Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [495,4,Mod(1,495)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(495, 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("495.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 495 = 3^{2} \cdot 5 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 495.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: | \(29.2059454528\) |
Analytic rank: | \(0\) |
Dimension: | \(7\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{7} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{7} - 2x^{6} - 41x^{5} + 40x^{4} + 424x^{3} - 168x^{2} - 1042x - 388 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.7 | ||
Root | \(-4.54090\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 495.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 5.54090 | 1.95900 | 0.979502 | − | 0.201434i | \(-0.0645601\pi\) | ||||
0.979502 | + | 0.201434i | \(0.0645601\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 22.7016 | 2.83770 | ||||||||
\(5\) | 5.00000 | 0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 17.7319 | 0.957434 | 0.478717 | − | 0.877969i | \(-0.341102\pi\) | ||||
0.478717 | + | 0.877969i | \(0.341102\pi\) | |||||||
\(8\) | 81.4600 | 3.60006 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 27.7045 | 0.876093 | ||||||||
\(11\) | 11.0000 | 0.301511 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −53.5704 | −1.14290 | −0.571452 | − | 0.820635i | \(-0.693620\pi\) | ||||
−0.571452 | + | 0.820635i | \(0.693620\pi\) | |||||||
\(14\) | 98.2508 | 1.87562 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 269.749 | 4.21483 | ||||||||
\(17\) | −112.431 | −1.60403 | −0.802014 | − | 0.597305i | \(-0.796238\pi\) | ||||
−0.802014 | + | 0.597305i | \(0.796238\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.24467 | −0.0150288 | −0.00751439 | − | 0.999972i | \(-0.502392\pi\) | ||||
−0.00751439 | + | 0.999972i | \(0.502392\pi\) | |||||||
\(20\) | 113.508 | 1.26906 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 60.9499 | 0.590662 | ||||||||
\(23\) | 78.4188 | 0.710933 | 0.355466 | − | 0.934689i | \(-0.384322\pi\) | ||||
0.355466 | + | 0.934689i | \(0.384322\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 25.0000 | 0.200000 | ||||||||
\(26\) | −296.828 | −2.23896 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 402.543 | 2.71691 | ||||||||
\(29\) | −174.127 | −1.11498 | −0.557492 | − | 0.830182i | \(-0.688236\pi\) | ||||
−0.557492 | + | 0.830182i | \(0.688236\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 82.5240 | 0.478121 | 0.239060 | − | 0.971005i | \(-0.423161\pi\) | ||||
0.239060 | + | 0.971005i | \(0.423161\pi\) | |||||||
\(32\) | 842.973 | 4.65681 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −622.968 | −3.14230 | ||||||||
\(35\) | 88.6596 | 0.428178 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −149.081 | −0.662398 | −0.331199 | − | 0.943561i | \(-0.607453\pi\) | ||||
−0.331199 | + | 0.943561i | \(0.607453\pi\) | |||||||
\(38\) | −6.89659 | −0.0294414 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 407.300 | 1.60999 | ||||||||
\(41\) | −414.603 | −1.57927 | −0.789635 | − | 0.613577i | \(-0.789730\pi\) | ||||
−0.789635 | + | 0.613577i | \(0.789730\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −182.535 | −0.647357 | −0.323679 | − | 0.946167i | \(-0.604920\pi\) | ||||
−0.323679 | + | 0.946167i | \(0.604920\pi\) | |||||||
\(44\) | 249.717 | 0.855598 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 434.511 | 1.39272 | ||||||||
\(47\) | 438.738 | 1.36163 | 0.680815 | − | 0.732456i | \(-0.261626\pi\) | ||||
0.680815 | + | 0.732456i | \(0.261626\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −28.5788 | −0.0833201 | ||||||||
\(50\) | 138.523 | 0.391801 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −1216.13 | −3.24322 | ||||||||
\(53\) | 490.962 | 1.27243 | 0.636216 | − | 0.771511i | \(-0.280499\pi\) | ||||
0.636216 | + | 0.771511i | \(0.280499\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 55.0000 | 0.134840 | ||||||||
\(56\) | 1444.44 | 3.44682 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −964.819 | −2.18426 | ||||||||
\(59\) | 6.02762 | 0.0133005 | 0.00665025 | − | 0.999978i | \(-0.497883\pi\) | ||||
0.00665025 | + | 0.999978i | \(0.497883\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 434.789 | 0.912606 | 0.456303 | − | 0.889824i | \(-0.349173\pi\) | ||||
0.456303 | + | 0.889824i | \(0.349173\pi\) | |||||||
\(62\) | 457.257 | 0.936640 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 2512.84 | 4.90789 | ||||||||
\(65\) | −267.852 | −0.511123 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 935.150 | 1.70518 | 0.852588 | − | 0.522584i | \(-0.175032\pi\) | ||||
0.852588 | + | 0.522584i | \(0.175032\pi\) | |||||||
\(68\) | −2552.36 | −4.55175 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 491.254 | 0.838802 | ||||||||
\(71\) | 510.132 | 0.852698 | 0.426349 | − | 0.904559i | \(-0.359800\pi\) | ||||
0.426349 | + | 0.904559i | \(0.359800\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −1045.70 | −1.67658 | −0.838290 | − | 0.545225i | \(-0.816444\pi\) | ||||
−0.838290 | + | 0.545225i | \(0.816444\pi\) | |||||||
\(74\) | −826.042 | −1.29764 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −28.2560 | −0.0426471 | ||||||||
\(77\) | 195.051 | 0.288677 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 226.439 | 0.322485 | 0.161243 | − | 0.986915i | \(-0.448450\pi\) | ||||
0.161243 | + | 0.986915i | \(0.448450\pi\) | |||||||
\(80\) | 1348.75 | 1.88493 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −2297.27 | −3.09380 | ||||||||
\(83\) | −1185.72 | −1.56807 | −0.784035 | − | 0.620716i | \(-0.786842\pi\) | ||||
−0.784035 | + | 0.620716i | \(0.786842\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −562.154 | −0.717344 | ||||||||
\(86\) | −1011.41 | −1.26818 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 896.060 | 1.08546 | ||||||||
\(89\) | −1443.15 | −1.71880 | −0.859400 | − | 0.511303i | \(-0.829163\pi\) | ||||
−0.859400 | + | 0.511303i | \(0.829163\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −949.907 | −1.09426 | ||||||||
\(92\) | 1780.23 | 2.01741 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 2431.01 | 2.66744 | ||||||||
\(95\) | −6.22335 | −0.00672107 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 825.703 | 0.864303 | 0.432152 | − | 0.901801i | \(-0.357755\pi\) | ||||
0.432152 | + | 0.901801i | \(0.357755\pi\) | |||||||
\(98\) | −158.352 | −0.163224 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 567.540 | 0.567540 | ||||||||
\(101\) | 18.3996 | 0.0181270 | 0.00906349 | − | 0.999959i | \(-0.497115\pi\) | ||||
0.00906349 | + | 0.999959i | \(0.497115\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 955.858 | 0.914402 | 0.457201 | − | 0.889363i | \(-0.348852\pi\) | ||||
0.457201 | + | 0.889363i | \(0.348852\pi\) | |||||||
\(104\) | −4363.85 | −4.11452 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 2720.37 | 2.49270 | ||||||||
\(107\) | −1500.76 | −1.35593 | −0.677963 | − | 0.735096i | \(-0.737137\pi\) | ||||
−0.677963 | + | 0.735096i | \(0.737137\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −727.915 | −0.639648 | −0.319824 | − | 0.947477i | \(-0.603624\pi\) | ||||
−0.319824 | + | 0.947477i | \(0.603624\pi\) | |||||||
\(110\) | 304.750 | 0.264152 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 4783.17 | 4.03542 | ||||||||
\(113\) | −1341.55 | −1.11684 | −0.558419 | − | 0.829559i | \(-0.688592\pi\) | ||||
−0.558419 | + | 0.829559i | \(0.688592\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 392.094 | 0.317939 | ||||||||
\(116\) | −3952.95 | −3.16399 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 33.3985 | 0.0260557 | ||||||||
\(119\) | −1993.62 | −1.53575 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 121.000 | 0.0909091 | ||||||||
\(122\) | 2409.12 | 1.78780 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 1873.42 | 1.35676 | ||||||||
\(125\) | 125.000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1685.73 | 1.17783 | 0.588914 | − | 0.808196i | \(-0.299556\pi\) | ||||
0.588914 | + | 0.808196i | \(0.299556\pi\) | |||||||
\(128\) | 7179.60 | 4.95776 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −1484.14 | −1.00129 | ||||||||
\(131\) | −473.852 | −0.316035 | −0.158018 | − | 0.987436i | \(-0.550510\pi\) | ||||
−0.158018 | + | 0.987436i | \(0.550510\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −22.0704 | −0.0143891 | ||||||||
\(134\) | 5181.57 | 3.34045 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −9158.62 | −5.77460 | ||||||||
\(137\) | 724.768 | 0.451979 | 0.225990 | − | 0.974130i | \(-0.427438\pi\) | ||||
0.225990 | + | 0.974130i | \(0.427438\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 2396.73 | 1.46250 | 0.731251 | − | 0.682108i | \(-0.238937\pi\) | ||||
0.731251 | + | 0.682108i | \(0.238937\pi\) | |||||||
\(140\) | 2012.71 | 1.21504 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 2826.59 | 1.67044 | ||||||||
\(143\) | −589.275 | −0.344599 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −870.634 | −0.498636 | ||||||||
\(146\) | −5794.14 | −3.28443 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −3384.37 | −1.87969 | ||||||||
\(149\) | −693.282 | −0.381180 | −0.190590 | − | 0.981670i | \(-0.561040\pi\) | ||||
−0.190590 | + | 0.981670i | \(0.561040\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −2682.28 | −1.44557 | −0.722785 | − | 0.691073i | \(-0.757138\pi\) | ||||
−0.722785 | + | 0.691073i | \(0.757138\pi\) | |||||||
\(152\) | −101.391 | −0.0541045 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 1080.76 | 0.565520 | ||||||||
\(155\) | 412.620 | 0.213822 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −1209.54 | −0.614852 | −0.307426 | − | 0.951572i | \(-0.599468\pi\) | ||||
−0.307426 | + | 0.951572i | \(0.599468\pi\) | |||||||
\(158\) | 1254.67 | 0.631750 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 4214.87 | 2.08259 | ||||||||
\(161\) | 1390.52 | 0.680671 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −3429.67 | −1.64805 | −0.824026 | − | 0.566553i | \(-0.808277\pi\) | ||||
−0.824026 | + | 0.566553i | \(0.808277\pi\) | |||||||
\(164\) | −9412.14 | −4.48149 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −6569.97 | −3.07186 | ||||||||
\(167\) | −1523.60 | −0.705986 | −0.352993 | − | 0.935626i | \(-0.614836\pi\) | ||||
−0.352993 | + | 0.935626i | \(0.614836\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 672.791 | 0.306232 | ||||||||
\(170\) | −3114.84 | −1.40528 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −4143.84 | −1.83700 | ||||||||
\(173\) | −739.726 | −0.325089 | −0.162544 | − | 0.986701i | \(-0.551970\pi\) | ||||
−0.162544 | + | 0.986701i | \(0.551970\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 443.298 | 0.191487 | ||||||||
\(176\) | 2967.24 | 1.27082 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −7996.33 | −3.36714 | ||||||||
\(179\) | 2090.21 | 0.872791 | 0.436395 | − | 0.899755i | \(-0.356255\pi\) | ||||
0.436395 | + | 0.899755i | \(0.356255\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 521.612 | 0.214205 | 0.107103 | − | 0.994248i | \(-0.465843\pi\) | ||||
0.107103 | + | 0.994248i | \(0.465843\pi\) | |||||||
\(182\) | −5263.34 | −2.14365 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 6388.00 | 2.55940 | ||||||||
\(185\) | −745.404 | −0.296233 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −1236.74 | −0.483633 | ||||||||
\(188\) | 9960.06 | 3.86389 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −34.4830 | −0.0131666 | ||||||||
\(191\) | −1336.98 | −0.506494 | −0.253247 | − | 0.967402i | \(-0.581499\pi\) | ||||
−0.253247 | + | 0.967402i | \(0.581499\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 4650.76 | 1.73455 | 0.867277 | − | 0.497825i | \(-0.165868\pi\) | ||||
0.867277 | + | 0.497825i | \(0.165868\pi\) | |||||||
\(194\) | 4575.14 | 1.69317 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −648.784 | −0.236437 | ||||||||
\(197\) | −3293.66 | −1.19118 | −0.595592 | − | 0.803287i | \(-0.703083\pi\) | ||||
−0.595592 | + | 0.803287i | \(0.703083\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 3613.76 | 1.28730 | 0.643650 | − | 0.765320i | \(-0.277419\pi\) | ||||
0.643650 | + | 0.765320i | \(0.277419\pi\) | |||||||
\(200\) | 2036.50 | 0.720012 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 101.950 | 0.0355108 | ||||||||
\(203\) | −3087.60 | −1.06752 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −2073.01 | −0.706271 | ||||||||
\(206\) | 5296.31 | 1.79132 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −14450.6 | −4.81715 | ||||||||
\(209\) | −13.6914 | −0.00453135 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 5661.64 | 1.84722 | 0.923609 | − | 0.383335i | \(-0.125225\pi\) | ||||
0.923609 | + | 0.383335i | \(0.125225\pi\) | |||||||
\(212\) | 11145.6 | 3.61078 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −8315.57 | −2.65626 | ||||||||
\(215\) | −912.676 | −0.289507 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1463.31 | 0.457769 | ||||||||
\(218\) | −4033.31 | −1.25307 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 1248.59 | 0.382635 | ||||||||
\(221\) | 6022.97 | 1.83325 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 5866.64 | 1.76170 | 0.880850 | − | 0.473396i | \(-0.156972\pi\) | ||||
0.880850 | + | 0.473396i | \(0.156972\pi\) | |||||||
\(224\) | 14947.5 | 4.45859 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −7433.41 | −2.18789 | ||||||||
\(227\) | 671.916 | 0.196461 | 0.0982304 | − | 0.995164i | \(-0.468682\pi\) | ||||
0.0982304 | + | 0.995164i | \(0.468682\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −1265.84 | −0.365281 | −0.182640 | − | 0.983180i | \(-0.558464\pi\) | ||||
−0.182640 | + | 0.983180i | \(0.558464\pi\) | |||||||
\(230\) | 2172.55 | 0.622844 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −14184.4 | −4.01401 | ||||||||
\(233\) | −173.516 | −0.0487873 | −0.0243936 | − | 0.999702i | \(-0.507766\pi\) | ||||
−0.0243936 | + | 0.999702i | \(0.507766\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 2193.69 | 0.608939 | ||||||||
\(236\) | 136.837 | 0.0377428 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −11046.4 | −3.00854 | ||||||||
\(239\) | −2261.08 | −0.611955 | −0.305977 | − | 0.952039i | \(-0.598983\pi\) | ||||
−0.305977 | + | 0.952039i | \(0.598983\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 2069.83 | 0.553233 | 0.276617 | − | 0.960980i | \(-0.410787\pi\) | ||||
0.276617 | + | 0.960980i | \(0.410787\pi\) | |||||||
\(242\) | 670.449 | 0.178091 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 9870.39 | 2.58970 | ||||||||
\(245\) | −142.894 | −0.0372619 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 66.6775 | 0.0171765 | ||||||||
\(248\) | 6722.40 | 1.72126 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 692.613 | 0.175219 | ||||||||
\(251\) | −2511.60 | −0.631597 | −0.315798 | − | 0.948826i | \(-0.602272\pi\) | ||||
−0.315798 | + | 0.948826i | \(0.602272\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 862.607 | 0.214354 | ||||||||
\(254\) | 9340.45 | 2.30737 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 19678.8 | 4.80438 | ||||||||
\(257\) | 261.418 | 0.0634506 | 0.0317253 | − | 0.999497i | \(-0.489900\pi\) | ||||
0.0317253 | + | 0.999497i | \(0.489900\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −2643.49 | −0.634202 | ||||||||
\(260\) | −6080.67 | −1.45041 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −2625.56 | −0.619114 | ||||||||
\(263\) | 2015.73 | 0.472605 | 0.236303 | − | 0.971680i | \(-0.424064\pi\) | ||||
0.236303 | + | 0.971680i | \(0.424064\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 2454.81 | 0.569049 | ||||||||
\(266\) | −122.290 | −0.0281882 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 21229.4 | 4.83877 | ||||||||
\(269\) | −1638.25 | −0.371324 | −0.185662 | − | 0.982614i | \(-0.559443\pi\) | ||||
−0.185662 | + | 0.982614i | \(0.559443\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 2200.32 | 0.493209 | 0.246605 | − | 0.969116i | \(-0.420685\pi\) | ||||
0.246605 | + | 0.969116i | \(0.420685\pi\) | |||||||
\(272\) | −30328.1 | −6.76071 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 4015.87 | 0.885429 | ||||||||
\(275\) | 275.000 | 0.0603023 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 6953.40 | 1.50827 | 0.754133 | − | 0.656722i | \(-0.228057\pi\) | ||||
0.754133 | + | 0.656722i | \(0.228057\pi\) | |||||||
\(278\) | 13280.0 | 2.86505 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 7222.21 | 1.54146 | ||||||||
\(281\) | −6425.61 | −1.36413 | −0.682063 | − | 0.731293i | \(-0.738917\pi\) | ||||
−0.682063 | + | 0.731293i | \(0.738917\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −1799.64 | −0.378013 | −0.189006 | − | 0.981976i | \(-0.560527\pi\) | ||||
−0.189006 | + | 0.981976i | \(0.560527\pi\) | |||||||
\(284\) | 11580.8 | 2.41970 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −3265.11 | −0.675071 | ||||||||
\(287\) | −7351.70 | −1.51205 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 7727.70 | 1.57291 | ||||||||
\(290\) | −4824.10 | −0.976830 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −23739.1 | −4.75763 | ||||||||
\(293\) | 4715.83 | 0.940279 | 0.470140 | − | 0.882592i | \(-0.344204\pi\) | ||||
0.470140 | + | 0.882592i | \(0.344204\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 30.1381 | 0.00594817 | ||||||||
\(296\) | −12144.1 | −2.38467 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −3841.41 | −0.746734 | ||||||||
\(299\) | −4200.93 | −0.812529 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −3236.70 | −0.619802 | ||||||||
\(302\) | −14862.3 | −2.83188 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −335.749 | −0.0633438 | ||||||||
\(305\) | 2173.94 | 0.408130 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −3963.76 | −0.736885 | −0.368442 | − | 0.929651i | \(-0.620109\pi\) | ||||
−0.368442 | + | 0.929651i | \(0.620109\pi\) | |||||||
\(308\) | 4427.97 | 0.819179 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 2286.29 | 0.418878 | ||||||||
\(311\) | 6788.34 | 1.23772 | 0.618861 | − | 0.785501i | \(-0.287595\pi\) | ||||
0.618861 | + | 0.785501i | \(0.287595\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 3894.31 | 0.703256 | 0.351628 | − | 0.936140i | \(-0.385628\pi\) | ||||
0.351628 | + | 0.936140i | \(0.385628\pi\) | |||||||
\(314\) | −6701.94 | −1.20450 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 5140.52 | 0.915116 | ||||||||
\(317\) | 7108.82 | 1.25953 | 0.629766 | − | 0.776785i | \(-0.283151\pi\) | ||||
0.629766 | + | 0.776785i | \(0.283151\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −1915.39 | −0.336180 | ||||||||
\(320\) | 12564.2 | 2.19487 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 7704.72 | 1.33344 | ||||||||
\(323\) | 139.939 | 0.0241066 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −1339.26 | −0.228581 | ||||||||
\(326\) | −19003.5 | −3.22854 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −33773.5 | −5.68546 | ||||||||
\(329\) | 7779.68 | 1.30367 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −7241.67 | −1.20253 | −0.601266 | − | 0.799049i | \(-0.705337\pi\) | ||||
−0.601266 | + | 0.799049i | \(0.705337\pi\) | |||||||
\(332\) | −26917.8 | −4.44971 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −8442.11 | −1.38303 | ||||||||
\(335\) | 4675.75 | 0.762578 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 7982.45 | 1.29030 | 0.645151 | − | 0.764055i | \(-0.276794\pi\) | ||||
0.645151 | + | 0.764055i | \(0.276794\pi\) | |||||||
\(338\) | 3727.87 | 0.599909 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −12761.8 | −2.03560 | ||||||||
\(341\) | 907.764 | 0.144159 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −6588.81 | −1.03721 | ||||||||
\(344\) | −14869.3 | −2.33052 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −4098.75 | −0.636850 | ||||||||
\(347\) | 3956.38 | 0.612074 | 0.306037 | − | 0.952020i | \(-0.400997\pi\) | ||||
0.306037 | + | 0.952020i | \(0.400997\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −1242.91 | −0.190635 | −0.0953174 | − | 0.995447i | \(-0.530387\pi\) | ||||
−0.0953174 | + | 0.995447i | \(0.530387\pi\) | |||||||
\(350\) | 2456.27 | 0.375123 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 9272.71 | 1.40408 | ||||||||
\(353\) | −9549.18 | −1.43981 | −0.719903 | − | 0.694075i | \(-0.755814\pi\) | ||||
−0.719903 | + | 0.694075i | \(0.755814\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 2550.66 | 0.381338 | ||||||||
\(356\) | −32761.7 | −4.87744 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 11581.6 | 1.70980 | ||||||||
\(359\) | 8171.34 | 1.20130 | 0.600650 | − | 0.799512i | \(-0.294909\pi\) | ||||
0.600650 | + | 0.799512i | \(0.294909\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −6857.45 | −0.999774 | ||||||||
\(362\) | 2890.20 | 0.419629 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −21564.4 | −3.10517 | ||||||||
\(365\) | −5228.52 | −0.749789 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 7101.30 | 1.01004 | 0.505020 | − | 0.863107i | \(-0.331485\pi\) | ||||
0.505020 | + | 0.863107i | \(0.331485\pi\) | |||||||
\(368\) | 21153.4 | 2.99646 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −4130.21 | −0.580322 | ||||||||
\(371\) | 8705.71 | 1.21827 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 12150.0 | 1.68661 | 0.843304 | − | 0.537437i | \(-0.180607\pi\) | ||||
0.843304 | + | 0.537437i | \(0.180607\pi\) | |||||||
\(374\) | −6852.65 | −0.947439 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 35739.6 | 4.90194 | ||||||||
\(377\) | 9328.05 | 1.27432 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 1034.28 | 0.140177 | 0.0700887 | − | 0.997541i | \(-0.477672\pi\) | ||||
0.0700887 | + | 0.997541i | \(0.477672\pi\) | |||||||
\(380\) | −141.280 | −0.0190724 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −7408.07 | −0.992224 | ||||||||
\(383\) | −5508.99 | −0.734977 | −0.367489 | − | 0.930028i | \(-0.619782\pi\) | ||||
−0.367489 | + | 0.930028i | \(0.619782\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 975.256 | 0.129100 | ||||||||
\(386\) | 25769.4 | 3.39800 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 18744.8 | 2.45263 | ||||||||
\(389\) | 8347.36 | 1.08799 | 0.543995 | − | 0.839089i | \(-0.316911\pi\) | ||||
0.543995 | + | 0.839089i | \(0.316911\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −8816.70 | −1.14036 | ||||||||
\(392\) | −2328.03 | −0.299957 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −18249.8 | −2.33354 | ||||||||
\(395\) | 1132.19 | 0.144220 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −1233.32 | −0.155916 | −0.0779581 | − | 0.996957i | \(-0.524840\pi\) | ||||
−0.0779581 | + | 0.996957i | \(0.524840\pi\) | |||||||
\(398\) | 20023.5 | 2.52182 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 6743.73 | 0.842966 | ||||||||
\(401\) | −3405.69 | −0.424120 | −0.212060 | − | 0.977257i | \(-0.568017\pi\) | ||||
−0.212060 | + | 0.977257i | \(0.568017\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −4420.84 | −0.546446 | ||||||||
\(404\) | 417.699 | 0.0514389 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −17108.1 | −2.09128 | ||||||||
\(407\) | −1639.89 | −0.199720 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −2468.78 | −0.298468 | −0.149234 | − | 0.988802i | \(-0.547681\pi\) | ||||
−0.149234 | + | 0.988802i | \(0.547681\pi\) | |||||||
\(410\) | −11486.4 | −1.38359 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 21699.5 | 2.59480 | ||||||||
\(413\) | 106.881 | 0.0127344 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −5928.61 | −0.701262 | ||||||||
\(416\) | −45158.4 | −5.32230 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −75.8625 | −0.00887693 | ||||||||
\(419\) | 1712.51 | 0.199670 | 0.0998349 | − | 0.995004i | \(-0.468169\pi\) | ||||
0.0998349 | + | 0.995004i | \(0.468169\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −6612.82 | −0.765533 | −0.382766 | − | 0.923845i | \(-0.625029\pi\) | ||||
−0.382766 | + | 0.923845i | \(0.625029\pi\) | |||||||
\(422\) | 31370.6 | 3.61871 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 39993.8 | 4.58083 | ||||||||
\(425\) | −2810.77 | −0.320806 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 7709.64 | 0.873760 | ||||||||
\(428\) | −34069.7 | −3.84771 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −5057.05 | −0.567145 | ||||||||
\(431\) | 15380.0 | 1.71886 | 0.859432 | − | 0.511250i | \(-0.170817\pi\) | ||||
0.859432 | + | 0.511250i | \(0.170817\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −9228.58 | −1.02424 | −0.512121 | − | 0.858913i | \(-0.671140\pi\) | ||||
−0.512121 | + | 0.858913i | \(0.671140\pi\) | |||||||
\(434\) | 8108.05 | 0.896771 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −16524.8 | −1.81513 | ||||||||
\(437\) | −97.6055 | −0.0106845 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 3483.80 | 0.378753 | 0.189376 | − | 0.981905i | \(-0.439353\pi\) | ||||
0.189376 | + | 0.981905i | \(0.439353\pi\) | |||||||
\(440\) | 4480.30 | 0.485432 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 33372.7 | 3.59135 | ||||||||
\(443\) | −4979.97 | −0.534099 | −0.267049 | − | 0.963683i | \(-0.586049\pi\) | ||||
−0.267049 | + | 0.963683i | \(0.586049\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −7215.73 | −0.768671 | ||||||||
\(446\) | 32506.5 | 3.45118 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 44557.5 | 4.69898 | ||||||||
\(449\) | −4167.11 | −0.437991 | −0.218996 | − | 0.975726i | \(-0.570278\pi\) | ||||
−0.218996 | + | 0.975726i | \(0.570278\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −4560.63 | −0.476168 | ||||||||
\(452\) | −30455.4 | −3.16925 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 3723.02 | 0.384868 | ||||||||
\(455\) | −4749.53 | −0.489366 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 865.844 | 0.0886269 | 0.0443134 | − | 0.999018i | \(-0.485890\pi\) | ||||
0.0443134 | + | 0.999018i | \(0.485890\pi\) | |||||||
\(458\) | −7013.91 | −0.715587 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 8901.16 | 0.902214 | ||||||||
\(461\) | 5354.67 | 0.540980 | 0.270490 | − | 0.962723i | \(-0.412814\pi\) | ||||
0.270490 | + | 0.962723i | \(0.412814\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 2232.71 | 0.224110 | 0.112055 | − | 0.993702i | \(-0.464257\pi\) | ||||
0.112055 | + | 0.993702i | \(0.464257\pi\) | |||||||
\(464\) | −46970.6 | −4.69947 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −961.437 | −0.0955744 | ||||||||
\(467\) | 18874.0 | 1.87020 | 0.935102 | − | 0.354377i | \(-0.115307\pi\) | ||||
0.935102 | + | 0.354377i | \(0.115307\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 16582.0 | 1.63259 | ||||||||
\(470\) | 12155.0 | 1.19291 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 491.010 | 0.0478826 | ||||||||
\(473\) | −2007.89 | −0.195186 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −31.1167 | −0.00300576 | ||||||||
\(476\) | −45258.2 | −4.35800 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −12528.4 | −1.19882 | ||||||||
\(479\) | 4981.32 | 0.475161 | 0.237580 | − | 0.971368i | \(-0.423646\pi\) | ||||
0.237580 | + | 0.971368i | \(0.423646\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 7986.32 | 0.757058 | ||||||||
\(482\) | 11468.7 | 1.08379 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 2746.89 | 0.257973 | ||||||||
\(485\) | 4128.51 | 0.386528 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 3704.78 | 0.344722 | 0.172361 | − | 0.985034i | \(-0.444860\pi\) | ||||
0.172361 | + | 0.985034i | \(0.444860\pi\) | |||||||
\(488\) | 35417.9 | 3.28543 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −791.761 | −0.0729962 | ||||||||
\(491\) | 1746.76 | 0.160550 | 0.0802751 | − | 0.996773i | \(-0.474420\pi\) | ||||
0.0802751 | + | 0.996773i | \(0.474420\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 19577.2 | 1.78847 | ||||||||
\(494\) | 369.453 | 0.0336488 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 22260.8 | 2.01520 | ||||||||
\(497\) | 9045.63 | 0.816402 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 8368.30 | 0.750735 | 0.375367 | − | 0.926876i | \(-0.377517\pi\) | ||||
0.375367 | + | 0.926876i | \(0.377517\pi\) | |||||||
\(500\) | 2837.70 | 0.253811 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −13916.5 | −1.23730 | ||||||||
\(503\) | −2647.07 | −0.234646 | −0.117323 | − | 0.993094i | \(-0.537431\pi\) | ||||
−0.117323 | + | 0.993094i | \(0.537431\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 91.9978 | 0.00810663 | ||||||||
\(506\) | 4779.62 | 0.419921 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 38268.7 | 3.34232 | ||||||||
\(509\) | −9531.20 | −0.829987 | −0.414993 | − | 0.909824i | \(-0.636216\pi\) | ||||
−0.414993 | + | 0.909824i | \(0.636216\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −18542.3 | −1.60521 | ||||||||
\(512\) | 51601.2 | 4.45405 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 1448.49 | 0.124300 | ||||||||
\(515\) | 4779.29 | 0.408933 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 4826.12 | 0.410547 | ||||||||
\(518\) | −14647.3 | −1.24241 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −21819.2 | −1.84007 | ||||||||
\(521\) | −3791.36 | −0.318815 | −0.159407 | − | 0.987213i | \(-0.550958\pi\) | ||||
−0.159407 | + | 0.987213i | \(0.550958\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 5578.17 | 0.466379 | 0.233190 | − | 0.972431i | \(-0.425084\pi\) | ||||
0.233190 | + | 0.972431i | \(0.425084\pi\) | |||||||
\(524\) | −10757.2 | −0.896812 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 11169.0 | 0.925836 | ||||||||
\(527\) | −9278.24 | −0.766919 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −6017.49 | −0.494574 | ||||||||
\(530\) | 13601.9 | 1.11477 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −501.033 | −0.0408318 | ||||||||
\(533\) | 22210.4 | 1.80495 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −7503.81 | −0.606389 | ||||||||
\(536\) | 76177.3 | 6.13873 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −9077.40 | −0.727425 | ||||||||
\(539\) | −314.367 | −0.0251220 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −11942.4 | −0.949061 | −0.474531 | − | 0.880239i | \(-0.657382\pi\) | ||||
−0.474531 | + | 0.880239i | \(0.657382\pi\) | |||||||
\(542\) | 12191.7 | 0.966200 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −94776.2 | −7.46966 | ||||||||
\(545\) | −3639.58 | −0.286059 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −6873.38 | −0.537266 | −0.268633 | − | 0.963243i | \(-0.586572\pi\) | ||||
−0.268633 | + | 0.963243i | \(0.586572\pi\) | |||||||
\(548\) | 16453.4 | 1.28258 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 1523.75 | 0.118132 | ||||||||
\(551\) | 216.730 | 0.0167568 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 4015.19 | 0.308758 | ||||||||
\(554\) | 38528.1 | 2.95470 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 54409.5 | 4.15014 | ||||||||
\(557\) | 26189.4 | 1.99225 | 0.996123 | − | 0.0879714i | \(-0.0280384\pi\) | ||||
0.996123 | + | 0.0879714i | \(0.0280384\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 9778.49 | 0.739868 | ||||||||
\(560\) | 23915.9 | 1.80470 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −35603.7 | −2.67233 | ||||||||
\(563\) | −2732.90 | −0.204579 | −0.102289 | − | 0.994755i | \(-0.532617\pi\) | ||||
−0.102289 | + | 0.994755i | \(0.532617\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −6707.76 | −0.499465 | ||||||||
\(566\) | −9971.64 | −0.740529 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 41555.4 | 3.06976 | ||||||||
\(569\) | −23590.4 | −1.73807 | −0.869034 | − | 0.494753i | \(-0.835259\pi\) | ||||
−0.869034 | + | 0.494753i | \(0.835259\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −24477.2 | −1.79394 | −0.896969 | − | 0.442093i | \(-0.854236\pi\) | ||||
−0.896969 | + | 0.442093i | \(0.854236\pi\) | |||||||
\(572\) | −13377.5 | −0.977867 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −40735.1 | −2.96211 | ||||||||
\(575\) | 1960.47 | 0.142187 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 23152.4 | 1.67044 | 0.835221 | − | 0.549914i | \(-0.185340\pi\) | ||||
0.835221 | + | 0.549914i | \(0.185340\pi\) | |||||||
\(578\) | 42818.4 | 3.08133 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −19764.8 | −1.41498 | ||||||||
\(581\) | −21025.1 | −1.50132 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 5400.59 | 0.383653 | ||||||||
\(584\) | −85183.0 | −6.03578 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 26130.0 | 1.84201 | ||||||||
\(587\) | −4917.15 | −0.345746 | −0.172873 | − | 0.984944i | \(-0.555305\pi\) | ||||
−0.172873 | + | 0.984944i | \(0.555305\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −102.715 | −0.00718557 | ||||||||
\(590\) | 166.992 | 0.0116525 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −40214.4 | −2.79190 | ||||||||
\(593\) | 24489.7 | 1.69591 | 0.847953 | − | 0.530071i | \(-0.177835\pi\) | ||||
0.847953 | + | 0.530071i | \(0.177835\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −9968.08 | −0.686809 | ||||||||
\(596\) | −15738.6 | −1.08167 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −23276.9 | −1.59175 | ||||||||
\(599\) | −5515.59 | −0.376229 | −0.188114 | − | 0.982147i | \(-0.560238\pi\) | ||||
−0.188114 | + | 0.982147i | \(0.560238\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 17496.2 | 1.18750 | 0.593749 | − | 0.804651i | \(-0.297647\pi\) | ||||
0.593749 | + | 0.804651i | \(0.297647\pi\) | |||||||
\(602\) | −17934.2 | −1.21419 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −60892.0 | −4.10209 | ||||||||
\(605\) | 605.000 | 0.0406558 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 5146.06 | 0.344106 | 0.172053 | − | 0.985088i | \(-0.444960\pi\) | ||||
0.172053 | + | 0.985088i | \(0.444960\pi\) | |||||||
\(608\) | −1049.22 | −0.0699862 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 12045.6 | 0.799528 | ||||||||
\(611\) | −23503.4 | −1.55621 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −16329.5 | −1.07593 | −0.537963 | − | 0.842969i | \(-0.680806\pi\) | ||||
−0.537963 | + | 0.842969i | \(0.680806\pi\) | |||||||
\(614\) | −21962.8 | −1.44356 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 15888.9 | 1.03925 | ||||||||
\(617\) | −7734.93 | −0.504695 | −0.252347 | − | 0.967637i | \(-0.581203\pi\) | ||||
−0.252347 | + | 0.967637i | \(0.581203\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −966.773 | −0.0627753 | −0.0313876 | − | 0.999507i | \(-0.509993\pi\) | ||||
−0.0313876 | + | 0.999507i | \(0.509993\pi\) | |||||||
\(620\) | 9367.12 | 0.606762 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 37613.5 | 2.42470 | ||||||||
\(623\) | −25589.8 | −1.64564 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 625.000 | 0.0400000 | ||||||||
\(626\) | 21578.0 | 1.37768 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −27458.5 | −1.74477 | ||||||||
\(629\) | 16761.3 | 1.06251 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 22262.9 | 1.40455 | 0.702275 | − | 0.711906i | \(-0.252168\pi\) | ||||
0.702275 | + | 0.711906i | \(0.252168\pi\) | |||||||
\(632\) | 18445.7 | 1.16097 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 39389.3 | 2.46743 | ||||||||
\(635\) | 8428.64 | 0.526741 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1530.98 | 0.0952270 | ||||||||
\(638\) | −10613.0 | −0.658579 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 35898.0 | 2.21718 | ||||||||
\(641\) | −9081.43 | −0.559587 | −0.279793 | − | 0.960060i | \(-0.590266\pi\) | ||||
−0.279793 | + | 0.960060i | \(0.590266\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −26891.9 | −1.64932 | −0.824661 | − | 0.565628i | \(-0.808634\pi\) | ||||
−0.824661 | + | 0.565628i | \(0.808634\pi\) | |||||||
\(644\) | 31566.9 | 1.93154 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 775.390 | 0.0472249 | ||||||||
\(647\) | 30371.4 | 1.84548 | 0.922738 | − | 0.385429i | \(-0.125947\pi\) | ||||
0.922738 | + | 0.385429i | \(0.125947\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 66.3039 | 0.00401025 | ||||||||
\(650\) | −7420.71 | −0.447791 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −77858.9 | −4.67667 | ||||||||
\(653\) | −16502.1 | −0.988941 | −0.494471 | − | 0.869194i | \(-0.664638\pi\) | ||||
−0.494471 | + | 0.869194i | \(0.664638\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −2369.26 | −0.141335 | ||||||||
\(656\) | −111839. | −6.65635 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 43106.4 | 2.55390 | ||||||||
\(659\) | 18549.5 | 1.09649 | 0.548244 | − | 0.836319i | \(-0.315297\pi\) | ||||
0.548244 | + | 0.836319i | \(0.315297\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −13963.5 | −0.821662 | −0.410831 | − | 0.911711i | \(-0.634761\pi\) | ||||
−0.410831 | + | 0.911711i | \(0.634761\pi\) | |||||||
\(662\) | −40125.4 | −2.35577 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −96588.9 | −5.64514 | ||||||||
\(665\) | −110.352 | −0.00643498 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −13654.8 | −0.792679 | ||||||||
\(668\) | −34588.1 | −2.00337 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 25907.9 | 1.49389 | ||||||||
\(671\) | 4782.67 | 0.275161 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −10248.0 | −0.586972 | −0.293486 | − | 0.955963i | \(-0.594815\pi\) | ||||
−0.293486 | + | 0.955963i | \(0.594815\pi\) | |||||||
\(674\) | 44230.0 | 2.52771 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 15273.4 | 0.868993 | ||||||||
\(677\) | −1595.91 | −0.0905994 | −0.0452997 | − | 0.998973i | \(-0.514424\pi\) | ||||
−0.0452997 | + | 0.998973i | \(0.514424\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 14641.3 | 0.827513 | ||||||||
\(680\) | −45793.1 | −2.58248 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 5029.83 | 0.282408 | ||||||||
\(683\) | 6165.40 | 0.345406 | 0.172703 | − | 0.984974i | \(-0.444750\pi\) | ||||
0.172703 | + | 0.984974i | \(0.444750\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 3623.84 | 0.202131 | ||||||||
\(686\) | −36507.9 | −2.03189 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −49238.7 | −2.72850 | ||||||||
\(689\) | −26301.1 | −1.45427 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −13398.1 | −0.737609 | −0.368804 | − | 0.929507i | \(-0.620233\pi\) | ||||
−0.368804 | + | 0.929507i | \(0.620233\pi\) | |||||||
\(692\) | −16792.9 | −0.922503 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 21921.9 | 1.19906 | ||||||||
\(695\) | 11983.6 | 0.654051 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 46614.1 | 2.53319 | ||||||||
\(698\) | −6886.85 | −0.373455 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 10063.6 | 0.543382 | ||||||||
\(701\) | 19182.6 | 1.03354 | 0.516772 | − | 0.856123i | \(-0.327133\pi\) | ||||
0.516772 | + | 0.856123i | \(0.327133\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 185.556 | 0.00995503 | ||||||||
\(704\) | 27641.2 | 1.47978 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −52911.0 | −2.82059 | ||||||||
\(707\) | 326.260 | 0.0173554 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −14076.7 | −0.745641 | −0.372821 | − | 0.927903i | \(-0.621609\pi\) | ||||
−0.372821 | + | 0.927903i | \(0.621609\pi\) | |||||||
\(710\) | 14133.0 | 0.747043 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −117559. | −6.18778 | ||||||||
\(713\) | 6471.43 | 0.339912 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −2946.37 | −0.154109 | ||||||||
\(716\) | 47451.0 | 2.47672 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 45276.6 | 2.35335 | ||||||||
\(719\) | −30477.5 | −1.58083 | −0.790417 | − | 0.612569i | \(-0.790136\pi\) | ||||
−0.790417 | + | 0.612569i | \(0.790136\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 16949.2 | 0.875480 | ||||||||
\(722\) | −37996.5 | −1.95856 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 11841.4 | 0.607849 | ||||||||
\(725\) | −4353.17 | −0.222997 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 16141.1 | 0.823440 | 0.411720 | − | 0.911310i | \(-0.364928\pi\) | ||||
0.411720 | + | 0.911310i | \(0.364928\pi\) | |||||||
\(728\) | −77379.4 | −3.93939 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −28970.7 | −1.46884 | ||||||||
\(731\) | 20522.6 | 1.03838 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 32962.3 | 1.66097 | 0.830484 | − | 0.557043i | \(-0.188064\pi\) | ||||
0.830484 | + | 0.557043i | \(0.188064\pi\) | |||||||
\(734\) | 39347.6 | 1.97867 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 66105.0 | 3.31068 | ||||||||
\(737\) | 10286.7 | 0.514130 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 1509.25 | 0.0751267 | 0.0375634 | − | 0.999294i | \(-0.488040\pi\) | ||||
0.0375634 | + | 0.999294i | \(0.488040\pi\) | |||||||
\(740\) | −16921.8 | −0.840621 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 48237.5 | 2.38659 | ||||||||
\(743\) | 14601.9 | 0.720984 | 0.360492 | − | 0.932762i | \(-0.382609\pi\) | ||||
0.360492 | + | 0.932762i | \(0.382609\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −3466.41 | −0.170469 | ||||||||
\(746\) | 67322.1 | 3.30407 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −28075.9 | −1.37240 | ||||||||
\(749\) | −26611.4 | −1.29821 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −17830.7 | −0.866381 | −0.433191 | − | 0.901302i | \(-0.642612\pi\) | ||||
−0.433191 | + | 0.901302i | \(0.642612\pi\) | |||||||
\(752\) | 118349. | 5.73904 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 51685.8 | 2.49640 | ||||||||
\(755\) | −13411.4 | −0.646478 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 15800.6 | 0.758632 | 0.379316 | − | 0.925267i | \(-0.376159\pi\) | ||||
0.379316 | + | 0.925267i | \(0.376159\pi\) | |||||||
\(758\) | 5730.83 | 0.274608 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −506.954 | −0.0241963 | ||||||||
\(761\) | −1707.35 | −0.0813292 | −0.0406646 | − | 0.999173i | \(-0.512948\pi\) | ||||
−0.0406646 | + | 0.999173i | \(0.512948\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −12907.3 | −0.612421 | ||||||||
\(764\) | −30351.5 | −1.43728 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −30524.8 | −1.43982 | ||||||||
\(767\) | −322.902 | −0.0152012 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −13359.8 | −0.626486 | −0.313243 | − | 0.949673i | \(-0.601415\pi\) | ||||
−0.313243 | + | 0.949673i | \(0.601415\pi\) | |||||||
\(770\) | 5403.80 | 0.252908 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 105580. | 4.92214 | ||||||||
\(773\) | −28990.9 | −1.34894 | −0.674469 | − | 0.738303i | \(-0.735628\pi\) | ||||
−0.674469 | + | 0.738303i | \(0.735628\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 2063.10 | 0.0956241 | ||||||||
\(776\) | 67261.8 | 3.11154 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 46251.9 | 2.13138 | ||||||||
\(779\) | 516.043 | 0.0237345 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 5611.45 | 0.257098 | ||||||||
\(782\) | −48852.4 | −2.23396 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −7709.11 | −0.351180 | ||||||||
\(785\) | −6047.70 | −0.274970 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −22010.7 | −0.996947 | −0.498473 | − | 0.866905i | \(-0.666106\pi\) | ||||
−0.498473 | + | 0.866905i | \(0.666106\pi\) | |||||||
\(788\) | −74771.2 | −3.38022 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 6273.37 | 0.282527 | ||||||||
\(791\) | −23788.3 | −1.06930 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −23291.8 | −1.04302 | ||||||||
\(794\) | −6833.73 | −0.305441 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 82038.0 | 3.65297 | ||||||||
\(797\) | −26709.2 | −1.18706 | −0.593531 | − | 0.804811i | \(-0.702267\pi\) | ||||
−0.593531 | + | 0.804811i | \(0.702267\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −49327.7 | −2.18409 | ||||||||
\(800\) | 21074.3 | 0.931363 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −18870.6 | −0.830853 | ||||||||
\(803\) | −11502.7 | −0.505508 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 6952.58 | 0.304405 | ||||||||
\(806\) | −24495.5 | −1.07049 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 1498.83 | 0.0652582 | ||||||||
\(809\) | 11202.0 | 0.486823 | 0.243412 | − | 0.969923i | \(-0.421733\pi\) | ||||
0.243412 | + | 0.969923i | \(0.421733\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −34979.8 | −1.51456 | −0.757280 | − | 0.653091i | \(-0.773472\pi\) | ||||
−0.757280 | + | 0.653091i | \(0.773472\pi\) | |||||||
\(812\) | −70093.5 | −3.02931 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −9086.46 | −0.391253 | ||||||||
\(815\) | −17148.3 | −0.737031 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 227.196 | 0.00972899 | ||||||||
\(818\) | −13679.3 | −0.584700 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −47060.7 | −2.00418 | ||||||||
\(821\) | −3802.17 | −0.161628 | −0.0808140 | − | 0.996729i | \(-0.525752\pi\) | ||||
−0.0808140 | + | 0.996729i | \(0.525752\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 4717.91 | 0.199825 | 0.0999126 | − | 0.994996i | \(-0.468144\pi\) | ||||
0.0999126 | + | 0.994996i | \(0.468144\pi\) | |||||||
\(824\) | 77864.2 | 3.29190 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 592.219 | 0.0249467 | ||||||||
\(827\) | −30244.0 | −1.27169 | −0.635845 | − | 0.771817i | \(-0.719348\pi\) | ||||
−0.635845 | + | 0.771817i | \(0.719348\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 26008.5 | 1.08964 | 0.544821 | − | 0.838552i | \(-0.316597\pi\) | ||||
0.544821 | + | 0.838552i | \(0.316597\pi\) | |||||||
\(830\) | −32849.8 | −1.37378 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −134614. | −5.60925 | ||||||||
\(833\) | 3213.14 | 0.133648 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −7617.99 | −0.315726 | ||||||||
\(836\) | −310.816 | −0.0128586 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 9488.86 | 0.391154 | ||||||||
\(839\) | 5360.85 | 0.220593 | 0.110296 | − | 0.993899i | \(-0.464820\pi\) | ||||
0.110296 | + | 0.993899i | \(0.464820\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 5931.14 | 0.243189 | ||||||||
\(842\) | −36641.0 | −1.49968 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 128528. | 5.24185 | ||||||||
\(845\) | 3363.96 | 0.136951 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 2145.56 | 0.0870395 | ||||||||
\(848\) | 132437. | 5.36308 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −15574.2 | −0.628460 | ||||||||
\(851\) | −11690.7 | −0.470920 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −31301.1 | −1.25642 | −0.628212 | − | 0.778043i | \(-0.716213\pi\) | ||||
−0.628212 | + | 0.778043i | \(0.716213\pi\) | |||||||
\(854\) | 42718.3 | 1.71170 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −122252. | −4.88141 | ||||||||
\(857\) | 1445.51 | 0.0576167 | 0.0288084 | − | 0.999585i | \(-0.490829\pi\) | ||||
0.0288084 | + | 0.999585i | \(0.490829\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −27178.3 | −1.07953 | −0.539763 | − | 0.841817i | \(-0.681486\pi\) | ||||
−0.539763 | + | 0.841817i | \(0.681486\pi\) | |||||||
\(860\) | −20719.2 | −0.821533 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 85219.3 | 3.36726 | ||||||||
\(863\) | 1232.36 | 0.0486097 | 0.0243049 | − | 0.999705i | \(-0.492263\pi\) | ||||
0.0243049 | + | 0.999705i | \(0.492263\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −3698.63 | −0.145384 | ||||||||
\(866\) | −51134.6 | −2.00650 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 33219.4 | 1.29901 | ||||||||
\(869\) | 2490.82 | 0.0972330 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −50096.4 | −1.94885 | ||||||||
\(872\) | −59296.0 | −2.30277 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −540.823 | −0.0209309 | ||||||||
\(875\) | 2216.49 | 0.0856355 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −22320.0 | −0.859399 | −0.429699 | − | 0.902972i | \(-0.641380\pi\) | ||||
−0.429699 | + | 0.902972i | \(0.641380\pi\) | |||||||
\(878\) | 19303.4 | 0.741979 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 14836.2 | 0.568328 | ||||||||
\(881\) | 22244.7 | 0.850674 | 0.425337 | − | 0.905035i | \(-0.360156\pi\) | ||||
0.425337 | + | 0.905035i | \(0.360156\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 35958.1 | 1.37043 | 0.685214 | − | 0.728342i | \(-0.259709\pi\) | ||||
0.685214 | + | 0.728342i | \(0.259709\pi\) | |||||||
\(884\) | 136731. | 5.20222 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −27593.5 | −1.04630 | ||||||||
\(887\) | 26277.0 | 0.994696 | 0.497348 | − | 0.867551i | \(-0.334307\pi\) | ||||
0.497348 | + | 0.867551i | \(0.334307\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 29891.2 | 1.12769 | ||||||||
\(890\) | −39981.7 | −1.50583 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 133182. | 4.99917 | ||||||||
\(893\) | −546.084 | −0.0204636 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 10451.0 | 0.390324 | ||||||||
\(896\) | 127308. | 4.74673 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −23089.5 | −0.858027 | ||||||||
\(899\) | −14369.6 | −0.533097 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −55199.3 | −2.04102 | ||||||||
\(902\) | −25270.0 | −0.932815 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −109283. | −4.02068 | ||||||||
\(905\) | 2608.06 | 0.0957954 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 30458.2 | 1.11505 | 0.557523 | − | 0.830161i | \(-0.311752\pi\) | ||||
0.557523 | + | 0.830161i | \(0.311752\pi\) | |||||||
\(908\) | 15253.5 | 0.557496 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −26316.7 | −0.958670 | ||||||||
\(911\) | −44396.7 | −1.61463 | −0.807315 | − | 0.590120i | \(-0.799080\pi\) | ||||
−0.807315 | + | 0.590120i | \(0.799080\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −13042.9 | −0.472791 | ||||||||
\(914\) | 4797.56 | 0.173620 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −28736.7 | −1.03656 | ||||||||
\(917\) | −8402.30 | −0.302583 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 23498.2 | 0.843454 | 0.421727 | − | 0.906723i | \(-0.361424\pi\) | ||||
0.421727 | + | 0.906723i | \(0.361424\pi\) | |||||||
\(920\) | 31940.0 | 1.14460 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 29669.7 | 1.05978 | ||||||||
\(923\) | −27328.0 | −0.974553 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −3727.02 | −0.132480 | ||||||||
\(926\) | 12371.2 | 0.439032 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −146784. | −5.19227 | ||||||||
\(929\) | −40096.3 | −1.41606 | −0.708029 | − | 0.706184i | \(-0.750415\pi\) | ||||
−0.708029 | + | 0.706184i | \(0.750415\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 35.5712 | 0.00125220 | ||||||||
\(932\) | −3939.09 | −0.138443 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 104579. | 3.66374 | ||||||||
\(935\) | −6183.70 | −0.216287 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −36306.5 | −1.26583 | −0.632914 | − | 0.774222i | \(-0.718141\pi\) | ||||
−0.632914 | + | 0.774222i | \(0.718141\pi\) | |||||||
\(938\) | 91879.3 | 3.19826 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 49800.3 | 1.72799 | ||||||||
\(941\) | −25929.1 | −0.898262 | −0.449131 | − | 0.893466i | \(-0.648266\pi\) | ||||
−0.449131 | + | 0.893466i | \(0.648266\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −32512.7 | −1.12275 | ||||||||
\(944\) | 1625.95 | 0.0560594 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −11125.5 | −0.382369 | ||||||||
\(947\) | 13367.3 | 0.458689 | 0.229345 | − | 0.973345i | \(-0.426342\pi\) | ||||
0.229345 | + | 0.973345i | \(0.426342\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 56018.8 | 1.91617 | ||||||||
\(950\) | −172.415 | −0.00588829 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −162400. | −5.52880 | ||||||||
\(953\) | 35619.6 | 1.21074 | 0.605368 | − | 0.795946i | \(-0.293026\pi\) | ||||
0.605368 | + | 0.795946i | \(0.293026\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −6684.89 | −0.226511 | ||||||||
\(956\) | −51330.1 | −1.73654 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 27601.0 | 0.930842 | ||||||||
\(959\) | 12851.5 | 0.432740 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −22980.8 | −0.771401 | ||||||||
\(962\) | 44251.4 | 1.48308 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 46988.3 | 1.56991 | ||||||||
\(965\) | 23253.8 | 0.775716 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 14921.5 | 0.496217 | 0.248109 | − | 0.968732i | \(-0.420191\pi\) | ||||
0.248109 | + | 0.968732i | \(0.420191\pi\) | |||||||
\(968\) | 9856.66 | 0.327278 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 22875.7 | 0.757210 | ||||||||
\(971\) | 32520.5 | 1.07480 | 0.537401 | − | 0.843327i | \(-0.319406\pi\) | ||||
0.537401 | + | 0.843327i | \(0.319406\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 42498.6 | 1.40025 | ||||||||
\(974\) | 20527.8 | 0.675313 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 117284. | 3.84648 | ||||||||
\(977\) | 28946.6 | 0.947884 | 0.473942 | − | 0.880556i | \(-0.342831\pi\) | ||||
0.473942 | + | 0.880556i | \(0.342831\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −15874.6 | −0.518238 | ||||||||
\(980\) | −3243.92 | −0.105738 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 9678.63 | 0.314519 | ||||||||
\(983\) | −1920.56 | −0.0623158 | −0.0311579 | − | 0.999514i | \(-0.509919\pi\) | ||||
−0.0311579 | + | 0.999514i | \(0.509919\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −16468.3 | −0.532714 | ||||||||
\(986\) | 108475. | 3.50361 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 1513.68 | 0.0487416 | ||||||||
\(989\) | −14314.2 | −0.460228 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −30472.4 | −0.976780 | −0.488390 | − | 0.872625i | \(-0.662416\pi\) | ||||
−0.488390 | + | 0.872625i | \(0.662416\pi\) | |||||||
\(992\) | 69565.5 | 2.22652 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 50120.9 | 1.59934 | ||||||||
\(995\) | 18068.8 | 0.575698 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 52854.5 | 1.67895 | 0.839477 | − | 0.543395i | \(-0.182861\pi\) | ||||
0.839477 | + | 0.543395i | \(0.182861\pi\) | |||||||
\(998\) | 46367.9 | 1.47069 | ||||||||
\(999\) | 0 | 0 |
(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 | 495.4.a.p.1.7 | yes | 7 | |
3.2 | odd | 2 | 495.4.a.o.1.1 | ✓ | 7 | ||
5.4 | even | 2 | 2475.4.a.bp.1.1 | 7 | |||
15.14 | odd | 2 | 2475.4.a.bt.1.7 | 7 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
495.4.a.o.1.1 | ✓ | 7 | 3.2 | odd | 2 | ||
495.4.a.p.1.7 | yes | 7 | 1.1 | even | 1 | trivial | |
2475.4.a.bp.1.1 | 7 | 5.4 | even | 2 | |||
2475.4.a.bt.1.7 | 7 | 15.14 | odd | 2 |