Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [784,5,Mod(97,784)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(784, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 1]))
N = Newforms(chi, 5, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("784.97");
S:= CuspForms(chi, 5);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 784 = 2^{4} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 5 \) |
Character orbit: | \([\chi]\) | \(=\) | 784.c (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: | \(81.0420510577\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | 4.0.2048.2 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 4x^{2} + 2 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 98) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 97.2 | ||
Root | \(1.84776i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 784.97 |
Dual form | 784.5.c.a.97.3 |
$q$-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 \(\left(\mathbb{Z}/784\mathbb{Z}\right)^\times\).
\(n\) | \(197\) | \(687\) | \(689\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | − 2.03347i | − 0.225941i | −0.993598 | − | 0.112970i | \(-0.963963\pi\) | ||||
0.993598 | − | 0.112970i | \(-0.0360365\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.710974i | 0.0284390i | 0.999899 | + | 0.0142195i | \(0.00452635\pi\) | ||||
−0.999899 | + | 0.0142195i | \(0.995474\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 76.8650 | 0.948951 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −151.664 | −1.25342 | −0.626711 | − | 0.779252i | \(-0.715599\pi\) | ||||
−0.626711 | + | 0.779252i | \(0.715599\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 260.864i | 1.54358i | 0.635880 | + | 0.771788i | \(0.280637\pi\) | ||||
−0.635880 | + | 0.771788i | \(0.719363\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.44574 | 0.00642552 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − 385.598i | − 1.33425i | −0.744946 | − | 0.667125i | \(-0.767525\pi\) | ||||
0.744946 | − | 0.667125i | \(-0.232475\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − 390.140i | − 1.08072i | −0.841434 | − | 0.540360i | \(-0.818288\pi\) | ||||
0.841434 | − | 0.540360i | \(-0.181712\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 177.647 | 0.335816 | 0.167908 | − | 0.985803i | \(-0.446299\pi\) | ||||
0.167908 | + | 0.985803i | \(0.446299\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 624.495 | 0.999191 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − 321.013i | − 0.440348i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −320.887 | −0.381554 | −0.190777 | − | 0.981633i | \(-0.561101\pi\) | ||||
−0.190777 | + | 0.981633i | \(0.561101\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1346.37i | 1.40101i | 0.713646 | + | 0.700506i | \(0.247042\pi\) | ||||
−0.713646 | + | 0.700506i | \(0.752958\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 308.404i | 0.283199i | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −797.088 | −0.582241 | −0.291121 | − | 0.956686i | \(-0.594028\pi\) | ||||
−0.291121 | + | 0.956686i | \(0.594028\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 530.459 | 0.348757 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 815.856i | 0.485340i | 0.970109 | + | 0.242670i | \(0.0780232\pi\) | ||||
−0.970109 | + | 0.242670i | \(0.921977\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2167.70 | 1.17236 | 0.586182 | − | 0.810179i | \(-0.300630\pi\) | ||||
0.586182 | + | 0.810179i | \(0.300630\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 54.6490i | 0.0269872i | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 4285.61i | 1.94007i | 0.242970 | + | 0.970034i | \(0.421878\pi\) | ||||
−0.242970 | + | 0.970034i | \(0.578122\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −784.102 | −0.301462 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −3171.57 | −1.12907 | −0.564536 | − | 0.825408i | \(-0.690945\pi\) | ||||
−0.564536 | + | 0.825408i | \(0.690945\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − 107.829i | − 0.0356460i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −793.337 | −0.244179 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − 4706.39i | − 1.35202i | −0.736891 | − | 0.676012i | \(-0.763707\pi\) | ||||
0.736891 | − | 0.676012i | \(-0.236293\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − 2534.78i | − 0.681209i | −0.940207 | − | 0.340604i | \(-0.889368\pi\) | ||||
0.940207 | − | 0.340604i | \(-0.110632\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −185.468 | −0.0438977 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 4092.43 | 0.911657 | 0.455828 | − | 0.890068i | \(-0.349343\pi\) | ||||
0.455828 | + | 0.890068i | \(0.349343\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | − 361.239i | − 0.0758746i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 2255.28 | 0.447388 | 0.223694 | − | 0.974659i | \(-0.428188\pi\) | ||||
0.223694 | + | 0.974659i | \(0.428188\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − 4653.19i | − 0.873183i | −0.899660 | − | 0.436591i | \(-0.856186\pi\) | ||||
0.899660 | − | 0.436591i | \(-0.143814\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | − 1269.89i | − 0.225758i | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 4193.74 | 0.671965 | 0.335983 | − | 0.941868i | \(-0.390932\pi\) | ||||
0.335983 | + | 0.941868i | \(0.390932\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 5573.29 | 0.849458 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 7799.12i | 1.13211i | 0.824367 | + | 0.566056i | \(0.191532\pi\) | ||||
−0.824367 | + | 0.566056i | \(0.808468\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 274.150 | 0.0379447 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 652.514i | 0.0862088i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 9469.11i | 1.19544i | 0.801704 | + | 0.597722i | \(0.203927\pi\) | ||||
−0.801704 | + | 0.597722i | \(0.796073\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 2737.81 | 0.316546 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 277.379 | 0.0307345 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 9945.39i | 1.05701i | 0.848931 | + | 0.528504i | \(0.177247\pi\) | ||||
−0.848931 | + | 0.528504i | \(0.822753\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −11657.7 | −1.18944 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 2068.32i | 0.202756i | 0.994848 | + | 0.101378i | \(0.0323252\pi\) | ||||
−0.994848 | + | 0.101378i | \(0.967675\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − 2504.76i | − 0.236098i | −0.993008 | − | 0.118049i | \(-0.962336\pi\) | ||||
0.993008 | − | 0.118049i | \(-0.0376639\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −6443.39 | −0.562791 | −0.281395 | − | 0.959592i | \(-0.590797\pi\) | ||||
−0.281395 | + | 0.959592i | \(0.590797\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 23546.0 | 1.98182 | 0.990912 | − | 0.134515i | \(-0.0429477\pi\) | ||||
0.990912 | + | 0.134515i | \(0.0429477\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 1620.85i | 0.131552i | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 19692.2 | 1.54219 | 0.771096 | − | 0.636719i | \(-0.219709\pi\) | ||||
0.771096 | + | 0.636719i | \(0.219709\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 126.302i | 0.00955026i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 20051.3i | 1.46478i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 8360.97 | 0.571065 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 1659.02 | 0.109658 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 888.358i | 0.0568549i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 12550.5 | 0.778135 | 0.389067 | − | 0.921209i | \(-0.372797\pi\) | ||||
0.389067 | + | 0.921209i | \(0.372797\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | − 4407.95i | − 0.264885i | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 19323.3i | 1.12600i | 0.826457 | + | 0.562999i | \(0.190353\pi\) | ||||
−0.826457 | + | 0.562999i | \(0.809647\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 228.232 | 0.0125230 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 3708.59 | 0.197591 | 0.0987955 | − | 0.995108i | \(-0.468501\pi\) | ||||
0.0987955 | + | 0.995108i | \(0.468501\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − 1096.09i | − 0.0567307i | −0.999598 | − | 0.0283653i | \(-0.990970\pi\) | ||||
0.999598 | − | 0.0283653i | \(-0.00903018\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 8714.65 | 0.438341 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − 39563.7i | − 1.93475i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − 228.143i | − 0.0108510i | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −1233.82 | −0.0555748 | −0.0277874 | − | 0.999614i | \(-0.508846\pi\) | ||||
−0.0277874 | + | 0.999614i | \(0.508846\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 42672.8 | 1.87153 | 0.935766 | − | 0.352622i | \(-0.114710\pi\) | ||||
0.935766 | + | 0.352622i | \(0.114710\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | − 29639.0i | − 1.26614i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −957.236 | −0.0398433 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − 29884.9i | − 1.21242i | −0.795305 | − | 0.606209i | \(-0.792689\pi\) | ||||
0.795305 | − | 0.606209i | \(-0.207311\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 6449.28i | 0.255104i | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 26205.2 | 0.986308 | 0.493154 | − | 0.869942i | \(-0.335844\pi\) | ||||
0.493154 | + | 0.869942i | \(0.335844\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −219.267 | −0.00805389 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 35887.5i | 1.28680i | 0.765532 | + | 0.643398i | \(0.222476\pi\) | ||||
−0.765532 | + | 0.643398i | \(0.777524\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −39489.2 | −1.38263 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | − 29988.1i | − 1.02555i | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 10972.7i | 0.366625i | 0.983055 | + | 0.183312i | \(0.0586820\pi\) | ||||
−0.983055 | + | 0.183312i | \(0.941318\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −9570.30 | −0.305477 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 33844.1 | 1.05628 | 0.528138 | − | 0.849159i | \(-0.322891\pi\) | ||||
0.528138 | + | 0.849159i | \(0.322891\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 50094.5i | 1.52909i | 0.644571 | + | 0.764545i | \(0.277036\pi\) | ||||
−0.644571 | + | 0.764545i | \(0.722964\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −5154.39 | −0.153913 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | − 566.709i | − 0.0165583i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 58481.4i | 1.67238i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −17612.9 | −0.482798 | −0.241399 | − | 0.970426i | \(-0.577606\pi\) | ||||
−0.241399 | + | 0.970426i | \(0.577606\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 13264.2 | 0.356097 | 0.178048 | − | 0.984022i | \(-0.443022\pi\) | ||||
0.178048 | + | 0.984022i | \(0.443022\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 377.143i | 0.00991828i | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 5362.20 | 0.138169 | 0.0690844 | − | 0.997611i | \(-0.477992\pi\) | ||||
0.0690844 | + | 0.997611i | \(0.477992\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 42230.6i | 1.06640i | 0.845988 | + | 0.533202i | \(0.179011\pi\) | ||||
−0.845988 | + | 0.533202i | \(0.820989\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | − 8321.82i | − 0.205981i | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −580.053 | −0.0138026 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 13654.8 | 0.318673 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 59170.2i | 1.35460i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 77049.0 | 1.73062 | 0.865311 | − | 0.501236i | \(-0.167121\pi\) | ||||
0.865311 | + | 0.501236i | \(0.167121\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | − 4586.04i | − 0.101083i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 1541.18i | 0.0333408i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −9462.11 | −0.197288 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 100589. | 2.05951 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − 3702.60i | − 0.0744555i | −0.999307 | − | 0.0372278i | \(-0.988147\pi\) | ||||
0.999307 | − | 0.0372278i | \(-0.0118527\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 48001.8 | 0.948183 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 12018.8i | 0.233243i | 0.993176 | + | 0.116621i | \(0.0372064\pi\) | ||||
−0.993176 | + | 0.116621i | \(0.962794\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 33360.5i | 0.636153i | 0.948065 | + | 0.318076i | \(0.103037\pi\) | ||||
−0.948065 | + | 0.318076i | \(0.896963\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 54138.9 | 0.997235 | 0.498618 | − | 0.866822i | \(-0.333841\pi\) | ||||
0.498618 | + | 0.866822i | \(0.333841\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −3046.96 | −0.0551735 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | − 8527.83i | − 0.151824i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −29165.4 | −0.510590 | −0.255295 | − | 0.966863i | \(-0.582173\pi\) | ||||
−0.255295 | + | 0.966863i | \(0.582173\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − 100130.i | − 1.72398i | −0.506929 | − | 0.861988i | \(-0.669219\pi\) | ||||
0.506929 | − | 0.861988i | \(-0.330781\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | − 37335.2i | − 0.632275i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 101774. | 1.66817 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 15859.3 | 0.255791 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − 81988.2i | − 1.30138i | −0.759344 | − | 0.650690i | \(-0.774480\pi\) | ||||
0.759344 | − | 0.650690i | \(-0.225520\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −26942.6 | −0.420919 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | − 557.476i | − 0.00857325i | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 73774.8i | 1.11697i | 0.829515 | + | 0.558485i | \(0.188617\pi\) | ||||
−0.829515 | + | 0.558485i | \(0.811383\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −24665.0 | −0.362076 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −39243.6 | −0.567358 | −0.283679 | − | 0.958919i | \(-0.591555\pi\) | ||||
−0.283679 | + | 0.958919i | \(0.591555\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − 2254.90i | − 0.0321096i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 19255.1 | 0.270100 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − 10311.6i | − 0.142502i | −0.997458 | − | 0.0712509i | \(-0.977301\pi\) | ||||
0.997458 | − | 0.0712509i | \(-0.0226991\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 36969.3i | 0.503388i | 0.967807 | + | 0.251694i | \(0.0809876\pi\) | ||||
−0.967807 | + | 0.251694i | \(0.919012\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −94713.3 | −1.25241 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −92405.8 | −1.20431 | −0.602157 | − | 0.798378i | \(-0.705692\pi\) | ||||
−0.602157 | + | 0.798378i | \(0.705692\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 103489.i | 1.32949i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 21171.6 | 0.268128 | 0.134064 | − | 0.990973i | \(-0.457197\pi\) | ||||
0.134064 | + | 0.990973i | \(0.457197\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − 48065.2i | − 0.600147i | −0.953916 | − | 0.300074i | \(-0.902989\pi\) | ||||
0.953916 | − | 0.300074i | \(-0.0970112\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | − 564.042i | − 0.00694419i | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −65164.9 | −0.780222 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 20223.6 | 0.238821 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − 26781.1i | − 0.311956i | −0.987761 | − | 0.155978i | \(-0.950147\pi\) | ||||
0.987761 | − | 0.155978i | \(-0.0498528\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 3346.12 | 0.0384501 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 48686.2i | 0.551941i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 46341.7i | 0.518358i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 4205.85 | 0.0458109 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 1802.16 | 0.0193729 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 69996.0i | 0.742671i | 0.928499 | + | 0.371336i | \(0.121100\pi\) | ||||
−0.928499 | + | 0.371336i | \(0.878900\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −5093.35 | −0.0533441 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − 86961.6i | − 0.899097i | −0.893256 | − | 0.449549i | \(-0.851585\pi\) | ||||
0.893256 | − | 0.449549i | \(-0.148415\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − 33163.2i | − 0.338507i | −0.985573 | − | 0.169253i | \(-0.945864\pi\) | ||||
0.985573 | − | 0.169253i | \(-0.0541357\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 29206.0 | 0.290639 | 0.145319 | − | 0.989385i | \(-0.453579\pi\) | ||||
0.145319 | + | 0.989385i | \(0.453579\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 48667.1 | 0.478249 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 13102.4i | 0.127157i | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −150437. | −1.44195 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 162908.i | 1.54233i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | − 47880.1i | − 0.447775i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −166993. | −1.52420 | −0.762102 | − | 0.647457i | \(-0.775832\pi\) | ||||
−0.762102 | + | 0.647457i | \(0.775832\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −61268.2 | −0.552518 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 2909.61i | 0.0259266i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 16126.0 | 0.141993 | 0.0709964 | − | 0.997477i | \(-0.477382\pi\) | ||||
0.0709964 | + | 0.997477i | \(0.477382\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | − 40043.5i | − 0.348444i | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − 204196.i | − 1.75606i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 256.832 | 0.00215779 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −10071.3 | −0.0836428 | −0.0418214 | − | 0.999125i | \(-0.513316\pi\) | ||||
−0.0418214 | + | 0.999125i | \(0.513316\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − 97674.1i | − 0.801915i | −0.916097 | − | 0.400958i | \(-0.868677\pi\) | ||||
0.916097 | − | 0.400958i | \(-0.131323\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 83740.9 | 0.679710 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 85255.3i | 0.684182i | 0.939667 | + | 0.342091i | \(0.111135\pi\) | ||||
−0.939667 | + | 0.342091i | \(0.888865\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 1603.45i | 0.0127232i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 142240. | 1.10365 | 0.551826 | − | 0.833959i | \(-0.313931\pi\) | ||||
0.551826 | + | 0.833959i | \(0.313931\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −21888.1 | −0.167955 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − 17001.8i | − 0.129027i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 3308.30 | 0.0248324 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 177841.i | 1.32038i | 0.751098 | + | 0.660191i | \(0.229525\pi\) | ||||
−0.751098 | + | 0.660191i | \(0.770475\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 62710.8i | 0.460564i | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −21670.8 | −0.155761 | −0.0778803 | − | 0.996963i | \(-0.524815\pi\) | ||||
−0.0778803 | + | 0.996963i | \(0.524815\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 1806.45 | 0.0128459 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − 83708.0i | − 0.588958i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −125199. | −0.871608 | −0.435804 | − | 0.900042i | \(-0.643536\pi\) | ||||
−0.435804 | + | 0.900042i | \(0.643536\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | − 25521.1i | − 0.175812i | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − 211410.i | − 1.44121i | −0.693345 | − | 0.720605i | \(-0.743864\pi\) | ||||
0.693345 | − | 0.720605i | \(-0.256136\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 166620. | 1.11252 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −39160.8 | −0.258793 | −0.129396 | − | 0.991593i | \(-0.541304\pi\) | ||||
−0.129396 | + | 0.991593i | \(0.541304\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − 68500.3i | − 0.448063i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 39293.2 | 0.254409 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 2981.64i | 0.0191100i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 196525.i | 1.24691i | 0.781858 | + | 0.623456i | \(0.214272\pi\) | ||||
−0.781858 | + | 0.623456i | \(0.785728\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 213650. | 1.32866 | 0.664330 | − | 0.747439i | \(-0.268717\pi\) | ||||
0.664330 | + | 0.747439i | \(0.268717\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −351221. | −2.16257 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 3962.47i | 0.0241577i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 120890. | 0.729794 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − 35604.1i | − 0.212840i | −0.994321 | − | 0.106420i | \(-0.966061\pi\) | ||||
0.994321 | − | 0.106420i | \(-0.0339388\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | − 7541.29i | − 0.0446439i | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −5544.97 | −0.0321961 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −2228.87 | −0.0128178 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − 254947.i | − 1.45219i | −0.687597 | − | 0.726093i | \(-0.741334\pi\) | ||||
0.687597 | − | 0.726093i | \(-0.258666\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 107186. | 0.604748 | 0.302374 | − | 0.953189i | \(-0.402221\pi\) | ||||
0.302374 | + | 0.953189i | \(0.402221\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 329413.i | 1.84103i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | − 240804.i | − 1.33317i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −80451.6 | −0.437139 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −119958. | −0.645768 | −0.322884 | − | 0.946439i | \(-0.604652\pi\) | ||||
−0.322884 | + | 0.946439i | \(0.604652\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − 110159.i | − 0.587547i | −0.955875 | − | 0.293773i | \(-0.905089\pi\) | ||||
0.955875 | − | 0.293773i | \(-0.0949111\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −463.921 | −0.00245169 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − 69307.1i | − 0.362923i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − 352295.i | − 1.82801i | −0.405708 | − | 0.914003i | \(-0.632975\pi\) | ||||
0.405708 | − | 0.914003i | \(-0.367025\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −285732. | −1.45597 | −0.727984 | − | 0.685594i | \(-0.759543\pi\) | ||||
−0.727984 | + | 0.685594i | \(0.759543\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −6732.29 | −0.0339972 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 2508.92i | 0.0125566i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −342184. | −1.69733 | −0.848667 | − | 0.528927i | \(-0.822594\pi\) | ||||
−0.848667 | + | 0.528927i | \(0.822594\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − 123736.i | − 0.608335i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | − 86773.8i | − 0.422856i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −277624. | −1.32931 | −0.664653 | − | 0.747152i | \(-0.731421\pi\) | ||||
−0.664653 | + | 0.747152i | \(0.731421\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −123782. | −0.587534 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 361934.i | 1.70305i | 0.524315 | + | 0.851524i | \(0.324322\pi\) | ||||
−0.524315 | + | 0.851524i | \(0.675678\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −146876. | −0.685153 | −0.342577 | − | 0.939490i | \(-0.611300\pi\) | ||||
−0.342577 | + | 0.939490i | \(0.611300\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 1946.51i | 0.00900224i | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 268410.i | 1.23073i | 0.788241 | + | 0.615367i | \(0.210992\pi\) | ||||
−0.788241 | + | 0.615367i | \(0.789008\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −60770.0 | −0.273935 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −328762. | −1.46947 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − 243640.i | − 1.07985i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −243782. | −1.07143 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 155285.i | 0.676797i | 0.941003 | + | 0.338399i | \(0.109885\pi\) | ||||
−0.941003 | + | 0.338399i | \(0.890115\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | − 207932.i | − 0.898733i | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −7070.91 | −0.0300602 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 155628. | 0.656190 | 0.328095 | − | 0.944645i | \(-0.393593\pi\) | ||||
0.328095 | + | 0.944645i | \(0.393593\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | − 53287.5i | − 0.222847i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −37550.7 | −0.155760 | −0.0778798 | − | 0.996963i | \(-0.524815\pi\) | ||||
−0.0778798 | + | 0.996963i | \(0.524815\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 123734.i | 0.509089i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | − 8288.29i | − 0.0338263i | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −167820. | −0.673975 | −0.336987 | − | 0.941509i | \(-0.609408\pi\) | ||||
−0.336987 | + | 0.941509i | \(0.609408\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 72976.0 | 0.290740 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 133035.i | 0.525810i | 0.964822 | + | 0.262905i | \(0.0846806\pi\) | ||||
−0.964822 | + | 0.262905i | \(0.915319\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −1470.52 | −0.00576617 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 80299.9i | 0.312392i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − 227994.i | − 0.880011i | −0.897995 | − | 0.440005i | \(-0.854976\pi\) | ||||
0.897995 | − | 0.440005i | \(-0.145024\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −125240. | −0.475892 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 1780.82 | 0.00671437 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − 649973.i | − 2.43172i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 22312.7 | 0.0828355 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 341411.i | 1.25777i | 0.777498 | + | 0.628885i | \(0.216489\pi\) | ||||
−0.777498 | + | 0.628885i | \(0.783511\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − 62912.0i | − 0.230001i | −0.993365 | − | 0.115001i | \(-0.963313\pi\) | ||||
0.993365 | − | 0.115001i | \(-0.0366870\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 519159. | 1.86930 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −248283. | −0.887228 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − 361757.i | − 1.28300i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −212828. | −0.749159 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − 4581.08i | − 0.0160052i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | − 68820.9i | − 0.238656i | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 251203. | 0.858282 | 0.429141 | − | 0.903237i | \(-0.358816\pi\) | ||||
0.429141 | + | 0.903237i | \(0.358816\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 101866. | 0.345484 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 16740.6i | 0.0563610i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 153431. | 0.512789 | 0.256395 | − | 0.966572i | \(-0.417465\pi\) | ||||
0.256395 | + | 0.966572i | \(0.417465\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | − 194836.i | − 0.646434i | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 125191.i | 0.412353i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −1152.38 | −0.00374121 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −475151. | −1.53152 | −0.765758 | − | 0.643129i | \(-0.777636\pi\) | ||||
−0.765758 | + | 0.643129i | \(0.777636\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 565476.i | 1.80963i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 118920. | 0.377858 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 39487.0i | 0.124577i | 0.998058 | + | 0.0622884i | \(0.0198398\pi\) | ||||
−0.998058 | + | 0.0622884i | \(0.980160\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 14000.7i | 0.0438583i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −85307.7 | −0.263490 | −0.131745 | − | 0.991284i | \(-0.542058\pi\) | ||||
−0.131745 | + | 0.991284i | \(0.542058\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −89099.0 | −0.273276 | −0.136638 | − | 0.990621i | \(-0.543630\pi\) | ||||
−0.136638 | + | 0.990621i | \(0.543630\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 35815.4i | 0.109084i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 110939. | 0.335545 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 311076.i | 0.934362i | 0.884162 | + | 0.467181i | \(0.154730\pi\) | ||||
−0.884162 | + | 0.467181i | \(0.845270\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | − 26972.4i | − 0.0804568i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 481012. | 1.41520 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −14256.0 | −0.0416567 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − 62466.3i | − 0.181288i | −0.995883 | − | 0.0906440i | \(-0.971107\pi\) | ||||
0.995883 | − | 0.0906440i | \(-0.0288926\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 525274. | 1.51410 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | − 10903.9i | − 0.0312180i | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − 47567.3i | − 0.135269i | −0.997710 | − | 0.0676346i | \(-0.978455\pi\) | ||||
0.997710 | − | 0.0676346i | \(-0.0215452\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 85874.6 | 0.240944 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −564035. | −1.57200 | −0.785999 | − | 0.618227i | \(-0.787851\pi\) | ||||
−0.785999 | + | 0.618227i | \(0.787851\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 255637.i | 0.707740i | 0.935295 | + | 0.353870i | \(0.115135\pi\) | ||||
−0.935295 | + | 0.353870i | \(0.884865\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 314565. | 0.865118 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 5944.43i | 0.0162405i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − 572699.i | − 1.55435i | −0.629284 | − | 0.777176i | \(-0.716652\pi\) | ||||
0.629284 | − | 0.777176i | \(-0.283348\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −1.11796e6 | −2.99464 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 283002. | 0.753127 | 0.376563 | − | 0.926391i | \(-0.377106\pi\) | ||||
0.376563 | + | 0.926391i | \(0.377106\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 1179.52i | 0.00311856i | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 248170. | 0.651896 | 0.325948 | − | 0.945388i | \(-0.394317\pi\) | ||||
0.325948 | + | 0.945388i | \(0.394317\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − 56588.1i | − 0.147688i | −0.997270 | − | 0.0738438i | \(-0.976473\pi\) | ||||
0.997270 | − | 0.0738438i | \(-0.0235266\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | − 57027.0i | − 0.147876i | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 389677. | 0.997574 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 120321. | 0.306059 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 307356.i | 0.776855i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −681448. | −1.71149 | −0.855744 | − | 0.517399i | \(-0.826900\pi\) | ||||
−0.855744 | + | 0.517399i | \(0.826900\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | − 156677.i | − 0.391018i | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 8923.10i | 0.0221293i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 173352. | 0.424549 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 678114. | 1.65039 | 0.825195 | − | 0.564848i | \(-0.191065\pi\) | ||||
0.825195 | + | 0.564848i | \(0.191065\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − 345520.i | − 0.835701i | −0.908516 | − | 0.417851i | \(-0.862784\pi\) | ||||
0.908516 | − | 0.417851i | \(-0.137216\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 3133.94 | 0.00753305 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 7757.50i | 0.0185316i | 0.999957 | + | 0.00926581i | \(0.00294944\pi\) | ||||
−0.999957 | + | 0.00926581i | \(0.997051\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 713791.i | 1.69466i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −448473. | −1.05174 | −0.525872 | − | 0.850564i | \(-0.676261\pi\) | ||||
−0.525872 | + | 0.850564i | \(0.676261\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −13738.3 | −0.0320222 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | − 357667.i | − 0.828607i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −583660. | −1.34397 | −0.671984 | − | 0.740565i | \(-0.734558\pi\) | ||||
−0.671984 | + | 0.740565i | \(0.734558\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 382886.i | 0.876327i | 0.898895 | + | 0.438164i | \(0.144371\pi\) | ||||
−0.898895 | + | 0.438164i | \(0.855629\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | − 204544.i | − 0.465329i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −57004.6 | −0.128132 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −7529.12 | −0.0168226 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 384435.i | 0.853842i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −323802. | −0.714907 | −0.357453 | − | 0.933931i | \(-0.616355\pi\) | ||||
−0.357453 | + | 0.933931i | \(0.616355\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | − 200471.i | − 0.439992i | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 374803.i | 0.817760i | 0.912588 | + | 0.408880i | \(0.134081\pi\) | ||||
−0.912588 | + | 0.408880i | \(0.865919\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 24439.8 | 0.0526990 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −97364.5 | −0.208718 | −0.104359 | − | 0.994540i | \(-0.533279\pi\) | ||||
−0.104359 | + | 0.994540i | \(0.533279\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 2636.71i | 0.00561928i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 67837.5 | 0.143733 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − 827348.i | − 1.74281i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 787116.i | 1.64848i | 0.566244 | + | 0.824238i | \(0.308396\pi\) | ||||
−0.566244 | + | 0.824238i | \(0.691604\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 779.294 | 0.00161336 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 314593. | 0.647564 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | − 110090.i | − 0.225316i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −232522. | −0.473182 | −0.236591 | − | 0.971609i | \(-0.576030\pi\) | ||||
−0.236591 | + | 0.971609i | \(0.576030\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 310976.i | 0.629240i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 6195.89i | 0.0124659i | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 151049. | 0.300487 | 0.150243 | − | 0.988649i | \(-0.451994\pi\) | ||||
0.150243 | + | 0.988649i | \(0.451994\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 322351. | 0.637662 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 239179.i | 0.470483i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 28128.8 | 0.0550223 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 59306.9i | 0.115363i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | − 712110.i | − 1.37749i | −0.725002 | − | 0.688746i | \(-0.758161\pi\) | ||||
0.725002 | − | 0.688746i | \(-0.241839\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −203612. | −0.389517 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −200392. | −0.381246 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 693160.i | 1.31149i | 0.754983 | + | 0.655744i | \(0.227645\pi\) | ||||
−0.754983 | + | 0.655744i | \(0.772355\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 375517. | 0.706601 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − 835861.i | − 1.56423i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − 269107.i | − 0.500861i | −0.968135 | − | 0.250431i | \(-0.919428\pi\) | ||||
0.968135 | − | 0.250431i | \(-0.0805722\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −620674. | −1.14269 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −86185.1 | −0.157813 | −0.0789066 | − | 0.996882i | \(-0.525143\pi\) | ||||
−0.0789066 | + | 0.996882i | \(0.525143\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | − 206953.i | − 0.376908i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 457439. | 0.828620 | 0.414310 | − | 0.910136i | \(-0.364023\pi\) | ||||
0.414310 | + | 0.910136i | \(0.364023\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | − 877.210i | − 0.00158049i | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 599480.i | 1.07432i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 581442. | 1.03092 | 0.515462 | − | 0.856913i | \(-0.327620\pi\) | ||||
0.515462 | + | 0.856913i | \(0.327620\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −166720. | −0.294035 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 30339.2i | 0.0532244i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 398071. | 0.694655 | 0.347327 | − | 0.937744i | \(-0.387089\pi\) | ||||
0.347327 | + | 0.937744i | \(0.387089\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 54787.0i | 0.0951029i | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 323965.i | 0.559408i | 0.960086 | + | 0.279704i | \(0.0902363\pi\) | ||||
−0.960086 | + | 0.279704i | \(0.909764\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 21072.6 | 0.0360076 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 1.22773e6 | 2.08695 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 318602.i | 0.538760i | 0.963034 | + | 0.269380i | \(0.0868187\pi\) | ||||
−0.963034 | + | 0.269380i | \(0.913181\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 150019. | 0.252369 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − 512015.i | − 0.856887i | −0.903569 | − | 0.428443i | \(-0.859062\pi\) | ||||
0.903569 | − | 0.428443i | \(-0.140938\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 840803.i | 1.39988i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 318298. | 0.524516 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −342045. | −0.560765 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 103009.i | 0.168017i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 21247.4 | 0.0344799 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − 644919.i | − 1.04125i | −0.853785 | − | 0.520626i | \(-0.825699\pi\) | ||||
0.853785 | − | 0.520626i | \(-0.174301\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 79800.5i | 0.128189i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 661233. | 1.05150 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −4585.27 | −0.00725488 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − 278844.i | − 0.438980i | −0.975615 | − | 0.219490i | \(-0.929561\pi\) | ||||
0.975615 | − | 0.219490i | \(-0.0704393\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1.65252e6 | 2.58853 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 727843.i | 1.13442i | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 705721.i | 1.09447i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −20968.2 | −0.0321970 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 662520. | 1.01228 | 0.506142 | − | 0.862450i | \(-0.331071\pi\) | ||||
0.506142 | + | 0.862450i | \(0.331071\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − 586078.i | − 0.891073i | −0.895264 | − | 0.445537i | \(-0.853013\pi\) | ||||
0.895264 | − | 0.445537i | \(-0.146987\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 75175.9 | 0.113736 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 18631.2i | 0.0280496i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − 845706.i | − 1.26700i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 790534. | 1.17283 | 0.586414 | − | 0.810012i | \(-0.300539\pi\) | ||||
0.586414 | + | 0.810012i | \(0.300539\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 1.15645e6 | 1.70737 | 0.853684 | − | 0.520791i | \(-0.174363\pi\) | ||||
0.853684 | + | 0.520791i | \(0.174363\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 192597.i | 0.282970i | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −390408. | −0.570832 | −0.285416 | − | 0.958404i | \(-0.592132\pi\) | ||||
−0.285416 | + | 0.958404i | \(0.592132\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − 531226.i | − 0.772984i | −0.922293 | − | 0.386492i | \(-0.873687\pi\) | ||||
0.922293 | − | 0.386492i | \(-0.126313\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 187904.i | 0.272104i | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −25515.1 | −0.0365951 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 432204. | 0.616933 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 263842.i | 0.374817i | 0.982282 | + | 0.187409i | \(0.0600089\pi\) | ||||
−0.982282 | + | 0.187409i | \(0.939991\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −604312. | −0.854416 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | − 43051.9i | − 0.0605811i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | − 28075.8i | − 0.0393204i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −97739.0 | −0.135598 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −141600. | −0.195526 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 1.17089e6i | 1.60923i | 0.593798 | + | 0.804614i | \(0.297628\pi\) | ||||
−0.593798 | + | 0.804614i | \(0.702372\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 21320.8 | 0.0291656 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − 424840.i | − 0.578447i | −0.957262 | − | 0.289223i | \(-0.906603\pi\) | ||||
0.957262 | − | 0.289223i | \(-0.0933970\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 408175.i | 0.553172i | 0.960989 | + | 0.276586i | \(0.0892030\pi\) | ||||
−0.960989 | + | 0.276586i | \(0.910797\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 882741. | 1.18525 | 0.592627 | − | 0.805477i | \(-0.298091\pi\) | ||||
0.592627 | + | 0.805477i | \(0.298091\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −7801.31 | −0.0104264 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 132511.i | 0.176284i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −636039. | −0.842256 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1.06757e6i | 1.40721i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 764452.i | 1.00305i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −595392. | −0.774112 | −0.387056 | − | 0.922056i | \(-0.626508\pi\) | ||||
−0.387056 | + | 0.922056i | \(0.626508\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −54458.5 | −0.0704835 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 238444.i | 0.307209i | 0.988132 | + | 0.153605i | \(0.0490882\pi\) | ||||
−0.988132 | + | 0.153605i | \(0.950912\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −189523. | −0.243076 | −0.121538 | − | 0.992587i | \(-0.538783\pi\) | ||||
−0.121538 | + | 0.992587i | \(0.538783\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | − 6804.24i | − 0.00868746i | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − 819553.i | − 1.04167i | −0.853658 | − | 0.520834i | \(-0.825621\pi\) | ||||
0.853658 | − | 0.520834i | \(-0.174379\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −845268. | −1.06473 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 1.67199e6 | 2.09667 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 24062.3i | 0.0300394i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 94234.3 | 0.117118 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − 432034.i | − 0.534563i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1.22295e6i | 1.50646i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −35615.9 | −0.0434857 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 657619. | 0.799392 | 0.399696 | − | 0.916648i | \(-0.369116\pi\) | ||||
0.399696 | + | 0.916648i | \(0.369116\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 158981.i | 0.192406i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −1.32632e6 | −1.59812 | −0.799061 | − | 0.601250i | \(-0.794670\pi\) | ||||
−0.799061 | + | 0.601250i | \(0.794670\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − 1.18285e6i | − 1.41901i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | − 3664.64i | − 0.00437712i | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 236310. | 0.279803 | 0.139901 | − | 0.990165i | \(-0.455321\pi\) | ||||
0.139901 | + | 0.990165i | \(0.455321\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 142335. | 0.167800 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 588322.i | 0.690577i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −497777. | −0.581770 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | − 192528.i | − 0.224045i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 352762.i | 0.408743i | 0.978893 | + | 0.204372i | \(0.0655151\pi\) | ||||
−0.978893 | + | 0.204372i | \(0.934485\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −176834. | −0.203143 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −41578.7 | −0.0475607 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − 113445.i | − 0.129213i | −0.997911 | − | 0.0646066i | \(-0.979421\pi\) | ||||
0.997911 | − | 0.0646066i | \(-0.0205793\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −67436.3 | −0.0764826 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − 1.17351e6i | − 1.32528i | −0.748937 | − | 0.662642i | \(-0.769435\pi\) | ||||
0.748937 | − | 0.662642i | \(-0.230565\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 144934.i | 0.162985i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −271958. | −0.303250 | −0.151625 | − | 0.988438i | \(-0.548451\pi\) | ||||
−0.151625 | + | 0.988438i | \(0.548451\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 1.21385e6 | 1.34782 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | − 59389.5i | − 0.0656672i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 465476. | 0.512520 | 0.256260 | − | 0.966608i | \(-0.417510\pi\) | ||||
0.256260 | + | 0.966608i | \(0.417510\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − 12522.3i | − 0.0137303i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | − 98962.9i | − 0.108056i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −889199. | −0.962836 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −495271. | −0.534061 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 9430.53i | 0.0101270i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 1.49573e6 | 1.59956 | 0.799782 | − | 0.600291i | \(-0.204949\pi\) | ||||
0.799782 | + | 0.600291i | \(0.204949\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 305909.i | 0.325795i | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − 404524.i | − 0.429048i | −0.976719 | − | 0.214524i | \(-0.931180\pi\) | ||||
0.976719 | − | 0.214524i | \(-0.0688201\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 331269. | 0.348475 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −1.65194e6 | −1.73063 | −0.865315 | − | 0.501229i | \(-0.832882\pi\) | ||||
−0.865315 | + | 0.501229i | \(0.832882\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − 1.43612e6i | − 1.49839i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 1.80987e6 | 1.88065 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − 978562.i | − 1.01270i | −0.862328 | − | 0.506350i | \(-0.830994\pi\) | ||||
0.862328 | − | 0.506350i | \(-0.169006\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 3812.38i | 0.00392938i | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 385085. | 0.393699 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −1.26854e6 | −1.29168 | −0.645841 | − | 0.763472i | \(-0.723493\pi\) | ||||
−0.645841 | + | 0.763472i | \(0.723493\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 339575.i | 0.344380i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −30024.9 | −0.0303274 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 2071.33i | 0.00208382i | 0.999999 | + | 0.00104191i | \(0.000331650\pi\) | ||||
−0.999999 | + | 0.00104191i | \(0.999668\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 255876.i | 0.256389i |
(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 | 784.5.c.a.97.2 | 4 | ||
4.3 | odd | 2 | 98.5.b.a.97.4 | yes | 4 | ||
7.6 | odd | 2 | inner | 784.5.c.a.97.3 | 4 | ||
12.11 | even | 2 | 882.5.c.c.685.1 | 4 | |||
28.3 | even | 6 | 98.5.d.c.19.1 | 8 | |||
28.11 | odd | 6 | 98.5.d.c.19.2 | 8 | |||
28.19 | even | 6 | 98.5.d.c.31.2 | 8 | |||
28.23 | odd | 6 | 98.5.d.c.31.1 | 8 | |||
28.27 | even | 2 | 98.5.b.a.97.3 | ✓ | 4 | ||
84.83 | odd | 2 | 882.5.c.c.685.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
98.5.b.a.97.3 | ✓ | 4 | 28.27 | even | 2 | ||
98.5.b.a.97.4 | yes | 4 | 4.3 | odd | 2 | ||
98.5.d.c.19.1 | 8 | 28.3 | even | 6 | |||
98.5.d.c.19.2 | 8 | 28.11 | odd | 6 | |||
98.5.d.c.31.1 | 8 | 28.23 | odd | 6 | |||
98.5.d.c.31.2 | 8 | 28.19 | even | 6 | |||
784.5.c.a.97.2 | 4 | 1.1 | even | 1 | trivial | ||
784.5.c.a.97.3 | 4 | 7.6 | odd | 2 | inner | ||
882.5.c.c.685.1 | 4 | 12.11 | even | 2 | |||
882.5.c.c.685.2 | 4 | 84.83 | odd | 2 |