Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1216,3,Mod(1025,1216)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1216, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1216.1025");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1216 = 2^{6} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 1216.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: | \(33.1336001462\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{-2}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} + 2 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 38) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1025.2 | ||
Root | \(1.41421i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1216.1025 |
Dual form | 1216.3.e.j.1025.1 |
$q$-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 \(\left(\mathbb{Z}/1216\mathbb{Z}\right)^\times\).
\(n\) | \(191\) | \(705\) | \(837\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) |
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 | ||||||||
\(3\) | 2.82843i | 0.942809i | 0.881917 | + | 0.471405i | \(0.156253\pi\) | ||||
−0.881917 | + | 0.471405i | \(0.843747\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.00000 | 0.200000 | 0.100000 | − | 0.994987i | \(-0.468116\pi\) | ||||
0.100000 | + | 0.994987i | \(0.468116\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 5.00000 | 0.714286 | 0.357143 | − | 0.934050i | \(-0.383751\pi\) | ||||
0.357143 | + | 0.934050i | \(0.383751\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.111111 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −5.00000 | −0.454545 | −0.227273 | − | 0.973831i | \(-0.572981\pi\) | ||||
−0.227273 | + | 0.973831i | \(0.572981\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − 16.9706i | − 1.30543i | −0.757604 | − | 0.652714i | \(-0.773630\pi\) | ||||
0.757604 | − | 0.652714i | \(-0.226370\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 2.82843i | 0.188562i | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −25.0000 | −1.47059 | −0.735294 | − | 0.677748i | \(-0.762956\pi\) | ||||
−0.735294 | + | 0.677748i | \(0.762956\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −19.0000 | −1.00000 | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 14.1421i | 0.673435i | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −10.0000 | −0.434783 | −0.217391 | − | 0.976085i | \(-0.569755\pi\) | ||||
−0.217391 | + | 0.976085i | \(0.569755\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −24.0000 | −0.960000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 28.2843i | 1.04757i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 42.4264i | 1.46298i | 0.681852 | + | 0.731490i | \(0.261175\pi\) | ||||
−0.681852 | + | 0.731490i | \(0.738825\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 42.4264i | 1.36859i | 0.729204 | + | 0.684297i | \(0.239891\pi\) | ||||
−0.729204 | + | 0.684297i | \(0.760109\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | − 14.1421i | − 0.428550i | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 5.00000 | 0.142857 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − 25.4558i | − 0.687996i | −0.938970 | − | 0.343998i | \(-0.888219\pi\) | ||||
0.938970 | − | 0.343998i | \(-0.111781\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 48.0000 | 1.23077 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 42.4264i | 1.03479i | 0.855747 | + | 0.517395i | \(0.173098\pi\) | ||||
−0.855747 | + | 0.517395i | \(0.826902\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −5.00000 | −0.116279 | −0.0581395 | − | 0.998308i | \(-0.518517\pi\) | ||||
−0.0581395 | + | 0.998308i | \(0.518517\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 1.00000 | 0.0222222 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 5.00000 | 0.106383 | 0.0531915 | − | 0.998584i | \(-0.483061\pi\) | ||||
0.0531915 | + | 0.998584i | \(0.483061\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −24.0000 | −0.489796 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | − 70.7107i | − 1.38648i | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − 25.4558i | − 0.480299i | −0.970736 | − | 0.240149i | \(-0.922804\pi\) | ||||
0.970736 | − | 0.240149i | \(-0.0771965\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −5.00000 | −0.0909091 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − 53.7401i | − 0.942809i | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 84.8528i | 1.43818i | 0.694915 | + | 0.719092i | \(0.255442\pi\) | ||||
−0.694915 | + | 0.719092i | \(0.744558\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −95.0000 | −1.55738 | −0.778689 | − | 0.627411i | \(-0.784115\pi\) | ||||
−0.778689 | + | 0.627411i | \(0.784115\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 5.00000 | 0.0793651 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | − 16.9706i | − 0.261086i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 110.309i | 1.64640i | 0.567753 | + | 0.823199i | \(0.307813\pi\) | ||||
−0.567753 | + | 0.823199i | \(0.692187\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | − 28.2843i | − 0.409917i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −25.0000 | −0.342466 | −0.171233 | − | 0.985231i | \(-0.554775\pi\) | ||||
−0.171233 | + | 0.985231i | \(0.554775\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | − 67.8823i | − 0.905097i | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −25.0000 | −0.324675 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − 42.4264i | − 0.537043i | −0.963274 | − | 0.268522i | \(-0.913465\pi\) | ||||
0.963274 | − | 0.268522i | \(-0.0865351\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −71.0000 | −0.876543 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 130.000 | 1.56627 | 0.783133 | − | 0.621855i | \(-0.213621\pi\) | ||||
0.783133 | + | 0.621855i | \(0.213621\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −25.0000 | −0.294118 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −120.000 | −1.37931 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 127.279i | 1.43010i | 0.699071 | + | 0.715052i | \(0.253597\pi\) | ||||
−0.699071 | + | 0.715052i | \(0.746403\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − 84.8528i | − 0.932449i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −120.000 | −1.29032 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −19.0000 | −0.200000 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − 16.9706i | − 0.174954i | −0.996167 | − | 0.0874771i | \(-0.972120\pi\) | ||||
0.996167 | − | 0.0874771i | \(-0.0278805\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −5.00000 | −0.0505051 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −50.0000 | −0.495050 | −0.247525 | − | 0.968882i | \(-0.579617\pi\) | ||||
−0.247525 | + | 0.968882i | \(0.579617\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 16.9706i | 0.164763i | 0.996601 | + | 0.0823814i | \(0.0262526\pi\) | ||||
−0.996601 | + | 0.0823814i | \(0.973747\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 14.1421i | 0.134687i | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − 101.823i | − 0.951620i | −0.879548 | − | 0.475810i | \(-0.842155\pi\) | ||||
0.879548 | − | 0.475810i | \(-0.157845\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 127.279i | 1.16770i | 0.811862 | + | 0.583850i | \(0.198454\pi\) | ||||
−0.811862 | + | 0.583850i | \(0.801546\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 72.0000 | 0.648649 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − 110.309i | − 0.976183i | −0.872793 | − | 0.488091i | \(-0.837693\pi\) | ||||
0.872793 | − | 0.488091i | \(-0.162307\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −10.0000 | −0.0869565 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | − 16.9706i | − 0.145048i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −125.000 | −1.05042 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −96.0000 | −0.793388 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −120.000 | −0.975610 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −49.0000 | −0.392000 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − 229.103i | − 1.80396i | −0.431780 | − | 0.901979i | \(-0.642114\pi\) | ||||
0.431780 | − | 0.901979i | \(-0.357886\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | − 14.1421i | − 0.109629i | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 163.000 | 1.24427 | 0.622137 | − | 0.782908i | \(-0.286265\pi\) | ||||
0.622137 | + | 0.782908i | \(0.286265\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −95.0000 | −0.714286 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 28.2843i | 0.209513i | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 95.0000 | 0.693431 | 0.346715 | − | 0.937970i | \(-0.387297\pi\) | ||||
0.346715 | + | 0.937970i | \(0.387297\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −125.000 | −0.899281 | −0.449640 | − | 0.893210i | \(-0.648448\pi\) | ||||
−0.449640 | + | 0.893210i | \(0.648448\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 14.1421i | 0.100299i | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 84.8528i | 0.593376i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 42.4264i | 0.292596i | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | − 67.8823i | − 0.461784i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −215.000 | −1.44295 | −0.721477 | − | 0.692439i | \(-0.756536\pi\) | ||||
−0.721477 | + | 0.692439i | \(0.756536\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 84.8528i | 0.561939i | 0.959717 | + | 0.280970i | \(0.0906560\pi\) | ||||
−0.959717 | + | 0.280970i | \(0.909344\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −25.0000 | −0.163399 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 42.4264i | 0.273719i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 190.000 | 1.21019 | 0.605096 | − | 0.796153i | \(-0.293135\pi\) | ||||
0.605096 | + | 0.796153i | \(0.293135\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 72.0000 | 0.452830 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −50.0000 | −0.310559 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −110.000 | −0.674847 | −0.337423 | − | 0.941353i | \(-0.609555\pi\) | ||||
−0.337423 | + | 0.941353i | \(0.609555\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | − 14.1421i | − 0.0857099i | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − 59.3970i | − 0.355670i | −0.984060 | − | 0.177835i | \(-0.943091\pi\) | ||||
0.984060 | − | 0.177835i | \(-0.0569094\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −119.000 | −0.704142 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −19.0000 | −0.111111 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − 186.676i | − 1.07905i | −0.841969 | − | 0.539527i | \(-0.818603\pi\) | ||||
0.841969 | − | 0.539527i | \(-0.181397\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −120.000 | −0.685714 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −240.000 | −1.35593 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − 127.279i | − 0.711057i | −0.934665 | − | 0.355529i | \(-0.884301\pi\) | ||||
0.934665 | − | 0.355529i | \(-0.115699\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − 254.558i | − 1.40640i | −0.710992 | − | 0.703200i | \(-0.751754\pi\) | ||||
0.710992 | − | 0.703200i | \(-0.248246\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − 268.701i | − 1.46831i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | − 25.4558i | − 0.137599i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 125.000 | 0.668449 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 141.421i | 0.748261i | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 293.000 | 1.53403 | 0.767016 | − | 0.641628i | \(-0.221741\pi\) | ||||
0.767016 | + | 0.641628i | \(0.221741\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − 59.3970i | − 0.307756i | −0.988090 | − | 0.153878i | \(-0.950824\pi\) | ||||
0.988090 | − | 0.153878i | \(-0.0491763\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 48.0000 | 0.246154 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 70.0000 | 0.355330 | 0.177665 | − | 0.984091i | \(-0.443146\pi\) | ||||
0.177665 | + | 0.984091i | \(0.443146\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 173.000 | 0.869347 | 0.434673 | − | 0.900588i | \(-0.356864\pi\) | ||||
0.434673 | + | 0.900588i | \(0.356864\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −312.000 | −1.55224 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 212.132i | 1.04499i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 42.4264i | 0.206958i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −10.0000 | −0.0483092 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 95.0000 | 0.454545 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 84.8528i | 0.402146i | 0.979576 | + | 0.201073i | \(0.0644429\pi\) | ||||
−0.979576 | + | 0.201073i | \(0.935557\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −5.00000 | −0.0232558 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 212.132i | 0.977567i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | − 70.7107i | − 0.322880i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 424.264i | 1.91975i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 364.867i | 1.63618i | 0.575094 | + | 0.818088i | \(0.304966\pi\) | ||||
−0.575094 | + | 0.818088i | \(0.695034\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −24.0000 | −0.106667 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 67.8823i | 0.299041i | 0.988759 | + | 0.149520i | \(0.0477730\pi\) | ||||
−0.988759 | + | 0.149520i | \(0.952227\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 145.000 | 0.633188 | 0.316594 | − | 0.948561i | \(-0.397461\pi\) | ||||
0.316594 | + | 0.948561i | \(0.397461\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | − 70.7107i | − 0.306107i | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 335.000 | 1.43777 | 0.718884 | − | 0.695130i | \(-0.244653\pi\) | ||||
0.718884 | + | 0.695130i | \(0.244653\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 5.00000 | 0.0212766 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 120.000 | 0.506329 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 197.000 | 0.824268 | 0.412134 | − | 0.911123i | \(-0.364784\pi\) | ||||
0.412134 | + | 0.911123i | \(0.364784\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − 296.985i | − 1.23230i | −0.787628 | − | 0.616151i | \(-0.788691\pi\) | ||||
0.787628 | − | 0.616151i | \(-0.211309\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 53.7401i | 0.221153i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −24.0000 | −0.0979592 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 322.441i | 1.30543i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 367.696i | 1.47669i | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −173.000 | −0.689243 | −0.344622 | − | 0.938742i | \(-0.611993\pi\) | ||||
−0.344622 | + | 0.938742i | \(0.611993\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 50.0000 | 0.197628 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | − 70.7107i | − 0.277297i | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 67.8823i | 0.264133i | 0.991241 | + | 0.132067i | \(0.0421613\pi\) | ||||
−0.991241 | + | 0.132067i | \(0.957839\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − 127.279i | − 0.491426i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 42.4264i | 0.162553i | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −355.000 | −1.34981 | −0.674905 | − | 0.737905i | \(-0.735815\pi\) | ||||
−0.674905 | + | 0.737905i | \(0.735815\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − 25.4558i | − 0.0960598i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −360.000 | −1.34831 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − 381.838i | − 1.41947i | −0.704468 | − | 0.709735i | \(-0.748814\pi\) | ||||
0.704468 | − | 0.709735i | \(-0.251186\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 110.000 | 0.405904 | 0.202952 | − | 0.979189i | \(-0.434946\pi\) | ||||
0.202952 | + | 0.979189i | \(0.434946\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 240.000 | 0.879121 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 120.000 | 0.436364 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 265.000 | 0.956679 | 0.478339 | − | 0.878175i | \(-0.341239\pi\) | ||||
0.478339 | + | 0.878175i | \(0.341239\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 42.4264i | 0.152066i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − 424.264i | − 1.50984i | −0.655819 | − | 0.754918i | \(-0.727677\pi\) | ||||
0.655819 | − | 0.754918i | \(-0.272323\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −125.000 | −0.441696 | −0.220848 | − | 0.975308i | \(-0.570882\pi\) | ||||
−0.220848 | + | 0.975308i | \(0.570882\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | − 53.7401i | − 0.188562i | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 212.132i | 0.739136i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 336.000 | 1.16263 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 48.0000 | 0.164948 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 186.676i | 0.637120i | 0.947903 | + | 0.318560i | \(0.103199\pi\) | ||||
−0.947903 | + | 0.318560i | \(0.896801\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 84.8528i | 0.287637i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | − 141.421i | − 0.476166i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 169.706i | 0.567577i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −25.0000 | −0.0830565 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | − 141.421i | − 0.466737i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −95.0000 | −0.311475 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 280.014i | 0.912099i | 0.889955 | + | 0.456049i | \(0.150736\pi\) | ||||
−0.889955 | + | 0.456049i | \(0.849264\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −48.0000 | −0.155340 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −235.000 | −0.755627 | −0.377814 | − | 0.925882i | \(-0.623324\pi\) | ||||
−0.377814 | + | 0.925882i | \(0.623324\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −310.000 | −0.990415 | −0.495208 | − | 0.868775i | \(-0.664908\pi\) | ||||
−0.495208 | + | 0.868775i | \(0.664908\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 5.00000 | 0.0158730 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − 186.676i | − 0.588884i | −0.955669 | − | 0.294442i | \(-0.904866\pi\) | ||||
0.955669 | − | 0.294442i | \(-0.0951338\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − 212.132i | − 0.664991i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 288.000 | 0.897196 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 475.000 | 1.47059 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 407.294i | 1.25321i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −360.000 | −1.10092 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 25.0000 | 0.0759878 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 296.985i | 0.897235i | 0.893724 | + | 0.448618i | \(0.148083\pi\) | ||||
−0.893724 | + | 0.448618i | \(0.851917\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | − 25.4558i | − 0.0764440i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 110.309i | 0.329280i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 526.087i | 1.56109i | 0.625099 | + | 0.780545i | \(0.285058\pi\) | ||||
−0.625099 | + | 0.780545i | \(0.714942\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 312.000 | 0.920354 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − 212.132i | − 0.622088i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −365.000 | −1.06414 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | − 28.2843i | − 0.0819834i | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −125.000 | −0.360231 | −0.180115 | − | 0.983646i | \(-0.557647\pi\) | ||||
−0.180115 | + | 0.983646i | \(0.557647\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −23.0000 | −0.0659026 | −0.0329513 | − | 0.999457i | \(-0.510491\pi\) | ||||
−0.0329513 | + | 0.999457i | \(0.510491\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 480.000 | 1.36752 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 410.000 | 1.16147 | 0.580737 | − | 0.814092i | \(-0.302765\pi\) | ||||
0.580737 | + | 0.814092i | \(0.302765\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | − 353.553i | − 0.990346i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −475.000 | −1.32312 | −0.661560 | − | 0.749892i | \(-0.730105\pi\) | ||||
−0.661560 | + | 0.749892i | \(0.730105\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 361.000 | 1.00000 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − 271.529i | − 0.748014i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −25.0000 | −0.0684932 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 230.000 | 0.626703 | 0.313351 | − | 0.949637i | \(-0.398548\pi\) | ||||
0.313351 | + | 0.949637i | \(0.398548\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 42.4264i | 0.114977i | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − 127.279i | − 0.343071i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − 67.8823i | − 0.181990i | −0.995851 | − | 0.0909950i | \(-0.970995\pi\) | ||||
0.995851 | − | 0.0909950i | \(-0.0290047\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | − 138.593i | − 0.369581i | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 720.000 | 1.90981 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − 254.558i | − 0.671658i | −0.941923 | − | 0.335829i | \(-0.890984\pi\) | ||||
0.941923 | − | 0.335829i | \(-0.109016\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 648.000 | 1.70079 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 144.250i | 0.376631i | 0.982109 | + | 0.188316i | \(0.0603028\pi\) | ||||
−0.982109 | + | 0.188316i | \(0.939697\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −25.0000 | −0.0649351 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −5.00000 | −0.0129199 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 553.000 | 1.42159 | 0.710797 | − | 0.703397i | \(-0.248334\pi\) | ||||
0.710797 | + | 0.703397i | \(0.248334\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 250.000 | 0.639386 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 461.034i | 1.17311i | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | − 42.4264i | − 0.107409i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −335.000 | −0.843829 | −0.421914 | − | 0.906636i | \(-0.638642\pi\) | ||||
−0.421914 | + | 0.906636i | \(0.638642\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | − 268.701i | − 0.673435i | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − 212.132i | − 0.529008i | −0.964385 | − | 0.264504i | \(-0.914792\pi\) | ||||
0.964385 | − | 0.264504i | \(-0.0852082\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 720.000 | 1.78660 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −71.0000 | −0.175309 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 127.279i | 0.312725i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − 721.249i | − 1.76344i | −0.471769 | − | 0.881722i | \(-0.656384\pi\) | ||||
0.471769 | − | 0.881722i | \(-0.343616\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 268.701i | 0.653773i | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 424.264i | 1.02727i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 130.000 | 0.313253 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | − 353.553i | − 0.847850i | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −62.0000 | −0.147971 | −0.0739857 | − | 0.997259i | \(-0.523572\pi\) | ||||
−0.0739857 | + | 0.997259i | \(0.523572\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 296.985i | 0.705427i | 0.935731 | + | 0.352714i | \(0.114741\pi\) | ||||
−0.935731 | + | 0.352714i | \(0.885259\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 5.00000 | 0.0118203 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 600.000 | 1.41176 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −475.000 | −1.11241 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −240.000 | −0.559441 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 509.117i | 1.18125i | 0.806948 | + | 0.590623i | \(0.201118\pi\) | ||||
−0.806948 | + | 0.590623i | \(0.798882\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 229.103i | 0.529105i | 0.964371 | + | 0.264553i | \(0.0852243\pi\) | ||||
−0.964371 | + | 0.264553i | \(0.914776\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −120.000 | −0.275862 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 190.000 | 0.434783 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − 806.102i | − 1.83622i | −0.396323 | − | 0.918111i | \(-0.629714\pi\) | ||||
0.396323 | − | 0.918111i | \(-0.370286\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −24.0000 | −0.0544218 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −365.000 | −0.823928 | −0.411964 | − | 0.911200i | \(-0.635157\pi\) | ||||
−0.411964 | + | 0.911200i | \(0.635157\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 127.279i | 0.286021i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | − 608.112i | − 1.36043i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 763.675i | 1.70084i | 0.526108 | + | 0.850418i | \(0.323651\pi\) | ||||
−0.526108 | + | 0.850418i | \(0.676349\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − 212.132i | − 0.470359i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −240.000 | −0.529801 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | − 84.8528i | − 0.186490i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −265.000 | −0.579869 | −0.289934 | − | 0.957047i | \(-0.593633\pi\) | ||||
−0.289934 | + | 0.957047i | \(0.593633\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | − 707.107i | − 1.54054i | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 553.000 | 1.19957 | 0.599783 | − | 0.800163i | \(-0.295254\pi\) | ||||
0.599783 | + | 0.800163i | \(0.295254\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 485.000 | 1.04752 | 0.523758 | − | 0.851867i | \(-0.324530\pi\) | ||||
0.523758 | + | 0.851867i | \(0.324530\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −120.000 | −0.258065 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 115.000 | 0.246253 | 0.123126 | − | 0.992391i | \(-0.460708\pi\) | ||||
0.123126 | + | 0.992391i | \(0.460708\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 551.543i | 1.17600i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 537.401i | 1.14098i | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 25.0000 | 0.0528541 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 456.000 | 0.960000 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | − 25.4558i | − 0.0533665i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −490.000 | −1.02296 | −0.511482 | − | 0.859294i | \(-0.670903\pi\) | ||||
−0.511482 | + | 0.859294i | \(0.670903\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −432.000 | −0.898129 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | − 141.421i | − 0.292798i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − 16.9706i | − 0.0349909i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 610.940i | 1.25450i | 0.778819 | + | 0.627249i | \(0.215819\pi\) | ||||
−0.778819 | + | 0.627249i | \(0.784181\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | − 311.127i | − 0.636252i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 82.0000 | 0.167006 | 0.0835031 | − | 0.996508i | \(-0.473389\pi\) | ||||
0.0835031 | + | 0.996508i | \(0.473389\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − 1060.66i | − 2.15144i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −5.00000 | −0.0101010 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −485.000 | −0.971944 | −0.485972 | − | 0.873974i | \(-0.661534\pi\) | ||||
−0.485972 | + | 0.873974i | \(0.661534\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 168.000 | 0.335329 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −250.000 | −0.497018 | −0.248509 | − | 0.968630i | \(-0.579941\pi\) | ||||
−0.248509 | + | 0.968630i | \(0.579941\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −50.0000 | −0.0990099 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | − 336.583i | − 0.663871i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − 169.706i | − 0.333410i | −0.986007 | − | 0.166705i | \(-0.946687\pi\) | ||||
0.986007 | − | 0.166705i | \(-0.0533127\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −125.000 | −0.244618 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | − 537.401i | − 1.04757i | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 16.9706i | 0.0329525i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −25.0000 | −0.0483559 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 528.000 | 1.01734 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 127.279i | 0.244298i | 0.992512 | + | 0.122149i | \(0.0389786\pi\) | ||||
−0.992512 | + | 0.122149i | \(0.961021\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 356.382i | 0.681418i | 0.940169 | + | 0.340709i | \(0.110667\pi\) | ||||
−0.940169 | + | 0.340709i | \(0.889333\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | − 339.411i | − 0.646498i | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − 1060.66i | − 2.01264i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −429.000 | −0.810964 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 84.8528i | 0.159798i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 720.000 | 1.35084 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − 101.823i | − 0.190324i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 360.000 | 0.670391 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 120.000 | 0.222635 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 25.0000 | 0.0462107 | 0.0231054 | − | 0.999733i | \(-0.492645\pi\) | ||||
0.0231054 | + | 0.999733i | \(0.492645\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 720.000 | 1.32597 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 127.279i | 0.233540i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 16.9706i | 0.0310248i | 0.999880 | + | 0.0155124i | \(0.00493795\pi\) | ||||
−0.999880 | + | 0.0155124i | \(0.995062\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −95.0000 | −0.173042 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − 806.102i | − 1.46298i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − 212.132i | − 0.383602i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 72.0000 | 0.129730 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 745.000 | 1.33752 | 0.668761 | − | 0.743477i | \(-0.266825\pi\) | ||||
0.668761 | + | 0.743477i | \(0.266825\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 84.8528i | 0.151794i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 353.553i | 0.630220i | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 313.955i | 0.557647i | 0.960342 | + | 0.278824i | \(0.0899445\pi\) | ||||
−0.960342 | + | 0.278824i | \(0.910056\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − 110.309i | − 0.195237i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −355.000 | −0.626102 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − 424.264i | − 0.745631i | −0.927905 | − | 0.372816i | \(-0.878392\pi\) | ||||
0.927905 | − | 0.372816i | \(-0.121608\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −1070.00 | −1.87391 | −0.936953 | − | 0.349456i | \(-0.886366\pi\) | ||||
−0.936953 | + | 0.349456i | \(0.886366\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 828.729i | 1.44630i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 240.000 | 0.417391 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −25.0000 | −0.0433276 | −0.0216638 | − | 0.999765i | \(-0.506896\pi\) | ||||
−0.0216638 | + | 0.999765i | \(0.506896\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 168.000 | 0.290155 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 650.000 | 1.11876 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 127.279i | 0.218318i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | − 16.9706i | − 0.0290095i | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −725.000 | −1.23509 | −0.617547 | − | 0.786534i | \(-0.711873\pi\) | ||||
−0.617547 | + | 0.786534i | \(0.711873\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − 806.102i | − 1.36859i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 197.990i | 0.335008i | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 650.000 | 1.09612 | 0.548061 | − | 0.836439i | \(-0.315366\pi\) | ||||
0.548061 | + | 0.836439i | \(0.315366\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −125.000 | −0.210084 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 489.318i | 0.819628i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 296.985i | 0.495801i | 0.968785 | + | 0.247901i | \(0.0797406\pi\) | ||||
−0.968785 | + | 0.247901i | \(0.920259\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 848.528i | 1.41186i | 0.708281 | + | 0.705930i | \(0.249471\pi\) | ||||
−0.708281 | + | 0.705930i | \(0.750529\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 110.309i | 0.182933i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −96.0000 | −0.158678 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 271.529i | 0.447329i | 0.974666 | + | 0.223665i | \(0.0718021\pi\) | ||||
−0.974666 | + | 0.223665i | \(0.928198\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −600.000 | −0.985222 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − 84.8528i | − 0.138875i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −1055.00 | −1.72104 | −0.860522 | − | 0.509413i | \(-0.829862\pi\) | ||||
−0.860522 | + | 0.509413i | \(0.829862\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −120.000 | −0.195122 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −505.000 | −0.818476 | −0.409238 | − | 0.912428i | \(-0.634206\pi\) | ||||
−0.409238 | + | 0.912428i | \(0.634206\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 130.000 | 0.210016 | 0.105008 | − | 0.994471i | \(-0.466513\pi\) | ||||
0.105008 | + | 0.994471i | \(0.466513\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | − 282.843i | − 0.455463i | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 636.396i | 1.02150i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 551.000 | 0.881600 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 268.701i | 0.428550i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 636.396i | 1.01176i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −475.000 | −0.752773 | −0.376387 | − | 0.926463i | \(-0.622834\pi\) | ||||
−0.376387 | + | 0.926463i | \(0.622834\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −240.000 | −0.379147 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | − 229.103i | − 0.360791i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 407.294i | 0.639393i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 848.528i | 1.32376i | 0.749611 | + | 0.661878i | \(0.230240\pi\) | ||||
−0.749611 | + | 0.661878i | \(0.769760\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 955.000 | 1.48523 | 0.742613 | − | 0.669721i | \(-0.233586\pi\) | ||||
0.742613 | + | 0.669721i | \(0.233586\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | − 14.1421i | − 0.0219258i | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 965.000 | 1.49150 | 0.745750 | − | 0.666226i | \(-0.232092\pi\) | ||||
0.745750 | + | 0.666226i | \(0.232092\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − 424.264i | − 0.653720i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −600.000 | −0.921659 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −935.000 | −1.43185 | −0.715926 | − | 0.698176i | \(-0.753995\pi\) | ||||
−0.715926 | + | 0.698176i | \(0.753995\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 163.000 | 0.248855 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −25.0000 | −0.0380518 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − 84.8528i | − 0.128760i | −0.997925 | − | 0.0643800i | \(-0.979493\pi\) | ||||
0.997925 | − | 0.0643800i | \(-0.0205070\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − 678.823i | − 1.02696i | −0.858101 | − | 0.513481i | \(-0.828356\pi\) | ||||
0.858101 | − | 0.513481i | \(-0.171644\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −1200.00 | −1.80995 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −95.0000 | −0.142857 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − 424.264i | − 0.636078i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −1032.00 | −1.54260 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 475.000 | 0.707899 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 186.676i | 0.277379i | 0.990336 | + | 0.138690i | \(0.0442890\pi\) | ||||
−0.990336 | + | 0.138690i | \(0.955711\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | − 678.823i | − 1.00566i | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 907.925i | 1.34110i | 0.741864 | + | 0.670550i | \(0.233942\pi\) | ||||
−0.741864 | + | 0.670550i | \(0.766058\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − 84.8528i | − 0.124967i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −192.000 | −0.281938 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 1120.06i | 1.63991i | 0.572429 | + | 0.819954i | \(0.306001\pi\) | ||||
−0.572429 | + | 0.819954i | \(0.693999\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 95.0000 | 0.138686 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 410.122i | 0.596975i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −432.000 | −0.626996 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 715.000 | 1.03473 | 0.517366 | − | 0.855764i | \(-0.326913\pi\) | ||||
0.517366 | + | 0.855764i | \(0.326913\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −25.0000 | −0.0360750 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −125.000 | −0.179856 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − 1060.66i | − 1.52175i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 947.523i | 1.35554i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 430.000 | 0.613409 | 0.306705 | − | 0.951805i | \(-0.400774\pi\) | ||||
0.306705 | + | 0.951805i | \(0.400774\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 483.661i | 0.687996i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 14.1421i | 0.0200598i | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −250.000 | −0.353607 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 382.000 | 0.538787 | 0.269394 | − | 0.963030i | \(-0.413177\pi\) | ||||
0.269394 | + | 0.963030i | \(0.413177\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | − 42.4264i | − 0.0596715i | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − 424.264i | − 0.595041i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 84.8528i | 0.118675i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 557.200i | 0.777127i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −115.000 | −0.159944 | −0.0799722 | − | 0.996797i | \(-0.525483\pi\) | ||||
−0.0799722 | + | 0.996797i | \(0.525483\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 84.8528i | 0.117688i | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 840.000 | 1.16183 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | − 1018.23i | − 1.40446i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −1075.00 | −1.47868 | −0.739340 | − | 0.673333i | \(-0.764862\pi\) | ||||
−0.739340 | + | 0.673333i | \(0.764862\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −791.000 | −1.08505 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 125.000 | 0.170999 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −530.000 | −0.723056 | −0.361528 | − | 0.932361i | \(-0.617745\pi\) | ||||
−0.361528 | + | 0.932361i | \(0.617745\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | − 67.8823i | − 0.0923568i | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − 551.543i | − 0.748363i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 547.000 | 0.740189 | 0.370095 | − | 0.928994i | \(-0.379325\pi\) | ||||
0.370095 | + | 0.928994i | \(0.379325\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −912.000 | −1.23077 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 958.837i | 1.29049i | 0.763974 | + | 0.645247i | \(0.223245\pi\) | ||||
−0.763974 | + | 0.645247i | \(0.776755\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −215.000 | −0.288591 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 130.000 | 0.174029 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − 509.117i | − 0.679729i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 169.706i | 0.225973i | 0.993597 | + | 0.112986i | \(0.0360417\pi\) | ||||
−0.993597 | + | 0.112986i | \(0.963958\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | − 489.318i | − 0.649825i | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 84.8528i | 0.112388i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −1055.00 | −1.39366 | −0.696830 | − | 0.717237i | \(-0.745407\pi\) | ||||
−0.696830 | + | 0.717237i | \(0.745407\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 141.421i | 0.186326i | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 215.000 | 0.282523 | 0.141261 | − | 0.989972i | \(-0.454884\pi\) | ||||
0.141261 | + | 0.989972i | \(0.454884\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 636.396i | 0.834071i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −25.0000 | −0.0326797 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 1440.00 | 1.87744 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −145.000 | −0.188557 | −0.0942783 | − | 0.995546i | \(-0.530054\pi\) | ||||
−0.0942783 | + | 0.995546i | \(0.530054\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −192.000 | −0.249027 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 407.294i | 0.526900i | 0.964673 | + | 0.263450i | \(0.0848604\pi\) | ||||
−0.964673 | + | 0.263450i | \(0.915140\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − 1018.23i | − 1.31385i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 360.000 | 0.463320 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | − 806.102i | − 1.03479i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −1200.00 | −1.53257 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 190.000 | 0.242038 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 186.676i | 0.237200i | 0.992942 | + | 0.118600i | \(0.0378406\pi\) | ||||
−0.992942 | + | 0.118600i | \(0.962159\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | − 1004.09i | − 1.27261i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − 551.543i | − 0.697273i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1612.20i | 2.03304i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 72.0000 | 0.0905660 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − 704.278i | − 0.883662i | −0.897098 | − | 0.441831i | \(-0.854329\pi\) | ||||
0.897098 | − | 0.441831i | \(-0.145671\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −125.000 | −0.156446 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 127.279i | 0.158900i | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 125.000 | 0.155666 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −50.0000 | −0.0621118 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 1080.00 | 1.33829 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −457.000 | −0.564895 | −0.282447 | − | 0.959283i | \(-0.591146\pi\) | ||||
−0.282447 | + | 0.959283i | \(0.591146\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 509.117i | 0.627764i | 0.949462 | + | 0.313882i | \(0.101630\pi\) | ||||
−0.949462 | + | 0.313882i | \(0.898370\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 311.127i | 0.382690i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −110.000 | −0.134969 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 95.0000 | 0.116279 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | − 84.8528i | − 0.103605i | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −167.000 | −0.203410 | −0.101705 | − | 0.994815i | \(-0.532430\pi\) | ||||
−0.101705 | + | 0.994815i | \(0.532430\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −1315.00 | −1.59781 | −0.798906 | − | 0.601455i | \(-0.794588\pi\) | ||||
−0.798906 | + | 0.601455i | \(0.794588\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 339.411i | 0.411408i | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − 534.573i | − 0.646400i | −0.946331 | − | 0.323200i | \(-0.895241\pi\) | ||||
0.946331 | − | 0.323200i | \(-0.104759\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 763.675i | 0.921201i | 0.887608 | + | 0.460600i | \(0.152366\pi\) | ||||
−0.887608 | + | 0.460600i | \(0.847634\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 749.533i | 0.901965i | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 600.000 | 0.720288 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − 59.3970i | − 0.0711341i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −1200.00 | −1.43369 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 339.411i | 0.404543i | 0.979330 | + | 0.202271i | \(0.0648323\pi\) | ||||
−0.979330 | + | 0.202271i | \(0.935168\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −959.000 | −1.14031 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 1200.00 | 1.42349 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −119.000 | −0.140828 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −480.000 | −0.566706 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | − 353.553i | − 0.416435i | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 254.558i | 0.299129i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −770.000 | −0.902696 | −0.451348 | − | 0.892348i | \(-0.649057\pi\) | ||||
−0.451348 | + | 0.892348i | \(0.649057\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −19.0000 | −0.0222222 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 1255.82i | 1.46537i | 0.680568 | + | 0.732685i | \(0.261733\pi\) | ||||
−0.680568 | + | 0.732685i | \(0.738267\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −557.000 | −0.648428 | −0.324214 | − | 0.945984i | \(-0.605100\pi\) | ||||
−0.324214 | + | 0.945984i | \(0.605100\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −600.000 | −0.696864 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − 992.778i | − 1.15038i | −0.818020 | − | 0.575190i | \(-0.804928\pi\) | ||||
0.818020 | − | 0.575190i | \(-0.195072\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | − 186.676i | − 0.215811i | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 950.352i | 1.09614i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 212.132i | 0.244111i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1872.00 | 2.14925 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | − 16.9706i | − 0.0194394i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −245.000 | −0.280000 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 186.676i | 0.212858i | 0.994320 | + | 0.106429i | \(0.0339416\pi\) | ||||
−0.994320 | + | 0.106429i | \(0.966058\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −528.000 | −0.600683 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −25.0000 | −0.0283768 | −0.0141884 | − | 0.999899i | \(-0.504516\pi\) | ||||
−0.0141884 | + | 0.999899i | \(0.504516\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −965.000 | −1.09287 | −0.546433 | − | 0.837503i | \(-0.684015\pi\) | ||||
−0.546433 | + | 0.837503i | \(0.684015\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −240.000 | −0.271186 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 780.646i | 0.880097i | 0.897974 | + | 0.440048i | \(0.145039\pi\) | ||||
−0.897974 | + | 0.440048i | \(0.854961\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − 1145.51i | − 1.28854i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 355.000 | 0.398429 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −95.0000 | −0.106383 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − 127.279i | − 0.142211i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −480.000 | −0.535117 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −1800.00 | −2.00222 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 636.396i | 0.706322i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | − 70.7107i | − 0.0783064i | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | − 254.558i | − 0.281280i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − 313.955i | − 0.346147i | −0.984909 | − | 0.173074i | \(-0.944630\pi\) | ||||
0.984909 | − | 0.173074i | \(-0.0553698\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −50.0000 | −0.0550055 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − 933.381i | − 1.02457i | −0.858816 | − | 0.512284i | \(-0.828800\pi\) | ||||
0.858816 | − | 0.512284i | \(-0.171200\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −650.000 | −0.711939 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | − 268.701i | − 0.293662i | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 815.000 | 0.888768 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −538.000 | −0.585419 | −0.292709 | − | 0.956201i | \(-0.594557\pi\) | ||||
−0.292709 | + | 0.956201i | \(0.594557\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −792.000 | −0.859935 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 610.940i | 0.660476i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 16.9706i | 0.0183070i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −742.000 | −0.798708 | −0.399354 | − | 0.916797i | \(-0.630766\pi\) | ||||
−0.399354 | + | 0.916797i | \(0.630766\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 456.000 | 0.489796 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | − 664.680i | − 0.712412i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 125.000 | 0.133690 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 335.000 | 0.357524 | 0.178762 | − | 0.983892i | \(-0.442791\pi\) | ||||
0.178762 | + | 0.983892i | \(0.442791\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | − 876.812i | − 0.933773i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − 424.264i | − 0.450865i | −0.974259 | − | 0.225433i | \(-0.927620\pi\) | ||||
0.974259 | − | 0.225433i | \(-0.0723795\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − 424.264i | − 0.449909i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 141.421i | 0.149652i | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 1210.00 | 1.27772 | 0.638860 | − | 0.769323i | \(-0.279406\pi\) | ||||
0.638860 | + | 0.769323i | \(0.279406\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 424.264i | 0.447064i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 528.000 | 0.555205 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − 992.778i | − 1.04174i | −0.853636 | − | 0.520870i | \(-0.825608\pi\) | ||||
0.853636 | − | 0.520870i | \(-0.174392\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 293.000 | 0.306806 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 600.000 | 0.626959 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 475.000 | 0.495308 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −839.000 | −0.873049 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | − 101.823i | − 0.105736i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | − 59.3970i | − 0.0615513i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 350.000 | 0.361944 | 0.180972 | − | 0.983488i | \(-0.442076\pi\) | ||||
0.180972 | + | 0.983488i | \(0.442076\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 1343.50i | 1.38648i | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 254.558i | 0.262161i | 0.991372 | + | 0.131081i | \(0.0418447\pi\) | ||||
−0.991372 | + | 0.131081i | \(0.958155\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −625.000 | −0.642343 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −1152.00 | −1.18154 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 398.808i | 0.408197i | 0.978950 | + | 0.204098i | \(0.0654262\pi\) | ||||
−0.978950 | + | 0.204098i | \(0.934574\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − 636.396i | − 0.650047i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 127.279i | 0.129744i | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 695.793i | 0.707826i | 0.935278 | + | 0.353913i | \(0.115149\pi\) | ||||
−0.935278 | + | 0.353913i | \(0.884851\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 70.0000 | 0.0710660 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 70.7107i | 0.0716420i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 50.0000 | 0.0505561 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − 381.838i | − 0.385305i | −0.981267 | − | 0.192653i | \(-0.938291\pi\) | ||||
0.981267 | − | 0.192653i | \(-0.0617091\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −840.000 | −0.845921 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 173.000 | 0.173869 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 265.000 | 0.265797 | 0.132899 | − | 0.991130i | \(-0.457572\pi\) | ||||
0.132899 | + | 0.991130i | \(0.457572\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 720.000 | 0.720721 |
(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 | 1216.3.e.j.1025.2 | 2 | ||
4.3 | odd | 2 | 1216.3.e.i.1025.1 | 2 | |||
8.3 | odd | 2 | 304.3.e.c.113.2 | 2 | |||
8.5 | even | 2 | 38.3.b.a.37.1 | ✓ | 2 | ||
19.18 | odd | 2 | inner | 1216.3.e.j.1025.1 | 2 | ||
24.5 | odd | 2 | 342.3.d.a.37.2 | 2 | |||
24.11 | even | 2 | 2736.3.o.h.721.2 | 2 | |||
40.13 | odd | 4 | 950.3.d.a.949.1 | 4 | |||
40.29 | even | 2 | 950.3.c.a.151.2 | 2 | |||
40.37 | odd | 4 | 950.3.d.a.949.4 | 4 | |||
76.75 | even | 2 | 1216.3.e.i.1025.2 | 2 | |||
152.37 | odd | 2 | 38.3.b.a.37.2 | yes | 2 | ||
152.75 | even | 2 | 304.3.e.c.113.1 | 2 | |||
456.227 | odd | 2 | 2736.3.o.h.721.1 | 2 | |||
456.341 | even | 2 | 342.3.d.a.37.1 | 2 | |||
760.37 | even | 4 | 950.3.d.a.949.2 | 4 | |||
760.189 | odd | 2 | 950.3.c.a.151.1 | 2 | |||
760.493 | even | 4 | 950.3.d.a.949.3 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
38.3.b.a.37.1 | ✓ | 2 | 8.5 | even | 2 | ||
38.3.b.a.37.2 | yes | 2 | 152.37 | odd | 2 | ||
304.3.e.c.113.1 | 2 | 152.75 | even | 2 | |||
304.3.e.c.113.2 | 2 | 8.3 | odd | 2 | |||
342.3.d.a.37.1 | 2 | 456.341 | even | 2 | |||
342.3.d.a.37.2 | 2 | 24.5 | odd | 2 | |||
950.3.c.a.151.1 | 2 | 760.189 | odd | 2 | |||
950.3.c.a.151.2 | 2 | 40.29 | even | 2 | |||
950.3.d.a.949.1 | 4 | 40.13 | odd | 4 | |||
950.3.d.a.949.2 | 4 | 760.37 | even | 4 | |||
950.3.d.a.949.3 | 4 | 760.493 | even | 4 | |||
950.3.d.a.949.4 | 4 | 40.37 | odd | 4 | |||
1216.3.e.i.1025.1 | 2 | 4.3 | odd | 2 | |||
1216.3.e.i.1025.2 | 2 | 76.75 | even | 2 | |||
1216.3.e.j.1025.1 | 2 | 19.18 | odd | 2 | inner | ||
1216.3.e.j.1025.2 | 2 | 1.1 | even | 1 | trivial | ||
2736.3.o.h.721.1 | 2 | 456.227 | odd | 2 | |||
2736.3.o.h.721.2 | 2 | 24.11 | even | 2 |