Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1280,3,Mod(1279,1280)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1280, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1280.1279");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1280 = 2^{8} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 1280.h (of order \(2\), degree \(1\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(34.8774738381\) |
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: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{34} \) |
Twist minimal: | no (minimal twist has level 320) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1279.14 | ||
Root | \(-0.940543 + 1.62907i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1280.1279 |
Dual form | 1280.3.h.n.1279.13 |
$q$-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 \(\left(\mathbb{Z}/1280\mathbb{Z}\right)^\times\).
\(n\) | \(257\) | \(261\) | \(511\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(-1\) |
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 | ||||||||
\(5\) | −4.14474 | + | 2.79662i | −0.828949 | + | 0.559324i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 6.19337 | 0.884767 | 0.442383 | − | 0.896826i | \(-0.354133\pi\) | ||||
0.442383 | + | 0.896826i | \(0.354133\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 17.3578 | 1.92865 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − | 20.0431i | − | 1.82210i | −0.412298 | − | 0.911049i | \(-0.635274\pi\) | ||
0.412298 | − | 0.911049i | \(-0.364726\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 15.8612i | − | 1.22009i | −0.792365 | − | 0.610047i | \(-0.791151\pi\) | ||
0.792365 | − | 0.610047i | \(-0.208849\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −21.2791 | + | 14.3578i | −1.41860 | + | 0.957188i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − | 6.98882i | − | 0.411107i | −0.978646 | − | 0.205554i | \(-0.934100\pi\) | ||
0.978646 | − | 0.205554i | \(-0.0658995\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 10.3923i | − | 0.546963i | −0.961877 | − | 0.273482i | \(-0.911825\pi\) | ||
0.961877 | − | 0.273482i | \(-0.0881753\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 31.7967 | 1.51413 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −22.3871 | −0.973353 | −0.486676 | − | 0.873582i | \(-0.661791\pi\) | ||||
−0.486676 | + | 0.873582i | \(0.661791\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 9.35782 | − | 23.1826i | 0.374313 | − | 0.927303i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 42.9089 | 1.58922 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 4.20563 | 0.145022 | 0.0725109 | − | 0.997368i | \(-0.476899\pi\) | ||||
0.0725109 | + | 0.997368i | \(0.476899\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 20.7156i | 0.668246i | 0.942529 | + | 0.334123i | \(0.108440\pi\) | ||||
−0.942529 | + | 0.334123i | \(0.891560\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | − | 102.901i | − | 3.11821i | ||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −25.6699 | + | 17.3205i | −0.733427 | + | 0.494872i | ||||
\(36\) | 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 | \(-0.350670\pi\) | ||||
0.452115 | + | 0.891960i | \(0.350670\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −23.8329 | −0.554254 | −0.277127 | − | 0.960833i | \(-0.589382\pi\) | ||||
−0.277127 | + | 0.960833i | \(0.589382\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −71.9437 | + | 48.5432i | −1.59875 | + | 1.07874i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −48.7515 | −1.03727 | −0.518633 | − | 0.854997i | \(-0.673559\pi\) | ||||
−0.518633 | + | 0.854997i | \(0.673559\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −10.6422 | −0.217187 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | − | 35.8805i | − | 0.703540i | ||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 77.4691i | 1.46168i | 0.682549 | + | 0.730840i | \(0.260872\pi\) | ||||
−0.682549 | + | 0.730840i | \(0.739128\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 56.0529 | + | 83.0735i | 1.01914 | + | 1.51043i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − | 53.3540i | − | 0.936034i | ||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − | 0.497984i | − | 0.00844041i | −0.999991 | − | 0.00422020i | \(-0.998657\pi\) | ||
0.999991 | − | 0.00422020i | \(-0.00134334\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 60.7490 | 0.995885 | 0.497943 | − | 0.867210i | \(-0.334089\pi\) | ||||
0.497943 | + | 0.867210i | \(0.334089\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 107.503 | 1.70640 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 44.3578 | + | 65.7407i | 0.682428 | + | 1.01140i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 82.5209 | 1.23165 | 0.615827 | − | 0.787881i | \(-0.288822\pi\) | ||||
0.615827 | + | 0.787881i | \(0.288822\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −114.935 | −1.66573 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 28.7156i | 0.404446i | 0.979340 | + | 0.202223i | \(0.0648165\pi\) | ||||
−0.979340 | + | 0.202223i | \(0.935183\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 10.1706i | − | 0.139324i | −0.997571 | − | 0.0696620i | \(-0.977808\pi\) | ||
0.997571 | − | 0.0696620i | \(-0.0221921\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 48.0429 | − | 119.019i | 0.640572 | − | 1.58692i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − | 124.134i | − | 1.61213i | ||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 87.5782i | − | 1.10858i | −0.832322 | − | 0.554292i | \(-0.812989\pi\) | ||
0.832322 | − | 0.554292i | \(-0.187011\pi\) | |||||||
\(80\) | 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 | ||||||||
\(85\) | 19.5451 | + | 28.9669i | 0.229942 | + | 0.340787i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 21.5917 | 0.248180 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 49.2844 | 0.553757 | 0.276878 | − | 0.960905i | \(-0.410700\pi\) | ||||
0.276878 | + | 0.960905i | \(0.410700\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − | 98.2344i | − | 1.07950i | ||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 106.354i | 1.14359i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 29.0633 | + | 43.0735i | 0.305930 | + | 0.453405i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 84.4911i | 0.871042i | 0.900179 | + | 0.435521i | \(0.143436\pi\) | ||||
−0.900179 | + | 0.435521i | \(0.856564\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | − | 347.904i | − | 3.51418i | ||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 92.7892 | 0.918705 | 0.459353 | − | 0.888254i | \(-0.348081\pi\) | ||||
0.459353 | + | 0.888254i | \(0.348081\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −42.7284 | −0.414839 | −0.207419 | − | 0.978252i | \(-0.566506\pi\) | ||||
−0.207419 | + | 0.978252i | \(0.566506\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −131.789 | + | 88.9233i | −1.25513 | + | 0.846888i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 29.3440 | 0.274243 | 0.137121 | − | 0.990554i | \(-0.456215\pi\) | ||||
0.137121 | + | 0.990554i | \(0.456215\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 163.433 | 1.49938 | 0.749691 | − | 0.661789i | \(-0.230202\pi\) | ||||
0.749691 | + | 0.661789i | \(0.230202\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | − | 182.147i | − | 1.64096i | ||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 120.686i | 1.06801i | 0.845480 | + | 0.534007i | \(0.179314\pi\) | ||||
−0.845480 | + | 0.534007i | \(0.820686\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 92.7888 | − | 62.6083i | 0.806860 | − | 0.544420i | ||||
\(116\) | 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 | ||||||||
\(125\) | 26.0471 | + | 122.256i | 0.208377 | + | 0.978049i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 227.564 | 1.79184 | 0.895920 | − | 0.444215i | \(-0.146517\pi\) | ||||
0.895920 | + | 0.444215i | \(0.146517\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −122.358 | −0.948510 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 34.1430i | 0.260634i | 0.991472 | + | 0.130317i | \(0.0415995\pi\) | ||||
−0.991472 | + | 0.130317i | \(0.958401\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − | 64.3634i | − | 0.483935i | ||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −177.847 | + | 120.000i | −1.31738 | + | 0.888889i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 216.598i | 1.58100i | 0.612459 | + | 0.790502i | \(0.290180\pi\) | ||||
−0.612459 | + | 0.790502i | \(0.709820\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 113.076i | 0.813495i | 0.913541 | + | 0.406748i | \(0.133337\pi\) | ||||
−0.913541 | + | 0.406748i | \(0.866663\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −250.290 | −1.77510 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −317.908 | −2.22313 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −17.4313 | + | 11.7616i | −0.120216 | + | 0.0811142i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −54.6368 | −0.371679 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −171.844 | −1.15331 | −0.576657 | − | 0.816986i | \(-0.695643\pi\) | ||||
−0.576657 | + | 0.816986i | \(0.695643\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 30.5687i | − | 0.202442i | −0.994864 | − | 0.101221i | \(-0.967725\pi\) | ||
0.994864 | − | 0.101221i | \(-0.0322749\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | − | 121.311i | − | 0.792881i | ||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −57.9338 | − | 85.8610i | −0.373766 | − | 0.553942i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 265.212i | − | 1.68925i | −0.535357 | − | 0.844626i | \(-0.679823\pi\) | ||
0.535357 | − | 0.844626i | \(-0.320177\pi\) | |||||||
\(158\) | 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 | ||||||||
\(165\) | 287.775 | + | 426.498i | 1.74409 | + | 2.58484i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −101.140 | −0.605627 | −0.302814 | − | 0.953050i | \(-0.597926\pi\) | ||||
−0.302814 | + | 0.953050i | \(0.597926\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −82.5782 | −0.488628 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | − | 180.388i | − | 1.05490i | ||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 65.5284i | 0.378777i | 0.981902 | + | 0.189388i | \(0.0606505\pi\) | ||||
−0.981902 | + | 0.189388i | \(0.939349\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 57.9564 | − | 143.578i | 0.331179 | − | 0.820447i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | − | 2.55664i | − | 0.0144443i | ||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 47.2688i | 0.264072i | 0.991245 | + | 0.132036i | \(0.0421514\pi\) | ||||
−0.991245 | + | 0.132036i | \(0.957849\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −255.613 | −1.41223 | −0.706113 | − | 0.708099i | \(-0.749553\pi\) | ||||
−0.706113 | + | 0.708099i | \(0.749553\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 311.885 | 1.70429 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 99.2204 | + | 147.050i | 0.536326 | + | 0.794865i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −140.078 | −0.749078 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 265.751 | 1.40609 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 67.7062i | − | 0.354483i | −0.984167 | − | 0.177241i | \(-0.943283\pi\) | ||
0.984167 | − | 0.177241i | \(-0.0567173\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 327.113i | 1.69488i | 0.530888 | + | 0.847442i | \(0.321858\pi\) | ||||
−0.530888 | + | 0.847442i | \(0.678142\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 227.732 | + | 337.512i | 1.16786 | + | 1.73083i | ||||
\(196\) | 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 | ||||||||
\(205\) | −153.660 | + | 103.680i | −0.749561 | + | 0.505758i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −388.591 | −1.87725 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −208.294 | −0.996621 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 237.053i | − | 1.12347i | −0.827316 | − | 0.561737i | \(-0.810133\pi\) | ||
0.827316 | − | 0.561737i | \(-0.189867\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 147.426i | 0.692139i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 98.7813 | − | 66.6516i | 0.459448 | − | 0.310008i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 128.300i | 0.591242i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | − | 52.2160i | − | 0.238429i | ||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −110.851 | −0.501589 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −13.8074 | −0.0619165 | −0.0309582 | − | 0.999521i | \(-0.509856\pi\) | ||||
−0.0309582 | + | 0.999521i | \(0.509856\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 162.431 | − | 402.399i | 0.721917 | − | 1.78844i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −2.21412 | −0.00975382 | −0.00487691 | − | 0.999988i | \(-0.501552\pi\) | ||||
−0.00487691 | + | 0.999988i | \(0.501552\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 241.756 | 1.05571 | 0.527853 | − | 0.849336i | \(-0.322997\pi\) | ||||
0.527853 | + | 0.849336i | \(0.322997\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | − | 637.303i | − | 2.75889i | ||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 30.5119i | 0.130953i | 0.997854 | + | 0.0654763i | \(0.0208567\pi\) | ||||
−0.997854 | + | 0.0654763i | \(0.979143\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 202.062 | − | 136.339i | 0.859840 | − | 0.580168i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | − | 449.625i | − | 1.89715i | ||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 426.441i | 1.78427i | 0.451768 | + | 0.892135i | \(0.350793\pi\) | ||||
−0.451768 | + | 0.892135i | \(0.649207\pi\) | |||||||
\(240\) | 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 | ||||||||
\(245\) | 44.1091 | − | 29.7622i | 0.180037 | − | 0.121478i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −164.835 | −0.667347 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 529.092 | 2.12487 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 97.7364i | − | 0.389388i | −0.980864 | − | 0.194694i | \(-0.937629\pi\) | ||
0.980864 | − | 0.194694i | \(-0.0623714\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 448.707i | 1.77354i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 100.344 | + | 148.716i | 0.393507 | + | 0.583199i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − | 354.443i | − | 1.37915i | −0.724212 | − | 0.689577i | \(-0.757796\pi\) | ||
0.724212 | − | 0.689577i | \(-0.242204\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − | 219.732i | − | 0.848387i | ||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 73.0006 | 0.279696 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −44.6039 | −0.169597 | −0.0847984 | − | 0.996398i | \(-0.527025\pi\) | ||||
−0.0847984 | + | 0.996398i | \(0.527025\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −216.652 | − | 321.089i | −0.817553 | − | 1.21166i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 253.025 | 0.947660 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −314.879 | −1.17055 | −0.585277 | − | 0.810834i | \(-0.699014\pi\) | ||||
−0.585277 | + | 0.810834i | \(0.699014\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 449.009i | − | 1.65686i | −0.560092 | − | 0.828431i | \(-0.689234\pi\) | ||
0.560092 | − | 0.828431i | \(-0.310766\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | − | 504.334i | − | 1.84738i | ||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −464.650 | − | 187.559i | −1.68964 | − | 0.682034i | ||||
\(276\) | 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 | \(-0.684584\pi\) | ||||
−0.547929 | + | 0.836525i | \(0.684584\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 182.609 | 0.645263 | 0.322631 | − | 0.946525i | \(-0.395433\pi\) | ||||
0.322631 | + | 0.946525i | \(0.395433\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 149.211 | + | 221.139i | 0.523547 | + | 0.775925i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 229.610 | 0.800033 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 240.156 | 0.830991 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 433.776i | 1.49064i | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 259.373i | 0.885231i | 0.896711 | + | 0.442616i | \(0.145949\pi\) | ||||
−0.896711 | + | 0.442616i | \(0.854051\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 1.39267 | + | 2.06402i | 0.00472092 | + | 0.00699667i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | − | 860.027i | − | 2.89571i | ||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 355.087i | 1.18758i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −147.606 | −0.490385 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 476.379 | 1.57221 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −251.789 | + | 169.892i | −0.825538 | + | 0.557023i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 209.411 | 0.682119 | 0.341060 | − | 0.940042i | \(-0.389214\pi\) | ||||
0.341060 | + | 0.940042i | \(0.389214\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −219.367 | −0.709926 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 149.137i | − | 0.479542i | −0.970830 | − | 0.239771i | \(-0.922928\pi\) | ||
0.970830 | − | 0.239771i | \(-0.0770723\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 296.601i | 0.947606i | 0.880631 | + | 0.473803i | \(0.157119\pi\) | ||||
−0.880631 | + | 0.473803i | \(0.842881\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −445.574 | + | 300.646i | −1.41452 | + | 0.954432i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 23.0450i | 0.0726971i | 0.999339 | + | 0.0363486i | \(0.0115727\pi\) | ||||
−0.999339 | + | 0.0363486i | \(0.988427\pi\) | |||||||
\(318\) | 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 | ||||||||
\(325\) | −367.704 | − | 148.426i | −1.13140 | − | 0.456696i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 839.060 | 2.56593 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −301.936 | −0.917739 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 419.665i | 1.26787i | 0.773386 | + | 0.633935i | \(0.218561\pi\) | ||||
−0.773386 | + | 0.633935i | \(0.781439\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | − | 615.832i | − | 1.84934i | ||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −342.028 | + | 230.780i | −1.02098 | + | 0.688894i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 52.0477i | − | 0.154444i | −0.997014 | − | 0.0772221i | \(-0.975395\pi\) | ||
0.997014 | − | 0.0772221i | \(-0.0246050\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 619.598i | 1.82772i | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 415.205 | 1.21761 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −369.386 | −1.07693 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 476.377 | − | 321.430i | 1.38080 | − | 0.931681i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −329.706 | −0.950163 | −0.475081 | − | 0.879942i | \(-0.657581\pi\) | ||||
−0.475081 | + | 0.879942i | \(0.657581\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 517.423 | 1.48259 | 0.741294 | − | 0.671180i | \(-0.234212\pi\) | ||||
0.741294 | + | 0.671180i | \(0.234212\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | − | 680.588i | − | 1.93900i | ||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − | 44.4337i | − | 0.125874i | −0.998017 | − | 0.0629372i | \(-0.979953\pi\) | ||
0.998017 | − | 0.0629372i | \(-0.0200468\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −80.3068 | − | 119.019i | −0.226216 | − | 0.335265i | ||||
\(356\) | 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 | ||||||||
\(365\) | 28.4434 | + | 42.1547i | 0.0779273 | + | 0.115492i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 374.954 | 1.02167 | 0.510837 | − | 0.859678i | \(-0.329336\pi\) | ||||
0.510837 | + | 0.859678i | \(0.329336\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 643.514 | 1.74394 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 479.794i | 1.29325i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 24.6208i | 0.0660076i | 0.999455 | + | 0.0330038i | \(0.0105073\pi\) | ||||
−0.999455 | + | 0.0330038i | \(0.989493\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 133.725 | + | 627.661i | 0.356601 | + | 1.67376i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 66.7064i | − | 0.176940i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 170.472i | − | 0.449793i | −0.974383 | − | 0.224897i | \(-0.927796\pi\) | ||
0.974383 | − | 0.224897i | \(-0.0722044\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 1168.31 | 3.06643 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 136.084 | 0.355310 | 0.177655 | − | 0.984093i | \(-0.443149\pi\) | ||||
0.177655 | + | 0.984093i | \(0.443149\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 347.156 | + | 514.505i | 0.901705 | + | 1.33638i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −413.687 | −1.06896 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −60.5055 | −0.155541 | −0.0777705 | − | 0.996971i | \(-0.524780\pi\) | ||||
−0.0777705 | + | 0.996971i | \(0.524780\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 156.460i | 0.400152i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 175.290i | 0.446030i | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 244.923 | + | 362.989i | 0.620058 | + | 0.918960i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 124.216i | 0.312888i | 0.987687 | + | 0.156444i | \(0.0500030\pi\) | ||||
−0.987687 | + | 0.156444i | \(0.949997\pi\) | |||||||
\(398\) | 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 | ||||||||
\(405\) | −265.568 | + | 179.189i | −0.655724 | + | 0.442442i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −711.101 | −1.74718 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −582.377 | −1.42390 | −0.711952 | − | 0.702228i | \(-0.752189\pi\) | ||||
−0.711952 | + | 0.702228i | \(0.752189\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 1112.01i | 2.70562i | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − | 3.08420i | − | 0.00746779i | ||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −427.144 | + | 288.211i | −1.02926 | + | 0.694484i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 580.530i | 1.39216i | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 479.296i | 1.14391i | 0.820287 | + | 0.571953i | \(0.193814\pi\) | ||||
−0.820287 | + | 0.571953i | \(0.806186\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −116.905 | −0.277685 | −0.138842 | − | 0.990314i | \(-0.544338\pi\) | ||||
−0.138842 | + | 0.990314i | \(0.544338\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −846.220 | −2.00052 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −162.019 | − | 65.4001i | −0.381221 | − | 0.153883i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 376.241 | 0.881126 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −1632.13 | −3.80451 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 204.460i | 0.474384i | 0.971463 | + | 0.237192i | \(0.0762271\pi\) | ||||
−0.971463 | + | 0.237192i | \(0.923773\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 403.364i | 0.931558i | 0.884901 | + | 0.465779i | \(0.154226\pi\) | ||||
−0.884901 | + | 0.465779i | \(0.845774\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −89.4919 | + | 60.3837i | −0.205728 | + | 0.138813i | ||||
\(436\) | 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 | \(-0.178524\pi\) | ||||
0.846803 | + | 0.531906i | \(0.178524\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −204.271 | + | 137.830i | −0.459036 | + | 0.309730i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −882.244 | −1.97370 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −554.377 | −1.23469 | −0.617346 | − | 0.786692i | \(-0.711792\pi\) | ||||
−0.617346 | + | 0.786692i | \(0.711792\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 743.066i | − | 1.64760i | ||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | − | 156.939i | − | 0.346445i | ||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 274.724 | + | 407.156i | 0.603790 | + | 0.894849i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 870.823i | 1.90552i | 0.303724 | + | 0.952760i | \(0.401770\pi\) | ||||
−0.303724 | + | 0.952760i | \(0.598230\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | − | 299.883i | − | 0.653340i | ||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 37.3636 | 0.0810490 | 0.0405245 | − | 0.999179i | \(-0.487097\pi\) | ||||
0.0405245 | + | 0.999179i | \(0.487097\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 228.189 | 0.492849 | 0.246424 | − | 0.969162i | \(-0.420744\pi\) | ||||
0.246424 | + | 0.969162i | \(0.420744\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −297.431 | − | 440.809i | −0.639637 | − | 0.947977i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −414.441 | −0.887455 | −0.443727 | − | 0.896162i | \(-0.646344\pi\) | ||||
−0.443727 | + | 0.896162i | \(0.646344\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 511.082 | 1.08973 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | − | 1361.60i | − | 2.89086i | ||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 477.685i | 1.00990i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −240.920 | − | 97.2493i | −0.507201 | − | 0.204735i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 1344.69i | 2.81906i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | − | 871.744i | − | 1.81992i | −0.414691 | − | 0.909962i | \(-0.636110\pi\) | ||
0.414691 | − | 0.909962i | \(-0.363890\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −562.735 | −1.16993 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −711.836 | −1.47378 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −236.290 | − | 350.194i | −0.487195 | − | 0.722049i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −316.431 | −0.649756 | −0.324878 | − | 0.945756i | \(-0.605323\pi\) | ||||
−0.324878 | + | 0.945756i | \(0.605323\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −357.642 | −0.731375 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 372.142i | − | 0.757927i | −0.925412 | − | 0.378963i | \(-0.876281\pi\) | ||
0.925412 | − | 0.378963i | \(-0.123719\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 29.3924i | − | 0.0596195i | ||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 972.956 | + | 1441.97i | 1.96557 | + | 2.91308i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 177.847i | 0.357840i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 198.184i | 0.397163i | 0.980084 | + | 0.198582i | \(0.0636335\pi\) | ||||
−0.980084 | + | 0.198582i | \(0.936367\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −519.250 | −1.03643 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 638.202 | 1.26879 | 0.634395 | − | 0.773009i | \(-0.281249\pi\) | ||||
0.634395 | + | 0.773009i | \(0.281249\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −384.588 | + | 259.496i | −0.761560 | + | 0.513854i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −423.955 | −0.836204 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 58.6571 | 0.115240 | 0.0576199 | − | 0.998339i | \(-0.481649\pi\) | ||||
0.0576199 | + | 0.998339i | \(0.481649\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − | 62.9906i | − | 0.123269i | ||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | − | 445.923i | − | 0.869245i | ||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 177.098 | − | 119.495i | 0.343880 | − | 0.232029i | ||||
\(516\) | 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 | \(-0.552608\pi\) | ||||
−0.164521 | + | 0.986374i | \(0.552608\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −407.751 | −0.779638 | −0.389819 | − | 0.920892i | \(-0.627462\pi\) | ||||
−0.389819 | + | 0.920892i | \(0.627462\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 297.547 | − | 737.128i | 0.566757 | − | 1.40405i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 144.778 | 0.274721 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −27.8174 | −0.0525848 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − | 8.64391i | − | 0.0162786i | ||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 588.030i | − | 1.10325i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −121.623 | + | 82.0640i | −0.227333 | + | 0.153391i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 242.677i | 0.451913i | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 213.302i | 0.395737i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −144.762 | −0.267582 | −0.133791 | − | 0.991010i | \(-0.542715\pi\) | ||||
−0.133791 | + | 0.991010i | \(0.542715\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −1312.31 | −2.41678 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −677.386 | + | 457.059i | −1.24291 | + | 0.838640i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 570.627 | 1.04319 | 0.521597 | − | 0.853192i | \(-0.325337\pi\) | ||||
0.521597 | + | 0.853192i | \(0.325337\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 1054.47 | 1.92071 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 43.7062i | − | 0.0793216i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − | 542.404i | − | 0.980839i | ||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 509.396 | + | 754.952i | 0.917831 | + | 1.36027i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − | 824.208i | − | 1.47973i | −0.672757 | − | 0.739864i | \(-0.734890\pi\) | ||
0.672757 | − | 0.739864i | \(-0.265110\pi\) | |||||||
\(558\) | 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 | ||||||||
\(565\) | −337.512 | − | 500.211i | −0.597366 | − | 0.885329i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 396.831 | 0.699877 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 468.230 | 0.822899 | 0.411450 | − | 0.911432i | \(-0.365023\pi\) | ||||
0.411450 | + | 0.911432i | \(0.365023\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 759.434i | − | 1.33001i | −0.746840 | − | 0.665004i | \(-0.768430\pi\) | ||
0.746840 | − | 0.665004i | \(-0.231570\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − | 347.603i | − | 0.606636i | ||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −209.494 | + | 518.991i | −0.364338 | + | 0.902592i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 29.2057i | 0.0506164i | 0.999680 | + | 0.0253082i | \(0.00805671\pi\) | ||||
−0.999680 | + | 0.0253082i | \(0.991943\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 1679.39i | 2.90050i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 638.269 | 1.09857 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 1552.72 | 2.66332 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 769.955 | + | 1141.11i | 1.31616 | + | 1.95062i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −1014.74 | −1.72869 | −0.864345 | − | 0.502900i | \(-0.832266\pi\) | ||||
−0.864345 | + | 0.502900i | \(0.832266\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 215.283 | 0.365506 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | − | 618.863i | − | 1.04714i | ||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 835.823i | 1.40948i | 0.709465 | + | 0.704741i | \(0.248937\pi\) | ||||
−0.709465 | + | 0.704741i | \(0.751063\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 121.050 | + | 179.403i | 0.203445 | + | 0.301517i | ||||
\(596\) | 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 | \(-0.327994\pi\) | ||||
0.514456 | + | 0.857516i | \(0.327994\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 1432.38 | 2.37543 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 1163.53 | − | 785.082i | 1.92320 | − | 1.29766i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 182.393 | 0.300483 | 0.150241 | − | 0.988649i | \(-0.451995\pi\) | ||||
0.150241 | + | 0.988649i | \(0.451995\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 133.725 | 0.219581 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 773.258i | 1.26556i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 638.630i | 1.04181i | 0.853614 | + | 0.520906i | \(0.174406\pi\) | ||||
−0.853614 | + | 0.520906i | \(0.825594\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −788.888 | + | 532.294i | −1.28275 | + | 0.865518i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 416.661i | 0.675301i | 0.941271 | + | 0.337651i | \(0.109632\pi\) | ||||
−0.941271 | + | 0.337651i | \(0.890368\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 1090.24i | − | 1.76129i | −0.473775 | − | 0.880646i | \(-0.657109\pi\) | ||
0.473775 | − | 0.880646i | \(-0.342891\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −960.607 | −1.54687 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 305.236 | 0.489946 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −449.863 | − | 433.876i | −0.719780 | − | 0.694202i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −1069.38 | −1.70555 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −247.954 | −0.394204 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 574.569i | − | 0.910569i | −0.890346 | − | 0.455284i | \(-0.849538\pi\) | ||
0.890346 | − | 0.455284i | \(-0.150462\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | − | 1217.03i | − | 1.92263i | ||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −943.194 | + | 636.410i | −1.48534 | + | 1.00222i | ||||
\(636\) | 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 | ||||||||
\(645\) | 507.142 | − | 342.188i | 0.786267 | − | 0.530525i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 737.921 | 1.14053 | 0.570263 | − | 0.821462i | \(-0.306841\pi\) | ||||
0.570263 | + | 0.821462i | \(0.306841\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −9.98113 | −0.0153792 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 658.688i | 1.01181i | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 771.853i | 1.18201i | 0.806668 | + | 0.591005i | \(0.201269\pi\) | ||||
−0.806668 | + | 0.591005i | \(0.798731\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −95.4851 | − | 141.514i | −0.145779 | − | 0.216052i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | − | 176.540i | − | 0.268707i | ||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 814.838i | − | 1.23648i | −0.785991 | − | 0.618238i | \(-0.787847\pi\) | ||
0.785991 | − | 0.618238i | \(-0.212153\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −1038.13 | −1.57055 | −0.785276 | − | 0.619146i | \(-0.787479\pi\) | ||||
−0.785276 | + | 0.619146i | \(0.787479\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −569.109 | −0.858384 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 180.000 | + | 266.770i | 0.270677 | + | 0.401158i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −94.1519 | −0.141157 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −70.8869 | −0.105959 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 1217.60i | − | 1.81460i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 367.795i | − | 0.546501i | −0.961943 | − | 0.273250i | \(-0.911901\pi\) | ||
0.961943 | − | 0.273250i | \(-0.0880988\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 401.534 | − | 994.739i | 0.594865 | − | 1.47369i | ||||
\(676\) | 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 | \(-0.653255\pi\) | ||||
−0.463077 | + | 0.886318i | \(0.653255\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −605.742 | − | 897.742i | −0.884294 | − | 1.31057i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 1241.17 | 1.80666 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 1228.75 | 1.78339 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 436.001i | − | 0.630970i | −0.948930 | − | 0.315485i | \(-0.897833\pi\) | ||
0.948930 | − | 0.315485i | \(-0.102167\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | − | 2154.70i | − | 3.10923i | ||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −316.230 | − | 468.670i | −0.455008 | − | 0.674346i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 259.100i | − | 0.371736i | ||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 156.648i | 0.224103i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −364.085 | −0.519380 | −0.259690 | − | 0.965692i | \(-0.583620\pi\) | ||||
−0.259690 | + | 0.965692i | \(0.583620\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −368.705 | −0.524474 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 1037.39 | − | 699.965i | 1.47147 | − | 0.992858i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 574.678 | 0.812840 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 789.593 | 1.11367 | 0.556836 | − | 0.830622i | \(-0.312015\pi\) | ||||
0.556836 | + | 0.830622i | \(0.312015\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | − | 1520.17i | − | 2.13807i | ||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 463.763i | − | 0.650439i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1317.65 | − | 889.067i | 1.84286 | − | 1.24345i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 2189.34i | 3.05347i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 168.422i | 0.234245i | 0.993118 | + | 0.117122i | \(0.0373669\pi\) | ||||
−0.993118 | + | 0.117122i | \(0.962633\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −264.633 | −0.367036 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 759.501 | 1.05049 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 39.3555 | − | 97.4973i | 0.0542835 | − | 0.134479i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −382.568 | −0.526229 | −0.263114 | − | 0.964765i | \(-0.584750\pi\) | ||||
−0.263114 | + | 0.964765i | \(0.584750\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −870.469 | −1.19406 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 166.564i | 0.227858i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 74.5492i | − | 0.101704i | −0.998706 | − | 0.0508521i | \(-0.983806\pi\) | ||
0.998706 | − | 0.0508521i | \(-0.0161937\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 226.456 | − | 152.799i | 0.308103 | − | 0.207889i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − | 1653.97i | − | 2.24420i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 682.206i | − | 0.923148i | −0.887102 | − | 0.461574i | \(-0.847285\pi\) | ||
0.887102 | − | 0.461574i | \(-0.152715\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −846.259 | −1.14205 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 359.274 | 0.483545 | 0.241772 | − | 0.970333i | \(-0.422271\pi\) | ||||
0.241772 | + | 0.970333i | \(0.422271\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 712.249 | − | 480.582i | 0.956038 | − | 0.645077i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 1788.84 | 2.39470 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 181.738 | 0.242641 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 532.038i | 0.708439i | 0.935162 | + | 0.354220i | \(0.115253\pi\) | ||||
−0.935162 | + | 0.354220i | \(0.884747\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | − | 501.777i | − | 0.666371i | ||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 85.4892 | + | 126.700i | 0.113231 | + | 0.167814i | ||||
\(756\) | 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 | \(-0.448593\pi\) | ||||
0.160798 | + | 0.986987i | \(0.448593\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 1012.20 | 1.32660 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 339.260 | + | 502.802i | 0.443477 | + | 0.657258i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −7.89863 | −0.0102981 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −1131.73 | −1.47168 | −0.735842 | − | 0.677153i | \(-0.763213\pi\) | ||||
−0.735842 | + | 0.677153i | \(0.763213\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | − | 1819.70i | − | 2.36019i | ||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 294.508i | 0.380994i | 0.981688 | + | 0.190497i | \(0.0610099\pi\) | ||||
−0.981688 | + | 0.190497i | \(0.938990\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 480.241 | + | 193.853i | 0.619666 | + | 0.250133i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | − | 1128.10i | − | 1.45187i | ||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | − | 385.279i | − | 0.494581i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 575.550 | 0.736939 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 180.459 | 0.230471 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 741.699 | + | 1099.24i | 0.944839 | + | 1.40030i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 1017.00 | 1.29225 | 0.646127 | − | 0.763230i | \(-0.276388\pi\) | ||||
0.646127 | + | 0.763230i | \(0.276388\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −228.996 | −0.290236 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 747.450i | 0.944943i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 963.553i | − | 1.21507i | ||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −1112.29 | − | 1648.47i | −1.39910 | − | 2.07355i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 1105.61i | 1.38722i | 0.720353 | + | 0.693608i | \(0.243980\pi\) | ||||
−0.720353 | + | 0.693608i | \(0.756020\pi\) | |||||||
\(798\) | 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 | ||||||||
\(805\) | 574.676 | − | 387.756i | 0.713883 | − | 0.481685i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −1616.58 | −2.00320 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 594.881 | 0.735329 | 0.367665 | − | 0.929958i | \(-0.380157\pi\) | ||||
0.367665 | + | 0.929958i | \(0.380157\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 45.3204i | − | 0.0558822i | −0.999610 | − | 0.0279411i | \(-0.991105\pi\) | ||
0.999610 | − | 0.0279411i | \(-0.00889508\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − | 2305.21i | − | 2.83543i | ||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 288.730 | − | 194.817i | 0.354270 | − | 0.239040i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 247.679i | 0.303156i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | − | 1705.13i | − | 2.08197i | ||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −310.208 | −0.377842 | −0.188921 | − | 0.981992i | \(-0.560499\pi\) | ||||
−0.188921 | + | 0.981992i | \(0.560499\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −660.022 | −0.801971 | −0.400985 | − | 0.916084i | \(-0.631332\pi\) | ||||
−0.400985 | + | 0.916084i | \(0.631332\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −2385.51 | − | 962.928i | −2.89152 | − | 1.16719i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 168.339 | 0.203553 | 0.101777 | − | 0.994807i | \(-0.467547\pi\) | ||||
0.101777 | + | 0.994807i | \(0.467547\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −597.939 | −0.721278 | −0.360639 | − | 0.932706i | \(-0.617441\pi\) | ||||
−0.360639 | + | 0.932706i | \(0.617441\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | − | 1695.91i | − | 2.04081i | ||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 74.3764i | 0.0892873i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 419.198 | − | 282.849i | 0.502034 | − | 0.338742i | ||||
\(836\) | 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 | ||||||||
\(845\) | 342.265 | − | 230.940i | 0.405048 | − | 0.273302i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −1738.63 | −2.05270 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 937.514 | 1.10426 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 794.264i | 0.933331i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 889.393i | 1.04266i | 0.853354 | + | 0.521332i | \(0.174565\pi\) | ||||
−0.853354 | + | 0.521332i | \(0.825435\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 504.476 | + | 747.661i | 0.590031 | + | 0.874457i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − | 1246.97i | − | 1.45504i | −0.686087 | − | 0.727520i | \(-0.740673\pi\) | ||
0.686087 | − | 0.727520i | \(-0.259327\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 977.927i | − | 1.13845i | −0.822182 | − | 0.569224i | \(-0.807244\pi\) | ||
0.822182 | − | 0.569224i | \(-0.192756\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 1178.81 | 1.36912 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 1366.41 | 1.58332 | 0.791661 | − | 0.610961i | \(-0.209217\pi\) | ||||
0.791661 | + | 0.610961i | \(0.209217\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −183.258 | − | 271.598i | −0.211859 | − | 0.313987i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 1232.96 | 1.42210 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −1755.34 | −2.01995 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 1308.88i | − | 1.50273i | ||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 1466.58i | 1.67993i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 161.319 | + | 757.177i | 0.184365 | + | 0.865345i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − | 87.0797i | − | 0.0992927i | −0.998767 | − | 0.0496464i | \(-0.984191\pi\) | ||
0.998767 | − | 0.0496464i | \(-0.0158094\pi\) | |||||||
\(878\) | 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 | ||||||||
\(885\) | 7.14996 | + | 10.5966i | 0.00807905 | + | 0.0119736i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 196.767 | 0.221834 | 0.110917 | − | 0.993830i | \(-0.464621\pi\) | ||||
0.110917 | + | 0.993830i | \(0.464621\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1409.39 | 1.58536 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | − | 1284.23i | − | 1.44133i | ||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 506.640i | 0.567346i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −132.193 | − | 195.917i | −0.147702 | − | 0.218902i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 1823.01i | 2.03234i | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 87.1223i | 0.0969102i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 541.418 | 0.600907 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −757.807 | −0.839210 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 1059.45 | − | 714.852i | 1.17066 | − | 0.789892i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 1079.04 | 1.18968 | 0.594838 | − | 0.803845i | \(-0.297216\pi\) | ||||
0.594838 | + | 0.803845i | \(0.297216\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 1610.62 | 1.77186 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 1815.91i | − | 1.99331i | −0.0816953 | − | 0.996657i | \(-0.526033\pi\) | ||
0.0816953 | − | 0.996657i | \(-0.473967\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 2065.58i | − | 2.26241i | ||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −1292.68 | + | 872.223i | −1.41277 | + | 0.953249i | ||||
\(916\) | 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 | ||||||||
\(925\) | −822.486 | − | 332.003i | −0.889174 | − | 0.358922i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −741.672 | −0.800077 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −164.320 | −0.176878 | −0.0884392 | − | 0.996082i | \(-0.528188\pi\) | ||||
−0.0884392 | + | 0.996082i | \(0.528188\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 110.597i | 0.118794i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | − | 765.670i | − | 0.820654i | ||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 580.586 | − | 391.744i | 0.620947 | − | 0.418977i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 1238.62i | 1.32190i | 0.750431 | + | 0.660949i | \(0.229846\pi\) | ||||
−0.750431 | + | 0.660949i | \(0.770154\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 1522.74i | 1.62167i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −1846.13 | −1.96188 | −0.980942 | − | 0.194299i | \(-0.937757\pi\) | ||||
−0.980942 | + | 0.194299i | \(0.937757\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −829.967 | −0.880135 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −1101.47 | + | 743.204i | −1.16558 | + | 0.786460i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −466.767 | −0.492890 | −0.246445 | − | 0.969157i | \(-0.579263\pi\) | ||||
−0.246445 | + | 0.969157i | \(0.579263\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −161.319 | −0.169988 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 118.313i | 0.124409i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 1316.75i | 1.38168i | 0.723006 | + | 0.690842i | \(0.242760\pi\) | ||||
−0.723006 | + | 0.690842i | \(0.757240\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 189.349 | + | 280.625i | 0.198271 | + | 0.293848i | ||||
\(956\) | 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 | ||||||||
\(965\) | −914.810 | − | 1355.80i | −0.947990 | − | 1.40497i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 572.176 | 0.591702 | 0.295851 | − | 0.955234i | \(-0.404397\pi\) | ||||
0.295851 | + | 0.955234i | \(0.404397\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −372.881 | −0.384811 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 881.863i | − | 0.908201i | −0.890951 | − | 0.454100i | \(-0.849961\pi\) | ||
0.890951 | − | 0.454100i | \(-0.150039\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 700.320i | 0.719754i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −1887.79 | − | 762.019i | −1.93619 | − | 0.781558i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 512.461i | 0.524525i | 0.964997 | + | 0.262263i | \(0.0844687\pi\) | ||||
−0.964997 | + | 0.262263i | \(0.915531\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 987.811i | − | 1.00900i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 2836.83 | 2.89178 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −1665.68 | −1.69448 | −0.847241 | − | 0.531209i | \(-0.821738\pi\) | ||||
−0.847241 | + | 0.531209i | \(0.821738\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 337.111 | + | 499.617i | 0.342245 | + | 0.507225i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −1550.14 | −1.57055 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 533.550 | 0.539484 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1696.66i | 1.71207i | 0.516916 | + | 0.856036i | \(0.327080\pi\) | ||||
−0.516916 | + | 0.856036i | \(0.672920\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 2154.56i | 2.16974i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −491.026 | − | 727.727i | −0.493493 | − | 0.731384i | ||||
\(996\) | 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 | 1280.3.h.n.1279.14 | 16 | ||
4.3 | odd | 2 | inner | 1280.3.h.n.1279.2 | 16 | ||
5.4 | even | 2 | inner | 1280.3.h.n.1279.1 | 16 | ||
8.3 | odd | 2 | inner | 1280.3.h.n.1279.15 | 16 | ||
8.5 | even | 2 | inner | 1280.3.h.n.1279.3 | 16 | ||
16.3 | odd | 4 | 320.3.e.b.159.4 | yes | 16 | ||
16.5 | even | 4 | 320.3.e.b.159.1 | ✓ | 16 | ||
16.11 | odd | 4 | 320.3.e.b.159.13 | yes | 16 | ||
16.13 | even | 4 | 320.3.e.b.159.16 | yes | 16 | ||
20.19 | odd | 2 | inner | 1280.3.h.n.1279.13 | 16 | ||
40.19 | odd | 2 | inner | 1280.3.h.n.1279.4 | 16 | ||
40.29 | even | 2 | inner | 1280.3.h.n.1279.16 | 16 | ||
80.3 | even | 4 | 1600.3.g.k.351.14 | 16 | |||
80.13 | odd | 4 | 1600.3.g.k.351.3 | 16 | |||
80.19 | odd | 4 | 320.3.e.b.159.14 | yes | 16 | ||
80.27 | even | 4 | 1600.3.g.k.351.15 | 16 | |||
80.29 | even | 4 | 320.3.e.b.159.2 | yes | 16 | ||
80.37 | odd | 4 | 1600.3.g.k.351.2 | 16 | |||
80.43 | even | 4 | 1600.3.g.k.351.1 | 16 | |||
80.53 | odd | 4 | 1600.3.g.k.351.16 | 16 | |||
80.59 | odd | 4 | 320.3.e.b.159.3 | yes | 16 | ||
80.67 | even | 4 | 1600.3.g.k.351.4 | 16 | |||
80.69 | even | 4 | 320.3.e.b.159.15 | yes | 16 | ||
80.77 | odd | 4 | 1600.3.g.k.351.13 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
320.3.e.b.159.1 | ✓ | 16 | 16.5 | even | 4 | ||
320.3.e.b.159.2 | yes | 16 | 80.29 | even | 4 | ||
320.3.e.b.159.3 | yes | 16 | 80.59 | odd | 4 | ||
320.3.e.b.159.4 | yes | 16 | 16.3 | odd | 4 | ||
320.3.e.b.159.13 | yes | 16 | 16.11 | odd | 4 | ||
320.3.e.b.159.14 | yes | 16 | 80.19 | odd | 4 | ||
320.3.e.b.159.15 | yes | 16 | 80.69 | even | 4 | ||
320.3.e.b.159.16 | yes | 16 | 16.13 | even | 4 | ||
1280.3.h.n.1279.1 | 16 | 5.4 | even | 2 | inner | ||
1280.3.h.n.1279.2 | 16 | 4.3 | odd | 2 | inner | ||
1280.3.h.n.1279.3 | 16 | 8.5 | even | 2 | inner | ||
1280.3.h.n.1279.4 | 16 | 40.19 | odd | 2 | inner | ||
1280.3.h.n.1279.13 | 16 | 20.19 | odd | 2 | inner | ||
1280.3.h.n.1279.14 | 16 | 1.1 | even | 1 | trivial | ||
1280.3.h.n.1279.15 | 16 | 8.3 | odd | 2 | inner | ||
1280.3.h.n.1279.16 | 16 | 40.29 | even | 2 | inner | ||
1600.3.g.k.351.1 | 16 | 80.43 | even | 4 | |||
1600.3.g.k.351.2 | 16 | 80.37 | odd | 4 | |||
1600.3.g.k.351.3 | 16 | 80.13 | odd | 4 | |||
1600.3.g.k.351.4 | 16 | 80.67 | even | 4 | |||
1600.3.g.k.351.13 | 16 | 80.77 | odd | 4 | |||
1600.3.g.k.351.14 | 16 | 80.3 | even | 4 | |||
1600.3.g.k.351.15 | 16 | 80.27 | even | 4 | |||
1600.3.g.k.351.16 | 16 | 80.53 | odd | 4 |