Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2312,4,Mod(1,2312)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2312, 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("2312.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2312 = 2^{3} \cdot 17^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 2312.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: | \(136.412415933\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 95x^{6} + 756x^{4} - 1780x^{2} + 1152 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{13} \) |
Twist minimal: | no (minimal twist has level 136) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.6 | ||
Root | \(-1.60125\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2312.1 |
$q$-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 | ||||||||
\(3\) | 2.95309 | 0.568322 | 0.284161 | − | 0.958777i | \(-0.408285\pi\) | ||||
0.284161 | + | 0.958777i | \(0.408285\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 4.89575 | 0.437889 | 0.218944 | − | 0.975737i | \(-0.429739\pi\) | ||||
0.218944 | + | 0.975737i | \(0.429739\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 4.46235 | 0.240944 | 0.120472 | − | 0.992717i | \(-0.461559\pi\) | ||||
0.120472 | + | 0.992717i | \(0.461559\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −18.2793 | −0.677010 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −60.3865 | −1.65520 | −0.827600 | − | 0.561318i | \(-0.810294\pi\) | ||||
−0.827600 | + | 0.561318i | \(0.810294\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −56.1938 | −1.19887 | −0.599437 | − | 0.800422i | \(-0.704609\pi\) | ||||
−0.599437 | + | 0.800422i | \(0.704609\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 14.4576 | 0.248862 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 0 | 0 | ||||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 134.845 | 1.62819 | 0.814095 | − | 0.580731i | \(-0.197233\pi\) | ||||
0.814095 | + | 0.580731i | \(0.197233\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 13.1777 | 0.136934 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −39.1633 | −0.355049 | −0.177524 | − | 0.984116i | \(-0.556809\pi\) | ||||
−0.177524 | + | 0.984116i | \(0.556809\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −101.032 | −0.808253 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −133.714 | −0.953082 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −113.700 | −0.728053 | −0.364027 | − | 0.931389i | \(-0.618598\pi\) | ||||
−0.364027 | + | 0.931389i | \(0.618598\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 306.516 | 1.77587 | 0.887935 | − | 0.459969i | \(-0.152139\pi\) | ||||
0.887935 | + | 0.459969i | \(0.152139\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −178.326 | −0.940686 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 21.8465 | 0.105507 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −61.9621 | −0.275311 | −0.137656 | − | 0.990480i | \(-0.543957\pi\) | ||||
−0.137656 | + | 0.990480i | \(0.543957\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −165.945 | −0.681346 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 317.272 | 1.20853 | 0.604263 | − | 0.796785i | \(-0.293468\pi\) | ||||
0.604263 | + | 0.796785i | \(0.293468\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −122.660 | −0.435009 | −0.217505 | − | 0.976059i | \(-0.569792\pi\) | ||||
−0.217505 | + | 0.976059i | \(0.569792\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −89.4907 | −0.296455 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 303.233 | 0.941086 | 0.470543 | − | 0.882377i | \(-0.344058\pi\) | ||||
0.470543 | + | 0.882377i | \(0.344058\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −323.087 | −0.941946 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −133.743 | −0.346623 | −0.173311 | − | 0.984867i | \(-0.555447\pi\) | ||||
−0.173311 | + | 0.984867i | \(0.555447\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −295.637 | −0.724794 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 398.210 | 0.925336 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 130.660 | 0.288312 | 0.144156 | − | 0.989555i | \(-0.453953\pi\) | ||||
0.144156 | + | 0.989555i | \(0.453953\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 772.618 | 1.62170 | 0.810849 | − | 0.585256i | \(-0.199006\pi\) | ||||
0.810849 | + | 0.585256i | \(0.199006\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −81.5685 | −0.163122 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −275.111 | −0.524974 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 378.907 | 0.690909 | 0.345455 | − | 0.938435i | \(-0.387725\pi\) | ||||
0.345455 | + | 0.938435i | \(0.387725\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −115.653 | −0.201782 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −465.116 | −0.777452 | −0.388726 | − | 0.921353i | \(-0.627085\pi\) | ||||
−0.388726 | + | 0.921353i | \(0.627085\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 664.801 | 1.06588 | 0.532939 | − | 0.846154i | \(-0.321087\pi\) | ||||
0.532939 | + | 0.846154i | \(0.321087\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −298.355 | −0.459348 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −269.466 | −0.398811 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 925.763 | 1.31844 | 0.659218 | − | 0.751952i | \(-0.270887\pi\) | ||||
0.659218 | + | 0.751952i | \(0.270887\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 98.6724 | 0.135353 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 723.561 | 0.956882 | 0.478441 | − | 0.878120i | \(-0.341202\pi\) | ||||
0.478441 | + | 0.878120i | \(0.341202\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −335.766 | −0.413769 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 889.439 | 1.05933 | 0.529665 | − | 0.848207i | \(-0.322318\pi\) | ||||
0.529665 | + | 0.848207i | \(0.322318\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −250.757 | −0.288862 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 905.170 | 1.00927 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 660.168 | 0.712967 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1506.43 | 1.57686 | 0.788428 | − | 0.615127i | \(-0.210895\pi\) | ||||
0.788428 | + | 0.615127i | \(0.210895\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 1103.82 | 1.12059 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 606.815 | 0.597825 | 0.298912 | − | 0.954281i | \(-0.403376\pi\) | ||||
0.298912 | + | 0.954281i | \(0.403376\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 582.633 | 0.557364 | 0.278682 | − | 0.960383i | \(-0.410102\pi\) | ||||
0.278682 | + | 0.960383i | \(0.410102\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 64.5147 | 0.0599619 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 14.1057 | 0.0127444 | 0.00637221 | − | 0.999980i | \(-0.497972\pi\) | ||||
0.00637221 | + | 0.999980i | \(0.497972\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1599.48 | −1.40553 | −0.702765 | − | 0.711422i | \(-0.748051\pi\) | ||||
−0.702765 | + | 0.711422i | \(0.748051\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −182.980 | −0.156465 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 620.655 | 0.516693 | 0.258347 | − | 0.966052i | \(-0.416822\pi\) | ||||
0.258347 | + | 0.966052i | \(0.416822\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −191.734 | −0.155472 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 1027.18 | 0.811650 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 2315.52 | 1.73969 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 936.932 | 0.686832 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1106.59 | −0.791814 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 970.396 | 0.678021 | 0.339011 | − | 0.940783i | \(-0.389908\pi\) | ||||
0.339011 | + | 0.940783i | \(0.389908\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −362.224 | −0.247225 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 705.717 | 0.470678 | 0.235339 | − | 0.971913i | \(-0.424380\pi\) | ||||
0.235339 | + | 0.971913i | \(0.424380\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 601.727 | 0.392303 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −654.628 | −0.417344 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −2470.01 | −1.54035 | −0.770173 | − | 0.637835i | \(-0.779830\pi\) | ||||
−0.770173 | + | 0.637835i | \(0.779830\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 435.484 | 0.265736 | 0.132868 | − | 0.991134i | \(-0.457581\pi\) | ||||
0.132868 | + | 0.991134i | \(0.457581\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 895.473 | 0.534840 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 3393.35 | 1.98438 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −556.646 | −0.318806 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −954.105 | −0.535328 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 2428.83 | 1.33542 | 0.667709 | − | 0.744422i | \(-0.267275\pi\) | ||||
0.667709 | + | 0.744422i | \(0.267275\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −2608.09 | −1.40558 | −0.702792 | − | 0.711396i | \(-0.748063\pi\) | ||||
−0.702792 | + | 0.711396i | \(0.748063\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 1500.63 | 0.777634 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 164.006 | 0.0833703 | 0.0416851 | − | 0.999131i | \(-0.486727\pi\) | ||||
0.0416851 | + | 0.999131i | \(0.486727\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −394.955 | −0.196993 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −174.760 | −0.0855469 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −289.416 | −0.139072 | −0.0695362 | − | 0.997579i | \(-0.522152\pi\) | ||||
−0.0695362 | + | 0.997579i | \(0.522152\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −873.041 | −0.411916 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −2147.52 | −0.995090 | −0.497545 | − | 0.867438i | \(-0.665765\pi\) | ||||
−0.497545 | + | 0.867438i | \(0.665765\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 960.747 | 0.437299 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −2464.87 | −1.10230 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −4383.99 | −1.92664 | −0.963320 | − | 0.268357i | \(-0.913519\pi\) | ||||
−0.963320 | + | 0.268357i | \(0.913519\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −450.839 | −0.194744 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 385.849 | 0.163854 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −3793.10 | −1.58385 | −0.791926 | − | 0.610617i | \(-0.790921\pi\) | ||||
−0.791926 | + | 0.610617i | \(0.790921\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −1726.75 | −0.709108 | −0.354554 | − | 0.935036i | \(-0.615367\pi\) | ||||
−0.354554 | + | 0.935036i | \(0.615367\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 2281.61 | 0.921646 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −303.351 | −0.120556 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −596.677 | −0.229640 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 1286.01 | 0.487184 | 0.243592 | − | 0.969878i | \(-0.421674\pi\) | ||||
0.243592 | + | 0.969878i | \(0.421674\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 1682.07 | 0.627349 | 0.313674 | − | 0.949531i | \(-0.398440\pi\) | ||||
0.313674 | + | 0.949531i | \(0.398440\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −812.426 | −0.298354 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −415.578 | −0.150298 | −0.0751489 | − | 0.997172i | \(-0.523943\pi\) | ||||
−0.0751489 | + | 0.997172i | \(0.523943\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −2761.31 | −0.983637 | −0.491819 | − | 0.870698i | \(-0.663668\pi\) | ||||
−0.491819 | + | 0.870698i | \(0.663668\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 1118.95 | 0.392659 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −507.369 | −0.175420 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1553.28 | 0.529200 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 715.877 | 0.240372 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −8142.83 | −2.69498 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2713.80 | 0.885431 | 0.442715 | − | 0.896662i | \(-0.354015\pi\) | ||||
0.442715 | + | 0.896662i | \(0.354015\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −1373.53 | −0.441843 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −600.510 | −0.190486 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1367.78 | 0.427886 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 1963.22 | 0.605762 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 6395.76 | 1.92059 | 0.960296 | − | 0.278984i | \(-0.0899978\pi\) | ||||
0.960296 | + | 0.278984i | \(0.0899978\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1846.79 | 0.547196 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −3844.30 | −1.12403 | −0.562016 | − | 0.827127i | \(-0.689974\pi\) | ||||
−0.562016 | + | 0.827127i | \(0.689974\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 4849.35 | 1.39936 | 0.699682 | − | 0.714455i | \(-0.253325\pi\) | ||||
0.699682 | + | 0.714455i | \(0.253325\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −795.755 | −0.226653 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 2719.86 | 0.764738 | 0.382369 | − | 0.924010i | \(-0.375108\pi\) | ||||
0.382369 | + | 0.924010i | \(0.375108\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1484.55 | 0.412091 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 2733.86 | 0.749296 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 2524.92 | 0.683362 | 0.341681 | − | 0.939816i | \(-0.389004\pi\) | ||||
0.341681 | + | 0.939816i | \(0.389004\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1943.29 | 0.519413 | 0.259706 | − | 0.965688i | \(-0.416374\pi\) | ||||
0.259706 | + | 0.965688i | \(0.416374\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 3901.66 | 1.03001 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −1581.75 | −0.412468 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −7577.47 | −1.95200 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 2136.74 | 0.543817 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 2332.58 | 0.586578 | 0.293289 | − | 0.956024i | \(-0.405250\pi\) | ||||
0.293289 | + | 0.956024i | \(0.405250\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 2364.93 | 0.587676 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 807.810 | 0.196069 | 0.0980346 | − | 0.995183i | \(-0.468744\pi\) | ||||
0.0980346 | + | 0.995183i | \(0.468744\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −276.497 | −0.0663347 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 2078.35 | 0.492900 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 6420.82 | 1.50542 | 0.752708 | − | 0.658354i | \(-0.228747\pi\) | ||||
0.752708 | + | 0.658354i | \(0.228747\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −654.772 | −0.151782 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 2626.59 | 0.602040 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −6335.06 | −1.43589 | −0.717947 | − | 0.696097i | \(-0.754918\pi\) | ||||
−0.717947 | + | 0.696097i | \(0.754918\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −1429.35 | −0.320394 | −0.160197 | − | 0.987085i | \(-0.551213\pi\) | ||||
−0.160197 | + | 0.987085i | \(0.551213\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −740.506 | −0.164167 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 6100.94 | 1.33782 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 7878.89 | 1.70901 | 0.854506 | − | 0.519441i | \(-0.173860\pi\) | ||||
0.854506 | + | 0.519441i | \(0.173860\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −5602.90 | −1.20228 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −2967.99 | −0.630090 | −0.315045 | − | 0.949077i | \(-0.602020\pi\) | ||||
−0.315045 | + | 0.949077i | \(0.602020\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −401.204 | −0.0842725 | −0.0421363 | − | 0.999112i | \(-0.513416\pi\) | ||||
−0.0421363 | + | 0.999112i | \(0.513416\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 1949.53 | 0.405195 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 1415.78 | 0.291188 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 0 | 0 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 4448.63 | 0.896162 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 7390.62 | 1.47360 | 0.736800 | − | 0.676111i | \(-0.236336\pi\) | ||||
0.736800 | + | 0.676111i | \(0.236336\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 639.676 | 0.126249 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 8074.49 | 1.57754 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 2200.74 | 0.425659 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −547.350 | −0.104813 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 1791.98 | 0.339757 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 3782.54 | 0.710123 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −50.2688 | −0.00934524 | −0.00467262 | − | 0.999989i | \(-0.501487\pi\) | ||||
−0.00467262 | + | 0.999989i | \(0.501487\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 1720.57 | 0.316762 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 215.028 | 0.0392062 | 0.0196031 | − | 0.999808i | \(-0.493760\pi\) | ||||
0.0196031 | + | 0.999808i | \(0.493760\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −4639.52 | −0.837831 | −0.418915 | − | 0.908025i | \(-0.637590\pi\) | ||||
−0.418915 | + | 0.908025i | \(0.637590\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −399.339 | −0.0714292 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −3965.63 | −0.702624 | −0.351312 | − | 0.936259i | \(-0.614264\pi\) | ||||
−0.351312 | + | 0.936259i | \(0.614264\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 6865.94 | 1.20507 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 41.6554 | 0.00724293 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 5677.36 | 0.968994 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −4723.41 | −0.798793 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 1353.13 | 0.226749 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −7497.94 | −1.24509 | −0.622544 | − | 0.782585i | \(-0.713901\pi\) | ||||
−0.622544 | + | 0.782585i | \(0.713901\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 1132.62 | 0.186388 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 1855.03 | 0.302541 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −798.500 | −0.129071 | −0.0645357 | − | 0.997915i | \(-0.520557\pi\) | ||||
−0.0645357 | + | 0.997915i | \(0.520557\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 1832.85 | 0.293648 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −18509.4 | −2.93942 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −2972.32 | −0.467901 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −566.206 | −0.0883581 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −4014.43 | −0.621054 | −0.310527 | − | 0.950564i | \(-0.600506\pi\) | ||||
−0.310527 | + | 0.950564i | \(0.600506\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −4747.53 | −0.728165 | −0.364083 | − | 0.931367i | \(-0.618617\pi\) | ||||
−0.364083 | + | 0.931367i | \(0.618617\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 7513.88 | 1.14262 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 9653.02 | 1.45546 | 0.727731 | − | 0.685862i | \(-0.240575\pi\) | ||||
0.727731 | + | 0.685862i | \(0.240575\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −2277.09 | −0.340438 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 6641.04 | 0.976325 | 0.488162 | − | 0.872753i | \(-0.337667\pi\) | ||||
0.488162 | + | 0.872753i | \(0.337667\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 11324.2 | 1.65100 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 6837.94 | 0.988703 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 3254.70 | 0.466736 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −3305.96 | −0.470217 | −0.235108 | − | 0.971969i | \(-0.575545\pi\) | ||||
−0.235108 | + | 0.971969i | \(0.575545\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −5799.50 | −0.818185 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −596.808 | −0.0835168 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 238.635 | 0.0331261 | 0.0165631 | − | 0.999863i | \(-0.494728\pi\) | ||||
0.0165631 | + | 0.999863i | \(0.494728\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −3267.87 | −0.450005 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 6389.23 | 0.872844 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −11081.6 | −1.50191 | −0.750955 | − | 0.660353i | \(-0.770407\pi\) | ||||
−0.750955 | + | 0.660353i | \(0.770407\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 2865.66 | 0.385334 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −7956.45 | −1.06150 | −0.530752 | − | 0.847527i | \(-0.678090\pi\) | ||||
−0.530752 | + | 0.847527i | \(0.678090\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −1319.24 | −0.174635 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 2242.13 | 0.294506 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −5128.06 | −0.668388 | −0.334194 | − | 0.942504i | \(-0.608464\pi\) | ||||
−0.334194 | + | 0.942504i | \(0.608464\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 2084.04 | 0.267496 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 4532.30 | 0.577329 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 2933.96 | 0.370910 | 0.185455 | − | 0.982653i | \(-0.440624\pi\) | ||||
0.185455 | + | 0.982653i | \(0.440624\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 1776.95 | 0.222955 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −5278.07 | −0.657293 | −0.328646 | − | 0.944453i | \(-0.606592\pi\) | ||||
−0.328646 | + | 0.944453i | \(0.606592\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −17224.3 | −2.12904 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 483.075 | 0.0592696 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 3741.67 | 0.455695 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −6880.00 | −0.831770 | −0.415885 | − | 0.909417i | \(-0.636528\pi\) | ||||
−0.415885 | + | 0.909417i | \(0.636528\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −7294.16 | −0.875412 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 583.049 | 0.0694672 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 3542.37 | 0.419008 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 1286.02 | 0.151024 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 3048.43 | 0.355431 | 0.177715 | − | 0.984082i | \(-0.443129\pi\) | ||||
0.177715 | + | 0.984082i | \(0.443129\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 3607.83 | 0.417660 | 0.208830 | − | 0.977952i | \(-0.433034\pi\) | ||||
0.208830 | + | 0.977952i | \(0.433034\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −5542.88 | −0.637125 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 3447.69 | 0.390739 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 10020.8 | 1.12776 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −8866.93 | −0.990962 | −0.495481 | − | 0.868619i | \(-0.665008\pi\) | ||||
−0.495481 | + | 0.868619i | \(0.665008\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 11353.2 | 1.26005 | 0.630024 | − | 0.776575i | \(-0.283045\pi\) | ||||
0.630024 | + | 0.776575i | \(0.283045\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −1643.82 | −0.181185 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −5280.99 | −0.578087 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −2786.53 | −0.302947 | −0.151474 | − | 0.988461i | \(-0.548402\pi\) | ||||
−0.151474 | + | 0.988461i | \(0.548402\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 5905.80 | 0.637707 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 15244.4 | 1.63495 | 0.817474 | − | 0.575965i | \(-0.195374\pi\) | ||||
0.817474 | + | 0.575965i | \(0.195374\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 4354.47 | 0.463869 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 7172.54 | 0.758947 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 17473.1 | 1.83654 | 0.918269 | − | 0.395958i | \(-0.129587\pi\) | ||||
0.918269 | + | 0.395958i | \(0.129587\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −19158.9 | −2.00035 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −7701.91 | −0.798824 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −1227.64 | −0.126489 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 16422.8 | 1.68102 | 0.840508 | − | 0.541800i | \(-0.182257\pi\) | ||||
0.840508 | + | 0.541800i | \(0.182257\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 12802.9 | 1.29347 | 0.646737 | − | 0.762713i | \(-0.276133\pi\) | ||||
0.646737 | + | 0.762713i | \(0.276133\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −2291.00 | −0.229961 | −0.114980 | − | 0.993368i | \(-0.536680\pi\) | ||||
−0.114980 | + | 0.993368i | \(0.536680\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 4431.48 | 0.441946 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 14464.0 | 1.43322 | 0.716610 | − | 0.697474i | \(-0.245693\pi\) | ||||
0.716610 | + | 0.697474i | \(0.245693\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 1690.82 | 0.166471 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 484.325 | 0.0473812 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 7406.97 | 0.720028 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −13623.6 | −1.31599 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 2444.72 | 0.234667 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 6988.15 | 0.666590 | 0.333295 | − | 0.942823i | \(-0.391839\pi\) | ||||
0.333295 | + | 0.942823i | \(0.391839\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 3481.89 | 0.330063 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −516.083 | −0.0486182 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 7375.11 | 0.690488 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −8494.76 | −0.790420 | −0.395210 | − | 0.918591i | \(-0.629328\pi\) | ||||
−0.395210 | + | 0.918591i | \(0.629328\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −854.670 | −0.0790379 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 5195.82 | 0.477565 | 0.238782 | − | 0.971073i | \(-0.423252\pi\) | ||||
0.238782 | + | 0.971073i | \(0.423252\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 5404.03 | 0.490693 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −2075.51 | −0.187323 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 8790.68 | 0.788627 | 0.394313 | − | 0.918976i | \(-0.370982\pi\) | ||||
0.394313 | + | 0.918976i | \(0.370982\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −6341.81 | −0.565531 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −7764.74 | −0.688295 | −0.344148 | − | 0.938916i | \(-0.611832\pi\) | ||||
−0.344148 | + | 0.938916i | \(0.611832\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 2970.81 | 0.261781 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 2837.17 | 0.248527 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 9919.29 | 0.863782 | 0.431891 | − | 0.901926i | \(-0.357847\pi\) | ||||
0.431891 | + | 0.901926i | \(0.357847\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 2966.58 | 0.256817 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −18030.6 | −1.55180 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 2852.42 | 0.244064 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −18311.2 | −1.55769 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −12946.3 | −1.09495 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −4230.44 | −0.355737 | −0.177868 | − | 0.984054i | \(-0.556920\pi\) | ||||
−0.177868 | + | 0.984054i | \(0.556920\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 10566.8 | 0.883465 | 0.441732 | − | 0.897147i | \(-0.354364\pi\) | ||||
0.441732 | + | 0.897147i | \(0.354364\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −1331.37 | −0.110677 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −10633.2 | −0.873941 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −2388.36 | −0.195190 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −17828.7 | −1.44887 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 69.0581 | 0.00558064 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −11201.3 | −0.900138 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 19510.1 | 1.55911 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −1980.86 | −0.157419 | −0.0787094 | − | 0.996898i | \(-0.525080\pi\) | ||||
−0.0787094 | + | 0.996898i | \(0.525080\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −5099.25 | −0.403001 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −7830.67 | −0.615466 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 3940.22 | 0.307992 | 0.153996 | − | 0.988071i | \(-0.450786\pi\) | ||||
0.153996 | + | 0.988071i | \(0.450786\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −14122.9 | −1.09791 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −15331.9 | −1.18541 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 4131.08 | 0.317670 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −895.822 | −0.0685145 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 3709.12 | 0.282155 | 0.141077 | − | 0.989999i | \(-0.454943\pi\) | ||||
0.141077 | + | 0.989999i | \(0.454943\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 6892.71 | 0.521522 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 3393.34 | 0.254018 | 0.127009 | − | 0.991902i | \(-0.459462\pi\) | ||||
0.127009 | + | 0.991902i | \(0.459462\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 3038.57 | 0.226254 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 440.311 | 0.0326125 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 2927.65 | 0.215700 | 0.107850 | − | 0.994167i | \(-0.465603\pi\) | ||||
0.107850 | + | 0.994167i | \(0.465603\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 19781.8 | 1.44981 | 0.724907 | − | 0.688846i | \(-0.241883\pi\) | ||||
0.724907 | + | 0.688846i | \(0.241883\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 3797.69 | 0.276877 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 3956.74 | 0.286969 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 17520.1 | 1.26407 | 0.632037 | − | 0.774938i | \(-0.282219\pi\) | ||||
0.632037 | + | 0.774938i | \(0.282219\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 4967.31 | 0.356536 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 3228.79 | 0.230555 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 8076.26 | 0.573730 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 5028.83 | 0.355413 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −7846.90 | −0.551748 | −0.275874 | − | 0.961194i | \(-0.588967\pi\) | ||||
−0.275874 | + | 0.961194i | \(0.588967\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 41332.3 | 2.89145 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −1227.24 | −0.0854175 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −10572.9 | −0.732173 | −0.366086 | − | 0.930581i | \(-0.619303\pi\) | ||||
−0.366086 | + | 0.930581i | \(0.619303\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −8154.38 | −0.559023 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −27156.5 | −1.85240 | −0.926198 | − | 0.377038i | \(-0.876943\pi\) | ||||
−0.926198 | + | 0.377038i | \(0.876943\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −11180.6 | −0.758849 | −0.379424 | − | 0.925223i | \(-0.623878\pi\) | ||||
−0.379424 | + | 0.925223i | \(0.623878\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −6926.15 | −0.467752 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 11336.2 | 0.761790 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 19444.2 | 1.30019 | 0.650097 | − | 0.759851i | \(-0.274728\pi\) | ||||
0.650097 | + | 0.759851i | \(0.274728\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −1498.30 | −0.0996952 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −17039.8 | −1.12824 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −16630.9 | −1.09579 | −0.547893 | − | 0.836548i | \(-0.684570\pi\) | ||||
−0.547893 | + | 0.836548i | \(0.684570\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 4586.98 | 0.300756 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 8035.03 | 0.524276 | 0.262138 | − | 0.965030i | \(-0.415572\pi\) | ||||
0.262138 | + | 0.965030i | \(0.415572\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 16161.6 | 1.04942 | 0.524709 | − | 0.851282i | \(-0.324174\pi\) | ||||
0.524709 | + | 0.851282i | \(0.324174\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 5236.67 | 0.338390 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 3968.99 | 0.255239 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 7211.35 | 0.461527 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −24046.5 | −1.53162 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 10043.9 | 0.633665 | 0.316833 | − | 0.948481i | \(-0.397381\pi\) | ||||
0.316833 | + | 0.948481i | \(0.397381\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 8014.09 | 0.503210 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 4750.81 | 0.296898 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 18155.5 | 1.12927 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 8501.98 | 0.526343 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −15316.1 | −0.943757 | −0.471879 | − | 0.881664i | \(-0.656424\pi\) | ||||
−0.471879 | + | 0.881664i | \(0.656424\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −24684.6 | −1.51394 | −0.756970 | − | 0.653449i | \(-0.773321\pi\) | ||||
−0.756970 | + | 0.653449i | \(0.773321\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −1773.36 | −0.108257 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 7774.11 | 0.472383 | 0.236192 | − | 0.971707i | \(-0.424101\pi\) | ||||
0.236192 | + | 0.971707i | \(0.424101\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −7890.07 | −0.477214 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 4039.18 | 0.243177 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 752.623 | 0.0451032 | 0.0225516 | − | 0.999746i | \(-0.492821\pi\) | ||||
0.0225516 | + | 0.999746i | \(0.492821\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 3455.01 | 0.206105 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −12152.1 | −0.721611 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −4887.68 | −0.288918 | −0.144459 | − | 0.989511i | \(-0.546144\pi\) | ||||
−0.144459 | + | 0.989511i | \(0.546144\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 7122.91 | 0.419136 | 0.209568 | − | 0.977794i | \(-0.432794\pi\) | ||||
0.209568 | + | 0.977794i | \(0.432794\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 2945.90 | 0.171785 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 4452.87 | 0.258494 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 18887.2 | 1.09151 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −46655.6 | −2.68423 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 32249.6 | 1.84715 | 0.923574 | − | 0.383421i | \(-0.125254\pi\) | ||||
0.923574 | + | 0.383421i | \(0.125254\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 13509.3 | 0.770331 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 17447.9 | 0.990511 | 0.495255 | − | 0.868748i | \(-0.335075\pi\) | ||||
0.495255 | + | 0.868748i | \(0.335075\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 6722.23 | 0.379934 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −11352.6 | −0.638812 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −13935.3 | −0.780701 | −0.390351 | − | 0.920666i | \(-0.627646\pi\) | ||||
−0.390351 | + | 0.920666i | \(0.627646\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −12092.6 | −0.674500 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 14320.6 | 0.795289 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 7515.53 | 0.415557 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −22358.6 | −1.23092 | −0.615458 | − | 0.788170i | \(-0.711029\pi\) | ||||
−0.615458 | + | 0.788170i | \(0.711029\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 4925.64 | 0.269999 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 2132.02 | 0.116363 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 8031.99 | 0.434617 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 30456.5 | 1.64098 | 0.820491 | − | 0.571660i | \(-0.193700\pi\) | ||||
0.820491 | + | 0.571660i | \(0.193700\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −8355.30 | −0.448259 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 4384.01 | 0.234201 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 2707.82 | 0.144042 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 36945.7 | 1.95702 | 0.978508 | − | 0.206210i | \(-0.0661130\pi\) | ||||
0.978508 | + | 0.206210i | \(0.0661130\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −16922.3 | −0.892595 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −12004.2 | −0.630520 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 16613.0 | 0.868937 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 7456.31 | 0.388369 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −12442.4 | −0.645375 | −0.322687 | − | 0.946506i | \(-0.604586\pi\) | ||||
−0.322687 | + | 0.946506i | \(0.604586\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 2599.91 | 0.134294 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 5738.71 | 0.295194 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 11487.3 | 0.588451 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −29943.3 | −1.52756 | −0.763780 | − | 0.645477i | \(-0.776659\pi\) | ||||
−0.763780 | + | 0.645477i | \(0.776659\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 8857.78 | 0.450022 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −19615.5 | −0.988423 | −0.494212 | − | 0.869342i | \(-0.664543\pi\) | ||||
−0.494212 | + | 0.869342i | \(0.664543\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −4671.06 | −0.234414 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −22880.9 | −1.14359 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 3459.26 | 0.172194 | 0.0860968 | − | 0.996287i | \(-0.472561\pi\) | ||||
0.0860968 | + | 0.996287i | \(0.472561\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −22376.9 | −1.10936 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −37392.9 | −1.84632 | −0.923158 | − | 0.384421i | \(-0.874401\pi\) | ||||
−0.923158 | + | 0.384421i | \(0.874401\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 11890.9 | 0.584765 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −13226.2 | −0.647819 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 62.9447 | 0.00307069 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −34379.7 | −1.67048 | −0.835241 | − | 0.549884i | \(-0.814672\pi\) | ||||
−0.835241 | + | 0.549884i | \(0.814672\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 6888.31 | 0.333365 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −12768.5 | −0.615489 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 20120.9 | 0.966057 | 0.483028 | − | 0.875605i | \(-0.339537\pi\) | ||||
0.483028 | + | 0.875605i | \(0.339537\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 6983.86 | 0.333989 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −21739.7 | −1.03556 | −0.517781 | − | 0.855513i | \(-0.673242\pi\) | ||||
−0.517781 | + | 0.855513i | \(0.673242\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −7137.46 | −0.338654 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −7342.26 | −0.345650 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 26884.9 | 1.26072 | 0.630360 | − | 0.776303i | \(-0.282907\pi\) | ||||
0.630360 | + | 0.776303i | \(0.282907\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 2385.53 | 0.111430 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 21927.0 | 1.02026 | 0.510128 | − | 0.860099i | \(-0.329598\pi\) | ||||
0.510128 | + | 0.860099i | \(0.329598\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −30967.9 | −1.43535 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −816.519 | −0.0376994 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 42782.6 | 1.96771 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 28086.7 | 1.28684 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 15203.2 | 0.693894 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 802.934 | 0.0365069 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −28401.4 | −1.28641 | −0.643203 | − | 0.765695i | \(-0.722395\pi\) | ||||
−0.643203 | + | 0.765695i | \(0.722395\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 18961.2 | 0.855561 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 2769.58 | 0.124494 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −43416.3 | −1.94421 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −1933.60 | −0.0862612 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 19462.7 | 0.864999 | 0.432499 | − | 0.901634i | \(-0.357632\pi\) | ||||
0.432499 | + | 0.901634i | \(0.357632\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −16258.3 | −0.717177 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −40145.0 | −1.76424 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −855.583 | −0.0374601 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −18708.0 | −0.816050 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −11073.0 | −0.481220 | −0.240610 | − | 0.970622i | \(-0.577347\pi\) | ||||
−0.240610 | + | 0.970622i | \(0.577347\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −8512.57 | −0.368578 | −0.184289 | − | 0.982872i | \(-0.558998\pi\) | ||||
−0.184289 | + | 0.982872i | \(0.558998\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −4220.99 | −0.182087 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −1416.91 | −0.0608983 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −16540.1 | −0.708278 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 4583.65 | 0.195562 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 26291.2 | 1.11762 | 0.558812 | − | 0.829294i | \(-0.311257\pi\) | ||||
0.558812 | + | 0.829294i | \(0.311257\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 4379.37 | 0.185486 | 0.0927432 | − | 0.995690i | \(-0.470436\pi\) | ||||
0.0927432 | + | 0.995690i | \(0.470436\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 18016.6 | 0.760313 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 2994.98 | 0.125932 | 0.0629659 | − | 0.998016i | \(-0.479944\pi\) | ||||
0.0629659 | + | 0.998016i | \(0.479944\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −33497.1 | −1.40338 | −0.701690 | − | 0.712482i | \(-0.747571\pi\) | ||||
−0.701690 | + | 0.712482i | \(0.747571\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 23267.0 | 0.971269 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −10513.7 | −0.435739 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −40985.4 | −1.69255 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 25588.9 | 1.05295 | 0.526477 | − | 0.850189i | \(-0.323513\pi\) | ||||
0.526477 | + | 0.850189i | \(0.323513\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −11461.3 | −0.469938 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −8764.73 | −0.358094 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 4703.57 | 0.191489 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 10332.7 | 0.419168 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −1184.79 | −0.0478939 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 2426.64 | 0.0977488 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 31609.1 | 1.26879 | 0.634394 | − | 0.773010i | \(-0.281250\pi\) | ||||
0.634394 | + | 0.773010i | \(0.281250\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −12067.4 | −0.482686 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 7519.34 | 0.299715 | 0.149858 | − | 0.988708i | \(-0.452119\pi\) | ||||
0.149858 | + | 0.988708i | \(0.452119\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 3923.30 | 0.155834 | 0.0779169 | − | 0.996960i | \(-0.475173\pi\) | ||||
0.0779169 | + | 0.996960i | \(0.475173\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 4180.92 | 0.165488 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 32254.8 | 1.27227 | 0.636133 | − | 0.771580i | \(-0.280533\pi\) | ||||
0.636133 | + | 0.771580i | \(0.280533\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −21462.9 | −0.843654 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −55903.5 | −2.18228 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −21292.3 | −0.828313 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −27536.5 | −1.06755 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −4938.01 | −0.190783 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 9587.97 | 0.369171 | 0.184585 | − | 0.982816i | \(-0.440906\pi\) | ||||
0.184585 | + | 0.982816i | \(0.440906\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 21825.2 | 0.837479 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −10243.5 | −0.391726 | −0.195863 | − | 0.980631i | \(-0.562751\pi\) | ||||
−0.195863 | + | 0.980631i | \(0.562751\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −17802.2 | −0.678474 | −0.339237 | − | 0.940701i | \(-0.610169\pi\) | ||||
−0.339237 | + | 0.940701i | \(0.610169\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 1889.02 | 0.0717499 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 5409.67 | 0.204779 | 0.102389 | − | 0.994744i | \(-0.467351\pi\) | ||||
0.102389 | + | 0.994744i | \(0.467351\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 4330.25 | 0.163365 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −5958.47 | −0.224036 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 40889.5 | 1.53227 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −18570.1 | −0.693551 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 6498.97 | 0.241911 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −34850.9 | −1.29293 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −1616.37 | −0.0595675 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −8453.74 | −0.310510 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −27596.6 | −1.01029 | −0.505143 | − | 0.863036i | \(-0.668560\pi\) | ||||
−0.505143 | + | 0.863036i | \(0.668560\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −11092.1 | −0.404733 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 47306.9 | 1.72047 | 0.860235 | − | 0.509898i | \(-0.170317\pi\) | ||||
0.860235 | + | 0.509898i | \(0.170317\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −43693.3 | −1.58383 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 11170.2 | 0.403579 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 3149.16 | 0.113407 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 40635.5 | 1.45859 | 0.729293 | − | 0.684202i | \(-0.239849\pi\) | ||||
0.729293 | + | 0.684202i | \(0.239849\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −148.448 | −0.00531111 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 26136.6 | 0.932067 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 6260.14 | 0.222521 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −10650.1 | −0.377341 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 34143.2 | 1.20582 | 0.602908 | − | 0.797811i | \(-0.294009\pi\) | ||||
0.602908 | + | 0.797811i | \(0.294009\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −43566.8 | −1.53367 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 634.997 | 0.0222817 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −4097.67 | −0.142865 | −0.0714327 | − | 0.997445i | \(-0.522757\pi\) | ||||
−0.0714327 | + | 0.997445i | \(0.522757\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −13700.9 | −0.476157 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 32801.4 | 1.13634 | 0.568169 | − | 0.822912i | \(-0.307652\pi\) | ||||
0.568169 | + | 0.822912i | \(0.307652\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −12425.4 | −0.429086 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −2921.18 | −0.100557 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −32528.3 | −1.11618 | −0.558092 | − | 0.829779i | \(-0.688466\pi\) | ||||
−0.558092 | + | 0.829779i | \(0.688466\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −37357.7 | −1.27785 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −11710.8 | −0.399316 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 14335.6 | 0.487276 | 0.243638 | − | 0.969866i | \(-0.421659\pi\) | ||||
0.243638 | + | 0.969866i | \(0.421659\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 6295.96 | 0.213332 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 20275.7 | 0.684870 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −11022.1 | −0.371138 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 64161.3 | 2.15371 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −257.842 | −0.00862810 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 8235.01 | 0.274709 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 688.081 | 0.0228823 | 0.0114412 | − | 0.999935i | \(-0.496358\pi\) | ||||
0.0114412 | + | 0.999935i | \(0.496358\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −49985.2 | −1.65201 | −0.826005 | − | 0.563663i | \(-0.809391\pi\) | ||||
−0.826005 | + | 0.563663i | \(0.809391\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 1943.28 | 0.0640276 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 16765.7 | 0.550701 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −38752.4 | −1.26899 | −0.634493 | − | 0.772929i | \(-0.718791\pi\) | ||||
−0.634493 | + | 0.772929i | \(0.718791\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −53710.1 | −1.75340 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 29237.4 | 0.951558 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −21516.4 | −0.698135 | −0.349067 | − | 0.937098i | \(-0.613502\pi\) | ||||
−0.349067 | + | 0.937098i | \(0.613502\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −2034.56 | −0.0658138 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 3995.92 | 0.128867 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 4803.75 | 0.154449 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −6941.00 | −0.222491 | −0.111245 | − | 0.993793i | \(-0.535484\pi\) | ||||
−0.111245 | + | 0.993793i | \(0.535484\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −22142.1 | −0.707611 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −13518.7 | −0.430724 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 44135.5 | 1.40199 | 0.700996 | − | 0.713165i | \(-0.252739\pi\) | ||||
0.700996 | + | 0.713165i | \(0.252739\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 8285.18 | 0.262394 |
(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 | 2312.4.a.k.1.6 | 8 | ||
17.4 | even | 4 | 136.4.b.b.33.3 | ✓ | 8 | ||
17.13 | even | 4 | 136.4.b.b.33.6 | yes | 8 | ||
17.16 | even | 2 | inner | 2312.4.a.k.1.3 | 8 | ||
51.38 | odd | 4 | 1224.4.c.e.577.5 | 8 | |||
51.47 | odd | 4 | 1224.4.c.e.577.4 | 8 | |||
68.47 | odd | 4 | 272.4.b.f.33.3 | 8 | |||
68.55 | odd | 4 | 272.4.b.f.33.6 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
136.4.b.b.33.3 | ✓ | 8 | 17.4 | even | 4 | ||
136.4.b.b.33.6 | yes | 8 | 17.13 | even | 4 | ||
272.4.b.f.33.3 | 8 | 68.47 | odd | 4 | |||
272.4.b.f.33.6 | 8 | 68.55 | odd | 4 | |||
1224.4.c.e.577.4 | 8 | 51.47 | odd | 4 | |||
1224.4.c.e.577.5 | 8 | 51.38 | odd | 4 | |||
2312.4.a.k.1.3 | 8 | 17.16 | even | 2 | inner | ||
2312.4.a.k.1.6 | 8 | 1.1 | even | 1 | trivial |