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: | \(8\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 19x^{6} + 92x^{4} - 51x^{2} + 5 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{10}\cdot 5 \) |
Twist minimal: | no (minimal twist has level 928) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(-3.34163\) 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 | ||||||||
\(3\) | −3.89793 | −0.750157 | −0.375078 | − | 0.926993i | \(-0.622384\pi\) | ||||
−0.375078 | + | 0.926993i | \(0.622384\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 15.3330 | 1.37142 | 0.685710 | − | 0.727874i | \(-0.259492\pi\) | ||||
0.685710 | + | 0.727874i | \(0.259492\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 5.27577 | 0.284865 | 0.142432 | − | 0.989805i | \(-0.454508\pi\) | ||||
0.142432 | + | 0.989805i | \(0.454508\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −11.8061 | −0.437265 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −28.3477 | −0.777015 | −0.388507 | − | 0.921446i | \(-0.627009\pi\) | ||||
−0.388507 | + | 0.921446i | \(0.627009\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −61.6285 | −1.31482 | −0.657411 | − | 0.753533i | \(-0.728348\pi\) | ||||
−0.657411 | + | 0.753533i | \(0.728348\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −59.7668 | −1.02878 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 39.9279 | 0.569643 | 0.284822 | − | 0.958581i | \(-0.408066\pi\) | ||||
0.284822 | + | 0.958581i | \(0.408066\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 146.682 | 1.77112 | 0.885558 | − | 0.464528i | \(-0.153776\pi\) | ||||
0.885558 | + | 0.464528i | \(0.153776\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −20.5646 | −0.213693 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −43.8973 | −0.397966 | −0.198983 | − | 0.980003i | \(-0.563764\pi\) | ||||
−0.198983 | + | 0.980003i | \(0.563764\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 110.099 | 0.880795 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 151.264 | 1.07817 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −29.0000 | −0.185695 | ||||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 169.034 | 0.979337 | 0.489669 | − | 0.871909i | \(-0.337118\pi\) | ||||
0.489669 | + | 0.871909i | \(0.337118\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 110.497 | 0.582883 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 80.8931 | 0.390670 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −69.8939 | −0.310554 | −0.155277 | − | 0.987871i | \(-0.549627\pi\) | ||||
−0.155277 | + | 0.987871i | \(0.549627\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 240.224 | 0.986322 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −229.327 | −0.873533 | −0.436766 | − | 0.899575i | \(-0.643876\pi\) | ||||
−0.436766 | + | 0.899575i | \(0.643876\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −150.534 | −0.533864 | −0.266932 | − | 0.963715i | \(-0.586010\pi\) | ||||
−0.266932 | + | 0.963715i | \(0.586010\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −181.023 | −0.599674 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −237.886 | −0.738282 | −0.369141 | − | 0.929373i | \(-0.620348\pi\) | ||||
−0.369141 | + | 0.929373i | \(0.620348\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −315.166 | −0.918852 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −155.636 | −0.427322 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 218.454 | 0.566169 | 0.283084 | − | 0.959095i | \(-0.408642\pi\) | ||||
0.283084 | + | 0.959095i | \(0.408642\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −434.654 | −1.06561 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −571.757 | −1.32862 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 115.370 | 0.254575 | 0.127287 | − | 0.991866i | \(-0.459373\pi\) | ||||
0.127287 | + | 0.991866i | \(0.459373\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −211.782 | −0.444524 | −0.222262 | − | 0.974987i | \(-0.571344\pi\) | ||||
−0.222262 | + | 0.974987i | \(0.571344\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −62.2865 | −0.124561 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −944.947 | −1.80317 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 442.508 | 0.806880 | 0.403440 | − | 0.915006i | \(-0.367814\pi\) | ||||
0.403440 | + | 0.915006i | \(0.367814\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 171.109 | 0.298537 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 663.263 | 1.10866 | 0.554330 | − | 0.832297i | \(-0.312975\pi\) | ||||
0.554330 | + | 0.832297i | \(0.312975\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −676.680 | −1.08492 | −0.542462 | − | 0.840081i | \(-0.682508\pi\) | ||||
−0.542462 | + | 0.840081i | \(0.682508\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −429.160 | −0.660735 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −149.556 | −0.221344 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −1319.35 | −1.87897 | −0.939486 | − | 0.342588i | \(-0.888696\pi\) | ||||
−0.939486 | + | 0.342588i | \(0.888696\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −270.849 | −0.371535 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 1266.38 | 1.67473 | 0.837367 | − | 0.546641i | \(-0.184094\pi\) | ||||
0.837367 | + | 0.546641i | \(0.184094\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 612.212 | 0.781221 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 113.040 | 0.139301 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −1356.44 | −1.61553 | −0.807763 | − | 0.589507i | \(-0.799322\pi\) | ||||
−0.807763 | + | 0.589507i | \(0.799322\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −325.138 | −0.374546 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −658.884 | −0.734656 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 2249.07 | 2.42895 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 823.177 | 0.861659 | 0.430830 | − | 0.902433i | \(-0.358221\pi\) | ||||
0.430830 | + | 0.902433i | \(0.358221\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 334.678 | 0.339761 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 895.738 | 0.882468 | 0.441234 | − | 0.897392i | \(-0.354541\pi\) | ||||
0.441234 | + | 0.897392i | \(0.354541\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −774.903 | −0.741296 | −0.370648 | − | 0.928773i | \(-0.620864\pi\) | ||||
−0.370648 | + | 0.928773i | \(0.620864\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −315.316 | −0.293063 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −868.181 | −0.784394 | −0.392197 | − | 0.919881i | \(-0.628285\pi\) | ||||
−0.392197 | + | 0.919881i | \(0.628285\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 328.137 | 0.288347 | 0.144173 | − | 0.989552i | \(-0.453948\pi\) | ||||
0.144173 | + | 0.989552i | \(0.453948\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 272.441 | 0.232964 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −1095.47 | −0.911971 | −0.455986 | − | 0.889987i | \(-0.650713\pi\) | ||||
−0.455986 | + | 0.889987i | \(0.650713\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −673.076 | −0.545779 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 727.595 | 0.574925 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 210.650 | 0.162271 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −527.406 | −0.396248 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 893.900 | 0.655286 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −228.470 | −0.163480 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 948.925 | 0.663019 | 0.331510 | − | 0.943452i | \(-0.392442\pi\) | ||||
0.331510 | + | 0.943452i | \(0.392442\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 586.769 | 0.400482 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −45.1750 | −0.0301294 | −0.0150647 | − | 0.999887i | \(-0.504795\pi\) | ||||
−0.0150647 | + | 0.999887i | \(0.504795\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 773.862 | 0.504529 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 2319.32 | 1.47863 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −1006.30 | −0.627550 | −0.313775 | − | 0.949497i | \(-0.601594\pi\) | ||||
−0.313775 | + | 0.949497i | \(0.601594\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 177.789 | 0.108488 | 0.0542441 | − | 0.998528i | \(-0.482725\pi\) | ||||
0.0542441 | + | 0.998528i | \(0.482725\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 927.263 | 0.553827 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 1747.03 | 1.02164 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −444.656 | −0.254666 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 1228.50 | 0.689283 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 2275.95 | 1.25136 | 0.625682 | − | 0.780078i | \(-0.284821\pi\) | ||||
0.625682 | + | 0.780078i | \(0.284821\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −22.3187 | −0.0120283 | −0.00601414 | − | 0.999982i | \(-0.501914\pi\) | ||||
−0.00601414 | + | 0.999982i | \(0.501914\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −471.395 | −0.249085 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 2591.79 | 1.34308 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −2749.00 | −1.39741 | −0.698707 | − | 0.715408i | \(-0.746241\pi\) | ||||
−0.698707 | + | 0.715408i | \(0.746241\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −851.517 | −0.424715 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −231.592 | −0.113367 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −1552.50 | −0.746018 | −0.373009 | − | 0.927828i | \(-0.621674\pi\) | ||||
−0.373009 | + | 0.927828i | \(0.621674\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 1694.25 | 0.799378 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −2322.26 | −1.07606 | −0.538029 | − | 0.842926i | \(-0.680831\pi\) | ||||
−0.538029 | + | 0.842926i | \(0.680831\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1601.07 | 0.728755 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −1731.75 | −0.774447 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −363.841 | −0.159898 | −0.0799490 | − | 0.996799i | \(-0.525476\pi\) | ||||
−0.0799490 | + | 0.996799i | \(0.525476\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 580.859 | 0.250908 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −449.705 | −0.190971 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −2532.15 | −1.05733 | −0.528665 | − | 0.848831i | \(-0.677307\pi\) | ||||
−0.528665 | + | 0.848831i | \(0.677307\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1163.94 | 0.477982 | 0.238991 | − | 0.971022i | \(-0.423183\pi\) | ||||
0.238991 | + | 0.971022i | \(0.423183\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 825.512 | 0.333462 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −1071.68 | −0.425900 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −1131.87 | −0.442621 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 798.032 | 0.307134 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −1677.77 | −0.635599 | −0.317799 | − | 0.948158i | \(-0.602944\pi\) | ||||
−0.317799 | + | 0.948158i | \(0.602944\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 2249.50 | 0.838978 | 0.419489 | − | 0.907760i | \(-0.362209\pi\) | ||||
0.419489 | + | 0.907760i | \(0.362209\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 3683.34 | 1.35266 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −2233.37 | −0.807720 | −0.403860 | − | 0.914821i | \(-0.632332\pi\) | ||||
−0.403860 | + | 0.914821i | \(0.632332\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −2986.69 | −1.06392 | −0.531962 | − | 0.846768i | \(-0.678545\pi\) | ||||
−0.531962 | + | 0.846768i | \(0.678545\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −1724.86 | −0.605286 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −152.997 | −0.0528981 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −3516.26 | −1.19798 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 518.259 | 0.174017 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −4158.11 | −1.37618 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −5179.02 | −1.68975 | −0.844877 | − | 0.534960i | \(-0.820327\pi\) | ||||
−0.844877 | + | 0.534960i | \(0.820327\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −2585.35 | −0.831669 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −2308.13 | −0.732153 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 891.786 | 0.278979 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 2637.65 | 0.813863 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −2460.70 | −0.748979 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 5527.03 | 1.65972 | 0.829859 | − | 0.557973i | \(-0.188421\pi\) | ||||
0.829859 | + | 0.557973i | \(0.188421\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −1299.85 | −0.385141 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −2788.28 | −0.815262 | −0.407631 | − | 0.913147i | \(-0.633645\pi\) | ||||
−0.407631 | + | 0.913147i | \(0.633645\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 2527.23 | 0.729274 | 0.364637 | − | 0.931150i | \(-0.381193\pi\) | ||||
0.364637 | + | 0.931150i | \(0.381193\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 582.959 | 0.166043 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −5606.98 | −1.57650 | −0.788252 | − | 0.615352i | \(-0.789014\pi\) | ||||
−0.788252 | + | 0.615352i | \(0.789014\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −3647.49 | −1.01249 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 5142.74 | 1.40952 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −5924.09 | −1.60334 | −0.801668 | − | 0.597769i | \(-0.796054\pi\) | ||||
−0.801668 | + | 0.597769i | \(0.796054\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −876.073 | −0.234161 | −0.117081 | − | 0.993122i | \(-0.537354\pi\) | ||||
−0.117081 | + | 0.993122i | \(0.537354\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −3028.37 | −0.799465 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −4832.43 | −1.26013 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −9039.81 | −2.32870 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −4936.25 | −1.25631 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 5914.86 | 1.48742 | 0.743711 | − | 0.668502i | \(-0.233064\pi\) | ||||
0.743711 | + | 0.668502i | \(0.233064\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1244.39 | 0.309226 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −2386.36 | −0.586038 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −1589.22 | −0.385730 | −0.192865 | − | 0.981225i | \(-0.561778\pi\) | ||||
−0.192865 | + | 0.981225i | \(0.561778\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −368.744 | −0.0884658 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 342.378 | 0.0811980 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 7777.46 | 1.82349 | 0.911747 | − | 0.410752i | \(-0.134734\pi\) | ||||
0.911747 | + | 0.410752i | \(0.134734\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 3349.54 | 0.776456 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 5287.29 | 1.21190 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 925.953 | 0.209875 | 0.104937 | − | 0.994479i | \(-0.466536\pi\) | ||||
0.104937 | + | 0.994479i | \(0.466536\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 2235.53 | 0.501103 | 0.250551 | − | 0.968103i | \(-0.419388\pi\) | ||||
0.250551 | + | 0.968103i | \(0.419388\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 1267.36 | 0.280968 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −3121.07 | −0.684391 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −1810.59 | −0.392736 | −0.196368 | − | 0.980530i | \(-0.562915\pi\) | ||||
−0.196368 | + | 0.980530i | \(0.562915\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −1995.64 | −0.428230 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −7795.69 | −1.65499 | −0.827495 | − | 0.561474i | \(-0.810235\pi\) | ||||
−0.827495 | + | 0.561474i | \(0.810235\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 7693.60 | 1.61603 | 0.808016 | − | 0.589160i | \(-0.200541\pi\) | ||||
0.808016 | + | 0.589160i | \(0.200541\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −8766.72 | −1.82209 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −1209.88 | −0.248839 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −3318.76 | −0.675507 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −3208.69 | −0.646380 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 2093.31 | 0.417381 | 0.208691 | − | 0.977982i | \(-0.433080\pi\) | ||||
0.208691 | + | 0.977982i | \(0.433080\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 1768.97 | 0.349129 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −4287.98 | −0.837757 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 2705.33 | 0.523255 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −794.181 | −0.152079 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −3491.52 | −0.661989 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −3247.25 | −0.609629 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −3700.08 | −0.687865 | −0.343933 | − | 0.938994i | \(-0.611759\pi\) | ||||
−0.343933 | + | 0.938994i | \(0.611759\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 3020.52 | 0.556088 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −758.661 | −0.138327 | −0.0691635 | − | 0.997605i | \(-0.522033\pi\) | ||||
−0.0691635 | + | 0.997605i | \(0.522033\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 2441.99 | 0.440989 | 0.220494 | − | 0.975388i | \(-0.429233\pi\) | ||||
0.220494 | + | 0.975388i | \(0.429233\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −955.036 | −0.170826 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −5664.85 | −1.00369 | −0.501845 | − | 0.864958i | \(-0.667345\pi\) | ||||
−0.501845 | + | 0.864958i | \(0.667345\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 822.084 | 0.144288 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 3384.11 | 0.588419 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 5856.71 | 1.00890 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −6785.26 | −1.15809 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −1279.05 | −0.216305 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −1255.03 | −0.210310 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −5046.15 | −0.837950 | −0.418975 | − | 0.907998i | \(-0.637611\pi\) | ||||
−0.418975 | + | 0.907998i | \(0.637611\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 825.178 | 0.135794 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 6784.95 | 1.10657 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −2064.77 | −0.333754 | −0.166877 | − | 0.985978i | \(-0.553368\pi\) | ||||
−0.166877 | + | 0.985978i | \(0.553368\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 4270.05 | 0.684121 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −4791.74 | −0.760959 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −3472.33 | −0.546613 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 2623.60 | 0.409420 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −10261.9 | −1.58757 | −0.793785 | − | 0.608199i | \(-0.791892\pi\) | ||||
−0.793785 | + | 0.608199i | \(0.791892\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −9965.45 | −1.52848 | −0.764238 | − | 0.644934i | \(-0.776885\pi\) | ||||
−0.764238 | + | 0.644934i | \(0.776885\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −9322.15 | −1.41761 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −2978.90 | −0.449153 | −0.224576 | − | 0.974457i | \(-0.572100\pi\) | ||||
−0.224576 | + | 0.974457i | \(0.572100\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 10169.8 | 1.52044 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −821.100 | −0.121729 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −8156.81 | −1.19916 | −0.599582 | − | 0.800313i | \(-0.704667\pi\) | ||||
−0.599582 | + | 0.800313i | \(0.704667\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 14656.7 | 2.13686 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 2055.79 | 0.297248 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −10375.5 | −1.48789 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 6202.75 | 0.882237 | 0.441119 | − | 0.897449i | \(-0.354582\pi\) | ||||
0.441119 | + | 0.897449i | \(0.354582\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 2707.47 | 0.381965 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 1152.51 | 0.161282 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −5940.53 | −0.824635 | −0.412317 | − | 0.911040i | \(-0.635281\pi\) | ||||
−0.412317 | + | 0.911040i | \(0.635281\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 890.559 | 0.122635 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 1787.23 | 0.244156 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −3283.69 | −0.445045 | −0.222522 | − | 0.974928i | \(-0.571429\pi\) | ||||
−0.222522 | + | 0.974928i | \(0.571429\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −3698.84 | −0.497369 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 6651.64 | 0.887423 | 0.443712 | − | 0.896170i | \(-0.353661\pi\) | ||||
0.443712 | + | 0.896170i | \(0.353661\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −2293.14 | −0.303556 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 1777.22 | 0.233440 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −10607.5 | −1.38257 | −0.691285 | − | 0.722582i | \(-0.742955\pi\) | ||||
−0.691285 | + | 0.722582i | \(0.742955\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −1752.73 | −0.226699 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 176.089 | 0.0226018 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −20229.6 | −2.57686 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −4945.27 | −0.625178 | −0.312589 | − | 0.949888i | \(-0.601196\pi\) | ||||
−0.312589 | + | 0.949888i | \(0.601196\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −3016.46 | −0.378476 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 14041.2 | 1.74859 | 0.874295 | − | 0.485396i | \(-0.161324\pi\) | ||||
0.874295 | + | 0.485396i | \(0.161324\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −10417.3 | −1.28765 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −4152.91 | −0.509531 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 1981.33 | 0.241305 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −11566.1 | −1.39830 | −0.699150 | − | 0.714975i | \(-0.746438\pi\) | ||||
−0.699150 | + | 0.714975i | \(0.746438\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 3922.50 | 0.470761 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 608.666 | 0.0725194 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 19417.3 | 2.29677 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −693.008 | −0.0813831 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −10233.3 | −1.19314 | −0.596572 | − | 0.802560i | \(-0.703471\pi\) | ||||
−0.596572 | + | 0.802560i | \(0.703471\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 11582.5 | 1.34085 | 0.670423 | − | 0.741979i | \(-0.266113\pi\) | ||||
0.670423 | + | 0.741979i | \(0.266113\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 2808.52 | 0.322825 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 4396.04 | 0.501739 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −1117.31 | −0.126629 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −6809.79 | −0.766387 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −1754.30 | −0.196060 | −0.0980299 | − | 0.995183i | \(-0.531254\pi\) | ||||
−0.0980299 | + | 0.995183i | \(0.531254\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 1060.29 | 0.117677 | 0.0588387 | − | 0.998268i | \(-0.481260\pi\) | ||||
0.0588387 | + | 0.998268i | \(0.481260\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 1733.24 | 0.191040 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −6438.96 | −0.704845 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 11608.1 | 1.26202 | 0.631008 | − | 0.775776i | \(-0.282641\pi\) | ||||
0.631008 | + | 0.775776i | \(0.282641\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 3720.90 | 0.401782 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 4090.97 | 0.438754 | 0.219377 | − | 0.975640i | \(-0.429598\pi\) | ||||
0.219377 | + | 0.975640i | \(0.429598\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −20798.2 | −2.21557 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −8871.50 | −0.938720 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −16360.6 | −1.71961 | −0.859807 | − | 0.510620i | \(-0.829416\pi\) | ||||
−0.859807 | + | 0.510620i | \(0.829416\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 6500.90 | 0.678748 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 86.9967 | 0.00902309 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −4985.32 | −0.513661 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 11693.7 | 1.19696 | 0.598479 | − | 0.801138i | \(-0.295772\pi\) | ||||
0.598479 | + | 0.801138i | \(0.295772\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 6039.64 | 0.614175 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 14730.0 | 1.48817 | 0.744084 | − | 0.668086i | \(-0.232886\pi\) | ||||
0.744084 | + | 0.668086i | \(0.232886\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −12020.1 | −1.20653 | −0.603263 | − | 0.797542i | \(-0.706133\pi\) | ||||
−0.603263 | + | 0.797542i | \(0.706133\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −10102.6 | −1.00752 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 5973.63 | 0.591920 | 0.295960 | − | 0.955200i | \(-0.404360\pi\) | ||||
0.295960 | + | 0.955200i | \(0.404360\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 2334.57 | 0.229852 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 10715.4 | 1.04828 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 4267.29 | 0.414820 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 16149.6 | 1.55999 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −2579.10 | −0.247566 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 17413.9 | 1.66109 | 0.830545 | − | 0.556951i | \(-0.188029\pi\) | ||||
0.830545 | + | 0.556951i | \(0.188029\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 4307.46 | 0.408322 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 902.730 | 0.0850427 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 12621.7 | 1.18170 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −3885.79 | −0.361565 | −0.180782 | − | 0.983523i | \(-0.557863\pi\) | ||||
−0.180782 | + | 0.983523i | \(0.557863\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 6051.53 | 0.559631 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 14369.1 | 1.32071 | 0.660354 | − | 0.750954i | \(-0.270406\pi\) | ||||
0.660354 | + | 0.750954i | \(0.270406\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −1157.91 | −0.105780 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 5131.60 | 0.465956 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 3499.22 | 0.315818 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −466.364 | −0.0418383 | −0.0209191 | − | 0.999781i | \(-0.506659\pi\) | ||||
−0.0209191 | + | 0.999781i | \(0.506659\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 9052.00 | 0.807212 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 3145.80 | 0.278856 | 0.139428 | − | 0.990232i | \(-0.455474\pi\) | ||||
0.139428 | + | 0.990232i | \(0.455474\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 13734.3 | 1.21024 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −6240.87 | −0.546680 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 1033.27 | 0.0899779 | 0.0449889 | − | 0.998987i | \(-0.485675\pi\) | ||||
0.0449889 | + | 0.998987i | \(0.485675\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −3570.01 | −0.309056 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 22187.7 | 1.90957 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −11881.6 | −1.01663 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 6743.53 | 0.573656 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 1418.23 | 0.119949 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −11615.8 | −0.976767 | −0.488384 | − | 0.872629i | \(-0.662413\pi\) | ||||
−0.488384 | + | 0.872629i | \(0.662413\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 14249.8 | 1.19140 | 0.595700 | − | 0.803207i | \(-0.296875\pi\) | ||||
0.595700 | + | 0.803207i | \(0.296875\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −2264.15 | −0.188220 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 6749.18 | 0.557873 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −10240.0 | −0.841623 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −1362.08 | −0.111317 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 14133.1 | 1.14854 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −13311.8 | −1.07573 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 9870.15 | 0.793163 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 8934.25 | 0.713962 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 1221.09 | 0.0970404 | 0.0485202 | − | 0.998822i | \(-0.484549\pi\) | ||||
0.0485202 | + | 0.998822i | \(0.484549\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −4536.95 | −0.358562 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 5031.30 | 0.395445 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −23448.2 | −1.83285 | −0.916427 | − | 0.400201i | \(-0.868940\pi\) | ||||
−0.916427 | + | 0.400201i | \(0.868940\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 2500.33 | 0.194375 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −4253.79 | −0.328888 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −6960.60 | −0.535253 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 4177.33 | 0.319492 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 14174.7 | 1.07828 | 0.539140 | − | 0.842216i | \(-0.318749\pi\) | ||||
0.539140 | + | 0.842216i | \(0.318749\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 9277.16 | 0.701936 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 4411.93 | 0.332035 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 3348.85 | 0.250688 | 0.125344 | − | 0.992113i | \(-0.459997\pi\) | ||||
0.125344 | + | 0.992113i | \(0.459997\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −16796.7 | −1.25070 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −1428.94 | −0.105837 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 10533.7 | 0.776091 | 0.388045 | − | 0.921640i | \(-0.373150\pi\) | ||||
0.388045 | + | 0.921640i | \(0.373150\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −19267.0 | −1.41208 | −0.706041 | − | 0.708171i | \(-0.749520\pi\) | ||||
−0.706041 | + | 0.708171i | \(0.749520\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 6539.84 | 0.476799 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −4833.07 | −0.350527 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 4747.42 | 0.342526 | 0.171263 | − | 0.985225i | \(-0.445215\pi\) | ||||
0.171263 | + | 0.985225i | \(0.445215\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −8768.41 | −0.629365 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 6681.11 | 0.477073 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −6192.67 | −0.439921 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 11156.2 | 0.788464 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −7603.14 | −0.534608 | −0.267304 | − | 0.963612i | \(-0.586133\pi\) | ||||
−0.267304 | + | 0.963612i | \(0.586133\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 24794.3 | 1.73452 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 8705.51 | 0.605917 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 1892.76 | 0.131073 | 0.0655366 | − | 0.997850i | \(-0.479124\pi\) | ||||
0.0655366 | + | 0.997850i | \(0.479124\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 3229.89 | 0.222542 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 11641.9 | 0.798110 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −18998.8 | −1.29594 | −0.647970 | − | 0.761665i | \(-0.724382\pi\) | ||||
−0.647970 | + | 0.761665i | \(0.724382\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 2034.70 | 0.138098 | 0.0690491 | − | 0.997613i | \(-0.478003\pi\) | ||||
0.0690491 | + | 0.997613i | \(0.478003\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −5224.31 | −0.352820 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −8086.69 | −0.543423 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −1691.66 | −0.113117 | −0.0565587 | − | 0.998399i | \(-0.518013\pi\) | ||||
−0.0565587 | + | 0.998399i | \(0.518013\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 596.373 | 0.0396818 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 14660.6 | 0.970708 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 2051.86 | 0.135194 | 0.0675969 | − | 0.997713i | \(-0.478467\pi\) | ||||
0.0675969 | + | 0.997713i | \(0.478467\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 13706.1 | 0.898674 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −21839.0 | −1.42497 | −0.712483 | − | 0.701690i | \(-0.752429\pi\) | ||||
−0.712483 | + | 0.701690i | \(0.752429\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 5707.58 | 0.370609 | 0.185305 | − | 0.982681i | \(-0.440673\pi\) | ||||
0.185305 | + | 0.982681i | \(0.440673\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −6640.07 | −0.429077 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −7156.24 | −0.460207 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −17265.5 | −1.10499 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 16208.0 | 1.03235 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −2790.72 | −0.176905 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 848.735 | 0.0535461 | 0.0267731 | − | 0.999642i | \(-0.491477\pi\) | ||||
0.0267731 | + | 0.999642i | \(0.491477\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 20187.4 | 1.26758 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 14549.8 | 0.909279 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 19423.2 | 1.20813 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −7830.59 | −0.484778 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −25537.5 | −1.57359 | −0.786796 | − | 0.617213i | \(-0.788262\pi\) | ||||
−0.786796 | + | 0.617213i | \(0.788262\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −4902.36 | −0.300669 | −0.150334 | − | 0.988635i | \(-0.548035\pi\) | ||||
−0.150334 | + | 0.988635i | \(0.548035\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 8996.91 | 0.549229 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −3920.19 | −0.238205 | −0.119103 | − | 0.992882i | \(-0.538002\pi\) | ||||
−0.119103 | + | 0.992882i | \(0.538002\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −3270.48 | −0.197808 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −3476.12 | −0.209278 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 3640.59 | 0.218174 | 0.109087 | − | 0.994032i | \(-0.465207\pi\) | ||||
0.109087 | + | 0.994032i | \(0.465207\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −692.666 | −0.0413201 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 7988.99 | 0.474399 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −14826.8 | −0.876437 | −0.438219 | − | 0.898868i | \(-0.644390\pi\) | ||||
−0.438219 | + | 0.898868i | \(0.644390\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −25302.1 | −1.48886 | −0.744432 | − | 0.667698i | \(-0.767280\pi\) | ||||
−0.744432 | + | 0.667698i | \(0.767280\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 9591.62 | 0.561852 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 11865.6 | 0.691921 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1273.02 | 0.0739005 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −21544.0 | −1.24505 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 6003.55 | 0.345402 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −18983.4 | −1.08730 | −0.543652 | − | 0.839311i | \(-0.682959\pi\) | ||||
−0.543652 | + | 0.839311i | \(0.682959\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 16654.0 | 0.949651 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −16033.8 | −0.910236 | −0.455118 | − | 0.890431i | \(-0.650403\pi\) | ||||
−0.455118 | + | 0.890431i | \(0.650403\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 4342.89 | 0.245456 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 10868.5 | 0.611574 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −1451.21 | −0.0813017 | −0.0406509 | − | 0.999173i | \(-0.512943\pi\) | ||||
−0.0406509 | + | 0.999173i | \(0.512943\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −15429.6 | −0.860635 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −9850.95 | −0.547070 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −13463.0 | −0.744410 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 8126.55 | 0.447393 | 0.223697 | − | 0.974659i | \(-0.428188\pi\) | ||||
0.223697 | + | 0.974659i | \(0.428188\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 1765.68 | 0.0967860 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 2726.03 | 0.148783 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −9156.54 | −0.497602 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 21855.6 | 1.18263 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −1475.94 | −0.0795229 | −0.0397614 | − | 0.999209i | \(-0.512660\pi\) | ||||
−0.0397614 | + | 0.999209i | \(0.512660\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −10252.2 | −0.550027 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 14217.7 | 0.759530 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 4725.71 | 0.251384 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 228.875 | 0.0121235 | 0.00606177 | − | 0.999982i | \(-0.498070\pi\) | ||||
0.00606177 | + | 0.999982i | \(0.498070\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 15576.5 | 0.821608 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −7420.15 | −0.389743 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 26787.1 | 1.40109 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 23091.7 | 1.20275 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 15696.4 | 0.814155 | 0.407077 | − | 0.913394i | \(-0.366548\pi\) | ||||
0.407077 | + | 0.913394i | \(0.366548\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −4088.21 | −0.211169 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 3414.87 | 0.175658 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −3192.88 | −0.163560 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 14329.5 | 0.731020 | 0.365510 | − | 0.930807i | \(-0.380895\pi\) | ||||
0.365510 | + | 0.930807i | \(0.380895\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 19117.3 | 0.971259 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −6010.49 | −0.304112 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 15912.1 | 0.801810 | 0.400905 | − | 0.916120i | \(-0.368696\pi\) | ||||
0.400905 | + | 0.916120i | \(0.368696\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 18836.5 | 0.945297 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −12544.1 | −0.626958 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 12354.6 | 0.614983 | 0.307492 | − | 0.951551i | \(-0.400510\pi\) | ||||
0.307492 | + | 0.951551i | \(0.400510\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 35236.5 | 1.74689 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −5080.77 | −0.250869 | −0.125434 | − | 0.992102i | \(-0.540032\pi\) | ||||
−0.125434 | + | 0.992102i | \(0.540032\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 34897.1 | 1.71615 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −14951.0 | −0.732302 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −4580.32 | −0.223446 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −34750.4 | −1.68850 | −0.844248 | − | 0.535952i | \(-0.819953\pi\) | ||||
−0.844248 | + | 0.535952i | \(0.819953\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −23055.7 | −1.11580 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −342.212 | −0.0164958 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 2602.27 | 0.124942 | 0.0624709 | − | 0.998047i | \(-0.480102\pi\) | ||||
0.0624709 | + | 0.998047i | \(0.480102\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −4850.54 | −0.231968 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 26480.5 | 1.26139 | 0.630694 | − | 0.776031i | \(-0.282770\pi\) | ||||
0.630694 | + | 0.776031i | \(0.282770\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 1731.17 | 0.0821398 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −7227.87 | −0.341600 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −7110.09 | −0.334720 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −7464.68 | −0.350043 | −0.175022 | − | 0.984565i | \(-0.556000\pi\) | ||||
−0.175022 | + | 0.984565i | \(0.556000\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 6194.65 | 0.289358 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 39751.4 | 1.84962 | 0.924812 | − | 0.380424i | \(-0.124222\pi\) | ||||
0.924812 | + | 0.380424i | \(0.124222\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 18610.6 | 0.862596 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 1437.34 | 0.0663632 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −33638.2 | −1.54713 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −18802.0 | −0.861446 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −4386.64 | −0.200212 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −42150.3 | −1.91644 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −16132.1 | −0.730681 | −0.365341 | − | 0.930874i | \(-0.619048\pi\) | ||||
−0.365341 | + | 0.930874i | \(0.619048\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −30316.0 | −1.36791 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −5779.42 | −0.259788 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 13051.8 | 0.584469 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −13056.3 | −0.582463 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 30649.4 | 1.36218 | 0.681089 | − | 0.732201i | \(-0.261507\pi\) | ||||
0.681089 | + | 0.732201i | \(0.261507\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −9498.28 | −0.420557 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 16014.3 | 0.706413 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 19182.3 | 0.843002 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −3550.99 | −0.155473 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −3609.30 | −0.157439 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 31988.2 | 1.39017 | 0.695083 | − | 0.718929i | \(-0.255367\pi\) | ||||
0.695083 | + | 0.718929i | \(0.255367\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −39086.8 | −1.69238 | −0.846192 | − | 0.532877i | \(-0.821111\pi\) | ||||
−0.846192 | + | 0.532877i | \(0.821111\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −8713.94 | −0.375906 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −23804.4 | −1.02311 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −22080.6 | −0.945536 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 3838.63 | 0.163776 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 20056.3 | 0.852582 | 0.426291 | − | 0.904586i | \(-0.359820\pi\) | ||||
0.426291 | + | 0.904586i | \(0.359820\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 24931.0 | 1.05594 | 0.527970 | − | 0.849263i | \(-0.322953\pi\) | ||||
0.527970 | + | 0.849263i | \(0.322953\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 12165.7 | 0.513401 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −40104.5 | −1.68630 | −0.843150 | − | 0.537678i | \(-0.819302\pi\) | ||||
−0.843150 | + | 0.537678i | \(0.819302\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 35722.2 | 1.49660 | 0.748300 | − | 0.663360i | \(-0.230870\pi\) | ||||
0.748300 | + | 0.663360i | \(0.230870\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 7057.56 | 0.294614 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −12583.9 | −0.523418 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −35607.1 | −1.47573 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 25568.7 | 1.05590 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −185.813 | −0.00764598 | −0.00382299 | − | 0.999993i | \(-0.501217\pi\) | ||||
−0.00382299 | + | 0.999993i | \(0.501217\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 841.000 | 0.0344828 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 30387.1 | 1.24150 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 24549.2 | 0.999429 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −2782.47 | −0.112877 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −29989.1 | −1.21228 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 3068.16 | 0.123590 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 32958.5 | 1.32295 | 0.661475 | − | 0.749967i | \(-0.269931\pi\) | ||||
0.661475 | + | 0.749967i | \(0.269931\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −26552.9 | −1.06209 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −36681.9 | −1.46211 | −0.731056 | − | 0.682318i | \(-0.760972\pi\) | ||||
−0.731056 | + | 0.682318i | \(0.760972\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 25084.0 | 0.996340 | 0.498170 | − | 0.867079i | \(-0.334006\pi\) | ||||
0.498170 | + | 0.867079i | \(0.334006\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 4716.01 | 0.186668 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 6552.57 | 0.258461 | 0.129231 | − | 0.991615i | \(-0.458749\pi\) | ||||
0.129231 | + | 0.991615i | \(0.458749\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −5578.76 | −0.219287 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 12936.3 | 0.506736 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 37400.6 | 1.45999 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −27271.1 | −1.06090 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −9718.55 | −0.376773 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −1205.35 | −0.0465696 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 39373.9 | 1.51603 | 0.758017 | − | 0.652234i | \(-0.226168\pi\) | ||||
0.758017 | + | 0.652234i | \(0.226168\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −8159.59 | −0.313101 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −8182.51 | −0.312912 | −0.156456 | − | 0.987685i | \(-0.550007\pi\) | ||||
−0.156456 | + | 0.987685i | \(0.550007\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −7461.63 | −0.284376 | −0.142188 | − | 0.989840i | \(-0.545414\pi\) | ||||
−0.142188 | + | 0.989840i | \(0.545414\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −6895.30 | −0.261902 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 29745.2 | 1.12598 | 0.562990 | − | 0.826463i | \(-0.309651\pi\) | ||||
0.562990 | + | 0.826463i | \(0.309651\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 5006.31 | 0.188871 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 7677.95 | 0.288688 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −34893.7 | −1.30758 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −38825.4 | −1.45004 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −10545.2 | −0.392523 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −4901.99 | −0.181858 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 8722.40 | 0.322514 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 3095.66 | 0.114083 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 17846.6 | 0.655515 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −34626.6 | −1.26765 | −0.633825 | − | 0.773476i | \(-0.718516\pi\) | ||||
−0.633825 | + | 0.773476i | \(0.718516\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −10575.2 | −0.385872 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −6172.29 | −0.224476 | −0.112238 | − | 0.993681i | \(-0.535802\pi\) | ||||
−0.112238 | + | 0.993681i | \(0.535802\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −35898.9 | −1.30129 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 12657.5 | 0.457317 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −238.333 | −0.00858281 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −15779.0 | −0.566376 | −0.283188 | − | 0.959064i | \(-0.591392\pi\) | ||||
−0.283188 | + | 0.959064i | \(0.591392\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 14422.6 | 0.516007 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −40875.9 | −1.45769 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −7695.28 | −0.273534 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 9148.62 | 0.324143 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −9692.85 | −0.342316 | −0.171158 | − | 0.985244i | \(-0.554751\pi\) | ||||
−0.171158 | + | 0.985244i | \(0.554751\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −46229.3 | −1.62739 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 2957.21 | 0.103767 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −17354.8 | −0.607020 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 17253.8 | 0.601554 | 0.300777 | − | 0.953694i | \(-0.402754\pi\) | ||||
0.300777 | + | 0.953694i | \(0.402754\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −9518.70 | −0.330811 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −6249.78 | −0.216511 | −0.108256 | − | 0.994123i | \(-0.534526\pi\) | ||||
−0.108256 | + | 0.994123i | \(0.534526\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 10066.8 | 0.347637 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 12236.2 | 0.421210 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −38713.7 | −1.32843 | −0.664217 | − | 0.747540i | \(-0.731235\pi\) | ||||
−0.664217 | + | 0.747540i | \(0.731235\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 41702.8 | 1.42648 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 22081.2 | 0.752924 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 28936.5 | 0.983573 | 0.491787 | − | 0.870716i | \(-0.336344\pi\) | ||||
0.491787 | + | 0.870716i | \(0.336344\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −25725.2 | −0.871673 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −3204.43 | −0.108239 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −5309.03 | −0.178767 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −1218.42 | −0.0408989 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 10249.9 | 0.342988 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 34491.5 | 1.15059 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −8697.74 | −0.289245 | −0.144623 | − | 0.989487i | \(-0.546197\pi\) | ||||
−0.144623 | + | 0.989487i | \(0.546197\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −22829.1 | −0.756837 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 41062.0 | 1.35710 | 0.678549 | − | 0.734555i | \(-0.262609\pi\) | ||||
0.678549 | + | 0.734555i | \(0.262609\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 937.973 | 0.0309045 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 26448.5 | 0.868748 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 35397.4 | 1.15912 | 0.579561 | − | 0.814929i | \(-0.303224\pi\) | ||||
0.579561 | + | 0.814929i | \(0.303224\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 38451.9 | 1.25529 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −3874.03 | −0.126084 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 51453.4 | 1.66949 | 0.834746 | − | 0.550636i | \(-0.185615\pi\) | ||||
0.834746 | + | 0.550636i | \(0.185615\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −34244.1 | −1.10772 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 4892.02 | 0.157766 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 6608.03 | 0.212460 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 43563.5 | 1.39641 | 0.698205 | − | 0.715898i | \(-0.253983\pi\) | ||||
0.698205 | + | 0.715898i | \(0.253983\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 19669.5 | 0.628594 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −45794.8 | −1.45909 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 45472.8 | 1.44447 | 0.722236 | − | 0.691647i | \(-0.243114\pi\) | ||||
0.722236 | + | 0.691647i | \(0.243114\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −10572.4 | −0.334831 |
(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.be.1.3 | 8 | ||
4.3 | odd | 2 | inner | 1856.4.a.be.1.6 | 8 | ||
8.3 | odd | 2 | 928.4.a.c.1.3 | ✓ | 8 | ||
8.5 | even | 2 | 928.4.a.c.1.6 | yes | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
928.4.a.c.1.3 | ✓ | 8 | 8.3 | odd | 2 | ||
928.4.a.c.1.6 | yes | 8 | 8.5 | even | 2 | ||
1856.4.a.be.1.3 | 8 | 1.1 | even | 1 | trivial | ||
1856.4.a.be.1.6 | 8 | 4.3 | odd | 2 | inner |