Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1815,4,Mod(1,1815)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1815, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1815.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1815 = 3 \cdot 5 \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1815.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: | \(107.088466660\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{12})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - 3 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{17}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-1.73205\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1815.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −3.46410 | −1.22474 | −0.612372 | − | 0.790569i | \(-0.709785\pi\) | ||||
−0.612372 | + | 0.790569i | \(0.709785\pi\) | |||||||
\(3\) | 3.00000 | 0.577350 | ||||||||
\(4\) | 4.00000 | 0.500000 | ||||||||
\(5\) | 5.00000 | 0.447214 | ||||||||
\(6\) | −10.3923 | −0.707107 | ||||||||
\(7\) | −31.1769 | −1.68340 | −0.841698 | − | 0.539949i | \(-0.818443\pi\) | ||||
−0.841698 | + | 0.539949i | \(0.818443\pi\) | |||||||
\(8\) | 13.8564 | 0.612372 | ||||||||
\(9\) | 9.00000 | 0.333333 | ||||||||
\(10\) | −17.3205 | −0.547723 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | 12.0000 | 0.288675 | ||||||||
\(13\) | 76.2102 | 1.62592 | 0.812958 | − | 0.582322i | \(-0.197856\pi\) | ||||
0.812958 | + | 0.582322i | \(0.197856\pi\) | |||||||
\(14\) | 108.000 | 2.06173 | ||||||||
\(15\) | 15.0000 | 0.258199 | ||||||||
\(16\) | −80.0000 | −1.25000 | ||||||||
\(17\) | −46.7654 | −0.667192 | −0.333596 | − | 0.942716i | \(-0.608262\pi\) | ||||
−0.333596 | + | 0.942716i | \(0.608262\pi\) | |||||||
\(18\) | −31.1769 | −0.408248 | ||||||||
\(19\) | 31.1769 | 0.376446 | 0.188223 | − | 0.982126i | \(-0.439727\pi\) | ||||
0.188223 | + | 0.982126i | \(0.439727\pi\) | |||||||
\(20\) | 20.0000 | 0.223607 | ||||||||
\(21\) | −93.5307 | −0.971909 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 195.000 | 1.76784 | 0.883920 | − | 0.467639i | \(-0.154895\pi\) | ||||
0.883920 | + | 0.467639i | \(0.154895\pi\) | |||||||
\(24\) | 41.5692 | 0.353553 | ||||||||
\(25\) | 25.0000 | 0.200000 | ||||||||
\(26\) | −264.000 | −1.99133 | ||||||||
\(27\) | 27.0000 | 0.192450 | ||||||||
\(28\) | −124.708 | −0.841698 | ||||||||
\(29\) | −34.6410 | −0.221816 | −0.110908 | − | 0.993831i | \(-0.535376\pi\) | ||||
−0.110908 | + | 0.993831i | \(0.535376\pi\) | |||||||
\(30\) | −51.9615 | −0.316228 | ||||||||
\(31\) | 97.0000 | 0.561991 | 0.280995 | − | 0.959709i | \(-0.409335\pi\) | ||||
0.280995 | + | 0.959709i | \(0.409335\pi\) | |||||||
\(32\) | 166.277 | 0.918559 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 162.000 | 0.817140 | ||||||||
\(35\) | −155.885 | −0.752837 | ||||||||
\(36\) | 36.0000 | 0.166667 | ||||||||
\(37\) | 274.000 | 1.21744 | 0.608721 | − | 0.793385i | \(-0.291683\pi\) | ||||
0.608721 | + | 0.793385i | \(0.291683\pi\) | |||||||
\(38\) | −108.000 | −0.461050 | ||||||||
\(39\) | 228.631 | 0.938723 | ||||||||
\(40\) | 69.2820 | 0.273861 | ||||||||
\(41\) | −384.515 | −1.46466 | −0.732332 | − | 0.680948i | \(-0.761568\pi\) | ||||
−0.732332 | + | 0.680948i | \(0.761568\pi\) | |||||||
\(42\) | 324.000 | 1.19034 | ||||||||
\(43\) | −415.692 | −1.47424 | −0.737122 | − | 0.675760i | \(-0.763816\pi\) | ||||
−0.737122 | + | 0.675760i | \(0.763816\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 45.0000 | 0.149071 | ||||||||
\(46\) | −675.500 | −2.16515 | ||||||||
\(47\) | 3.00000 | 0.00931053 | 0.00465527 | − | 0.999989i | \(-0.498518\pi\) | ||||
0.00465527 | + | 0.999989i | \(0.498518\pi\) | |||||||
\(48\) | −240.000 | −0.721688 | ||||||||
\(49\) | 629.000 | 1.83382 | ||||||||
\(50\) | −86.6025 | −0.244949 | ||||||||
\(51\) | −140.296 | −0.385204 | ||||||||
\(52\) | 304.841 | 0.812958 | ||||||||
\(53\) | 3.00000 | 0.00777513 | 0.00388756 | − | 0.999992i | \(-0.498763\pi\) | ||||
0.00388756 | + | 0.999992i | \(0.498763\pi\) | |||||||
\(54\) | −93.5307 | −0.235702 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −432.000 | −1.03086 | ||||||||
\(57\) | 93.5307 | 0.217341 | ||||||||
\(58\) | 120.000 | 0.271668 | ||||||||
\(59\) | −648.000 | −1.42987 | −0.714936 | − | 0.699190i | \(-0.753544\pi\) | ||||
−0.714936 | + | 0.699190i | \(0.753544\pi\) | |||||||
\(60\) | 60.0000 | 0.129099 | ||||||||
\(61\) | 458.993 | 0.963411 | 0.481706 | − | 0.876333i | \(-0.340017\pi\) | ||||
0.481706 | + | 0.876333i | \(0.340017\pi\) | |||||||
\(62\) | −336.018 | −0.688295 | ||||||||
\(63\) | −280.592 | −0.561132 | ||||||||
\(64\) | 64.0000 | 0.125000 | ||||||||
\(65\) | 381.051 | 0.727132 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 70.0000 | 0.127640 | 0.0638199 | − | 0.997961i | \(-0.479672\pi\) | ||||
0.0638199 | + | 0.997961i | \(0.479672\pi\) | |||||||
\(68\) | −187.061 | −0.333596 | ||||||||
\(69\) | 585.000 | 1.02066 | ||||||||
\(70\) | 540.000 | 0.922033 | ||||||||
\(71\) | −372.000 | −0.621807 | −0.310903 | − | 0.950442i | \(-0.600632\pi\) | ||||
−0.310903 | + | 0.950442i | \(0.600632\pi\) | |||||||
\(72\) | 124.708 | 0.204124 | ||||||||
\(73\) | −935.307 | −1.49958 | −0.749791 | − | 0.661675i | \(-0.769846\pi\) | ||||
−0.749791 | + | 0.661675i | \(0.769846\pi\) | |||||||
\(74\) | −949.164 | −1.49105 | ||||||||
\(75\) | 75.0000 | 0.115470 | ||||||||
\(76\) | 124.708 | 0.188223 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −792.000 | −1.14970 | ||||||||
\(79\) | −521.347 | −0.742483 | −0.371241 | − | 0.928536i | \(-0.621068\pi\) | ||||
−0.371241 | + | 0.928536i | \(0.621068\pi\) | |||||||
\(80\) | −400.000 | −0.559017 | ||||||||
\(81\) | 81.0000 | 0.111111 | ||||||||
\(82\) | 1332.00 | 1.79384 | ||||||||
\(83\) | −45.0333 | −0.0595548 | −0.0297774 | − | 0.999557i | \(-0.509480\pi\) | ||||
−0.0297774 | + | 0.999557i | \(0.509480\pi\) | |||||||
\(84\) | −374.123 | −0.485954 | ||||||||
\(85\) | −233.827 | −0.298377 | ||||||||
\(86\) | 1440.00 | 1.80557 | ||||||||
\(87\) | −103.923 | −0.128066 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 1122.00 | 1.33631 | 0.668156 | − | 0.744021i | \(-0.267084\pi\) | ||||
0.668156 | + | 0.744021i | \(0.267084\pi\) | |||||||
\(90\) | −155.885 | −0.182574 | ||||||||
\(91\) | −2376.00 | −2.73706 | ||||||||
\(92\) | 780.000 | 0.883920 | ||||||||
\(93\) | 291.000 | 0.324466 | ||||||||
\(94\) | −10.3923 | −0.0114030 | ||||||||
\(95\) | 155.885 | 0.168352 | ||||||||
\(96\) | 498.831 | 0.530330 | ||||||||
\(97\) | 470.000 | 0.491972 | 0.245986 | − | 0.969273i | \(-0.420888\pi\) | ||||
0.245986 | + | 0.969273i | \(0.420888\pi\) | |||||||
\(98\) | −2178.92 | −2.24596 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 100.000 | 0.100000 | ||||||||
\(101\) | 1932.97 | 1.90433 | 0.952166 | − | 0.305581i | \(-0.0988505\pi\) | ||||
0.952166 | + | 0.305581i | \(0.0988505\pi\) | |||||||
\(102\) | 486.000 | 0.471776 | ||||||||
\(103\) | 968.000 | 0.926018 | 0.463009 | − | 0.886354i | \(-0.346770\pi\) | ||||
0.463009 | + | 0.886354i | \(0.346770\pi\) | |||||||
\(104\) | 1056.00 | 0.995667 | ||||||||
\(105\) | −467.654 | −0.434651 | ||||||||
\(106\) | −10.3923 | −0.00952255 | ||||||||
\(107\) | 161.081 | 0.145535 | 0.0727676 | − | 0.997349i | \(-0.476817\pi\) | ||||
0.0727676 | + | 0.997349i | \(0.476817\pi\) | |||||||
\(108\) | 108.000 | 0.0962250 | ||||||||
\(109\) | 235.559 | 0.206995 | 0.103497 | − | 0.994630i | \(-0.466997\pi\) | ||||
0.103497 | + | 0.994630i | \(0.466997\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 822.000 | 0.702890 | ||||||||
\(112\) | 2494.15 | 2.10424 | ||||||||
\(113\) | −1653.00 | −1.37612 | −0.688058 | − | 0.725655i | \(-0.741537\pi\) | ||||
−0.688058 | + | 0.725655i | \(0.741537\pi\) | |||||||
\(114\) | −324.000 | −0.266188 | ||||||||
\(115\) | 975.000 | 0.790602 | ||||||||
\(116\) | −138.564 | −0.110908 | ||||||||
\(117\) | 685.892 | 0.541972 | ||||||||
\(118\) | 2244.74 | 1.75123 | ||||||||
\(119\) | 1458.00 | 1.12315 | ||||||||
\(120\) | 207.846 | 0.158114 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | −1590.00 | −1.17993 | ||||||||
\(123\) | −1153.55 | −0.845624 | ||||||||
\(124\) | 388.000 | 0.280995 | ||||||||
\(125\) | 125.000 | 0.0894427 | ||||||||
\(126\) | 972.000 | 0.687243 | ||||||||
\(127\) | 2057.68 | 1.43771 | 0.718855 | − | 0.695160i | \(-0.244666\pi\) | ||||
0.718855 | + | 0.695160i | \(0.244666\pi\) | |||||||
\(128\) | −1551.92 | −1.07165 | ||||||||
\(129\) | −1247.08 | −0.851155 | ||||||||
\(130\) | −1320.00 | −0.890551 | ||||||||
\(131\) | 2151.21 | 1.43475 | 0.717373 | − | 0.696689i | \(-0.245344\pi\) | ||||
0.717373 | + | 0.696689i | \(0.245344\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −972.000 | −0.633707 | ||||||||
\(134\) | −242.487 | −0.156326 | ||||||||
\(135\) | 135.000 | 0.0860663 | ||||||||
\(136\) | −648.000 | −0.408570 | ||||||||
\(137\) | 921.000 | 0.574353 | 0.287176 | − | 0.957878i | \(-0.407283\pi\) | ||||
0.287176 | + | 0.957878i | \(0.407283\pi\) | |||||||
\(138\) | −2026.50 | −1.25005 | ||||||||
\(139\) | −1726.85 | −1.05374 | −0.526870 | − | 0.849946i | \(-0.676635\pi\) | ||||
−0.526870 | + | 0.849946i | \(0.676635\pi\) | |||||||
\(140\) | −623.538 | −0.376419 | ||||||||
\(141\) | 9.00000 | 0.00537544 | ||||||||
\(142\) | 1288.65 | 0.761555 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −720.000 | −0.416667 | ||||||||
\(145\) | −173.205 | −0.0991993 | ||||||||
\(146\) | 3240.00 | 1.83660 | ||||||||
\(147\) | 1887.00 | 1.05876 | ||||||||
\(148\) | 1096.00 | 0.608721 | ||||||||
\(149\) | 2016.11 | 1.10850 | 0.554248 | − | 0.832352i | \(-0.313006\pi\) | ||||
0.554248 | + | 0.832352i | \(0.313006\pi\) | |||||||
\(150\) | −259.808 | −0.141421 | ||||||||
\(151\) | 774.227 | 0.417256 | 0.208628 | − | 0.977995i | \(-0.433100\pi\) | ||||
0.208628 | + | 0.977995i | \(0.433100\pi\) | |||||||
\(152\) | 432.000 | 0.230525 | ||||||||
\(153\) | −420.888 | −0.222397 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 485.000 | 0.251330 | ||||||||
\(156\) | 914.523 | 0.469362 | ||||||||
\(157\) | −3602.00 | −1.83102 | −0.915512 | − | 0.402290i | \(-0.868214\pi\) | ||||
−0.915512 | + | 0.402290i | \(0.868214\pi\) | |||||||
\(158\) | 1806.00 | 0.909352 | ||||||||
\(159\) | 9.00000 | 0.00448897 | ||||||||
\(160\) | 831.384 | 0.410792 | ||||||||
\(161\) | −6079.50 | −2.97597 | ||||||||
\(162\) | −280.592 | −0.136083 | ||||||||
\(163\) | −1672.00 | −0.803443 | −0.401721 | − | 0.915762i | \(-0.631588\pi\) | ||||
−0.401721 | + | 0.915762i | \(0.631588\pi\) | |||||||
\(164\) | −1538.06 | −0.732332 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 156.000 | 0.0729394 | ||||||||
\(167\) | −2527.06 | −1.17096 | −0.585479 | − | 0.810688i | \(-0.699093\pi\) | ||||
−0.585479 | + | 0.810688i | \(0.699093\pi\) | |||||||
\(168\) | −1296.00 | −0.595170 | ||||||||
\(169\) | 3611.00 | 1.64360 | ||||||||
\(170\) | 810.000 | 0.365436 | ||||||||
\(171\) | 280.592 | 0.125482 | ||||||||
\(172\) | −1662.77 | −0.737122 | ||||||||
\(173\) | −1745.91 | −0.767277 | −0.383638 | − | 0.923483i | \(-0.625329\pi\) | ||||
−0.383638 | + | 0.923483i | \(0.625329\pi\) | |||||||
\(174\) | 360.000 | 0.156848 | ||||||||
\(175\) | −779.423 | −0.336679 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −1944.00 | −0.825537 | ||||||||
\(178\) | −3886.72 | −1.63664 | ||||||||
\(179\) | 1998.00 | 0.834288 | 0.417144 | − | 0.908840i | \(-0.363031\pi\) | ||||
0.417144 | + | 0.908840i | \(0.363031\pi\) | |||||||
\(180\) | 180.000 | 0.0745356 | ||||||||
\(181\) | −4534.00 | −1.86193 | −0.930966 | − | 0.365107i | \(-0.881032\pi\) | ||||
−0.930966 | + | 0.365107i | \(0.881032\pi\) | |||||||
\(182\) | 8230.71 | 3.35220 | ||||||||
\(183\) | 1376.98 | 0.556226 | ||||||||
\(184\) | 2702.00 | 1.08258 | ||||||||
\(185\) | 1370.00 | 0.544456 | ||||||||
\(186\) | −1008.05 | −0.397387 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 12.0000 | 0.00465527 | ||||||||
\(189\) | −841.777 | −0.323970 | ||||||||
\(190\) | −540.000 | −0.206188 | ||||||||
\(191\) | 2754.00 | 1.04331 | 0.521656 | − | 0.853156i | \(-0.325315\pi\) | ||||
0.521656 | + | 0.853156i | \(0.325315\pi\) | |||||||
\(192\) | 192.000 | 0.0721688 | ||||||||
\(193\) | 772.495 | 0.288111 | 0.144055 | − | 0.989570i | \(-0.453986\pi\) | ||||
0.144055 | + | 0.989570i | \(0.453986\pi\) | |||||||
\(194\) | −1628.13 | −0.602540 | ||||||||
\(195\) | 1143.15 | 0.419810 | ||||||||
\(196\) | 2516.00 | 0.916910 | ||||||||
\(197\) | 2757.42 | 0.997251 | 0.498625 | − | 0.866818i | \(-0.333838\pi\) | ||||
0.498625 | + | 0.866818i | \(0.333838\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −731.000 | −0.260398 | −0.130199 | − | 0.991488i | \(-0.541562\pi\) | ||||
−0.130199 | + | 0.991488i | \(0.541562\pi\) | |||||||
\(200\) | 346.410 | 0.122474 | ||||||||
\(201\) | 210.000 | 0.0736928 | ||||||||
\(202\) | −6696.00 | −2.33232 | ||||||||
\(203\) | 1080.00 | 0.373405 | ||||||||
\(204\) | −561.184 | −0.192602 | ||||||||
\(205\) | −1922.58 | −0.655017 | ||||||||
\(206\) | −3353.25 | −1.13414 | ||||||||
\(207\) | 1755.00 | 0.589280 | ||||||||
\(208\) | −6096.82 | −2.03240 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 1620.00 | 0.532336 | ||||||||
\(211\) | −2069.80 | −0.675313 | −0.337656 | − | 0.941269i | \(-0.609634\pi\) | ||||
−0.337656 | + | 0.941269i | \(0.609634\pi\) | |||||||
\(212\) | 12.0000 | 0.00388756 | ||||||||
\(213\) | −1116.00 | −0.359000 | ||||||||
\(214\) | −558.000 | −0.178243 | ||||||||
\(215\) | −2078.46 | −0.659302 | ||||||||
\(216\) | 374.123 | 0.117851 | ||||||||
\(217\) | −3024.16 | −0.946053 | ||||||||
\(218\) | −816.000 | −0.253516 | ||||||||
\(219\) | −2805.92 | −0.865784 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −3564.00 | −1.08480 | ||||||||
\(222\) | −2847.49 | −0.860861 | ||||||||
\(223\) | 5438.00 | 1.63298 | 0.816492 | − | 0.577357i | \(-0.195916\pi\) | ||||
0.816492 | + | 0.577357i | \(0.195916\pi\) | |||||||
\(224\) | −5184.00 | −1.54630 | ||||||||
\(225\) | 225.000 | 0.0666667 | ||||||||
\(226\) | 5726.16 | 1.68539 | ||||||||
\(227\) | −2177.19 | −0.636586 | −0.318293 | − | 0.947992i | \(-0.603110\pi\) | ||||
−0.318293 | + | 0.947992i | \(0.603110\pi\) | |||||||
\(228\) | 374.123 | 0.108671 | ||||||||
\(229\) | 6073.00 | 1.75247 | 0.876234 | − | 0.481886i | \(-0.160048\pi\) | ||||
0.876234 | + | 0.481886i | \(0.160048\pi\) | |||||||
\(230\) | −3377.50 | −0.968286 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −480.000 | −0.135834 | ||||||||
\(233\) | −1574.43 | −0.442681 | −0.221340 | − | 0.975197i | \(-0.571043\pi\) | ||||
−0.221340 | + | 0.975197i | \(0.571043\pi\) | |||||||
\(234\) | −2376.00 | −0.663778 | ||||||||
\(235\) | 15.0000 | 0.00416380 | ||||||||
\(236\) | −2592.00 | −0.714936 | ||||||||
\(237\) | −1564.04 | −0.428673 | ||||||||
\(238\) | −5050.66 | −1.37557 | ||||||||
\(239\) | 6290.81 | 1.70259 | 0.851294 | − | 0.524689i | \(-0.175818\pi\) | ||||
0.851294 | + | 0.524689i | \(0.175818\pi\) | |||||||
\(240\) | −1200.00 | −0.322749 | ||||||||
\(241\) | 3257.99 | 0.870811 | 0.435405 | − | 0.900234i | \(-0.356605\pi\) | ||||
0.435405 | + | 0.900234i | \(0.356605\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 243.000 | 0.0641500 | ||||||||
\(244\) | 1835.97 | 0.481706 | ||||||||
\(245\) | 3145.00 | 0.820109 | ||||||||
\(246\) | 3996.00 | 1.03567 | ||||||||
\(247\) | 2376.00 | 0.612070 | ||||||||
\(248\) | 1344.07 | 0.344148 | ||||||||
\(249\) | −135.100 | −0.0343840 | ||||||||
\(250\) | −433.013 | −0.109545 | ||||||||
\(251\) | 660.000 | 0.165971 | 0.0829857 | − | 0.996551i | \(-0.473554\pi\) | ||||
0.0829857 | + | 0.996551i | \(0.473554\pi\) | |||||||
\(252\) | −1122.37 | −0.280566 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | −7128.00 | −1.76083 | ||||||||
\(255\) | −701.481 | −0.172268 | ||||||||
\(256\) | 4864.00 | 1.18750 | ||||||||
\(257\) | −1641.00 | −0.398299 | −0.199149 | − | 0.979969i | \(-0.563818\pi\) | ||||
−0.199149 | + | 0.979969i | \(0.563818\pi\) | |||||||
\(258\) | 4320.00 | 1.04245 | ||||||||
\(259\) | −8542.47 | −2.04943 | ||||||||
\(260\) | 1524.20 | 0.363566 | ||||||||
\(261\) | −311.769 | −0.0739388 | ||||||||
\(262\) | −7452.00 | −1.75720 | ||||||||
\(263\) | −2558.24 | −0.599801 | −0.299901 | − | 0.953970i | \(-0.596954\pi\) | ||||
−0.299901 | + | 0.953970i | \(0.596954\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 15.0000 | 0.00347714 | ||||||||
\(266\) | 3367.11 | 0.776130 | ||||||||
\(267\) | 3366.00 | 0.771520 | ||||||||
\(268\) | 280.000 | 0.0638199 | ||||||||
\(269\) | 60.0000 | 0.0135995 | 0.00679975 | − | 0.999977i | \(-0.497836\pi\) | ||||
0.00679975 | + | 0.999977i | \(0.497836\pi\) | |||||||
\(270\) | −467.654 | −0.105409 | ||||||||
\(271\) | −2818.05 | −0.631676 | −0.315838 | − | 0.948813i | \(-0.602286\pi\) | ||||
−0.315838 | + | 0.948813i | \(0.602286\pi\) | |||||||
\(272\) | 3741.23 | 0.833990 | ||||||||
\(273\) | −7128.00 | −1.58024 | ||||||||
\(274\) | −3190.44 | −0.703436 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 2340.00 | 0.510331 | ||||||||
\(277\) | 4205.42 | 0.912199 | 0.456100 | − | 0.889929i | \(-0.349246\pi\) | ||||
0.456100 | + | 0.889929i | \(0.349246\pi\) | |||||||
\(278\) | 5982.00 | 1.29056 | ||||||||
\(279\) | 873.000 | 0.187330 | ||||||||
\(280\) | −2160.00 | −0.461017 | ||||||||
\(281\) | 5220.40 | 1.10827 | 0.554133 | − | 0.832428i | \(-0.313050\pi\) | ||||
0.554133 | + | 0.832428i | \(0.313050\pi\) | |||||||
\(282\) | −31.1769 | −0.00658354 | ||||||||
\(283\) | 4077.25 | 0.856421 | 0.428211 | − | 0.903679i | \(-0.359144\pi\) | ||||
0.428211 | + | 0.903679i | \(0.359144\pi\) | |||||||
\(284\) | −1488.00 | −0.310903 | ||||||||
\(285\) | 467.654 | 0.0971979 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 11988.0 | 2.46561 | ||||||||
\(288\) | 1496.49 | 0.306186 | ||||||||
\(289\) | −2726.00 | −0.554854 | ||||||||
\(290\) | 600.000 | 0.121494 | ||||||||
\(291\) | 1410.00 | 0.284040 | ||||||||
\(292\) | −3741.23 | −0.749791 | ||||||||
\(293\) | 6576.60 | 1.31129 | 0.655647 | − | 0.755068i | \(-0.272396\pi\) | ||||
0.655647 | + | 0.755068i | \(0.272396\pi\) | |||||||
\(294\) | −6536.76 | −1.29671 | ||||||||
\(295\) | −3240.00 | −0.639458 | ||||||||
\(296\) | 3796.66 | 0.745527 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −6984.00 | −1.35763 | ||||||||
\(299\) | 14861.0 | 2.87436 | ||||||||
\(300\) | 300.000 | 0.0577350 | ||||||||
\(301\) | 12960.0 | 2.48173 | ||||||||
\(302\) | −2682.00 | −0.511032 | ||||||||
\(303\) | 5798.91 | 1.09947 | ||||||||
\(304\) | −2494.15 | −0.470558 | ||||||||
\(305\) | 2294.97 | 0.430851 | ||||||||
\(306\) | 1458.00 | 0.272380 | ||||||||
\(307\) | −6786.18 | −1.26159 | −0.630794 | − | 0.775950i | \(-0.717271\pi\) | ||||
−0.630794 | + | 0.775950i | \(0.717271\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 2904.00 | 0.534637 | ||||||||
\(310\) | −1680.09 | −0.307815 | ||||||||
\(311\) | 2934.00 | 0.534958 | 0.267479 | − | 0.963564i | \(-0.413809\pi\) | ||||
0.267479 | + | 0.963564i | \(0.413809\pi\) | |||||||
\(312\) | 3168.00 | 0.574848 | ||||||||
\(313\) | 7180.00 | 1.29661 | 0.648303 | − | 0.761383i | \(-0.275479\pi\) | ||||
0.648303 | + | 0.761383i | \(0.275479\pi\) | |||||||
\(314\) | 12477.7 | 2.24254 | ||||||||
\(315\) | −1402.96 | −0.250946 | ||||||||
\(316\) | −2085.39 | −0.371241 | ||||||||
\(317\) | 7713.00 | 1.36658 | 0.683289 | − | 0.730148i | \(-0.260549\pi\) | ||||
0.683289 | + | 0.730148i | \(0.260549\pi\) | |||||||
\(318\) | −31.1769 | −0.00549784 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 320.000 | 0.0559017 | ||||||||
\(321\) | 483.242 | 0.0840248 | ||||||||
\(322\) | 21060.0 | 3.64481 | ||||||||
\(323\) | −1458.00 | −0.251162 | ||||||||
\(324\) | 324.000 | 0.0555556 | ||||||||
\(325\) | 1905.26 | 0.325183 | ||||||||
\(326\) | 5791.98 | 0.984012 | ||||||||
\(327\) | 706.677 | 0.119509 | ||||||||
\(328\) | −5328.00 | −0.896919 | ||||||||
\(329\) | −93.5307 | −0.0156733 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −9349.00 | −1.55247 | −0.776235 | − | 0.630444i | \(-0.782873\pi\) | ||||
−0.776235 | + | 0.630444i | \(0.782873\pi\) | |||||||
\(332\) | −180.133 | −0.0297774 | ||||||||
\(333\) | 2466.00 | 0.405814 | ||||||||
\(334\) | 8754.00 | 1.43412 | ||||||||
\(335\) | 350.000 | 0.0570822 | ||||||||
\(336\) | 7482.46 | 1.21489 | ||||||||
\(337\) | 3183.51 | 0.514590 | 0.257295 | − | 0.966333i | \(-0.417169\pi\) | ||||
0.257295 | + | 0.966333i | \(0.417169\pi\) | |||||||
\(338\) | −12508.9 | −2.01300 | ||||||||
\(339\) | −4959.00 | −0.794501 | ||||||||
\(340\) | −935.307 | −0.149189 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | −972.000 | −0.153683 | ||||||||
\(343\) | −8916.60 | −1.40365 | ||||||||
\(344\) | −5760.00 | −0.902786 | ||||||||
\(345\) | 2925.00 | 0.456454 | ||||||||
\(346\) | 6048.00 | 0.939718 | ||||||||
\(347\) | 1470.51 | 0.227496 | 0.113748 | − | 0.993510i | \(-0.463714\pi\) | ||||
0.113748 | + | 0.993510i | \(0.463714\pi\) | |||||||
\(348\) | −415.692 | −0.0640329 | ||||||||
\(349\) | 5326.06 | 0.816898 | 0.408449 | − | 0.912781i | \(-0.366070\pi\) | ||||
0.408449 | + | 0.912781i | \(0.366070\pi\) | |||||||
\(350\) | 2700.00 | 0.412346 | ||||||||
\(351\) | 2057.68 | 0.312908 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 11547.0 | 1.74103 | 0.870517 | − | 0.492139i | \(-0.163785\pi\) | ||||
0.870517 | + | 0.492139i | \(0.163785\pi\) | |||||||
\(354\) | 6734.21 | 1.01107 | ||||||||
\(355\) | −1860.00 | −0.278080 | ||||||||
\(356\) | 4488.00 | 0.668156 | ||||||||
\(357\) | 4374.00 | 0.648450 | ||||||||
\(358\) | −6921.28 | −1.02179 | ||||||||
\(359\) | 3547.24 | 0.521494 | 0.260747 | − | 0.965407i | \(-0.416031\pi\) | ||||
0.260747 | + | 0.965407i | \(0.416031\pi\) | |||||||
\(360\) | 623.538 | 0.0912871 | ||||||||
\(361\) | −5887.00 | −0.858288 | ||||||||
\(362\) | 15706.2 | 2.28039 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −9504.00 | −1.36853 | ||||||||
\(365\) | −4676.54 | −0.670633 | ||||||||
\(366\) | −4770.00 | −0.681235 | ||||||||
\(367\) | 5894.00 | 0.838322 | 0.419161 | − | 0.907912i | \(-0.362324\pi\) | ||||
0.419161 | + | 0.907912i | \(0.362324\pi\) | |||||||
\(368\) | −15600.0 | −2.20980 | ||||||||
\(369\) | −3460.64 | −0.488221 | ||||||||
\(370\) | −4745.82 | −0.666820 | ||||||||
\(371\) | −93.5307 | −0.0130886 | ||||||||
\(372\) | 1164.00 | 0.162233 | ||||||||
\(373\) | −3838.22 | −0.532804 | −0.266402 | − | 0.963862i | \(-0.585835\pi\) | ||||
−0.266402 | + | 0.963862i | \(0.585835\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 375.000 | 0.0516398 | ||||||||
\(376\) | 41.5692 | 0.00570151 | ||||||||
\(377\) | −2640.00 | −0.360655 | ||||||||
\(378\) | 2916.00 | 0.396780 | ||||||||
\(379\) | −5431.00 | −0.736073 | −0.368037 | − | 0.929811i | \(-0.619970\pi\) | ||||
−0.368037 | + | 0.929811i | \(0.619970\pi\) | |||||||
\(380\) | 623.538 | 0.0841759 | ||||||||
\(381\) | 6173.03 | 0.830063 | ||||||||
\(382\) | −9540.14 | −1.27779 | ||||||||
\(383\) | 312.000 | 0.0416252 | 0.0208126 | − | 0.999783i | \(-0.493375\pi\) | ||||
0.0208126 | + | 0.999783i | \(0.493375\pi\) | |||||||
\(384\) | −4655.75 | −0.618718 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −2676.00 | −0.352862 | ||||||||
\(387\) | −3741.23 | −0.491414 | ||||||||
\(388\) | 1880.00 | 0.245986 | ||||||||
\(389\) | 1512.00 | 0.197073 | 0.0985366 | − | 0.995133i | \(-0.468584\pi\) | ||||
0.0985366 | + | 0.995133i | \(0.468584\pi\) | |||||||
\(390\) | −3960.00 | −0.514160 | ||||||||
\(391\) | −9119.25 | −1.17949 | ||||||||
\(392\) | 8715.68 | 1.12298 | ||||||||
\(393\) | 6453.62 | 0.828351 | ||||||||
\(394\) | −9552.00 | −1.22138 | ||||||||
\(395\) | −2606.74 | −0.332048 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −10210.0 | −1.29074 | −0.645372 | − | 0.763869i | \(-0.723298\pi\) | ||||
−0.645372 | + | 0.763869i | \(0.723298\pi\) | |||||||
\(398\) | 2532.26 | 0.318921 | ||||||||
\(399\) | −2916.00 | −0.365871 | ||||||||
\(400\) | −2000.00 | −0.250000 | ||||||||
\(401\) | −10368.0 | −1.29116 | −0.645578 | − | 0.763695i | \(-0.723383\pi\) | ||||
−0.645578 | + | 0.763695i | \(0.723383\pi\) | |||||||
\(402\) | −727.461 | −0.0902549 | ||||||||
\(403\) | 7392.39 | 0.913750 | ||||||||
\(404\) | 7731.87 | 0.952166 | ||||||||
\(405\) | 405.000 | 0.0496904 | ||||||||
\(406\) | −3741.23 | −0.457325 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | −1944.00 | −0.235888 | ||||||||
\(409\) | 15611.0 | 1.88732 | 0.943659 | − | 0.330920i | \(-0.107359\pi\) | ||||
0.943659 | + | 0.330920i | \(0.107359\pi\) | |||||||
\(410\) | 6660.00 | 0.802229 | ||||||||
\(411\) | 2763.00 | 0.331603 | ||||||||
\(412\) | 3872.00 | 0.463009 | ||||||||
\(413\) | 20202.6 | 2.40704 | ||||||||
\(414\) | −6079.50 | −0.721717 | ||||||||
\(415\) | −225.167 | −0.0266337 | ||||||||
\(416\) | 12672.0 | 1.49350 | ||||||||
\(417\) | −5180.56 | −0.608377 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 8802.00 | 1.02627 | 0.513133 | − | 0.858309i | \(-0.328485\pi\) | ||||
0.513133 | + | 0.858309i | \(0.328485\pi\) | |||||||
\(420\) | −1870.61 | −0.217325 | ||||||||
\(421\) | −2537.00 | −0.293696 | −0.146848 | − | 0.989159i | \(-0.546913\pi\) | ||||
−0.146848 | + | 0.989159i | \(0.546913\pi\) | |||||||
\(422\) | 7170.00 | 0.827086 | ||||||||
\(423\) | 27.0000 | 0.00310351 | ||||||||
\(424\) | 41.5692 | 0.00476127 | ||||||||
\(425\) | −1169.13 | −0.133438 | ||||||||
\(426\) | 3865.94 | 0.439684 | ||||||||
\(427\) | −14310.0 | −1.62180 | ||||||||
\(428\) | 644.323 | 0.0727676 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 7200.00 | 0.807476 | ||||||||
\(431\) | 3824.37 | 0.427409 | 0.213705 | − | 0.976898i | \(-0.431447\pi\) | ||||
0.213705 | + | 0.976898i | \(0.431447\pi\) | |||||||
\(432\) | −2160.00 | −0.240563 | ||||||||
\(433\) | −12004.0 | −1.33228 | −0.666138 | − | 0.745829i | \(-0.732054\pi\) | ||||
−0.666138 | + | 0.745829i | \(0.732054\pi\) | |||||||
\(434\) | 10476.0 | 1.15867 | ||||||||
\(435\) | −519.615 | −0.0572727 | ||||||||
\(436\) | 942.236 | 0.103497 | ||||||||
\(437\) | 6079.50 | 0.665496 | ||||||||
\(438\) | 9720.00 | 1.06036 | ||||||||
\(439\) | 13127.2 | 1.42717 | 0.713585 | − | 0.700569i | \(-0.247070\pi\) | ||||
0.713585 | + | 0.700569i | \(0.247070\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 5661.00 | 0.611273 | ||||||||
\(442\) | 12346.1 | 1.32860 | ||||||||
\(443\) | 1560.00 | 0.167309 | 0.0836544 | − | 0.996495i | \(-0.473341\pi\) | ||||
0.0836544 | + | 0.996495i | \(0.473341\pi\) | |||||||
\(444\) | 3288.00 | 0.351445 | ||||||||
\(445\) | 5610.00 | 0.597617 | ||||||||
\(446\) | −18837.8 | −1.99999 | ||||||||
\(447\) | 6048.32 | 0.639991 | ||||||||
\(448\) | −1995.32 | −0.210424 | ||||||||
\(449\) | 10890.0 | 1.14461 | 0.572306 | − | 0.820040i | \(-0.306049\pi\) | ||||
0.572306 | + | 0.820040i | \(0.306049\pi\) | |||||||
\(450\) | −779.423 | −0.0816497 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | −6612.00 | −0.688058 | ||||||||
\(453\) | 2322.68 | 0.240903 | ||||||||
\(454\) | 7542.00 | 0.779656 | ||||||||
\(455\) | −11880.0 | −1.22405 | ||||||||
\(456\) | 1296.00 | 0.133094 | ||||||||
\(457\) | 17746.6 | 1.81652 | 0.908261 | − | 0.418404i | \(-0.137410\pi\) | ||||
0.908261 | + | 0.418404i | \(0.137410\pi\) | |||||||
\(458\) | −21037.5 | −2.14633 | ||||||||
\(459\) | −1262.67 | −0.128401 | ||||||||
\(460\) | 3900.00 | 0.395301 | ||||||||
\(461\) | 10274.5 | 1.03803 | 0.519016 | − | 0.854765i | \(-0.326299\pi\) | ||||
0.519016 | + | 0.854765i | \(0.326299\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 8978.00 | 0.901173 | 0.450586 | − | 0.892733i | \(-0.351215\pi\) | ||||
0.450586 | + | 0.892733i | \(0.351215\pi\) | |||||||
\(464\) | 2771.28 | 0.277270 | ||||||||
\(465\) | 1455.00 | 0.145105 | ||||||||
\(466\) | 5454.00 | 0.542171 | ||||||||
\(467\) | 9111.00 | 0.902798 | 0.451399 | − | 0.892322i | \(-0.350925\pi\) | ||||
0.451399 | + | 0.892322i | \(0.350925\pi\) | |||||||
\(468\) | 2743.57 | 0.270986 | ||||||||
\(469\) | −2182.38 | −0.214868 | ||||||||
\(470\) | −51.9615 | −0.00509959 | ||||||||
\(471\) | −10806.0 | −1.05714 | ||||||||
\(472\) | −8978.95 | −0.875614 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 5418.00 | 0.525015 | ||||||||
\(475\) | 779.423 | 0.0752892 | ||||||||
\(476\) | 5832.00 | 0.561574 | ||||||||
\(477\) | 27.0000 | 0.00259171 | ||||||||
\(478\) | −21792.0 | −2.08524 | ||||||||
\(479\) | 13225.9 | 1.26160 | 0.630802 | − | 0.775944i | \(-0.282726\pi\) | ||||
0.630802 | + | 0.775944i | \(0.282726\pi\) | |||||||
\(480\) | 2494.15 | 0.237171 | ||||||||
\(481\) | 20881.6 | 1.97946 | ||||||||
\(482\) | −11286.0 | −1.06652 | ||||||||
\(483\) | −18238.5 | −1.71818 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 2350.00 | 0.220017 | ||||||||
\(486\) | −841.777 | −0.0785674 | ||||||||
\(487\) | −9200.00 | −0.856041 | −0.428020 | − | 0.903769i | \(-0.640789\pi\) | ||||
−0.428020 | + | 0.903769i | \(0.640789\pi\) | |||||||
\(488\) | 6360.00 | 0.589967 | ||||||||
\(489\) | −5016.00 | −0.463868 | ||||||||
\(490\) | −10894.6 | −1.00442 | ||||||||
\(491\) | 1170.87 | 0.107618 | 0.0538090 | − | 0.998551i | \(-0.482864\pi\) | ||||
0.0538090 | + | 0.998551i | \(0.482864\pi\) | |||||||
\(492\) | −4614.18 | −0.422812 | ||||||||
\(493\) | 1620.00 | 0.147994 | ||||||||
\(494\) | −8230.71 | −0.749629 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −7760.00 | −0.702488 | ||||||||
\(497\) | 11597.8 | 1.04675 | ||||||||
\(498\) | 468.000 | 0.0421116 | ||||||||
\(499\) | −3872.00 | −0.347364 | −0.173682 | − | 0.984802i | \(-0.555566\pi\) | ||||
−0.173682 | + | 0.984802i | \(0.555566\pi\) | |||||||
\(500\) | 500.000 | 0.0447214 | ||||||||
\(501\) | −7581.19 | −0.676053 | ||||||||
\(502\) | −2286.31 | −0.203273 | ||||||||
\(503\) | 19476.9 | 1.72651 | 0.863253 | − | 0.504771i | \(-0.168423\pi\) | ||||
0.863253 | + | 0.504771i | \(0.168423\pi\) | |||||||
\(504\) | −3888.00 | −0.343622 | ||||||||
\(505\) | 9664.84 | 0.851643 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 10833.0 | 0.948936 | ||||||||
\(508\) | 8230.71 | 0.718855 | ||||||||
\(509\) | 14010.0 | 1.22000 | 0.610002 | − | 0.792400i | \(-0.291169\pi\) | ||||
0.610002 | + | 0.792400i | \(0.291169\pi\) | |||||||
\(510\) | 2430.00 | 0.210985 | ||||||||
\(511\) | 29160.0 | 2.52439 | ||||||||
\(512\) | −4434.05 | −0.382733 | ||||||||
\(513\) | 841.777 | 0.0724471 | ||||||||
\(514\) | 5684.59 | 0.487814 | ||||||||
\(515\) | 4840.00 | 0.414128 | ||||||||
\(516\) | −4988.31 | −0.425577 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 29592.0 | 2.51003 | ||||||||
\(519\) | −5237.72 | −0.442987 | ||||||||
\(520\) | 5280.00 | 0.445276 | ||||||||
\(521\) | 9900.00 | 0.832489 | 0.416245 | − | 0.909253i | \(-0.363346\pi\) | ||||
0.416245 | + | 0.909253i | \(0.363346\pi\) | |||||||
\(522\) | 1080.00 | 0.0905562 | ||||||||
\(523\) | −16090.8 | −1.34531 | −0.672657 | − | 0.739954i | \(-0.734847\pi\) | ||||
−0.672657 | + | 0.739954i | \(0.734847\pi\) | |||||||
\(524\) | 8604.83 | 0.717373 | ||||||||
\(525\) | −2338.27 | −0.194382 | ||||||||
\(526\) | 8862.00 | 0.734604 | ||||||||
\(527\) | −4536.24 | −0.374956 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 25858.0 | 2.12526 | ||||||||
\(530\) | −51.9615 | −0.00425861 | ||||||||
\(531\) | −5832.00 | −0.476624 | ||||||||
\(532\) | −3888.00 | −0.316854 | ||||||||
\(533\) | −29304.0 | −2.38142 | ||||||||
\(534\) | −11660.2 | −0.944915 | ||||||||
\(535\) | 805.404 | 0.0650853 | ||||||||
\(536\) | 969.948 | 0.0781630 | ||||||||
\(537\) | 5994.00 | 0.481676 | ||||||||
\(538\) | −207.846 | −0.0166559 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 540.000 | 0.0430331 | ||||||||
\(541\) | 15013.4 | 1.19312 | 0.596559 | − | 0.802569i | \(-0.296534\pi\) | ||||
0.596559 | + | 0.802569i | \(0.296534\pi\) | |||||||
\(542\) | 9762.00 | 0.773642 | ||||||||
\(543\) | −13602.0 | −1.07499 | ||||||||
\(544\) | −7776.00 | −0.612855 | ||||||||
\(545\) | 1177.79 | 0.0925710 | ||||||||
\(546\) | 24692.1 | 1.93539 | ||||||||
\(547\) | −15429.1 | −1.20603 | −0.603017 | − | 0.797728i | \(-0.706035\pi\) | ||||
−0.603017 | + | 0.797728i | \(0.706035\pi\) | |||||||
\(548\) | 3684.00 | 0.287176 | ||||||||
\(549\) | 4130.94 | 0.321137 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −1080.00 | −0.0835019 | ||||||||
\(552\) | 8106.00 | 0.625026 | ||||||||
\(553\) | 16254.0 | 1.24989 | ||||||||
\(554\) | −14568.0 | −1.11721 | ||||||||
\(555\) | 4110.00 | 0.314342 | ||||||||
\(556\) | −6907.42 | −0.526870 | ||||||||
\(557\) | −8395.25 | −0.638632 | −0.319316 | − | 0.947648i | \(-0.603453\pi\) | ||||
−0.319316 | + | 0.947648i | \(0.603453\pi\) | |||||||
\(558\) | −3024.16 | −0.229432 | ||||||||
\(559\) | −31680.0 | −2.39700 | ||||||||
\(560\) | 12470.8 | 0.941046 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −18084.0 | −1.35734 | ||||||||
\(563\) | −7271.15 | −0.544303 | −0.272151 | − | 0.962254i | \(-0.587735\pi\) | ||||
−0.272151 | + | 0.962254i | \(0.587735\pi\) | |||||||
\(564\) | 36.0000 | 0.00268772 | ||||||||
\(565\) | −8265.00 | −0.615418 | ||||||||
\(566\) | −14124.0 | −1.04890 | ||||||||
\(567\) | −2525.33 | −0.187044 | ||||||||
\(568\) | −5154.58 | −0.380777 | ||||||||
\(569\) | 8182.21 | 0.602840 | 0.301420 | − | 0.953491i | \(-0.402539\pi\) | ||||
0.301420 | + | 0.953491i | \(0.402539\pi\) | |||||||
\(570\) | −1620.00 | −0.119043 | ||||||||
\(571\) | 16414.6 | 1.20303 | 0.601516 | − | 0.798861i | \(-0.294564\pi\) | ||||
0.601516 | + | 0.798861i | \(0.294564\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 8262.00 | 0.602356 | ||||||||
\(574\) | −41527.7 | −3.01974 | ||||||||
\(575\) | 4875.00 | 0.353568 | ||||||||
\(576\) | 576.000 | 0.0416667 | ||||||||
\(577\) | 7300.00 | 0.526695 | 0.263347 | − | 0.964701i | \(-0.415173\pi\) | ||||
0.263347 | + | 0.964701i | \(0.415173\pi\) | |||||||
\(578\) | 9443.14 | 0.679555 | ||||||||
\(579\) | 2317.48 | 0.166341 | ||||||||
\(580\) | −692.820 | −0.0495997 | ||||||||
\(581\) | 1404.00 | 0.100254 | ||||||||
\(582\) | −4884.38 | −0.347877 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | −12960.0 | −0.918302 | ||||||||
\(585\) | 3429.46 | 0.242377 | ||||||||
\(586\) | −22782.0 | −1.60600 | ||||||||
\(587\) | −5703.00 | −0.401002 | −0.200501 | − | 0.979694i | \(-0.564257\pi\) | ||||
−0.200501 | + | 0.979694i | \(0.564257\pi\) | |||||||
\(588\) | 7548.00 | 0.529378 | ||||||||
\(589\) | 3024.16 | 0.211559 | ||||||||
\(590\) | 11223.7 | 0.783173 | ||||||||
\(591\) | 8272.27 | 0.575763 | ||||||||
\(592\) | −21920.0 | −1.52180 | ||||||||
\(593\) | −16717.8 | −1.15770 | −0.578850 | − | 0.815434i | \(-0.696498\pi\) | ||||
−0.578850 | + | 0.815434i | \(0.696498\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 7290.00 | 0.502287 | ||||||||
\(596\) | 8064.43 | 0.554248 | ||||||||
\(597\) | −2193.00 | −0.150341 | ||||||||
\(598\) | −51480.0 | −3.52036 | ||||||||
\(599\) | 12630.0 | 0.861516 | 0.430758 | − | 0.902468i | \(-0.358246\pi\) | ||||
0.430758 | + | 0.902468i | \(0.358246\pi\) | |||||||
\(600\) | 1039.23 | 0.0707107 | ||||||||
\(601\) | −2757.42 | −0.187151 | −0.0935755 | − | 0.995612i | \(-0.529830\pi\) | ||||
−0.0935755 | + | 0.995612i | \(0.529830\pi\) | |||||||
\(602\) | −44894.8 | −3.03949 | ||||||||
\(603\) | 630.000 | 0.0425466 | ||||||||
\(604\) | 3096.91 | 0.208628 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −20088.0 | −1.34657 | ||||||||
\(607\) | −13035.4 | −0.871649 | −0.435825 | − | 0.900032i | \(-0.643543\pi\) | ||||
−0.435825 | + | 0.900032i | \(0.643543\pi\) | |||||||
\(608\) | 5184.00 | 0.345788 | ||||||||
\(609\) | 3240.00 | 0.215585 | ||||||||
\(610\) | −7950.00 | −0.527682 | ||||||||
\(611\) | 228.631 | 0.0151381 | ||||||||
\(612\) | −1683.55 | −0.111199 | ||||||||
\(613\) | 28142.4 | 1.85426 | 0.927128 | − | 0.374744i | \(-0.122269\pi\) | ||||
0.927128 | + | 0.374744i | \(0.122269\pi\) | |||||||
\(614\) | 23508.0 | 1.54512 | ||||||||
\(615\) | −5767.73 | −0.378174 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −6942.00 | −0.452957 | −0.226478 | − | 0.974016i | \(-0.572721\pi\) | ||||
−0.226478 | + | 0.974016i | \(0.572721\pi\) | |||||||
\(618\) | −10059.8 | −0.654794 | ||||||||
\(619\) | −9220.00 | −0.598680 | −0.299340 | − | 0.954146i | \(-0.596767\pi\) | ||||
−0.299340 | + | 0.954146i | \(0.596767\pi\) | |||||||
\(620\) | 1940.00 | 0.125665 | ||||||||
\(621\) | 5265.00 | 0.340221 | ||||||||
\(622\) | −10163.7 | −0.655187 | ||||||||
\(623\) | −34980.5 | −2.24954 | ||||||||
\(624\) | −18290.5 | −1.17340 | ||||||||
\(625\) | 625.000 | 0.0400000 | ||||||||
\(626\) | −24872.2 | −1.58801 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −14408.0 | −0.915512 | ||||||||
\(629\) | −12813.7 | −0.812267 | ||||||||
\(630\) | 4860.00 | 0.307344 | ||||||||
\(631\) | 7393.00 | 0.466419 | 0.233210 | − | 0.972426i | \(-0.425077\pi\) | ||||
0.233210 | + | 0.972426i | \(0.425077\pi\) | |||||||
\(632\) | −7224.00 | −0.454676 | ||||||||
\(633\) | −6209.40 | −0.389892 | ||||||||
\(634\) | −26718.6 | −1.67371 | ||||||||
\(635\) | 10288.4 | 0.642964 | ||||||||
\(636\) | 36.0000 | 0.00224449 | ||||||||
\(637\) | 47936.2 | 2.98164 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −3348.00 | −0.207269 | ||||||||
\(640\) | −7759.59 | −0.479257 | ||||||||
\(641\) | −15390.0 | −0.948313 | −0.474156 | − | 0.880441i | \(-0.657247\pi\) | ||||
−0.474156 | + | 0.880441i | \(0.657247\pi\) | |||||||
\(642\) | −1674.00 | −0.102909 | ||||||||
\(643\) | −12598.0 | −0.772654 | −0.386327 | − | 0.922362i | \(-0.626256\pi\) | ||||
−0.386327 | + | 0.922362i | \(0.626256\pi\) | |||||||
\(644\) | −24318.0 | −1.48799 | ||||||||
\(645\) | −6235.38 | −0.380648 | ||||||||
\(646\) | 5050.66 | 0.307609 | ||||||||
\(647\) | 7131.00 | 0.433305 | 0.216653 | − | 0.976249i | \(-0.430486\pi\) | ||||
0.216653 | + | 0.976249i | \(0.430486\pi\) | |||||||
\(648\) | 1122.37 | 0.0680414 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | −6600.00 | −0.398267 | ||||||||
\(651\) | −9072.48 | −0.546204 | ||||||||
\(652\) | −6688.00 | −0.401721 | ||||||||
\(653\) | −4890.00 | −0.293048 | −0.146524 | − | 0.989207i | \(-0.546809\pi\) | ||||
−0.146524 | + | 0.989207i | \(0.546809\pi\) | |||||||
\(654\) | −2448.00 | −0.146368 | ||||||||
\(655\) | 10756.0 | 0.641638 | ||||||||
\(656\) | 30761.2 | 1.83083 | ||||||||
\(657\) | −8417.77 | −0.499861 | ||||||||
\(658\) | 324.000 | 0.0191958 | ||||||||
\(659\) | −4569.15 | −0.270089 | −0.135045 | − | 0.990840i | \(-0.543118\pi\) | ||||
−0.135045 | + | 0.990840i | \(0.543118\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −14438.0 | −0.849581 | −0.424791 | − | 0.905292i | \(-0.639652\pi\) | ||||
−0.424791 | + | 0.905292i | \(0.639652\pi\) | |||||||
\(662\) | 32385.9 | 1.90138 | ||||||||
\(663\) | −10692.0 | −0.626309 | ||||||||
\(664\) | −624.000 | −0.0364697 | ||||||||
\(665\) | −4860.00 | −0.283403 | ||||||||
\(666\) | −8542.47 | −0.497018 | ||||||||
\(667\) | −6755.00 | −0.392136 | ||||||||
\(668\) | −10108.2 | −0.585479 | ||||||||
\(669\) | 16314.0 | 0.942804 | ||||||||
\(670\) | −1212.44 | −0.0699112 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | −15552.0 | −0.892755 | ||||||||
\(673\) | −10728.3 | −0.614482 | −0.307241 | − | 0.951632i | \(-0.599406\pi\) | ||||
−0.307241 | + | 0.951632i | \(0.599406\pi\) | |||||||
\(674\) | −11028.0 | −0.630241 | ||||||||
\(675\) | 675.000 | 0.0384900 | ||||||||
\(676\) | 14444.0 | 0.821802 | ||||||||
\(677\) | −13461.5 | −0.764206 | −0.382103 | − | 0.924120i | \(-0.624800\pi\) | ||||
−0.382103 | + | 0.924120i | \(0.624800\pi\) | |||||||
\(678\) | 17178.5 | 0.973061 | ||||||||
\(679\) | −14653.1 | −0.828183 | ||||||||
\(680\) | −3240.00 | −0.182718 | ||||||||
\(681\) | −6531.56 | −0.367533 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −4068.00 | −0.227903 | −0.113951 | − | 0.993486i | \(-0.536351\pi\) | ||||
−0.113951 | + | 0.993486i | \(0.536351\pi\) | |||||||
\(684\) | 1122.37 | 0.0627410 | ||||||||
\(685\) | 4605.00 | 0.256858 | ||||||||
\(686\) | 30888.0 | 1.71911 | ||||||||
\(687\) | 18219.0 | 1.01179 | ||||||||
\(688\) | 33255.4 | 1.84280 | ||||||||
\(689\) | 228.631 | 0.0126417 | ||||||||
\(690\) | −10132.5 | −0.559040 | ||||||||
\(691\) | 3065.00 | 0.168738 | 0.0843691 | − | 0.996435i | \(-0.473113\pi\) | ||||
0.0843691 | + | 0.996435i | \(0.473113\pi\) | |||||||
\(692\) | −6983.63 | −0.383638 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −5094.00 | −0.278625 | ||||||||
\(695\) | −8634.27 | −0.471247 | ||||||||
\(696\) | −1440.00 | −0.0784239 | ||||||||
\(697\) | 17982.0 | 0.977212 | ||||||||
\(698\) | −18450.0 | −1.00049 | ||||||||
\(699\) | −4723.30 | −0.255582 | ||||||||
\(700\) | −3117.69 | −0.168340 | ||||||||
\(701\) | −2303.63 | −0.124118 | −0.0620591 | − | 0.998072i | \(-0.519767\pi\) | ||||
−0.0620591 | + | 0.998072i | \(0.519767\pi\) | |||||||
\(702\) | −7128.00 | −0.383232 | ||||||||
\(703\) | 8542.47 | 0.458301 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 45.0000 | 0.00240397 | ||||||||
\(706\) | −40000.0 | −2.13232 | ||||||||
\(707\) | −60264.0 | −3.20574 | ||||||||
\(708\) | −7776.00 | −0.412768 | ||||||||
\(709\) | 13795.0 | 0.730722 | 0.365361 | − | 0.930866i | \(-0.380946\pi\) | ||||
0.365361 | + | 0.930866i | \(0.380946\pi\) | |||||||
\(710\) | 6443.23 | 0.340578 | ||||||||
\(711\) | −4692.13 | −0.247494 | ||||||||
\(712\) | 15546.9 | 0.818321 | ||||||||
\(713\) | 18915.0 | 0.993510 | ||||||||
\(714\) | −15152.0 | −0.794186 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 7992.00 | 0.417144 | ||||||||
\(717\) | 18872.4 | 0.982990 | ||||||||
\(718\) | −12288.0 | −0.638697 | ||||||||
\(719\) | −23406.0 | −1.21404 | −0.607021 | − | 0.794686i | \(-0.707636\pi\) | ||||
−0.607021 | + | 0.794686i | \(0.707636\pi\) | |||||||
\(720\) | −3600.00 | −0.186339 | ||||||||
\(721\) | −30179.3 | −1.55885 | ||||||||
\(722\) | 20393.2 | 1.05118 | ||||||||
\(723\) | 9773.96 | 0.502763 | ||||||||
\(724\) | −18136.0 | −0.930966 | ||||||||
\(725\) | −866.025 | −0.0443633 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −6518.00 | −0.332516 | −0.166258 | − | 0.986082i | \(-0.553168\pi\) | ||||
−0.166258 | + | 0.986082i | \(0.553168\pi\) | |||||||
\(728\) | −32922.8 | −1.67610 | ||||||||
\(729\) | 729.000 | 0.0370370 | ||||||||
\(730\) | 16200.0 | 0.821355 | ||||||||
\(731\) | 19440.0 | 0.983604 | ||||||||
\(732\) | 5507.92 | 0.278113 | ||||||||
\(733\) | −266.736 | −0.0134408 | −0.00672040 | − | 0.999977i | \(-0.502139\pi\) | ||||
−0.00672040 | + | 0.999977i | \(0.502139\pi\) | |||||||
\(734\) | −20417.4 | −1.02673 | ||||||||
\(735\) | 9435.00 | 0.473490 | ||||||||
\(736\) | 32424.0 | 1.62386 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 11988.0 | 0.597946 | ||||||||
\(739\) | 33388.7 | 1.66201 | 0.831005 | − | 0.556266i | \(-0.187766\pi\) | ||||
0.831005 | + | 0.556266i | \(0.187766\pi\) | |||||||
\(740\) | 5480.00 | 0.272228 | ||||||||
\(741\) | 7128.00 | 0.353379 | ||||||||
\(742\) | 324.000 | 0.0160302 | ||||||||
\(743\) | −34362.2 | −1.69667 | −0.848335 | − | 0.529460i | \(-0.822394\pi\) | ||||
−0.848335 | + | 0.529460i | \(0.822394\pi\) | |||||||
\(744\) | 4032.21 | 0.198694 | ||||||||
\(745\) | 10080.5 | 0.495735 | ||||||||
\(746\) | 13296.0 | 0.652548 | ||||||||
\(747\) | −405.300 | −0.0198516 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −5022.00 | −0.244993 | ||||||||
\(750\) | −1299.04 | −0.0632456 | ||||||||
\(751\) | 6301.00 | 0.306161 | 0.153080 | − | 0.988214i | \(-0.451081\pi\) | ||||
0.153080 | + | 0.988214i | \(0.451081\pi\) | |||||||
\(752\) | −240.000 | −0.0116382 | ||||||||
\(753\) | 1980.00 | 0.0958237 | ||||||||
\(754\) | 9145.23 | 0.441710 | ||||||||
\(755\) | 3871.13 | 0.186603 | ||||||||
\(756\) | −3367.11 | −0.161985 | ||||||||
\(757\) | 17026.0 | 0.817464 | 0.408732 | − | 0.912654i | \(-0.365971\pi\) | ||||
0.408732 | + | 0.912654i | \(0.365971\pi\) | |||||||
\(758\) | 18813.5 | 0.901502 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 2160.00 | 0.103094 | ||||||||
\(761\) | −12574.7 | −0.598991 | −0.299495 | − | 0.954098i | \(-0.596818\pi\) | ||||
−0.299495 | + | 0.954098i | \(0.596818\pi\) | |||||||
\(762\) | −21384.0 | −1.01661 | ||||||||
\(763\) | −7344.00 | −0.348454 | ||||||||
\(764\) | 11016.0 | 0.521656 | ||||||||
\(765\) | −2104.44 | −0.0994592 | ||||||||
\(766\) | −1080.80 | −0.0509803 | ||||||||
\(767\) | −49384.2 | −2.32485 | ||||||||
\(768\) | 14592.0 | 0.685603 | ||||||||
\(769\) | 13702.3 | 0.642543 | 0.321272 | − | 0.946987i | \(-0.395890\pi\) | ||||
0.321272 | + | 0.946987i | \(0.395890\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −4923.00 | −0.229958 | ||||||||
\(772\) | 3089.98 | 0.144055 | ||||||||
\(773\) | −10155.0 | −0.472510 | −0.236255 | − | 0.971691i | \(-0.575920\pi\) | ||||
−0.236255 | + | 0.971691i | \(0.575920\pi\) | |||||||
\(774\) | 12960.0 | 0.601857 | ||||||||
\(775\) | 2425.00 | 0.112398 | ||||||||
\(776\) | 6512.51 | 0.301270 | ||||||||
\(777\) | −25627.4 | −1.18324 | ||||||||
\(778\) | −5237.72 | −0.241364 | ||||||||
\(779\) | −11988.0 | −0.551367 | ||||||||
\(780\) | 4572.61 | 0.209905 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 31590.0 | 1.44457 | ||||||||
\(783\) | −935.307 | −0.0426886 | ||||||||
\(784\) | −50320.0 | −2.29227 | ||||||||
\(785\) | −18010.0 | −0.818859 | ||||||||
\(786\) | −22356.0 | −1.01452 | ||||||||
\(787\) | −33671.1 | −1.52509 | −0.762544 | − | 0.646937i | \(-0.776050\pi\) | ||||
−0.762544 | + | 0.646937i | \(0.776050\pi\) | |||||||
\(788\) | 11029.7 | 0.498625 | ||||||||
\(789\) | −7674.72 | −0.346296 | ||||||||
\(790\) | 9030.00 | 0.406675 | ||||||||
\(791\) | 51535.4 | 2.31655 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 34980.0 | 1.56643 | ||||||||
\(794\) | 35368.5 | 1.58083 | ||||||||
\(795\) | 45.0000 | 0.00200753 | ||||||||
\(796\) | −2924.00 | −0.130199 | ||||||||
\(797\) | 14106.0 | 0.626926 | 0.313463 | − | 0.949600i | \(-0.398511\pi\) | ||||
0.313463 | + | 0.949600i | \(0.398511\pi\) | |||||||
\(798\) | 10101.3 | 0.448099 | ||||||||
\(799\) | −140.296 | −0.00621191 | ||||||||
\(800\) | 4156.92 | 0.183712 | ||||||||
\(801\) | 10098.0 | 0.445437 | ||||||||
\(802\) | 35915.8 | 1.58134 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 840.000 | 0.0368464 | ||||||||
\(805\) | −30397.5 | −1.33090 | ||||||||
\(806\) | −25608.0 | −1.11911 | ||||||||
\(807\) | 180.000 | 0.00785167 | ||||||||
\(808\) | 26784.0 | 1.16616 | ||||||||
\(809\) | −533.472 | −0.0231840 | −0.0115920 | − | 0.999933i | \(-0.503690\pi\) | ||||
−0.0115920 | + | 0.999933i | \(0.503690\pi\) | |||||||
\(810\) | −1402.96 | −0.0608581 | ||||||||
\(811\) | 12870.9 | 0.557284 | 0.278642 | − | 0.960395i | \(-0.410116\pi\) | ||||
0.278642 | + | 0.960395i | \(0.410116\pi\) | |||||||
\(812\) | 4320.00 | 0.186702 | ||||||||
\(813\) | −8454.14 | −0.364698 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −8360.00 | −0.359310 | ||||||||
\(816\) | 11223.7 | 0.481505 | ||||||||
\(817\) | −12960.0 | −0.554973 | ||||||||
\(818\) | −54078.0 | −2.31148 | ||||||||
\(819\) | −21384.0 | −0.912353 | ||||||||
\(820\) | −7690.31 | −0.327509 | ||||||||
\(821\) | 2975.66 | 0.126494 | 0.0632469 | − | 0.997998i | \(-0.479854\pi\) | ||||
0.0632469 | + | 0.997998i | \(0.479854\pi\) | |||||||
\(822\) | −9571.31 | −0.406129 | ||||||||
\(823\) | −3664.00 | −0.155187 | −0.0775936 | − | 0.996985i | \(-0.524724\pi\) | ||||
−0.0775936 | + | 0.996985i | \(0.524724\pi\) | |||||||
\(824\) | 13413.0 | 0.567068 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −69984.0 | −2.94801 | ||||||||
\(827\) | −31547.6 | −1.32650 | −0.663251 | − | 0.748397i | \(-0.730824\pi\) | ||||
−0.663251 | + | 0.748397i | \(0.730824\pi\) | |||||||
\(828\) | 7020.00 | 0.294640 | ||||||||
\(829\) | −24829.0 | −1.04023 | −0.520113 | − | 0.854098i | \(-0.674110\pi\) | ||||
−0.520113 | + | 0.854098i | \(0.674110\pi\) | |||||||
\(830\) | 780.000 | 0.0326195 | ||||||||
\(831\) | 12616.3 | 0.526658 | ||||||||
\(832\) | 4877.46 | 0.203240 | ||||||||
\(833\) | −29415.4 | −1.22351 | ||||||||
\(834\) | 17946.0 | 0.745107 | ||||||||
\(835\) | −12635.3 | −0.523668 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 2619.00 | 0.108155 | ||||||||
\(838\) | −30491.0 | −1.25692 | ||||||||
\(839\) | −6048.00 | −0.248868 | −0.124434 | − | 0.992228i | \(-0.539711\pi\) | ||||
−0.124434 | + | 0.992228i | \(0.539711\pi\) | |||||||
\(840\) | −6480.00 | −0.266168 | ||||||||
\(841\) | −23189.0 | −0.950797 | ||||||||
\(842\) | 8788.43 | 0.359702 | ||||||||
\(843\) | 15661.2 | 0.639858 | ||||||||
\(844\) | −8279.20 | −0.337656 | ||||||||
\(845\) | 18055.0 | 0.735042 | ||||||||
\(846\) | −93.5307 | −0.00380101 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −240.000 | −0.00971891 | ||||||||
\(849\) | 12231.7 | 0.494455 | ||||||||
\(850\) | 4050.00 | 0.163428 | ||||||||
\(851\) | 53430.0 | 2.15224 | ||||||||
\(852\) | −4464.00 | −0.179500 | ||||||||
\(853\) | −11656.7 | −0.467899 | −0.233950 | − | 0.972249i | \(-0.575165\pi\) | ||||
−0.233950 | + | 0.972249i | \(0.575165\pi\) | |||||||
\(854\) | 49571.3 | 1.98629 | ||||||||
\(855\) | 1402.96 | 0.0561173 | ||||||||
\(856\) | 2232.00 | 0.0891217 | ||||||||
\(857\) | 33198.2 | 1.32325 | 0.661627 | − | 0.749833i | \(-0.269866\pi\) | ||||
0.661627 | + | 0.749833i | \(0.269866\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 16196.0 | 0.643307 | 0.321653 | − | 0.946858i | \(-0.395761\pi\) | ||||
0.321653 | + | 0.946858i | \(0.395761\pi\) | |||||||
\(860\) | −8313.84 | −0.329651 | ||||||||
\(861\) | 35964.0 | 1.42352 | ||||||||
\(862\) | −13248.0 | −0.523467 | ||||||||
\(863\) | 10728.0 | 0.423158 | 0.211579 | − | 0.977361i | \(-0.432139\pi\) | ||||
0.211579 | + | 0.977361i | \(0.432139\pi\) | |||||||
\(864\) | 4489.48 | 0.176777 | ||||||||
\(865\) | −8729.54 | −0.343137 | ||||||||
\(866\) | 41583.1 | 1.63170 | ||||||||
\(867\) | −8178.00 | −0.320345 | ||||||||
\(868\) | −12096.6 | −0.473026 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 1800.00 | 0.0701445 | ||||||||
\(871\) | 5334.72 | 0.207532 | ||||||||
\(872\) | 3264.00 | 0.126758 | ||||||||
\(873\) | 4230.00 | 0.163991 | ||||||||
\(874\) | −21060.0 | −0.815063 | ||||||||
\(875\) | −3897.11 | −0.150567 | ||||||||
\(876\) | −11223.7 | −0.432892 | ||||||||
\(877\) | 47392.4 | 1.82477 | 0.912387 | − | 0.409329i | \(-0.134237\pi\) | ||||
0.912387 | + | 0.409329i | \(0.134237\pi\) | |||||||
\(878\) | −45474.0 | −1.74792 | ||||||||
\(879\) | 19729.8 | 0.757075 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 20664.0 | 0.790225 | 0.395112 | − | 0.918633i | \(-0.370706\pi\) | ||||
0.395112 | + | 0.918633i | \(0.370706\pi\) | |||||||
\(882\) | −19610.3 | −0.748654 | ||||||||
\(883\) | 27532.0 | 1.04929 | 0.524646 | − | 0.851320i | \(-0.324198\pi\) | ||||
0.524646 | + | 0.851320i | \(0.324198\pi\) | |||||||
\(884\) | −14256.0 | −0.542400 | ||||||||
\(885\) | −9720.00 | −0.369191 | ||||||||
\(886\) | −5404.00 | −0.204911 | ||||||||
\(887\) | 29822.5 | 1.12891 | 0.564453 | − | 0.825465i | \(-0.309087\pi\) | ||||
0.564453 | + | 0.825465i | \(0.309087\pi\) | |||||||
\(888\) | 11390.0 | 0.430430 | ||||||||
\(889\) | −64152.0 | −2.42024 | ||||||||
\(890\) | −19433.6 | −0.731928 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 21752.0 | 0.816492 | ||||||||
\(893\) | 93.5307 | 0.00350491 | ||||||||
\(894\) | −20952.0 | −0.783825 | ||||||||
\(895\) | 9990.00 | 0.373105 | ||||||||
\(896\) | 48384.0 | 1.80401 | ||||||||
\(897\) | 44583.0 | 1.65951 | ||||||||
\(898\) | −37724.1 | −1.40186 | ||||||||
\(899\) | −3360.18 | −0.124659 | ||||||||
\(900\) | 900.000 | 0.0333333 | ||||||||
\(901\) | −140.296 | −0.00518750 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 38880.0 | 1.43283 | ||||||||
\(904\) | −22904.6 | −0.842696 | ||||||||
\(905\) | −22670.0 | −0.832681 | ||||||||
\(906\) | −8046.00 | −0.295045 | ||||||||
\(907\) | −6406.00 | −0.234518 | −0.117259 | − | 0.993101i | \(-0.537411\pi\) | ||||
−0.117259 | + | 0.993101i | \(0.537411\pi\) | |||||||
\(908\) | −8708.75 | −0.318293 | ||||||||
\(909\) | 17396.7 | 0.634777 | ||||||||
\(910\) | 41153.5 | 1.49915 | ||||||||
\(911\) | 35046.0 | 1.27456 | 0.637281 | − | 0.770632i | \(-0.280059\pi\) | ||||
0.637281 | + | 0.770632i | \(0.280059\pi\) | |||||||
\(912\) | −7482.46 | −0.271677 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | −61476.0 | −2.22478 | ||||||||
\(915\) | 6884.90 | 0.248752 | ||||||||
\(916\) | 24292.0 | 0.876234 | ||||||||
\(917\) | −67068.0 | −2.41525 | ||||||||
\(918\) | 4374.00 | 0.157259 | ||||||||
\(919\) | 23801.8 | 0.854353 | 0.427176 | − | 0.904168i | \(-0.359508\pi\) | ||||
0.427176 | + | 0.904168i | \(0.359508\pi\) | |||||||
\(920\) | 13510.0 | 0.484143 | ||||||||
\(921\) | −20358.5 | −0.728378 | ||||||||
\(922\) | −35592.0 | −1.27132 | ||||||||
\(923\) | −28350.2 | −1.01101 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 6850.00 | 0.243488 | ||||||||
\(926\) | −31100.7 | −1.10371 | ||||||||
\(927\) | 8712.00 | 0.308673 | ||||||||
\(928\) | −5760.00 | −0.203751 | ||||||||
\(929\) | −42558.0 | −1.50300 | −0.751498 | − | 0.659736i | \(-0.770668\pi\) | ||||
−0.751498 | + | 0.659736i | \(0.770668\pi\) | |||||||
\(930\) | −5040.27 | −0.177717 | ||||||||
\(931\) | 19610.3 | 0.690334 | ||||||||
\(932\) | −6297.74 | −0.221340 | ||||||||
\(933\) | 8802.00 | 0.308858 | ||||||||
\(934\) | −31561.4 | −1.10570 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 9504.00 | 0.331889 | ||||||||
\(937\) | −10049.4 | −0.350372 | −0.175186 | − | 0.984535i | \(-0.556053\pi\) | ||||
−0.175186 | + | 0.984535i | \(0.556053\pi\) | |||||||
\(938\) | 7560.00 | 0.263159 | ||||||||
\(939\) | 21540.0 | 0.748596 | ||||||||
\(940\) | 60.0000 | 0.00208190 | ||||||||
\(941\) | 13343.7 | 0.462267 | 0.231133 | − | 0.972922i | \(-0.425757\pi\) | ||||
0.231133 | + | 0.972922i | \(0.425757\pi\) | |||||||
\(942\) | 37433.1 | 1.29473 | ||||||||
\(943\) | −74980.5 | −2.58929 | ||||||||
\(944\) | 51840.0 | 1.78734 | ||||||||
\(945\) | −4208.88 | −0.144884 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −1899.00 | −0.0651628 | −0.0325814 | − | 0.999469i | \(-0.510373\pi\) | ||||
−0.0325814 | + | 0.999469i | \(0.510373\pi\) | |||||||
\(948\) | −6256.17 | −0.214336 | ||||||||
\(949\) | −71280.0 | −2.43819 | ||||||||
\(950\) | −2700.00 | −0.0922101 | ||||||||
\(951\) | 23139.0 | 0.788994 | ||||||||
\(952\) | 20202.6 | 0.687785 | ||||||||
\(953\) | −25766.0 | −0.875805 | −0.437903 | − | 0.899022i | \(-0.644279\pi\) | ||||
−0.437903 | + | 0.899022i | \(0.644279\pi\) | |||||||
\(954\) | −93.5307 | −0.00317418 | ||||||||
\(955\) | 13770.0 | 0.466583 | ||||||||
\(956\) | 25163.2 | 0.851294 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −45816.0 | −1.54514 | ||||||||
\(959\) | −28713.9 | −0.966863 | ||||||||
\(960\) | 960.000 | 0.0322749 | ||||||||
\(961\) | −20382.0 | −0.684166 | ||||||||
\(962\) | −72336.0 | −2.42433 | ||||||||
\(963\) | 1449.73 | 0.0485117 | ||||||||
\(964\) | 13032.0 | 0.435405 | ||||||||
\(965\) | 3862.47 | 0.128847 | ||||||||
\(966\) | 63180.0 | 2.10433 | ||||||||
\(967\) | −45005.6 | −1.49667 | −0.748336 | − | 0.663319i | \(-0.769147\pi\) | ||||
−0.748336 | + | 0.663319i | \(0.769147\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −4374.00 | −0.145008 | ||||||||
\(970\) | −8140.64 | −0.269464 | ||||||||
\(971\) | −51840.0 | −1.71331 | −0.856655 | − | 0.515889i | \(-0.827462\pi\) | ||||
−0.856655 | + | 0.515889i | \(0.827462\pi\) | |||||||
\(972\) | 972.000 | 0.0320750 | ||||||||
\(973\) | 53838.0 | 1.77386 | ||||||||
\(974\) | 31869.7 | 1.04843 | ||||||||
\(975\) | 5715.77 | 0.187745 | ||||||||
\(976\) | −36719.5 | −1.20426 | ||||||||
\(977\) | −17133.0 | −0.561037 | −0.280519 | − | 0.959849i | \(-0.590506\pi\) | ||||
−0.280519 | + | 0.959849i | \(0.590506\pi\) | |||||||
\(978\) | 17375.9 | 0.568120 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 12580.0 | 0.410054 | ||||||||
\(981\) | 2120.03 | 0.0689983 | ||||||||
\(982\) | −4056.00 | −0.131805 | ||||||||
\(983\) | 11241.0 | 0.364733 | 0.182366 | − | 0.983231i | \(-0.441624\pi\) | ||||
0.182366 | + | 0.983231i | \(0.441624\pi\) | |||||||
\(984\) | −15984.0 | −0.517837 | ||||||||
\(985\) | 13787.1 | 0.445984 | ||||||||
\(986\) | −5611.84 | −0.181255 | ||||||||
\(987\) | −280.592 | −0.00904899 | ||||||||
\(988\) | 9504.00 | 0.306035 | ||||||||
\(989\) | −81060.0 | −2.60623 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −14567.0 | −0.466938 | −0.233469 | − | 0.972364i | \(-0.575008\pi\) | ||||
−0.233469 | + | 0.972364i | \(0.575008\pi\) | |||||||
\(992\) | 16128.9 | 0.516221 | ||||||||
\(993\) | −28047.0 | −0.896319 | ||||||||
\(994\) | −40176.0 | −1.28200 | ||||||||
\(995\) | −3655.00 | −0.116454 | ||||||||
\(996\) | −540.400 | −0.0171920 | ||||||||
\(997\) | −29874.4 | −0.948979 | −0.474490 | − | 0.880261i | \(-0.657367\pi\) | ||||
−0.474490 | + | 0.880261i | \(0.657367\pi\) | |||||||
\(998\) | 13413.0 | 0.425432 | ||||||||
\(999\) | 7398.00 | 0.234297 |
(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 | 1815.4.a.l.1.1 | ✓ | 2 | |
11.10 | odd | 2 | inner | 1815.4.a.l.1.2 | yes | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1815.4.a.l.1.1 | ✓ | 2 | 1.1 | even | 1 | trivial | |
1815.4.a.l.1.2 | yes | 2 | 11.10 | odd | 2 | inner |