Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1140,2,Mod(1,1140)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1140, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1140.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1140 = 2^{2} \cdot 3 \cdot 5 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1140.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: | \(9.10294583043\) |
Analytic rank: | \(0\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.1524.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 7x + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(3.13264\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1140.1 |
$q$-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 | ||||||||
\(7\) | −4.81342 | −1.81930 | −0.909650 | − | 0.415375i | \(-0.863650\pi\) | ||||
−0.909650 | + | 0.415375i | \(0.863650\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.45186 | −0.437751 | −0.218876 | − | 0.975753i | \(-0.570239\pi\) | ||||
−0.218876 | + | 0.975753i | \(0.570239\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.81342 | −0.780302 | −0.390151 | − | 0.920751i | \(-0.627577\pi\) | ||||
−0.390151 | + | 0.920751i | \(0.627577\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.00000 | −0.258199 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 6.26527 | 1.51955 | 0.759776 | − | 0.650185i | \(-0.225308\pi\) | ||||
0.759776 | + | 0.650185i | \(0.225308\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.00000 | 0.229416 | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 4.81342 | 1.05037 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 6.26527 | 1.30640 | 0.653200 | − | 0.757185i | \(-0.273426\pi\) | ||||
0.653200 | + | 0.757185i | \(0.273426\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0.548143 | 0.101788 | 0.0508938 | − | 0.998704i | \(-0.483793\pi\) | ||||
0.0508938 | + | 0.998704i | \(0.483793\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 8.26527 | 1.48449 | 0.742244 | − | 0.670130i | \(-0.233762\pi\) | ||||
0.742244 | + | 0.670130i | \(0.233762\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 1.45186 | 0.252736 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −4.81342 | −0.813616 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 6.81342 | 1.12012 | 0.560059 | − | 0.828452i | \(-0.310778\pi\) | ||||
0.560059 | + | 0.828452i | \(0.310778\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 2.81342 | 0.450507 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 4.54814 | 0.710301 | 0.355150 | − | 0.934809i | \(-0.384430\pi\) | ||||
0.355150 | + | 0.934809i | \(0.384430\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −7.71713 | −1.17685 | −0.588426 | − | 0.808551i | \(-0.700252\pi\) | ||||
−0.588426 | + | 0.808551i | \(0.700252\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 1.00000 | 0.149071 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −10.2653 | −1.49734 | −0.748672 | − | 0.662940i | \(-0.769308\pi\) | ||||
−0.748672 | + | 0.662940i | \(0.769308\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 16.1690 | 2.30986 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −6.26527 | −0.877314 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −0.265275 | −0.0364383 | −0.0182192 | − | 0.999834i | \(-0.505800\pi\) | ||||
−0.0182192 | + | 0.999834i | \(0.505800\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −1.45186 | −0.195768 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −1.00000 | −0.132453 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 2.90371 | 0.378031 | 0.189016 | − | 0.981974i | \(-0.439470\pi\) | ||||
0.189016 | + | 0.981974i | \(0.439470\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 11.3616 | 1.45470 | 0.727349 | − | 0.686267i | \(-0.240752\pi\) | ||||
0.727349 | + | 0.686267i | \(0.240752\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −4.81342 | −0.606434 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −2.81342 | −0.348962 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −6.26527 | −0.754250 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 6.90371 | 0.819320 | 0.409660 | − | 0.912238i | \(-0.365647\pi\) | ||||
0.409660 | + | 0.912238i | \(0.365647\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −6.53055 | −0.764343 | −0.382172 | − | 0.924091i | \(-0.624824\pi\) | ||||
−0.382172 | + | 0.924091i | \(0.624824\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −1.00000 | −0.115470 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 6.98840 | 0.796402 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 10.7231 | 1.20645 | 0.603223 | − | 0.797573i | \(-0.293883\pi\) | ||||
0.603223 | + | 0.797573i | \(0.293883\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 9.16899 | 1.00643 | 0.503214 | − | 0.864162i | \(-0.332151\pi\) | ||||
0.503214 | + | 0.864162i | \(0.332151\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 6.26527 | 0.679564 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −0.548143 | −0.0587671 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −18.7055 | −1.98278 | −0.991391 | − | 0.130935i | \(-0.958202\pi\) | ||||
−0.991391 | + | 0.130935i | \(0.958202\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 13.5422 | 1.41960 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −8.26527 | −0.857069 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 1.00000 | 0.102598 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −6.81342 | −0.691798 | −0.345899 | − | 0.938272i | \(-0.612426\pi\) | ||||
−0.345899 | + | 0.938272i | \(0.612426\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −1.45186 | −0.145917 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 17.4343 | 1.73477 | 0.867387 | − | 0.497634i | \(-0.165798\pi\) | ||||
0.867387 | + | 0.497634i | \(0.165798\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 16.5305 | 1.62880 | 0.814402 | − | 0.580301i | \(-0.197065\pi\) | ||||
0.814402 | + | 0.580301i | \(0.197065\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 4.81342 | 0.469741 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −16.0000 | −1.54678 | −0.773389 | − | 0.633932i | \(-0.781440\pi\) | ||||
−0.773389 | + | 0.633932i | \(0.781440\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 3.09629 | 0.296570 | 0.148285 | − | 0.988945i | \(-0.452625\pi\) | ||||
0.148285 | + | 0.988945i | \(0.452625\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −6.81342 | −0.646701 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 13.3616 | 1.25695 | 0.628475 | − | 0.777830i | \(-0.283679\pi\) | ||||
0.628475 | + | 0.777830i | \(0.283679\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 6.26527 | 0.584240 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −2.81342 | −0.260101 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −30.1574 | −2.76452 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −8.89211 | −0.808374 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −4.54814 | −0.410092 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 4.00000 | 0.354943 | 0.177471 | − | 0.984126i | \(-0.443208\pi\) | ||||
0.177471 | + | 0.984126i | \(0.443208\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 7.71713 | 0.679456 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −4.35557 | −0.380548 | −0.190274 | − | 0.981731i | \(-0.560938\pi\) | ||||
−0.190274 | + | 0.981731i | \(0.560938\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −4.81342 | −0.417376 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −1.00000 | −0.0860663 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −6.00000 | −0.512615 | −0.256307 | − | 0.966595i | \(-0.582506\pi\) | ||||
−0.256307 | + | 0.966595i | \(0.582506\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −2.90371 | −0.246290 | −0.123145 | − | 0.992389i | \(-0.539298\pi\) | ||||
−0.123145 | + | 0.992389i | \(0.539298\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 10.2653 | 0.864492 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 4.08468 | 0.341578 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0.548143 | 0.0455208 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −16.1690 | −1.33360 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 6.53055 | 0.535003 | 0.267502 | − | 0.963557i | \(-0.413802\pi\) | ||||
0.267502 | + | 0.963557i | \(0.413802\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 18.9884 | 1.54525 | 0.772627 | − | 0.634860i | \(-0.218942\pi\) | ||||
0.772627 | + | 0.634860i | \(0.218942\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 6.26527 | 0.506517 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 8.26527 | 0.663883 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 16.1574 | 1.28950 | 0.644750 | − | 0.764394i | \(-0.276962\pi\) | ||||
0.644750 | + | 0.764394i | \(0.276962\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0.265275 | 0.0210377 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −30.1574 | −2.37673 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 10.4403 | 0.817744 | 0.408872 | − | 0.912592i | \(-0.365922\pi\) | ||||
0.408872 | + | 0.912592i | \(0.365922\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 1.45186 | 0.113027 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −13.8921 | −1.07500 | −0.537502 | − | 0.843263i | \(-0.680632\pi\) | ||||
−0.537502 | + | 0.843263i | \(0.680632\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −5.08468 | −0.391129 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1.00000 | 0.0764719 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −2.63844 | −0.200597 | −0.100298 | − | 0.994957i | \(-0.531980\pi\) | ||||
−0.100298 | + | 0.994957i | \(0.531980\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −4.81342 | −0.363860 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −2.90371 | −0.218257 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −2.37316 | −0.177379 | −0.0886893 | − | 0.996059i | \(-0.528268\pi\) | ||||
−0.0886893 | + | 0.996059i | \(0.528268\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 0.373165 | 0.0277371 | 0.0138686 | − | 0.999904i | \(-0.495585\pi\) | ||||
0.0138686 | + | 0.999904i | \(0.495585\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −11.3616 | −0.839871 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 6.81342 | 0.500932 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −9.09629 | −0.665186 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 4.81342 | 0.350125 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 4.17498 | 0.302091 | 0.151045 | − | 0.988527i | \(-0.451736\pi\) | ||||
0.151045 | + | 0.988527i | \(0.451736\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 15.3440 | 1.10448 | 0.552241 | − | 0.833684i | \(-0.313773\pi\) | ||||
0.552241 | + | 0.833684i | \(0.313773\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 2.81342 | 0.201473 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −22.2653 | −1.58634 | −0.793168 | − | 0.609003i | \(-0.791570\pi\) | ||||
−0.793168 | + | 0.609003i | \(0.791570\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 6.15739 | 0.436485 | 0.218243 | − | 0.975895i | \(-0.429968\pi\) | ||||
0.218243 | + | 0.975895i | \(0.429968\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −2.63844 | −0.185182 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 4.54814 | 0.317656 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 6.26527 | 0.435467 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −1.45186 | −0.100427 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −23.7842 | −1.63737 | −0.818687 | − | 0.574241i | \(-0.805297\pi\) | ||||
−0.818687 | + | 0.574241i | \(0.805297\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −6.90371 | −0.473035 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −7.71713 | −0.526304 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −39.7842 | −2.70073 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 6.53055 | 0.441294 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −17.6268 | −1.18571 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 16.5305 | 1.10697 | 0.553484 | − | 0.832860i | \(-0.313298\pi\) | ||||
0.553484 | + | 0.832860i | \(0.313298\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1.00000 | 0.0666667 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −20.0847 | −1.33307 | −0.666534 | − | 0.745475i | \(-0.732223\pi\) | ||||
−0.666534 | + | 0.745475i | \(0.732223\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −27.8921 | −1.84316 | −0.921581 | − | 0.388185i | \(-0.873102\pi\) | ||||
−0.921581 | + | 0.388185i | \(0.873102\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −6.98840 | −0.459803 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 20.3380 | 1.33239 | 0.666193 | − | 0.745780i | \(-0.267923\pi\) | ||||
0.666193 | + | 0.745780i | \(0.267923\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −10.2653 | −0.669633 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −10.7231 | −0.696542 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −0.921307 | −0.0595944 | −0.0297972 | − | 0.999556i | \(-0.509486\pi\) | ||||
−0.0297972 | + | 0.999556i | \(0.509486\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −2.00000 | −0.128831 | −0.0644157 | − | 0.997923i | \(-0.520518\pi\) | ||||
−0.0644157 | + | 0.997923i | \(0.520518\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 16.1690 | 1.03300 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −2.81342 | −0.179013 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −9.16899 | −0.581061 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 15.6092 | 0.985247 | 0.492623 | − | 0.870243i | \(-0.336038\pi\) | ||||
0.492623 | + | 0.870243i | \(0.336038\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −9.09629 | −0.571879 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −6.26527 | −0.392347 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 7.16899 | 0.447189 | 0.223595 | − | 0.974682i | \(-0.428221\pi\) | ||||
0.223595 | + | 0.974682i | \(0.428221\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −32.7958 | −2.03783 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0.548143 | 0.0339292 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −24.4227 | −1.50597 | −0.752983 | − | 0.658040i | \(-0.771386\pi\) | ||||
−0.752983 | + | 0.658040i | \(0.771386\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −0.265275 | −0.0162957 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 18.7055 | 1.14476 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −10.1750 | −0.620379 | −0.310190 | − | 0.950675i | \(-0.600393\pi\) | ||||
−0.310190 | + | 0.950675i | \(0.600393\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 2.37316 | 0.144159 | 0.0720797 | − | 0.997399i | \(-0.477036\pi\) | ||||
0.0720797 | + | 0.997399i | \(0.477036\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −13.5422 | −0.819608 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −1.45186 | −0.0875503 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −16.3380 | −0.981654 | −0.490827 | − | 0.871257i | \(-0.663305\pi\) | ||||
−0.490827 | + | 0.871257i | \(0.663305\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 8.26527 | 0.494829 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 5.64443 | 0.336718 | 0.168359 | − | 0.985726i | \(-0.446153\pi\) | ||||
0.168359 | + | 0.985726i | \(0.446153\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −21.3440 | −1.26877 | −0.634384 | − | 0.773018i | \(-0.718746\pi\) | ||||
−0.634384 | + | 0.773018i | \(0.718746\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −1.00000 | −0.0592349 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −21.8921 | −1.29225 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 22.2537 | 1.30904 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 6.81342 | 0.399410 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 10.6384 | 0.621504 | 0.310752 | − | 0.950491i | \(-0.399419\pi\) | ||||
0.310752 | + | 0.950491i | \(0.399419\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 2.90371 | 0.169061 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 1.45186 | 0.0842453 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −17.6268 | −1.01939 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 37.1458 | 2.14105 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −17.4343 | −1.00157 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 11.3616 | 0.650561 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 22.1574 | 1.26459 | 0.632294 | − | 0.774728i | \(-0.282113\pi\) | ||||
0.632294 | + | 0.774728i | \(0.282113\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −16.5305 | −0.940390 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 4.17498 | 0.236741 | 0.118371 | − | 0.992969i | \(-0.462233\pi\) | ||||
0.118371 | + | 0.992969i | \(0.462233\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −12.3732 | −0.699373 | −0.349686 | − | 0.936867i | \(-0.613712\pi\) | ||||
−0.349686 | + | 0.936867i | \(0.613712\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −4.81342 | −0.271205 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −3.73473 | −0.209763 | −0.104882 | − | 0.994485i | \(-0.533446\pi\) | ||||
−0.104882 | + | 0.994485i | \(0.533446\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −0.795825 | −0.0445576 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 16.0000 | 0.893033 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 6.26527 | 0.348609 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −2.81342 | −0.156060 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −3.09629 | −0.171225 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 49.4111 | 2.72412 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 14.9884 | 0.823837 | 0.411918 | − | 0.911221i | \(-0.364859\pi\) | ||||
0.411918 | + | 0.911221i | \(0.364859\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 6.81342 | 0.373373 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 32.9708 | 1.79603 | 0.898017 | − | 0.439961i | \(-0.145008\pi\) | ||||
0.898017 | + | 0.439961i | \(0.145008\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −13.3616 | −0.725700 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −12.0000 | −0.649836 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −44.1342 | −2.38302 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −6.26527 | −0.337311 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 35.1458 | 1.88672 | 0.943362 | − | 0.331765i | \(-0.107644\pi\) | ||||
0.943362 | + | 0.331765i | \(0.107644\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −4.19257 | −0.224423 | −0.112212 | − | 0.993684i | \(-0.535793\pi\) | ||||
−0.112212 | + | 0.993684i | \(0.535793\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 2.81342 | 0.150169 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −3.80743 | −0.202649 | −0.101325 | − | 0.994853i | \(-0.532308\pi\) | ||||
−0.101325 | + | 0.994853i | \(0.532308\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 6.90371 | 0.366411 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 30.1574 | 1.59610 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −1.27126 | −0.0670947 | −0.0335474 | − | 0.999437i | \(-0.510680\pi\) | ||||
−0.0335474 | + | 0.999437i | \(0.510680\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 8.89211 | 0.466715 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −6.53055 | −0.341825 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 10.0903 | 0.526709 | 0.263355 | − | 0.964699i | \(-0.415171\pi\) | ||||
0.263355 | + | 0.964699i | \(0.415171\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 4.54814 | 0.236767 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 1.27688 | 0.0662923 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −14.2829 | −0.739539 | −0.369769 | − | 0.929124i | \(-0.620563\pi\) | ||||
−0.369769 | + | 0.929124i | \(0.620563\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −1.00000 | −0.0516398 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −1.54215 | −0.0794250 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 20.7958 | 1.06821 | 0.534105 | − | 0.845418i | \(-0.320649\pi\) | ||||
0.534105 | + | 0.845418i | \(0.320649\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −4.00000 | −0.204926 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 3.46945 | 0.177281 | 0.0886403 | − | 0.996064i | \(-0.471748\pi\) | ||||
0.0886403 | + | 0.996064i | \(0.471748\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 6.98840 | 0.356162 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −7.71713 | −0.392284 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 8.72312 | 0.442280 | 0.221140 | − | 0.975242i | \(-0.429022\pi\) | ||||
0.221140 | + | 0.975242i | \(0.429022\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 39.2537 | 1.98514 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 4.35557 | 0.219710 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 10.7231 | 0.539539 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 19.4462 | 0.975979 | 0.487989 | − | 0.872850i | \(-0.337730\pi\) | ||||
0.487989 | + | 0.872850i | \(0.337730\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 4.81342 | 0.240972 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 27.9824 | 1.39737 | 0.698687 | − | 0.715427i | \(-0.253768\pi\) | ||||
0.698687 | + | 0.715427i | \(0.253768\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −23.2537 | −1.15835 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 1.00000 | 0.0496904 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −9.89211 | −0.490334 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −25.9648 | −1.28388 | −0.641939 | − | 0.766756i | \(-0.721870\pi\) | ||||
−0.641939 | + | 0.766756i | \(0.721870\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 6.00000 | 0.295958 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −13.9768 | −0.687753 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 9.16899 | 0.450088 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 2.90371 | 0.142196 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −28.7055 | −1.40236 | −0.701178 | − | 0.712986i | \(-0.747342\pi\) | ||||
−0.701178 | + | 0.712986i | \(0.747342\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 10.0000 | 0.487370 | 0.243685 | − | 0.969854i | \(-0.421644\pi\) | ||||
0.243685 | + | 0.969854i | \(0.421644\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −10.2653 | −0.499115 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 6.26527 | 0.303910 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −54.6879 | −2.64653 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −4.08468 | −0.197210 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 22.6879 | 1.09284 | 0.546420 | − | 0.837512i | \(-0.315990\pi\) | ||||
0.546420 | + | 0.837512i | \(0.315990\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 31.3440 | 1.50629 | 0.753147 | − | 0.657852i | \(-0.228535\pi\) | ||||
0.753147 | + | 0.657852i | \(0.228535\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −0.548143 | −0.0262814 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 6.26527 | 0.299709 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −10.1926 | −0.486465 | −0.243232 | − | 0.969968i | \(-0.578208\pi\) | ||||
−0.243232 | + | 0.969968i | \(0.578208\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 16.1690 | 0.769952 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −13.5189 | −0.642304 | −0.321152 | − | 0.947028i | \(-0.604070\pi\) | ||||
−0.321152 | + | 0.947028i | \(0.604070\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −18.7055 | −0.886727 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −6.53055 | −0.308884 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −15.9824 | −0.754256 | −0.377128 | − | 0.926161i | \(-0.623088\pi\) | ||||
−0.377128 | + | 0.926161i | \(0.623088\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −6.60325 | −0.310935 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −18.9884 | −0.892153 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 13.5422 | 0.634866 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −23.0963 | −1.08040 | −0.540199 | − | 0.841537i | \(-0.681651\pi\) | ||||
−0.540199 | + | 0.841537i | \(0.681651\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −6.26527 | −0.292438 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −29.2537 | −1.36248 | −0.681240 | − | 0.732060i | \(-0.738559\pi\) | ||||
−0.681240 | + | 0.732060i | \(0.738559\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 15.5365 | 0.722044 | 0.361022 | − | 0.932557i | \(-0.382428\pi\) | ||||
0.361022 | + | 0.932557i | \(0.382428\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −8.26527 | −0.383293 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −11.5422 | −0.534107 | −0.267054 | − | 0.963682i | \(-0.586050\pi\) | ||||
−0.267054 | + | 0.963682i | \(0.586050\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −16.1574 | −0.744493 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 11.2042 | 0.515169 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1.00000 | 0.0458831 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −0.265275 | −0.0121461 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −16.3556 | −0.747305 | −0.373653 | − | 0.927569i | \(-0.621895\pi\) | ||||
−0.373653 | + | 0.927569i | \(0.621895\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −19.1690 | −0.874031 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 30.1574 | 1.37221 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −6.81342 | −0.309381 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 41.4111 | 1.87651 | 0.938257 | − | 0.345939i | \(-0.112440\pi\) | ||||
0.938257 | + | 0.345939i | \(0.112440\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −10.4403 | −0.472125 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −11.0787 | −0.499974 | −0.249987 | − | 0.968249i | \(-0.580426\pi\) | ||||
−0.249987 | + | 0.968249i | \(0.580426\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 3.43426 | 0.154671 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −1.45186 | −0.0652561 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −33.2305 | −1.49059 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −16.3500 | −0.731925 | −0.365962 | − | 0.930630i | \(-0.619260\pi\) | ||||
−0.365962 | + | 0.930630i | \(0.619260\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 13.8921 | 0.620654 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 11.8921 | 0.530243 | 0.265121 | − | 0.964215i | \(-0.414588\pi\) | ||||
0.265121 | + | 0.964215i | \(0.414588\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 17.4343 | 0.775815 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 5.08468 | 0.225819 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 32.8981 | 1.45818 | 0.729091 | − | 0.684416i | \(-0.239943\pi\) | ||||
0.729091 | + | 0.684416i | \(0.239943\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 31.4343 | 1.39057 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −1.00000 | −0.0441511 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 16.5305 | 0.728423 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 14.9037 | 0.655465 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 2.63844 | 0.115815 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −25.0787 | −1.09872 | −0.549359 | − | 0.835587i | \(-0.685128\pi\) | ||||
−0.549359 | + | 0.835587i | \(0.685128\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 23.9648 | 1.04791 | 0.523954 | − | 0.851747i | \(-0.324456\pi\) | ||||
0.523954 | + | 0.851747i | \(0.324456\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 4.81342 | 0.210075 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 51.7842 | 2.25576 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 16.2537 | 0.706681 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 2.90371 | 0.126010 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −12.7958 | −0.554249 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −16.0000 | −0.691740 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 2.37316 | 0.102410 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −23.4751 | −1.01114 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 11.0611 | 0.475554 | 0.237777 | − | 0.971320i | \(-0.423581\pi\) | ||||
0.237777 | + | 0.971320i | \(0.423581\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −0.373165 | −0.0160140 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 3.09629 | 0.132630 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 21.0963 | 0.902012 | 0.451006 | − | 0.892521i | \(-0.351065\pi\) | ||||
0.451006 | + | 0.892521i | \(0.351065\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 11.3616 | 0.484900 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0.548143 | 0.0233517 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −51.6149 | −2.19489 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −6.81342 | −0.289213 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −39.5916 | −1.67755 | −0.838776 | − | 0.544477i | \(-0.816728\pi\) | ||||
−0.838776 | + | 0.544477i | \(0.816728\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 21.7115 | 0.918299 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 9.09629 | 0.384045 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −28.0847 | −1.18363 | −0.591814 | − | 0.806074i | \(-0.701588\pi\) | ||||
−0.591814 | + | 0.806074i | \(0.701588\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 13.3616 | 0.562125 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −4.81342 | −0.202145 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 41.0787 | 1.72211 | 0.861054 | − | 0.508513i | \(-0.169805\pi\) | ||||
0.861054 | + | 0.508513i | \(0.169805\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −11.8194 | −0.494627 | −0.247313 | − | 0.968936i | \(-0.579548\pi\) | ||||
−0.247313 | + | 0.968936i | \(0.579548\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −4.17498 | −0.174412 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 6.26527 | 0.261280 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −29.4343 | −1.22536 | −0.612682 | − | 0.790329i | \(-0.709909\pi\) | ||||
−0.612682 | + | 0.790329i | \(0.709909\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −15.3440 | −0.637674 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −44.1342 | −1.83099 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0.385141 | 0.0159509 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −2.81342 | −0.116321 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 31.7115 | 1.30887 | 0.654437 | − | 0.756116i | \(-0.272906\pi\) | ||||
0.654437 | + | 0.756116i | \(0.272906\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 8.26527 | 0.340565 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 22.2653 | 0.915871 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 14.5305 | 0.596698 | 0.298349 | − | 0.954457i | \(-0.403564\pi\) | ||||
0.298349 | + | 0.954457i | \(0.403564\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −30.1574 | −1.23633 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −6.15739 | −0.252005 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 17.8074 | 0.727592 | 0.363796 | − | 0.931479i | \(-0.381481\pi\) | ||||
0.363796 | + | 0.931479i | \(0.381481\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 20.6879 | 0.843878 | 0.421939 | − | 0.906624i | \(-0.361350\pi\) | ||||
0.421939 | + | 0.906624i | \(0.361350\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −8.89211 | −0.361516 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −17.2417 | −0.699819 | −0.349909 | − | 0.936784i | \(-0.613788\pi\) | ||||
−0.349909 | + | 0.936784i | \(0.613788\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 2.63844 | 0.106915 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 28.8805 | 1.16838 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −3.62684 | −0.146486 | −0.0732432 | − | 0.997314i | \(-0.523335\pi\) | ||||
−0.0732432 | + | 0.997314i | \(0.523335\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −4.54814 | −0.183399 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 23.3264 | 0.939084 | 0.469542 | − | 0.882910i | \(-0.344419\pi\) | ||||
0.469542 | + | 0.882910i | \(0.344419\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −24.8805 | −1.00003 | −0.500016 | − | 0.866016i | \(-0.666673\pi\) | ||||
−0.500016 | + | 0.866016i | \(0.666673\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −6.26527 | −0.251417 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 90.0375 | 3.60728 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 1.45186 | 0.0579816 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 42.6879 | 1.70208 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −36.3148 | −1.44567 | −0.722834 | − | 0.691022i | \(-0.757161\pi\) | ||||
−0.722834 | + | 0.691022i | \(0.757161\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 23.7842 | 0.945338 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 4.00000 | 0.158735 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −45.4901 | −1.80238 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 6.90371 | 0.273107 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 14.3556 | 0.567011 | 0.283506 | − | 0.958971i | \(-0.408503\pi\) | ||||
0.283506 | + | 0.958971i | \(0.408503\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 37.1634 | 1.46558 | 0.732790 | − | 0.680455i | \(-0.238218\pi\) | ||||
0.732790 | + | 0.680455i | \(0.238218\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 7.71713 | 0.303862 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 40.9532 | 1.61004 | 0.805018 | − | 0.593250i | \(-0.202155\pi\) | ||||
0.805018 | + | 0.593250i | \(0.202155\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −4.21578 | −0.165484 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 39.7842 | 1.55927 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −18.7958 | −0.735537 | −0.367769 | − | 0.929917i | \(-0.619878\pi\) | ||||
−0.367769 | + | 0.929917i | \(0.619878\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −4.35557 | −0.170186 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −6.53055 | −0.254781 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 8.53055 | 0.332303 | 0.166152 | − | 0.986100i | \(-0.446866\pi\) | ||||
0.166152 | + | 0.986100i | \(0.446866\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 13.4343 | 0.522532 | 0.261266 | − | 0.965267i | \(-0.415860\pi\) | ||||
0.261266 | + | 0.965267i | \(0.415860\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 17.6268 | 0.684570 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −4.81342 | −0.186656 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 3.43426 | 0.132975 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −16.5305 | −0.639108 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −16.4954 | −0.636796 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −6.81342 | −0.262638 | −0.131319 | − | 0.991340i | \(-0.541921\pi\) | ||||
−0.131319 | + | 0.991340i | \(0.541921\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −1.00000 | −0.0384900 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 47.3032 | 1.81801 | 0.909004 | − | 0.416787i | \(-0.136844\pi\) | ||||
0.909004 | + | 0.416787i | \(0.136844\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 32.7958 | 1.25859 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 20.0847 | 0.769647 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −11.2537 | −0.430610 | −0.215305 | − | 0.976547i | \(-0.569075\pi\) | ||||
−0.215305 | + | 0.976547i | \(0.569075\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −6.00000 | −0.229248 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 27.8921 | 1.06415 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 0.746329 | 0.0284329 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 9.62684 | 0.366222 | 0.183111 | − | 0.983092i | \(-0.441383\pi\) | ||||
0.183111 | + | 0.983092i | \(0.441383\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 6.98840 | 0.265467 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −2.90371 | −0.110144 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 28.4954 | 1.07934 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −20.3380 | −0.769253 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 16.7231 | 0.631624 | 0.315812 | − | 0.948822i | \(-0.397723\pi\) | ||||
0.315812 | + | 0.948822i | \(0.397723\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 6.81342 | 0.256973 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 10.2653 | 0.386613 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −83.9184 | −3.15608 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −32.9532 | −1.23758 | −0.618792 | − | 0.785555i | \(-0.712378\pi\) | ||||
−0.618792 | + | 0.785555i | \(0.712378\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 10.7231 | 0.402148 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 51.7842 | 1.93933 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 4.08468 | 0.152758 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0.921307 | 0.0344069 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −15.6444 | −0.583439 | −0.291719 | − | 0.956504i | \(-0.594227\pi\) | ||||
−0.291719 | + | 0.956504i | \(0.594227\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −79.5684 | −2.96328 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 2.00000 | 0.0743808 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0.548143 | 0.0203575 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 24.2829 | 0.900602 | 0.450301 | − | 0.892877i | \(-0.351317\pi\) | ||||
0.450301 | + | 0.892877i | \(0.351317\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −48.3500 | −1.78829 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −18.5305 | −0.684441 | −0.342221 | − | 0.939620i | \(-0.611179\pi\) | ||||
−0.342221 | + | 0.939620i | \(0.611179\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −16.1690 | −0.596402 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −9.44624 | −0.347486 | −0.173743 | − | 0.984791i | \(-0.555586\pi\) | ||||
−0.173743 | + | 0.984791i | \(0.555586\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 2.81342 | 0.103353 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 41.9768 | 1.53998 | 0.769990 | − | 0.638056i | \(-0.220261\pi\) | ||||
0.769990 | + | 0.638056i | \(0.220261\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 6.53055 | 0.239261 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 9.16899 | 0.335476 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 77.0147 | 2.81406 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 26.4578 | 0.965461 | 0.482730 | − | 0.875769i | \(-0.339645\pi\) | ||||
0.482730 | + | 0.875769i | \(0.339645\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −15.6092 | −0.568832 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 18.9884 | 0.691058 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 12.9037 | 0.468993 | 0.234497 | − | 0.972117i | \(-0.424656\pi\) | ||||
0.234497 | + | 0.972117i | \(0.424656\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 9.09629 | 0.330174 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −40.7231 | −1.47621 | −0.738106 | − | 0.674685i | \(-0.764280\pi\) | ||||
−0.738106 | + | 0.674685i | \(0.764280\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −14.9037 | −0.539551 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 6.26527 | 0.226521 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −8.16936 | −0.294979 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −5.25367 | −0.189452 | −0.0947261 | − | 0.995503i | \(-0.530198\pi\) | ||||
−0.0947261 | + | 0.995503i | \(0.530198\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −7.16899 | −0.258185 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −38.9884 | −1.40232 | −0.701158 | − | 0.713006i | \(-0.747333\pi\) | ||||
−0.701158 | + | 0.713006i | \(0.747333\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 8.26527 | 0.296897 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 32.7958 | 1.17654 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 4.54814 | 0.162954 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −10.0232 | −0.358659 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −0.548143 | −0.0195890 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 16.1574 | 0.576682 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −11.2889 | −0.402404 | −0.201202 | − | 0.979550i | \(-0.564485\pi\) | ||||
−0.201202 | + | 0.979550i | \(0.564485\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 24.4227 | 0.869470 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −64.3148 | −2.28677 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −31.9648 | −1.13510 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0.265275 | 0.00940833 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −27.6995 | −0.981168 | −0.490584 | − | 0.871394i | \(-0.663217\pi\) | ||||
−0.490584 | + | 0.871394i | \(0.663217\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −64.3148 | −2.27529 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −18.7055 | −0.660927 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 9.48143 | 0.334592 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −30.1574 | −1.06291 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 10.1750 | 0.358176 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −0.723121 | −0.0254236 | −0.0127118 | − | 0.999919i | \(-0.504046\pi\) | ||||
−0.0127118 | + | 0.999919i | \(0.504046\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −42.5073 | −1.49263 | −0.746317 | − | 0.665590i | \(-0.768180\pi\) | ||||
−0.746317 | + | 0.665590i | \(0.768180\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −2.37316 | −0.0832305 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 10.4403 | 0.365706 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −7.71713 | −0.269988 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 13.5422 | 0.473201 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −4.90371 | −0.171141 | −0.0855704 | − | 0.996332i | \(-0.527271\pi\) | ||||
−0.0855704 | + | 0.996332i | \(0.527271\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −1.37915 | −0.0480743 | −0.0240371 | − | 0.999711i | \(-0.507652\pi\) | ||||
−0.0240371 | + | 0.999711i | \(0.507652\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 1.45186 | 0.0505472 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −16.9764 | −0.590328 | −0.295164 | − | 0.955447i | \(-0.595374\pi\) | ||||
−0.295164 | + | 0.955447i | \(0.595374\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −13.4343 | −0.466591 | −0.233296 | − | 0.972406i | \(-0.574951\pi\) | ||||
−0.233296 | + | 0.972406i | \(0.574951\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 16.3380 | 0.566758 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 101.303 | 3.50995 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −13.8921 | −0.480756 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −8.26527 | −0.285690 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −43.2185 | −1.49207 | −0.746034 | − | 0.665908i | \(-0.768044\pi\) | ||||
−0.746034 | + | 0.665908i | \(0.768044\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −28.6995 | −0.989639 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −5.64443 | −0.194404 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −5.08468 | −0.174918 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 42.8014 | 1.47067 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 21.3440 | 0.732523 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 42.6879 | 1.46332 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −19.0963 | −0.653844 | −0.326922 | − | 0.945051i | \(-0.606012\pi\) | ||||
−0.326922 | + | 0.945051i | \(0.606012\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 1.00000 | 0.0341993 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −25.5422 | −0.872503 | −0.436252 | − | 0.899825i | \(-0.643694\pi\) | ||||
−0.436252 | + | 0.899825i | \(0.643694\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 51.3991 | 1.75371 | 0.876857 | − | 0.480751i | \(-0.159636\pi\) | ||||
0.876857 | + | 0.480751i | \(0.159636\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 21.8921 | 0.746081 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 44.0000 | 1.49778 | 0.748889 | − | 0.662696i | \(-0.230588\pi\) | ||||
0.748889 | + | 0.662696i | \(0.230588\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −2.63844 | −0.0897096 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −22.2537 | −0.755774 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −15.5684 | −0.528123 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −6.81342 | −0.230599 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −4.81342 | −0.162723 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −49.6819 | −1.67764 | −0.838820 | − | 0.544409i | \(-0.816754\pi\) | ||||
−0.838820 | + | 0.544409i | \(0.816754\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −10.6384 | −0.358826 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −21.2889 | −0.717240 | −0.358620 | − | 0.933484i | \(-0.616753\pi\) | ||||
−0.358620 | + | 0.933484i | \(0.616753\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −30.6208 | −1.03047 | −0.515237 | − | 0.857048i | \(-0.672296\pi\) | ||||
−0.515237 | + | 0.857048i | \(0.672296\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −2.90371 | −0.0976073 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −33.0611 | −1.11008 | −0.555042 | − | 0.831823i | \(-0.687298\pi\) | ||||
−0.555042 | + | 0.831823i | \(0.687298\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −19.2537 | −0.645747 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −1.45186 | −0.0486391 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −10.2653 | −0.343514 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −2.37316 | −0.0793261 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 17.6268 | 0.588543 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 4.53055 | 0.151102 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −1.66202 | −0.0553699 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −37.1458 | −1.23613 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0.373165 | 0.0124044 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 51.7490 | 1.71830 | 0.859149 | − | 0.511725i | \(-0.170993\pi\) | ||||
0.859149 | + | 0.511725i | \(0.170993\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 17.4343 | 0.578258 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 3.78422 | 0.125377 | 0.0626884 | − | 0.998033i | \(-0.480033\pi\) | ||||
0.0626884 | + | 0.998033i | \(0.480033\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −13.3121 | −0.440565 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −11.3616 | −0.375602 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 20.9652 | 0.692331 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −2.72312 | −0.0898275 | −0.0449137 | − | 0.998991i | \(-0.514301\pi\) | ||||
−0.0449137 | + | 0.998991i | \(0.514301\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −22.1574 | −0.730111 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −19.4230 | −0.639317 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 6.81342 | 0.224024 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 16.5305 | 0.542934 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 19.8426 | 0.651015 | 0.325508 | − | 0.945539i | \(-0.394465\pi\) | ||||
0.325508 | + | 0.945539i | \(0.394465\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 16.1690 | 0.529917 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −4.17498 | −0.136683 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −9.09629 | −0.297480 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −1.28886 | −0.0421051 | −0.0210525 | − | 0.999778i | \(-0.506702\pi\) | ||||
−0.0210525 | + | 0.999778i | \(0.506702\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 12.3732 | 0.403783 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −21.7898 | −0.710328 | −0.355164 | − | 0.934804i | \(-0.615575\pi\) | ||||
−0.355164 | + | 0.934804i | \(0.615575\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 28.4954 | 0.927937 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 4.81342 | 0.156580 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 12.6384 | 0.410694 | 0.205347 | − | 0.978689i | \(-0.434168\pi\) | ||||
0.205347 | + | 0.978689i | \(0.434168\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 18.3732 | 0.596418 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 3.73473 | 0.121107 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 29.6763 | 0.961311 | 0.480655 | − | 0.876910i | \(-0.340399\pi\) | ||||
0.480655 | + | 0.876910i | \(0.340399\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 4.17498 | 0.135099 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0.795825 | 0.0257254 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 28.8805 | 0.932600 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 37.3148 | 1.20370 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −16.0000 | −0.515593 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 15.3440 | 0.493940 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 10.2597 | 0.329928 | 0.164964 | − | 0.986300i | \(-0.447249\pi\) | ||||
0.164964 | + | 0.986300i | \(0.447249\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −6.26527 | −0.201270 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −49.5916 | −1.59147 | −0.795736 | − | 0.605644i | \(-0.792916\pi\) | ||||
−0.795736 | + | 0.605644i | \(0.792916\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 13.9768 | 0.448075 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 2.81342 | 0.0901015 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −9.71152 | −0.310699 | −0.155349 | − | 0.987860i | \(-0.549650\pi\) | ||||
−0.155349 | + | 0.987860i | \(0.549650\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 27.1578 | 0.867966 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 3.09629 | 0.0988568 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 4.83101 | 0.154085 | 0.0770427 | − | 0.997028i | \(-0.475452\pi\) | ||||
0.0770427 | + | 0.997028i | \(0.475452\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −22.2653 | −0.709431 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −49.4111 | −1.57277 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −48.3500 | −1.53744 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −10.1926 | −0.323778 | −0.161889 | − | 0.986809i | \(-0.551759\pi\) | ||||
−0.161889 | + | 0.986809i | \(0.551759\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −14.9884 | −0.475642 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 6.15739 | 0.195202 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −17.9648 | −0.568951 | −0.284476 | − | 0.958683i | \(-0.591820\pi\) | ||||
−0.284476 | + | 0.958683i | \(0.591820\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −6.81342 | −0.215567 |
(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 | 1140.2.a.f.1.1 | ✓ | 3 | |
3.2 | odd | 2 | 3420.2.a.k.1.1 | 3 | |||
4.3 | odd | 2 | 4560.2.a.bu.1.3 | 3 | |||
5.2 | odd | 4 | 5700.2.f.p.3649.4 | 6 | |||
5.3 | odd | 4 | 5700.2.f.p.3649.3 | 6 | |||
5.4 | even | 2 | 5700.2.a.z.1.3 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1140.2.a.f.1.1 | ✓ | 3 | 1.1 | even | 1 | trivial | |
3420.2.a.k.1.1 | 3 | 3.2 | odd | 2 | |||
4560.2.a.bu.1.3 | 3 | 4.3 | odd | 2 | |||
5700.2.a.z.1.3 | 3 | 5.4 | even | 2 | |||
5700.2.f.p.3649.3 | 6 | 5.3 | odd | 4 | |||
5700.2.f.p.3649.4 | 6 | 5.2 | odd | 4 |