Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1216,2,Mod(1215,1216)]
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([1, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1216.1215");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1216 = 2^{6} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1216.h (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: | \(9.70980888579\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\sqrt{-3}, \sqrt{7})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 7x^{2} + 49 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 304) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1215.2 | ||
Root | \(1.32288 + 2.29129i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1216.1215 |
Dual form | 1216.2.h.c.1215.1 |
$q$-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 | ||||||||
\(3\) | −2.64575 | −1.52753 | −0.763763 | − | 0.645497i | \(-0.776650\pi\) | ||||
−0.763763 | + | 0.645497i | \(0.776650\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.73205i | 0.654654i | 0.944911 | + | 0.327327i | \(0.106148\pi\) | ||||
−0.944911 | + | 0.327327i | \(0.893852\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 4.00000 | 1.33333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 3.46410i | 1.04447i | 0.852803 | + | 0.522233i | \(0.174901\pi\) | ||||
−0.852803 | + | 0.522233i | \(0.825099\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 4.58258i | − | 1.27098i | −0.772110 | − | 0.635489i | \(-0.780799\pi\) | ||
0.772110 | − | 0.635489i | \(-0.219201\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 3.00000 | 0.727607 | 0.363803 | − | 0.931476i | \(-0.381478\pi\) | ||||
0.363803 | + | 0.931476i | \(0.381478\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.64575 | + | 3.46410i | 0.606977 | + | 0.794719i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | − | 4.58258i | − | 1.00000i | ||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − | 5.19615i | − | 1.08347i | −0.840548 | − | 0.541736i | \(-0.817767\pi\) | ||
0.840548 | − | 0.541736i | \(-0.182233\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −5.00000 | −1.00000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −2.64575 | −0.509175 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 4.58258i | − | 0.850963i | −0.904967 | − | 0.425481i | \(-0.860105\pi\) | ||
0.904967 | − | 0.425481i | \(-0.139895\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −5.29150 | −0.950382 | −0.475191 | − | 0.879883i | \(-0.657621\pi\) | ||||
−0.475191 | + | 0.879883i | \(0.657621\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | − | 9.16515i | − | 1.59545i | ||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 9.16515i | 1.50674i | 0.657596 | + | 0.753371i | \(0.271573\pi\) | ||||
−0.657596 | + | 0.753371i | \(0.728427\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 12.1244i | 1.94145i | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 9.16515i | 1.43136i | 0.698430 | + | 0.715678i | \(0.253882\pi\) | ||||
−0.698430 | + | 0.715678i | \(0.746118\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 3.46410i | 0.505291i | 0.967559 | + | 0.252646i | \(0.0813007\pi\) | ||||
−0.967559 | + | 0.252646i | \(0.918699\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 4.00000 | 0.571429 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −7.93725 | −1.11144 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 4.58258i | 0.629465i | 0.949180 | + | 0.314733i | \(0.101915\pi\) | ||||
−0.949180 | + | 0.314733i | \(0.898085\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −7.00000 | − | 9.16515i | −0.927173 | − | 1.21395i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −7.93725 | −1.03334 | −0.516671 | − | 0.856184i | \(-0.672829\pi\) | ||||
−0.516671 | + | 0.856184i | \(0.672829\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 8.00000 | 1.02430 | 0.512148 | − | 0.858898i | \(-0.328850\pi\) | ||||
0.512148 | + | 0.858898i | \(0.328850\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 6.92820i | 0.872872i | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −2.64575 | −0.323230 | −0.161615 | − | 0.986854i | \(-0.551670\pi\) | ||||
−0.161615 | + | 0.986854i | \(0.551670\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 13.7477i | 1.65503i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −15.8745 | −1.88396 | −0.941979 | − | 0.335673i | \(-0.891036\pi\) | ||||
−0.941979 | + | 0.335673i | \(0.891036\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −11.0000 | −1.28745 | −0.643726 | − | 0.765256i | \(-0.722612\pi\) | ||||
−0.643726 | + | 0.765256i | \(0.722612\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 13.2288 | 1.52753 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −6.00000 | −0.683763 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 5.29150 | 0.595341 | 0.297670 | − | 0.954669i | \(-0.403790\pi\) | ||||
0.297670 | + | 0.954669i | \(0.403790\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −5.00000 | −0.555556 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 6.92820i | 0.760469i | 0.924890 | + | 0.380235i | \(0.124157\pi\) | ||||
−0.924890 | + | 0.380235i | \(0.875843\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 12.1244i | 1.29987i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 18.3303i | 1.94301i | 0.237023 | + | 0.971504i | \(0.423828\pi\) | ||||
−0.237023 | + | 0.971504i | \(0.576172\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 7.93725 | 0.832050 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 14.0000 | 1.45173 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 9.16515i | 0.930580i | 0.885158 | + | 0.465290i | \(0.154050\pi\) | ||||
−0.885158 | + | 0.465290i | \(0.845950\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 13.8564i | 1.39262i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −18.0000 | −1.79107 | −0.895533 | − | 0.444994i | \(-0.853206\pi\) | ||||
−0.895533 | + | 0.444994i | \(0.853206\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −10.5830 | −1.04277 | −0.521387 | − | 0.853320i | \(-0.674585\pi\) | ||||
−0.521387 | + | 0.853320i | \(0.674585\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −7.93725 | −0.767323 | −0.383662 | − | 0.923474i | \(-0.625337\pi\) | ||||
−0.383662 | + | 0.923474i | \(0.625337\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 13.7477i | 1.31679i | 0.752671 | + | 0.658397i | \(0.228765\pi\) | ||||
−0.752671 | + | 0.658397i | \(0.771235\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | − | 24.2487i | − | 2.30159i | ||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 9.16515i | − | 0.862185i | −0.902308 | − | 0.431092i | \(-0.858128\pi\) | ||
0.902308 | − | 0.431092i | \(-0.141872\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | − | 18.3303i | − | 1.69464i | ||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 5.19615i | 0.476331i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1.00000 | −0.0909091 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | − | 24.2487i | − | 2.18643i | ||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 10.5830 | 0.939090 | 0.469545 | − | 0.882909i | \(-0.344418\pi\) | ||||
0.469545 | + | 0.882909i | \(0.344418\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 20.7846i | 1.81596i | 0.419014 | + | 0.907980i | \(0.362376\pi\) | ||||
−0.419014 | + | 0.907980i | \(0.637624\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −6.00000 | + | 4.58258i | −0.520266 | + | 0.397360i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 9.00000 | 0.768922 | 0.384461 | − | 0.923141i | \(-0.374387\pi\) | ||||
0.384461 | + | 0.923141i | \(0.374387\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 17.3205i | − | 1.46911i | −0.678551 | − | 0.734553i | \(-0.737392\pi\) | ||
0.678551 | − | 0.734553i | \(-0.262608\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | − | 9.16515i | − | 0.771845i | ||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 15.8745 | 1.32749 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −10.5830 | −0.872872 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −6.00000 | −0.491539 | −0.245770 | − | 0.969328i | \(-0.579041\pi\) | ||||
−0.245770 | + | 0.969328i | \(0.579041\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 5.29150 | 0.430616 | 0.215308 | − | 0.976546i | \(-0.430924\pi\) | ||||
0.215308 | + | 0.976546i | \(0.430924\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 12.0000 | 0.970143 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −10.0000 | −0.798087 | −0.399043 | − | 0.916932i | \(-0.630658\pi\) | ||||
−0.399043 | + | 0.916932i | \(0.630658\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | − | 12.1244i | − | 0.961524i | ||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 9.00000 | 0.709299 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 17.3205i | − | 1.35665i | −0.734763 | − | 0.678323i | \(-0.762707\pi\) | ||
0.734763 | − | 0.678323i | \(-0.237293\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 15.8745 | 1.22841 | 0.614203 | − | 0.789148i | \(-0.289478\pi\) | ||||
0.614203 | + | 0.789148i | \(0.289478\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −8.00000 | −0.615385 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 10.5830 | + | 13.8564i | 0.809303 | + | 1.05963i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − | 9.16515i | − | 0.696814i | −0.937343 | − | 0.348407i | \(-0.886723\pi\) | ||
0.937343 | − | 0.348407i | \(-0.113277\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − | 8.66025i | − | 0.654654i | ||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 21.0000 | 1.57846 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −15.8745 | −1.18652 | −0.593258 | − | 0.805012i | \(-0.702159\pi\) | ||||
−0.593258 | + | 0.805012i | \(0.702159\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 9.16515i | − | 0.681240i | −0.940201 | − | 0.340620i | \(-0.889363\pi\) | ||
0.940201 | − | 0.340620i | \(-0.110637\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −21.1660 | −1.56464 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 10.3923i | 0.759961i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | − | 4.58258i | − | 0.333333i | ||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 12.1244i | 0.877288i | 0.898661 | + | 0.438644i | \(0.144541\pi\) | ||||
−0.898661 | + | 0.438644i | \(0.855459\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − | 9.16515i | − | 0.659722i | −0.944030 | − | 0.329861i | \(-0.892998\pi\) | ||
0.944030 | − | 0.329861i | \(-0.107002\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 6.00000 | 0.427482 | 0.213741 | − | 0.976890i | \(-0.431435\pi\) | ||||
0.213741 | + | 0.976890i | \(0.431435\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 8.66025i | 0.613909i | 0.951724 | + | 0.306955i | \(0.0993100\pi\) | ||||
−0.951724 | + | 0.306955i | \(0.900690\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 7.00000 | 0.493742 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 7.93725 | 0.557086 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | − | 20.7846i | − | 1.44463i | ||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −12.0000 | + | 9.16515i | −0.830057 | + | 0.633967i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −2.64575 | −0.182141 | −0.0910705 | − | 0.995844i | \(-0.529029\pi\) | ||||
−0.0910705 | + | 0.995844i | \(0.529029\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 42.0000 | 2.87779 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 9.16515i | − | 0.622171i | ||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 29.1033 | 1.96662 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 13.7477i | − | 0.924772i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −10.5830 | −0.708690 | −0.354345 | − | 0.935115i | \(-0.615296\pi\) | ||||
−0.354345 | + | 0.935115i | \(0.615296\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −20.0000 | −1.33333 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 7.93725 | 0.526814 | 0.263407 | − | 0.964685i | \(-0.415154\pi\) | ||||
0.263407 | + | 0.964685i | \(0.415154\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −8.00000 | −0.528655 | −0.264327 | − | 0.964433i | \(-0.585150\pi\) | ||||
−0.264327 | + | 0.964433i | \(0.585150\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 15.8745 | 1.04447 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 18.0000 | 1.17922 | 0.589610 | − | 0.807688i | \(-0.299282\pi\) | ||||
0.589610 | + | 0.807688i | \(0.299282\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −14.0000 | −0.909398 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 1.73205i | − | 0.112037i | −0.998430 | − | 0.0560185i | \(-0.982159\pi\) | ||
0.998430 | − | 0.0560185i | \(-0.0178406\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 9.16515i | − | 0.590379i | −0.955439 | − | 0.295190i | \(-0.904617\pi\) | ||
0.955439 | − | 0.295190i | \(-0.0953828\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 21.1660 | 1.35780 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 15.8745 | − | 12.1244i | 1.01007 | − | 0.771454i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | − | 18.3303i | − | 1.16164i | ||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 10.3923i | 0.655956i | 0.944685 | + | 0.327978i | \(0.106367\pi\) | ||||
−0.944685 | + | 0.327978i | \(0.893633\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 18.0000 | 1.13165 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −15.8745 | −0.986394 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | − | 18.3303i | − | 1.13462i | ||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − | 3.46410i | − | 0.213606i | −0.994280 | − | 0.106803i | \(-0.965939\pi\) | ||
0.994280 | − | 0.106803i | \(-0.0340614\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − | 48.4974i | − | 2.96799i | ||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 27.4955i | 1.67643i | 0.545342 | + | 0.838214i | \(0.316400\pi\) | ||||
−0.545342 | + | 0.838214i | \(0.683600\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 8.66025i | − | 0.526073i | −0.964786 | − | 0.263036i | \(-0.915276\pi\) | ||
0.964786 | − | 0.263036i | \(-0.0847240\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −21.0000 | −1.27098 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | − | 17.3205i | − | 1.04447i | ||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −2.00000 | −0.120168 | −0.0600842 | − | 0.998193i | \(-0.519137\pi\) | ||||
−0.0600842 | + | 0.998193i | \(0.519137\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −21.1660 | −1.26718 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 20.7846i | − | 1.23552i | −0.786368 | − | 0.617758i | \(-0.788041\pi\) | ||
0.786368 | − | 0.617758i | \(-0.211959\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −15.8745 | −0.937043 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −8.00000 | −0.470588 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | − | 24.2487i | − | 1.42148i | ||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 22.9129i | 1.33858i | 0.742999 | + | 0.669292i | \(0.233403\pi\) | ||||
−0.742999 | + | 0.669292i | \(0.766597\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | − | 9.16515i | − | 0.531816i | ||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −23.8118 | −1.37707 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 47.6235 | 2.73590 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 26.4575 | 1.51001 | 0.755005 | − | 0.655719i | \(-0.227634\pi\) | ||||
0.755005 | + | 0.655719i | \(0.227634\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 28.0000 | 1.59286 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 22.5167i | 1.27680i | 0.769704 | + | 0.638401i | \(0.220404\pi\) | ||||
−0.769704 | + | 0.638401i | \(0.779596\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 1.00000 | 0.0565233 | 0.0282617 | − | 0.999601i | \(-0.491003\pi\) | ||||
0.0282617 | + | 0.999601i | \(0.491003\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 13.7477i | 0.772149i | 0.922468 | + | 0.386075i | \(0.126169\pi\) | ||||
−0.922468 | + | 0.386075i | \(0.873831\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 15.8745 | 0.888802 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 21.0000 | 1.17211 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 7.93725 | + | 10.3923i | 0.441641 | + | 0.578243i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 22.9129i | 1.27098i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | − | 36.3731i | − | 2.01144i | ||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −6.00000 | −0.330791 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 2.64575 | 0.145424 | 0.0727118 | − | 0.997353i | \(-0.476835\pi\) | ||||
0.0727118 | + | 0.997353i | \(0.476835\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 36.6606i | 2.00899i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 18.3303i | 0.998515i | 0.866454 | + | 0.499258i | \(0.166394\pi\) | ||||
−0.866454 | + | 0.499258i | \(0.833606\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 24.2487i | 1.31701i | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 18.3303i | − | 0.992642i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 19.0526i | 1.02874i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −26.0000 | −1.39175 | −0.695874 | − | 0.718164i | \(-0.744983\pi\) | ||||
−0.695874 | + | 0.718164i | \(0.744983\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 12.1244i | 0.647150i | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −21.0000 | −1.11772 | −0.558859 | − | 0.829263i | \(-0.688761\pi\) | ||||
−0.558859 | + | 0.829263i | \(0.688761\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | − | 13.7477i | − | 0.727607i | ||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 5.19615i | − | 0.274242i | −0.990554 | − | 0.137121i | \(-0.956215\pi\) | ||
0.990554 | − | 0.137121i | \(-0.0437850\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −5.00000 | + | 18.3303i | −0.263158 | + | 0.964753i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 2.64575 | 0.138866 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 3.46410i | 0.180825i | 0.995904 | + | 0.0904123i | \(0.0288185\pi\) | ||||
−0.995904 | + | 0.0904123i | \(0.971182\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 36.6606i | 1.90847i | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −7.93725 | −0.412082 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 32.0780i | − | 1.66094i | −0.557065 | − | 0.830469i | \(-0.688073\pi\) | ||
0.557065 | − | 0.830469i | \(-0.311927\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −21.0000 | −1.08156 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 34.3948 | 1.76674 | 0.883370 | − | 0.468676i | \(-0.155269\pi\) | ||||
0.883370 | + | 0.468676i | \(0.155269\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −28.0000 | −1.43448 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −31.7490 | −1.62230 | −0.811149 | − | 0.584839i | \(-0.801158\pi\) | ||||
−0.811149 | + | 0.584839i | \(0.801158\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −30.0000 | −1.52106 | −0.760530 | − | 0.649303i | \(-0.775061\pi\) | ||||
−0.760530 | + | 0.649303i | \(0.775061\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 15.5885i | − | 0.788342i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − | 54.9909i | − | 2.77392i | ||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 22.0000 | 1.10415 | 0.552074 | − | 0.833795i | \(-0.313837\pi\) | ||||
0.552074 | + | 0.833795i | \(0.313837\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 15.8745 | − | 12.1244i | 0.794719 | − | 0.606977i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 24.2487i | 1.20791i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −31.7490 | −1.57374 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 9.16515i | 0.453188i | 0.973989 | + | 0.226594i | \(0.0727590\pi\) | ||||
−0.973989 | + | 0.226594i | \(0.927241\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −23.8118 | −1.17455 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − | 13.7477i | − | 0.676481i | ||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 45.8258i | 2.24410i | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 6.92820i | 0.338465i | 0.985576 | + | 0.169232i | \(0.0541289\pi\) | ||||
−0.985576 | + | 0.169232i | \(0.945871\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 22.9129i | 1.11671i | 0.829604 | + | 0.558353i | \(0.188566\pi\) | ||||
−0.829604 | + | 0.558353i | \(0.811434\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 13.8564i | 0.673722i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −15.0000 | −0.727607 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 13.8564i | 0.670559i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −42.0000 | −2.02778 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 18.0000 | − | 13.7477i | 0.861057 | − | 0.657643i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −10.5830 | −0.505099 | −0.252550 | − | 0.967584i | \(-0.581269\pi\) | ||||
−0.252550 | + | 0.967584i | \(0.581269\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 16.0000 | 0.761905 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 17.3205i | 0.822922i | 0.911427 | + | 0.411461i | \(0.134981\pi\) | ||||
−0.911427 | + | 0.411461i | \(0.865019\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 15.8745 | 0.750838 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 9.16515i | 0.432530i | 0.976335 | + | 0.216265i | \(0.0693876\pi\) | ||||
−0.976335 | + | 0.216265i | \(0.930612\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −31.7490 | −1.49500 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −14.0000 | −0.657777 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 25.0000 | 1.16945 | 0.584725 | − | 0.811231i | \(-0.301202\pi\) | ||||
0.584725 | + | 0.811231i | \(0.301202\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −7.93725 | −0.370479 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 12.0000 | 0.558896 | 0.279448 | − | 0.960161i | \(-0.409849\pi\) | ||||
0.279448 | + | 0.960161i | \(0.409849\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 38.1051i | − | 1.77090i | −0.464739 | − | 0.885448i | \(-0.653852\pi\) | ||
0.464739 | − | 0.885448i | \(-0.346148\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − | 3.46410i | − | 0.160300i | −0.996783 | − | 0.0801498i | \(-0.974460\pi\) | ||
0.996783 | − | 0.0801498i | \(-0.0255399\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − | 4.58258i | − | 0.211604i | ||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 26.4575 | 1.21910 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −13.2288 | − | 17.3205i | −0.606977 | − | 0.794719i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 18.3303i | 0.839287i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 10.3923i | 0.474837i | 0.971408 | + | 0.237418i | \(0.0763012\pi\) | ||||
−0.971408 | + | 0.237418i | \(0.923699\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 42.0000 | 1.91504 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −23.8118 | −1.08347 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 10.5830 | 0.479562 | 0.239781 | − | 0.970827i | \(-0.422924\pi\) | ||||
0.239781 | + | 0.970827i | \(0.422924\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 45.8258i | 2.07231i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 13.8564i | − | 0.625331i | −0.949863 | − | 0.312665i | \(-0.898778\pi\) | ||
0.949863 | − | 0.312665i | \(-0.101222\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 13.7477i | − | 0.619166i | ||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − | 27.4955i | − | 1.23334i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −42.0000 | −1.87642 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 43.3013i | 1.93071i | 0.260943 | + | 0.965354i | \(0.415966\pi\) | ||||
−0.260943 | + | 0.965354i | \(0.584034\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 21.1660 | 0.940016 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − | 9.16515i | − | 0.406238i | −0.979154 | − | 0.203119i | \(-0.934892\pi\) | ||
0.979154 | − | 0.203119i | \(-0.0651079\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − | 19.0526i | − | 0.842836i | ||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −7.00000 | − | 9.16515i | −0.309058 | − | 0.404651i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −12.0000 | −0.527759 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 24.2487i | 1.06440i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 27.4955i | − | 1.20460i | −0.798271 | − | 0.602299i | \(-0.794252\pi\) | ||
0.798271 | − | 0.602299i | \(-0.205748\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 13.2288 | 0.578453 | 0.289227 | − | 0.957261i | \(-0.406602\pi\) | ||||
0.289227 | + | 0.957261i | \(0.406602\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 22.9129i | 1.00000i | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −15.8745 | −0.691504 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −4.00000 | −0.173913 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −31.7490 | −1.37779 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 42.0000 | 1.81922 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 42.0000 | 1.81243 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 13.8564i | 0.596838i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 20.0000 | 0.859867 | 0.429934 | − | 0.902861i | \(-0.358537\pi\) | ||||
0.429934 | + | 0.902861i | \(0.358537\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 24.2487i | 1.04061i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 26.4575 | 1.13124 | 0.565621 | − | 0.824665i | \(-0.308637\pi\) | ||||
0.565621 | + | 0.824665i | \(0.308637\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 32.0000 | 1.36573 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 15.8745 | − | 12.1244i | 0.676277 | − | 0.516515i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 9.16515i | 0.389742i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 24.0000 | 1.01691 | 0.508456 | − | 0.861088i | \(-0.330216\pi\) | ||||
0.508456 | + | 0.861088i | \(0.330216\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | − | 27.4955i | − | 1.16086i | ||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −15.8745 | −0.669031 | −0.334515 | − | 0.942390i | \(-0.608573\pi\) | ||||
−0.334515 | + | 0.942390i | \(0.608573\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | − | 8.66025i | − | 0.363696i | ||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 27.4955i | − | 1.15267i | −0.817214 | − | 0.576335i | \(-0.804482\pi\) | ||
0.817214 | − | 0.576335i | \(-0.195518\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 3.46410i | 0.144968i | 0.997370 | + | 0.0724841i | \(0.0230926\pi\) | ||||
−0.997370 | + | 0.0724841i | \(0.976907\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − | 32.0780i | − | 1.34008i | ||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 25.9808i | 1.08347i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −17.0000 | −0.707719 | −0.353860 | − | 0.935299i | \(-0.615131\pi\) | ||||
−0.353860 | + | 0.935299i | \(0.615131\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 24.2487i | 1.00774i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −12.0000 | −0.497844 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −15.8745 | −0.657455 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 41.5692i | 1.71575i | 0.513862 | + | 0.857873i | \(0.328214\pi\) | ||||
−0.513862 | + | 0.857873i | \(0.671786\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −14.0000 | − | 18.3303i | −0.576860 | − | 0.755287i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −15.8745 | −0.652990 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 6.00000 | 0.246390 | 0.123195 | − | 0.992382i | \(-0.460686\pi\) | ||||
0.123195 | + | 0.992382i | \(0.460686\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | − | 22.9129i | − | 0.937762i | ||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −31.7490 | −1.29723 | −0.648615 | − | 0.761117i | \(-0.724651\pi\) | ||||
−0.648615 | + | 0.761117i | \(0.724651\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 27.4955i | 1.12156i | 0.827964 | + | 0.560781i | \(0.189499\pi\) | ||||
−0.827964 | + | 0.560781i | \(0.810501\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −10.5830 | −0.430973 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 26.4575 | 1.07388 | 0.536939 | − | 0.843621i | \(-0.319581\pi\) | ||||
0.536939 | + | 0.843621i | \(0.319581\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −21.0000 | −0.850963 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 15.8745 | 0.642214 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 44.0000 | 1.77714 | 0.888572 | − | 0.458738i | \(-0.151698\pi\) | ||||
0.888572 | + | 0.458738i | \(0.151698\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −30.0000 | −1.20775 | −0.603877 | − | 0.797077i | \(-0.706378\pi\) | ||||
−0.603877 | + | 0.797077i | \(0.706378\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 13.8564i | − | 0.556936i | −0.960446 | − | 0.278468i | \(-0.910173\pi\) | ||
0.960446 | − | 0.278468i | \(-0.0898266\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 13.7477i | 0.551677i | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −31.7490 | −1.27200 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 25.0000 | 1.00000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 31.7490 | − | 24.2487i | 1.26793 | − | 0.968400i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 27.4955i | 1.09632i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 24.2487i | 0.965326i | 0.875806 | + | 0.482663i | \(0.160330\pi\) | ||||
−0.875806 | + | 0.482663i | \(0.839670\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 7.00000 | 0.278225 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − | 18.3303i | − | 0.726273i | ||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −63.4980 | −2.51194 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 36.6606i | − | 1.44801i | −0.689796 | − | 0.724003i | \(-0.742300\pi\) | ||
0.689796 | − | 0.724003i | \(-0.257700\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 31.1769i | 1.22950i | 0.788723 | + | 0.614749i | \(0.210743\pi\) | ||||
−0.788723 | + | 0.614749i | \(0.789257\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − | 32.9090i | − | 1.29378i | −0.762581 | − | 0.646892i | \(-0.776068\pi\) | ||
0.762581 | − | 0.646892i | \(-0.223932\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 27.4955i | − | 1.07929i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 24.2487i | 0.950382i | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 18.0000 | 0.704394 | 0.352197 | − | 0.935926i | \(-0.385435\pi\) | ||||
0.352197 | + | 0.935926i | \(0.385435\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −44.0000 | −1.71660 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −23.8118 | −0.927575 | −0.463787 | − | 0.885947i | \(-0.653510\pi\) | ||||
−0.463787 | + | 0.885947i | \(0.653510\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 4.58258i | 0.178242i | 0.996021 | + | 0.0891208i | \(0.0284057\pi\) | ||||
−0.996021 | + | 0.0891208i | \(0.971594\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 36.3731i | 1.41261i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −23.8118 | −0.921995 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 28.0000 | 1.08254 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 27.7128i | 1.06984i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 45.8258i | − | 1.76645i | −0.468947 | − | 0.883227i | \(-0.655366\pi\) | ||
0.468947 | − | 0.883227i | \(-0.344634\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 13.2288 | 0.509175 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − | 13.7477i | − | 0.528368i | −0.964472 | − | 0.264184i | \(-0.914897\pi\) | ||
0.964472 | − | 0.264184i | \(-0.0851026\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −15.8745 | −0.609208 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −21.0000 | −0.804722 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 15.8745 | 0.607421 | 0.303711 | − | 0.952764i | \(-0.401774\pi\) | ||||
0.303711 | + | 0.952764i | \(0.401774\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 21.1660 | 0.807534 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 21.0000 | 0.800036 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 20.7846i | − | 0.790684i | −0.918534 | − | 0.395342i | \(-0.870626\pi\) | ||
0.918534 | − | 0.395342i | \(-0.129374\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −24.0000 | −0.911685 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 27.4955i | 1.04146i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −47.6235 | −1.80129 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 36.0000 | 1.35970 | 0.679851 | − | 0.733351i | \(-0.262045\pi\) | ||||
0.679851 | + | 0.733351i | \(0.262045\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −31.7490 | + | 24.2487i | −1.19744 | + | 0.914557i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − | 31.1769i | − | 1.17253i | ||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −4.00000 | −0.150223 | −0.0751116 | − | 0.997175i | \(-0.523931\pi\) | ||||
−0.0751116 | + | 0.997175i | \(0.523931\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 21.1660 | 0.793787 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 27.4955i | 1.02971i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 4.58258i | 0.171139i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 39.8372i | 1.48568i | 0.669471 | + | 0.742838i | \(0.266521\pi\) | ||||
−0.669471 | + | 0.742838i | \(0.733479\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | − | 18.3303i | − | 0.682656i | ||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 24.2487i | 0.901819i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 22.9129i | 0.850963i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 25.9808i | − | 0.963573i | −0.876289 | − | 0.481787i | \(-0.839988\pi\) | ||
0.876289 | − | 0.481787i | \(-0.160012\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −41.0000 | −1.51852 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −28.0000 | −1.03420 | −0.517102 | − | 0.855924i | \(-0.672989\pi\) | ||||
−0.517102 | + | 0.855924i | \(0.672989\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − | 9.16515i | − | 0.337603i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 20.7846i | − | 0.764574i | −0.924044 | − | 0.382287i | \(-0.875137\pi\) | ||
0.924044 | − | 0.382287i | \(-0.124863\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −42.0000 | + | 32.0780i | −1.54291 | + | 1.17842i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 15.8745 | 0.582379 | 0.291190 | − | 0.956665i | \(-0.405949\pi\) | ||||
0.291190 | + | 0.956665i | \(0.405949\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 27.7128i | 1.01396i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − | 13.7477i | − | 0.502331i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 37.0405 | 1.35163 | 0.675814 | − | 0.737072i | \(-0.263792\pi\) | ||||
0.675814 | + | 0.737072i | \(0.263792\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | − | 27.4955i | − | 1.00199i | ||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −20.0000 | −0.726912 | −0.363456 | − | 0.931611i | \(-0.618403\pi\) | ||||
−0.363456 | + | 0.931611i | \(0.618403\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −47.6235 | −1.72862 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 21.0000 | 0.761249 | 0.380625 | − | 0.924730i | \(-0.375709\pi\) | ||||
0.380625 | + | 0.924730i | \(0.375709\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −23.8118 | −0.862044 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 36.3731i | 1.31336i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 7.00000 | 0.252426 | 0.126213 | − | 0.992003i | \(-0.459718\pi\) | ||||
0.126213 | + | 0.992003i | \(0.459718\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 4.58258i | 0.164824i | 0.996598 | + | 0.0824119i | \(0.0262623\pi\) | ||||
−0.996598 | + | 0.0824119i | \(0.973738\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 26.4575 | 0.950382 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 42.0000 | 1.50674 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −31.7490 | + | 24.2487i | −1.13753 | + | 0.868800i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − | 54.9909i | − | 1.96773i | ||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 12.1244i | 0.433289i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −2.64575 | −0.0943108 | −0.0471554 | − | 0.998888i | \(-0.515016\pi\) | ||||
−0.0471554 | + | 0.998888i | \(0.515016\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 9.16515i | 0.326288i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 15.8745 | 0.564433 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 36.6606i | − | 1.30186i | ||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 32.0780i | 1.13626i | 0.822938 | + | 0.568131i | \(0.192333\pi\) | ||||
−0.822938 | + | 0.568131i | \(0.807667\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 10.3923i | 0.367653i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 73.3212i | 2.59068i | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − | 38.1051i | − | 1.34470i | ||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | − | 72.7461i | − | 2.56079i | ||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −39.0000 | −1.37117 | −0.685583 | − | 0.727994i | \(-0.740453\pi\) | ||||
−0.685583 | + | 0.727994i | \(0.740453\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 2.64575 | 0.0929049 | 0.0464524 | − | 0.998921i | \(-0.485208\pi\) | ||||
0.0464524 | + | 0.998921i | \(0.485208\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 22.9129i | 0.803590i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 31.7490 | 1.10940 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 18.0000 | 0.628204 | 0.314102 | − | 0.949389i | \(-0.398297\pi\) | ||||
0.314102 | + | 0.949389i | \(0.398297\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 32.9090i | − | 1.14713i | −0.819159 | − | 0.573567i | \(-0.805559\pi\) | ||
0.819159 | − | 0.573567i | \(-0.194441\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 45.8258i | 1.59545i | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −7.93725 | −0.276005 | −0.138003 | − | 0.990432i | \(-0.544068\pi\) | ||||
−0.138003 | + | 0.990432i | \(0.544068\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 32.0780i | 1.11412i | 0.830474 | + | 0.557058i | \(0.188070\pi\) | ||||
−0.830474 | + | 0.557058i | \(0.811930\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 5.29150 | 0.183560 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 12.0000 | 0.415775 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 14.0000 | 0.483911 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 31.7490 | 1.09610 | 0.548049 | − | 0.836446i | \(-0.315371\pi\) | ||||
0.548049 | + | 0.836446i | \(0.315371\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 8.00000 | 0.275862 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 1.73205i | − | 0.0595140i | ||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 54.9909i | 1.88728i | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 47.6235 | 1.63251 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −44.0000 | −1.50653 | −0.753266 | − | 0.657716i | \(-0.771523\pi\) | ||||
−0.753266 | + | 0.657716i | \(0.771523\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 18.3303i | 0.626151i | 0.949728 | + | 0.313076i | \(0.101359\pi\) | ||||
−0.949728 | + | 0.313076i | \(0.898641\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 6.92820i | − | 0.236387i | −0.992991 | − | 0.118194i | \(-0.962290\pi\) | ||
0.992991 | − | 0.118194i | \(-0.0377103\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 42.0000 | 1.43136 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −31.7490 | −1.08075 | −0.540375 | − | 0.841425i | \(-0.681717\pi\) | ||||
−0.540375 | + | 0.841425i | \(0.681717\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 21.1660 | 0.718835 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 18.3303i | 0.621813i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 12.1244i | 0.410818i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 36.6606i | 1.24077i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − | 22.9129i | − | 0.773713i | −0.922140 | − | 0.386856i | \(-0.873561\pi\) | ||
0.922140 | − | 0.386856i | \(-0.126439\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | − | 60.6218i | − | 2.04472i | ||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 30.0000 | 1.01073 | 0.505363 | − | 0.862907i | \(-0.331359\pi\) | ||||
0.505363 | + | 0.862907i | \(0.331359\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 13.8564i | 0.466305i | 0.972440 | + | 0.233153i | \(0.0749042\pi\) | ||||
−0.972440 | + | 0.233153i | \(0.925096\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 31.7490 | 1.06603 | 0.533014 | − | 0.846107i | \(-0.321059\pi\) | ||||
0.533014 | + | 0.846107i | \(0.321059\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 18.3303i | 0.614779i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | − | 17.3205i | − | 0.580259i | ||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −12.0000 | + | 9.16515i | −0.401565 | + | 0.306700i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 63.0000 | 2.10351 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 24.2487i | 0.808740i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 13.7477i | 0.458003i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 44.9778 | 1.49346 | 0.746731 | − | 0.665126i | \(-0.231622\pi\) | ||||
0.746731 | + | 0.665126i | \(0.231622\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −72.0000 | −2.38809 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −24.0000 | −0.794284 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −36.0000 | −1.18882 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 5.19615i | − | 0.171405i | −0.996321 | − | 0.0857026i | \(-0.972687\pi\) | ||
0.996321 | − | 0.0857026i | \(-0.0273135\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −70.0000 | −2.30658 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 72.7461i | 2.39447i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − | 45.8258i | − | 1.50674i | ||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −42.3320 | −1.39037 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 15.0000 | 0.492134 | 0.246067 | − | 0.969253i | \(-0.420862\pi\) | ||||
0.246067 | + | 0.969253i | \(0.420862\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 10.5830 | + | 13.8564i | 0.346844 | + | 0.454125i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | − | 59.5735i | − | 1.95035i | ||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −7.00000 | −0.228680 | −0.114340 | − | 0.993442i | \(-0.536475\pi\) | ||||
−0.114340 | + | 0.993442i | \(0.536475\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −2.64575 | −0.0863408 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 41.2432i | − | 1.34449i | −0.740329 | − | 0.672245i | \(-0.765330\pi\) | ||
0.740329 | − | 0.672245i | \(-0.234670\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 47.6235 | 1.55084 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − | 48.4974i | − | 1.57595i | −0.615704 | − | 0.787977i | \(-0.711128\pi\) | ||
0.615704 | − | 0.787977i | \(-0.288872\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 50.4083i | 1.63632i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | − | 36.3731i | − | 1.17948i | ||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 36.6606i | 1.18755i | 0.804630 | + | 0.593777i | \(0.202364\pi\) | ||||
−0.804630 | + | 0.593777i | \(0.797636\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −42.0000 | −1.35767 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 15.5885i | 0.503378i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −3.00000 | −0.0967742 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −31.7490 | −1.02310 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 24.2487i | 0.779786i | 0.920860 | + | 0.389893i | \(0.127488\pi\) | ||||
−0.920860 | + | 0.389893i | \(0.872512\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −21.0000 | − | 27.4955i | −0.674617 | − | 0.883281i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −47.6235 | −1.52831 | −0.764156 | − | 0.645032i | \(-0.776844\pi\) | ||||
−0.764156 | + | 0.645032i | \(0.776844\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 30.0000 | 0.961756 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | − | 60.6218i | − | 1.94145i | ||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 9.16515i | 0.293219i | 0.989194 | + | 0.146610i | \(0.0468361\pi\) | ||||
−0.989194 | + | 0.146610i | \(0.953164\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −63.4980 | −2.02941 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 54.9909i | 1.75572i | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 15.8745 | 0.505291 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −52.9150 | −1.68090 | −0.840451 | − | 0.541888i | \(-0.817710\pi\) | ||||
−0.840451 | + | 0.541888i | \(0.817710\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −7.00000 | −0.222138 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −10.0000 | −0.316703 | −0.158352 | − | 0.987383i | \(-0.550618\pi\) | ||||
−0.158352 | + | 0.987383i | \(0.550618\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | − | 24.2487i | − | 0.767195i |
(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 | 1216.2.h.c.1215.2 | 4 | ||
4.3 | odd | 2 | inner | 1216.2.h.c.1215.3 | 4 | ||
8.3 | odd | 2 | 304.2.h.b.303.1 | ✓ | 4 | ||
8.5 | even | 2 | 304.2.h.b.303.4 | yes | 4 | ||
19.18 | odd | 2 | inner | 1216.2.h.c.1215.4 | 4 | ||
24.5 | odd | 2 | 2736.2.k.k.2431.4 | 4 | |||
24.11 | even | 2 | 2736.2.k.k.2431.2 | 4 | |||
76.75 | even | 2 | inner | 1216.2.h.c.1215.1 | 4 | ||
152.37 | odd | 2 | 304.2.h.b.303.2 | yes | 4 | ||
152.75 | even | 2 | 304.2.h.b.303.3 | yes | 4 | ||
456.227 | odd | 2 | 2736.2.k.k.2431.1 | 4 | |||
456.341 | even | 2 | 2736.2.k.k.2431.3 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
304.2.h.b.303.1 | ✓ | 4 | 8.3 | odd | 2 | ||
304.2.h.b.303.2 | yes | 4 | 152.37 | odd | 2 | ||
304.2.h.b.303.3 | yes | 4 | 152.75 | even | 2 | ||
304.2.h.b.303.4 | yes | 4 | 8.5 | even | 2 | ||
1216.2.h.c.1215.1 | 4 | 76.75 | even | 2 | inner | ||
1216.2.h.c.1215.2 | 4 | 1.1 | even | 1 | trivial | ||
1216.2.h.c.1215.3 | 4 | 4.3 | odd | 2 | inner | ||
1216.2.h.c.1215.4 | 4 | 19.18 | odd | 2 | inner | ||
2736.2.k.k.2431.1 | 4 | 456.227 | odd | 2 | |||
2736.2.k.k.2431.2 | 4 | 24.11 | even | 2 | |||
2736.2.k.k.2431.3 | 4 | 456.341 | even | 2 | |||
2736.2.k.k.2431.4 | 4 | 24.5 | odd | 2 |