Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1575,4,Mod(1,1575)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1575, 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("1575.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1575 = 3^{2} \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1575.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: | \(92.9280082590\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 50x^{6} + 698x^{4} - 2653x^{2} + 2268 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2\cdot 3 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.8 | ||
Root | \(5.38335\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1575.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 5.38335 | 1.90330 | 0.951651 | − | 0.307182i | \(-0.0993860\pi\) | ||||
0.951651 | + | 0.307182i | \(0.0993860\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 20.9805 | 2.62256 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −7.00000 | −0.377964 | ||||||||
\(8\) | 69.8783 | 3.08822 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 15.8856 | 0.435426 | 0.217713 | − | 0.976013i | \(-0.430140\pi\) | ||||
0.217713 | + | 0.976013i | \(0.430140\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 40.8573 | 0.871676 | 0.435838 | − | 0.900025i | \(-0.356452\pi\) | ||||
0.435838 | + | 0.900025i | \(0.356452\pi\) | |||||||
\(14\) | −37.6834 | −0.719380 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 208.336 | 3.25525 | ||||||||
\(17\) | −47.2555 | −0.674185 | −0.337093 | − | 0.941471i | \(-0.609444\pi\) | ||||
−0.337093 | + | 0.941471i | \(0.609444\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 141.113 | 1.70388 | 0.851938 | − | 0.523643i | \(-0.175427\pi\) | ||||
0.851938 | + | 0.523643i | \(0.175427\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 85.5176 | 0.828746 | ||||||||
\(23\) | 97.3015 | 0.882120 | 0.441060 | − | 0.897478i | \(-0.354603\pi\) | ||||
0.441060 | + | 0.897478i | \(0.354603\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 219.949 | 1.65906 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −146.863 | −0.991233 | ||||||||
\(29\) | −236.682 | −1.51555 | −0.757773 | − | 0.652519i | \(-0.773712\pi\) | ||||
−0.757773 | + | 0.652519i | \(0.773712\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 95.7947 | 0.555008 | 0.277504 | − | 0.960725i | \(-0.410493\pi\) | ||||
0.277504 | + | 0.960725i | \(0.410493\pi\) | |||||||
\(32\) | 562.518 | 3.10750 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −254.393 | −1.28318 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −33.8738 | −0.150509 | −0.0752544 | − | 0.997164i | \(-0.523977\pi\) | ||||
−0.0752544 | + | 0.997164i | \(0.523977\pi\) | |||||||
\(38\) | 759.663 | 3.24299 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −197.295 | −0.751520 | −0.375760 | − | 0.926717i | \(-0.622618\pi\) | ||||
−0.375760 | + | 0.926717i | \(0.622618\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −437.132 | −1.55028 | −0.775140 | − | 0.631790i | \(-0.782321\pi\) | ||||
−0.775140 | + | 0.631790i | \(0.782321\pi\) | |||||||
\(44\) | 333.287 | 1.14193 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 523.808 | 1.67894 | ||||||||
\(47\) | 256.598 | 0.796354 | 0.398177 | − | 0.917309i | \(-0.369643\pi\) | ||||
0.398177 | + | 0.917309i | \(0.369643\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 49.0000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 857.205 | 2.28602 | ||||||||
\(53\) | −64.7048 | −0.167696 | −0.0838480 | − | 0.996479i | \(-0.526721\pi\) | ||||
−0.0838480 | + | 0.996479i | \(0.526721\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −489.148 | −1.16724 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −1274.14 | −2.88454 | ||||||||
\(59\) | 809.137 | 1.78543 | 0.892717 | − | 0.450618i | \(-0.148796\pi\) | ||||
0.892717 | + | 0.450618i | \(0.148796\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 318.721 | 0.668985 | 0.334492 | − | 0.942398i | \(-0.391435\pi\) | ||||
0.334492 | + | 0.942398i | \(0.391435\pi\) | |||||||
\(62\) | 515.696 | 1.05635 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1361.55 | 2.65927 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 726.284 | 1.32432 | 0.662162 | − | 0.749361i | \(-0.269639\pi\) | ||||
0.662162 | + | 0.749361i | \(0.269639\pi\) | |||||||
\(68\) | −991.443 | −1.76809 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 68.6547 | 0.114758 | 0.0573790 | − | 0.998352i | \(-0.481726\pi\) | ||||
0.0573790 | + | 0.998352i | \(0.481726\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 680.433 | 1.09094 | 0.545471 | − | 0.838130i | \(-0.316351\pi\) | ||||
0.545471 | + | 0.838130i | \(0.316351\pi\) | |||||||
\(74\) | −182.355 | −0.286464 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 2960.62 | 4.46851 | ||||||||
\(77\) | −111.199 | −0.164575 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1169.94 | 1.66619 | 0.833093 | − | 0.553132i | \(-0.186568\pi\) | ||||
0.833093 | + | 0.553132i | \(0.186568\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −1062.11 | −1.43037 | ||||||||
\(83\) | −642.901 | −0.850211 | −0.425105 | − | 0.905144i | \(-0.639763\pi\) | ||||
−0.425105 | + | 0.905144i | \(0.639763\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −2353.24 | −2.95065 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 1110.06 | 1.34469 | ||||||||
\(89\) | 1382.18 | 1.64619 | 0.823096 | − | 0.567903i | \(-0.192245\pi\) | ||||
0.823096 | + | 0.567903i | \(0.192245\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −286.001 | −0.329462 | ||||||||
\(92\) | 2041.43 | 2.31341 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 1381.36 | 1.51570 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 317.080 | 0.331903 | 0.165951 | − | 0.986134i | \(-0.446930\pi\) | ||||
0.165951 | + | 0.986134i | \(0.446930\pi\) | |||||||
\(98\) | 263.784 | 0.271900 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1140.37 | −1.12347 | −0.561736 | − | 0.827316i | \(-0.689866\pi\) | ||||
−0.561736 | + | 0.827316i | \(0.689866\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −970.893 | −0.928786 | −0.464393 | − | 0.885629i | \(-0.653727\pi\) | ||||
−0.464393 | + | 0.885629i | \(0.653727\pi\) | |||||||
\(104\) | 2855.04 | 2.69192 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −348.329 | −0.319176 | ||||||||
\(107\) | 707.342 | 0.639078 | 0.319539 | − | 0.947573i | \(-0.396472\pi\) | ||||
0.319539 | + | 0.947573i | \(0.396472\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1538.49 | −1.35193 | −0.675967 | − | 0.736932i | \(-0.736274\pi\) | ||||
−0.675967 | + | 0.736932i | \(0.736274\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −1458.35 | −1.23037 | ||||||||
\(113\) | −465.734 | −0.387722 | −0.193861 | − | 0.981029i | \(-0.562101\pi\) | ||||
−0.193861 | + | 0.981029i | \(0.562101\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −4965.70 | −3.97460 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 4355.87 | 3.39822 | ||||||||
\(119\) | 330.789 | 0.254818 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1078.65 | −0.810405 | ||||||||
\(122\) | 1715.79 | 1.27328 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 2009.82 | 1.45554 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −964.749 | −0.674076 | −0.337038 | − | 0.941491i | \(-0.609425\pi\) | ||||
−0.337038 | + | 0.941491i | \(0.609425\pi\) | |||||||
\(128\) | 2829.53 | 1.95389 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 2733.39 | 1.82303 | 0.911517 | − | 0.411262i | \(-0.134912\pi\) | ||||
0.911517 | + | 0.411262i | \(0.134912\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −987.794 | −0.644005 | ||||||||
\(134\) | 3909.84 | 2.52059 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −3302.14 | −2.08203 | ||||||||
\(137\) | −2707.00 | −1.68813 | −0.844067 | − | 0.536238i | \(-0.819845\pi\) | ||||
−0.844067 | + | 0.536238i | \(0.819845\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −2459.38 | −1.50073 | −0.750367 | − | 0.661021i | \(-0.770123\pi\) | ||||
−0.750367 | + | 0.661021i | \(0.770123\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 369.592 | 0.218419 | ||||||||
\(143\) | 649.042 | 0.379550 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 3663.01 | 2.07639 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −710.689 | −0.394718 | ||||||||
\(149\) | −3484.84 | −1.91604 | −0.958018 | − | 0.286707i | \(-0.907439\pi\) | ||||
−0.958018 | + | 0.286707i | \(0.907439\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 444.052 | 0.239314 | 0.119657 | − | 0.992815i | \(-0.461820\pi\) | ||||
0.119657 | + | 0.992815i | \(0.461820\pi\) | |||||||
\(152\) | 9860.77 | 5.26194 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −598.623 | −0.313237 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 831.556 | 0.422709 | 0.211355 | − | 0.977409i | \(-0.432212\pi\) | ||||
0.211355 | + | 0.977409i | \(0.432212\pi\) | |||||||
\(158\) | 6298.21 | 3.17126 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −681.110 | −0.333410 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 419.137 | 0.201407 | 0.100703 | − | 0.994916i | \(-0.467891\pi\) | ||||
0.100703 | + | 0.994916i | \(0.467891\pi\) | |||||||
\(164\) | −4139.34 | −1.97090 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −3460.96 | −1.61821 | ||||||||
\(167\) | 2441.03 | 1.13109 | 0.565547 | − | 0.824716i | \(-0.308665\pi\) | ||||
0.565547 | + | 0.824716i | \(0.308665\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −527.678 | −0.240181 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −9171.23 | −4.06570 | ||||||||
\(173\) | −2630.72 | −1.15613 | −0.578064 | − | 0.815991i | \(-0.696192\pi\) | ||||
−0.578064 | + | 0.815991i | \(0.696192\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 3309.54 | 1.41742 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 7440.77 | 3.13320 | ||||||||
\(179\) | 739.987 | 0.308990 | 0.154495 | − | 0.987994i | \(-0.450625\pi\) | ||||
0.154495 | + | 0.987994i | \(0.450625\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −2061.53 | −0.846588 | −0.423294 | − | 0.905992i | \(-0.639126\pi\) | ||||
−0.423294 | + | 0.905992i | \(0.639126\pi\) | |||||||
\(182\) | −1539.65 | −0.627066 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 6799.27 | 2.72418 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −750.681 | −0.293558 | ||||||||
\(188\) | 5383.54 | 2.08848 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −4047.47 | −1.53332 | −0.766662 | − | 0.642051i | \(-0.778084\pi\) | ||||
−0.766662 | + | 0.642051i | \(0.778084\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 2100.96 | 0.783578 | 0.391789 | − | 0.920055i | \(-0.371856\pi\) | ||||
0.391789 | + | 0.920055i | \(0.371856\pi\) | |||||||
\(194\) | 1706.95 | 0.631711 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1028.04 | 0.374651 | ||||||||
\(197\) | 3057.94 | 1.10594 | 0.552968 | − | 0.833202i | \(-0.313495\pi\) | ||||
0.552968 | + | 0.833202i | \(0.313495\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 2915.91 | 1.03871 | 0.519356 | − | 0.854558i | \(-0.326172\pi\) | ||||
0.519356 | + | 0.854558i | \(0.326172\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −6138.99 | −2.13831 | ||||||||
\(203\) | 1656.78 | 0.572822 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −5226.66 | −1.76776 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 8512.05 | 2.83752 | ||||||||
\(209\) | 2241.67 | 0.741911 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 3626.89 | 1.18334 | 0.591671 | − | 0.806179i | \(-0.298468\pi\) | ||||
0.591671 | + | 0.806179i | \(0.298468\pi\) | |||||||
\(212\) | −1357.54 | −0.439792 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 3807.87 | 1.21636 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −670.563 | −0.209773 | ||||||||
\(218\) | −8282.24 | −2.57314 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1930.74 | −0.587671 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −5661.60 | −1.70013 | −0.850064 | − | 0.526679i | \(-0.823437\pi\) | ||||
−0.850064 | + | 0.526679i | \(0.823437\pi\) | |||||||
\(224\) | −3937.63 | −1.17453 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −2507.21 | −0.737951 | ||||||||
\(227\) | −5746.85 | −1.68032 | −0.840158 | − | 0.542342i | \(-0.817538\pi\) | ||||
−0.840158 | + | 0.542342i | \(0.817538\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −1702.78 | −0.491367 | −0.245684 | − | 0.969350i | \(-0.579012\pi\) | ||||
−0.245684 | + | 0.969350i | \(0.579012\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −16539.0 | −4.68033 | ||||||||
\(233\) | −988.387 | −0.277903 | −0.138951 | − | 0.990299i | \(-0.544373\pi\) | ||||
−0.138951 | + | 0.990299i | \(0.544373\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 16976.1 | 4.68240 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 1780.75 | 0.484996 | ||||||||
\(239\) | −301.963 | −0.0817255 | −0.0408627 | − | 0.999165i | \(-0.513011\pi\) | ||||
−0.0408627 | + | 0.999165i | \(0.513011\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −4054.29 | −1.08365 | −0.541826 | − | 0.840491i | \(-0.682267\pi\) | ||||
−0.541826 | + | 0.840491i | \(0.682267\pi\) | |||||||
\(242\) | −5806.74 | −1.54244 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 6686.92 | 1.75445 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 5765.52 | 1.48523 | ||||||||
\(248\) | 6693.97 | 1.71398 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −6426.79 | −1.61616 | −0.808079 | − | 0.589074i | \(-0.799493\pi\) | ||||
−0.808079 | + | 0.589074i | \(0.799493\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1545.69 | 0.384098 | ||||||||
\(254\) | −5193.58 | −1.28297 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 4339.98 | 1.05957 | ||||||||
\(257\) | 991.869 | 0.240744 | 0.120372 | − | 0.992729i | \(-0.461591\pi\) | ||||
0.120372 | + | 0.992729i | \(0.461591\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 237.117 | 0.0568870 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 14714.8 | 3.46978 | ||||||||
\(263\) | −5394.91 | −1.26488 | −0.632442 | − | 0.774608i | \(-0.717947\pi\) | ||||
−0.632442 | + | 0.774608i | \(0.717947\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −5317.64 | −1.22573 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 15237.8 | 3.47311 | ||||||||
\(269\) | 7111.53 | 1.61189 | 0.805944 | − | 0.591992i | \(-0.201658\pi\) | ||||
0.805944 | + | 0.591992i | \(0.201658\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 609.090 | 0.136530 | 0.0682649 | − | 0.997667i | \(-0.478254\pi\) | ||||
0.0682649 | + | 0.997667i | \(0.478254\pi\) | |||||||
\(272\) | −9845.02 | −2.19464 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −14572.7 | −3.21303 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −3015.06 | −0.653998 | −0.326999 | − | 0.945025i | \(-0.606037\pi\) | ||||
−0.326999 | + | 0.945025i | \(0.606037\pi\) | |||||||
\(278\) | −13239.7 | −2.85635 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −416.706 | −0.0884648 | −0.0442324 | − | 0.999021i | \(-0.514084\pi\) | ||||
−0.0442324 | + | 0.999021i | \(0.514084\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −4483.54 | −0.941763 | −0.470882 | − | 0.882196i | \(-0.656064\pi\) | ||||
−0.470882 | + | 0.882196i | \(0.656064\pi\) | |||||||
\(284\) | 1440.41 | 0.300959 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 3494.02 | 0.722398 | ||||||||
\(287\) | 1381.07 | 0.284048 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −2679.91 | −0.545474 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 14275.8 | 2.86106 | ||||||||
\(293\) | −8198.32 | −1.63464 | −0.817322 | − | 0.576181i | \(-0.804542\pi\) | ||||
−0.817322 | + | 0.576181i | \(0.804542\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −2367.05 | −0.464804 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −18760.1 | −3.64680 | ||||||||
\(299\) | 3975.48 | 0.768923 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 3059.93 | 0.585951 | ||||||||
\(302\) | 2390.49 | 0.455487 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 29399.0 | 5.54654 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −5568.07 | −1.03514 | −0.517568 | − | 0.855642i | \(-0.673163\pi\) | ||||
−0.517568 | + | 0.855642i | \(0.673163\pi\) | |||||||
\(308\) | −2333.01 | −0.431608 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 979.150 | 0.178529 | 0.0892645 | − | 0.996008i | \(-0.471548\pi\) | ||||
0.0892645 | + | 0.996008i | \(0.471548\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 1466.51 | 0.264831 | 0.132415 | − | 0.991194i | \(-0.457727\pi\) | ||||
0.132415 | + | 0.991194i | \(0.457727\pi\) | |||||||
\(314\) | 4476.56 | 0.804544 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 24545.9 | 4.36967 | ||||||||
\(317\) | −9413.22 | −1.66782 | −0.833910 | − | 0.551900i | \(-0.813903\pi\) | ||||
−0.833910 | + | 0.551900i | \(0.813903\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −3759.84 | −0.659907 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −3666.66 | −0.634580 | ||||||||
\(323\) | −6668.39 | −1.14873 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 2256.36 | 0.383338 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −13786.6 | −2.32085 | ||||||||
\(329\) | −1796.18 | −0.300993 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 6614.38 | 1.09837 | 0.549183 | − | 0.835702i | \(-0.314939\pi\) | ||||
0.549183 | + | 0.835702i | \(0.314939\pi\) | |||||||
\(332\) | −13488.3 | −2.22973 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 13140.9 | 2.15281 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −717.673 | −0.116006 | −0.0580032 | − | 0.998316i | \(-0.518473\pi\) | ||||
−0.0580032 | + | 0.998316i | \(0.518473\pi\) | |||||||
\(338\) | −2840.68 | −0.457137 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 1521.75 | 0.241665 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −343.000 | −0.0539949 | ||||||||
\(344\) | −30546.1 | −4.78760 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −14162.1 | −2.20046 | ||||||||
\(347\) | −6994.59 | −1.08210 | −0.541051 | − | 0.840990i | \(-0.681973\pi\) | ||||
−0.541051 | + | 0.840990i | \(0.681973\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 9941.33 | 1.52478 | 0.762388 | − | 0.647120i | \(-0.224027\pi\) | ||||
0.762388 | + | 0.647120i | \(0.224027\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 8935.93 | 1.35309 | ||||||||
\(353\) | −1997.26 | −0.301143 | −0.150572 | − | 0.988599i | \(-0.548111\pi\) | ||||
−0.150572 | + | 0.988599i | \(0.548111\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 28998.8 | 4.31723 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 3983.61 | 0.588101 | ||||||||
\(359\) | 3272.07 | 0.481040 | 0.240520 | − | 0.970644i | \(-0.422682\pi\) | ||||
0.240520 | + | 0.970644i | \(0.422682\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 13054.0 | 1.90319 | ||||||||
\(362\) | −11098.0 | −1.61131 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −6000.44 | −0.864034 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 12744.7 | 1.81272 | 0.906359 | − | 0.422509i | \(-0.138850\pi\) | ||||
0.906359 | + | 0.422509i | \(0.138850\pi\) | |||||||
\(368\) | 20271.4 | 2.87152 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 452.934 | 0.0633831 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −1849.96 | −0.256803 | −0.128401 | − | 0.991722i | \(-0.540985\pi\) | ||||
−0.128401 | + | 0.991722i | \(0.540985\pi\) | |||||||
\(374\) | −4041.18 | −0.558729 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 17930.6 | 2.45931 | ||||||||
\(377\) | −9670.21 | −1.32106 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 4832.69 | 0.654983 | 0.327491 | − | 0.944854i | \(-0.393797\pi\) | ||||
0.327491 | + | 0.944854i | \(0.393797\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −21789.0 | −2.91838 | ||||||||
\(383\) | −3561.98 | −0.475218 | −0.237609 | − | 0.971361i | \(-0.576364\pi\) | ||||
−0.237609 | + | 0.971361i | \(0.576364\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 11310.2 | 1.49139 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 6652.48 | 0.870434 | ||||||||
\(389\) | −5095.14 | −0.664097 | −0.332048 | − | 0.943262i | \(-0.607740\pi\) | ||||
−0.332048 | + | 0.943262i | \(0.607740\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −4598.03 | −0.594712 | ||||||||
\(392\) | 3424.04 | 0.441174 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 16462.0 | 2.10493 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 14511.4 | 1.83453 | 0.917263 | − | 0.398283i | \(-0.130394\pi\) | ||||
0.917263 | + | 0.398283i | \(0.130394\pi\) | |||||||
\(398\) | 15697.4 | 1.97698 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −4973.55 | −0.619370 | −0.309685 | − | 0.950839i | \(-0.600224\pi\) | ||||
−0.309685 | + | 0.950839i | \(0.600224\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 3913.92 | 0.483787 | ||||||||
\(404\) | −23925.4 | −2.94637 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 8919.01 | 1.09025 | ||||||||
\(407\) | −538.106 | −0.0655354 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 2841.63 | 0.343545 | 0.171772 | − | 0.985137i | \(-0.445051\pi\) | ||||
0.171772 | + | 0.985137i | \(0.445051\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −20369.8 | −2.43579 | ||||||||
\(413\) | −5663.96 | −0.674831 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 22983.0 | 2.70874 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 12067.7 | 1.41208 | ||||||||
\(419\) | 12983.2 | 1.51377 | 0.756886 | − | 0.653547i | \(-0.226720\pi\) | ||||
0.756886 | + | 0.653547i | \(0.226720\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 6323.41 | 0.732029 | 0.366015 | − | 0.930609i | \(-0.380722\pi\) | ||||
0.366015 | + | 0.930609i | \(0.380722\pi\) | |||||||
\(422\) | 19524.8 | 2.25226 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −4521.46 | −0.517881 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −2231.05 | −0.252852 | ||||||||
\(428\) | 14840.4 | 1.67602 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 2421.08 | 0.270579 | 0.135289 | − | 0.990806i | \(-0.456804\pi\) | ||||
0.135289 | + | 0.990806i | \(0.456804\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −3187.12 | −0.353726 | −0.176863 | − | 0.984235i | \(-0.556595\pi\) | ||||
−0.176863 | + | 0.984235i | \(0.556595\pi\) | |||||||
\(434\) | −3609.87 | −0.399262 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −32278.3 | −3.54553 | ||||||||
\(437\) | 13730.5 | 1.50302 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −2492.32 | −0.270961 | −0.135480 | − | 0.990780i | \(-0.543258\pi\) | ||||
−0.135480 | + | 0.990780i | \(0.543258\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −10393.8 | −1.11852 | ||||||||
\(443\) | −5862.02 | −0.628698 | −0.314349 | − | 0.949308i | \(-0.601786\pi\) | ||||
−0.314349 | + | 0.949308i | \(0.601786\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −30478.4 | −3.23586 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −9530.82 | −1.00511 | ||||||||
\(449\) | 9655.80 | 1.01489 | 0.507445 | − | 0.861684i | \(-0.330590\pi\) | ||||
0.507445 | + | 0.861684i | \(0.330590\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −3134.15 | −0.327231 | ||||||||
\(452\) | −9771.31 | −1.01682 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −30937.3 | −3.19815 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 12608.4 | 1.29059 | 0.645293 | − | 0.763935i | \(-0.276735\pi\) | ||||
0.645293 | + | 0.763935i | \(0.276735\pi\) | |||||||
\(458\) | −9166.68 | −0.935220 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 4611.99 | 0.465947 | 0.232974 | − | 0.972483i | \(-0.425154\pi\) | ||||
0.232974 | + | 0.972483i | \(0.425154\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −11150.2 | −1.11921 | −0.559603 | − | 0.828761i | \(-0.689046\pi\) | ||||
−0.559603 | + | 0.828761i | \(0.689046\pi\) | |||||||
\(464\) | −49309.4 | −4.93348 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −5320.83 | −0.528933 | ||||||||
\(467\) | −4106.72 | −0.406930 | −0.203465 | − | 0.979082i | \(-0.565220\pi\) | ||||
−0.203465 | + | 0.979082i | \(0.565220\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −5083.99 | −0.500547 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 56541.1 | 5.51380 | ||||||||
\(473\) | −6944.10 | −0.675032 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 6940.10 | 0.668275 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −1625.57 | −0.155548 | ||||||||
\(479\) | −4559.73 | −0.434947 | −0.217473 | − | 0.976066i | \(-0.569782\pi\) | ||||
−0.217473 | + | 0.976066i | \(0.569782\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1383.99 | −0.131195 | ||||||||
\(482\) | −21825.7 | −2.06252 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −22630.5 | −2.12533 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −3854.56 | −0.358659 | −0.179329 | − | 0.983789i | \(-0.557393\pi\) | ||||
−0.179329 | + | 0.983789i | \(0.557393\pi\) | |||||||
\(488\) | 22271.7 | 2.06597 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −10619.9 | −0.976110 | −0.488055 | − | 0.872813i | \(-0.662293\pi\) | ||||
−0.488055 | + | 0.872813i | \(0.662293\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 11184.6 | 1.02176 | ||||||||
\(494\) | 31037.8 | 2.82684 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 19957.5 | 1.80669 | ||||||||
\(497\) | −480.583 | −0.0433744 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −4544.53 | −0.407698 | −0.203849 | − | 0.979002i | \(-0.565345\pi\) | ||||
−0.203849 | + | 0.979002i | \(0.565345\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −34597.7 | −3.07604 | ||||||||
\(503\) | 8793.98 | 0.779531 | 0.389766 | − | 0.920914i | \(-0.372556\pi\) | ||||
0.389766 | + | 0.920914i | \(0.372556\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 8320.99 | 0.731054 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −20240.9 | −1.76780 | ||||||||
\(509\) | −10573.9 | −0.920782 | −0.460391 | − | 0.887716i | \(-0.652291\pi\) | ||||
−0.460391 | + | 0.887716i | \(0.652291\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −4763.03 | −0.412337 | ||||||||
\(512\) | 727.414 | 0.0627880 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 5339.58 | 0.458208 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 4076.20 | 0.346753 | ||||||||
\(518\) | 1276.48 | 0.108273 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −15708.4 | −1.32092 | −0.660458 | − | 0.750863i | \(-0.729638\pi\) | ||||
−0.660458 | + | 0.750863i | \(0.729638\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −2656.84 | −0.222133 | −0.111067 | − | 0.993813i | \(-0.535427\pi\) | ||||
−0.111067 | + | 0.993813i | \(0.535427\pi\) | |||||||
\(524\) | 57347.8 | 4.78101 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −29042.7 | −2.40745 | ||||||||
\(527\) | −4526.83 | −0.374178 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −2699.42 | −0.221864 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −20724.4 | −1.68894 | ||||||||
\(533\) | −8060.95 | −0.655081 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 50751.5 | 4.08980 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 38283.9 | 3.06791 | ||||||||
\(539\) | 778.393 | 0.0622037 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −6340.08 | −0.503847 | −0.251924 | − | 0.967747i | \(-0.581063\pi\) | ||||
−0.251924 | + | 0.967747i | \(0.581063\pi\) | |||||||
\(542\) | 3278.94 | 0.259857 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −26582.1 | −2.09503 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −22317.5 | −1.74447 | −0.872235 | − | 0.489087i | \(-0.837330\pi\) | ||||
−0.872235 | + | 0.489087i | \(0.837330\pi\) | |||||||
\(548\) | −56794.0 | −4.42723 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −33399.1 | −2.58230 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −8189.59 | −0.629759 | ||||||||
\(554\) | −16231.1 | −1.24476 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −51599.0 | −3.93576 | ||||||||
\(557\) | 9476.86 | 0.720911 | 0.360455 | − | 0.932776i | \(-0.382621\pi\) | ||||
0.360455 | + | 0.932776i | \(0.382621\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −17860.1 | −1.35134 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −2243.28 | −0.168375 | ||||||||
\(563\) | −21003.7 | −1.57229 | −0.786144 | − | 0.618043i | \(-0.787926\pi\) | ||||
−0.786144 | + | 0.618043i | \(0.787926\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −24136.5 | −1.79246 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 4797.48 | 0.354397 | ||||||||
\(569\) | 22905.7 | 1.68762 | 0.843811 | − | 0.536640i | \(-0.180307\pi\) | ||||
0.843811 | + | 0.536640i | \(0.180307\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 5035.60 | 0.369060 | 0.184530 | − | 0.982827i | \(-0.440924\pi\) | ||||
0.184530 | + | 0.982827i | \(0.440924\pi\) | |||||||
\(572\) | 13617.2 | 0.995392 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 7434.76 | 0.540628 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −7692.81 | −0.555036 | −0.277518 | − | 0.960720i | \(-0.589512\pi\) | ||||
−0.277518 | + | 0.960720i | \(0.589512\pi\) | |||||||
\(578\) | −14426.9 | −1.03820 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 4500.30 | 0.321350 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −1027.87 | −0.0730191 | ||||||||
\(584\) | 47547.6 | 3.36906 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −44134.4 | −3.11122 | ||||||||
\(587\) | −4219.62 | −0.296699 | −0.148350 | − | 0.988935i | \(-0.547396\pi\) | ||||
−0.148350 | + | 0.988935i | \(0.547396\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 13517.9 | 0.945664 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −7057.14 | −0.489943 | ||||||||
\(593\) | −10710.9 | −0.741730 | −0.370865 | − | 0.928687i | \(-0.620939\pi\) | ||||
−0.370865 | + | 0.928687i | \(0.620939\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −73113.6 | −5.02492 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 21401.4 | 1.46349 | ||||||||
\(599\) | 25086.1 | 1.71117 | 0.855584 | − | 0.517663i | \(-0.173198\pi\) | ||||
0.855584 | + | 0.517663i | \(0.173198\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 25399.6 | 1.72391 | 0.861957 | − | 0.506982i | \(-0.169239\pi\) | ||||
0.861957 | + | 0.506982i | \(0.169239\pi\) | |||||||
\(602\) | 16472.6 | 1.11524 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 9316.42 | 0.627616 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 14501.2 | 0.969665 | 0.484833 | − | 0.874607i | \(-0.338881\pi\) | ||||
0.484833 | + | 0.874607i | \(0.338881\pi\) | |||||||
\(608\) | 79378.9 | 5.29480 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 10483.9 | 0.694162 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 3673.43 | 0.242036 | 0.121018 | − | 0.992650i | \(-0.461384\pi\) | ||||
0.121018 | + | 0.992650i | \(0.461384\pi\) | |||||||
\(614\) | −29974.9 | −1.97018 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −7770.40 | −0.508244 | ||||||||
\(617\) | −9857.06 | −0.643161 | −0.321581 | − | 0.946882i | \(-0.604214\pi\) | ||||
−0.321581 | + | 0.946882i | \(0.604214\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 29100.2 | 1.88956 | 0.944778 | − | 0.327712i | \(-0.106277\pi\) | ||||
0.944778 | + | 0.327712i | \(0.106277\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 5271.11 | 0.339794 | ||||||||
\(623\) | −9675.28 | −0.622202 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 7894.74 | 0.504053 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 17446.4 | 1.10858 | ||||||||
\(629\) | 1600.73 | 0.101471 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −5707.06 | −0.360055 | −0.180027 | − | 0.983662i | \(-0.557619\pi\) | ||||
−0.180027 | + | 0.983662i | \(0.557619\pi\) | |||||||
\(632\) | 81753.6 | 5.14554 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −50674.7 | −3.17437 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 2002.01 | 0.124525 | ||||||||
\(638\) | −20240.5 | −1.25600 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 7664.18 | 0.472257 | 0.236129 | − | 0.971722i | \(-0.424121\pi\) | ||||
0.236129 | + | 0.971722i | \(0.424121\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 15108.9 | 0.926653 | 0.463326 | − | 0.886188i | \(-0.346656\pi\) | ||||
0.463326 | + | 0.886188i | \(0.346656\pi\) | |||||||
\(644\) | −14290.0 | −0.874387 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −35898.3 | −2.18638 | ||||||||
\(647\) | −26190.4 | −1.59142 | −0.795712 | − | 0.605675i | \(-0.792903\pi\) | ||||
−0.795712 | + | 0.605675i | \(0.792903\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 12853.6 | 0.777424 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 8793.68 | 0.528201 | ||||||||
\(653\) | 609.867 | 0.0365482 | 0.0182741 | − | 0.999833i | \(-0.494183\pi\) | ||||
0.0182741 | + | 0.999833i | \(0.494183\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −41103.6 | −2.44638 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −9669.49 | −0.572881 | ||||||||
\(659\) | −8456.98 | −0.499905 | −0.249952 | − | 0.968258i | \(-0.580415\pi\) | ||||
−0.249952 | + | 0.968258i | \(0.580415\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 11260.1 | 0.662582 | 0.331291 | − | 0.943529i | \(-0.392516\pi\) | ||||
0.331291 | + | 0.943529i | \(0.392516\pi\) | |||||||
\(662\) | 35607.5 | 2.09052 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −44924.8 | −2.62563 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −23029.5 | −1.33689 | ||||||||
\(668\) | 51213.9 | 2.96636 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 5063.07 | 0.291293 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −21034.3 | −1.20477 | −0.602386 | − | 0.798205i | \(-0.705783\pi\) | ||||
−0.602386 | + | 0.798205i | \(0.705783\pi\) | |||||||
\(674\) | −3863.48 | −0.220795 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −11070.9 | −0.629889 | ||||||||
\(677\) | 6576.39 | 0.373340 | 0.186670 | − | 0.982423i | \(-0.440230\pi\) | ||||
0.186670 | + | 0.982423i | \(0.440230\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −2219.56 | −0.125448 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 8192.14 | 0.459961 | ||||||||
\(683\) | −19573.4 | −1.09657 | −0.548283 | − | 0.836293i | \(-0.684718\pi\) | ||||
−0.548283 | + | 0.836293i | \(0.684718\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −1846.49 | −0.102769 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −91070.3 | −5.04655 | ||||||||
\(689\) | −2643.67 | −0.146177 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 10921.3 | 0.601251 | 0.300626 | − | 0.953742i | \(-0.402805\pi\) | ||||
0.300626 | + | 0.953742i | \(0.402805\pi\) | |||||||
\(692\) | −55193.8 | −3.03201 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −37654.3 | −2.05957 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 9323.28 | 0.506663 | ||||||||
\(698\) | 53517.6 | 2.90211 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −15067.7 | −0.811839 | −0.405920 | − | 0.913909i | \(-0.633049\pi\) | ||||
−0.405920 | + | 0.913909i | \(0.633049\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −4780.05 | −0.256448 | ||||||||
\(704\) | 21628.9 | 1.15791 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −10752.0 | −0.573166 | ||||||||
\(707\) | 7982.57 | 0.424633 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 27173.9 | 1.43940 | 0.719702 | − | 0.694283i | \(-0.244279\pi\) | ||||
0.719702 | + | 0.694283i | \(0.244279\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 96584.6 | 5.08379 | ||||||||
\(713\) | 9320.97 | 0.489583 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 15525.3 | 0.810344 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 17614.7 | 0.915564 | ||||||||
\(719\) | 11572.1 | 0.600233 | 0.300117 | − | 0.953902i | \(-0.402974\pi\) | ||||
0.300117 | + | 0.953902i | \(0.402974\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 6796.25 | 0.351048 | ||||||||
\(722\) | 70274.2 | 3.62235 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −43251.9 | −2.22023 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 10390.6 | 0.530075 | 0.265038 | − | 0.964238i | \(-0.414616\pi\) | ||||
0.265038 | + | 0.964238i | \(0.414616\pi\) | |||||||
\(728\) | −19985.3 | −1.01745 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 20656.9 | 1.04518 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −20807.9 | −1.04851 | −0.524255 | − | 0.851562i | \(-0.675656\pi\) | ||||
−0.524255 | + | 0.851562i | \(0.675656\pi\) | |||||||
\(734\) | 68609.1 | 3.45015 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 54733.9 | 2.74119 | ||||||||
\(737\) | 11537.4 | 0.576644 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 8201.89 | 0.408270 | 0.204135 | − | 0.978943i | \(-0.434562\pi\) | ||||
0.204135 | + | 0.978943i | \(0.434562\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 2438.30 | 0.120637 | ||||||||
\(743\) | 6711.14 | 0.331370 | 0.165685 | − | 0.986179i | \(-0.447017\pi\) | ||||
0.165685 | + | 0.986179i | \(0.447017\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −9958.99 | −0.488773 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −15749.6 | −0.769871 | ||||||||
\(749\) | −4951.39 | −0.241549 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 28845.5 | 1.40158 | 0.700789 | − | 0.713368i | \(-0.252831\pi\) | ||||
0.700789 | + | 0.713368i | \(0.252831\pi\) | |||||||
\(752\) | 53458.5 | 2.59233 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −52058.1 | −2.51438 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 18678.9 | 0.896822 | 0.448411 | − | 0.893827i | \(-0.351990\pi\) | ||||
0.448411 | + | 0.893827i | \(0.351990\pi\) | |||||||
\(758\) | 26016.0 | 1.24663 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −22486.7 | −1.07115 | −0.535573 | − | 0.844489i | \(-0.679904\pi\) | ||||
−0.535573 | + | 0.844489i | \(0.679904\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 10769.4 | 0.510983 | ||||||||
\(764\) | −84917.8 | −4.02123 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −19175.4 | −0.904483 | ||||||||
\(767\) | 33059.2 | 1.55632 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 3982.98 | 0.186775 | 0.0933874 | − | 0.995630i | \(-0.470230\pi\) | ||||
0.0933874 | + | 0.995630i | \(0.470230\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 44079.1 | 2.05498 | ||||||||
\(773\) | 8594.11 | 0.399882 | 0.199941 | − | 0.979808i | \(-0.435925\pi\) | ||||
0.199941 | + | 0.979808i | \(0.435925\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 22157.0 | 1.02499 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −27428.9 | −1.26398 | ||||||||
\(779\) | −27841.0 | −1.28050 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1090.62 | 0.0499685 | ||||||||
\(782\) | −24752.8 | −1.13192 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 10208.5 | 0.465035 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 21490.9 | 0.973403 | 0.486702 | − | 0.873568i | \(-0.338200\pi\) | ||||
0.486702 | + | 0.873568i | \(0.338200\pi\) | |||||||
\(788\) | 64157.0 | 2.90038 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 3260.14 | 0.146545 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 13022.1 | 0.583138 | ||||||||
\(794\) | 78120.0 | 3.49165 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 61177.2 | 2.72408 | ||||||||
\(797\) | −2703.13 | −0.120138 | −0.0600688 | − | 0.998194i | \(-0.519132\pi\) | ||||
−0.0600688 | + | 0.998194i | \(0.519132\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −12125.7 | −0.536890 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −26774.4 | −1.17885 | ||||||||
\(803\) | 10809.1 | 0.475024 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 21070.0 | 0.920792 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −79686.9 | −3.46952 | ||||||||
\(809\) | 16331.3 | 0.709738 | 0.354869 | − | 0.934916i | \(-0.384526\pi\) | ||||
0.354869 | + | 0.934916i | \(0.384526\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 14503.0 | 0.627953 | 0.313977 | − | 0.949431i | \(-0.398339\pi\) | ||||
0.313977 | + | 0.949431i | \(0.398339\pi\) | |||||||
\(812\) | 34759.9 | 1.50226 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −2896.81 | −0.124734 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −61685.2 | −2.64148 | ||||||||
\(818\) | 15297.5 | 0.653869 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −27641.5 | −1.17503 | −0.587513 | − | 0.809215i | \(-0.699893\pi\) | ||||
−0.587513 | + | 0.809215i | \(0.699893\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −20193.2 | −0.855273 | −0.427636 | − | 0.903951i | \(-0.640654\pi\) | ||||
−0.427636 | + | 0.903951i | \(0.640654\pi\) | |||||||
\(824\) | −67844.4 | −2.86829 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −30491.1 | −1.28441 | ||||||||
\(827\) | 14333.6 | 0.602696 | 0.301348 | − | 0.953514i | \(-0.402563\pi\) | ||||
0.301348 | + | 0.953514i | \(0.402563\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 3214.10 | 0.134657 | 0.0673283 | − | 0.997731i | \(-0.478553\pi\) | ||||
0.0673283 | + | 0.997731i | \(0.478553\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 55629.1 | 2.31802 | ||||||||
\(833\) | −2315.52 | −0.0963122 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 47031.2 | 1.94570 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 69893.1 | 2.88117 | ||||||||
\(839\) | −729.209 | −0.0300061 | −0.0150030 | − | 0.999887i | \(-0.504776\pi\) | ||||
−0.0150030 | + | 0.999887i | \(0.504776\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 31629.5 | 1.29688 | ||||||||
\(842\) | 34041.1 | 1.39327 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 76093.8 | 3.10338 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 7550.54 | 0.306304 | ||||||||
\(848\) | −13480.3 | −0.545892 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −3295.98 | −0.132767 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −41938.2 | −1.68340 | −0.841698 | − | 0.539949i | \(-0.818443\pi\) | ||||
−0.841698 | + | 0.539949i | \(0.818443\pi\) | |||||||
\(854\) | −12010.5 | −0.481254 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 49427.9 | 1.97361 | ||||||||
\(857\) | −19103.8 | −0.761464 | −0.380732 | − | 0.924685i | \(-0.624328\pi\) | ||||
−0.380732 | + | 0.924685i | \(0.624328\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 13341.8 | 0.529936 | 0.264968 | − | 0.964257i | \(-0.414639\pi\) | ||||
0.264968 | + | 0.964257i | \(0.414639\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 13033.5 | 0.514993 | ||||||||
\(863\) | −38561.8 | −1.52104 | −0.760522 | − | 0.649313i | \(-0.775057\pi\) | ||||
−0.760522 | + | 0.649313i | \(0.775057\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −17157.4 | −0.673247 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −14068.7 | −0.550142 | ||||||||
\(869\) | 18585.2 | 0.725500 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 29674.0 | 1.15438 | ||||||||
\(872\) | −107507. | −4.17507 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 73916.3 | 2.86071 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 28097.0 | 1.08183 | 0.540917 | − | 0.841076i | \(-0.318077\pi\) | ||||
0.540917 | + | 0.841076i | \(0.318077\pi\) | |||||||
\(878\) | −13417.0 | −0.515720 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 12677.3 | 0.484801 | 0.242400 | − | 0.970176i | \(-0.422065\pi\) | ||||
0.242400 | + | 0.970176i | \(0.422065\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 26590.0 | 1.01339 | 0.506695 | − | 0.862125i | \(-0.330867\pi\) | ||||
0.506695 | + | 0.862125i | \(0.330867\pi\) | |||||||
\(884\) | −40507.7 | −1.54120 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −31557.3 | −1.19660 | ||||||||
\(887\) | −10754.1 | −0.407090 | −0.203545 | − | 0.979066i | \(-0.565246\pi\) | ||||
−0.203545 | + | 0.979066i | \(0.565246\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 6753.24 | 0.254777 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −118783. | −4.45868 | ||||||||
\(893\) | 36209.4 | 1.35689 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −19806.7 | −0.738500 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 51980.5 | 1.93164 | ||||||||
\(899\) | −22672.9 | −0.841139 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 3057.66 | 0.113058 | ||||||||
\(902\) | −16872.2 | −0.622819 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −32544.7 | −1.19737 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 40275.4 | 1.47445 | 0.737224 | − | 0.675649i | \(-0.236136\pi\) | ||||
0.737224 | + | 0.675649i | \(0.236136\pi\) | |||||||
\(908\) | −120572. | −4.40672 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 19797.9 | 0.720015 | 0.360007 | − | 0.932949i | \(-0.382774\pi\) | ||||
0.360007 | + | 0.932949i | \(0.382774\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −10212.8 | −0.370204 | ||||||||
\(914\) | 67875.7 | 2.45638 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −35725.2 | −1.28864 | ||||||||
\(917\) | −19133.7 | −0.689042 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −40237.3 | −1.44429 | −0.722146 | − | 0.691740i | \(-0.756844\pi\) | ||||
−0.722146 | + | 0.691740i | \(0.756844\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 24827.9 | 0.886838 | ||||||||
\(923\) | 2805.05 | 0.100032 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −60025.3 | −2.13019 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −133138. | −4.70956 | ||||||||
\(929\) | 13545.9 | 0.478391 | 0.239195 | − | 0.970971i | \(-0.423116\pi\) | ||||
0.239195 | + | 0.970971i | \(0.423116\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 6914.56 | 0.243411 | ||||||||
\(932\) | −20736.8 | −0.728816 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −22107.9 | −0.774511 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 32849.2 | 1.14529 | 0.572645 | − | 0.819803i | \(-0.305917\pi\) | ||||
0.572645 | + | 0.819803i | \(0.305917\pi\) | |||||||
\(938\) | −27368.9 | −0.952692 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −44538.0 | −1.54293 | −0.771464 | − | 0.636272i | \(-0.780475\pi\) | ||||
−0.771464 | + | 0.636272i | \(0.780475\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −19197.1 | −0.662931 | ||||||||
\(944\) | 168572. | 5.81203 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −37382.5 | −1.28479 | ||||||||
\(947\) | 1052.01 | 0.0360991 | 0.0180496 | − | 0.999837i | \(-0.494254\pi\) | ||||
0.0180496 | + | 0.999837i | \(0.494254\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 27800.7 | 0.950947 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 23115.0 | 0.786933 | ||||||||
\(953\) | −35657.1 | −1.21201 | −0.606005 | − | 0.795461i | \(-0.707229\pi\) | ||||
−0.606005 | + | 0.795461i | \(0.707229\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −6335.33 | −0.214330 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −24546.6 | −0.827835 | ||||||||
\(959\) | 18949.0 | 0.638055 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −20614.4 | −0.691967 | ||||||||
\(962\) | −7450.53 | −0.249703 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −85060.9 | −2.84194 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 3425.21 | 0.113906 | 0.0569531 | − | 0.998377i | \(-0.481861\pi\) | ||||
0.0569531 | + | 0.998377i | \(0.481861\pi\) | |||||||
\(968\) | −75374.2 | −2.50270 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 15544.8 | 0.513754 | 0.256877 | − | 0.966444i | \(-0.417306\pi\) | ||||
0.256877 | + | 0.966444i | \(0.417306\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 17215.7 | 0.567224 | ||||||||
\(974\) | −20750.5 | −0.682636 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 66401.1 | 2.17771 | ||||||||
\(977\) | −48799.1 | −1.59798 | −0.798988 | − | 0.601347i | \(-0.794631\pi\) | ||||
−0.798988 | + | 0.601347i | \(0.794631\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 21956.8 | 0.716794 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −57170.7 | −1.85783 | ||||||||
\(983\) | 39839.1 | 1.29264 | 0.646322 | − | 0.763065i | \(-0.276306\pi\) | ||||
0.646322 | + | 0.763065i | \(0.276306\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 60210.4 | 1.94471 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 120963. | 3.89509 | ||||||||
\(989\) | −42533.6 | −1.36753 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 4833.44 | 0.154934 | 0.0774668 | − | 0.996995i | \(-0.475317\pi\) | ||||
0.0774668 | + | 0.996995i | \(0.475317\pi\) | |||||||
\(992\) | 53886.3 | 1.72469 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −2587.15 | −0.0825546 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −2299.66 | −0.0730502 | −0.0365251 | − | 0.999333i | \(-0.511629\pi\) | ||||
−0.0365251 | + | 0.999333i | \(0.511629\pi\) | |||||||
\(998\) | −24464.8 | −0.775971 | ||||||||
\(999\) | 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 | 1575.4.a.br.1.8 | yes | 8 | |
3.2 | odd | 2 | inner | 1575.4.a.br.1.1 | ✓ | 8 | |
5.4 | even | 2 | 1575.4.a.bs.1.1 | yes | 8 | ||
15.14 | odd | 2 | 1575.4.a.bs.1.8 | yes | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1575.4.a.br.1.1 | ✓ | 8 | 3.2 | odd | 2 | inner | |
1575.4.a.br.1.8 | yes | 8 | 1.1 | even | 1 | trivial | |
1575.4.a.bs.1.1 | yes | 8 | 5.4 | even | 2 | ||
1575.4.a.bs.1.8 | yes | 8 | 15.14 | odd | 2 |