Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4140,2,Mod(1,4140)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4140, 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("4140.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4140 = 2^{2} \cdot 3^{2} \cdot 5 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4140.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(33.0580664368\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{6}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - 6 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 1380) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(2.44949\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4140.1 |
$q$-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 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.00000 | 0.377964 | 0.188982 | − | 0.981981i | \(-0.439481\pi\) | ||||
0.188982 | + | 0.981981i | \(0.439481\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.449490 | −0.135526 | −0.0677631 | − | 0.997701i | \(-0.521586\pi\) | ||||
−0.0677631 | + | 0.997701i | \(0.521586\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.44949 | −0.679366 | −0.339683 | − | 0.940540i | \(-0.610320\pi\) | ||||
−0.339683 | + | 0.940540i | \(0.610320\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −1.44949 | −0.351553 | −0.175776 | − | 0.984430i | \(-0.556244\pi\) | ||||
−0.175776 | + | 0.984430i | \(0.556244\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −7.34847 | −1.68585 | −0.842927 | − | 0.538028i | \(-0.819170\pi\) | ||||
−0.842927 | + | 0.538028i | \(0.819170\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −1.00000 | −0.208514 | ||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 4.55051 | 0.845009 | 0.422504 | − | 0.906361i | \(-0.361151\pi\) | ||||
0.422504 | + | 0.906361i | \(0.361151\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 7.89898 | 1.41870 | 0.709349 | − | 0.704857i | \(-0.248989\pi\) | ||||
0.709349 | + | 0.704857i | \(0.248989\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 1.00000 | 0.169031 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −0.101021 | −0.0166077 | −0.00830384 | − | 0.999966i | \(-0.502643\pi\) | ||||
−0.00830384 | + | 0.999966i | \(0.502643\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 5.44949 | 0.851067 | 0.425534 | − | 0.904943i | \(-0.360086\pi\) | ||||
0.425534 | + | 0.904943i | \(0.360086\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 11.7980 | 1.79917 | 0.899586 | − | 0.436744i | \(-0.143868\pi\) | ||||
0.899586 | + | 0.436744i | \(0.143868\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 7.34847 | 1.07188 | 0.535942 | − | 0.844255i | \(-0.319956\pi\) | ||||
0.535942 | + | 0.844255i | \(0.319956\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.00000 | −0.857143 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 10.3485 | 1.42147 | 0.710736 | − | 0.703459i | \(-0.248362\pi\) | ||||
0.710736 | + | 0.703459i | \(0.248362\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −0.449490 | −0.0606092 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 11.4495 | 1.49060 | 0.745298 | − | 0.666731i | \(-0.232307\pi\) | ||||
0.745298 | + | 0.666731i | \(0.232307\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −4.44949 | −0.569699 | −0.284849 | − | 0.958572i | \(-0.591944\pi\) | ||||
−0.284849 | + | 0.958572i | \(0.591944\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −2.44949 | −0.303822 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −10.7980 | −1.31918 | −0.659590 | − | 0.751625i | \(-0.729270\pi\) | ||||
−0.659590 | + | 0.751625i | \(0.729270\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 12.3485 | 1.46549 | 0.732747 | − | 0.680501i | \(-0.238238\pi\) | ||||
0.732747 | + | 0.680501i | \(0.238238\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 7.34847 | 0.860073 | 0.430037 | − | 0.902811i | \(-0.358501\pi\) | ||||
0.430037 | + | 0.902811i | \(0.358501\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −0.449490 | −0.0512241 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 5.79796 | 0.652321 | 0.326161 | − | 0.945314i | \(-0.394245\pi\) | ||||
0.326161 | + | 0.945314i | \(0.394245\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 10.5505 | 1.15807 | 0.579034 | − | 0.815303i | \(-0.303430\pi\) | ||||
0.579034 | + | 0.815303i | \(0.303430\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1.44949 | −0.157219 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 12.8990 | 1.36729 | 0.683645 | − | 0.729815i | \(-0.260394\pi\) | ||||
0.683645 | + | 0.729815i | \(0.260394\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −2.44949 | −0.256776 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −7.34847 | −0.753937 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −4.89898 | −0.497416 | −0.248708 | − | 0.968579i | \(-0.580006\pi\) | ||||
−0.248708 | + | 0.968579i | \(0.580006\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1.65153 | 0.164333 | 0.0821667 | − | 0.996619i | \(-0.473816\pi\) | ||||
0.0821667 | + | 0.996619i | \(0.473816\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −6.89898 | −0.679777 | −0.339888 | − | 0.940466i | \(-0.610389\pi\) | ||||
−0.339888 | + | 0.940466i | \(0.610389\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −16.3485 | −1.58047 | −0.790233 | − | 0.612806i | \(-0.790041\pi\) | ||||
−0.790233 | + | 0.612806i | \(0.790041\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −13.5505 | −1.29790 | −0.648952 | − | 0.760830i | \(-0.724792\pi\) | ||||
−0.648952 | + | 0.760830i | \(0.724792\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −9.24745 | −0.869927 | −0.434963 | − | 0.900448i | \(-0.643239\pi\) | ||||
−0.434963 | + | 0.900448i | \(0.643239\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1.00000 | −0.0932505 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −1.44949 | −0.132875 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.7980 | −0.981633 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 18.2474 | 1.61920 | 0.809600 | − | 0.586983i | \(-0.199684\pi\) | ||||
0.809600 | + | 0.586983i | \(0.199684\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −7.34847 | −0.637193 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 10.6969 | 0.913901 | 0.456951 | − | 0.889492i | \(-0.348942\pi\) | ||||
0.456951 | + | 0.889492i | \(0.348942\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 8.79796 | 0.746233 | 0.373117 | − | 0.927784i | \(-0.378289\pi\) | ||||
0.373117 | + | 0.927784i | \(0.378289\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 1.10102 | 0.0920720 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 4.55051 | 0.377899 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 10.4495 | 0.856056 | 0.428028 | − | 0.903766i | \(-0.359209\pi\) | ||||
0.428028 | + | 0.903766i | \(0.359209\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 15.7980 | 1.28562 | 0.642810 | − | 0.766026i | \(-0.277769\pi\) | ||||
0.642810 | + | 0.766026i | \(0.277769\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 7.89898 | 0.634461 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 11.0000 | 0.877896 | 0.438948 | − | 0.898513i | \(-0.355351\pi\) | ||||
0.438948 | + | 0.898513i | \(0.355351\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −1.00000 | −0.0788110 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −17.5959 | −1.37822 | −0.689109 | − | 0.724657i | \(-0.741998\pi\) | ||||
−0.689109 | + | 0.724657i | \(0.741998\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −9.55051 | −0.739041 | −0.369520 | − | 0.929223i | \(-0.620478\pi\) | ||||
−0.369520 | + | 0.929223i | \(0.620478\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −7.00000 | −0.538462 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 9.79796 | 0.744925 | 0.372463 | − | 0.928047i | \(-0.378514\pi\) | ||||
0.372463 | + | 0.928047i | \(0.378514\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1.00000 | 0.0755929 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −10.0000 | −0.747435 | −0.373718 | − | 0.927543i | \(-0.621917\pi\) | ||||
−0.373718 | + | 0.927543i | \(0.621917\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 4.89898 | 0.364138 | 0.182069 | − | 0.983286i | \(-0.441721\pi\) | ||||
0.182069 | + | 0.983286i | \(0.441721\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −0.101021 | −0.00742718 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0.651531 | 0.0476446 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −17.1464 | −1.24067 | −0.620336 | − | 0.784336i | \(-0.713004\pi\) | ||||
−0.620336 | + | 0.784336i | \(0.713004\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 8.89898 | 0.640563 | 0.320281 | − | 0.947322i | \(-0.396223\pi\) | ||||
0.320281 | + | 0.947322i | \(0.396223\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 1.10102 | 0.0784445 | 0.0392222 | − | 0.999231i | \(-0.487512\pi\) | ||||
0.0392222 | + | 0.999231i | \(0.487512\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −4.69694 | −0.332957 | −0.166479 | − | 0.986045i | \(-0.553240\pi\) | ||||
−0.166479 | + | 0.986045i | \(0.553240\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 4.55051 | 0.319383 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 5.44949 | 0.380609 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 3.30306 | 0.228478 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 25.0000 | 1.72107 | 0.860535 | − | 0.509390i | \(-0.170129\pi\) | ||||
0.860535 | + | 0.509390i | \(0.170129\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 11.7980 | 0.804614 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 7.89898 | 0.536218 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 3.55051 | 0.238833 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 14.0000 | 0.937509 | 0.468755 | − | 0.883328i | \(-0.344703\pi\) | ||||
0.468755 | + | 0.883328i | \(0.344703\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −21.7980 | −1.44678 | −0.723391 | − | 0.690439i | \(-0.757417\pi\) | ||||
−0.723391 | + | 0.690439i | \(0.757417\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 6.69694 | 0.442546 | 0.221273 | − | 0.975212i | \(-0.428979\pi\) | ||||
0.221273 | + | 0.975212i | \(0.428979\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 15.5959 | 1.02172 | 0.510861 | − | 0.859663i | \(-0.329327\pi\) | ||||
0.510861 | + | 0.859663i | \(0.329327\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 7.34847 | 0.479361 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 21.0454 | 1.36131 | 0.680657 | − | 0.732602i | \(-0.261694\pi\) | ||||
0.680657 | + | 0.732602i | \(0.261694\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −30.0454 | −1.93539 | −0.967697 | − | 0.252114i | \(-0.918874\pi\) | ||||
−0.967697 | + | 0.252114i | \(0.918874\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −6.00000 | −0.383326 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 18.0000 | 1.14531 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 18.0000 | 1.13615 | 0.568075 | − | 0.822977i | \(-0.307688\pi\) | ||||
0.568075 | + | 0.822977i | \(0.307688\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0.449490 | 0.0282592 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 4.24745 | 0.264949 | 0.132474 | − | 0.991186i | \(-0.457708\pi\) | ||||
0.132474 | + | 0.991186i | \(0.457708\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −0.101021 | −0.00627711 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 0.348469 | 0.0214875 | 0.0107438 | − | 0.999942i | \(-0.496580\pi\) | ||||
0.0107438 | + | 0.999942i | \(0.496580\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 10.3485 | 0.635701 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −15.2474 | −0.929653 | −0.464827 | − | 0.885402i | \(-0.653883\pi\) | ||||
−0.464827 | + | 0.885402i | \(0.653883\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 6.10102 | 0.370611 | 0.185305 | − | 0.982681i | \(-0.440673\pi\) | ||||
0.185305 | + | 0.982681i | \(0.440673\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −0.449490 | −0.0271053 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −0.202041 | −0.0121395 | −0.00606973 | − | 0.999982i | \(-0.501932\pi\) | ||||
−0.00606973 | + | 0.999982i | \(0.501932\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 2.65153 | 0.158177 | 0.0790885 | − | 0.996868i | \(-0.474799\pi\) | ||||
0.0790885 | + | 0.996868i | \(0.474799\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 3.89898 | 0.231770 | 0.115885 | − | 0.993263i | \(-0.463030\pi\) | ||||
0.115885 | + | 0.993263i | \(0.463030\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 5.44949 | 0.321673 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −14.8990 | −0.876411 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −27.0454 | −1.58001 | −0.790005 | − | 0.613101i | \(-0.789922\pi\) | ||||
−0.790005 | + | 0.613101i | \(0.789922\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 11.4495 | 0.666615 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 2.44949 | 0.141658 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 11.7980 | 0.680023 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −4.44949 | −0.254777 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −20.2474 | −1.15558 | −0.577791 | − | 0.816184i | \(-0.696085\pi\) | ||||
−0.577791 | + | 0.816184i | \(0.696085\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 15.5959 | 0.884363 | 0.442182 | − | 0.896926i | \(-0.354205\pi\) | ||||
0.442182 | + | 0.896926i | \(0.354205\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −4.30306 | −0.243223 | −0.121612 | − | 0.992578i | \(-0.538806\pi\) | ||||
−0.121612 | + | 0.992578i | \(0.538806\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −27.3485 | −1.53604 | −0.768022 | − | 0.640424i | \(-0.778759\pi\) | ||||
−0.768022 | + | 0.640424i | \(0.778759\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −2.04541 | −0.114521 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 10.6515 | 0.592667 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −2.44949 | −0.135873 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 7.34847 | 0.405134 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 20.7980 | 1.14316 | 0.571580 | − | 0.820547i | \(-0.306331\pi\) | ||||
0.571580 | + | 0.820547i | \(0.306331\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −10.7980 | −0.589956 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 23.7980 | 1.29636 | 0.648179 | − | 0.761488i | \(-0.275531\pi\) | ||||
0.648179 | + | 0.761488i | \(0.275531\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −3.55051 | −0.192271 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −13.0000 | −0.701934 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −28.4949 | −1.52969 | −0.764843 | − | 0.644217i | \(-0.777184\pi\) | ||||
−0.764843 | + | 0.644217i | \(0.777184\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −33.4949 | −1.79294 | −0.896470 | − | 0.443104i | \(-0.853877\pi\) | ||||
−0.896470 | + | 0.443104i | \(0.853877\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −5.55051 | −0.295424 | −0.147712 | − | 0.989030i | \(-0.547191\pi\) | ||||
−0.147712 | + | 0.989030i | \(0.547191\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 12.3485 | 0.655389 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 9.55051 | 0.504057 | 0.252028 | − | 0.967720i | \(-0.418902\pi\) | ||||
0.252028 | + | 0.967720i | \(0.418902\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 35.0000 | 1.84211 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 7.34847 | 0.384636 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 29.8990 | 1.56071 | 0.780357 | − | 0.625334i | \(-0.215037\pi\) | ||||
0.780357 | + | 0.625334i | \(0.215037\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 10.3485 | 0.537266 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 10.2020 | 0.528242 | 0.264121 | − | 0.964490i | \(-0.414918\pi\) | ||||
0.264121 | + | 0.964490i | \(0.414918\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −11.1464 | −0.574070 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 13.7980 | 0.708754 | 0.354377 | − | 0.935103i | \(-0.384693\pi\) | ||||
0.354377 | + | 0.935103i | \(0.384693\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −21.2474 | −1.08569 | −0.542847 | − | 0.839832i | \(-0.682654\pi\) | ||||
−0.542847 | + | 0.839832i | \(0.682654\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −0.449490 | −0.0229081 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 14.4949 | 0.734920 | 0.367460 | − | 0.930039i | \(-0.380227\pi\) | ||||
0.367460 | + | 0.930039i | \(0.380227\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1.44949 | 0.0733038 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 5.79796 | 0.291727 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −37.7980 | −1.89703 | −0.948513 | − | 0.316739i | \(-0.897412\pi\) | ||||
−0.948513 | + | 0.316739i | \(0.897412\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −13.1010 | −0.654234 | −0.327117 | − | 0.944984i | \(-0.606077\pi\) | ||||
−0.327117 | + | 0.944984i | \(0.606077\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −19.3485 | −0.963816 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0.0454077 | 0.00225078 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 19.6969 | 0.973951 | 0.486975 | − | 0.873416i | \(-0.338100\pi\) | ||||
0.486975 | + | 0.873416i | \(0.338100\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 11.4495 | 0.563393 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 10.5505 | 0.517904 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 18.6515 | 0.911187 | 0.455593 | − | 0.890188i | \(-0.349427\pi\) | ||||
0.455593 | + | 0.890188i | \(0.349427\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −7.34847 | −0.358142 | −0.179071 | − | 0.983836i | \(-0.557309\pi\) | ||||
−0.179071 | + | 0.983836i | \(0.557309\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −1.44949 | −0.0703106 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −4.44949 | −0.215326 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 36.4949 | 1.75790 | 0.878949 | − | 0.476916i | \(-0.158246\pi\) | ||||
0.878949 | + | 0.476916i | \(0.158246\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −5.20204 | −0.249994 | −0.124997 | − | 0.992157i | \(-0.539892\pi\) | ||||
−0.124997 | + | 0.992157i | \(0.539892\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 7.34847 | 0.351525 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 4.69694 | 0.224173 | 0.112086 | − | 0.993698i | \(-0.464247\pi\) | ||||
0.112086 | + | 0.993698i | \(0.464247\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 22.4495 | 1.06661 | 0.533304 | − | 0.845924i | \(-0.320950\pi\) | ||||
0.533304 | + | 0.845924i | \(0.320950\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 12.8990 | 0.611470 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −24.8434 | −1.17243 | −0.586215 | − | 0.810155i | \(-0.699383\pi\) | ||||
−0.586215 | + | 0.810155i | \(0.699383\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −2.44949 | −0.115342 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −2.44949 | −0.114834 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −27.4949 | −1.28616 | −0.643079 | − | 0.765800i | \(-0.722343\pi\) | ||||
−0.643079 | + | 0.765800i | \(0.722343\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 12.6969 | 0.591355 | 0.295678 | − | 0.955288i | \(-0.404455\pi\) | ||||
0.295678 | + | 0.955288i | \(0.404455\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −7.34847 | −0.341512 | −0.170756 | − | 0.985313i | \(-0.554621\pi\) | ||||
−0.170756 | + | 0.985313i | \(0.554621\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −2.14643 | −0.0993249 | −0.0496624 | − | 0.998766i | \(-0.515815\pi\) | ||||
−0.0496624 | + | 0.998766i | \(0.515815\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −10.7980 | −0.498603 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −5.30306 | −0.243835 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −7.34847 | −0.337171 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −22.9444 | −1.04836 | −0.524178 | − | 0.851609i | \(-0.675627\pi\) | ||||
−0.524178 | + | 0.851609i | \(0.675627\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0.247449 | 0.0112827 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −4.89898 | −0.222451 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 25.8434 | 1.17107 | 0.585537 | − | 0.810645i | \(-0.300884\pi\) | ||||
0.585537 | + | 0.810645i | \(0.300884\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 21.2474 | 0.958884 | 0.479442 | − | 0.877574i | \(-0.340839\pi\) | ||||
0.479442 | + | 0.877574i | \(0.340839\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −6.59592 | −0.297065 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 12.3485 | 0.553905 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 26.7980 | 1.19964 | 0.599821 | − | 0.800134i | \(-0.295239\pi\) | ||||
0.599821 | + | 0.800134i | \(0.295239\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 16.1464 | 0.719934 | 0.359967 | − | 0.932965i | \(-0.382788\pi\) | ||||
0.359967 | + | 0.932965i | \(0.382788\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 1.65153 | 0.0734922 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −30.6969 | −1.36062 | −0.680309 | − | 0.732925i | \(-0.738154\pi\) | ||||
−0.680309 | + | 0.732925i | \(0.738154\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 7.34847 | 0.325077 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −6.89898 | −0.304005 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −3.30306 | −0.145268 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −14.2474 | −0.624192 | −0.312096 | − | 0.950051i | \(-0.601031\pi\) | ||||
−0.312096 | + | 0.950051i | \(0.601031\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −10.2020 | −0.446104 | −0.223052 | − | 0.974807i | \(-0.571602\pi\) | ||||
−0.223052 | + | 0.974807i | \(0.571602\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −11.4495 | −0.498748 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −13.3485 | −0.578186 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −16.3485 | −0.706806 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 2.69694 | 0.116165 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 32.4949 | 1.39706 | 0.698532 | − | 0.715578i | \(-0.253837\pi\) | ||||
0.698532 | + | 0.715578i | \(0.253837\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −13.5505 | −0.580440 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −21.7980 | −0.932013 | −0.466007 | − | 0.884781i | \(-0.654308\pi\) | ||||
−0.466007 | + | 0.884781i | \(0.654308\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −33.4393 | −1.42456 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 5.79796 | 0.246554 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −21.6515 | −0.917405 | −0.458702 | − | 0.888590i | \(-0.651686\pi\) | ||||
−0.458702 | + | 0.888590i | \(0.651686\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −28.8990 | −1.22230 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 32.3485 | 1.36333 | 0.681663 | − | 0.731667i | \(-0.261257\pi\) | ||||
0.681663 | + | 0.731667i | \(0.261257\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −9.24745 | −0.389043 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 20.6969 | 0.867661 | 0.433830 | − | 0.900995i | \(-0.357162\pi\) | ||||
0.433830 | + | 0.900995i | \(0.357162\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −8.44949 | −0.353600 | −0.176800 | − | 0.984247i | \(-0.556575\pi\) | ||||
−0.176800 | + | 0.984247i | \(0.556575\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −1.00000 | −0.0417029 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −13.7980 | −0.574417 | −0.287208 | − | 0.957868i | \(-0.592727\pi\) | ||||
−0.287208 | + | 0.957868i | \(0.592727\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 10.5505 | 0.437709 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −4.65153 | −0.192647 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 39.3939 | 1.62596 | 0.812980 | − | 0.582292i | \(-0.197844\pi\) | ||||
0.812980 | + | 0.582292i | \(0.197844\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −58.0454 | −2.39172 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −0.247449 | −0.0101615 | −0.00508075 | − | 0.999987i | \(-0.501617\pi\) | ||||
−0.00508075 | + | 0.999987i | \(0.501617\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −1.44949 | −0.0594233 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −24.4949 | −1.00083 | −0.500417 | − | 0.865784i | \(-0.666820\pi\) | ||||
−0.500417 | + | 0.865784i | \(0.666820\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 22.3939 | 0.913465 | 0.456733 | − | 0.889604i | \(-0.349020\pi\) | ||||
0.456733 | + | 0.889604i | \(0.349020\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −10.7980 | −0.438999 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −12.0454 | −0.488908 | −0.244454 | − | 0.969661i | \(-0.578609\pi\) | ||||
−0.244454 | + | 0.969661i | \(0.578609\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −18.0000 | −0.728202 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 14.0000 | 0.565455 | 0.282727 | − | 0.959200i | \(-0.408761\pi\) | ||||
0.282727 | + | 0.959200i | \(0.408761\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −7.85357 | −0.316173 | −0.158086 | − | 0.987425i | \(-0.550532\pi\) | ||||
−0.158086 | + | 0.987425i | \(0.550532\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −45.7980 | −1.84078 | −0.920388 | − | 0.391007i | \(-0.872127\pi\) | ||||
−0.920388 | + | 0.391007i | \(0.872127\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 12.8990 | 0.516787 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 0.146428 | 0.00583847 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −8.04541 | −0.320283 | −0.160141 | − | 0.987094i | \(-0.551195\pi\) | ||||
−0.160141 | + | 0.987094i | \(0.551195\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 18.2474 | 0.724128 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 14.6969 | 0.582314 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −0.449490 | −0.0177538 | −0.00887689 | − | 0.999961i | \(-0.502826\pi\) | ||||
−0.00887689 | + | 0.999961i | \(0.502826\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −25.4949 | −1.00542 | −0.502710 | − | 0.864455i | \(-0.667664\pi\) | ||||
−0.502710 | + | 0.864455i | \(0.667664\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −25.3485 | −0.996551 | −0.498276 | − | 0.867019i | \(-0.666033\pi\) | ||||
−0.498276 | + | 0.867019i | \(0.666033\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −5.14643 | −0.202015 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −5.34847 | −0.209302 | −0.104651 | − | 0.994509i | \(-0.533373\pi\) | ||||
−0.104651 | + | 0.994509i | \(0.533373\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 32.9444 | 1.28333 | 0.641666 | − | 0.766985i | \(-0.278244\pi\) | ||||
0.641666 | + | 0.766985i | \(0.278244\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 15.3031 | 0.595220 | 0.297610 | − | 0.954688i | \(-0.403810\pi\) | ||||
0.297610 | + | 0.954688i | \(0.403810\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −7.34847 | −0.284961 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −4.55051 | −0.176196 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 2.00000 | 0.0772091 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −32.4495 | −1.25084 | −0.625418 | − | 0.780290i | \(-0.715072\pi\) | ||||
−0.625418 | + | 0.780290i | \(0.715072\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −6.34847 | −0.243991 | −0.121996 | − | 0.992531i | \(-0.538929\pi\) | ||||
−0.121996 | + | 0.992531i | \(0.538929\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −4.89898 | −0.188006 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −46.0454 | −1.76188 | −0.880939 | − | 0.473229i | \(-0.843088\pi\) | ||||
−0.880939 | + | 0.473229i | \(0.843088\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 10.6969 | 0.408709 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −25.3485 | −0.965700 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −9.59592 | −0.365046 | −0.182523 | − | 0.983202i | \(-0.558426\pi\) | ||||
−0.182523 | + | 0.983202i | \(0.558426\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 8.79796 | 0.333726 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −7.89898 | −0.299195 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 31.3485 | 1.18402 | 0.592008 | − | 0.805932i | \(-0.298336\pi\) | ||||
0.592008 | + | 0.805932i | \(0.298336\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0.742346 | 0.0279981 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 1.65153 | 0.0621122 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −18.6515 | −0.700473 | −0.350236 | − | 0.936661i | \(-0.613899\pi\) | ||||
−0.350236 | + | 0.936661i | \(0.613899\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −7.89898 | −0.295819 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1.10102 | 0.0411758 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 4.34847 | 0.162171 | 0.0810853 | − | 0.996707i | \(-0.474161\pi\) | ||||
0.0810853 | + | 0.996707i | \(0.474161\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −6.89898 | −0.256931 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 4.55051 | 0.169002 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −17.8990 | −0.663836 | −0.331918 | − | 0.943308i | \(-0.607696\pi\) | ||||
−0.331918 | + | 0.943308i | \(0.607696\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −17.1010 | −0.632504 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 32.3939 | 1.19650 | 0.598248 | − | 0.801311i | \(-0.295864\pi\) | ||||
0.598248 | + | 0.801311i | \(0.295864\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 4.85357 | 0.178784 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 46.5959 | 1.71406 | 0.857029 | − | 0.515268i | \(-0.172308\pi\) | ||||
0.857029 | + | 0.515268i | \(0.172308\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 53.7980 | 1.97366 | 0.986828 | − | 0.161774i | \(-0.0517215\pi\) | ||||
0.986828 | + | 0.161774i | \(0.0517215\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 10.4495 | 0.382840 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −16.3485 | −0.597360 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 10.8536 | 0.396052 | 0.198026 | − | 0.980197i | \(-0.436547\pi\) | ||||
0.198026 | + | 0.980197i | \(0.436547\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 15.7980 | 0.574947 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 9.69694 | 0.352441 | 0.176221 | − | 0.984351i | \(-0.443613\pi\) | ||||
0.176221 | + | 0.984351i | \(0.443613\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 42.1464 | 1.52781 | 0.763903 | − | 0.645331i | \(-0.223280\pi\) | ||||
0.763903 | + | 0.645331i | \(0.223280\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −13.5505 | −0.490561 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −28.0454 | −1.01266 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −0.853572 | −0.0307806 | −0.0153903 | − | 0.999882i | \(-0.504899\pi\) | ||||
−0.0153903 | + | 0.999882i | \(0.504899\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −1.10102 | −0.0396010 | −0.0198005 | − | 0.999804i | \(-0.506303\pi\) | ||||
−0.0198005 | + | 0.999804i | \(0.506303\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 7.89898 | 0.283740 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −40.0454 | −1.43478 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −5.55051 | −0.198613 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 11.0000 | 0.392607 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 21.2929 | 0.759008 | 0.379504 | − | 0.925190i | \(-0.376095\pi\) | ||||
0.379504 | + | 0.925190i | \(0.376095\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −9.24745 | −0.328801 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 10.8990 | 0.387034 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −32.5505 | −1.15300 | −0.576499 | − | 0.817098i | \(-0.695582\pi\) | ||||
−0.576499 | + | 0.817098i | \(0.695582\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −10.6515 | −0.376824 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −3.30306 | −0.116563 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −1.00000 | −0.0352454 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −41.4495 | −1.45729 | −0.728643 | − | 0.684893i | \(-0.759849\pi\) | ||||
−0.728643 | + | 0.684893i | \(0.759849\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −13.2020 | −0.463586 | −0.231793 | − | 0.972765i | \(-0.574459\pi\) | ||||
−0.231793 | + | 0.972765i | \(0.574459\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −17.5959 | −0.616358 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −86.6969 | −3.03314 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 4.49490 | 0.156873 | 0.0784365 | − | 0.996919i | \(-0.475007\pi\) | ||||
0.0784365 | + | 0.996919i | \(0.475007\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −1.79796 | −0.0626729 | −0.0313365 | − | 0.999509i | \(-0.509976\pi\) | ||||
−0.0313365 | + | 0.999509i | \(0.509976\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 52.4393 | 1.82349 | 0.911746 | − | 0.410754i | \(-0.134734\pi\) | ||||
0.911746 | + | 0.410754i | \(0.134734\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −31.6969 | −1.10088 | −0.550440 | − | 0.834875i | \(-0.685540\pi\) | ||||
−0.550440 | + | 0.834875i | \(0.685540\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 8.69694 | 0.301331 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −9.55051 | −0.330509 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 2.00000 | 0.0690477 | 0.0345238 | − | 0.999404i | \(-0.489009\pi\) | ||||
0.0345238 | + | 0.999404i | \(0.489009\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −8.29286 | −0.285961 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −7.00000 | −0.240807 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −10.7980 | −0.371022 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0.101021 | 0.00346294 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −14.8990 | −0.510131 | −0.255066 | − | 0.966924i | \(-0.582097\pi\) | ||||
−0.255066 | + | 0.966924i | \(0.582097\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −25.5959 | −0.874340 | −0.437170 | − | 0.899379i | \(-0.644019\pi\) | ||||
−0.437170 | + | 0.899379i | \(0.644019\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 16.5959 | 0.566245 | 0.283123 | − | 0.959084i | \(-0.408630\pi\) | ||||
0.283123 | + | 0.959084i | \(0.408630\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −40.2929 | −1.37158 | −0.685792 | − | 0.727797i | \(-0.740544\pi\) | ||||
−0.685792 | + | 0.727797i | \(0.740544\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 9.79796 | 0.333141 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −2.60612 | −0.0884067 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 26.4495 | 0.896207 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 1.00000 | 0.0338062 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −4.69694 | −0.158604 | −0.0793022 | − | 0.996851i | \(-0.525269\pi\) | ||||
−0.0793022 | + | 0.996851i | \(0.525269\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 44.2474 | 1.49073 | 0.745367 | − | 0.666654i | \(-0.232274\pi\) | ||||
0.745367 | + | 0.666654i | \(0.232274\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −17.7526 | −0.597421 | −0.298710 | − | 0.954344i | \(-0.596556\pi\) | ||||
−0.298710 | + | 0.954344i | \(0.596556\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −3.30306 | −0.110906 | −0.0554530 | − | 0.998461i | \(-0.517660\pi\) | ||||
−0.0554530 | + | 0.998461i | \(0.517660\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 18.2474 | 0.612000 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −54.0000 | −1.80704 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −10.0000 | −0.334263 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 35.9444 | 1.19881 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −15.0000 | −0.499722 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 4.89898 | 0.162848 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −45.0000 | −1.49420 | −0.747100 | − | 0.664711i | \(-0.768555\pi\) | ||||
−0.747100 | + | 0.664711i | \(0.768555\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −43.5959 | −1.44440 | −0.722199 | − | 0.691686i | \(-0.756868\pi\) | ||||
−0.722199 | + | 0.691686i | \(0.756868\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −4.74235 | −0.156949 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 6.20204 | 0.204586 | 0.102293 | − | 0.994754i | \(-0.467382\pi\) | ||||
0.102293 | + | 0.994754i | \(0.467382\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −30.2474 | −0.995607 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −0.101021 | −0.00332153 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 34.8434 | 1.14317 | 0.571587 | − | 0.820542i | \(-0.306328\pi\) | ||||
0.571587 | + | 0.820542i | \(0.306328\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 44.0908 | 1.44502 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0.651531 | 0.0213073 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −36.4949 | −1.19224 | −0.596118 | − | 0.802897i | \(-0.703291\pi\) | ||||
−0.596118 | + | 0.802897i | \(0.703291\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 25.5505 | 0.832923 | 0.416461 | − | 0.909153i | \(-0.363270\pi\) | ||||
0.416461 | + | 0.909153i | \(0.363270\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −5.44949 | −0.177460 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 13.3031 | 0.432291 | 0.216146 | − | 0.976361i | \(-0.430651\pi\) | ||||
0.216146 | + | 0.976361i | \(0.430651\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −18.0000 | −0.584305 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −33.5959 | −1.08828 | −0.544139 | − | 0.838995i | \(-0.683144\pi\) | ||||
−0.544139 | + | 0.838995i | \(0.683144\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −17.1464 | −0.554845 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 10.6969 | 0.345422 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 31.3939 | 1.01271 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 8.89898 | 0.286468 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −21.3485 | −0.686520 | −0.343260 | − | 0.939240i | \(-0.611531\pi\) | ||||
−0.343260 | + | 0.939240i | \(0.611531\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 35.1010 | 1.12645 | 0.563223 | − | 0.826305i | \(-0.309561\pi\) | ||||
0.563223 | + | 0.826305i | \(0.309561\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 8.79796 | 0.282050 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 7.65153 | 0.244794 | 0.122397 | − | 0.992481i | \(-0.460942\pi\) | ||||
0.122397 | + | 0.992481i | \(0.460942\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −5.79796 | −0.185304 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 26.1464 | 0.833942 | 0.416971 | − | 0.908920i | \(-0.363092\pi\) | ||||
0.416971 | + | 0.908920i | \(0.363092\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 1.10102 | 0.0350814 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −11.7980 | −0.375153 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 20.5959 | 0.654251 | 0.327125 | − | 0.944981i | \(-0.393920\pi\) | ||||
0.327125 | + | 0.944981i | \(0.393920\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −4.69694 | −0.148903 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −27.1010 | −0.858298 | −0.429149 | − | 0.903234i | \(-0.641186\pi\) | ||||
−0.429149 | + | 0.903234i | \(0.641186\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 4140.2.a.r.1.1 | 2 | ||
3.2 | odd | 2 | 1380.2.a.f.1.2 | ✓ | 2 | ||
12.11 | even | 2 | 5520.2.a.bl.1.1 | 2 | |||
15.2 | even | 4 | 6900.2.f.h.6349.4 | 4 | |||
15.8 | even | 4 | 6900.2.f.h.6349.2 | 4 | |||
15.14 | odd | 2 | 6900.2.a.r.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1380.2.a.f.1.2 | ✓ | 2 | 3.2 | odd | 2 | ||
4140.2.a.r.1.1 | 2 | 1.1 | even | 1 | trivial | ||
5520.2.a.bl.1.1 | 2 | 12.11 | even | 2 | |||
6900.2.a.r.1.2 | 2 | 15.14 | odd | 2 | |||
6900.2.f.h.6349.2 | 4 | 15.8 | even | 4 | |||
6900.2.f.h.6349.4 | 4 | 15.2 | even | 4 |