Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [396,4,Mod(1,396)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(396, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("396.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 396 = 2^{2} \cdot 3^{2} \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 396.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: | \(23.3647563623\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{31}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - 31 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Fricke sign: | \(+1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(5.56776\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 396.1 |
$q$-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 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 5.13553 | 0.459336 | 0.229668 | − | 0.973269i | \(-0.426236\pi\) | ||||
0.229668 | + | 0.973269i | \(0.426236\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.864471 | −0.0466771 | −0.0233385 | − | 0.999728i | \(-0.507430\pi\) | ||||
−0.0233385 | + | 0.999728i | \(0.507430\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 11.0000 | 0.301511 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 51.6776 | 1.10252 | 0.551262 | − | 0.834333i | \(-0.314147\pi\) | ||||
0.551262 | + | 0.834333i | \(0.314147\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −52.8132 | −0.753475 | −0.376738 | − | 0.926320i | \(-0.622954\pi\) | ||||
−0.376738 | + | 0.926320i | \(0.622954\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −56.2711 | −0.679446 | −0.339723 | − | 0.940526i | \(-0.610333\pi\) | ||||
−0.339723 | + | 0.940526i | \(0.610333\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 211.949 | 1.92149 | 0.960747 | − | 0.277426i | \(-0.0894814\pi\) | ||||
0.960747 | + | 0.277426i | \(0.0894814\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −98.6263 | −0.789011 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 174.542 | 1.11764 | 0.558822 | − | 0.829288i | \(-0.311254\pi\) | ||||
0.558822 | + | 0.829288i | \(0.311254\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 211.897 | 1.22767 | 0.613837 | − | 0.789433i | \(-0.289625\pi\) | ||||
0.613837 | + | 0.789433i | \(0.289625\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −4.43952 | −0.0214404 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −86.9816 | −0.386478 | −0.193239 | − | 0.981152i | \(-0.561899\pi\) | ||||
−0.193239 | + | 0.981152i | \(0.561899\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 151.084 | 0.575497 | 0.287749 | − | 0.957706i | \(-0.407093\pi\) | ||||
0.287749 | + | 0.957706i | \(0.407093\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −74.0000 | −0.262439 | −0.131220 | − | 0.991353i | \(-0.541889\pi\) | ||||
−0.131220 | + | 0.991353i | \(0.541889\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 163.509 | 0.507452 | 0.253726 | − | 0.967276i | \(-0.418344\pi\) | ||||
0.253726 | + | 0.967276i | \(0.418344\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −342.253 | −0.997821 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 539.099 | 1.39719 | 0.698594 | − | 0.715519i | \(-0.253810\pi\) | ||||
0.698594 | + | 0.715519i | \(0.253810\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 56.4908 | 0.138495 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 365.187 | 0.805818 | 0.402909 | − | 0.915240i | \(-0.367999\pi\) | ||||
0.402909 | + | 0.915240i | \(0.367999\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 499.912 | 1.04930 | 0.524649 | − | 0.851319i | \(-0.324197\pi\) | ||||
0.524649 | + | 0.851319i | \(0.324197\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 265.392 | 0.506428 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 189.421 | 0.345395 | 0.172698 | − | 0.984975i | \(-0.444752\pi\) | ||||
0.172698 | + | 0.984975i | \(0.444752\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 751.744 | 1.25656 | 0.628278 | − | 0.777989i | \(-0.283760\pi\) | ||||
0.628278 | + | 0.777989i | \(0.283760\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 352.374 | 0.564962 | 0.282481 | − | 0.959273i | \(-0.408843\pi\) | ||||
0.282481 | + | 0.959273i | \(0.408843\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −9.50918 | −0.0140737 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −319.678 | −0.455273 | −0.227636 | − | 0.973746i | \(-0.573100\pi\) | ||||
−0.227636 | + | 0.973746i | \(0.573100\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 811.018 | 1.07254 | 0.536270 | − | 0.844046i | \(-0.319833\pi\) | ||||
0.536270 | + | 0.844046i | \(0.319833\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −271.224 | −0.346098 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −1103.18 | −1.31390 | −0.656948 | − | 0.753936i | \(-0.728153\pi\) | ||||
−0.656948 | + | 0.753936i | \(0.728153\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −44.6738 | −0.0514625 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −288.982 | −0.312094 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −551.758 | −0.577552 | −0.288776 | − | 0.957397i | \(-0.593248\pi\) | ||||
−0.288776 | + | 0.957397i | \(0.593248\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 196.476 | 0.193566 | 0.0967828 | − | 0.995306i | \(-0.469145\pi\) | ||||
0.0967828 | + | 0.995306i | \(0.469145\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 261.832 | 0.250476 | 0.125238 | − | 0.992127i | \(-0.460031\pi\) | ||||
0.125238 | + | 0.992127i | \(0.460031\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 1393.68 | 1.25918 | 0.629591 | − | 0.776926i | \(-0.283222\pi\) | ||||
0.629591 | + | 0.776926i | \(0.283222\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −190.491 | −0.167392 | −0.0836959 | − | 0.996491i | \(-0.526672\pi\) | ||||
−0.0836959 | + | 0.996491i | \(0.526672\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 226.095 | 0.188223 | 0.0941116 | − | 0.995562i | \(-0.469999\pi\) | ||||
0.0941116 | + | 0.995562i | \(0.469999\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1088.47 | 0.882611 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 45.6555 | 0.0351700 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 121.000 | 0.0909091 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1148.44 | −0.821756 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −2585.70 | −1.80664 | −0.903322 | − | 0.428964i | \(-0.858879\pi\) | ||||
−0.903322 | + | 0.428964i | \(0.858879\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −1867.55 | −1.24556 | −0.622779 | − | 0.782398i | \(-0.713997\pi\) | ||||
−0.622779 | + | 0.782398i | \(0.713997\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 48.6447 | 0.0317145 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −1447.56 | −0.902726 | −0.451363 | − | 0.892340i | \(-0.649062\pi\) | ||||
−0.451363 | + | 0.892340i | \(0.649062\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 298.513 | 0.182155 | 0.0910775 | − | 0.995844i | \(-0.470969\pi\) | ||||
0.0910775 | + | 0.995844i | \(0.470969\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 568.454 | 0.332423 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 896.366 | 0.513373 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −3240.09 | −1.78147 | −0.890735 | − | 0.454524i | \(-0.849809\pi\) | ||||
−0.890735 | + | 0.454524i | \(0.849809\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 169.875 | 0.0915513 | 0.0457757 | − | 0.998952i | \(-0.485424\pi\) | ||||
0.0457757 | + | 0.998952i | \(0.485424\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 1088.21 | 0.563914 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 2622.42 | 1.33307 | 0.666536 | − | 0.745473i | \(-0.267776\pi\) | ||||
0.666536 | + | 0.745473i | \(0.267776\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −183.224 | −0.0896897 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −684.879 | −0.329103 | −0.164552 | − | 0.986368i | \(-0.552618\pi\) | ||||
−0.164552 | + | 0.986368i | \(0.552618\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −1302.51 | −0.603538 | −0.301769 | − | 0.953381i | \(-0.597577\pi\) | ||||
−0.301769 | + | 0.953381i | \(0.597577\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 473.579 | 0.215557 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −3157.79 | −1.38776 | −0.693881 | − | 0.720090i | \(-0.744100\pi\) | ||||
−0.693881 | + | 0.720090i | \(0.744100\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 85.2596 | 0.0368287 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −843.619 | −0.352263 | −0.176131 | − | 0.984367i | \(-0.556358\pi\) | ||||
−0.176131 | + | 0.984367i | \(0.556358\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −2539.42 | −1.04284 | −0.521419 | − | 0.853301i | \(-0.674597\pi\) | ||||
−0.521419 | + | 0.853301i | \(0.674597\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −446.697 | −0.177523 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −580.945 | −0.227181 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 365.883 | 0.138609 | 0.0693046 | − | 0.997596i | \(-0.477922\pi\) | ||||
0.0693046 | + | 0.997596i | \(0.477922\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −1566.10 | −0.584096 | −0.292048 | − | 0.956404i | \(-0.594337\pi\) | ||||
−0.292048 | + | 0.956404i | \(0.594337\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −2487.39 | −0.899591 | −0.449795 | − | 0.893132i | \(-0.648503\pi\) | ||||
−0.449795 | + | 0.893132i | \(0.648503\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 4288.44 | 1.52764 | 0.763818 | − | 0.645432i | \(-0.223323\pi\) | ||||
0.763818 | + | 0.645432i | \(0.223323\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −150.887 | −0.0521683 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 775.897 | 0.264346 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −618.982 | −0.204861 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1667.95 | −0.544200 | −0.272100 | − | 0.962269i | \(-0.587718\pi\) | ||||
−0.272100 | + | 0.962269i | \(0.587718\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −380.029 | −0.120548 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −183.179 | −0.0573042 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −2729.26 | −0.830724 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −301.479 | −0.0905316 | −0.0452658 | − | 0.998975i | \(-0.514413\pi\) | ||||
−0.0452658 | + | 0.998975i | \(0.514413\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 1153.01 | 0.337128 | 0.168564 | − | 0.985691i | \(-0.446087\pi\) | ||||
0.168564 | + | 0.985691i | \(0.446087\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 495.861 | 0.143089 | 0.0715445 | − | 0.997437i | \(-0.477207\pi\) | ||||
0.0715445 | + | 0.997437i | \(0.477207\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −5009.50 | −1.40851 | −0.704256 | − | 0.709946i | \(-0.748719\pi\) | ||||
−0.704256 | + | 0.709946i | \(0.748719\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 839.706 | 0.233091 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 1971.52 | 0.533585 | 0.266792 | − | 0.963754i | \(-0.414036\pi\) | ||||
0.266792 | + | 0.963754i | \(0.414036\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −5622.20 | −1.50273 | −0.751365 | − | 0.659887i | \(-0.770604\pi\) | ||||
−0.751365 | + | 0.659887i | \(0.770604\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −1757.65 | −0.458335 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −2907.96 | −0.749104 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 2142.29 | 0.538725 | 0.269362 | − | 0.963039i | \(-0.413187\pi\) | ||||
0.269362 | + | 0.963039i | \(0.413187\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 2331.44 | 0.579352 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −1393.29 | −0.338175 | −0.169088 | − | 0.985601i | \(-0.554082\pi\) | ||||
−0.169088 | + | 0.985601i | \(0.554082\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 75.1931 | 0.0180397 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 7244.29 | 1.69849 | 0.849244 | − | 0.528001i | \(-0.177058\pi\) | ||||
0.849244 | + | 0.528001i | \(0.177058\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 2768.56 | 0.641778 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 3082.48 | 0.698670 | 0.349335 | − | 0.936998i | \(-0.386407\pi\) | ||||
0.349335 | + | 0.936998i | \(0.386407\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 5463.79 | 1.22473 | 0.612365 | − | 0.790575i | \(-0.290218\pi\) | ||||
0.612365 | + | 0.790575i | \(0.290218\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −1084.89 | −0.237896 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 2395.43 | 0.519593 | 0.259797 | − | 0.965663i | \(-0.416344\pi\) | ||||
0.259797 | + | 0.965663i | \(0.416344\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 6345.21 | 1.34706 | 0.673529 | − | 0.739161i | \(-0.264778\pi\) | ||||
0.673529 | + | 0.739161i | \(0.264778\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −6903.80 | −1.45014 | −0.725068 | − | 0.688677i | \(-0.758192\pi\) | ||||
−0.725068 | + | 0.688677i | \(0.758192\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −130.608 | −0.0268625 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −2123.77 | −0.432275 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −7349.12 | −1.46532 | −0.732662 | − | 0.680592i | \(-0.761723\pi\) | ||||
−0.732662 | + | 0.680592i | \(0.761723\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 1875.43 | 0.370141 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 10953.0 | 2.11849 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 63.9709 | 0.0122499 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 2567.31 | 0.481980 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 621.325 | 0.115508 | 0.0577539 | − | 0.998331i | \(-0.481606\pi\) | ||||
0.0577539 | + | 0.998331i | \(0.481606\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 674.748 | 0.123027 | 0.0615136 | − | 0.998106i | \(-0.480407\pi\) | ||||
0.0615136 | + | 0.998106i | \(0.480407\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −367.510 | −0.0663670 | −0.0331835 | − | 0.999449i | \(-0.510565\pi\) | ||||
−0.0331835 | + | 0.999449i | \(0.510565\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −3027.35 | −0.536381 | −0.268190 | − | 0.963366i | \(-0.586426\pi\) | ||||
−0.268190 | + | 0.963366i | \(0.586426\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1919.96 | 0.336982 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 2971.85 | 0.511945 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −5096.78 | −0.869903 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −141.349 | −0.0236864 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 8180.62 | 1.35845 | 0.679226 | − | 0.733930i | \(-0.262316\pi\) | ||||
0.679226 | + | 0.733930i | \(0.262316\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 972.778 | 0.158652 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 8582.67 | 1.38732 | 0.693662 | − | 0.720301i | \(-0.255996\pi\) | ||||
0.693662 | + | 0.720301i | \(0.255996\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 2330.87 | 0.370158 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 592.381 | 0.0932524 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 169.435 | 0.0262125 | 0.0131063 | − | 0.999914i | \(-0.495828\pi\) | ||||
0.0131063 | + | 0.999914i | \(0.495828\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −6107.13 | −0.936697 | −0.468349 | − | 0.883544i | \(-0.655151\pi\) | ||||
−0.468349 | + | 0.883544i | \(0.655151\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 10191.0 | 1.53658 | 0.768292 | − | 0.640100i | \(-0.221107\pi\) | ||||
0.768292 | + | 0.640100i | \(0.221107\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 3860.60 | 0.577181 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 13015.3 | 1.91343 | 0.956716 | − | 0.291025i | \(-0.0939962\pi\) | ||||
0.956716 | + | 0.291025i | \(0.0939962\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −3692.57 | −0.538354 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 1809.63 | 0.259507 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −7541.19 | −1.07261 | −0.536303 | − | 0.844025i | \(-0.680180\pi\) | ||||
−0.536303 | + | 0.844025i | \(0.680180\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −466.035 | −0.0652166 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −3186.02 | −0.442268 | −0.221134 | − | 0.975243i | \(-0.570976\pi\) | ||||
−0.221134 | + | 0.975243i | \(0.570976\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 9019.93 | 1.23223 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −10641.9 | −1.44232 | −0.721159 | − | 0.692769i | \(-0.756390\pi\) | ||||
−0.721159 | + | 0.692769i | \(0.756390\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −1845.84 | −0.246261 | −0.123130 | − | 0.992391i | \(-0.539293\pi\) | ||||
−0.123130 | + | 0.992391i | \(0.539293\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −48.8347 | −0.00646454 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 4615.33 | 0.601560 | 0.300780 | − | 0.953694i | \(-0.402753\pi\) | ||||
0.300780 | + | 0.953694i | \(0.402753\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −11193.7 | −1.44780 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −1641.71 | −0.209123 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 10168.0 | 1.28544 | 0.642719 | − | 0.766102i | \(-0.277806\pi\) | ||||
0.642719 | + | 0.766102i | \(0.277806\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −9577.61 | −1.19273 | −0.596363 | − | 0.802715i | \(-0.703388\pi\) | ||||
−0.596363 | + | 0.802715i | \(0.703388\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 10950.4 | 1.35354 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −956.798 | −0.116528 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −3895.73 | −0.470981 | −0.235491 | − | 0.971877i | \(-0.575670\pi\) | ||||
−0.235491 | + | 0.971877i | \(0.575670\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −315.694 | −0.0376132 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 4165.01 | 0.492656 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 163.208 | 0.0190292 | 0.00951462 | − | 0.999955i | \(-0.496971\pi\) | ||||
0.00951462 | + | 0.999955i | \(0.496971\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 13611.6 | 1.57574 | 0.787871 | − | 0.615841i | \(-0.211183\pi\) | ||||
0.787871 | + | 0.615841i | \(0.211183\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 5208.77 | 0.594500 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −432.160 | −0.0489781 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 309.524 | 0.0345922 | 0.0172961 | − | 0.999850i | \(-0.494494\pi\) | ||||
0.0172961 | + | 0.999850i | \(0.494494\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 11406.1 | 1.26592 | 0.632960 | − | 0.774185i | \(-0.281840\pi\) | ||||
0.632960 | + | 0.774185i | \(0.281840\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −11926.6 | −1.30555 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −16541.7 | −1.79838 | −0.899192 | − | 0.437554i | \(-0.855845\pi\) | ||||
−0.899192 | + | 0.437554i | \(0.855845\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 3728.94 | 0.399926 | 0.199963 | − | 0.979803i | \(-0.435918\pi\) | ||||
0.199963 | + | 0.979803i | \(0.435918\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −5665.41 | −0.603519 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −3344.45 | −0.351524 | −0.175762 | − | 0.984433i | \(-0.556239\pi\) | ||||
−0.175762 | + | 0.984433i | \(0.556239\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1661.93 | 0.173519 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −229.424 | −0.0236386 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −16692.1 | −1.70858 | −0.854291 | − | 0.519795i | \(-0.826008\pi\) | ||||
−0.854291 | + | 0.519795i | \(0.826008\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 8755.78 | 0.884593 | 0.442297 | − | 0.896869i | \(-0.354164\pi\) | ||||
0.442297 | + | 0.896869i | \(0.354164\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 11017.1 | 1.10585 | 0.552924 | − | 0.833232i | \(-0.313512\pi\) | ||||
0.552924 | + | 0.833232i | \(0.313512\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 3146.12 | 0.311746 | 0.155873 | − | 0.987777i | \(-0.450181\pi\) | ||||
0.155873 | + | 0.987777i | \(0.450181\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −163.749 | −0.0161220 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −814.000 | −0.0791285 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 5549.81 | 0.536090 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −1789.35 | −0.170683 | −0.0853417 | − | 0.996352i | \(-0.527198\pi\) | ||||
−0.0853417 | + | 0.996352i | \(0.527198\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −4495.01 | −0.426101 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −2833.57 | −0.265290 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 7891.84 | 0.734319 | 0.367160 | − | 0.930158i | \(-0.380330\pi\) | ||||
0.367160 | + | 0.930158i | \(0.380330\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −12340.1 | −1.13422 | −0.567111 | − | 0.823641i | \(-0.691939\pi\) | ||||
−0.567111 | + | 0.823641i | \(0.691939\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −9218.12 | −0.842116 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −649.861 | −0.0586524 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 13615.4 | 1.22146 | 0.610732 | − | 0.791837i | \(-0.290875\pi\) | ||||
0.610732 | + | 0.791837i | \(0.290875\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −4092.13 | −0.362742 | −0.181371 | − | 0.983415i | \(-0.558053\pi\) | ||||
−0.181371 | + | 0.983415i | \(0.558053\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 1009.01 | 0.0889115 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −18821.2 | −1.63897 | −0.819483 | − | 0.573104i | \(-0.805739\pi\) | ||||
−0.819483 | + | 0.573104i | \(0.805739\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −304.617 | −0.0263708 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 1344.64 | 0.115053 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1798.60 | 0.153003 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −6851.87 | −0.576172 | −0.288086 | − | 0.957605i | \(-0.593019\pi\) | ||||
−0.288086 | + | 0.957605i | \(0.593019\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −20338.2 | −1.70043 | −0.850216 | − | 0.526433i | \(-0.823529\pi\) | ||||
−0.850216 | + | 0.526433i | \(0.823529\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −11191.0 | −0.925022 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 32755.3 | 2.69214 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 7807.68 | 0.634499 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 7157.31 | 0.578388 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −3764.78 | −0.300854 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −6446.58 | −0.512311 | −0.256155 | − | 0.966636i | \(-0.582456\pi\) | ||||
−0.256155 | + | 0.966636i | \(0.582456\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −978.271 | −0.0768890 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −20285.9 | −1.58567 | −0.792834 | − | 0.609438i | \(-0.791395\pi\) | ||||
−0.792834 | + | 0.609438i | \(0.791395\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −9821.67 | −0.759378 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 276.352 | 0.0212508 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −18441.2 | −1.40284 | −0.701418 | − | 0.712750i | \(-0.747449\pi\) | ||||
−0.701418 | + | 0.712750i | \(0.747449\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −3824.15 | −0.289345 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −20335.0 | −1.52224 | −0.761118 | − | 0.648614i | \(-0.775349\pi\) | ||||
−0.761118 | + | 0.648614i | \(0.775349\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 1161.12 | 0.0864576 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 22960.4 | 1.69165 | 0.845825 | − | 0.533460i | \(-0.179109\pi\) | ||||
0.845825 | + | 0.533460i | \(0.179109\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −13239.5 | −0.970323 | −0.485161 | − | 0.874425i | \(-0.661239\pi\) | ||||
−0.485161 | + | 0.874425i | \(0.661239\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −20903.7 | −1.51608 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −11439.5 | −0.825361 | −0.412681 | − | 0.910876i | \(-0.635407\pi\) | ||||
−0.412681 | + | 0.910876i | \(0.635407\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −701.102 | −0.0500630 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 5930.09 | 0.421268 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −8474.43 | −0.595873 | −0.297936 | − | 0.954586i | \(-0.596298\pi\) | ||||
−0.297936 | + | 0.954586i | \(0.596298\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −11923.7 | −0.834138 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 16321.7 | 1.13027 | 0.565136 | − | 0.824998i | \(-0.308824\pi\) | ||||
0.565136 | + | 0.824998i | \(0.308824\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 234.465 | 0.0161548 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −11407.4 | −0.778117 | −0.389059 | − | 0.921213i | \(-0.627200\pi\) | ||||
−0.389059 | + | 0.921213i | \(0.627200\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 22493.8 | 1.52669 | 0.763347 | − | 0.645989i | \(-0.223555\pi\) | ||||
0.763347 | + | 0.645989i | \(0.223555\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 621.399 | 0.0417578 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 14720.9 | 0.984354 | 0.492177 | − | 0.870495i | \(-0.336201\pi\) | ||||
0.492177 | + | 0.870495i | \(0.336201\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 8449.77 | 0.559478 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −10291.2 | −0.678068 | −0.339034 | − | 0.940774i | \(-0.610100\pi\) | ||||
−0.339034 | + | 0.940774i | \(0.610100\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −5682.09 | −0.370750 | −0.185375 | − | 0.982668i | \(-0.559350\pi\) | ||||
−0.185375 | + | 0.982668i | \(0.559350\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 19433.1 | 1.26184 | 0.630922 | − | 0.775847i | \(-0.282677\pi\) | ||||
0.630922 | + | 0.775847i | \(0.282677\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 953.667 | 0.0613288 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 6430.45 | 0.411549 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 4593.78 | 0.291202 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −15008.3 | −0.946863 | −0.473432 | − | 0.880831i | \(-0.656985\pi\) | ||||
−0.473432 | + | 0.880831i | \(0.656985\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −13278.9 | −0.829856 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −17686.8 | −1.10012 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 26697.2 | 1.64505 | 0.822524 | − | 0.568731i | \(-0.192565\pi\) | ||||
0.822524 | + | 0.568731i | \(0.192565\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −17052.5 | −1.04586 | −0.522928 | − | 0.852377i | \(-0.675161\pi\) | ||||
−0.522928 | + | 0.852377i | \(0.675161\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −19430.9 | −1.18069 | −0.590345 | − | 0.807151i | \(-0.701008\pi\) | ||||
−0.590345 | + | 0.807151i | \(0.701008\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 4017.06 | 0.242963 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −13484.8 | −0.808116 | −0.404058 | − | 0.914733i | \(-0.632401\pi\) | ||||
−0.404058 | + | 0.914733i | \(0.632401\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −9590.83 | −0.572130 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −23752.4 | −1.40404 | −0.702020 | − | 0.712157i | \(-0.747718\pi\) | ||||
−0.702020 | + | 0.712157i | \(0.747718\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 22078.0 | 1.29914 | 0.649571 | − | 0.760301i | \(-0.274949\pi\) | ||||
0.649571 | + | 0.760301i | \(0.274949\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 249.816 | 0.0145676 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 36994.0 | 2.14754 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 5499.03 | 0.316375 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −20273.4 | −1.16119 | −0.580595 | − | 0.814192i | \(-0.697180\pi\) | ||||
−0.580595 | + | 0.814192i | \(0.697180\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −25947.6 | −1.47304 | −0.736519 | − | 0.676417i | \(-0.763532\pi\) | ||||
−0.736519 | + | 0.676417i | \(0.763532\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 476.979 | 0.0269584 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 9293.09 | 0.520630 | 0.260315 | − | 0.965524i | \(-0.416174\pi\) | ||||
0.260315 | + | 0.965524i | \(0.416174\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −7433.99 | −0.414654 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 27859.4 | 1.54043 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 2879.37 | 0.158518 | 0.0792592 | − | 0.996854i | \(-0.474745\pi\) | ||||
0.0792592 | + | 0.996854i | \(0.474745\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 1533.02 | 0.0836703 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −7979.24 | −0.433623 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −14194.6 | −0.764795 | −0.382398 | − | 0.923998i | \(-0.624902\pi\) | ||||
−0.382398 | + | 0.923998i | \(0.624902\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 4894.55 | 0.262591 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −169.848 | −0.00903507 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −19233.2 | −1.01879 | −0.509393 | − | 0.860534i | \(-0.670130\pi\) | ||||
−0.509393 | + | 0.860534i | \(0.670130\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 44911.4 | 2.35897 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 2919.31 | 0.152694 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 32319.6 | 1.67638 | 0.838190 | − | 0.545378i | \(-0.183614\pi\) | ||||
0.838190 | + | 0.545378i | \(0.183614\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −226.346 | −0.0116915 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −17214.5 | −0.881833 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 26551.7 | 1.35454 | 0.677268 | − | 0.735737i | \(-0.263164\pi\) | ||||
0.677268 | + | 0.735737i | \(0.263164\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 3908.17 | 0.197742 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 31494.5 | 1.58701 | 0.793504 | − | 0.608565i | \(-0.208255\pi\) | ||||
0.793504 | + | 0.608565i | \(0.208255\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 2083.63 | 0.104141 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 14450.0 | 0.719283 | 0.359642 | − | 0.933091i | \(-0.382899\pi\) | ||||
0.359642 | + | 0.933091i | \(0.382899\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −11693.6 | −0.577383 | −0.288692 | − | 0.957422i | \(-0.593220\pi\) | ||||
−0.288692 | + | 0.957422i | \(0.593220\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −16639.6 | −0.818292 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −1204.80 | −0.0587750 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −1082.31 | −0.0525888 | −0.0262944 | − | 0.999654i | \(-0.508371\pi\) | ||||
−0.0262944 | + | 0.999654i | \(0.508371\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 872.399 | 0.0420528 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 3150.38 | 0.151258 | 0.0756291 | − | 0.997136i | \(-0.475904\pi\) | ||||
0.0756291 | + | 0.997136i | \(0.475904\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 16026.3 | 0.763406 | 0.381703 | − | 0.924285i | \(-0.375338\pi\) | ||||
0.381703 | + | 0.924285i | \(0.375338\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 164.674 | 0.00781336 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 18872.0 | 0.888433 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −24674.3 | −1.15706 | −0.578528 | − | 0.815662i | \(-0.696373\pi\) | ||||
−0.578528 | + | 0.815662i | \(0.696373\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 28881.8 | 1.34386 | 0.671932 | − | 0.740613i | \(-0.265465\pi\) | ||||
0.671932 | + | 0.740613i | \(0.265465\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −20898.7 | −0.968648 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −8501.67 | −0.391019 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 8269.18 | 0.378866 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 13467.5 | 0.612327 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −24240.9 | −1.09796 | −0.548981 | − | 0.835835i | \(-0.684984\pi\) | ||||
−0.548981 | + | 0.835835i | \(0.684984\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −195.453 | −0.00878571 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 25834.3 | 1.15688 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 1476.34 | 0.0656145 | 0.0328072 | − | 0.999462i | \(-0.489555\pi\) | ||||
0.0328072 | + | 0.999462i | \(0.489555\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −8635.44 | −0.382353 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 3876.11 | 0.170342 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −940.950 | −0.0411977 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 36215.0 | 1.57386 | 0.786930 | − | 0.617042i | \(-0.211669\pi\) | ||||
0.786930 | + | 0.617042i | \(0.211669\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −36279.6 | −1.57084 | −0.785419 | − | 0.618964i | \(-0.787553\pi\) | ||||
−0.785419 | + | 0.618964i | \(0.787553\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −3517.22 | −0.151169 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 4164.06 | 0.178313 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 15206.6 | 0.646422 | 0.323211 | − | 0.946327i | \(-0.395238\pi\) | ||||
0.323211 | + | 0.946327i | \(0.395238\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −15023.1 | −0.636296 | −0.318148 | − | 0.948041i | \(-0.603061\pi\) | ||||
−0.318148 | + | 0.948041i | \(0.603061\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 1108.16 | 0.0465957 | 0.0232978 | − | 0.999729i | \(-0.492583\pi\) | ||||
0.0232978 | + | 0.999729i | \(0.492583\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 37519.7 | 1.57191 | 0.785955 | − | 0.618283i | \(-0.212172\pi\) | ||||
0.785955 | + | 0.618283i | \(0.212172\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 18075.5 | 0.751833 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −6689.05 | −0.277227 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −112.813 | −0.00464210 | −0.00232105 | − | 0.999997i | \(-0.500739\pi\) | ||||
−0.00232105 | + | 0.999997i | \(0.500739\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 6075.95 | 0.249127 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 2432.08 | 0.0990130 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −104.601 | −0.00424337 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −18435.6 | −0.742615 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −15005.7 | −0.602326 | −0.301163 | − | 0.953573i | \(-0.597375\pi\) | ||||
−0.301163 | + | 0.953573i | \(0.597375\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 16517.0 | 0.658353 | 0.329177 | − | 0.944268i | \(-0.393229\pi\) | ||||
0.329177 | + | 0.944268i | \(0.393229\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 21272.5 | 0.844945 | 0.422473 | − | 0.906376i | \(-0.361162\pi\) | ||||
0.422473 | + | 0.906376i | \(0.361162\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −1173.70 | −0.0462959 | −0.0231479 | − | 0.999732i | \(-0.507369\pi\) | ||||
−0.0231479 | + | 0.999732i | \(0.507369\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −16216.9 | −0.637448 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −3516.45 | −0.137270 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 9788.84 | 0.380806 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 992.793 | 0.0383572 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 5338.75 | 0.205561 | 0.102780 | − | 0.994704i | \(-0.467226\pi\) | ||||
0.102780 | + | 0.994704i | \(0.467226\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 21936.8 | 0.838898 | 0.419449 | − | 0.907779i | \(-0.362223\pi\) | ||||
0.419449 | + | 0.907779i | \(0.362223\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 30167.4 | 1.14973 | 0.574866 | − | 0.818247i | \(-0.305054\pi\) | ||||
0.574866 | + | 0.818247i | \(0.305054\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −22302.6 | −0.844250 | −0.422125 | − | 0.906538i | \(-0.638716\pi\) | ||||
−0.422125 | + | 0.906538i | \(0.638716\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 2235.26 | 0.0843288 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −9200.83 | −0.344786 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −4332.43 | −0.161807 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 36985.0 | 1.37210 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −28471.5 | −1.05275 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −13041.3 | −0.479013 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −1261.17 | −0.0461704 | −0.0230852 | − | 0.999734i | \(-0.507349\pi\) | ||||
−0.0230852 | + | 0.999734i | \(0.507349\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 33089.3 | 1.20340 | 0.601700 | − | 0.798722i | \(-0.294490\pi\) | ||||
0.601700 | + | 0.798722i | \(0.294490\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 8921.20 | 0.323383 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 1614.44 | 0.0581390 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −43973.8 | −1.57841 | −0.789207 | − | 0.614128i | \(-0.789508\pi\) | ||||
−0.789207 | + | 0.614128i | \(0.789508\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 38848.3 | 1.38538 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 8578.68 | 0.304935 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 51539.4 | 1.82019 | 0.910093 | − | 0.414403i | \(-0.136010\pi\) | ||||
0.910093 | + | 0.414403i | \(0.136010\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 19258.9 | 0.677965 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −2983.46 | −0.104352 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −4384.73 | −0.152874 | −0.0764369 | − | 0.997074i | \(-0.524354\pi\) | ||||
−0.0764369 | + | 0.997074i | \(0.524354\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 23862.3 | 0.826663 | 0.413332 | − | 0.910581i | \(-0.364365\pi\) | ||||
0.413332 | + | 0.910581i | \(0.364365\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 32022.1 | 1.10581 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −33377.7 | −1.14533 | −0.572666 | − | 0.819789i | \(-0.694091\pi\) | ||||
−0.572666 | + | 0.819789i | \(0.694091\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 18209.8 | 0.622883 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −25097.9 | −0.853095 | −0.426547 | − | 0.904465i | \(-0.640270\pi\) | ||||
−0.426547 | + | 0.904465i | \(0.640270\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 1879.00 | 0.0636681 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 1251.37 | 0.0421366 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 15109.5 | 0.507184 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −8042.76 | −0.268296 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 963.547 | 0.0320430 | 0.0160215 | − | 0.999872i | \(-0.494900\pi\) | ||||
0.0160215 | + | 0.999872i | \(0.494900\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −28702.2 | −0.948607 | −0.474304 | − | 0.880361i | \(-0.657300\pi\) | ||||
−0.474304 | + | 0.880361i | \(0.657300\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −258.056 | −0.00850246 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −18696.2 | −0.612226 | −0.306113 | − | 0.951995i | \(-0.599028\pi\) | ||||
−0.306113 | + | 0.951995i | \(0.599028\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −12135.0 | −0.396155 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −35820.2 | −1.16224 | −0.581122 | − | 0.813817i | \(-0.697386\pi\) | ||||
−0.581122 | + | 0.813817i | \(0.697386\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −12774.1 | −0.413214 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −15684.2 | −0.504276 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 32090.3 | 1.02864 | 0.514320 | − | 0.857598i | \(-0.328044\pi\) | ||||
0.514320 | + | 0.857598i | \(0.328044\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 22023.4 | 0.701697 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 3963.89 | 0.125915 | 0.0629577 | − | 0.998016i | \(-0.479947\pi\) | ||||
0.0629577 | + | 0.998016i | \(0.479947\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(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 | 396.4.a.h.1.2 | ✓ | 2 | |
3.2 | odd | 2 | 396.4.a.j.1.1 | yes | 2 | ||
4.3 | odd | 2 | 1584.4.a.y.1.2 | 2 | |||
12.11 | even | 2 | 1584.4.a.bi.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
396.4.a.h.1.2 | ✓ | 2 | 1.1 | even | 1 | trivial | |
396.4.a.j.1.1 | yes | 2 | 3.2 | odd | 2 | ||
1584.4.a.y.1.2 | 2 | 4.3 | odd | 2 | |||
1584.4.a.bi.1.1 | 2 | 12.11 | even | 2 |