Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1600,3,Mod(351,1600)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1600, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1, 0]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1600.351");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1600 = 2^{6} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 1600.g (of order \(2\), degree \(1\), 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: | \(43.5968422976\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} + 19x^{14} + 301x^{12} + 1102x^{10} + 3238x^{8} + 1102x^{6} + 301x^{4} + 19x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{29}]\) |
Coefficient ring index: | \( 2^{37} \) |
Twist minimal: | no (minimal twist has level 320) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 351.13 | ||
Root | \(0.265804 - 0.460386i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1600.351 |
Dual form | 1600.3.g.k.351.15 |
$q$-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 \(\left(\mathbb{Z}/1600\mathbb{Z}\right)^\times\).
\(n\) | \(577\) | \(901\) | \(1151\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(-1\) |
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 | ||||||||
\(3\) | 5.13399 | 1.71133 | 0.855664 | − | 0.517531i | \(-0.173149\pi\) | ||||
0.855664 | + | 0.517531i | \(0.173149\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − 6.19337i | − 0.884767i | −0.896826 | − | 0.442383i | \(-0.854133\pi\) | ||||
0.896826 | − | 0.442383i | \(-0.145867\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 17.3578 | 1.92865 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −20.0431 | −1.82210 | −0.911049 | − | 0.412298i | \(-0.864726\pi\) | ||||
−0.911049 | + | 0.412298i | \(0.864726\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − 15.8612i | − 1.22009i | −0.792365 | − | 0.610047i | \(-0.791151\pi\) | ||||
0.792365 | − | 0.610047i | \(-0.208849\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 6.98882 | 0.411107 | 0.205554 | − | 0.978646i | \(-0.434100\pi\) | ||||
0.205554 | + | 0.978646i | \(0.434100\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −10.3923 | −0.546963 | −0.273482 | − | 0.961877i | \(-0.588175\pi\) | ||||
−0.273482 | + | 0.961877i | \(0.588175\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | − 31.7967i | − 1.51413i | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − 22.3871i | − 0.973353i | −0.873582 | − | 0.486676i | \(-0.838209\pi\) | ||||
0.873582 | − | 0.486676i | \(-0.161791\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 42.9089 | 1.58922 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − 4.20563i | − 0.145022i | −0.997368 | − | 0.0725109i | \(-0.976899\pi\) | ||||
0.997368 | − | 0.0725109i | \(-0.0231012\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 20.7156i | 0.668246i | 0.942529 | + | 0.334123i | \(0.108440\pi\) | ||||
−0.942529 | + | 0.334123i | \(0.891560\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −102.901 | −3.11821 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − 35.4786i | − 0.958882i | −0.877574 | − | 0.479441i | \(-0.840839\pi\) | ||||
0.877574 | − | 0.479441i | \(-0.159161\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | − 81.4313i | − 2.08798i | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −37.0735 | −0.904230 | −0.452115 | − | 0.891960i | \(-0.649330\pi\) | ||||
−0.452115 | + | 0.891960i | \(0.649330\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 23.8329 | 0.554254 | 0.277127 | − | 0.960833i | \(-0.410618\pi\) | ||||
0.277127 | + | 0.960833i | \(0.410618\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − 48.7515i | − 1.03727i | −0.854997 | − | 0.518633i | \(-0.826441\pi\) | ||||
0.854997 | − | 0.518633i | \(-0.173559\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 10.6422 | 0.217187 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 35.8805 | 0.703540 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − 77.4691i | − 1.46168i | −0.682549 | − | 0.730840i | \(-0.739128\pi\) | ||||
0.682549 | − | 0.730840i | \(-0.260872\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −53.3540 | −0.936034 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 0.497984 | 0.00844041 | 0.00422020 | − | 0.999991i | \(-0.498657\pi\) | ||||
0.00422020 | + | 0.999991i | \(0.498657\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 60.7490i | 0.995885i | 0.867210 | + | 0.497943i | \(0.165911\pi\) | ||||
−0.867210 | + | 0.497943i | \(0.834089\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | − 107.503i | − 1.70640i | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −82.5209 | −1.23165 | −0.615827 | − | 0.787881i | \(-0.711178\pi\) | ||||
−0.615827 | + | 0.787881i | \(0.711178\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | − 114.935i | − 1.66573i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − 28.7156i | − 0.404446i | −0.979340 | − | 0.202223i | \(-0.935183\pi\) | ||||
0.979340 | − | 0.202223i | \(-0.0648165\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 10.1706 | 0.139324 | 0.0696620 | − | 0.997571i | \(-0.477808\pi\) | ||||
0.0696620 | + | 0.997571i | \(0.477808\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 124.134i | 1.61213i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 87.5782i | 1.10858i | 0.832322 | + | 0.554292i | \(0.187011\pi\) | ||||
−0.832322 | + | 0.554292i | \(0.812989\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 64.0735 | 0.791030 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 103.057 | 1.24165 | 0.620824 | − | 0.783950i | \(-0.286798\pi\) | ||||
0.620824 | + | 0.783950i | \(0.286798\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | − 21.5917i | − 0.248180i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 49.2844 | 0.553757 | 0.276878 | − | 0.960905i | \(-0.410700\pi\) | ||||
0.276878 | + | 0.960905i | \(0.410700\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −98.2344 | −1.07950 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 106.354i | 1.14359i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −84.4911 | −0.871042 | −0.435521 | − | 0.900179i | \(-0.643436\pi\) | ||||
−0.435521 | + | 0.900179i | \(0.643436\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −347.904 | −3.51418 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − 92.7892i | − 0.918705i | −0.888254 | − | 0.459353i | \(-0.848081\pi\) | ||||
0.888254 | − | 0.459353i | \(-0.151919\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − 42.7284i | − 0.414839i | −0.978252 | − | 0.207419i | \(-0.933494\pi\) | ||||
0.978252 | − | 0.207419i | \(-0.0665065\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 29.3440 | 0.274243 | 0.137121 | − | 0.990554i | \(-0.456215\pi\) | ||||
0.137121 | + | 0.990554i | \(0.456215\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − 163.433i | − 1.49938i | −0.661789 | − | 0.749691i | \(-0.730202\pi\) | ||||
0.661789 | − | 0.749691i | \(-0.269798\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | − 182.147i | − 1.64096i | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 120.686 | 1.06801 | 0.534007 | − | 0.845480i | \(-0.320686\pi\) | ||||
0.534007 | + | 0.845480i | \(0.320686\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | − 275.316i | − 2.35313i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | − 43.2844i | − 0.363734i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 280.725 | 2.32004 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −190.335 | −1.54744 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 227.564i | 1.79184i | 0.444215 | + | 0.895920i | \(0.353483\pi\) | ||||
−0.444215 | + | 0.895920i | \(0.646517\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 122.358 | 0.948510 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −34.1430 | −0.260634 | −0.130317 | − | 0.991472i | \(-0.541599\pi\) | ||||
−0.130317 | + | 0.991472i | \(0.541599\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 64.3634i | 0.483935i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 216.598 | 1.58100 | 0.790502 | − | 0.612459i | \(-0.209820\pi\) | ||||
0.790502 | + | 0.612459i | \(0.209820\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −113.076 | −0.813495 | −0.406748 | − | 0.913541i | \(-0.633337\pi\) | ||||
−0.406748 | + | 0.913541i | \(0.633337\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | − 250.290i | − 1.77510i | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 317.908i | 2.22313i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 54.6368 | 0.371679 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − 171.844i | − 1.15331i | −0.816986 | − | 0.576657i | \(-0.804357\pi\) | ||||
0.816986 | − | 0.576657i | \(-0.195643\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 30.5687i | 0.202442i | 0.994864 | + | 0.101221i | \(0.0322749\pi\) | ||||
−0.994864 | + | 0.101221i | \(0.967725\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 121.311 | 0.792881 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 265.212i | 1.68925i | 0.535357 | + | 0.844626i | \(0.320177\pi\) | ||||
−0.535357 | + | 0.844626i | \(0.679823\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | − 397.725i | − 2.50142i | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −138.652 | −0.861190 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −69.6617 | −0.427372 | −0.213686 | − | 0.976902i | \(-0.568547\pi\) | ||||
−0.213686 | + | 0.976902i | \(0.568547\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 101.140i | 0.605627i | 0.953050 | + | 0.302814i | \(0.0979259\pi\) | ||||
−0.953050 | + | 0.302814i | \(0.902074\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −82.5782 | −0.488628 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −180.388 | −1.05490 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 65.5284i | 0.378777i | 0.981902 | + | 0.189388i | \(0.0606505\pi\) | ||||
−0.981902 | + | 0.189388i | \(0.939349\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 2.55664 | 0.0144443 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 47.2688 | 0.264072 | 0.132036 | − | 0.991245i | \(-0.457849\pi\) | ||||
0.132036 | + | 0.991245i | \(0.457849\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 255.613i | 1.41223i | 0.708099 | + | 0.706113i | \(0.249553\pi\) | ||||
−0.708099 | + | 0.706113i | \(0.750447\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 311.885i | 1.70429i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −140.078 | −0.749078 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | − 265.751i | − 1.40609i | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − 67.7062i | − 0.354483i | −0.984167 | − | 0.177241i | \(-0.943283\pi\) | ||||
0.984167 | − | 0.177241i | \(-0.0567173\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 327.113 | 1.69488 | 0.847442 | − | 0.530888i | \(-0.178142\pi\) | ||||
0.847442 | + | 0.530888i | \(0.178142\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − 120.542i | − 0.611890i | −0.952049 | − | 0.305945i | \(-0.901028\pi\) | ||||
0.952049 | − | 0.305945i | \(-0.0989723\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 175.578i | 0.882302i | 0.897433 | + | 0.441151i | \(0.145430\pi\) | ||||
−0.897433 | + | 0.441151i | \(0.854570\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −423.661 | −2.10777 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −26.0470 | −0.128310 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | − 388.591i | − 1.87725i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 208.294 | 0.996621 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 237.053 | 1.12347 | 0.561737 | − | 0.827316i | \(-0.310133\pi\) | ||||
0.561737 | + | 0.827316i | \(0.310133\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | − 147.426i | − 0.692139i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 128.300 | 0.591242 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 52.2160 | 0.238429 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − 110.851i | − 0.501589i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 13.8074i | 0.0619165i | 0.999521 | + | 0.0309582i | \(0.00985589\pi\) | ||||
−0.999521 | + | 0.0309582i | \(0.990144\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 2.21412 | 0.00975382 | 0.00487691 | − | 0.999988i | \(-0.498448\pi\) | ||||
0.00487691 | + | 0.999988i | \(0.498448\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 241.756i | 1.05571i | 0.849336 | + | 0.527853i | \(0.177003\pi\) | ||||
−0.849336 | + | 0.527853i | \(0.822997\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 637.303i | 2.75889i | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −30.5119 | −0.130953 | −0.0654763 | − | 0.997854i | \(-0.520857\pi\) | ||||
−0.0654763 | + | 0.997854i | \(0.520857\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 449.625i | 1.89715i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − 426.441i | − 1.78427i | −0.451768 | − | 0.892135i | \(-0.649207\pi\) | ||||
0.451768 | − | 0.892135i | \(-0.350793\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 147.936 | 0.613842 | 0.306921 | − | 0.951735i | \(-0.400701\pi\) | ||||
0.306921 | + | 0.951735i | \(0.400701\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −57.2280 | −0.235506 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 164.835i | 0.667347i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 529.092 | 2.12487 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −97.7364 | −0.389388 | −0.194694 | − | 0.980864i | \(-0.562371\pi\) | ||||
−0.194694 | + | 0.980864i | \(0.562371\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 448.707i | 1.77354i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 354.443 | 1.37915 | 0.689577 | − | 0.724212i | \(-0.257796\pi\) | ||||
0.689577 | + | 0.724212i | \(0.257796\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −219.732 | −0.848387 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | − 73.0006i | − 0.279696i | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − 44.6039i | − 0.169597i | −0.996398 | − | 0.0847984i | \(-0.972975\pi\) | ||||
0.996398 | − | 0.0847984i | \(-0.0270246\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 253.025 | 0.947660 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 314.879i | 1.17055i | 0.810834 | + | 0.585277i | \(0.199014\pi\) | ||||
−0.810834 | + | 0.585277i | \(0.800986\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − 449.009i | − 1.65686i | −0.560092 | − | 0.828431i | \(-0.689234\pi\) | ||||
0.560092 | − | 0.828431i | \(-0.310766\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −504.334 | −1.84738 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − 330.330i | − 1.19253i | −0.802789 | − | 0.596264i | \(-0.796651\pi\) | ||||
0.802789 | − | 0.596264i | \(-0.203349\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 359.578i | 1.28881i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 307.936 | 1.09586 | 0.547929 | − | 0.836525i | \(-0.315416\pi\) | ||||
0.547929 | + | 0.836525i | \(0.315416\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −182.609 | −0.645263 | −0.322631 | − | 0.946525i | \(-0.604567\pi\) | ||||
−0.322631 | + | 0.946525i | \(0.604567\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 229.610i | 0.800033i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −240.156 | −0.830991 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −433.776 | −1.49064 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − 259.373i | − 0.885231i | −0.896711 | − | 0.442616i | \(-0.854051\pi\) | ||||
0.896711 | − | 0.442616i | \(-0.145949\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −860.027 | −2.89571 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −355.087 | −1.18758 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | − 147.606i | − 0.490385i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | − 476.379i | − 1.57221i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −209.411 | −0.682119 | −0.341060 | − | 0.940042i | \(-0.610786\pi\) | ||||
−0.341060 | + | 0.940042i | \(0.610786\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | − 219.367i | − 0.709926i | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 149.137i | 0.479542i | 0.970830 | + | 0.239771i | \(0.0770723\pi\) | ||||
−0.970830 | + | 0.239771i | \(0.922928\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −296.601 | −0.947606 | −0.473803 | − | 0.880631i | \(-0.657119\pi\) | ||||
−0.473803 | + | 0.880631i | \(0.657119\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − 23.0450i | − 0.0726971i | −0.999339 | − | 0.0363486i | \(-0.988427\pi\) | ||||
0.999339 | − | 0.0363486i | \(-0.0115727\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 84.2938i | 0.264244i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 150.652 | 0.469320 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −72.6300 | −0.224861 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | − 839.060i | − 2.56593i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −301.936 | −0.917739 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 419.665 | 1.26787 | 0.633935 | − | 0.773386i | \(-0.281439\pi\) | ||||
0.633935 | + | 0.773386i | \(0.281439\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | − 615.832i | − 1.84934i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 52.0477 | 0.154444 | 0.0772221 | − | 0.997014i | \(-0.475395\pi\) | ||||
0.0772221 | + | 0.997014i | \(0.475395\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 619.598 | 1.82772 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − 415.205i | − 1.21761i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − 369.386i | − 1.07693i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −329.706 | −0.950163 | −0.475081 | − | 0.879942i | \(-0.657581\pi\) | ||||
−0.475081 | + | 0.879942i | \(0.657581\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − 517.423i | − 1.48259i | −0.671180 | − | 0.741294i | \(-0.734212\pi\) | ||||
0.671180 | − | 0.741294i | \(-0.265788\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | − 680.588i | − 1.93900i | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −44.4337 | −0.125874 | −0.0629372 | − | 0.998017i | \(-0.520047\pi\) | ||||
−0.0629372 | + | 0.998017i | \(0.520047\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | − 222.221i | − 0.622469i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 53.1375i | 0.148015i | 0.997258 | + | 0.0740076i | \(0.0235789\pi\) | ||||
−0.997258 | + | 0.0740076i | \(0.976421\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −253.000 | −0.700831 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 1441.24 | 3.97035 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 374.954i | 1.02167i | 0.859678 | + | 0.510837i | \(0.170664\pi\) | ||||
−0.859678 | + | 0.510837i | \(0.829336\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −643.514 | −1.74394 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −479.794 | −1.29325 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − 24.6208i | − 0.0660076i | −0.999455 | − | 0.0330038i | \(-0.989493\pi\) | ||||
0.999455 | − | 0.0330038i | \(-0.0105073\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −66.7064 | −0.176940 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 170.472 | 0.449793 | 0.224897 | − | 0.974383i | \(-0.427796\pi\) | ||||
0.224897 | + | 0.974383i | \(0.427796\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 1168.31i | 3.06643i | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − 136.084i | − 0.355310i | −0.984093 | − | 0.177655i | \(-0.943149\pi\) | ||||
0.984093 | − | 0.177655i | \(-0.0568512\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 413.687 | 1.06896 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − 60.5055i | − 0.155541i | −0.996971 | − | 0.0777705i | \(-0.975220\pi\) | ||||
0.996971 | − | 0.0777705i | \(-0.0247801\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − 156.460i | − 0.400152i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −175.290 | −0.446030 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − 124.216i | − 0.312888i | −0.987687 | − | 0.156444i | \(-0.949997\pi\) | ||||
0.987687 | − | 0.156444i | \(-0.0500030\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 330.441i | 0.828172i | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 46.7156 | 0.116498 | 0.0582489 | − | 0.998302i | \(-0.481448\pi\) | ||||
0.0582489 | + | 0.998302i | \(0.481448\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 328.575 | 0.815323 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 711.101i | 1.74718i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −582.377 | −1.42390 | −0.711952 | − | 0.702228i | \(-0.752189\pi\) | ||||
−0.711952 | + | 0.702228i | \(0.752189\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 1112.01 | 2.70562 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − 3.08420i | − 0.00746779i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −580.530 | −1.39216 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 479.296 | 1.14391 | 0.571953 | − | 0.820287i | \(-0.306186\pi\) | ||||
0.571953 | + | 0.820287i | \(0.306186\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 116.905i | 0.277685i | 0.990314 | + | 0.138842i | \(0.0443381\pi\) | ||||
−0.990314 | + | 0.138842i | \(0.955662\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | − 846.220i | − 2.00052i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 376.241 | 0.881126 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 1632.13i | 3.80451i | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 204.460i | 0.474384i | 0.971463 | + | 0.237192i | \(0.0762271\pi\) | ||||
−0.971463 | + | 0.237192i | \(0.923773\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 403.364 | 0.931558 | 0.465779 | − | 0.884901i | \(-0.345774\pi\) | ||||
0.465779 | + | 0.884901i | \(0.345774\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 232.654i | 0.532388i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 114.275i | 0.260307i | 0.991494 | + | 0.130154i | \(0.0415471\pi\) | ||||
−0.991494 | + | 0.130154i | \(0.958453\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 184.725 | 0.418878 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −750.268 | −1.69361 | −0.846803 | − | 0.531906i | \(-0.821476\pi\) | ||||
−0.846803 | + | 0.531906i | \(0.821476\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | − 882.244i | − 1.97370i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 554.377 | 1.23469 | 0.617346 | − | 0.786692i | \(-0.288208\pi\) | ||||
0.617346 | + | 0.786692i | \(0.288208\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 743.066 | 1.64760 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 156.939i | 0.346445i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 870.823 | 1.90552 | 0.952760 | − | 0.303724i | \(-0.0982301\pi\) | ||||
0.952760 | + | 0.303724i | \(0.0982301\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 299.883 | 0.653340 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 37.3636i | 0.0810490i | 0.999179 | + | 0.0405245i | \(0.0129029\pi\) | ||||
−0.999179 | + | 0.0405245i | \(0.987097\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − 228.189i | − 0.492849i | −0.969162 | − | 0.246424i | \(-0.920744\pi\) | ||||
0.969162 | − | 0.246424i | \(-0.0792557\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 414.441 | 0.887455 | 0.443727 | − | 0.896162i | \(-0.353656\pi\) | ||||
0.443727 | + | 0.896162i | \(0.353656\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 511.082i | 1.08973i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 1361.60i | 2.89086i | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −477.685 | −1.00990 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | − 1344.69i | − 2.81906i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 871.744i | 1.81992i | 0.414691 | + | 0.909962i | \(0.363890\pi\) | ||||
−0.414691 | + | 0.909962i | \(0.636110\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −562.735 | −1.16993 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −711.836 | −1.47378 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 316.431i | 0.649756i | 0.945756 | + | 0.324878i | \(0.105323\pi\) | ||||
−0.945756 | + | 0.324878i | \(0.894677\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −357.642 | −0.731375 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −372.142 | −0.757927 | −0.378963 | − | 0.925412i | \(-0.623719\pi\) | ||||
−0.378963 | + | 0.925412i | \(0.623719\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − 29.3924i | − 0.0596195i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −177.847 | −0.357840 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 198.184 | 0.397163 | 0.198582 | − | 0.980084i | \(-0.436367\pi\) | ||||
0.198582 | + | 0.980084i | \(0.436367\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 519.250i | 1.03643i | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 638.202i | 1.26879i | 0.773009 | + | 0.634395i | \(0.218751\pi\) | ||||
−0.773009 | + | 0.634395i | \(0.781249\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −423.955 | −0.836204 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − 58.6571i | − 0.115240i | −0.998339 | − | 0.0576199i | \(-0.981649\pi\) | ||||
0.998339 | − | 0.0576199i | \(-0.0183512\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − 62.9906i | − 0.123269i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −445.923 | −0.869245 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 977.130i | 1.89000i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 336.422i | 0.648212i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 171.431 | 0.329043 | 0.164521 | − | 0.986374i | \(-0.447392\pi\) | ||||
0.164521 | + | 0.986374i | \(0.447392\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 407.751 | 0.779638 | 0.389819 | − | 0.920892i | \(-0.372538\pi\) | ||||
0.389819 | + | 0.920892i | \(0.372538\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 144.778i | 0.274721i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 27.8174 | 0.0525848 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 8.64391 | 0.0162786 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 588.030i | 1.10325i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 242.677 | 0.451913 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −213.302 | −0.395737 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − 144.762i | − 0.267582i | −0.991010 | − | 0.133791i | \(-0.957285\pi\) | ||||
0.991010 | − | 0.133791i | \(-0.0427150\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 1312.31i | 2.41678i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −570.627 | −1.04319 | −0.521597 | − | 0.853192i | \(-0.674663\pi\) | ||||
−0.521597 | + | 0.853192i | \(0.674663\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 1054.47i | 1.92071i | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 43.7062i | 0.0793216i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 542.404 | 0.980839 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 824.208i | 1.47973i | 0.672757 | + | 0.739864i | \(0.265110\pi\) | ||||
−0.672757 | + | 0.739864i | \(0.734890\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − 378.019i | − 0.676241i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −719.156 | −1.28192 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 216.333 | 0.384251 | 0.192125 | − | 0.981370i | \(-0.438462\pi\) | ||||
0.192125 | + | 0.981370i | \(0.438462\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | − 396.831i | − 0.699877i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 468.230 | 0.822899 | 0.411450 | − | 0.911432i | \(-0.365023\pi\) | ||||
0.411450 | + | 0.911432i | \(0.365023\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −759.434 | −1.33001 | −0.665004 | − | 0.746840i | \(-0.731570\pi\) | ||||
−0.665004 | + | 0.746840i | \(0.731570\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − 347.603i | − 0.606636i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −29.2057 | −0.0506164 | −0.0253082 | − | 0.999680i | \(-0.508057\pi\) | ||||
−0.0253082 | + | 0.999680i | \(0.508057\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 1679.39 | 2.90050 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | − 638.269i | − 1.09857i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 1552.72i | 2.66332i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −1014.74 | −1.72869 | −0.864345 | − | 0.502900i | \(-0.832266\pi\) | ||||
−0.864345 | + | 0.502900i | \(0.832266\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − 215.283i | − 0.365506i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | − 618.863i | − 1.04714i | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 835.823 | 1.40948 | 0.704741 | − | 0.709465i | \(-0.251063\pi\) | ||||
0.704741 | + | 0.709465i | \(0.251063\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 901.416i | 1.50991i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − 851.616i | − 1.42173i | −0.703329 | − | 0.710865i | \(-0.748304\pi\) | ||||
0.703329 | − | 0.710865i | \(-0.251696\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −618.377 | −1.02891 | −0.514456 | − | 0.857516i | \(-0.672006\pi\) | ||||
−0.514456 | + | 0.857516i | \(0.672006\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −1432.38 | −2.37543 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 182.393i | 0.300483i | 0.988649 | + | 0.150241i | \(0.0480051\pi\) | ||||
−0.988649 | + | 0.150241i | \(0.951995\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −133.725 | −0.219581 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −773.258 | −1.26556 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − 638.630i | − 1.04181i | −0.853614 | − | 0.520906i | \(-0.825594\pi\) | ||||
0.853614 | − | 0.520906i | \(-0.174406\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 416.661 | 0.675301 | 0.337651 | − | 0.941271i | \(-0.390368\pi\) | ||||
0.337651 | + | 0.941271i | \(0.390368\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 1090.24 | 1.76129 | 0.880646 | − | 0.473775i | \(-0.157109\pi\) | ||||
0.880646 | + | 0.473775i | \(0.157109\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | − 960.607i | − 1.54687i | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − 305.236i | − 0.489946i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 1069.38 | 1.70555 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − 247.954i | − 0.394204i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 574.569i | 0.910569i | 0.890346 | + | 0.455284i | \(0.150462\pi\) | ||||
−0.890346 | + | 0.455284i | \(0.849538\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 1217.03 | 1.92263 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − 168.798i | − 0.264989i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | − 498.441i | − 0.780032i | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 893.367 | 1.39371 | 0.696854 | − | 0.717213i | \(-0.254582\pi\) | ||||
0.696854 | + | 0.717213i | \(0.254582\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −675.801 | −1.05101 | −0.525506 | − | 0.850790i | \(-0.676124\pi\) | ||||
−0.525506 | + | 0.850790i | \(0.676124\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − 737.921i | − 1.14053i | −0.821462 | − | 0.570263i | \(-0.806841\pi\) | ||||
0.821462 | − | 0.570263i | \(-0.193159\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −9.98113 | −0.0153792 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 658.688 | 1.01181 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 771.853i | 1.18201i | 0.806668 | + | 0.591005i | \(0.201269\pi\) | ||||
−0.806668 | + | 0.591005i | \(0.798731\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 176.540 | 0.268707 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −814.838 | −1.23648 | −0.618238 | − | 0.785991i | \(-0.712153\pi\) | ||||
−0.618238 | + | 0.785991i | \(0.712153\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 1038.13i | 1.57055i | 0.619146 | + | 0.785276i | \(0.287479\pi\) | ||||
−0.619146 | + | 0.785276i | \(0.712521\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | − 569.109i | − 0.858384i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −94.1519 | −0.141157 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 70.8869i | 0.105959i | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − 1217.60i | − 1.81460i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −367.795 | −0.546501 | −0.273250 | − | 0.961943i | \(-0.588099\pi\) | ||||
−0.273250 | + | 0.961943i | \(0.588099\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 463.978i | 0.685344i | 0.939455 | + | 0.342672i | \(0.111332\pi\) | ||||
−0.939455 | + | 0.342672i | \(0.888668\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 523.284i | 0.770669i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 11.3673 | 0.0166920 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 632.563 | 0.926154 | 0.463077 | − | 0.886318i | \(-0.346745\pi\) | ||||
0.463077 | + | 0.886318i | \(0.346745\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 1241.17i | 1.80666i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −1228.75 | −1.78339 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 436.001 | 0.630970 | 0.315485 | − | 0.948930i | \(-0.397833\pi\) | ||||
0.315485 | + | 0.948930i | \(0.397833\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 2154.70i | 3.10923i | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −259.100 | −0.371736 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −156.648 | −0.224103 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − 364.085i | − 0.519380i | −0.965692 | − | 0.259690i | \(-0.916380\pi\) | ||||
0.965692 | − | 0.259690i | \(-0.0836203\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 368.705i | 0.524474i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −574.678 | −0.812840 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 789.593i | 1.11367i | 0.830622 | + | 0.556836i | \(0.187985\pi\) | ||||
−0.830622 | + | 0.556836i | \(0.812015\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 1520.17i | 2.13807i | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 463.763 | 0.650439 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | − 2189.34i | − 3.05347i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | − 168.422i | − 0.234245i | −0.993118 | − | 0.117122i | \(-0.962633\pi\) | ||||
0.993118 | − | 0.117122i | \(-0.0373669\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −264.633 | −0.367036 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 759.501 | 1.05049 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 382.568i | 0.526229i | 0.964765 | + | 0.263114i | \(0.0847496\pi\) | ||||
−0.964765 | + | 0.263114i | \(0.915250\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −870.469 | −1.19406 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 166.564 | 0.227858 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − 74.5492i | − 0.101704i | −0.998706 | − | 0.0508521i | \(-0.983806\pi\) | ||||
0.998706 | − | 0.0508521i | \(-0.0161937\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 1653.97 | 2.24420 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −682.206 | −0.923148 | −0.461574 | − | 0.887102i | \(-0.652715\pi\) | ||||
−0.461574 | + | 0.887102i | \(0.652715\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 846.259i | 1.14205i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 359.274i | 0.483545i | 0.970333 | + | 0.241772i | \(0.0777287\pi\) | ||||
−0.970333 | + | 0.241772i | \(0.922271\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 1788.84 | 2.39470 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − 181.738i | − 0.242641i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 532.038i | 0.708439i | 0.935162 | + | 0.354220i | \(0.115253\pi\) | ||||
−0.935162 | + | 0.354220i | \(0.884747\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −501.777 | −0.666371 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 444.854i | 0.587653i | 0.955859 | + | 0.293827i | \(0.0949288\pi\) | ||||
−0.955859 | + | 0.293827i | \(0.905071\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 2303.65i | 3.03512i | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −244.735 | −0.321596 | −0.160798 | − | 0.986987i | \(-0.551407\pi\) | ||||
−0.160798 | + | 0.986987i | \(0.551407\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −1012.20 | −1.32660 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − 7.89863i | − 0.0102981i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 1131.73 | 1.47168 | 0.735842 | − | 0.677153i | \(-0.236787\pi\) | ||||
0.735842 | + | 0.677153i | \(0.236787\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 1819.70 | 2.36019 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − 294.508i | − 0.380994i | −0.981688 | − | 0.190497i | \(-0.938990\pi\) | ||||
0.981688 | − | 0.190497i | \(-0.0610099\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −1128.10 | −1.45187 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 385.279 | 0.494581 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 575.550i | 0.736939i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | − 180.459i | − 0.230471i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −1017.00 | −1.29225 | −0.646127 | − | 0.763230i | \(-0.723612\pi\) | ||||
−0.646127 | + | 0.763230i | \(0.723612\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | − 228.996i | − 0.290236i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − 747.450i | − 0.944943i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 963.553 | 1.21507 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − 1105.61i | − 1.38722i | −0.720353 | − | 0.693608i | \(-0.756020\pi\) | ||||
0.720353 | − | 0.693608i | \(-0.243980\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − 340.716i | − 0.426428i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 855.469 | 1.06800 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −203.851 | −0.253862 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 1616.58i | 2.00320i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 594.881 | 0.735329 | 0.367665 | − | 0.929958i | \(-0.380157\pi\) | ||||
0.367665 | + | 0.929958i | \(0.380157\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −45.3204 | −0.0558822 | −0.0279411 | − | 0.999610i | \(-0.508895\pi\) | ||||
−0.0279411 | + | 0.999610i | \(0.508895\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − 2305.21i | − 2.83543i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −247.679 | −0.303156 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −1705.13 | −2.08197 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 310.208i | 0.377842i | 0.981992 | + | 0.188921i | \(0.0604989\pi\) | ||||
−0.981992 | + | 0.188921i | \(0.939501\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − 660.022i | − 0.801971i | −0.916084 | − | 0.400985i | \(-0.868668\pi\) | ||||
0.916084 | − | 0.400985i | \(-0.131332\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 168.339 | 0.203553 | 0.101777 | − | 0.994807i | \(-0.467547\pi\) | ||||
0.101777 | + | 0.994807i | \(0.467547\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 597.939i | 0.721278i | 0.932706 | + | 0.360639i | \(0.117441\pi\) | ||||
−0.932706 | + | 0.360639i | \(0.882559\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | − 1695.91i | − 2.04081i | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 74.3764 | 0.0892873 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 888.885i | 1.06199i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 1113.51i | 1.32718i | 0.748095 | + | 0.663592i | \(0.230969\pi\) | ||||
−0.748095 | + | 0.663592i | \(0.769031\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 823.313 | 0.978969 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 1580.94 | 1.87537 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − 1738.63i | − 2.05270i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −937.514 | −1.10426 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −794.264 | −0.933331 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − 889.393i | − 1.04266i | −0.853354 | − | 0.521332i | \(-0.825435\pi\) | ||||
0.853354 | − | 0.521332i | \(-0.174565\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −1246.97 | −1.45504 | −0.727520 | − | 0.686087i | \(-0.759327\pi\) | ||||
−0.727520 | + | 0.686087i | \(0.759327\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 977.927 | 1.13845 | 0.569224 | − | 0.822182i | \(-0.307244\pi\) | ||||
0.569224 | + | 0.822182i | \(0.307244\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 1178.81i | 1.36912i | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − 1366.41i | − 1.58332i | −0.610961 | − | 0.791661i | \(-0.709217\pi\) | ||||
0.610961 | − | 0.791661i | \(-0.290783\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −1232.96 | −1.42210 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − 1755.34i | − 2.01995i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1308.88i | 1.50273i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −1466.58 | −1.67993 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 87.0797i | 0.0992927i | 0.998767 | + | 0.0496464i | \(0.0158094\pi\) | ||||
−0.998767 | + | 0.0496464i | \(0.984191\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | − 1331.62i | − 1.51492i | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 154.927 | 0.175853 | 0.0879265 | − | 0.996127i | \(-0.471976\pi\) | ||||
0.0879265 | + | 0.996127i | \(0.471976\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 1604.11 | 1.81666 | 0.908332 | − | 0.418249i | \(-0.137356\pi\) | ||||
0.908332 | + | 0.418249i | \(0.137356\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − 196.767i | − 0.221834i | −0.993830 | − | 0.110917i | \(-0.964621\pi\) | ||||
0.993830 | − | 0.110917i | \(-0.0353788\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1409.39 | 1.58536 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −1284.23 | −1.44133 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 506.640i | 0.567346i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −1823.01 | −2.03234 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 87.1223 | 0.0969102 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − 541.418i | − 0.600907i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | − 757.807i | − 0.839210i | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 1079.04 | 1.18968 | 0.594838 | − | 0.803845i | \(-0.297216\pi\) | ||||
0.594838 | + | 0.803845i | \(0.297216\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | − 1610.62i | − 1.77186i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − 1815.91i | − 1.99331i | −0.0816953 | − | 0.996657i | \(-0.526033\pi\) | ||||
0.0816953 | − | 0.996657i | \(-0.473967\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −2065.58 | −2.26241 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 211.460i | 0.230600i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − 437.303i | − 0.475847i | −0.971284 | − | 0.237923i | \(-0.923533\pi\) | ||||
0.971284 | − | 0.237923i | \(-0.0764667\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −1075.11 | −1.16733 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −455.465 | −0.493461 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | − 741.672i | − 0.800077i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 164.320 | 0.176878 | 0.0884392 | − | 0.996082i | \(-0.471812\pi\) | ||||
0.0884392 | + | 0.996082i | \(0.471812\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −110.597 | −0.118794 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 765.670i | 0.820654i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 1238.62 | 1.32190 | 0.660949 | − | 0.750431i | \(-0.270154\pi\) | ||||
0.660949 | + | 0.750431i | \(0.270154\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −1522.74 | −1.62167 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − 1846.13i | − 1.96188i | −0.194299 | − | 0.980942i | \(-0.562243\pi\) | ||||
0.194299 | − | 0.980942i | \(-0.437757\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 829.967i | 0.880135i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 466.767 | 0.492890 | 0.246445 | − | 0.969157i | \(-0.420737\pi\) | ||||
0.246445 | + | 0.969157i | \(0.420737\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − 161.319i | − 0.169988i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | − 118.313i | − 0.124409i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −1316.75 | −1.38168 | −0.690842 | − | 0.723006i | \(-0.742760\pi\) | ||||
−0.690842 | + | 0.723006i | \(0.742760\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 432.763i | 0.452208i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | − 1341.47i | − 1.39882i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 531.863 | 0.553447 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 509.347 | 0.528917 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − 572.176i | − 0.591702i | −0.955234 | − | 0.295851i | \(-0.904397\pi\) | ||||
0.955234 | − | 0.295851i | \(-0.0956033\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −372.881 | −0.384811 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −881.863 | −0.908201 | −0.454100 | − | 0.890951i | \(-0.650039\pi\) | ||||
−0.454100 | + | 0.890951i | \(0.650039\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 700.320i | 0.719754i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −512.461 | −0.524525 | −0.262263 | − | 0.964997i | \(-0.584469\pi\) | ||||
−0.262263 | + | 0.964997i | \(0.584469\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −987.811 | −1.00900 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | − 2836.83i | − 2.89178i | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − 1665.68i | − 1.69448i | −0.531209 | − | 0.847241i | \(-0.678262\pi\) | ||||
0.531209 | − | 0.847241i | \(-0.321738\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −1550.14 | −1.57055 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − 533.550i | − 0.539484i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1696.66i | 1.71207i | 0.516916 | + | 0.856036i | \(0.327080\pi\) | ||||
−0.516916 | + | 0.856036i | \(0.672920\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 2154.56 | 2.16974 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − 1405.45i | − 1.40968i | −0.709367 | − | 0.704840i | \(-0.751019\pi\) | ||||
0.709367 | − | 0.704840i | \(-0.248981\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | − 1522.35i | − 1.52387i |
(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 | 1600.3.g.k.351.13 | 16 | ||
4.3 | odd | 2 | inner | 1600.3.g.k.351.4 | 16 | ||
5.2 | odd | 4 | 320.3.e.b.159.2 | yes | 16 | ||
5.3 | odd | 4 | 320.3.e.b.159.16 | yes | 16 | ||
5.4 | even | 2 | inner | 1600.3.g.k.351.3 | 16 | ||
8.3 | odd | 2 | inner | 1600.3.g.k.351.15 | 16 | ||
8.5 | even | 2 | inner | 1600.3.g.k.351.2 | 16 | ||
20.3 | even | 4 | 320.3.e.b.159.4 | yes | 16 | ||
20.7 | even | 4 | 320.3.e.b.159.14 | yes | 16 | ||
20.19 | odd | 2 | inner | 1600.3.g.k.351.14 | 16 | ||
40.3 | even | 4 | 320.3.e.b.159.13 | yes | 16 | ||
40.13 | odd | 4 | 320.3.e.b.159.1 | ✓ | 16 | ||
40.19 | odd | 2 | inner | 1600.3.g.k.351.1 | 16 | ||
40.27 | even | 4 | 320.3.e.b.159.3 | yes | 16 | ||
40.29 | even | 2 | inner | 1600.3.g.k.351.16 | 16 | ||
40.37 | odd | 4 | 320.3.e.b.159.15 | yes | 16 | ||
80.3 | even | 4 | 1280.3.h.n.1279.15 | 16 | |||
80.13 | odd | 4 | 1280.3.h.n.1279.3 | 16 | |||
80.27 | even | 4 | 1280.3.h.n.1279.13 | 16 | |||
80.37 | odd | 4 | 1280.3.h.n.1279.1 | 16 | |||
80.43 | even | 4 | 1280.3.h.n.1279.2 | 16 | |||
80.53 | odd | 4 | 1280.3.h.n.1279.14 | 16 | |||
80.67 | even | 4 | 1280.3.h.n.1279.4 | 16 | |||
80.77 | odd | 4 | 1280.3.h.n.1279.16 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
320.3.e.b.159.1 | ✓ | 16 | 40.13 | odd | 4 | ||
320.3.e.b.159.2 | yes | 16 | 5.2 | odd | 4 | ||
320.3.e.b.159.3 | yes | 16 | 40.27 | even | 4 | ||
320.3.e.b.159.4 | yes | 16 | 20.3 | even | 4 | ||
320.3.e.b.159.13 | yes | 16 | 40.3 | even | 4 | ||
320.3.e.b.159.14 | yes | 16 | 20.7 | even | 4 | ||
320.3.e.b.159.15 | yes | 16 | 40.37 | odd | 4 | ||
320.3.e.b.159.16 | yes | 16 | 5.3 | odd | 4 | ||
1280.3.h.n.1279.1 | 16 | 80.37 | odd | 4 | |||
1280.3.h.n.1279.2 | 16 | 80.43 | even | 4 | |||
1280.3.h.n.1279.3 | 16 | 80.13 | odd | 4 | |||
1280.3.h.n.1279.4 | 16 | 80.67 | even | 4 | |||
1280.3.h.n.1279.13 | 16 | 80.27 | even | 4 | |||
1280.3.h.n.1279.14 | 16 | 80.53 | odd | 4 | |||
1280.3.h.n.1279.15 | 16 | 80.3 | even | 4 | |||
1280.3.h.n.1279.16 | 16 | 80.77 | odd | 4 | |||
1600.3.g.k.351.1 | 16 | 40.19 | odd | 2 | inner | ||
1600.3.g.k.351.2 | 16 | 8.5 | even | 2 | inner | ||
1600.3.g.k.351.3 | 16 | 5.4 | even | 2 | inner | ||
1600.3.g.k.351.4 | 16 | 4.3 | odd | 2 | inner | ||
1600.3.g.k.351.13 | 16 | 1.1 | even | 1 | trivial | ||
1600.3.g.k.351.14 | 16 | 20.19 | odd | 2 | inner | ||
1600.3.g.k.351.15 | 16 | 8.3 | odd | 2 | inner | ||
1600.3.g.k.351.16 | 16 | 40.29 | even | 2 | inner |