Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [448,4,Mod(1,448)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(448, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("448.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 448 = 2^{6} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 448.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: | \(26.4328556826\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{37}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 9 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 224) |
Fricke sign: | \(+1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-2.54138\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 448.1 |
$q$-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 | ||||||||
\(3\) | −3.08276 | −0.593278 | −0.296639 | − | 0.954990i | \(-0.595866\pi\) | ||||
−0.296639 | + | 0.954990i | \(0.595866\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 9.08276 | 0.812387 | 0.406193 | − | 0.913787i | \(-0.366856\pi\) | ||||
0.406193 | + | 0.913787i | \(0.366856\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 7.00000 | 0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −17.4966 | −0.648021 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 34.1655 | 0.936481 | 0.468241 | − | 0.883601i | \(-0.344888\pi\) | ||||
0.468241 | + | 0.883601i | \(0.344888\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −13.0828 | −0.279116 | −0.139558 | − | 0.990214i | \(-0.544568\pi\) | ||||
−0.139558 | + | 0.990214i | \(0.544568\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −28.0000 | −0.481971 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −12.8276 | −0.183009 | −0.0915046 | − | 0.995805i | \(-0.529168\pi\) | ||||
−0.0915046 | + | 0.995805i | \(0.529168\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 139.745 | 1.68735 | 0.843676 | − | 0.536853i | \(-0.180387\pi\) | ||||
0.843676 | + | 0.536853i | \(0.180387\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −21.5793 | −0.224238 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 21.3242 | 0.193322 | 0.0966609 | − | 0.995317i | \(-0.469184\pi\) | ||||
0.0966609 | + | 0.995317i | \(0.469184\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −42.5034 | −0.340027 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 137.172 | 0.977735 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −142.814 | −0.914479 | −0.457239 | − | 0.889344i | \(-0.651162\pi\) | ||||
−0.457239 | + | 0.889344i | \(0.651162\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −192.152 | −1.11327 | −0.556637 | − | 0.830756i | \(-0.687909\pi\) | ||||
−0.556637 | + | 0.830756i | \(0.687909\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −105.324 | −0.555594 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 63.5793 | 0.307053 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 115.834 | 0.514678 | 0.257339 | − | 0.966321i | \(-0.417154\pi\) | ||||
0.257339 | + | 0.966321i | \(0.417154\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 40.3311 | 0.165593 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 396.800 | 1.51146 | 0.755729 | − | 0.654884i | \(-0.227283\pi\) | ||||
0.755729 | + | 0.654884i | \(0.227283\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 252.510 | 0.895522 | 0.447761 | − | 0.894153i | \(-0.352222\pi\) | ||||
0.447761 | + | 0.894153i | \(0.352222\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −158.917 | −0.526444 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −11.8208 | −0.0366859 | −0.0183430 | − | 0.999832i | \(-0.505839\pi\) | ||||
−0.0183430 | + | 0.999832i | \(0.505839\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 49.0000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 39.5445 | 0.108575 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 295.297 | 0.765323 | 0.382662 | − | 0.923889i | \(-0.375008\pi\) | ||||
0.382662 | + | 0.923889i | \(0.375008\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 310.317 | 0.760785 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −430.800 | −1.00107 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 269.731 | 0.595187 | 0.297593 | − | 0.954693i | \(-0.403816\pi\) | ||||
0.297593 | + | 0.954693i | \(0.403816\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 233.745 | 0.490622 | 0.245311 | − | 0.969444i | \(-0.421110\pi\) | ||||
0.245311 | + | 0.969444i | \(0.421110\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −122.476 | −0.244929 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −118.828 | −0.226750 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 975.918 | 1.77951 | 0.889756 | − | 0.456436i | \(-0.150874\pi\) | ||||
0.889756 | + | 0.456436i | \(0.150874\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −65.7374 | −0.114694 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 870.317 | 1.45476 | 0.727378 | − | 0.686237i | \(-0.240739\pi\) | ||||
0.727378 | + | 0.686237i | \(0.240739\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 391.600 | 0.627854 | 0.313927 | − | 0.949447i | \(-0.398355\pi\) | ||||
0.313927 | + | 0.949447i | \(0.398355\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 131.028 | 0.201731 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 239.159 | 0.353957 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 897.573 | 1.27829 | 0.639145 | − | 0.769087i | \(-0.279289\pi\) | ||||
0.639145 | + | 0.769087i | \(0.279289\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 49.5377 | 0.0679529 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −658.159 | −0.870390 | −0.435195 | − | 0.900336i | \(-0.643321\pi\) | ||||
−0.435195 | + | 0.900336i | \(0.643321\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −116.510 | −0.148674 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 440.261 | 0.542540 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 32.6210 | 0.0388519 | 0.0194260 | − | 0.999811i | \(-0.493816\pi\) | ||||
0.0194260 | + | 0.999811i | \(0.493816\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −91.5793 | −0.105496 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 592.358 | 0.660481 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 1269.27 | 1.37078 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 991.145 | 1.03748 | 0.518740 | − | 0.854932i | \(-0.326401\pi\) | ||||
0.518740 | + | 0.854932i | \(0.326401\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −597.780 | −0.606860 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −501.180 | −0.493755 | −0.246877 | − | 0.969047i | \(-0.579405\pi\) | ||||
−0.246877 | + | 0.969047i | \(0.579405\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 709.503 | 0.678733 | 0.339366 | − | 0.940654i | \(-0.389787\pi\) | ||||
0.339366 | + | 0.940654i | \(0.389787\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −196.000 | −0.182168 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −860.304 | −0.777278 | −0.388639 | − | 0.921390i | \(-0.627055\pi\) | ||||
−0.388639 | + | 0.921390i | \(0.627055\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1415.72 | −1.24405 | −0.622027 | − | 0.782996i | \(-0.713691\pi\) | ||||
−0.622027 | + | 0.782996i | \(0.713691\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −357.090 | −0.305347 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −1621.82 | −1.35016 | −0.675080 | − | 0.737745i | \(-0.735891\pi\) | ||||
−0.675080 | + | 0.737745i | \(0.735891\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 193.683 | 0.157052 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 228.904 | 0.180873 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −89.7934 | −0.0691710 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −163.717 | −0.123003 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −1223.24 | −0.896715 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1521.39 | −1.08862 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1964.91 | −1.37289 | −0.686447 | − | 0.727179i | \(-0.740831\pi\) | ||||
−0.686447 | + | 0.727179i | \(0.740831\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −778.429 | −0.531294 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1023.97 | 0.682934 | 0.341467 | − | 0.939894i | \(-0.389076\pi\) | ||||
0.341467 | + | 0.939894i | \(0.389076\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 978.214 | 0.637759 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 1245.90 | 0.794299 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 2534.94 | 1.58084 | 0.790418 | − | 0.612568i | \(-0.209864\pi\) | ||||
0.790418 | + | 0.612568i | \(0.209864\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −509.676 | −0.311009 | −0.155504 | − | 0.987835i | \(-0.549700\pi\) | ||||
−0.155504 | + | 0.987835i | \(0.549700\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 36.4406 | 0.0217649 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −446.979 | −0.261387 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −1297.14 | −0.742911 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −151.055 | −0.0847540 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 2263.55 | 1.24454 | 0.622271 | − | 0.782802i | \(-0.286210\pi\) | ||||
0.622271 | + | 0.782802i | \(0.286210\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1184.44 | −0.638334 | −0.319167 | − | 0.947699i | \(-0.603403\pi\) | ||||
−0.319167 | + | 0.947699i | \(0.603403\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 224.440 | 0.118594 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −1745.27 | −0.904409 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1426.70 | 0.725241 | 0.362621 | − | 0.931937i | \(-0.381882\pi\) | ||||
0.362621 | + | 0.931937i | \(0.381882\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −910.330 | −0.454049 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 149.269 | 0.0730688 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 2473.04 | 1.18836 | 0.594181 | − | 0.804331i | \(-0.297476\pi\) | ||||
0.594181 | + | 0.804331i | \(0.297476\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −956.635 | −0.451357 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −338.083 | −0.156657 | −0.0783284 | − | 0.996928i | \(-0.524958\pi\) | ||||
−0.0783284 | + | 0.996928i | \(0.524958\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −2025.84 | −0.922094 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −2445.06 | −1.09344 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −967.482 | −0.425181 | −0.212591 | − | 0.977141i | \(-0.568190\pi\) | ||||
−0.212591 | + | 0.977141i | \(0.568190\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −297.524 | −0.128518 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −831.517 | −0.353111 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 2438.13 | 1.01807 | 0.509034 | − | 0.860747i | \(-0.330003\pi\) | ||||
0.509034 | + | 0.860747i | \(0.330003\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −4711.93 | −1.93500 | −0.967499 | − | 0.252875i | \(-0.918624\pi\) | ||||
−0.967499 | + | 0.252875i | \(0.918624\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −720.580 | −0.291075 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 1052.10 | 0.418117 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −438.263 | −0.171385 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 960.207 | 0.369549 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −5172.66 | −1.95959 | −0.979793 | − | 0.200015i | \(-0.935901\pi\) | ||||
−0.979793 | + | 0.200015i | \(0.935901\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 2199.06 | 0.820166 | 0.410083 | − | 0.912048i | \(-0.365500\pi\) | ||||
0.410083 | + | 0.912048i | \(0.365500\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 366.317 | 0.134526 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 3572.73 | 1.29212 | 0.646058 | − | 0.763289i | \(-0.276417\pi\) | ||||
0.646058 | + | 0.763289i | \(0.276417\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −3198.17 | −1.13926 | −0.569628 | − | 0.821903i | \(-0.692913\pi\) | ||||
−0.569628 | + | 0.821903i | \(0.692913\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −3008.52 | −1.05575 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −999.697 | −0.345640 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 3604.04 | 1.22789 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −373.100 | −0.125277 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 4774.46 | 1.58017 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2686.70 | 0.876589 | 0.438294 | − | 0.898831i | \(-0.355583\pi\) | ||||
0.438294 | + | 0.898831i | \(0.355583\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −2682.98 | −0.863075 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 2293.49 | 0.727511 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1345.06 | −0.420778 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −1207.21 | −0.372492 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 167.821 | 0.0510808 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −6352.75 | −1.90767 | −0.953837 | − | 0.300324i | \(-0.902905\pi\) | ||||
−0.953837 | + | 0.300324i | \(0.902905\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 743.664 | 0.220345 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 1205.23 | 0.352397 | 0.176199 | − | 0.984355i | \(-0.443620\pi\) | ||||
0.176199 | + | 0.984355i | \(0.443620\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −867.345 | −0.250287 | −0.125144 | − | 0.992139i | \(-0.539939\pi\) | ||||
−0.125144 | + | 0.992139i | \(0.539939\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −737.269 | −0.209995 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −232.151 | −0.0652734 | −0.0326367 | − | 0.999467i | \(-0.510390\pi\) | ||||
−0.0326367 | + | 0.999467i | \(0.510390\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −107.365 | −0.0298031 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −2767.00 | −0.758381 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −131.283 | −0.0355314 | −0.0177657 | − | 0.999842i | \(-0.505655\pi\) | ||||
−0.0177657 | + | 0.999842i | \(0.505655\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 5858.79 | 1.56597 | 0.782983 | − | 0.622043i | \(-0.213697\pi\) | ||||
0.782983 | + | 0.622043i | \(0.213697\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −3856.37 | −1.01805 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 445.055 | 0.116055 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1828.25 | −0.470966 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 2028.95 | 0.516383 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −1795.55 | −0.451531 | −0.225765 | − | 0.974182i | \(-0.572488\pi\) | ||||
−0.225765 | + | 0.974182i | \(0.572488\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 728.553 | 0.181042 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 359.174 | 0.0882052 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −7753.70 | −1.88195 | −0.940977 | − | 0.338469i | \(-0.890091\pi\) | ||||
−0.940977 | + | 0.338469i | \(0.890091\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 810.841 | 0.194530 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 2498.75 | 0.592602 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 5937.02 | 1.39199 | 0.695993 | − | 0.718048i | \(-0.254964\pi\) | ||||
0.695993 | + | 0.718048i | \(0.254964\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 2682.11 | 0.621739 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −100.563 | −0.0230500 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 2313.02 | 0.524264 | 0.262132 | − | 0.965032i | \(-0.415574\pi\) | ||||
0.262132 | + | 0.965032i | \(0.415574\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −5212.08 | −1.16831 | −0.584154 | − | 0.811643i | \(-0.698574\pi\) | ||||
−0.584154 | + | 0.811643i | \(0.698574\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 282.317 | 0.0625884 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −1452.15 | −0.318429 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 6984.74 | 1.51506 | 0.757531 | − | 0.652799i | \(-0.226406\pi\) | ||||
0.757531 | + | 0.652799i | \(0.226406\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 3362.00 | 0.721425 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −6845.51 | −1.45327 | −0.726635 | − | 0.687024i | \(-0.758917\pi\) | ||||
−0.726635 | + | 0.687024i | \(0.758917\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −7726.11 | −1.62286 | −0.811430 | − | 0.584450i | \(-0.801310\pi\) | ||||
−0.811430 | + | 0.584450i | \(0.801310\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −3912.86 | −0.813255 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 2777.60 | 0.571277 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −4748.45 | −0.966508 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −3055.46 | −0.615514 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −9674.17 | −1.92891 | −0.964456 | − | 0.264243i | \(-0.914878\pi\) | ||||
−0.964456 | + | 0.264243i | \(0.914878\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 2449.90 | 0.483522 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 4686.57 | 0.915630 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −278.979 | −0.0539592 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1767.57 | 0.338476 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 1545.02 | 0.292934 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 2123.05 | 0.398575 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 2131.55 | 0.396267 | 0.198134 | − | 0.980175i | \(-0.436512\pi\) | ||||
0.198134 | + | 0.980175i | \(0.436512\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −2187.23 | −0.402677 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 6502.68 | 1.18564 | 0.592818 | − | 0.805336i | \(-0.298015\pi\) | ||||
0.592818 | + | 0.805336i | \(0.298015\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −8879.89 | −1.60358 | −0.801791 | − | 0.597604i | \(-0.796119\pi\) | ||||
−0.801791 | + | 0.597604i | \(0.796119\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −1112.42 | −0.198977 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 2818.86 | 0.499441 | 0.249720 | − | 0.968318i | \(-0.419661\pi\) | ||||
0.249720 | + | 0.968318i | \(0.419661\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −4879.31 | −0.856392 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 2652.11 | 0.461142 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −1792.59 | −0.308801 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 556.062 | 0.0949070 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 4364.34 | 0.738070 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −82.7454 | −0.0138660 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 5572.13 | 0.925292 | 0.462646 | − | 0.886543i | \(-0.346900\pi\) | ||||
0.462646 | + | 0.886543i | \(0.346900\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −2026.71 | −0.333522 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 8864.03 | 1.44565 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 1014.24 | 0.163944 | 0.0819718 | − | 0.996635i | \(-0.473878\pi\) | ||||
0.0819718 | + | 0.996635i | \(0.473878\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 4999.69 | 0.801020 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −6564.97 | −1.04256 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 343.000 | 0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −597.078 | −0.0931756 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −863.408 | −0.133574 | −0.0667870 | − | 0.997767i | \(-0.521275\pi\) | ||||
−0.0667870 | + | 0.997767i | \(0.521275\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −2772.92 | −0.425303 | −0.212652 | − | 0.977128i | \(-0.568210\pi\) | ||||
−0.212652 | + | 0.977128i | \(0.568210\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1794.59 | −0.272901 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −350.333 | −0.0528226 | −0.0264113 | − | 0.999651i | \(-0.508408\pi\) | ||||
−0.0264113 | + | 0.999651i | \(0.508408\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 7904.89 | 1.18182 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 276.812 | 0.0410376 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 12932.4 | 1.90124 | 0.950618 | − | 0.310362i | \(-0.100450\pi\) | ||||
0.950618 | + | 0.310362i | \(0.100450\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 12669.6 | 1.84715 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 504.700 | 0.0729749 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 3556.81 | 0.510061 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −969.349 | −0.137874 | −0.0689368 | − | 0.997621i | \(-0.521961\pi\) | ||||
−0.0689368 | + | 0.997621i | \(0.521961\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −6942.64 | −0.979457 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 2067.08 | 0.289265 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 5399.55 | 0.749539 | 0.374769 | − | 0.927118i | \(-0.377722\pi\) | ||||
0.374769 | + | 0.927118i | \(0.377722\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 4690.10 | 0.645855 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 1868.40 | 0.255245 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −2296.87 | −0.311299 | −0.155650 | − | 0.987812i | \(-0.549747\pi\) | ||||
−0.155650 | + | 0.987812i | \(0.549747\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 6057.35 | 0.814508 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 9908.90 | 1.32199 | 0.660993 | − | 0.750392i | \(-0.270135\pi\) | ||||
0.660993 | + | 0.750392i | \(0.270135\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 2172.22 | 0.287550 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −4418.07 | −0.580317 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 3858.40 | 0.502901 | 0.251451 | − | 0.967870i | \(-0.419092\pi\) | ||||
0.251451 | + | 0.967870i | \(0.419092\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −273.539 | −0.0353797 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −3156.64 | −0.405170 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 8152.44 | 1.03847 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −8571.26 | −1.08357 | −0.541787 | − | 0.840516i | \(-0.682252\pi\) | ||||
−0.541787 | + | 0.840516i | \(0.682252\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −3015.60 | −0.378368 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 8756.14 | 1.09043 | 0.545213 | − | 0.838298i | \(-0.316449\pi\) | ||||
0.545213 | + | 0.838298i | \(0.316449\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 2513.88 | 0.310732 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 449.939 | 0.0552041 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 3957.55 | 0.481986 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −1739.67 | −0.210321 | −0.105160 | − | 0.994455i | \(-0.533536\pi\) | ||||
−0.105160 | + | 0.994455i | \(0.533536\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −7814.61 | −0.937875 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 1888.12 | 0.224959 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −5977.90 | −0.707093 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 1571.21 | 0.184514 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 7998.16 | 0.932543 | 0.466272 | − | 0.884642i | \(-0.345597\pi\) | ||||
0.466272 | + | 0.884642i | \(0.345597\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −8002.03 | −0.926354 | −0.463177 | − | 0.886266i | \(-0.653291\pi\) | ||||
−0.463177 | + | 0.886266i | \(0.653291\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 206.823 | 0.0237732 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 545.218 | 0.0622281 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 1636.21 | 0.185438 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 1377.93 | 0.155075 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −8374.93 | −0.935977 | −0.467989 | − | 0.883734i | \(-0.655021\pi\) | ||||
−0.467989 | + | 0.883734i | \(0.655021\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −10136.5 | −1.12501 | −0.562505 | − | 0.826794i | \(-0.690162\pi\) | ||||
−0.562505 | + | 0.826794i | \(0.690162\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 3998.79 | 0.440752 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 2979.95 | 0.326202 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −11505.6 | −1.25087 | −0.625433 | − | 0.780278i | \(-0.715078\pi\) | ||||
−0.625433 | + | 0.780278i | \(0.715078\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −857.332 | −0.0925745 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 3045.88 | 0.326668 | 0.163334 | − | 0.986571i | \(-0.447775\pi\) | ||||
0.163334 | + | 0.986571i | \(0.447775\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 296.289 | 0.0315628 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −6977.97 | −0.738360 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −8831.38 | −0.928238 | −0.464119 | − | 0.885773i | \(-0.653629\pi\) | ||||
−0.464119 | + | 0.885773i | \(0.653629\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 13556.9 | 1.41545 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 3651.35 | 0.378709 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −831.793 | −0.0857035 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 4058.54 | 0.415428 | 0.207714 | − | 0.978190i | \(-0.433398\pi\) | ||||
0.207714 | + | 0.978190i | \(0.433398\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −1759.60 | −0.178934 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 6858.56 | 0.692917 | 0.346459 | − | 0.938065i | \(-0.387384\pi\) | ||||
0.346459 | + | 0.938065i | \(0.387384\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 3587.32 | 0.360079 | 0.180040 | − | 0.983659i | \(-0.442377\pi\) | ||||
0.180040 | + | 0.983659i | \(0.442377\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 5380.25 | 0.536566 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 12553.5 | 1.24391 | 0.621954 | − | 0.783054i | \(-0.286339\pi\) | ||||
0.621954 | + | 0.783054i | \(0.286339\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 6831.42 | 0.672592 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −4398.17 | −0.430270 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 8627.15 | 0.838640 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −5939.64 | −0.573746 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −5166.68 | −0.495946 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 7622.42 | 0.727092 | 0.363546 | − | 0.931576i | \(-0.381566\pi\) | ||||
0.363546 | + | 0.931576i | \(0.381566\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1515.43 | −0.143655 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −460.162 | −0.0433501 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 9002.33 | 0.842835 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −19040.9 | −1.77171 | −0.885856 | − | 0.463960i | \(-0.846428\pi\) | ||||
−0.885856 | + | 0.463960i | \(0.846428\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −7623.78 | −0.705029 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 14451.3 | 1.32827 | 0.664134 | − | 0.747613i | \(-0.268800\pi\) | ||||
0.664134 | + | 0.747613i | \(0.268800\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 1831.96 | 0.167358 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −5429.49 | −0.493005 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 6092.22 | 0.549846 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −8904.70 | −0.798856 | −0.399428 | − | 0.916765i | \(-0.630791\pi\) | ||||
−0.399428 | + | 0.916765i | \(0.630791\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 1042.23 | 0.0929410 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 14787.6 | 1.31083 | 0.655413 | − | 0.755271i | \(-0.272495\pi\) | ||||
0.655413 | + | 0.755271i | \(0.272495\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −4552.10 | −0.401120 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 6245.19 | 0.547058 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −20698.0 | −1.80240 | −0.901201 | − | 0.433401i | \(-0.857313\pi\) | ||||
−0.901201 | + | 0.433401i | \(0.857313\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 2741.20 | 0.237307 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 19169.1 | 1.64978 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 6444.25 | 0.551393 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −403.863 | −0.0343557 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 2982.52 | 0.252251 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −5283.86 | −0.444319 | −0.222159 | − | 0.975010i | \(-0.571311\pi\) | ||||
−0.222159 | + | 0.975010i | \(0.571311\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −1489.36 | −0.124522 | −0.0622611 | − | 0.998060i | \(-0.519831\pi\) | ||||
−0.0622611 | + | 0.998060i | \(0.519831\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 917.196 | 0.0762471 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 2464.85 | 0.203739 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −11712.3 | −0.962627 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −4719.37 | −0.385694 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −5191.24 | −0.421872 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −7813.93 | −0.631450 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −7516.16 | −0.603997 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 1674.11 | 0.133783 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −5574.20 | −0.442982 | −0.221491 | − | 0.975162i | \(-0.571092\pi\) | ||||
−0.221491 | + | 0.975162i | \(0.571092\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 14525.7 | 1.14799 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −12858.7 | −1.01065 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 809.449 | 0.0632715 | 0.0316358 | − | 0.999499i | \(-0.489928\pi\) | ||||
0.0316358 | + | 0.999499i | \(0.489928\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −4089.73 | −0.317934 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −19957.5 | −1.54305 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 6283.01 | 0.483148 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −3243.37 | −0.248060 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 12199.2 | 0.927998 | 0.463999 | − | 0.885836i | \(-0.346414\pi\) | ||||
0.463999 | + | 0.885836i | \(0.346414\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −3303.53 | −0.249954 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 1351.06 | 0.101679 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −22708.9 | −1.69994 | −0.849971 | − | 0.526829i | \(-0.823381\pi\) | ||||
−0.849971 | + | 0.526829i | \(0.823381\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −14730.6 | −1.09685 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 346.764 | 0.0256838 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 19186.3 | 1.41359 | 0.706793 | − | 0.707421i | \(-0.250141\pi\) | ||||
0.706793 | + | 0.707421i | \(0.250141\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −15757.5 | −1.15487 | −0.577433 | − | 0.816438i | \(-0.695946\pi\) | ||||
−0.577433 | + | 0.816438i | \(0.695946\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 15946.1 | 1.16258 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −906.352 | −0.0657347 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 4445.32 | 0.320729 | 0.160365 | − | 0.987058i | \(-0.448733\pi\) | ||||
0.160365 | + | 0.987058i | \(0.448733\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −6779.19 | −0.486586 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −4607.11 | −0.328976 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 10089.0 | 0.716711 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 2079.08 | 0.146939 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 23183.2 | 1.63011 | 0.815054 | − | 0.579385i | \(-0.196707\pi\) | ||||
0.815054 | + | 0.579385i | \(0.196707\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −26852.2 | −1.87848 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −11013.9 | −0.766583 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −9639.30 | −0.667519 | −0.333759 | − | 0.942658i | \(-0.608317\pi\) | ||||
−0.333759 | + | 0.942658i | \(0.608317\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −815.572 | −0.0561936 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 9859.18 | 0.675895 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −1294.46 | −0.0882976 | −0.0441488 | − | 0.999025i | \(-0.514058\pi\) | ||||
−0.0441488 | + | 0.999025i | \(0.514058\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −3912.65 | −0.265558 | −0.132779 | − | 0.991146i | \(-0.542390\pi\) | ||||
−0.132779 | + | 0.991146i | \(0.542390\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −17075.2 | −1.15316 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −1487.00 | −0.0999260 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 20986.8 | 1.40334 | 0.701670 | − | 0.712503i | \(-0.252438\pi\) | ||||
0.701670 | + | 0.712503i | \(0.252438\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 3081.83 | 0.205061 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 154.648 | 0.0102396 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 14701.1 | 0.968633 | 0.484316 | − | 0.874893i | \(-0.339068\pi\) | ||||
0.484316 | + | 0.874893i | \(0.339068\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −11110.4 | −0.728479 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −3795.09 | −0.247625 | −0.123812 | − | 0.992306i | \(-0.539512\pi\) | ||||
−0.123812 | + | 0.992306i | \(0.539512\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −11335.1 | −0.736020 | −0.368010 | − | 0.929822i | \(-0.619961\pi\) | ||||
−0.368010 | + | 0.929822i | \(0.619961\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 2925.09 | 0.189017 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 228.347 | 0.0146846 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −8505.53 | −0.544354 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −14718.5 | −0.937482 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −1485.88 | −0.0941907 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −17565.2 | −1.10817 | −0.554087 | − | 0.832459i | \(-0.686933\pi\) | ||||
−0.554087 | + | 0.832459i | \(0.686933\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −8282.47 | −0.520061 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −17846.8 | −1.11532 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −641.055 | −0.0398737 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −15227.6 | −0.942713 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −10053.0 | −0.619451 | −0.309726 | − | 0.950826i | \(-0.600237\pi\) | ||||
−0.309726 | + | 0.950826i | \(0.600237\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −26476.7 | −1.62386 | −0.811928 | − | 0.583757i | \(-0.801582\pi\) | ||||
−0.811928 | + | 0.583757i | \(0.801582\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −7070.29 | −0.431616 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −4372.68 | −0.265700 | −0.132850 | − | 0.991136i | \(-0.542413\pi\) | ||||
−0.132850 | + | 0.991136i | \(0.542413\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 9215.51 | 0.557381 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 4146.51 | 0.249638 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −18328.4 | −1.09839 | −0.549193 | − | 0.835696i | \(-0.685065\pi\) | ||||
−0.549193 | + | 0.835696i | \(0.685065\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 9300.44 | 0.554807 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −6851.67 | −0.406863 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −19536.1 | −1.15481 | −0.577404 | − | 0.816458i | \(-0.695934\pi\) | ||||
−0.577404 | + | 0.816458i | \(0.695934\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 23169.3 | 1.36336 | 0.681679 | − | 0.731651i | \(-0.261250\pi\) | ||||
0.681679 | + | 0.731651i | \(0.261250\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −517.352 | −0.0303051 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 8884.89 | 0.518107 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −3045.39 | −0.176789 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 19584.0 | 1.13178 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 7986.02 | 0.459459 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 11370.9 | 0.651287 | 0.325644 | − | 0.945493i | \(-0.394419\pi\) | ||||
0.325644 | + | 0.945493i | \(0.394419\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −5830.30 | −0.332457 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 3556.00 | 0.201873 | 0.100937 | − | 0.994893i | \(-0.467816\pi\) | ||||
0.100937 | + | 0.994893i | \(0.467816\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 6938.01 | 0.392130 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −3715.45 | −0.209069 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 16124.8 | 0.903367 | 0.451683 | − | 0.892178i | \(-0.350824\pi\) | ||||
0.451683 | + | 0.892178i | \(0.350824\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 23024.2 | 1.28425 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 2673.82 | 0.148490 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −3863.30 | −0.213614 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −14358.8 | −0.790499 | −0.395250 | − | 0.918574i | \(-0.629342\pi\) | ||||
−0.395250 | + | 0.918574i | \(0.629342\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −4184.46 | −0.229371 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −4629.27 | −0.252659 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −5090.00 | −0.276611 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 715.665 | 0.0387253 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −16098.4 | −0.867374 | −0.433687 | − | 0.901064i | \(-0.642788\pi\) | ||||
−0.433687 | + | 0.901064i | \(0.642788\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 16187.3 | 0.868442 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 330.982 | 0.0176815 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −3508.26 | −0.186622 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −6849.63 | −0.362826 | −0.181413 | − | 0.983407i | \(-0.558067\pi\) | ||||
−0.181413 | + | 0.983407i | \(0.558067\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −15704.5 | −0.828359 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −4097.48 | −0.215220 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −4059.81 | −0.212347 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 404.715 | 0.0210800 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 9257.56 | 0.480179 | 0.240090 | − | 0.970751i | \(-0.422823\pi\) | ||||
0.240090 | + | 0.970751i | \(0.422823\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 4966.52 | 0.256537 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −18061.3 | −0.929053 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 6070.08 | 0.310948 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 7188.96 | 0.366745 | 0.183373 | − | 0.983043i | \(-0.441299\pi\) | ||||
0.183373 | + | 0.983043i | \(0.441299\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 10550.7 | 0.536033 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −3239.11 | −0.163889 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −19359.3 | −0.975515 | −0.487757 | − | 0.872979i | \(-0.662185\pi\) | ||||
−0.487757 | + | 0.872979i | \(0.662185\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −1372.00 | −0.0688530 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 33342.7 | 1.66648 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −1159.95 | −0.0577395 | −0.0288697 | − | 0.999583i | \(-0.509191\pi\) | ||||
−0.0288697 | + | 0.999583i | \(0.509191\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 5636.06 | 0.279414 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 12095.9 | 0.597248 | 0.298624 | − | 0.954371i | \(-0.403472\pi\) | ||||
0.298624 | + | 0.954371i | \(0.403472\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 20559.2 | 1.01105 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 11515.5 | 0.564031 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −6022.13 | −0.293783 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −22296.3 | −1.08336 | −0.541679 | − | 0.840585i | \(-0.682211\pi\) | ||||
−0.541679 | + | 0.840585i | \(0.682211\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 5535.26 | 0.267883 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −10758.0 | −0.518574 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −17611.2 | −0.845563 | −0.422782 | − | 0.906232i | \(-0.638946\pi\) | ||||
−0.422782 | + | 0.906232i | \(0.638946\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −2245.95 | −0.107408 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −28792.7 | −1.37153 | −0.685765 | − | 0.727823i | \(-0.740532\pi\) | ||||
−0.685765 | + | 0.727823i | \(0.740532\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −9910.07 | −0.470208 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 2038.53 | 0.0963441 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −3528.83 | −0.166126 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −34104.7 | −1.59928 | −0.799640 | − | 0.600480i | \(-0.794976\pi\) | ||||
−0.799640 | + | 0.600480i | \(0.794976\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 23902.8 | 1.11652 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −3821.35 | −0.177807 | −0.0889033 | − | 0.996040i | \(-0.528336\pi\) | ||||
−0.0889033 | + | 0.996040i | \(0.528336\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 8167.11 | 0.378544 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −2499.63 | −0.115410 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 55450.8 | 2.55036 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 29734.8 | 1.36235 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −19590.1 | −0.894117 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 12958.4 | 0.589177 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 3580.88 | 0.162191 | 0.0810956 | − | 0.996706i | \(-0.474158\pi\) | ||||
0.0810956 | + | 0.996706i | \(0.474158\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −18302.4 | −0.825835 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −11352.7 | −0.510312 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −3058.03 | −0.136940 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −8268.31 | −0.368864 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 31970.7 | 1.42091 | 0.710453 | − | 0.703745i | \(-0.248490\pi\) | ||||
0.710453 | + | 0.703745i | \(0.248490\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 151.632 | 0.00671386 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −570.756 | −0.0251769 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 13379.2 | 0.587974 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 1355.78 | 0.0593601 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −7130.48 | −0.311034 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 5730.20 | 0.249027 | 0.124514 | − | 0.992218i | \(-0.460263\pi\) | ||||
0.124514 | + | 0.992218i | \(0.460263\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 16525.5 | 0.715523 | 0.357761 | − | 0.933813i | \(-0.383540\pi\) | ||||
0.357761 | + | 0.933813i | \(0.383540\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 16067.6 | 0.693131 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 22462.0 | 0.965410 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 35287.0 | 1.51106 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 1602.32 | 0.0683636 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −9304.93 | −0.395547 | −0.197774 | − | 0.980248i | \(-0.563371\pi\) | ||||
−0.197774 | + | 0.980248i | \(0.563371\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 20220.8 | 0.856443 | 0.428222 | − | 0.903674i | \(-0.359140\pi\) | ||||
0.428222 | + | 0.903674i | \(0.359140\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 4476.64 | 0.188917 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 37983.5 | 1.59712 | 0.798558 | − | 0.601919i | \(-0.205597\pi\) | ||||
0.798558 | + | 0.601919i | \(0.205597\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 24674.8 | 1.03376 | 0.516882 | − | 0.856056i | \(-0.327092\pi\) | ||||
0.516882 | + | 0.856056i | \(0.327092\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −21532.3 | −0.898853 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −628.554 | −0.0261442 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −3070.73 | −0.127266 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −26357.9 | −1.08849 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −41574.9 | −1.71076 | −0.855378 | − | 0.518005i | \(-0.826675\pi\) | ||||
−0.855378 | + | 0.518005i | \(0.826675\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −3993.18 | −0.163729 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 21103.1 | 0.862193 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −18400.2 | −0.749097 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −1146.02 | −0.0464907 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 23817.8 | 0.962807 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 2470.08 | 0.0994984 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −13103.0 | −0.525953 | −0.262976 | − | 0.964802i | \(-0.584704\pi\) | ||||
−0.262976 | + | 0.964802i | \(0.584704\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −22207.9 | −0.888296 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −4100.11 | −0.163427 | −0.0817135 | − | 0.996656i | \(-0.526039\pi\) | ||||
−0.0817135 | + | 0.996656i | \(0.526039\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 17741.5 | 0.704695 | 0.352347 | − | 0.935869i | \(-0.385384\pi\) | ||||
0.352347 | + | 0.935869i | \(0.385384\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −8562.69 | −0.338926 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 41942.8 | 1.65440 | 0.827201 | − | 0.561907i | \(-0.189932\pi\) | ||||
0.827201 | + | 0.561907i | \(0.189932\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −8787.41 | −0.345412 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 14638.3 | 0.573408 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 30666.1 | 1.19709 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −12767.7 | −0.496690 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −17341.6 | −0.672309 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −10649.8 | −0.411460 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −27562.4 | −1.06125 | −0.530625 | − | 0.847607i | \(-0.678043\pi\) | ||||
−0.530625 | + | 0.847607i | \(0.678043\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 29823.2 | 1.14438 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −39863.8 | −1.52446 | −0.762228 | − | 0.647308i | \(-0.775895\pi\) | ||||
−0.762228 | + | 0.647308i | \(0.775895\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −38030.3 | −1.44940 | −0.724701 | − | 0.689064i | \(-0.758022\pi\) | ||||
−0.724701 | + | 0.689064i | \(0.758022\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −7552.47 | −0.286863 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 12130.5 | 0.459190 | 0.229595 | − | 0.973286i | \(-0.426260\pi\) | ||||
0.229595 | + | 0.973286i | \(0.426260\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −13754.4 | −0.518905 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 1692.48 | 0.0636366 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −1651.89 | −0.0619020 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 22144.9 | 0.827065 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 860.027 | 0.0320128 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 27442.0 | 1.01807 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −3787.96 | −0.140061 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −5449.00 | −0.200810 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −42797.3 | −1.57197 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 42557.0 | 1.55797 | 0.778987 | − | 0.627039i | \(-0.215734\pi\) | ||||
0.778987 | + | 0.627039i | \(0.215734\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 8768.93 | 0.319964 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −9996.30 | −0.363548 | −0.181774 | − | 0.983340i | \(-0.558184\pi\) | ||||
−0.181774 | + | 0.983340i | \(0.558184\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −22486.4 | −0.815104 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −6544.86 | −0.236466 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 7167.76 | 0.258125 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 8273.88 | 0.296986 | 0.148493 | − | 0.988913i | \(-0.452558\pi\) | ||||
0.148493 | + | 0.988913i | \(0.452558\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −6571.06 | −0.235097 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −11386.2 | −0.406045 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −4923.36 | −0.175004 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −12413.9 | −0.439833 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 8388.40 | 0.296248 | 0.148124 | − | 0.988969i | \(-0.452677\pi\) | ||||
0.148124 | + | 0.988969i | \(0.452677\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 6847.50 | 0.241050 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −20046.2 | −0.703412 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −3980.63 | −0.139231 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −3757.33 | −0.130999 | −0.0654997 | − | 0.997853i | \(-0.520864\pi\) | ||||
−0.0654997 | + | 0.997853i | \(0.520864\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 27374.6 | 0.951370 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −10842.3 | −0.375610 | −0.187805 | − | 0.982206i | \(-0.560137\pi\) | ||||
−0.187805 | + | 0.982206i | \(0.560137\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 8461.45 | 0.292198 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 8721.33 | 0.300217 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 9717.58 | 0.333452 | 0.166726 | − | 0.986003i | \(-0.446681\pi\) | ||||
0.166726 | + | 0.986003i | \(0.446681\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −5123.22 | −0.175244 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −8689.86 | −0.296307 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 30184.9 | 1.02601 | 0.513003 | − | 0.858387i | \(-0.328533\pi\) | ||||
0.513003 | + | 0.858387i | \(0.328533\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −46982.1 | −1.59194 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 15041.8 | 0.508079 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 17744.6 | 0.597499 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 7131.32 | 0.239378 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 15052.4 | 0.503692 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 19973.6 | 0.666292 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 9170.72 | 0.304975 | 0.152487 | − | 0.988305i | \(-0.451272\pi\) | ||||
0.152487 | + | 0.988305i | \(0.451272\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 5526.14 | 0.183205 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 52443.9 | 1.73327 | 0.866634 | − | 0.498944i | \(-0.166279\pi\) | ||||
0.866634 | + | 0.498944i | \(0.166279\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −3567.73 | −0.117550 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −1714.21 | −0.0563062 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 9348.90 | 0.306139 | 0.153070 | − | 0.988215i | \(-0.451084\pi\) | ||||
0.153070 | + | 0.988215i | \(0.451084\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 1114.51 | 0.0363841 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 24770.3 | 0.806173 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −23736.4 | −0.770167 | −0.385084 | − | 0.922882i | \(-0.625827\pi\) | ||||
−0.385084 | + | 0.922882i | \(0.625827\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 32450.3 | 1.04970 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 255.085 | 0.00822637 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 5384.58 | 0.173124 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −15639.9 | −0.501330 | −0.250665 | − | 0.968074i | \(-0.580649\pi\) | ||||
−0.250665 | + | 0.968074i | \(0.580649\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −17177.5 | −0.548956 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −29048.2 | −0.925517 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 17347.8 | 0.551064 | 0.275532 | − | 0.961292i | \(-0.411146\pi\) | ||||
0.275532 | + | 0.961292i | \(0.411146\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 15889.3 | 0.503218 |
(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 | 448.4.a.t.1.1 | 2 | ||
4.3 | odd | 2 | 448.4.a.q.1.2 | 2 | |||
8.3 | odd | 2 | 224.4.a.d.1.1 | yes | 2 | ||
8.5 | even | 2 | 224.4.a.c.1.2 | ✓ | 2 | ||
24.5 | odd | 2 | 2016.4.a.p.1.2 | 2 | |||
24.11 | even | 2 | 2016.4.a.o.1.2 | 2 | |||
56.13 | odd | 2 | 1568.4.a.u.1.1 | 2 | |||
56.27 | even | 2 | 1568.4.a.p.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
224.4.a.c.1.2 | ✓ | 2 | 8.5 | even | 2 | ||
224.4.a.d.1.1 | yes | 2 | 8.3 | odd | 2 | ||
448.4.a.q.1.2 | 2 | 4.3 | odd | 2 | |||
448.4.a.t.1.1 | 2 | 1.1 | even | 1 | trivial | ||
1568.4.a.p.1.2 | 2 | 56.27 | even | 2 | |||
1568.4.a.u.1.1 | 2 | 56.13 | odd | 2 | |||
2016.4.a.o.1.2 | 2 | 24.11 | even | 2 | |||
2016.4.a.p.1.2 | 2 | 24.5 | odd | 2 |