Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [5625,2,Mod(1,5625)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(5625, 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("5625.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 5625 = 3^{2} \cdot 5^{4} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 5625.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: | \(44.9158511370\) |
Analytic rank: | \(1\) |
Dimension: | \(8\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 15x^{6} + 70x^{4} - 105x^{2} + 45 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(-1.23762\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 5625.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.23762 | −0.875127 | −0.437563 | − | 0.899188i | \(-0.644158\pi\) | ||||
−0.437563 | + | 0.899188i | \(0.644158\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −0.468306 | −0.234153 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.08634 | 0.788563 | 0.394281 | − | 0.918990i | \(-0.370994\pi\) | ||||
0.394281 | + | 0.918990i | \(0.370994\pi\) | |||||||
\(8\) | 3.05482 | 1.08004 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2.65287 | −0.799870 | −0.399935 | − | 0.916543i | \(-0.630967\pi\) | ||||
−0.399935 | + | 0.916543i | \(0.630967\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −0.149728 | −0.0415269 | −0.0207635 | − | 0.999784i | \(-0.506610\pi\) | ||||
−0.0207635 | + | 0.999784i | \(0.506610\pi\) | |||||||
\(14\) | −2.58209 | −0.690092 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −2.84408 | −0.711019 | ||||||||
\(17\) | 5.12810 | 1.24375 | 0.621874 | − | 0.783118i | \(-0.286372\pi\) | ||||
0.621874 | + | 0.783118i | \(0.286372\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −3.08634 | −0.708055 | −0.354028 | − | 0.935235i | \(-0.615188\pi\) | ||||
−0.354028 | + | 0.935235i | \(0.615188\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 3.28323 | 0.699988 | ||||||||
\(23\) | −2.76265 | −0.576053 | −0.288027 | − | 0.957622i | \(-0.592999\pi\) | ||||
−0.288027 | + | 0.957622i | \(0.592999\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0.185305 | 0.0363413 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −0.977047 | −0.184644 | ||||||||
\(29\) | 6.94530 | 1.28971 | 0.644855 | − | 0.764305i | \(-0.276918\pi\) | ||||
0.644855 | + | 0.764305i | \(0.276918\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.52550 | 0.273987 | 0.136994 | − | 0.990572i | \(-0.456256\pi\) | ||||
0.136994 | + | 0.990572i | \(0.456256\pi\) | |||||||
\(32\) | −2.58976 | −0.457809 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −6.34662 | −1.08844 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −8.52550 | −1.40158 | −0.700792 | − | 0.713366i | \(-0.747170\pi\) | ||||
−0.700792 | + | 0.713366i | \(0.747170\pi\) | |||||||
\(38\) | 3.81970 | 0.619638 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −9.82722 | −1.53475 | −0.767377 | − | 0.641196i | \(-0.778438\pi\) | ||||
−0.767377 | + | 0.641196i | \(0.778438\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −3.43296 | −0.523522 | −0.261761 | − | 0.965133i | \(-0.584303\pi\) | ||||
−0.261761 | + | 0.965133i | \(0.584303\pi\) | |||||||
\(44\) | 1.24236 | 0.187292 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 3.41911 | 0.504120 | ||||||||
\(47\) | 4.00501 | 0.584191 | 0.292095 | − | 0.956389i | \(-0.405648\pi\) | ||||
0.292095 | + | 0.956389i | \(0.405648\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −2.64718 | −0.378169 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0.0701184 | 0.00972367 | ||||||||
\(53\) | 0.945455 | 0.129868 | 0.0649341 | − | 0.997890i | \(-0.479316\pi\) | ||||
0.0649341 | + | 0.997890i | \(0.479316\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 6.37339 | 0.851679 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −8.59562 | −1.12866 | ||||||||
\(59\) | 8.18766 | 1.06594 | 0.532971 | − | 0.846133i | \(-0.321075\pi\) | ||||
0.532971 | + | 0.846133i | \(0.321075\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −4.47450 | −0.572901 | −0.286451 | − | 0.958095i | \(-0.592475\pi\) | ||||
−0.286451 | + | 0.958095i | \(0.592475\pi\) | |||||||
\(62\) | −1.88798 | −0.239774 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 8.89328 | 1.11166 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 3.34042 | 0.408098 | 0.204049 | − | 0.978961i | \(-0.434590\pi\) | ||||
0.204049 | + | 0.978961i | \(0.434590\pi\) | |||||||
\(68\) | −2.40152 | −0.291227 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −12.4801 | −1.48111 | −0.740557 | − | 0.671994i | \(-0.765438\pi\) | ||||
−0.740557 | + | 0.671994i | \(0.765438\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −11.6018 | −1.35789 | −0.678945 | − | 0.734189i | \(-0.737562\pi\) | ||||
−0.678945 | + | 0.734189i | \(0.737562\pi\) | |||||||
\(74\) | 10.5513 | 1.22656 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 1.44535 | 0.165793 | ||||||||
\(77\) | −5.53479 | −0.630748 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 11.3696 | 1.27918 | 0.639588 | − | 0.768717i | \(-0.279105\pi\) | ||||
0.639588 | + | 0.768717i | \(0.279105\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 12.1623 | 1.34310 | ||||||||
\(83\) | −3.45676 | −0.379429 | −0.189715 | − | 0.981839i | \(-0.560756\pi\) | ||||
−0.189715 | + | 0.981839i | \(0.560756\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 4.24869 | 0.458148 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −8.10403 | −0.863892 | ||||||||
\(89\) | 14.8875 | 1.57807 | 0.789034 | − | 0.614349i | \(-0.210581\pi\) | ||||
0.789034 | + | 0.614349i | \(0.210581\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −0.312383 | −0.0327466 | ||||||||
\(92\) | 1.29377 | 0.134885 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −4.95666 | −0.511241 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 0.0571908 | 0.00580685 | 0.00290342 | − | 0.999996i | \(-0.499076\pi\) | ||||
0.00290342 | + | 0.999996i | \(0.499076\pi\) | |||||||
\(98\) | 3.27620 | 0.330946 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 16.2980 | 1.62171 | 0.810855 | − | 0.585247i | \(-0.199003\pi\) | ||||
0.810855 | + | 0.585247i | \(0.199003\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −5.37814 | −0.529924 | −0.264962 | − | 0.964259i | \(-0.585359\pi\) | ||||
−0.264962 | + | 0.964259i | \(0.585359\pi\) | |||||||
\(104\) | −0.457390 | −0.0448508 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −1.17011 | −0.113651 | ||||||||
\(107\) | −20.2611 | −1.95871 | −0.979355 | − | 0.202147i | \(-0.935208\pi\) | ||||
−0.979355 | + | 0.202147i | \(0.935208\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −16.0778 | −1.53997 | −0.769986 | − | 0.638061i | \(-0.779737\pi\) | ||||
−0.769986 | + | 0.638061i | \(0.779737\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −5.93371 | −0.560683 | ||||||||
\(113\) | −8.40723 | −0.790885 | −0.395443 | − | 0.918491i | \(-0.629409\pi\) | ||||
−0.395443 | + | 0.918491i | \(0.629409\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −3.25253 | −0.301990 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −10.1332 | −0.932834 | ||||||||
\(119\) | 10.6990 | 0.980772 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −3.96229 | −0.360208 | ||||||||
\(122\) | 5.53772 | 0.501361 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −0.714400 | −0.0641550 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −21.8709 | −1.94072 | −0.970362 | − | 0.241654i | \(-0.922310\pi\) | ||||
−0.970362 | + | 0.241654i | \(0.922310\pi\) | |||||||
\(128\) | −5.82695 | −0.515034 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 14.1197 | 1.23364 | 0.616820 | − | 0.787104i | \(-0.288421\pi\) | ||||
0.616820 | + | 0.787104i | \(0.288421\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −6.43916 | −0.558346 | ||||||||
\(134\) | −4.13416 | −0.357137 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 15.6654 | 1.34330 | ||||||||
\(137\) | 9.59817 | 0.820027 | 0.410013 | − | 0.912079i | \(-0.365524\pi\) | ||||
0.410013 | + | 0.912079i | \(0.365524\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 17.7945 | 1.50931 | 0.754657 | − | 0.656120i | \(-0.227803\pi\) | ||||
0.754657 | + | 0.656120i | \(0.227803\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 15.4456 | 1.29616 | ||||||||
\(143\) | 0.397208 | 0.0332162 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 14.3586 | 1.18833 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 3.99255 | 0.328185 | ||||||||
\(149\) | −1.01331 | −0.0830132 | −0.0415066 | − | 0.999138i | \(-0.513216\pi\) | ||||
−0.0415066 | + | 0.999138i | \(0.513216\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −13.2809 | −1.08078 | −0.540391 | − | 0.841414i | \(-0.681724\pi\) | ||||
−0.540391 | + | 0.841414i | \(0.681724\pi\) | |||||||
\(152\) | −9.42820 | −0.764728 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 6.84994 | 0.551984 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 21.5579 | 1.72051 | 0.860254 | − | 0.509866i | \(-0.170305\pi\) | ||||
0.860254 | + | 0.509866i | \(0.170305\pi\) | |||||||
\(158\) | −14.0712 | −1.11944 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −5.76384 | −0.454254 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −4.99144 | −0.390960 | −0.195480 | − | 0.980708i | \(-0.562626\pi\) | ||||
−0.195480 | + | 0.980708i | \(0.562626\pi\) | |||||||
\(164\) | 4.60215 | 0.359368 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 4.27815 | 0.332048 | ||||||||
\(167\) | 22.9559 | 1.77638 | 0.888189 | − | 0.459478i | \(-0.151964\pi\) | ||||
0.888189 | + | 0.459478i | \(0.151964\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.9776 | −0.998276 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 1.60768 | 0.122584 | ||||||||
\(173\) | 6.17748 | 0.469665 | 0.234833 | − | 0.972036i | \(-0.424546\pi\) | ||||
0.234833 | + | 0.972036i | \(0.424546\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 7.54496 | 0.568723 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −18.4250 | −1.38101 | ||||||||
\(179\) | −14.6584 | −1.09562 | −0.547811 | − | 0.836602i | \(-0.684539\pi\) | ||||
−0.547811 | + | 0.836602i | \(0.684539\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −2.87559 | −0.213741 | −0.106871 | − | 0.994273i | \(-0.534083\pi\) | ||||
−0.106871 | + | 0.994273i | \(0.534083\pi\) | |||||||
\(182\) | 0.386610 | 0.0286574 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −8.43940 | −0.622161 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −13.6042 | −0.994836 | ||||||||
\(188\) | −1.87557 | −0.136790 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −12.6216 | −0.913270 | −0.456635 | − | 0.889654i | \(-0.650946\pi\) | ||||
−0.456635 | + | 0.889654i | \(0.650946\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −7.02059 | −0.505353 | −0.252676 | − | 0.967551i | \(-0.581311\pi\) | ||||
−0.252676 | + | 0.967551i | \(0.581311\pi\) | |||||||
\(194\) | −0.0707803 | −0.00508173 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1.23969 | 0.0885495 | ||||||||
\(197\) | 11.3056 | 0.805489 | 0.402745 | − | 0.915312i | \(-0.368056\pi\) | ||||
0.402745 | + | 0.915312i | \(0.368056\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 13.4827 | 0.955763 | 0.477882 | − | 0.878424i | \(-0.341405\pi\) | ||||
0.477882 | + | 0.878424i | \(0.341405\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −20.1706 | −1.41920 | ||||||||
\(203\) | 14.4903 | 1.01702 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 6.65607 | 0.463750 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0.425837 | 0.0295265 | ||||||||
\(209\) | 8.18766 | 0.566352 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −10.1297 | −0.697356 | −0.348678 | − | 0.937243i | \(-0.613369\pi\) | ||||
−0.348678 | + | 0.937243i | \(0.613369\pi\) | |||||||
\(212\) | −0.442762 | −0.0304091 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 25.0754 | 1.71412 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 3.18271 | 0.216056 | ||||||||
\(218\) | 19.8981 | 1.34767 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −0.767818 | −0.0516490 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −22.6330 | −1.51562 | −0.757809 | − | 0.652477i | \(-0.773730\pi\) | ||||
−0.757809 | + | 0.652477i | \(0.773730\pi\) | |||||||
\(224\) | −5.40311 | −0.361011 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 10.4049 | 0.692125 | ||||||||
\(227\) | −5.12810 | −0.340364 | −0.170182 | − | 0.985413i | \(-0.554436\pi\) | ||||
−0.170182 | + | 0.985413i | \(0.554436\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 20.8709 | 1.37919 | 0.689593 | − | 0.724198i | \(-0.257790\pi\) | ||||
0.689593 | + | 0.724198i | \(0.257790\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 21.2166 | 1.39294 | ||||||||
\(233\) | 17.3988 | 1.13983 | 0.569916 | − | 0.821703i | \(-0.306976\pi\) | ||||
0.569916 | + | 0.821703i | \(0.306976\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −3.83433 | −0.249594 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −13.2412 | −0.858300 | ||||||||
\(239\) | 4.66304 | 0.301627 | 0.150814 | − | 0.988562i | \(-0.451811\pi\) | ||||
0.150814 | + | 0.988562i | \(0.451811\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 13.3242 | 0.858287 | 0.429144 | − | 0.903236i | \(-0.358815\pi\) | ||||
0.429144 | + | 0.903236i | \(0.358815\pi\) | |||||||
\(242\) | 4.90379 | 0.315228 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 2.09544 | 0.134147 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0.462110 | 0.0294034 | ||||||||
\(248\) | 4.66011 | 0.295917 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −13.1063 | −0.827265 | −0.413633 | − | 0.910444i | \(-0.635740\pi\) | ||||
−0.413633 | + | 0.910444i | \(0.635740\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 7.32896 | 0.460768 | ||||||||
\(254\) | 27.0677 | 1.69838 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −10.5750 | −0.660939 | ||||||||
\(257\) | 5.19595 | 0.324115 | 0.162057 | − | 0.986781i | \(-0.448187\pi\) | ||||
0.162057 | + | 0.986781i | \(0.448187\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −17.7871 | −1.10524 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −17.4747 | −1.07959 | ||||||||
\(263\) | 0.145861 | 0.00899420 | 0.00449710 | − | 0.999990i | \(-0.498569\pi\) | ||||
0.00449710 | + | 0.999990i | \(0.498569\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 7.96920 | 0.488623 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −1.56434 | −0.0955574 | ||||||||
\(269\) | 13.8640 | 0.845303 | 0.422652 | − | 0.906292i | \(-0.361099\pi\) | ||||
0.422652 | + | 0.906292i | \(0.361099\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −3.09196 | −0.187823 | −0.0939117 | − | 0.995581i | \(-0.529937\pi\) | ||||
−0.0939117 | + | 0.995581i | \(0.529937\pi\) | |||||||
\(272\) | −14.5847 | −0.884328 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −11.8788 | −0.717627 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −11.3301 | −0.680758 | −0.340379 | − | 0.940288i | \(-0.610555\pi\) | ||||
−0.340379 | + | 0.940288i | \(0.610555\pi\) | |||||||
\(278\) | −22.0228 | −1.32084 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −3.42069 | −0.204061 | −0.102031 | − | 0.994781i | \(-0.532534\pi\) | ||||
−0.102031 | + | 0.994781i | \(0.532534\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −27.4747 | −1.63320 | −0.816601 | − | 0.577203i | \(-0.804144\pi\) | ||||
−0.816601 | + | 0.577203i | \(0.804144\pi\) | |||||||
\(284\) | 5.84451 | 0.346808 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −0.491590 | −0.0290684 | ||||||||
\(287\) | −20.5029 | −1.21025 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 9.29742 | 0.546907 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 5.43320 | 0.317954 | ||||||||
\(293\) | −23.5916 | −1.37824 | −0.689118 | − | 0.724649i | \(-0.742002\pi\) | ||||
−0.689118 | + | 0.724649i | \(0.742002\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −26.0438 | −1.51377 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 1.25408 | 0.0726471 | ||||||||
\(299\) | 0.413645 | 0.0239217 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −7.16232 | −0.412830 | ||||||||
\(302\) | 16.4366 | 0.945821 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 8.77779 | 0.503441 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −4.34390 | −0.247919 | −0.123960 | − | 0.992287i | \(-0.539559\pi\) | ||||
−0.123960 | + | 0.992287i | \(0.539559\pi\) | |||||||
\(308\) | 2.59198 | 0.147692 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 6.69981 | 0.379912 | 0.189956 | − | 0.981793i | \(-0.439166\pi\) | ||||
0.189956 | + | 0.981793i | \(0.439166\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −16.0033 | −0.904558 | −0.452279 | − | 0.891877i | \(-0.649389\pi\) | ||||
−0.452279 | + | 0.891877i | \(0.649389\pi\) | |||||||
\(314\) | −26.6804 | −1.50566 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −5.32444 | −0.299523 | ||||||||
\(317\) | −21.0650 | −1.18313 | −0.591563 | − | 0.806259i | \(-0.701489\pi\) | ||||
−0.591563 | + | 0.806259i | \(0.701489\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −18.4250 | −1.03160 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 7.13342 | 0.397530 | ||||||||
\(323\) | −15.8271 | −0.880641 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 6.17748 | 0.342139 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −30.0203 | −1.65760 | ||||||||
\(329\) | 8.35581 | 0.460671 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 30.4432 | 1.67331 | 0.836655 | − | 0.547731i | \(-0.184508\pi\) | ||||
0.836655 | + | 0.547731i | \(0.184508\pi\) | |||||||
\(332\) | 1.61882 | 0.0888445 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −28.4105 | −1.55456 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −28.9925 | −1.57932 | −0.789662 | − | 0.613542i | \(-0.789744\pi\) | ||||
−0.789662 | + | 0.613542i | \(0.789744\pi\) | |||||||
\(338\) | 16.0613 | 0.873618 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −4.04694 | −0.219154 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −20.1273 | −1.08677 | ||||||||
\(344\) | −10.4871 | −0.565424 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −7.64535 | −0.411017 | ||||||||
\(347\) | −5.55708 | −0.298320 | −0.149160 | − | 0.988813i | \(-0.547657\pi\) | ||||
−0.149160 | + | 0.988813i | \(0.547657\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −13.9703 | −0.747812 | −0.373906 | − | 0.927467i | \(-0.621982\pi\) | ||||
−0.373906 | + | 0.927467i | \(0.621982\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 6.87029 | 0.366187 | ||||||||
\(353\) | 19.7642 | 1.05194 | 0.525972 | − | 0.850502i | \(-0.323702\pi\) | ||||
0.525972 | + | 0.850502i | \(0.323702\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −6.97190 | −0.369510 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 18.1415 | 0.958808 | ||||||||
\(359\) | −11.6083 | −0.612665 | −0.306332 | − | 0.951925i | \(-0.599102\pi\) | ||||
−0.306332 | + | 0.951925i | \(0.599102\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −9.47450 | −0.498658 | ||||||||
\(362\) | 3.55888 | 0.187051 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0.146291 | 0.00766772 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 0.0182198 | 0.000951065 0 | 0.000475533 | − | 1.00000i | \(-0.499849\pi\) | ||||
0.000475533 | 1.00000i | \(0.499849\pi\) | ||||||||
\(368\) | 7.85720 | 0.409585 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 1.97254 | 0.102409 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −16.5665 | −0.857779 | −0.428890 | − | 0.903357i | \(-0.641095\pi\) | ||||
−0.428890 | + | 0.903357i | \(0.641095\pi\) | |||||||
\(374\) | 16.8368 | 0.870608 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 12.2346 | 0.630950 | ||||||||
\(377\) | −1.03990 | −0.0535577 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −2.52370 | −0.129634 | −0.0648170 | − | 0.997897i | \(-0.520646\pi\) | ||||
−0.0648170 | + | 0.997897i | \(0.520646\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 15.6208 | 0.799227 | ||||||||
\(383\) | 15.7910 | 0.806882 | 0.403441 | − | 0.915006i | \(-0.367814\pi\) | ||||
0.403441 | + | 0.915006i | \(0.367814\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 8.68879 | 0.442248 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −0.0267828 | −0.00135969 | ||||||||
\(389\) | 4.36976 | 0.221556 | 0.110778 | − | 0.993845i | \(-0.464666\pi\) | ||||
0.110778 | + | 0.993845i | \(0.464666\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −14.1672 | −0.716465 | ||||||||
\(392\) | −8.08666 | −0.408438 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −13.9920 | −0.704905 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −11.6729 | −0.585844 | −0.292922 | − | 0.956136i | \(-0.594628\pi\) | ||||
−0.292922 | + | 0.956136i | \(0.594628\pi\) | |||||||
\(398\) | −16.6864 | −0.836414 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −19.8999 | −0.993755 | −0.496877 | − | 0.867821i | \(-0.665520\pi\) | ||||
−0.496877 | + | 0.867821i | \(0.665520\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −0.228409 | −0.0113779 | ||||||||
\(404\) | −7.63245 | −0.379729 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −17.9334 | −0.890019 | ||||||||
\(407\) | 22.6170 | 1.12108 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −10.2084 | −0.504772 | −0.252386 | − | 0.967627i | \(-0.581215\pi\) | ||||
−0.252386 | + | 0.967627i | \(0.581215\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 2.51862 | 0.124083 | ||||||||
\(413\) | 17.0822 | 0.840562 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0.387758 | 0.0190114 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −10.1332 | −0.495630 | ||||||||
\(419\) | −37.8375 | −1.84848 | −0.924241 | − | 0.381810i | \(-0.875301\pi\) | ||||
−0.924241 | + | 0.381810i | \(0.875301\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 10.1730 | 0.495802 | 0.247901 | − | 0.968785i | \(-0.420259\pi\) | ||||
0.247901 | + | 0.968785i | \(0.420259\pi\) | |||||||
\(422\) | 12.5366 | 0.610275 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 2.88819 | 0.140263 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −9.33534 | −0.451769 | ||||||||
\(428\) | 9.48838 | 0.458638 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −37.9626 | −1.82859 | −0.914297 | − | 0.405045i | \(-0.867256\pi\) | ||||
−0.914297 | + | 0.405045i | \(0.867256\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −16.4745 | −0.791714 | −0.395857 | − | 0.918312i | \(-0.629552\pi\) | ||||
−0.395857 | + | 0.918312i | \(0.629552\pi\) | |||||||
\(434\) | −3.93897 | −0.189077 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 7.52933 | 0.360589 | ||||||||
\(437\) | 8.52649 | 0.407877 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 16.4231 | 0.783834 | 0.391917 | − | 0.920001i | \(-0.371812\pi\) | ||||
0.391917 | + | 0.920001i | \(0.371812\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0.950264 | 0.0451994 | ||||||||
\(443\) | −34.6321 | −1.64542 | −0.822709 | − | 0.568462i | \(-0.807539\pi\) | ||||
−0.822709 | + | 0.568462i | \(0.807539\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 28.0110 | 1.32636 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 18.5544 | 0.876613 | ||||||||
\(449\) | −14.7835 | −0.697678 | −0.348839 | − | 0.937183i | \(-0.613424\pi\) | ||||
−0.348839 | + | 0.937183i | \(0.613424\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 26.0703 | 1.22760 | ||||||||
\(452\) | 3.93716 | 0.185188 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 6.34662 | 0.297862 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 23.8075 | 1.11367 | 0.556833 | − | 0.830624i | \(-0.312016\pi\) | ||||
0.556833 | + | 0.830624i | \(0.312016\pi\) | |||||||
\(458\) | −25.8301 | −1.20696 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −23.1017 | −1.07595 | −0.537977 | − | 0.842959i | \(-0.680811\pi\) | ||||
−0.537977 | + | 0.842959i | \(0.680811\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 0.884510 | 0.0411067 | 0.0205533 | − | 0.999789i | \(-0.493457\pi\) | ||||
0.0205533 | + | 0.999789i | \(0.493457\pi\) | |||||||
\(464\) | −19.7530 | −0.917008 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −21.5330 | −0.997497 | ||||||||
\(467\) | −19.3835 | −0.896959 | −0.448480 | − | 0.893793i | \(-0.648034\pi\) | ||||
−0.448480 | + | 0.893793i | \(0.648034\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 6.96926 | 0.321811 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 25.0118 | 1.15126 | ||||||||
\(473\) | 9.10719 | 0.418749 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −5.01039 | −0.229651 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −5.77106 | −0.263962 | ||||||||
\(479\) | −32.8149 | −1.49935 | −0.749674 | − | 0.661807i | \(-0.769790\pi\) | ||||
−0.749674 | + | 0.661807i | \(0.769790\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1.27650 | 0.0582035 | ||||||||
\(482\) | −16.4902 | −0.751110 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 1.85556 | 0.0843439 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −18.5956 | −0.842648 | −0.421324 | − | 0.906910i | \(-0.638434\pi\) | ||||
−0.421324 | + | 0.906910i | \(0.638434\pi\) | |||||||
\(488\) | −13.6688 | −0.618757 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 27.3676 | 1.23508 | 0.617540 | − | 0.786539i | \(-0.288129\pi\) | ||||
0.617540 | + | 0.786539i | \(0.288129\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 35.6162 | 1.60407 | ||||||||
\(494\) | −0.571915 | −0.0257317 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −4.33863 | −0.194810 | ||||||||
\(497\) | −26.0377 | −1.16795 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −0.852639 | −0.0381694 | −0.0190847 | − | 0.999818i | \(-0.506075\pi\) | ||||
−0.0190847 | + | 0.999818i | \(0.506075\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 16.2206 | 0.723962 | ||||||||
\(503\) | −30.4176 | −1.35626 | −0.678128 | − | 0.734944i | \(-0.737208\pi\) | ||||
−0.678128 | + | 0.734944i | \(0.737208\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −9.07044 | −0.403230 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 10.2423 | 0.454427 | ||||||||
\(509\) | −4.30887 | −0.190987 | −0.0954936 | − | 0.995430i | \(-0.530443\pi\) | ||||
−0.0954936 | + | 0.995430i | \(0.530443\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −24.2053 | −1.07078 | ||||||||
\(512\) | 24.7417 | 1.09344 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −6.43059 | −0.283641 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −10.6248 | −0.467277 | ||||||||
\(518\) | 22.0136 | 0.967222 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 9.99538 | 0.437905 | 0.218953 | − | 0.975735i | \(-0.429736\pi\) | ||||
0.218953 | + | 0.975735i | \(0.429736\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −13.1913 | −0.576814 | −0.288407 | − | 0.957508i | \(-0.593126\pi\) | ||||
−0.288407 | + | 0.957508i | \(0.593126\pi\) | |||||||
\(524\) | −6.61232 | −0.288861 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −0.180521 | −0.00787107 | ||||||||
\(527\) | 7.82290 | 0.340771 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −15.3677 | −0.668163 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 3.01550 | 0.130738 | ||||||||
\(533\) | 1.47141 | 0.0637336 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 10.2044 | 0.440762 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −17.1583 | −0.739747 | ||||||||
\(539\) | 7.02263 | 0.302486 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 35.6710 | 1.53362 | 0.766809 | − | 0.641876i | \(-0.221844\pi\) | ||||
0.766809 | + | 0.641876i | \(0.221844\pi\) | |||||||
\(542\) | 3.82666 | 0.164369 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −13.2805 | −0.569398 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 16.6018 | 0.709842 | 0.354921 | − | 0.934896i | \(-0.384508\pi\) | ||||
0.354921 | + | 0.934896i | \(0.384508\pi\) | |||||||
\(548\) | −4.49488 | −0.192012 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −21.4356 | −0.913186 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 23.7208 | 1.00871 | ||||||||
\(554\) | 14.0223 | 0.595749 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −8.33330 | −0.353411 | ||||||||
\(557\) | 14.8875 | 0.630802 | 0.315401 | − | 0.948958i | \(-0.397861\pi\) | ||||
0.315401 | + | 0.948958i | \(0.397861\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0.514009 | 0.0217403 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 4.23350 | 0.178579 | ||||||||
\(563\) | −46.4541 | −1.95781 | −0.978904 | − | 0.204322i | \(-0.934501\pi\) | ||||
−0.978904 | + | 0.204322i | \(0.934501\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 34.0031 | 1.42926 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −38.1244 | −1.59966 | ||||||||
\(569\) | −9.57157 | −0.401261 | −0.200631 | − | 0.979667i | \(-0.564299\pi\) | ||||
−0.200631 | + | 0.979667i | \(0.564299\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 0.921854 | 0.0385784 | 0.0192892 | − | 0.999814i | \(-0.493860\pi\) | ||||
0.0192892 | + | 0.999814i | \(0.493860\pi\) | |||||||
\(572\) | −0.186015 | −0.00777767 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 25.3747 | 1.05912 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −20.5519 | −0.855589 | −0.427794 | − | 0.903876i | \(-0.640709\pi\) | ||||
−0.427794 | + | 0.903876i | \(0.640709\pi\) | |||||||
\(578\) | −11.5066 | −0.478613 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −7.21198 | −0.299204 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −2.50817 | −0.103878 | ||||||||
\(584\) | −35.4414 | −1.46658 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 29.1973 | 1.20613 | ||||||||
\(587\) | 0.487355 | 0.0201153 | 0.0100576 | − | 0.999949i | \(-0.496798\pi\) | ||||
0.0100576 | + | 0.999949i | \(0.496798\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −4.70820 | −0.193998 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 24.2472 | 0.996552 | ||||||||
\(593\) | 34.3654 | 1.41122 | 0.705608 | − | 0.708602i | \(-0.250674\pi\) | ||||
0.705608 | + | 0.708602i | \(0.250674\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0.474538 | 0.0194378 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −0.511934 | −0.0209345 | ||||||||
\(599\) | −39.2856 | −1.60517 | −0.802583 | − | 0.596540i | \(-0.796542\pi\) | ||||
−0.802583 | + | 0.596540i | \(0.796542\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −48.6333 | −1.98379 | −0.991897 | − | 0.127044i | \(-0.959451\pi\) | ||||
−0.991897 | + | 0.127044i | \(0.959451\pi\) | |||||||
\(602\) | 8.86421 | 0.361278 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 6.21952 | 0.253068 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −37.4916 | −1.52174 | −0.760869 | − | 0.648906i | \(-0.775227\pi\) | ||||
−0.760869 | + | 0.648906i | \(0.775227\pi\) | |||||||
\(608\) | 7.99287 | 0.324154 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −0.599660 | −0.0242597 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 37.7346 | 1.52409 | 0.762043 | − | 0.647526i | \(-0.224196\pi\) | ||||
0.762043 | + | 0.647526i | \(0.224196\pi\) | |||||||
\(614\) | 5.37608 | 0.216961 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −16.9078 | −0.681233 | ||||||||
\(617\) | −41.3260 | −1.66372 | −0.831861 | − | 0.554984i | \(-0.812724\pi\) | ||||
−0.831861 | + | 0.554984i | \(0.812724\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 11.7256 | 0.471294 | 0.235647 | − | 0.971839i | \(-0.424279\pi\) | ||||
0.235647 | + | 0.971839i | \(0.424279\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −8.29180 | −0.332471 | ||||||||
\(623\) | 31.0603 | 1.24441 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 19.8059 | 0.791602 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −10.0957 | −0.402862 | ||||||||
\(629\) | −43.7196 | −1.74322 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 24.4523 | 0.973430 | 0.486715 | − | 0.873561i | \(-0.338195\pi\) | ||||
0.486715 | + | 0.873561i | \(0.338195\pi\) | |||||||
\(632\) | 34.7320 | 1.38156 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 26.0703 | 1.03538 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0.396356 | 0.0157042 | ||||||||
\(638\) | 22.8030 | 0.902781 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 20.8359 | 0.822969 | 0.411484 | − | 0.911417i | \(-0.365010\pi\) | ||||
0.411484 | + | 0.911417i | \(0.365010\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 20.6793 | 0.815510 | 0.407755 | − | 0.913091i | \(-0.366312\pi\) | ||||
0.407755 | + | 0.913091i | \(0.366312\pi\) | |||||||
\(644\) | 2.69924 | 0.106365 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 19.5878 | 0.770673 | ||||||||
\(647\) | −15.5302 | −0.610554 | −0.305277 | − | 0.952264i | \(-0.598749\pi\) | ||||
−0.305277 | + | 0.952264i | \(0.598749\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −21.7208 | −0.852615 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 2.33752 | 0.0915444 | ||||||||
\(653\) | 28.4323 | 1.11264 | 0.556320 | − | 0.830968i | \(-0.312213\pi\) | ||||
0.556320 | + | 0.830968i | \(0.312213\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 27.9494 | 1.09124 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −10.3413 | −0.403145 | ||||||||
\(659\) | 17.9375 | 0.698748 | 0.349374 | − | 0.936983i | \(-0.386394\pi\) | ||||
0.349374 | + | 0.936983i | \(0.386394\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −5.32444 | −0.207097 | −0.103548 | − | 0.994624i | \(-0.533020\pi\) | ||||
−0.103548 | + | 0.994624i | \(0.533020\pi\) | |||||||
\(662\) | −37.6770 | −1.46436 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −10.5598 | −0.409799 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −19.1875 | −0.742942 | ||||||||
\(668\) | −10.7504 | −0.415945 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 11.8703 | 0.458247 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 7.66248 | 0.295367 | 0.147683 | − | 0.989035i | \(-0.452818\pi\) | ||||
0.147683 | + | 0.989035i | \(0.452818\pi\) | |||||||
\(674\) | 35.8816 | 1.38211 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 6.07749 | 0.233749 | ||||||||
\(677\) | 37.4111 | 1.43783 | 0.718914 | − | 0.695099i | \(-0.244640\pi\) | ||||
0.718914 | + | 0.695099i | \(0.244640\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0.119320 | 0.00457906 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 5.00856 | 0.191788 | ||||||||
\(683\) | −18.3023 | −0.700318 | −0.350159 | − | 0.936690i | \(-0.613872\pi\) | ||||
−0.350159 | + | 0.936690i | \(0.613872\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 24.9099 | 0.951064 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 9.76360 | 0.372234 | ||||||||
\(689\) | −0.141561 | −0.00539303 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 19.9505 | 0.758952 | 0.379476 | − | 0.925202i | \(-0.376104\pi\) | ||||
0.379476 | + | 0.925202i | \(0.376104\pi\) | |||||||
\(692\) | −2.89295 | −0.109974 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 6.87754 | 0.261068 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −50.3950 | −1.90885 | ||||||||
\(698\) | 17.2898 | 0.654430 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −41.9220 | −1.58337 | −0.791687 | − | 0.610927i | \(-0.790797\pi\) | ||||
−0.791687 | + | 0.610927i | \(0.790797\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 26.3126 | 0.992398 | ||||||||
\(704\) | −23.5927 | −0.889183 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −24.4605 | −0.920584 | ||||||||
\(707\) | 34.0031 | 1.27882 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 6.12755 | 0.230125 | 0.115063 | − | 0.993358i | \(-0.463293\pi\) | ||||
0.115063 | + | 0.993358i | \(0.463293\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 45.4785 | 1.70438 | ||||||||
\(713\) | −4.21442 | −0.157831 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 6.86463 | 0.256543 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 14.3667 | 0.536159 | ||||||||
\(719\) | 40.2449 | 1.50088 | 0.750440 | − | 0.660939i | \(-0.229842\pi\) | ||||
0.750440 | + | 0.660939i | \(0.229842\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −11.2206 | −0.417878 | ||||||||
\(722\) | 11.7258 | 0.436389 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 1.34666 | 0.0500482 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 9.61564 | 0.356624 | 0.178312 | − | 0.983974i | \(-0.442936\pi\) | ||||
0.178312 | + | 0.983974i | \(0.442936\pi\) | |||||||
\(728\) | −0.954271 | −0.0353676 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −17.6046 | −0.651128 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −9.23751 | −0.341195 | −0.170598 | − | 0.985341i | \(-0.554570\pi\) | ||||
−0.170598 | + | 0.985341i | \(0.554570\pi\) | |||||||
\(734\) | −0.0225491 | −0.000832303 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 7.15460 | 0.263722 | ||||||||
\(737\) | −8.86171 | −0.326425 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 11.7962 | 0.433931 | 0.216966 | − | 0.976179i | \(-0.430384\pi\) | ||||
0.216966 | + | 0.976179i | \(0.430384\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −2.44125 | −0.0896210 | ||||||||
\(743\) | −7.23858 | −0.265558 | −0.132779 | − | 0.991146i | \(-0.542390\pi\) | ||||
−0.132779 | + | 0.991146i | \(0.542390\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 20.5029 | 0.750665 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 6.37092 | 0.232944 | ||||||||
\(749\) | −42.2715 | −1.54457 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 4.76976 | 0.174051 | 0.0870255 | − | 0.996206i | \(-0.472264\pi\) | ||||
0.0870255 | + | 0.996206i | \(0.472264\pi\) | |||||||
\(752\) | −11.3906 | −0.415371 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 1.28700 | 0.0468698 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −15.7834 | −0.573658 | −0.286829 | − | 0.957982i | \(-0.592601\pi\) | ||||
−0.286829 | + | 0.957982i | \(0.592601\pi\) | |||||||
\(758\) | 3.12338 | 0.113446 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 28.6365 | 1.03807 | 0.519036 | − | 0.854752i | \(-0.326291\pi\) | ||||
0.519036 | + | 0.854752i | \(0.326291\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −33.5437 | −1.21436 | ||||||||
\(764\) | 5.91080 | 0.213845 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −19.5432 | −0.706124 | ||||||||
\(767\) | −1.22592 | −0.0442653 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 44.2898 | 1.59713 | 0.798566 | − | 0.601907i | \(-0.205592\pi\) | ||||
0.798566 | + | 0.601907i | \(0.205592\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 3.28779 | 0.118330 | ||||||||
\(773\) | −14.3392 | −0.515746 | −0.257873 | − | 0.966179i | \(-0.583022\pi\) | ||||
−0.257873 | + | 0.966179i | \(0.583022\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0.174707 | 0.00627163 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −5.40809 | −0.193889 | ||||||||
\(779\) | 30.3301 | 1.08669 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 33.1080 | 1.18470 | ||||||||
\(782\) | 17.5335 | 0.626997 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 7.52879 | 0.268885 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 49.6574 | 1.77009 | 0.885047 | − | 0.465501i | \(-0.154126\pi\) | ||||
0.885047 | + | 0.465501i | \(0.154126\pi\) | |||||||
\(788\) | −5.29448 | −0.188608 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −17.5403 | −0.623663 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0.669956 | 0.0237908 | ||||||||
\(794\) | 14.4465 | 0.512688 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −6.31403 | −0.223795 | ||||||||
\(797\) | −3.33054 | −0.117974 | −0.0589869 | − | 0.998259i | \(-0.518787\pi\) | ||||
−0.0589869 | + | 0.998259i | \(0.518787\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 20.5381 | 0.726586 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 24.6285 | 0.869661 | ||||||||
\(803\) | 30.7781 | 1.08614 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0.282683 | 0.00995707 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 49.7873 | 1.75151 | ||||||||
\(809\) | −22.9978 | −0.808559 | −0.404280 | − | 0.914635i | \(-0.632478\pi\) | ||||
−0.404280 | + | 0.914635i | \(0.632478\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 1.70528 | 0.0598804 | 0.0299402 | − | 0.999552i | \(-0.490468\pi\) | ||||
0.0299402 | + | 0.999552i | \(0.490468\pi\) | |||||||
\(812\) | −6.78588 | −0.238138 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −27.9912 | −0.981091 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 10.5953 | 0.370682 | ||||||||
\(818\) | 12.6341 | 0.441739 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −19.5935 | −0.683819 | −0.341910 | − | 0.939733i | \(-0.611074\pi\) | ||||
−0.341910 | + | 0.939733i | \(0.611074\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −6.41237 | −0.223521 | −0.111761 | − | 0.993735i | \(-0.535649\pi\) | ||||
−0.111761 | + | 0.993735i | \(0.535649\pi\) | |||||||
\(824\) | −16.4292 | −0.572339 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −21.1413 | −0.735598 | ||||||||
\(827\) | 31.6309 | 1.09991 | 0.549957 | − | 0.835193i | \(-0.314644\pi\) | ||||
0.549957 | + | 0.835193i | \(0.314644\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −3.08634 | −0.107193 | −0.0535965 | − | 0.998563i | \(-0.517068\pi\) | ||||
−0.0535965 | + | 0.998563i | \(0.517068\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −1.33157 | −0.0461638 | ||||||||
\(833\) | −13.5750 | −0.470347 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −3.83433 | −0.132613 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 46.8283 | 1.61766 | ||||||||
\(839\) | −15.2136 | −0.525233 | −0.262616 | − | 0.964900i | \(-0.584585\pi\) | ||||
−0.262616 | + | 0.964900i | \(0.584585\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 19.2372 | 0.663352 | ||||||||
\(842\) | −12.5903 | −0.433890 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 4.74379 | 0.163288 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −8.26668 | −0.284046 | ||||||||
\(848\) | −2.68894 | −0.0923387 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 23.5530 | 0.807386 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 25.1005 | 0.859426 | 0.429713 | − | 0.902966i | \(-0.358615\pi\) | ||||
0.429713 | + | 0.902966i | \(0.358615\pi\) | |||||||
\(854\) | 11.5536 | 0.395355 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −61.8938 | −2.11549 | ||||||||
\(857\) | −34.7042 | −1.18547 | −0.592737 | − | 0.805396i | \(-0.701952\pi\) | ||||
−0.592737 | + | 0.805396i | \(0.701952\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 38.5260 | 1.31449 | 0.657246 | − | 0.753676i | \(-0.271721\pi\) | ||||
0.657246 | + | 0.753676i | \(0.271721\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 46.9831 | 1.60025 | ||||||||
\(863\) | 45.6656 | 1.55447 | 0.777237 | − | 0.629208i | \(-0.216621\pi\) | ||||
0.777237 | + | 0.629208i | \(0.216621\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 20.3891 | 0.692850 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −1.49048 | −0.0505903 | ||||||||
\(869\) | −30.1620 | −1.02318 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −0.500153 | −0.0169471 | ||||||||
\(872\) | −49.1146 | −1.66323 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −10.5525 | −0.356944 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 6.58359 | 0.222312 | 0.111156 | − | 0.993803i | \(-0.464545\pi\) | ||||
0.111156 | + | 0.993803i | \(0.464545\pi\) | |||||||
\(878\) | −20.3255 | −0.685954 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −42.9142 | −1.44581 | −0.722907 | − | 0.690945i | \(-0.757195\pi\) | ||||
−0.722907 | + | 0.690945i | \(0.757195\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −35.4942 | −1.19447 | −0.597237 | − | 0.802065i | \(-0.703735\pi\) | ||||
−0.597237 | + | 0.802065i | \(0.703735\pi\) | |||||||
\(884\) | 0.359574 | 0.0120938 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 42.8612 | 1.43995 | ||||||||
\(887\) | 24.5790 | 0.825282 | 0.412641 | − | 0.910894i | \(-0.364606\pi\) | ||||
0.412641 | + | 0.910894i | \(0.364606\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −45.6301 | −1.53038 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 10.5992 | 0.354887 | ||||||||
\(893\) | −12.3608 | −0.413639 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −12.1570 | −0.406137 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 18.2963 | 0.610557 | ||||||||
\(899\) | 10.5950 | 0.353364 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 4.84839 | 0.161523 | ||||||||
\(902\) | −32.2651 | −1.07431 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −25.6825 | −0.854188 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −46.5140 | −1.54447 | −0.772236 | − | 0.635336i | \(-0.780862\pi\) | ||||
−0.772236 | + | 0.635336i | \(0.780862\pi\) | |||||||
\(908\) | 2.40152 | 0.0796973 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −15.2581 | −0.505523 | −0.252761 | − | 0.967529i | \(-0.581339\pi\) | ||||
−0.252761 | + | 0.967529i | \(0.581339\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 9.17034 | 0.303494 | ||||||||
\(914\) | −29.4645 | −0.974599 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −9.77396 | −0.322941 | ||||||||
\(917\) | 29.4584 | 0.972802 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −12.0177 | −0.396427 | −0.198213 | − | 0.980159i | \(-0.563514\pi\) | ||||
−0.198213 | + | 0.980159i | \(0.563514\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 28.5911 | 0.941597 | ||||||||
\(923\) | 1.86861 | 0.0615061 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −1.09468 | −0.0359735 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −17.9866 | −0.590440 | ||||||||
\(929\) | −1.48156 | −0.0486086 | −0.0243043 | − | 0.999705i | \(-0.507737\pi\) | ||||
−0.0243043 | + | 0.999705i | \(0.507737\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 8.17011 | 0.267765 | ||||||||
\(932\) | −8.14796 | −0.266895 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 23.9893 | 0.784953 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −38.5057 | −1.25793 | −0.628963 | − | 0.777435i | \(-0.716520\pi\) | ||||
−0.628963 | + | 0.777435i | \(0.716520\pi\) | |||||||
\(938\) | −8.62527 | −0.281625 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 24.8562 | 0.810291 | 0.405145 | − | 0.914252i | \(-0.367221\pi\) | ||||
0.405145 | + | 0.914252i | \(0.367221\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 27.1492 | 0.884100 | ||||||||
\(944\) | −23.2863 | −0.757905 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −11.2712 | −0.366459 | ||||||||
\(947\) | 10.6476 | 0.345999 | 0.172999 | − | 0.984922i | \(-0.444654\pi\) | ||||
0.172999 | + | 0.984922i | \(0.444654\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 1.73711 | 0.0563890 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 32.6834 | 1.05927 | ||||||||
\(953\) | −27.2483 | −0.882659 | −0.441329 | − | 0.897345i | \(-0.645493\pi\) | ||||
−0.441329 | + | 0.897345i | \(0.645493\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −2.18373 | −0.0706270 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 40.6122 | 1.31212 | ||||||||
\(959\) | 20.0250 | 0.646643 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −28.6729 | −0.924931 | ||||||||
\(962\) | −1.57982 | −0.0509354 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −6.23981 | −0.200971 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −37.9832 | −1.22146 | −0.610729 | − | 0.791840i | \(-0.709123\pi\) | ||||
−0.610729 | + | 0.791840i | \(0.709123\pi\) | |||||||
\(968\) | −12.1041 | −0.389039 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −4.14071 | −0.132882 | −0.0664409 | − | 0.997790i | \(-0.521164\pi\) | ||||
−0.0664409 | + | 0.997790i | \(0.521164\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 37.1255 | 1.19019 | ||||||||
\(974\) | 23.0142 | 0.737424 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 12.7258 | 0.407344 | ||||||||
\(977\) | −50.3811 | −1.61183 | −0.805917 | − | 0.592028i | \(-0.798327\pi\) | ||||
−0.805917 | + | 0.592028i | \(0.798327\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −39.4945 | −1.26225 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −33.8705 | −1.08085 | ||||||||
\(983\) | 30.0565 | 0.958654 | 0.479327 | − | 0.877637i | \(-0.340881\pi\) | ||||
0.479327 | + | 0.877637i | \(0.340881\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −44.0792 | −1.40377 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −0.216409 | −0.00688489 | ||||||||
\(989\) | 9.48408 | 0.301576 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 4.37287 | 0.138909 | 0.0694544 | − | 0.997585i | \(-0.477874\pi\) | ||||
0.0694544 | + | 0.997585i | \(0.477874\pi\) | |||||||
\(992\) | −3.95067 | −0.125434 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 32.2247 | 1.02211 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 2.57051 | 0.0814090 | 0.0407045 | − | 0.999171i | \(-0.487040\pi\) | ||||
0.0407045 | + | 0.999171i | \(0.487040\pi\) | |||||||
\(998\) | 1.05524 | 0.0334030 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 5625.2.a.z.1.3 | ✓ | 8 | |
3.2 | odd | 2 | inner | 5625.2.a.z.1.6 | yes | 8 | |
5.4 | even | 2 | 5625.2.a.bb.1.6 | yes | 8 | ||
15.14 | odd | 2 | 5625.2.a.bb.1.3 | yes | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
5625.2.a.z.1.3 | ✓ | 8 | 1.1 | even | 1 | trivial | |
5625.2.a.z.1.6 | yes | 8 | 3.2 | odd | 2 | inner | |
5625.2.a.bb.1.3 | yes | 8 | 15.14 | odd | 2 | ||
5625.2.a.bb.1.6 | yes | 8 | 5.4 | even | 2 |