Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4320,2,Mod(2161,4320)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4320, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4320.2161");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4320 = 2^{5} \cdot 3^{3} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4320.k (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: | \(34.4953736732\) |
Analytic rank: | \(0\) |
Dimension: | \(20\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} - x^{18} + 5x^{16} + 28x^{12} - 28x^{10} + 112x^{8} + 320x^{4} - 256x^{2} + 1024 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{19}]\) |
Coefficient ring index: | \( 2^{24} \) |
Twist minimal: | no (minimal twist has level 1080) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 2161.15 | ||
Root | \(0.662801 + 1.24928i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4320.2161 |
Dual form | 4320.2.k.d.2161.6 |
$q$-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 \(\left(\mathbb{Z}/4320\mathbb{Z}\right)^\times\).
\(n\) | \(2081\) | \(2431\) | \(3457\) | \(3781\) |
\(\chi(n)\) | \(1\) | \(1\) | \(1\) | \(-1\) |
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 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.00000i | 0.447214i | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.52861 | 0.577761 | 0.288880 | − | 0.957365i | \(-0.406717\pi\) | ||||
0.288880 | + | 0.957365i | \(0.406717\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − 5.34793i | − 1.61246i | −0.591601 | − | 0.806231i | \(-0.701504\pi\) | ||||
0.591601 | − | 0.806231i | \(-0.298496\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − 0.986544i | − 0.273618i | −0.990597 | − | 0.136809i | \(-0.956315\pi\) | ||||
0.990597 | − | 0.136809i | \(-0.0436847\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 5.84354 | 1.41727 | 0.708633 | − | 0.705577i | \(-0.249312\pi\) | ||||
0.708633 | + | 0.705577i | \(0.249312\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − 7.86987i | − 1.80547i | −0.430195 | − | 0.902736i | \(-0.641555\pi\) | ||||
0.430195 | − | 0.902736i | \(-0.358445\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −4.41839 | −0.921298 | −0.460649 | − | 0.887582i | \(-0.652383\pi\) | ||||
−0.460649 | + | 0.887582i | \(0.652383\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.00000 | −0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − 9.95406i | − 1.84842i | −0.381882 | − | 0.924211i | \(-0.624724\pi\) | ||||
0.381882 | − | 0.924211i | \(-0.375276\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −3.04016 | −0.546030 | −0.273015 | − | 0.962010i | \(-0.588021\pi\) | ||||
−0.273015 | + | 0.962010i | \(0.588021\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 1.52861i | 0.258382i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 11.2485i | 1.84924i | 0.380894 | + | 0.924619i | \(0.375616\pi\) | ||||
−0.380894 | + | 0.924619i | \(0.624384\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −8.75389 | −1.36713 | −0.683564 | − | 0.729891i | \(-0.739571\pi\) | ||||
−0.683564 | + | 0.729891i | \(0.739571\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 3.01287i | 0.459459i | 0.973255 | + | 0.229729i | \(0.0737841\pi\) | ||||
−0.973255 | + | 0.229729i | \(0.926216\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −9.74043 | −1.42079 | −0.710394 | − | 0.703804i | \(-0.751483\pi\) | ||||
−0.710394 | + | 0.703804i | \(0.751483\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −4.66335 | −0.666193 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 5.83638i | 0.801688i | 0.916146 | + | 0.400844i | \(0.131283\pi\) | ||||
−0.916146 | + | 0.400844i | \(0.868717\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 5.34793 | 0.721115 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − 5.85948i | − 0.762840i | −0.924402 | − | 0.381420i | \(-0.875435\pi\) | ||||
0.924402 | − | 0.381420i | \(-0.124565\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 6.88333i | 0.881320i | 0.897674 | + | 0.440660i | \(0.145255\pi\) | ||||
−0.897674 | + | 0.440660i | \(0.854745\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0.986544 | 0.122366 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − 3.97298i | − 0.485376i | −0.970104 | − | 0.242688i | \(-0.921971\pi\) | ||||
0.970104 | − | 0.242688i | \(-0.0780292\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −10.2619 | −1.21787 | −0.608934 | − | 0.793221i | \(-0.708402\pi\) | ||||
−0.608934 | + | 0.793221i | \(0.708402\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −6.83638 | −0.800137 | −0.400069 | − | 0.916485i | \(-0.631014\pi\) | ||||
−0.400069 | + | 0.916485i | \(0.631014\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − 8.17490i | − 0.931617i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 2.07752 | 0.233739 | 0.116869 | − | 0.993147i | \(-0.462714\pi\) | ||||
0.116869 | + | 0.993147i | \(0.462714\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 4.30777i | 0.472839i | 0.971651 | + | 0.236419i | \(0.0759739\pi\) | ||||
−0.971651 | + | 0.236419i | \(0.924026\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 5.84354i | 0.633821i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 3.01287 | 0.319364 | 0.159682 | − | 0.987169i | \(-0.448953\pi\) | ||||
0.159682 | + | 0.987169i | \(0.448953\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − 1.50804i | − 0.158086i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 7.86987 | 0.807432 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −5.12708 | −0.520576 | −0.260288 | − | 0.965531i | \(-0.583818\pi\) | ||||
−0.260288 | + | 0.965531i | \(0.583818\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − 10.5399i | − 1.04876i | −0.851485 | − | 0.524379i | \(-0.824297\pi\) | ||||
0.851485 | − | 0.524379i | \(-0.175703\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 3.84403 | 0.378764 | 0.189382 | − | 0.981904i | \(-0.439352\pi\) | ||||
0.189382 | + | 0.981904i | \(0.439352\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − 16.3592i | − 1.58150i | −0.612136 | − | 0.790752i | \(-0.709690\pi\) | ||||
0.612136 | − | 0.790752i | \(-0.290310\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − 6.90977i | − 0.661836i | −0.943660 | − | 0.330918i | \(-0.892642\pi\) | ||||
0.943660 | − | 0.330918i | \(-0.107358\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 8.41100 | 0.791240 | 0.395620 | − | 0.918414i | \(-0.370530\pi\) | ||||
0.395620 | + | 0.918414i | \(0.370530\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − 4.41839i | − 0.412017i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 8.93250 | 0.818841 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −17.6003 | −1.60003 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − 1.00000i | − 0.0894427i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1.84403 | −0.163631 | −0.0818156 | − | 0.996647i | \(-0.526072\pi\) | ||||
−0.0818156 | + | 0.996647i | \(0.526072\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − 12.7810i | − 1.11668i | −0.829611 | − | 0.558342i | \(-0.811438\pi\) | ||||
0.829611 | − | 0.558342i | \(-0.188562\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − 12.0300i | − 1.04313i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −12.6540 | −1.08110 | −0.540552 | − | 0.841311i | \(-0.681784\pi\) | ||||
−0.540552 | + | 0.841311i | \(0.681784\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 18.9626i | 1.60838i | 0.594369 | + | 0.804192i | \(0.297402\pi\) | ||||
−0.594369 | + | 0.804192i | \(0.702598\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −5.27597 | −0.441199 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 9.95406 | 0.826639 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − 3.95406i | − 0.323929i | −0.986797 | − | 0.161964i | \(-0.948217\pi\) | ||||
0.986797 | − | 0.161964i | \(-0.0517830\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −2.76210 | −0.224776 | −0.112388 | − | 0.993664i | \(-0.535850\pi\) | ||||
−0.112388 | + | 0.993664i | \(0.535850\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − 3.04016i | − 0.244192i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 7.85024i | 0.626517i | 0.949668 | + | 0.313259i | \(0.101421\pi\) | ||||
−0.949668 | + | 0.313259i | \(0.898579\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −6.75400 | −0.532290 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − 14.5778i | − 1.14182i | −0.821012 | − | 0.570911i | \(-0.806590\pi\) | ||||
0.821012 | − | 0.570911i | \(-0.193410\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −8.13307 | −0.629356 | −0.314678 | − | 0.949198i | \(-0.601897\pi\) | ||||
−0.314678 | + | 0.949198i | \(0.601897\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 12.0267 | 0.925133 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 0.0170573i | 0.00129684i | 1.00000 | 0.000648420i | \(0.000206399\pi\) | |||||
−1.00000 | 0.000648420i | \(0.999794\pi\) | ||||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1.52861 | −0.115552 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 11.6386i | 0.869913i | 0.900452 | + | 0.434956i | \(0.143236\pi\) | ||||
−0.900452 | + | 0.434956i | \(0.856764\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 4.41839i | 0.328416i | 0.986426 | + | 0.164208i | \(0.0525069\pi\) | ||||
−0.986426 | + | 0.164208i | \(0.947493\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −11.2485 | −0.827004 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − 31.2508i | − 2.28529i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 16.1783 | 1.17062 | 0.585312 | − | 0.810808i | \(-0.300972\pi\) | ||||
0.585312 | + | 0.810808i | \(0.300972\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 14.4052 | 1.03691 | 0.518453 | − | 0.855106i | \(-0.326508\pi\) | ||||
0.518453 | + | 0.855106i | \(0.326508\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − 12.4981i | − 0.890454i | −0.895418 | − | 0.445227i | \(-0.853123\pi\) | ||||
0.895418 | − | 0.445227i | \(-0.146877\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 22.7242 | 1.61088 | 0.805438 | − | 0.592680i | \(-0.201930\pi\) | ||||
0.805438 | + | 0.592680i | \(0.201930\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − 15.2159i | − 1.06795i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | − 8.75389i | − 0.611398i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −42.0875 | −2.91125 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 8.29565i | 0.571096i | 0.958364 | + | 0.285548i | \(0.0921756\pi\) | ||||
−0.958364 | + | 0.285548i | \(0.907824\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −3.01287 | −0.205476 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −4.64723 | −0.315474 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − 5.76491i | − 0.387790i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 26.4139 | 1.76880 | 0.884402 | − | 0.466725i | \(-0.154566\pi\) | ||||
0.884402 | + | 0.466725i | \(0.154566\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 4.75886i | 0.315857i | 0.987451 | + | 0.157928i | \(0.0504815\pi\) | ||||
−0.987451 | + | 0.157928i | \(0.949519\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − 14.3374i | − 0.947444i | −0.880674 | − | 0.473722i | \(-0.842910\pi\) | ||||
0.880674 | − | 0.473722i | \(-0.157090\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 5.97287 | 0.391295 | 0.195648 | − | 0.980674i | \(-0.437319\pi\) | ||||
0.195648 | + | 0.980674i | \(0.437319\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − 9.74043i | − 0.635396i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −7.79379 | −0.504138 | −0.252069 | − | 0.967709i | \(-0.581111\pi\) | ||||
−0.252069 | + | 0.967709i | \(0.581111\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 8.54891 | 0.550683 | 0.275342 | − | 0.961346i | \(-0.411209\pi\) | ||||
0.275342 | + | 0.961346i | \(0.411209\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | − 4.66335i | − 0.297930i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −7.76397 | −0.494010 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − 19.9081i | − 1.25659i | −0.777976 | − | 0.628294i | \(-0.783753\pi\) | ||||
0.777976 | − | 0.628294i | \(-0.216247\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 23.6292i | 1.48556i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 11.4042 | 0.711377 | 0.355689 | − | 0.934605i | \(-0.384246\pi\) | ||||
0.355689 | + | 0.934605i | \(0.384246\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 17.1945i | 1.06842i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −2.46493 | −0.151994 | −0.0759972 | − | 0.997108i | \(-0.524214\pi\) | ||||
−0.0759972 | + | 0.997108i | \(0.524214\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −5.83638 | −0.358526 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − 12.1144i | − 0.738631i | −0.929304 | − | 0.369315i | \(-0.879592\pi\) | ||||
0.929304 | − | 0.369315i | \(-0.120408\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −6.01128 | −0.365159 | −0.182580 | − | 0.983191i | \(-0.558445\pi\) | ||||
−0.182580 | + | 0.983191i | \(0.558445\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 5.34793i | 0.322492i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 13.1122i | 0.787837i | 0.919145 | + | 0.393919i | \(0.128881\pi\) | ||||
−0.919145 | + | 0.393919i | \(0.871119\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 16.6730 | 0.994630 | 0.497315 | − | 0.867570i | \(-0.334319\pi\) | ||||
0.497315 | + | 0.867570i | \(0.334319\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 9.79688i | 0.582364i | 0.956668 | + | 0.291182i | \(0.0940486\pi\) | ||||
−0.956668 | + | 0.291182i | \(0.905951\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −13.3813 | −0.789872 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 17.1470 | 1.00864 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − 14.4981i | − 0.846989i | −0.905899 | − | 0.423495i | \(-0.860803\pi\) | ||||
0.905899 | − | 0.423495i | \(-0.139197\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 5.85948 | 0.341152 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 4.35894i | 0.252084i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 4.60551i | 0.265457i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −6.88333 | −0.394138 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 11.7936i | 0.673094i | 0.941667 | + | 0.336547i | \(0.109259\pi\) | ||||
−0.941667 | + | 0.336547i | \(0.890741\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −1.53163 | −0.0868509 | −0.0434255 | − | 0.999057i | \(-0.513827\pi\) | ||||
−0.0434255 | + | 0.999057i | \(0.513827\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 25.7415 | 1.45500 | 0.727498 | − | 0.686109i | \(-0.240683\pi\) | ||||
0.727498 | + | 0.686109i | \(0.240683\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − 6.59847i | − 0.370607i | −0.982681 | − | 0.185304i | \(-0.940673\pi\) | ||||
0.982681 | − | 0.185304i | \(-0.0593268\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −53.2336 | −2.98051 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − 45.9879i | − 2.55883i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0.986544i | 0.0547236i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −14.8893 | −0.820875 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 1.45480i | 0.0799630i | 0.999200 | + | 0.0399815i | \(0.0127299\pi\) | ||||
−0.999200 | + | 0.0399815i | \(0.987270\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 3.97298 | 0.217067 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −27.9624 | −1.52321 | −0.761604 | − | 0.648043i | \(-0.775588\pi\) | ||||
−0.761604 | + | 0.648043i | \(0.775588\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 16.2586i | 0.880452i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −17.8287 | −0.962660 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 3.79945i | 0.203965i | 0.994786 | + | 0.101983i | \(0.0325186\pi\) | ||||
−0.994786 | + | 0.101983i | \(0.967481\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 0.0196324i | 0.00105090i | 1.00000 | 0.000525448i | \(0.000167255\pi\) | |||||
−1.00000 | 0.000525448i | \(0.999833\pi\) | ||||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −4.92987 | −0.262390 | −0.131195 | − | 0.991357i | \(-0.541881\pi\) | ||||
−0.131195 | + | 0.991357i | \(0.541881\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − 10.2619i | − 0.544647i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 11.3550 | 0.599292 | 0.299646 | − | 0.954050i | \(-0.403131\pi\) | ||||
0.299646 | + | 0.954050i | \(0.403131\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −42.9348 | −2.25973 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − 6.83638i | − 0.357832i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 1.68458 | 0.0879344 | 0.0439672 | − | 0.999033i | \(-0.486000\pi\) | ||||
0.0439672 | + | 0.999033i | \(0.486000\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 8.92155i | 0.463184i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − 20.9625i | − 1.08540i | −0.839928 | − | 0.542698i | \(-0.817403\pi\) | ||||
0.839928 | − | 0.542698i | \(-0.182597\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −9.82012 | −0.505762 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − 5.84354i | − 0.300162i | −0.988674 | − | 0.150081i | \(-0.952046\pi\) | ||||
0.988674 | − | 0.150081i | \(-0.0479535\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −29.3803 | −1.50126 | −0.750631 | − | 0.660722i | \(-0.770250\pi\) | ||||
−0.750631 | + | 0.660722i | \(0.770250\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 8.17490 | 0.416632 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − 24.2470i | − 1.22937i | −0.788772 | − | 0.614687i | \(-0.789283\pi\) | ||||
0.788772 | − | 0.614687i | \(-0.210717\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −25.8190 | −1.30572 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 2.07752i | 0.104531i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − 27.9219i | − 1.40136i | −0.713476 | − | 0.700679i | \(-0.752880\pi\) | ||||
0.713476 | − | 0.700679i | \(-0.247120\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −1.01620 | −0.0507464 | −0.0253732 | − | 0.999678i | \(-0.508077\pi\) | ||||
−0.0253732 | + | 0.999678i | \(0.508077\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 2.99926i | 0.149404i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 60.1560 | 2.98182 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −29.4054 | −1.45400 | −0.727002 | − | 0.686635i | \(-0.759087\pi\) | ||||
−0.727002 | + | 0.686635i | \(0.759087\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − 8.95687i | − 0.440739i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −4.30777 | −0.211460 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − 5.07845i | − 0.248099i | −0.992276 | − | 0.124049i | \(-0.960412\pi\) | ||||
0.992276 | − | 0.124049i | \(-0.0395881\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − 16.8024i | − 0.818897i | −0.912333 | − | 0.409449i | \(-0.865721\pi\) | ||||
0.912333 | − | 0.409449i | \(-0.134279\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −5.84354 | −0.283453 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 10.5219i | 0.509192i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −13.5116 | −0.650829 | −0.325415 | − | 0.945571i | \(-0.605504\pi\) | ||||
−0.325415 | + | 0.945571i | \(0.605504\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 31.7335 | 1.52501 | 0.762507 | − | 0.646980i | \(-0.223968\pi\) | ||||
0.762507 | + | 0.646980i | \(0.223968\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 34.7722i | 1.66338i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 21.7302 | 1.03713 | 0.518564 | − | 0.855039i | \(-0.326467\pi\) | ||||
0.518564 | + | 0.855039i | \(0.326467\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − 8.22744i | − 0.390897i | −0.980714 | − | 0.195449i | \(-0.937384\pi\) | ||||
0.980714 | − | 0.195449i | \(-0.0626163\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 3.01287i | 0.142824i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 8.83357 | 0.416882 | 0.208441 | − | 0.978035i | \(-0.433161\pi\) | ||||
0.208441 | + | 0.978035i | \(0.433161\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 46.8152i | 2.20444i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 1.50804 | 0.0706981 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 16.0924 | 0.752772 | 0.376386 | − | 0.926463i | \(-0.377167\pi\) | ||||
0.376386 | + | 0.926463i | \(0.377167\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 22.1038i | 1.02948i | 0.857347 | + | 0.514739i | \(0.172111\pi\) | ||||
−0.857347 | + | 0.514739i | \(0.827889\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 8.06502 | 0.374813 | 0.187407 | − | 0.982282i | \(-0.439992\pi\) | ||||
0.187407 | + | 0.982282i | \(0.439992\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 4.53303i | 0.209764i | 0.994485 | + | 0.104882i | \(0.0334464\pi\) | ||||
−0.994485 | + | 0.104882i | \(0.966554\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − 6.07314i | − 0.280431i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 16.1126 | 0.740860 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 7.86987i | 0.361094i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 16.2348 | 0.741787 | 0.370893 | − | 0.928675i | \(-0.379052\pi\) | ||||
0.370893 | + | 0.928675i | \(0.379052\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 11.0971 | 0.505985 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − 5.12708i | − 0.232809i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −14.4136 | −0.653143 | −0.326572 | − | 0.945172i | \(-0.605893\pi\) | ||||
−0.326572 | + | 0.945172i | \(0.605893\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 37.9033i | 1.71055i | 0.518174 | + | 0.855275i | \(0.326612\pi\) | ||||
−0.518174 | + | 0.855275i | \(0.673388\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − 58.1669i | − 2.61971i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −15.6865 | −0.703636 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 29.8032i | 1.33417i | 0.744980 | + | 0.667087i | \(0.232459\pi\) | ||||
−0.744980 | + | 0.667087i | \(0.767541\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −36.6293 | −1.63322 | −0.816611 | − | 0.577189i | \(-0.804150\pi\) | ||||
−0.816611 | + | 0.577189i | \(0.804150\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 10.5399 | 0.469019 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − 16.1891i | − 0.717571i | −0.933420 | − | 0.358786i | \(-0.883191\pi\) | ||||
0.933420 | − | 0.358786i | \(-0.116809\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −10.4502 | −0.462288 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 3.84403i | 0.169388i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 52.0911i | 2.29097i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 40.1269 | 1.75799 | 0.878995 | − | 0.476830i | \(-0.158214\pi\) | ||||
0.878995 | + | 0.476830i | \(0.158214\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − 8.54884i | − 0.373815i | −0.982378 | − | 0.186907i | \(-0.940154\pi\) | ||||
0.982378 | − | 0.186907i | \(-0.0598464\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −17.7653 | −0.773869 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −3.47782 | −0.151210 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 8.63610i | 0.374071i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 16.3592 | 0.707270 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 24.9393i | 1.07421i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − 18.2047i | − 0.782680i | −0.920246 | − | 0.391340i | \(-0.872012\pi\) | ||||
0.920246 | − | 0.391340i | \(-0.127988\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 6.90977 | 0.295982 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 13.7431i | 0.587611i | 0.955865 | + | 0.293805i | \(0.0949218\pi\) | ||||
−0.955865 | + | 0.293805i | \(0.905078\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −78.3371 | −3.33727 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 3.17571 | 0.135045 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 14.6098i | 0.619035i | 0.950894 | + | 0.309518i | \(0.100168\pi\) | ||||
−0.950894 | + | 0.309518i | \(0.899832\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 2.97233 | 0.125716 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − 8.20995i | − 0.346008i | −0.984921 | − | 0.173004i | \(-0.944653\pi\) | ||||
0.984921 | − | 0.173004i | \(-0.0553474\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 8.41100i | 0.353853i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −4.72803 | −0.198209 | −0.0991046 | − | 0.995077i | \(-0.531598\pi\) | ||||
−0.0991046 | + | 0.995077i | \(0.531598\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 14.2702i | 0.597190i | 0.954380 | + | 0.298595i | \(0.0965180\pi\) | ||||
−0.954380 | + | 0.298595i | \(0.903482\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 4.41839 | 0.184260 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 39.2496 | 1.63398 | 0.816990 | − | 0.576651i | \(-0.195641\pi\) | ||||
0.816990 | + | 0.576651i | \(0.195641\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 6.58490i | 0.273188i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 31.2125 | 1.29269 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − 1.14493i | − 0.0472565i | −0.999721 | − | 0.0236282i | \(-0.992478\pi\) | ||||
0.999721 | − | 0.0236282i | \(-0.00752180\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 23.9257i | 0.985841i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 23.2964 | 0.956667 | 0.478334 | − | 0.878178i | \(-0.341241\pi\) | ||||
0.478334 | + | 0.878178i | \(0.341241\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 8.93250i | 0.366197i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 39.4568 | 1.61216 | 0.806080 | − | 0.591806i | \(-0.201585\pi\) | ||||
0.806080 | + | 0.591806i | \(0.201585\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 0.728368 | 0.0297108 | 0.0148554 | − | 0.999890i | \(-0.495271\pi\) | ||||
0.0148554 | + | 0.999890i | \(0.495271\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | − 17.6003i | − 0.715556i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −18.0003 | −0.730608 | −0.365304 | − | 0.930888i | \(-0.619035\pi\) | ||||
−0.365304 | + | 0.930888i | \(0.619035\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 9.60937i | 0.388753i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − 43.1802i | − 1.74403i | −0.489478 | − | 0.872015i | \(-0.662813\pi\) | ||||
0.489478 | − | 0.872015i | \(-0.337187\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 43.6681 | 1.75801 | 0.879005 | − | 0.476813i | \(-0.158208\pi\) | ||||
0.879005 | + | 0.476813i | \(0.158208\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − 28.2112i | − 1.13390i | −0.823751 | − | 0.566951i | \(-0.808123\pi\) | ||||
0.823751 | − | 0.566951i | \(-0.191877\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 4.60551 | 0.184516 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 65.7309i | 2.62086i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −42.6068 | −1.69615 | −0.848075 | − | 0.529877i | \(-0.822238\pi\) | ||||
−0.848075 | + | 0.529877i | \(0.822238\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | − 1.84403i | − 0.0731781i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 4.60060i | 0.182282i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 29.1556 | 1.15158 | 0.575788 | − | 0.817599i | \(-0.304695\pi\) | ||||
0.575788 | + | 0.817599i | \(0.304695\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − 21.3586i | − 0.842301i | −0.906991 | − | 0.421150i | \(-0.861626\pi\) | ||||
0.906991 | − | 0.421150i | \(-0.138374\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −8.33813 | −0.327806 | −0.163903 | − | 0.986476i | \(-0.552408\pi\) | ||||
−0.163903 | + | 0.986476i | \(0.552408\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −31.3361 | −1.23005 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 38.3458i | 1.50059i | 0.661105 | + | 0.750293i | \(0.270088\pi\) | ||||
−0.661105 | + | 0.750293i | \(0.729912\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 12.7810 | 0.499396 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − 24.5080i | − 0.954698i | −0.878714 | − | 0.477349i | \(-0.841598\pi\) | ||||
0.878714 | − | 0.477349i | \(-0.158402\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 27.2089i | 1.05831i | 0.848527 | + | 0.529153i | \(0.177490\pi\) | ||||
−0.848527 | + | 0.529153i | \(0.822510\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 12.0300 | 0.466502 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 43.9809i | 1.70295i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 36.8115 | 1.42109 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 38.4788 | 1.48325 | 0.741624 | − | 0.670816i | \(-0.234056\pi\) | ||||
0.741624 | + | 0.670816i | \(0.234056\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − 6.83595i | − 0.262727i | −0.991334 | − | 0.131363i | \(-0.958065\pi\) | ||||
0.991334 | − | 0.131363i | \(-0.0419355\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −7.83732 | −0.300769 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 36.3056i | 1.38920i | 0.719398 | + | 0.694598i | \(0.244418\pi\) | ||||
−0.719398 | + | 0.694598i | \(0.755582\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − 12.6540i | − 0.483484i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 5.75784 | 0.219356 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − 44.4920i | − 1.69256i | −0.532741 | − | 0.846278i | \(-0.678838\pi\) | ||||
0.532741 | − | 0.846278i | \(-0.321162\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −18.9626 | −0.719292 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −51.1537 | −1.93758 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − 22.7347i | − 0.858676i | −0.903144 | − | 0.429338i | \(-0.858747\pi\) | ||||
0.903144 | − | 0.429338i | \(-0.141253\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 88.5240 | 3.33875 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − 16.1114i | − 0.605931i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − 47.2538i | − 1.77465i | −0.461142 | − | 0.887326i | \(-0.652560\pi\) | ||||
0.461142 | − | 0.887326i | \(-0.347440\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 13.4326 | 0.503056 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − 5.27597i | − 0.197310i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 48.8415 | 1.82148 | 0.910740 | − | 0.412979i | \(-0.135512\pi\) | ||||
0.910740 | + | 0.412979i | \(0.135512\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 5.87603 | 0.218835 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 9.95406i | 0.369684i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 3.90811 | 0.144944 | 0.0724720 | − | 0.997370i | \(-0.476911\pi\) | ||||
0.0724720 | + | 0.997370i | \(0.476911\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 17.6058i | 0.651176i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 0.332121i | 0.0122672i | 0.999981 | + | 0.00613358i | \(0.00195239\pi\) | ||||
−0.999981 | + | 0.00613358i | \(0.998048\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −21.2472 | −0.782651 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − 14.6274i | − 0.538079i | −0.963129 | − | 0.269039i | \(-0.913294\pi\) | ||||
0.963129 | − | 0.269039i | \(-0.0867062\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 17.0424 | 0.625224 | 0.312612 | − | 0.949881i | \(-0.398796\pi\) | ||||
0.312612 | + | 0.949881i | \(0.398796\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 3.95406 | 0.144865 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − 25.0069i | − 0.913731i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −12.3129 | −0.449303 | −0.224652 | − | 0.974439i | \(-0.572124\pi\) | ||||
−0.224652 | + | 0.974439i | \(0.572124\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − 2.76210i | − 0.100523i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − 36.8680i | − 1.33999i | −0.742366 | − | 0.669995i | \(-0.766296\pi\) | ||||
0.742366 | − | 0.669995i | \(-0.233704\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −16.6730 | −0.604397 | −0.302199 | − | 0.953245i | \(-0.597721\pi\) | ||||
−0.302199 | + | 0.953245i | \(0.597721\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − 10.5623i | − 0.382383i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −5.78064 | −0.208727 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 24.0819 | 0.868417 | 0.434208 | − | 0.900812i | \(-0.357028\pi\) | ||||
0.434208 | + | 0.900812i | \(0.357028\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 5.88458i | 0.211654i | 0.994385 | + | 0.105827i | \(0.0337489\pi\) | ||||
−0.994385 | + | 0.105827i | \(0.966251\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 3.04016 | 0.109206 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 68.8920i | 2.46831i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 54.8801i | 1.96376i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −7.85024 | −0.280187 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − 33.5218i | − 1.19492i | −0.801897 | − | 0.597462i | \(-0.796176\pi\) | ||||
0.801897 | − | 0.597462i | \(-0.203824\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 12.8571 | 0.457147 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 6.79070 | 0.241145 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 8.39899i | 0.297507i | 0.988874 | + | 0.148754i | \(0.0475262\pi\) | ||||
−0.988874 | + | 0.148754i | \(0.952474\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −56.9186 | −2.01364 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 36.5605i | 1.29019i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | − 6.75400i | − 0.238047i | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −37.4680 | −1.31731 | −0.658653 | − | 0.752447i | \(-0.728873\pi\) | ||||
−0.658653 | + | 0.752447i | \(0.728873\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − 19.2209i | − 0.674936i | −0.941337 | − | 0.337468i | \(-0.890430\pi\) | ||||
0.941337 | − | 0.337468i | \(-0.109570\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 14.5778 | 0.510638 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 23.7109 | 0.829540 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 26.3571i | 0.919867i | 0.887953 | + | 0.459934i | \(0.152127\pi\) | ||||
−0.887953 | + | 0.459934i | \(0.847873\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −20.2586 | −0.706170 | −0.353085 | − | 0.935591i | \(-0.614867\pi\) | ||||
−0.353085 | + | 0.935591i | \(0.614867\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − 10.3325i | − 0.359295i | −0.983731 | − | 0.179648i | \(-0.942504\pi\) | ||||
0.983731 | − | 0.179648i | \(-0.0574958\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 53.2266i | 1.84864i | 0.381621 | + | 0.924319i | \(0.375366\pi\) | ||||
−0.381621 | + | 0.924319i | \(0.624634\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −27.2505 | −0.944173 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − 8.13307i | − 0.281457i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 5.86638 | 0.202530 | 0.101265 | − | 0.994859i | \(-0.467711\pi\) | ||||
0.101265 | + | 0.994859i | \(0.467711\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −70.0832 | −2.41666 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 12.0267i | 0.413732i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −26.9041 | −0.924435 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − 49.7002i | − 1.70370i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 48.3015i | 1.65381i | 0.562341 | + | 0.826906i | \(0.309901\pi\) | ||||
−0.562341 | + | 0.826906i | \(0.690099\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 2.68171 | 0.0916054 | 0.0458027 | − | 0.998951i | \(-0.485415\pi\) | ||||
0.0458027 | + | 0.998951i | \(0.485415\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 3.19829i | 0.109124i | 0.998510 | + | 0.0545622i | \(0.0173763\pi\) | ||||
−0.998510 | + | 0.0545622i | \(0.982624\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −10.4441 | −0.355523 | −0.177761 | − | 0.984074i | \(-0.556885\pi\) | ||||
−0.177761 | + | 0.984074i | \(0.556885\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −0.0170573 | −0.000579964 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − 11.1104i | − 0.376895i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −3.91952 | −0.132808 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | − 1.52861i | − 0.0516765i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 2.26309i | 0.0764192i | 0.999270 | + | 0.0382096i | \(0.0121655\pi\) | ||||
−0.999270 | + | 0.0382096i | \(0.987835\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 15.6176 | 0.526170 | 0.263085 | − | 0.964773i | \(-0.415260\pi\) | ||||
0.263085 | + | 0.964773i | \(0.415260\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − 21.6433i | − 0.728356i | −0.931329 | − | 0.364178i | \(-0.881350\pi\) | ||||
0.931329 | − | 0.364178i | \(-0.118650\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −32.2570 | −1.08308 | −0.541542 | − | 0.840674i | \(-0.682159\pi\) | ||||
−0.541542 | + | 0.840674i | \(0.682159\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −2.81880 | −0.0945397 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 76.6559i | 2.56519i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −11.6386 | −0.389037 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 30.2620i | 1.00929i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 34.1051i | 1.13621i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −4.41839 | −0.146872 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 33.2207i | 1.10308i | 0.834150 | + | 0.551538i | \(0.185959\pi\) | ||||
−0.834150 | + | 0.551538i | \(0.814041\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 5.56561 | 0.184397 | 0.0921985 | − | 0.995741i | \(-0.470611\pi\) | ||||
0.0921985 | + | 0.995741i | \(0.470611\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 23.0376 | 0.762434 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − 19.5372i | − 0.645176i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −2.80883 | −0.0926549 | −0.0463274 | − | 0.998926i | \(-0.514752\pi\) | ||||
−0.0463274 | + | 0.998926i | \(0.514752\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 10.1238i | 0.333230i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − 11.2485i | − 0.369848i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 20.7121 | 0.679541 | 0.339771 | − | 0.940508i | \(-0.389651\pi\) | ||||
0.339771 | + | 0.940508i | \(0.389651\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 36.6999i | 1.20279i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 31.2508 | 1.02201 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −41.6066 | −1.35923 | −0.679615 | − | 0.733569i | \(-0.737853\pi\) | ||||
−0.679615 | + | 0.733569i | \(0.737853\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 16.6771i | 0.543656i | 0.962346 | + | 0.271828i | \(0.0876282\pi\) | ||||
−0.962346 | + | 0.271828i | \(0.912372\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 38.6781 | 1.25953 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 38.5829i | 1.25377i | 0.779110 | + | 0.626887i | \(0.215671\pi\) | ||||
−0.779110 | + | 0.626887i | \(0.784329\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 6.74439i | 0.218932i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −31.6927 | −1.02663 | −0.513313 | − | 0.858202i | \(-0.671582\pi\) | ||||
−0.513313 | + | 0.858202i | \(0.671582\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 16.1783i | 0.523519i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −19.3430 | −0.624619 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −21.7574 | −0.701852 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 14.4052i | 0.463718i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 10.1657 | 0.326905 | 0.163453 | − | 0.986551i | \(-0.447737\pi\) | ||||
0.163453 | + | 0.986551i | \(0.447737\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − 19.4769i | − 0.625043i | −0.949911 | − | 0.312522i | \(-0.898826\pi\) | ||||
0.949911 | − | 0.312522i | \(-0.101174\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 28.9864i | 0.929261i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −7.99884 | −0.255905 | −0.127953 | − | 0.991780i | \(-0.540841\pi\) | ||||
−0.127953 | + | 0.991780i | \(0.540841\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − 16.1126i | − 0.514962i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 26.1856 | 0.835190 | 0.417595 | − | 0.908633i | \(-0.362873\pi\) | ||||
0.417595 | + | 0.908633i | \(0.362873\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 12.4981 | 0.398223 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − 13.3121i | − 0.423299i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 43.1761 | 1.37153 | 0.685767 | − | 0.727821i | \(-0.259467\pi\) | ||||
0.685767 | + | 0.727821i | \(0.259467\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 22.7242i | 0.720405i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − 14.4809i | − 0.458615i | −0.973354 | − | 0.229308i | \(-0.926354\pi\) | ||||
0.973354 | − | 0.229308i | \(-0.0736462\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 4320.2.k.d.2161.15 | 20 | ||
3.2 | odd | 2 | inner | 4320.2.k.d.2161.5 | 20 | ||
4.3 | odd | 2 | 1080.2.k.d.541.13 | yes | 20 | ||
8.3 | odd | 2 | 1080.2.k.d.541.14 | yes | 20 | ||
8.5 | even | 2 | inner | 4320.2.k.d.2161.6 | 20 | ||
12.11 | even | 2 | 1080.2.k.d.541.8 | yes | 20 | ||
24.5 | odd | 2 | inner | 4320.2.k.d.2161.16 | 20 | ||
24.11 | even | 2 | 1080.2.k.d.541.7 | ✓ | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1080.2.k.d.541.7 | ✓ | 20 | 24.11 | even | 2 | ||
1080.2.k.d.541.8 | yes | 20 | 12.11 | even | 2 | ||
1080.2.k.d.541.13 | yes | 20 | 4.3 | odd | 2 | ||
1080.2.k.d.541.14 | yes | 20 | 8.3 | odd | 2 | ||
4320.2.k.d.2161.5 | 20 | 3.2 | odd | 2 | inner | ||
4320.2.k.d.2161.6 | 20 | 8.5 | even | 2 | inner | ||
4320.2.k.d.2161.15 | 20 | 1.1 | even | 1 | trivial | ||
4320.2.k.d.2161.16 | 20 | 24.5 | odd | 2 | inner |