Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8550,2,Mod(1,8550)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8550, 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("8550.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8550 = 2 \cdot 3^{2} \cdot 5^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8550.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: | \(68.2720937282\) |
Analytic rank: | \(0\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.993.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 6x + 3 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 950) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(2.77339\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8550.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.69168 | −1.01736 | −0.508679 | − | 0.860956i | \(-0.669866\pi\) | ||||
−0.508679 | + | 0.860956i | \(0.669866\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −5.54677 | −1.67242 | −0.836208 | − | 0.548413i | \(-0.815232\pi\) | ||||
−0.836208 | + | 0.548413i | \(0.815232\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.91829 | −0.809388 | −0.404694 | − | 0.914452i | \(-0.632622\pi\) | ||||
−0.404694 | + | 0.914452i | \(0.632622\pi\) | |||||||
\(14\) | 2.69168 | 0.719381 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −4.91829 | −1.19286 | −0.596430 | − | 0.802665i | \(-0.703415\pi\) | ||||
−0.596430 | + | 0.802665i | \(0.703415\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.00000 | 0.229416 | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 5.54677 | 1.18258 | ||||||||
\(23\) | −3.60997 | −0.752730 | −0.376365 | − | 0.926471i | \(-0.622826\pi\) | ||||
−0.376365 | + | 0.926471i | \(0.622826\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 2.91829 | 0.572324 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −2.69168 | −0.508679 | ||||||||
\(29\) | −1.08171 | −0.200868 | −0.100434 | − | 0.994944i | \(-0.532023\pi\) | ||||
−0.100434 | + | 0.994944i | \(0.532023\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 7.54677 | 1.35544 | 0.677720 | − | 0.735320i | \(-0.262968\pi\) | ||||
0.677720 | + | 0.735320i | \(0.262968\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 4.91829 | 0.843480 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 4.54677 | 0.747485 | 0.373743 | − | 0.927532i | \(-0.378074\pi\) | ||||
0.373743 | + | 0.927532i | \(0.378074\pi\) | |||||||
\(38\) | −1.00000 | −0.162221 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −9.54677 | −1.45587 | −0.727935 | − | 0.685646i | \(-0.759520\pi\) | ||||
−0.727935 | + | 0.685646i | \(0.759520\pi\) | |||||||
\(44\) | −5.54677 | −0.836208 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 3.60997 | 0.532261 | ||||||||
\(47\) | 0.836581 | 0.122028 | 0.0610139 | − | 0.998137i | \(-0.480567\pi\) | ||||
0.0610139 | + | 0.998137i | \(0.480567\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0.245129 | 0.0350184 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −2.91829 | −0.404694 | ||||||||
\(53\) | −9.78523 | −1.34410 | −0.672052 | − | 0.740504i | \(-0.734587\pi\) | ||||
−0.672052 | + | 0.740504i | \(0.734587\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 2.69168 | 0.359691 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 1.08171 | 0.142035 | ||||||||
\(59\) | −12.9933 | −1.69159 | −0.845793 | − | 0.533511i | \(-0.820872\pi\) | ||||
−0.845793 | + | 0.533511i | \(0.820872\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −7.38336 | −0.945342 | −0.472671 | − | 0.881239i | \(-0.656710\pi\) | ||||
−0.472671 | + | 0.881239i | \(0.656710\pi\) | |||||||
\(62\) | −7.54677 | −0.958441 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 2.85510 | 0.348806 | 0.174403 | − | 0.984674i | \(-0.444201\pi\) | ||||
0.174403 | + | 0.984674i | \(0.444201\pi\) | |||||||
\(68\) | −4.91829 | −0.596430 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −14.4769 | −1.71809 | −0.859046 | − | 0.511898i | \(-0.828943\pi\) | ||||
−0.859046 | + | 0.511898i | \(0.828943\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 5.15674 | 0.603551 | 0.301776 | − | 0.953379i | \(-0.402421\pi\) | ||||
0.301776 | + | 0.953379i | \(0.402421\pi\) | |||||||
\(74\) | −4.54677 | −0.528552 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 1.00000 | 0.114708 | ||||||||
\(77\) | 14.9301 | 1.70145 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −3.09355 | −0.348052 | −0.174026 | − | 0.984741i | \(-0.555678\pi\) | ||||
−0.174026 | + | 0.984741i | \(0.555678\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −1.71019 | −0.187718 | −0.0938591 | − | 0.995585i | \(-0.529920\pi\) | ||||
−0.0938591 | + | 0.995585i | \(0.529920\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 9.54677 | 1.02946 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 5.54677 | 0.591288 | ||||||||
\(89\) | 5.09355 | 0.539915 | 0.269958 | − | 0.962872i | \(-0.412990\pi\) | ||||
0.269958 | + | 0.962872i | \(0.412990\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 7.85510 | 0.823438 | ||||||||
\(92\) | −3.60997 | −0.376365 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −0.836581 | −0.0862867 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −17.2570 | −1.75218 | −0.876090 | − | 0.482148i | \(-0.839857\pi\) | ||||
−0.876090 | + | 0.482148i | \(0.839857\pi\) | |||||||
\(98\) | −0.245129 | −0.0247618 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 9.38336 | 0.933679 | 0.466839 | − | 0.884342i | \(-0.345393\pi\) | ||||
0.466839 | + | 0.884342i | \(0.345393\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −12.9301 | −1.27404 | −0.637022 | − | 0.770846i | \(-0.719834\pi\) | ||||
−0.637022 | + | 0.770846i | \(0.719834\pi\) | |||||||
\(104\) | 2.91829 | 0.286162 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 9.78523 | 0.950425 | ||||||||
\(107\) | −18.9420 | −1.83119 | −0.915595 | − | 0.402102i | \(-0.868280\pi\) | ||||
−0.915595 | + | 0.402102i | \(0.868280\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −2.69168 | −0.257816 | −0.128908 | − | 0.991657i | \(-0.541147\pi\) | ||||
−0.128908 | + | 0.991657i | \(0.541147\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −2.69168 | −0.254340 | ||||||||
\(113\) | 6.00000 | 0.564433 | 0.282216 | − | 0.959351i | \(-0.408930\pi\) | ||||
0.282216 | + | 0.959351i | \(0.408930\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −1.08171 | −0.100434 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 12.9933 | 1.19613 | ||||||||
\(119\) | 13.2385 | 1.21357 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 19.7667 | 1.79697 | ||||||||
\(122\) | 7.38336 | 0.668458 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 7.54677 | 0.677720 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1.87361 | −0.166256 | −0.0831282 | − | 0.996539i | \(-0.526491\pi\) | ||||
−0.0831282 | + | 0.996539i | \(0.526491\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 11.5468 | 1.00885 | 0.504423 | − | 0.863457i | \(-0.331705\pi\) | ||||
0.504423 | + | 0.863457i | \(0.331705\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −2.69168 | −0.233398 | ||||||||
\(134\) | −2.85510 | −0.246643 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 4.91829 | 0.421740 | ||||||||
\(137\) | −4.23845 | −0.362115 | −0.181058 | − | 0.983472i | \(-0.557952\pi\) | ||||
−0.181058 | + | 0.983472i | \(0.557952\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 9.21994 | 0.782025 | 0.391012 | − | 0.920385i | \(-0.372125\pi\) | ||||
0.391012 | + | 0.920385i | \(0.372125\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 14.4769 | 1.21487 | ||||||||
\(143\) | 16.1871 | 1.35363 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −5.15674 | −0.426775 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 4.54677 | 0.373743 | ||||||||
\(149\) | 7.25697 | 0.594514 | 0.297257 | − | 0.954797i | \(-0.403928\pi\) | ||||
0.297257 | + | 0.954797i | \(0.403928\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 20.0000 | 1.62758 | 0.813788 | − | 0.581161i | \(-0.197401\pi\) | ||||
0.813788 | + | 0.581161i | \(0.197401\pi\) | |||||||
\(152\) | −1.00000 | −0.0811107 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −14.9301 | −1.20310 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −9.54677 | −0.761916 | −0.380958 | − | 0.924592i | \(-0.624406\pi\) | ||||
−0.380958 | + | 0.924592i | \(0.624406\pi\) | |||||||
\(158\) | 3.09355 | 0.246110 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 9.71687 | 0.765797 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 15.7102 | 1.23052 | 0.615259 | − | 0.788325i | \(-0.289052\pi\) | ||||
0.615259 | + | 0.788325i | \(0.289052\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 1.71019 | 0.132737 | ||||||||
\(167\) | −6.45323 | −0.499366 | −0.249683 | − | 0.968328i | \(-0.580326\pi\) | ||||
−0.249683 | + | 0.968328i | \(0.580326\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −4.48358 | −0.344891 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −9.54677 | −0.727935 | ||||||||
\(173\) | 0.873614 | 0.0664196 | 0.0332098 | − | 0.999448i | \(-0.489427\pi\) | ||||
0.0332098 | + | 0.999448i | \(0.489427\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −5.54677 | −0.418104 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −5.09355 | −0.381778 | ||||||||
\(179\) | 12.3834 | 0.925575 | 0.462788 | − | 0.886469i | \(-0.346849\pi\) | ||||
0.462788 | + | 0.886469i | \(0.346849\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −17.6403 | −1.31119 | −0.655597 | − | 0.755111i | \(-0.727583\pi\) | ||||
−0.655597 | + | 0.755111i | \(0.727583\pi\) | |||||||
\(182\) | −7.85510 | −0.582259 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 3.60997 | 0.266130 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 27.2806 | 1.99496 | ||||||||
\(188\) | 0.836581 | 0.0610139 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 15.1567 | 1.09670 | 0.548352 | − | 0.836248i | \(-0.315256\pi\) | ||||
0.548352 | + | 0.836248i | \(0.315256\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 23.3834 | 1.68317 | 0.841585 | − | 0.540124i | \(-0.181623\pi\) | ||||
0.841585 | + | 0.540124i | \(0.181623\pi\) | |||||||
\(194\) | 17.2570 | 1.23898 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0.245129 | 0.0175092 | ||||||||
\(197\) | 23.0935 | 1.64535 | 0.822674 | − | 0.568514i | \(-0.192481\pi\) | ||||
0.822674 | + | 0.568514i | \(0.192481\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −25.7852 | −1.82787 | −0.913933 | − | 0.405865i | \(-0.866970\pi\) | ||||
−0.913933 | + | 0.405865i | \(0.866970\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −9.38336 | −0.660211 | ||||||||
\(203\) | 2.91161 | 0.204355 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 12.9301 | 0.900885 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −2.91829 | −0.202347 | ||||||||
\(209\) | −5.54677 | −0.383678 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 14.2266 | 0.979400 | 0.489700 | − | 0.871891i | \(-0.337106\pi\) | ||||
0.489700 | + | 0.871891i | \(0.337106\pi\) | |||||||
\(212\) | −9.78523 | −0.672052 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 18.9420 | 1.29485 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −20.3135 | −1.37897 | ||||||||
\(218\) | 2.69168 | 0.182303 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 14.3530 | 0.965487 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −4.45323 | −0.298210 | −0.149105 | − | 0.988821i | \(-0.547639\pi\) | ||||
−0.149105 | + | 0.988821i | \(0.547639\pi\) | |||||||
\(224\) | 2.69168 | 0.179845 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −6.00000 | −0.399114 | ||||||||
\(227\) | −5.94865 | −0.394826 | −0.197413 | − | 0.980320i | \(-0.563254\pi\) | ||||
−0.197413 | + | 0.980320i | \(0.563254\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 1.09355 | 0.0722638 | 0.0361319 | − | 0.999347i | \(-0.488496\pi\) | ||||
0.0361319 | + | 0.999347i | \(0.488496\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 1.08171 | 0.0710177 | ||||||||
\(233\) | −14.0935 | −0.923299 | −0.461650 | − | 0.887062i | \(-0.652742\pi\) | ||||
−0.461650 | + | 0.887062i | \(0.652742\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −12.9933 | −0.845793 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −13.2385 | −0.858121 | ||||||||
\(239\) | −15.6100 | −1.00972 | −0.504862 | − | 0.863200i | \(-0.668457\pi\) | ||||
−0.504862 | + | 0.863200i | \(0.668457\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −5.21994 | −0.336246 | −0.168123 | − | 0.985766i | \(-0.553771\pi\) | ||||
−0.168123 | + | 0.985766i | \(0.553771\pi\) | |||||||
\(242\) | −19.7667 | −1.27065 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −7.38336 | −0.472671 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −2.91829 | −0.185686 | ||||||||
\(248\) | −7.54677 | −0.479221 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 28.6403 | 1.80776 | 0.903881 | − | 0.427785i | \(-0.140706\pi\) | ||||
0.903881 | + | 0.427785i | \(0.140706\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 20.0237 | 1.25888 | ||||||||
\(254\) | 1.87361 | 0.117561 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −6.45323 | −0.402541 | −0.201271 | − | 0.979536i | \(-0.564507\pi\) | ||||
−0.201271 | + | 0.979536i | \(0.564507\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −12.2385 | −0.760460 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −11.5468 | −0.713362 | ||||||||
\(263\) | −22.1871 | −1.36812 | −0.684058 | − | 0.729428i | \(-0.739786\pi\) | ||||
−0.684058 | + | 0.729428i | \(0.739786\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 2.69168 | 0.165037 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 2.85510 | 0.174403 | ||||||||
\(269\) | 20.4070 | 1.24424 | 0.622119 | − | 0.782922i | \(-0.286272\pi\) | ||||
0.622119 | + | 0.782922i | \(0.286272\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 15.9368 | 0.968092 | 0.484046 | − | 0.875043i | \(-0.339167\pi\) | ||||
0.484046 | + | 0.875043i | \(0.339167\pi\) | |||||||
\(272\) | −4.91829 | −0.298215 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 4.23845 | 0.256054 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 4.02368 | 0.241759 | 0.120880 | − | 0.992667i | \(-0.461428\pi\) | ||||
0.120880 | + | 0.992667i | \(0.461428\pi\) | |||||||
\(278\) | −9.21994 | −0.552975 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −1.67316 | −0.0998124 | −0.0499062 | − | 0.998754i | \(-0.515892\pi\) | ||||
−0.0499062 | + | 0.998754i | \(0.515892\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 16.8931 | 1.00419 | 0.502095 | − | 0.864812i | \(-0.332563\pi\) | ||||
0.502095 | + | 0.864812i | \(0.332563\pi\) | |||||||
\(284\) | −14.4769 | −0.859046 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −16.1871 | −0.957163 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 7.18958 | 0.422916 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 5.15674 | 0.301776 | ||||||||
\(293\) | 1.08171 | 0.0631942 | 0.0315971 | − | 0.999501i | \(-0.489941\pi\) | ||||
0.0315971 | + | 0.999501i | \(0.489941\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −4.54677 | −0.264276 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −7.25697 | −0.420385 | ||||||||
\(299\) | 10.5349 | 0.609251 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 25.6968 | 1.48114 | ||||||||
\(302\) | −20.0000 | −1.15087 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 1.00000 | 0.0573539 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 2.38336 | 0.136025 | 0.0680126 | − | 0.997684i | \(-0.478334\pi\) | ||||
0.0680126 | + | 0.997684i | \(0.478334\pi\) | |||||||
\(308\) | 14.9301 | 0.850723 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 29.4584 | 1.67043 | 0.835216 | − | 0.549922i | \(-0.185343\pi\) | ||||
0.835216 | + | 0.549922i | \(0.185343\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 32.0355 | 1.81075 | 0.905377 | − | 0.424608i | \(-0.139588\pi\) | ||||
0.905377 | + | 0.424608i | \(0.139588\pi\) | |||||||
\(314\) | 9.54677 | 0.538756 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −3.09355 | −0.174026 | ||||||||
\(317\) | 26.6665 | 1.49774 | 0.748870 | − | 0.662717i | \(-0.230597\pi\) | ||||
0.748870 | + | 0.662717i | \(0.230597\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 6.00000 | 0.335936 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −9.71687 | −0.541500 | ||||||||
\(323\) | −4.91829 | −0.273661 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −15.7102 | −0.870107 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −2.25181 | −0.124146 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −19.8721 | −1.09227 | −0.546135 | − | 0.837697i | \(-0.683901\pi\) | ||||
−0.546135 | + | 0.837697i | \(0.683901\pi\) | |||||||
\(332\) | −1.71019 | −0.0938591 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 6.45323 | 0.353105 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 27.5705 | 1.50186 | 0.750929 | − | 0.660383i | \(-0.229606\pi\) | ||||
0.750929 | + | 0.660383i | \(0.229606\pi\) | |||||||
\(338\) | 4.48358 | 0.243875 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −41.8603 | −2.26686 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 18.1819 | 0.981732 | ||||||||
\(344\) | 9.54677 | 0.514728 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −0.873614 | −0.0469658 | ||||||||
\(347\) | 27.2806 | 1.46450 | 0.732251 | − | 0.681035i | \(-0.238470\pi\) | ||||
0.732251 | + | 0.681035i | \(0.238470\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 30.9538 | 1.65692 | 0.828460 | − | 0.560049i | \(-0.189218\pi\) | ||||
0.828460 | + | 0.560049i | \(0.189218\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 5.54677 | 0.295644 | ||||||||
\(353\) | −11.1819 | −0.595154 | −0.297577 | − | 0.954698i | \(-0.596179\pi\) | ||||
−0.297577 | + | 0.954698i | \(0.596179\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 5.09355 | 0.269958 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −12.3834 | −0.654481 | ||||||||
\(359\) | −20.3387 | −1.07343 | −0.536717 | − | 0.843762i | \(-0.680336\pi\) | ||||
−0.536717 | + | 0.843762i | \(0.680336\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | 17.6403 | 0.927155 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 7.85510 | 0.411719 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −32.9538 | −1.72017 | −0.860087 | − | 0.510147i | \(-0.829591\pi\) | ||||
−0.860087 | + | 0.510147i | \(0.829591\pi\) | |||||||
\(368\) | −3.60997 | −0.188183 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 26.3387 | 1.36744 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −10.0869 | −0.522278 | −0.261139 | − | 0.965301i | \(-0.584098\pi\) | ||||
−0.261139 | + | 0.965301i | \(0.584098\pi\) | |||||||
\(374\) | −27.2806 | −1.41065 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −0.836581 | −0.0431434 | ||||||||
\(377\) | 3.15674 | 0.162581 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −18.4256 | −0.946457 | −0.473229 | − | 0.880940i | \(-0.656912\pi\) | ||||
−0.473229 | + | 0.880940i | \(0.656912\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −15.1567 | −0.775486 | ||||||||
\(383\) | −28.1871 | −1.44029 | −0.720147 | − | 0.693822i | \(-0.755926\pi\) | ||||
−0.720147 | + | 0.693822i | \(0.755926\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −23.3834 | −1.19018 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −17.2570 | −0.876090 | ||||||||
\(389\) | −20.0237 | −1.01524 | −0.507620 | − | 0.861581i | \(-0.669475\pi\) | ||||
−0.507620 | + | 0.861581i | \(0.669475\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 17.7549 | 0.897902 | ||||||||
\(392\) | −0.245129 | −0.0123809 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −23.0935 | −1.16344 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −8.32684 | −0.417912 | −0.208956 | − | 0.977925i | \(-0.567007\pi\) | ||||
−0.208956 | + | 0.977925i | \(0.567007\pi\) | |||||||
\(398\) | 25.7852 | 1.29250 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 22.1501 | 1.10612 | 0.553061 | − | 0.833141i | \(-0.313460\pi\) | ||||
0.553061 | + | 0.833141i | \(0.313460\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −22.0237 | −1.09708 | ||||||||
\(404\) | 9.38336 | 0.466839 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −2.91161 | −0.144501 | ||||||||
\(407\) | −25.2199 | −1.25011 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 34.0237 | 1.68236 | 0.841181 | − | 0.540753i | \(-0.181861\pi\) | ||||
0.841181 | + | 0.540753i | \(0.181861\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −12.9301 | −0.637022 | ||||||||
\(413\) | 34.9738 | 1.72095 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 2.91829 | 0.143081 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 5.54677 | 0.271302 | ||||||||
\(419\) | −37.5334 | −1.83363 | −0.916814 | − | 0.399315i | \(-0.869248\pi\) | ||||
−0.916814 | + | 0.399315i | \(0.869248\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 33.8341 | 1.64897 | 0.824487 | − | 0.565882i | \(-0.191464\pi\) | ||||
0.824487 | + | 0.565882i | \(0.191464\pi\) | |||||||
\(422\) | −14.2266 | −0.692541 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 9.78523 | 0.475213 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 19.8736 | 0.961752 | ||||||||
\(428\) | −18.9420 | −0.915595 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −24.8037 | −1.19475 | −0.597377 | − | 0.801960i | \(-0.703790\pi\) | ||||
−0.597377 | + | 0.801960i | \(0.703790\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 1.68651 | 0.0810487 | 0.0405244 | − | 0.999179i | \(-0.487097\pi\) | ||||
0.0405244 | + | 0.999179i | \(0.487097\pi\) | |||||||
\(434\) | 20.3135 | 0.975079 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −2.69168 | −0.128908 | ||||||||
\(437\) | −3.60997 | −0.172688 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 0.326839 | 0.0155992 | 0.00779958 | − | 0.999970i | \(-0.497517\pi\) | ||||
0.00779958 | + | 0.999970i | \(0.497517\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −14.3530 | −0.682703 | ||||||||
\(443\) | −0.490258 | −0.0232929 | −0.0116464 | − | 0.999932i | \(-0.503707\pi\) | ||||
−0.0116464 | + | 0.999932i | \(0.503707\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 4.45323 | 0.210866 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −2.69168 | −0.127170 | ||||||||
\(449\) | −23.5468 | −1.11124 | −0.555621 | − | 0.831436i | \(-0.687519\pi\) | ||||
−0.555621 | + | 0.831436i | \(0.687519\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 6.00000 | 0.282216 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 5.94865 | 0.279184 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −8.01184 | −0.374778 | −0.187389 | − | 0.982286i | \(-0.560003\pi\) | ||||
−0.187389 | + | 0.982286i | \(0.560003\pi\) | |||||||
\(458\) | −1.09355 | −0.0510982 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −3.83658 | −0.178687 | −0.0893437 | − | 0.996001i | \(-0.528477\pi\) | ||||
−0.0893437 | + | 0.996001i | \(0.528477\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −6.58381 | −0.305975 | −0.152988 | − | 0.988228i | \(-0.548890\pi\) | ||||
−0.152988 | + | 0.988228i | \(0.548890\pi\) | |||||||
\(464\) | −1.08171 | −0.0502171 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 14.0935 | 0.652871 | ||||||||
\(467\) | −22.6033 | −1.04596 | −0.522978 | − | 0.852346i | \(-0.675179\pi\) | ||||
−0.522978 | + | 0.852346i | \(0.675179\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −7.68500 | −0.354860 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 12.9933 | 0.598066 | ||||||||
\(473\) | 52.9538 | 2.43482 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 13.2385 | 0.606783 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 15.6100 | 0.713983 | ||||||||
\(479\) | 35.7904 | 1.63530 | 0.817652 | − | 0.575712i | \(-0.195275\pi\) | ||||
0.817652 | + | 0.575712i | \(0.195275\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −13.2688 | −0.605006 | ||||||||
\(482\) | 5.21994 | 0.237762 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 19.7667 | 0.898487 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −21.4070 | −0.970045 | −0.485023 | − | 0.874502i | \(-0.661189\pi\) | ||||
−0.485023 | + | 0.874502i | \(0.661189\pi\) | |||||||
\(488\) | 7.38336 | 0.334229 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 4.32684 | 0.195267 | 0.0976337 | − | 0.995222i | \(-0.468873\pi\) | ||||
0.0976337 | + | 0.995222i | \(0.468873\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 5.32016 | 0.239608 | ||||||||
\(494\) | 2.91829 | 0.131300 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 7.54677 | 0.338860 | ||||||||
\(497\) | 38.9672 | 1.74792 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −37.6968 | −1.68754 | −0.843771 | − | 0.536703i | \(-0.819670\pi\) | ||||
−0.843771 | + | 0.536703i | \(0.819670\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −28.6403 | −1.27828 | ||||||||
\(503\) | 16.9183 | 0.754349 | 0.377175 | − | 0.926142i | \(-0.376896\pi\) | ||||
0.377175 | + | 0.926142i | \(0.376896\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −20.0237 | −0.890161 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −1.87361 | −0.0831282 | ||||||||
\(509\) | 6.79955 | 0.301385 | 0.150692 | − | 0.988581i | \(-0.451850\pi\) | ||||
0.150692 | + | 0.988581i | \(0.451850\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −13.8803 | −0.614028 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 6.45323 | 0.284640 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −4.64032 | −0.204081 | ||||||||
\(518\) | 12.2385 | 0.537727 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 1.35968 | 0.0595685 | 0.0297842 | − | 0.999556i | \(-0.490518\pi\) | ||||
0.0297842 | + | 0.999556i | \(0.490518\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −21.9486 | −0.959747 | −0.479874 | − | 0.877338i | \(-0.659318\pi\) | ||||
−0.479874 | + | 0.877338i | \(0.659318\pi\) | |||||||
\(524\) | 11.5468 | 0.504423 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 22.1871 | 0.967404 | ||||||||
\(527\) | −37.1172 | −1.61685 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −9.96813 | −0.433397 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −2.69168 | −0.116699 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −2.85510 | −0.123321 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −20.4070 | −0.879810 | ||||||||
\(539\) | −1.35968 | −0.0585654 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −39.8973 | −1.71532 | −0.857659 | − | 0.514218i | \(-0.828082\pi\) | ||||
−0.857659 | + | 0.514218i | \(0.828082\pi\) | |||||||
\(542\) | −15.9368 | −0.684544 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 4.91829 | 0.210870 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −7.34632 | −0.314106 | −0.157053 | − | 0.987590i | \(-0.550199\pi\) | ||||
−0.157053 | + | 0.987590i | \(0.550199\pi\) | |||||||
\(548\) | −4.23845 | −0.181058 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −1.08171 | −0.0460824 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 8.32684 | 0.354093 | ||||||||
\(554\) | −4.02368 | −0.170950 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 9.21994 | 0.391012 | ||||||||
\(557\) | 26.9672 | 1.14264 | 0.571318 | − | 0.820729i | \(-0.306432\pi\) | ||||
0.571318 | + | 0.820729i | \(0.306432\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 27.8603 | 1.17836 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 1.67316 | 0.0705780 | ||||||||
\(563\) | 44.8973 | 1.89220 | 0.946098 | − | 0.323881i | \(-0.104988\pi\) | ||||
0.946098 | + | 0.323881i | \(0.104988\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −16.8931 | −0.710070 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 14.4769 | 0.607437 | ||||||||
\(569\) | −31.1172 | −1.30450 | −0.652251 | − | 0.758003i | \(-0.726175\pi\) | ||||
−0.652251 | + | 0.758003i | \(0.726175\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 33.2570 | 1.39176 | 0.695880 | − | 0.718158i | \(-0.255014\pi\) | ||||
0.695880 | + | 0.718158i | \(0.255014\pi\) | |||||||
\(572\) | 16.1871 | 0.676817 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 23.4702 | 0.977078 | 0.488539 | − | 0.872542i | \(-0.337530\pi\) | ||||
0.488539 | + | 0.872542i | \(0.337530\pi\) | |||||||
\(578\) | −7.18958 | −0.299047 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 4.60329 | 0.190977 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 54.2765 | 2.24790 | ||||||||
\(584\) | −5.15674 | −0.213388 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −1.08171 | −0.0446850 | ||||||||
\(587\) | 10.1501 | 0.418938 | 0.209469 | − | 0.977815i | \(-0.432826\pi\) | ||||
0.209469 | + | 0.977815i | \(0.432826\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 7.54677 | 0.310959 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 4.54677 | 0.186871 | ||||||||
\(593\) | 16.6732 | 0.684685 | 0.342342 | − | 0.939575i | \(-0.388780\pi\) | ||||
0.342342 | + | 0.939575i | \(0.388780\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 7.25697 | 0.297257 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −10.5349 | −0.430806 | ||||||||
\(599\) | −18.2765 | −0.746756 | −0.373378 | − | 0.927679i | \(-0.621800\pi\) | ||||
−0.373378 | + | 0.927679i | \(0.621800\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 7.96297 | 0.324816 | 0.162408 | − | 0.986724i | \(-0.448074\pi\) | ||||
0.162408 | + | 0.986724i | \(0.448074\pi\) | |||||||
\(602\) | −25.6968 | −1.04733 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 20.0000 | 0.813788 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −6.93013 | −0.281285 | −0.140643 | − | 0.990060i | \(-0.544917\pi\) | ||||
−0.140643 | + | 0.990060i | \(0.544917\pi\) | |||||||
\(608\) | −1.00000 | −0.0405554 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −2.44139 | −0.0987679 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −34.2765 | −1.38441 | −0.692206 | − | 0.721700i | \(-0.743361\pi\) | ||||
−0.692206 | + | 0.721700i | \(0.743361\pi\) | |||||||
\(614\) | −2.38336 | −0.0961844 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −14.9301 | −0.601552 | ||||||||
\(617\) | −35.5139 | −1.42974 | −0.714869 | − | 0.699259i | \(-0.753514\pi\) | ||||
−0.714869 | + | 0.699259i | \(0.753514\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −29.5334 | −1.18705 | −0.593524 | − | 0.804816i | \(-0.702264\pi\) | ||||
−0.593524 | + | 0.804816i | \(0.702264\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −29.4584 | −1.18117 | ||||||||
\(623\) | −13.7102 | −0.549287 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −32.0355 | −1.28040 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −9.54677 | −0.380958 | ||||||||
\(629\) | −22.3624 | −0.891646 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −15.1634 | −0.603646 | −0.301823 | − | 0.953364i | \(-0.597595\pi\) | ||||
−0.301823 | + | 0.953364i | \(0.597595\pi\) | |||||||
\(632\) | 3.09355 | 0.123055 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −26.6665 | −1.05906 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −0.715358 | −0.0283435 | ||||||||
\(638\) | −6.00000 | −0.237542 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 25.0802 | 0.990608 | 0.495304 | − | 0.868720i | \(-0.335057\pi\) | ||||
0.495304 | + | 0.868720i | \(0.335057\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 19.1306 | 0.754437 | 0.377218 | − | 0.926124i | \(-0.376881\pi\) | ||||
0.377218 | + | 0.926124i | \(0.376881\pi\) | |||||||
\(644\) | 9.71687 | 0.382898 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 4.91829 | 0.193508 | ||||||||
\(647\) | −12.4019 | −0.487568 | −0.243784 | − | 0.969830i | \(-0.578389\pi\) | ||||
−0.243784 | + | 0.969830i | \(0.578389\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 72.0710 | 2.82904 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 15.7102 | 0.615259 | ||||||||
\(653\) | 10.7801 | 0.421856 | 0.210928 | − | 0.977502i | \(-0.432351\pi\) | ||||
0.210928 | + | 0.977502i | \(0.432351\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 2.25181 | 0.0877845 | ||||||||
\(659\) | −8.56529 | −0.333656 | −0.166828 | − | 0.985986i | \(-0.553353\pi\) | ||||
−0.166828 | + | 0.985986i | \(0.553353\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −26.2883 | −1.02250 | −0.511248 | − | 0.859433i | \(-0.670817\pi\) | ||||
−0.511248 | + | 0.859433i | \(0.670817\pi\) | |||||||
\(662\) | 19.8721 | 0.772351 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 1.71019 | 0.0663684 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 3.90494 | 0.151200 | ||||||||
\(668\) | −6.45323 | −0.249683 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 40.9538 | 1.58100 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −12.9301 | −0.498420 | −0.249210 | − | 0.968449i | \(-0.580171\pi\) | ||||
−0.249210 | + | 0.968449i | \(0.580171\pi\) | |||||||
\(674\) | −27.5705 | −1.06197 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −4.48358 | −0.172445 | ||||||||
\(677\) | 15.9250 | 0.612046 | 0.306023 | − | 0.952024i | \(-0.401002\pi\) | ||||
0.306023 | + | 0.952024i | \(0.401002\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 46.4502 | 1.78260 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 41.8603 | 1.60291 | ||||||||
\(683\) | −13.2898 | −0.508520 | −0.254260 | − | 0.967136i | \(-0.581832\pi\) | ||||
−0.254260 | + | 0.967136i | \(0.581832\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −18.1819 | −0.694190 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −9.54677 | −0.363967 | ||||||||
\(689\) | 28.5561 | 1.08790 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 27.2570 | 1.03690 | 0.518452 | − | 0.855107i | \(-0.326508\pi\) | ||||
0.518452 | + | 0.855107i | \(0.326508\pi\) | |||||||
\(692\) | 0.873614 | 0.0332098 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −27.2806 | −1.03556 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | −30.9538 | −1.17162 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 41.4441 | 1.56532 | 0.782660 | − | 0.622449i | \(-0.213862\pi\) | ||||
0.782660 | + | 0.622449i | \(0.213862\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 4.54677 | 0.171485 | ||||||||
\(704\) | −5.54677 | −0.209052 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 11.1819 | 0.420838 | ||||||||
\(707\) | −25.2570 | −0.949886 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −36.7904 | −1.38169 | −0.690846 | − | 0.723002i | \(-0.742762\pi\) | ||||
−0.690846 | + | 0.723002i | \(0.742762\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −5.09355 | −0.190889 | ||||||||
\(713\) | −27.2436 | −1.02028 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 12.3834 | 0.462788 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 20.3387 | 0.759033 | ||||||||
\(719\) | 4.13726 | 0.154294 | 0.0771469 | − | 0.997020i | \(-0.475419\pi\) | ||||
0.0771469 | + | 0.997020i | \(0.475419\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 34.8037 | 1.29616 | ||||||||
\(722\) | −1.00000 | −0.0372161 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −17.6403 | −0.655597 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −40.4374 | −1.49974 | −0.749870 | − | 0.661585i | \(-0.769884\pi\) | ||||
−0.749870 | + | 0.661585i | \(0.769884\pi\) | |||||||
\(728\) | −7.85510 | −0.291129 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 46.9538 | 1.73665 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 28.1264 | 1.03887 | 0.519436 | − | 0.854509i | \(-0.326142\pi\) | ||||
0.519436 | + | 0.854509i | \(0.326142\pi\) | |||||||
\(734\) | 32.9538 | 1.21635 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 3.60997 | 0.133065 | ||||||||
\(737\) | −15.8366 | −0.583348 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −38.1501 | −1.40337 | −0.701686 | − | 0.712486i | \(-0.747569\pi\) | ||||
−0.701686 | + | 0.712486i | \(0.747569\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −26.3387 | −0.966923 | ||||||||
\(743\) | 17.8232 | 0.653871 | 0.326935 | − | 0.945047i | \(-0.393984\pi\) | ||||
0.326935 | + | 0.945047i | \(0.393984\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 10.0869 | 0.369307 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 27.2806 | 0.997479 | ||||||||
\(749\) | 50.9857 | 1.86298 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 23.6968 | 0.864710 | 0.432355 | − | 0.901703i | \(-0.357683\pi\) | ||||
0.432355 | + | 0.901703i | \(0.357683\pi\) | |||||||
\(752\) | 0.836581 | 0.0305070 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −3.15674 | −0.114962 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −6.51394 | −0.236753 | −0.118377 | − | 0.992969i | \(-0.537769\pi\) | ||||
−0.118377 | + | 0.992969i | \(0.537769\pi\) | |||||||
\(758\) | 18.4256 | 0.669246 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −34.7786 | −1.26072 | −0.630361 | − | 0.776302i | \(-0.717093\pi\) | ||||
−0.630361 | + | 0.776302i | \(0.717093\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 7.24513 | 0.262291 | ||||||||
\(764\) | 15.1567 | 0.548352 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 28.1871 | 1.01844 | ||||||||
\(767\) | 37.9183 | 1.36915 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −27.6850 | −0.998347 | −0.499173 | − | 0.866502i | \(-0.666363\pi\) | ||||
−0.499173 | + | 0.866502i | \(0.666363\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 23.3834 | 0.841585 | ||||||||
\(773\) | 19.9738 | 0.718409 | 0.359205 | − | 0.933259i | \(-0.383048\pi\) | ||||
0.359205 | + | 0.933259i | \(0.383048\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 17.2570 | 0.619489 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 20.0237 | 0.717884 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 80.3001 | 2.87336 | ||||||||
\(782\) | −17.7549 | −0.634913 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0.245129 | 0.00875461 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 42.0118 | 1.49756 | 0.748780 | − | 0.662818i | \(-0.230640\pi\) | ||||
0.748780 | + | 0.662818i | \(0.230640\pi\) | |||||||
\(788\) | 23.0935 | 0.822674 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −16.1501 | −0.574230 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 21.5468 | 0.765148 | ||||||||
\(794\) | 8.32684 | 0.295508 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −25.7852 | −0.913933 | ||||||||
\(797\) | 45.1054 | 1.59771 | 0.798857 | − | 0.601520i | \(-0.205438\pi\) | ||||
0.798857 | + | 0.601520i | \(0.205438\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −4.11455 | −0.145562 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −22.1501 | −0.782146 | ||||||||
\(803\) | −28.6033 | −1.00939 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 22.0237 | 0.775751 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −9.38336 | −0.330105 | ||||||||
\(809\) | −6.85510 | −0.241012 | −0.120506 | − | 0.992713i | \(-0.538452\pi\) | ||||
−0.120506 | + | 0.992713i | \(0.538452\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −15.1819 | −0.533110 | −0.266555 | − | 0.963820i | \(-0.585885\pi\) | ||||
−0.266555 | + | 0.963820i | \(0.585885\pi\) | |||||||
\(812\) | 2.91161 | 0.102178 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 25.2199 | 0.883958 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −9.54677 | −0.333999 | ||||||||
\(818\) | −34.0237 | −1.18961 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −22.5006 | −0.785276 | −0.392638 | − | 0.919693i | \(-0.628437\pi\) | ||||
−0.392638 | + | 0.919693i | \(0.628437\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −16.1896 | −0.564333 | −0.282167 | − | 0.959365i | \(-0.591053\pi\) | ||||
−0.282167 | + | 0.959365i | \(0.591053\pi\) | |||||||
\(824\) | 12.9301 | 0.450442 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −34.9738 | −1.21690 | ||||||||
\(827\) | 25.0817 | 0.872177 | 0.436088 | − | 0.899904i | \(-0.356364\pi\) | ||||
0.436088 | + | 0.899904i | \(0.356364\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 21.3068 | 0.740016 | 0.370008 | − | 0.929029i | \(-0.379355\pi\) | ||||
0.370008 | + | 0.929029i | \(0.379355\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −2.91829 | −0.101174 | ||||||||
\(833\) | −1.20562 | −0.0417721 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −5.54677 | −0.191839 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 37.5334 | 1.29657 | ||||||||
\(839\) | 11.4727 | 0.396082 | 0.198041 | − | 0.980194i | \(-0.436542\pi\) | ||||
0.198041 | + | 0.980194i | \(0.436542\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −27.8299 | −0.959652 | ||||||||
\(842\) | −33.8341 | −1.16600 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 14.2266 | 0.489700 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −53.2056 | −1.82817 | ||||||||
\(848\) | −9.78523 | −0.336026 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −16.4137 | −0.562655 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −38.9908 | −1.33502 | −0.667511 | − | 0.744600i | \(-0.732640\pi\) | ||||
−0.667511 | + | 0.744600i | \(0.732640\pi\) | |||||||
\(854\) | −19.8736 | −0.680061 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 18.9420 | 0.647423 | ||||||||
\(857\) | 29.8973 | 1.02127 | 0.510636 | − | 0.859797i | \(-0.329410\pi\) | ||||
0.510636 | + | 0.859797i | \(0.329410\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −6.47691 | −0.220989 | −0.110495 | − | 0.993877i | \(-0.535243\pi\) | ||||
−0.110495 | + | 0.993877i | \(0.535243\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 24.8037 | 0.844819 | ||||||||
\(863\) | 5.09355 | 0.173386 | 0.0866932 | − | 0.996235i | \(-0.472370\pi\) | ||||
0.0866932 | + | 0.996235i | \(0.472370\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −1.68651 | −0.0573101 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −20.3135 | −0.689485 | ||||||||
\(869\) | 17.1592 | 0.582087 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −8.33200 | −0.282319 | ||||||||
\(872\) | 2.69168 | 0.0911517 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 3.60997 | 0.122109 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −29.8341 | −1.00743 | −0.503713 | − | 0.863871i | \(-0.668033\pi\) | ||||
−0.503713 | + | 0.863871i | \(0.668033\pi\) | |||||||
\(878\) | −0.326839 | −0.0110303 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 11.5796 | 0.390127 | 0.195064 | − | 0.980791i | \(-0.437509\pi\) | ||||
0.195064 | + | 0.980791i | \(0.437509\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −48.0237 | −1.61613 | −0.808063 | − | 0.589096i | \(-0.799484\pi\) | ||||
−0.808063 | + | 0.589096i | \(0.799484\pi\) | |||||||
\(884\) | 14.3530 | 0.482744 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0.490258 | 0.0164705 | ||||||||
\(887\) | −9.38336 | −0.315062 | −0.157531 | − | 0.987514i | \(-0.550353\pi\) | ||||
−0.157531 | + | 0.987514i | \(0.550353\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 5.04316 | 0.169142 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −4.45323 | −0.149105 | ||||||||
\(893\) | 0.836581 | 0.0279951 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 2.69168 | 0.0899226 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 23.5468 | 0.785766 | ||||||||
\(899\) | −8.16342 | −0.272265 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 48.1266 | 1.60333 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −6.00000 | −0.199557 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −19.4347 | −0.645319 | −0.322659 | − | 0.946515i | \(-0.604577\pi\) | ||||
−0.322659 | + | 0.946515i | \(0.604577\pi\) | |||||||
\(908\) | −5.94865 | −0.197413 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 19.9866 | 0.662187 | 0.331094 | − | 0.943598i | \(-0.392582\pi\) | ||||
0.331094 | + | 0.943598i | \(0.392582\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 9.48606 | 0.313943 | ||||||||
\(914\) | 8.01184 | 0.265008 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 1.09355 | 0.0361319 | ||||||||
\(917\) | −31.0802 | −1.02636 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 6.15158 | 0.202922 | 0.101461 | − | 0.994840i | \(-0.467648\pi\) | ||||
0.101461 | + | 0.994840i | \(0.467648\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 3.83658 | 0.126351 | ||||||||
\(923\) | 42.2478 | 1.39060 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 6.58381 | 0.216357 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 1.08171 | 0.0355089 | ||||||||
\(929\) | 7.17010 | 0.235243 | 0.117622 | − | 0.993058i | \(-0.462473\pi\) | ||||
0.117622 | + | 0.993058i | \(0.462473\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0.245129 | 0.00803378 | ||||||||
\(932\) | −14.0935 | −0.461650 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 22.6033 | 0.739602 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −24.2646 | −0.792690 | −0.396345 | − | 0.918102i | \(-0.629722\pi\) | ||||
−0.396345 | + | 0.918102i | \(0.629722\pi\) | |||||||
\(938\) | 7.68500 | 0.250924 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 7.44806 | 0.242800 | 0.121400 | − | 0.992604i | \(-0.461262\pi\) | ||||
0.121400 | + | 0.992604i | \(0.461262\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | −12.9933 | −0.422897 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −52.9538 | −1.72168 | ||||||||
\(947\) | 52.9538 | 1.72077 | 0.860384 | − | 0.509647i | \(-0.170224\pi\) | ||||
0.860384 | + | 0.509647i | \(0.170224\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −15.0489 | −0.488507 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −13.2385 | −0.429061 | ||||||||
\(953\) | 12.8694 | 0.416881 | 0.208441 | − | 0.978035i | \(-0.433161\pi\) | ||||
0.208441 | + | 0.978035i | \(0.433161\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −15.6100 | −0.504862 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −35.7904 | −1.15634 | ||||||||
\(959\) | 11.4085 | 0.368401 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 25.9538 | 0.837220 | ||||||||
\(962\) | 13.2688 | 0.427804 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −5.21994 | −0.168123 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 25.8603 | 0.831610 | 0.415805 | − | 0.909454i | \(-0.363500\pi\) | ||||
0.415805 | + | 0.909454i | \(0.363500\pi\) | |||||||
\(968\) | −19.7667 | −0.635326 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −35.0935 | −1.12621 | −0.563103 | − | 0.826387i | \(-0.690392\pi\) | ||||
−0.563103 | + | 0.826387i | \(0.690392\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −24.8171 | −0.795600 | ||||||||
\(974\) | 21.4070 | 0.685926 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −7.38336 | −0.236335 | ||||||||
\(977\) | 42.1737 | 1.34926 | 0.674629 | − | 0.738157i | \(-0.264304\pi\) | ||||
0.674629 | + | 0.738157i | \(0.264304\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −28.2528 | −0.902963 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −4.32684 | −0.138075 | ||||||||
\(983\) | 42.6270 | 1.35959 | 0.679795 | − | 0.733403i | \(-0.262069\pi\) | ||||
0.679795 | + | 0.733403i | \(0.262069\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −5.32016 | −0.169428 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −2.91829 | −0.0928432 | ||||||||
\(989\) | 34.4636 | 1.09588 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −34.1737 | −1.08556 | −0.542782 | − | 0.839873i | \(-0.682629\pi\) | ||||
−0.542782 | + | 0.839873i | \(0.682629\pi\) | |||||||
\(992\) | −7.54677 | −0.239610 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −38.9672 | −1.23596 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 29.3834 | 0.930580 | 0.465290 | − | 0.885158i | \(-0.345950\pi\) | ||||
0.465290 | + | 0.885158i | \(0.345950\pi\) | |||||||
\(998\) | 37.6968 | 1.19327 | ||||||||
\(999\) | 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 | 8550.2.a.ci.1.1 | 3 | ||
3.2 | odd | 2 | 950.2.a.l.1.1 | yes | 3 | ||
5.4 | even | 2 | 8550.2.a.cp.1.3 | 3 | |||
12.11 | even | 2 | 7600.2.a.bk.1.3 | 3 | |||
15.2 | even | 4 | 950.2.b.h.799.6 | 6 | |||
15.8 | even | 4 | 950.2.b.h.799.1 | 6 | |||
15.14 | odd | 2 | 950.2.a.j.1.3 | ✓ | 3 | ||
60.59 | even | 2 | 7600.2.a.bz.1.1 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
950.2.a.j.1.3 | ✓ | 3 | 15.14 | odd | 2 | ||
950.2.a.l.1.1 | yes | 3 | 3.2 | odd | 2 | ||
950.2.b.h.799.1 | 6 | 15.8 | even | 4 | |||
950.2.b.h.799.6 | 6 | 15.2 | even | 4 | |||
7600.2.a.bk.1.3 | 3 | 12.11 | even | 2 | |||
7600.2.a.bz.1.1 | 3 | 60.59 | even | 2 | |||
8550.2.a.ci.1.1 | 3 | 1.1 | even | 1 | trivial | ||
8550.2.a.cp.1.3 | 3 | 5.4 | even | 2 |