Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [5796,2,Mod(1,5796)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(5796, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("5796.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 5796 = 2^{2} \cdot 3^{2} \cdot 7 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 5796.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: | \(46.2812930115\) |
Analytic rank: | \(1\) |
Dimension: | \(4\) |
Coefficient field: | 4.4.140608.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 26x^{2} + 52 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(+1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(4.88023\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 5796.1 |
$q$-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 | ||||||||
\(5\) | 1.30278 | 0.582619 | 0.291309 | − | 0.956629i | \(-0.405909\pi\) | ||||
0.291309 | + | 0.956629i | \(0.405909\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −5.88023 | −1.77296 | −0.886478 | − | 0.462770i | \(-0.846855\pi\) | ||||
−0.886478 | + | 0.462770i | \(0.846855\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.78039 | 1.04849 | 0.524246 | − | 0.851567i | \(-0.324347\pi\) | ||||
0.524246 | + | 0.851567i | \(0.324347\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −5.60555 | −1.35955 | −0.679773 | − | 0.733423i | \(-0.737922\pi\) | ||||
−0.679773 | + | 0.733423i | \(0.737922\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 4.40262 | 1.01003 | 0.505015 | − | 0.863111i | \(-0.331487\pi\) | ||||
0.505015 | + | 0.863111i | \(0.331487\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −1.00000 | −0.208514 | ||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −3.30278 | −0.660555 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −0.202935 | −0.0376842 | −0.0188421 | − | 0.999822i | \(-0.505998\pi\) | ||||
−0.0188421 | + | 0.999822i | \(0.505998\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −0.725320 | −0.130271 | −0.0651357 | − | 0.997876i | \(-0.520748\pi\) | ||||
−0.0651357 | + | 0.997876i | \(0.520748\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 1.30278 | 0.220209 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1.52238 | 0.250279 | 0.125139 | − | 0.992139i | \(-0.460062\pi\) | ||||
0.125139 | + | 0.992139i | \(0.460062\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −6.47762 | −1.01163 | −0.505817 | − | 0.862641i | \(-0.668809\pi\) | ||||
−0.505817 | + | 0.862641i | \(0.668809\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.44952 | 0.221050 | 0.110525 | − | 0.993873i | \(-0.464747\pi\) | ||||
0.110525 | + | 0.993873i | \(0.464747\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 1.66062 | 0.228104 | 0.114052 | − | 0.993475i | \(-0.463617\pi\) | ||||
0.114052 | + | 0.993475i | \(0.463617\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −7.66062 | −1.03296 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 2.53269 | 0.329728 | 0.164864 | − | 0.986316i | \(-0.447282\pi\) | ||||
0.164864 | + | 0.986316i | \(0.447282\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −5.18301 | −0.663616 | −0.331808 | − | 0.943347i | \(-0.607659\pi\) | ||||
−0.331808 | + | 0.943347i | \(0.607659\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 4.92500 | 0.610871 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −5.57746 | −0.681395 | −0.340697 | − | 0.940173i | \(-0.610663\pi\) | ||||
−0.340697 | + | 0.940173i | \(0.610663\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −10.5775 | −1.25531 | −0.627656 | − | 0.778490i | \(-0.715986\pi\) | ||||
−0.627656 | + | 0.778490i | \(0.715986\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −11.6969 | −1.36902 | −0.684508 | − | 0.729005i | \(-0.739983\pi\) | ||||
−0.684508 | + | 0.729005i | \(0.739983\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −5.88023 | −0.670115 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 8.23808 | 0.926856 | 0.463428 | − | 0.886135i | \(-0.346619\pi\) | ||||
0.463428 | + | 0.886135i | \(0.346619\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −1.34968 | −0.148146 | −0.0740732 | − | 0.997253i | \(-0.523600\pi\) | ||||
−0.0740732 | + | 0.997253i | \(0.523600\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −7.30278 | −0.792097 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −9.10801 | −0.965447 | −0.482723 | − | 0.875773i | \(-0.660352\pi\) | ||||
−0.482723 | + | 0.875773i | \(0.660352\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 3.78039 | 0.396293 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 5.73562 | 0.588462 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −16.5128 | −1.67662 | −0.838308 | − | 0.545197i | \(-0.816455\pi\) | ||||
−0.838308 | + | 0.545197i | \(0.816455\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 0.0728659 | 0.00725043 | 0.00362522 | − | 0.999993i | \(-0.498846\pi\) | ||||
0.00362522 | + | 0.999993i | \(0.498846\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −0.605551 | −0.0596667 | −0.0298334 | − | 0.999555i | \(-0.509498\pi\) | ||||
−0.0298334 | + | 0.999555i | \(0.509498\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 17.1016 | 1.65328 | 0.826639 | − | 0.562733i | \(-0.190250\pi\) | ||||
0.826639 | + | 0.562733i | \(0.190250\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −9.83333 | −0.941862 | −0.470931 | − | 0.882170i | \(-0.656082\pi\) | ||||
−0.470931 | + | 0.882170i | \(0.656082\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 3.31094 | 0.311467 | 0.155734 | − | 0.987799i | \(-0.450226\pi\) | ||||
0.155734 | + | 0.987799i | \(0.450226\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1.30278 | −0.121484 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −5.60555 | −0.513860 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 23.5771 | 2.14337 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −10.8167 | −0.967471 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −8.85213 | −0.785500 | −0.392750 | − | 0.919645i | \(-0.628476\pi\) | ||||
−0.392750 | + | 0.919645i | \(0.628476\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −2.67730 | −0.233916 | −0.116958 | − | 0.993137i | \(-0.537314\pi\) | ||||
−0.116958 | + | 0.993137i | \(0.537314\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 4.40262 | 0.381755 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 3.44101 | 0.293986 | 0.146993 | − | 0.989138i | \(-0.453041\pi\) | ||||
0.146993 | + | 0.989138i | \(0.453041\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 11.7168 | 0.993807 | 0.496904 | − | 0.867806i | \(-0.334470\pi\) | ||||
0.496904 | + | 0.867806i | \(0.334470\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −22.2296 | −1.85893 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −0.264379 | −0.0219555 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −3.39445 | −0.278084 | −0.139042 | − | 0.990286i | \(-0.544402\pi\) | ||||
−0.139042 | + | 0.990286i | \(0.544402\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −21.6873 | −1.76488 | −0.882442 | − | 0.470421i | \(-0.844102\pi\) | ||||
−0.882442 | + | 0.470421i | \(0.844102\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −0.944930 | −0.0758986 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −20.2765 | −1.61824 | −0.809119 | − | 0.587644i | \(-0.800055\pi\) | ||||
−0.809119 | + | 0.587644i | \(0.800055\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −1.00000 | −0.0788110 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 10.1642 | 0.796122 | 0.398061 | − | 0.917359i | \(-0.369683\pi\) | ||||
0.398061 | + | 0.917359i | \(0.369683\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −5.92826 | −0.458742 | −0.229371 | − | 0.973339i | \(-0.573667\pi\) | ||||
−0.229371 | + | 0.973339i | \(0.573667\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.29135 | 0.0993349 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 11.4492 | 0.870465 | 0.435232 | − | 0.900318i | \(-0.356666\pi\) | ||||
0.435232 | + | 0.900318i | \(0.356666\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −3.30278 | −0.249666 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −6.98007 | −0.521715 | −0.260858 | − | 0.965377i | \(-0.584005\pi\) | ||||
−0.260858 | + | 0.965377i | \(0.584005\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −15.5575 | −1.15638 | −0.578191 | − | 0.815902i | \(-0.696241\pi\) | ||||
−0.578191 | + | 0.815902i | \(0.696241\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 1.98333 | 0.145817 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 32.9619 | 2.41042 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −6.16633 | −0.446180 | −0.223090 | − | 0.974798i | \(-0.571614\pi\) | ||||
−0.223090 | + | 0.974798i | \(0.571614\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 27.1712 | 1.95583 | 0.977915 | − | 0.209005i | \(-0.0670226\pi\) | ||||
0.977915 | + | 0.209005i | \(0.0670226\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −26.3046 | −1.87412 | −0.937061 | − | 0.349164i | \(-0.886465\pi\) | ||||
−0.937061 | + | 0.349164i | \(0.886465\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 26.3575 | 1.86843 | 0.934217 | − | 0.356705i | \(-0.116100\pi\) | ||||
0.934217 | + | 0.356705i | \(0.116100\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −0.202935 | −0.0142433 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −8.43888 | −0.589397 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −25.8884 | −1.79074 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 21.1827 | 1.45827 | 0.729137 | − | 0.684367i | \(-0.239921\pi\) | ||||
0.729137 | + | 0.684367i | \(0.239921\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 1.88840 | 0.128788 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −0.725320 | −0.0492380 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −21.1912 | −1.42547 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 1.05507 | 0.0706527 | 0.0353264 | − | 0.999376i | \(-0.488753\pi\) | ||||
0.0353264 | + | 0.999376i | \(0.488753\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −14.9737 | −0.993839 | −0.496920 | − | 0.867797i | \(-0.665536\pi\) | ||||
−0.496920 | + | 0.867797i | \(0.665536\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 14.4307 | 0.953608 | 0.476804 | − | 0.879010i | \(-0.341795\pi\) | ||||
0.476804 | + | 0.879010i | \(0.341795\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −27.6062 | −1.80854 | −0.904272 | − | 0.426957i | \(-0.859586\pi\) | ||||
−0.904272 | + | 0.426957i | \(0.859586\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 8.34117 | 0.539546 | 0.269773 | − | 0.962924i | \(-0.413051\pi\) | ||||
0.269773 | + | 0.962924i | \(0.413051\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −16.6585 | −1.07307 | −0.536534 | − | 0.843879i | \(-0.680267\pi\) | ||||
−0.536534 | + | 0.843879i | \(0.680267\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 1.30278 | 0.0832313 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 16.6436 | 1.05901 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 19.5771 | 1.23570 | 0.617848 | − | 0.786297i | \(-0.288005\pi\) | ||||
0.617848 | + | 0.786297i | \(0.288005\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 5.88023 | 0.369687 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −21.4670 | −1.33907 | −0.669537 | − | 0.742779i | \(-0.733507\pi\) | ||||
−0.669537 | + | 0.742779i | \(0.733507\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1.52238 | 0.0945964 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 15.4907 | 0.955197 | 0.477599 | − | 0.878578i | \(-0.341507\pi\) | ||||
0.477599 | + | 0.878578i | \(0.341507\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 2.16342 | 0.132898 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 24.2377 | 1.47780 | 0.738900 | − | 0.673815i | \(-0.235345\pi\) | ||||
0.738900 | + | 0.673815i | \(0.235345\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −30.4126 | −1.84743 | −0.923716 | − | 0.383077i | \(-0.874864\pi\) | ||||
−0.923716 | + | 0.383077i | \(0.874864\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 19.4211 | 1.17114 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −1.89690 | −0.113974 | −0.0569870 | − | 0.998375i | \(-0.518149\pi\) | ||||
−0.0569870 | + | 0.998375i | \(0.518149\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −11.9062 | −0.710264 | −0.355132 | − | 0.934816i | \(-0.615564\pi\) | ||||
−0.355132 | + | 0.934816i | \(0.615564\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −2.37452 | −0.141151 | −0.0705753 | − | 0.997506i | \(-0.522483\pi\) | ||||
−0.0705753 | + | 0.997506i | \(0.522483\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −6.47762 | −0.382362 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 14.4222 | 0.848365 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 1.41078 | 0.0824188 | 0.0412094 | − | 0.999151i | \(-0.486879\pi\) | ||||
0.0412094 | + | 0.999151i | \(0.486879\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 3.29952 | 0.192106 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −3.78039 | −0.218626 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1.44952 | 0.0835489 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −6.75229 | −0.386635 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −15.7345 | −0.898015 | −0.449008 | − | 0.893528i | \(-0.648222\pi\) | ||||
−0.449008 | + | 0.893528i | \(0.648222\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 14.7502 | 0.836405 | 0.418202 | − | 0.908354i | \(-0.362660\pi\) | ||||
0.418202 | + | 0.908354i | \(0.362660\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 8.45555 | 0.477936 | 0.238968 | − | 0.971027i | \(-0.423191\pi\) | ||||
0.238968 | + | 0.971027i | \(0.423191\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −10.6866 | −0.600218 | −0.300109 | − | 0.953905i | \(-0.597023\pi\) | ||||
−0.300109 | + | 0.953905i | \(0.597023\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1.19331 | 0.0668124 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −24.6791 | −1.37318 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −12.4858 | −0.692587 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −11.9105 | −0.654658 | −0.327329 | − | 0.944910i | \(-0.606149\pi\) | ||||
−0.327329 | + | 0.944910i | \(0.606149\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −7.26617 | −0.396993 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 32.3315 | 1.76121 | 0.880606 | − | 0.473850i | \(-0.157136\pi\) | ||||
0.880606 | + | 0.473850i | \(0.157136\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 4.26505 | 0.230965 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −26.7124 | −1.43400 | −0.716999 | − | 0.697074i | \(-0.754485\pi\) | ||||
−0.716999 | + | 0.697074i | \(0.754485\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 8.87172 | 0.474893 | 0.237446 | − | 0.971401i | \(-0.423690\pi\) | ||||
0.237446 | + | 0.971401i | \(0.423690\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 13.2665 | 0.706105 | 0.353053 | − | 0.935603i | \(-0.385144\pi\) | ||||
0.353053 | + | 0.935603i | \(0.385144\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −13.7801 | −0.731369 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 7.51713 | 0.396739 | 0.198370 | − | 0.980127i | \(-0.436435\pi\) | ||||
0.198370 | + | 0.980127i | \(0.436435\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 0.383027 | 0.0201593 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −15.2384 | −0.797615 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −3.03301 | −0.158322 | −0.0791609 | − | 0.996862i | \(-0.525224\pi\) | ||||
−0.0791609 | + | 0.996862i | \(0.525224\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 1.66062 | 0.0862152 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 13.4492 | 0.696372 | 0.348186 | − | 0.937425i | \(-0.386798\pi\) | ||||
0.348186 | + | 0.937425i | \(0.386798\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −0.767175 | −0.0395115 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 10.0562 | 0.516552 | 0.258276 | − | 0.966071i | \(-0.416846\pi\) | ||||
0.258276 | + | 0.966071i | \(0.416846\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −9.02060 | −0.460931 | −0.230466 | − | 0.973080i | \(-0.574025\pi\) | ||||
−0.230466 | + | 0.973080i | \(0.574025\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −7.66062 | −0.390421 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 18.5021 | 0.938095 | 0.469047 | − | 0.883173i | \(-0.344597\pi\) | ||||
0.469047 | + | 0.883173i | \(0.344597\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 5.60555 | 0.283485 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 10.7324 | 0.540004 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −18.1265 | −0.909742 | −0.454871 | − | 0.890557i | \(-0.650315\pi\) | ||||
−0.454871 | + | 0.890557i | \(0.650315\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −9.42041 | −0.470433 | −0.235216 | − | 0.971943i | \(-0.575580\pi\) | ||||
−0.235216 | + | 0.971943i | \(0.575580\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −2.74199 | −0.136588 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −8.95198 | −0.443733 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −10.9812 | −0.542985 | −0.271493 | − | 0.962441i | \(-0.587517\pi\) | ||||
−0.271493 | + | 0.962441i | \(0.587517\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 2.53269 | 0.124625 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −1.75833 | −0.0863130 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −18.1080 | −0.884634 | −0.442317 | − | 0.896859i | \(-0.645843\pi\) | ||||
−0.442317 | + | 0.896859i | \(0.645843\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −4.55048 | −0.221777 | −0.110888 | − | 0.993833i | \(-0.535370\pi\) | ||||
−0.110888 | + | 0.993833i | \(0.535370\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 18.5139 | 0.898055 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −5.18301 | −0.250823 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −25.1578 | −1.21181 | −0.605905 | − | 0.795537i | \(-0.707189\pi\) | ||||
−0.605905 | + | 0.795537i | \(0.707189\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 15.7206 | 0.755484 | 0.377742 | − | 0.925911i | \(-0.376701\pi\) | ||||
0.377742 | + | 0.925911i | \(0.376701\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −4.40262 | −0.210606 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −7.99261 | −0.381467 | −0.190733 | − | 0.981642i | \(-0.561087\pi\) | ||||
−0.190733 | + | 0.981642i | \(0.561087\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −23.1173 | −1.09834 | −0.549168 | − | 0.835712i | \(-0.685055\pi\) | ||||
−0.549168 | + | 0.835712i | \(0.685055\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −11.8657 | −0.562488 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 12.1180 | 0.571882 | 0.285941 | − | 0.958247i | \(-0.407694\pi\) | ||||
0.285941 | + | 0.958247i | \(0.407694\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 38.0899 | 1.79358 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 4.92500 | 0.230888 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −12.8425 | −0.600747 | −0.300374 | − | 0.953822i | \(-0.597111\pi\) | ||||
−0.300374 | + | 0.953822i | \(0.597111\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −22.0870 | −1.02869 | −0.514346 | − | 0.857583i | \(-0.671965\pi\) | ||||
−0.514346 | + | 0.857583i | \(0.671965\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −33.9360 | −1.57714 | −0.788569 | − | 0.614946i | \(-0.789178\pi\) | ||||
−0.788569 | + | 0.614946i | \(0.789178\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 41.6758 | 1.92853 | 0.964264 | − | 0.264944i | \(-0.0853535\pi\) | ||||
0.964264 | + | 0.264944i | \(0.0853535\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −5.57746 | −0.257543 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −8.52351 | −0.391911 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −14.5409 | −0.667180 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 9.26014 | 0.423107 | 0.211553 | − | 0.977366i | \(-0.432148\pi\) | ||||
0.211553 | + | 0.977366i | \(0.432148\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 5.75521 | 0.262415 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −21.5124 | −0.976829 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −10.4670 | −0.474304 | −0.237152 | − | 0.971473i | \(-0.576214\pi\) | ||||
−0.237152 | + | 0.971473i | \(0.576214\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −9.52842 | −0.430012 | −0.215006 | − | 0.976613i | \(-0.568977\pi\) | ||||
−0.215006 | + | 0.976613i | \(0.568977\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 1.13756 | 0.0512333 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −10.5775 | −0.474464 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 5.19264 | 0.232454 | 0.116227 | − | 0.993223i | \(-0.462920\pi\) | ||||
0.116227 | + | 0.993223i | \(0.462920\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −3.81452 | −0.170081 | −0.0850405 | − | 0.996377i | \(-0.527102\pi\) | ||||
−0.0850405 | + | 0.996377i | \(0.527102\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0.0949280 | 0.00422424 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −29.3546 | −1.30112 | −0.650560 | − | 0.759455i | \(-0.725466\pi\) | ||||
−0.650560 | + | 0.759455i | \(0.725466\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −11.6969 | −0.517440 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −0.788897 | −0.0347630 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 31.5771 | 1.38342 | 0.691709 | − | 0.722176i | \(-0.256858\pi\) | ||||
0.691709 | + | 0.722176i | \(0.256858\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −29.1712 | −1.27557 | −0.637785 | − | 0.770215i | \(-0.720149\pi\) | ||||
−0.637785 | + | 0.770215i | \(0.720149\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 4.06582 | 0.177110 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −24.4879 | −1.06069 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 22.2796 | 0.963231 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −5.88023 | −0.253279 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −34.1663 | −1.46893 | −0.734463 | − | 0.678649i | \(-0.762566\pi\) | ||||
−0.734463 | + | 0.678649i | \(0.762566\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −12.8106 | −0.548747 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 19.1756 | 0.819890 | 0.409945 | − | 0.912110i | \(-0.365548\pi\) | ||||
0.409945 | + | 0.912110i | \(0.365548\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −0.893447 | −0.0380621 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 8.23808 | 0.350319 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −19.3611 | −0.820356 | −0.410178 | − | 0.912005i | \(-0.634533\pi\) | ||||
−0.410178 | + | 0.912005i | \(0.634533\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 5.47975 | 0.231769 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 28.2296 | 1.18973 | 0.594867 | − | 0.803824i | \(-0.297205\pi\) | ||||
0.594867 | + | 0.803824i | \(0.297205\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 4.31342 | 0.181467 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 23.3774 | 0.980033 | 0.490017 | − | 0.871713i | \(-0.336991\pi\) | ||||
0.490017 | + | 0.871713i | \(0.336991\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −29.6489 | −1.24077 | −0.620383 | − | 0.784299i | \(-0.713023\pi\) | ||||
−0.620383 | + | 0.784299i | \(0.713023\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 3.30278 | 0.137735 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −24.2928 | −1.01132 | −0.505661 | − | 0.862732i | \(-0.668751\pi\) | ||||
−0.505661 | + | 0.862732i | \(0.668751\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −1.34968 | −0.0559941 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −9.76484 | −0.404418 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 43.7423 | 1.80544 | 0.902720 | − | 0.430230i | \(-0.141567\pi\) | ||||
0.902720 | + | 0.430230i | \(0.141567\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −3.19331 | −0.131578 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −44.1471 | −1.81290 | −0.906452 | − | 0.422310i | \(-0.861219\pi\) | ||||
−0.906452 | + | 0.422310i | \(0.861219\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −7.30278 | −0.299385 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −13.2768 | −0.542476 | −0.271238 | − | 0.962512i | \(-0.587433\pi\) | ||||
−0.271238 | + | 0.962512i | \(0.587433\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 30.2868 | 1.23542 | 0.617712 | − | 0.786405i | \(-0.288060\pi\) | ||||
0.617712 | + | 0.786405i | \(0.288060\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 30.7157 | 1.24877 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −38.3127 | −1.55507 | −0.777533 | − | 0.628842i | \(-0.783529\pi\) | ||||
−0.777533 | + | 0.628842i | \(0.783529\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 22.2943 | 0.900457 | 0.450229 | − | 0.892913i | \(-0.351343\pi\) | ||||
0.450229 | + | 0.892913i | \(0.351343\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 43.7569 | 1.76159 | 0.880793 | − | 0.473502i | \(-0.157010\pi\) | ||||
0.880793 | + | 0.473502i | \(0.157010\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 8.92287 | 0.358640 | 0.179320 | − | 0.983791i | \(-0.442610\pi\) | ||||
0.179320 | + | 0.983791i | \(0.442610\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −9.10801 | −0.364905 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 2.42221 | 0.0968882 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −8.53381 | −0.340265 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 12.2047 | 0.485863 | 0.242931 | − | 0.970043i | \(-0.421891\pi\) | ||||
0.242931 | + | 0.970043i | \(0.421891\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −11.5323 | −0.457647 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 3.78039 | 0.149785 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −42.6787 | −1.68571 | −0.842855 | − | 0.538141i | \(-0.819127\pi\) | ||||
−0.842855 | + | 0.538141i | \(0.819127\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −3.27255 | −0.129057 | −0.0645283 | − | 0.997916i | \(-0.520554\pi\) | ||||
−0.0645283 | + | 0.997916i | \(0.520554\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 23.5213 | 0.924716 | 0.462358 | − | 0.886693i | \(-0.347003\pi\) | ||||
0.462358 | + | 0.886693i | \(0.347003\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −14.8928 | −0.584593 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 0.168330 | 0.00658725 | 0.00329362 | − | 0.999995i | \(-0.498952\pi\) | ||||
0.00329362 | + | 0.999995i | \(0.498952\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −3.48792 | −0.136284 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −0.669128 | −0.0260655 | −0.0130328 | − | 0.999915i | \(-0.504149\pi\) | ||||
−0.0130328 | + | 0.999915i | \(0.504149\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 7.81767 | 0.304072 | 0.152036 | − | 0.988375i | \(-0.451417\pi\) | ||||
0.152036 | + | 0.988375i | \(0.451417\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 5.73562 | 0.222418 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0.202935 | 0.00785769 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 30.4773 | 1.17656 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 29.0931 | 1.12146 | 0.560729 | − | 0.828000i | \(-0.310521\pi\) | ||||
0.560729 | + | 0.828000i | \(0.310521\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −5.01847 | −0.192875 | −0.0964377 | − | 0.995339i | \(-0.530745\pi\) | ||||
−0.0964377 | + | 0.995339i | \(0.530745\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −16.5128 | −0.633701 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 3.97973 | 0.152280 | 0.0761401 | − | 0.997097i | \(-0.475740\pi\) | ||||
0.0761401 | + | 0.997097i | \(0.475740\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 4.48287 | 0.171282 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 6.27780 | 0.239165 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 14.6062 | 0.555647 | 0.277823 | − | 0.960632i | \(-0.410387\pi\) | ||||
0.277823 | + | 0.960632i | \(0.410387\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 15.2644 | 0.579011 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 36.3106 | 1.37536 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −36.8717 | −1.39263 | −0.696313 | − | 0.717738i | \(-0.745177\pi\) | ||||
−0.696313 | + | 0.717738i | \(0.745177\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 6.70248 | 0.252789 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0.0728659 | 0.00274041 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −18.9165 | −0.710424 | −0.355212 | − | 0.934786i | \(-0.615591\pi\) | ||||
−0.355212 | + | 0.934786i | \(0.615591\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 0.725320 | 0.0271635 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −28.9601 | −1.08305 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 29.4492 | 1.09827 | 0.549135 | − | 0.835734i | \(-0.314957\pi\) | ||||
0.549135 | + | 0.835734i | \(0.314957\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −0.605551 | −0.0225519 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0.670250 | 0.0248925 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 5.11899 | 0.189853 | 0.0949264 | − | 0.995484i | \(-0.469738\pi\) | ||||
0.0949264 | + | 0.995484i | \(0.469738\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −8.12535 | −0.300527 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −7.56078 | −0.279264 | −0.139632 | − | 0.990203i | \(-0.544592\pi\) | ||||
−0.139632 | + | 0.990203i | \(0.544592\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 32.7967 | 1.20808 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −5.20619 | −0.191513 | −0.0957564 | − | 0.995405i | \(-0.530527\pi\) | ||||
−0.0957564 | + | 0.995405i | \(0.530527\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 9.54824 | 0.350291 | 0.175145 | − | 0.984543i | \(-0.443960\pi\) | ||||
0.175145 | + | 0.984543i | \(0.443960\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −4.42221 | −0.162017 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 17.1016 | 0.624880 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −12.6052 | −0.459971 | −0.229985 | − | 0.973194i | \(-0.573868\pi\) | ||||
−0.229985 | + | 0.973194i | \(0.573868\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −28.2536 | −1.02825 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −42.3874 | −1.54060 | −0.770298 | − | 0.637684i | \(-0.779893\pi\) | ||||
−0.770298 | + | 0.637684i | \(0.779893\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 39.2977 | 1.42454 | 0.712271 | − | 0.701905i | \(-0.247667\pi\) | ||||
0.712271 | + | 0.701905i | \(0.247667\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −9.83333 | −0.355990 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 9.57454 | 0.345717 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 43.3333 | 1.56264 | 0.781320 | − | 0.624131i | \(-0.214547\pi\) | ||||
0.781320 | + | 0.624131i | \(0.214547\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −13.1827 | −0.474148 | −0.237074 | − | 0.971492i | \(-0.576188\pi\) | ||||
−0.237074 | + | 0.971492i | \(0.576188\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 2.39557 | 0.0860514 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −28.5185 | −1.02178 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 62.1979 | 2.22562 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −26.4157 | −0.942817 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −8.75979 | −0.312253 | −0.156126 | − | 0.987737i | \(-0.549901\pi\) | ||||
−0.156126 | + | 0.987737i | \(0.549901\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 3.31094 | 0.117724 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −19.5938 | −0.695796 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −22.2559 | −0.788343 | −0.394172 | − | 0.919037i | \(-0.628968\pi\) | ||||
−0.394172 | + | 0.919037i | \(0.628968\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 68.7804 | 2.42721 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −1.30278 | −0.0459168 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −39.0722 | −1.37370 | −0.686852 | − | 0.726797i | \(-0.741008\pi\) | ||||
−0.686852 | + | 0.726797i | \(0.741008\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 6.99528 | 0.245638 | 0.122819 | − | 0.992429i | \(-0.460807\pi\) | ||||
0.122819 | + | 0.992429i | \(0.460807\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 13.2417 | 0.463836 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 6.38168 | 0.223267 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 51.5601 | 1.79946 | 0.899730 | − | 0.436447i | \(-0.143763\pi\) | ||||
0.899730 | + | 0.436447i | \(0.143763\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 21.8727 | 0.762436 | 0.381218 | − | 0.924485i | \(-0.375505\pi\) | ||||
0.381218 | + | 0.924485i | \(0.375505\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 4.40966 | 0.153339 | 0.0766695 | − | 0.997057i | \(-0.475571\pi\) | ||||
0.0766695 | + | 0.997057i | \(0.475571\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 24.3727 | 0.846500 | 0.423250 | − | 0.906013i | \(-0.360889\pi\) | ||||
0.423250 | + | 0.906013i | \(0.360889\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −5.60555 | −0.194221 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −7.72319 | −0.267272 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 29.6639 | 1.02411 | 0.512055 | − | 0.858952i | \(-0.328884\pi\) | ||||
0.512055 | + | 0.858952i | \(0.328884\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −28.9588 | −0.998580 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 1.68234 | 0.0578744 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 23.5771 | 0.810119 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −1.52238 | −0.0521867 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 7.78331 | 0.266495 | 0.133248 | − | 0.991083i | \(-0.457459\pi\) | ||||
0.133248 | + | 0.991083i | \(0.457459\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 36.5722 | 1.24928 | 0.624641 | − | 0.780912i | \(-0.285245\pi\) | ||||
0.624641 | + | 0.780912i | \(0.285245\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 9.41078 | 0.321092 | 0.160546 | − | 0.987028i | \(-0.448675\pi\) | ||||
0.160546 | + | 0.987028i | \(0.448675\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 54.9546 | 1.87067 | 0.935337 | − | 0.353757i | \(-0.115096\pi\) | ||||
0.935337 | + | 0.353757i | \(0.115096\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 14.9157 | 0.507149 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −48.4418 | −1.64328 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −21.0850 | −0.714437 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −10.8167 | −0.365670 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 41.0107 | 1.38483 | 0.692417 | − | 0.721497i | \(-0.256546\pi\) | ||||
0.692417 | + | 0.721497i | \(0.256546\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −23.6170 | −0.795676 | −0.397838 | − | 0.917456i | \(-0.630239\pi\) | ||||
−0.397838 | + | 0.917456i | \(0.630239\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 3.71783 | 0.125115 | 0.0625574 | − | 0.998041i | \(-0.480074\pi\) | ||||
0.0625574 | + | 0.998041i | \(0.480074\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −8.19788 | −0.275258 | −0.137629 | − | 0.990484i | \(-0.543948\pi\) | ||||
−0.137629 | + | 0.990484i | \(0.543948\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −8.85213 | −0.296891 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −9.09347 | −0.303961 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 0.147193 | 0.00490917 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −9.30870 | −0.310118 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −20.2680 | −0.673730 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −17.9370 | −0.595587 | −0.297793 | − | 0.954630i | \(-0.596251\pi\) | ||||
−0.297793 | + | 0.954630i | \(0.596251\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 52.1330 | 1.72724 | 0.863621 | − | 0.504141i | \(-0.168191\pi\) | ||||
0.863621 | + | 0.504141i | \(0.168191\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 7.93642 | 0.262657 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −2.67730 | −0.0884121 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 55.1136 | 1.81803 | 0.909015 | − | 0.416764i | \(-0.136836\pi\) | ||||
0.909015 | + | 0.416764i | \(0.136836\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −39.9869 | −1.31619 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −5.02810 | −0.165323 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 16.3287 | 0.535729 | 0.267864 | − | 0.963457i | \(-0.413682\pi\) | ||||
0.267864 | + | 0.963457i | \(0.413682\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 4.40262 | 0.144290 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 42.9420 | 1.40435 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 16.5454 | 0.540515 | 0.270258 | − | 0.962788i | \(-0.412891\pi\) | ||||
0.270258 | + | 0.962788i | \(0.412891\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −12.5990 | −0.410717 | −0.205359 | − | 0.978687i | \(-0.565836\pi\) | ||||
−0.205359 | + | 0.978687i | \(0.565836\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 6.47762 | 0.210940 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 40.9510 | 1.33073 | 0.665364 | − | 0.746519i | \(-0.268276\pi\) | ||||
0.665364 | + | 0.746519i | \(0.268276\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −44.2188 | −1.43540 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −30.3461 | −0.983006 | −0.491503 | − | 0.870876i | \(-0.663552\pi\) | ||||
−0.491503 | + | 0.870876i | \(0.663552\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −8.03335 | −0.259953 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 3.44101 | 0.111116 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −30.4739 | −0.983029 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 35.3980 | 1.13950 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −34.2160 | −1.10031 | −0.550156 | − | 0.835062i | \(-0.685432\pi\) | ||||
−0.550156 | + | 0.835062i | \(0.685432\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −35.5465 | −1.14074 | −0.570371 | − | 0.821387i | \(-0.693201\pi\) | ||||
−0.570371 | + | 0.821387i | \(0.693201\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 11.7168 | 0.375624 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −18.1072 | −0.579301 | −0.289651 | − | 0.957132i | \(-0.593539\pi\) | ||||
−0.289651 | + | 0.957132i | \(0.593539\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 53.5572 | 1.71170 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 49.5885 | 1.58163 | 0.790814 | − | 0.612056i | \(-0.209657\pi\) | ||||
0.790814 | + | 0.612056i | \(0.209657\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −34.2690 | −1.09190 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −1.44952 | −0.0460920 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 45.8897 | 1.45773 | 0.728867 | − | 0.684655i | \(-0.240047\pi\) | ||||
0.728867 | + | 0.684655i | \(0.240047\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 34.3379 | 1.08859 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −19.6577 | −0.622566 | −0.311283 | − | 0.950317i | \(-0.600759\pi\) | ||||
−0.311283 | + | 0.950317i | \(0.600759\pi\) | |||||||
\(998\) | 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 | 5796.2.a.q.1.3 | ✓ | 4 | |
3.2 | odd | 2 | 5796.2.a.r.1.2 | yes | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
5796.2.a.q.1.3 | ✓ | 4 | 1.1 | even | 1 | trivial | |
5796.2.a.r.1.2 | yes | 4 | 3.2 | odd | 2 |