.443568 | ||||||||
\(612\) | 13.1423 | 0.531244 | ||||||||
\(613\) | 19.3275 | 0.780632 | 0.390316 | − | 0.920681i | \(-0.372366\pi\) | ||||
0.390316 | + | 0.920681i | \(0.372366\pi\) | |||||||
\(614\) | −8.81240 | −0.355640 | ||||||||
\(615\) | −56.5340 | −2.27967 | ||||||||
\(616\) | 2.03152 | 0.0818521 | ||||||||
\(617\) | −44.7037 | −1.79970 | −0.899851 | − | 0.436197i | \(-0.856325\pi\) | ||||
−0.899851 | + | 0.436197i | \(0.856325\pi\) | |||||||
\(618\) | −3.74710 | −0.150730 | ||||||||
\(619\) | 35.3049 | 1.41902 | 0.709512 | − | 0.704693i | \(-0.248915\pi\) | ||||
0.709512 | + | 0.704693i | \(0.248915\pi\) | |||||||
\(620\) | 9.14286 | 0.367186 | ||||||||
\(621\) | −3.06746 | −0.123093 | ||||||||
\(622\) | −26.7512 | −1.07263 | ||||||||
\(623\) | 10.1184 | 0.405385 | ||||||||
\(624\) | −8.58834 | −0.343809 | ||||||||
\(625\) | 56.1948 | 2.24779 | ||||||||
\(626\) | 19.5340 | 0.780737 | ||||||||
\(627\) | 24.3629 | 0.972961 | ||||||||
\(628\) | −4.24098 | −0.169234 | ||||||||
\(629\) | −11.9690 | −0.477236 | ||||||||
\(630\) | −12.5270 | −0.499090 | ||||||||
\(631\) | −16.5494 | −0.658823 | −0.329412 | − | 0.944186i | \(-0.606850\pi\) | ||||
−0.329412 | + | 0.944186i | \(0.606850\pi\) | |||||||
\(632\) | 8.34555 | 0.331968 | ||||||||
\(633\) | −18.2373 | −0.724867 | ||||||||
\(634\) | −13.9817 | −0.555284 | ||||||||
\(635\) | −29.1942 | −1.15854 | ||||||||
\(636\) | 5.39071 | 0.213756 | ||||||||
\(637\) | −21.0286 | −0.833185 | ||||||||
\(638\) | 22.5183 | 0.891507 | ||||||||
\(639\) | 35.2155 | 1.39311 | ||||||||
\(640\) | −4.10502 | −0.162265 | ||||||||
\(641\) | 8.08076 | 0.319171 | 0.159585 | − | 0.987184i | \(-0.448984\pi\) | ||||
0.159585 | + | 0.987184i | \(0.448984\pi\) | |||||||
\(642\) | 0.460347 | 0.0181685 | ||||||||
\(643\) | −23.9090 | −0.942880 | −0.471440 | − | 0.881898i | \(-0.656266\pi\) | ||||
−0.471440 | + | 0.881898i | \(0.656266\pi\) | |||||||
\(644\) | 2.64193 | 0.104107 | ||||||||
\(645\) | 15.5217 | 0.611164 | ||||||||
\(646\) | −16.3333 | −0.642626 | ||||||||
\(647\) | −6.29349 | −0.247422 | −0.123711 | − | 0.992318i | \(-0.539480\pi\) | ||||
−0.123711 | + | 0.992318i | \(0.539480\pi\) | |||||||
\(648\) | 7.60057 | 0.298579 | ||||||||
\(649\) | 9.46329 | 0.371467 | ||||||||
\(650\) | −40.2004 | −1.57679 | ||||||||
\(651\) | −5.04594 | −0.197766 | ||||||||
\(652\) | 13.4953 | 0.528515 | ||||||||
\(653\) | −12.0440 | −0.471317 | −0.235659 | − | 0.971836i | \(-0.575725\pi\) | ||||
−0.235659 | + | 0.971836i | \(0.575725\pi\) | |||||||
\(654\) | −15.1670 | −0.593075 | ||||||||
\(655\) | −7.37278 | −0.288078 | ||||||||
\(656\) | 5.43943 | 0.212374 | ||||||||
\(657\) | 50.5724 | 1.97302 | ||||||||
\(658\) | 2.89232 | 0.112754 | ||||||||
\(659\) | −3.73022 | −0.145309 | −0.0726544 | − | 0.997357i | \(-0.523147\pi\) | ||||
−0.0726544 | + | 0.997357i | \(0.523147\pi\) | |||||||
\(660\) | 23.5962 | 0.918480 | ||||||||
\(661\) | 30.3974 | 1.18232 | 0.591160 | − | 0.806554i | \(-0.298670\pi\) | ||||
0.591160 | + | 0.806554i | \(0.298670\pi\) | |||||||
\(662\) | 16.2256 | 0.630624 | ||||||||
\(663\) | −33.0964 | −1.28536 | ||||||||
\(664\) | 10.1561 | 0.394133 | ||||||||
\(665\) | 15.5687 | 0.603730 | ||||||||
\(666\) | 10.5922 | 0.410439 | ||||||||
\(667\) | 29.2844 | 1.13389 | ||||||||
\(668\) | −9.02394 | −0.349147 | ||||||||
\(669\) | −9.41612 | −0.364048 | ||||||||
\(670\) | −50.3555 | −1.94540 | ||||||||
\(671\) | −12.3458 | −0.476606 | ||||||||
\(672\) | 2.26556 | 0.0873959 | ||||||||
\(673\) | 7.50398 | 0.289257 | 0.144629 | − | 0.989486i | \(-0.453801\pi\) | ||||
0.144629 | + | 0.989486i | \(0.453801\pi\) | |||||||
\(674\) | −14.0146 | −0.539822 | ||||||||
\(675\) | −12.3127 | −0.473917 | ||||||||
\(676\) | −1.49365 | −0.0574483 | ||||||||
\(677\) | 35.1058 | 1.34923 | 0.674613 | − | 0.738171i | \(-0.264310\pi\) | ||||
0.674613 | + | 0.738171i | \(0.264310\pi\) | |||||||
\(678\) | 7.56987 | 0.290719 | ||||||||
\(679\) | −4.74242 | −0.181997 | ||||||||
\(680\) | −15.8193 | −0.606642 | ||||||||
\(681\) | 13.4884 | 0.516878 | ||||||||
\(682\) | 5.05652 | 0.193624 | ||||||||
\(683\) | −17.3374 | −0.663399 | −0.331699 | − | 0.943385i | \(-0.607622\pi\) | ||||
−0.331699 | + | 0.943385i | \(0.607622\pi\) | |||||||
\(684\) | 14.4545 | 0.552680 | ||||||||
\(685\) | −21.5739 | −0.824295 | ||||||||
\(686\) | 11.8110 | 0.450945 | ||||||||
\(687\) | 38.3499 | 1.46314 | ||||||||
\(688\) | −1.49342 | −0.0569361 | ||||||||
\(689\) | −7.22227 | −0.275147 | ||||||||
\(690\) | 30.6861 | 1.16820 | ||||||||
\(691\) | 19.7711 | 0.752130 | 0.376065 | − | 0.926593i | \(-0.377277\pi\) | ||||
0.376065 | + | 0.926593i | \(0.377277\pi\) | |||||||
\(692\) | −18.0592 | −0.686508 | ||||||||
\(693\) | −6.92818 | −0.263180 | ||||||||
\(694\) | 28.1431 | 1.06830 | ||||||||
\(695\) | 42.3493 | 1.60640 | ||||||||
\(696\) | 25.1125 | 0.951888 | ||||||||
\(697\) | 20.9616 | 0.793978 | ||||||||
\(698\) | −30.4236 | −1.15155 | ||||||||
\(699\) | −13.2119 | −0.499720 | ||||||||
\(700\) | 10.6047 | 0.400819 | ||||||||
\(701\) | 24.2040 | 0.914173 | 0.457087 | − | 0.889422i | \(-0.348893\pi\) | ||||
0.457087 | + | 0.889422i | \(0.348893\pi\) | |||||||
\(702\) | 3.52420 | 0.133012 | ||||||||
\(703\) | −13.1641 | −0.496493 | ||||||||
\(704\) | −2.27031 | −0.0855656 | ||||||||
\(705\) | 33.5945 | 1.26524 | ||||||||
\(706\) | −17.6425 | −0.663984 | ||||||||
\(707\) | 6.24018 | 0.234686 | ||||||||
\(708\) | 10.5535 | 0.396626 | ||||||||
\(709\) | 34.8797 | 1.30993 | 0.654967 | − | 0.755657i | \(-0.272682\pi\) | ||||
0.654967 | + | 0.755657i | \(0.272682\pi\) | |||||||
\(710\) | −42.3888 | −1.59082 | ||||||||
\(711\) | −28.4612 | −1.06738 | ||||||||
\(712\) | −11.3078 | −0.423777 | ||||||||
\(713\) | 6.57586 | 0.246268 | ||||||||
\(714\) | 8.73066 | 0.326737 | ||||||||
\(715\) | −31.6133 | −1.18227 | ||||||||
\(716\) | −13.0145 | −0.486375 | ||||||||
\(717\) | 10.5759 | 0.394966 | ||||||||
\(718\) | −30.1434 | −1.12494 | ||||||||
\(719\) | −9.39032 | −0.350200 | −0.175100 | − | 0.984551i | \(-0.556025\pi\) | ||||
−0.175100 | + | 0.984551i | \(0.556025\pi\) | |||||||
\(720\) | 13.9995 | 0.521732 | ||||||||
\(721\) | −1.32431 | −0.0493198 | ||||||||
\(722\) | 1.03587 | 0.0385509 | ||||||||
\(723\) | 20.1332 | 0.748761 | ||||||||
\(724\) | 15.0458 | 0.559173 | ||||||||
\(725\) | 117.547 | 4.36559 | ||||||||
\(726\) | −14.8005 | −0.549298 | ||||||||
\(727\) | 26.6314 | 0.987704 | 0.493852 | − | 0.869546i | \(-0.335588\pi\) | ||||
0.493852 | + | 0.869546i | \(0.335588\pi\) | |||||||
\(728\) | −3.03531 | −0.112496 | ||||||||
\(729\) | −33.8120 | −1.25230 | ||||||||
\(730\) | −60.8738 | −2.25304 | ||||||||
\(731\) | −5.75510 | −0.212860 | ||||||||
\(732\) | −13.7682 | −0.508886 | ||||||||
\(733\) | 19.5989 | 0.723901 | 0.361950 | − | 0.932197i | \(-0.382111\pi\) | ||||
0.361950 | + | 0.932197i | \(0.382111\pi\) | |||||||
\(734\) | −10.9556 | −0.404377 | ||||||||
\(735\) | 64.4316 | 2.37659 | ||||||||
\(736\) | −2.95247 | −0.108830 | ||||||||
\(737\) | −27.8495 | −1.02585 | ||||||||
\(738\) | −18.5504 | −0.682848 | ||||||||
\(739\) | −24.0248 | −0.883766 | −0.441883 | − | 0.897073i | \(-0.645689\pi\) | ||||
−0.441883 | + | 0.897073i | \(0.645689\pi\) | |||||||
\(740\) | −12.7498 | −0.468691 | ||||||||
\(741\) | −36.4009 | −1.33722 | ||||||||
\(742\) | 1.90520 | 0.0699420 | ||||||||
\(743\) | −15.6874 | −0.575515 | −0.287758 | − | 0.957703i | \(-0.592910\pi\) | ||||
−0.287758 | + | 0.957703i | \(0.592910\pi\) | |||||||
\(744\) | 5.63907 | 0.206738 | ||||||||
\(745\) | −39.5538 | −1.44914 | ||||||||
\(746\) | 16.6269 | 0.608755 | ||||||||
\(747\) | −34.6358 | −1.26726 | ||||||||
\(748\) | −8.74897 | −0.319894 | ||||||||
\(749\) | 0.162697 | 0.00594482 | ||||||||
\(750\) | 71.2069 | 2.60011 | ||||||||
\(751\) | 29.3428 | 1.07073 | 0.535367 | − | 0.844619i | \(-0.320173\pi\) | ||||
0.535367 | + | 0.844619i | \(0.320173\pi\) | |||||||
\(752\) | −3.23230 | −0.117870 | ||||||||
\(753\) | 60.1581 | 2.19228 | ||||||||
\(754\) | −33.6448 | −1.22527 | ||||||||
\(755\) | −10.3000 | −0.374856 | ||||||||
\(756\) | −0.929666 | −0.0338116 | ||||||||
\(757\) | −5.33901 | −0.194050 | −0.0970249 | − | 0.995282i | \(-0.530933\pi\) | ||||
−0.0970249 | + | 0.995282i | \(0.530933\pi\) | |||||||
\(758\) | −4.80098 | −0.174379 | ||||||||
\(759\) | 16.9712 | 0.616015 | ||||||||
\(760\) | −17.3988 | −0.631120 | ||||||||
\(761\) | −38.4634 | −1.39430 | −0.697148 | − | 0.716927i | \(-0.745548\pi\) | ||||
−0.697148 | + | 0.716927i | \(0.745548\pi\) | |||||||
\(762\) | −18.0062 | −0.652296 | ||||||||
\(763\) | −5.36034 | −0.194057 | ||||||||
\(764\) | −7.62970 | −0.276033 | ||||||||
\(765\) | 53.9492 | 1.95054 | ||||||||
\(766\) | −2.69820 | −0.0974899 | ||||||||
\(767\) | −14.1392 | −0.510538 | ||||||||
\(768\) | −2.53187 | −0.0913609 | ||||||||
\(769\) | −29.0978 | −1.04929 | −0.524646 | − | 0.851320i | \(-0.675802\pi\) | ||||
−0.524646 | + | 0.851320i | \(0.675802\pi\) | |||||||
\(770\) | 8.33942 | 0.300532 | ||||||||
\(771\) | 33.7988 | 1.21723 | ||||||||
\(772\) | 7.96623 | 0.286711 | ||||||||
\(773\) | −51.7135 | −1.86000 | −0.930002 | − | 0.367555i | \(-0.880195\pi\) | ||||
−0.930002 | + | 0.367555i | \(0.880195\pi\) | |||||||
\(774\) | 5.09308 | 0.183067 | ||||||||
\(775\) | 26.3954 | 0.948152 | ||||||||
\(776\) | 5.29986 | 0.190254 | ||||||||
\(777\) | 7.03660 | 0.252437 | ||||||||
\(778\) | 10.2263 | 0.366631 | ||||||||
\(779\) | 23.0546 | 0.826015 | ||||||||
\(780\) | −35.2553 | −1.26234 | ||||||||
\(781\) | −23.4434 | −0.838872 | ||||||||
\(782\) | −11.3778 | −0.406868 | ||||||||
\(783\) | −10.3049 | −0.368265 | ||||||||
\(784\) | −6.19930 | −0.221404 | ||||||||
\(785\) | −17.4093 | −0.621365 | ||||||||
\(786\) | −4.54733 | −0.162198 | ||||||||
\(787\) | −10.6768 | −0.380588 | −0.190294 | − | 0.981727i | \(-0.560944\pi\) | ||||
−0.190294 | + | 0.981727i | \(0.560944\pi\) | |||||||
\(788\) | 0.887818 | 0.0316272 | ||||||||
\(789\) | −6.58873 | −0.234565 | ||||||||
\(790\) | 34.2586 | 1.21887 | ||||||||
\(791\) | 2.67536 | 0.0951249 | ||||||||
\(792\) | 7.74255 | 0.275120 | ||||||||
\(793\) | 18.4461 | 0.655039 | ||||||||
\(794\) | 1.61933 | 0.0574679 | ||||||||
\(795\) | 22.1290 | 0.784834 | ||||||||
\(796\) | 5.87976 | 0.208403 | ||||||||
\(797\) | 14.3788 | 0.509324 | 0.254662 | − | 0.967030i | \(-0.418036\pi\) | ||||
0.254662 | + | 0.967030i | \(0.418036\pi\) | |||||||
\(798\) | 9.60238 | 0.339921 | ||||||||
\(799\) | −12.4561 | −0.440666 | ||||||||
\(800\) | −11.8512 | −0.419003 | ||||||||
\(801\) | 38.5635 | 1.36257 | ||||||||
\(802\) | −9.85489 | −0.347988 | ||||||||
\(803\) | −33.6667 | −1.18807 | ||||||||
\(804\) | −31.0579 | −1.09533 | ||||||||
\(805\) | 10.8452 | 0.382242 | ||||||||
\(806\) | −7.55501 | −0.266114 | ||||||||
\(807\) | 0.669037 | 0.0235512 | ||||||||
\(808\) | −6.97368 | −0.245333 | ||||||||
\(809\) | 9.47631 | 0.333169 | 0.166585 | − | 0.986027i | \(-0.446726\pi\) | ||||
0.166585 | + | 0.986027i | \(0.446726\pi\) | |||||||
\(810\) | 31.2005 | 1.09627 | ||||||||
\(811\) | 6.58696 | 0.231299 | 0.115650 | − | 0.993290i | \(-0.463105\pi\) | ||||
0.115650 | + | 0.993290i | \(0.463105\pi\) | |||||||
\(812\) | 8.87533 | 0.311463 | ||||||||
\(813\) | 41.5595 | 1.45755 | ||||||||
\(814\) | −7.05136 | −0.247150 | ||||||||
\(815\) | 55.3983 | 1.94052 | ||||||||
\(816\) | −9.75691 | −0.341560 | ||||||||
\(817\) | −6.32973 | −0.221449 | ||||||||
\(818\) | 10.5522 | 0.368949 | ||||||||
\(819\) | 10.3515 | 0.361710 | ||||||||
\(820\) | 22.3290 | 0.779762 | ||||||||
\(821\) | 6.81114 | 0.237710 | 0.118855 | − | 0.992912i | \(-0.462078\pi\) | ||||
0.118855 | + | 0.992912i | \(0.462078\pi\) | |||||||
\(822\) | −13.3062 | −0.464106 | ||||||||
\(823\) | −41.6119 | −1.45050 | −0.725250 | − | 0.688486i | \(-0.758276\pi\) | ||||
−0.725250 | + | 0.688486i | \(0.758276\pi\) | |||||||
\(824\) | 1.47997 | 0.0515573 | ||||||||
\(825\) | 68.1221 | 2.37171 | ||||||||
\(826\) | 3.72985 | 0.129778 | ||||||||
\(827\) | −38.3990 | −1.33526 | −0.667632 | − | 0.744492i | \(-0.732692\pi\) | ||||
−0.667632 | + | 0.744492i | \(0.732692\pi\) | |||||||
\(828\) | 10.0690 | 0.349921 | ||||||||
\(829\) | 28.1534 | 0.977809 | 0.488905 | − | 0.872337i | \(-0.337397\pi\) | ||||
0.488905 | + | 0.872337i | \(0.337397\pi\) | |||||||
\(830\) | 41.6910 | 1.44712 | ||||||||
\(831\) | 23.2040 | 0.804938 | ||||||||
\(832\) | 3.39210 | 0.117600 | ||||||||
\(833\) | −23.8899 | −0.827735 | ||||||||
\(834\) | 26.1199 | 0.904459 | ||||||||
\(835\) | −37.0435 | −1.28194 | ||||||||
\(836\) | −9.62252 | −0.332802 | ||||||||
\(837\) | −2.31398 | −0.0799827 | ||||||||
\(838\) | −19.6283 | −0.678047 | ||||||||
\(839\) | −26.7873 | −0.924799 | −0.462399 | − | 0.886672i | \(-0.653011\pi\) | ||||
−0.462399 | + | 0.886672i | \(0.653011\pi\) | |||||||
\(840\) | 9.30017 | 0.320886 | ||||||||
\(841\) | 69.3783 | 2.39235 | ||||||||
\(842\) | 22.0430 | 0.759651 | ||||||||
\(843\) | 55.6241 | 1.91580 | ||||||||
\(844\) | 7.20309 | 0.247941 | ||||||||
\(845\) | −6.13148 | −0.210929 | ||||||||
\(846\) | 11.0233 | 0.378988 | ||||||||
\(847\) | −5.23083 | −0.179733 | ||||||||
\(848\) | −2.12914 | −0.0731151 | ||||||||
\(849\) | 78.6958 | 2.70083 | ||||||||
\(850\) | −45.6702 | −1.56648 | ||||||||
\(851\) | −9.17009 | −0.314347 | ||||||||
\(852\) | −26.1443 | −0.895688 | ||||||||
\(853\) | −30.3376 | −1.03874 | −0.519370 | − | 0.854549i | \(-0.673834\pi\) | ||||
−0.519370 | + | 0.854549i | \(0.673834\pi\) | |||||||
\(854\) | −4.86598 | −0.166510 | ||||||||
\(855\) | 59.3358 | 2.02924 | ||||||||
\(856\) | −0.181821 | −0.00621453 | ||||||||
\(857\) | 4.65447 | 0.158994 | 0.0794968 | − | 0.996835i | \(-0.474669\pi\) | ||||
0.0794968 | + | 0.996835i | \(0.474669\pi\) | |||||||
\(858\) | −19.4982 | −0.665658 | ||||||||
\(859\) | 11.9948 | 0.409256 | 0.204628 | − | 0.978840i | \(-0.434402\pi\) | ||||
0.204628 | + | 0.978840i | \(0.434402\pi\) | |||||||
\(860\) | −6.13052 | −0.209049 | ||||||||
\(861\) | −12.3234 | −0.419979 | ||||||||
\(862\) | 25.5575 | 0.870492 | ||||||||
\(863\) | −27.4448 | −0.934233 | −0.467116 | − | 0.884196i | \(-0.654707\pi\) | ||||
−0.467116 | + | 0.884196i | \(0.654707\pi\) | |||||||
\(864\) | 1.03894 | 0.0353456 | ||||||||
\(865\) | −74.1334 | −2.52061 | ||||||||
\(866\) | −5.85717 | −0.199035 | ||||||||
\(867\) | 5.44211 | 0.184824 | ||||||||
\(868\) | 1.99297 | 0.0676459 | ||||||||
\(869\) | 18.9470 | 0.642733 | ||||||||
\(870\) | 103.087 | 3.49499 | ||||||||
\(871\) | 41.6102 | 1.40991 | ||||||||
\(872\) | 5.99043 | 0.202861 | ||||||||
\(873\) | −18.0744 | −0.611725 | ||||||||
\(874\) | −12.5138 | −0.423286 | ||||||||
\(875\) | 25.1661 | 0.850770 | ||||||||
\(876\) | −37.5453 | −1.26854 | ||||||||
\(877\) | −5.63566 | −0.190303 | −0.0951513 | − | 0.995463i | \(-0.530333\pi\) | ||||
−0.0951513 | + | 0.995463i | \(0.530333\pi\) | |||||||
\(878\) | 16.8707 | 0.569358 | ||||||||
\(879\) | 78.5675 | 2.65002 | ||||||||
\(880\) | −9.31968 | −0.314166 | ||||||||
\(881\) | −1.72951 | −0.0582686 | −0.0291343 | − | 0.999576i | \(-0.509275\pi\) | ||||
−0.0291343 | + | 0.999576i | \(0.509275\pi\) | |||||||
\(882\) | 21.1418 | 0.711880 | ||||||||
\(883\) | −33.5110 | −1.12773 | −0.563867 | − | 0.825866i | \(-0.690687\pi\) | ||||
−0.563867 | + | 0.825866i | \(0.690687\pi\) | |||||||
\(884\) | 13.0719 | 0.439657 | ||||||||
\(885\) | 43.3224 | 1.45627 | ||||||||
\(886\) | 7.90860 | 0.265694 | ||||||||
\(887\) | −5.90531 | −0.198281 | −0.0991405 | − | 0.995073i | \(-0.531609\pi\) | ||||
−0.0991405 | + | 0.995073i | \(0.531609\pi\) | |||||||
\(888\) | −7.86372 | −0.263889 | ||||||||
\(889\) | −6.36380 | −0.213435 | ||||||||
\(890\) | −46.4187 | −1.55596 | ||||||||
\(891\) | 17.2557 | 0.578087 | ||||||||
\(892\) | 3.71904 | 0.124523 | ||||||||
\(893\) | −13.6998 | −0.458447 | ||||||||
\(894\) | −24.3957 | −0.815915 | ||||||||
\(895\) | −53.4248 | −1.78579 | ||||||||
\(896\) | −0.894818 | −0.0298938 | ||||||||
\(897\) | −25.3569 | −0.846641 | ||||||||
\(898\) | 25.1035 | 0.837716 | ||||||||
\(899\) | 22.0910 | 0.736778 | ||||||||
\(900\) | 40.4167 | 1.34722 | ||||||||
\(901\) | −8.20496 | −0.273347 | ||||||||
\(902\) | 12.3492 | 0.411184 | ||||||||
\(903\) | 3.38343 | 0.112594 | ||||||||
\(904\) | −2.98984 | −0.0994405 | ||||||||
\(905\) | 61.7634 | 2.05308 | ||||||||
\(906\) | −6.35277 | −0.211057 | ||||||||
\(907\) | −7.10973 | −0.236075 | −0.118037 | − | 0.993009i | \(-0.537660\pi\) | ||||
−0.118037 | + | 0.993009i | \(0.537660\pi\) | |||||||
\(908\) | −5.32747 | −0.176798 | ||||||||
\(909\) | 23.7827 | 0.788821 | ||||||||
\(910\) | −12.4600 | −0.413046 | ||||||||
\(911\) | 35.8358 | 1.18729 | 0.593647 | − | 0.804726i | \(-0.297688\pi\) | ||||
0.593647 | + | 0.804726i | \(0.297688\pi\) | |||||||
\(912\) | −10.7311 | −0.355342 | ||||||||
\(913\) | 23.0575 | 0.763093 | ||||||||
\(914\) | −22.4161 | −0.741460 | ||||||||
\(915\) | −56.5186 | −1.86845 | ||||||||
\(916\) | −15.1469 | −0.500468 | ||||||||
\(917\) | −1.60713 | −0.0530721 | ||||||||
\(918\) | 4.00372 | 0.132142 | ||||||||
\(919\) | 45.7182 | 1.50810 | 0.754052 | − | 0.656815i | \(-0.228097\pi\) | ||||
0.754052 | + | 0.656815i | \(0.228097\pi\) | |||||||
\(920\) | −12.1200 | −0.399583 | ||||||||
\(921\) | −22.3118 | −0.735200 | ||||||||
\(922\) | −24.7103 | −0.813790 | ||||||||
\(923\) | 35.0271 | 1.15293 | ||||||||
\(924\) | 5.14353 | 0.169210 | ||||||||
\(925\) | −36.8086 | −1.21026 | ||||||||
\(926\) | 39.7700 | 1.30692 | ||||||||
\(927\) | −5.04722 | −0.165773 | ||||||||
\(928\) | −9.91858 | −0.325593 | ||||||||
\(929\) | 15.9162 | 0.522193 | 0.261097 | − | 0.965313i | \(-0.415916\pi\) | ||||
0.261097 | + | 0.965313i | \(0.415916\pi\) | |||||||
\(930\) | 23.1485 | 0.759069 | ||||||||
\(931\) | −26.2752 | −0.861134 | ||||||||
\(932\) | 5.21825 | 0.170929 | ||||||||
\(933\) | −67.7306 | −2.21740 | ||||||||
\(934\) | −14.2231 | −0.465395 | ||||||||
\(935\) | −35.9147 | −1.17454 | ||||||||
\(936\) | −11.5682 | −0.378120 | ||||||||
\(937\) | 27.6752 | 0.904109 | 0.452054 | − | 0.891990i | \(-0.350691\pi\) | ||||
0.452054 | + | 0.891990i | \(0.350691\pi\) | |||||||
\(938\) | −10.9766 | −0.358397 | ||||||||
\(939\) | 49.4575 | 1.61399 | ||||||||
\(940\) | −13.2687 | −0.432776 | ||||||||
\(941\) | 15.0285 | 0.489914 | 0.244957 | − | 0.969534i | \(-0.421226\pi\) | ||||
0.244957 | + | 0.969534i | \(0.421226\pi\) | |||||||
\(942\) | −10.7376 | −0.349850 | ||||||||
\(943\) | 16.0598 | 0.522979 | ||||||||
\(944\) | −4.16828 | −0.135666 | ||||||||
\(945\) | −3.81630 | −0.124144 | ||||||||
\(946\) | −3.39053 | −0.110236 | ||||||||
\(947\) | 19.1997 | 0.623906 | 0.311953 | − | 0.950098i | \(-0.399017\pi\) | ||||
0.311953 | + | 0.950098i | \(0.399017\pi\) | |||||||
\(948\) | 21.1298 | 0.686264 | ||||||||
\(949\) | 50.3018 | 1.63287 | ||||||||
\(950\) | −50.2302 | −1.62968 | ||||||||
\(951\) | −35.3998 | −1.14792 | ||||||||
\(952\) | −3.44831 | −0.111760 | ||||||||
\(953\) | 12.8441 | 0.416060 | 0.208030 | − | 0.978122i | \(-0.433295\pi\) | ||||
0.208030 | + | 0.978122i | \(0.433295\pi\) | |||||||
\(954\) | 7.26112 | 0.235088 | ||||||||
\(955\) | −31.3201 | −1.01349 | ||||||||
\(956\) | −4.17713 | −0.135098 | ||||||||
\(957\) | 57.0133 | 1.84298 | ||||||||
\(958\) | −35.2372 | −1.13846 | ||||||||
\(959\) | −4.70270 | −0.151858 | ||||||||
\(960\) | −10.3934 | −0.335444 | ||||||||
\(961\) | −26.0394 | −0.839981 | ||||||||
\(962\) | 10.5355 | 0.339679 | ||||||||
\(963\) | 0.620074 | 0.0199816 | ||||||||
\(964\) | −7.95191 | −0.256114 | ||||||||
\(965\) | 32.7016 | 1.05270 | ||||||||
\(966\) | 6.68901 | 0.215215 | ||||||||
\(967\) | 41.8395 | 1.34547 | 0.672734 | − | 0.739885i | \(-0.265120\pi\) | ||||
0.672734 | + | 0.739885i | \(0.265120\pi\) | |||||||
\(968\) | 5.84568 | 0.187887 | ||||||||
\(969\) | −41.3538 | −1.32847 | ||||||||
\(970\) | 21.7560 | 0.698545 | ||||||||
\(971\) | 33.4610 | 1.07382 | 0.536908 | − | 0.843641i | \(-0.319592\pi\) | ||||
0.536908 | + | 0.843641i | \(0.319592\pi\) | |||||||
\(972\) | 22.3605 | 0.717212 | ||||||||
\(973\) | 9.23137 | 0.295944 | ||||||||
\(974\) | 18.4206 | 0.590233 | ||||||||
\(975\) | −101.782 | −3.25964 | ||||||||
\(976\) | 5.43795 | 0.174064 | ||||||||
\(977\) | −30.8467 | −0.986874 | −0.493437 | − | 0.869781i | \(-0.664260\pi\) | ||||
−0.493437 | + | 0.869781i | \(0.664260\pi\) | |||||||
\(978\) | 34.1682 | 1.09258 | ||||||||
\(979\) | −25.6722 | −0.820487 | ||||||||
\(980\) | −25.4483 | −0.812915 | ||||||||
\(981\) | −20.4294 | −0.652262 | ||||||||
\(982\) | 26.4977 | 0.845577 | ||||||||
\(983\) | 42.5800 | 1.35809 | 0.679046 | − | 0.734096i | \(-0.262394\pi\) | ||||
0.679046 | + | 0.734096i | \(0.262394\pi\) | |||||||
\(984\) | 13.7719 | 0.439033 | ||||||||
\(985\) | 3.64451 | 0.116124 | ||||||||
\(986\) | −38.2227 | −1.21726 | ||||||||
\(987\) | 7.32297 | 0.233093 | ||||||||
\(988\) | 14.3771 | 0.457397 | ||||||||
\(989\) | −4.40928 | −0.140207 | ||||||||
\(990\) | 31.7833 | 1.01014 | ||||||||
\(991\) | 46.1656 | 1.46650 | 0.733250 | − | 0.679960i | \(-0.238003\pi\) | ||||
0.733250 | + | 0.679960i | \(0.238003\pi\) | |||||||
\(992\) | −2.22724 | −0.0707149 | ||||||||
\(993\) | 41.0809 | 1.30366 | ||||||||
\(994\) | −9.23997 | −0.293074 | ||||||||
\(995\) | 24.1365 | 0.765180 | ||||||||
\(996\) | 25.7139 | 0.814776 | ||||||||
\(997\) | −35.1743 | −1.11398 | −0.556991 | − | 0.830519i | \(-0.688044\pi\) | ||||
−0.556991 | + | 0.830519i | \(0.688044\pi\) | |||||||
\(998\) | −34.6603 | −1.09715 | ||||||||
\(999\) | 3.22686 | 0.102093 |
(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 | 8006.2.a.c.1.13 | ✓ | 92 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8006.2.a.c.1.13 | ✓ | 92 | 1.1 | even | 1 | trivial |