Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3584,2,Mod(1,3584)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3584, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("3584.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3584 = 2^{9} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3584.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: | \(28.6183840844\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\zeta_{16})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 4x^{2} + 2 \) |
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 | 1.2 | ||
Root | \(-0.765367\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3584.1 |
$q$-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 | ||||||||
\(3\) | −0.765367 | −0.441885 | −0.220942 | − | 0.975287i | \(-0.570913\pi\) | ||||
−0.220942 | + | 0.975287i | \(0.570913\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.84776 | −0.826343 | −0.413171 | − | 0.910653i | \(-0.635579\pi\) | ||||
−0.413171 | + | 0.910653i | \(0.635579\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.41421 | −0.804738 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −3.69552 | −1.11424 | −0.557120 | − | 0.830432i | \(-0.688094\pi\) | ||||
−0.557120 | + | 0.830432i | \(0.688094\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.29610 | −0.636824 | −0.318412 | − | 0.947952i | \(-0.603149\pi\) | ||||
−0.318412 | + | 0.947952i | \(0.603149\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.41421 | 0.365148 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 0.828427 | 0.200923 | 0.100462 | − | 0.994941i | \(-0.467968\pi\) | ||||
0.100462 | + | 0.994941i | \(0.467968\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −3.37849 | −0.775079 | −0.387540 | − | 0.921853i | \(-0.626675\pi\) | ||||
−0.387540 | + | 0.921853i | \(0.626675\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.765367 | 0.167017 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0.585786 | 0.122145 | 0.0610725 | − | 0.998133i | \(-0.480548\pi\) | ||||
0.0610725 | + | 0.998133i | \(0.480548\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.58579 | −0.317157 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 4.14386 | 0.797486 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −8.92177 | −1.65673 | −0.828366 | − | 0.560188i | \(-0.810729\pi\) | ||||
−0.828366 | + | 0.560188i | \(0.810729\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.17157 | 0.210421 | 0.105210 | − | 0.994450i | \(-0.466448\pi\) | ||||
0.105210 | + | 0.994450i | \(0.466448\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 2.82843 | 0.492366 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 1.84776 | 0.312328 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 0.634051 | 0.104237 | 0.0521186 | − | 0.998641i | \(-0.483403\pi\) | ||||
0.0521186 | + | 0.998641i | \(0.483403\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 1.75736 | 0.281403 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −6.48528 | −1.01283 | −0.506415 | − | 0.862290i | \(-0.669030\pi\) | ||||
−0.506415 | + | 0.862290i | \(0.669030\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1.53073 | −0.233435 | −0.116717 | − | 0.993165i | \(-0.537237\pi\) | ||||
−0.116717 | + | 0.993165i | \(0.537237\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 4.46088 | 0.664989 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 4.00000 | 0.583460 | 0.291730 | − | 0.956501i | \(-0.405769\pi\) | ||||
0.291730 | + | 0.956501i | \(0.405769\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −0.634051 | −0.0887849 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 7.39104 | 1.01524 | 0.507618 | − | 0.861582i | \(-0.330526\pi\) | ||||
0.507618 | + | 0.861582i | \(0.330526\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 6.82843 | 0.920745 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 2.58579 | 0.342496 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −15.0991 | −1.96574 | −0.982868 | − | 0.184313i | \(-0.940994\pi\) | ||||
−0.982868 | + | 0.184313i | \(0.940994\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.84776 | 0.236581 | 0.118291 | − | 0.992979i | \(-0.462259\pi\) | ||||
0.118291 | + | 0.992979i | \(0.462259\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 2.41421 | 0.304162 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 4.24264 | 0.526235 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 6.49435 | 0.793412 | 0.396706 | − | 0.917946i | \(-0.370153\pi\) | ||||
0.396706 | + | 0.917946i | \(0.370153\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −0.448342 | −0.0539740 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 4.82843 | 0.573029 | 0.286514 | − | 0.958076i | \(-0.407503\pi\) | ||||
0.286514 | + | 0.958076i | \(0.407503\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −10.4853 | −1.22721 | −0.613605 | − | 0.789613i | \(-0.710281\pi\) | ||||
−0.613605 | + | 0.789613i | \(0.710281\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 1.21371 | 0.140147 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 3.69552 | 0.421143 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 8.82843 | 0.993276 | 0.496638 | − | 0.867958i | \(-0.334568\pi\) | ||||
0.496638 | + | 0.867958i | \(0.334568\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 4.07107 | 0.452341 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 2.29610 | 0.252030 | 0.126015 | − | 0.992028i | \(-0.459781\pi\) | ||||
0.126015 | + | 0.992028i | \(0.459781\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1.53073 | −0.166031 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 6.82843 | 0.732084 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 6.00000 | 0.635999 | 0.317999 | − | 0.948091i | \(-0.396989\pi\) | ||||
0.317999 | + | 0.948091i | \(0.396989\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 2.29610 | 0.240697 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −0.896683 | −0.0929817 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 6.24264 | 0.640481 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −2.00000 | −0.203069 | −0.101535 | − | 0.994832i | \(-0.532375\pi\) | ||||
−0.101535 | + | 0.994832i | \(0.532375\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 8.92177 | 0.896672 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −14.0167 | −1.39471 | −0.697357 | − | 0.716724i | \(-0.745641\pi\) | ||||
−0.697357 | + | 0.716724i | \(0.745641\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 16.4853 | 1.62434 | 0.812172 | − | 0.583419i | \(-0.198285\pi\) | ||||
0.812172 | + | 0.583419i | \(0.198285\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −1.41421 | −0.138013 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 2.16478 | 0.209278 | 0.104639 | − | 0.994510i | \(-0.466631\pi\) | ||||
0.104639 | + | 0.994510i | \(0.466631\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −13.2513 | −1.26925 | −0.634624 | − | 0.772821i | \(-0.718845\pi\) | ||||
−0.634624 | + | 0.772821i | \(0.718845\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −0.485281 | −0.0460609 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 13.8995 | 1.30755 | 0.653777 | − | 0.756687i | \(-0.273183\pi\) | ||||
0.653777 | + | 0.756687i | \(0.273183\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1.08239 | −0.100934 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 5.54328 | 0.512476 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −0.828427 | −0.0759418 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 2.65685 | 0.241532 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 4.96362 | 0.447554 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 12.1689 | 1.08842 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 9.75736 | 0.865826 | 0.432913 | − | 0.901436i | \(-0.357486\pi\) | ||||
0.432913 | + | 0.901436i | \(0.357486\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 1.17157 | 0.103151 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 3.56420 | 0.311406 | 0.155703 | − | 0.987804i | \(-0.450236\pi\) | ||||
0.155703 | + | 0.987804i | \(0.450236\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 3.37849 | 0.292952 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −7.65685 | −0.658997 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −20.9706 | −1.79164 | −0.895818 | − | 0.444421i | \(-0.853409\pi\) | ||||
−0.895818 | + | 0.444421i | \(0.853409\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 11.4036 | 0.967239 | 0.483620 | − | 0.875278i | \(-0.339322\pi\) | ||||
0.483620 | + | 0.875278i | \(0.339322\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −3.06147 | −0.257822 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 8.48528 | 0.709575 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 16.4853 | 1.36903 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −0.765367 | −0.0631264 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −15.6788 | −1.28445 | −0.642227 | − | 0.766515i | \(-0.721989\pi\) | ||||
−0.642227 | + | 0.766515i | \(0.721989\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 8.58579 | 0.698701 | 0.349351 | − | 0.936992i | \(-0.386402\pi\) | ||||
0.349351 | + | 0.936992i | \(0.386402\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −2.00000 | −0.161690 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −2.16478 | −0.173880 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 5.35757 | 0.427580 | 0.213790 | − | 0.976880i | \(-0.431419\pi\) | ||||
0.213790 | + | 0.976880i | \(0.431419\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −5.65685 | −0.448618 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −0.585786 | −0.0461664 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −22.4357 | −1.75730 | −0.878651 | − | 0.477464i | \(-0.841556\pi\) | ||||
−0.878651 | + | 0.477464i | \(0.841556\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −5.22625 | −0.406863 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 17.6569 | 1.36633 | 0.683164 | − | 0.730265i | \(-0.260603\pi\) | ||||
0.683164 | + | 0.730265i | \(0.260603\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −7.72792 | −0.594456 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 8.15640 | 0.623736 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 15.8101 | 1.20202 | 0.601009 | − | 0.799242i | \(-0.294766\pi\) | ||||
0.601009 | + | 0.799242i | \(0.294766\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1.58579 | 0.119874 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 11.5563 | 0.868628 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −12.6173 | −0.943060 | −0.471530 | − | 0.881850i | \(-0.656298\pi\) | ||||
−0.471530 | + | 0.881850i | \(0.656298\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 3.64113 | 0.270643 | 0.135321 | − | 0.990802i | \(-0.456793\pi\) | ||||
0.135321 | + | 0.990802i | \(0.456793\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −1.41421 | −0.104542 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −1.17157 | −0.0861358 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −3.06147 | −0.223877 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −4.14386 | −0.301421 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 13.6569 | 0.988175 | 0.494088 | − | 0.869412i | \(-0.335502\pi\) | ||||
0.494088 | + | 0.869412i | \(0.335502\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −10.5858 | −0.761982 | −0.380991 | − | 0.924579i | \(-0.624417\pi\) | ||||
−0.380991 | + | 0.924579i | \(0.624417\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −3.24718 | −0.232535 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −10.8239 | −0.771173 | −0.385586 | − | 0.922672i | \(-0.626001\pi\) | ||||
−0.385586 | + | 0.922672i | \(0.626001\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −6.14214 | −0.435404 | −0.217702 | − | 0.976015i | \(-0.569856\pi\) | ||||
−0.217702 | + | 0.976015i | \(0.569856\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −4.97056 | −0.350596 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 8.92177 | 0.626185 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 11.9832 | 0.836946 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −1.41421 | −0.0982946 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 12.4853 | 0.863625 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 23.9665 | 1.64992 | 0.824960 | − | 0.565191i | \(-0.191198\pi\) | ||||
0.824960 | + | 0.565191i | \(0.191198\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −3.69552 | −0.253213 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 2.82843 | 0.192897 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1.17157 | −0.0795315 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 8.02509 | 0.542285 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1.90215 | −0.127953 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −1.17157 | −0.0784543 | −0.0392272 | − | 0.999230i | \(-0.512490\pi\) | ||||
−0.0392272 | + | 0.999230i | \(0.512490\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 3.82843 | 0.255228 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 16.2584 | 1.07911 | 0.539554 | − | 0.841951i | \(-0.318593\pi\) | ||||
0.539554 | + | 0.841951i | \(0.318593\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 25.7373 | 1.70077 | 0.850385 | − | 0.526161i | \(-0.176369\pi\) | ||||
0.850385 | + | 0.526161i | \(0.176369\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −2.82843 | −0.186097 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −24.6274 | −1.61340 | −0.806698 | − | 0.590964i | \(-0.798747\pi\) | ||||
−0.806698 | + | 0.590964i | \(0.798747\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −7.39104 | −0.482138 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −6.75699 | −0.438913 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −3.89949 | −0.252237 | −0.126119 | − | 0.992015i | \(-0.540252\pi\) | ||||
−0.126119 | + | 0.992015i | \(0.540252\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −0.343146 | −0.0221040 | −0.0110520 | − | 0.999939i | \(-0.503518\pi\) | ||||
−0.0110520 | + | 0.999939i | \(0.503518\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −15.5474 | −0.997369 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −1.84776 | −0.118049 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 7.75736 | 0.493589 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −1.75736 | −0.111368 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −0.502734 | −0.0317323 | −0.0158662 | − | 0.999874i | \(-0.505051\pi\) | ||||
−0.0158662 | + | 0.999874i | \(0.505051\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −2.16478 | −0.136099 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 1.17157 | 0.0733667 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 18.0000 | 1.12281 | 0.561405 | − | 0.827541i | \(-0.310261\pi\) | ||||
0.561405 | + | 0.827541i | \(0.310261\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −0.634051 | −0.0393980 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 21.5391 | 1.33323 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −15.1716 | −0.935519 | −0.467760 | − | 0.883856i | \(-0.654939\pi\) | ||||
−0.467760 | + | 0.883856i | \(0.654939\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −13.6569 | −0.838934 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −4.59220 | −0.281038 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −8.41904 | −0.513318 | −0.256659 | − | 0.966502i | \(-0.582622\pi\) | ||||
−0.256659 | + | 0.966502i | \(0.582622\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −2.14214 | −0.130125 | −0.0650627 | − | 0.997881i | \(-0.520725\pi\) | ||||
−0.0650627 | + | 0.997881i | \(0.520725\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −1.75736 | −0.106360 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 5.86030 | 0.353390 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 3.43289 | 0.206262 | 0.103131 | − | 0.994668i | \(-0.467114\pi\) | ||||
0.103131 | + | 0.994668i | \(0.467114\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −2.82843 | −0.169334 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 12.9706 | 0.773759 | 0.386879 | − | 0.922130i | \(-0.373553\pi\) | ||||
0.386879 | + | 0.922130i | \(0.373553\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 20.1396 | 1.19718 | 0.598589 | − | 0.801057i | \(-0.295728\pi\) | ||||
0.598589 | + | 0.801057i | \(0.295728\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −4.77791 | −0.283019 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 6.48528 | 0.382814 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −16.3137 | −0.959630 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 1.53073 | 0.0897332 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 9.68714 | 0.565929 | 0.282964 | − | 0.959130i | \(-0.408682\pi\) | ||||
0.282964 | + | 0.959130i | \(0.408682\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 27.8995 | 1.62437 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −15.3137 | −0.888591 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −1.34502 | −0.0777848 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1.53073 | 0.0882300 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 10.7279 | 0.616303 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −3.41421 | −0.195497 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 0.765367 | 0.0436818 | 0.0218409 | − | 0.999761i | \(-0.493047\pi\) | ||||
0.0218409 | + | 0.999761i | \(0.493047\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −12.6173 | −0.717772 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 4.00000 | 0.226819 | 0.113410 | − | 0.993548i | \(-0.463823\pi\) | ||||
0.113410 | + | 0.993548i | \(0.463823\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 28.1421 | 1.59069 | 0.795344 | − | 0.606159i | \(-0.207290\pi\) | ||||
0.795344 | + | 0.606159i | \(0.207290\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −4.46088 | −0.251342 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −5.59767 | −0.314396 | −0.157198 | − | 0.987567i | \(-0.550246\pi\) | ||||
−0.157198 | + | 0.987567i | \(0.550246\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 32.9706 | 1.84600 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −1.65685 | −0.0924766 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −2.79884 | −0.155731 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 3.64113 | 0.201973 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 10.1421 | 0.560861 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −4.00000 | −0.220527 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −23.7038 | −1.30288 | −0.651441 | − | 0.758700i | \(-0.725835\pi\) | ||||
−0.651441 | + | 0.758700i | \(0.725835\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −1.53073 | −0.0838837 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −12.0000 | −0.655630 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 6.58579 | 0.358751 | 0.179375 | − | 0.983781i | \(-0.442592\pi\) | ||||
0.179375 | + | 0.983781i | \(0.442592\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −10.6382 | −0.577788 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −4.32957 | −0.234459 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0.828427 | 0.0446010 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −19.0029 | −1.02013 | −0.510063 | − | 0.860137i | \(-0.670378\pi\) | ||||
−0.510063 | + | 0.860137i | \(0.670378\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 30.7779 | 1.64750 | 0.823750 | − | 0.566953i | \(-0.191878\pi\) | ||||
0.823750 | + | 0.566953i | \(0.191878\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −9.51472 | −0.507858 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −3.85786 | −0.205333 | −0.102667 | − | 0.994716i | \(-0.532738\pi\) | ||||
−0.102667 | + | 0.994716i | \(0.532738\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −8.92177 | −0.473518 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0.634051 | 0.0335575 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −9.55635 | −0.504365 | −0.252182 | − | 0.967680i | \(-0.581148\pi\) | ||||
−0.252182 | + | 0.967680i | \(0.581148\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −7.58579 | −0.399252 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −2.03347 | −0.106729 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 19.3743 | 1.01410 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 33.4558 | 1.74638 | 0.873190 | − | 0.487379i | \(-0.162047\pi\) | ||||
0.873190 | + | 0.487379i | \(0.162047\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 15.6569 | 0.815063 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −7.39104 | −0.383723 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 27.9246 | 1.44588 | 0.722941 | − | 0.690910i | \(-0.242790\pi\) | ||||
0.722941 | + | 0.690910i | \(0.242790\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −9.31371 | −0.480958 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 20.4853 | 1.05505 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −8.02509 | −0.412221 | −0.206111 | − | 0.978529i | \(-0.566081\pi\) | ||||
−0.206111 | + | 0.978529i | \(0.566081\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −7.46796 | −0.382595 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −29.9411 | −1.52992 | −0.764960 | − | 0.644078i | \(-0.777241\pi\) | ||||
−0.764960 | + | 0.644078i | \(0.777241\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −6.82843 | −0.348009 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 3.69552 | 0.187854 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 20.6424 | 1.04661 | 0.523305 | − | 0.852145i | \(-0.324699\pi\) | ||||
0.523305 | + | 0.852145i | \(0.324699\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0.485281 | 0.0245417 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −2.72792 | −0.137605 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −16.3128 | −0.820786 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −29.5098 | −1.48105 | −0.740526 | − | 0.672028i | \(-0.765424\pi\) | ||||
−0.740526 | + | 0.672028i | \(0.765424\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −2.58579 | −0.129451 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −23.0711 | −1.15211 | −0.576057 | − | 0.817409i | \(-0.695409\pi\) | ||||
−0.576057 | + | 0.817409i | \(0.695409\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −2.69005 | −0.134001 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −7.52235 | −0.373789 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −2.34315 | −0.116145 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 18.9706 | 0.938034 | 0.469017 | − | 0.883189i | \(-0.344608\pi\) | ||||
0.469017 | + | 0.883189i | \(0.344608\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 16.0502 | 0.791697 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 15.0991 | 0.742978 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −4.24264 | −0.208263 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −8.72792 | −0.427408 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −29.0614 | −1.41974 | −0.709871 | − | 0.704331i | \(-0.751247\pi\) | ||||
−0.709871 | + | 0.704331i | \(0.751247\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −22.5445 | −1.09875 | −0.549377 | − | 0.835575i | \(-0.685135\pi\) | ||||
−0.549377 | + | 0.835575i | \(0.685135\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −9.65685 | −0.469532 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −1.31371 | −0.0637242 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −1.84776 | −0.0894193 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −6.49435 | −0.313550 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 7.41421 | 0.357130 | 0.178565 | − | 0.983928i | \(-0.442855\pi\) | ||||
0.178565 | + | 0.983928i | \(0.442855\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 0.828427 | 0.0398117 | 0.0199058 | − | 0.999802i | \(-0.493663\pi\) | ||||
0.0199058 | + | 0.999802i | \(0.493663\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −12.6173 | −0.604953 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −1.97908 | −0.0946720 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 21.4558 | 1.02403 | 0.512016 | − | 0.858976i | \(-0.328899\pi\) | ||||
0.512016 | + | 0.858976i | \(0.328899\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −2.41421 | −0.114963 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 14.4107 | 0.684671 | 0.342335 | − | 0.939578i | \(-0.388782\pi\) | ||||
0.342335 | + | 0.939578i | \(0.388782\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −11.0866 | −0.525553 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 12.0000 | 0.567581 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 10.0000 | 0.471929 | 0.235965 | − | 0.971762i | \(-0.424175\pi\) | ||||
0.235965 | + | 0.971762i | \(0.424175\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 23.9665 | 1.12854 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −6.57128 | −0.308746 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −4.24264 | −0.198898 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −4.92893 | −0.230566 | −0.115283 | − | 0.993333i | \(-0.536777\pi\) | ||||
−0.115283 | + | 0.993333i | \(0.536777\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 3.43289 | 0.160233 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −9.23880 | −0.430294 | −0.215147 | − | 0.976582i | \(-0.569023\pi\) | ||||
−0.215147 | + | 0.976582i | \(0.569023\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −36.2843 | −1.68627 | −0.843137 | − | 0.537700i | \(-0.819293\pi\) | ||||
−0.843137 | + | 0.537700i | \(0.819293\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 1.65685 | 0.0768348 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −23.6494 | −1.09437 | −0.547183 | − | 0.837013i | \(-0.684300\pi\) | ||||
−0.547183 | + | 0.837013i | \(0.684300\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −6.49435 | −0.299881 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −4.10051 | −0.188941 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 5.65685 | 0.260102 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 5.35757 | 0.245822 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −17.8435 | −0.817000 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −35.7990 | −1.63570 | −0.817849 | − | 0.575433i | \(-0.804833\pi\) | ||||
−0.817849 | + | 0.575433i | \(0.804833\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1.45584 | −0.0663808 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0.448342 | 0.0204002 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 3.69552 | 0.167805 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −1.55635 | −0.0705249 | −0.0352625 | − | 0.999378i | \(-0.511227\pi\) | ||||
−0.0352625 | + | 0.999378i | \(0.511227\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 17.1716 | 0.776525 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 7.91630 | 0.357258 | 0.178629 | − | 0.983917i | \(-0.442834\pi\) | ||||
0.178629 | + | 0.983917i | \(0.442834\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −7.39104 | −0.332876 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −16.4853 | −0.740958 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −4.82843 | −0.216585 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 41.2848 | 1.84816 | 0.924080 | − | 0.382200i | \(-0.124833\pi\) | ||||
0.924080 | + | 0.382200i | \(0.124833\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −13.5140 | −0.603760 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −16.4853 | −0.735042 | −0.367521 | − | 0.930015i | \(-0.619793\pi\) | ||||
−0.367521 | + | 0.930015i | \(0.619793\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 25.8995 | 1.15251 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 5.91470 | 0.262681 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −7.97069 | −0.353295 | −0.176647 | − | 0.984274i | \(-0.556525\pi\) | ||||
−0.176647 | + | 0.984274i | \(0.556525\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 10.4853 | 0.463842 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −14.0000 | −0.618115 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −30.4608 | −1.34226 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −14.7821 | −0.650115 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −12.1005 | −0.531153 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −14.0000 | −0.613351 | −0.306676 | − | 0.951814i | \(-0.599217\pi\) | ||||
−0.306676 | + | 0.951814i | \(0.599217\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 13.8310 | 0.604787 | 0.302394 | − | 0.953183i | \(-0.402214\pi\) | ||||
0.302394 | + | 0.953183i | \(0.402214\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −1.21371 | −0.0529706 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0.970563 | 0.0422784 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −22.6569 | −0.985081 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 36.4524 | 1.58190 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 14.8909 | 0.644995 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −4.00000 | −0.172935 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 9.65685 | 0.416724 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −3.69552 | −0.159177 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 1.26810 | 0.0545199 | 0.0272600 | − | 0.999628i | \(-0.491322\pi\) | ||||
0.0272600 | + | 0.999628i | \(0.491322\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −2.78680 | −0.119593 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 24.4853 | 1.04883 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −13.2513 | −0.566586 | −0.283293 | − | 0.959033i | \(-0.591427\pi\) | ||||
−0.283293 | + | 0.959033i | \(0.591427\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −4.46088 | −0.190386 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 30.1421 | 1.28410 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −8.82843 | −0.375423 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0.896683 | 0.0380621 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 18.7402 | 0.794049 | 0.397024 | − | 0.917808i | \(-0.370043\pi\) | ||||
0.397024 | + | 0.917808i | \(0.370043\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 3.51472 | 0.148657 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 2.34315 | 0.0989277 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 23.7582 | 1.00129 | 0.500645 | − | 0.865653i | \(-0.333096\pi\) | ||||
0.500645 | + | 0.865653i | \(0.333096\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −25.6829 | −1.08049 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −4.07107 | −0.170969 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −8.44365 | −0.353976 | −0.176988 | − | 0.984213i | \(-0.556635\pi\) | ||||
−0.176988 | + | 0.984213i | \(0.556635\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −24.0753 | −1.00752 | −0.503759 | − | 0.863844i | \(-0.668050\pi\) | ||||
−0.503759 | + | 0.863844i | \(0.668050\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −10.4525 | −0.436660 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −0.928932 | −0.0387392 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −33.1127 | −1.37850 | −0.689250 | − | 0.724524i | \(-0.742060\pi\) | ||||
−0.689250 | + | 0.724524i | \(0.742060\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 8.10201 | 0.336708 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −2.29610 | −0.0952583 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −27.3137 | −1.13122 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −10.2426 | −0.423481 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −9.61021 | −0.396656 | −0.198328 | − | 0.980136i | \(-0.563551\pi\) | ||||
−0.198328 | + | 0.980136i | \(0.563551\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −3.95815 | −0.163093 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 8.28427 | 0.340769 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 18.6863 | 0.767354 | 0.383677 | − | 0.923467i | \(-0.374658\pi\) | ||||
0.383677 | + | 0.923467i | \(0.374658\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 1.53073 | 0.0627540 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 4.70099 | 0.192399 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −44.2843 | −1.80941 | −0.904703 | − | 0.426043i | \(-0.859907\pi\) | ||||
−0.904703 | + | 0.426043i | \(0.859907\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 35.9411 | 1.46607 | 0.733035 | − | 0.680191i | \(-0.238103\pi\) | ||||
0.733035 | + | 0.680191i | \(0.238103\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −15.6788 | −0.638488 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −4.90923 | −0.199588 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −42.6274 | −1.73019 | −0.865097 | − | 0.501605i | \(-0.832743\pi\) | ||||
−0.865097 | + | 0.501605i | \(0.832743\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −6.82843 | −0.276702 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −9.18440 | −0.371561 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −26.3939 | −1.06604 | −0.533020 | − | 0.846103i | \(-0.678943\pi\) | ||||
−0.533020 | + | 0.846103i | \(0.678943\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −9.17157 | −0.369834 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −1.41421 | −0.0569341 | −0.0284670 | − | 0.999595i | \(-0.509063\pi\) | ||||
−0.0284670 | + | 0.999595i | \(0.509063\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 39.5139 | 1.58820 | 0.794099 | − | 0.607788i | \(-0.207943\pi\) | ||||
0.794099 | + | 0.607788i | \(0.207943\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 2.42742 | 0.0974089 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −6.00000 | −0.240385 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −14.5563 | −0.582254 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −9.55582 | −0.381623 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 0.525265 | 0.0209437 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 21.6569 | 0.862146 | 0.431073 | − | 0.902317i | \(-0.358135\pi\) | ||||
0.431073 | + | 0.902317i | \(0.358135\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −18.3431 | −0.729075 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −18.0292 | −0.715469 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −2.29610 | −0.0909748 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −11.6569 | −0.461138 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −11.2721 | −0.445220 | −0.222610 | − | 0.974908i | \(-0.571458\pi\) | ||||
−0.222610 | + | 0.974908i | \(0.571458\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 26.7109 | 1.05338 | 0.526688 | − | 0.850059i | \(-0.323434\pi\) | ||||
0.526688 | + | 0.850059i | \(0.323434\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −2.16478 | −0.0852383 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −48.4853 | −1.90615 | −0.953077 | − | 0.302729i | \(-0.902102\pi\) | ||||
−0.953077 | + | 0.302729i | \(0.902102\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 55.7990 | 2.19030 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0.896683 | 0.0351438 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −3.69552 | −0.144617 | −0.0723084 | − | 0.997382i | \(-0.523037\pi\) | ||||
−0.0723084 | + | 0.997382i | \(0.523037\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −6.58579 | −0.257328 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 25.3137 | 0.987582 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 21.9105 | 0.853511 | 0.426755 | − | 0.904367i | \(-0.359656\pi\) | ||||
0.426755 | + | 0.904367i | \(0.359656\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 27.5307 | 1.07082 | 0.535410 | − | 0.844593i | \(-0.320157\pi\) | ||||
0.535410 | + | 0.844593i | \(0.320157\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 1.45584 | 0.0565403 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −6.24264 | −0.242079 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −5.22625 | −0.202361 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0.896683 | 0.0346678 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −6.82843 | −0.263609 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −16.2843 | −0.627713 | −0.313856 | − | 0.949471i | \(-0.601621\pi\) | ||||
−0.313856 | + | 0.949471i | \(0.601621\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −6.57128 | −0.252929 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 11.1409 | 0.428181 | 0.214091 | − | 0.976814i | \(-0.431321\pi\) | ||||
0.214091 | + | 0.976814i | \(0.431321\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 2.00000 | 0.0767530 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −12.4437 | −0.476842 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −12.2459 | −0.468575 | −0.234288 | − | 0.972167i | \(-0.575276\pi\) | ||||
−0.234288 | + | 0.972167i | \(0.575276\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 38.7485 | 1.48051 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −19.6985 | −0.751544 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −16.9706 | −0.646527 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 37.4579 | 1.42497 | 0.712483 | − | 0.701689i | \(-0.247570\pi\) | ||||
0.712483 | + | 0.701689i | \(0.247570\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −8.92177 | −0.338910 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −21.0711 | −0.799271 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −5.37258 | −0.203501 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 18.8490 | 0.712935 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 35.9497 | 1.35780 | 0.678901 | − | 0.734230i | \(-0.262457\pi\) | ||||
0.678901 | + | 0.734230i | \(0.262457\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −2.14214 | −0.0807922 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 5.65685 | 0.213049 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 14.0167 | 0.527152 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −35.0530 | −1.31644 | −0.658222 | − | 0.752824i | \(-0.728691\pi\) | ||||
−0.658222 | + | 0.752824i | \(0.728691\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −21.3137 | −0.799327 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 0.686292 | 0.0257018 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −15.6788 | −0.586352 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 2.98454 | 0.111460 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −49.6569 | −1.85189 | −0.925944 | − | 0.377661i | \(-0.876729\pi\) | ||||
−0.925944 | + | 0.377661i | \(0.876729\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −16.4853 | −0.613944 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0.262632 | 0.00976740 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 14.1480 | 0.525444 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −0.313708 | −0.0116188 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −1.26810 | −0.0469024 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 30.7779 | 1.13681 | 0.568403 | − | 0.822750i | \(-0.307561\pi\) | ||||
0.568403 | + | 0.822750i | \(0.307561\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 1.41421 | 0.0521641 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −24.0000 | −0.884051 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 23.7038 | 0.871960 | 0.435980 | − | 0.899956i | \(-0.356402\pi\) | ||||
0.435980 | + | 0.899956i | \(0.356402\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −5.93723 | −0.218109 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 12.8701 | 0.472157 | 0.236078 | − | 0.971734i | \(-0.424138\pi\) | ||||
0.236078 | + | 0.971734i | \(0.424138\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 28.9706 | 1.06140 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −5.54328 | −0.202818 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −2.16478 | −0.0790995 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 41.3553 | 1.50908 | 0.754539 | − | 0.656255i | \(-0.227861\pi\) | ||||
0.754539 | + | 0.656255i | \(0.227861\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0.384776 | 0.0140220 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −15.8645 | −0.577367 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 40.6507 | 1.47747 | 0.738737 | − | 0.673993i | \(-0.235422\pi\) | ||||
0.738737 | + | 0.673993i | \(0.235422\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 1.65685 | 0.0601400 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 46.4853 | 1.68509 | 0.842545 | − | 0.538626i | \(-0.181056\pi\) | ||||
0.842545 | + | 0.538626i | \(0.181056\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 13.2513 | 0.479731 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 3.69552 | 0.133612 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 34.6690 | 1.25183 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −26.2843 | −0.947835 | −0.473918 | − | 0.880569i | \(-0.657161\pi\) | ||||
−0.473918 | + | 0.880569i | \(0.657161\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −13.7766 | −0.496152 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 12.3003 | 0.442410 | 0.221205 | − | 0.975227i | \(-0.429001\pi\) | ||||
0.221205 | + | 0.975227i | \(0.429001\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −1.85786 | −0.0667365 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0.485281 | 0.0174094 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 21.9105 | 0.785024 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −17.8435 | −0.638492 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −36.9706 | −1.32122 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −9.89949 | −0.353328 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −31.1493 | −1.11035 | −0.555176 | − | 0.831733i | \(-0.687349\pi\) | ||||
−0.555176 | + | 0.831733i | \(0.687349\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 11.6118 | 0.413392 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −13.8995 | −0.494209 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −4.24264 | −0.150661 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 10.4525 | 0.370712 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −47.4302 | −1.68006 | −0.840032 | − | 0.542537i | \(-0.817464\pi\) | ||||
−0.840032 | + | 0.542537i | \(0.817464\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 3.31371 | 0.117231 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −14.4853 | −0.511812 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 38.7485 | 1.36741 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 1.08239 | 0.0381493 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 6.44365 | 0.226827 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 1.21320 | 0.0426540 | 0.0213270 | − | 0.999773i | \(-0.493211\pi\) | ||||
0.0213270 | + | 0.999773i | \(0.493211\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −21.6704 | −0.760950 | −0.380475 | − | 0.924791i | \(-0.624239\pi\) | ||||
−0.380475 | + | 0.924791i | \(0.624239\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 1.63952 | 0.0575005 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 41.4558 | 1.45213 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 5.17157 | 0.180930 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −5.54328 | −0.193698 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −20.3797 | −0.711258 | −0.355629 | − | 0.934627i | \(-0.615733\pi\) | ||||
−0.355629 | + | 0.934627i | \(0.615733\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −33.7990 | −1.17816 | −0.589079 | − | 0.808075i | \(-0.700509\pi\) | ||||
−0.589079 | + | 0.808075i | \(0.700509\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −4.48528 | −0.156157 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 48.6758 | 1.69262 | 0.846311 | − | 0.532688i | \(-0.178818\pi\) | ||||
0.846311 | + | 0.532688i | \(0.178818\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −0.0543929 | −0.00188915 | −0.000944573 | − | 1.00000i | \(-0.500301\pi\) | ||||
−0.000944573 | 1.00000i | \(0.500301\pi\) | ||||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −2.62742 | −0.0911441 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0.828427 | 0.0287033 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −32.6256 | −1.12906 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 4.85483 | 0.167808 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −15.5147 | −0.535628 | −0.267814 | − | 0.963471i | \(-0.586301\pi\) | ||||
−0.267814 | + | 0.963471i | \(0.586301\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 50.5980 | 1.74476 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −9.92724 | −0.341912 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 14.2793 | 0.491224 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −2.65685 | −0.0912906 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −15.4142 | −0.529014 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0.371418 | 0.0127321 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −46.6423 | −1.59700 | −0.798501 | − | 0.601993i | \(-0.794373\pi\) | ||||
−0.798501 | + | 0.601993i | \(0.794373\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −15.0711 | −0.515420 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −7.65685 | −0.261553 | −0.130777 | − | 0.991412i | \(-0.541747\pi\) | ||||
−0.130777 | + | 0.991412i | \(0.541747\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −34.6591 | −1.18255 | −0.591276 | − | 0.806469i | \(-0.701376\pi\) | ||||
−0.591276 | + | 0.806469i | \(0.701376\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −4.96362 | −0.169160 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −48.0000 | −1.63394 | −0.816970 | − | 0.576681i | \(-0.804348\pi\) | ||||
−0.816970 | + | 0.576681i | \(0.804348\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −29.2132 | −0.993279 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 12.4860 | 0.424046 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −32.6256 | −1.10675 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −14.9117 | −0.505263 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 4.82843 | 0.163417 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −12.1689 | −0.411385 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −19.8995 | −0.671960 | −0.335980 | − | 0.941869i | \(-0.609067\pi\) | ||||
−0.335980 | + | 0.941869i | \(0.609067\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −7.41421 | −0.250075 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −36.4264 | −1.22724 | −0.613618 | − | 0.789603i | \(-0.710287\pi\) | ||||
−0.613618 | + | 0.789603i | \(0.710287\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −42.1814 | −1.41952 | −0.709759 | − | 0.704444i | \(-0.751196\pi\) | ||||
−0.709759 | + | 0.704444i | \(0.751196\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −21.3533 | −0.717785 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 55.5980 | 1.86680 | 0.933399 | − | 0.358841i | \(-0.116828\pi\) | ||||
0.933399 | + | 0.358841i | \(0.116828\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −9.75736 | −0.327251 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −15.0447 | −0.504017 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −13.5140 | −0.452228 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 23.3137 | 0.779291 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 1.02944 | 0.0343719 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −10.4525 | −0.348611 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 6.12293 | 0.203985 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −1.17157 | −0.0389875 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −6.72792 | −0.223644 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 43.0781 | 1.43039 | 0.715193 | − | 0.698927i | \(-0.246339\pi\) | ||||
0.715193 | + | 0.698927i | \(0.246339\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 33.8393 | 1.12238 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −48.1838 | −1.59640 | −0.798200 | − | 0.602393i | \(-0.794214\pi\) | ||||
−0.798200 | + | 0.602393i | \(0.794214\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −8.48528 | −0.280822 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 2.61313 | 0.0863873 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −3.56420 | −0.117700 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −13.1127 | −0.432548 | −0.216274 | − | 0.976333i | \(-0.569390\pi\) | ||||
−0.216274 | + | 0.976333i | \(0.569390\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −0.585786 | −0.0193023 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −11.0866 | −0.364918 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −1.00547 | −0.0330596 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −39.7990 | −1.30717 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 33.7990 | 1.10891 | 0.554454 | − | 0.832214i | \(-0.312927\pi\) | ||||
0.554454 | + | 0.832214i | \(0.312927\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −3.37849 | −0.110726 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −3.06147 | −0.100228 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 5.65685 | 0.184999 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 50.0833 | 1.63615 | 0.818074 | − | 0.575112i | \(-0.195042\pi\) | ||||
0.818074 | + | 0.575112i | \(0.195042\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −21.5391 | −0.702901 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 29.3240 | 0.955936 | 0.477968 | − | 0.878377i | \(-0.341373\pi\) | ||||
0.477968 | + | 0.878377i | \(0.341373\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −3.79899 | −0.123712 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 7.65685 | 0.249077 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −4.06694 | −0.132158 | −0.0660788 | − | 0.997814i | \(-0.521049\pi\) | ||||
−0.0660788 | + | 0.997814i | \(0.521049\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 24.0753 | 0.781516 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 4.28427 | 0.138927 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 12.3431 | 0.399834 | 0.199917 | − | 0.979813i | \(-0.435933\pi\) | ||||
0.199917 | + | 0.979813i | \(0.435933\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −25.2346 | −0.816572 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −25.2346 | −0.815718 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 20.9706 | 0.677175 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −29.6274 | −0.955723 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −5.22625 | −0.168414 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 19.5600 | 0.629658 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 25.3553 | 0.815373 | 0.407686 | − | 0.913122i | \(-0.366336\pi\) | ||||
0.407686 | + | 0.913122i | \(0.366336\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 2.14214 | 0.0688153 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −11.9288 | −0.382815 | −0.191407 | − | 0.981511i | \(-0.561305\pi\) | ||||
−0.191407 | + | 0.981511i | \(0.561305\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −11.4036 | −0.365582 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −2.78680 | −0.0892489 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −29.3137 | −0.937829 | −0.468914 | − | 0.883244i | \(-0.655355\pi\) | ||||
−0.468914 | + | 0.883244i | \(0.655355\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −22.1731 | −0.708656 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 31.9916 | 1.02141 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −25.1716 | −0.802848 | −0.401424 | − | 0.915892i | \(-0.631485\pi\) | ||||
−0.401424 | + | 0.915892i | \(0.631485\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 20.0000 | 0.637253 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 3.06147 | 0.0974476 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −0.896683 | −0.0285129 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 17.7990 | 0.565404 | 0.282702 | − | 0.959208i | \(-0.408769\pi\) | ||||
0.282702 | + | 0.959208i | \(0.408769\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 18.1421 | 0.575723 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 11.3492 | 0.359793 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −17.2639 | −0.546753 | −0.273376 | − | 0.961907i | \(-0.588140\pi\) | ||||
−0.273376 | + | 0.961907i | \(0.588140\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 2.62742 | 0.0831278 |
(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 | 3584.2.a.c.1.2 | ✓ | 4 | |
4.3 | odd | 2 | 3584.2.a.d.1.3 | yes | 4 | ||
8.3 | odd | 2 | 3584.2.a.d.1.2 | yes | 4 | ||
8.5 | even | 2 | inner | 3584.2.a.c.1.3 | yes | 4 | |
16.3 | odd | 4 | 3584.2.b.c.1793.3 | 4 | |||
16.5 | even | 4 | 3584.2.b.d.1793.3 | 4 | |||
16.11 | odd | 4 | 3584.2.b.c.1793.2 | 4 | |||
16.13 | even | 4 | 3584.2.b.d.1793.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
3584.2.a.c.1.2 | ✓ | 4 | 1.1 | even | 1 | trivial | |
3584.2.a.c.1.3 | yes | 4 | 8.5 | even | 2 | inner | |
3584.2.a.d.1.2 | yes | 4 | 8.3 | odd | 2 | ||
3584.2.a.d.1.3 | yes | 4 | 4.3 | odd | 2 | ||
3584.2.b.c.1793.2 | 4 | 16.11 | odd | 4 | |||
3584.2.b.c.1793.3 | 4 | 16.3 | odd | 4 | |||
3584.2.b.d.1793.2 | 4 | 16.13 | even | 4 | |||
3584.2.b.d.1793.3 | 4 | 16.5 | even | 4 |