Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [38,4,Mod(1,38)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(38, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("38.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 38 = 2 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 38.a (trivial) |
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: | yes |
Analytic conductor: | \(2.24207258022\) |
Analytic rank: | \(1\) |
Dimension: | \(1\) |
Coefficient field: | \(\mathbb{Q}\) |
Coefficient ring: | \(\mathbb{Z}\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Character | \(\chi\) | \(=\) | 38.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.00000 | −0.707107 | ||||||||
\(3\) | −2.00000 | −0.384900 | −0.192450 | − | 0.981307i | \(-0.561643\pi\) | ||||
−0.192450 | + | 0.981307i | \(0.561643\pi\) | |||||||
\(4\) | 4.00000 | 0.500000 | ||||||||
\(5\) | −9.00000 | −0.804984 | −0.402492 | − | 0.915423i | \(-0.631856\pi\) | ||||
−0.402492 | + | 0.915423i | \(0.631856\pi\) | |||||||
\(6\) | 4.00000 | 0.272166 | ||||||||
\(7\) | −31.0000 | −1.67384 | −0.836921 | − | 0.547323i | \(-0.815647\pi\) | ||||
−0.836921 | + | 0.547323i | \(0.815647\pi\) | |||||||
\(8\) | −8.00000 | −0.353553 | ||||||||
\(9\) | −23.0000 | −0.851852 | ||||||||
\(10\) | 18.0000 | 0.569210 | ||||||||
\(11\) | 57.0000 | 1.56238 | 0.781188 | − | 0.624295i | \(-0.214614\pi\) | ||||
0.781188 | + | 0.624295i | \(0.214614\pi\) | |||||||
\(12\) | −8.00000 | −0.192450 | ||||||||
\(13\) | −52.0000 | −1.10940 | −0.554700 | − | 0.832050i | \(-0.687167\pi\) | ||||
−0.554700 | + | 0.832050i | \(0.687167\pi\) | |||||||
\(14\) | 62.0000 | 1.18359 | ||||||||
\(15\) | 18.0000 | 0.309839 | ||||||||
\(16\) | 16.0000 | 0.250000 | ||||||||
\(17\) | 69.0000 | 0.984409 | 0.492205 | − | 0.870480i | \(-0.336191\pi\) | ||||
0.492205 | + | 0.870480i | \(0.336191\pi\) | |||||||
\(18\) | 46.0000 | 0.602350 | ||||||||
\(19\) | 19.0000 | 0.229416 | ||||||||
\(20\) | −36.0000 | −0.402492 | ||||||||
\(21\) | 62.0000 | 0.644262 | ||||||||
\(22\) | −114.000 | −1.10477 | ||||||||
\(23\) | −72.0000 | −0.652741 | −0.326370 | − | 0.945242i | \(-0.605826\pi\) | ||||
−0.326370 | + | 0.945242i | \(0.605826\pi\) | |||||||
\(24\) | 16.0000 | 0.136083 | ||||||||
\(25\) | −44.0000 | −0.352000 | ||||||||
\(26\) | 104.000 | 0.784465 | ||||||||
\(27\) | 100.000 | 0.712778 | ||||||||
\(28\) | −124.000 | −0.836921 | ||||||||
\(29\) | −150.000 | −0.960493 | −0.480247 | − | 0.877134i | \(-0.659453\pi\) | ||||
−0.480247 | + | 0.877134i | \(0.659453\pi\) | |||||||
\(30\) | −36.0000 | −0.219089 | ||||||||
\(31\) | 32.0000 | 0.185399 | 0.0926995 | − | 0.995694i | \(-0.470450\pi\) | ||||
0.0926995 | + | 0.995694i | \(0.470450\pi\) | |||||||
\(32\) | −32.0000 | −0.176777 | ||||||||
\(33\) | −114.000 | −0.601359 | ||||||||
\(34\) | −138.000 | −0.696082 | ||||||||
\(35\) | 279.000 | 1.34742 | ||||||||
\(36\) | −92.0000 | −0.425926 | ||||||||
\(37\) | −226.000 | −1.00417 | −0.502083 | − | 0.864819i | \(-0.667433\pi\) | ||||
−0.502083 | + | 0.864819i | \(0.667433\pi\) | |||||||
\(38\) | −38.0000 | −0.162221 | ||||||||
\(39\) | 104.000 | 0.427008 | ||||||||
\(40\) | 72.0000 | 0.284605 | ||||||||
\(41\) | −258.000 | −0.982752 | −0.491376 | − | 0.870948i | \(-0.663506\pi\) | ||||
−0.491376 | + | 0.870948i | \(0.663506\pi\) | |||||||
\(42\) | −124.000 | −0.455562 | ||||||||
\(43\) | −67.0000 | −0.237614 | −0.118807 | − | 0.992917i | \(-0.537907\pi\) | ||||
−0.118807 | + | 0.992917i | \(0.537907\pi\) | |||||||
\(44\) | 228.000 | 0.781188 | ||||||||
\(45\) | 207.000 | 0.685728 | ||||||||
\(46\) | 144.000 | 0.461557 | ||||||||
\(47\) | 579.000 | 1.79693 | 0.898466 | − | 0.439043i | \(-0.144682\pi\) | ||||
0.898466 | + | 0.439043i | \(0.144682\pi\) | |||||||
\(48\) | −32.0000 | −0.0962250 | ||||||||
\(49\) | 618.000 | 1.80175 | ||||||||
\(50\) | 88.0000 | 0.248902 | ||||||||
\(51\) | −138.000 | −0.378899 | ||||||||
\(52\) | −208.000 | −0.554700 | ||||||||
\(53\) | −432.000 | −1.11962 | −0.559809 | − | 0.828622i | \(-0.689126\pi\) | ||||
−0.559809 | + | 0.828622i | \(0.689126\pi\) | |||||||
\(54\) | −200.000 | −0.504010 | ||||||||
\(55\) | −513.000 | −1.25769 | ||||||||
\(56\) | 248.000 | 0.591793 | ||||||||
\(57\) | −38.0000 | −0.0883022 | ||||||||
\(58\) | 300.000 | 0.679171 | ||||||||
\(59\) | −330.000 | −0.728175 | −0.364088 | − | 0.931365i | \(-0.618619\pi\) | ||||
−0.364088 | + | 0.931365i | \(0.618619\pi\) | |||||||
\(60\) | 72.0000 | 0.154919 | ||||||||
\(61\) | −13.0000 | −0.0272865 | −0.0136433 | − | 0.999907i | \(-0.504343\pi\) | ||||
−0.0136433 | + | 0.999907i | \(0.504343\pi\) | |||||||
\(62\) | −64.0000 | −0.131097 | ||||||||
\(63\) | 713.000 | 1.42587 | ||||||||
\(64\) | 64.0000 | 0.125000 | ||||||||
\(65\) | 468.000 | 0.893050 | ||||||||
\(66\) | 228.000 | 0.425225 | ||||||||
\(67\) | −856.000 | −1.56085 | −0.780426 | − | 0.625249i | \(-0.784998\pi\) | ||||
−0.780426 | + | 0.625249i | \(0.784998\pi\) | |||||||
\(68\) | 276.000 | 0.492205 | ||||||||
\(69\) | 144.000 | 0.251240 | ||||||||
\(70\) | −558.000 | −0.952768 | ||||||||
\(71\) | 642.000 | 1.07312 | 0.536559 | − | 0.843863i | \(-0.319724\pi\) | ||||
0.536559 | + | 0.843863i | \(0.319724\pi\) | |||||||
\(72\) | 184.000 | 0.301175 | ||||||||
\(73\) | −487.000 | −0.780809 | −0.390404 | − | 0.920643i | \(-0.627665\pi\) | ||||
−0.390404 | + | 0.920643i | \(0.627665\pi\) | |||||||
\(74\) | 452.000 | 0.710053 | ||||||||
\(75\) | 88.0000 | 0.135485 | ||||||||
\(76\) | 76.0000 | 0.114708 | ||||||||
\(77\) | −1767.00 | −2.61517 | ||||||||
\(78\) | −208.000 | −0.301941 | ||||||||
\(79\) | −700.000 | −0.996913 | −0.498457 | − | 0.866915i | \(-0.666100\pi\) | ||||
−0.498457 | + | 0.866915i | \(0.666100\pi\) | |||||||
\(80\) | −144.000 | −0.201246 | ||||||||
\(81\) | 421.000 | 0.577503 | ||||||||
\(82\) | 516.000 | 0.694911 | ||||||||
\(83\) | −12.0000 | −0.0158695 | −0.00793477 | − | 0.999969i | \(-0.502526\pi\) | ||||
−0.00793477 | + | 0.999969i | \(0.502526\pi\) | |||||||
\(84\) | 248.000 | 0.322131 | ||||||||
\(85\) | −621.000 | −0.792434 | ||||||||
\(86\) | 134.000 | 0.168019 | ||||||||
\(87\) | 300.000 | 0.369694 | ||||||||
\(88\) | −456.000 | −0.552384 | ||||||||
\(89\) | −600.000 | −0.714605 | −0.357303 | − | 0.933989i | \(-0.616304\pi\) | ||||
−0.357303 | + | 0.933989i | \(0.616304\pi\) | |||||||
\(90\) | −414.000 | −0.484883 | ||||||||
\(91\) | 1612.00 | 1.85696 | ||||||||
\(92\) | −288.000 | −0.326370 | ||||||||
\(93\) | −64.0000 | −0.0713601 | ||||||||
\(94\) | −1158.00 | −1.27062 | ||||||||
\(95\) | −171.000 | −0.184676 | ||||||||
\(96\) | 64.0000 | 0.0680414 | ||||||||
\(97\) | 1424.00 | 1.49057 | 0.745285 | − | 0.666746i | \(-0.232313\pi\) | ||||
0.745285 | + | 0.666746i | \(0.232313\pi\) | |||||||
\(98\) | −1236.00 | −1.27403 | ||||||||
\(99\) | −1311.00 | −1.33091 | ||||||||
\(100\) | −176.000 | −0.176000 | ||||||||
\(101\) | 1062.00 | 1.04627 | 0.523133 | − | 0.852251i | \(-0.324763\pi\) | ||||
0.523133 | + | 0.852251i | \(0.324763\pi\) | |||||||
\(102\) | 276.000 | 0.267922 | ||||||||
\(103\) | 1178.00 | 1.12691 | 0.563455 | − | 0.826147i | \(-0.309472\pi\) | ||||
0.563455 | + | 0.826147i | \(0.309472\pi\) | |||||||
\(104\) | 416.000 | 0.392232 | ||||||||
\(105\) | −558.000 | −0.518621 | ||||||||
\(106\) | 864.000 | 0.791690 | ||||||||
\(107\) | 114.000 | 0.102998 | 0.0514990 | − | 0.998673i | \(-0.483600\pi\) | ||||
0.0514990 | + | 0.998673i | \(0.483600\pi\) | |||||||
\(108\) | 400.000 | 0.356389 | ||||||||
\(109\) | 1460.00 | 1.28296 | 0.641480 | − | 0.767140i | \(-0.278321\pi\) | ||||
0.641480 | + | 0.767140i | \(0.278321\pi\) | |||||||
\(110\) | 1026.00 | 0.889321 | ||||||||
\(111\) | 452.000 | 0.386504 | ||||||||
\(112\) | −496.000 | −0.418461 | ||||||||
\(113\) | −822.000 | −0.684312 | −0.342156 | − | 0.939643i | \(-0.611157\pi\) | ||||
−0.342156 | + | 0.939643i | \(0.611157\pi\) | |||||||
\(114\) | 76.0000 | 0.0624391 | ||||||||
\(115\) | 648.000 | 0.525446 | ||||||||
\(116\) | −600.000 | −0.480247 | ||||||||
\(117\) | 1196.00 | 0.945045 | ||||||||
\(118\) | 660.000 | 0.514898 | ||||||||
\(119\) | −2139.00 | −1.64775 | ||||||||
\(120\) | −144.000 | −0.109545 | ||||||||
\(121\) | 1918.00 | 1.44102 | ||||||||
\(122\) | 26.0000 | 0.0192945 | ||||||||
\(123\) | 516.000 | 0.378261 | ||||||||
\(124\) | 128.000 | 0.0926995 | ||||||||
\(125\) | 1521.00 | 1.08834 | ||||||||
\(126\) | −1426.00 | −1.00824 | ||||||||
\(127\) | −2086.00 | −1.45750 | −0.728750 | − | 0.684780i | \(-0.759898\pi\) | ||||
−0.728750 | + | 0.684780i | \(0.759898\pi\) | |||||||
\(128\) | −128.000 | −0.0883883 | ||||||||
\(129\) | 134.000 | 0.0914577 | ||||||||
\(130\) | −936.000 | −0.631482 | ||||||||
\(131\) | −93.0000 | −0.0620263 | −0.0310132 | − | 0.999519i | \(-0.509873\pi\) | ||||
−0.0310132 | + | 0.999519i | \(0.509873\pi\) | |||||||
\(132\) | −456.000 | −0.300680 | ||||||||
\(133\) | −589.000 | −0.384006 | ||||||||
\(134\) | 1712.00 | 1.10369 | ||||||||
\(135\) | −900.000 | −0.573775 | ||||||||
\(136\) | −552.000 | −0.348041 | ||||||||
\(137\) | 1269.00 | 0.791372 | 0.395686 | − | 0.918386i | \(-0.370507\pi\) | ||||
0.395686 | + | 0.918386i | \(0.370507\pi\) | |||||||
\(138\) | −288.000 | −0.177654 | ||||||||
\(139\) | −1975.00 | −1.20516 | −0.602580 | − | 0.798058i | \(-0.705861\pi\) | ||||
−0.602580 | + | 0.798058i | \(0.705861\pi\) | |||||||
\(140\) | 1116.00 | 0.673709 | ||||||||
\(141\) | −1158.00 | −0.691640 | ||||||||
\(142\) | −1284.00 | −0.758809 | ||||||||
\(143\) | −2964.00 | −1.73330 | ||||||||
\(144\) | −368.000 | −0.212963 | ||||||||
\(145\) | 1350.00 | 0.773182 | ||||||||
\(146\) | 974.000 | 0.552115 | ||||||||
\(147\) | −1236.00 | −0.693494 | ||||||||
\(148\) | −904.000 | −0.502083 | ||||||||
\(149\) | −1695.00 | −0.931945 | −0.465973 | − | 0.884799i | \(-0.654295\pi\) | ||||
−0.465973 | + | 0.884799i | \(0.654295\pi\) | |||||||
\(150\) | −176.000 | −0.0958023 | ||||||||
\(151\) | 1802.00 | 0.971157 | 0.485578 | − | 0.874193i | \(-0.338609\pi\) | ||||
0.485578 | + | 0.874193i | \(0.338609\pi\) | |||||||
\(152\) | −152.000 | −0.0811107 | ||||||||
\(153\) | −1587.00 | −0.838571 | ||||||||
\(154\) | 3534.00 | 1.84921 | ||||||||
\(155\) | −288.000 | −0.149243 | ||||||||
\(156\) | 416.000 | 0.213504 | ||||||||
\(157\) | −3226.00 | −1.63989 | −0.819945 | − | 0.572442i | \(-0.805996\pi\) | ||||
−0.819945 | + | 0.572442i | \(0.805996\pi\) | |||||||
\(158\) | 1400.00 | 0.704924 | ||||||||
\(159\) | 864.000 | 0.430941 | ||||||||
\(160\) | 288.000 | 0.142302 | ||||||||
\(161\) | 2232.00 | 1.09259 | ||||||||
\(162\) | −842.000 | −0.408357 | ||||||||
\(163\) | 1268.00 | 0.609309 | 0.304655 | − | 0.952463i | \(-0.401459\pi\) | ||||
0.304655 | + | 0.952463i | \(0.401459\pi\) | |||||||
\(164\) | −1032.00 | −0.491376 | ||||||||
\(165\) | 1026.00 | 0.484085 | ||||||||
\(166\) | 24.0000 | 0.0112215 | ||||||||
\(167\) | 654.000 | 0.303042 | 0.151521 | − | 0.988454i | \(-0.451583\pi\) | ||||
0.151521 | + | 0.988454i | \(0.451583\pi\) | |||||||
\(168\) | −496.000 | −0.227781 | ||||||||
\(169\) | 507.000 | 0.230769 | ||||||||
\(170\) | 1242.00 | 0.560336 | ||||||||
\(171\) | −437.000 | −0.195428 | ||||||||
\(172\) | −268.000 | −0.118807 | ||||||||
\(173\) | −1362.00 | −0.598560 | −0.299280 | − | 0.954165i | \(-0.596747\pi\) | ||||
−0.299280 | + | 0.954165i | \(0.596747\pi\) | |||||||
\(174\) | −600.000 | −0.261413 | ||||||||
\(175\) | 1364.00 | 0.589193 | ||||||||
\(176\) | 912.000 | 0.390594 | ||||||||
\(177\) | 660.000 | 0.280275 | ||||||||
\(178\) | 1200.00 | 0.505302 | ||||||||
\(179\) | −210.000 | −0.0876879 | −0.0438440 | − | 0.999038i | \(-0.513960\pi\) | ||||
−0.0438440 | + | 0.999038i | \(0.513960\pi\) | |||||||
\(180\) | 828.000 | 0.342864 | ||||||||
\(181\) | 2.00000 | 0.000821319 0 | 0.000410660 | − | 1.00000i | \(-0.499869\pi\) | ||||
0.000410660 | 1.00000i | \(0.499869\pi\) | ||||||||
\(182\) | −3224.00 | −1.31307 | ||||||||
\(183\) | 26.0000 | 0.0105026 | ||||||||
\(184\) | 576.000 | 0.230779 | ||||||||
\(185\) | 2034.00 | 0.808339 | ||||||||
\(186\) | 128.000 | 0.0504592 | ||||||||
\(187\) | 3933.00 | 1.53802 | ||||||||
\(188\) | 2316.00 | 0.898466 | ||||||||
\(189\) | −3100.00 | −1.19308 | ||||||||
\(190\) | 342.000 | 0.130586 | ||||||||
\(191\) | −2643.00 | −1.00126 | −0.500630 | − | 0.865661i | \(-0.666898\pi\) | ||||
−0.500630 | + | 0.865661i | \(0.666898\pi\) | |||||||
\(192\) | −128.000 | −0.0481125 | ||||||||
\(193\) | 3248.00 | 1.21138 | 0.605690 | − | 0.795701i | \(-0.292897\pi\) | ||||
0.605690 | + | 0.795701i | \(0.292897\pi\) | |||||||
\(194\) | −2848.00 | −1.05399 | ||||||||
\(195\) | −936.000 | −0.343735 | ||||||||
\(196\) | 2472.00 | 0.900875 | ||||||||
\(197\) | −3126.00 | −1.13055 | −0.565275 | − | 0.824903i | \(-0.691230\pi\) | ||||
−0.565275 | + | 0.824903i | \(0.691230\pi\) | |||||||
\(198\) | 2622.00 | 0.941098 | ||||||||
\(199\) | −2995.00 | −1.06688 | −0.533442 | − | 0.845837i | \(-0.679102\pi\) | ||||
−0.533442 | + | 0.845837i | \(0.679102\pi\) | |||||||
\(200\) | 352.000 | 0.124451 | ||||||||
\(201\) | 1712.00 | 0.600772 | ||||||||
\(202\) | −2124.00 | −0.739822 | ||||||||
\(203\) | 4650.00 | 1.60771 | ||||||||
\(204\) | −552.000 | −0.189450 | ||||||||
\(205\) | 2322.00 | 0.791100 | ||||||||
\(206\) | −2356.00 | −0.796846 | ||||||||
\(207\) | 1656.00 | 0.556038 | ||||||||
\(208\) | −832.000 | −0.277350 | ||||||||
\(209\) | 1083.00 | 0.358434 | ||||||||
\(210\) | 1116.00 | 0.366721 | ||||||||
\(211\) | −4318.00 | −1.40883 | −0.704416 | − | 0.709788i | \(-0.748791\pi\) | ||||
−0.704416 | + | 0.709788i | \(0.748791\pi\) | |||||||
\(212\) | −1728.00 | −0.559809 | ||||||||
\(213\) | −1284.00 | −0.413043 | ||||||||
\(214\) | −228.000 | −0.0728307 | ||||||||
\(215\) | 603.000 | 0.191276 | ||||||||
\(216\) | −800.000 | −0.252005 | ||||||||
\(217\) | −992.000 | −0.310329 | ||||||||
\(218\) | −2920.00 | −0.907190 | ||||||||
\(219\) | 974.000 | 0.300533 | ||||||||
\(220\) | −2052.00 | −0.628845 | ||||||||
\(221\) | −3588.00 | −1.09210 | ||||||||
\(222\) | −904.000 | −0.273300 | ||||||||
\(223\) | 518.000 | 0.155551 | 0.0777754 | − | 0.996971i | \(-0.475218\pi\) | ||||
0.0777754 | + | 0.996971i | \(0.475218\pi\) | |||||||
\(224\) | 992.000 | 0.295896 | ||||||||
\(225\) | 1012.00 | 0.299852 | ||||||||
\(226\) | 1644.00 | 0.483882 | ||||||||
\(227\) | 2844.00 | 0.831555 | 0.415777 | − | 0.909466i | \(-0.363510\pi\) | ||||
0.415777 | + | 0.909466i | \(0.363510\pi\) | |||||||
\(228\) | −152.000 | −0.0441511 | ||||||||
\(229\) | 1745.00 | 0.503550 | 0.251775 | − | 0.967786i | \(-0.418986\pi\) | ||||
0.251775 | + | 0.967786i | \(0.418986\pi\) | |||||||
\(230\) | −1296.00 | −0.371547 | ||||||||
\(231\) | 3534.00 | 1.00658 | ||||||||
\(232\) | 1200.00 | 0.339586 | ||||||||
\(233\) | 5283.00 | 1.48541 | 0.742706 | − | 0.669618i | \(-0.233542\pi\) | ||||
0.742706 | + | 0.669618i | \(0.233542\pi\) | |||||||
\(234\) | −2392.00 | −0.668248 | ||||||||
\(235\) | −5211.00 | −1.44650 | ||||||||
\(236\) | −1320.00 | −0.364088 | ||||||||
\(237\) | 1400.00 | 0.383712 | ||||||||
\(238\) | 4278.00 | 1.16513 | ||||||||
\(239\) | 465.000 | 0.125851 | 0.0629254 | − | 0.998018i | \(-0.479957\pi\) | ||||
0.0629254 | + | 0.998018i | \(0.479957\pi\) | |||||||
\(240\) | 288.000 | 0.0774597 | ||||||||
\(241\) | −7078.00 | −1.89184 | −0.945921 | − | 0.324396i | \(-0.894839\pi\) | ||||
−0.945921 | + | 0.324396i | \(0.894839\pi\) | |||||||
\(242\) | −3836.00 | −1.01896 | ||||||||
\(243\) | −3542.00 | −0.935059 | ||||||||
\(244\) | −52.0000 | −0.0136433 | ||||||||
\(245\) | −5562.00 | −1.45038 | ||||||||
\(246\) | −1032.00 | −0.267471 | ||||||||
\(247\) | −988.000 | −0.254514 | ||||||||
\(248\) | −256.000 | −0.0655485 | ||||||||
\(249\) | 24.0000 | 0.00610819 | ||||||||
\(250\) | −3042.00 | −0.769572 | ||||||||
\(251\) | 3567.00 | 0.897000 | 0.448500 | − | 0.893783i | \(-0.351958\pi\) | ||||
0.448500 | + | 0.893783i | \(0.351958\pi\) | |||||||
\(252\) | 2852.00 | 0.712933 | ||||||||
\(253\) | −4104.00 | −1.01983 | ||||||||
\(254\) | 4172.00 | 1.03061 | ||||||||
\(255\) | 1242.00 | 0.305008 | ||||||||
\(256\) | 256.000 | 0.0625000 | ||||||||
\(257\) | −1896.00 | −0.460192 | −0.230096 | − | 0.973168i | \(-0.573904\pi\) | ||||
−0.230096 | + | 0.973168i | \(0.573904\pi\) | |||||||
\(258\) | −268.000 | −0.0646704 | ||||||||
\(259\) | 7006.00 | 1.68082 | ||||||||
\(260\) | 1872.00 | 0.446525 | ||||||||
\(261\) | 3450.00 | 0.818198 | ||||||||
\(262\) | 186.000 | 0.0438592 | ||||||||
\(263\) | −57.0000 | −0.0133641 | −0.00668207 | − | 0.999978i | \(-0.502127\pi\) | ||||
−0.00668207 | + | 0.999978i | \(0.502127\pi\) | |||||||
\(264\) | 912.000 | 0.212613 | ||||||||
\(265\) | 3888.00 | 0.901275 | ||||||||
\(266\) | 1178.00 | 0.271533 | ||||||||
\(267\) | 1200.00 | 0.275052 | ||||||||
\(268\) | −3424.00 | −0.780426 | ||||||||
\(269\) | 2700.00 | 0.611977 | 0.305989 | − | 0.952035i | \(-0.401013\pi\) | ||||
0.305989 | + | 0.952035i | \(0.401013\pi\) | |||||||
\(270\) | 1800.00 | 0.405720 | ||||||||
\(271\) | 3872.00 | 0.867923 | 0.433962 | − | 0.900931i | \(-0.357115\pi\) | ||||
0.433962 | + | 0.900931i | \(0.357115\pi\) | |||||||
\(272\) | 1104.00 | 0.246102 | ||||||||
\(273\) | −3224.00 | −0.714745 | ||||||||
\(274\) | −2538.00 | −0.559585 | ||||||||
\(275\) | −2508.00 | −0.549957 | ||||||||
\(276\) | 576.000 | 0.125620 | ||||||||
\(277\) | −7711.00 | −1.67260 | −0.836298 | − | 0.548275i | \(-0.815285\pi\) | ||||
−0.836298 | + | 0.548275i | \(0.815285\pi\) | |||||||
\(278\) | 3950.00 | 0.852177 | ||||||||
\(279\) | −736.000 | −0.157932 | ||||||||
\(280\) | −2232.00 | −0.476384 | ||||||||
\(281\) | −6858.00 | −1.45592 | −0.727961 | − | 0.685619i | \(-0.759532\pi\) | ||||
−0.727961 | + | 0.685619i | \(0.759532\pi\) | |||||||
\(282\) | 2316.00 | 0.489063 | ||||||||
\(283\) | −1807.00 | −0.379558 | −0.189779 | − | 0.981827i | \(-0.560777\pi\) | ||||
−0.189779 | + | 0.981827i | \(0.560777\pi\) | |||||||
\(284\) | 2568.00 | 0.536559 | ||||||||
\(285\) | 342.000 | 0.0710819 | ||||||||
\(286\) | 5928.00 | 1.22563 | ||||||||
\(287\) | 7998.00 | 1.64497 | ||||||||
\(288\) | 736.000 | 0.150588 | ||||||||
\(289\) | −152.000 | −0.0309383 | ||||||||
\(290\) | −2700.00 | −0.546722 | ||||||||
\(291\) | −2848.00 | −0.573721 | ||||||||
\(292\) | −1948.00 | −0.390404 | ||||||||
\(293\) | −3012.00 | −0.600556 | −0.300278 | − | 0.953852i | \(-0.597079\pi\) | ||||
−0.300278 | + | 0.953852i | \(0.597079\pi\) | |||||||
\(294\) | 2472.00 | 0.490374 | ||||||||
\(295\) | 2970.00 | 0.586170 | ||||||||
\(296\) | 1808.00 | 0.355027 | ||||||||
\(297\) | 5700.00 | 1.11363 | ||||||||
\(298\) | 3390.00 | 0.658985 | ||||||||
\(299\) | 3744.00 | 0.724151 | ||||||||
\(300\) | 352.000 | 0.0677424 | ||||||||
\(301\) | 2077.00 | 0.397729 | ||||||||
\(302\) | −3604.00 | −0.686712 | ||||||||
\(303\) | −2124.00 | −0.402708 | ||||||||
\(304\) | 304.000 | 0.0573539 | ||||||||
\(305\) | 117.000 | 0.0219652 | ||||||||
\(306\) | 3174.00 | 0.592959 | ||||||||
\(307\) | −1096.00 | −0.203753 | −0.101876 | − | 0.994797i | \(-0.532485\pi\) | ||||
−0.101876 | + | 0.994797i | \(0.532485\pi\) | |||||||
\(308\) | −7068.00 | −1.30759 | ||||||||
\(309\) | −2356.00 | −0.433748 | ||||||||
\(310\) | 576.000 | 0.105531 | ||||||||
\(311\) | 1947.00 | 0.354998 | 0.177499 | − | 0.984121i | \(-0.443199\pi\) | ||||
0.177499 | + | 0.984121i | \(0.443199\pi\) | |||||||
\(312\) | −832.000 | −0.150970 | ||||||||
\(313\) | 7598.00 | 1.37209 | 0.686045 | − | 0.727559i | \(-0.259345\pi\) | ||||
0.686045 | + | 0.727559i | \(0.259345\pi\) | |||||||
\(314\) | 6452.00 | 1.15958 | ||||||||
\(315\) | −6417.00 | −1.14780 | ||||||||
\(316\) | −2800.00 | −0.498457 | ||||||||
\(317\) | 8334.00 | 1.47661 | 0.738303 | − | 0.674469i | \(-0.235627\pi\) | ||||
0.738303 | + | 0.674469i | \(0.235627\pi\) | |||||||
\(318\) | −1728.00 | −0.304721 | ||||||||
\(319\) | −8550.00 | −1.50065 | ||||||||
\(320\) | −576.000 | −0.100623 | ||||||||
\(321\) | −228.000 | −0.0396440 | ||||||||
\(322\) | −4464.00 | −0.772575 | ||||||||
\(323\) | 1311.00 | 0.225839 | ||||||||
\(324\) | 1684.00 | 0.288752 | ||||||||
\(325\) | 2288.00 | 0.390509 | ||||||||
\(326\) | −2536.00 | −0.430847 | ||||||||
\(327\) | −2920.00 | −0.493812 | ||||||||
\(328\) | 2064.00 | 0.347455 | ||||||||
\(329\) | −17949.0 | −3.00778 | ||||||||
\(330\) | −2052.00 | −0.342300 | ||||||||
\(331\) | −8368.00 | −1.38957 | −0.694784 | − | 0.719219i | \(-0.744500\pi\) | ||||
−0.694784 | + | 0.719219i | \(0.744500\pi\) | |||||||
\(332\) | −48.0000 | −0.00793477 | ||||||||
\(333\) | 5198.00 | 0.855401 | ||||||||
\(334\) | −1308.00 | −0.214283 | ||||||||
\(335\) | 7704.00 | 1.25646 | ||||||||
\(336\) | 992.000 | 0.161066 | ||||||||
\(337\) | −10336.0 | −1.67074 | −0.835368 | − | 0.549692i | \(-0.814745\pi\) | ||||
−0.835368 | + | 0.549692i | \(0.814745\pi\) | |||||||
\(338\) | −1014.00 | −0.163178 | ||||||||
\(339\) | 1644.00 | 0.263392 | ||||||||
\(340\) | −2484.00 | −0.396217 | ||||||||
\(341\) | 1824.00 | 0.289663 | ||||||||
\(342\) | 874.000 | 0.138189 | ||||||||
\(343\) | −8525.00 | −1.34200 | ||||||||
\(344\) | 536.000 | 0.0840093 | ||||||||
\(345\) | −1296.00 | −0.202244 | ||||||||
\(346\) | 2724.00 | 0.423246 | ||||||||
\(347\) | 6879.00 | 1.06422 | 0.532110 | − | 0.846675i | \(-0.321399\pi\) | ||||
0.532110 | + | 0.846675i | \(0.321399\pi\) | |||||||
\(348\) | 1200.00 | 0.184847 | ||||||||
\(349\) | −6355.00 | −0.974714 | −0.487357 | − | 0.873203i | \(-0.662039\pi\) | ||||
−0.487357 | + | 0.873203i | \(0.662039\pi\) | |||||||
\(350\) | −2728.00 | −0.416622 | ||||||||
\(351\) | −5200.00 | −0.790756 | ||||||||
\(352\) | −1824.00 | −0.276192 | ||||||||
\(353\) | 7218.00 | 1.08832 | 0.544158 | − | 0.838983i | \(-0.316849\pi\) | ||||
0.544158 | + | 0.838983i | \(0.316849\pi\) | |||||||
\(354\) | −1320.00 | −0.198184 | ||||||||
\(355\) | −5778.00 | −0.863843 | ||||||||
\(356\) | −2400.00 | −0.357303 | ||||||||
\(357\) | 4278.00 | 0.634218 | ||||||||
\(358\) | 420.000 | 0.0620047 | ||||||||
\(359\) | 1665.00 | 0.244778 | 0.122389 | − | 0.992482i | \(-0.460944\pi\) | ||||
0.122389 | + | 0.992482i | \(0.460944\pi\) | |||||||
\(360\) | −1656.00 | −0.242441 | ||||||||
\(361\) | 361.000 | 0.0526316 | ||||||||
\(362\) | −4.00000 | −0.000580761 0 | ||||||||
\(363\) | −3836.00 | −0.554650 | ||||||||
\(364\) | 6448.00 | 0.928481 | ||||||||
\(365\) | 4383.00 | 0.628539 | ||||||||
\(366\) | −52.0000 | −0.00742646 | ||||||||
\(367\) | 13064.0 | 1.85813 | 0.929067 | − | 0.369911i | \(-0.120612\pi\) | ||||
0.929067 | + | 0.369911i | \(0.120612\pi\) | |||||||
\(368\) | −1152.00 | −0.163185 | ||||||||
\(369\) | 5934.00 | 0.837159 | ||||||||
\(370\) | −4068.00 | −0.571582 | ||||||||
\(371\) | 13392.0 | 1.87406 | ||||||||
\(372\) | −256.000 | −0.0356801 | ||||||||
\(373\) | −10492.0 | −1.45645 | −0.728224 | − | 0.685339i | \(-0.759654\pi\) | ||||
−0.728224 | + | 0.685339i | \(0.759654\pi\) | |||||||
\(374\) | −7866.00 | −1.08754 | ||||||||
\(375\) | −3042.00 | −0.418902 | ||||||||
\(376\) | −4632.00 | −0.635312 | ||||||||
\(377\) | 7800.00 | 1.06557 | ||||||||
\(378\) | 6200.00 | 0.843634 | ||||||||
\(379\) | 7610.00 | 1.03140 | 0.515698 | − | 0.856770i | \(-0.327532\pi\) | ||||
0.515698 | + | 0.856770i | \(0.327532\pi\) | |||||||
\(380\) | −684.000 | −0.0923381 | ||||||||
\(381\) | 4172.00 | 0.560992 | ||||||||
\(382\) | 5286.00 | 0.707998 | ||||||||
\(383\) | 4008.00 | 0.534724 | 0.267362 | − | 0.963596i | \(-0.413848\pi\) | ||||
0.267362 | + | 0.963596i | \(0.413848\pi\) | |||||||
\(384\) | 256.000 | 0.0340207 | ||||||||
\(385\) | 15903.0 | 2.10517 | ||||||||
\(386\) | −6496.00 | −0.856574 | ||||||||
\(387\) | 1541.00 | 0.202412 | ||||||||
\(388\) | 5696.00 | 0.745285 | ||||||||
\(389\) | −3525.00 | −0.459446 | −0.229723 | − | 0.973256i | \(-0.573782\pi\) | ||||
−0.229723 | + | 0.973256i | \(0.573782\pi\) | |||||||
\(390\) | 1872.00 | 0.243057 | ||||||||
\(391\) | −4968.00 | −0.642564 | ||||||||
\(392\) | −4944.00 | −0.637015 | ||||||||
\(393\) | 186.000 | 0.0238739 | ||||||||
\(394\) | 6252.00 | 0.799419 | ||||||||
\(395\) | 6300.00 | 0.802500 | ||||||||
\(396\) | −5244.00 | −0.665457 | ||||||||
\(397\) | 6629.00 | 0.838035 | 0.419018 | − | 0.907978i | \(-0.362375\pi\) | ||||
0.419018 | + | 0.907978i | \(0.362375\pi\) | |||||||
\(398\) | 5990.00 | 0.754401 | ||||||||
\(399\) | 1178.00 | 0.147804 | ||||||||
\(400\) | −704.000 | −0.0880000 | ||||||||
\(401\) | −10848.0 | −1.35093 | −0.675465 | − | 0.737392i | \(-0.736057\pi\) | ||||
−0.675465 | + | 0.737392i | \(0.736057\pi\) | |||||||
\(402\) | −3424.00 | −0.424810 | ||||||||
\(403\) | −1664.00 | −0.205682 | ||||||||
\(404\) | 4248.00 | 0.523133 | ||||||||
\(405\) | −3789.00 | −0.464881 | ||||||||
\(406\) | −9300.00 | −1.13683 | ||||||||
\(407\) | −12882.0 | −1.56889 | ||||||||
\(408\) | 1104.00 | 0.133961 | ||||||||
\(409\) | −3040.00 | −0.367526 | −0.183763 | − | 0.982971i | \(-0.558828\pi\) | ||||
−0.183763 | + | 0.982971i | \(0.558828\pi\) | |||||||
\(410\) | −4644.00 | −0.559392 | ||||||||
\(411\) | −2538.00 | −0.304599 | ||||||||
\(412\) | 4712.00 | 0.563455 | ||||||||
\(413\) | 10230.0 | 1.21885 | ||||||||
\(414\) | −3312.00 | −0.393179 | ||||||||
\(415\) | 108.000 | 0.0127747 | ||||||||
\(416\) | 1664.00 | 0.196116 | ||||||||
\(417\) | 3950.00 | 0.463867 | ||||||||
\(418\) | −2166.00 | −0.253451 | ||||||||
\(419\) | −3900.00 | −0.454719 | −0.227360 | − | 0.973811i | \(-0.573009\pi\) | ||||
−0.227360 | + | 0.973811i | \(0.573009\pi\) | |||||||
\(420\) | −2232.00 | −0.259311 | ||||||||
\(421\) | 4412.00 | 0.510755 | 0.255377 | − | 0.966841i | \(-0.417800\pi\) | ||||
0.255377 | + | 0.966841i | \(0.417800\pi\) | |||||||
\(422\) | 8636.00 | 0.996194 | ||||||||
\(423\) | −13317.0 | −1.53072 | ||||||||
\(424\) | 3456.00 | 0.395845 | ||||||||
\(425\) | −3036.00 | −0.346512 | ||||||||
\(426\) | 2568.00 | 0.292066 | ||||||||
\(427\) | 403.000 | 0.0456734 | ||||||||
\(428\) | 456.000 | 0.0514990 | ||||||||
\(429\) | 5928.00 | 0.667148 | ||||||||
\(430\) | −1206.00 | −0.135252 | ||||||||
\(431\) | 432.000 | 0.0482801 | 0.0241400 | − | 0.999709i | \(-0.492315\pi\) | ||||
0.0241400 | + | 0.999709i | \(0.492315\pi\) | |||||||
\(432\) | 1600.00 | 0.178195 | ||||||||
\(433\) | −2002.00 | −0.222194 | −0.111097 | − | 0.993810i | \(-0.535436\pi\) | ||||
−0.111097 | + | 0.993810i | \(0.535436\pi\) | |||||||
\(434\) | 1984.00 | 0.219436 | ||||||||
\(435\) | −2700.00 | −0.297598 | ||||||||
\(436\) | 5840.00 | 0.641480 | ||||||||
\(437\) | −1368.00 | −0.149749 | ||||||||
\(438\) | −1948.00 | −0.212509 | ||||||||
\(439\) | −1690.00 | −0.183734 | −0.0918671 | − | 0.995771i | \(-0.529283\pi\) | ||||
−0.0918671 | + | 0.995771i | \(0.529283\pi\) | |||||||
\(440\) | 4104.00 | 0.444660 | ||||||||
\(441\) | −14214.0 | −1.53482 | ||||||||
\(442\) | 7176.00 | 0.772234 | ||||||||
\(443\) | −1977.00 | −0.212032 | −0.106016 | − | 0.994364i | \(-0.533809\pi\) | ||||
−0.106016 | + | 0.994364i | \(0.533809\pi\) | |||||||
\(444\) | 1808.00 | 0.193252 | ||||||||
\(445\) | 5400.00 | 0.575246 | ||||||||
\(446\) | −1036.00 | −0.109991 | ||||||||
\(447\) | 3390.00 | 0.358706 | ||||||||
\(448\) | −1984.00 | −0.209230 | ||||||||
\(449\) | −2760.00 | −0.290095 | −0.145047 | − | 0.989425i | \(-0.546333\pi\) | ||||
−0.145047 | + | 0.989425i | \(0.546333\pi\) | |||||||
\(450\) | −2024.00 | −0.212027 | ||||||||
\(451\) | −14706.0 | −1.53543 | ||||||||
\(452\) | −3288.00 | −0.342156 | ||||||||
\(453\) | −3604.00 | −0.373798 | ||||||||
\(454\) | −5688.00 | −0.587998 | ||||||||
\(455\) | −14508.0 | −1.49483 | ||||||||
\(456\) | 304.000 | 0.0312195 | ||||||||
\(457\) | 4499.00 | 0.460513 | 0.230256 | − | 0.973130i | \(-0.426044\pi\) | ||||
0.230256 | + | 0.973130i | \(0.426044\pi\) | |||||||
\(458\) | −3490.00 | −0.356063 | ||||||||
\(459\) | 6900.00 | 0.701665 | ||||||||
\(460\) | 2592.00 | 0.262723 | ||||||||
\(461\) | −11643.0 | −1.17629 | −0.588144 | − | 0.808756i | \(-0.700141\pi\) | ||||
−0.588144 | + | 0.808756i | \(0.700141\pi\) | |||||||
\(462\) | −7068.00 | −0.711760 | ||||||||
\(463\) | −1537.00 | −0.154277 | −0.0771387 | − | 0.997020i | \(-0.524578\pi\) | ||||
−0.0771387 | + | 0.997020i | \(0.524578\pi\) | |||||||
\(464\) | −2400.00 | −0.240123 | ||||||||
\(465\) | 576.000 | 0.0574438 | ||||||||
\(466\) | −10566.0 | −1.05034 | ||||||||
\(467\) | −7641.00 | −0.757138 | −0.378569 | − | 0.925573i | \(-0.623584\pi\) | ||||
−0.378569 | + | 0.925573i | \(0.623584\pi\) | |||||||
\(468\) | 4784.00 | 0.472522 | ||||||||
\(469\) | 26536.0 | 2.61262 | ||||||||
\(470\) | 10422.0 | 1.02283 | ||||||||
\(471\) | 6452.00 | 0.631194 | ||||||||
\(472\) | 2640.00 | 0.257449 | ||||||||
\(473\) | −3819.00 | −0.371243 | ||||||||
\(474\) | −2800.00 | −0.271325 | ||||||||
\(475\) | −836.000 | −0.0807543 | ||||||||
\(476\) | −8556.00 | −0.823873 | ||||||||
\(477\) | 9936.00 | 0.953749 | ||||||||
\(478\) | −930.000 | −0.0889900 | ||||||||
\(479\) | −8580.00 | −0.818435 | −0.409217 | − | 0.912437i | \(-0.634198\pi\) | ||||
−0.409217 | + | 0.912437i | \(0.634198\pi\) | |||||||
\(480\) | −576.000 | −0.0547723 | ||||||||
\(481\) | 11752.0 | 1.11402 | ||||||||
\(482\) | 14156.0 | 1.33773 | ||||||||
\(483\) | −4464.00 | −0.420536 | ||||||||
\(484\) | 7672.00 | 0.720511 | ||||||||
\(485\) | −12816.0 | −1.19989 | ||||||||
\(486\) | 7084.00 | 0.661187 | ||||||||
\(487\) | 12134.0 | 1.12904 | 0.564522 | − | 0.825418i | \(-0.309061\pi\) | ||||
0.564522 | + | 0.825418i | \(0.309061\pi\) | |||||||
\(488\) | 104.000 | 0.00964725 | ||||||||
\(489\) | −2536.00 | −0.234523 | ||||||||
\(490\) | 11124.0 | 1.02557 | ||||||||
\(491\) | −5508.00 | −0.506258 | −0.253129 | − | 0.967433i | \(-0.581460\pi\) | ||||
−0.253129 | + | 0.967433i | \(0.581460\pi\) | |||||||
\(492\) | 2064.00 | 0.189131 | ||||||||
\(493\) | −10350.0 | −0.945518 | ||||||||
\(494\) | 1976.00 | 0.179969 | ||||||||
\(495\) | 11799.0 | 1.07136 | ||||||||
\(496\) | 512.000 | 0.0463498 | ||||||||
\(497\) | −19902.0 | −1.79623 | ||||||||
\(498\) | −48.0000 | −0.00431914 | ||||||||
\(499\) | −11905.0 | −1.06802 | −0.534009 | − | 0.845479i | \(-0.679315\pi\) | ||||
−0.534009 | + | 0.845479i | \(0.679315\pi\) | |||||||
\(500\) | 6084.00 | 0.544170 | ||||||||
\(501\) | −1308.00 | −0.116641 | ||||||||
\(502\) | −7134.00 | −0.634275 | ||||||||
\(503\) | 9108.00 | 0.807367 | 0.403684 | − | 0.914899i | \(-0.367730\pi\) | ||||
0.403684 | + | 0.914899i | \(0.367730\pi\) | |||||||
\(504\) | −5704.00 | −0.504120 | ||||||||
\(505\) | −9558.00 | −0.842229 | ||||||||
\(506\) | 8208.00 | 0.721127 | ||||||||
\(507\) | −1014.00 | −0.0888231 | ||||||||
\(508\) | −8344.00 | −0.728750 | ||||||||
\(509\) | −2520.00 | −0.219444 | −0.109722 | − | 0.993962i | \(-0.534996\pi\) | ||||
−0.109722 | + | 0.993962i | \(0.534996\pi\) | |||||||
\(510\) | −2484.00 | −0.215673 | ||||||||
\(511\) | 15097.0 | 1.30695 | ||||||||
\(512\) | −512.000 | −0.0441942 | ||||||||
\(513\) | 1900.00 | 0.163523 | ||||||||
\(514\) | 3792.00 | 0.325405 | ||||||||
\(515\) | −10602.0 | −0.907146 | ||||||||
\(516\) | 536.000 | 0.0457288 | ||||||||
\(517\) | 33003.0 | 2.80749 | ||||||||
\(518\) | −14012.0 | −1.18852 | ||||||||
\(519\) | 2724.00 | 0.230386 | ||||||||
\(520\) | −3744.00 | −0.315741 | ||||||||
\(521\) | 21612.0 | 1.81735 | 0.908675 | − | 0.417505i | \(-0.137095\pi\) | ||||
0.908675 | + | 0.417505i | \(0.137095\pi\) | |||||||
\(522\) | −6900.00 | −0.578553 | ||||||||
\(523\) | −9022.00 | −0.754311 | −0.377155 | − | 0.926150i | \(-0.623098\pi\) | ||||
−0.377155 | + | 0.926150i | \(0.623098\pi\) | |||||||
\(524\) | −372.000 | −0.0310132 | ||||||||
\(525\) | −2728.00 | −0.226780 | ||||||||
\(526\) | 114.000 | 0.00944988 | ||||||||
\(527\) | 2208.00 | 0.182509 | ||||||||
\(528\) | −1824.00 | −0.150340 | ||||||||
\(529\) | −6983.00 | −0.573929 | ||||||||
\(530\) | −7776.00 | −0.637298 | ||||||||
\(531\) | 7590.00 | 0.620297 | ||||||||
\(532\) | −2356.00 | −0.192003 | ||||||||
\(533\) | 13416.0 | 1.09027 | ||||||||
\(534\) | −2400.00 | −0.194491 | ||||||||
\(535\) | −1026.00 | −0.0829119 | ||||||||
\(536\) | 6848.00 | 0.551844 | ||||||||
\(537\) | 420.000 | 0.0337511 | ||||||||
\(538\) | −5400.00 | −0.432733 | ||||||||
\(539\) | 35226.0 | 2.81501 | ||||||||
\(540\) | −3600.00 | −0.286888 | ||||||||
\(541\) | −9253.00 | −0.735337 | −0.367669 | − | 0.929957i | \(-0.619844\pi\) | ||||
−0.367669 | + | 0.929957i | \(0.619844\pi\) | |||||||
\(542\) | −7744.00 | −0.613715 | ||||||||
\(543\) | −4.00000 | −0.000316126 0 | ||||||||
\(544\) | −2208.00 | −0.174021 | ||||||||
\(545\) | −13140.0 | −1.03276 | ||||||||
\(546\) | 6448.00 | 0.505401 | ||||||||
\(547\) | 13244.0 | 1.03523 | 0.517617 | − | 0.855613i | \(-0.326819\pi\) | ||||
0.517617 | + | 0.855613i | \(0.326819\pi\) | |||||||
\(548\) | 5076.00 | 0.395686 | ||||||||
\(549\) | 299.000 | 0.0232441 | ||||||||
\(550\) | 5016.00 | 0.388878 | ||||||||
\(551\) | −2850.00 | −0.220352 | ||||||||
\(552\) | −1152.00 | −0.0888268 | ||||||||
\(553\) | 21700.0 | 1.66868 | ||||||||
\(554\) | 15422.0 | 1.18270 | ||||||||
\(555\) | −4068.00 | −0.311130 | ||||||||
\(556\) | −7900.00 | −0.602580 | ||||||||
\(557\) | 1569.00 | 0.119355 | 0.0596774 | − | 0.998218i | \(-0.480993\pi\) | ||||
0.0596774 | + | 0.998218i | \(0.480993\pi\) | |||||||
\(558\) | 1472.00 | 0.111675 | ||||||||
\(559\) | 3484.00 | 0.263609 | ||||||||
\(560\) | 4464.00 | 0.336854 | ||||||||
\(561\) | −7866.00 | −0.591984 | ||||||||
\(562\) | 13716.0 | 1.02949 | ||||||||
\(563\) | −15762.0 | −1.17991 | −0.589955 | − | 0.807436i | \(-0.700854\pi\) | ||||
−0.589955 | + | 0.807436i | \(0.700854\pi\) | |||||||
\(564\) | −4632.00 | −0.345820 | ||||||||
\(565\) | 7398.00 | 0.550861 | ||||||||
\(566\) | 3614.00 | 0.268388 | ||||||||
\(567\) | −13051.0 | −0.966650 | ||||||||
\(568\) | −5136.00 | −0.379405 | ||||||||
\(569\) | −13800.0 | −1.01674 | −0.508371 | − | 0.861138i | \(-0.669752\pi\) | ||||
−0.508371 | + | 0.861138i | \(0.669752\pi\) | |||||||
\(570\) | −684.000 | −0.0502625 | ||||||||
\(571\) | −4348.00 | −0.318666 | −0.159333 | − | 0.987225i | \(-0.550934\pi\) | ||||
−0.159333 | + | 0.987225i | \(0.550934\pi\) | |||||||
\(572\) | −11856.0 | −0.866651 | ||||||||
\(573\) | 5286.00 | 0.385385 | ||||||||
\(574\) | −15996.0 | −1.16317 | ||||||||
\(575\) | 3168.00 | 0.229765 | ||||||||
\(576\) | −1472.00 | −0.106481 | ||||||||
\(577\) | 3539.00 | 0.255339 | 0.127669 | − | 0.991817i | \(-0.459250\pi\) | ||||
0.127669 | + | 0.991817i | \(0.459250\pi\) | |||||||
\(578\) | 304.000 | 0.0218767 | ||||||||
\(579\) | −6496.00 | −0.466260 | ||||||||
\(580\) | 5400.00 | 0.386591 | ||||||||
\(581\) | 372.000 | 0.0265631 | ||||||||
\(582\) | 5696.00 | 0.405682 | ||||||||
\(583\) | −24624.0 | −1.74927 | ||||||||
\(584\) | 3896.00 | 0.276058 | ||||||||
\(585\) | −10764.0 | −0.760746 | ||||||||
\(586\) | 6024.00 | 0.424657 | ||||||||
\(587\) | −6321.00 | −0.444456 | −0.222228 | − | 0.974995i | \(-0.571333\pi\) | ||||
−0.222228 | + | 0.974995i | \(0.571333\pi\) | |||||||
\(588\) | −4944.00 | −0.346747 | ||||||||
\(589\) | 608.000 | 0.0425335 | ||||||||
\(590\) | −5940.00 | −0.414485 | ||||||||
\(591\) | 6252.00 | 0.435149 | ||||||||
\(592\) | −3616.00 | −0.251042 | ||||||||
\(593\) | 13278.0 | 0.919498 | 0.459749 | − | 0.888049i | \(-0.347939\pi\) | ||||
0.459749 | + | 0.888049i | \(0.347939\pi\) | |||||||
\(594\) | −11400.0 | −0.787454 | ||||||||
\(595\) | 19251.0 | 1.32641 | ||||||||
\(596\) | −6780.00 | −0.465973 | ||||||||
\(597\) | 5990.00 | 0.410644 | ||||||||
\(598\) | −7488.00 | −0.512052 | ||||||||
\(599\) | 20400.0 | 1.39152 | 0.695761 | − | 0.718274i | \(-0.255067\pi\) | ||||
0.695761 | + | 0.718274i | \(0.255067\pi\) | |||||||
\(600\) | −704.000 | −0.0479011 | ||||||||
\(601\) | −22198.0 | −1.50661 | −0.753307 | − | 0.657669i | \(-0.771543\pi\) | ||||
−0.753307 | + | 0.657669i | \(0.771543\pi\) | |||||||
\(602\) | −4154.00 | −0.281237 | ||||||||
\(603\) | 19688.0 | 1.32961 | ||||||||
\(604\) | 7208.00 | 0.485578 | ||||||||
\(605\) | −17262.0 | −1.16000 | ||||||||
\(606\) | 4248.00 | 0.284758 | ||||||||
\(607\) | 9824.00 | 0.656909 | 0.328455 | − | 0.944520i | \(-0.393472\pi\) | ||||
0.328455 | + | 0.944520i | \(0.393472\pi\) | |||||||
\(608\) | −608.000 | −0.0405554 | ||||||||
\(609\) | −9300.00 | −0.618810 | ||||||||
\(610\) | −234.000 | −0.0155318 | ||||||||
\(611\) | −30108.0 | −1.99352 | ||||||||
\(612\) | −6348.00 | −0.419285 | ||||||||
\(613\) | −4327.00 | −0.285099 | −0.142550 | − | 0.989788i | \(-0.545530\pi\) | ||||
−0.142550 | + | 0.989788i | \(0.545530\pi\) | |||||||
\(614\) | 2192.00 | 0.144075 | ||||||||
\(615\) | −4644.00 | −0.304495 | ||||||||
\(616\) | 14136.0 | 0.924603 | ||||||||
\(617\) | −14151.0 | −0.923335 | −0.461668 | − | 0.887053i | \(-0.652749\pi\) | ||||
−0.461668 | + | 0.887053i | \(0.652749\pi\) | |||||||
\(618\) | 4712.00 | 0.306706 | ||||||||
\(619\) | 22460.0 | 1.45839 | 0.729195 | − | 0.684306i | \(-0.239895\pi\) | ||||
0.729195 | + | 0.684306i | \(0.239895\pi\) | |||||||
\(620\) | −1152.00 | −0.0746217 | ||||||||
\(621\) | −7200.00 | −0.465259 | ||||||||
\(622\) | −3894.00 | −0.251021 | ||||||||
\(623\) | 18600.0 | 1.19614 | ||||||||
\(624\) | 1664.00 | 0.106752 | ||||||||
\(625\) | −8189.00 | −0.524096 | ||||||||
\(626\) | −15196.0 | −0.970215 | ||||||||
\(627\) | −2166.00 | −0.137961 | ||||||||
\(628\) | −12904.0 | −0.819945 | ||||||||
\(629\) | −15594.0 | −0.988511 | ||||||||
\(630\) | 12834.0 | 0.811617 | ||||||||
\(631\) | −16363.0 | −1.03233 | −0.516165 | − | 0.856489i | \(-0.672641\pi\) | ||||
−0.516165 | + | 0.856489i | \(0.672641\pi\) | |||||||
\(632\) | 5600.00 | 0.352462 | ||||||||
\(633\) | 8636.00 | 0.542259 | ||||||||
\(634\) | −16668.0 | −1.04412 | ||||||||
\(635\) | 18774.0 | 1.17327 | ||||||||
\(636\) | 3456.00 | 0.215471 | ||||||||
\(637\) | −32136.0 | −1.99886 | ||||||||
\(638\) | 17100.0 | 1.06112 | ||||||||
\(639\) | −14766.0 | −0.914138 | ||||||||
\(640\) | 1152.00 | 0.0711512 | ||||||||
\(641\) | 5592.00 | 0.344572 | 0.172286 | − | 0.985047i | \(-0.444885\pi\) | ||||
0.172286 | + | 0.985047i | \(0.444885\pi\) | |||||||
\(642\) | 456.000 | 0.0280325 | ||||||||
\(643\) | 16553.0 | 1.01522 | 0.507610 | − | 0.861587i | \(-0.330529\pi\) | ||||
0.507610 | + | 0.861587i | \(0.330529\pi\) | |||||||
\(644\) | 8928.00 | 0.546293 | ||||||||
\(645\) | −1206.00 | −0.0736220 | ||||||||
\(646\) | −2622.00 | −0.159692 | ||||||||
\(647\) | −4611.00 | −0.280181 | −0.140091 | − | 0.990139i | \(-0.544739\pi\) | ||||
−0.140091 | + | 0.990139i | \(0.544739\pi\) | |||||||
\(648\) | −3368.00 | −0.204178 | ||||||||
\(649\) | −18810.0 | −1.13768 | ||||||||
\(650\) | −4576.00 | −0.276132 | ||||||||
\(651\) | 1984.00 | 0.119446 | ||||||||
\(652\) | 5072.00 | 0.304655 | ||||||||
\(653\) | 16413.0 | 0.983599 | 0.491800 | − | 0.870708i | \(-0.336339\pi\) | ||||
0.491800 | + | 0.870708i | \(0.336339\pi\) | |||||||
\(654\) | 5840.00 | 0.349177 | ||||||||
\(655\) | 837.000 | 0.0499302 | ||||||||
\(656\) | −4128.00 | −0.245688 | ||||||||
\(657\) | 11201.0 | 0.665133 | ||||||||
\(658\) | 35898.0 | 2.12682 | ||||||||
\(659\) | 27390.0 | 1.61906 | 0.809532 | − | 0.587076i | \(-0.199721\pi\) | ||||
0.809532 | + | 0.587076i | \(0.199721\pi\) | |||||||
\(660\) | 4104.00 | 0.242042 | ||||||||
\(661\) | 26912.0 | 1.58359 | 0.791797 | − | 0.610784i | \(-0.209146\pi\) | ||||
0.791797 | + | 0.610784i | \(0.209146\pi\) | |||||||
\(662\) | 16736.0 | 0.982573 | ||||||||
\(663\) | 7176.00 | 0.420351 | ||||||||
\(664\) | 96.0000 | 0.00561073 | ||||||||
\(665\) | 5301.00 | 0.309119 | ||||||||
\(666\) | −10396.0 | −0.604860 | ||||||||
\(667\) | 10800.0 | 0.626953 | ||||||||
\(668\) | 2616.00 | 0.151521 | ||||||||
\(669\) | −1036.00 | −0.0598716 | ||||||||
\(670\) | −15408.0 | −0.888452 | ||||||||
\(671\) | −741.000 | −0.0426319 | ||||||||
\(672\) | −1984.00 | −0.113891 | ||||||||
\(673\) | −21562.0 | −1.23500 | −0.617499 | − | 0.786571i | \(-0.711854\pi\) | ||||
−0.617499 | + | 0.786571i | \(0.711854\pi\) | |||||||
\(674\) | 20672.0 | 1.18139 | ||||||||
\(675\) | −4400.00 | −0.250898 | ||||||||
\(676\) | 2028.00 | 0.115385 | ||||||||
\(677\) | −21966.0 | −1.24700 | −0.623502 | − | 0.781822i | \(-0.714291\pi\) | ||||
−0.623502 | + | 0.781822i | \(0.714291\pi\) | |||||||
\(678\) | −3288.00 | −0.186246 | ||||||||
\(679\) | −44144.0 | −2.49498 | ||||||||
\(680\) | 4968.00 | 0.280168 | ||||||||
\(681\) | −5688.00 | −0.320066 | ||||||||
\(682\) | −3648.00 | −0.204823 | ||||||||
\(683\) | 15348.0 | 0.859846 | 0.429923 | − | 0.902866i | \(-0.358541\pi\) | ||||
0.429923 | + | 0.902866i | \(0.358541\pi\) | |||||||
\(684\) | −1748.00 | −0.0977141 | ||||||||
\(685\) | −11421.0 | −0.637042 | ||||||||
\(686\) | 17050.0 | 0.948939 | ||||||||
\(687\) | −3490.00 | −0.193816 | ||||||||
\(688\) | −1072.00 | −0.0594035 | ||||||||
\(689\) | 22464.0 | 1.24210 | ||||||||
\(690\) | 2592.00 | 0.143008 | ||||||||
\(691\) | 8147.00 | 0.448519 | 0.224259 | − | 0.974529i | \(-0.428004\pi\) | ||||
0.224259 | + | 0.974529i | \(0.428004\pi\) | |||||||
\(692\) | −5448.00 | −0.299280 | ||||||||
\(693\) | 40641.0 | 2.22774 | ||||||||
\(694\) | −13758.0 | −0.752517 | ||||||||
\(695\) | 17775.0 | 0.970136 | ||||||||
\(696\) | −2400.00 | −0.130707 | ||||||||
\(697\) | −17802.0 | −0.967430 | ||||||||
\(698\) | 12710.0 | 0.689227 | ||||||||
\(699\) | −10566.0 | −0.571735 | ||||||||
\(700\) | 5456.00 | 0.294596 | ||||||||
\(701\) | 14982.0 | 0.807222 | 0.403611 | − | 0.914931i | \(-0.367755\pi\) | ||||
0.403611 | + | 0.914931i | \(0.367755\pi\) | |||||||
\(702\) | 10400.0 | 0.559149 | ||||||||
\(703\) | −4294.00 | −0.230372 | ||||||||
\(704\) | 3648.00 | 0.195297 | ||||||||
\(705\) | 10422.0 | 0.556759 | ||||||||
\(706\) | −14436.0 | −0.769555 | ||||||||
\(707\) | −32922.0 | −1.75129 | ||||||||
\(708\) | 2640.00 | 0.140137 | ||||||||
\(709\) | 21890.0 | 1.15952 | 0.579758 | − | 0.814789i | \(-0.303147\pi\) | ||||
0.579758 | + | 0.814789i | \(0.303147\pi\) | |||||||
\(710\) | 11556.0 | 0.610830 | ||||||||
\(711\) | 16100.0 | 0.849222 | ||||||||
\(712\) | 4800.00 | 0.252651 | ||||||||
\(713\) | −2304.00 | −0.121018 | ||||||||
\(714\) | −8556.00 | −0.448460 | ||||||||
\(715\) | 26676.0 | 1.39528 | ||||||||
\(716\) | −840.000 | −0.0438440 | ||||||||
\(717\) | −930.000 | −0.0484400 | ||||||||
\(718\) | −3330.00 | −0.173084 | ||||||||
\(719\) | −27015.0 | −1.40124 | −0.700619 | − | 0.713536i | \(-0.747093\pi\) | ||||
−0.700619 | + | 0.713536i | \(0.747093\pi\) | |||||||
\(720\) | 3312.00 | 0.171432 | ||||||||
\(721\) | −36518.0 | −1.88627 | ||||||||
\(722\) | −722.000 | −0.0372161 | ||||||||
\(723\) | 14156.0 | 0.728171 | ||||||||
\(724\) | 8.00000 | 0.000410660 0 | ||||||||
\(725\) | 6600.00 | 0.338094 | ||||||||
\(726\) | 7672.00 | 0.392196 | ||||||||
\(727\) | −13021.0 | −0.664267 | −0.332134 | − | 0.943232i | \(-0.607768\pi\) | ||||
−0.332134 | + | 0.943232i | \(0.607768\pi\) | |||||||
\(728\) | −12896.0 | −0.656535 | ||||||||
\(729\) | −4283.00 | −0.217599 | ||||||||
\(730\) | −8766.00 | −0.444444 | ||||||||
\(731\) | −4623.00 | −0.233909 | ||||||||
\(732\) | 104.000 | 0.00525130 | ||||||||
\(733\) | −6262.00 | −0.315542 | −0.157771 | − | 0.987476i | \(-0.550431\pi\) | ||||
−0.157771 | + | 0.987476i | \(0.550431\pi\) | |||||||
\(734\) | −26128.0 | −1.31390 | ||||||||
\(735\) | 11124.0 | 0.558252 | ||||||||
\(736\) | 2304.00 | 0.115389 | ||||||||
\(737\) | −48792.0 | −2.43864 | ||||||||
\(738\) | −11868.0 | −0.591961 | ||||||||
\(739\) | −10855.0 | −0.540335 | −0.270168 | − | 0.962813i | \(-0.587079\pi\) | ||||
−0.270168 | + | 0.962813i | \(0.587079\pi\) | |||||||
\(740\) | 8136.00 | 0.404169 | ||||||||
\(741\) | 1976.00 | 0.0979624 | ||||||||
\(742\) | −26784.0 | −1.32516 | ||||||||
\(743\) | −14892.0 | −0.735309 | −0.367654 | − | 0.929962i | \(-0.619839\pi\) | ||||
−0.367654 | + | 0.929962i | \(0.619839\pi\) | |||||||
\(744\) | 512.000 | 0.0252296 | ||||||||
\(745\) | 15255.0 | 0.750201 | ||||||||
\(746\) | 20984.0 | 1.02986 | ||||||||
\(747\) | 276.000 | 0.0135185 | ||||||||
\(748\) | 15732.0 | 0.769009 | ||||||||
\(749\) | −3534.00 | −0.172403 | ||||||||
\(750\) | 6084.00 | 0.296208 | ||||||||
\(751\) | 28952.0 | 1.40676 | 0.703378 | − | 0.710816i | \(-0.251674\pi\) | ||||
0.703378 | + | 0.710816i | \(0.251674\pi\) | |||||||
\(752\) | 9264.00 | 0.449233 | ||||||||
\(753\) | −7134.00 | −0.345256 | ||||||||
\(754\) | −15600.0 | −0.753473 | ||||||||
\(755\) | −16218.0 | −0.781766 | ||||||||
\(756\) | −12400.0 | −0.596539 | ||||||||
\(757\) | −3541.00 | −0.170013 | −0.0850065 | − | 0.996380i | \(-0.527091\pi\) | ||||
−0.0850065 | + | 0.996380i | \(0.527091\pi\) | |||||||
\(758\) | −15220.0 | −0.729308 | ||||||||
\(759\) | 8208.00 | 0.392532 | ||||||||
\(760\) | 1368.00 | 0.0652929 | ||||||||
\(761\) | 22617.0 | 1.07735 | 0.538676 | − | 0.842513i | \(-0.318925\pi\) | ||||
0.538676 | + | 0.842513i | \(0.318925\pi\) | |||||||
\(762\) | −8344.00 | −0.396681 | ||||||||
\(763\) | −45260.0 | −2.14747 | ||||||||
\(764\) | −10572.0 | −0.500630 | ||||||||
\(765\) | 14283.0 | 0.675037 | ||||||||
\(766\) | −8016.00 | −0.378107 | ||||||||
\(767\) | 17160.0 | 0.807838 | ||||||||
\(768\) | −512.000 | −0.0240563 | ||||||||
\(769\) | 11495.0 | 0.539038 | 0.269519 | − | 0.962995i | \(-0.413135\pi\) | ||||
0.269519 | + | 0.962995i | \(0.413135\pi\) | |||||||
\(770\) | −31806.0 | −1.48858 | ||||||||
\(771\) | 3792.00 | 0.177128 | ||||||||
\(772\) | 12992.0 | 0.605690 | ||||||||
\(773\) | −14622.0 | −0.680358 | −0.340179 | − | 0.940361i | \(-0.610488\pi\) | ||||
−0.340179 | + | 0.940361i | \(0.610488\pi\) | |||||||
\(774\) | −3082.00 | −0.143127 | ||||||||
\(775\) | −1408.00 | −0.0652605 | ||||||||
\(776\) | −11392.0 | −0.526996 | ||||||||
\(777\) | −14012.0 | −0.646947 | ||||||||
\(778\) | 7050.00 | 0.324878 | ||||||||
\(779\) | −4902.00 | −0.225459 | ||||||||
\(780\) | −3744.00 | −0.171868 | ||||||||
\(781\) | 36594.0 | 1.67661 | ||||||||
\(782\) | 9936.00 | 0.454361 | ||||||||
\(783\) | −15000.0 | −0.684618 | ||||||||
\(784\) | 9888.00 | 0.450437 | ||||||||
\(785\) | 29034.0 | 1.32009 | ||||||||
\(786\) | −372.000 | −0.0168814 | ||||||||
\(787\) | 7124.00 | 0.322672 | 0.161336 | − | 0.986900i | \(-0.448420\pi\) | ||||
0.161336 | + | 0.986900i | \(0.448420\pi\) | |||||||
\(788\) | −12504.0 | −0.565275 | ||||||||
\(789\) | 114.000 | 0.00514386 | ||||||||
\(790\) | −12600.0 | −0.567453 | ||||||||
\(791\) | 25482.0 | 1.14543 | ||||||||
\(792\) | 10488.0 | 0.470549 | ||||||||
\(793\) | 676.000 | 0.0302717 | ||||||||
\(794\) | −13258.0 | −0.592580 | ||||||||
\(795\) | −7776.00 | −0.346901 | ||||||||
\(796\) | −11980.0 | −0.533442 | ||||||||
\(797\) | −3576.00 | −0.158932 | −0.0794658 | − | 0.996838i | \(-0.525321\pi\) | ||||
−0.0794658 | + | 0.996838i | \(0.525321\pi\) | |||||||
\(798\) | −2356.00 | −0.104513 | ||||||||
\(799\) | 39951.0 | 1.76892 | ||||||||
\(800\) | 1408.00 | 0.0622254 | ||||||||
\(801\) | 13800.0 | 0.608738 | ||||||||
\(802\) | 21696.0 | 0.955252 | ||||||||
\(803\) | −27759.0 | −1.21992 | ||||||||
\(804\) | 6848.00 | 0.300386 | ||||||||
\(805\) | −20088.0 | −0.879514 | ||||||||
\(806\) | 3328.00 | 0.145439 | ||||||||
\(807\) | −5400.00 | −0.235550 | ||||||||
\(808\) | −8496.00 | −0.369911 | ||||||||
\(809\) | 42855.0 | 1.86242 | 0.931212 | − | 0.364477i | \(-0.118752\pi\) | ||||
0.931212 | + | 0.364477i | \(0.118752\pi\) | |||||||
\(810\) | 7578.00 | 0.328721 | ||||||||
\(811\) | −15568.0 | −0.674065 | −0.337032 | − | 0.941493i | \(-0.609423\pi\) | ||||
−0.337032 | + | 0.941493i | \(0.609423\pi\) | |||||||
\(812\) | 18600.0 | 0.803857 | ||||||||
\(813\) | −7744.00 | −0.334064 | ||||||||
\(814\) | 25764.0 | 1.10937 | ||||||||
\(815\) | −11412.0 | −0.490485 | ||||||||
\(816\) | −2208.00 | −0.0947248 | ||||||||
\(817\) | −1273.00 | −0.0545124 | ||||||||
\(818\) | 6080.00 | 0.259880 | ||||||||
\(819\) | −37076.0 | −1.58186 | ||||||||
\(820\) | 9288.00 | 0.395550 | ||||||||
\(821\) | 2517.00 | 0.106996 | 0.0534981 | − | 0.998568i | \(-0.482963\pi\) | ||||
0.0534981 | + | 0.998568i | \(0.482963\pi\) | |||||||
\(822\) | 5076.00 | 0.215384 | ||||||||
\(823\) | −9727.00 | −0.411983 | −0.205991 | − | 0.978554i | \(-0.566042\pi\) | ||||
−0.205991 | + | 0.978554i | \(0.566042\pi\) | |||||||
\(824\) | −9424.00 | −0.398423 | ||||||||
\(825\) | 5016.00 | 0.211678 | ||||||||
\(826\) | −20460.0 | −0.861858 | ||||||||
\(827\) | 28224.0 | 1.18675 | 0.593376 | − | 0.804925i | \(-0.297795\pi\) | ||||
0.593376 | + | 0.804925i | \(0.297795\pi\) | |||||||
\(828\) | 6624.00 | 0.278019 | ||||||||
\(829\) | 3080.00 | 0.129038 | 0.0645192 | − | 0.997916i | \(-0.479449\pi\) | ||||
0.0645192 | + | 0.997916i | \(0.479449\pi\) | |||||||
\(830\) | −216.000 | −0.00903310 | ||||||||
\(831\) | 15422.0 | 0.643782 | ||||||||
\(832\) | −3328.00 | −0.138675 | ||||||||
\(833\) | 42642.0 | 1.77366 | ||||||||
\(834\) | −7900.00 | −0.328003 | ||||||||
\(835\) | −5886.00 | −0.243944 | ||||||||
\(836\) | 4332.00 | 0.179217 | ||||||||
\(837\) | 3200.00 | 0.132148 | ||||||||
\(838\) | 7800.00 | 0.321535 | ||||||||
\(839\) | 26790.0 | 1.10238 | 0.551188 | − | 0.834381i | \(-0.314175\pi\) | ||||
0.551188 | + | 0.834381i | \(0.314175\pi\) | |||||||
\(840\) | 4464.00 | 0.183360 | ||||||||
\(841\) | −1889.00 | −0.0774530 | ||||||||
\(842\) | −8824.00 | −0.361158 | ||||||||
\(843\) | 13716.0 | 0.560385 | ||||||||
\(844\) | −17272.0 | −0.704416 | ||||||||
\(845\) | −4563.00 | −0.185766 | ||||||||
\(846\) | 26634.0 | 1.08238 | ||||||||
\(847\) | −59458.0 | −2.41204 | ||||||||
\(848\) | −6912.00 | −0.279905 | ||||||||
\(849\) | 3614.00 | 0.146092 | ||||||||
\(850\) | 6072.00 | 0.245021 | ||||||||
\(851\) | 16272.0 | 0.655461 | ||||||||
\(852\) | −5136.00 | −0.206522 | ||||||||
\(853\) | 19178.0 | 0.769803 | 0.384902 | − | 0.922958i | \(-0.374235\pi\) | ||||
0.384902 | + | 0.922958i | \(0.374235\pi\) | |||||||
\(854\) | −806.000 | −0.0322960 | ||||||||
\(855\) | 3933.00 | 0.157317 | ||||||||
\(856\) | −912.000 | −0.0364153 | ||||||||
\(857\) | −2406.00 | −0.0959013 | −0.0479506 | − | 0.998850i | \(-0.515269\pi\) | ||||
−0.0479506 | + | 0.998850i | \(0.515269\pi\) | |||||||
\(858\) | −11856.0 | −0.471745 | ||||||||
\(859\) | 9125.00 | 0.362446 | 0.181223 | − | 0.983442i | \(-0.441994\pi\) | ||||
0.181223 | + | 0.983442i | \(0.441994\pi\) | |||||||
\(860\) | 2412.00 | 0.0956378 | ||||||||
\(861\) | −15996.0 | −0.633150 | ||||||||
\(862\) | −864.000 | −0.0341392 | ||||||||
\(863\) | 8898.00 | 0.350975 | 0.175488 | − | 0.984482i | \(-0.443850\pi\) | ||||
0.175488 | + | 0.984482i | \(0.443850\pi\) | |||||||
\(864\) | −3200.00 | −0.126003 | ||||||||
\(865\) | 12258.0 | 0.481832 | ||||||||
\(866\) | 4004.00 | 0.157115 | ||||||||
\(867\) | 304.000 | 0.0119082 | ||||||||
\(868\) | −3968.00 | −0.155164 | ||||||||
\(869\) | −39900.0 | −1.55755 | ||||||||
\(870\) | 5400.00 | 0.210434 | ||||||||
\(871\) | 44512.0 | 1.73161 | ||||||||
\(872\) | −11680.0 | −0.453595 | ||||||||
\(873\) | −32752.0 | −1.26974 | ||||||||
\(874\) | 2736.00 | 0.105889 | ||||||||
\(875\) | −47151.0 | −1.82171 | ||||||||
\(876\) | 3896.00 | 0.150267 | ||||||||
\(877\) | −15886.0 | −0.611667 | −0.305834 | − | 0.952085i | \(-0.598935\pi\) | ||||
−0.305834 | + | 0.952085i | \(0.598935\pi\) | |||||||
\(878\) | 3380.00 | 0.129920 | ||||||||
\(879\) | 6024.00 | 0.231154 | ||||||||
\(880\) | −8208.00 | −0.314422 | ||||||||
\(881\) | −25683.0 | −0.982159 | −0.491080 | − | 0.871115i | \(-0.663398\pi\) | ||||
−0.491080 | + | 0.871115i | \(0.663398\pi\) | |||||||
\(882\) | 28428.0 | 1.08528 | ||||||||
\(883\) | −28267.0 | −1.07730 | −0.538652 | − | 0.842528i | \(-0.681066\pi\) | ||||
−0.538652 | + | 0.842528i | \(0.681066\pi\) | |||||||
\(884\) | −14352.0 | −0.546052 | ||||||||
\(885\) | −5940.00 | −0.225617 | ||||||||
\(886\) | 3954.00 | 0.149929 | ||||||||
\(887\) | −2466.00 | −0.0933486 | −0.0466743 | − | 0.998910i | \(-0.514862\pi\) | ||||
−0.0466743 | + | 0.998910i | \(0.514862\pi\) | |||||||
\(888\) | −3616.00 | −0.136650 | ||||||||
\(889\) | 64666.0 | 2.43963 | ||||||||
\(890\) | −10800.0 | −0.406760 | ||||||||
\(891\) | 23997.0 | 0.902278 | ||||||||
\(892\) | 2072.00 | 0.0777754 | ||||||||
\(893\) | 11001.0 | 0.412245 | ||||||||
\(894\) | −6780.00 | −0.253643 | ||||||||
\(895\) | 1890.00 | 0.0705874 | ||||||||
\(896\) | 3968.00 | 0.147948 | ||||||||
\(897\) | −7488.00 | −0.278726 | ||||||||
\(898\) | 5520.00 | 0.205128 | ||||||||
\(899\) | −4800.00 | −0.178074 | ||||||||
\(900\) | 4048.00 | 0.149926 | ||||||||
\(901\) | −29808.0 | −1.10216 | ||||||||
\(902\) | 29412.0 | 1.08571 | ||||||||
\(903\) | −4154.00 | −0.153086 | ||||||||
\(904\) | 6576.00 | 0.241941 | ||||||||
\(905\) | −18.0000 | −0.000661149 0 | ||||||||
\(906\) | 7208.00 | 0.264315 | ||||||||
\(907\) | 29324.0 | 1.07353 | 0.536763 | − | 0.843733i | \(-0.319647\pi\) | ||||
0.536763 | + | 0.843733i | \(0.319647\pi\) | |||||||
\(908\) | 11376.0 | 0.415777 | ||||||||
\(909\) | −24426.0 | −0.891264 | ||||||||
\(910\) | 29016.0 | 1.05700 | ||||||||
\(911\) | 47142.0 | 1.71447 | 0.857236 | − | 0.514924i | \(-0.172180\pi\) | ||||
0.857236 | + | 0.514924i | \(0.172180\pi\) | |||||||
\(912\) | −608.000 | −0.0220755 | ||||||||
\(913\) | −684.000 | −0.0247942 | ||||||||
\(914\) | −8998.00 | −0.325632 | ||||||||
\(915\) | −234.000 | −0.00845443 | ||||||||
\(916\) | 6980.00 | 0.251775 | ||||||||
\(917\) | 2883.00 | 0.103822 | ||||||||
\(918\) | −13800.0 | −0.496152 | ||||||||
\(919\) | −39940.0 | −1.43362 | −0.716811 | − | 0.697267i | \(-0.754399\pi\) | ||||
−0.716811 | + | 0.697267i | \(0.754399\pi\) | |||||||
\(920\) | −5184.00 | −0.185773 | ||||||||
\(921\) | 2192.00 | 0.0784244 | ||||||||
\(922\) | 23286.0 | 0.831761 | ||||||||
\(923\) | −33384.0 | −1.19052 | ||||||||
\(924\) | 14136.0 | 0.503290 | ||||||||
\(925\) | 9944.00 | 0.353467 | ||||||||
\(926\) | 3074.00 | 0.109091 | ||||||||
\(927\) | −27094.0 | −0.959961 | ||||||||
\(928\) | 4800.00 | 0.169793 | ||||||||
\(929\) | −4410.00 | −0.155745 | −0.0778727 | − | 0.996963i | \(-0.524813\pi\) | ||||
−0.0778727 | + | 0.996963i | \(0.524813\pi\) | |||||||
\(930\) | −1152.00 | −0.0406189 | ||||||||
\(931\) | 11742.0 | 0.413350 | ||||||||
\(932\) | 21132.0 | 0.742706 | ||||||||
\(933\) | −3894.00 | −0.136639 | ||||||||
\(934\) | 15282.0 | 0.535377 | ||||||||
\(935\) | −35397.0 | −1.23808 | ||||||||
\(936\) | −9568.00 | −0.334124 | ||||||||
\(937\) | −41671.0 | −1.45286 | −0.726431 | − | 0.687239i | \(-0.758822\pi\) | ||||
−0.726431 | + | 0.687239i | \(0.758822\pi\) | |||||||
\(938\) | −53072.0 | −1.84740 | ||||||||
\(939\) | −15196.0 | −0.528118 | ||||||||
\(940\) | −20844.0 | −0.723251 | ||||||||
\(941\) | 4062.00 | 0.140720 | 0.0703599 | − | 0.997522i | \(-0.477585\pi\) | ||||
0.0703599 | + | 0.997522i | \(0.477585\pi\) | |||||||
\(942\) | −12904.0 | −0.446322 | ||||||||
\(943\) | 18576.0 | 0.641482 | ||||||||
\(944\) | −5280.00 | −0.182044 | ||||||||
\(945\) | 27900.0 | 0.960410 | ||||||||
\(946\) | 7638.00 | 0.262508 | ||||||||
\(947\) | −45036.0 | −1.54538 | −0.772689 | − | 0.634785i | \(-0.781089\pi\) | ||||
−0.772689 | + | 0.634785i | \(0.781089\pi\) | |||||||
\(948\) | 5600.00 | 0.191856 | ||||||||
\(949\) | 25324.0 | 0.866230 | ||||||||
\(950\) | 1672.00 | 0.0571019 | ||||||||
\(951\) | −16668.0 | −0.568346 | ||||||||
\(952\) | 17112.0 | 0.582566 | ||||||||
\(953\) | 26508.0 | 0.901027 | 0.450513 | − | 0.892770i | \(-0.351241\pi\) | ||||
0.450513 | + | 0.892770i | \(0.351241\pi\) | |||||||
\(954\) | −19872.0 | −0.674402 | ||||||||
\(955\) | 23787.0 | 0.805999 | ||||||||
\(956\) | 1860.00 | 0.0629254 | ||||||||
\(957\) | 17100.0 | 0.577601 | ||||||||
\(958\) | 17160.0 | 0.578721 | ||||||||
\(959\) | −39339.0 | −1.32463 | ||||||||
\(960\) | 1152.00 | 0.0387298 | ||||||||
\(961\) | −28767.0 | −0.965627 | ||||||||
\(962\) | −23504.0 | −0.787733 | ||||||||
\(963\) | −2622.00 | −0.0877391 | ||||||||
\(964\) | −28312.0 | −0.945921 | ||||||||
\(965\) | −29232.0 | −0.975141 | ||||||||
\(966\) | 8928.00 | 0.297364 | ||||||||
\(967\) | −15976.0 | −0.531286 | −0.265643 | − | 0.964071i | \(-0.585584\pi\) | ||||
−0.265643 | + | 0.964071i | \(0.585584\pi\) | |||||||
\(968\) | −15344.0 | −0.509478 | ||||||||
\(969\) | −2622.00 | −0.0869255 | ||||||||
\(970\) | 25632.0 | 0.848447 | ||||||||
\(971\) | −39468.0 | −1.30442 | −0.652208 | − | 0.758040i | \(-0.726157\pi\) | ||||
−0.652208 | + | 0.758040i | \(0.726157\pi\) | |||||||
\(972\) | −14168.0 | −0.467530 | ||||||||
\(973\) | 61225.0 | 2.01725 | ||||||||
\(974\) | −24268.0 | −0.798354 | ||||||||
\(975\) | −4576.00 | −0.150307 | ||||||||
\(976\) | −208.000 | −0.00682164 | ||||||||
\(977\) | 21804.0 | 0.713994 | 0.356997 | − | 0.934106i | \(-0.383801\pi\) | ||||
0.356997 | + | 0.934106i | \(0.383801\pi\) | |||||||
\(978\) | 5072.00 | 0.165833 | ||||||||
\(979\) | −34200.0 | −1.11648 | ||||||||
\(980\) | −22248.0 | −0.725190 | ||||||||
\(981\) | −33580.0 | −1.09289 | ||||||||
\(982\) | 11016.0 | 0.357978 | ||||||||
\(983\) | 11268.0 | 0.365609 | 0.182804 | − | 0.983149i | \(-0.441483\pi\) | ||||
0.182804 | + | 0.983149i | \(0.441483\pi\) | |||||||
\(984\) | −4128.00 | −0.133736 | ||||||||
\(985\) | 28134.0 | 0.910075 | ||||||||
\(986\) | 20700.0 | 0.668582 | ||||||||
\(987\) | 35898.0 | 1.15770 | ||||||||
\(988\) | −3952.00 | −0.127257 | ||||||||
\(989\) | 4824.00 | 0.155100 | ||||||||
\(990\) | −23598.0 | −0.757569 | ||||||||
\(991\) | −778.000 | −0.0249384 | −0.0124692 | − | 0.999922i | \(-0.503969\pi\) | ||||
−0.0124692 | + | 0.999922i | \(0.503969\pi\) | |||||||
\(992\) | −1024.00 | −0.0327742 | ||||||||
\(993\) | 16736.0 | 0.534845 | ||||||||
\(994\) | 39804.0 | 1.27013 | ||||||||
\(995\) | 26955.0 | 0.858825 | ||||||||
\(996\) | 96.0000 | 0.00305409 | ||||||||
\(997\) | 389.000 | 0.0123568 | 0.00617841 | − | 0.999981i | \(-0.498033\pi\) | ||||
0.00617841 | + | 0.999981i | \(0.498033\pi\) | |||||||
\(998\) | 23810.0 | 0.755203 | ||||||||
\(999\) | −22600.0 | −0.715748 |
(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 | 38.4.a.a.1.1 | ✓ | 1 | |
3.2 | odd | 2 | 342.4.a.d.1.1 | 1 | |||
4.3 | odd | 2 | 304.4.a.a.1.1 | 1 | |||
5.2 | odd | 4 | 950.4.b.d.799.1 | 2 | |||
5.3 | odd | 4 | 950.4.b.d.799.2 | 2 | |||
5.4 | even | 2 | 950.4.a.d.1.1 | 1 | |||
7.6 | odd | 2 | 1862.4.a.a.1.1 | 1 | |||
8.3 | odd | 2 | 1216.4.a.b.1.1 | 1 | |||
8.5 | even | 2 | 1216.4.a.e.1.1 | 1 | |||
19.18 | odd | 2 | 722.4.a.d.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
38.4.a.a.1.1 | ✓ | 1 | 1.1 | even | 1 | trivial | |
304.4.a.a.1.1 | 1 | 4.3 | odd | 2 | |||
342.4.a.d.1.1 | 1 | 3.2 | odd | 2 | |||
722.4.a.d.1.1 | 1 | 19.18 | odd | 2 | |||
950.4.a.d.1.1 | 1 | 5.4 | even | 2 | |||
950.4.b.d.799.1 | 2 | 5.2 | odd | 4 | |||
950.4.b.d.799.2 | 2 | 5.3 | odd | 4 | |||
1216.4.a.b.1.1 | 1 | 8.3 | odd | 2 | |||
1216.4.a.e.1.1 | 1 | 8.5 | even | 2 | |||
1862.4.a.a.1.1 | 1 | 7.6 | odd | 2 |