Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4011,2,Mod(1,4011)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4011, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4011.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4011 = 3 \cdot 7 \cdot 191 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4011.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(32.0279962507\) |
Analytic rank: | \(0\) |
Dimension: | \(26\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.9 | ||
Character | \(\chi\) | \(=\) | 4011.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.07123 | −0.757472 | −0.378736 | − | 0.925505i | \(-0.623641\pi\) | ||||
−0.378736 | + | 0.925505i | \(0.623641\pi\) | |||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | −0.852471 | −0.426236 | ||||||||
\(5\) | −1.60541 | −0.717960 | −0.358980 | − | 0.933345i | \(-0.616875\pi\) | ||||
−0.358980 | + | 0.933345i | \(0.616875\pi\) | |||||||
\(6\) | 1.07123 | 0.437327 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | 3.05565 | 1.08033 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 1.71976 | 0.543835 | ||||||||
\(11\) | 3.95375 | 1.19210 | 0.596050 | − | 0.802947i | \(-0.296736\pi\) | ||||
0.596050 | + | 0.802947i | \(0.296736\pi\) | |||||||
\(12\) | 0.852471 | 0.246087 | ||||||||
\(13\) | 2.25813 | 0.626292 | 0.313146 | − | 0.949705i | \(-0.398617\pi\) | ||||
0.313146 | + | 0.949705i | \(0.398617\pi\) | |||||||
\(14\) | 1.07123 | 0.286298 | ||||||||
\(15\) | 1.60541 | 0.414514 | ||||||||
\(16\) | −1.56835 | −0.392088 | ||||||||
\(17\) | 7.21920 | 1.75091 | 0.875456 | − | 0.483297i | \(-0.160561\pi\) | ||||
0.875456 | + | 0.483297i | \(0.160561\pi\) | |||||||
\(18\) | −1.07123 | −0.252491 | ||||||||
\(19\) | 3.29499 | 0.755924 | 0.377962 | − | 0.925821i | \(-0.376625\pi\) | ||||
0.377962 | + | 0.925821i | \(0.376625\pi\) | |||||||
\(20\) | 1.36856 | 0.306020 | ||||||||
\(21\) | 1.00000 | 0.218218 | ||||||||
\(22\) | −4.23537 | −0.902983 | ||||||||
\(23\) | 7.63636 | 1.59229 | 0.796146 | − | 0.605105i | \(-0.206869\pi\) | ||||
0.796146 | + | 0.605105i | \(0.206869\pi\) | |||||||
\(24\) | −3.05565 | −0.623731 | ||||||||
\(25\) | −2.42267 | −0.484533 | ||||||||
\(26\) | −2.41897 | −0.474399 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 0.852471 | 0.161102 | ||||||||
\(29\) | 2.20779 | 0.409975 | 0.204988 | − | 0.978765i | \(-0.434285\pi\) | ||||
0.204988 | + | 0.978765i | \(0.434285\pi\) | |||||||
\(30\) | −1.71976 | −0.313983 | ||||||||
\(31\) | 3.76529 | 0.676265 | 0.338133 | − | 0.941098i | \(-0.390205\pi\) | ||||
0.338133 | + | 0.941098i | \(0.390205\pi\) | |||||||
\(32\) | −4.43123 | −0.783338 | ||||||||
\(33\) | −3.95375 | −0.688259 | ||||||||
\(34\) | −7.73341 | −1.32627 | ||||||||
\(35\) | 1.60541 | 0.271363 | ||||||||
\(36\) | −0.852471 | −0.142079 | ||||||||
\(37\) | 7.13126 | 1.17237 | 0.586186 | − | 0.810177i | \(-0.300629\pi\) | ||||
0.586186 | + | 0.810177i | \(0.300629\pi\) | |||||||
\(38\) | −3.52969 | −0.572591 | ||||||||
\(39\) | −2.25813 | −0.361590 | ||||||||
\(40\) | −4.90556 | −0.775637 | ||||||||
\(41\) | 2.60553 | 0.406915 | 0.203458 | − | 0.979084i | \(-0.434782\pi\) | ||||
0.203458 | + | 0.979084i | \(0.434782\pi\) | |||||||
\(42\) | −1.07123 | −0.165294 | ||||||||
\(43\) | −4.92670 | −0.751314 | −0.375657 | − | 0.926759i | \(-0.622583\pi\) | ||||
−0.375657 | + | 0.926759i | \(0.622583\pi\) | |||||||
\(44\) | −3.37046 | −0.508116 | ||||||||
\(45\) | −1.60541 | −0.239320 | ||||||||
\(46\) | −8.18029 | −1.20612 | ||||||||
\(47\) | −3.37970 | −0.492980 | −0.246490 | − | 0.969145i | \(-0.579277\pi\) | ||||
−0.246490 | + | 0.969145i | \(0.579277\pi\) | |||||||
\(48\) | 1.56835 | 0.226372 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 2.59523 | 0.367021 | ||||||||
\(51\) | −7.21920 | −1.01089 | ||||||||
\(52\) | −1.92499 | −0.266948 | ||||||||
\(53\) | −6.43059 | −0.883309 | −0.441655 | − | 0.897185i | \(-0.645608\pi\) | ||||
−0.441655 | + | 0.897185i | \(0.645608\pi\) | |||||||
\(54\) | 1.07123 | 0.145776 | ||||||||
\(55\) | −6.34738 | −0.855880 | ||||||||
\(56\) | −3.05565 | −0.408328 | ||||||||
\(57\) | −3.29499 | −0.436433 | ||||||||
\(58\) | −2.36504 | −0.310545 | ||||||||
\(59\) | 7.10117 | 0.924494 | 0.462247 | − | 0.886751i | \(-0.347043\pi\) | ||||
0.462247 | + | 0.886751i | \(0.347043\pi\) | |||||||
\(60\) | −1.36856 | −0.176681 | ||||||||
\(61\) | 9.46455 | 1.21181 | 0.605906 | − | 0.795536i | \(-0.292811\pi\) | ||||
0.605906 | + | 0.795536i | \(0.292811\pi\) | |||||||
\(62\) | −4.03348 | −0.512252 | ||||||||
\(63\) | −1.00000 | −0.125988 | ||||||||
\(64\) | 7.88356 | 0.985445 | ||||||||
\(65\) | −3.62521 | −0.449652 | ||||||||
\(66\) | 4.23537 | 0.521338 | ||||||||
\(67\) | −2.59510 | −0.317042 | −0.158521 | − | 0.987356i | \(-0.550673\pi\) | ||||
−0.158521 | + | 0.987356i | \(0.550673\pi\) | |||||||
\(68\) | −6.15416 | −0.746301 | ||||||||
\(69\) | −7.63636 | −0.919310 | ||||||||
\(70\) | −1.71976 | −0.205550 | ||||||||
\(71\) | −3.53690 | −0.419753 | −0.209877 | − | 0.977728i | \(-0.567306\pi\) | ||||
−0.209877 | + | 0.977728i | \(0.567306\pi\) | |||||||
\(72\) | 3.05565 | 0.360111 | ||||||||
\(73\) | −12.6813 | −1.48424 | −0.742119 | − | 0.670268i | \(-0.766179\pi\) | ||||
−0.742119 | + | 0.670268i | \(0.766179\pi\) | |||||||
\(74\) | −7.63920 | −0.888039 | ||||||||
\(75\) | 2.42267 | 0.279745 | ||||||||
\(76\) | −2.80889 | −0.322202 | ||||||||
\(77\) | −3.95375 | −0.450572 | ||||||||
\(78\) | 2.41897 | 0.273894 | ||||||||
\(79\) | 9.03996 | 1.01707 | 0.508537 | − | 0.861040i | \(-0.330186\pi\) | ||||
0.508537 | + | 0.861040i | \(0.330186\pi\) | |||||||
\(80\) | 2.51784 | 0.281503 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −2.79112 | −0.308227 | ||||||||
\(83\) | 1.94384 | 0.213364 | 0.106682 | − | 0.994293i | \(-0.465977\pi\) | ||||
0.106682 | + | 0.994293i | \(0.465977\pi\) | |||||||
\(84\) | −0.852471 | −0.0930122 | ||||||||
\(85\) | −11.5898 | −1.25709 | ||||||||
\(86\) | 5.27761 | 0.569100 | ||||||||
\(87\) | −2.20779 | −0.236699 | ||||||||
\(88\) | 12.0813 | 1.28787 | ||||||||
\(89\) | −1.89187 | −0.200538 | −0.100269 | − | 0.994960i | \(-0.531970\pi\) | ||||
−0.100269 | + | 0.994960i | \(0.531970\pi\) | |||||||
\(90\) | 1.71976 | 0.181278 | ||||||||
\(91\) | −2.25813 | −0.236716 | ||||||||
\(92\) | −6.50978 | −0.678691 | ||||||||
\(93\) | −3.76529 | −0.390442 | ||||||||
\(94\) | 3.62043 | 0.373419 | ||||||||
\(95\) | −5.28981 | −0.542723 | ||||||||
\(96\) | 4.43123 | 0.452261 | ||||||||
\(97\) | 10.9501 | 1.11181 | 0.555906 | − | 0.831245i | \(-0.312372\pi\) | ||||
0.555906 | + | 0.831245i | \(0.312372\pi\) | |||||||
\(98\) | −1.07123 | −0.108210 | ||||||||
\(99\) | 3.95375 | 0.397367 | ||||||||
\(100\) | 2.06525 | 0.206525 | ||||||||
\(101\) | −16.7754 | −1.66921 | −0.834606 | − | 0.550847i | \(-0.814305\pi\) | ||||
−0.834606 | + | 0.550847i | \(0.814305\pi\) | |||||||
\(102\) | 7.73341 | 0.765721 | ||||||||
\(103\) | 7.97639 | 0.785937 | 0.392968 | − | 0.919552i | \(-0.371448\pi\) | ||||
0.392968 | + | 0.919552i | \(0.371448\pi\) | |||||||
\(104\) | 6.90004 | 0.676604 | ||||||||
\(105\) | −1.60541 | −0.156672 | ||||||||
\(106\) | 6.88862 | 0.669082 | ||||||||
\(107\) | −5.72343 | −0.553305 | −0.276653 | − | 0.960970i | \(-0.589225\pi\) | ||||
−0.276653 | + | 0.960970i | \(0.589225\pi\) | |||||||
\(108\) | 0.852471 | 0.0820291 | ||||||||
\(109\) | 4.81420 | 0.461117 | 0.230558 | − | 0.973058i | \(-0.425945\pi\) | ||||
0.230558 | + | 0.973058i | \(0.425945\pi\) | |||||||
\(110\) | 6.79949 | 0.648306 | ||||||||
\(111\) | −7.13126 | −0.676869 | ||||||||
\(112\) | 1.56835 | 0.148195 | ||||||||
\(113\) | 6.71853 | 0.632026 | 0.316013 | − | 0.948755i | \(-0.397656\pi\) | ||||
0.316013 | + | 0.948755i | \(0.397656\pi\) | |||||||
\(114\) | 3.52969 | 0.330586 | ||||||||
\(115\) | −12.2595 | −1.14320 | ||||||||
\(116\) | −1.88207 | −0.174746 | ||||||||
\(117\) | 2.25813 | 0.208764 | ||||||||
\(118\) | −7.60697 | −0.700279 | ||||||||
\(119\) | −7.21920 | −0.661783 | ||||||||
\(120\) | 4.90556 | 0.447814 | ||||||||
\(121\) | 4.63214 | 0.421103 | ||||||||
\(122\) | −10.1387 | −0.917914 | ||||||||
\(123\) | −2.60553 | −0.234933 | ||||||||
\(124\) | −3.20980 | −0.288248 | ||||||||
\(125\) | 11.9164 | 1.06584 | ||||||||
\(126\) | 1.07123 | 0.0954326 | ||||||||
\(127\) | 8.46541 | 0.751184 | 0.375592 | − | 0.926785i | \(-0.377439\pi\) | ||||
0.375592 | + | 0.926785i | \(0.377439\pi\) | |||||||
\(128\) | 0.417375 | 0.0368911 | ||||||||
\(129\) | 4.92670 | 0.433771 | ||||||||
\(130\) | 3.88343 | 0.340599 | ||||||||
\(131\) | −7.42020 | −0.648306 | −0.324153 | − | 0.946005i | \(-0.605079\pi\) | ||||
−0.324153 | + | 0.946005i | \(0.605079\pi\) | |||||||
\(132\) | 3.37046 | 0.293361 | ||||||||
\(133\) | −3.29499 | −0.285712 | ||||||||
\(134\) | 2.77995 | 0.240151 | ||||||||
\(135\) | 1.60541 | 0.138171 | ||||||||
\(136\) | 22.0593 | 1.89157 | ||||||||
\(137\) | 1.68559 | 0.144010 | 0.0720050 | − | 0.997404i | \(-0.477060\pi\) | ||||
0.0720050 | + | 0.997404i | \(0.477060\pi\) | |||||||
\(138\) | 8.18029 | 0.696352 | ||||||||
\(139\) | −9.79050 | −0.830419 | −0.415210 | − | 0.909726i | \(-0.636292\pi\) | ||||
−0.415210 | + | 0.909726i | \(0.636292\pi\) | |||||||
\(140\) | −1.36856 | −0.115665 | ||||||||
\(141\) | 3.37970 | 0.284622 | ||||||||
\(142\) | 3.78883 | 0.317952 | ||||||||
\(143\) | 8.92807 | 0.746602 | ||||||||
\(144\) | −1.56835 | −0.130696 | ||||||||
\(145\) | −3.54439 | −0.294346 | ||||||||
\(146\) | 13.5846 | 1.12427 | ||||||||
\(147\) | −1.00000 | −0.0824786 | ||||||||
\(148\) | −6.07919 | −0.499706 | ||||||||
\(149\) | 0.674214 | 0.0552338 | 0.0276169 | − | 0.999619i | \(-0.491208\pi\) | ||||
0.0276169 | + | 0.999619i | \(0.491208\pi\) | |||||||
\(150\) | −2.59523 | −0.211899 | ||||||||
\(151\) | 6.29611 | 0.512370 | 0.256185 | − | 0.966628i | \(-0.417534\pi\) | ||||
0.256185 | + | 0.966628i | \(0.417534\pi\) | |||||||
\(152\) | 10.0683 | 0.816650 | ||||||||
\(153\) | 7.21920 | 0.583638 | ||||||||
\(154\) | 4.23537 | 0.341296 | ||||||||
\(155\) | −6.04482 | −0.485531 | ||||||||
\(156\) | 1.92499 | 0.154122 | ||||||||
\(157\) | −17.4938 | −1.39616 | −0.698078 | − | 0.716022i | \(-0.745961\pi\) | ||||
−0.698078 | + | 0.716022i | \(0.745961\pi\) | |||||||
\(158\) | −9.68385 | −0.770406 | ||||||||
\(159\) | 6.43059 | 0.509979 | ||||||||
\(160\) | 7.11393 | 0.562406 | ||||||||
\(161\) | −7.63636 | −0.601830 | ||||||||
\(162\) | −1.07123 | −0.0841636 | ||||||||
\(163\) | 22.3848 | 1.75332 | 0.876658 | − | 0.481114i | \(-0.159768\pi\) | ||||
0.876658 | + | 0.481114i | \(0.159768\pi\) | |||||||
\(164\) | −2.22114 | −0.173442 | ||||||||
\(165\) | 6.34738 | 0.494143 | ||||||||
\(166\) | −2.08229 | −0.161617 | ||||||||
\(167\) | −24.6831 | −1.91004 | −0.955018 | − | 0.296548i | \(-0.904165\pi\) | ||||
−0.955018 | + | 0.296548i | \(0.904165\pi\) | |||||||
\(168\) | 3.05565 | 0.235748 | ||||||||
\(169\) | −7.90087 | −0.607759 | ||||||||
\(170\) | 12.4153 | 0.952207 | ||||||||
\(171\) | 3.29499 | 0.251975 | ||||||||
\(172\) | 4.19987 | 0.320237 | ||||||||
\(173\) | 11.6998 | 0.889519 | 0.444759 | − | 0.895650i | \(-0.353289\pi\) | ||||
0.444759 | + | 0.895650i | \(0.353289\pi\) | |||||||
\(174\) | 2.36504 | 0.179293 | ||||||||
\(175\) | 2.42267 | 0.183136 | ||||||||
\(176\) | −6.20087 | −0.467408 | ||||||||
\(177\) | −7.10117 | −0.533757 | ||||||||
\(178\) | 2.02663 | 0.151902 | ||||||||
\(179\) | −8.71883 | −0.651676 | −0.325838 | − | 0.945426i | \(-0.605646\pi\) | ||||
−0.325838 | + | 0.945426i | \(0.605646\pi\) | |||||||
\(180\) | 1.36856 | 0.102007 | ||||||||
\(181\) | 15.5238 | 1.15387 | 0.576936 | − | 0.816790i | \(-0.304248\pi\) | ||||
0.576936 | + | 0.816790i | \(0.304248\pi\) | |||||||
\(182\) | 2.41897 | 0.179306 | ||||||||
\(183\) | −9.46455 | −0.699640 | ||||||||
\(184\) | 23.3340 | 1.72021 | ||||||||
\(185\) | −11.4486 | −0.841716 | ||||||||
\(186\) | 4.03348 | 0.295749 | ||||||||
\(187\) | 28.5429 | 2.08726 | ||||||||
\(188\) | 2.88110 | 0.210126 | ||||||||
\(189\) | 1.00000 | 0.0727393 | ||||||||
\(190\) | 5.66659 | 0.411098 | ||||||||
\(191\) | 1.00000 | 0.0723575 | ||||||||
\(192\) | −7.88356 | −0.568947 | ||||||||
\(193\) | 8.77267 | 0.631470 | 0.315735 | − | 0.948847i | \(-0.397749\pi\) | ||||
0.315735 | + | 0.948847i | \(0.397749\pi\) | |||||||
\(194\) | −11.7300 | −0.842166 | ||||||||
\(195\) | 3.62521 | 0.259607 | ||||||||
\(196\) | −0.852471 | −0.0608908 | ||||||||
\(197\) | 20.1146 | 1.43311 | 0.716554 | − | 0.697532i | \(-0.245718\pi\) | ||||
0.716554 | + | 0.697532i | \(0.245718\pi\) | |||||||
\(198\) | −4.23537 | −0.300994 | ||||||||
\(199\) | −9.89253 | −0.701263 | −0.350631 | − | 0.936514i | \(-0.614033\pi\) | ||||
−0.350631 | + | 0.936514i | \(0.614033\pi\) | |||||||
\(200\) | −7.40281 | −0.523458 | ||||||||
\(201\) | 2.59510 | 0.183044 | ||||||||
\(202\) | 17.9702 | 1.26438 | ||||||||
\(203\) | −2.20779 | −0.154956 | ||||||||
\(204\) | 6.15416 | 0.430877 | ||||||||
\(205\) | −4.18294 | −0.292149 | ||||||||
\(206\) | −8.54453 | −0.595325 | ||||||||
\(207\) | 7.63636 | 0.530764 | ||||||||
\(208\) | −3.54153 | −0.245561 | ||||||||
\(209\) | 13.0276 | 0.901137 | ||||||||
\(210\) | 1.71976 | 0.118675 | ||||||||
\(211\) | 10.9634 | 0.754750 | 0.377375 | − | 0.926061i | \(-0.376827\pi\) | ||||
0.377375 | + | 0.926061i | \(0.376827\pi\) | |||||||
\(212\) | 5.48189 | 0.376498 | ||||||||
\(213\) | 3.53690 | 0.242345 | ||||||||
\(214\) | 6.13110 | 0.419113 | ||||||||
\(215\) | 7.90935 | 0.539413 | ||||||||
\(216\) | −3.05565 | −0.207910 | ||||||||
\(217\) | −3.76529 | −0.255604 | ||||||||
\(218\) | −5.15710 | −0.349283 | ||||||||
\(219\) | 12.6813 | 0.856925 | ||||||||
\(220\) | 5.41096 | 0.364807 | ||||||||
\(221\) | 16.3019 | 1.09658 | ||||||||
\(222\) | 7.63920 | 0.512709 | ||||||||
\(223\) | 5.73082 | 0.383764 | 0.191882 | − | 0.981418i | \(-0.438541\pi\) | ||||
0.191882 | + | 0.981418i | \(0.438541\pi\) | |||||||
\(224\) | 4.43123 | 0.296074 | ||||||||
\(225\) | −2.42267 | −0.161511 | ||||||||
\(226\) | −7.19708 | −0.478743 | ||||||||
\(227\) | −18.8079 | −1.24832 | −0.624162 | − | 0.781295i | \(-0.714560\pi\) | ||||
−0.624162 | + | 0.781295i | \(0.714560\pi\) | |||||||
\(228\) | 2.80889 | 0.186023 | ||||||||
\(229\) | −6.31690 | −0.417432 | −0.208716 | − | 0.977976i | \(-0.566928\pi\) | ||||
−0.208716 | + | 0.977976i | \(0.566928\pi\) | |||||||
\(230\) | 13.1327 | 0.865944 | ||||||||
\(231\) | 3.95375 | 0.260138 | ||||||||
\(232\) | 6.74621 | 0.442910 | ||||||||
\(233\) | −1.27413 | −0.0834710 | −0.0417355 | − | 0.999129i | \(-0.513289\pi\) | ||||
−0.0417355 | + | 0.999129i | \(0.513289\pi\) | |||||||
\(234\) | −2.41897 | −0.158133 | ||||||||
\(235\) | 5.42579 | 0.353940 | ||||||||
\(236\) | −6.05354 | −0.394052 | ||||||||
\(237\) | −9.03996 | −0.587208 | ||||||||
\(238\) | 7.73341 | 0.501282 | ||||||||
\(239\) | −22.0775 | −1.42807 | −0.714036 | − | 0.700109i | \(-0.753135\pi\) | ||||
−0.714036 | + | 0.700109i | \(0.753135\pi\) | |||||||
\(240\) | −2.51784 | −0.162526 | ||||||||
\(241\) | −18.2835 | −1.17774 | −0.588871 | − | 0.808227i | \(-0.700427\pi\) | ||||
−0.588871 | + | 0.808227i | \(0.700427\pi\) | |||||||
\(242\) | −4.96207 | −0.318974 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | −8.06826 | −0.516517 | ||||||||
\(245\) | −1.60541 | −0.102566 | ||||||||
\(246\) | 2.79112 | 0.177955 | ||||||||
\(247\) | 7.44051 | 0.473429 | ||||||||
\(248\) | 11.5054 | 0.730592 | ||||||||
\(249\) | −1.94384 | −0.123186 | ||||||||
\(250\) | −12.7652 | −0.807341 | ||||||||
\(251\) | 24.5159 | 1.54743 | 0.773715 | − | 0.633533i | \(-0.218396\pi\) | ||||
0.773715 | + | 0.633533i | \(0.218396\pi\) | |||||||
\(252\) | 0.852471 | 0.0537006 | ||||||||
\(253\) | 30.1923 | 1.89817 | ||||||||
\(254\) | −9.06839 | −0.569001 | ||||||||
\(255\) | 11.5898 | 0.725779 | ||||||||
\(256\) | −16.2142 | −1.01339 | ||||||||
\(257\) | 1.86568 | 0.116378 | 0.0581889 | − | 0.998306i | \(-0.481467\pi\) | ||||
0.0581889 | + | 0.998306i | \(0.481467\pi\) | |||||||
\(258\) | −5.27761 | −0.328570 | ||||||||
\(259\) | −7.13126 | −0.443115 | ||||||||
\(260\) | 3.09039 | 0.191658 | ||||||||
\(261\) | 2.20779 | 0.136658 | ||||||||
\(262\) | 7.94872 | 0.491074 | ||||||||
\(263\) | −13.3481 | −0.823076 | −0.411538 | − | 0.911392i | \(-0.635008\pi\) | ||||
−0.411538 | + | 0.911392i | \(0.635008\pi\) | |||||||
\(264\) | −12.0813 | −0.743550 | ||||||||
\(265\) | 10.3237 | 0.634181 | ||||||||
\(266\) | 3.52969 | 0.216419 | ||||||||
\(267\) | 1.89187 | 0.115781 | ||||||||
\(268\) | 2.21225 | 0.135135 | ||||||||
\(269\) | 8.19868 | 0.499883 | 0.249941 | − | 0.968261i | \(-0.419589\pi\) | ||||
0.249941 | + | 0.968261i | \(0.419589\pi\) | |||||||
\(270\) | −1.71976 | −0.104661 | ||||||||
\(271\) | −24.3911 | −1.48165 | −0.740826 | − | 0.671697i | \(-0.765566\pi\) | ||||
−0.740826 | + | 0.671697i | \(0.765566\pi\) | |||||||
\(272\) | −11.3222 | −0.686511 | ||||||||
\(273\) | 2.25813 | 0.136668 | ||||||||
\(274\) | −1.80565 | −0.109084 | ||||||||
\(275\) | −9.57862 | −0.577612 | ||||||||
\(276\) | 6.50978 | 0.391843 | ||||||||
\(277\) | −1.15495 | −0.0693943 | −0.0346972 | − | 0.999398i | \(-0.511047\pi\) | ||||
−0.0346972 | + | 0.999398i | \(0.511047\pi\) | |||||||
\(278\) | 10.4879 | 0.629020 | ||||||||
\(279\) | 3.76529 | 0.225422 | ||||||||
\(280\) | 4.90556 | 0.293163 | ||||||||
\(281\) | −7.98233 | −0.476186 | −0.238093 | − | 0.971242i | \(-0.576522\pi\) | ||||
−0.238093 | + | 0.971242i | \(0.576522\pi\) | |||||||
\(282\) | −3.62043 | −0.215593 | ||||||||
\(283\) | 27.6027 | 1.64081 | 0.820406 | − | 0.571781i | \(-0.193747\pi\) | ||||
0.820406 | + | 0.571781i | \(0.193747\pi\) | |||||||
\(284\) | 3.01511 | 0.178914 | ||||||||
\(285\) | 5.28981 | 0.313341 | ||||||||
\(286\) | −9.56399 | −0.565531 | ||||||||
\(287\) | −2.60553 | −0.153800 | ||||||||
\(288\) | −4.43123 | −0.261113 | ||||||||
\(289\) | 35.1168 | 2.06570 | ||||||||
\(290\) | 3.79685 | 0.222959 | ||||||||
\(291\) | −10.9501 | −0.641904 | ||||||||
\(292\) | 10.8105 | 0.632635 | ||||||||
\(293\) | 10.6042 | 0.619505 | 0.309752 | − | 0.950817i | \(-0.399754\pi\) | ||||
0.309752 | + | 0.950817i | \(0.399754\pi\) | |||||||
\(294\) | 1.07123 | 0.0624753 | ||||||||
\(295\) | −11.4003 | −0.663750 | ||||||||
\(296\) | 21.7906 | 1.26655 | ||||||||
\(297\) | −3.95375 | −0.229420 | ||||||||
\(298\) | −0.722237 | −0.0418381 | ||||||||
\(299\) | 17.2439 | 0.997239 | ||||||||
\(300\) | −2.06525 | −0.119237 | ||||||||
\(301\) | 4.92670 | 0.283970 | ||||||||
\(302\) | −6.74457 | −0.388106 | ||||||||
\(303\) | 16.7754 | 0.963720 | ||||||||
\(304\) | −5.16771 | −0.296388 | ||||||||
\(305\) | −15.1945 | −0.870033 | ||||||||
\(306\) | −7.73341 | −0.442089 | ||||||||
\(307\) | −0.647153 | −0.0369350 | −0.0184675 | − | 0.999829i | \(-0.505879\pi\) | ||||
−0.0184675 | + | 0.999829i | \(0.505879\pi\) | |||||||
\(308\) | 3.37046 | 0.192050 | ||||||||
\(309\) | −7.97639 | −0.453761 | ||||||||
\(310\) | 6.47538 | 0.367777 | ||||||||
\(311\) | 1.95496 | 0.110856 | 0.0554279 | − | 0.998463i | \(-0.482348\pi\) | ||||
0.0554279 | + | 0.998463i | \(0.482348\pi\) | |||||||
\(312\) | −6.90004 | −0.390638 | ||||||||
\(313\) | 4.32445 | 0.244432 | 0.122216 | − | 0.992503i | \(-0.461000\pi\) | ||||
0.122216 | + | 0.992503i | \(0.461000\pi\) | |||||||
\(314\) | 18.7398 | 1.05755 | ||||||||
\(315\) | 1.60541 | 0.0904545 | ||||||||
\(316\) | −7.70630 | −0.433513 | ||||||||
\(317\) | −8.61346 | −0.483780 | −0.241890 | − | 0.970304i | \(-0.577767\pi\) | ||||
−0.241890 | + | 0.970304i | \(0.577767\pi\) | |||||||
\(318\) | −6.88862 | −0.386295 | ||||||||
\(319\) | 8.72903 | 0.488732 | ||||||||
\(320\) | −12.6563 | −0.707510 | ||||||||
\(321\) | 5.72343 | 0.319451 | ||||||||
\(322\) | 8.18029 | 0.455869 | ||||||||
\(323\) | 23.7872 | 1.32356 | ||||||||
\(324\) | −0.852471 | −0.0473595 | ||||||||
\(325\) | −5.47069 | −0.303459 | ||||||||
\(326\) | −23.9793 | −1.32809 | ||||||||
\(327\) | −4.81420 | −0.266226 | ||||||||
\(328\) | 7.96158 | 0.439605 | ||||||||
\(329\) | 3.37970 | 0.186329 | ||||||||
\(330\) | −6.79949 | −0.374300 | ||||||||
\(331\) | 33.1706 | 1.82322 | 0.911610 | − | 0.411057i | \(-0.134840\pi\) | ||||
0.911610 | + | 0.411057i | \(0.134840\pi\) | |||||||
\(332\) | −1.65706 | −0.0909433 | ||||||||
\(333\) | 7.13126 | 0.390790 | ||||||||
\(334\) | 26.4412 | 1.44680 | ||||||||
\(335\) | 4.16620 | 0.227624 | ||||||||
\(336\) | −1.56835 | −0.0855605 | ||||||||
\(337\) | 24.7860 | 1.35018 | 0.675090 | − | 0.737735i | \(-0.264105\pi\) | ||||
0.675090 | + | 0.737735i | \(0.264105\pi\) | |||||||
\(338\) | 8.46363 | 0.460361 | ||||||||
\(339\) | −6.71853 | −0.364901 | ||||||||
\(340\) | 9.87993 | 0.535814 | ||||||||
\(341\) | 14.8870 | 0.806176 | ||||||||
\(342\) | −3.52969 | −0.190864 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | −15.0542 | −0.811670 | ||||||||
\(345\) | 12.2595 | 0.660028 | ||||||||
\(346\) | −12.5331 | −0.673786 | ||||||||
\(347\) | −15.3519 | −0.824134 | −0.412067 | − | 0.911154i | \(-0.635193\pi\) | ||||
−0.412067 | + | 0.911154i | \(0.635193\pi\) | |||||||
\(348\) | 1.88207 | 0.100890 | ||||||||
\(349\) | −31.4705 | −1.68458 | −0.842288 | − | 0.539027i | \(-0.818792\pi\) | ||||
−0.842288 | + | 0.539027i | \(0.818792\pi\) | |||||||
\(350\) | −2.59523 | −0.138721 | ||||||||
\(351\) | −2.25813 | −0.120530 | ||||||||
\(352\) | −17.5200 | −0.933818 | ||||||||
\(353\) | −26.5844 | −1.41495 | −0.707474 | − | 0.706740i | \(-0.750165\pi\) | ||||
−0.707474 | + | 0.706740i | \(0.750165\pi\) | |||||||
\(354\) | 7.60697 | 0.404306 | ||||||||
\(355\) | 5.67817 | 0.301366 | ||||||||
\(356\) | 1.61277 | 0.0854765 | ||||||||
\(357\) | 7.21920 | 0.382080 | ||||||||
\(358\) | 9.33985 | 0.493626 | ||||||||
\(359\) | 7.32424 | 0.386559 | 0.193279 | − | 0.981144i | \(-0.438088\pi\) | ||||
0.193279 | + | 0.981144i | \(0.438088\pi\) | |||||||
\(360\) | −4.90556 | −0.258546 | ||||||||
\(361\) | −8.14301 | −0.428580 | ||||||||
\(362\) | −16.6295 | −0.874026 | ||||||||
\(363\) | −4.63214 | −0.243124 | ||||||||
\(364\) | 1.92499 | 0.100897 | ||||||||
\(365\) | 20.3587 | 1.06562 | ||||||||
\(366\) | 10.1387 | 0.529958 | ||||||||
\(367\) | −36.3112 | −1.89543 | −0.947714 | − | 0.319121i | \(-0.896612\pi\) | ||||
−0.947714 | + | 0.319121i | \(0.896612\pi\) | |||||||
\(368\) | −11.9765 | −0.624318 | ||||||||
\(369\) | 2.60553 | 0.135638 | ||||||||
\(370\) | 12.2640 | 0.637576 | ||||||||
\(371\) | 6.43059 | 0.333859 | ||||||||
\(372\) | 3.20980 | 0.166420 | ||||||||
\(373\) | 9.04125 | 0.468138 | 0.234069 | − | 0.972220i | \(-0.424796\pi\) | ||||
0.234069 | + | 0.972220i | \(0.424796\pi\) | |||||||
\(374\) | −30.5759 | −1.58104 | ||||||||
\(375\) | −11.9164 | −0.615360 | ||||||||
\(376\) | −10.3272 | −0.532583 | ||||||||
\(377\) | 4.98546 | 0.256764 | ||||||||
\(378\) | −1.07123 | −0.0550980 | ||||||||
\(379\) | 16.9931 | 0.872879 | 0.436440 | − | 0.899734i | \(-0.356239\pi\) | ||||
0.436440 | + | 0.899734i | \(0.356239\pi\) | |||||||
\(380\) | 4.50941 | 0.231328 | ||||||||
\(381\) | −8.46541 | −0.433696 | ||||||||
\(382\) | −1.07123 | −0.0548088 | ||||||||
\(383\) | −2.75744 | −0.140899 | −0.0704494 | − | 0.997515i | \(-0.522443\pi\) | ||||
−0.0704494 | + | 0.997515i | \(0.522443\pi\) | |||||||
\(384\) | −0.417375 | −0.0212991 | ||||||||
\(385\) | 6.34738 | 0.323492 | ||||||||
\(386\) | −9.39752 | −0.478321 | ||||||||
\(387\) | −4.92670 | −0.250438 | ||||||||
\(388\) | −9.33462 | −0.473893 | ||||||||
\(389\) | 24.7868 | 1.25674 | 0.628369 | − | 0.777915i | \(-0.283723\pi\) | ||||
0.628369 | + | 0.777915i | \(0.283723\pi\) | |||||||
\(390\) | −3.88343 | −0.196645 | ||||||||
\(391\) | 55.1284 | 2.78796 | ||||||||
\(392\) | 3.05565 | 0.154333 | ||||||||
\(393\) | 7.42020 | 0.374299 | ||||||||
\(394\) | −21.5473 | −1.08554 | ||||||||
\(395\) | −14.5128 | −0.730219 | ||||||||
\(396\) | −3.37046 | −0.169372 | ||||||||
\(397\) | −22.4693 | −1.12770 | −0.563851 | − | 0.825877i | \(-0.690681\pi\) | ||||
−0.563851 | + | 0.825877i | \(0.690681\pi\) | |||||||
\(398\) | 10.5972 | 0.531187 | ||||||||
\(399\) | 3.29499 | 0.164956 | ||||||||
\(400\) | 3.79959 | 0.189980 | ||||||||
\(401\) | 13.0849 | 0.653431 | 0.326715 | − | 0.945123i | \(-0.394058\pi\) | ||||
0.326715 | + | 0.945123i | \(0.394058\pi\) | |||||||
\(402\) | −2.77995 | −0.138651 | ||||||||
\(403\) | 8.50249 | 0.423539 | ||||||||
\(404\) | 14.3005 | 0.711478 | ||||||||
\(405\) | −1.60541 | −0.0797733 | ||||||||
\(406\) | 2.36504 | 0.117375 | ||||||||
\(407\) | 28.1952 | 1.39758 | ||||||||
\(408\) | −22.0593 | −1.09210 | ||||||||
\(409\) | −9.41484 | −0.465534 | −0.232767 | − | 0.972533i | \(-0.574778\pi\) | ||||
−0.232767 | + | 0.972533i | \(0.574778\pi\) | |||||||
\(410\) | 4.48088 | 0.221295 | ||||||||
\(411\) | −1.68559 | −0.0831442 | ||||||||
\(412\) | −6.79964 | −0.334994 | ||||||||
\(413\) | −7.10117 | −0.349426 | ||||||||
\(414\) | −8.18029 | −0.402039 | ||||||||
\(415\) | −3.12065 | −0.153187 | ||||||||
\(416\) | −10.0063 | −0.490598 | ||||||||
\(417\) | 9.79050 | 0.479443 | ||||||||
\(418\) | −13.9555 | −0.682586 | ||||||||
\(419\) | −27.5630 | −1.34654 | −0.673270 | − | 0.739397i | \(-0.735111\pi\) | ||||
−0.673270 | + | 0.739397i | \(0.735111\pi\) | |||||||
\(420\) | 1.36856 | 0.0667791 | ||||||||
\(421\) | −0.485100 | −0.0236423 | −0.0118212 | − | 0.999930i | \(-0.503763\pi\) | ||||
−0.0118212 | + | 0.999930i | \(0.503763\pi\) | |||||||
\(422\) | −11.7443 | −0.571702 | ||||||||
\(423\) | −3.37970 | −0.164327 | ||||||||
\(424\) | −19.6496 | −0.954269 | ||||||||
\(425\) | −17.4897 | −0.848376 | ||||||||
\(426\) | −3.78883 | −0.183569 | ||||||||
\(427\) | −9.46455 | −0.458022 | ||||||||
\(428\) | 4.87906 | 0.235838 | ||||||||
\(429\) | −8.92807 | −0.431051 | ||||||||
\(430\) | −8.47272 | −0.408591 | ||||||||
\(431\) | 40.3460 | 1.94340 | 0.971699 | − | 0.236224i | \(-0.0759099\pi\) | ||||
0.971699 | + | 0.236224i | \(0.0759099\pi\) | |||||||
\(432\) | 1.56835 | 0.0754573 | ||||||||
\(433\) | 3.01364 | 0.144826 | 0.0724132 | − | 0.997375i | \(-0.476930\pi\) | ||||
0.0724132 | + | 0.997375i | \(0.476930\pi\) | |||||||
\(434\) | 4.03348 | 0.193613 | ||||||||
\(435\) | 3.54439 | 0.169941 | ||||||||
\(436\) | −4.10397 | −0.196544 | ||||||||
\(437\) | 25.1618 | 1.20365 | ||||||||
\(438\) | −13.5846 | −0.649097 | ||||||||
\(439\) | 10.7374 | 0.512469 | 0.256235 | − | 0.966615i | \(-0.417518\pi\) | ||||
0.256235 | + | 0.966615i | \(0.417518\pi\) | |||||||
\(440\) | −19.3953 | −0.924637 | ||||||||
\(441\) | 1.00000 | 0.0476190 | ||||||||
\(442\) | −17.4630 | −0.830631 | ||||||||
\(443\) | −22.1940 | −1.05447 | −0.527234 | − | 0.849720i | \(-0.676771\pi\) | ||||
−0.527234 | + | 0.849720i | \(0.676771\pi\) | |||||||
\(444\) | 6.07919 | 0.288506 | ||||||||
\(445\) | 3.03723 | 0.143978 | ||||||||
\(446\) | −6.13902 | −0.290691 | ||||||||
\(447\) | −0.674214 | −0.0318892 | ||||||||
\(448\) | −7.88356 | −0.372463 | ||||||||
\(449\) | 24.0274 | 1.13392 | 0.566962 | − | 0.823744i | \(-0.308119\pi\) | ||||
0.566962 | + | 0.823744i | \(0.308119\pi\) | |||||||
\(450\) | 2.59523 | 0.122340 | ||||||||
\(451\) | 10.3016 | 0.485084 | ||||||||
\(452\) | −5.72736 | −0.269392 | ||||||||
\(453\) | −6.29611 | −0.295817 | ||||||||
\(454\) | 20.1475 | 0.945571 | ||||||||
\(455\) | 3.62521 | 0.169953 | ||||||||
\(456\) | −10.0683 | −0.471493 | ||||||||
\(457\) | −20.1053 | −0.940484 | −0.470242 | − | 0.882537i | \(-0.655833\pi\) | ||||
−0.470242 | + | 0.882537i | \(0.655833\pi\) | |||||||
\(458\) | 6.76684 | 0.316194 | ||||||||
\(459\) | −7.21920 | −0.336963 | ||||||||
\(460\) | 10.4508 | 0.487273 | ||||||||
\(461\) | −30.3736 | −1.41464 | −0.707319 | − | 0.706895i | \(-0.750095\pi\) | ||||
−0.707319 | + | 0.706895i | \(0.750095\pi\) | |||||||
\(462\) | −4.23537 | −0.197047 | ||||||||
\(463\) | 14.1708 | 0.658574 | 0.329287 | − | 0.944230i | \(-0.393192\pi\) | ||||
0.329287 | + | 0.944230i | \(0.393192\pi\) | |||||||
\(464\) | −3.46258 | −0.160746 | ||||||||
\(465\) | 6.04482 | 0.280322 | ||||||||
\(466\) | 1.36488 | 0.0632270 | ||||||||
\(467\) | −36.9095 | −1.70797 | −0.853984 | − | 0.520300i | \(-0.825820\pi\) | ||||
−0.853984 | + | 0.520300i | \(0.825820\pi\) | |||||||
\(468\) | −1.92499 | −0.0889826 | ||||||||
\(469\) | 2.59510 | 0.119831 | ||||||||
\(470\) | −5.81226 | −0.268100 | ||||||||
\(471\) | 17.4938 | 0.806071 | ||||||||
\(472\) | 21.6987 | 0.998762 | ||||||||
\(473\) | −19.4789 | −0.895642 | ||||||||
\(474\) | 9.68385 | 0.444794 | ||||||||
\(475\) | −7.98267 | −0.366270 | ||||||||
\(476\) | 6.15416 | 0.282075 | ||||||||
\(477\) | −6.43059 | −0.294436 | ||||||||
\(478\) | 23.6500 | 1.08173 | ||||||||
\(479\) | −31.4445 | −1.43674 | −0.718368 | − | 0.695664i | \(-0.755110\pi\) | ||||
−0.718368 | + | 0.695664i | \(0.755110\pi\) | |||||||
\(480\) | −7.11393 | −0.324705 | ||||||||
\(481\) | 16.1033 | 0.734246 | ||||||||
\(482\) | 19.5858 | 0.892107 | ||||||||
\(483\) | 7.63636 | 0.347467 | ||||||||
\(484\) | −3.94876 | −0.179489 | ||||||||
\(485\) | −17.5793 | −0.798236 | ||||||||
\(486\) | 1.07123 | 0.0485919 | ||||||||
\(487\) | 17.6044 | 0.797732 | 0.398866 | − | 0.917009i | \(-0.369404\pi\) | ||||
0.398866 | + | 0.917009i | \(0.369404\pi\) | |||||||
\(488\) | 28.9203 | 1.30916 | ||||||||
\(489\) | −22.3848 | −1.01228 | ||||||||
\(490\) | 1.71976 | 0.0776907 | ||||||||
\(491\) | 0.926528 | 0.0418136 | 0.0209068 | − | 0.999781i | \(-0.493345\pi\) | ||||
0.0209068 | + | 0.999781i | \(0.493345\pi\) | |||||||
\(492\) | 2.22114 | 0.100137 | ||||||||
\(493\) | 15.9384 | 0.717831 | ||||||||
\(494\) | −7.97048 | −0.358609 | ||||||||
\(495\) | −6.34738 | −0.285293 | ||||||||
\(496\) | −5.90529 | −0.265155 | ||||||||
\(497\) | 3.53690 | 0.158652 | ||||||||
\(498\) | 2.08229 | 0.0933097 | ||||||||
\(499\) | −16.1234 | −0.721780 | −0.360890 | − | 0.932608i | \(-0.617527\pi\) | ||||
−0.360890 | + | 0.932608i | \(0.617527\pi\) | |||||||
\(500\) | −10.1584 | −0.454297 | ||||||||
\(501\) | 24.6831 | 1.10276 | ||||||||
\(502\) | −26.2621 | −1.17214 | ||||||||
\(503\) | 40.0355 | 1.78509 | 0.892547 | − | 0.450954i | \(-0.148916\pi\) | ||||
0.892547 | + | 0.450954i | \(0.148916\pi\) | |||||||
\(504\) | −3.05565 | −0.136109 | ||||||||
\(505\) | 26.9313 | 1.19843 | ||||||||
\(506\) | −32.3428 | −1.43781 | ||||||||
\(507\) | 7.90087 | 0.350890 | ||||||||
\(508\) | −7.21652 | −0.320181 | ||||||||
\(509\) | −10.9560 | −0.485617 | −0.242809 | − | 0.970074i | \(-0.578069\pi\) | ||||
−0.242809 | + | 0.970074i | \(0.578069\pi\) | |||||||
\(510\) | −12.4153 | −0.549757 | ||||||||
\(511\) | 12.6813 | 0.560989 | ||||||||
\(512\) | 16.5344 | 0.730723 | ||||||||
\(513\) | −3.29499 | −0.145478 | ||||||||
\(514\) | −1.99857 | −0.0881530 | ||||||||
\(515\) | −12.8053 | −0.564271 | ||||||||
\(516\) | −4.19987 | −0.184889 | ||||||||
\(517\) | −13.3625 | −0.587681 | ||||||||
\(518\) | 7.63920 | 0.335647 | ||||||||
\(519\) | −11.6998 | −0.513564 | ||||||||
\(520\) | −11.0774 | −0.485775 | ||||||||
\(521\) | −3.93778 | −0.172517 | −0.0862585 | − | 0.996273i | \(-0.527491\pi\) | ||||
−0.0862585 | + | 0.996273i | \(0.527491\pi\) | |||||||
\(522\) | −2.36504 | −0.103515 | ||||||||
\(523\) | 15.8233 | 0.691903 | 0.345952 | − | 0.938252i | \(-0.387556\pi\) | ||||
0.345952 | + | 0.938252i | \(0.387556\pi\) | |||||||
\(524\) | 6.32550 | 0.276331 | ||||||||
\(525\) | −2.42267 | −0.105734 | ||||||||
\(526\) | 14.2988 | 0.623458 | ||||||||
\(527\) | 27.1823 | 1.18408 | ||||||||
\(528\) | 6.20087 | 0.269858 | ||||||||
\(529\) | 35.3141 | 1.53539 | ||||||||
\(530\) | −11.0590 | −0.480374 | ||||||||
\(531\) | 7.10117 | 0.308165 | ||||||||
\(532\) | 2.80889 | 0.121781 | ||||||||
\(533\) | 5.88361 | 0.254848 | ||||||||
\(534\) | −2.02663 | −0.0877007 | ||||||||
\(535\) | 9.18844 | 0.397251 | ||||||||
\(536\) | −7.92971 | −0.342511 | ||||||||
\(537\) | 8.71883 | 0.376245 | ||||||||
\(538\) | −8.78266 | −0.378647 | ||||||||
\(539\) | 3.95375 | 0.170300 | ||||||||
\(540\) | −1.36856 | −0.0588936 | ||||||||
\(541\) | 31.8076 | 1.36752 | 0.683758 | − | 0.729709i | \(-0.260344\pi\) | ||||
0.683758 | + | 0.729709i | \(0.260344\pi\) | |||||||
\(542\) | 26.1284 | 1.12231 | ||||||||
\(543\) | −15.5238 | −0.666188 | ||||||||
\(544\) | −31.9899 | −1.37156 | ||||||||
\(545\) | −7.72875 | −0.331063 | ||||||||
\(546\) | −2.41897 | −0.103522 | ||||||||
\(547\) | −7.75499 | −0.331579 | −0.165790 | − | 0.986161i | \(-0.553017\pi\) | ||||
−0.165790 | + | 0.986161i | \(0.553017\pi\) | |||||||
\(548\) | −1.43692 | −0.0613822 | ||||||||
\(549\) | 9.46455 | 0.403937 | ||||||||
\(550\) | 10.2609 | 0.437525 | ||||||||
\(551\) | 7.27464 | 0.309910 | ||||||||
\(552\) | −23.3340 | −0.993162 | ||||||||
\(553\) | −9.03996 | −0.384418 | ||||||||
\(554\) | 1.23722 | 0.0525643 | ||||||||
\(555\) | 11.4486 | 0.485965 | ||||||||
\(556\) | 8.34612 | 0.353954 | ||||||||
\(557\) | −40.0002 | −1.69486 | −0.847431 | − | 0.530905i | \(-0.821852\pi\) | ||||
−0.847431 | + | 0.530905i | \(0.821852\pi\) | |||||||
\(558\) | −4.03348 | −0.170751 | ||||||||
\(559\) | −11.1251 | −0.470542 | ||||||||
\(560\) | −2.51784 | −0.106398 | ||||||||
\(561\) | −28.5429 | −1.20508 | ||||||||
\(562\) | 8.55089 | 0.360698 | ||||||||
\(563\) | −15.8098 | −0.666302 | −0.333151 | − | 0.942873i | \(-0.608112\pi\) | ||||
−0.333151 | + | 0.942873i | \(0.608112\pi\) | |||||||
\(564\) | −2.88110 | −0.121316 | ||||||||
\(565\) | −10.7860 | −0.453770 | ||||||||
\(566\) | −29.5688 | −1.24287 | ||||||||
\(567\) | −1.00000 | −0.0419961 | ||||||||
\(568\) | −10.8075 | −0.453474 | ||||||||
\(569\) | −6.48696 | −0.271947 | −0.135974 | − | 0.990712i | \(-0.543416\pi\) | ||||
−0.135974 | + | 0.990712i | \(0.543416\pi\) | |||||||
\(570\) | −5.66659 | −0.237347 | ||||||||
\(571\) | 25.5999 | 1.07132 | 0.535661 | − | 0.844433i | \(-0.320063\pi\) | ||||
0.535661 | + | 0.844433i | \(0.320063\pi\) | |||||||
\(572\) | −7.61092 | −0.318228 | ||||||||
\(573\) | −1.00000 | −0.0417756 | ||||||||
\(574\) | 2.79112 | 0.116499 | ||||||||
\(575\) | −18.5004 | −0.771519 | ||||||||
\(576\) | 7.88356 | 0.328482 | ||||||||
\(577\) | 42.8974 | 1.78584 | 0.892920 | − | 0.450215i | \(-0.148653\pi\) | ||||
0.892920 | + | 0.450215i | \(0.148653\pi\) | |||||||
\(578\) | −37.6181 | −1.56471 | ||||||||
\(579\) | −8.77267 | −0.364580 | ||||||||
\(580\) | 3.02149 | 0.125461 | ||||||||
\(581\) | −1.94384 | −0.0806439 | ||||||||
\(582\) | 11.7300 | 0.486225 | ||||||||
\(583\) | −25.4249 | −1.05299 | ||||||||
\(584\) | −38.7497 | −1.60347 | ||||||||
\(585\) | −3.62521 | −0.149884 | ||||||||
\(586\) | −11.3595 | −0.469258 | ||||||||
\(587\) | 12.3490 | 0.509698 | 0.254849 | − | 0.966981i | \(-0.417974\pi\) | ||||
0.254849 | + | 0.966981i | \(0.417974\pi\) | |||||||
\(588\) | 0.852471 | 0.0351553 | ||||||||
\(589\) | 12.4066 | 0.511205 | ||||||||
\(590\) | 12.2123 | 0.502772 | ||||||||
\(591\) | −20.1146 | −0.827405 | ||||||||
\(592\) | −11.1843 | −0.459672 | ||||||||
\(593\) | 18.0381 | 0.740736 | 0.370368 | − | 0.928885i | \(-0.379232\pi\) | ||||
0.370368 | + | 0.928885i | \(0.379232\pi\) | |||||||
\(594\) | 4.23537 | 0.173779 | ||||||||
\(595\) | 11.5898 | 0.475134 | ||||||||
\(596\) | −0.574748 | −0.0235426 | ||||||||
\(597\) | 9.89253 | 0.404874 | ||||||||
\(598\) | −18.4721 | −0.755381 | ||||||||
\(599\) | 28.1439 | 1.14993 | 0.574964 | − | 0.818179i | \(-0.305016\pi\) | ||||
0.574964 | + | 0.818179i | \(0.305016\pi\) | |||||||
\(600\) | 7.40281 | 0.302219 | ||||||||
\(601\) | 39.4164 | 1.60783 | 0.803915 | − | 0.594744i | \(-0.202747\pi\) | ||||
0.803915 | + | 0.594744i | \(0.202747\pi\) | |||||||
\(602\) | −5.27761 | −0.215099 | ||||||||
\(603\) | −2.59510 | −0.105681 | ||||||||
\(604\) | −5.36725 | −0.218390 | ||||||||
\(605\) | −7.43647 | −0.302335 | ||||||||
\(606\) | −17.9702 | −0.729991 | ||||||||
\(607\) | −30.3092 | −1.23021 | −0.615106 | − | 0.788445i | \(-0.710887\pi\) | ||||
−0.615106 | + | 0.788445i | \(0.710887\pi\) | |||||||
\(608\) | −14.6009 | −0.592144 | ||||||||
\(609\) | 2.20779 | 0.0894640 | ||||||||
\(610\) | 16.2767 | 0.659026 | ||||||||
\(611\) | −7.63179 | −0.308749 | ||||||||
\(612\) | −6.15416 | −0.248767 | ||||||||
\(613\) | 6.88568 | 0.278110 | 0.139055 | − | 0.990285i | \(-0.455594\pi\) | ||||
0.139055 | + | 0.990285i | \(0.455594\pi\) | |||||||
\(614\) | 0.693249 | 0.0279772 | ||||||||
\(615\) | 4.18294 | 0.168672 | ||||||||
\(616\) | −12.0813 | −0.486768 | ||||||||
\(617\) | 2.49816 | 0.100572 | 0.0502860 | − | 0.998735i | \(-0.483987\pi\) | ||||
0.0502860 | + | 0.998735i | \(0.483987\pi\) | |||||||
\(618\) | 8.54453 | 0.343711 | ||||||||
\(619\) | 3.82063 | 0.153564 | 0.0767820 | − | 0.997048i | \(-0.475535\pi\) | ||||
0.0767820 | + | 0.997048i | \(0.475535\pi\) | |||||||
\(620\) | 5.15303 | 0.206951 | ||||||||
\(621\) | −7.63636 | −0.306437 | ||||||||
\(622\) | −2.09421 | −0.0839702 | ||||||||
\(623\) | 1.89187 | 0.0757963 | ||||||||
\(624\) | 3.54153 | 0.141775 | ||||||||
\(625\) | −7.01735 | −0.280694 | ||||||||
\(626\) | −4.63247 | −0.185151 | ||||||||
\(627\) | −13.0276 | −0.520272 | ||||||||
\(628\) | 14.9129 | 0.595091 | ||||||||
\(629\) | 51.4819 | 2.05272 | ||||||||
\(630\) | −1.71976 | −0.0685168 | ||||||||
\(631\) | −4.87731 | −0.194163 | −0.0970813 | − | 0.995276i | \(-0.530951\pi\) | ||||
−0.0970813 | + | 0.995276i | \(0.530951\pi\) | |||||||
\(632\) | 27.6229 | 1.09878 | ||||||||
\(633\) | −10.9634 | −0.435755 | ||||||||
\(634\) | 9.22697 | 0.366450 | ||||||||
\(635\) | −13.5904 | −0.539320 | ||||||||
\(636\) | −5.48189 | −0.217371 | ||||||||
\(637\) | 2.25813 | 0.0894702 | ||||||||
\(638\) | −9.35078 | −0.370201 | ||||||||
\(639\) | −3.53690 | −0.139918 | ||||||||
\(640\) | −0.670057 | −0.0264863 | ||||||||
\(641\) | 4.66421 | 0.184225 | 0.0921127 | − | 0.995749i | \(-0.470638\pi\) | ||||
0.0921127 | + | 0.995749i | \(0.470638\pi\) | |||||||
\(642\) | −6.13110 | −0.241975 | ||||||||
\(643\) | 3.55725 | 0.140284 | 0.0701421 | − | 0.997537i | \(-0.477655\pi\) | ||||
0.0701421 | + | 0.997537i | \(0.477655\pi\) | |||||||
\(644\) | 6.50978 | 0.256521 | ||||||||
\(645\) | −7.90935 | −0.311431 | ||||||||
\(646\) | −25.4815 | −1.00256 | ||||||||
\(647\) | 16.0468 | 0.630866 | 0.315433 | − | 0.948948i | \(-0.397850\pi\) | ||||
0.315433 | + | 0.948948i | \(0.397850\pi\) | |||||||
\(648\) | 3.05565 | 0.120037 | ||||||||
\(649\) | 28.0763 | 1.10209 | ||||||||
\(650\) | 5.86035 | 0.229862 | ||||||||
\(651\) | 3.76529 | 0.147573 | ||||||||
\(652\) | −19.0824 | −0.747326 | ||||||||
\(653\) | 25.5154 | 0.998496 | 0.499248 | − | 0.866459i | \(-0.333610\pi\) | ||||
0.499248 | + | 0.866459i | \(0.333610\pi\) | |||||||
\(654\) | 5.15710 | 0.201659 | ||||||||
\(655\) | 11.9124 | 0.465458 | ||||||||
\(656\) | −4.08638 | −0.159546 | ||||||||
\(657\) | −12.6813 | −0.494746 | ||||||||
\(658\) | −3.62043 | −0.141139 | ||||||||
\(659\) | −27.3209 | −1.06427 | −0.532135 | − | 0.846660i | \(-0.678610\pi\) | ||||
−0.532135 | + | 0.846660i | \(0.678610\pi\) | |||||||
\(660\) | −5.41096 | −0.210621 | ||||||||
\(661\) | 25.3809 | 0.987204 | 0.493602 | − | 0.869688i | \(-0.335680\pi\) | ||||
0.493602 | + | 0.869688i | \(0.335680\pi\) | |||||||
\(662\) | −35.5332 | −1.38104 | ||||||||
\(663\) | −16.3019 | −0.633112 | ||||||||
\(664\) | 5.93968 | 0.230504 | ||||||||
\(665\) | 5.28981 | 0.205130 | ||||||||
\(666\) | −7.63920 | −0.296013 | ||||||||
\(667\) | 16.8595 | 0.652801 | ||||||||
\(668\) | 21.0416 | 0.814125 | ||||||||
\(669\) | −5.73082 | −0.221566 | ||||||||
\(670\) | −4.46294 | −0.172419 | ||||||||
\(671\) | 37.4205 | 1.44460 | ||||||||
\(672\) | −4.43123 | −0.170938 | ||||||||
\(673\) | −2.95341 | −0.113846 | −0.0569229 | − | 0.998379i | \(-0.518129\pi\) | ||||
−0.0569229 | + | 0.998379i | \(0.518129\pi\) | |||||||
\(674\) | −26.5515 | −1.02272 | ||||||||
\(675\) | 2.42267 | 0.0932485 | ||||||||
\(676\) | 6.73526 | 0.259048 | ||||||||
\(677\) | −37.7680 | −1.45154 | −0.725770 | − | 0.687937i | \(-0.758516\pi\) | ||||
−0.725770 | + | 0.687937i | \(0.758516\pi\) | |||||||
\(678\) | 7.19708 | 0.276402 | ||||||||
\(679\) | −10.9501 | −0.420225 | ||||||||
\(680\) | −35.4142 | −1.35807 | ||||||||
\(681\) | 18.8079 | 0.720720 | ||||||||
\(682\) | −15.9474 | −0.610656 | ||||||||
\(683\) | −15.4844 | −0.592493 | −0.296246 | − | 0.955112i | \(-0.595735\pi\) | ||||
−0.296246 | + | 0.955112i | \(0.595735\pi\) | |||||||
\(684\) | −2.80889 | −0.107401 | ||||||||
\(685\) | −2.70606 | −0.103393 | ||||||||
\(686\) | 1.07123 | 0.0408997 | ||||||||
\(687\) | 6.31690 | 0.241005 | ||||||||
\(688\) | 7.72679 | 0.294581 | ||||||||
\(689\) | −14.5211 | −0.553209 | ||||||||
\(690\) | −13.1327 | −0.499953 | ||||||||
\(691\) | −1.27832 | −0.0486297 | −0.0243148 | − | 0.999704i | \(-0.507740\pi\) | ||||
−0.0243148 | + | 0.999704i | \(0.507740\pi\) | |||||||
\(692\) | −9.97373 | −0.379144 | ||||||||
\(693\) | −3.95375 | −0.150191 | ||||||||
\(694\) | 16.4454 | 0.624259 | ||||||||
\(695\) | 15.7177 | 0.596208 | ||||||||
\(696\) | −6.74621 | −0.255714 | ||||||||
\(697\) | 18.8098 | 0.712473 | ||||||||
\(698\) | 33.7121 | 1.27602 | ||||||||
\(699\) | 1.27413 | 0.0481920 | ||||||||
\(700\) | −2.06525 | −0.0780593 | ||||||||
\(701\) | 17.6475 | 0.666536 | 0.333268 | − | 0.942832i | \(-0.391849\pi\) | ||||
0.333268 | + | 0.942832i | \(0.391849\pi\) | |||||||
\(702\) | 2.41897 | 0.0912980 | ||||||||
\(703\) | 23.4974 | 0.886223 | ||||||||
\(704\) | 31.1696 | 1.17475 | ||||||||
\(705\) | −5.42579 | −0.204347 | ||||||||
\(706\) | 28.4780 | 1.07178 | ||||||||
\(707\) | 16.7754 | 0.630903 | ||||||||
\(708\) | 6.05354 | 0.227506 | ||||||||
\(709\) | 53.1278 | 1.99526 | 0.997628 | − | 0.0688293i | \(-0.0219264\pi\) | ||||
0.997628 | + | 0.0688293i | \(0.0219264\pi\) | |||||||
\(710\) | −6.08262 | −0.228277 | ||||||||
\(711\) | 9.03996 | 0.339025 | ||||||||
\(712\) | −5.78089 | −0.216648 | ||||||||
\(713\) | 28.7531 | 1.07681 | ||||||||
\(714\) | −7.73341 | −0.289415 | ||||||||
\(715\) | −14.3332 | −0.536031 | ||||||||
\(716\) | 7.43255 | 0.277767 | ||||||||
\(717\) | 22.0775 | 0.824498 | ||||||||
\(718\) | −7.84593 | −0.292808 | ||||||||
\(719\) | −3.94431 | −0.147098 | −0.0735490 | − | 0.997292i | \(-0.523433\pi\) | ||||
−0.0735490 | + | 0.997292i | \(0.523433\pi\) | |||||||
\(720\) | 2.51784 | 0.0938344 | ||||||||
\(721\) | −7.97639 | −0.297056 | ||||||||
\(722\) | 8.72302 | 0.324637 | ||||||||
\(723\) | 18.2835 | 0.679970 | ||||||||
\(724\) | −13.2335 | −0.491821 | ||||||||
\(725\) | −5.34873 | −0.198647 | ||||||||
\(726\) | 4.96207 | 0.184160 | ||||||||
\(727\) | −26.8457 | −0.995650 | −0.497825 | − | 0.867277i | \(-0.665868\pi\) | ||||
−0.497825 | + | 0.867277i | \(0.665868\pi\) | |||||||
\(728\) | −6.90004 | −0.255732 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −21.8088 | −0.807180 | ||||||||
\(731\) | −35.5668 | −1.31549 | ||||||||
\(732\) | 8.06826 | 0.298211 | ||||||||
\(733\) | −11.1232 | −0.410845 | −0.205423 | − | 0.978673i | \(-0.565857\pi\) | ||||
−0.205423 | + | 0.978673i | \(0.565857\pi\) | |||||||
\(734\) | 38.8975 | 1.43573 | ||||||||
\(735\) | 1.60541 | 0.0592163 | ||||||||
\(736\) | −33.8385 | −1.24730 | ||||||||
\(737\) | −10.2604 | −0.377946 | ||||||||
\(738\) | −2.79112 | −0.102742 | ||||||||
\(739\) | −27.5864 | −1.01478 | −0.507391 | − | 0.861716i | \(-0.669390\pi\) | ||||
−0.507391 | + | 0.861716i | \(0.669390\pi\) | |||||||
\(740\) | 9.75958 | 0.358769 | ||||||||
\(741\) | −7.44051 | −0.273334 | ||||||||
\(742\) | −6.88862 | −0.252889 | ||||||||
\(743\) | −26.4082 | −0.968823 | −0.484411 | − | 0.874840i | \(-0.660966\pi\) | ||||
−0.484411 | + | 0.874840i | \(0.660966\pi\) | |||||||
\(744\) | −11.5054 | −0.421808 | ||||||||
\(745\) | −1.08239 | −0.0396557 | ||||||||
\(746\) | −9.68524 | −0.354602 | ||||||||
\(747\) | 1.94384 | 0.0711213 | ||||||||
\(748\) | −24.3320 | −0.889666 | ||||||||
\(749\) | 5.72343 | 0.209130 | ||||||||
\(750\) | 12.7652 | 0.466119 | ||||||||
\(751\) | −53.4551 | −1.95060 | −0.975301 | − | 0.220878i | \(-0.929108\pi\) | ||||
−0.975301 | + | 0.220878i | \(0.929108\pi\) | |||||||
\(752\) | 5.30055 | 0.193291 | ||||||||
\(753\) | −24.5159 | −0.893410 | ||||||||
\(754\) | −5.34056 | −0.194492 | ||||||||
\(755\) | −10.1078 | −0.367861 | ||||||||
\(756\) | −0.852471 | −0.0310041 | ||||||||
\(757\) | −50.7130 | −1.84320 | −0.921598 | − | 0.388145i | \(-0.873116\pi\) | ||||
−0.921598 | + | 0.388145i | \(0.873116\pi\) | |||||||
\(758\) | −18.2035 | −0.661182 | ||||||||
\(759\) | −30.1923 | −1.09591 | ||||||||
\(760\) | −16.1638 | −0.586322 | ||||||||
\(761\) | 32.0694 | 1.16251 | 0.581257 | − | 0.813720i | \(-0.302561\pi\) | ||||
0.581257 | + | 0.813720i | \(0.302561\pi\) | |||||||
\(762\) | 9.06839 | 0.328513 | ||||||||
\(763\) | −4.81420 | −0.174286 | ||||||||
\(764\) | −0.852471 | −0.0308413 | ||||||||
\(765\) | −11.5898 | −0.419028 | ||||||||
\(766\) | 2.95385 | 0.106727 | ||||||||
\(767\) | 16.0353 | 0.579003 | ||||||||
\(768\) | 16.2142 | 0.585080 | ||||||||
\(769\) | 22.0829 | 0.796330 | 0.398165 | − | 0.917314i | \(-0.369647\pi\) | ||||
0.398165 | + | 0.917314i | \(0.369647\pi\) | |||||||
\(770\) | −6.79949 | −0.245037 | ||||||||
\(771\) | −1.86568 | −0.0671908 | ||||||||
\(772\) | −7.47844 | −0.269155 | ||||||||
\(773\) | −16.9475 | −0.609558 | −0.304779 | − | 0.952423i | \(-0.598583\pi\) | ||||
−0.304779 | + | 0.952423i | \(0.598583\pi\) | |||||||
\(774\) | 5.27761 | 0.189700 | ||||||||
\(775\) | −9.12203 | −0.327673 | ||||||||
\(776\) | 33.4595 | 1.20113 | ||||||||
\(777\) | 7.13126 | 0.255832 | ||||||||
\(778\) | −26.5523 | −0.951945 | ||||||||
\(779\) | 8.58521 | 0.307597 | ||||||||
\(780\) | −3.09039 | −0.110654 | ||||||||
\(781\) | −13.9840 | −0.500388 | ||||||||
\(782\) | −59.0551 | −2.11181 | ||||||||
\(783\) | −2.20779 | −0.0788998 | ||||||||
\(784\) | −1.56835 | −0.0560125 | ||||||||
\(785\) | 28.0846 | 1.00238 | ||||||||
\(786\) | −7.94872 | −0.283522 | ||||||||
\(787\) | −13.6816 | −0.487696 | −0.243848 | − | 0.969813i | \(-0.578410\pi\) | ||||
−0.243848 | + | 0.969813i | \(0.578410\pi\) | |||||||
\(788\) | −17.1471 | −0.610841 | ||||||||
\(789\) | 13.3481 | 0.475203 | ||||||||
\(790\) | 15.5465 | 0.553121 | ||||||||
\(791\) | −6.71853 | −0.238884 | ||||||||
\(792\) | 12.0813 | 0.429289 | ||||||||
\(793\) | 21.3722 | 0.758948 | ||||||||
\(794\) | 24.0697 | 0.854202 | ||||||||
\(795\) | −10.3237 | −0.366144 | ||||||||
\(796\) | 8.43310 | 0.298903 | ||||||||
\(797\) | −23.7100 | −0.839853 | −0.419926 | − | 0.907558i | \(-0.637944\pi\) | ||||
−0.419926 | + | 0.907558i | \(0.637944\pi\) | |||||||
\(798\) | −3.52969 | −0.124950 | ||||||||
\(799\) | −24.3987 | −0.863165 | ||||||||
\(800\) | 10.7354 | 0.379554 | ||||||||
\(801\) | −1.89187 | −0.0668460 | ||||||||
\(802\) | −14.0169 | −0.494956 | ||||||||
\(803\) | −50.1388 | −1.76936 | ||||||||
\(804\) | −2.21225 | −0.0780200 | ||||||||
\(805\) | 12.2595 | 0.432090 | ||||||||
\(806\) | −9.10810 | −0.320819 | ||||||||
\(807\) | −8.19868 | −0.288607 | ||||||||
\(808\) | −51.2596 | −1.80331 | ||||||||
\(809\) | 11.4257 | 0.401707 | 0.200854 | − | 0.979621i | \(-0.435628\pi\) | ||||
0.200854 | + | 0.979621i | \(0.435628\pi\) | |||||||
\(810\) | 1.71976 | 0.0604261 | ||||||||
\(811\) | 21.8387 | 0.766859 | 0.383430 | − | 0.923570i | \(-0.374743\pi\) | ||||
0.383430 | + | 0.923570i | \(0.374743\pi\) | |||||||
\(812\) | 1.88207 | 0.0660478 | ||||||||
\(813\) | 24.3911 | 0.855432 | ||||||||
\(814\) | −30.2035 | −1.05863 | ||||||||
\(815\) | −35.9368 | −1.25881 | ||||||||
\(816\) | 11.3222 | 0.396358 | ||||||||
\(817\) | −16.2334 | −0.567936 | ||||||||
\(818\) | 10.0854 | 0.352629 | ||||||||
\(819\) | −2.25813 | −0.0789053 | ||||||||
\(820\) | 3.56583 | 0.124524 | ||||||||
\(821\) | 10.4364 | 0.364233 | 0.182116 | − | 0.983277i | \(-0.441705\pi\) | ||||
0.182116 | + | 0.983277i | \(0.441705\pi\) | |||||||
\(822\) | 1.80565 | 0.0629794 | ||||||||
\(823\) | −34.9451 | −1.21811 | −0.609055 | − | 0.793128i | \(-0.708451\pi\) | ||||
−0.609055 | + | 0.793128i | \(0.708451\pi\) | |||||||
\(824\) | 24.3730 | 0.849074 | ||||||||
\(825\) | 9.57862 | 0.333485 | ||||||||
\(826\) | 7.60697 | 0.264680 | ||||||||
\(827\) | −30.0929 | −1.04643 | −0.523217 | − | 0.852200i | \(-0.675268\pi\) | ||||
−0.523217 | + | 0.852200i | \(0.675268\pi\) | |||||||
\(828\) | −6.50978 | −0.226230 | ||||||||
\(829\) | 33.1864 | 1.15261 | 0.576306 | − | 0.817234i | \(-0.304493\pi\) | ||||
0.576306 | + | 0.817234i | \(0.304493\pi\) | |||||||
\(830\) | 3.34293 | 0.116035 | ||||||||
\(831\) | 1.15495 | 0.0400648 | ||||||||
\(832\) | 17.8021 | 0.617176 | ||||||||
\(833\) | 7.21920 | 0.250130 | ||||||||
\(834\) | −10.4879 | −0.363165 | ||||||||
\(835\) | 39.6264 | 1.37133 | ||||||||
\(836\) | −11.1056 | −0.384097 | ||||||||
\(837\) | −3.76529 | −0.130147 | ||||||||
\(838\) | 29.5262 | 1.01997 | ||||||||
\(839\) | 37.8509 | 1.30676 | 0.653380 | − | 0.757031i | \(-0.273351\pi\) | ||||
0.653380 | + | 0.757031i | \(0.273351\pi\) | |||||||
\(840\) | −4.90556 | −0.169258 | ||||||||
\(841\) | −24.1257 | −0.831920 | ||||||||
\(842\) | 0.519653 | 0.0179084 | ||||||||
\(843\) | 7.98233 | 0.274926 | ||||||||
\(844\) | −9.34596 | −0.321701 | ||||||||
\(845\) | 12.6841 | 0.436347 | ||||||||
\(846\) | 3.62043 | 0.124473 | ||||||||
\(847\) | −4.63214 | −0.159162 | ||||||||
\(848\) | 10.0854 | 0.346335 | ||||||||
\(849\) | −27.6027 | −0.947323 | ||||||||
\(850\) | 18.7355 | 0.642621 | ||||||||
\(851\) | 54.4569 | 1.86676 | ||||||||
\(852\) | −3.01511 | −0.103296 | ||||||||
\(853\) | 29.5727 | 1.01255 | 0.506275 | − | 0.862372i | \(-0.331022\pi\) | ||||
0.506275 | + | 0.862372i | \(0.331022\pi\) | |||||||
\(854\) | 10.1387 | 0.346939 | ||||||||
\(855\) | −5.28981 | −0.180908 | ||||||||
\(856\) | −17.4888 | −0.597755 | ||||||||
\(857\) | −2.93843 | −0.100375 | −0.0501873 | − | 0.998740i | \(-0.515982\pi\) | ||||
−0.0501873 | + | 0.998740i | \(0.515982\pi\) | |||||||
\(858\) | 9.56399 | 0.326509 | ||||||||
\(859\) | 13.2384 | 0.451687 | 0.225844 | − | 0.974164i | \(-0.427486\pi\) | ||||
0.225844 | + | 0.974164i | \(0.427486\pi\) | |||||||
\(860\) | −6.74250 | −0.229917 | ||||||||
\(861\) | 2.60553 | 0.0887962 | ||||||||
\(862\) | −43.2197 | −1.47207 | ||||||||
\(863\) | −55.8000 | −1.89945 | −0.949727 | − | 0.313079i | \(-0.898640\pi\) | ||||
−0.949727 | + | 0.313079i | \(0.898640\pi\) | |||||||
\(864\) | 4.43123 | 0.150754 | ||||||||
\(865\) | −18.7829 | −0.638639 | ||||||||
\(866\) | −3.22830 | −0.109702 | ||||||||
\(867\) | −35.1168 | −1.19263 | ||||||||
\(868\) | 3.20980 | 0.108948 | ||||||||
\(869\) | 35.7417 | 1.21246 | ||||||||
\(870\) | −3.79685 | −0.128725 | ||||||||
\(871\) | −5.86007 | −0.198561 | ||||||||
\(872\) | 14.7105 | 0.498160 | ||||||||
\(873\) | 10.9501 | 0.370604 | ||||||||
\(874\) | −26.9540 | −0.911732 | ||||||||
\(875\) | −11.9164 | −0.402848 | ||||||||
\(876\) | −10.8105 | −0.365252 | ||||||||
\(877\) | 54.4379 | 1.83824 | 0.919119 | − | 0.393979i | \(-0.128902\pi\) | ||||
0.919119 | + | 0.393979i | \(0.128902\pi\) | |||||||
\(878\) | −11.5022 | −0.388181 | ||||||||
\(879\) | −10.6042 | −0.357671 | ||||||||
\(880\) | 9.95492 | 0.335580 | ||||||||
\(881\) | −5.81193 | −0.195809 | −0.0979044 | − | 0.995196i | \(-0.531214\pi\) | ||||
−0.0979044 | + | 0.995196i | \(0.531214\pi\) | |||||||
\(882\) | −1.07123 | −0.0360701 | ||||||||
\(883\) | −50.2967 | −1.69262 | −0.846309 | − | 0.532692i | \(-0.821180\pi\) | ||||
−0.846309 | + | 0.532692i | \(0.821180\pi\) | |||||||
\(884\) | −13.8969 | −0.467402 | ||||||||
\(885\) | 11.4003 | 0.383216 | ||||||||
\(886\) | 23.7748 | 0.798731 | ||||||||
\(887\) | −24.5730 | −0.825079 | −0.412540 | − | 0.910940i | \(-0.635358\pi\) | ||||
−0.412540 | + | 0.910940i | \(0.635358\pi\) | |||||||
\(888\) | −21.7906 | −0.731244 | ||||||||
\(889\) | −8.46541 | −0.283921 | ||||||||
\(890\) | −3.25356 | −0.109060 | ||||||||
\(891\) | 3.95375 | 0.132456 | ||||||||
\(892\) | −4.88536 | −0.163574 | ||||||||
\(893\) | −11.1361 | −0.372655 | ||||||||
\(894\) | 0.722237 | 0.0241552 | ||||||||
\(895\) | 13.9973 | 0.467877 | ||||||||
\(896\) | −0.417375 | −0.0139435 | ||||||||
\(897\) | −17.2439 | −0.575756 | ||||||||
\(898\) | −25.7388 | −0.858916 | ||||||||
\(899\) | 8.31294 | 0.277252 | ||||||||
\(900\) | 2.06525 | 0.0688418 | ||||||||
\(901\) | −46.4237 | −1.54660 | ||||||||
\(902\) | −11.0354 | −0.367438 | ||||||||
\(903\) | −4.92670 | −0.163950 | ||||||||
\(904\) | 20.5295 | 0.682800 | ||||||||
\(905\) | −24.9219 | −0.828433 | ||||||||
\(906\) | 6.74457 | 0.224073 | ||||||||
\(907\) | 22.0175 | 0.731079 | 0.365539 | − | 0.930796i | \(-0.380885\pi\) | ||||
0.365539 | + | 0.930796i | \(0.380885\pi\) | |||||||
\(908\) | 16.0332 | 0.532080 | ||||||||
\(909\) | −16.7754 | −0.556404 | ||||||||
\(910\) | −3.88343 | −0.128734 | ||||||||
\(911\) | −6.73977 | −0.223298 | −0.111649 | − | 0.993748i | \(-0.535613\pi\) | ||||
−0.111649 | + | 0.993748i | \(0.535613\pi\) | |||||||
\(912\) | 5.16771 | 0.171120 | ||||||||
\(913\) | 7.68545 | 0.254351 | ||||||||
\(914\) | 21.5373 | 0.712391 | ||||||||
\(915\) | 15.1945 | 0.502314 | ||||||||
\(916\) | 5.38497 | 0.177925 | ||||||||
\(917\) | 7.42020 | 0.245037 | ||||||||
\(918\) | 7.73341 | 0.255240 | ||||||||
\(919\) | 33.3112 | 1.09884 | 0.549418 | − | 0.835548i | \(-0.314849\pi\) | ||||
0.549418 | + | 0.835548i | \(0.314849\pi\) | |||||||
\(920\) | −37.4606 | −1.23504 | ||||||||
\(921\) | 0.647153 | 0.0213244 | ||||||||
\(922\) | 32.5370 | 1.07155 | ||||||||
\(923\) | −7.98678 | −0.262888 | ||||||||
\(924\) | −3.37046 | −0.110880 | ||||||||
\(925\) | −17.2767 | −0.568053 | ||||||||
\(926\) | −15.1802 | −0.498852 | ||||||||
\(927\) | 7.97639 | 0.261979 | ||||||||
\(928\) | −9.78321 | −0.321150 | ||||||||
\(929\) | 34.3536 | 1.12711 | 0.563553 | − | 0.826080i | \(-0.309434\pi\) | ||||
0.563553 | + | 0.826080i | \(0.309434\pi\) | |||||||
\(930\) | −6.47538 | −0.212336 | ||||||||
\(931\) | 3.29499 | 0.107989 | ||||||||
\(932\) | 1.08616 | 0.0355783 | ||||||||
\(933\) | −1.95496 | −0.0640026 | ||||||||
\(934\) | 39.5385 | 1.29374 | ||||||||
\(935\) | −45.8230 | −1.49857 | ||||||||
\(936\) | 6.90004 | 0.225535 | ||||||||
\(937\) | −26.1880 | −0.855525 | −0.427763 | − | 0.903891i | \(-0.640698\pi\) | ||||
−0.427763 | + | 0.903891i | \(0.640698\pi\) | |||||||
\(938\) | −2.77995 | −0.0907684 | ||||||||
\(939\) | −4.32445 | −0.141123 | ||||||||
\(940\) | −4.62533 | −0.150862 | ||||||||
\(941\) | 9.53035 | 0.310681 | 0.155340 | − | 0.987861i | \(-0.450353\pi\) | ||||
0.155340 | + | 0.987861i | \(0.450353\pi\) | |||||||
\(942\) | −18.7398 | −0.610576 | ||||||||
\(943\) | 19.8968 | 0.647928 | ||||||||
\(944\) | −11.1371 | −0.362483 | ||||||||
\(945\) | −1.60541 | −0.0522239 | ||||||||
\(946\) | 20.8664 | 0.678424 | ||||||||
\(947\) | −15.5422 | −0.505054 | −0.252527 | − | 0.967590i | \(-0.581262\pi\) | ||||
−0.252527 | + | 0.967590i | \(0.581262\pi\) | |||||||
\(948\) | 7.70630 | 0.250289 | ||||||||
\(949\) | −28.6361 | −0.929566 | ||||||||
\(950\) | 8.55126 | 0.277440 | ||||||||
\(951\) | 8.61346 | 0.279310 | ||||||||
\(952\) | −22.0593 | −0.714947 | ||||||||
\(953\) | −0.154260 | −0.00499696 | −0.00249848 | − | 0.999997i | \(-0.500795\pi\) | ||||
−0.00249848 | + | 0.999997i | \(0.500795\pi\) | |||||||
\(954\) | 6.88862 | 0.223027 | ||||||||
\(955\) | −1.60541 | −0.0519498 | ||||||||
\(956\) | 18.8204 | 0.608695 | ||||||||
\(957\) | −8.72903 | −0.282169 | ||||||||
\(958\) | 33.6842 | 1.08829 | ||||||||
\(959\) | −1.68559 | −0.0544306 | ||||||||
\(960\) | 12.6563 | 0.408481 | ||||||||
\(961\) | −16.8226 | −0.542665 | ||||||||
\(962\) | −17.2503 | −0.556171 | ||||||||
\(963\) | −5.72343 | −0.184435 | ||||||||
\(964\) | 15.5861 | 0.501995 | ||||||||
\(965\) | −14.0837 | −0.453370 | ||||||||
\(966\) | −8.18029 | −0.263196 | ||||||||
\(967\) | −22.9884 | −0.739256 | −0.369628 | − | 0.929180i | \(-0.620515\pi\) | ||||
−0.369628 | + | 0.929180i | \(0.620515\pi\) | |||||||
\(968\) | 14.1542 | 0.454932 | ||||||||
\(969\) | −23.7872 | −0.764156 | ||||||||
\(970\) | 18.8315 | 0.604642 | ||||||||
\(971\) | 55.8595 | 1.79262 | 0.896308 | − | 0.443432i | \(-0.146239\pi\) | ||||
0.896308 | + | 0.443432i | \(0.146239\pi\) | |||||||
\(972\) | 0.852471 | 0.0273430 | ||||||||
\(973\) | 9.79050 | 0.313869 | ||||||||
\(974\) | −18.8583 | −0.604260 | ||||||||
\(975\) | 5.47069 | 0.175202 | ||||||||
\(976\) | −14.8437 | −0.475137 | ||||||||
\(977\) | −23.8934 | −0.764416 | −0.382208 | − | 0.924076i | \(-0.624836\pi\) | ||||
−0.382208 | + | 0.924076i | \(0.624836\pi\) | |||||||
\(978\) | 23.9793 | 0.766772 | ||||||||
\(979\) | −7.47999 | −0.239062 | ||||||||
\(980\) | 1.36856 | 0.0437172 | ||||||||
\(981\) | 4.81420 | 0.153706 | ||||||||
\(982\) | −0.992522 | −0.0316727 | ||||||||
\(983\) | −36.3132 | −1.15821 | −0.579106 | − | 0.815252i | \(-0.696598\pi\) | ||||
−0.579106 | + | 0.815252i | \(0.696598\pi\) | |||||||
\(984\) | −7.96158 | −0.253806 | ||||||||
\(985\) | −32.2922 | −1.02891 | ||||||||
\(986\) | −17.0737 | −0.543737 | ||||||||
\(987\) | −3.37970 | −0.107577 | ||||||||
\(988\) | −6.34282 | −0.201792 | ||||||||
\(989\) | −37.6220 | −1.19631 | ||||||||
\(990\) | 6.79949 | 0.216102 | ||||||||
\(991\) | 3.43443 | 0.109098 | 0.0545492 | − | 0.998511i | \(-0.482628\pi\) | ||||
0.0545492 | + | 0.998511i | \(0.482628\pi\) | |||||||
\(992\) | −16.6849 | −0.529745 | ||||||||
\(993\) | −33.1706 | −1.05264 | ||||||||
\(994\) | −3.78883 | −0.120174 | ||||||||
\(995\) | 15.8815 | 0.503479 | ||||||||
\(996\) | 1.65706 | 0.0525061 | ||||||||
\(997\) | −16.2980 | −0.516161 | −0.258081 | − | 0.966123i | \(-0.583090\pi\) | ||||
−0.258081 | + | 0.966123i | \(0.583090\pi\) | |||||||
\(998\) | 17.2718 | 0.546729 | ||||||||
\(999\) | −7.13126 | −0.225623 |
(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 | 4011.2.a.j.1.9 | ✓ | 26 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4011.2.a.j.1.9 | ✓ | 26 | 1.1 | even | 1 | trivial |