Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8001,2,Mod(1,8001)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8001, 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("8001.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8001 = 3^{2} \cdot 7 \cdot 127 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8001.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(63.8883066572\) |
Analytic rank: | \(1\) |
Dimension: | \(32\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.10 | ||
Character | \(\chi\) | \(=\) | 8001.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.18013 | −0.834479 | −0.417239 | − | 0.908797i | \(-0.637002\pi\) | ||||
−0.417239 | + | 0.908797i | \(0.637002\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −0.607291 | −0.303645 | ||||||||
\(5\) | 4.43826 | 1.98485 | 0.992425 | − | 0.122856i | \(-0.0392053\pi\) | ||||
0.992425 | + | 0.122856i | \(0.0392053\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | 3.07694 | 1.08786 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −5.23773 | −1.65631 | ||||||||
\(11\) | −5.41915 | −1.63393 | −0.816967 | − | 0.576685i | \(-0.804346\pi\) | ||||
−0.816967 | + | 0.576685i | \(0.804346\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.38471 | −0.661398 | −0.330699 | − | 0.943736i | \(-0.607285\pi\) | ||||
−0.330699 | + | 0.943736i | \(0.607285\pi\) | |||||||
\(14\) | 1.18013 | 0.315403 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −2.41662 | −0.604154 | ||||||||
\(17\) | 2.36152 | 0.572753 | 0.286377 | − | 0.958117i | \(-0.407549\pi\) | ||||
0.286377 | + | 0.958117i | \(0.407549\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2.75497 | −0.632034 | −0.316017 | − | 0.948753i | \(-0.602346\pi\) | ||||
−0.316017 | + | 0.948753i | \(0.602346\pi\) | |||||||
\(20\) | −2.69531 | −0.602690 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 6.39530 | 1.36348 | ||||||||
\(23\) | −5.73685 | −1.19622 | −0.598108 | − | 0.801416i | \(-0.704081\pi\) | ||||
−0.598108 | + | 0.801416i | \(0.704081\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 14.6981 | 2.93963 | ||||||||
\(26\) | 2.81427 | 0.551923 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0.607291 | 0.114767 | ||||||||
\(29\) | −3.90830 | −0.725754 | −0.362877 | − | 0.931837i | \(-0.618205\pi\) | ||||
−0.362877 | + | 0.931837i | \(0.618205\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.83738 | 0.509609 | 0.254804 | − | 0.966993i | \(-0.417989\pi\) | ||||
0.254804 | + | 0.966993i | \(0.417989\pi\) | |||||||
\(32\) | −3.30196 | −0.583710 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −2.78691 | −0.477950 | ||||||||
\(35\) | −4.43826 | −0.750202 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −3.58729 | −0.589747 | −0.294874 | − | 0.955536i | \(-0.595278\pi\) | ||||
−0.294874 | + | 0.955536i | \(0.595278\pi\) | |||||||
\(38\) | 3.25123 | 0.527419 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 13.6563 | 2.15925 | ||||||||
\(41\) | −0.707118 | −0.110433 | −0.0552166 | − | 0.998474i | \(-0.517585\pi\) | ||||
−0.0552166 | + | 0.998474i | \(0.517585\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 9.07783 | 1.38436 | 0.692178 | − | 0.721727i | \(-0.256651\pi\) | ||||
0.692178 | + | 0.721727i | \(0.256651\pi\) | |||||||
\(44\) | 3.29100 | 0.496136 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 6.77024 | 0.998217 | ||||||||
\(47\) | 4.92884 | 0.718945 | 0.359473 | − | 0.933156i | \(-0.382957\pi\) | ||||
0.359473 | + | 0.933156i | \(0.382957\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | −17.3457 | −2.45306 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 1.44821 | 0.200830 | ||||||||
\(53\) | 10.8388 | 1.48883 | 0.744414 | − | 0.667719i | \(-0.232729\pi\) | ||||
0.744414 | + | 0.667719i | \(0.232729\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −24.0516 | −3.24311 | ||||||||
\(56\) | −3.07694 | −0.411174 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 4.61231 | 0.605626 | ||||||||
\(59\) | 8.70245 | 1.13296 | 0.566481 | − | 0.824075i | \(-0.308304\pi\) | ||||
0.566481 | + | 0.824075i | \(0.308304\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 15.4770 | 1.98163 | 0.990816 | − | 0.135214i | \(-0.0431723\pi\) | ||||
0.990816 | + | 0.135214i | \(0.0431723\pi\) | |||||||
\(62\) | −3.34848 | −0.425258 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 8.72998 | 1.09125 | ||||||||
\(65\) | −10.5839 | −1.31278 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 5.37268 | 0.656377 | 0.328189 | − | 0.944612i | \(-0.393562\pi\) | ||||
0.328189 | + | 0.944612i | \(0.393562\pi\) | |||||||
\(68\) | −1.43413 | −0.173914 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 5.23773 | 0.626028 | ||||||||
\(71\) | −8.79079 | −1.04327 | −0.521637 | − | 0.853167i | \(-0.674679\pi\) | ||||
−0.521637 | + | 0.853167i | \(0.674679\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −14.5845 | −1.70698 | −0.853492 | − | 0.521107i | \(-0.825519\pi\) | ||||
−0.853492 | + | 0.521107i | \(0.825519\pi\) | |||||||
\(74\) | 4.23348 | 0.492132 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 1.67307 | 0.191914 | ||||||||
\(77\) | 5.41915 | 0.617569 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −13.5647 | −1.52615 | −0.763077 | − | 0.646308i | \(-0.776312\pi\) | ||||
−0.763077 | + | 0.646308i | \(0.776312\pi\) | |||||||
\(80\) | −10.7256 | −1.19915 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0.834492 | 0.0921542 | ||||||||
\(83\) | −5.85553 | −0.642728 | −0.321364 | − | 0.946956i | \(-0.604141\pi\) | ||||
−0.321364 | + | 0.946956i | \(0.604141\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 10.4810 | 1.13683 | ||||||||
\(86\) | −10.7130 | −1.15522 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −16.6744 | −1.77750 | ||||||||
\(89\) | 5.77576 | 0.612229 | 0.306114 | − | 0.951995i | \(-0.400971\pi\) | ||||
0.306114 | + | 0.951995i | \(0.400971\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 2.38471 | 0.249985 | ||||||||
\(92\) | 3.48394 | 0.363225 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −5.81668 | −0.599944 | ||||||||
\(95\) | −12.2273 | −1.25449 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 13.8577 | 1.40703 | 0.703517 | − | 0.710678i | \(-0.251612\pi\) | ||||
0.703517 | + | 0.710678i | \(0.251612\pi\) | |||||||
\(98\) | −1.18013 | −0.119211 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −8.92604 | −0.892604 | ||||||||
\(101\) | −1.80702 | −0.179806 | −0.0899028 | − | 0.995951i | \(-0.528656\pi\) | ||||
−0.0899028 | + | 0.995951i | \(0.528656\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −10.8246 | −1.06658 | −0.533288 | − | 0.845934i | \(-0.679044\pi\) | ||||
−0.533288 | + | 0.845934i | \(0.679044\pi\) | |||||||
\(104\) | −7.33761 | −0.719512 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −12.7912 | −1.24239 | ||||||||
\(107\) | −12.8202 | −1.23937 | −0.619686 | − | 0.784849i | \(-0.712740\pi\) | ||||
−0.619686 | + | 0.784849i | \(0.712740\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −9.99649 | −0.957490 | −0.478745 | − | 0.877954i | \(-0.658908\pi\) | ||||
−0.478745 | + | 0.877954i | \(0.658908\pi\) | |||||||
\(110\) | 28.3840 | 2.70631 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 2.41662 | 0.228349 | ||||||||
\(113\) | −8.33535 | −0.784124 | −0.392062 | − | 0.919939i | \(-0.628238\pi\) | ||||
−0.392062 | + | 0.919939i | \(0.628238\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −25.4616 | −2.37431 | ||||||||
\(116\) | 2.37348 | 0.220372 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −10.2700 | −0.945433 | ||||||||
\(119\) | −2.36152 | −0.216480 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 18.3671 | 1.66974 | ||||||||
\(122\) | −18.2649 | −1.65363 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −1.72311 | −0.154740 | ||||||||
\(125\) | 43.0428 | 3.84986 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1.00000 | −0.0887357 | ||||||||
\(128\) | −3.69860 | −0.326913 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 12.4904 | 1.09548 | ||||||||
\(131\) | −9.14569 | −0.799062 | −0.399531 | − | 0.916720i | \(-0.630827\pi\) | ||||
−0.399531 | + | 0.916720i | \(0.630827\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 2.75497 | 0.238886 | ||||||||
\(134\) | −6.34047 | −0.547733 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 7.26627 | 0.623078 | ||||||||
\(137\) | 13.9083 | 1.18826 | 0.594132 | − | 0.804368i | \(-0.297496\pi\) | ||||
0.594132 | + | 0.804368i | \(0.297496\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −17.0334 | −1.44476 | −0.722379 | − | 0.691497i | \(-0.756951\pi\) | ||||
−0.722379 | + | 0.691497i | \(0.756951\pi\) | |||||||
\(140\) | 2.69531 | 0.227795 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 10.3743 | 0.870590 | ||||||||
\(143\) | 12.9231 | 1.08068 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −17.3461 | −1.44051 | ||||||||
\(146\) | 17.2116 | 1.42444 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 2.17853 | 0.179074 | ||||||||
\(149\) | 12.3798 | 1.01419 | 0.507097 | − | 0.861889i | \(-0.330719\pi\) | ||||
0.507097 | + | 0.861889i | \(0.330719\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −12.4328 | −1.01176 | −0.505882 | − | 0.862603i | \(-0.668833\pi\) | ||||
−0.505882 | + | 0.862603i | \(0.668833\pi\) | |||||||
\(152\) | −8.47690 | −0.687567 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −6.39530 | −0.515348 | ||||||||
\(155\) | 12.5930 | 1.01150 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −19.3845 | −1.54705 | −0.773524 | − | 0.633767i | \(-0.781508\pi\) | ||||
−0.773524 | + | 0.633767i | \(0.781508\pi\) | |||||||
\(158\) | 16.0082 | 1.27354 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −14.6550 | −1.15858 | ||||||||
\(161\) | 5.73685 | 0.452127 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −3.46010 | −0.271016 | −0.135508 | − | 0.990776i | \(-0.543267\pi\) | ||||
−0.135508 | + | 0.990776i | \(0.543267\pi\) | |||||||
\(164\) | 0.429426 | 0.0335325 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 6.91029 | 0.536343 | ||||||||
\(167\) | −19.5272 | −1.51106 | −0.755531 | − | 0.655113i | \(-0.772621\pi\) | ||||
−0.755531 | + | 0.655113i | \(0.772621\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −7.31318 | −0.562552 | ||||||||
\(170\) | −12.3690 | −0.948659 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −5.51288 | −0.420353 | ||||||||
\(173\) | −19.1759 | −1.45792 | −0.728959 | − | 0.684558i | \(-0.759995\pi\) | ||||
−0.728959 | + | 0.684558i | \(0.759995\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −14.6981 | −1.11107 | ||||||||
\(176\) | 13.0960 | 0.987148 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −6.81615 | −0.510892 | ||||||||
\(179\) | −7.02739 | −0.525252 | −0.262626 | − | 0.964898i | \(-0.584588\pi\) | ||||
−0.262626 | + | 0.964898i | \(0.584588\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −15.3645 | −1.14203 | −0.571017 | − | 0.820938i | \(-0.693451\pi\) | ||||
−0.571017 | + | 0.820938i | \(0.693451\pi\) | |||||||
\(182\) | −2.81427 | −0.208607 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −17.6520 | −1.30132 | ||||||||
\(185\) | −15.9213 | −1.17056 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −12.7974 | −0.935841 | ||||||||
\(188\) | −2.99324 | −0.218304 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 14.4298 | 1.04685 | ||||||||
\(191\) | −7.76445 | −0.561816 | −0.280908 | − | 0.959735i | \(-0.590636\pi\) | ||||
−0.280908 | + | 0.959735i | \(0.590636\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −24.7433 | −1.78106 | −0.890529 | − | 0.454926i | \(-0.849666\pi\) | ||||
−0.890529 | + | 0.454926i | \(0.849666\pi\) | |||||||
\(194\) | −16.3539 | −1.17414 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −0.607291 | −0.0433779 | ||||||||
\(197\) | −10.5794 | −0.753754 | −0.376877 | − | 0.926263i | \(-0.623002\pi\) | ||||
−0.376877 | + | 0.926263i | \(0.623002\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 0.813046 | 0.0576353 | 0.0288177 | − | 0.999585i | \(-0.490826\pi\) | ||||
0.0288177 | + | 0.999585i | \(0.490826\pi\) | |||||||
\(200\) | 45.2253 | 3.19791 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 2.13253 | 0.150044 | ||||||||
\(203\) | 3.90830 | 0.274309 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −3.13837 | −0.219193 | ||||||||
\(206\) | 12.7744 | 0.890035 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 5.76292 | 0.399587 | ||||||||
\(209\) | 14.9296 | 1.03270 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −2.74396 | −0.188902 | −0.0944509 | − | 0.995530i | \(-0.530110\pi\) | ||||
−0.0944509 | + | 0.995530i | \(0.530110\pi\) | |||||||
\(212\) | −6.58232 | −0.452075 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 15.1295 | 1.03423 | ||||||||
\(215\) | 40.2897 | 2.74774 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −2.83738 | −0.192614 | ||||||||
\(218\) | 11.7972 | 0.799005 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 14.6063 | 0.984756 | ||||||||
\(221\) | −5.63153 | −0.378818 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 19.4867 | 1.30493 | 0.652464 | − | 0.757820i | \(-0.273735\pi\) | ||||
0.652464 | + | 0.757820i | \(0.273735\pi\) | |||||||
\(224\) | 3.30196 | 0.220622 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 9.83680 | 0.654334 | ||||||||
\(227\) | 12.5024 | 0.829813 | 0.414906 | − | 0.909864i | \(-0.363814\pi\) | ||||
0.414906 | + | 0.909864i | \(0.363814\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −25.3292 | −1.67380 | −0.836900 | − | 0.547356i | \(-0.815634\pi\) | ||||
−0.836900 | + | 0.547356i | \(0.815634\pi\) | |||||||
\(230\) | 30.0480 | 1.98131 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −12.0256 | −0.789521 | ||||||||
\(233\) | −9.91538 | −0.649578 | −0.324789 | − | 0.945786i | \(-0.605293\pi\) | ||||
−0.324789 | + | 0.945786i | \(0.605293\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 21.8755 | 1.42700 | ||||||||
\(236\) | −5.28491 | −0.344019 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 2.78691 | 0.180648 | ||||||||
\(239\) | 18.4248 | 1.19180 | 0.595900 | − | 0.803058i | \(-0.296795\pi\) | ||||
0.595900 | + | 0.803058i | \(0.296795\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 8.87131 | 0.571451 | 0.285725 | − | 0.958312i | \(-0.407765\pi\) | ||||
0.285725 | + | 0.958312i | \(0.407765\pi\) | |||||||
\(242\) | −21.6756 | −1.39336 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −9.39906 | −0.601713 | ||||||||
\(245\) | 4.43826 | 0.283550 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 6.56980 | 0.418026 | ||||||||
\(248\) | 8.73046 | 0.554385 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −50.7961 | −3.21263 | ||||||||
\(251\) | 0.561631 | 0.0354498 | 0.0177249 | − | 0.999843i | \(-0.494358\pi\) | ||||
0.0177249 | + | 0.999843i | \(0.494358\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 31.0888 | 1.95454 | ||||||||
\(254\) | 1.18013 | 0.0740480 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −13.0951 | −0.818446 | ||||||||
\(257\) | −3.53641 | −0.220595 | −0.110298 | − | 0.993899i | \(-0.535180\pi\) | ||||
−0.110298 | + | 0.993899i | \(0.535180\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 3.58729 | 0.222904 | ||||||||
\(260\) | 6.42753 | 0.398618 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 10.7931 | 0.666801 | ||||||||
\(263\) | −10.8675 | −0.670118 | −0.335059 | − | 0.942197i | \(-0.608756\pi\) | ||||
−0.335059 | + | 0.942197i | \(0.608756\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 48.1055 | 2.95510 | ||||||||
\(266\) | −3.25123 | −0.199346 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −3.26278 | −0.199306 | ||||||||
\(269\) | −15.7001 | −0.957254 | −0.478627 | − | 0.878018i | \(-0.658865\pi\) | ||||
−0.478627 | + | 0.878018i | \(0.658865\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −27.0181 | −1.64123 | −0.820617 | − | 0.571478i | \(-0.806370\pi\) | ||||
−0.820617 | + | 0.571478i | \(0.806370\pi\) | |||||||
\(272\) | −5.70689 | −0.346031 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −16.4136 | −0.991581 | ||||||||
\(275\) | −79.6513 | −4.80315 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −20.7983 | −1.24965 | −0.624823 | − | 0.780766i | \(-0.714829\pi\) | ||||
−0.624823 | + | 0.780766i | \(0.714829\pi\) | |||||||
\(278\) | 20.1017 | 1.20562 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −13.6563 | −0.816118 | ||||||||
\(281\) | 11.3243 | 0.675554 | 0.337777 | − | 0.941226i | \(-0.390325\pi\) | ||||
0.337777 | + | 0.941226i | \(0.390325\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 7.09116 | 0.421526 | 0.210763 | − | 0.977537i | \(-0.432405\pi\) | ||||
0.210763 | + | 0.977537i | \(0.432405\pi\) | |||||||
\(284\) | 5.33856 | 0.316785 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −15.2509 | −0.901805 | ||||||||
\(287\) | 0.707118 | 0.0417398 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −11.4232 | −0.671954 | ||||||||
\(290\) | 20.4706 | 1.20208 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 8.85701 | 0.518317 | ||||||||
\(293\) | 1.07254 | 0.0626582 | 0.0313291 | − | 0.999509i | \(-0.490026\pi\) | ||||
0.0313291 | + | 0.999509i | \(0.490026\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 38.6237 | 2.24876 | ||||||||
\(296\) | −11.0379 | −0.641565 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −14.6098 | −0.846324 | ||||||||
\(299\) | 13.6807 | 0.791175 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −9.07783 | −0.523237 | ||||||||
\(302\) | 14.6723 | 0.844296 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 6.65772 | 0.381846 | ||||||||
\(305\) | 68.6911 | 3.93324 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 18.1259 | 1.03450 | 0.517249 | − | 0.855835i | \(-0.326956\pi\) | ||||
0.517249 | + | 0.855835i | \(0.326956\pi\) | |||||||
\(308\) | −3.29100 | −0.187522 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −14.8614 | −0.844072 | ||||||||
\(311\) | 6.03589 | 0.342264 | 0.171132 | − | 0.985248i | \(-0.445258\pi\) | ||||
0.171132 | + | 0.985248i | \(0.445258\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 16.9041 | 0.955475 | 0.477737 | − | 0.878503i | \(-0.341457\pi\) | ||||
0.477737 | + | 0.878503i | \(0.341457\pi\) | |||||||
\(314\) | 22.8762 | 1.29098 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 8.23774 | 0.463409 | ||||||||
\(317\) | −18.1372 | −1.01868 | −0.509342 | − | 0.860564i | \(-0.670111\pi\) | ||||
−0.509342 | + | 0.860564i | \(0.670111\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 21.1797 | 1.18583 | ||||||||
\(320\) | 38.7459 | 2.16596 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −6.77024 | −0.377290 | ||||||||
\(323\) | −6.50593 | −0.362000 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −35.0507 | −1.94426 | ||||||||
\(326\) | 4.08337 | 0.226157 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −2.17576 | −0.120136 | ||||||||
\(329\) | −4.92884 | −0.271736 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −8.15730 | −0.448366 | −0.224183 | − | 0.974547i | \(-0.571971\pi\) | ||||
−0.224183 | + | 0.974547i | \(0.571971\pi\) | |||||||
\(332\) | 3.55601 | 0.195161 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 23.0447 | 1.26095 | ||||||||
\(335\) | 23.8453 | 1.30281 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −9.35375 | −0.509531 | −0.254765 | − | 0.967003i | \(-0.581998\pi\) | ||||
−0.254765 | + | 0.967003i | \(0.581998\pi\) | |||||||
\(338\) | 8.63051 | 0.469438 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −6.36504 | −0.345193 | ||||||||
\(341\) | −15.3762 | −0.832667 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | 27.9320 | 1.50599 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 22.6301 | 1.21660 | ||||||||
\(347\) | −2.98500 | −0.160243 | −0.0801216 | − | 0.996785i | \(-0.525531\pi\) | ||||
−0.0801216 | + | 0.996785i | \(0.525531\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 30.6058 | 1.63829 | 0.819146 | − | 0.573585i | \(-0.194448\pi\) | ||||
0.819146 | + | 0.573585i | \(0.194448\pi\) | |||||||
\(350\) | 17.3457 | 0.927168 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 17.8938 | 0.953744 | ||||||||
\(353\) | 6.64509 | 0.353682 | 0.176841 | − | 0.984239i | \(-0.443412\pi\) | ||||
0.176841 | + | 0.984239i | \(0.443412\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −39.0158 | −2.07074 | ||||||||
\(356\) | −3.50756 | −0.185900 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 8.29324 | 0.438311 | ||||||||
\(359\) | −32.2341 | −1.70125 | −0.850626 | − | 0.525772i | \(-0.823777\pi\) | ||||
−0.850626 | + | 0.525772i | \(0.823777\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −11.4101 | −0.600533 | ||||||||
\(362\) | 18.1321 | 0.953003 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −1.44821 | −0.0759068 | ||||||||
\(365\) | −64.7296 | −3.38810 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 12.1394 | 0.633670 | 0.316835 | − | 0.948481i | \(-0.397380\pi\) | ||||
0.316835 | + | 0.948481i | \(0.397380\pi\) | |||||||
\(368\) | 13.8638 | 0.722699 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 18.7893 | 0.976807 | ||||||||
\(371\) | −10.8388 | −0.562724 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −32.5972 | −1.68782 | −0.843910 | − | 0.536485i | \(-0.819752\pi\) | ||||
−0.843910 | + | 0.536485i | \(0.819752\pi\) | |||||||
\(374\) | 15.1026 | 0.780939 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 15.1658 | 0.782115 | ||||||||
\(377\) | 9.32015 | 0.480012 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 21.7712 | 1.11831 | 0.559155 | − | 0.829063i | \(-0.311126\pi\) | ||||
0.559155 | + | 0.829063i | \(0.311126\pi\) | |||||||
\(380\) | 7.42551 | 0.380921 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 9.16307 | 0.468824 | ||||||||
\(383\) | 3.86635 | 0.197561 | 0.0987806 | − | 0.995109i | \(-0.468506\pi\) | ||||
0.0987806 | + | 0.995109i | \(0.468506\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 24.0516 | 1.22578 | ||||||||
\(386\) | 29.2003 | 1.48626 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −8.41564 | −0.427239 | ||||||||
\(389\) | 17.3609 | 0.880230 | 0.440115 | − | 0.897941i | \(-0.354938\pi\) | ||||
0.440115 | + | 0.897941i | \(0.354938\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −13.5477 | −0.685137 | ||||||||
\(392\) | 3.07694 | 0.155409 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 12.4851 | 0.628991 | ||||||||
\(395\) | −60.2038 | −3.02918 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −36.5315 | −1.83346 | −0.916732 | − | 0.399502i | \(-0.869183\pi\) | ||||
−0.916732 | + | 0.399502i | \(0.869183\pi\) | |||||||
\(398\) | −0.959501 | −0.0480955 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −35.5197 | −1.77599 | ||||||||
\(401\) | 15.3087 | 0.764482 | 0.382241 | − | 0.924063i | \(-0.375152\pi\) | ||||
0.382241 | + | 0.924063i | \(0.375152\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −6.76632 | −0.337054 | ||||||||
\(404\) | 1.09739 | 0.0545971 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −4.61231 | −0.228905 | ||||||||
\(407\) | 19.4401 | 0.963608 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 27.7504 | 1.37217 | 0.686083 | − | 0.727523i | \(-0.259328\pi\) | ||||
0.686083 | + | 0.727523i | \(0.259328\pi\) | |||||||
\(410\) | 3.70369 | 0.182912 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 6.57366 | 0.323861 | ||||||||
\(413\) | −8.70245 | −0.428219 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −25.9883 | −1.27572 | ||||||||
\(416\) | 7.87421 | 0.386065 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −17.6189 | −0.861768 | ||||||||
\(419\) | −7.51179 | −0.366975 | −0.183488 | − | 0.983022i | \(-0.558739\pi\) | ||||
−0.183488 | + | 0.983022i | \(0.558739\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 6.05425 | 0.295066 | 0.147533 | − | 0.989057i | \(-0.452867\pi\) | ||||
0.147533 | + | 0.989057i | \(0.452867\pi\) | |||||||
\(422\) | 3.23823 | 0.157634 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 33.3505 | 1.61964 | ||||||||
\(425\) | 34.7100 | 1.68368 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −15.4770 | −0.748987 | ||||||||
\(428\) | 7.78557 | 0.376330 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −47.5472 | −2.29293 | ||||||||
\(431\) | 33.5629 | 1.61667 | 0.808334 | − | 0.588724i | \(-0.200369\pi\) | ||||
0.808334 | + | 0.588724i | \(0.200369\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 14.8488 | 0.713586 | 0.356793 | − | 0.934183i | \(-0.383870\pi\) | ||||
0.356793 | + | 0.934183i | \(0.383870\pi\) | |||||||
\(434\) | 3.34848 | 0.160732 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 6.07078 | 0.290737 | ||||||||
\(437\) | 15.8049 | 0.756049 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 18.5869 | 0.887103 | 0.443552 | − | 0.896249i | \(-0.353718\pi\) | ||||
0.443552 | + | 0.896249i | \(0.353718\pi\) | |||||||
\(440\) | −74.0053 | −3.52807 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 6.64595 | 0.316116 | ||||||||
\(443\) | 2.21728 | 0.105346 | 0.0526730 | − | 0.998612i | \(-0.483226\pi\) | ||||
0.0526730 | + | 0.998612i | \(0.483226\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 25.6343 | 1.21518 | ||||||||
\(446\) | −22.9969 | −1.08893 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −8.72998 | −0.412453 | ||||||||
\(449\) | 12.9587 | 0.611558 | 0.305779 | − | 0.952102i | \(-0.401083\pi\) | ||||
0.305779 | + | 0.952102i | \(0.401083\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 3.83197 | 0.180441 | ||||||||
\(452\) | 5.06198 | 0.238095 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −14.7545 | −0.692461 | ||||||||
\(455\) | 10.5839 | 0.496183 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −36.1883 | −1.69282 | −0.846410 | − | 0.532532i | \(-0.821240\pi\) | ||||
−0.846410 | + | 0.532532i | \(0.821240\pi\) | |||||||
\(458\) | 29.8918 | 1.39675 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 15.4626 | 0.720948 | ||||||||
\(461\) | 41.2133 | 1.91949 | 0.959747 | − | 0.280866i | \(-0.0906217\pi\) | ||||
0.959747 | + | 0.280866i | \(0.0906217\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −39.1721 | −1.82048 | −0.910240 | − | 0.414080i | \(-0.864103\pi\) | ||||
−0.910240 | + | 0.414080i | \(0.864103\pi\) | |||||||
\(464\) | 9.44487 | 0.438467 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 11.7014 | 0.542059 | ||||||||
\(467\) | −27.5007 | −1.27258 | −0.636291 | − | 0.771449i | \(-0.719532\pi\) | ||||
−0.636291 | + | 0.771449i | \(0.719532\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −5.37268 | −0.248087 | ||||||||
\(470\) | −25.8159 | −1.19080 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 26.7769 | 1.23251 | ||||||||
\(473\) | −49.1941 | −2.26195 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −40.4930 | −1.85794 | ||||||||
\(476\) | 1.43413 | 0.0657332 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −21.7437 | −0.994532 | ||||||||
\(479\) | −2.25308 | −0.102946 | −0.0514728 | − | 0.998674i | \(-0.516392\pi\) | ||||
−0.0514728 | + | 0.998674i | \(0.516392\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 8.55464 | 0.390058 | ||||||||
\(482\) | −10.4693 | −0.476864 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −11.1542 | −0.507009 | ||||||||
\(485\) | 61.5039 | 2.79275 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 4.33373 | 0.196380 | 0.0981901 | − | 0.995168i | \(-0.468695\pi\) | ||||
0.0981901 | + | 0.995168i | \(0.468695\pi\) | |||||||
\(488\) | 47.6220 | 2.15575 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −5.23773 | −0.236616 | ||||||||
\(491\) | −3.53012 | −0.159312 | −0.0796560 | − | 0.996822i | \(-0.525382\pi\) | ||||
−0.0796560 | + | 0.996822i | \(0.525382\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −9.22954 | −0.415678 | ||||||||
\(494\) | −7.75323 | −0.348834 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −6.85686 | −0.307882 | ||||||||
\(497\) | 8.79079 | 0.394321 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −19.5211 | −0.873884 | −0.436942 | − | 0.899490i | \(-0.643939\pi\) | ||||
−0.436942 | + | 0.899490i | \(0.643939\pi\) | |||||||
\(500\) | −26.1395 | −1.16899 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −0.662798 | −0.0295821 | ||||||||
\(503\) | −25.9921 | −1.15893 | −0.579465 | − | 0.814997i | \(-0.696739\pi\) | ||||
−0.579465 | + | 0.814997i | \(0.696739\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −8.02004 | −0.356887 | ||||||||
\(506\) | −36.6889 | −1.63102 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0.607291 | 0.0269442 | ||||||||
\(509\) | 39.4799 | 1.74992 | 0.874959 | − | 0.484198i | \(-0.160888\pi\) | ||||
0.874959 | + | 0.484198i | \(0.160888\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 14.5845 | 0.645179 | ||||||||
\(512\) | 22.8512 | 1.00989 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 4.17343 | 0.184082 | ||||||||
\(515\) | −48.0422 | −2.11699 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −26.7101 | −1.17471 | ||||||||
\(518\) | −4.23348 | −0.186008 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −32.5662 | −1.42812 | ||||||||
\(521\) | −10.6512 | −0.466639 | −0.233320 | − | 0.972400i | \(-0.574959\pi\) | ||||
−0.233320 | + | 0.972400i | \(0.574959\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 25.7574 | 1.12629 | 0.563147 | − | 0.826357i | \(-0.309591\pi\) | ||||
0.563147 | + | 0.826357i | \(0.309591\pi\) | |||||||
\(524\) | 5.55409 | 0.242632 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 12.8251 | 0.559199 | ||||||||
\(527\) | 6.70054 | 0.291880 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 9.91145 | 0.430933 | ||||||||
\(530\) | −56.7708 | −2.46597 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −1.67307 | −0.0725368 | ||||||||
\(533\) | 1.68627 | 0.0730404 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −56.8992 | −2.45997 | ||||||||
\(536\) | 16.5314 | 0.714049 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 18.5282 | 0.798808 | ||||||||
\(539\) | −5.41915 | −0.233419 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −27.6386 | −1.18828 | −0.594138 | − | 0.804363i | \(-0.702507\pi\) | ||||
−0.594138 | + | 0.804363i | \(0.702507\pi\) | |||||||
\(542\) | 31.8849 | 1.36958 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −7.79766 | −0.334322 | ||||||||
\(545\) | −44.3670 | −1.90047 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 19.2255 | 0.822024 | 0.411012 | − | 0.911630i | \(-0.365175\pi\) | ||||
0.411012 | + | 0.911630i | \(0.365175\pi\) | |||||||
\(548\) | −8.44636 | −0.360811 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 93.9990 | 4.00813 | ||||||||
\(551\) | 10.7673 | 0.458701 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 13.5647 | 0.576832 | ||||||||
\(554\) | 24.5447 | 1.04280 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 10.3442 | 0.438694 | ||||||||
\(557\) | −29.8537 | −1.26494 | −0.632471 | − | 0.774584i | \(-0.717959\pi\) | ||||
−0.632471 | + | 0.774584i | \(0.717959\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −21.6480 | −0.915611 | ||||||||
\(560\) | 10.7256 | 0.453238 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −13.3642 | −0.563735 | ||||||||
\(563\) | −32.2423 | −1.35885 | −0.679425 | − | 0.733745i | \(-0.737771\pi\) | ||||
−0.679425 | + | 0.733745i | \(0.737771\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −36.9944 | −1.55637 | ||||||||
\(566\) | −8.36850 | −0.351754 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −27.0488 | −1.13494 | ||||||||
\(569\) | 27.2451 | 1.14217 | 0.571086 | − | 0.820890i | \(-0.306522\pi\) | ||||
0.571086 | + | 0.820890i | \(0.306522\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −23.3646 | −0.977779 | −0.488890 | − | 0.872346i | \(-0.662598\pi\) | ||||
−0.488890 | + | 0.872346i | \(0.662598\pi\) | |||||||
\(572\) | −7.84806 | −0.328144 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −0.834492 | −0.0348310 | ||||||||
\(575\) | −84.3210 | −3.51643 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −14.4610 | −0.602018 | −0.301009 | − | 0.953621i | \(-0.597323\pi\) | ||||
−0.301009 | + | 0.953621i | \(0.597323\pi\) | |||||||
\(578\) | 13.4809 | 0.560731 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 10.5341 | 0.437404 | ||||||||
\(581\) | 5.85553 | 0.242928 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −58.7372 | −2.43265 | ||||||||
\(584\) | −44.8756 | −1.85697 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −1.26573 | −0.0522870 | ||||||||
\(587\) | 15.5314 | 0.641049 | 0.320524 | − | 0.947240i | \(-0.396141\pi\) | ||||
0.320524 | + | 0.947240i | \(0.396141\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −7.81691 | −0.322090 | ||||||||
\(590\) | −45.5810 | −1.87654 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 8.66911 | 0.356298 | ||||||||
\(593\) | 15.6281 | 0.641769 | 0.320884 | − | 0.947118i | \(-0.396020\pi\) | ||||
0.320884 | + | 0.947118i | \(0.396020\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −10.4810 | −0.429681 | ||||||||
\(596\) | −7.51815 | −0.307955 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −16.1450 | −0.660219 | ||||||||
\(599\) | 8.04131 | 0.328559 | 0.164280 | − | 0.986414i | \(-0.447470\pi\) | ||||
0.164280 | + | 0.986414i | \(0.447470\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −46.7643 | −1.90755 | −0.953777 | − | 0.300514i | \(-0.902842\pi\) | ||||
−0.953777 | + | 0.300514i | \(0.902842\pi\) | |||||||
\(602\) | 10.7130 | 0.436630 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 7.55030 | 0.307217 | ||||||||
\(605\) | 81.5181 | 3.31418 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 4.05313 | 0.164511 | 0.0822557 | − | 0.996611i | \(-0.473788\pi\) | ||||
0.0822557 | + | 0.996611i | \(0.473788\pi\) | |||||||
\(608\) | 9.09682 | 0.368925 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −81.0645 | −3.28221 | ||||||||
\(611\) | −11.7538 | −0.475509 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 7.60595 | 0.307201 | 0.153601 | − | 0.988133i | \(-0.450913\pi\) | ||||
0.153601 | + | 0.988133i | \(0.450913\pi\) | |||||||
\(614\) | −21.3909 | −0.863267 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 16.6744 | 0.671831 | ||||||||
\(617\) | 23.6786 | 0.953265 | 0.476632 | − | 0.879103i | \(-0.341857\pi\) | ||||
0.476632 | + | 0.879103i | \(0.341857\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 30.7464 | 1.23580 | 0.617901 | − | 0.786256i | \(-0.287983\pi\) | ||||
0.617901 | + | 0.786256i | \(0.287983\pi\) | |||||||
\(620\) | −7.64763 | −0.307136 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −7.12314 | −0.285612 | ||||||||
\(623\) | −5.77576 | −0.231401 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 117.544 | 4.70177 | ||||||||
\(626\) | −19.9490 | −0.797323 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 11.7720 | 0.469754 | ||||||||
\(629\) | −8.47147 | −0.337780 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −39.5487 | −1.57441 | −0.787205 | − | 0.616691i | \(-0.788473\pi\) | ||||
−0.787205 | + | 0.616691i | \(0.788473\pi\) | |||||||
\(632\) | −41.7380 | −1.66025 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 21.4042 | 0.850071 | ||||||||
\(635\) | −4.43826 | −0.176127 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −2.38471 | −0.0944855 | ||||||||
\(638\) | −24.9948 | −0.989553 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −16.4153 | −0.648873 | ||||||||
\(641\) | −21.3454 | −0.843091 | −0.421546 | − | 0.906807i | \(-0.638512\pi\) | ||||
−0.421546 | + | 0.906807i | \(0.638512\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 9.79675 | 0.386346 | 0.193173 | − | 0.981165i | \(-0.438122\pi\) | ||||
0.193173 | + | 0.981165i | \(0.438122\pi\) | |||||||
\(644\) | −3.48394 | −0.137286 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 7.67785 | 0.302081 | ||||||||
\(647\) | 9.33818 | 0.367122 | 0.183561 | − | 0.983008i | \(-0.441238\pi\) | ||||
0.183561 | + | 0.983008i | \(0.441238\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −47.1598 | −1.85118 | ||||||||
\(650\) | 41.3644 | 1.62245 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 2.10129 | 0.0822927 | ||||||||
\(653\) | 1.02438 | 0.0400872 | 0.0200436 | − | 0.999799i | \(-0.493620\pi\) | ||||
0.0200436 | + | 0.999799i | \(0.493620\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −40.5909 | −1.58602 | ||||||||
\(656\) | 1.70883 | 0.0667187 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 5.81668 | 0.226758 | ||||||||
\(659\) | −18.9099 | −0.736623 | −0.368312 | − | 0.929702i | \(-0.620064\pi\) | ||||
−0.368312 | + | 0.929702i | \(0.620064\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −27.3932 | −1.06547 | −0.532736 | − | 0.846282i | \(-0.678836\pi\) | ||||
−0.532736 | + | 0.846282i | \(0.678836\pi\) | |||||||
\(662\) | 9.62668 | 0.374152 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −18.0171 | −0.699200 | ||||||||
\(665\) | 12.2273 | 0.474154 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 22.4213 | 0.868158 | ||||||||
\(668\) | 11.8587 | 0.458827 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −28.1406 | −1.08717 | ||||||||
\(671\) | −83.8724 | −3.23786 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 11.6979 | 0.450920 | 0.225460 | − | 0.974252i | \(-0.427611\pi\) | ||||
0.225460 | + | 0.974252i | \(0.427611\pi\) | |||||||
\(674\) | 11.0386 | 0.425193 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 4.44122 | 0.170816 | ||||||||
\(677\) | 12.2230 | 0.469768 | 0.234884 | − | 0.972023i | \(-0.424529\pi\) | ||||
0.234884 | + | 0.972023i | \(0.424529\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −13.8577 | −0.531809 | ||||||||
\(680\) | 32.2496 | 1.23672 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 18.1459 | 0.694843 | ||||||||
\(683\) | −45.0284 | −1.72296 | −0.861482 | − | 0.507788i | \(-0.830463\pi\) | ||||
−0.861482 | + | 0.507788i | \(0.830463\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 61.7285 | 2.35852 | ||||||||
\(686\) | 1.18013 | 0.0450576 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −21.9376 | −0.836365 | ||||||||
\(689\) | −25.8474 | −0.984708 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 18.8479 | 0.717009 | 0.358504 | − | 0.933528i | \(-0.383287\pi\) | ||||
0.358504 | + | 0.933528i | \(0.383287\pi\) | |||||||
\(692\) | 11.6453 | 0.442690 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 3.52269 | 0.133719 | ||||||||
\(695\) | −75.5988 | −2.86763 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −1.66987 | −0.0632510 | ||||||||
\(698\) | −36.1189 | −1.36712 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 8.92604 | 0.337372 | ||||||||
\(701\) | −6.02478 | −0.227553 | −0.113776 | − | 0.993506i | \(-0.536295\pi\) | ||||
−0.113776 | + | 0.993506i | \(0.536295\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 9.88290 | 0.372740 | ||||||||
\(704\) | −47.3091 | −1.78303 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −7.84208 | −0.295140 | ||||||||
\(707\) | 1.80702 | 0.0679601 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 2.99684 | 0.112549 | 0.0562744 | − | 0.998415i | \(-0.482078\pi\) | ||||
0.0562744 | + | 0.998415i | \(0.482078\pi\) | |||||||
\(710\) | 46.0437 | 1.72799 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 17.7717 | 0.666022 | ||||||||
\(713\) | −16.2776 | −0.609602 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 57.3559 | 2.14499 | ||||||||
\(716\) | 4.26767 | 0.159490 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 38.0405 | 1.41966 | ||||||||
\(719\) | −36.4922 | −1.36093 | −0.680465 | − | 0.732781i | \(-0.738222\pi\) | ||||
−0.680465 | + | 0.732781i | \(0.738222\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 10.8246 | 0.403128 | ||||||||
\(722\) | 13.4654 | 0.501132 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 9.33071 | 0.346773 | ||||||||
\(725\) | −57.4447 | −2.13344 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 8.36457 | 0.310225 | 0.155112 | − | 0.987897i | \(-0.450426\pi\) | ||||
0.155112 | + | 0.987897i | \(0.450426\pi\) | |||||||
\(728\) | 7.33761 | 0.271950 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 76.3895 | 2.82730 | ||||||||
\(731\) | 21.4375 | 0.792894 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 28.0240 | 1.03509 | 0.517545 | − | 0.855656i | \(-0.326846\pi\) | ||||
0.517545 | + | 0.855656i | \(0.326846\pi\) | |||||||
\(734\) | −14.3260 | −0.528784 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 18.9429 | 0.698244 | ||||||||
\(737\) | −29.1153 | −1.07248 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −44.3664 | −1.63204 | −0.816022 | − | 0.578021i | \(-0.803825\pi\) | ||||
−0.816022 | + | 0.578021i | \(0.803825\pi\) | |||||||
\(740\) | 9.66887 | 0.355435 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 12.7912 | 0.469581 | ||||||||
\(743\) | −27.2520 | −0.999778 | −0.499889 | − | 0.866089i | \(-0.666626\pi\) | ||||
−0.499889 | + | 0.866089i | \(0.666626\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 54.9448 | 2.01302 | ||||||||
\(746\) | 38.4690 | 1.40845 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 7.77176 | 0.284164 | ||||||||
\(749\) | 12.8202 | 0.468439 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 20.4756 | 0.747167 | 0.373583 | − | 0.927597i | \(-0.378129\pi\) | ||||
0.373583 | + | 0.927597i | \(0.378129\pi\) | |||||||
\(752\) | −11.9111 | −0.434354 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −10.9990 | −0.400560 | ||||||||
\(755\) | −55.1798 | −2.00820 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 3.88978 | 0.141376 | 0.0706882 | − | 0.997498i | \(-0.477480\pi\) | ||||
0.0706882 | + | 0.997498i | \(0.477480\pi\) | |||||||
\(758\) | −25.6928 | −0.933206 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −37.6227 | −1.36472 | ||||||||
\(761\) | 2.39284 | 0.0867405 | 0.0433702 | − | 0.999059i | \(-0.486190\pi\) | ||||
0.0433702 | + | 0.999059i | \(0.486190\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 9.99649 | 0.361897 | ||||||||
\(764\) | 4.71528 | 0.170593 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −4.56280 | −0.164861 | ||||||||
\(767\) | −20.7528 | −0.749339 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 17.0826 | 0.616014 | 0.308007 | − | 0.951384i | \(-0.400338\pi\) | ||||
0.308007 | + | 0.951384i | \(0.400338\pi\) | |||||||
\(770\) | −28.3840 | −1.02289 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 15.0263 | 0.540810 | ||||||||
\(773\) | 38.7362 | 1.39324 | 0.696621 | − | 0.717439i | \(-0.254686\pi\) | ||||
0.696621 | + | 0.717439i | \(0.254686\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 41.7042 | 1.49806 | ||||||||
\(776\) | 42.6393 | 1.53066 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −20.4881 | −0.734533 | ||||||||
\(779\) | 1.94809 | 0.0697976 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 47.6385 | 1.70464 | ||||||||
\(782\) | 15.9881 | 0.571732 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −2.41662 | −0.0863077 | ||||||||
\(785\) | −86.0332 | −3.07066 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 13.3375 | 0.475430 | 0.237715 | − | 0.971335i | \(-0.423602\pi\) | ||||
0.237715 | + | 0.971335i | \(0.423602\pi\) | |||||||
\(788\) | 6.42479 | 0.228874 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 71.0484 | 2.52779 | ||||||||
\(791\) | 8.33535 | 0.296371 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −36.9082 | −1.31065 | ||||||||
\(794\) | 43.1120 | 1.52999 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −0.493755 | −0.0175007 | ||||||||
\(797\) | −5.73847 | −0.203267 | −0.101633 | − | 0.994822i | \(-0.532407\pi\) | ||||
−0.101633 | + | 0.994822i | \(0.532407\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 11.6396 | 0.411778 | ||||||||
\(800\) | −48.5327 | −1.71589 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −18.0663 | −0.637944 | ||||||||
\(803\) | 79.0354 | 2.78910 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 25.4616 | 0.897404 | ||||||||
\(806\) | 7.98514 | 0.281265 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −5.56011 | −0.195604 | ||||||||
\(809\) | 32.9630 | 1.15892 | 0.579458 | − | 0.815002i | \(-0.303264\pi\) | ||||
0.579458 | + | 0.815002i | \(0.303264\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 35.8058 | 1.25731 | 0.628656 | − | 0.777684i | \(-0.283605\pi\) | ||||
0.628656 | + | 0.777684i | \(0.283605\pi\) | |||||||
\(812\) | −2.37348 | −0.0832927 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −22.9418 | −0.804110 | ||||||||
\(815\) | −15.3568 | −0.537926 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −25.0092 | −0.874960 | ||||||||
\(818\) | −32.7491 | −1.14504 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 1.90590 | 0.0665570 | ||||||||
\(821\) | −45.5266 | −1.58889 | −0.794445 | − | 0.607336i | \(-0.792238\pi\) | ||||
−0.794445 | + | 0.607336i | \(0.792238\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 4.84441 | 0.168866 | 0.0844328 | − | 0.996429i | \(-0.473092\pi\) | ||||
0.0844328 | + | 0.996429i | \(0.473092\pi\) | |||||||
\(824\) | −33.3066 | −1.16029 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 10.2700 | 0.357340 | ||||||||
\(827\) | 29.6775 | 1.03199 | 0.515993 | − | 0.856593i | \(-0.327423\pi\) | ||||
0.515993 | + | 0.856593i | \(0.327423\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −38.9206 | −1.35177 | −0.675884 | − | 0.737008i | \(-0.736238\pi\) | ||||
−0.675884 | + | 0.737008i | \(0.736238\pi\) | |||||||
\(830\) | 30.6696 | 1.06456 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −20.8184 | −0.721750 | ||||||||
\(833\) | 2.36152 | 0.0818219 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −86.6668 | −2.99923 | ||||||||
\(836\) | −9.06661 | −0.313575 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 8.86490 | 0.306233 | ||||||||
\(839\) | 11.2390 | 0.388015 | 0.194007 | − | 0.981000i | \(-0.437851\pi\) | ||||
0.194007 | + | 0.981000i | \(0.437851\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −13.7252 | −0.473282 | ||||||||
\(842\) | −7.14480 | −0.246226 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 1.66638 | 0.0573591 | ||||||||
\(845\) | −32.4578 | −1.11658 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −18.3671 | −0.631102 | ||||||||
\(848\) | −26.1933 | −0.899481 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −40.9623 | −1.40500 | ||||||||
\(851\) | 20.5798 | 0.705465 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −3.28040 | −0.112319 | −0.0561594 | − | 0.998422i | \(-0.517885\pi\) | ||||
−0.0561594 | + | 0.998422i | \(0.517885\pi\) | |||||||
\(854\) | 18.2649 | 0.625014 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −39.4470 | −1.34827 | ||||||||
\(857\) | −18.3698 | −0.627499 | −0.313750 | − | 0.949506i | \(-0.601585\pi\) | ||||
−0.313750 | + | 0.949506i | \(0.601585\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −39.9179 | −1.36198 | −0.680991 | − | 0.732292i | \(-0.738451\pi\) | ||||
−0.680991 | + | 0.732292i | \(0.738451\pi\) | |||||||
\(860\) | −24.4676 | −0.834338 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −39.6086 | −1.34908 | ||||||||
\(863\) | 2.21429 | 0.0753753 | 0.0376876 | − | 0.999290i | \(-0.488001\pi\) | ||||
0.0376876 | + | 0.999290i | \(0.488001\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −85.1076 | −2.89375 | ||||||||
\(866\) | −17.5235 | −0.595472 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 1.72311 | 0.0584863 | ||||||||
\(869\) | 73.5093 | 2.49363 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −12.8123 | −0.434127 | ||||||||
\(872\) | −30.7586 | −1.04162 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −18.6518 | −0.630907 | ||||||||
\(875\) | −43.0428 | −1.45511 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −34.7091 | −1.17204 | −0.586021 | − | 0.810296i | \(-0.699306\pi\) | ||||
−0.586021 | + | 0.810296i | \(0.699306\pi\) | |||||||
\(878\) | −21.9349 | −0.740269 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 58.1234 | 1.95934 | ||||||||
\(881\) | 0.174959 | 0.00589451 | 0.00294725 | − | 0.999996i | \(-0.499062\pi\) | ||||
0.00294725 | + | 0.999996i | \(0.499062\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 47.3602 | 1.59380 | 0.796899 | − | 0.604113i | \(-0.206473\pi\) | ||||
0.796899 | + | 0.604113i | \(0.206473\pi\) | |||||||
\(884\) | 3.41998 | 0.115026 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −2.61668 | −0.0879090 | ||||||||
\(887\) | 40.2851 | 1.35264 | 0.676321 | − | 0.736607i | \(-0.263573\pi\) | ||||
0.676321 | + | 0.736607i | \(0.263573\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1.00000 | 0.0335389 | ||||||||
\(890\) | −30.2518 | −1.01404 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −11.8341 | −0.396235 | ||||||||
\(893\) | −13.5788 | −0.454398 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −31.1894 | −1.04255 | ||||||||
\(896\) | 3.69860 | 0.123561 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −15.2929 | −0.510332 | ||||||||
\(899\) | −11.0893 | −0.369850 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 25.5961 | 0.852731 | ||||||||
\(902\) | −4.52223 | −0.150574 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −25.6474 | −0.853020 | ||||||||
\(905\) | −68.1916 | −2.26677 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −16.1755 | −0.537100 | −0.268550 | − | 0.963266i | \(-0.586544\pi\) | ||||
−0.268550 | + | 0.963266i | \(0.586544\pi\) | |||||||
\(908\) | −7.59259 | −0.251969 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −12.4904 | −0.414054 | ||||||||
\(911\) | −5.34893 | −0.177218 | −0.0886090 | − | 0.996066i | \(-0.528242\pi\) | ||||
−0.0886090 | + | 0.996066i | \(0.528242\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 31.7320 | 1.05017 | ||||||||
\(914\) | 42.7070 | 1.41262 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 15.3822 | 0.508242 | ||||||||
\(917\) | 9.14569 | 0.302017 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −26.5607 | −0.876156 | −0.438078 | − | 0.898937i | \(-0.644341\pi\) | ||||
−0.438078 | + | 0.898937i | \(0.644341\pi\) | |||||||
\(920\) | −78.3440 | −2.58292 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −48.6371 | −1.60178 | ||||||||
\(923\) | 20.9634 | 0.690020 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −52.7265 | −1.73364 | ||||||||
\(926\) | 46.2282 | 1.51915 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 12.9051 | 0.423630 | ||||||||
\(929\) | 42.5323 | 1.39544 | 0.697719 | − | 0.716371i | \(-0.254198\pi\) | ||||
0.697719 | + | 0.716371i | \(0.254198\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −2.75497 | −0.0902906 | ||||||||
\(932\) | 6.02152 | 0.197241 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 32.4545 | 1.06194 | ||||||||
\(935\) | −56.7983 | −1.85750 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 8.57209 | 0.280038 | 0.140019 | − | 0.990149i | \(-0.455284\pi\) | ||||
0.140019 | + | 0.990149i | \(0.455284\pi\) | |||||||
\(938\) | 6.34047 | 0.207024 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −13.2848 | −0.433301 | ||||||||
\(941\) | 30.0271 | 0.978857 | 0.489428 | − | 0.872044i | \(-0.337205\pi\) | ||||
0.489428 | + | 0.872044i | \(0.337205\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 4.05663 | 0.132102 | ||||||||
\(944\) | −21.0305 | −0.684484 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 58.0555 | 1.88755 | ||||||||
\(947\) | 27.6070 | 0.897108 | 0.448554 | − | 0.893756i | \(-0.351939\pi\) | ||||
0.448554 | + | 0.893756i | \(0.351939\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 34.7797 | 1.12900 | ||||||||
\(950\) | 47.7870 | 1.55041 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −7.26627 | −0.235501 | ||||||||
\(953\) | 56.3567 | 1.82557 | 0.912786 | − | 0.408437i | \(-0.133926\pi\) | ||||
0.912786 | + | 0.408437i | \(0.133926\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −34.4606 | −1.11512 | ||||||||
\(956\) | −11.1892 | −0.361885 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 2.65893 | 0.0859060 | ||||||||
\(959\) | −13.9083 | −0.449121 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −22.9493 | −0.740299 | ||||||||
\(962\) | −10.0956 | −0.325495 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −5.38746 | −0.173518 | ||||||||
\(965\) | −109.817 | −3.53513 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −10.0649 | −0.323664 | −0.161832 | − | 0.986818i | \(-0.551740\pi\) | ||||
−0.161832 | + | 0.986818i | \(0.551740\pi\) | |||||||
\(968\) | 56.5147 | 1.81645 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −72.5827 | −2.33049 | ||||||||
\(971\) | 47.6227 | 1.52829 | 0.764143 | − | 0.645047i | \(-0.223162\pi\) | ||||
0.764143 | + | 0.645047i | \(0.223162\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 17.0334 | 0.546067 | ||||||||
\(974\) | −5.11437 | −0.163875 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −37.4021 | −1.19721 | ||||||||
\(977\) | −2.84827 | −0.0911243 | −0.0455621 | − | 0.998962i | \(-0.514508\pi\) | ||||
−0.0455621 | + | 0.998962i | \(0.514508\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −31.2997 | −1.00034 | ||||||||
\(980\) | −2.69531 | −0.0860986 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 4.16600 | 0.132942 | ||||||||
\(983\) | −37.5274 | −1.19694 | −0.598470 | − | 0.801146i | \(-0.704224\pi\) | ||||
−0.598470 | + | 0.801146i | \(0.704224\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −46.9543 | −1.49609 | ||||||||
\(986\) | 10.8921 | 0.346874 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −3.98978 | −0.126932 | ||||||||
\(989\) | −52.0782 | −1.65599 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −42.7222 | −1.35711 | −0.678557 | − | 0.734547i | \(-0.737395\pi\) | ||||
−0.678557 | + | 0.734547i | \(0.737395\pi\) | |||||||
\(992\) | −9.36893 | −0.297464 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −10.3743 | −0.329052 | ||||||||
\(995\) | 3.60851 | 0.114397 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 3.76493 | 0.119237 | 0.0596183 | − | 0.998221i | \(-0.481012\pi\) | ||||
0.0596183 | + | 0.998221i | \(0.481012\pi\) | |||||||
\(998\) | 23.0374 | 0.729238 | ||||||||
\(999\) | 0 | 0 |
(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 | 8001.2.a.z.1.10 | ✓ | 32 | |
3.2 | odd | 2 | inner | 8001.2.a.z.1.23 | yes | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8001.2.a.z.1.10 | ✓ | 32 | 1.1 | even | 1 | trivial | |
8001.2.a.z.1.23 | yes | 32 | 3.2 | odd | 2 | inner |