Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4560,2,Mod(1,4560)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4560, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("4560.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4560 = 2^{4} \cdot 3 \cdot 5 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4560.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(36.4117833217\) |
Analytic rank: | \(0\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.1772.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 12x + 8 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 2280) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(3.67370\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4560.1 |
$q$-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 | ||||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.911179 | −0.344393 | −0.172197 | − | 0.985063i | \(-0.555086\pi\) | ||||
−0.172197 | + | 0.985063i | \(0.555086\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2.91118 | −0.877753 | −0.438877 | − | 0.898547i | \(-0.644624\pi\) | ||||
−0.438877 | + | 0.898547i | \(0.644624\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −6.25857 | −1.73582 | −0.867908 | − | 0.496725i | \(-0.834536\pi\) | ||||
−0.867908 | + | 0.496725i | \(0.834536\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.00000 | −0.258199 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 4.00000 | 0.970143 | 0.485071 | − | 0.874475i | \(-0.338794\pi\) | ||||
0.485071 | + | 0.874475i | \(0.338794\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.00000 | −0.229416 | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.911179 | 0.198836 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −5.34740 | −1.11501 | −0.557505 | − | 0.830174i | \(-0.688241\pi\) | ||||
−0.557505 | + | 0.830174i | \(0.688241\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −0.911179 | −0.169202 | −0.0846008 | − | 0.996415i | \(-0.526962\pi\) | ||||
−0.0846008 | + | 0.996415i | \(0.526962\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.00000 | 0.359211 | 0.179605 | − | 0.983739i | \(-0.442518\pi\) | ||||
0.179605 | + | 0.983739i | \(0.442518\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 2.91118 | 0.506771 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −0.911179 | −0.154017 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 4.43622 | 0.729310 | 0.364655 | − | 0.931143i | \(-0.381187\pi\) | ||||
0.364655 | + | 0.931143i | \(0.381187\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 6.25857 | 1.00217 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 6.43622 | 1.00517 | 0.502584 | − | 0.864528i | \(-0.332383\pi\) | ||||
0.502584 | + | 0.864528i | \(0.332383\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −8.25857 | −1.25942 | −0.629710 | − | 0.776830i | \(-0.716826\pi\) | ||||
−0.629710 | + | 0.776830i | \(0.716826\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 1.00000 | 0.149071 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 5.34740 | 0.779998 | 0.389999 | − | 0.920815i | \(-0.372475\pi\) | ||||
0.389999 | + | 0.920815i | \(0.372475\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.16975 | −0.881393 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −4.00000 | −0.560112 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 3.34740 | 0.459800 | 0.229900 | − | 0.973214i | \(-0.426160\pi\) | ||||
0.229900 | + | 0.973214i | \(0.426160\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −2.91118 | −0.392543 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 1.00000 | 0.132453 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −5.52504 | −0.719299 | −0.359649 | − | 0.933088i | \(-0.617104\pi\) | ||||
−0.359649 | + | 0.933088i | \(0.617104\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 13.1698 | 1.68621 | 0.843107 | − | 0.537746i | \(-0.180724\pi\) | ||||
0.843107 | + | 0.537746i | \(0.180724\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −0.911179 | −0.114798 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −6.25857 | −0.776281 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −4.00000 | −0.488678 | −0.244339 | − | 0.969690i | \(-0.578571\pi\) | ||||
−0.244339 | + | 0.969690i | \(0.578571\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 5.34740 | 0.643751 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 16.5171 | 1.96022 | 0.980112 | − | 0.198443i | \(-0.0635884\pi\) | ||||
0.980112 | + | 0.198443i | \(0.0635884\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 6.00000 | 0.702247 | 0.351123 | − | 0.936329i | \(-0.385800\pi\) | ||||
0.351123 | + | 0.936329i | \(0.385800\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −1.00000 | −0.115470 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 2.65260 | 0.302292 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 10.9921 | 1.23671 | 0.618355 | − | 0.785899i | \(-0.287800\pi\) | ||||
0.618355 | + | 0.785899i | \(0.287800\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 3.82236 | 0.419558 | 0.209779 | − | 0.977749i | \(-0.432726\pi\) | ||||
0.209779 | + | 0.977749i | \(0.432726\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 4.00000 | 0.433861 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0.911179 | 0.0976886 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −2.43622 | −0.258238 | −0.129119 | − | 0.991629i | \(-0.541215\pi\) | ||||
−0.129119 | + | 0.991629i | \(0.541215\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 5.70268 | 0.597803 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −2.00000 | −0.207390 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −1.00000 | −0.102598 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 16.4362 | 1.66884 | 0.834422 | − | 0.551125i | \(-0.185801\pi\) | ||||
0.834422 | + | 0.551125i | \(0.185801\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −2.91118 | −0.292584 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −0.177642 | −0.0176761 | −0.00883804 | − | 0.999961i | \(-0.502813\pi\) | ||||
−0.00883804 | + | 0.999961i | \(0.502813\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 3.64472 | 0.359124 | 0.179562 | − | 0.983747i | \(-0.442532\pi\) | ||||
0.179562 | + | 0.983747i | \(0.442532\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0.911179 | 0.0889219 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 3.64472 | 0.352348 | 0.176174 | − | 0.984359i | \(-0.443628\pi\) | ||||
0.176174 | + | 0.984359i | \(0.443628\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −3.52504 | −0.337637 | −0.168819 | − | 0.985647i | \(-0.553995\pi\) | ||||
−0.168819 | + | 0.985647i | \(0.553995\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −4.43622 | −0.421067 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −13.5250 | −1.27233 | −0.636164 | − | 0.771554i | \(-0.719480\pi\) | ||||
−0.636164 | + | 0.771554i | \(0.719480\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −5.34740 | −0.498647 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −6.25857 | −0.578605 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −3.64472 | −0.334110 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −2.52504 | −0.229549 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −6.43622 | −0.580334 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −22.3395 | −1.98231 | −0.991155 | − | 0.132707i | \(-0.957633\pi\) | ||||
−0.991155 | + | 0.132707i | \(0.957633\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 8.25857 | 0.727127 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 8.73354 | 0.763053 | 0.381526 | − | 0.924358i | \(-0.375399\pi\) | ||||
0.381526 | + | 0.924358i | \(0.375399\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0.911179 | 0.0790092 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −1.00000 | −0.0860663 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 13.3474 | 1.14034 | 0.570172 | − | 0.821525i | \(-0.306876\pi\) | ||||
0.570172 | + | 0.821525i | \(0.306876\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −1.82236 | −0.154570 | −0.0772852 | − | 0.997009i | \(-0.524625\pi\) | ||||
−0.0772852 | + | 0.997009i | \(0.524625\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −5.34740 | −0.450332 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 18.2198 | 1.52362 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −0.911179 | −0.0756693 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 6.16975 | 0.508873 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 4.69479 | 0.384612 | 0.192306 | − | 0.981335i | \(-0.438403\pi\) | ||||
0.192306 | + | 0.981335i | \(0.438403\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −4.69479 | −0.382057 | −0.191028 | − | 0.981585i | \(-0.561182\pi\) | ||||
−0.191028 | + | 0.981585i | \(0.561182\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 4.00000 | 0.323381 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 2.00000 | 0.160644 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −3.16975 | −0.252974 | −0.126487 | − | 0.991968i | \(-0.540370\pi\) | ||||
−0.126487 | + | 0.991968i | \(0.540370\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −3.34740 | −0.265466 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 4.87243 | 0.384002 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 6.43622 | 0.504123 | 0.252062 | − | 0.967711i | \(-0.418891\pi\) | ||||
0.252062 | + | 0.967711i | \(0.418891\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 2.91118 | 0.226635 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −3.16975 | −0.245283 | −0.122641 | − | 0.992451i | \(-0.539137\pi\) | ||||
−0.122641 | + | 0.992451i | \(0.539137\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 26.1698 | 2.01306 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −1.00000 | −0.0764719 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −9.52504 | −0.724175 | −0.362088 | − | 0.932144i | \(-0.617936\pi\) | ||||
−0.362088 | + | 0.932144i | \(0.617936\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −0.911179 | −0.0688786 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 5.52504 | 0.415287 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −5.16975 | −0.386405 | −0.193203 | − | 0.981159i | \(-0.561888\pi\) | ||||
−0.193203 | + | 0.981159i | \(0.561888\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 18.8145 | 1.39847 | 0.699234 | − | 0.714893i | \(-0.253524\pi\) | ||||
0.699234 | + | 0.714893i | \(0.253524\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −13.1698 | −0.973536 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 4.43622 | 0.326157 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −11.6447 | −0.851546 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0.911179 | 0.0662785 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −7.78361 | −0.563202 | −0.281601 | − | 0.959532i | \(-0.590866\pi\) | ||||
−0.281601 | + | 0.959532i | \(0.590866\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −15.7256 | −1.13196 | −0.565978 | − | 0.824420i | \(-0.691501\pi\) | ||||
−0.565978 | + | 0.824420i | \(0.691501\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 6.25857 | 0.448186 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −7.70268 | −0.548793 | −0.274397 | − | 0.961617i | \(-0.588478\pi\) | ||||
−0.274397 | + | 0.961617i | \(0.588478\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 20.5171 | 1.45442 | 0.727211 | − | 0.686414i | \(-0.240816\pi\) | ||||
0.727211 | + | 0.686414i | \(0.240816\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 4.00000 | 0.282138 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0.830247 | 0.0582719 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 6.43622 | 0.449525 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −5.34740 | −0.371670 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 2.91118 | 0.201370 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 22.3395 | 1.53792 | 0.768958 | − | 0.639300i | \(-0.220776\pi\) | ||||
0.768958 | + | 0.639300i | \(0.220776\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −16.5171 | −1.13174 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −8.25857 | −0.563230 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1.82236 | −0.123710 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −6.00000 | −0.405442 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −25.0343 | −1.68399 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 18.3395 | 1.22810 | 0.614052 | − | 0.789266i | \(-0.289538\pi\) | ||||
0.614052 | + | 0.789266i | \(0.289538\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1.00000 | 0.0666667 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 17.8645 | 1.18571 | 0.592856 | − | 0.805309i | \(-0.298000\pi\) | ||||
0.592856 | + | 0.805309i | \(0.298000\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 25.1698 | 1.66326 | 0.831632 | − | 0.555327i | \(-0.187407\pi\) | ||||
0.831632 | + | 0.555327i | \(0.187407\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −2.65260 | −0.174529 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 15.6869 | 1.02768 | 0.513842 | − | 0.857885i | \(-0.328222\pi\) | ||||
0.513842 | + | 0.857885i | \(0.328222\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 5.34740 | 0.348826 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −10.9921 | −0.714014 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −3.42833 | −0.221760 | −0.110880 | − | 0.993834i | \(-0.535367\pi\) | ||||
−0.110880 | + | 0.993834i | \(0.535367\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −23.0343 | −1.48377 | −0.741885 | − | 0.670527i | \(-0.766068\pi\) | ||||
−0.741885 | + | 0.670527i | \(0.766068\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −6.16975 | −0.394171 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 6.25857 | 0.398224 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −3.82236 | −0.242232 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −19.0730 | −1.20388 | −0.601940 | − | 0.798541i | \(-0.705605\pi\) | ||||
−0.601940 | + | 0.798541i | \(0.705605\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 15.5672 | 0.978703 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −4.00000 | −0.250490 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −15.8645 | −0.989603 | −0.494802 | − | 0.869006i | \(-0.664759\pi\) | ||||
−0.494802 | + | 0.869006i | \(0.664759\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −4.04219 | −0.251169 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −0.911179 | −0.0564006 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 3.16975 | 0.195455 | 0.0977277 | − | 0.995213i | \(-0.468843\pi\) | ||||
0.0977277 | + | 0.995213i | \(0.468843\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 3.34740 | 0.205629 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 2.43622 | 0.149094 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −13.7836 | −0.840402 | −0.420201 | − | 0.907431i | \(-0.638040\pi\) | ||||
−0.420201 | + | 0.907431i | \(0.638040\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 17.8224 | 1.08263 | 0.541316 | − | 0.840820i | \(-0.317926\pi\) | ||||
0.541316 | + | 0.840820i | \(0.317926\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −5.70268 | −0.345142 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −2.91118 | −0.175551 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 21.3474 | 1.28264 | 0.641320 | − | 0.767273i | \(-0.278387\pi\) | ||||
0.641320 | + | 0.767273i | \(0.278387\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 2.00000 | 0.119737 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 14.4362 | 0.861192 | 0.430596 | − | 0.902545i | \(-0.358303\pi\) | ||||
0.430596 | + | 0.902545i | \(0.358303\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 6.08093 | 0.361474 | 0.180737 | − | 0.983531i | \(-0.442152\pi\) | ||||
0.180737 | + | 0.983531i | \(0.442152\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 1.00000 | 0.0592349 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −5.86454 | −0.346173 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −1.00000 | −0.0588235 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −16.4362 | −0.963508 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −25.1698 | −1.47043 | −0.735216 | − | 0.677833i | \(-0.762919\pi\) | ||||
−0.735216 | + | 0.677833i | \(0.762919\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −5.52504 | −0.321680 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 2.91118 | 0.168924 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 33.4671 | 1.93545 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 7.52504 | 0.433736 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0.177642 | 0.0102053 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 13.1698 | 0.754098 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −22.1776 | −1.26574 | −0.632872 | − | 0.774256i | \(-0.718124\pi\) | ||||
−0.632872 | + | 0.774256i | \(0.718124\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −3.64472 | −0.207341 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 23.7836 | 1.34864 | 0.674322 | − | 0.738437i | \(-0.264436\pi\) | ||||
0.674322 | + | 0.738437i | \(0.264436\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 15.4671 | 0.874251 | 0.437125 | − | 0.899401i | \(-0.355997\pi\) | ||||
0.437125 | + | 0.899401i | \(0.355997\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −0.911179 | −0.0513391 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 32.3817 | 1.81874 | 0.909369 | − | 0.415991i | \(-0.136565\pi\) | ||||
0.909369 | + | 0.415991i | \(0.136565\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 2.65260 | 0.148517 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −3.64472 | −0.203428 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −4.00000 | −0.222566 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −6.25857 | −0.347163 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 3.52504 | 0.194935 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −4.87243 | −0.268626 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 20.0422 | 1.10162 | 0.550809 | − | 0.834631i | \(-0.314319\pi\) | ||||
0.550809 | + | 0.834631i | \(0.314319\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 4.43622 | 0.243103 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −4.00000 | −0.218543 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 13.9033 | 0.757360 | 0.378680 | − | 0.925528i | \(-0.376378\pi\) | ||||
0.378680 | + | 0.925528i | \(0.376378\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 13.5250 | 0.734579 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −5.82236 | −0.315298 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 12.0000 | 0.647939 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 5.34740 | 0.287894 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −7.46707 | −0.400853 | −0.200427 | − | 0.979709i | \(-0.564233\pi\) | ||||
−0.200427 | + | 0.979709i | \(0.564233\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 16.6948 | 0.893652 | 0.446826 | − | 0.894621i | \(-0.352554\pi\) | ||||
0.446826 | + | 0.894621i | \(0.352554\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 6.25857 | 0.334058 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −9.70268 | −0.516422 | −0.258211 | − | 0.966089i | \(-0.583133\pi\) | ||||
−0.258211 | + | 0.966089i | \(0.583133\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 16.5171 | 0.876639 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 3.64472 | 0.192899 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 29.6060 | 1.56254 | 0.781272 | − | 0.624191i | \(-0.214571\pi\) | ||||
0.781272 | + | 0.624191i | \(0.214571\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 2.52504 | 0.132530 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 6.00000 | 0.314054 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 13.7836 | 0.719499 | 0.359749 | − | 0.933049i | \(-0.382862\pi\) | ||||
0.359749 | + | 0.933049i | \(0.382862\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 6.43622 | 0.335056 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −3.05008 | −0.158352 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −2.25857 | −0.116945 | −0.0584723 | − | 0.998289i | \(-0.518623\pi\) | ||||
−0.0584723 | + | 0.998289i | \(0.518623\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −1.00000 | −0.0516398 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 5.70268 | 0.293703 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 17.7027 | 0.909326 | 0.454663 | − | 0.890664i | \(-0.349760\pi\) | ||||
0.454663 | + | 0.890664i | \(0.349760\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 22.3395 | 1.14449 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −15.0501 | −0.769023 | −0.384511 | − | 0.923120i | \(-0.625630\pi\) | ||||
−0.384511 | + | 0.923120i | \(0.625630\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 2.65260 | 0.135189 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −8.25857 | −0.419807 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −14.0000 | −0.709828 | −0.354914 | − | 0.934899i | \(-0.615490\pi\) | ||||
−0.354914 | + | 0.934899i | \(0.615490\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −21.3896 | −1.08172 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −8.73354 | −0.440549 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 10.9921 | 0.553073 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 0.313098 | 0.0157139 | 0.00785697 | − | 0.999969i | \(-0.497499\pi\) | ||||
0.00785697 | + | 0.999969i | \(0.497499\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −0.911179 | −0.0456160 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −7.03086 | −0.351104 | −0.175552 | − | 0.984470i | \(-0.556171\pi\) | ||||
−0.175552 | + | 0.984470i | \(0.556171\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −12.5171 | −0.623524 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 1.00000 | 0.0496904 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −12.9146 | −0.640154 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 20.1776 | 0.997720 | 0.498860 | − | 0.866683i | \(-0.333752\pi\) | ||||
0.498860 | + | 0.866683i | \(0.333752\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −13.3474 | −0.658378 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 5.03430 | 0.247722 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 3.82236 | 0.187632 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 1.82236 | 0.0892412 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 15.4283 | 0.753723 | 0.376862 | − | 0.926270i | \(-0.377003\pi\) | ||||
0.376862 | + | 0.926270i | \(0.377003\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 27.3316 | 1.33206 | 0.666031 | − | 0.745924i | \(-0.267992\pi\) | ||||
0.666031 | + | 0.745924i | \(0.267992\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 5.34740 | 0.259999 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 4.00000 | 0.194029 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −12.0000 | −0.580721 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −18.2198 | −0.879662 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 1.22772 | 0.0591371 | 0.0295686 | − | 0.999563i | \(-0.490587\pi\) | ||||
0.0295686 | + | 0.999563i | \(0.490587\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −24.4362 | −1.17433 | −0.587165 | − | 0.809467i | \(-0.699756\pi\) | ||||
−0.587165 | + | 0.809467i | \(0.699756\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0.911179 | 0.0436877 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 5.34740 | 0.255801 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 34.9921 | 1.67008 | 0.835041 | − | 0.550187i | \(-0.185444\pi\) | ||||
0.835041 | + | 0.550187i | \(0.185444\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −6.16975 | −0.293798 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 31.3896 | 1.49136 | 0.745682 | − | 0.666302i | \(-0.232124\pi\) | ||||
0.745682 | + | 0.666302i | \(0.232124\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −2.43622 | −0.115488 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −4.69479 | −0.222056 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −12.2586 | −0.578518 | −0.289259 | − | 0.957251i | \(-0.593409\pi\) | ||||
−0.289259 | + | 0.957251i | \(0.593409\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −18.7370 | −0.882290 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 4.69479 | 0.220581 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 5.70268 | 0.267346 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −17.2119 | −0.805141 | −0.402570 | − | 0.915389i | \(-0.631883\pi\) | ||||
−0.402570 | + | 0.915389i | \(0.631883\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −4.00000 | −0.186704 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −28.6948 | −1.33645 | −0.668225 | − | 0.743959i | \(-0.732946\pi\) | ||||
−0.668225 | + | 0.743959i | \(0.732946\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 7.08882 | 0.329445 | 0.164723 | − | 0.986340i | \(-0.447327\pi\) | ||||
0.164723 | + | 0.986340i | \(0.447327\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −2.00000 | −0.0927478 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 26.6790 | 1.23456 | 0.617279 | − | 0.786745i | \(-0.288235\pi\) | ||||
0.617279 | + | 0.786745i | \(0.288235\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 3.64472 | 0.168297 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 3.16975 | 0.146055 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 24.0422 | 1.10546 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −1.00000 | −0.0458831 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 3.34740 | 0.153267 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 29.0888 | 1.32910 | 0.664551 | − | 0.747243i | \(-0.268623\pi\) | ||||
0.664551 | + | 0.747243i | \(0.268623\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −27.7644 | −1.26595 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −4.87243 | −0.221703 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 16.4362 | 0.746330 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −23.8066 | −1.07878 | −0.539390 | − | 0.842056i | \(-0.681345\pi\) | ||||
−0.539390 | + | 0.842056i | \(0.681345\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −6.43622 | −0.291056 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 13.6060 | 0.614029 | 0.307014 | − | 0.951705i | \(-0.400670\pi\) | ||||
0.307014 | + | 0.951705i | \(0.400670\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −3.64472 | −0.164150 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −2.91118 | −0.130848 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −15.0501 | −0.675088 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 6.17764 | 0.276549 | 0.138275 | − | 0.990394i | \(-0.455844\pi\) | ||||
0.138275 | + | 0.990394i | \(0.455844\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 3.16975 | 0.141614 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −2.81447 | −0.125491 | −0.0627455 | − | 0.998030i | \(-0.519986\pi\) | ||||
−0.0627455 | + | 0.998030i | \(0.519986\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −0.177642 | −0.00790498 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −26.1698 | −1.16224 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −39.7678 | −1.76268 | −0.881339 | − | 0.472484i | \(-0.843357\pi\) | ||||
−0.881339 | + | 0.472484i | \(0.843357\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −5.46707 | −0.241849 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 1.00000 | 0.0441511 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 3.64472 | 0.160605 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −15.5672 | −0.684646 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 9.52504 | 0.418103 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −38.5981 | −1.69101 | −0.845506 | − | 0.533965i | \(-0.820701\pi\) | ||||
−0.845506 | + | 0.533965i | \(0.820701\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −38.5014 | −1.68355 | −0.841774 | − | 0.539831i | \(-0.818488\pi\) | ||||
−0.841774 | + | 0.539831i | \(0.818488\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0.911179 | 0.0397671 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 8.00000 | 0.348485 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 5.59464 | 0.243245 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −5.52504 | −0.239766 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −40.2815 | −1.74479 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 3.64472 | 0.157575 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 5.16975 | 0.223091 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 17.9613 | 0.773646 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −10.0000 | −0.429934 | −0.214967 | − | 0.976621i | \(-0.568964\pi\) | ||||
−0.214967 | + | 0.976621i | \(0.568964\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −18.8145 | −0.807406 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −3.52504 | −0.150996 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −14.1776 | −0.606192 | −0.303096 | − | 0.952960i | \(-0.598020\pi\) | ||||
−0.303096 | + | 0.952960i | \(0.598020\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 13.1698 | 0.562071 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0.911179 | 0.0388175 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −10.0158 | −0.425914 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −4.43622 | −0.188307 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 6.00000 | 0.254228 | 0.127114 | − | 0.991888i | \(-0.459429\pi\) | ||||
0.127114 | + | 0.991888i | \(0.459429\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 51.6869 | 2.18612 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 11.6447 | 0.491640 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −28.8302 | −1.21505 | −0.607525 | − | 0.794301i | \(-0.707838\pi\) | ||||
−0.607525 | + | 0.794301i | \(0.707838\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −13.5250 | −0.569003 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −0.911179 | −0.0382659 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −28.2586 | −1.18466 | −0.592331 | − | 0.805695i | \(-0.701792\pi\) | ||||
−0.592331 | + | 0.805695i | \(0.701792\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −0.872434 | −0.0365102 | −0.0182551 | − | 0.999833i | \(-0.505811\pi\) | ||||
−0.0182551 | + | 0.999833i | \(0.505811\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 7.78361 | 0.325165 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −5.34740 | −0.223002 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 25.8066 | 1.07434 | 0.537171 | − | 0.843473i | \(-0.319493\pi\) | ||||
0.537171 | + | 0.843473i | \(0.319493\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 15.7256 | 0.653536 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −3.48285 | −0.144493 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −9.74487 | −0.403591 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −6.25857 | −0.258760 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −16.6948 | −0.689068 | −0.344534 | − | 0.938774i | \(-0.611963\pi\) | ||||
−0.344534 | + | 0.938774i | \(0.611963\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −2.00000 | −0.0824086 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 7.70268 | 0.316846 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −20.6368 | −0.847453 | −0.423726 | − | 0.905790i | \(-0.639278\pi\) | ||||
−0.423726 | + | 0.905790i | \(0.639278\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −3.64472 | −0.149419 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −20.5171 | −0.839711 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 14.9341 | 0.610193 | 0.305096 | − | 0.952321i | \(-0.401311\pi\) | ||||
0.305096 | + | 0.952321i | \(0.401311\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −6.51715 | −0.265840 | −0.132920 | − | 0.991127i | \(-0.542435\pi\) | ||||
−0.132920 | + | 0.991127i | \(0.542435\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −4.00000 | −0.162893 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −2.52504 | −0.102657 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 34.5014 | 1.40037 | 0.700184 | − | 0.713963i | \(-0.253101\pi\) | ||||
0.700184 | + | 0.713963i | \(0.253101\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −0.830247 | −0.0336433 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −33.4671 | −1.35393 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −28.5593 | −1.15350 | −0.576750 | − | 0.816920i | \(-0.695679\pi\) | ||||
−0.576750 | + | 0.816920i | \(0.695679\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −6.43622 | −0.259533 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 25.9842 | 1.04609 | 0.523043 | − | 0.852306i | \(-0.324797\pi\) | ||||
0.523043 | + | 0.852306i | \(0.324797\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −5.22772 | −0.210120 | −0.105060 | − | 0.994466i | \(-0.533503\pi\) | ||||
−0.105060 | + | 0.994466i | \(0.533503\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 5.34740 | 0.214584 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 2.21983 | 0.0889356 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −2.91118 | −0.116261 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 17.7449 | 0.707534 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 45.3896 | 1.80693 | 0.903465 | − | 0.428661i | \(-0.141015\pi\) | ||||
0.903465 | + | 0.428661i | \(0.141015\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −22.3395 | −0.887916 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −22.3395 | −0.886516 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 38.6139 | 1.52994 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 16.5171 | 0.653408 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 11.5480 | 0.456119 | 0.228059 | − | 0.973647i | \(-0.426762\pi\) | ||||
0.228059 | + | 0.973647i | \(0.426762\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −15.7414 | −0.620781 | −0.310391 | − | 0.950609i | \(-0.600460\pi\) | ||||
−0.310391 | + | 0.950609i | \(0.600460\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 8.25857 | 0.325181 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 17.8645 | 0.702328 | 0.351164 | − | 0.936314i | \(-0.385786\pi\) | ||||
0.351164 | + | 0.936314i | \(0.385786\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 16.0844 | 0.631367 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 1.82236 | 0.0714238 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −42.9921 | −1.68241 | −0.841206 | − | 0.540715i | \(-0.818154\pi\) | ||||
−0.841206 | + | 0.540715i | \(0.818154\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 8.73354 | 0.341248 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 6.00000 | 0.234082 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −48.3817 | −1.88468 | −0.942342 | − | 0.334653i | \(-0.891381\pi\) | ||||
−0.942342 | + | 0.334653i | \(0.891381\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −25.8645 | −1.00601 | −0.503007 | − | 0.864282i | \(-0.667773\pi\) | ||||
−0.503007 | + | 0.864282i | \(0.667773\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 25.0343 | 0.972252 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0.911179 | 0.0353340 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 4.87243 | 0.188661 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −18.3395 | −0.709046 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −38.3395 | −1.48008 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 42.9376 | 1.65512 | 0.827561 | − | 0.561376i | \(-0.189728\pi\) | ||||
0.827561 | + | 0.561376i | \(0.189728\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −1.00000 | −0.0384900 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 10.0422 | 0.385953 | 0.192976 | − | 0.981203i | \(-0.438186\pi\) | ||||
0.192976 | + | 0.981203i | \(0.438186\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −14.9763 | −0.574739 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −17.8645 | −0.684571 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −30.6948 | −1.17450 | −0.587252 | − | 0.809404i | \(-0.699790\pi\) | ||||
−0.587252 | + | 0.809404i | \(0.699790\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 13.3474 | 0.509978 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −25.1698 | −0.960286 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −20.9499 | −0.798129 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 3.48285 | 0.132494 | 0.0662470 | − | 0.997803i | \(-0.478897\pi\) | ||||
0.0662470 | + | 0.997803i | \(0.478897\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 2.65260 | 0.100764 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −1.82236 | −0.0691260 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 25.7449 | 0.975156 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −15.6869 | −0.593333 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −23.3896 | −0.883412 | −0.441706 | − | 0.897160i | \(-0.645627\pi\) | ||||
−0.441706 | + | 0.897160i | \(0.645627\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −4.43622 | −0.167315 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −5.34740 | −0.201395 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0.161864 | 0.00608752 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −20.4592 | −0.768361 | −0.384180 | − | 0.923258i | \(-0.625516\pi\) | ||||
−0.384180 | + | 0.923258i | \(0.625516\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 10.9921 | 0.412236 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −10.6948 | −0.400523 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 18.2198 | 0.681383 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 3.42833 | 0.128033 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −12.3783 | −0.461631 | −0.230815 | − | 0.972998i | \(-0.574139\pi\) | ||||
−0.230815 | + | 0.972998i | \(0.574139\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −3.32099 | −0.123680 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 23.0343 | 0.856655 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −0.911179 | −0.0338403 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −2.49418 | −0.0925041 | −0.0462520 | − | 0.998930i | \(-0.514728\pi\) | ||||
−0.0462520 | + | 0.998930i | \(0.514728\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −33.0343 | −1.22182 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 14.6526 | 0.541206 | 0.270603 | − | 0.962691i | \(-0.412777\pi\) | ||||
0.270603 | + | 0.962691i | \(0.412777\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 6.16975 | 0.227575 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 11.6447 | 0.428939 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −21.0343 | −0.773759 | −0.386880 | − | 0.922130i | \(-0.626447\pi\) | ||||
−0.386880 | + | 0.922130i | \(0.626447\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −6.25857 | −0.229914 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 0.949924 | 0.0348493 | 0.0174247 | − | 0.999848i | \(-0.494453\pi\) | ||||
0.0174247 | + | 0.999848i | \(0.494453\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 4.69479 | 0.172004 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 3.82236 | 0.139853 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −3.32099 | −0.121346 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 20.6948 | 0.755164 | 0.377582 | − | 0.925976i | \(-0.376756\pi\) | ||||
0.377582 | + | 0.925976i | \(0.376756\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 19.0730 | 0.695060 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −4.69479 | −0.170861 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 23.8803 | 0.867945 | 0.433973 | − | 0.900926i | \(-0.357111\pi\) | ||||
0.433973 | + | 0.900926i | \(0.357111\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −15.5672 | −0.565054 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 53.3738 | 1.93480 | 0.967399 | − | 0.253255i | \(-0.0815013\pi\) | ||||
0.967399 | + | 0.253255i | \(0.0815013\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 3.21194 | 0.116280 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 4.00000 | 0.144620 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 34.5789 | 1.24857 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 29.0501 | 1.04757 | 0.523786 | − | 0.851850i | \(-0.324519\pi\) | ||||
0.523786 | + | 0.851850i | \(0.324519\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 15.8645 | 0.571348 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −31.3474 | −1.12749 | −0.563744 | − | 0.825950i | \(-0.690639\pi\) | ||||
−0.563744 | + | 0.825950i | \(0.690639\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 2.00000 | 0.0718421 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 4.04219 | 0.145013 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −6.43622 | −0.230601 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −48.0844 | −1.72059 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0.911179 | 0.0325629 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −3.16975 | −0.113133 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −23.2119 | −0.827416 | −0.413708 | − | 0.910410i | \(-0.635767\pi\) | ||||
−0.413708 | + | 0.910410i | \(0.635767\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −3.16975 | −0.112846 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 12.3237 | 0.438181 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −82.4239 | −2.92696 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −3.34740 | −0.118720 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −35.8645 | −1.27039 | −0.635194 | − | 0.772353i | \(-0.719080\pi\) | ||||
−0.635194 | + | 0.772353i | \(0.719080\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 21.3896 | 0.756709 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −2.43622 | −0.0860795 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −17.4671 | −0.616400 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 4.87243 | 0.171731 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 13.7836 | 0.485206 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 2.35528 | 0.0828074 | 0.0414037 | − | 0.999142i | \(-0.486817\pi\) | ||||
0.0414037 | + | 0.999142i | \(0.486817\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 43.0185 | 1.51058 | 0.755292 | − | 0.655388i | \(-0.227495\pi\) | ||||
0.755292 | + | 0.655388i | \(0.227495\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −17.8224 | −0.625057 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 6.43622 | 0.225451 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 8.25857 | 0.288931 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 5.70268 | 0.199268 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 47.9067 | 1.67196 | 0.835978 | − | 0.548763i | \(-0.184901\pi\) | ||||
0.835978 | + | 0.548763i | \(0.184901\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 12.3940 | 0.432029 | 0.216014 | − | 0.976390i | \(-0.430694\pi\) | ||||
0.216014 | + | 0.976390i | \(0.430694\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 2.91118 | 0.101354 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −11.1698 | −0.388410 | −0.194205 | − | 0.980961i | \(-0.562213\pi\) | ||||
−0.194205 | + | 0.980961i | \(0.562213\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −0.830247 | −0.0288357 | −0.0144178 | − | 0.999896i | \(-0.504589\pi\) | ||||
−0.0144178 | + | 0.999896i | \(0.504589\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −21.3474 | −0.740533 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −24.6790 | −0.855077 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −3.16975 | −0.109694 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −2.00000 | −0.0691301 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 12.8724 | 0.444406 | 0.222203 | − | 0.975000i | \(-0.428675\pi\) | ||||
0.222203 | + | 0.975000i | \(0.428675\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −28.1698 | −0.971371 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −14.4362 | −0.497210 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 26.1698 | 0.900267 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 2.30076 | 0.0790551 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −6.08093 | −0.208697 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −23.7222 | −0.813187 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 12.8302 | 0.439299 | 0.219650 | − | 0.975579i | \(-0.429509\pi\) | ||||
0.219650 | + | 0.975579i | \(0.429509\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −1.00000 | −0.0341993 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −35.0765 | −1.19819 | −0.599095 | − | 0.800678i | \(-0.704473\pi\) | ||||
−0.599095 | + | 0.800678i | \(0.704473\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 22.6948 | 0.774336 | 0.387168 | − | 0.922009i | \(-0.373453\pi\) | ||||
0.387168 | + | 0.922009i | \(0.373453\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 5.86454 | 0.199863 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 18.6948 | 0.636378 | 0.318189 | − | 0.948027i | \(-0.396925\pi\) | ||||
0.318189 | + | 0.948027i | \(0.396925\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −9.52504 | −0.323861 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 1.00000 | 0.0339618 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −32.0000 | −1.08553 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 25.0343 | 0.848255 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 16.4362 | 0.556282 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −0.911179 | −0.0308035 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −10.7757 | −0.363870 | −0.181935 | − | 0.983311i | \(-0.558236\pi\) | ||||
−0.181935 | + | 0.983311i | \(0.558236\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 25.1698 | 0.848955 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 1.56722 | 0.0528011 | 0.0264006 | − | 0.999651i | \(-0.491595\pi\) | ||||
0.0264006 | + | 0.999651i | \(0.491595\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 5.13101 | 0.172672 | 0.0863361 | − | 0.996266i | \(-0.472484\pi\) | ||||
0.0863361 | + | 0.996266i | \(0.472484\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 5.52504 | 0.185722 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 9.74487 | 0.327201 | 0.163600 | − | 0.986527i | \(-0.447689\pi\) | ||||
0.163600 | + | 0.986527i | \(0.447689\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 20.3553 | 0.682694 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −2.91118 | −0.0975282 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −5.34740 | −0.178944 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −5.16975 | −0.172806 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −33.4671 | −1.11743 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −1.82236 | −0.0607790 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 13.3896 | 0.446072 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −7.52504 | −0.250418 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 18.8145 | 0.625414 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 4.51715 | 0.149989 | 0.0749947 | − | 0.997184i | \(-0.476106\pi\) | ||||
0.0749947 | + | 0.997184i | \(0.476106\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −0.177642 | −0.00589203 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −21.0343 | −0.696897 | −0.348449 | − | 0.937328i | \(-0.613291\pi\) | ||||
−0.348449 | + | 0.937328i | \(0.613291\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −11.1276 | −0.368269 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −13.1698 | −0.435379 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −7.95781 | −0.262790 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 0.949924 | 0.0313351 | 0.0156676 | − | 0.999877i | \(-0.495013\pi\) | ||||
0.0156676 | + | 0.999877i | \(0.495013\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 22.1776 | 0.730778 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −103.374 | −3.40259 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 4.43622 | 0.145862 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 3.64472 | 0.119708 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 29.4513 | 0.966266 | 0.483133 | − | 0.875547i | \(-0.339499\pi\) | ||||
0.483133 | + | 0.875547i | \(0.339499\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 6.16975 | 0.202205 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −23.7836 | −0.778641 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −11.6447 | −0.380823 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −54.6015 | −1.78375 | −0.891877 | − | 0.452278i | \(-0.850611\pi\) | ||||
−0.891877 | + | 0.452278i | \(0.850611\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −15.4671 | −0.504749 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 32.2006 | 1.04971 | 0.524855 | − | 0.851192i | \(-0.324120\pi\) | ||||
0.524855 | + | 0.851192i | \(0.324120\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −34.4170 | −1.12077 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0.911179 | 0.0296406 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −42.5171 | −1.38162 | −0.690811 | − | 0.723036i | \(-0.742746\pi\) | ||||
−0.690811 | + | 0.723036i | \(0.742746\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −37.5514 | −1.21897 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −32.3817 | −1.05005 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 28.1039 | 0.910375 | 0.455187 | − | 0.890396i | \(-0.349572\pi\) | ||||
0.455187 | + | 0.890396i | \(0.349572\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −7.78361 | −0.251872 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −2.65260 | −0.0857465 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −12.1619 | −0.392727 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −27.0000 | −0.870968 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 3.64472 | 0.117449 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −15.7256 | −0.506226 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −42.4626 | −1.36551 | −0.682753 | − | 0.730649i | \(-0.739217\pi\) | ||||
−0.682753 | + | 0.730649i | \(0.739217\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 4.00000 | 0.128499 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 22.0422 | 0.707367 | 0.353684 | − | 0.935365i | \(-0.384929\pi\) | ||||
0.353684 | + | 0.935365i | \(0.384929\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 1.66049 | 0.0532330 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 6.25857 | 0.200435 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −15.3474 | −0.491007 | −0.245503 | − | 0.969396i | \(-0.578953\pi\) | ||||
−0.245503 | + | 0.969396i | \(0.578953\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 7.09226 | 0.226670 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −3.52504 | −0.112546 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 5.78017 | 0.184359 | 0.0921794 | − | 0.995742i | \(-0.470617\pi\) | ||||
0.0921794 | + | 0.995742i | \(0.470617\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −7.70268 | −0.245428 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 4.87243 | 0.155091 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 44.1619 | 1.40427 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −60.7370 | −1.92937 | −0.964687 | − | 0.263399i | \(-0.915156\pi\) | ||||
−0.964687 | + | 0.263399i | \(0.915156\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −20.0422 | −0.636020 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 20.5171 | 0.650437 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 41.5093 | 1.31461 | 0.657306 | − | 0.753624i | \(-0.271696\pi\) | ||||
0.657306 | + | 0.753624i | \(0.271696\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −4.43622 | −0.140356 |
(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 | 4560.2.a.bs.1.2 | 3 | ||
4.3 | odd | 2 | 2280.2.a.u.1.2 | ✓ | 3 | ||
12.11 | even | 2 | 6840.2.a.bh.1.2 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2280.2.a.u.1.2 | ✓ | 3 | 4.3 | odd | 2 | ||
4560.2.a.bs.1.2 | 3 | 1.1 | even | 1 | trivial | ||
6840.2.a.bh.1.2 | 3 | 12.11 | even | 2 |