Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1900,2,Mod(1749,1900)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1900, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1900.1749");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1900 = 2^{2} \cdot 5^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1900.c (of order \(2\), degree \(1\), not minimal) |
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: | no |
Analytic conductor: | \(15.1715763840\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | 6.0.4227136.2 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} + 9x^{4} + 22x^{2} + 9 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 5^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1749.1 | ||
Root | \(-1.91223i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1900.1749 |
Dual form | 1900.2.c.g.1749.6 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1900\mathbb{Z}\right)^\times\).
\(n\) | \(77\) | \(401\) | \(951\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | − 2.91223i | − 1.68138i | −0.541520 | − | 0.840688i | \(-0.682151\pi\) | ||||
0.541520 | − | 0.840688i | \(-0.317849\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.91223i | 1.10072i | 0.834928 | + | 0.550360i | \(0.185509\pi\) | ||||
−0.834928 | + | 0.550360i | \(0.814491\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −5.48108 | −1.82703 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.598988 | 0.180602 | 0.0903009 | − | 0.995915i | \(-0.471217\pi\) | ||||
0.0903009 | + | 0.995915i | \(0.471217\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.56885i | 0.712471i | 0.934396 | + | 0.356235i | \(0.115940\pi\) | ||||
−0.934396 | + | 0.356235i | \(0.884060\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 2.91223i | 0.706319i | 0.935563 | + | 0.353160i | \(0.114893\pi\) | ||||
−0.935563 | + | 0.353160i | \(0.885107\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.00000 | 0.229416 | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 8.48108 | 1.85072 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.16784i | 0.243511i | 0.992560 | + | 0.121756i | \(0.0388524\pi\) | ||||
−0.992560 | + | 0.121756i | \(0.961148\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 7.22547i | 1.39054i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1.40101 | 0.260161 | 0.130081 | − | 0.991503i | \(-0.458476\pi\) | ||||
0.130081 | + | 0.991503i | \(0.458476\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 7.88209 | 1.41567 | 0.707833 | − | 0.706380i | \(-0.249673\pi\) | ||||
0.707833 | + | 0.706380i | \(0.249673\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | − 1.74439i | − 0.303660i | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − 6.53871i | − 1.07496i | −0.843277 | − | 0.537479i | \(-0.819377\pi\) | ||||
0.843277 | − | 0.537479i | \(-0.180623\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 7.48108 | 1.19793 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 9.48108 | 1.48070 | 0.740348 | − | 0.672224i | \(-0.234661\pi\) | ||||
0.740348 | + | 0.672224i | \(0.234661\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0.824458i | 0.125729i | 0.998022 | + | 0.0628644i | \(0.0200236\pi\) | ||||
−0.998022 | + | 0.0628644i | \(0.979976\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 6.05763i | 0.883596i | 0.897114 | + | 0.441798i | \(0.145659\pi\) | ||||
−0.897114 | + | 0.441798i | \(0.854341\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.48108 | −0.211583 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 8.48108 | 1.18759 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 0.824458i | 0.113248i | 0.998396 | + | 0.0566240i | \(0.0180336\pi\) | ||||
−0.998396 | + | 0.0566240i | \(0.981966\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − 2.91223i | − 0.385734i | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 14.1601 | 1.84349 | 0.921746 | − | 0.387794i | \(-0.126763\pi\) | ||||
0.921746 | + | 0.387794i | \(0.126763\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.88209 | −0.240977 | −0.120488 | − | 0.992715i | \(-0.538446\pi\) | ||||
−0.120488 | + | 0.992715i | \(0.538446\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | − 15.9622i | − 2.01104i | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 5.11021i | 0.624311i | 0.950031 | + | 0.312156i | \(0.101051\pi\) | ||||
−0.950031 | + | 0.312156i | \(0.898949\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 3.40101 | 0.409434 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −11.9622 | −1.41965 | −0.709823 | − | 0.704380i | \(-0.751225\pi\) | ||||
−0.709823 | + | 0.704380i | \(0.751225\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − 1.03014i | − 0.120569i | −0.998181 | − | 0.0602843i | \(-0.980799\pi\) | ||||
0.998181 | − | 0.0602843i | \(-0.0192007\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 1.74439i | 0.198792i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 15.3632 | 1.72849 | 0.864246 | − | 0.503070i | \(-0.167796\pi\) | ||||
0.864246 | + | 0.503070i | \(0.167796\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 4.59899 | 0.510999 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 15.7565i | 1.72950i | 0.502204 | + | 0.864749i | \(0.332523\pi\) | ||||
−0.502204 | + | 0.864749i | \(0.667477\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | − 4.08007i | − 0.437429i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −15.4432 | −1.63698 | −0.818490 | − | 0.574521i | \(-0.805188\pi\) | ||||
−0.818490 | + | 0.574521i | \(0.805188\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −7.48108 | −0.784230 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | − 22.9545i | − 2.38027i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 7.70655i | 0.782481i | 0.920288 | + | 0.391241i | \(0.127954\pi\) | ||||
−0.920288 | + | 0.391241i | \(0.872046\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −3.28310 | −0.329964 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 4.40101 | 0.437917 | 0.218959 | − | 0.975734i | \(-0.429734\pi\) | ||||
0.218959 | + | 0.975734i | \(0.429734\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − 17.3632i | − 1.71084i | −0.517932 | − | 0.855422i | \(-0.673298\pi\) | ||||
0.517932 | − | 0.855422i | \(-0.326702\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 14.1903i | 1.37183i | 0.727684 | + | 0.685913i | \(0.240597\pi\) | ||||
−0.727684 | + | 0.685913i | \(0.759403\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 10.6791 | 1.02287 | 0.511434 | − | 0.859323i | \(-0.329114\pi\) | ||||
0.511434 | + | 0.859323i | \(0.329114\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −19.0422 | −1.80741 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − 8.25561i | − 0.776622i | −0.921528 | − | 0.388311i | \(-0.873059\pi\) | ||||
0.921528 | − | 0.388311i | \(-0.126941\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | − 14.0801i | − 1.30170i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −8.48108 | −0.777459 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.6412 | −0.967383 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | − 27.6111i | − 2.48961i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − 12.1300i | − 1.07636i | −0.842829 | − | 0.538182i | \(-0.819111\pi\) | ||||
0.842829 | − | 0.538182i | \(-0.180889\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 2.40101 | 0.211397 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 5.48108 | 0.478884 | 0.239442 | − | 0.970911i | \(-0.423035\pi\) | ||||
0.239442 | + | 0.970911i | \(0.423035\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 2.91223i | 0.252522i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 7.59634i | 0.648999i | 0.945886 | + | 0.324500i | \(0.105196\pi\) | ||||
−0.945886 | + | 0.324500i | \(0.894804\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −7.16013 | −0.607315 | −0.303657 | − | 0.952781i | \(-0.598208\pi\) | ||||
−0.303657 | + | 0.952781i | \(0.598208\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 17.6412 | 1.48566 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 1.53871i | 0.128673i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 4.31324i | 0.355750i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 18.4432 | 1.51093 | 0.755464 | − | 0.655190i | \(-0.227411\pi\) | ||||
0.755464 | + | 0.655190i | \(0.227411\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −9.27804 | −0.755036 | −0.377518 | − | 0.926002i | \(-0.623222\pi\) | ||||
−0.377518 | + | 0.926002i | \(0.623222\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | − 15.9622i | − 1.29046i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − 14.1903i | − 1.13251i | −0.824231 | − | 0.566254i | \(-0.808392\pi\) | ||||
0.824231 | − | 0.566254i | \(-0.191608\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 2.40101 | 0.190413 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −3.40101 | −0.268037 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 25.1799i | 1.97224i | 0.166023 | + | 0.986122i | \(0.446907\pi\) | ||||
−0.166023 | + | 0.986122i | \(0.553093\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 11.0301i | 0.853538i | 0.904361 | + | 0.426769i | \(0.140348\pi\) | ||||
−0.904361 | + | 0.426769i | \(0.859652\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 6.40101 | 0.492386 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −5.48108 | −0.419149 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − 15.3029i | − 1.16346i | −0.813383 | − | 0.581729i | \(-0.802377\pi\) | ||||
0.813383 | − | 0.581729i | \(-0.197623\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | − 41.2376i | − 3.09960i | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 14.9243 | 1.11550 | 0.557748 | − | 0.830010i | \(-0.311666\pi\) | ||||
0.557748 | + | 0.830010i | \(0.311666\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 3.80202 | 0.282602 | 0.141301 | − | 0.989967i | \(-0.454871\pi\) | ||||
0.141301 | + | 0.989967i | \(0.454871\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 5.48108i | 0.405173i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1.74439i | 0.127563i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −21.0422 | −1.53060 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −10.5990 | −0.766916 | −0.383458 | − | 0.923558i | \(-0.625267\pi\) | ||||
−0.383458 | + | 0.923558i | \(0.625267\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − 22.2677i | − 1.60286i | −0.598086 | − | 0.801432i | \(-0.704072\pi\) | ||||
0.598086 | − | 0.801432i | \(-0.295928\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − 15.1652i | − 1.08048i | −0.841513 | − | 0.540238i | \(-0.818334\pi\) | ||||
0.841513 | − | 0.540238i | \(-0.181666\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −16.3632 | −1.15995 | −0.579977 | − | 0.814633i | \(-0.696939\pi\) | ||||
−0.579977 | + | 0.814633i | \(0.696939\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 14.8821 | 1.04970 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 4.08007i | 0.286365i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | − 6.40101i | − 0.444901i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0.598988 | 0.0414329 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −5.80202 | −0.399428 | −0.199714 | − | 0.979854i | \(-0.564001\pi\) | ||||
−0.199714 | + | 0.979854i | \(0.564001\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 34.8365i | 2.38696i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 22.9545i | 1.55825i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −3.00000 | −0.202721 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −7.48108 | −0.503232 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 10.1377i | 0.678871i | 0.940629 | + | 0.339435i | \(0.110236\pi\) | ||||
−0.940629 | + | 0.339435i | \(0.889764\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 14.5189i | 0.963655i | 0.876266 | + | 0.481827i | \(0.160027\pi\) | ||||
−0.876266 | + | 0.481827i | \(0.839973\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 27.2024 | 1.79758 | 0.898791 | − | 0.438377i | \(-0.144446\pi\) | ||||
0.898791 | + | 0.438377i | \(0.144446\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 5.08007 | 0.334244 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 1.40101i | 0.0917833i | 0.998946 | + | 0.0458917i | \(0.0146129\pi\) | ||||
−0.998946 | + | 0.0458917i | \(0.985387\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | − 44.7411i | − 2.90624i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −9.88209 | −0.639219 | −0.319610 | − | 0.947549i | \(-0.603552\pi\) | ||||
−0.319610 | + | 0.947549i | \(0.603552\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −3.08513 | −0.198730 | −0.0993652 | − | 0.995051i | \(-0.531681\pi\) | ||||
−0.0993652 | + | 0.995051i | \(0.531681\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 8.28310i | 0.531361i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 2.56885i | 0.163452i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 45.8865 | 2.90794 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 6.08007 | 0.383770 | 0.191885 | − | 0.981417i | \(-0.438540\pi\) | ||||
0.191885 | + | 0.981417i | \(0.438540\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0.699521i | 0.0439785i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 19.0121i | 1.18594i | 0.805224 | + | 0.592971i | \(0.202045\pi\) | ||||
−0.805224 | + | 0.592971i | \(0.797955\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 19.0422 | 1.18323 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −7.67906 | −0.475322 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 0.453585i | 0.0279693i | 0.999902 | + | 0.0139846i | \(0.00445159\pi\) | ||||
−0.999902 | + | 0.0139846i | \(0.995548\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 44.9742i | 2.75238i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −23.8442 | −1.45381 | −0.726905 | − | 0.686738i | \(-0.759042\pi\) | ||||
−0.726905 | + | 0.686738i | \(0.759042\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 12.7591 | 0.775061 | 0.387531 | − | 0.921857i | \(-0.373328\pi\) | ||||
0.387531 | + | 0.921857i | \(0.373328\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 21.7866i | 1.31859i | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 8.29783i | 0.498568i | 0.968430 | + | 0.249284i | \(0.0801953\pi\) | ||||
−0.968430 | + | 0.249284i | \(0.919805\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −43.2024 | −2.58646 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −9.19798 | −0.548705 | −0.274353 | − | 0.961629i | \(-0.588464\pi\) | ||||
−0.274353 | + | 0.961629i | \(0.588464\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 19.8770i | 1.18157i | 0.806830 | + | 0.590783i | \(0.201181\pi\) | ||||
−0.806830 | + | 0.590783i | \(0.798819\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 27.6111i | 1.62983i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 8.51892 | 0.501113 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 22.4432 | 1.31565 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 8.14540i | 0.475860i | 0.971282 | + | 0.237930i | \(0.0764688\pi\) | ||||
−0.971282 | + | 0.237930i | \(0.923531\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 4.32797i | 0.251134i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −3.00000 | −0.173494 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −2.40101 | −0.138392 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | − 12.8168i | − 0.736303i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 10.7565i | 0.613905i | 0.951725 | + | 0.306952i | \(0.0993092\pi\) | ||||
−0.951725 | + | 0.306952i | \(0.900691\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −50.5655 | −2.87657 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −30.8442 | −1.74902 | −0.874508 | − | 0.485010i | \(-0.838816\pi\) | ||||
−0.874508 | + | 0.485010i | \(0.838816\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − 6.53871i | − 0.369590i | −0.982777 | − | 0.184795i | \(-0.940838\pi\) | ||||
0.982777 | − | 0.184795i | \(-0.0591621\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 11.3055i | 0.634982i | 0.948261 | + | 0.317491i | \(0.102840\pi\) | ||||
−0.948261 | + | 0.317491i | \(0.897160\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0.839190 | 0.0469856 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 41.3253 | 2.30655 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 2.91223i | 0.162041i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | − 31.0999i | − 1.71983i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −17.6412 | −0.972592 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 22.8064 | 1.25355 | 0.626777 | − | 0.779199i | \(-0.284374\pi\) | ||||
0.626777 | + | 0.779199i | \(0.284374\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 35.8392i | 1.96398i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − 17.7065i | − 0.964537i | −0.876023 | − | 0.482269i | \(-0.839813\pi\) | ||||
0.876023 | − | 0.482269i | \(-0.160187\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −24.0422 | −1.30579 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 4.72128 | 0.255672 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 16.0724i | 0.867826i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 6.26331i | 0.336232i | 0.985767 | + | 0.168116i | \(0.0537684\pi\) | ||||
−0.985767 | + | 0.168116i | \(0.946232\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 14.8821 | 0.796620 | 0.398310 | − | 0.917251i | \(-0.369597\pi\) | ||||
0.398310 | + | 0.917251i | \(0.369597\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −18.5611 | −0.990721 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 5.45359i | 0.290265i | 0.989412 | + | 0.145133i | \(0.0463609\pi\) | ||||
−0.989412 | + | 0.145133i | \(0.953639\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 24.6988i | 1.30720i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −2.11791 | −0.111779 | −0.0558895 | − | 0.998437i | \(-0.517799\pi\) | ||||
−0.0558895 | + | 0.998437i | \(0.517799\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 30.9897i | 1.62653i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − 17.5414i | − 0.915651i | −0.889042 | − | 0.457826i | \(-0.848628\pi\) | ||||
0.889042 | − | 0.457826i | \(-0.151372\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −51.9665 | −2.70527 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −2.40101 | −0.124654 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 29.0801i | 1.50571i | 0.658187 | + | 0.752854i | \(0.271324\pi\) | ||||
−0.658187 | + | 0.752854i | \(0.728676\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 3.59899i | 0.185357i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −26.2780 | −1.34981 | −0.674906 | − | 0.737904i | \(-0.735816\pi\) | ||||
−0.674906 | + | 0.737904i | \(0.735816\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −35.3253 | −1.80977 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − 21.6911i | − 1.10837i | −0.832395 | − | 0.554183i | \(-0.813031\pi\) | ||||
0.832395 | − | 0.554183i | \(-0.186969\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | − 4.51892i | − 0.229710i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −2.43380 | −0.123398 | −0.0616992 | − | 0.998095i | \(-0.519652\pi\) | ||||
−0.0616992 | + | 0.998095i | \(0.519652\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −3.40101 | −0.171997 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − 15.9622i | − 0.805184i | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − 31.2780i | − 1.56980i | −0.619622 | − | 0.784900i | \(-0.712714\pi\) | ||||
0.619622 | − | 0.784900i | \(-0.287286\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 8.48108 | 0.424585 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −8.95710 | −0.447296 | −0.223648 | − | 0.974670i | \(-0.571797\pi\) | ||||
−0.223648 | + | 0.974670i | \(0.571797\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 20.2479i | 1.00862i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − 3.91661i | − 0.194139i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 24.6412 | 1.21843 | 0.609215 | − | 0.793005i | \(-0.291485\pi\) | ||||
0.609215 | + | 0.793005i | \(0.291485\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 22.1223 | 1.09121 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 41.2376i | 2.02917i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 20.8520i | 1.02112i | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −13.9199 | −0.680033 | −0.340017 | − | 0.940419i | \(-0.610433\pi\) | ||||
−0.340017 | + | 0.940419i | \(0.610433\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 4.91993 | 0.239783 | 0.119891 | − | 0.992787i | \(-0.461745\pi\) | ||||
0.119891 | + | 0.992787i | \(0.461745\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | − 33.2024i | − 1.61435i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − 5.48108i | − 0.265248i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 4.48108 | 0.216349 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 20.2875 | 0.977214 | 0.488607 | − | 0.872504i | \(-0.337505\pi\) | ||||
0.488607 | + | 0.872504i | \(0.337505\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 20.9769i | 1.00808i | 0.863679 | + | 0.504042i | \(0.168155\pi\) | ||||
−0.863679 | + | 0.504042i | \(0.831845\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 1.16784i | 0.0558653i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 18.7591 | 0.895324 | 0.447662 | − | 0.894203i | \(-0.352257\pi\) | ||||
0.447662 | + | 0.894203i | \(0.352257\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 8.11791 | 0.386567 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − 40.4828i | − 1.92340i | −0.274110 | − | 0.961698i | \(-0.588383\pi\) | ||||
0.274110 | − | 0.961698i | \(-0.411617\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | − 53.7109i | − 2.54044i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 19.2402 | 0.908001 | 0.454001 | − | 0.891001i | \(-0.349996\pi\) | ||||
0.454001 | + | 0.891001i | \(0.349996\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 5.67906 | 0.267416 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 27.0198i | 1.26950i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − 8.44829i | − 0.395195i | −0.980283 | − | 0.197597i | \(-0.936686\pi\) | ||||
0.980283 | − | 0.197597i | \(-0.0633138\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −21.0422 | −0.982167 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −25.2780 | −1.17732 | −0.588658 | − | 0.808382i | \(-0.700343\pi\) | ||||
−0.588658 | + | 0.808382i | \(0.700343\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − 7.15749i | − 0.332637i | −0.986072 | − | 0.166318i | \(-0.946812\pi\) | ||||
0.986072 | − | 0.166318i | \(-0.0531879\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 1.71690i | 0.0794486i | 0.999211 | + | 0.0397243i | \(0.0126480\pi\) | ||||
−0.999211 | + | 0.0397243i | \(0.987352\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −14.8821 | −0.687191 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −41.3253 | −1.90417 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0.493841i | 0.0227068i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | − 4.51892i | − 0.206907i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 31.6885 | 1.44788 | 0.723942 | − | 0.689861i | \(-0.242328\pi\) | ||||
0.723942 | + | 0.689861i | \(0.242328\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 16.7970 | 0.765876 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 9.90453i | 0.450672i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 1.08513i | 0.0491717i | 0.999698 | + | 0.0245859i | \(0.00782671\pi\) | ||||
−0.999698 | + | 0.0245859i | \(0.992173\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 73.3297 | 3.31608 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −10.9149 | −0.492581 | −0.246291 | − | 0.969196i | \(-0.579212\pi\) | ||||
−0.246291 | + | 0.969196i | \(0.579212\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 4.08007i | 0.183757i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − 34.8365i | − 1.56263i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −38.8814 | −1.74057 | −0.870286 | − | 0.492547i | \(-0.836066\pi\) | ||||
−0.870286 | + | 0.492547i | \(0.836066\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 32.1223 | 1.43512 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − 20.3306i | − 0.906497i | −0.891384 | − | 0.453249i | \(-0.850265\pi\) | ||||
0.891384 | − | 0.453249i | \(-0.149735\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | − 18.6412i | − 0.827885i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −10.5189 | −0.466243 | −0.233121 | − | 0.972448i | \(-0.574894\pi\) | ||||
−0.233121 | + | 0.972448i | \(0.574894\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 3.00000 | 0.132712 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 7.22547i | 0.319012i | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 3.62845i | 0.159579i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −44.5655 | −1.95621 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −25.7642 | −1.12875 | −0.564375 | − | 0.825519i | \(-0.690883\pi\) | ||||
−0.564375 | + | 0.825519i | \(0.690883\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − 30.8814i | − 1.35035i | −0.737658 | − | 0.675175i | \(-0.764068\pi\) | ||||
0.737658 | − | 0.675175i | \(-0.235932\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 22.9545i | 0.999912i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 21.6362 | 0.940702 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −77.6128 | −3.36811 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 24.3555i | 1.05495i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | − 43.4630i | − 1.87557i | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −0.887149 | −0.0382122 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 13.3253 | 0.572901 | 0.286450 | − | 0.958095i | \(-0.407525\pi\) | ||||
0.286450 | + | 0.958095i | \(0.407525\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | − 11.0724i | − 0.475161i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 26.8821i | 1.14940i | 0.818366 | + | 0.574698i | \(0.194880\pi\) | ||||
−0.818366 | + | 0.574698i | \(0.805120\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 10.3159 | 0.440271 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1.40101 | 0.0596851 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 44.7411i | 1.90258i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − 27.3082i | − 1.15708i | −0.815652 | − | 0.578542i | \(-0.803622\pi\) | ||||
0.815652 | − | 0.578542i | \(-0.196378\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −2.11791 | −0.0895780 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 5.08007 | 0.214481 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 40.3324i | 1.69981i | 0.526939 | + | 0.849903i | \(0.323340\pi\) | ||||
−0.526939 | + | 0.849903i | \(0.676660\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 13.3933i | 0.562466i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −11.8399 | −0.496353 | −0.248176 | − | 0.968715i | \(-0.579831\pi\) | ||||
−0.248176 | + | 0.968715i | \(0.579831\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −1.71690 | −0.0718499 | −0.0359250 | − | 0.999354i | \(-0.511438\pi\) | ||||
−0.0359250 | + | 0.999354i | \(0.511438\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 30.8667i | 1.28947i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − 0.0552190i | − 0.00229880i | −0.999999 | − | 0.00114940i | \(-0.999634\pi\) | ||||
0.999999 | − | 0.00114940i | \(-0.000365865\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −64.8486 | −2.69502 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −45.8865 | −1.90369 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0.493841i | 0.0204528i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − 11.4010i | − 0.470570i | −0.971926 | − | 0.235285i | \(-0.924398\pi\) | ||||
0.971926 | − | 0.235285i | \(-0.0756024\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 7.88209 | 0.324776 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −44.1645 | −1.81669 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − 36.8288i | − 1.51238i | −0.654353 | − | 0.756190i | \(-0.727059\pi\) | ||||
0.654353 | − | 0.756190i | \(-0.272941\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 47.6533i | 1.95032i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 22.7591 | 0.929913 | 0.464956 | − | 0.885334i | \(-0.346070\pi\) | ||||
0.464956 | + | 0.885334i | \(0.346070\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −36.5277 | −1.49000 | −0.744998 | − | 0.667067i | \(-0.767549\pi\) | ||||
−0.744998 | + | 0.667067i | \(0.767549\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − 28.0094i | − 1.14063i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 10.1230i | 0.410879i | 0.978670 | + | 0.205439i | \(0.0658623\pi\) | ||||
−0.978670 | + | 0.205439i | \(0.934138\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 11.8821 | 0.481487 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −15.5611 | −0.629537 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − 35.5930i | − 1.43759i | −0.695223 | − | 0.718794i | \(-0.744694\pi\) | ||||
0.695223 | − | 0.718794i | \(-0.255306\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 13.2134i | 0.531951i | 0.963980 | + | 0.265975i | \(0.0856940\pi\) | ||||
−0.963980 | + | 0.265975i | \(0.914306\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 23.2453 | 0.934306 | 0.467153 | − | 0.884177i | \(-0.345280\pi\) | ||||
0.467153 | + | 0.884177i | \(0.345280\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −8.43818 | −0.338612 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − 44.9742i | − 1.80186i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | − 1.74439i | − 0.0696643i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 19.0422 | 0.759263 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 3.88715 | 0.154745 | 0.0773725 | − | 0.997002i | \(-0.475347\pi\) | ||||
0.0773725 | + | 0.997002i | \(0.475347\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 16.8968i | 0.671588i | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − 3.80467i | − 0.150746i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 65.5655 | 2.59373 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −34.1223 | −1.34775 | −0.673875 | − | 0.738846i | \(-0.735371\pi\) | ||||
−0.673875 | + | 0.738846i | \(0.735371\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − 31.9243i | − 1.25897i | −0.777012 | − | 0.629486i | \(-0.783265\pi\) | ||||
0.777012 | − | 0.629486i | \(-0.216735\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 35.3434i | 1.38949i | 0.719255 | + | 0.694746i | \(0.244483\pi\) | ||||
−0.719255 | + | 0.694746i | \(0.755517\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 8.48175 | 0.332938 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 66.8486 | 2.62000 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − 27.5431i | − 1.07784i | −0.842356 | − | 0.538922i | \(-0.818832\pi\) | ||||
0.842356 | − | 0.538922i | \(-0.181168\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 5.64627i | 0.220282i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −29.6740 | −1.15593 | −0.577967 | − | 0.816060i | \(-0.696154\pi\) | ||||
−0.577967 | + | 0.816060i | \(0.696154\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −16.3159 | −0.634614 | −0.317307 | − | 0.948323i | \(-0.602779\pi\) | ||||
−0.317307 | + | 0.948323i | \(0.602779\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 21.7866i | 0.846122i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1.63615i | 0.0633522i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 29.5233 | 1.14144 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −1.12735 | −0.0435209 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − 13.6945i | − 0.527883i | −0.964539 | − | 0.263941i | \(-0.914977\pi\) | ||||
0.964539 | − | 0.263941i | \(-0.0850225\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 18.2426i | 0.701121i | 0.936540 | + | 0.350560i | \(0.114009\pi\) | ||||
−0.936540 | + | 0.350560i | \(0.885991\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −22.4432 | −0.861292 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 42.2824 | 1.62027 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − 8.92764i | − 0.341607i | −0.985305 | − | 0.170803i | \(-0.945364\pi\) | ||||
0.985305 | − | 0.170803i | \(-0.0546363\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − 79.2195i | − 3.02241i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −2.11791 | −0.0806859 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 37.5284 | 1.42765 | 0.713823 | − | 0.700326i | \(-0.246962\pi\) | ||||
0.713823 | + | 0.700326i | \(0.246962\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | − 9.56115i | − 0.363198i | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 27.6111i | 1.04584i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 4.08007 | 0.154322 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −42.1746 | −1.59291 | −0.796457 | − | 0.604695i | \(-0.793295\pi\) | ||||
−0.796457 | + | 0.604695i | \(0.793295\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − 6.53871i | − 0.246612i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 12.8168i | 0.482024i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 4.35373 | 0.163508 | 0.0817539 | − | 0.996653i | \(-0.473948\pi\) | ||||
0.0817539 | + | 0.996653i | \(0.473948\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −84.2067 | −3.15800 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 9.20500i | 0.344730i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 28.7789i | 1.07477i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −14.2780 | −0.532481 | −0.266241 | − | 0.963907i | \(-0.585782\pi\) | ||||
−0.266241 | + | 0.963907i | \(0.585782\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 50.5655 | 1.88316 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 8.98459i | 0.334141i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − 29.7538i | − 1.10351i | −0.834007 | − | 0.551754i | \(-0.813959\pi\) | ||||
0.834007 | − | 0.551754i | \(-0.186041\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 37.9193 | 1.40442 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −2.40101 | −0.0888046 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − 16.4580i | − 0.607889i | −0.952690 | − | 0.303944i | \(-0.901696\pi\) | ||||
0.952690 | − | 0.303944i | \(-0.0983037\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 3.06095i | 0.112752i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −11.2024 | −0.412085 | −0.206043 | − | 0.978543i | \(-0.566059\pi\) | ||||
−0.206043 | + | 0.978543i | \(0.566059\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 7.48108 | 0.274824 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 28.5053i | 1.04576i | 0.852407 | + | 0.522878i | \(0.175142\pi\) | ||||
−0.852407 | + | 0.522878i | \(0.824858\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | − 86.3625i | − 3.15984i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −41.3253 | −1.50999 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −24.9716 | −0.911227 | −0.455613 | − | 0.890178i | \(-0.650580\pi\) | ||||
−0.455613 | + | 0.890178i | \(0.650580\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | − 17.7065i | − 0.645263i | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − 12.8717i | − 0.467831i | −0.972257 | − | 0.233916i | \(-0.924846\pi\) | ||||
0.972257 | − | 0.233916i | \(-0.0751540\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 2.03717 | 0.0739445 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −26.6791 | −0.967115 | −0.483558 | − | 0.875313i | \(-0.660656\pi\) | ||||
−0.483558 | + | 0.875313i | \(0.660656\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 31.0999i | 1.12589i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 36.3753i | 1.31343i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −29.7541 | −1.07296 | −0.536479 | − | 0.843913i | \(-0.680246\pi\) | ||||
−0.536479 | + | 0.843913i | \(0.680246\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 55.3676 | 1.99401 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − 50.5655i | − 1.81872i | −0.416015 | − | 0.909358i | \(-0.636574\pi\) | ||||
0.416015 | − | 0.909358i | \(-0.363426\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | − 55.4553i | − 1.98945i | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 9.48108 | 0.339695 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −7.16519 | −0.256391 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 10.1230i | 0.361765i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − 54.8530i | − 1.95530i | −0.210242 | − | 0.977649i | \(-0.567425\pi\) | ||||
0.210242 | − | 0.977649i | \(-0.432575\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 1.32094 | 0.0470269 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 24.0422 | 0.854843 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − 4.83481i | − 0.171689i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 30.3434i | 1.07482i | 0.843322 | + | 0.537409i | \(0.180597\pi\) | ||||
−0.843322 | + | 0.537409i | \(0.819403\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −17.6412 | −0.624101 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 84.6456 | 2.99081 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − 0.617041i | − 0.0217749i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 69.4399i | 2.44440i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 11.0801 | 0.389554 | 0.194777 | − | 0.980848i | \(-0.437602\pi\) | ||||
0.194777 | + | 0.980848i | \(0.437602\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 39.3625 | 1.38220 | 0.691102 | − | 0.722757i | \(-0.257126\pi\) | ||||
0.691102 | + | 0.722757i | \(0.257126\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − 37.1575i | − 1.30317i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0.824458i | 0.0288441i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 41.0044 | 1.43281 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 34.8493 | 1.21625 | 0.608125 | − | 0.793842i | \(-0.291922\pi\) | ||||
0.608125 | + | 0.793842i | \(0.291922\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 22.7615i | 0.793417i | 0.917945 | + | 0.396709i | \(0.129848\pi\) | ||||
−0.917945 | + | 0.396709i | \(0.870152\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 32.7615i | 1.13923i | 0.821912 | + | 0.569615i | \(0.192908\pi\) | ||||
−0.821912 | + | 0.569615i | \(0.807092\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −36.4905 | −1.26737 | −0.633684 | − | 0.773592i | \(-0.718458\pi\) | ||||
−0.633684 | + | 0.773592i | \(0.718458\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 24.1652 | 0.838281 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − 4.31324i | − 0.149445i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 56.9518i | 1.96854i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −47.4949 | −1.63971 | −0.819853 | − | 0.572574i | \(-0.805945\pi\) | ||||
−0.819853 | + | 0.572574i | \(0.805945\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −27.0372 | −0.932316 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 26.7866i | 0.922580i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − 30.9897i | − 1.06482i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 57.8865 | 1.98666 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 7.63615 | 0.261764 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − 1.86736i | − 0.0639372i | −0.999489 | − | 0.0319686i | \(-0.989822\pi\) | ||||
0.999489 | − | 0.0319686i | \(-0.0101776\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 16.3608i | 0.558873i | 0.960164 | + | 0.279436i | \(0.0901476\pi\) | ||||
−0.960164 | + | 0.279436i | \(0.909852\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 21.0851 | 0.719415 | 0.359708 | − | 0.933065i | \(-0.382876\pi\) | ||||
0.359708 | + | 0.933065i | \(0.382876\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 80.4098 | 2.74036 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − 25.6868i | − 0.874387i | −0.899367 | − | 0.437194i | \(-0.855972\pi\) | ||||
0.899367 | − | 0.437194i | \(-0.144028\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | − 24.8091i | − 0.842560i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 9.20236 | 0.312169 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −13.1274 | −0.444803 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | − 42.2402i | − 1.42961i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − 43.2978i | − 1.46206i | −0.682343 | − | 0.731032i | \(-0.739039\pi\) | ||||
0.682343 | − | 0.731032i | \(-0.260961\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 23.7213 | 0.800099 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 22.0750 | 0.743726 | 0.371863 | − | 0.928288i | \(-0.378719\pi\) | ||||
0.371863 | + | 0.928288i | \(0.378719\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 0.385604i | 0.0129766i | 0.999979 | + | 0.00648831i | \(0.00206531\pi\) | ||||
−0.999979 | + | 0.00648831i | \(0.997935\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − 54.9210i | − 1.84407i | −0.387111 | − | 0.922033i | \(-0.626527\pi\) | ||||
0.387111 | − | 0.922033i | \(-0.373473\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 35.3253 | 1.18477 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 2.75474 | 0.0922873 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 6.05763i | 0.202711i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 8.73669i | 0.291710i | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 11.0429 | 0.368301 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −2.40101 | −0.0799893 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 6.99230i | 0.232689i | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 41.4727i | 1.37708i | 0.725199 | + | 0.688539i | \(0.241748\pi\) | ||||
−0.725199 | + | 0.688539i | \(0.758252\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −24.1223 | −0.800086 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 41.8909 | 1.38791 | 0.693953 | − | 0.720020i | \(-0.255868\pi\) | ||||
0.693953 | + | 0.720020i | \(0.255868\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 9.43795i | 0.312350i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 15.9622i | 0.527117i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 36.0044 | 1.18767 | 0.593837 | − | 0.804585i | \(-0.297612\pi\) | ||||
0.593837 | + | 0.804585i | \(0.297612\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 31.3253 | 1.03220 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − 30.7290i | − 1.01146i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 95.1689i | 3.12576i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −59.4898 | −1.95180 | −0.975899 | − | 0.218222i | \(-0.929974\pi\) | ||||
−0.975899 | + | 0.218222i | \(0.929974\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1.48108 | −0.0485404 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 89.8255i | 2.94076i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − 35.7143i | − 1.16673i | −0.812209 | − | 0.583367i | \(-0.801735\pi\) | ||||
0.812209 | − | 0.583367i | \(-0.198265\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −19.0422 | −0.621420 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 20.2074 | 0.658743 | 0.329371 | − | 0.944200i | \(-0.393163\pi\) | ||||
0.329371 | + | 0.944200i | \(0.393163\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 11.0724i | 0.360566i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 51.4982i | 1.67347i | 0.547610 | + | 0.836734i | \(0.315538\pi\) | ||||
−0.547610 | + | 0.836734i | \(0.684462\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 2.64627 | 0.0859016 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 32.9243 | 1.06764 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − 7.95272i | − 0.257614i | −0.991670 | − | 0.128807i | \(-0.958885\pi\) | ||||
0.991670 | − | 0.128807i | \(-0.0411147\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | − 2.44391i | − 0.0790005i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −22.1223 | −0.714366 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 31.1274 | 1.00411 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | − 77.7780i | − 2.50636i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 32.5706i | 1.04740i | 0.851903 | + | 0.523700i | \(0.175449\pi\) | ||||
−0.851903 | + | 0.523700i | \(0.824551\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 8.48108 | 0.272452 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 21.0378 | 0.675136 | 0.337568 | − | 0.941301i | \(-0.390396\pi\) | ||||
0.337568 | + | 0.941301i | \(0.390396\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − 20.8520i | − 0.668483i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 46.9648i | 1.50254i | 0.659997 | + | 0.751269i | \(0.270558\pi\) | ||||
−0.659997 | + | 0.751269i | \(0.729442\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −9.25032 | −0.295641 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −58.5327 | −1.86881 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 18.5182i | 0.590640i | 0.955398 | + | 0.295320i | \(0.0954263\pi\) | ||||
−0.955398 | + | 0.295320i | \(0.904574\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 51.3753i | 1.63529i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −0.962834 | −0.0306163 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −5.40539 | −0.171708 | −0.0858540 | − | 0.996308i | \(-0.527362\pi\) | ||||
−0.0858540 | + | 0.996308i | \(0.527362\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | − 66.4175i | − 2.10770i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 8.55676i | 0.270995i | 0.990778 | + | 0.135498i | \(0.0432633\pi\) | ||||
−0.990778 | + | 0.135498i | \(0.956737\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 47.2453 | 1.49477 |
(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 | 1900.2.c.g.1749.1 | 6 | ||
5.2 | odd | 4 | 1900.2.a.f.1.1 | ✓ | 3 | ||
5.3 | odd | 4 | 1900.2.a.h.1.3 | yes | 3 | ||
5.4 | even | 2 | inner | 1900.2.c.g.1749.6 | 6 | ||
20.3 | even | 4 | 7600.2.a.bj.1.1 | 3 | |||
20.7 | even | 4 | 7600.2.a.by.1.3 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1900.2.a.f.1.1 | ✓ | 3 | 5.2 | odd | 4 | ||
1900.2.a.h.1.3 | yes | 3 | 5.3 | odd | 4 | ||
1900.2.c.g.1749.1 | 6 | 1.1 | even | 1 | trivial | ||
1900.2.c.g.1749.6 | 6 | 5.4 | even | 2 | inner | ||
7600.2.a.bj.1.1 | 3 | 20.3 | even | 4 | |||
7600.2.a.by.1.3 | 3 | 20.7 | even | 4 |