Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2070,4,Mod(1,2070)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2070, 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("2070.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2070 = 2 \cdot 3^{2} \cdot 5 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 2070.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: | \(122.133953712\) |
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 | \(\chi\) | \(=\) | 2070.1 |
$q$-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 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 4.00000 | 0.500000 | ||||||||
\(5\) | 5.00000 | 0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −18.0000 | −0.971909 | −0.485954 | − | 0.873984i | \(-0.661528\pi\) | ||||
−0.485954 | + | 0.873984i | \(0.661528\pi\) | |||||||
\(8\) | −8.00000 | −0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −10.0000 | −0.316228 | ||||||||
\(11\) | 32.0000 | 0.877124 | 0.438562 | − | 0.898701i | \(-0.355488\pi\) | ||||
0.438562 | + | 0.898701i | \(0.355488\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −47.0000 | −1.00273 | −0.501364 | − | 0.865237i | \(-0.667168\pi\) | ||||
−0.501364 | + | 0.865237i | \(0.667168\pi\) | |||||||
\(14\) | 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 | \(0.545568\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 36.0000 | 0.434682 | 0.217341 | − | 0.976096i | \(-0.430262\pi\) | ||||
0.217341 | + | 0.976096i | \(0.430262\pi\) | |||||||
\(20\) | 20.0000 | 0.223607 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −64.0000 | −0.620220 | ||||||||
\(23\) | 23.0000 | 0.208514 | ||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 25.0000 | 0.200000 | ||||||||
\(26\) | 94.0000 | 0.709035 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −72.0000 | −0.485954 | ||||||||
\(29\) | 27.0000 | 0.172889 | 0.0864444 | − | 0.996257i | \(-0.472450\pi\) | ||||
0.0864444 | + | 0.996257i | \(0.472450\pi\) | |||||||
\(30\) | 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 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 40.0000 | 0.201763 | ||||||||
\(35\) | −90.0000 | −0.434651 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 56.0000 | 0.248820 | 0.124410 | − | 0.992231i | \(-0.460296\pi\) | ||||
0.124410 | + | 0.992231i | \(0.460296\pi\) | |||||||
\(38\) | −72.0000 | −0.307367 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −40.0000 | −0.158114 | ||||||||
\(41\) | 157.000 | 0.598031 | 0.299016 | − | 0.954248i | \(-0.403342\pi\) | ||||
0.299016 | + | 0.954248i | \(0.403342\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 18.0000 | 0.0638366 | 0.0319183 | − | 0.999490i | \(-0.489838\pi\) | ||||
0.0319183 | + | 0.999490i | \(0.489838\pi\) | |||||||
\(44\) | 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 | \(0.532161\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −19.0000 | −0.0553936 | ||||||||
\(50\) | −50.0000 | −0.141421 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −188.000 | −0.501364 | ||||||||
\(53\) | 14.0000 | 0.0362839 | 0.0181420 | − | 0.999835i | \(-0.494225\pi\) | ||||
0.0181420 | + | 0.999835i | \(0.494225\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 160.000 | 0.392262 | ||||||||
\(56\) | 144.000 | 0.343622 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −54.0000 | −0.122251 | ||||||||
\(59\) | 744.000 | 1.64170 | 0.820852 | − | 0.571141i | \(-0.193499\pi\) | ||||
0.820852 | + | 0.571141i | \(0.193499\pi\) | |||||||
\(60\) | 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 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 64.0000 | 0.125000 | ||||||||
\(65\) | −235.000 | −0.448433 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −156.000 | −0.284454 | −0.142227 | − | 0.989834i | \(-0.545426\pi\) | ||||
−0.142227 | + | 0.989834i | \(0.545426\pi\) | |||||||
\(68\) | −80.0000 | −0.142668 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 180.000 | 0.307344 | ||||||||
\(71\) | −699.000 | −1.16839 | −0.584197 | − | 0.811612i | \(-0.698591\pi\) | ||||
−0.584197 | + | 0.811612i | \(0.698591\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −609.000 | −0.976412 | −0.488206 | − | 0.872728i | \(-0.662348\pi\) | ||||
−0.488206 | + | 0.872728i | \(0.662348\pi\) | |||||||
\(74\) | −112.000 | −0.175942 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 144.000 | 0.217341 | ||||||||
\(77\) | −576.000 | −0.852484 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −644.000 | −0.917160 | −0.458580 | − | 0.888653i | \(-0.651642\pi\) | ||||
−0.458580 | + | 0.888653i | \(0.651642\pi\) | |||||||
\(80\) | 80.0000 | 0.111803 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −314.000 | −0.422872 | ||||||||
\(83\) | −512.000 | −0.677100 | −0.338550 | − | 0.940948i | \(-0.609936\pi\) | ||||
−0.338550 | + | 0.940948i | \(0.609936\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −100.000 | −0.127606 | ||||||||
\(86\) | −36.0000 | −0.0451393 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −256.000 | −0.310110 | ||||||||
\(89\) | 102.000 | 0.121483 | 0.0607415 | − | 0.998154i | \(-0.480653\pi\) | ||||
0.0607415 | + | 0.998154i | \(0.480653\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 846.000 | 0.974559 | ||||||||
\(92\) | 92.0000 | 0.104257 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 130.000 | 0.142643 | ||||||||
\(95\) | 180.000 | 0.194396 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 578.000 | 0.605021 | 0.302510 | − | 0.953146i | \(-0.402175\pi\) | ||||
0.302510 | + | 0.953146i | \(0.402175\pi\) | |||||||
\(98\) | 38.0000 | 0.0391692 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 100.000 | 0.100000 | ||||||||
\(101\) | 6.00000 | 0.00591111 | 0.00295556 | − | 0.999996i | \(-0.499059\pi\) | ||||
0.00295556 | + | 0.999996i | \(0.499059\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −160.000 | −0.153061 | −0.0765304 | − | 0.997067i | \(-0.524384\pi\) | ||||
−0.0765304 | + | 0.997067i | \(0.524384\pi\) | |||||||
\(104\) | 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 | \(0.554914\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 250.000 | 0.219685 | 0.109842 | − | 0.993949i | \(-0.464965\pi\) | ||||
0.109842 | + | 0.993949i | \(0.464965\pi\) | |||||||
\(110\) | −320.000 | −0.277371 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −288.000 | −0.242977 | ||||||||
\(113\) | 390.000 | 0.324674 | 0.162337 | − | 0.986735i | \(-0.448097\pi\) | ||||
0.162337 | + | 0.986735i | \(0.448097\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 115.000 | 0.0932505 | ||||||||
\(116\) | 108.000 | 0.0864444 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −1488.00 | −1.16086 | ||||||||
\(119\) | 360.000 | 0.277321 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −307.000 | −0.230654 | ||||||||
\(122\) | −1104.00 | −0.819274 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −132.000 | −0.0955964 | ||||||||
\(125\) | 125.000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −769.000 | −0.537305 | −0.268652 | − | 0.963237i | \(-0.586578\pi\) | ||||
−0.268652 | + | 0.963237i | \(0.586578\pi\) | |||||||
\(128\) | −128.000 | −0.0883883 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 470.000 | 0.317090 | ||||||||
\(131\) | 213.000 | 0.142060 | 0.0710301 | − | 0.997474i | \(-0.477371\pi\) | ||||
0.0710301 | + | 0.997474i | \(0.477371\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −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 | \(0.845358\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −1631.00 | −0.995249 | −0.497625 | − | 0.867393i | \(-0.665794\pi\) | ||||
−0.497625 | + | 0.867393i | \(0.665794\pi\) | |||||||
\(140\) | −360.000 | −0.217325 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 1398.00 | 0.826180 | ||||||||
\(143\) | −1504.00 | −0.879516 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 135.000 | 0.0773182 | ||||||||
\(146\) | 1218.00 | 0.690427 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 224.000 | 0.124410 | ||||||||
\(149\) | 1966.00 | 1.08095 | 0.540473 | − | 0.841361i | \(-0.318245\pi\) | ||||
0.540473 | + | 0.841361i | \(0.318245\pi\) | |||||||
\(150\) | 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 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 1152.00 | 0.602797 | ||||||||
\(155\) | −165.000 | −0.0855040 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1702.00 | 0.865187 | 0.432594 | − | 0.901589i | \(-0.357599\pi\) | ||||
0.432594 | + | 0.901589i | \(0.357599\pi\) | |||||||
\(158\) | 1288.00 | 0.648530 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −160.000 | −0.0790569 | ||||||||
\(161\) | −414.000 | −0.202657 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −2045.00 | −0.982680 | −0.491340 | − | 0.870968i | \(-0.663493\pi\) | ||||
−0.491340 | + | 0.870968i | \(0.663493\pi\) | |||||||
\(164\) | 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 | \(0.575637\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 12.0000 | 0.00546199 | ||||||||
\(170\) | 200.000 | 0.0902312 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 72.0000 | 0.0319183 | ||||||||
\(173\) | −598.000 | −0.262804 | −0.131402 | − | 0.991329i | \(-0.541948\pi\) | ||||
−0.131402 | + | 0.991329i | \(0.541948\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −450.000 | −0.194382 | ||||||||
\(176\) | 512.000 | 0.219281 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −204.000 | −0.0859014 | ||||||||
\(179\) | 4607.00 | 1.92371 | 0.961853 | − | 0.273567i | \(-0.0882036\pi\) | ||||
0.961853 | + | 0.273567i | \(0.0882036\pi\) | |||||||
\(180\) | 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 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −184.000 | −0.0737210 | ||||||||
\(185\) | 280.000 | 0.111276 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −640.000 | −0.250275 | ||||||||
\(188\) | −260.000 | −0.100864 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −360.000 | −0.137459 | ||||||||
\(191\) | 1058.00 | 0.400807 | 0.200404 | − | 0.979713i | \(-0.435775\pi\) | ||||
0.200404 | + | 0.979713i | \(0.435775\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 1047.00 | 0.390491 | 0.195245 | − | 0.980754i | \(-0.437450\pi\) | ||||
0.195245 | + | 0.980754i | \(0.437450\pi\) | |||||||
\(194\) | −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 | \(0.514453\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −3508.00 | −1.24963 | −0.624813 | − | 0.780775i | \(-0.714825\pi\) | ||||
−0.624813 | + | 0.780775i | \(0.714825\pi\) | |||||||
\(200\) | −200.000 | −0.0707107 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −12.0000 | −0.00417979 | ||||||||
\(203\) | −486.000 | −0.168032 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 785.000 | 0.267448 | ||||||||
\(206\) | 320.000 | 0.108230 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −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 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 760.000 | 0.242769 | ||||||||
\(215\) | 90.0000 | 0.0285486 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 594.000 | 0.185822 | ||||||||
\(218\) | −500.000 | −0.155341 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 640.000 | 0.196131 | ||||||||
\(221\) | 940.000 | 0.286114 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −2720.00 | −0.816792 | −0.408396 | − | 0.912805i | \(-0.633912\pi\) | ||||
−0.408396 | + | 0.912805i | \(0.633912\pi\) | |||||||
\(224\) | 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 | \(0.293426\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −4510.00 | −1.30144 | −0.650719 | − | 0.759319i | \(-0.725532\pi\) | ||||
−0.650719 | + | 0.759319i | \(0.725532\pi\) | |||||||
\(230\) | −230.000 | −0.0659380 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −216.000 | −0.0611254 | ||||||||
\(233\) | 5003.00 | 1.40668 | 0.703342 | − | 0.710852i | \(-0.251690\pi\) | ||||
0.703342 | + | 0.710852i | \(0.251690\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −325.000 | −0.0902156 | ||||||||
\(236\) | 2976.00 | 0.820852 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −720.000 | −0.196095 | ||||||||
\(239\) | 6309.00 | 1.70751 | 0.853756 | − | 0.520674i | \(-0.174319\pi\) | ||||
0.853756 | + | 0.520674i | \(0.174319\pi\) | |||||||
\(240\) | 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 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 2208.00 | 0.579314 | ||||||||
\(245\) | −95.0000 | −0.0247728 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1692.00 | −0.435868 | ||||||||
\(248\) | 264.000 | 0.0675968 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −250.000 | −0.0632456 | ||||||||
\(251\) | 1332.00 | 0.334961 | 0.167480 | − | 0.985875i | \(-0.446437\pi\) | ||||
0.167480 | + | 0.985875i | \(0.446437\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 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 | \(0.631200\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −1008.00 | −0.241830 | ||||||||
\(260\) | −940.000 | −0.224217 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −426.000 | −0.100452 | ||||||||
\(263\) | −2072.00 | −0.485798 | −0.242899 | − | 0.970052i | \(-0.578098\pi\) | ||||
−0.242899 | + | 0.970052i | \(0.578098\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 70.0000 | 0.0162267 | ||||||||
\(266\) | 1296.00 | 0.298733 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −624.000 | −0.142227 | ||||||||
\(269\) | −5721.00 | −1.29671 | −0.648356 | − | 0.761337i | \(-0.724543\pi\) | ||||
−0.648356 | + | 0.761337i | \(0.724543\pi\) | |||||||
\(270\) | 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 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 5672.00 | 1.25058 | ||||||||
\(275\) | 800.000 | 0.175425 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 6371.00 | 1.38194 | 0.690968 | − | 0.722885i | \(-0.257185\pi\) | ||||
0.690968 | + | 0.722885i | \(0.257185\pi\) | |||||||
\(278\) | 3262.00 | 0.703747 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 720.000 | 0.153672 | ||||||||
\(281\) | −3190.00 | −0.677222 | −0.338611 | − | 0.940926i | \(-0.609957\pi\) | ||||
−0.338611 | + | 0.940926i | \(0.609957\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −4226.00 | −0.887667 | −0.443833 | − | 0.896109i | \(-0.646382\pi\) | ||||
−0.443833 | + | 0.896109i | \(0.646382\pi\) | |||||||
\(284\) | −2796.00 | −0.584197 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 3008.00 | 0.621912 | ||||||||
\(287\) | −2826.00 | −0.581232 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −4513.00 | −0.918583 | ||||||||
\(290\) | −270.000 | −0.0546722 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −2436.00 | −0.488206 | ||||||||
\(293\) | −6048.00 | −1.20590 | −0.602949 | − | 0.797780i | \(-0.706008\pi\) | ||||
−0.602949 | + | 0.797780i | \(0.706008\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 3720.00 | 0.734192 | ||||||||
\(296\) | −448.000 | −0.0879712 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −3932.00 | −0.764344 | ||||||||
\(299\) | −1081.00 | −0.209083 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −324.000 | −0.0620434 | ||||||||
\(302\) | −70.0000 | −0.0133379 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 576.000 | 0.108671 | ||||||||
\(305\) | 2760.00 | 0.518155 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 8628.00 | 1.60399 | 0.801997 | − | 0.597328i | \(-0.203771\pi\) | ||||
0.801997 | + | 0.597328i | \(0.203771\pi\) | |||||||
\(308\) | −2304.00 | −0.426242 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 330.000 | 0.0604605 | ||||||||
\(311\) | −8247.00 | −1.50368 | −0.751840 | − | 0.659346i | \(-0.770833\pi\) | ||||
−0.751840 | + | 0.659346i | \(0.770833\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 2620.00 | 0.473135 | 0.236567 | − | 0.971615i | \(-0.423978\pi\) | ||||
0.236567 | + | 0.971615i | \(0.423978\pi\) | |||||||
\(314\) | −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 | \(0.840834\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 864.000 | 0.151645 | ||||||||
\(320\) | 320.000 | 0.0559017 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 828.000 | 0.143300 | ||||||||
\(323\) | −720.000 | −0.124031 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −1175.00 | −0.200545 | ||||||||
\(326\) | 4090.00 | 0.694859 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −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 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 2032.00 | 0.332892 | ||||||||
\(335\) | −780.000 | −0.127212 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −7586.00 | −1.22622 | −0.613109 | − | 0.789998i | \(-0.710082\pi\) | ||||
−0.613109 | + | 0.789998i | \(0.710082\pi\) | |||||||
\(338\) | −24.0000 | −0.00386221 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −400.000 | −0.0638031 | ||||||||
\(341\) | −1056.00 | −0.167700 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 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 | \(0.533449\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 6649.00 | 1.01981 | 0.509904 | − | 0.860231i | \(-0.329681\pi\) | ||||
0.509904 | + | 0.860231i | \(0.329681\pi\) | |||||||
\(350\) | 900.000 | 0.137449 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −1024.00 | −0.155055 | ||||||||
\(353\) | −10691.0 | −1.61197 | −0.805984 | − | 0.591938i | \(-0.798363\pi\) | ||||
−0.805984 | + | 0.591938i | \(0.798363\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −3495.00 | −0.522522 | ||||||||
\(356\) | 408.000 | 0.0607415 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −9214.00 | −1.36027 | ||||||||
\(359\) | 6420.00 | 0.943829 | 0.471915 | − | 0.881644i | \(-0.343563\pi\) | ||||
0.471915 | + | 0.881644i | \(0.343563\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −5563.00 | −0.811051 | ||||||||
\(362\) | 2424.00 | 0.351941 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 3384.00 | 0.487280 | ||||||||
\(365\) | −3045.00 | −0.436665 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −524.000 | −0.0745302 | −0.0372651 | − | 0.999305i | \(-0.511865\pi\) | ||||
−0.0372651 | + | 0.999305i | \(0.511865\pi\) | |||||||
\(368\) | 368.000 | 0.0521286 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −560.000 | −0.0786838 | ||||||||
\(371\) | −252.000 | −0.0352647 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 5566.00 | 0.772645 | 0.386322 | − | 0.922364i | \(-0.373745\pi\) | ||||
0.386322 | + | 0.922364i | \(0.373745\pi\) | |||||||
\(374\) | 1280.00 | 0.176971 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 520.000 | 0.0713217 | ||||||||
\(377\) | −1269.00 | −0.173360 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 2240.00 | 0.303591 | 0.151796 | − | 0.988412i | \(-0.451494\pi\) | ||||
0.151796 | + | 0.988412i | \(0.451494\pi\) | |||||||
\(380\) | 720.000 | 0.0971979 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −2116.00 | −0.283414 | ||||||||
\(383\) | −8778.00 | −1.17111 | −0.585555 | − | 0.810633i | \(-0.699123\pi\) | ||||
−0.585555 | + | 0.810633i | \(0.699123\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −2880.00 | −0.381243 | ||||||||
\(386\) | −2094.00 | −0.276119 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 2312.00 | 0.302510 | ||||||||
\(389\) | −4056.00 | −0.528656 | −0.264328 | − | 0.964433i | \(-0.585150\pi\) | ||||
−0.264328 | + | 0.964433i | \(0.585150\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −460.000 | −0.0594967 | ||||||||
\(392\) | 152.000 | 0.0195846 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 502.000 | 0.0641888 | ||||||||
\(395\) | −3220.00 | −0.410167 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −9151.00 | −1.15687 | −0.578433 | − | 0.815730i | \(-0.696335\pi\) | ||||
−0.578433 | + | 0.815730i | \(0.696335\pi\) | |||||||
\(398\) | 7016.00 | 0.883619 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 400.000 | 0.0500000 | ||||||||
\(401\) | −15930.0 | −1.98381 | −0.991903 | − | 0.126997i | \(-0.959466\pi\) | ||||
−0.991903 | + | 0.126997i | \(0.959466\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1551.00 | 0.191714 | ||||||||
\(404\) | 24.0000 | 0.00295556 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 972.000 | 0.118817 | ||||||||
\(407\) | 1792.00 | 0.218246 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −5891.00 | −0.712203 | −0.356102 | − | 0.934447i | \(-0.615894\pi\) | ||||
−0.356102 | + | 0.934447i | \(0.615894\pi\) | |||||||
\(410\) | −1570.00 | −0.189114 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −640.000 | −0.0765304 | ||||||||
\(413\) | −13392.0 | −1.59559 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −2560.00 | −0.302808 | ||||||||
\(416\) | 1504.00 | 0.177259 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −2304.00 | −0.269599 | ||||||||
\(419\) | −15282.0 | −1.78180 | −0.890900 | − | 0.454199i | \(-0.849926\pi\) | ||||
−0.890900 | + | 0.454199i | \(0.849926\pi\) | |||||||
\(420\) | 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 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −112.000 | −0.0128283 | ||||||||
\(425\) | −500.000 | −0.0570672 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −9936.00 | −1.12608 | ||||||||
\(428\) | −1520.00 | −0.171663 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −180.000 | −0.0201869 | ||||||||
\(431\) | 2794.00 | 0.312256 | 0.156128 | − | 0.987737i | \(-0.450099\pi\) | ||||
0.156128 | + | 0.987737i | \(0.450099\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −15062.0 | −1.67167 | −0.835835 | − | 0.548980i | \(-0.815016\pi\) | ||||
−0.835835 | + | 0.548980i | \(0.815016\pi\) | |||||||
\(434\) | −1188.00 | −0.131396 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 1000.00 | 0.109842 | ||||||||
\(437\) | 828.000 | 0.0906376 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 261.000 | 0.0283755 | 0.0141878 | − | 0.999899i | \(-0.495484\pi\) | ||||
0.0141878 | + | 0.999899i | \(0.495484\pi\) | |||||||
\(440\) | −1280.00 | −0.138685 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −1880.00 | −0.202313 | ||||||||
\(443\) | 7083.00 | 0.759647 | 0.379823 | − | 0.925059i | \(-0.375985\pi\) | ||||
0.379823 | + | 0.925059i | \(0.375985\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 510.000 | 0.0543288 | ||||||||
\(446\) | 5440.00 | 0.577559 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −1152.00 | −0.121489 | ||||||||
\(449\) | 10370.0 | 1.08996 | 0.544978 | − | 0.838450i | \(-0.316538\pi\) | ||||
0.544978 | + | 0.838450i | \(0.316538\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 5024.00 | 0.524547 | ||||||||
\(452\) | 1560.00 | 0.162337 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −8268.00 | −0.854706 | ||||||||
\(455\) | 4230.00 | 0.435836 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −10496.0 | −1.07436 | −0.537180 | − | 0.843468i | \(-0.680510\pi\) | ||||
−0.537180 | + | 0.843468i | \(0.680510\pi\) | |||||||
\(458\) | 9020.00 | 0.920255 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 460.000 | 0.0466252 | ||||||||
\(461\) | −18021.0 | −1.82065 | −0.910327 | − | 0.413889i | \(-0.864170\pi\) | ||||
−0.910327 | + | 0.413889i | \(0.864170\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −17188.0 | −1.72526 | −0.862629 | − | 0.505838i | \(-0.831183\pi\) | ||||
−0.862629 | + | 0.505838i | \(0.831183\pi\) | |||||||
\(464\) | 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 | \(0.227465\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 2808.00 | 0.276464 | ||||||||
\(470\) | 650.000 | 0.0637921 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −5952.00 | −0.580430 | ||||||||
\(473\) | 576.000 | 0.0559926 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 900.000 | 0.0869365 | ||||||||
\(476\) | 1440.00 | 0.138660 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −12618.0 | −1.20739 | ||||||||
\(479\) | 8556.00 | 0.816145 | 0.408073 | − | 0.912949i | \(-0.366201\pi\) | ||||
0.408073 | + | 0.912949i | \(0.366201\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −2632.00 | −0.249499 | ||||||||
\(482\) | −6076.00 | −0.574179 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −1228.00 | −0.115327 | ||||||||
\(485\) | 2890.00 | 0.270573 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −1805.00 | −0.167951 | −0.0839757 | − | 0.996468i | \(-0.526762\pi\) | ||||
−0.0839757 | + | 0.996468i | \(0.526762\pi\) | |||||||
\(488\) | −4416.00 | −0.409637 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 190.000 | 0.0175170 | ||||||||
\(491\) | −5245.00 | −0.482085 | −0.241042 | − | 0.970515i | \(-0.577489\pi\) | ||||
−0.241042 | + | 0.970515i | \(0.577489\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −540.000 | −0.0493314 | ||||||||
\(494\) | 3384.00 | 0.308205 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −528.000 | −0.0477982 | ||||||||
\(497\) | 12582.0 | 1.13557 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 9027.00 | 0.809828 | 0.404914 | − | 0.914355i | \(-0.367302\pi\) | ||||
0.404914 | + | 0.914355i | \(0.367302\pi\) | |||||||
\(500\) | 500.000 | 0.0447214 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −2664.00 | −0.236853 | ||||||||
\(503\) | −3522.00 | −0.312203 | −0.156102 | − | 0.987741i | \(-0.549893\pi\) | ||||
−0.156102 | + | 0.987741i | \(0.549893\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 30.0000 | 0.00264353 | ||||||||
\(506\) | −1472.00 | −0.129325 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −3076.00 | −0.268652 | ||||||||
\(509\) | −3949.00 | −0.343883 | −0.171941 | − | 0.985107i | \(-0.555004\pi\) | ||||
−0.171941 | + | 0.985107i | \(0.555004\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 10962.0 | 0.948983 | ||||||||
\(512\) | −512.000 | −0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 6602.00 | 0.566540 | ||||||||
\(515\) | −800.000 | −0.0684509 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −2080.00 | −0.176941 | ||||||||
\(518\) | 2016.00 | 0.171000 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 1880.00 | 0.158545 | ||||||||
\(521\) | −3236.00 | −0.272115 | −0.136057 | − | 0.990701i | \(-0.543443\pi\) | ||||
−0.136057 | + | 0.990701i | \(0.543443\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 12394.0 | 1.03624 | 0.518118 | − | 0.855309i | \(-0.326633\pi\) | ||||
0.518118 | + | 0.855309i | \(0.326633\pi\) | |||||||
\(524\) | 852.000 | 0.0710301 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 4144.00 | 0.343511 | ||||||||
\(527\) | 660.000 | 0.0545542 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 529.000 | 0.0434783 | ||||||||
\(530\) | −140.000 | −0.0114740 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −2592.00 | −0.211236 | ||||||||
\(533\) | −7379.00 | −0.599662 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −1900.00 | −0.153540 | ||||||||
\(536\) | 1248.00 | 0.100570 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 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 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 640.000 | 0.0504408 | ||||||||
\(545\) | 1250.00 | 0.0982461 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −19761.0 | −1.54464 | −0.772321 | − | 0.635232i | \(-0.780904\pi\) | ||||
−0.772321 | + | 0.635232i | \(0.780904\pi\) | |||||||
\(548\) | −11344.0 | −0.884291 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −1600.00 | −0.124044 | ||||||||
\(551\) | 972.000 | 0.0751517 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 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 | \(0.740205\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −846.000 | −0.0640107 | ||||||||
\(560\) | −1440.00 | −0.108663 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 6380.00 | 0.478868 | ||||||||
\(563\) | 2648.00 | 0.198224 | 0.0991118 | − | 0.995076i | \(-0.468400\pi\) | ||||
0.0991118 | + | 0.995076i | \(0.468400\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 1950.00 | 0.145198 | ||||||||
\(566\) | 8452.00 | 0.627675 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 5592.00 | 0.413090 | ||||||||
\(569\) | 1566.00 | 0.115378 | 0.0576890 | − | 0.998335i | \(-0.481627\pi\) | ||||
0.0576890 | + | 0.998335i | \(0.481627\pi\) | |||||||
\(570\) | 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 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 5652.00 | 0.410993 | ||||||||
\(575\) | 575.000 | 0.0417029 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −929.000 | −0.0670273 | −0.0335137 | − | 0.999438i | \(-0.510670\pi\) | ||||
−0.0335137 | + | 0.999438i | \(0.510670\pi\) | |||||||
\(578\) | 9026.00 | 0.649537 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 540.000 | 0.0386591 | ||||||||
\(581\) | 9216.00 | 0.658079 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 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 | \(0.259571\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −1188.00 | −0.0831081 | ||||||||
\(590\) | −7440.00 | −0.519152 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 896.000 | 0.0622050 | ||||||||
\(593\) | −6570.00 | −0.454971 | −0.227485 | − | 0.973782i | \(-0.573050\pi\) | ||||
−0.227485 | + | 0.973782i | \(0.573050\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 1800.00 | 0.124022 | ||||||||
\(596\) | 7864.00 | 0.540473 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 2162.00 | 0.147844 | ||||||||
\(599\) | −1880.00 | −0.128238 | −0.0641191 | − | 0.997942i | \(-0.520424\pi\) | ||||
−0.0641191 | + | 0.997942i | \(0.520424\pi\) | |||||||
\(600\) | 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 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 140.000 | 0.00943132 | ||||||||
\(605\) | −1535.00 | −0.103151 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −3080.00 | −0.205953 | −0.102976 | − | 0.994684i | \(-0.532837\pi\) | ||||
−0.102976 | + | 0.994684i | \(0.532837\pi\) | |||||||
\(608\) | −1152.00 | −0.0768417 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −5520.00 | −0.366391 | ||||||||
\(611\) | 3055.00 | 0.202278 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 24004.0 | 1.58159 | 0.790793 | − | 0.612083i | \(-0.209668\pi\) | ||||
0.790793 | + | 0.612083i | \(0.209668\pi\) | |||||||
\(614\) | −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 | \(0.508101\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 21892.0 | 1.42151 | 0.710754 | − | 0.703440i | \(-0.248354\pi\) | ||||
0.710754 | + | 0.703440i | \(0.248354\pi\) | |||||||
\(620\) | −660.000 | −0.0427520 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 16494.0 | 1.06326 | ||||||||
\(623\) | −1836.00 | −0.118070 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 625.000 | 0.0400000 | ||||||||
\(626\) | −5240.00 | −0.334557 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 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 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 19812.0 | 1.24106 | ||||||||
\(635\) | −3845.00 | −0.240290 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 893.000 | 0.0555447 | ||||||||
\(638\) | −1728.00 | −0.107229 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −640.000 | −0.0395285 | ||||||||
\(641\) | 25890.0 | 1.59531 | 0.797655 | − | 0.603114i | \(-0.206074\pi\) | ||||
0.797655 | + | 0.603114i | \(0.206074\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 4774.00 | 0.292797 | 0.146398 | − | 0.989226i | \(-0.453232\pi\) | ||||
0.146398 | + | 0.989226i | \(0.453232\pi\) | |||||||
\(644\) | −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 | \(0.532444\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 23808.0 | 1.43998 | ||||||||
\(650\) | 2350.00 | 0.141807 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −8180.00 | −0.491340 | ||||||||
\(653\) | −24813.0 | −1.48699 | −0.743497 | − | 0.668739i | \(-0.766834\pi\) | ||||
−0.743497 | + | 0.668739i | \(0.766834\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 1065.00 | 0.0635313 | ||||||||
\(656\) | 2512.00 | 0.149508 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −2340.00 | −0.138636 | ||||||||
\(659\) | −18180.0 | −1.07465 | −0.537323 | − | 0.843376i | \(-0.680565\pi\) | ||||
−0.537323 | + | 0.843376i | \(0.680565\pi\) | |||||||
\(660\) | 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 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 4096.00 | 0.239391 | ||||||||
\(665\) | −3240.00 | −0.188935 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 621.000 | 0.0360498 | ||||||||
\(668\) | −4064.00 | −0.235391 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 1560.00 | 0.0899523 | ||||||||
\(671\) | 17664.0 | 1.01626 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −23027.0 | −1.31891 | −0.659454 | − | 0.751745i | \(-0.729213\pi\) | ||||
−0.659454 | + | 0.751745i | \(0.729213\pi\) | |||||||
\(674\) | 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 | \(0.693331\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −10404.0 | −0.588025 | ||||||||
\(680\) | 800.000 | 0.0451156 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 2112.00 | 0.118582 | ||||||||
\(683\) | 18745.0 | 1.05016 | 0.525079 | − | 0.851054i | \(-0.324036\pi\) | ||||
0.525079 | + | 0.851054i | \(0.324036\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −14180.0 | −0.790934 | ||||||||
\(686\) | −13032.0 | −0.725312 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 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 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 2712.00 | 0.148337 | ||||||||
\(695\) | −8155.00 | −0.445089 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −3140.00 | −0.170640 | ||||||||
\(698\) | −13298.0 | −0.721113 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −1800.00 | −0.0971909 | ||||||||
\(701\) | 27278.0 | 1.46972 | 0.734862 | − | 0.678217i | \(-0.237247\pi\) | ||||
0.734862 | + | 0.678217i | \(0.237247\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 2016.00 | 0.108158 | ||||||||
\(704\) | 2048.00 | 0.109640 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 21382.0 | 1.13983 | ||||||||
\(707\) | −108.000 | −0.00574506 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 12214.0 | 0.646977 | 0.323488 | − | 0.946232i | \(-0.395144\pi\) | ||||
0.323488 | + | 0.946232i | \(0.395144\pi\) | |||||||
\(710\) | 6990.00 | 0.369479 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −816.000 | −0.0429507 | ||||||||
\(713\) | −759.000 | −0.0398664 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −7520.00 | −0.393332 | ||||||||
\(716\) | 18428.0 | 0.961853 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −12840.0 | −0.667388 | ||||||||
\(719\) | −12932.0 | −0.670768 | −0.335384 | − | 0.942082i | \(-0.608866\pi\) | ||||
−0.335384 | + | 0.942082i | \(0.608866\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 2880.00 | 0.148761 | ||||||||
\(722\) | 11126.0 | 0.573500 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −4848.00 | −0.248860 | ||||||||
\(725\) | 675.000 | 0.0345778 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 10046.0 | 0.512497 | 0.256249 | − | 0.966611i | \(-0.417513\pi\) | ||||
0.256249 | + | 0.966611i | \(0.417513\pi\) | |||||||
\(728\) | −6768.00 | −0.344559 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 6090.00 | 0.308769 | ||||||||
\(731\) | −360.000 | −0.0182149 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −5924.00 | −0.298510 | −0.149255 | − | 0.988799i | \(-0.547688\pi\) | ||||
−0.149255 | + | 0.988799i | \(0.547688\pi\) | |||||||
\(734\) | 1048.00 | 0.0527008 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −736.000 | −0.0368605 | ||||||||
\(737\) | −4992.00 | −0.249502 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 829.000 | 0.0412656 | 0.0206328 | − | 0.999787i | \(-0.493432\pi\) | ||||
0.0206328 | + | 0.999787i | \(0.493432\pi\) | |||||||
\(740\) | 1120.00 | 0.0556379 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 504.000 | 0.0249359 | ||||||||
\(743\) | −7072.00 | −0.349188 | −0.174594 | − | 0.984641i | \(-0.555861\pi\) | ||||
−0.174594 | + | 0.984641i | \(0.555861\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 9830.00 | 0.483414 | ||||||||
\(746\) | −11132.0 | −0.546342 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −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 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 2538.00 | 0.122584 | ||||||||
\(755\) | 175.000 | 0.00843563 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 9128.00 | 0.438260 | 0.219130 | − | 0.975696i | \(-0.429678\pi\) | ||||
0.219130 | + | 0.975696i | \(0.429678\pi\) | |||||||
\(758\) | −4480.00 | −0.214671 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −1440.00 | −0.0687293 | ||||||||
\(761\) | −165.000 | −0.00785972 | −0.00392986 | − | 0.999992i | \(-0.501251\pi\) | ||||
−0.00392986 | + | 0.999992i | \(0.501251\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −4500.00 | −0.213514 | ||||||||
\(764\) | 4232.00 | 0.200404 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 17556.0 | 0.828099 | ||||||||
\(767\) | −34968.0 | −1.64618 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −20834.0 | −0.976974 | −0.488487 | − | 0.872571i | \(-0.662451\pi\) | ||||
−0.488487 | + | 0.872571i | \(0.662451\pi\) | |||||||
\(770\) | 5760.00 | 0.269579 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 4188.00 | 0.195245 | ||||||||
\(773\) | 31782.0 | 1.47881 | 0.739404 | − | 0.673262i | \(-0.235107\pi\) | ||||
0.739404 | + | 0.673262i | \(0.235107\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −825.000 | −0.0382385 | ||||||||
\(776\) | −4624.00 | −0.213907 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 8112.00 | 0.373817 | ||||||||
\(779\) | 5652.00 | 0.259954 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −22368.0 | −1.02483 | ||||||||
\(782\) | 920.000 | 0.0420705 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −304.000 | −0.0138484 | ||||||||
\(785\) | 8510.00 | 0.386923 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 33104.0 | 1.49940 | 0.749701 | − | 0.661776i | \(-0.230197\pi\) | ||||
0.749701 | + | 0.661776i | \(0.230197\pi\) | |||||||
\(788\) | −1004.00 | −0.0453883 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 6440.00 | 0.290032 | ||||||||
\(791\) | −7020.00 | −0.315553 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −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 | \(0.533562\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1300.00 | 0.0575603 | ||||||||
\(800\) | −800.000 | −0.0353553 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 31860.0 | 1.40276 | ||||||||
\(803\) | −19488.0 | −0.856434 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −2070.00 | −0.0906309 | ||||||||
\(806\) | −3102.00 | −0.135562 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −48.0000 | −0.00208989 | ||||||||
\(809\) | 7470.00 | 0.324637 | 0.162318 | − | 0.986738i | \(-0.448103\pi\) | ||||
0.162318 | + | 0.986738i | \(0.448103\pi\) | |||||||
\(810\) | 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 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −3584.00 | −0.154323 | ||||||||
\(815\) | −10225.0 | −0.439468 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 648.000 | 0.0277487 | ||||||||
\(818\) | 11782.0 | 0.503604 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 3140.00 | 0.133724 | ||||||||
\(821\) | 22694.0 | 0.964709 | 0.482354 | − | 0.875976i | \(-0.339782\pi\) | ||||
0.482354 | + | 0.875976i | \(0.339782\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −31907.0 | −1.35141 | −0.675704 | − | 0.737173i | \(-0.736160\pi\) | ||||
−0.675704 | + | 0.737173i | \(0.736160\pi\) | |||||||
\(824\) | 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 | \(0.396210\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 27286.0 | 1.14316 | 0.571581 | − | 0.820545i | \(-0.306330\pi\) | ||||
0.571581 | + | 0.820545i | \(0.306330\pi\) | |||||||
\(830\) | 5120.00 | 0.214118 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −3008.00 | −0.125341 | ||||||||
\(833\) | 380.000 | 0.0158058 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −5080.00 | −0.210540 | ||||||||
\(836\) | 4608.00 | 0.190635 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 30564.0 | 1.25992 | ||||||||
\(839\) | −23054.0 | −0.948644 | −0.474322 | − | 0.880351i | \(-0.657307\pi\) | ||||
−0.474322 | + | 0.880351i | \(0.657307\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −23660.0 | −0.970109 | ||||||||
\(842\) | 21868.0 | 0.895037 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −13184.0 | −0.537692 | ||||||||
\(845\) | 60.0000 | 0.00244268 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 5526.00 | 0.224174 | ||||||||
\(848\) | 224.000 | 0.00907098 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 1000.00 | 0.0403526 | ||||||||
\(851\) | 1288.00 | 0.0518826 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −34506.0 | −1.38507 | −0.692534 | − | 0.721385i | \(-0.743506\pi\) | ||||
−0.692534 | + | 0.721385i | \(0.743506\pi\) | |||||||
\(854\) | 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 | \(0.353668\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 12851.0 | 0.510443 | 0.255221 | − | 0.966883i | \(-0.417852\pi\) | ||||
0.255221 | + | 0.966883i | \(0.417852\pi\) | |||||||
\(860\) | 360.000 | 0.0142743 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −5588.00 | −0.220798 | ||||||||
\(863\) | −15723.0 | −0.620182 | −0.310091 | − | 0.950707i | \(-0.600360\pi\) | ||||
−0.310091 | + | 0.950707i | \(0.600360\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −2990.00 | −0.117530 | ||||||||
\(866\) | 30124.0 | 1.18205 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 2376.00 | 0.0929109 | ||||||||
\(869\) | −20608.0 | −0.804463 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 7332.00 | 0.285230 | ||||||||
\(872\) | −2000.00 | −0.0776704 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −1656.00 | −0.0640904 | ||||||||
\(875\) | −2250.00 | −0.0869302 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −886.000 | −0.0341141 | −0.0170571 | − | 0.999855i | \(-0.505430\pi\) | ||||
−0.0170571 | + | 0.999855i | \(0.505430\pi\) | |||||||
\(878\) | −522.000 | −0.0200645 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 2560.00 | 0.0980654 | ||||||||
\(881\) | 37120.0 | 1.41953 | 0.709764 | − | 0.704439i | \(-0.248801\pi\) | ||||
0.709764 | + | 0.704439i | \(0.248801\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −7524.00 | −0.286753 | −0.143376 | − | 0.989668i | \(-0.545796\pi\) | ||||
−0.143376 | + | 0.989668i | \(0.545796\pi\) | |||||||
\(884\) | 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 | \(0.555840\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 13842.0 | 0.522211 | ||||||||
\(890\) | −1020.00 | −0.0384163 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −10880.0 | −0.408396 | ||||||||
\(893\) | −2340.00 | −0.0876877 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 23035.0 | 0.860307 | ||||||||
\(896\) | 2304.00 | 0.0859054 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −20740.0 | −0.770716 | ||||||||
\(899\) | −891.000 | −0.0330551 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −280.000 | −0.0103531 | ||||||||
\(902\) | −10048.0 | −0.370911 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −3120.00 | −0.114789 | ||||||||
\(905\) | −6060.00 | −0.222587 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 29116.0 | 1.06591 | 0.532955 | − | 0.846143i | \(-0.321081\pi\) | ||||
0.532955 | + | 0.846143i | \(0.321081\pi\) | |||||||
\(908\) | 16536.0 | 0.604368 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −8460.00 | −0.308183 | ||||||||
\(911\) | −11440.0 | −0.416053 | −0.208026 | − | 0.978123i | \(-0.566704\pi\) | ||||
−0.208026 | + | 0.978123i | \(0.566704\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −16384.0 | −0.593901 | ||||||||
\(914\) | 20992.0 | 0.759687 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −18040.0 | −0.650719 | ||||||||
\(917\) | −3834.00 | −0.138070 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 2958.00 | 0.106176 | 0.0530878 | − | 0.998590i | \(-0.483094\pi\) | ||||
0.0530878 | + | 0.998590i | \(0.483094\pi\) | |||||||
\(920\) | −920.000 | −0.0329690 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 36042.0 | 1.28740 | ||||||||
\(923\) | 32853.0 | 1.17158 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1400.00 | 0.0497640 | ||||||||
\(926\) | 34376.0 | 1.21994 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −864.000 | −0.0305627 | ||||||||
\(929\) | −20907.0 | −0.738360 | −0.369180 | − | 0.929358i | \(-0.620361\pi\) | ||||
−0.369180 | + | 0.929358i | \(0.620361\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −684.000 | −0.0240786 | ||||||||
\(932\) | 20012.0 | 0.703342 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −30492.0 | −1.06823 | ||||||||
\(935\) | −3200.00 | −0.111926 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 9748.00 | 0.339865 | 0.169932 | − | 0.985456i | \(-0.445645\pi\) | ||||
0.169932 | + | 0.985456i | \(0.445645\pi\) | |||||||
\(938\) | −5616.00 | −0.195489 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −1300.00 | −0.0451078 | ||||||||
\(941\) | −19624.0 | −0.679834 | −0.339917 | − | 0.940455i | \(-0.610399\pi\) | ||||
−0.339917 | + | 0.940455i | \(0.610399\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 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 | \(0.244975\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 28623.0 | 0.979075 | ||||||||
\(950\) | −1800.00 | −0.0614734 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −2880.00 | −0.0980476 | ||||||||
\(953\) | −29226.0 | −0.993413 | −0.496707 | − | 0.867918i | \(-0.665458\pi\) | ||||
−0.496707 | + | 0.867918i | \(0.665458\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 5290.00 | 0.179246 | ||||||||
\(956\) | 25236.0 | 0.853756 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −17112.0 | −0.577102 | ||||||||
\(959\) | 51048.0 | 1.71890 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −28702.0 | −0.963445 | ||||||||
\(962\) | 5264.00 | 0.176422 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 12152.0 | 0.406006 | ||||||||
\(965\) | 5235.00 | 0.174633 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −29849.0 | −0.992636 | −0.496318 | − | 0.868141i | \(-0.665315\pi\) | ||||
−0.496318 | + | 0.868141i | \(0.665315\pi\) | |||||||
\(968\) | 2456.00 | 0.0815484 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −5780.00 | −0.191324 | ||||||||
\(971\) | 9390.00 | 0.310339 | 0.155170 | − | 0.987888i | \(-0.450408\pi\) | ||||
0.155170 | + | 0.987888i | \(0.450408\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 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 | \(0.685024\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 3264.00 | 0.106556 | ||||||||
\(980\) | −380.000 | −0.0123864 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 10490.0 | 0.340885 | ||||||||
\(983\) | −28994.0 | −0.940758 | −0.470379 | − | 0.882465i | \(-0.655883\pi\) | ||||
−0.470379 | + | 0.882465i | \(0.655883\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −1255.00 | −0.0405966 | ||||||||
\(986\) | 1080.00 | 0.0348826 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −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 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −25164.0 | −0.802971 | ||||||||
\(995\) | −17540.0 | −0.558850 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 61186.0 | 1.94361 | 0.971805 | − | 0.235784i | \(-0.0757658\pi\) | ||||
0.971805 | + | 0.235784i | \(0.0757658\pi\) | |||||||
\(998\) | −18054.0 | −0.572635 | ||||||||
\(999\) | 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 | 2070.4.a.e.1.1 | 1 | ||
3.2 | odd | 2 | 230.4.a.e.1.1 | ✓ | 1 | ||
12.11 | even | 2 | 1840.4.a.d.1.1 | 1 | |||
15.2 | even | 4 | 1150.4.b.f.599.2 | 2 | |||
15.8 | even | 4 | 1150.4.b.f.599.1 | 2 | |||
15.14 | odd | 2 | 1150.4.a.b.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
230.4.a.e.1.1 | ✓ | 1 | 3.2 | odd | 2 | ||
1150.4.a.b.1.1 | 1 | 15.14 | odd | 2 | |||
1150.4.b.f.599.1 | 2 | 15.8 | even | 4 | |||
1150.4.b.f.599.2 | 2 | 15.2 | even | 4 | |||
1840.4.a.d.1.1 | 1 | 12.11 | even | 2 | |||
2070.4.a.e.1.1 | 1 | 1.1 | even | 1 | trivial |