Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [425,4,Mod(1,425)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(425, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("425.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 425 = 5^{2} \cdot 17 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 425.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: | \(25.0758117524\) |
Analytic rank: | \(1\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.2636.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - 14x - 4 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 17) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-0.287410\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 425.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −4.67129 | −1.65155 | −0.825775 | − | 0.564000i | \(-0.809262\pi\) | ||||
−0.825775 | + | 0.564000i | \(0.809262\pi\) | |||||||
\(3\) | 7.62999 | 1.46839 | 0.734196 | − | 0.678938i | \(-0.237559\pi\) | ||||
0.734196 | + | 0.678938i | \(0.237559\pi\) | |||||||
\(4\) | 13.8209 | 1.72762 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −35.6419 | −2.42512 | ||||||||
\(7\) | −26.1222 | −1.41047 | −0.705233 | − | 0.708975i | \(-0.749158\pi\) | ||||
−0.705233 | + | 0.708975i | \(0.749158\pi\) | |||||||
\(8\) | −27.1912 | −1.20169 | ||||||||
\(9\) | 31.2167 | 1.15617 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −3.24412 | −0.0889216 | −0.0444608 | − | 0.999011i | \(-0.514157\pi\) | ||||
−0.0444608 | + | 0.999011i | \(0.514157\pi\) | |||||||
\(12\) | 105.453 | 2.53682 | ||||||||
\(13\) | 20.0515 | 0.427790 | 0.213895 | − | 0.976857i | \(-0.431385\pi\) | ||||
0.213895 | + | 0.976857i | \(0.431385\pi\) | |||||||
\(14\) | 122.024 | 2.32945 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 16.4506 | 0.257041 | ||||||||
\(17\) | 17.0000 | 0.242536 | ||||||||
\(18\) | −145.822 | −1.90948 | ||||||||
\(19\) | 57.3466 | 0.692432 | 0.346216 | − | 0.938155i | \(-0.387466\pi\) | ||||
0.346216 | + | 0.938155i | \(0.387466\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −199.312 | −2.07112 | ||||||||
\(22\) | 15.1542 | 0.146858 | ||||||||
\(23\) | −77.0438 | −0.698467 | −0.349233 | − | 0.937036i | \(-0.613558\pi\) | ||||
−0.349233 | + | 0.937036i | \(0.613558\pi\) | |||||||
\(24\) | −207.469 | −1.76456 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −93.6662 | −0.706517 | ||||||||
\(27\) | 32.1732 | 0.229323 | ||||||||
\(28\) | −361.033 | −2.43674 | ||||||||
\(29\) | −286.162 | −1.83238 | −0.916190 | − | 0.400744i | \(-0.868752\pi\) | ||||
−0.916190 | + | 0.400744i | \(0.868752\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −8.54816 | −0.0495256 | −0.0247628 | − | 0.999693i | \(-0.507883\pi\) | ||||
−0.0247628 | + | 0.999693i | \(0.507883\pi\) | |||||||
\(32\) | 140.684 | 0.777178 | ||||||||
\(33\) | −24.7526 | −0.130572 | ||||||||
\(34\) | −79.4119 | −0.400560 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 431.443 | 1.99742 | ||||||||
\(37\) | −357.982 | −1.59059 | −0.795296 | − | 0.606221i | \(-0.792685\pi\) | ||||
−0.795296 | + | 0.606221i | \(0.792685\pi\) | |||||||
\(38\) | −267.882 | −1.14359 | ||||||||
\(39\) | 152.992 | 0.628164 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 194.467 | 0.740748 | 0.370374 | − | 0.928883i | \(-0.379230\pi\) | ||||
0.370374 | + | 0.928883i | \(0.379230\pi\) | |||||||
\(42\) | 931.044 | 3.42055 | ||||||||
\(43\) | 74.2619 | 0.263368 | 0.131684 | − | 0.991292i | \(-0.457962\pi\) | ||||
0.131684 | + | 0.991292i | \(0.457962\pi\) | |||||||
\(44\) | −44.8367 | −0.153622 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 359.894 | 1.15355 | ||||||||
\(47\) | −23.6130 | −0.0732831 | −0.0366416 | − | 0.999328i | \(-0.511666\pi\) | ||||
−0.0366416 | + | 0.999328i | \(0.511666\pi\) | |||||||
\(48\) | 125.518 | 0.377437 | ||||||||
\(49\) | 339.369 | 0.989415 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 129.710 | 0.356137 | ||||||||
\(52\) | 277.130 | 0.739058 | ||||||||
\(53\) | −104.330 | −0.270393 | −0.135197 | − | 0.990819i | \(-0.543167\pi\) | ||||
−0.135197 | + | 0.990819i | \(0.543167\pi\) | |||||||
\(54\) | −150.290 | −0.378739 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 710.295 | 1.69495 | ||||||||
\(57\) | 437.553 | 1.01676 | ||||||||
\(58\) | 1336.75 | 3.02627 | ||||||||
\(59\) | 249.363 | 0.550243 | 0.275122 | − | 0.961409i | \(-0.411282\pi\) | ||||
0.275122 | + | 0.961409i | \(0.411282\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −370.384 | −0.777424 | −0.388712 | − | 0.921359i | \(-0.627080\pi\) | ||||
−0.388712 | + | 0.921359i | \(0.627080\pi\) | |||||||
\(62\) | 39.9309 | 0.0817940 | ||||||||
\(63\) | −815.448 | −1.63074 | ||||||||
\(64\) | −788.781 | −1.54059 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 115.626 | 0.215646 | ||||||||
\(67\) | −939.650 | −1.71338 | −0.856691 | − | 0.515830i | \(-0.827483\pi\) | ||||
−0.856691 | + | 0.515830i | \(0.827483\pi\) | |||||||
\(68\) | 234.956 | 0.419008 | ||||||||
\(69\) | −587.843 | −1.02562 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −520.197 | −0.869522 | −0.434761 | − | 0.900546i | \(-0.643167\pi\) | ||||
−0.434761 | + | 0.900546i | \(0.643167\pi\) | |||||||
\(72\) | −848.820 | −1.38937 | ||||||||
\(73\) | −348.741 | −0.559137 | −0.279568 | − | 0.960126i | \(-0.590191\pi\) | ||||
−0.279568 | + | 0.960126i | \(0.590191\pi\) | |||||||
\(74\) | 1672.24 | 2.62694 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 792.583 | 1.19626 | ||||||||
\(77\) | 84.7434 | 0.125421 | ||||||||
\(78\) | −714.672 | −1.03744 | ||||||||
\(79\) | −953.827 | −1.35840 | −0.679202 | − | 0.733951i | \(-0.737674\pi\) | ||||
−0.679202 | + | 0.733951i | \(0.737674\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −597.369 | −0.819437 | ||||||||
\(82\) | −908.412 | −1.22338 | ||||||||
\(83\) | 1414.28 | 1.87033 | 0.935166 | − | 0.354211i | \(-0.115250\pi\) | ||||
0.935166 | + | 0.354211i | \(0.115250\pi\) | |||||||
\(84\) | −2754.68 | −3.57809 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −346.899 | −0.434966 | ||||||||
\(87\) | −2183.41 | −2.69065 | ||||||||
\(88\) | 88.2115 | 0.106857 | ||||||||
\(89\) | −486.132 | −0.578987 | −0.289493 | − | 0.957180i | \(-0.593487\pi\) | ||||
−0.289493 | + | 0.957180i | \(0.593487\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −523.788 | −0.603384 | ||||||||
\(92\) | −1064.82 | −1.20668 | ||||||||
\(93\) | −65.2223 | −0.0727230 | ||||||||
\(94\) | 110.303 | 0.121031 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 1073.42 | 1.14120 | ||||||||
\(97\) | 685.281 | 0.717317 | 0.358659 | − | 0.933469i | \(-0.383234\pi\) | ||||
0.358659 | + | 0.933469i | \(0.383234\pi\) | |||||||
\(98\) | −1585.29 | −1.63407 | ||||||||
\(99\) | −101.271 | −0.102809 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 864.755 | 0.851944 | 0.425972 | − | 0.904736i | \(-0.359932\pi\) | ||||
0.425972 | + | 0.904736i | \(0.359932\pi\) | |||||||
\(102\) | −605.912 | −0.588178 | ||||||||
\(103\) | −1880.91 | −1.79933 | −0.899665 | − | 0.436580i | \(-0.856190\pi\) | ||||
−0.899665 | + | 0.436580i | \(0.856190\pi\) | |||||||
\(104\) | −545.224 | −0.514073 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 487.355 | 0.446567 | ||||||||
\(107\) | 32.8149 | 0.0296480 | 0.0148240 | − | 0.999890i | \(-0.495281\pi\) | ||||
0.0148240 | + | 0.999890i | \(0.495281\pi\) | |||||||
\(108\) | 444.663 | 0.396183 | ||||||||
\(109\) | 528.727 | 0.464613 | 0.232307 | − | 0.972643i | \(-0.425373\pi\) | ||||
0.232307 | + | 0.972643i | \(0.425373\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −2731.40 | −2.33561 | ||||||||
\(112\) | −429.727 | −0.362548 | ||||||||
\(113\) | −414.691 | −0.345229 | −0.172614 | − | 0.984989i | \(-0.555221\pi\) | ||||
−0.172614 | + | 0.984989i | \(0.555221\pi\) | |||||||
\(114\) | −2043.94 | −1.67923 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −3955.03 | −3.16565 | ||||||||
\(117\) | 625.940 | 0.494600 | ||||||||
\(118\) | −1164.85 | −0.908754 | ||||||||
\(119\) | −444.077 | −0.342088 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1320.48 | −0.992093 | ||||||||
\(122\) | 1730.17 | 1.28395 | ||||||||
\(123\) | 1483.78 | 1.08771 | ||||||||
\(124\) | −118.143 | −0.0855613 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 3809.19 | 2.69325 | ||||||||
\(127\) | −596.093 | −0.416494 | −0.208247 | − | 0.978076i | \(-0.566776\pi\) | ||||
−0.208247 | + | 0.978076i | \(0.566776\pi\) | |||||||
\(128\) | 2559.15 | 1.76718 | ||||||||
\(129\) | 566.617 | 0.386728 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 121.819 | 0.0812472 | 0.0406236 | − | 0.999175i | \(-0.487066\pi\) | ||||
0.0406236 | + | 0.999175i | \(0.487066\pi\) | |||||||
\(132\) | −342.103 | −0.225578 | ||||||||
\(133\) | −1498.02 | −0.976652 | ||||||||
\(134\) | 4389.38 | 2.82973 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −462.251 | −0.291454 | ||||||||
\(137\) | 897.365 | 0.559614 | 0.279807 | − | 0.960056i | \(-0.409730\pi\) | ||||
0.279807 | + | 0.960056i | \(0.409730\pi\) | |||||||
\(138\) | 2745.98 | 1.69387 | ||||||||
\(139\) | −2113.61 | −1.28974 | −0.644871 | − | 0.764292i | \(-0.723089\pi\) | ||||
−0.644871 | + | 0.764292i | \(0.723089\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −180.167 | −0.107608 | ||||||||
\(142\) | 2429.99 | 1.43606 | ||||||||
\(143\) | −65.0493 | −0.0380398 | ||||||||
\(144\) | 513.534 | 0.297184 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 1629.07 | 0.923442 | ||||||||
\(147\) | 2589.38 | 1.45285 | ||||||||
\(148\) | −4947.65 | −2.74793 | ||||||||
\(149\) | 2580.76 | 1.41895 | 0.709476 | − | 0.704729i | \(-0.248932\pi\) | ||||
0.709476 | + | 0.704729i | \(0.248932\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1342.77 | 0.723662 | 0.361831 | − | 0.932244i | \(-0.382152\pi\) | ||||
0.361831 | + | 0.932244i | \(0.382152\pi\) | |||||||
\(152\) | −1559.32 | −0.832091 | ||||||||
\(153\) | 530.683 | 0.280413 | ||||||||
\(154\) | −395.861 | −0.207139 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 2114.50 | 1.08523 | ||||||||
\(157\) | 2495.82 | 1.26871 | 0.634357 | − | 0.773041i | \(-0.281265\pi\) | ||||
0.634357 | + | 0.773041i | \(0.281265\pi\) | |||||||
\(158\) | 4455.60 | 2.24347 | ||||||||
\(159\) | −796.036 | −0.397043 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 2012.55 | 0.985164 | ||||||||
\(162\) | 2790.48 | 1.35334 | ||||||||
\(163\) | −1961.58 | −0.942595 | −0.471297 | − | 0.881974i | \(-0.656214\pi\) | ||||
−0.471297 | + | 0.881974i | \(0.656214\pi\) | |||||||
\(164\) | 2687.72 | 1.27973 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −6606.51 | −3.08894 | ||||||||
\(167\) | −2179.24 | −1.00979 | −0.504894 | − | 0.863182i | \(-0.668468\pi\) | ||||
−0.504894 | + | 0.863182i | \(0.668468\pi\) | |||||||
\(168\) | 5419.54 | 2.48885 | ||||||||
\(169\) | −1794.94 | −0.816995 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1790.17 | 0.800571 | ||||||||
\(172\) | 1026.37 | 0.454999 | ||||||||
\(173\) | −3111.45 | −1.36739 | −0.683697 | − | 0.729766i | \(-0.739629\pi\) | ||||
−0.683697 | + | 0.729766i | \(0.739629\pi\) | |||||||
\(174\) | 10199.4 | 4.44374 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −53.3677 | −0.0228565 | ||||||||
\(177\) | 1902.64 | 0.807972 | ||||||||
\(178\) | 2270.86 | 0.956226 | ||||||||
\(179\) | 810.106 | 0.338269 | 0.169135 | − | 0.985593i | \(-0.445903\pi\) | ||||
0.169135 | + | 0.985593i | \(0.445903\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −3356.23 | −1.37827 | −0.689134 | − | 0.724634i | \(-0.742009\pi\) | ||||
−0.689134 | + | 0.724634i | \(0.742009\pi\) | |||||||
\(182\) | 2446.77 | 0.996519 | ||||||||
\(183\) | −2826.03 | −1.14156 | ||||||||
\(184\) | 2094.92 | 0.839343 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 304.672 | 0.120106 | ||||||||
\(187\) | −55.1500 | −0.0215667 | ||||||||
\(188\) | −326.353 | −0.126605 | ||||||||
\(189\) | −840.434 | −0.323453 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 1338.41 | 0.507038 | 0.253519 | − | 0.967330i | \(-0.418412\pi\) | ||||
0.253519 | + | 0.967330i | \(0.418412\pi\) | |||||||
\(192\) | −6018.39 | −2.26219 | ||||||||
\(193\) | 227.465 | 0.0848358 | 0.0424179 | − | 0.999100i | \(-0.486494\pi\) | ||||
0.0424179 | + | 0.999100i | \(0.486494\pi\) | |||||||
\(194\) | −3201.15 | −1.18468 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 4690.40 | 1.70933 | ||||||||
\(197\) | −815.549 | −0.294952 | −0.147476 | − | 0.989066i | \(-0.547115\pi\) | ||||
−0.147476 | + | 0.989066i | \(0.547115\pi\) | |||||||
\(198\) | 473.064 | 0.169794 | ||||||||
\(199\) | 1866.90 | 0.665030 | 0.332515 | − | 0.943098i | \(-0.392103\pi\) | ||||
0.332515 | + | 0.943098i | \(0.392103\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −7169.52 | −2.51591 | ||||||||
\(202\) | −4039.52 | −1.40703 | ||||||||
\(203\) | 7475.19 | 2.58451 | ||||||||
\(204\) | 1792.71 | 0.615268 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 8786.25 | 2.97168 | ||||||||
\(207\) | −2405.05 | −0.807549 | ||||||||
\(208\) | 329.859 | 0.109960 | ||||||||
\(209\) | −186.039 | −0.0615721 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1102.88 | −0.359836 | −0.179918 | − | 0.983682i | \(-0.557583\pi\) | ||||
−0.179918 | + | 0.983682i | \(0.557583\pi\) | |||||||
\(212\) | −1441.94 | −0.467135 | ||||||||
\(213\) | −3969.10 | −1.27680 | ||||||||
\(214\) | −153.288 | −0.0489651 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −874.828 | −0.275576 | ||||||||
\(217\) | 223.297 | 0.0698542 | ||||||||
\(218\) | −2469.84 | −0.767332 | ||||||||
\(219\) | −2660.89 | −0.821032 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 340.875 | 0.103754 | ||||||||
\(222\) | 12759.2 | 3.85738 | ||||||||
\(223\) | 568.848 | 0.170820 | 0.0854100 | − | 0.996346i | \(-0.472780\pi\) | ||||
0.0854100 | + | 0.996346i | \(0.472780\pi\) | |||||||
\(224\) | −3674.98 | −1.09618 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 1937.14 | 0.570163 | ||||||||
\(227\) | −2106.99 | −0.616061 | −0.308030 | − | 0.951377i | \(-0.599670\pi\) | ||||
−0.308030 | + | 0.951377i | \(0.599670\pi\) | |||||||
\(228\) | 6047.39 | 1.75657 | ||||||||
\(229\) | 4336.30 | 1.25131 | 0.625656 | − | 0.780099i | \(-0.284831\pi\) | ||||
0.625656 | + | 0.780099i | \(0.284831\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 646.591 | 0.184167 | ||||||||
\(232\) | 7781.11 | 2.20196 | ||||||||
\(233\) | 4517.39 | 1.27014 | 0.635072 | − | 0.772453i | \(-0.280970\pi\) | ||||
0.635072 | + | 0.772453i | \(0.280970\pi\) | |||||||
\(234\) | −2923.95 | −0.816856 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 3446.43 | 0.950609 | ||||||||
\(237\) | −7277.69 | −1.99467 | ||||||||
\(238\) | 2074.41 | 0.564976 | ||||||||
\(239\) | 5300.88 | 1.43467 | 0.717333 | − | 0.696731i | \(-0.245363\pi\) | ||||
0.717333 | + | 0.696731i | \(0.245363\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1368.82 | −0.365864 | −0.182932 | − | 0.983126i | \(-0.558559\pi\) | ||||
−0.182932 | + | 0.983126i | \(0.558559\pi\) | |||||||
\(242\) | 6168.32 | 1.63849 | ||||||||
\(243\) | −5426.60 | −1.43258 | ||||||||
\(244\) | −5119.05 | −1.34309 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −6931.17 | −1.79640 | ||||||||
\(247\) | 1149.88 | 0.296216 | ||||||||
\(248\) | 232.435 | 0.0595146 | ||||||||
\(249\) | 10790.9 | 2.74638 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −5547.63 | −1.39507 | −0.697536 | − | 0.716549i | \(-0.745720\pi\) | ||||
−0.697536 | + | 0.716549i | \(0.745720\pi\) | |||||||
\(252\) | −11270.3 | −2.81730 | ||||||||
\(253\) | 249.939 | 0.0621088 | ||||||||
\(254\) | 2784.52 | 0.687860 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −5644.28 | −1.37800 | ||||||||
\(257\) | 193.949 | 0.0470748 | 0.0235374 | − | 0.999723i | \(-0.492507\pi\) | ||||
0.0235374 | + | 0.999723i | \(0.492507\pi\) | |||||||
\(258\) | −2646.83 | −0.638700 | ||||||||
\(259\) | 9351.29 | 2.24348 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −8933.04 | −2.11855 | ||||||||
\(262\) | −569.052 | −0.134184 | ||||||||
\(263\) | 1345.63 | 0.315494 | 0.157747 | − | 0.987480i | \(-0.449577\pi\) | ||||
0.157747 | + | 0.987480i | \(0.449577\pi\) | |||||||
\(264\) | 673.052 | 0.156907 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 6997.67 | 1.61299 | ||||||||
\(267\) | −3709.18 | −0.850180 | ||||||||
\(268\) | −12986.8 | −2.96007 | ||||||||
\(269\) | −3083.04 | −0.698797 | −0.349398 | − | 0.936974i | \(-0.613614\pi\) | ||||
−0.349398 | + | 0.936974i | \(0.613614\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −422.163 | −0.0946294 | −0.0473147 | − | 0.998880i | \(-0.515066\pi\) | ||||
−0.0473147 | + | 0.998880i | \(0.515066\pi\) | |||||||
\(272\) | 279.661 | 0.0623416 | ||||||||
\(273\) | −3996.50 | −0.886004 | ||||||||
\(274\) | −4191.85 | −0.924230 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −8124.54 | −1.77188 | ||||||||
\(277\) | 8260.00 | 1.79168 | 0.895840 | − | 0.444377i | \(-0.146575\pi\) | ||||
0.895840 | + | 0.444377i | \(0.146575\pi\) | |||||||
\(278\) | 9873.28 | 2.13007 | ||||||||
\(279\) | −266.845 | −0.0572602 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 3321.91 | 0.705226 | 0.352613 | − | 0.935769i | \(-0.385293\pi\) | ||||
0.352613 | + | 0.935769i | \(0.385293\pi\) | |||||||
\(282\) | 841.611 | 0.177721 | ||||||||
\(283\) | 7954.43 | 1.67082 | 0.835409 | − | 0.549629i | \(-0.185231\pi\) | ||||
0.835409 | + | 0.549629i | \(0.185231\pi\) | |||||||
\(284\) | −7189.61 | −1.50220 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 303.864 | 0.0628246 | ||||||||
\(287\) | −5079.91 | −1.04480 | ||||||||
\(288\) | 4391.69 | 0.898552 | ||||||||
\(289\) | 289.000 | 0.0588235 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 5228.69 | 1.05330 | ||||||||
\(292\) | −4819.92 | −0.965974 | ||||||||
\(293\) | 1171.99 | 0.233681 | 0.116841 | − | 0.993151i | \(-0.462723\pi\) | ||||
0.116841 | + | 0.993151i | \(0.462723\pi\) | |||||||
\(294\) | −12095.8 | −2.39945 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 9733.98 | 1.91141 | ||||||||
\(297\) | −104.374 | −0.0203918 | ||||||||
\(298\) | −12055.5 | −2.34347 | ||||||||
\(299\) | −1544.84 | −0.298798 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1939.88 | −0.371472 | ||||||||
\(302\) | −6272.46 | −1.19516 | ||||||||
\(303\) | 6598.07 | 1.25099 | ||||||||
\(304\) | 943.387 | 0.177983 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −2478.98 | −0.463116 | ||||||||
\(307\) | −865.763 | −0.160950 | −0.0804751 | − | 0.996757i | \(-0.525644\pi\) | ||||
−0.0804751 | + | 0.996757i | \(0.525644\pi\) | |||||||
\(308\) | 1171.23 | 0.216679 | ||||||||
\(309\) | −14351.3 | −2.64212 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 6994.83 | 1.27537 | 0.637685 | − | 0.770297i | \(-0.279892\pi\) | ||||
0.637685 | + | 0.770297i | \(0.279892\pi\) | |||||||
\(312\) | −4160.05 | −0.754861 | ||||||||
\(313\) | −3442.33 | −0.621635 | −0.310818 | − | 0.950470i | \(-0.600603\pi\) | ||||
−0.310818 | + | 0.950470i | \(0.600603\pi\) | |||||||
\(314\) | −11658.7 | −2.09534 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −13182.8 | −2.34680 | ||||||||
\(317\) | −2066.15 | −0.366078 | −0.183039 | − | 0.983106i | \(-0.558593\pi\) | ||||
−0.183039 | + | 0.983106i | \(0.558593\pi\) | |||||||
\(318\) | 3718.52 | 0.655736 | ||||||||
\(319\) | 928.344 | 0.162938 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 250.377 | 0.0435349 | ||||||||
\(322\) | −9401.21 | −1.62705 | ||||||||
\(323\) | 974.892 | 0.167939 | ||||||||
\(324\) | −8256.20 | −1.41567 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 9163.11 | 1.55674 | ||||||||
\(327\) | 4034.18 | 0.682234 | ||||||||
\(328\) | −5287.80 | −0.890152 | ||||||||
\(329\) | 616.823 | 0.103363 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 9027.44 | 1.49907 | 0.749536 | − | 0.661964i | \(-0.230277\pi\) | ||||
0.749536 | + | 0.661964i | \(0.230277\pi\) | |||||||
\(332\) | 19546.7 | 3.23121 | ||||||||
\(333\) | −11175.0 | −1.83900 | ||||||||
\(334\) | 10179.8 | 1.66771 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −3278.81 | −0.532362 | ||||||||
\(337\) | −204.309 | −0.0330250 | −0.0165125 | − | 0.999864i | \(-0.505256\pi\) | ||||
−0.0165125 | + | 0.999864i | \(0.505256\pi\) | |||||||
\(338\) | 8384.67 | 1.34931 | ||||||||
\(339\) | −3164.09 | −0.506931 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 27.7312 | 0.00440390 | ||||||||
\(342\) | −8362.39 | −1.32218 | ||||||||
\(343\) | 94.8397 | 0.0149296 | ||||||||
\(344\) | −2019.27 | −0.316488 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 14534.5 | 2.25832 | ||||||||
\(347\) | −143.063 | −0.0221326 | −0.0110663 | − | 0.999939i | \(-0.503523\pi\) | ||||
−0.0110663 | + | 0.999939i | \(0.503523\pi\) | |||||||
\(348\) | −30176.8 | −4.64841 | ||||||||
\(349\) | −3998.42 | −0.613268 | −0.306634 | − | 0.951828i | \(-0.599203\pi\) | ||||
−0.306634 | + | 0.951828i | \(0.599203\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 645.119 | 0.0981024 | ||||||||
\(352\) | −456.396 | −0.0691079 | ||||||||
\(353\) | 5809.57 | 0.875956 | 0.437978 | − | 0.898986i | \(-0.355695\pi\) | ||||
0.437978 | + | 0.898986i | \(0.355695\pi\) | |||||||
\(354\) | −8887.77 | −1.33441 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −6718.79 | −1.00027 | ||||||||
\(357\) | −3388.30 | −0.502320 | ||||||||
\(358\) | −3784.24 | −0.558668 | ||||||||
\(359\) | −4895.37 | −0.719687 | −0.359844 | − | 0.933013i | \(-0.617170\pi\) | ||||
−0.359844 | + | 0.933013i | \(0.617170\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −3570.37 | −0.520538 | ||||||||
\(362\) | 15677.9 | 2.27628 | ||||||||
\(363\) | −10075.2 | −1.45678 | ||||||||
\(364\) | −7239.24 | −1.04242 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 13201.2 | 1.88535 | ||||||||
\(367\) | −528.151 | −0.0751206 | −0.0375603 | − | 0.999294i | \(-0.511959\pi\) | ||||
−0.0375603 | + | 0.999294i | \(0.511959\pi\) | |||||||
\(368\) | −1267.42 | −0.179535 | ||||||||
\(369\) | 6070.62 | 0.856433 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 2725.33 | 0.381380 | ||||||||
\(372\) | −901.433 | −0.125637 | ||||||||
\(373\) | 10113.5 | 1.40390 | 0.701950 | − | 0.712226i | \(-0.252313\pi\) | ||||
0.701950 | + | 0.712226i | \(0.252313\pi\) | |||||||
\(374\) | 257.621 | 0.0356184 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 642.066 | 0.0880639 | ||||||||
\(377\) | −5737.98 | −0.783875 | ||||||||
\(378\) | 3925.91 | 0.534198 | ||||||||
\(379\) | 729.385 | 0.0988548 | 0.0494274 | − | 0.998778i | \(-0.484260\pi\) | ||||
0.0494274 | + | 0.998778i | \(0.484260\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −4548.18 | −0.611576 | ||||||||
\(382\) | −6252.12 | −0.837399 | ||||||||
\(383\) | 1608.08 | 0.214540 | 0.107270 | − | 0.994230i | \(-0.465789\pi\) | ||||
0.107270 | + | 0.994230i | \(0.465789\pi\) | |||||||
\(384\) | 19526.3 | 2.59491 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −1062.56 | −0.140111 | ||||||||
\(387\) | 2318.21 | 0.304499 | ||||||||
\(388\) | 9471.22 | 1.23925 | ||||||||
\(389\) | 9824.09 | 1.28047 | 0.640233 | − | 0.768181i | \(-0.278838\pi\) | ||||
0.640233 | + | 0.768181i | \(0.278838\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −1309.74 | −0.169403 | ||||||||
\(392\) | −9227.87 | −1.18897 | ||||||||
\(393\) | 929.478 | 0.119303 | ||||||||
\(394\) | 3809.66 | 0.487127 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −1399.65 | −0.177614 | ||||||||
\(397\) | −2876.88 | −0.363694 | −0.181847 | − | 0.983327i | \(-0.558208\pi\) | ||||
−0.181847 | + | 0.983327i | \(0.558208\pi\) | |||||||
\(398\) | −8720.82 | −1.09833 | ||||||||
\(399\) | −11429.9 | −1.43411 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −6515.91 | −0.811444 | −0.405722 | − | 0.913996i | \(-0.632980\pi\) | ||||
−0.405722 | + | 0.913996i | \(0.632980\pi\) | |||||||
\(402\) | 33490.9 | 4.15516 | ||||||||
\(403\) | −171.403 | −0.0211866 | ||||||||
\(404\) | 11951.7 | 1.47183 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −34918.8 | −4.26845 | ||||||||
\(407\) | 1161.34 | 0.141438 | ||||||||
\(408\) | −3526.97 | −0.427968 | ||||||||
\(409\) | −8870.10 | −1.07237 | −0.536183 | − | 0.844101i | \(-0.680134\pi\) | ||||
−0.536183 | + | 0.844101i | \(0.680134\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 6846.89 | 0.821732 | ||||||||
\(412\) | −25995.9 | −3.10855 | ||||||||
\(413\) | −6513.92 | −0.776099 | ||||||||
\(414\) | 11234.7 | 1.33371 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 2820.93 | 0.332469 | ||||||||
\(417\) | −16126.8 | −1.89385 | ||||||||
\(418\) | 869.041 | 0.101689 | ||||||||
\(419\) | −1009.53 | −0.117706 | −0.0588531 | − | 0.998267i | \(-0.518744\pi\) | ||||
−0.0588531 | + | 0.998267i | \(0.518744\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −3253.60 | −0.376652 | −0.188326 | − | 0.982107i | \(-0.560306\pi\) | ||||
−0.188326 | + | 0.982107i | \(0.560306\pi\) | |||||||
\(422\) | 5151.87 | 0.594287 | ||||||||
\(423\) | −737.119 | −0.0847280 | ||||||||
\(424\) | 2836.86 | 0.324930 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 18540.8 | 2.10870 | ||||||||
\(427\) | 9675.25 | 1.09653 | ||||||||
\(428\) | 453.532 | 0.0512203 | ||||||||
\(429\) | −496.325 | −0.0558573 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −2352.51 | −0.262915 | −0.131457 | − | 0.991322i | \(-0.541966\pi\) | ||||
−0.131457 | + | 0.991322i | \(0.541966\pi\) | |||||||
\(432\) | 529.269 | 0.0589455 | ||||||||
\(433\) | 5860.51 | 0.650434 | 0.325217 | − | 0.945639i | \(-0.394563\pi\) | ||||
0.325217 | + | 0.945639i | \(0.394563\pi\) | |||||||
\(434\) | −1043.08 | −0.115368 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 7307.50 | 0.802674 | ||||||||
\(437\) | −4418.20 | −0.483641 | ||||||||
\(438\) | 12429.8 | 1.35597 | ||||||||
\(439\) | 2894.17 | 0.314650 | 0.157325 | − | 0.987547i | \(-0.449713\pi\) | ||||
0.157325 | + | 0.987547i | \(0.449713\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 10594.0 | 1.14394 | ||||||||
\(442\) | −1592.32 | −0.171356 | ||||||||
\(443\) | 8256.85 | 0.885541 | 0.442771 | − | 0.896635i | \(-0.353996\pi\) | ||||
0.442771 | + | 0.896635i | \(0.353996\pi\) | |||||||
\(444\) | −37750.5 | −4.03504 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −2657.25 | −0.282118 | ||||||||
\(447\) | 19691.1 | 2.08358 | ||||||||
\(448\) | 20604.7 | 2.17295 | ||||||||
\(449\) | 15487.1 | 1.62779 | 0.813897 | − | 0.581009i | \(-0.197342\pi\) | ||||
0.813897 | + | 0.581009i | \(0.197342\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −630.874 | −0.0658685 | ||||||||
\(452\) | −5731.42 | −0.596423 | ||||||||
\(453\) | 10245.3 | 1.06262 | ||||||||
\(454\) | 9842.35 | 1.01745 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −11897.6 | −1.22184 | ||||||||
\(457\) | 16055.6 | 1.64343 | 0.821716 | − | 0.569897i | \(-0.193017\pi\) | ||||
0.821716 | + | 0.569897i | \(0.193017\pi\) | |||||||
\(458\) | −20256.1 | −2.06661 | ||||||||
\(459\) | 546.944 | 0.0556191 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 14064.0 | 1.42088 | 0.710440 | − | 0.703758i | \(-0.248496\pi\) | ||||
0.710440 | + | 0.703758i | \(0.248496\pi\) | |||||||
\(462\) | −3020.41 | −0.304161 | ||||||||
\(463\) | 8071.30 | 0.810162 | 0.405081 | − | 0.914281i | \(-0.367243\pi\) | ||||
0.405081 | + | 0.914281i | \(0.367243\pi\) | |||||||
\(464\) | −4707.55 | −0.470997 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −21102.0 | −2.09771 | ||||||||
\(467\) | −8582.41 | −0.850421 | −0.425211 | − | 0.905094i | \(-0.639800\pi\) | ||||
−0.425211 | + | 0.905094i | \(0.639800\pi\) | |||||||
\(468\) | 8651.07 | 0.854479 | ||||||||
\(469\) | 24545.7 | 2.41667 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 19043.1 | 1.86297 | ||||||||
\(472\) | −6780.49 | −0.661224 | ||||||||
\(473\) | −240.914 | −0.0234191 | ||||||||
\(474\) | 33996.2 | 3.29429 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −6137.56 | −0.590997 | ||||||||
\(477\) | −3256.84 | −0.312621 | ||||||||
\(478\) | −24761.9 | −2.36942 | ||||||||
\(479\) | −6320.96 | −0.602948 | −0.301474 | − | 0.953474i | \(-0.597479\pi\) | ||||
−0.301474 | + | 0.953474i | \(0.597479\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −7178.07 | −0.680441 | ||||||||
\(482\) | 6394.13 | 0.604242 | ||||||||
\(483\) | 15355.8 | 1.44661 | ||||||||
\(484\) | −18250.2 | −1.71396 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 25349.2 | 2.36597 | ||||||||
\(487\) | −7336.47 | −0.682643 | −0.341321 | − | 0.939947i | \(-0.610874\pi\) | ||||
−0.341321 | + | 0.939947i | \(0.610874\pi\) | |||||||
\(488\) | 10071.2 | 0.934225 | ||||||||
\(489\) | −14966.8 | −1.38410 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 6672.53 | 0.613294 | 0.306647 | − | 0.951823i | \(-0.400793\pi\) | ||||
0.306647 | + | 0.951823i | \(0.400793\pi\) | |||||||
\(492\) | 20507.2 | 1.87914 | ||||||||
\(493\) | −4864.76 | −0.444417 | ||||||||
\(494\) | −5371.43 | −0.489215 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −140.623 | −0.0127301 | ||||||||
\(497\) | 13588.7 | 1.22643 | ||||||||
\(498\) | −50407.6 | −4.53578 | ||||||||
\(499\) | 17920.9 | 1.60772 | 0.803858 | − | 0.594821i | \(-0.202777\pi\) | ||||
0.803858 | + | 0.594821i | \(0.202777\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −16627.6 | −1.48276 | ||||||||
\(502\) | 25914.6 | 2.30403 | ||||||||
\(503\) | 11325.3 | 1.00392 | 0.501959 | − | 0.864891i | \(-0.332613\pi\) | ||||
0.501959 | + | 0.864891i | \(0.332613\pi\) | |||||||
\(504\) | 22173.0 | 1.95965 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −1167.54 | −0.102576 | ||||||||
\(507\) | −13695.4 | −1.19967 | ||||||||
\(508\) | −8238.56 | −0.719541 | ||||||||
\(509\) | −8313.78 | −0.723972 | −0.361986 | − | 0.932184i | \(-0.617901\pi\) | ||||
−0.361986 | + | 0.932184i | \(0.617901\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 9109.87 | 0.788644 | ||||||||
\(512\) | 5892.85 | 0.508651 | ||||||||
\(513\) | 1845.02 | 0.158791 | ||||||||
\(514\) | −905.993 | −0.0777464 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 7831.17 | 0.668117 | ||||||||
\(517\) | 76.6033 | 0.00651646 | ||||||||
\(518\) | −43682.6 | −3.70521 | ||||||||
\(519\) | −23740.3 | −2.00787 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 5121.64 | 0.430677 | 0.215339 | − | 0.976539i | \(-0.430914\pi\) | ||||
0.215339 | + | 0.976539i | \(0.430914\pi\) | |||||||
\(522\) | 41728.8 | 3.49889 | ||||||||
\(523\) | −13378.5 | −1.11855 | −0.559275 | − | 0.828982i | \(-0.688920\pi\) | ||||
−0.559275 | + | 0.828982i | \(0.688920\pi\) | |||||||
\(524\) | 1683.65 | 0.140364 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −6285.81 | −0.521054 | ||||||||
\(527\) | −145.319 | −0.0120117 | ||||||||
\(528\) | −407.195 | −0.0335623 | ||||||||
\(529\) | −6231.26 | −0.512144 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 7784.29 | 0.636176 | ||||||||
\(532\) | −20704.0 | −1.68728 | ||||||||
\(533\) | 3899.35 | 0.316885 | ||||||||
\(534\) | 17326.6 | 1.40411 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 25550.2 | 2.05896 | ||||||||
\(537\) | 6181.10 | 0.496712 | ||||||||
\(538\) | 14401.8 | 1.15410 | ||||||||
\(539\) | −1100.95 | −0.0879804 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 9906.81 | 0.787296 | 0.393648 | − | 0.919261i | \(-0.371213\pi\) | ||||
0.393648 | + | 0.919261i | \(0.371213\pi\) | |||||||
\(542\) | 1972.04 | 0.156285 | ||||||||
\(543\) | −25608.0 | −2.02384 | ||||||||
\(544\) | 2391.63 | 0.188493 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 18668.8 | 1.46328 | ||||||||
\(547\) | −16399.6 | −1.28189 | −0.640947 | − | 0.767585i | \(-0.721458\pi\) | ||||
−0.640947 | + | 0.767585i | \(0.721458\pi\) | |||||||
\(548\) | 12402.4 | 0.966798 | ||||||||
\(549\) | −11562.2 | −0.898836 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −16410.4 | −1.26880 | ||||||||
\(552\) | 15984.2 | 1.23248 | ||||||||
\(553\) | 24916.1 | 1.91598 | ||||||||
\(554\) | −38584.8 | −2.95905 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −29212.0 | −2.22818 | ||||||||
\(557\) | −22044.3 | −1.67692 | −0.838461 | − | 0.544962i | \(-0.816544\pi\) | ||||
−0.838461 | + | 0.544962i | \(0.816544\pi\) | |||||||
\(558\) | 1246.51 | 0.0945681 | ||||||||
\(559\) | 1489.06 | 0.112666 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −420.793 | −0.0316683 | ||||||||
\(562\) | −15517.6 | −1.16472 | ||||||||
\(563\) | −12048.8 | −0.901947 | −0.450973 | − | 0.892537i | \(-0.648923\pi\) | ||||
−0.450973 | + | 0.892537i | \(0.648923\pi\) | |||||||
\(564\) | −2490.07 | −0.185906 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −37157.4 | −2.75944 | ||||||||
\(567\) | 15604.6 | 1.15579 | ||||||||
\(568\) | 14144.8 | 1.04490 | ||||||||
\(569\) | −23785.4 | −1.75243 | −0.876217 | − | 0.481916i | \(-0.839941\pi\) | ||||
−0.876217 | + | 0.481916i | \(0.839941\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −10878.3 | −0.797271 | −0.398635 | − | 0.917110i | \(-0.630516\pi\) | ||||
−0.398635 | + | 0.917110i | \(0.630516\pi\) | |||||||
\(572\) | −899.041 | −0.0657182 | ||||||||
\(573\) | 10212.1 | 0.744531 | ||||||||
\(574\) | 23729.7 | 1.72554 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −24623.1 | −1.78119 | ||||||||
\(577\) | −6315.86 | −0.455689 | −0.227845 | − | 0.973698i | \(-0.573168\pi\) | ||||
−0.227845 | + | 0.973698i | \(0.573168\pi\) | |||||||
\(578\) | −1350.00 | −0.0971500 | ||||||||
\(579\) | 1735.56 | 0.124572 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −36944.1 | −2.63804 | ||||||||
\(582\) | −24424.7 | −1.73958 | ||||||||
\(583\) | 338.459 | 0.0240438 | ||||||||
\(584\) | 9482.69 | 0.671912 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −5474.72 | −0.385936 | ||||||||
\(587\) | −18192.1 | −1.27916 | −0.639581 | − | 0.768724i | \(-0.720892\pi\) | ||||
−0.639581 | + | 0.768724i | \(0.720892\pi\) | |||||||
\(588\) | 35787.7 | 2.50996 | ||||||||
\(589\) | −490.207 | −0.0342931 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −6222.63 | −0.433104 | ||||||||
\(592\) | −5889.03 | −0.408848 | ||||||||
\(593\) | 9828.72 | 0.680636 | 0.340318 | − | 0.940310i | \(-0.389465\pi\) | ||||
0.340318 | + | 0.940310i | \(0.389465\pi\) | |||||||
\(594\) | 487.559 | 0.0336781 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 35668.5 | 2.45140 | ||||||||
\(597\) | 14244.4 | 0.976524 | ||||||||
\(598\) | 7216.40 | 0.493479 | ||||||||
\(599\) | 4662.57 | 0.318043 | 0.159021 | − | 0.987275i | \(-0.449166\pi\) | ||||
0.159021 | + | 0.987275i | \(0.449166\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 21658.6 | 1.47000 | 0.735001 | − | 0.678066i | \(-0.237182\pi\) | ||||
0.735001 | + | 0.678066i | \(0.237182\pi\) | |||||||
\(602\) | 9061.76 | 0.613504 | ||||||||
\(603\) | −29332.8 | −1.98097 | ||||||||
\(604\) | 18558.3 | 1.25021 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −30821.5 | −2.06607 | ||||||||
\(607\) | −25764.7 | −1.72283 | −0.861415 | − | 0.507902i | \(-0.830421\pi\) | ||||
−0.861415 | + | 0.507902i | \(0.830421\pi\) | |||||||
\(608\) | 8067.76 | 0.538143 | ||||||||
\(609\) | 57035.6 | 3.79507 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −473.475 | −0.0313498 | ||||||||
\(612\) | 7334.54 | 0.484446 | ||||||||
\(613\) | −16018.1 | −1.05541 | −0.527705 | − | 0.849428i | \(-0.676947\pi\) | ||||
−0.527705 | + | 0.849428i | \(0.676947\pi\) | |||||||
\(614\) | 4044.23 | 0.265817 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −2304.28 | −0.150718 | ||||||||
\(617\) | −22250.3 | −1.45180 | −0.725902 | − | 0.687798i | \(-0.758578\pi\) | ||||
−0.725902 | + | 0.687798i | \(0.758578\pi\) | |||||||
\(618\) | 67038.9 | 4.36360 | ||||||||
\(619\) | −3765.95 | −0.244534 | −0.122267 | − | 0.992497i | \(-0.539016\pi\) | ||||
−0.122267 | + | 0.992497i | \(0.539016\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −2478.74 | −0.160175 | ||||||||
\(622\) | −32674.9 | −2.10634 | ||||||||
\(623\) | 12698.8 | 0.816642 | ||||||||
\(624\) | 2516.82 | 0.161464 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 16080.1 | 1.02666 | ||||||||
\(627\) | −1419.47 | −0.0904120 | ||||||||
\(628\) | 34494.5 | 2.19185 | ||||||||
\(629\) | −6085.70 | −0.385775 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −20806.5 | −1.31267 | −0.656334 | − | 0.754470i | \(-0.727894\pi\) | ||||
−0.656334 | + | 0.754470i | \(0.727894\pi\) | |||||||
\(632\) | 25935.7 | 1.63239 | ||||||||
\(633\) | −8414.96 | −0.528380 | ||||||||
\(634\) | 9651.60 | 0.604596 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −11002.0 | −0.685937 | ||||||||
\(637\) | 6804.85 | 0.423262 | ||||||||
\(638\) | −4336.56 | −0.269100 | ||||||||
\(639\) | −16238.8 | −1.00532 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 2439.58 | 0.150324 | 0.0751620 | − | 0.997171i | \(-0.476053\pi\) | ||||
0.0751620 | + | 0.997171i | \(0.476053\pi\) | |||||||
\(642\) | −1169.58 | −0.0719000 | ||||||||
\(643\) | 19320.1 | 1.18493 | 0.592466 | − | 0.805595i | \(-0.298154\pi\) | ||||
0.592466 | + | 0.805595i | \(0.298154\pi\) | |||||||
\(644\) | 27815.4 | 1.70199 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −4554.00 | −0.277360 | ||||||||
\(647\) | 14067.1 | 0.854766 | 0.427383 | − | 0.904071i | \(-0.359436\pi\) | ||||
0.427383 | + | 0.904071i | \(0.359436\pi\) | |||||||
\(648\) | 16243.2 | 0.984712 | ||||||||
\(649\) | −808.963 | −0.0489285 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 1703.75 | 0.102573 | ||||||||
\(652\) | −27110.9 | −1.62844 | ||||||||
\(653\) | −15893.7 | −0.952478 | −0.476239 | − | 0.879316i | \(-0.658000\pi\) | ||||
−0.476239 | + | 0.879316i | \(0.658000\pi\) | |||||||
\(654\) | −18844.8 | −1.12674 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 3199.11 | 0.190403 | ||||||||
\(657\) | −10886.5 | −0.646459 | ||||||||
\(658\) | −2881.36 | −0.170710 | ||||||||
\(659\) | −9653.54 | −0.570635 | −0.285318 | − | 0.958433i | \(-0.592099\pi\) | ||||
−0.285318 | + | 0.958433i | \(0.592099\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 5389.06 | 0.317111 | 0.158555 | − | 0.987350i | \(-0.449316\pi\) | ||||
0.158555 | + | 0.987350i | \(0.449316\pi\) | |||||||
\(662\) | −42169.7 | −2.47579 | ||||||||
\(663\) | 2600.87 | 0.152352 | ||||||||
\(664\) | −38456.0 | −2.24757 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 52201.7 | 3.03720 | ||||||||
\(667\) | 22047.0 | 1.27986 | ||||||||
\(668\) | −30119.1 | −1.74453 | ||||||||
\(669\) | 4340.30 | 0.250831 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 1201.57 | 0.0691297 | ||||||||
\(672\) | −28040.1 | −1.60963 | ||||||||
\(673\) | 3032.18 | 0.173673 | 0.0868366 | − | 0.996223i | \(-0.472324\pi\) | ||||
0.0868366 | + | 0.996223i | \(0.472324\pi\) | |||||||
\(674\) | 954.386 | 0.0545424 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −24807.7 | −1.41145 | ||||||||
\(677\) | 22029.2 | 1.25059 | 0.625295 | − | 0.780388i | \(-0.284979\pi\) | ||||
0.625295 | + | 0.780388i | \(0.284979\pi\) | |||||||
\(678\) | 14780.4 | 0.837222 | ||||||||
\(679\) | −17901.1 | −1.01175 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −16076.3 | −0.904618 | ||||||||
\(682\) | −129.540 | −0.00727326 | ||||||||
\(683\) | 9040.72 | 0.506491 | 0.253246 | − | 0.967402i | \(-0.418502\pi\) | ||||
0.253246 | + | 0.967402i | \(0.418502\pi\) | |||||||
\(684\) | 24741.8 | 1.38308 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −443.023 | −0.0246570 | ||||||||
\(687\) | 33085.9 | 1.83742 | ||||||||
\(688\) | 1221.65 | 0.0676964 | ||||||||
\(689\) | −2091.97 | −0.115672 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −22863.5 | −1.25871 | −0.629355 | − | 0.777118i | \(-0.716681\pi\) | ||||
−0.629355 | + | 0.777118i | \(0.716681\pi\) | |||||||
\(692\) | −43003.1 | −2.36233 | ||||||||
\(693\) | 2645.41 | 0.145008 | ||||||||
\(694\) | 668.288 | 0.0365531 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 59369.7 | 3.23334 | ||||||||
\(697\) | 3305.94 | 0.179658 | ||||||||
\(698\) | 18677.8 | 1.01284 | ||||||||
\(699\) | 34467.6 | 1.86507 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 1753.00 | 0.0944507 | 0.0472253 | − | 0.998884i | \(-0.484962\pi\) | ||||
0.0472253 | + | 0.998884i | \(0.484962\pi\) | |||||||
\(702\) | −3013.54 | −0.162021 | ||||||||
\(703\) | −20529.1 | −1.10138 | ||||||||
\(704\) | 2558.90 | 0.136992 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −27138.2 | −1.44668 | ||||||||
\(707\) | −22589.3 | −1.20164 | ||||||||
\(708\) | 26296.2 | 1.39587 | ||||||||
\(709\) | 11547.0 | 0.611645 | 0.305823 | − | 0.952089i | \(-0.401069\pi\) | ||||
0.305823 | + | 0.952089i | \(0.401069\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −29775.3 | −1.57055 | ||||||||
\(712\) | 13218.5 | 0.695765 | ||||||||
\(713\) | 658.582 | 0.0345920 | ||||||||
\(714\) | 15827.7 | 0.829606 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 11196.4 | 0.584399 | ||||||||
\(717\) | 40445.6 | 2.10665 | ||||||||
\(718\) | 22867.7 | 1.18860 | ||||||||
\(719\) | −10289.8 | −0.533720 | −0.266860 | − | 0.963735i | \(-0.585986\pi\) | ||||
−0.266860 | + | 0.963735i | \(0.585986\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 49133.4 | 2.53790 | ||||||||
\(722\) | 16678.2 | 0.859695 | ||||||||
\(723\) | −10444.0 | −0.537231 | ||||||||
\(724\) | −46386.2 | −2.38112 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 47064.2 | 2.40595 | ||||||||
\(727\) | −2950.10 | −0.150499 | −0.0752497 | − | 0.997165i | \(-0.523975\pi\) | ||||
−0.0752497 | + | 0.997165i | \(0.523975\pi\) | |||||||
\(728\) | 14242.5 | 0.725083 | ||||||||
\(729\) | −25275.9 | −1.28415 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 1262.45 | 0.0638762 | ||||||||
\(732\) | −39058.3 | −1.97218 | ||||||||
\(733\) | −24348.2 | −1.22691 | −0.613453 | − | 0.789731i | \(-0.710220\pi\) | ||||
−0.613453 | + | 0.789731i | \(0.710220\pi\) | |||||||
\(734\) | 2467.15 | 0.124065 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −10838.8 | −0.542833 | ||||||||
\(737\) | 3048.33 | 0.152357 | ||||||||
\(738\) | −28357.6 | −1.41444 | ||||||||
\(739\) | −29233.5 | −1.45517 | −0.727585 | − | 0.686017i | \(-0.759358\pi\) | ||||
−0.727585 | + | 0.686017i | \(0.759358\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 8773.59 | 0.434961 | ||||||||
\(742\) | −12730.8 | −0.629868 | ||||||||
\(743\) | −15340.6 | −0.757457 | −0.378729 | − | 0.925508i | \(-0.623639\pi\) | ||||
−0.378729 | + | 0.925508i | \(0.623639\pi\) | |||||||
\(744\) | 1773.47 | 0.0873908 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −47242.9 | −2.31861 | ||||||||
\(747\) | 44149.2 | 2.16243 | ||||||||
\(748\) | −762.224 | −0.0372589 | ||||||||
\(749\) | −857.197 | −0.0418175 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 39862.6 | 1.93689 | 0.968446 | − | 0.249223i | \(-0.0801752\pi\) | ||||
0.968446 | + | 0.249223i | \(0.0801752\pi\) | |||||||
\(752\) | −388.448 | −0.0188368 | ||||||||
\(753\) | −42328.3 | −2.04851 | ||||||||
\(754\) | 26803.7 | 1.29461 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −11615.6 | −0.558802 | ||||||||
\(757\) | −26375.1 | −1.26634 | −0.633169 | − | 0.774013i | \(-0.718246\pi\) | ||||
−0.633169 | + | 0.774013i | \(0.718246\pi\) | |||||||
\(758\) | −3407.17 | −0.163264 | ||||||||
\(759\) | 1907.03 | 0.0912000 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 7848.63 | 0.373867 | 0.186933 | − | 0.982373i | \(-0.440145\pi\) | ||||
0.186933 | + | 0.982373i | \(0.440145\pi\) | |||||||
\(762\) | 21245.9 | 1.01005 | ||||||||
\(763\) | −13811.5 | −0.655322 | ||||||||
\(764\) | 18498.1 | 0.875967 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −7511.78 | −0.354323 | ||||||||
\(767\) | 5000.10 | 0.235389 | ||||||||
\(768\) | −43065.8 | −2.02344 | ||||||||
\(769\) | 31818.9 | 1.49209 | 0.746046 | − | 0.665895i | \(-0.231950\pi\) | ||||
0.746046 | + | 0.665895i | \(0.231950\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 1479.83 | 0.0691242 | ||||||||
\(772\) | 3143.78 | 0.146564 | ||||||||
\(773\) | 29559.8 | 1.37541 | 0.687706 | − | 0.725990i | \(-0.258618\pi\) | ||||
0.687706 | + | 0.725990i | \(0.258618\pi\) | |||||||
\(774\) | −10829.0 | −0.502896 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −18633.6 | −0.861996 | ||||||||
\(777\) | 71350.2 | 3.29430 | ||||||||
\(778\) | −45891.2 | −2.11475 | ||||||||
\(779\) | 11152.0 | 0.512917 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1687.58 | 0.0773193 | ||||||||
\(782\) | 6118.19 | 0.279778 | ||||||||
\(783\) | −9206.75 | −0.420208 | ||||||||
\(784\) | 5582.84 | 0.254320 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −4341.86 | −0.197034 | ||||||||
\(787\) | 28038.7 | 1.26998 | 0.634989 | − | 0.772521i | \(-0.281005\pi\) | ||||
0.634989 | + | 0.772521i | \(0.281005\pi\) | |||||||
\(788\) | −11271.6 | −0.509563 | ||||||||
\(789\) | 10267.1 | 0.463269 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 10832.6 | 0.486934 | ||||||||
\(792\) | 2753.67 | 0.123545 | ||||||||
\(793\) | −7426.75 | −0.332574 | ||||||||
\(794\) | 13438.7 | 0.600659 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 25802.3 | 1.14892 | ||||||||
\(797\) | −5320.45 | −0.236462 | −0.118231 | − | 0.992986i | \(-0.537722\pi\) | ||||
−0.118231 | + | 0.992986i | \(0.537722\pi\) | |||||||
\(798\) | 53392.2 | 2.36850 | ||||||||
\(799\) | −401.421 | −0.0177738 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −15175.4 | −0.669409 | ||||||||
\(802\) | 30437.7 | 1.34014 | ||||||||
\(803\) | 1131.35 | 0.0497194 | ||||||||
\(804\) | −99089.4 | −4.34653 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 800.673 | 0.0349907 | ||||||||
\(807\) | −23523.6 | −1.02611 | ||||||||
\(808\) | −23513.8 | −1.02378 | ||||||||
\(809\) | 30934.0 | 1.34435 | 0.672177 | − | 0.740390i | \(-0.265359\pi\) | ||||
0.672177 | + | 0.740390i | \(0.265359\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −40364.5 | −1.74771 | −0.873854 | − | 0.486189i | \(-0.838387\pi\) | ||||
−0.873854 | + | 0.486189i | \(0.838387\pi\) | |||||||
\(812\) | 103314. | 4.46504 | ||||||||
\(813\) | −3221.10 | −0.138953 | ||||||||
\(814\) | −5424.94 | −0.233592 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 2133.81 | 0.0915419 | ||||||||
\(817\) | 4258.66 | 0.182364 | ||||||||
\(818\) | 41434.8 | 1.77107 | ||||||||
\(819\) | −16350.9 | −0.697616 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 19799.7 | 0.841672 | 0.420836 | − | 0.907137i | \(-0.361737\pi\) | ||||
0.420836 | + | 0.907137i | \(0.361737\pi\) | |||||||
\(822\) | −31983.8 | −1.35713 | ||||||||
\(823\) | −18756.4 | −0.794419 | −0.397210 | − | 0.917728i | \(-0.630021\pi\) | ||||
−0.397210 | + | 0.917728i | \(0.630021\pi\) | |||||||
\(824\) | 51144.1 | 2.16225 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 30428.4 | 1.28177 | ||||||||
\(827\) | −20958.0 | −0.881234 | −0.440617 | − | 0.897695i | \(-0.645240\pi\) | ||||
−0.440617 | + | 0.897695i | \(0.645240\pi\) | |||||||
\(828\) | −33240.0 | −1.39513 | ||||||||
\(829\) | −31320.3 | −1.31218 | −0.656091 | − | 0.754682i | \(-0.727791\pi\) | ||||
−0.656091 | + | 0.754682i | \(0.727791\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 63023.7 | 2.63089 | ||||||||
\(832\) | −15816.2 | −0.659049 | ||||||||
\(833\) | 5769.28 | 0.239968 | ||||||||
\(834\) | 75333.0 | 3.12778 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −2571.23 | −0.106373 | ||||||||
\(837\) | −275.021 | −0.0113574 | ||||||||
\(838\) | 4715.82 | 0.194398 | ||||||||
\(839\) | −30290.6 | −1.24642 | −0.623212 | − | 0.782053i | \(-0.714173\pi\) | ||||
−0.623212 | + | 0.782053i | \(0.714173\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 57499.9 | 2.35762 | ||||||||
\(842\) | 15198.5 | 0.622060 | ||||||||
\(843\) | 25346.1 | 1.03555 | ||||||||
\(844\) | −15242.8 | −0.621659 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 3443.29 | 0.139933 | ||||||||
\(847\) | 34493.7 | 1.39931 | ||||||||
\(848\) | −1716.29 | −0.0695021 | ||||||||
\(849\) | 60692.2 | 2.45342 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 27580.3 | 1.11098 | ||||||||
\(852\) | −54856.6 | −2.20582 | ||||||||
\(853\) | 21111.8 | 0.847425 | 0.423712 | − | 0.905797i | \(-0.360727\pi\) | ||||
0.423712 | + | 0.905797i | \(0.360727\pi\) | |||||||
\(854\) | −45195.9 | −1.81097 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −892.277 | −0.0356278 | ||||||||
\(857\) | 39983.0 | 1.59369 | 0.796845 | − | 0.604184i | \(-0.206501\pi\) | ||||
0.796845 | + | 0.604184i | \(0.206501\pi\) | |||||||
\(858\) | 2318.48 | 0.0922512 | ||||||||
\(859\) | −39503.3 | −1.56907 | −0.784537 | − | 0.620082i | \(-0.787099\pi\) | ||||
−0.784537 | + | 0.620082i | \(0.787099\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −38759.6 | −1.53418 | ||||||||
\(862\) | 10989.2 | 0.434217 | ||||||||
\(863\) | −26019.9 | −1.02634 | −0.513168 | − | 0.858288i | \(-0.671528\pi\) | ||||
−0.513168 | + | 0.858288i | \(0.671528\pi\) | |||||||
\(864\) | 4526.26 | 0.178225 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −27376.1 | −1.07422 | ||||||||
\(867\) | 2205.07 | 0.0863760 | ||||||||
\(868\) | 3086.17 | 0.120681 | ||||||||
\(869\) | 3094.33 | 0.120791 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −18841.4 | −0.732968 | ||||||||
\(872\) | −14376.7 | −0.558323 | ||||||||
\(873\) | 21392.2 | 0.829343 | ||||||||
\(874\) | 20638.7 | 0.798757 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −36775.9 | −1.41843 | ||||||||
\(877\) | −15038.3 | −0.579027 | −0.289514 | − | 0.957174i | \(-0.593494\pi\) | ||||
−0.289514 | + | 0.957174i | \(0.593494\pi\) | |||||||
\(878\) | −13519.5 | −0.519660 | ||||||||
\(879\) | 8942.30 | 0.343136 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −18334.3 | −0.701133 | −0.350567 | − | 0.936538i | \(-0.614011\pi\) | ||||
−0.350567 | + | 0.936538i | \(0.614011\pi\) | |||||||
\(882\) | −49487.5 | −1.88927 | ||||||||
\(883\) | −26659.5 | −1.01604 | −0.508020 | − | 0.861345i | \(-0.669622\pi\) | ||||
−0.508020 | + | 0.861345i | \(0.669622\pi\) | |||||||
\(884\) | 4711.21 | 0.179248 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −38570.1 | −1.46251 | ||||||||
\(887\) | −11473.7 | −0.434327 | −0.217163 | − | 0.976135i | \(-0.569680\pi\) | ||||
−0.217163 | + | 0.976135i | \(0.569680\pi\) | |||||||
\(888\) | 74270.1 | 2.80669 | ||||||||
\(889\) | 15571.3 | 0.587450 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 1937.94 | 0.0728656 | ||||||||
\(892\) | 7862.01 | 0.295111 | ||||||||
\(893\) | −1354.12 | −0.0507436 | ||||||||
\(894\) | −91983.0 | −3.44113 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −66850.7 | −2.49255 | ||||||||
\(897\) | −11787.1 | −0.438752 | ||||||||
\(898\) | −72344.6 | −2.68838 | ||||||||
\(899\) | 2446.16 | 0.0907498 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −1773.61 | −0.0655799 | ||||||||
\(902\) | 2946.99 | 0.108785 | ||||||||
\(903\) | −14801.3 | −0.545466 | ||||||||
\(904\) | 11276.0 | 0.414860 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −47858.8 | −1.75497 | ||||||||
\(907\) | 20361.6 | 0.745421 | 0.372710 | − | 0.927948i | \(-0.378429\pi\) | ||||
0.372710 | + | 0.927948i | \(0.378429\pi\) | |||||||
\(908\) | −29120.5 | −1.06432 | ||||||||
\(909\) | 26994.8 | 0.984995 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −19261.9 | −0.700523 | −0.350262 | − | 0.936652i | \(-0.613907\pi\) | ||||
−0.350262 | + | 0.936652i | \(0.613907\pi\) | |||||||
\(912\) | 7198.03 | 0.261349 | ||||||||
\(913\) | −4588.09 | −0.166313 | ||||||||
\(914\) | −75000.3 | −2.71421 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 59931.7 | 2.16179 | ||||||||
\(917\) | −3182.18 | −0.114596 | ||||||||
\(918\) | −2554.93 | −0.0918577 | ||||||||
\(919\) | −21191.8 | −0.760666 | −0.380333 | − | 0.924850i | \(-0.624191\pi\) | ||||
−0.380333 | + | 0.924850i | \(0.624191\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −6605.76 | −0.236338 | ||||||||
\(922\) | −65697.0 | −2.34665 | ||||||||
\(923\) | −10430.7 | −0.371973 | ||||||||
\(924\) | 8936.49 | 0.318170 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −37703.4 | −1.33802 | ||||||||
\(927\) | −58715.6 | −2.08034 | ||||||||
\(928\) | −40258.5 | −1.42409 | ||||||||
\(929\) | 40815.0 | 1.44144 | 0.720719 | − | 0.693227i | \(-0.243812\pi\) | ||||
0.720719 | + | 0.693227i | \(0.243812\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 19461.7 | 0.685102 | ||||||||
\(932\) | 62434.5 | 2.19432 | ||||||||
\(933\) | 53370.4 | 1.87274 | ||||||||
\(934\) | 40090.9 | 1.40451 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −17020.1 | −0.594358 | ||||||||
\(937\) | 38439.1 | 1.34018 | 0.670092 | − | 0.742278i | \(-0.266255\pi\) | ||||
0.670092 | + | 0.742278i | \(0.266255\pi\) | |||||||
\(938\) | −114660. | −3.99124 | ||||||||
\(939\) | −26264.9 | −0.912804 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −2244.08 | −0.0777415 | −0.0388708 | − | 0.999244i | \(-0.512376\pi\) | ||||
−0.0388708 | + | 0.999244i | \(0.512376\pi\) | |||||||
\(942\) | −88955.6 | −3.07678 | ||||||||
\(943\) | −14982.5 | −0.517388 | ||||||||
\(944\) | 4102.18 | 0.141435 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 1125.38 | 0.0386778 | ||||||||
\(947\) | 42289.0 | 1.45112 | 0.725559 | − | 0.688160i | \(-0.241581\pi\) | ||||
0.725559 | + | 0.688160i | \(0.241581\pi\) | |||||||
\(948\) | −100584. | −3.44602 | ||||||||
\(949\) | −6992.76 | −0.239193 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −15764.7 | −0.537546 | ||||||||
\(952\) | 12075.0 | 0.411085 | ||||||||
\(953\) | −37426.2 | −1.27214 | −0.636072 | − | 0.771629i | \(-0.719442\pi\) | ||||
−0.636072 | + | 0.771629i | \(0.719442\pi\) | |||||||
\(954\) | 15213.6 | 0.516309 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 73263.0 | 2.47855 | ||||||||
\(957\) | 7083.25 | 0.239257 | ||||||||
\(958\) | 29527.0 | 0.995799 | ||||||||
\(959\) | −23441.2 | −0.789317 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −29717.9 | −0.997547 | ||||||||
\(962\) | 33530.8 | 1.12378 | ||||||||
\(963\) | 1024.37 | 0.0342782 | ||||||||
\(964\) | −18918.3 | −0.632072 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −71731.1 | −2.38914 | ||||||||
\(967\) | −1088.56 | −0.0362003 | −0.0181001 | − | 0.999836i | \(-0.505762\pi\) | ||||
−0.0181001 | + | 0.999836i | \(0.505762\pi\) | |||||||
\(968\) | 35905.4 | 1.19219 | ||||||||
\(969\) | 7438.41 | 0.246601 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 39506.5 | 1.30569 | 0.652845 | − | 0.757491i | \(-0.273575\pi\) | ||||
0.652845 | + | 0.757491i | \(0.273575\pi\) | |||||||
\(972\) | −75000.6 | −2.47494 | ||||||||
\(973\) | 55212.1 | 1.81914 | ||||||||
\(974\) | 34270.8 | 1.12742 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −6093.05 | −0.199830 | ||||||||
\(977\) | 43326.8 | 1.41878 | 0.709389 | − | 0.704817i | \(-0.248971\pi\) | ||||
0.709389 | + | 0.704817i | \(0.248971\pi\) | |||||||
\(978\) | 69914.4 | 2.28591 | ||||||||
\(979\) | 1577.07 | 0.0514845 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 16505.1 | 0.537174 | ||||||||
\(982\) | −31169.3 | −1.01288 | ||||||||
\(983\) | −10664.1 | −0.346014 | −0.173007 | − | 0.984921i | \(-0.555348\pi\) | ||||
−0.173007 | + | 0.984921i | \(0.555348\pi\) | |||||||
\(984\) | −40345.9 | −1.30709 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 22724.7 | 0.733977 | ||||||||
\(987\) | 4706.35 | 0.151778 | ||||||||
\(988\) | 15892.4 | 0.511747 | ||||||||
\(989\) | −5721.42 | −0.183954 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 15461.4 | 0.495609 | 0.247804 | − | 0.968810i | \(-0.420291\pi\) | ||||
0.247804 | + | 0.968810i | \(0.420291\pi\) | |||||||
\(992\) | −1202.59 | −0.0384902 | ||||||||
\(993\) | 68879.2 | 2.20122 | ||||||||
\(994\) | −63476.7 | −2.02551 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 149141. | 4.74469 | ||||||||
\(997\) | −46061.1 | −1.46316 | −0.731579 | − | 0.681756i | \(-0.761216\pi\) | ||||
−0.731579 | + | 0.681756i | \(0.761216\pi\) | |||||||
\(998\) | −83713.7 | −2.65522 | ||||||||
\(999\) | −11517.4 | −0.364760 |
(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 | 425.4.a.g.1.1 | 3 | ||
5.2 | odd | 4 | 425.4.b.f.324.2 | 6 | |||
5.3 | odd | 4 | 425.4.b.f.324.5 | 6 | |||
5.4 | even | 2 | 17.4.a.b.1.3 | ✓ | 3 | ||
15.14 | odd | 2 | 153.4.a.g.1.1 | 3 | |||
20.19 | odd | 2 | 272.4.a.h.1.3 | 3 | |||
35.34 | odd | 2 | 833.4.a.d.1.3 | 3 | |||
40.19 | odd | 2 | 1088.4.a.x.1.1 | 3 | |||
40.29 | even | 2 | 1088.4.a.v.1.3 | 3 | |||
55.54 | odd | 2 | 2057.4.a.e.1.1 | 3 | |||
60.59 | even | 2 | 2448.4.a.bi.1.3 | 3 | |||
85.4 | even | 4 | 289.4.b.b.288.2 | 6 | |||
85.64 | even | 4 | 289.4.b.b.288.1 | 6 | |||
85.84 | even | 2 | 289.4.a.b.1.3 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
17.4.a.b.1.3 | ✓ | 3 | 5.4 | even | 2 | ||
153.4.a.g.1.1 | 3 | 15.14 | odd | 2 | |||
272.4.a.h.1.3 | 3 | 20.19 | odd | 2 | |||
289.4.a.b.1.3 | 3 | 85.84 | even | 2 | |||
289.4.b.b.288.1 | 6 | 85.64 | even | 4 | |||
289.4.b.b.288.2 | 6 | 85.4 | even | 4 | |||
425.4.a.g.1.1 | 3 | 1.1 | even | 1 | trivial | ||
425.4.b.f.324.2 | 6 | 5.2 | odd | 4 | |||
425.4.b.f.324.5 | 6 | 5.3 | odd | 4 | |||
833.4.a.d.1.3 | 3 | 35.34 | odd | 2 | |||
1088.4.a.v.1.3 | 3 | 40.29 | even | 2 | |||
1088.4.a.x.1.1 | 3 | 40.19 | odd | 2 | |||
2057.4.a.e.1.1 | 3 | 55.54 | odd | 2 | |||
2448.4.a.bi.1.3 | 3 | 60.59 | even | 2 |