Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8015,2,Mod(1,8015)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8015, 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("8015.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8015 = 5 \cdot 7 \cdot 229 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8015.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: | \(64.0000972201\) |
Analytic rank: | \(0\) |
Dimension: | \(62\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.21 | ||
Character | \(\chi\) | \(=\) | 8015.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.05535 | −0.746245 | −0.373122 | − | 0.927782i | \(-0.621713\pi\) | ||||
−0.373122 | + | 0.927782i | \(0.621713\pi\) | |||||||
\(3\) | 0.176354 | 0.101818 | 0.0509090 | − | 0.998703i | \(-0.483788\pi\) | ||||
0.0509090 | + | 0.998703i | \(0.483788\pi\) | |||||||
\(4\) | −0.886237 | −0.443119 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | −0.186115 | −0.0759812 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | 3.04599 | 1.07692 | ||||||||
\(9\) | −2.96890 | −0.989633 | ||||||||
\(10\) | 1.05535 | 0.333731 | ||||||||
\(11\) | 3.44108 | 1.03752 | 0.518762 | − | 0.854919i | \(-0.326393\pi\) | ||||
0.518762 | + | 0.854919i | \(0.326393\pi\) | |||||||
\(12\) | −0.156292 | −0.0451175 | ||||||||
\(13\) | 6.99973 | 1.94137 | 0.970687 | − | 0.240346i | \(-0.0772609\pi\) | ||||
0.970687 | + | 0.240346i | \(0.0772609\pi\) | |||||||
\(14\) | 1.05535 | 0.282054 | ||||||||
\(15\) | −0.176354 | −0.0455344 | ||||||||
\(16\) | −1.44211 | −0.360527 | ||||||||
\(17\) | −1.17778 | −0.285654 | −0.142827 | − | 0.989748i | \(-0.545619\pi\) | ||||
−0.142827 | + | 0.989748i | \(0.545619\pi\) | |||||||
\(18\) | 3.13323 | 0.738509 | ||||||||
\(19\) | 1.90054 | 0.436015 | 0.218007 | − | 0.975947i | \(-0.430044\pi\) | ||||
0.218007 | + | 0.975947i | \(0.430044\pi\) | |||||||
\(20\) | 0.886237 | 0.198169 | ||||||||
\(21\) | −0.176354 | −0.0384836 | ||||||||
\(22\) | −3.63154 | −0.774246 | ||||||||
\(23\) | 7.72001 | 1.60973 | 0.804866 | − | 0.593456i | \(-0.202237\pi\) | ||||
0.804866 | + | 0.593456i | \(0.202237\pi\) | |||||||
\(24\) | 0.537173 | 0.109650 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | −7.38716 | −1.44874 | ||||||||
\(27\) | −1.05264 | −0.202581 | ||||||||
\(28\) | 0.886237 | 0.167483 | ||||||||
\(29\) | 9.32486 | 1.73158 | 0.865791 | − | 0.500405i | \(-0.166816\pi\) | ||||
0.865791 | + | 0.500405i | \(0.166816\pi\) | |||||||
\(30\) | 0.186115 | 0.0339798 | ||||||||
\(31\) | −5.28696 | −0.949567 | −0.474783 | − | 0.880103i | \(-0.657474\pi\) | ||||
−0.474783 | + | 0.880103i | \(0.657474\pi\) | |||||||
\(32\) | −4.57005 | −0.807878 | ||||||||
\(33\) | 0.606848 | 0.105639 | ||||||||
\(34\) | 1.24297 | 0.213167 | ||||||||
\(35\) | 1.00000 | 0.169031 | ||||||||
\(36\) | 2.63115 | 0.438525 | ||||||||
\(37\) | −8.69853 | −1.43003 | −0.715015 | − | 0.699109i | \(-0.753580\pi\) | ||||
−0.715015 | + | 0.699109i | \(0.753580\pi\) | |||||||
\(38\) | −2.00574 | −0.325374 | ||||||||
\(39\) | 1.23443 | 0.197667 | ||||||||
\(40\) | −3.04599 | −0.481613 | ||||||||
\(41\) | 7.81091 | 1.21986 | 0.609930 | − | 0.792456i | \(-0.291198\pi\) | ||||
0.609930 | + | 0.792456i | \(0.291198\pi\) | |||||||
\(42\) | 0.186115 | 0.0287182 | ||||||||
\(43\) | 2.29810 | 0.350458 | 0.175229 | − | 0.984528i | \(-0.443933\pi\) | ||||
0.175229 | + | 0.984528i | \(0.443933\pi\) | |||||||
\(44\) | −3.04961 | −0.459746 | ||||||||
\(45\) | 2.96890 | 0.442577 | ||||||||
\(46\) | −8.14731 | −1.20125 | ||||||||
\(47\) | 8.63688 | 1.25982 | 0.629909 | − | 0.776669i | \(-0.283092\pi\) | ||||
0.629909 | + | 0.776669i | \(0.283092\pi\) | |||||||
\(48\) | −0.254322 | −0.0367082 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | −1.05535 | −0.149249 | ||||||||
\(51\) | −0.207706 | −0.0290847 | ||||||||
\(52\) | −6.20342 | −0.860259 | ||||||||
\(53\) | 5.56374 | 0.764238 | 0.382119 | − | 0.924113i | \(-0.375194\pi\) | ||||
0.382119 | + | 0.924113i | \(0.375194\pi\) | |||||||
\(54\) | 1.11090 | 0.151175 | ||||||||
\(55\) | −3.44108 | −0.463995 | ||||||||
\(56\) | −3.04599 | −0.407037 | ||||||||
\(57\) | 0.335169 | 0.0443942 | ||||||||
\(58\) | −9.84099 | −1.29218 | ||||||||
\(59\) | 1.85923 | 0.242051 | 0.121026 | − | 0.992649i | \(-0.461382\pi\) | ||||
0.121026 | + | 0.992649i | \(0.461382\pi\) | |||||||
\(60\) | 0.156292 | 0.0201772 | ||||||||
\(61\) | 0.0439074 | 0.00562177 | 0.00281088 | − | 0.999996i | \(-0.499105\pi\) | ||||
0.00281088 | + | 0.999996i | \(0.499105\pi\) | |||||||
\(62\) | 5.57960 | 0.708609 | ||||||||
\(63\) | 2.96890 | 0.374046 | ||||||||
\(64\) | 7.70722 | 0.963402 | ||||||||
\(65\) | −6.99973 | −0.868209 | ||||||||
\(66\) | −0.640437 | −0.0788323 | ||||||||
\(67\) | −2.23381 | −0.272903 | −0.136452 | − | 0.990647i | \(-0.543570\pi\) | ||||
−0.136452 | + | 0.990647i | \(0.543570\pi\) | |||||||
\(68\) | 1.04379 | 0.126578 | ||||||||
\(69\) | 1.36145 | 0.163900 | ||||||||
\(70\) | −1.05535 | −0.126138 | ||||||||
\(71\) | 15.3936 | 1.82688 | 0.913440 | − | 0.406972i | \(-0.133415\pi\) | ||||
0.913440 | + | 0.406972i | \(0.133415\pi\) | |||||||
\(72\) | −9.04324 | −1.06576 | ||||||||
\(73\) | 8.20243 | 0.960022 | 0.480011 | − | 0.877262i | \(-0.340633\pi\) | ||||
0.480011 | + | 0.877262i | \(0.340633\pi\) | |||||||
\(74\) | 9.17999 | 1.06715 | ||||||||
\(75\) | 0.176354 | 0.0203636 | ||||||||
\(76\) | −1.68433 | −0.193206 | ||||||||
\(77\) | −3.44108 | −0.392147 | ||||||||
\(78\) | −1.30276 | −0.147508 | ||||||||
\(79\) | −4.53514 | −0.510243 | −0.255121 | − | 0.966909i | \(-0.582115\pi\) | ||||
−0.255121 | + | 0.966909i | \(0.582115\pi\) | |||||||
\(80\) | 1.44211 | 0.161233 | ||||||||
\(81\) | 8.72106 | 0.969007 | ||||||||
\(82\) | −8.24324 | −0.910314 | ||||||||
\(83\) | −7.32652 | −0.804190 | −0.402095 | − | 0.915598i | \(-0.631718\pi\) | ||||
−0.402095 | + | 0.915598i | \(0.631718\pi\) | |||||||
\(84\) | 0.156292 | 0.0170528 | ||||||||
\(85\) | 1.17778 | 0.127748 | ||||||||
\(86\) | −2.42530 | −0.261527 | ||||||||
\(87\) | 1.64448 | 0.176306 | ||||||||
\(88\) | 10.4815 | 1.11733 | ||||||||
\(89\) | −14.6526 | −1.55317 | −0.776587 | − | 0.630010i | \(-0.783051\pi\) | ||||
−0.776587 | + | 0.630010i | \(0.783051\pi\) | |||||||
\(90\) | −3.13323 | −0.330271 | ||||||||
\(91\) | −6.99973 | −0.733771 | ||||||||
\(92\) | −6.84176 | −0.713303 | ||||||||
\(93\) | −0.932378 | −0.0966831 | ||||||||
\(94\) | −9.11492 | −0.940133 | ||||||||
\(95\) | −1.90054 | −0.194992 | ||||||||
\(96\) | −0.805947 | −0.0822566 | ||||||||
\(97\) | −8.10190 | −0.822624 | −0.411312 | − | 0.911495i | \(-0.634929\pi\) | ||||
−0.411312 | + | 0.911495i | \(0.634929\pi\) | |||||||
\(98\) | −1.05535 | −0.106606 | ||||||||
\(99\) | −10.2162 | −1.02677 | ||||||||
\(100\) | −0.886237 | −0.0886237 | ||||||||
\(101\) | 6.83585 | 0.680193 | 0.340096 | − | 0.940391i | \(-0.389540\pi\) | ||||
0.340096 | + | 0.940391i | \(0.389540\pi\) | |||||||
\(102\) | 0.219203 | 0.0217043 | ||||||||
\(103\) | 12.1047 | 1.19271 | 0.596354 | − | 0.802722i | \(-0.296616\pi\) | ||||
0.596354 | + | 0.802722i | \(0.296616\pi\) | |||||||
\(104\) | 21.3211 | 2.09070 | ||||||||
\(105\) | 0.176354 | 0.0172104 | ||||||||
\(106\) | −5.87169 | −0.570309 | ||||||||
\(107\) | −3.99447 | −0.386160 | −0.193080 | − | 0.981183i | \(-0.561848\pi\) | ||||
−0.193080 | + | 0.981183i | \(0.561848\pi\) | |||||||
\(108\) | 0.932888 | 0.0897672 | ||||||||
\(109\) | −8.18543 | −0.784022 | −0.392011 | − | 0.919960i | \(-0.628221\pi\) | ||||
−0.392011 | + | 0.919960i | \(0.628221\pi\) | |||||||
\(110\) | 3.63154 | 0.346254 | ||||||||
\(111\) | −1.53402 | −0.145603 | ||||||||
\(112\) | 1.44211 | 0.136267 | ||||||||
\(113\) | −16.8701 | −1.58701 | −0.793504 | − | 0.608566i | \(-0.791745\pi\) | ||||
−0.793504 | + | 0.608566i | \(0.791745\pi\) | |||||||
\(114\) | −0.353720 | −0.0331289 | ||||||||
\(115\) | −7.72001 | −0.719894 | ||||||||
\(116\) | −8.26404 | −0.767296 | ||||||||
\(117\) | −20.7815 | −1.92125 | ||||||||
\(118\) | −1.96214 | −0.180629 | ||||||||
\(119\) | 1.17778 | 0.107967 | ||||||||
\(120\) | −0.537173 | −0.0490369 | ||||||||
\(121\) | 0.841001 | 0.0764546 | ||||||||
\(122\) | −0.0463377 | −0.00419522 | ||||||||
\(123\) | 1.37749 | 0.124204 | ||||||||
\(124\) | 4.68550 | 0.420771 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | −3.13323 | −0.279130 | ||||||||
\(127\) | −14.1236 | −1.25327 | −0.626634 | − | 0.779313i | \(-0.715568\pi\) | ||||
−0.626634 | + | 0.779313i | \(0.715568\pi\) | |||||||
\(128\) | 1.00629 | 0.0889441 | ||||||||
\(129\) | 0.405280 | 0.0356829 | ||||||||
\(130\) | 7.38716 | 0.647897 | ||||||||
\(131\) | −12.0149 | −1.04975 | −0.524874 | − | 0.851180i | \(-0.675887\pi\) | ||||
−0.524874 | + | 0.851180i | \(0.675887\pi\) | |||||||
\(132\) | −0.537811 | −0.0468104 | ||||||||
\(133\) | −1.90054 | −0.164798 | ||||||||
\(134\) | 2.35745 | 0.203653 | ||||||||
\(135\) | 1.05264 | 0.0905968 | ||||||||
\(136\) | −3.58750 | −0.307626 | ||||||||
\(137\) | 8.09677 | 0.691754 | 0.345877 | − | 0.938280i | \(-0.387581\pi\) | ||||
0.345877 | + | 0.938280i | \(0.387581\pi\) | |||||||
\(138\) | −1.43681 | −0.122309 | ||||||||
\(139\) | 4.28815 | 0.363716 | 0.181858 | − | 0.983325i | \(-0.441789\pi\) | ||||
0.181858 | + | 0.983325i | \(0.441789\pi\) | |||||||
\(140\) | −0.886237 | −0.0749007 | ||||||||
\(141\) | 1.52315 | 0.128272 | ||||||||
\(142\) | −16.2456 | −1.36330 | ||||||||
\(143\) | 24.0866 | 2.01422 | ||||||||
\(144\) | 4.28148 | 0.356790 | ||||||||
\(145\) | −9.32486 | −0.774387 | ||||||||
\(146\) | −8.65643 | −0.716412 | ||||||||
\(147\) | 0.176354 | 0.0145454 | ||||||||
\(148\) | 7.70896 | 0.633673 | ||||||||
\(149\) | 6.63875 | 0.543867 | 0.271934 | − | 0.962316i | \(-0.412337\pi\) | ||||
0.271934 | + | 0.962316i | \(0.412337\pi\) | |||||||
\(150\) | −0.186115 | −0.0151962 | ||||||||
\(151\) | −0.535768 | −0.0436002 | −0.0218001 | − | 0.999762i | \(-0.506940\pi\) | ||||
−0.0218001 | + | 0.999762i | \(0.506940\pi\) | |||||||
\(152\) | 5.78903 | 0.469553 | ||||||||
\(153\) | 3.49671 | 0.282692 | ||||||||
\(154\) | 3.63154 | 0.292638 | ||||||||
\(155\) | 5.28696 | 0.424659 | ||||||||
\(156\) | −1.09400 | −0.0875899 | ||||||||
\(157\) | 8.74303 | 0.697769 | 0.348885 | − | 0.937166i | \(-0.386560\pi\) | ||||
0.348885 | + | 0.937166i | \(0.386560\pi\) | |||||||
\(158\) | 4.78615 | 0.380766 | ||||||||
\(159\) | 0.981188 | 0.0778132 | ||||||||
\(160\) | 4.57005 | 0.361294 | ||||||||
\(161\) | −7.72001 | −0.608422 | ||||||||
\(162\) | −9.20377 | −0.723116 | ||||||||
\(163\) | −17.0760 | −1.33749 | −0.668747 | − | 0.743490i | \(-0.733169\pi\) | ||||
−0.668747 | + | 0.743490i | \(0.733169\pi\) | |||||||
\(164\) | −6.92232 | −0.540542 | ||||||||
\(165\) | −0.606848 | −0.0472430 | ||||||||
\(166\) | 7.73204 | 0.600122 | ||||||||
\(167\) | 6.63610 | 0.513517 | 0.256758 | − | 0.966476i | \(-0.417346\pi\) | ||||
0.256758 | + | 0.966476i | \(0.417346\pi\) | |||||||
\(168\) | −0.537173 | −0.0414438 | ||||||||
\(169\) | 35.9962 | 2.76894 | ||||||||
\(170\) | −1.24297 | −0.0953314 | ||||||||
\(171\) | −5.64252 | −0.431494 | ||||||||
\(172\) | −2.03667 | −0.155294 | ||||||||
\(173\) | −10.7189 | −0.814939 | −0.407470 | − | 0.913219i | \(-0.633589\pi\) | ||||
−0.407470 | + | 0.913219i | \(0.633589\pi\) | |||||||
\(174\) | −1.73550 | −0.131568 | ||||||||
\(175\) | −1.00000 | −0.0755929 | ||||||||
\(176\) | −4.96241 | −0.374056 | ||||||||
\(177\) | 0.327883 | 0.0246452 | ||||||||
\(178\) | 15.4636 | 1.15905 | ||||||||
\(179\) | −18.7926 | −1.40462 | −0.702312 | − | 0.711870i | \(-0.747849\pi\) | ||||
−0.702312 | + | 0.711870i | \(0.747849\pi\) | |||||||
\(180\) | −2.63115 | −0.196114 | ||||||||
\(181\) | 0.679653 | 0.0505182 | 0.0252591 | − | 0.999681i | \(-0.491959\pi\) | ||||
0.0252591 | + | 0.999681i | \(0.491959\pi\) | |||||||
\(182\) | 7.38716 | 0.547573 | ||||||||
\(183\) | 0.00774325 | 0.000572398 0 | ||||||||
\(184\) | 23.5151 | 1.73355 | ||||||||
\(185\) | 8.69853 | 0.639529 | ||||||||
\(186\) | 0.983985 | 0.0721492 | ||||||||
\(187\) | −4.05283 | −0.296372 | ||||||||
\(188\) | −7.65432 | −0.558249 | ||||||||
\(189\) | 1.05264 | 0.0765683 | ||||||||
\(190\) | 2.00574 | 0.145512 | ||||||||
\(191\) | 9.78238 | 0.707828 | 0.353914 | − | 0.935278i | \(-0.384850\pi\) | ||||
0.353914 | + | 0.935278i | \(0.384850\pi\) | |||||||
\(192\) | 1.35920 | 0.0980918 | ||||||||
\(193\) | −11.3460 | −0.816706 | −0.408353 | − | 0.912824i | \(-0.633897\pi\) | ||||
−0.408353 | + | 0.912824i | \(0.633897\pi\) | |||||||
\(194\) | 8.55034 | 0.613879 | ||||||||
\(195\) | −1.23443 | −0.0883994 | ||||||||
\(196\) | −0.886237 | −0.0633027 | ||||||||
\(197\) | −13.0279 | −0.928201 | −0.464100 | − | 0.885783i | \(-0.653622\pi\) | ||||
−0.464100 | + | 0.885783i | \(0.653622\pi\) | |||||||
\(198\) | 10.7817 | 0.766220 | ||||||||
\(199\) | 6.11713 | 0.433632 | 0.216816 | − | 0.976212i | \(-0.430433\pi\) | ||||
0.216816 | + | 0.976212i | \(0.430433\pi\) | |||||||
\(200\) | 3.04599 | 0.215384 | ||||||||
\(201\) | −0.393942 | −0.0277865 | ||||||||
\(202\) | −7.21422 | −0.507590 | ||||||||
\(203\) | −9.32486 | −0.654477 | ||||||||
\(204\) | 0.184077 | 0.0128880 | ||||||||
\(205\) | −7.81091 | −0.545538 | ||||||||
\(206\) | −12.7747 | −0.890052 | ||||||||
\(207\) | −22.9199 | −1.59304 | ||||||||
\(208\) | −10.0944 | −0.699919 | ||||||||
\(209\) | 6.53991 | 0.452375 | ||||||||
\(210\) | −0.186115 | −0.0128432 | ||||||||
\(211\) | 5.38574 | 0.370770 | 0.185385 | − | 0.982666i | \(-0.440647\pi\) | ||||
0.185385 | + | 0.982666i | \(0.440647\pi\) | |||||||
\(212\) | −4.93079 | −0.338648 | ||||||||
\(213\) | 2.71472 | 0.186010 | ||||||||
\(214\) | 4.21556 | 0.288170 | ||||||||
\(215\) | −2.29810 | −0.156729 | ||||||||
\(216\) | −3.20633 | −0.218163 | ||||||||
\(217\) | 5.28696 | 0.358903 | ||||||||
\(218\) | 8.63849 | 0.585073 | ||||||||
\(219\) | 1.44653 | 0.0977476 | ||||||||
\(220\) | 3.04961 | 0.205605 | ||||||||
\(221\) | −8.24413 | −0.554560 | ||||||||
\(222\) | 1.61893 | 0.108655 | ||||||||
\(223\) | 2.53650 | 0.169857 | 0.0849284 | − | 0.996387i | \(-0.472934\pi\) | ||||
0.0849284 | + | 0.996387i | \(0.472934\pi\) | |||||||
\(224\) | 4.57005 | 0.305349 | ||||||||
\(225\) | −2.96890 | −0.197927 | ||||||||
\(226\) | 17.8039 | 1.18430 | ||||||||
\(227\) | −14.8731 | −0.987164 | −0.493582 | − | 0.869699i | \(-0.664313\pi\) | ||||
−0.493582 | + | 0.869699i | \(0.664313\pi\) | |||||||
\(228\) | −0.297039 | −0.0196719 | ||||||||
\(229\) | 1.00000 | 0.0660819 | ||||||||
\(230\) | 8.14731 | 0.537218 | ||||||||
\(231\) | −0.606848 | −0.0399277 | ||||||||
\(232\) | 28.4034 | 1.86478 | ||||||||
\(233\) | −6.46901 | −0.423799 | −0.211899 | − | 0.977292i | \(-0.567965\pi\) | ||||
−0.211899 | + | 0.977292i | \(0.567965\pi\) | |||||||
\(234\) | 21.9317 | 1.43372 | ||||||||
\(235\) | −8.63688 | −0.563408 | ||||||||
\(236\) | −1.64772 | −0.107257 | ||||||||
\(237\) | −0.799790 | −0.0519519 | ||||||||
\(238\) | −1.24297 | −0.0805697 | ||||||||
\(239\) | 10.3407 | 0.668882 | 0.334441 | − | 0.942417i | \(-0.391452\pi\) | ||||
0.334441 | + | 0.942417i | \(0.391452\pi\) | |||||||
\(240\) | 0.254322 | 0.0164164 | ||||||||
\(241\) | −11.1851 | −0.720497 | −0.360249 | − | 0.932856i | \(-0.617308\pi\) | ||||
−0.360249 | + | 0.932856i | \(0.617308\pi\) | |||||||
\(242\) | −0.887550 | −0.0570539 | ||||||||
\(243\) | 4.69591 | 0.301243 | ||||||||
\(244\) | −0.0389124 | −0.00249111 | ||||||||
\(245\) | −1.00000 | −0.0638877 | ||||||||
\(246\) | −1.45373 | −0.0926864 | ||||||||
\(247\) | 13.3033 | 0.846468 | ||||||||
\(248\) | −16.1040 | −1.02261 | ||||||||
\(249\) | −1.29206 | −0.0818810 | ||||||||
\(250\) | 1.05535 | 0.0667462 | ||||||||
\(251\) | 14.7123 | 0.928633 | 0.464316 | − | 0.885669i | \(-0.346300\pi\) | ||||
0.464316 | + | 0.885669i | \(0.346300\pi\) | |||||||
\(252\) | −2.63115 | −0.165747 | ||||||||
\(253\) | 26.5651 | 1.67014 | ||||||||
\(254\) | 14.9054 | 0.935245 | ||||||||
\(255\) | 0.207706 | 0.0130071 | ||||||||
\(256\) | −16.4764 | −1.02978 | ||||||||
\(257\) | 31.0456 | 1.93657 | 0.968286 | − | 0.249845i | \(-0.0803796\pi\) | ||||
0.968286 | + | 0.249845i | \(0.0803796\pi\) | |||||||
\(258\) | −0.427712 | −0.0266282 | ||||||||
\(259\) | 8.69853 | 0.540501 | ||||||||
\(260\) | 6.20342 | 0.384720 | ||||||||
\(261\) | −27.6846 | −1.71363 | ||||||||
\(262\) | 12.6799 | 0.783369 | ||||||||
\(263\) | 13.4504 | 0.829384 | 0.414692 | − | 0.909962i | \(-0.363889\pi\) | ||||
0.414692 | + | 0.909962i | \(0.363889\pi\) | |||||||
\(264\) | 1.84845 | 0.113764 | ||||||||
\(265\) | −5.56374 | −0.341778 | ||||||||
\(266\) | 2.00574 | 0.122980 | ||||||||
\(267\) | −2.58405 | −0.158141 | ||||||||
\(268\) | 1.97969 | 0.120929 | ||||||||
\(269\) | −2.69957 | −0.164596 | −0.0822980 | − | 0.996608i | \(-0.526226\pi\) | ||||
−0.0822980 | + | 0.996608i | \(0.526226\pi\) | |||||||
\(270\) | −1.11090 | −0.0676074 | ||||||||
\(271\) | 3.68602 | 0.223910 | 0.111955 | − | 0.993713i | \(-0.464289\pi\) | ||||
0.111955 | + | 0.993713i | \(0.464289\pi\) | |||||||
\(272\) | 1.69849 | 0.102986 | ||||||||
\(273\) | −1.23443 | −0.0747111 | ||||||||
\(274\) | −8.54493 | −0.516218 | ||||||||
\(275\) | 3.44108 | 0.207505 | ||||||||
\(276\) | −1.20657 | −0.0726271 | ||||||||
\(277\) | 25.9698 | 1.56037 | 0.780187 | − | 0.625547i | \(-0.215124\pi\) | ||||
0.780187 | + | 0.625547i | \(0.215124\pi\) | |||||||
\(278\) | −4.52550 | −0.271421 | ||||||||
\(279\) | 15.6965 | 0.939723 | ||||||||
\(280\) | 3.04599 | 0.182033 | ||||||||
\(281\) | 3.83290 | 0.228652 | 0.114326 | − | 0.993443i | \(-0.463529\pi\) | ||||
0.114326 | + | 0.993443i | \(0.463529\pi\) | |||||||
\(282\) | −1.60745 | −0.0957225 | ||||||||
\(283\) | −24.3622 | −1.44818 | −0.724092 | − | 0.689704i | \(-0.757741\pi\) | ||||
−0.724092 | + | 0.689704i | \(0.757741\pi\) | |||||||
\(284\) | −13.6424 | −0.809525 | ||||||||
\(285\) | −0.335169 | −0.0198537 | ||||||||
\(286\) | −25.4198 | −1.50310 | ||||||||
\(287\) | −7.81091 | −0.461064 | ||||||||
\(288\) | 13.5680 | 0.799503 | ||||||||
\(289\) | −15.6128 | −0.918402 | ||||||||
\(290\) | 9.84099 | 0.577883 | ||||||||
\(291\) | −1.42880 | −0.0837580 | ||||||||
\(292\) | −7.26930 | −0.425404 | ||||||||
\(293\) | −11.2255 | −0.655804 | −0.327902 | − | 0.944712i | \(-0.606342\pi\) | ||||
−0.327902 | + | 0.944712i | \(0.606342\pi\) | |||||||
\(294\) | −0.186115 | −0.0108545 | ||||||||
\(295\) | −1.85923 | −0.108249 | ||||||||
\(296\) | −26.4956 | −1.54003 | ||||||||
\(297\) | −3.62221 | −0.210182 | ||||||||
\(298\) | −7.00620 | −0.405858 | ||||||||
\(299\) | 54.0379 | 3.12509 | ||||||||
\(300\) | −0.156292 | −0.00902350 | ||||||||
\(301\) | −2.29810 | −0.132461 | ||||||||
\(302\) | 0.565423 | 0.0325364 | ||||||||
\(303\) | 1.20553 | 0.0692559 | ||||||||
\(304\) | −2.74079 | −0.157195 | ||||||||
\(305\) | −0.0439074 | −0.00251413 | ||||||||
\(306\) | −3.69025 | −0.210958 | ||||||||
\(307\) | 34.5744 | 1.97326 | 0.986631 | − | 0.162967i | \(-0.0521065\pi\) | ||||
0.986631 | + | 0.162967i | \(0.0521065\pi\) | |||||||
\(308\) | 3.04961 | 0.173768 | ||||||||
\(309\) | 2.13471 | 0.121439 | ||||||||
\(310\) | −5.57960 | −0.316900 | ||||||||
\(311\) | −18.8728 | −1.07018 | −0.535090 | − | 0.844795i | \(-0.679722\pi\) | ||||
−0.535090 | + | 0.844795i | \(0.679722\pi\) | |||||||
\(312\) | 3.76006 | 0.212872 | ||||||||
\(313\) | 22.2370 | 1.25691 | 0.628455 | − | 0.777846i | \(-0.283688\pi\) | ||||
0.628455 | + | 0.777846i | \(0.283688\pi\) | |||||||
\(314\) | −9.22695 | −0.520707 | ||||||||
\(315\) | −2.96890 | −0.167279 | ||||||||
\(316\) | 4.01921 | 0.226098 | ||||||||
\(317\) | 14.7211 | 0.826822 | 0.413411 | − | 0.910545i | \(-0.364337\pi\) | ||||
0.413411 | + | 0.910545i | \(0.364337\pi\) | |||||||
\(318\) | −1.03550 | −0.0580677 | ||||||||
\(319\) | 32.0875 | 1.79656 | ||||||||
\(320\) | −7.70722 | −0.430847 | ||||||||
\(321\) | −0.704441 | −0.0393181 | ||||||||
\(322\) | 8.14731 | 0.454032 | ||||||||
\(323\) | −2.23842 | −0.124549 | ||||||||
\(324\) | −7.72893 | −0.429385 | ||||||||
\(325\) | 6.99973 | 0.388275 | ||||||||
\(326\) | 18.0211 | 0.998098 | ||||||||
\(327\) | −1.44353 | −0.0798276 | ||||||||
\(328\) | 23.7920 | 1.31369 | ||||||||
\(329\) | −8.63688 | −0.476166 | ||||||||
\(330\) | 0.640437 | 0.0352549 | ||||||||
\(331\) | 29.4760 | 1.62015 | 0.810074 | − | 0.586327i | \(-0.199427\pi\) | ||||
0.810074 | + | 0.586327i | \(0.199427\pi\) | |||||||
\(332\) | 6.49303 | 0.356351 | ||||||||
\(333\) | 25.8251 | 1.41521 | ||||||||
\(334\) | −7.00340 | −0.383209 | ||||||||
\(335\) | 2.23381 | 0.122046 | ||||||||
\(336\) | 0.254322 | 0.0138744 | ||||||||
\(337\) | 20.5174 | 1.11765 | 0.558827 | − | 0.829284i | \(-0.311252\pi\) | ||||
0.558827 | + | 0.829284i | \(0.311252\pi\) | |||||||
\(338\) | −37.9885 | −2.06630 | ||||||||
\(339\) | −2.97511 | −0.161586 | ||||||||
\(340\) | −1.04379 | −0.0566076 | ||||||||
\(341\) | −18.1928 | −0.985198 | ||||||||
\(342\) | 5.95483 | 0.322001 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | 7.00000 | 0.377415 | ||||||||
\(345\) | −1.36145 | −0.0732983 | ||||||||
\(346\) | 11.3121 | 0.608144 | ||||||||
\(347\) | 15.9899 | 0.858384 | 0.429192 | − | 0.903213i | \(-0.358798\pi\) | ||||
0.429192 | + | 0.903213i | \(0.358798\pi\) | |||||||
\(348\) | −1.45740 | −0.0781246 | ||||||||
\(349\) | 15.5304 | 0.831326 | 0.415663 | − | 0.909519i | \(-0.363550\pi\) | ||||
0.415663 | + | 0.909519i | \(0.363550\pi\) | |||||||
\(350\) | 1.05535 | 0.0564108 | ||||||||
\(351\) | −7.36819 | −0.393285 | ||||||||
\(352\) | −15.7259 | −0.838192 | ||||||||
\(353\) | −16.1927 | −0.861852 | −0.430926 | − | 0.902387i | \(-0.641813\pi\) | ||||
−0.430926 | + | 0.902387i | \(0.641813\pi\) | |||||||
\(354\) | −0.346031 | −0.0183913 | ||||||||
\(355\) | −15.3936 | −0.817006 | ||||||||
\(356\) | 12.9857 | 0.688240 | ||||||||
\(357\) | 0.207706 | 0.0109930 | ||||||||
\(358\) | 19.8327 | 1.04819 | ||||||||
\(359\) | 29.1666 | 1.53935 | 0.769677 | − | 0.638434i | \(-0.220417\pi\) | ||||
0.769677 | + | 0.638434i | \(0.220417\pi\) | |||||||
\(360\) | 9.04324 | 0.476620 | ||||||||
\(361\) | −15.3879 | −0.809891 | ||||||||
\(362\) | −0.717271 | −0.0376989 | ||||||||
\(363\) | 0.148314 | 0.00778446 | ||||||||
\(364\) | 6.20342 | 0.325147 | ||||||||
\(365\) | −8.20243 | −0.429335 | ||||||||
\(366\) | −0.00817184 | −0.000427149 0 | ||||||||
\(367\) | −5.07904 | −0.265124 | −0.132562 | − | 0.991175i | \(-0.542320\pi\) | ||||
−0.132562 | + | 0.991175i | \(0.542320\pi\) | |||||||
\(368\) | −11.1331 | −0.580353 | ||||||||
\(369\) | −23.1898 | −1.20721 | ||||||||
\(370\) | −9.17999 | −0.477245 | ||||||||
\(371\) | −5.56374 | −0.288855 | ||||||||
\(372\) | 0.826308 | 0.0428421 | ||||||||
\(373\) | 21.3097 | 1.10338 | 0.551688 | − | 0.834050i | \(-0.313984\pi\) | ||||
0.551688 | + | 0.834050i | \(0.313984\pi\) | |||||||
\(374\) | 4.27715 | 0.221166 | ||||||||
\(375\) | −0.176354 | −0.00910689 | ||||||||
\(376\) | 26.3078 | 1.35672 | ||||||||
\(377\) | 65.2714 | 3.36165 | ||||||||
\(378\) | −1.11090 | −0.0571387 | ||||||||
\(379\) | −36.5100 | −1.87539 | −0.937697 | − | 0.347455i | \(-0.887046\pi\) | ||||
−0.937697 | + | 0.347455i | \(0.887046\pi\) | |||||||
\(380\) | 1.68433 | 0.0864044 | ||||||||
\(381\) | −2.49076 | −0.127605 | ||||||||
\(382\) | −10.3238 | −0.528213 | ||||||||
\(383\) | 4.21828 | 0.215544 | 0.107772 | − | 0.994176i | \(-0.465628\pi\) | ||||
0.107772 | + | 0.994176i | \(0.465628\pi\) | |||||||
\(384\) | 0.177463 | 0.00905612 | ||||||||
\(385\) | 3.44108 | 0.175373 | ||||||||
\(386\) | 11.9740 | 0.609462 | ||||||||
\(387\) | −6.82284 | −0.346824 | ||||||||
\(388\) | 7.18021 | 0.364520 | ||||||||
\(389\) | −2.43112 | −0.123263 | −0.0616313 | − | 0.998099i | \(-0.519630\pi\) | ||||
−0.0616313 | + | 0.998099i | \(0.519630\pi\) | |||||||
\(390\) | 1.30276 | 0.0659676 | ||||||||
\(391\) | −9.09247 | −0.459826 | ||||||||
\(392\) | 3.04599 | 0.153846 | ||||||||
\(393\) | −2.11888 | −0.106883 | ||||||||
\(394\) | 13.7490 | 0.692665 | ||||||||
\(395\) | 4.53514 | 0.228187 | ||||||||
\(396\) | 9.05398 | 0.454980 | ||||||||
\(397\) | 3.62747 | 0.182057 | 0.0910287 | − | 0.995848i | \(-0.470984\pi\) | ||||
0.0910287 | + | 0.995848i | \(0.470984\pi\) | |||||||
\(398\) | −6.45571 | −0.323596 | ||||||||
\(399\) | −0.335169 | −0.0167794 | ||||||||
\(400\) | −1.44211 | −0.0721055 | ||||||||
\(401\) | 17.3416 | 0.866000 | 0.433000 | − | 0.901394i | \(-0.357455\pi\) | ||||
0.433000 | + | 0.901394i | \(0.357455\pi\) | |||||||
\(402\) | 0.415746 | 0.0207355 | ||||||||
\(403\) | −37.0073 | −1.84346 | ||||||||
\(404\) | −6.05819 | −0.301406 | ||||||||
\(405\) | −8.72106 | −0.433353 | ||||||||
\(406\) | 9.84099 | 0.488400 | ||||||||
\(407\) | −29.9323 | −1.48369 | ||||||||
\(408\) | −0.632671 | −0.0313219 | ||||||||
\(409\) | 2.41659 | 0.119493 | 0.0597465 | − | 0.998214i | \(-0.480971\pi\) | ||||
0.0597465 | + | 0.998214i | \(0.480971\pi\) | |||||||
\(410\) | 8.24324 | 0.407105 | ||||||||
\(411\) | 1.42790 | 0.0704331 | ||||||||
\(412\) | −10.7276 | −0.528511 | ||||||||
\(413\) | −1.85923 | −0.0914868 | ||||||||
\(414\) | 24.1885 | 1.18880 | ||||||||
\(415\) | 7.32652 | 0.359644 | ||||||||
\(416\) | −31.9891 | −1.56839 | ||||||||
\(417\) | 0.756233 | 0.0370329 | ||||||||
\(418\) | −6.90190 | −0.337583 | ||||||||
\(419\) | 7.35049 | 0.359095 | 0.179548 | − | 0.983749i | \(-0.442537\pi\) | ||||
0.179548 | + | 0.983749i | \(0.442537\pi\) | |||||||
\(420\) | −0.156292 | −0.00762625 | ||||||||
\(421\) | 8.66867 | 0.422485 | 0.211243 | − | 0.977434i | \(-0.432249\pi\) | ||||
0.211243 | + | 0.977434i | \(0.432249\pi\) | |||||||
\(422\) | −5.68384 | −0.276685 | ||||||||
\(423\) | −25.6420 | −1.24676 | ||||||||
\(424\) | 16.9471 | 0.823023 | ||||||||
\(425\) | −1.17778 | −0.0571307 | ||||||||
\(426\) | −2.86498 | −0.138809 | ||||||||
\(427\) | −0.0439074 | −0.00212483 | ||||||||
\(428\) | 3.54005 | 0.171115 | ||||||||
\(429\) | 4.24777 | 0.205084 | ||||||||
\(430\) | 2.42530 | 0.116959 | ||||||||
\(431\) | 18.9096 | 0.910842 | 0.455421 | − | 0.890276i | \(-0.349489\pi\) | ||||
0.455421 | + | 0.890276i | \(0.349489\pi\) | |||||||
\(432\) | 1.51802 | 0.0730359 | ||||||||
\(433\) | 30.7692 | 1.47867 | 0.739337 | − | 0.673335i | \(-0.235139\pi\) | ||||
0.739337 | + | 0.673335i | \(0.235139\pi\) | |||||||
\(434\) | −5.57960 | −0.267829 | ||||||||
\(435\) | −1.64448 | −0.0788466 | ||||||||
\(436\) | 7.25423 | 0.347415 | ||||||||
\(437\) | 14.6722 | 0.701867 | ||||||||
\(438\) | −1.52660 | −0.0729437 | ||||||||
\(439\) | −25.3465 | −1.20972 | −0.604861 | − | 0.796331i | \(-0.706771\pi\) | ||||
−0.604861 | + | 0.796331i | \(0.706771\pi\) | |||||||
\(440\) | −10.4815 | −0.499685 | ||||||||
\(441\) | −2.96890 | −0.141376 | ||||||||
\(442\) | 8.70044 | 0.413838 | ||||||||
\(443\) | −16.2193 | −0.770604 | −0.385302 | − | 0.922790i | \(-0.625903\pi\) | ||||
−0.385302 | + | 0.922790i | \(0.625903\pi\) | |||||||
\(444\) | 1.35951 | 0.0645194 | ||||||||
\(445\) | 14.6526 | 0.694601 | ||||||||
\(446\) | −2.67690 | −0.126755 | ||||||||
\(447\) | 1.17077 | 0.0553755 | ||||||||
\(448\) | −7.70722 | −0.364132 | ||||||||
\(449\) | −33.2507 | −1.56920 | −0.784599 | − | 0.620003i | \(-0.787131\pi\) | ||||
−0.784599 | + | 0.620003i | \(0.787131\pi\) | |||||||
\(450\) | 3.13323 | 0.147702 | ||||||||
\(451\) | 26.8779 | 1.26563 | ||||||||
\(452\) | 14.9509 | 0.703232 | ||||||||
\(453\) | −0.0944849 | −0.00443929 | ||||||||
\(454\) | 15.6963 | 0.736666 | ||||||||
\(455\) | 6.99973 | 0.328152 | ||||||||
\(456\) | 1.02092 | 0.0478090 | ||||||||
\(457\) | −14.7416 | −0.689583 | −0.344792 | − | 0.938679i | \(-0.612050\pi\) | ||||
−0.344792 | + | 0.938679i | \(0.612050\pi\) | |||||||
\(458\) | −1.05535 | −0.0493132 | ||||||||
\(459\) | 1.23978 | 0.0578679 | ||||||||
\(460\) | 6.84176 | 0.318999 | ||||||||
\(461\) | 20.2338 | 0.942382 | 0.471191 | − | 0.882031i | \(-0.343824\pi\) | ||||
0.471191 | + | 0.882031i | \(0.343824\pi\) | |||||||
\(462\) | 0.640437 | 0.0297958 | ||||||||
\(463\) | 9.79492 | 0.455209 | 0.227604 | − | 0.973754i | \(-0.426911\pi\) | ||||
0.227604 | + | 0.973754i | \(0.426911\pi\) | |||||||
\(464\) | −13.4475 | −0.624283 | ||||||||
\(465\) | 0.932378 | 0.0432380 | ||||||||
\(466\) | 6.82706 | 0.316258 | ||||||||
\(467\) | −0.857035 | −0.0396589 | −0.0198294 | − | 0.999803i | \(-0.506312\pi\) | ||||
−0.0198294 | + | 0.999803i | \(0.506312\pi\) | |||||||
\(468\) | 18.4173 | 0.851341 | ||||||||
\(469\) | 2.23381 | 0.103148 | ||||||||
\(470\) | 9.11492 | 0.420440 | ||||||||
\(471\) | 1.54187 | 0.0710456 | ||||||||
\(472\) | 5.66320 | 0.260670 | ||||||||
\(473\) | 7.90795 | 0.363608 | ||||||||
\(474\) | 0.844058 | 0.0387689 | ||||||||
\(475\) | 1.90054 | 0.0872029 | ||||||||
\(476\) | −1.04379 | −0.0478421 | ||||||||
\(477\) | −16.5182 | −0.756315 | ||||||||
\(478\) | −10.9130 | −0.499150 | ||||||||
\(479\) | −27.9193 | −1.27567 | −0.637834 | − | 0.770174i | \(-0.720169\pi\) | ||||
−0.637834 | + | 0.770174i | \(0.720169\pi\) | |||||||
\(480\) | 0.805947 | 0.0367863 | ||||||||
\(481\) | −60.8873 | −2.77622 | ||||||||
\(482\) | 11.8042 | 0.537668 | ||||||||
\(483\) | −1.36145 | −0.0619483 | ||||||||
\(484\) | −0.745326 | −0.0338785 | ||||||||
\(485\) | 8.10190 | 0.367888 | ||||||||
\(486\) | −4.95583 | −0.224801 | ||||||||
\(487\) | 30.3011 | 1.37307 | 0.686537 | − | 0.727095i | \(-0.259130\pi\) | ||||
0.686537 | + | 0.727095i | \(0.259130\pi\) | |||||||
\(488\) | 0.133742 | 0.00605419 | ||||||||
\(489\) | −3.01142 | −0.136181 | ||||||||
\(490\) | 1.05535 | 0.0476758 | ||||||||
\(491\) | −8.69063 | −0.392203 | −0.196101 | − | 0.980584i | \(-0.562828\pi\) | ||||
−0.196101 | + | 0.980584i | \(0.562828\pi\) | |||||||
\(492\) | −1.22078 | −0.0550370 | ||||||||
\(493\) | −10.9826 | −0.494633 | ||||||||
\(494\) | −14.0396 | −0.631672 | ||||||||
\(495\) | 10.2162 | 0.459184 | ||||||||
\(496\) | 7.62438 | 0.342345 | ||||||||
\(497\) | −15.3936 | −0.690496 | ||||||||
\(498\) | 1.36358 | 0.0611033 | ||||||||
\(499\) | 11.1086 | 0.497290 | 0.248645 | − | 0.968595i | \(-0.420015\pi\) | ||||
0.248645 | + | 0.968595i | \(0.420015\pi\) | |||||||
\(500\) | 0.886237 | 0.0396337 | ||||||||
\(501\) | 1.17030 | 0.0522853 | ||||||||
\(502\) | −15.5266 | −0.692987 | ||||||||
\(503\) | 1.81849 | 0.0810823 | 0.0405412 | − | 0.999178i | \(-0.487092\pi\) | ||||
0.0405412 | + | 0.999178i | \(0.487092\pi\) | |||||||
\(504\) | 9.04324 | 0.402818 | ||||||||
\(505\) | −6.83585 | −0.304192 | ||||||||
\(506\) | −28.0355 | −1.24633 | ||||||||
\(507\) | 6.34807 | 0.281928 | ||||||||
\(508\) | 12.5169 | 0.555347 | ||||||||
\(509\) | 23.4429 | 1.03909 | 0.519544 | − | 0.854443i | \(-0.326102\pi\) | ||||
0.519544 | + | 0.854443i | \(0.326102\pi\) | |||||||
\(510\) | −0.219203 | −0.00970646 | ||||||||
\(511\) | −8.20243 | −0.362854 | ||||||||
\(512\) | 15.3758 | 0.679521 | ||||||||
\(513\) | −2.00059 | −0.0883281 | ||||||||
\(514\) | −32.7640 | −1.44516 | ||||||||
\(515\) | −12.1047 | −0.533395 | ||||||||
\(516\) | −0.359174 | −0.0158118 | ||||||||
\(517\) | 29.7201 | 1.30709 | ||||||||
\(518\) | −9.17999 | −0.403346 | ||||||||
\(519\) | −1.89031 | −0.0829756 | ||||||||
\(520\) | −21.3211 | −0.934992 | ||||||||
\(521\) | −25.8648 | −1.13316 | −0.566579 | − | 0.824007i | \(-0.691733\pi\) | ||||
−0.566579 | + | 0.824007i | \(0.691733\pi\) | |||||||
\(522\) | 29.2169 | 1.27879 | ||||||||
\(523\) | −1.38587 | −0.0605997 | −0.0302999 | − | 0.999541i | \(-0.509646\pi\) | ||||
−0.0302999 | + | 0.999541i | \(0.509646\pi\) | |||||||
\(524\) | 10.6481 | 0.465163 | ||||||||
\(525\) | −0.176354 | −0.00769672 | ||||||||
\(526\) | −14.1948 | −0.618924 | ||||||||
\(527\) | 6.22688 | 0.271247 | ||||||||
\(528\) | −0.875141 | −0.0380856 | ||||||||
\(529\) | 36.5985 | 1.59124 | ||||||||
\(530\) | 5.87169 | 0.255050 | ||||||||
\(531\) | −5.51987 | −0.239542 | ||||||||
\(532\) | 1.68433 | 0.0730251 | ||||||||
\(533\) | 54.6742 | 2.36820 | ||||||||
\(534\) | 2.72707 | 0.118012 | ||||||||
\(535\) | 3.99447 | 0.172696 | ||||||||
\(536\) | −6.80416 | −0.293895 | ||||||||
\(537\) | −3.31415 | −0.143016 | ||||||||
\(538\) | 2.84900 | 0.122829 | ||||||||
\(539\) | 3.44108 | 0.148218 | ||||||||
\(540\) | −0.932888 | −0.0401451 | ||||||||
\(541\) | 0.469849 | 0.0202004 | 0.0101002 | − | 0.999949i | \(-0.496785\pi\) | ||||
0.0101002 | + | 0.999949i | \(0.496785\pi\) | |||||||
\(542\) | −3.89004 | −0.167092 | ||||||||
\(543\) | 0.119860 | 0.00514367 | ||||||||
\(544\) | 5.38251 | 0.230773 | ||||||||
\(545\) | 8.18543 | 0.350625 | ||||||||
\(546\) | 1.30276 | 0.0557528 | ||||||||
\(547\) | 22.5965 | 0.966156 | 0.483078 | − | 0.875577i | \(-0.339519\pi\) | ||||
0.483078 | + | 0.875577i | \(0.339519\pi\) | |||||||
\(548\) | −7.17566 | −0.306529 | ||||||||
\(549\) | −0.130357 | −0.00556349 | ||||||||
\(550\) | −3.63154 | −0.154849 | ||||||||
\(551\) | 17.7223 | 0.754995 | ||||||||
\(552\) | 4.14698 | 0.176507 | ||||||||
\(553\) | 4.53514 | 0.192854 | ||||||||
\(554\) | −27.4072 | −1.16442 | ||||||||
\(555\) | 1.53402 | 0.0651156 | ||||||||
\(556\) | −3.80032 | −0.161169 | ||||||||
\(557\) | −11.2564 | −0.476949 | −0.238474 | − | 0.971149i | \(-0.576647\pi\) | ||||
−0.238474 | + | 0.971149i | \(0.576647\pi\) | |||||||
\(558\) | −16.5653 | −0.701263 | ||||||||
\(559\) | 16.0861 | 0.680369 | ||||||||
\(560\) | −1.44211 | −0.0609402 | ||||||||
\(561\) | −0.714733 | −0.0301760 | ||||||||
\(562\) | −4.04505 | −0.170630 | ||||||||
\(563\) | −16.8583 | −0.710493 | −0.355246 | − | 0.934773i | \(-0.615603\pi\) | ||||
−0.355246 | + | 0.934773i | \(0.615603\pi\) | |||||||
\(564\) | −1.34987 | −0.0568398 | ||||||||
\(565\) | 16.8701 | 0.709731 | ||||||||
\(566\) | 25.7107 | 1.08070 | ||||||||
\(567\) | −8.72106 | −0.366250 | ||||||||
\(568\) | 46.8887 | 1.96740 | ||||||||
\(569\) | −21.2557 | −0.891084 | −0.445542 | − | 0.895261i | \(-0.646989\pi\) | ||||
−0.445542 | + | 0.895261i | \(0.646989\pi\) | |||||||
\(570\) | 0.353720 | 0.0148157 | ||||||||
\(571\) | 32.7283 | 1.36964 | 0.684819 | − | 0.728713i | \(-0.259881\pi\) | ||||
0.684819 | + | 0.728713i | \(0.259881\pi\) | |||||||
\(572\) | −21.3464 | −0.892539 | ||||||||
\(573\) | 1.72516 | 0.0720697 | ||||||||
\(574\) | 8.24324 | 0.344066 | ||||||||
\(575\) | 7.72001 | 0.321947 | ||||||||
\(576\) | −22.8820 | −0.953415 | ||||||||
\(577\) | −4.36463 | −0.181702 | −0.0908510 | − | 0.995864i | \(-0.528959\pi\) | ||||
−0.0908510 | + | 0.995864i | \(0.528959\pi\) | |||||||
\(578\) | 16.4770 | 0.685353 | ||||||||
\(579\) | −2.00092 | −0.0831554 | ||||||||
\(580\) | 8.26404 | 0.343145 | ||||||||
\(581\) | 7.32652 | 0.303955 | ||||||||
\(582\) | 1.50789 | 0.0625039 | ||||||||
\(583\) | 19.1452 | 0.792915 | ||||||||
\(584\) | 24.9845 | 1.03387 | ||||||||
\(585\) | 20.7815 | 0.859208 | ||||||||
\(586\) | 11.8469 | 0.489390 | ||||||||
\(587\) | 25.0269 | 1.03297 | 0.516485 | − | 0.856296i | \(-0.327240\pi\) | ||||
0.516485 | + | 0.856296i | \(0.327240\pi\) | |||||||
\(588\) | −0.156292 | −0.00644535 | ||||||||
\(589\) | −10.0481 | −0.414025 | ||||||||
\(590\) | 1.96214 | 0.0807800 | ||||||||
\(591\) | −2.29753 | −0.0945076 | ||||||||
\(592\) | 12.5442 | 0.515565 | ||||||||
\(593\) | 21.3000 | 0.874685 | 0.437342 | − | 0.899295i | \(-0.355920\pi\) | ||||
0.437342 | + | 0.899295i | \(0.355920\pi\) | |||||||
\(594\) | 3.82270 | 0.156847 | ||||||||
\(595\) | −1.17778 | −0.0482843 | ||||||||
\(596\) | −5.88351 | −0.240998 | ||||||||
\(597\) | 1.07878 | 0.0441516 | ||||||||
\(598\) | −57.0289 | −2.33209 | ||||||||
\(599\) | 10.6826 | 0.436478 | 0.218239 | − | 0.975895i | \(-0.429969\pi\) | ||||
0.218239 | + | 0.975895i | \(0.429969\pi\) | |||||||
\(600\) | 0.537173 | 0.0219300 | ||||||||
\(601\) | −32.1515 | −1.31149 | −0.655744 | − | 0.754984i | \(-0.727645\pi\) | ||||
−0.655744 | + | 0.754984i | \(0.727645\pi\) | |||||||
\(602\) | 2.42530 | 0.0988480 | ||||||||
\(603\) | 6.63196 | 0.270074 | ||||||||
\(604\) | 0.474818 | 0.0193201 | ||||||||
\(605\) | −0.841001 | −0.0341915 | ||||||||
\(606\) | −1.27226 | −0.0516819 | ||||||||
\(607\) | −7.63372 | −0.309843 | −0.154922 | − | 0.987927i | \(-0.549512\pi\) | ||||
−0.154922 | + | 0.987927i | \(0.549512\pi\) | |||||||
\(608\) | −8.68558 | −0.352247 | ||||||||
\(609\) | −1.64448 | −0.0666376 | ||||||||
\(610\) | 0.0463377 | 0.00187616 | ||||||||
\(611\) | 60.4558 | 2.44578 | ||||||||
\(612\) | −3.09891 | −0.125266 | ||||||||
\(613\) | 41.3140 | 1.66866 | 0.834329 | − | 0.551267i | \(-0.185856\pi\) | ||||
0.834329 | + | 0.551267i | \(0.185856\pi\) | |||||||
\(614\) | −36.4880 | −1.47254 | ||||||||
\(615\) | −1.37749 | −0.0555456 | ||||||||
\(616\) | −10.4815 | −0.422311 | ||||||||
\(617\) | −37.6139 | −1.51428 | −0.757140 | − | 0.653252i | \(-0.773404\pi\) | ||||
−0.757140 | + | 0.653252i | \(0.773404\pi\) | |||||||
\(618\) | −2.25286 | −0.0906234 | ||||||||
\(619\) | 8.96197 | 0.360212 | 0.180106 | − | 0.983647i | \(-0.442356\pi\) | ||||
0.180106 | + | 0.983647i | \(0.442356\pi\) | |||||||
\(620\) | −4.68550 | −0.188174 | ||||||||
\(621\) | −8.12639 | −0.326101 | ||||||||
\(622\) | 19.9174 | 0.798617 | ||||||||
\(623\) | 14.6526 | 0.587045 | ||||||||
\(624\) | −1.78018 | −0.0712644 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | −23.4678 | −0.937962 | ||||||||
\(627\) | 1.15334 | 0.0460600 | ||||||||
\(628\) | −7.74839 | −0.309195 | ||||||||
\(629\) | 10.2450 | 0.408493 | ||||||||
\(630\) | 3.13323 | 0.124831 | ||||||||
\(631\) | −23.8093 | −0.947835 | −0.473917 | − | 0.880569i | \(-0.657160\pi\) | ||||
−0.473917 | + | 0.880569i | \(0.657160\pi\) | |||||||
\(632\) | −13.8140 | −0.549490 | ||||||||
\(633\) | 0.949797 | 0.0377510 | ||||||||
\(634\) | −15.5360 | −0.617011 | ||||||||
\(635\) | 14.1236 | 0.560479 | ||||||||
\(636\) | −0.869565 | −0.0344805 | ||||||||
\(637\) | 6.99973 | 0.277339 | ||||||||
\(638\) | −33.8636 | −1.34067 | ||||||||
\(639\) | −45.7020 | −1.80794 | ||||||||
\(640\) | −1.00629 | −0.0397770 | ||||||||
\(641\) | −39.3068 | −1.55252 | −0.776262 | − | 0.630411i | \(-0.782887\pi\) | ||||
−0.776262 | + | 0.630411i | \(0.782887\pi\) | |||||||
\(642\) | 0.743432 | 0.0293409 | ||||||||
\(643\) | −30.3638 | −1.19743 | −0.598715 | − | 0.800962i | \(-0.704322\pi\) | ||||
−0.598715 | + | 0.800962i | \(0.704322\pi\) | |||||||
\(644\) | 6.84176 | 0.269603 | ||||||||
\(645\) | −0.405280 | −0.0159579 | ||||||||
\(646\) | 2.36232 | 0.0929441 | ||||||||
\(647\) | 19.4049 | 0.762884 | 0.381442 | − | 0.924393i | \(-0.375428\pi\) | ||||
0.381442 | + | 0.924393i | \(0.375428\pi\) | |||||||
\(648\) | 26.5643 | 1.04354 | ||||||||
\(649\) | 6.39775 | 0.251134 | ||||||||
\(650\) | −7.38716 | −0.289748 | ||||||||
\(651\) | 0.932378 | 0.0365428 | ||||||||
\(652\) | 15.1334 | 0.592668 | ||||||||
\(653\) | −37.5277 | −1.46857 | −0.734285 | − | 0.678841i | \(-0.762483\pi\) | ||||
−0.734285 | + | 0.678841i | \(0.762483\pi\) | |||||||
\(654\) | 1.52343 | 0.0595710 | ||||||||
\(655\) | 12.0149 | 0.469461 | ||||||||
\(656\) | −11.2642 | −0.439793 | ||||||||
\(657\) | −24.3522 | −0.950070 | ||||||||
\(658\) | 9.11492 | 0.355337 | ||||||||
\(659\) | −7.91358 | −0.308269 | −0.154135 | − | 0.988050i | \(-0.549259\pi\) | ||||
−0.154135 | + | 0.988050i | \(0.549259\pi\) | |||||||
\(660\) | 0.537811 | 0.0209343 | ||||||||
\(661\) | −9.73139 | −0.378507 | −0.189254 | − | 0.981928i | \(-0.560607\pi\) | ||||
−0.189254 | + | 0.981928i | \(0.560607\pi\) | |||||||
\(662\) | −31.1075 | −1.20903 | ||||||||
\(663\) | −1.45389 | −0.0564643 | ||||||||
\(664\) | −22.3165 | −0.866048 | ||||||||
\(665\) | 1.90054 | 0.0736999 | ||||||||
\(666\) | −27.2545 | −1.05609 | ||||||||
\(667\) | 71.9880 | 2.78739 | ||||||||
\(668\) | −5.88116 | −0.227549 | ||||||||
\(669\) | 0.447323 | 0.0172945 | ||||||||
\(670\) | −2.35745 | −0.0910763 | ||||||||
\(671\) | 0.151089 | 0.00583272 | ||||||||
\(672\) | 0.805947 | 0.0310901 | ||||||||
\(673\) | 13.7602 | 0.530417 | 0.265208 | − | 0.964191i | \(-0.414559\pi\) | ||||
0.265208 | + | 0.964191i | \(0.414559\pi\) | |||||||
\(674\) | −21.6530 | −0.834044 | ||||||||
\(675\) | −1.05264 | −0.0405161 | ||||||||
\(676\) | −31.9011 | −1.22697 | ||||||||
\(677\) | −36.7348 | −1.41183 | −0.705917 | − | 0.708295i | \(-0.749465\pi\) | ||||
−0.705917 | + | 0.708295i | \(0.749465\pi\) | |||||||
\(678\) | 3.13979 | 0.120583 | ||||||||
\(679\) | 8.10190 | 0.310922 | ||||||||
\(680\) | 3.58750 | 0.137575 | ||||||||
\(681\) | −2.62294 | −0.100511 | ||||||||
\(682\) | 19.1998 | 0.735199 | ||||||||
\(683\) | 39.9800 | 1.52979 | 0.764895 | − | 0.644155i | \(-0.222791\pi\) | ||||
0.764895 | + | 0.644155i | \(0.222791\pi\) | |||||||
\(684\) | 5.00061 | 0.191203 | ||||||||
\(685\) | −8.09677 | −0.309362 | ||||||||
\(686\) | 1.05535 | 0.0402934 | ||||||||
\(687\) | 0.176354 | 0.00672833 | ||||||||
\(688\) | −3.31412 | −0.126350 | ||||||||
\(689\) | 38.9446 | 1.48367 | ||||||||
\(690\) | 1.43681 | 0.0546985 | ||||||||
\(691\) | −21.4525 | −0.816092 | −0.408046 | − | 0.912961i | \(-0.633790\pi\) | ||||
−0.408046 | + | 0.912961i | \(0.633790\pi\) | |||||||
\(692\) | 9.49945 | 0.361115 | ||||||||
\(693\) | 10.2162 | 0.388082 | ||||||||
\(694\) | −16.8750 | −0.640565 | ||||||||
\(695\) | −4.28815 | −0.162659 | ||||||||
\(696\) | 5.00906 | 0.189868 | ||||||||
\(697\) | −9.19953 | −0.348457 | ||||||||
\(698\) | −16.3900 | −0.620373 | ||||||||
\(699\) | −1.14084 | −0.0431504 | ||||||||
\(700\) | 0.886237 | 0.0334966 | ||||||||
\(701\) | 13.2233 | 0.499439 | 0.249720 | − | 0.968318i | \(-0.419662\pi\) | ||||
0.249720 | + | 0.968318i | \(0.419662\pi\) | |||||||
\(702\) | 7.77602 | 0.293487 | ||||||||
\(703\) | −16.5319 | −0.623514 | ||||||||
\(704\) | 26.5211 | 0.999552 | ||||||||
\(705\) | −1.52315 | −0.0573651 | ||||||||
\(706\) | 17.0890 | 0.643152 | ||||||||
\(707\) | −6.83585 | −0.257089 | ||||||||
\(708\) | −0.290582 | −0.0109207 | ||||||||
\(709\) | −22.7931 | −0.856014 | −0.428007 | − | 0.903775i | \(-0.640784\pi\) | ||||
−0.428007 | + | 0.903775i | \(0.640784\pi\) | |||||||
\(710\) | 16.2456 | 0.609687 | ||||||||
\(711\) | 13.4644 | 0.504953 | ||||||||
\(712\) | −44.6317 | −1.67264 | ||||||||
\(713\) | −40.8154 | −1.52855 | ||||||||
\(714\) | −0.219203 | −0.00820346 | ||||||||
\(715\) | −24.0866 | −0.900787 | ||||||||
\(716\) | 16.6547 | 0.622415 | ||||||||
\(717\) | 1.82362 | 0.0681043 | ||||||||
\(718\) | −30.7810 | −1.14873 | ||||||||
\(719\) | −23.9806 | −0.894325 | −0.447163 | − | 0.894453i | \(-0.647565\pi\) | ||||
−0.447163 | + | 0.894453i | \(0.647565\pi\) | |||||||
\(720\) | −4.28148 | −0.159561 | ||||||||
\(721\) | −12.1047 | −0.450801 | ||||||||
\(722\) | 16.2397 | 0.604377 | ||||||||
\(723\) | −1.97254 | −0.0733597 | ||||||||
\(724\) | −0.602334 | −0.0223856 | ||||||||
\(725\) | 9.32486 | 0.346317 | ||||||||
\(726\) | −0.156523 | −0.00580911 | ||||||||
\(727\) | −14.9127 | −0.553080 | −0.276540 | − | 0.961002i | \(-0.589188\pi\) | ||||
−0.276540 | + | 0.961002i | \(0.589188\pi\) | |||||||
\(728\) | −21.3211 | −0.790212 | ||||||||
\(729\) | −25.3350 | −0.938335 | ||||||||
\(730\) | 8.65643 | 0.320389 | ||||||||
\(731\) | −2.70666 | −0.100109 | ||||||||
\(732\) | −0.00686236 | −0.000253640 0 | ||||||||
\(733\) | 41.8848 | 1.54705 | 0.773526 | − | 0.633764i | \(-0.218491\pi\) | ||||
0.773526 | + | 0.633764i | \(0.218491\pi\) | |||||||
\(734\) | 5.36016 | 0.197847 | ||||||||
\(735\) | −0.176354 | −0.00650492 | ||||||||
\(736\) | −35.2808 | −1.30047 | ||||||||
\(737\) | −7.68671 | −0.283144 | ||||||||
\(738\) | 24.4734 | 0.900877 | ||||||||
\(739\) | 23.6216 | 0.868933 | 0.434467 | − | 0.900688i | \(-0.356937\pi\) | ||||
0.434467 | + | 0.900688i | \(0.356937\pi\) | |||||||
\(740\) | −7.70896 | −0.283387 | ||||||||
\(741\) | 2.34609 | 0.0861857 | ||||||||
\(742\) | 5.87169 | 0.215556 | ||||||||
\(743\) | 36.0578 | 1.32283 | 0.661416 | − | 0.750020i | \(-0.269956\pi\) | ||||
0.661416 | + | 0.750020i | \(0.269956\pi\) | |||||||
\(744\) | −2.84001 | −0.104120 | ||||||||
\(745\) | −6.63875 | −0.243225 | ||||||||
\(746\) | −22.4892 | −0.823389 | ||||||||
\(747\) | 21.7517 | 0.795853 | ||||||||
\(748\) | 3.59177 | 0.131328 | ||||||||
\(749\) | 3.99447 | 0.145955 | ||||||||
\(750\) | 0.186115 | 0.00679597 | ||||||||
\(751\) | −9.26373 | −0.338038 | −0.169019 | − | 0.985613i | \(-0.554060\pi\) | ||||
−0.169019 | + | 0.985613i | \(0.554060\pi\) | |||||||
\(752\) | −12.4553 | −0.454199 | ||||||||
\(753\) | 2.59458 | 0.0945516 | ||||||||
\(754\) | −68.8842 | −2.50861 | ||||||||
\(755\) | 0.535768 | 0.0194986 | ||||||||
\(756\) | −0.932888 | −0.0339288 | ||||||||
\(757\) | −33.0741 | −1.20210 | −0.601050 | − | 0.799212i | \(-0.705251\pi\) | ||||
−0.601050 | + | 0.799212i | \(0.705251\pi\) | |||||||
\(758\) | 38.5308 | 1.39950 | ||||||||
\(759\) | 4.68487 | 0.170050 | ||||||||
\(760\) | −5.78903 | −0.209990 | ||||||||
\(761\) | 10.4377 | 0.378368 | 0.189184 | − | 0.981942i | \(-0.439416\pi\) | ||||
0.189184 | + | 0.981942i | \(0.439416\pi\) | |||||||
\(762\) | 2.62862 | 0.0952249 | ||||||||
\(763\) | 8.18543 | 0.296333 | ||||||||
\(764\) | −8.66951 | −0.313652 | ||||||||
\(765\) | −3.49671 | −0.126424 | ||||||||
\(766\) | −4.45176 | −0.160849 | ||||||||
\(767\) | 13.0141 | 0.469912 | ||||||||
\(768\) | −2.90568 | −0.104850 | ||||||||
\(769\) | 6.24782 | 0.225302 | 0.112651 | − | 0.993635i | \(-0.464066\pi\) | ||||
0.112651 | + | 0.993635i | \(0.464066\pi\) | |||||||
\(770\) | −3.63154 | −0.130872 | ||||||||
\(771\) | 5.47502 | 0.197178 | ||||||||
\(772\) | 10.0553 | 0.361897 | ||||||||
\(773\) | 37.3719 | 1.34417 | 0.672087 | − | 0.740473i | \(-0.265398\pi\) | ||||
0.672087 | + | 0.740473i | \(0.265398\pi\) | |||||||
\(774\) | 7.20048 | 0.258816 | ||||||||
\(775\) | −5.28696 | −0.189913 | ||||||||
\(776\) | −24.6783 | −0.885900 | ||||||||
\(777\) | 1.53402 | 0.0550327 | ||||||||
\(778\) | 2.56568 | 0.0919841 | ||||||||
\(779\) | 14.8450 | 0.531876 | ||||||||
\(780\) | 1.09400 | 0.0391714 | ||||||||
\(781\) | 52.9704 | 1.89543 | ||||||||
\(782\) | 9.59573 | 0.343143 | ||||||||
\(783\) | −9.81572 | −0.350785 | ||||||||
\(784\) | −1.44211 | −0.0515039 | ||||||||
\(785\) | −8.74303 | −0.312052 | ||||||||
\(786\) | 2.23616 | 0.0797611 | ||||||||
\(787\) | 10.6026 | 0.377940 | 0.188970 | − | 0.981983i | \(-0.439485\pi\) | ||||
0.188970 | + | 0.981983i | \(0.439485\pi\) | |||||||
\(788\) | 11.5458 | 0.411303 | ||||||||
\(789\) | 2.37202 | 0.0844463 | ||||||||
\(790\) | −4.78615 | −0.170284 | ||||||||
\(791\) | 16.8701 | 0.599832 | ||||||||
\(792\) | −31.1185 | −1.10575 | ||||||||
\(793\) | 0.307340 | 0.0109140 | ||||||||
\(794\) | −3.82825 | −0.135859 | ||||||||
\(795\) | −0.981188 | −0.0347991 | ||||||||
\(796\) | −5.42123 | −0.192150 | ||||||||
\(797\) | 4.88587 | 0.173066 | 0.0865332 | − | 0.996249i | \(-0.472421\pi\) | ||||
0.0865332 | + | 0.996249i | \(0.472421\pi\) | |||||||
\(798\) | 0.353720 | 0.0125216 | ||||||||
\(799\) | −10.1723 | −0.359871 | ||||||||
\(800\) | −4.57005 | −0.161576 | ||||||||
\(801\) | 43.5021 | 1.53707 | ||||||||
\(802\) | −18.3015 | −0.646248 | ||||||||
\(803\) | 28.2252 | 0.996045 | ||||||||
\(804\) | 0.349126 | 0.0123127 | ||||||||
\(805\) | 7.72001 | 0.272095 | ||||||||
\(806\) | 39.0556 | 1.37568 | ||||||||
\(807\) | −0.476081 | −0.0167588 | ||||||||
\(808\) | 20.8219 | 0.732513 | ||||||||
\(809\) | 8.15712 | 0.286789 | 0.143395 | − | 0.989666i | \(-0.454198\pi\) | ||||
0.143395 | + | 0.989666i | \(0.454198\pi\) | |||||||
\(810\) | 9.20377 | 0.323387 | ||||||||
\(811\) | 20.0066 | 0.702527 | 0.351264 | − | 0.936277i | \(-0.385752\pi\) | ||||
0.351264 | + | 0.936277i | \(0.385752\pi\) | |||||||
\(812\) | 8.26404 | 0.290011 | ||||||||
\(813\) | 0.650045 | 0.0227981 | ||||||||
\(814\) | 31.5891 | 1.10720 | ||||||||
\(815\) | 17.0760 | 0.598145 | ||||||||
\(816\) | 0.299535 | 0.0104858 | ||||||||
\(817\) | 4.36765 | 0.152805 | ||||||||
\(818\) | −2.55035 | −0.0891710 | ||||||||
\(819\) | 20.7815 | 0.726164 | ||||||||
\(820\) | 6.92232 | 0.241738 | ||||||||
\(821\) | −21.3976 | −0.746783 | −0.373391 | − | 0.927674i | \(-0.621805\pi\) | ||||
−0.373391 | + | 0.927674i | \(0.621805\pi\) | |||||||
\(822\) | −1.50693 | −0.0525603 | ||||||||
\(823\) | −49.0475 | −1.70969 | −0.854844 | − | 0.518885i | \(-0.826347\pi\) | ||||
−0.854844 | + | 0.518885i | \(0.826347\pi\) | |||||||
\(824\) | 36.8707 | 1.28445 | ||||||||
\(825\) | 0.606848 | 0.0211277 | ||||||||
\(826\) | 1.96214 | 0.0682715 | ||||||||
\(827\) | 6.48400 | 0.225471 | 0.112735 | − | 0.993625i | \(-0.464039\pi\) | ||||
0.112735 | + | 0.993625i | \(0.464039\pi\) | |||||||
\(828\) | 20.3125 | 0.705908 | ||||||||
\(829\) | −5.09284 | −0.176882 | −0.0884408 | − | 0.996081i | \(-0.528188\pi\) | ||||
−0.0884408 | + | 0.996081i | \(0.528188\pi\) | |||||||
\(830\) | −7.73204 | −0.268383 | ||||||||
\(831\) | 4.57988 | 0.158874 | ||||||||
\(832\) | 53.9484 | 1.87032 | ||||||||
\(833\) | −1.17778 | −0.0408076 | ||||||||
\(834\) | −0.798090 | −0.0276356 | ||||||||
\(835\) | −6.63610 | −0.229652 | ||||||||
\(836\) | −5.79591 | −0.200456 | ||||||||
\(837\) | 5.56527 | 0.192364 | ||||||||
\(838\) | −7.75734 | −0.267973 | ||||||||
\(839\) | −0.820289 | −0.0283195 | −0.0141598 | − | 0.999900i | \(-0.504507\pi\) | ||||
−0.0141598 | + | 0.999900i | \(0.504507\pi\) | |||||||
\(840\) | 0.537173 | 0.0185342 | ||||||||
\(841\) | 57.9530 | 1.99838 | ||||||||
\(842\) | −9.14848 | −0.315277 | ||||||||
\(843\) | 0.675948 | 0.0232809 | ||||||||
\(844\) | −4.77304 | −0.164295 | ||||||||
\(845\) | −35.9962 | −1.23831 | ||||||||
\(846\) | 27.0613 | 0.930386 | ||||||||
\(847\) | −0.841001 | −0.0288971 | ||||||||
\(848\) | −8.02352 | −0.275529 | ||||||||
\(849\) | −4.29638 | −0.147451 | ||||||||
\(850\) | 1.24297 | 0.0426335 | ||||||||
\(851\) | −67.1527 | −2.30197 | ||||||||
\(852\) | −2.40589 | −0.0824243 | ||||||||
\(853\) | −40.9686 | −1.40274 | −0.701370 | − | 0.712798i | \(-0.747428\pi\) | ||||
−0.701370 | + | 0.712798i | \(0.747428\pi\) | |||||||
\(854\) | 0.0463377 | 0.00158564 | ||||||||
\(855\) | 5.64252 | 0.192970 | ||||||||
\(856\) | −12.1671 | −0.415863 | ||||||||
\(857\) | 54.4420 | 1.85970 | 0.929852 | − | 0.367935i | \(-0.119935\pi\) | ||||
0.929852 | + | 0.367935i | \(0.119935\pi\) | |||||||
\(858\) | −4.48288 | −0.153043 | ||||||||
\(859\) | −39.6992 | −1.35452 | −0.677260 | − | 0.735744i | \(-0.736833\pi\) | ||||
−0.677260 | + | 0.735744i | \(0.736833\pi\) | |||||||
\(860\) | 2.03667 | 0.0694497 | ||||||||
\(861\) | −1.37749 | −0.0469446 | ||||||||
\(862\) | −19.9562 | −0.679711 | ||||||||
\(863\) | 14.8822 | 0.506595 | 0.253298 | − | 0.967388i | \(-0.418485\pi\) | ||||
0.253298 | + | 0.967388i | \(0.418485\pi\) | |||||||
\(864\) | 4.81062 | 0.163660 | ||||||||
\(865\) | 10.7189 | 0.364452 | ||||||||
\(866\) | −32.4723 | −1.10345 | ||||||||
\(867\) | −2.75339 | −0.0935099 | ||||||||
\(868\) | −4.68550 | −0.159036 | ||||||||
\(869\) | −15.6057 | −0.529389 | ||||||||
\(870\) | 1.73550 | 0.0588389 | ||||||||
\(871\) | −15.6361 | −0.529808 | ||||||||
\(872\) | −24.9327 | −0.844329 | ||||||||
\(873\) | 24.0537 | 0.814095 | ||||||||
\(874\) | −15.4843 | −0.523765 | ||||||||
\(875\) | 1.00000 | 0.0338062 | ||||||||
\(876\) | −1.28197 | −0.0433138 | ||||||||
\(877\) | −37.4492 | −1.26457 | −0.632284 | − | 0.774736i | \(-0.717883\pi\) | ||||
−0.632284 | + | 0.774736i | \(0.717883\pi\) | |||||||
\(878\) | 26.7494 | 0.902748 | ||||||||
\(879\) | −1.97967 | −0.0667727 | ||||||||
\(880\) | 4.96241 | 0.167283 | ||||||||
\(881\) | 11.0613 | 0.372664 | 0.186332 | − | 0.982487i | \(-0.440340\pi\) | ||||
0.186332 | + | 0.982487i | \(0.440340\pi\) | |||||||
\(882\) | 3.13323 | 0.105501 | ||||||||
\(883\) | 4.25775 | 0.143285 | 0.0716423 | − | 0.997430i | \(-0.477176\pi\) | ||||
0.0716423 | + | 0.997430i | \(0.477176\pi\) | |||||||
\(884\) | 7.30626 | 0.245736 | ||||||||
\(885\) | −0.327883 | −0.0110217 | ||||||||
\(886\) | 17.1171 | 0.575060 | ||||||||
\(887\) | 8.24772 | 0.276931 | 0.138466 | − | 0.990367i | \(-0.455783\pi\) | ||||
0.138466 | + | 0.990367i | \(0.455783\pi\) | |||||||
\(888\) | −4.67261 | −0.156803 | ||||||||
\(889\) | 14.1236 | 0.473691 | ||||||||
\(890\) | −15.4636 | −0.518342 | ||||||||
\(891\) | 30.0098 | 1.00537 | ||||||||
\(892\) | −2.24794 | −0.0752667 | ||||||||
\(893\) | 16.4148 | 0.549299 | ||||||||
\(894\) | −1.23557 | −0.0413237 | ||||||||
\(895\) | 18.7926 | 0.628167 | ||||||||
\(896\) | −1.00629 | −0.0336177 | ||||||||
\(897\) | 9.52981 | 0.318191 | ||||||||
\(898\) | 35.0911 | 1.17101 | ||||||||
\(899\) | −49.3002 | −1.64425 | ||||||||
\(900\) | 2.63115 | 0.0877050 | ||||||||
\(901\) | −6.55286 | −0.218307 | ||||||||
\(902\) | −28.3656 | −0.944472 | ||||||||
\(903\) | −0.405280 | −0.0134869 | ||||||||
\(904\) | −51.3862 | −1.70908 | ||||||||
\(905\) | −0.679653 | −0.0225924 | ||||||||
\(906\) | 0.0997147 | 0.00331280 | ||||||||
\(907\) | 37.9050 | 1.25862 | 0.629308 | − | 0.777156i | \(-0.283338\pi\) | ||||
0.629308 | + | 0.777156i | \(0.283338\pi\) | |||||||
\(908\) | 13.1811 | 0.437431 | ||||||||
\(909\) | −20.2950 | −0.673141 | ||||||||
\(910\) | −7.38716 | −0.244882 | ||||||||
\(911\) | 0.389540 | 0.0129060 | 0.00645302 | − | 0.999979i | \(-0.497946\pi\) | ||||
0.00645302 | + | 0.999979i | \(0.497946\pi\) | |||||||
\(912\) | −0.483350 | −0.0160053 | ||||||||
\(913\) | −25.2111 | −0.834365 | ||||||||
\(914\) | 15.5576 | 0.514598 | ||||||||
\(915\) | −0.00774325 | −0.000255984 0 | ||||||||
\(916\) | −0.886237 | −0.0292821 | ||||||||
\(917\) | 12.0149 | 0.396767 | ||||||||
\(918\) | −1.30840 | −0.0431836 | ||||||||
\(919\) | −22.0521 | −0.727431 | −0.363715 | − | 0.931510i | \(-0.618492\pi\) | ||||
−0.363715 | + | 0.931510i | \(0.618492\pi\) | |||||||
\(920\) | −23.5151 | −0.775269 | ||||||||
\(921\) | 6.09733 | 0.200914 | ||||||||
\(922\) | −21.3537 | −0.703248 | ||||||||
\(923\) | 107.751 | 3.54666 | ||||||||
\(924\) | 0.537811 | 0.0176927 | ||||||||
\(925\) | −8.69853 | −0.286006 | ||||||||
\(926\) | −10.3371 | −0.339697 | ||||||||
\(927\) | −35.9375 | −1.18034 | ||||||||
\(928\) | −42.6151 | −1.39891 | ||||||||
\(929\) | 23.2441 | 0.762614 | 0.381307 | − | 0.924449i | \(-0.375474\pi\) | ||||
0.381307 | + | 0.924449i | \(0.375474\pi\) | |||||||
\(930\) | −0.983985 | −0.0322661 | ||||||||
\(931\) | 1.90054 | 0.0622878 | ||||||||
\(932\) | 5.73307 | 0.187793 | ||||||||
\(933\) | −3.32830 | −0.108964 | ||||||||
\(934\) | 0.904472 | 0.0295952 | ||||||||
\(935\) | 4.05283 | 0.132542 | ||||||||
\(936\) | −63.3002 | −2.06903 | ||||||||
\(937\) | 28.3995 | 0.927771 | 0.463885 | − | 0.885895i | \(-0.346455\pi\) | ||||
0.463885 | + | 0.885895i | \(0.346455\pi\) | |||||||
\(938\) | −2.35745 | −0.0769735 | ||||||||
\(939\) | 3.92159 | 0.127976 | ||||||||
\(940\) | 7.65432 | 0.249656 | ||||||||
\(941\) | −8.65126 | −0.282023 | −0.141012 | − | 0.990008i | \(-0.545035\pi\) | ||||
−0.141012 | + | 0.990008i | \(0.545035\pi\) | |||||||
\(942\) | −1.62721 | −0.0530174 | ||||||||
\(943\) | 60.3003 | 1.96365 | ||||||||
\(944\) | −2.68121 | −0.0872661 | ||||||||
\(945\) | −1.05264 | −0.0342424 | ||||||||
\(946\) | −8.34565 | −0.271341 | ||||||||
\(947\) | −57.0061 | −1.85245 | −0.926224 | − | 0.376974i | \(-0.876965\pi\) | ||||
−0.926224 | + | 0.376974i | \(0.876965\pi\) | |||||||
\(948\) | 0.708803 | 0.0230209 | ||||||||
\(949\) | 57.4148 | 1.86376 | ||||||||
\(950\) | −2.00574 | −0.0650747 | ||||||||
\(951\) | 2.59613 | 0.0841854 | ||||||||
\(952\) | 3.58750 | 0.116272 | ||||||||
\(953\) | −18.9213 | −0.612921 | −0.306461 | − | 0.951883i | \(-0.599145\pi\) | ||||
−0.306461 | + | 0.951883i | \(0.599145\pi\) | |||||||
\(954\) | 17.4324 | 0.564396 | ||||||||
\(955\) | −9.78238 | −0.316550 | ||||||||
\(956\) | −9.16428 | −0.296394 | ||||||||
\(957\) | 5.65877 | 0.182922 | ||||||||
\(958\) | 29.4647 | 0.951960 | ||||||||
\(959\) | −8.09677 | −0.261458 | ||||||||
\(960\) | −1.35920 | −0.0438680 | ||||||||
\(961\) | −3.04801 | −0.0983228 | ||||||||
\(962\) | 64.2574 | 2.07174 | ||||||||
\(963\) | 11.8592 | 0.382157 | ||||||||
\(964\) | 9.91268 | 0.319266 | ||||||||
\(965\) | 11.3460 | 0.365242 | ||||||||
\(966\) | 1.43681 | 0.0462286 | ||||||||
\(967\) | 6.72890 | 0.216387 | 0.108193 | − | 0.994130i | \(-0.465493\pi\) | ||||
0.108193 | + | 0.994130i | \(0.465493\pi\) | |||||||
\(968\) | 2.56168 | 0.0823355 | ||||||||
\(969\) | −0.394755 | −0.0126814 | ||||||||
\(970\) | −8.55034 | −0.274535 | ||||||||
\(971\) | 20.8492 | 0.669083 | 0.334541 | − | 0.942381i | \(-0.391419\pi\) | ||||
0.334541 | + | 0.942381i | \(0.391419\pi\) | |||||||
\(972\) | −4.16169 | −0.133486 | ||||||||
\(973\) | −4.28815 | −0.137472 | ||||||||
\(974\) | −31.9783 | −1.02465 | ||||||||
\(975\) | 1.23443 | 0.0395334 | ||||||||
\(976\) | −0.0633193 | −0.00202680 | ||||||||
\(977\) | −47.1315 | −1.50787 | −0.753935 | − | 0.656949i | \(-0.771847\pi\) | ||||
−0.753935 | + | 0.656949i | \(0.771847\pi\) | |||||||
\(978\) | 3.17810 | 0.101624 | ||||||||
\(979\) | −50.4208 | −1.61145 | ||||||||
\(980\) | 0.886237 | 0.0283098 | ||||||||
\(981\) | 24.3017 | 0.775894 | ||||||||
\(982\) | 9.17165 | 0.292679 | ||||||||
\(983\) | 42.2594 | 1.34787 | 0.673933 | − | 0.738793i | \(-0.264604\pi\) | ||||
0.673933 | + | 0.738793i | \(0.264604\pi\) | |||||||
\(984\) | 4.19581 | 0.133757 | ||||||||
\(985\) | 13.0279 | 0.415104 | ||||||||
\(986\) | 11.5905 | 0.369117 | ||||||||
\(987\) | −1.52315 | −0.0484823 | ||||||||
\(988\) | −11.7899 | −0.375086 | ||||||||
\(989\) | 17.7414 | 0.564143 | ||||||||
\(990\) | −10.7817 | −0.342664 | ||||||||
\(991\) | −39.1637 | −1.24408 | −0.622038 | − | 0.782987i | \(-0.713695\pi\) | ||||
−0.622038 | + | 0.782987i | \(0.713695\pi\) | |||||||
\(992\) | 24.1617 | 0.767134 | ||||||||
\(993\) | 5.19822 | 0.164960 | ||||||||
\(994\) | 16.2456 | 0.515279 | ||||||||
\(995\) | −6.11713 | −0.193926 | ||||||||
\(996\) | 1.14507 | 0.0362830 | ||||||||
\(997\) | 11.3276 | 0.358749 | 0.179375 | − | 0.983781i | \(-0.442593\pi\) | ||||
0.179375 | + | 0.983781i | \(0.442593\pi\) | |||||||
\(998\) | −11.7235 | −0.371100 | ||||||||
\(999\) | 9.15642 | 0.289696 |
(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 | 8015.2.a.l.1.21 | ✓ | 62 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8015.2.a.l.1.21 | ✓ | 62 | 1.1 | even | 1 | trivial |