Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4900,2,Mod(2549,4900)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4900, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4900.2549");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4900 = 2^{2} \cdot 5^{2} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4900.e (of order \(2\), degree \(1\), not minimal) |
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: | no |
Analytic conductor: | \(39.1266969904\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | 6.0.4227136.2 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} + 9x^{4} + 22x^{2} + 9 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{17}]\) |
Coefficient ring index: | \( 3^{2} \) |
Twist minimal: | no (minimal twist has level 700) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 2549.6 | ||
Root | \(0.713538i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4900.2549 |
Dual form | 4900.2.e.s.2549.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/4900\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(1177\) | \(2451\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) |
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 | ||||||||
\(3\) | 3.20440i | 1.85006i | 0.379892 | + | 0.925031i | \(0.375961\pi\) | ||||
−0.379892 | + | 0.925031i | \(0.624039\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −7.26819 | −2.42273 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 4.20440 | 1.26767 | 0.633837 | − | 0.773466i | \(-0.281479\pi\) | ||||
0.633837 | + | 0.773466i | \(0.281479\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − 0.204402i | − 0.0566908i | −0.999598 | − | 0.0283454i | \(-0.990976\pi\) | ||||
0.999598 | − | 0.0283454i | \(-0.00902383\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − 5.06379i | − 1.22815i | −0.789248 | − | 0.614074i | \(-0.789529\pi\) | ||||
0.789248 | − | 0.614074i | \(-0.210471\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.06379 | 0.244050 | 0.122025 | − | 0.992527i | \(-0.461061\pi\) | ||||
0.122025 | + | 0.992527i | \(0.461061\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 2.14061i | 0.446349i | 0.974779 | + | 0.223174i | \(0.0716419\pi\) | ||||
−0.974779 | + | 0.223174i | \(0.928358\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − 13.6770i | − 2.63214i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 7.47259 | 1.38763 | 0.693813 | − | 0.720156i | \(-0.255930\pi\) | ||||
0.693813 | + | 0.720156i | \(0.255930\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 8.47259 | 1.52172 | 0.760861 | − | 0.648915i | \(-0.224777\pi\) | ||||
0.760861 | + | 0.648915i | \(0.224777\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 13.4726i | 2.34528i | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 10.6132i | 1.74480i | 0.488793 | + | 0.872400i | \(0.337437\pi\) | ||||
−0.488793 | + | 0.872400i | \(0.662563\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0.654985 | 0.104881 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −10.5494 | −1.64754 | −0.823771 | − | 0.566923i | \(-0.808134\pi\) | ||||
−0.823771 | + | 0.566923i | \(0.808134\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 8.26819i | 1.26089i | 0.776235 | + | 0.630444i | \(0.217127\pi\) | ||||
−0.776235 | + | 0.630444i | \(0.782873\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 3.26819i | 0.476714i | 0.971178 | + | 0.238357i | \(0.0766089\pi\) | ||||
−0.971178 | + | 0.238357i | \(0.923391\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 16.2264 | 2.27215 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 5.67699i | 0.779795i | 0.920858 | + | 0.389897i | \(0.127490\pi\) | ||||
−0.920858 | + | 0.389897i | \(0.872510\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 3.40880i | 0.451507i | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 1.20440 | 0.156800 | 0.0783999 | − | 0.996922i | \(-0.475019\pi\) | ||||
0.0783999 | + | 0.996922i | \(0.475019\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.65498 | −0.211899 | −0.105950 | − | 0.994372i | \(-0.533788\pi\) | ||||
−0.105950 | + | 0.994372i | \(0.533788\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 12.4088i | 1.51598i | 0.652268 | + | 0.757988i | \(0.273818\pi\) | ||||
−0.652268 | + | 0.757988i | \(0.726182\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −6.85939 | −0.825773 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −0.591197 | −0.0701622 | −0.0350811 | − | 0.999384i | \(-0.511169\pi\) | ||||
−0.0350811 | + | 0.999384i | \(0.511169\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 4.00000i | 0.468165i | 0.972217 | + | 0.234082i | \(0.0752085\pi\) | ||||
−0.972217 | + | 0.234082i | \(0.924791\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −6.54942 | −0.736867 | −0.368433 | − | 0.929654i | \(-0.620106\pi\) | ||||
−0.368433 | + | 0.929654i | \(0.620106\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 22.0220 | 2.44689 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − 3.88139i | − 0.426038i | −0.977048 | − | 0.213019i | \(-0.931670\pi\) | ||||
0.977048 | − | 0.213019i | \(-0.0683297\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 23.9452i | 2.56719i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −9.26819 | −0.982426 | −0.491213 | − | 0.871039i | \(-0.663446\pi\) | ||||
−0.491213 | + | 0.871039i | \(0.663446\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 27.1496i | 2.81528i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1.33198i | 0.135242i | 0.997711 | + | 0.0676209i | \(0.0215408\pi\) | ||||
−0.997711 | + | 0.0676209i | \(0.978459\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −30.5584 | −3.07123 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −6.19136 | −0.616064 | −0.308032 | − | 0.951376i | \(-0.599670\pi\) | ||||
−0.308032 | + | 0.951376i | \(0.599670\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − 9.74078i | − 0.959788i | −0.877327 | − | 0.479894i | \(-0.840675\pi\) | ||||
0.877327 | − | 0.479894i | \(-0.159325\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − 9.85939i | − 0.953143i | −0.879136 | − | 0.476571i | \(-0.841879\pi\) | ||||
0.879136 | − | 0.476571i | \(-0.158121\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 4.07683 | 0.390489 | 0.195245 | − | 0.980755i | \(-0.437450\pi\) | ||||
0.195245 | + | 0.980755i | \(0.437450\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −34.0090 | −3.22799 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 2.21744i | 0.208599i | 0.994546 | + | 0.104300i | \(0.0332601\pi\) | ||||
−0.994546 | + | 0.104300i | \(0.966740\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 1.48563i | 0.137346i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 6.67699 | 0.606999 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | − 33.8046i | − 3.04806i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − 6.54942i | − 0.581167i | −0.956850 | − | 0.290583i | \(-0.906151\pi\) | ||||
0.956850 | − | 0.290583i | \(-0.0938494\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −26.4946 | −2.33272 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 17.0090 | 1.48608 | 0.743040 | − | 0.669247i | \(-0.233383\pi\) | ||||
0.743040 | + | 0.669247i | \(0.233383\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 17.0858i | 1.45974i | 0.683587 | + | 0.729869i | \(0.260419\pi\) | ||||
−0.683587 | + | 0.729869i | \(0.739581\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 0.740780 | 0.0628322 | 0.0314161 | − | 0.999506i | \(-0.489998\pi\) | ||||
0.0314161 | + | 0.999506i | \(0.489998\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −10.4726 | −0.881951 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − 0.859386i | − 0.0718655i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 16.4178 | 1.34500 | 0.672498 | − | 0.740099i | \(-0.265221\pi\) | ||||
0.672498 | + | 0.740099i | \(0.265221\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 0.527409 | 0.0429199 | 0.0214600 | − | 0.999770i | \(-0.493169\pi\) | ||||
0.0214600 | + | 0.999770i | \(0.493169\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 36.8046i | 2.97547i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − 9.48563i | − 0.757036i | −0.925594 | − | 0.378518i | \(-0.876434\pi\) | ||||
0.925594 | − | 0.378518i | \(-0.123566\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −18.1914 | −1.44267 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 8.85939i | 0.693921i | 0.937880 | + | 0.346960i | \(0.112786\pi\) | ||||
−0.937880 | + | 0.346960i | \(0.887214\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 8.33198i | 0.644748i | 0.946612 | + | 0.322374i | \(0.104481\pi\) | ||||
−0.946612 | + | 0.322374i | \(0.895519\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 12.9582 | 0.996786 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −7.73181 | −0.591266 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 18.3450i | 1.39475i | 0.716709 | + | 0.697373i | \(0.245648\pi\) | ||||
−0.716709 | + | 0.697373i | \(0.754352\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 3.85939i | 0.290089i | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 4.28123 | 0.319994 | 0.159997 | − | 0.987118i | \(-0.448852\pi\) | ||||
0.159997 | + | 0.987118i | \(0.448852\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −2.93621 | −0.218247 | −0.109123 | − | 0.994028i | \(-0.534804\pi\) | ||||
−0.109123 | + | 0.994028i | \(0.534804\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − 5.30324i | − 0.392026i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − 21.2902i | − 1.55689i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −11.9452 | −0.864323 | −0.432162 | − | 0.901796i | \(-0.642249\pi\) | ||||
−0.432162 | + | 0.901796i | \(0.642249\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 7.08580i | 0.510047i | 0.966935 | + | 0.255023i | \(0.0820832\pi\) | ||||
−0.966935 | + | 0.255023i | \(0.917917\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 5.48563i | 0.390835i | 0.980720 | + | 0.195417i | \(0.0626062\pi\) | ||||
−0.980720 | + | 0.195417i | \(0.937394\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 16.0858 | 1.14029 | 0.570146 | − | 0.821543i | \(-0.306887\pi\) | ||||
0.570146 | + | 0.821543i | \(0.306887\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −39.7628 | −2.80465 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | − 15.5584i | − 1.08138i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 4.47259 | 0.309376 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 16.6002 | 1.14280 | 0.571401 | − | 0.820671i | \(-0.306400\pi\) | ||||
0.571401 | + | 0.820671i | \(0.306400\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | − 1.89443i | − 0.129804i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −12.8176 | −0.866134 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1.03505 | −0.0696247 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 15.4856i | 1.03699i | 0.855079 | + | 0.518497i | \(0.173508\pi\) | ||||
−0.855079 | + | 0.518497i | \(0.826492\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − 3.78256i | − 0.251057i | −0.992090 | − | 0.125529i | \(-0.959937\pi\) | ||||
0.992090 | − | 0.125529i | \(-0.0400627\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −11.2044 | −0.740408 | −0.370204 | − | 0.928951i | \(-0.620712\pi\) | ||||
−0.370204 | + | 0.928951i | \(0.620712\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − 11.9452i | − 0.782555i | −0.920273 | − | 0.391277i | \(-0.872033\pi\) | ||||
0.920273 | − | 0.391277i | \(-0.127967\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | − 20.9870i | − 1.36325i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −15.3450 | −0.992587 | −0.496293 | − | 0.868155i | \(-0.665306\pi\) | ||||
−0.496293 | + | 0.868155i | \(0.665306\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 14.3958 | 0.927313 | 0.463656 | − | 0.886015i | \(-0.346537\pi\) | ||||
0.463656 | + | 0.886015i | \(0.346537\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 29.5364i | 1.89476i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − 0.217440i | − 0.0138354i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 12.4375 | 0.788197 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 19.4178 | 1.22564 | 0.612819 | − | 0.790223i | \(-0.290035\pi\) | ||||
0.612819 | + | 0.790223i | \(0.290035\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 9.00000i | 0.565825i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − 13.8724i | − 0.865338i | −0.901553 | − | 0.432669i | \(-0.857572\pi\) | ||||
0.901553 | − | 0.432669i | \(-0.142428\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −54.3122 | −3.36184 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 3.45955i | 0.213325i | 0.994295 | + | 0.106663i | \(0.0340165\pi\) | ||||
−0.994295 | + | 0.106663i | \(0.965984\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − 29.6990i | − 1.81755i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 25.6640 | 1.56476 | 0.782379 | − | 0.622802i | \(-0.214006\pi\) | ||||
0.782379 | + | 0.622802i | \(0.214006\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −19.6770 | −1.19529 | −0.597646 | − | 0.801760i | \(-0.703897\pi\) | ||||
−0.597646 | + | 0.801760i | \(0.703897\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − 18.1496i | − 1.09050i | −0.838273 | − | 0.545251i | \(-0.816434\pi\) | ||||
0.838273 | − | 0.545251i | \(-0.183566\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −61.5804 | −3.68672 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −18.5364 | −1.10579 | −0.552894 | − | 0.833252i | \(-0.686476\pi\) | ||||
−0.552894 | + | 0.833252i | \(0.686476\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 28.5584i | 1.69762i | 0.528698 | + | 0.848810i | \(0.322680\pi\) | ||||
−0.528698 | + | 0.848810i | \(0.677320\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −8.64195 | −0.508350 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −4.26819 | −0.250206 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 25.5494i | 1.49261i | 0.665603 | + | 0.746306i | \(0.268175\pi\) | ||||
−0.665603 | + | 0.746306i | \(0.731825\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | − 57.5036i | − 3.33670i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0.437545 | 0.0253039 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | − 19.8396i | − 1.13976i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − 10.1145i | − 0.577267i | −0.957440 | − | 0.288634i | \(-0.906799\pi\) | ||||
0.957440 | − | 0.288634i | \(-0.0932009\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 31.2134 | 1.77567 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −34.1716 | −1.93769 | −0.968847 | − | 0.247662i | \(-0.920338\pi\) | ||||
−0.968847 | + | 0.247662i | \(0.920338\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − 8.61320i | − 0.486847i | −0.969920 | − | 0.243424i | \(-0.921730\pi\) | ||||
0.969920 | − | 0.243424i | \(-0.0782705\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − 7.81761i | − 0.439081i | −0.975603 | − | 0.219540i | \(-0.929544\pi\) | ||||
0.975603 | − | 0.219540i | \(-0.0704557\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 31.4178 | 1.75906 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 31.5934 | 1.76337 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − 5.38680i | − 0.299729i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 13.0638i | 0.722429i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −22.0988 | −1.21466 | −0.607331 | − | 0.794449i | \(-0.707760\pi\) | ||||
−0.607331 | + | 0.794449i | \(0.707760\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | − 77.1388i | − 4.22718i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 1.29020i | 0.0702815i | 0.999382 | + | 0.0351408i | \(0.0111880\pi\) | ||||
−0.999382 | + | 0.0351408i | \(0.988812\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −7.10557 | −0.385921 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 35.6222 | 1.92905 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 9.45955i | 0.507815i | 0.967228 | + | 0.253908i | \(0.0817159\pi\) | ||||
−0.967228 | + | 0.253908i | \(0.918284\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 15.5494 | 0.832341 | 0.416171 | − | 0.909287i | \(-0.363372\pi\) | ||||
0.416171 | + | 0.909287i | \(0.363372\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −2.79560 | −0.149218 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − 15.1365i | − 0.805637i | −0.915280 | − | 0.402818i | \(-0.868031\pi\) | ||||
0.915280 | − | 0.402818i | \(-0.131969\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −10.3189 | −0.544613 | −0.272306 | − | 0.962211i | \(-0.587786\pi\) | ||||
−0.272306 | + | 0.962211i | \(0.587786\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −17.8684 | −0.940440 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 21.3958i | 1.12299i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 17.9362i | 0.936263i | 0.883659 | + | 0.468131i | \(0.155073\pi\) | ||||
−0.883659 | + | 0.468131i | \(0.844927\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 76.6752 | 3.99155 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − 16.1914i | − 0.838357i | −0.907904 | − | 0.419179i | \(-0.862318\pi\) | ||||
0.907904 | − | 0.419179i | \(-0.137682\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − 1.52741i | − 0.0786656i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 12.6002 | 0.647227 | 0.323614 | − | 0.946189i | \(-0.395102\pi\) | ||||
0.323614 | + | 0.946189i | \(0.395102\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 20.9870 | 1.07519 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − 15.1757i | − 0.775440i | −0.921777 | − | 0.387720i | \(-0.873263\pi\) | ||||
0.921777 | − | 0.387720i | \(-0.126737\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | − 60.0948i | − 3.05479i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 29.2394 | 1.48250 | 0.741249 | − | 0.671230i | \(-0.234234\pi\) | ||||
0.741249 | + | 0.671230i | \(0.234234\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 10.8396 | 0.548183 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 54.5036i | 2.74934i | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 11.2682i | 0.565534i | 0.959189 | + | 0.282767i | \(0.0912524\pi\) | ||||
−0.959189 | + | 0.282767i | \(0.908748\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −18.0220 | −0.899976 | −0.449988 | − | 0.893035i | \(-0.648572\pi\) | ||||
−0.449988 | + | 0.893035i | \(0.648572\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − 1.73181i | − 0.0862676i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 44.6222i | 2.21184i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −15.7915 | −0.780841 | −0.390420 | − | 0.920637i | \(-0.627670\pi\) | ||||
−0.390420 | + | 0.920637i | \(0.627670\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −54.7497 | −2.70061 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 2.37376i | 0.116243i | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −13.4726 | −0.658179 | −0.329090 | − | 0.944299i | \(-0.606742\pi\) | ||||
−0.329090 | + | 0.944299i | \(0.606742\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −26.8396 | −1.30808 | −0.654041 | − | 0.756459i | \(-0.726928\pi\) | ||||
−0.654041 | + | 0.756459i | \(0.726928\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | − 23.7538i | − 1.15495i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 2.75382 | 0.132956 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 16.0507 | 0.773137 | 0.386569 | − | 0.922261i | \(-0.373660\pi\) | ||||
0.386569 | + | 0.922261i | \(0.373660\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − 0.910136i | − 0.0437383i | −0.999761 | − | 0.0218692i | \(-0.993038\pi\) | ||||
0.999761 | − | 0.0218692i | \(-0.00696173\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 2.27716i | 0.108931i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −37.9034 | −1.80903 | −0.904515 | − | 0.426441i | \(-0.859767\pi\) | ||||
−0.904515 | + | 0.426441i | \(0.859767\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − 6.88139i | − 0.326945i | −0.986548 | − | 0.163472i | \(-0.947731\pi\) | ||||
0.986548 | − | 0.163472i | \(-0.0522695\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 52.6091i | 2.48833i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −6.43754 | −0.303807 | −0.151903 | − | 0.988395i | \(-0.548540\pi\) | ||||
−0.151903 | + | 0.988395i | \(0.548540\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −44.3540 | −2.08855 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 1.69003i | 0.0794046i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 9.29427i | 0.434767i | 0.976086 | + | 0.217384i | \(0.0697523\pi\) | ||||
−0.976086 | + | 0.217384i | \(0.930248\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −69.2574 | −3.23266 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −9.29020 | −0.432688 | −0.216344 | − | 0.976317i | \(-0.569413\pi\) | ||||
−0.216344 | + | 0.976317i | \(0.569413\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − 29.6091i | − 1.37605i | −0.725685 | − | 0.688027i | \(-0.758477\pi\) | ||||
0.725685 | − | 0.688027i | \(-0.241523\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − 26.0638i | − 1.20609i | −0.797708 | − | 0.603044i | \(-0.793954\pi\) | ||||
0.797708 | − | 0.603044i | \(-0.206046\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 30.3958 | 1.40056 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 34.7628i | 1.59839i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | − 41.2615i | − 1.88923i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −1.10557 | −0.0505147 | −0.0252573 | − | 0.999681i | \(-0.508041\pi\) | ||||
−0.0252573 | + | 0.999681i | \(0.508041\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 2.16936 | 0.0989141 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − 5.19136i | − 0.235243i | −0.993058 | − | 0.117622i | \(-0.962473\pi\) | ||||
0.993058 | − | 0.117622i | \(-0.0375270\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −28.3890 | −1.28380 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −28.6640 | −1.29359 | −0.646793 | − | 0.762666i | \(-0.723890\pi\) | ||||
−0.646793 | + | 0.762666i | \(0.723890\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − 37.8396i | − 1.70421i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 26.0728 | 1.16718 | 0.583588 | − | 0.812050i | \(-0.301648\pi\) | ||||
0.583588 | + | 0.812050i | \(0.301648\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −26.6990 | −1.19282 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − 8.80864i | − 0.392758i | −0.980528 | − | 0.196379i | \(-0.937082\pi\) | ||||
0.980528 | − | 0.196379i | \(-0.0629182\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 41.5233i | 1.84412i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −22.0179 | −0.975928 | −0.487964 | − | 0.872864i | \(-0.662260\pi\) | ||||
−0.487964 | + | 0.872864i | \(0.662260\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | − 14.5494i | − 0.642372i | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 13.7408i | 0.604319i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −58.7848 | −2.58037 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 15.0988 | 0.661492 | 0.330746 | − | 0.943720i | \(-0.392700\pi\) | ||||
0.330746 | + | 0.943720i | \(0.392700\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 4.59120i | 0.200759i | 0.994949 | + | 0.100380i | \(0.0320057\pi\) | ||||
−0.994949 | + | 0.100380i | \(0.967994\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − 42.9034i | − 1.86890i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 18.4178 | 0.800773 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −8.75382 | −0.379883 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 2.15632i | 0.0934005i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 13.7188i | 0.592009i | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 13.6770 | 0.588020 | 0.294010 | − | 0.955802i | \(-0.405010\pi\) | ||||
0.294010 | + | 0.955802i | \(0.405010\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | − 9.40880i | − 0.403770i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 11.3581i | 0.485635i | 0.970072 | + | 0.242818i | \(0.0780717\pi\) | ||||
−0.970072 | + | 0.242818i | \(0.921928\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 12.0287 | 0.513374 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 7.94925 | 0.338649 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − 16.3958i | − 0.694711i | −0.937734 | − | 0.347355i | \(-0.887080\pi\) | ||||
0.937734 | − | 0.347355i | \(-0.112920\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 1.69003 | 0.0714807 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 68.2223 | 2.88035 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 4.87242i | 0.205348i | 0.994715 | + | 0.102674i | \(0.0327399\pi\) | ||||
−0.994715 | + | 0.102674i | \(0.967260\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 37.8553 | 1.58698 | 0.793489 | − | 0.608585i | \(-0.208263\pi\) | ||||
0.793489 | + | 0.608585i | \(0.208263\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −41.7408 | −1.74680 | −0.873399 | − | 0.487006i | \(-0.838089\pi\) | ||||
−0.873399 | + | 0.487006i | \(0.838089\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − 38.2772i | − 1.59905i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 43.0530i | 1.79232i | 0.443732 | + | 0.896160i | \(0.353654\pi\) | ||||
−0.443732 | + | 0.896160i | \(0.646346\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −22.7057 | −0.943618 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 23.8684i | 0.988526i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − 5.67699i | − 0.234315i | −0.993113 | − | 0.117157i | \(-0.962622\pi\) | ||||
0.993113 | − | 0.117157i | \(-0.0373782\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 9.01304 | 0.371376 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −17.5782 | −0.723069 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − 8.94518i | − 0.367335i | −0.982988 | − | 0.183667i | \(-0.941203\pi\) | ||||
0.982988 | − | 0.183667i | \(-0.0587969\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 51.5453i | 2.10961i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 25.2264 | 1.03072 | 0.515362 | − | 0.856973i | \(-0.327658\pi\) | ||||
0.515362 | + | 0.856973i | \(0.327658\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −15.3409 | −0.625770 | −0.312885 | − | 0.949791i | \(-0.601295\pi\) | ||||
−0.312885 | + | 0.949791i | \(0.601295\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − 90.1895i | − 3.67280i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 20.9362i | 0.849775i | 0.905246 | + | 0.424887i | \(0.139686\pi\) | ||||
−0.905246 | + | 0.424887i | \(0.860314\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0.668023 | 0.0270253 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − 5.31894i | − 0.214830i | −0.994214 | − | 0.107415i | \(-0.965743\pi\) | ||||
0.994214 | − | 0.107415i | \(-0.0342573\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 28.6262i | 1.15245i | 0.817291 | + | 0.576225i | \(0.195475\pi\) | ||||
−0.817291 | + | 0.576225i | \(0.804525\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −21.5625 | −0.866668 | −0.433334 | − | 0.901233i | \(-0.642663\pi\) | ||||
−0.433334 | + | 0.901233i | \(0.642663\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 29.2772 | 1.17485 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 14.3320i | 0.572364i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 53.7430 | 2.14287 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −25.1365 | −1.00067 | −0.500335 | − | 0.865832i | \(-0.666790\pi\) | ||||
−0.500335 | + | 0.865832i | \(0.666790\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 53.1936i | 2.11426i | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 4.29693 | 0.169984 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 44.1078 | 1.74215 | 0.871077 | − | 0.491147i | \(-0.163422\pi\) | ||||
0.871077 | + | 0.491147i | \(0.163422\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 16.4816i | 0.649969i | 0.945719 | + | 0.324985i | \(0.105359\pi\) | ||||
−0.945719 | + | 0.324985i | \(0.894641\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − 31.4398i | − 1.23603i | −0.786168 | − | 0.618013i | \(-0.787938\pi\) | ||||
0.786168 | − | 0.618013i | \(-0.212062\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 5.06379 | 0.198771 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 40.8773i | 1.59965i | 0.600231 | + | 0.799827i | \(0.295075\pi\) | ||||
−0.600231 | + | 0.799827i | \(0.704925\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | − 29.0728i | − 1.13424i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 46.6860 | 1.81863 | 0.909313 | − | 0.416112i | \(-0.136608\pi\) | ||||
0.909313 | + | 0.416112i | \(0.136608\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −0.127575 | −0.00496211 | −0.00248106 | − | 0.999997i | \(-0.500790\pi\) | ||||
−0.00248106 | + | 0.999997i | \(0.500790\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | − 3.31670i | − 0.128810i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 15.9959i | 0.619365i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −49.6222 | −1.91850 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −6.95822 | −0.268619 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 48.1936i | 1.85773i | 0.370423 | + | 0.928863i | \(0.379213\pi\) | ||||
−0.370423 | + | 0.928863i | \(0.620787\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − 46.4178i | − 1.78398i | −0.452055 | − | 0.891990i | \(-0.649309\pi\) | ||||
0.452055 | − | 0.891990i | \(-0.350691\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 12.1208 | 0.464472 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 43.5494i | 1.66637i | 0.552993 | + | 0.833186i | \(0.313486\pi\) | ||||
−0.552993 | + | 0.833186i | \(0.686514\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − 35.9034i | − 1.36980i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 1.16039 | 0.0442072 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 26.0948 | 0.992692 | 0.496346 | − | 0.868125i | \(-0.334675\pi\) | ||||
0.496346 | + | 0.868125i | \(0.334675\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 53.4200i | 2.02343i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 38.2772 | 1.44778 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 21.7277 | 0.820645 | 0.410323 | − | 0.911940i | \(-0.365416\pi\) | ||||
0.410323 | + | 0.911940i | \(0.365416\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 11.2902i | 0.425818i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −17.0768 | −0.641334 | −0.320667 | − | 0.947192i | \(-0.603907\pi\) | ||||
−0.320667 | + | 0.947192i | \(0.603907\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 47.6024 | 1.78523 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 18.1365i | 0.679219i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | − 49.1716i | − 1.83635i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 27.2462 | 1.01611 | 0.508056 | − | 0.861324i | \(-0.330364\pi\) | ||||
0.508056 | + | 0.861324i | \(0.330364\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 46.1298i | 1.71559i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 19.9232i | 0.738910i | 0.929249 | + | 0.369455i | \(0.120456\pi\) | ||||
−0.929249 | + | 0.369455i | \(0.879544\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −28.5804 | −1.05853 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 41.8684 | 1.54856 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − 31.1626i | − 1.15102i | −0.817796 | − | 0.575509i | \(-0.804804\pi\) | ||||
0.817796 | − | 0.575509i | \(-0.195196\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 52.1716i | 1.92177i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −1.90117 | −0.0699355 | −0.0349678 | − | 0.999388i | \(-0.511133\pi\) | ||||
−0.0349678 | + | 0.999388i | \(0.511133\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0.696765 | 0.0255963 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 36.0660i | 1.32313i | 0.749886 | + | 0.661567i | \(0.230108\pi\) | ||||
−0.749886 | + | 0.661567i | \(0.769892\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 28.2107i | 1.03218i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −0.769522 | −0.0280803 | −0.0140401 | − | 0.999901i | \(-0.504469\pi\) | ||||
−0.0140401 | + | 0.999901i | \(0.504469\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 62.2223i | 2.26751i | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 14.9542i | 0.543518i | 0.962365 | + | 0.271759i | \(0.0876053\pi\) | ||||
−0.962365 | + | 0.271759i | \(0.912395\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −28.8396 | −1.04681 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −19.1716 | −0.694970 | −0.347485 | − | 0.937686i | \(-0.612964\pi\) | ||||
−0.347485 | + | 0.937686i | \(0.612964\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − 0.246182i | − 0.00888910i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 36.3189 | 1.30969 | 0.654847 | − | 0.755761i | \(-0.272733\pi\) | ||||
0.654847 | + | 0.755761i | \(0.272733\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 44.4528 | 1.60093 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 47.4685i | 1.70732i | 0.520827 | + | 0.853662i | \(0.325624\pi\) | ||||
−0.520827 | + | 0.853662i | \(0.674376\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −11.2223 | −0.402082 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −2.48563 | −0.0889428 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | − 102.203i | − 3.65242i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 7.88546i | 0.281086i | 0.990075 | + | 0.140543i | \(0.0448849\pi\) | ||||
−0.990075 | + | 0.140543i | \(0.955115\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −11.0858 | −0.394665 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0.338281i | 0.0120127i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − 33.6132i | − 1.19064i | −0.803488 | − | 0.595320i | \(-0.797025\pi\) | ||||
0.803488 | − | 0.595320i | \(-0.202975\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 16.5494 | 0.585476 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 67.3630 | 2.38015 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 16.8176i | 0.593480i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 82.2376i | 2.89490i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 9.19136 | 0.323151 | 0.161576 | − | 0.986860i | \(-0.448342\pi\) | ||||
0.161576 | + | 0.986860i | \(0.448342\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −21.6483 | −0.760173 | −0.380086 | − | 0.924951i | \(-0.624106\pi\) | ||||
−0.380086 | + | 0.924951i | \(0.624106\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − 63.0530i | − 2.21136i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 8.79560i | 0.307719i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 32.2615 | 1.12593 | 0.562966 | − | 0.826480i | \(-0.309660\pi\) | ||||
0.562966 | + | 0.826480i | \(0.309660\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 11.4438i | 0.398908i | 0.979907 | + | 0.199454i | \(0.0639168\pi\) | ||||
−0.979907 | + | 0.199454i | \(0.936083\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − 9.82658i | − 0.341704i | −0.985297 | − | 0.170852i | \(-0.945348\pi\) | ||||
0.985297 | − | 0.170852i | \(-0.0546519\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 38.2574 | 1.32873 | 0.664367 | − | 0.747407i | \(-0.268701\pi\) | ||||
0.664367 | + | 0.747407i | \(0.268701\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 58.1586 | 2.01750 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | − 115.880i | − 4.00538i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 30.6900 | 1.05954 | 0.529769 | − | 0.848142i | \(-0.322279\pi\) | ||||
0.529769 | + | 0.848142i | \(0.322279\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 26.8396 | 0.925504 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | − 59.3980i | − 2.04578i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −91.5125 | −3.14070 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −22.7188 | −0.778789 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − 39.4569i | − 1.35098i | −0.737370 | − | 0.675489i | \(-0.763933\pi\) | ||||
0.737370 | − | 0.675489i | \(-0.236067\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − 39.8594i | − 1.36157i | −0.732483 | − | 0.680785i | \(-0.761639\pi\) | ||||
0.732483 | − | 0.680785i | \(-0.238361\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −19.5144 | −0.665822 | −0.332911 | − | 0.942958i | \(-0.608031\pi\) | ||||
−0.332911 | + | 0.942958i | \(0.608031\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − 37.9321i | − 1.29123i | −0.763665 | − | 0.645613i | \(-0.776602\pi\) | ||||
0.763665 | − | 0.645613i | \(-0.223398\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | − 27.6923i | − 0.940479i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −27.5364 | −0.934108 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 2.53638 | 0.0859419 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | − 9.68106i | − 0.327654i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − 10.9452i | − 0.369593i | −0.982777 | − | 0.184796i | \(-0.940837\pi\) | ||||
0.982777 | − | 0.184796i | \(-0.0591625\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −81.8706 | −2.76143 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 16.2592 | 0.547787 | 0.273894 | − | 0.961760i | \(-0.411688\pi\) | ||||
0.273894 | + | 0.961760i | \(0.411688\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 23.2511i | 0.782461i | 0.920293 | + | 0.391231i | \(0.127951\pi\) | ||||
−0.920293 | + | 0.391231i | \(0.872049\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − 23.2394i | − 0.780304i | −0.920750 | − | 0.390152i | \(-0.872422\pi\) | ||||
0.920750 | − | 0.390152i | \(-0.127578\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 92.5894 | 3.10186 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 3.47666i | 0.116342i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 1.40207i | 0.0468137i | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 63.3122 | 2.11158 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 28.7471 | 0.957704 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 44.2264i | 1.46851i | 0.678872 | + | 0.734257i | \(0.262469\pi\) | ||||
−0.678872 | + | 0.734257i | \(0.737531\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 45.0000 | 1.49256 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −27.4218 | −0.908526 | −0.454263 | − | 0.890868i | \(-0.650097\pi\) | ||||
−0.454263 | + | 0.890868i | \(0.650097\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − 16.3189i | − 0.540078i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 33.3163 | 1.09900 | 0.549501 | − | 0.835493i | \(-0.314818\pi\) | ||||
0.549501 | + | 0.835493i | \(0.314818\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 32.4110 | 1.06798 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0.120842i | 0.00397755i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 70.7978i | 2.32531i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −13.2484 | −0.434666 | −0.217333 | − | 0.976097i | \(-0.569736\pi\) | ||||
−0.217333 | + | 0.976097i | \(0.569736\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | − 109.499i | − 3.58485i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − 10.1365i | − 0.331146i | −0.986197 | − | 0.165573i | \(-0.947053\pi\) | ||||
0.986197 | − | 0.165573i | \(-0.0529474\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 27.6002 | 0.900697 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 32.8684 | 1.07148 | 0.535739 | − | 0.844384i | \(-0.320033\pi\) | ||||
0.535739 | + | 0.844384i | \(0.320033\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − 22.5822i | − 0.735379i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 22.3252i | 0.725473i | 0.931892 | + | 0.362736i | \(0.118157\pi\) | ||||
−0.931892 | + | 0.362736i | \(0.881843\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0.817606 | 0.0265406 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 25.0507 | 0.812326 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − 47.4685i | − 1.53766i | −0.639455 | − | 0.768828i | \(-0.720840\pi\) | ||||
0.639455 | − | 0.768828i | \(-0.279160\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 100.675i | 3.25437i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 40.7848 | 1.31564 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 71.6599i | 2.30921i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − 21.3189i | − 0.685571i | −0.939414 | − | 0.342785i | \(-0.888630\pi\) | ||||
0.939414 | − | 0.342785i | \(-0.111370\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 17.2615 | 0.554518 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 29.5625 | 0.948704 | 0.474352 | − | 0.880335i | \(-0.342682\pi\) | ||||
0.474352 | + | 0.880335i | \(0.342682\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 1.83961i | 0.0588545i | 0.999567 | + | 0.0294272i | \(0.00936833\pi\) | ||||
−0.999567 | + | 0.0294272i | \(0.990632\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −38.9672 | −1.24540 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −29.6311 | −0.946050 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 11.3760i | 0.362838i | 0.983406 | + | 0.181419i | \(0.0580690\pi\) | ||||
−0.983406 | + | 0.181419i | \(0.941931\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −17.6990 | −0.562795 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 7.79153 | 0.247506 | 0.123753 | − | 0.992313i | \(-0.460507\pi\) | ||||
0.123753 | + | 0.992313i | \(0.460507\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | − 70.8135i | − 2.24720i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 11.4218i | 0.361733i | 0.983508 | + | 0.180867i | \(0.0578903\pi\) | ||||
−0.983508 | + | 0.180867i | \(0.942110\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 145.157 | 4.59256 |
(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 | 4900.2.e.s.2549.6 | 6 | ||
5.2 | odd | 4 | 4900.2.a.bd.1.3 | 3 | |||
5.3 | odd | 4 | 4900.2.a.bb.1.1 | 3 | |||
5.4 | even | 2 | inner | 4900.2.e.s.2549.1 | 6 | ||
7.3 | odd | 6 | 700.2.r.d.149.1 | 12 | |||
7.5 | odd | 6 | 700.2.r.d.249.6 | 12 | |||
7.6 | odd | 2 | 4900.2.e.t.2549.1 | 6 | |||
35.3 | even | 12 | 700.2.i.d.401.1 | ✓ | 6 | ||
35.12 | even | 12 | 700.2.i.e.501.3 | yes | 6 | ||
35.13 | even | 4 | 4900.2.a.bc.1.3 | 3 | |||
35.17 | even | 12 | 700.2.i.e.401.3 | yes | 6 | ||
35.19 | odd | 6 | 700.2.r.d.249.1 | 12 | |||
35.24 | odd | 6 | 700.2.r.d.149.6 | 12 | |||
35.27 | even | 4 | 4900.2.a.ba.1.1 | 3 | |||
35.33 | even | 12 | 700.2.i.d.501.1 | yes | 6 | ||
35.34 | odd | 2 | 4900.2.e.t.2549.6 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
700.2.i.d.401.1 | ✓ | 6 | 35.3 | even | 12 | ||
700.2.i.d.501.1 | yes | 6 | 35.33 | even | 12 | ||
700.2.i.e.401.3 | yes | 6 | 35.17 | even | 12 | ||
700.2.i.e.501.3 | yes | 6 | 35.12 | even | 12 | ||
700.2.r.d.149.1 | 12 | 7.3 | odd | 6 | |||
700.2.r.d.149.6 | 12 | 35.24 | odd | 6 | |||
700.2.r.d.249.1 | 12 | 35.19 | odd | 6 | |||
700.2.r.d.249.6 | 12 | 7.5 | odd | 6 | |||
4900.2.a.ba.1.1 | 3 | 35.27 | even | 4 | |||
4900.2.a.bb.1.1 | 3 | 5.3 | odd | 4 | |||
4900.2.a.bc.1.3 | 3 | 35.13 | even | 4 | |||
4900.2.a.bd.1.3 | 3 | 5.2 | odd | 4 | |||
4900.2.e.s.2549.1 | 6 | 5.4 | even | 2 | inner | ||
4900.2.e.s.2549.6 | 6 | 1.1 | even | 1 | trivial | ||
4900.2.e.t.2549.1 | 6 | 7.6 | odd | 2 | |||
4900.2.e.t.2549.6 | 6 | 35.34 | odd | 2 |