Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1200,4,Mod(1,1200)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1200, 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("1200.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1200 = 2^{4} \cdot 3 \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1200.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: | \(70.8022920069\) |
Analytic rank: | \(1\) |
Dimension: | \(1\) |
Coefficient field: | \(\mathbb{Q}\) |
Coefficient ring: | \(\mathbb{Z}\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 600) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Character | \(\chi\) | \(=\) | 1200.1 |
$q$-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 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −19.0000 | −1.02590 | −0.512952 | − | 0.858417i | \(-0.671448\pi\) | ||||
−0.512952 | + | 0.858417i | \(0.671448\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 9.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −22.0000 | −0.603023 | −0.301511 | − | 0.953463i | \(-0.597491\pi\) | ||||
−0.301511 | + | 0.953463i | \(0.597491\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.00000 | −0.0213346 | −0.0106673 | − | 0.999943i | \(-0.503396\pi\) | ||||
−0.0106673 | + | 0.999943i | \(0.503396\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 58.0000 | 0.827474 | 0.413737 | − | 0.910396i | \(-0.364223\pi\) | ||||
0.413737 | + | 0.910396i | \(0.364223\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 53.0000 | 0.639949 | 0.319975 | − | 0.947426i | \(-0.396326\pi\) | ||||
0.319975 | + | 0.947426i | \(0.396326\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −57.0000 | −0.592306 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 58.0000 | 0.525819 | 0.262909 | − | 0.964821i | \(-0.415318\pi\) | ||||
0.262909 | + | 0.964821i | \(0.415318\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 27.0000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 22.0000 | 0.140872 | 0.0704362 | − | 0.997516i | \(-0.477561\pi\) | ||||
0.0704362 | + | 0.997516i | \(0.477561\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 35.0000 | 0.202780 | 0.101390 | − | 0.994847i | \(-0.467671\pi\) | ||||
0.101390 | + | 0.994847i | \(0.467671\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −66.0000 | −0.348155 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 270.000 | 1.19967 | 0.599834 | − | 0.800124i | \(-0.295233\pi\) | ||||
0.599834 | + | 0.800124i | \(0.295233\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −3.00000 | −0.0123176 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −468.000 | −1.78267 | −0.891333 | − | 0.453349i | \(-0.850229\pi\) | ||||
−0.891333 | + | 0.453349i | \(0.850229\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −431.000 | −1.52853 | −0.764266 | − | 0.644901i | \(-0.776899\pi\) | ||||
−0.764266 | + | 0.644901i | \(0.776899\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −230.000 | −0.713807 | −0.356904 | − | 0.934141i | \(-0.616168\pi\) | ||||
−0.356904 | + | 0.934141i | \(0.616168\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 18.0000 | 0.0524781 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 174.000 | 0.477743 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 159.000 | 0.369475 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −446.000 | −0.984140 | −0.492070 | − | 0.870556i | \(-0.663760\pi\) | ||||
−0.492070 | + | 0.870556i | \(0.663760\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 127.000 | 0.266569 | 0.133284 | − | 0.991078i | \(-0.457448\pi\) | ||||
0.133284 | + | 0.991078i | \(0.457448\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −171.000 | −0.341968 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −811.000 | −1.47880 | −0.739399 | − | 0.673268i | \(-0.764890\pi\) | ||||
−0.739399 | + | 0.673268i | \(0.764890\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 174.000 | 0.303582 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −36.0000 | −0.0601748 | −0.0300874 | − | 0.999547i | \(-0.509579\pi\) | ||||
−0.0300874 | + | 0.999547i | \(0.509579\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −522.000 | −0.836924 | −0.418462 | − | 0.908234i | \(-0.637431\pi\) | ||||
−0.418462 | + | 0.908234i | \(0.637431\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 418.000 | 0.618643 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −1368.00 | −1.94825 | −0.974127 | − | 0.226002i | \(-0.927434\pi\) | ||||
−0.974127 | + | 0.226002i | \(0.927434\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 81.0000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −1138.00 | −1.50496 | −0.752480 | − | 0.658615i | \(-0.771143\pi\) | ||||
−0.752480 | + | 0.658615i | \(0.771143\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 66.0000 | 0.0813327 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 144.000 | 0.171505 | 0.0857526 | − | 0.996316i | \(-0.472671\pi\) | ||||
0.0857526 | + | 0.996316i | \(0.472671\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 19.0000 | 0.0218873 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 105.000 | 0.117075 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1079.00 | 1.12944 | 0.564721 | − | 0.825282i | \(-0.308984\pi\) | ||||
0.564721 | + | 0.825282i | \(0.308984\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −198.000 | −0.201008 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1440.00 | −1.41867 | −0.709333 | − | 0.704873i | \(-0.751004\pi\) | ||||
−0.709333 | + | 0.704873i | \(0.751004\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 124.000 | 0.118622 | 0.0593111 | − | 0.998240i | \(-0.481110\pi\) | ||||
0.0593111 | + | 0.998240i | \(0.481110\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −432.000 | −0.390309 | −0.195154 | − | 0.980773i | \(-0.562521\pi\) | ||||
−0.195154 | + | 0.980773i | \(0.562521\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 701.000 | 0.615997 | 0.307998 | − | 0.951387i | \(-0.400341\pi\) | ||||
0.307998 | + | 0.951387i | \(0.400341\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 810.000 | 0.692629 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1044.00 | 0.869126 | 0.434563 | − | 0.900641i | \(-0.356903\pi\) | ||||
0.434563 | + | 0.900641i | \(0.356903\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −9.00000 | −0.00711154 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −1102.00 | −0.848909 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −847.000 | −0.636364 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −1404.00 | −1.02922 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 504.000 | 0.352148 | 0.176074 | − | 0.984377i | \(-0.443660\pi\) | ||||
0.176074 | + | 0.984377i | \(0.443660\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −1293.00 | −0.882498 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −72.0000 | −0.0480204 | −0.0240102 | − | 0.999712i | \(-0.507643\pi\) | ||||
−0.0240102 | + | 0.999712i | \(0.507643\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1007.00 | −0.656526 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 1850.00 | 1.15369 | 0.576847 | − | 0.816852i | \(-0.304283\pi\) | ||||
0.576847 | + | 0.816852i | \(0.304283\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −1836.00 | −1.12034 | −0.560171 | − | 0.828377i | \(-0.689265\pi\) | ||||
−0.560171 | + | 0.828377i | \(0.689265\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −690.000 | −0.412117 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 22.0000 | 0.0128653 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 54.0000 | 0.0302983 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −2398.00 | −1.31847 | −0.659234 | − | 0.751938i | \(-0.729119\pi\) | ||||
−0.659234 | + | 0.751938i | \(0.729119\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1871.00 | −1.00834 | −0.504172 | − | 0.863604i | \(-0.668202\pi\) | ||||
−0.504172 | + | 0.863604i | \(0.668202\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 522.000 | 0.275825 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 3293.00 | 1.67395 | 0.836975 | − | 0.547242i | \(-0.184322\pi\) | ||||
0.836975 | + | 0.547242i | \(0.184322\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −1102.00 | −0.539440 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 883.000 | 0.424306 | 0.212153 | − | 0.977236i | \(-0.431952\pi\) | ||||
0.212153 | + | 0.977236i | \(0.431952\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 4104.00 | 1.90166 | 0.950830 | − | 0.309715i | \(-0.100234\pi\) | ||||
0.950830 | + | 0.309715i | \(0.100234\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −2196.00 | −0.999545 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 477.000 | 0.213316 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −1706.00 | −0.749739 | −0.374869 | − | 0.927078i | \(-0.622312\pi\) | ||||
−0.374869 | + | 0.927078i | \(0.622312\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −1338.00 | −0.568193 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −662.000 | −0.276426 | −0.138213 | − | 0.990403i | \(-0.544136\pi\) | ||||
−0.138213 | + | 0.990403i | \(0.544136\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 4121.00 | 1.69233 | 0.846164 | − | 0.532922i | \(-0.178906\pi\) | ||||
0.846164 | + | 0.532922i | \(0.178906\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 381.000 | 0.153903 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −1276.00 | −0.498986 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −513.000 | −0.197435 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 958.000 | 0.362924 | 0.181462 | − | 0.983398i | \(-0.441917\pi\) | ||||
0.181462 | + | 0.983398i | \(0.441917\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −3187.00 | −1.18863 | −0.594314 | − | 0.804233i | \(-0.702576\pi\) | ||||
−0.594314 | + | 0.804233i | \(0.702576\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 2282.00 | 0.825308 | 0.412654 | − | 0.910888i | \(-0.364602\pi\) | ||||
0.412654 | + | 0.910888i | \(0.364602\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −1043.00 | −0.371539 | −0.185770 | − | 0.982593i | \(-0.559478\pi\) | ||||
−0.185770 | + | 0.982593i | \(0.559478\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −2433.00 | −0.853784 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −418.000 | −0.144521 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 522.000 | 0.175273 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −1166.00 | −0.385904 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −4139.00 | −1.35043 | −0.675214 | − | 0.737621i | \(-0.735949\pi\) | ||||
−0.675214 | + | 0.737621i | \(0.735949\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −108.000 | −0.0347420 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −665.000 | −0.208033 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −1566.00 | −0.483199 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −58.0000 | −0.0176539 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 413.000 | 0.124020 | 0.0620101 | − | 0.998076i | \(-0.480249\pi\) | ||||
0.0620101 | + | 0.998076i | \(0.480249\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 5652.00 | 1.65258 | 0.826292 | − | 0.563242i | \(-0.190446\pi\) | ||||
0.826292 | + | 0.563242i | \(0.190446\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −4391.00 | −1.26710 | −0.633549 | − | 0.773703i | \(-0.718403\pi\) | ||||
−0.633549 | + | 0.773703i | \(0.718403\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 1254.00 | 0.357174 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 2052.00 | 0.576957 | 0.288479 | − | 0.957486i | \(-0.406851\pi\) | ||||
0.288479 | + | 0.957486i | \(0.406851\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −4104.00 | −1.12482 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 4320.00 | 1.16919 | 0.584597 | − | 0.811324i | \(-0.301252\pi\) | ||||
0.584597 | + | 0.811324i | \(0.301252\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 4265.00 | 1.13997 | 0.569985 | − | 0.821655i | \(-0.306949\pi\) | ||||
0.569985 | + | 0.821655i | \(0.306949\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 243.000 | 0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −53.0000 | −0.0136531 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −3414.00 | −0.868889 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 2412.00 | 0.606550 | 0.303275 | − | 0.952903i | \(-0.401920\pi\) | ||||
0.303275 | + | 0.952903i | \(0.401920\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1276.00 | −0.317081 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −6948.00 | −1.68640 | −0.843199 | − | 0.537601i | \(-0.819331\pi\) | ||||
−0.843199 | + | 0.537601i | \(0.819331\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −5130.00 | −1.23074 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 198.000 | 0.0469574 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −3564.00 | −0.835611 | −0.417805 | − | 0.908537i | \(-0.637201\pi\) | ||||
−0.417805 | + | 0.908537i | \(0.637201\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 432.000 | 0.0990186 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −1534.00 | −0.347694 | −0.173847 | − | 0.984773i | \(-0.555620\pi\) | ||||
−0.173847 | + | 0.984773i | \(0.555620\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −7704.00 | −1.72688 | −0.863440 | − | 0.504451i | \(-0.831695\pi\) | ||||
−0.863440 | + | 0.504451i | \(0.831695\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 57.0000 | 0.0126366 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −4877.00 | −1.05787 | −0.528936 | − | 0.848662i | \(-0.677409\pi\) | ||||
−0.528936 | + | 0.848662i | \(0.677409\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 315.000 | 0.0675934 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −3758.00 | −0.797806 | −0.398903 | − | 0.916993i | \(-0.630609\pi\) | ||||
−0.398903 | + | 0.916993i | \(0.630609\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 935.000 | 0.196396 | 0.0981978 | − | 0.995167i | \(-0.468692\pi\) | ||||
0.0981978 | + | 0.995167i | \(0.468692\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 8892.00 | 1.82884 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −1549.00 | −0.315286 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 3237.00 | 0.652084 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −6214.00 | −1.23900 | −0.619498 | − | 0.784998i | \(-0.712664\pi\) | ||||
−0.619498 | + | 0.784998i | \(0.712664\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −594.000 | −0.116052 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −58.0000 | −0.0112181 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 8189.00 | 1.56813 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −4320.00 | −0.819068 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −3905.00 | −0.725961 | −0.362981 | − | 0.931797i | \(-0.618241\pi\) | ||||
−0.362981 | + | 0.931797i | \(0.618241\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 372.000 | 0.0684865 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −9662.00 | −1.76168 | −0.880839 | − | 0.473416i | \(-0.843021\pi\) | ||||
−0.880839 | + | 0.473416i | \(0.843021\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −5147.00 | −0.929475 | −0.464737 | − | 0.885449i | \(-0.653851\pi\) | ||||
−0.464737 | + | 0.885449i | \(0.653851\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 9216.00 | 1.63288 | 0.816439 | − | 0.577432i | \(-0.195945\pi\) | ||||
0.816439 | + | 0.577432i | \(0.195945\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −484.000 | −0.0849492 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −1296.00 | −0.225345 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 3074.00 | 0.529542 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 2103.00 | 0.355646 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 4370.00 | 0.732298 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −2196.00 | −0.364662 | −0.182331 | − | 0.983237i | \(-0.558364\pi\) | ||||
−0.182331 | + | 0.983237i | \(0.558364\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 2430.00 | 0.399889 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −2521.00 | −0.407500 | −0.203750 | − | 0.979023i | \(-0.565313\pi\) | ||||
−0.203750 | + | 0.979023i | \(0.565313\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 3132.00 | 0.501790 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −770.000 | −0.122281 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 6175.00 | 0.972066 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 7034.00 | 1.08820 | 0.544099 | − | 0.839021i | \(-0.316871\pi\) | ||||
0.544099 | + | 0.839021i | \(0.316871\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 7362.00 | 1.12917 | 0.564583 | − | 0.825376i | \(-0.309037\pi\) | ||||
0.564583 | + | 0.825376i | \(0.309037\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −27.0000 | −0.00410585 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 9382.00 | 1.41460 | 0.707300 | − | 0.706914i | \(-0.249913\pi\) | ||||
0.707300 | + | 0.706914i | \(0.249913\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −3306.00 | −0.490118 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 10116.0 | 1.48719 | 0.743596 | − | 0.668629i | \(-0.233119\pi\) | ||||
0.743596 | + | 0.668629i | \(0.233119\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −4050.00 | −0.590465 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −2541.00 | −0.367405 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −3277.00 | −0.466098 | −0.233049 | − | 0.972465i | \(-0.574870\pi\) | ||||
−0.233049 | + | 0.972465i | \(0.574870\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −4212.00 | −0.594222 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −10891.0 | −1.51184 | −0.755918 | − | 0.654667i | \(-0.772809\pi\) | ||||
−0.755918 | + | 0.654667i | \(0.772809\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −22.0000 | −0.00300546 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 2591.00 | 0.351163 | 0.175581 | − | 0.984465i | \(-0.443819\pi\) | ||||
0.175581 | + | 0.984465i | \(0.443819\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 1512.00 | 0.203313 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −612.000 | −0.0816494 | −0.0408247 | − | 0.999166i | \(-0.512999\pi\) | ||||
−0.0408247 | + | 0.999166i | \(0.512999\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −3879.00 | −0.509511 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 3708.00 | 0.483298 | 0.241649 | − | 0.970364i | \(-0.422312\pi\) | ||||
0.241649 | + | 0.970364i | \(0.422312\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 3364.00 | 0.435102 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −216.000 | −0.0277246 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 3833.00 | 0.484566 | 0.242283 | − | 0.970206i | \(-0.422104\pi\) | ||||
0.242283 | + | 0.970206i | \(0.422104\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −3021.00 | −0.379046 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −9288.00 | −1.15666 | −0.578330 | − | 0.815803i | \(-0.696295\pi\) | ||||
−0.578330 | + | 0.815803i | \(0.696295\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −35.0000 | −0.00432624 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −5940.00 | −0.723427 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −755.000 | −0.0912771 | −0.0456386 | − | 0.998958i | \(-0.514532\pi\) | ||||
−0.0456386 | + | 0.998958i | \(0.514532\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 5550.00 | 0.666086 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 8474.00 | 1.00963 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −5508.00 | −0.646830 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 9576.00 | 1.11651 | 0.558256 | − | 0.829669i | \(-0.311471\pi\) | ||||
0.558256 | + | 0.829669i | \(0.311471\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 9414.00 | 1.08981 | 0.544905 | − | 0.838498i | \(-0.316566\pi\) | ||||
0.544905 | + | 0.838498i | \(0.316566\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −2070.00 | −0.237936 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −2413.00 | −0.273474 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 66.0000 | 0.00742776 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 2254.00 | 0.251906 | 0.125953 | − | 0.992036i | \(-0.459801\pi\) | ||||
0.125953 | + | 0.992036i | \(0.459801\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 6301.00 | 0.699323 | 0.349661 | − | 0.936876i | \(-0.386297\pi\) | ||||
0.349661 | + | 0.936876i | \(0.386297\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 3074.00 | 0.336497 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 3779.00 | 0.410847 | 0.205423 | − | 0.978673i | \(-0.434143\pi\) | ||||
0.205423 | + | 0.978673i | \(0.434143\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 162.000 | 0.0174927 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 7632.00 | 0.818527 | 0.409263 | − | 0.912416i | \(-0.365786\pi\) | ||||
0.409263 | + | 0.912416i | \(0.365786\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −7194.00 | −0.761218 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 2988.00 | 0.314059 | 0.157029 | − | 0.987594i | \(-0.449808\pi\) | ||||
0.157029 | + | 0.987594i | \(0.449808\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 10296.0 | 1.07499 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −5613.00 | −0.582167 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 1370.00 | 0.140232 | 0.0701159 | − | 0.997539i | \(-0.477663\pi\) | ||||
0.0701159 | + | 0.997539i | \(0.477663\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 1566.00 | 0.159248 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −7992.00 | −0.807429 | −0.403714 | − | 0.914885i | \(-0.632281\pi\) | ||||
−0.403714 | + | 0.914885i | \(0.632281\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −3096.00 | −0.310763 | −0.155382 | − | 0.987855i | \(-0.549661\pi\) | ||||
−0.155382 | + | 0.987855i | \(0.549661\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −8338.00 | −0.826203 | −0.413101 | − | 0.910685i | \(-0.635554\pi\) | ||||
−0.413101 | + | 0.910685i | \(0.635554\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 15409.0 | 1.51710 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 9879.00 | 0.966455 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 9482.00 | 0.921740 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −4918.00 | −0.469121 | −0.234561 | − | 0.972101i | \(-0.575365\pi\) | ||||
−0.234561 | + | 0.972101i | \(0.575365\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −270.000 | −0.0255945 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −3306.00 | −0.311446 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −19637.0 | −1.82718 | −0.913591 | − | 0.406635i | \(-0.866702\pi\) | ||||
−0.913591 | + | 0.406635i | \(0.866702\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 2649.00 | 0.244973 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −3096.00 | −0.284563 | −0.142282 | − | 0.989826i | \(-0.545444\pi\) | ||||
−0.142282 | + | 0.989826i | \(0.545444\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 1276.00 | 0.116568 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 684.000 | 0.0617336 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −6875.00 | −0.616768 | −0.308384 | − | 0.951262i | \(-0.599788\pi\) | ||||
−0.308384 | + | 0.951262i | \(0.599788\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 12312.0 | 1.09792 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 11268.0 | 0.998838 | 0.499419 | − | 0.866361i | \(-0.333547\pi\) | ||||
0.499419 | + | 0.866361i | \(0.333547\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −6588.00 | −0.577087 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 16078.0 | 1.40009 | 0.700044 | − | 0.714100i | \(-0.253164\pi\) | ||||
0.700044 | + | 0.714100i | \(0.253164\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 9918.00 | 0.858604 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 1431.00 | 0.123158 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 5060.00 | 0.430442 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −5118.00 | −0.432862 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −17366.0 | −1.46030 | −0.730152 | − | 0.683285i | \(-0.760551\pi\) | ||||
−0.730152 | + | 0.683285i | \(0.760551\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −4913.00 | −0.410766 | −0.205383 | − | 0.978682i | \(-0.565844\pi\) | ||||
−0.205383 | + | 0.978682i | \(0.565844\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 2030.00 | 0.167795 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −8803.00 | −0.723514 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −4014.00 | −0.328047 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 468.000 | 0.0380325 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −1986.00 | −0.159594 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −396.000 | −0.0316455 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 17605.0 | 1.39907 | 0.699536 | − | 0.714597i | \(-0.253390\pi\) | ||||
0.699536 | + | 0.714597i | \(0.253390\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 12363.0 | 0.977067 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −14560.0 | −1.13810 | −0.569050 | − | 0.822303i | \(-0.692689\pi\) | ||||
−0.569050 | + | 0.822303i | \(0.692689\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 1143.00 | 0.0888562 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1166.00 | 0.0901511 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 25992.0 | 1.99872 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 20614.0 | 1.56812 | 0.784060 | − | 0.620685i | \(-0.213145\pi\) | ||||
0.784060 | + | 0.620685i | \(0.213145\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 431.000 | 0.0326107 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −3828.00 | −0.288090 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 3442.00 | 0.257661 | 0.128830 | − | 0.991667i | \(-0.458878\pi\) | ||||
0.128830 | + | 0.991667i | \(0.458878\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −1539.00 | −0.113989 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 22082.0 | 1.62693 | 0.813467 | − | 0.581611i | \(-0.197577\pi\) | ||||
0.813467 | + | 0.581611i | \(0.197577\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −451.000 | −0.0330539 | −0.0165269 | − | 0.999863i | \(-0.505261\pi\) | ||||
−0.0165269 | + | 0.999863i | \(0.505261\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 2874.00 | 0.209534 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −20987.0 | −1.51421 | −0.757106 | − | 0.653292i | \(-0.773387\pi\) | ||||
−0.757106 | + | 0.653292i | \(0.773387\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −9561.00 | −0.686255 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 21622.0 | 1.54394 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 3888.00 | 0.273381 | 0.136691 | − | 0.990614i | \(-0.456353\pi\) | ||||
0.136691 | + | 0.990614i | \(0.456353\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1855.00 | 0.129769 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 6846.00 | 0.476492 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 11268.0 | 0.780306 | 0.390153 | − | 0.920750i | \(-0.372422\pi\) | ||||
0.390153 | + | 0.920750i | \(0.372422\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −3129.00 | −0.214508 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 3996.00 | 0.272575 | 0.136287 | − | 0.990669i | \(-0.456483\pi\) | ||||
0.136287 | + | 0.990669i | \(0.456483\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −24965.0 | −1.69442 | −0.847208 | − | 0.531262i | \(-0.821718\pi\) | ||||
−0.847208 | + | 0.531262i | \(0.821718\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −7299.00 | −0.492932 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 4176.00 | 0.279240 | 0.139620 | − | 0.990205i | \(-0.455412\pi\) | ||||
0.139620 | + | 0.990205i | \(0.455412\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −1254.00 | −0.0834395 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 230.000 | 0.0152288 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 9558.00 | 0.629762 | 0.314881 | − | 0.949131i | \(-0.398035\pi\) | ||||
0.314881 | + | 0.949131i | \(0.398035\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 9000.00 | 0.587239 | 0.293619 | − | 0.955922i | \(-0.405140\pi\) | ||||
0.293619 | + | 0.955922i | \(0.405140\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 15625.0 | 1.01457 | 0.507287 | − | 0.861777i | \(-0.330648\pi\) | ||||
0.507287 | + | 0.861777i | \(0.330648\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1566.00 | 0.101194 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −2736.00 | −0.175948 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −3498.00 | −0.222802 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 15660.0 | 0.992695 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 31175.0 | 1.96681 | 0.983405 | − | 0.181424i | \(-0.0580705\pi\) | ||||
0.983405 | + | 0.181424i | \(0.0580705\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −12417.0 | −0.779671 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −18.0000 | −0.00111960 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −324.000 | −0.0200583 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −6732.00 | −0.414817 | −0.207409 | − | 0.978254i | \(-0.566503\pi\) | ||||
−0.207409 | + | 0.978254i | \(0.566503\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −6228.00 | −0.381973 | −0.190986 | − | 0.981593i | \(-0.561169\pi\) | ||||
−0.190986 | + | 0.981593i | \(0.561169\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −396.000 | −0.0240624 | −0.0120312 | − | 0.999928i | \(-0.503830\pi\) | ||||
−0.0120312 | + | 0.999928i | \(0.503830\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 9812.00 | 0.593459 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −1995.00 | −0.120108 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 4702.00 | 0.281782 | 0.140891 | − | 0.990025i | \(-0.455003\pi\) | ||||
0.140891 | + | 0.990025i | \(0.455003\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −4698.00 | −0.278975 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 22140.0 | 1.30873 | 0.654364 | − | 0.756180i | \(-0.272936\pi\) | ||||
0.654364 | + | 0.756180i | \(0.272936\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −13518.0 | −0.795445 | −0.397723 | − | 0.917506i | \(-0.630199\pi\) | ||||
−0.397723 | + | 0.917506i | \(0.630199\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −174.000 | −0.0101925 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1276.00 | 0.0740733 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 1239.00 | 0.0716032 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −2794.00 | −0.160747 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 11250.0 | 0.644362 | 0.322181 | − | 0.946678i | \(-0.395584\pi\) | ||||
0.322181 | + | 0.946678i | \(0.395584\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 15170.0 | 0.861197 | 0.430599 | − | 0.902544i | \(-0.358302\pi\) | ||||
0.430599 | + | 0.902544i | \(0.358302\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −20501.0 | −1.15870 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 16956.0 | 0.954119 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 22680.0 | 1.27061 | 0.635305 | − | 0.772262i | \(-0.280875\pi\) | ||||
0.635305 | + | 0.772262i | \(0.280875\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −13173.0 | −0.731559 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −128.000 | −0.00704682 | −0.00352341 | − | 0.999994i | \(-0.501122\pi\) | ||||
−0.00352341 | + | 0.999994i | \(0.501122\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 3762.00 | 0.206214 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −27144.0 | −1.47511 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 6156.00 | 0.333106 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 25682.0 | 1.38373 | 0.691866 | − | 0.722026i | \(-0.256789\pi\) | ||||
0.691866 | + | 0.722026i | \(0.256789\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 14310.0 | 0.767727 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 27360.0 | 1.45542 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −4951.00 | −0.262255 | −0.131127 | − | 0.991366i | \(-0.541860\pi\) | ||||
−0.131127 | + | 0.991366i | \(0.541860\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −12312.0 | −0.649418 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 2030.00 | 0.106626 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 12960.0 | 0.675035 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 22190.0 | 1.15097 | 0.575485 | − | 0.817812i | \(-0.304813\pi\) | ||||
0.575485 | + | 0.817812i | \(0.304813\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −2356.00 | −0.121695 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 12795.0 | 0.658162 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 7685.00 | 0.392051 | 0.196025 | − | 0.980599i | \(-0.437197\pi\) | ||||
0.196025 | + | 0.980599i | \(0.437197\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 729.000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −24998.0 | −1.26482 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −29574.0 | −1.49023 | −0.745116 | − | 0.666934i | \(-0.767606\pi\) | ||||
−0.745116 | + | 0.666934i | \(0.767606\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 17842.0 | 0.891748 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 32580.0 | 1.62175 | 0.810876 | − | 0.585218i | \(-0.198991\pi\) | ||||
0.810876 | + | 0.585218i | \(0.198991\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −159.000 | −0.00788261 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −3060.00 | −0.151091 | −0.0755454 | − | 0.997142i | \(-0.524070\pi\) | ||||
−0.0755454 | + | 0.997142i | \(0.524070\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −10242.0 | −0.501654 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 8208.00 | 0.400419 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 7992.00 | 0.388325 | 0.194163 | − | 0.980969i | \(-0.437801\pi\) | ||||
0.194163 | + | 0.980969i | \(0.437801\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 7236.00 | 0.350192 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −22841.0 | −1.09666 | −0.548329 | − | 0.836263i | \(-0.684736\pi\) | ||||
−0.548329 | + | 0.836263i | \(0.684736\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −3828.00 | −0.183067 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −17172.0 | −0.817982 | −0.408991 | − | 0.912538i | \(-0.634119\pi\) | ||||
−0.408991 | + | 0.912538i | \(0.634119\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −13319.0 | −0.631953 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 446.000 | 0.0209963 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −30869.0 | −1.44755 | −0.723774 | − | 0.690037i | \(-0.757594\pi\) | ||||
−0.723774 | + | 0.690037i | \(0.757594\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −20844.0 | −0.973642 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −34884.0 | −1.62314 | −0.811572 | − | 0.584252i | \(-0.801388\pi\) | ||||
−0.811572 | + | 0.584252i | \(0.801388\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −15390.0 | −0.710570 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −24804.0 | −1.14082 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 792.000 | 0.0362868 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 594.000 | 0.0271109 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 5039.00 | 0.228235 | 0.114118 | − | 0.993467i | \(-0.463596\pi\) | ||||
0.114118 | + | 0.993467i | \(0.463596\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −10692.0 | −0.482440 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −19836.0 | −0.891640 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −127.000 | −0.00568714 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −540.000 | −0.0239997 | −0.0119999 | − | 0.999928i | \(-0.503820\pi\) | ||||
−0.0119999 | + | 0.999928i | \(0.503820\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −13340.0 | −0.590657 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 1296.00 | 0.0571684 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 11484.0 | 0.504684 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −4602.00 | −0.200741 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −41328.0 | −1.79606 | −0.898032 | − | 0.439931i | \(-0.855003\pi\) | ||||
−0.898032 | + | 0.439931i | \(0.855003\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 12853.0 | 0.556510 | 0.278255 | − | 0.960507i | \(-0.410244\pi\) | ||||
0.278255 | + | 0.960507i | \(0.410244\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −23112.0 | −0.997015 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −22843.0 | −0.978183 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 171.000 | 0.00729576 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 29470.0 | 1.25275 | 0.626376 | − | 0.779521i | \(-0.284537\pi\) | ||||
0.626376 | + | 0.779521i | \(0.284537\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −24407.0 | −1.03375 | −0.516874 | − | 0.856062i | \(-0.672904\pi\) | ||||
−0.516874 | + | 0.856062i | \(0.672904\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 15048.0 | 0.632733 | 0.316367 | − | 0.948637i | \(-0.397537\pi\) | ||||
0.316367 | + | 0.948637i | \(0.397537\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −28406.0 | −1.19009 | −0.595043 | − | 0.803694i | \(-0.702865\pi\) | ||||
−0.595043 | + | 0.803694i | \(0.702865\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −14631.0 | −0.610763 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 1044.00 | 0.0434243 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 945.000 | 0.0390251 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 26914.0 | 1.10748 | 0.553739 | − | 0.832690i | \(-0.313200\pi\) | ||||
0.553739 | + | 0.832690i | \(0.313200\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −23905.0 | −0.980155 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −11274.0 | −0.460614 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 16093.0 | 0.652848 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 2805.00 | 0.113389 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 15660.0 | 0.630808 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −21275.0 | −0.853977 | −0.426988 | − | 0.904257i | \(-0.640425\pi\) | ||||
−0.426988 | + | 0.904257i | \(0.640425\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −39132.0 | −1.55977 | −0.779885 | − | 0.625922i | \(-0.784723\pi\) | ||||
−0.779885 | + | 0.625922i | \(0.784723\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 448.000 | 0.0177946 | 0.00889730 | − | 0.999960i | \(-0.497168\pi\) | ||||
0.00889730 | + | 0.999960i | \(0.497168\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 26676.0 | 1.05588 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −26856.0 | −1.05932 | −0.529658 | − | 0.848212i | \(-0.677680\pi\) | ||||
−0.529658 | + | 0.848212i | \(0.677680\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −4647.00 | −0.182030 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 30096.0 | 1.17484 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 811.000 | 0.0315496 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 9711.00 | 0.376481 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 3653.00 | 0.140653 | 0.0703267 | − | 0.997524i | \(-0.477596\pi\) | ||||
0.0703267 | + | 0.997524i | \(0.477596\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −18642.0 | −0.715335 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −6552.00 | −0.250559 | −0.125280 | − | 0.992121i | \(-0.539983\pi\) | ||||
−0.125280 | + | 0.992121i | \(0.539983\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 4481.00 | 0.170779 | 0.0853894 | − | 0.996348i | \(-0.472787\pi\) | ||||
0.0853894 | + | 0.996348i | \(0.472787\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −14666.0 | −0.555170 | −0.277585 | − | 0.960701i | \(-0.589534\pi\) | ||||
−0.277585 | + | 0.960701i | \(0.589534\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −9576.00 | −0.361270 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −1782.00 | −0.0670025 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −12190.0 | −0.456800 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −174.000 | −0.00647680 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 770.000 | 0.0285661 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 24567.0 | 0.905358 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 51804.0 | 1.89650 | 0.948249 | − | 0.317528i | \(-0.102853\pi\) | ||||
0.948249 | + | 0.317528i | \(0.102853\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −12960.0 | −0.472889 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −31198.0 | −1.13462 | −0.567308 | − | 0.823505i | \(-0.692015\pi\) | ||||
−0.567308 | + | 0.823505i | \(0.692015\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 25036.0 | 0.907525 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 1368.00 | 0.0492643 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 27001.0 | 0.969185 | 0.484592 | − | 0.874740i | \(-0.338968\pi\) | ||||
0.484592 | + | 0.874740i | \(0.338968\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −11715.0 | −0.419134 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 36.0000 | 0.00128381 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 1116.00 | 0.0395407 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −22694.0 | −0.801470 | −0.400735 | − | 0.916194i | \(-0.631245\pi\) | ||||
−0.400735 | + | 0.916194i | \(0.631245\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 954.000 | 0.0335833 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −28986.0 | −1.01711 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −29503.0 | −1.02862 | −0.514312 | − | 0.857603i | \(-0.671953\pi\) | ||||
−0.514312 | + | 0.857603i | \(0.671953\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −15441.0 | −0.536633 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 14566.0 | 0.504610 | 0.252305 | − | 0.967648i | \(-0.418811\pi\) | ||||
0.252305 | + | 0.967648i | \(0.418811\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −27144.0 | −0.937360 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 42322.0 | 1.45225 | 0.726125 | − | 0.687563i | \(-0.241319\pi\) | ||||
0.726125 | + | 0.687563i | \(0.241319\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 522.000 | 0.0178555 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 27648.0 | 0.942742 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −43416.0 | −1.47574 | −0.737871 | − | 0.674942i | \(-0.764169\pi\) | ||||
−0.737871 | + | 0.674942i | \(0.764169\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −1452.00 | −0.0490454 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −35150.0 | −1.18358 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −28566.0 | −0.958880 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −3888.00 | −0.130103 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 21528.0 | 0.715919 | 0.357960 | − | 0.933737i | \(-0.383473\pi\) | ||||
0.357960 | + | 0.933737i | \(0.383473\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 9222.00 | 0.305731 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −27050.0 | −0.894002 | −0.447001 | − | 0.894533i | \(-0.647508\pi\) | ||||
−0.447001 | + | 0.894533i | \(0.647508\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 34884.0 | 1.14936 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 24934.0 | 0.816489 | 0.408244 | − | 0.912873i | \(-0.366141\pi\) | ||||
0.408244 | + | 0.912873i | \(0.366141\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −3168.00 | −0.103422 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 6309.00 | 0.205332 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 8388.00 | 0.272162 | 0.136081 | − | 0.990698i | \(-0.456549\pi\) | ||||
0.136081 | + | 0.990698i | \(0.456549\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 13110.0 | 0.422792 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −24998.0 | −0.803731 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −29033.0 | −0.930639 | −0.465320 | − | 0.885143i | \(-0.654061\pi\) | ||||
−0.465320 | + | 0.885143i | \(0.654061\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −6588.00 | −0.210538 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 25326.0 | 0.804496 | 0.402248 | − | 0.915531i | \(-0.368229\pi\) | ||||
0.402248 | + | 0.915531i | \(0.368229\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 7290.00 | 0.230876 |
(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 | 1200.4.a.x.1.1 | 1 | ||
4.3 | odd | 2 | 600.4.a.g.1.1 | ✓ | 1 | ||
5.2 | odd | 4 | 1200.4.f.f.49.1 | 2 | |||
5.3 | odd | 4 | 1200.4.f.f.49.2 | 2 | |||
5.4 | even | 2 | 1200.4.a.n.1.1 | 1 | |||
12.11 | even | 2 | 1800.4.a.bf.1.1 | 1 | |||
20.3 | even | 4 | 600.4.f.h.49.1 | 2 | |||
20.7 | even | 4 | 600.4.f.h.49.2 | 2 | |||
20.19 | odd | 2 | 600.4.a.j.1.1 | yes | 1 | ||
60.23 | odd | 4 | 1800.4.f.g.649.1 | 2 | |||
60.47 | odd | 4 | 1800.4.f.g.649.2 | 2 | |||
60.59 | even | 2 | 1800.4.a.g.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
600.4.a.g.1.1 | ✓ | 1 | 4.3 | odd | 2 | ||
600.4.a.j.1.1 | yes | 1 | 20.19 | odd | 2 | ||
600.4.f.h.49.1 | 2 | 20.3 | even | 4 | |||
600.4.f.h.49.2 | 2 | 20.7 | even | 4 | |||
1200.4.a.n.1.1 | 1 | 5.4 | even | 2 | |||
1200.4.a.x.1.1 | 1 | 1.1 | even | 1 | trivial | ||
1200.4.f.f.49.1 | 2 | 5.2 | odd | 4 | |||
1200.4.f.f.49.2 | 2 | 5.3 | odd | 4 | |||
1800.4.a.g.1.1 | 1 | 60.59 | even | 2 | |||
1800.4.a.bf.1.1 | 1 | 12.11 | even | 2 | |||
1800.4.f.g.649.1 | 2 | 60.23 | odd | 4 | |||
1800.4.f.g.649.2 | 2 | 60.47 | odd | 4 |