Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [164,2,Mod(1,164)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(164, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("164.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 164 = 2^{2} \cdot 41 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 164.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: | \(1.30954659315\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | 4.4.25808.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 10x^{2} - 6x + 9 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(0.707500\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 164.1 |
$q$-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 | ||||||||
\(3\) | −3.24028 | −1.87078 | −0.935390 | − | 0.353619i | \(-0.884951\pi\) | ||||
−0.935390 | + | 0.353619i | \(0.884951\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 2.56613 | 1.14761 | 0.573803 | − | 0.818993i | \(-0.305467\pi\) | ||||
0.573803 | + | 0.818993i | \(0.305467\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.858626 | −0.324530 | −0.162265 | − | 0.986747i | \(-0.551880\pi\) | ||||
−0.162265 | + | 0.986747i | \(0.551880\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 7.49944 | 2.49981 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 6.20694 | 1.87146 | 0.935732 | − | 0.352712i | \(-0.114740\pi\) | ||||
0.935732 | + | 0.352712i | \(0.114740\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.41500 | 0.392450 | 0.196225 | − | 0.980559i | \(-0.437132\pi\) | ||||
0.196225 | + | 0.980559i | \(0.437132\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −8.31498 | −2.14692 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −3.93332 | −0.953970 | −0.476985 | − | 0.878911i | \(-0.658270\pi\) | ||||
−0.476985 | + | 0.878911i | \(0.658270\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 3.82529 | 0.877581 | 0.438790 | − | 0.898589i | \(-0.355407\pi\) | ||||
0.438790 | + | 0.898589i | \(0.355407\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 2.78219 | 0.607124 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 3.06557 | 0.639215 | 0.319608 | − | 0.947550i | \(-0.396449\pi\) | ||||
0.319608 | + | 0.947550i | \(0.396449\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.58500 | 0.317000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −14.5795 | −2.80582 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −8.48057 | −1.57480 | −0.787401 | − | 0.616441i | \(-0.788574\pi\) | ||||
−0.787401 | + | 0.616441i | \(0.788574\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.13225 | 0.203358 | 0.101679 | − | 0.994817i | \(-0.467578\pi\) | ||||
0.101679 | + | 0.994817i | \(0.467578\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −20.1123 | −3.50110 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −2.20334 | −0.372433 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 8.49944 | 1.39730 | 0.698650 | − | 0.715464i | \(-0.253784\pi\) | ||||
0.698650 | + | 0.715464i | \(0.253784\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −4.58500 | −0.734188 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −1.00000 | −0.156174 | ||||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 5.34832 | 0.815611 | 0.407805 | − | 0.913069i | \(-0.366294\pi\) | ||||
0.407805 | + | 0.913069i | \(0.366294\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 19.2445 | 2.86880 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −6.65528 | −0.970773 | −0.485386 | − | 0.874300i | \(-0.661321\pi\) | ||||
−0.485386 | + | 0.874300i | \(0.661321\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.26276 | −0.894680 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 12.7451 | 1.78467 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 6.41389 | 0.881015 | 0.440508 | − | 0.897749i | \(-0.354798\pi\) | ||||
0.440508 | + | 0.897749i | \(0.354798\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 15.9278 | 2.14770 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −12.3950 | −1.64176 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −3.06557 | −0.399103 | −0.199552 | − | 0.979887i | \(-0.563949\pi\) | ||||
−0.199552 | + | 0.979887i | \(0.563949\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 7.41500 | 0.949393 | 0.474697 | − | 0.880149i | \(-0.342558\pi\) | ||||
0.474697 | + | 0.880149i | \(0.342558\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −6.43922 | −0.811265 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 3.63107 | 0.450378 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1.79306 | 0.219057 | 0.109528 | − | 0.993984i | \(-0.465066\pi\) | ||||
0.109528 | + | 0.993984i | \(0.465066\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −9.93332 | −1.19583 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −3.02422 | −0.358909 | −0.179454 | − | 0.983766i | \(-0.557433\pi\) | ||||
−0.179454 | + | 0.983766i | \(0.557433\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 0.632807 | 0.0740645 | 0.0370322 | − | 0.999314i | \(-0.488210\pi\) | ||||
0.0370322 | + | 0.999314i | \(0.488210\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −5.13585 | −0.593037 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −5.32944 | −0.607346 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −14.3059 | −1.60953 | −0.804767 | − | 0.593591i | \(-0.797710\pi\) | ||||
−0.804767 | + | 0.593591i | \(0.797710\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 24.7433 | 2.74926 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −8.76332 | −0.961899 | −0.480950 | − | 0.876748i | \(-0.659708\pi\) | ||||
−0.480950 | + | 0.876748i | \(0.659708\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −10.0934 | −1.09478 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 27.4795 | 2.94611 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −7.89557 | −0.836929 | −0.418464 | − | 0.908233i | \(-0.637431\pi\) | ||||
−0.418464 | + | 0.908233i | \(0.637431\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.21496 | −0.127362 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −3.66882 | −0.380439 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 9.81616 | 1.00712 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 9.86664 | 1.00181 | 0.500903 | − | 0.865504i | \(-0.333001\pi\) | ||||
0.500903 | + | 0.865504i | \(0.333001\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 46.5486 | 4.67831 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −4.51832 | −0.449590 | −0.224795 | − | 0.974406i | \(-0.572171\pi\) | ||||
−0.224795 | + | 0.974406i | \(0.572171\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −16.4139 | −1.61731 | −0.808654 | − | 0.588284i | \(-0.799804\pi\) | ||||
−0.808654 | + | 0.588284i | \(0.799804\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 7.13946 | 0.696739 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −16.0645 | −1.55301 | −0.776505 | − | 0.630111i | \(-0.783009\pi\) | ||||
−0.776505 | + | 0.630111i | \(0.783009\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −5.61282 | −0.537611 | −0.268805 | − | 0.963195i | \(-0.586629\pi\) | ||||
−0.268805 | + | 0.963195i | \(0.586629\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −27.5406 | −2.61404 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 5.63170 | 0.529785 | 0.264893 | − | 0.964278i | \(-0.414663\pi\) | ||||
0.264893 | + | 0.964278i | \(0.414663\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 7.86664 | 0.733568 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 10.6117 | 0.981053 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 3.37725 | 0.309592 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 27.5262 | 2.50238 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 3.24028 | 0.292167 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −8.76332 | −0.783815 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1.69775 | 0.150651 | 0.0753254 | − | 0.997159i | \(-0.476000\pi\) | ||||
0.0753254 | + | 0.997159i | \(0.476000\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −17.3301 | −1.52583 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −2.48057 | −0.216728 | −0.108364 | − | 0.994111i | \(-0.534561\pi\) | ||||
−0.108364 | + | 0.994111i | \(0.534561\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −3.28449 | −0.284801 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −37.4128 | −3.21998 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 2.76332 | 0.236086 | 0.118043 | − | 0.993008i | \(-0.462338\pi\) | ||||
0.118043 | + | 0.993008i | \(0.462338\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 8.99889 | 0.763276 | 0.381638 | − | 0.924312i | \(-0.375360\pi\) | ||||
0.381638 | + | 0.924312i | \(0.375360\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 21.5650 | 1.81610 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 8.78282 | 0.734456 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −21.7622 | −1.80725 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 20.2931 | 1.67375 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −8.48057 | −0.694755 | −0.347378 | − | 0.937725i | \(-0.612928\pi\) | ||||
−0.347378 | + | 0.937725i | \(0.612928\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −7.58971 | −0.617642 | −0.308821 | − | 0.951120i | \(-0.599934\pi\) | ||||
−0.308821 | + | 0.951120i | \(0.599934\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −29.4977 | −2.38475 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 2.90550 | 0.233375 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −6.78282 | −0.541328 | −0.270664 | − | 0.962674i | \(-0.587243\pi\) | ||||
−0.270664 | + | 0.962674i | \(0.587243\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −20.7828 | −1.64818 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −2.63218 | −0.207445 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 15.0278 | 1.17707 | 0.588535 | − | 0.808472i | \(-0.299705\pi\) | ||||
0.588535 | + | 0.808472i | \(0.299705\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −51.6106 | −4.01788 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 5.79306 | 0.448280 | 0.224140 | − | 0.974557i | \(-0.428043\pi\) | ||||
0.224140 | + | 0.974557i | \(0.428043\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −10.9978 | −0.845983 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 28.6875 | 2.19379 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −5.43450 | −0.413178 | −0.206589 | − | 0.978428i | \(-0.566236\pi\) | ||||
−0.206589 | + | 0.978428i | \(0.566236\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1.36092 | −0.102876 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 9.93332 | 0.746634 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 8.10251 | 0.605610 | 0.302805 | − | 0.953052i | \(-0.402077\pi\) | ||||
0.302805 | + | 0.953052i | \(0.402077\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −9.24389 | −0.687093 | −0.343546 | − | 0.939136i | \(-0.611628\pi\) | ||||
−0.343546 | + | 0.939136i | \(0.611628\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −24.0267 | −1.77611 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 21.8106 | 1.60355 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −24.4139 | −1.78532 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 12.5183 | 0.910574 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 24.3381 | 1.76104 | 0.880521 | − | 0.474007i | \(-0.157193\pi\) | ||||
0.880521 | + | 0.474007i | \(0.157193\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 13.2634 | 0.954720 | 0.477360 | − | 0.878708i | \(-0.341594\pi\) | ||||
0.477360 | + | 0.878708i | \(0.341594\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −11.7657 | −0.842558 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −18.1116 | −1.29040 | −0.645200 | − | 0.764013i | \(-0.723226\pi\) | ||||
−0.645200 | + | 0.764013i | \(0.723226\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 19.7726 | 1.40164 | 0.700821 | − | 0.713337i | \(-0.252817\pi\) | ||||
0.700821 | + | 0.713337i | \(0.252817\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −5.81001 | −0.409807 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 7.28164 | 0.511071 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −2.56613 | −0.179226 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 22.9901 | 1.59792 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 23.7433 | 1.64236 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1.53924 | 0.105966 | 0.0529828 | − | 0.998595i | \(-0.483127\pi\) | ||||
0.0529828 | + | 0.998595i | \(0.483127\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 9.79933 | 0.671439 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 13.7245 | 0.936000 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −0.972180 | −0.0659959 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −2.05047 | −0.138558 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −5.56564 | −0.374386 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −27.6578 | −1.85210 | −0.926051 | − | 0.377399i | \(-0.876819\pi\) | ||||
−0.926051 | + | 0.377399i | \(0.876819\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 11.8866 | 0.792442 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −1.79635 | −0.119228 | −0.0596141 | − | 0.998221i | \(-0.518987\pi\) | ||||
−0.0596141 | + | 0.998221i | \(0.518987\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 21.6128 | 1.42822 | 0.714108 | − | 0.700036i | \(-0.246833\pi\) | ||||
0.714108 | + | 0.700036i | \(0.246833\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 17.2689 | 1.13621 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −18.3312 | −1.20092 | −0.600458 | − | 0.799656i | \(-0.705015\pi\) | ||||
−0.600458 | + | 0.799656i | \(0.705015\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −17.0783 | −1.11407 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 46.3550 | 3.01108 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 11.9586 | 0.773541 | 0.386770 | − | 0.922176i | \(-0.373591\pi\) | ||||
0.386770 | + | 0.922176i | \(0.373591\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 7.41500 | 0.477642 | 0.238821 | − | 0.971064i | \(-0.423239\pi\) | ||||
0.238821 | + | 0.971064i | \(0.423239\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −36.4370 | −2.33743 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −16.0710 | −1.02674 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 5.41278 | 0.344407 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 28.3956 | 1.79950 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −1.91507 | −0.120878 | −0.0604392 | − | 0.998172i | \(-0.519250\pi\) | ||||
−0.0604392 | + | 0.998172i | \(0.519250\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 19.0278 | 1.19627 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 32.7055 | 2.04810 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 2.93443 | 0.183045 | 0.0915224 | − | 0.995803i | \(-0.470827\pi\) | ||||
0.0915224 | + | 0.995803i | \(0.470827\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −7.29784 | −0.453466 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −63.5996 | −3.93671 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −3.10692 | −0.191581 | −0.0957905 | − | 0.995402i | \(-0.530538\pi\) | ||||
−0.0957905 | + | 0.995402i | \(0.530538\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 16.4588 | 1.01106 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 25.5839 | 1.56571 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −10.2450 | −0.624649 | −0.312324 | − | 0.949976i | \(-0.601108\pi\) | ||||
−0.312324 | + | 0.949976i | \(0.601108\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −11.1989 | −0.680287 | −0.340143 | − | 0.940374i | \(-0.610476\pi\) | ||||
−0.340143 | + | 0.940374i | \(0.610476\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 3.93680 | 0.238266 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 9.83801 | 0.593254 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 2.52838 | 0.151915 | 0.0759577 | − | 0.997111i | \(-0.475799\pi\) | ||||
0.0759577 | + | 0.997111i | \(0.475799\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 8.49125 | 0.508358 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −23.5656 | −1.40581 | −0.702904 | − | 0.711285i | \(-0.748114\pi\) | ||||
−0.702904 | + | 0.711285i | \(0.748114\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 8.99889 | 0.534928 | 0.267464 | − | 0.963568i | \(-0.413814\pi\) | ||||
0.267464 | + | 0.963568i | \(0.413814\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −31.8072 | −1.88409 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0.858626 | 0.0506831 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −1.52900 | −0.0899415 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −31.9707 | −1.87416 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 3.17721 | 0.185614 | 0.0928072 | − | 0.995684i | \(-0.470416\pi\) | ||||
0.0928072 | + | 0.995684i | \(0.470416\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −7.86664 | −0.458013 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −90.4940 | −5.25100 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 4.33778 | 0.250860 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −4.59220 | −0.264690 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 14.6406 | 0.841083 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 19.0278 | 1.08953 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −17.5839 | −1.00357 | −0.501783 | − | 0.864994i | \(-0.667322\pi\) | ||||
−0.501783 | + | 0.864994i | \(0.667322\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 53.1857 | 3.02563 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 1.55749 | 0.0883169 | 0.0441584 | − | 0.999025i | \(-0.485939\pi\) | ||||
0.0441584 | + | 0.999025i | \(0.485939\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 20.5255 | 1.16017 | 0.580086 | − | 0.814556i | \(-0.303019\pi\) | ||||
0.580086 | + | 0.814556i | \(0.303019\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −16.5238 | −0.931013 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 26.1094 | 1.46645 | 0.733225 | − | 0.679986i | \(-0.238014\pi\) | ||||
0.733225 | + | 0.679986i | \(0.238014\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −52.6384 | −2.94719 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 52.0534 | 2.90534 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −15.0461 | −0.837185 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 2.24277 | 0.124407 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 18.1871 | 1.00575 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 5.71440 | 0.315045 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 3.68862 | 0.202745 | 0.101373 | − | 0.994849i | \(-0.467677\pi\) | ||||
0.101373 | + | 0.994849i | \(0.467677\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 63.7411 | 3.49299 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 4.60121 | 0.251391 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 30.9240 | 1.68454 | 0.842269 | − | 0.539057i | \(-0.181219\pi\) | ||||
0.842269 | + | 0.539057i | \(0.181219\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −18.2483 | −0.991111 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 7.02782 | 0.380578 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 11.3878 | 0.614881 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −25.4901 | −1.37234 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 27.1264 | 1.45622 | 0.728111 | − | 0.685459i | \(-0.240398\pi\) | ||||
0.728111 | + | 0.685459i | \(0.240398\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −9.30051 | −0.497845 | −0.248922 | − | 0.968523i | \(-0.580076\pi\) | ||||
−0.248922 | + | 0.968523i | \(0.580076\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −20.6300 | −1.10115 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 13.3961 | 0.713004 | 0.356502 | − | 0.934295i | \(-0.383969\pi\) | ||||
0.356502 | + | 0.934295i | \(0.383969\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −7.76052 | −0.411886 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −10.9432 | −0.579178 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −28.9611 | −1.52851 | −0.764255 | − | 0.644914i | \(-0.776893\pi\) | ||||
−0.764255 | + | 0.644914i | \(0.776893\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −4.36719 | −0.229852 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −89.1926 | −4.68140 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 1.62386 | 0.0849968 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −31.4795 | −1.64321 | −0.821607 | − | 0.570054i | \(-0.806922\pi\) | ||||
−0.821607 | + | 0.570054i | \(0.806922\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −7.49944 | −0.390405 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −5.50713 | −0.285916 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −15.5266 | −0.803939 | −0.401969 | − | 0.915653i | \(-0.631674\pi\) | ||||
−0.401969 | + | 0.915653i | \(0.631674\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 28.3956 | 1.46634 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −12.0000 | −0.618031 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 1.97107 | 0.101247 | 0.0506235 | − | 0.998718i | \(-0.483879\pi\) | ||||
0.0506235 | + | 0.998718i | \(0.483879\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −5.50119 | −0.281834 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −12.8404 | −0.656113 | −0.328056 | − | 0.944658i | \(-0.606394\pi\) | ||||
−0.328056 | + | 0.944658i | \(0.606394\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −13.6760 | −0.696995 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 40.1094 | 2.03888 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 1.03886 | 0.0526724 | 0.0263362 | − | 0.999653i | \(-0.491616\pi\) | ||||
0.0263362 | + | 0.999653i | \(0.491616\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −12.0579 | −0.609792 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 8.03775 | 0.405451 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −36.7106 | −1.84711 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −24.6406 | −1.23668 | −0.618339 | − | 0.785911i | \(-0.712194\pi\) | ||||
−0.618339 | + | 0.785911i | \(0.712194\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 10.6427 | 0.532800 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 0.397236 | 0.0198370 | 0.00991851 | − | 0.999951i | \(-0.496843\pi\) | ||||
0.00991851 | + | 0.999951i | \(0.496843\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1.60213 | 0.0798080 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 63.4945 | 3.15507 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 52.7556 | 2.61500 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −2.76395 | −0.136668 | −0.0683342 | − | 0.997662i | \(-0.521768\pi\) | ||||
−0.0683342 | + | 0.997662i | \(0.521768\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −8.95393 | −0.441665 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 2.63218 | 0.129521 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −22.4878 | −1.10388 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −29.1590 | −1.42792 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 1.48168 | 0.0723848 | 0.0361924 | − | 0.999345i | \(-0.488477\pi\) | ||||
0.0361924 | + | 0.999345i | \(0.488477\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −18.9039 | −0.921319 | −0.460659 | − | 0.887577i | \(-0.652387\pi\) | ||||
−0.460659 | + | 0.887577i | \(0.652387\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −49.9109 | −2.42675 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −6.23431 | −0.302409 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −6.36671 | −0.308107 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −28.4588 | −1.37401 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −7.28164 | −0.350744 | −0.175372 | − | 0.984502i | \(-0.556113\pi\) | ||||
−0.175372 | + | 0.984502i | \(0.556113\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −0.397865 | −0.0191202 | −0.00956009 | − | 0.999954i | \(-0.503043\pi\) | ||||
−0.00956009 | + | 0.999954i | \(0.503043\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 70.5157 | 3.38097 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 11.7267 | 0.560963 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 33.9798 | 1.62177 | 0.810885 | − | 0.585206i | \(-0.198986\pi\) | ||||
0.810885 | + | 0.585206i | \(0.198986\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −46.9672 | −2.23653 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 16.2050 | 0.769924 | 0.384962 | − | 0.922932i | \(-0.374215\pi\) | ||||
0.384962 | + | 0.922932i | \(0.374215\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −20.2610 | −0.960464 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 27.4795 | 1.29973 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −23.1118 | −1.09071 | −0.545356 | − | 0.838204i | \(-0.683606\pi\) | ||||
−0.545356 | + | 0.838204i | \(0.683606\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −6.20694 | −0.292274 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 24.5928 | 1.15547 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −3.11773 | −0.146161 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 35.6301 | 1.66671 | 0.833353 | − | 0.552741i | \(-0.186418\pi\) | ||||
0.833353 | + | 0.552741i | \(0.186418\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 57.3457 | 2.67667 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 6.63058 | 0.308817 | 0.154409 | − | 0.988007i | \(-0.450653\pi\) | ||||
0.154409 | + | 0.988007i | \(0.450653\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −21.0220 | −0.976975 | −0.488487 | − | 0.872571i | \(-0.662451\pi\) | ||||
−0.488487 | + | 0.872571i | \(0.662451\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −9.41464 | −0.436594 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 15.8933 | 0.735456 | 0.367728 | − | 0.929933i | \(-0.380136\pi\) | ||||
0.367728 | + | 0.929933i | \(0.380136\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −1.53956 | −0.0710905 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 21.9783 | 1.01271 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 33.1967 | 1.52639 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 6.06308 | 0.278193 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 48.1006 | 2.20237 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −34.8564 | −1.59263 | −0.796315 | − | 0.604882i | \(-0.793220\pi\) | ||||
−0.796315 | + | 0.604882i | \(0.793220\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 12.0267 | 0.548371 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 8.52900 | 0.388083 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 25.3190 | 1.14968 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −9.44393 | −0.427945 | −0.213973 | − | 0.976840i | \(-0.568640\pi\) | ||||
−0.213973 | + | 0.976840i | \(0.568640\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −48.6944 | −2.20204 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 33.1577 | 1.49639 | 0.748193 | − | 0.663481i | \(-0.230922\pi\) | ||||
0.748193 | + | 0.663481i | \(0.230922\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 33.3568 | 1.50231 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 119.450 | 5.36886 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 2.59667 | 0.116477 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 12.7597 | 0.571203 | 0.285602 | − | 0.958348i | \(-0.407807\pi\) | ||||
0.285602 | + | 0.958348i | \(0.407807\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −18.7712 | −0.838633 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −17.0025 | −0.758104 | −0.379052 | − | 0.925375i | \(-0.623750\pi\) | ||||
−0.379052 | + | 0.925375i | \(0.623750\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −11.5946 | −0.515952 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 35.6359 | 1.58265 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −2.50950 | −0.111232 | −0.0556158 | − | 0.998452i | \(-0.517712\pi\) | ||||
−0.0556158 | + | 0.998452i | \(0.517712\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −0.543345 | −0.0240361 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −55.7707 | −2.46234 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −42.1201 | −1.85603 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −41.3090 | −1.81677 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 17.6093 | 0.772964 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 13.1300 | 0.575237 | 0.287618 | − | 0.957745i | \(-0.407136\pi\) | ||||
0.287618 | + | 0.957745i | \(0.407136\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 23.8301 | 1.04202 | 0.521010 | − | 0.853551i | \(-0.325556\pi\) | ||||
0.521010 | + | 0.853551i | \(0.325556\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 4.40978 | 0.192458 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −4.45350 | −0.193998 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −13.6023 | −0.591404 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −22.9901 | −0.997684 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −1.41500 | −0.0612904 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −41.2234 | −1.78224 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −26.2544 | −1.13296 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −38.8726 | −1.67436 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 14.6995 | 0.631980 | 0.315990 | − | 0.948762i | \(-0.397663\pi\) | ||||
0.315990 | + | 0.948762i | \(0.397663\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 29.9528 | 1.28540 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −14.4032 | −0.616965 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 20.2209 | 0.864584 | 0.432292 | − | 0.901734i | \(-0.357705\pi\) | ||||
0.432292 | + | 0.901734i | \(0.357705\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 55.6084 | 2.37331 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −32.4406 | −1.38202 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 12.2834 | 0.522342 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −70.6727 | −2.99989 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −40.6784 | −1.72360 | −0.861799 | − | 0.507249i | \(-0.830662\pi\) | ||||
−0.861799 | + | 0.507249i | \(0.830662\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 7.56787 | 0.320087 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 79.1079 | 3.33994 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −19.4486 | −0.819661 | −0.409831 | − | 0.912162i | \(-0.634412\pi\) | ||||
−0.409831 | + | 0.912162i | \(0.634412\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 14.4516 | 0.607985 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −21.2453 | −0.892217 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −31.1850 | −1.30734 | −0.653672 | − | 0.756778i | \(-0.726773\pi\) | ||||
−0.653672 | + | 0.756778i | \(0.726773\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −0.190921 | −0.00798981 | −0.00399491 | − | 0.999992i | \(-0.501272\pi\) | ||||
−0.00399491 | + | 0.999992i | \(0.501272\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −78.8623 | −3.29452 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 4.85893 | 0.202631 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −29.0278 | −1.20844 | −0.604222 | − | 0.796816i | \(-0.706516\pi\) | ||||
−0.604222 | + | 0.796816i | \(0.706516\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −42.9772 | −1.78607 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 7.52441 | 0.312165 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 39.8106 | 1.64879 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 27.2310 | 1.12586 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −11.5735 | −0.477690 | −0.238845 | − | 0.971058i | \(-0.576769\pi\) | ||||
−0.238845 | + | 0.971058i | \(0.576769\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 4.33118 | 0.178463 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 58.6869 | 2.41405 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 34.5557 | 1.41903 | 0.709517 | − | 0.704689i | \(-0.248913\pi\) | ||||
0.709517 | + | 0.704689i | \(0.248913\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 8.66645 | 0.355290 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −64.0688 | −2.62216 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 26.9967 | 1.10305 | 0.551527 | − | 0.834157i | \(-0.314045\pi\) | ||||
0.551527 | + | 0.834157i | \(0.314045\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 47.8534 | 1.95198 | 0.975990 | − | 0.217816i | \(-0.0698932\pi\) | ||||
0.975990 | + | 0.217816i | \(0.0698932\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 13.4469 | 0.547601 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 70.6356 | 2.87174 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 12.3761 | 0.502332 | 0.251166 | − | 0.967944i | \(-0.419186\pi\) | ||||
0.251166 | + | 0.967944i | \(0.419186\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −23.5946 | −0.956100 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −9.41722 | −0.380980 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 12.9061 | 0.521274 | 0.260637 | − | 0.965437i | \(-0.416067\pi\) | ||||
0.260637 | + | 0.965437i | \(0.416067\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 8.31498 | 0.335292 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −40.5268 | −1.63155 | −0.815773 | − | 0.578372i | \(-0.803688\pi\) | ||||
−0.815773 | + | 0.578372i | \(0.803688\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −2.65889 | −0.106870 | −0.0534348 | − | 0.998571i | \(-0.517017\pi\) | ||||
−0.0534348 | + | 0.998571i | \(0.517017\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −44.6944 | −1.79353 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 6.77934 | 0.271609 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −30.4128 | −1.21651 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −76.9351 | −3.07249 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −33.4310 | −1.33298 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −0.139958 | −0.00557165 | −0.00278583 | − | 0.999996i | \(-0.500887\pi\) | ||||
−0.00278583 | + | 0.999996i | \(0.500887\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −4.98757 | −0.198238 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 4.35663 | 0.172888 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −8.86180 | −0.351117 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −22.6800 | −0.897205 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 9.39675 | 0.371149 | 0.185575 | − | 0.982630i | \(-0.440585\pi\) | ||||
0.185575 | + | 0.982630i | \(0.440585\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 6.02863 | 0.237746 | 0.118873 | − | 0.992909i | \(-0.462072\pi\) | ||||
0.118873 | + | 0.992909i | \(0.462072\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −44.4711 | −1.75105 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 17.3861 | 0.683517 | 0.341758 | − | 0.939788i | \(-0.388978\pi\) | ||||
0.341758 | + | 0.939788i | \(0.388978\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −19.0278 | −0.746907 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 3.15014 | 0.123464 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −8.02832 | −0.314173 | −0.157086 | − | 0.987585i | \(-0.550210\pi\) | ||||
−0.157086 | + | 0.987585i | \(0.550210\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −6.36545 | −0.248719 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 4.74570 | 0.185147 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −33.8809 | −1.31981 | −0.659907 | − | 0.751348i | \(-0.729404\pi\) | ||||
−0.659907 | + | 0.751348i | \(0.729404\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 34.3840 | 1.33738 | 0.668691 | − | 0.743541i | \(-0.266855\pi\) | ||||
0.668691 | + | 0.743541i | \(0.266855\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 18.0343 | 0.700393 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −8.42841 | −0.326840 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −25.9978 | −1.00664 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 89.6191 | 3.46487 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 46.0245 | 1.77676 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 10.3689 | 0.399693 | 0.199847 | − | 0.979827i | \(-0.435956\pi\) | ||||
0.199847 | + | 0.979827i | \(0.435956\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −23.1085 | −0.889446 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 28.0616 | 1.07850 | 0.539248 | − | 0.842147i | \(-0.318709\pi\) | ||||
0.539248 | + | 0.842147i | \(0.318709\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −8.47175 | −0.325116 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 5.82070 | 0.223050 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 12.2209 | 0.467621 | 0.233810 | − | 0.972282i | \(-0.424881\pi\) | ||||
0.233810 | + | 0.972282i | \(0.424881\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 7.09102 | 0.270934 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −70.0317 | −2.67188 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 9.07565 | 0.345755 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 46.1797 | 1.75676 | 0.878379 | − | 0.477964i | \(-0.158625\pi\) | ||||
0.878379 | + | 0.477964i | \(0.158625\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −39.9679 | −1.51825 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 23.0923 | 0.875940 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 3.93332 | 0.148985 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 59.3983 | 2.24665 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −46.8161 | −1.76822 | −0.884110 | − | 0.467279i | \(-0.845234\pi\) | ||||
−0.884110 | + | 0.467279i | \(0.845234\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 32.5128 | 1.22624 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 55.3385 | 2.08417 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 3.87955 | 0.145905 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 42.0840 | 1.58050 | 0.790248 | − | 0.612787i | \(-0.209952\pi\) | ||||
0.790248 | + | 0.612787i | \(0.209952\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −107.286 | −4.02354 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 3.47100 | 0.129990 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 22.5378 | 0.842867 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −38.7494 | −1.44712 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 1.77685 | 0.0662653 | 0.0331327 | − | 0.999451i | \(-0.489452\pi\) | ||||
0.0331327 | + | 0.999451i | \(0.489452\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 14.0934 | 0.524865 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −24.0267 | −0.893563 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −13.4417 | −0.499212 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −17.4346 | −0.646614 | −0.323307 | − | 0.946294i | \(-0.604795\pi\) | ||||
−0.323307 | + | 0.946294i | \(0.604795\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 43.8362 | 1.62356 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −21.0366 | −0.778068 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −8.31827 | −0.307242 | −0.153621 | − | 0.988130i | \(-0.549094\pi\) | ||||
−0.153621 | + | 0.988130i | \(0.549094\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 52.0747 | 1.92080 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 11.1294 | 0.409957 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −0.139958 | −0.00514845 | −0.00257422 | − | 0.999997i | \(-0.500819\pi\) | ||||
−0.00257422 | + | 0.999997i | \(0.500819\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −17.5389 | −0.644309 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −3.92389 | −0.143954 | −0.0719768 | − | 0.997406i | \(-0.522931\pi\) | ||||
−0.0719768 | + | 0.997406i | \(0.522931\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −21.7622 | −0.797306 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −65.7200 | −2.40457 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 13.7934 | 0.503998 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 38.2786 | 1.39681 | 0.698403 | − | 0.715705i | \(-0.253894\pi\) | ||||
0.698403 | + | 0.715705i | \(0.253894\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 6.20538 | 0.226137 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −19.4762 | −0.708810 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −31.0640 | −1.12904 | −0.564519 | − | 0.825420i | \(-0.690938\pi\) | ||||
−0.564519 | + | 0.825420i | \(0.690938\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −61.6556 | −2.23795 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −2.83945 | −0.102930 | −0.0514649 | − | 0.998675i | \(-0.516389\pi\) | ||||
−0.0514649 | + | 0.998675i | \(0.516389\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 4.81931 | 0.174471 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −75.6948 | −2.73675 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −4.33778 | −0.156628 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 38.7888 | 1.39876 | 0.699379 | − | 0.714751i | \(-0.253460\pi\) | ||||
0.699379 | + | 0.714751i | \(0.253460\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −9.50839 | −0.342436 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 25.7150 | 0.924905 | 0.462453 | − | 0.886644i | \(-0.346970\pi\) | ||||
0.462453 | + | 0.886644i | \(0.346970\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 1.79462 | 0.0644646 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 23.6471 | 0.848335 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −3.82529 | −0.137055 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −18.7712 | −0.671685 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 123.642 | 4.41861 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −17.4056 | −0.621232 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 41.7817 | 1.48936 | 0.744679 | − | 0.667423i | \(-0.232603\pi\) | ||||
0.744679 | + | 0.667423i | \(0.232603\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 10.0673 | 0.358406 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −4.83552 | −0.171931 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 10.4922 | 0.372590 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −53.3313 | −1.89147 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 36.2818 | 1.28517 | 0.642583 | − | 0.766216i | \(-0.277863\pi\) | ||||
0.642583 | + | 0.766216i | \(0.277863\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 26.1774 | 0.926088 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −59.2124 | −2.09217 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 3.92780 | 0.138609 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −6.75450 | −0.238065 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 33.1967 | 1.16858 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −37.8556 | −1.33093 | −0.665466 | − | 0.746428i | \(-0.731767\pi\) | ||||
−0.665466 | + | 0.746428i | \(0.731767\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −15.5751 | −0.546915 | −0.273457 | − | 0.961884i | \(-0.588167\pi\) | ||||
−0.273457 | + | 0.961884i | \(0.588167\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 36.2877 | 1.27267 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 38.5633 | 1.35081 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 20.4588 | 0.715764 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −9.11149 | −0.318381 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −9.42283 | −0.328859 | −0.164430 | − | 0.986389i | \(-0.552578\pi\) | ||||
−0.164430 | + | 0.986389i | \(0.552578\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −13.9636 | −0.486741 | −0.243371 | − | 0.969933i | \(-0.578253\pi\) | ||||
−0.243371 | + | 0.969933i | \(0.578253\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −31.8780 | −1.10985 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 19.6886 | 0.684641 | 0.342320 | − | 0.939583i | \(-0.388787\pi\) | ||||
0.342320 | + | 0.939583i | \(0.388787\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 52.9595 | 1.83936 | 0.919681 | − | 0.392668i | \(-0.128448\pi\) | ||||
0.919681 | + | 0.392668i | \(0.128448\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −8.19266 | −0.284200 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 24.6334 | 0.853498 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 14.8657 | 0.514449 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −16.5076 | −0.570587 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −17.1392 | −0.591709 | −0.295855 | − | 0.955233i | \(-0.595604\pi\) | ||||
−0.295855 | + | 0.955233i | \(0.595604\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 42.9201 | 1.48000 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 76.3594 | 2.62996 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −28.2217 | −0.970855 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −23.6347 | −0.812097 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −29.1590 | −1.00073 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 26.0556 | 0.893176 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −24.8256 | −0.850011 | −0.425005 | − | 0.905191i | \(-0.639728\pi\) | ||||
−0.425005 | + | 0.905191i | \(0.639728\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 73.6158 | 2.51761 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 25.6584 | 0.876474 | 0.438237 | − | 0.898859i | \(-0.355603\pi\) | ||||
0.438237 | + | 0.898859i | \(0.355603\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 11.9818 | 0.408812 | 0.204406 | − | 0.978886i | \(-0.434474\pi\) | ||||
0.204406 | + | 0.978886i | \(0.434474\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −2.78219 | −0.0948169 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −33.9138 | −1.15444 | −0.577220 | − | 0.816589i | \(-0.695862\pi\) | ||||
−0.577220 | + | 0.816589i | \(0.695862\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −13.9456 | −0.474165 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 4.95441 | 0.168261 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −88.7956 | −3.01219 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 2.53717 | 0.0859688 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 73.9943 | 2.50433 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 7.52441 | 0.254372 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −14.1871 | −0.479066 | −0.239533 | − | 0.970888i | \(-0.576994\pi\) | ||||
−0.239533 | + | 0.970888i | \(0.576994\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −10.2950 | −0.347243 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 42.3201 | 1.42580 | 0.712901 | − | 0.701265i | \(-0.247381\pi\) | ||||
0.712901 | + | 0.701265i | \(0.247381\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 51.7258 | 1.74071 | 0.870356 | − | 0.492422i | \(-0.163888\pi\) | ||||
0.870356 | + | 0.492422i | \(0.163888\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 25.4901 | 0.856842 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 30.1270 | 1.01157 | 0.505783 | − | 0.862661i | \(-0.331204\pi\) | ||||
0.505783 | + | 0.862661i | \(0.331204\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −1.45773 | −0.0488907 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 153.580 | 5.14514 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −25.4584 | −0.851932 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 20.7921 | 0.695002 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −14.0556 | −0.469304 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −9.60213 | −0.320249 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −25.2279 | −0.840462 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 14.8800 | 0.495177 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −23.7210 | −0.788512 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −4.24848 | −0.141068 | −0.0705342 | − | 0.997509i | \(-0.522470\pi\) | ||||
−0.0705342 | + | 0.997509i | \(0.522470\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −33.8849 | −1.12389 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −49.1395 | −1.62806 | −0.814031 | − | 0.580821i | \(-0.802732\pi\) | ||||
−0.814031 | + | 0.580821i | \(0.802732\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −54.3934 | −1.80016 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −61.6556 | −2.03827 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 2.12988 | 0.0703349 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 6.59412 | 0.217520 | 0.108760 | − | 0.994068i | \(-0.465312\pi\) | ||||
0.108760 | + | 0.994068i | \(0.465312\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 56.9768 | 1.87745 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −4.27927 | −0.140854 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 13.4716 | 0.442944 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −123.095 | −4.04297 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 54.3833 | 1.78426 | 0.892130 | − | 0.451779i | \(-0.149211\pi\) | ||||
0.892130 | + | 0.451779i | \(0.149211\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −23.9568 | −0.785154 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −5.04669 | −0.165221 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −62.6491 | −2.04884 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −43.0888 | −1.40765 | −0.703825 | − | 0.710374i | \(-0.748526\pi\) | ||||
−0.703825 | + | 0.710374i | \(0.748526\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −66.5085 | −2.17042 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 12.6966 | 0.413899 | 0.206949 | − | 0.978352i | \(-0.433646\pi\) | ||||
0.206949 | + | 0.978352i | \(0.433646\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −3.06557 | −0.0998287 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 32.1236 | 1.04498 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 29.6867 | 0.964688 | 0.482344 | − | 0.875982i | \(-0.339785\pi\) | ||||
0.482344 | + | 0.875982i | \(0.339785\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0.895422 | 0.0290666 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −84.6019 | −2.74341 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 7.62947 | 0.247143 | 0.123571 | − | 0.992336i | \(-0.460565\pi\) | ||||
0.123571 | + | 0.992336i | \(0.460565\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 62.4546 | 2.02098 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 170.563 | 5.51353 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −2.37266 | −0.0766171 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −29.7180 | −0.958645 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −120.475 | −3.88224 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 34.0355 | 1.09564 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −37.0187 | −1.19044 | −0.595221 | − | 0.803562i | \(-0.702935\pi\) | ||||
−0.595221 | + | 0.803562i | \(0.702935\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 48.7535 | 1.56619 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −17.2425 | −0.553338 | −0.276669 | − | 0.960965i | \(-0.589231\pi\) | ||||
−0.276669 | + | 0.960965i | \(0.589231\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −7.72668 | −0.247706 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −7.26723 | −0.232738 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −31.6112 | −1.01133 | −0.505666 | − | 0.862729i | \(-0.668753\pi\) | ||||
−0.505666 | + | 0.862729i | \(0.668753\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −49.0074 | −1.56628 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −42.0930 | −1.34393 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 51.8543 | 1.65390 | 0.826948 | − | 0.562278i | \(-0.190075\pi\) | ||||
0.826948 | + | 0.562278i | \(0.190075\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −46.4767 | −1.48087 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −18.5163 | −0.589380 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 16.3956 | 0.521351 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −37.7209 | −1.19824 | −0.599121 | − | 0.800658i | \(-0.704483\pi\) | ||||
−0.599121 | + | 0.800658i | \(0.704483\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −11.9522 | −0.379291 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 50.7389 | 1.60853 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −19.1882 | −0.607698 | −0.303849 | − | 0.952720i | \(-0.598272\pi\) | ||||
−0.303849 | + | 0.952720i | \(0.598272\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −123.917 | −3.92058 |
(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 | 164.2.a.a.1.1 | ✓ | 4 | |
3.2 | odd | 2 | 1476.2.a.g.1.2 | 4 | |||
4.3 | odd | 2 | 656.2.a.i.1.4 | 4 | |||
5.2 | odd | 4 | 4100.2.d.c.1149.8 | 8 | |||
5.3 | odd | 4 | 4100.2.d.c.1149.1 | 8 | |||
5.4 | even | 2 | 4100.2.a.c.1.4 | 4 | |||
7.6 | odd | 2 | 8036.2.a.i.1.4 | 4 | |||
8.3 | odd | 2 | 2624.2.a.y.1.1 | 4 | |||
8.5 | even | 2 | 2624.2.a.v.1.4 | 4 | |||
12.11 | even | 2 | 5904.2.a.bp.1.2 | 4 | |||
41.40 | even | 2 | 6724.2.a.c.1.4 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
164.2.a.a.1.1 | ✓ | 4 | 1.1 | even | 1 | trivial | |
656.2.a.i.1.4 | 4 | 4.3 | odd | 2 | |||
1476.2.a.g.1.2 | 4 | 3.2 | odd | 2 | |||
2624.2.a.v.1.4 | 4 | 8.5 | even | 2 | |||
2624.2.a.y.1.1 | 4 | 8.3 | odd | 2 | |||
4100.2.a.c.1.4 | 4 | 5.4 | even | 2 | |||
4100.2.d.c.1149.1 | 8 | 5.3 | odd | 4 | |||
4100.2.d.c.1149.8 | 8 | 5.2 | odd | 4 | |||
5904.2.a.bp.1.2 | 4 | 12.11 | even | 2 | |||
6724.2.a.c.1.4 | 4 | 41.40 | even | 2 | |||
8036.2.a.i.1.4 | 4 | 7.6 | odd | 2 |