Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6040,2,Mod(1,6040)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6040, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("6040.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6040 = 2^{3} \cdot 5 \cdot 151 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6040.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: | \(48.2296428209\) |
Analytic rank: | \(1\) |
Dimension: | \(9\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{9} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{9} - x^{8} - 11x^{7} + 9x^{6} + 32x^{5} - 17x^{4} - 27x^{3} + 10x^{2} + 3x - 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(0.390645\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6040.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −1.96251 | −1.13305 | −0.566527 | − | 0.824043i | \(-0.691713\pi\) | ||||
−0.566527 | + | 0.824043i | \(0.691713\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.16922 | −0.819890 | −0.409945 | − | 0.912110i | \(-0.634452\pi\) | ||||
−0.409945 | + | 0.912110i | \(0.634452\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0.851433 | 0.283811 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 3.01214 | 0.908193 | 0.454097 | − | 0.890952i | \(-0.349962\pi\) | ||||
0.454097 | + | 0.890952i | \(0.349962\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.71469 | −0.752919 | −0.376460 | − | 0.926433i | \(-0.622859\pi\) | ||||
−0.376460 | + | 0.926433i | \(0.622859\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.96251 | −0.506717 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 0.748145 | 0.181452 | 0.0907259 | − | 0.995876i | \(-0.471081\pi\) | ||||
0.0907259 | + | 0.995876i | \(0.471081\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −4.29171 | −0.984585 | −0.492293 | − | 0.870430i | \(-0.663841\pi\) | ||||
−0.492293 | + | 0.870430i | \(0.663841\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 4.25712 | 0.928979 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.71882 | 0.358398 | 0.179199 | − | 0.983813i | \(-0.442649\pi\) | ||||
0.179199 | + | 0.983813i | \(0.442649\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 4.21658 | 0.811481 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −1.74832 | −0.324654 | −0.162327 | − | 0.986737i | \(-0.551900\pi\) | ||||
−0.162327 | + | 0.986737i | \(0.551900\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.16689 | 0.748396 | 0.374198 | − | 0.927349i | \(-0.377918\pi\) | ||||
0.374198 | + | 0.927349i | \(0.377918\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −5.91134 | −1.02903 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −2.16922 | −0.366666 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 4.69387 | 0.771668 | 0.385834 | − | 0.922568i | \(-0.373914\pi\) | ||||
0.385834 | + | 0.922568i | \(0.373914\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 5.32759 | 0.853098 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −9.89262 | −1.54497 | −0.772484 | − | 0.635034i | \(-0.780986\pi\) | ||||
−0.772484 | + | 0.635034i | \(0.780986\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 8.49792 | 1.29592 | 0.647960 | − | 0.761674i | \(-0.275622\pi\) | ||||
0.647960 | + | 0.761674i | \(0.275622\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0.851433 | 0.126924 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 12.8181 | 1.86971 | 0.934856 | − | 0.355028i | \(-0.115529\pi\) | ||||
0.934856 | + | 0.355028i | \(0.115529\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −2.29447 | −0.327781 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −1.46824 | −0.205595 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −7.88590 | −1.08321 | −0.541606 | − | 0.840633i | \(-0.682183\pi\) | ||||
−0.541606 | + | 0.840633i | \(0.682183\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 3.01214 | 0.406156 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 8.42251 | 1.11559 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 6.20478 | 0.807793 | 0.403897 | − | 0.914805i | \(-0.367656\pi\) | ||||
0.403897 | + | 0.914805i | \(0.367656\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −9.79583 | −1.25423 | −0.627114 | − | 0.778927i | \(-0.715764\pi\) | ||||
−0.627114 | + | 0.778927i | \(0.715764\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −1.84695 | −0.232694 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −2.71469 | −0.336716 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 2.54968 | 0.311493 | 0.155746 | − | 0.987797i | \(-0.450222\pi\) | ||||
0.155746 | + | 0.987797i | \(0.450222\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −3.37319 | −0.406084 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −6.64355 | −0.788445 | −0.394222 | − | 0.919015i | \(-0.628986\pi\) | ||||
−0.394222 | + | 0.919015i | \(0.628986\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −6.53691 | −0.765088 | −0.382544 | − | 0.923937i | \(-0.624952\pi\) | ||||
−0.382544 | + | 0.923937i | \(0.624952\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −1.96251 | −0.226611 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −6.53400 | −0.744618 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −5.44102 | −0.612163 | −0.306081 | − | 0.952005i | \(-0.599018\pi\) | ||||
−0.306081 | + | 0.952005i | \(0.599018\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −10.8294 | −1.20326 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 4.01722 | 0.440947 | 0.220473 | − | 0.975393i | \(-0.429240\pi\) | ||||
0.220473 | + | 0.975393i | \(0.429240\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0.748145 | 0.0811477 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 3.43108 | 0.367850 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 15.0573 | 1.59607 | 0.798036 | − | 0.602610i | \(-0.205873\pi\) | ||||
0.798036 | + | 0.602610i | \(0.205873\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 5.88877 | 0.617311 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −8.17755 | −0.847973 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −4.29171 | −0.440320 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −2.91029 | −0.295495 | −0.147748 | − | 0.989025i | \(-0.547202\pi\) | ||||
−0.147748 | + | 0.989025i | \(0.547202\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 2.56463 | 0.257755 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 2.73382 | 0.272025 | 0.136013 | − | 0.990707i | \(-0.456571\pi\) | ||||
0.136013 | + | 0.990707i | \(0.456571\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 3.62541 | 0.357222 | 0.178611 | − | 0.983920i | \(-0.442840\pi\) | ||||
0.178611 | + | 0.983920i | \(0.442840\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 4.25712 | 0.415452 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −3.20902 | −0.310227 | −0.155114 | − | 0.987897i | \(-0.549574\pi\) | ||||
−0.155114 | + | 0.987897i | \(0.549574\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −4.88474 | −0.467873 | −0.233936 | − | 0.972252i | \(-0.575161\pi\) | ||||
−0.233936 | + | 0.972252i | \(0.575161\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −9.21176 | −0.874341 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 8.30803 | 0.781554 | 0.390777 | − | 0.920485i | \(-0.372206\pi\) | ||||
0.390777 | + | 0.920485i | \(0.372206\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1.71882 | 0.160281 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −2.31138 | −0.213687 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −1.62289 | −0.148770 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1.92703 | −0.175185 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 19.4143 | 1.75053 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 2.07348 | 0.183992 | 0.0919958 | − | 0.995759i | \(-0.470675\pi\) | ||||
0.0919958 | + | 0.995759i | \(0.470675\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −16.6772 | −1.46835 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −13.3055 | −1.16251 | −0.581253 | − | 0.813723i | \(-0.697437\pi\) | ||||
−0.581253 | + | 0.813723i | \(0.697437\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 9.30968 | 0.807251 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 4.21658 | 0.362905 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 18.3490 | 1.56766 | 0.783832 | − | 0.620973i | \(-0.213262\pi\) | ||||
0.783832 | + | 0.620973i | \(0.213262\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −0.0634977 | −0.00538581 | −0.00269290 | − | 0.999996i | \(-0.500857\pi\) | ||||
−0.00269290 | + | 0.999996i | \(0.500857\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −25.1556 | −2.11848 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −8.17701 | −0.683796 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −1.74832 | −0.145190 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 4.50291 | 0.371393 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 11.4828 | 0.940711 | 0.470356 | − | 0.882477i | \(-0.344126\pi\) | ||||
0.470356 | + | 0.882477i | \(0.344126\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1.00000 | −0.0813788 | ||||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0.636995 | 0.0514980 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 4.16689 | 0.334693 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 2.26410 | 0.180695 | 0.0903475 | − | 0.995910i | \(-0.471202\pi\) | ||||
0.0903475 | + | 0.995910i | \(0.471202\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 15.4761 | 1.22734 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −3.72850 | −0.293847 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −18.5884 | −1.45595 | −0.727976 | − | 0.685602i | \(-0.759539\pi\) | ||||
−0.727976 | + | 0.685602i | \(0.759539\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −5.91134 | −0.460197 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 1.75344 | 0.135685 | 0.0678426 | − | 0.997696i | \(-0.478388\pi\) | ||||
0.0678426 | + | 0.997696i | \(0.478388\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −5.63047 | −0.433113 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −3.65410 | −0.279436 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 17.5676 | 1.33564 | 0.667819 | − | 0.744324i | \(-0.267228\pi\) | ||||
0.667819 | + | 0.744324i | \(0.267228\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −2.16922 | −0.163978 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −12.1769 | −0.915273 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −16.1306 | −1.20566 | −0.602829 | − | 0.797870i | \(-0.705960\pi\) | ||||
−0.602829 | + | 0.797870i | \(0.705960\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −16.9945 | −1.26319 | −0.631596 | − | 0.775298i | \(-0.717600\pi\) | ||||
−0.631596 | + | 0.775298i | \(0.717600\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 19.2244 | 1.42111 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 4.69387 | 0.345100 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 2.25352 | 0.164793 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −9.14670 | −0.665325 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −8.52383 | −0.616763 | −0.308381 | − | 0.951263i | \(-0.599787\pi\) | ||||
−0.308381 | + | 0.951263i | \(0.599787\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −21.7917 | −1.56860 | −0.784300 | − | 0.620382i | \(-0.786977\pi\) | ||||
−0.784300 | + | 0.620382i | \(0.786977\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 5.32759 | 0.381517 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 11.6273 | 0.828408 | 0.414204 | − | 0.910184i | \(-0.364060\pi\) | ||||
0.414204 | + | 0.910184i | \(0.364060\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −20.9477 | −1.48495 | −0.742473 | − | 0.669876i | \(-0.766347\pi\) | ||||
−0.742473 | + | 0.669876i | \(0.766347\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −5.00376 | −0.352938 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 3.79249 | 0.266180 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −9.89262 | −0.690931 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 1.46346 | 0.101717 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −12.9272 | −0.894194 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −9.21057 | −0.634082 | −0.317041 | − | 0.948412i | \(-0.602689\pi\) | ||||
−0.317041 | + | 0.948412i | \(0.602689\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 13.0380 | 0.893350 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 8.49792 | 0.579553 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −9.03892 | −0.613602 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 12.8287 | 0.866886 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −2.03098 | −0.136619 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 13.4874 | 0.903185 | 0.451592 | − | 0.892224i | \(-0.350856\pi\) | ||||
0.451592 | + | 0.892224i | \(0.350856\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0.851433 | 0.0567622 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 10.3020 | 0.683765 | 0.341882 | − | 0.939743i | \(-0.388936\pi\) | ||||
0.341882 | + | 0.939743i | \(0.388936\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −14.3497 | −0.948258 | −0.474129 | − | 0.880455i | \(-0.657237\pi\) | ||||
−0.474129 | + | 0.880455i | \(0.657237\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 12.8230 | 0.843693 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −20.7413 | −1.35881 | −0.679404 | − | 0.733764i | \(-0.737762\pi\) | ||||
−0.679404 | + | 0.733764i | \(0.737762\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 12.8181 | 0.836160 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 10.6780 | 0.693613 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 6.25664 | 0.404708 | 0.202354 | − | 0.979312i | \(-0.435141\pi\) | ||||
0.202354 | + | 0.979312i | \(0.435141\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 20.1542 | 1.29825 | 0.649125 | − | 0.760682i | \(-0.275135\pi\) | ||||
0.649125 | + | 0.760682i | \(0.275135\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 8.60296 | 0.551880 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −2.29447 | −0.146588 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 11.6506 | 0.741313 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −7.88381 | −0.499616 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 4.67467 | 0.295063 | 0.147531 | − | 0.989057i | \(-0.452867\pi\) | ||||
0.147531 | + | 0.989057i | \(0.452867\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 5.17731 | 0.325495 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −1.46824 | −0.0919447 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −4.57646 | −0.285472 | −0.142736 | − | 0.989761i | \(-0.545590\pi\) | ||||
−0.142736 | + | 0.989761i | \(0.545590\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −10.1821 | −0.632683 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −1.48857 | −0.0921404 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −16.0834 | −0.991745 | −0.495873 | − | 0.868395i | \(-0.665152\pi\) | ||||
−0.495873 | + | 0.868395i | \(0.665152\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −7.88590 | −0.484427 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −29.5501 | −1.80843 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −1.32579 | −0.0808347 | −0.0404174 | − | 0.999183i | \(-0.512869\pi\) | ||||
−0.0404174 | + | 0.999183i | \(0.512869\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 6.50832 | 0.395353 | 0.197676 | − | 0.980267i | \(-0.436661\pi\) | ||||
0.197676 | + | 0.980267i | \(0.436661\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −11.5567 | −0.699446 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 3.01214 | 0.181639 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −14.4607 | −0.868859 | −0.434430 | − | 0.900706i | \(-0.643050\pi\) | ||||
−0.434430 | + | 0.900706i | \(0.643050\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 3.54783 | 0.212403 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −6.05087 | −0.360964 | −0.180482 | − | 0.983578i | \(-0.557766\pi\) | ||||
−0.180482 | + | 0.983578i | \(0.557766\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −20.6207 | −1.22577 | −0.612887 | − | 0.790170i | \(-0.709992\pi\) | ||||
−0.612887 | + | 0.790170i | \(0.709992\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 8.42251 | 0.498906 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 21.4593 | 1.26670 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −16.4403 | −0.967075 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 5.71147 | 0.334812 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 16.7712 | 0.979786 | 0.489893 | − | 0.871783i | \(-0.337036\pi\) | ||||
0.489893 | + | 0.871783i | \(0.337036\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 6.20478 | 0.361256 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 12.7009 | 0.736981 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −4.66605 | −0.269845 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −18.4339 | −1.06251 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −5.36514 | −0.308219 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −9.79583 | −0.560908 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 10.7421 | 0.613081 | 0.306541 | − | 0.951858i | \(-0.400828\pi\) | ||||
0.306541 | + | 0.951858i | \(0.400828\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −7.11489 | −0.404752 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 2.82492 | 0.160186 | 0.0800932 | − | 0.996787i | \(-0.474478\pi\) | ||||
0.0800932 | + | 0.996787i | \(0.474478\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −28.7090 | −1.62273 | −0.811365 | − | 0.584540i | \(-0.801275\pi\) | ||||
−0.811365 | + | 0.584540i | \(0.801275\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −1.84695 | −0.104064 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −9.72265 | −0.546078 | −0.273039 | − | 0.962003i | \(-0.588029\pi\) | ||||
−0.273039 | + | 0.962003i | \(0.588029\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −5.26616 | −0.294849 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 6.29772 | 0.351504 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −3.21082 | −0.178655 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −2.71469 | −0.150584 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 9.58633 | 0.530125 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −27.8053 | −1.53296 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 0.830070 | 0.0456248 | 0.0228124 | − | 0.999740i | \(-0.492738\pi\) | ||||
0.0228124 | + | 0.999740i | \(0.492738\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 3.99652 | 0.219008 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 2.54968 | 0.139304 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −26.9322 | −1.46709 | −0.733544 | − | 0.679642i | \(-0.762135\pi\) | ||||
−0.733544 | + | 0.679642i | \(0.762135\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −16.3046 | −0.885542 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 12.5512 | 0.679688 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 20.1618 | 1.08863 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −3.37319 | −0.181606 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −26.5136 | −1.42332 | −0.711662 | − | 0.702522i | \(-0.752057\pi\) | ||||
−0.711662 | + | 0.702522i | \(0.752057\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −16.3698 | −0.876254 | −0.438127 | − | 0.898913i | \(-0.644358\pi\) | ||||
−0.438127 | + | 0.898913i | \(0.644358\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −11.4467 | −0.610979 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −8.02380 | −0.427064 | −0.213532 | − | 0.976936i | \(-0.568497\pi\) | ||||
−0.213532 | + | 0.976936i | \(0.568497\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −6.64355 | −0.352603 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 3.18494 | 0.168565 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 4.18033 | 0.220629 | 0.110315 | − | 0.993897i | \(-0.464814\pi\) | ||||
0.110315 | + | 0.993897i | \(0.464814\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −0.581244 | −0.0305918 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 3.78181 | 0.198494 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −6.53691 | −0.342158 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −20.8757 | −1.08970 | −0.544851 | − | 0.838533i | \(-0.683414\pi\) | ||||
−0.544851 | + | 0.838533i | \(0.683414\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −8.42290 | −0.438479 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 17.1063 | 0.888114 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −31.6271 | −1.63759 | −0.818796 | − | 0.574085i | \(-0.805358\pi\) | ||||
−0.818796 | + | 0.574085i | \(0.805358\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −1.96251 | −0.101343 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 4.74613 | 0.244438 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −7.38975 | −0.379586 | −0.189793 | − | 0.981824i | \(-0.560782\pi\) | ||||
−0.189793 | + | 0.981824i | \(0.560782\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −4.06922 | −0.208472 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −30.4978 | −1.55836 | −0.779182 | − | 0.626798i | \(-0.784365\pi\) | ||||
−0.779182 | + | 0.626798i | \(0.784365\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −6.53400 | −0.333003 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 7.23541 | 0.367796 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 27.2328 | 1.38076 | 0.690379 | − | 0.723448i | \(-0.257444\pi\) | ||||
0.690379 | + | 0.723448i | \(0.257444\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1.28592 | 0.0650320 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 26.1121 | 1.31718 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −5.44102 | −0.273768 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 13.2555 | 0.665273 | 0.332637 | − | 0.943055i | \(-0.392062\pi\) | ||||
0.332637 | + | 0.943055i | \(0.392062\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −18.2703 | −0.914659 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −20.4575 | −1.02160 | −0.510800 | − | 0.859699i | \(-0.670651\pi\) | ||||
−0.510800 | + | 0.859699i | \(0.670651\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −11.3118 | −0.563481 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −10.8294 | −0.538115 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 14.1386 | 0.700824 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 21.9027 | 1.08302 | 0.541509 | − | 0.840695i | \(-0.317853\pi\) | ||||
0.541509 | + | 0.840695i | \(0.317853\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −36.0101 | −1.77625 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −13.4596 | −0.662301 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 4.01722 | 0.197197 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0.124615 | 0.00610241 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 33.9905 | 1.66055 | 0.830273 | − | 0.557357i | \(-0.188185\pi\) | ||||
0.830273 | + | 0.557357i | \(0.188185\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 4.66631 | 0.227422 | 0.113711 | − | 0.993514i | \(-0.463726\pi\) | ||||
0.113711 | + | 0.993514i | \(0.463726\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 10.9137 | 0.530645 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0.748145 | 0.0362904 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 21.2494 | 1.02833 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 16.0474 | 0.774778 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −11.8922 | −0.572829 | −0.286414 | − | 0.958106i | \(-0.592463\pi\) | ||||
−0.286414 | + | 0.958106i | \(0.592463\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 2.07028 | 0.0994911 | 0.0497455 | − | 0.998762i | \(-0.484159\pi\) | ||||
0.0497455 | + | 0.998762i | \(0.484159\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 3.43108 | 0.164508 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −7.37666 | −0.352874 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −19.5142 | −0.931361 | −0.465680 | − | 0.884953i | \(-0.654190\pi\) | ||||
−0.465680 | + | 0.884953i | \(0.654190\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −1.95358 | −0.0930278 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 26.5032 | 1.25920 | 0.629601 | − | 0.776918i | \(-0.283218\pi\) | ||||
0.629601 | + | 0.776918i | \(0.283218\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 15.0573 | 0.713785 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −22.5352 | −1.06588 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −37.4184 | −1.76588 | −0.882941 | − | 0.469484i | \(-0.844440\pi\) | ||||
−0.882941 | + | 0.469484i | \(0.844440\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −29.7979 | −1.40313 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 1.96251 | 0.0922066 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 5.88877 | 0.276070 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −5.56466 | −0.260304 | −0.130152 | − | 0.991494i | \(-0.541547\pi\) | ||||
−0.130152 | + | 0.991494i | \(0.541547\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 3.15461 | 0.147245 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 0.103086 | 0.00480120 | 0.00240060 | − | 0.999997i | \(-0.499236\pi\) | ||||
0.00240060 | + | 0.999997i | \(0.499236\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −25.5155 | −1.18581 | −0.592904 | − | 0.805273i | \(-0.702019\pi\) | ||||
−0.592904 | + | 0.805273i | \(0.702019\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −8.17755 | −0.379225 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 4.88782 | 0.226181 | 0.113091 | − | 0.993585i | \(-0.463925\pi\) | ||||
0.113091 | + | 0.993585i | \(0.463925\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −5.53083 | −0.255390 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −4.44331 | −0.204737 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 25.5969 | 1.17695 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −4.29171 | −0.196917 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −6.71432 | −0.307427 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 7.80514 | 0.356626 | 0.178313 | − | 0.983974i | \(-0.442936\pi\) | ||||
0.178313 | + | 0.983974i | \(0.442936\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −12.7424 | −0.581004 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 7.31721 | 0.332944 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −2.91029 | −0.132150 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −11.3311 | −0.513462 | −0.256731 | − | 0.966483i | \(-0.582645\pi\) | ||||
−0.256731 | + | 0.966483i | \(0.582645\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 36.4798 | 1.64967 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −0.687619 | −0.0310318 | −0.0155159 | − | 0.999880i | \(-0.504939\pi\) | ||||
−0.0155159 | + | 0.999880i | \(0.504939\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −1.30799 | −0.0589091 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 2.56463 | 0.115272 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 14.4114 | 0.646438 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 18.6479 | 0.834793 | 0.417396 | − | 0.908725i | \(-0.362943\pi\) | ||||
0.417396 | + | 0.908725i | \(0.362943\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −3.44114 | −0.153739 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −24.8823 | −1.10945 | −0.554724 | − | 0.832035i | \(-0.687176\pi\) | ||||
−0.554724 | + | 0.832035i | \(0.687176\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 2.73382 | 0.121653 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 11.0498 | 0.490740 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −18.0862 | −0.801658 | −0.400829 | − | 0.916153i | \(-0.631278\pi\) | ||||
−0.400829 | + | 0.916153i | \(0.631278\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 14.1800 | 0.627288 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −18.0963 | −0.798972 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 3.62541 | 0.159755 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 38.6099 | 1.69806 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −34.4765 | −1.51335 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −3.52627 | −0.154489 | −0.0772444 | − | 0.997012i | \(-0.524612\pi\) | ||||
−0.0772444 | + | 0.997012i | \(0.524612\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −1.83625 | −0.0802934 | −0.0401467 | − | 0.999194i | \(-0.512783\pi\) | ||||
−0.0401467 | + | 0.999194i | \(0.512783\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 4.25712 | 0.185796 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 3.11744 | 0.135798 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −20.0457 | −0.871551 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 5.28295 | 0.229261 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 26.8554 | 1.16324 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −3.20902 | −0.138738 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 31.6564 | 1.36608 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −6.91125 | −0.297688 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 5.43440 | 0.233643 | 0.116822 | − | 0.993153i | \(-0.462729\pi\) | ||||
0.116822 | + | 0.993153i | \(0.462729\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 33.3518 | 1.43126 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −4.88474 | −0.209239 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −13.7390 | −0.587436 | −0.293718 | − | 0.955892i | \(-0.594893\pi\) | ||||
−0.293718 | + | 0.955892i | \(0.594893\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −8.34050 | −0.355964 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 7.50326 | 0.319650 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 11.8028 | 0.501906 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −9.21176 | −0.391017 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −30.8848 | −1.30863 | −0.654315 | − | 0.756222i | \(-0.727043\pi\) | ||||
−0.654315 | + | 0.756222i | \(0.727043\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −23.0692 | −0.975723 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −4.42254 | −0.186720 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −34.0179 | −1.43368 | −0.716842 | − | 0.697235i | \(-0.754413\pi\) | ||||
−0.716842 | + | 0.697235i | \(0.754413\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 8.30803 | 0.349521 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 23.4913 | 0.986542 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −16.6839 | −0.699425 | −0.349712 | − | 0.936857i | \(-0.613721\pi\) | ||||
−0.349712 | + | 0.936857i | \(0.613721\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 13.6448 | 0.571016 | 0.285508 | − | 0.958376i | \(-0.407838\pi\) | ||||
0.285508 | + | 0.958376i | \(0.407838\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 16.7281 | 0.698825 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 1.71882 | 0.0716796 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 34.1896 | 1.42333 | 0.711666 | − | 0.702518i | \(-0.247941\pi\) | ||||
0.711666 | + | 0.702518i | \(0.247941\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 42.7663 | 1.77731 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −8.71424 | −0.361528 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −23.7534 | −0.983766 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −2.31138 | −0.0955636 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 9.60515 | 0.396447 | 0.198223 | − | 0.980157i | \(-0.436483\pi\) | ||||
0.198223 | + | 0.980157i | \(0.436483\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −17.8831 | −0.736859 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −22.8186 | −0.938631 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 11.4144 | 0.468733 | 0.234366 | − | 0.972148i | \(-0.424698\pi\) | ||||
0.234366 | + | 0.972148i | \(0.424698\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −1.62289 | −0.0665322 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 41.1101 | 1.68252 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 23.1359 | 0.945307 | 0.472653 | − | 0.881248i | \(-0.343296\pi\) | ||||
0.472653 | + | 0.881248i | \(0.343296\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −31.2599 | −1.27512 | −0.637559 | − | 0.770402i | \(-0.720056\pi\) | ||||
−0.637559 | + | 0.770402i | \(0.720056\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 2.17088 | 0.0884051 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −1.92703 | −0.0783450 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 26.2273 | 1.06453 | 0.532267 | − | 0.846577i | \(-0.321340\pi\) | ||||
0.532267 | + | 0.846577i | \(0.321340\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −7.44278 | −0.301597 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −34.7971 | −1.40774 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 24.3200 | 0.982275 | 0.491138 | − | 0.871082i | \(-0.336581\pi\) | ||||
0.491138 | + | 0.871082i | \(0.336581\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 19.4143 | 0.782862 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 6.43402 | 0.259024 | 0.129512 | − | 0.991578i | \(-0.458659\pi\) | ||||
0.129512 | + | 0.991578i | \(0.458659\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 42.7419 | 1.71794 | 0.858971 | − | 0.512024i | \(-0.171104\pi\) | ||||
0.858971 | + | 0.512024i | \(0.171104\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 7.24753 | 0.290833 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −32.6627 | −1.30860 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 25.3697 | 1.01317 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 3.51170 | 0.140021 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 23.1177 | 0.920303 | 0.460151 | − | 0.887840i | \(-0.347795\pi\) | ||||
0.460151 | + | 0.887840i | \(0.347795\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 18.0758 | 0.718449 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 2.07348 | 0.0822836 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 6.22876 | 0.246793 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −5.65654 | −0.223769 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 4.45325 | 0.175893 | 0.0879464 | − | 0.996125i | \(-0.471970\pi\) | ||||
0.0879464 | + | 0.996125i | \(0.471970\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 0.00677368 | 0.000267128 0 | 0.000133564 | − | 1.00000i | \(-0.499957\pi\) | ||||
0.000133564 | 1.00000i | \(0.499957\pi\) | ||||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −16.6772 | −0.656665 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −45.8824 | −1.80383 | −0.901913 | − | 0.431919i | \(-0.857837\pi\) | ||||
−0.901913 | + | 0.431919i | \(0.857837\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 18.6896 | 0.733632 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 17.7389 | 0.695244 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −43.3779 | −1.69751 | −0.848754 | − | 0.528788i | \(-0.822647\pi\) | ||||
−0.848754 | + | 0.528788i | \(0.822647\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −13.3055 | −0.519889 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −5.56574 | −0.217140 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −30.8265 | −1.20083 | −0.600414 | − | 0.799689i | \(-0.704998\pi\) | ||||
−0.600414 | + | 0.799689i | \(0.704998\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −3.59334 | −0.139765 | −0.0698824 | − | 0.997555i | \(-0.522262\pi\) | ||||
−0.0698824 | + | 0.997555i | \(0.522262\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 3.98581 | 0.154796 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 9.30968 | 0.361014 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −3.00503 | −0.116355 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −26.4692 | −1.02336 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −29.5064 | −1.13908 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 17.8727 | 0.688942 | 0.344471 | − | 0.938797i | \(-0.388058\pi\) | ||||
0.344471 | + | 0.938797i | \(0.388058\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 4.21658 | 0.162296 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −50.1714 | −1.92824 | −0.964122 | − | 0.265460i | \(-0.914476\pi\) | ||||
−0.964122 | + | 0.265460i | \(0.914476\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 6.31308 | 0.242274 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −20.2177 | −0.774742 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −43.2419 | −1.65461 | −0.827303 | − | 0.561756i | \(-0.810126\pi\) | ||||
−0.827303 | + | 0.561756i | \(0.810126\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 18.3490 | 0.701081 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 28.1615 | 1.07443 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 21.4078 | 0.815571 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −11.3083 | −0.430188 | −0.215094 | − | 0.976593i | \(-0.569006\pi\) | ||||
−0.215094 | + | 0.976593i | \(0.569006\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −5.56326 | −0.211331 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −0.0634977 | −0.00240861 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −7.40112 | −0.280337 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 40.7050 | 1.53960 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 16.5642 | 0.625620 | 0.312810 | − | 0.949816i | \(-0.398730\pi\) | ||||
0.312810 | + | 0.949816i | \(0.398730\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −20.1447 | −0.759773 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −25.1556 | −0.947415 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −5.93027 | −0.223031 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 46.7990 | 1.75757 | 0.878786 | − | 0.477216i | \(-0.158354\pi\) | ||||
0.878786 | + | 0.477216i | \(0.158354\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −4.63267 | −0.173739 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 7.16212 | 0.268224 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −8.17701 | −0.305803 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −12.2787 | −0.458556 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −31.6279 | −1.17952 | −0.589760 | − | 0.807578i | \(-0.700778\pi\) | ||||
−0.589760 | + | 0.807578i | \(0.700778\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −7.86432 | −0.292883 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −39.5528 | −1.47099 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −1.74832 | −0.0649308 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −16.5897 | −0.615277 | −0.307639 | − | 0.951503i | \(-0.599539\pi\) | ||||
−0.307639 | + | 0.951503i | \(0.599539\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 15.6047 | 0.577952 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 6.35768 | 0.235147 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −29.1792 | −1.07776 | −0.538880 | − | 0.842383i | \(-0.681152\pi\) | ||||
−0.538880 | + | 0.842383i | \(0.681152\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 4.50291 | 0.166092 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 7.67998 | 0.282896 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −0.503787 | −0.0185321 | −0.00926604 | − | 0.999957i | \(-0.502950\pi\) | ||||
−0.00926604 | + | 0.999957i | \(0.502950\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −22.8645 | −0.839948 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −26.4912 | −0.971868 | −0.485934 | − | 0.873995i | \(-0.661521\pi\) | ||||
−0.485934 | + | 0.873995i | \(0.661521\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 11.4828 | 0.420699 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 3.42039 | 0.125146 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 6.96108 | 0.254352 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 48.4483 | 1.76790 | 0.883952 | − | 0.467577i | \(-0.154873\pi\) | ||||
0.883952 | + | 0.467577i | \(0.154873\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −9.17408 | −0.334322 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −1.00000 | −0.0363937 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 6.76709 | 0.245954 | 0.122977 | − | 0.992410i | \(-0.460756\pi\) | ||||
0.122977 | + | 0.992410i | \(0.460756\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −10.1605 | −0.368803 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 8.93154 | 0.323768 | 0.161884 | − | 0.986810i | \(-0.448243\pi\) | ||||
0.161884 | + | 0.986810i | \(0.448243\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 10.5961 | 0.383604 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0.636995 | 0.0230306 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −16.8440 | −0.608203 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −15.1159 | −0.545095 | −0.272548 | − | 0.962142i | \(-0.587866\pi\) | ||||
−0.272548 | + | 0.962142i | \(0.587866\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 8.98134 | 0.323455 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 0.404826 | 0.0145606 | 0.00728028 | − | 0.999973i | \(-0.497683\pi\) | ||||
0.00728028 | + | 0.999973i | \(0.497683\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 4.16689 | 0.149679 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 19.9824 | 0.716863 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 42.4562 | 1.52115 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −20.0113 | −0.716060 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −7.37191 | −0.263450 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 2.26410 | 0.0808092 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 42.2257 | 1.50519 | 0.752593 | − | 0.658486i | \(-0.228803\pi\) | ||||
0.752593 | + | 0.658486i | \(0.228803\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 31.5638 | 1.12370 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −18.0220 | −0.640788 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 26.5926 | 0.944332 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 15.4761 | 0.548882 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −0.488145 | −0.0172910 | −0.00864549 | − | 0.999963i | \(-0.502752\pi\) | ||||
−0.00864549 | + | 0.999963i | \(0.502752\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 9.58980 | 0.339263 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 12.8203 | 0.452983 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −19.6901 | −0.694848 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −3.72850 | −0.131412 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 2.60187 | 0.0915901 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −21.1286 | −0.742843 | −0.371422 | − | 0.928464i | \(-0.621130\pi\) | ||||
−0.371422 | + | 0.928464i | \(0.621130\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −20.8571 | −0.732392 | −0.366196 | − | 0.930538i | \(-0.619340\pi\) | ||||
−0.366196 | + | 0.930538i | \(0.619340\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −12.7726 | −0.447956 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −18.5884 | −0.651122 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −36.4706 | −1.27594 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 5.01389 | 0.175200 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −30.9000 | −1.07842 | −0.539209 | − | 0.842172i | \(-0.681277\pi\) | ||||
−0.539209 | + | 0.842172i | \(0.681277\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 3.04961 | 0.106303 | 0.0531513 | − | 0.998586i | \(-0.483073\pi\) | ||||
0.0531513 | + | 0.998586i | \(0.483073\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −5.91134 | −0.205806 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 41.4450 | 1.44118 | 0.720591 | − | 0.693360i | \(-0.243870\pi\) | ||||
0.720591 | + | 0.693360i | \(0.243870\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −3.61104 | −0.125417 | −0.0627083 | − | 0.998032i | \(-0.519974\pi\) | ||||
−0.0627083 | + | 0.998032i | \(0.519974\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 28.3792 | 0.984464 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −1.71659 | −0.0594764 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 1.75344 | 0.0606803 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 17.5700 | 0.607309 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 7.85452 | 0.271168 | 0.135584 | − | 0.990766i | \(-0.456709\pi\) | ||||
0.135584 | + | 0.990766i | \(0.456709\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −25.9434 | −0.894600 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 11.8749 | 0.408992 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −5.63047 | −0.193694 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 4.18017 | 0.143632 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 40.4683 | 1.38887 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 8.06791 | 0.276564 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 33.5124 | 1.14744 | 0.573721 | − | 0.819051i | \(-0.305500\pi\) | ||||
0.573721 | + | 0.819051i | \(0.305500\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −3.65410 | −0.124968 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −24.7458 | −0.845299 | −0.422649 | − | 0.906293i | \(-0.638900\pi\) | ||||
−0.422649 | + | 0.906293i | \(0.638900\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 20.9899 | 0.716166 | 0.358083 | − | 0.933690i | \(-0.383430\pi\) | ||||
0.358083 | + | 0.933690i | \(0.383430\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −42.1140 | −1.43524 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 28.6868 | 0.976510 | 0.488255 | − | 0.872701i | \(-0.337634\pi\) | ||||
0.488255 | + | 0.872701i | \(0.337634\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 17.5676 | 0.597315 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 32.2642 | 1.09575 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −16.3891 | −0.555962 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −6.92159 | −0.234529 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −2.47792 | −0.0838649 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −2.16922 | −0.0733332 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 38.5479 | 1.30167 | 0.650835 | − | 0.759219i | \(-0.274419\pi\) | ||||
0.650835 | + | 0.759219i | \(0.274419\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −32.9137 | −1.11015 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 53.0568 | 1.78753 | 0.893765 | − | 0.448535i | \(-0.148054\pi\) | ||||
0.893765 | + | 0.448535i | \(0.148054\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 28.7759 | 0.968386 | 0.484193 | − | 0.874961i | \(-0.339113\pi\) | ||||
0.484193 | + | 0.874961i | \(0.339113\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −12.1769 | −0.409323 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 42.2665 | 1.41917 | 0.709586 | − | 0.704619i | \(-0.248882\pi\) | ||||
0.709586 | + | 0.704619i | \(0.248882\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −4.49784 | −0.150853 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −32.6195 | −1.09279 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −55.0115 | −1.84089 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −16.1306 | −0.539187 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 9.15716 | 0.305749 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −7.28504 | −0.242970 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −5.89980 | −0.196551 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 36.1766 | 1.20388 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −16.9945 | −0.564916 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 7.95833 | 0.264252 | 0.132126 | − | 0.991233i | \(-0.457820\pi\) | ||||
0.132126 | + | 0.991233i | \(0.457820\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 2.32767 | 0.0772038 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −22.4319 | −0.743201 | −0.371600 | − | 0.928393i | \(-0.621191\pi\) | ||||
−0.371600 | + | 0.928393i | \(0.621191\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 12.1004 | 0.400465 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 19.2244 | 0.635539 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 28.8626 | 0.953127 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −47.4862 | −1.56642 | −0.783212 | − | 0.621755i | \(-0.786420\pi\) | ||||
−0.783212 | + | 0.621755i | \(0.786420\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −21.0813 | −0.694654 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 18.0352 | 0.593635 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 4.69387 | 0.154334 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 3.08679 | 0.101384 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 13.1937 | 0.432871 | 0.216436 | − | 0.976297i | \(-0.430557\pi\) | ||||
0.216436 | + | 0.976297i | \(0.430557\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 9.84718 | 0.322728 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −5.54392 | −0.181500 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 2.25352 | 0.0736978 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −36.0411 | −1.17741 | −0.588706 | − | 0.808347i | \(-0.700363\pi\) | ||||
−0.588706 | + | 0.808347i | \(0.700363\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 56.3416 | 1.83864 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 41.8765 | 1.36514 | 0.682568 | − | 0.730822i | \(-0.260863\pi\) | ||||
0.682568 | + | 0.730822i | \(0.260863\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −17.0036 | −0.553714 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −9.14670 | −0.297542 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −27.3169 | −0.887679 | −0.443840 | − | 0.896106i | \(-0.646384\pi\) | ||||
−0.443840 | + | 0.896106i | \(0.646384\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 17.7457 | 0.576049 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 19.0808 | 0.618736 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −14.3197 | −0.463861 | −0.231931 | − | 0.972732i | \(-0.574504\pi\) | ||||
−0.231931 | + | 0.972732i | \(0.574504\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −8.52383 | −0.275825 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 10.3349 | 0.334079 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −39.8032 | −1.28531 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −13.6370 | −0.439904 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −2.73226 | −0.0880459 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −21.7917 | −0.701499 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 40.2007 | 1.29277 | 0.646384 | − | 0.763013i | \(-0.276281\pi\) | ||||
0.646384 | + | 0.763013i | \(0.276281\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 6.30126 | 0.202426 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −40.0498 | −1.28526 | −0.642630 | − | 0.766177i | \(-0.722157\pi\) | ||||
−0.642630 | + | 0.766177i | \(0.722157\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0.137741 | 0.00441577 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 5.32759 | 0.170620 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −48.8020 | −1.56131 | −0.780657 | − | 0.624959i | \(-0.785116\pi\) | ||||
−0.780657 | + | 0.624959i | \(0.785116\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 45.3547 | 1.44954 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −4.15903 | −0.132787 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 20.1288 | 0.642009 | 0.321004 | − | 0.947078i | \(-0.395980\pi\) | ||||
0.321004 | + | 0.947078i | \(0.395980\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 11.6273 | 0.370475 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 54.5681 | 1.73692 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 14.6064 | 0.464456 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −21.8226 | −0.693219 | −0.346609 | − | 0.938010i | \(-0.612667\pi\) | ||||
−0.346609 | + | 0.938010i | \(0.612667\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −1.62902 | −0.0516953 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −20.9477 | −0.664088 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 27.6835 | 0.876745 | 0.438373 | − | 0.898793i | \(-0.355555\pi\) | ||||
0.438373 | + | 0.898793i | \(0.355555\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 19.7921 | 0.626194 |
(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 | 6040.2.a.l.1.1 | ✓ | 9 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6040.2.a.l.1.1 | ✓ | 9 | 1.1 | even | 1 | trivial |