Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [320,3,Mod(159,320)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(320, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("320.159");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 320 = 2^{6} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 320.e (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: | \(8.71936845953\) |
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: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 159.16 | ||
Root | \(0.265804 + 0.460386i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 320.159 |
Dual form | 320.3.e.b.159.3 |
$q$-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 \(\left(\mathbb{Z}/320\mathbb{Z}\right)^\times\).
\(n\) | \(191\) | \(257\) | \(261\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(-1\) |
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 | ||||||||
\(3\) | 5.13399i | 1.71133i | 0.517531 | + | 0.855664i | \(0.326851\pi\) | ||||
−0.517531 | + | 0.855664i | \(0.673149\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 2.79662 | + | 4.14474i | 0.559324 | + | 0.828949i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −6.19337 | −0.884767 | −0.442383 | − | 0.896826i | \(-0.645867\pi\) | ||||
−0.442383 | + | 0.896826i | \(0.645867\pi\) | |||||||
\(8\) | 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 | ||||||||
\(13\) | 15.8612 | 1.22009 | 0.610047 | − | 0.792365i | \(-0.291151\pi\) | ||||
0.610047 | + | 0.792365i | \(0.291151\pi\) | |||||||
\(14\) | 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 | ||||||||
\(19\) | 10.3923 | 0.546963 | 0.273482 | − | 0.961877i | \(-0.411825\pi\) | ||||
0.273482 | + | 0.961877i | \(0.411825\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | − | 31.7967i | − | 1.51413i | ||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 22.3871 | 0.973353 | 0.486676 | − | 0.873582i | \(-0.338209\pi\) | ||||
0.486676 | + | 0.873582i | \(0.338209\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −9.35782 | + | 23.1826i | −0.374313 | + | 0.927303i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − | 42.9089i | − | 1.58922i | ||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 4.20563i | 0.145022i | 0.997368 | + | 0.0725109i | \(0.0231012\pi\) | ||||
−0.997368 | + | 0.0725109i | \(0.976899\pi\) | |||||||
\(30\) | 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 | ||||||||
\(35\) | −17.3205 | − | 25.6699i | −0.494872 | − | 0.733427i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −35.4786 | −0.958882 | −0.479441 | − | 0.877574i | \(-0.659161\pi\) | ||||
−0.479441 | + | 0.877574i | \(0.659161\pi\) | |||||||
\(38\) | 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 | ||||||||
\(43\) | 23.8329i | 0.554254i | 0.960833 | + | 0.277127i | \(0.0893822\pi\) | ||||
−0.960833 | + | 0.277127i | \(0.910618\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −48.5432 | − | 71.9437i | −1.07874 | − | 1.59875i | ||||
\(46\) | 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 | ||||||||
\(51\) | 35.8805 | 0.703540 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 77.4691 | 1.46168 | 0.730840 | − | 0.682549i | \(-0.239128\pi\) | ||||
0.730840 | + | 0.682549i | \(0.239128\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −56.0529 | − | 83.0735i | −1.01914 | − | 1.51043i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 53.3540i | 0.936034i | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −0.497984 | −0.00844041 | −0.00422020 | − | 0.999991i | \(-0.501343\pi\) | ||||
−0.00422020 | + | 0.999991i | \(0.501343\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 60.7490i | 0.995885i | 0.867210 | + | 0.497943i | \(0.165911\pi\) | ||||
−0.867210 | + | 0.497943i | \(0.834089\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 107.503 | 1.70640 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 44.3578 | + | 65.7407i | 0.682428 | + | 1.01140i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 82.5209i | 1.23165i | 0.787881 | + | 0.615827i | \(0.211178\pi\) | ||||
−0.787881 | + | 0.615827i | \(0.788822\pi\) | |||||||
\(68\) | 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 | ||||||||
\(73\) | 10.1706i | 0.139324i | 0.997571 | + | 0.0696620i | \(0.0221921\pi\) | ||||
−0.997571 | + | 0.0696620i | \(0.977808\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −119.019 | − | 48.0429i | −1.58692 | − | 0.640572i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 124.134 | 1.61213 | ||||||||
\(78\) | 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 | ||||||||
\(83\) | 103.057i | 1.24165i | 0.783950 | + | 0.620824i | \(0.213202\pi\) | ||||
−0.783950 | + | 0.620824i | \(0.786798\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 28.9669 | − | 19.5451i | 0.340787 | − | 0.229942i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −21.5917 | −0.248180 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −49.2844 | −0.553757 | −0.276878 | − | 0.960905i | \(-0.589300\pi\) | ||||
−0.276878 | + | 0.960905i | \(0.589300\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −98.2344 | −1.07950 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −106.354 | −1.14359 | ||||||||
\(94\) | 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 | ||||||||
\(99\) | 347.904 | 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 | ||||||||
\(103\) | 42.7284 | 0.414839 | 0.207419 | − | 0.978252i | \(-0.433494\pi\) | ||||
0.207419 | + | 0.978252i | \(0.433494\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 131.789 | − | 88.9233i | 1.25513 | − | 0.846888i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − | 29.3440i | − | 0.274243i | −0.990554 | − | 0.137121i | \(-0.956215\pi\) | ||
0.990554 | − | 0.137121i | \(-0.0437851\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 163.433i | 1.49938i | 0.661789 | + | 0.749691i | \(0.269798\pi\) | ||||
−0.661789 | + | 0.749691i | \(0.730202\pi\) | |||||||
\(110\) | 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 | ||||||||
\(115\) | 62.6083 | + | 92.7888i | 0.544420 | + | 0.806860i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −275.316 | −2.35313 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 43.2844i | 0.363734i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 280.725 | 2.32004 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | − | 190.335i | − | 1.54744i | ||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −122.256 | + | 26.0471i | −0.978049 | + | 0.208377i | ||||
\(126\) | 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 | ||||||||
\(131\) | −34.1430 | −0.260634 | −0.130317 | − | 0.991472i | \(-0.541599\pi\) | ||||
−0.130317 | + | 0.991472i | \(0.541599\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −64.3634 | −0.483935 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 177.847 | − | 120.000i | 1.31738 | − | 0.888889i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − | 216.598i | − | 1.58100i | −0.612459 | − | 0.790502i | \(-0.709820\pi\) | ||
0.612459 | − | 0.790502i | \(-0.290180\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 113.076 | 0.813495 | 0.406748 | − | 0.913541i | \(-0.366663\pi\) | ||||
0.406748 | + | 0.913541i | \(0.366663\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | − | 250.290i | − | 1.77510i | ||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −317.908 | −2.22313 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −17.4313 | + | 11.7616i | −0.120216 | + | 0.0811142i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | − | 54.6368i | − | 0.371679i | ||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 171.844i | 1.15331i | 0.816986 | + | 0.576657i | \(0.195643\pi\) | ||||
−0.816986 | + | 0.576657i | \(0.804357\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 30.5687i | 0.202442i | 0.994864 | + | 0.101221i | \(0.0322749\pi\) | ||||
−0.994864 | + | 0.101221i | \(0.967725\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 121.311i | 0.792881i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −85.8610 | + | 57.9338i | −0.553942 | + | 0.373766i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 265.212 | 1.68925 | 0.844626 | − | 0.535357i | \(-0.179823\pi\) | ||||
0.844626 | + | 0.535357i | \(0.179823\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 397.725i | 2.50142i | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −138.652 | −0.861190 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 69.6617i | − | 0.427372i | −0.976902 | − | 0.213686i | \(-0.931453\pi\) | ||
0.976902 | − | 0.213686i | \(-0.0685470\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 426.498 | − | 287.775i | 2.58484 | − | 1.74409i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 101.140 | 0.605627 | 0.302814 | − | 0.953050i | \(-0.402074\pi\) | ||||
0.302814 | + | 0.953050i | \(0.402074\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 82.5782 | 0.488628 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −180.388 | −1.05490 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −65.5284 | −0.378777 | −0.189388 | − | 0.981902i | \(-0.560651\pi\) | ||||
−0.189388 | + | 0.981902i | \(0.560651\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 57.9564 | − | 143.578i | 0.331179 | − | 0.820447i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | − | 2.55664i | − | 0.0144443i | ||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −47.2688 | −0.264072 | −0.132036 | − | 0.991245i | \(-0.542151\pi\) | ||||
−0.132036 | + | 0.991245i | \(0.542151\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 255.613i | 1.41223i | 0.708099 | + | 0.706113i | \(0.249553\pi\) | ||||
−0.708099 | + | 0.706113i | \(0.750447\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −311.885 | −1.70429 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −99.2204 | − | 147.050i | −0.536326 | − | 0.794865i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 140.078i | 0.749078i | ||||||||
\(188\) | 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 | ||||||||
\(193\) | 327.113i | 1.69488i | 0.530888 | + | 0.847442i | \(0.321858\pi\) | ||||
−0.530888 | + | 0.847442i | \(0.678142\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −337.512 | + | 227.732i | −1.73083 | + | 1.16786i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −120.542 | −0.611890 | −0.305945 | − | 0.952049i | \(-0.598972\pi\) | ||||
−0.305945 | + | 0.952049i | \(0.598972\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 175.578i | − | 0.882302i | −0.897433 | − | 0.441151i | \(-0.854570\pi\) | ||
0.897433 | − | 0.441151i | \(-0.145430\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −423.661 | −2.10777 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − | 26.0470i | − | 0.128310i | ||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −103.680 | − | 153.660i | −0.505758 | − | 0.749561i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −388.591 | −1.87725 | ||||||||
\(208\) | 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 | ||||||||
\(213\) | 147.426 | 0.692139 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −98.7813 | + | 66.6516i | −0.459448 | + | 0.310008i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 128.300i | − | 0.591242i | ||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −52.2160 | −0.238429 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 110.851i | − | 0.501589i | ||||||
\(222\) | 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 | ||||||||
\(227\) | − | 2.21412i | − | 0.00975382i | −0.999988 | − | 0.00487691i | \(-0.998448\pi\) | ||
0.999988 | − | 0.00487691i | \(-0.00155238\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 241.756i | − | 1.05571i | −0.849336 | − | 0.527853i | \(-0.822997\pi\) | ||
0.849336 | − | 0.527853i | \(-0.177003\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 637.303i | 2.75889i | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 30.5119i | − | 0.130953i | −0.997854 | − | 0.0654763i | \(-0.979143\pi\) | ||
0.997854 | − | 0.0654763i | \(-0.0208567\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −136.339 | − | 202.062i | −0.580168 | − | 0.859840i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 449.625 | 1.89715 | ||||||||
\(238\) | 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 | ||||||||
\(243\) | − | 57.2280i | − | 0.235506i | ||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −29.7622 | − | 44.1091i | −0.121478 | − | 0.180037i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 164.835 | 0.667347 | ||||||||
\(248\) | 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 | ||||||||
\(253\) | −448.707 | −1.77354 | ||||||||
\(254\) | 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 | ||||||||
\(259\) | 219.732 | 0.848387 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | − | 73.0006i | − | 0.279696i | ||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 44.6039 | 0.169597 | 0.0847984 | − | 0.996398i | \(-0.472975\pi\) | ||||
0.0847984 | + | 0.996398i | \(0.472975\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 216.652 | + | 321.089i | 0.817553 | + | 1.21166i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − | 253.025i | − | 0.947660i | ||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − | 314.879i | − | 1.17055i | −0.810834 | − | 0.585277i | \(-0.800986\pi\) | ||
0.810834 | − | 0.585277i | \(-0.199014\pi\) | |||||||
\(270\) | 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 | ||||||||
\(275\) | 187.559 | − | 464.650i | 0.682034 | − | 1.68964i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −330.330 | −1.19253 | −0.596264 | − | 0.802789i | \(-0.703349\pi\) | ||||
−0.596264 | + | 0.802789i | \(0.703349\pi\) | |||||||
\(278\) | 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 | ||||||||
\(283\) | − | 182.609i | − | 0.645263i | −0.946525 | − | 0.322631i | \(-0.895433\pi\) | ||
0.946525 | − | 0.322631i | \(-0.104567\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −221.139 | + | 149.211i | −0.775925 | + | 0.523547i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 229.610 | 0.800033 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 240.156 | 0.830991 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −433.776 | −1.49064 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 259.373 | 0.885231 | 0.442616 | − | 0.896711i | \(-0.354051\pi\) | ||||
0.442616 | + | 0.896711i | \(0.354051\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −1.39267 | − | 2.06402i | −0.00472092 | − | 0.00699667i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 860.027i | 2.89571i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 355.087 | 1.18758 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | − | 147.606i | − | 0.490385i | ||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 476.379 | 1.57221 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −251.789 | + | 169.892i | −0.825538 | + | 0.557023i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 209.411i | 0.682119i | 0.940042 | + | 0.341060i | \(0.110786\pi\) | ||||
−0.940042 | + | 0.341060i | \(0.889214\pi\) | |||||||
\(308\) | 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 | ||||||||
\(313\) | − | 296.601i | − | 0.947606i | −0.880631 | − | 0.473803i | \(-0.842881\pi\) | ||
0.880631 | − | 0.473803i | \(-0.157119\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 300.646 | + | 445.574i | 0.954432 | + | 1.41452i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −23.0450 | −0.0726971 | −0.0363486 | − | 0.999339i | \(-0.511573\pi\) | ||||
−0.0363486 | + | 0.999339i | \(0.511573\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 84.2938i | − | 0.264244i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 150.652 | 0.469320 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 72.6300i | − | 0.224861i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −148.426 | + | 367.704i | −0.456696 | + | 1.13140i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −839.060 | −2.56593 | ||||||||
\(328\) | 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 | ||||||||
\(333\) | 615.832 | 1.84934 | ||||||||
\(334\) | 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 | ||||||||
\(339\) | −619.598 | −1.82772 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 415.205i | − | 1.21761i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 369.386 | 1.07693 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −476.377 | + | 321.430i | −1.38080 | + | 0.931681i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 329.706i | 0.950163i | 0.879942 | + | 0.475081i | \(0.157581\pi\) | ||||
−0.879942 | + | 0.475081i | \(0.842419\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 517.423i | 1.48259i | 0.671180 | + | 0.741294i | \(0.265788\pi\) | ||||
−0.671180 | + | 0.741294i | \(0.734212\pi\) | |||||||
\(350\) | 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 | ||||||||
\(355\) | 119.019 | − | 80.3068i | 0.335265 | − | 0.226216i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −222.221 | −0.622469 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 53.1375i | − | 0.148015i | −0.997258 | − | 0.0740076i | \(-0.976421\pi\) | ||
0.997258 | − | 0.0740076i | \(-0.0235789\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −253.000 | −0.700831 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 1441.24i | 3.97035i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −42.1547 | + | 28.4434i | −0.115492 | + | 0.0779273i | ||||
\(366\) | 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 | ||||||||
\(371\) | −479.794 | −1.29325 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 24.6208 | 0.0660076 | 0.0330038 | − | 0.999455i | \(-0.489493\pi\) | ||||
0.0330038 | + | 0.999455i | \(0.489493\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −133.725 | − | 627.661i | −0.356601 | − | 1.67376i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 66.7064i | 0.176940i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −170.472 | −0.449793 | −0.224897 | − | 0.974383i | \(-0.572204\pi\) | ||||
−0.224897 | + | 0.974383i | \(0.572204\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 1168.31i | 3.06643i | ||||||||
\(382\) | 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 | ||||||||
\(387\) | − | 413.687i | − | 1.06896i | ||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 60.5055i | 0.155541i | 0.996971 | + | 0.0777705i | \(0.0247801\pi\) | ||||
−0.996971 | + | 0.0777705i | \(0.975220\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 156.460i | − | 0.400152i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − | 175.290i | − | 0.446030i | ||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 362.989 | − | 244.923i | 0.918960 | − | 0.620058i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −124.216 | −0.312888 | −0.156444 | − | 0.987687i | \(-0.550003\pi\) | ||||
−0.156444 | + | 0.987687i | \(0.550003\pi\) | |||||||
\(398\) | 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 | ||||||||
\(403\) | 328.575i | 0.815323i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 179.189 | + | 265.568i | 0.442442 | + | 0.655724i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 711.101 | 1.74718 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 582.377 | 1.42390 | 0.711952 | − | 0.702228i | \(-0.247811\pi\) | ||||
0.711952 | + | 0.702228i | \(0.247811\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 1112.01 | 2.70562 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 3.08420 | 0.00746779 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −427.144 | + | 288.211i | −1.02926 | + | 0.694484i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 580.530i | 1.39216i | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −479.296 | −1.14391 | −0.571953 | − | 0.820287i | \(-0.693814\pi\) | ||||
−0.571953 | + | 0.820287i | \(0.693814\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 116.905i | 0.277685i | 0.990314 | + | 0.138842i | \(0.0443381\pi\) | ||||
−0.990314 | + | 0.138842i | \(0.955662\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 846.220 | 2.00052 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 162.019 | + | 65.4001i | 0.381221 | + | 0.153883i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − | 376.241i | − | 0.881126i | ||||||
\(428\) | 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 | ||||||||
\(433\) | 403.364i | 0.931558i | 0.884901 | + | 0.465779i | \(0.154226\pi\) | ||||
−0.884901 | + | 0.465779i | \(0.845774\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −60.3837 | − | 89.4919i | −0.138813 | − | 0.205728i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 232.654 | 0.532388 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 114.275i | − | 0.260307i | −0.991494 | − | 0.130154i | \(-0.958453\pi\) | ||
0.991494 | − | 0.130154i | \(-0.0415471\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 184.725 | 0.418878 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − | 750.268i | − | 1.69361i | −0.531906 | − | 0.846803i | \(-0.678524\pi\) | ||
0.531906 | − | 0.846803i | \(-0.321476\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −137.830 | − | 204.271i | −0.309730 | − | 0.459036i | ||||
\(446\) | 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 | ||||||||
\(451\) | 743.066 | 1.64760 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −156.939 | −0.346445 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −274.724 | − | 407.156i | −0.603790 | − | 0.894849i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 870.823i | − | 1.90552i | −0.303724 | − | 0.952760i | \(-0.598230\pi\) | ||
0.303724 | − | 0.952760i | \(-0.401770\pi\) | |||||||
\(458\) | 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 | ||||||||
\(463\) | 228.189 | 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 | ||||||||
\(467\) | − | 414.441i | − | 0.887455i | −0.896162 | − | 0.443727i | \(-0.853656\pi\) | ||
0.896162 | − | 0.443727i | \(-0.146344\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − | 511.082i | − | 1.08973i | ||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 1361.60i | 2.89086i | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − | 477.685i | − | 1.00990i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −97.2493 | + | 240.920i | −0.204735 | + | 0.507201i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −1344.69 | −2.81906 | ||||||||
\(478\) | 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 | ||||||||
\(483\) | − | 711.836i | − | 1.47378i | ||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −350.194 | + | 236.290i | −0.722049 | + | 0.487195i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 316.431 | 0.649756 | 0.324878 | − | 0.945756i | \(-0.394677\pi\) | ||||
0.324878 | + | 0.945756i | \(0.394677\pi\) | |||||||
\(488\) | 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 | ||||||||
\(493\) | 29.3924 | 0.0596195 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 972.956 | + | 1441.97i | 1.96557 | + | 2.91308i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 177.847i | 0.357840i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −198.184 | −0.397163 | −0.198582 | − | 0.980084i | \(-0.563633\pi\) | ||||
−0.198582 | + | 0.980084i | \(0.563633\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 519.250i | 1.03643i | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −638.202 | −1.26879 | −0.634395 | − | 0.773009i | \(-0.718751\pi\) | ||||
−0.634395 | + | 0.773009i | \(0.718751\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 384.588 | − | 259.496i | 0.761560 | − | 0.513854i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 423.955i | 0.836204i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 58.6571i | 0.115240i | 0.998339 | + | 0.0576199i | \(0.0183512\pi\) | ||||
−0.998339 | + | 0.0576199i | \(0.981649\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − | 62.9906i | − | 0.123269i | ||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | − | 445.923i | − | 0.869245i | ||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 119.495 | + | 177.098i | 0.232029 | + | 0.343880i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 977.130 | 1.89000 | ||||||||
\(518\) | 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 | ||||||||
\(523\) | 407.751i | 0.779638i | 0.920892 | + | 0.389819i | \(0.127462\pi\) | ||||
−0.920892 | + | 0.389819i | \(0.872538\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 737.128 | + | 297.547i | 1.40405 | + | 0.566757i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 144.778 | 0.274721 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −27.8174 | −0.0525848 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 8.64391 | 0.0162786 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −588.030 | −1.10325 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 121.623 | − | 82.0640i | 0.227333 | − | 0.153391i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | − | 242.677i | − | 0.451913i | ||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 213.302 | 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 | ||||||||
\(543\) | −1312.31 | −2.41678 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −677.386 | + | 457.059i | −1.24291 | + | 0.838640i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 570.627i | 1.04319i | 0.853192 | + | 0.521597i | \(0.174663\pi\) | ||||
−0.853192 | + | 0.521597i | \(0.825337\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | − | 1054.47i | − | 1.92071i | ||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 43.7062i | 0.0793216i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 542.404i | 0.980839i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 754.952 | − | 509.396i | 1.36027 | − | 0.917831i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 824.208 | 1.47973 | 0.739864 | − | 0.672757i | \(-0.234890\pi\) | ||||
0.739864 | + | 0.672757i | \(0.234890\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 378.019i | 0.676241i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −719.156 | −1.28192 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 216.333i | 0.384251i | 0.981370 | + | 0.192125i | \(0.0615380\pi\) | ||||
−0.981370 | + | 0.192125i | \(0.938462\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −500.211 | + | 337.512i | −0.885329 | + | 0.597366i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −396.831 | −0.699877 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −468.230 | −0.822899 | −0.411450 | − | 0.911432i | \(-0.634977\pi\) | ||||
−0.411450 | + | 0.911432i | \(0.634977\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −759.434 | −1.33001 | −0.665004 | − | 0.746840i | \(-0.731570\pi\) | ||||
−0.665004 | + | 0.746840i | \(0.731570\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 347.603 | 0.606636 | ||||||||
\(574\) | 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 | ||||||||
\(579\) | −1679.39 | −2.90050 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | − | 638.269i | − | 1.09857i | ||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −1552.72 | −2.66332 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −769.955 | − | 1141.11i | −1.31616 | − | 1.95062i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 1014.74i | 1.72869i | 0.502900 | + | 0.864345i | \(0.332266\pi\) | ||||
−0.502900 | + | 0.864345i | \(0.667734\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 215.283i | 0.365506i | ||||||||
\(590\) | 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 | ||||||||
\(595\) | −179.403 | + | 121.050i | −0.301517 | + | 0.203445i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 901.416 | 1.50991 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 851.616i | 1.42173i | 0.703329 | + | 0.710865i | \(0.251696\pi\) | ||||
−0.703329 | + | 0.710865i | \(0.748304\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −618.377 | −1.02891 | −0.514456 | − | 0.857516i | \(-0.672006\pi\) | ||||
−0.514456 | + | 0.857516i | \(0.672006\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − | 1432.38i | − | 2.37543i | ||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 785.082 | + | 1163.53i | 1.29766 | + | 1.92320i | ||||
\(606\) | 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 | ||||||||
\(611\) | −773.258 | −1.26556 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 638.630 | 1.04181 | 0.520906 | − | 0.853614i | \(-0.325594\pi\) | ||||
0.520906 | + | 0.853614i | \(0.325594\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 788.888 | − | 532.294i | 1.28275 | − | 0.865518i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 416.661i | − | 0.675301i | −0.941271 | − | 0.337651i | \(-0.890368\pi\) | ||
0.941271 | − | 0.337651i | \(-0.109632\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −1090.24 | −1.76129 | −0.880646 | − | 0.473775i | \(-0.842891\pi\) | ||||
−0.880646 | + | 0.473775i | \(0.842891\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | − | 960.607i | − | 1.54687i | ||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 305.236 | 0.489946 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −449.863 | − | 433.876i | −0.719780 | − | 0.694202i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | − | 1069.38i | − | 1.70555i | ||||||
\(628\) | 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 | ||||||||
\(633\) | 1217.03i | 1.92263i | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 636.410 | + | 943.194i | 1.00222 | + | 1.48534i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −168.798 | −0.264989 | ||||||||
\(638\) | 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 | ||||||||
\(643\) | − | 675.801i | − | 1.05101i | −0.850790 | − | 0.525506i | \(-0.823876\pi\) | ||
0.850790 | − | 0.525506i | \(-0.176124\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −342.188 | − | 507.142i | −0.530525 | − | 0.786267i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −737.921 | −1.14053 | −0.570263 | − | 0.821462i | \(-0.693159\pi\) | ||||
−0.570263 | + | 0.821462i | \(0.693159\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 9.98113 | 0.0153792 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 658.688 | 1.01181 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −771.853 | −1.18201 | −0.591005 | − | 0.806668i | \(-0.701269\pi\) | ||||
−0.591005 | + | 0.806668i | \(0.701269\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −95.4851 | − | 141.514i | −0.145779 | − | 0.216052i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | − | 176.540i | − | 0.268707i | ||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 814.838 | 1.23648 | 0.618238 | − | 0.785991i | \(-0.287847\pi\) | ||||
0.618238 | + | 0.785991i | \(0.287847\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 1038.13i | 1.57055i | 0.619146 | + | 0.785276i | \(0.287479\pi\) | ||||
−0.619146 | + | 0.785276i | \(0.712521\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 569.109 | 0.858384 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −180.000 | − | 266.770i | −0.270677 | − | 0.401158i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 94.1519i | 0.141157i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | − | 70.8869i | − | 0.105959i | ||||||
\(670\) | 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 | ||||||||
\(675\) | 994.739 | + | 401.534i | 1.47369 | + | 0.594865i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 463.978 | 0.685344 | 0.342672 | − | 0.939455i | \(-0.388668\pi\) | ||||
0.342672 | + | 0.939455i | \(0.388668\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − | 523.284i | − | 0.770669i | ||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 11.3673 | 0.0166920 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 632.563i | 0.926154i | 0.886318 | + | 0.463077i | \(0.153255\pi\) | ||||
−0.886318 | + | 0.463077i | \(0.846745\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 897.742 | − | 605.742i | 1.31057 | − | 0.884294i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 1241.17 | 1.80666 | ||||||||
\(688\) | 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 | ||||||||
\(693\) | −2154.70 | −3.10923 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 316.230 | + | 468.670i | 0.455008 | + | 0.674346i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 259.100i | 0.371736i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 156.648 | 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 | ||||||||
\(703\) | −368.705 | −0.524474 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 1037.39 | − | 699.965i | 1.47147 | − | 0.992858i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 574.678i | 0.812840i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − | 789.593i | − | 1.11367i | −0.830622 | − | 0.556836i | \(-0.812015\pi\) | ||
0.830622 | − | 0.556836i | \(-0.187985\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 1520.17i | 2.13807i | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 463.763i | 0.650439i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −889.067 | − | 1317.65i | −1.24345 | − | 1.84286i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −2189.34 | −3.05347 | ||||||||
\(718\) | 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 | ||||||||
\(723\) | 759.501i | 1.05049i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −97.4973 | − | 39.3555i | −0.134479 | − | 0.0542835i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 382.568 | 0.526229 | 0.263114 | − | 0.964765i | \(-0.415250\pi\) | ||||
0.263114 | + | 0.964765i | \(0.415250\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 870.469 | 1.19406 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 166.564 | 0.227858 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 74.5492 | 0.101704 | 0.0508521 | − | 0.998706i | \(-0.483806\pi\) | ||||
0.0508521 | + | 0.998706i | \(0.483806\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 226.456 | − | 152.799i | 0.308103 | − | 0.207889i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − | 1653.97i | − | 2.24420i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 682.206 | 0.923148 | 0.461574 | − | 0.887102i | \(-0.347285\pi\) | ||||
0.461574 | + | 0.887102i | \(0.347285\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 846.259i | 1.14205i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −359.274 | −0.483545 | −0.241772 | − | 0.970333i | \(-0.577729\pi\) | ||||
−0.241772 | + | 0.970333i | \(0.577729\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −712.249 | + | 480.582i | −0.956038 | + | 0.645077i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | − | 1788.84i | − | 2.39470i | ||||||
\(748\) | 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 | ||||||||
\(753\) | − | 501.777i | − | 0.666371i | ||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −126.700 | + | 85.4892i | −0.167814 | + | 0.113231i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 444.854 | 0.587653 | 0.293827 | − | 0.955859i | \(-0.405071\pi\) | ||||
0.293827 | + | 0.955859i | \(0.405071\pi\) | |||||||
\(758\) | 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 | ||||||||
\(763\) | − | 1012.20i | − | 1.32660i | ||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −502.802 | + | 339.260i | −0.657258 | + | 0.443477i | ||||
\(766\) | 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 | ||||||||
\(771\) | 1819.70 | 2.36019 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 294.508 | 0.380994 | 0.190497 | − | 0.981688i | \(-0.438990\pi\) | ||||
0.190497 | + | 0.981688i | \(0.438990\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −480.241 | − | 193.853i | −0.619666 | − | 0.250133i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 1128.10i | 1.45187i | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −385.279 | −0.494581 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 575.550i | 0.736939i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 180.459 | 0.230471 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 741.699 | + | 1099.24i | 0.944839 | + | 1.40030i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 1017.00i | 1.29225i | 0.763230 | + | 0.646127i | \(0.223612\pi\) | ||||
−0.763230 | + | 0.646127i | \(0.776388\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 228.996i | 0.290236i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 747.450i | − | 0.944943i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 963.553i | 1.21507i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −1648.47 | + | 1112.29i | −2.07355 | + | 1.39910i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −1105.61 | −1.38722 | −0.693608 | − | 0.720353i | \(-0.743980\pi\) | ||||
−0.693608 | + | 0.720353i | \(0.743980\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 340.716i | 0.426428i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 855.469 | 1.06800 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − | 203.851i | − | 0.253862i | ||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −387.756 | − | 574.676i | −0.481685 | − | 0.713883i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 1616.58 | 2.00320 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −594.881 | −0.735329 | −0.367665 | − | 0.929958i | \(-0.619843\pi\) | ||||
−0.367665 | + | 0.929958i | \(0.619843\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −45.3204 | −0.0558822 | −0.0279411 | − | 0.999610i | \(-0.508895\pi\) | ||||
−0.0279411 | + | 0.999610i | \(0.508895\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 2305.21 | 2.83543 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 288.730 | − | 194.817i | 0.354270 | − | 0.239040i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 247.679i | 0.303156i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 1705.13 | 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 | ||||||||
\(823\) | 660.022 | 0.801971 | 0.400985 | − | 0.916084i | \(-0.368668\pi\) | ||||
0.400985 | + | 0.916084i | \(0.368668\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 2385.51 | + | 962.928i | 2.89152 | + | 1.16719i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 168.339i | − | 0.203553i | −0.994807 | − | 0.101777i | \(-0.967547\pi\) | ||
0.994807 | − | 0.101777i | \(-0.0324527\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 597.939i | − | 0.721278i | −0.932706 | − | 0.360639i | \(-0.882559\pi\) | ||
0.932706 | − | 0.360639i | \(-0.117441\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | − | 1695.91i | − | 2.04081i | ||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 74.3764i | 0.0892873i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 282.849 | + | 419.198i | 0.338742 | + | 0.502034i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 888.885 | 1.06199 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − | 1113.51i | − | 1.32718i | −0.748095 | − | 0.663592i | \(-0.769031\pi\) | ||
0.748095 | − | 0.663592i | \(-0.230969\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 823.313 | 0.978969 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 1580.94i | 1.87537i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 230.940 | + | 342.265i | 0.273302 | + | 0.405048i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −1738.63 | −2.05270 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 937.514 | 1.10426 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −794.264 | −0.933331 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 889.393 | 1.04266 | 0.521332 | − | 0.853354i | \(-0.325435\pi\) | ||||
0.521332 | + | 0.853354i | \(0.325435\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −504.476 | − | 747.661i | −0.590031 | − | 0.874457i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 1246.97i | 1.45504i | 0.686087 | + | 0.727520i | \(0.259327\pi\) | ||||
−0.686087 | + | 0.727520i | \(0.740673\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −977.927 | −1.13845 | −0.569224 | − | 0.822182i | \(-0.692756\pi\) | ||||
−0.569224 | + | 0.822182i | \(0.692756\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 1178.81i | 1.36912i | ||||||||
\(862\) | 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 | ||||||||
\(867\) | 1232.96i | 1.42210i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 1755.34i | 2.01995i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1308.88i | 1.50273i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | − | 1466.58i | − | 1.67993i | ||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 757.177 | − | 161.319i | 0.865345 | − | 0.184365i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 87.0797 | 0.0992927 | 0.0496464 | − | 0.998767i | \(-0.484191\pi\) | ||||
0.0496464 | + | 0.998767i | \(0.484191\pi\) | |||||||
\(878\) | 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 | ||||||||
\(883\) | 1604.11i | 1.81666i | 0.418249 | + | 0.908332i | \(0.362644\pi\) | ||||
−0.418249 | + | 0.908332i | \(0.637356\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 10.5966 | − | 7.14996i | 0.0119736 | − | 0.00807905i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −196.767 | −0.221834 | −0.110917 | − | 0.993830i | \(-0.535379\pi\) | ||||
−0.110917 | + | 0.993830i | \(0.535379\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −1409.39 | −1.58536 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −1284.23 | −1.44133 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −506.640 | −0.567346 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −132.193 | − | 195.917i | −0.147702 | − | 0.218902i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 1823.01i | 2.03234i | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −87.1223 | −0.0969102 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 541.418i | − | 0.600907i | ||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 757.807 | 0.839210 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −1059.45 | + | 714.852i | −1.17066 | + | 0.789892i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 1079.04i | − | 1.18968i | −0.803845 | − | 0.594838i | \(-0.797216\pi\) | ||
0.803845 | − | 0.594838i | \(-0.202784\pi\) | |||||||
\(908\) | 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 | ||||||||
\(913\) | − | 2065.58i | − | 2.26241i | ||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −872.223 | − | 1292.68i | −0.953249 | − | 1.41277i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 211.460 | 0.230600 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 437.303i | 0.475847i | 0.971284 | + | 0.237923i | \(0.0764667\pi\) | ||||
−0.971284 | + | 0.237923i | \(0.923533\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −1075.11 | −1.16733 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − | 455.465i | − | 0.493461i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 332.003 | − | 822.486i | 0.358922 | − | 0.889174i | ||||
\(926\) | 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 | ||||||||
\(931\) | −110.597 | −0.118794 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −765.670 | −0.820654 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −580.586 | + | 391.744i | −0.620947 | + | 0.418977i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 1238.62i | − | 1.32190i | −0.750431 | − | 0.660949i | \(-0.770154\pi\) | ||
0.750431 | − | 0.660949i | \(-0.229846\pi\) | |||||||
\(938\) | 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 | ||||||||
\(943\) | −829.967 | −0.880135 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −1101.47 | + | 743.204i | −1.16558 | + | 0.786460i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − | 466.767i | − | 0.492890i | −0.969157 | − | 0.246445i | \(-0.920737\pi\) | ||
0.969157 | − | 0.246445i | \(-0.0792625\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 161.319i | 0.169988i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | − | 118.313i | − | 0.124409i | ||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 1316.75i | − | 1.38168i | −0.723006 | − | 0.690842i | \(-0.757240\pi\) | ||
0.723006 | − | 0.690842i | \(-0.242760\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 280.625 | − | 189.349i | 0.293848 | − | 0.198271i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 432.763 | 0.452208 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 1341.47i | 1.39882i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 531.863 | 0.553447 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 509.347i | 0.528917i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −1355.80 | + | 914.810i | −1.40497 | + | 0.947990i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −572.176 | −0.591702 | −0.295851 | − | 0.955234i | \(-0.595603\pi\) | ||||
−0.295851 | + | 0.955234i | \(0.595603\pi\) | |||||||
\(968\) | 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 | ||||||||
\(973\) | −700.320 | −0.719754 | ||||||||
\(974\) | 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 | ||||||||
\(979\) | 987.811 | 1.00900 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | − | 2836.83i | − | 2.89178i | ||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 1665.68 | 1.69448 | 0.847241 | − | 0.531209i | \(-0.178262\pi\) | ||||
0.847241 | + | 0.531209i | \(0.178262\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −337.111 | − | 499.617i | −0.342245 | − | 0.507225i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 1550.14i | 1.57055i | ||||||||
\(988\) | 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 | ||||||||
\(993\) | 2154.56i | 2.16974i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 727.727 | − | 491.026i | 0.731384 | − | 0.493493i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −1405.45 | −1.40968 | −0.704840 | − | 0.709367i | \(-0.748981\pi\) | ||||
−0.704840 | + | 0.709367i | \(0.748981\pi\) | |||||||
\(998\) | 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 | 320.3.e.b.159.16 | yes | 16 | |
4.3 | odd | 2 | inner | 320.3.e.b.159.4 | yes | 16 | |
5.2 | odd | 4 | 1600.3.g.k.351.13 | 16 | |||
5.3 | odd | 4 | 1600.3.g.k.351.3 | 16 | |||
5.4 | even | 2 | inner | 320.3.e.b.159.2 | yes | 16 | |
8.3 | odd | 2 | inner | 320.3.e.b.159.13 | yes | 16 | |
8.5 | even | 2 | inner | 320.3.e.b.159.1 | ✓ | 16 | |
16.3 | odd | 4 | 1280.3.h.n.1279.15 | 16 | |||
16.5 | even | 4 | 1280.3.h.n.1279.14 | 16 | |||
16.11 | odd | 4 | 1280.3.h.n.1279.2 | 16 | |||
16.13 | even | 4 | 1280.3.h.n.1279.3 | 16 | |||
20.3 | even | 4 | 1600.3.g.k.351.14 | 16 | |||
20.7 | even | 4 | 1600.3.g.k.351.4 | 16 | |||
20.19 | odd | 2 | inner | 320.3.e.b.159.14 | yes | 16 | |
40.3 | even | 4 | 1600.3.g.k.351.1 | 16 | |||
40.13 | odd | 4 | 1600.3.g.k.351.16 | 16 | |||
40.19 | odd | 2 | inner | 320.3.e.b.159.3 | yes | 16 | |
40.27 | even | 4 | 1600.3.g.k.351.15 | 16 | |||
40.29 | even | 2 | inner | 320.3.e.b.159.15 | yes | 16 | |
40.37 | odd | 4 | 1600.3.g.k.351.2 | 16 | |||
80.19 | odd | 4 | 1280.3.h.n.1279.4 | 16 | |||
80.29 | even | 4 | 1280.3.h.n.1279.16 | 16 | |||
80.59 | odd | 4 | 1280.3.h.n.1279.13 | 16 | |||
80.69 | even | 4 | 1280.3.h.n.1279.1 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
320.3.e.b.159.1 | ✓ | 16 | 8.5 | even | 2 | inner | |
320.3.e.b.159.2 | yes | 16 | 5.4 | even | 2 | inner | |
320.3.e.b.159.3 | yes | 16 | 40.19 | odd | 2 | inner | |
320.3.e.b.159.4 | yes | 16 | 4.3 | odd | 2 | inner | |
320.3.e.b.159.13 | yes | 16 | 8.3 | odd | 2 | inner | |
320.3.e.b.159.14 | yes | 16 | 20.19 | odd | 2 | inner | |
320.3.e.b.159.15 | yes | 16 | 40.29 | even | 2 | inner | |
320.3.e.b.159.16 | yes | 16 | 1.1 | even | 1 | trivial | |
1280.3.h.n.1279.1 | 16 | 80.69 | even | 4 | |||
1280.3.h.n.1279.2 | 16 | 16.11 | odd | 4 | |||
1280.3.h.n.1279.3 | 16 | 16.13 | even | 4 | |||
1280.3.h.n.1279.4 | 16 | 80.19 | odd | 4 | |||
1280.3.h.n.1279.13 | 16 | 80.59 | odd | 4 | |||
1280.3.h.n.1279.14 | 16 | 16.5 | even | 4 | |||
1280.3.h.n.1279.15 | 16 | 16.3 | odd | 4 | |||
1280.3.h.n.1279.16 | 16 | 80.29 | even | 4 | |||
1600.3.g.k.351.1 | 16 | 40.3 | even | 4 | |||
1600.3.g.k.351.2 | 16 | 40.37 | odd | 4 | |||
1600.3.g.k.351.3 | 16 | 5.3 | odd | 4 | |||
1600.3.g.k.351.4 | 16 | 20.7 | even | 4 | |||
1600.3.g.k.351.13 | 16 | 5.2 | odd | 4 | |||
1600.3.g.k.351.14 | 16 | 20.3 | even | 4 | |||
1600.3.g.k.351.15 | 16 | 40.27 | even | 4 | |||
1600.3.g.k.351.16 | 16 | 40.13 | odd | 4 |