Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1859,2,Mod(1,1859)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1859, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("1859.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1859 = 11 \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1859.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: | \(14.8441897358\) |
Analytic rank: | \(1\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.756.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - 6x - 2 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 143) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-2.26180\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1859.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | −0.353553 | − | 0.935414i | \(-0.615027\pi\) | ||||
−0.353553 | + | 0.935414i | \(0.615027\pi\) | |||||||
\(3\) | −2.26180 | −1.30585 | −0.652926 | − | 0.757422i | \(-0.726459\pi\) | ||||
−0.652926 | + | 0.757422i | \(0.726459\pi\) | |||||||
\(4\) | −1.00000 | −0.500000 | ||||||||
\(5\) | −2.11575 | −0.946192 | −0.473096 | − | 0.881011i | \(-0.656864\pi\) | ||||
−0.473096 | + | 0.881011i | \(0.656864\pi\) | |||||||
\(6\) | 2.26180 | 0.923377 | ||||||||
\(7\) | −3.37755 | −1.27659 | −0.638297 | − | 0.769790i | \(-0.720361\pi\) | ||||
−0.638297 | + | 0.769790i | \(0.720361\pi\) | |||||||
\(8\) | 3.00000 | 1.06066 | ||||||||
\(9\) | 2.11575 | 0.705250 | ||||||||
\(10\) | 2.11575 | 0.669059 | ||||||||
\(11\) | −1.00000 | −0.301511 | ||||||||
\(12\) | 2.26180 | 0.652926 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | 3.37755 | 0.902689 | ||||||||
\(15\) | 4.78541 | 1.23559 | ||||||||
\(16\) | −1.00000 | −0.250000 | ||||||||
\(17\) | −2.14605 | −0.520494 | −0.260247 | − | 0.965542i | \(-0.583804\pi\) | ||||
−0.260247 | + | 0.965542i | \(0.583804\pi\) | |||||||
\(18\) | −2.11575 | −0.498687 | ||||||||
\(19\) | −3.14605 | −0.721754 | −0.360877 | − | 0.932613i | \(-0.617523\pi\) | ||||
−0.360877 | + | 0.932613i | \(0.617523\pi\) | |||||||
\(20\) | 2.11575 | 0.473096 | ||||||||
\(21\) | 7.63935 | 1.66704 | ||||||||
\(22\) | 1.00000 | 0.213201 | ||||||||
\(23\) | 4.52360 | 0.943237 | 0.471618 | − | 0.881803i | \(-0.343670\pi\) | ||||
0.471618 | + | 0.881803i | \(0.343670\pi\) | |||||||
\(24\) | −6.78541 | −1.38507 | ||||||||
\(25\) | −0.523604 | −0.104721 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 2.00000 | 0.384900 | ||||||||
\(28\) | 3.37755 | 0.638297 | ||||||||
\(29\) | 3.49330 | 0.648690 | 0.324345 | − | 0.945939i | \(-0.394856\pi\) | ||||
0.324345 | + | 0.945939i | \(0.394856\pi\) | |||||||
\(30\) | −4.78541 | −0.873692 | ||||||||
\(31\) | 9.27871 | 1.66651 | 0.833253 | − | 0.552893i | \(-0.186476\pi\) | ||||
0.833253 | + | 0.552893i | \(0.186476\pi\) | |||||||
\(32\) | −5.00000 | −0.883883 | ||||||||
\(33\) | 2.26180 | 0.393729 | ||||||||
\(34\) | 2.14605 | 0.368045 | ||||||||
\(35\) | 7.14605 | 1.20790 | ||||||||
\(36\) | −2.11575 | −0.352625 | ||||||||
\(37\) | 9.16296 | 1.50638 | 0.753191 | − | 0.657802i | \(-0.228514\pi\) | ||||
0.753191 | + | 0.657802i | \(0.228514\pi\) | |||||||
\(38\) | 3.14605 | 0.510357 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −6.34725 | −1.00359 | ||||||||
\(41\) | −10.0169 | −1.56438 | −0.782189 | − | 0.623041i | \(-0.785897\pi\) | ||||
−0.782189 | + | 0.623041i | \(0.785897\pi\) | |||||||
\(42\) | −7.63935 | −1.17878 | ||||||||
\(43\) | 2.52360 | 0.384846 | 0.192423 | − | 0.981312i | \(-0.438365\pi\) | ||||
0.192423 | + | 0.981312i | \(0.438365\pi\) | |||||||
\(44\) | 1.00000 | 0.150756 | ||||||||
\(45\) | −4.47640 | −0.667302 | ||||||||
\(46\) | −4.52360 | −0.666969 | ||||||||
\(47\) | 1.96970 | 0.287310 | 0.143655 | − | 0.989628i | \(-0.454114\pi\) | ||||
0.143655 | + | 0.989628i | \(0.454114\pi\) | |||||||
\(48\) | 2.26180 | 0.326463 | ||||||||
\(49\) | 4.40786 | 0.629694 | ||||||||
\(50\) | 0.523604 | 0.0740489 | ||||||||
\(51\) | 4.85395 | 0.679689 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 7.75510 | 1.06525 | 0.532623 | − | 0.846353i | \(-0.321206\pi\) | ||||
0.532623 | + | 0.846353i | \(0.321206\pi\) | |||||||
\(54\) | −2.00000 | −0.272166 | ||||||||
\(55\) | 2.11575 | 0.285288 | ||||||||
\(56\) | −10.1327 | −1.35403 | ||||||||
\(57\) | 7.11575 | 0.942504 | ||||||||
\(58\) | −3.49330 | −0.458693 | ||||||||
\(59\) | 6.03030 | 0.785079 | 0.392539 | − | 0.919735i | \(-0.371597\pi\) | ||||
0.392539 | + | 0.919735i | \(0.371597\pi\) | |||||||
\(60\) | −4.78541 | −0.617793 | ||||||||
\(61\) | 9.78541 | 1.25289 | 0.626446 | − | 0.779464i | \(-0.284509\pi\) | ||||
0.626446 | + | 0.779464i | \(0.284509\pi\) | |||||||
\(62\) | −9.27871 | −1.17840 | ||||||||
\(63\) | −7.14605 | −0.900318 | ||||||||
\(64\) | 7.00000 | 0.875000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −2.26180 | −0.278409 | ||||||||
\(67\) | −4.03030 | −0.492380 | −0.246190 | − | 0.969222i | \(-0.579179\pi\) | ||||
−0.246190 | + | 0.969222i | \(0.579179\pi\) | |||||||
\(68\) | 2.14605 | 0.260247 | ||||||||
\(69\) | −10.2315 | −1.23173 | ||||||||
\(70\) | −7.14605 | −0.854117 | ||||||||
\(71\) | −6.00000 | −0.712069 | −0.356034 | − | 0.934473i | \(-0.615871\pi\) | ||||
−0.356034 | + | 0.934473i | \(0.615871\pi\) | |||||||
\(72\) | 6.34725 | 0.748030 | ||||||||
\(73\) | −10.8405 | −1.26879 | −0.634395 | − | 0.773009i | \(-0.718751\pi\) | ||||
−0.634395 | + | 0.773009i | \(0.718751\pi\) | |||||||
\(74\) | −9.16296 | −1.06517 | ||||||||
\(75\) | 1.18429 | 0.136750 | ||||||||
\(76\) | 3.14605 | 0.360877 | ||||||||
\(77\) | 3.37755 | 0.384908 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1.66966 | 0.187851 | 0.0939256 | − | 0.995579i | \(-0.470058\pi\) | ||||
0.0939256 | + | 0.995579i | \(0.470058\pi\) | |||||||
\(80\) | 2.11575 | 0.236548 | ||||||||
\(81\) | −10.8709 | −1.20787 | ||||||||
\(82\) | 10.0169 | 1.10618 | ||||||||
\(83\) | −5.66966 | −0.622326 | −0.311163 | − | 0.950357i | \(-0.600718\pi\) | ||||
−0.311163 | + | 0.950357i | \(0.600718\pi\) | |||||||
\(84\) | −7.63935 | −0.833522 | ||||||||
\(85\) | 4.54051 | 0.492487 | ||||||||
\(86\) | −2.52360 | −0.272127 | ||||||||
\(87\) | −7.90116 | −0.847093 | ||||||||
\(88\) | −3.00000 | −0.319801 | ||||||||
\(89\) | −9.34725 | −0.990806 | −0.495403 | − | 0.868663i | \(-0.664980\pi\) | ||||
−0.495403 | + | 0.868663i | \(0.664980\pi\) | |||||||
\(90\) | 4.47640 | 0.471854 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −4.52360 | −0.471618 | ||||||||
\(93\) | −20.9866 | −2.17621 | ||||||||
\(94\) | −1.96970 | −0.203159 | ||||||||
\(95\) | 6.65626 | 0.682918 | ||||||||
\(96\) | 11.3090 | 1.15422 | ||||||||
\(97\) | −11.6394 | −1.18180 | −0.590899 | − | 0.806746i | \(-0.701227\pi\) | ||||
−0.590899 | + | 0.806746i | \(0.701227\pi\) | |||||||
\(98\) | −4.40786 | −0.445261 | ||||||||
\(99\) | −2.11575 | −0.212641 | ||||||||
\(100\) | 0.523604 | 0.0523604 | ||||||||
\(101\) | 0.901156 | 0.0896684 | 0.0448342 | − | 0.998994i | \(-0.485724\pi\) | ||||
0.0448342 | + | 0.998994i | \(0.485724\pi\) | |||||||
\(102\) | −4.85395 | −0.480612 | ||||||||
\(103\) | 13.0472 | 1.28558 | 0.642790 | − | 0.766043i | \(-0.277777\pi\) | ||||
0.642790 | + | 0.766043i | \(0.277777\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −16.1630 | −1.57734 | ||||||||
\(106\) | −7.75510 | −0.753242 | ||||||||
\(107\) | −13.6091 | −1.31564 | −0.657818 | − | 0.753177i | \(-0.728521\pi\) | ||||
−0.657818 | + | 0.753177i | \(0.728521\pi\) | |||||||
\(108\) | −2.00000 | −0.192450 | ||||||||
\(109\) | −18.6866 | −1.78985 | −0.894924 | − | 0.446218i | \(-0.852770\pi\) | ||||
−0.894924 | + | 0.446218i | \(0.852770\pi\) | |||||||
\(110\) | −2.11575 | −0.201729 | ||||||||
\(111\) | −20.7248 | −1.96711 | ||||||||
\(112\) | 3.37755 | 0.319149 | ||||||||
\(113\) | 12.6394 | 1.18901 | 0.594505 | − | 0.804092i | \(-0.297348\pi\) | ||||
0.594505 | + | 0.804092i | \(0.297348\pi\) | |||||||
\(114\) | −7.11575 | −0.666451 | ||||||||
\(115\) | −9.57081 | −0.892483 | ||||||||
\(116\) | −3.49330 | −0.324345 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −6.03030 | −0.555134 | ||||||||
\(119\) | 7.24840 | 0.664460 | ||||||||
\(120\) | 14.3562 | 1.31054 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | −9.78541 | −0.885929 | ||||||||
\(123\) | 22.6563 | 2.04285 | ||||||||
\(124\) | −9.27871 | −0.833253 | ||||||||
\(125\) | 11.6866 | 1.04528 | ||||||||
\(126\) | 7.14605 | 0.636621 | ||||||||
\(127\) | 11.5102 | 1.02137 | 0.510683 | − | 0.859769i | \(-0.329393\pi\) | ||||
0.510683 | + | 0.859769i | \(0.329393\pi\) | |||||||
\(128\) | 3.00000 | 0.265165 | ||||||||
\(129\) | −5.70789 | −0.502552 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 13.6091 | 1.18903 | 0.594514 | − | 0.804085i | \(-0.297344\pi\) | ||||
0.594514 | + | 0.804085i | \(0.297344\pi\) | |||||||
\(132\) | −2.26180 | −0.196865 | ||||||||
\(133\) | 10.6260 | 0.921387 | ||||||||
\(134\) | 4.03030 | 0.348165 | ||||||||
\(135\) | −4.23150 | −0.364189 | ||||||||
\(136\) | −6.43816 | −0.552068 | ||||||||
\(137\) | 15.1024 | 1.29028 | 0.645140 | − | 0.764064i | \(-0.276799\pi\) | ||||
0.645140 | + | 0.764064i | \(0.276799\pi\) | |||||||
\(138\) | 10.2315 | 0.870963 | ||||||||
\(139\) | −15.2787 | −1.29592 | −0.647962 | − | 0.761673i | \(-0.724378\pi\) | ||||
−0.647962 | + | 0.761673i | \(0.724378\pi\) | |||||||
\(140\) | −7.14605 | −0.603952 | ||||||||
\(141\) | −4.45506 | −0.375184 | ||||||||
\(142\) | 6.00000 | 0.503509 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −2.11575 | −0.176312 | ||||||||
\(145\) | −7.39095 | −0.613785 | ||||||||
\(146\) | 10.8405 | 0.897170 | ||||||||
\(147\) | −9.96970 | −0.822287 | ||||||||
\(148\) | −9.16296 | −0.753191 | ||||||||
\(149\) | −4.37755 | −0.358623 | −0.179312 | − | 0.983792i | \(-0.557387\pi\) | ||||
−0.179312 | + | 0.983792i | \(0.557387\pi\) | |||||||
\(150\) | −1.18429 | −0.0966969 | ||||||||
\(151\) | −2.29211 | −0.186529 | −0.0932645 | − | 0.995641i | \(-0.529730\pi\) | ||||
−0.0932645 | + | 0.995641i | \(0.529730\pi\) | |||||||
\(152\) | −9.43816 | −0.765536 | ||||||||
\(153\) | −4.54051 | −0.367078 | ||||||||
\(154\) | −3.37755 | −0.272171 | ||||||||
\(155\) | −19.6314 | −1.57683 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −24.0472 | −1.91918 | −0.959588 | − | 0.281408i | \(-0.909198\pi\) | ||||
−0.959588 | + | 0.281408i | \(0.909198\pi\) | |||||||
\(158\) | −1.66966 | −0.132831 | ||||||||
\(159\) | −17.5405 | −1.39105 | ||||||||
\(160\) | 10.5787 | 0.836323 | ||||||||
\(161\) | −15.2787 | −1.20413 | ||||||||
\(162\) | 10.8709 | 0.854095 | ||||||||
\(163\) | 6.55391 | 0.513342 | 0.256671 | − | 0.966499i | \(-0.417374\pi\) | ||||
0.256671 | + | 0.966499i | \(0.417374\pi\) | |||||||
\(164\) | 10.0169 | 0.782189 | ||||||||
\(165\) | −4.78541 | −0.372543 | ||||||||
\(166\) | 5.66966 | 0.440051 | ||||||||
\(167\) | 18.3259 | 1.41810 | 0.709051 | − | 0.705157i | \(-0.249124\pi\) | ||||
0.709051 | + | 0.705157i | \(0.249124\pi\) | |||||||
\(168\) | 22.9181 | 1.76817 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | −4.54051 | −0.348241 | ||||||||
\(171\) | −6.65626 | −0.509017 | ||||||||
\(172\) | −2.52360 | −0.192423 | ||||||||
\(173\) | 14.6866 | 1.11660 | 0.558299 | − | 0.829640i | \(-0.311454\pi\) | ||||
0.558299 | + | 0.829640i | \(0.311454\pi\) | |||||||
\(174\) | 7.90116 | 0.598985 | ||||||||
\(175\) | 1.76850 | 0.133686 | ||||||||
\(176\) | 1.00000 | 0.0753778 | ||||||||
\(177\) | −13.6394 | −1.02520 | ||||||||
\(178\) | 9.34725 | 0.700606 | ||||||||
\(179\) | −6.49330 | −0.485332 | −0.242666 | − | 0.970110i | \(-0.578022\pi\) | ||||
−0.242666 | + | 0.970110i | \(0.578022\pi\) | |||||||
\(180\) | 4.47640 | 0.333651 | ||||||||
\(181\) | −17.1630 | −1.27571 | −0.637856 | − | 0.770155i | \(-0.720179\pi\) | ||||
−0.637856 | + | 0.770155i | \(0.720179\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −22.1327 | −1.63609 | ||||||||
\(184\) | 13.5708 | 1.00045 | ||||||||
\(185\) | −19.3865 | −1.42533 | ||||||||
\(186\) | 20.9866 | 1.53881 | ||||||||
\(187\) | 2.14605 | 0.156935 | ||||||||
\(188\) | −1.96970 | −0.143655 | ||||||||
\(189\) | −6.75510 | −0.491361 | ||||||||
\(190\) | −6.65626 | −0.482896 | ||||||||
\(191\) | 17.9697 | 1.30024 | 0.650121 | − | 0.759831i | \(-0.274718\pi\) | ||||
0.650121 | + | 0.759831i | \(0.274718\pi\) | |||||||
\(192\) | −15.8326 | −1.14262 | ||||||||
\(193\) | 2.96970 | 0.213763 | 0.106882 | − | 0.994272i | \(-0.465913\pi\) | ||||
0.106882 | + | 0.994272i | \(0.465913\pi\) | |||||||
\(194\) | 11.6394 | 0.835657 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −4.40786 | −0.314847 | ||||||||
\(197\) | −12.2315 | −0.871458 | −0.435729 | − | 0.900078i | \(-0.643509\pi\) | ||||
−0.435729 | + | 0.900078i | \(0.643509\pi\) | |||||||
\(198\) | 2.11575 | 0.150360 | ||||||||
\(199\) | −0.201195 | −0.0142624 | −0.00713118 | − | 0.999975i | \(-0.502270\pi\) | ||||
−0.00713118 | + | 0.999975i | \(0.502270\pi\) | |||||||
\(200\) | −1.57081 | −0.111073 | ||||||||
\(201\) | 9.11575 | 0.642975 | ||||||||
\(202\) | −0.901156 | −0.0634051 | ||||||||
\(203\) | −11.7988 | −0.828114 | ||||||||
\(204\) | −4.85395 | −0.339844 | ||||||||
\(205\) | 21.1933 | 1.48020 | ||||||||
\(206\) | −13.0472 | −0.909042 | ||||||||
\(207\) | 9.57081 | 0.665218 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 3.14605 | 0.217617 | ||||||||
\(210\) | 16.1630 | 1.11535 | ||||||||
\(211\) | 11.6697 | 0.803372 | 0.401686 | − | 0.915777i | \(-0.368424\pi\) | ||||
0.401686 | + | 0.915777i | \(0.368424\pi\) | |||||||
\(212\) | −7.75510 | −0.532623 | ||||||||
\(213\) | 13.5708 | 0.929857 | ||||||||
\(214\) | 13.6091 | 0.930296 | ||||||||
\(215\) | −5.33931 | −0.364138 | ||||||||
\(216\) | 6.00000 | 0.408248 | ||||||||
\(217\) | −31.3393 | −2.12745 | ||||||||
\(218\) | 18.6866 | 1.26561 | ||||||||
\(219\) | 24.5192 | 1.65685 | ||||||||
\(220\) | −2.11575 | −0.142644 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 20.7248 | 1.39096 | ||||||||
\(223\) | 7.50670 | 0.502686 | 0.251343 | − | 0.967898i | \(-0.419128\pi\) | ||||
0.251343 | + | 0.967898i | \(0.419128\pi\) | |||||||
\(224\) | 16.8878 | 1.12836 | ||||||||
\(225\) | −1.10782 | −0.0738544 | ||||||||
\(226\) | −12.6394 | −0.840757 | ||||||||
\(227\) | 3.47640 | 0.230736 | 0.115368 | − | 0.993323i | \(-0.463195\pi\) | ||||
0.115368 | + | 0.993323i | \(0.463195\pi\) | |||||||
\(228\) | −7.11575 | −0.471252 | ||||||||
\(229\) | −13.4079 | −0.886016 | −0.443008 | − | 0.896518i | \(-0.646089\pi\) | ||||
−0.443008 | + | 0.896518i | \(0.646089\pi\) | |||||||
\(230\) | 9.57081 | 0.631081 | ||||||||
\(231\) | −7.63935 | −0.502633 | ||||||||
\(232\) | 10.4799 | 0.688039 | ||||||||
\(233\) | 0.292106 | 0.0191365 | 0.00956824 | − | 0.999954i | \(-0.496954\pi\) | ||||
0.00956824 | + | 0.999954i | \(0.496954\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −4.16738 | −0.271850 | ||||||||
\(236\) | −6.03030 | −0.392539 | ||||||||
\(237\) | −3.77643 | −0.245306 | ||||||||
\(238\) | −7.24840 | −0.469844 | ||||||||
\(239\) | 21.8023 | 1.41027 | 0.705137 | − | 0.709071i | \(-0.250885\pi\) | ||||
0.705137 | + | 0.709071i | \(0.250885\pi\) | |||||||
\(240\) | −4.78541 | −0.308897 | ||||||||
\(241\) | 2.54844 | 0.164160 | 0.0820798 | − | 0.996626i | \(-0.473844\pi\) | ||||
0.0820798 | + | 0.996626i | \(0.473844\pi\) | |||||||
\(242\) | −1.00000 | −0.0642824 | ||||||||
\(243\) | 18.5877 | 1.19240 | ||||||||
\(244\) | −9.78541 | −0.626446 | ||||||||
\(245\) | −9.32592 | −0.595811 | ||||||||
\(246\) | −22.6563 | −1.44451 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 27.8361 | 1.76760 | ||||||||
\(249\) | 12.8236 | 0.812665 | ||||||||
\(250\) | −11.6866 | −0.739123 | ||||||||
\(251\) | −26.8192 | −1.69281 | −0.846407 | − | 0.532537i | \(-0.821239\pi\) | ||||
−0.846407 | + | 0.532537i | \(0.821239\pi\) | |||||||
\(252\) | 7.14605 | 0.450159 | ||||||||
\(253\) | −4.52360 | −0.284397 | ||||||||
\(254\) | −11.5102 | −0.722215 | ||||||||
\(255\) | −10.2697 | −0.643116 | ||||||||
\(256\) | −17.0000 | −1.06250 | ||||||||
\(257\) | 3.06854 | 0.191410 | 0.0957051 | − | 0.995410i | \(-0.469489\pi\) | ||||
0.0957051 | + | 0.995410i | \(0.469489\pi\) | |||||||
\(258\) | 5.70789 | 0.355358 | ||||||||
\(259\) | −30.9484 | −1.92304 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 7.39095 | 0.457488 | ||||||||
\(262\) | −13.6091 | −0.840770 | ||||||||
\(263\) | 2.29211 | 0.141337 | 0.0706686 | − | 0.997500i | \(-0.477487\pi\) | ||||
0.0706686 | + | 0.997500i | \(0.477487\pi\) | |||||||
\(264\) | 6.78541 | 0.417613 | ||||||||
\(265\) | −16.4079 | −1.00793 | ||||||||
\(266\) | −10.6260 | −0.651519 | ||||||||
\(267\) | 21.1416 | 1.29385 | ||||||||
\(268\) | 4.03030 | 0.246190 | ||||||||
\(269\) | 11.2449 | 0.685613 | 0.342807 | − | 0.939406i | \(-0.388622\pi\) | ||||
0.342807 | + | 0.939406i | \(0.388622\pi\) | |||||||
\(270\) | 4.23150 | 0.257521 | ||||||||
\(271\) | 4.29211 | 0.260727 | 0.130363 | − | 0.991466i | \(-0.458386\pi\) | ||||
0.130363 | + | 0.991466i | \(0.458386\pi\) | |||||||
\(272\) | 2.14605 | 0.130124 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −15.1024 | −0.912366 | ||||||||
\(275\) | 0.523604 | 0.0315745 | ||||||||
\(276\) | 10.2315 | 0.615864 | ||||||||
\(277\) | −4.83262 | −0.290364 | −0.145182 | − | 0.989405i | \(-0.546377\pi\) | ||||
−0.145182 | + | 0.989405i | \(0.546377\pi\) | |||||||
\(278\) | 15.2787 | 0.916356 | ||||||||
\(279\) | 19.6314 | 1.17530 | ||||||||
\(280\) | 21.4382 | 1.28118 | ||||||||
\(281\) | −3.78541 | −0.225818 | −0.112909 | − | 0.993605i | \(-0.536017\pi\) | ||||
−0.112909 | + | 0.993605i | \(0.536017\pi\) | |||||||
\(282\) | 4.45506 | 0.265295 | ||||||||
\(283\) | −12.4248 | −0.738575 | −0.369288 | − | 0.929315i | \(-0.620398\pi\) | ||||
−0.369288 | + | 0.929315i | \(0.620398\pi\) | |||||||
\(284\) | 6.00000 | 0.356034 | ||||||||
\(285\) | −15.0551 | −0.891790 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 33.8326 | 1.99708 | ||||||||
\(288\) | −10.5787 | −0.623359 | ||||||||
\(289\) | −12.3945 | −0.729086 | ||||||||
\(290\) | 7.39095 | 0.434012 | ||||||||
\(291\) | 26.3259 | 1.54325 | ||||||||
\(292\) | 10.8405 | 0.634395 | ||||||||
\(293\) | −16.9012 | −0.987376 | −0.493688 | − | 0.869639i | \(-0.664352\pi\) | ||||
−0.493688 | + | 0.869639i | \(0.664352\pi\) | |||||||
\(294\) | 9.96970 | 0.581445 | ||||||||
\(295\) | −12.7586 | −0.742835 | ||||||||
\(296\) | 27.4889 | 1.59776 | ||||||||
\(297\) | −2.00000 | −0.116052 | ||||||||
\(298\) | 4.37755 | 0.253585 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | −1.18429 | −0.0683750 | ||||||||
\(301\) | −8.52360 | −0.491292 | ||||||||
\(302\) | 2.29211 | 0.131896 | ||||||||
\(303\) | −2.03824 | −0.117094 | ||||||||
\(304\) | 3.14605 | 0.180439 | ||||||||
\(305\) | −20.7035 | −1.18548 | ||||||||
\(306\) | 4.54051 | 0.259564 | ||||||||
\(307\) | 8.42476 | 0.480826 | 0.240413 | − | 0.970671i | \(-0.422717\pi\) | ||||
0.240413 | + | 0.970671i | \(0.422717\pi\) | |||||||
\(308\) | −3.37755 | −0.192454 | ||||||||
\(309\) | −29.5102 | −1.67878 | ||||||||
\(310\) | 19.6314 | 1.11499 | ||||||||
\(311\) | −28.5877 | −1.62106 | −0.810530 | − | 0.585697i | \(-0.800821\pi\) | ||||
−0.810530 | + | 0.585697i | \(0.800821\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 22.3945 | 1.26581 | 0.632905 | − | 0.774230i | \(-0.281862\pi\) | ||||
0.632905 | + | 0.774230i | \(0.281862\pi\) | |||||||
\(314\) | 24.0472 | 1.35706 | ||||||||
\(315\) | 15.1193 | 0.851874 | ||||||||
\(316\) | −1.66966 | −0.0939256 | ||||||||
\(317\) | 26.2708 | 1.47551 | 0.737757 | − | 0.675067i | \(-0.235885\pi\) | ||||
0.737757 | + | 0.675067i | \(0.235885\pi\) | |||||||
\(318\) | 17.5405 | 0.983623 | ||||||||
\(319\) | −3.49330 | −0.195587 | ||||||||
\(320\) | −14.8102 | −0.827918 | ||||||||
\(321\) | 30.7810 | 1.71803 | ||||||||
\(322\) | 15.2787 | 0.851449 | ||||||||
\(323\) | 6.75160 | 0.375669 | ||||||||
\(324\) | 10.8709 | 0.603936 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −6.55391 | −0.362987 | ||||||||
\(327\) | 42.2653 | 2.33728 | ||||||||
\(328\) | −30.0507 | −1.65927 | ||||||||
\(329\) | −6.65275 | −0.366778 | ||||||||
\(330\) | 4.78541 | 0.263428 | ||||||||
\(331\) | 8.29211 | 0.455775 | 0.227888 | − | 0.973687i | \(-0.426818\pi\) | ||||
0.227888 | + | 0.973687i | \(0.426818\pi\) | |||||||
\(332\) | 5.66966 | 0.311163 | ||||||||
\(333\) | 19.3865 | 1.06237 | ||||||||
\(334\) | −18.3259 | −1.00275 | ||||||||
\(335\) | 8.52711 | 0.465886 | ||||||||
\(336\) | −7.63935 | −0.416761 | ||||||||
\(337\) | −0.0516349 | −0.00281273 | −0.00140637 | − | 0.999999i | \(-0.500448\pi\) | ||||
−0.00140637 | + | 0.999999i | \(0.500448\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −28.5877 | −1.55267 | ||||||||
\(340\) | −4.54051 | −0.246244 | ||||||||
\(341\) | −9.27871 | −0.502470 | ||||||||
\(342\) | 6.65626 | 0.359929 | ||||||||
\(343\) | 8.75510 | 0.472731 | ||||||||
\(344\) | 7.57081 | 0.408191 | ||||||||
\(345\) | 21.6473 | 1.16545 | ||||||||
\(346\) | −14.6866 | −0.789555 | ||||||||
\(347\) | −8.62245 | −0.462877 | −0.231439 | − | 0.972850i | \(-0.574343\pi\) | ||||
−0.231439 | + | 0.972850i | \(0.574343\pi\) | |||||||
\(348\) | 7.90116 | 0.423546 | ||||||||
\(349\) | −30.0000 | −1.60586 | −0.802932 | − | 0.596071i | \(-0.796728\pi\) | ||||
−0.802932 | + | 0.596071i | \(0.796728\pi\) | |||||||
\(350\) | −1.76850 | −0.0945304 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 5.00000 | 0.266501 | ||||||||
\(353\) | 0.476396 | 0.0253560 | 0.0126780 | − | 0.999920i | \(-0.495964\pi\) | ||||
0.0126780 | + | 0.999920i | \(0.495964\pi\) | |||||||
\(354\) | 13.6394 | 0.724923 | ||||||||
\(355\) | 12.6945 | 0.673754 | ||||||||
\(356\) | 9.34725 | 0.495403 | ||||||||
\(357\) | −16.3945 | −0.867687 | ||||||||
\(358\) | 6.49330 | 0.343182 | ||||||||
\(359\) | 10.2315 | 0.539998 | 0.269999 | − | 0.962861i | \(-0.412977\pi\) | ||||
0.269999 | + | 0.962861i | \(0.412977\pi\) | |||||||
\(360\) | −13.4292 | −0.707780 | ||||||||
\(361\) | −9.10235 | −0.479071 | ||||||||
\(362\) | 17.1630 | 0.902065 | ||||||||
\(363\) | −2.26180 | −0.118714 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 22.9359 | 1.20052 | ||||||||
\(366\) | 22.1327 | 1.15689 | ||||||||
\(367\) | 21.3393 | 1.11390 | 0.556952 | − | 0.830545i | \(-0.311971\pi\) | ||||
0.556952 | + | 0.830545i | \(0.311971\pi\) | |||||||
\(368\) | −4.52360 | −0.235809 | ||||||||
\(369\) | −21.1933 | −1.10328 | ||||||||
\(370\) | 19.3865 | 1.00786 | ||||||||
\(371\) | −26.1933 | −1.35989 | ||||||||
\(372\) | 20.9866 | 1.08810 | ||||||||
\(373\) | 21.2271 | 1.09910 | 0.549548 | − | 0.835462i | \(-0.314800\pi\) | ||||
0.549548 | + | 0.835462i | \(0.314800\pi\) | |||||||
\(374\) | −2.14605 | −0.110970 | ||||||||
\(375\) | −26.4327 | −1.36498 | ||||||||
\(376\) | 5.90909 | 0.304738 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 6.75510 | 0.347445 | ||||||||
\(379\) | 1.04721 | 0.0537915 | 0.0268958 | − | 0.999638i | \(-0.491438\pi\) | ||||
0.0268958 | + | 0.999638i | \(0.491438\pi\) | |||||||
\(380\) | −6.65626 | −0.341459 | ||||||||
\(381\) | −26.0338 | −1.33375 | ||||||||
\(382\) | −17.9697 | −0.919410 | ||||||||
\(383\) | 28.9866 | 1.48115 | 0.740573 | − | 0.671976i | \(-0.234554\pi\) | ||||
0.740573 | + | 0.671976i | \(0.234554\pi\) | |||||||
\(384\) | −6.78541 | −0.346266 | ||||||||
\(385\) | −7.14605 | −0.364197 | ||||||||
\(386\) | −2.96970 | −0.151154 | ||||||||
\(387\) | 5.33931 | 0.271413 | ||||||||
\(388\) | 11.6394 | 0.590899 | ||||||||
\(389\) | 15.5653 | 0.789195 | 0.394597 | − | 0.918854i | \(-0.370884\pi\) | ||||
0.394597 | + | 0.918854i | \(0.370884\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −9.70789 | −0.490949 | ||||||||
\(392\) | 13.2236 | 0.667891 | ||||||||
\(393\) | −30.7810 | −1.55270 | ||||||||
\(394\) | 12.2315 | 0.616214 | ||||||||
\(395\) | −3.53258 | −0.177743 | ||||||||
\(396\) | 2.11575 | 0.106320 | ||||||||
\(397\) | −18.9787 | −0.952512 | −0.476256 | − | 0.879307i | \(-0.658006\pi\) | ||||
−0.476256 | + | 0.879307i | \(0.658006\pi\) | |||||||
\(398\) | 0.201195 | 0.0100850 | ||||||||
\(399\) | −24.0338 | −1.20320 | ||||||||
\(400\) | 0.523604 | 0.0261802 | ||||||||
\(401\) | 9.52360 | 0.475586 | 0.237793 | − | 0.971316i | \(-0.423576\pi\) | ||||
0.237793 | + | 0.971316i | \(0.423576\pi\) | |||||||
\(402\) | −9.11575 | −0.454652 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | −0.901156 | −0.0448342 | ||||||||
\(405\) | 23.0000 | 1.14288 | ||||||||
\(406\) | 11.7988 | 0.585565 | ||||||||
\(407\) | −9.16296 | −0.454191 | ||||||||
\(408\) | 14.5618 | 0.720919 | ||||||||
\(409\) | −9.91455 | −0.490243 | −0.245122 | − | 0.969492i | \(-0.578828\pi\) | ||||
−0.245122 | + | 0.969492i | \(0.578828\pi\) | |||||||
\(410\) | −21.1933 | −1.04666 | ||||||||
\(411\) | −34.1585 | −1.68492 | ||||||||
\(412\) | −13.0472 | −0.642790 | ||||||||
\(413\) | −20.3677 | −1.00223 | ||||||||
\(414\) | −9.57081 | −0.470380 | ||||||||
\(415\) | 11.9956 | 0.588840 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 34.5574 | 1.69228 | ||||||||
\(418\) | −3.14605 | −0.153878 | ||||||||
\(419\) | 7.01340 | 0.342627 | 0.171313 | − | 0.985217i | \(-0.445199\pi\) | ||||
0.171313 | + | 0.985217i | \(0.445199\pi\) | |||||||
\(420\) | 16.1630 | 0.788672 | ||||||||
\(421\) | −33.9787 | −1.65602 | −0.828009 | − | 0.560714i | \(-0.810527\pi\) | ||||
−0.828009 | + | 0.560714i | \(0.810527\pi\) | |||||||
\(422\) | −11.6697 | −0.568070 | ||||||||
\(423\) | 4.16738 | 0.202625 | ||||||||
\(424\) | 23.2653 | 1.12986 | ||||||||
\(425\) | 1.12368 | 0.0545066 | ||||||||
\(426\) | −13.5708 | −0.657508 | ||||||||
\(427\) | −33.0507 | −1.59944 | ||||||||
\(428\) | 13.6091 | 0.657818 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 5.33931 | 0.257485 | ||||||||
\(431\) | −7.86735 | −0.378957 | −0.189478 | − | 0.981885i | \(-0.560680\pi\) | ||||
−0.189478 | + | 0.981885i | \(0.560680\pi\) | |||||||
\(432\) | −2.00000 | −0.0962250 | ||||||||
\(433\) | −13.6528 | −0.656109 | −0.328055 | − | 0.944659i | \(-0.606393\pi\) | ||||
−0.328055 | + | 0.944659i | \(0.606393\pi\) | |||||||
\(434\) | 31.3393 | 1.50434 | ||||||||
\(435\) | 16.7169 | 0.801512 | ||||||||
\(436\) | 18.6866 | 0.894924 | ||||||||
\(437\) | −14.2315 | −0.680785 | ||||||||
\(438\) | −24.5192 | −1.17157 | ||||||||
\(439\) | −8.33034 | −0.397586 | −0.198793 | − | 0.980042i | \(-0.563702\pi\) | ||||
−0.198793 | + | 0.980042i | \(0.563702\pi\) | |||||||
\(440\) | 6.34725 | 0.302593 | ||||||||
\(441\) | 9.32592 | 0.444091 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −25.2484 | −1.19959 | −0.599794 | − | 0.800154i | \(-0.704751\pi\) | ||||
−0.599794 | + | 0.800154i | \(0.704751\pi\) | |||||||
\(444\) | 20.7248 | 0.983555 | ||||||||
\(445\) | 19.7764 | 0.937493 | ||||||||
\(446\) | −7.50670 | −0.355452 | ||||||||
\(447\) | 9.90116 | 0.468309 | ||||||||
\(448\) | −23.6429 | −1.11702 | ||||||||
\(449\) | 37.2708 | 1.75892 | 0.879458 | − | 0.475976i | \(-0.157905\pi\) | ||||
0.879458 | + | 0.475976i | \(0.157905\pi\) | |||||||
\(450\) | 1.10782 | 0.0522229 | ||||||||
\(451\) | 10.0169 | 0.471678 | ||||||||
\(452\) | −12.6394 | −0.594505 | ||||||||
\(453\) | 5.18429 | 0.243579 | ||||||||
\(454\) | −3.47640 | −0.163155 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 21.3472 | 0.999676 | ||||||||
\(457\) | 3.09091 | 0.144587 | 0.0722933 | − | 0.997383i | \(-0.476968\pi\) | ||||
0.0722933 | + | 0.997383i | \(0.476968\pi\) | |||||||
\(458\) | 13.4079 | 0.626508 | ||||||||
\(459\) | −4.29211 | −0.200338 | ||||||||
\(460\) | 9.57081 | 0.446241 | ||||||||
\(461\) | 22.4799 | 1.04699 | 0.523497 | − | 0.852028i | \(-0.324627\pi\) | ||||
0.523497 | + | 0.852028i | \(0.324627\pi\) | |||||||
\(462\) | 7.63935 | 0.355415 | ||||||||
\(463\) | 29.0507 | 1.35010 | 0.675051 | − | 0.737771i | \(-0.264122\pi\) | ||||
0.675051 | + | 0.737771i | \(0.264122\pi\) | |||||||
\(464\) | −3.49330 | −0.162172 | ||||||||
\(465\) | 44.4024 | 2.05911 | ||||||||
\(466\) | −0.292106 | −0.0135315 | ||||||||
\(467\) | −7.47990 | −0.346129 | −0.173064 | − | 0.984911i | \(-0.555367\pi\) | ||||
−0.173064 | + | 0.984911i | \(0.555367\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 13.6126 | 0.628570 | ||||||||
\(470\) | 4.16738 | 0.192227 | ||||||||
\(471\) | 54.3900 | 2.50616 | ||||||||
\(472\) | 18.0909 | 0.832702 | ||||||||
\(473\) | −2.52360 | −0.116035 | ||||||||
\(474\) | 3.77643 | 0.173457 | ||||||||
\(475\) | 1.64729 | 0.0755827 | ||||||||
\(476\) | −7.24840 | −0.332230 | ||||||||
\(477\) | 16.4079 | 0.751264 | ||||||||
\(478\) | −21.8023 | −0.997215 | ||||||||
\(479\) | −8.62245 | −0.393970 | −0.196985 | − | 0.980407i | \(-0.563115\pi\) | ||||
−0.196985 | + | 0.980407i | \(0.563115\pi\) | |||||||
\(480\) | −23.9270 | −1.09211 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | −2.54844 | −0.116078 | ||||||||
\(483\) | 34.5574 | 1.57242 | ||||||||
\(484\) | −1.00000 | −0.0454545 | ||||||||
\(485\) | 24.6260 | 1.11821 | ||||||||
\(486\) | −18.5877 | −0.843156 | ||||||||
\(487\) | −8.09091 | −0.366634 | −0.183317 | − | 0.983054i | \(-0.558683\pi\) | ||||
−0.183317 | + | 0.983054i | \(0.558683\pi\) | |||||||
\(488\) | 29.3562 | 1.32889 | ||||||||
\(489\) | −14.8236 | −0.670348 | ||||||||
\(490\) | 9.32592 | 0.421302 | ||||||||
\(491\) | 4.62245 | 0.208608 | 0.104304 | − | 0.994545i | \(-0.466738\pi\) | ||||
0.104304 | + | 0.994545i | \(0.466738\pi\) | |||||||
\(492\) | −22.6563 | −1.02142 | ||||||||
\(493\) | −7.49681 | −0.337639 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 4.47640 | 0.201199 | ||||||||
\(496\) | −9.27871 | −0.416626 | ||||||||
\(497\) | 20.2653 | 0.909023 | ||||||||
\(498\) | −12.8236 | −0.574641 | ||||||||
\(499\) | −39.5137 | −1.76888 | −0.884438 | − | 0.466657i | \(-0.845458\pi\) | ||||
−0.884438 | + | 0.466657i | \(0.845458\pi\) | |||||||
\(500\) | −11.6866 | −0.522639 | ||||||||
\(501\) | −41.4496 | −1.85183 | ||||||||
\(502\) | 26.8192 | 1.19700 | ||||||||
\(503\) | −37.7035 | −1.68111 | −0.840557 | − | 0.541723i | \(-0.817772\pi\) | ||||
−0.840557 | + | 0.541723i | \(0.817772\pi\) | |||||||
\(504\) | −21.4382 | −0.954931 | ||||||||
\(505\) | −1.90662 | −0.0848435 | ||||||||
\(506\) | 4.52360 | 0.201099 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −11.5102 | −0.510683 | ||||||||
\(509\) | 7.72129 | 0.342240 | 0.171120 | − | 0.985250i | \(-0.445261\pi\) | ||||
0.171120 | + | 0.985250i | \(0.445261\pi\) | |||||||
\(510\) | 10.2697 | 0.454752 | ||||||||
\(511\) | 36.6145 | 1.61973 | ||||||||
\(512\) | 11.0000 | 0.486136 | ||||||||
\(513\) | −6.29211 | −0.277803 | ||||||||
\(514\) | −3.06854 | −0.135348 | ||||||||
\(515\) | −27.6046 | −1.21641 | ||||||||
\(516\) | 5.70789 | 0.251276 | ||||||||
\(517\) | −1.96970 | −0.0866272 | ||||||||
\(518\) | 30.9484 | 1.35979 | ||||||||
\(519\) | −33.2181 | −1.45811 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 5.48979 | 0.240512 | 0.120256 | − | 0.992743i | \(-0.461628\pi\) | ||||
0.120256 | + | 0.992743i | \(0.461628\pi\) | |||||||
\(522\) | −7.39095 | −0.323493 | ||||||||
\(523\) | 41.2137 | 1.80215 | 0.901074 | − | 0.433665i | \(-0.142780\pi\) | ||||
0.901074 | + | 0.433665i | \(0.142780\pi\) | |||||||
\(524\) | −13.6091 | −0.594514 | ||||||||
\(525\) | −4.00000 | −0.174574 | ||||||||
\(526\) | −2.29211 | −0.0999406 | ||||||||
\(527\) | −19.9126 | −0.867406 | ||||||||
\(528\) | −2.26180 | −0.0984323 | ||||||||
\(529\) | −2.53700 | −0.110304 | ||||||||
\(530\) | 16.4079 | 0.712712 | ||||||||
\(531\) | 12.7586 | 0.553677 | ||||||||
\(532\) | −10.6260 | −0.460694 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | −21.1416 | −0.914888 | ||||||||
\(535\) | 28.7933 | 1.24484 | ||||||||
\(536\) | −12.0909 | −0.522248 | ||||||||
\(537\) | 14.6866 | 0.633772 | ||||||||
\(538\) | −11.2449 | −0.484802 | ||||||||
\(539\) | −4.40786 | −0.189860 | ||||||||
\(540\) | 4.23150 | 0.182095 | ||||||||
\(541\) | −31.2539 | −1.34371 | −0.671854 | − | 0.740683i | \(-0.734502\pi\) | ||||
−0.671854 | + | 0.740683i | \(0.734502\pi\) | |||||||
\(542\) | −4.29211 | −0.184362 | ||||||||
\(543\) | 38.8192 | 1.66589 | ||||||||
\(544\) | 10.7303 | 0.460056 | ||||||||
\(545\) | 39.5361 | 1.69354 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 2.40239 | 0.102719 | 0.0513594 | − | 0.998680i | \(-0.483645\pi\) | ||||
0.0513594 | + | 0.998680i | \(0.483645\pi\) | |||||||
\(548\) | −15.1024 | −0.645140 | ||||||||
\(549\) | 20.7035 | 0.883602 | ||||||||
\(550\) | −0.523604 | −0.0223266 | ||||||||
\(551\) | −10.9901 | −0.468194 | ||||||||
\(552\) | −30.6945 | −1.30644 | ||||||||
\(553\) | −5.63935 | −0.239810 | ||||||||
\(554\) | 4.83262 | 0.205318 | ||||||||
\(555\) | 43.8485 | 1.86126 | ||||||||
\(556\) | 15.2787 | 0.647962 | ||||||||
\(557\) | −2.44609 | −0.103644 | −0.0518221 | − | 0.998656i | \(-0.516503\pi\) | ||||
−0.0518221 | + | 0.998656i | \(0.516503\pi\) | |||||||
\(558\) | −19.6314 | −0.831064 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | −7.14605 | −0.301976 | ||||||||
\(561\) | −4.85395 | −0.204934 | ||||||||
\(562\) | 3.78541 | 0.159678 | ||||||||
\(563\) | 38.4586 | 1.62084 | 0.810418 | − | 0.585852i | \(-0.199240\pi\) | ||||
0.810418 | + | 0.585852i | \(0.199240\pi\) | |||||||
\(564\) | 4.45506 | 0.187592 | ||||||||
\(565\) | −26.7417 | −1.12503 | ||||||||
\(566\) | 12.4248 | 0.522252 | ||||||||
\(567\) | 36.7169 | 1.54196 | ||||||||
\(568\) | −18.0000 | −0.755263 | ||||||||
\(569\) | 39.2519 | 1.64553 | 0.822763 | − | 0.568385i | \(-0.192431\pi\) | ||||
0.822763 | + | 0.568385i | \(0.192431\pi\) | |||||||
\(570\) | 15.0551 | 0.630591 | ||||||||
\(571\) | −39.3349 | −1.64611 | −0.823057 | − | 0.567959i | \(-0.807733\pi\) | ||||
−0.823057 | + | 0.567959i | \(0.807733\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −40.6439 | −1.69792 | ||||||||
\(574\) | −33.8326 | −1.41215 | ||||||||
\(575\) | −2.36858 | −0.0987766 | ||||||||
\(576\) | 14.8102 | 0.617094 | ||||||||
\(577\) | 24.0890 | 1.00284 | 0.501418 | − | 0.865205i | \(-0.332812\pi\) | ||||
0.501418 | + | 0.865205i | \(0.332812\pi\) | |||||||
\(578\) | 12.3945 | 0.515541 | ||||||||
\(579\) | −6.71687 | −0.279143 | ||||||||
\(580\) | 7.39095 | 0.306892 | ||||||||
\(581\) | 19.1496 | 0.794458 | ||||||||
\(582\) | −26.3259 | −1.09124 | ||||||||
\(583\) | −7.75510 | −0.321184 | ||||||||
\(584\) | −32.5216 | −1.34576 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 16.9012 | 0.698180 | ||||||||
\(587\) | −24.4665 | −1.00984 | −0.504920 | − | 0.863166i | \(-0.668478\pi\) | ||||
−0.504920 | + | 0.863166i | \(0.668478\pi\) | |||||||
\(588\) | 9.96970 | 0.411143 | ||||||||
\(589\) | −29.1913 | −1.20281 | ||||||||
\(590\) | 12.7586 | 0.525264 | ||||||||
\(591\) | 27.6652 | 1.13800 | ||||||||
\(592\) | −9.16296 | −0.376595 | ||||||||
\(593\) | −33.6215 | −1.38067 | −0.690335 | − | 0.723490i | \(-0.742537\pi\) | ||||
−0.690335 | + | 0.723490i | \(0.742537\pi\) | |||||||
\(594\) | 2.00000 | 0.0820610 | ||||||||
\(595\) | −15.3358 | −0.628707 | ||||||||
\(596\) | 4.37755 | 0.179312 | ||||||||
\(597\) | 0.455064 | 0.0186245 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 3.01340 | 0.123124 | 0.0615621 | − | 0.998103i | \(-0.480392\pi\) | ||||
0.0615621 | + | 0.998103i | \(0.480392\pi\) | |||||||
\(600\) | 3.55287 | 0.145045 | ||||||||
\(601\) | −18.5743 | −0.757662 | −0.378831 | − | 0.925466i | \(-0.623674\pi\) | ||||
−0.378831 | + | 0.925466i | \(0.623674\pi\) | |||||||
\(602\) | 8.52360 | 0.347396 | ||||||||
\(603\) | −8.52711 | −0.347251 | ||||||||
\(604\) | 2.29211 | 0.0932645 | ||||||||
\(605\) | −2.11575 | −0.0860174 | ||||||||
\(606\) | 2.03824 | 0.0827977 | ||||||||
\(607\) | −19.2137 | −0.779859 | −0.389930 | − | 0.920845i | \(-0.627501\pi\) | ||||
−0.389930 | + | 0.920845i | \(0.627501\pi\) | |||||||
\(608\) | 15.7303 | 0.637946 | ||||||||
\(609\) | 26.6866 | 1.08139 | ||||||||
\(610\) | 20.7035 | 0.838259 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 4.54051 | 0.183539 | ||||||||
\(613\) | −18.9350 | −0.764776 | −0.382388 | − | 0.924002i | \(-0.624898\pi\) | ||||
−0.382388 | + | 0.924002i | \(0.624898\pi\) | |||||||
\(614\) | −8.42476 | −0.339996 | ||||||||
\(615\) | −47.9350 | −1.93292 | ||||||||
\(616\) | 10.1327 | 0.408256 | ||||||||
\(617\) | 1.72129 | 0.0692966 | 0.0346483 | − | 0.999400i | \(-0.488969\pi\) | ||||
0.0346483 | + | 0.999400i | \(0.488969\pi\) | |||||||
\(618\) | 29.5102 | 1.18707 | ||||||||
\(619\) | −16.3562 | −0.657412 | −0.328706 | − | 0.944432i | \(-0.606613\pi\) | ||||
−0.328706 | + | 0.944432i | \(0.606613\pi\) | |||||||
\(620\) | 19.6314 | 0.788417 | ||||||||
\(621\) | 9.04721 | 0.363052 | ||||||||
\(622\) | 28.5877 | 1.14626 | ||||||||
\(623\) | 31.5708 | 1.26486 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −22.1078 | −0.884313 | ||||||||
\(626\) | −22.3945 | −0.895063 | ||||||||
\(627\) | −7.11575 | −0.284176 | ||||||||
\(628\) | 24.0472 | 0.959588 | ||||||||
\(629\) | −19.6642 | −0.784063 | ||||||||
\(630\) | −15.1193 | −0.602366 | ||||||||
\(631\) | 21.0775 | 0.839083 | 0.419541 | − | 0.907736i | \(-0.362191\pi\) | ||||
0.419541 | + | 0.907736i | \(0.362191\pi\) | |||||||
\(632\) | 5.00897 | 0.199246 | ||||||||
\(633\) | −26.3945 | −1.04909 | ||||||||
\(634\) | −26.2708 | −1.04335 | ||||||||
\(635\) | −24.3527 | −0.966408 | ||||||||
\(636\) | 17.5405 | 0.695526 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 3.49330 | 0.138301 | ||||||||
\(639\) | −12.6945 | −0.502187 | ||||||||
\(640\) | −6.34725 | −0.250897 | ||||||||
\(641\) | −4.53700 | −0.179201 | −0.0896004 | − | 0.995978i | \(-0.528559\pi\) | ||||
−0.0896004 | + | 0.995978i | \(0.528559\pi\) | |||||||
\(642\) | −30.7810 | −1.21483 | ||||||||
\(643\) | 0.983094 | 0.0387695 | 0.0193847 | − | 0.999812i | \(-0.493829\pi\) | ||||
0.0193847 | + | 0.999812i | \(0.493829\pi\) | |||||||
\(644\) | 15.2787 | 0.602065 | ||||||||
\(645\) | 12.0765 | 0.475511 | ||||||||
\(646\) | −6.75160 | −0.265638 | ||||||||
\(647\) | −46.6856 | −1.83540 | −0.917701 | − | 0.397272i | \(-0.869957\pi\) | ||||
−0.917701 | + | 0.397272i | \(0.869957\pi\) | |||||||
\(648\) | −32.6126 | −1.28114 | ||||||||
\(649\) | −6.03030 | −0.236710 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 70.8833 | 2.77814 | ||||||||
\(652\) | −6.55391 | −0.256671 | ||||||||
\(653\) | −25.8709 | −1.01240 | −0.506202 | − | 0.862415i | \(-0.668951\pi\) | ||||
−0.506202 | + | 0.862415i | \(0.668951\pi\) | |||||||
\(654\) | −42.2653 | −1.65270 | ||||||||
\(655\) | −28.7933 | −1.12505 | ||||||||
\(656\) | 10.0169 | 0.391094 | ||||||||
\(657\) | −22.9359 | −0.894814 | ||||||||
\(658\) | 6.65275 | 0.259351 | ||||||||
\(659\) | 17.4988 | 0.681655 | 0.340828 | − | 0.940126i | \(-0.389293\pi\) | ||||
0.340828 | + | 0.940126i | \(0.389293\pi\) | |||||||
\(660\) | 4.78541 | 0.186272 | ||||||||
\(661\) | −21.6528 | −0.842194 | −0.421097 | − | 0.907016i | \(-0.638355\pi\) | ||||
−0.421097 | + | 0.907016i | \(0.638355\pi\) | |||||||
\(662\) | −8.29211 | −0.322282 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −17.0090 | −0.660076 | ||||||||
\(665\) | −22.4819 | −0.871809 | ||||||||
\(666\) | −19.3865 | −0.751213 | ||||||||
\(667\) | 15.8023 | 0.611868 | ||||||||
\(668\) | −18.3259 | −0.709051 | ||||||||
\(669\) | −16.9787 | −0.656433 | ||||||||
\(670\) | −8.52711 | −0.329431 | ||||||||
\(671\) | −9.78541 | −0.377761 | ||||||||
\(672\) | −38.1968 | −1.47347 | ||||||||
\(673\) | −23.8798 | −0.920500 | −0.460250 | − | 0.887789i | \(-0.652240\pi\) | ||||
−0.460250 | + | 0.887789i | \(0.652240\pi\) | |||||||
\(674\) | 0.0516349 | 0.00198890 | ||||||||
\(675\) | −1.04721 | −0.0403071 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −12.6945 | −0.487889 | −0.243945 | − | 0.969789i | \(-0.578441\pi\) | ||||
−0.243945 | + | 0.969789i | \(0.578441\pi\) | |||||||
\(678\) | 28.5877 | 1.09790 | ||||||||
\(679\) | 39.3125 | 1.50868 | ||||||||
\(680\) | 13.6215 | 0.522362 | ||||||||
\(681\) | −7.86292 | −0.301308 | ||||||||
\(682\) | 9.27871 | 0.355300 | ||||||||
\(683\) | 37.8699 | 1.44905 | 0.724526 | − | 0.689247i | \(-0.242059\pi\) | ||||
0.724526 | + | 0.689247i | \(0.242059\pi\) | |||||||
\(684\) | 6.65626 | 0.254508 | ||||||||
\(685\) | −31.9528 | −1.22085 | ||||||||
\(686\) | −8.75510 | −0.334271 | ||||||||
\(687\) | 30.3259 | 1.15701 | ||||||||
\(688\) | −2.52360 | −0.0962115 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | −21.6473 | −0.824098 | ||||||||
\(691\) | −25.7417 | −0.979261 | −0.489630 | − | 0.871930i | \(-0.662868\pi\) | ||||
−0.489630 | + | 0.871930i | \(0.662868\pi\) | |||||||
\(692\) | −14.6866 | −0.558299 | ||||||||
\(693\) | 7.14605 | 0.271456 | ||||||||
\(694\) | 8.62245 | 0.327304 | ||||||||
\(695\) | 32.3259 | 1.22619 | ||||||||
\(696\) | −23.7035 | −0.898478 | ||||||||
\(697\) | 21.4968 | 0.814250 | ||||||||
\(698\) | 30.0000 | 1.13552 | ||||||||
\(699\) | −0.660685 | −0.0249894 | ||||||||
\(700\) | −1.76850 | −0.0668431 | ||||||||
\(701\) | −33.5023 | −1.26536 | −0.632682 | − | 0.774412i | \(-0.718046\pi\) | ||||
−0.632682 | + | 0.774412i | \(0.718046\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −28.8272 | −1.08724 | ||||||||
\(704\) | −7.00000 | −0.263822 | ||||||||
\(705\) | 9.42580 | 0.354996 | ||||||||
\(706\) | −0.476396 | −0.0179294 | ||||||||
\(707\) | −3.04370 | −0.114470 | ||||||||
\(708\) | 13.6394 | 0.512598 | ||||||||
\(709\) | 30.9235 | 1.16136 | 0.580679 | − | 0.814133i | \(-0.302787\pi\) | ||||
0.580679 | + | 0.814133i | \(0.302787\pi\) | |||||||
\(710\) | −12.6945 | −0.476416 | ||||||||
\(711\) | 3.53258 | 0.132482 | ||||||||
\(712\) | −28.0417 | −1.05091 | ||||||||
\(713\) | 41.9732 | 1.57191 | ||||||||
\(714\) | 16.3945 | 0.613547 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 6.49330 | 0.242666 | ||||||||
\(717\) | −49.3125 | −1.84161 | ||||||||
\(718\) | −10.2315 | −0.381836 | ||||||||
\(719\) | 9.21810 | 0.343777 | 0.171889 | − | 0.985116i | \(-0.445013\pi\) | ||||
0.171889 | + | 0.985116i | \(0.445013\pi\) | |||||||
\(720\) | 4.47640 | 0.166825 | ||||||||
\(721\) | −44.0676 | −1.64116 | ||||||||
\(722\) | 9.10235 | 0.338754 | ||||||||
\(723\) | −5.76408 | −0.214368 | ||||||||
\(724\) | 17.1630 | 0.637856 | ||||||||
\(725\) | −1.82911 | −0.0679314 | ||||||||
\(726\) | 2.26180 | 0.0839434 | ||||||||
\(727\) | 33.5102 | 1.24282 | 0.621412 | − | 0.783484i | \(-0.286559\pi\) | ||||
0.621412 | + | 0.783484i | \(0.286559\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −9.42919 | −0.349229 | ||||||||
\(730\) | −22.9359 | −0.848895 | ||||||||
\(731\) | −5.41579 | −0.200310 | ||||||||
\(732\) | 22.1327 | 0.818046 | ||||||||
\(733\) | 1.29561 | 0.0478546 | 0.0239273 | − | 0.999714i | \(-0.492383\pi\) | ||||
0.0239273 | + | 0.999714i | \(0.492383\pi\) | |||||||
\(734\) | −21.3393 | −0.787648 | ||||||||
\(735\) | 21.0934 | 0.778041 | ||||||||
\(736\) | −22.6180 | −0.833711 | ||||||||
\(737\) | 4.03030 | 0.148458 | ||||||||
\(738\) | 21.1933 | 0.780135 | ||||||||
\(739\) | −28.8495 | −1.06125 | −0.530623 | − | 0.847608i | \(-0.678042\pi\) | ||||
−0.530623 | + | 0.847608i | \(0.678042\pi\) | |||||||
\(740\) | 19.3865 | 0.712663 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 26.1933 | 0.961585 | ||||||||
\(743\) | 31.7373 | 1.16433 | 0.582164 | − | 0.813071i | \(-0.302206\pi\) | ||||
0.582164 | + | 0.813071i | \(0.302206\pi\) | |||||||
\(744\) | −62.9598 | −2.30822 | ||||||||
\(745\) | 9.26180 | 0.339326 | ||||||||
\(746\) | −21.2271 | −0.777178 | ||||||||
\(747\) | −11.9956 | −0.438895 | ||||||||
\(748\) | −2.14605 | −0.0784675 | ||||||||
\(749\) | 45.9653 | 1.67953 | ||||||||
\(750\) | 26.4327 | 0.965186 | ||||||||
\(751\) | −36.1282 | −1.31834 | −0.659169 | − | 0.751995i | \(-0.729092\pi\) | ||||
−0.659169 | + | 0.751995i | \(0.729092\pi\) | |||||||
\(752\) | −1.96970 | −0.0718274 | ||||||||
\(753\) | 60.6598 | 2.21056 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 4.84952 | 0.176492 | ||||||||
\(756\) | 6.75510 | 0.245681 | ||||||||
\(757\) | −22.0527 | −0.801518 | −0.400759 | − | 0.916183i | \(-0.631254\pi\) | ||||
−0.400759 | + | 0.916183i | \(0.631254\pi\) | |||||||
\(758\) | −1.04721 | −0.0380363 | ||||||||
\(759\) | 10.2315 | 0.371380 | ||||||||
\(760\) | 19.9688 | 0.724344 | ||||||||
\(761\) | −40.1620 | −1.45587 | −0.727936 | − | 0.685645i | \(-0.759520\pi\) | ||||
−0.727936 | + | 0.685645i | \(0.759520\pi\) | |||||||
\(762\) | 26.0338 | 0.943105 | ||||||||
\(763\) | 63.1148 | 2.28491 | ||||||||
\(764\) | −17.9697 | −0.650121 | ||||||||
\(765\) | 9.60658 | 0.347327 | ||||||||
\(766\) | −28.9866 | −1.04733 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 38.4506 | 1.38747 | ||||||||
\(769\) | 24.9598 | 0.900074 | 0.450037 | − | 0.893010i | \(-0.351411\pi\) | ||||
0.450037 | + | 0.893010i | \(0.351411\pi\) | |||||||
\(770\) | 7.14605 | 0.257526 | ||||||||
\(771\) | −6.94043 | −0.249954 | ||||||||
\(772\) | −2.96970 | −0.106882 | ||||||||
\(773\) | −5.46846 | −0.196687 | −0.0983435 | − | 0.995153i | \(-0.531354\pi\) | ||||
−0.0983435 | + | 0.995153i | \(0.531354\pi\) | |||||||
\(774\) | −5.33931 | −0.191918 | ||||||||
\(775\) | −4.85837 | −0.174518 | ||||||||
\(776\) | −34.9181 | −1.25349 | ||||||||
\(777\) | 69.9991 | 2.51120 | ||||||||
\(778\) | −15.5653 | −0.558045 | ||||||||
\(779\) | 31.5137 | 1.12910 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 6.00000 | 0.214697 | ||||||||
\(782\) | 9.70789 | 0.347154 | ||||||||
\(783\) | 6.98660 | 0.249681 | ||||||||
\(784\) | −4.40786 | −0.157423 | ||||||||
\(785\) | 50.8779 | 1.81591 | ||||||||
\(786\) | 30.7810 | 1.09792 | ||||||||
\(787\) | −37.5484 | −1.33846 | −0.669229 | − | 0.743056i | \(-0.733375\pi\) | ||||
−0.669229 | + | 0.743056i | \(0.733375\pi\) | |||||||
\(788\) | 12.2315 | 0.435729 | ||||||||
\(789\) | −5.18429 | −0.184566 | ||||||||
\(790\) | 3.53258 | 0.125683 | ||||||||
\(791\) | −42.6901 | −1.51788 | ||||||||
\(792\) | −6.34725 | −0.225540 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 18.9787 | 0.673528 | ||||||||
\(795\) | 37.1113 | 1.31620 | ||||||||
\(796\) | 0.201195 | 0.00713118 | ||||||||
\(797\) | 7.76057 | 0.274893 | 0.137447 | − | 0.990509i | \(-0.456110\pi\) | ||||
0.137447 | + | 0.990509i | \(0.456110\pi\) | |||||||
\(798\) | 24.0338 | 0.850788 | ||||||||
\(799\) | −4.22707 | −0.149543 | ||||||||
\(800\) | 2.61802 | 0.0925611 | ||||||||
\(801\) | −19.7764 | −0.698766 | ||||||||
\(802\) | −9.52360 | −0.336290 | ||||||||
\(803\) | 10.8405 | 0.382555 | ||||||||
\(804\) | −9.11575 | −0.321488 | ||||||||
\(805\) | 32.3259 | 1.13934 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −25.4337 | −0.895310 | ||||||||
\(808\) | 2.70347 | 0.0951077 | ||||||||
\(809\) | −6.80674 | −0.239312 | −0.119656 | − | 0.992815i | \(-0.538179\pi\) | ||||
−0.119656 | + | 0.992815i | \(0.538179\pi\) | |||||||
\(810\) | −23.0000 | −0.808138 | ||||||||
\(811\) | 37.0810 | 1.30209 | 0.651045 | − | 0.759039i | \(-0.274331\pi\) | ||||
0.651045 | + | 0.759039i | \(0.274331\pi\) | |||||||
\(812\) | 11.7988 | 0.414057 | ||||||||
\(813\) | −9.70789 | −0.340471 | ||||||||
\(814\) | 9.16296 | 0.321162 | ||||||||
\(815\) | −13.8664 | −0.485720 | ||||||||
\(816\) | −4.85395 | −0.169922 | ||||||||
\(817\) | −7.93939 | −0.277764 | ||||||||
\(818\) | 9.91455 | 0.346654 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −21.1933 | −0.740101 | ||||||||
\(821\) | 0.170892 | 0.00596417 | 0.00298208 | − | 0.999996i | \(-0.499051\pi\) | ||||
0.00298208 | + | 0.999996i | \(0.499051\pi\) | |||||||
\(822\) | 34.1585 | 1.19142 | ||||||||
\(823\) | 14.9260 | 0.520287 | 0.260144 | − | 0.965570i | \(-0.416230\pi\) | ||||
0.260144 | + | 0.965570i | \(0.416230\pi\) | |||||||
\(824\) | 39.1416 | 1.36356 | ||||||||
\(825\) | −1.18429 | −0.0412317 | ||||||||
\(826\) | 20.3677 | 0.708682 | ||||||||
\(827\) | −10.0114 | −0.348132 | −0.174066 | − | 0.984734i | \(-0.555691\pi\) | ||||
−0.174066 | + | 0.984734i | \(0.555691\pi\) | |||||||
\(828\) | −9.57081 | −0.332609 | ||||||||
\(829\) | −3.59214 | −0.124760 | −0.0623802 | − | 0.998052i | \(-0.519869\pi\) | ||||
−0.0623802 | + | 0.998052i | \(0.519869\pi\) | |||||||
\(830\) | −11.9956 | −0.416372 | ||||||||
\(831\) | 10.9304 | 0.379172 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −9.45949 | −0.327752 | ||||||||
\(834\) | −34.5574 | −1.19663 | ||||||||
\(835\) | −38.7730 | −1.34180 | ||||||||
\(836\) | −3.14605 | −0.108809 | ||||||||
\(837\) | 18.5574 | 0.641438 | ||||||||
\(838\) | −7.01340 | −0.242274 | ||||||||
\(839\) | 27.2216 | 0.939794 | 0.469897 | − | 0.882721i | \(-0.344291\pi\) | ||||
0.469897 | + | 0.882721i | \(0.344291\pi\) | |||||||
\(840\) | −48.4889 | −1.67303 | ||||||||
\(841\) | −16.7968 | −0.579202 | ||||||||
\(842\) | 33.9787 | 1.17098 | ||||||||
\(843\) | 8.56184 | 0.294885 | ||||||||
\(844\) | −11.6697 | −0.401686 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −4.16738 | −0.143278 | ||||||||
\(847\) | −3.37755 | −0.116054 | ||||||||
\(848\) | −7.75510 | −0.266311 | ||||||||
\(849\) | 28.1024 | 0.964470 | ||||||||
\(850\) | −1.12368 | −0.0385420 | ||||||||
\(851\) | 41.4496 | 1.42087 | ||||||||
\(852\) | −13.5708 | −0.464928 | ||||||||
\(853\) | −26.7114 | −0.914581 | −0.457290 | − | 0.889317i | \(-0.651180\pi\) | ||||
−0.457290 | + | 0.889317i | \(0.651180\pi\) | |||||||
\(854\) | 33.0507 | 1.13097 | ||||||||
\(855\) | 14.0830 | 0.481628 | ||||||||
\(856\) | −40.8272 | −1.39544 | ||||||||
\(857\) | −26.6955 | −0.911902 | −0.455951 | − | 0.890005i | \(-0.650701\pi\) | ||||
−0.455951 | + | 0.890005i | \(0.650701\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −21.3855 | −0.729663 | −0.364832 | − | 0.931073i | \(-0.618873\pi\) | ||||
−0.364832 | + | 0.931073i | \(0.618873\pi\) | |||||||
\(860\) | 5.33931 | 0.182069 | ||||||||
\(861\) | −76.5227 | −2.60789 | ||||||||
\(862\) | 7.86735 | 0.267963 | ||||||||
\(863\) | −0.694496 | −0.0236409 | −0.0118205 | − | 0.999930i | \(-0.503763\pi\) | ||||
−0.0118205 | + | 0.999930i | \(0.503763\pi\) | |||||||
\(864\) | −10.0000 | −0.340207 | ||||||||
\(865\) | −31.0731 | −1.05652 | ||||||||
\(866\) | 13.6528 | 0.463939 | ||||||||
\(867\) | 28.0338 | 0.952078 | ||||||||
\(868\) | 31.3393 | 1.06373 | ||||||||
\(869\) | −1.66966 | −0.0566392 | ||||||||
\(870\) | −16.7169 | −0.566755 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | −56.0597 | −1.89842 | ||||||||
\(873\) | −24.6260 | −0.833462 | ||||||||
\(874\) | 14.2315 | 0.481388 | ||||||||
\(875\) | −39.4720 | −1.33440 | ||||||||
\(876\) | −24.5192 | −0.828426 | ||||||||
\(877\) | 17.2609 | 0.582859 | 0.291429 | − | 0.956592i | \(-0.405869\pi\) | ||||
0.291429 | + | 0.956592i | \(0.405869\pi\) | |||||||
\(878\) | 8.33034 | 0.281135 | ||||||||
\(879\) | 38.2271 | 1.28937 | ||||||||
\(880\) | −2.11575 | −0.0713219 | ||||||||
\(881\) | 27.7889 | 0.936232 | 0.468116 | − | 0.883667i | \(-0.344933\pi\) | ||||
0.468116 | + | 0.883667i | \(0.344933\pi\) | |||||||
\(882\) | −9.32592 | −0.314020 | ||||||||
\(883\) | 13.1505 | 0.442549 | 0.221274 | − | 0.975212i | \(-0.428978\pi\) | ||||
0.221274 | + | 0.975212i | \(0.428978\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 28.8575 | 0.970033 | ||||||||
\(886\) | 25.2484 | 0.848237 | ||||||||
\(887\) | −53.0204 | −1.78025 | −0.890126 | − | 0.455715i | \(-0.849384\pi\) | ||||
−0.890126 | + | 0.455715i | \(0.849384\pi\) | |||||||
\(888\) | −62.1744 | −2.08644 | ||||||||
\(889\) | −38.8763 | −1.30387 | ||||||||
\(890\) | −19.7764 | −0.662908 | ||||||||
\(891\) | 10.8709 | 0.364187 | ||||||||
\(892\) | −7.50670 | −0.251343 | ||||||||
\(893\) | −6.19677 | −0.207367 | ||||||||
\(894\) | −9.90116 | −0.331144 | ||||||||
\(895\) | 13.7382 | 0.459217 | ||||||||
\(896\) | −10.1327 | −0.338508 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −37.2708 | −1.24374 | ||||||||
\(899\) | 32.4133 | 1.08104 | ||||||||
\(900\) | 1.10782 | 0.0369272 | ||||||||
\(901\) | −16.6429 | −0.554454 | ||||||||
\(902\) | −10.0169 | −0.333526 | ||||||||
\(903\) | 19.2787 | 0.641555 | ||||||||
\(904\) | 37.9181 | 1.26114 | ||||||||
\(905\) | 36.3125 | 1.20707 | ||||||||
\(906\) | −5.18429 | −0.172236 | ||||||||
\(907\) | −54.8192 | −1.82024 | −0.910121 | − | 0.414342i | \(-0.864012\pi\) | ||||
−0.910121 | + | 0.414342i | \(0.864012\pi\) | |||||||
\(908\) | −3.47640 | −0.115368 | ||||||||
\(909\) | 1.90662 | 0.0632386 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −25.4799 | −0.844187 | −0.422093 | − | 0.906552i | \(-0.638705\pi\) | ||||
−0.422093 | + | 0.906552i | \(0.638705\pi\) | |||||||
\(912\) | −7.11575 | −0.235626 | ||||||||
\(913\) | 5.66966 | 0.187638 | ||||||||
\(914\) | −3.09091 | −0.102238 | ||||||||
\(915\) | 46.8272 | 1.54806 | ||||||||
\(916\) | 13.4079 | 0.443008 | ||||||||
\(917\) | −45.9653 | −1.51791 | ||||||||
\(918\) | 4.29211 | 0.141661 | ||||||||
\(919\) | −14.2156 | −0.468930 | −0.234465 | − | 0.972125i | \(-0.575334\pi\) | ||||
−0.234465 | + | 0.972125i | \(0.575334\pi\) | |||||||
\(920\) | −28.7124 | −0.946621 | ||||||||
\(921\) | −19.0551 | −0.627888 | ||||||||
\(922\) | −22.4799 | −0.740336 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 7.63935 | 0.251316 | ||||||||
\(925\) | −4.79777 | −0.157750 | ||||||||
\(926\) | −29.0507 | −0.954666 | ||||||||
\(927\) | 27.6046 | 0.906655 | ||||||||
\(928\) | −17.4665 | −0.573366 | ||||||||
\(929\) | 4.60462 | 0.151073 | 0.0755364 | − | 0.997143i | \(-0.475933\pi\) | ||||
0.0755364 | + | 0.997143i | \(0.475933\pi\) | |||||||
\(930\) | −44.4024 | −1.45601 | ||||||||
\(931\) | −13.8673 | −0.454484 | ||||||||
\(932\) | −0.292106 | −0.00956824 | ||||||||
\(933\) | 64.6598 | 2.11687 | ||||||||
\(934\) | 7.47990 | 0.244750 | ||||||||
\(935\) | −4.54051 | −0.148491 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −54.9002 | −1.79351 | −0.896756 | − | 0.442525i | \(-0.854083\pi\) | ||||
−0.896756 | + | 0.442525i | \(0.854083\pi\) | |||||||
\(938\) | −13.6126 | −0.444466 | ||||||||
\(939\) | −50.6518 | −1.65296 | ||||||||
\(940\) | 4.16738 | 0.135925 | ||||||||
\(941\) | 0.292106 | 0.00952237 | 0.00476119 | − | 0.999989i | \(-0.498484\pi\) | ||||
0.00476119 | + | 0.999989i | \(0.498484\pi\) | |||||||
\(942\) | −54.3900 | −1.77212 | ||||||||
\(943\) | −45.3125 | −1.47558 | ||||||||
\(944\) | −6.03030 | −0.196270 | ||||||||
\(945\) | 14.2921 | 0.464922 | ||||||||
\(946\) | 2.52360 | 0.0820495 | ||||||||
\(947\) | 4.46300 | 0.145028 | 0.0725140 | − | 0.997367i | \(-0.476898\pi\) | ||||
0.0725140 | + | 0.997367i | \(0.476898\pi\) | |||||||
\(948\) | 3.77643 | 0.122653 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | −1.64729 | −0.0534451 | ||||||||
\(951\) | −59.4193 | −1.92680 | ||||||||
\(952\) | 21.7452 | 0.704766 | ||||||||
\(953\) | −40.4809 | −1.31131 | −0.655653 | − | 0.755062i | \(-0.727607\pi\) | ||||
−0.655653 | + | 0.755062i | \(0.727607\pi\) | |||||||
\(954\) | −16.4079 | −0.531224 | ||||||||
\(955\) | −38.0194 | −1.23028 | ||||||||
\(956\) | −21.8023 | −0.705137 | ||||||||
\(957\) | 7.90116 | 0.255408 | ||||||||
\(958\) | 8.62245 | 0.278579 | ||||||||
\(959\) | −51.0090 | −1.64717 | ||||||||
\(960\) | 33.4978 | 1.08114 | ||||||||
\(961\) | 55.0944 | 1.77724 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −28.7933 | −0.927852 | ||||||||
\(964\) | −2.54844 | −0.0820798 | ||||||||
\(965\) | −6.28313 | −0.202261 | ||||||||
\(966\) | −34.5574 | −1.11187 | ||||||||
\(967\) | 1.00897 | 0.0324464 | 0.0162232 | − | 0.999868i | \(-0.494836\pi\) | ||||
0.0162232 | + | 0.999868i | \(0.494836\pi\) | |||||||
\(968\) | 3.00000 | 0.0964237 | ||||||||
\(969\) | −15.2708 | −0.490568 | ||||||||
\(970\) | −24.6260 | −0.790692 | ||||||||
\(971\) | 25.8664 | 0.830093 | 0.415047 | − | 0.909800i | \(-0.363765\pi\) | ||||
0.415047 | + | 0.909800i | \(0.363765\pi\) | |||||||
\(972\) | −18.5877 | −0.596201 | ||||||||
\(973\) | 51.6046 | 1.65437 | ||||||||
\(974\) | 8.09091 | 0.259249 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −9.78541 | −0.313223 | ||||||||
\(977\) | 43.3677 | 1.38745 | 0.693727 | − | 0.720238i | \(-0.255967\pi\) | ||||
0.693727 | + | 0.720238i | \(0.255967\pi\) | |||||||
\(978\) | 14.8236 | 0.474008 | ||||||||
\(979\) | 9.34725 | 0.298739 | ||||||||
\(980\) | 9.32592 | 0.297905 | ||||||||
\(981\) | −39.5361 | −1.26229 | ||||||||
\(982\) | −4.62245 | −0.147508 | ||||||||
\(983\) | 17.0472 | 0.543722 | 0.271861 | − | 0.962337i | \(-0.412361\pi\) | ||||
0.271861 | + | 0.962337i | \(0.412361\pi\) | |||||||
\(984\) | 67.9688 | 2.16677 | ||||||||
\(985\) | 25.8788 | 0.824567 | ||||||||
\(986\) | 7.49681 | 0.238747 | ||||||||
\(987\) | 15.0472 | 0.478958 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 11.4158 | 0.363001 | ||||||||
\(990\) | −4.47640 | −0.142269 | ||||||||
\(991\) | −40.0979 | −1.27375 | −0.636876 | − | 0.770966i | \(-0.719774\pi\) | ||||
−0.636876 | + | 0.770966i | \(0.719774\pi\) | |||||||
\(992\) | −46.3935 | −1.47300 | ||||||||
\(993\) | −18.7551 | −0.595175 | ||||||||
\(994\) | −20.2653 | −0.642777 | ||||||||
\(995\) | 0.425679 | 0.0134949 | ||||||||
\(996\) | −12.8236 | −0.406333 | ||||||||
\(997\) | −54.0428 | −1.71155 | −0.855776 | − | 0.517346i | \(-0.826920\pi\) | ||||
−0.855776 | + | 0.517346i | \(0.826920\pi\) | |||||||
\(998\) | 39.5137 | 1.25078 | ||||||||
\(999\) | 18.3259 | 0.579806 |
(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 | 1859.2.a.e.1.1 | 3 | ||
13.4 | even | 6 | 143.2.e.a.133.3 | yes | 6 | ||
13.10 | even | 6 | 143.2.e.a.100.3 | ✓ | 6 | ||
13.12 | even | 2 | 1859.2.a.h.1.1 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
143.2.e.a.100.3 | ✓ | 6 | 13.10 | even | 6 | ||
143.2.e.a.133.3 | yes | 6 | 13.4 | even | 6 | ||
1859.2.a.e.1.1 | 3 | 1.1 | even | 1 | trivial | ||
1859.2.a.h.1.1 | 3 | 13.12 | even | 2 |