Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1521,4,Mod(1,1521)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1521, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1521.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1521 = 3^{2} \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1521.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: | \(89.7419051187\) |
Analytic rank: | \(0\) |
Dimension: | \(9\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{9} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{9} - x^{8} - 48x^{7} + 29x^{6} + 772x^{5} - 150x^{4} - 4745x^{3} - 966x^{2} + 9428x + 5144 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 13^{2} \) |
Twist minimal: | no (minimal twist has level 507) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.9 | ||
Root | \(-4.48584\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1521.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 5.48584 | 1.93954 | 0.969769 | − | 0.244025i | \(-0.0784677\pi\) | ||||
0.969769 | + | 0.244025i | \(0.0784677\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 22.0945 | 2.76181 | ||||||||
\(5\) | 13.3185 | 1.19125 | 0.595624 | − | 0.803264i | \(-0.296905\pi\) | ||||
0.595624 | + | 0.803264i | \(0.296905\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −21.4234 | −1.15675 | −0.578377 | − | 0.815770i | \(-0.696314\pi\) | ||||
−0.578377 | + | 0.815770i | \(0.696314\pi\) | |||||||
\(8\) | 77.3200 | 3.41709 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 73.0635 | 2.31047 | ||||||||
\(11\) | −19.0520 | −0.522217 | −0.261108 | − | 0.965310i | \(-0.584088\pi\) | ||||
−0.261108 | + | 0.965310i | \(0.584088\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | −117.525 | −2.24357 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 247.410 | 3.86578 | ||||||||
\(17\) | 71.7906 | 1.02422 | 0.512111 | − | 0.858919i | \(-0.328864\pi\) | ||||
0.512111 | + | 0.858919i | \(0.328864\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 102.134 | 1.23322 | 0.616611 | − | 0.787268i | \(-0.288505\pi\) | ||||
0.616611 | + | 0.787268i | \(0.288505\pi\) | |||||||
\(20\) | 294.266 | 3.29000 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −104.516 | −1.01286 | ||||||||
\(23\) | 37.8302 | 0.342962 | 0.171481 | − | 0.985187i | \(-0.445145\pi\) | ||||
0.171481 | + | 0.985187i | \(0.445145\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 52.3838 | 0.419070 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −473.338 | −3.19473 | ||||||||
\(29\) | −40.8605 | −0.261642 | −0.130821 | − | 0.991406i | \(-0.541761\pi\) | ||||
−0.130821 | + | 0.991406i | \(0.541761\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 6.05542 | 0.0350834 | 0.0175417 | − | 0.999846i | \(-0.494416\pi\) | ||||
0.0175417 | + | 0.999846i | \(0.494416\pi\) | |||||||
\(32\) | 738.690 | 4.08073 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 393.832 | 1.98652 | ||||||||
\(35\) | −285.328 | −1.37798 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 285.682 | 1.26935 | 0.634673 | − | 0.772781i | \(-0.281135\pi\) | ||||
0.634673 | + | 0.772781i | \(0.281135\pi\) | |||||||
\(38\) | 560.293 | 2.39188 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 1029.79 | 4.07060 | ||||||||
\(41\) | −342.705 | −1.30540 | −0.652702 | − | 0.757615i | \(-0.726364\pi\) | ||||
−0.652702 | + | 0.757615i | \(0.726364\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 306.458 | 1.08685 | 0.543424 | − | 0.839458i | \(-0.317128\pi\) | ||||
0.543424 | + | 0.839458i | \(0.317128\pi\) | |||||||
\(44\) | −420.943 | −1.44226 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 207.530 | 0.665188 | ||||||||
\(47\) | 346.863 | 1.07649 | 0.538246 | − | 0.842788i | \(-0.319087\pi\) | ||||
0.538246 | + | 0.842788i | \(0.319087\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 115.961 | 0.338079 | ||||||||
\(50\) | 287.369 | 0.812802 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −398.219 | −1.03207 | −0.516034 | − | 0.856568i | \(-0.672592\pi\) | ||||
−0.516034 | + | 0.856568i | \(0.672592\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −253.745 | −0.622089 | ||||||||
\(56\) | −1656.46 | −3.95274 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −224.155 | −0.507464 | ||||||||
\(59\) | −208.497 | −0.460067 | −0.230034 | − | 0.973183i | \(-0.573884\pi\) | ||||
−0.230034 | + | 0.973183i | \(0.573884\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 546.936 | 1.14800 | 0.574000 | − | 0.818855i | \(-0.305391\pi\) | ||||
0.574000 | + | 0.818855i | \(0.305391\pi\) | |||||||
\(62\) | 33.2191 | 0.0680456 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 2073.06 | 4.04895 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 678.268 | 1.23677 | 0.618386 | − | 0.785875i | \(-0.287787\pi\) | ||||
0.618386 | + | 0.785875i | \(0.287787\pi\) | |||||||
\(68\) | 1586.18 | 2.82871 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −1565.27 | −2.67264 | ||||||||
\(71\) | 957.777 | 1.60095 | 0.800474 | − | 0.599368i | \(-0.204581\pi\) | ||||
0.800474 | + | 0.599368i | \(0.204581\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −270.360 | −0.433469 | −0.216734 | − | 0.976231i | \(-0.569541\pi\) | ||||
−0.216734 | + | 0.976231i | \(0.569541\pi\) | |||||||
\(74\) | 1567.21 | 2.46195 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 2256.60 | 3.40592 | ||||||||
\(77\) | 408.157 | 0.604076 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −1032.86 | −1.47096 | −0.735482 | − | 0.677544i | \(-0.763044\pi\) | ||||
−0.735482 | + | 0.677544i | \(0.763044\pi\) | |||||||
\(80\) | 3295.14 | 4.60510 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −1880.03 | −2.53188 | ||||||||
\(83\) | −1065.90 | −1.40961 | −0.704806 | − | 0.709400i | \(-0.748966\pi\) | ||||
−0.704806 | + | 0.709400i | \(0.748966\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 956.147 | 1.22010 | ||||||||
\(86\) | 1681.18 | 2.10798 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −1473.10 | −1.78446 | ||||||||
\(89\) | 427.185 | 0.508782 | 0.254391 | − | 0.967101i | \(-0.418125\pi\) | ||||
0.254391 | + | 0.967101i | \(0.418125\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 835.837 | 0.947196 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 1902.83 | 2.08790 | ||||||||
\(95\) | 1360.28 | 1.46907 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −698.084 | −0.730718 | −0.365359 | − | 0.930867i | \(-0.619054\pi\) | ||||
−0.365359 | + | 0.930867i | \(0.619054\pi\) | |||||||
\(98\) | 636.144 | 0.655717 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 1157.39 | 1.15739 | ||||||||
\(101\) | −88.7364 | −0.0874218 | −0.0437109 | − | 0.999044i | \(-0.513918\pi\) | ||||
−0.0437109 | + | 0.999044i | \(0.513918\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1427.61 | −1.36570 | −0.682849 | − | 0.730560i | \(-0.739259\pi\) | ||||
−0.682849 | + | 0.730560i | \(0.739259\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −2184.57 | −2.00173 | ||||||||
\(107\) | 15.0233 | 0.0135735 | 0.00678673 | − | 0.999977i | \(-0.497840\pi\) | ||||
0.00678673 | + | 0.999977i | \(0.497840\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −2053.56 | −1.80455 | −0.902274 | − | 0.431163i | \(-0.858104\pi\) | ||||
−0.902274 | + | 0.431163i | \(0.858104\pi\) | |||||||
\(110\) | −1392.00 | −1.20657 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −5300.35 | −4.47175 | ||||||||
\(113\) | −717.456 | −0.597280 | −0.298640 | − | 0.954366i | \(-0.596533\pi\) | ||||
−0.298640 | + | 0.954366i | \(0.596533\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 503.843 | 0.408553 | ||||||||
\(116\) | −902.792 | −0.722605 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −1143.78 | −0.892318 | ||||||||
\(119\) | −1538.00 | −1.18477 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −968.023 | −0.727290 | ||||||||
\(122\) | 3000.41 | 2.22659 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 133.791 | 0.0968937 | ||||||||
\(125\) | −967.143 | −0.692031 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −117.640 | −0.0821955 | −0.0410978 | − | 0.999155i | \(-0.513086\pi\) | ||||
−0.0410978 | + | 0.999155i | \(0.513086\pi\) | |||||||
\(128\) | 5462.96 | 3.77236 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 262.376 | 0.174991 | 0.0874957 | − | 0.996165i | \(-0.472114\pi\) | ||||
0.0874957 | + | 0.996165i | \(0.472114\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −2188.06 | −1.42653 | ||||||||
\(134\) | 3720.87 | 2.39876 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 5550.85 | 3.49986 | ||||||||
\(137\) | −1317.41 | −0.821563 | −0.410782 | − | 0.911734i | \(-0.634744\pi\) | ||||
−0.410782 | + | 0.911734i | \(0.634744\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −6.43478 | −0.00392656 | −0.00196328 | − | 0.999998i | \(-0.500625\pi\) | ||||
−0.00196328 | + | 0.999998i | \(0.500625\pi\) | |||||||
\(140\) | −6304.18 | −3.80572 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 5254.22 | 3.10510 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −544.203 | −0.311680 | ||||||||
\(146\) | −1483.15 | −0.840729 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 6311.99 | 3.50569 | ||||||||
\(149\) | 548.312 | 0.301473 | 0.150736 | − | 0.988574i | \(-0.451836\pi\) | ||||
0.150736 | + | 0.988574i | \(0.451836\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1485.90 | −0.800799 | −0.400399 | − | 0.916341i | \(-0.631129\pi\) | ||||
−0.400399 | + | 0.916341i | \(0.631129\pi\) | |||||||
\(152\) | 7897.03 | 4.21404 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 2239.09 | 1.17163 | ||||||||
\(155\) | 80.6494 | 0.0417930 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 2132.36 | 1.08396 | 0.541978 | − | 0.840393i | \(-0.317676\pi\) | ||||
0.541978 | + | 0.840393i | \(0.317676\pi\) | |||||||
\(158\) | −5666.13 | −2.85299 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 9838.28 | 4.86115 | ||||||||
\(161\) | −810.450 | −0.396723 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −480.633 | −0.230957 | −0.115479 | − | 0.993310i | \(-0.536840\pi\) | ||||
−0.115479 | + | 0.993310i | \(0.536840\pi\) | |||||||
\(164\) | −7571.88 | −3.60527 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −5847.36 | −2.73400 | ||||||||
\(167\) | −2919.71 | −1.35290 | −0.676448 | − | 0.736490i | \(-0.736482\pi\) | ||||
−0.676448 | + | 0.736490i | \(0.736482\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | 5245.27 | 2.36643 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 6771.04 | 3.00167 | ||||||||
\(173\) | 2339.62 | 1.02820 | 0.514098 | − | 0.857731i | \(-0.328127\pi\) | ||||
0.514098 | + | 0.857731i | \(0.328127\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1122.24 | −0.484761 | ||||||||
\(176\) | −4713.64 | −2.01877 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 2343.47 | 0.986802 | ||||||||
\(179\) | 4558.71 | 1.90354 | 0.951772 | − | 0.306808i | \(-0.0992608\pi\) | ||||
0.951772 | + | 0.306808i | \(0.0992608\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −3524.56 | −1.44739 | −0.723696 | − | 0.690118i | \(-0.757558\pi\) | ||||
−0.723696 | + | 0.690118i | \(0.757558\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 2925.03 | 1.17193 | ||||||||
\(185\) | 3804.87 | 1.51211 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −1367.75 | −0.534866 | ||||||||
\(188\) | 7663.75 | 2.97306 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 7462.29 | 2.84932 | ||||||||
\(191\) | −3343.27 | −1.26655 | −0.633273 | − | 0.773929i | \(-0.718289\pi\) | ||||
−0.633273 | + | 0.773929i | \(0.718289\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −3341.33 | −1.24619 | −0.623094 | − | 0.782147i | \(-0.714124\pi\) | ||||
−0.623094 | + | 0.782147i | \(0.714124\pi\) | |||||||
\(194\) | −3829.58 | −1.41726 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 2562.10 | 0.933709 | ||||||||
\(197\) | 3653.95 | 1.32149 | 0.660745 | − | 0.750611i | \(-0.270241\pi\) | ||||
0.660745 | + | 0.750611i | \(0.270241\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1126.55 | 0.401301 | 0.200651 | − | 0.979663i | \(-0.435694\pi\) | ||||
0.200651 | + | 0.979663i | \(0.435694\pi\) | |||||||
\(200\) | 4050.31 | 1.43200 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −486.794 | −0.169558 | ||||||||
\(203\) | 875.371 | 0.302655 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −4564.33 | −1.55506 | ||||||||
\(206\) | −7831.66 | −2.64882 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −1945.86 | −0.644009 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −74.5243 | −0.0243150 | −0.0121575 | − | 0.999926i | \(-0.503870\pi\) | ||||
−0.0121575 | + | 0.999926i | \(0.503870\pi\) | |||||||
\(212\) | −8798.44 | −2.85037 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 82.4156 | 0.0263262 | ||||||||
\(215\) | 4081.58 | 1.29471 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −129.728 | −0.0405829 | ||||||||
\(218\) | −11265.5 | −3.49999 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −5606.35 | −1.71809 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 3178.62 | 0.954512 | 0.477256 | − | 0.878764i | \(-0.341631\pi\) | ||||
0.477256 | + | 0.878764i | \(0.341631\pi\) | |||||||
\(224\) | −15825.2 | −4.72039 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −3935.85 | −1.15845 | ||||||||
\(227\) | 1349.76 | 0.394655 | 0.197327 | − | 0.980338i | \(-0.436774\pi\) | ||||
0.197327 | + | 0.980338i | \(0.436774\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −4821.46 | −1.39131 | −0.695657 | − | 0.718374i | \(-0.744887\pi\) | ||||
−0.695657 | + | 0.718374i | \(0.744887\pi\) | |||||||
\(230\) | 2764.00 | 0.792404 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −3159.34 | −0.894055 | ||||||||
\(233\) | 2400.88 | 0.675050 | 0.337525 | − | 0.941317i | \(-0.390410\pi\) | ||||
0.337525 | + | 0.941317i | \(0.390410\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 4619.71 | 1.28237 | ||||||||
\(236\) | −4606.63 | −1.27062 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −8437.21 | −2.29791 | ||||||||
\(239\) | 1880.85 | 0.509047 | 0.254523 | − | 0.967067i | \(-0.418081\pi\) | ||||
0.254523 | + | 0.967067i | \(0.418081\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 5435.01 | 1.45270 | 0.726349 | − | 0.687327i | \(-0.241216\pi\) | ||||
0.726349 | + | 0.687327i | \(0.241216\pi\) | |||||||
\(242\) | −5310.42 | −1.41061 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 12084.3 | 3.17056 | ||||||||
\(245\) | 1544.43 | 0.402736 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 468.205 | 0.119883 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −5305.59 | −1.34222 | ||||||||
\(251\) | −1256.70 | −0.316024 | −0.158012 | − | 0.987437i | \(-0.550508\pi\) | ||||
−0.158012 | + | 0.987437i | \(0.550508\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −720.739 | −0.179101 | ||||||||
\(254\) | −645.353 | −0.159421 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 13384.5 | 3.26769 | ||||||||
\(257\) | −5504.87 | −1.33612 | −0.668062 | − | 0.744105i | \(-0.732876\pi\) | ||||
−0.668062 | + | 0.744105i | \(0.732876\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −6120.27 | −1.46832 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 1439.35 | 0.339402 | ||||||||
\(263\) | −2032.44 | −0.476522 | −0.238261 | − | 0.971201i | \(-0.576577\pi\) | ||||
−0.238261 | + | 0.971201i | \(0.576577\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −5303.70 | −1.22945 | ||||||||
\(266\) | −12003.4 | −2.76682 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 14986.0 | 3.41572 | ||||||||
\(269\) | −5523.82 | −1.25202 | −0.626009 | − | 0.779816i | \(-0.715313\pi\) | ||||
−0.626009 | + | 0.779816i | \(0.715313\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 3918.69 | 0.878389 | 0.439194 | − | 0.898392i | \(-0.355264\pi\) | ||||
0.439194 | + | 0.898392i | \(0.355264\pi\) | |||||||
\(272\) | 17761.7 | 3.95941 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −7227.12 | −1.59345 | ||||||||
\(275\) | −998.013 | −0.218845 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −2944.56 | −0.638705 | −0.319353 | − | 0.947636i | \(-0.603465\pi\) | ||||
−0.319353 | + | 0.947636i | \(0.603465\pi\) | |||||||
\(278\) | −35.3002 | −0.00761570 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −22061.6 | −4.70869 | ||||||||
\(281\) | 5048.76 | 1.07183 | 0.535914 | − | 0.844273i | \(-0.319967\pi\) | ||||
0.535914 | + | 0.844273i | \(0.319967\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 4491.66 | 0.943469 | 0.471734 | − | 0.881741i | \(-0.343628\pi\) | ||||
0.471734 | + | 0.881741i | \(0.343628\pi\) | |||||||
\(284\) | 21161.6 | 4.42151 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 7341.90 | 1.51003 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 240.893 | 0.0490318 | ||||||||
\(290\) | −2985.41 | −0.604515 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −5973.45 | −1.19716 | ||||||||
\(293\) | 4754.86 | 0.948061 | 0.474031 | − | 0.880508i | \(-0.342799\pi\) | ||||
0.474031 | + | 0.880508i | \(0.342799\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −2776.88 | −0.548054 | ||||||||
\(296\) | 22088.9 | 4.33747 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 3007.95 | 0.584718 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −6565.38 | −1.25722 | ||||||||
\(302\) | −8151.40 | −1.55318 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 25269.0 | 4.76736 | ||||||||
\(305\) | 7284.40 | 1.36755 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −1623.31 | −0.301783 | −0.150891 | − | 0.988550i | \(-0.548214\pi\) | ||||
−0.150891 | + | 0.988550i | \(0.548214\pi\) | |||||||
\(308\) | 9018.02 | 1.66834 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 442.430 | 0.0810592 | ||||||||
\(311\) | −6683.49 | −1.21860 | −0.609302 | − | 0.792938i | \(-0.708550\pi\) | ||||
−0.609302 | + | 0.792938i | \(0.708550\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 1584.55 | 0.286147 | 0.143073 | − | 0.989712i | \(-0.454301\pi\) | ||||
0.143073 | + | 0.989712i | \(0.454301\pi\) | |||||||
\(314\) | 11697.8 | 2.10237 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −22820.6 | −4.06252 | ||||||||
\(317\) | 787.932 | 0.139605 | 0.0698023 | − | 0.997561i | \(-0.477763\pi\) | ||||
0.0698023 | + | 0.997561i | \(0.477763\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 778.474 | 0.136634 | ||||||||
\(320\) | 27610.2 | 4.82330 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −4446.00 | −0.769459 | ||||||||
\(323\) | 7332.28 | 1.26309 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −2636.67 | −0.447951 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −26498.0 | −4.46069 | ||||||||
\(329\) | −7430.97 | −1.24524 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 9493.56 | 1.57647 | 0.788237 | − | 0.615371i | \(-0.210994\pi\) | ||||
0.788237 | + | 0.615371i | \(0.210994\pi\) | |||||||
\(332\) | −23550.5 | −3.89308 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −16017.1 | −2.62399 | ||||||||
\(335\) | 9033.55 | 1.47330 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −4123.06 | −0.666461 | −0.333230 | − | 0.942845i | \(-0.608139\pi\) | ||||
−0.333230 | + | 0.942845i | \(0.608139\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 21125.6 | 3.36969 | ||||||||
\(341\) | −115.368 | −0.0183211 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 4863.94 | 0.765680 | ||||||||
\(344\) | 23695.4 | 3.71386 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 12834.8 | 1.99423 | ||||||||
\(347\) | −2320.76 | −0.359034 | −0.179517 | − | 0.983755i | \(-0.557454\pi\) | ||||
−0.179517 | + | 0.983755i | \(0.557454\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −3818.85 | −0.585726 | −0.292863 | − | 0.956154i | \(-0.594608\pi\) | ||||
−0.292863 | + | 0.956154i | \(0.594608\pi\) | |||||||
\(350\) | −6156.41 | −0.940212 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −14073.5 | −2.13102 | ||||||||
\(353\) | −6065.53 | −0.914549 | −0.457274 | − | 0.889326i | \(-0.651174\pi\) | ||||
−0.457274 | + | 0.889326i | \(0.651174\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 12756.2 | 1.90712 | ||||||||
\(356\) | 9438.43 | 1.40516 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 25008.4 | 3.69199 | ||||||||
\(359\) | 7406.02 | 1.08879 | 0.544394 | − | 0.838830i | \(-0.316760\pi\) | ||||
0.544394 | + | 0.838830i | \(0.316760\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 3572.42 | 0.520836 | ||||||||
\(362\) | −19335.2 | −2.80727 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −3600.80 | −0.516368 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −4754.23 | −0.676209 | −0.338105 | − | 0.941109i | \(-0.609786\pi\) | ||||
−0.338105 | + | 0.941109i | \(0.609786\pi\) | |||||||
\(368\) | 9359.55 | 1.32582 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 20872.9 | 2.93279 | ||||||||
\(371\) | 8531.20 | 1.19385 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −4684.13 | −0.650229 | −0.325114 | − | 0.945675i | \(-0.605403\pi\) | ||||
−0.325114 | + | 0.945675i | \(0.605403\pi\) | |||||||
\(374\) | −7503.27 | −1.03739 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 26819.4 | 3.67847 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −12103.9 | −1.64047 | −0.820233 | − | 0.572030i | \(-0.806156\pi\) | ||||
−0.820233 | + | 0.572030i | \(0.806156\pi\) | |||||||
\(380\) | 30054.7 | 4.05730 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −18340.6 | −2.45651 | ||||||||
\(383\) | −5601.56 | −0.747327 | −0.373663 | − | 0.927564i | \(-0.621898\pi\) | ||||
−0.373663 | + | 0.927564i | \(0.621898\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 5436.06 | 0.719604 | ||||||||
\(386\) | −18330.0 | −2.41703 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −15423.8 | −2.01810 | ||||||||
\(389\) | −9450.46 | −1.23177 | −0.615883 | − | 0.787837i | \(-0.711201\pi\) | ||||
−0.615883 | + | 0.787837i | \(0.711201\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2715.85 | 0.351270 | ||||||||
\(392\) | 8966.11 | 1.15525 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 20045.0 | 2.56308 | ||||||||
\(395\) | −13756.2 | −1.75228 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 2723.98 | 0.344364 | 0.172182 | − | 0.985065i | \(-0.444918\pi\) | ||||
0.172182 | + | 0.985065i | \(0.444918\pi\) | |||||||
\(398\) | 6180.07 | 0.778339 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 12960.2 | 1.62003 | ||||||||
\(401\) | 4680.46 | 0.582870 | 0.291435 | − | 0.956591i | \(-0.405867\pi\) | ||||
0.291435 | + | 0.956591i | \(0.405867\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | −1960.58 | −0.241442 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 4802.15 | 0.587011 | ||||||||
\(407\) | −5442.80 | −0.662874 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 3272.70 | 0.395659 | 0.197830 | − | 0.980236i | \(-0.436611\pi\) | ||||
0.197830 | + | 0.980236i | \(0.436611\pi\) | |||||||
\(410\) | −25039.2 | −3.01609 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −31542.3 | −3.77179 | ||||||||
\(413\) | 4466.71 | 0.532185 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −14196.2 | −1.67920 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −10674.7 | −1.24908 | ||||||||
\(419\) | −1501.48 | −0.175065 | −0.0875323 | − | 0.996162i | \(-0.527898\pi\) | ||||
−0.0875323 | + | 0.996162i | \(0.527898\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 16578.1 | 1.91916 | 0.959580 | − | 0.281436i | \(-0.0908106\pi\) | ||||
0.959580 | + | 0.281436i | \(0.0908106\pi\) | |||||||
\(422\) | −408.828 | −0.0471598 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −30790.3 | −3.52667 | ||||||||
\(425\) | 3760.66 | 0.429221 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −11717.2 | −1.32795 | ||||||||
\(428\) | 331.933 | 0.0374873 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 22390.9 | 2.51113 | ||||||||
\(431\) | −3776.55 | −0.422065 | −0.211032 | − | 0.977479i | \(-0.567683\pi\) | ||||
−0.211032 | + | 0.977479i | \(0.567683\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −709.953 | −0.0787948 | −0.0393974 | − | 0.999224i | \(-0.512544\pi\) | ||||
−0.0393974 | + | 0.999224i | \(0.512544\pi\) | |||||||
\(434\) | −711.665 | −0.0787120 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −45372.4 | −4.98382 | ||||||||
\(437\) | 3863.76 | 0.422949 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −16262.2 | −1.76800 | −0.884002 | − | 0.467484i | \(-0.845161\pi\) | ||||
−0.884002 | + | 0.467484i | \(0.845161\pi\) | |||||||
\(440\) | −19619.5 | −2.12574 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −2899.45 | −0.310964 | −0.155482 | − | 0.987839i | \(-0.549693\pi\) | ||||
−0.155482 | + | 0.987839i | \(0.549693\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 5689.49 | 0.606085 | ||||||||
\(446\) | 17437.4 | 1.85131 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −44412.0 | −4.68363 | ||||||||
\(449\) | 7817.78 | 0.821701 | 0.410851 | − | 0.911703i | \(-0.365232\pi\) | ||||
0.410851 | + | 0.911703i | \(0.365232\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 6529.20 | 0.681703 | ||||||||
\(452\) | −15851.8 | −1.64957 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 7404.57 | 0.765448 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −14452.9 | −1.47939 | −0.739694 | − | 0.672943i | \(-0.765030\pi\) | ||||
−0.739694 | + | 0.672943i | \(0.765030\pi\) | |||||||
\(458\) | −26449.8 | −2.69851 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 11132.1 | 1.12834 | ||||||||
\(461\) | −2891.46 | −0.292123 | −0.146061 | − | 0.989276i | \(-0.546660\pi\) | ||||
−0.146061 | + | 0.989276i | \(0.546660\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 9223.83 | 0.925848 | 0.462924 | − | 0.886398i | \(-0.346800\pi\) | ||||
0.462924 | + | 0.886398i | \(0.346800\pi\) | |||||||
\(464\) | −10109.3 | −1.01145 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 13170.8 | 1.30929 | ||||||||
\(467\) | 7988.25 | 0.791546 | 0.395773 | − | 0.918348i | \(-0.370477\pi\) | ||||
0.395773 | + | 0.918348i | \(0.370477\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −14530.8 | −1.43064 | ||||||||
\(470\) | 25343.0 | 2.48720 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −16121.0 | −1.57209 | ||||||||
\(473\) | −5838.64 | −0.567570 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 5350.18 | 0.516806 | ||||||||
\(476\) | −33981.2 | −3.27212 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 10318.1 | 0.987315 | ||||||||
\(479\) | 6908.64 | 0.659006 | 0.329503 | − | 0.944155i | \(-0.393119\pi\) | ||||
0.329503 | + | 0.944155i | \(0.393119\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 29815.6 | 2.81756 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −21387.9 | −2.00863 | ||||||||
\(485\) | −9297.47 | −0.870466 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 13455.0 | 1.25196 | 0.625978 | − | 0.779841i | \(-0.284700\pi\) | ||||
0.625978 | + | 0.779841i | \(0.284700\pi\) | |||||||
\(488\) | 42289.1 | 3.92282 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 8472.52 | 0.781121 | ||||||||
\(491\) | 1044.02 | 0.0959589 | 0.0479795 | − | 0.998848i | \(-0.484722\pi\) | ||||
0.0479795 | + | 0.998848i | \(0.484722\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −2933.40 | −0.267979 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 1498.17 | 0.135625 | ||||||||
\(497\) | −20518.8 | −1.85190 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −16190.7 | −1.45249 | −0.726246 | − | 0.687435i | \(-0.758737\pi\) | ||||
−0.726246 | + | 0.687435i | \(0.758737\pi\) | |||||||
\(500\) | −21368.5 | −1.91126 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −6894.04 | −0.612940 | ||||||||
\(503\) | 11854.8 | 1.05086 | 0.525429 | − | 0.850838i | \(-0.323905\pi\) | ||||
0.525429 | + | 0.850838i | \(0.323905\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −1181.84 | −0.104141 | ||||||||
\(506\) | −3953.86 | −0.347372 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −2599.19 | −0.227008 | ||||||||
\(509\) | −6647.07 | −0.578834 | −0.289417 | − | 0.957203i | \(-0.593461\pi\) | ||||
−0.289417 | + | 0.957203i | \(0.593461\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 5792.02 | 0.501416 | ||||||||
\(512\) | 29721.4 | 2.56545 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −30198.8 | −2.59146 | ||||||||
\(515\) | −19013.7 | −1.62688 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −6608.42 | −0.562162 | ||||||||
\(518\) | −33574.8 | −2.84786 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −16839.6 | −1.41604 | −0.708019 | − | 0.706193i | \(-0.750411\pi\) | ||||
−0.708019 | + | 0.706193i | \(0.750411\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 10414.1 | 0.870701 | 0.435351 | − | 0.900261i | \(-0.356624\pi\) | ||||
0.435351 | + | 0.900261i | \(0.356624\pi\) | |||||||
\(524\) | 5797.05 | 0.483293 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −11149.6 | −0.924233 | ||||||||
\(527\) | 434.723 | 0.0359332 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −10735.9 | −0.882377 | ||||||||
\(530\) | −29095.3 | −2.38456 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −48344.1 | −3.93981 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 200.089 | 0.0161694 | ||||||||
\(536\) | 52443.7 | 4.22616 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −30302.8 | −2.42834 | ||||||||
\(539\) | −2209.29 | −0.176550 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −5464.03 | −0.434227 | −0.217114 | − | 0.976146i | \(-0.569664\pi\) | ||||
−0.217114 | + | 0.976146i | \(0.569664\pi\) | |||||||
\(542\) | 21497.3 | 1.70367 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 53031.0 | 4.17957 | ||||||||
\(545\) | −27350.5 | −2.14966 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 24902.3 | 1.94652 | 0.973261 | − | 0.229702i | \(-0.0737753\pi\) | ||||
0.973261 | + | 0.229702i | \(0.0737753\pi\) | |||||||
\(548\) | −29107.5 | −2.26900 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −5474.94 | −0.424459 | ||||||||
\(551\) | −4173.26 | −0.322662 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 22127.4 | 1.70154 | ||||||||
\(554\) | −16153.4 | −1.23879 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −142.173 | −0.0108444 | ||||||||
\(557\) | 9817.71 | 0.746840 | 0.373420 | − | 0.927662i | \(-0.378185\pi\) | ||||
0.373420 | + | 0.927662i | \(0.378185\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | −70593.0 | −5.32696 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 27696.7 | 2.07885 | ||||||||
\(563\) | 23333.7 | 1.74671 | 0.873356 | − | 0.487083i | \(-0.161939\pi\) | ||||
0.873356 | + | 0.487083i | \(0.161939\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −9555.48 | −0.711508 | ||||||||
\(566\) | 24640.6 | 1.82989 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 74055.4 | 5.47059 | ||||||||
\(569\) | −24543.9 | −1.80832 | −0.904160 | − | 0.427194i | \(-0.859502\pi\) | ||||
−0.904160 | + | 0.427194i | \(0.859502\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −10562.5 | −0.774126 | −0.387063 | − | 0.922053i | \(-0.626510\pi\) | ||||
−0.387063 | + | 0.922053i | \(0.626510\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 40276.5 | 2.92876 | ||||||||
\(575\) | 1981.69 | 0.143725 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −18922.5 | −1.36526 | −0.682629 | − | 0.730765i | \(-0.739163\pi\) | ||||
−0.682629 | + | 0.730765i | \(0.739163\pi\) | |||||||
\(578\) | 1321.50 | 0.0950991 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −12023.9 | −0.860801 | ||||||||
\(581\) | 22835.2 | 1.63057 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 7586.85 | 0.538963 | ||||||||
\(584\) | −20904.2 | −1.48120 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 26084.4 | 1.83880 | ||||||||
\(587\) | 7989.65 | 0.561786 | 0.280893 | − | 0.959739i | \(-0.409369\pi\) | ||||
0.280893 | + | 0.959739i | \(0.409369\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 618.466 | 0.0432656 | ||||||||
\(590\) | −15233.5 | −1.06297 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 70680.4 | 4.90701 | ||||||||
\(593\) | 25239.2 | 1.74781 | 0.873905 | − | 0.486097i | \(-0.161580\pi\) | ||||
0.873905 | + | 0.486097i | \(0.161580\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −20483.9 | −1.41136 | ||||||||
\(596\) | 12114.7 | 0.832610 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 7412.19 | 0.505599 | 0.252800 | − | 0.967519i | \(-0.418649\pi\) | ||||
0.252800 | + | 0.967519i | \(0.418649\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −21459.2 | −1.45647 | −0.728236 | − | 0.685327i | \(-0.759659\pi\) | ||||
−0.728236 | + | 0.685327i | \(0.759659\pi\) | |||||||
\(602\) | −36016.6 | −2.43842 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −32830.1 | −2.21165 | ||||||||
\(605\) | −12892.7 | −0.866382 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −18246.7 | −1.22011 | −0.610057 | − | 0.792358i | \(-0.708853\pi\) | ||||
−0.610057 | + | 0.792358i | \(0.708853\pi\) | |||||||
\(608\) | 75445.6 | 5.03244 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 39961.1 | 2.65242 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −24087.5 | −1.58709 | −0.793545 | − | 0.608512i | \(-0.791767\pi\) | ||||
−0.793545 | + | 0.608512i | \(0.791767\pi\) | |||||||
\(614\) | −8905.23 | −0.585319 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 31558.7 | 2.06418 | ||||||||
\(617\) | 14400.6 | 0.939621 | 0.469811 | − | 0.882767i | \(-0.344322\pi\) | ||||
0.469811 | + | 0.882767i | \(0.344322\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 25635.8 | 1.66460 | 0.832302 | − | 0.554322i | \(-0.187022\pi\) | ||||
0.832302 | + | 0.554322i | \(0.187022\pi\) | |||||||
\(620\) | 1781.91 | 0.115424 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −36664.6 | −2.36353 | ||||||||
\(623\) | −9151.76 | −0.588535 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −19428.9 | −1.24345 | ||||||||
\(626\) | 8692.58 | 0.554993 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 47113.4 | 2.99368 | ||||||||
\(629\) | 20509.3 | 1.30009 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −2757.17 | −0.173948 | −0.0869741 | − | 0.996211i | \(-0.527720\pi\) | ||||
−0.0869741 | + | 0.996211i | \(0.527720\pi\) | |||||||
\(632\) | −79861.0 | −5.02643 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 4322.47 | 0.270768 | ||||||||
\(635\) | −1566.79 | −0.0979152 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 4270.58 | 0.265006 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 72758.7 | 4.49382 | ||||||||
\(641\) | −14317.0 | −0.882196 | −0.441098 | − | 0.897459i | \(-0.645411\pi\) | ||||
−0.441098 | + | 0.897459i | \(0.645411\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −51.9171 | −0.00318415 | −0.00159208 | − | 0.999999i | \(-0.500507\pi\) | ||||
−0.00159208 | + | 0.999999i | \(0.500507\pi\) | |||||||
\(644\) | −17906.5 | −1.09567 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 40223.8 | 2.44982 | ||||||||
\(647\) | 9735.07 | 0.591538 | 0.295769 | − | 0.955260i | \(-0.404424\pi\) | ||||
0.295769 | + | 0.955260i | \(0.404424\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 3972.27 | 0.240255 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −10619.3 | −0.637860 | ||||||||
\(653\) | −10842.6 | −0.649778 | −0.324889 | − | 0.945752i | \(-0.605327\pi\) | ||||
−0.324889 | + | 0.945752i | \(0.605327\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 3494.46 | 0.208458 | ||||||||
\(656\) | −84788.5 | −5.04640 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −40765.1 | −2.41518 | ||||||||
\(659\) | −28940.9 | −1.71074 | −0.855369 | − | 0.518020i | \(-0.826669\pi\) | ||||
−0.855369 | + | 0.518020i | \(0.826669\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −3108.58 | −0.182919 | −0.0914597 | − | 0.995809i | \(-0.529153\pi\) | ||||
−0.0914597 | + | 0.995809i | \(0.529153\pi\) | |||||||
\(662\) | 52080.2 | 3.05763 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −82415.4 | −4.81677 | ||||||||
\(665\) | −29141.8 | −1.69935 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −1545.76 | −0.0897333 | ||||||||
\(668\) | −64509.4 | −3.73644 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 49556.6 | 2.85752 | ||||||||
\(671\) | −10420.2 | −0.599505 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −9950.09 | −0.569908 | −0.284954 | − | 0.958541i | \(-0.591978\pi\) | ||||
−0.284954 | + | 0.958541i | \(0.591978\pi\) | |||||||
\(674\) | −22618.4 | −1.29263 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 3483.60 | 0.197763 | 0.0988816 | − | 0.995099i | \(-0.468473\pi\) | ||||
0.0988816 | + | 0.995099i | \(0.468473\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 14955.3 | 0.845261 | ||||||||
\(680\) | 73929.3 | 4.16920 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −632.889 | −0.0355346 | ||||||||
\(683\) | −16811.4 | −0.941829 | −0.470915 | − | 0.882179i | \(-0.656076\pi\) | ||||
−0.470915 | + | 0.882179i | \(0.656076\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −17546.0 | −0.978685 | ||||||||
\(686\) | 26682.8 | 1.48506 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 75820.8 | 4.20151 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 3078.78 | 0.169497 | 0.0847484 | − | 0.996402i | \(-0.472991\pi\) | ||||
0.0847484 | + | 0.996402i | \(0.472991\pi\) | |||||||
\(692\) | 51692.6 | 2.83968 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −12731.3 | −0.696361 | ||||||||
\(695\) | −85.7020 | −0.00467750 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −24603.0 | −1.33702 | ||||||||
\(698\) | −20949.6 | −1.13604 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −24795.2 | −1.33882 | ||||||||
\(701\) | 18608.6 | 1.00262 | 0.501311 | − | 0.865267i | \(-0.332851\pi\) | ||||
0.501311 | + | 0.865267i | \(0.332851\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 29177.9 | 1.56539 | ||||||||
\(704\) | −39495.9 | −2.11443 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −33274.5 | −1.77380 | ||||||||
\(707\) | 1901.03 | 0.101126 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −19046.2 | −1.00888 | −0.504439 | − | 0.863448i | \(-0.668301\pi\) | ||||
−0.504439 | + | 0.863448i | \(0.668301\pi\) | |||||||
\(710\) | 69978.5 | 3.69894 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 33030.0 | 1.73855 | ||||||||
\(713\) | 229.078 | 0.0120323 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 100722. | 5.25722 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 40628.2 | 2.11174 | ||||||||
\(719\) | 14013.4 | 0.726859 | 0.363430 | − | 0.931622i | \(-0.381606\pi\) | ||||
0.363430 | + | 0.931622i | \(0.381606\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 30584.3 | 1.57978 | ||||||||
\(722\) | 19597.7 | 1.01018 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −77873.2 | −3.99742 | ||||||||
\(725\) | −2140.43 | −0.109646 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 2578.98 | 0.131567 | 0.0657834 | − | 0.997834i | \(-0.479045\pi\) | ||||
0.0657834 | + | 0.997834i | \(0.479045\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −19753.4 | −1.00152 | ||||||||
\(731\) | 22000.8 | 1.11317 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −5029.12 | −0.253417 | −0.126709 | − | 0.991940i | \(-0.540441\pi\) | ||||
−0.126709 | + | 0.991940i | \(0.540441\pi\) | |||||||
\(734\) | −26081.0 | −1.31153 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 27944.8 | 1.39954 | ||||||||
\(737\) | −12922.3 | −0.645863 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 23856.4 | 1.18751 | 0.593757 | − | 0.804644i | \(-0.297644\pi\) | ||||
0.593757 | + | 0.804644i | \(0.297644\pi\) | |||||||
\(740\) | 84066.5 | 4.17614 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 46800.8 | 2.31551 | ||||||||
\(743\) | 4887.62 | 0.241332 | 0.120666 | − | 0.992693i | \(-0.461497\pi\) | ||||
0.120666 | + | 0.992693i | \(0.461497\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 7302.72 | 0.359129 | ||||||||
\(746\) | −25696.4 | −1.26114 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −30219.8 | −1.47720 | ||||||||
\(749\) | −321.851 | −0.0157012 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 24814.3 | 1.20571 | 0.602854 | − | 0.797851i | \(-0.294030\pi\) | ||||
0.602854 | + | 0.797851i | \(0.294030\pi\) | |||||||
\(752\) | 85817.2 | 4.16148 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −19790.0 | −0.953949 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −6552.91 | −0.314623 | −0.157311 | − | 0.987549i | \(-0.550283\pi\) | ||||
−0.157311 | + | 0.987549i | \(0.550283\pi\) | |||||||
\(758\) | −66400.2 | −3.18175 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 105177. | 5.01996 | ||||||||
\(761\) | 20351.4 | 0.969431 | 0.484715 | − | 0.874672i | \(-0.338923\pi\) | ||||
0.484715 | + | 0.874672i | \(0.338923\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 43994.3 | 2.08742 | ||||||||
\(764\) | −73867.7 | −3.49796 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −30729.3 | −1.44947 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 22209.7 | 1.04148 | 0.520742 | − | 0.853714i | \(-0.325655\pi\) | ||||
0.520742 | + | 0.853714i | \(0.325655\pi\) | |||||||
\(770\) | 29821.4 | 1.39570 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −73824.9 | −3.44173 | ||||||||
\(773\) | 28496.6 | 1.32594 | 0.662971 | − | 0.748645i | \(-0.269295\pi\) | ||||
0.662971 | + | 0.748645i | \(0.269295\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 317.206 | 0.0147024 | ||||||||
\(776\) | −53975.9 | −2.49693 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −51843.7 | −2.38906 | ||||||||
\(779\) | −35001.9 | −1.60985 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −18247.5 | −0.836041 | ||||||||
\(782\) | 14898.7 | 0.681301 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 28689.9 | 1.30694 | ||||||||
\(785\) | 28400.0 | 1.29126 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 2394.07 | 0.108436 | 0.0542181 | − | 0.998529i | \(-0.482733\pi\) | ||||
0.0542181 | + | 0.998529i | \(0.482733\pi\) | |||||||
\(788\) | 80732.2 | 3.64970 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −75464.6 | −3.39862 | ||||||||
\(791\) | 15370.3 | 0.690906 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 14943.3 | 0.667907 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 24890.5 | 1.10832 | ||||||||
\(797\) | 37996.7 | 1.68872 | 0.844362 | − | 0.535773i | \(-0.179980\pi\) | ||||
0.844362 | + | 0.535773i | \(0.179980\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 24901.5 | 1.10257 | ||||||||
\(800\) | 38695.4 | 1.71011 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 25676.3 | 1.13050 | ||||||||
\(803\) | 5150.88 | 0.226364 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −10794.0 | −0.472595 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −6861.10 | −0.298729 | ||||||||
\(809\) | 25993.4 | 1.12964 | 0.564821 | − | 0.825213i | \(-0.308945\pi\) | ||||
0.564821 | + | 0.825213i | \(0.308945\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 15524.4 | 0.672176 | 0.336088 | − | 0.941831i | \(-0.390896\pi\) | ||||
0.336088 | + | 0.941831i | \(0.390896\pi\) | |||||||
\(812\) | 19340.9 | 0.835875 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −29858.3 | −1.28567 | ||||||||
\(815\) | −6401.33 | −0.275127 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 31299.9 | 1.34033 | ||||||||
\(818\) | 17953.5 | 0.767396 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −100847. | −4.29477 | ||||||||
\(821\) | −2029.40 | −0.0862684 | −0.0431342 | − | 0.999069i | \(-0.513734\pi\) | ||||
−0.0431342 | + | 0.999069i | \(0.513734\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −42010.4 | −1.77933 | −0.889667 | − | 0.456610i | \(-0.849064\pi\) | ||||
−0.889667 | + | 0.456610i | \(0.849064\pi\) | |||||||
\(824\) | −110383. | −4.66672 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 24503.6 | 1.03219 | ||||||||
\(827\) | 3941.24 | 0.165720 | 0.0828599 | − | 0.996561i | \(-0.473595\pi\) | ||||
0.0828599 | + | 0.996561i | \(0.473595\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 11264.7 | 0.471941 | 0.235970 | − | 0.971760i | \(-0.424173\pi\) | ||||
0.235970 | + | 0.971760i | \(0.424173\pi\) | |||||||
\(830\) | −77878.4 | −3.25686 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 8324.92 | 0.346268 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −38886.3 | −1.61163 | ||||||||
\(836\) | −42992.7 | −1.77863 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −8236.88 | −0.339544 | ||||||||
\(839\) | 35221.1 | 1.44931 | 0.724653 | − | 0.689114i | \(-0.242000\pi\) | ||||
0.724653 | + | 0.689114i | \(0.242000\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −22719.4 | −0.931544 | ||||||||
\(842\) | 90944.8 | 3.72228 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −1646.57 | −0.0671533 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 20738.3 | 0.841295 | ||||||||
\(848\) | −98523.2 | −3.98974 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 20630.4 | 0.832490 | ||||||||
\(851\) | 10807.4 | 0.435338 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 37662.7 | 1.51178 | 0.755888 | − | 0.654701i | \(-0.227205\pi\) | ||||
0.755888 | + | 0.654701i | \(0.227205\pi\) | |||||||
\(854\) | −64278.8 | −2.57562 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 1161.60 | 0.0463818 | ||||||||
\(857\) | −800.368 | −0.0319020 | −0.0159510 | − | 0.999873i | \(-0.505078\pi\) | ||||
−0.0159510 | + | 0.999873i | \(0.505078\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −8800.69 | −0.349564 | −0.174782 | − | 0.984607i | \(-0.555922\pi\) | ||||
−0.174782 | + | 0.984607i | \(0.555922\pi\) | |||||||
\(860\) | 90180.4 | 3.57573 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −20717.6 | −0.818611 | ||||||||
\(863\) | 17991.0 | 0.709641 | 0.354821 | − | 0.934934i | \(-0.384542\pi\) | ||||
0.354821 | + | 0.934934i | \(0.384542\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 31160.3 | 1.22484 | ||||||||
\(866\) | −3894.69 | −0.152826 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −2866.26 | −0.112082 | ||||||||
\(869\) | 19678.1 | 0.768162 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | −158782. | −6.16631 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 21196.0 | 0.820325 | ||||||||
\(875\) | 20719.5 | 0.800510 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −44304.5 | −1.70588 | −0.852940 | − | 0.522008i | \(-0.825183\pi\) | ||||
−0.852940 | + | 0.522008i | \(0.825183\pi\) | |||||||
\(878\) | −89212.0 | −3.42911 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −62778.8 | −2.40486 | ||||||||
\(881\) | −10814.6 | −0.413567 | −0.206783 | − | 0.978387i | \(-0.566300\pi\) | ||||
−0.206783 | + | 0.978387i | \(0.566300\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 14530.8 | 0.553793 | 0.276897 | − | 0.960900i | \(-0.410694\pi\) | ||||
0.276897 | + | 0.960900i | \(0.410694\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −15905.9 | −0.603126 | ||||||||
\(887\) | 3385.82 | 0.128168 | 0.0640838 | − | 0.997945i | \(-0.479588\pi\) | ||||
0.0640838 | + | 0.997945i | \(0.479588\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 2520.24 | 0.0950800 | ||||||||
\(890\) | 31211.7 | 1.17552 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 70229.9 | 2.63618 | ||||||||
\(893\) | 35426.6 | 1.32755 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 60715.4 | 2.26759 | ||||||||
\(896\) | −117035. | −4.36369 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 42887.1 | 1.59372 | ||||||||
\(899\) | −247.428 | −0.00917929 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −28588.4 | −1.05707 | ||||||||
\(902\) | 35818.2 | 1.32219 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −55473.7 | −2.04096 | ||||||||
\(905\) | −46942.0 | −1.72420 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 38174.2 | 1.39752 | 0.698762 | − | 0.715354i | \(-0.253735\pi\) | ||||
0.698762 | + | 0.715354i | \(0.253735\pi\) | |||||||
\(908\) | 29822.2 | 1.08996 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 11699.5 | 0.425489 | 0.212745 | − | 0.977108i | \(-0.431760\pi\) | ||||
0.212745 | + | 0.977108i | \(0.431760\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 20307.5 | 0.736123 | ||||||||
\(914\) | −79286.6 | −2.86933 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −106528. | −3.84254 | ||||||||
\(917\) | −5620.97 | −0.202422 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 21615.6 | 0.775879 | 0.387939 | − | 0.921685i | \(-0.373187\pi\) | ||||
0.387939 | + | 0.921685i | \(0.373187\pi\) | |||||||
\(920\) | 38957.1 | 1.39606 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −15862.1 | −0.566583 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 14965.1 | 0.531945 | ||||||||
\(926\) | 50600.5 | 1.79572 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −30183.3 | −1.06769 | ||||||||
\(929\) | 22325.9 | 0.788471 | 0.394236 | − | 0.919009i | \(-0.371009\pi\) | ||||
0.394236 | + | 0.919009i | \(0.371009\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 11843.6 | 0.416926 | ||||||||
\(932\) | 53046.1 | 1.86436 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 43822.3 | 1.53523 | ||||||||
\(935\) | −18216.5 | −0.637158 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −29401.5 | −1.02509 | −0.512543 | − | 0.858661i | \(-0.671297\pi\) | ||||
−0.512543 | + | 0.858661i | \(0.671297\pi\) | |||||||
\(938\) | −79713.7 | −2.77478 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 102070. | 3.54166 | ||||||||
\(941\) | 30280.7 | 1.04902 | 0.524508 | − | 0.851406i | \(-0.324249\pi\) | ||||
0.524508 | + | 0.851406i | \(0.324249\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −12964.6 | −0.447704 | ||||||||
\(944\) | −51584.1 | −1.77852 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −32029.8 | −1.10082 | ||||||||
\(947\) | 25226.1 | 0.865617 | 0.432809 | − | 0.901486i | \(-0.357523\pi\) | ||||
0.432809 | + | 0.901486i | \(0.357523\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 29350.2 | 1.00237 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −118918. | −4.04848 | ||||||||
\(953\) | 11893.7 | 0.404275 | 0.202137 | − | 0.979357i | \(-0.435211\pi\) | ||||
0.202137 | + | 0.979357i | \(0.435211\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −44527.5 | −1.50877 | ||||||||
\(956\) | 41556.4 | 1.40589 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 37899.7 | 1.27817 | ||||||||
\(959\) | 28223.4 | 0.950346 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −29754.3 | −0.998769 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 120084. | 4.01207 | ||||||||
\(965\) | −44501.7 | −1.48452 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −8534.72 | −0.283824 | −0.141912 | − | 0.989879i | \(-0.545325\pi\) | ||||
−0.141912 | + | 0.989879i | \(0.545325\pi\) | |||||||
\(968\) | −74847.5 | −2.48522 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −51004.4 | −1.68830 | ||||||||
\(971\) | −25615.3 | −0.846585 | −0.423292 | − | 0.905993i | \(-0.639126\pi\) | ||||
−0.423292 | + | 0.905993i | \(0.639126\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 137.855 | 0.00454206 | ||||||||
\(974\) | 73811.8 | 2.42822 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 135317. | 4.43791 | ||||||||
\(977\) | −22995.5 | −0.753011 | −0.376506 | − | 0.926414i | \(-0.622874\pi\) | ||||
−0.376506 | + | 0.926414i | \(0.622874\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −8138.72 | −0.265694 | ||||||||
\(980\) | 34123.4 | 1.11228 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 5727.31 | 0.186116 | ||||||||
\(983\) | −20592.1 | −0.668144 | −0.334072 | − | 0.942548i | \(-0.608423\pi\) | ||||
−0.334072 | + | 0.942548i | \(0.608423\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 48665.4 | 1.57422 | ||||||||
\(986\) | −16092.2 | −0.519756 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 11593.4 | 0.372748 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −11557.9 | −0.370485 | −0.185242 | − | 0.982693i | \(-0.559307\pi\) | ||||
−0.185242 | + | 0.982693i | \(0.559307\pi\) | |||||||
\(992\) | 4473.08 | 0.143166 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −112563. | −3.59183 | ||||||||
\(995\) | 15004.0 | 0.478049 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −15481.5 | −0.491778 | −0.245889 | − | 0.969298i | \(-0.579080\pi\) | ||||
−0.245889 | + | 0.969298i | \(0.579080\pi\) | |||||||
\(998\) | −88819.4 | −2.81716 | ||||||||
\(999\) | 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 | 1521.4.a.bj.1.9 | 9 | ||
3.2 | odd | 2 | 507.4.a.n.1.1 | ✓ | 9 | ||
13.12 | even | 2 | 1521.4.a.be.1.1 | 9 | |||
39.5 | even | 4 | 507.4.b.j.337.18 | 18 | |||
39.8 | even | 4 | 507.4.b.j.337.1 | 18 | |||
39.38 | odd | 2 | 507.4.a.q.1.9 | yes | 9 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
507.4.a.n.1.1 | ✓ | 9 | 3.2 | odd | 2 | ||
507.4.a.q.1.9 | yes | 9 | 39.38 | odd | 2 | ||
507.4.b.j.337.1 | 18 | 39.8 | even | 4 | |||
507.4.b.j.337.18 | 18 | 39.5 | even | 4 | |||
1521.4.a.be.1.1 | 9 | 13.12 | even | 2 | |||
1521.4.a.bj.1.9 | 9 | 1.1 | even | 1 | trivial |