Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2352,4,Mod(1,2352)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2352, 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("2352.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2352 = 2^{4} \cdot 3 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 2352.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: | \(138.772492334\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | 4.4.145408.2 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 24x^{2} + 142 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{3} \) |
Twist minimal: | no (minimal twist has level 1176) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(3.66254\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2352.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −3.00000 | −0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 4.11659 | 0.368199 | 0.184100 | − | 0.982908i | \(-0.441063\pi\) | ||||
0.184100 | + | 0.982908i | \(0.441063\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 9.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −17.9344 | −0.491585 | −0.245792 | − | 0.969323i | \(-0.579048\pi\) | ||||
−0.245792 | + | 0.969323i | \(0.579048\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −23.4236 | −0.499733 | −0.249867 | − | 0.968280i | \(-0.580387\pi\) | ||||
−0.249867 | + | 0.968280i | \(0.580387\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −12.3498 | −0.212580 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −76.2280 | −1.08753 | −0.543765 | − | 0.839237i | \(-0.683002\pi\) | ||||
−0.543765 | + | 0.839237i | \(0.683002\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 35.5964 | 0.429809 | 0.214905 | − | 0.976635i | \(-0.431056\pi\) | ||||
0.214905 | + | 0.976635i | \(0.431056\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 40.7918 | 0.369812 | 0.184906 | − | 0.982756i | \(-0.440802\pi\) | ||||
0.184906 | + | 0.982756i | \(0.440802\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −108.054 | −0.864429 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −27.0000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −178.805 | −1.14494 | −0.572471 | − | 0.819925i | \(-0.694015\pi\) | ||||
−0.572471 | + | 0.819925i | \(0.694015\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 31.6797 | 0.183543 | 0.0917717 | − | 0.995780i | \(-0.470747\pi\) | ||||
0.0917717 | + | 0.995780i | \(0.470747\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 53.8032 | 0.283816 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −54.8450 | −0.243688 | −0.121844 | − | 0.992549i | \(-0.538881\pi\) | ||||
−0.121844 | + | 0.992549i | \(0.538881\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 70.2708 | 0.288521 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 190.547 | 0.725815 | 0.362907 | − | 0.931825i | \(-0.381784\pi\) | ||||
0.362907 | + | 0.931825i | \(0.381784\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 131.964 | 0.468009 | 0.234004 | − | 0.972236i | \(-0.424817\pi\) | ||||
0.234004 | + | 0.972236i | \(0.424817\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 37.0493 | 0.122733 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 199.573 | 0.619377 | 0.309689 | − | 0.950838i | \(-0.399775\pi\) | ||||
0.309689 | + | 0.950838i | \(0.399775\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 228.684 | 0.627886 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 321.907 | 0.834289 | 0.417145 | − | 0.908840i | \(-0.363031\pi\) | ||||
0.417145 | + | 0.908840i | \(0.363031\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −73.8287 | −0.181001 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −106.789 | −0.248150 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 163.392 | 0.360540 | 0.180270 | − | 0.983617i | \(-0.442303\pi\) | ||||
0.180270 | + | 0.983617i | \(0.442303\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −265.230 | −0.556710 | −0.278355 | − | 0.960478i | \(-0.589789\pi\) | ||||
−0.278355 | + | 0.960478i | \(0.589789\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −96.4254 | −0.184001 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −278.127 | −0.507144 | −0.253572 | − | 0.967316i | \(-0.581606\pi\) | ||||
−0.253572 | + | 0.967316i | \(0.581606\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −122.375 | −0.213511 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 10.5794 | 0.0176836 | 0.00884182 | − | 0.999961i | \(-0.497186\pi\) | ||||
0.00884182 | + | 0.999961i | \(0.497186\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −584.292 | −0.936797 | −0.468398 | − | 0.883517i | \(-0.655169\pi\) | ||||
−0.468398 | + | 0.883517i | \(0.655169\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 324.161 | 0.499079 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 183.078 | 0.260733 | 0.130366 | − | 0.991466i | \(-0.458385\pi\) | ||||
0.130366 | + | 0.991466i | \(0.458385\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 81.0000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −175.117 | −0.231585 | −0.115792 | − | 0.993273i | \(-0.536941\pi\) | ||||
−0.115792 | + | 0.993273i | \(0.536941\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −313.800 | −0.400428 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 536.416 | 0.661033 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −47.1437 | −0.0561485 | −0.0280743 | − | 0.999606i | \(-0.508937\pi\) | ||||
−0.0280743 | + | 0.999606i | \(0.508937\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −95.0391 | −0.105969 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 146.536 | 0.158255 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 556.805 | 0.582834 | 0.291417 | − | 0.956596i | \(-0.405873\pi\) | ||||
0.291417 | + | 0.956596i | \(0.405873\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −161.410 | −0.163862 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −128.804 | −0.126895 | −0.0634477 | − | 0.997985i | \(-0.520210\pi\) | ||||
−0.0634477 | + | 0.997985i | \(0.520210\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 2043.48 | 1.95485 | 0.977427 | − | 0.211271i | \(-0.0677604\pi\) | ||||
0.977427 | + | 0.211271i | \(0.0677604\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 268.860 | 0.242913 | 0.121456 | − | 0.992597i | \(-0.461244\pi\) | ||||
0.121456 | + | 0.992597i | \(0.461244\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1335.64 | 1.17368 | 0.586841 | − | 0.809702i | \(-0.300371\pi\) | ||||
0.586841 | + | 0.809702i | \(0.300371\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 164.535 | 0.140693 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −1675.40 | −1.39476 | −0.697382 | − | 0.716700i | \(-0.745652\pi\) | ||||
−0.697382 | + | 0.716700i | \(0.745652\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 167.923 | 0.136164 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −210.812 | −0.166578 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1009.36 | −0.758345 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −571.640 | −0.419049 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −959.387 | −0.686481 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1626.28 | −1.13629 | −0.568144 | − | 0.822929i | \(-0.692338\pi\) | ||||
−0.568144 | + | 0.822929i | \(0.692338\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −395.893 | −0.270205 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1534.98 | 1.02375 | 0.511877 | − | 0.859059i | \(-0.328950\pi\) | ||||
0.511877 | + | 0.859059i | \(0.328950\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −111.148 | −0.0708600 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 2466.49 | 1.53815 | 0.769076 | − | 0.639158i | \(-0.220717\pi\) | ||||
0.769076 | + | 0.639158i | \(0.220717\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1322.68 | 0.807107 | 0.403554 | − | 0.914956i | \(-0.367775\pi\) | ||||
0.403554 | + | 0.914956i | \(0.367775\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −598.719 | −0.357598 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 420.088 | 0.245661 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −736.069 | −0.421567 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −648.069 | −0.356321 | −0.178161 | − | 0.984001i | \(-0.557015\pi\) | ||||
−0.178161 | + | 0.984001i | \(0.557015\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −2003.70 | −1.07986 | −0.539930 | − | 0.841710i | \(-0.681549\pi\) | ||||
−0.539930 | + | 0.841710i | \(0.681549\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −686.052 | −0.362510 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 130.412 | 0.0675805 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 773.589 | 0.393243 | 0.196622 | − | 0.980479i | \(-0.437003\pi\) | ||||
0.196622 | + | 0.980479i | \(0.437003\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −965.721 | −0.481677 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −66.4286 | −0.0319208 | −0.0159604 | − | 0.999873i | \(-0.505081\pi\) | ||||
−0.0159604 | + | 0.999873i | \(0.505081\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 221.486 | 0.104501 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 842.616 | 0.390441 | 0.195220 | − | 0.980759i | \(-0.437458\pi\) | ||||
0.195220 | + | 0.980759i | \(0.437458\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1648.34 | −0.750266 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 320.368 | 0.143270 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −1570.69 | −0.690275 | −0.345138 | − | 0.938552i | \(-0.612168\pi\) | ||||
−0.345138 | + | 0.938552i | \(0.612168\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −490.177 | −0.208158 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −3670.74 | −1.53276 | −0.766380 | − | 0.642387i | \(-0.777944\pi\) | ||||
−0.766380 | + | 0.642387i | \(0.777944\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 802.417 | 0.329520 | 0.164760 | − | 0.986334i | \(-0.447315\pi\) | ||||
0.164760 | + | 0.986334i | \(0.447315\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 795.691 | 0.321416 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −225.775 | −0.0897258 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1367.11 | 0.534613 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 4559.10 | 1.72714 | 0.863572 | − | 0.504225i | \(-0.168222\pi\) | ||||
0.863572 | + | 0.504225i | \(0.168222\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 3133.71 | 1.16875 | 0.584377 | − | 0.811482i | \(-0.301339\pi\) | ||||
0.584377 | + | 0.811482i | \(0.301339\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 289.276 | 0.106233 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −2805.70 | −1.01471 | −0.507354 | − | 0.861738i | \(-0.669376\pi\) | ||||
−0.507354 | + | 0.861738i | \(0.669376\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 5257.19 | 1.87272 | 0.936362 | − | 0.351036i | \(-0.114171\pi\) | ||||
0.936362 | + | 0.351036i | \(0.114171\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 834.382 | 0.292800 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 784.403 | 0.267244 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 367.126 | 0.123271 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −638.400 | −0.211287 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −3230.30 | −1.05395 | −0.526974 | − | 0.849882i | \(-0.676673\pi\) | ||||
−0.526974 | + | 0.849882i | \(0.676673\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −31.7381 | −0.0102097 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 543.243 | 0.172320 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 1752.87 | 0.540860 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1785.53 | 0.543475 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 433.169 | 0.130077 | 0.0650385 | − | 0.997883i | \(-0.479283\pi\) | ||||
0.0650385 | + | 0.997883i | \(0.479283\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −972.483 | −0.288143 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 4108.60 | 1.20131 | 0.600655 | − | 0.799509i | \(-0.294907\pi\) | ||||
0.600655 | + | 0.799509i | \(0.294907\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −4633.01 | −1.33693 | −0.668467 | − | 0.743742i | \(-0.733049\pi\) | ||||
−0.668467 | + | 0.743742i | \(0.733049\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 643.222 | 0.180853 | 0.0904267 | − | 0.995903i | \(-0.471177\pi\) | ||||
0.0904267 | + | 0.995903i | \(0.471177\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 821.561 | 0.228054 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −549.235 | −0.150534 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −783.612 | −0.212082 | −0.106041 | − | 0.994362i | \(-0.533818\pi\) | ||||
−0.106041 | + | 0.994362i | \(0.533818\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 6338.58 | 1.69421 | 0.847103 | − | 0.531429i | \(-0.178345\pi\) | ||||
0.847103 | + | 0.531429i | \(0.178345\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −243.000 | −0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −833.795 | −0.214790 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 525.350 | 0.133706 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 5863.01 | 1.47438 | 0.737191 | − | 0.675685i | \(-0.236152\pi\) | ||||
0.737191 | + | 0.675685i | \(0.236152\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −731.577 | −0.181794 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 941.399 | 0.231187 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 4213.76 | 1.02275 | 0.511376 | − | 0.859357i | \(-0.329136\pi\) | ||||
0.511376 | + | 0.859357i | \(0.329136\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −1609.25 | −0.381648 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 1955.85 | 0.458566 | 0.229283 | − | 0.973360i | \(-0.426362\pi\) | ||||
0.229283 | + | 0.973360i | \(0.426362\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 1325.16 | 0.307185 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 141.431 | 0.0324174 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −1527.99 | −0.346332 | −0.173166 | − | 0.984893i | \(-0.555400\pi\) | ||||
−0.173166 | + | 0.984893i | \(0.555400\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 7673.88 | 1.72013 | 0.860064 | − | 0.510185i | \(-0.170423\pi\) | ||||
0.860064 | + | 0.510185i | \(0.170423\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 1937.88 | 0.424940 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 6312.20 | 1.36918 | 0.684591 | − | 0.728927i | \(-0.259981\pi\) | ||||
0.684591 | + | 0.728927i | \(0.259981\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 285.117 | 0.0611811 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −3334.66 | −0.707932 | −0.353966 | − | 0.935258i | \(-0.615167\pi\) | ||||
−0.353966 | + | 0.935258i | \(0.615167\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −725.900 | −0.152474 | −0.0762372 | − | 0.997090i | \(-0.524291\pi\) | ||||
−0.0762372 | + | 0.997090i | \(0.524291\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −439.607 | −0.0913688 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 897.713 | 0.182722 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −1670.41 | −0.336500 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 5681.47 | 1.13282 | 0.566408 | − | 0.824125i | \(-0.308333\pi\) | ||||
0.566408 | + | 0.824125i | \(0.308333\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 672.620 | 0.132751 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 484.229 | 0.0946055 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −955.490 | −0.184807 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 386.411 | 0.0732631 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −1091.85 | −0.204980 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −2469.04 | −0.459008 | −0.229504 | − | 0.973308i | \(-0.573710\pi\) | ||||
−0.229504 | + | 0.973308i | \(0.573710\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −6130.44 | −1.12864 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 4068.00 | 0.741721 | 0.370860 | − | 0.928689i | \(-0.379063\pi\) | ||||
0.370860 | + | 0.928689i | \(0.379063\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −4912.13 | −0.887062 | −0.443531 | − | 0.896259i | \(-0.646274\pi\) | ||||
−0.443531 | + | 0.896259i | \(0.646274\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 2761.17 | 0.489219 | 0.244610 | − | 0.969622i | \(-0.421340\pi\) | ||||
0.244610 | + | 0.969622i | \(0.421340\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 3206.77 | 0.562836 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −806.579 | −0.140246 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −2713.44 | −0.467430 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 2531.00 | 0.431984 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −4006.93 | −0.677626 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −1191.72 | −0.197894 | −0.0989470 | − | 0.995093i | \(-0.531547\pi\) | ||||
−0.0989470 | + | 0.995093i | \(0.531547\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −493.605 | −0.0812294 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −1144.94 | −0.186730 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 4336.34 | 0.700937 | 0.350468 | − | 0.936575i | \(-0.386022\pi\) | ||||
0.350468 | + | 0.936575i | \(0.386022\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 5026.20 | 0.805267 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −568.157 | −0.0902271 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −503.769 | −0.0786146 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 9450.20 | 1.46200 | 0.730999 | − | 0.682379i | \(-0.239054\pi\) | ||||
0.730999 | + | 0.682379i | \(0.239054\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 10654.7 | 1.63418 | 0.817092 | − | 0.576507i | \(-0.195585\pi\) | ||||
0.817092 | + | 0.576507i | \(0.195585\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 632.437 | 0.0961738 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 1702.81 | 0.256746 | 0.128373 | − | 0.991726i | \(-0.459025\pi\) | ||||
0.128373 | + | 0.991726i | \(0.459025\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 43.5509 | 0.00651110 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 4108.61 | 0.604023 | 0.302011 | − | 0.953304i | \(-0.402342\pi\) | ||||
0.302011 | + | 0.953304i | \(0.402342\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −5591.90 | −0.815264 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 3028.07 | 0.437830 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −2405.29 | −0.344928 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 1179.35 | 0.167743 | 0.0838715 | − | 0.996477i | \(-0.473271\pi\) | ||||
0.0838715 | + | 0.996477i | \(0.473271\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 1714.92 | 0.241938 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 7865.22 | 1.09181 | 0.545906 | − | 0.837846i | \(-0.316186\pi\) | ||||
0.545906 | + | 0.837846i | \(0.316186\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 2878.16 | 0.396340 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 4188.27 | 0.572166 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −13076.8 | −1.77233 | −0.886164 | − | 0.463372i | \(-0.846640\pi\) | ||||
−0.886164 | + | 0.463372i | \(0.846640\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 4878.83 | 0.656036 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −2410.38 | −0.321578 | −0.160789 | − | 0.986989i | \(-0.551404\pi\) | ||||
−0.160789 | + | 0.986989i | \(0.551404\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 1187.68 | 0.156003 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 6178.78 | 0.805339 | 0.402669 | − | 0.915346i | \(-0.368082\pi\) | ||||
0.402669 | + | 0.915346i | \(0.368082\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −3109.48 | −0.402182 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −4604.94 | −0.591064 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 753.658 | 0.0960017 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −4809.52 | −0.608017 | −0.304009 | − | 0.952669i | \(-0.598325\pi\) | ||||
−0.304009 | + | 0.952669i | \(0.598325\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 6088.29 | 0.758191 | 0.379096 | − | 0.925357i | \(-0.376235\pi\) | ||||
0.379096 | + | 0.925357i | \(0.376235\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −742.053 | −0.0917228 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 333.444 | 0.0409110 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 983.613 | 0.119793 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 7869.74 | 0.951426 | 0.475713 | − | 0.879600i | \(-0.342190\pi\) | ||||
0.475713 | + | 0.879600i | \(0.342190\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −7399.48 | −0.888052 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −720.884 | −0.0852694 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −3968.03 | −0.465984 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 15279.0 | 1.78145 | 0.890724 | − | 0.454544i | \(-0.150198\pi\) | ||||
0.890724 | + | 0.454544i | \(0.150198\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 6909.70 | 0.799900 | 0.399950 | − | 0.916537i | \(-0.369027\pi\) | ||||
0.399950 | + | 0.916537i | \(0.369027\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 1796.16 | 0.206459 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 8236.72 | 0.940093 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −1260.27 | −0.141833 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 12627.4 | 1.41124 | 0.705618 | − | 0.708592i | \(-0.250669\pi\) | ||||
0.705618 | + | 0.708592i | \(0.250669\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 6738.74 | 0.747906 | 0.373953 | − | 0.927448i | \(-0.378002\pi\) | ||||
0.373953 | + | 0.927448i | \(0.378002\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 2208.21 | 0.243392 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 1452.04 | 0.158948 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −1752.54 | −0.190533 | −0.0952667 | − | 0.995452i | \(-0.530370\pi\) | ||||
−0.0952667 | + | 0.995452i | \(0.530370\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 14286.9 | 1.53226 | 0.766130 | − | 0.642686i | \(-0.222180\pi\) | ||||
0.766130 | + | 0.642686i | \(0.222180\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −194.071 | −0.0206738 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 1944.21 | 0.205722 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −7524.11 | −0.790835 | −0.395417 | − | 0.918501i | \(-0.629400\pi\) | ||||
−0.395417 | + | 0.918501i | \(0.629400\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −3417.35 | −0.356799 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 6011.10 | 0.623457 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 10579.4 | 1.08290 | 0.541448 | − | 0.840734i | \(-0.317876\pi\) | ||||
0.541448 | + | 0.840734i | \(0.317876\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 2058.16 | 0.209295 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −5889.66 | −0.595030 | −0.297515 | − | 0.954717i | \(-0.596158\pi\) | ||||
−0.297515 | + | 0.954717i | \(0.596158\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −12716.5 | −1.27643 | −0.638215 | − | 0.769858i | \(-0.720327\pi\) | ||||
−0.638215 | + | 0.769858i | \(0.720327\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −391.237 | −0.0390176 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −8362.46 | −0.828626 | −0.414313 | − | 0.910134i | \(-0.635978\pi\) | ||||
−0.414313 | + | 0.910134i | \(0.635978\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −2320.77 | −0.227039 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −2366.70 | −0.230066 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −3846.32 | −0.371540 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 2897.16 | 0.278096 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −5404.57 | −0.515535 | −0.257768 | − | 0.966207i | \(-0.582987\pi\) | ||||
−0.257768 | + | 0.966207i | \(0.582987\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1284.67 | 0.121779 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 2292.14 | 0.214599 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 10659.5 | 0.991842 | 0.495921 | − | 0.868368i | \(-0.334831\pi\) | ||||
0.495921 | + | 0.868368i | \(0.334831\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 199.286 | 0.0184295 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 277.130 | 0.0254719 | 0.0127360 | − | 0.999919i | \(-0.495946\pi\) | ||||
0.0127360 | + | 0.999919i | \(0.495946\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 13630.0 | 1.24516 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −664.458 | −0.0603337 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −18108.3 | −1.62453 | −0.812266 | − | 0.583288i | \(-0.801766\pi\) | ||||
−0.812266 | + | 0.583288i | \(0.801766\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −2527.85 | −0.225421 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −3671.00 | −0.325411 | −0.162706 | − | 0.986675i | \(-0.552022\pi\) | ||||
−0.162706 | + | 0.986675i | \(0.552022\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −530.232 | −0.0467228 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 4945.01 | 0.433167 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 17364.1 | 1.51208 | 0.756040 | − | 0.654526i | \(-0.227132\pi\) | ||||
0.756040 | + | 0.654526i | \(0.227132\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −961.103 | −0.0827168 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 8412.17 | 0.719776 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −3579.23 | −0.304476 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 4712.08 | 0.398531 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −2870.45 | −0.241376 | −0.120688 | − | 0.992690i | \(-0.538510\pi\) | ||||
−0.120688 | + | 0.992690i | \(0.538510\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 5735.39 | 0.479524 | 0.239762 | − | 0.970832i | \(-0.422931\pi\) | ||||
0.239762 | + | 0.970832i | \(0.422931\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −2414.88 | −0.199609 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −10503.0 | −0.863239 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 1470.53 | 0.120180 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −4463.29 | −0.362714 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 1106.79 | 0.0894402 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 11012.2 | 0.884940 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 2014.27 | 0.160074 | 0.0800372 | − | 0.996792i | \(-0.474496\pi\) | ||||
0.0800372 | + | 0.996792i | \(0.474496\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −2407.25 | −0.190249 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 5498.30 | 0.432149 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −18005.2 | −1.40740 | −0.703699 | − | 0.710498i | \(-0.748470\pi\) | ||||
−0.703699 | + | 0.710498i | \(0.748470\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −2387.07 | −0.185570 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −6364.83 | −0.492107 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 677.324 | 0.0518032 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 3093.70 | 0.235340 | 0.117670 | − | 0.993053i | \(-0.462458\pi\) | ||||
0.117670 | + | 0.993053i | \(0.462458\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −3091.08 | −0.233880 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −4101.32 | −0.308659 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −18245.4 | −1.36581 | −0.682907 | − | 0.730505i | \(-0.739285\pi\) | ||||
−0.682907 | + | 0.730505i | \(0.739285\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −6896.94 | −0.513551 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 17456.7 | 1.28616 | 0.643079 | − | 0.765800i | \(-0.277657\pi\) | ||||
0.643079 | + | 0.765800i | \(0.277657\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −10013.7 | −0.733902 | −0.366951 | − | 0.930240i | \(-0.619598\pi\) | ||||
−0.366951 | + | 0.930240i | \(0.619598\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −13677.3 | −0.997167 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −4407.70 | −0.319676 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 26521.5 | 1.91353 | 0.956764 | − | 0.290867i | \(-0.0939436\pi\) | ||||
0.956764 | + | 0.290867i | \(0.0939436\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −9401.14 | −0.674781 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −5773.21 | −0.410124 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −867.828 | −0.0613338 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 6734.74 | 0.473547 | 0.236774 | − | 0.971565i | \(-0.423910\pi\) | ||||
0.236774 | + | 0.971565i | \(0.423910\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1127.68 | 0.0788886 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 8417.09 | 0.585842 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 26173.3 | 1.81250 | 0.906248 | − | 0.422746i | \(-0.138934\pi\) | ||||
0.906248 | + | 0.422746i | \(0.138934\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −15771.6 | −1.08122 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 5944.71 | 0.405499 | 0.202750 | − | 0.979231i | \(-0.435012\pi\) | ||||
0.202750 | + | 0.979231i | \(0.435012\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 1988.96 | 0.134994 | 0.0674970 | − | 0.997719i | \(-0.478499\pi\) | ||||
0.0674970 | + | 0.997719i | \(0.478499\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −2503.15 | −0.169048 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −4155.11 | −0.279222 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 1383.89 | 0.0925376 | 0.0462688 | − | 0.998929i | \(-0.485267\pi\) | ||||
0.0462688 | + | 0.998929i | \(0.485267\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −4674.72 | −0.309524 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 1500.35 | 0.0988558 | 0.0494279 | − | 0.998778i | \(-0.484260\pi\) | ||||
0.0494279 | + | 0.998778i | \(0.484260\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −2353.21 | −0.154294 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 15497.7 | 1.01121 | 0.505604 | − | 0.862766i | \(-0.331270\pi\) | ||||
0.505604 | + | 0.862766i | \(0.331270\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 515.002 | 0.0334405 | 0.0167203 | − | 0.999860i | \(-0.494678\pi\) | ||||
0.0167203 | + | 0.999860i | \(0.494678\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −1101.38 | −0.0711703 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 9557.30 | 0.611667 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 1915.20 | 0.121987 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 4180.73 | 0.265018 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −22060.1 | −1.39176 | −0.695880 | − | 0.718158i | \(-0.744985\pi\) | ||||
−0.695880 | + | 0.718158i | \(0.744985\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 9690.89 | 0.608497 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −6694.71 | −0.418380 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 95.2142 | 0.00589455 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −17094.1 | −1.05332 | −0.526660 | − | 0.850076i | \(-0.676556\pi\) | ||||
−0.526660 | + | 0.850076i | \(0.676556\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 2999.98 | 0.183993 | 0.0919965 | − | 0.995759i | \(-0.470675\pi\) | ||||
0.0919965 | + | 0.995759i | \(0.470675\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −1629.73 | −0.0994892 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −8255.72 | −0.501648 | −0.250824 | − | 0.968033i | \(-0.580701\pi\) | ||||
−0.250824 | + | 0.968033i | \(0.580701\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −2930.35 | −0.177236 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −7953.02 | −0.476609 | −0.238304 | − | 0.971191i | \(-0.576592\pi\) | ||||
−0.238304 | + | 0.971191i | \(0.576592\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 6318.88 | 0.376945 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −5258.62 | −0.312266 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 4420.98 | 0.261331 | 0.130665 | − | 0.991427i | \(-0.458289\pi\) | ||||
0.130665 | + | 0.991427i | \(0.458289\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −5830.81 | −0.343105 | −0.171552 | − | 0.985175i | \(-0.554878\pi\) | ||||
−0.171552 | + | 0.985175i | \(0.554878\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −5356.60 | −0.313776 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −7293.79 | −0.423413 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −1299.51 | −0.0751000 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 4756.75 | 0.273670 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 24614.2 | 1.40982 | 0.704910 | − | 0.709297i | \(-0.250987\pi\) | ||||
0.704910 | + | 0.709297i | \(0.250987\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 2917.45 | 0.166360 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −130.989 | −0.00743619 | −0.00371810 | − | 0.999993i | \(-0.501184\pi\) | ||||
−0.00371810 | + | 0.999993i | \(0.501184\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −12325.8 | −0.693576 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 4912.86 | 0.275235 | 0.137617 | − | 0.990485i | \(-0.456056\pi\) | ||||
0.137617 | + | 0.990485i | \(0.456056\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 10153.5 | 0.566346 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 13899.0 | 0.771879 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −7540.22 | −0.416922 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 9639.37 | 0.530678 | 0.265339 | − | 0.964155i | \(-0.414516\pi\) | ||||
0.265339 | + | 0.964155i | \(0.414516\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 5444.92 | 0.297176 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −14525.0 | −0.789346 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −1929.66 | −0.104416 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −18377.9 | −0.990188 | −0.495094 | − | 0.868839i | \(-0.664866\pi\) | ||||
−0.495094 | + | 0.868839i | \(0.664866\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −1952.28 | −0.104739 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −2464.68 | −0.131667 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −8667.23 | −0.459104 | −0.229552 | − | 0.973296i | \(-0.573726\pi\) | ||||
−0.229552 | + | 0.973296i | \(0.573726\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 1647.70 | 0.0869110 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 1292.27 | 0.0678765 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1729.33 | 0.0904523 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 2350.84 | 0.122446 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 13439.1 | 0.697070 | 0.348535 | − | 0.937296i | \(-0.386679\pi\) | ||||
0.348535 | + | 0.937296i | \(0.386679\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −19015.7 | −0.978150 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 19320.6 | 0.989722 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −25085.9 | −1.27976 | −0.639879 | − | 0.768476i | \(-0.721015\pi\) | ||||
−0.639879 | + | 0.768476i | \(0.721015\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 729.000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −10059.4 | −0.508973 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −31020.6 | −1.56313 | −0.781563 | − | 0.623826i | \(-0.785577\pi\) | ||||
−0.781563 | + | 0.623826i | \(0.785577\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 4988.05 | 0.249304 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −12992.4 | −0.646730 | −0.323365 | − | 0.946274i | \(-0.604814\pi\) | ||||
−0.323365 | + | 0.946274i | \(0.604814\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 2501.39 | 0.124009 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 23950.7 | 1.18259 | 0.591297 | − | 0.806454i | \(-0.298616\pi\) | ||||
0.591297 | + | 0.806454i | \(0.298616\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −2667.83 | −0.131197 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −1576.05 | −0.0771950 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −13677.5 | −0.664580 | −0.332290 | − | 0.943177i | \(-0.607821\pi\) | ||||
−0.332290 | + | 0.943177i | \(0.607821\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −17589.0 | −0.851235 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −8248.41 | −0.397603 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −9295.64 | −0.446309 | −0.223154 | − | 0.974783i | \(-0.571635\pi\) | ||||
−0.223154 | + | 0.974783i | \(0.571635\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 2194.73 | 0.104959 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 19586.0 | 0.932970 | 0.466485 | − | 0.884529i | \(-0.345520\pi\) | ||||
0.466485 | + | 0.884529i | \(0.345520\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −2824.20 | −0.133476 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −3827.24 | −0.180174 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −5952.29 | −0.279122 | −0.139561 | − | 0.990213i | \(-0.544569\pi\) | ||||
−0.139561 | + | 0.990213i | \(0.544569\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −12641.3 | −0.590486 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −34379.6 | −1.59968 | −0.799838 | − | 0.600216i | \(-0.795081\pi\) | ||||
−0.799838 | + | 0.600216i | \(0.795081\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −3423.11 | −0.158660 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 6782.78 | 0.311962 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −189.735 | −0.00869300 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 4827.75 | 0.220344 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 3184.55 | 0.144792 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −19167.6 | −0.868172 | −0.434086 | − | 0.900872i | \(-0.642929\pi\) | ||||
−0.434086 | + | 0.900872i | \(0.642929\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −5867.55 | −0.264753 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 6212.65 | 0.278206 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −3975.48 | −0.177353 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −2679.24 | −0.119076 | −0.0595380 | − | 0.998226i | \(-0.518963\pi\) | ||||
−0.0595380 | + | 0.998226i | \(0.518963\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −15213.1 | −0.673592 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −424.293 | −0.0187162 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 10478.9 | 0.460515 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 4583.98 | 0.199955 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 8075.98 | 0.350972 | 0.175486 | − | 0.984482i | \(-0.443850\pi\) | ||||
0.175486 | + | 0.984482i | \(0.443850\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −31378.3 | −1.35862 | −0.679311 | − | 0.733851i | \(-0.737721\pi\) | ||||
−0.679311 | + | 0.733851i | \(0.737721\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −23021.6 | −0.993117 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −273.459 | −0.0117532 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 4697.45 | 0.201154 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 3099.20 | 0.131745 | 0.0658726 | − | 0.997828i | \(-0.479017\pi\) | ||||
0.0658726 | + | 0.997828i | \(0.479017\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 965.740 | 0.0409035 | 0.0204517 | − | 0.999791i | \(-0.493490\pi\) | ||||
0.0204517 | + | 0.999791i | \(0.493490\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −5813.64 | −0.245339 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 7538.11 | 0.316960 | 0.158480 | − | 0.987362i | \(-0.449341\pi\) | ||||
0.158480 | + | 0.987362i | \(0.449341\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −12841.2 | −0.537991 | −0.268995 | − | 0.963141i | \(-0.586692\pi\) | ||||
−0.268995 | + | 0.963141i | \(0.586692\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −18936.6 | −0.790498 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 3468.71 | 0.143760 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −855.352 | −0.0353229 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 13909.3 | 0.572351 | 0.286176 | − | 0.958177i | \(-0.407616\pi\) | ||||
0.286176 | + | 0.958177i | \(0.407616\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 7582.39 | 0.310894 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 10004.0 | 0.408725 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −6785.52 | −0.276248 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 2177.70 | 0.0880311 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −2237.22 | −0.0901188 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −33036.0 | −1.32606 | −0.663030 | − | 0.748593i | \(-0.730730\pi\) | ||||
−0.663030 | + | 0.748593i | \(0.730730\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 1318.82 | 0.0527518 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −15827.5 | −0.630873 | −0.315437 | − | 0.948947i | \(-0.602151\pi\) | ||||
−0.315437 | + | 0.948947i | \(0.602151\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 6933.95 | 0.275417 | 0.137709 | − | 0.990473i | \(-0.456026\pi\) | ||||
0.137709 | + | 0.990473i | \(0.456026\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 25595.4 | 1.00959 | 0.504795 | − | 0.863239i | \(-0.331568\pi\) | ||||
0.504795 | + | 0.863239i | \(0.331568\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −6465.91 | −0.254159 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −2693.14 | −0.105495 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −3283.40 | −0.128172 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 6514.74 | 0.253437 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 5011.24 | 0.194278 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −44274.9 | −1.70474 | −0.852369 | − | 0.522940i | \(-0.824835\pi\) | ||||
−0.852369 | + | 0.522940i | \(0.824835\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −17044.4 | −0.654032 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −5773.97 | −0.220806 | −0.110403 | − | 0.993887i | \(-0.535214\pi\) | ||||
−0.110403 | + | 0.993887i | \(0.535214\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 48171.4 | 1.83590 | 0.917948 | − | 0.396701i | \(-0.129845\pi\) | ||||
0.917948 | + | 0.396701i | \(0.129845\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −2017.86 | −0.0766437 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 48168.5 | 1.82338 | 0.911692 | − | 0.410875i | \(-0.134777\pi\) | ||||
0.911692 | + | 0.410875i | \(0.134777\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −1452.69 | −0.0546205 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 7104.08 | 0.266214 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −15110.9 | −0.564361 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 2866.47 | 0.106699 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −5664.51 | −0.210147 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −24538.3 | −0.907315 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 3303.22 | 0.121329 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −31992.5 | −1.17122 | −0.585608 | − | 0.810595i | \(-0.699144\pi\) | ||||
−0.585608 | + | 0.810595i | \(0.699144\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −1159.23 | −0.0422985 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 21184.7 | 0.770450 | 0.385225 | − | 0.922823i | \(-0.374124\pi\) | ||||
0.385225 | + | 0.922823i | \(0.374124\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 3140.61 | 0.113844 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 3275.54 | 0.118345 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −21647.9 | −0.777040 | −0.388520 | − | 0.921440i | \(-0.627014\pi\) | ||||
−0.388520 | + | 0.921440i | \(0.627014\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 7407.11 | 0.265008 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −247.807 | −0.00883711 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 5926.20 | 0.210651 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 18391.3 | 0.651618 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −9480.99 | −0.334834 | −0.167417 | − | 0.985886i | \(-0.553543\pi\) | ||||
−0.167417 | + | 0.985886i | \(0.553543\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −12204.0 | −0.428233 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 5627.82 | 0.196844 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 2941.86 | 0.102568 | 0.0512841 | − | 0.998684i | \(-0.483669\pi\) | ||||
0.0512841 | + | 0.998684i | \(0.483669\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 14736.4 | 0.512145 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −52683.8 | −1.82513 | −0.912563 | − | 0.408937i | \(-0.865900\pi\) | ||||
−0.912563 | + | 0.408937i | \(0.865900\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 7772.74 | 0.268415 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 45003.1 | 1.54425 | 0.772125 | − | 0.635471i | \(-0.219194\pi\) | ||||
0.772125 | + | 0.635471i | \(0.219194\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 13686.2 | 0.468149 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −8283.50 | −0.282451 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 40137.2 | 1.36429 | 0.682146 | − | 0.731216i | \(-0.261047\pi\) | ||||
0.682146 | + | 0.731216i | \(0.261047\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 18767.9 | 0.635933 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −9620.31 | −0.324954 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −28787.4 | −0.966312 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 2419.74 | 0.0809709 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 12900.2 | 0.430335 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 42055.0 | 1.39855 | 0.699276 | − | 0.714852i | \(-0.253506\pi\) | ||||
0.699276 | + | 0.714852i | \(0.253506\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 8140.33 | 0.269871 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −9772.69 | −0.322987 | −0.161494 | − | 0.986874i | \(-0.551631\pi\) | ||||
−0.161494 | + | 0.986874i | \(0.551631\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −7593.01 | −0.249406 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −11978.1 | −0.392236 | −0.196118 | − | 0.980580i | \(-0.562834\pi\) | ||||
−0.196118 | + | 0.980580i | \(0.562834\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 845.494 | 0.0276018 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 12020.8 | 0.391228 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −56474.0 | −1.83239 | −0.916197 | − | 0.400729i | \(-0.868757\pi\) | ||||
−0.916197 | + | 0.400729i | \(0.868757\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −11549.9 | −0.373615 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 5383.06 | 0.173075 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −48427.6 | −1.55233 | −0.776163 | − | 0.630533i | \(-0.782837\pi\) | ||||
−0.776163 | + | 0.630533i | \(0.782837\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 3575.16 | 0.114254 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 21641.7 | 0.689535 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −29268.6 | −0.929734 | −0.464867 | − | 0.885381i | \(-0.653898\pi\) | ||||
−0.464867 | + | 0.885381i | \(0.653898\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 1480.81 | 0.0468978 |
(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 | 2352.4.a.ck.1.3 | 4 | ||
4.3 | odd | 2 | 1176.4.a.bc.1.3 | yes | 4 | ||
7.6 | odd | 2 | 2352.4.a.cr.1.2 | 4 | |||
28.27 | even | 2 | 1176.4.a.bb.1.2 | ✓ | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1176.4.a.bb.1.2 | ✓ | 4 | 28.27 | even | 2 | ||
1176.4.a.bc.1.3 | yes | 4 | 4.3 | odd | 2 | ||
2352.4.a.ck.1.3 | 4 | 1.1 | even | 1 | trivial | ||
2352.4.a.cr.1.2 | 4 | 7.6 | odd | 2 |