Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [624,4,Mod(1,624)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(624, 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("624.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 624 = 2^{4} \cdot 3 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 624.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: | \(36.8171918436\) |
Analytic rank: | \(0\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.3144.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 16x - 8 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{3} \) |
Twist minimal: | no (minimal twist has level 39) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-3.20905\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 624.1 |
$q$-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 | ||||||||
\(5\) | −11.4322 | −1.02253 | −0.511264 | − | 0.859424i | \(-0.670822\pi\) | ||||
−0.511264 | + | 0.859424i | \(0.670822\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 11.2543 | 0.607675 | 0.303838 | − | 0.952724i | \(-0.401732\pi\) | ||||
0.303838 | + | 0.952724i | \(0.401732\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 9.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −25.8785 | −0.709333 | −0.354666 | − | 0.934993i | \(-0.615406\pi\) | ||||
−0.354666 | + | 0.934993i | \(0.615406\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 13.0000 | 0.277350 | ||||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 34.2966 | 0.590356 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −20.3276 | −0.290010 | −0.145005 | − | 0.989431i | \(-0.546320\pi\) | ||||
−0.145005 | + | 0.989431i | \(0.546320\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −154.712 | −1.86807 | −0.934035 | − | 0.357181i | \(-0.883738\pi\) | ||||
−0.934035 | + | 0.357181i | \(0.883738\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −33.7629 | −0.350841 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 180.418 | 1.63565 | 0.817823 | − | 0.575471i | \(-0.195181\pi\) | ||||
0.817823 | + | 0.575471i | \(0.195181\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 5.69520 | 0.0455616 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −27.0000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −20.4522 | −0.130961 | −0.0654806 | − | 0.997854i | \(-0.520858\pi\) | ||||
−0.0654806 | + | 0.997854i | \(0.520858\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −266.424 | −1.54359 | −0.771794 | − | 0.635873i | \(-0.780640\pi\) | ||||
−0.771794 | + | 0.635873i | \(0.780640\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 77.6355 | 0.409534 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −128.661 | −0.621364 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 115.984 | 0.515340 | 0.257670 | − | 0.966233i | \(-0.417045\pi\) | ||||
0.257670 | + | 0.966233i | \(0.417045\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −39.0000 | −0.160128 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 391.184 | 1.49006 | 0.745032 | − | 0.667029i | \(-0.232434\pi\) | ||||
0.745032 | + | 0.667029i | \(0.232434\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −151.407 | −0.536963 | −0.268482 | − | 0.963285i | \(-0.586522\pi\) | ||||
−0.268482 | + | 0.963285i | \(0.586522\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −102.890 | −0.340842 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 467.365 | 1.45047 | 0.725236 | − | 0.688500i | \(-0.241731\pi\) | ||||
0.725236 | + | 0.688500i | \(0.241731\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −216.341 | −0.630731 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 60.9828 | 0.167437 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 79.9842 | 0.207296 | 0.103648 | − | 0.994614i | \(-0.466949\pi\) | ||||
0.103648 | + | 0.994614i | \(0.466949\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 295.848 | 0.725312 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 464.136 | 1.07853 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 873.710 | 1.92792 | 0.963960 | − | 0.266045i | \(-0.0857171\pi\) | ||||
0.963960 | + | 0.266045i | \(0.0857171\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −187.068 | −0.392649 | −0.196325 | − | 0.980539i | \(-0.562901\pi\) | ||||
−0.196325 | + | 0.980539i | \(0.562901\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 101.289 | 0.202558 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −148.619 | −0.283598 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 609.204 | 1.11084 | 0.555418 | − | 0.831571i | \(-0.312558\pi\) | ||||
0.555418 | + | 0.831571i | \(0.312558\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −541.255 | −0.944340 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −248.038 | −0.414601 | −0.207301 | − | 0.978277i | \(-0.566468\pi\) | ||||
−0.207301 | + | 0.978277i | \(0.566468\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 852.765 | 1.36724 | 0.683621 | − | 0.729838i | \(-0.260404\pi\) | ||||
0.683621 | + | 0.729838i | \(0.260404\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −17.0856 | −0.0263050 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −291.244 | −0.431044 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 331.221 | 0.471712 | 0.235856 | − | 0.971788i | \(-0.424211\pi\) | ||||
0.235856 | + | 0.971788i | \(0.424211\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 81.0000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 435.432 | 0.575842 | 0.287921 | − | 0.957654i | \(-0.407036\pi\) | ||||
0.287921 | + | 0.957654i | \(0.407036\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 232.389 | 0.296543 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 61.3566 | 0.0756105 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 259.233 | 0.308749 | 0.154375 | − | 0.988012i | \(-0.450664\pi\) | ||||
0.154375 | + | 0.988012i | \(0.450664\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 146.306 | 0.168539 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 799.273 | 0.891191 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 1768.70 | 1.91015 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1225.17 | 1.28245 | 0.641223 | − | 0.767355i | \(-0.278428\pi\) | ||||
0.641223 | + | 0.767355i | \(0.278428\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −232.907 | −0.236444 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 645.416 | 0.635855 | 0.317927 | − | 0.948115i | \(-0.397013\pi\) | ||||
0.317927 | + | 0.948115i | \(0.397013\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 511.137 | 0.488969 | 0.244484 | − | 0.969653i | \(-0.421381\pi\) | ||||
0.244484 | + | 0.969653i | \(0.421381\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 385.984 | 0.358745 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −608.195 | −0.549499 | −0.274750 | − | 0.961516i | \(-0.588595\pi\) | ||||
−0.274750 | + | 0.961516i | \(0.588595\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1300.04 | −1.14239 | −0.571197 | − | 0.820813i | \(-0.693521\pi\) | ||||
−0.571197 | + | 0.820813i | \(0.693521\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −347.951 | −0.297532 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 42.1953 | 0.0351274 | 0.0175637 | − | 0.999846i | \(-0.494409\pi\) | ||||
0.0175637 | + | 0.999846i | \(0.494409\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −2062.58 | −1.67249 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 117.000 | 0.0924500 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −228.773 | −0.176232 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −661.303 | −0.496847 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −1173.55 | −0.860289 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1363.92 | 0.975939 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 311.018 | 0.217310 | 0.108655 | − | 0.994080i | \(-0.465346\pi\) | ||||
0.108655 | + | 0.994080i | \(0.465346\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 454.222 | 0.310016 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −2000.98 | −1.33456 | −0.667278 | − | 0.744809i | \(-0.732541\pi\) | ||||
−0.667278 | + | 0.744809i | \(0.732541\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1741.17 | −1.13518 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 308.669 | 0.196785 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 1038.53 | 0.647644 | 0.323822 | − | 0.946118i | \(-0.395032\pi\) | ||||
0.323822 | + | 0.946118i | \(0.395032\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 2858.46 | 1.74426 | 0.872128 | − | 0.489277i | \(-0.162739\pi\) | ||||
0.872128 | + | 0.489277i | \(0.162739\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −1402.09 | −0.837430 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −336.421 | −0.196734 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 233.814 | 0.133911 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 649.022 | 0.364153 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 743.479 | 0.408780 | 0.204390 | − | 0.978890i | \(-0.434479\pi\) | ||||
0.204390 | + | 0.978890i | \(0.434479\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −2277.24 | −1.22728 | −0.613640 | − | 0.789586i | \(-0.710295\pi\) | ||||
−0.613640 | + | 0.789586i | \(0.710295\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −182.948 | −0.0966700 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 3045.82 | 1.57836 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 3173.51 | 1.61321 | 0.806605 | − | 0.591091i | \(-0.201303\pi\) | ||||
0.806605 | + | 0.591091i | \(0.201303\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −239.953 | −0.119682 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 2030.48 | 0.993941 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 2314.65 | 1.11225 | 0.556126 | − | 0.831098i | \(-0.312287\pi\) | ||||
0.556126 | + | 0.831098i | \(0.312287\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −887.545 | −0.418759 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 2665.65 | 1.23517 | 0.617587 | − | 0.786502i | \(-0.288110\pi\) | ||||
0.617587 | + | 0.786502i | \(0.288110\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 169.000 | 0.0769231 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −1392.41 | −0.622690 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −165.243 | −0.0726198 | −0.0363099 | − | 0.999341i | \(-0.511560\pi\) | ||||
−0.0363099 | + | 0.999341i | \(0.511560\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 64.0954 | 0.0276866 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −2621.13 | −1.11309 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −712.339 | −0.297446 | −0.148723 | − | 0.988879i | \(-0.547516\pi\) | ||||
−0.148723 | + | 0.988879i | \(0.547516\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 2206.53 | 0.906133 | 0.453066 | − | 0.891477i | \(-0.350330\pi\) | ||||
0.453066 | + | 0.891477i | \(0.350330\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 561.204 | 0.226696 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −1325.95 | −0.526949 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 526.048 | 0.205714 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −303.866 | −0.116947 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −1470.64 | −0.557129 | −0.278565 | − | 0.960417i | \(-0.589859\pi\) | ||||
−0.278565 | + | 0.960417i | \(0.589859\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 369.560 | 0.137832 | 0.0689158 | − | 0.997622i | \(-0.478046\pi\) | ||||
0.0689158 | + | 0.997622i | \(0.478046\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 445.856 | 0.163735 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −4273.41 | −1.54552 | −0.772761 | − | 0.634697i | \(-0.781125\pi\) | ||||
−0.772761 | + | 0.634697i | \(0.781125\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −4154.31 | −1.47985 | −0.739927 | − | 0.672687i | \(-0.765140\pi\) | ||||
−0.739927 | + | 0.672687i | \(0.765140\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −1827.61 | −0.641342 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −230.175 | −0.0795819 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −4472.09 | −1.52363 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 1623.77 | 0.545215 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 4003.71 | 1.32508 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1231.59 | −0.401830 | −0.200915 | − | 0.979609i | \(-0.564392\pi\) | ||||
−0.200915 | + | 0.979609i | \(0.564392\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 744.114 | 0.239370 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 1730.92 | 0.549059 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −2998.42 | −0.938000 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −2558.30 | −0.789377 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −264.259 | −0.0804343 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 2187.24 | 0.656809 | 0.328404 | − | 0.944537i | \(-0.393489\pi\) | ||||
0.328404 | + | 0.944537i | \(0.393489\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 51.2568 | 0.0151872 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −4138.67 | −1.21010 | −0.605051 | − | 0.796187i | \(-0.706847\pi\) | ||||
−0.605051 | + | 0.796187i | \(0.706847\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −835.354 | −0.241056 | −0.120528 | − | 0.992710i | \(-0.538459\pi\) | ||||
−0.120528 | + | 0.992710i | \(0.538459\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 873.733 | 0.248863 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 3685.51 | 1.03625 | 0.518124 | − | 0.855305i | \(-0.326630\pi\) | ||||
0.518124 | + | 0.855305i | \(0.326630\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −5343.01 | −1.48315 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −993.662 | −0.272343 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −3026.21 | −0.819034 | −0.409517 | − | 0.912303i | \(-0.634303\pi\) | ||||
−0.409517 | + | 0.912303i | \(0.634303\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 3265.58 | 0.872839 | 0.436420 | − | 0.899743i | \(-0.356246\pi\) | ||||
0.436420 | + | 0.899743i | \(0.356246\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −243.000 | −0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 2473.25 | 0.644940 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −2011.25 | −0.518110 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −1306.30 | −0.332463 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 6363.16 | 1.60016 | 0.800078 | − | 0.599897i | \(-0.204792\pi\) | ||||
0.800078 | + | 0.599897i | \(0.204792\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −4668.96 | −1.16022 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −697.168 | −0.171209 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −6085.36 | −1.47702 | −0.738511 | − | 0.674242i | \(-0.764471\pi\) | ||||
−0.738511 | + | 0.674242i | \(0.764471\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1305.31 | 0.313159 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −184.070 | −0.0436538 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −123.227 | −0.0288916 | −0.0144458 | − | 0.999896i | \(-0.504598\pi\) | ||||
−0.0144458 | + | 0.999896i | \(0.504598\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −914.395 | −0.211965 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −777.700 | −0.178256 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −1935.79 | −0.438763 | −0.219381 | − | 0.975639i | \(-0.570404\pi\) | ||||
−0.219381 | + | 0.975639i | \(0.570404\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 4612.69 | 1.03395 | 0.516976 | − | 0.856000i | \(-0.327058\pi\) | ||||
0.516976 | + | 0.856000i | \(0.327058\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −438.918 | −0.0973059 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −147.383 | −0.0323183 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −5834.30 | −1.26552 | −0.632761 | − | 0.774347i | \(-0.718078\pi\) | ||||
−0.632761 | + | 0.774347i | \(0.718078\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −2397.82 | −0.514529 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 4691.91 | 0.996071 | 0.498036 | − | 0.867157i | \(-0.334055\pi\) | ||||
0.498036 | + | 0.867157i | \(0.334055\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −3465.60 | −0.727945 | −0.363973 | − | 0.931410i | \(-0.618580\pi\) | ||||
−0.363973 | + | 0.931410i | \(0.618580\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −5306.09 | −1.10283 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 4402.50 | 0.905475 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −4499.79 | −0.915894 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −3675.51 | −0.740420 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 2677.31 | 0.533822 | 0.266911 | − | 0.963721i | \(-0.413997\pi\) | ||||
0.266911 | + | 0.963721i | \(0.413997\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −9988.43 | −1.97135 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 698.720 | 0.136511 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 2345.44 | 0.453646 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1703.98 | −0.326299 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −1936.25 | −0.367111 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 2138.60 | 0.401494 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −471.915 | −0.0877316 | −0.0438658 | − | 0.999037i | \(-0.513967\pi\) | ||||
−0.0438658 | + | 0.999037i | \(0.513967\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −1533.41 | −0.282306 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 1518.52 | 0.276872 | 0.138436 | − | 0.990371i | \(-0.455793\pi\) | ||||
0.138436 | + | 0.990371i | \(0.455793\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 4049.86 | 0.731348 | 0.365674 | − | 0.930743i | \(-0.380839\pi\) | ||||
0.365674 | + | 0.930743i | \(0.380839\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −1157.95 | −0.207121 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 3253.96 | 0.576532 | 0.288266 | − | 0.957550i | \(-0.406921\pi\) | ||||
0.288266 | + | 0.957550i | \(0.406921\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 529.272 | 0.0928951 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 1824.59 | 0.317254 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 3144.92 | 0.541759 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 74.0375 | 0.0126365 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 3900.11 | 0.659561 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 5259.86 | 0.881415 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 3422.45 | 0.568322 | 0.284161 | − | 0.958777i | \(-0.408285\pi\) | ||||
0.284161 | + | 0.958777i | \(0.408285\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 1043.85 | 0.171780 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −6964.54 | −1.13586 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −9301.67 | −1.50354 | −0.751772 | − | 0.659423i | \(-0.770801\pi\) | ||||
−0.751772 | + | 0.659423i | \(0.770801\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −126.586 | −0.0202808 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 6894.66 | 1.09492 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −6294.99 | −0.990955 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 6187.74 | 0.965613 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −216.898 | −0.0335554 | −0.0167777 | − | 0.999859i | \(-0.505341\pi\) | ||||
−0.0167777 | + | 0.999859i | \(0.505341\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −4809.84 | −0.737721 | −0.368861 | − | 0.929485i | \(-0.620252\pi\) | ||||
−0.368861 | + | 0.929485i | \(0.620252\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −351.000 | −0.0533761 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −2859.64 | −0.431170 | −0.215585 | − | 0.976485i | \(-0.569166\pi\) | ||||
−0.215585 | + | 0.976485i | \(0.569166\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 2835.62 | 0.423941 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 686.319 | 0.101747 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −3686.04 | −0.541899 | −0.270949 | − | 0.962594i | \(-0.587338\pi\) | ||||
−0.270949 | + | 0.962594i | \(0.587338\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 17076.8 | 2.48969 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 1983.91 | 0.286855 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −9748.98 | −1.39804 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 3470.59 | 0.493633 | 0.246816 | − | 0.969062i | \(-0.420616\pi\) | ||||
0.246816 | + | 0.969062i | \(0.420616\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 3520.65 | 0.496688 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 900.166 | 0.125968 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −11963.4 | −1.66070 | −0.830352 | − | 0.557240i | \(-0.811860\pi\) | ||||
−0.830352 | + | 0.557240i | \(0.811860\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −4091.75 | −0.563459 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −265.879 | −0.0363221 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −345.604 | −0.0468403 | −0.0234202 | − | 0.999726i | \(-0.507456\pi\) | ||||
−0.0234202 | + | 0.999726i | \(0.507456\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −933.055 | −0.125464 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 3386.40 | 0.451793 | 0.225897 | − | 0.974151i | \(-0.427469\pi\) | ||||
0.225897 | + | 0.974151i | \(0.427469\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 3329.56 | 0.440754 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −1362.67 | −0.178988 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −1629.88 | −0.212438 | −0.106219 | − | 0.994343i | \(-0.533874\pi\) | ||||
−0.106219 | + | 0.994343i | \(0.533874\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −3667.47 | −0.474353 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 6002.95 | 0.770506 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −3786.58 | −0.482338 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 7938.94 | 1.00364 | 0.501819 | − | 0.864973i | \(-0.332664\pi\) | ||||
0.501819 | + | 0.864973i | \(0.332664\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 5223.52 | 0.655396 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 214.402 | 0.0267001 | 0.0133500 | − | 0.999911i | \(-0.495750\pi\) | ||||
0.0133500 | + | 0.999911i | \(0.495750\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −3463.52 | −0.428114 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −926.008 | −0.113614 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −3001.48 | −0.365548 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −4783.73 | −0.578338 | −0.289169 | − | 0.957278i | \(-0.593379\pi\) | ||||
−0.289169 | + | 0.957278i | \(0.593379\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −3115.58 | −0.373917 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 9832.99 | 1.17155 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −4977.95 | −0.588815 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −8575.39 | −1.00705 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 9903.67 | 1.15472 | 0.577358 | − | 0.816491i | \(-0.304084\pi\) | ||||
0.577358 | + | 0.816491i | \(0.304084\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −12120.6 | −1.40314 | −0.701572 | − | 0.712598i | \(-0.747518\pi\) | ||||
−0.701572 | + | 0.712598i | \(0.747518\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 4206.28 | 0.483491 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −115.770 | −0.0132133 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −2105.32 | −0.238603 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 1009.26 | 0.113584 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 13672.6 | 1.52805 | 0.764023 | − | 0.645189i | \(-0.223221\pi\) | ||||
0.764023 | + | 0.645189i | \(0.223221\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 7113.10 | 0.789455 | 0.394727 | − | 0.918798i | \(-0.370839\pi\) | ||||
0.394727 | + | 0.918798i | \(0.370839\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −701.441 | −0.0773138 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −27912.9 | −3.05550 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 6022.04 | 0.654707 | 0.327353 | − | 0.944902i | \(-0.393843\pi\) | ||||
0.327353 | + | 0.944902i | \(0.393843\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −1947.07 | −0.210244 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 12994.4 | 1.39364 | 0.696821 | − | 0.717245i | \(-0.254597\pi\) | ||||
0.696821 | + | 0.717245i | \(0.254597\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −2963.61 | −0.315704 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −2230.44 | −0.236009 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 10984.3 | 1.15452 | 0.577260 | − | 0.816560i | \(-0.304122\pi\) | ||||
0.577260 | + | 0.816560i | \(0.304122\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −10123.2 | −1.05695 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 6831.72 | 0.708570 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −1672.60 | −0.172335 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 9834.10 | 1.00661 | 0.503304 | − | 0.864109i | \(-0.332118\pi\) | ||||
0.503304 | + | 0.864109i | \(0.332118\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 548.845 | 0.0558124 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 3401.42 | 0.343644 | 0.171822 | − | 0.985128i | \(-0.445035\pi\) | ||||
0.171822 | + | 0.985128i | \(0.445035\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −1739.42 | −0.174596 | −0.0872979 | − | 0.996182i | \(-0.527823\pi\) | ||||
−0.0872979 | + | 0.996182i | \(0.527823\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −9137.45 | −0.911267 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 7958.82 | 0.788630 | 0.394315 | − | 0.918975i | \(-0.370982\pi\) | ||||
0.394315 | + | 0.918975i | \(0.370982\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 6856.16 | 0.675028 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −9520.54 | −0.931387 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 3918.20 | 0.380886 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −881.114 | −0.0851122 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 719.858 | 0.0690986 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −8431.98 | −0.804315 | −0.402158 | − | 0.915570i | \(-0.631740\pi\) | ||||
−0.402158 | + | 0.915570i | \(0.631740\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1507.79 | 0.142930 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −6091.45 | −0.573852 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −14006.4 | −1.31133 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 11684.7 | 1.08723 | 0.543617 | − | 0.839334i | \(-0.317055\pi\) | ||||
0.543617 | + | 0.839334i | \(0.317055\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −6943.94 | −0.642159 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 3954.70 | 0.363489 | 0.181745 | − | 0.983346i | \(-0.441826\pi\) | ||||
0.181745 | + | 0.983346i | \(0.441826\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 415.744 | 0.0379801 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 2662.63 | 0.241771 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −2791.49 | −0.251943 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 5690.37 | 0.510493 | 0.255246 | − | 0.966876i | \(-0.417843\pi\) | ||||
0.255246 | + | 0.966876i | \(0.417843\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −7996.95 | −0.713128 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −10859.1 | −0.962595 | −0.481298 | − | 0.876557i | \(-0.659834\pi\) | ||||
−0.481298 | + | 0.876557i | \(0.659834\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −7378.53 | −0.650178 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −507.000 | −0.0444116 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −18558.6 | −1.61610 | −0.808049 | − | 0.589115i | \(-0.799476\pi\) | ||||
−0.808049 | + | 0.589115i | \(0.799476\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 9597.27 | 0.830838 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 4177.22 | 0.359510 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −5843.42 | −0.499984 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −12094.7 | −1.02887 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 495.730 | 0.0419271 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 17297.5 | 1.45454 | 0.727271 | − | 0.686350i | \(-0.240788\pi\) | ||||
0.727271 | + | 0.686350i | \(0.240788\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 5016.11 | 0.419386 | 0.209693 | − | 0.977767i | \(-0.432753\pi\) | ||||
0.209693 | + | 0.977767i | \(0.432753\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −192.286 | −0.0159849 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 5415.77 | 0.447656 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 20383.8 | 1.67533 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 7863.39 | 0.642640 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 5085.39 | 0.413269 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 6953.01 | 0.561878 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 2137.02 | 0.171730 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 5598.57 | 0.447398 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 17642.3 | 1.40204 | 0.701018 | − | 0.713144i | \(-0.252729\pi\) | ||||
0.701018 | + | 0.713144i | \(0.252729\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −6619.59 | −0.523156 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 14862.3 | 1.16813 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 18414.9 | 1.43943 | 0.719713 | − | 0.694271i | \(-0.244273\pi\) | ||||
0.719713 | + | 0.694271i | \(0.244273\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −1683.61 | −0.130883 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 3164.20 | 0.244645 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 3727.66 | 0.286648 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 3977.84 | 0.304234 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 8179.15 | 0.622193 | 0.311096 | − | 0.950378i | \(-0.399304\pi\) | ||||
0.311096 | + | 0.950378i | \(0.399304\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −1968.30 | −0.148927 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −1578.14 | −0.118769 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 1880.07 | 0.140738 | 0.0703690 | − | 0.997521i | \(-0.477582\pi\) | ||||
0.0703690 | + | 0.997521i | \(0.477582\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −482.385 | −0.0359187 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 911.598 | 0.0675194 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 10118.3 | 0.745485 | 0.372743 | − | 0.927935i | \(-0.378417\pi\) | ||||
0.372743 | + | 0.927935i | \(0.378417\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −23428.9 | −1.71711 | −0.858555 | − | 0.512721i | \(-0.828638\pi\) | ||||
−0.858555 | + | 0.512721i | \(0.828638\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 4411.92 | 0.321659 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 1027.52 | 0.0745225 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 20508.1 | 1.47966 | 0.739831 | − | 0.672793i | \(-0.234906\pi\) | ||||
0.739831 | + | 0.672793i | \(0.234906\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −1108.68 | −0.0795771 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 4900.49 | 0.349925 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −2069.87 | −0.147042 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −1337.57 | −0.0945327 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 5968.43 | 0.419665 | 0.209833 | − | 0.977737i | \(-0.432708\pi\) | ||||
0.209833 | + | 0.977737i | \(0.432708\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 41219.0 | 2.88353 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 12820.2 | 0.892308 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −14659.5 | −1.01517 | −0.507584 | − | 0.861602i | \(-0.669461\pi\) | ||||
−0.507584 | + | 0.861602i | \(0.669461\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 2615.38 | 0.180202 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 12462.9 | 0.854394 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −23635.9 | −1.61225 | −0.806125 | − | 0.591746i | \(-0.798439\pi\) | ||||
−0.806125 | + | 0.591746i | \(0.798439\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −11527.0 | −0.782356 | −0.391178 | − | 0.920315i | \(-0.627932\pi\) | ||||
−0.391178 | + | 0.920315i | \(0.627932\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 5482.83 | 0.370279 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 7560.15 | 0.508039 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 5098.56 | 0.340930 | 0.170465 | − | 0.985364i | \(-0.445473\pi\) | ||||
0.170465 | + | 0.985364i | \(0.445473\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 690.525 | 0.0459466 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 6075.74 | 0.402288 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 1516.39 | 0.0999128 | 0.0499564 | − | 0.998751i | \(-0.484092\pi\) | ||||
0.0499564 | + | 0.998751i | \(0.484092\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 13416.3 | 0.879668 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 18539.3 | 1.20966 | 0.604832 | − | 0.796353i | \(-0.293240\pi\) | ||||
0.604832 | + | 0.796353i | \(0.293240\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −25684.9 | −1.66779 | −0.833897 | − | 0.551920i | \(-0.813895\pi\) | ||||
−0.833897 | + | 0.551920i | \(0.813895\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −4871.30 | −0.314780 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 2917.49 | 0.187619 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −16304.5 | −1.04349 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −12011.1 | −0.765038 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −2357.67 | −0.149454 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 22410.9 | 1.41389 | 0.706945 | − | 0.707269i | \(-0.250073\pi\) | ||||
0.706945 | + | 0.707269i | \(0.250073\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 3694.77 | 0.231997 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −3555.62 | −0.222206 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −2812.43 | −0.174933 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −2232.34 | −0.138200 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 6827.81 | 0.420721 | 0.210361 | − | 0.977624i | \(-0.432536\pi\) | ||||
0.210361 | + | 0.977624i | \(0.432536\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 23264.3 | 1.42684 | 0.713418 | − | 0.700738i | \(-0.247146\pi\) | ||||
0.713418 | + | 0.700738i | \(0.247146\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −5192.76 | −0.316999 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −14745.9 | −0.896014 | −0.448007 | − | 0.894030i | \(-0.647866\pi\) | ||||
−0.448007 | + | 0.894030i | \(0.647866\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −22610.3 | −1.36754 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 8995.26 | 0.541554 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 10909.0 | 0.653755 | 0.326878 | − | 0.945067i | \(-0.394003\pi\) | ||||
0.326878 | + | 0.945067i | \(0.394003\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 22875.7 | 1.36462 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 7674.89 | 0.455747 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 4182.99 | 0.247263 | 0.123631 | − | 0.992328i | \(-0.460546\pi\) | ||||
0.123631 | + | 0.992328i | \(0.460546\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 2224.23 | 0.130881 | 0.0654406 | − | 0.997856i | \(-0.479155\pi\) | ||||
0.0654406 | + | 0.997856i | \(0.479155\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 792.776 | 0.0464387 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 19905.4 | 1.16075 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −3689.95 | −0.214206 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −6561.72 | −0.379209 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 4841.04 | 0.278519 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −24152.5 | −1.38337 | −0.691687 | − | 0.722197i | \(-0.743132\pi\) | ||||
−0.691687 | + | 0.722197i | \(0.743132\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −153.770 | −0.00876833 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −15310.7 | −0.869187 | −0.434593 | − | 0.900627i | \(-0.643108\pi\) | ||||
−0.434593 | + | 0.900627i | \(0.643108\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 13788.4 | 0.779310 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 12416.0 | 0.698652 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −11399.6 | −0.638646 | −0.319323 | − | 0.947646i | \(-0.603455\pi\) | ||||
−0.319323 | + | 0.947646i | \(0.603455\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −11872.6 | −0.662233 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 2506.06 | 0.139174 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 1039.79 | 0.0574935 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 3323.23 | 0.182955 | 0.0914773 | − | 0.995807i | \(-0.470841\pi\) | ||||
0.0914773 | + | 0.995807i | \(0.470841\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −2621.20 | −0.143681 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −32678.5 | −1.78355 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −7951.82 | −0.432133 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −11056.5 | −0.598279 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −12670.4 | −0.682673 | −0.341336 | − | 0.939941i | \(-0.610880\pi\) | ||||
−0.341336 | + | 0.939941i | \(0.610880\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −17944.0 | −0.962692 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 16029.0 | 0.856295 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 7263.71 | 0.386393 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 13075.2 | 0.692594 | 0.346297 | − | 0.938125i | \(-0.387439\pi\) | ||||
0.346297 | + | 0.938125i | \(0.387439\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 2980.99 | 0.157237 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −48067.8 | −2.52476 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 3846.03 | 0.201165 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 9078.62 | 0.472869 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 2988.41 | 0.155005 | 0.0775026 | − | 0.996992i | \(-0.475305\pi\) | ||||
0.0775026 | + | 0.996992i | \(0.475305\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 5752.48 | 0.297134 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −9796.73 | −0.503934 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −116.479 | −0.00596680 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 5507.46 | 0.280963 | 0.140482 | − | 0.990083i | \(-0.455135\pi\) | ||||
0.140482 | + | 0.990083i | \(0.455135\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 729.000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 3077.75 | 0.155725 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −36585.2 | −1.84353 | −0.921764 | − | 0.387751i | \(-0.873252\pi\) | ||||
−0.921764 | + | 0.387751i | \(0.873252\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −7419.75 | −0.372356 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −15765.3 | −0.787953 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −6425.89 | −0.319865 | −0.159933 | − | 0.987128i | \(-0.551128\pi\) | ||||
−0.159933 | + | 0.987128i | \(0.551128\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 6033.76 | 0.299131 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −20411.0 | −1.00782 | −0.503908 | − | 0.863757i | \(-0.668105\pi\) | ||||
−0.503908 | + | 0.863757i | \(0.668105\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −8499.60 | −0.417988 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 3918.89 | 0.191947 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −6844.81 | −0.333917 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 24259.5 | 1.17875 | 0.589375 | − | 0.807860i | \(-0.299374\pi\) | ||||
0.589375 | + | 0.807860i | \(0.299374\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −19089.5 | −0.923850 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 26033.9 | 1.25493 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 9295.39 | 0.446297 | 0.223148 | − | 0.974785i | \(-0.428367\pi\) | ||||
0.223148 | + | 0.974785i | \(0.428367\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 14006.9 | 0.669851 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −21974.7 | −1.04676 | −0.523378 | − | 0.852101i | \(-0.675328\pi\) | ||||
−0.523378 | + | 0.852101i | \(0.675328\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −14631.0 | −0.694204 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 2091.50 | 0.0988476 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 11358.2 | 0.534709 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 22987.4 | 1.07795 | 0.538977 | − | 0.842320i | \(-0.318811\pi\) | ||||
0.538977 | + | 0.842320i | \(0.318811\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 18256.1 | 0.852759 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 31970.9 | 1.48760 | 0.743799 | − | 0.668404i | \(-0.233022\pi\) | ||||
0.743799 | + | 0.668404i | \(0.233022\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −1517.34 | −0.0703283 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −3915.94 | −0.180803 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −60520.8 | −2.78354 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 6418.85 | 0.294090 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 552.209 | 0.0252035 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −36280.2 | −1.64955 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −6087.26 | −0.275715 | −0.137857 | − | 0.990452i | \(-0.544022\pi\) | ||||
−0.137857 | + | 0.990452i | \(0.544022\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 369.680 | 0.0166805 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 474.878 | 0.0213460 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −2431.88 | −0.108901 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 2743.19 | 0.122378 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 23080.0 | 1.02577 | 0.512883 | − | 0.858458i | \(-0.328577\pi\) | ||||
0.512883 | + | 0.858458i | \(0.328577\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −9500.41 | −0.420651 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 2333.10 | 0.102916 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −22068.3 | −0.969829 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −23212.9 | −1.01633 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 5807.37 | 0.253320 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −32377.8 | −1.40710 | −0.703550 | − | 0.710646i | \(-0.748403\pi\) | ||||
−0.703550 | + | 0.710646i | \(0.748403\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −26352.8 | −1.14103 | −0.570513 | − | 0.821288i | \(-0.693256\pi\) | ||||
−0.570513 | + | 0.821288i | \(0.693256\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −13838.1 | −0.596952 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −26461.5 | −1.13731 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 23424.5 | 1.00308 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 1316.75 | 0.0561796 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 35355.3 | 1.50294 | 0.751468 | − | 0.659770i | \(-0.229346\pi\) | ||||
0.751468 | + | 0.659770i | \(0.229346\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 12663.3 | 0.536347 | 0.268173 | − | 0.963371i | \(-0.413580\pi\) | ||||
0.268173 | + | 0.963371i | \(0.413580\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 442.149 | 0.0186590 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 16295.2 | 0.685176 | 0.342588 | − | 0.939486i | \(-0.388697\pi\) | ||||
0.342588 | + | 0.939486i | \(0.388697\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 13638.9 | 0.571411 | 0.285705 | − | 0.958318i | \(-0.407772\pi\) | ||||
0.285705 | + | 0.958318i | \(0.407772\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 17502.9 | 0.730649 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 4397.69 | 0.182918 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −30474.2 | −1.26300 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 7193.46 | 0.297064 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 1890.31 | 0.0777838 | 0.0388919 | − | 0.999243i | \(-0.487617\pi\) | ||||
0.0388919 | + | 0.999243i | \(0.487617\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −23970.7 | −0.982849 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −14075.7 | −0.575082 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −1932.04 | −0.0786559 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −7442.50 | −0.301921 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 10396.8 | 0.420279 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 20925.6 | 0.842914 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 1620.21 | 0.0650351 | 0.0325175 | − | 0.999471i | \(-0.489648\pi\) | ||||
0.0325175 | + | 0.999471i | \(0.489648\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 15918.3 | 0.636718 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −14508.4 | −0.578292 | −0.289146 | − | 0.957285i | \(-0.593371\pi\) | ||||
−0.289146 | + | 0.957285i | \(0.593371\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −29639.8 | −1.17730 | −0.588648 | − | 0.808389i | \(-0.700340\pi\) | ||||
−0.588648 | + | 0.808389i | \(0.700340\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −13207.5 | −0.522776 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −21528.8 | −0.849186 | −0.424593 | − | 0.905384i | \(-0.639583\pi\) | ||||
−0.424593 | + | 0.905384i | \(0.639583\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 1889.10 | 0.0742557 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 13499.4 | 0.528792 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −8571.50 | −0.334601 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 7919.65 | 0.308091 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 11026.5 | 0.427482 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 15349.9 | 0.593054 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 14865.3 | 0.572366 | 0.286183 | − | 0.958175i | \(-0.407613\pi\) | ||||
0.286183 | + | 0.958175i | \(0.407613\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −8031.92 | −0.308202 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −21336.0 | −0.815921 | −0.407961 | − | 0.913000i | \(-0.633760\pi\) | ||||
−0.407961 | + | 0.913000i | \(0.633760\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −37538.2 | −1.43065 | −0.715323 | − | 0.698794i | \(-0.753720\pi\) | ||||
−0.715323 | + | 0.698794i | \(0.753720\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 29965.3 | 1.13816 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −34575.0 | −1.30881 | −0.654406 | − | 0.756144i | \(-0.727081\pi\) | ||||
−0.654406 | + | 0.756144i | \(0.727081\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 3500.29 | 0.132054 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −2096.16 | −0.0788148 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −72306.9 | −2.70958 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 8143.61 | 0.304146 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −7036.32 | −0.261913 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 5448.96 | 0.202150 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −1625.89 | −0.0601178 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 5111.95 | 0.188389 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −25225.5 | −0.926545 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 10424.8 | 0.381641 | 0.190820 | − | 0.981625i | \(-0.438885\pi\) | ||||
0.190820 | + | 0.981625i | \(0.438885\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 5808.75 | 0.211952 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −10961.8 | −0.398661 | −0.199331 | − | 0.979932i | \(-0.563877\pi\) | ||||
−0.199331 | + | 0.979932i | \(0.563877\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −11268.3 | −0.408464 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −6415.80 | −0.231803 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −22519.7 | −0.810976 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 10779.2 | 0.386914 | 0.193457 | − | 0.981109i | \(-0.438030\pi\) | ||||
0.193457 | + | 0.981109i | \(0.438030\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 1415.74 | 0.0506519 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −3224.49 | −0.114990 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 660.549 | 0.0234797 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 4600.23 | 0.162990 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 5429.07 | 0.191735 | 0.0958675 | − | 0.995394i | \(-0.469437\pi\) | ||||
0.0958675 | + | 0.995394i | \(0.469437\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 33470.5 | 1.17825 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −4555.55 | −0.159852 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −6013.88 | −0.210348 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −21300.1 | −0.742631 | −0.371315 | − | 0.928507i | \(-0.621093\pi\) | ||||
−0.371315 | + | 0.928507i | \(0.621093\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −12149.6 | −0.422244 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 26851.2 | 0.930207 | 0.465103 | − | 0.885256i | \(-0.346017\pi\) | ||||
0.465103 | + | 0.885256i | \(0.346017\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 70576.7 | 2.43722 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 3473.86 | 0.119582 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 8021.68 | 0.275258 | 0.137629 | − | 0.990484i | \(-0.456052\pi\) | ||||
0.137629 | + | 0.990484i | \(0.456052\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 11085.9 | 0.379204 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −9761.88 | −0.332861 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 35715.0 | 1.21398 | 0.606990 | − | 0.794709i | \(-0.292377\pi\) | ||||
0.606990 | + | 0.794709i | \(0.292377\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 16812.6 | 0.569680 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −1587.82 | −0.0536330 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 11687.9 | 0.393557 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 41190.9 | 1.38266 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −5473.76 | −0.183166 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −4224.88 | −0.140936 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −53338.8 | −1.77380 | −0.886898 | − | 0.461965i | \(-0.847145\pi\) | ||||
−0.886898 | + | 0.461965i | \(0.847145\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −9434.77 | −0.312785 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −23112.9 | −0.763882 | −0.381941 | − | 0.924187i | \(-0.624744\pi\) | ||||
−0.381941 | + | 0.924187i | \(0.624744\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 32170.0 | 1.05994 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −222.113 | −0.00729569 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −52874.6 | −1.73143 | −0.865715 | − | 0.500538i | \(-0.833136\pi\) | ||||
−0.865715 | + | 0.500538i | \(0.833136\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −6708.57 | −0.219006 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −11700.3 | −0.380798 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −45173.1 | −1.46572 | −0.732858 | − | 0.680381i | \(-0.761814\pi\) | ||||
−0.732858 | + | 0.680381i | \(0.761814\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 48854.5 | 1.58034 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −15779.6 | −0.508885 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −27316.7 | −0.878281 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −60485.6 | −1.93884 | −0.969418 | − | 0.245414i | \(-0.921076\pi\) | ||||
−0.969418 | + | 0.245414i | \(0.921076\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −10267.3 | −0.328121 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 47492.8 | 1.51319 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −18108.1 | −0.575214 | −0.287607 | − | 0.957749i | \(-0.592860\pi\) | ||||
−0.287607 | + | 0.957749i | \(0.592860\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −3131.56 | −0.0991773 |
(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 | 624.4.a.t.1.1 | 3 | ||
3.2 | odd | 2 | 1872.4.a.bk.1.3 | 3 | |||
4.3 | odd | 2 | 39.4.a.c.1.3 | ✓ | 3 | ||
8.3 | odd | 2 | 2496.4.a.bl.1.3 | 3 | |||
8.5 | even | 2 | 2496.4.a.bp.1.3 | 3 | |||
12.11 | even | 2 | 117.4.a.f.1.1 | 3 | |||
20.19 | odd | 2 | 975.4.a.l.1.1 | 3 | |||
28.27 | even | 2 | 1911.4.a.k.1.3 | 3 | |||
52.31 | even | 4 | 507.4.b.g.337.1 | 6 | |||
52.47 | even | 4 | 507.4.b.g.337.6 | 6 | |||
52.51 | odd | 2 | 507.4.a.h.1.1 | 3 | |||
156.155 | even | 2 | 1521.4.a.u.1.3 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
39.4.a.c.1.3 | ✓ | 3 | 4.3 | odd | 2 | ||
117.4.a.f.1.1 | 3 | 12.11 | even | 2 | |||
507.4.a.h.1.1 | 3 | 52.51 | odd | 2 | |||
507.4.b.g.337.1 | 6 | 52.31 | even | 4 | |||
507.4.b.g.337.6 | 6 | 52.47 | even | 4 | |||
624.4.a.t.1.1 | 3 | 1.1 | even | 1 | trivial | ||
975.4.a.l.1.1 | 3 | 20.19 | odd | 2 | |||
1521.4.a.u.1.3 | 3 | 156.155 | even | 2 | |||
1872.4.a.bk.1.3 | 3 | 3.2 | odd | 2 | |||
1911.4.a.k.1.3 | 3 | 28.27 | even | 2 | |||
2496.4.a.bl.1.3 | 3 | 8.3 | odd | 2 | |||
2496.4.a.bp.1.3 | 3 | 8.5 | even | 2 |