Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1232,4,Mod(1,1232)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1232, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("1232.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1232 = 2^{4} \cdot 7 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1232.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: | \(72.6903531271\) |
Analytic rank: | \(1\) |
Dimension: | \(4\) |
Coefficient field: | 4.4.522072.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} - 12x^{2} + 5x + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 77) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(0.555307\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1232.1 |
$q$-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 | ||||||||
\(3\) | 5.49244 | 1.05702 | 0.528510 | − | 0.848927i | \(-0.322751\pi\) | ||||
0.528510 | + | 0.848927i | \(0.322751\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −16.0955 | −1.43962 | −0.719812 | − | 0.694169i | \(-0.755772\pi\) | ||||
−0.719812 | + | 0.694169i | \(0.755772\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 7.00000 | 0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 3.16692 | 0.117293 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 11.0000 | 0.301511 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 35.3712 | 0.754631 | 0.377316 | − | 0.926085i | \(-0.376847\pi\) | ||||
0.377316 | + | 0.926085i | \(0.376847\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −88.4036 | −1.52171 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 40.4757 | 0.577459 | 0.288730 | − | 0.957411i | \(-0.406767\pi\) | ||||
0.288730 | + | 0.957411i | \(0.406767\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −118.159 | −1.42672 | −0.713359 | − | 0.700799i | \(-0.752827\pi\) | ||||
−0.713359 | + | 0.700799i | \(0.752827\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 38.4471 | 0.399516 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 174.510 | 1.58208 | 0.791039 | − | 0.611766i | \(-0.209541\pi\) | ||||
0.791039 | + | 0.611766i | \(0.209541\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 134.065 | 1.07252 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −130.902 | −0.933040 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −262.725 | −1.68230 | −0.841152 | − | 0.540799i | \(-0.818122\pi\) | ||||
−0.841152 | + | 0.540799i | \(0.818122\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 36.1894 | 0.209671 | 0.104836 | − | 0.994490i | \(-0.466568\pi\) | ||||
0.104836 | + | 0.994490i | \(0.466568\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 60.4169 | 0.318704 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −112.668 | −0.544127 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 19.0464 | 0.0846274 | 0.0423137 | − | 0.999104i | \(-0.486527\pi\) | ||||
0.0423137 | + | 0.999104i | \(0.486527\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 194.274 | 0.797661 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 156.996 | 0.598017 | 0.299008 | − | 0.954250i | \(-0.403344\pi\) | ||||
0.299008 | + | 0.954250i | \(0.403344\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −287.182 | −1.01849 | −0.509243 | − | 0.860623i | \(-0.670074\pi\) | ||||
−0.509243 | + | 0.860623i | \(0.670074\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −50.9731 | −0.168858 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −397.244 | −1.23285 | −0.616425 | − | 0.787413i | \(-0.711420\pi\) | ||||
−0.616425 | + | 0.787413i | \(0.711420\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 49.0000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 222.311 | 0.610386 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 272.483 | 0.706196 | 0.353098 | − | 0.935586i | \(-0.385128\pi\) | ||||
0.353098 | + | 0.935586i | \(0.385128\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −177.050 | −0.434063 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −648.984 | −1.50807 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 507.466 | 1.11977 | 0.559885 | − | 0.828570i | \(-0.310845\pi\) | ||||
0.559885 | + | 0.828570i | \(0.310845\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 35.5608 | 0.0746409 | 0.0373205 | − | 0.999303i | \(-0.488118\pi\) | ||||
0.0373205 | + | 0.999303i | \(0.488118\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 22.1684 | 0.0443326 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −569.317 | −1.08639 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −979.229 | −1.78555 | −0.892775 | − | 0.450502i | \(-0.851245\pi\) | ||||
−0.892775 | + | 0.450502i | \(0.851245\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 958.484 | 1.67229 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −750.404 | −1.25432 | −0.627159 | − | 0.778891i | \(-0.715782\pi\) | ||||
−0.627159 | + | 0.778891i | \(0.715782\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 395.594 | 0.634257 | 0.317129 | − | 0.948383i | \(-0.397281\pi\) | ||||
0.317129 | + | 0.948383i | \(0.397281\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 736.344 | 1.13368 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 77.0000 | 0.113961 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 736.516 | 1.04892 | 0.524459 | − | 0.851436i | \(-0.324268\pi\) | ||||
0.524459 | + | 0.851436i | \(0.324268\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −804.477 | −1.10354 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −582.975 | −0.770962 | −0.385481 | − | 0.922716i | \(-0.625964\pi\) | ||||
−0.385481 | + | 0.922716i | \(0.625964\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −651.477 | −0.831325 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −1443.00 | −1.77823 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −806.201 | −0.960192 | −0.480096 | − | 0.877216i | \(-0.659398\pi\) | ||||
−0.480096 | + | 0.877216i | \(0.659398\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 247.598 | 0.285224 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 198.768 | 0.221627 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 1901.84 | 2.05394 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −957.232 | −1.00198 | −0.500991 | − | 0.865453i | \(-0.667031\pi\) | ||||
−0.500991 | + | 0.865453i | \(0.667031\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 34.8361 | 0.0353652 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −996.143 | −0.981386 | −0.490693 | − | 0.871333i | \(-0.663256\pi\) | ||||
−0.490693 | + | 0.871333i | \(0.663256\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1338.55 | −1.28050 | −0.640248 | − | 0.768169i | \(-0.721168\pi\) | ||||
−0.640248 | + | 0.768169i | \(0.721168\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −618.825 | −0.575154 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −1449.25 | −1.30939 | −0.654693 | − | 0.755895i | \(-0.727202\pi\) | ||||
−0.654693 | + | 0.755895i | \(0.727202\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −654.535 | −0.575166 | −0.287583 | − | 0.957756i | \(-0.592852\pi\) | ||||
−0.287583 | + | 0.957756i | \(0.592852\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 104.611 | 0.0894529 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −1160.63 | −0.966223 | −0.483111 | − | 0.875559i | \(-0.660493\pi\) | ||||
−0.483111 | + | 0.875559i | \(0.660493\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −2808.82 | −2.27760 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 112.018 | 0.0885131 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 283.330 | 0.218259 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 121.000 | 0.0909091 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 862.293 | 0.632116 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −145.906 | −0.104402 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1055.41 | 0.737420 | 0.368710 | − | 0.929545i | \(-0.379800\pi\) | ||||
0.368710 | + | 0.929545i | \(0.379800\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −1577.33 | −1.07656 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −2657.40 | −1.77235 | −0.886175 | − | 0.463351i | \(-0.846647\pi\) | ||||
−0.886175 | + | 0.463351i | \(0.846647\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −827.116 | −0.539249 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 2106.93 | 1.34323 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −147.314 | −0.0918676 | −0.0459338 | − | 0.998944i | \(-0.514626\pi\) | ||||
−0.0459338 | + | 0.998944i | \(0.514626\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −902.634 | −0.550794 | −0.275397 | − | 0.961331i | \(-0.588809\pi\) | ||||
−0.275397 | + | 0.961331i | \(0.588809\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −2181.84 | −1.30315 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 389.083 | 0.227530 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 4228.69 | 2.42189 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 269.130 | 0.151003 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 1212.63 | 0.666727 | 0.333363 | − | 0.942798i | \(-0.391816\pi\) | ||||
0.333363 | + | 0.942798i | \(0.391816\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −2565.33 | −1.38254 | −0.691270 | − | 0.722597i | \(-0.742948\pi\) | ||||
−0.691270 | + | 0.722597i | \(0.742948\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 128.183 | 0.0677320 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −582.486 | −0.301848 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 702.237 | 0.356972 | 0.178486 | − | 0.983942i | \(-0.442880\pi\) | ||||
0.178486 | + | 0.983942i | \(0.442880\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 1496.60 | 0.746464 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1221.57 | 0.597969 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 1146.27 | 0.550814 | 0.275407 | − | 0.961328i | \(-0.411187\pi\) | ||||
0.275407 | + | 0.961328i | \(0.411187\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −972.439 | −0.458814 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 3255.04 | 1.50828 | 0.754140 | − | 0.656714i | \(-0.228054\pi\) | ||||
0.754140 | + | 0.656714i | \(0.228054\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −945.879 | −0.430532 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −374.201 | −0.167344 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 4024.24 | 1.76854 | 0.884269 | − | 0.466977i | \(-0.154657\pi\) | ||||
0.884269 | + | 0.466977i | \(0.154657\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 938.455 | 0.405374 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 2787.23 | 1.18362 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −706.090 | −0.294836 | −0.147418 | − | 0.989074i | \(-0.547096\pi\) | ||||
−0.147418 | + | 0.989074i | \(0.547096\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −1268.90 | −0.521087 | −0.260544 | − | 0.965462i | \(-0.583902\pi\) | ||||
−0.260544 | + | 0.965462i | \(0.583902\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 195.316 | 0.0788970 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −306.562 | −0.121832 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 445.233 | 0.174110 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −916.313 | −0.352656 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −4864.58 | −1.84287 | −0.921436 | − | 0.388529i | \(-0.872983\pi\) | ||||
−0.921436 | + | 0.388529i | \(0.872983\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −2675.49 | −0.997855 | −0.498928 | − | 0.866644i | \(-0.666273\pi\) | ||||
−0.498928 | + | 0.866644i | \(0.666273\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −3126.94 | −1.14833 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 1627.73 | 0.588684 | 0.294342 | − | 0.955700i | \(-0.404899\pi\) | ||||
0.294342 | + | 0.955700i | \(0.404899\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 2254.07 | 0.802947 | 0.401474 | − | 0.915871i | \(-0.368498\pi\) | ||||
0.401474 | + | 0.915871i | \(0.368498\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −5378.36 | −1.88736 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −1839.08 | −0.635851 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −2526.93 | −0.860920 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 552.657 | 0.185567 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −1299.75 | −0.430172 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −3112.07 | −1.01537 | −0.507687 | − | 0.861542i | \(-0.669499\pi\) | ||||
−0.507687 | + | 0.861542i | \(0.669499\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −4121.55 | −1.32584 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 4622.34 | 1.46624 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 253.326 | 0.0792482 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 2172.78 | 0.670423 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1431.67 | 0.435769 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 3558.38 | 1.06855 | 0.534275 | − | 0.845311i | \(-0.320585\pi\) | ||||
0.534275 | + | 0.845311i | \(0.320585\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 424.572 | 0.125799 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 2330.51 | 0.681416 | 0.340708 | − | 0.940169i | \(-0.389333\pi\) | ||||
0.340708 | + | 0.940169i | \(0.389333\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 676.106 | 0.195102 | 0.0975509 | − | 0.995231i | \(-0.468899\pi\) | ||||
0.0975509 | + | 0.995231i | \(0.468899\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 422.918 | 0.120459 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 1620.20 | 0.455548 | 0.227774 | − | 0.973714i | \(-0.426855\pi\) | ||||
0.227774 | + | 0.973714i | \(0.426855\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 6393.84 | 1.77484 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 4045.27 | 1.10873 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 2001.39 | 0.541669 | 0.270835 | − | 0.962626i | \(-0.412700\pi\) | ||||
0.270835 | + | 0.962626i | \(0.412700\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1586.39 | −0.424018 | −0.212009 | − | 0.977268i | \(-0.568001\pi\) | ||||
−0.212009 | + | 0.977268i | \(0.568001\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −884.196 | −0.233420 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −788.679 | −0.205661 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −4179.44 | −1.07665 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −3201.96 | −0.814923 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −2612.23 | −0.656902 | −0.328451 | − | 0.944521i | \(-0.606527\pi\) | ||||
−0.328451 | + | 0.944521i | \(0.606527\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1919.61 | 0.477014 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −3578.20 | −0.878727 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 4198.23 | 1.01898 | 0.509491 | − | 0.860476i | \(-0.329834\pi\) | ||||
0.509491 | + | 0.860476i | \(0.329834\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 133.325 | 0.0319861 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −832.028 | −0.197323 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 5170.31 | 1.21222 | 0.606112 | − | 0.795380i | \(-0.292728\pi\) | ||||
0.606112 | + | 0.795380i | \(0.292728\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −4385.74 | −1.01666 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −4428.01 | −1.01494 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 1648.20 | 0.373578 | 0.186789 | − | 0.982400i | \(-0.440192\pi\) | ||||
0.186789 | + | 0.982400i | \(0.440192\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −2562.79 | −0.574459 | −0.287230 | − | 0.957862i | \(-0.592734\pi\) | ||||
−0.287230 | + | 0.957862i | \(0.592734\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 1359.92 | 0.301487 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 1474.72 | 0.323377 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 2762.94 | 0.599310 | 0.299655 | − | 0.954048i | \(-0.403128\pi\) | ||||
0.299655 | + | 0.954048i | \(0.403128\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 114.609 | 0.0245930 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 6453.68 | 1.37009 | 0.685044 | − | 0.728502i | \(-0.259783\pi\) | ||||
0.685044 | + | 0.728502i | \(0.259783\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −4540.78 | −0.953787 | −0.476893 | − | 0.878961i | \(-0.658237\pi\) | ||||
−0.476893 | + | 0.878961i | \(0.658237\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 10445.7 | 2.17106 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 1098.97 | 0.226029 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −3274.72 | −0.666541 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −5257.54 | −1.05912 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 1916.34 | 0.382094 | 0.191047 | − | 0.981581i | \(-0.438812\pi\) | ||||
0.191047 | + | 0.981581i | \(0.438812\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −8167.92 | −1.61205 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −1439.92 | −0.281322 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 6172.61 | 1.19388 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −2010.28 | −0.384951 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −5471.26 | −1.03735 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −572.369 | −0.107455 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −6876.30 | −1.27834 | −0.639171 | − | 0.769064i | \(-0.720722\pi\) | ||||
−0.639171 | + | 0.769064i | \(0.720722\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −7351.89 | −1.35351 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −8469.32 | −1.54422 | −0.772108 | − | 0.635492i | \(-0.780797\pi\) | ||||
−0.772108 | + | 0.635492i | \(0.780797\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −2882.28 | −0.520498 | −0.260249 | − | 0.965542i | \(-0.583805\pi\) | ||||
−0.260249 | + | 0.965542i | \(0.583805\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −356.812 | −0.0638224 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 9795.31 | 1.73552 | 0.867759 | − | 0.496985i | \(-0.165560\pi\) | ||||
0.867759 | + | 0.496985i | \(0.165560\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −2889.98 | −0.507234 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −7959.92 | −1.38405 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −4782.59 | −0.823871 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 4742.04 | 0.809357 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −3595.00 | −0.607963 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −2780.71 | −0.465974 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −1813.70 | −0.301178 | −0.150589 | − | 0.988596i | \(-0.548117\pi\) | ||||
−0.150589 | + | 0.988596i | \(0.548117\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 60.3184 | 0.00992621 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 15761.2 | 2.57052 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −11964.2 | −1.93393 | −0.966964 | − | 0.254913i | \(-0.917953\pi\) | ||||
−0.966964 | + | 0.254913i | \(0.917953\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −6374.71 | −1.02132 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 398.083 | 0.0632182 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 343.000 | 0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −15427.3 | −2.40747 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 2283.89 | 0.353330 | 0.176665 | − | 0.984271i | \(-0.443469\pi\) | ||||
0.176665 | + | 0.984271i | \(0.443469\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −2472.48 | −0.379223 | −0.189612 | − | 0.981859i | \(-0.560723\pi\) | ||||
−0.189612 | + | 0.981859i | \(0.560723\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −4630.15 | −0.704101 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 10190.0 | 1.53642 | 0.768211 | − | 0.640197i | \(-0.221147\pi\) | ||||
0.768211 | + | 0.640197i | \(0.221147\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 12078.1 | 1.80575 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 1556.17 | 0.230704 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 43.4294 | 0.00638473 | 0.00319236 | − | 0.999995i | \(-0.498984\pi\) | ||||
0.00319236 | + | 0.999995i | \(0.498984\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 7102.66 | 1.03552 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 664.585 | 0.0960928 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −6367.28 | −0.913093 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −8775.78 | −1.24821 | −0.624104 | − | 0.781342i | \(-0.714536\pi\) | ||||
−0.624104 | + | 0.781342i | \(0.714536\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 497.194 | 0.0701433 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 1907.38 | 0.266917 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −2751.89 | −0.382004 | −0.191002 | − | 0.981590i | \(-0.561174\pi\) | ||||
−0.191002 | + | 0.981590i | \(0.561174\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −801.379 | −0.110355 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −9292.90 | −1.26952 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −2605.59 | −0.353141 | −0.176570 | − | 0.984288i | \(-0.556500\pi\) | ||||
−0.176570 | + | 0.984288i | \(0.556500\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 5796.77 | 0.779468 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 14360.5 | 1.91590 | 0.957949 | − | 0.286940i | \(-0.0926380\pi\) | ||||
0.957949 | + | 0.286940i | \(0.0926380\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −1239.35 | −0.164060 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −909.482 | −0.119461 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −10607.9 | −1.38262 | −0.691311 | − | 0.722557i | \(-0.742967\pi\) | ||||
−0.691311 | + | 0.722557i | \(0.742967\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 7063.40 | 0.913585 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −14595.6 | −1.87341 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −11854.6 | −1.51005 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 7362.35 | 0.930745 | 0.465373 | − | 0.885115i | \(-0.345920\pi\) | ||||
0.465373 | + | 0.885115i | \(0.345920\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −4542.89 | −0.569997 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −264.514 | −0.0329406 | −0.0164703 | − | 0.999864i | \(-0.505243\pi\) | ||||
−0.0164703 | + | 0.999864i | \(0.505243\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1280.06 | 0.158224 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 12948.5 | 1.58868 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 209.511 | 0.0255161 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −1244.03 | −0.150400 | −0.0751999 | − | 0.997168i | \(-0.523959\pi\) | ||||
−0.0751999 | + | 0.997168i | \(0.523959\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −809.112 | −0.0971060 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 3552.26 | 0.423233 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 9383.27 | 1.10990 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −4957.66 | −0.582201 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −3974.76 | −0.463436 | −0.231718 | − | 0.972783i | \(-0.574435\pi\) | ||||
−0.231718 | + | 0.972783i | \(0.574435\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −14910.2 | −1.72608 | −0.863041 | − | 0.505134i | \(-0.831443\pi\) | ||||
−0.863041 | + | 0.505134i | \(0.831443\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −1258.04 | −0.144605 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 5426.38 | 0.619336 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 248.926 | 0.0282116 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 2137.02 | 0.240504 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 10622.4 | 1.18715 | 0.593574 | − | 0.804779i | \(-0.297716\pi\) | ||||
0.593574 | + | 0.804779i | \(0.297716\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 17440.5 | 1.93565 | 0.967823 | − | 0.251630i | \(-0.0809667\pi\) | ||||
0.967823 | + | 0.251630i | \(0.0809667\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 23225.8 | 2.55999 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −20620.0 | −2.25718 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −13627.1 | −1.48151 | −0.740756 | − | 0.671774i | \(-0.765533\pi\) | ||||
−0.740756 | + | 0.671774i | \(0.765533\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 155.179 | 0.0167562 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −2135.29 | −0.229008 | −0.114504 | − | 0.993423i | \(-0.536528\pi\) | ||||
−0.114504 | + | 0.993423i | \(0.536528\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 12976.2 | 1.38232 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 6660.28 | 0.704744 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 17780.8 | 1.86889 | 0.934443 | − | 0.356113i | \(-0.115898\pi\) | ||||
0.934443 | + | 0.356113i | \(0.115898\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1726.96 | 0.180309 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −14089.9 | −1.46137 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −3985.22 | −0.410615 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 10357.0 | 1.06013 | 0.530064 | − | 0.847957i | \(-0.322168\pi\) | ||||
0.530064 | + | 0.847957i | \(0.322168\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −5298.35 | −0.538792 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −19679.5 | −1.98821 | −0.994106 | − | 0.108410i | \(-0.965424\pi\) | ||||
−0.994106 | + | 0.108410i | \(0.965424\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 7171.43 | 0.719838 | 0.359919 | − | 0.932984i | \(-0.382804\pi\) | ||||
0.359919 | + | 0.932984i | \(0.382804\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −3199.27 | −0.319059 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 12192.8 | 1.20817 | 0.604085 | − | 0.796920i | \(-0.293539\pi\) | ||||
0.604085 | + | 0.796920i | \(0.293539\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −6854.61 | −0.674875 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 3856.99 | 0.377327 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −3159.00 | −0.307085 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −15841.1 | −1.53018 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 862.930 | 0.0828319 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −8475.11 | −0.808429 | −0.404215 | − | 0.914664i | \(-0.632455\pi\) | ||||
−0.404215 | + | 0.914664i | \(0.632455\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 673.695 | 0.0638624 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 6709.39 | 0.632066 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 15407.1 | 1.44248 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −2735.29 | −0.254513 | −0.127257 | − | 0.991870i | \(-0.540617\pi\) | ||||
−0.127257 | + | 0.991870i | \(0.540617\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 6295.81 | 0.582222 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 2233.82 | 0.205317 | 0.102659 | − | 0.994717i | \(-0.467265\pi\) | ||||
0.102659 | + | 0.994717i | \(0.467265\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −10634.0 | −0.971462 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −560.704 | −0.0509126 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −5252.83 | −0.474088 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 18100.3 | 1.62381 | 0.811904 | − | 0.583791i | \(-0.198431\pi\) | ||||
0.811904 | + | 0.583791i | \(0.198431\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 17878.1 | 1.59428 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −6149.06 | −0.545076 | −0.272538 | − | 0.962145i | \(-0.587863\pi\) | ||||
−0.272538 | + | 0.962145i | \(0.587863\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 16033.4 | 1.41283 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −5195.18 | −0.455081 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 14193.9 | 1.23602 | 0.618008 | − | 0.786172i | \(-0.287940\pi\) | ||||
0.618008 | + | 0.786172i | \(0.287940\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 2769.16 | 0.239727 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 15467.3 | 1.33118 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 21544.6 | 1.84343 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −4369.68 | −0.371718 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 22102.9 | 1.86938 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 10371.8 | 0.872163 | 0.436082 | − | 0.899907i | \(-0.356366\pi\) | ||||
0.436082 | + | 0.899907i | \(0.356366\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 11369.4 | 0.950569 | 0.475285 | − | 0.879832i | \(-0.342345\pi\) | ||||
0.475285 | + | 0.879832i | \(0.342345\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 5154.41 | 0.428489 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 1464.79 | 0.121076 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 18286.6 | 1.50297 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 1607.10 | 0.131341 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 5553.14 | 0.451282 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 23326.4 | 1.88503 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −3878.16 | −0.311648 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 539.000 | 0.0430730 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 5386.88 | 0.428096 | 0.214048 | − | 0.976823i | \(-0.431335\pi\) | ||||
0.214048 | + | 0.976823i | \(0.431335\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −6969.38 | −0.550800 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 10535.1 | 0.828024 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −13890.8 | −1.08579 | −0.542894 | − | 0.839801i | \(-0.682672\pi\) | ||||
−0.542894 | + | 0.839801i | \(0.682672\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 112.618 | 0.00875487 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 31043.5 | 2.40017 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 5155.61 | 0.396454 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −1683.77 | −0.128779 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 17498.3 | 1.33111 | 0.665553 | − | 0.746351i | \(-0.268196\pi\) | ||||
0.665553 | + | 0.746351i | \(0.268196\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −10158.0 | −0.768581 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 2445.42 | 0.184038 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −147.373 | −0.0110320 | −0.00551600 | − | 0.999985i | \(-0.501756\pi\) | ||||
−0.00551600 | + | 0.999985i | \(0.501756\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 18681.0 | 1.39100 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −5631.34 | −0.417097 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −14155.3 | −1.04292 | −0.521459 | − | 0.853276i | \(-0.674612\pi\) | ||||
−0.521459 | + | 0.853276i | \(0.674612\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 248.361 | 0.0182025 | 0.00910123 | − | 0.999959i | \(-0.497103\pi\) | ||||
0.00910123 | + | 0.999959i | \(0.497103\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −26718.4 | −1.94795 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 23395.6 | 1.69681 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 19364.6 | 1.39715 | 0.698576 | − | 0.715536i | \(-0.253817\pi\) | ||||
0.698576 | + | 0.715536i | \(0.253817\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −14695.0 | −1.05475 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −4080.83 | −0.291396 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 2997.31 | 0.212926 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −1802.98 | −0.127426 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 9135.18 | 0.642332 | 0.321166 | − | 0.947023i | \(-0.395925\pi\) | ||||
0.321166 | + | 0.947023i | \(0.395925\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −4276.12 | −0.299141 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 8940.20 | 0.622252 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −12287.6 | −0.850916 | −0.425458 | − | 0.904978i | \(-0.639887\pi\) | ||||
−0.425458 | + | 0.904978i | \(0.639887\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −4560.34 | −0.314211 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 12380.3 | 0.848732 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −12351.9 | −0.842549 | −0.421275 | − | 0.906933i | \(-0.638417\pi\) | ||||
−0.421275 | + | 0.906933i | \(0.638417\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 21624.2 | 1.46767 | 0.733836 | − | 0.679327i | \(-0.237728\pi\) | ||||
0.733836 | + | 0.679327i | \(0.237728\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −3101.14 | −0.209433 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −1947.56 | −0.130875 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 2086.03 | 0.139488 | 0.0697442 | − | 0.997565i | \(-0.477782\pi\) | ||||
0.0697442 | + | 0.997565i | \(0.477782\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −10101.0 | −0.672108 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −14051.0 | −0.930347 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −8338.46 | −0.549408 | −0.274704 | − | 0.961529i | \(-0.588580\pi\) | ||||
−0.274704 | + | 0.961529i | \(0.588580\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −13879.0 | −0.910011 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −4771.20 | −0.311315 | −0.155657 | − | 0.987811i | \(-0.549750\pi\) | ||||
−0.155657 | + | 0.987811i | \(0.549750\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 16609.4 | 1.07850 | 0.539248 | − | 0.842147i | \(-0.318708\pi\) | ||||
0.539248 | + | 0.842147i | \(0.318708\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −22843.6 | −1.47614 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −5643.40 | −0.362919 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −14409.7 | −0.922221 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −7138.82 | −0.454700 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 770.918 | 0.0488688 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −17254.9 | −1.08860 | −0.544299 | − | 0.838891i | \(-0.683204\pi\) | ||||
−0.544299 | + | 0.838891i | \(0.683204\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −17092.9 | −1.07327 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −16987.3 | −1.06161 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1733.19 | 0.107804 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −2376.47 | −0.147123 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −7350.77 | −0.452945 | −0.226473 | − | 0.974018i | \(-0.572719\pi\) | ||||
−0.226473 | + | 0.974018i | \(0.572719\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −10117.8 | −0.620542 | −0.310271 | − | 0.950648i | \(-0.600420\pi\) | ||||
−0.310271 | + | 0.950648i | \(0.600420\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 25387.9 | 1.54984 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 24590.9 | 1.49423 | 0.747116 | − | 0.664693i | \(-0.231438\pi\) | ||||
0.747116 | + | 0.664693i | \(0.231438\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 5582.13 | 0.337624 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 1391.38 | 0.0837670 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 2339.03 | 0.140173 | 0.0700867 | − | 0.997541i | \(-0.477672\pi\) | ||||
0.0700867 | + | 0.997541i | \(0.477672\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 42772.1 | 2.55152 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 1252.81 | 0.0743940 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 15735.7 | 0.930162 | 0.465081 | − | 0.885268i | \(-0.346025\pi\) | ||||
0.465081 | + | 0.885268i | \(0.346025\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 4846.75 | 0.285199 | 0.142600 | − | 0.989780i | \(-0.454454\pi\) | ||||
0.142600 | + | 0.989780i | \(0.454454\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 7863.39 | 0.460617 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 13312.8 | 0.776316 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −45848.1 | −2.66154 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 19544.2 | 1.12948 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 391.169 | 0.0225051 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 15716.8 | 0.900205 | 0.450103 | − | 0.892977i | \(-0.351387\pi\) | ||||
0.450103 | + | 0.892977i | \(0.351387\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −17549.4 | −1.00070 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −856.968 | −0.0486499 | −0.0243249 | − | 0.999704i | \(-0.507744\pi\) | ||||
−0.0243249 | + | 0.999704i | \(0.507744\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −6700.63 | −0.378713 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 12800.2 | 0.720271 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −24804.0 | −1.38960 | −0.694801 | − | 0.719202i | \(-0.744508\pi\) | ||||
−0.694801 | + | 0.719202i | \(0.744508\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 2371.09 | 0.132255 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 3713.47 | 0.206227 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 9638.04 | 0.532917 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −3475.97 | −0.191364 | −0.0956818 | − | 0.995412i | \(-0.530503\pi\) | ||||
−0.0956818 | + | 0.995412i | \(0.530503\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 243.852 | 0.0133668 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 14528.3 | 0.792937 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 6354.54 | 0.345330 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 8898.85 | 0.481524 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 17461.0 | 0.940790 | 0.470395 | − | 0.882456i | \(-0.344111\pi\) | ||||
0.470395 | + | 0.882456i | \(0.344111\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −2250.52 | −0.120739 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 35117.8 | 1.87605 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −6973.00 | −0.370929 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −18405.7 | −0.974950 | −0.487475 | − | 0.873137i | \(-0.662082\pi\) | ||||
−0.487475 | + | 0.873137i | \(0.662082\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 2332.48 | 0.123031 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 6315.39 | 0.331716 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −6262.49 | −0.327558 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 10992.5 | 0.572555 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 892.380 | 0.0462867 | 0.0231434 | − | 0.999732i | \(-0.492633\pi\) | ||||
0.0231434 | + | 0.999732i | \(0.492633\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −9369.83 | −0.483982 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −8713.15 | −0.448196 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −35222.2 | −1.80431 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −27919.2 | −1.42430 | −0.712149 | − | 0.702028i | \(-0.752278\pi\) | ||||
−0.712149 | + | 0.702028i | \(0.752278\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 16864.5 | 0.856805 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −11623.9 | −0.588134 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −4769.38 | −0.240329 | −0.120164 | − | 0.992754i | \(-0.538342\pi\) | ||||
−0.120164 | + | 0.992754i | \(0.538342\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −4331.78 | −0.217388 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −10771.5 | −0.538364 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 5170.63 | 0.257381 | 0.128691 | − | 0.991685i | \(-0.458923\pi\) | ||||
0.128691 | + | 0.991685i | \(0.458923\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −22955.3 | −1.13804 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 29407.9 | 1.45205 | 0.726024 | − | 0.687669i | \(-0.241366\pi\) | ||||
0.726024 | + | 0.687669i | \(0.241366\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −19517.8 | −0.959836 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −1846.23 | −0.0904286 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −10144.8 | −0.494902 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 16956.5 | 0.823905 | 0.411952 | − | 0.911205i | \(-0.364847\pi\) | ||||
0.411952 | + | 0.911205i | \(0.364847\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −14347.5 | −0.694360 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 41290.3 | 1.99034 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −21322.0 | −1.02373 | −0.511864 | − | 0.859067i | \(-0.671045\pi\) | ||||
−0.511864 | + | 0.859067i | \(0.671045\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 10543.3 | 0.504214 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −23548.0 | −1.12170 | −0.560851 | − | 0.827917i | \(-0.689526\pi\) | ||||
−0.560851 | + | 0.827917i | \(0.689526\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −4581.75 | −0.217392 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −2063.17 | −0.0975087 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 17949.7 | 0.845014 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −17230.9 | −0.808015 | −0.404007 | − | 0.914756i | \(-0.632383\pi\) | ||||
−0.404007 | + | 0.914756i | \(0.632383\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 23058.5 | 1.07709 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 12285.8 | 0.571655 | 0.285828 | − | 0.958281i | \(-0.407732\pi\) | ||||
0.285828 | + | 0.958281i | \(0.407732\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 4851.73 | 0.224876 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 732.280 | 0.0338100 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −18550.6 | −0.853202 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −8254.45 | −0.378191 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 34391.2 | 1.56966 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −11302.8 | −0.513906 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −663.152 | −0.0300366 | −0.0150183 | − | 0.999887i | \(-0.504781\pi\) | ||||
−0.0150183 | + | 0.999887i | \(0.504781\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 28397.6 | 1.28135 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −8124.43 | −0.365198 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1257.83 | 0.0563264 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −24088.4 | −1.07463 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 19216.3 | 0.854050 | 0.427025 | − | 0.904240i | \(-0.359562\pi\) | ||||
0.427025 | + | 0.904240i | \(0.359562\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −16078.7 | −0.711921 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −2553.17 | −0.112624 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 4351.53 | 0.191236 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −19661.7 | −0.860851 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 9052.65 | 0.394880 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −42881.8 | −1.86359 | −0.931794 | − | 0.362989i | \(-0.881756\pi\) | ||||
−0.931794 | + | 0.362989i | \(0.881756\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 1205.73 | 0.0522058 | 0.0261029 | − | 0.999659i | \(-0.491690\pi\) | ||||
0.0261029 | + | 0.999659i | \(0.491690\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −14076.0 | −0.607215 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −18449.8 | −0.792966 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 33933.3 | 1.45309 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 784.123 | 0.0334548 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −28577.6 | −1.21482 | −0.607408 | − | 0.794390i | \(-0.707791\pi\) | ||||
−0.607408 | + | 0.794390i | \(0.707791\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −42524.8 | −1.80112 | −0.900561 | − | 0.434730i | \(-0.856844\pi\) | ||||
−0.900561 | + | 0.434730i | \(0.856844\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 8099.79 | 0.341816 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −30768.7 | −1.29375 | −0.646876 | − | 0.762595i | \(-0.723925\pi\) | ||||
−0.646876 | + | 0.762595i | \(0.723925\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −17583.3 | −0.736661 | −0.368330 | − | 0.929695i | \(-0.620070\pi\) | ||||
−0.368330 | + | 0.929695i | \(0.620070\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 15175.3 | 0.633484 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 1983.31 | 0.0824942 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −52391.5 | −2.17136 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −4737.25 | −0.195631 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −19552.8 | −0.804573 | −0.402287 | − | 0.915514i | \(-0.631784\pi\) | ||||
−0.402287 | + | 0.915514i | \(0.631784\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 44635.5 | 1.83015 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 35446.5 | 1.44821 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 15224.4 | 0.619805 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 847.000 | 0.0343604 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −24940.0 | −1.00817 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 3323.78 | 0.133887 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −18524.1 | −0.743557 | −0.371779 | − | 0.928321i | \(-0.621252\pi\) | ||||
−0.371779 | + | 0.928321i | \(0.621252\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 6022.95 | 0.240913 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 24439.0 | 0.974118 | 0.487059 | − | 0.873369i | \(-0.338070\pi\) | ||||
0.487059 | + | 0.873369i | \(0.338070\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −11301.4 | −0.448893 | −0.224447 | − | 0.974486i | \(-0.572057\pi\) | ||||
−0.224447 | + | 0.974486i | \(0.572057\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 6036.05 | 0.238918 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 26377.3 | 1.04043 | 0.520217 | − | 0.854034i | \(-0.325851\pi\) | ||||
0.520217 | + | 0.854034i | \(0.325851\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −64772.1 | −2.54603 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −17986.2 | −0.704548 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 8101.68 | 0.316261 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −34636.5 | −1.34743 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −3031.47 | −0.117526 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −1021.34 | −0.0394601 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −28425.0 | −1.09446 | −0.547232 | − | 0.836981i | \(-0.684319\pi\) | ||||
−0.547232 | + | 0.836981i | \(0.684319\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 10525.4 | 0.403882 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 16897.1 | 0.646171 | 0.323086 | − | 0.946370i | \(-0.395280\pi\) | ||||
0.323086 | + | 0.946370i | \(0.395280\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 25538.9 | 0.973331 | 0.486665 | − | 0.873588i | \(-0.338213\pi\) | ||||
0.486665 | + | 0.873588i | \(0.338213\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −44861.8 | −1.70397 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −6478.48 | −0.245238 | −0.122619 | − | 0.992454i | \(-0.539129\pi\) | ||||
−0.122619 | + | 0.992454i | \(0.539129\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 7387.85 | 0.278718 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −8849.25 | −0.332728 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 46938.1 | 1.75893 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 11364.9 | 0.424453 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 33902.7 | 1.26196 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −9507.86 | −0.352731 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 11028.9 | 0.407799 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −11041.3 | −0.406902 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 20423.6 | 0.750171 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 9356.17 | 0.342521 | 0.171260 | − | 0.985226i | \(-0.445216\pi\) | ||||
0.171260 | + | 0.985226i | \(0.445216\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −3154.70 | −0.115110 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 16574.0 | 0.602768 | 0.301384 | − | 0.953503i | \(-0.402551\pi\) | ||||
0.301384 | + | 0.953503i | \(0.402551\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −6412.73 | −0.232454 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −3143.70 | −0.113582 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −18601.8 | −0.669885 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −8214.92 | −0.294870 | −0.147435 | − | 0.989072i | \(-0.547102\pi\) | ||||
−0.147435 | + | 0.989072i | \(0.547102\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −37767.7 | −1.35123 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −26542.7 | −0.946548 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 2553.46 | 0.0907646 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −4239.07 | −0.150193 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 42653.9 | 1.50638 | 0.753192 | − | 0.657801i | \(-0.228513\pi\) | ||||
0.753192 | + | 0.657801i | \(0.228513\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −5789.81 | −0.203817 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −46517.2 | −1.63227 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −7166.25 | −0.250654 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −18484.8 | −0.644473 | −0.322237 | − | 0.946659i | \(-0.604435\pi\) | ||||
−0.322237 | + | 0.946659i | \(0.604435\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −15830.7 | −0.550177 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −7183.03 | −0.248842 | −0.124421 | − | 0.992230i | \(-0.539707\pi\) | ||||
−0.124421 | + | 0.992230i | \(0.539707\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 27397.4 | 0.946109 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 14748.5 | 0.507692 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −41443.3 | −1.42210 | −0.711049 | − | 0.703143i | \(-0.751779\pi\) | ||||
−0.711049 | + | 0.703143i | \(0.751779\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 13992.6 | 0.478630 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 53800.2 | 1.83448 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 7981.30 | 0.271290 | 0.135645 | − | 0.990757i | \(-0.456689\pi\) | ||||
0.135645 | + | 0.990757i | \(0.456689\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 78297.8 | 2.65305 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −15873.0 | −0.536157 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −1031.20 | −0.0347227 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −28481.3 | −0.956038 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −4589.65 | −0.153582 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 43063.3 | 1.43654 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 18745.7 | 0.623394 | 0.311697 | − | 0.950182i | \(-0.399103\pi\) | ||||
0.311697 | + | 0.950182i | \(0.399103\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −26268.1 | −0.870849 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −3096.87 | −0.102351 | −0.0511757 | − | 0.998690i | \(-0.516297\pi\) | ||||
−0.0511757 | + | 0.998690i | \(0.516297\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −6318.44 | −0.208181 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 26045.4 | 0.855507 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 19960.2 | 0.653618 | 0.326809 | − | 0.945090i | \(-0.394027\pi\) | ||||
0.326809 | + | 0.945090i | \(0.394027\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −8868.21 | −0.289509 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −2072.86 | −0.0674631 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 33434.5 | 1.08484 | 0.542419 | − | 0.840108i | \(-0.317509\pi\) | ||||
0.542419 | + | 0.840108i | \(0.317509\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −26199.1 | −0.847485 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −15272.9 | −0.492544 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −50116.1 | −1.61132 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −24855.2 | −0.796722 | −0.398361 | − | 0.917229i | \(-0.630421\pi\) | ||||
−0.398361 | + | 0.917229i | \(0.630421\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −9961.63 | −0.318351 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −36280.3 | −1.15594 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −7810.38 | −0.248102 | −0.124051 | − | 0.992276i | \(-0.539589\pi\) | ||||
−0.124051 | + | 0.992276i | \(0.539589\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −2493.21 | −0.0789607 |
(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 | 1232.4.a.s.1.4 | 4 | ||
4.3 | odd | 2 | 77.4.a.d.1.2 | ✓ | 4 | ||
12.11 | even | 2 | 693.4.a.l.1.3 | 4 | |||
20.19 | odd | 2 | 1925.4.a.p.1.3 | 4 | |||
28.27 | even | 2 | 539.4.a.g.1.2 | 4 | |||
44.43 | even | 2 | 847.4.a.d.1.3 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
77.4.a.d.1.2 | ✓ | 4 | 4.3 | odd | 2 | ||
539.4.a.g.1.2 | 4 | 28.27 | even | 2 | |||
693.4.a.l.1.3 | 4 | 12.11 | even | 2 | |||
847.4.a.d.1.3 | 4 | 44.43 | even | 2 | |||
1232.4.a.s.1.4 | 4 | 1.1 | even | 1 | trivial | ||
1925.4.a.p.1.3 | 4 | 20.19 | odd | 2 |