Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [539,2,Mod(1,539)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(539, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("539.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 539 = 7^{2} \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 539.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: | \(4.30393666895\) |
Analytic rank: | \(0\) |
Dimension: | \(10\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{10} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{10} - 26x^{8} + 245x^{6} - 1038x^{4} + 1884x^{2} - 968 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.8 | ||
Root | \(3.27614\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 539.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.70296 | 1.20417 | 0.602087 | − | 0.798430i | \(-0.294336\pi\) | ||||
0.602087 | + | 0.798430i | \(0.294336\pi\) | |||||||
\(3\) | 3.27614 | 1.89148 | 0.945740 | − | 0.324924i | \(-0.105339\pi\) | ||||
0.945740 | + | 0.324924i | \(0.105339\pi\) | |||||||
\(4\) | 0.900071 | 0.450036 | ||||||||
\(5\) | −0.246676 | −0.110317 | −0.0551584 | − | 0.998478i | \(-0.517566\pi\) | ||||
−0.0551584 | + | 0.998478i | \(0.517566\pi\) | |||||||
\(6\) | 5.57913 | 2.27767 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −1.87313 | −0.662253 | ||||||||
\(9\) | 7.73309 | 2.57770 | ||||||||
\(10\) | −0.420079 | −0.132841 | ||||||||
\(11\) | 1.00000 | 0.301511 | ||||||||
\(12\) | 2.94876 | 0.851233 | ||||||||
\(13\) | −3.17078 | −0.879417 | −0.439709 | − | 0.898140i | \(-0.644918\pi\) | ||||
−0.439709 | + | 0.898140i | \(0.644918\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −0.808144 | −0.208662 | ||||||||
\(16\) | −4.99001 | −1.24750 | ||||||||
\(17\) | −6.49256 | −1.57468 | −0.787339 | − | 0.616520i | \(-0.788542\pi\) | ||||
−0.787339 | + | 0.616520i | \(0.788542\pi\) | |||||||
\(18\) | 13.1691 | 3.10400 | ||||||||
\(19\) | −4.32335 | −0.991844 | −0.495922 | − | 0.868367i | \(-0.665170\pi\) | ||||
−0.495922 | + | 0.868367i | \(0.665170\pi\) | |||||||
\(20\) | −0.222026 | −0.0496464 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 1.70296 | 0.363072 | ||||||||
\(23\) | 3.15700 | 0.658279 | 0.329140 | − | 0.944281i | \(-0.393241\pi\) | ||||
0.329140 | + | 0.944281i | \(0.393241\pi\) | |||||||
\(24\) | −6.13665 | −1.25264 | ||||||||
\(25\) | −4.93915 | −0.987830 | ||||||||
\(26\) | −5.39972 | −1.05897 | ||||||||
\(27\) | 15.5063 | 2.98418 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 6.48417 | 1.20408 | 0.602040 | − | 0.798466i | \(-0.294355\pi\) | ||||
0.602040 | + | 0.798466i | \(0.294355\pi\) | |||||||
\(30\) | −1.37624 | −0.251265 | ||||||||
\(31\) | 1.78122 | 0.319917 | 0.159958 | − | 0.987124i | \(-0.448864\pi\) | ||||
0.159958 | + | 0.987124i | \(0.448864\pi\) | |||||||
\(32\) | −4.75152 | −0.839959 | ||||||||
\(33\) | 3.27614 | 0.570303 | ||||||||
\(34\) | −11.0566 | −1.89619 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 6.96033 | 1.16006 | ||||||||
\(37\) | 8.38424 | 1.37836 | 0.689180 | − | 0.724590i | \(-0.257971\pi\) | ||||
0.689180 | + | 0.724590i | \(0.257971\pi\) | |||||||
\(38\) | −7.36248 | −1.19435 | ||||||||
\(39\) | −10.3879 | −1.66340 | ||||||||
\(40\) | 0.462057 | 0.0730576 | ||||||||
\(41\) | −0.553067 | −0.0863746 | −0.0431873 | − | 0.999067i | \(-0.513751\pi\) | ||||
−0.0431873 | + | 0.999067i | \(0.513751\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 5.69023 | 0.867752 | 0.433876 | − | 0.900973i | \(-0.357146\pi\) | ||||
0.433876 | + | 0.900973i | \(0.357146\pi\) | |||||||
\(44\) | 0.900071 | 0.135691 | ||||||||
\(45\) | −1.90756 | −0.284363 | ||||||||
\(46\) | 5.37624 | 0.792683 | ||||||||
\(47\) | 10.2971 | 1.50199 | 0.750995 | − | 0.660308i | \(-0.229574\pi\) | ||||
0.750995 | + | 0.660308i | \(0.229574\pi\) | |||||||
\(48\) | −16.3480 | −2.35963 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −8.41117 | −1.18952 | ||||||||
\(51\) | −21.2705 | −2.97847 | ||||||||
\(52\) | −2.85393 | −0.395769 | ||||||||
\(53\) | −10.1744 | −1.39756 | −0.698780 | − | 0.715336i | \(-0.746273\pi\) | ||||
−0.698780 | + | 0.715336i | \(0.746273\pi\) | |||||||
\(54\) | 26.4065 | 3.59347 | ||||||||
\(55\) | −0.246676 | −0.0332617 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −14.1639 | −1.87605 | ||||||||
\(58\) | 11.0423 | 1.44992 | ||||||||
\(59\) | −6.45660 | −0.840577 | −0.420289 | − | 0.907390i | \(-0.638071\pi\) | ||||
−0.420289 | + | 0.907390i | \(0.638071\pi\) | |||||||
\(60\) | −0.727387 | −0.0939053 | ||||||||
\(61\) | −3.38149 | −0.432956 | −0.216478 | − | 0.976287i | \(-0.569457\pi\) | ||||
−0.216478 | + | 0.976287i | \(0.569457\pi\) | |||||||
\(62\) | 3.03335 | 0.385235 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.88838 | 0.236047 | ||||||||
\(65\) | 0.782155 | 0.0970144 | ||||||||
\(66\) | 5.57913 | 0.686744 | ||||||||
\(67\) | −3.65484 | −0.446510 | −0.223255 | − | 0.974760i | \(-0.571668\pi\) | ||||
−0.223255 | + | 0.974760i | \(0.571668\pi\) | |||||||
\(68\) | −5.84377 | −0.708661 | ||||||||
\(69\) | 10.3428 | 1.24512 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0.345158 | 0.0409627 | 0.0204813 | − | 0.999790i | \(-0.493480\pi\) | ||||
0.0204813 | + | 0.999790i | \(0.493480\pi\) | |||||||
\(72\) | −14.4851 | −1.70709 | ||||||||
\(73\) | 2.97942 | 0.348715 | 0.174357 | − | 0.984682i | \(-0.444215\pi\) | ||||
0.174357 | + | 0.984682i | \(0.444215\pi\) | |||||||
\(74\) | 14.2780 | 1.65979 | ||||||||
\(75\) | −16.1813 | −1.86846 | ||||||||
\(76\) | −3.89132 | −0.446365 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −17.6902 | −2.00302 | ||||||||
\(79\) | −3.77595 | −0.424828 | −0.212414 | − | 0.977180i | \(-0.568132\pi\) | ||||
−0.212414 | + | 0.977180i | \(0.568132\pi\) | |||||||
\(80\) | 1.23091 | 0.137620 | ||||||||
\(81\) | 27.6014 | 3.06682 | ||||||||
\(82\) | −0.941851 | −0.104010 | ||||||||
\(83\) | −6.34157 | −0.696078 | −0.348039 | − | 0.937480i | \(-0.613152\pi\) | ||||
−0.348039 | + | 0.937480i | \(0.613152\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.60156 | 0.173713 | ||||||||
\(86\) | 9.69023 | 1.04492 | ||||||||
\(87\) | 21.2430 | 2.27749 | ||||||||
\(88\) | −1.87313 | −0.199677 | ||||||||
\(89\) | −0.246676 | −0.0261476 | −0.0130738 | − | 0.999915i | \(-0.504162\pi\) | ||||
−0.0130738 | + | 0.999915i | \(0.504162\pi\) | |||||||
\(90\) | −3.24851 | −0.342423 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 2.84152 | 0.296249 | ||||||||
\(93\) | 5.83553 | 0.605116 | ||||||||
\(94\) | 17.5356 | 1.80866 | ||||||||
\(95\) | 1.06646 | 0.109417 | ||||||||
\(96\) | −15.5667 | −1.58877 | ||||||||
\(97\) | −4.81068 | −0.488451 | −0.244226 | − | 0.969718i | \(-0.578534\pi\) | ||||
−0.244226 | + | 0.969718i | \(0.578534\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 7.73309 | 0.777205 | ||||||||
\(100\) | −4.44559 | −0.444559 | ||||||||
\(101\) | −6.86468 | −0.683061 | −0.341531 | − | 0.939871i | \(-0.610945\pi\) | ||||
−0.341531 | + | 0.939871i | \(0.610945\pi\) | |||||||
\(102\) | −36.2229 | −3.58660 | ||||||||
\(103\) | 5.07835 | 0.500385 | 0.250192 | − | 0.968196i | \(-0.419506\pi\) | ||||
0.250192 | + | 0.968196i | \(0.419506\pi\) | |||||||
\(104\) | 5.93930 | 0.582397 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −17.3266 | −1.68291 | ||||||||
\(107\) | 0.897562 | 0.0867706 | 0.0433853 | − | 0.999058i | \(-0.486186\pi\) | ||||
0.0433853 | + | 0.999058i | \(0.486186\pi\) | |||||||
\(108\) | 13.9567 | 1.34299 | ||||||||
\(109\) | 5.71569 | 0.547464 | 0.273732 | − | 0.961806i | \(-0.411742\pi\) | ||||
0.273732 | + | 0.961806i | \(0.411742\pi\) | |||||||
\(110\) | −0.420079 | −0.0400529 | ||||||||
\(111\) | 27.4679 | 2.60714 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −5.99001 | −0.563493 | −0.281747 | − | 0.959489i | \(-0.590914\pi\) | ||||
−0.281747 | + | 0.959489i | \(0.590914\pi\) | |||||||
\(114\) | −24.1205 | −2.25909 | ||||||||
\(115\) | −0.778754 | −0.0726192 | ||||||||
\(116\) | 5.83621 | 0.541879 | ||||||||
\(117\) | −24.5200 | −2.26687 | ||||||||
\(118\) | −10.9953 | −1.01220 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 1.51376 | 0.138187 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | −5.75855 | −0.521354 | ||||||||
\(123\) | −1.81193 | −0.163376 | ||||||||
\(124\) | 1.60323 | 0.143974 | ||||||||
\(125\) | 2.45175 | 0.219291 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 2.31399 | 0.205334 | 0.102667 | − | 0.994716i | \(-0.467262\pi\) | ||||
0.102667 | + | 0.994716i | \(0.467262\pi\) | |||||||
\(128\) | 12.7189 | 1.12420 | ||||||||
\(129\) | 18.6420 | 1.64133 | ||||||||
\(130\) | 1.33198 | 0.116822 | ||||||||
\(131\) | 14.4800 | 1.26513 | 0.632564 | − | 0.774508i | \(-0.282003\pi\) | ||||
0.632564 | + | 0.774508i | \(0.282003\pi\) | |||||||
\(132\) | 2.94876 | 0.256657 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −6.22405 | −0.537676 | ||||||||
\(135\) | −3.82502 | −0.329205 | ||||||||
\(136\) | 12.1614 | 1.04284 | ||||||||
\(137\) | −10.9962 | −0.939470 | −0.469735 | − | 0.882807i | \(-0.655651\pi\) | ||||
−0.469735 | + | 0.882807i | \(0.655651\pi\) | |||||||
\(138\) | 17.6133 | 1.49934 | ||||||||
\(139\) | 1.05087 | 0.0891334 | 0.0445667 | − | 0.999006i | \(-0.485809\pi\) | ||||
0.0445667 | + | 0.999006i | \(0.485809\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 33.7348 | 2.84098 | ||||||||
\(142\) | 0.587790 | 0.0493262 | ||||||||
\(143\) | −3.17078 | −0.265154 | ||||||||
\(144\) | −38.5882 | −3.21569 | ||||||||
\(145\) | −1.59949 | −0.132830 | ||||||||
\(146\) | 5.07383 | 0.419913 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 7.54641 | 0.620311 | ||||||||
\(149\) | 18.4185 | 1.50890 | 0.754452 | − | 0.656356i | \(-0.227903\pi\) | ||||
0.754452 | + | 0.656356i | \(0.227903\pi\) | |||||||
\(150\) | −27.5562 | −2.24995 | ||||||||
\(151\) | 19.1564 | 1.55893 | 0.779463 | − | 0.626448i | \(-0.215492\pi\) | ||||
0.779463 | + | 0.626448i | \(0.215492\pi\) | |||||||
\(152\) | 8.09821 | 0.656851 | ||||||||
\(153\) | −50.2076 | −4.05904 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −0.439384 | −0.0352922 | ||||||||
\(156\) | −9.34988 | −0.748589 | ||||||||
\(157\) | 23.0214 | 1.83731 | 0.918653 | − | 0.395065i | \(-0.129278\pi\) | ||||
0.918653 | + | 0.395065i | \(0.129278\pi\) | |||||||
\(158\) | −6.43029 | −0.511567 | ||||||||
\(159\) | −33.3327 | −2.64346 | ||||||||
\(160\) | 1.17209 | 0.0926615 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 47.0041 | 3.69299 | ||||||||
\(163\) | −4.93865 | −0.386825 | −0.193412 | − | 0.981118i | \(-0.561956\pi\) | ||||
−0.193412 | + | 0.981118i | \(0.561956\pi\) | |||||||
\(164\) | −0.497800 | −0.0388716 | ||||||||
\(165\) | −0.808144 | −0.0629139 | ||||||||
\(166\) | −10.7994 | −0.838199 | ||||||||
\(167\) | 7.39244 | 0.572044 | 0.286022 | − | 0.958223i | \(-0.407667\pi\) | ||||
0.286022 | + | 0.958223i | \(0.407667\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −2.94613 | −0.226625 | ||||||||
\(170\) | 2.72739 | 0.209181 | ||||||||
\(171\) | −33.4328 | −2.55667 | ||||||||
\(172\) | 5.12161 | 0.390519 | ||||||||
\(173\) | −18.2383 | −1.38663 | −0.693316 | − | 0.720634i | \(-0.743851\pi\) | ||||
−0.693316 | + | 0.720634i | \(0.743851\pi\) | |||||||
\(174\) | 36.1760 | 2.74250 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −4.99001 | −0.376136 | ||||||||
\(177\) | −21.1527 | −1.58994 | ||||||||
\(178\) | −0.420079 | −0.0314862 | ||||||||
\(179\) | −2.37373 | −0.177421 | −0.0887103 | − | 0.996057i | \(-0.528275\pi\) | ||||
−0.0887103 | + | 0.996057i | \(0.528275\pi\) | |||||||
\(180\) | −1.71694 | −0.127973 | ||||||||
\(181\) | −21.6459 | −1.60893 | −0.804463 | − | 0.594002i | \(-0.797547\pi\) | ||||
−0.804463 | + | 0.594002i | \(0.797547\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −11.0782 | −0.818928 | ||||||||
\(184\) | −5.91348 | −0.435947 | ||||||||
\(185\) | −2.06819 | −0.152056 | ||||||||
\(186\) | 9.93767 | 0.728665 | ||||||||
\(187\) | −6.49256 | −0.474783 | ||||||||
\(188\) | 9.26814 | 0.675949 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 1.81615 | 0.131757 | ||||||||
\(191\) | 7.22154 | 0.522532 | 0.261266 | − | 0.965267i | \(-0.415860\pi\) | ||||
0.261266 | + | 0.965267i | \(0.415860\pi\) | |||||||
\(192\) | 6.18658 | 0.446478 | ||||||||
\(193\) | −3.66604 | −0.263887 | −0.131944 | − | 0.991257i | \(-0.542122\pi\) | ||||
−0.131944 | + | 0.991257i | \(0.542122\pi\) | |||||||
\(194\) | −8.19240 | −0.588180 | ||||||||
\(195\) | 2.56245 | 0.183501 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −3.81615 | −0.271889 | −0.135945 | − | 0.990716i | \(-0.543407\pi\) | ||||
−0.135945 | + | 0.990716i | \(0.543407\pi\) | |||||||
\(198\) | 13.1691 | 0.935890 | ||||||||
\(199\) | −19.3819 | −1.37395 | −0.686973 | − | 0.726683i | \(-0.741061\pi\) | ||||
−0.686973 | + | 0.726683i | \(0.741061\pi\) | |||||||
\(200\) | 9.25169 | 0.654193 | ||||||||
\(201\) | −11.9738 | −0.844565 | ||||||||
\(202\) | −11.6903 | −0.822525 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −19.1450 | −1.34042 | ||||||||
\(205\) | 0.136428 | 0.00952856 | ||||||||
\(206\) | 8.64822 | 0.602550 | ||||||||
\(207\) | 24.4133 | 1.69684 | ||||||||
\(208\) | 15.8223 | 1.09708 | ||||||||
\(209\) | −4.32335 | −0.299052 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 24.1279 | 1.66103 | 0.830517 | − | 0.556993i | \(-0.188045\pi\) | ||||
0.830517 | + | 0.556993i | \(0.188045\pi\) | |||||||
\(212\) | −9.15768 | −0.628952 | ||||||||
\(213\) | 1.13078 | 0.0774801 | ||||||||
\(214\) | 1.52851 | 0.104487 | ||||||||
\(215\) | −1.40364 | −0.0957275 | ||||||||
\(216\) | −29.0453 | −1.97628 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 9.73359 | 0.659242 | ||||||||
\(219\) | 9.76100 | 0.659587 | ||||||||
\(220\) | −0.222026 | −0.0149690 | ||||||||
\(221\) | 20.5865 | 1.38480 | ||||||||
\(222\) | 46.7768 | 3.13945 | ||||||||
\(223\) | 14.6952 | 0.984061 | 0.492030 | − | 0.870578i | \(-0.336255\pi\) | ||||
0.492030 | + | 0.870578i | \(0.336255\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −38.1949 | −2.54633 | ||||||||
\(226\) | −10.2008 | −0.678544 | ||||||||
\(227\) | 9.19531 | 0.610314 | 0.305157 | − | 0.952302i | \(-0.401291\pi\) | ||||
0.305157 | + | 0.952302i | \(0.401291\pi\) | |||||||
\(228\) | −12.7485 | −0.844290 | ||||||||
\(229\) | 17.4339 | 1.15207 | 0.576033 | − | 0.817427i | \(-0.304600\pi\) | ||||
0.576033 | + | 0.817427i | \(0.304600\pi\) | |||||||
\(230\) | −1.32619 | −0.0874461 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −12.1457 | −0.797405 | ||||||||
\(233\) | −27.7505 | −1.81799 | −0.908997 | − | 0.416802i | \(-0.863151\pi\) | ||||
−0.908997 | + | 0.416802i | \(0.863151\pi\) | |||||||
\(234\) | −41.7565 | −2.72971 | ||||||||
\(235\) | −2.54005 | −0.165695 | ||||||||
\(236\) | −5.81140 | −0.378290 | ||||||||
\(237\) | −12.3705 | −0.803553 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −22.5326 | −1.45752 | −0.728758 | − | 0.684772i | \(-0.759902\pi\) | ||||
−0.728758 | + | 0.684772i | \(0.759902\pi\) | |||||||
\(240\) | 4.03265 | 0.260306 | ||||||||
\(241\) | −7.22658 | −0.465505 | −0.232752 | − | 0.972536i | \(-0.574773\pi\) | ||||
−0.232752 | + | 0.972536i | \(0.574773\pi\) | |||||||
\(242\) | 1.70296 | 0.109470 | ||||||||
\(243\) | 43.9073 | 2.81665 | ||||||||
\(244\) | −3.04359 | −0.194846 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −3.08564 | −0.196733 | ||||||||
\(247\) | 13.7084 | 0.872244 | ||||||||
\(248\) | −3.33647 | −0.211866 | ||||||||
\(249\) | −20.7759 | −1.31662 | ||||||||
\(250\) | 4.17523 | 0.264064 | ||||||||
\(251\) | 12.8842 | 0.813245 | 0.406622 | − | 0.913596i | \(-0.366706\pi\) | ||||
0.406622 | + | 0.913596i | \(0.366706\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 3.15700 | 0.198479 | ||||||||
\(254\) | 3.94063 | 0.247257 | ||||||||
\(255\) | 5.24692 | 0.328575 | ||||||||
\(256\) | 17.8830 | 1.11769 | ||||||||
\(257\) | 31.0932 | 1.93954 | 0.969771 | − | 0.244016i | \(-0.0784650\pi\) | ||||
0.969771 | + | 0.244016i | \(0.0784650\pi\) | |||||||
\(258\) | 31.7465 | 1.97645 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0.703995 | 0.0436599 | ||||||||
\(261\) | 50.1426 | 3.10375 | ||||||||
\(262\) | 24.6589 | 1.52343 | ||||||||
\(263\) | −7.50215 | −0.462603 | −0.231301 | − | 0.972882i | \(-0.574298\pi\) | ||||
−0.231301 | + | 0.972882i | \(0.574298\pi\) | |||||||
\(264\) | −6.13665 | −0.377685 | ||||||||
\(265\) | 2.50978 | 0.154174 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −0.808144 | −0.0494576 | ||||||||
\(268\) | −3.28962 | −0.200945 | ||||||||
\(269\) | −1.93752 | −0.118133 | −0.0590663 | − | 0.998254i | \(-0.518812\pi\) | ||||
−0.0590663 | + | 0.998254i | \(0.518812\pi\) | |||||||
\(270\) | −6.51385 | −0.396420 | ||||||||
\(271\) | 22.9786 | 1.39585 | 0.697926 | − | 0.716170i | \(-0.254107\pi\) | ||||
0.697926 | + | 0.716170i | \(0.254107\pi\) | |||||||
\(272\) | 32.3980 | 1.96442 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −18.7261 | −1.13129 | ||||||||
\(275\) | −4.93915 | −0.297842 | ||||||||
\(276\) | 9.30922 | 0.560349 | ||||||||
\(277\) | −5.52095 | −0.331722 | −0.165861 | − | 0.986149i | \(-0.553040\pi\) | ||||
−0.165861 | + | 0.986149i | \(0.553040\pi\) | |||||||
\(278\) | 1.78958 | 0.107332 | ||||||||
\(279\) | 13.7743 | 0.824648 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −7.28000 | −0.434288 | −0.217144 | − | 0.976140i | \(-0.569674\pi\) | ||||
−0.217144 | + | 0.976140i | \(0.569674\pi\) | |||||||
\(282\) | 57.4490 | 3.42104 | ||||||||
\(283\) | −13.2600 | −0.788225 | −0.394113 | − | 0.919062i | \(-0.628948\pi\) | ||||
−0.394113 | + | 0.919062i | \(0.628948\pi\) | |||||||
\(284\) | 0.310666 | 0.0184347 | ||||||||
\(285\) | 3.49389 | 0.206960 | ||||||||
\(286\) | −5.39972 | −0.319292 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −36.7440 | −2.16516 | ||||||||
\(289\) | 25.1534 | 1.47961 | ||||||||
\(290\) | −2.72386 | −0.159951 | ||||||||
\(291\) | −15.7605 | −0.923895 | ||||||||
\(292\) | 2.68169 | 0.156934 | ||||||||
\(293\) | −5.56718 | −0.325238 | −0.162619 | − | 0.986689i | \(-0.551994\pi\) | ||||
−0.162619 | + | 0.986689i | \(0.551994\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 1.59269 | 0.0927297 | ||||||||
\(296\) | −15.7048 | −0.912823 | ||||||||
\(297\) | 15.5063 | 0.899765 | ||||||||
\(298\) | 31.3660 | 1.81698 | ||||||||
\(299\) | −10.0102 | −0.578902 | ||||||||
\(300\) | −14.5644 | −0.840874 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 32.6226 | 1.87722 | ||||||||
\(303\) | −22.4897 | −1.29200 | ||||||||
\(304\) | 21.5736 | 1.23733 | ||||||||
\(305\) | 0.834132 | 0.0477623 | ||||||||
\(306\) | −85.5015 | −4.88779 | ||||||||
\(307\) | −14.2467 | −0.813102 | −0.406551 | − | 0.913628i | \(-0.633269\pi\) | ||||
−0.406551 | + | 0.913628i | \(0.633269\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 16.6374 | 0.946468 | ||||||||
\(310\) | −0.748253 | −0.0424979 | ||||||||
\(311\) | −3.56834 | −0.202342 | −0.101171 | − | 0.994869i | \(-0.532259\pi\) | ||||
−0.101171 | + | 0.994869i | \(0.532259\pi\) | |||||||
\(312\) | 19.4580 | 1.10159 | ||||||||
\(313\) | 9.11394 | 0.515150 | 0.257575 | − | 0.966258i | \(-0.417076\pi\) | ||||
0.257575 | + | 0.966258i | \(0.417076\pi\) | |||||||
\(314\) | 39.2045 | 2.21244 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −3.39863 | −0.191188 | ||||||||
\(317\) | −11.7542 | −0.660181 | −0.330090 | − | 0.943949i | \(-0.607079\pi\) | ||||
−0.330090 | + | 0.943949i | \(0.607079\pi\) | |||||||
\(318\) | −56.7643 | −3.18318 | ||||||||
\(319\) | 6.48417 | 0.363044 | ||||||||
\(320\) | −0.465816 | −0.0260399 | ||||||||
\(321\) | 2.94054 | 0.164125 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 28.0696 | 1.56183 | ||||||||
\(324\) | 24.8432 | 1.38018 | ||||||||
\(325\) | 15.6610 | 0.868715 | ||||||||
\(326\) | −8.41032 | −0.465805 | ||||||||
\(327\) | 18.7254 | 1.03552 | ||||||||
\(328\) | 1.03597 | 0.0572018 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −1.37624 | −0.0757593 | ||||||||
\(331\) | −25.6748 | −1.41122 | −0.705609 | − | 0.708602i | \(-0.749326\pi\) | ||||
−0.705609 | + | 0.708602i | \(0.749326\pi\) | |||||||
\(332\) | −5.70786 | −0.313260 | ||||||||
\(333\) | 64.8361 | 3.55299 | ||||||||
\(334\) | 12.5890 | 0.688841 | ||||||||
\(335\) | 0.901561 | 0.0492575 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 33.5644 | 1.82837 | 0.914185 | − | 0.405298i | \(-0.132832\pi\) | ||||
0.914185 | + | 0.405298i | \(0.132832\pi\) | |||||||
\(338\) | −5.01713 | −0.272896 | ||||||||
\(339\) | −19.6241 | −1.06584 | ||||||||
\(340\) | 1.44152 | 0.0781772 | ||||||||
\(341\) | 1.78122 | 0.0964585 | ||||||||
\(342\) | −56.9347 | −3.07868 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −10.6586 | −0.574671 | ||||||||
\(345\) | −2.55131 | −0.137358 | ||||||||
\(346\) | −31.0591 | −1.66975 | ||||||||
\(347\) | −26.7567 | −1.43637 | −0.718187 | − | 0.695850i | \(-0.755028\pi\) | ||||
−0.718187 | + | 0.695850i | \(0.755028\pi\) | |||||||
\(348\) | 19.1202 | 1.02495 | ||||||||
\(349\) | 19.9411 | 1.06742 | 0.533711 | − | 0.845667i | \(-0.320797\pi\) | ||||
0.533711 | + | 0.845667i | \(0.320797\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −49.1670 | −2.62434 | ||||||||
\(352\) | −4.75152 | −0.253257 | ||||||||
\(353\) | 10.0436 | 0.534566 | 0.267283 | − | 0.963618i | \(-0.413874\pi\) | ||||
0.267283 | + | 0.963618i | \(0.413874\pi\) | |||||||
\(354\) | −36.0222 | −1.91456 | ||||||||
\(355\) | −0.0851420 | −0.00451887 | ||||||||
\(356\) | −0.222026 | −0.0117673 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −4.04236 | −0.213645 | ||||||||
\(359\) | −17.0519 | −0.899964 | −0.449982 | − | 0.893038i | \(-0.648570\pi\) | ||||
−0.449982 | + | 0.893038i | \(0.648570\pi\) | |||||||
\(360\) | 3.57313 | 0.188320 | ||||||||
\(361\) | −0.308682 | −0.0162464 | ||||||||
\(362\) | −36.8621 | −1.93743 | ||||||||
\(363\) | 3.27614 | 0.171953 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −0.734951 | −0.0384691 | ||||||||
\(366\) | −18.8658 | −0.986132 | ||||||||
\(367\) | −0.115028 | −0.00600443 | −0.00300221 | − | 0.999995i | \(-0.500956\pi\) | ||||
−0.00300221 | + | 0.999995i | \(0.500956\pi\) | |||||||
\(368\) | −15.7535 | −0.821206 | ||||||||
\(369\) | −4.27692 | −0.222648 | ||||||||
\(370\) | −3.52204 | −0.183102 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 5.25239 | 0.272324 | ||||||||
\(373\) | −17.5106 | −0.906664 | −0.453332 | − | 0.891342i | \(-0.649765\pi\) | ||||
−0.453332 | + | 0.891342i | \(0.649765\pi\) | |||||||
\(374\) | −11.0566 | −0.571722 | ||||||||
\(375\) | 8.03226 | 0.414784 | ||||||||
\(376\) | −19.2879 | −0.994697 | ||||||||
\(377\) | −20.5599 | −1.05889 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 7.72561 | 0.396838 | 0.198419 | − | 0.980117i | \(-0.436419\pi\) | ||||
0.198419 | + | 0.980117i | \(0.436419\pi\) | |||||||
\(380\) | 0.959894 | 0.0492415 | ||||||||
\(381\) | 7.58096 | 0.388384 | ||||||||
\(382\) | 12.2980 | 0.629220 | ||||||||
\(383\) | −10.6044 | −0.541860 | −0.270930 | − | 0.962599i | \(-0.587331\pi\) | ||||
−0.270930 | + | 0.962599i | \(0.587331\pi\) | |||||||
\(384\) | 41.6688 | 2.12640 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −6.24311 | −0.317766 | ||||||||
\(387\) | 44.0030 | 2.23680 | ||||||||
\(388\) | −4.32996 | −0.219820 | ||||||||
\(389\) | −22.2172 | −1.12646 | −0.563228 | − | 0.826302i | \(-0.690441\pi\) | ||||
−0.563228 | + | 0.826302i | \(0.690441\pi\) | |||||||
\(390\) | 4.36375 | 0.220967 | ||||||||
\(391\) | −20.4970 | −1.03658 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 47.4386 | 2.39296 | ||||||||
\(394\) | −6.49874 | −0.327402 | ||||||||
\(395\) | 0.931435 | 0.0468656 | ||||||||
\(396\) | 6.96033 | 0.349770 | ||||||||
\(397\) | 19.8781 | 0.997654 | 0.498827 | − | 0.866702i | \(-0.333764\pi\) | ||||
0.498827 | + | 0.866702i | \(0.333764\pi\) | |||||||
\(398\) | −33.0066 | −1.65447 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 24.6464 | 1.23232 | ||||||||
\(401\) | −24.7759 | −1.23725 | −0.618624 | − | 0.785687i | \(-0.712309\pi\) | ||||
−0.618624 | + | 0.785687i | \(0.712309\pi\) | |||||||
\(402\) | −20.3909 | −1.01700 | ||||||||
\(403\) | −5.64787 | −0.281340 | ||||||||
\(404\) | −6.17870 | −0.307402 | ||||||||
\(405\) | −6.80859 | −0.338322 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 8.38424 | 0.415591 | ||||||||
\(408\) | 39.8426 | 1.97250 | ||||||||
\(409\) | −21.7215 | −1.07406 | −0.537029 | − | 0.843564i | \(-0.680454\pi\) | ||||
−0.537029 | + | 0.843564i | \(0.680454\pi\) | |||||||
\(410\) | 0.232332 | 0.0114740 | ||||||||
\(411\) | −36.0251 | −1.77699 | ||||||||
\(412\) | 4.57088 | 0.225191 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 41.5749 | 2.04330 | ||||||||
\(415\) | 1.56431 | 0.0767890 | ||||||||
\(416\) | 15.0661 | 0.738674 | ||||||||
\(417\) | 3.44279 | 0.168594 | ||||||||
\(418\) | −7.36248 | −0.360111 | ||||||||
\(419\) | −25.6815 | −1.25462 | −0.627311 | − | 0.778769i | \(-0.715845\pi\) | ||||
−0.627311 | + | 0.778769i | \(0.715845\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 28.7580 | 1.40158 | 0.700789 | − | 0.713369i | \(-0.252832\pi\) | ||||
0.700789 | + | 0.713369i | \(0.252832\pi\) | |||||||
\(422\) | 41.0889 | 2.00017 | ||||||||
\(423\) | 79.6285 | 3.87167 | ||||||||
\(424\) | 19.0580 | 0.925539 | ||||||||
\(425\) | 32.0677 | 1.55551 | ||||||||
\(426\) | 1.92568 | 0.0932995 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0.807869 | 0.0390498 | ||||||||
\(429\) | −10.3879 | −0.501534 | ||||||||
\(430\) | −2.39034 | −0.115273 | ||||||||
\(431\) | −9.84034 | −0.473992 | −0.236996 | − | 0.971511i | \(-0.576163\pi\) | ||||
−0.236996 | + | 0.971511i | \(0.576163\pi\) | |||||||
\(432\) | −77.3765 | −3.72278 | ||||||||
\(433\) | −0.424750 | −0.0204122 | −0.0102061 | − | 0.999948i | \(-0.503249\pi\) | ||||
−0.0102061 | + | 0.999948i | \(0.503249\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −5.24014 | −0.251245 | ||||||||
\(436\) | 5.14453 | 0.246378 | ||||||||
\(437\) | −13.6488 | −0.652910 | ||||||||
\(438\) | 16.6226 | 0.794258 | ||||||||
\(439\) | −3.98983 | −0.190424 | −0.0952121 | − | 0.995457i | \(-0.530353\pi\) | ||||
−0.0952121 | + | 0.995457i | \(0.530353\pi\) | |||||||
\(440\) | 0.462057 | 0.0220277 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 35.0580 | 1.66754 | ||||||||
\(443\) | −19.9380 | −0.947285 | −0.473642 | − | 0.880717i | \(-0.657061\pi\) | ||||
−0.473642 | + | 0.880717i | \(0.657061\pi\) | |||||||
\(444\) | 24.7231 | 1.17331 | ||||||||
\(445\) | 0.0608489 | 0.00288451 | ||||||||
\(446\) | 25.0253 | 1.18498 | ||||||||
\(447\) | 60.3416 | 2.85406 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 9.97100 | 0.470561 | 0.235280 | − | 0.971928i | \(-0.424399\pi\) | ||||
0.235280 | + | 0.971928i | \(0.424399\pi\) | |||||||
\(450\) | −65.0444 | −3.06622 | ||||||||
\(451\) | −0.553067 | −0.0260429 | ||||||||
\(452\) | −5.39144 | −0.253592 | ||||||||
\(453\) | 62.7591 | 2.94868 | ||||||||
\(454\) | 15.6592 | 0.734925 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 26.5309 | 1.24242 | ||||||||
\(457\) | 34.9248 | 1.63371 | 0.816856 | − | 0.576841i | \(-0.195715\pi\) | ||||
0.816856 | + | 0.576841i | \(0.195715\pi\) | |||||||
\(458\) | 29.6893 | 1.38729 | ||||||||
\(459\) | −100.675 | −4.69912 | ||||||||
\(460\) | −0.700934 | −0.0326812 | ||||||||
\(461\) | 26.8042 | 1.24839 | 0.624197 | − | 0.781267i | \(-0.285426\pi\) | ||||
0.624197 | + | 0.781267i | \(0.285426\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −28.1253 | −1.30709 | −0.653547 | − | 0.756886i | \(-0.726720\pi\) | ||||
−0.653547 | + | 0.756886i | \(0.726720\pi\) | |||||||
\(464\) | −32.3561 | −1.50209 | ||||||||
\(465\) | −1.43948 | −0.0667544 | ||||||||
\(466\) | −47.2580 | −2.18918 | ||||||||
\(467\) | −27.7857 | −1.28577 | −0.642884 | − | 0.765964i | \(-0.722262\pi\) | ||||
−0.642884 | + | 0.765964i | \(0.722262\pi\) | |||||||
\(468\) | −22.0697 | −1.02017 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −4.32560 | −0.199525 | ||||||||
\(471\) | 75.4213 | 3.47523 | ||||||||
\(472\) | 12.0941 | 0.556675 | ||||||||
\(473\) | 5.69023 | 0.261637 | ||||||||
\(474\) | −21.0665 | −0.967618 | ||||||||
\(475\) | 21.3537 | 0.979773 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −78.6795 | −3.60249 | ||||||||
\(478\) | −38.3722 | −1.75510 | ||||||||
\(479\) | −9.27456 | −0.423766 | −0.211883 | − | 0.977295i | \(-0.567960\pi\) | ||||
−0.211883 | + | 0.977295i | \(0.567960\pi\) | |||||||
\(480\) | 3.83991 | 0.175267 | ||||||||
\(481\) | −26.5846 | −1.21215 | ||||||||
\(482\) | −12.3066 | −0.560549 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0.900071 | 0.0409123 | ||||||||
\(485\) | 1.18668 | 0.0538843 | ||||||||
\(486\) | 74.7723 | 3.39174 | ||||||||
\(487\) | 10.6356 | 0.481944 | 0.240972 | − | 0.970532i | \(-0.422534\pi\) | ||||
0.240972 | + | 0.970532i | \(0.422534\pi\) | |||||||
\(488\) | 6.33399 | 0.286726 | ||||||||
\(489\) | −16.1797 | −0.731672 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −19.9832 | −0.901829 | −0.450915 | − | 0.892567i | \(-0.648902\pi\) | ||||
−0.450915 | + | 0.892567i | \(0.648902\pi\) | |||||||
\(492\) | −1.63086 | −0.0735249 | ||||||||
\(493\) | −42.0989 | −1.89604 | ||||||||
\(494\) | 23.3448 | 1.05033 | ||||||||
\(495\) | −1.90756 | −0.0857387 | ||||||||
\(496\) | −8.88832 | −0.399097 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −35.3805 | −1.58544 | ||||||||
\(499\) | −10.9536 | −0.490351 | −0.245175 | − | 0.969479i | \(-0.578846\pi\) | ||||
−0.245175 | + | 0.969479i | \(0.578846\pi\) | |||||||
\(500\) | 2.20675 | 0.0986887 | ||||||||
\(501\) | 24.2187 | 1.08201 | ||||||||
\(502\) | 21.9413 | 0.979288 | ||||||||
\(503\) | −25.5069 | −1.13729 | −0.568647 | − | 0.822582i | \(-0.692533\pi\) | ||||
−0.568647 | + | 0.822582i | \(0.692533\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 1.69335 | 0.0753531 | ||||||||
\(506\) | 5.37624 | 0.239003 | ||||||||
\(507\) | −9.65192 | −0.428657 | ||||||||
\(508\) | 2.08276 | 0.0924074 | ||||||||
\(509\) | 5.16877 | 0.229102 | 0.114551 | − | 0.993417i | \(-0.463457\pi\) | ||||
0.114551 | + | 0.993417i | \(0.463457\pi\) | |||||||
\(510\) | 8.93530 | 0.395662 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 5.01624 | 0.221689 | ||||||||
\(513\) | −67.0389 | −2.95984 | ||||||||
\(514\) | 52.9505 | 2.33555 | ||||||||
\(515\) | −1.25271 | −0.0552008 | ||||||||
\(516\) | 16.7791 | 0.738659 | ||||||||
\(517\) | 10.2971 | 0.452867 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −59.7512 | −2.62279 | ||||||||
\(520\) | −1.46508 | −0.0642481 | ||||||||
\(521\) | 15.4837 | 0.678352 | 0.339176 | − | 0.940723i | \(-0.389852\pi\) | ||||
0.339176 | + | 0.940723i | \(0.389852\pi\) | |||||||
\(522\) | 85.3909 | 3.73746 | ||||||||
\(523\) | −10.2761 | −0.449344 | −0.224672 | − | 0.974434i | \(-0.572131\pi\) | ||||
−0.224672 | + | 0.974434i | \(0.572131\pi\) | |||||||
\(524\) | 13.0331 | 0.569352 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −12.7759 | −0.557054 | ||||||||
\(527\) | −11.5647 | −0.503766 | ||||||||
\(528\) | −16.3480 | −0.711455 | ||||||||
\(529\) | −13.0334 | −0.566669 | ||||||||
\(530\) | 4.27405 | 0.185653 | ||||||||
\(531\) | −49.9294 | −2.16675 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 1.75366 | 0.0759593 | ||||||||
\(534\) | −1.37624 | −0.0595556 | ||||||||
\(535\) | −0.221407 | −0.00957224 | ||||||||
\(536\) | 6.84601 | 0.295703 | ||||||||
\(537\) | −7.77666 | −0.335588 | ||||||||
\(538\) | −3.29952 | −0.142252 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −3.44279 | −0.148154 | ||||||||
\(541\) | 32.5212 | 1.39820 | 0.699099 | − | 0.715025i | \(-0.253585\pi\) | ||||
0.699099 | + | 0.715025i | \(0.253585\pi\) | |||||||
\(542\) | 39.1317 | 1.68085 | ||||||||
\(543\) | −70.9150 | −3.04325 | ||||||||
\(544\) | 30.8496 | 1.32266 | ||||||||
\(545\) | −1.40992 | −0.0603944 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −32.7759 | −1.40139 | −0.700697 | − | 0.713459i | \(-0.747128\pi\) | ||||
−0.700697 | + | 0.713459i | \(0.747128\pi\) | |||||||
\(548\) | −9.89738 | −0.422795 | ||||||||
\(549\) | −26.1494 | −1.11603 | ||||||||
\(550\) | −8.41117 | −0.358654 | ||||||||
\(551\) | −28.0333 | −1.19426 | ||||||||
\(552\) | −19.3734 | −0.824586 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −9.40195 | −0.399451 | ||||||||
\(555\) | −6.77567 | −0.287611 | ||||||||
\(556\) | 0.945855 | 0.0401132 | ||||||||
\(557\) | −14.3574 | −0.608341 | −0.304170 | − | 0.952618i | \(-0.598379\pi\) | ||||
−0.304170 | + | 0.952618i | \(0.598379\pi\) | |||||||
\(558\) | 23.4571 | 0.993020 | ||||||||
\(559\) | −18.0425 | −0.763116 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −21.2705 | −0.898043 | ||||||||
\(562\) | −12.3975 | −0.522959 | ||||||||
\(563\) | −13.3422 | −0.562305 | −0.281152 | − | 0.959663i | \(-0.590717\pi\) | ||||
−0.281152 | + | 0.959663i | \(0.590717\pi\) | |||||||
\(564\) | 30.3637 | 1.27854 | ||||||||
\(565\) | 1.47759 | 0.0621627 | ||||||||
\(566\) | −22.5812 | −0.949160 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −0.646527 | −0.0271277 | ||||||||
\(569\) | −18.6491 | −0.781809 | −0.390904 | − | 0.920431i | \(-0.627838\pi\) | ||||
−0.390904 | + | 0.920431i | \(0.627838\pi\) | |||||||
\(570\) | 5.94994 | 0.249216 | ||||||||
\(571\) | 32.0508 | 1.34128 | 0.670642 | − | 0.741781i | \(-0.266019\pi\) | ||||
0.670642 | + | 0.741781i | \(0.266019\pi\) | |||||||
\(572\) | −2.85393 | −0.119329 | ||||||||
\(573\) | 23.6588 | 0.988359 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −15.5929 | −0.650268 | ||||||||
\(576\) | 14.6030 | 0.608457 | ||||||||
\(577\) | −16.4352 | −0.684206 | −0.342103 | − | 0.939662i | \(-0.611139\pi\) | ||||
−0.342103 | + | 0.939662i | \(0.611139\pi\) | |||||||
\(578\) | 42.8352 | 1.78171 | ||||||||
\(579\) | −12.0104 | −0.499137 | ||||||||
\(580\) | −1.43965 | −0.0597783 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −26.8394 | −1.11253 | ||||||||
\(583\) | −10.1744 | −0.421380 | ||||||||
\(584\) | −5.58086 | −0.230937 | ||||||||
\(585\) | 6.04848 | 0.250074 | ||||||||
\(586\) | −9.48069 | −0.391644 | ||||||||
\(587\) | 11.8148 | 0.487647 | 0.243824 | − | 0.969820i | \(-0.421598\pi\) | ||||
0.243824 | + | 0.969820i | \(0.421598\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −7.70083 | −0.317307 | ||||||||
\(590\) | 2.71228 | 0.111663 | ||||||||
\(591\) | −12.5022 | −0.514273 | ||||||||
\(592\) | −41.8375 | −1.71951 | ||||||||
\(593\) | −20.7452 | −0.851905 | −0.425952 | − | 0.904746i | \(-0.640061\pi\) | ||||
−0.425952 | + | 0.904746i | \(0.640061\pi\) | |||||||
\(594\) | 26.4065 | 1.08347 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 16.5780 | 0.679060 | ||||||||
\(597\) | −63.4978 | −2.59879 | ||||||||
\(598\) | −17.0469 | −0.697099 | ||||||||
\(599\) | 8.71038 | 0.355897 | 0.177948 | − | 0.984040i | \(-0.443054\pi\) | ||||
0.177948 | + | 0.984040i | \(0.443054\pi\) | |||||||
\(600\) | 30.3098 | 1.23739 | ||||||||
\(601\) | 46.2310 | 1.88580 | 0.942902 | − | 0.333072i | \(-0.108085\pi\) | ||||
0.942902 | + | 0.333072i | \(0.108085\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −28.2632 | −1.15097 | ||||||||
\(604\) | 17.2421 | 0.701572 | ||||||||
\(605\) | −0.246676 | −0.0100288 | ||||||||
\(606\) | −38.2990 | −1.55579 | ||||||||
\(607\) | −30.1304 | −1.22295 | −0.611477 | − | 0.791262i | \(-0.709424\pi\) | ||||
−0.611477 | + | 0.791262i | \(0.709424\pi\) | |||||||
\(608\) | 20.5425 | 0.833108 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 1.42049 | 0.0575141 | ||||||||
\(611\) | −32.6499 | −1.32088 | ||||||||
\(612\) | −45.1904 | −1.82671 | ||||||||
\(613\) | 41.7643 | 1.68684 | 0.843421 | − | 0.537253i | \(-0.180538\pi\) | ||||
0.843421 | + | 0.537253i | \(0.180538\pi\) | |||||||
\(614\) | −24.2616 | −0.979117 | ||||||||
\(615\) | 0.446958 | 0.0180231 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 8.94182 | 0.359984 | 0.179992 | − | 0.983668i | \(-0.442393\pi\) | ||||
0.179992 | + | 0.983668i | \(0.442393\pi\) | |||||||
\(618\) | 28.3328 | 1.13971 | ||||||||
\(619\) | −30.9126 | −1.24248 | −0.621241 | − | 0.783620i | \(-0.713371\pi\) | ||||
−0.621241 | + | 0.783620i | \(0.713371\pi\) | |||||||
\(620\) | −0.395477 | −0.0158827 | ||||||||
\(621\) | 48.9532 | 1.96442 | ||||||||
\(622\) | −6.07674 | −0.243655 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 51.8359 | 2.07510 | ||||||||
\(625\) | 24.0910 | 0.963639 | ||||||||
\(626\) | 15.5207 | 0.620331 | ||||||||
\(627\) | −14.1639 | −0.565651 | ||||||||
\(628\) | 20.7209 | 0.826853 | ||||||||
\(629\) | −54.4352 | −2.17047 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 30.5300 | 1.21538 | 0.607691 | − | 0.794174i | \(-0.292096\pi\) | ||||
0.607691 | + | 0.794174i | \(0.292096\pi\) | |||||||
\(632\) | 7.07286 | 0.281343 | ||||||||
\(633\) | 79.0464 | 3.14181 | ||||||||
\(634\) | −20.0169 | −0.794973 | ||||||||
\(635\) | −0.570805 | −0.0226517 | ||||||||
\(636\) | −30.0018 | −1.18965 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 11.0423 | 0.437168 | ||||||||
\(639\) | 2.66914 | 0.105589 | ||||||||
\(640\) | −3.13744 | −0.124018 | ||||||||
\(641\) | −10.4287 | −0.411907 | −0.205953 | − | 0.978562i | \(-0.566030\pi\) | ||||
−0.205953 | + | 0.978562i | \(0.566030\pi\) | |||||||
\(642\) | 5.00762 | 0.197635 | ||||||||
\(643\) | −16.4973 | −0.650590 | −0.325295 | − | 0.945613i | \(-0.605464\pi\) | ||||
−0.325295 | + | 0.945613i | \(0.605464\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −4.59852 | −0.181067 | ||||||||
\(646\) | 47.8014 | 1.88072 | ||||||||
\(647\) | 41.0615 | 1.61429 | 0.807147 | − | 0.590350i | \(-0.201010\pi\) | ||||
0.807147 | + | 0.590350i | \(0.201010\pi\) | |||||||
\(648\) | −51.7011 | −2.03101 | ||||||||
\(649\) | −6.45660 | −0.253444 | ||||||||
\(650\) | 26.6700 | 1.04608 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −4.44514 | −0.174085 | ||||||||
\(653\) | −20.1454 | −0.788350 | −0.394175 | − | 0.919035i | \(-0.628970\pi\) | ||||
−0.394175 | + | 0.919035i | \(0.628970\pi\) | |||||||
\(654\) | 31.8886 | 1.24694 | ||||||||
\(655\) | −3.57187 | −0.139565 | ||||||||
\(656\) | 2.75981 | 0.107753 | ||||||||
\(657\) | 23.0401 | 0.898881 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 6.46125 | 0.251694 | 0.125847 | − | 0.992050i | \(-0.459835\pi\) | ||||
0.125847 | + | 0.992050i | \(0.459835\pi\) | |||||||
\(660\) | −0.727387 | −0.0283135 | ||||||||
\(661\) | 14.3775 | 0.559221 | 0.279611 | − | 0.960114i | \(-0.409795\pi\) | ||||
0.279611 | + | 0.960114i | \(0.409795\pi\) | |||||||
\(662\) | −43.7232 | −1.69935 | ||||||||
\(663\) | 67.4443 | 2.61932 | ||||||||
\(664\) | 11.8786 | 0.460979 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 110.413 | 4.27842 | ||||||||
\(667\) | 20.4705 | 0.792620 | ||||||||
\(668\) | 6.65372 | 0.257440 | ||||||||
\(669\) | 48.1434 | 1.86133 | ||||||||
\(670\) | 1.53532 | 0.0593146 | ||||||||
\(671\) | −3.38149 | −0.130541 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 27.0790 | 1.04382 | 0.521909 | − | 0.853001i | \(-0.325220\pi\) | ||||
0.521909 | + | 0.853001i | \(0.325220\pi\) | |||||||
\(674\) | 57.1588 | 2.20168 | ||||||||
\(675\) | −76.5878 | −2.94786 | ||||||||
\(676\) | −2.65172 | −0.101989 | ||||||||
\(677\) | 15.8329 | 0.608506 | 0.304253 | − | 0.952591i | \(-0.401593\pi\) | ||||
0.304253 | + | 0.952591i | \(0.401593\pi\) | |||||||
\(678\) | −33.4191 | −1.28345 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −2.99993 | −0.115042 | ||||||||
\(681\) | 30.1251 | 1.15440 | ||||||||
\(682\) | 3.03335 | 0.116153 | ||||||||
\(683\) | 37.0041 | 1.41592 | 0.707962 | − | 0.706251i | \(-0.249615\pi\) | ||||
0.707962 | + | 0.706251i | \(0.249615\pi\) | |||||||
\(684\) | −30.0919 | −1.15059 | ||||||||
\(685\) | 2.71250 | 0.103639 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 57.1159 | 2.17911 | ||||||||
\(688\) | −28.3943 | −1.08252 | ||||||||
\(689\) | 32.2608 | 1.22904 | ||||||||
\(690\) | −4.34477 | −0.165403 | ||||||||
\(691\) | 14.5966 | 0.555283 | 0.277641 | − | 0.960685i | \(-0.410447\pi\) | ||||
0.277641 | + | 0.960685i | \(0.410447\pi\) | |||||||
\(692\) | −16.4158 | −0.624034 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −45.5656 | −1.72965 | ||||||||
\(695\) | −0.259223 | −0.00983290 | ||||||||
\(696\) | −39.7911 | −1.50828 | ||||||||
\(697\) | 3.59082 | 0.136012 | ||||||||
\(698\) | 33.9589 | 1.28536 | ||||||||
\(699\) | −90.9145 | −3.43870 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −40.3475 | −1.52390 | −0.761952 | − | 0.647633i | \(-0.775759\pi\) | ||||
−0.761952 | + | 0.647633i | \(0.775759\pi\) | |||||||
\(702\) | −83.7294 | −3.16016 | ||||||||
\(703\) | −36.2480 | −1.36712 | ||||||||
\(704\) | 1.88838 | 0.0711708 | ||||||||
\(705\) | −8.32155 | −0.313408 | ||||||||
\(706\) | 17.1038 | 0.643710 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −19.0389 | −0.715527 | ||||||||
\(709\) | 0.763572 | 0.0286766 | 0.0143383 | − | 0.999897i | \(-0.495436\pi\) | ||||
0.0143383 | + | 0.999897i | \(0.495436\pi\) | |||||||
\(710\) | −0.144993 | −0.00544150 | ||||||||
\(711\) | −29.1998 | −1.09508 | ||||||||
\(712\) | 0.462057 | 0.0173163 | ||||||||
\(713\) | 5.62331 | 0.210594 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0.782155 | 0.0292509 | ||||||||
\(716\) | −2.13652 | −0.0798456 | ||||||||
\(717\) | −73.8201 | −2.75686 | ||||||||
\(718\) | −29.0387 | −1.08371 | ||||||||
\(719\) | −7.59172 | −0.283123 | −0.141562 | − | 0.989929i | \(-0.545212\pi\) | ||||
−0.141562 | + | 0.989929i | \(0.545212\pi\) | |||||||
\(720\) | 9.51878 | 0.354744 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −0.525673 | −0.0195635 | ||||||||
\(723\) | −23.6753 | −0.880493 | ||||||||
\(724\) | −19.4828 | −0.724074 | ||||||||
\(725\) | −32.0263 | −1.18943 | ||||||||
\(726\) | 5.57913 | 0.207061 | ||||||||
\(727\) | 2.08478 | 0.0773204 | 0.0386602 | − | 0.999252i | \(-0.487691\pi\) | ||||
0.0386602 | + | 0.999252i | \(0.487691\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 61.0421 | 2.26082 | ||||||||
\(730\) | −1.25159 | −0.0463235 | ||||||||
\(731\) | −36.9442 | −1.36643 | ||||||||
\(732\) | −9.97121 | −0.368547 | ||||||||
\(733\) | −37.7859 | −1.39566 | −0.697828 | − | 0.716266i | \(-0.745850\pi\) | ||||
−0.697828 | + | 0.716266i | \(0.745850\pi\) | |||||||
\(734\) | −0.195889 | −0.00723038 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −15.0005 | −0.552927 | ||||||||
\(737\) | −3.65484 | −0.134628 | ||||||||
\(738\) | −7.28342 | −0.268106 | ||||||||
\(739\) | 36.8466 | 1.35543 | 0.677713 | − | 0.735327i | \(-0.262971\pi\) | ||||
0.677713 | + | 0.735327i | \(0.262971\pi\) | |||||||
\(740\) | −1.86152 | −0.0684307 | ||||||||
\(741\) | 44.9106 | 1.64983 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −44.4863 | −1.63204 | −0.816022 | − | 0.578020i | \(-0.803825\pi\) | ||||
−0.816022 | + | 0.578020i | \(0.803825\pi\) | |||||||
\(744\) | −10.9307 | −0.400740 | ||||||||
\(745\) | −4.54340 | −0.166457 | ||||||||
\(746\) | −29.8198 | −1.09178 | ||||||||
\(747\) | −49.0399 | −1.79428 | ||||||||
\(748\) | −5.84377 | −0.213669 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 13.6786 | 0.499473 | ||||||||
\(751\) | 26.6146 | 0.971179 | 0.485590 | − | 0.874187i | \(-0.338605\pi\) | ||||
0.485590 | + | 0.874187i | \(0.338605\pi\) | |||||||
\(752\) | −51.3828 | −1.87374 | ||||||||
\(753\) | 42.2105 | 1.53824 | ||||||||
\(754\) | −35.0127 | −1.27509 | ||||||||
\(755\) | −4.72542 | −0.171976 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −6.38731 | −0.232151 | −0.116075 | − | 0.993240i | \(-0.537031\pi\) | ||||
−0.116075 | + | 0.993240i | \(0.537031\pi\) | |||||||
\(758\) | 13.1564 | 0.477862 | ||||||||
\(759\) | 10.3428 | 0.375418 | ||||||||
\(760\) | −1.99763 | −0.0724617 | ||||||||
\(761\) | 40.1614 | 1.45585 | 0.727925 | − | 0.685657i | \(-0.240485\pi\) | ||||
0.727925 | + | 0.685657i | \(0.240485\pi\) | |||||||
\(762\) | 12.9101 | 0.467682 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 6.49990 | 0.235158 | ||||||||
\(765\) | 12.3850 | 0.447780 | ||||||||
\(766\) | −18.0589 | −0.652494 | ||||||||
\(767\) | 20.4725 | 0.739218 | ||||||||
\(768\) | 58.5871 | 2.11408 | ||||||||
\(769\) | −0.481136 | −0.0173502 | −0.00867510 | − | 0.999962i | \(-0.502761\pi\) | ||||
−0.00867510 | + | 0.999962i | \(0.502761\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 101.866 | 3.66861 | ||||||||
\(772\) | −3.29969 | −0.118759 | ||||||||
\(773\) | 24.1864 | 0.869924 | 0.434962 | − | 0.900449i | \(-0.356762\pi\) | ||||
0.434962 | + | 0.900449i | \(0.356762\pi\) | |||||||
\(774\) | 74.9354 | 2.69350 | ||||||||
\(775\) | −8.79772 | −0.316023 | ||||||||
\(776\) | 9.01106 | 0.323478 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −37.8349 | −1.35645 | ||||||||
\(779\) | 2.39110 | 0.0856701 | ||||||||
\(780\) | 2.30639 | 0.0825819 | ||||||||
\(781\) | 0.345158 | 0.0123507 | ||||||||
\(782\) | −34.9056 | −1.24822 | ||||||||
\(783\) | 100.545 | 3.59319 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −5.67881 | −0.202686 | ||||||||
\(786\) | 80.7861 | 2.88154 | ||||||||
\(787\) | 37.8595 | 1.34954 | 0.674772 | − | 0.738026i | \(-0.264242\pi\) | ||||
0.674772 | + | 0.738026i | \(0.264242\pi\) | |||||||
\(788\) | −3.43480 | −0.122360 | ||||||||
\(789\) | −24.5781 | −0.875004 | ||||||||
\(790\) | 1.58620 | 0.0564343 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −14.4851 | −0.514706 | ||||||||
\(793\) | 10.7220 | 0.380749 | ||||||||
\(794\) | 33.8516 | 1.20135 | ||||||||
\(795\) | 8.22237 | 0.291618 | ||||||||
\(796\) | −17.4451 | −0.618325 | ||||||||
\(797\) | −27.0930 | −0.959683 | −0.479842 | − | 0.877355i | \(-0.659306\pi\) | ||||
−0.479842 | + | 0.877355i | \(0.659306\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −66.8547 | −2.36515 | ||||||||
\(800\) | 23.4685 | 0.829737 | ||||||||
\(801\) | −1.90756 | −0.0674005 | ||||||||
\(802\) | −42.1923 | −1.48986 | ||||||||
\(803\) | 2.97942 | 0.105141 | ||||||||
\(804\) | −10.7772 | −0.380084 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −9.61809 | −0.338783 | ||||||||
\(807\) | −6.34758 | −0.223445 | ||||||||
\(808\) | 12.8585 | 0.452359 | ||||||||
\(809\) | 15.7254 | 0.552876 | 0.276438 | − | 0.961032i | \(-0.410846\pi\) | ||||
0.276438 | + | 0.961032i | \(0.410846\pi\) | |||||||
\(810\) | −11.5948 | −0.407398 | ||||||||
\(811\) | 32.3327 | 1.13536 | 0.567678 | − | 0.823251i | \(-0.307842\pi\) | ||||
0.567678 | + | 0.823251i | \(0.307842\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 75.2811 | 2.64023 | ||||||||
\(814\) | 14.2780 | 0.500444 | ||||||||
\(815\) | 1.21824 | 0.0426732 | ||||||||
\(816\) | 106.140 | 3.71565 | ||||||||
\(817\) | −24.6008 | −0.860674 | ||||||||
\(818\) | −36.9908 | −1.29335 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0.122795 | 0.00428819 | ||||||||
\(821\) | 9.55190 | 0.333364 | 0.166682 | − | 0.986011i | \(-0.446695\pi\) | ||||
0.166682 | + | 0.986011i | \(0.446695\pi\) | |||||||
\(822\) | −61.3494 | −2.13980 | ||||||||
\(823\) | 28.6991 | 1.00039 | 0.500194 | − | 0.865913i | \(-0.333262\pi\) | ||||
0.500194 | + | 0.865913i | \(0.333262\pi\) | |||||||
\(824\) | −9.51243 | −0.331381 | ||||||||
\(825\) | −16.1813 | −0.563362 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −9.66064 | −0.335933 | −0.167967 | − | 0.985793i | \(-0.553720\pi\) | ||||
−0.167967 | + | 0.985793i | \(0.553720\pi\) | |||||||
\(828\) | 21.9737 | 0.763640 | ||||||||
\(829\) | 16.4010 | 0.569629 | 0.284815 | − | 0.958583i | \(-0.408068\pi\) | ||||
0.284815 | + | 0.958583i | \(0.408068\pi\) | |||||||
\(830\) | 2.66396 | 0.0924673 | ||||||||
\(831\) | −18.0874 | −0.627445 | ||||||||
\(832\) | −5.98763 | −0.207584 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 5.86293 | 0.203017 | ||||||||
\(835\) | −1.82353 | −0.0631060 | ||||||||
\(836\) | −3.89132 | −0.134584 | ||||||||
\(837\) | 27.6201 | 0.954690 | ||||||||
\(838\) | −43.7345 | −1.51078 | ||||||||
\(839\) | −15.0128 | −0.518301 | −0.259150 | − | 0.965837i | \(-0.583443\pi\) | ||||
−0.259150 | + | 0.965837i | \(0.583443\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 13.0444 | 0.449807 | ||||||||
\(842\) | 48.9736 | 1.68774 | ||||||||
\(843\) | −23.8503 | −0.821448 | ||||||||
\(844\) | 21.7168 | 0.747524 | ||||||||
\(845\) | 0.726738 | 0.0250005 | ||||||||
\(846\) | 135.604 | 4.66217 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 50.7704 | 1.74346 | ||||||||
\(849\) | −43.4416 | −1.49091 | ||||||||
\(850\) | 54.6101 | 1.87311 | ||||||||
\(851\) | 26.4690 | 0.907346 | ||||||||
\(852\) | 1.01779 | 0.0348688 | ||||||||
\(853\) | 57.4026 | 1.96543 | 0.982714 | − | 0.185133i | \(-0.0592715\pi\) | ||||
0.982714 | + | 0.185133i | \(0.0592715\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 8.24706 | 0.282044 | ||||||||
\(856\) | −1.68125 | −0.0574641 | ||||||||
\(857\) | 32.1817 | 1.09931 | 0.549654 | − | 0.835393i | \(-0.314760\pi\) | ||||
0.549654 | + | 0.835393i | \(0.314760\pi\) | |||||||
\(858\) | −17.6902 | −0.603934 | ||||||||
\(859\) | 23.9856 | 0.818380 | 0.409190 | − | 0.912449i | \(-0.365811\pi\) | ||||
0.409190 | + | 0.912449i | \(0.365811\pi\) | |||||||
\(860\) | −1.26338 | −0.0430808 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −16.7577 | −0.570769 | ||||||||
\(863\) | 36.7485 | 1.25093 | 0.625467 | − | 0.780251i | \(-0.284909\pi\) | ||||
0.625467 | + | 0.780251i | \(0.284909\pi\) | |||||||
\(864\) | −73.6784 | −2.50659 | ||||||||
\(865\) | 4.49894 | 0.152969 | ||||||||
\(866\) | −0.723331 | −0.0245798 | ||||||||
\(867\) | 82.4060 | 2.79865 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −3.77595 | −0.128090 | ||||||||
\(870\) | −8.92374 | −0.302543 | ||||||||
\(871\) | 11.5887 | 0.392669 | ||||||||
\(872\) | −10.7063 | −0.362560 | ||||||||
\(873\) | −37.2015 | −1.25908 | ||||||||
\(874\) | −23.2433 | −0.786217 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 8.78559 | 0.296838 | ||||||||
\(877\) | −25.3446 | −0.855826 | −0.427913 | − | 0.903820i | \(-0.640751\pi\) | ||||
−0.427913 | + | 0.903820i | \(0.640751\pi\) | |||||||
\(878\) | −6.79452 | −0.229304 | ||||||||
\(879\) | −18.2389 | −0.615182 | ||||||||
\(880\) | 1.23091 | 0.0414941 | ||||||||
\(881\) | −12.7302 | −0.428890 | −0.214445 | − | 0.976736i | \(-0.568794\pi\) | ||||
−0.214445 | + | 0.976736i | \(0.568794\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 10.0508 | 0.338235 | 0.169117 | − | 0.985596i | \(-0.445908\pi\) | ||||
0.169117 | + | 0.985596i | \(0.445908\pi\) | |||||||
\(884\) | 18.5293 | 0.623209 | ||||||||
\(885\) | 5.21786 | 0.175396 | ||||||||
\(886\) | −33.9537 | −1.14070 | ||||||||
\(887\) | −18.9974 | −0.637871 | −0.318936 | − | 0.947776i | \(-0.603325\pi\) | ||||
−0.318936 | + | 0.947776i | \(0.603325\pi\) | |||||||
\(888\) | −51.4511 | −1.72659 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0.103623 | 0.00347346 | ||||||||
\(891\) | 27.6014 | 0.924682 | ||||||||
\(892\) | 13.2267 | 0.442862 | ||||||||
\(893\) | −44.5180 | −1.48974 | ||||||||
\(894\) | 102.759 | 3.43679 | ||||||||
\(895\) | 0.585541 | 0.0195725 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −32.7947 | −1.09498 | ||||||||
\(898\) | 16.9802 | 0.566637 | ||||||||
\(899\) | 11.5497 | 0.385205 | ||||||||
\(900\) | −34.3781 | −1.14594 | ||||||||
\(901\) | 66.0579 | 2.20071 | ||||||||
\(902\) | −0.941851 | −0.0313602 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 11.2201 | 0.373175 | ||||||||
\(905\) | 5.33951 | 0.177491 | ||||||||
\(906\) | 106.876 | 3.55072 | ||||||||
\(907\) | −59.1419 | −1.96378 | −0.981888 | − | 0.189464i | \(-0.939325\pi\) | ||||
−0.981888 | + | 0.189464i | \(0.939325\pi\) | |||||||
\(908\) | 8.27643 | 0.274663 | ||||||||
\(909\) | −53.0852 | −1.76073 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −11.5307 | −0.382028 | −0.191014 | − | 0.981587i | \(-0.561178\pi\) | ||||
−0.191014 | + | 0.981587i | \(0.561178\pi\) | |||||||
\(912\) | 70.6780 | 2.34038 | ||||||||
\(913\) | −6.34157 | −0.209875 | ||||||||
\(914\) | 59.4755 | 1.96728 | ||||||||
\(915\) | 2.73273 | 0.0903414 | ||||||||
\(916\) | 15.6918 | 0.518471 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −171.446 | −5.65856 | ||||||||
\(919\) | 27.8583 | 0.918962 | 0.459481 | − | 0.888188i | \(-0.348036\pi\) | ||||
0.459481 | + | 0.888188i | \(0.348036\pi\) | |||||||
\(920\) | 1.45871 | 0.0480923 | ||||||||
\(921\) | −46.6742 | −1.53797 | ||||||||
\(922\) | 45.6464 | 1.50328 | ||||||||
\(923\) | −1.09442 | −0.0360233 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −41.4110 | −1.36159 | ||||||||
\(926\) | −47.8963 | −1.57397 | ||||||||
\(927\) | 39.2713 | 1.28984 | ||||||||
\(928\) | −30.8097 | −1.01138 | ||||||||
\(929\) | −51.3944 | −1.68619 | −0.843097 | − | 0.537761i | \(-0.819270\pi\) | ||||
−0.843097 | + | 0.537761i | \(0.819270\pi\) | |||||||
\(930\) | −2.45138 | −0.0803839 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −24.9774 | −0.818162 | ||||||||
\(933\) | −11.6904 | −0.382726 | ||||||||
\(934\) | −47.3179 | −1.54829 | ||||||||
\(935\) | 1.60156 | 0.0523765 | ||||||||
\(936\) | 45.9292 | 1.50124 | ||||||||
\(937\) | 8.07437 | 0.263778 | 0.131889 | − | 0.991264i | \(-0.457896\pi\) | ||||
0.131889 | + | 0.991264i | \(0.457896\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 29.8585 | 0.974397 | ||||||||
\(940\) | −2.28622 | −0.0745684 | ||||||||
\(941\) | −24.3020 | −0.792223 | −0.396112 | − | 0.918202i | \(-0.629641\pi\) | ||||
−0.396112 | + | 0.918202i | \(0.629641\pi\) | |||||||
\(942\) | 128.439 | 4.18478 | ||||||||
\(943\) | −1.74603 | −0.0568586 | ||||||||
\(944\) | 32.2185 | 1.04862 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 9.69023 | 0.315056 | ||||||||
\(947\) | 40.5660 | 1.31822 | 0.659109 | − | 0.752047i | \(-0.270933\pi\) | ||||
0.659109 | + | 0.752047i | \(0.270933\pi\) | |||||||
\(948\) | −11.1344 | −0.361628 | ||||||||
\(949\) | −9.44710 | −0.306666 | ||||||||
\(950\) | 36.3644 | 1.17982 | ||||||||
\(951\) | −38.5083 | −1.24872 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −4.52347 | −0.146529 | −0.0732647 | − | 0.997313i | \(-0.523342\pi\) | ||||
−0.0732647 | + | 0.997313i | \(0.523342\pi\) | |||||||
\(954\) | −133.988 | −4.33802 | ||||||||
\(955\) | −1.78138 | −0.0576440 | ||||||||
\(956\) | −20.2810 | −0.655934 | ||||||||
\(957\) | 21.2430 | 0.686690 | ||||||||
\(958\) | −15.7942 | −0.510288 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −1.52608 | −0.0492540 | ||||||||
\(961\) | −27.8273 | −0.897653 | ||||||||
\(962\) | −45.2725 | −1.45964 | ||||||||
\(963\) | 6.94092 | 0.223668 | ||||||||
\(964\) | −6.50443 | −0.209494 | ||||||||
\(965\) | 0.904322 | 0.0291112 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −48.3508 | −1.55486 | −0.777428 | − | 0.628972i | \(-0.783476\pi\) | ||||
−0.777428 | + | 0.628972i | \(0.783476\pi\) | |||||||
\(968\) | −1.87313 | −0.0602048 | ||||||||
\(969\) | 91.9599 | 2.95418 | ||||||||
\(970\) | 2.02087 | 0.0648861 | ||||||||
\(971\) | 12.7515 | 0.409217 | 0.204608 | − | 0.978844i | \(-0.434408\pi\) | ||||
0.204608 | + | 0.978844i | \(0.434408\pi\) | |||||||
\(972\) | 39.5197 | 1.26759 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 18.1120 | 0.580345 | ||||||||
\(975\) | 51.3076 | 1.64316 | ||||||||
\(976\) | 16.8737 | 0.540114 | ||||||||
\(977\) | 21.9973 | 0.703757 | 0.351879 | − | 0.936046i | \(-0.385543\pi\) | ||||
0.351879 | + | 0.936046i | \(0.385543\pi\) | |||||||
\(978\) | −27.5534 | −0.881060 | ||||||||
\(979\) | −0.246676 | −0.00788379 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 44.2000 | 1.41120 | ||||||||
\(982\) | −34.0306 | −1.08596 | ||||||||
\(983\) | −51.4813 | −1.64200 | −0.820999 | − | 0.570930i | \(-0.806583\pi\) | ||||
−0.820999 | + | 0.570930i | \(0.806583\pi\) | |||||||
\(984\) | 3.39398 | 0.108196 | ||||||||
\(985\) | 0.941350 | 0.0299939 | ||||||||
\(986\) | −71.6927 | −2.28316 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 12.3385 | 0.392541 | ||||||||
\(989\) | 17.9640 | 0.571223 | ||||||||
\(990\) | −3.24851 | −0.103244 | ||||||||
\(991\) | −12.8667 | −0.408724 | −0.204362 | − | 0.978895i | \(-0.565512\pi\) | ||||
−0.204362 | + | 0.978895i | \(0.565512\pi\) | |||||||
\(992\) | −8.46351 | −0.268717 | ||||||||
\(993\) | −84.1144 | −2.66929 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 4.78104 | 0.151569 | ||||||||
\(996\) | −18.6998 | −0.592524 | ||||||||
\(997\) | −30.0438 | −0.951496 | −0.475748 | − | 0.879582i | \(-0.657823\pi\) | ||||
−0.475748 | + | 0.879582i | \(0.657823\pi\) | |||||||
\(998\) | −18.6535 | −0.590468 | ||||||||
\(999\) | 130.008 | 4.11328 |
(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 | 539.2.a.l.1.8 | yes | 10 | |
3.2 | odd | 2 | 4851.2.a.cg.1.4 | 10 | |||
4.3 | odd | 2 | 8624.2.a.df.1.1 | 10 | |||
7.2 | even | 3 | 539.2.e.o.67.3 | 20 | |||
7.3 | odd | 6 | 539.2.e.o.177.4 | 20 | |||
7.4 | even | 3 | 539.2.e.o.177.3 | 20 | |||
7.5 | odd | 6 | 539.2.e.o.67.4 | 20 | |||
7.6 | odd | 2 | inner | 539.2.a.l.1.7 | ✓ | 10 | |
11.10 | odd | 2 | 5929.2.a.bv.1.4 | 10 | |||
21.20 | even | 2 | 4851.2.a.cg.1.3 | 10 | |||
28.27 | even | 2 | 8624.2.a.df.1.10 | 10 | |||
77.76 | even | 2 | 5929.2.a.bv.1.3 | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
539.2.a.l.1.7 | ✓ | 10 | 7.6 | odd | 2 | inner | |
539.2.a.l.1.8 | yes | 10 | 1.1 | even | 1 | trivial | |
539.2.e.o.67.3 | 20 | 7.2 | even | 3 | |||
539.2.e.o.67.4 | 20 | 7.5 | odd | 6 | |||
539.2.e.o.177.3 | 20 | 7.4 | even | 3 | |||
539.2.e.o.177.4 | 20 | 7.3 | odd | 6 | |||
4851.2.a.cg.1.3 | 10 | 21.20 | even | 2 | |||
4851.2.a.cg.1.4 | 10 | 3.2 | odd | 2 | |||
5929.2.a.bv.1.3 | 10 | 77.76 | even | 2 | |||
5929.2.a.bv.1.4 | 10 | 11.10 | odd | 2 | |||
8624.2.a.df.1.1 | 10 | 4.3 | odd | 2 | |||
8624.2.a.df.1.10 | 10 | 28.27 | even | 2 |