Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1849,2,Mod(1,1849)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1849, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1849.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1849 = 43^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1849.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: | \(14.7643393337\) |
Analytic rank: | \(0\) |
Dimension: | \(18\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{18} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{18} - 5 x^{17} - 15 x^{16} + 106 x^{15} + 47 x^{14} - 897 x^{13} + 364 x^{12} + 3855 x^{11} - 3223 x^{10} - 8851 x^{9} + 9909 x^{8} + 10400 x^{7} - 14483 x^{6} - 5118 x^{5} + \cdots - 27 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 43) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.11 | ||
Root | \(1.04477\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1849.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.04477 | 0.738766 | 0.369383 | − | 0.929277i | \(-0.379569\pi\) | ||||
0.369383 | + | 0.929277i | \(0.379569\pi\) | |||||||
\(3\) | −2.52412 | −1.45730 | −0.728651 | − | 0.684885i | \(-0.759853\pi\) | ||||
−0.728651 | + | 0.684885i | \(0.759853\pi\) | |||||||
\(4\) | −0.908449 | −0.454224 | ||||||||
\(5\) | 0.499809 | 0.223521 | 0.111761 | − | 0.993735i | \(-0.464351\pi\) | ||||
0.111761 | + | 0.993735i | \(0.464351\pi\) | |||||||
\(6\) | −2.63714 | −1.07661 | ||||||||
\(7\) | −3.30668 | −1.24981 | −0.624904 | − | 0.780702i | \(-0.714862\pi\) | ||||
−0.624904 | + | 0.780702i | \(0.714862\pi\) | |||||||
\(8\) | −3.03867 | −1.07433 | ||||||||
\(9\) | 3.37119 | 1.12373 | ||||||||
\(10\) | 0.522187 | 0.165130 | ||||||||
\(11\) | −3.72276 | −1.12245 | −0.561227 | − | 0.827662i | \(-0.689670\pi\) | ||||
−0.561227 | + | 0.827662i | \(0.689670\pi\) | |||||||
\(12\) | 2.29304 | 0.661942 | ||||||||
\(13\) | −4.68695 | −1.29993 | −0.649963 | − | 0.759966i | \(-0.725216\pi\) | ||||
−0.649963 | + | 0.759966i | \(0.725216\pi\) | |||||||
\(14\) | −3.45473 | −0.923316 | ||||||||
\(15\) | −1.26158 | −0.325738 | ||||||||
\(16\) | −1.35782 | −0.339456 | ||||||||
\(17\) | −4.59028 | −1.11331 | −0.556653 | − | 0.830745i | \(-0.687915\pi\) | ||||
−0.556653 | + | 0.830745i | \(0.687915\pi\) | |||||||
\(18\) | 3.52213 | 0.830175 | ||||||||
\(19\) | 6.05844 | 1.38990 | 0.694951 | − | 0.719057i | \(-0.255426\pi\) | ||||
0.694951 | + | 0.719057i | \(0.255426\pi\) | |||||||
\(20\) | −0.454051 | −0.101529 | ||||||||
\(21\) | 8.34647 | 1.82135 | ||||||||
\(22\) | −3.88944 | −0.829231 | ||||||||
\(23\) | −0.388946 | −0.0811008 | −0.0405504 | − | 0.999177i | \(-0.512911\pi\) | ||||
−0.0405504 | + | 0.999177i | \(0.512911\pi\) | |||||||
\(24\) | 7.66997 | 1.56563 | ||||||||
\(25\) | −4.75019 | −0.950038 | ||||||||
\(26\) | −4.89680 | −0.960342 | ||||||||
\(27\) | −0.936938 | −0.180314 | ||||||||
\(28\) | 3.00395 | 0.567693 | ||||||||
\(29\) | 3.53498 | 0.656429 | 0.328215 | − | 0.944603i | \(-0.393553\pi\) | ||||
0.328215 | + | 0.944603i | \(0.393553\pi\) | |||||||
\(30\) | −1.31806 | −0.240644 | ||||||||
\(31\) | −0.870839 | −0.156407 | −0.0782037 | − | 0.996937i | \(-0.524918\pi\) | ||||
−0.0782037 | + | 0.996937i | \(0.524918\pi\) | |||||||
\(32\) | 4.65872 | 0.823553 | ||||||||
\(33\) | 9.39670 | 1.63575 | ||||||||
\(34\) | −4.79580 | −0.822473 | ||||||||
\(35\) | −1.65271 | −0.279359 | ||||||||
\(36\) | −3.06256 | −0.510426 | ||||||||
\(37\) | −3.93313 | −0.646602 | −0.323301 | − | 0.946296i | \(-0.604793\pi\) | ||||
−0.323301 | + | 0.946296i | \(0.604793\pi\) | |||||||
\(38\) | 6.32970 | 1.02681 | ||||||||
\(39\) | 11.8304 | 1.89439 | ||||||||
\(40\) | −1.51875 | −0.240136 | ||||||||
\(41\) | −10.7837 | −1.68412 | −0.842062 | − | 0.539380i | \(-0.818659\pi\) | ||||
−0.842062 | + | 0.539380i | \(0.818659\pi\) | |||||||
\(42\) | 8.72017 | 1.34555 | ||||||||
\(43\) | 0 | 0 | ||||||||
\(44\) | 3.38193 | 0.509846 | ||||||||
\(45\) | 1.68495 | 0.251178 | ||||||||
\(46\) | −0.406360 | −0.0599146 | ||||||||
\(47\) | 3.49088 | 0.509197 | 0.254599 | − | 0.967047i | \(-0.418057\pi\) | ||||
0.254599 | + | 0.967047i | \(0.418057\pi\) | |||||||
\(48\) | 3.42731 | 0.494690 | ||||||||
\(49\) | 3.93414 | 0.562020 | ||||||||
\(50\) | −4.96287 | −0.701856 | ||||||||
\(51\) | 11.5864 | 1.62242 | ||||||||
\(52\) | 4.25785 | 0.590458 | ||||||||
\(53\) | 4.77361 | 0.655706 | 0.327853 | − | 0.944729i | \(-0.393675\pi\) | ||||
0.327853 | + | 0.944729i | \(0.393675\pi\) | |||||||
\(54\) | −0.978888 | −0.133210 | ||||||||
\(55\) | −1.86067 | −0.250892 | ||||||||
\(56\) | 10.0479 | 1.34271 | ||||||||
\(57\) | −15.2923 | −2.02551 | ||||||||
\(58\) | 3.69325 | 0.484948 | ||||||||
\(59\) | 6.72259 | 0.875207 | 0.437603 | − | 0.899168i | \(-0.355827\pi\) | ||||
0.437603 | + | 0.899168i | \(0.355827\pi\) | |||||||
\(60\) | 1.14608 | 0.147958 | ||||||||
\(61\) | −5.24696 | −0.671805 | −0.335902 | − | 0.941897i | \(-0.609041\pi\) | ||||
−0.335902 | + | 0.941897i | \(0.609041\pi\) | |||||||
\(62\) | −0.909829 | −0.115548 | ||||||||
\(63\) | −11.1475 | −1.40445 | ||||||||
\(64\) | 7.58295 | 0.947869 | ||||||||
\(65\) | −2.34258 | −0.290561 | ||||||||
\(66\) | 9.81742 | 1.20844 | ||||||||
\(67\) | 10.5533 | 1.28929 | 0.644645 | − | 0.764482i | \(-0.277005\pi\) | ||||
0.644645 | + | 0.764482i | \(0.277005\pi\) | |||||||
\(68\) | 4.17003 | 0.505691 | ||||||||
\(69\) | 0.981747 | 0.118188 | ||||||||
\(70\) | −1.72670 | −0.206381 | ||||||||
\(71\) | −0.899542 | −0.106756 | −0.0533780 | − | 0.998574i | \(-0.516999\pi\) | ||||
−0.0533780 | + | 0.998574i | \(0.516999\pi\) | |||||||
\(72\) | −10.2439 | −1.20726 | ||||||||
\(73\) | 0.966562 | 0.113128 | 0.0565638 | − | 0.998399i | \(-0.481986\pi\) | ||||
0.0565638 | + | 0.998399i | \(0.481986\pi\) | |||||||
\(74\) | −4.10922 | −0.477688 | ||||||||
\(75\) | 11.9901 | 1.38449 | ||||||||
\(76\) | −5.50379 | −0.631328 | ||||||||
\(77\) | 12.3100 | 1.40285 | ||||||||
\(78\) | 12.3601 | 1.39951 | ||||||||
\(79\) | −1.00197 | −0.112730 | −0.0563650 | − | 0.998410i | \(-0.517951\pi\) | ||||
−0.0563650 | + | 0.998410i | \(0.517951\pi\) | |||||||
\(80\) | −0.678652 | −0.0758756 | ||||||||
\(81\) | −7.74863 | −0.860959 | ||||||||
\(82\) | −11.2665 | −1.24417 | ||||||||
\(83\) | −3.41592 | −0.374946 | −0.187473 | − | 0.982270i | \(-0.560030\pi\) | ||||
−0.187473 | + | 0.982270i | \(0.560030\pi\) | |||||||
\(84\) | −7.58234 | −0.827301 | ||||||||
\(85\) | −2.29426 | −0.248847 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −8.92272 | −0.956616 | ||||||||
\(88\) | 11.3122 | 1.20589 | ||||||||
\(89\) | 1.84065 | 0.195108 | 0.0975542 | − | 0.995230i | \(-0.468898\pi\) | ||||
0.0975542 | + | 0.995230i | \(0.468898\pi\) | |||||||
\(90\) | 1.76039 | 0.185562 | ||||||||
\(91\) | 15.4982 | 1.62466 | ||||||||
\(92\) | 0.353338 | 0.0368380 | ||||||||
\(93\) | 2.19810 | 0.227933 | ||||||||
\(94\) | 3.64718 | 0.376178 | ||||||||
\(95\) | 3.02806 | 0.310673 | ||||||||
\(96\) | −11.7592 | −1.20017 | ||||||||
\(97\) | 0.960596 | 0.0975337 | 0.0487669 | − | 0.998810i | \(-0.484471\pi\) | ||||
0.0487669 | + | 0.998810i | \(0.484471\pi\) | |||||||
\(98\) | 4.11028 | 0.415201 | ||||||||
\(99\) | −12.5501 | −1.26134 | ||||||||
\(100\) | 4.31531 | 0.431531 | ||||||||
\(101\) | 16.4388 | 1.63572 | 0.817862 | − | 0.575414i | \(-0.195159\pi\) | ||||
0.817862 | + | 0.575414i | \(0.195159\pi\) | |||||||
\(102\) | 12.1052 | 1.19859 | ||||||||
\(103\) | −0.572128 | −0.0563735 | −0.0281867 | − | 0.999603i | \(-0.508973\pi\) | ||||
−0.0281867 | + | 0.999603i | \(0.508973\pi\) | |||||||
\(104\) | 14.2421 | 1.39655 | ||||||||
\(105\) | 4.17164 | 0.407110 | ||||||||
\(106\) | 4.98734 | 0.484413 | ||||||||
\(107\) | −16.1723 | −1.56343 | −0.781716 | − | 0.623634i | \(-0.785656\pi\) | ||||
−0.781716 | + | 0.623634i | \(0.785656\pi\) | |||||||
\(108\) | 0.851160 | 0.0819029 | ||||||||
\(109\) | −6.52710 | −0.625182 | −0.312591 | − | 0.949888i | \(-0.601197\pi\) | ||||
−0.312591 | + | 0.949888i | \(0.601197\pi\) | |||||||
\(110\) | −1.94397 | −0.185351 | ||||||||
\(111\) | 9.92769 | 0.942295 | ||||||||
\(112\) | 4.48989 | 0.424255 | ||||||||
\(113\) | 1.70054 | 0.159974 | 0.0799868 | − | 0.996796i | \(-0.474512\pi\) | ||||
0.0799868 | + | 0.996796i | \(0.474512\pi\) | |||||||
\(114\) | −15.9769 | −1.49638 | ||||||||
\(115\) | −0.194399 | −0.0181278 | ||||||||
\(116\) | −3.21135 | −0.298166 | ||||||||
\(117\) | −15.8006 | −1.46077 | ||||||||
\(118\) | 7.02358 | 0.646573 | ||||||||
\(119\) | 15.1786 | 1.39142 | ||||||||
\(120\) | 3.83352 | 0.349951 | ||||||||
\(121\) | 2.85893 | 0.259902 | ||||||||
\(122\) | −5.48189 | −0.496307 | ||||||||
\(123\) | 27.2193 | 2.45428 | ||||||||
\(124\) | 0.791113 | 0.0710440 | ||||||||
\(125\) | −4.87323 | −0.435875 | ||||||||
\(126\) | −11.6466 | −1.03756 | ||||||||
\(127\) | 15.6958 | 1.39277 | 0.696387 | − | 0.717666i | \(-0.254790\pi\) | ||||
0.696387 | + | 0.717666i | \(0.254790\pi\) | |||||||
\(128\) | −1.39498 | −0.123300 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −2.44746 | −0.214657 | ||||||||
\(131\) | 10.7262 | 0.937151 | 0.468576 | − | 0.883423i | \(-0.344767\pi\) | ||||
0.468576 | + | 0.883423i | \(0.344767\pi\) | |||||||
\(132\) | −8.53642 | −0.743000 | ||||||||
\(133\) | −20.0333 | −1.73711 | ||||||||
\(134\) | 11.0258 | 0.952484 | ||||||||
\(135\) | −0.468290 | −0.0403040 | ||||||||
\(136\) | 13.9483 | 1.19606 | ||||||||
\(137\) | 8.08569 | 0.690807 | 0.345404 | − | 0.938454i | \(-0.387742\pi\) | ||||
0.345404 | + | 0.938454i | \(0.387742\pi\) | |||||||
\(138\) | 1.02570 | 0.0873137 | ||||||||
\(139\) | 12.8655 | 1.09124 | 0.545620 | − | 0.838032i | \(-0.316294\pi\) | ||||
0.545620 | + | 0.838032i | \(0.316294\pi\) | |||||||
\(140\) | 1.50140 | 0.126891 | ||||||||
\(141\) | −8.81141 | −0.742054 | ||||||||
\(142\) | −0.939817 | −0.0788677 | ||||||||
\(143\) | 17.4484 | 1.45911 | ||||||||
\(144\) | −4.57748 | −0.381457 | ||||||||
\(145\) | 1.76681 | 0.146726 | ||||||||
\(146\) | 1.00984 | 0.0835748 | ||||||||
\(147\) | −9.93025 | −0.819033 | ||||||||
\(148\) | 3.57304 | 0.293702 | ||||||||
\(149\) | 7.44008 | 0.609515 | 0.304757 | − | 0.952430i | \(-0.401425\pi\) | ||||
0.304757 | + | 0.952430i | \(0.401425\pi\) | |||||||
\(150\) | 12.5269 | 1.02282 | ||||||||
\(151\) | 4.77560 | 0.388633 | 0.194316 | − | 0.980939i | \(-0.437751\pi\) | ||||
0.194316 | + | 0.980939i | \(0.437751\pi\) | |||||||
\(152\) | −18.4096 | −1.49322 | ||||||||
\(153\) | −15.4747 | −1.25106 | ||||||||
\(154\) | 12.8611 | 1.03638 | ||||||||
\(155\) | −0.435253 | −0.0349604 | ||||||||
\(156\) | −10.7473 | −0.860476 | ||||||||
\(157\) | −13.4410 | −1.07271 | −0.536354 | − | 0.843993i | \(-0.680199\pi\) | ||||
−0.536354 | + | 0.843993i | \(0.680199\pi\) | |||||||
\(158\) | −1.04683 | −0.0832811 | ||||||||
\(159\) | −12.0492 | −0.955562 | ||||||||
\(160\) | 2.32847 | 0.184082 | ||||||||
\(161\) | 1.28612 | 0.101360 | ||||||||
\(162\) | −8.09557 | −0.636048 | ||||||||
\(163\) | −18.7293 | −1.46699 | −0.733496 | − | 0.679694i | \(-0.762113\pi\) | ||||
−0.733496 | + | 0.679694i | \(0.762113\pi\) | |||||||
\(164\) | 9.79640 | 0.764970 | ||||||||
\(165\) | 4.69655 | 0.365626 | ||||||||
\(166\) | −3.56886 | −0.276997 | ||||||||
\(167\) | −13.8552 | −1.07215 | −0.536075 | − | 0.844170i | \(-0.680094\pi\) | ||||
−0.536075 | + | 0.844170i | \(0.680094\pi\) | |||||||
\(168\) | −25.3622 | −1.95673 | ||||||||
\(169\) | 8.96750 | 0.689808 | ||||||||
\(170\) | −2.39698 | −0.183840 | ||||||||
\(171\) | 20.4242 | 1.56188 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −13.8705 | −1.05456 | −0.527278 | − | 0.849693i | \(-0.676787\pi\) | ||||
−0.527278 | + | 0.849693i | \(0.676787\pi\) | |||||||
\(174\) | −9.32222 | −0.706716 | ||||||||
\(175\) | 15.7074 | 1.18737 | ||||||||
\(176\) | 5.05485 | 0.381023 | ||||||||
\(177\) | −16.9686 | −1.27544 | ||||||||
\(178\) | 1.92306 | 0.144140 | ||||||||
\(179\) | −6.18438 | −0.462242 | −0.231121 | − | 0.972925i | \(-0.574239\pi\) | ||||
−0.231121 | + | 0.972925i | \(0.574239\pi\) | |||||||
\(180\) | −1.53069 | −0.114091 | ||||||||
\(181\) | 3.70276 | 0.275224 | 0.137612 | − | 0.990486i | \(-0.456057\pi\) | ||||
0.137612 | + | 0.990486i | \(0.456057\pi\) | |||||||
\(182\) | 16.1922 | 1.20024 | ||||||||
\(183\) | 13.2440 | 0.979023 | ||||||||
\(184\) | 1.18188 | 0.0871292 | ||||||||
\(185\) | −1.96581 | −0.144529 | ||||||||
\(186\) | 2.29652 | 0.168389 | ||||||||
\(187\) | 17.0885 | 1.24963 | ||||||||
\(188\) | −3.17128 | −0.231290 | ||||||||
\(189\) | 3.09815 | 0.225358 | ||||||||
\(190\) | 3.16364 | 0.229515 | ||||||||
\(191\) | −11.4154 | −0.825991 | −0.412995 | − | 0.910733i | \(-0.635517\pi\) | ||||
−0.412995 | + | 0.910733i | \(0.635517\pi\) | |||||||
\(192\) | −19.1403 | −1.38133 | ||||||||
\(193\) | −8.44971 | −0.608223 | −0.304112 | − | 0.952636i | \(-0.598360\pi\) | ||||
−0.304112 | + | 0.952636i | \(0.598360\pi\) | |||||||
\(194\) | 1.00360 | 0.0720546 | ||||||||
\(195\) | 5.91295 | 0.423435 | ||||||||
\(196\) | −3.57396 | −0.255283 | ||||||||
\(197\) | −21.6649 | −1.54356 | −0.771780 | − | 0.635890i | \(-0.780633\pi\) | ||||
−0.771780 | + | 0.635890i | \(0.780633\pi\) | |||||||
\(198\) | −13.1120 | −0.931833 | ||||||||
\(199\) | 9.87849 | 0.700267 | 0.350134 | − | 0.936700i | \(-0.386136\pi\) | ||||
0.350134 | + | 0.936700i | \(0.386136\pi\) | |||||||
\(200\) | 14.4343 | 1.02066 | ||||||||
\(201\) | −26.6378 | −1.87889 | ||||||||
\(202\) | 17.1748 | 1.20842 | ||||||||
\(203\) | −11.6890 | −0.820410 | ||||||||
\(204\) | −10.5257 | −0.736944 | ||||||||
\(205\) | −5.38977 | −0.376438 | ||||||||
\(206\) | −0.597744 | −0.0416468 | ||||||||
\(207\) | −1.31121 | −0.0911356 | ||||||||
\(208\) | 6.36405 | 0.441267 | ||||||||
\(209\) | −22.5541 | −1.56010 | ||||||||
\(210\) | 4.35841 | 0.300759 | ||||||||
\(211\) | 15.2999 | 1.05329 | 0.526644 | − | 0.850086i | \(-0.323450\pi\) | ||||
0.526644 | + | 0.850086i | \(0.323450\pi\) | |||||||
\(212\) | −4.33658 | −0.297838 | ||||||||
\(213\) | 2.27055 | 0.155576 | ||||||||
\(214\) | −16.8964 | −1.15501 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 2.84704 | 0.193717 | ||||||||
\(217\) | 2.87959 | 0.195479 | ||||||||
\(218\) | −6.81934 | −0.461864 | ||||||||
\(219\) | −2.43972 | −0.164861 | ||||||||
\(220\) | 1.69032 | 0.113961 | ||||||||
\(221\) | 21.5144 | 1.44722 | ||||||||
\(222\) | 10.3722 | 0.696135 | ||||||||
\(223\) | −11.7167 | −0.784608 | −0.392304 | − | 0.919836i | \(-0.628322\pi\) | ||||
−0.392304 | + | 0.919836i | \(0.628322\pi\) | |||||||
\(224\) | −15.4049 | −1.02928 | ||||||||
\(225\) | −16.0138 | −1.06759 | ||||||||
\(226\) | 1.77668 | 0.118183 | ||||||||
\(227\) | −9.03975 | −0.599989 | −0.299995 | − | 0.953941i | \(-0.596985\pi\) | ||||
−0.299995 | + | 0.953941i | \(0.596985\pi\) | |||||||
\(228\) | 13.8922 | 0.920035 | ||||||||
\(229\) | −15.5978 | −1.03073 | −0.515366 | − | 0.856970i | \(-0.672344\pi\) | ||||
−0.515366 | + | 0.856970i | \(0.672344\pi\) | |||||||
\(230\) | −0.203102 | −0.0133922 | ||||||||
\(231\) | −31.0719 | −2.04438 | ||||||||
\(232\) | −10.7416 | −0.705223 | ||||||||
\(233\) | 4.69718 | 0.307722 | 0.153861 | − | 0.988092i | \(-0.450829\pi\) | ||||
0.153861 | + | 0.988092i | \(0.450829\pi\) | |||||||
\(234\) | −16.5081 | −1.07917 | ||||||||
\(235\) | 1.74477 | 0.113816 | ||||||||
\(236\) | −6.10713 | −0.397540 | ||||||||
\(237\) | 2.52908 | 0.164282 | ||||||||
\(238\) | 15.8582 | 1.02793 | ||||||||
\(239\) | −4.11467 | −0.266156 | −0.133078 | − | 0.991106i | \(-0.542486\pi\) | ||||
−0.133078 | + | 0.991106i | \(0.542486\pi\) | |||||||
\(240\) | 1.71300 | 0.110574 | ||||||||
\(241\) | −3.26436 | −0.210276 | −0.105138 | − | 0.994458i | \(-0.533528\pi\) | ||||
−0.105138 | + | 0.994458i | \(0.533528\pi\) | |||||||
\(242\) | 2.98693 | 0.192007 | ||||||||
\(243\) | 22.3693 | 1.43499 | ||||||||
\(244\) | 4.76660 | 0.305150 | ||||||||
\(245\) | 1.96632 | 0.125623 | ||||||||
\(246\) | 28.4380 | 1.81314 | ||||||||
\(247\) | −28.3956 | −1.80677 | ||||||||
\(248\) | 2.64619 | 0.168033 | ||||||||
\(249\) | 8.62220 | 0.546410 | ||||||||
\(250\) | −5.09142 | −0.322010 | ||||||||
\(251\) | 5.47251 | 0.345422 | 0.172711 | − | 0.984973i | \(-0.444747\pi\) | ||||
0.172711 | + | 0.984973i | \(0.444747\pi\) | |||||||
\(252\) | 10.1269 | 0.637935 | ||||||||
\(253\) | 1.44795 | 0.0910319 | ||||||||
\(254\) | 16.3985 | 1.02893 | ||||||||
\(255\) | 5.79099 | 0.362646 | ||||||||
\(256\) | −16.6233 | −1.03896 | ||||||||
\(257\) | 8.41973 | 0.525208 | 0.262604 | − | 0.964904i | \(-0.415419\pi\) | ||||
0.262604 | + | 0.964904i | \(0.415419\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 13.0056 | 0.808128 | ||||||||
\(260\) | 2.12811 | 0.131980 | ||||||||
\(261\) | 11.9171 | 0.737650 | ||||||||
\(262\) | 11.2064 | 0.692336 | ||||||||
\(263\) | −6.11997 | −0.377374 | −0.188687 | − | 0.982037i | \(-0.560423\pi\) | ||||
−0.188687 | + | 0.982037i | \(0.560423\pi\) | |||||||
\(264\) | −28.5535 | −1.75734 | ||||||||
\(265\) | 2.38589 | 0.146564 | ||||||||
\(266\) | −20.9303 | −1.28332 | ||||||||
\(267\) | −4.64602 | −0.284332 | ||||||||
\(268\) | −9.58712 | −0.585627 | ||||||||
\(269\) | 2.29453 | 0.139900 | 0.0699500 | − | 0.997550i | \(-0.477716\pi\) | ||||
0.0699500 | + | 0.997550i | \(0.477716\pi\) | |||||||
\(270\) | −0.489256 | −0.0297752 | ||||||||
\(271\) | 27.3969 | 1.66425 | 0.832123 | − | 0.554591i | \(-0.187125\pi\) | ||||
0.832123 | + | 0.554591i | \(0.187125\pi\) | |||||||
\(272\) | 6.23279 | 0.377918 | ||||||||
\(273\) | −39.1195 | −2.36762 | ||||||||
\(274\) | 8.44771 | 0.510345 | ||||||||
\(275\) | 17.6838 | 1.06637 | ||||||||
\(276\) | −0.891867 | −0.0536841 | ||||||||
\(277\) | 26.5986 | 1.59815 | 0.799077 | − | 0.601229i | \(-0.205322\pi\) | ||||
0.799077 | + | 0.601229i | \(0.205322\pi\) | |||||||
\(278\) | 13.4416 | 0.806172 | ||||||||
\(279\) | −2.93577 | −0.175760 | ||||||||
\(280\) | 5.02203 | 0.300124 | ||||||||
\(281\) | 16.6768 | 0.994852 | 0.497426 | − | 0.867506i | \(-0.334279\pi\) | ||||
0.497426 | + | 0.867506i | \(0.334279\pi\) | |||||||
\(282\) | −9.20592 | −0.548205 | ||||||||
\(283\) | 17.1076 | 1.01694 | 0.508471 | − | 0.861079i | \(-0.330211\pi\) | ||||
0.508471 | + | 0.861079i | \(0.330211\pi\) | |||||||
\(284\) | 0.817188 | 0.0484912 | ||||||||
\(285\) | −7.64320 | −0.452744 | ||||||||
\(286\) | 18.2296 | 1.07794 | ||||||||
\(287\) | 35.6581 | 2.10483 | ||||||||
\(288\) | 15.7055 | 0.925453 | ||||||||
\(289\) | 4.07065 | 0.239450 | ||||||||
\(290\) | 1.84592 | 0.108396 | ||||||||
\(291\) | −2.42466 | −0.142136 | ||||||||
\(292\) | −0.878072 | −0.0513853 | ||||||||
\(293\) | −29.9122 | −1.74749 | −0.873744 | − | 0.486387i | \(-0.838315\pi\) | ||||
−0.873744 | + | 0.486387i | \(0.838315\pi\) | |||||||
\(294\) | −10.3749 | −0.605074 | ||||||||
\(295\) | 3.36001 | 0.195627 | ||||||||
\(296\) | 11.9515 | 0.694665 | ||||||||
\(297\) | 3.48799 | 0.202394 | ||||||||
\(298\) | 7.77319 | 0.450289 | ||||||||
\(299\) | 1.82297 | 0.105425 | ||||||||
\(300\) | −10.8924 | −0.628871 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 4.98942 | 0.287109 | ||||||||
\(303\) | −41.4936 | −2.38375 | ||||||||
\(304\) | −8.22630 | −0.471810 | ||||||||
\(305\) | −2.62248 | −0.150163 | ||||||||
\(306\) | −16.1676 | −0.924238 | ||||||||
\(307\) | −13.4430 | −0.767230 | −0.383615 | − | 0.923493i | \(-0.625321\pi\) | ||||
−0.383615 | + | 0.923493i | \(0.625321\pi\) | |||||||
\(308\) | −11.1830 | −0.637209 | ||||||||
\(309\) | 1.44412 | 0.0821532 | ||||||||
\(310\) | −0.454741 | −0.0258275 | ||||||||
\(311\) | 15.1900 | 0.861347 | 0.430673 | − | 0.902508i | \(-0.358276\pi\) | ||||
0.430673 | + | 0.902508i | \(0.358276\pi\) | |||||||
\(312\) | −35.9488 | −2.03520 | ||||||||
\(313\) | −11.3920 | −0.643913 | −0.321956 | − | 0.946754i | \(-0.604340\pi\) | ||||
−0.321956 | + | 0.946754i | \(0.604340\pi\) | |||||||
\(314\) | −14.0428 | −0.792480 | ||||||||
\(315\) | −5.57160 | −0.313924 | ||||||||
\(316\) | 0.910235 | 0.0512047 | ||||||||
\(317\) | −22.8190 | −1.28164 | −0.640822 | − | 0.767689i | \(-0.721406\pi\) | ||||
−0.640822 | + | 0.767689i | \(0.721406\pi\) | |||||||
\(318\) | −12.5887 | −0.705937 | ||||||||
\(319\) | −13.1599 | −0.736811 | ||||||||
\(320\) | 3.79003 | 0.211869 | ||||||||
\(321\) | 40.8208 | 2.27840 | ||||||||
\(322\) | 1.34370 | 0.0748817 | ||||||||
\(323\) | −27.8099 | −1.54739 | ||||||||
\(324\) | 7.03924 | 0.391069 | ||||||||
\(325\) | 22.2639 | 1.23498 | ||||||||
\(326\) | −19.5679 | −1.08376 | ||||||||
\(327\) | 16.4752 | 0.911080 | ||||||||
\(328\) | 32.7680 | 1.80931 | ||||||||
\(329\) | −11.5432 | −0.636399 | ||||||||
\(330\) | 4.90683 | 0.270112 | ||||||||
\(331\) | −15.5508 | −0.854747 | −0.427373 | − | 0.904075i | \(-0.640561\pi\) | ||||
−0.427373 | + | 0.904075i | \(0.640561\pi\) | |||||||
\(332\) | 3.10319 | 0.170310 | ||||||||
\(333\) | −13.2593 | −0.726607 | ||||||||
\(334\) | −14.4756 | −0.792068 | ||||||||
\(335\) | 5.27463 | 0.288184 | ||||||||
\(336\) | −11.3330 | −0.618267 | ||||||||
\(337\) | 14.9040 | 0.811871 | 0.405935 | − | 0.913902i | \(-0.366946\pi\) | ||||
0.405935 | + | 0.913902i | \(0.366946\pi\) | |||||||
\(338\) | 9.36901 | 0.509607 | ||||||||
\(339\) | −4.29238 | −0.233130 | ||||||||
\(340\) | 2.08422 | 0.113033 | ||||||||
\(341\) | 3.24192 | 0.175560 | ||||||||
\(342\) | 21.3386 | 1.15386 | ||||||||
\(343\) | 10.1378 | 0.547391 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0.490686 | 0.0264176 | ||||||||
\(346\) | −14.4915 | −0.779071 | ||||||||
\(347\) | −27.1661 | −1.45835 | −0.729177 | − | 0.684325i | \(-0.760097\pi\) | ||||
−0.729177 | + | 0.684325i | \(0.760097\pi\) | |||||||
\(348\) | 8.10583 | 0.434518 | ||||||||
\(349\) | −28.3556 | −1.51784 | −0.758920 | − | 0.651184i | \(-0.774273\pi\) | ||||
−0.758920 | + | 0.651184i | \(0.774273\pi\) | |||||||
\(350\) | 16.4106 | 0.877185 | ||||||||
\(351\) | 4.39138 | 0.234395 | ||||||||
\(352\) | −17.3433 | −0.924401 | ||||||||
\(353\) | −19.7233 | −1.04977 | −0.524883 | − | 0.851175i | \(-0.675891\pi\) | ||||
−0.524883 | + | 0.851175i | \(0.675891\pi\) | |||||||
\(354\) | −17.7284 | −0.942253 | ||||||||
\(355\) | −0.449599 | −0.0238622 | ||||||||
\(356\) | −1.67214 | −0.0886230 | ||||||||
\(357\) | −38.3126 | −2.02772 | ||||||||
\(358\) | −6.46127 | −0.341489 | ||||||||
\(359\) | −28.1781 | −1.48718 | −0.743592 | − | 0.668633i | \(-0.766880\pi\) | ||||
−0.743592 | + | 0.668633i | \(0.766880\pi\) | |||||||
\(360\) | −5.12001 | −0.269848 | ||||||||
\(361\) | 17.7047 | 0.931829 | ||||||||
\(362\) | 3.86854 | 0.203326 | ||||||||
\(363\) | −7.21628 | −0.378756 | ||||||||
\(364\) | −14.0794 | −0.737959 | ||||||||
\(365\) | 0.483096 | 0.0252864 | ||||||||
\(366\) | 13.8370 | 0.723269 | ||||||||
\(367\) | −29.5394 | −1.54194 | −0.770972 | − | 0.636869i | \(-0.780229\pi\) | ||||
−0.770972 | + | 0.636869i | \(0.780229\pi\) | |||||||
\(368\) | 0.528120 | 0.0275302 | ||||||||
\(369\) | −36.3538 | −1.89250 | ||||||||
\(370\) | −2.05383 | −0.106773 | ||||||||
\(371\) | −15.7848 | −0.819506 | ||||||||
\(372\) | −1.99687 | −0.103533 | ||||||||
\(373\) | 32.1477 | 1.66454 | 0.832272 | − | 0.554367i | \(-0.187040\pi\) | ||||
0.832272 | + | 0.554367i | \(0.187040\pi\) | |||||||
\(374\) | 17.8536 | 0.923188 | ||||||||
\(375\) | 12.3006 | 0.635202 | ||||||||
\(376\) | −10.6076 | −0.547047 | ||||||||
\(377\) | −16.5683 | −0.853309 | ||||||||
\(378\) | 3.23687 | 0.166487 | ||||||||
\(379\) | −18.0279 | −0.926033 | −0.463017 | − | 0.886350i | \(-0.653233\pi\) | ||||
−0.463017 | + | 0.886350i | \(0.653233\pi\) | |||||||
\(380\) | −2.75084 | −0.141115 | ||||||||
\(381\) | −39.6180 | −2.02969 | ||||||||
\(382\) | −11.9265 | −0.610214 | ||||||||
\(383\) | 22.9648 | 1.17345 | 0.586724 | − | 0.809787i | \(-0.300417\pi\) | ||||
0.586724 | + | 0.809787i | \(0.300417\pi\) | |||||||
\(384\) | 3.52109 | 0.179685 | ||||||||
\(385\) | 6.15263 | 0.313567 | ||||||||
\(386\) | −8.82803 | −0.449335 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −0.872652 | −0.0443022 | ||||||||
\(389\) | 22.8174 | 1.15689 | 0.578445 | − | 0.815721i | \(-0.303660\pi\) | ||||
0.578445 | + | 0.815721i | \(0.303660\pi\) | |||||||
\(390\) | 6.17770 | 0.312820 | ||||||||
\(391\) | 1.78537 | 0.0902901 | ||||||||
\(392\) | −11.9545 | −0.603796 | ||||||||
\(393\) | −27.0742 | −1.36571 | ||||||||
\(394\) | −22.6349 | −1.14033 | ||||||||
\(395\) | −0.500791 | −0.0251975 | ||||||||
\(396\) | 11.4012 | 0.572930 | ||||||||
\(397\) | −8.63189 | −0.433222 | −0.216611 | − | 0.976258i | \(-0.569500\pi\) | ||||
−0.216611 | + | 0.976258i | \(0.569500\pi\) | |||||||
\(398\) | 10.3208 | 0.517334 | ||||||||
\(399\) | 50.5666 | 2.53150 | ||||||||
\(400\) | 6.44992 | 0.322496 | ||||||||
\(401\) | 33.8253 | 1.68916 | 0.844578 | − | 0.535433i | \(-0.179852\pi\) | ||||
0.844578 | + | 0.535433i | \(0.179852\pi\) | |||||||
\(402\) | −27.8305 | −1.38806 | ||||||||
\(403\) | 4.08158 | 0.203318 | ||||||||
\(404\) | −14.9338 | −0.742986 | ||||||||
\(405\) | −3.87283 | −0.192443 | ||||||||
\(406\) | −12.2124 | −0.606091 | ||||||||
\(407\) | 14.6421 | 0.725781 | ||||||||
\(408\) | −35.2073 | −1.74302 | ||||||||
\(409\) | 25.6569 | 1.26865 | 0.634326 | − | 0.773065i | \(-0.281278\pi\) | ||||
0.634326 | + | 0.773065i | \(0.281278\pi\) | |||||||
\(410\) | −5.63108 | −0.278099 | ||||||||
\(411\) | −20.4093 | −1.00672 | ||||||||
\(412\) | 0.519749 | 0.0256062 | ||||||||
\(413\) | −22.2295 | −1.09384 | ||||||||
\(414\) | −1.36992 | −0.0673279 | ||||||||
\(415\) | −1.70731 | −0.0838083 | ||||||||
\(416\) | −21.8352 | −1.07056 | ||||||||
\(417\) | −32.4742 | −1.59027 | ||||||||
\(418\) | −23.5639 | −1.15255 | ||||||||
\(419\) | 24.8323 | 1.21314 | 0.606570 | − | 0.795030i | \(-0.292545\pi\) | ||||
0.606570 | + | 0.795030i | \(0.292545\pi\) | |||||||
\(420\) | −3.78972 | −0.184919 | ||||||||
\(421\) | −19.2945 | −0.940356 | −0.470178 | − | 0.882571i | \(-0.655810\pi\) | ||||
−0.470178 | + | 0.882571i | \(0.655810\pi\) | |||||||
\(422\) | 15.9849 | 0.778134 | ||||||||
\(423\) | 11.7684 | 0.572201 | ||||||||
\(424\) | −14.5054 | −0.704446 | ||||||||
\(425\) | 21.8047 | 1.05768 | ||||||||
\(426\) | 2.37221 | 0.114934 | ||||||||
\(427\) | 17.3500 | 0.839627 | ||||||||
\(428\) | 14.6917 | 0.710149 | ||||||||
\(429\) | −44.0418 | −2.12636 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 32.4273 | 1.56197 | 0.780983 | − | 0.624552i | \(-0.214718\pi\) | ||||
0.780983 | + | 0.624552i | \(0.214718\pi\) | |||||||
\(432\) | 1.27220 | 0.0612085 | ||||||||
\(433\) | 17.1636 | 0.824828 | 0.412414 | − | 0.910997i | \(-0.364686\pi\) | ||||
0.412414 | + | 0.910997i | \(0.364686\pi\) | |||||||
\(434\) | 3.00852 | 0.144413 | ||||||||
\(435\) | −4.45965 | −0.213824 | ||||||||
\(436\) | 5.92953 | 0.283973 | ||||||||
\(437\) | −2.35641 | −0.112722 | ||||||||
\(438\) | −2.54896 | −0.121794 | ||||||||
\(439\) | 14.4303 | 0.688720 | 0.344360 | − | 0.938838i | \(-0.388096\pi\) | ||||
0.344360 | + | 0.938838i | \(0.388096\pi\) | |||||||
\(440\) | 5.65395 | 0.269542 | ||||||||
\(441\) | 13.2627 | 0.631559 | ||||||||
\(442\) | 22.4777 | 1.06915 | ||||||||
\(443\) | 19.0065 | 0.903024 | 0.451512 | − | 0.892265i | \(-0.350885\pi\) | ||||
0.451512 | + | 0.892265i | \(0.350885\pi\) | |||||||
\(444\) | −9.01880 | −0.428013 | ||||||||
\(445\) | 0.919972 | 0.0436109 | ||||||||
\(446\) | −12.2413 | −0.579642 | ||||||||
\(447\) | −18.7797 | −0.888248 | ||||||||
\(448\) | −25.0744 | −1.18465 | ||||||||
\(449\) | −5.33116 | −0.251593 | −0.125797 | − | 0.992056i | \(-0.540149\pi\) | ||||
−0.125797 | + | 0.992056i | \(0.540149\pi\) | |||||||
\(450\) | −16.7308 | −0.788698 | ||||||||
\(451\) | 40.1449 | 1.89035 | ||||||||
\(452\) | −1.54486 | −0.0726639 | ||||||||
\(453\) | −12.0542 | −0.566355 | ||||||||
\(454\) | −9.44449 | −0.443252 | ||||||||
\(455\) | 7.74616 | 0.363146 | ||||||||
\(456\) | 46.4681 | 2.17607 | ||||||||
\(457\) | −7.95238 | −0.371997 | −0.185998 | − | 0.982550i | \(-0.559552\pi\) | ||||
−0.185998 | + | 0.982550i | \(0.559552\pi\) | |||||||
\(458\) | −16.2962 | −0.761470 | ||||||||
\(459\) | 4.30080 | 0.200744 | ||||||||
\(460\) | 0.176601 | 0.00823407 | ||||||||
\(461\) | 42.5990 | 1.98403 | 0.992016 | − | 0.126115i | \(-0.0402510\pi\) | ||||
0.992016 | + | 0.126115i | \(0.0402510\pi\) | |||||||
\(462\) | −32.4631 | −1.51032 | ||||||||
\(463\) | 5.69293 | 0.264573 | 0.132286 | − | 0.991212i | \(-0.457768\pi\) | ||||
0.132286 | + | 0.991212i | \(0.457768\pi\) | |||||||
\(464\) | −4.79988 | −0.222829 | ||||||||
\(465\) | 1.09863 | 0.0509478 | ||||||||
\(466\) | 4.90749 | 0.227335 | ||||||||
\(467\) | 7.38749 | 0.341852 | 0.170926 | − | 0.985284i | \(-0.445324\pi\) | ||||
0.170926 | + | 0.985284i | \(0.445324\pi\) | |||||||
\(468\) | 14.3541 | 0.663516 | ||||||||
\(469\) | −34.8964 | −1.61136 | ||||||||
\(470\) | 1.82289 | 0.0840837 | ||||||||
\(471\) | 33.9267 | 1.56326 | ||||||||
\(472\) | −20.4277 | −0.940263 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 2.64232 | 0.121366 | ||||||||
\(475\) | −28.7788 | −1.32046 | ||||||||
\(476\) | −13.7890 | −0.632016 | ||||||||
\(477\) | 16.0928 | 0.736837 | ||||||||
\(478\) | −4.29889 | −0.196627 | ||||||||
\(479\) | 20.7081 | 0.946177 | 0.473089 | − | 0.881015i | \(-0.343139\pi\) | ||||
0.473089 | + | 0.881015i | \(0.343139\pi\) | |||||||
\(480\) | −5.87734 | −0.268263 | ||||||||
\(481\) | 18.4344 | 0.840535 | ||||||||
\(482\) | −3.41051 | −0.155345 | ||||||||
\(483\) | −3.24633 | −0.147713 | ||||||||
\(484\) | −2.59719 | −0.118054 | ||||||||
\(485\) | 0.480114 | 0.0218009 | ||||||||
\(486\) | 23.3709 | 1.06012 | ||||||||
\(487\) | 35.6007 | 1.61322 | 0.806610 | − | 0.591084i | \(-0.201300\pi\) | ||||
0.806610 | + | 0.591084i | \(0.201300\pi\) | |||||||
\(488\) | 15.9438 | 0.721741 | ||||||||
\(489\) | 47.2750 | 2.13785 | ||||||||
\(490\) | 2.05436 | 0.0928063 | ||||||||
\(491\) | −0.665932 | −0.0300531 | −0.0150265 | − | 0.999887i | \(-0.504783\pi\) | ||||
−0.0150265 | + | 0.999887i | \(0.504783\pi\) | |||||||
\(492\) | −24.7273 | −1.11479 | ||||||||
\(493\) | −16.2265 | −0.730806 | ||||||||
\(494\) | −29.6670 | −1.33478 | ||||||||
\(495\) | −6.27267 | −0.281935 | ||||||||
\(496\) | 1.18245 | 0.0530934 | ||||||||
\(497\) | 2.97450 | 0.133424 | ||||||||
\(498\) | 9.00824 | 0.403669 | ||||||||
\(499\) | 7.19573 | 0.322125 | 0.161063 | − | 0.986944i | \(-0.448508\pi\) | ||||
0.161063 | + | 0.986944i | \(0.448508\pi\) | |||||||
\(500\) | 4.42708 | 0.197985 | ||||||||
\(501\) | 34.9723 | 1.56245 | ||||||||
\(502\) | 5.71753 | 0.255186 | ||||||||
\(503\) | 41.5468 | 1.85248 | 0.926240 | − | 0.376935i | \(-0.123022\pi\) | ||||
0.926240 | + | 0.376935i | \(0.123022\pi\) | |||||||
\(504\) | 33.8735 | 1.50884 | ||||||||
\(505\) | 8.21627 | 0.365619 | ||||||||
\(506\) | 1.51278 | 0.0672513 | ||||||||
\(507\) | −22.6351 | −1.00526 | ||||||||
\(508\) | −14.2588 | −0.632632 | ||||||||
\(509\) | −30.7587 | −1.36335 | −0.681677 | − | 0.731653i | \(-0.738749\pi\) | ||||
−0.681677 | + | 0.731653i | \(0.738749\pi\) | |||||||
\(510\) | 6.05028 | 0.267911 | ||||||||
\(511\) | −3.19611 | −0.141388 | ||||||||
\(512\) | −14.5777 | −0.644248 | ||||||||
\(513\) | −5.67639 | −0.250619 | ||||||||
\(514\) | 8.79671 | 0.388006 | ||||||||
\(515\) | −0.285955 | −0.0126007 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −12.9957 | −0.571550 | ||||||||
\(518\) | 13.5879 | 0.597018 | ||||||||
\(519\) | 35.0109 | 1.53681 | ||||||||
\(520\) | 7.11832 | 0.312159 | ||||||||
\(521\) | 15.3022 | 0.670402 | 0.335201 | − | 0.942147i | \(-0.391196\pi\) | ||||
0.335201 | + | 0.942147i | \(0.391196\pi\) | |||||||
\(522\) | 12.4507 | 0.544951 | ||||||||
\(523\) | −1.34406 | −0.0587716 | −0.0293858 | − | 0.999568i | \(-0.509355\pi\) | ||||
−0.0293858 | + | 0.999568i | \(0.509355\pi\) | |||||||
\(524\) | −9.74419 | −0.425677 | ||||||||
\(525\) | −39.6473 | −1.73035 | ||||||||
\(526\) | −6.39399 | −0.278791 | ||||||||
\(527\) | 3.99739 | 0.174129 | ||||||||
\(528\) | −12.7591 | −0.555266 | ||||||||
\(529\) | −22.8487 | −0.993423 | ||||||||
\(530\) | 2.49272 | 0.108277 | ||||||||
\(531\) | 22.6632 | 0.983497 | ||||||||
\(532\) | 18.1993 | 0.789038 | ||||||||
\(533\) | 50.5425 | 2.18924 | ||||||||
\(534\) | −4.85404 | −0.210055 | ||||||||
\(535\) | −8.08304 | −0.349460 | ||||||||
\(536\) | −32.0680 | −1.38512 | ||||||||
\(537\) | 15.6101 | 0.673627 | ||||||||
\(538\) | 2.39727 | 0.103353 | ||||||||
\(539\) | −14.6458 | −0.630841 | ||||||||
\(540\) | 0.425417 | 0.0183070 | ||||||||
\(541\) | −0.198489 | −0.00853373 | −0.00426686 | − | 0.999991i | \(-0.501358\pi\) | ||||
−0.00426686 | + | 0.999991i | \(0.501358\pi\) | |||||||
\(542\) | 28.6236 | 1.22949 | ||||||||
\(543\) | −9.34621 | −0.401084 | ||||||||
\(544\) | −21.3848 | −0.916867 | ||||||||
\(545\) | −3.26230 | −0.139742 | ||||||||
\(546\) | −40.8710 | −1.74912 | ||||||||
\(547\) | 7.93941 | 0.339465 | 0.169732 | − | 0.985490i | \(-0.445710\pi\) | ||||
0.169732 | + | 0.985490i | \(0.445710\pi\) | |||||||
\(548\) | −7.34544 | −0.313782 | ||||||||
\(549\) | −17.6885 | −0.754928 | ||||||||
\(550\) | 18.4756 | 0.787801 | ||||||||
\(551\) | 21.4165 | 0.912372 | ||||||||
\(552\) | −2.98321 | −0.126974 | ||||||||
\(553\) | 3.31318 | 0.140891 | ||||||||
\(554\) | 27.7895 | 1.18066 | ||||||||
\(555\) | 4.96194 | 0.210623 | ||||||||
\(556\) | −11.6877 | −0.495668 | ||||||||
\(557\) | −17.5130 | −0.742048 | −0.371024 | − | 0.928623i | \(-0.620993\pi\) | ||||
−0.371024 | + | 0.928623i | \(0.620993\pi\) | |||||||
\(558\) | −3.06721 | −0.129845 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 2.24408 | 0.0948299 | ||||||||
\(561\) | −43.1334 | −1.82110 | ||||||||
\(562\) | 17.4234 | 0.734963 | ||||||||
\(563\) | 24.8082 | 1.04554 | 0.522771 | − | 0.852473i | \(-0.324898\pi\) | ||||
0.522771 | + | 0.852473i | \(0.324898\pi\) | |||||||
\(564\) | 8.00471 | 0.337059 | ||||||||
\(565\) | 0.849946 | 0.0357575 | ||||||||
\(566\) | 17.8736 | 0.751283 | ||||||||
\(567\) | 25.6223 | 1.07603 | ||||||||
\(568\) | 2.73341 | 0.114691 | ||||||||
\(569\) | −28.8478 | −1.20936 | −0.604681 | − | 0.796468i | \(-0.706699\pi\) | ||||
−0.604681 | + | 0.796468i | \(0.706699\pi\) | |||||||
\(570\) | −7.98541 | −0.334472 | ||||||||
\(571\) | −32.6060 | −1.36452 | −0.682259 | − | 0.731111i | \(-0.739002\pi\) | ||||
−0.682259 | + | 0.731111i | \(0.739002\pi\) | |||||||
\(572\) | −15.8510 | −0.662762 | ||||||||
\(573\) | 28.8139 | 1.20372 | ||||||||
\(574\) | 37.2547 | 1.55498 | ||||||||
\(575\) | 1.84757 | 0.0770489 | ||||||||
\(576\) | 25.5636 | 1.06515 | ||||||||
\(577\) | 33.6229 | 1.39974 | 0.699870 | − | 0.714270i | \(-0.253241\pi\) | ||||
0.699870 | + | 0.714270i | \(0.253241\pi\) | |||||||
\(578\) | 4.25291 | 0.176898 | ||||||||
\(579\) | 21.3281 | 0.886366 | ||||||||
\(580\) | −1.60506 | −0.0666465 | ||||||||
\(581\) | 11.2954 | 0.468610 | ||||||||
\(582\) | −2.53322 | −0.105005 | ||||||||
\(583\) | −17.7710 | −0.735999 | ||||||||
\(584\) | −2.93706 | −0.121537 | ||||||||
\(585\) | −7.89728 | −0.326513 | ||||||||
\(586\) | −31.2514 | −1.29098 | ||||||||
\(587\) | −16.2192 | −0.669439 | −0.334720 | − | 0.942318i | \(-0.608642\pi\) | ||||
−0.334720 | + | 0.942318i | \(0.608642\pi\) | |||||||
\(588\) | 9.02112 | 0.372025 | ||||||||
\(589\) | −5.27593 | −0.217391 | ||||||||
\(590\) | 3.51045 | 0.144523 | ||||||||
\(591\) | 54.6848 | 2.24943 | ||||||||
\(592\) | 5.34049 | 0.219493 | ||||||||
\(593\) | 44.2180 | 1.81582 | 0.907909 | − | 0.419168i | \(-0.137678\pi\) | ||||
0.907909 | + | 0.419168i | \(0.137678\pi\) | |||||||
\(594\) | 3.64416 | 0.149522 | ||||||||
\(595\) | 7.58639 | 0.311012 | ||||||||
\(596\) | −6.75893 | −0.276857 | ||||||||
\(597\) | −24.9345 | −1.02050 | ||||||||
\(598\) | 1.90459 | 0.0778845 | ||||||||
\(599\) | 4.14316 | 0.169285 | 0.0846425 | − | 0.996411i | \(-0.473025\pi\) | ||||
0.0846425 | + | 0.996411i | \(0.473025\pi\) | |||||||
\(600\) | −36.4338 | −1.48741 | ||||||||
\(601\) | −19.9921 | −0.815496 | −0.407748 | − | 0.913094i | \(-0.633686\pi\) | ||||
−0.407748 | + | 0.913094i | \(0.633686\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 35.5772 | 1.44881 | ||||||||
\(604\) | −4.33839 | −0.176526 | ||||||||
\(605\) | 1.42892 | 0.0580937 | ||||||||
\(606\) | −43.3514 | −1.76103 | ||||||||
\(607\) | 18.0883 | 0.734183 | 0.367091 | − | 0.930185i | \(-0.380354\pi\) | ||||
0.367091 | + | 0.930185i | \(0.380354\pi\) | |||||||
\(608\) | 28.2246 | 1.14466 | ||||||||
\(609\) | 29.5046 | 1.19559 | ||||||||
\(610\) | −2.73989 | −0.110935 | ||||||||
\(611\) | −16.3616 | −0.661919 | ||||||||
\(612\) | 14.0580 | 0.568260 | ||||||||
\(613\) | 37.5137 | 1.51516 | 0.757582 | − | 0.652740i | \(-0.226380\pi\) | ||||
0.757582 | + | 0.652740i | \(0.226380\pi\) | |||||||
\(614\) | −14.0448 | −0.566804 | ||||||||
\(615\) | 13.6044 | 0.548583 | ||||||||
\(616\) | −37.4059 | −1.50713 | ||||||||
\(617\) | −9.05821 | −0.364670 | −0.182335 | − | 0.983236i | \(-0.558366\pi\) | ||||
−0.182335 | + | 0.983236i | \(0.558366\pi\) | |||||||
\(618\) | 1.50878 | 0.0606920 | ||||||||
\(619\) | 4.96217 | 0.199446 | 0.0997232 | − | 0.995015i | \(-0.468204\pi\) | ||||
0.0997232 | + | 0.995015i | \(0.468204\pi\) | |||||||
\(620\) | 0.395405 | 0.0158798 | ||||||||
\(621\) | 0.364418 | 0.0146236 | ||||||||
\(622\) | 15.8701 | 0.636334 | ||||||||
\(623\) | −6.08644 | −0.243848 | ||||||||
\(624\) | −16.0636 | −0.643060 | ||||||||
\(625\) | 21.3153 | 0.852611 | ||||||||
\(626\) | −11.9020 | −0.475701 | ||||||||
\(627\) | 56.9294 | 2.27354 | ||||||||
\(628\) | 12.2104 | 0.487250 | ||||||||
\(629\) | 18.0541 | 0.719866 | ||||||||
\(630\) | −5.82106 | −0.231916 | ||||||||
\(631\) | −34.8666 | −1.38802 | −0.694009 | − | 0.719966i | \(-0.744157\pi\) | ||||
−0.694009 | + | 0.719966i | \(0.744157\pi\) | |||||||
\(632\) | 3.04464 | 0.121109 | ||||||||
\(633\) | −38.6188 | −1.53496 | ||||||||
\(634\) | −23.8407 | −0.946836 | ||||||||
\(635\) | 7.84488 | 0.311315 | ||||||||
\(636\) | 10.9461 | 0.434039 | ||||||||
\(637\) | −18.4391 | −0.730584 | ||||||||
\(638\) | −13.7491 | −0.544331 | ||||||||
\(639\) | −3.03253 | −0.119965 | ||||||||
\(640\) | −0.697221 | −0.0275601 | ||||||||
\(641\) | 43.9244 | 1.73491 | 0.867454 | − | 0.497518i | \(-0.165755\pi\) | ||||
0.867454 | + | 0.497518i | \(0.165755\pi\) | |||||||
\(642\) | 42.6485 | 1.68320 | ||||||||
\(643\) | 23.0813 | 0.910236 | 0.455118 | − | 0.890431i | \(-0.349597\pi\) | ||||
0.455118 | + | 0.890431i | \(0.349597\pi\) | |||||||
\(644\) | −1.16837 | −0.0460404 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −29.0551 | −1.14316 | ||||||||
\(647\) | 44.1509 | 1.73575 | 0.867876 | − | 0.496780i | \(-0.165485\pi\) | ||||
0.867876 | + | 0.496780i | \(0.165485\pi\) | |||||||
\(648\) | 23.5455 | 0.924956 | ||||||||
\(649\) | −25.0266 | −0.982379 | ||||||||
\(650\) | 23.2607 | 0.912361 | ||||||||
\(651\) | −7.26843 | −0.284872 | ||||||||
\(652\) | 17.0146 | 0.666344 | ||||||||
\(653\) | −6.65908 | −0.260590 | −0.130295 | − | 0.991475i | \(-0.541592\pi\) | ||||
−0.130295 | + | 0.991475i | \(0.541592\pi\) | |||||||
\(654\) | 17.2128 | 0.673075 | ||||||||
\(655\) | 5.36104 | 0.209473 | ||||||||
\(656\) | 14.6423 | 0.571686 | ||||||||
\(657\) | 3.25847 | 0.127125 | ||||||||
\(658\) | −12.0601 | −0.470150 | ||||||||
\(659\) | −9.47092 | −0.368935 | −0.184467 | − | 0.982839i | \(-0.559056\pi\) | ||||
−0.184467 | + | 0.982839i | \(0.559056\pi\) | |||||||
\(660\) | −4.26658 | −0.166076 | ||||||||
\(661\) | 16.8401 | 0.655005 | 0.327503 | − | 0.944850i | \(-0.393793\pi\) | ||||
0.327503 | + | 0.944850i | \(0.393793\pi\) | |||||||
\(662\) | −16.2470 | −0.631458 | ||||||||
\(663\) | −54.3050 | −2.10903 | ||||||||
\(664\) | 10.3798 | 0.402816 | ||||||||
\(665\) | −10.0128 | −0.388281 | ||||||||
\(666\) | −13.8530 | −0.536792 | ||||||||
\(667\) | −1.37492 | −0.0532370 | ||||||||
\(668\) | 12.5868 | 0.486997 | ||||||||
\(669\) | 29.5744 | 1.14341 | ||||||||
\(670\) | 5.51079 | 0.212900 | ||||||||
\(671\) | 19.5332 | 0.754070 | ||||||||
\(672\) | 38.8839 | 1.49998 | ||||||||
\(673\) | −18.0156 | −0.694449 | −0.347225 | − | 0.937782i | \(-0.612876\pi\) | ||||
−0.347225 | + | 0.937782i | \(0.612876\pi\) | |||||||
\(674\) | 15.5713 | 0.599783 | ||||||||
\(675\) | 4.45063 | 0.171305 | ||||||||
\(676\) | −8.14652 | −0.313328 | ||||||||
\(677\) | −5.40686 | −0.207802 | −0.103901 | − | 0.994588i | \(-0.533133\pi\) | ||||
−0.103901 | + | 0.994588i | \(0.533133\pi\) | |||||||
\(678\) | −4.48456 | −0.172229 | ||||||||
\(679\) | −3.17638 | −0.121898 | ||||||||
\(680\) | 6.97150 | 0.267345 | ||||||||
\(681\) | 22.8174 | 0.874366 | ||||||||
\(682\) | 3.38707 | 0.129698 | ||||||||
\(683\) | −36.8545 | −1.41020 | −0.705099 | − | 0.709109i | \(-0.749098\pi\) | ||||
−0.705099 | + | 0.709109i | \(0.749098\pi\) | |||||||
\(684\) | −18.5543 | −0.709443 | ||||||||
\(685\) | 4.04130 | 0.154410 | ||||||||
\(686\) | 10.5917 | 0.404394 | ||||||||
\(687\) | 39.3708 | 1.50209 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −22.3737 | −0.852369 | ||||||||
\(690\) | 0.512655 | 0.0195165 | ||||||||
\(691\) | −9.97585 | −0.379499 | −0.189750 | − | 0.981833i | \(-0.560768\pi\) | ||||
−0.189750 | + | 0.981833i | \(0.560768\pi\) | |||||||
\(692\) | 12.6007 | 0.479005 | ||||||||
\(693\) | 41.4993 | 1.57643 | ||||||||
\(694\) | −28.3824 | −1.07738 | ||||||||
\(695\) | 6.43031 | 0.243915 | ||||||||
\(696\) | 27.1132 | 1.02772 | ||||||||
\(697\) | 49.5000 | 1.87495 | ||||||||
\(698\) | −29.6252 | −1.12133 | ||||||||
\(699\) | −11.8562 | −0.448445 | ||||||||
\(700\) | −14.2693 | −0.539330 | ||||||||
\(701\) | 11.6450 | 0.439827 | 0.219913 | − | 0.975519i | \(-0.429422\pi\) | ||||
0.219913 | + | 0.975519i | \(0.429422\pi\) | |||||||
\(702\) | 4.58800 | 0.173163 | ||||||||
\(703\) | −23.8286 | −0.898713 | ||||||||
\(704\) | −28.2295 | −1.06394 | ||||||||
\(705\) | −4.40402 | −0.165865 | ||||||||
\(706\) | −20.6064 | −0.775531 | ||||||||
\(707\) | −54.3580 | −2.04434 | ||||||||
\(708\) | 15.4151 | 0.579337 | ||||||||
\(709\) | 16.6947 | 0.626981 | 0.313491 | − | 0.949591i | \(-0.398502\pi\) | ||||
0.313491 | + | 0.949591i | \(0.398502\pi\) | |||||||
\(710\) | −0.469729 | −0.0176286 | ||||||||
\(711\) | −3.37782 | −0.126678 | ||||||||
\(712\) | −5.59312 | −0.209611 | ||||||||
\(713\) | 0.338709 | 0.0126848 | ||||||||
\(714\) | −40.0280 | −1.49801 | ||||||||
\(715\) | 8.72085 | 0.326141 | ||||||||
\(716\) | 5.61819 | 0.209962 | ||||||||
\(717\) | 10.3859 | 0.387869 | ||||||||
\(718\) | −29.4398 | −1.09868 | ||||||||
\(719\) | −32.2362 | −1.20221 | −0.601104 | − | 0.799170i | \(-0.705272\pi\) | ||||
−0.601104 | + | 0.799170i | \(0.705272\pi\) | |||||||
\(720\) | −2.28787 | −0.0852637 | ||||||||
\(721\) | 1.89184 | 0.0704560 | ||||||||
\(722\) | 18.4974 | 0.688404 | ||||||||
\(723\) | 8.23964 | 0.306435 | ||||||||
\(724\) | −3.36376 | −0.125013 | ||||||||
\(725\) | −16.7918 | −0.623633 | ||||||||
\(726\) | −7.53937 | −0.279812 | ||||||||
\(727\) | −21.0335 | −0.780088 | −0.390044 | − | 0.920796i | \(-0.627540\pi\) | ||||
−0.390044 | + | 0.920796i | \(0.627540\pi\) | |||||||
\(728\) | −47.0941 | −1.74542 | ||||||||
\(729\) | −33.2170 | −1.23026 | ||||||||
\(730\) | 0.504726 | 0.0186807 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | −12.0315 | −0.444696 | ||||||||
\(733\) | −4.52071 | −0.166976 | −0.0834881 | − | 0.996509i | \(-0.526606\pi\) | ||||
−0.0834881 | + | 0.996509i | \(0.526606\pi\) | |||||||
\(734\) | −30.8620 | −1.13914 | ||||||||
\(735\) | −4.96322 | −0.183071 | ||||||||
\(736\) | −1.81199 | −0.0667909 | ||||||||
\(737\) | −39.2873 | −1.44717 | ||||||||
\(738\) | −37.9815 | −1.39812 | ||||||||
\(739\) | 6.99980 | 0.257492 | 0.128746 | − | 0.991678i | \(-0.458905\pi\) | ||||
0.128746 | + | 0.991678i | \(0.458905\pi\) | |||||||
\(740\) | 1.78584 | 0.0656487 | ||||||||
\(741\) | 71.6740 | 2.63301 | ||||||||
\(742\) | −16.4915 | −0.605424 | ||||||||
\(743\) | 23.0203 | 0.844532 | 0.422266 | − | 0.906472i | \(-0.361235\pi\) | ||||
0.422266 | + | 0.906472i | \(0.361235\pi\) | |||||||
\(744\) | −6.67931 | −0.244876 | ||||||||
\(745\) | 3.71861 | 0.136240 | ||||||||
\(746\) | 33.5870 | 1.22971 | ||||||||
\(747\) | −11.5157 | −0.421338 | ||||||||
\(748\) | −15.5240 | −0.567614 | ||||||||
\(749\) | 53.4766 | 1.95399 | ||||||||
\(750\) | 12.8514 | 0.469266 | ||||||||
\(751\) | −14.3313 | −0.522957 | −0.261478 | − | 0.965209i | \(-0.584210\pi\) | ||||
−0.261478 | + | 0.965209i | \(0.584210\pi\) | |||||||
\(752\) | −4.74000 | −0.172850 | ||||||||
\(753\) | −13.8133 | −0.503384 | ||||||||
\(754\) | −17.3101 | −0.630396 | ||||||||
\(755\) | 2.38689 | 0.0868676 | ||||||||
\(756\) | −2.81451 | −0.102363 | ||||||||
\(757\) | −36.4497 | −1.32479 | −0.662393 | − | 0.749156i | \(-0.730459\pi\) | ||||
−0.662393 | + | 0.749156i | \(0.730459\pi\) | |||||||
\(758\) | −18.8351 | −0.684122 | ||||||||
\(759\) | −3.65481 | −0.132661 | ||||||||
\(760\) | −9.20128 | −0.333766 | ||||||||
\(761\) | 44.4716 | 1.61209 | 0.806047 | − | 0.591852i | \(-0.201603\pi\) | ||||
0.806047 | + | 0.591852i | \(0.201603\pi\) | |||||||
\(762\) | −41.3919 | −1.49947 | ||||||||
\(763\) | 21.5830 | 0.781358 | ||||||||
\(764\) | 10.3703 | 0.375185 | ||||||||
\(765\) | −7.73440 | −0.279638 | ||||||||
\(766\) | 23.9931 | 0.866904 | ||||||||
\(767\) | −31.5084 | −1.13770 | ||||||||
\(768\) | 41.9593 | 1.51408 | ||||||||
\(769\) | 2.51601 | 0.0907298 | 0.0453649 | − | 0.998970i | \(-0.485555\pi\) | ||||
0.0453649 | + | 0.998970i | \(0.485555\pi\) | |||||||
\(770\) | 6.42810 | 0.231653 | ||||||||
\(771\) | −21.2524 | −0.765387 | ||||||||
\(772\) | 7.67613 | 0.276270 | ||||||||
\(773\) | 44.8085 | 1.61165 | 0.805824 | − | 0.592155i | \(-0.201723\pi\) | ||||
0.805824 | + | 0.592155i | \(0.201723\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 4.13665 | 0.148593 | ||||||||
\(776\) | −2.91893 | −0.104784 | ||||||||
\(777\) | −32.8277 | −1.17769 | ||||||||
\(778\) | 23.8391 | 0.854672 | ||||||||
\(779\) | −65.3322 | −2.34077 | ||||||||
\(780\) | −5.37162 | −0.192335 | ||||||||
\(781\) | 3.34878 | 0.119829 | ||||||||
\(782\) | 1.86531 | 0.0667032 | ||||||||
\(783\) | −3.31206 | −0.118363 | ||||||||
\(784\) | −5.34187 | −0.190781 | ||||||||
\(785\) | −6.71792 | −0.239773 | ||||||||
\(786\) | −28.2864 | −1.00894 | ||||||||
\(787\) | 2.59659 | 0.0925583 | 0.0462792 | − | 0.998929i | \(-0.485264\pi\) | ||||
0.0462792 | + | 0.998929i | \(0.485264\pi\) | |||||||
\(788\) | 19.6814 | 0.701122 | ||||||||
\(789\) | 15.4476 | 0.549948 | ||||||||
\(790\) | −0.523213 | −0.0186151 | ||||||||
\(791\) | −5.62315 | −0.199936 | ||||||||
\(792\) | 38.1357 | 1.35509 | ||||||||
\(793\) | 24.5922 | 0.873296 | ||||||||
\(794\) | −9.01836 | −0.320050 | ||||||||
\(795\) | −6.02228 | −0.213588 | ||||||||
\(796\) | −8.97410 | −0.318078 | ||||||||
\(797\) | 23.6408 | 0.837400 | 0.418700 | − | 0.908124i | \(-0.362486\pi\) | ||||
0.418700 | + | 0.908124i | \(0.362486\pi\) | |||||||
\(798\) | 52.8306 | 1.87018 | ||||||||
\(799\) | −16.0241 | −0.566892 | ||||||||
\(800\) | −22.1298 | −0.782407 | ||||||||
\(801\) | 6.20518 | 0.219249 | ||||||||
\(802\) | 35.3398 | 1.24789 | ||||||||
\(803\) | −3.59828 | −0.126980 | ||||||||
\(804\) | 24.1991 | 0.853435 | ||||||||
\(805\) | 0.642814 | 0.0226562 | ||||||||
\(806\) | 4.26433 | 0.150204 | ||||||||
\(807\) | −5.79168 | −0.203877 | ||||||||
\(808\) | −49.9522 | −1.75731 | ||||||||
\(809\) | 40.0359 | 1.40759 | 0.703793 | − | 0.710405i | \(-0.251488\pi\) | ||||
0.703793 | + | 0.710405i | \(0.251488\pi\) | |||||||
\(810\) | −4.04623 | −0.142170 | ||||||||
\(811\) | 9.32389 | 0.327406 | 0.163703 | − | 0.986510i | \(-0.447656\pi\) | ||||
0.163703 | + | 0.986510i | \(0.447656\pi\) | |||||||
\(812\) | 10.6189 | 0.372650 | ||||||||
\(813\) | −69.1533 | −2.42531 | ||||||||
\(814\) | 15.2976 | 0.536182 | ||||||||
\(815\) | −9.36107 | −0.327904 | ||||||||
\(816\) | −15.7323 | −0.550741 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | 26.8057 | 0.937238 | ||||||||
\(819\) | 52.2476 | 1.82568 | ||||||||
\(820\) | 4.89633 | 0.170987 | ||||||||
\(821\) | −1.87089 | −0.0652944 | −0.0326472 | − | 0.999467i | \(-0.510394\pi\) | ||||
−0.0326472 | + | 0.999467i | \(0.510394\pi\) | |||||||
\(822\) | −21.3231 | −0.743727 | ||||||||
\(823\) | 7.72253 | 0.269191 | 0.134595 | − | 0.990901i | \(-0.457027\pi\) | ||||
0.134595 | + | 0.990901i | \(0.457027\pi\) | |||||||
\(824\) | 1.73851 | 0.0605638 | ||||||||
\(825\) | −44.6361 | −1.55403 | ||||||||
\(826\) | −23.2247 | −0.808092 | ||||||||
\(827\) | 10.8269 | 0.376490 | 0.188245 | − | 0.982122i | \(-0.439720\pi\) | ||||
0.188245 | + | 0.982122i | \(0.439720\pi\) | |||||||
\(828\) | 1.19117 | 0.0413960 | ||||||||
\(829\) | 16.7060 | 0.580223 | 0.290111 | − | 0.956993i | \(-0.406308\pi\) | ||||
0.290111 | + | 0.956993i | \(0.406308\pi\) | |||||||
\(830\) | −1.78375 | −0.0619148 | ||||||||
\(831\) | −67.1380 | −2.32899 | ||||||||
\(832\) | −35.5409 | −1.23216 | ||||||||
\(833\) | −18.0588 | −0.625700 | ||||||||
\(834\) | −33.9282 | −1.17484 | ||||||||
\(835\) | −6.92497 | −0.239648 | ||||||||
\(836\) | 20.4893 | 0.708636 | ||||||||
\(837\) | 0.815922 | 0.0282024 | ||||||||
\(838\) | 25.9442 | 0.896226 | ||||||||
\(839\) | −2.28441 | −0.0788666 | −0.0394333 | − | 0.999222i | \(-0.512555\pi\) | ||||
−0.0394333 | + | 0.999222i | \(0.512555\pi\) | |||||||
\(840\) | −12.6762 | −0.437371 | ||||||||
\(841\) | −16.5039 | −0.569101 | ||||||||
\(842\) | −20.1584 | −0.694704 | ||||||||
\(843\) | −42.0942 | −1.44980 | ||||||||
\(844\) | −13.8992 | −0.478429 | ||||||||
\(845\) | 4.48203 | 0.154187 | ||||||||
\(846\) | 12.2953 | 0.422723 | ||||||||
\(847\) | −9.45356 | −0.324828 | ||||||||
\(848\) | −6.48172 | −0.222583 | ||||||||
\(849\) | −43.1817 | −1.48199 | ||||||||
\(850\) | 22.7810 | 0.781381 | ||||||||
\(851\) | 1.52977 | 0.0524400 | ||||||||
\(852\) | −2.06268 | −0.0706663 | ||||||||
\(853\) | 14.0427 | 0.480811 | 0.240406 | − | 0.970673i | \(-0.422720\pi\) | ||||
0.240406 | + | 0.970673i | \(0.422720\pi\) | |||||||
\(854\) | 18.1268 | 0.620288 | ||||||||
\(855\) | 10.2082 | 0.349113 | ||||||||
\(856\) | 49.1422 | 1.67965 | ||||||||
\(857\) | −40.2306 | −1.37425 | −0.687126 | − | 0.726538i | \(-0.741128\pi\) | ||||
−0.687126 | + | 0.726538i | \(0.741128\pi\) | |||||||
\(858\) | −46.0137 | −1.57088 | ||||||||
\(859\) | 34.4229 | 1.17449 | 0.587247 | − | 0.809407i | \(-0.300212\pi\) | ||||
0.587247 | + | 0.809407i | \(0.300212\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −90.0055 | −3.06738 | ||||||||
\(862\) | 33.8791 | 1.15393 | ||||||||
\(863\) | −20.2575 | −0.689575 | −0.344787 | − | 0.938681i | \(-0.612049\pi\) | ||||
−0.344787 | + | 0.938681i | \(0.612049\pi\) | |||||||
\(864\) | −4.36493 | −0.148498 | ||||||||
\(865\) | −6.93261 | −0.235716 | ||||||||
\(866\) | 17.9320 | 0.609355 | ||||||||
\(867\) | −10.2748 | −0.348951 | ||||||||
\(868\) | −2.61596 | −0.0887914 | ||||||||
\(869\) | 3.73008 | 0.126534 | ||||||||
\(870\) | −4.65933 | −0.157966 | ||||||||
\(871\) | −49.4627 | −1.67598 | ||||||||
\(872\) | 19.8337 | 0.671653 | ||||||||
\(873\) | 3.23835 | 0.109602 | ||||||||
\(874\) | −2.46191 | −0.0832754 | ||||||||
\(875\) | 16.1142 | 0.544760 | ||||||||
\(876\) | 2.21636 | 0.0748839 | ||||||||
\(877\) | −43.7768 | −1.47824 | −0.739119 | − | 0.673575i | \(-0.764758\pi\) | ||||
−0.739119 | + | 0.673575i | \(0.764758\pi\) | |||||||
\(878\) | 15.0764 | 0.508803 | ||||||||
\(879\) | 75.5020 | 2.54662 | ||||||||
\(880\) | 2.52646 | 0.0851668 | ||||||||
\(881\) | 3.24793 | 0.109426 | 0.0547128 | − | 0.998502i | \(-0.482576\pi\) | ||||
0.0547128 | + | 0.998502i | \(0.482576\pi\) | |||||||
\(882\) | 13.8566 | 0.466575 | ||||||||
\(883\) | −15.3073 | −0.515131 | −0.257565 | − | 0.966261i | \(-0.582920\pi\) | ||||
−0.257565 | + | 0.966261i | \(0.582920\pi\) | |||||||
\(884\) | −19.5447 | −0.657361 | ||||||||
\(885\) | −8.48107 | −0.285088 | ||||||||
\(886\) | 19.8574 | 0.667124 | ||||||||
\(887\) | 10.3041 | 0.345977 | 0.172988 | − | 0.984924i | \(-0.444658\pi\) | ||||
0.172988 | + | 0.984924i | \(0.444658\pi\) | |||||||
\(888\) | −30.1670 | −1.01234 | ||||||||
\(889\) | −51.9009 | −1.74070 | ||||||||
\(890\) | 0.961162 | 0.0322182 | ||||||||
\(891\) | 28.8463 | 0.966387 | ||||||||
\(892\) | 10.6440 | 0.356388 | ||||||||
\(893\) | 21.1493 | 0.707734 | ||||||||
\(894\) | −19.6205 | −0.656207 | ||||||||
\(895\) | −3.09101 | −0.103321 | ||||||||
\(896\) | 4.61274 | 0.154101 | ||||||||
\(897\) | −4.60140 | −0.153636 | ||||||||
\(898\) | −5.56986 | −0.185868 | ||||||||
\(899\) | −3.07840 | −0.102670 | ||||||||
\(900\) | 14.5477 | 0.484924 | ||||||||
\(901\) | −21.9122 | −0.730001 | ||||||||
\(902\) | 41.9424 | 1.39653 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −5.16739 | −0.171865 | ||||||||
\(905\) | 1.85067 | 0.0615183 | ||||||||
\(906\) | −12.5939 | −0.418404 | ||||||||
\(907\) | −44.5746 | −1.48008 | −0.740038 | − | 0.672565i | \(-0.765192\pi\) | ||||
−0.740038 | + | 0.672565i | \(0.765192\pi\) | |||||||
\(908\) | 8.21215 | 0.272530 | ||||||||
\(909\) | 55.4185 | 1.83811 | ||||||||
\(910\) | 8.09298 | 0.268280 | ||||||||
\(911\) | −9.12024 | −0.302167 | −0.151084 | − | 0.988521i | \(-0.548276\pi\) | ||||
−0.151084 | + | 0.988521i | \(0.548276\pi\) | |||||||
\(912\) | 20.7642 | 0.687571 | ||||||||
\(913\) | 12.7166 | 0.420859 | ||||||||
\(914\) | −8.30843 | −0.274819 | ||||||||
\(915\) | 6.61945 | 0.218832 | ||||||||
\(916\) | 14.1698 | 0.468184 | ||||||||
\(917\) | −35.4681 | −1.17126 | ||||||||
\(918\) | 4.49337 | 0.148303 | ||||||||
\(919\) | −27.4060 | −0.904039 | −0.452020 | − | 0.892008i | \(-0.649296\pi\) | ||||
−0.452020 | + | 0.892008i | \(0.649296\pi\) | |||||||
\(920\) | 0.590713 | 0.0194752 | ||||||||
\(921\) | 33.9317 | 1.11809 | ||||||||
\(922\) | 44.5062 | 1.46574 | ||||||||
\(923\) | 4.21611 | 0.138775 | ||||||||
\(924\) | 28.2272 | 0.928607 | ||||||||
\(925\) | 18.6831 | 0.614296 | ||||||||
\(926\) | 5.94782 | 0.195458 | ||||||||
\(927\) | −1.92875 | −0.0633486 | ||||||||
\(928\) | 16.4685 | 0.540604 | ||||||||
\(929\) | −8.08472 | −0.265251 | −0.132625 | − | 0.991166i | \(-0.542341\pi\) | ||||
−0.132625 | + | 0.991166i | \(0.542341\pi\) | |||||||
\(930\) | 1.14782 | 0.0376385 | ||||||||
\(931\) | 23.8348 | 0.781153 | ||||||||
\(932\) | −4.26714 | −0.139775 | ||||||||
\(933\) | −38.3415 | −1.25524 | ||||||||
\(934\) | 7.71825 | 0.252549 | ||||||||
\(935\) | 8.54098 | 0.279320 | ||||||||
\(936\) | 48.0129 | 1.56935 | ||||||||
\(937\) | −37.2600 | −1.21723 | −0.608615 | − | 0.793465i | \(-0.708275\pi\) | ||||
−0.608615 | + | 0.793465i | \(0.708275\pi\) | |||||||
\(938\) | −36.4588 | −1.19042 | ||||||||
\(939\) | 28.7548 | 0.938376 | ||||||||
\(940\) | −1.58504 | −0.0516982 | ||||||||
\(941\) | 36.3058 | 1.18354 | 0.591768 | − | 0.806108i | \(-0.298430\pi\) | ||||
0.591768 | + | 0.806108i | \(0.298430\pi\) | |||||||
\(942\) | 35.4457 | 1.15488 | ||||||||
\(943\) | 4.19426 | 0.136584 | ||||||||
\(944\) | −9.12809 | −0.297094 | ||||||||
\(945\) | 1.54848 | 0.0503722 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 46.5566 | 1.51288 | 0.756442 | − | 0.654060i | \(-0.226936\pi\) | ||||
0.756442 | + | 0.654060i | \(0.226936\pi\) | |||||||
\(948\) | −2.29754 | −0.0746207 | ||||||||
\(949\) | −4.53023 | −0.147057 | ||||||||
\(950\) | −30.0673 | −0.975512 | ||||||||
\(951\) | 57.5980 | 1.86774 | ||||||||
\(952\) | −46.1227 | −1.49485 | ||||||||
\(953\) | −31.4936 | −1.02018 | −0.510089 | − | 0.860122i | \(-0.670388\pi\) | ||||
−0.510089 | + | 0.860122i | \(0.670388\pi\) | |||||||
\(954\) | 16.8133 | 0.544350 | ||||||||
\(955\) | −5.70552 | −0.184626 | ||||||||
\(956\) | 3.73796 | 0.120894 | ||||||||
\(957\) | 33.2171 | 1.07376 | ||||||||
\(958\) | 21.6353 | 0.699004 | ||||||||
\(959\) | −26.7368 | −0.863376 | ||||||||
\(960\) | −9.56649 | −0.308757 | ||||||||
\(961\) | −30.2416 | −0.975537 | ||||||||
\(962\) | 19.2597 | 0.620959 | ||||||||
\(963\) | −54.5199 | −1.75688 | ||||||||
\(964\) | 2.96550 | 0.0955124 | ||||||||
\(965\) | −4.22324 | −0.135951 | ||||||||
\(966\) | −3.39167 | −0.109125 | ||||||||
\(967\) | −1.18018 | −0.0379519 | −0.0189760 | − | 0.999820i | \(-0.506041\pi\) | ||||
−0.0189760 | + | 0.999820i | \(0.506041\pi\) | |||||||
\(968\) | −8.68733 | −0.279221 | ||||||||
\(969\) | 70.1957 | 2.25501 | ||||||||
\(970\) | 0.501610 | 0.0161057 | ||||||||
\(971\) | −39.8983 | −1.28040 | −0.640199 | − | 0.768209i | \(-0.721148\pi\) | ||||
−0.640199 | + | 0.768209i | \(0.721148\pi\) | |||||||
\(972\) | −20.3214 | −0.651809 | ||||||||
\(973\) | −42.5422 | −1.36384 | ||||||||
\(974\) | 37.1946 | 1.19179 | ||||||||
\(975\) | −56.1968 | −1.79974 | ||||||||
\(976\) | 7.12445 | 0.228048 | ||||||||
\(977\) | −31.6088 | −1.01125 | −0.505627 | − | 0.862752i | \(-0.668739\pi\) | ||||
−0.505627 | + | 0.862752i | \(0.668739\pi\) | |||||||
\(978\) | 49.3917 | 1.57937 | ||||||||
\(979\) | −6.85229 | −0.219000 | ||||||||
\(980\) | −1.78630 | −0.0570612 | ||||||||
\(981\) | −22.0041 | −0.702537 | ||||||||
\(982\) | −0.695748 | −0.0222022 | ||||||||
\(983\) | 24.3164 | 0.775573 | 0.387787 | − | 0.921749i | \(-0.373240\pi\) | ||||
0.387787 | + | 0.921749i | \(0.373240\pi\) | |||||||
\(984\) | −82.7104 | −2.63671 | ||||||||
\(985\) | −10.8283 | −0.345018 | ||||||||
\(986\) | −16.9531 | −0.539895 | ||||||||
\(987\) | 29.1365 | 0.927425 | ||||||||
\(988\) | 25.7960 | 0.820679 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | −6.55351 | −0.208284 | ||||||||
\(991\) | 3.22998 | 0.102604 | 0.0513019 | − | 0.998683i | \(-0.483663\pi\) | ||||
0.0513019 | + | 0.998683i | \(0.483663\pi\) | |||||||
\(992\) | −4.05700 | −0.128810 | ||||||||
\(993\) | 39.2520 | 1.24562 | ||||||||
\(994\) | 3.10768 | 0.0985695 | ||||||||
\(995\) | 4.93735 | 0.156525 | ||||||||
\(996\) | −7.83283 | −0.248193 | ||||||||
\(997\) | 14.7265 | 0.466394 | 0.233197 | − | 0.972430i | \(-0.425081\pi\) | ||||
0.233197 | + | 0.972430i | \(0.425081\pi\) | |||||||
\(998\) | 7.51791 | 0.237975 | ||||||||
\(999\) | 3.68509 | 0.116591 |
(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 | 1849.2.a.o.1.11 | 18 | ||
43.12 | odd | 42 | 43.2.g.a.15.2 | ✓ | 36 | ||
43.18 | odd | 42 | 43.2.g.a.23.2 | yes | 36 | ||
43.42 | odd | 2 | 1849.2.a.n.1.8 | 18 | |||
129.98 | even | 42 | 387.2.y.c.316.2 | 36 | |||
129.104 | even | 42 | 387.2.y.c.109.2 | 36 | |||
172.55 | even | 42 | 688.2.bg.c.273.1 | 36 | |||
172.147 | even | 42 | 688.2.bg.c.625.1 | 36 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
43.2.g.a.15.2 | ✓ | 36 | 43.12 | odd | 42 | ||
43.2.g.a.23.2 | yes | 36 | 43.18 | odd | 42 | ||
387.2.y.c.109.2 | 36 | 129.104 | even | 42 | |||
387.2.y.c.316.2 | 36 | 129.98 | even | 42 | |||
688.2.bg.c.273.1 | 36 | 172.55 | even | 42 | |||
688.2.bg.c.625.1 | 36 | 172.147 | even | 42 | |||
1849.2.a.n.1.8 | 18 | 43.42 | odd | 2 | |||
1849.2.a.o.1.11 | 18 | 1.1 | even | 1 | trivial |