Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4017,2,Mod(1,4017)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4017, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("4017.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4017 = 3 \cdot 13 \cdot 103 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4017.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: | \(32.0759064919\) |
Analytic rank: | \(1\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 21 x^{14} - 3 x^{13} + 177 x^{12} + 45 x^{11} - 763 x^{10} - 251 x^{9} + 1771 x^{8} + 639 x^{7} - 2118 x^{6} - 710 x^{5} + 1113 x^{4} + 243 x^{3} - 183 x^{2} - 10 x + 7 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(2.37644\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4017.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.37644 | −1.68040 | −0.840200 | − | 0.542277i | \(-0.817562\pi\) | ||||
−0.840200 | + | 0.542277i | \(0.817562\pi\) | |||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 3.64749 | 1.82374 | ||||||||
\(5\) | 1.54914 | 0.692798 | 0.346399 | − | 0.938087i | \(-0.387404\pi\) | ||||
0.346399 | + | 0.938087i | \(0.387404\pi\) | |||||||
\(6\) | −2.37644 | −0.970179 | ||||||||
\(7\) | 1.30434 | 0.492996 | 0.246498 | − | 0.969143i | \(-0.420720\pi\) | ||||
0.246498 | + | 0.969143i | \(0.420720\pi\) | |||||||
\(8\) | −3.91517 | −1.38422 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −3.68145 | −1.16418 | ||||||||
\(11\) | 0.998212 | 0.300972 | 0.150486 | − | 0.988612i | \(-0.451916\pi\) | ||||
0.150486 | + | 0.988612i | \(0.451916\pi\) | |||||||
\(12\) | 3.64749 | 1.05294 | ||||||||
\(13\) | −1.00000 | −0.277350 | ||||||||
\(14\) | −3.09970 | −0.828430 | ||||||||
\(15\) | 1.54914 | 0.399987 | ||||||||
\(16\) | 2.00920 | 0.502299 | ||||||||
\(17\) | −6.18975 | −1.50123 | −0.750617 | − | 0.660737i | \(-0.770244\pi\) | ||||
−0.750617 | + | 0.660737i | \(0.770244\pi\) | |||||||
\(18\) | −2.37644 | −0.560133 | ||||||||
\(19\) | −3.83531 | −0.879880 | −0.439940 | − | 0.898027i | \(-0.645000\pi\) | ||||
−0.439940 | + | 0.898027i | \(0.645000\pi\) | |||||||
\(20\) | 5.65049 | 1.26349 | ||||||||
\(21\) | 1.30434 | 0.284631 | ||||||||
\(22\) | −2.37219 | −0.505754 | ||||||||
\(23\) | 3.79897 | 0.792139 | 0.396070 | − | 0.918220i | \(-0.370374\pi\) | ||||
0.396070 | + | 0.918220i | \(0.370374\pi\) | |||||||
\(24\) | −3.91517 | −0.799180 | ||||||||
\(25\) | −2.60015 | −0.520031 | ||||||||
\(26\) | 2.37644 | 0.466059 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 4.75758 | 0.899099 | ||||||||
\(29\) | 2.72405 | 0.505843 | 0.252921 | − | 0.967487i | \(-0.418609\pi\) | ||||
0.252921 | + | 0.967487i | \(0.418609\pi\) | |||||||
\(30\) | −3.68145 | −0.672139 | ||||||||
\(31\) | −3.88694 | −0.698114 | −0.349057 | − | 0.937101i | \(-0.613498\pi\) | ||||
−0.349057 | + | 0.937101i | \(0.613498\pi\) | |||||||
\(32\) | 3.05559 | 0.540157 | ||||||||
\(33\) | 0.998212 | 0.173766 | ||||||||
\(34\) | 14.7096 | 2.52268 | ||||||||
\(35\) | 2.02062 | 0.341547 | ||||||||
\(36\) | 3.64749 | 0.607915 | ||||||||
\(37\) | −4.36970 | −0.718374 | −0.359187 | − | 0.933266i | \(-0.616946\pi\) | ||||
−0.359187 | + | 0.933266i | \(0.616946\pi\) | |||||||
\(38\) | 9.11440 | 1.47855 | ||||||||
\(39\) | −1.00000 | −0.160128 | ||||||||
\(40\) | −6.06516 | −0.958985 | ||||||||
\(41\) | 1.99305 | 0.311262 | 0.155631 | − | 0.987815i | \(-0.450259\pi\) | ||||
0.155631 | + | 0.987815i | \(0.450259\pi\) | |||||||
\(42\) | −3.09970 | −0.478295 | ||||||||
\(43\) | −4.74274 | −0.723262 | −0.361631 | − | 0.932321i | \(-0.617780\pi\) | ||||
−0.361631 | + | 0.932321i | \(0.617780\pi\) | |||||||
\(44\) | 3.64097 | 0.548896 | ||||||||
\(45\) | 1.54914 | 0.230933 | ||||||||
\(46\) | −9.02803 | −1.33111 | ||||||||
\(47\) | −10.7060 | −1.56163 | −0.780814 | − | 0.624764i | \(-0.785195\pi\) | ||||
−0.780814 | + | 0.624764i | \(0.785195\pi\) | |||||||
\(48\) | 2.00920 | 0.290003 | ||||||||
\(49\) | −5.29868 | −0.756955 | ||||||||
\(50\) | 6.17912 | 0.873859 | ||||||||
\(51\) | −6.18975 | −0.866738 | ||||||||
\(52\) | −3.64749 | −0.505816 | ||||||||
\(53\) | 1.58834 | 0.218176 | 0.109088 | − | 0.994032i | \(-0.465207\pi\) | ||||
0.109088 | + | 0.994032i | \(0.465207\pi\) | |||||||
\(54\) | −2.37644 | −0.323393 | ||||||||
\(55\) | 1.54637 | 0.208513 | ||||||||
\(56\) | −5.10673 | −0.682415 | ||||||||
\(57\) | −3.83531 | −0.507999 | ||||||||
\(58\) | −6.47355 | −0.850018 | ||||||||
\(59\) | −9.55468 | −1.24391 | −0.621957 | − | 0.783051i | \(-0.713662\pi\) | ||||
−0.621957 | + | 0.783051i | \(0.713662\pi\) | |||||||
\(60\) | 5.65049 | 0.729474 | ||||||||
\(61\) | 0.815146 | 0.104369 | 0.0521844 | − | 0.998637i | \(-0.483382\pi\) | ||||
0.0521844 | + | 0.998637i | \(0.483382\pi\) | |||||||
\(62\) | 9.23709 | 1.17311 | ||||||||
\(63\) | 1.30434 | 0.164332 | ||||||||
\(64\) | −11.2798 | −1.40998 | ||||||||
\(65\) | −1.54914 | −0.192148 | ||||||||
\(66\) | −2.37219 | −0.291997 | ||||||||
\(67\) | −8.73068 | −1.06662 | −0.533311 | − | 0.845919i | \(-0.679053\pi\) | ||||
−0.533311 | + | 0.845919i | \(0.679053\pi\) | |||||||
\(68\) | −22.5770 | −2.73787 | ||||||||
\(69\) | 3.79897 | 0.457342 | ||||||||
\(70\) | −4.80189 | −0.573935 | ||||||||
\(71\) | 11.8921 | 1.41133 | 0.705667 | − | 0.708544i | \(-0.250647\pi\) | ||||
0.705667 | + | 0.708544i | \(0.250647\pi\) | |||||||
\(72\) | −3.91517 | −0.461407 | ||||||||
\(73\) | −3.23415 | −0.378529 | −0.189265 | − | 0.981926i | \(-0.560610\pi\) | ||||
−0.189265 | + | 0.981926i | \(0.560610\pi\) | |||||||
\(74\) | 10.3843 | 1.20716 | ||||||||
\(75\) | −2.60015 | −0.300240 | ||||||||
\(76\) | −13.9892 | −1.60468 | ||||||||
\(77\) | 1.30201 | 0.148378 | ||||||||
\(78\) | 2.37644 | 0.269079 | ||||||||
\(79\) | −8.61766 | −0.969563 | −0.484781 | − | 0.874635i | \(-0.661101\pi\) | ||||
−0.484781 | + | 0.874635i | \(0.661101\pi\) | |||||||
\(80\) | 3.11253 | 0.347992 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −4.73638 | −0.523045 | ||||||||
\(83\) | 7.32306 | 0.803810 | 0.401905 | − | 0.915681i | \(-0.368348\pi\) | ||||
0.401905 | + | 0.915681i | \(0.368348\pi\) | |||||||
\(84\) | 4.75758 | 0.519095 | ||||||||
\(85\) | −9.58881 | −1.04005 | ||||||||
\(86\) | 11.2709 | 1.21537 | ||||||||
\(87\) | 2.72405 | 0.292048 | ||||||||
\(88\) | −3.90816 | −0.416612 | ||||||||
\(89\) | −12.5308 | −1.32826 | −0.664129 | − | 0.747618i | \(-0.731197\pi\) | ||||
−0.664129 | + | 0.747618i | \(0.731197\pi\) | |||||||
\(90\) | −3.68145 | −0.388059 | ||||||||
\(91\) | −1.30434 | −0.136732 | ||||||||
\(92\) | 13.8567 | 1.44466 | ||||||||
\(93\) | −3.88694 | −0.403056 | ||||||||
\(94\) | 25.4422 | 2.62416 | ||||||||
\(95\) | −5.94145 | −0.609580 | ||||||||
\(96\) | 3.05559 | 0.311860 | ||||||||
\(97\) | 7.89294 | 0.801407 | 0.400703 | − | 0.916208i | \(-0.368766\pi\) | ||||
0.400703 | + | 0.916208i | \(0.368766\pi\) | |||||||
\(98\) | 12.5920 | 1.27199 | ||||||||
\(99\) | 0.998212 | 0.100324 | ||||||||
\(100\) | −9.48403 | −0.948403 | ||||||||
\(101\) | 10.7172 | 1.06640 | 0.533200 | − | 0.845989i | \(-0.320989\pi\) | ||||
0.533200 | + | 0.845989i | \(0.320989\pi\) | |||||||
\(102\) | 14.7096 | 1.45647 | ||||||||
\(103\) | 1.00000 | 0.0985329 | ||||||||
\(104\) | 3.91517 | 0.383914 | ||||||||
\(105\) | 2.02062 | 0.197192 | ||||||||
\(106\) | −3.77461 | −0.366623 | ||||||||
\(107\) | −19.7317 | −1.90753 | −0.953766 | − | 0.300549i | \(-0.902830\pi\) | ||||
−0.953766 | + | 0.300549i | \(0.902830\pi\) | |||||||
\(108\) | 3.64749 | 0.350980 | ||||||||
\(109\) | 2.32319 | 0.222521 | 0.111260 | − | 0.993791i | \(-0.464511\pi\) | ||||
0.111260 | + | 0.993791i | \(0.464511\pi\) | |||||||
\(110\) | −3.67487 | −0.350385 | ||||||||
\(111\) | −4.36970 | −0.414754 | ||||||||
\(112\) | 2.62068 | 0.247631 | ||||||||
\(113\) | −14.1085 | −1.32721 | −0.663607 | − | 0.748081i | \(-0.730975\pi\) | ||||
−0.663607 | + | 0.748081i | \(0.730975\pi\) | |||||||
\(114\) | 9.11440 | 0.853642 | ||||||||
\(115\) | 5.88515 | 0.548793 | ||||||||
\(116\) | 9.93593 | 0.922528 | ||||||||
\(117\) | −1.00000 | −0.0924500 | ||||||||
\(118\) | 22.7062 | 2.09027 | ||||||||
\(119\) | −8.07357 | −0.740103 | ||||||||
\(120\) | −6.06516 | −0.553670 | ||||||||
\(121\) | −10.0036 | −0.909416 | ||||||||
\(122\) | −1.93715 | −0.175381 | ||||||||
\(123\) | 1.99305 | 0.179707 | ||||||||
\(124\) | −14.1776 | −1.27318 | ||||||||
\(125\) | −11.7737 | −1.05307 | ||||||||
\(126\) | −3.09970 | −0.276143 | ||||||||
\(127\) | −3.67047 | −0.325702 | −0.162851 | − | 0.986651i | \(-0.552069\pi\) | ||||
−0.162851 | + | 0.986651i | \(0.552069\pi\) | |||||||
\(128\) | 20.6947 | 1.82917 | ||||||||
\(129\) | −4.74274 | −0.417575 | ||||||||
\(130\) | 3.68145 | 0.322885 | ||||||||
\(131\) | 1.83891 | 0.160666 | 0.0803330 | − | 0.996768i | \(-0.474402\pi\) | ||||
0.0803330 | + | 0.996768i | \(0.474402\pi\) | |||||||
\(132\) | 3.64097 | 0.316905 | ||||||||
\(133\) | −5.00257 | −0.433777 | ||||||||
\(134\) | 20.7480 | 1.79235 | ||||||||
\(135\) | 1.54914 | 0.133329 | ||||||||
\(136\) | 24.2339 | 2.07804 | ||||||||
\(137\) | −4.15752 | −0.355201 | −0.177601 | − | 0.984103i | \(-0.556834\pi\) | ||||
−0.177601 | + | 0.984103i | \(0.556834\pi\) | |||||||
\(138\) | −9.02803 | −0.768517 | ||||||||
\(139\) | −16.1928 | −1.37346 | −0.686728 | − | 0.726915i | \(-0.740954\pi\) | ||||
−0.686728 | + | 0.726915i | \(0.740954\pi\) | |||||||
\(140\) | 7.37018 | 0.622894 | ||||||||
\(141\) | −10.7060 | −0.901606 | ||||||||
\(142\) | −28.2609 | −2.37161 | ||||||||
\(143\) | −0.998212 | −0.0834747 | ||||||||
\(144\) | 2.00920 | 0.167433 | ||||||||
\(145\) | 4.21994 | 0.350447 | ||||||||
\(146\) | 7.68579 | 0.636080 | ||||||||
\(147\) | −5.29868 | −0.437028 | ||||||||
\(148\) | −15.9384 | −1.31013 | ||||||||
\(149\) | 16.1197 | 1.32058 | 0.660288 | − | 0.751013i | \(-0.270434\pi\) | ||||
0.660288 | + | 0.751013i | \(0.270434\pi\) | |||||||
\(150\) | 6.17912 | 0.504523 | ||||||||
\(151\) | 7.13374 | 0.580536 | 0.290268 | − | 0.956945i | \(-0.406256\pi\) | ||||
0.290268 | + | 0.956945i | \(0.406256\pi\) | |||||||
\(152\) | 15.0159 | 1.21795 | ||||||||
\(153\) | −6.18975 | −0.500412 | ||||||||
\(154\) | −3.09416 | −0.249334 | ||||||||
\(155\) | −6.02142 | −0.483652 | ||||||||
\(156\) | −3.64749 | −0.292033 | ||||||||
\(157\) | −3.13762 | −0.250409 | −0.125205 | − | 0.992131i | \(-0.539959\pi\) | ||||
−0.125205 | + | 0.992131i | \(0.539959\pi\) | |||||||
\(158\) | 20.4794 | 1.62925 | ||||||||
\(159\) | 1.58834 | 0.125964 | ||||||||
\(160\) | 4.73354 | 0.374220 | ||||||||
\(161\) | 4.95516 | 0.390521 | ||||||||
\(162\) | −2.37644 | −0.186711 | ||||||||
\(163\) | 5.91150 | 0.463024 | 0.231512 | − | 0.972832i | \(-0.425633\pi\) | ||||
0.231512 | + | 0.972832i | \(0.425633\pi\) | |||||||
\(164\) | 7.26963 | 0.567663 | ||||||||
\(165\) | 1.54637 | 0.120385 | ||||||||
\(166\) | −17.4028 | −1.35072 | ||||||||
\(167\) | 24.5246 | 1.89777 | 0.948886 | − | 0.315619i | \(-0.102212\pi\) | ||||
0.948886 | + | 0.315619i | \(0.102212\pi\) | |||||||
\(168\) | −5.10673 | −0.393992 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | 22.7873 | 1.74770 | ||||||||
\(171\) | −3.83531 | −0.293293 | ||||||||
\(172\) | −17.2991 | −1.31904 | ||||||||
\(173\) | −7.07942 | −0.538239 | −0.269119 | − | 0.963107i | \(-0.586733\pi\) | ||||
−0.269119 | + | 0.963107i | \(0.586733\pi\) | |||||||
\(174\) | −6.47355 | −0.490758 | ||||||||
\(175\) | −3.39150 | −0.256373 | ||||||||
\(176\) | 2.00560 | 0.151178 | ||||||||
\(177\) | −9.55468 | −0.718174 | ||||||||
\(178\) | 29.7787 | 2.23200 | ||||||||
\(179\) | −6.28398 | −0.469686 | −0.234843 | − | 0.972033i | \(-0.575458\pi\) | ||||
−0.234843 | + | 0.972033i | \(0.575458\pi\) | |||||||
\(180\) | 5.65049 | 0.421162 | ||||||||
\(181\) | −15.9763 | −1.18751 | −0.593754 | − | 0.804647i | \(-0.702355\pi\) | ||||
−0.593754 | + | 0.804647i | \(0.702355\pi\) | |||||||
\(182\) | 3.09970 | 0.229765 | ||||||||
\(183\) | 0.815146 | 0.0602573 | ||||||||
\(184\) | −14.8736 | −1.09650 | ||||||||
\(185\) | −6.76929 | −0.497688 | ||||||||
\(186\) | 9.23709 | 0.677296 | ||||||||
\(187\) | −6.17868 | −0.451830 | ||||||||
\(188\) | −39.0499 | −2.84801 | ||||||||
\(189\) | 1.30434 | 0.0948771 | ||||||||
\(190\) | 14.1195 | 1.02434 | ||||||||
\(191\) | 17.1115 | 1.23814 | 0.619072 | − | 0.785334i | \(-0.287509\pi\) | ||||
0.619072 | + | 0.785334i | \(0.287509\pi\) | |||||||
\(192\) | −11.2798 | −0.814051 | ||||||||
\(193\) | −8.19444 | −0.589849 | −0.294925 | − | 0.955521i | \(-0.595295\pi\) | ||||
−0.294925 | + | 0.955521i | \(0.595295\pi\) | |||||||
\(194\) | −18.7571 | −1.34668 | ||||||||
\(195\) | −1.54914 | −0.110937 | ||||||||
\(196\) | −19.3269 | −1.38049 | ||||||||
\(197\) | 22.4587 | 1.60011 | 0.800057 | − | 0.599924i | \(-0.204803\pi\) | ||||
0.800057 | + | 0.599924i | \(0.204803\pi\) | |||||||
\(198\) | −2.37219 | −0.168585 | ||||||||
\(199\) | 18.5204 | 1.31288 | 0.656439 | − | 0.754379i | \(-0.272062\pi\) | ||||
0.656439 | + | 0.754379i | \(0.272062\pi\) | |||||||
\(200\) | 10.1800 | 0.719837 | ||||||||
\(201\) | −8.73068 | −0.615815 | ||||||||
\(202\) | −25.4688 | −1.79198 | ||||||||
\(203\) | 3.55310 | 0.249378 | ||||||||
\(204\) | −22.5770 | −1.58071 | ||||||||
\(205\) | 3.08752 | 0.215642 | ||||||||
\(206\) | −2.37644 | −0.165575 | ||||||||
\(207\) | 3.79897 | 0.264046 | ||||||||
\(208\) | −2.00920 | −0.139313 | ||||||||
\(209\) | −3.82845 | −0.264819 | ||||||||
\(210\) | −4.80189 | −0.331362 | ||||||||
\(211\) | 21.9114 | 1.50845 | 0.754223 | − | 0.656619i | \(-0.228014\pi\) | ||||
0.754223 | + | 0.656619i | \(0.228014\pi\) | |||||||
\(212\) | 5.79347 | 0.397897 | ||||||||
\(213\) | 11.8921 | 0.814834 | ||||||||
\(214\) | 46.8912 | 3.20542 | ||||||||
\(215\) | −7.34719 | −0.501074 | ||||||||
\(216\) | −3.91517 | −0.266393 | ||||||||
\(217\) | −5.06990 | −0.344167 | ||||||||
\(218\) | −5.52092 | −0.373924 | ||||||||
\(219\) | −3.23415 | −0.218544 | ||||||||
\(220\) | 5.64038 | 0.380274 | ||||||||
\(221\) | 6.18975 | 0.416368 | ||||||||
\(222\) | 10.3843 | 0.696952 | ||||||||
\(223\) | 6.00131 | 0.401878 | 0.200939 | − | 0.979604i | \(-0.435601\pi\) | ||||
0.200939 | + | 0.979604i | \(0.435601\pi\) | |||||||
\(224\) | 3.98554 | 0.266295 | ||||||||
\(225\) | −2.60015 | −0.173344 | ||||||||
\(226\) | 33.5280 | 2.23025 | ||||||||
\(227\) | 7.52318 | 0.499331 | 0.249666 | − | 0.968332i | \(-0.419679\pi\) | ||||
0.249666 | + | 0.968332i | \(0.419679\pi\) | |||||||
\(228\) | −13.9892 | −0.926461 | ||||||||
\(229\) | −9.53118 | −0.629838 | −0.314919 | − | 0.949119i | \(-0.601977\pi\) | ||||
−0.314919 | + | 0.949119i | \(0.601977\pi\) | |||||||
\(230\) | −13.9857 | −0.922191 | ||||||||
\(231\) | 1.30201 | 0.0856661 | ||||||||
\(232\) | −10.6651 | −0.700198 | ||||||||
\(233\) | 13.0635 | 0.855820 | 0.427910 | − | 0.903821i | \(-0.359250\pi\) | ||||
0.427910 | + | 0.903821i | \(0.359250\pi\) | |||||||
\(234\) | 2.37644 | 0.155353 | ||||||||
\(235\) | −16.5851 | −1.08189 | ||||||||
\(236\) | −34.8506 | −2.26858 | ||||||||
\(237\) | −8.61766 | −0.559777 | ||||||||
\(238\) | 19.1864 | 1.24367 | ||||||||
\(239\) | −2.04869 | −0.132518 | −0.0662592 | − | 0.997802i | \(-0.521106\pi\) | ||||
−0.0662592 | + | 0.997802i | \(0.521106\pi\) | |||||||
\(240\) | 3.11253 | 0.200913 | ||||||||
\(241\) | 0.454757 | 0.0292935 | 0.0146467 | − | 0.999893i | \(-0.495338\pi\) | ||||
0.0146467 | + | 0.999893i | \(0.495338\pi\) | |||||||
\(242\) | 23.7729 | 1.52818 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 2.97323 | 0.190342 | ||||||||
\(245\) | −8.20843 | −0.524417 | ||||||||
\(246\) | −4.73638 | −0.301980 | ||||||||
\(247\) | 3.83531 | 0.244035 | ||||||||
\(248\) | 15.2180 | 0.966344 | ||||||||
\(249\) | 7.32306 | 0.464080 | ||||||||
\(250\) | 27.9796 | 1.76959 | ||||||||
\(251\) | 29.5491 | 1.86512 | 0.932561 | − | 0.361011i | \(-0.117568\pi\) | ||||
0.932561 | + | 0.361011i | \(0.117568\pi\) | |||||||
\(252\) | 4.75758 | 0.299700 | ||||||||
\(253\) | 3.79217 | 0.238412 | ||||||||
\(254\) | 8.72267 | 0.547309 | ||||||||
\(255\) | −9.58881 | −0.600475 | ||||||||
\(256\) | −26.6202 | −1.66376 | ||||||||
\(257\) | 4.57116 | 0.285141 | 0.142571 | − | 0.989785i | \(-0.454463\pi\) | ||||
0.142571 | + | 0.989785i | \(0.454463\pi\) | |||||||
\(258\) | 11.2709 | 0.701694 | ||||||||
\(259\) | −5.69959 | −0.354156 | ||||||||
\(260\) | −5.65049 | −0.350428 | ||||||||
\(261\) | 2.72405 | 0.168614 | ||||||||
\(262\) | −4.37006 | −0.269983 | ||||||||
\(263\) | −8.65184 | −0.533495 | −0.266748 | − | 0.963766i | \(-0.585949\pi\) | ||||
−0.266748 | + | 0.963766i | \(0.585949\pi\) | |||||||
\(264\) | −3.90816 | −0.240531 | ||||||||
\(265\) | 2.46057 | 0.151152 | ||||||||
\(266\) | 11.8883 | 0.728920 | ||||||||
\(267\) | −12.5308 | −0.766870 | ||||||||
\(268\) | −31.8451 | −1.94525 | ||||||||
\(269\) | −5.54940 | −0.338353 | −0.169176 | − | 0.985586i | \(-0.554111\pi\) | ||||
−0.169176 | + | 0.985586i | \(0.554111\pi\) | |||||||
\(270\) | −3.68145 | −0.224046 | ||||||||
\(271\) | 21.6564 | 1.31553 | 0.657766 | − | 0.753222i | \(-0.271502\pi\) | ||||
0.657766 | + | 0.753222i | \(0.271502\pi\) | |||||||
\(272\) | −12.4364 | −0.754069 | ||||||||
\(273\) | −1.30434 | −0.0789425 | ||||||||
\(274\) | 9.88012 | 0.596880 | ||||||||
\(275\) | −2.59550 | −0.156515 | ||||||||
\(276\) | 13.8567 | 0.834075 | ||||||||
\(277\) | 4.52966 | 0.272161 | 0.136080 | − | 0.990698i | \(-0.456549\pi\) | ||||
0.136080 | + | 0.990698i | \(0.456549\pi\) | |||||||
\(278\) | 38.4813 | 2.30795 | ||||||||
\(279\) | −3.88694 | −0.232705 | ||||||||
\(280\) | −7.91105 | −0.472776 | ||||||||
\(281\) | −11.8177 | −0.704983 | −0.352491 | − | 0.935815i | \(-0.614665\pi\) | ||||
−0.352491 | + | 0.935815i | \(0.614665\pi\) | |||||||
\(282\) | 25.4422 | 1.51506 | ||||||||
\(283\) | −14.2567 | −0.847471 | −0.423735 | − | 0.905786i | \(-0.639281\pi\) | ||||
−0.423735 | + | 0.905786i | \(0.639281\pi\) | |||||||
\(284\) | 43.3763 | 2.57391 | ||||||||
\(285\) | −5.94145 | −0.351941 | ||||||||
\(286\) | 2.37219 | 0.140271 | ||||||||
\(287\) | 2.59963 | 0.153451 | ||||||||
\(288\) | 3.05559 | 0.180052 | ||||||||
\(289\) | 21.3130 | 1.25371 | ||||||||
\(290\) | −10.0285 | −0.588891 | ||||||||
\(291\) | 7.89294 | 0.462692 | ||||||||
\(292\) | −11.7965 | −0.690340 | ||||||||
\(293\) | 3.73104 | 0.217970 | 0.108985 | − | 0.994043i | \(-0.465240\pi\) | ||||
0.108985 | + | 0.994043i | \(0.465240\pi\) | |||||||
\(294\) | 12.5920 | 0.734382 | ||||||||
\(295\) | −14.8016 | −0.861781 | ||||||||
\(296\) | 17.1081 | 0.994388 | ||||||||
\(297\) | 0.998212 | 0.0579221 | ||||||||
\(298\) | −38.3075 | −2.21910 | ||||||||
\(299\) | −3.79897 | −0.219700 | ||||||||
\(300\) | −9.48403 | −0.547561 | ||||||||
\(301\) | −6.18617 | −0.356565 | ||||||||
\(302\) | −16.9529 | −0.975532 | ||||||||
\(303\) | 10.7172 | 0.615687 | ||||||||
\(304\) | −7.70589 | −0.441963 | ||||||||
\(305\) | 1.26278 | 0.0723065 | ||||||||
\(306\) | 14.7096 | 0.840892 | ||||||||
\(307\) | −2.73282 | −0.155970 | −0.0779851 | − | 0.996955i | \(-0.524849\pi\) | ||||
−0.0779851 | + | 0.996955i | \(0.524849\pi\) | |||||||
\(308\) | 4.74907 | 0.270604 | ||||||||
\(309\) | 1.00000 | 0.0568880 | ||||||||
\(310\) | 14.3096 | 0.812729 | ||||||||
\(311\) | −13.4725 | −0.763955 | −0.381978 | − | 0.924172i | \(-0.624757\pi\) | ||||
−0.381978 | + | 0.924172i | \(0.624757\pi\) | |||||||
\(312\) | 3.91517 | 0.221653 | ||||||||
\(313\) | −17.5971 | −0.994647 | −0.497323 | − | 0.867565i | \(-0.665684\pi\) | ||||
−0.497323 | + | 0.867565i | \(0.665684\pi\) | |||||||
\(314\) | 7.45637 | 0.420787 | ||||||||
\(315\) | 2.02062 | 0.113849 | ||||||||
\(316\) | −31.4328 | −1.76823 | ||||||||
\(317\) | 13.0410 | 0.732457 | 0.366229 | − | 0.930525i | \(-0.380649\pi\) | ||||
0.366229 | + | 0.930525i | \(0.380649\pi\) | |||||||
\(318\) | −3.77461 | −0.211670 | ||||||||
\(319\) | 2.71917 | 0.152245 | ||||||||
\(320\) | −17.4741 | −0.976831 | ||||||||
\(321\) | −19.7317 | −1.10131 | ||||||||
\(322\) | −11.7757 | −0.656232 | ||||||||
\(323\) | 23.7396 | 1.32091 | ||||||||
\(324\) | 3.64749 | 0.202638 | ||||||||
\(325\) | 2.60015 | 0.144231 | ||||||||
\(326\) | −14.0484 | −0.778066 | ||||||||
\(327\) | 2.32319 | 0.128472 | ||||||||
\(328\) | −7.80313 | −0.430856 | ||||||||
\(329\) | −13.9643 | −0.769876 | ||||||||
\(330\) | −3.67487 | −0.202295 | ||||||||
\(331\) | 29.9797 | 1.64783 | 0.823916 | − | 0.566711i | \(-0.191784\pi\) | ||||
0.823916 | + | 0.566711i | \(0.191784\pi\) | |||||||
\(332\) | 26.7108 | 1.46594 | ||||||||
\(333\) | −4.36970 | −0.239458 | ||||||||
\(334\) | −58.2814 | −3.18902 | ||||||||
\(335\) | −13.5251 | −0.738954 | ||||||||
\(336\) | 2.62068 | 0.142970 | ||||||||
\(337\) | −6.99406 | −0.380991 | −0.190495 | − | 0.981688i | \(-0.561009\pi\) | ||||
−0.190495 | + | 0.981688i | \(0.561009\pi\) | |||||||
\(338\) | −2.37644 | −0.129262 | ||||||||
\(339\) | −14.1085 | −0.766268 | ||||||||
\(340\) | −34.9751 | −1.89679 | ||||||||
\(341\) | −3.87998 | −0.210113 | ||||||||
\(342\) | 9.11440 | 0.492850 | ||||||||
\(343\) | −16.0417 | −0.866172 | ||||||||
\(344\) | 18.5686 | 1.00115 | ||||||||
\(345\) | 5.88515 | 0.316846 | ||||||||
\(346\) | 16.8239 | 0.904456 | ||||||||
\(347\) | −35.9879 | −1.93193 | −0.965965 | − | 0.258675i | \(-0.916714\pi\) | ||||
−0.965965 | + | 0.258675i | \(0.916714\pi\) | |||||||
\(348\) | 9.93593 | 0.532622 | ||||||||
\(349\) | −2.81375 | −0.150617 | −0.0753084 | − | 0.997160i | \(-0.523994\pi\) | ||||
−0.0753084 | + | 0.997160i | \(0.523994\pi\) | |||||||
\(350\) | 8.05970 | 0.430809 | ||||||||
\(351\) | −1.00000 | −0.0533761 | ||||||||
\(352\) | 3.05012 | 0.162572 | ||||||||
\(353\) | 4.97986 | 0.265051 | 0.132526 | − | 0.991180i | \(-0.457691\pi\) | ||||
0.132526 | + | 0.991180i | \(0.457691\pi\) | |||||||
\(354\) | 22.7062 | 1.20682 | ||||||||
\(355\) | 18.4226 | 0.977770 | ||||||||
\(356\) | −45.7058 | −2.42240 | ||||||||
\(357\) | −8.07357 | −0.427298 | ||||||||
\(358\) | 14.9335 | 0.789261 | ||||||||
\(359\) | −14.2904 | −0.754221 | −0.377110 | − | 0.926168i | \(-0.623082\pi\) | ||||
−0.377110 | + | 0.926168i | \(0.623082\pi\) | |||||||
\(360\) | −6.06516 | −0.319662 | ||||||||
\(361\) | −4.29040 | −0.225811 | ||||||||
\(362\) | 37.9667 | 1.99549 | ||||||||
\(363\) | −10.0036 | −0.525051 | ||||||||
\(364\) | −4.75758 | −0.249365 | ||||||||
\(365\) | −5.01017 | −0.262244 | ||||||||
\(366\) | −1.93715 | −0.101256 | ||||||||
\(367\) | −16.8112 | −0.877539 | −0.438770 | − | 0.898600i | \(-0.644586\pi\) | ||||
−0.438770 | + | 0.898600i | \(0.644586\pi\) | |||||||
\(368\) | 7.63287 | 0.397891 | ||||||||
\(369\) | 1.99305 | 0.103754 | ||||||||
\(370\) | 16.0869 | 0.836316 | ||||||||
\(371\) | 2.07175 | 0.107560 | ||||||||
\(372\) | −14.1776 | −0.735072 | ||||||||
\(373\) | −8.90595 | −0.461132 | −0.230566 | − | 0.973057i | \(-0.574058\pi\) | ||||
−0.230566 | + | 0.973057i | \(0.574058\pi\) | |||||||
\(374\) | 14.6833 | 0.759255 | ||||||||
\(375\) | −11.7737 | −0.607993 | ||||||||
\(376\) | 41.9157 | 2.16164 | ||||||||
\(377\) | −2.72405 | −0.140296 | ||||||||
\(378\) | −3.09970 | −0.159432 | ||||||||
\(379\) | −6.07179 | −0.311887 | −0.155943 | − | 0.987766i | \(-0.549842\pi\) | ||||
−0.155943 | + | 0.987766i | \(0.549842\pi\) | |||||||
\(380\) | −21.6714 | −1.11172 | ||||||||
\(381\) | −3.67047 | −0.188044 | ||||||||
\(382\) | −40.6645 | −2.08058 | ||||||||
\(383\) | 9.80223 | 0.500871 | 0.250435 | − | 0.968133i | \(-0.419426\pi\) | ||||
0.250435 | + | 0.968133i | \(0.419426\pi\) | |||||||
\(384\) | 20.6947 | 1.05607 | ||||||||
\(385\) | 2.01700 | 0.102796 | ||||||||
\(386\) | 19.4736 | 0.991182 | ||||||||
\(387\) | −4.74274 | −0.241087 | ||||||||
\(388\) | 28.7894 | 1.46156 | ||||||||
\(389\) | −26.9054 | −1.36416 | −0.682078 | − | 0.731279i | \(-0.738924\pi\) | ||||
−0.682078 | + | 0.731279i | \(0.738924\pi\) | |||||||
\(390\) | 3.68145 | 0.186418 | ||||||||
\(391\) | −23.5147 | −1.18919 | ||||||||
\(392\) | 20.7452 | 1.04779 | ||||||||
\(393\) | 1.83891 | 0.0927606 | ||||||||
\(394\) | −53.3718 | −2.68883 | ||||||||
\(395\) | −13.3500 | −0.671711 | ||||||||
\(396\) | 3.64097 | 0.182965 | ||||||||
\(397\) | −10.1821 | −0.511026 | −0.255513 | − | 0.966806i | \(-0.582244\pi\) | ||||
−0.255513 | + | 0.966806i | \(0.582244\pi\) | |||||||
\(398\) | −44.0128 | −2.20616 | ||||||||
\(399\) | −5.00257 | −0.250442 | ||||||||
\(400\) | −5.22422 | −0.261211 | ||||||||
\(401\) | 13.1041 | 0.654387 | 0.327193 | − | 0.944957i | \(-0.393897\pi\) | ||||
0.327193 | + | 0.944957i | \(0.393897\pi\) | |||||||
\(402\) | 20.7480 | 1.03482 | ||||||||
\(403\) | 3.88694 | 0.193622 | ||||||||
\(404\) | 39.0908 | 1.94484 | ||||||||
\(405\) | 1.54914 | 0.0769776 | ||||||||
\(406\) | −8.44373 | −0.419055 | ||||||||
\(407\) | −4.36189 | −0.216211 | ||||||||
\(408\) | 24.2339 | 1.19976 | ||||||||
\(409\) | 38.0991 | 1.88388 | 0.941939 | − | 0.335783i | \(-0.109001\pi\) | ||||
0.941939 | + | 0.335783i | \(0.109001\pi\) | |||||||
\(410\) | −7.33733 | −0.362365 | ||||||||
\(411\) | −4.15752 | −0.205076 | ||||||||
\(412\) | 3.64749 | 0.179699 | ||||||||
\(413\) | −12.4626 | −0.613244 | ||||||||
\(414\) | −9.02803 | −0.443704 | ||||||||
\(415\) | 11.3445 | 0.556878 | ||||||||
\(416\) | −3.05559 | −0.149812 | ||||||||
\(417\) | −16.1928 | −0.792965 | ||||||||
\(418\) | 9.09810 | 0.445003 | ||||||||
\(419\) | 10.3491 | 0.505585 | 0.252792 | − | 0.967521i | \(-0.418651\pi\) | ||||
0.252792 | + | 0.967521i | \(0.418651\pi\) | |||||||
\(420\) | 7.37018 | 0.359628 | ||||||||
\(421\) | −20.5052 | −0.999364 | −0.499682 | − | 0.866209i | \(-0.666550\pi\) | ||||
−0.499682 | + | 0.866209i | \(0.666550\pi\) | |||||||
\(422\) | −52.0713 | −2.53479 | ||||||||
\(423\) | −10.7060 | −0.520543 | ||||||||
\(424\) | −6.21863 | −0.302003 | ||||||||
\(425\) | 16.0943 | 0.780688 | ||||||||
\(426\) | −28.2609 | −1.36925 | ||||||||
\(427\) | 1.06323 | 0.0514534 | ||||||||
\(428\) | −71.9711 | −3.47885 | ||||||||
\(429\) | −0.998212 | −0.0481941 | ||||||||
\(430\) | 17.4602 | 0.842005 | ||||||||
\(431\) | 25.7240 | 1.23908 | 0.619540 | − | 0.784965i | \(-0.287319\pi\) | ||||
0.619540 | + | 0.784965i | \(0.287319\pi\) | |||||||
\(432\) | 2.00920 | 0.0966675 | ||||||||
\(433\) | 11.9162 | 0.572654 | 0.286327 | − | 0.958132i | \(-0.407566\pi\) | ||||
0.286327 | + | 0.958132i | \(0.407566\pi\) | |||||||
\(434\) | 12.0483 | 0.578339 | ||||||||
\(435\) | 4.21994 | 0.202331 | ||||||||
\(436\) | 8.47379 | 0.405821 | ||||||||
\(437\) | −14.5702 | −0.696988 | ||||||||
\(438\) | 7.68579 | 0.367241 | ||||||||
\(439\) | −1.60422 | −0.0765653 | −0.0382826 | − | 0.999267i | \(-0.512189\pi\) | ||||
−0.0382826 | + | 0.999267i | \(0.512189\pi\) | |||||||
\(440\) | −6.05431 | −0.288628 | ||||||||
\(441\) | −5.29868 | −0.252318 | ||||||||
\(442\) | −14.7096 | −0.699664 | ||||||||
\(443\) | −25.1699 | −1.19586 | −0.597929 | − | 0.801549i | \(-0.704010\pi\) | ||||
−0.597929 | + | 0.801549i | \(0.704010\pi\) | |||||||
\(444\) | −15.9384 | −0.756404 | ||||||||
\(445\) | −19.4119 | −0.920215 | ||||||||
\(446\) | −14.2618 | −0.675315 | ||||||||
\(447\) | 16.1197 | 0.762435 | ||||||||
\(448\) | −14.7128 | −0.695114 | ||||||||
\(449\) | −15.1160 | −0.713368 | −0.356684 | − | 0.934225i | \(-0.616093\pi\) | ||||
−0.356684 | + | 0.934225i | \(0.616093\pi\) | |||||||
\(450\) | 6.17912 | 0.291286 | ||||||||
\(451\) | 1.98949 | 0.0936813 | ||||||||
\(452\) | −51.4605 | −2.42050 | ||||||||
\(453\) | 7.13374 | 0.335172 | ||||||||
\(454\) | −17.8784 | −0.839076 | ||||||||
\(455\) | −2.02062 | −0.0947280 | ||||||||
\(456\) | 15.0159 | 0.703183 | ||||||||
\(457\) | −17.5065 | −0.818921 | −0.409460 | − | 0.912328i | \(-0.634283\pi\) | ||||
−0.409460 | + | 0.912328i | \(0.634283\pi\) | |||||||
\(458\) | 22.6503 | 1.05838 | ||||||||
\(459\) | −6.18975 | −0.288913 | ||||||||
\(460\) | 21.4660 | 1.00086 | ||||||||
\(461\) | 28.8415 | 1.34328 | 0.671642 | − | 0.740876i | \(-0.265589\pi\) | ||||
0.671642 | + | 0.740876i | \(0.265589\pi\) | |||||||
\(462\) | −3.09416 | −0.143953 | ||||||||
\(463\) | −29.9946 | −1.39397 | −0.696985 | − | 0.717086i | \(-0.745475\pi\) | ||||
−0.696985 | + | 0.717086i | \(0.745475\pi\) | |||||||
\(464\) | 5.47314 | 0.254084 | ||||||||
\(465\) | −6.02142 | −0.279237 | ||||||||
\(466\) | −31.0448 | −1.43812 | ||||||||
\(467\) | 29.6606 | 1.37253 | 0.686265 | − | 0.727352i | \(-0.259249\pi\) | ||||
0.686265 | + | 0.727352i | \(0.259249\pi\) | |||||||
\(468\) | −3.64749 | −0.168605 | ||||||||
\(469\) | −11.3878 | −0.525841 | ||||||||
\(470\) | 39.4136 | 1.81801 | ||||||||
\(471\) | −3.13762 | −0.144574 | ||||||||
\(472\) | 37.4082 | 1.72185 | ||||||||
\(473\) | −4.73426 | −0.217682 | ||||||||
\(474\) | 20.4794 | 0.940650 | ||||||||
\(475\) | 9.97239 | 0.457565 | ||||||||
\(476\) | −29.4482 | −1.34976 | ||||||||
\(477\) | 1.58834 | 0.0727253 | ||||||||
\(478\) | 4.86859 | 0.222684 | ||||||||
\(479\) | 19.8032 | 0.904831 | 0.452416 | − | 0.891807i | \(-0.350562\pi\) | ||||
0.452416 | + | 0.891807i | \(0.350562\pi\) | |||||||
\(480\) | 4.73354 | 0.216056 | ||||||||
\(481\) | 4.36970 | 0.199241 | ||||||||
\(482\) | −1.08071 | −0.0492248 | ||||||||
\(483\) | 4.95516 | 0.225468 | ||||||||
\(484\) | −36.4879 | −1.65854 | ||||||||
\(485\) | 12.2273 | 0.555213 | ||||||||
\(486\) | −2.37644 | −0.107798 | ||||||||
\(487\) | 43.3406 | 1.96395 | 0.981976 | − | 0.189005i | \(-0.0605263\pi\) | ||||
0.981976 | + | 0.189005i | \(0.0605263\pi\) | |||||||
\(488\) | −3.19143 | −0.144469 | ||||||||
\(489\) | 5.91150 | 0.267327 | ||||||||
\(490\) | 19.5069 | 0.881231 | ||||||||
\(491\) | −29.4802 | −1.33042 | −0.665212 | − | 0.746654i | \(-0.731659\pi\) | ||||
−0.665212 | + | 0.746654i | \(0.731659\pi\) | |||||||
\(492\) | 7.26963 | 0.327740 | ||||||||
\(493\) | −16.8612 | −0.759389 | ||||||||
\(494\) | −9.11440 | −0.410076 | ||||||||
\(495\) | 1.54637 | 0.0695043 | ||||||||
\(496\) | −7.80962 | −0.350662 | ||||||||
\(497\) | 15.5114 | 0.695782 | ||||||||
\(498\) | −17.4028 | −0.779840 | ||||||||
\(499\) | −30.9431 | −1.38520 | −0.692602 | − | 0.721320i | \(-0.743536\pi\) | ||||
−0.692602 | + | 0.721320i | \(0.743536\pi\) | |||||||
\(500\) | −42.9446 | −1.92054 | ||||||||
\(501\) | 24.5246 | 1.09568 | ||||||||
\(502\) | −70.2218 | −3.13415 | ||||||||
\(503\) | −31.9197 | −1.42323 | −0.711614 | − | 0.702571i | \(-0.752035\pi\) | ||||
−0.711614 | + | 0.702571i | \(0.752035\pi\) | |||||||
\(504\) | −5.10673 | −0.227472 | ||||||||
\(505\) | 16.6025 | 0.738800 | ||||||||
\(506\) | −9.01189 | −0.400627 | ||||||||
\(507\) | 1.00000 | 0.0444116 | ||||||||
\(508\) | −13.3880 | −0.593996 | ||||||||
\(509\) | −19.1063 | −0.846873 | −0.423436 | − | 0.905926i | \(-0.639176\pi\) | ||||
−0.423436 | + | 0.905926i | \(0.639176\pi\) | |||||||
\(510\) | 22.7873 | 1.00904 | ||||||||
\(511\) | −4.21845 | −0.186613 | ||||||||
\(512\) | 21.8719 | 0.966613 | ||||||||
\(513\) | −3.83531 | −0.169333 | ||||||||
\(514\) | −10.8631 | −0.479151 | ||||||||
\(515\) | 1.54914 | 0.0682634 | ||||||||
\(516\) | −17.2991 | −0.761551 | ||||||||
\(517\) | −10.6868 | −0.470006 | ||||||||
\(518\) | 13.5448 | 0.595123 | ||||||||
\(519\) | −7.07942 | −0.310752 | ||||||||
\(520\) | 6.06516 | 0.265975 | ||||||||
\(521\) | −31.6998 | −1.38879 | −0.694396 | − | 0.719593i | \(-0.744328\pi\) | ||||
−0.694396 | + | 0.719593i | \(0.744328\pi\) | |||||||
\(522\) | −6.47355 | −0.283339 | ||||||||
\(523\) | −33.2108 | −1.45221 | −0.726104 | − | 0.687585i | \(-0.758671\pi\) | ||||
−0.726104 | + | 0.687585i | \(0.758671\pi\) | |||||||
\(524\) | 6.70739 | 0.293014 | ||||||||
\(525\) | −3.39150 | −0.148017 | ||||||||
\(526\) | 20.5606 | 0.896485 | ||||||||
\(527\) | 24.0592 | 1.04803 | ||||||||
\(528\) | 2.00560 | 0.0872827 | ||||||||
\(529\) | −8.56785 | −0.372515 | ||||||||
\(530\) | −5.84742 | −0.253996 | ||||||||
\(531\) | −9.55468 | −0.414638 | ||||||||
\(532\) | −18.2468 | −0.791099 | ||||||||
\(533\) | −1.99305 | −0.0863286 | ||||||||
\(534\) | 29.7787 | 1.28865 | ||||||||
\(535\) | −30.5672 | −1.32154 | ||||||||
\(536\) | 34.1821 | 1.47644 | ||||||||
\(537\) | −6.28398 | −0.271174 | ||||||||
\(538\) | 13.1878 | 0.568568 | ||||||||
\(539\) | −5.28921 | −0.227822 | ||||||||
\(540\) | 5.65049 | 0.243158 | ||||||||
\(541\) | 2.37553 | 0.102132 | 0.0510661 | − | 0.998695i | \(-0.483738\pi\) | ||||
0.0510661 | + | 0.998695i | \(0.483738\pi\) | |||||||
\(542\) | −51.4652 | −2.21062 | ||||||||
\(543\) | −15.9763 | −0.685607 | ||||||||
\(544\) | −18.9133 | −0.810902 | ||||||||
\(545\) | 3.59895 | 0.154162 | ||||||||
\(546\) | 3.09970 | 0.132655 | ||||||||
\(547\) | −11.0030 | −0.470454 | −0.235227 | − | 0.971941i | \(-0.575583\pi\) | ||||
−0.235227 | + | 0.971941i | \(0.575583\pi\) | |||||||
\(548\) | −15.1645 | −0.647796 | ||||||||
\(549\) | 0.815146 | 0.0347896 | ||||||||
\(550\) | 6.16807 | 0.263007 | ||||||||
\(551\) | −10.4476 | −0.445081 | ||||||||
\(552\) | −14.8736 | −0.633062 | ||||||||
\(553\) | −11.2404 | −0.477990 | ||||||||
\(554\) | −10.7645 | −0.457339 | ||||||||
\(555\) | −6.76929 | −0.287341 | ||||||||
\(556\) | −59.0631 | −2.50483 | ||||||||
\(557\) | 14.7101 | 0.623288 | 0.311644 | − | 0.950199i | \(-0.399120\pi\) | ||||
0.311644 | + | 0.950199i | \(0.399120\pi\) | |||||||
\(558\) | 9.23709 | 0.391037 | ||||||||
\(559\) | 4.74274 | 0.200597 | ||||||||
\(560\) | 4.05982 | 0.171559 | ||||||||
\(561\) | −6.17868 | −0.260864 | ||||||||
\(562\) | 28.0840 | 1.18465 | ||||||||
\(563\) | 24.0877 | 1.01518 | 0.507588 | − | 0.861600i | \(-0.330537\pi\) | ||||
0.507588 | + | 0.861600i | \(0.330537\pi\) | |||||||
\(564\) | −39.0499 | −1.64430 | ||||||||
\(565\) | −21.8561 | −0.919492 | ||||||||
\(566\) | 33.8802 | 1.42409 | ||||||||
\(567\) | 1.30434 | 0.0547773 | ||||||||
\(568\) | −46.5596 | −1.95360 | ||||||||
\(569\) | 13.7005 | 0.574354 | 0.287177 | − | 0.957878i | \(-0.407283\pi\) | ||||
0.287177 | + | 0.957878i | \(0.407283\pi\) | |||||||
\(570\) | 14.1195 | 0.591402 | ||||||||
\(571\) | 34.7830 | 1.45562 | 0.727811 | − | 0.685778i | \(-0.240538\pi\) | ||||
0.727811 | + | 0.685778i | \(0.240538\pi\) | |||||||
\(572\) | −3.64097 | −0.152236 | ||||||||
\(573\) | 17.1115 | 0.714843 | ||||||||
\(574\) | −6.17787 | −0.257859 | ||||||||
\(575\) | −9.87789 | −0.411937 | ||||||||
\(576\) | −11.2798 | −0.469993 | ||||||||
\(577\) | −18.4334 | −0.767391 | −0.383696 | − | 0.923460i | \(-0.625349\pi\) | ||||
−0.383696 | + | 0.923460i | \(0.625349\pi\) | |||||||
\(578\) | −50.6492 | −2.10673 | ||||||||
\(579\) | −8.19444 | −0.340549 | ||||||||
\(580\) | 15.3922 | 0.639126 | ||||||||
\(581\) | 9.55180 | 0.396275 | ||||||||
\(582\) | −18.7571 | −0.777508 | ||||||||
\(583\) | 1.58550 | 0.0656649 | ||||||||
\(584\) | 12.6622 | 0.523968 | ||||||||
\(585\) | −1.54914 | −0.0640492 | ||||||||
\(586\) | −8.86661 | −0.366276 | ||||||||
\(587\) | −41.5828 | −1.71631 | −0.858153 | − | 0.513394i | \(-0.828388\pi\) | ||||
−0.858153 | + | 0.513394i | \(0.828388\pi\) | |||||||
\(588\) | −19.3269 | −0.797028 | ||||||||
\(589\) | 14.9076 | 0.614257 | ||||||||
\(590\) | 35.1751 | 1.44814 | ||||||||
\(591\) | 22.4587 | 0.923826 | ||||||||
\(592\) | −8.77958 | −0.360839 | ||||||||
\(593\) | −15.6620 | −0.643161 | −0.321581 | − | 0.946882i | \(-0.604214\pi\) | ||||
−0.321581 | + | 0.946882i | \(0.604214\pi\) | |||||||
\(594\) | −2.37219 | −0.0973323 | ||||||||
\(595\) | −12.5071 | −0.512742 | ||||||||
\(596\) | 58.7963 | 2.40839 | ||||||||
\(597\) | 18.5204 | 0.757991 | ||||||||
\(598\) | 9.02803 | 0.369184 | ||||||||
\(599\) | −16.4211 | −0.670948 | −0.335474 | − | 0.942050i | \(-0.608896\pi\) | ||||
−0.335474 | + | 0.942050i | \(0.608896\pi\) | |||||||
\(600\) | 10.1800 | 0.415598 | ||||||||
\(601\) | 13.0892 | 0.533918 | 0.266959 | − | 0.963708i | \(-0.413981\pi\) | ||||
0.266959 | + | 0.963708i | \(0.413981\pi\) | |||||||
\(602\) | 14.7011 | 0.599172 | ||||||||
\(603\) | −8.73068 | −0.355541 | ||||||||
\(604\) | 26.0202 | 1.05875 | ||||||||
\(605\) | −15.4970 | −0.630042 | ||||||||
\(606\) | −25.4688 | −1.03460 | ||||||||
\(607\) | 17.5766 | 0.713413 | 0.356707 | − | 0.934216i | \(-0.383900\pi\) | ||||
0.356707 | + | 0.934216i | \(0.383900\pi\) | |||||||
\(608\) | −11.7191 | −0.475273 | ||||||||
\(609\) | 3.55310 | 0.143979 | ||||||||
\(610\) | −3.00092 | −0.121504 | ||||||||
\(611\) | 10.7060 | 0.433118 | ||||||||
\(612\) | −22.5770 | −0.912623 | ||||||||
\(613\) | 10.5398 | 0.425699 | 0.212849 | − | 0.977085i | \(-0.431726\pi\) | ||||
0.212849 | + | 0.977085i | \(0.431726\pi\) | |||||||
\(614\) | 6.49439 | 0.262092 | ||||||||
\(615\) | 3.08752 | 0.124501 | ||||||||
\(616\) | −5.09759 | −0.205388 | ||||||||
\(617\) | 14.8994 | 0.599825 | 0.299913 | − | 0.953967i | \(-0.403042\pi\) | ||||
0.299913 | + | 0.953967i | \(0.403042\pi\) | |||||||
\(618\) | −2.37644 | −0.0955946 | ||||||||
\(619\) | −24.6412 | −0.990413 | −0.495207 | − | 0.868775i | \(-0.664908\pi\) | ||||
−0.495207 | + | 0.868775i | \(0.664908\pi\) | |||||||
\(620\) | −21.9631 | −0.882058 | ||||||||
\(621\) | 3.79897 | 0.152447 | ||||||||
\(622\) | 32.0166 | 1.28375 | ||||||||
\(623\) | −16.3444 | −0.654826 | ||||||||
\(624\) | −2.00920 | −0.0804322 | ||||||||
\(625\) | −5.23844 | −0.209538 | ||||||||
\(626\) | 41.8185 | 1.67140 | ||||||||
\(627\) | −3.82845 | −0.152894 | ||||||||
\(628\) | −11.4444 | −0.456682 | ||||||||
\(629\) | 27.0473 | 1.07845 | ||||||||
\(630\) | −4.80189 | −0.191312 | ||||||||
\(631\) | 34.9645 | 1.39192 | 0.695958 | − | 0.718082i | \(-0.254980\pi\) | ||||
0.695958 | + | 0.718082i | \(0.254980\pi\) | |||||||
\(632\) | 33.7396 | 1.34209 | ||||||||
\(633\) | 21.9114 | 0.870901 | ||||||||
\(634\) | −30.9913 | −1.23082 | ||||||||
\(635\) | −5.68609 | −0.225645 | ||||||||
\(636\) | 5.79347 | 0.229726 | ||||||||
\(637\) | 5.29868 | 0.209942 | ||||||||
\(638\) | −6.46197 | −0.255832 | ||||||||
\(639\) | 11.8921 | 0.470445 | ||||||||
\(640\) | 32.0591 | 1.26725 | ||||||||
\(641\) | −32.0423 | −1.26560 | −0.632798 | − | 0.774317i | \(-0.718094\pi\) | ||||
−0.632798 | + | 0.774317i | \(0.718094\pi\) | |||||||
\(642\) | 46.8912 | 1.85065 | ||||||||
\(643\) | −37.0823 | −1.46238 | −0.731192 | − | 0.682172i | \(-0.761036\pi\) | ||||
−0.731192 | + | 0.682172i | \(0.761036\pi\) | |||||||
\(644\) | 18.0739 | 0.712211 | ||||||||
\(645\) | −7.34719 | −0.289295 | ||||||||
\(646\) | −56.4159 | −2.21965 | ||||||||
\(647\) | 30.1877 | 1.18680 | 0.593401 | − | 0.804907i | \(-0.297785\pi\) | ||||
0.593401 | + | 0.804907i | \(0.297785\pi\) | |||||||
\(648\) | −3.91517 | −0.153802 | ||||||||
\(649\) | −9.53760 | −0.374383 | ||||||||
\(650\) | −6.17912 | −0.242365 | ||||||||
\(651\) | −5.06990 | −0.198705 | ||||||||
\(652\) | 21.5621 | 0.844438 | ||||||||
\(653\) | −37.4278 | −1.46466 | −0.732331 | − | 0.680949i | \(-0.761568\pi\) | ||||
−0.732331 | + | 0.680949i | \(0.761568\pi\) | |||||||
\(654\) | −5.52092 | −0.215885 | ||||||||
\(655\) | 2.84873 | 0.111309 | ||||||||
\(656\) | 4.00443 | 0.156347 | ||||||||
\(657\) | −3.23415 | −0.126176 | ||||||||
\(658\) | 33.1854 | 1.29370 | ||||||||
\(659\) | −15.2056 | −0.592327 | −0.296164 | − | 0.955137i | \(-0.595707\pi\) | ||||
−0.296164 | + | 0.955137i | \(0.595707\pi\) | |||||||
\(660\) | 5.64038 | 0.219552 | ||||||||
\(661\) | 30.1880 | 1.17418 | 0.587088 | − | 0.809523i | \(-0.300274\pi\) | ||||
0.587088 | + | 0.809523i | \(0.300274\pi\) | |||||||
\(662\) | −71.2451 | −2.76902 | ||||||||
\(663\) | 6.18975 | 0.240390 | ||||||||
\(664\) | −28.6710 | −1.11265 | ||||||||
\(665\) | −7.74969 | −0.300520 | ||||||||
\(666\) | 10.3843 | 0.402385 | ||||||||
\(667\) | 10.3486 | 0.400698 | ||||||||
\(668\) | 89.4533 | 3.46105 | ||||||||
\(669\) | 6.00131 | 0.232024 | ||||||||
\(670\) | 32.1416 | 1.24174 | ||||||||
\(671\) | 0.813688 | 0.0314121 | ||||||||
\(672\) | 3.98554 | 0.153746 | ||||||||
\(673\) | 40.3310 | 1.55465 | 0.777323 | − | 0.629102i | \(-0.216577\pi\) | ||||
0.777323 | + | 0.629102i | \(0.216577\pi\) | |||||||
\(674\) | 16.6210 | 0.640217 | ||||||||
\(675\) | −2.60015 | −0.100080 | ||||||||
\(676\) | 3.64749 | 0.140288 | ||||||||
\(677\) | 17.2813 | 0.664175 | 0.332087 | − | 0.943249i | \(-0.392247\pi\) | ||||
0.332087 | + | 0.943249i | \(0.392247\pi\) | |||||||
\(678\) | 33.5280 | 1.28764 | ||||||||
\(679\) | 10.2951 | 0.395090 | ||||||||
\(680\) | 37.5418 | 1.43966 | ||||||||
\(681\) | 7.52318 | 0.288289 | ||||||||
\(682\) | 9.22057 | 0.353074 | ||||||||
\(683\) | −38.8489 | −1.48651 | −0.743256 | − | 0.669007i | \(-0.766719\pi\) | ||||
−0.743256 | + | 0.669007i | \(0.766719\pi\) | |||||||
\(684\) | −13.9892 | −0.534892 | ||||||||
\(685\) | −6.44060 | −0.246083 | ||||||||
\(686\) | 38.1223 | 1.45551 | ||||||||
\(687\) | −9.53118 | −0.363637 | ||||||||
\(688\) | −9.52910 | −0.363294 | ||||||||
\(689\) | −1.58834 | −0.0605111 | ||||||||
\(690\) | −13.9857 | −0.532427 | ||||||||
\(691\) | 32.3528 | 1.23076 | 0.615379 | − | 0.788231i | \(-0.289003\pi\) | ||||
0.615379 | + | 0.788231i | \(0.289003\pi\) | |||||||
\(692\) | −25.8221 | −0.981609 | ||||||||
\(693\) | 1.30201 | 0.0494594 | ||||||||
\(694\) | 85.5231 | 3.24641 | ||||||||
\(695\) | −25.0850 | −0.951528 | ||||||||
\(696\) | −10.6651 | −0.404259 | ||||||||
\(697\) | −12.3365 | −0.467278 | ||||||||
\(698\) | 6.68673 | 0.253096 | ||||||||
\(699\) | 13.0635 | 0.494108 | ||||||||
\(700\) | −12.3704 | −0.467559 | ||||||||
\(701\) | 50.4385 | 1.90503 | 0.952517 | − | 0.304485i | \(-0.0984844\pi\) | ||||
0.952517 | + | 0.304485i | \(0.0984844\pi\) | |||||||
\(702\) | 2.37644 | 0.0896931 | ||||||||
\(703\) | 16.7591 | 0.632083 | ||||||||
\(704\) | −11.2597 | −0.424364 | ||||||||
\(705\) | −16.5851 | −0.624631 | ||||||||
\(706\) | −11.8344 | −0.445392 | ||||||||
\(707\) | 13.9789 | 0.525731 | ||||||||
\(708\) | −34.8506 | −1.30977 | ||||||||
\(709\) | 19.7175 | 0.740506 | 0.370253 | − | 0.928931i | \(-0.379271\pi\) | ||||
0.370253 | + | 0.928931i | \(0.379271\pi\) | |||||||
\(710\) | −43.7803 | −1.64304 | ||||||||
\(711\) | −8.61766 | −0.323188 | ||||||||
\(712\) | 49.0600 | 1.83860 | ||||||||
\(713\) | −14.7663 | −0.553004 | ||||||||
\(714\) | 19.1864 | 0.718032 | ||||||||
\(715\) | −1.54637 | −0.0578311 | ||||||||
\(716\) | −22.9207 | −0.856588 | ||||||||
\(717\) | −2.04869 | −0.0765096 | ||||||||
\(718\) | 33.9604 | 1.26739 | ||||||||
\(719\) | −31.6734 | −1.18122 | −0.590609 | − | 0.806958i | \(-0.701112\pi\) | ||||
−0.590609 | + | 0.806958i | \(0.701112\pi\) | |||||||
\(720\) | 3.11253 | 0.115997 | ||||||||
\(721\) | 1.30434 | 0.0485763 | ||||||||
\(722\) | 10.1959 | 0.379452 | ||||||||
\(723\) | 0.454757 | 0.0169126 | ||||||||
\(724\) | −58.2733 | −2.16571 | ||||||||
\(725\) | −7.08294 | −0.263054 | ||||||||
\(726\) | 23.7729 | 0.882296 | ||||||||
\(727\) | −37.7524 | −1.40016 | −0.700079 | − | 0.714065i | \(-0.746852\pi\) | ||||
−0.700079 | + | 0.714065i | \(0.746852\pi\) | |||||||
\(728\) | 5.10673 | 0.189268 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 11.9064 | 0.440675 | ||||||||
\(731\) | 29.3564 | 1.08579 | ||||||||
\(732\) | 2.97323 | 0.109894 | ||||||||
\(733\) | 21.7447 | 0.803160 | 0.401580 | − | 0.915824i | \(-0.368461\pi\) | ||||
0.401580 | + | 0.915824i | \(0.368461\pi\) | |||||||
\(734\) | 39.9510 | 1.47462 | ||||||||
\(735\) | −8.20843 | −0.302772 | ||||||||
\(736\) | 11.6081 | 0.427879 | ||||||||
\(737\) | −8.71507 | −0.321024 | ||||||||
\(738\) | −4.73638 | −0.174348 | ||||||||
\(739\) | −35.9828 | −1.32365 | −0.661824 | − | 0.749659i | \(-0.730218\pi\) | ||||
−0.661824 | + | 0.749659i | \(0.730218\pi\) | |||||||
\(740\) | −24.6909 | −0.907656 | ||||||||
\(741\) | 3.83531 | 0.140894 | ||||||||
\(742\) | −4.92339 | −0.180744 | ||||||||
\(743\) | −44.9581 | −1.64935 | −0.824676 | − | 0.565606i | \(-0.808642\pi\) | ||||
−0.824676 | + | 0.565606i | \(0.808642\pi\) | |||||||
\(744\) | 15.2180 | 0.557919 | ||||||||
\(745\) | 24.9717 | 0.914892 | ||||||||
\(746\) | 21.1645 | 0.774887 | ||||||||
\(747\) | 7.32306 | 0.267937 | ||||||||
\(748\) | −22.5367 | −0.824022 | ||||||||
\(749\) | −25.7369 | −0.940406 | ||||||||
\(750\) | 27.9796 | 1.02167 | ||||||||
\(751\) | −13.6203 | −0.497012 | −0.248506 | − | 0.968630i | \(-0.579940\pi\) | ||||
−0.248506 | + | 0.968630i | \(0.579940\pi\) | |||||||
\(752\) | −21.5104 | −0.784404 | ||||||||
\(753\) | 29.5491 | 1.07683 | ||||||||
\(754\) | 6.47355 | 0.235753 | ||||||||
\(755\) | 11.0512 | 0.402194 | ||||||||
\(756\) | 4.75758 | 0.173032 | ||||||||
\(757\) | 30.3825 | 1.10427 | 0.552135 | − | 0.833755i | \(-0.313813\pi\) | ||||
0.552135 | + | 0.833755i | \(0.313813\pi\) | |||||||
\(758\) | 14.4293 | 0.524095 | ||||||||
\(759\) | 3.79217 | 0.137647 | ||||||||
\(760\) | 23.2617 | 0.843792 | ||||||||
\(761\) | 11.1454 | 0.404020 | 0.202010 | − | 0.979383i | \(-0.435253\pi\) | ||||
0.202010 | + | 0.979383i | \(0.435253\pi\) | |||||||
\(762\) | 8.72267 | 0.315989 | ||||||||
\(763\) | 3.03023 | 0.109702 | ||||||||
\(764\) | 62.4140 | 2.25806 | ||||||||
\(765\) | −9.58881 | −0.346684 | ||||||||
\(766\) | −23.2945 | −0.841663 | ||||||||
\(767\) | 9.55468 | 0.345000 | ||||||||
\(768\) | −26.6202 | −0.960573 | ||||||||
\(769\) | 26.3612 | 0.950609 | 0.475304 | − | 0.879821i | \(-0.342338\pi\) | ||||
0.475304 | + | 0.879821i | \(0.342338\pi\) | |||||||
\(770\) | −4.79330 | −0.172738 | ||||||||
\(771\) | 4.57116 | 0.164626 | ||||||||
\(772\) | −29.8891 | −1.07573 | ||||||||
\(773\) | 1.19513 | 0.0429858 | 0.0214929 | − | 0.999769i | \(-0.493158\pi\) | ||||
0.0214929 | + | 0.999769i | \(0.493158\pi\) | |||||||
\(774\) | 11.2709 | 0.405123 | ||||||||
\(775\) | 10.1066 | 0.363041 | ||||||||
\(776\) | −30.9022 | −1.10932 | ||||||||
\(777\) | −5.69959 | −0.204472 | ||||||||
\(778\) | 63.9391 | 2.29233 | ||||||||
\(779\) | −7.64397 | −0.273874 | ||||||||
\(780\) | −5.65049 | −0.202320 | ||||||||
\(781\) | 11.8708 | 0.424772 | ||||||||
\(782\) | 55.8813 | 1.99831 | ||||||||
\(783\) | 2.72405 | 0.0973495 | ||||||||
\(784\) | −10.6461 | −0.380218 | ||||||||
\(785\) | −4.86062 | −0.173483 | ||||||||
\(786\) | −4.37006 | −0.155875 | ||||||||
\(787\) | 21.6949 | 0.773340 | 0.386670 | − | 0.922218i | \(-0.373625\pi\) | ||||
0.386670 | + | 0.922218i | \(0.373625\pi\) | |||||||
\(788\) | 81.9177 | 2.91820 | ||||||||
\(789\) | −8.65184 | −0.308014 | ||||||||
\(790\) | 31.7255 | 1.12874 | ||||||||
\(791\) | −18.4023 | −0.654311 | ||||||||
\(792\) | −3.90816 | −0.138871 | ||||||||
\(793\) | −0.815146 | −0.0289467 | ||||||||
\(794\) | 24.1972 | 0.858727 | ||||||||
\(795\) | 2.46057 | 0.0872676 | ||||||||
\(796\) | 67.5531 | 2.39435 | ||||||||
\(797\) | 13.8975 | 0.492275 | 0.246137 | − | 0.969235i | \(-0.420839\pi\) | ||||
0.246137 | + | 0.969235i | \(0.420839\pi\) | |||||||
\(798\) | 11.8883 | 0.420842 | ||||||||
\(799\) | 66.2673 | 2.34437 | ||||||||
\(800\) | −7.94499 | −0.280898 | ||||||||
\(801\) | −12.5308 | −0.442753 | ||||||||
\(802\) | −31.1411 | −1.09963 | ||||||||
\(803\) | −3.22837 | −0.113927 | ||||||||
\(804\) | −31.8451 | −1.12309 | ||||||||
\(805\) | 7.67626 | 0.270553 | ||||||||
\(806\) | −9.23709 | −0.325363 | ||||||||
\(807\) | −5.54940 | −0.195348 | ||||||||
\(808\) | −41.9596 | −1.47613 | ||||||||
\(809\) | −30.4630 | −1.07102 | −0.535511 | − | 0.844529i | \(-0.679881\pi\) | ||||
−0.535511 | + | 0.844529i | \(0.679881\pi\) | |||||||
\(810\) | −3.68145 | −0.129353 | ||||||||
\(811\) | −7.87483 | −0.276523 | −0.138261 | − | 0.990396i | \(-0.544151\pi\) | ||||
−0.138261 | + | 0.990396i | \(0.544151\pi\) | |||||||
\(812\) | 12.9599 | 0.454802 | ||||||||
\(813\) | 21.6564 | 0.759523 | ||||||||
\(814\) | 10.3658 | 0.363320 | ||||||||
\(815\) | 9.15776 | 0.320783 | ||||||||
\(816\) | −12.4364 | −0.435362 | ||||||||
\(817\) | 18.1899 | 0.636384 | ||||||||
\(818\) | −90.5404 | −3.16567 | ||||||||
\(819\) | −1.30434 | −0.0455775 | ||||||||
\(820\) | 11.2617 | 0.393276 | ||||||||
\(821\) | 21.7907 | 0.760501 | 0.380250 | − | 0.924884i | \(-0.375838\pi\) | ||||
0.380250 | + | 0.924884i | \(0.375838\pi\) | |||||||
\(822\) | 9.88012 | 0.344609 | ||||||||
\(823\) | −29.5397 | −1.02969 | −0.514844 | − | 0.857284i | \(-0.672150\pi\) | ||||
−0.514844 | + | 0.857284i | \(0.672150\pi\) | |||||||
\(824\) | −3.91517 | −0.136391 | ||||||||
\(825\) | −2.59550 | −0.0903638 | ||||||||
\(826\) | 29.6167 | 1.03050 | ||||||||
\(827\) | −20.4485 | −0.711062 | −0.355531 | − | 0.934664i | \(-0.615700\pi\) | ||||
−0.355531 | + | 0.934664i | \(0.615700\pi\) | |||||||
\(828\) | 13.8567 | 0.481553 | ||||||||
\(829\) | −15.2614 | −0.530049 | −0.265024 | − | 0.964242i | \(-0.585380\pi\) | ||||
−0.265024 | + | 0.964242i | \(0.585380\pi\) | |||||||
\(830\) | −26.9595 | −0.935779 | ||||||||
\(831\) | 4.52966 | 0.157132 | ||||||||
\(832\) | 11.2798 | 0.391058 | ||||||||
\(833\) | 32.7975 | 1.13637 | ||||||||
\(834\) | 38.4813 | 1.33250 | ||||||||
\(835\) | 37.9922 | 1.31477 | ||||||||
\(836\) | −13.9642 | −0.482963 | ||||||||
\(837\) | −3.88694 | −0.134352 | ||||||||
\(838\) | −24.5940 | −0.849585 | ||||||||
\(839\) | −50.3094 | −1.73687 | −0.868437 | − | 0.495799i | \(-0.834875\pi\) | ||||
−0.868437 | + | 0.495799i | \(0.834875\pi\) | |||||||
\(840\) | −7.91105 | −0.272957 | ||||||||
\(841\) | −21.5796 | −0.744123 | ||||||||
\(842\) | 48.7295 | 1.67933 | ||||||||
\(843\) | −11.8177 | −0.407022 | ||||||||
\(844\) | 79.9217 | 2.75102 | ||||||||
\(845\) | 1.54914 | 0.0532922 | ||||||||
\(846\) | 25.4422 | 0.874720 | ||||||||
\(847\) | −13.0481 | −0.448338 | ||||||||
\(848\) | 3.19130 | 0.109590 | ||||||||
\(849\) | −14.2567 | −0.489287 | ||||||||
\(850\) | −38.2472 | −1.31187 | ||||||||
\(851\) | −16.6003 | −0.569052 | ||||||||
\(852\) | 43.3763 | 1.48605 | ||||||||
\(853\) | 11.0233 | 0.377430 | 0.188715 | − | 0.982032i | \(-0.439568\pi\) | ||||
0.188715 | + | 0.982032i | \(0.439568\pi\) | |||||||
\(854\) | −2.52671 | −0.0864622 | ||||||||
\(855\) | −5.94145 | −0.203193 | ||||||||
\(856\) | 77.2528 | 2.64045 | ||||||||
\(857\) | 4.33332 | 0.148023 | 0.0740117 | − | 0.997257i | \(-0.476420\pi\) | ||||
0.0740117 | + | 0.997257i | \(0.476420\pi\) | |||||||
\(858\) | 2.37219 | 0.0809854 | ||||||||
\(859\) | 10.9554 | 0.373792 | 0.186896 | − | 0.982380i | \(-0.440157\pi\) | ||||
0.186896 | + | 0.982380i | \(0.440157\pi\) | |||||||
\(860\) | −26.7988 | −0.913832 | ||||||||
\(861\) | 2.59963 | 0.0885950 | ||||||||
\(862\) | −61.1316 | −2.08215 | ||||||||
\(863\) | −42.7748 | −1.45607 | −0.728035 | − | 0.685540i | \(-0.759566\pi\) | ||||
−0.728035 | + | 0.685540i | \(0.759566\pi\) | |||||||
\(864\) | 3.05559 | 0.103953 | ||||||||
\(865\) | −10.9670 | −0.372891 | ||||||||
\(866\) | −28.3181 | −0.962288 | ||||||||
\(867\) | 21.3130 | 0.723827 | ||||||||
\(868\) | −18.4924 | −0.627674 | ||||||||
\(869\) | −8.60225 | −0.291811 | ||||||||
\(870\) | −10.0285 | −0.339996 | ||||||||
\(871\) | 8.73068 | 0.295828 | ||||||||
\(872\) | −9.09566 | −0.308018 | ||||||||
\(873\) | 7.89294 | 0.267136 | ||||||||
\(874\) | 34.6253 | 1.17122 | ||||||||
\(875\) | −15.3570 | −0.519161 | ||||||||
\(876\) | −11.7965 | −0.398568 | ||||||||
\(877\) | 4.60259 | 0.155418 | 0.0777092 | − | 0.996976i | \(-0.475239\pi\) | ||||
0.0777092 | + | 0.996976i | \(0.475239\pi\) | |||||||
\(878\) | 3.81234 | 0.128660 | ||||||||
\(879\) | 3.73104 | 0.125845 | ||||||||
\(880\) | 3.10697 | 0.104736 | ||||||||
\(881\) | 12.9976 | 0.437901 | 0.218951 | − | 0.975736i | \(-0.429737\pi\) | ||||
0.218951 | + | 0.975736i | \(0.429737\pi\) | |||||||
\(882\) | 12.5920 | 0.423996 | ||||||||
\(883\) | 5.87431 | 0.197686 | 0.0988432 | − | 0.995103i | \(-0.468486\pi\) | ||||
0.0988432 | + | 0.995103i | \(0.468486\pi\) | |||||||
\(884\) | 22.5770 | 0.759348 | ||||||||
\(885\) | −14.8016 | −0.497550 | ||||||||
\(886\) | 59.8149 | 2.00952 | ||||||||
\(887\) | 0.861770 | 0.0289354 | 0.0144677 | − | 0.999895i | \(-0.495395\pi\) | ||||
0.0144677 | + | 0.999895i | \(0.495395\pi\) | |||||||
\(888\) | 17.1081 | 0.574110 | ||||||||
\(889\) | −4.78756 | −0.160570 | ||||||||
\(890\) | 46.1314 | 1.54633 | ||||||||
\(891\) | 0.998212 | 0.0334414 | ||||||||
\(892\) | 21.8897 | 0.732922 | ||||||||
\(893\) | 41.0607 | 1.37405 | ||||||||
\(894\) | −38.3075 | −1.28120 | ||||||||
\(895\) | −9.73479 | −0.325398 | ||||||||
\(896\) | 26.9930 | 0.901774 | ||||||||
\(897\) | −3.79897 | −0.126844 | ||||||||
\(898\) | 35.9223 | 1.19874 | ||||||||
\(899\) | −10.5882 | −0.353136 | ||||||||
\(900\) | −9.48403 | −0.316134 | ||||||||
\(901\) | −9.83145 | −0.327533 | ||||||||
\(902\) | −4.72791 | −0.157422 | ||||||||
\(903\) | −6.18617 | −0.205863 | ||||||||
\(904\) | 55.2371 | 1.83716 | ||||||||
\(905\) | −24.7495 | −0.822703 | ||||||||
\(906\) | −16.9529 | −0.563224 | ||||||||
\(907\) | −23.3940 | −0.776786 | −0.388393 | − | 0.921494i | \(-0.626970\pi\) | ||||
−0.388393 | + | 0.921494i | \(0.626970\pi\) | |||||||
\(908\) | 27.4407 | 0.910652 | ||||||||
\(909\) | 10.7172 | 0.355467 | ||||||||
\(910\) | 4.80189 | 0.159181 | ||||||||
\(911\) | 55.6209 | 1.84280 | 0.921401 | − | 0.388613i | \(-0.127046\pi\) | ||||
0.921401 | + | 0.388613i | \(0.127046\pi\) | |||||||
\(912\) | −7.70589 | −0.255167 | ||||||||
\(913\) | 7.30997 | 0.241925 | ||||||||
\(914\) | 41.6033 | 1.37611 | ||||||||
\(915\) | 1.26278 | 0.0417462 | ||||||||
\(916\) | −34.7649 | −1.14866 | ||||||||
\(917\) | 2.39857 | 0.0792077 | ||||||||
\(918\) | 14.7096 | 0.485489 | ||||||||
\(919\) | 35.9293 | 1.18520 | 0.592599 | − | 0.805498i | \(-0.298102\pi\) | ||||
0.592599 | + | 0.805498i | \(0.298102\pi\) | |||||||
\(920\) | −23.0413 | −0.759650 | ||||||||
\(921\) | −2.73282 | −0.0900494 | ||||||||
\(922\) | −68.5403 | −2.25726 | ||||||||
\(923\) | −11.8921 | −0.391434 | ||||||||
\(924\) | 4.74907 | 0.156233 | ||||||||
\(925\) | 11.3619 | 0.373577 | ||||||||
\(926\) | 71.2806 | 2.34243 | ||||||||
\(927\) | 1.00000 | 0.0328443 | ||||||||
\(928\) | 8.32356 | 0.273234 | ||||||||
\(929\) | 30.0078 | 0.984524 | 0.492262 | − | 0.870447i | \(-0.336170\pi\) | ||||
0.492262 | + | 0.870447i | \(0.336170\pi\) | |||||||
\(930\) | 14.3096 | 0.469230 | ||||||||
\(931\) | 20.3221 | 0.666030 | ||||||||
\(932\) | 47.6491 | 1.56080 | ||||||||
\(933\) | −13.4725 | −0.441070 | ||||||||
\(934\) | −70.4868 | −2.30640 | ||||||||
\(935\) | −9.57167 | −0.313027 | ||||||||
\(936\) | 3.91517 | 0.127971 | ||||||||
\(937\) | 30.9226 | 1.01020 | 0.505098 | − | 0.863062i | \(-0.331456\pi\) | ||||
0.505098 | + | 0.863062i | \(0.331456\pi\) | |||||||
\(938\) | 27.0625 | 0.883622 | ||||||||
\(939\) | −17.5971 | −0.574260 | ||||||||
\(940\) | −60.4940 | −1.97310 | ||||||||
\(941\) | 16.6465 | 0.542662 | 0.271331 | − | 0.962486i | \(-0.412536\pi\) | ||||
0.271331 | + | 0.962486i | \(0.412536\pi\) | |||||||
\(942\) | 7.45637 | 0.242942 | ||||||||
\(943\) | 7.57154 | 0.246563 | ||||||||
\(944\) | −19.1972 | −0.624817 | ||||||||
\(945\) | 2.02062 | 0.0657307 | ||||||||
\(946\) | 11.2507 | 0.365792 | ||||||||
\(947\) | −39.7813 | −1.29272 | −0.646360 | − | 0.763033i | \(-0.723709\pi\) | ||||
−0.646360 | + | 0.763033i | \(0.723709\pi\) | |||||||
\(948\) | −31.4328 | −1.02089 | ||||||||
\(949\) | 3.23415 | 0.104985 | ||||||||
\(950\) | −23.6988 | −0.768892 | ||||||||
\(951\) | 13.0410 | 0.422884 | ||||||||
\(952\) | 31.6094 | 1.02446 | ||||||||
\(953\) | 1.86533 | 0.0604238 | 0.0302119 | − | 0.999544i | \(-0.490382\pi\) | ||||
0.0302119 | + | 0.999544i | \(0.490382\pi\) | |||||||
\(954\) | −3.77461 | −0.122208 | ||||||||
\(955\) | 26.5082 | 0.857784 | ||||||||
\(956\) | −7.47256 | −0.241680 | ||||||||
\(957\) | 2.71917 | 0.0878984 | ||||||||
\(958\) | −47.0612 | −1.52048 | ||||||||
\(959\) | −5.42284 | −0.175113 | ||||||||
\(960\) | −17.4741 | −0.563973 | ||||||||
\(961\) | −15.8917 | −0.512637 | ||||||||
\(962\) | −10.3843 | −0.334805 | ||||||||
\(963\) | −19.7317 | −0.635844 | ||||||||
\(964\) | 1.65872 | 0.0534238 | ||||||||
\(965\) | −12.6944 | −0.408646 | ||||||||
\(966\) | −11.7757 | −0.378876 | ||||||||
\(967\) | −32.3041 | −1.03883 | −0.519414 | − | 0.854522i | \(-0.673850\pi\) | ||||
−0.519414 | + | 0.854522i | \(0.673850\pi\) | |||||||
\(968\) | 39.1656 | 1.25883 | ||||||||
\(969\) | 23.7396 | 0.762626 | ||||||||
\(970\) | −29.0575 | −0.932980 | ||||||||
\(971\) | 20.8391 | 0.668758 | 0.334379 | − | 0.942439i | \(-0.391474\pi\) | ||||
0.334379 | + | 0.942439i | \(0.391474\pi\) | |||||||
\(972\) | 3.64749 | 0.116993 | ||||||||
\(973\) | −21.1210 | −0.677108 | ||||||||
\(974\) | −102.997 | −3.30023 | ||||||||
\(975\) | 2.60015 | 0.0832715 | ||||||||
\(976\) | 1.63779 | 0.0524243 | ||||||||
\(977\) | −5.98592 | −0.191506 | −0.0957532 | − | 0.995405i | \(-0.530526\pi\) | ||||
−0.0957532 | + | 0.995405i | \(0.530526\pi\) | |||||||
\(978\) | −14.0484 | −0.449217 | ||||||||
\(979\) | −12.5083 | −0.399769 | ||||||||
\(980\) | −29.9401 | −0.956403 | ||||||||
\(981\) | 2.32319 | 0.0741736 | ||||||||
\(982\) | 70.0582 | 2.23565 | ||||||||
\(983\) | 39.7389 | 1.26747 | 0.633736 | − | 0.773549i | \(-0.281520\pi\) | ||||
0.633736 | + | 0.773549i | \(0.281520\pi\) | |||||||
\(984\) | −7.80313 | −0.248755 | ||||||||
\(985\) | 34.7917 | 1.10856 | ||||||||
\(986\) | 40.0696 | 1.27608 | ||||||||
\(987\) | −13.9643 | −0.444488 | ||||||||
\(988\) | 13.9892 | 0.445057 | ||||||||
\(989\) | −18.0175 | −0.572924 | ||||||||
\(990\) | −3.67487 | −0.116795 | ||||||||
\(991\) | −5.50656 | −0.174922 | −0.0874609 | − | 0.996168i | \(-0.527875\pi\) | ||||
−0.0874609 | + | 0.996168i | \(0.527875\pi\) | |||||||
\(992\) | −11.8769 | −0.377091 | ||||||||
\(993\) | 29.9797 | 0.951377 | ||||||||
\(994\) | −36.8620 | −1.16919 | ||||||||
\(995\) | 28.6908 | 0.909560 | ||||||||
\(996\) | 26.7108 | 0.846364 | ||||||||
\(997\) | −28.2905 | −0.895968 | −0.447984 | − | 0.894041i | \(-0.647858\pi\) | ||||
−0.447984 | + | 0.894041i | \(0.647858\pi\) | |||||||
\(998\) | 73.5346 | 2.32770 | ||||||||
\(999\) | −4.36970 | −0.138251 |
(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 | 4017.2.a.e.1.2 | ✓ | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4017.2.a.e.1.2 | ✓ | 16 | 1.1 | even | 1 | trivial |