Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [495,4,Mod(1,495)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(495, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("495.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 495 = 3^{2} \cdot 5 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 495.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(29.2059454528\) |
Analytic rank: | \(1\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.1957.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 9x + 10 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 165) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(1.12946\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 495.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −4.59486 | −1.62453 | −0.812263 | − | 0.583291i | \(-0.801765\pi\) | ||||
−0.812263 | + | 0.583291i | \(0.801765\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 13.1127 | 1.63909 | ||||||||
\(5\) | −5.00000 | −0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 20.6383 | 1.11437 | 0.557183 | − | 0.830390i | \(-0.311882\pi\) | ||||
0.557183 | + | 0.830390i | \(0.311882\pi\) | |||||||
\(8\) | −23.4921 | −1.03822 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 22.9743 | 0.726511 | ||||||||
\(11\) | −11.0000 | −0.301511 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −15.6584 | −0.334067 | −0.167033 | − | 0.985951i | \(-0.553419\pi\) | ||||
−0.167033 | + | 0.985951i | \(0.553419\pi\) | |||||||
\(14\) | −94.8302 | −1.81032 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 3.04132 | 0.0475206 | ||||||||
\(17\) | −72.9507 | −1.04077 | −0.520387 | − | 0.853931i | \(-0.674212\pi\) | ||||
−0.520387 | + | 0.853931i | \(0.674212\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 61.0513 | 0.737165 | 0.368582 | − | 0.929595i | \(-0.379843\pi\) | ||||
0.368582 | + | 0.929595i | \(0.379843\pi\) | |||||||
\(20\) | −65.5635 | −0.733022 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 50.5434 | 0.489813 | ||||||||
\(23\) | 13.6605 | 0.123844 | 0.0619218 | − | 0.998081i | \(-0.480277\pi\) | ||||
0.0619218 | + | 0.998081i | \(0.480277\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 25.0000 | 0.200000 | ||||||||
\(26\) | 71.9483 | 0.542701 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 270.624 | 1.82654 | ||||||||
\(29\) | 31.4663 | 0.201487 | 0.100744 | − | 0.994912i | \(-0.467878\pi\) | ||||
0.100744 | + | 0.994912i | \(0.467878\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −243.008 | −1.40792 | −0.703961 | − | 0.710239i | \(-0.748587\pi\) | ||||
−0.703961 | + | 0.710239i | \(0.748587\pi\) | |||||||
\(32\) | 173.963 | 0.961016 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 335.198 | 1.69076 | ||||||||
\(35\) | −103.192 | −0.498360 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −65.4018 | −0.290594 | −0.145297 | − | 0.989388i | \(-0.546414\pi\) | ||||
−0.145297 | + | 0.989388i | \(0.546414\pi\) | |||||||
\(38\) | −280.522 | −1.19754 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 117.461 | 0.464304 | ||||||||
\(41\) | 109.087 | 0.415524 | 0.207762 | − | 0.978179i | \(-0.433382\pi\) | ||||
0.207762 | + | 0.978179i | \(0.433382\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −121.750 | −0.431783 | −0.215891 | − | 0.976417i | \(-0.569266\pi\) | ||||
−0.215891 | + | 0.976417i | \(0.569266\pi\) | |||||||
\(44\) | −144.240 | −0.494204 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −62.7678 | −0.201187 | ||||||||
\(47\) | 519.530 | 1.61237 | 0.806184 | − | 0.591665i | \(-0.201529\pi\) | ||||
0.806184 | + | 0.591665i | \(0.201529\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 82.9413 | 0.241811 | ||||||||
\(50\) | −114.871 | −0.324905 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −205.324 | −0.547565 | ||||||||
\(53\) | 542.673 | 1.40645 | 0.703226 | − | 0.710967i | \(-0.251742\pi\) | ||||
0.703226 | + | 0.710967i | \(0.251742\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 55.0000 | 0.134840 | ||||||||
\(56\) | −484.839 | −1.15695 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −144.583 | −0.327322 | ||||||||
\(59\) | −109.478 | −0.241574 | −0.120787 | − | 0.992678i | \(-0.538542\pi\) | ||||
−0.120787 | + | 0.992678i | \(0.538542\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −89.6156 | −0.188100 | −0.0940501 | − | 0.995567i | \(-0.529981\pi\) | ||||
−0.0940501 | + | 0.995567i | \(0.529981\pi\) | |||||||
\(62\) | 1116.59 | 2.28721 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −823.664 | −1.60872 | ||||||||
\(65\) | 78.2922 | 0.149399 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 488.446 | 0.890644 | 0.445322 | − | 0.895371i | \(-0.353089\pi\) | ||||
0.445322 | + | 0.895371i | \(0.353089\pi\) | |||||||
\(68\) | −956.581 | −1.70592 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 474.151 | 0.809599 | ||||||||
\(71\) | −837.423 | −1.39977 | −0.699887 | − | 0.714254i | \(-0.746766\pi\) | ||||
−0.699887 | + | 0.714254i | \(0.746766\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 351.216 | 0.563105 | 0.281553 | − | 0.959546i | \(-0.409151\pi\) | ||||
0.281553 | + | 0.959546i | \(0.409151\pi\) | |||||||
\(74\) | 300.512 | 0.472078 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 800.547 | 1.20828 | ||||||||
\(77\) | −227.022 | −0.335994 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −831.205 | −1.18377 | −0.591885 | − | 0.806022i | \(-0.701616\pi\) | ||||
−0.591885 | + | 0.806022i | \(0.701616\pi\) | |||||||
\(80\) | −15.2066 | −0.0212519 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −501.238 | −0.675031 | ||||||||
\(83\) | −1389.13 | −1.83707 | −0.918537 | − | 0.395335i | \(-0.870629\pi\) | ||||
−0.918537 | + | 0.395335i | \(0.870629\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 364.754 | 0.465448 | ||||||||
\(86\) | 559.423 | 0.701443 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 258.413 | 0.313034 | ||||||||
\(89\) | −1523.70 | −1.81474 | −0.907369 | − | 0.420335i | \(-0.861912\pi\) | ||||
−0.907369 | + | 0.420335i | \(0.861912\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −323.164 | −0.372273 | ||||||||
\(92\) | 179.125 | 0.202990 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −2387.17 | −2.61933 | ||||||||
\(95\) | −305.256 | −0.329670 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −426.612 | −0.446555 | −0.223278 | − | 0.974755i | \(-0.571676\pi\) | ||||
−0.223278 | + | 0.974755i | \(0.571676\pi\) | |||||||
\(98\) | −381.103 | −0.392829 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 327.818 | 0.327818 | ||||||||
\(101\) | −74.1387 | −0.0730403 | −0.0365202 | − | 0.999333i | \(-0.511627\pi\) | ||||
−0.0365202 | + | 0.999333i | \(0.511627\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −69.3916 | −0.0663821 | −0.0331911 | − | 0.999449i | \(-0.510567\pi\) | ||||
−0.0331911 | + | 0.999449i | \(0.510567\pi\) | |||||||
\(104\) | 367.850 | 0.346833 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −2493.51 | −2.28482 | ||||||||
\(107\) | −1141.71 | −1.03152 | −0.515761 | − | 0.856733i | \(-0.672491\pi\) | ||||
−0.515761 | + | 0.856733i | \(0.672491\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −2226.85 | −1.95682 | −0.978409 | − | 0.206680i | \(-0.933734\pi\) | ||||
−0.978409 | + | 0.206680i | \(0.933734\pi\) | |||||||
\(110\) | −252.717 | −0.219051 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 62.7678 | 0.0529554 | ||||||||
\(113\) | 1719.76 | 1.43169 | 0.715847 | − | 0.698257i | \(-0.246041\pi\) | ||||
0.715847 | + | 0.698257i | \(0.246041\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −68.3023 | −0.0553845 | ||||||||
\(116\) | 412.608 | 0.330256 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 503.038 | 0.392444 | ||||||||
\(119\) | −1505.58 | −1.15980 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 121.000 | 0.0909091 | ||||||||
\(122\) | 411.771 | 0.305574 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −3186.49 | −2.30771 | ||||||||
\(125\) | −125.000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1601.63 | −1.11907 | −0.559534 | − | 0.828807i | \(-0.689020\pi\) | ||||
−0.559534 | + | 0.828807i | \(0.689020\pi\) | |||||||
\(128\) | 2392.91 | 1.65239 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −359.741 | −0.242703 | ||||||||
\(131\) | −2004.13 | −1.33665 | −0.668327 | − | 0.743868i | \(-0.732989\pi\) | ||||
−0.668327 | + | 0.743868i | \(0.732989\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1260.00 | 0.821471 | ||||||||
\(134\) | −2244.34 | −1.44687 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 1713.77 | 1.08055 | ||||||||
\(137\) | 1672.85 | 1.04322 | 0.521610 | − | 0.853184i | \(-0.325331\pi\) | ||||
0.521610 | + | 0.853184i | \(0.325331\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 2540.38 | 1.55016 | 0.775080 | − | 0.631863i | \(-0.217709\pi\) | ||||
0.775080 | + | 0.631863i | \(0.217709\pi\) | |||||||
\(140\) | −1353.12 | −0.816855 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 3847.84 | 2.27397 | ||||||||
\(143\) | 172.243 | 0.100725 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −157.331 | −0.0901079 | ||||||||
\(146\) | −1613.79 | −0.914780 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −857.594 | −0.476310 | ||||||||
\(149\) | −3090.68 | −1.69932 | −0.849658 | − | 0.527334i | \(-0.823192\pi\) | ||||
−0.849658 | + | 0.527334i | \(0.823192\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1358.74 | 0.732267 | 0.366134 | − | 0.930562i | \(-0.380681\pi\) | ||||
0.366134 | + | 0.930562i | \(0.380681\pi\) | |||||||
\(152\) | −1434.22 | −0.765335 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 1043.13 | 0.545831 | ||||||||
\(155\) | 1215.04 | 0.629642 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −1011.95 | −0.514411 | −0.257205 | − | 0.966357i | \(-0.582802\pi\) | ||||
−0.257205 | + | 0.966357i | \(0.582802\pi\) | |||||||
\(158\) | 3819.27 | 1.92307 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −869.813 | −0.429780 | ||||||||
\(161\) | 281.929 | 0.138007 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −2816.37 | −1.35334 | −0.676672 | − | 0.736285i | \(-0.736578\pi\) | ||||
−0.676672 | + | 0.736285i | \(0.736578\pi\) | |||||||
\(164\) | 1430.42 | 0.681081 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 6382.87 | 2.98438 | ||||||||
\(167\) | −3448.89 | −1.59810 | −0.799052 | − | 0.601262i | \(-0.794665\pi\) | ||||
−0.799052 | + | 0.601262i | \(0.794665\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1951.81 | −0.888399 | ||||||||
\(170\) | −1675.99 | −0.756133 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −1596.47 | −0.707730 | ||||||||
\(173\) | 2287.85 | 1.00545 | 0.502723 | − | 0.864448i | \(-0.332332\pi\) | ||||
0.502723 | + | 0.864448i | \(0.332332\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 515.959 | 0.222873 | ||||||||
\(176\) | −33.4545 | −0.0143280 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 7001.17 | 2.94809 | ||||||||
\(179\) | −3249.06 | −1.35668 | −0.678340 | − | 0.734748i | \(-0.737300\pi\) | ||||
−0.678340 | + | 0.734748i | \(0.737300\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1170.45 | 0.480655 | 0.240328 | − | 0.970692i | \(-0.422745\pi\) | ||||
0.240328 | + | 0.970692i | \(0.422745\pi\) | |||||||
\(182\) | 1484.89 | 0.604767 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −320.913 | −0.128576 | ||||||||
\(185\) | 327.009 | 0.129958 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 802.458 | 0.313805 | ||||||||
\(188\) | 6812.44 | 2.64281 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 1402.61 | 0.535558 | ||||||||
\(191\) | 2760.35 | 1.04572 | 0.522859 | − | 0.852419i | \(-0.324866\pi\) | ||||
0.522859 | + | 0.852419i | \(0.324866\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −1250.61 | −0.466430 | −0.233215 | − | 0.972425i | \(-0.574925\pi\) | ||||
−0.233215 | + | 0.972425i | \(0.574925\pi\) | |||||||
\(194\) | 1960.22 | 0.725441 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1087.58 | 0.396350 | ||||||||
\(197\) | 143.991 | 0.0520756 | 0.0260378 | − | 0.999661i | \(-0.491711\pi\) | ||||
0.0260378 | + | 0.999661i | \(0.491711\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 761.249 | 0.271174 | 0.135587 | − | 0.990765i | \(-0.456708\pi\) | ||||
0.135587 | + | 0.990765i | \(0.456708\pi\) | |||||||
\(200\) | −587.303 | −0.207643 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 340.657 | 0.118656 | ||||||||
\(203\) | 649.411 | 0.224531 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −545.434 | −0.185828 | ||||||||
\(206\) | 318.844 | 0.107840 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −47.6223 | −0.0158751 | ||||||||
\(209\) | −671.564 | −0.222263 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 3976.58 | 1.29743 | 0.648717 | − | 0.761029i | \(-0.275306\pi\) | ||||
0.648717 | + | 0.761029i | \(0.275306\pi\) | |||||||
\(212\) | 7115.91 | 2.30530 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 5245.97 | 1.67573 | ||||||||
\(215\) | 608.749 | 0.193099 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −5015.29 | −1.56894 | ||||||||
\(218\) | 10232.0 | 3.17890 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 721.199 | 0.221015 | ||||||||
\(221\) | 1142.29 | 0.347688 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 908.084 | 0.272690 | 0.136345 | − | 0.990661i | \(-0.456464\pi\) | ||||
0.136345 | + | 0.990661i | \(0.456464\pi\) | |||||||
\(224\) | 3590.30 | 1.07092 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −7902.05 | −2.32583 | ||||||||
\(227\) | 2062.15 | 0.602951 | 0.301475 | − | 0.953474i | \(-0.402521\pi\) | ||||
0.301475 | + | 0.953474i | \(0.402521\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 4077.47 | 1.17662 | 0.588312 | − | 0.808634i | \(-0.299793\pi\) | ||||
0.588312 | + | 0.808634i | \(0.299793\pi\) | |||||||
\(230\) | 313.839 | 0.0899737 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −739.209 | −0.209187 | ||||||||
\(233\) | −1682.76 | −0.473138 | −0.236569 | − | 0.971615i | \(-0.576023\pi\) | ||||
−0.236569 | + | 0.971615i | \(0.576023\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −2597.65 | −0.721073 | ||||||||
\(236\) | −1435.56 | −0.395961 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 6917.93 | 1.88413 | ||||||||
\(239\) | −4024.96 | −1.08934 | −0.544672 | − | 0.838649i | \(-0.683346\pi\) | ||||
−0.544672 | + | 0.838649i | \(0.683346\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −2784.27 | −0.744194 | −0.372097 | − | 0.928194i | \(-0.621361\pi\) | ||||
−0.372097 | + | 0.928194i | \(0.621361\pi\) | |||||||
\(242\) | −555.978 | −0.147684 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −1175.10 | −0.308313 | ||||||||
\(245\) | −414.707 | −0.108141 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −955.968 | −0.246262 | ||||||||
\(248\) | 5708.78 | 1.46173 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 574.357 | 0.145302 | ||||||||
\(251\) | 1827.60 | 0.459591 | 0.229796 | − | 0.973239i | \(-0.426194\pi\) | ||||
0.229796 | + | 0.973239i | \(0.426194\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −150.265 | −0.0373402 | ||||||||
\(254\) | 7359.26 | 1.81796 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −4405.79 | −1.07563 | ||||||||
\(257\) | −585.171 | −0.142031 | −0.0710155 | − | 0.997475i | \(-0.522624\pi\) | ||||
−0.0710155 | + | 0.997475i | \(0.522624\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −1349.78 | −0.323828 | ||||||||
\(260\) | 1026.62 | 0.244878 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 9208.69 | 2.17143 | ||||||||
\(263\) | 238.098 | 0.0558241 | 0.0279120 | − | 0.999610i | \(-0.491114\pi\) | ||||
0.0279120 | + | 0.999610i | \(0.491114\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −2713.37 | −0.628984 | ||||||||
\(266\) | −5789.51 | −1.33450 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 6404.84 | 1.45984 | ||||||||
\(269\) | −4618.46 | −1.04681 | −0.523406 | − | 0.852083i | \(-0.675339\pi\) | ||||
−0.523406 | + | 0.852083i | \(0.675339\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −143.439 | −0.0321525 | −0.0160762 | − | 0.999871i | \(-0.505117\pi\) | ||||
−0.0160762 | + | 0.999871i | \(0.505117\pi\) | |||||||
\(272\) | −221.867 | −0.0494582 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −7686.51 | −1.69474 | ||||||||
\(275\) | −275.000 | −0.0603023 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −8602.51 | −1.86597 | −0.932987 | − | 0.359911i | \(-0.882807\pi\) | ||||
−0.932987 | + | 0.359911i | \(0.882807\pi\) | |||||||
\(278\) | −11672.7 | −2.51828 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 2424.19 | 0.517404 | ||||||||
\(281\) | 2992.81 | 0.635360 | 0.317680 | − | 0.948198i | \(-0.397096\pi\) | ||||
0.317680 | + | 0.948198i | \(0.397096\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −6858.89 | −1.44070 | −0.720351 | − | 0.693610i | \(-0.756019\pi\) | ||||
−0.720351 | + | 0.693610i | \(0.756019\pi\) | |||||||
\(284\) | −10980.9 | −2.29435 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −791.431 | −0.163630 | ||||||||
\(287\) | 2251.37 | 0.463046 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 408.809 | 0.0832096 | ||||||||
\(290\) | 722.915 | 0.146383 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 4605.39 | 0.922979 | ||||||||
\(293\) | −4049.70 | −0.807461 | −0.403731 | − | 0.914878i | \(-0.632287\pi\) | ||||
−0.403731 | + | 0.914878i | \(0.632287\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 547.392 | 0.108035 | ||||||||
\(296\) | 1536.43 | 0.301699 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 14201.2 | 2.76059 | ||||||||
\(299\) | −213.901 | −0.0413720 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −2512.71 | −0.481164 | ||||||||
\(302\) | −6243.20 | −1.18959 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 185.677 | 0.0350305 | ||||||||
\(305\) | 448.078 | 0.0841209 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −9572.69 | −1.77962 | −0.889808 | − | 0.456335i | \(-0.849162\pi\) | ||||
−0.889808 | + | 0.456335i | \(0.849162\pi\) | |||||||
\(308\) | −2976.87 | −0.550724 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −5582.94 | −1.02287 | ||||||||
\(311\) | −5396.42 | −0.983932 | −0.491966 | − | 0.870614i | \(-0.663722\pi\) | ||||
−0.491966 | + | 0.870614i | \(0.663722\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 9755.04 | 1.76162 | 0.880811 | − | 0.473469i | \(-0.156998\pi\) | ||||
0.880811 | + | 0.473469i | \(0.156998\pi\) | |||||||
\(314\) | 4649.77 | 0.835674 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −10899.3 | −1.94030 | ||||||||
\(317\) | 4353.75 | 0.771391 | 0.385695 | − | 0.922626i | \(-0.373962\pi\) | ||||
0.385695 | + | 0.922626i | \(0.373962\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −346.129 | −0.0607508 | ||||||||
\(320\) | 4118.32 | 0.719440 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −1295.42 | −0.224196 | ||||||||
\(323\) | −4453.74 | −0.767221 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −391.461 | −0.0668134 | ||||||||
\(326\) | 12940.8 | 2.19854 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −2562.68 | −0.431404 | ||||||||
\(329\) | 10722.2 | 1.79677 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 5387.64 | 0.894656 | 0.447328 | − | 0.894370i | \(-0.352376\pi\) | ||||
0.447328 | + | 0.894370i | \(0.352376\pi\) | |||||||
\(332\) | −18215.3 | −3.01113 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 15847.2 | 2.59616 | ||||||||
\(335\) | −2442.23 | −0.398308 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −4500.27 | −0.727434 | −0.363717 | − | 0.931509i | \(-0.618492\pi\) | ||||
−0.363717 | + | 0.931509i | \(0.618492\pi\) | |||||||
\(338\) | 8968.30 | 1.44323 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 4782.91 | 0.762910 | ||||||||
\(341\) | 2673.09 | 0.424504 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −5367.18 | −0.844899 | ||||||||
\(344\) | 2860.16 | 0.448283 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −10512.4 | −1.63337 | ||||||||
\(347\) | −5906.32 | −0.913740 | −0.456870 | − | 0.889533i | \(-0.651030\pi\) | ||||
−0.456870 | + | 0.889533i | \(0.651030\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 3636.26 | 0.557721 | 0.278860 | − | 0.960332i | \(-0.410043\pi\) | ||||
0.278860 | + | 0.960332i | \(0.410043\pi\) | |||||||
\(350\) | −2370.76 | −0.362063 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −1913.59 | −0.289757 | ||||||||
\(353\) | −210.408 | −0.0317248 | −0.0158624 | − | 0.999874i | \(-0.505049\pi\) | ||||
−0.0158624 | + | 0.999874i | \(0.505049\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 4187.12 | 0.625998 | ||||||||
\(356\) | −19979.8 | −2.97451 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 14928.9 | 2.20396 | ||||||||
\(359\) | −2499.68 | −0.367488 | −0.183744 | − | 0.982974i | \(-0.558822\pi\) | ||||
−0.183744 | + | 0.982974i | \(0.558822\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −3131.74 | −0.456588 | ||||||||
\(362\) | −5378.03 | −0.780837 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −4237.56 | −0.610188 | ||||||||
\(365\) | −1756.08 | −0.251828 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 5748.70 | 0.817656 | 0.408828 | − | 0.912612i | \(-0.365938\pi\) | ||||
0.408828 | + | 0.912612i | \(0.365938\pi\) | |||||||
\(368\) | 41.5458 | 0.00588512 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −1502.56 | −0.211120 | ||||||||
\(371\) | 11199.9 | 1.56730 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 4467.78 | 0.620196 | 0.310098 | − | 0.950705i | \(-0.399638\pi\) | ||||
0.310098 | + | 0.950705i | \(0.399638\pi\) | |||||||
\(374\) | −3687.18 | −0.509785 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −12204.9 | −1.67398 | ||||||||
\(377\) | −492.712 | −0.0673103 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 7804.08 | 1.05770 | 0.528851 | − | 0.848715i | \(-0.322623\pi\) | ||||
0.528851 | + | 0.848715i | \(0.322623\pi\) | |||||||
\(380\) | −4002.74 | −0.540358 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −12683.4 | −1.69880 | ||||||||
\(383\) | 11161.1 | 1.48904 | 0.744522 | − | 0.667597i | \(-0.232677\pi\) | ||||
0.744522 | + | 0.667597i | \(0.232677\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 1135.11 | 0.150261 | ||||||||
\(386\) | 5746.38 | 0.757728 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −5594.04 | −0.731944 | ||||||||
\(389\) | −8490.24 | −1.10661 | −0.553306 | − | 0.832978i | \(-0.686634\pi\) | ||||
−0.553306 | + | 0.832978i | \(0.686634\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −996.540 | −0.128893 | ||||||||
\(392\) | −1948.47 | −0.251052 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −661.616 | −0.0845983 | ||||||||
\(395\) | 4156.03 | 0.529398 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 6019.74 | 0.761013 | 0.380507 | − | 0.924778i | \(-0.375750\pi\) | ||||
0.380507 | + | 0.924778i | \(0.375750\pi\) | |||||||
\(398\) | −3497.83 | −0.440529 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 76.0330 | 0.00950413 | ||||||||
\(401\) | 10398.8 | 1.29499 | 0.647495 | − | 0.762069i | \(-0.275816\pi\) | ||||
0.647495 | + | 0.762069i | \(0.275816\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 3805.13 | 0.470340 | ||||||||
\(404\) | −972.158 | −0.119720 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −2983.95 | −0.364756 | ||||||||
\(407\) | 719.420 | 0.0876175 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −4733.68 | −0.572287 | −0.286144 | − | 0.958187i | \(-0.592373\pi\) | ||||
−0.286144 | + | 0.958187i | \(0.592373\pi\) | |||||||
\(410\) | 2506.19 | 0.301883 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −909.911 | −0.108806 | ||||||||
\(413\) | −2259.45 | −0.269202 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 6945.67 | 0.821565 | ||||||||
\(416\) | −2723.98 | −0.321044 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 3085.74 | 0.361073 | ||||||||
\(419\) | 8117.57 | 0.946466 | 0.473233 | − | 0.880937i | \(-0.343087\pi\) | ||||
0.473233 | + | 0.880937i | \(0.343087\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −9484.27 | −1.09795 | −0.548973 | − | 0.835840i | \(-0.684981\pi\) | ||||
−0.548973 | + | 0.835840i | \(0.684981\pi\) | |||||||
\(422\) | −18271.8 | −2.10772 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −12748.5 | −1.46020 | ||||||||
\(425\) | −1823.77 | −0.208155 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −1849.52 | −0.209612 | ||||||||
\(428\) | −14970.8 | −1.69075 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −2797.11 | −0.313695 | ||||||||
\(431\) | −9335.16 | −1.04329 | −0.521646 | − | 0.853162i | \(-0.674682\pi\) | ||||
−0.521646 | + | 0.853162i | \(0.674682\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −2983.02 | −0.331074 | −0.165537 | − | 0.986204i | \(-0.552936\pi\) | ||||
−0.165537 | + | 0.986204i | \(0.552936\pi\) | |||||||
\(434\) | 23044.5 | 2.54878 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −29200.0 | −3.20739 | ||||||||
\(437\) | 833.988 | 0.0912931 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −5232.32 | −0.568850 | −0.284425 | − | 0.958698i | \(-0.591803\pi\) | ||||
−0.284425 | + | 0.958698i | \(0.591803\pi\) | |||||||
\(440\) | −1292.07 | −0.139993 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −5248.68 | −0.564828 | ||||||||
\(443\) | −7517.71 | −0.806269 | −0.403135 | − | 0.915141i | \(-0.632079\pi\) | ||||
−0.403135 | + | 0.915141i | \(0.632079\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 7618.49 | 0.811575 | ||||||||
\(446\) | −4172.52 | −0.442992 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −16999.1 | −1.79270 | ||||||||
\(449\) | −16070.9 | −1.68916 | −0.844581 | − | 0.535428i | \(-0.820150\pi\) | ||||
−0.844581 | + | 0.535428i | \(0.820150\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1199.96 | −0.125285 | ||||||||
\(452\) | 22550.7 | 2.34667 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −9475.29 | −0.979510 | ||||||||
\(455\) | 1615.82 | 0.166485 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 9718.51 | 0.994776 | 0.497388 | − | 0.867528i | \(-0.334293\pi\) | ||||
0.497388 | + | 0.867528i | \(0.334293\pi\) | |||||||
\(458\) | −18735.4 | −1.91146 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −895.627 | −0.0907801 | ||||||||
\(461\) | 14538.0 | 1.46877 | 0.734385 | − | 0.678733i | \(-0.237471\pi\) | ||||
0.734385 | + | 0.678733i | \(0.237471\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −9978.17 | −1.00157 | −0.500783 | − | 0.865573i | \(-0.666955\pi\) | ||||
−0.500783 | + | 0.865573i | \(0.666955\pi\) | |||||||
\(464\) | 95.6990 | 0.00957481 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 7732.03 | 0.768625 | ||||||||
\(467\) | −15188.2 | −1.50498 | −0.752489 | − | 0.658605i | \(-0.771147\pi\) | ||||
−0.752489 | + | 0.658605i | \(0.771147\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 10080.7 | 0.992503 | ||||||||
\(470\) | 11935.8 | 1.17140 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 2571.88 | 0.250806 | ||||||||
\(473\) | 1339.25 | 0.130187 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1526.28 | 0.147433 | ||||||||
\(476\) | −19742.3 | −1.90102 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 18494.1 | 1.76967 | ||||||||
\(479\) | −11330.8 | −1.08083 | −0.540415 | − | 0.841399i | \(-0.681733\pi\) | ||||
−0.540415 | + | 0.841399i | \(0.681733\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1024.09 | 0.0970779 | ||||||||
\(482\) | 12793.3 | 1.20896 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 1586.64 | 0.149008 | ||||||||
\(485\) | 2133.06 | 0.199706 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 19086.9 | 1.77599 | 0.887997 | − | 0.459850i | \(-0.152097\pi\) | ||||
0.887997 | + | 0.459850i | \(0.152097\pi\) | |||||||
\(488\) | 2105.26 | 0.195288 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 1905.52 | 0.175679 | ||||||||
\(491\) | 8112.85 | 0.745677 | 0.372839 | − | 0.927896i | \(-0.378384\pi\) | ||||
0.372839 | + | 0.927896i | \(0.378384\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −2295.49 | −0.209703 | ||||||||
\(494\) | 4392.53 | 0.400060 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −739.066 | −0.0669053 | ||||||||
\(497\) | −17283.0 | −1.55986 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 18329.1 | 1.64433 | 0.822167 | − | 0.569246i | \(-0.192765\pi\) | ||||
0.822167 | + | 0.569246i | \(0.192765\pi\) | |||||||
\(500\) | −1639.09 | −0.146604 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −8397.58 | −0.746618 | ||||||||
\(503\) | −7739.57 | −0.686064 | −0.343032 | − | 0.939324i | \(-0.611454\pi\) | ||||
−0.343032 | + | 0.939324i | \(0.611454\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 370.693 | 0.0326646 | ||||||||
\(506\) | 690.446 | 0.0606602 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −21001.7 | −1.83425 | ||||||||
\(509\) | −15914.9 | −1.38589 | −0.692943 | − | 0.720993i | \(-0.743686\pi\) | ||||
−0.692943 | + | 0.720993i | \(0.743686\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 7248.51 | 0.627505 | ||||||||
\(512\) | 1100.65 | 0.0950048 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 2688.78 | 0.230733 | ||||||||
\(515\) | 346.958 | 0.0296870 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −5714.83 | −0.486147 | ||||||||
\(518\) | 6202.07 | 0.526068 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −1839.25 | −0.155109 | ||||||||
\(521\) | −2274.50 | −0.191262 | −0.0956312 | − | 0.995417i | \(-0.530487\pi\) | ||||
−0.0956312 | + | 0.995417i | \(0.530487\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 10971.1 | 0.917274 | 0.458637 | − | 0.888624i | \(-0.348338\pi\) | ||||
0.458637 | + | 0.888624i | \(0.348338\pi\) | |||||||
\(524\) | −26279.6 | −2.19089 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −1094.02 | −0.0906877 | ||||||||
\(527\) | 17727.6 | 1.46533 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −11980.4 | −0.984663 | ||||||||
\(530\) | 12467.5 | 1.02180 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 16522.0 | 1.34646 | ||||||||
\(533\) | −1708.13 | −0.138813 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 5708.53 | 0.461310 | ||||||||
\(536\) | −11474.6 | −0.924680 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 21221.2 | 1.70058 | ||||||||
\(539\) | −912.355 | −0.0729089 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 5313.05 | 0.422229 | 0.211115 | − | 0.977461i | \(-0.432291\pi\) | ||||
0.211115 | + | 0.977461i | \(0.432291\pi\) | |||||||
\(542\) | 659.084 | 0.0522326 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −12690.7 | −1.00020 | ||||||||
\(545\) | 11134.2 | 0.875115 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 20685.1 | 1.61688 | 0.808439 | − | 0.588581i | \(-0.200313\pi\) | ||||
0.808439 | + | 0.588581i | \(0.200313\pi\) | |||||||
\(548\) | 21935.6 | 1.70993 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 1263.59 | 0.0979627 | ||||||||
\(551\) | 1921.06 | 0.148529 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −17154.7 | −1.31915 | ||||||||
\(554\) | 39527.3 | 3.03132 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 33311.2 | 2.54085 | ||||||||
\(557\) | 10853.8 | 0.825659 | 0.412830 | − | 0.910808i | \(-0.364540\pi\) | ||||
0.412830 | + | 0.910808i | \(0.364540\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 1906.41 | 0.144244 | ||||||||
\(560\) | −313.839 | −0.0236824 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −13751.5 | −1.03216 | ||||||||
\(563\) | 15381.2 | 1.15141 | 0.575704 | − | 0.817658i | \(-0.304728\pi\) | ||||
0.575704 | + | 0.817658i | \(0.304728\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −8598.80 | −0.640273 | ||||||||
\(566\) | 31515.6 | 2.34046 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 19672.9 | 1.45327 | ||||||||
\(569\) | 1348.88 | 0.0993814 | 0.0496907 | − | 0.998765i | \(-0.484176\pi\) | ||||
0.0496907 | + | 0.998765i | \(0.484176\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 3463.51 | 0.253841 | 0.126920 | − | 0.991913i | \(-0.459491\pi\) | ||||
0.126920 | + | 0.991913i | \(0.459491\pi\) | |||||||
\(572\) | 2258.57 | 0.165097 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −10344.7 | −0.752231 | ||||||||
\(575\) | 341.511 | 0.0247687 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 12052.6 | 0.869598 | 0.434799 | − | 0.900528i | \(-0.356819\pi\) | ||||
0.434799 | + | 0.900528i | \(0.356819\pi\) | |||||||
\(578\) | −1878.42 | −0.135176 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −2063.04 | −0.147695 | ||||||||
\(581\) | −28669.4 | −2.04717 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −5969.41 | −0.424061 | ||||||||
\(584\) | −8250.80 | −0.584624 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 18607.8 | 1.31174 | ||||||||
\(587\) | 11133.1 | 0.782813 | 0.391407 | − | 0.920218i | \(-0.371989\pi\) | ||||
0.391407 | + | 0.920218i | \(0.371989\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −14836.0 | −1.03787 | ||||||||
\(590\) | −2515.19 | −0.175506 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −198.908 | −0.0138092 | ||||||||
\(593\) | 7939.69 | 0.549821 | 0.274911 | − | 0.961470i | \(-0.411352\pi\) | ||||
0.274911 | + | 0.961470i | \(0.411352\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 7527.91 | 0.518680 | ||||||||
\(596\) | −40527.1 | −2.78533 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 982.846 | 0.0672100 | ||||||||
\(599\) | 19474.7 | 1.32840 | 0.664202 | − | 0.747553i | \(-0.268771\pi\) | ||||
0.664202 | + | 0.747553i | \(0.268771\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −19946.1 | −1.35377 | −0.676887 | − | 0.736087i | \(-0.736671\pi\) | ||||
−0.676887 | + | 0.736087i | \(0.736671\pi\) | |||||||
\(602\) | 11545.6 | 0.781664 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 17816.7 | 1.20025 | ||||||||
\(605\) | −605.000 | −0.0406558 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 1427.44 | 0.0954496 | 0.0477248 | − | 0.998861i | \(-0.484803\pi\) | ||||
0.0477248 | + | 0.998861i | \(0.484803\pi\) | |||||||
\(608\) | 10620.6 | 0.708427 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −2058.85 | −0.136657 | ||||||||
\(611\) | −8135.03 | −0.538638 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −8029.40 | −0.529045 | −0.264522 | − | 0.964380i | \(-0.585214\pi\) | ||||
−0.264522 | + | 0.964380i | \(0.585214\pi\) | |||||||
\(614\) | 43985.1 | 2.89103 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 5333.22 | 0.348834 | ||||||||
\(617\) | −20795.5 | −1.35688 | −0.678440 | − | 0.734655i | \(-0.737344\pi\) | ||||
−0.678440 | + | 0.734655i | \(0.737344\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 1677.43 | 0.108920 | 0.0544602 | − | 0.998516i | \(-0.482656\pi\) | ||||
0.0544602 | + | 0.998516i | \(0.482656\pi\) | |||||||
\(620\) | 15932.5 | 1.03204 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 24795.8 | 1.59842 | ||||||||
\(623\) | −31446.6 | −2.02228 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 625.000 | 0.0400000 | ||||||||
\(626\) | −44823.0 | −2.86180 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −13269.4 | −0.843165 | ||||||||
\(629\) | 4771.11 | 0.302443 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −25225.2 | −1.59144 | −0.795719 | − | 0.605666i | \(-0.792907\pi\) | ||||
−0.795719 | + | 0.605666i | \(0.792907\pi\) | |||||||
\(632\) | 19526.8 | 1.22901 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −20004.8 | −1.25315 | ||||||||
\(635\) | 8008.15 | 0.500462 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1298.73 | −0.0807812 | ||||||||
\(638\) | 1590.41 | 0.0986912 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −11964.6 | −0.738971 | ||||||||
\(641\) | −15165.3 | −0.934468 | −0.467234 | − | 0.884134i | \(-0.654749\pi\) | ||||
−0.467234 | + | 0.884134i | \(0.654749\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 27156.1 | 1.66553 | 0.832763 | − | 0.553630i | \(-0.186758\pi\) | ||||
0.832763 | + | 0.553630i | \(0.186758\pi\) | |||||||
\(644\) | 3696.85 | 0.226206 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 20464.3 | 1.24637 | ||||||||
\(647\) | −29154.9 | −1.77156 | −0.885778 | − | 0.464110i | \(-0.846374\pi\) | ||||
−0.885778 | + | 0.464110i | \(0.846374\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 1204.26 | 0.0728374 | ||||||||
\(650\) | 1798.71 | 0.108540 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −36930.2 | −2.21825 | ||||||||
\(653\) | 19141.7 | 1.14713 | 0.573564 | − | 0.819161i | \(-0.305560\pi\) | ||||
0.573564 | + | 0.819161i | \(0.305560\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 10020.7 | 0.597770 | ||||||||
\(656\) | 331.768 | 0.0197460 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −49267.2 | −2.91890 | ||||||||
\(659\) | 24939.6 | 1.47422 | 0.737110 | − | 0.675773i | \(-0.236190\pi\) | ||||
0.737110 | + | 0.675773i | \(0.236190\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 22617.7 | 1.33090 | 0.665452 | − | 0.746440i | \(-0.268239\pi\) | ||||
0.665452 | + | 0.746440i | \(0.268239\pi\) | |||||||
\(662\) | −24755.4 | −1.45339 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 32633.7 | 1.90728 | ||||||||
\(665\) | −6299.99 | −0.367373 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 429.843 | 0.0249529 | ||||||||
\(668\) | −45224.3 | −2.61943 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 11221.7 | 0.647062 | ||||||||
\(671\) | 985.772 | 0.0567143 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −13855.8 | −0.793615 | −0.396807 | − | 0.917902i | \(-0.629882\pi\) | ||||
−0.396807 | + | 0.917902i | \(0.629882\pi\) | |||||||
\(674\) | 20678.1 | 1.18174 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −25593.5 | −1.45616 | ||||||||
\(677\) | 24992.8 | 1.41884 | 0.709419 | − | 0.704787i | \(-0.248957\pi\) | ||||
0.709419 | + | 0.704787i | \(0.248957\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −8804.57 | −0.497626 | ||||||||
\(680\) | −8568.84 | −0.483235 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −12282.5 | −0.689619 | ||||||||
\(683\) | 14420.5 | 0.807887 | 0.403943 | − | 0.914784i | \(-0.367639\pi\) | ||||
0.403943 | + | 0.914784i | \(0.367639\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −8364.25 | −0.466543 | ||||||||
\(686\) | 24661.4 | 1.37256 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −370.280 | −0.0205186 | ||||||||
\(689\) | −8497.42 | −0.469849 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 30552.4 | 1.68201 | 0.841005 | − | 0.541027i | \(-0.181964\pi\) | ||||
0.841005 | + | 0.541027i | \(0.181964\pi\) | |||||||
\(692\) | 29999.9 | 1.64801 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 27138.7 | 1.48440 | ||||||||
\(695\) | −12701.9 | −0.693253 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −7957.96 | −0.432467 | ||||||||
\(698\) | −16708.1 | −0.906032 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 6765.61 | 0.365309 | ||||||||
\(701\) | 9151.47 | 0.493076 | 0.246538 | − | 0.969133i | \(-0.420707\pi\) | ||||
0.246538 | + | 0.969133i | \(0.420707\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −3992.86 | −0.214216 | ||||||||
\(704\) | 9060.30 | 0.485047 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 966.793 | 0.0515378 | ||||||||
\(707\) | −1530.10 | −0.0813937 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −6261.96 | −0.331697 | −0.165848 | − | 0.986151i | \(-0.553036\pi\) | ||||
−0.165848 | + | 0.986151i | \(0.553036\pi\) | |||||||
\(710\) | −19239.2 | −1.01695 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 35794.9 | 1.88409 | ||||||||
\(713\) | −3319.60 | −0.174362 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −861.214 | −0.0450456 | ||||||||
\(716\) | −42603.9 | −2.22372 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 11485.7 | 0.596995 | ||||||||
\(719\) | 18228.7 | 0.945500 | 0.472750 | − | 0.881197i | \(-0.343261\pi\) | ||||
0.472750 | + | 0.881197i | \(0.343261\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −1432.13 | −0.0739740 | ||||||||
\(722\) | 14389.9 | 0.741740 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 15347.7 | 0.787836 | ||||||||
\(725\) | 786.656 | 0.0402975 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −7233.66 | −0.369026 | −0.184513 | − | 0.982830i | \(-0.559071\pi\) | ||||
−0.184513 | + | 0.982830i | \(0.559071\pi\) | |||||||
\(728\) | 7591.81 | 0.386499 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 8068.93 | 0.409102 | ||||||||
\(731\) | 8881.73 | 0.449388 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −13444.8 | −0.677485 | −0.338743 | − | 0.940879i | \(-0.610002\pi\) | ||||
−0.338743 | + | 0.940879i | \(0.610002\pi\) | |||||||
\(734\) | −26414.4 | −1.32830 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 2376.41 | 0.119016 | ||||||||
\(737\) | −5372.90 | −0.268539 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 18490.9 | 0.920432 | 0.460216 | − | 0.887807i | \(-0.347772\pi\) | ||||
0.460216 | + | 0.887807i | \(0.347772\pi\) | |||||||
\(740\) | 4287.97 | 0.213012 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −51461.8 | −2.54612 | ||||||||
\(743\) | 25160.9 | 1.24235 | 0.621173 | − | 0.783674i | \(-0.286657\pi\) | ||||
0.621173 | + | 0.783674i | \(0.286657\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 15453.4 | 0.759957 | ||||||||
\(746\) | −20528.8 | −1.00752 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 10522.4 | 0.514354 | ||||||||
\(749\) | −23562.9 | −1.14949 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −13419.5 | −0.652045 | −0.326023 | − | 0.945362i | \(-0.605709\pi\) | ||||
−0.326023 | + | 0.945362i | \(0.605709\pi\) | |||||||
\(752\) | 1580.06 | 0.0766207 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 2263.94 | 0.109347 | ||||||||
\(755\) | −6793.68 | −0.327480 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −7014.90 | −0.336804 | −0.168402 | − | 0.985718i | \(-0.553861\pi\) | ||||
−0.168402 | + | 0.985718i | \(0.553861\pi\) | |||||||
\(758\) | −35858.6 | −1.71826 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 7171.12 | 0.342268 | ||||||||
\(761\) | 30156.9 | 1.43651 | 0.718256 | − | 0.695779i | \(-0.244941\pi\) | ||||
0.718256 | + | 0.695779i | \(0.244941\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −45958.4 | −2.18061 | ||||||||
\(764\) | 36195.7 | 1.71402 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −51283.5 | −2.41899 | ||||||||
\(767\) | 1714.26 | 0.0807019 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 11292.2 | 0.529530 | 0.264765 | − | 0.964313i | \(-0.414706\pi\) | ||||
0.264765 | + | 0.964313i | \(0.414706\pi\) | |||||||
\(770\) | −5215.66 | −0.244103 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −16398.9 | −0.764519 | ||||||||
\(773\) | −8524.10 | −0.396624 | −0.198312 | − | 0.980139i | \(-0.563546\pi\) | ||||
−0.198312 | + | 0.980139i | \(0.563546\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −6075.21 | −0.281584 | ||||||||
\(776\) | 10022.0 | 0.463621 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 39011.4 | 1.79772 | ||||||||
\(779\) | 6659.89 | 0.306310 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 9211.66 | 0.422047 | ||||||||
\(782\) | 4578.96 | 0.209390 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 252.251 | 0.0114910 | ||||||||
\(785\) | 5059.76 | 0.230052 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −14983.9 | −0.678676 | −0.339338 | − | 0.940665i | \(-0.610203\pi\) | ||||
−0.339338 | + | 0.940665i | \(0.610203\pi\) | |||||||
\(788\) | 1888.10 | 0.0853565 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −19096.3 | −0.860022 | ||||||||
\(791\) | 35493.0 | 1.59543 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1403.24 | 0.0628380 | ||||||||
\(794\) | −27659.9 | −1.23629 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 9982.04 | 0.444477 | ||||||||
\(797\) | −37172.3 | −1.65208 | −0.826041 | − | 0.563610i | \(-0.809412\pi\) | ||||
−0.826041 | + | 0.563610i | \(0.809412\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −37900.1 | −1.67811 | ||||||||
\(800\) | 4349.06 | 0.192203 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −47781.0 | −2.10375 | ||||||||
\(803\) | −3863.37 | −0.169783 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −1409.65 | −0.0617186 | ||||||||
\(806\) | −17484.0 | −0.764080 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 1741.68 | 0.0758316 | ||||||||
\(809\) | −23797.1 | −1.03419 | −0.517096 | − | 0.855928i | \(-0.672987\pi\) | ||||
−0.517096 | + | 0.855928i | \(0.672987\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 8988.35 | 0.389178 | 0.194589 | − | 0.980885i | \(-0.437663\pi\) | ||||
0.194589 | + | 0.980885i | \(0.437663\pi\) | |||||||
\(812\) | 8515.54 | 0.368026 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −3305.63 | −0.142337 | ||||||||
\(815\) | 14081.8 | 0.605234 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −7432.98 | −0.318295 | ||||||||
\(818\) | 21750.6 | 0.929696 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −7152.11 | −0.304589 | ||||||||
\(821\) | 25156.8 | 1.06940 | 0.534702 | − | 0.845041i | \(-0.320424\pi\) | ||||
0.534702 | + | 0.845041i | \(0.320424\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 1318.51 | 0.0558447 | 0.0279224 | − | 0.999610i | \(-0.491111\pi\) | ||||
0.0279224 | + | 0.999610i | \(0.491111\pi\) | |||||||
\(824\) | 1630.16 | 0.0689189 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 10381.9 | 0.437326 | ||||||||
\(827\) | −124.982 | −0.00525519 | −0.00262760 | − | 0.999997i | \(-0.500836\pi\) | ||||
−0.00262760 | + | 0.999997i | \(0.500836\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −8886.80 | −0.372318 | −0.186159 | − | 0.982520i | \(-0.559604\pi\) | ||||
−0.186159 | + | 0.982520i | \(0.559604\pi\) | |||||||
\(830\) | −31914.3 | −1.33465 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 12897.3 | 0.537419 | ||||||||
\(833\) | −6050.63 | −0.251671 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 17244.5 | 0.714694 | ||||||||
\(836\) | −8806.02 | −0.364309 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −37299.1 | −1.53756 | ||||||||
\(839\) | −2995.21 | −0.123249 | −0.0616247 | − | 0.998099i | \(-0.519628\pi\) | ||||
−0.0616247 | + | 0.998099i | \(0.519628\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −23398.9 | −0.959403 | ||||||||
\(842\) | 43578.8 | 1.78364 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 52143.6 | 2.12661 | ||||||||
\(845\) | 9759.07 | 0.397304 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 2497.24 | 0.101306 | ||||||||
\(848\) | 1650.44 | 0.0668355 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 8379.95 | 0.338153 | ||||||||
\(851\) | −893.418 | −0.0359882 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 18130.5 | 0.727757 | 0.363878 | − | 0.931446i | \(-0.381452\pi\) | ||||
0.363878 | + | 0.931446i | \(0.381452\pi\) | |||||||
\(854\) | 8498.27 | 0.340521 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 26821.1 | 1.07094 | ||||||||
\(857\) | −26394.1 | −1.05205 | −0.526024 | − | 0.850470i | \(-0.676318\pi\) | ||||
−0.526024 | + | 0.850470i | \(0.676318\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −29456.2 | −1.17000 | −0.585002 | − | 0.811032i | \(-0.698906\pi\) | ||||
−0.585002 | + | 0.811032i | \(0.698906\pi\) | |||||||
\(860\) | 7982.34 | 0.316506 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 42893.7 | 1.69486 | ||||||||
\(863\) | 762.616 | 0.0300808 | 0.0150404 | − | 0.999887i | \(-0.495212\pi\) | ||||
0.0150404 | + | 0.999887i | \(0.495212\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −11439.3 | −0.449649 | ||||||||
\(866\) | 13706.6 | 0.537838 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −65764.0 | −2.57163 | ||||||||
\(869\) | 9143.26 | 0.356920 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −7648.29 | −0.297535 | ||||||||
\(872\) | 52313.3 | 2.03160 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −3832.06 | −0.148308 | ||||||||
\(875\) | −2579.79 | −0.0996719 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 44767.2 | 1.72369 | 0.861847 | − | 0.507168i | \(-0.169308\pi\) | ||||
0.861847 | + | 0.507168i | \(0.169308\pi\) | |||||||
\(878\) | 24041.8 | 0.924112 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 167.273 | 0.00640768 | ||||||||
\(881\) | 32057.9 | 1.22595 | 0.612973 | − | 0.790104i | \(-0.289973\pi\) | ||||
0.612973 | + | 0.790104i | \(0.289973\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 7078.95 | 0.269791 | 0.134896 | − | 0.990860i | \(-0.456930\pi\) | ||||
0.134896 | + | 0.990860i | \(0.456930\pi\) | |||||||
\(884\) | 14978.6 | 0.569891 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 34542.8 | 1.30981 | ||||||||
\(887\) | 25148.1 | 0.951964 | 0.475982 | − | 0.879455i | \(-0.342093\pi\) | ||||
0.475982 | + | 0.879455i | \(0.342093\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −33055.0 | −1.24705 | ||||||||
\(890\) | −35005.9 | −1.31843 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 11907.4 | 0.446963 | ||||||||
\(893\) | 31718.0 | 1.18858 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 16245.3 | 0.606726 | ||||||||
\(896\) | 49385.8 | 1.84137 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 73843.6 | 2.74409 | ||||||||
\(899\) | −7646.56 | −0.283679 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −39588.4 | −1.46380 | ||||||||
\(902\) | 5513.62 | 0.203529 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −40400.8 | −1.48641 | ||||||||
\(905\) | −5852.23 | −0.214955 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 1269.76 | 0.0464848 | 0.0232424 | − | 0.999730i | \(-0.492601\pi\) | ||||
0.0232424 | + | 0.999730i | \(0.492601\pi\) | |||||||
\(908\) | 27040.4 | 0.988289 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −7424.47 | −0.270460 | ||||||||
\(911\) | 33783.1 | 1.22863 | 0.614316 | − | 0.789060i | \(-0.289432\pi\) | ||||
0.614316 | + | 0.789060i | \(0.289432\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 15280.5 | 0.553899 | ||||||||
\(914\) | −44655.1 | −1.61604 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 53466.6 | 1.92859 | ||||||||
\(917\) | −41361.9 | −1.48952 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 39262.5 | 1.40930 | 0.704652 | − | 0.709553i | \(-0.251103\pi\) | ||||
0.704652 | + | 0.709553i | \(0.251103\pi\) | |||||||
\(920\) | 1604.57 | 0.0575010 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −66800.1 | −2.38606 | ||||||||
\(923\) | 13112.7 | 0.467618 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −1635.04 | −0.0581189 | ||||||||
\(926\) | 45848.3 | 1.62707 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 5473.95 | 0.193633 | ||||||||
\(929\) | 21175.0 | 0.747825 | 0.373913 | − | 0.927464i | \(-0.378016\pi\) | ||||
0.373913 | + | 0.927464i | \(0.378016\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 5063.68 | 0.178255 | ||||||||
\(932\) | −22065.5 | −0.775515 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 69787.5 | 2.44488 | ||||||||
\(935\) | −4012.29 | −0.140338 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −5135.11 | −0.179036 | −0.0895180 | − | 0.995985i | \(-0.528533\pi\) | ||||
−0.0895180 | + | 0.995985i | \(0.528533\pi\) | |||||||
\(938\) | −46319.4 | −1.61235 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −34062.2 | −1.18190 | ||||||||
\(941\) | 9702.77 | 0.336133 | 0.168067 | − | 0.985776i | \(-0.446248\pi\) | ||||
0.168067 | + | 0.985776i | \(0.446248\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 1490.18 | 0.0514600 | ||||||||
\(944\) | −332.959 | −0.0114798 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −6153.65 | −0.211493 | ||||||||
\(947\) | 699.579 | 0.0240055 | 0.0120028 | − | 0.999928i | \(-0.496179\pi\) | ||||
0.0120028 | + | 0.999928i | \(0.496179\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −5499.49 | −0.188115 | ||||||||
\(950\) | −7013.05 | −0.239509 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 35369.3 | 1.20412 | ||||||||
\(953\) | −42039.3 | −1.42895 | −0.714473 | − | 0.699663i | \(-0.753333\pi\) | ||||
−0.714473 | + | 0.699663i | \(0.753333\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −13801.8 | −0.467659 | ||||||||
\(956\) | −52778.1 | −1.78553 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 52063.4 | 1.75584 | ||||||||
\(959\) | 34524.9 | 1.16253 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 29262.0 | 0.982243 | ||||||||
\(962\) | −4705.55 | −0.157706 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −36509.3 | −1.21980 | ||||||||
\(965\) | 6253.05 | 0.208594 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −32794.8 | −1.09060 | −0.545299 | − | 0.838242i | \(-0.683584\pi\) | ||||
−0.545299 | + | 0.838242i | \(0.683584\pi\) | |||||||
\(968\) | −2842.55 | −0.0943832 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −9801.10 | −0.324427 | ||||||||
\(971\) | 3322.53 | 0.109810 | 0.0549048 | − | 0.998492i | \(-0.482514\pi\) | ||||
0.0549048 | + | 0.998492i | \(0.482514\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 52429.3 | 1.72745 | ||||||||
\(974\) | −87701.4 | −2.88515 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −272.550 | −0.00893864 | ||||||||
\(977\) | −22192.5 | −0.726716 | −0.363358 | − | 0.931650i | \(-0.618370\pi\) | ||||
−0.363358 | + | 0.931650i | \(0.618370\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 16760.7 | 0.547164 | ||||||||
\(980\) | −5437.92 | −0.177253 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −37277.4 | −1.21137 | ||||||||
\(983\) | −7383.09 | −0.239556 | −0.119778 | − | 0.992801i | \(-0.538218\pi\) | ||||
−0.119778 | + | 0.992801i | \(0.538218\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −719.953 | −0.0232889 | ||||||||
\(986\) | 10547.4 | 0.340668 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −12535.3 | −0.403645 | ||||||||
\(989\) | −1663.16 | −0.0534735 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 46260.8 | 1.48287 | 0.741434 | − | 0.671026i | \(-0.234146\pi\) | ||||
0.741434 | + | 0.671026i | \(0.234146\pi\) | |||||||
\(992\) | −42274.3 | −1.35304 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 79413.1 | 2.53403 | ||||||||
\(995\) | −3806.25 | −0.121273 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 41196.8 | 1.30864 | 0.654320 | − | 0.756217i | \(-0.272955\pi\) | ||||
0.654320 | + | 0.756217i | \(0.272955\pi\) | |||||||
\(998\) | −84219.5 | −2.67127 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 495.4.a.i.1.1 | 3 | ||
3.2 | odd | 2 | 165.4.a.g.1.3 | ✓ | 3 | ||
5.4 | even | 2 | 2475.4.a.z.1.3 | 3 | |||
15.2 | even | 4 | 825.4.c.m.199.6 | 6 | |||
15.8 | even | 4 | 825.4.c.m.199.1 | 6 | |||
15.14 | odd | 2 | 825.4.a.p.1.1 | 3 | |||
33.32 | even | 2 | 1815.4.a.q.1.1 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
165.4.a.g.1.3 | ✓ | 3 | 3.2 | odd | 2 | ||
495.4.a.i.1.1 | 3 | 1.1 | even | 1 | trivial | ||
825.4.a.p.1.1 | 3 | 15.14 | odd | 2 | |||
825.4.c.m.199.1 | 6 | 15.8 | even | 4 | |||
825.4.c.m.199.6 | 6 | 15.2 | even | 4 | |||
1815.4.a.q.1.1 | 3 | 33.32 | even | 2 | |||
2475.4.a.z.1.3 | 3 | 5.4 | even | 2 |