Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1150,4,Mod(1,1150)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1150, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1150.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1150 = 2 \cdot 5^{2} \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1150.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: | \(67.8521965066\) |
Analytic rank: | \(1\) |
Dimension: | \(1\) |
Coefficient field: | \(\mathbb{Q}\) |
Coefficient ring: | \(\mathbb{Z}\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 230) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Character | \(\chi\) | \(=\) | 1150.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.00000 | −0.707107 | ||||||||
\(3\) | −1.00000 | −0.192450 | −0.0962250 | − | 0.995360i | \(-0.530677\pi\) | ||||
−0.0962250 | + | 0.995360i | \(0.530677\pi\) | |||||||
\(4\) | 4.00000 | 0.500000 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 2.00000 | 0.136083 | ||||||||
\(7\) | 18.0000 | 0.971909 | 0.485954 | − | 0.873984i | \(-0.338472\pi\) | ||||
0.485954 | + | 0.873984i | \(0.338472\pi\) | |||||||
\(8\) | −8.00000 | −0.353553 | ||||||||
\(9\) | −26.0000 | −0.962963 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −32.0000 | −0.877124 | −0.438562 | − | 0.898701i | \(-0.644512\pi\) | ||||
−0.438562 | + | 0.898701i | \(0.644512\pi\) | |||||||
\(12\) | −4.00000 | −0.0962250 | ||||||||
\(13\) | 47.0000 | 1.00273 | 0.501364 | − | 0.865237i | \(-0.332832\pi\) | ||||
0.501364 | + | 0.865237i | \(0.332832\pi\) | |||||||
\(14\) | −36.0000 | −0.687243 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 16.0000 | 0.250000 | ||||||||
\(17\) | −20.0000 | −0.285336 | −0.142668 | − | 0.989771i | \(-0.545568\pi\) | ||||
−0.142668 | + | 0.989771i | \(0.545568\pi\) | |||||||
\(18\) | 52.0000 | 0.680918 | ||||||||
\(19\) | 36.0000 | 0.434682 | 0.217341 | − | 0.976096i | \(-0.430262\pi\) | ||||
0.217341 | + | 0.976096i | \(0.430262\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −18.0000 | −0.187044 | ||||||||
\(22\) | 64.0000 | 0.620220 | ||||||||
\(23\) | 23.0000 | 0.208514 | ||||||||
\(24\) | 8.00000 | 0.0680414 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −94.0000 | −0.709035 | ||||||||
\(27\) | 53.0000 | 0.377772 | ||||||||
\(28\) | 72.0000 | 0.485954 | ||||||||
\(29\) | −27.0000 | −0.172889 | −0.0864444 | − | 0.996257i | \(-0.527550\pi\) | ||||
−0.0864444 | + | 0.996257i | \(0.527550\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −33.0000 | −0.191193 | −0.0955964 | − | 0.995420i | \(-0.530476\pi\) | ||||
−0.0955964 | + | 0.995420i | \(0.530476\pi\) | |||||||
\(32\) | −32.0000 | −0.176777 | ||||||||
\(33\) | 32.0000 | 0.168803 | ||||||||
\(34\) | 40.0000 | 0.201763 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −104.000 | −0.481481 | ||||||||
\(37\) | −56.0000 | −0.248820 | −0.124410 | − | 0.992231i | \(-0.539704\pi\) | ||||
−0.124410 | + | 0.992231i | \(0.539704\pi\) | |||||||
\(38\) | −72.0000 | −0.307367 | ||||||||
\(39\) | −47.0000 | −0.192975 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −157.000 | −0.598031 | −0.299016 | − | 0.954248i | \(-0.596658\pi\) | ||||
−0.299016 | + | 0.954248i | \(0.596658\pi\) | |||||||
\(42\) | 36.0000 | 0.132260 | ||||||||
\(43\) | −18.0000 | −0.0638366 | −0.0319183 | − | 0.999490i | \(-0.510162\pi\) | ||||
−0.0319183 | + | 0.999490i | \(0.510162\pi\) | |||||||
\(44\) | −128.000 | −0.438562 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −46.0000 | −0.147442 | ||||||||
\(47\) | −65.0000 | −0.201728 | −0.100864 | − | 0.994900i | \(-0.532161\pi\) | ||||
−0.100864 | + | 0.994900i | \(0.532161\pi\) | |||||||
\(48\) | −16.0000 | −0.0481125 | ||||||||
\(49\) | −19.0000 | −0.0553936 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 20.0000 | 0.0549129 | ||||||||
\(52\) | 188.000 | 0.501364 | ||||||||
\(53\) | 14.0000 | 0.0362839 | 0.0181420 | − | 0.999835i | \(-0.494225\pi\) | ||||
0.0181420 | + | 0.999835i | \(0.494225\pi\) | |||||||
\(54\) | −106.000 | −0.267125 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −144.000 | −0.343622 | ||||||||
\(57\) | −36.0000 | −0.0836547 | ||||||||
\(58\) | 54.0000 | 0.122251 | ||||||||
\(59\) | −744.000 | −1.64170 | −0.820852 | − | 0.571141i | \(-0.806501\pi\) | ||||
−0.820852 | + | 0.571141i | \(0.806501\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 552.000 | 1.15863 | 0.579314 | − | 0.815104i | \(-0.303320\pi\) | ||||
0.579314 | + | 0.815104i | \(0.303320\pi\) | |||||||
\(62\) | 66.0000 | 0.135194 | ||||||||
\(63\) | −468.000 | −0.935912 | ||||||||
\(64\) | 64.0000 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −64.0000 | −0.119361 | ||||||||
\(67\) | 156.000 | 0.284454 | 0.142227 | − | 0.989834i | \(-0.454574\pi\) | ||||
0.142227 | + | 0.989834i | \(0.454574\pi\) | |||||||
\(68\) | −80.0000 | −0.142668 | ||||||||
\(69\) | −23.0000 | −0.0401286 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 699.000 | 1.16839 | 0.584197 | − | 0.811612i | \(-0.301409\pi\) | ||||
0.584197 | + | 0.811612i | \(0.301409\pi\) | |||||||
\(72\) | 208.000 | 0.340459 | ||||||||
\(73\) | 609.000 | 0.976412 | 0.488206 | − | 0.872728i | \(-0.337652\pi\) | ||||
0.488206 | + | 0.872728i | \(0.337652\pi\) | |||||||
\(74\) | 112.000 | 0.175942 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 144.000 | 0.217341 | ||||||||
\(77\) | −576.000 | −0.852484 | ||||||||
\(78\) | 94.0000 | 0.136454 | ||||||||
\(79\) | −644.000 | −0.917160 | −0.458580 | − | 0.888653i | \(-0.651642\pi\) | ||||
−0.458580 | + | 0.888653i | \(0.651642\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 649.000 | 0.890261 | ||||||||
\(82\) | 314.000 | 0.422872 | ||||||||
\(83\) | −512.000 | −0.677100 | −0.338550 | − | 0.940948i | \(-0.609936\pi\) | ||||
−0.338550 | + | 0.940948i | \(0.609936\pi\) | |||||||
\(84\) | −72.0000 | −0.0935220 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 36.0000 | 0.0451393 | ||||||||
\(87\) | 27.0000 | 0.0332725 | ||||||||
\(88\) | 256.000 | 0.310110 | ||||||||
\(89\) | −102.000 | −0.121483 | −0.0607415 | − | 0.998154i | \(-0.519347\pi\) | ||||
−0.0607415 | + | 0.998154i | \(0.519347\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 846.000 | 0.974559 | ||||||||
\(92\) | 92.0000 | 0.104257 | ||||||||
\(93\) | 33.0000 | 0.0367951 | ||||||||
\(94\) | 130.000 | 0.142643 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 32.0000 | 0.0340207 | ||||||||
\(97\) | −578.000 | −0.605021 | −0.302510 | − | 0.953146i | \(-0.597825\pi\) | ||||
−0.302510 | + | 0.953146i | \(0.597825\pi\) | |||||||
\(98\) | 38.0000 | 0.0391692 | ||||||||
\(99\) | 832.000 | 0.844638 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −6.00000 | −0.00591111 | −0.00295556 | − | 0.999996i | \(-0.500941\pi\) | ||||
−0.00295556 | + | 0.999996i | \(0.500941\pi\) | |||||||
\(102\) | −40.0000 | −0.0388293 | ||||||||
\(103\) | 160.000 | 0.153061 | 0.0765304 | − | 0.997067i | \(-0.475616\pi\) | ||||
0.0765304 | + | 0.997067i | \(0.475616\pi\) | |||||||
\(104\) | −376.000 | −0.354518 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −28.0000 | −0.0256566 | ||||||||
\(107\) | −380.000 | −0.343327 | −0.171663 | − | 0.985156i | \(-0.554914\pi\) | ||||
−0.171663 | + | 0.985156i | \(0.554914\pi\) | |||||||
\(108\) | 212.000 | 0.188886 | ||||||||
\(109\) | 250.000 | 0.219685 | 0.109842 | − | 0.993949i | \(-0.464965\pi\) | ||||
0.109842 | + | 0.993949i | \(0.464965\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 56.0000 | 0.0478854 | ||||||||
\(112\) | 288.000 | 0.242977 | ||||||||
\(113\) | 390.000 | 0.324674 | 0.162337 | − | 0.986735i | \(-0.448097\pi\) | ||||
0.162337 | + | 0.986735i | \(0.448097\pi\) | |||||||
\(114\) | 72.0000 | 0.0591528 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −108.000 | −0.0864444 | ||||||||
\(117\) | −1222.00 | −0.965589 | ||||||||
\(118\) | 1488.00 | 1.16086 | ||||||||
\(119\) | −360.000 | −0.277321 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −307.000 | −0.230654 | ||||||||
\(122\) | −1104.00 | −0.819274 | ||||||||
\(123\) | 157.000 | 0.115091 | ||||||||
\(124\) | −132.000 | −0.0955964 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 936.000 | 0.661790 | ||||||||
\(127\) | 769.000 | 0.537305 | 0.268652 | − | 0.963237i | \(-0.413422\pi\) | ||||
0.268652 | + | 0.963237i | \(0.413422\pi\) | |||||||
\(128\) | −128.000 | −0.0883883 | ||||||||
\(129\) | 18.0000 | 0.0122854 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −213.000 | −0.142060 | −0.0710301 | − | 0.997474i | \(-0.522629\pi\) | ||||
−0.0710301 | + | 0.997474i | \(0.522629\pi\) | |||||||
\(132\) | 128.000 | 0.0844013 | ||||||||
\(133\) | 648.000 | 0.422472 | ||||||||
\(134\) | −312.000 | −0.201140 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 160.000 | 0.100882 | ||||||||
\(137\) | −2836.00 | −1.76858 | −0.884291 | − | 0.466936i | \(-0.845358\pi\) | ||||
−0.884291 | + | 0.466936i | \(0.845358\pi\) | |||||||
\(138\) | 46.0000 | 0.0283752 | ||||||||
\(139\) | −1631.00 | −0.995249 | −0.497625 | − | 0.867393i | \(-0.665794\pi\) | ||||
−0.497625 | + | 0.867393i | \(0.665794\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 65.0000 | 0.0388226 | ||||||||
\(142\) | −1398.00 | −0.826180 | ||||||||
\(143\) | −1504.00 | −0.879516 | ||||||||
\(144\) | −416.000 | −0.240741 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −1218.00 | −0.690427 | ||||||||
\(147\) | 19.0000 | 0.0106605 | ||||||||
\(148\) | −224.000 | −0.124410 | ||||||||
\(149\) | −1966.00 | −1.08095 | −0.540473 | − | 0.841361i | \(-0.681755\pi\) | ||||
−0.540473 | + | 0.841361i | \(0.681755\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 35.0000 | 0.0188626 | 0.00943132 | − | 0.999956i | \(-0.496998\pi\) | ||||
0.00943132 | + | 0.999956i | \(0.496998\pi\) | |||||||
\(152\) | −288.000 | −0.153683 | ||||||||
\(153\) | 520.000 | 0.274768 | ||||||||
\(154\) | 1152.00 | 0.602797 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −188.000 | −0.0964875 | ||||||||
\(157\) | −1702.00 | −0.865187 | −0.432594 | − | 0.901589i | \(-0.642401\pi\) | ||||
−0.432594 | + | 0.901589i | \(0.642401\pi\) | |||||||
\(158\) | 1288.00 | 0.648530 | ||||||||
\(159\) | −14.0000 | −0.00698284 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 414.000 | 0.202657 | ||||||||
\(162\) | −1298.00 | −0.629509 | ||||||||
\(163\) | 2045.00 | 0.982680 | 0.491340 | − | 0.870968i | \(-0.336507\pi\) | ||||
0.491340 | + | 0.870968i | \(0.336507\pi\) | |||||||
\(164\) | −628.000 | −0.299016 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 1024.00 | 0.478782 | ||||||||
\(167\) | −1016.00 | −0.470781 | −0.235391 | − | 0.971901i | \(-0.575637\pi\) | ||||
−0.235391 | + | 0.971901i | \(0.575637\pi\) | |||||||
\(168\) | 144.000 | 0.0661300 | ||||||||
\(169\) | 12.0000 | 0.00546199 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −936.000 | −0.418583 | ||||||||
\(172\) | −72.0000 | −0.0319183 | ||||||||
\(173\) | −598.000 | −0.262804 | −0.131402 | − | 0.991329i | \(-0.541948\pi\) | ||||
−0.131402 | + | 0.991329i | \(0.541948\pi\) | |||||||
\(174\) | −54.0000 | −0.0235272 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −512.000 | −0.219281 | ||||||||
\(177\) | 744.000 | 0.315946 | ||||||||
\(178\) | 204.000 | 0.0859014 | ||||||||
\(179\) | −4607.00 | −1.92371 | −0.961853 | − | 0.273567i | \(-0.911796\pi\) | ||||
−0.961853 | + | 0.273567i | \(0.911796\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −1212.00 | −0.497720 | −0.248860 | − | 0.968540i | \(-0.580056\pi\) | ||||
−0.248860 | + | 0.968540i | \(0.580056\pi\) | |||||||
\(182\) | −1692.00 | −0.689117 | ||||||||
\(183\) | −552.000 | −0.222978 | ||||||||
\(184\) | −184.000 | −0.0737210 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −66.0000 | −0.0260180 | ||||||||
\(187\) | 640.000 | 0.250275 | ||||||||
\(188\) | −260.000 | −0.100864 | ||||||||
\(189\) | 954.000 | 0.367160 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −1058.00 | −0.400807 | −0.200404 | − | 0.979713i | \(-0.564225\pi\) | ||||
−0.200404 | + | 0.979713i | \(0.564225\pi\) | |||||||
\(192\) | −64.0000 | −0.0240563 | ||||||||
\(193\) | −1047.00 | −0.390491 | −0.195245 | − | 0.980754i | \(-0.562550\pi\) | ||||
−0.195245 | + | 0.980754i | \(0.562550\pi\) | |||||||
\(194\) | 1156.00 | 0.427814 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −76.0000 | −0.0276968 | ||||||||
\(197\) | −251.000 | −0.0907767 | −0.0453883 | − | 0.998969i | \(-0.514453\pi\) | ||||
−0.0453883 | + | 0.998969i | \(0.514453\pi\) | |||||||
\(198\) | −1664.00 | −0.597249 | ||||||||
\(199\) | −3508.00 | −1.24963 | −0.624813 | − | 0.780775i | \(-0.714825\pi\) | ||||
−0.624813 | + | 0.780775i | \(0.714825\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −156.000 | −0.0547432 | ||||||||
\(202\) | 12.0000 | 0.00417979 | ||||||||
\(203\) | −486.000 | −0.168032 | ||||||||
\(204\) | 80.0000 | 0.0274565 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −320.000 | −0.108230 | ||||||||
\(207\) | −598.000 | −0.200792 | ||||||||
\(208\) | 752.000 | 0.250682 | ||||||||
\(209\) | −1152.00 | −0.381270 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −3296.00 | −1.07538 | −0.537692 | − | 0.843141i | \(-0.680704\pi\) | ||||
−0.537692 | + | 0.843141i | \(0.680704\pi\) | |||||||
\(212\) | 56.0000 | 0.0181420 | ||||||||
\(213\) | −699.000 | −0.224858 | ||||||||
\(214\) | 760.000 | 0.242769 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −424.000 | −0.133563 | ||||||||
\(217\) | −594.000 | −0.185822 | ||||||||
\(218\) | −500.000 | −0.155341 | ||||||||
\(219\) | −609.000 | −0.187911 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −940.000 | −0.286114 | ||||||||
\(222\) | −112.000 | −0.0338601 | ||||||||
\(223\) | 2720.00 | 0.816792 | 0.408396 | − | 0.912805i | \(-0.366088\pi\) | ||||
0.408396 | + | 0.912805i | \(0.366088\pi\) | |||||||
\(224\) | −576.000 | −0.171811 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −780.000 | −0.229579 | ||||||||
\(227\) | 4134.00 | 1.20874 | 0.604368 | − | 0.796705i | \(-0.293426\pi\) | ||||
0.604368 | + | 0.796705i | \(0.293426\pi\) | |||||||
\(228\) | −144.000 | −0.0418273 | ||||||||
\(229\) | −4510.00 | −1.30144 | −0.650719 | − | 0.759319i | \(-0.725532\pi\) | ||||
−0.650719 | + | 0.759319i | \(0.725532\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 576.000 | 0.164061 | ||||||||
\(232\) | 216.000 | 0.0611254 | ||||||||
\(233\) | 5003.00 | 1.40668 | 0.703342 | − | 0.710852i | \(-0.251690\pi\) | ||||
0.703342 | + | 0.710852i | \(0.251690\pi\) | |||||||
\(234\) | 2444.00 | 0.682775 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −2976.00 | −0.820852 | ||||||||
\(237\) | 644.000 | 0.176508 | ||||||||
\(238\) | 720.000 | 0.196095 | ||||||||
\(239\) | −6309.00 | −1.70751 | −0.853756 | − | 0.520674i | \(-0.825681\pi\) | ||||
−0.853756 | + | 0.520674i | \(0.825681\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 3038.00 | 0.812012 | 0.406006 | − | 0.913871i | \(-0.366921\pi\) | ||||
0.406006 | + | 0.913871i | \(0.366921\pi\) | |||||||
\(242\) | 614.000 | 0.163097 | ||||||||
\(243\) | −2080.00 | −0.549103 | ||||||||
\(244\) | 2208.00 | 0.579314 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −314.000 | −0.0813817 | ||||||||
\(247\) | 1692.00 | 0.435868 | ||||||||
\(248\) | 264.000 | 0.0675968 | ||||||||
\(249\) | 512.000 | 0.130308 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −1332.00 | −0.334961 | −0.167480 | − | 0.985875i | \(-0.553563\pi\) | ||||
−0.167480 | + | 0.985875i | \(0.553563\pi\) | |||||||
\(252\) | −1872.00 | −0.467956 | ||||||||
\(253\) | −736.000 | −0.182893 | ||||||||
\(254\) | −1538.00 | −0.379932 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 256.000 | 0.0625000 | ||||||||
\(257\) | −3301.00 | −0.801209 | −0.400605 | − | 0.916251i | \(-0.631200\pi\) | ||||
−0.400605 | + | 0.916251i | \(0.631200\pi\) | |||||||
\(258\) | −36.0000 | −0.00868706 | ||||||||
\(259\) | −1008.00 | −0.241830 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 702.000 | 0.166485 | ||||||||
\(262\) | 426.000 | 0.100452 | ||||||||
\(263\) | −2072.00 | −0.485798 | −0.242899 | − | 0.970052i | \(-0.578098\pi\) | ||||
−0.242899 | + | 0.970052i | \(0.578098\pi\) | |||||||
\(264\) | −256.000 | −0.0596807 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −1296.00 | −0.298733 | ||||||||
\(267\) | 102.000 | 0.0233794 | ||||||||
\(268\) | 624.000 | 0.142227 | ||||||||
\(269\) | 5721.00 | 1.29671 | 0.648356 | − | 0.761337i | \(-0.275457\pi\) | ||||
0.648356 | + | 0.761337i | \(0.275457\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −5900.00 | −1.32251 | −0.661254 | − | 0.750162i | \(-0.729975\pi\) | ||||
−0.661254 | + | 0.750162i | \(0.729975\pi\) | |||||||
\(272\) | −320.000 | −0.0713340 | ||||||||
\(273\) | −846.000 | −0.187554 | ||||||||
\(274\) | 5672.00 | 1.25058 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −92.0000 | −0.0200643 | ||||||||
\(277\) | −6371.00 | −1.38194 | −0.690968 | − | 0.722885i | \(-0.742815\pi\) | ||||
−0.690968 | + | 0.722885i | \(0.742815\pi\) | |||||||
\(278\) | 3262.00 | 0.703747 | ||||||||
\(279\) | 858.000 | 0.184112 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 3190.00 | 0.677222 | 0.338611 | − | 0.940926i | \(-0.390043\pi\) | ||||
0.338611 | + | 0.940926i | \(0.390043\pi\) | |||||||
\(282\) | −130.000 | −0.0274517 | ||||||||
\(283\) | 4226.00 | 0.887667 | 0.443833 | − | 0.896109i | \(-0.353618\pi\) | ||||
0.443833 | + | 0.896109i | \(0.353618\pi\) | |||||||
\(284\) | 2796.00 | 0.584197 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 3008.00 | 0.621912 | ||||||||
\(287\) | −2826.00 | −0.581232 | ||||||||
\(288\) | 832.000 | 0.170229 | ||||||||
\(289\) | −4513.00 | −0.918583 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 578.000 | 0.116436 | ||||||||
\(292\) | 2436.00 | 0.488206 | ||||||||
\(293\) | −6048.00 | −1.20590 | −0.602949 | − | 0.797780i | \(-0.706008\pi\) | ||||
−0.602949 | + | 0.797780i | \(0.706008\pi\) | |||||||
\(294\) | −38.0000 | −0.00753811 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 448.000 | 0.0879712 | ||||||||
\(297\) | −1696.00 | −0.331353 | ||||||||
\(298\) | 3932.00 | 0.764344 | ||||||||
\(299\) | 1081.00 | 0.209083 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −324.000 | −0.0620434 | ||||||||
\(302\) | −70.0000 | −0.0133379 | ||||||||
\(303\) | 6.00000 | 0.00113759 | ||||||||
\(304\) | 576.000 | 0.108671 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −1040.00 | −0.194290 | ||||||||
\(307\) | −8628.00 | −1.60399 | −0.801997 | − | 0.597328i | \(-0.796229\pi\) | ||||
−0.801997 | + | 0.597328i | \(0.796229\pi\) | |||||||
\(308\) | −2304.00 | −0.426242 | ||||||||
\(309\) | −160.000 | −0.0294566 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 8247.00 | 1.50368 | 0.751840 | − | 0.659346i | \(-0.229167\pi\) | ||||
0.751840 | + | 0.659346i | \(0.229167\pi\) | |||||||
\(312\) | 376.000 | 0.0682269 | ||||||||
\(313\) | −2620.00 | −0.473135 | −0.236567 | − | 0.971615i | \(-0.576022\pi\) | ||||
−0.236567 | + | 0.971615i | \(0.576022\pi\) | |||||||
\(314\) | 3404.00 | 0.611780 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −2576.00 | −0.458580 | ||||||||
\(317\) | −9906.00 | −1.75513 | −0.877565 | − | 0.479457i | \(-0.840834\pi\) | ||||
−0.877565 | + | 0.479457i | \(0.840834\pi\) | |||||||
\(318\) | 28.0000 | 0.00493762 | ||||||||
\(319\) | 864.000 | 0.151645 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 380.000 | 0.0660733 | ||||||||
\(322\) | −828.000 | −0.143300 | ||||||||
\(323\) | −720.000 | −0.124031 | ||||||||
\(324\) | 2596.00 | 0.445130 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −4090.00 | −0.694859 | ||||||||
\(327\) | −250.000 | −0.0422784 | ||||||||
\(328\) | 1256.00 | 0.211436 | ||||||||
\(329\) | −1170.00 | −0.196061 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −8115.00 | −1.34756 | −0.673778 | − | 0.738934i | \(-0.735329\pi\) | ||||
−0.673778 | + | 0.738934i | \(0.735329\pi\) | |||||||
\(332\) | −2048.00 | −0.338550 | ||||||||
\(333\) | 1456.00 | 0.239605 | ||||||||
\(334\) | 2032.00 | 0.332892 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −288.000 | −0.0467610 | ||||||||
\(337\) | 7586.00 | 1.22622 | 0.613109 | − | 0.789998i | \(-0.289918\pi\) | ||||
0.613109 | + | 0.789998i | \(0.289918\pi\) | |||||||
\(338\) | −24.0000 | −0.00386221 | ||||||||
\(339\) | −390.000 | −0.0624835 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 1056.00 | 0.167700 | ||||||||
\(342\) | 1872.00 | 0.295983 | ||||||||
\(343\) | −6516.00 | −1.02575 | ||||||||
\(344\) | 144.000 | 0.0225697 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 1196.00 | 0.185831 | ||||||||
\(347\) | −1356.00 | −0.209781 | −0.104890 | − | 0.994484i | \(-0.533449\pi\) | ||||
−0.104890 | + | 0.994484i | \(0.533449\pi\) | |||||||
\(348\) | 108.000 | 0.0166362 | ||||||||
\(349\) | 6649.00 | 1.01981 | 0.509904 | − | 0.860231i | \(-0.329681\pi\) | ||||
0.509904 | + | 0.860231i | \(0.329681\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 2491.00 | 0.378803 | ||||||||
\(352\) | 1024.00 | 0.155055 | ||||||||
\(353\) | −10691.0 | −1.61197 | −0.805984 | − | 0.591938i | \(-0.798363\pi\) | ||||
−0.805984 | + | 0.591938i | \(0.798363\pi\) | |||||||
\(354\) | −1488.00 | −0.223408 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −408.000 | −0.0607415 | ||||||||
\(357\) | 360.000 | 0.0533704 | ||||||||
\(358\) | 9214.00 | 1.36027 | ||||||||
\(359\) | −6420.00 | −0.943829 | −0.471915 | − | 0.881644i | \(-0.656437\pi\) | ||||
−0.471915 | + | 0.881644i | \(0.656437\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −5563.00 | −0.811051 | ||||||||
\(362\) | 2424.00 | 0.351941 | ||||||||
\(363\) | 307.000 | 0.0443893 | ||||||||
\(364\) | 3384.00 | 0.487280 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 1104.00 | 0.157669 | ||||||||
\(367\) | 524.000 | 0.0745302 | 0.0372651 | − | 0.999305i | \(-0.488135\pi\) | ||||
0.0372651 | + | 0.999305i | \(0.488135\pi\) | |||||||
\(368\) | 368.000 | 0.0521286 | ||||||||
\(369\) | 4082.00 | 0.575882 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 252.000 | 0.0352647 | ||||||||
\(372\) | 132.000 | 0.0183975 | ||||||||
\(373\) | −5566.00 | −0.772645 | −0.386322 | − | 0.922364i | \(-0.626255\pi\) | ||||
−0.386322 | + | 0.922364i | \(0.626255\pi\) | |||||||
\(374\) | −1280.00 | −0.176971 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 520.000 | 0.0713217 | ||||||||
\(377\) | −1269.00 | −0.173360 | ||||||||
\(378\) | −1908.00 | −0.259622 | ||||||||
\(379\) | 2240.00 | 0.303591 | 0.151796 | − | 0.988412i | \(-0.451494\pi\) | ||||
0.151796 | + | 0.988412i | \(0.451494\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −769.000 | −0.103404 | ||||||||
\(382\) | 2116.00 | 0.283414 | ||||||||
\(383\) | −8778.00 | −1.17111 | −0.585555 | − | 0.810633i | \(-0.699123\pi\) | ||||
−0.585555 | + | 0.810633i | \(0.699123\pi\) | |||||||
\(384\) | 128.000 | 0.0170103 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 2094.00 | 0.276119 | ||||||||
\(387\) | 468.000 | 0.0614723 | ||||||||
\(388\) | −2312.00 | −0.302510 | ||||||||
\(389\) | 4056.00 | 0.528656 | 0.264328 | − | 0.964433i | \(-0.414850\pi\) | ||||
0.264328 | + | 0.964433i | \(0.414850\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −460.000 | −0.0594967 | ||||||||
\(392\) | 152.000 | 0.0195846 | ||||||||
\(393\) | 213.000 | 0.0273395 | ||||||||
\(394\) | 502.000 | 0.0641888 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 3328.00 | 0.422319 | ||||||||
\(397\) | 9151.00 | 1.15687 | 0.578433 | − | 0.815730i | \(-0.303665\pi\) | ||||
0.578433 | + | 0.815730i | \(0.303665\pi\) | |||||||
\(398\) | 7016.00 | 0.883619 | ||||||||
\(399\) | −648.000 | −0.0813047 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 15930.0 | 1.98381 | 0.991903 | − | 0.126997i | \(-0.0405340\pi\) | ||||
0.991903 | + | 0.126997i | \(0.0405340\pi\) | |||||||
\(402\) | 312.000 | 0.0387093 | ||||||||
\(403\) | −1551.00 | −0.191714 | ||||||||
\(404\) | −24.0000 | −0.00295556 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 972.000 | 0.118817 | ||||||||
\(407\) | 1792.00 | 0.218246 | ||||||||
\(408\) | −160.000 | −0.0194147 | ||||||||
\(409\) | −5891.00 | −0.712203 | −0.356102 | − | 0.934447i | \(-0.615894\pi\) | ||||
−0.356102 | + | 0.934447i | \(0.615894\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 2836.00 | 0.340364 | ||||||||
\(412\) | 640.000 | 0.0765304 | ||||||||
\(413\) | −13392.0 | −1.59559 | ||||||||
\(414\) | 1196.00 | 0.141981 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −1504.00 | −0.177259 | ||||||||
\(417\) | 1631.00 | 0.191536 | ||||||||
\(418\) | 2304.00 | 0.269599 | ||||||||
\(419\) | 15282.0 | 1.78180 | 0.890900 | − | 0.454199i | \(-0.150074\pi\) | ||||
0.890900 | + | 0.454199i | \(0.150074\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −10934.0 | −1.26577 | −0.632887 | − | 0.774244i | \(-0.718130\pi\) | ||||
−0.632887 | + | 0.774244i | \(0.718130\pi\) | |||||||
\(422\) | 6592.00 | 0.760411 | ||||||||
\(423\) | 1690.00 | 0.194257 | ||||||||
\(424\) | −112.000 | −0.0128283 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 1398.00 | 0.158998 | ||||||||
\(427\) | 9936.00 | 1.12608 | ||||||||
\(428\) | −1520.00 | −0.171663 | ||||||||
\(429\) | 1504.00 | 0.169263 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −2794.00 | −0.312256 | −0.156128 | − | 0.987737i | \(-0.549901\pi\) | ||||
−0.156128 | + | 0.987737i | \(0.549901\pi\) | |||||||
\(432\) | 848.000 | 0.0944431 | ||||||||
\(433\) | 15062.0 | 1.67167 | 0.835835 | − | 0.548980i | \(-0.184984\pi\) | ||||
0.835835 | + | 0.548980i | \(0.184984\pi\) | |||||||
\(434\) | 1188.00 | 0.131396 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 1000.00 | 0.109842 | ||||||||
\(437\) | 828.000 | 0.0906376 | ||||||||
\(438\) | 1218.00 | 0.132873 | ||||||||
\(439\) | 261.000 | 0.0283755 | 0.0141878 | − | 0.999899i | \(-0.495484\pi\) | ||||
0.0141878 | + | 0.999899i | \(0.495484\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 494.000 | 0.0533420 | ||||||||
\(442\) | 1880.00 | 0.202313 | ||||||||
\(443\) | 7083.00 | 0.759647 | 0.379823 | − | 0.925059i | \(-0.375985\pi\) | ||||
0.379823 | + | 0.925059i | \(0.375985\pi\) | |||||||
\(444\) | 224.000 | 0.0239427 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −5440.00 | −0.577559 | ||||||||
\(447\) | 1966.00 | 0.208028 | ||||||||
\(448\) | 1152.00 | 0.121489 | ||||||||
\(449\) | −10370.0 | −1.08996 | −0.544978 | − | 0.838450i | \(-0.683462\pi\) | ||||
−0.544978 | + | 0.838450i | \(0.683462\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 5024.00 | 0.524547 | ||||||||
\(452\) | 1560.00 | 0.162337 | ||||||||
\(453\) | −35.0000 | −0.00363012 | ||||||||
\(454\) | −8268.00 | −0.854706 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 288.000 | 0.0295764 | ||||||||
\(457\) | 10496.0 | 1.07436 | 0.537180 | − | 0.843468i | \(-0.319490\pi\) | ||||
0.537180 | + | 0.843468i | \(0.319490\pi\) | |||||||
\(458\) | 9020.00 | 0.920255 | ||||||||
\(459\) | −1060.00 | −0.107792 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 18021.0 | 1.82065 | 0.910327 | − | 0.413889i | \(-0.135830\pi\) | ||||
0.910327 | + | 0.413889i | \(0.135830\pi\) | |||||||
\(462\) | −1152.00 | −0.116008 | ||||||||
\(463\) | 17188.0 | 1.72526 | 0.862629 | − | 0.505838i | \(-0.168817\pi\) | ||||
0.862629 | + | 0.505838i | \(0.168817\pi\) | |||||||
\(464\) | −432.000 | −0.0432222 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −10006.0 | −0.994676 | ||||||||
\(467\) | 15246.0 | 1.51071 | 0.755354 | − | 0.655317i | \(-0.227465\pi\) | ||||
0.755354 | + | 0.655317i | \(0.227465\pi\) | |||||||
\(468\) | −4888.00 | −0.482795 | ||||||||
\(469\) | 2808.00 | 0.276464 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 1702.00 | 0.166505 | ||||||||
\(472\) | 5952.00 | 0.580430 | ||||||||
\(473\) | 576.000 | 0.0559926 | ||||||||
\(474\) | −1288.00 | −0.124810 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −1440.00 | −0.138660 | ||||||||
\(477\) | −364.000 | −0.0349401 | ||||||||
\(478\) | 12618.0 | 1.20739 | ||||||||
\(479\) | −8556.00 | −0.816145 | −0.408073 | − | 0.912949i | \(-0.633799\pi\) | ||||
−0.408073 | + | 0.912949i | \(0.633799\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −2632.00 | −0.249499 | ||||||||
\(482\) | −6076.00 | −0.574179 | ||||||||
\(483\) | −414.000 | −0.0390014 | ||||||||
\(484\) | −1228.00 | −0.115327 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 4160.00 | 0.388275 | ||||||||
\(487\) | 1805.00 | 0.167951 | 0.0839757 | − | 0.996468i | \(-0.473238\pi\) | ||||
0.0839757 | + | 0.996468i | \(0.473238\pi\) | |||||||
\(488\) | −4416.00 | −0.409637 | ||||||||
\(489\) | −2045.00 | −0.189117 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 5245.00 | 0.482085 | 0.241042 | − | 0.970515i | \(-0.422511\pi\) | ||||
0.241042 | + | 0.970515i | \(0.422511\pi\) | |||||||
\(492\) | 628.000 | 0.0575456 | ||||||||
\(493\) | 540.000 | 0.0493314 | ||||||||
\(494\) | −3384.00 | −0.308205 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −528.000 | −0.0477982 | ||||||||
\(497\) | 12582.0 | 1.13557 | ||||||||
\(498\) | −1024.00 | −0.0921416 | ||||||||
\(499\) | 9027.00 | 0.809828 | 0.404914 | − | 0.914355i | \(-0.367302\pi\) | ||||
0.404914 | + | 0.914355i | \(0.367302\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 1016.00 | 0.0906019 | ||||||||
\(502\) | 2664.00 | 0.236853 | ||||||||
\(503\) | −3522.00 | −0.312203 | −0.156102 | − | 0.987741i | \(-0.549893\pi\) | ||||
−0.156102 | + | 0.987741i | \(0.549893\pi\) | |||||||
\(504\) | 3744.00 | 0.330895 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 1472.00 | 0.129325 | ||||||||
\(507\) | −12.0000 | −0.00105116 | ||||||||
\(508\) | 3076.00 | 0.268652 | ||||||||
\(509\) | 3949.00 | 0.343883 | 0.171941 | − | 0.985107i | \(-0.444996\pi\) | ||||
0.171941 | + | 0.985107i | \(0.444996\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 10962.0 | 0.948983 | ||||||||
\(512\) | −512.000 | −0.0441942 | ||||||||
\(513\) | 1908.00 | 0.164211 | ||||||||
\(514\) | 6602.00 | 0.566540 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 72.0000 | 0.00614268 | ||||||||
\(517\) | 2080.00 | 0.176941 | ||||||||
\(518\) | 2016.00 | 0.171000 | ||||||||
\(519\) | 598.000 | 0.0505767 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 3236.00 | 0.272115 | 0.136057 | − | 0.990701i | \(-0.456557\pi\) | ||||
0.136057 | + | 0.990701i | \(0.456557\pi\) | |||||||
\(522\) | −1404.00 | −0.117723 | ||||||||
\(523\) | −12394.0 | −1.03624 | −0.518118 | − | 0.855309i | \(-0.673367\pi\) | ||||
−0.518118 | + | 0.855309i | \(0.673367\pi\) | |||||||
\(524\) | −852.000 | −0.0710301 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 4144.00 | 0.343511 | ||||||||
\(527\) | 660.000 | 0.0545542 | ||||||||
\(528\) | 512.000 | 0.0422006 | ||||||||
\(529\) | 529.000 | 0.0434783 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 19344.0 | 1.58090 | ||||||||
\(532\) | 2592.00 | 0.211236 | ||||||||
\(533\) | −7379.00 | −0.599662 | ||||||||
\(534\) | −204.000 | −0.0165317 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −1248.00 | −0.100570 | ||||||||
\(537\) | 4607.00 | 0.370217 | ||||||||
\(538\) | −11442.0 | −0.916914 | ||||||||
\(539\) | 608.000 | 0.0485870 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −7159.00 | −0.568927 | −0.284463 | − | 0.958687i | \(-0.591815\pi\) | ||||
−0.284463 | + | 0.958687i | \(0.591815\pi\) | |||||||
\(542\) | 11800.0 | 0.935154 | ||||||||
\(543\) | 1212.00 | 0.0957862 | ||||||||
\(544\) | 640.000 | 0.0504408 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 1692.00 | 0.132621 | ||||||||
\(547\) | 19761.0 | 1.54464 | 0.772321 | − | 0.635232i | \(-0.219096\pi\) | ||||
0.772321 | + | 0.635232i | \(0.219096\pi\) | |||||||
\(548\) | −11344.0 | −0.884291 | ||||||||
\(549\) | −14352.0 | −1.11572 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −972.000 | −0.0751517 | ||||||||
\(552\) | 184.000 | 0.0141876 | ||||||||
\(553\) | −11592.0 | −0.891396 | ||||||||
\(554\) | 12742.0 | 0.977176 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −6524.00 | −0.497625 | ||||||||
\(557\) | −18010.0 | −1.37003 | −0.685016 | − | 0.728528i | \(-0.740205\pi\) | ||||
−0.685016 | + | 0.728528i | \(0.740205\pi\) | |||||||
\(558\) | −1716.00 | −0.130187 | ||||||||
\(559\) | −846.000 | −0.0640107 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −640.000 | −0.0481655 | ||||||||
\(562\) | −6380.00 | −0.478868 | ||||||||
\(563\) | 2648.00 | 0.198224 | 0.0991118 | − | 0.995076i | \(-0.468400\pi\) | ||||
0.0991118 | + | 0.995076i | \(0.468400\pi\) | |||||||
\(564\) | 260.000 | 0.0194113 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −8452.00 | −0.627675 | ||||||||
\(567\) | 11682.0 | 0.865252 | ||||||||
\(568\) | −5592.00 | −0.413090 | ||||||||
\(569\) | −1566.00 | −0.115378 | −0.0576890 | − | 0.998335i | \(-0.518373\pi\) | ||||
−0.0576890 | + | 0.998335i | \(0.518373\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 2864.00 | 0.209903 | 0.104952 | − | 0.994477i | \(-0.466531\pi\) | ||||
0.104952 | + | 0.994477i | \(0.466531\pi\) | |||||||
\(572\) | −6016.00 | −0.439758 | ||||||||
\(573\) | 1058.00 | 0.0771354 | ||||||||
\(574\) | 5652.00 | 0.410993 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −1664.00 | −0.120370 | ||||||||
\(577\) | 929.000 | 0.0670273 | 0.0335137 | − | 0.999438i | \(-0.489330\pi\) | ||||
0.0335137 | + | 0.999438i | \(0.489330\pi\) | |||||||
\(578\) | 9026.00 | 0.649537 | ||||||||
\(579\) | 1047.00 | 0.0751500 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −9216.00 | −0.658079 | ||||||||
\(582\) | −1156.00 | −0.0823329 | ||||||||
\(583\) | −448.000 | −0.0318255 | ||||||||
\(584\) | −4872.00 | −0.345214 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 12096.0 | 0.852698 | ||||||||
\(587\) | 19499.0 | 1.37106 | 0.685528 | − | 0.728046i | \(-0.259571\pi\) | ||||
0.685528 | + | 0.728046i | \(0.259571\pi\) | |||||||
\(588\) | 76.0000 | 0.00533025 | ||||||||
\(589\) | −1188.00 | −0.0831081 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 251.000 | 0.0174700 | ||||||||
\(592\) | −896.000 | −0.0622050 | ||||||||
\(593\) | −6570.00 | −0.454971 | −0.227485 | − | 0.973782i | \(-0.573050\pi\) | ||||
−0.227485 | + | 0.973782i | \(0.573050\pi\) | |||||||
\(594\) | 3392.00 | 0.234302 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −7864.00 | −0.540473 | ||||||||
\(597\) | 3508.00 | 0.240491 | ||||||||
\(598\) | −2162.00 | −0.147844 | ||||||||
\(599\) | 1880.00 | 0.128238 | 0.0641191 | − | 0.997942i | \(-0.479576\pi\) | ||||
0.0641191 | + | 0.997942i | \(0.479576\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 3701.00 | 0.251193 | 0.125596 | − | 0.992081i | \(-0.459916\pi\) | ||||
0.125596 | + | 0.992081i | \(0.459916\pi\) | |||||||
\(602\) | 648.000 | 0.0438713 | ||||||||
\(603\) | −4056.00 | −0.273919 | ||||||||
\(604\) | 140.000 | 0.00943132 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −12.0000 | −0.000804400 0 | ||||||||
\(607\) | 3080.00 | 0.205953 | 0.102976 | − | 0.994684i | \(-0.467163\pi\) | ||||
0.102976 | + | 0.994684i | \(0.467163\pi\) | |||||||
\(608\) | −1152.00 | −0.0768417 | ||||||||
\(609\) | 486.000 | 0.0323378 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −3055.00 | −0.202278 | ||||||||
\(612\) | 2080.00 | 0.137384 | ||||||||
\(613\) | −24004.0 | −1.58159 | −0.790793 | − | 0.612083i | \(-0.790332\pi\) | ||||
−0.790793 | + | 0.612083i | \(0.790332\pi\) | |||||||
\(614\) | 17256.0 | 1.13419 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 4608.00 | 0.301399 | ||||||||
\(617\) | −780.000 | −0.0508940 | −0.0254470 | − | 0.999676i | \(-0.508101\pi\) | ||||
−0.0254470 | + | 0.999676i | \(0.508101\pi\) | |||||||
\(618\) | 320.000 | 0.0208289 | ||||||||
\(619\) | 21892.0 | 1.42151 | 0.710754 | − | 0.703440i | \(-0.248354\pi\) | ||||
0.710754 | + | 0.703440i | \(0.248354\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1219.00 | 0.0787710 | ||||||||
\(622\) | −16494.0 | −1.06326 | ||||||||
\(623\) | −1836.00 | −0.118070 | ||||||||
\(624\) | −752.000 | −0.0482437 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 5240.00 | 0.334557 | ||||||||
\(627\) | 1152.00 | 0.0733755 | ||||||||
\(628\) | −6808.00 | −0.432594 | ||||||||
\(629\) | 1120.00 | 0.0709973 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 8050.00 | 0.507869 | 0.253935 | − | 0.967221i | \(-0.418275\pi\) | ||||
0.253935 | + | 0.967221i | \(0.418275\pi\) | |||||||
\(632\) | 5152.00 | 0.324265 | ||||||||
\(633\) | 3296.00 | 0.206958 | ||||||||
\(634\) | 19812.0 | 1.24106 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −56.0000 | −0.00349142 | ||||||||
\(637\) | −893.000 | −0.0555447 | ||||||||
\(638\) | −1728.00 | −0.107229 | ||||||||
\(639\) | −18174.0 | −1.12512 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −25890.0 | −1.59531 | −0.797655 | − | 0.603114i | \(-0.793926\pi\) | ||||
−0.797655 | + | 0.603114i | \(0.793926\pi\) | |||||||
\(642\) | −760.000 | −0.0467209 | ||||||||
\(643\) | −4774.00 | −0.292797 | −0.146398 | − | 0.989226i | \(-0.546768\pi\) | ||||
−0.146398 | + | 0.989226i | \(0.546768\pi\) | |||||||
\(644\) | 1656.00 | 0.101328 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 1440.00 | 0.0877029 | ||||||||
\(647\) | −3349.00 | −0.203497 | −0.101749 | − | 0.994810i | \(-0.532444\pi\) | ||||
−0.101749 | + | 0.994810i | \(0.532444\pi\) | |||||||
\(648\) | −5192.00 | −0.314755 | ||||||||
\(649\) | 23808.0 | 1.43998 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 594.000 | 0.0357614 | ||||||||
\(652\) | 8180.00 | 0.491340 | ||||||||
\(653\) | −24813.0 | −1.48699 | −0.743497 | − | 0.668739i | \(-0.766834\pi\) | ||||
−0.743497 | + | 0.668739i | \(0.766834\pi\) | |||||||
\(654\) | 500.000 | 0.0298953 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −2512.00 | −0.149508 | ||||||||
\(657\) | −15834.0 | −0.940248 | ||||||||
\(658\) | 2340.00 | 0.138636 | ||||||||
\(659\) | 18180.0 | 1.07465 | 0.537323 | − | 0.843376i | \(-0.319435\pi\) | ||||
0.537323 | + | 0.843376i | \(0.319435\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −29250.0 | −1.72117 | −0.860585 | − | 0.509307i | \(-0.829902\pi\) | ||||
−0.860585 | + | 0.509307i | \(0.829902\pi\) | |||||||
\(662\) | 16230.0 | 0.952865 | ||||||||
\(663\) | 940.000 | 0.0550627 | ||||||||
\(664\) | 4096.00 | 0.239391 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −2912.00 | −0.169426 | ||||||||
\(667\) | −621.000 | −0.0360498 | ||||||||
\(668\) | −4064.00 | −0.235391 | ||||||||
\(669\) | −2720.00 | −0.157192 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −17664.0 | −1.01626 | ||||||||
\(672\) | 576.000 | 0.0330650 | ||||||||
\(673\) | 23027.0 | 1.31891 | 0.659454 | − | 0.751745i | \(-0.270787\pi\) | ||||
0.659454 | + | 0.751745i | \(0.270787\pi\) | |||||||
\(674\) | −15172.0 | −0.867068 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 48.0000 | 0.00273100 | ||||||||
\(677\) | −20106.0 | −1.14141 | −0.570706 | − | 0.821154i | \(-0.693331\pi\) | ||||
−0.570706 | + | 0.821154i | \(0.693331\pi\) | |||||||
\(678\) | 780.000 | 0.0441825 | ||||||||
\(679\) | −10404.0 | −0.588025 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −4134.00 | −0.232621 | ||||||||
\(682\) | −2112.00 | −0.118582 | ||||||||
\(683\) | 18745.0 | 1.05016 | 0.525079 | − | 0.851054i | \(-0.324036\pi\) | ||||
0.525079 | + | 0.851054i | \(0.324036\pi\) | |||||||
\(684\) | −3744.00 | −0.209292 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 13032.0 | 0.725312 | ||||||||
\(687\) | 4510.00 | 0.250462 | ||||||||
\(688\) | −288.000 | −0.0159592 | ||||||||
\(689\) | 658.000 | 0.0363829 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 24424.0 | 1.34462 | 0.672310 | − | 0.740270i | \(-0.265302\pi\) | ||||
0.672310 | + | 0.740270i | \(0.265302\pi\) | |||||||
\(692\) | −2392.00 | −0.131402 | ||||||||
\(693\) | 14976.0 | 0.820911 | ||||||||
\(694\) | 2712.00 | 0.148337 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −216.000 | −0.0117636 | ||||||||
\(697\) | 3140.00 | 0.170640 | ||||||||
\(698\) | −13298.0 | −0.721113 | ||||||||
\(699\) | −5003.00 | −0.270717 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −27278.0 | −1.46972 | −0.734862 | − | 0.678217i | \(-0.762753\pi\) | ||||
−0.734862 | + | 0.678217i | \(0.762753\pi\) | |||||||
\(702\) | −4982.00 | −0.267854 | ||||||||
\(703\) | −2016.00 | −0.108158 | ||||||||
\(704\) | −2048.00 | −0.109640 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 21382.0 | 1.13983 | ||||||||
\(707\) | −108.000 | −0.00574506 | ||||||||
\(708\) | 2976.00 | 0.157973 | ||||||||
\(709\) | 12214.0 | 0.646977 | 0.323488 | − | 0.946232i | \(-0.395144\pi\) | ||||
0.323488 | + | 0.946232i | \(0.395144\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 16744.0 | 0.883191 | ||||||||
\(712\) | 816.000 | 0.0429507 | ||||||||
\(713\) | −759.000 | −0.0398664 | ||||||||
\(714\) | −720.000 | −0.0377385 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −18428.0 | −0.961853 | ||||||||
\(717\) | 6309.00 | 0.328611 | ||||||||
\(718\) | 12840.0 | 0.667388 | ||||||||
\(719\) | 12932.0 | 0.670768 | 0.335384 | − | 0.942082i | \(-0.391134\pi\) | ||||
0.335384 | + | 0.942082i | \(0.391134\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 2880.00 | 0.148761 | ||||||||
\(722\) | 11126.0 | 0.573500 | ||||||||
\(723\) | −3038.00 | −0.156272 | ||||||||
\(724\) | −4848.00 | −0.248860 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −614.000 | −0.0313880 | ||||||||
\(727\) | −10046.0 | −0.512497 | −0.256249 | − | 0.966611i | \(-0.582487\pi\) | ||||
−0.256249 | + | 0.966611i | \(0.582487\pi\) | |||||||
\(728\) | −6768.00 | −0.344559 | ||||||||
\(729\) | −15443.0 | −0.784586 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 360.000 | 0.0182149 | ||||||||
\(732\) | −2208.00 | −0.111489 | ||||||||
\(733\) | 5924.00 | 0.298510 | 0.149255 | − | 0.988799i | \(-0.452312\pi\) | ||||
0.149255 | + | 0.988799i | \(0.452312\pi\) | |||||||
\(734\) | −1048.00 | −0.0527008 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −736.000 | −0.0368605 | ||||||||
\(737\) | −4992.00 | −0.249502 | ||||||||
\(738\) | −8164.00 | −0.407210 | ||||||||
\(739\) | 829.000 | 0.0412656 | 0.0206328 | − | 0.999787i | \(-0.493432\pi\) | ||||
0.0206328 | + | 0.999787i | \(0.493432\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −1692.00 | −0.0838828 | ||||||||
\(742\) | −504.000 | −0.0249359 | ||||||||
\(743\) | −7072.00 | −0.349188 | −0.174594 | − | 0.984641i | \(-0.555861\pi\) | ||||
−0.174594 | + | 0.984641i | \(0.555861\pi\) | |||||||
\(744\) | −264.000 | −0.0130090 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 11132.0 | 0.546342 | ||||||||
\(747\) | 13312.0 | 0.652022 | ||||||||
\(748\) | 2560.00 | 0.125138 | ||||||||
\(749\) | −6840.00 | −0.333682 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 16234.0 | 0.788798 | 0.394399 | − | 0.918939i | \(-0.370953\pi\) | ||||
0.394399 | + | 0.918939i | \(0.370953\pi\) | |||||||
\(752\) | −1040.00 | −0.0504320 | ||||||||
\(753\) | 1332.00 | 0.0644632 | ||||||||
\(754\) | 2538.00 | 0.122584 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 3816.00 | 0.183580 | ||||||||
\(757\) | −9128.00 | −0.438260 | −0.219130 | − | 0.975696i | \(-0.570322\pi\) | ||||
−0.219130 | + | 0.975696i | \(0.570322\pi\) | |||||||
\(758\) | −4480.00 | −0.214671 | ||||||||
\(759\) | 736.000 | 0.0351978 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 165.000 | 0.00785972 | 0.00392986 | − | 0.999992i | \(-0.498749\pi\) | ||||
0.00392986 | + | 0.999992i | \(0.498749\pi\) | |||||||
\(762\) | 1538.00 | 0.0731179 | ||||||||
\(763\) | 4500.00 | 0.213514 | ||||||||
\(764\) | −4232.00 | −0.200404 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 17556.0 | 0.828099 | ||||||||
\(767\) | −34968.0 | −1.64618 | ||||||||
\(768\) | −256.000 | −0.0120281 | ||||||||
\(769\) | −20834.0 | −0.976974 | −0.488487 | − | 0.872571i | \(-0.662451\pi\) | ||||
−0.488487 | + | 0.872571i | \(0.662451\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 3301.00 | 0.154193 | ||||||||
\(772\) | −4188.00 | −0.195245 | ||||||||
\(773\) | 31782.0 | 1.47881 | 0.739404 | − | 0.673262i | \(-0.235107\pi\) | ||||
0.739404 | + | 0.673262i | \(0.235107\pi\) | |||||||
\(774\) | −936.000 | −0.0434675 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 4624.00 | 0.213907 | ||||||||
\(777\) | 1008.00 | 0.0465403 | ||||||||
\(778\) | −8112.00 | −0.373817 | ||||||||
\(779\) | −5652.00 | −0.259954 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −22368.0 | −1.02483 | ||||||||
\(782\) | 920.000 | 0.0420705 | ||||||||
\(783\) | −1431.00 | −0.0653126 | ||||||||
\(784\) | −304.000 | −0.0138484 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −426.000 | −0.0193320 | ||||||||
\(787\) | −33104.0 | −1.49940 | −0.749701 | − | 0.661776i | \(-0.769803\pi\) | ||||
−0.749701 | + | 0.661776i | \(0.769803\pi\) | |||||||
\(788\) | −1004.00 | −0.0453883 | ||||||||
\(789\) | 2072.00 | 0.0934920 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 7020.00 | 0.315553 | ||||||||
\(792\) | −6656.00 | −0.298625 | ||||||||
\(793\) | 25944.0 | 1.16179 | ||||||||
\(794\) | −18302.0 | −0.818027 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −14032.0 | −0.624813 | ||||||||
\(797\) | −4736.00 | −0.210486 | −0.105243 | − | 0.994447i | \(-0.533562\pi\) | ||||
−0.105243 | + | 0.994447i | \(0.533562\pi\) | |||||||
\(798\) | 1296.00 | 0.0574911 | ||||||||
\(799\) | 1300.00 | 0.0575603 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 2652.00 | 0.116984 | ||||||||
\(802\) | −31860.0 | −1.40276 | ||||||||
\(803\) | −19488.0 | −0.856434 | ||||||||
\(804\) | −624.000 | −0.0273716 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 3102.00 | 0.135562 | ||||||||
\(807\) | −5721.00 | −0.249552 | ||||||||
\(808\) | 48.0000 | 0.00208989 | ||||||||
\(809\) | −7470.00 | −0.324637 | −0.162318 | − | 0.986738i | \(-0.551897\pi\) | ||||
−0.162318 | + | 0.986738i | \(0.551897\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 19919.0 | 0.862455 | 0.431227 | − | 0.902243i | \(-0.358081\pi\) | ||||
0.431227 | + | 0.902243i | \(0.358081\pi\) | |||||||
\(812\) | −1944.00 | −0.0840160 | ||||||||
\(813\) | 5900.00 | 0.254517 | ||||||||
\(814\) | −3584.00 | −0.154323 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 320.000 | 0.0137282 | ||||||||
\(817\) | −648.000 | −0.0277487 | ||||||||
\(818\) | 11782.0 | 0.503604 | ||||||||
\(819\) | −21996.0 | −0.938465 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −22694.0 | −0.964709 | −0.482354 | − | 0.875976i | \(-0.660218\pi\) | ||||
−0.482354 | + | 0.875976i | \(0.660218\pi\) | |||||||
\(822\) | −5672.00 | −0.240674 | ||||||||
\(823\) | 31907.0 | 1.35141 | 0.675704 | − | 0.737173i | \(-0.263840\pi\) | ||||
0.675704 | + | 0.737173i | \(0.263840\pi\) | |||||||
\(824\) | −1280.00 | −0.0541152 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 26784.0 | 1.12825 | ||||||||
\(827\) | 15236.0 | 0.640638 | 0.320319 | − | 0.947310i | \(-0.396210\pi\) | ||||
0.320319 | + | 0.947310i | \(0.396210\pi\) | |||||||
\(828\) | −2392.00 | −0.100396 | ||||||||
\(829\) | 27286.0 | 1.14316 | 0.571581 | − | 0.820545i | \(-0.306330\pi\) | ||||
0.571581 | + | 0.820545i | \(0.306330\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 6371.00 | 0.265954 | ||||||||
\(832\) | 3008.00 | 0.125341 | ||||||||
\(833\) | 380.000 | 0.0158058 | ||||||||
\(834\) | −3262.00 | −0.135436 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −4608.00 | −0.190635 | ||||||||
\(837\) | −1749.00 | −0.0722273 | ||||||||
\(838\) | −30564.0 | −1.25992 | ||||||||
\(839\) | 23054.0 | 0.948644 | 0.474322 | − | 0.880351i | \(-0.342693\pi\) | ||||
0.474322 | + | 0.880351i | \(0.342693\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −23660.0 | −0.970109 | ||||||||
\(842\) | 21868.0 | 0.895037 | ||||||||
\(843\) | −3190.00 | −0.130331 | ||||||||
\(844\) | −13184.0 | −0.537692 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −3380.00 | −0.137360 | ||||||||
\(847\) | −5526.00 | −0.224174 | ||||||||
\(848\) | 224.000 | 0.00907098 | ||||||||
\(849\) | −4226.00 | −0.170832 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −1288.00 | −0.0518826 | ||||||||
\(852\) | −2796.00 | −0.112429 | ||||||||
\(853\) | 34506.0 | 1.38507 | 0.692534 | − | 0.721385i | \(-0.256494\pi\) | ||||
0.692534 | + | 0.721385i | \(0.256494\pi\) | |||||||
\(854\) | −19872.0 | −0.796260 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 3040.00 | 0.121384 | ||||||||
\(857\) | 22263.0 | 0.887386 | 0.443693 | − | 0.896179i | \(-0.353668\pi\) | ||||
0.443693 | + | 0.896179i | \(0.353668\pi\) | |||||||
\(858\) | −3008.00 | −0.119687 | ||||||||
\(859\) | 12851.0 | 0.510443 | 0.255221 | − | 0.966883i | \(-0.417852\pi\) | ||||
0.255221 | + | 0.966883i | \(0.417852\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 2826.00 | 0.111858 | ||||||||
\(862\) | 5588.00 | 0.220798 | ||||||||
\(863\) | −15723.0 | −0.620182 | −0.310091 | − | 0.950707i | \(-0.600360\pi\) | ||||
−0.310091 | + | 0.950707i | \(0.600360\pi\) | |||||||
\(864\) | −1696.00 | −0.0667814 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −30124.0 | −1.18205 | ||||||||
\(867\) | 4513.00 | 0.176781 | ||||||||
\(868\) | −2376.00 | −0.0929109 | ||||||||
\(869\) | 20608.0 | 0.804463 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 7332.00 | 0.285230 | ||||||||
\(872\) | −2000.00 | −0.0776704 | ||||||||
\(873\) | 15028.0 | 0.582613 | ||||||||
\(874\) | −1656.00 | −0.0640904 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −2436.00 | −0.0939553 | ||||||||
\(877\) | 886.000 | 0.0341141 | 0.0170571 | − | 0.999855i | \(-0.494570\pi\) | ||||
0.0170571 | + | 0.999855i | \(0.494570\pi\) | |||||||
\(878\) | −522.000 | −0.0200645 | ||||||||
\(879\) | 6048.00 | 0.232075 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −37120.0 | −1.41953 | −0.709764 | − | 0.704439i | \(-0.751199\pi\) | ||||
−0.709764 | + | 0.704439i | \(0.751199\pi\) | |||||||
\(882\) | −988.000 | −0.0377185 | ||||||||
\(883\) | 7524.00 | 0.286753 | 0.143376 | − | 0.989668i | \(-0.454204\pi\) | ||||
0.143376 | + | 0.989668i | \(0.454204\pi\) | |||||||
\(884\) | −3760.00 | −0.143057 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −14166.0 | −0.537151 | ||||||||
\(887\) | −9221.00 | −0.349054 | −0.174527 | − | 0.984652i | \(-0.555840\pi\) | ||||
−0.174527 | + | 0.984652i | \(0.555840\pi\) | |||||||
\(888\) | −448.000 | −0.0169301 | ||||||||
\(889\) | 13842.0 | 0.522211 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −20768.0 | −0.780869 | ||||||||
\(892\) | 10880.0 | 0.408396 | ||||||||
\(893\) | −2340.00 | −0.0876877 | ||||||||
\(894\) | −3932.00 | −0.147098 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −2304.00 | −0.0859054 | ||||||||
\(897\) | −1081.00 | −0.0402381 | ||||||||
\(898\) | 20740.0 | 0.770716 | ||||||||
\(899\) | 891.000 | 0.0330551 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −280.000 | −0.0103531 | ||||||||
\(902\) | −10048.0 | −0.370911 | ||||||||
\(903\) | 324.000 | 0.0119402 | ||||||||
\(904\) | −3120.00 | −0.114789 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 70.0000 | 0.00256688 | ||||||||
\(907\) | −29116.0 | −1.06591 | −0.532955 | − | 0.846143i | \(-0.678919\pi\) | ||||
−0.532955 | + | 0.846143i | \(0.678919\pi\) | |||||||
\(908\) | 16536.0 | 0.604368 | ||||||||
\(909\) | 156.000 | 0.00569218 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 11440.0 | 0.416053 | 0.208026 | − | 0.978123i | \(-0.433296\pi\) | ||||
0.208026 | + | 0.978123i | \(0.433296\pi\) | |||||||
\(912\) | −576.000 | −0.0209137 | ||||||||
\(913\) | 16384.0 | 0.593901 | ||||||||
\(914\) | −20992.0 | −0.759687 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −18040.0 | −0.650719 | ||||||||
\(917\) | −3834.00 | −0.138070 | ||||||||
\(918\) | 2120.00 | 0.0762205 | ||||||||
\(919\) | 2958.00 | 0.106176 | 0.0530878 | − | 0.998590i | \(-0.483094\pi\) | ||||
0.0530878 | + | 0.998590i | \(0.483094\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 8628.00 | 0.308689 | ||||||||
\(922\) | −36042.0 | −1.28740 | ||||||||
\(923\) | 32853.0 | 1.17158 | ||||||||
\(924\) | 2304.00 | 0.0820303 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −34376.0 | −1.21994 | ||||||||
\(927\) | −4160.00 | −0.147392 | ||||||||
\(928\) | 864.000 | 0.0305627 | ||||||||
\(929\) | 20907.0 | 0.738360 | 0.369180 | − | 0.929358i | \(-0.379639\pi\) | ||||
0.369180 | + | 0.929358i | \(0.379639\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −684.000 | −0.0240786 | ||||||||
\(932\) | 20012.0 | 0.703342 | ||||||||
\(933\) | −8247.00 | −0.289383 | ||||||||
\(934\) | −30492.0 | −1.06823 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 9776.00 | 0.341387 | ||||||||
\(937\) | −9748.00 | −0.339865 | −0.169932 | − | 0.985456i | \(-0.554355\pi\) | ||||
−0.169932 | + | 0.985456i | \(0.554355\pi\) | |||||||
\(938\) | −5616.00 | −0.195489 | ||||||||
\(939\) | 2620.00 | 0.0910548 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 19624.0 | 0.679834 | 0.339917 | − | 0.940455i | \(-0.389601\pi\) | ||||
0.339917 | + | 0.940455i | \(0.389601\pi\) | |||||||
\(942\) | −3404.00 | −0.117737 | ||||||||
\(943\) | −3611.00 | −0.124698 | ||||||||
\(944\) | −11904.0 | −0.410426 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −1152.00 | −0.0395928 | ||||||||
\(947\) | 41859.0 | 1.43636 | 0.718181 | − | 0.695856i | \(-0.244975\pi\) | ||||
0.718181 | + | 0.695856i | \(0.244975\pi\) | |||||||
\(948\) | 2576.00 | 0.0882538 | ||||||||
\(949\) | 28623.0 | 0.979075 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 9906.00 | 0.337775 | ||||||||
\(952\) | 2880.00 | 0.0980476 | ||||||||
\(953\) | −29226.0 | −0.993413 | −0.496707 | − | 0.867918i | \(-0.665458\pi\) | ||||
−0.496707 | + | 0.867918i | \(0.665458\pi\) | |||||||
\(954\) | 728.000 | 0.0247064 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −25236.0 | −0.853756 | ||||||||
\(957\) | −864.000 | −0.0291841 | ||||||||
\(958\) | 17112.0 | 0.577102 | ||||||||
\(959\) | −51048.0 | −1.71890 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −28702.0 | −0.963445 | ||||||||
\(962\) | 5264.00 | 0.176422 | ||||||||
\(963\) | 9880.00 | 0.330611 | ||||||||
\(964\) | 12152.0 | 0.406006 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 828.000 | 0.0275781 | ||||||||
\(967\) | 29849.0 | 0.992636 | 0.496318 | − | 0.868141i | \(-0.334685\pi\) | ||||
0.496318 | + | 0.868141i | \(0.334685\pi\) | |||||||
\(968\) | 2456.00 | 0.0815484 | ||||||||
\(969\) | 720.000 | 0.0238697 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −9390.00 | −0.310339 | −0.155170 | − | 0.987888i | \(-0.549592\pi\) | ||||
−0.155170 | + | 0.987888i | \(0.549592\pi\) | |||||||
\(972\) | −8320.00 | −0.274552 | ||||||||
\(973\) | −29358.0 | −0.967291 | ||||||||
\(974\) | −3610.00 | −0.118760 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 8832.00 | 0.289657 | ||||||||
\(977\) | −33536.0 | −1.09817 | −0.549085 | − | 0.835767i | \(-0.685024\pi\) | ||||
−0.549085 | + | 0.835767i | \(0.685024\pi\) | |||||||
\(978\) | 4090.00 | 0.133726 | ||||||||
\(979\) | 3264.00 | 0.106556 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −6500.00 | −0.211548 | ||||||||
\(982\) | −10490.0 | −0.340885 | ||||||||
\(983\) | −28994.0 | −0.940758 | −0.470379 | − | 0.882465i | \(-0.655883\pi\) | ||||
−0.470379 | + | 0.882465i | \(0.655883\pi\) | |||||||
\(984\) | −1256.00 | −0.0406909 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −1080.00 | −0.0348826 | ||||||||
\(987\) | 1170.00 | 0.0377320 | ||||||||
\(988\) | 6768.00 | 0.217934 | ||||||||
\(989\) | −414.000 | −0.0133109 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 11272.0 | 0.361319 | 0.180659 | − | 0.983546i | \(-0.442177\pi\) | ||||
0.180659 | + | 0.983546i | \(0.442177\pi\) | |||||||
\(992\) | 1056.00 | 0.0337984 | ||||||||
\(993\) | 8115.00 | 0.259337 | ||||||||
\(994\) | −25164.0 | −0.802971 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 2048.00 | 0.0651540 | ||||||||
\(997\) | −61186.0 | −1.94361 | −0.971805 | − | 0.235784i | \(-0.924234\pi\) | ||||
−0.971805 | + | 0.235784i | \(0.924234\pi\) | |||||||
\(998\) | −18054.0 | −0.572635 | ||||||||
\(999\) | −2968.00 | −0.0939974 |
(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 | 1150.4.a.b.1.1 | 1 | ||
5.2 | odd | 4 | 1150.4.b.f.599.1 | 2 | |||
5.3 | odd | 4 | 1150.4.b.f.599.2 | 2 | |||
5.4 | even | 2 | 230.4.a.e.1.1 | ✓ | 1 | ||
15.14 | odd | 2 | 2070.4.a.e.1.1 | 1 | |||
20.19 | odd | 2 | 1840.4.a.d.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
230.4.a.e.1.1 | ✓ | 1 | 5.4 | even | 2 | ||
1150.4.a.b.1.1 | 1 | 1.1 | even | 1 | trivial | ||
1150.4.b.f.599.1 | 2 | 5.2 | odd | 4 | |||
1150.4.b.f.599.2 | 2 | 5.3 | odd | 4 | |||
1840.4.a.d.1.1 | 1 | 20.19 | odd | 2 | |||
2070.4.a.e.1.1 | 1 | 15.14 | odd | 2 |