Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1380,4,Mod(1,1380)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1380, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("1380.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1380 = 2^{2} \cdot 3 \cdot 5 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1380.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: | \(81.4226358079\) |
Analytic rank: | \(1\) |
Dimension: | \(1\) |
Coefficient field: | \(\mathbb{Q}\) |
Coefficient ring: | \(\mathbb{Z}\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Character | \(\chi\) | \(=\) | 1380.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −3.00000 | −0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −5.00000 | −0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −16.0000 | −0.863919 | −0.431959 | − | 0.901893i | \(-0.642178\pi\) | ||||
−0.431959 | + | 0.901893i | \(0.642178\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 9.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 30.0000 | 0.822304 | 0.411152 | − | 0.911567i | \(-0.365127\pi\) | ||||
0.411152 | + | 0.911567i | \(0.365127\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −28.0000 | −0.597369 | −0.298685 | − | 0.954352i | \(-0.596548\pi\) | ||||
−0.298685 | + | 0.954352i | \(0.596548\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 15.0000 | 0.258199 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 78.0000 | 1.11281 | 0.556405 | − | 0.830911i | \(-0.312180\pi\) | ||||
0.556405 | + | 0.830911i | \(0.312180\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −52.0000 | −0.627875 | −0.313937 | − | 0.949444i | \(-0.601648\pi\) | ||||
−0.313937 | + | 0.949444i | \(0.601648\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 48.0000 | 0.498784 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −23.0000 | −0.208514 | ||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 25.0000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −27.0000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −252.000 | −1.61363 | −0.806814 | − | 0.590805i | \(-0.798810\pi\) | ||||
−0.806814 | + | 0.590805i | \(0.798810\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 200.000 | 1.15874 | 0.579372 | − | 0.815063i | \(-0.303298\pi\) | ||||
0.579372 | + | 0.815063i | \(0.303298\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −90.0000 | −0.474757 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 80.0000 | 0.386356 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 146.000 | 0.648710 | 0.324355 | − | 0.945936i | \(-0.394853\pi\) | ||||
0.324355 | + | 0.945936i | \(0.394853\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 84.0000 | 0.344891 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 438.000 | 1.66839 | 0.834196 | − | 0.551467i | \(-0.185932\pi\) | ||||
0.834196 | + | 0.551467i | \(0.185932\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −46.0000 | −0.163138 | −0.0815690 | − | 0.996668i | \(-0.525993\pi\) | ||||
−0.0815690 | + | 0.996668i | \(0.525993\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −45.0000 | −0.149071 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 588.000 | 1.82486 | 0.912432 | − | 0.409228i | \(-0.134202\pi\) | ||||
0.912432 | + | 0.409228i | \(0.134202\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −87.0000 | −0.253644 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −234.000 | −0.642481 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 438.000 | 1.13517 | 0.567584 | − | 0.823315i | \(-0.307878\pi\) | ||||
0.567584 | + | 0.823315i | \(0.307878\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −150.000 | −0.367745 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 156.000 | 0.362504 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −168.000 | −0.370707 | −0.185354 | − | 0.982672i | \(-0.559343\pi\) | ||||
−0.185354 | + | 0.982672i | \(0.559343\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −586.000 | −1.22999 | −0.614997 | − | 0.788530i | \(-0.710843\pi\) | ||||
−0.614997 | + | 0.788530i | \(0.710843\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −144.000 | −0.287973 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 140.000 | 0.267152 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −94.0000 | −0.171402 | −0.0857010 | − | 0.996321i | \(-0.527313\pi\) | ||||
−0.0857010 | + | 0.996321i | \(0.527313\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 69.0000 | 0.120386 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −30.0000 | −0.0501457 | −0.0250729 | − | 0.999686i | \(-0.507982\pi\) | ||||
−0.0250729 | + | 0.999686i | \(0.507982\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −466.000 | −0.747139 | −0.373570 | − | 0.927602i | \(-0.621866\pi\) | ||||
−0.373570 | + | 0.927602i | \(0.621866\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −75.0000 | −0.115470 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −480.000 | −0.710404 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −520.000 | −0.740564 | −0.370282 | − | 0.928919i | \(-0.620739\pi\) | ||||
−0.370282 | + | 0.928919i | \(0.620739\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 81.0000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 708.000 | 0.936302 | 0.468151 | − | 0.883648i | \(-0.344920\pi\) | ||||
0.468151 | + | 0.883648i | \(0.344920\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −390.000 | −0.497664 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 756.000 | 0.931629 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −600.000 | −0.714605 | −0.357303 | − | 0.933989i | \(-0.616304\pi\) | ||||
−0.357303 | + | 0.933989i | \(0.616304\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 448.000 | 0.516079 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −600.000 | −0.669001 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 260.000 | 0.280794 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −340.000 | −0.355895 | −0.177947 | − | 0.984040i | \(-0.556946\pi\) | ||||
−0.177947 | + | 0.984040i | \(0.556946\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 270.000 | 0.274101 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1164.00 | −1.14676 | −0.573378 | − | 0.819291i | \(-0.694367\pi\) | ||||
−0.573378 | + | 0.819291i | \(0.694367\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 656.000 | 0.627550 | 0.313775 | − | 0.949497i | \(-0.398406\pi\) | ||||
0.313775 | + | 0.949497i | \(0.398406\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −240.000 | −0.223063 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −1992.00 | −1.79976 | −0.899878 | − | 0.436142i | \(-0.856345\pi\) | ||||
−0.899878 | + | 0.436142i | \(0.856345\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1226.00 | 1.07733 | 0.538667 | − | 0.842518i | \(-0.318928\pi\) | ||||
0.538667 | + | 0.842518i | \(0.318928\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −438.000 | −0.374533 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 954.000 | 0.794202 | 0.397101 | − | 0.917775i | \(-0.370016\pi\) | ||||
0.397101 | + | 0.917775i | \(0.370016\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 115.000 | 0.0932505 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −252.000 | −0.199123 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −1248.00 | −0.961378 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −431.000 | −0.323817 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −1314.00 | −0.963247 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −125.000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 962.000 | 0.672155 | 0.336078 | − | 0.941834i | \(-0.390900\pi\) | ||||
0.336078 | + | 0.941834i | \(0.390900\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 138.000 | 0.0941878 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −2484.00 | −1.65670 | −0.828351 | − | 0.560209i | \(-0.810721\pi\) | ||||
−0.828351 | + | 0.560209i | \(0.810721\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 832.000 | 0.542433 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 135.000 | 0.0860663 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −1134.00 | −0.707184 | −0.353592 | − | 0.935400i | \(-0.615040\pi\) | ||||
−0.353592 | + | 0.935400i | \(0.615040\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −1636.00 | −0.998300 | −0.499150 | − | 0.866516i | \(-0.666354\pi\) | ||||
−0.499150 | + | 0.866516i | \(0.666354\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −1764.00 | −1.05359 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −840.000 | −0.491219 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 1260.00 | 0.721637 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 261.000 | 0.146442 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −1566.00 | −0.861018 | −0.430509 | − | 0.902586i | \(-0.641666\pi\) | ||||
−0.430509 | + | 0.902586i | \(0.641666\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 788.000 | 0.424679 | 0.212340 | − | 0.977196i | \(-0.431892\pi\) | ||||
0.212340 | + | 0.977196i | \(0.431892\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 702.000 | 0.370937 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −1000.00 | −0.518206 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 2.00000 | 0.00101667 | 0.000508336 | − | 1.00000i | \(-0.499838\pi\) | ||||
0.000508336 | 1.00000i | \(0.499838\pi\) | ||||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −1314.00 | −0.655390 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 368.000 | 0.180140 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −448.000 | −0.215276 | −0.107638 | − | 0.994190i | \(-0.534329\pi\) | ||||
−0.107638 | + | 0.994190i | \(0.534329\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 450.000 | 0.212318 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 2904.00 | 1.34562 | 0.672809 | − | 0.739816i | \(-0.265087\pi\) | ||||
0.672809 | + | 0.739816i | \(0.265087\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1413.00 | −0.643150 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −468.000 | −0.209292 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −2322.00 | −1.02045 | −0.510227 | − | 0.860040i | \(-0.670438\pi\) | ||||
−0.510227 | + | 0.860040i | \(0.670438\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −400.000 | −0.172784 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 504.000 | 0.214028 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −96.0000 | −0.0400859 | −0.0200430 | − | 0.999799i | \(-0.506380\pi\) | ||||
−0.0200430 | + | 0.999799i | \(0.506380\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −1906.00 | −0.782717 | −0.391359 | − | 0.920238i | \(-0.627995\pi\) | ||||
−0.391359 | + | 0.920238i | \(0.627995\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 1758.00 | 0.710137 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −730.000 | −0.290112 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 2340.00 | 0.915068 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 432.000 | 0.166261 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −2520.00 | −0.954664 | −0.477332 | − | 0.878723i | \(-0.658396\pi\) | ||||
−0.477332 | + | 0.878723i | \(0.658396\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −4366.00 | −1.62835 | −0.814175 | − | 0.580620i | \(-0.802810\pi\) | ||||
−0.814175 | + | 0.580620i | \(0.802810\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −420.000 | −0.154240 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 3750.00 | 1.35623 | 0.678113 | − | 0.734958i | \(-0.262798\pi\) | ||||
0.678113 | + | 0.734958i | \(0.262798\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −1576.00 | −0.561405 | −0.280703 | − | 0.959795i | \(-0.590567\pi\) | ||||
−0.280703 | + | 0.959795i | \(0.590567\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 282.000 | 0.0989589 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 4032.00 | 1.39404 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −2190.00 | −0.746128 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −207.000 | −0.0695048 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −1560.00 | −0.516304 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 284.000 | 0.0926605 | 0.0463303 | − | 0.998926i | \(-0.485247\pi\) | ||||
0.0463303 | + | 0.998926i | \(0.485247\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 90.0000 | 0.0289516 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 230.000 | 0.0729575 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −3200.00 | −1.00106 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 1398.00 | 0.431361 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −2184.00 | −0.664759 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 2294.00 | 0.688868 | 0.344434 | − | 0.938811i | \(-0.388071\pi\) | ||||
0.344434 | + | 0.938811i | \(0.388071\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 225.000 | 0.0666667 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −4584.00 | −1.34031 | −0.670156 | − | 0.742220i | \(-0.733773\pi\) | ||||
−0.670156 | + | 0.742220i | \(0.733773\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 4634.00 | 1.33722 | 0.668610 | − | 0.743613i | \(-0.266890\pi\) | ||||
0.668610 | + | 0.743613i | \(0.266890\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 1440.00 | 0.410152 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −5082.00 | −1.42890 | −0.714448 | − | 0.699688i | \(-0.753322\pi\) | ||||
−0.714448 | + | 0.699688i | \(0.753322\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −2940.00 | −0.816104 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 1560.00 | 0.427565 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −606.000 | −0.164012 | −0.0820060 | − | 0.996632i | \(-0.526133\pi\) | ||||
−0.0820060 | + | 0.996632i | \(0.526133\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −3454.00 | −0.923202 | −0.461601 | − | 0.887088i | \(-0.652725\pi\) | ||||
−0.461601 | + | 0.887088i | \(0.652725\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −243.000 | −0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 435.000 | 0.113433 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1456.00 | 0.375073 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −2124.00 | −0.540574 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −1758.00 | −0.442088 | −0.221044 | − | 0.975264i | \(-0.570946\pi\) | ||||
−0.221044 | + | 0.975264i | \(0.570946\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −690.000 | −0.171462 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 1170.00 | 0.287326 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −3546.00 | −0.860675 | −0.430337 | − | 0.902668i | \(-0.641605\pi\) | ||||
−0.430337 | + | 0.902668i | \(0.641605\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −2336.00 | −0.560432 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −2268.00 | −0.537876 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −168.000 | −0.0393891 | −0.0196945 | − | 0.999806i | \(-0.506269\pi\) | ||||
−0.0196945 | + | 0.999806i | \(0.506269\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −2190.00 | −0.507663 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 1800.00 | 0.412578 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −360.000 | −0.0815970 | −0.0407985 | − | 0.999167i | \(-0.512990\pi\) | ||||
−0.0407985 | + | 0.999167i | \(0.512990\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 7208.00 | 1.61570 | 0.807850 | − | 0.589388i | \(-0.200631\pi\) | ||||
0.807850 | + | 0.589388i | \(0.200631\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −1344.00 | −0.297958 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 750.000 | 0.164461 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 2012.00 | 0.436424 | 0.218212 | − | 0.975901i | \(-0.429978\pi\) | ||||
0.218212 | + | 0.975901i | \(0.429978\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 1800.00 | 0.386248 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −5520.00 | −1.17187 | −0.585935 | − | 0.810358i | \(-0.699273\pi\) | ||||
−0.585935 | + | 0.810358i | \(0.699273\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 998.000 | 0.209629 | 0.104814 | − | 0.994492i | \(-0.466575\pi\) | ||||
0.104814 | + | 0.994492i | \(0.466575\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −780.000 | −0.162117 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −7008.00 | −1.44136 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1171.00 | 0.238347 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 1020.00 | 0.205476 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −6834.00 | −1.36262 | −0.681308 | − | 0.731997i | \(-0.738589\pi\) | ||||
−0.681308 | + | 0.731997i | \(0.738589\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 840.000 | 0.165785 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −810.000 | −0.158252 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 644.000 | 0.124560 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 736.000 | 0.140938 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 3492.00 | 0.662080 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 2930.00 | 0.550070 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −5380.00 | −1.00017 | −0.500086 | − | 0.865976i | \(-0.666698\pi\) | ||||
−0.500086 | + | 0.865976i | \(0.666698\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −1968.00 | −0.362316 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 4650.00 | 0.847837 | 0.423919 | − | 0.905700i | \(-0.360654\pi\) | ||||
0.423919 | + | 0.905700i | \(0.360654\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −9232.00 | −1.66717 | −0.833584 | − | 0.552393i | \(-0.813715\pi\) | ||||
−0.833584 | + | 0.552393i | \(0.813715\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 720.000 | 0.128785 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −4566.00 | −0.808997 | −0.404499 | − | 0.914539i | \(-0.632554\pi\) | ||||
−0.404499 | + | 0.914539i | \(0.632554\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −7560.00 | −1.32689 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 5976.00 | 1.03909 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −4056.00 | −0.698706 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −700.000 | −0.119474 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −3678.00 | −0.622000 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −9408.00 | −1.57653 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 3140.00 | 0.521420 | 0.260710 | − | 0.965417i | \(-0.416043\pi\) | ||||
0.260710 | + | 0.965417i | \(0.416043\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 1314.00 | 0.216237 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 470.000 | 0.0766533 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 6896.00 | 1.11469 | 0.557343 | − | 0.830282i | \(-0.311821\pi\) | ||||
0.557343 | + | 0.830282i | \(0.311821\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −2862.00 | −0.458532 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 6000.00 | 0.952839 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 6880.00 | 1.08305 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −345.000 | −0.0538382 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −3084.00 | −0.477112 | −0.238556 | − | 0.971129i | \(-0.576674\pi\) | ||||
−0.238556 | + | 0.971129i | \(0.576674\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 1226.00 | 0.188041 | 0.0940205 | − | 0.995570i | \(-0.470028\pi\) | ||||
0.0940205 | + | 0.995570i | \(0.470028\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 756.000 | 0.114964 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 8394.00 | 1.26563 | 0.632815 | − | 0.774303i | \(-0.281899\pi\) | ||||
0.632815 | + | 0.774303i | \(0.281899\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 150.000 | 0.0224258 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 3744.00 | 0.555052 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −12480.0 | −1.83473 | −0.917367 | − | 0.398043i | \(-0.869689\pi\) | ||||
−0.917367 | + | 0.398043i | \(0.869689\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −4155.00 | −0.605773 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 1293.00 | 0.186956 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 2330.00 | 0.334131 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 5312.00 | 0.755543 | 0.377771 | − | 0.925899i | \(-0.376691\pi\) | ||||
0.377771 | + | 0.925899i | \(0.376691\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 3942.00 | 0.556131 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −7008.00 | −0.980693 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 1490.00 | 0.206835 | 0.103417 | − | 0.994638i | \(-0.467022\pi\) | ||||
0.103417 | + | 0.994638i | \(0.467022\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 375.000 | 0.0516398 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 7056.00 | 0.963932 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 6968.00 | 0.944386 | 0.472193 | − | 0.881495i | \(-0.343463\pi\) | ||||
0.472193 | + | 0.881495i | \(0.343463\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −2886.00 | −0.388069 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 1512.00 | 0.201722 | 0.100861 | − | 0.994901i | \(-0.467840\pi\) | ||||
0.100861 | + | 0.994901i | \(0.467840\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 2400.00 | 0.317702 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −414.000 | −0.0543793 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −2514.00 | −0.327673 | −0.163837 | − | 0.986487i | \(-0.552387\pi\) | ||||
−0.163837 | + | 0.986487i | \(0.552387\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −1794.00 | −0.232037 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 7452.00 | 0.956498 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 2600.00 | 0.331190 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −2548.00 | −0.322117 | −0.161059 | − | 0.986945i | \(-0.551491\pi\) | ||||
−0.161059 | + | 0.986945i | \(0.551491\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −2496.00 | −0.313174 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 15324.0 | 1.90834 | 0.954170 | − | 0.299266i | \(-0.0967419\pi\) | ||||
0.954170 | + | 0.299266i | \(0.0967419\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −5600.00 | −0.692198 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −405.000 | −0.0496904 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 4380.00 | 0.533436 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −14362.0 | −1.73632 | −0.868160 | − | 0.496284i | \(-0.834698\pi\) | ||||
−0.868160 | + | 0.496284i | \(0.834698\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 3402.00 | 0.408293 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 2688.00 | 0.320261 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −3540.00 | −0.418727 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 4908.00 | 0.576369 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 6774.00 | 0.789813 | 0.394906 | − | 0.918721i | \(-0.370777\pi\) | ||||
0.394906 | + | 0.918721i | \(0.370777\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 15662.0 | 1.81311 | 0.906555 | − | 0.422088i | \(-0.138703\pi\) | ||||
0.906555 | + | 0.422088i | \(0.138703\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 5292.00 | 0.608288 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 1950.00 | 0.222562 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 9376.00 | 1.06261 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 2520.00 | 0.283605 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −11688.0 | −1.30624 | −0.653122 | − | 0.757253i | \(-0.726541\pi\) | ||||
−0.653122 | + | 0.757253i | \(0.726541\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −1588.00 | −0.176246 | −0.0881229 | − | 0.996110i | \(-0.528087\pi\) | ||||
−0.0881229 | + | 0.996110i | \(0.528087\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −3780.00 | −0.416637 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 1196.00 | 0.130921 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 8300.00 | 0.902363 | 0.451182 | − | 0.892432i | \(-0.351003\pi\) | ||||
0.451182 | + | 0.892432i | \(0.351003\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −783.000 | −0.0845481 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 2988.00 | 0.320461 | 0.160230 | − | 0.987080i | \(-0.448776\pi\) | ||||
0.160230 | + | 0.987080i | \(0.448776\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 3000.00 | 0.319581 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 4698.00 | 0.497109 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −9546.00 | −1.00335 | −0.501674 | − | 0.865057i | \(-0.667282\pi\) | ||||
−0.501674 | + | 0.865057i | \(0.667282\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 13140.0 | 1.37193 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −2364.00 | −0.245189 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −2240.00 | −0.230797 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −10540.0 | −1.07886 | −0.539432 | − | 0.842029i | \(-0.681361\pi\) | ||||
−0.539432 | + | 0.842029i | \(0.681361\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −2106.00 | −0.214160 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 11988.0 | 1.21114 | 0.605571 | − | 0.795791i | \(-0.292945\pi\) | ||||
0.605571 | + | 0.795791i | \(0.292945\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 19382.0 | 1.94548 | 0.972741 | − | 0.231895i | \(-0.0744927\pi\) | ||||
0.972741 | + | 0.231895i | \(0.0744927\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 3000.00 | 0.299186 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −9180.00 | −0.909635 | −0.454818 | − | 0.890585i | \(-0.650296\pi\) | ||||
−0.454818 | + | 0.890585i | \(0.650296\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 1504.00 | 0.148077 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −6.00000 | −0.000586975 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −1380.00 | −0.134149 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −1300.00 | −0.125575 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 3942.00 | 0.378389 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −192.000 | −0.0183146 | −0.00915731 | − | 0.999958i | \(-0.502915\pi\) | ||||
−0.00915731 | + | 0.999958i | \(0.502915\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −4088.00 | −0.387519 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −1104.00 | −0.104004 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 1700.00 | 0.159161 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 3446.00 | 0.320643 | 0.160322 | − | 0.987065i | \(-0.448747\pi\) | ||||
0.160322 | + | 0.987065i | \(0.448747\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 1344.00 | 0.124290 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 10068.0 | 0.925382 | 0.462691 | − | 0.886520i | \(-0.346884\pi\) | ||||
0.462691 | + | 0.886520i | \(0.346884\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −19656.0 | −1.79566 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −1350.00 | −0.122582 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 480.000 | 0.0433218 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −14020.0 | −1.25776 | −0.628879 | − | 0.777503i | \(-0.716486\pi\) | ||||
−0.628879 | + | 0.777503i | \(0.716486\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −8712.00 | −0.776893 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −14952.0 | −1.32540 | −0.662701 | − | 0.748885i | \(-0.730590\pi\) | ||||
−0.662701 | + | 0.748885i | \(0.730590\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 5820.00 | 0.512845 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 4239.00 | 0.371323 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −13692.0 | −1.19231 | −0.596156 | − | 0.802868i | \(-0.703306\pi\) | ||||
−0.596156 | + | 0.802868i | \(0.703306\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 7456.00 | 0.645468 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 1404.00 | 0.120835 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −3280.00 | −0.280649 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 17640.0 | 1.50059 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 6966.00 | 0.589159 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −13704.0 | −1.15237 | −0.576183 | − | 0.817320i | \(-0.695459\pi\) | ||||
−0.576183 | + | 0.817320i | \(0.695459\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −17026.0 | −1.42351 | −0.711754 | − | 0.702429i | \(-0.752099\pi\) | ||||
−0.711754 | + | 0.702429i | \(0.752099\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 1200.00 | 0.0997567 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 15600.0 | 1.28946 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 529.000 | 0.0434783 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −1512.00 | −0.123569 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −12264.0 | −0.996647 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 9960.00 | 0.804875 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 288.000 | 0.0231436 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −2610.00 | −0.208573 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −1942.00 | −0.154331 | −0.0771655 | − | 0.997018i | \(-0.524587\pi\) | ||||
−0.0771655 | + | 0.997018i | \(0.524587\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 5718.00 | 0.451902 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −6130.00 | −0.481799 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 13988.0 | 1.09339 | 0.546694 | − | 0.837332i | \(-0.315886\pi\) | ||||
0.546694 | + | 0.837332i | \(0.315886\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −5274.00 | −0.409998 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 13104.0 | 1.01316 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 8320.00 | 0.639787 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 2190.00 | 0.167496 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −11382.0 | −0.865836 | −0.432918 | − | 0.901433i | \(-0.642516\pi\) | ||||
−0.432918 | + | 0.901433i | \(0.642516\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 1288.00 | 0.0974537 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −7020.00 | −0.528315 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 20844.0 | 1.56034 | 0.780169 | − | 0.625569i | \(-0.215133\pi\) | ||||
0.780169 | + | 0.625569i | \(0.215133\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −4770.00 | −0.355178 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −1296.00 | −0.0959910 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 5676.00 | 0.418190 | 0.209095 | − | 0.977895i | \(-0.432948\pi\) | ||||
0.209095 | + | 0.977895i | \(0.432948\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 11936.0 | 0.874792 | 0.437396 | − | 0.899269i | \(-0.355901\pi\) | ||||
0.437396 | + | 0.899269i | \(0.355901\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 7560.00 | 0.551175 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −575.000 | −0.0417029 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −7594.00 | −0.547907 | −0.273954 | − | 0.961743i | \(-0.588331\pi\) | ||||
−0.273954 | + | 0.961743i | \(0.588331\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 13098.0 | 0.940128 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −11328.0 | −0.808889 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 13140.0 | 0.933453 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 1260.00 | 0.0890506 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 26172.0 | 1.84026 | 0.920131 | − | 0.391610i | \(-0.128082\pi\) | ||||
0.920131 | + | 0.391610i | \(0.128082\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −10400.0 | −0.727546 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −11250.0 | −0.783017 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −15786.0 | −1.09318 | −0.546588 | − | 0.837402i | \(-0.684074\pi\) | ||||
−0.546588 | + | 0.837402i | \(0.684074\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 6240.00 | 0.429941 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 4728.00 | 0.324128 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −15714.0 | −1.07188 | −0.535940 | − | 0.844256i | \(-0.680043\pi\) | ||||
−0.535940 | + | 0.844256i | \(0.680043\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −16714.0 | −1.13441 | −0.567203 | − | 0.823578i | \(-0.691975\pi\) | ||||
−0.567203 | + | 0.823578i | \(0.691975\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −846.000 | −0.0571340 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 2155.00 | 0.144815 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 8606.00 | 0.575464 | 0.287732 | − | 0.957711i | \(-0.407099\pi\) | ||||
0.287732 | + | 0.957711i | \(0.407099\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −12096.0 | −0.804852 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −16464.0 | −1.09012 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 24038.0 | 1.58383 | 0.791913 | − | 0.610634i | \(-0.209085\pi\) | ||||
0.791913 | + | 0.610634i | \(0.209085\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 6570.00 | 0.430777 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 13134.0 | 0.856977 | 0.428489 | − | 0.903547i | \(-0.359046\pi\) | ||||
0.428489 | + | 0.903547i | \(0.359046\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 11660.0 | 0.757116 | 0.378558 | − | 0.925578i | \(-0.376420\pi\) | ||||
0.378558 | + | 0.925578i | \(0.376420\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 621.000 | 0.0401286 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 9600.00 | 0.617361 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 625.000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 4680.00 | 0.298088 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 11388.0 | 0.721891 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 24680.0 | 1.55704 | 0.778522 | − | 0.627617i | \(-0.215970\pi\) | ||||
0.778522 | + | 0.627617i | \(0.215970\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −852.000 | −0.0534976 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −4810.00 | −0.300597 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 2436.00 | 0.151519 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −270.000 | −0.0167152 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 8184.00 | 0.504288 | 0.252144 | − | 0.967690i | \(-0.418864\pi\) | ||||
0.252144 | + | 0.967690i | \(0.418864\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 3998.00 | 0.245203 | 0.122602 | − | 0.992456i | \(-0.460876\pi\) | ||||
0.122602 | + | 0.992456i | \(0.460876\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −690.000 | −0.0421221 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 25476.0 | 1.54801 | 0.774007 | − | 0.633177i | \(-0.218250\pi\) | ||||
0.774007 | + | 0.633177i | \(0.218250\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −5040.00 | −0.304834 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 9600.00 | 0.577963 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 10146.0 | 0.608030 | 0.304015 | − | 0.952667i | \(-0.401673\pi\) | ||||
0.304015 | + | 0.952667i | \(0.401673\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 12420.0 | 0.740900 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −4194.00 | −0.249046 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −25986.0 | −1.53607 | −0.768036 | − | 0.640407i | \(-0.778766\pi\) | ||||
−0.768036 | + | 0.640407i | \(0.778766\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 4034.00 | 0.237374 | 0.118687 | − | 0.992932i | \(-0.462131\pi\) | ||||
0.118687 | + | 0.992932i | \(0.462131\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 6552.00 | 0.383799 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −4160.00 | −0.242583 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 5796.00 | 0.336465 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −6882.00 | −0.397718 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −17580.0 | −1.01143 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −13954.0 | −0.799238 | −0.399619 | − | 0.916681i | \(-0.630858\pi\) | ||||
−0.399619 | + | 0.916681i | \(0.630858\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −675.000 | −0.0384900 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −14814.0 | −0.840987 | −0.420494 | − | 0.907296i | \(-0.638143\pi\) | ||||
−0.420494 | + | 0.907296i | \(0.638143\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 5440.00 | 0.307464 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 13752.0 | 0.773829 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −20388.0 | −1.14220 | −0.571102 | − | 0.820879i | \(-0.693484\pi\) | ||||
−0.571102 | + | 0.820879i | \(0.693484\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 5670.00 | 0.316262 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −13902.0 | −0.772044 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −12264.0 | −0.678115 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −9508.00 | −0.523446 | −0.261723 | − | 0.965143i | \(-0.584291\pi\) | ||||
−0.261723 | + | 0.965143i | \(0.584291\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −4320.00 | −0.236801 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 8180.00 | 0.446453 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 34164.0 | 1.85661 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 15246.0 | 0.824974 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 5790.00 | 0.311962 | 0.155981 | − | 0.987760i | \(-0.450146\pi\) | ||||
0.155981 | + | 0.987760i | \(0.450146\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −7592.00 | −0.407308 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 8820.00 | 0.471178 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 18624.0 | 0.990704 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −6238.00 | −0.330427 | −0.165214 | − | 0.986258i | \(-0.552831\pi\) | ||||
−0.165214 | + | 0.986258i | \(0.552831\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −4680.00 | −0.246855 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −4600.00 | −0.241615 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 4200.00 | 0.219680 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 1818.00 | 0.0946924 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −5010.00 | −0.259863 | −0.129931 | − | 0.991523i | \(-0.541476\pi\) | ||||
−0.129931 | + | 0.991523i | \(0.541476\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −10496.0 | −0.542152 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 10362.0 | 0.533011 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −6300.00 | −0.322726 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −13876.0 | −0.707885 | −0.353942 | − | 0.935267i | \(-0.615159\pi\) | ||||
−0.353942 | + | 0.935267i | \(0.615159\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 729.000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −3588.00 | −0.181542 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −9766.00 | −0.492108 | −0.246054 | − | 0.969256i | \(-0.579134\pi\) | ||||
−0.246054 | + | 0.969256i | \(0.579134\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −1305.00 | −0.0654907 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −2820.00 | −0.140944 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −8740.00 | −0.435056 | −0.217528 | − | 0.976054i | \(-0.569799\pi\) | ||||
−0.217528 | + | 0.976054i | \(0.569799\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −4368.00 | −0.216549 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −5952.00 | −0.293887 | −0.146943 | − | 0.989145i | \(-0.546943\pi\) | ||||
−0.146943 | + | 0.989145i | \(0.546943\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 7830.00 | 0.385059 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 6372.00 | 0.312101 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 31872.0 | 1.55484 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −6784.00 | −0.329629 | −0.164815 | − | 0.986325i | \(-0.552703\pi\) | ||||
−0.164815 | + | 0.986325i | \(0.552703\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 5274.00 | 0.255239 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −3940.00 | −0.189922 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 10550.0 | 0.506534 | 0.253267 | − | 0.967396i | \(-0.418495\pi\) | ||||
0.253267 | + | 0.967396i | \(0.418495\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 2070.00 | 0.0989937 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −38430.0 | −1.83060 | −0.915300 | − | 0.402773i | \(-0.868046\pi\) | ||||
−0.915300 | + | 0.402773i | \(0.868046\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −19616.0 | −0.930730 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −3510.00 | −0.165888 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 4704.00 | 0.221449 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 19358.0 | 0.907760 | 0.453880 | − | 0.891063i | \(-0.350039\pi\) | ||||
0.453880 | + | 0.891063i | \(0.350039\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 10638.0 | 0.496911 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 7182.00 | 0.334177 | 0.167088 | − | 0.985942i | \(-0.446563\pi\) | ||||
0.167088 | + | 0.985942i | \(0.446563\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 5000.00 | 0.231749 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 7008.00 | 0.323566 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −22776.0 | −1.04754 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −900.000 | −0.0412350 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 6804.00 | 0.310543 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −10.0000 | −0.000454669 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 28190.0 | 1.27683 | 0.638415 | − | 0.769692i | \(-0.279590\pi\) | ||||
0.638415 | + | 0.769692i | \(0.279590\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 504.000 | 0.0227413 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −15264.0 | −0.686126 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 16408.0 | 0.734761 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 6570.00 | 0.293099 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −29310.0 | −1.30265 | −0.651326 | − | 0.758798i | \(-0.725787\pi\) | ||||
−0.651326 | + | 0.758798i | \(0.725787\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 45864.0 | 2.03073 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −5400.00 | −0.238202 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −13980.0 | −0.614375 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −1840.00 | −0.0805608 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 1080.00 | 0.0471100 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 30330.0 | 1.31810 | 0.659052 | − | 0.752097i | \(-0.270958\pi\) | ||||
0.659052 | + | 0.752097i | \(0.270958\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 28508.0 | 1.23434 | 0.617171 | − | 0.786829i | \(-0.288279\pi\) | ||||
0.617171 | + | 0.786829i | \(0.288279\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −21624.0 | −0.932825 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 2240.00 | 0.0962746 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 2392.00 | 0.102430 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 4032.00 | 0.172026 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −8616.00 | −0.366261 | −0.183131 | − | 0.983089i | \(-0.558623\pi\) | ||||
−0.183131 | + | 0.983089i | \(0.558623\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −16702.0 | −0.707406 | −0.353703 | − | 0.935358i | \(-0.615078\pi\) | ||||
−0.353703 | + | 0.935358i | \(0.615078\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −2250.00 | −0.0949514 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 27648.0 | 1.16253 | 0.581267 | − | 0.813713i | \(-0.302557\pi\) | ||||
0.581267 | + | 0.813713i | \(0.302557\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −40678.0 | −1.70423 | −0.852114 | − | 0.523356i | \(-0.824680\pi\) | ||||
−0.852114 | + | 0.523356i | \(0.824680\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −6036.00 | −0.251969 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −6786.00 | −0.282258 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −14520.0 | −0.601779 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −5400.00 | −0.223000 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 6372.00 | 0.262200 | 0.131100 | − | 0.991369i | \(-0.458149\pi\) | ||||
0.131100 | + | 0.991369i | \(0.458149\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 39115.0 | 1.60380 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 16560.0 | 0.676580 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 7065.00 | 0.287625 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 6896.00 | 0.279751 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −2994.00 | −0.121029 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −3358.00 | −0.135265 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −42844.0 | −1.71975 | −0.859877 | − | 0.510501i | \(-0.829460\pi\) | ||||
−0.859877 | + | 0.510501i | \(0.829460\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 2340.00 | 0.0935980 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −16686.0 | −0.665091 | −0.332545 | − | 0.943087i | \(-0.607907\pi\) | ||||
−0.332545 | + | 0.943087i | \(0.607907\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −27196.0 | −1.08023 | −0.540114 | − | 0.841592i | \(-0.681619\pi\) | ||||
−0.540114 | + | 0.841592i | \(0.681619\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 21024.0 | 0.832167 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 24828.0 | 0.979322 | 0.489661 | − | 0.871913i | \(-0.337121\pi\) | ||||
0.489661 | + | 0.871913i | \(0.337121\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 11610.0 | 0.456361 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −3513.00 | −0.137610 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −15600.0 | −0.608969 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 2632.00 | 0.102390 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −3060.00 | −0.118632 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 2000.00 | 0.0772712 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 4340.00 | 0.167105 | 0.0835527 | − | 0.996503i | \(-0.473373\pi\) | ||||
0.0835527 | + | 0.996503i | \(0.473373\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 20502.0 | 0.786707 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −21240.0 | −0.812252 | −0.406126 | − | 0.913817i | \(-0.633121\pi\) | ||||
−0.406126 | + | 0.913817i | \(0.633121\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 12944.0 | 0.493319 | 0.246659 | − | 0.969102i | \(-0.420667\pi\) | ||||
0.246659 | + | 0.969102i | \(0.420667\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −2520.00 | −0.0957162 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 1308.00 | 0.0495134 | 0.0247567 | − | 0.999694i | \(-0.492119\pi\) | ||||
0.0247567 | + | 0.999694i | \(0.492119\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −15392.0 | −0.580687 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 2430.00 | 0.0913671 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −30576.0 | −1.14579 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 480.000 | 0.0179270 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −1932.00 | −0.0719148 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −50400.0 | −1.86978 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 34164.0 | 1.26323 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −2208.00 | −0.0813706 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 9530.00 | 0.350042 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −14710.0 | −0.538520 | −0.269260 | − | 0.963068i | \(-0.586779\pi\) | ||||
−0.269260 | + | 0.963068i | \(0.586779\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −10476.0 | −0.382252 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 7548.00 | 0.274508 | 0.137254 | − | 0.990536i | \(-0.456172\pi\) | ||||
0.137254 | + | 0.990536i | \(0.456172\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 21240.0 | 0.769925 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −8790.00 | −0.317583 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 39744.0 | 1.43126 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −17728.0 | −0.636336 | −0.318168 | − | 0.948034i | \(-0.603068\pi\) | ||||
−0.318168 | + | 0.948034i | \(0.603068\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 16140.0 | 0.577450 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 840.000 | 0.0299555 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 3650.00 | 0.129742 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 5904.00 | 0.209183 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 19110.0 | 0.674896 | 0.337448 | − | 0.941344i | \(-0.390436\pi\) | ||||
0.337448 | + | 0.941344i | \(0.390436\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 4524.00 | 0.159257 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −13950.0 | −0.489499 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −11700.0 | −0.409231 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 16004.0 | 0.557981 | 0.278990 | − | 0.960294i | \(-0.410000\pi\) | ||||
0.278990 | + | 0.960294i | \(0.410000\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 27696.0 | 0.962540 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −30510.0 | −1.05696 | −0.528479 | − | 0.848946i | \(-0.677237\pi\) | ||||
−0.528479 | + | 0.848946i | \(0.677237\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −10074.0 | −0.347884 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −2160.00 | −0.0743543 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 37044.0 | 1.27114 | 0.635569 | − | 0.772044i | \(-0.280765\pi\) | ||||
0.635569 | + | 0.772044i | \(0.280765\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 13048.0 | 0.446318 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 13698.0 | 0.467075 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −34998.0 | −1.18961 | −0.594804 | − | 0.803871i | \(-0.702770\pi\) | ||||
−0.594804 | + | 0.803871i | \(0.702770\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 12600.0 | 0.426939 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 22680.0 | 0.766082 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 18144.0 | 0.610949 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 10209.0 | 0.342687 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −17928.0 | −0.599919 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 21830.0 | 0.728220 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 13454.0 | 0.447416 | 0.223708 | − | 0.974656i | \(-0.428184\pi\) | ||||
0.223708 | + | 0.974656i | \(0.428184\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 12168.0 | 0.403398 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −57222.0 | −1.89119 | −0.945593 | − | 0.325352i | \(-0.894517\pi\) | ||||
−0.945593 | + | 0.325352i | \(0.894517\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 26176.0 | 0.862450 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 2100.00 | 0.0689783 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −5874.00 | −0.192350 | −0.0961750 | − | 0.995364i | \(-0.530661\pi\) | ||||
−0.0961750 | + | 0.995364i | \(0.530661\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −18000.0 | −0.587623 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 11034.0 | 0.359112 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −22944.0 | −0.744456 | −0.372228 | − | 0.928141i | \(-0.621406\pi\) | ||||
−0.372228 | + | 0.928141i | \(0.621406\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −18750.0 | −0.606523 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 28224.0 | 0.910213 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 1058.00 | 0.0340166 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −14956.0 | −0.479408 | −0.239704 | − | 0.970846i | \(-0.577050\pi\) | ||||
−0.239704 | + | 0.970846i | \(0.577050\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −9420.00 | −0.301042 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 7880.00 | 0.251068 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −34396.0 | −1.09261 | −0.546305 | − | 0.837586i | \(-0.683966\pi\) | ||||
−0.546305 | + | 0.837586i | \(0.683966\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −3942.00 | −0.124844 |
(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 | 1380.4.a.a.1.1 | ✓ | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1380.4.a.a.1.1 | ✓ | 1 | 1.1 | even | 1 | trivial |