Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1014,2,Mod(1,1014)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1014, 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("1014.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1014 = 2 \cdot 3 \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1014.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: | \(8.09683076496\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{12})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - 3 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 78) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-1.73205\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1014.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −1.73205 | −0.774597 | −0.387298 | − | 0.921954i | \(-0.626592\pi\) | ||||
−0.387298 | + | 0.921954i | \(0.626592\pi\) | |||||||
\(6\) | 1.00000 | 0.408248 | ||||||||
\(7\) | 4.73205 | 1.78855 | 0.894274 | − | 0.447521i | \(-0.147693\pi\) | ||||
0.894274 | + | 0.447521i | \(0.147693\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 1.73205 | 0.547723 | ||||||||
\(11\) | 4.73205 | 1.42677 | 0.713384 | − | 0.700774i | \(-0.247162\pi\) | ||||
0.713384 | + | 0.700774i | \(0.247162\pi\) | |||||||
\(12\) | −1.00000 | −0.288675 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | −4.73205 | −1.26469 | ||||||||
\(15\) | 1.73205 | 0.447214 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −5.19615 | −1.26025 | −0.630126 | − | 0.776493i | \(-0.716997\pi\) | ||||
−0.630126 | + | 0.776493i | \(0.716997\pi\) | |||||||
\(18\) | −1.00000 | −0.235702 | ||||||||
\(19\) | 1.26795 | 0.290887 | 0.145444 | − | 0.989367i | \(-0.453539\pi\) | ||||
0.145444 | + | 0.989367i | \(0.453539\pi\) | |||||||
\(20\) | −1.73205 | −0.387298 | ||||||||
\(21\) | −4.73205 | −1.03262 | ||||||||
\(22\) | −4.73205 | −1.00888 | ||||||||
\(23\) | 2.19615 | 0.457929 | 0.228965 | − | 0.973435i | \(-0.426466\pi\) | ||||
0.228965 | + | 0.973435i | \(0.426466\pi\) | |||||||
\(24\) | 1.00000 | 0.204124 | ||||||||
\(25\) | −2.00000 | −0.400000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 4.73205 | 0.894274 | ||||||||
\(29\) | −3.00000 | −0.557086 | −0.278543 | − | 0.960424i | \(-0.589851\pi\) | ||||
−0.278543 | + | 0.960424i | \(0.589851\pi\) | |||||||
\(30\) | −1.73205 | −0.316228 | ||||||||
\(31\) | 2.53590 | 0.455461 | 0.227730 | − | 0.973724i | \(-0.426870\pi\) | ||||
0.227730 | + | 0.973724i | \(0.426870\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | −4.73205 | −0.823744 | ||||||||
\(34\) | 5.19615 | 0.891133 | ||||||||
\(35\) | −8.19615 | −1.38540 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | 3.00000 | 0.493197 | 0.246598 | − | 0.969118i | \(-0.420687\pi\) | ||||
0.246598 | + | 0.969118i | \(0.420687\pi\) | |||||||
\(38\) | −1.26795 | −0.205689 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 1.73205 | 0.273861 | ||||||||
\(41\) | −0.464102 | −0.0724805 | −0.0362402 | − | 0.999343i | \(-0.511538\pi\) | ||||
−0.0362402 | + | 0.999343i | \(0.511538\pi\) | |||||||
\(42\) | 4.73205 | 0.730171 | ||||||||
\(43\) | 6.19615 | 0.944904 | 0.472452 | − | 0.881356i | \(-0.343369\pi\) | ||||
0.472452 | + | 0.881356i | \(0.343369\pi\) | |||||||
\(44\) | 4.73205 | 0.713384 | ||||||||
\(45\) | −1.73205 | −0.258199 | ||||||||
\(46\) | −2.19615 | −0.323805 | ||||||||
\(47\) | −1.26795 | −0.184949 | −0.0924747 | − | 0.995715i | \(-0.529478\pi\) | ||||
−0.0924747 | + | 0.995715i | \(0.529478\pi\) | |||||||
\(48\) | −1.00000 | −0.144338 | ||||||||
\(49\) | 15.3923 | 2.19890 | ||||||||
\(50\) | 2.00000 | 0.282843 | ||||||||
\(51\) | 5.19615 | 0.727607 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 3.00000 | 0.412082 | 0.206041 | − | 0.978543i | \(-0.433942\pi\) | ||||
0.206041 | + | 0.978543i | \(0.433942\pi\) | |||||||
\(54\) | 1.00000 | 0.136083 | ||||||||
\(55\) | −8.19615 | −1.10517 | ||||||||
\(56\) | −4.73205 | −0.632347 | ||||||||
\(57\) | −1.26795 | −0.167944 | ||||||||
\(58\) | 3.00000 | 0.393919 | ||||||||
\(59\) | 13.8564 | 1.80395 | 0.901975 | − | 0.431788i | \(-0.142117\pi\) | ||||
0.901975 | + | 0.431788i | \(0.142117\pi\) | |||||||
\(60\) | 1.73205 | 0.223607 | ||||||||
\(61\) | 4.80385 | 0.615070 | 0.307535 | − | 0.951537i | \(-0.400496\pi\) | ||||
0.307535 | + | 0.951537i | \(0.400496\pi\) | |||||||
\(62\) | −2.53590 | −0.322059 | ||||||||
\(63\) | 4.73205 | 0.596182 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 4.73205 | 0.582475 | ||||||||
\(67\) | 10.7321 | 1.31113 | 0.655564 | − | 0.755139i | \(-0.272431\pi\) | ||||
0.655564 | + | 0.755139i | \(0.272431\pi\) | |||||||
\(68\) | −5.19615 | −0.630126 | ||||||||
\(69\) | −2.19615 | −0.264386 | ||||||||
\(70\) | 8.19615 | 0.979628 | ||||||||
\(71\) | 8.19615 | 0.972704 | 0.486352 | − | 0.873763i | \(-0.338327\pi\) | ||||
0.486352 | + | 0.873763i | \(0.338327\pi\) | |||||||
\(72\) | −1.00000 | −0.117851 | ||||||||
\(73\) | −12.1244 | −1.41905 | −0.709524 | − | 0.704681i | \(-0.751090\pi\) | ||||
−0.709524 | + | 0.704681i | \(0.751090\pi\) | |||||||
\(74\) | −3.00000 | −0.348743 | ||||||||
\(75\) | 2.00000 | 0.230940 | ||||||||
\(76\) | 1.26795 | 0.145444 | ||||||||
\(77\) | 22.3923 | 2.55184 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −12.3923 | −1.39424 | −0.697122 | − | 0.716953i | \(-0.745536\pi\) | ||||
−0.697122 | + | 0.716953i | \(0.745536\pi\) | |||||||
\(80\) | −1.73205 | −0.193649 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0.464102 | 0.0512514 | ||||||||
\(83\) | −11.6603 | −1.27988 | −0.639940 | − | 0.768425i | \(-0.721041\pi\) | ||||
−0.639940 | + | 0.768425i | \(0.721041\pi\) | |||||||
\(84\) | −4.73205 | −0.516309 | ||||||||
\(85\) | 9.00000 | 0.976187 | ||||||||
\(86\) | −6.19615 | −0.668148 | ||||||||
\(87\) | 3.00000 | 0.321634 | ||||||||
\(88\) | −4.73205 | −0.504438 | ||||||||
\(89\) | 2.53590 | 0.268805 | 0.134402 | − | 0.990927i | \(-0.457089\pi\) | ||||
0.134402 | + | 0.990927i | \(0.457089\pi\) | |||||||
\(90\) | 1.73205 | 0.182574 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 2.19615 | 0.228965 | ||||||||
\(93\) | −2.53590 | −0.262960 | ||||||||
\(94\) | 1.26795 | 0.130779 | ||||||||
\(95\) | −2.19615 | −0.225320 | ||||||||
\(96\) | 1.00000 | 0.102062 | ||||||||
\(97\) | 6.00000 | 0.609208 | 0.304604 | − | 0.952479i | \(-0.401476\pi\) | ||||
0.304604 | + | 0.952479i | \(0.401476\pi\) | |||||||
\(98\) | −15.3923 | −1.55486 | ||||||||
\(99\) | 4.73205 | 0.475589 | ||||||||
\(100\) | −2.00000 | −0.200000 | ||||||||
\(101\) | −1.39230 | −0.138540 | −0.0692698 | − | 0.997598i | \(-0.522067\pi\) | ||||
−0.0692698 | + | 0.997598i | \(0.522067\pi\) | |||||||
\(102\) | −5.19615 | −0.514496 | ||||||||
\(103\) | −4.19615 | −0.413459 | −0.206730 | − | 0.978398i | \(-0.566282\pi\) | ||||
−0.206730 | + | 0.978398i | \(0.566282\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 8.19615 | 0.799863 | ||||||||
\(106\) | −3.00000 | −0.291386 | ||||||||
\(107\) | 8.19615 | 0.792352 | 0.396176 | − | 0.918175i | \(-0.370337\pi\) | ||||
0.396176 | + | 0.918175i | \(0.370337\pi\) | |||||||
\(108\) | −1.00000 | −0.0962250 | ||||||||
\(109\) | 16.3923 | 1.57010 | 0.785049 | − | 0.619434i | \(-0.212638\pi\) | ||||
0.785049 | + | 0.619434i | \(0.212638\pi\) | |||||||
\(110\) | 8.19615 | 0.781472 | ||||||||
\(111\) | −3.00000 | −0.284747 | ||||||||
\(112\) | 4.73205 | 0.447137 | ||||||||
\(113\) | 11.1962 | 1.05325 | 0.526623 | − | 0.850099i | \(-0.323458\pi\) | ||||
0.526623 | + | 0.850099i | \(0.323458\pi\) | |||||||
\(114\) | 1.26795 | 0.118754 | ||||||||
\(115\) | −3.80385 | −0.354711 | ||||||||
\(116\) | −3.00000 | −0.278543 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −13.8564 | −1.27559 | ||||||||
\(119\) | −24.5885 | −2.25402 | ||||||||
\(120\) | −1.73205 | −0.158114 | ||||||||
\(121\) | 11.3923 | 1.03566 | ||||||||
\(122\) | −4.80385 | −0.434920 | ||||||||
\(123\) | 0.464102 | 0.0418466 | ||||||||
\(124\) | 2.53590 | 0.227730 | ||||||||
\(125\) | 12.1244 | 1.08444 | ||||||||
\(126\) | −4.73205 | −0.421565 | ||||||||
\(127\) | −4.00000 | −0.354943 | −0.177471 | − | 0.984126i | \(-0.556792\pi\) | ||||
−0.177471 | + | 0.984126i | \(0.556792\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | −6.19615 | −0.545541 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 16.3923 | 1.43220 | 0.716101 | − | 0.697997i | \(-0.245925\pi\) | ||||
0.716101 | + | 0.697997i | \(0.245925\pi\) | |||||||
\(132\) | −4.73205 | −0.411872 | ||||||||
\(133\) | 6.00000 | 0.520266 | ||||||||
\(134\) | −10.7321 | −0.927108 | ||||||||
\(135\) | 1.73205 | 0.149071 | ||||||||
\(136\) | 5.19615 | 0.445566 | ||||||||
\(137\) | −9.00000 | −0.768922 | −0.384461 | − | 0.923141i | \(-0.625613\pi\) | ||||
−0.384461 | + | 0.923141i | \(0.625613\pi\) | |||||||
\(138\) | 2.19615 | 0.186949 | ||||||||
\(139\) | −4.00000 | −0.339276 | −0.169638 | − | 0.985506i | \(-0.554260\pi\) | ||||
−0.169638 | + | 0.985506i | \(0.554260\pi\) | |||||||
\(140\) | −8.19615 | −0.692701 | ||||||||
\(141\) | 1.26795 | 0.106781 | ||||||||
\(142\) | −8.19615 | −0.687806 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | 5.19615 | 0.431517 | ||||||||
\(146\) | 12.1244 | 1.00342 | ||||||||
\(147\) | −15.3923 | −1.26954 | ||||||||
\(148\) | 3.00000 | 0.246598 | ||||||||
\(149\) | −18.1244 | −1.48481 | −0.742403 | − | 0.669954i | \(-0.766314\pi\) | ||||
−0.742403 | + | 0.669954i | \(0.766314\pi\) | |||||||
\(150\) | −2.00000 | −0.163299 | ||||||||
\(151\) | 7.26795 | 0.591457 | 0.295729 | − | 0.955272i | \(-0.404438\pi\) | ||||
0.295729 | + | 0.955272i | \(0.404438\pi\) | |||||||
\(152\) | −1.26795 | −0.102844 | ||||||||
\(153\) | −5.19615 | −0.420084 | ||||||||
\(154\) | −22.3923 | −1.80442 | ||||||||
\(155\) | −4.39230 | −0.352798 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −3.19615 | −0.255081 | −0.127540 | − | 0.991833i | \(-0.540708\pi\) | ||||
−0.127540 | + | 0.991833i | \(0.540708\pi\) | |||||||
\(158\) | 12.3923 | 0.985879 | ||||||||
\(159\) | −3.00000 | −0.237915 | ||||||||
\(160\) | 1.73205 | 0.136931 | ||||||||
\(161\) | 10.3923 | 0.819028 | ||||||||
\(162\) | −1.00000 | −0.0785674 | ||||||||
\(163\) | 9.46410 | 0.741286 | 0.370643 | − | 0.928775i | \(-0.379137\pi\) | ||||
0.370643 | + | 0.928775i | \(0.379137\pi\) | |||||||
\(164\) | −0.464102 | −0.0362402 | ||||||||
\(165\) | 8.19615 | 0.638070 | ||||||||
\(166\) | 11.6603 | 0.905011 | ||||||||
\(167\) | −2.53590 | −0.196234 | −0.0981169 | − | 0.995175i | \(-0.531282\pi\) | ||||
−0.0981169 | + | 0.995175i | \(0.531282\pi\) | |||||||
\(168\) | 4.73205 | 0.365086 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | −9.00000 | −0.690268 | ||||||||
\(171\) | 1.26795 | 0.0969625 | ||||||||
\(172\) | 6.19615 | 0.472452 | ||||||||
\(173\) | 16.3923 | 1.24628 | 0.623142 | − | 0.782109i | \(-0.285856\pi\) | ||||
0.623142 | + | 0.782109i | \(0.285856\pi\) | |||||||
\(174\) | −3.00000 | −0.227429 | ||||||||
\(175\) | −9.46410 | −0.715419 | ||||||||
\(176\) | 4.73205 | 0.356692 | ||||||||
\(177\) | −13.8564 | −1.04151 | ||||||||
\(178\) | −2.53590 | −0.190074 | ||||||||
\(179\) | −8.19615 | −0.612609 | −0.306305 | − | 0.951934i | \(-0.599093\pi\) | ||||
−0.306305 | + | 0.951934i | \(0.599093\pi\) | |||||||
\(180\) | −1.73205 | −0.129099 | ||||||||
\(181\) | −11.5885 | −0.861363 | −0.430682 | − | 0.902504i | \(-0.641727\pi\) | ||||
−0.430682 | + | 0.902504i | \(0.641727\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −4.80385 | −0.355111 | ||||||||
\(184\) | −2.19615 | −0.161903 | ||||||||
\(185\) | −5.19615 | −0.382029 | ||||||||
\(186\) | 2.53590 | 0.185941 | ||||||||
\(187\) | −24.5885 | −1.79809 | ||||||||
\(188\) | −1.26795 | −0.0924747 | ||||||||
\(189\) | −4.73205 | −0.344206 | ||||||||
\(190\) | 2.19615 | 0.159326 | ||||||||
\(191\) | 20.7846 | 1.50392 | 0.751961 | − | 0.659208i | \(-0.229108\pi\) | ||||
0.751961 | + | 0.659208i | \(0.229108\pi\) | |||||||
\(192\) | −1.00000 | −0.0721688 | ||||||||
\(193\) | −12.8038 | −0.921641 | −0.460821 | − | 0.887493i | \(-0.652445\pi\) | ||||
−0.460821 | + | 0.887493i | \(0.652445\pi\) | |||||||
\(194\) | −6.00000 | −0.430775 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 15.3923 | 1.09945 | ||||||||
\(197\) | 6.92820 | 0.493614 | 0.246807 | − | 0.969065i | \(-0.420619\pi\) | ||||
0.246807 | + | 0.969065i | \(0.420619\pi\) | |||||||
\(198\) | −4.73205 | −0.336292 | ||||||||
\(199\) | 8.58846 | 0.608820 | 0.304410 | − | 0.952541i | \(-0.401541\pi\) | ||||
0.304410 | + | 0.952541i | \(0.401541\pi\) | |||||||
\(200\) | 2.00000 | 0.141421 | ||||||||
\(201\) | −10.7321 | −0.756980 | ||||||||
\(202\) | 1.39230 | 0.0979622 | ||||||||
\(203\) | −14.1962 | −0.996375 | ||||||||
\(204\) | 5.19615 | 0.363803 | ||||||||
\(205\) | 0.803848 | 0.0561432 | ||||||||
\(206\) | 4.19615 | 0.292360 | ||||||||
\(207\) | 2.19615 | 0.152643 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 6.00000 | 0.415029 | ||||||||
\(210\) | −8.19615 | −0.565588 | ||||||||
\(211\) | −3.60770 | −0.248364 | −0.124182 | − | 0.992259i | \(-0.539631\pi\) | ||||
−0.124182 | + | 0.992259i | \(0.539631\pi\) | |||||||
\(212\) | 3.00000 | 0.206041 | ||||||||
\(213\) | −8.19615 | −0.561591 | ||||||||
\(214\) | −8.19615 | −0.560277 | ||||||||
\(215\) | −10.7321 | −0.731920 | ||||||||
\(216\) | 1.00000 | 0.0680414 | ||||||||
\(217\) | 12.0000 | 0.814613 | ||||||||
\(218\) | −16.3923 | −1.11023 | ||||||||
\(219\) | 12.1244 | 0.819288 | ||||||||
\(220\) | −8.19615 | −0.552584 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 3.00000 | 0.201347 | ||||||||
\(223\) | −18.9282 | −1.26753 | −0.633763 | − | 0.773527i | \(-0.718491\pi\) | ||||
−0.633763 | + | 0.773527i | \(0.718491\pi\) | |||||||
\(224\) | −4.73205 | −0.316173 | ||||||||
\(225\) | −2.00000 | −0.133333 | ||||||||
\(226\) | −11.1962 | −0.744757 | ||||||||
\(227\) | −9.80385 | −0.650704 | −0.325352 | − | 0.945593i | \(-0.605483\pi\) | ||||
−0.325352 | + | 0.945593i | \(0.605483\pi\) | |||||||
\(228\) | −1.26795 | −0.0839720 | ||||||||
\(229\) | 19.8564 | 1.31215 | 0.656074 | − | 0.754696i | \(-0.272216\pi\) | ||||
0.656074 | + | 0.754696i | \(0.272216\pi\) | |||||||
\(230\) | 3.80385 | 0.250818 | ||||||||
\(231\) | −22.3923 | −1.47331 | ||||||||
\(232\) | 3.00000 | 0.196960 | ||||||||
\(233\) | −18.0000 | −1.17922 | −0.589610 | − | 0.807688i | \(-0.700718\pi\) | ||||
−0.589610 | + | 0.807688i | \(0.700718\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 2.19615 | 0.143261 | ||||||||
\(236\) | 13.8564 | 0.901975 | ||||||||
\(237\) | 12.3923 | 0.804967 | ||||||||
\(238\) | 24.5885 | 1.59383 | ||||||||
\(239\) | −24.5885 | −1.59050 | −0.795248 | − | 0.606285i | \(-0.792659\pi\) | ||||
−0.795248 | + | 0.606285i | \(0.792659\pi\) | |||||||
\(240\) | 1.73205 | 0.111803 | ||||||||
\(241\) | 0.803848 | 0.0517804 | 0.0258902 | − | 0.999665i | \(-0.491758\pi\) | ||||
0.0258902 | + | 0.999665i | \(0.491758\pi\) | |||||||
\(242\) | −11.3923 | −0.732325 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 4.80385 | 0.307535 | ||||||||
\(245\) | −26.6603 | −1.70326 | ||||||||
\(246\) | −0.464102 | −0.0295900 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | −2.53590 | −0.161030 | ||||||||
\(249\) | 11.6603 | 0.738939 | ||||||||
\(250\) | −12.1244 | −0.766812 | ||||||||
\(251\) | −4.39230 | −0.277240 | −0.138620 | − | 0.990346i | \(-0.544267\pi\) | ||||
−0.138620 | + | 0.990346i | \(0.544267\pi\) | |||||||
\(252\) | 4.73205 | 0.298091 | ||||||||
\(253\) | 10.3923 | 0.653359 | ||||||||
\(254\) | 4.00000 | 0.250982 | ||||||||
\(255\) | −9.00000 | −0.563602 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 12.8038 | 0.798682 | 0.399341 | − | 0.916802i | \(-0.369239\pi\) | ||||
0.399341 | + | 0.916802i | \(0.369239\pi\) | |||||||
\(258\) | 6.19615 | 0.385756 | ||||||||
\(259\) | 14.1962 | 0.882106 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −3.00000 | −0.185695 | ||||||||
\(262\) | −16.3923 | −1.01272 | ||||||||
\(263\) | −2.19615 | −0.135421 | −0.0677103 | − | 0.997705i | \(-0.521569\pi\) | ||||
−0.0677103 | + | 0.997705i | \(0.521569\pi\) | |||||||
\(264\) | 4.73205 | 0.291238 | ||||||||
\(265\) | −5.19615 | −0.319197 | ||||||||
\(266\) | −6.00000 | −0.367884 | ||||||||
\(267\) | −2.53590 | −0.155194 | ||||||||
\(268\) | 10.7321 | 0.655564 | ||||||||
\(269\) | −28.3923 | −1.73111 | −0.865555 | − | 0.500814i | \(-0.833034\pi\) | ||||
−0.865555 | + | 0.500814i | \(0.833034\pi\) | |||||||
\(270\) | −1.73205 | −0.105409 | ||||||||
\(271\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(272\) | −5.19615 | −0.315063 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 9.00000 | 0.543710 | ||||||||
\(275\) | −9.46410 | −0.570707 | ||||||||
\(276\) | −2.19615 | −0.132193 | ||||||||
\(277\) | 15.1962 | 0.913048 | 0.456524 | − | 0.889711i | \(-0.349094\pi\) | ||||
0.456524 | + | 0.889711i | \(0.349094\pi\) | |||||||
\(278\) | 4.00000 | 0.239904 | ||||||||
\(279\) | 2.53590 | 0.151820 | ||||||||
\(280\) | 8.19615 | 0.489814 | ||||||||
\(281\) | 24.4641 | 1.45941 | 0.729703 | − | 0.683764i | \(-0.239658\pi\) | ||||
0.729703 | + | 0.683764i | \(0.239658\pi\) | |||||||
\(282\) | −1.26795 | −0.0755053 | ||||||||
\(283\) | −30.1962 | −1.79497 | −0.897487 | − | 0.441040i | \(-0.854610\pi\) | ||||
−0.897487 | + | 0.441040i | \(0.854610\pi\) | |||||||
\(284\) | 8.19615 | 0.486352 | ||||||||
\(285\) | 2.19615 | 0.130089 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −2.19615 | −0.129635 | ||||||||
\(288\) | −1.00000 | −0.0589256 | ||||||||
\(289\) | 10.0000 | 0.588235 | ||||||||
\(290\) | −5.19615 | −0.305129 | ||||||||
\(291\) | −6.00000 | −0.351726 | ||||||||
\(292\) | −12.1244 | −0.709524 | ||||||||
\(293\) | −14.6603 | −0.856461 | −0.428231 | − | 0.903669i | \(-0.640863\pi\) | ||||
−0.428231 | + | 0.903669i | \(0.640863\pi\) | |||||||
\(294\) | 15.3923 | 0.897697 | ||||||||
\(295\) | −24.0000 | −1.39733 | ||||||||
\(296\) | −3.00000 | −0.174371 | ||||||||
\(297\) | −4.73205 | −0.274581 | ||||||||
\(298\) | 18.1244 | 1.04992 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 2.00000 | 0.115470 | ||||||||
\(301\) | 29.3205 | 1.69001 | ||||||||
\(302\) | −7.26795 | −0.418223 | ||||||||
\(303\) | 1.39230 | 0.0799858 | ||||||||
\(304\) | 1.26795 | 0.0727219 | ||||||||
\(305\) | −8.32051 | −0.476431 | ||||||||
\(306\) | 5.19615 | 0.297044 | ||||||||
\(307\) | 10.7321 | 0.612510 | 0.306255 | − | 0.951949i | \(-0.400924\pi\) | ||||
0.306255 | + | 0.951949i | \(0.400924\pi\) | |||||||
\(308\) | 22.3923 | 1.27592 | ||||||||
\(309\) | 4.19615 | 0.238711 | ||||||||
\(310\) | 4.39230 | 0.249466 | ||||||||
\(311\) | 2.19615 | 0.124532 | 0.0622662 | − | 0.998060i | \(-0.480167\pi\) | ||||
0.0622662 | + | 0.998060i | \(0.480167\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −24.3923 | −1.37873 | −0.689367 | − | 0.724412i | \(-0.742111\pi\) | ||||
−0.689367 | + | 0.724412i | \(0.742111\pi\) | |||||||
\(314\) | 3.19615 | 0.180369 | ||||||||
\(315\) | −8.19615 | −0.461801 | ||||||||
\(316\) | −12.3923 | −0.697122 | ||||||||
\(317\) | 6.12436 | 0.343978 | 0.171989 | − | 0.985099i | \(-0.444981\pi\) | ||||
0.171989 | + | 0.985099i | \(0.444981\pi\) | |||||||
\(318\) | 3.00000 | 0.168232 | ||||||||
\(319\) | −14.1962 | −0.794832 | ||||||||
\(320\) | −1.73205 | −0.0968246 | ||||||||
\(321\) | −8.19615 | −0.457465 | ||||||||
\(322\) | −10.3923 | −0.579141 | ||||||||
\(323\) | −6.58846 | −0.366592 | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −9.46410 | −0.524168 | ||||||||
\(327\) | −16.3923 | −0.906497 | ||||||||
\(328\) | 0.464102 | 0.0256257 | ||||||||
\(329\) | −6.00000 | −0.330791 | ||||||||
\(330\) | −8.19615 | −0.451183 | ||||||||
\(331\) | 12.0000 | 0.659580 | 0.329790 | − | 0.944054i | \(-0.393022\pi\) | ||||
0.329790 | + | 0.944054i | \(0.393022\pi\) | |||||||
\(332\) | −11.6603 | −0.639940 | ||||||||
\(333\) | 3.00000 | 0.164399 | ||||||||
\(334\) | 2.53590 | 0.138758 | ||||||||
\(335\) | −18.5885 | −1.01560 | ||||||||
\(336\) | −4.73205 | −0.258155 | ||||||||
\(337\) | −31.0000 | −1.68868 | −0.844339 | − | 0.535810i | \(-0.820006\pi\) | ||||
−0.844339 | + | 0.535810i | \(0.820006\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −11.1962 | −0.608092 | ||||||||
\(340\) | 9.00000 | 0.488094 | ||||||||
\(341\) | 12.0000 | 0.649836 | ||||||||
\(342\) | −1.26795 | −0.0685628 | ||||||||
\(343\) | 39.7128 | 2.14429 | ||||||||
\(344\) | −6.19615 | −0.334074 | ||||||||
\(345\) | 3.80385 | 0.204792 | ||||||||
\(346\) | −16.3923 | −0.881256 | ||||||||
\(347\) | −12.5885 | −0.675784 | −0.337892 | − | 0.941185i | \(-0.609714\pi\) | ||||
−0.337892 | + | 0.941185i | \(0.609714\pi\) | |||||||
\(348\) | 3.00000 | 0.160817 | ||||||||
\(349\) | 2.53590 | 0.135744 | 0.0678718 | − | 0.997694i | \(-0.478379\pi\) | ||||
0.0678718 | + | 0.997694i | \(0.478379\pi\) | |||||||
\(350\) | 9.46410 | 0.505878 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −4.73205 | −0.252219 | ||||||||
\(353\) | 5.78461 | 0.307884 | 0.153942 | − | 0.988080i | \(-0.450803\pi\) | ||||
0.153942 | + | 0.988080i | \(0.450803\pi\) | |||||||
\(354\) | 13.8564 | 0.736460 | ||||||||
\(355\) | −14.1962 | −0.753454 | ||||||||
\(356\) | 2.53590 | 0.134402 | ||||||||
\(357\) | 24.5885 | 1.30136 | ||||||||
\(358\) | 8.19615 | 0.433180 | ||||||||
\(359\) | 22.0526 | 1.16389 | 0.581945 | − | 0.813228i | \(-0.302292\pi\) | ||||
0.581945 | + | 0.813228i | \(0.302292\pi\) | |||||||
\(360\) | 1.73205 | 0.0912871 | ||||||||
\(361\) | −17.3923 | −0.915384 | ||||||||
\(362\) | 11.5885 | 0.609076 | ||||||||
\(363\) | −11.3923 | −0.597941 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 21.0000 | 1.09919 | ||||||||
\(366\) | 4.80385 | 0.251101 | ||||||||
\(367\) | −24.1962 | −1.26303 | −0.631514 | − | 0.775364i | \(-0.717566\pi\) | ||||
−0.631514 | + | 0.775364i | \(0.717566\pi\) | |||||||
\(368\) | 2.19615 | 0.114482 | ||||||||
\(369\) | −0.464102 | −0.0241602 | ||||||||
\(370\) | 5.19615 | 0.270135 | ||||||||
\(371\) | 14.1962 | 0.737028 | ||||||||
\(372\) | −2.53590 | −0.131480 | ||||||||
\(373\) | 23.9808 | 1.24168 | 0.620838 | − | 0.783939i | \(-0.286792\pi\) | ||||
0.620838 | + | 0.783939i | \(0.286792\pi\) | |||||||
\(374\) | 24.5885 | 1.27144 | ||||||||
\(375\) | −12.1244 | −0.626099 | ||||||||
\(376\) | 1.26795 | 0.0653895 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 4.73205 | 0.243390 | ||||||||
\(379\) | −18.2487 | −0.937373 | −0.468687 | − | 0.883364i | \(-0.655273\pi\) | ||||
−0.468687 | + | 0.883364i | \(0.655273\pi\) | |||||||
\(380\) | −2.19615 | −0.112660 | ||||||||
\(381\) | 4.00000 | 0.204926 | ||||||||
\(382\) | −20.7846 | −1.06343 | ||||||||
\(383\) | 11.3205 | 0.578451 | 0.289225 | − | 0.957261i | \(-0.406602\pi\) | ||||
0.289225 | + | 0.957261i | \(0.406602\pi\) | |||||||
\(384\) | 1.00000 | 0.0510310 | ||||||||
\(385\) | −38.7846 | −1.97665 | ||||||||
\(386\) | 12.8038 | 0.651699 | ||||||||
\(387\) | 6.19615 | 0.314968 | ||||||||
\(388\) | 6.00000 | 0.304604 | ||||||||
\(389\) | −13.3923 | −0.679017 | −0.339508 | − | 0.940603i | \(-0.610261\pi\) | ||||
−0.339508 | + | 0.940603i | \(0.610261\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −11.4115 | −0.577107 | ||||||||
\(392\) | −15.3923 | −0.777429 | ||||||||
\(393\) | −16.3923 | −0.826882 | ||||||||
\(394\) | −6.92820 | −0.349038 | ||||||||
\(395\) | 21.4641 | 1.07998 | ||||||||
\(396\) | 4.73205 | 0.237795 | ||||||||
\(397\) | −16.3923 | −0.822706 | −0.411353 | − | 0.911476i | \(-0.634944\pi\) | ||||
−0.411353 | + | 0.911476i | \(0.634944\pi\) | |||||||
\(398\) | −8.58846 | −0.430500 | ||||||||
\(399\) | −6.00000 | −0.300376 | ||||||||
\(400\) | −2.00000 | −0.100000 | ||||||||
\(401\) | 21.0000 | 1.04869 | 0.524345 | − | 0.851506i | \(-0.324310\pi\) | ||||
0.524345 | + | 0.851506i | \(0.324310\pi\) | |||||||
\(402\) | 10.7321 | 0.535266 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | −1.39230 | −0.0692698 | ||||||||
\(405\) | −1.73205 | −0.0860663 | ||||||||
\(406\) | 14.1962 | 0.704543 | ||||||||
\(407\) | 14.1962 | 0.703677 | ||||||||
\(408\) | −5.19615 | −0.257248 | ||||||||
\(409\) | −3.33975 | −0.165140 | −0.0825699 | − | 0.996585i | \(-0.526313\pi\) | ||||
−0.0825699 | + | 0.996585i | \(0.526313\pi\) | |||||||
\(410\) | −0.803848 | −0.0396992 | ||||||||
\(411\) | 9.00000 | 0.443937 | ||||||||
\(412\) | −4.19615 | −0.206730 | ||||||||
\(413\) | 65.5692 | 3.22645 | ||||||||
\(414\) | −2.19615 | −0.107935 | ||||||||
\(415\) | 20.1962 | 0.991390 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 4.00000 | 0.195881 | ||||||||
\(418\) | −6.00000 | −0.293470 | ||||||||
\(419\) | 16.3923 | 0.800816 | 0.400408 | − | 0.916337i | \(-0.368868\pi\) | ||||
0.400408 | + | 0.916337i | \(0.368868\pi\) | |||||||
\(420\) | 8.19615 | 0.399931 | ||||||||
\(421\) | 0.464102 | 0.0226189 | 0.0113095 | − | 0.999936i | \(-0.496400\pi\) | ||||
0.0113095 | + | 0.999936i | \(0.496400\pi\) | |||||||
\(422\) | 3.60770 | 0.175620 | ||||||||
\(423\) | −1.26795 | −0.0616498 | ||||||||
\(424\) | −3.00000 | −0.145693 | ||||||||
\(425\) | 10.3923 | 0.504101 | ||||||||
\(426\) | 8.19615 | 0.397105 | ||||||||
\(427\) | 22.7321 | 1.10008 | ||||||||
\(428\) | 8.19615 | 0.396176 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 10.7321 | 0.517545 | ||||||||
\(431\) | 27.8038 | 1.33926 | 0.669632 | − | 0.742693i | \(-0.266452\pi\) | ||||
0.669632 | + | 0.742693i | \(0.266452\pi\) | |||||||
\(432\) | −1.00000 | −0.0481125 | ||||||||
\(433\) | −33.7846 | −1.62358 | −0.811792 | − | 0.583946i | \(-0.801508\pi\) | ||||
−0.811792 | + | 0.583946i | \(0.801508\pi\) | |||||||
\(434\) | −12.0000 | −0.576018 | ||||||||
\(435\) | −5.19615 | −0.249136 | ||||||||
\(436\) | 16.3923 | 0.785049 | ||||||||
\(437\) | 2.78461 | 0.133206 | ||||||||
\(438\) | −12.1244 | −0.579324 | ||||||||
\(439\) | 16.5885 | 0.791724 | 0.395862 | − | 0.918310i | \(-0.370446\pi\) | ||||
0.395862 | + | 0.918310i | \(0.370446\pi\) | |||||||
\(440\) | 8.19615 | 0.390736 | ||||||||
\(441\) | 15.3923 | 0.732967 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −4.39230 | −0.208685 | −0.104342 | − | 0.994541i | \(-0.533274\pi\) | ||||
−0.104342 | + | 0.994541i | \(0.533274\pi\) | |||||||
\(444\) | −3.00000 | −0.142374 | ||||||||
\(445\) | −4.39230 | −0.208215 | ||||||||
\(446\) | 18.9282 | 0.896276 | ||||||||
\(447\) | 18.1244 | 0.857253 | ||||||||
\(448\) | 4.73205 | 0.223568 | ||||||||
\(449\) | 33.4641 | 1.57927 | 0.789634 | − | 0.613578i | \(-0.210270\pi\) | ||||
0.789634 | + | 0.613578i | \(0.210270\pi\) | |||||||
\(450\) | 2.00000 | 0.0942809 | ||||||||
\(451\) | −2.19615 | −0.103413 | ||||||||
\(452\) | 11.1962 | 0.526623 | ||||||||
\(453\) | −7.26795 | −0.341478 | ||||||||
\(454\) | 9.80385 | 0.460117 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 1.26795 | 0.0593772 | ||||||||
\(457\) | 19.9808 | 0.934661 | 0.467330 | − | 0.884083i | \(-0.345216\pi\) | ||||
0.467330 | + | 0.884083i | \(0.345216\pi\) | |||||||
\(458\) | −19.8564 | −0.927829 | ||||||||
\(459\) | 5.19615 | 0.242536 | ||||||||
\(460\) | −3.80385 | −0.177355 | ||||||||
\(461\) | −19.9808 | −0.930597 | −0.465298 | − | 0.885154i | \(-0.654053\pi\) | ||||
−0.465298 | + | 0.885154i | \(0.654053\pi\) | |||||||
\(462\) | 22.3923 | 1.04178 | ||||||||
\(463\) | −26.1962 | −1.21744 | −0.608719 | − | 0.793386i | \(-0.708316\pi\) | ||||
−0.608719 | + | 0.793386i | \(0.708316\pi\) | |||||||
\(464\) | −3.00000 | −0.139272 | ||||||||
\(465\) | 4.39230 | 0.203688 | ||||||||
\(466\) | 18.0000 | 0.833834 | ||||||||
\(467\) | 36.5885 | 1.69311 | 0.846556 | − | 0.532300i | \(-0.178672\pi\) | ||||
0.846556 | + | 0.532300i | \(0.178672\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 50.7846 | 2.34502 | ||||||||
\(470\) | −2.19615 | −0.101301 | ||||||||
\(471\) | 3.19615 | 0.147271 | ||||||||
\(472\) | −13.8564 | −0.637793 | ||||||||
\(473\) | 29.3205 | 1.34816 | ||||||||
\(474\) | −12.3923 | −0.569197 | ||||||||
\(475\) | −2.53590 | −0.116355 | ||||||||
\(476\) | −24.5885 | −1.12701 | ||||||||
\(477\) | 3.00000 | 0.137361 | ||||||||
\(478\) | 24.5885 | 1.12465 | ||||||||
\(479\) | −35.3205 | −1.61384 | −0.806918 | − | 0.590664i | \(-0.798866\pi\) | ||||
−0.806918 | + | 0.590664i | \(0.798866\pi\) | |||||||
\(480\) | −1.73205 | −0.0790569 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | −0.803848 | −0.0366143 | ||||||||
\(483\) | −10.3923 | −0.472866 | ||||||||
\(484\) | 11.3923 | 0.517832 | ||||||||
\(485\) | −10.3923 | −0.471890 | ||||||||
\(486\) | 1.00000 | 0.0453609 | ||||||||
\(487\) | 9.12436 | 0.413464 | 0.206732 | − | 0.978398i | \(-0.433717\pi\) | ||||
0.206732 | + | 0.978398i | \(0.433717\pi\) | |||||||
\(488\) | −4.80385 | −0.217460 | ||||||||
\(489\) | −9.46410 | −0.427981 | ||||||||
\(490\) | 26.6603 | 1.20439 | ||||||||
\(491\) | 0.588457 | 0.0265567 | 0.0132784 | − | 0.999912i | \(-0.495773\pi\) | ||||
0.0132784 | + | 0.999912i | \(0.495773\pi\) | |||||||
\(492\) | 0.464102 | 0.0209233 | ||||||||
\(493\) | 15.5885 | 0.702069 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −8.19615 | −0.368390 | ||||||||
\(496\) | 2.53590 | 0.113865 | ||||||||
\(497\) | 38.7846 | 1.73973 | ||||||||
\(498\) | −11.6603 | −0.522508 | ||||||||
\(499\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(500\) | 12.1244 | 0.542218 | ||||||||
\(501\) | 2.53590 | 0.113296 | ||||||||
\(502\) | 4.39230 | 0.196038 | ||||||||
\(503\) | −18.5885 | −0.828818 | −0.414409 | − | 0.910091i | \(-0.636012\pi\) | ||||
−0.414409 | + | 0.910091i | \(0.636012\pi\) | |||||||
\(504\) | −4.73205 | −0.210782 | ||||||||
\(505\) | 2.41154 | 0.107312 | ||||||||
\(506\) | −10.3923 | −0.461994 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −4.00000 | −0.177471 | ||||||||
\(509\) | 9.33975 | 0.413977 | 0.206988 | − | 0.978343i | \(-0.433634\pi\) | ||||
0.206988 | + | 0.978343i | \(0.433634\pi\) | |||||||
\(510\) | 9.00000 | 0.398527 | ||||||||
\(511\) | −57.3731 | −2.53804 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | −1.26795 | −0.0559813 | ||||||||
\(514\) | −12.8038 | −0.564754 | ||||||||
\(515\) | 7.26795 | 0.320264 | ||||||||
\(516\) | −6.19615 | −0.272770 | ||||||||
\(517\) | −6.00000 | −0.263880 | ||||||||
\(518\) | −14.1962 | −0.623743 | ||||||||
\(519\) | −16.3923 | −0.719542 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −18.8038 | −0.823812 | −0.411906 | − | 0.911226i | \(-0.635137\pi\) | ||||
−0.411906 | + | 0.911226i | \(0.635137\pi\) | |||||||
\(522\) | 3.00000 | 0.131306 | ||||||||
\(523\) | 1.41154 | 0.0617225 | 0.0308612 | − | 0.999524i | \(-0.490175\pi\) | ||||
0.0308612 | + | 0.999524i | \(0.490175\pi\) | |||||||
\(524\) | 16.3923 | 0.716101 | ||||||||
\(525\) | 9.46410 | 0.413047 | ||||||||
\(526\) | 2.19615 | 0.0957568 | ||||||||
\(527\) | −13.1769 | −0.573995 | ||||||||
\(528\) | −4.73205 | −0.205936 | ||||||||
\(529\) | −18.1769 | −0.790301 | ||||||||
\(530\) | 5.19615 | 0.225706 | ||||||||
\(531\) | 13.8564 | 0.601317 | ||||||||
\(532\) | 6.00000 | 0.260133 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 2.53590 | 0.109739 | ||||||||
\(535\) | −14.1962 | −0.613753 | ||||||||
\(536\) | −10.7321 | −0.463554 | ||||||||
\(537\) | 8.19615 | 0.353690 | ||||||||
\(538\) | 28.3923 | 1.22408 | ||||||||
\(539\) | 72.8372 | 3.13732 | ||||||||
\(540\) | 1.73205 | 0.0745356 | ||||||||
\(541\) | 16.8564 | 0.724714 | 0.362357 | − | 0.932039i | \(-0.381972\pi\) | ||||
0.362357 | + | 0.932039i | \(0.381972\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 11.5885 | 0.497308 | ||||||||
\(544\) | 5.19615 | 0.222783 | ||||||||
\(545\) | −28.3923 | −1.21619 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −6.19615 | −0.264928 | −0.132464 | − | 0.991188i | \(-0.542289\pi\) | ||||
−0.132464 | + | 0.991188i | \(0.542289\pi\) | |||||||
\(548\) | −9.00000 | −0.384461 | ||||||||
\(549\) | 4.80385 | 0.205023 | ||||||||
\(550\) | 9.46410 | 0.403551 | ||||||||
\(551\) | −3.80385 | −0.162049 | ||||||||
\(552\) | 2.19615 | 0.0934745 | ||||||||
\(553\) | −58.6410 | −2.49367 | ||||||||
\(554\) | −15.1962 | −0.645623 | ||||||||
\(555\) | 5.19615 | 0.220564 | ||||||||
\(556\) | −4.00000 | −0.169638 | ||||||||
\(557\) | 22.2679 | 0.943523 | 0.471762 | − | 0.881726i | \(-0.343618\pi\) | ||||
0.471762 | + | 0.881726i | \(0.343618\pi\) | |||||||
\(558\) | −2.53590 | −0.107353 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | −8.19615 | −0.346351 | ||||||||
\(561\) | 24.5885 | 1.03813 | ||||||||
\(562\) | −24.4641 | −1.03196 | ||||||||
\(563\) | 8.78461 | 0.370227 | 0.185114 | − | 0.982717i | \(-0.440735\pi\) | ||||
0.185114 | + | 0.982717i | \(0.440735\pi\) | |||||||
\(564\) | 1.26795 | 0.0533903 | ||||||||
\(565\) | −19.3923 | −0.815840 | ||||||||
\(566\) | 30.1962 | 1.26924 | ||||||||
\(567\) | 4.73205 | 0.198727 | ||||||||
\(568\) | −8.19615 | −0.343903 | ||||||||
\(569\) | −32.7846 | −1.37440 | −0.687201 | − | 0.726467i | \(-0.741161\pi\) | ||||
−0.687201 | + | 0.726467i | \(0.741161\pi\) | |||||||
\(570\) | −2.19615 | −0.0919867 | ||||||||
\(571\) | −13.8038 | −0.577673 | −0.288837 | − | 0.957378i | \(-0.593268\pi\) | ||||
−0.288837 | + | 0.957378i | \(0.593268\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −20.7846 | −0.868290 | ||||||||
\(574\) | 2.19615 | 0.0916656 | ||||||||
\(575\) | −4.39230 | −0.183172 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | −16.2679 | −0.677244 | −0.338622 | − | 0.940923i | \(-0.609961\pi\) | ||||
−0.338622 | + | 0.940923i | \(0.609961\pi\) | |||||||
\(578\) | −10.0000 | −0.415945 | ||||||||
\(579\) | 12.8038 | 0.532110 | ||||||||
\(580\) | 5.19615 | 0.215758 | ||||||||
\(581\) | −55.1769 | −2.28912 | ||||||||
\(582\) | 6.00000 | 0.248708 | ||||||||
\(583\) | 14.1962 | 0.587945 | ||||||||
\(584\) | 12.1244 | 0.501709 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 14.6603 | 0.605610 | ||||||||
\(587\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(588\) | −15.3923 | −0.634768 | ||||||||
\(589\) | 3.21539 | 0.132488 | ||||||||
\(590\) | 24.0000 | 0.988064 | ||||||||
\(591\) | −6.92820 | −0.284988 | ||||||||
\(592\) | 3.00000 | 0.123299 | ||||||||
\(593\) | −46.8564 | −1.92416 | −0.962081 | − | 0.272764i | \(-0.912062\pi\) | ||||
−0.962081 | + | 0.272764i | \(0.912062\pi\) | |||||||
\(594\) | 4.73205 | 0.194158 | ||||||||
\(595\) | 42.5885 | 1.74596 | ||||||||
\(596\) | −18.1244 | −0.742403 | ||||||||
\(597\) | −8.58846 | −0.351502 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −4.39230 | −0.179465 | −0.0897324 | − | 0.995966i | \(-0.528601\pi\) | ||||
−0.0897324 | + | 0.995966i | \(0.528601\pi\) | |||||||
\(600\) | −2.00000 | −0.0816497 | ||||||||
\(601\) | 21.7846 | 0.888613 | 0.444306 | − | 0.895875i | \(-0.353450\pi\) | ||||
0.444306 | + | 0.895875i | \(0.353450\pi\) | |||||||
\(602\) | −29.3205 | −1.19501 | ||||||||
\(603\) | 10.7321 | 0.437043 | ||||||||
\(604\) | 7.26795 | 0.295729 | ||||||||
\(605\) | −19.7321 | −0.802222 | ||||||||
\(606\) | −1.39230 | −0.0565585 | ||||||||
\(607\) | −48.7846 | −1.98011 | −0.990053 | − | 0.140694i | \(-0.955067\pi\) | ||||
−0.990053 | + | 0.140694i | \(0.955067\pi\) | |||||||
\(608\) | −1.26795 | −0.0514221 | ||||||||
\(609\) | 14.1962 | 0.575257 | ||||||||
\(610\) | 8.32051 | 0.336888 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | −5.19615 | −0.210042 | ||||||||
\(613\) | −40.8564 | −1.65017 | −0.825087 | − | 0.565005i | \(-0.808874\pi\) | ||||
−0.825087 | + | 0.565005i | \(0.808874\pi\) | |||||||
\(614\) | −10.7321 | −0.433110 | ||||||||
\(615\) | −0.803848 | −0.0324143 | ||||||||
\(616\) | −22.3923 | −0.902212 | ||||||||
\(617\) | 10.6077 | 0.427050 | 0.213525 | − | 0.976938i | \(-0.431506\pi\) | ||||
0.213525 | + | 0.976938i | \(0.431506\pi\) | |||||||
\(618\) | −4.19615 | −0.168794 | ||||||||
\(619\) | −7.60770 | −0.305779 | −0.152890 | − | 0.988243i | \(-0.548858\pi\) | ||||
−0.152890 | + | 0.988243i | \(0.548858\pi\) | |||||||
\(620\) | −4.39230 | −0.176399 | ||||||||
\(621\) | −2.19615 | −0.0881286 | ||||||||
\(622\) | −2.19615 | −0.0880577 | ||||||||
\(623\) | 12.0000 | 0.480770 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −11.0000 | −0.440000 | ||||||||
\(626\) | 24.3923 | 0.974913 | ||||||||
\(627\) | −6.00000 | −0.239617 | ||||||||
\(628\) | −3.19615 | −0.127540 | ||||||||
\(629\) | −15.5885 | −0.621552 | ||||||||
\(630\) | 8.19615 | 0.326543 | ||||||||
\(631\) | 25.8564 | 1.02933 | 0.514664 | − | 0.857392i | \(-0.327917\pi\) | ||||
0.514664 | + | 0.857392i | \(0.327917\pi\) | |||||||
\(632\) | 12.3923 | 0.492939 | ||||||||
\(633\) | 3.60770 | 0.143393 | ||||||||
\(634\) | −6.12436 | −0.243229 | ||||||||
\(635\) | 6.92820 | 0.274937 | ||||||||
\(636\) | −3.00000 | −0.118958 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 14.1962 | 0.562031 | ||||||||
\(639\) | 8.19615 | 0.324235 | ||||||||
\(640\) | 1.73205 | 0.0684653 | ||||||||
\(641\) | −30.8038 | −1.21668 | −0.608339 | − | 0.793677i | \(-0.708164\pi\) | ||||
−0.608339 | + | 0.793677i | \(0.708164\pi\) | |||||||
\(642\) | 8.19615 | 0.323476 | ||||||||
\(643\) | −27.7128 | −1.09289 | −0.546443 | − | 0.837496i | \(-0.684019\pi\) | ||||
−0.546443 | + | 0.837496i | \(0.684019\pi\) | |||||||
\(644\) | 10.3923 | 0.409514 | ||||||||
\(645\) | 10.7321 | 0.422574 | ||||||||
\(646\) | 6.58846 | 0.259219 | ||||||||
\(647\) | 13.1769 | 0.518038 | 0.259019 | − | 0.965872i | \(-0.416601\pi\) | ||||
0.259019 | + | 0.965872i | \(0.416601\pi\) | |||||||
\(648\) | −1.00000 | −0.0392837 | ||||||||
\(649\) | 65.5692 | 2.57382 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −12.0000 | −0.470317 | ||||||||
\(652\) | 9.46410 | 0.370643 | ||||||||
\(653\) | −49.1769 | −1.92444 | −0.962221 | − | 0.272271i | \(-0.912225\pi\) | ||||
−0.962221 | + | 0.272271i | \(0.912225\pi\) | |||||||
\(654\) | 16.3923 | 0.640990 | ||||||||
\(655\) | −28.3923 | −1.10938 | ||||||||
\(656\) | −0.464102 | −0.0181201 | ||||||||
\(657\) | −12.1244 | −0.473016 | ||||||||
\(658\) | 6.00000 | 0.233904 | ||||||||
\(659\) | 25.1769 | 0.980753 | 0.490377 | − | 0.871511i | \(-0.336859\pi\) | ||||
0.490377 | + | 0.871511i | \(0.336859\pi\) | |||||||
\(660\) | 8.19615 | 0.319035 | ||||||||
\(661\) | 9.00000 | 0.350059 | 0.175030 | − | 0.984563i | \(-0.443998\pi\) | ||||
0.175030 | + | 0.984563i | \(0.443998\pi\) | |||||||
\(662\) | −12.0000 | −0.466393 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 11.6603 | 0.452506 | ||||||||
\(665\) | −10.3923 | −0.402996 | ||||||||
\(666\) | −3.00000 | −0.116248 | ||||||||
\(667\) | −6.58846 | −0.255106 | ||||||||
\(668\) | −2.53590 | −0.0981169 | ||||||||
\(669\) | 18.9282 | 0.731807 | ||||||||
\(670\) | 18.5885 | 0.718135 | ||||||||
\(671\) | 22.7321 | 0.877561 | ||||||||
\(672\) | 4.73205 | 0.182543 | ||||||||
\(673\) | 1.00000 | 0.0385472 | 0.0192736 | − | 0.999814i | \(-0.493865\pi\) | ||||
0.0192736 | + | 0.999814i | \(0.493865\pi\) | |||||||
\(674\) | 31.0000 | 1.19408 | ||||||||
\(675\) | 2.00000 | 0.0769800 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 4.39230 | 0.168810 | 0.0844050 | − | 0.996432i | \(-0.473101\pi\) | ||||
0.0844050 | + | 0.996432i | \(0.473101\pi\) | |||||||
\(678\) | 11.1962 | 0.429986 | ||||||||
\(679\) | 28.3923 | 1.08960 | ||||||||
\(680\) | −9.00000 | −0.345134 | ||||||||
\(681\) | 9.80385 | 0.375684 | ||||||||
\(682\) | −12.0000 | −0.459504 | ||||||||
\(683\) | 27.7128 | 1.06040 | 0.530201 | − | 0.847872i | \(-0.322117\pi\) | ||||
0.530201 | + | 0.847872i | \(0.322117\pi\) | |||||||
\(684\) | 1.26795 | 0.0484812 | ||||||||
\(685\) | 15.5885 | 0.595604 | ||||||||
\(686\) | −39.7128 | −1.51624 | ||||||||
\(687\) | −19.8564 | −0.757569 | ||||||||
\(688\) | 6.19615 | 0.236226 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | −3.80385 | −0.144810 | ||||||||
\(691\) | −19.5167 | −0.742449 | −0.371224 | − | 0.928543i | \(-0.621062\pi\) | ||||
−0.371224 | + | 0.928543i | \(0.621062\pi\) | |||||||
\(692\) | 16.3923 | 0.623142 | ||||||||
\(693\) | 22.3923 | 0.850613 | ||||||||
\(694\) | 12.5885 | 0.477851 | ||||||||
\(695\) | 6.92820 | 0.262802 | ||||||||
\(696\) | −3.00000 | −0.113715 | ||||||||
\(697\) | 2.41154 | 0.0913437 | ||||||||
\(698\) | −2.53590 | −0.0959852 | ||||||||
\(699\) | 18.0000 | 0.680823 | ||||||||
\(700\) | −9.46410 | −0.357709 | ||||||||
\(701\) | 4.39230 | 0.165895 | 0.0829475 | − | 0.996554i | \(-0.473567\pi\) | ||||
0.0829475 | + | 0.996554i | \(0.473567\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 3.80385 | 0.143465 | ||||||||
\(704\) | 4.73205 | 0.178346 | ||||||||
\(705\) | −2.19615 | −0.0827119 | ||||||||
\(706\) | −5.78461 | −0.217707 | ||||||||
\(707\) | −6.58846 | −0.247784 | ||||||||
\(708\) | −13.8564 | −0.520756 | ||||||||
\(709\) | 3.24871 | 0.122008 | 0.0610040 | − | 0.998138i | \(-0.480570\pi\) | ||||
0.0610040 | + | 0.998138i | \(0.480570\pi\) | |||||||
\(710\) | 14.1962 | 0.532772 | ||||||||
\(711\) | −12.3923 | −0.464748 | ||||||||
\(712\) | −2.53590 | −0.0950368 | ||||||||
\(713\) | 5.56922 | 0.208569 | ||||||||
\(714\) | −24.5885 | −0.920200 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −8.19615 | −0.306305 | ||||||||
\(717\) | 24.5885 | 0.918273 | ||||||||
\(718\) | −22.0526 | −0.822994 | ||||||||
\(719\) | 52.3923 | 1.95390 | 0.976952 | − | 0.213461i | \(-0.0684736\pi\) | ||||
0.976952 | + | 0.213461i | \(0.0684736\pi\) | |||||||
\(720\) | −1.73205 | −0.0645497 | ||||||||
\(721\) | −19.8564 | −0.739491 | ||||||||
\(722\) | 17.3923 | 0.647275 | ||||||||
\(723\) | −0.803848 | −0.0298954 | ||||||||
\(724\) | −11.5885 | −0.430682 | ||||||||
\(725\) | 6.00000 | 0.222834 | ||||||||
\(726\) | 11.3923 | 0.422808 | ||||||||
\(727\) | −24.1962 | −0.897386 | −0.448693 | − | 0.893686i | \(-0.648110\pi\) | ||||
−0.448693 | + | 0.893686i | \(0.648110\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −21.0000 | −0.777245 | ||||||||
\(731\) | −32.1962 | −1.19082 | ||||||||
\(732\) | −4.80385 | −0.177555 | ||||||||
\(733\) | −14.3205 | −0.528940 | −0.264470 | − | 0.964394i | \(-0.585197\pi\) | ||||
−0.264470 | + | 0.964394i | \(0.585197\pi\) | |||||||
\(734\) | 24.1962 | 0.893096 | ||||||||
\(735\) | 26.6603 | 0.983378 | ||||||||
\(736\) | −2.19615 | −0.0809513 | ||||||||
\(737\) | 50.7846 | 1.87068 | ||||||||
\(738\) | 0.464102 | 0.0170838 | ||||||||
\(739\) | −18.9282 | −0.696285 | −0.348143 | − | 0.937442i | \(-0.613188\pi\) | ||||
−0.348143 | + | 0.937442i | \(0.613188\pi\) | |||||||
\(740\) | −5.19615 | −0.191014 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −14.1962 | −0.521157 | ||||||||
\(743\) | 4.39230 | 0.161138 | 0.0805690 | − | 0.996749i | \(-0.474326\pi\) | ||||
0.0805690 | + | 0.996749i | \(0.474326\pi\) | |||||||
\(744\) | 2.53590 | 0.0929705 | ||||||||
\(745\) | 31.3923 | 1.15013 | ||||||||
\(746\) | −23.9808 | −0.877998 | ||||||||
\(747\) | −11.6603 | −0.426626 | ||||||||
\(748\) | −24.5885 | −0.899043 | ||||||||
\(749\) | 38.7846 | 1.41716 | ||||||||
\(750\) | 12.1244 | 0.442719 | ||||||||
\(751\) | −24.9808 | −0.911561 | −0.455780 | − | 0.890092i | \(-0.650640\pi\) | ||||
−0.455780 | + | 0.890092i | \(0.650640\pi\) | |||||||
\(752\) | −1.26795 | −0.0462373 | ||||||||
\(753\) | 4.39230 | 0.160064 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −12.5885 | −0.458141 | ||||||||
\(756\) | −4.73205 | −0.172103 | ||||||||
\(757\) | 18.7846 | 0.682738 | 0.341369 | − | 0.939929i | \(-0.389109\pi\) | ||||
0.341369 | + | 0.939929i | \(0.389109\pi\) | |||||||
\(758\) | 18.2487 | 0.662823 | ||||||||
\(759\) | −10.3923 | −0.377217 | ||||||||
\(760\) | 2.19615 | 0.0796628 | ||||||||
\(761\) | −4.39230 | −0.159221 | −0.0796105 | − | 0.996826i | \(-0.525368\pi\) | ||||
−0.0796105 | + | 0.996826i | \(0.525368\pi\) | |||||||
\(762\) | −4.00000 | −0.144905 | ||||||||
\(763\) | 77.5692 | 2.80819 | ||||||||
\(764\) | 20.7846 | 0.751961 | ||||||||
\(765\) | 9.00000 | 0.325396 | ||||||||
\(766\) | −11.3205 | −0.409027 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | −1.00000 | −0.0360844 | ||||||||
\(769\) | 33.7128 | 1.21572 | 0.607858 | − | 0.794046i | \(-0.292029\pi\) | ||||
0.607858 | + | 0.794046i | \(0.292029\pi\) | |||||||
\(770\) | 38.7846 | 1.39770 | ||||||||
\(771\) | −12.8038 | −0.461119 | ||||||||
\(772\) | −12.8038 | −0.460821 | ||||||||
\(773\) | −50.7846 | −1.82660 | −0.913298 | − | 0.407293i | \(-0.866473\pi\) | ||||
−0.913298 | + | 0.407293i | \(0.866473\pi\) | |||||||
\(774\) | −6.19615 | −0.222716 | ||||||||
\(775\) | −5.07180 | −0.182184 | ||||||||
\(776\) | −6.00000 | −0.215387 | ||||||||
\(777\) | −14.1962 | −0.509284 | ||||||||
\(778\) | 13.3923 | 0.480137 | ||||||||
\(779\) | −0.588457 | −0.0210837 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 38.7846 | 1.38782 | ||||||||
\(782\) | 11.4115 | 0.408076 | ||||||||
\(783\) | 3.00000 | 0.107211 | ||||||||
\(784\) | 15.3923 | 0.549725 | ||||||||
\(785\) | 5.53590 | 0.197585 | ||||||||
\(786\) | 16.3923 | 0.584694 | ||||||||
\(787\) | −14.5359 | −0.518149 | −0.259074 | − | 0.965857i | \(-0.583417\pi\) | ||||
−0.259074 | + | 0.965857i | \(0.583417\pi\) | |||||||
\(788\) | 6.92820 | 0.246807 | ||||||||
\(789\) | 2.19615 | 0.0781851 | ||||||||
\(790\) | −21.4641 | −0.763658 | ||||||||
\(791\) | 52.9808 | 1.88378 | ||||||||
\(792\) | −4.73205 | −0.168146 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 16.3923 | 0.581741 | ||||||||
\(795\) | 5.19615 | 0.184289 | ||||||||
\(796\) | 8.58846 | 0.304410 | ||||||||
\(797\) | 6.00000 | 0.212531 | 0.106265 | − | 0.994338i | \(-0.466111\pi\) | ||||
0.106265 | + | 0.994338i | \(0.466111\pi\) | |||||||
\(798\) | 6.00000 | 0.212398 | ||||||||
\(799\) | 6.58846 | 0.233083 | ||||||||
\(800\) | 2.00000 | 0.0707107 | ||||||||
\(801\) | 2.53590 | 0.0896016 | ||||||||
\(802\) | −21.0000 | −0.741536 | ||||||||
\(803\) | −57.3731 | −2.02465 | ||||||||
\(804\) | −10.7321 | −0.378490 | ||||||||
\(805\) | −18.0000 | −0.634417 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 28.3923 | 0.999456 | ||||||||
\(808\) | 1.39230 | 0.0489811 | ||||||||
\(809\) | −47.1962 | −1.65933 | −0.829664 | − | 0.558263i | \(-0.811468\pi\) | ||||
−0.829664 | + | 0.558263i | \(0.811468\pi\) | |||||||
\(810\) | 1.73205 | 0.0608581 | ||||||||
\(811\) | 4.39230 | 0.154235 | 0.0771173 | − | 0.997022i | \(-0.475428\pi\) | ||||
0.0771173 | + | 0.997022i | \(0.475428\pi\) | |||||||
\(812\) | −14.1962 | −0.498187 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −14.1962 | −0.497575 | ||||||||
\(815\) | −16.3923 | −0.574197 | ||||||||
\(816\) | 5.19615 | 0.181902 | ||||||||
\(817\) | 7.85641 | 0.274861 | ||||||||
\(818\) | 3.33975 | 0.116771 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0.803848 | 0.0280716 | ||||||||
\(821\) | −40.6410 | −1.41838 | −0.709191 | − | 0.705017i | \(-0.750939\pi\) | ||||
−0.709191 | + | 0.705017i | \(0.750939\pi\) | |||||||
\(822\) | −9.00000 | −0.313911 | ||||||||
\(823\) | −32.0000 | −1.11545 | −0.557725 | − | 0.830026i | \(-0.688326\pi\) | ||||
−0.557725 | + | 0.830026i | \(0.688326\pi\) | |||||||
\(824\) | 4.19615 | 0.146180 | ||||||||
\(825\) | 9.46410 | 0.329498 | ||||||||
\(826\) | −65.5692 | −2.28144 | ||||||||
\(827\) | −32.1051 | −1.11640 | −0.558202 | − | 0.829705i | \(-0.688509\pi\) | ||||
−0.558202 | + | 0.829705i | \(0.688509\pi\) | |||||||
\(828\) | 2.19615 | 0.0763216 | ||||||||
\(829\) | −11.9808 | −0.416109 | −0.208055 | − | 0.978117i | \(-0.566713\pi\) | ||||
−0.208055 | + | 0.978117i | \(0.566713\pi\) | |||||||
\(830\) | −20.1962 | −0.701019 | ||||||||
\(831\) | −15.1962 | −0.527149 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −79.9808 | −2.77117 | ||||||||
\(834\) | −4.00000 | −0.138509 | ||||||||
\(835\) | 4.39230 | 0.152002 | ||||||||
\(836\) | 6.00000 | 0.207514 | ||||||||
\(837\) | −2.53590 | −0.0876535 | ||||||||
\(838\) | −16.3923 | −0.566263 | ||||||||
\(839\) | −12.0000 | −0.414286 | −0.207143 | − | 0.978311i | \(-0.566417\pi\) | ||||
−0.207143 | + | 0.978311i | \(0.566417\pi\) | |||||||
\(840\) | −8.19615 | −0.282794 | ||||||||
\(841\) | −20.0000 | −0.689655 | ||||||||
\(842\) | −0.464102 | −0.0159940 | ||||||||
\(843\) | −24.4641 | −0.842588 | ||||||||
\(844\) | −3.60770 | −0.124182 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 1.26795 | 0.0435930 | ||||||||
\(847\) | 53.9090 | 1.85233 | ||||||||
\(848\) | 3.00000 | 0.103020 | ||||||||
\(849\) | 30.1962 | 1.03633 | ||||||||
\(850\) | −10.3923 | −0.356453 | ||||||||
\(851\) | 6.58846 | 0.225849 | ||||||||
\(852\) | −8.19615 | −0.280796 | ||||||||
\(853\) | 9.00000 | 0.308154 | 0.154077 | − | 0.988059i | \(-0.450760\pi\) | ||||
0.154077 | + | 0.988059i | \(0.450760\pi\) | |||||||
\(854\) | −22.7321 | −0.777875 | ||||||||
\(855\) | −2.19615 | −0.0751068 | ||||||||
\(856\) | −8.19615 | −0.280139 | ||||||||
\(857\) | −54.3731 | −1.85735 | −0.928674 | − | 0.370896i | \(-0.879051\pi\) | ||||
−0.928674 | + | 0.370896i | \(0.879051\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 10.5885 | 0.361273 | 0.180637 | − | 0.983550i | \(-0.442184\pi\) | ||||
0.180637 | + | 0.983550i | \(0.442184\pi\) | |||||||
\(860\) | −10.7321 | −0.365960 | ||||||||
\(861\) | 2.19615 | 0.0748447 | ||||||||
\(862\) | −27.8038 | −0.947003 | ||||||||
\(863\) | 4.48334 | 0.152615 | 0.0763073 | − | 0.997084i | \(-0.475687\pi\) | ||||
0.0763073 | + | 0.997084i | \(0.475687\pi\) | |||||||
\(864\) | 1.00000 | 0.0340207 | ||||||||
\(865\) | −28.3923 | −0.965367 | ||||||||
\(866\) | 33.7846 | 1.14805 | ||||||||
\(867\) | −10.0000 | −0.339618 | ||||||||
\(868\) | 12.0000 | 0.407307 | ||||||||
\(869\) | −58.6410 | −1.98926 | ||||||||
\(870\) | 5.19615 | 0.176166 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | −16.3923 | −0.555113 | ||||||||
\(873\) | 6.00000 | 0.203069 | ||||||||
\(874\) | −2.78461 | −0.0941908 | ||||||||
\(875\) | 57.3731 | 1.93956 | ||||||||
\(876\) | 12.1244 | 0.409644 | ||||||||
\(877\) | 43.3923 | 1.46525 | 0.732627 | − | 0.680630i | \(-0.238294\pi\) | ||||
0.732627 | + | 0.680630i | \(0.238294\pi\) | |||||||
\(878\) | −16.5885 | −0.559833 | ||||||||
\(879\) | 14.6603 | 0.494478 | ||||||||
\(880\) | −8.19615 | −0.276292 | ||||||||
\(881\) | 37.9808 | 1.27960 | 0.639802 | − | 0.768540i | \(-0.279016\pi\) | ||||
0.639802 | + | 0.768540i | \(0.279016\pi\) | |||||||
\(882\) | −15.3923 | −0.518286 | ||||||||
\(883\) | −24.7846 | −0.834069 | −0.417034 | − | 0.908891i | \(-0.636930\pi\) | ||||
−0.417034 | + | 0.908891i | \(0.636930\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 24.0000 | 0.806751 | ||||||||
\(886\) | 4.39230 | 0.147562 | ||||||||
\(887\) | 48.0000 | 1.61168 | 0.805841 | − | 0.592132i | \(-0.201714\pi\) | ||||
0.805841 | + | 0.592132i | \(0.201714\pi\) | |||||||
\(888\) | 3.00000 | 0.100673 | ||||||||
\(889\) | −18.9282 | −0.634832 | ||||||||
\(890\) | 4.39230 | 0.147230 | ||||||||
\(891\) | 4.73205 | 0.158530 | ||||||||
\(892\) | −18.9282 | −0.633763 | ||||||||
\(893\) | −1.60770 | −0.0537995 | ||||||||
\(894\) | −18.1244 | −0.606169 | ||||||||
\(895\) | 14.1962 | 0.474525 | ||||||||
\(896\) | −4.73205 | −0.158087 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −33.4641 | −1.11671 | ||||||||
\(899\) | −7.60770 | −0.253731 | ||||||||
\(900\) | −2.00000 | −0.0666667 | ||||||||
\(901\) | −15.5885 | −0.519327 | ||||||||
\(902\) | 2.19615 | 0.0731239 | ||||||||
\(903\) | −29.3205 | −0.975725 | ||||||||
\(904\) | −11.1962 | −0.372378 | ||||||||
\(905\) | 20.0718 | 0.667209 | ||||||||
\(906\) | 7.26795 | 0.241461 | ||||||||
\(907\) | −41.1769 | −1.36726 | −0.683629 | − | 0.729830i | \(-0.739599\pi\) | ||||
−0.683629 | + | 0.729830i | \(0.739599\pi\) | |||||||
\(908\) | −9.80385 | −0.325352 | ||||||||
\(909\) | −1.39230 | −0.0461798 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 37.1769 | 1.23173 | 0.615863 | − | 0.787853i | \(-0.288807\pi\) | ||||
0.615863 | + | 0.787853i | \(0.288807\pi\) | |||||||
\(912\) | −1.26795 | −0.0419860 | ||||||||
\(913\) | −55.1769 | −1.82609 | ||||||||
\(914\) | −19.9808 | −0.660905 | ||||||||
\(915\) | 8.32051 | 0.275068 | ||||||||
\(916\) | 19.8564 | 0.656074 | ||||||||
\(917\) | 77.5692 | 2.56156 | ||||||||
\(918\) | −5.19615 | −0.171499 | ||||||||
\(919\) | 32.3923 | 1.06852 | 0.534262 | − | 0.845319i | \(-0.320590\pi\) | ||||
0.534262 | + | 0.845319i | \(0.320590\pi\) | |||||||
\(920\) | 3.80385 | 0.125409 | ||||||||
\(921\) | −10.7321 | −0.353633 | ||||||||
\(922\) | 19.9808 | 0.658031 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | −22.3923 | −0.736653 | ||||||||
\(925\) | −6.00000 | −0.197279 | ||||||||
\(926\) | 26.1962 | 0.860859 | ||||||||
\(927\) | −4.19615 | −0.137820 | ||||||||
\(928\) | 3.00000 | 0.0984798 | ||||||||
\(929\) | −34.6077 | −1.13544 | −0.567721 | − | 0.823221i | \(-0.692175\pi\) | ||||
−0.567721 | + | 0.823221i | \(0.692175\pi\) | |||||||
\(930\) | −4.39230 | −0.144029 | ||||||||
\(931\) | 19.5167 | 0.639633 | ||||||||
\(932\) | −18.0000 | −0.589610 | ||||||||
\(933\) | −2.19615 | −0.0718988 | ||||||||
\(934\) | −36.5885 | −1.19721 | ||||||||
\(935\) | 42.5885 | 1.39279 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 5.39230 | 0.176159 | 0.0880795 | − | 0.996113i | \(-0.471927\pi\) | ||||
0.0880795 | + | 0.996113i | \(0.471927\pi\) | |||||||
\(938\) | −50.7846 | −1.65818 | ||||||||
\(939\) | 24.3923 | 0.796013 | ||||||||
\(940\) | 2.19615 | 0.0716306 | ||||||||
\(941\) | 2.78461 | 0.0907757 | 0.0453878 | − | 0.998969i | \(-0.485548\pi\) | ||||
0.0453878 | + | 0.998969i | \(0.485548\pi\) | |||||||
\(942\) | −3.19615 | −0.104136 | ||||||||
\(943\) | −1.01924 | −0.0331910 | ||||||||
\(944\) | 13.8564 | 0.450988 | ||||||||
\(945\) | 8.19615 | 0.266621 | ||||||||
\(946\) | −29.3205 | −0.953292 | ||||||||
\(947\) | −42.9282 | −1.39498 | −0.697490 | − | 0.716595i | \(-0.745700\pi\) | ||||
−0.697490 | + | 0.716595i | \(0.745700\pi\) | |||||||
\(948\) | 12.3923 | 0.402483 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 2.53590 | 0.0822754 | ||||||||
\(951\) | −6.12436 | −0.198596 | ||||||||
\(952\) | 24.5885 | 0.796916 | ||||||||
\(953\) | −24.0000 | −0.777436 | −0.388718 | − | 0.921357i | \(-0.627082\pi\) | ||||
−0.388718 | + | 0.921357i | \(0.627082\pi\) | |||||||
\(954\) | −3.00000 | −0.0971286 | ||||||||
\(955\) | −36.0000 | −1.16493 | ||||||||
\(956\) | −24.5885 | −0.795248 | ||||||||
\(957\) | 14.1962 | 0.458896 | ||||||||
\(958\) | 35.3205 | 1.14115 | ||||||||
\(959\) | −42.5885 | −1.37525 | ||||||||
\(960\) | 1.73205 | 0.0559017 | ||||||||
\(961\) | −24.5692 | −0.792555 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 8.19615 | 0.264117 | ||||||||
\(964\) | 0.803848 | 0.0258902 | ||||||||
\(965\) | 22.1769 | 0.713900 | ||||||||
\(966\) | 10.3923 | 0.334367 | ||||||||
\(967\) | −14.8756 | −0.478368 | −0.239184 | − | 0.970974i | \(-0.576880\pi\) | ||||
−0.239184 | + | 0.970974i | \(0.576880\pi\) | |||||||
\(968\) | −11.3923 | −0.366163 | ||||||||
\(969\) | 6.58846 | 0.211652 | ||||||||
\(970\) | 10.3923 | 0.333677 | ||||||||
\(971\) | −13.1769 | −0.422867 | −0.211434 | − | 0.977392i | \(-0.567813\pi\) | ||||
−0.211434 | + | 0.977392i | \(0.567813\pi\) | |||||||
\(972\) | −1.00000 | −0.0320750 | ||||||||
\(973\) | −18.9282 | −0.606810 | ||||||||
\(974\) | −9.12436 | −0.292363 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 4.80385 | 0.153767 | ||||||||
\(977\) | −16.8564 | −0.539284 | −0.269642 | − | 0.962961i | \(-0.586905\pi\) | ||||
−0.269642 | + | 0.962961i | \(0.586905\pi\) | |||||||
\(978\) | 9.46410 | 0.302629 | ||||||||
\(979\) | 12.0000 | 0.383522 | ||||||||
\(980\) | −26.6603 | −0.851631 | ||||||||
\(981\) | 16.3923 | 0.523366 | ||||||||
\(982\) | −0.588457 | −0.0187784 | ||||||||
\(983\) | −20.7846 | −0.662926 | −0.331463 | − | 0.943468i | \(-0.607542\pi\) | ||||
−0.331463 | + | 0.943468i | \(0.607542\pi\) | |||||||
\(984\) | −0.464102 | −0.0147950 | ||||||||
\(985\) | −12.0000 | −0.382352 | ||||||||
\(986\) | −15.5885 | −0.496438 | ||||||||
\(987\) | 6.00000 | 0.190982 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 13.6077 | 0.432700 | ||||||||
\(990\) | 8.19615 | 0.260491 | ||||||||
\(991\) | 29.3731 | 0.933066 | 0.466533 | − | 0.884504i | \(-0.345503\pi\) | ||||
0.466533 | + | 0.884504i | \(0.345503\pi\) | |||||||
\(992\) | −2.53590 | −0.0805149 | ||||||||
\(993\) | −12.0000 | −0.380808 | ||||||||
\(994\) | −38.7846 | −1.23017 | ||||||||
\(995\) | −14.8756 | −0.471590 | ||||||||
\(996\) | 11.6603 | 0.369469 | ||||||||
\(997\) | 13.1962 | 0.417926 | 0.208963 | − | 0.977924i | \(-0.432991\pi\) | ||||
0.208963 | + | 0.977924i | \(0.432991\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −3.00000 | −0.0949158 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))