Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1088,4,Mod(1,1088)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1088, 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("1088.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1088 = 2^{6} \cdot 17 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1088.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: | \(64.1940780862\) |
Analytic rank: | \(0\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.2636.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - 14x - 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 17) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(-0.287410\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1088.1 |
$q$-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 | ||||||||
\(3\) | 7.62999 | 1.46839 | 0.734196 | − | 0.678938i | \(-0.237559\pi\) | ||||
0.734196 | + | 0.678938i | \(0.237559\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 11.9174 | 1.06592 | 0.532962 | − | 0.846139i | \(-0.321079\pi\) | ||||
0.532962 | + | 0.846139i | \(0.321079\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 26.1222 | 1.41047 | 0.705233 | − | 0.708975i | \(-0.250842\pi\) | ||||
0.705233 | + | 0.708975i | \(0.250842\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 31.2167 | 1.15617 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 3.24412 | 0.0889216 | 0.0444608 | − | 0.999011i | \(-0.485843\pi\) | ||||
0.0444608 | + | 0.999011i | \(0.485843\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 20.0515 | 0.427790 | 0.213895 | − | 0.976857i | \(-0.431385\pi\) | ||||
0.213895 | + | 0.976857i | \(0.431385\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 90.9296 | 1.56519 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −17.0000 | −0.242536 | ||||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −57.3466 | −0.692432 | −0.346216 | − | 0.938155i | \(-0.612534\pi\) | ||||
−0.346216 | + | 0.938155i | \(0.612534\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 199.312 | 2.07112 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 77.0438 | 0.698467 | 0.349233 | − | 0.937036i | \(-0.386442\pi\) | ||||
0.349233 | + | 0.937036i | \(0.386442\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 17.0243 | 0.136195 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 32.1732 | 0.229323 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 286.162 | 1.83238 | 0.916190 | − | 0.400744i | \(-0.131248\pi\) | ||||
0.916190 | + | 0.400744i | \(0.131248\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −8.54816 | −0.0495256 | −0.0247628 | − | 0.999693i | \(-0.507883\pi\) | ||||
−0.0247628 | + | 0.999693i | \(0.507883\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 24.7526 | 0.130572 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 311.309 | 1.50345 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −357.982 | −1.59059 | −0.795296 | − | 0.606221i | \(-0.792685\pi\) | ||||
−0.795296 | + | 0.606221i | \(0.792685\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 152.992 | 0.628164 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 194.467 | 0.740748 | 0.370374 | − | 0.928883i | \(-0.379230\pi\) | ||||
0.370374 | + | 0.928883i | \(0.379230\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 74.2619 | 0.263368 | 0.131684 | − | 0.991292i | \(-0.457962\pi\) | ||||
0.131684 | + | 0.991292i | \(0.457962\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 372.021 | 1.23239 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 23.6130 | 0.0732831 | 0.0366416 | − | 0.999328i | \(-0.488334\pi\) | ||||
0.0366416 | + | 0.999328i | \(0.488334\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 339.369 | 0.989415 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −129.710 | −0.356137 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −104.330 | −0.270393 | −0.135197 | − | 0.990819i | \(-0.543167\pi\) | ||||
−0.135197 | + | 0.990819i | \(0.543167\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 38.6614 | 0.0947837 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −437.553 | −1.01676 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −249.363 | −0.550243 | −0.275122 | − | 0.961409i | \(-0.588718\pi\) | ||||
−0.275122 | + | 0.961409i | \(0.588718\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 370.384 | 0.777424 | 0.388712 | − | 0.921359i | \(-0.372920\pi\) | ||||
0.388712 | + | 0.921359i | \(0.372920\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 815.448 | 1.63074 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 238.961 | 0.455992 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −939.650 | −1.71338 | −0.856691 | − | 0.515830i | \(-0.827483\pi\) | ||||
−0.856691 | + | 0.515830i | \(0.827483\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 587.843 | 1.02562 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −520.197 | −0.869522 | −0.434761 | − | 0.900546i | \(-0.643167\pi\) | ||||
−0.434761 | + | 0.900546i | \(0.643167\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 348.741 | 0.559137 | 0.279568 | − | 0.960126i | \(-0.409809\pi\) | ||||
0.279568 | + | 0.960126i | \(0.409809\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 129.895 | 0.199987 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 84.7434 | 0.125421 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −953.827 | −1.35840 | −0.679202 | − | 0.733951i | \(-0.737674\pi\) | ||||
−0.679202 | + | 0.733951i | \(0.737674\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −597.369 | −0.819437 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 1414.28 | 1.87033 | 0.935166 | − | 0.354211i | \(-0.115250\pi\) | ||||
0.935166 | + | 0.354211i | \(0.115250\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −202.596 | −0.258525 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 2183.41 | 2.69065 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −486.132 | −0.578987 | −0.289493 | − | 0.957180i | \(-0.593487\pi\) | ||||
−0.289493 | + | 0.957180i | \(0.593487\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 523.788 | 0.603384 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −65.2223 | −0.0727230 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −683.422 | −0.738080 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −685.281 | −0.717317 | −0.358659 | − | 0.933469i | \(-0.616766\pi\) | ||||
−0.358659 | + | 0.933469i | \(0.616766\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 101.271 | 0.102809 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −864.755 | −0.851944 | −0.425972 | − | 0.904736i | \(-0.640068\pi\) | ||||
−0.425972 | + | 0.904736i | \(0.640068\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1880.91 | 1.79933 | 0.899665 | − | 0.436580i | \(-0.143810\pi\) | ||||
0.899665 | + | 0.436580i | \(0.143810\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 2375.28 | 2.20765 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 32.8149 | 0.0296480 | 0.0148240 | − | 0.999890i | \(-0.495281\pi\) | ||||
0.0148240 | + | 0.999890i | \(0.495281\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −528.727 | −0.464613 | −0.232307 | − | 0.972643i | \(-0.574627\pi\) | ||||
−0.232307 | + | 0.972643i | \(0.574627\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −2731.40 | −2.33561 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 414.691 | 0.345229 | 0.172614 | − | 0.984989i | \(-0.444779\pi\) | ||||
0.172614 | + | 0.984989i | \(0.444779\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 918.161 | 0.744513 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 625.940 | 0.494600 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −444.077 | −0.342088 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1320.48 | −0.992093 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 1483.78 | 1.08771 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1286.79 | −0.920751 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 596.093 | 0.416494 | 0.208247 | − | 0.978076i | \(-0.433224\pi\) | ||||
0.208247 | + | 0.978076i | \(0.433224\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 566.617 | 0.386728 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −121.819 | −0.0812472 | −0.0406236 | − | 0.999175i | \(-0.512934\pi\) | ||||
−0.0406236 | + | 0.999175i | \(0.512934\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1498.02 | −0.976652 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 383.420 | 0.244441 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −897.365 | −0.559614 | −0.279807 | − | 0.960056i | \(-0.590270\pi\) | ||||
−0.279807 | + | 0.960056i | \(0.590270\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 2113.61 | 1.28974 | 0.644871 | − | 0.764292i | \(-0.276911\pi\) | ||||
0.644871 | + | 0.764292i | \(0.276911\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 180.167 | 0.107608 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 65.0493 | 0.0380398 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 3410.31 | 1.95318 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 2589.38 | 1.45285 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −2580.76 | −1.41895 | −0.709476 | − | 0.704729i | \(-0.751068\pi\) | ||||
−0.709476 | + | 0.704729i | \(0.751068\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1342.77 | 0.723662 | 0.361831 | − | 0.932244i | \(-0.382152\pi\) | ||||
0.361831 | + | 0.932244i | \(0.382152\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −530.683 | −0.280413 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −101.872 | −0.0527906 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 2495.82 | 1.26871 | 0.634357 | − | 0.773041i | \(-0.281265\pi\) | ||||
0.634357 | + | 0.773041i | \(0.281265\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −796.036 | −0.397043 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 2012.55 | 0.985164 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −1961.58 | −0.942595 | −0.471297 | − | 0.881974i | \(-0.656214\pi\) | ||||
−0.471297 | + | 0.881974i | \(0.656214\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 294.986 | 0.139180 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 2179.24 | 1.00979 | 0.504894 | − | 0.863182i | \(-0.331532\pi\) | ||||
0.504894 | + | 0.863182i | \(0.331532\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1794.94 | −0.816995 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −1790.17 | −0.800571 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −3111.45 | −1.36739 | −0.683697 | − | 0.729766i | \(-0.739629\pi\) | ||||
−0.683697 | + | 0.729766i | \(0.739629\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 444.713 | 0.192098 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −1902.64 | −0.807972 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −810.106 | −0.338269 | −0.169135 | − | 0.985593i | \(-0.554097\pi\) | ||||
−0.169135 | + | 0.985593i | \(0.554097\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 3356.23 | 1.37827 | 0.689134 | − | 0.724634i | \(-0.257991\pi\) | ||||
0.689134 | + | 0.724634i | \(0.257991\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 2826.03 | 1.14156 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −4266.22 | −1.69545 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −55.1500 | −0.0215667 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 840.434 | 0.323453 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 1338.41 | 0.507038 | 0.253519 | − | 0.967330i | \(-0.418412\pi\) | ||||
0.253519 | + | 0.967330i | \(0.418412\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −227.465 | −0.0848358 | −0.0424179 | − | 0.999100i | \(-0.513506\pi\) | ||||
−0.0424179 | + | 0.999100i | \(0.513506\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 1823.27 | 0.669575 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −815.549 | −0.294952 | −0.147476 | − | 0.989066i | \(-0.547115\pi\) | ||||
−0.147476 | + | 0.989066i | \(0.547115\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1866.90 | 0.665030 | 0.332515 | − | 0.943098i | \(-0.392103\pi\) | ||||
0.332515 | + | 0.943098i | \(0.392103\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −7169.52 | −2.51591 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 7475.19 | 2.58451 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 2317.54 | 0.789581 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 2405.05 | 0.807549 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −186.039 | −0.0615721 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1102.88 | 0.359836 | 0.179918 | − | 0.983682i | \(-0.442417\pi\) | ||||
0.179918 | + | 0.983682i | \(0.442417\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −3969.10 | −1.27680 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 885.008 | 0.280731 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −223.297 | −0.0698542 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 2660.89 | 0.821032 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −340.875 | −0.103754 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −568.848 | −0.170820 | −0.0854100 | − | 0.996346i | \(-0.527220\pi\) | ||||
−0.0854100 | + | 0.996346i | \(0.527220\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 531.442 | 0.157464 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −2106.99 | −0.616061 | −0.308030 | − | 0.951377i | \(-0.599670\pi\) | ||||
−0.308030 | + | 0.951377i | \(0.599670\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −4336.30 | −1.25131 | −0.625656 | − | 0.780099i | \(-0.715169\pi\) | ||||
−0.625656 | + | 0.780099i | \(0.715169\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 646.591 | 0.184167 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −4517.39 | −1.27014 | −0.635072 | − | 0.772453i | \(-0.719030\pi\) | ||||
−0.635072 | + | 0.772453i | \(0.719030\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 281.405 | 0.0781143 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −7277.69 | −1.99467 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 5300.88 | 1.43467 | 0.717333 | − | 0.696731i | \(-0.245363\pi\) | ||||
0.717333 | + | 0.696731i | \(0.245363\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1368.82 | −0.365864 | −0.182932 | − | 0.983126i | \(-0.558559\pi\) | ||||
−0.182932 | + | 0.983126i | \(0.558559\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −5426.60 | −1.43258 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 4044.40 | 1.05464 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1149.88 | −0.296216 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 10790.9 | 2.74638 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 5547.63 | 1.39507 | 0.697536 | − | 0.716549i | \(-0.254280\pi\) | ||||
0.697536 | + | 0.716549i | \(0.254280\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 249.939 | 0.0621088 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −1545.80 | −0.379615 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −193.949 | −0.0470748 | −0.0235374 | − | 0.999723i | \(-0.507493\pi\) | ||||
−0.0235374 | + | 0.999723i | \(0.507493\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −9351.29 | −2.24348 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 8933.04 | 2.11855 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −1345.63 | −0.315494 | −0.157747 | − | 0.987480i | \(-0.550423\pi\) | ||||
−0.157747 | + | 0.987480i | \(0.550423\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −1243.34 | −0.288218 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −3709.18 | −0.850180 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 3083.04 | 0.698797 | 0.349398 | − | 0.936974i | \(-0.386386\pi\) | ||||
0.349398 | + | 0.936974i | \(0.386386\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −422.163 | −0.0946294 | −0.0473147 | − | 0.998880i | \(-0.515066\pi\) | ||||
−0.0473147 | + | 0.998880i | \(0.515066\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 3996.50 | 0.886004 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 55.2288 | 0.0121106 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 8260.00 | 1.79168 | 0.895840 | − | 0.444377i | \(-0.146575\pi\) | ||||
0.895840 | + | 0.444377i | \(0.146575\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −266.845 | −0.0572602 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 3321.91 | 0.705226 | 0.352613 | − | 0.935769i | \(-0.385293\pi\) | ||||
0.352613 | + | 0.935769i | \(0.385293\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 7954.43 | 1.67082 | 0.835409 | − | 0.549629i | \(-0.185231\pi\) | ||||
0.835409 | + | 0.549629i | \(0.185231\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −5214.50 | −1.08379 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 5079.91 | 1.04480 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 289.000 | 0.0588235 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −5228.69 | −1.05330 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 1171.99 | 0.233681 | 0.116841 | − | 0.993151i | \(-0.462723\pi\) | ||||
0.116841 | + | 0.993151i | \(0.462723\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −2971.76 | −0.586517 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 104.374 | 0.0203918 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 1544.84 | 0.298798 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1939.88 | 0.371472 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −6598.07 | −1.25099 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 4414.01 | 0.828675 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −865.763 | −0.160950 | −0.0804751 | − | 0.996757i | \(-0.525644\pi\) | ||||
−0.0804751 | + | 0.996757i | \(0.525644\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 14351.3 | 2.64212 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 6994.83 | 1.27537 | 0.637685 | − | 0.770297i | \(-0.279892\pi\) | ||||
0.637685 | + | 0.770297i | \(0.279892\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 3442.33 | 0.621635 | 0.310818 | − | 0.950470i | \(-0.399397\pi\) | ||||
0.310818 | + | 0.950470i | \(0.399397\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 9718.02 | 1.73825 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −2066.15 | −0.366078 | −0.183039 | − | 0.983106i | \(-0.558593\pi\) | ||||
−0.183039 | + | 0.983106i | \(0.558593\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 928.344 | 0.162938 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 250.377 | 0.0435349 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 974.892 | 0.167939 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 341.362 | 0.0582627 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −4034.18 | −0.682234 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 616.823 | 0.103363 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −9027.44 | −1.49907 | −0.749536 | − | 0.661964i | \(-0.769723\pi\) | ||||
−0.749536 | + | 0.661964i | \(0.769723\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −11175.0 | −1.83900 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −11198.2 | −1.82633 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 204.309 | 0.0330250 | 0.0165125 | − | 0.999864i | \(-0.494744\pi\) | ||||
0.0165125 | + | 0.999864i | \(0.494744\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 3164.09 | 0.506931 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −27.7312 | −0.00440390 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −94.8397 | −0.0149296 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 7005.56 | 1.09324 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −143.063 | −0.0221326 | −0.0110663 | − | 0.999939i | \(-0.503523\pi\) | ||||
−0.0110663 | + | 0.999939i | \(0.503523\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 3998.42 | 0.613268 | 0.306634 | − | 0.951828i | \(-0.400797\pi\) | ||||
0.306634 | + | 0.951828i | \(0.400797\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 645.119 | 0.0981024 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −5809.57 | −0.875956 | −0.437978 | − | 0.898986i | \(-0.644305\pi\) | ||||
−0.437978 | + | 0.898986i | \(0.644305\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −6199.39 | −0.926844 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −3388.30 | −0.502320 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −4895.37 | −0.719687 | −0.359844 | − | 0.933013i | \(-0.617170\pi\) | ||||
−0.359844 | + | 0.933013i | \(0.617170\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −3570.37 | −0.520538 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −10075.2 | −1.45678 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 4156.08 | 0.595998 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 528.151 | 0.0751206 | 0.0375603 | − | 0.999294i | \(-0.488041\pi\) | ||||
0.0375603 | + | 0.999294i | \(0.488041\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 6070.62 | 0.856433 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −2725.33 | −0.381380 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 10113.5 | 1.40390 | 0.701950 | − | 0.712226i | \(-0.252313\pi\) | ||||
0.701950 | + | 0.712226i | \(0.252313\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −9818.18 | −1.35202 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 5737.98 | 0.783875 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −729.385 | −0.0988548 | −0.0494274 | − | 0.998778i | \(-0.515740\pi\) | ||||
−0.0494274 | + | 0.998778i | \(0.515740\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 4548.18 | 0.611576 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −1608.08 | −0.214540 | −0.107270 | − | 0.994230i | \(-0.534211\pi\) | ||||
−0.107270 | + | 0.994230i | \(0.534211\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 1009.92 | 0.133689 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 2318.21 | 0.304499 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −9824.09 | −1.28047 | −0.640233 | − | 0.768181i | \(-0.721162\pi\) | ||||
−0.640233 | + | 0.768181i | \(0.721162\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −1309.74 | −0.169403 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −929.478 | −0.119303 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −11367.1 | −1.44796 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −2876.88 | −0.363694 | −0.181847 | − | 0.983327i | \(-0.558208\pi\) | ||||
−0.181847 | + | 0.983327i | \(0.558208\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −11429.9 | −1.43411 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −6515.91 | −0.811444 | −0.405722 | − | 0.913996i | \(-0.632980\pi\) | ||||
−0.405722 | + | 0.913996i | \(0.632980\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −171.403 | −0.0211866 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −7119.09 | −0.873457 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −1161.34 | −0.141438 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −8870.10 | −1.07237 | −0.536183 | − | 0.844101i | \(-0.680134\pi\) | ||||
−0.536183 | + | 0.844101i | \(0.680134\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −6846.89 | −0.821732 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −6513.92 | −0.776099 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 16854.5 | 1.99363 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 16126.8 | 1.89385 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 1009.53 | 0.117706 | 0.0588531 | − | 0.998267i | \(-0.481256\pi\) | ||||
0.0588531 | + | 0.998267i | \(0.481256\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 3253.60 | 0.376652 | 0.188326 | − | 0.982107i | \(-0.439694\pi\) | ||||
0.188326 | + | 0.982107i | \(0.439694\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 737.119 | 0.0847280 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −289.413 | −0.0330320 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 9675.25 | 1.09653 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 496.325 | 0.0558573 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −2352.51 | −0.262915 | −0.131457 | − | 0.991322i | \(-0.541966\pi\) | ||||
−0.131457 | + | 0.991322i | \(0.541966\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −5860.51 | −0.650434 | −0.325217 | − | 0.945639i | \(-0.605437\pi\) | ||||
−0.325217 | + | 0.945639i | \(0.605437\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 26020.6 | 2.86803 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −4418.20 | −0.483641 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 2894.17 | 0.314650 | 0.157325 | − | 0.987547i | \(-0.449713\pi\) | ||||
0.157325 | + | 0.987547i | \(0.449713\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 10594.0 | 1.14394 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 8256.85 | 0.885541 | 0.442771 | − | 0.896635i | \(-0.353996\pi\) | ||||
0.442771 | + | 0.896635i | \(0.353996\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −5793.42 | −0.617156 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −19691.1 | −2.08358 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 15487.1 | 1.62779 | 0.813897 | − | 0.581009i | \(-0.197342\pi\) | ||||
0.813897 | + | 0.581009i | \(0.197342\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 630.874 | 0.0658685 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 10245.3 | 1.06262 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 6242.19 | 0.643162 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −16055.6 | −1.64343 | −0.821716 | − | 0.569897i | \(-0.806983\pi\) | ||||
−0.821716 | + | 0.569897i | \(0.806983\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −546.944 | −0.0556191 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −14064.0 | −1.42088 | −0.710440 | − | 0.703758i | \(-0.751504\pi\) | ||||
−0.710440 | + | 0.703758i | \(0.751504\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −8071.30 | −0.810162 | −0.405081 | − | 0.914281i | \(-0.632757\pi\) | ||||
−0.405081 | + | 0.914281i | \(0.632757\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −777.280 | −0.0775172 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −8582.41 | −0.850421 | −0.425211 | − | 0.905094i | \(-0.639800\pi\) | ||||
−0.425211 | + | 0.905094i | \(0.639800\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −24545.7 | −2.41667 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 19043.1 | 1.86297 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 240.914 | 0.0234191 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −976.286 | −0.0943054 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −3256.84 | −0.312621 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −6320.96 | −0.602948 | −0.301474 | − | 0.953474i | \(-0.597479\pi\) | ||||
−0.301474 | + | 0.953474i | \(0.597479\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −7178.07 | −0.680441 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 15355.8 | 1.44661 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −8166.77 | −0.764606 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 7336.47 | 0.682643 | 0.341321 | − | 0.939947i | \(-0.389126\pi\) | ||||
0.341321 | + | 0.939947i | \(0.389126\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −14966.8 | −1.38410 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −6672.53 | −0.613294 | −0.306647 | − | 0.951823i | \(-0.599207\pi\) | ||||
−0.306647 | + | 0.951823i | \(0.599207\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −4864.76 | −0.444417 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 1206.88 | 0.109586 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −13588.7 | −1.22643 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −17920.9 | −1.60772 | −0.803858 | − | 0.594821i | \(-0.797223\pi\) | ||||
−0.803858 | + | 0.594821i | \(0.797223\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 16627.6 | 1.48276 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −11325.3 | −1.00392 | −0.501959 | − | 0.864891i | \(-0.667387\pi\) | ||||
−0.501959 | + | 0.864891i | \(0.667387\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −10305.6 | −0.908108 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −13695.4 | −1.19967 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 8313.78 | 0.723972 | 0.361986 | − | 0.932184i | \(-0.382099\pi\) | ||||
0.361986 | + | 0.932184i | \(0.382099\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 9109.87 | 0.788644 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −1845.02 | −0.158791 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 22415.5 | 1.91795 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 76.6033 | 0.00651646 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −23740.3 | −2.00787 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 5121.64 | 0.430677 | 0.215339 | − | 0.976539i | \(-0.430914\pi\) | ||||
0.215339 | + | 0.976539i | \(0.430914\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −13378.5 | −1.11855 | −0.559275 | − | 0.828982i | \(-0.688920\pi\) | ||||
−0.559275 | + | 0.828982i | \(0.688920\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 3393.15 | 0.282075 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 145.319 | 0.0120117 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −6231.26 | −0.512144 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −7784.29 | −0.636176 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 3899.35 | 0.316885 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 391.068 | 0.0316025 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −6181.10 | −0.496712 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 1100.95 | 0.0879804 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −9906.81 | −0.787296 | −0.393648 | − | 0.919261i | \(-0.628787\pi\) | ||||
−0.393648 | + | 0.919261i | \(0.628787\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 25608.0 | 2.02384 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −6301.05 | −0.495243 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −16399.6 | −1.28189 | −0.640947 | − | 0.767585i | \(-0.721458\pi\) | ||||
−0.640947 | + | 0.767585i | \(0.721458\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 11562.2 | 0.898836 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −16410.4 | −1.26880 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −24916.1 | −1.91598 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −32551.2 | −2.48959 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −22044.3 | −1.67692 | −0.838461 | − | 0.544962i | \(-0.816544\pi\) | ||||
−0.838461 | + | 0.544962i | \(0.816544\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 1489.06 | 0.112666 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −420.793 | −0.0316683 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −12048.8 | −0.901947 | −0.450973 | − | 0.892537i | \(-0.648923\pi\) | ||||
−0.450973 | + | 0.892537i | \(0.648923\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 4942.04 | 0.367988 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −15604.6 | −1.15579 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −23785.4 | −1.75243 | −0.876217 | − | 0.481916i | \(-0.839941\pi\) | ||||
−0.876217 | + | 0.481916i | \(0.839941\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 10878.3 | 0.797271 | 0.398635 | − | 0.917110i | \(-0.369484\pi\) | ||||
0.398635 | + | 0.917110i | \(0.369484\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 10212.1 | 0.744531 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 1311.62 | 0.0951274 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 6315.86 | 0.455689 | 0.227845 | − | 0.973698i | \(-0.426832\pi\) | ||||
0.227845 | + | 0.973698i | \(0.426832\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −1735.56 | −0.124572 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 36944.1 | 2.63804 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −338.459 | −0.0240438 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 7459.58 | 0.527206 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −18192.1 | −1.27916 | −0.639581 | − | 0.768724i | \(-0.720892\pi\) | ||||
−0.639581 | + | 0.768724i | \(0.720892\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 490.207 | 0.0342931 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −6222.63 | −0.433104 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −9828.72 | −0.680636 | −0.340318 | − | 0.940310i | \(-0.610535\pi\) | ||||
−0.340318 | + | 0.940310i | \(0.610535\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −5292.25 | −0.364640 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 14244.4 | 0.976524 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 4662.57 | 0.318043 | 0.159021 | − | 0.987275i | \(-0.449166\pi\) | ||||
0.159021 | + | 0.987275i | \(0.449166\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 21658.6 | 1.47000 | 0.735001 | − | 0.678066i | \(-0.237182\pi\) | ||||
0.735001 | + | 0.678066i | \(0.237182\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −29332.8 | −1.98097 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −15736.6 | −1.05750 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 25764.7 | 1.72283 | 0.861415 | − | 0.507902i | \(-0.169579\pi\) | ||||
0.861415 | + | 0.507902i | \(0.169579\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 57035.6 | 3.79507 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 473.475 | 0.0313498 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −16018.1 | −1.05541 | −0.527705 | − | 0.849428i | \(-0.676947\pi\) | ||||
−0.527705 | + | 0.849428i | \(0.676947\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 17682.8 | 1.15941 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 22250.3 | 1.45180 | 0.725902 | − | 0.687798i | \(-0.241422\pi\) | ||||
0.725902 | + | 0.687798i | \(0.241422\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 3765.95 | 0.244534 | 0.122267 | − | 0.992497i | \(-0.460984\pi\) | ||||
0.122267 | + | 0.992497i | \(0.460984\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 2478.74 | 0.160175 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −12698.8 | −0.816642 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −17463.2 | −1.11765 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −1419.47 | −0.0904120 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 6085.70 | 0.385775 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −20806.5 | −1.31267 | −0.656334 | − | 0.754470i | \(-0.727894\pi\) | ||||
−0.656334 | + | 0.754470i | \(0.727894\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 8414.96 | 0.528380 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 7103.88 | 0.443951 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 6804.85 | 0.423262 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −16238.8 | −1.00532 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 2439.58 | 0.150324 | 0.0751620 | − | 0.997171i | \(-0.476053\pi\) | ||||
0.0751620 | + | 0.997171i | \(0.476053\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 19320.1 | 1.18493 | 0.592466 | − | 0.805595i | \(-0.298154\pi\) | ||||
0.592466 | + | 0.805595i | \(0.298154\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 6752.60 | 0.412222 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −14067.1 | −0.854766 | −0.427383 | − | 0.904071i | \(-0.640564\pi\) | ||||
−0.427383 | + | 0.904071i | \(0.640564\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −808.963 | −0.0489285 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −1703.75 | −0.102573 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −15893.7 | −0.952478 | −0.476239 | − | 0.879316i | \(-0.658000\pi\) | ||||
−0.476239 | + | 0.879316i | \(0.658000\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −1451.77 | −0.0866033 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 10886.5 | 0.646459 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 9653.54 | 0.570635 | 0.285318 | − | 0.958433i | \(-0.407901\pi\) | ||||
0.285318 | + | 0.958433i | \(0.407901\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −5389.06 | −0.317111 | −0.158555 | − | 0.987350i | \(-0.550684\pi\) | ||||
−0.158555 | + | 0.987350i | \(0.550684\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −2600.87 | −0.152352 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −17852.5 | −1.04104 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 22047.0 | 1.27986 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −4340.30 | −0.250831 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 1201.57 | 0.0691297 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −3032.18 | −0.173673 | −0.0868366 | − | 0.996223i | \(-0.527676\pi\) | ||||
−0.0868366 | + | 0.996223i | \(0.527676\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 547.726 | 0.0312326 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 22029.2 | 1.25059 | 0.625295 | − | 0.780388i | \(-0.284979\pi\) | ||||
0.625295 | + | 0.780388i | \(0.284979\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −17901.1 | −1.01175 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −16076.3 | −0.904618 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 9040.72 | 0.506491 | 0.253246 | − | 0.967402i | \(-0.418502\pi\) | ||||
0.253246 | + | 0.967402i | \(0.418502\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −10694.3 | −0.596506 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −33085.9 | −1.83742 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −2091.97 | −0.115672 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 22863.5 | 1.25871 | 0.629355 | − | 0.777118i | \(-0.283319\pi\) | ||||
0.629355 | + | 0.777118i | \(0.283319\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 2645.41 | 0.145008 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 25188.7 | 1.37477 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −3305.94 | −0.179658 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −34467.6 | −1.86507 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −1753.00 | −0.0944507 | −0.0472253 | − | 0.998884i | \(-0.515038\pi\) | ||||
−0.0472253 | + | 0.998884i | \(0.515038\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 20529.1 | 1.10138 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 2147.12 | 0.114702 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −22589.3 | −1.20164 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −11547.0 | −0.611645 | −0.305823 | − | 0.952089i | \(-0.598931\pi\) | ||||
−0.305823 | + | 0.952089i | \(0.598931\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −29775.3 | −1.57055 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −658.582 | −0.0345920 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 775.218 | 0.0405476 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 40445.6 | 2.10665 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −10289.8 | −0.533720 | −0.266860 | − | 0.963735i | \(-0.585986\pi\) | ||||
−0.266860 | + | 0.963735i | \(0.585986\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 49133.4 | 2.53790 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −10444.0 | −0.537231 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 4871.72 | 0.249560 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 2950.10 | 0.150499 | 0.0752497 | − | 0.997165i | \(-0.476025\pi\) | ||||
0.0752497 | + | 0.997165i | \(0.476025\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −25275.9 | −1.28415 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −1262.45 | −0.0638762 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −24348.2 | −1.22691 | −0.613453 | − | 0.789731i | \(-0.710220\pi\) | ||||
−0.613453 | + | 0.789731i | \(0.710220\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 30858.7 | 1.54863 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −3048.33 | −0.152357 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 29233.5 | 1.45517 | 0.727585 | − | 0.686017i | \(-0.240642\pi\) | ||||
0.727585 | + | 0.686017i | \(0.240642\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −8773.59 | −0.434961 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 15340.6 | 0.757457 | 0.378729 | − | 0.925508i | \(-0.376361\pi\) | ||||
0.378729 | + | 0.925508i | \(0.376361\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −30755.9 | −1.51250 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 44149.2 | 2.16243 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 857.197 | 0.0418175 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 39862.6 | 1.93689 | 0.968446 | − | 0.249223i | \(-0.0801752\pi\) | ||||
0.968446 | + | 0.249223i | \(0.0801752\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 42328.3 | 2.04851 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 16002.3 | 0.771369 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −26375.1 | −1.26634 | −0.633169 | − | 0.774013i | \(-0.718246\pi\) | ||||
−0.633169 | + | 0.774013i | \(0.718246\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 1907.03 | 0.0912000 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 7848.63 | 0.373867 | 0.186933 | − | 0.982373i | \(-0.440145\pi\) | ||||
0.186933 | + | 0.982373i | \(0.440145\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −13811.5 | −0.655322 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −6324.37 | −0.298899 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −5000.10 | −0.235389 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 31818.9 | 1.49209 | 0.746046 | − | 0.665895i | \(-0.231950\pi\) | ||||
0.746046 | + | 0.665895i | \(0.231950\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −1479.83 | −0.0691242 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 29559.8 | 1.37541 | 0.687706 | − | 0.725990i | \(-0.258618\pi\) | ||||
0.687706 | + | 0.725990i | \(0.258618\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −145.527 | −0.00674512 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −71350.2 | −3.29430 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −11152.0 | −0.512917 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −1687.58 | −0.0773193 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 9206.75 | 0.420208 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 29743.6 | 1.35235 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 28038.7 | 1.26998 | 0.634989 | − | 0.772521i | \(-0.281005\pi\) | ||||
0.634989 | + | 0.772521i | \(0.281005\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −10267.1 | −0.463269 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 10832.6 | 0.486934 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 7426.75 | 0.332574 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −9486.68 | −0.423217 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −5320.45 | −0.236462 | −0.118231 | − | 0.992986i | \(-0.537722\pi\) | ||||
−0.118231 | + | 0.992986i | \(0.537722\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −401.421 | −0.0177738 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −15175.4 | −0.669409 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 1131.35 | 0.0497194 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 23984.4 | 1.05011 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 23523.6 | 1.02611 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 30934.0 | 1.34435 | 0.672177 | − | 0.740390i | \(-0.265359\pi\) | ||||
0.672177 | + | 0.740390i | \(0.265359\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 40364.5 | 1.74771 | 0.873854 | − | 0.486189i | \(-0.161613\pi\) | ||||
0.873854 | + | 0.486189i | \(0.161613\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −3221.10 | −0.138953 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −23376.9 | −1.00473 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −4258.66 | −0.182364 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 16350.9 | 0.697616 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −19799.7 | −0.841672 | −0.420836 | − | 0.907137i | \(-0.638263\pi\) | ||||
−0.420836 | + | 0.907137i | \(0.638263\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 18756.4 | 0.794419 | 0.397210 | − | 0.917728i | \(-0.369979\pi\) | ||||
0.397210 | + | 0.917728i | \(0.369979\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 421.395 | 0.0177832 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −20958.0 | −0.881234 | −0.440617 | − | 0.897695i | \(-0.645240\pi\) | ||||
−0.440617 | + | 0.897695i | \(0.645240\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 31320.3 | 1.31218 | 0.656091 | − | 0.754682i | \(-0.272209\pi\) | ||||
0.656091 | + | 0.754682i | \(0.272209\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 63023.7 | 2.63089 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −5769.28 | −0.239968 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 25970.8 | 1.07636 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −275.021 | −0.0113574 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −30290.6 | −1.24642 | −0.623212 | − | 0.782053i | \(-0.714173\pi\) | ||||
−0.623212 | + | 0.782053i | \(0.714173\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 57499.9 | 2.35762 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 25346.1 | 1.03555 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −21391.0 | −0.870855 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −34493.7 | −1.39931 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 60692.2 | 2.45342 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −27580.3 | −1.11098 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 21111.8 | 0.847425 | 0.423712 | − | 0.905797i | \(-0.360727\pi\) | ||||
0.423712 | + | 0.905797i | \(0.360727\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −21334.2 | −0.853348 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −39983.0 | −1.59369 | −0.796845 | − | 0.604184i | \(-0.793499\pi\) | ||||
−0.796845 | + | 0.604184i | \(0.793499\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 39503.3 | 1.56907 | 0.784537 | − | 0.620082i | \(-0.212901\pi\) | ||||
0.784537 | + | 0.620082i | \(0.212901\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 38759.6 | 1.53418 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 26019.9 | 1.02634 | 0.513168 | − | 0.858288i | \(-0.328472\pi\) | ||||
0.513168 | + | 0.858288i | \(0.328472\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −37080.4 | −1.45754 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 2205.07 | 0.0863760 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −3094.33 | −0.120791 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −18841.4 | −0.732968 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −21392.2 | −0.829343 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −33613.8 | −1.29869 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −15038.3 | −0.579027 | −0.289514 | − | 0.957174i | \(-0.593494\pi\) | ||||
−0.289514 | + | 0.957174i | \(0.593494\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 8942.30 | 0.343136 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −18334.3 | −0.701133 | −0.350567 | − | 0.936538i | \(-0.614011\pi\) | ||||
−0.350567 | + | 0.936538i | \(0.614011\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −26659.5 | −1.01604 | −0.508020 | − | 0.861345i | \(-0.669622\pi\) | ||||
−0.508020 | + | 0.861345i | \(0.669622\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −22674.5 | −0.861237 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 11473.7 | 0.434327 | 0.217163 | − | 0.976135i | \(-0.430320\pi\) | ||||
0.217163 | + | 0.976135i | \(0.430320\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 15571.3 | 0.587450 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −1937.94 | −0.0728656 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −1354.12 | −0.0507436 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −9654.36 | −0.360569 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 11787.1 | 0.438752 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −2446.16 | −0.0907498 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1773.61 | 0.0655799 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 14801.3 | 0.545466 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 39997.5 | 1.46913 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 20361.6 | 0.745421 | 0.372710 | − | 0.927948i | \(-0.378429\pi\) | ||||
0.372710 | + | 0.927948i | \(0.378429\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −26994.8 | −0.984995 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −19261.9 | −0.700523 | −0.350262 | − | 0.936652i | \(-0.613907\pi\) | ||||
−0.350262 | + | 0.936652i | \(0.613907\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 4588.09 | 0.166313 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 33678.9 | 1.21682 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −3182.18 | −0.114596 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −21191.8 | −0.760666 | −0.380333 | − | 0.924850i | \(-0.624191\pi\) | ||||
−0.380333 | + | 0.924850i | \(0.624191\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −6605.76 | −0.236338 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −10430.7 | −0.371973 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −6094.40 | −0.216630 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 58715.6 | 2.08034 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 40815.0 | 1.44144 | 0.720719 | − | 0.693227i | \(-0.243812\pi\) | ||||
0.720719 | + | 0.693227i | \(0.243812\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −19461.7 | −0.685102 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 53370.4 | 1.87274 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −657.244 | −0.0229884 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −38439.1 | −1.34018 | −0.670092 | − | 0.742278i | \(-0.733745\pi\) | ||||
−0.670092 | + | 0.742278i | \(0.733745\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 26264.9 | 0.912804 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 2244.08 | 0.0777415 | 0.0388708 | − | 0.999244i | \(-0.487624\pi\) | ||||
0.0388708 | + | 0.999244i | \(0.487624\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 14982.5 | 0.517388 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 10015.8 | 0.344776 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 42289.0 | 1.45112 | 0.725559 | − | 0.688160i | \(-0.241581\pi\) | ||||
0.725559 | + | 0.688160i | \(0.241581\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 6992.76 | 0.239193 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −15764.7 | −0.537546 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 37426.2 | 1.27214 | 0.636072 | − | 0.771629i | \(-0.280558\pi\) | ||||
0.636072 | + | 0.771629i | \(0.280558\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 15950.4 | 0.540464 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 7083.25 | 0.239257 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −23441.2 | −0.789317 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −29717.9 | −0.997547 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 1024.37 | 0.0342782 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −2710.80 | −0.0904286 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 1088.56 | 0.0362003 | 0.0181001 | − | 0.999836i | \(-0.494238\pi\) | ||||
0.0181001 | + | 0.999836i | \(0.494238\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 7438.41 | 0.246601 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −39506.5 | −1.30569 | −0.652845 | − | 0.757491i | \(-0.726425\pi\) | ||||
−0.652845 | + | 0.757491i | \(0.726425\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 55212.1 | 1.81914 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 2604.59 | 0.0855525 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −43326.8 | −1.41878 | −0.709389 | − | 0.704817i | \(-0.751029\pi\) | ||||
−0.709389 | + | 0.704817i | \(0.751029\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −1577.07 | −0.0514845 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −16505.1 | −0.537174 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 10664.1 | 0.346014 | 0.173007 | − | 0.984921i | \(-0.444652\pi\) | ||||
0.173007 | + | 0.984921i | \(0.444652\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −9719.22 | −0.314396 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 4706.35 | 0.151778 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 5721.42 | 0.183954 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 15461.4 | 0.495609 | 0.247804 | − | 0.968810i | \(-0.420291\pi\) | ||||
0.247804 | + | 0.968810i | \(0.420291\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −68879.2 | −2.20122 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 22248.6 | 0.708871 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −46061.1 | −1.46316 | −0.731579 | − | 0.681756i | \(-0.761216\pi\) | ||||
−0.731579 | + | 0.681756i | \(0.761216\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −11517.4 | −0.364760 |
(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 | 1088.4.a.v.1.3 | 3 | ||
4.3 | odd | 2 | 1088.4.a.x.1.1 | 3 | |||
8.3 | odd | 2 | 272.4.a.h.1.3 | 3 | |||
8.5 | even | 2 | 17.4.a.b.1.3 | ✓ | 3 | ||
24.5 | odd | 2 | 153.4.a.g.1.1 | 3 | |||
24.11 | even | 2 | 2448.4.a.bi.1.3 | 3 | |||
40.13 | odd | 4 | 425.4.b.f.324.2 | 6 | |||
40.29 | even | 2 | 425.4.a.g.1.1 | 3 | |||
40.37 | odd | 4 | 425.4.b.f.324.5 | 6 | |||
56.13 | odd | 2 | 833.4.a.d.1.3 | 3 | |||
88.21 | odd | 2 | 2057.4.a.e.1.1 | 3 | |||
136.13 | even | 4 | 289.4.b.b.288.1 | 6 | |||
136.21 | even | 4 | 289.4.b.b.288.2 | 6 | |||
136.101 | even | 2 | 289.4.a.b.1.3 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
17.4.a.b.1.3 | ✓ | 3 | 8.5 | even | 2 | ||
153.4.a.g.1.1 | 3 | 24.5 | odd | 2 | |||
272.4.a.h.1.3 | 3 | 8.3 | odd | 2 | |||
289.4.a.b.1.3 | 3 | 136.101 | even | 2 | |||
289.4.b.b.288.1 | 6 | 136.13 | even | 4 | |||
289.4.b.b.288.2 | 6 | 136.21 | even | 4 | |||
425.4.a.g.1.1 | 3 | 40.29 | even | 2 | |||
425.4.b.f.324.2 | 6 | 40.13 | odd | 4 | |||
425.4.b.f.324.5 | 6 | 40.37 | odd | 4 | |||
833.4.a.d.1.3 | 3 | 56.13 | odd | 2 | |||
1088.4.a.v.1.3 | 3 | 1.1 | even | 1 | trivial | ||
1088.4.a.x.1.1 | 3 | 4.3 | odd | 2 | |||
2057.4.a.e.1.1 | 3 | 88.21 | odd | 2 | |||
2448.4.a.bi.1.3 | 3 | 24.11 | even | 2 |