Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1638,4,Mod(1,1638)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1638, 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("1638.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1638 = 2 \cdot 3^{2} \cdot 7 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1638.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: | \(96.6451285894\) |
Analytic rank: | \(0\) |
Dimension: | \(1\) |
Coefficient field: | \(\mathbb{Q}\) |
Coefficient ring: | \(\mathbb{Z}\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 182) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Character | \(\chi\) | \(=\) | 1638.1 |
$q$-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 | ||||||||
\(5\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 7.00000 | 0.377964 | ||||||||
\(8\) | 8.00000 | 0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −39.0000 | −1.06899 | −0.534497 | − | 0.845170i | \(-0.679499\pi\) | ||||
−0.534497 | + | 0.845170i | \(0.679499\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 13.0000 | 0.277350 | ||||||||
\(14\) | 14.0000 | 0.267261 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 16.0000 | 0.250000 | ||||||||
\(17\) | −24.0000 | −0.342403 | −0.171202 | − | 0.985236i | \(-0.554765\pi\) | ||||
−0.171202 | + | 0.985236i | \(0.554765\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 38.0000 | 0.458831 | 0.229416 | − | 0.973329i | \(-0.426318\pi\) | ||||
0.229416 | + | 0.973329i | \(0.426318\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −78.0000 | −0.755893 | ||||||||
\(23\) | −39.0000 | −0.353568 | −0.176784 | − | 0.984250i | \(-0.556569\pi\) | ||||
−0.176784 | + | 0.984250i | \(0.556569\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −125.000 | −1.00000 | ||||||||
\(26\) | 26.0000 | 0.196116 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 28.0000 | 0.188982 | ||||||||
\(29\) | 96.0000 | 0.614716 | 0.307358 | − | 0.951594i | \(-0.400555\pi\) | ||||
0.307358 | + | 0.951594i | \(0.400555\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 227.000 | 1.31517 | 0.657587 | − | 0.753378i | \(-0.271577\pi\) | ||||
0.657587 | + | 0.753378i | \(0.271577\pi\) | |||||||
\(32\) | 32.0000 | 0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −48.0000 | −0.242116 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 425.000 | 1.88837 | 0.944183 | − | 0.329420i | \(-0.106853\pi\) | ||||
0.944183 | + | 0.329420i | \(0.106853\pi\) | |||||||
\(38\) | 76.0000 | 0.324443 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 105.000 | 0.399957 | 0.199979 | − | 0.979800i | \(-0.435913\pi\) | ||||
0.199979 | + | 0.979800i | \(0.435913\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 344.000 | 1.21999 | 0.609994 | − | 0.792406i | \(-0.291172\pi\) | ||||
0.609994 | + | 0.792406i | \(0.291172\pi\) | |||||||
\(44\) | −156.000 | −0.534497 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −78.0000 | −0.250010 | ||||||||
\(47\) | −99.0000 | −0.307248 | −0.153624 | − | 0.988129i | \(-0.549094\pi\) | ||||
−0.153624 | + | 0.988129i | \(0.549094\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 49.0000 | 0.142857 | ||||||||
\(50\) | −250.000 | −0.707107 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 52.0000 | 0.138675 | ||||||||
\(53\) | 540.000 | 1.39952 | 0.699761 | − | 0.714377i | \(-0.253290\pi\) | ||||
0.699761 | + | 0.714377i | \(0.253290\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 56.0000 | 0.133631 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 192.000 | 0.434670 | ||||||||
\(59\) | −114.000 | −0.251551 | −0.125776 | − | 0.992059i | \(-0.540142\pi\) | ||||
−0.125776 | + | 0.992059i | \(0.540142\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −565.000 | −1.18592 | −0.592958 | − | 0.805234i | \(-0.702040\pi\) | ||||
−0.592958 | + | 0.805234i | \(0.702040\pi\) | |||||||
\(62\) | 454.000 | 0.929969 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 64.0000 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −385.000 | −0.702018 | −0.351009 | − | 0.936372i | \(-0.614161\pi\) | ||||
−0.351009 | + | 0.936372i | \(0.614161\pi\) | |||||||
\(68\) | −96.0000 | −0.171202 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 156.000 | 0.260758 | 0.130379 | − | 0.991464i | \(-0.458381\pi\) | ||||
0.130379 | + | 0.991464i | \(0.458381\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −673.000 | −1.07902 | −0.539512 | − | 0.841978i | \(-0.681391\pi\) | ||||
−0.539512 | + | 0.841978i | \(0.681391\pi\) | |||||||
\(74\) | 850.000 | 1.33528 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 152.000 | 0.229416 | ||||||||
\(77\) | −273.000 | −0.404042 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 749.000 | 1.06670 | 0.533349 | − | 0.845896i | \(-0.320933\pi\) | ||||
0.533349 | + | 0.845896i | \(0.320933\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 210.000 | 0.282812 | ||||||||
\(83\) | 1044.00 | 1.38065 | 0.690325 | − | 0.723500i | \(-0.257468\pi\) | ||||
0.690325 | + | 0.723500i | \(0.257468\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 688.000 | 0.862662 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −312.000 | −0.377947 | ||||||||
\(89\) | 690.000 | 0.821796 | 0.410898 | − | 0.911681i | \(-0.365215\pi\) | ||||
0.410898 | + | 0.911681i | \(0.365215\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 91.0000 | 0.104828 | ||||||||
\(92\) | −156.000 | −0.176784 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −198.000 | −0.217257 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 317.000 | 0.331819 | 0.165910 | − | 0.986141i | \(-0.446944\pi\) | ||||
0.165910 | + | 0.986141i | \(0.446944\pi\) | |||||||
\(98\) | 98.0000 | 0.101015 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −500.000 | −0.500000 | ||||||||
\(101\) | 663.000 | 0.653178 | 0.326589 | − | 0.945166i | \(-0.394101\pi\) | ||||
0.326589 | + | 0.945166i | \(0.394101\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −646.000 | −0.617983 | −0.308992 | − | 0.951065i | \(-0.599992\pi\) | ||||
−0.308992 | + | 0.951065i | \(0.599992\pi\) | |||||||
\(104\) | 104.000 | 0.0980581 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 1080.00 | 0.989612 | ||||||||
\(107\) | 744.000 | 0.672198 | 0.336099 | − | 0.941827i | \(-0.390892\pi\) | ||||
0.336099 | + | 0.941827i | \(0.390892\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 218.000 | 0.191565 | 0.0957826 | − | 0.995402i | \(-0.469465\pi\) | ||||
0.0957826 | + | 0.995402i | \(0.469465\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 112.000 | 0.0944911 | ||||||||
\(113\) | 1623.00 | 1.35114 | 0.675571 | − | 0.737295i | \(-0.263897\pi\) | ||||
0.675571 | + | 0.737295i | \(0.263897\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 384.000 | 0.307358 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −228.000 | −0.177874 | ||||||||
\(119\) | −168.000 | −0.129416 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 190.000 | 0.142750 | ||||||||
\(122\) | −1130.00 | −0.838569 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 908.000 | 0.657587 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 659.000 | 0.460447 | 0.230224 | − | 0.973138i | \(-0.426054\pi\) | ||||
0.230224 | + | 0.973138i | \(0.426054\pi\) | |||||||
\(128\) | 128.000 | 0.0883883 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 216.000 | 0.144061 | 0.0720306 | − | 0.997402i | \(-0.477052\pi\) | ||||
0.0720306 | + | 0.997402i | \(0.477052\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 266.000 | 0.173422 | ||||||||
\(134\) | −770.000 | −0.496402 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −192.000 | −0.121058 | ||||||||
\(137\) | −1842.00 | −1.14871 | −0.574353 | − | 0.818608i | \(-0.694746\pi\) | ||||
−0.574353 | + | 0.818608i | \(0.694746\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −628.000 | −0.383211 | −0.191605 | − | 0.981472i | \(-0.561369\pi\) | ||||
−0.191605 | + | 0.981472i | \(0.561369\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 312.000 | 0.184384 | ||||||||
\(143\) | −507.000 | −0.296486 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −1346.00 | −0.762985 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 1700.00 | 0.944183 | ||||||||
\(149\) | −321.000 | −0.176492 | −0.0882461 | − | 0.996099i | \(-0.528126\pi\) | ||||
−0.0882461 | + | 0.996099i | \(0.528126\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1600.00 | −0.862292 | −0.431146 | − | 0.902282i | \(-0.641891\pi\) | ||||
−0.431146 | + | 0.902282i | \(0.641891\pi\) | |||||||
\(152\) | 304.000 | 0.162221 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −546.000 | −0.285701 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1127.00 | 0.572894 | 0.286447 | − | 0.958096i | \(-0.407526\pi\) | ||||
0.286447 | + | 0.958096i | \(0.407526\pi\) | |||||||
\(158\) | 1498.00 | 0.754269 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −273.000 | −0.133636 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −1204.00 | −0.578556 | −0.289278 | − | 0.957245i | \(-0.593415\pi\) | ||||
−0.289278 | + | 0.957245i | \(0.593415\pi\) | |||||||
\(164\) | 420.000 | 0.199979 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 2088.00 | 0.976266 | ||||||||
\(167\) | 600.000 | 0.278020 | 0.139010 | − | 0.990291i | \(-0.455608\pi\) | ||||
0.139010 | + | 0.990291i | \(0.455608\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 169.000 | 0.0769231 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 1376.00 | 0.609994 | ||||||||
\(173\) | 2154.00 | 0.946622 | 0.473311 | − | 0.880895i | \(-0.343059\pi\) | ||||
0.473311 | + | 0.880895i | \(0.343059\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −875.000 | −0.377964 | ||||||||
\(176\) | −624.000 | −0.267249 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 1380.00 | 0.581098 | ||||||||
\(179\) | 2850.00 | 1.19005 | 0.595025 | − | 0.803707i | \(-0.297142\pi\) | ||||
0.595025 | + | 0.803707i | \(0.297142\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 4205.00 | 1.72682 | 0.863412 | − | 0.504499i | \(-0.168323\pi\) | ||||
0.863412 | + | 0.504499i | \(0.168323\pi\) | |||||||
\(182\) | 182.000 | 0.0741249 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −312.000 | −0.125005 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 936.000 | 0.366027 | ||||||||
\(188\) | −396.000 | −0.153624 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 4152.00 | 1.57292 | 0.786461 | − | 0.617640i | \(-0.211911\pi\) | ||||
0.786461 | + | 0.617640i | \(0.211911\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −3148.00 | −1.17408 | −0.587041 | − | 0.809557i | \(-0.699707\pi\) | ||||
−0.587041 | + | 0.809557i | \(0.699707\pi\) | |||||||
\(194\) | 634.000 | 0.234632 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 196.000 | 0.0714286 | ||||||||
\(197\) | −1173.00 | −0.424227 | −0.212114 | − | 0.977245i | \(-0.568035\pi\) | ||||
−0.212114 | + | 0.977245i | \(0.568035\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 3512.00 | 1.25105 | 0.625525 | − | 0.780204i | \(-0.284885\pi\) | ||||
0.625525 | + | 0.780204i | \(0.284885\pi\) | |||||||
\(200\) | −1000.00 | −0.353553 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 1326.00 | 0.461867 | ||||||||
\(203\) | 672.000 | 0.232341 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −1292.00 | −0.436980 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 208.000 | 0.0693375 | ||||||||
\(209\) | −1482.00 | −0.490488 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −3418.00 | −1.11519 | −0.557594 | − | 0.830114i | \(-0.688276\pi\) | ||||
−0.557594 | + | 0.830114i | \(0.688276\pi\) | |||||||
\(212\) | 2160.00 | 0.699761 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 1488.00 | 0.475316 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1589.00 | 0.497089 | ||||||||
\(218\) | 436.000 | 0.135457 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −312.000 | −0.0949656 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 4241.00 | 1.27354 | 0.636768 | − | 0.771056i | \(-0.280271\pi\) | ||||
0.636768 | + | 0.771056i | \(0.280271\pi\) | |||||||
\(224\) | 224.000 | 0.0668153 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 3246.00 | 0.955401 | ||||||||
\(227\) | −888.000 | −0.259642 | −0.129821 | − | 0.991537i | \(-0.541440\pi\) | ||||
−0.129821 | + | 0.991537i | \(0.541440\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 4700.00 | 1.35627 | 0.678133 | − | 0.734940i | \(-0.262789\pi\) | ||||
0.678133 | + | 0.734940i | \(0.262789\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 768.000 | 0.217335 | ||||||||
\(233\) | −6363.00 | −1.78907 | −0.894536 | − | 0.446995i | \(-0.852494\pi\) | ||||
−0.894536 | + | 0.446995i | \(0.852494\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −456.000 | −0.125776 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −336.000 | −0.0915111 | ||||||||
\(239\) | 3078.00 | 0.833051 | 0.416526 | − | 0.909124i | \(-0.363248\pi\) | ||||
0.416526 | + | 0.909124i | \(0.363248\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 3674.00 | 0.982005 | 0.491002 | − | 0.871158i | \(-0.336631\pi\) | ||||
0.491002 | + | 0.871158i | \(0.336631\pi\) | |||||||
\(242\) | 380.000 | 0.100939 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −2260.00 | −0.592958 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 494.000 | 0.127257 | ||||||||
\(248\) | 1816.00 | 0.464984 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 345.000 | 0.0867578 | 0.0433789 | − | 0.999059i | \(-0.486188\pi\) | ||||
0.0433789 | + | 0.999059i | \(0.486188\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1521.00 | 0.377962 | ||||||||
\(254\) | 1318.00 | 0.325585 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 256.000 | 0.0625000 | ||||||||
\(257\) | −6888.00 | −1.67184 | −0.835918 | − | 0.548855i | \(-0.815064\pi\) | ||||
−0.835918 | + | 0.548855i | \(0.815064\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 2975.00 | 0.713736 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 432.000 | 0.101867 | ||||||||
\(263\) | 1248.00 | 0.292604 | 0.146302 | − | 0.989240i | \(-0.453263\pi\) | ||||
0.146302 | + | 0.989240i | \(0.453263\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 532.000 | 0.122628 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −1540.00 | −0.351009 | ||||||||
\(269\) | 2253.00 | 0.510661 | 0.255331 | − | 0.966854i | \(-0.417816\pi\) | ||||
0.255331 | + | 0.966854i | \(0.417816\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1397.00 | 0.313143 | 0.156571 | − | 0.987667i | \(-0.449956\pi\) | ||||
0.156571 | + | 0.987667i | \(0.449956\pi\) | |||||||
\(272\) | −384.000 | −0.0856008 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −3684.00 | −0.812258 | ||||||||
\(275\) | 4875.00 | 1.06899 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −2302.00 | −0.499328 | −0.249664 | − | 0.968333i | \(-0.580320\pi\) | ||||
−0.249664 | + | 0.968333i | \(0.580320\pi\) | |||||||
\(278\) | −1256.00 | −0.270971 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −8532.00 | −1.81130 | −0.905652 | − | 0.424022i | \(-0.860618\pi\) | ||||
−0.905652 | + | 0.424022i | \(0.860618\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −3769.00 | −0.791674 | −0.395837 | − | 0.918321i | \(-0.629546\pi\) | ||||
−0.395837 | + | 0.918321i | \(0.629546\pi\) | |||||||
\(284\) | 624.000 | 0.130379 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −1014.00 | −0.209647 | ||||||||
\(287\) | 735.000 | 0.151170 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −4337.00 | −0.882760 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −2692.00 | −0.539512 | ||||||||
\(293\) | 6150.00 | 1.22623 | 0.613117 | − | 0.789992i | \(-0.289915\pi\) | ||||
0.613117 | + | 0.789992i | \(0.289915\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 3400.00 | 0.667638 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −642.000 | −0.124799 | ||||||||
\(299\) | −507.000 | −0.0980621 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 2408.00 | 0.461112 | ||||||||
\(302\) | −3200.00 | −0.609733 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 608.000 | 0.114708 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 4592.00 | 0.853678 | 0.426839 | − | 0.904328i | \(-0.359627\pi\) | ||||
0.426839 | + | 0.904328i | \(0.359627\pi\) | |||||||
\(308\) | −1092.00 | −0.202021 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −6498.00 | −1.18478 | −0.592392 | − | 0.805650i | \(-0.701816\pi\) | ||||
−0.592392 | + | 0.805650i | \(0.701816\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 5762.00 | 1.04054 | 0.520268 | − | 0.854003i | \(-0.325832\pi\) | ||||
0.520268 | + | 0.854003i | \(0.325832\pi\) | |||||||
\(314\) | 2254.00 | 0.405097 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 2996.00 | 0.533349 | ||||||||
\(317\) | −2565.00 | −0.454463 | −0.227231 | − | 0.973841i | \(-0.572967\pi\) | ||||
−0.227231 | + | 0.973841i | \(0.572967\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −3744.00 | −0.657128 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −546.000 | −0.0944950 | ||||||||
\(323\) | −912.000 | −0.157105 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −1625.00 | −0.277350 | ||||||||
\(326\) | −2408.00 | −0.409101 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 840.000 | 0.141406 | ||||||||
\(329\) | −693.000 | −0.116129 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −745.000 | −0.123713 | −0.0618563 | − | 0.998085i | \(-0.519702\pi\) | ||||
−0.0618563 | + | 0.998085i | \(0.519702\pi\) | |||||||
\(332\) | 4176.00 | 0.690325 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 1200.00 | 0.196590 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 8345.00 | 1.34891 | 0.674453 | − | 0.738318i | \(-0.264380\pi\) | ||||
0.674453 | + | 0.738318i | \(0.264380\pi\) | |||||||
\(338\) | 338.000 | 0.0543928 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −8853.00 | −1.40591 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 343.000 | 0.0539949 | ||||||||
\(344\) | 2752.00 | 0.431331 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 4308.00 | 0.669363 | ||||||||
\(347\) | 1776.00 | 0.274757 | 0.137378 | − | 0.990519i | \(-0.456132\pi\) | ||||
0.137378 | + | 0.990519i | \(0.456132\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −8602.00 | −1.31935 | −0.659677 | − | 0.751549i | \(-0.729307\pi\) | ||||
−0.659677 | + | 0.751549i | \(0.729307\pi\) | |||||||
\(350\) | −1750.00 | −0.267261 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −1248.00 | −0.188973 | ||||||||
\(353\) | 6477.00 | 0.976589 | 0.488295 | − | 0.872679i | \(-0.337619\pi\) | ||||
0.488295 | + | 0.872679i | \(0.337619\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 2760.00 | 0.410898 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 5700.00 | 0.841493 | ||||||||
\(359\) | −7920.00 | −1.16435 | −0.582175 | − | 0.813064i | \(-0.697798\pi\) | ||||
−0.582175 | + | 0.813064i | \(0.697798\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −5415.00 | −0.789474 | ||||||||
\(362\) | 8410.00 | 1.22105 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 364.000 | 0.0524142 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 3404.00 | 0.484162 | 0.242081 | − | 0.970256i | \(-0.422170\pi\) | ||||
0.242081 | + | 0.970256i | \(0.422170\pi\) | |||||||
\(368\) | −624.000 | −0.0883920 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 3780.00 | 0.528970 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 10604.0 | 1.47200 | 0.735998 | − | 0.676984i | \(-0.236713\pi\) | ||||
0.735998 | + | 0.676984i | \(0.236713\pi\) | |||||||
\(374\) | 1872.00 | 0.258820 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −792.000 | −0.108628 | ||||||||
\(377\) | 1248.00 | 0.170491 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −11680.0 | −1.58301 | −0.791506 | − | 0.611162i | \(-0.790702\pi\) | ||||
−0.791506 | + | 0.611162i | \(0.790702\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 8304.00 | 1.11222 | ||||||||
\(383\) | −8133.00 | −1.08506 | −0.542529 | − | 0.840037i | \(-0.682533\pi\) | ||||
−0.542529 | + | 0.840037i | \(0.682533\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −6296.00 | −0.830202 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 1268.00 | 0.165910 | ||||||||
\(389\) | −2556.00 | −0.333147 | −0.166574 | − | 0.986029i | \(-0.553270\pi\) | ||||
−0.166574 | + | 0.986029i | \(0.553270\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 936.000 | 0.121063 | ||||||||
\(392\) | 392.000 | 0.0505076 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −2346.00 | −0.299974 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 12620.0 | 1.59541 | 0.797707 | − | 0.603045i | \(-0.206046\pi\) | ||||
0.797707 | + | 0.603045i | \(0.206046\pi\) | |||||||
\(398\) | 7024.00 | 0.884626 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −2000.00 | −0.250000 | ||||||||
\(401\) | −2064.00 | −0.257036 | −0.128518 | − | 0.991707i | \(-0.541022\pi\) | ||||
−0.128518 | + | 0.991707i | \(0.541022\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 2951.00 | 0.364764 | ||||||||
\(404\) | 2652.00 | 0.326589 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 1344.00 | 0.164290 | ||||||||
\(407\) | −16575.0 | −2.01865 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −5974.00 | −0.722238 | −0.361119 | − | 0.932520i | \(-0.617605\pi\) | ||||
−0.361119 | + | 0.932520i | \(0.617605\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −2584.00 | −0.308992 | ||||||||
\(413\) | −798.000 | −0.0950775 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 416.000 | 0.0490290 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −2964.00 | −0.346828 | ||||||||
\(419\) | −12459.0 | −1.45265 | −0.726327 | − | 0.687349i | \(-0.758774\pi\) | ||||
−0.726327 | + | 0.687349i | \(0.758774\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −2221.00 | −0.257114 | −0.128557 | − | 0.991702i | \(-0.541034\pi\) | ||||
−0.128557 | + | 0.991702i | \(0.541034\pi\) | |||||||
\(422\) | −6836.00 | −0.788558 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 4320.00 | 0.494806 | ||||||||
\(425\) | 3000.00 | 0.342403 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −3955.00 | −0.448234 | ||||||||
\(428\) | 2976.00 | 0.336099 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 15162.0 | 1.69450 | 0.847248 | − | 0.531197i | \(-0.178258\pi\) | ||||
0.847248 | + | 0.531197i | \(0.178258\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −10978.0 | −1.21840 | −0.609202 | − | 0.793015i | \(-0.708510\pi\) | ||||
−0.609202 | + | 0.793015i | \(0.708510\pi\) | |||||||
\(434\) | 3178.00 | 0.351495 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 872.000 | 0.0957826 | ||||||||
\(437\) | −1482.00 | −0.162228 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −3274.00 | −0.355944 | −0.177972 | − | 0.984036i | \(-0.556954\pi\) | ||||
−0.177972 | + | 0.984036i | \(0.556954\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −624.000 | −0.0671508 | ||||||||
\(443\) | −3888.00 | −0.416985 | −0.208493 | − | 0.978024i | \(-0.566856\pi\) | ||||
−0.208493 | + | 0.978024i | \(0.566856\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 8482.00 | 0.900525 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 448.000 | 0.0472456 | ||||||||
\(449\) | 11262.0 | 1.18371 | 0.591856 | − | 0.806044i | \(-0.298395\pi\) | ||||
0.591856 | + | 0.806044i | \(0.298395\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −4095.00 | −0.427552 | ||||||||
\(452\) | 6492.00 | 0.675571 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −1776.00 | −0.183594 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −9718.00 | −0.994724 | −0.497362 | − | 0.867543i | \(-0.665698\pi\) | ||||
−0.497362 | + | 0.867543i | \(0.665698\pi\) | |||||||
\(458\) | 9400.00 | 0.959024 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 13656.0 | 1.37966 | 0.689830 | − | 0.723971i | \(-0.257685\pi\) | ||||
0.689830 | + | 0.723971i | \(0.257685\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 12008.0 | 1.20531 | 0.602656 | − | 0.798001i | \(-0.294109\pi\) | ||||
0.602656 | + | 0.798001i | \(0.294109\pi\) | |||||||
\(464\) | 1536.00 | 0.153679 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −12726.0 | −1.26507 | ||||||||
\(467\) | −2268.00 | −0.224733 | −0.112367 | − | 0.993667i | \(-0.535843\pi\) | ||||
−0.112367 | + | 0.993667i | \(0.535843\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −2695.00 | −0.265338 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −912.000 | −0.0889369 | ||||||||
\(473\) | −13416.0 | −1.30416 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −4750.00 | −0.458831 | ||||||||
\(476\) | −672.000 | −0.0647081 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 6156.00 | 0.589056 | ||||||||
\(479\) | 10536.0 | 1.00501 | 0.502507 | − | 0.864573i | \(-0.332411\pi\) | ||||
0.502507 | + | 0.864573i | \(0.332411\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 5525.00 | 0.523739 | ||||||||
\(482\) | 7348.00 | 0.694382 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 760.000 | 0.0713749 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 12566.0 | 1.16924 | 0.584620 | − | 0.811307i | \(-0.301244\pi\) | ||||
0.584620 | + | 0.811307i | \(0.301244\pi\) | |||||||
\(488\) | −4520.00 | −0.419284 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 12444.0 | 1.14377 | 0.571884 | − | 0.820335i | \(-0.306213\pi\) | ||||
0.571884 | + | 0.820335i | \(0.306213\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −2304.00 | −0.210481 | ||||||||
\(494\) | 988.000 | 0.0899843 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 3632.00 | 0.328794 | ||||||||
\(497\) | 1092.00 | 0.0985571 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −6091.00 | −0.546434 | −0.273217 | − | 0.961952i | \(-0.588088\pi\) | ||||
−0.273217 | + | 0.961952i | \(0.588088\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 690.000 | 0.0613470 | ||||||||
\(503\) | −9204.00 | −0.815877 | −0.407938 | − | 0.913009i | \(-0.633752\pi\) | ||||
−0.407938 | + | 0.913009i | \(0.633752\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 3042.00 | 0.267260 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 2636.00 | 0.230224 | ||||||||
\(509\) | −21522.0 | −1.87416 | −0.937078 | − | 0.349119i | \(-0.886481\pi\) | ||||
−0.937078 | + | 0.349119i | \(0.886481\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −4711.00 | −0.407832 | ||||||||
\(512\) | 512.000 | 0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −13776.0 | −1.18217 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 3861.00 | 0.328446 | ||||||||
\(518\) | 5950.00 | 0.504687 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 12474.0 | 1.04894 | 0.524468 | − | 0.851430i | \(-0.324264\pi\) | ||||
0.524468 | + | 0.851430i | \(0.324264\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 16607.0 | 1.38848 | 0.694238 | − | 0.719745i | \(-0.255741\pi\) | ||||
0.694238 | + | 0.719745i | \(0.255741\pi\) | |||||||
\(524\) | 864.000 | 0.0720306 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 2496.00 | 0.206903 | ||||||||
\(527\) | −5448.00 | −0.450320 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −10646.0 | −0.874990 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 1064.00 | 0.0867110 | ||||||||
\(533\) | 1365.00 | 0.110928 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −3080.00 | −0.248201 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 4506.00 | 0.361092 | ||||||||
\(539\) | −1911.00 | −0.152714 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −19690.0 | −1.56477 | −0.782384 | − | 0.622797i | \(-0.785996\pi\) | ||||
−0.782384 | + | 0.622797i | \(0.785996\pi\) | |||||||
\(542\) | 2794.00 | 0.221425 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −768.000 | −0.0605289 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −19960.0 | −1.56020 | −0.780099 | − | 0.625656i | \(-0.784831\pi\) | ||||
−0.780099 | + | 0.625656i | \(0.784831\pi\) | |||||||
\(548\) | −7368.00 | −0.574353 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 9750.00 | 0.755893 | ||||||||
\(551\) | 3648.00 | 0.282051 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 5243.00 | 0.403174 | ||||||||
\(554\) | −4604.00 | −0.353078 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −2512.00 | −0.191605 | ||||||||
\(557\) | −19137.0 | −1.45576 | −0.727882 | − | 0.685702i | \(-0.759495\pi\) | ||||
−0.727882 | + | 0.685702i | \(0.759495\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 4472.00 | 0.338364 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −17064.0 | −1.28079 | ||||||||
\(563\) | −6711.00 | −0.502371 | −0.251186 | − | 0.967939i | \(-0.580820\pi\) | ||||
−0.251186 | + | 0.967939i | \(0.580820\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −7538.00 | −0.559798 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 1248.00 | 0.0921918 | ||||||||
\(569\) | 5595.00 | 0.412222 | 0.206111 | − | 0.978529i | \(-0.433919\pi\) | ||||
0.206111 | + | 0.978529i | \(0.433919\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −21274.0 | −1.55918 | −0.779588 | − | 0.626293i | \(-0.784571\pi\) | ||||
−0.779588 | + | 0.626293i | \(0.784571\pi\) | |||||||
\(572\) | −2028.00 | −0.148243 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 1470.00 | 0.106893 | ||||||||
\(575\) | 4875.00 | 0.353568 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −15694.0 | −1.13232 | −0.566161 | − | 0.824295i | \(-0.691572\pi\) | ||||
−0.566161 | + | 0.824295i | \(0.691572\pi\) | |||||||
\(578\) | −8674.00 | −0.624206 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 7308.00 | 0.521836 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −21060.0 | −1.49608 | ||||||||
\(584\) | −5384.00 | −0.381492 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 12300.0 | 0.867079 | ||||||||
\(587\) | −21054.0 | −1.48039 | −0.740197 | − | 0.672390i | \(-0.765268\pi\) | ||||
−0.740197 | + | 0.672390i | \(0.765268\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 8626.00 | 0.603443 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 6800.00 | 0.472092 | ||||||||
\(593\) | 17910.0 | 1.24026 | 0.620131 | − | 0.784498i | \(-0.287079\pi\) | ||||
0.620131 | + | 0.784498i | \(0.287079\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −1284.00 | −0.0882461 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −1014.00 | −0.0693404 | ||||||||
\(599\) | −3213.00 | −0.219165 | −0.109582 | − | 0.993978i | \(-0.534951\pi\) | ||||
−0.109582 | + | 0.993978i | \(0.534951\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 15158.0 | 1.02880 | 0.514399 | − | 0.857551i | \(-0.328015\pi\) | ||||
0.514399 | + | 0.857551i | \(0.328015\pi\) | |||||||
\(602\) | 4816.00 | 0.326056 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −6400.00 | −0.431146 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −26206.0 | −1.75234 | −0.876169 | − | 0.482005i | \(-0.839909\pi\) | ||||
−0.876169 | + | 0.482005i | \(0.839909\pi\) | |||||||
\(608\) | 1216.00 | 0.0811107 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −1287.00 | −0.0852151 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −6145.00 | −0.404885 | −0.202442 | − | 0.979294i | \(-0.564888\pi\) | ||||
−0.202442 | + | 0.979294i | \(0.564888\pi\) | |||||||
\(614\) | 9184.00 | 0.603642 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −2184.00 | −0.142850 | ||||||||
\(617\) | −9474.00 | −0.618167 | −0.309083 | − | 0.951035i | \(-0.600022\pi\) | ||||
−0.309083 | + | 0.951035i | \(0.600022\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −14326.0 | −0.930227 | −0.465114 | − | 0.885251i | \(-0.653987\pi\) | ||||
−0.465114 | + | 0.885251i | \(0.653987\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −12996.0 | −0.837769 | ||||||||
\(623\) | 4830.00 | 0.310610 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 15625.0 | 1.00000 | ||||||||
\(626\) | 11524.0 | 0.735769 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 4508.00 | 0.286447 | ||||||||
\(629\) | −10200.0 | −0.646583 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −15478.0 | −0.976497 | −0.488248 | − | 0.872705i | \(-0.662364\pi\) | ||||
−0.488248 | + | 0.872705i | \(0.662364\pi\) | |||||||
\(632\) | 5992.00 | 0.377134 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −5130.00 | −0.321354 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 637.000 | 0.0396214 | ||||||||
\(638\) | −7488.00 | −0.464659 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −17439.0 | −1.07457 | −0.537285 | − | 0.843401i | \(-0.680550\pi\) | ||||
−0.537285 | + | 0.843401i | \(0.680550\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 30296.0 | 1.85810 | 0.929049 | − | 0.369956i | \(-0.120627\pi\) | ||||
0.929049 | + | 0.369956i | \(0.120627\pi\) | |||||||
\(644\) | −1092.00 | −0.0668181 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −1824.00 | −0.111090 | ||||||||
\(647\) | 17124.0 | 1.04052 | 0.520258 | − | 0.854009i | \(-0.325836\pi\) | ||||
0.520258 | + | 0.854009i | \(0.325836\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 4446.00 | 0.268907 | ||||||||
\(650\) | −3250.00 | −0.196116 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −4816.00 | −0.289278 | ||||||||
\(653\) | −27120.0 | −1.62525 | −0.812625 | − | 0.582788i | \(-0.801962\pi\) | ||||
−0.812625 | + | 0.582788i | \(0.801962\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 1680.00 | 0.0999893 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −1386.00 | −0.0821154 | ||||||||
\(659\) | 138.000 | 0.00815739 | 0.00407869 | − | 0.999992i | \(-0.498702\pi\) | ||||
0.00407869 | + | 0.999992i | \(0.498702\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 29720.0 | 1.74883 | 0.874413 | − | 0.485182i | \(-0.161247\pi\) | ||||
0.874413 | + | 0.485182i | \(0.161247\pi\) | |||||||
\(662\) | −1490.00 | −0.0874781 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 8352.00 | 0.488133 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −3744.00 | −0.217344 | ||||||||
\(668\) | 2400.00 | 0.139010 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 22035.0 | 1.26774 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −32929.0 | −1.88606 | −0.943031 | − | 0.332705i | \(-0.892039\pi\) | ||||
−0.943031 | + | 0.332705i | \(0.892039\pi\) | |||||||
\(674\) | 16690.0 | 0.953820 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 676.000 | 0.0384615 | ||||||||
\(677\) | −33021.0 | −1.87459 | −0.937297 | − | 0.348532i | \(-0.886680\pi\) | ||||
−0.937297 | + | 0.348532i | \(0.886680\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 2219.00 | 0.125416 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −17706.0 | −0.994132 | ||||||||
\(683\) | −18519.0 | −1.03750 | −0.518748 | − | 0.854927i | \(-0.673602\pi\) | ||||
−0.518748 | + | 0.854927i | \(0.673602\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 686.000 | 0.0381802 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 5504.00 | 0.304997 | ||||||||
\(689\) | 7020.00 | 0.388158 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 15248.0 | 0.839452 | 0.419726 | − | 0.907651i | \(-0.362126\pi\) | ||||
0.419726 | + | 0.907651i | \(0.362126\pi\) | |||||||
\(692\) | 8616.00 | 0.473311 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 3552.00 | 0.194283 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −2520.00 | −0.136947 | ||||||||
\(698\) | −17204.0 | −0.932924 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −3500.00 | −0.188982 | ||||||||
\(701\) | 7740.00 | 0.417027 | 0.208513 | − | 0.978020i | \(-0.433138\pi\) | ||||
0.208513 | + | 0.978020i | \(0.433138\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 16150.0 | 0.866442 | ||||||||
\(704\) | −2496.00 | −0.133624 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 12954.0 | 0.690553 | ||||||||
\(707\) | 4641.00 | 0.246878 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 29747.0 | 1.57570 | 0.787851 | − | 0.615867i | \(-0.211194\pi\) | ||||
0.787851 | + | 0.615867i | \(0.211194\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 5520.00 | 0.290549 | ||||||||
\(713\) | −8853.00 | −0.465003 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 11400.0 | 0.595025 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −15840.0 | −0.823320 | ||||||||
\(719\) | −10266.0 | −0.532486 | −0.266243 | − | 0.963906i | \(-0.585782\pi\) | ||||
−0.266243 | + | 0.963906i | \(0.585782\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −4522.00 | −0.233576 | ||||||||
\(722\) | −10830.0 | −0.558242 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 16820.0 | 0.863412 | ||||||||
\(725\) | −12000.0 | −0.614716 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −8026.00 | −0.409447 | −0.204723 | − | 0.978820i | \(-0.565629\pi\) | ||||
−0.204723 | + | 0.978820i | \(0.565629\pi\) | |||||||
\(728\) | 728.000 | 0.0370625 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −8256.00 | −0.417728 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 13268.0 | 0.668574 | 0.334287 | − | 0.942471i | \(-0.391505\pi\) | ||||
0.334287 | + | 0.942471i | \(0.391505\pi\) | |||||||
\(734\) | 6808.00 | 0.342354 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −1248.00 | −0.0625026 | ||||||||
\(737\) | 15015.0 | 0.750454 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −8080.00 | −0.402202 | −0.201101 | − | 0.979570i | \(-0.564452\pi\) | ||||
−0.201101 | + | 0.979570i | \(0.564452\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 7560.00 | 0.374038 | ||||||||
\(743\) | 27096.0 | 1.33789 | 0.668947 | − | 0.743310i | \(-0.266745\pi\) | ||||
0.668947 | + | 0.743310i | \(0.266745\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 21208.0 | 1.04086 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 3744.00 | 0.183014 | ||||||||
\(749\) | 5208.00 | 0.254067 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 25067.0 | 1.21799 | 0.608993 | − | 0.793175i | \(-0.291574\pi\) | ||||
0.608993 | + | 0.793175i | \(0.291574\pi\) | |||||||
\(752\) | −1584.00 | −0.0768119 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 2496.00 | 0.120556 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −6442.00 | −0.309298 | −0.154649 | − | 0.987969i | \(-0.549425\pi\) | ||||
−0.154649 | + | 0.987969i | \(0.549425\pi\) | |||||||
\(758\) | −23360.0 | −1.11936 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −26511.0 | −1.26284 | −0.631421 | − | 0.775440i | \(-0.717528\pi\) | ||||
−0.631421 | + | 0.775440i | \(0.717528\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 1526.00 | 0.0724049 | ||||||||
\(764\) | 16608.0 | 0.786461 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −16266.0 | −0.767251 | ||||||||
\(767\) | −1482.00 | −0.0697678 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −17665.0 | −0.828370 | −0.414185 | − | 0.910193i | \(-0.635933\pi\) | ||||
−0.414185 | + | 0.910193i | \(0.635933\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −12592.0 | −0.587041 | ||||||||
\(773\) | −36258.0 | −1.68708 | −0.843538 | − | 0.537070i | \(-0.819531\pi\) | ||||
−0.843538 | + | 0.537070i | \(0.819531\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −28375.0 | −1.31517 | ||||||||
\(776\) | 2536.00 | 0.117316 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −5112.00 | −0.235571 | ||||||||
\(779\) | 3990.00 | 0.183513 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −6084.00 | −0.278749 | ||||||||
\(782\) | 1872.00 | 0.0856043 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 784.000 | 0.0357143 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 21296.0 | 0.964575 | 0.482287 | − | 0.876013i | \(-0.339806\pi\) | ||||
0.482287 | + | 0.876013i | \(0.339806\pi\) | |||||||
\(788\) | −4692.00 | −0.212114 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 11361.0 | 0.510684 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −7345.00 | −0.328914 | ||||||||
\(794\) | 25240.0 | 1.12813 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 14048.0 | 0.625525 | ||||||||
\(797\) | 28947.0 | 1.28652 | 0.643259 | − | 0.765648i | \(-0.277582\pi\) | ||||
0.643259 | + | 0.765648i | \(0.277582\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 2376.00 | 0.105203 | ||||||||
\(800\) | −4000.00 | −0.176777 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −4128.00 | −0.181752 | ||||||||
\(803\) | 26247.0 | 1.15347 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 5902.00 | 0.257927 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 5304.00 | 0.230933 | ||||||||
\(809\) | 20418.0 | 0.887341 | 0.443670 | − | 0.896190i | \(-0.353676\pi\) | ||||
0.443670 | + | 0.896190i | \(0.353676\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −14524.0 | −0.628861 | −0.314431 | − | 0.949280i | \(-0.601814\pi\) | ||||
−0.314431 | + | 0.949280i | \(0.601814\pi\) | |||||||
\(812\) | 2688.00 | 0.116170 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −33150.0 | −1.42740 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 13072.0 | 0.559769 | ||||||||
\(818\) | −11948.0 | −0.510699 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 7710.00 | 0.327748 | 0.163874 | − | 0.986481i | \(-0.447601\pi\) | ||||
0.163874 | + | 0.986481i | \(0.447601\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 2531.00 | 0.107199 | 0.0535997 | − | 0.998563i | \(-0.482931\pi\) | ||||
0.0535997 | + | 0.998563i | \(0.482931\pi\) | |||||||
\(824\) | −5168.00 | −0.218490 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −1596.00 | −0.0672300 | ||||||||
\(827\) | −24516.0 | −1.03084 | −0.515420 | − | 0.856938i | \(-0.672364\pi\) | ||||
−0.515420 | + | 0.856938i | \(0.672364\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −15586.0 | −0.652985 | −0.326492 | − | 0.945200i | \(-0.605867\pi\) | ||||
−0.326492 | + | 0.945200i | \(0.605867\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 832.000 | 0.0346688 | ||||||||
\(833\) | −1176.00 | −0.0489147 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −5928.00 | −0.245244 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −24918.0 | −1.02718 | ||||||||
\(839\) | 24915.0 | 1.02522 | 0.512611 | − | 0.858621i | \(-0.328678\pi\) | ||||
0.512611 | + | 0.858621i | \(0.328678\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −15173.0 | −0.622125 | ||||||||
\(842\) | −4442.00 | −0.181807 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −13672.0 | −0.557594 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 1330.00 | 0.0539544 | ||||||||
\(848\) | 8640.00 | 0.349881 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 6000.00 | 0.242116 | ||||||||
\(851\) | −16575.0 | −0.667666 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −20500.0 | −0.822868 | −0.411434 | − | 0.911439i | \(-0.634972\pi\) | ||||
−0.411434 | + | 0.911439i | \(0.634972\pi\) | |||||||
\(854\) | −7910.00 | −0.316949 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 5952.00 | 0.237658 | ||||||||
\(857\) | −26694.0 | −1.06400 | −0.532001 | − | 0.846744i | \(-0.678560\pi\) | ||||
−0.532001 | + | 0.846744i | \(0.678560\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 20801.0 | 0.826218 | 0.413109 | − | 0.910682i | \(-0.364443\pi\) | ||||
0.413109 | + | 0.910682i | \(0.364443\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 30324.0 | 1.19819 | ||||||||
\(863\) | 37404.0 | 1.47537 | 0.737687 | − | 0.675143i | \(-0.235918\pi\) | ||||
0.737687 | + | 0.675143i | \(0.235918\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −21956.0 | −0.861542 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 6356.00 | 0.248545 | ||||||||
\(869\) | −29211.0 | −1.14029 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −5005.00 | −0.194705 | ||||||||
\(872\) | 1744.00 | 0.0677285 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −2964.00 | −0.114713 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −20581.0 | −0.792441 | −0.396221 | − | 0.918155i | \(-0.629678\pi\) | ||||
−0.396221 | + | 0.918155i | \(0.629678\pi\) | |||||||
\(878\) | −6548.00 | −0.251691 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 34314.0 | 1.31222 | 0.656111 | − | 0.754664i | \(-0.272200\pi\) | ||||
0.656111 | + | 0.754664i | \(0.272200\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −12058.0 | −0.459552 | −0.229776 | − | 0.973244i | \(-0.573799\pi\) | ||||
−0.229776 | + | 0.973244i | \(0.573799\pi\) | |||||||
\(884\) | −1248.00 | −0.0474828 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −7776.00 | −0.294853 | ||||||||
\(887\) | −20406.0 | −0.772454 | −0.386227 | − | 0.922404i | \(-0.626222\pi\) | ||||
−0.386227 | + | 0.922404i | \(0.626222\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 4613.00 | 0.174033 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 16964.0 | 0.636768 | ||||||||
\(893\) | −3762.00 | −0.140975 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 896.000 | 0.0334077 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 22524.0 | 0.837011 | ||||||||
\(899\) | 21792.0 | 0.808458 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −12960.0 | −0.479201 | ||||||||
\(902\) | −8190.00 | −0.302325 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 12984.0 | 0.477701 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −2914.00 | −0.106679 | −0.0533395 | − | 0.998576i | \(-0.516987\pi\) | ||||
−0.0533395 | + | 0.998576i | \(0.516987\pi\) | |||||||
\(908\) | −3552.00 | −0.129821 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 1044.00 | 0.0379685 | 0.0189842 | − | 0.999820i | \(-0.493957\pi\) | ||||
0.0189842 | + | 0.999820i | \(0.493957\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −40716.0 | −1.47591 | ||||||||
\(914\) | −19436.0 | −0.703376 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 18800.0 | 0.678133 | ||||||||
\(917\) | 1512.00 | 0.0544500 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 20693.0 | 0.742763 | 0.371381 | − | 0.928480i | \(-0.378884\pi\) | ||||
0.371381 | + | 0.928480i | \(0.378884\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 27312.0 | 0.975567 | ||||||||
\(923\) | 2028.00 | 0.0723212 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −53125.0 | −1.88837 | ||||||||
\(926\) | 24016.0 | 0.852284 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 3072.00 | 0.108667 | ||||||||
\(929\) | 52653.0 | 1.85951 | 0.929757 | − | 0.368173i | \(-0.120017\pi\) | ||||
0.929757 | + | 0.368173i | \(0.120017\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1862.00 | 0.0655474 | ||||||||
\(932\) | −25452.0 | −0.894536 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −4536.00 | −0.158911 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 34868.0 | 1.21568 | 0.607838 | − | 0.794061i | \(-0.292037\pi\) | ||||
0.607838 | + | 0.794061i | \(0.292037\pi\) | |||||||
\(938\) | −5390.00 | −0.187622 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −25542.0 | −0.884852 | −0.442426 | − | 0.896805i | \(-0.645882\pi\) | ||||
−0.442426 | + | 0.896805i | \(0.645882\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −4095.00 | −0.141412 | ||||||||
\(944\) | −1824.00 | −0.0628879 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −26832.0 | −0.922181 | ||||||||
\(947\) | 672.000 | 0.0230592 | 0.0115296 | − | 0.999934i | \(-0.496330\pi\) | ||||
0.0115296 | + | 0.999934i | \(0.496330\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −8749.00 | −0.299267 | ||||||||
\(950\) | −9500.00 | −0.324443 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −1344.00 | −0.0457556 | ||||||||
\(953\) | −52278.0 | −1.77697 | −0.888484 | − | 0.458908i | \(-0.848241\pi\) | ||||
−0.888484 | + | 0.458908i | \(0.848241\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 12312.0 | 0.416526 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 21072.0 | 0.710653 | ||||||||
\(959\) | −12894.0 | −0.434170 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 21738.0 | 0.729683 | ||||||||
\(962\) | 11050.0 | 0.370339 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 14696.0 | 0.491002 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 758.000 | 0.0252075 | 0.0126037 | − | 0.999921i | \(-0.495988\pi\) | ||||
0.0126037 | + | 0.999921i | \(0.495988\pi\) | |||||||
\(968\) | 1520.00 | 0.0504697 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −27285.0 | −0.901769 | −0.450884 | − | 0.892582i | \(-0.648891\pi\) | ||||
−0.450884 | + | 0.892582i | \(0.648891\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −4396.00 | −0.144840 | ||||||||
\(974\) | 25132.0 | 0.826777 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −9040.00 | −0.296479 | ||||||||
\(977\) | −18786.0 | −0.615166 | −0.307583 | − | 0.951521i | \(-0.599520\pi\) | ||||
−0.307583 | + | 0.951521i | \(0.599520\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −26910.0 | −0.878496 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 24888.0 | 0.808766 | ||||||||
\(983\) | −37152.0 | −1.20546 | −0.602729 | − | 0.797946i | \(-0.705920\pi\) | ||||
−0.602729 | + | 0.797946i | \(0.705920\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −4608.00 | −0.148832 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 1976.00 | 0.0636285 | ||||||||
\(989\) | −13416.0 | −0.431349 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −17143.0 | −0.549511 | −0.274755 | − | 0.961514i | \(-0.588597\pi\) | ||||
−0.274755 | + | 0.961514i | \(0.588597\pi\) | |||||||
\(992\) | 7264.00 | 0.232492 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 2184.00 | 0.0696904 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −14137.0 | −0.449070 | −0.224535 | − | 0.974466i | \(-0.572086\pi\) | ||||
−0.224535 | + | 0.974466i | \(0.572086\pi\) | |||||||
\(998\) | −12182.0 | −0.386387 | ||||||||
\(999\) | 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 | 1638.4.a.j.1.1 | 1 | ||
3.2 | odd | 2 | 182.4.a.a.1.1 | ✓ | 1 | ||
12.11 | even | 2 | 1456.4.a.b.1.1 | 1 | |||
21.20 | even | 2 | 1274.4.a.a.1.1 | 1 | |||
39.38 | odd | 2 | 2366.4.a.g.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
182.4.a.a.1.1 | ✓ | 1 | 3.2 | odd | 2 | ||
1274.4.a.a.1.1 | 1 | 21.20 | even | 2 | |||
1456.4.a.b.1.1 | 1 | 12.11 | even | 2 | |||
1638.4.a.j.1.1 | 1 | 1.1 | even | 1 | trivial | ||
2366.4.a.g.1.1 | 1 | 39.38 | odd | 2 |