Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4225,2,Mod(1,4225)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4225, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4225.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4225 = 5^{2} \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4225.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: | \(33.7367948540\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | 6.6.199374400.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - 8x^{4} + 10x^{2} - 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 65) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-1.18733\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4225.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.18733 | −0.839571 | −0.419786 | − | 0.907623i | \(-0.637895\pi\) | ||||
−0.419786 | + | 0.907623i | \(0.637895\pi\) | |||||||
\(3\) | 0.345110 | 0.199249 | 0.0996247 | − | 0.995025i | \(-0.468236\pi\) | ||||
0.0996247 | + | 0.995025i | \(0.468236\pi\) | |||||||
\(4\) | −0.590239 | −0.295120 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −0.409761 | −0.167284 | ||||||||
\(7\) | −2.02956 | −0.767100 | −0.383550 | − | 0.923520i | \(-0.625299\pi\) | ||||
−0.383550 | + | 0.923520i | \(0.625299\pi\) | |||||||
\(8\) | 3.07548 | 1.08735 | ||||||||
\(9\) | −2.88090 | −0.960300 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −3.88090 | −1.17014 | −0.585068 | − | 0.810985i | \(-0.698932\pi\) | ||||
−0.585068 | + | 0.810985i | \(0.698932\pi\) | |||||||
\(12\) | −0.203698 | −0.0588024 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | 2.40976 | 0.644036 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −2.47114 | −0.617785 | ||||||||
\(17\) | −5.45014 | −1.32185 | −0.660927 | − | 0.750450i | \(-0.729837\pi\) | ||||
−0.660927 | + | 0.750450i | \(0.729837\pi\) | |||||||
\(18\) | 3.42059 | 0.806240 | ||||||||
\(19\) | −5.88090 | −1.34917 | −0.674585 | − | 0.738197i | \(-0.735678\pi\) | ||||
−0.674585 | + | 0.738197i | \(0.735678\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −0.700420 | −0.152844 | ||||||||
\(22\) | 4.60792 | 0.982412 | ||||||||
\(23\) | −0.345110 | −0.0719604 | −0.0359802 | − | 0.999353i | \(-0.511455\pi\) | ||||
−0.0359802 | + | 0.999353i | \(0.511455\pi\) | |||||||
\(24\) | 1.06138 | 0.216653 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −2.02956 | −0.390588 | ||||||||
\(28\) | 1.19792 | 0.226386 | ||||||||
\(29\) | 3.00000 | 0.557086 | 0.278543 | − | 0.960424i | \(-0.410149\pi\) | ||||
0.278543 | + | 0.960424i | \(0.410149\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.18048 | −0.212020 | −0.106010 | − | 0.994365i | \(-0.533808\pi\) | ||||
−0.106010 | + | 0.994365i | \(0.533808\pi\) | |||||||
\(32\) | −3.21689 | −0.568671 | ||||||||
\(33\) | −1.33934 | −0.233149 | ||||||||
\(34\) | 6.47114 | 1.10979 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 1.70042 | 0.283403 | ||||||||
\(37\) | −5.45014 | −0.895998 | −0.447999 | − | 0.894034i | \(-0.647863\pi\) | ||||
−0.447999 | + | 0.894034i | \(0.647863\pi\) | |||||||
\(38\) | 6.98259 | 1.13273 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −0.180479 | −0.0281861 | −0.0140930 | − | 0.999901i | \(-0.504486\pi\) | ||||
−0.0140930 | + | 0.999901i | \(0.504486\pi\) | |||||||
\(42\) | 0.831632 | 0.128324 | ||||||||
\(43\) | −1.33934 | −0.204247 | −0.102123 | − | 0.994772i | \(-0.532564\pi\) | ||||
−0.102123 | + | 0.994772i | \(0.532564\pi\) | |||||||
\(44\) | 2.29066 | 0.345330 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0.409761 | 0.0604159 | ||||||||
\(47\) | −12.2807 | −1.79133 | −0.895664 | − | 0.444731i | \(-0.853299\pi\) | ||||
−0.895664 | + | 0.444731i | \(0.853299\pi\) | |||||||
\(48\) | −0.852815 | −0.123093 | ||||||||
\(49\) | −2.88090 | −0.411557 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −1.88090 | −0.263379 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 2.42636 | 0.333286 | 0.166643 | − | 0.986017i | \(-0.446707\pi\) | ||||
0.166643 | + | 0.986017i | \(0.446707\pi\) | |||||||
\(54\) | 2.40976 | 0.327927 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −6.24186 | −0.834103 | ||||||||
\(57\) | −2.02956 | −0.268821 | ||||||||
\(58\) | −3.56200 | −0.467714 | ||||||||
\(59\) | 7.06138 | 0.919313 | 0.459657 | − | 0.888097i | \(-0.347973\pi\) | ||||
0.459657 | + | 0.888097i | \(0.347973\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 6.76180 | 0.865760 | 0.432880 | − | 0.901452i | \(-0.357497\pi\) | ||||
0.432880 | + | 0.901452i | \(0.357497\pi\) | |||||||
\(62\) | 1.40162 | 0.178006 | ||||||||
\(63\) | 5.84695 | 0.736646 | ||||||||
\(64\) | 8.76180 | 1.09522 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 1.59024 | 0.195745 | ||||||||
\(67\) | 4.40422 | 0.538062 | 0.269031 | − | 0.963132i | \(-0.413297\pi\) | ||||
0.269031 | + | 0.963132i | \(0.413297\pi\) | |||||||
\(68\) | 3.21689 | 0.390105 | ||||||||
\(69\) | −0.119101 | −0.0143381 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 1.88090 | 0.223222 | 0.111611 | − | 0.993752i | \(-0.464399\pi\) | ||||
0.111611 | + | 0.993752i | \(0.464399\pi\) | |||||||
\(72\) | −8.86014 | −1.04418 | ||||||||
\(73\) | −8.86014 | −1.03700 | −0.518501 | − | 0.855077i | \(-0.673510\pi\) | ||||
−0.518501 | + | 0.855077i | \(0.673510\pi\) | |||||||
\(74\) | 6.47114 | 0.752255 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 3.47114 | 0.398167 | ||||||||
\(77\) | 7.87651 | 0.897611 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 11.1805 | 1.25790 | 0.628951 | − | 0.777445i | \(-0.283485\pi\) | ||||
0.628951 | + | 0.777445i | \(0.283485\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 7.94228 | 0.882475 | ||||||||
\(82\) | 0.214289 | 0.0236642 | ||||||||
\(83\) | −7.83540 | −0.860047 | −0.430024 | − | 0.902818i | \(-0.641495\pi\) | ||||
−0.430024 | + | 0.902818i | \(0.641495\pi\) | |||||||
\(84\) | 0.413416 | 0.0451073 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 1.59024 | 0.171480 | ||||||||
\(87\) | 1.03533 | 0.110999 | ||||||||
\(88\) | −11.9356 | −1.27234 | ||||||||
\(89\) | −12.2419 | −1.29763 | −0.648817 | − | 0.760944i | \(-0.724736\pi\) | ||||
−0.648817 | + | 0.760944i | \(0.724736\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0.203698 | 0.0212369 | ||||||||
\(93\) | −0.407395 | −0.0422449 | ||||||||
\(94\) | 14.5813 | 1.50395 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −1.11018 | −0.113307 | ||||||||
\(97\) | 5.80585 | 0.589494 | 0.294747 | − | 0.955575i | \(-0.404765\pi\) | ||||
0.294747 | + | 0.955575i | \(0.404765\pi\) | |||||||
\(98\) | 3.42059 | 0.345532 | ||||||||
\(99\) | 11.1805 | 1.12368 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −5.94228 | −0.591279 | −0.295639 | − | 0.955300i | \(-0.595533\pi\) | ||||
−0.295639 | + | 0.955300i | \(0.595533\pi\) | |||||||
\(102\) | 2.23325 | 0.221125 | ||||||||
\(103\) | −6.43378 | −0.633939 | −0.316970 | − | 0.948436i | \(-0.602665\pi\) | ||||
−0.316970 | + | 0.948436i | \(0.602665\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −2.88090 | −0.279818 | ||||||||
\(107\) | 17.6792 | 1.70911 | 0.854555 | − | 0.519360i | \(-0.173830\pi\) | ||||
0.854555 | + | 0.519360i | \(0.173830\pi\) | |||||||
\(108\) | 1.19792 | 0.115270 | ||||||||
\(109\) | −5.76180 | −0.551880 | −0.275940 | − | 0.961175i | \(-0.588989\pi\) | ||||
−0.275940 | + | 0.961175i | \(0.588989\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −1.88090 | −0.178527 | ||||||||
\(112\) | 5.01532 | 0.473903 | ||||||||
\(113\) | −4.75992 | −0.447776 | −0.223888 | − | 0.974615i | \(-0.571875\pi\) | ||||
−0.223888 | + | 0.974615i | \(0.571875\pi\) | |||||||
\(114\) | 2.40976 | 0.225695 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −1.77072 | −0.164407 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −8.38421 | −0.771829 | ||||||||
\(119\) | 11.0614 | 1.01399 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 4.06138 | 0.369216 | ||||||||
\(122\) | −8.02851 | −0.726867 | ||||||||
\(123\) | −0.0622851 | −0.00561605 | ||||||||
\(124\) | 0.696765 | 0.0625714 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −6.94228 | −0.618467 | ||||||||
\(127\) | −16.7061 | −1.48243 | −0.741215 | − | 0.671268i | \(-0.765750\pi\) | ||||
−0.741215 | + | 0.671268i | \(0.765750\pi\) | |||||||
\(128\) | −3.96940 | −0.350848 | ||||||||
\(129\) | −0.462218 | −0.0406961 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 10.0000 | 0.873704 | 0.436852 | − | 0.899533i | \(-0.356093\pi\) | ||||
0.436852 | + | 0.899533i | \(0.356093\pi\) | |||||||
\(132\) | 0.790529 | 0.0688068 | ||||||||
\(133\) | 11.9356 | 1.03495 | ||||||||
\(134\) | −5.22928 | −0.451741 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −16.7618 | −1.43731 | ||||||||
\(137\) | −1.97786 | −0.168980 | −0.0844901 | − | 0.996424i | \(-0.526926\pi\) | ||||
−0.0844901 | + | 0.996424i | \(0.526926\pi\) | |||||||
\(138\) | 0.141412 | 0.0120378 | ||||||||
\(139\) | 8.70042 | 0.737960 | 0.368980 | − | 0.929437i | \(-0.379707\pi\) | ||||
0.368980 | + | 0.929437i | \(0.379707\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −4.23820 | −0.356921 | ||||||||
\(142\) | −2.23325 | −0.187411 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 7.11910 | 0.593258 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 10.5199 | 0.870637 | ||||||||
\(147\) | −0.994227 | −0.0820025 | ||||||||
\(148\) | 3.21689 | 0.264427 | ||||||||
\(149\) | −22.3032 | −1.82715 | −0.913576 | − | 0.406668i | \(-0.866691\pi\) | ||||
−0.913576 | + | 0.406668i | \(0.866691\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 19.1626 | 1.55943 | 0.779717 | − | 0.626132i | \(-0.215363\pi\) | ||||
0.779717 | + | 0.626132i | \(0.215363\pi\) | |||||||
\(152\) | −18.0866 | −1.46701 | ||||||||
\(153\) | 15.7013 | 1.26938 | ||||||||
\(154\) | −9.35204 | −0.753609 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −6.20265 | −0.495025 | −0.247513 | − | 0.968885i | \(-0.579613\pi\) | ||||
−0.247513 | + | 0.968885i | \(0.579613\pi\) | |||||||
\(158\) | −13.2750 | −1.05610 | ||||||||
\(159\) | 0.837361 | 0.0664071 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0.700420 | 0.0552008 | ||||||||
\(162\) | −9.43013 | −0.740901 | ||||||||
\(163\) | −11.9356 | −0.934870 | −0.467435 | − | 0.884027i | \(-0.654822\pi\) | ||||
−0.467435 | + | 0.884027i | \(0.654822\pi\) | |||||||
\(164\) | 0.106526 | 0.00831826 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 9.30323 | 0.722071 | ||||||||
\(167\) | 2.02956 | 0.157052 | 0.0785259 | − | 0.996912i | \(-0.474979\pi\) | ||||
0.0785259 | + | 0.996912i | \(0.474979\pi\) | |||||||
\(168\) | −2.15413 | −0.166195 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 16.9423 | 1.29561 | ||||||||
\(172\) | 0.790529 | 0.0602773 | ||||||||
\(173\) | 1.33934 | 0.101828 | 0.0509139 | − | 0.998703i | \(-0.483787\pi\) | ||||
0.0509139 | + | 0.998703i | \(0.483787\pi\) | |||||||
\(174\) | −1.22928 | −0.0931916 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 9.59024 | 0.722891 | ||||||||
\(177\) | 2.43695 | 0.183173 | ||||||||
\(178\) | 14.5352 | 1.08946 | ||||||||
\(179\) | 20.2240 | 1.51161 | 0.755807 | − | 0.654794i | \(-0.227245\pi\) | ||||
0.755807 | + | 0.654794i | \(0.227245\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 19.8232 | 1.47345 | 0.736723 | − | 0.676195i | \(-0.236372\pi\) | ||||
0.736723 | + | 0.676195i | \(0.236372\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 2.33356 | 0.172502 | ||||||||
\(184\) | −1.06138 | −0.0782458 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0.483714 | 0.0354676 | ||||||||
\(187\) | 21.1515 | 1.54675 | ||||||||
\(188\) | 7.24857 | 0.528656 | ||||||||
\(189\) | 4.11910 | 0.299621 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 1.53778 | 0.111270 | 0.0556350 | − | 0.998451i | \(-0.482282\pi\) | ||||
0.0556350 | + | 0.998451i | \(0.482282\pi\) | |||||||
\(192\) | 3.02378 | 0.218223 | ||||||||
\(193\) | −21.2032 | −1.52624 | −0.763118 | − | 0.646259i | \(-0.776333\pi\) | ||||
−0.763118 | + | 0.646259i | \(0.776333\pi\) | |||||||
\(194\) | −6.89347 | −0.494923 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1.70042 | 0.121459 | ||||||||
\(197\) | 9.25695 | 0.659530 | 0.329765 | − | 0.944063i | \(-0.393030\pi\) | ||||
0.329765 | + | 0.944063i | \(0.393030\pi\) | |||||||
\(198\) | −13.2750 | −0.943410 | ||||||||
\(199\) | −17.4045 | −1.23377 | −0.616886 | − | 0.787053i | \(-0.711606\pi\) | ||||
−0.616886 | + | 0.787053i | \(0.711606\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 1.51994 | 0.107208 | ||||||||
\(202\) | 7.05546 | 0.496421 | ||||||||
\(203\) | −6.08867 | −0.427341 | ||||||||
\(204\) | 1.11018 | 0.0777282 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 7.63904 | 0.532237 | ||||||||
\(207\) | 0.994227 | 0.0691036 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 22.8232 | 1.57871 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −7.28174 | −0.501296 | −0.250648 | − | 0.968078i | \(-0.580644\pi\) | ||||
−0.250648 | + | 0.968078i | \(0.580644\pi\) | |||||||
\(212\) | −1.43213 | −0.0983594 | ||||||||
\(213\) | 0.649117 | 0.0444768 | ||||||||
\(214\) | −20.9911 | −1.43492 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −6.24186 | −0.424705 | ||||||||
\(217\) | 2.39585 | 0.162641 | ||||||||
\(218\) | 6.84118 | 0.463343 | ||||||||
\(219\) | −3.05772 | −0.206622 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 2.23325 | 0.149886 | ||||||||
\(223\) | 19.4670 | 1.30361 | 0.651804 | − | 0.758388i | \(-0.274013\pi\) | ||||
0.651804 | + | 0.758388i | \(0.274013\pi\) | |||||||
\(224\) | 6.52886 | 0.436228 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 5.65162 | 0.375940 | ||||||||
\(227\) | −4.81162 | −0.319358 | −0.159679 | − | 0.987169i | \(-0.551046\pi\) | ||||
−0.159679 | + | 0.987169i | \(0.551046\pi\) | |||||||
\(228\) | 1.19792 | 0.0793345 | ||||||||
\(229\) | −1.52360 | −0.100682 | −0.0503410 | − | 0.998732i | \(-0.516031\pi\) | ||||
−0.0503410 | + | 0.998732i | \(0.516031\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 2.71826 | 0.178848 | ||||||||
\(232\) | 9.22643 | 0.605745 | ||||||||
\(233\) | −13.9652 | −0.914889 | −0.457445 | − | 0.889238i | \(-0.651235\pi\) | ||||
−0.457445 | + | 0.889238i | \(0.651235\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −4.16790 | −0.271307 | ||||||||
\(237\) | 3.85849 | 0.250636 | ||||||||
\(238\) | −13.1335 | −0.851321 | ||||||||
\(239\) | −4.00000 | −0.258738 | −0.129369 | − | 0.991596i | \(-0.541295\pi\) | ||||
−0.129369 | + | 0.991596i | \(0.541295\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 17.4659 | 1.12508 | 0.562538 | − | 0.826771i | \(-0.309825\pi\) | ||||
0.562538 | + | 0.826771i | \(0.309825\pi\) | |||||||
\(242\) | −4.82221 | −0.309983 | ||||||||
\(243\) | 8.82963 | 0.566421 | ||||||||
\(244\) | −3.99108 | −0.255503 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0.0739531 | 0.00471508 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | −3.63054 | −0.230539 | ||||||||
\(249\) | −2.70408 | −0.171364 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 9.29958 | 0.586984 | 0.293492 | − | 0.955961i | \(-0.405183\pi\) | ||||
0.293492 | + | 0.955961i | \(0.405183\pi\) | |||||||
\(252\) | −3.45110 | −0.217399 | ||||||||
\(253\) | 1.33934 | 0.0842034 | ||||||||
\(254\) | 19.8358 | 1.24461 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −12.8106 | −0.800663 | ||||||||
\(257\) | 10.8897 | 0.679281 | 0.339640 | − | 0.940555i | \(-0.389695\pi\) | ||||
0.339640 | + | 0.940555i | \(0.389695\pi\) | |||||||
\(258\) | 0.548807 | 0.0341673 | ||||||||
\(259\) | 11.0614 | 0.687321 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −8.64270 | −0.534970 | ||||||||
\(262\) | −11.8733 | −0.733537 | ||||||||
\(263\) | −13.4406 | −0.828785 | −0.414392 | − | 0.910098i | \(-0.636006\pi\) | ||||
−0.414392 | + | 0.910098i | \(0.636006\pi\) | |||||||
\(264\) | −4.11910 | −0.253513 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −14.1716 | −0.868914 | ||||||||
\(267\) | −4.22479 | −0.258553 | ||||||||
\(268\) | −2.59955 | −0.158793 | ||||||||
\(269\) | 3.66054 | 0.223187 | 0.111593 | − | 0.993754i | \(-0.464405\pi\) | ||||
0.111593 | + | 0.993754i | \(0.464405\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −22.0037 | −1.33663 | −0.668313 | − | 0.743880i | \(-0.732983\pi\) | ||||
−0.668313 | + | 0.743880i | \(0.732983\pi\) | |||||||
\(272\) | 13.4681 | 0.816621 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 2.34838 | 0.141871 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0.0702980 | 0.00423144 | ||||||||
\(277\) | 9.89547 | 0.594561 | 0.297281 | − | 0.954790i | \(-0.403920\pi\) | ||||
0.297281 | + | 0.954790i | \(0.403920\pi\) | |||||||
\(278\) | −10.3303 | −0.619570 | ||||||||
\(279\) | 3.40084 | 0.203603 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −4.06138 | −0.242281 | −0.121141 | − | 0.992635i | \(-0.538655\pi\) | ||||
−0.121141 | + | 0.992635i | \(0.538655\pi\) | |||||||
\(282\) | 5.03216 | 0.299661 | ||||||||
\(283\) | −6.08867 | −0.361934 | −0.180967 | − | 0.983489i | \(-0.557923\pi\) | ||||
−0.180967 | + | 0.983489i | \(0.557923\pi\) | |||||||
\(284\) | −1.11018 | −0.0658771 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0.366292 | 0.0216215 | ||||||||
\(288\) | 9.26754 | 0.546095 | ||||||||
\(289\) | 12.7041 | 0.747299 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 2.00366 | 0.117456 | ||||||||
\(292\) | 5.22960 | 0.306039 | ||||||||
\(293\) | 9.79208 | 0.572060 | 0.286030 | − | 0.958221i | \(-0.407664\pi\) | ||||
0.286030 | + | 0.958221i | \(0.407664\pi\) | |||||||
\(294\) | 1.18048 | 0.0688469 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −16.7618 | −0.974260 | ||||||||
\(297\) | 7.87651 | 0.457041 | ||||||||
\(298\) | 26.4814 | 1.53402 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 2.71826 | 0.156678 | ||||||||
\(302\) | −22.7524 | −1.30926 | ||||||||
\(303\) | −2.05074 | −0.117812 | ||||||||
\(304\) | 14.5325 | 0.833497 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −18.6427 | −1.06573 | ||||||||
\(307\) | 22.1046 | 1.26158 | 0.630788 | − | 0.775955i | \(-0.282732\pi\) | ||||
0.630788 | + | 0.775955i | \(0.282732\pi\) | |||||||
\(308\) | −4.64902 | −0.264903 | ||||||||
\(309\) | −2.22036 | −0.126312 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 7.63904 | 0.433170 | 0.216585 | − | 0.976264i | \(-0.430508\pi\) | ||||
0.216585 | + | 0.976264i | \(0.430508\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 26.1425 | 1.47766 | 0.738831 | − | 0.673891i | \(-0.235378\pi\) | ||||
0.738831 | + | 0.673891i | \(0.235378\pi\) | |||||||
\(314\) | 7.36461 | 0.415609 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −6.59916 | −0.371232 | ||||||||
\(317\) | −11.8428 | −0.665159 | −0.332580 | − | 0.943075i | \(-0.607919\pi\) | ||||
−0.332580 | + | 0.943075i | \(0.607919\pi\) | |||||||
\(318\) | −0.994227 | −0.0557535 | ||||||||
\(319\) | −11.6427 | −0.651866 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 6.10126 | 0.340539 | ||||||||
\(322\) | −0.831632 | −0.0463451 | ||||||||
\(323\) | 32.0518 | 1.78341 | ||||||||
\(324\) | −4.68785 | −0.260436 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 14.1716 | 0.784890 | ||||||||
\(327\) | −1.98845 | −0.109962 | ||||||||
\(328\) | −0.555059 | −0.0306480 | ||||||||
\(329\) | 24.9244 | 1.37413 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 12.7004 | 0.698078 | 0.349039 | − | 0.937108i | \(-0.386508\pi\) | ||||
0.349039 | + | 0.937108i | \(0.386508\pi\) | |||||||
\(332\) | 4.62476 | 0.253817 | ||||||||
\(333\) | 15.7013 | 0.860427 | ||||||||
\(334\) | −2.40976 | −0.131856 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 1.73084 | 0.0944248 | ||||||||
\(337\) | −15.2939 | −0.833113 | −0.416556 | − | 0.909110i | \(-0.636763\pi\) | ||||
−0.416556 | + | 0.909110i | \(0.636763\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −1.64270 | −0.0892191 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 4.58132 | 0.248092 | ||||||||
\(342\) | −20.1161 | −1.08776 | ||||||||
\(343\) | 20.0538 | 1.08281 | ||||||||
\(344\) | −4.11910 | −0.222087 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −1.59024 | −0.0854918 | ||||||||
\(347\) | 12.2396 | 0.657058 | 0.328529 | − | 0.944494i | \(-0.393447\pi\) | ||||
0.328529 | + | 0.944494i | \(0.393447\pi\) | |||||||
\(348\) | −0.611093 | −0.0327580 | ||||||||
\(349\) | −18.7004 | −1.00101 | −0.500505 | − | 0.865733i | \(-0.666852\pi\) | ||||
−0.500505 | + | 0.865733i | \(0.666852\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 12.4844 | 0.665422 | ||||||||
\(353\) | −1.30883 | −0.0696617 | −0.0348309 | − | 0.999393i | \(-0.511089\pi\) | ||||
−0.0348309 | + | 0.999393i | \(0.511089\pi\) | |||||||
\(354\) | −2.89347 | −0.153786 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 7.22563 | 0.382957 | ||||||||
\(357\) | 3.81739 | 0.202038 | ||||||||
\(358\) | −24.0127 | −1.26911 | ||||||||
\(359\) | 29.4082 | 1.55210 | 0.776051 | − | 0.630670i | \(-0.217220\pi\) | ||||
0.776051 | + | 0.630670i | \(0.217220\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 15.5850 | 0.820262 | ||||||||
\(362\) | −23.5367 | −1.23706 | ||||||||
\(363\) | 1.40162 | 0.0735661 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −2.77072 | −0.144828 | ||||||||
\(367\) | −33.4322 | −1.74515 | −0.872573 | − | 0.488484i | \(-0.837550\pi\) | ||||
−0.872573 | + | 0.488484i | \(0.837550\pi\) | |||||||
\(368\) | 0.852815 | 0.0444560 | ||||||||
\(369\) | 0.519941 | 0.0270671 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −4.92444 | −0.255664 | ||||||||
\(372\) | 0.240461 | 0.0124673 | ||||||||
\(373\) | −34.4781 | −1.78521 | −0.892604 | − | 0.450841i | \(-0.851124\pi\) | ||||
−0.892604 | + | 0.450841i | \(0.851124\pi\) | |||||||
\(374\) | −25.1138 | −1.29861 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −37.7691 | −1.94779 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | −4.89075 | −0.251553 | ||||||||
\(379\) | 17.4045 | 0.894009 | 0.447004 | − | 0.894532i | \(-0.352491\pi\) | ||||
0.447004 | + | 0.894532i | \(0.352491\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −5.76545 | −0.295373 | ||||||||
\(382\) | −1.82586 | −0.0934191 | ||||||||
\(383\) | −1.74673 | −0.0892538 | −0.0446269 | − | 0.999004i | \(-0.514210\pi\) | ||||
−0.0446269 | + | 0.999004i | \(0.514210\pi\) | |||||||
\(384\) | −1.36988 | −0.0699063 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 25.1752 | 1.28138 | ||||||||
\(387\) | 3.85849 | 0.196138 | ||||||||
\(388\) | −3.42684 | −0.173971 | ||||||||
\(389\) | 22.0435 | 1.11765 | 0.558826 | − | 0.829285i | \(-0.311252\pi\) | ||||
0.558826 | + | 0.829285i | \(0.311252\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1.88090 | 0.0951212 | ||||||||
\(392\) | −8.86014 | −0.447505 | ||||||||
\(393\) | 3.45110 | 0.174085 | ||||||||
\(394\) | −10.9911 | −0.553723 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −6.59916 | −0.331620 | ||||||||
\(397\) | 22.5319 | 1.13084 | 0.565422 | − | 0.824802i | \(-0.308713\pi\) | ||||
0.565422 | + | 0.824802i | \(0.308713\pi\) | |||||||
\(398\) | 20.6649 | 1.03584 | ||||||||
\(399\) | 4.11910 | 0.206213 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 3.70408 | 0.184973 | 0.0924863 | − | 0.995714i | \(-0.470519\pi\) | ||||
0.0924863 | + | 0.995714i | \(0.470519\pi\) | |||||||
\(402\) | −1.80468 | −0.0900091 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 3.50737 | 0.174498 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 7.22928 | 0.358783 | ||||||||
\(407\) | 21.1515 | 1.04844 | ||||||||
\(408\) | −5.78466 | −0.286384 | ||||||||
\(409\) | 13.4837 | 0.666727 | 0.333363 | − | 0.942798i | \(-0.391816\pi\) | ||||
0.333363 | + | 0.942798i | \(0.391816\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −0.682580 | −0.0336692 | ||||||||
\(412\) | 3.79747 | 0.187088 | ||||||||
\(413\) | −14.3315 | −0.705205 | ||||||||
\(414\) | −1.18048 | −0.0580174 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 3.00260 | 0.147038 | ||||||||
\(418\) | −27.0987 | −1.32544 | ||||||||
\(419\) | 16.8232 | 0.821866 | 0.410933 | − | 0.911666i | \(-0.365203\pi\) | ||||
0.410933 | + | 0.911666i | \(0.365203\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −17.1013 | −0.833464 | −0.416732 | − | 0.909029i | \(-0.636825\pi\) | ||||
−0.416732 | + | 0.909029i | \(0.636825\pi\) | |||||||
\(422\) | 8.64585 | 0.420874 | ||||||||
\(423\) | 35.3795 | 1.72021 | ||||||||
\(424\) | 7.46222 | 0.362397 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −0.770718 | −0.0373414 | ||||||||
\(427\) | −13.7235 | −0.664124 | ||||||||
\(428\) | −10.4349 | −0.504392 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −9.66054 | −0.465332 | −0.232666 | − | 0.972557i | \(-0.574745\pi\) | ||||
−0.232666 | + | 0.972557i | \(0.574745\pi\) | |||||||
\(432\) | 5.01532 | 0.241300 | ||||||||
\(433\) | 24.7727 | 1.19050 | 0.595249 | − | 0.803541i | \(-0.297053\pi\) | ||||
0.595249 | + | 0.803541i | \(0.297053\pi\) | |||||||
\(434\) | −2.84467 | −0.136549 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 3.40084 | 0.162871 | ||||||||
\(437\) | 2.02956 | 0.0970869 | ||||||||
\(438\) | 3.63054 | 0.173474 | ||||||||
\(439\) | 7.06138 | 0.337021 | 0.168511 | − | 0.985700i | \(-0.446104\pi\) | ||||
0.168511 | + | 0.985700i | \(0.446104\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 8.29958 | 0.395218 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −38.2438 | −1.81702 | −0.908509 | − | 0.417865i | \(-0.862778\pi\) | ||||
−0.908509 | + | 0.417865i | \(0.862778\pi\) | |||||||
\(444\) | 1.11018 | 0.0526869 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −23.1138 | −1.09447 | ||||||||
\(447\) | −7.69707 | −0.364059 | ||||||||
\(448\) | −17.7826 | −0.840147 | ||||||||
\(449\) | 12.4801 | 0.588970 | 0.294485 | − | 0.955656i | \(-0.404852\pi\) | ||||
0.294485 | + | 0.955656i | \(0.404852\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0.700420 | 0.0329815 | ||||||||
\(452\) | 2.80950 | 0.132148 | ||||||||
\(453\) | 6.61322 | 0.310716 | ||||||||
\(454\) | 5.71300 | 0.268124 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −6.24186 | −0.292302 | ||||||||
\(457\) | −8.23221 | −0.385086 | −0.192543 | − | 0.981289i | \(-0.561674\pi\) | ||||
−0.192543 | + | 0.981289i | \(0.561674\pi\) | |||||||
\(458\) | 1.80902 | 0.0845298 | ||||||||
\(459\) | 11.0614 | 0.516301 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 4.54144 | 0.211516 | 0.105758 | − | 0.994392i | \(-0.466273\pi\) | ||||
0.105758 | + | 0.994392i | \(0.466273\pi\) | |||||||
\(462\) | −3.22748 | −0.150156 | ||||||||
\(463\) | 1.98845 | 0.0924113 | 0.0462056 | − | 0.998932i | \(-0.485287\pi\) | ||||
0.0462056 | + | 0.998932i | \(0.485287\pi\) | |||||||
\(464\) | −7.41342 | −0.344159 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 16.5813 | 0.768115 | ||||||||
\(467\) | −32.8043 | −1.51800 | −0.759000 | − | 0.651091i | \(-0.774312\pi\) | ||||
−0.759000 | + | 0.651091i | \(0.774312\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −8.93862 | −0.412747 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −2.14060 | −0.0986335 | ||||||||
\(472\) | 21.7171 | 0.999611 | ||||||||
\(473\) | 5.19783 | 0.238997 | ||||||||
\(474\) | −4.58132 | −0.210427 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −6.52886 | −0.299250 | ||||||||
\(477\) | −6.99010 | −0.320055 | ||||||||
\(478\) | 4.74933 | 0.217229 | ||||||||
\(479\) | 30.8053 | 1.40753 | 0.703766 | − | 0.710432i | \(-0.251500\pi\) | ||||
0.703766 | + | 0.710432i | \(0.251500\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | −20.7378 | −0.944582 | ||||||||
\(483\) | 0.241722 | 0.0109987 | ||||||||
\(484\) | −2.39719 | −0.108963 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −10.4837 | −0.475551 | ||||||||
\(487\) | 22.3251 | 1.01165 | 0.505824 | − | 0.862637i | \(-0.331189\pi\) | ||||
0.505824 | + | 0.862637i | \(0.331189\pi\) | |||||||
\(488\) | 20.7958 | 0.941380 | ||||||||
\(489\) | −4.11910 | −0.186272 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 10.6826 | 0.482098 | 0.241049 | − | 0.970513i | \(-0.422509\pi\) | ||||
0.241049 | + | 0.970513i | \(0.422509\pi\) | |||||||
\(492\) | 0.0367631 | 0.00165741 | ||||||||
\(493\) | −16.3504 | −0.736386 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 2.91713 | 0.130983 | ||||||||
\(497\) | −3.81739 | −0.171233 | ||||||||
\(498\) | 3.21064 | 0.143872 | ||||||||
\(499\) | −18.8195 | −0.842477 | −0.421239 | − | 0.906950i | \(-0.638405\pi\) | ||||
−0.421239 | + | 0.906950i | \(0.638405\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0.700420 | 0.0312925 | ||||||||
\(502\) | −11.0417 | −0.492815 | ||||||||
\(503\) | −5.68128 | −0.253316 | −0.126658 | − | 0.991946i | \(-0.540425\pi\) | ||||
−0.126658 | + | 0.991946i | \(0.540425\pi\) | |||||||
\(504\) | 17.9822 | 0.800989 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −1.59024 | −0.0706948 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 9.86062 | 0.437494 | ||||||||
\(509\) | −27.9244 | −1.23773 | −0.618864 | − | 0.785498i | \(-0.712407\pi\) | ||||
−0.618864 | + | 0.785498i | \(0.712407\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 17.9822 | 0.795484 | ||||||||
\(512\) | 23.1492 | 1.02306 | ||||||||
\(513\) | 11.9356 | 0.526970 | ||||||||
\(514\) | −12.9297 | −0.570305 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0.272820 | 0.0120102 | ||||||||
\(517\) | 47.6603 | 2.09610 | ||||||||
\(518\) | −13.1335 | −0.577055 | ||||||||
\(519\) | 0.462218 | 0.0202891 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 6.29958 | 0.275990 | 0.137995 | − | 0.990433i | \(-0.455934\pi\) | ||||
0.137995 | + | 0.990433i | \(0.455934\pi\) | |||||||
\(522\) | 10.2618 | 0.449145 | ||||||||
\(523\) | 22.8571 | 0.999471 | 0.499735 | − | 0.866178i | \(-0.333431\pi\) | ||||
0.499735 | + | 0.866178i | \(0.333431\pi\) | |||||||
\(524\) | −5.90239 | −0.257847 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 15.9585 | 0.695824 | ||||||||
\(527\) | 6.43378 | 0.280260 | ||||||||
\(528\) | 3.30969 | 0.144036 | ||||||||
\(529\) | −22.8809 | −0.994822 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −20.3431 | −0.882816 | ||||||||
\(532\) | −7.04487 | −0.305434 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 5.01623 | 0.217074 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 13.5451 | 0.585059 | ||||||||
\(537\) | 6.97951 | 0.301188 | ||||||||
\(538\) | −4.34628 | −0.187381 | ||||||||
\(539\) | 11.1805 | 0.481577 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 9.48006 | 0.407580 | 0.203790 | − | 0.979015i | \(-0.434674\pi\) | ||||
0.203790 | + | 0.979015i | \(0.434674\pi\) | |||||||
\(542\) | 26.1257 | 1.12219 | ||||||||
\(543\) | 6.84118 | 0.293583 | ||||||||
\(544\) | 17.5325 | 0.751700 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 33.3911 | 1.42770 | 0.713850 | − | 0.700299i | \(-0.246950\pi\) | ||||
0.713850 | + | 0.700299i | \(0.246950\pi\) | |||||||
\(548\) | 1.16741 | 0.0498694 | ||||||||
\(549\) | −19.4801 | −0.831389 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −17.6427 | −0.751604 | ||||||||
\(552\) | −0.366292 | −0.0155904 | ||||||||
\(553\) | −22.6914 | −0.964937 | ||||||||
\(554\) | −11.7492 | −0.499177 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −5.13533 | −0.217787 | ||||||||
\(557\) | 37.7648 | 1.60015 | 0.800073 | − | 0.599903i | \(-0.204794\pi\) | ||||
0.800073 | + | 0.599903i | \(0.204794\pi\) | |||||||
\(558\) | −4.03793 | −0.170939 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 7.29958 | 0.308188 | ||||||||
\(562\) | 4.82221 | 0.203413 | ||||||||
\(563\) | 25.9008 | 1.09159 | 0.545794 | − | 0.837919i | \(-0.316228\pi\) | ||||
0.545794 | + | 0.837919i | \(0.316228\pi\) | |||||||
\(564\) | 2.50155 | 0.105334 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 7.22928 | 0.303869 | ||||||||
\(567\) | −16.1193 | −0.676947 | ||||||||
\(568\) | 5.78466 | 0.242719 | ||||||||
\(569\) | −21.5451 | −0.903217 | −0.451609 | − | 0.892216i | \(-0.649150\pi\) | ||||
−0.451609 | + | 0.892216i | \(0.649150\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −2.22036 | −0.0929192 | −0.0464596 | − | 0.998920i | \(-0.514794\pi\) | ||||
−0.0464596 | + | 0.998920i | \(0.514794\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0.530704 | 0.0221705 | ||||||||
\(574\) | −0.434911 | −0.0181528 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −25.2419 | −1.05174 | ||||||||
\(577\) | −6.20265 | −0.258220 | −0.129110 | − | 0.991630i | \(-0.541212\pi\) | ||||
−0.129110 | + | 0.991630i | \(0.541212\pi\) | |||||||
\(578\) | −15.0840 | −0.627411 | ||||||||
\(579\) | −7.31742 | −0.304102 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 15.9024 | 0.659742 | ||||||||
\(582\) | −2.37901 | −0.0986130 | ||||||||
\(583\) | −9.41646 | −0.389990 | ||||||||
\(584\) | −27.2492 | −1.12758 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −11.6265 | −0.480285 | ||||||||
\(587\) | −1.82894 | −0.0754883 | −0.0377442 | − | 0.999287i | \(-0.512017\pi\) | ||||
−0.0377442 | + | 0.999287i | \(0.512017\pi\) | |||||||
\(588\) | 0.586832 | 0.0242005 | ||||||||
\(589\) | 6.94228 | 0.286052 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 3.19466 | 0.131411 | ||||||||
\(592\) | 13.4681 | 0.553534 | ||||||||
\(593\) | −0.0728761 | −0.00299266 | −0.00149633 | − | 0.999999i | \(-0.500476\pi\) | ||||
−0.00149633 | + | 0.999999i | \(0.500476\pi\) | |||||||
\(594\) | −9.35204 | −0.383719 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 13.1642 | 0.539229 | ||||||||
\(597\) | −6.00646 | −0.245828 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −14.5813 | −0.595777 | −0.297888 | − | 0.954601i | \(-0.596282\pi\) | ||||
−0.297888 | + | 0.954601i | \(0.596282\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −44.4082 | −1.81145 | −0.905723 | − | 0.423870i | \(-0.860671\pi\) | ||||
−0.905723 | + | 0.423870i | \(0.860671\pi\) | |||||||
\(602\) | −3.22748 | −0.131542 | ||||||||
\(603\) | −12.6881 | −0.516700 | ||||||||
\(604\) | −11.3105 | −0.460220 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 2.43491 | 0.0989115 | ||||||||
\(607\) | −36.2354 | −1.47075 | −0.735375 | − | 0.677660i | \(-0.762994\pi\) | ||||
−0.735375 | + | 0.677660i | \(0.762994\pi\) | |||||||
\(608\) | 18.9182 | 0.767235 | ||||||||
\(609\) | −2.10126 | −0.0851474 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | −9.26754 | −0.374618 | ||||||||
\(613\) | 3.35830 | 0.135641 | 0.0678203 | − | 0.997698i | \(-0.478396\pi\) | ||||
0.0678203 | + | 0.997698i | \(0.478396\pi\) | |||||||
\(614\) | −26.2455 | −1.05918 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 24.2240 | 0.976013 | ||||||||
\(617\) | −21.1820 | −0.852754 | −0.426377 | − | 0.904546i | \(-0.640210\pi\) | ||||
−0.426377 | + | 0.904546i | \(0.640210\pi\) | |||||||
\(618\) | 2.63631 | 0.106048 | ||||||||
\(619\) | −25.4082 | −1.02124 | −0.510620 | − | 0.859807i | \(-0.670584\pi\) | ||||
−0.510620 | + | 0.859807i | \(0.670584\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0.700420 | 0.0281069 | ||||||||
\(622\) | −9.07009 | −0.363677 | ||||||||
\(623\) | 24.8455 | 0.995416 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −31.0399 | −1.24060 | ||||||||
\(627\) | 7.87651 | 0.314557 | ||||||||
\(628\) | 3.66105 | 0.146092 | ||||||||
\(629\) | 29.7041 | 1.18438 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −43.5451 | −1.73350 | −0.866751 | − | 0.498740i | \(-0.833796\pi\) | ||||
−0.866751 | + | 0.498740i | \(0.833796\pi\) | |||||||
\(632\) | 34.3853 | 1.36777 | ||||||||
\(633\) | −2.51300 | −0.0998828 | ||||||||
\(634\) | 14.0614 | 0.558449 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −0.494244 | −0.0195980 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 13.8238 | 0.547288 | ||||||||
\(639\) | −5.41868 | −0.214360 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 48.2854 | 1.90716 | 0.953579 | − | 0.301142i | \(-0.0973679\pi\) | ||||
0.953579 | + | 0.301142i | \(0.0973679\pi\) | |||||||
\(642\) | −7.24423 | −0.285907 | ||||||||
\(643\) | 42.3440 | 1.66989 | 0.834943 | − | 0.550337i | \(-0.185501\pi\) | ||||
0.834943 | + | 0.550337i | \(0.185501\pi\) | |||||||
\(644\) | −0.413416 | −0.0162909 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −38.0561 | −1.49730 | ||||||||
\(647\) | −34.4052 | −1.35261 | −0.676305 | − | 0.736622i | \(-0.736420\pi\) | ||||
−0.676305 | + | 0.736622i | \(0.736420\pi\) | |||||||
\(648\) | 24.4263 | 0.959556 | ||||||||
\(649\) | −27.4045 | −1.07572 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0.826831 | 0.0324061 | ||||||||
\(652\) | 7.04487 | 0.275899 | ||||||||
\(653\) | −14.3315 | −0.560834 | −0.280417 | − | 0.959878i | \(-0.590473\pi\) | ||||
−0.280417 | + | 0.959878i | \(0.590473\pi\) | |||||||
\(654\) | 2.36096 | 0.0923208 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0.445988 | 0.0174129 | ||||||||
\(657\) | 25.5252 | 0.995832 | ||||||||
\(658\) | −29.5936 | −1.15368 | ||||||||
\(659\) | 22.8232 | 0.889065 | 0.444532 | − | 0.895763i | \(-0.353370\pi\) | ||||
0.444532 | + | 0.895763i | \(0.353370\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −14.4187 | −0.560822 | −0.280411 | − | 0.959880i | \(-0.590471\pi\) | ||||
−0.280411 | + | 0.959880i | \(0.590471\pi\) | |||||||
\(662\) | −15.0796 | −0.586087 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −24.0976 | −0.935168 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −18.6427 | −0.722390 | ||||||||
\(667\) | −1.03533 | −0.0400881 | ||||||||
\(668\) | −1.19792 | −0.0463491 | ||||||||
\(669\) | 6.71826 | 0.259743 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −26.2419 | −1.01306 | ||||||||
\(672\) | 2.25318 | 0.0869181 | ||||||||
\(673\) | −34.1741 | −1.31731 | −0.658657 | − | 0.752443i | \(-0.728875\pi\) | ||||
−0.658657 | + | 0.752443i | \(0.728875\pi\) | |||||||
\(674\) | 18.1590 | 0.699458 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 5.84695 | 0.224716 | 0.112358 | − | 0.993668i | \(-0.464160\pi\) | ||||
0.112358 | + | 0.993668i | \(0.464160\pi\) | |||||||
\(678\) | 1.95043 | 0.0749058 | ||||||||
\(679\) | −11.7833 | −0.452201 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −1.66054 | −0.0636319 | ||||||||
\(682\) | −5.43955 | −0.208291 | ||||||||
\(683\) | 11.3488 | 0.434249 | 0.217125 | − | 0.976144i | \(-0.430332\pi\) | ||||
0.217125 | + | 0.976144i | \(0.430332\pi\) | |||||||
\(684\) | −10.0000 | −0.382360 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −23.8106 | −0.909093 | ||||||||
\(687\) | −0.525808 | −0.0200608 | ||||||||
\(688\) | 3.30969 | 0.126181 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 18.8232 | 0.716067 | 0.358034 | − | 0.933709i | \(-0.383447\pi\) | ||||
0.358034 | + | 0.933709i | \(0.383447\pi\) | |||||||
\(692\) | −0.790529 | −0.0300514 | ||||||||
\(693\) | −22.6914 | −0.861976 | ||||||||
\(694\) | −14.5325 | −0.551647 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 3.18413 | 0.120694 | ||||||||
\(697\) | 0.983636 | 0.0372579 | ||||||||
\(698\) | 22.2036 | 0.840420 | ||||||||
\(699\) | −4.81952 | −0.182291 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 19.1626 | 0.723763 | 0.361881 | − | 0.932224i | \(-0.382135\pi\) | ||||
0.361881 | + | 0.932224i | \(0.382135\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 32.0518 | 1.20885 | ||||||||
\(704\) | −34.0037 | −1.28156 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 1.55401 | 0.0584860 | ||||||||
\(707\) | 12.0602 | 0.453570 | ||||||||
\(708\) | −1.43839 | −0.0540578 | ||||||||
\(709\) | −23.4837 | −0.881949 | −0.440975 | − | 0.897520i | \(-0.645367\pi\) | ||||
−0.440975 | + | 0.897520i | \(0.645367\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −32.2098 | −1.20796 | ||||||||
\(712\) | −37.6496 | −1.41098 | ||||||||
\(713\) | 0.407395 | 0.0152571 | ||||||||
\(714\) | −4.53252 | −0.169625 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −11.9370 | −0.446107 | ||||||||
\(717\) | −1.38044 | −0.0515535 | ||||||||
\(718\) | −34.9173 | −1.30310 | ||||||||
\(719\) | −14.1086 | −0.526161 | −0.263080 | − | 0.964774i | \(-0.584738\pi\) | ||||
−0.263080 | + | 0.964774i | \(0.584738\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 13.0577 | 0.486295 | ||||||||
\(722\) | −18.5046 | −0.688668 | ||||||||
\(723\) | 6.02765 | 0.224171 | ||||||||
\(724\) | −11.7004 | −0.434843 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −1.66419 | −0.0617640 | ||||||||
\(727\) | 25.3762 | 0.941153 | 0.470576 | − | 0.882359i | \(-0.344046\pi\) | ||||
0.470576 | + | 0.882359i | \(0.344046\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −20.7796 | −0.769616 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 7.29958 | 0.269985 | ||||||||
\(732\) | −1.37736 | −0.0509087 | ||||||||
\(733\) | 10.6692 | 0.394074 | 0.197037 | − | 0.980396i | \(-0.436868\pi\) | ||||
0.197037 | + | 0.980396i | \(0.436868\pi\) | |||||||
\(734\) | 39.6952 | 1.46517 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 1.11018 | 0.0409218 | ||||||||
\(737\) | −17.0923 | −0.629605 | ||||||||
\(738\) | −0.617344 | −0.0227247 | ||||||||
\(739\) | 1.41503 | 0.0520526 | 0.0260263 | − | 0.999661i | \(-0.491715\pi\) | ||||
0.0260263 | + | 0.999661i | \(0.491715\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 5.84695 | 0.214648 | ||||||||
\(743\) | 29.8777 | 1.09611 | 0.548053 | − | 0.836443i | \(-0.315369\pi\) | ||||
0.548053 | + | 0.836443i | \(0.315369\pi\) | |||||||
\(744\) | −1.25293 | −0.0459348 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 40.9370 | 1.49881 | ||||||||
\(747\) | 22.5730 | 0.825903 | ||||||||
\(748\) | −12.4844 | −0.456476 | ||||||||
\(749\) | −35.8809 | −1.31106 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −19.9858 | −0.729293 | −0.364646 | − | 0.931146i | \(-0.618810\pi\) | ||||
−0.364646 | + | 0.931146i | \(0.618810\pi\) | |||||||
\(752\) | 30.3474 | 1.10666 | ||||||||
\(753\) | 3.20938 | 0.116956 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −2.43126 | −0.0884239 | ||||||||
\(757\) | −17.0923 | −0.621232 | −0.310616 | − | 0.950535i | \(-0.600535\pi\) | ||||
−0.310616 | + | 0.950535i | \(0.600535\pi\) | |||||||
\(758\) | −20.6649 | −0.750584 | ||||||||
\(759\) | 0.462218 | 0.0167775 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 42.2240 | 1.53062 | 0.765310 | − | 0.643662i | \(-0.222586\pi\) | ||||
0.765310 | + | 0.643662i | \(0.222586\pi\) | |||||||
\(762\) | 6.84552 | 0.247987 | ||||||||
\(763\) | 11.6939 | 0.423347 | ||||||||
\(764\) | −0.907659 | −0.0328380 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 2.07395 | 0.0749350 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | −4.42107 | −0.159531 | ||||||||
\(769\) | 23.7655 | 0.857004 | 0.428502 | − | 0.903541i | \(-0.359041\pi\) | ||||
0.428502 | + | 0.903541i | \(0.359041\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 3.75814 | 0.135346 | ||||||||
\(772\) | 12.5149 | 0.450422 | ||||||||
\(773\) | 0.284086 | 0.0102179 | 0.00510894 | − | 0.999987i | \(-0.498374\pi\) | ||||
0.00510894 | + | 0.999987i | \(0.498374\pi\) | |||||||
\(774\) | −4.58132 | −0.164672 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 17.8557 | 0.640984 | ||||||||
\(777\) | 3.81739 | 0.136948 | ||||||||
\(778\) | −26.1730 | −0.938349 | ||||||||
\(779\) | 1.06138 | 0.0380278 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −7.29958 | −0.261199 | ||||||||
\(782\) | −2.23325 | −0.0798610 | ||||||||
\(783\) | −6.08867 | −0.217591 | ||||||||
\(784\) | 7.11910 | 0.254254 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −4.09761 | −0.146157 | ||||||||
\(787\) | −24.1341 | −0.860289 | −0.430145 | − | 0.902760i | \(-0.641537\pi\) | ||||
−0.430145 | + | 0.902760i | \(0.641537\pi\) | |||||||
\(788\) | −5.46381 | −0.194640 | ||||||||
\(789\) | −4.63849 | −0.165135 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 9.66054 | 0.343489 | ||||||||
\(792\) | 34.3853 | 1.22183 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | −26.7529 | −0.949424 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 10.2728 | 0.364110 | ||||||||
\(797\) | −34.3442 | −1.21653 | −0.608267 | − | 0.793732i | \(-0.708135\pi\) | ||||
−0.608267 | + | 0.793732i | \(0.708135\pi\) | |||||||
\(798\) | −4.89075 | −0.173131 | ||||||||
\(799\) | 66.9317 | 2.36787 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 35.2676 | 1.24612 | ||||||||
\(802\) | −4.39797 | −0.155298 | ||||||||
\(803\) | 34.3853 | 1.21343 | ||||||||
\(804\) | −0.897129 | −0.0316393 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 1.26329 | 0.0444698 | ||||||||
\(808\) | −18.2753 | −0.642924 | ||||||||
\(809\) | −47.6862 | −1.67656 | −0.838279 | − | 0.545241i | \(-0.816438\pi\) | ||||
−0.838279 | + | 0.545241i | \(0.816438\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −24.5992 | −0.863793 | −0.431897 | − | 0.901923i | \(-0.642155\pi\) | ||||
−0.431897 | + | 0.901923i | \(0.642155\pi\) | |||||||
\(812\) | 3.59377 | 0.126117 | ||||||||
\(813\) | −7.59368 | −0.266322 | ||||||||
\(814\) | −25.1138 | −0.880239 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 4.64796 | 0.162711 | ||||||||
\(817\) | 7.87651 | 0.275564 | ||||||||
\(818\) | −16.0097 | −0.559765 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −17.2996 | −0.603759 | −0.301880 | − | 0.953346i | \(-0.597614\pi\) | ||||
−0.301880 | + | 0.953346i | \(0.597614\pi\) | |||||||
\(822\) | 0.810450 | 0.0282677 | ||||||||
\(823\) | −32.5625 | −1.13506 | −0.567529 | − | 0.823353i | \(-0.692101\pi\) | ||||
−0.567529 | + | 0.823353i | \(0.692101\pi\) | |||||||
\(824\) | −19.7869 | −0.689311 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 17.0162 | 0.592070 | ||||||||
\(827\) | 15.4702 | 0.537951 | 0.268976 | − | 0.963147i | \(-0.413315\pi\) | ||||
0.268976 | + | 0.963147i | \(0.413315\pi\) | |||||||
\(828\) | −0.586832 | −0.0203938 | ||||||||
\(829\) | −14.5236 | −0.504425 | −0.252213 | − | 0.967672i | \(-0.581158\pi\) | ||||
−0.252213 | + | 0.967672i | \(0.581158\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 3.41503 | 0.118466 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 15.7013 | 0.544018 | ||||||||
\(834\) | −3.56509 | −0.123449 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −13.4711 | −0.465909 | ||||||||
\(837\) | 2.39585 | 0.0828127 | ||||||||
\(838\) | −19.9747 | −0.690015 | ||||||||
\(839\) | −0.815866 | −0.0281668 | −0.0140834 | − | 0.999901i | \(-0.504483\pi\) | ||||
−0.0140834 | + | 0.999901i | \(0.504483\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −20.0000 | −0.689655 | ||||||||
\(842\) | 20.3049 | 0.699753 | ||||||||
\(843\) | −1.40162 | −0.0482744 | ||||||||
\(844\) | 4.29797 | 0.147942 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −42.0073 | −1.44424 | ||||||||
\(847\) | −8.24280 | −0.283226 | ||||||||
\(848\) | −5.99587 | −0.205899 | ||||||||
\(849\) | −2.10126 | −0.0721151 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 1.88090 | 0.0644764 | ||||||||
\(852\) | −0.383134 | −0.0131260 | ||||||||
\(853\) | −20.0856 | −0.687719 | −0.343859 | − | 0.939021i | \(-0.611734\pi\) | ||||
−0.343859 | + | 0.939021i | \(0.611734\pi\) | |||||||
\(854\) | 16.2943 | 0.557580 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 54.3719 | 1.85839 | ||||||||
\(857\) | 40.7886 | 1.39331 | 0.696656 | − | 0.717406i | \(-0.254671\pi\) | ||||
0.696656 | + | 0.717406i | \(0.254671\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −40.1301 | −1.36922 | −0.684610 | − | 0.728909i | \(-0.740028\pi\) | ||||
−0.684610 | + | 0.728909i | \(0.740028\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0.126411 | 0.00430808 | ||||||||
\(862\) | 11.4703 | 0.390679 | ||||||||
\(863\) | 20.8275 | 0.708977 | 0.354489 | − | 0.935060i | \(-0.384655\pi\) | ||||
0.354489 | + | 0.935060i | \(0.384655\pi\) | |||||||
\(864\) | 6.52886 | 0.222116 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −29.4134 | −0.999509 | ||||||||
\(867\) | 4.38430 | 0.148899 | ||||||||
\(868\) | −1.41412 | −0.0479985 | ||||||||
\(869\) | −43.3903 | −1.47192 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | −17.7203 | −0.600084 | ||||||||
\(873\) | −16.7261 | −0.566091 | ||||||||
\(874\) | −2.40976 | −0.0815114 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 1.80479 | 0.0609782 | ||||||||
\(877\) | −46.5944 | −1.57338 | −0.786691 | − | 0.617347i | \(-0.788207\pi\) | ||||
−0.786691 | + | 0.617347i | \(0.788207\pi\) | |||||||
\(878\) | −8.38421 | −0.282953 | ||||||||
\(879\) | 3.37935 | 0.113982 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 23.8447 | 0.803347 | 0.401674 | − | 0.915783i | \(-0.368429\pi\) | ||||
0.401674 | + | 0.915783i | \(0.368429\pi\) | |||||||
\(882\) | −9.85437 | −0.331814 | ||||||||
\(883\) | −37.2496 | −1.25355 | −0.626774 | − | 0.779201i | \(-0.715625\pi\) | ||||
−0.626774 | + | 0.779201i | \(0.715625\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 45.4082 | 1.52552 | ||||||||
\(887\) | 28.5795 | 0.959605 | 0.479802 | − | 0.877377i | \(-0.340708\pi\) | ||||
0.479802 | + | 0.877377i | \(0.340708\pi\) | |||||||
\(888\) | −5.78466 | −0.194121 | ||||||||
\(889\) | 33.9060 | 1.13717 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −30.8232 | −1.03262 | ||||||||
\(892\) | −11.4902 | −0.384720 | ||||||||
\(893\) | 72.2217 | 2.41681 | ||||||||
\(894\) | 9.13899 | 0.305653 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 8.05611 | 0.269136 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −14.8180 | −0.494483 | ||||||||
\(899\) | −3.54144 | −0.118114 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −13.2240 | −0.440556 | ||||||||
\(902\) | −0.831632 | −0.0276903 | ||||||||
\(903\) | 0.938099 | 0.0312180 | ||||||||
\(904\) | −14.6390 | −0.486887 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −7.85209 | −0.260868 | ||||||||
\(907\) | 6.41386 | 0.212969 | 0.106484 | − | 0.994314i | \(-0.466041\pi\) | ||||
0.106484 | + | 0.994314i | \(0.466041\pi\) | |||||||
\(908\) | 2.84001 | 0.0942489 | ||||||||
\(909\) | 17.1191 | 0.567805 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 22.2204 | 0.736193 | 0.368097 | − | 0.929788i | \(-0.380010\pi\) | ||||
0.368097 | + | 0.929788i | \(0.380010\pi\) | |||||||
\(912\) | 5.01532 | 0.166074 | ||||||||
\(913\) | 30.4084 | 1.00637 | ||||||||
\(914\) | 9.77437 | 0.323308 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0.899287 | 0.0297133 | ||||||||
\(917\) | −20.2956 | −0.670219 | ||||||||
\(918\) | −13.1335 | −0.433472 | ||||||||
\(919\) | 26.1264 | 0.861831 | 0.430915 | − | 0.902392i | \(-0.358191\pi\) | ||||
0.430915 | + | 0.902392i | \(0.358191\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 7.62851 | 0.251368 | ||||||||
\(922\) | −5.39220 | −0.177583 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | −1.60442 | −0.0527817 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −2.36096 | −0.0775859 | ||||||||
\(927\) | 18.5351 | 0.608772 | ||||||||
\(928\) | −9.65067 | −0.316799 | ||||||||
\(929\) | 23.9423 | 0.785521 | 0.392760 | − | 0.919641i | \(-0.371520\pi\) | ||||
0.392760 | + | 0.919641i | \(0.371520\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 16.9423 | 0.555261 | ||||||||
\(932\) | 8.24280 | 0.270002 | ||||||||
\(933\) | 2.63631 | 0.0863089 | ||||||||
\(934\) | 38.9496 | 1.27447 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −18.5046 | −0.604518 | −0.302259 | − | 0.953226i | \(-0.597741\pi\) | ||||
−0.302259 | + | 0.953226i | \(0.597741\pi\) | |||||||
\(938\) | 10.6131 | 0.346531 | ||||||||
\(939\) | 9.02204 | 0.294423 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 14.3788 | 0.468735 | 0.234368 | − | 0.972148i | \(-0.424698\pi\) | ||||
0.234368 | + | 0.972148i | \(0.424698\pi\) | |||||||
\(942\) | 2.54160 | 0.0828098 | ||||||||
\(943\) | 0.0622851 | 0.00202828 | ||||||||
\(944\) | −17.4496 | −0.567938 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −6.17156 | −0.200655 | ||||||||
\(947\) | −58.3188 | −1.89511 | −0.947554 | − | 0.319596i | \(-0.896453\pi\) | ||||
−0.947554 | + | 0.319596i | \(0.896453\pi\) | |||||||
\(948\) | −2.27744 | −0.0739677 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −4.08708 | −0.132533 | ||||||||
\(952\) | 34.0190 | 1.10256 | ||||||||
\(953\) | −13.7995 | −0.447010 | −0.223505 | − | 0.974703i | \(-0.571750\pi\) | ||||
−0.223505 | + | 0.974703i | \(0.571750\pi\) | |||||||
\(954\) | 8.29958 | 0.268709 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 2.36096 | 0.0763588 | ||||||||
\(957\) | −4.01801 | −0.129884 | ||||||||
\(958\) | −36.5762 | −1.18172 | ||||||||
\(959\) | 4.01419 | 0.129625 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −29.6065 | −0.955047 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −50.9319 | −1.64126 | ||||||||
\(964\) | −10.3090 | −0.332032 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −0.287005 | −0.00923422 | ||||||||
\(967\) | −30.3474 | −0.975906 | −0.487953 | − | 0.872870i | \(-0.662256\pi\) | ||||
−0.487953 | + | 0.872870i | \(0.662256\pi\) | |||||||
\(968\) | 12.4907 | 0.401466 | ||||||||
\(969\) | 11.0614 | 0.355343 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 44.1013 | 1.41528 | 0.707638 | − | 0.706575i | \(-0.249761\pi\) | ||||
0.707638 | + | 0.706575i | \(0.249761\pi\) | |||||||
\(972\) | −5.21160 | −0.167162 | ||||||||
\(973\) | −17.6580 | −0.566089 | ||||||||
\(974\) | −26.5074 | −0.849351 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −16.7093 | −0.534853 | ||||||||
\(977\) | 22.3220 | 0.714143 | 0.357071 | − | 0.934077i | \(-0.383775\pi\) | ||||
0.357071 | + | 0.934077i | \(0.383775\pi\) | |||||||
\(978\) | 4.89075 | 0.156389 | ||||||||
\(979\) | 47.5094 | 1.51841 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 16.5992 | 0.529970 | ||||||||
\(982\) | −12.6838 | −0.404756 | ||||||||
\(983\) | −4.03793 | −0.128790 | −0.0643950 | − | 0.997924i | \(-0.520512\pi\) | ||||
−0.0643950 | + | 0.997924i | \(0.520512\pi\) | |||||||
\(984\) | −0.191556 | −0.00610659 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 19.4134 | 0.618249 | ||||||||
\(987\) | 8.60167 | 0.273794 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 0.462218 | 0.0146977 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 29.6500 | 0.941864 | 0.470932 | − | 0.882170i | \(-0.343918\pi\) | ||||
0.470932 | + | 0.882170i | \(0.343918\pi\) | |||||||
\(992\) | 3.79747 | 0.120570 | ||||||||
\(993\) | 4.38304 | 0.139092 | ||||||||
\(994\) | 4.53252 | 0.143763 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 1.59605 | 0.0505728 | ||||||||
\(997\) | 22.1762 | 0.702327 | 0.351164 | − | 0.936314i | \(-0.385786\pi\) | ||||
0.351164 | + | 0.936314i | \(0.385786\pi\) | |||||||
\(998\) | 22.3450 | 0.707320 | ||||||||
\(999\) | 11.0614 | 0.349967 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))