Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [384,4,Mod(1,384)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(384, 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("384.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 384 = 2^{7} \cdot 3 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 384.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: | \(22.6567334422\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{7}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - 7 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-2.64575\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 384.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −3.00000 | −0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −18.5830 | −1.66211 | −0.831057 | − | 0.556187i | \(-0.812264\pi\) | ||||
−0.831057 | + | 0.556187i | \(0.812264\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −29.7490 | −1.60630 | −0.803148 | − | 0.595780i | \(-0.796843\pi\) | ||||
−0.803148 | + | 0.595780i | \(0.796843\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 9.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 9.16601 | 0.251241 | 0.125621 | − | 0.992078i | \(-0.459908\pi\) | ||||
0.125621 | + | 0.992078i | \(0.459908\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −80.3320 | −1.71385 | −0.856927 | − | 0.515438i | \(-0.827629\pi\) | ||||
−0.856927 | + | 0.515438i | \(0.827629\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 55.7490 | 0.959622 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −31.1660 | −0.444639 | −0.222320 | − | 0.974974i | \(-0.571363\pi\) | ||||
−0.222320 | + | 0.974974i | \(0.571363\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −89.8301 | −1.08465 | −0.542327 | − | 0.840167i | \(-0.682457\pi\) | ||||
−0.542327 | + | 0.840167i | \(0.682457\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 89.2470 | 0.927395 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 57.1660 | 0.518258 | 0.259129 | − | 0.965843i | \(-0.416564\pi\) | ||||
0.259129 | + | 0.965843i | \(0.416564\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 220.328 | 1.76262 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −27.0000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −167.085 | −1.06989 | −0.534947 | − | 0.844886i | \(-0.679668\pi\) | ||||
−0.534947 | + | 0.844886i | \(0.679668\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 270.915 | 1.56961 | 0.784803 | − | 0.619746i | \(-0.212764\pi\) | ||||
0.784803 | + | 0.619746i | \(0.212764\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −27.4980 | −0.145054 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 552.826 | 2.66985 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 157.498 | 0.699798 | 0.349899 | − | 0.936787i | \(-0.386216\pi\) | ||||
0.349899 | + | 0.936787i | \(0.386216\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 240.996 | 0.989494 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −404.154 | −1.53947 | −0.769735 | − | 0.638363i | \(-0.779612\pi\) | ||||
−0.769735 | + | 0.638363i | \(0.779612\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 317.166 | 1.12482 | 0.562411 | − | 0.826858i | \(-0.309874\pi\) | ||||
0.562411 | + | 0.826858i | \(0.309874\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −167.247 | −0.554038 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −63.1581 | −0.196012 | −0.0980060 | − | 0.995186i | \(-0.531246\pi\) | ||||
−0.0980060 | + | 0.995186i | \(0.531246\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 542.004 | 1.58019 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 93.4980 | 0.256713 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −616.737 | −1.59840 | −0.799202 | − | 0.601063i | \(-0.794744\pi\) | ||||
−0.799202 | + | 0.601063i | \(0.794744\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −170.332 | −0.417592 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 269.490 | 0.626225 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −137.992 | −0.304492 | −0.152246 | − | 0.988343i | \(-0.548651\pi\) | ||||
−0.152246 | + | 0.988343i | \(0.548651\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −200.170 | −0.420150 | −0.210075 | − | 0.977685i | \(-0.567371\pi\) | ||||
−0.210075 | + | 0.977685i | \(0.567371\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −267.741 | −0.535432 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 1492.81 | 2.84862 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 576.664 | 1.05150 | 0.525752 | − | 0.850638i | \(-0.323784\pi\) | ||||
0.525752 | + | 0.850638i | \(0.323784\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −171.498 | −0.299216 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 305.166 | 0.510092 | 0.255046 | − | 0.966929i | \(-0.417909\pi\) | ||||
0.255046 | + | 0.966929i | \(0.417909\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −198.988 | −0.319038 | −0.159519 | − | 0.987195i | \(-0.550994\pi\) | ||||
−0.159519 | + | 0.987195i | \(0.550994\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −660.984 | −1.01765 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −272.680 | −0.403568 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 335.563 | 0.477896 | 0.238948 | − | 0.971032i | \(-0.423197\pi\) | ||||
0.238948 | + | 0.971032i | \(0.423197\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 81.0000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −981.474 | −1.29796 | −0.648981 | − | 0.760805i | \(-0.724804\pi\) | ||||
−0.648981 | + | 0.760805i | \(0.724804\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 579.158 | 0.739041 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 501.255 | 0.617703 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −51.0197 | −0.0607649 | −0.0303824 | − | 0.999538i | \(-0.509673\pi\) | ||||
−0.0303824 | + | 0.999538i | \(0.509673\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 2389.80 | 2.75296 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −812.745 | −0.906212 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 1669.31 | 1.80282 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 678.340 | 0.710051 | 0.355026 | − | 0.934857i | \(-0.384472\pi\) | ||||
0.355026 | + | 0.934857i | \(0.384472\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 82.4941 | 0.0837472 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1334.91 | 1.31513 | 0.657565 | − | 0.753397i | \(-0.271586\pi\) | ||||
0.657565 | + | 0.753397i | \(0.271586\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −901.231 | −0.862145 | −0.431073 | − | 0.902317i | \(-0.641865\pi\) | ||||
−0.431073 | + | 0.902317i | \(0.641865\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −1658.48 | −1.54144 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −605.684 | −0.547230 | −0.273615 | − | 0.961839i | \(-0.588219\pi\) | ||||
−0.273615 | + | 0.961839i | \(0.588219\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −400.656 | −0.352072 | −0.176036 | − | 0.984384i | \(-0.556328\pi\) | ||||
−0.176036 | + | 0.984384i | \(0.556328\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −472.494 | −0.404028 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −1442.96 | −1.20126 | −0.600628 | − | 0.799529i | \(-0.705083\pi\) | ||||
−0.600628 | + | 0.799529i | \(0.705083\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1062.32 | −0.861404 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −722.988 | −0.571284 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 927.158 | 0.714222 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1246.98 | −0.936878 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 1212.46 | 0.888814 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1771.48 | −1.26757 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −2436.55 | −1.70243 | −0.851216 | − | 0.524815i | \(-0.824135\pi\) | ||||
−0.851216 | + | 0.524815i | \(0.824135\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −951.498 | −0.649417 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 983.953 | 0.656247 | 0.328123 | − | 0.944635i | \(-0.393584\pi\) | ||||
0.328123 | + | 0.944635i | \(0.393584\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 2672.36 | 1.74228 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 501.741 | 0.319874 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −633.205 | −0.394879 | −0.197439 | − | 0.980315i | \(-0.563263\pi\) | ||||
−0.197439 | + | 0.980315i | \(0.563263\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −1360.60 | −0.830249 | −0.415125 | − | 0.909765i | \(-0.636262\pi\) | ||||
−0.415125 | + | 0.909765i | \(0.636262\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 189.474 | 0.113168 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −736.324 | −0.430591 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 3104.94 | 1.77828 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −1626.01 | −0.912321 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 3079.33 | 1.69308 | 0.846539 | − | 0.532327i | \(-0.178682\pi\) | ||||
0.846539 | + | 0.532327i | \(0.178682\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −538.769 | −0.290360 | −0.145180 | − | 0.989405i | \(-0.546376\pi\) | ||||
−0.145180 | + | 0.989405i | \(0.546376\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −280.494 | −0.148213 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −5034.42 | −2.60886 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 586.842 | 0.298313 | 0.149156 | − | 0.988814i | \(-0.452344\pi\) | ||||
0.149156 | + | 0.988814i | \(0.452344\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 1850.21 | 0.922839 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −1700.63 | −0.832476 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 585.830 | 0.281508 | 0.140754 | − | 0.990045i | \(-0.455047\pi\) | ||||
0.140754 | + | 0.990045i | \(0.455047\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 510.996 | 0.241097 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −2369.36 | −1.09788 | −0.548942 | − | 0.835861i | \(-0.684969\pi\) | ||||
−0.548942 | + | 0.835861i | \(0.684969\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 4256.23 | 1.93729 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −808.470 | −0.361551 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −2329.84 | −1.02390 | −0.511949 | − | 0.859016i | \(-0.671076\pi\) | ||||
−0.511949 | + | 0.859016i | \(0.671076\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −6554.54 | −2.83130 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 413.976 | 0.175799 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −317.976 | −0.132775 | −0.0663873 | − | 0.997794i | \(-0.521147\pi\) | ||||
−0.0663873 | + | 0.997794i | \(0.521147\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 157.399 | 0.0646374 | 0.0323187 | − | 0.999478i | \(-0.489711\pi\) | ||||
0.0323187 | + | 0.999478i | \(0.489711\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 600.510 | 0.242574 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −2926.79 | −1.16314 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −285.668 | −0.111712 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 803.223 | 0.309132 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 636.727 | 0.241214 | 0.120607 | − | 0.992700i | \(-0.461516\pi\) | ||||
0.120607 | + | 0.992700i | \(0.461516\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −1344.93 | −0.501608 | −0.250804 | − | 0.968038i | \(-0.580695\pi\) | ||||
−0.250804 | + | 0.968038i | \(0.580695\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −4478.43 | −1.64465 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −1068.37 | −0.386385 | −0.193193 | − | 0.981161i | \(-0.561884\pi\) | ||||
−0.193193 | + | 0.981161i | \(0.561884\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −1537.60 | −0.547727 | −0.273864 | − | 0.961769i | \(-0.588302\pi\) | ||||
−0.273864 | + | 0.961769i | \(0.588302\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −1729.99 | −0.607086 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 4970.61 | 1.71856 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 7510.40 | 2.55878 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 514.494 | 0.172753 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −823.383 | −0.272510 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 5622.56 | 1.83447 | 0.917235 | − | 0.398347i | \(-0.130416\pi\) | ||||
0.917235 | + | 0.398347i | \(0.130416\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −915.498 | −0.294502 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −5893.90 | −1.86958 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −8059.46 | −2.52125 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 596.965 | 0.184197 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 2503.63 | 0.762047 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 4587.32 | 1.37753 | 0.688766 | − | 0.724983i | \(-0.258153\pi\) | ||||
0.688766 | + | 0.724983i | \(0.258153\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1982.95 | 0.587542 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 488.873 | 0.142941 | 0.0714706 | − | 0.997443i | \(-0.477231\pi\) | ||||
0.0714706 | + | 0.997443i | \(0.477231\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 4316.89 | 1.24571 | 0.622856 | − | 0.782337i | \(-0.285972\pi\) | ||||
0.622856 | + | 0.782337i | \(0.285972\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 818.039 | 0.233000 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −4591.62 | −1.29102 | −0.645509 | − | 0.763753i | \(-0.723355\pi\) | ||||
−0.645509 | + | 0.763753i | \(0.723355\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1173.67 | 0.325794 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −1006.69 | −0.275914 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 6358.19 | 1.72082 | 0.860412 | − | 0.509598i | \(-0.170206\pi\) | ||||
0.860412 | + | 0.509598i | \(0.170206\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 3118.65 | 0.833568 | 0.416784 | − | 0.909006i | \(-0.363157\pi\) | ||||
0.416784 | + | 0.909006i | \(0.363157\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −243.000 | −0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −10072.1 | −2.62645 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 7216.23 | 1.85894 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 2944.42 | 0.749378 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −6854.71 | −1.72377 | −0.861883 | − | 0.507107i | \(-0.830715\pi\) | ||||
−0.861883 | + | 0.507107i | \(0.830715\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 523.984 | 0.130208 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −1737.47 | −0.426686 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −234.696 | −0.0569646 | −0.0284823 | − | 0.999594i | \(-0.509067\pi\) | ||||
−0.0284823 | + | 0.999594i | \(0.509067\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −4685.41 | −1.12408 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −1503.76 | −0.356631 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −5862.58 | −1.37453 | −0.687266 | − | 0.726406i | \(-0.741189\pi\) | ||||
−0.687266 | + | 0.726406i | \(0.741189\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 11460.8 | 2.65673 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 153.059 | 0.0350826 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 1399.79 | 0.317273 | 0.158636 | − | 0.987337i | \(-0.449290\pi\) | ||||
0.158636 | + | 0.987337i | \(0.449290\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −7927.86 | −1.77706 | −0.888529 | − | 0.458820i | \(-0.848272\pi\) | ||||
−0.888529 | + | 0.458820i | \(0.848272\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −7169.40 | −1.58942 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 2019.53 | 0.442844 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1209.19 | 0.262287 | 0.131143 | − | 0.991363i | \(-0.458135\pi\) | ||||
0.131143 | + | 0.991363i | \(0.458135\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 2438.24 | 0.523202 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 8983.25 | 1.90710 | 0.953551 | − | 0.301231i | \(-0.0973976\pi\) | ||||
0.953551 | + | 0.301231i | \(0.0973976\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 2028.65 | 0.426115 | 0.213058 | − | 0.977040i | \(-0.431658\pi\) | ||||
0.213058 | + | 0.977040i | \(0.431658\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −5007.94 | −1.04086 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 12023.2 | 2.47284 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −3941.68 | −0.802296 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −2035.02 | −0.409948 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −14.8238 | −0.00295569 | −0.00147784 | − | 0.999999i | \(-0.500470\pi\) | ||||
−0.00147784 | + | 0.999999i | \(0.500470\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 2564.31 | 0.506101 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −247.482 | −0.0483514 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −4592.26 | −0.888218 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −9435.38 | −1.80680 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −4004.72 | −0.759291 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 3719.76 | 0.698337 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 5597.88 | 1.04068 | 0.520339 | − | 0.853960i | \(-0.325806\pi\) | ||||
0.520339 | + | 0.853960i | \(0.325806\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 2703.69 | 0.497760 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 6603.50 | 1.20402 | 0.602010 | − | 0.798488i | \(-0.294367\pi\) | ||||
0.602010 | + | 0.798488i | \(0.294367\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 6034.93 | 1.08982 | 0.544911 | − | 0.838494i | \(-0.316564\pi\) | ||||
0.544911 | + | 0.838494i | \(0.316564\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 4975.44 | 0.889949 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 4150.88 | 0.735446 | 0.367723 | − | 0.929935i | \(-0.380137\pi\) | ||||
0.367723 | + | 0.929935i | \(0.380137\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −1531.50 | −0.268802 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 1817.05 | 0.315944 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 2799.64 | 0.482280 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −17699.4 | −3.02088 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 1201.97 | 0.203269 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 1878.89 | 0.314853 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 5448.40 | 0.904747 | 0.452374 | − | 0.891829i | \(-0.350577\pi\) | ||||
0.452374 | + | 0.891829i | \(0.350577\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 1417.48 | 0.233266 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −10716.2 | −1.74772 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −9446.83 | −1.52701 | −0.763504 | − | 0.645803i | \(-0.776523\pi\) | ||||
−0.763504 | + | 0.645803i | \(0.776523\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 4328.87 | 0.693546 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 2483.21 | 0.394350 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −5920.17 | −0.931951 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 3186.95 | 0.497332 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 902.478 | 0.139618 | 0.0698092 | − | 0.997560i | \(-0.477761\pi\) | ||||
0.0698092 | + | 0.997560i | \(0.477761\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −2296.76 | −0.352271 | −0.176135 | − | 0.984366i | \(-0.556360\pi\) | ||||
−0.176135 | + | 0.984366i | \(0.556360\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 2168.96 | 0.329831 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −683.699 | −0.103087 | −0.0515434 | − | 0.998671i | \(-0.516414\pi\) | ||||
−0.0515434 | + | 0.998671i | \(0.516414\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −5670.90 | −0.847832 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −2781.47 | −0.412356 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 10440.2 | 1.53486 | 0.767430 | − | 0.641133i | \(-0.221535\pi\) | ||||
0.767430 | + | 0.641133i | \(0.221535\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1210.44 | 0.176474 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 3740.95 | 0.540907 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 3697.80 | 0.530278 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 4398.79 | 0.625654 | 0.312827 | − | 0.949810i | \(-0.398724\pi\) | ||||
0.312827 | + | 0.949810i | \(0.398724\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −3637.39 | −0.513157 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 18347.3 | 2.56751 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 341.111 | 0.0473513 | 0.0236757 | − | 0.999720i | \(-0.492463\pi\) | ||||
0.0236757 | + | 0.999720i | \(0.492463\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 5314.45 | 0.731832 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 13422.3 | 1.83364 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 11900.1 | 1.61284 | 0.806421 | − | 0.591342i | \(-0.201402\pi\) | ||||
0.806421 | + | 0.591342i | \(0.201402\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 7309.65 | 0.982900 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 13863.1 | 1.84953 | 0.924767 | − | 0.380535i | \(-0.124260\pi\) | ||||
0.924767 | + | 0.380535i | \(0.124260\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 5067.21 | 0.670776 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 2854.49 | 0.374941 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 335.006 | 0.0436645 | 0.0218322 | − | 0.999762i | \(-0.493050\pi\) | ||||
0.0218322 | + | 0.999762i | \(0.493050\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −1781.64 | −0.230438 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −2951.86 | −0.378884 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −6235.77 | −0.794319 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 8731.50 | 1.10383 | 0.551916 | − | 0.833900i | \(-0.313897\pi\) | ||||
0.551916 | + | 0.833900i | \(0.313897\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −8017.07 | −1.00590 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 382.565 | 0.0476419 | 0.0238209 | − | 0.999716i | \(-0.492417\pi\) | ||||
0.0238209 | + | 0.999716i | \(0.492417\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −21763.2 | −2.69007 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −1505.22 | −0.184679 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 1443.63 | 0.175818 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −1370.47 | −0.165685 | −0.0828425 | − | 0.996563i | \(-0.526400\pi\) | ||||
−0.0828425 | + | 0.996563i | \(0.526400\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 1899.62 | 0.227983 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 4105.13 | 0.489105 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 18238.7 | 2.15736 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 4081.80 | 0.479345 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 2389.63 | 0.278619 | 0.139309 | − | 0.990249i | \(-0.455512\pi\) | ||||
0.139309 | + | 0.990249i | \(0.455512\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 1144.48 | 0.132491 | 0.0662455 | − | 0.997803i | \(-0.478898\pi\) | ||||
0.0662455 | + | 0.997803i | \(0.478898\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −568.423 | −0.0653373 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −6866.75 | −0.783732 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 5954.86 | 0.674885 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 2208.97 | 0.248602 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −9624.10 | −1.07558 | −0.537792 | − | 0.843078i | \(-0.680741\pi\) | ||||
−0.537792 | + | 0.843078i | \(0.680741\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 3276.44 | 0.363638 | 0.181819 | − | 0.983332i | \(-0.441801\pi\) | ||||
0.181819 | + | 0.983332i | \(0.441801\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −9314.82 | −1.02669 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −5135.23 | −0.562131 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 12192.7 | 1.32557 | 0.662787 | − | 0.748808i | \(-0.269373\pi\) | ||||
0.662787 | + | 0.748808i | \(0.269373\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 4878.04 | 0.526729 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −101.632 | −0.0108999 | −0.00544997 | − | 0.999985i | \(-0.501735\pi\) | ||||
−0.00544997 | + | 0.999985i | \(0.501735\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 948.099 | 0.100998 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −9237.99 | −0.977499 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −7096.37 | −0.745876 | −0.372938 | − | 0.927856i | \(-0.621650\pi\) | ||||
−0.372938 | + | 0.927856i | \(0.621650\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −3704.48 | −0.386779 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 1616.31 | 0.167639 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −44409.6 | −4.57573 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −7377.47 | −0.755150 | −0.377575 | − | 0.925979i | \(-0.623242\pi\) | ||||
−0.377575 | + | 0.925979i | \(0.623242\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 841.482 | 0.0855709 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −13627.7 | −1.37680 | −0.688398 | − | 0.725333i | \(-0.741686\pi\) | ||||
−0.688398 | + | 0.725333i | \(0.741686\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −2160.46 | −0.216858 | −0.108429 | − | 0.994104i | \(-0.534582\pi\) | ||||
−0.108429 | + | 0.994104i | \(0.534582\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 15103.2 | 1.50623 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −2242.53 | −0.222209 | −0.111105 | − | 0.993809i | \(-0.535439\pi\) | ||||
−0.111105 | + | 0.993809i | \(0.535439\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −17155.2 | −1.68903 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −1760.53 | −0.172231 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 2907.15 | 0.282602 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −19792.1 | −1.91184 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −5550.63 | −0.532801 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −2155.89 | −0.205648 | −0.102824 | − | 0.994700i | \(-0.532788\pi\) | ||||
−0.102824 | + | 0.994700i | \(0.532788\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −12652.1 | −1.19935 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 5101.90 | 0.480630 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −12605.6 | −1.18019 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 4911.41 | 0.456996 | 0.228498 | − | 0.973544i | \(-0.426619\pi\) | ||||
0.228498 | + | 0.973544i | \(0.426619\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −1757.49 | −0.162529 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −3840.06 | −0.352952 | −0.176476 | − | 0.984305i | \(-0.556470\pi\) | ||||
−0.176476 | + | 0.984305i | \(0.556470\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 5207.37 | 0.475717 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −1532.99 | −0.139197 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −9078.39 | −0.819359 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −10463.4 | −0.938687 | −0.469343 | − | 0.883016i | \(-0.655509\pi\) | ||||
−0.469343 | + | 0.883016i | \(0.655509\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 7108.08 | 0.633863 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −2238.90 | −0.198464 | −0.0992321 | − | 0.995064i | \(-0.531639\pi\) | ||||
−0.0992321 | + | 0.995064i | \(0.531639\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −24806.6 | −2.18590 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −12768.7 | −1.11850 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 7481.43 | 0.651490 | 0.325745 | − | 0.945458i | \(-0.394385\pi\) | ||||
0.325745 | + | 0.945458i | \(0.394385\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 5919.70 | 0.512470 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 2425.41 | 0.208742 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 16747.6 | 1.43298 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −578.908 | −0.0492463 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 6989.52 | 0.591148 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 2231.61 | 0.187656 | 0.0938278 | − | 0.995588i | \(-0.470090\pi\) | ||||
0.0938278 | + | 0.995588i | \(0.470090\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −11380.5 | −0.951499 | −0.475749 | − | 0.879581i | \(-0.657823\pi\) | ||||
−0.475749 | + | 0.879581i | \(0.657823\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 19663.6 | 1.63465 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −8443.34 | −0.697908 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −8899.05 | −0.731409 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −1241.93 | −0.101497 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 32466.5 | 2.63843 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 11255.4 | 0.909560 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 953.929 | 0.0766575 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 4968.01 | 0.397008 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 2751.65 | 0.218674 | 0.109337 | − | 0.994005i | \(-0.465127\pi\) | ||||
0.109337 | + | 0.994005i | \(0.465127\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −472.197 | −0.0373184 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 7445.40 | 0.585185 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 20617.0 | 1.61155 | 0.805776 | − | 0.592220i | \(-0.201748\pi\) | ||||
0.805776 | + | 0.592220i | \(0.201748\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −1801.53 | −0.140050 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 15009.3 | 1.16046 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −9982.68 | −0.767643 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 8780.36 | 0.671542 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −12165.3 | −0.925420 | −0.462710 | − | 0.886510i | \(-0.653123\pi\) | ||||
−0.462710 | + | 0.886510i | \(0.653123\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −25478.6 | −1.92778 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 857.004 | 0.0644969 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −19095.1 | −1.42942 | −0.714708 | − | 0.699423i | \(-0.753440\pi\) | ||||
−0.714708 | + | 0.699423i | \(0.753440\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 26814.5 | 1.99663 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −2409.67 | −0.178477 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −18354.4 | −1.35229 | −0.676146 | − | 0.736767i | \(-0.736351\pi\) | ||||
−0.676146 | + | 0.736767i | \(0.736351\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −7264.64 | −0.532427 | −0.266213 | − | 0.963914i | \(-0.585773\pi\) | ||||
−0.266213 | + | 0.963914i | \(0.585773\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −1910.18 | −0.139265 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 12595.3 | 0.913495 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −4303.73 | −0.310514 | −0.155257 | − | 0.987874i | \(-0.549621\pi\) | ||||
−0.155257 | + | 0.987874i | \(0.549621\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 4034.80 | 0.289604 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 29197.9 | 2.08491 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −5653.02 | −0.401585 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 13435.3 | 0.949540 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −23123.2 | −1.62589 | −0.812943 | − | 0.582343i | \(-0.802136\pi\) | ||||
−0.812943 | + | 0.582343i | \(0.802136\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −24336.3 | −1.70248 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 3205.10 | 0.223080 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −15038.9 | −1.04144 | −0.520721 | − | 0.853727i | \(-0.674337\pi\) | ||||
−0.520721 | + | 0.853727i | \(0.674337\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −17229.4 | −1.18712 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 4612.81 | 0.316231 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −26909.4 | −1.83554 | −0.917769 | − | 0.397114i | \(-0.870012\pi\) | ||||
−0.917769 | + | 0.397114i | \(0.870012\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 9863.37 | 0.669443 | 0.334721 | − | 0.942317i | \(-0.391358\pi\) | ||||
0.334721 | + | 0.942317i | \(0.391358\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 5189.98 | 0.350501 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 23172.7 | 1.55720 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 17169.9 | 1.14812 | 0.574058 | − | 0.818815i | \(-0.305369\pi\) | ||||
0.574058 | + | 0.818815i | \(0.305369\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −14911.8 | −0.992214 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 5073.62 | 0.335936 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 6302.75 | 0.415279 | 0.207639 | − | 0.978205i | \(-0.433422\pi\) | ||||
0.207639 | + | 0.978205i | \(0.433422\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −22531.2 | −1.47731 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 24410.8 | 1.59277 | 0.796386 | − | 0.604789i | \(-0.206742\pi\) | ||||
0.796386 | + | 0.604789i | \(0.206742\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −16981.9 | −1.10268 | −0.551340 | − | 0.834280i | \(-0.685883\pi\) | ||||
−0.551340 | + | 0.834280i | \(0.685883\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −1543.48 | −0.0997388 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 1517.79 | 0.0976064 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 5378.45 | 0.344221 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 2470.15 | 0.157334 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −4908.59 | −0.311158 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 4791.04 | 0.302264 | 0.151132 | − | 0.988514i | \(-0.451708\pi\) | ||||
0.151132 | + | 0.988514i | \(0.451708\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −16867.7 | −1.05913 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 45278.4 | 2.82964 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −43540.3 | −2.70821 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 2746.49 | 0.170031 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 31537.4 | 1.94329 | 0.971647 | − | 0.236435i | \(-0.0759790\pi\) | ||||
0.971647 | + | 0.236435i | \(0.0759790\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −13428.9 | −0.823617 | −0.411809 | − | 0.911270i | \(-0.635103\pi\) | ||||
−0.411809 | + | 0.911270i | \(0.635103\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 17681.7 | 1.07940 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 1108.75 | 0.0673719 | 0.0336859 | − | 0.999432i | \(-0.489275\pi\) | ||||
0.0336859 | + | 0.999432i | \(0.489275\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −1264.84 | −0.0765011 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 24178.4 | 1.45564 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −9563.52 | −0.573123 | −0.286562 | − | 0.958062i | \(-0.592512\pi\) | ||||
−0.286562 | + | 0.958062i | \(0.592512\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −18284.8 | −1.09076 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −1790.89 | −0.106346 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 7239.84 | 0.427957 | 0.213979 | − | 0.976838i | \(-0.431358\pi\) | ||||
0.213979 | + | 0.976838i | \(0.431358\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −3653.77 | −0.215001 | −0.107500 | − | 0.994205i | \(-0.534285\pi\) | ||||
−0.107500 | + | 0.994205i | \(0.534285\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −7510.89 | −0.439968 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −49660.4 | −2.89586 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −9551.58 | −0.554481 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −13762.0 | −0.795319 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −1834.76 | −0.105559 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −2498.60 | −0.143111 | −0.0715557 | − | 0.997437i | \(-0.522796\pi\) | ||||
−0.0715557 | + | 0.997437i | \(0.522796\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −5948.86 | −0.339217 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 4198.61 | 0.238354 | 0.119177 | − | 0.992873i | \(-0.461974\pi\) | ||||
0.119177 | + | 0.992873i | \(0.461974\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −20179.9 | −1.14055 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −1466.62 | −0.0825272 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −22374.1 | −1.25347 | −0.626737 | − | 0.779231i | \(-0.715610\pi\) | ||||
−0.626737 | + | 0.779231i | \(0.715610\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 11766.9 | 0.656334 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −12950.7 | −0.719212 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 49543.7 | 2.73943 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 27217.7 | 1.49842 | 0.749212 | − | 0.662330i | \(-0.230432\pi\) | ||||
0.749212 | + | 0.662330i | \(0.230432\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −2454.12 | −0.134523 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 25284.1 | 1.37997 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 12595.9 | 0.684509 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 13774.9 | 0.745369 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 7516.46 | 0.404982 | 0.202491 | − | 0.979284i | \(-0.435096\pi\) | ||||
0.202491 | + | 0.979284i | \(0.435096\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −14148.1 | −0.759038 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −3521.00 | −0.188097 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −39712.2 | −2.11249 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −29538.0 | −1.56463 | −0.782314 | − | 0.622884i | \(-0.785961\pi\) | ||||
−0.782314 | + | 0.622884i | \(0.785961\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 3020.07 | 0.159299 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 15487.1 | 0.813461 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 13683.1 | 0.715692 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −19074.6 | −0.993519 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −1327.71 | −0.0688669 | −0.0344334 | − | 0.999407i | \(-0.510963\pi\) | ||||
−0.0344334 | + | 0.999407i | \(0.510963\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 26810.7 | 1.38486 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −9355.94 | −0.481260 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −36813.5 | −1.88582 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 13636.7 | 0.695678 | 0.347839 | − | 0.937554i | \(-0.386916\pi\) | ||||
0.347839 | + | 0.937554i | \(0.386916\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 729.000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −9884.80 | −0.500140 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 7587.21 | 0.382319 | 0.191160 | − | 0.981559i | \(-0.438775\pi\) | ||||
0.191160 | + | 0.981559i | \(0.438775\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 30216.2 | 1.51638 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 5285.71 | 0.264181 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −1550.27 | −0.0771686 | −0.0385843 | − | 0.999255i | \(-0.512285\pi\) | ||||
−0.0385843 | + | 0.999255i | \(0.512285\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −21648.7 | −1.07326 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 6931.44 | 0.342247 | 0.171124 | − | 0.985250i | \(-0.445260\pi\) | ||||
0.171124 | + | 0.985250i | \(0.445260\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −57223.2 | −2.81409 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −8833.27 | −0.432654 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 18018.5 | 0.879014 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 19674.1 | 0.955948 | 0.477974 | − | 0.878374i | \(-0.341371\pi\) | ||||
0.477974 | + | 0.878374i | \(0.341371\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 20564.1 | 0.995217 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 10011.9 | 0.482612 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 20509.6 | 0.984722 | 0.492361 | − | 0.870391i | \(-0.336134\pi\) | ||||
0.492361 | + | 0.870391i | \(0.336134\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −1571.95 | −0.0751756 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 10727.9 | 0.511018 | 0.255509 | − | 0.966807i | \(-0.417757\pi\) | ||||
0.255509 | + | 0.966807i | \(0.417757\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 11919.1 | 0.565533 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 5212.42 | 0.246347 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 11085.2 | 0.521855 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 13923.9 | 0.652935 | 0.326468 | − | 0.945208i | \(-0.394142\pi\) | ||||
0.326468 | + | 0.945208i | \(0.394142\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 704.087 | 0.0328885 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 16592.6 | 0.772051 | 0.386026 | − | 0.922488i | \(-0.373848\pi\) | ||||
0.386026 | + | 0.922488i | \(0.373848\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 59690.2 | 2.76663 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 14056.2 | 0.648989 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 36305.2 | 1.66979 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 2797.15 | 0.128156 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 4511.29 | 0.205901 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −10905.3 | −0.495830 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 28139.8 | 1.27455 | 0.637277 | − | 0.770635i | \(-0.280061\pi\) | ||||
0.637277 | + | 0.770635i | \(0.280061\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 17587.7 | 0.793587 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 42926.5 | 1.92957 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 16080.1 | 0.720075 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −34382.5 | −1.53386 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −12918.6 | −0.574156 | −0.287078 | − | 0.957907i | \(-0.592684\pi\) | ||||
−0.287078 | + | 0.957907i | \(0.592684\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1968.39 | 0.0871546 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −459.177 | −0.0202550 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −1823.93 | −0.0801557 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 31602.9 | 1.38367 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −4199.36 | −0.183178 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −28655.9 | −1.24535 | −0.622675 | − | 0.782481i | \(-0.713954\pi\) | ||||
−0.622675 | + | 0.782481i | \(0.713954\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 23687.0 | 1.02560 | 0.512802 | − | 0.858507i | \(-0.328608\pi\) | ||||
0.512802 | + | 0.858507i | \(0.328608\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 23783.6 | 1.02599 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −10886.5 | −0.467898 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −28491.0 | −1.22004 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 21508.2 | 0.917652 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −26268.3 | −1.11665 | −0.558326 | − | 0.829622i | \(-0.688556\pi\) | ||||
−0.558326 | + | 0.829622i | \(0.688556\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −17964.8 | −0.760893 | −0.380447 | − | 0.924803i | \(-0.624230\pi\) | ||||
−0.380447 | + | 0.924803i | \(0.624230\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −6058.59 | −0.255676 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 7957.87 | 0.334610 | 0.167305 | − | 0.985905i | \(-0.446494\pi\) | ||||
0.167305 | + | 0.985905i | \(0.446494\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −31973.7 | −1.33955 | −0.669777 | − | 0.742562i | \(-0.733610\pi\) | ||||
−0.669777 | + | 0.742562i | \(0.733610\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −3627.58 | −0.151431 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −16892.1 | −0.702613 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 44029.8 | 1.82481 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −7314.71 | −0.302071 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 13956.4 | 0.574289 | 0.287144 | − | 0.957887i | \(-0.407294\pi\) | ||||
0.287144 | + | 0.957887i | \(0.407294\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 3528.39 | 0.144671 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −26949.7 | −1.10107 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −79093.6 | −3.22000 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 37096.6 | 1.50490 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −6085.94 | −0.246018 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 9003.53 | 0.362676 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −30848.1 | −1.23824 | −0.619120 | − | 0.785296i | \(-0.712511\pi\) | ||||
−0.619120 | + | 0.785296i | \(0.712511\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 15023.8 | 0.600940 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 14292.3 | 0.569679 | 0.284839 | − | 0.958575i | \(-0.408060\pi\) | ||||
0.284839 | + | 0.958575i | \(0.408060\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −11549.7 | −0.458753 | −0.229377 | − | 0.973338i | \(-0.573669\pi\) | ||||
−0.229377 | + | 0.973338i | \(0.573669\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −36069.6 | −1.42770 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −29851.8 | −1.17748 | −0.588742 | − | 0.808321i | \(-0.700377\pi\) | ||||
−0.588742 | + | 0.808321i | \(0.700377\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 43295.4 | 1.70184 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 11825.0 | 0.463206 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 3075.78 | 0.120067 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −46324.6 | −1.80212 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 6105.06 | 0.236684 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 52699.9 | 2.03609 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 40261.8 | 1.55022 | 0.775110 | − | 0.631826i | \(-0.217694\pi\) | ||||
0.775110 | + | 0.631826i | \(0.217694\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 44.4715 | 0.00170647 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 2868.85 | 0.109709 | 0.0548546 | − | 0.998494i | \(-0.482530\pi\) | ||||
0.0548546 | + | 0.998494i | \(0.482530\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −697.808 | −0.0265947 | −0.0132973 | − | 0.999912i | \(-0.504233\pi\) | ||||
−0.0132973 | + | 0.999912i | \(0.504233\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −7692.93 | −0.292198 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −43009.9 | −1.62811 | −0.814054 | − | 0.580789i | \(-0.802744\pi\) | ||||
−0.814054 | + | 0.580789i | \(0.802744\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 72485.0 | 2.73461 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 742.447 | 0.0279157 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 5673.50 | 0.212605 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 5908.96 | 0.220687 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 13776.8 | 0.512813 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −45265.8 | −1.67931 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 19221.2 | 0.710713 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 28306.1 | 1.04316 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −2924.95 | −0.107435 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 13107.8 | 0.479867 | 0.239933 | − | 0.970789i | \(-0.422874\pi\) | ||||
0.239933 | + | 0.970789i | \(0.422874\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 12014.2 | 0.438377 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −24893.1 | −0.905320 | −0.452660 | − | 0.891683i | \(-0.649525\pi\) | ||||
−0.452660 | + | 0.891683i | \(0.649525\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −8996.20 | −0.326102 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −11159.3 | −0.403185 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −29271.6 | −1.05413 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −4809.81 | −0.172645 | −0.0863225 | − | 0.996267i | \(-0.527512\pi\) | ||||
−0.0863225 | + | 0.996267i | \(0.527512\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −16793.6 | −0.600835 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −24514.6 | −0.874223 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 34701.2 | 1.23348 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −8111.08 | −0.287382 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −32589.2 | −1.15093 | −0.575466 | − | 0.817826i | \(-0.695179\pi\) | ||||
−0.575466 | + | 0.817826i | \(0.695179\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −48688.2 | −1.71396 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −19810.5 | −0.695141 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 5308.57 | 0.185678 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 38928.7 | 1.35725 | 0.678627 | − | 0.734483i | \(-0.262575\pi\) | ||||
0.678627 | + | 0.734483i | \(0.262575\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −18104.8 | −0.629209 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −34383.5 | −1.19115 | −0.595574 | − | 0.803301i | \(-0.703075\pi\) | ||||
−0.595574 | + | 0.803301i | \(0.703075\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −23103.9 | −0.797843 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −14926.3 | −0.513812 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 32211.3 | 1.10531 | 0.552653 | − | 0.833411i | \(-0.313615\pi\) | ||||
0.552653 | + | 0.833411i | \(0.313615\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 15985.1 | 0.546785 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −12452.6 | −0.424610 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 20860.0 | 0.709046 | 0.354523 | − | 0.935047i | \(-0.384643\pi\) | ||||
0.354523 | + | 0.935047i | \(0.384643\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −11832.3 | −0.400926 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 4594.51 | 0.155193 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 18837.2 | 0.634292 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 43604.0 | 1.46366 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −5451.15 | −0.182410 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 24992.9 | 0.833730 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −41953.3 | −1.39517 | −0.697584 | − | 0.716503i | \(-0.745741\pi\) | ||||
−0.697584 | + | 0.716503i | \(0.745741\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −8398.93 | −0.278444 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 3032.34 | 0.100219 | 0.0501093 | − | 0.998744i | \(-0.484043\pi\) | ||||
0.0501093 | + | 0.998744i | \(0.484043\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 40476.5 | 1.33363 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 53098.2 | 1.74411 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −19012.9 | −0.622598 | −0.311299 | − | 0.950312i | \(-0.600764\pi\) | ||||
−0.311299 | + | 0.950312i | \(0.600764\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −467.647 | −0.0152667 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −3605.91 | −0.117357 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 22706.7 | 0.736756 | 0.368378 | − | 0.929676i | \(-0.379913\pi\) | ||||
0.368378 | + | 0.929676i | \(0.379913\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 19853.4 | 0.642217 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −5636.68 | −0.181781 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 18131.1 | 0.582948 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 9554.24 | 0.306257 | 0.153128 | − | 0.988206i | \(-0.451065\pi\) | ||||
0.153128 | + | 0.988206i | \(0.451065\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −16345.2 | −0.522356 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 28573.3 | 0.910386 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −15445.1 | −0.490623 | −0.245312 | − | 0.969444i | \(-0.578890\pi\) | ||||
−0.245312 | + | 0.969444i | \(0.578890\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −4252.45 | −0.134676 |
(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 | 384.4.a.i.1.1 | ✓ | 2 | |
3.2 | odd | 2 | 1152.4.a.x.1.2 | 2 | |||
4.3 | odd | 2 | 384.4.a.m.1.1 | yes | 2 | ||
8.3 | odd | 2 | 384.4.a.l.1.2 | yes | 2 | ||
8.5 | even | 2 | 384.4.a.p.1.2 | yes | 2 | ||
12.11 | even | 2 | 1152.4.a.w.1.2 | 2 | |||
16.3 | odd | 4 | 768.4.d.s.385.4 | 4 | |||
16.5 | even | 4 | 768.4.d.r.385.3 | 4 | |||
16.11 | odd | 4 | 768.4.d.s.385.1 | 4 | |||
16.13 | even | 4 | 768.4.d.r.385.2 | 4 | |||
24.5 | odd | 2 | 1152.4.a.n.1.1 | 2 | |||
24.11 | even | 2 | 1152.4.a.m.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
384.4.a.i.1.1 | ✓ | 2 | 1.1 | even | 1 | trivial | |
384.4.a.l.1.2 | yes | 2 | 8.3 | odd | 2 | ||
384.4.a.m.1.1 | yes | 2 | 4.3 | odd | 2 | ||
384.4.a.p.1.2 | yes | 2 | 8.5 | even | 2 | ||
768.4.d.r.385.2 | 4 | 16.13 | even | 4 | |||
768.4.d.r.385.3 | 4 | 16.5 | even | 4 | |||
768.4.d.s.385.1 | 4 | 16.11 | odd | 4 | |||
768.4.d.s.385.4 | 4 | 16.3 | odd | 4 | |||
1152.4.a.m.1.1 | 2 | 24.11 | even | 2 | |||
1152.4.a.n.1.1 | 2 | 24.5 | odd | 2 | |||
1152.4.a.w.1.2 | 2 | 12.11 | even | 2 | |||
1152.4.a.x.1.2 | 2 | 3.2 | odd | 2 |