Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2312,4,Mod(1,2312)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2312, 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("2312.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2312 = 2^{3} \cdot 17^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 2312.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: | \(136.412415933\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 95x^{6} + 756x^{4} - 1780x^{2} + 1152 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{13} \) |
Twist minimal: | no (minimal twist has level 136) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(2.20783\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2312.1 |
$q$-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 | ||||||||
\(3\) | −9.26065 | −1.78221 | −0.891107 | − | 0.453794i | \(-0.850070\pi\) | ||||
−0.891107 | + | 0.453794i | \(0.850070\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 16.4090 | 1.46766 | 0.733832 | − | 0.679331i | \(-0.237730\pi\) | ||||
0.733832 | + | 0.679331i | \(0.237730\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −34.5010 | −1.86288 | −0.931439 | − | 0.363898i | \(-0.881446\pi\) | ||||
−0.931439 | + | 0.363898i | \(0.881446\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 58.7597 | 2.17629 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −7.42843 | −0.203614 | −0.101807 | − | 0.994804i | \(-0.532462\pi\) | ||||
−0.101807 | + | 0.994804i | \(0.532462\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −42.0242 | −0.896571 | −0.448285 | − | 0.893890i | \(-0.647965\pi\) | ||||
−0.448285 | + | 0.893890i | \(0.647965\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −151.958 | −2.61569 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 0 | 0 | ||||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −59.9095 | −0.723378 | −0.361689 | − | 0.932299i | \(-0.617800\pi\) | ||||
−0.361689 | + | 0.932299i | \(0.617800\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 319.502 | 3.32005 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −49.4728 | −0.448513 | −0.224256 | − | 0.974530i | \(-0.571995\pi\) | ||||
−0.224256 | + | 0.974530i | \(0.571995\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 144.255 | 1.15404 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −294.116 | −2.09639 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −259.369 | −1.66081 | −0.830407 | − | 0.557157i | \(-0.811892\pi\) | ||||
−0.830407 | + | 0.557157i | \(0.811892\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −92.2215 | −0.534306 | −0.267153 | − | 0.963654i | \(-0.586083\pi\) | ||||
−0.267153 | + | 0.963654i | \(0.586083\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 68.7922 | 0.362884 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −566.126 | −2.73408 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 207.564 | 0.922252 | 0.461126 | − | 0.887335i | \(-0.347446\pi\) | ||||
0.461126 | + | 0.887335i | \(0.347446\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 389.172 | 1.59788 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −176.800 | −0.673454 | −0.336727 | − | 0.941602i | \(-0.609320\pi\) | ||||
−0.336727 | + | 0.941602i | \(0.609320\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 19.0809 | 0.0676700 | 0.0338350 | − | 0.999427i | \(-0.489228\pi\) | ||||
0.0338350 | + | 0.999427i | \(0.489228\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 964.188 | 3.19406 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 80.1389 | 0.248712 | 0.124356 | − | 0.992238i | \(-0.460314\pi\) | ||||
0.124356 | + | 0.992238i | \(0.460314\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 847.318 | 2.47031 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −319.869 | −0.829006 | −0.414503 | − | 0.910048i | \(-0.636045\pi\) | ||||
−0.414503 | + | 0.910048i | \(0.636045\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −121.893 | −0.298837 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 554.801 | 1.28921 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −11.0809 | −0.0244510 | −0.0122255 | − | 0.999925i | \(-0.503892\pi\) | ||||
−0.0122255 | + | 0.999925i | \(0.503892\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −712.648 | −1.49582 | −0.747912 | − | 0.663798i | \(-0.768943\pi\) | ||||
−0.747912 | + | 0.663798i | \(0.768943\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −2027.27 | −4.05415 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −689.575 | −1.31587 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 484.980 | 0.884325 | 0.442163 | − | 0.896935i | \(-0.354211\pi\) | ||||
0.442163 | + | 0.896935i | \(0.354211\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 458.150 | 0.799345 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −443.968 | −0.742103 | −0.371051 | − | 0.928612i | \(-0.621003\pi\) | ||||
−0.371051 | + | 0.928612i | \(0.621003\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 337.468 | 0.541063 | 0.270531 | − | 0.962711i | \(-0.412801\pi\) | ||||
0.270531 | + | 0.962711i | \(0.412801\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −1335.89 | −2.05674 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 256.288 | 0.379309 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −840.905 | −1.19759 | −0.598793 | − | 0.800904i | \(-0.704353\pi\) | ||||
−0.598793 | + | 0.800904i | \(0.704353\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1137.19 | 1.55993 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −456.004 | −0.603047 | −0.301524 | − | 0.953459i | \(-0.597495\pi\) | ||||
−0.301524 | + | 0.953459i | \(0.597495\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 2401.93 | 2.95993 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −1205.43 | −1.43568 | −0.717841 | − | 0.696207i | \(-0.754870\pi\) | ||||
−0.717841 | + | 0.696207i | \(0.754870\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1449.88 | 1.67020 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 854.032 | 0.952247 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −983.055 | −1.06168 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −638.484 | −0.668332 | −0.334166 | − | 0.942514i | \(-0.608455\pi\) | ||||
−0.334166 | + | 0.942514i | \(0.608455\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −436.493 | −0.443123 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 739.395 | 0.728441 | 0.364220 | − | 0.931313i | \(-0.381335\pi\) | ||||
0.364220 | + | 0.931313i | \(0.381335\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1588.54 | 1.51965 | 0.759824 | − | 0.650129i | \(-0.225285\pi\) | ||||
0.759824 | + | 0.650129i | \(0.225285\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 5242.70 | 4.87271 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 202.298 | 0.182775 | 0.0913875 | − | 0.995815i | \(-0.470870\pi\) | ||||
0.0913875 | + | 0.995815i | \(0.470870\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1244.71 | −1.09378 | −0.546890 | − | 0.837204i | \(-0.684188\pi\) | ||||
−0.546890 | + | 0.837204i | \(0.684188\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −1922.18 | −1.64365 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1492.28 | 1.24232 | 0.621159 | − | 0.783685i | \(-0.286662\pi\) | ||||
0.621159 | + | 0.783685i | \(0.286662\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −811.798 | −0.658266 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −2469.33 | −1.95119 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1275.82 | −0.958541 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 1637.29 | 1.20024 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 315.954 | 0.226078 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −2054.49 | −1.43548 | −0.717741 | − | 0.696311i | \(-0.754824\pi\) | ||||
−0.717741 | + | 0.696311i | \(0.754824\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −176.702 | −0.120602 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −1892.72 | −1.26235 | −0.631175 | − | 0.775640i | \(-0.717427\pi\) | ||||
−0.631175 | + | 0.775640i | \(0.717427\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 2066.94 | 1.34757 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −4826.14 | −3.07680 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −848.618 | −0.529214 | −0.264607 | − | 0.964356i | \(-0.585242\pi\) | ||||
−0.264607 | + | 0.964356i | \(0.585242\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −20.6414 | −0.0125955 | −0.00629777 | − | 0.999980i | \(-0.502005\pi\) | ||||
−0.00629777 | + | 0.999980i | \(0.502005\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −742.139 | −0.443258 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 312.174 | 0.182555 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −4255.98 | −2.43752 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −7846.71 | −4.40263 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −1202.59 | −0.661206 | −0.330603 | − | 0.943770i | \(-0.607252\pi\) | ||||
−0.330603 | + | 0.943770i | \(0.607252\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 2080.77 | 1.12140 | 0.560698 | − | 0.828020i | \(-0.310533\pi\) | ||||
0.560698 | + | 0.828020i | \(0.310533\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −1513.26 | −0.784182 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1153.74 | 0.586486 | 0.293243 | − | 0.956038i | \(-0.405266\pi\) | ||||
0.293243 | + | 0.956038i | \(0.405266\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 2962.19 | 1.47747 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1706.86 | 0.835524 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −1461.35 | −0.702221 | −0.351110 | − | 0.936334i | \(-0.614196\pi\) | ||||
−0.351110 | + | 0.936334i | \(0.614196\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 1128.81 | 0.532592 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −4157.98 | −1.92667 | −0.963337 | − | 0.268296i | \(-0.913539\pi\) | ||||
−0.963337 | + | 0.268296i | \(0.913539\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −430.965 | −0.196160 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −3520.27 | −1.57428 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 2504.08 | 1.10047 | 0.550235 | − | 0.835010i | \(-0.314538\pi\) | ||||
0.550235 | + | 0.835010i | \(0.314538\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −4976.94 | −2.14983 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 102.616 | 0.0435769 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −839.685 | −0.350620 | −0.175310 | − | 0.984513i | \(-0.556093\pi\) | ||||
−0.175310 | + | 0.984513i | \(0.556093\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 500.491 | 0.205532 | 0.102766 | − | 0.994706i | \(-0.467231\pi\) | ||||
0.102766 | + | 0.994706i | \(0.467231\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 6599.59 | 2.66588 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 3405.92 | 1.35356 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 10147.3 | 3.90532 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 199.937 | 0.0757430 | 0.0378715 | − | 0.999283i | \(-0.487942\pi\) | ||||
0.0378715 | + | 0.999283i | \(0.487942\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −2758.52 | −1.02882 | −0.514411 | − | 0.857544i | \(-0.671989\pi\) | ||||
−0.514411 | + | 0.857544i | \(0.671989\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 6385.92 | 2.34515 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 3379.87 | 1.22236 | 0.611182 | − | 0.791490i | \(-0.290694\pi\) | ||||
0.611182 | + | 0.791490i | \(0.290694\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 2729.46 | 0.972293 | 0.486147 | − | 0.873877i | \(-0.338402\pi\) | ||||
0.486147 | + | 0.873877i | \(0.338402\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −4491.24 | −1.57606 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 8948.48 | 3.09389 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −2901.12 | −0.988404 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −2907.01 | −0.976092 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 445.034 | 0.147290 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −2149.01 | −0.701157 | −0.350579 | − | 0.936533i | \(-0.614015\pi\) | ||||
−0.350579 | + | 0.936533i | \(0.614015\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 4111.43 | 1.32259 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 313.098 | 0.0993168 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 3181.73 | 0.995346 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −3125.17 | −0.964290 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 115.665 | 0.0347332 | 0.0173666 | − | 0.999849i | \(-0.494472\pi\) | ||||
0.0173666 | + | 0.999849i | \(0.494472\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 8476.38 | 2.51152 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 150.739 | 0.0440743 | 0.0220372 | − | 0.999757i | \(-0.492985\pi\) | ||||
0.0220372 | + | 0.999757i | \(0.492985\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 252.262 | 0.0727946 | 0.0363973 | − | 0.999337i | \(-0.488412\pi\) | ||||
0.0363973 | + | 0.999337i | \(0.488412\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −2373.40 | −0.676009 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −1025.45 | −0.288323 | −0.144161 | − | 0.989554i | \(-0.546048\pi\) | ||||
−0.144161 | + | 0.989554i | \(0.546048\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1315.00 | 0.365026 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 7787.33 | 2.13435 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 3803.45 | 1.02939 | 0.514696 | − | 0.857373i | \(-0.327905\pi\) | ||||
0.514696 | + | 0.857373i | \(0.327905\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −2073.99 | −0.554346 | −0.277173 | − | 0.960820i | \(-0.589397\pi\) | ||||
−0.277173 | + | 0.960820i | \(0.589397\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −2590.02 | −0.683743 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 13903.6 | 3.62559 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 2517.65 | 0.648560 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 4222.89 | 1.07476 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −1242.05 | −0.312341 | −0.156170 | − | 0.987730i | \(-0.549915\pi\) | ||||
−0.156170 | + | 0.987730i | \(0.549915\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 367.505 | 0.0913236 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −1469.82 | −0.356751 | −0.178375 | − | 0.983963i | \(-0.557084\pi\) | ||||
−0.178375 | + | 0.983963i | \(0.557084\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −7161.16 | −1.71804 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −15240.4 | −3.61441 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 4308.70 | 1.01021 | 0.505106 | − | 0.863057i | \(-0.331453\pi\) | ||||
0.505106 | + | 0.863057i | \(0.331453\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −5248.72 | −1.21670 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 11163.1 | 2.55869 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 3812.72 | 0.864184 | 0.432092 | − | 0.901830i | \(-0.357776\pi\) | ||||
0.432092 | + | 0.901830i | \(0.357776\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 2859.05 | 0.640868 | 0.320434 | − | 0.947271i | \(-0.396171\pi\) | ||||
0.320434 | + | 0.947271i | \(0.396171\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −13426.8 | −2.97666 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −1071.59 | −0.234979 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 5377.92 | 1.16653 | 0.583263 | − | 0.812283i | \(-0.301776\pi\) | ||||
0.583263 | + | 0.812283i | \(0.301776\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −5418.91 | −1.16280 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −1867.29 | −0.396418 | −0.198209 | − | 0.980160i | \(-0.563512\pi\) | ||||
−0.198209 | + | 0.980160i | \(0.563512\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 4296.76 | 0.902529 | 0.451265 | − | 0.892390i | \(-0.350973\pi\) | ||||
0.451265 | + | 0.892390i | \(0.350973\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 9103.73 | 1.89213 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 6099.79 | 1.25456 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 0 | 0 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 5912.78 | 1.19111 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 8816.10 | 1.75782 | 0.878911 | − | 0.476985i | \(-0.158270\pi\) | ||||
0.878911 | + | 0.476985i | \(0.158270\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −181.826 | −0.0358859 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 2184.82 | 0.426855 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 2079.06 | 0.402123 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −658.309 | −0.126061 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −6847.28 | −1.29824 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −11693.8 | −2.19537 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 6143.84 | 1.14217 | 0.571087 | − | 0.820890i | \(-0.306522\pi\) | ||||
0.571087 | + | 0.820890i | \(0.306522\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −14710.9 | −2.70834 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 7409.80 | 1.35103 | 0.675516 | − | 0.737345i | \(-0.263921\pi\) | ||||
0.675516 | + | 0.737345i | \(0.263921\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −9455.98 | −1.70761 | −0.853807 | − | 0.520589i | \(-0.825712\pi\) | ||||
−0.853807 | + | 0.520589i | \(0.825712\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −33265.4 | −5.95014 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −1045.23 | −0.185191 | −0.0925957 | − | 0.995704i | \(-0.529516\pi\) | ||||
−0.0925957 | + | 0.995704i | \(0.529516\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1926.71 | 0.338165 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −1873.42 | −0.325744 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −6062.20 | −1.03468 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 11526.9 | 1.94935 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −2764.87 | −0.463320 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 6370.04 | 1.05779 | 0.528896 | − | 0.848687i | \(-0.322606\pi\) | ||||
0.528896 | + | 0.848687i | \(0.322606\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 12196.4 | 2.00708 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 7958.04 | 1.29789 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 9216.37 | 1.48976 | 0.744878 | − | 0.667201i | \(-0.232508\pi\) | ||||
0.744878 | + | 0.667201i | \(0.232508\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −13819.5 | −2.21408 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 685.062 | 0.108792 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −17399.4 | −2.73901 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 7517.79 | 1.17317 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 7810.63 | 1.20835 | 0.604174 | − | 0.796852i | \(-0.293503\pi\) | ||||
0.604174 | + | 0.796852i | \(0.293503\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −8377.96 | −1.28499 | −0.642495 | − | 0.766290i | \(-0.722101\pi\) | ||||
−0.642495 | + | 0.766290i | \(0.722101\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 12360.0 | 1.87956 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 500.551 | 0.0754721 | 0.0377360 | − | 0.999288i | \(-0.487985\pi\) | ||||
0.0377360 | + | 0.999288i | \(0.487985\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −7285.06 | −1.08916 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 12643.0 | 1.85870 | 0.929351 | − | 0.369198i | \(-0.120368\pi\) | ||||
0.929351 | + | 0.369198i | \(0.120368\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −3269.85 | −0.476724 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 11814.9 | 1.70833 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 5537.50 | 0.794099 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 640.446 | 0.0910927 | 0.0455464 | − | 0.998962i | \(-0.485497\pi\) | ||||
0.0455464 | + | 0.998962i | \(0.485497\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −10388.7 | −1.46563 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 11035.8 | 1.54434 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −1138.01 | −0.157972 | −0.0789861 | − | 0.996876i | \(-0.525168\pi\) | ||||
−0.0789861 | + | 0.996876i | \(0.525168\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −2925.94 | −0.402920 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 10899.8 | 1.48904 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −12320.8 | −1.66987 | −0.834933 | − | 0.550352i | \(-0.814493\pi\) | ||||
−0.834933 | + | 0.550352i | \(0.814493\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 19025.9 | 2.55833 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 9934.77 | 1.32544 | 0.662719 | − | 0.748868i | \(-0.269402\pi\) | ||||
0.662719 | + | 0.748868i | \(0.269402\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 4205.43 | 0.556698 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 1121.19 | 0.147269 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −3323.46 | −0.433178 | −0.216589 | − | 0.976263i | \(-0.569493\pi\) | ||||
−0.216589 | + | 0.976263i | \(0.569493\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 17527.8 | 2.24978 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −13798.4 | −1.75765 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 3094.45 | 0.391199 | 0.195599 | − | 0.980684i | \(-0.437335\pi\) | ||||
0.195599 | + | 0.980684i | \(0.437335\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −19141.2 | −2.40165 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 6261.50 | 0.779761 | 0.389881 | − | 0.920865i | \(-0.372516\pi\) | ||||
0.389881 | + | 0.920865i | \(0.372516\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 3875.54 | 0.479043 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 18660.2 | 2.28946 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −1541.88 | −0.187784 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 13966.7 | 1.68853 | 0.844264 | − | 0.535927i | \(-0.180038\pi\) | ||||
0.844264 | + | 0.535927i | \(0.180038\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 7858.76 | 0.943172 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 382.302 | 0.0455492 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −7482.56 | −0.885071 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 191.153 | 0.0224479 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 6308.88 | 0.735582 | 0.367791 | − | 0.929908i | \(-0.380114\pi\) | ||||
0.367791 | + | 0.929908i | \(0.380114\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −3142.63 | −0.363806 | −0.181903 | − | 0.983317i | \(-0.558226\pi\) | ||||
−0.181903 | + | 0.983317i | \(0.558226\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 4708.94 | 0.541268 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 24587.1 | 2.78654 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −2890.94 | −0.325351 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −6900.34 | −0.771178 | −0.385589 | − | 0.922671i | \(-0.626002\pi\) | ||||
−0.385589 | + | 0.922671i | \(0.626002\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 15236.0 | 1.69098 | 0.845490 | − | 0.533991i | \(-0.179308\pi\) | ||||
0.845490 | + | 0.533991i | \(0.179308\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 39413.2 | 4.34418 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 2963.89 | 0.324444 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 9594.64 | 1.04311 | 0.521557 | − | 0.853216i | \(-0.325351\pi\) | ||||
0.521557 | + | 0.853216i | \(0.325351\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 49788.1 | 5.37611 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −3375.02 | −0.361968 | −0.180984 | − | 0.983486i | \(-0.557928\pi\) | ||||
−0.180984 | + | 0.983486i | \(0.557928\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −19780.0 | −2.10710 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 11136.7 | 1.17841 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 2918.05 | 0.306707 | 0.153354 | − | 0.988171i | \(-0.450993\pi\) | ||||
0.153354 | + | 0.988171i | \(0.450993\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1313.35 | 0.137125 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −19269.3 | −1.99857 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 23791.0 | 2.45130 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 3829.50 | 0.391983 | 0.195992 | − | 0.980606i | \(-0.437207\pi\) | ||||
0.195992 | + | 0.980606i | \(0.437207\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −6988.84 | −0.706080 | −0.353040 | − | 0.935608i | \(-0.614852\pi\) | ||||
−0.353040 | + | 0.935608i | \(0.614852\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 8669.67 | 0.870224 | 0.435112 | − | 0.900376i | \(-0.356709\pi\) | ||||
0.435112 | + | 0.900376i | \(0.356709\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 14013.8 | 1.39758 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −12728.0 | −1.26120 | −0.630600 | − | 0.776108i | \(-0.717191\pi\) | ||||
−0.630600 | + | 0.776108i | \(0.717191\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −16732.3 | −1.64739 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −10684.4 | −1.04524 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −141.741 | −0.0137786 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −8642.24 | −0.834807 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −18795.4 | −1.80415 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 13282.8 | 1.26703 | 0.633516 | − | 0.773730i | \(-0.281611\pi\) | ||||
0.633516 | + | 0.773730i | \(0.281611\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −8722.72 | −0.826864 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −15806.6 | −1.48908 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −10476.9 | −0.980888 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −5014.37 | −0.466577 | −0.233288 | − | 0.972408i | \(-0.574949\pi\) | ||||
−0.233288 | + | 0.972408i | \(0.574949\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 13533.1 | 1.25151 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −14518.4 | −1.33443 | −0.667217 | − | 0.744863i | \(-0.732515\pi\) | ||||
−0.667217 | + | 0.744863i | \(0.732515\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −7162.40 | −0.650356 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 15317.3 | 1.38245 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 18158.2 | 1.62901 | 0.814504 | − | 0.580158i | \(-0.197009\pi\) | ||||
0.814504 | + | 0.580158i | \(0.197009\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 38505.6 | 3.43374 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −12331.2 | −1.09309 | −0.546543 | − | 0.837431i | \(-0.684057\pi\) | ||||
−0.546543 | + | 0.837431i | \(0.684057\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 12132.7 | 1.06911 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 3991.01 | 0.349600 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −4051.78 | −0.352833 | −0.176417 | − | 0.984316i | \(-0.556451\pi\) | ||||
−0.176417 | + | 0.984316i | \(0.556451\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −11643.0 | −1.00793 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 17620.3 | 1.51648 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 26066.4 | 2.23033 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −595.307 | −0.0506413 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −23189.4 | −1.96127 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −6101.23 | −0.513052 | −0.256526 | − | 0.966537i | \(-0.582578\pi\) | ||||
−0.256526 | + | 0.966537i | \(0.582578\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −1233.70 | −0.103147 | −0.0515734 | − | 0.998669i | \(-0.516424\pi\) | ||||
−0.0515734 | + | 0.998669i | \(0.516424\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 46089.7 | 3.83146 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −9719.44 | −0.798836 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −651.110 | −0.0532124 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 7429.90 | 0.603799 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 3319.51 | 0.268252 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 7776.03 | 0.624880 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −6294.24 | −0.502991 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 8968.57 | 0.712734 | 0.356367 | − | 0.934346i | \(-0.384015\pi\) | ||||
0.356367 | + | 0.934346i | \(0.384015\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −4634.87 | −0.366301 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −20424.5 | −1.60530 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −7187.71 | −0.561836 | −0.280918 | − | 0.959732i | \(-0.590639\pi\) | ||||
−0.280918 | + | 0.959732i | \(0.590639\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −41875.0 | −3.25534 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 15538.7 | 1.20140 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 29012.0 | 2.23095 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −31541.0 | −2.41233 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 12502.2 | 0.951047 | 0.475524 | − | 0.879703i | \(-0.342259\pi\) | ||||
0.475524 | + | 0.879703i | \(0.342259\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −801.860 | −0.0606709 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −20391.1 | −1.52643 | −0.763216 | − | 0.646143i | \(-0.776381\pi\) | ||||
−0.763216 | + | 0.646143i | \(0.776381\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 24486.8 | 1.82331 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −39234.2 | −2.90597 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −3407.53 | −0.251057 | −0.125528 | − | 0.992090i | \(-0.540063\pi\) | ||||
−0.125528 | + | 0.992090i | \(0.540063\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −9682.41 | −0.709626 | −0.354813 | − | 0.934937i | \(-0.615455\pi\) | ||||
−0.354813 | + | 0.934937i | \(0.615455\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −1851.54 | −0.134990 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −7136.69 | −0.517601 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −10357.7 | −0.747309 | −0.373654 | − | 0.927568i | \(-0.621895\pi\) | ||||
−0.373654 | + | 0.927568i | \(0.621895\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 25545.7 | 1.83358 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 15732.6 | 1.12340 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 2376.12 | 0.168798 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −40519.2 | −2.86370 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 760.786 | 0.0534940 | 0.0267470 | − | 0.999642i | \(-0.491485\pi\) | ||||
0.0267470 | + | 0.999642i | \(0.491485\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 5524.95 | 0.386505 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −31299.8 | −2.17851 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −23861.5 | −1.65241 | −0.826203 | − | 0.563373i | \(-0.809503\pi\) | ||||
−0.826203 | + | 0.563373i | \(0.809503\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −25276.6 | −1.73283 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 40.2985 | 0.00274884 | 0.00137442 | − | 0.999999i | \(-0.499563\pi\) | ||||
0.00137442 | + | 0.999999i | \(0.499563\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 28351.4 | 1.92426 | 0.962129 | − | 0.272594i | \(-0.0878815\pi\) | ||||
0.962129 | + | 0.272594i | \(0.0878815\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 28497.3 | 1.92454 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −20934.9 | −1.40682 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 380.879 | 0.0254686 | 0.0127343 | − | 0.999919i | \(-0.495946\pi\) | ||||
0.0127343 | + | 0.999919i | \(0.495946\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −82868.8 | −5.51398 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −3367.78 | −0.222988 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −18449.5 | −1.21561 | −0.607804 | − | 0.794087i | \(-0.707949\pi\) | ||||
−0.607804 | + | 0.794087i | \(0.707949\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 26866.2 | 1.76155 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 13692.2 | 0.893397 | 0.446698 | − | 0.894685i | \(-0.352600\pi\) | ||||
0.446698 | + | 0.894685i | \(0.352600\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 15000.2 | 0.974004 | 0.487002 | − | 0.873401i | \(-0.338090\pi\) | ||||
0.487002 | + | 0.873401i | \(0.338090\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 14550.7 | 0.940259 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 41588.7 | 2.67450 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −12847.4 | −0.822232 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −4121.31 | −0.262503 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 25659.3 | 1.61883 | 0.809413 | − | 0.587240i | \(-0.199785\pi\) | ||||
0.809413 | + | 0.587240i | \(0.199785\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 19901.3 | 1.24961 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −33712.0 | −2.10680 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −35607.9 | −2.21481 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −26087.4 | −1.61503 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 6709.60 | 0.413437 | 0.206719 | − | 0.978400i | \(-0.433722\pi\) | ||||
0.206719 | + | 0.978400i | \(0.433722\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −11976.4 | −0.734528 | −0.367264 | − | 0.930117i | \(-0.619705\pi\) | ||||
−0.367264 | + | 0.930117i | \(0.619705\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −2899.49 | −0.177004 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 21265.3 | 1.29215 | 0.646077 | − | 0.763272i | \(-0.276408\pi\) | ||||
0.646077 | + | 0.763272i | \(0.276408\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 82.3137 | 0.00497857 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −29464.9 | −1.77392 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 19671.9 | 1.17890 | 0.589449 | − | 0.807806i | \(-0.299345\pi\) | ||||
0.589449 | + | 0.807806i | \(0.299345\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −31057.6 | −1.85271 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 19829.5 | 1.17751 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −14782.6 | −0.873824 | −0.436912 | − | 0.899504i | \(-0.643928\pi\) | ||||
−0.436912 | + | 0.899504i | \(0.643928\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −27770.8 | −1.63413 | −0.817063 | − | 0.576548i | \(-0.804399\pi\) | ||||
−0.817063 | + | 0.576548i | \(0.804399\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 33916.4 | 1.97777 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 12831.7 | 0.744896 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −1071.14 | −0.0619021 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 5293.86 | 0.304571 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −21891.3 | −1.25386 | −0.626929 | − | 0.779077i | \(-0.715688\pi\) | ||||
−0.626929 | + | 0.779077i | \(0.715688\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −42427.6 | −2.41932 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −1946.42 | −0.110498 | −0.0552488 | − | 0.998473i | \(-0.517595\pi\) | ||||
−0.0552488 | + | 0.998473i | \(0.517595\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 22028.3 | 1.24502 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −1395.94 | −0.0785498 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 10516.5 | 0.589169 | 0.294584 | − | 0.955625i | \(-0.404819\pi\) | ||||
0.294584 | + | 0.955625i | \(0.404819\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −13925.0 | −0.776709 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −2336.12 | −0.129736 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 13442.2 | 0.743263 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −26695.9 | −1.46970 | −0.734848 | − | 0.678232i | \(-0.762747\pi\) | ||||
−0.734848 | + | 0.678232i | \(0.762747\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 15059.4 | 0.825484 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −338.704 | −0.0184860 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 9496.30 | 0.513853 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −22317.0 | −1.20243 | −0.601214 | − | 0.799088i | \(-0.705316\pi\) | ||||
−0.601214 | + | 0.799088i | \(0.705316\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −12435.1 | −0.667137 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −12177.7 | −0.650554 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −25509.8 | −1.35700 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −28249.7 | −1.49639 | −0.748196 | − | 0.663478i | \(-0.769080\pi\) | ||||
−0.748196 | + | 0.663478i | \(0.769080\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −49411.3 | −2.60629 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 4562.46 | 0.239643 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 5122.46 | 0.267929 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −35222.4 | −1.83460 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 30991.2 | 1.60748 | 0.803739 | − | 0.594982i | \(-0.202841\pi\) | ||||
0.803739 | + | 0.594982i | \(0.202841\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −54806.3 | −2.83092 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 19206.5 | 0.987963 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −37415.2 | −1.91664 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 13328.0 | 0.679929 | 0.339965 | − | 0.940438i | \(-0.389585\pi\) | ||||
0.339965 | + | 0.940438i | \(0.389585\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −6718.94 | −0.341358 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 27976.7 | 1.40974 | 0.704872 | − | 0.709334i | \(-0.251004\pi\) | ||||
0.704872 | + | 0.709334i | \(0.251004\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −128757. | −6.46158 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −3602.64 | −0.180061 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −33971.2 | −1.69100 | −0.845501 | − | 0.533974i | \(-0.820698\pi\) | ||||
−0.845501 | + | 0.533974i | \(0.820698\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −23315.1 | −1.15587 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −25922.4 | −1.27995 | −0.639974 | − | 0.768397i | \(-0.721055\pi\) | ||||
−0.639974 | + | 0.768397i | \(0.721055\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −19733.2 | −0.970428 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −26794.6 | −1.31240 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −6979.49 | −0.340488 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −18950.5 | −0.920792 | −0.460396 | − | 0.887714i | \(-0.652293\pi\) | ||||
−0.460396 | + | 0.887714i | \(0.652293\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 11502.2 | 0.556658 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 34143.4 | 1.64583 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 8184.07 | 0.392940 | 0.196470 | − | 0.980510i | \(-0.437052\pi\) | ||||
0.196470 | + | 0.980510i | \(0.437052\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −3403.34 | −0.162758 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −25803.9 | −1.22916 | −0.614579 | − | 0.788855i | \(-0.710674\pi\) | ||||
−0.614579 | + | 0.788855i | \(0.710674\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 42943.9 | 2.03758 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 465.666 | 0.0219221 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 5222.53 | 0.244901 | 0.122451 | − | 0.992475i | \(-0.460925\pi\) | ||||
0.122451 | + | 0.992475i | \(0.460925\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 13611.5 | 0.635806 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −32636.6 | −1.51857 | −0.759286 | − | 0.650757i | \(-0.774452\pi\) | ||||
−0.759286 | + | 0.650757i | \(0.774452\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −13303.4 | −0.616610 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 66317.0 | 3.06192 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 10592.0 | 0.487162 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 3297.99 | 0.151103 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 76284.5 | 3.48172 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 18931.7 | 0.860764 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −17014.8 | −0.770664 | −0.385332 | − | 0.922778i | \(-0.625913\pi\) | ||||
−0.385332 | + | 0.922778i | \(0.625913\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −39901.4 | −1.80042 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −51485.1 | −2.31429 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 29948.5 | 1.34111 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 48606.6 | 2.16842 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 20826.6 | 0.925616 | 0.462808 | − | 0.886458i | \(-0.346842\pi\) | ||||
0.462808 | + | 0.886458i | \(0.346842\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −70831.0 | −3.12446 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −2506.86 | −0.110168 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 28007.8 | 1.22627 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −35308.2 | −1.54016 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 8639.25 | 0.375451 | 0.187726 | − | 0.982222i | \(-0.439888\pi\) | ||||
0.187726 | + | 0.982222i | \(0.439888\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 22319.6 | 0.966397 | 0.483199 | − | 0.875511i | \(-0.339475\pi\) | ||||
0.483199 | + | 0.875511i | \(0.339475\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −26476.7 | −1.14216 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −23979.3 | −1.03062 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −1143.13 | −0.0489510 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 85194.4 | 3.63484 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 9361.94 | 0.397971 | 0.198985 | − | 0.980002i | \(-0.436235\pi\) | ||||
0.198985 | + | 0.980002i | \(0.436235\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 19128.8 | 0.810192 | 0.405096 | − | 0.914274i | \(-0.367238\pi\) | ||||
0.405096 | + | 0.914274i | \(0.367238\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 9923.61 | 0.418783 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 40640.9 | 1.70886 | 0.854428 | − | 0.519570i | \(-0.173908\pi\) | ||||
0.854428 | + | 0.519570i | \(0.173908\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −25220.3 | −1.05662 | −0.528310 | − | 0.849052i | \(-0.677174\pi\) | ||||
−0.528310 | + | 0.849052i | \(0.677174\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −49803.0 | −2.07900 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −68228.3 | −2.82771 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 27123.8 | 1.12011 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 4544.50 | 0.187001 | 0.0935004 | − | 0.995619i | \(-0.470194\pi\) | ||||
0.0935004 | + | 0.995619i | \(0.470194\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 42883.3 | 1.75830 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 17292.4 | 0.706501 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −7071.69 | −0.287898 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 44017.0 | 1.78565 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −39790.8 | −1.60850 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −10268.8 | −0.413641 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 22395.8 | 0.898964 | 0.449482 | − | 0.893289i | \(-0.351609\pi\) | ||||
0.449482 | + | 0.893289i | \(0.351609\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −57764.0 | −2.31051 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −5735.42 | −0.228610 | −0.114305 | − | 0.993446i | \(-0.536464\pi\) | ||||
−0.114305 | + | 0.993446i | \(0.536464\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 34718.6 | 1.37903 | 0.689513 | − | 0.724273i | \(-0.257825\pi\) | ||||
0.689513 | + | 0.724273i | \(0.257825\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −56488.0 | −2.23590 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −22239.9 | −0.877237 | −0.438619 | − | 0.898673i | \(-0.644532\pi\) | ||||
−0.438619 | + | 0.898673i | \(0.644532\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 41089.4 | 1.61512 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 6246.61 | 0.243845 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −20380.9 | −0.792860 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −37517.1 | −1.45448 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −10900.7 | −0.421156 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −10379.6 | −0.399650 | −0.199825 | − | 0.979832i | \(-0.564037\pi\) | ||||
−0.199825 | + | 0.979832i | \(0.564037\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −81642.9 | −3.13282 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 44934.3 | 1.71836 | 0.859181 | − | 0.511672i | \(-0.170974\pi\) | ||||
0.859181 | + | 0.511672i | \(0.170974\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −15846.0 | −0.603918 | −0.301959 | − | 0.953321i | \(-0.597640\pi\) | ||||
−0.301959 | + | 0.953321i | \(0.597640\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 1683.83 | 0.0639563 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −30415.0 | −1.15134 | −0.575669 | − | 0.817683i | \(-0.695258\pi\) | ||||
−0.575669 | + | 0.817683i | \(0.695258\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 70881.8 | 2.67413 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −8447.56 | −0.317625 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −4801.08 | −0.179913 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −13778.4 | −0.514593 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −19253.4 | −0.716670 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 23919.4 | 0.887382 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 6096.38 | 0.224667 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 8212.55 | 0.301651 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −7288.75 | −0.266835 | −0.133417 | − | 0.991060i | \(-0.542595\pi\) | ||||
−0.133417 | + | 0.991060i | \(0.542595\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 43446.6 | 1.58530 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −10232.6 | −0.372140 | −0.186070 | − | 0.982536i | \(-0.559575\pi\) | ||||
−0.186070 | + | 0.982536i | \(0.559575\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 3387.39 | 0.122789 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 108293. | 3.91261 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 65300.8 | 2.35160 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −26533.8 | −0.952415 | −0.476207 | − | 0.879333i | \(-0.657989\pi\) | ||||
−0.476207 | + | 0.879333i | \(0.657989\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −56895.9 | −2.03560 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 18657.4 | 0.665348 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 29942.1 | 1.06431 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 93342.3 | 3.30719 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 7037.69 | 0.248546 | 0.124273 | − | 0.992248i | \(-0.460340\pi\) | ||||
0.124273 | + | 0.992248i | \(0.460340\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −50762.4 | −1.78697 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −68619.6 | −2.40783 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −16895.0 | −0.589047 | −0.294523 | − | 0.955644i | \(-0.595161\pi\) | ||||
−0.294523 | + | 0.955644i | \(0.595161\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 87568.5 | 3.04333 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 51103.6 | 1.77038 | 0.885190 | − | 0.465229i | \(-0.154028\pi\) | ||||
0.885190 | + | 0.465229i | \(0.154028\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 8746.81 | 0.302052 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 166507. | 5.73170 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 22510.4 | 0.772429 | 0.386215 | − | 0.922409i | \(-0.373782\pi\) | ||||
0.386215 | + | 0.922409i | \(0.373782\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −14181.8 | −0.485101 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 9679.47 | 0.330051 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −4260.98 | −0.144834 | −0.0724169 | − | 0.997374i | \(-0.523071\pi\) | ||||
−0.0724169 | + | 0.997374i | \(0.523071\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 3280.76 | 0.111165 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −17842.5 | −0.602683 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 29278.1 | 0.985861 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −21286.2 | −0.714517 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 11887.0 | 0.397771 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −45264.5 | −1.50996 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −5646.95 | −0.187791 | −0.0938953 | − | 0.995582i | \(-0.529932\pi\) | ||||
−0.0938953 | + | 0.995582i | \(0.529932\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −3320.02 | −0.109726 | −0.0548632 | − | 0.998494i | \(-0.517472\pi\) | ||||
−0.0548632 | + | 0.998494i | \(0.517472\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 712.148 | 0.0234639 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 56140.0 | 1.84402 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 5821.02 | 0.190615 | 0.0953076 | − | 0.995448i | \(-0.469617\pi\) | ||||
0.0953076 | + | 0.995448i | \(0.469617\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 8954.49 | 0.292326 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −73139.1 | −2.38038 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 234.506 | 0.00760894 | 0.00380447 | − | 0.999993i | \(-0.498789\pi\) | ||||
0.00380447 | + | 0.999993i | \(0.498789\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 55460.3 | 1.79402 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 25604.5 | 0.825735 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −943.985 | −0.0303508 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 16708.2 | 0.535573 | 0.267787 | − | 0.963478i | \(-0.413708\pi\) | ||||
0.267787 | + | 0.963478i | \(0.413708\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −58990.8 | −1.88521 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 44787.7 | 1.42700 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −10281.9 | −0.326611 | −0.163305 | − | 0.986576i | \(-0.552216\pi\) | ||||
−0.163305 | + | 0.986576i | \(0.552216\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −61047.8 | −1.93340 |
(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 | 2312.4.a.k.1.1 | 8 | ||
17.4 | even | 4 | 136.4.b.b.33.8 | yes | 8 | ||
17.13 | even | 4 | 136.4.b.b.33.1 | ✓ | 8 | ||
17.16 | even | 2 | inner | 2312.4.a.k.1.8 | 8 | ||
51.38 | odd | 4 | 1224.4.c.e.577.7 | 8 | |||
51.47 | odd | 4 | 1224.4.c.e.577.2 | 8 | |||
68.47 | odd | 4 | 272.4.b.f.33.8 | 8 | |||
68.55 | odd | 4 | 272.4.b.f.33.1 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
136.4.b.b.33.1 | ✓ | 8 | 17.13 | even | 4 | ||
136.4.b.b.33.8 | yes | 8 | 17.4 | even | 4 | ||
272.4.b.f.33.1 | 8 | 68.55 | odd | 4 | |||
272.4.b.f.33.8 | 8 | 68.47 | odd | 4 | |||
1224.4.c.e.577.2 | 8 | 51.47 | odd | 4 | |||
1224.4.c.e.577.7 | 8 | 51.38 | odd | 4 | |||
2312.4.a.k.1.1 | 8 | 1.1 | even | 1 | trivial | ||
2312.4.a.k.1.8 | 8 | 17.16 | even | 2 | inner |