Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1856,4,Mod(1,1856)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1856, 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("1856.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1856 = 2^{6} \cdot 29 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1856.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: | \(109.507544971\) |
Analytic rank: | \(1\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.19816.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 42x - 54 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 58) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(7.53003\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1856.1 |
$q$-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 | ||||||||
\(3\) | −6.53003 | −1.25670 | −0.628352 | − | 0.777929i | \(-0.716270\pi\) | ||||
−0.628352 | + | 0.777929i | \(0.716270\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −20.9205 | −1.87118 | −0.935591 | − | 0.353085i | \(-0.885133\pi\) | ||||
−0.935591 | + | 0.353085i | \(0.885133\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −8.55839 | −0.462110 | −0.231055 | − | 0.972941i | \(-0.574218\pi\) | ||||
−0.231055 | + | 0.972941i | \(0.574218\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 15.6413 | 0.579306 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 10.8092 | 0.296282 | 0.148141 | − | 0.988966i | \(-0.452671\pi\) | ||||
0.148141 | + | 0.988966i | \(0.452671\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −54.7046 | −1.16710 | −0.583551 | − | 0.812076i | \(-0.698337\pi\) | ||||
−0.583551 | + | 0.812076i | \(0.698337\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 136.611 | 2.35152 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −106.127 | −1.51409 | −0.757045 | − | 0.653363i | \(-0.773358\pi\) | ||||
−0.757045 | + | 0.653363i | \(0.773358\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −113.636 | −1.37210 | −0.686051 | − | 0.727554i | \(-0.740657\pi\) | ||||
−0.686051 | + | 0.727554i | \(0.740657\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 55.8865 | 0.580735 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 112.855 | 1.02313 | 0.511564 | − | 0.859245i | \(-0.329066\pi\) | ||||
0.511564 | + | 0.859245i | \(0.329066\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 312.666 | 2.50132 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 74.1729 | 0.528688 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −29.0000 | −0.185695 | ||||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 102.805 | 0.595622 | 0.297811 | − | 0.954625i | \(-0.403743\pi\) | ||||
0.297811 | + | 0.954625i | \(0.403743\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −70.5845 | −0.372339 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 179.045 | 0.864692 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 105.665 | 0.469493 | 0.234746 | − | 0.972057i | \(-0.424574\pi\) | ||||
0.234746 | + | 0.972057i | \(0.424574\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 357.223 | 1.46670 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 216.958 | 0.826417 | 0.413209 | − | 0.910636i | \(-0.364408\pi\) | ||||
0.413209 | + | 0.910636i | \(0.364408\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −102.230 | −0.362555 | −0.181278 | − | 0.983432i | \(-0.558023\pi\) | ||||
−0.181278 | + | 0.983432i | \(0.558023\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −327.222 | −1.08399 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −455.212 | −1.41275 | −0.706377 | − | 0.707836i | \(-0.749672\pi\) | ||||
−0.706377 | + | 0.707836i | \(0.749672\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −269.754 | −0.786455 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 693.011 | 1.90276 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 593.714 | 1.53873 | 0.769367 | − | 0.638807i | \(-0.220572\pi\) | ||||
0.769367 | + | 0.638807i | \(0.220572\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −226.134 | −0.554398 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 742.048 | 1.72433 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −558.141 | −1.23159 | −0.615794 | − | 0.787907i | \(-0.711165\pi\) | ||||
−0.615794 | + | 0.787907i | \(0.711165\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 473.986 | 0.994880 | 0.497440 | − | 0.867498i | \(-0.334273\pi\) | ||||
0.497440 | + | 0.867498i | \(0.334273\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −133.864 | −0.267703 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 1144.45 | 2.18386 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 193.132 | 0.352162 | 0.176081 | − | 0.984376i | \(-0.443658\pi\) | ||||
0.176081 | + | 0.984376i | \(0.443658\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −736.949 | −1.28577 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 2.38155 | 0.00398082 | 0.00199041 | − | 0.999998i | \(-0.499366\pi\) | ||||
0.00199041 | + | 0.999998i | \(0.499366\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 119.013 | 0.190814 | 0.0954071 | − | 0.995438i | \(-0.469585\pi\) | ||||
0.0954071 | + | 0.995438i | \(0.469585\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −2041.71 | −3.14343 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −92.5096 | −0.136915 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 964.306 | 1.37333 | 0.686664 | − | 0.726975i | \(-0.259074\pi\) | ||||
0.686664 | + | 0.726975i | \(0.259074\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −906.665 | −1.24371 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 1068.19 | 1.41264 | 0.706319 | − | 0.707893i | \(-0.250354\pi\) | ||||
0.706319 | + | 0.707893i | \(0.250354\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 2220.22 | 2.83314 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 189.371 | 0.233364 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 772.544 | 0.920106 | 0.460053 | − | 0.887891i | \(-0.347830\pi\) | ||||
0.460053 | + | 0.887891i | \(0.347830\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 468.184 | 0.539330 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −671.318 | −0.748521 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 2377.32 | 2.56745 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1344.03 | 1.40686 | 0.703431 | − | 0.710763i | \(-0.251650\pi\) | ||||
0.703431 | + | 0.710763i | \(0.251650\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 169.070 | 0.171638 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −986.733 | −0.972115 | −0.486057 | − | 0.873927i | \(-0.661565\pi\) | ||||
−0.486057 | + | 0.873927i | \(0.661565\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −548.272 | −0.524493 | −0.262247 | − | 0.965001i | \(-0.584463\pi\) | ||||
−0.262247 | + | 0.965001i | \(0.584463\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −1169.17 | −1.08666 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 1387.51 | 1.25361 | 0.626803 | − | 0.779178i | \(-0.284363\pi\) | ||||
0.626803 | + | 0.779178i | \(0.284363\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1293.32 | 1.13649 | 0.568246 | − | 0.822859i | \(-0.307622\pi\) | ||||
0.568246 | + | 0.822859i | \(0.307622\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −689.996 | −0.590014 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 302.883 | 0.252149 | 0.126075 | − | 0.992021i | \(-0.459762\pi\) | ||||
0.126075 | + | 0.992021i | \(0.459762\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −2360.99 | −1.91446 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −855.650 | −0.676110 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 908.274 | 0.699676 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1214.16 | −0.912217 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −1416.74 | −1.03856 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −3926.05 | −2.80925 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −2021.68 | −1.41256 | −0.706281 | − | 0.707931i | \(-0.749629\pi\) | ||||
−0.706281 | + | 0.707931i | \(0.749629\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 667.562 | 0.455625 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 854.726 | 0.570059 | 0.285030 | − | 0.958519i | \(-0.407997\pi\) | ||||
0.285030 | + | 0.958519i | \(0.407997\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 972.543 | 0.634062 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −1551.73 | −0.989272 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 365.024 | 0.227636 | 0.113818 | − | 0.993502i | \(-0.463692\pi\) | ||||
0.113818 | + | 0.993502i | \(0.463692\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −1010.10 | −0.616370 | −0.308185 | − | 0.951326i | \(-0.599722\pi\) | ||||
−0.308185 | + | 0.951326i | \(0.599722\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 2972.55 | 1.77541 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −591.315 | −0.345792 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 606.693 | 0.347470 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 1761.50 | 0.988341 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −819.765 | −0.450723 | −0.225362 | − | 0.974275i | \(-0.572356\pi\) | ||||
−0.225362 | + | 0.974275i | \(0.572356\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1000.25 | −0.539068 | −0.269534 | − | 0.962991i | \(-0.586870\pi\) | ||||
−0.269534 | + | 0.962991i | \(0.586870\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −1659.96 | −0.877121 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −2150.72 | −1.11452 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1702.38 | 0.865382 | 0.432691 | − | 0.901542i | \(-0.357564\pi\) | ||||
0.432691 | + | 0.901542i | \(0.357564\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −3876.97 | −1.93373 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −965.860 | −0.472798 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −3451.76 | −1.65867 | −0.829334 | − | 0.558753i | \(-0.811280\pi\) | ||||
−0.829334 | + | 0.558753i | \(0.811280\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 1476.66 | 0.696714 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −1409.23 | −0.652990 | −0.326495 | − | 0.945199i | \(-0.605868\pi\) | ||||
−0.326495 | + | 0.945199i | \(0.605868\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 795.598 | 0.362129 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −1777.41 | −0.794867 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −1358.39 | −0.596973 | −0.298487 | − | 0.954414i | \(-0.596482\pi\) | ||||
−0.298487 | + | 0.954414i | \(0.596482\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −2675.91 | −1.15589 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 3644.67 | 1.54774 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −1702.56 | −0.710924 | −0.355462 | − | 0.934691i | \(-0.615677\pi\) | ||||
−0.355462 | + | 0.934691i | \(0.615677\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 7.33698 | 0.00301300 | 0.00150650 | − | 0.999999i | \(-0.499520\pi\) | ||||
0.00150650 | + | 0.999999i | \(0.499520\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −3095.14 | −1.25027 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −2210.56 | −0.878507 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −1147.15 | −0.448598 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −634.801 | −0.244312 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −1324.78 | −0.501873 | −0.250936 | − | 0.968004i | \(-0.580738\pi\) | ||||
−0.250936 | + | 0.968004i | \(0.580738\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 1834.47 | 0.684187 | 0.342094 | − | 0.939666i | \(-0.388864\pi\) | ||||
0.342094 | + | 0.939666i | \(0.388864\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −7473.26 | −2.74447 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 4949.99 | 1.79021 | 0.895107 | − | 0.445851i | \(-0.147099\pi\) | ||||
0.895107 | + | 0.445851i | \(0.147099\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −3554.04 | −1.26603 | −0.633014 | − | 0.774140i | \(-0.718182\pi\) | ||||
−0.633014 | + | 0.774140i | \(0.718182\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −1261.16 | −0.442563 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 248.193 | 0.0858116 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −4538.85 | −1.54638 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 1765.20 | 0.592705 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −1228.32 | −0.406529 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2475.23 | 0.807590 | 0.403795 | − | 0.914849i | \(-0.367691\pi\) | ||||
0.403795 | + | 0.914849i | \(0.367691\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −15.5516 | −0.00500271 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 2138.69 | 0.678407 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −879.844 | −0.275243 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −777.159 | −0.239797 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 5805.63 | 1.76710 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −2381.72 | −0.715211 | −0.357605 | − | 0.933873i | \(-0.616407\pi\) | ||||
−0.357605 | + | 0.933873i | \(0.616407\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 4890.48 | 1.44903 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 5452.74 | 1.59432 | 0.797160 | − | 0.603768i | \(-0.206334\pi\) | ||||
0.797160 | + | 0.603768i | \(0.206334\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −596.232 | −0.172053 | −0.0860264 | − | 0.996293i | \(-0.527417\pi\) | ||||
−0.0860264 | + | 0.996293i | \(0.527417\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 604.090 | 0.172062 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −5623.04 | −1.58102 | −0.790509 | − | 0.612450i | \(-0.790184\pi\) | ||||
−0.790509 | + | 0.612450i | \(0.790184\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 9523.24 | 2.64352 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −6296.95 | −1.72587 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −1564.27 | −0.423366 | −0.211683 | − | 0.977338i | \(-0.567894\pi\) | ||||
−0.211683 | + | 0.977338i | \(0.567894\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −730.326 | −0.195205 | −0.0976026 | − | 0.995225i | \(-0.531117\pi\) | ||||
−0.0976026 | + | 0.995225i | \(0.531117\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 3917.88 | 1.03429 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 5643.38 | 1.47160 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 6216.43 | 1.60138 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −6975.31 | −1.77527 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −4244.39 | −1.06735 | −0.533673 | − | 0.845691i | \(-0.679189\pi\) | ||||
−0.533673 | + | 0.845691i | \(0.679189\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1219.88 | 0.303135 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −14498.1 | −3.56042 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −235.374 | −0.0571292 | −0.0285646 | − | 0.999592i | \(-0.509094\pi\) | ||||
−0.0285646 | + | 0.999592i | \(0.509094\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −904.323 | −0.216957 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −453.597 | −0.107574 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −3453.63 | −0.809734 | −0.404867 | − | 0.914376i | \(-0.632682\pi\) | ||||
−0.404867 | + | 0.914376i | \(0.632682\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −12420.8 | −2.87925 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −5044.73 | −1.15630 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 1921.31 | 0.435481 | 0.217741 | − | 0.976007i | \(-0.430131\pi\) | ||||
0.217741 | + | 0.976007i | \(0.430131\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 2480.09 | 0.555921 | 0.277961 | − | 0.960592i | \(-0.410342\pi\) | ||||
0.277961 | + | 0.960592i | \(0.410342\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −3057.25 | −0.677778 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 3379.67 | 0.741098 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 4766.90 | 1.03399 | 0.516995 | − | 0.855989i | \(-0.327051\pi\) | ||||
0.516995 | + | 0.855989i | \(0.327051\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 1608.00 | 0.345047 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 194.329 | 0.0412552 | 0.0206276 | − | 0.999787i | \(-0.493434\pi\) | ||||
0.0206276 | + | 0.999787i | \(0.493434\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −2817.42 | −0.591797 | −0.295898 | − | 0.955219i | \(-0.595619\pi\) | ||||
−0.295898 | + | 0.955219i | \(0.595619\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −15524.0 | −3.22653 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −1856.81 | −0.381895 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 6349.89 | 1.29247 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −8776.56 | −1.76801 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −4059.12 | −0.809339 | −0.404670 | − | 0.914463i | \(-0.632614\pi\) | ||||
−0.404670 | + | 0.914463i | \(0.632614\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 11676.6 | 2.30453 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 801.751 | 0.156641 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −6173.71 | −1.19410 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 874.921 | 0.167540 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 6443.39 | 1.22166 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −9916.01 | −1.86160 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −131.572 | −0.0244600 | −0.0122300 | − | 0.999925i | \(-0.503893\pi\) | ||||
−0.0122300 | + | 0.999925i | \(0.503893\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 3580.23 | 0.659133 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −1517.84 | −0.276748 | −0.138374 | − | 0.990380i | \(-0.544188\pi\) | ||||
−0.138374 | + | 0.990380i | \(0.544188\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 4244.17 | 0.766436 | 0.383218 | − | 0.923658i | \(-0.374816\pi\) | ||||
0.383218 | + | 0.923658i | \(0.374816\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 2800.50 | 0.500921 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −5596.56 | −0.991590 | −0.495795 | − | 0.868439i | \(-0.665123\pi\) | ||||
−0.495795 | + | 0.868439i | \(0.665123\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −313.467 | −0.0550182 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −9060.50 | −1.57541 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 12059.8 | 2.07748 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −17104.3 | −2.91930 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −8445.42 | −1.42824 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 3895.88 | 0.652848 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −8383.85 | −1.39220 | −0.696100 | − | 0.717945i | \(-0.745083\pi\) | ||||
−0.696100 | + | 0.717945i | \(0.745083\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 1652.73 | 0.271980 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −4040.41 | −0.658959 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 9887.12 | 1.59818 | 0.799089 | − | 0.601213i | \(-0.205316\pi\) | ||||
0.799089 | + | 0.601213i | \(0.205316\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −1977.84 | −0.316877 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 1111.24 | 0.176472 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 5244.19 | 0.825538 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 15417.3 | 2.40591 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 10678.8 | 1.65206 | 0.826032 | − | 0.563623i | \(-0.190593\pi\) | ||||
0.826032 | + | 0.563623i | \(0.190593\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 1457.88 | 0.223605 | 0.111803 | − | 0.993730i | \(-0.464338\pi\) | ||||
0.111803 | + | 0.993730i | \(0.464338\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −4057.60 | −0.617033 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 6737.20 | 1.01582 | 0.507911 | − | 0.861410i | \(-0.330418\pi\) | ||||
0.507911 | + | 0.861410i | \(0.330418\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −49.8232 | −0.00744884 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −5931.06 | −0.879285 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 3539.85 | 0.520407 | 0.260204 | − | 0.965554i | \(-0.416210\pi\) | ||||
0.260204 | + | 0.965554i | \(0.416210\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 6054.19 | 0.882663 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 7928.50 | 1.14639 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −2489.81 | −0.357048 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 4917.53 | 0.699436 | 0.349718 | − | 0.936855i | \(-0.386277\pi\) | ||||
0.349718 | + | 0.936855i | \(0.386277\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 3393.49 | 0.478748 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −5081.24 | −0.711064 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −2032.31 | −0.282115 | −0.141057 | − | 0.990001i | \(-0.545050\pi\) | ||||
−0.141057 | + | 0.990001i | \(0.545050\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 25637.2 | 3.53040 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 1586.43 | 0.216726 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −7051.47 | −0.955699 | −0.477849 | − | 0.878442i | \(-0.658584\pi\) | ||||
−0.477849 | + | 0.878442i | \(0.658584\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 13201.7 | 1.77517 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 9334.72 | 1.24538 | 0.622691 | − | 0.782467i | \(-0.286039\pi\) | ||||
0.622691 | + | 0.782467i | \(0.286039\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 1935.34 | 0.256193 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −1599.00 | −0.210030 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 1901.32 | 0.247816 | 0.123908 | − | 0.992294i | \(-0.460457\pi\) | ||||
0.123908 | + | 0.992294i | \(0.460457\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −11977.0 | −1.54911 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −5581.38 | −0.716396 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −20173.7 | −2.56975 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −1995.81 | −0.252309 | −0.126155 | − | 0.992011i | \(-0.540264\pi\) | ||||
−0.126155 | + | 0.992011i | \(0.540264\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −6350.73 | −0.796828 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 12920.6 | 1.60904 | 0.804520 | − | 0.593925i | \(-0.202422\pi\) | ||||
0.804520 | + | 0.593925i | \(0.202422\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −5623.90 | −0.695152 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 18967.8 | 2.32721 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 1142.16 | 0.139102 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −9713.54 | −1.17434 | −0.587168 | − | 0.809465i | \(-0.699757\pi\) | ||||
−0.587168 | + | 0.809465i | \(0.699757\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −2383.62 | −0.286071 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 4776.79 | 0.569129 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −22347.0 | −2.64330 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 6595.97 | 0.774595 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 15925.4 | 1.85682 | 0.928411 | − | 0.371555i | \(-0.121175\pi\) | ||||
0.928411 | + | 0.371555i | \(0.121175\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −10849.9 | −1.25604 | −0.628019 | − | 0.778198i | \(-0.716134\pi\) | ||||
−0.628019 | + | 0.778198i | \(0.716134\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −7120.09 | −0.818417 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −33182.2 | −3.78723 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −4056.56 | −0.459744 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 3861.30 | 0.434558 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 532.335 | 0.0594934 | 0.0297467 | − | 0.999557i | \(-0.490530\pi\) | ||||
0.0297467 | + | 0.999557i | \(0.490530\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −6995.94 | −0.776451 | −0.388225 | − | 0.921564i | \(-0.626912\pi\) | ||||
−0.388225 | + | 0.921564i | \(0.626912\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −3961.72 | −0.436667 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −12824.5 | −1.40384 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −3272.22 | −0.355750 | −0.177875 | − | 0.984053i | \(-0.556922\pi\) | ||||
−0.177875 | + | 0.984053i | \(0.556922\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −4219.29 | −0.455598 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −3818.14 | −0.409493 | −0.204746 | − | 0.978815i | \(-0.565637\pi\) | ||||
−0.204746 | + | 0.978815i | \(0.565637\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −16162.0 | −1.72169 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 5353.09 | 0.566426 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −4323.19 | −0.454396 | −0.227198 | − | 0.973849i | \(-0.572957\pi\) | ||||
−0.227198 | + | 0.973849i | \(0.572957\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 2345.14 | 0.244853 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 6531.66 | 0.677449 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −9794.62 | −1.00918 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −8367.43 | −0.856481 | −0.428240 | − | 0.903665i | \(-0.640866\pi\) | ||||
−0.428240 | + | 0.903665i | \(0.640866\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −7871.73 | −0.800481 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 17249.0 | 1.74266 | 0.871328 | − | 0.490701i | \(-0.163259\pi\) | ||||
0.871328 | + | 0.490701i | \(0.163259\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 16774.3 | 1.68373 | 0.841864 | − | 0.539690i | \(-0.181458\pi\) | ||||
0.841864 | + | 0.539690i | \(0.181458\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 14044.3 | 1.40062 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 7701.05 | 0.763088 | 0.381544 | − | 0.924351i | \(-0.375392\pi\) | ||||
0.381544 | + | 0.924351i | \(0.375392\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −1652.90 | −0.162737 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −11116.6 | −1.08753 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −1105.02 | −0.107419 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −35530.1 | −3.43207 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 9286.44 | 0.891398 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −5988.77 | −0.571261 | −0.285630 | − | 0.958340i | \(-0.592203\pi\) | ||||
−0.285630 | + | 0.958340i | \(0.592203\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −5780.37 | −0.547946 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 6307.09 | 0.594167 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −28117.7 | −2.63250 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −5790.34 | −0.538779 | −0.269390 | − | 0.963031i | \(-0.586822\pi\) | ||||
−0.269390 | + | 0.963031i | \(0.586822\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 22540.1 | 2.08446 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 19228.8 | 1.76738 | 0.883692 | − | 0.468069i | \(-0.155050\pi\) | ||||
0.883692 | + | 0.468069i | \(0.155050\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 3077.68 | 0.281159 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −3537.02 | −0.321166 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −20.3823 | −0.00183958 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −7081.65 | −0.635307 | −0.317653 | − | 0.948207i | \(-0.602895\pi\) | ||||
−0.317653 | + | 0.948207i | \(0.602895\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 9202.29 | 0.820615 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 5312.64 | 0.470932 | 0.235466 | − | 0.971883i | \(-0.424338\pi\) | ||||
0.235466 | + | 0.971883i | \(0.424338\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 20642.9 | 1.81900 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −5195.28 | −0.455089 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 13862.7 | 1.20717 | 0.603587 | − | 0.797297i | \(-0.293738\pi\) | ||||
0.603587 | + | 0.797297i | \(0.293738\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −1018.56 | −0.0881771 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −8428.72 | −0.725414 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 11470.1 | 0.981423 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −4920.49 | −0.418574 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 8870.32 | 0.750219 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 15447.5 | 1.29897 | 0.649487 | − | 0.760373i | \(-0.274984\pi\) | ||||
0.649487 | + | 0.760373i | \(0.274984\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 4349.54 | 0.363656 | 0.181828 | − | 0.983330i | \(-0.441799\pi\) | ||||
0.181828 | + | 0.983330i | \(0.441799\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 17473.8 | 1.45261 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −10910.3 | −0.901825 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 569.329 | 0.0467928 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −8730.03 | −0.713467 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −11868.6 | −0.964514 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −29027.4 | −2.34573 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 11117.8 | 0.893422 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −2915.83 | −0.233012 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −3206.84 | −0.254848 | −0.127424 | − | 0.991848i | \(-0.540671\pi\) | ||||
−0.127424 | + | 0.991848i | \(0.540671\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −47.9107 | −0.00378645 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −27056.9 | −2.12658 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −3289.81 | −0.257152 | −0.128576 | − | 0.991700i | \(-0.541041\pi\) | ||||
−0.128576 | + | 0.991700i | \(0.541041\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 7413.74 | 0.576340 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 3295.45 | 0.254793 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −8252.91 | −0.634628 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 14435.0 | 1.10402 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 313.140 | 0.0238207 | 0.0119104 | − | 0.999929i | \(-0.496209\pi\) | ||||
0.0119104 | + | 0.999929i | \(0.496209\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 5592.43 | 0.423139 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 7490.91 | 0.563755 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −3425.84 | −0.256451 | −0.128225 | − | 0.991745i | \(-0.540928\pi\) | ||||
−0.128225 | + | 0.991745i | \(0.540928\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −6336.46 | −0.471818 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 7759.60 | 0.574731 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 17763.8 | 1.30878 | 0.654390 | − | 0.756158i | \(-0.272926\pi\) | ||||
0.654390 | + | 0.756158i | \(0.272926\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 5741.80 | 0.420818 | 0.210409 | − | 0.977613i | \(-0.432520\pi\) | ||||
0.210409 | + | 0.977613i | \(0.432520\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 8650.85 | 0.630706 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 35286.0 | 2.55918 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 14477.5 | 1.04455 | 0.522275 | − | 0.852777i | \(-0.325083\pi\) | ||||
0.522275 | + | 0.852777i | \(0.325083\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −11979.1 | −0.859821 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −9141.98 | −0.652794 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 6417.59 | 0.455899 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 17900.6 | 1.26512 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −18082.8 | −1.27148 | −0.635738 | − | 0.771905i | \(-0.719304\pi\) | ||||
−0.635738 | + | 0.771905i | \(0.719304\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −11682.3 | −0.817254 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −32323.6 | −2.24977 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 1731.57 | 0.119911 | 0.0599553 | − | 0.998201i | \(-0.480904\pi\) | ||||
0.0599553 | + | 0.998201i | \(0.480904\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −19001.5 | −1.30922 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 23208.0 | 1.59102 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 11480.5 | 0.783105 | 0.391552 | − | 0.920156i | \(-0.371938\pi\) | ||||
0.391552 | + | 0.920156i | \(0.371938\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 2924.56 | 0.198495 | 0.0992474 | − | 0.995063i | \(-0.468356\pi\) | ||||
0.0992474 | + | 0.995063i | \(0.468356\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 3020.83 | 0.204009 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 25400.8 | 1.70692 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −3586.09 | −0.239794 | −0.119897 | − | 0.992786i | \(-0.538256\pi\) | ||||
−0.119897 | + | 0.992786i | \(0.538256\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −1620.71 | −0.107840 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 24902.2 | 1.64883 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 11679.8 | 0.769561 | 0.384781 | − | 0.923008i | \(-0.374277\pi\) | ||||
0.384781 | + | 0.923008i | \(0.374277\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 29638.8 | 1.94334 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 11063.0 | 0.721847 | 0.360924 | − | 0.932595i | \(-0.382461\pi\) | ||||
0.360924 | + | 0.932595i | \(0.382461\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −2463.60 | −0.159969 | −0.0799843 | − | 0.996796i | \(-0.525487\pi\) | ||||
−0.0799843 | + | 0.996796i | \(0.525487\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 8370.81 | 0.540916 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −6611.73 | −0.425190 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 43051.5 | 2.75530 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 8020.96 | 0.510887 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −11213.9 | −0.710854 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −1032.43 | −0.0651352 | −0.0325676 | − | 0.999470i | \(-0.510368\pi\) | ||||
−0.0325676 | + | 0.999470i | \(0.510368\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −16163.3 | −1.01490 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 42294.6 | 2.64316 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 14756.8 | 0.917873 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 37.2505 | 0.00230611 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 12841.6 | 0.791282 | 0.395641 | − | 0.918405i | \(-0.370522\pi\) | ||||
0.395641 | + | 0.918405i | \(0.370522\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 8449.14 | 0.518198 | 0.259099 | − | 0.965851i | \(-0.416574\pi\) | ||||
0.259099 | + | 0.965851i | \(0.416574\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −13965.7 | −0.852557 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 27036.8 | 1.64285 | 0.821426 | − | 0.570315i | \(-0.193179\pi\) | ||||
0.821426 | + | 0.570315i | \(0.193179\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −6033.07 | −0.364898 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 5745.40 | 0.345899 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 27105.2 | 1.62436 | 0.812181 | − | 0.583405i | \(-0.198280\pi\) | ||||
0.812181 | + | 0.583405i | \(0.198280\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −17881.3 | −1.06668 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 1861.52 | 0.110540 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −22622.4 | −1.33724 | −0.668621 | − | 0.743603i | \(-0.733115\pi\) | ||||
−0.668621 | + | 0.743603i | \(0.733115\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 21000.2 | 1.23572 | 0.617862 | − | 0.786287i | \(-0.287999\pi\) | ||||
0.617862 | + | 0.786287i | \(0.287999\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −37910.9 | −2.22072 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −20346.0 | −1.18645 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −3272.80 | −0.189990 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 15552.7 | 0.898809 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 5123.42 | 0.294765 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −13691.2 | −0.784186 | −0.392093 | − | 0.919926i | \(-0.628249\pi\) | ||||
−0.392093 | + | 0.919926i | \(0.628249\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 23191.3 | 1.32242 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −9694.60 | −0.550360 | −0.275180 | − | 0.961393i | \(-0.588737\pi\) | ||||
−0.275180 | + | 0.961393i | \(0.588737\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −11502.7 | −0.650125 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −35606.5 | −2.00359 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 6012.25 | 0.336826 | 0.168413 | − | 0.985717i | \(-0.446136\pi\) | ||||
0.168413 | + | 0.985717i | \(0.446136\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −7636.47 | −0.425948 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 3893.41 | 0.216220 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −32478.9 | −1.79586 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −10304.9 | −0.567317 | −0.283659 | − | 0.958925i | \(-0.591548\pi\) | ||||
−0.283659 | + | 0.958925i | \(0.591548\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −1446.97 | −0.0793156 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 21131.7 | 1.15334 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −23025.0 | −1.25127 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 36718.6 | 1.98687 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −11785.8 | −0.635011 | −0.317506 | − | 0.948256i | \(-0.602845\pi\) | ||||
−0.317506 | + | 0.948256i | \(0.602845\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −12007.4 | −0.644192 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −62187.0 | −3.32212 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 8444.85 | 0.449224 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −29226.1 | −1.54811 | −0.774054 | − | 0.633120i | \(-0.781774\pi\) | ||||
−0.774054 | + | 0.633120i | \(0.781774\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 15083.0 | 0.795577 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 11602.1 | 0.609398 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 12370.6 | 0.647040 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 10214.7 | 0.532045 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −14706.5 | −0.762809 | −0.381404 | − | 0.924408i | \(-0.624559\pi\) | ||||
−0.381404 | + | 0.924408i | \(0.624559\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 4692.32 | 0.242374 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 4769.05 | 0.245315 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −9067.30 | −0.464484 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 35975.1 | 1.83527 | 0.917637 | − | 0.397419i | \(-0.130094\pi\) | ||||
0.917637 | + | 0.397419i | \(0.130094\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −1103.91 | −0.0560843 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 10849.3 | 0.548941 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −10872.8 | −0.547879 | −0.273939 | − | 0.961747i | \(-0.588327\pi\) | ||||
−0.273939 | + | 0.961747i | \(0.588327\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −36851.4 | −1.84937 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 2087.61 | 0.104339 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −1078.25 | −0.0536727 | −0.0268363 | − | 0.999640i | \(-0.508543\pi\) | ||||
−0.0268363 | + | 0.999640i | \(0.508543\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −40593.4 | −2.01247 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 23176.4 | 1.14436 | 0.572180 | − | 0.820128i | \(-0.306098\pi\) | ||||
0.572180 | + | 0.820128i | \(0.306098\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 17149.9 | 0.843385 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 16707.8 | 0.818350 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −11874.9 | −0.579304 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −8738.85 | −0.424614 | −0.212307 | − | 0.977203i | \(-0.568098\pi\) | ||||
−0.212307 | + | 0.977203i | \(0.568098\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 27716.0 | 1.34134 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 20925.7 | 1.00869 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −4121.15 | −0.197868 | −0.0989338 | − | 0.995094i | \(-0.531543\pi\) | ||||
−0.0989338 | + | 0.995094i | \(0.531543\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −7965.84 | −0.380951 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 8706.54 | 0.414733 | 0.207367 | − | 0.978263i | \(-0.433511\pi\) | ||||
0.207367 | + | 0.978263i | \(0.433511\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −11068.7 | −0.525184 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 34727.0 | 1.64125 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 30532.9 | 1.43739 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −32258.8 | −1.51272 | −0.756361 | − | 0.654154i | \(-0.773025\pi\) | ||||
−0.756361 | + | 0.654154i | \(0.773025\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 1537.00 | 0.0717945 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −24794.1 | −1.15366 | −0.576832 | − | 0.816863i | \(-0.695711\pi\) | ||||
−0.576832 | + | 0.816863i | \(0.695711\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 32143.5 | 1.48984 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 5905.25 | 0.272651 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −24654.2 | −1.13393 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 25.7427 | 0.00117945 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −2151.01 | −0.0981749 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −35614.6 | −1.61929 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −11114.7 | −0.503427 | −0.251714 | − | 0.967802i | \(-0.580994\pi\) | ||||
−0.251714 | + | 0.967802i | \(0.580994\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 22552.3 | 1.01760 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −2592.20 | −0.116521 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −25929.2 | −1.16113 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 81108.0 | 3.61837 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 12329.8 | 0.547986 | 0.273993 | − | 0.961732i | \(-0.411656\pi\) | ||||
0.273993 | + | 0.961732i | \(0.411656\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 48310.1 | 2.13904 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 12083.6 | 0.533023 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 1286.44 | 0.0565348 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 20206.2 | 0.884691 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −12546.2 | −0.547271 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −36175.5 | −1.57214 | −0.786070 | − | 0.618138i | \(-0.787887\pi\) | ||||
−0.786070 | + | 0.618138i | \(0.787887\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −26581.0 | −1.15091 | −0.575453 | − | 0.817835i | \(-0.695174\pi\) | ||||
−0.575453 | + | 0.817835i | \(0.695174\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −16195.0 | −0.698629 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 72212.5 | 3.10367 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 11617.0 | 0.497462 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 7322.98 | 0.312437 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −10811.1 | −0.459574 | −0.229787 | − | 0.973241i | \(-0.573803\pi\) | ||||
−0.229787 | + | 0.973241i | \(0.573803\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −28625.1 | −1.21240 | −0.606202 | − | 0.795311i | \(-0.707308\pi\) | ||||
−0.606202 | + | 0.795311i | \(0.707308\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −22069.3 | −0.931341 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −9970.68 | −0.419244 | −0.209622 | − | 0.977783i | \(-0.567223\pi\) | ||||
−0.209622 | + | 0.977783i | \(0.567223\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −20201.0 | −0.846334 | −0.423167 | − | 0.906052i | \(-0.639082\pi\) | ||||
−0.423167 | + | 0.906052i | \(0.639082\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −31128.0 | −1.29942 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 28628.1 | 1.19076 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 29481.7 | 1.22186 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 7625.33 | 0.314898 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −28023.4 | −1.15313 | −0.576564 | − | 0.817052i | \(-0.695607\pi\) | ||||
−0.576564 | + | 0.817052i | \(0.695607\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 841.000 | 0.0344828 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −1268.98 | −0.0518456 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −16644.3 | −0.677610 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 10391.3 | 0.421544 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 18397.9 | 0.743714 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 11924.9 | 0.480352 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 26333.8 | 1.05704 | 0.528518 | − | 0.848922i | \(-0.322748\pi\) | ||||
0.528518 | + | 0.848922i | \(0.322748\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 37184.3 | 1.48734 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 36388.6 | 1.45042 | 0.725211 | − | 0.688527i | \(-0.241742\pi\) | ||||
0.725211 | + | 0.688527i | \(0.241742\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 14974.0 | 0.594770 | 0.297385 | − | 0.954758i | \(-0.403885\pi\) | ||||
0.297385 | + | 0.954758i | \(0.403885\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 12125.0 | 0.479930 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 40168.2 | 1.58440 | 0.792202 | − | 0.610259i | \(-0.208935\pi\) | ||||
0.792202 | + | 0.610259i | \(0.208935\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 28418.1 | 1.11705 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −41465.0 | −1.62425 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 10423.4 | 0.406893 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −10565.2 | −0.411009 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 21022.3 | 0.815004 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 33600.7 | 1.29818 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −32161.7 | −1.23834 | −0.619169 | − | 0.785258i | \(-0.712531\pi\) | ||||
−0.619169 | + | 0.785258i | \(0.712531\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 26506.2 | 1.01710 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −8870.49 | −0.339222 | −0.169611 | − | 0.985511i | \(-0.554251\pi\) | ||||
−0.169611 | + | 0.985511i | \(0.554251\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −24647.3 | −0.939351 | −0.469675 | − | 0.882839i | \(-0.655629\pi\) | ||||
−0.469675 | + | 0.882839i | \(0.655629\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −76248.3 | −2.89611 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −32371.7 | −1.22541 | −0.612703 | − | 0.790313i | \(-0.709918\pi\) | ||||
−0.612703 | + | 0.790313i | \(0.709918\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 17302.4 | 0.652759 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −9800.35 | −0.368489 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 51728.5 | 1.93844 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 35618.4 | 1.33027 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 40314.5 | 1.50063 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −2981.34 | −0.110604 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −63008.9 | −2.32978 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −5713.26 | −0.210549 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −153.493 | −0.00563787 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −43728.0 | −1.60084 | −0.800422 | − | 0.599437i | \(-0.795391\pi\) | ||||
−0.800422 | + | 0.599437i | \(0.795391\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −15433.7 | −0.563152 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −16033.6 | −0.583115 | −0.291557 | − | 0.956553i | \(-0.594173\pi\) | ||||
−0.291557 | + | 0.956553i | \(0.594173\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 11546.3 | 0.418540 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 64751.8 | 2.33948 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −7315.08 | −0.263430 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −29331.1 | −1.05282 | −0.526411 | − | 0.850230i | \(-0.676463\pi\) | ||||
−0.526411 | + | 0.850230i | \(0.676463\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 859.170 | 0.0307390 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −130.282 | −0.00464603 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 33037.8 | 1.17435 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −8575.66 | −0.303842 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −10024.6 | −0.354034 | −0.177017 | − | 0.984208i | \(-0.556645\pi\) | ||||
−0.177017 | + | 0.984208i | \(0.556645\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 30653.8 | 1.07910 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 9911.51 | 0.347790 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 23998.9 | 0.839408 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 21241.3 | 0.740578 | 0.370289 | − | 0.928917i | \(-0.379259\pi\) | ||||
0.370289 | + | 0.928917i | \(0.379259\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −27714.5 | −0.963184 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −11953.8 | −0.414115 | −0.207057 | − | 0.978329i | \(-0.566389\pi\) | ||||
−0.207057 | + | 0.978329i | \(0.566389\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 24484.8 | 0.845531 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 13280.3 | 0.457152 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −31650.6 | −1.08607 | −0.543034 | − | 0.839711i | \(-0.682725\pi\) | ||||
−0.543034 | + | 0.839711i | \(0.682725\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −6510.57 | −0.222700 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 36545.7 | 1.24614 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −17373.5 | −0.590539 | −0.295269 | − | 0.955414i | \(-0.595409\pi\) | ||||
−0.295269 | + | 0.955414i | \(0.595409\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 27715.0 | 0.939095 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 2046.95 | 0.0691416 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −3124.02 | −0.105193 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −19222.2 | −0.645234 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 21702.4 | 0.726222 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −38378.0 | −1.28024 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 11017.6 | 0.366394 | 0.183197 | − | 0.983076i | \(-0.441355\pi\) | ||||
0.183197 | + | 0.983076i | \(0.441355\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −78751.1 | −2.61078 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 17365.0 | 0.573912 | 0.286956 | − | 0.957944i | \(-0.407357\pi\) | ||||
0.286956 | + | 0.957944i | \(0.407357\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 8644.82 | 0.284831 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 111691. | 3.66870 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −29193.4 | −0.955967 | −0.477983 | − | 0.878369i | \(-0.658632\pi\) | ||||
−0.477983 | + | 0.878369i | \(0.658632\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 8350.60 | 0.272611 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 20229.2 | 0.658377 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −50359.8 | −1.63401 | −0.817003 | − | 0.576634i | \(-0.804366\pi\) | ||||
−0.817003 | + | 0.576634i | \(0.804366\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −103556. | −3.34982 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −25440.2 | −0.820436 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −11537.2 | −0.370941 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 20823.5 | 0.667488 | 0.333744 | − | 0.942664i | \(-0.391688\pi\) | ||||
0.333744 | + | 0.942664i | \(0.391688\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 54746.8 | 1.74958 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 74352.2 | 2.36897 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 27651.2 | 0.878356 | 0.439178 | − | 0.898400i | \(-0.355270\pi\) | ||||
0.439178 | + | 0.898400i | \(0.355270\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 7837.48 | 0.248215 |
(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 | 1856.4.a.s.1.1 | 3 | ||
4.3 | odd | 2 | 1856.4.a.r.1.3 | 3 | |||
8.3 | odd | 2 | 58.4.a.d.1.1 | ✓ | 3 | ||
8.5 | even | 2 | 464.4.a.i.1.3 | 3 | |||
24.11 | even | 2 | 522.4.a.k.1.1 | 3 | |||
40.19 | odd | 2 | 1450.4.a.h.1.3 | 3 | |||
232.115 | odd | 2 | 1682.4.a.d.1.3 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
58.4.a.d.1.1 | ✓ | 3 | 8.3 | odd | 2 | ||
464.4.a.i.1.3 | 3 | 8.5 | even | 2 | |||
522.4.a.k.1.1 | 3 | 24.11 | even | 2 | |||
1450.4.a.h.1.3 | 3 | 40.19 | odd | 2 | |||
1682.4.a.d.1.3 | 3 | 232.115 | odd | 2 | |||
1856.4.a.r.1.3 | 3 | 4.3 | odd | 2 | |||
1856.4.a.s.1.1 | 3 | 1.1 | even | 1 | trivial |