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: | \(1\) |
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 | ||||||||
\(5\) | 5.00000 | 0.447214 | 0.223607 | − | 0.974679i | \(-0.428217\pi\) | ||||
0.223607 | + | 0.974679i | \(0.428217\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −7.00000 | −0.377964 | ||||||||
\(8\) | −8.00000 | −0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −10.0000 | −0.316228 | ||||||||
\(11\) | 36.0000 | 0.986764 | 0.493382 | − | 0.869813i | \(-0.335760\pi\) | ||||
0.493382 | + | 0.869813i | \(0.335760\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −13.0000 | −0.277350 | ||||||||
\(14\) | 14.0000 | 0.267261 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 16.0000 | 0.250000 | ||||||||
\(17\) | −26.0000 | −0.370937 | −0.185468 | − | 0.982650i | \(-0.559380\pi\) | ||||
−0.185468 | + | 0.982650i | \(0.559380\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −47.0000 | −0.567502 | −0.283751 | − | 0.958898i | \(-0.591579\pi\) | ||||
−0.283751 | + | 0.958898i | \(0.591579\pi\) | |||||||
\(20\) | 20.0000 | 0.223607 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −72.0000 | −0.697748 | ||||||||
\(23\) | 99.0000 | 0.897519 | 0.448759 | − | 0.893653i | \(-0.351866\pi\) | ||||
0.448759 | + | 0.893653i | \(0.351866\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −100.000 | −0.800000 | ||||||||
\(26\) | 26.0000 | 0.196116 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −28.0000 | −0.188982 | ||||||||
\(29\) | 61.0000 | 0.390601 | 0.195300 | − | 0.980743i | \(-0.437432\pi\) | ||||
0.195300 | + | 0.980743i | \(0.437432\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −23.0000 | −0.133256 | −0.0666278 | − | 0.997778i | \(-0.521224\pi\) | ||||
−0.0666278 | + | 0.997778i | \(0.521224\pi\) | |||||||
\(32\) | −32.0000 | −0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 52.0000 | 0.262292 | ||||||||
\(35\) | −35.0000 | −0.169031 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −50.0000 | −0.222161 | −0.111080 | − | 0.993811i | \(-0.535431\pi\) | ||||
−0.111080 | + | 0.993811i | \(0.535431\pi\) | |||||||
\(38\) | 94.0000 | 0.401285 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −40.0000 | −0.158114 | ||||||||
\(41\) | −70.0000 | −0.266638 | −0.133319 | − | 0.991073i | \(-0.542564\pi\) | ||||
−0.133319 | + | 0.991073i | \(0.542564\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −19.0000 | −0.0673831 | −0.0336915 | − | 0.999432i | \(-0.510726\pi\) | ||||
−0.0336915 | + | 0.999432i | \(0.510726\pi\) | |||||||
\(44\) | 144.000 | 0.493382 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −198.000 | −0.634641 | ||||||||
\(47\) | −191.000 | −0.592770 | −0.296385 | − | 0.955068i | \(-0.595781\pi\) | ||||
−0.296385 | + | 0.955068i | \(0.595781\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 49.0000 | 0.142857 | ||||||||
\(50\) | 200.000 | 0.565685 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −52.0000 | −0.138675 | ||||||||
\(53\) | −195.000 | −0.505383 | −0.252692 | − | 0.967547i | \(-0.581316\pi\) | ||||
−0.252692 | + | 0.967547i | \(0.581316\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 180.000 | 0.441294 | ||||||||
\(56\) | 56.0000 | 0.133631 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −122.000 | −0.276196 | ||||||||
\(59\) | −264.000 | −0.582540 | −0.291270 | − | 0.956641i | \(-0.594078\pi\) | ||||
−0.291270 | + | 0.956641i | \(0.594078\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 310.000 | 0.650679 | 0.325340 | − | 0.945597i | \(-0.394521\pi\) | ||||
0.325340 | + | 0.945597i | \(0.394521\pi\) | |||||||
\(62\) | 46.0000 | 0.0942259 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 64.0000 | 0.125000 | ||||||||
\(65\) | −65.0000 | −0.124035 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −190.000 | −0.346451 | −0.173225 | − | 0.984882i | \(-0.555419\pi\) | ||||
−0.173225 | + | 0.984882i | \(0.555419\pi\) | |||||||
\(68\) | −104.000 | −0.185468 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 70.0000 | 0.119523 | ||||||||
\(71\) | 166.000 | 0.277473 | 0.138736 | − | 0.990329i | \(-0.455696\pi\) | ||||
0.138736 | + | 0.990329i | \(0.455696\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 873.000 | 1.39968 | 0.699842 | − | 0.714298i | \(-0.253254\pi\) | ||||
0.699842 | + | 0.714298i | \(0.253254\pi\) | |||||||
\(74\) | 100.000 | 0.157091 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −188.000 | −0.283751 | ||||||||
\(77\) | −252.000 | −0.372962 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −1191.00 | −1.69618 | −0.848088 | − | 0.529855i | \(-0.822246\pi\) | ||||
−0.848088 | + | 0.529855i | \(0.822246\pi\) | |||||||
\(80\) | 80.0000 | 0.111803 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 140.000 | 0.188542 | ||||||||
\(83\) | −259.000 | −0.342517 | −0.171259 | − | 0.985226i | \(-0.554783\pi\) | ||||
−0.171259 | + | 0.985226i | \(0.554783\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −130.000 | −0.165888 | ||||||||
\(86\) | 38.0000 | 0.0476470 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −288.000 | −0.348874 | ||||||||
\(89\) | 635.000 | 0.756291 | 0.378145 | − | 0.925746i | \(-0.376562\pi\) | ||||
0.378145 | + | 0.925746i | \(0.376562\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 91.0000 | 0.104828 | ||||||||
\(92\) | 396.000 | 0.448759 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 382.000 | 0.419152 | ||||||||
\(95\) | −235.000 | −0.253795 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 133.000 | 0.139218 | 0.0696088 | − | 0.997574i | \(-0.477825\pi\) | ||||
0.0696088 | + | 0.997574i | \(0.477825\pi\) | |||||||
\(98\) | −98.0000 | −0.101015 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −400.000 | −0.400000 | ||||||||
\(101\) | −152.000 | −0.149748 | −0.0748741 | − | 0.997193i | \(-0.523855\pi\) | ||||
−0.0748741 | + | 0.997193i | \(0.523855\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1664.00 | −1.59183 | −0.795916 | − | 0.605406i | \(-0.793011\pi\) | ||||
−0.795916 | + | 0.605406i | \(0.793011\pi\) | |||||||
\(104\) | 104.000 | 0.0980581 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 390.000 | 0.357360 | ||||||||
\(107\) | 36.0000 | 0.0325257 | 0.0162629 | − | 0.999868i | \(-0.494823\pi\) | ||||
0.0162629 | + | 0.999868i | \(0.494823\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −232.000 | −0.203868 | −0.101934 | − | 0.994791i | \(-0.532503\pi\) | ||||
−0.101934 | + | 0.994791i | \(0.532503\pi\) | |||||||
\(110\) | −360.000 | −0.312042 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −112.000 | −0.0944911 | ||||||||
\(113\) | −1353.00 | −1.12637 | −0.563184 | − | 0.826332i | \(-0.690424\pi\) | ||||
−0.563184 | + | 0.826332i | \(0.690424\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 495.000 | 0.401383 | ||||||||
\(116\) | 244.000 | 0.195300 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 528.000 | 0.411918 | ||||||||
\(119\) | 182.000 | 0.140201 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −35.0000 | −0.0262960 | ||||||||
\(122\) | −620.000 | −0.460100 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −92.0000 | −0.0666278 | ||||||||
\(125\) | −1125.00 | −0.804984 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 576.000 | 0.402455 | 0.201227 | − | 0.979545i | \(-0.435507\pi\) | ||||
0.201227 | + | 0.979545i | \(0.435507\pi\) | |||||||
\(128\) | −128.000 | −0.0883883 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 130.000 | 0.0877058 | ||||||||
\(131\) | 2056.00 | 1.37125 | 0.685624 | − | 0.727956i | \(-0.259529\pi\) | ||||
0.685624 | + | 0.727956i | \(0.259529\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 329.000 | 0.214496 | ||||||||
\(134\) | 380.000 | 0.244978 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 208.000 | 0.131146 | ||||||||
\(137\) | 1842.00 | 1.14871 | 0.574353 | − | 0.818608i | \(-0.305254\pi\) | ||||
0.574353 | + | 0.818608i | \(0.305254\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −1288.00 | −0.785948 | −0.392974 | − | 0.919550i | \(-0.628554\pi\) | ||||
−0.392974 | + | 0.919550i | \(0.628554\pi\) | |||||||
\(140\) | −140.000 | −0.0845154 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −332.000 | −0.196203 | ||||||||
\(143\) | −468.000 | −0.273679 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 305.000 | 0.174682 | ||||||||
\(146\) | −1746.00 | −0.989726 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −200.000 | −0.111080 | ||||||||
\(149\) | −1196.00 | −0.657585 | −0.328792 | − | 0.944402i | \(-0.606642\pi\) | ||||
−0.328792 | + | 0.944402i | \(0.606642\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −890.000 | −0.479650 | −0.239825 | − | 0.970816i | \(-0.577090\pi\) | ||||
−0.239825 | + | 0.970816i | \(0.577090\pi\) | |||||||
\(152\) | 376.000 | 0.200642 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 504.000 | 0.263724 | ||||||||
\(155\) | −115.000 | −0.0595937 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 138.000 | 0.0701503 | 0.0350752 | − | 0.999385i | \(-0.488833\pi\) | ||||
0.0350752 | + | 0.999385i | \(0.488833\pi\) | |||||||
\(158\) | 2382.00 | 1.19938 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −160.000 | −0.0790569 | ||||||||
\(161\) | −693.000 | −0.339230 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −3956.00 | −1.90097 | −0.950484 | − | 0.310773i | \(-0.899412\pi\) | ||||
−0.950484 | + | 0.310773i | \(0.899412\pi\) | |||||||
\(164\) | −280.000 | −0.133319 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 518.000 | 0.242196 | ||||||||
\(167\) | 3675.00 | 1.70287 | 0.851437 | − | 0.524457i | \(-0.175731\pi\) | ||||
0.851437 | + | 0.524457i | \(0.175731\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 169.000 | 0.0769231 | ||||||||
\(170\) | 260.000 | 0.117301 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −76.0000 | −0.0336915 | ||||||||
\(173\) | 2826.00 | 1.24195 | 0.620973 | − | 0.783832i | \(-0.286737\pi\) | ||||
0.620973 | + | 0.783832i | \(0.286737\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 700.000 | 0.302372 | ||||||||
\(176\) | 576.000 | 0.246691 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −1270.00 | −0.534778 | ||||||||
\(179\) | 3235.00 | 1.35081 | 0.675406 | − | 0.737446i | \(-0.263969\pi\) | ||||
0.675406 | + | 0.737446i | \(0.263969\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1260.00 | 0.517431 | 0.258716 | − | 0.965954i | \(-0.416701\pi\) | ||||
0.258716 | + | 0.965954i | \(0.416701\pi\) | |||||||
\(182\) | −182.000 | −0.0741249 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −792.000 | −0.317321 | ||||||||
\(185\) | −250.000 | −0.0993533 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −936.000 | −0.366027 | ||||||||
\(188\) | −764.000 | −0.296385 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 470.000 | 0.179460 | ||||||||
\(191\) | 232.000 | 0.0878897 | 0.0439448 | − | 0.999034i | \(-0.486007\pi\) | ||||
0.0439448 | + | 0.999034i | \(0.486007\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −5342.00 | −1.99236 | −0.996180 | − | 0.0873208i | \(-0.972169\pi\) | ||||
−0.996180 | + | 0.0873208i | \(0.972169\pi\) | |||||||
\(194\) | −266.000 | −0.0984417 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 196.000 | 0.0714286 | ||||||||
\(197\) | −1542.00 | −0.557680 | −0.278840 | − | 0.960338i | \(-0.589950\pi\) | ||||
−0.278840 | + | 0.960338i | \(0.589950\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 2182.00 | 0.777276 | 0.388638 | − | 0.921391i | \(-0.372946\pi\) | ||||
0.388638 | + | 0.921391i | \(0.372946\pi\) | |||||||
\(200\) | 800.000 | 0.282843 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 304.000 | 0.105888 | ||||||||
\(203\) | −427.000 | −0.147633 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −350.000 | −0.119244 | ||||||||
\(206\) | 3328.00 | 1.12560 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −208.000 | −0.0693375 | ||||||||
\(209\) | −1692.00 | −0.559991 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −523.000 | −0.170639 | −0.0853194 | − | 0.996354i | \(-0.527191\pi\) | ||||
−0.0853194 | + | 0.996354i | \(0.527191\pi\) | |||||||
\(212\) | −780.000 | −0.252692 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −72.0000 | −0.0229992 | ||||||||
\(215\) | −95.0000 | −0.0301346 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 161.000 | 0.0503659 | ||||||||
\(218\) | 464.000 | 0.144156 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 720.000 | 0.220647 | ||||||||
\(221\) | 338.000 | 0.102879 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −1981.00 | −0.594877 | −0.297439 | − | 0.954741i | \(-0.596132\pi\) | ||||
−0.297439 | + | 0.954741i | \(0.596132\pi\) | |||||||
\(224\) | 224.000 | 0.0668153 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 2706.00 | 0.796462 | ||||||||
\(227\) | −4352.00 | −1.27248 | −0.636239 | − | 0.771492i | \(-0.719511\pi\) | ||||
−0.636239 | + | 0.771492i | \(0.719511\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 2130.00 | 0.614648 | 0.307324 | − | 0.951605i | \(-0.400566\pi\) | ||||
0.307324 | + | 0.951605i | \(0.400566\pi\) | |||||||
\(230\) | −990.000 | −0.283820 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −488.000 | −0.138098 | ||||||||
\(233\) | −2687.00 | −0.755499 | −0.377749 | − | 0.925908i | \(-0.623302\pi\) | ||||
−0.377749 | + | 0.925908i | \(0.623302\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −955.000 | −0.265095 | ||||||||
\(236\) | −1056.00 | −0.291270 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −364.000 | −0.0991370 | ||||||||
\(239\) | −3852.00 | −1.04253 | −0.521266 | − | 0.853394i | \(-0.674540\pi\) | ||||
−0.521266 | + | 0.853394i | \(0.674540\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1069.00 | 0.285728 | 0.142864 | − | 0.989742i | \(-0.454369\pi\) | ||||
0.142864 | + | 0.989742i | \(0.454369\pi\) | |||||||
\(242\) | 70.0000 | 0.0185941 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 1240.00 | 0.325340 | ||||||||
\(245\) | 245.000 | 0.0638877 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 611.000 | 0.157397 | ||||||||
\(248\) | 184.000 | 0.0471130 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 2250.00 | 0.569210 | ||||||||
\(251\) | −5460.00 | −1.37304 | −0.686518 | − | 0.727113i | \(-0.740862\pi\) | ||||
−0.686518 | + | 0.727113i | \(0.740862\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 3564.00 | 0.885639 | ||||||||
\(254\) | −1152.00 | −0.284578 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 256.000 | 0.0625000 | ||||||||
\(257\) | −2172.00 | −0.527181 | −0.263591 | − | 0.964635i | \(-0.584907\pi\) | ||||
−0.263591 | + | 0.964635i | \(0.584907\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 350.000 | 0.0839689 | ||||||||
\(260\) | −260.000 | −0.0620174 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −4112.00 | −0.969619 | ||||||||
\(263\) | 3417.00 | 0.801145 | 0.400573 | − | 0.916265i | \(-0.368811\pi\) | ||||
0.400573 | + | 0.916265i | \(0.368811\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −975.000 | −0.226014 | ||||||||
\(266\) | −658.000 | −0.151671 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −760.000 | −0.173225 | ||||||||
\(269\) | −3792.00 | −0.859488 | −0.429744 | − | 0.902951i | \(-0.641396\pi\) | ||||
−0.429744 | + | 0.902951i | \(0.641396\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −4408.00 | −0.988070 | −0.494035 | − | 0.869442i | \(-0.664479\pi\) | ||||
−0.494035 | + | 0.869442i | \(0.664479\pi\) | |||||||
\(272\) | −416.000 | −0.0927342 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −3684.00 | −0.812258 | ||||||||
\(275\) | −3600.00 | −0.789412 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −1023.00 | −0.221899 | −0.110950 | − | 0.993826i | \(-0.535389\pi\) | ||||
−0.110950 | + | 0.993826i | \(0.535389\pi\) | |||||||
\(278\) | 2576.00 | 0.555749 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 280.000 | 0.0597614 | ||||||||
\(281\) | −7912.00 | −1.67968 | −0.839840 | − | 0.542833i | \(-0.817352\pi\) | ||||
−0.839840 | + | 0.542833i | \(0.817352\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −5336.00 | −1.12082 | −0.560410 | − | 0.828215i | \(-0.689357\pi\) | ||||
−0.560410 | + | 0.828215i | \(0.689357\pi\) | |||||||
\(284\) | 664.000 | 0.138736 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 936.000 | 0.193520 | ||||||||
\(287\) | 490.000 | 0.100780 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −4237.00 | −0.862406 | ||||||||
\(290\) | −610.000 | −0.123519 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 3492.00 | 0.699842 | ||||||||
\(293\) | −6615.00 | −1.31895 | −0.659475 | − | 0.751726i | \(-0.729221\pi\) | ||||
−0.659475 | + | 0.751726i | \(0.729221\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −1320.00 | −0.260520 | ||||||||
\(296\) | 400.000 | 0.0785457 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 2392.00 | 0.464983 | ||||||||
\(299\) | −1287.00 | −0.248927 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 133.000 | 0.0254684 | ||||||||
\(302\) | 1780.00 | 0.339164 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −752.000 | −0.141876 | ||||||||
\(305\) | 1550.00 | 0.290993 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 3843.00 | 0.714435 | 0.357218 | − | 0.934021i | \(-0.383725\pi\) | ||||
0.357218 | + | 0.934021i | \(0.383725\pi\) | |||||||
\(308\) | −1008.00 | −0.186481 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 230.000 | 0.0421391 | ||||||||
\(311\) | −1748.00 | −0.318714 | −0.159357 | − | 0.987221i | \(-0.550942\pi\) | ||||
−0.159357 | + | 0.987221i | \(0.550942\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −9392.00 | −1.69606 | −0.848031 | − | 0.529947i | \(-0.822212\pi\) | ||||
−0.848031 | + | 0.529947i | \(0.822212\pi\) | |||||||
\(314\) | −276.000 | −0.0496038 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −4764.00 | −0.848088 | ||||||||
\(317\) | −10380.0 | −1.83911 | −0.919557 | − | 0.392958i | \(-0.871452\pi\) | ||||
−0.919557 | + | 0.392958i | \(0.871452\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 2196.00 | 0.385431 | ||||||||
\(320\) | 320.000 | 0.0559017 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 1386.00 | 0.239872 | ||||||||
\(323\) | 1222.00 | 0.210507 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1300.00 | 0.221880 | ||||||||
\(326\) | 7912.00 | 1.34419 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 560.000 | 0.0942708 | ||||||||
\(329\) | 1337.00 | 0.224046 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 6250.00 | 1.03786 | 0.518929 | − | 0.854817i | \(-0.326331\pi\) | ||||
0.518929 | + | 0.854817i | \(0.326331\pi\) | |||||||
\(332\) | −1036.00 | −0.171259 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −7350.00 | −1.20411 | ||||||||
\(335\) | −950.000 | −0.154937 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −2315.00 | −0.374202 | −0.187101 | − | 0.982341i | \(-0.559909\pi\) | ||||
−0.187101 | + | 0.982341i | \(0.559909\pi\) | |||||||
\(338\) | −338.000 | −0.0543928 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −520.000 | −0.0829440 | ||||||||
\(341\) | −828.000 | −0.131492 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −343.000 | −0.0539949 | ||||||||
\(344\) | 152.000 | 0.0238235 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −5652.00 | −0.878189 | ||||||||
\(347\) | −3296.00 | −0.509909 | −0.254955 | − | 0.966953i | \(-0.582061\pi\) | ||||
−0.254955 | + | 0.966953i | \(0.582061\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −5607.00 | −0.859988 | −0.429994 | − | 0.902832i | \(-0.641484\pi\) | ||||
−0.429994 | + | 0.902832i | \(0.641484\pi\) | |||||||
\(350\) | −1400.00 | −0.213809 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −1152.00 | −0.174437 | ||||||||
\(353\) | −3722.00 | −0.561196 | −0.280598 | − | 0.959825i | \(-0.590533\pi\) | ||||
−0.280598 | + | 0.959825i | \(0.590533\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 830.000 | 0.124090 | ||||||||
\(356\) | 2540.00 | 0.378145 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −6470.00 | −0.955168 | ||||||||
\(359\) | 2430.00 | 0.357244 | 0.178622 | − | 0.983918i | \(-0.442836\pi\) | ||||
0.178622 | + | 0.983918i | \(0.442836\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −4650.00 | −0.677941 | ||||||||
\(362\) | −2520.00 | −0.365879 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 364.000 | 0.0524142 | ||||||||
\(365\) | 4365.00 | 0.625958 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −8584.00 | −1.22093 | −0.610465 | − | 0.792043i | \(-0.709017\pi\) | ||||
−0.610465 | + | 0.792043i | \(0.709017\pi\) | |||||||
\(368\) | 1584.00 | 0.224380 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 500.000 | 0.0702534 | ||||||||
\(371\) | 1365.00 | 0.191017 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −7274.00 | −1.00974 | −0.504871 | − | 0.863195i | \(-0.668460\pi\) | ||||
−0.504871 | + | 0.863195i | \(0.668460\pi\) | |||||||
\(374\) | 1872.00 | 0.258820 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 1528.00 | 0.209576 | ||||||||
\(377\) | −793.000 | −0.108333 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −1160.00 | −0.157217 | −0.0786084 | − | 0.996906i | \(-0.525048\pi\) | ||||
−0.0786084 | + | 0.996906i | \(0.525048\pi\) | |||||||
\(380\) | −940.000 | −0.126897 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −464.000 | −0.0621474 | ||||||||
\(383\) | 5528.00 | 0.737513 | 0.368757 | − | 0.929526i | \(-0.379784\pi\) | ||||
0.368757 | + | 0.929526i | \(0.379784\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −1260.00 | −0.166794 | ||||||||
\(386\) | 10684.0 | 1.40881 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 532.000 | 0.0696088 | ||||||||
\(389\) | −9666.00 | −1.25986 | −0.629930 | − | 0.776652i | \(-0.716916\pi\) | ||||
−0.629930 | + | 0.776652i | \(0.716916\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −2574.00 | −0.332923 | ||||||||
\(392\) | −392.000 | −0.0505076 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 3084.00 | 0.394339 | ||||||||
\(395\) | −5955.00 | −0.758553 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 4125.00 | 0.521481 | 0.260740 | − | 0.965409i | \(-0.416033\pi\) | ||||
0.260740 | + | 0.965409i | \(0.416033\pi\) | |||||||
\(398\) | −4364.00 | −0.549617 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −1600.00 | −0.200000 | ||||||||
\(401\) | 11796.0 | 1.46899 | 0.734494 | − | 0.678615i | \(-0.237420\pi\) | ||||
0.734494 | + | 0.678615i | \(0.237420\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 299.000 | 0.0369584 | ||||||||
\(404\) | −608.000 | −0.0748741 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 854.000 | 0.104392 | ||||||||
\(407\) | −1800.00 | −0.219220 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 8181.00 | 0.989057 | 0.494529 | − | 0.869161i | \(-0.335341\pi\) | ||||
0.494529 | + | 0.869161i | \(0.335341\pi\) | |||||||
\(410\) | 700.000 | 0.0843184 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −6656.00 | −0.795916 | ||||||||
\(413\) | 1848.00 | 0.220180 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −1295.00 | −0.153178 | ||||||||
\(416\) | 416.000 | 0.0490290 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 3384.00 | 0.395973 | ||||||||
\(419\) | 9296.00 | 1.08386 | 0.541932 | − | 0.840422i | \(-0.317693\pi\) | ||||
0.541932 | + | 0.840422i | \(0.317693\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 9074.00 | 1.05045 | 0.525225 | − | 0.850963i | \(-0.323981\pi\) | ||||
0.525225 | + | 0.850963i | \(0.323981\pi\) | |||||||
\(422\) | 1046.00 | 0.120660 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 1560.00 | 0.178680 | ||||||||
\(425\) | 2600.00 | 0.296749 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −2170.00 | −0.245934 | ||||||||
\(428\) | 144.000 | 0.0162629 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 190.000 | 0.0213084 | ||||||||
\(431\) | −9358.00 | −1.04584 | −0.522922 | − | 0.852380i | \(-0.675158\pi\) | ||||
−0.522922 | + | 0.852380i | \(0.675158\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −14392.0 | −1.59731 | −0.798655 | − | 0.601789i | \(-0.794455\pi\) | ||||
−0.798655 | + | 0.601789i | \(0.794455\pi\) | |||||||
\(434\) | −322.000 | −0.0356140 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −928.000 | −0.101934 | ||||||||
\(437\) | −4653.00 | −0.509344 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −6074.00 | −0.660356 | −0.330178 | − | 0.943919i | \(-0.607109\pi\) | ||||
−0.330178 | + | 0.943919i | \(0.607109\pi\) | |||||||
\(440\) | −1440.00 | −0.156021 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −676.000 | −0.0727467 | ||||||||
\(443\) | 6483.00 | 0.695297 | 0.347649 | − | 0.937625i | \(-0.386980\pi\) | ||||
0.347649 | + | 0.937625i | \(0.386980\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 3175.00 | 0.338223 | ||||||||
\(446\) | 3962.00 | 0.420642 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −448.000 | −0.0472456 | ||||||||
\(449\) | −15388.0 | −1.61738 | −0.808691 | − | 0.588234i | \(-0.799824\pi\) | ||||
−0.808691 | + | 0.588234i | \(0.799824\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −2520.00 | −0.263109 | ||||||||
\(452\) | −5412.00 | −0.563184 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 8704.00 | 0.899777 | ||||||||
\(455\) | 455.000 | 0.0468807 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −4642.00 | −0.475150 | −0.237575 | − | 0.971369i | \(-0.576353\pi\) | ||||
−0.237575 | + | 0.971369i | \(0.576353\pi\) | |||||||
\(458\) | −4260.00 | −0.434622 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 1980.00 | 0.200691 | ||||||||
\(461\) | 14266.0 | 1.44129 | 0.720644 | − | 0.693305i | \(-0.243846\pi\) | ||||
0.720644 | + | 0.693305i | \(0.243846\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 1472.00 | 0.147753 | 0.0738765 | − | 0.997267i | \(-0.476463\pi\) | ||||
0.0738765 | + | 0.997267i | \(0.476463\pi\) | |||||||
\(464\) | 976.000 | 0.0976501 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 5374.00 | 0.534218 | ||||||||
\(467\) | −1332.00 | −0.131986 | −0.0659932 | − | 0.997820i | \(-0.521022\pi\) | ||||
−0.0659932 | + | 0.997820i | \(0.521022\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 1330.00 | 0.130946 | ||||||||
\(470\) | 1910.00 | 0.187450 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 2112.00 | 0.205959 | ||||||||
\(473\) | −684.000 | −0.0664912 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 4700.00 | 0.454002 | ||||||||
\(476\) | 728.000 | 0.0701005 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 7704.00 | 0.737182 | ||||||||
\(479\) | −1629.00 | −0.155388 | −0.0776941 | − | 0.996977i | \(-0.524756\pi\) | ||||
−0.0776941 | + | 0.996977i | \(0.524756\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 650.000 | 0.0616163 | ||||||||
\(482\) | −2138.00 | −0.202040 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −140.000 | −0.0131480 | ||||||||
\(485\) | 665.000 | 0.0622600 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 13754.0 | 1.27978 | 0.639890 | − | 0.768466i | \(-0.278980\pi\) | ||||
0.639890 | + | 0.768466i | \(0.278980\pi\) | |||||||
\(488\) | −2480.00 | −0.230050 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −490.000 | −0.0451754 | ||||||||
\(491\) | 10904.0 | 1.00222 | 0.501111 | − | 0.865383i | \(-0.332925\pi\) | ||||
0.501111 | + | 0.865383i | \(0.332925\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −1586.00 | −0.144888 | ||||||||
\(494\) | −1222.00 | −0.111296 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −368.000 | −0.0333139 | ||||||||
\(497\) | −1162.00 | −0.104875 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 10394.0 | 0.932464 | 0.466232 | − | 0.884663i | \(-0.345611\pi\) | ||||
0.466232 | + | 0.884663i | \(0.345611\pi\) | |||||||
\(500\) | −4500.00 | −0.402492 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 10920.0 | 0.970883 | ||||||||
\(503\) | 5754.00 | 0.510056 | 0.255028 | − | 0.966934i | \(-0.417915\pi\) | ||||
0.255028 | + | 0.966934i | \(0.417915\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −760.000 | −0.0669694 | ||||||||
\(506\) | −7128.00 | −0.626242 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 2304.00 | 0.201227 | ||||||||
\(509\) | −13547.0 | −1.17969 | −0.589843 | − | 0.807518i | \(-0.700810\pi\) | ||||
−0.589843 | + | 0.807518i | \(0.700810\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −6111.00 | −0.529031 | ||||||||
\(512\) | −512.000 | −0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 4344.00 | 0.372774 | ||||||||
\(515\) | −8320.00 | −0.711889 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −6876.00 | −0.584925 | ||||||||
\(518\) | −700.000 | −0.0593750 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 520.000 | 0.0438529 | ||||||||
\(521\) | 7044.00 | 0.592329 | 0.296164 | − | 0.955137i | \(-0.404292\pi\) | ||||
0.296164 | + | 0.955137i | \(0.404292\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 9858.00 | 0.824207 | 0.412103 | − | 0.911137i | \(-0.364794\pi\) | ||||
0.412103 | + | 0.911137i | \(0.364794\pi\) | |||||||
\(524\) | 8224.00 | 0.685624 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −6834.00 | −0.566495 | ||||||||
\(527\) | 598.000 | 0.0494294 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −2366.00 | −0.194460 | ||||||||
\(530\) | 1950.00 | 0.159816 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 1316.00 | 0.107248 | ||||||||
\(533\) | 910.000 | 0.0739521 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 180.000 | 0.0145459 | ||||||||
\(536\) | 1520.00 | 0.122489 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 7584.00 | 0.607750 | ||||||||
\(539\) | 1764.00 | 0.140966 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −5650.00 | −0.449006 | −0.224503 | − | 0.974473i | \(-0.572076\pi\) | ||||
−0.224503 | + | 0.974473i | \(0.572076\pi\) | |||||||
\(542\) | 8816.00 | 0.698671 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 832.000 | 0.0655730 | ||||||||
\(545\) | −1160.00 | −0.0911724 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −14285.0 | −1.11660 | −0.558302 | − | 0.829638i | \(-0.688547\pi\) | ||||
−0.558302 | + | 0.829638i | \(0.688547\pi\) | |||||||
\(548\) | 7368.00 | 0.574353 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 7200.00 | 0.558198 | ||||||||
\(551\) | −2867.00 | −0.221667 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 8337.00 | 0.641095 | ||||||||
\(554\) | 2046.00 | 0.156907 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −5152.00 | −0.392974 | ||||||||
\(557\) | 2472.00 | 0.188047 | 0.0940233 | − | 0.995570i | \(-0.470027\pi\) | ||||
0.0940233 | + | 0.995570i | \(0.470027\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 247.000 | 0.0186887 | ||||||||
\(560\) | −560.000 | −0.0422577 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 15824.0 | 1.18771 | ||||||||
\(563\) | 3936.00 | 0.294641 | 0.147320 | − | 0.989089i | \(-0.452935\pi\) | ||||
0.147320 | + | 0.989089i | \(0.452935\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −6765.00 | −0.503727 | ||||||||
\(566\) | 10672.0 | 0.792540 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −1328.00 | −0.0981015 | ||||||||
\(569\) | −2995.00 | −0.220662 | −0.110331 | − | 0.993895i | \(-0.535191\pi\) | ||||
−0.110331 | + | 0.993895i | \(0.535191\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 19221.0 | 1.40871 | 0.704355 | − | 0.709848i | \(-0.251236\pi\) | ||||
0.704355 | + | 0.709848i | \(0.251236\pi\) | |||||||
\(572\) | −1872.00 | −0.136840 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −980.000 | −0.0712620 | ||||||||
\(575\) | −9900.00 | −0.718015 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −3166.00 | −0.228427 | −0.114213 | − | 0.993456i | \(-0.536435\pi\) | ||||
−0.114213 | + | 0.993456i | \(0.536435\pi\) | |||||||
\(578\) | 8474.00 | 0.609813 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 1220.00 | 0.0873409 | ||||||||
\(581\) | 1813.00 | 0.129459 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −7020.00 | −0.498694 | ||||||||
\(584\) | −6984.00 | −0.494863 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 13230.0 | 0.932639 | ||||||||
\(587\) | −13951.0 | −0.980953 | −0.490476 | − | 0.871454i | \(-0.663177\pi\) | ||||
−0.490476 | + | 0.871454i | \(0.663177\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1081.00 | 0.0756228 | ||||||||
\(590\) | 2640.00 | 0.184215 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −800.000 | −0.0555402 | ||||||||
\(593\) | 10645.0 | 0.737163 | 0.368582 | − | 0.929595i | \(-0.379844\pi\) | ||||
0.368582 | + | 0.929595i | \(0.379844\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 910.000 | 0.0626998 | ||||||||
\(596\) | −4784.00 | −0.328792 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 2574.00 | 0.176018 | ||||||||
\(599\) | −6313.00 | −0.430621 | −0.215311 | − | 0.976546i | \(-0.569076\pi\) | ||||
−0.215311 | + | 0.976546i | \(0.569076\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −22162.0 | −1.50417 | −0.752086 | − | 0.659065i | \(-0.770952\pi\) | ||||
−0.752086 | + | 0.659065i | \(0.770952\pi\) | |||||||
\(602\) | −266.000 | −0.0180089 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −3560.00 | −0.239825 | ||||||||
\(605\) | −175.000 | −0.0117599 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 28716.0 | 1.92018 | 0.960088 | − | 0.279699i | \(-0.0902347\pi\) | ||||
0.960088 | + | 0.279699i | \(0.0902347\pi\) | |||||||
\(608\) | 1504.00 | 0.100321 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −3100.00 | −0.205763 | ||||||||
\(611\) | 2483.00 | 0.164405 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −5860.00 | −0.386106 | −0.193053 | − | 0.981188i | \(-0.561839\pi\) | ||||
−0.193053 | + | 0.981188i | \(0.561839\pi\) | |||||||
\(614\) | −7686.00 | −0.505182 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 2016.00 | 0.131862 | ||||||||
\(617\) | 16154.0 | 1.05403 | 0.527014 | − | 0.849856i | \(-0.323311\pi\) | ||||
0.527014 | + | 0.849856i | \(0.323311\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 9644.00 | 0.626212 | 0.313106 | − | 0.949718i | \(-0.398631\pi\) | ||||
0.313106 | + | 0.949718i | \(0.398631\pi\) | |||||||
\(620\) | −460.000 | −0.0297968 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 3496.00 | 0.225365 | ||||||||
\(623\) | −4445.00 | −0.285851 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 6875.00 | 0.440000 | ||||||||
\(626\) | 18784.0 | 1.19930 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 552.000 | 0.0350752 | ||||||||
\(629\) | 1300.00 | 0.0824076 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 8682.00 | 0.547742 | 0.273871 | − | 0.961766i | \(-0.411696\pi\) | ||||
0.273871 | + | 0.961766i | \(0.411696\pi\) | |||||||
\(632\) | 9528.00 | 0.599689 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 20760.0 | 1.30045 | ||||||||
\(635\) | 2880.00 | 0.179983 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −637.000 | −0.0396214 | ||||||||
\(638\) | −4392.00 | −0.272541 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −640.000 | −0.0395285 | ||||||||
\(641\) | 13791.0 | 0.849784 | 0.424892 | − | 0.905244i | \(-0.360312\pi\) | ||||
0.424892 | + | 0.905244i | \(0.360312\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −15316.0 | −0.939353 | −0.469677 | − | 0.882839i | \(-0.655629\pi\) | ||||
−0.469677 | + | 0.882839i | \(0.655629\pi\) | |||||||
\(644\) | −2772.00 | −0.169615 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −2444.00 | −0.148851 | ||||||||
\(647\) | −15244.0 | −0.926280 | −0.463140 | − | 0.886285i | \(-0.653277\pi\) | ||||
−0.463140 | + | 0.886285i | \(0.653277\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −9504.00 | −0.574830 | ||||||||
\(650\) | −2600.00 | −0.156893 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −15824.0 | −0.950484 | ||||||||
\(653\) | −90.0000 | −0.00539353 | −0.00269676 | − | 0.999996i | \(-0.500858\pi\) | ||||
−0.00269676 | + | 0.999996i | \(0.500858\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 10280.0 | 0.613241 | ||||||||
\(656\) | −1120.00 | −0.0666595 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −2674.00 | −0.158425 | ||||||||
\(659\) | −10887.0 | −0.643547 | −0.321773 | − | 0.946817i | \(-0.604279\pi\) | ||||
−0.321773 | + | 0.946817i | \(0.604279\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −4475.00 | −0.263324 | −0.131662 | − | 0.991295i | \(-0.542031\pi\) | ||||
−0.131662 | + | 0.991295i | \(0.542031\pi\) | |||||||
\(662\) | −12500.0 | −0.733877 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 2072.00 | 0.121098 | ||||||||
\(665\) | 1645.00 | 0.0959254 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 6039.00 | 0.350571 | ||||||||
\(668\) | 14700.0 | 0.851437 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 1900.00 | 0.109557 | ||||||||
\(671\) | 11160.0 | 0.642067 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −33451.0 | −1.91596 | −0.957980 | − | 0.286834i | \(-0.907397\pi\) | ||||
−0.957980 | + | 0.286834i | \(0.907397\pi\) | |||||||
\(674\) | 4630.00 | 0.264601 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 676.000 | 0.0384615 | ||||||||
\(677\) | 5556.00 | 0.315413 | 0.157706 | − | 0.987486i | \(-0.449590\pi\) | ||||
0.157706 | + | 0.987486i | \(0.449590\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −931.000 | −0.0526193 | ||||||||
\(680\) | 1040.00 | 0.0586503 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 1656.00 | 0.0929788 | ||||||||
\(683\) | 6504.00 | 0.364376 | 0.182188 | − | 0.983264i | \(-0.441682\pi\) | ||||
0.182188 | + | 0.983264i | \(0.441682\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 9210.00 | 0.513717 | ||||||||
\(686\) | 686.000 | 0.0381802 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −304.000 | −0.0168458 | ||||||||
\(689\) | 2535.00 | 0.140168 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 16963.0 | 0.933868 | 0.466934 | − | 0.884292i | \(-0.345359\pi\) | ||||
0.466934 | + | 0.884292i | \(0.345359\pi\) | |||||||
\(692\) | 11304.0 | 0.620973 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 6592.00 | 0.360560 | ||||||||
\(695\) | −6440.00 | −0.351487 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1820.00 | 0.0989059 | ||||||||
\(698\) | 11214.0 | 0.608103 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 2800.00 | 0.151186 | ||||||||
\(701\) | −12805.0 | −0.689926 | −0.344963 | − | 0.938616i | \(-0.612109\pi\) | ||||
−0.344963 | + | 0.938616i | \(0.612109\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 2350.00 | 0.126077 | ||||||||
\(704\) | 2304.00 | 0.123346 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 7444.00 | 0.396825 | ||||||||
\(707\) | 1064.00 | 0.0565995 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 10772.0 | 0.570594 | 0.285297 | − | 0.958439i | \(-0.407908\pi\) | ||||
0.285297 | + | 0.958439i | \(0.407908\pi\) | |||||||
\(710\) | −1660.00 | −0.0877446 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −5080.00 | −0.267389 | ||||||||
\(713\) | −2277.00 | −0.119599 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −2340.00 | −0.122393 | ||||||||
\(716\) | 12940.0 | 0.675406 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −4860.00 | −0.252609 | ||||||||
\(719\) | 22524.0 | 1.16829 | 0.584147 | − | 0.811648i | \(-0.301429\pi\) | ||||
0.584147 | + | 0.811648i | \(0.301429\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 11648.0 | 0.601656 | ||||||||
\(722\) | 9300.00 | 0.479377 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 5040.00 | 0.258716 | ||||||||
\(725\) | −6100.00 | −0.312480 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −5754.00 | −0.293541 | −0.146770 | − | 0.989171i | \(-0.546888\pi\) | ||||
−0.146770 | + | 0.989171i | \(0.546888\pi\) | |||||||
\(728\) | −728.000 | −0.0370625 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −8730.00 | −0.442619 | ||||||||
\(731\) | 494.000 | 0.0249949 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 31817.0 | 1.60326 | 0.801629 | − | 0.597822i | \(-0.203967\pi\) | ||||
0.801629 | + | 0.597822i | \(0.203967\pi\) | |||||||
\(734\) | 17168.0 | 0.863328 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −3168.00 | −0.158660 | ||||||||
\(737\) | −6840.00 | −0.341865 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 30820.0 | 1.53414 | 0.767072 | − | 0.641561i | \(-0.221713\pi\) | ||||
0.767072 | + | 0.641561i | \(0.221713\pi\) | |||||||
\(740\) | −1000.00 | −0.0496767 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −2730.00 | −0.135069 | ||||||||
\(743\) | 5724.00 | 0.282629 | 0.141314 | − | 0.989965i | \(-0.454867\pi\) | ||||
0.141314 | + | 0.989965i | \(0.454867\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −5980.00 | −0.294081 | ||||||||
\(746\) | 14548.0 | 0.713995 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −3744.00 | −0.183014 | ||||||||
\(749\) | −252.000 | −0.0122936 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 20397.0 | 0.991075 | 0.495537 | − | 0.868587i | \(-0.334971\pi\) | ||||
0.495537 | + | 0.868587i | \(0.334971\pi\) | |||||||
\(752\) | −3056.00 | −0.148193 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 1586.00 | 0.0766031 | ||||||||
\(755\) | −4450.00 | −0.214506 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −21103.0 | −1.01321 | −0.506606 | − | 0.862178i | \(-0.669100\pi\) | ||||
−0.506606 | + | 0.862178i | \(0.669100\pi\) | |||||||
\(758\) | 2320.00 | 0.111169 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 1880.00 | 0.0897300 | ||||||||
\(761\) | 22209.0 | 1.05792 | 0.528959 | − | 0.848647i | \(-0.322583\pi\) | ||||
0.528959 | + | 0.848647i | \(0.322583\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 1624.00 | 0.0770547 | ||||||||
\(764\) | 928.000 | 0.0439448 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −11056.0 | −0.521501 | ||||||||
\(767\) | 3432.00 | 0.161568 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 27895.0 | 1.30809 | 0.654044 | − | 0.756457i | \(-0.273071\pi\) | ||||
0.654044 | + | 0.756457i | \(0.273071\pi\) | |||||||
\(770\) | 2520.00 | 0.117941 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −21368.0 | −0.996180 | ||||||||
\(773\) | −24722.0 | −1.15031 | −0.575154 | − | 0.818045i | \(-0.695058\pi\) | ||||
−0.575154 | + | 0.818045i | \(0.695058\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 2300.00 | 0.106604 | ||||||||
\(776\) | −1064.00 | −0.0492208 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 19332.0 | 0.890856 | ||||||||
\(779\) | 3290.00 | 0.151318 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 5976.00 | 0.273800 | ||||||||
\(782\) | 5148.00 | 0.235412 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 784.000 | 0.0357143 | ||||||||
\(785\) | 690.000 | 0.0313722 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −40091.0 | −1.81587 | −0.907935 | − | 0.419111i | \(-0.862342\pi\) | ||||
−0.907935 | + | 0.419111i | \(0.862342\pi\) | |||||||
\(788\) | −6168.00 | −0.278840 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 11910.0 | 0.536378 | ||||||||
\(791\) | 9471.00 | 0.425727 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −4030.00 | −0.180466 | ||||||||
\(794\) | −8250.00 | −0.368742 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 8728.00 | 0.388638 | ||||||||
\(797\) | −602.000 | −0.0267552 | −0.0133776 | − | 0.999911i | \(-0.504258\pi\) | ||||
−0.0133776 | + | 0.999911i | \(0.504258\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 4966.00 | 0.219880 | ||||||||
\(800\) | 3200.00 | 0.141421 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −23592.0 | −1.03873 | ||||||||
\(803\) | 31428.0 | 1.38116 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −3465.00 | −0.151708 | ||||||||
\(806\) | −598.000 | −0.0261336 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 1216.00 | 0.0529440 | ||||||||
\(809\) | 38963.0 | 1.69328 | 0.846642 | − | 0.532163i | \(-0.178621\pi\) | ||||
0.846642 | + | 0.532163i | \(0.178621\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 18116.0 | 0.784388 | 0.392194 | − | 0.919882i | \(-0.371716\pi\) | ||||
0.392194 | + | 0.919882i | \(0.371716\pi\) | |||||||
\(812\) | −1708.00 | −0.0738166 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 3600.00 | 0.155012 | ||||||||
\(815\) | −19780.0 | −0.850139 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 893.000 | 0.0382400 | ||||||||
\(818\) | −16362.0 | −0.699369 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −1400.00 | −0.0596221 | ||||||||
\(821\) | −8070.00 | −0.343051 | −0.171526 | − | 0.985180i | \(-0.554870\pi\) | ||||
−0.171526 | + | 0.985180i | \(0.554870\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 14664.0 | 0.621087 | 0.310544 | − | 0.950559i | \(-0.399489\pi\) | ||||
0.310544 | + | 0.950559i | \(0.399489\pi\) | |||||||
\(824\) | 13312.0 | 0.562798 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −3696.00 | −0.155690 | ||||||||
\(827\) | 12836.0 | 0.539724 | 0.269862 | − | 0.962899i | \(-0.413022\pi\) | ||||
0.269862 | + | 0.962899i | \(0.413022\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 22664.0 | 0.949521 | 0.474761 | − | 0.880115i | \(-0.342535\pi\) | ||||
0.474761 | + | 0.880115i | \(0.342535\pi\) | |||||||
\(830\) | 2590.00 | 0.108314 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −832.000 | −0.0346688 | ||||||||
\(833\) | −1274.00 | −0.0529910 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 18375.0 | 0.761549 | ||||||||
\(836\) | −6768.00 | −0.279995 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −18592.0 | −0.766408 | ||||||||
\(839\) | 420.000 | 0.0172825 | 0.00864125 | − | 0.999963i | \(-0.497249\pi\) | ||||
0.00864125 | + | 0.999963i | \(0.497249\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −20668.0 | −0.847431 | ||||||||
\(842\) | −18148.0 | −0.742781 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −2092.00 | −0.0853194 | ||||||||
\(845\) | 845.000 | 0.0344010 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 245.000 | 0.00993896 | ||||||||
\(848\) | −3120.00 | −0.126346 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −5200.00 | −0.209834 | ||||||||
\(851\) | −4950.00 | −0.199393 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −5425.00 | −0.217759 | −0.108880 | − | 0.994055i | \(-0.534726\pi\) | ||||
−0.108880 | + | 0.994055i | \(0.534726\pi\) | |||||||
\(854\) | 4340.00 | 0.173901 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −288.000 | −0.0114996 | ||||||||
\(857\) | 33294.0 | 1.32707 | 0.663536 | − | 0.748144i | \(-0.269055\pi\) | ||||
0.663536 | + | 0.748144i | \(0.269055\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 27386.0 | 1.08777 | 0.543887 | − | 0.839158i | \(-0.316952\pi\) | ||||
0.543887 | + | 0.839158i | \(0.316952\pi\) | |||||||
\(860\) | −380.000 | −0.0150673 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 18716.0 | 0.739524 | ||||||||
\(863\) | −12004.0 | −0.473489 | −0.236744 | − | 0.971572i | \(-0.576080\pi\) | ||||
−0.236744 | + | 0.971572i | \(0.576080\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 14130.0 | 0.555416 | ||||||||
\(866\) | 28784.0 | 1.12947 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 644.000 | 0.0251829 | ||||||||
\(869\) | −42876.0 | −1.67373 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 2470.00 | 0.0960881 | ||||||||
\(872\) | 1856.00 | 0.0720781 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 9306.00 | 0.360160 | ||||||||
\(875\) | 7875.00 | 0.304256 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 39346.0 | 1.51496 | 0.757480 | − | 0.652858i | \(-0.226430\pi\) | ||||
0.757480 | + | 0.652858i | \(0.226430\pi\) | |||||||
\(878\) | 12148.0 | 0.466942 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 2880.00 | 0.110324 | ||||||||
\(881\) | −50806.0 | −1.94290 | −0.971452 | − | 0.237238i | \(-0.923758\pi\) | ||||
−0.971452 | + | 0.237238i | \(0.923758\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −34592.0 | −1.31836 | −0.659181 | − | 0.751984i | \(-0.729097\pi\) | ||||
−0.659181 | + | 0.751984i | \(0.729097\pi\) | |||||||
\(884\) | 1352.00 | 0.0514397 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −12966.0 | −0.491649 | ||||||||
\(887\) | −34624.0 | −1.31067 | −0.655333 | − | 0.755340i | \(-0.727472\pi\) | ||||
−0.655333 | + | 0.755340i | \(0.727472\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −4032.00 | −0.152114 | ||||||||
\(890\) | −6350.00 | −0.239160 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −7924.00 | −0.297439 | ||||||||
\(893\) | 8977.00 | 0.336398 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 16175.0 | 0.604101 | ||||||||
\(896\) | 896.000 | 0.0334077 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 30776.0 | 1.14366 | ||||||||
\(899\) | −1403.00 | −0.0520497 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 5070.00 | 0.187465 | ||||||||
\(902\) | 5040.00 | 0.186046 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 10824.0 | 0.398231 | ||||||||
\(905\) | 6300.00 | 0.231402 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 10849.0 | 0.397172 | 0.198586 | − | 0.980083i | \(-0.436365\pi\) | ||||
0.198586 | + | 0.980083i | \(0.436365\pi\) | |||||||
\(908\) | −17408.0 | −0.636239 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −910.000 | −0.0331497 | ||||||||
\(911\) | −39671.0 | −1.44276 | −0.721382 | − | 0.692537i | \(-0.756493\pi\) | ||||
−0.721382 | + | 0.692537i | \(0.756493\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −9324.00 | −0.337984 | ||||||||
\(914\) | 9284.00 | 0.335982 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 8520.00 | 0.307324 | ||||||||
\(917\) | −14392.0 | −0.518283 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 27208.0 | 0.976615 | 0.488307 | − | 0.872672i | \(-0.337614\pi\) | ||||
0.488307 | + | 0.872672i | \(0.337614\pi\) | |||||||
\(920\) | −3960.00 | −0.141910 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −28532.0 | −1.01914 | ||||||||
\(923\) | −2158.00 | −0.0769571 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 5000.00 | 0.177729 | ||||||||
\(926\) | −2944.00 | −0.104477 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −1952.00 | −0.0690491 | ||||||||
\(929\) | 27193.0 | 0.960359 | 0.480179 | − | 0.877170i | \(-0.340572\pi\) | ||||
0.480179 | + | 0.877170i | \(0.340572\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −2303.00 | −0.0810717 | ||||||||
\(932\) | −10748.0 | −0.377749 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 2664.00 | 0.0933284 | ||||||||
\(935\) | −4680.00 | −0.163692 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 24262.0 | 0.845896 | 0.422948 | − | 0.906154i | \(-0.360995\pi\) | ||||
0.422948 | + | 0.906154i | \(0.360995\pi\) | |||||||
\(938\) | −2660.00 | −0.0925928 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −3820.00 | −0.132548 | ||||||||
\(941\) | 303.000 | 0.0104968 | 0.00524842 | − | 0.999986i | \(-0.498329\pi\) | ||||
0.00524842 | + | 0.999986i | \(0.498329\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −6930.00 | −0.239313 | ||||||||
\(944\) | −4224.00 | −0.145635 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 1368.00 | 0.0470164 | ||||||||
\(947\) | 20098.0 | 0.689649 | 0.344824 | − | 0.938667i | \(-0.387938\pi\) | ||||
0.344824 | + | 0.938667i | \(0.387938\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −11349.0 | −0.388202 | ||||||||
\(950\) | −9400.00 | −0.321028 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −1456.00 | −0.0495685 | ||||||||
\(953\) | −13477.0 | −0.458093 | −0.229047 | − | 0.973415i | \(-0.573561\pi\) | ||||
−0.229047 | + | 0.973415i | \(0.573561\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 1160.00 | 0.0393055 | ||||||||
\(956\) | −15408.0 | −0.521266 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 3258.00 | 0.109876 | ||||||||
\(959\) | −12894.0 | −0.434170 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −29262.0 | −0.982243 | ||||||||
\(962\) | −1300.00 | −0.0435693 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 4276.00 | 0.142864 | ||||||||
\(965\) | −26710.0 | −0.891011 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −14488.0 | −0.481802 | −0.240901 | − | 0.970550i | \(-0.577443\pi\) | ||||
−0.240901 | + | 0.970550i | \(0.577443\pi\) | |||||||
\(968\) | 280.000 | 0.00929705 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −1330.00 | −0.0440245 | ||||||||
\(971\) | −2830.00 | −0.0935314 | −0.0467657 | − | 0.998906i | \(-0.514891\pi\) | ||||
−0.0467657 | + | 0.998906i | \(0.514891\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 9016.00 | 0.297060 | ||||||||
\(974\) | −27508.0 | −0.904942 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 4960.00 | 0.162670 | ||||||||
\(977\) | 36016.0 | 1.17938 | 0.589690 | − | 0.807630i | \(-0.299250\pi\) | ||||
0.589690 | + | 0.807630i | \(0.299250\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 22860.0 | 0.746281 | ||||||||
\(980\) | 980.000 | 0.0319438 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −21808.0 | −0.708677 | ||||||||
\(983\) | 16907.0 | 0.548575 | 0.274288 | − | 0.961648i | \(-0.411558\pi\) | ||||
0.274288 | + | 0.961648i | \(0.411558\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −7710.00 | −0.249402 | ||||||||
\(986\) | 3172.00 | 0.102451 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 2444.00 | 0.0786984 | ||||||||
\(989\) | −1881.00 | −0.0604776 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −51528.0 | −1.65171 | −0.825853 | − | 0.563885i | \(-0.809306\pi\) | ||||
−0.825853 | + | 0.563885i | \(0.809306\pi\) | |||||||
\(992\) | 736.000 | 0.0235565 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 2324.00 | 0.0741578 | ||||||||
\(995\) | 10910.0 | 0.347608 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 46492.0 | 1.47685 | 0.738423 | − | 0.674337i | \(-0.235571\pi\) | ||||
0.738423 | + | 0.674337i | \(0.235571\pi\) | |||||||
\(998\) | −20788.0 | −0.659351 | ||||||||
\(999\) | 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.e.1.1 | 1 | ||
3.2 | odd | 2 | 182.4.a.c.1.1 | ✓ | 1 | ||
12.11 | even | 2 | 1456.4.a.f.1.1 | 1 | |||
21.20 | even | 2 | 1274.4.a.g.1.1 | 1 | |||
39.38 | odd | 2 | 2366.4.a.b.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
182.4.a.c.1.1 | ✓ | 1 | 3.2 | odd | 2 | ||
1274.4.a.g.1.1 | 1 | 21.20 | even | 2 | |||
1456.4.a.f.1.1 | 1 | 12.11 | even | 2 | |||
1638.4.a.e.1.1 | 1 | 1.1 | even | 1 | trivial | ||
2366.4.a.b.1.1 | 1 | 39.38 | odd | 2 |