Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3072,2,Mod(1,3072)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3072, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("3072.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3072 = 2^{10} \cdot 3 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3072.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: | \(24.5300435009\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | 4.4.4352.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 6x^{2} - 4x + 2 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 48) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(2.68554\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3072.1 |
$q$-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 | ||||||||
\(5\) | 3.79793 | 1.69849 | 0.849244 | − | 0.528001i | \(-0.177058\pi\) | ||||
0.849244 | + | 0.528001i | \(0.177058\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.15894 | −0.816003 | −0.408002 | − | 0.912981i | \(-0.633774\pi\) | ||||
−0.408002 | + | 0.912981i | \(0.633774\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2.54266 | −0.766641 | −0.383321 | − | 0.923615i | \(-0.625220\pi\) | ||||
−0.383321 | + | 0.923615i | \(0.625220\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.95687 | −0.542739 | −0.271370 | − | 0.962475i | \(-0.587477\pi\) | ||||
−0.271370 | + | 0.962475i | \(0.587477\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −3.79793 | −0.980622 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 0.224777 | 0.0545165 | 0.0272583 | − | 0.999628i | \(-0.491322\pi\) | ||||
0.0272583 | + | 0.999628i | \(0.491322\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.224777 | 0.0515675 | 0.0257837 | − | 0.999668i | \(-0.491792\pi\) | ||||
0.0257837 | + | 0.999668i | \(0.491792\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 2.15894 | 0.471120 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 2.82843 | 0.589768 | 0.294884 | − | 0.955533i | \(-0.404719\pi\) | ||||
0.294884 | + | 0.955533i | \(0.404719\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 9.42429 | 1.88486 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −2.62636 | −0.487703 | −0.243851 | − | 0.969813i | \(-0.578411\pi\) | ||||
−0.243851 | + | 0.969813i | \(0.578411\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.84106 | −0.330664 | −0.165332 | − | 0.986238i | \(-0.552870\pi\) | ||||
−0.165332 | + | 0.986238i | \(0.552870\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 2.54266 | 0.442620 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −8.19951 | −1.38597 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 5.18944 | 0.853138 | 0.426569 | − | 0.904455i | \(-0.359722\pi\) | ||||
0.426569 | + | 0.904455i | \(0.359722\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 1.95687 | 0.313351 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 5.88163 | 0.918557 | 0.459278 | − | 0.888292i | \(-0.348108\pi\) | ||||
0.459278 | + | 0.888292i | \(0.348108\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 10.9670 | 1.67244 | 0.836222 | − | 0.548391i | \(-0.184759\pi\) | ||||
0.836222 | + | 0.548391i | \(0.184759\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 3.79793 | 0.566162 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −2.82843 | −0.412568 | −0.206284 | − | 0.978492i | \(-0.566137\pi\) | ||||
−0.206284 | + | 0.978492i | \(0.566137\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −2.33897 | −0.334139 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −0.224777 | −0.0314751 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 10.6264 | 1.45964 | 0.729821 | − | 0.683638i | \(-0.239603\pi\) | ||||
0.729821 | + | 0.683638i | \(0.239603\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −9.65685 | −1.30213 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −0.224777 | −0.0297725 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 5.65685 | 0.736460 | 0.368230 | − | 0.929735i | \(-0.379964\pi\) | ||||
0.368230 | + | 0.929735i | \(0.379964\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 8.46742 | 1.08414 | 0.542071 | − | 0.840333i | \(-0.317640\pi\) | ||||
0.542071 | + | 0.840333i | \(0.317640\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −2.15894 | −0.272001 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −7.43208 | −0.921836 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 14.7422 | 1.80104 | 0.900522 | − | 0.434811i | \(-0.143185\pi\) | ||||
0.900522 | + | 0.434811i | \(0.143185\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −2.82843 | −0.340503 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 4.31788 | 0.512438 | 0.256219 | − | 0.966619i | \(-0.417523\pi\) | ||||
0.256219 | + | 0.966619i | \(0.417523\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 5.97474 | 0.699290 | 0.349645 | − | 0.936882i | \(-0.386302\pi\) | ||||
0.349645 | + | 0.936882i | \(0.386302\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −9.42429 | −1.08822 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 5.48946 | 0.625582 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 15.0075 | 1.68848 | 0.844239 | − | 0.535966i | \(-0.180053\pi\) | ||||
0.844239 | + | 0.535966i | \(0.180053\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −14.3059 | −1.57028 | −0.785140 | − | 0.619319i | \(-0.787409\pi\) | ||||
−0.785140 | + | 0.619319i | \(0.787409\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0.853690 | 0.0925956 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 2.62636 | 0.281575 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −1.42847 | −0.151417 | −0.0757086 | − | 0.997130i | \(-0.524122\pi\) | ||||
−0.0757086 | + | 0.997130i | \(0.524122\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 4.22478 | 0.442877 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 1.84106 | 0.190909 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0.853690 | 0.0875867 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −16.3990 | −1.66507 | −0.832535 | − | 0.553973i | \(-0.813111\pi\) | ||||
−0.832535 | + | 0.553973i | \(0.813111\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −2.54266 | −0.255547 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −0.115816 | −0.0115241 | −0.00576206 | − | 0.999983i | \(-0.501834\pi\) | ||||
−0.00576206 | + | 0.999983i | \(0.501834\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −13.3507 | −1.31548 | −0.657740 | − | 0.753245i | \(-0.728488\pi\) | ||||
−0.657740 | + | 0.753245i | \(0.728488\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 8.19951 | 0.800191 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 10.2926 | 0.995025 | 0.497513 | − | 0.867457i | \(-0.334247\pi\) | ||||
0.497513 | + | 0.867457i | \(0.334247\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 9.95687 | 0.953696 | 0.476848 | − | 0.878986i | \(-0.341779\pi\) | ||||
0.476848 | + | 0.878986i | \(0.341779\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −5.18944 | −0.492559 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −18.8486 | −1.77313 | −0.886563 | − | 0.462608i | \(-0.846914\pi\) | ||||
−0.886563 | + | 0.462608i | \(0.846914\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 10.7422 | 1.00171 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −1.95687 | −0.180913 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −0.485281 | −0.0444857 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −4.53488 | −0.412261 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −5.88163 | −0.530329 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 16.8032 | 1.50292 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 3.81580 | 0.338597 | 0.169299 | − | 0.985565i | \(-0.445850\pi\) | ||||
0.169299 | + | 0.985565i | \(0.445850\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −10.9670 | −0.965586 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1.08532 | 0.0948250 | 0.0474125 | − | 0.998875i | \(-0.484902\pi\) | ||||
0.0474125 | + | 0.998875i | \(0.484902\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −0.485281 | −0.0420792 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −3.79793 | −0.326874 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −5.31010 | −0.453672 | −0.226836 | − | 0.973933i | \(-0.572838\pi\) | ||||
−0.226836 | + | 0.973933i | \(0.572838\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −12.3990 | −1.05167 | −0.525836 | − | 0.850586i | \(-0.676247\pi\) | ||||
−0.525836 | + | 0.850586i | \(0.676247\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 2.82843 | 0.238197 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 4.97567 | 0.416086 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −9.97474 | −0.828357 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 2.33897 | 0.192915 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −1.45479 | −0.119181 | −0.0595904 | − | 0.998223i | \(-0.518979\pi\) | ||||
−0.0595904 | + | 0.998223i | \(0.518979\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −2.03696 | −0.165766 | −0.0828829 | − | 0.996559i | \(-0.526413\pi\) | ||||
−0.0828829 | + | 0.996559i | \(0.526413\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0.224777 | 0.0181722 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −6.99222 | −0.561628 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 8.61790 | 0.687784 | 0.343892 | − | 0.939009i | \(-0.388255\pi\) | ||||
0.343892 | + | 0.939009i | \(0.388255\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −10.6264 | −0.842725 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −6.10641 | −0.481252 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −4.86054 | −0.380707 | −0.190354 | − | 0.981716i | \(-0.560963\pi\) | ||||
−0.190354 | + | 0.981716i | \(0.560963\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 9.65685 | 0.751785 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 21.7023 | 1.67937 | 0.839686 | − | 0.543072i | \(-0.182739\pi\) | ||||
0.839686 | + | 0.543072i | \(0.182739\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −9.17064 | −0.705434 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0.224777 | 0.0171892 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 12.3695 | 0.940433 | 0.470217 | − | 0.882551i | \(-0.344176\pi\) | ||||
0.470217 | + | 0.882551i | \(0.344176\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −20.3465 | −1.53805 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −5.65685 | −0.425195 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 11.6413 | 0.870111 | 0.435055 | − | 0.900404i | \(-0.356729\pi\) | ||||
0.435055 | + | 0.900404i | \(0.356729\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 9.50732 | 0.706673 | 0.353337 | − | 0.935496i | \(-0.385047\pi\) | ||||
0.353337 | + | 0.935496i | \(0.385047\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −8.46742 | −0.625930 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 19.7091 | 1.44904 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −0.571533 | −0.0417946 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 2.15894 | 0.157040 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 20.8032 | 1.50526 | 0.752632 | − | 0.658441i | \(-0.228784\pi\) | ||||
0.752632 | + | 0.658441i | \(0.228784\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 14.1454 | 1.01821 | 0.509103 | − | 0.860705i | \(-0.329977\pi\) | ||||
0.509103 | + | 0.860705i | \(0.329977\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 7.43208 | 0.532222 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 3.43463 | 0.244707 | 0.122354 | − | 0.992487i | \(-0.460956\pi\) | ||||
0.122354 | + | 0.992487i | \(0.460956\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −0.306182 | −0.0217047 | −0.0108523 | − | 0.999941i | \(-0.503454\pi\) | ||||
−0.0108523 | + | 0.999941i | \(0.503454\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −14.7422 | −1.03983 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 5.67016 | 0.397967 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 22.3380 | 1.56016 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 2.82843 | 0.196589 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −0.571533 | −0.0395337 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 10.2284 | 0.704151 | 0.352076 | − | 0.935972i | \(-0.385476\pi\) | ||||
0.352076 | + | 0.935972i | \(0.385476\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −4.31788 | −0.295856 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 41.6517 | 2.84063 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 3.97474 | 0.269823 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −5.97474 | −0.403735 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −0.439861 | −0.0295883 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 1.71908 | 0.115118 | 0.0575591 | − | 0.998342i | \(-0.481668\pi\) | ||||
0.0575591 | + | 0.998342i | \(0.481668\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 9.42429 | 0.628286 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −14.3059 | −0.949518 | −0.474759 | − | 0.880116i | \(-0.657465\pi\) | ||||
−0.474759 | + | 0.880116i | \(0.657465\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 16.9981 | 1.12327 | 0.561634 | − | 0.827386i | \(-0.310173\pi\) | ||||
0.561634 | + | 0.827386i | \(0.310173\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −5.48946 | −0.361180 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 13.3779 | 0.876418 | 0.438209 | − | 0.898873i | \(-0.355613\pi\) | ||||
0.438209 | + | 0.898873i | \(0.355613\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −10.7422 | −0.700742 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −15.0075 | −0.974844 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 13.3675 | 0.864670 | 0.432335 | − | 0.901713i | \(-0.357690\pi\) | ||||
0.432335 | + | 0.901713i | \(0.357690\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −0.211474 | −0.0136222 | −0.00681112 | − | 0.999977i | \(-0.502168\pi\) | ||||
−0.00681112 | + | 0.999977i | \(0.502168\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −8.88325 | −0.567530 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −0.439861 | −0.0279877 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 14.3059 | 0.906601 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 14.7555 | 0.931358 | 0.465679 | − | 0.884954i | \(-0.345810\pi\) | ||||
0.465679 | + | 0.884954i | \(0.345810\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −7.19173 | −0.452140 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −0.853690 | −0.0534601 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −0.742176 | −0.0462957 | −0.0231478 | − | 0.999732i | \(-0.507369\pi\) | ||||
−0.0231478 | + | 0.999732i | \(0.507369\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −11.2037 | −0.696163 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −2.62636 | −0.162568 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −5.48435 | −0.338180 | −0.169090 | − | 0.985601i | \(-0.554083\pi\) | ||||
−0.169090 | + | 0.985601i | \(0.554083\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 40.3582 | 2.47918 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 1.42847 | 0.0874208 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −20.4694 | −1.24804 | −0.624021 | − | 0.781407i | \(-0.714502\pi\) | ||||
−0.624021 | + | 0.781407i | \(0.714502\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −14.0370 | −0.852685 | −0.426342 | − | 0.904562i | \(-0.640198\pi\) | ||||
−0.426342 | + | 0.904562i | \(0.640198\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −4.22478 | −0.255695 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −23.9628 | −1.44501 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 13.4211 | 0.806394 | 0.403197 | − | 0.915113i | \(-0.367899\pi\) | ||||
0.403197 | + | 0.915113i | \(0.367899\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −1.84106 | −0.110221 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 3.89359 | 0.232272 | 0.116136 | − | 0.993233i | \(-0.462949\pi\) | ||||
0.116136 | + | 0.993233i | \(0.462949\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −17.6569 | −1.04959 | −0.524796 | − | 0.851228i | \(-0.675858\pi\) | ||||
−0.524796 | + | 0.851228i | \(0.675858\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −0.853690 | −0.0505682 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −12.6981 | −0.749545 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −16.9495 | −0.997028 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 16.3990 | 0.961328 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 15.7759 | 0.921639 | 0.460819 | − | 0.887494i | \(-0.347556\pi\) | ||||
0.460819 | + | 0.887494i | \(0.347556\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 21.4844 | 1.25087 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 2.54266 | 0.147540 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −5.53488 | −0.320090 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −23.6770 | −1.36472 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0.115816 | 0.00665345 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 32.1587 | 1.84140 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −7.64129 | −0.436111 | −0.218056 | − | 0.975936i | \(-0.569971\pi\) | ||||
−0.218056 | + | 0.975936i | \(0.569971\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 13.3507 | 0.759493 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −24.1623 | −1.37012 | −0.685059 | − | 0.728488i | \(-0.740224\pi\) | ||||
−0.685059 | + | 0.728488i | \(0.740224\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −16.6105 | −0.938881 | −0.469441 | − | 0.882964i | \(-0.655544\pi\) | ||||
−0.469441 | + | 0.882964i | \(0.655544\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −8.19951 | −0.461990 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 2.56213 | 0.143903 | 0.0719517 | − | 0.997408i | \(-0.477077\pi\) | ||||
0.0719517 | + | 0.997408i | \(0.477077\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 6.67794 | 0.373893 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −10.2926 | −0.574478 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0.0505249 | 0.00281128 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −18.4422 | −1.02299 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −9.95687 | −0.550616 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 6.10641 | 0.336657 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −19.1275 | −1.05134 | −0.525671 | − | 0.850688i | \(-0.676186\pi\) | ||||
−0.525671 | + | 0.850688i | \(0.676186\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 5.18944 | 0.284379 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 55.9898 | 3.05905 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 1.12615 | 0.0613454 | 0.0306727 | − | 0.999529i | \(-0.490235\pi\) | ||||
0.0306727 | + | 0.999529i | \(0.490235\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 18.8486 | 1.02371 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 4.68119 | 0.253500 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 20.1623 | 1.08866 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −10.7422 | −0.578339 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 29.4068 | 1.57864 | 0.789320 | − | 0.613982i | \(-0.210433\pi\) | ||||
0.789320 | + | 0.613982i | \(0.210433\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −27.2738 | −1.45993 | −0.729967 | − | 0.683482i | \(-0.760465\pi\) | ||||
−0.729967 | + | 0.683482i | \(0.760465\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1.95687 | 0.104450 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 25.5908 | 1.36206 | 0.681029 | − | 0.732256i | \(-0.261533\pi\) | ||||
0.681029 | + | 0.732256i | \(0.261533\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 16.3990 | 0.870370 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0.485281 | 0.0256838 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −3.77296 | −0.199129 | −0.0995645 | − | 0.995031i | \(-0.531745\pi\) | ||||
−0.0995645 | + | 0.995031i | \(0.531745\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −18.9495 | −0.997341 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 4.53488 | 0.238019 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 22.6917 | 1.18774 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −27.4474 | −1.43274 | −0.716371 | − | 0.697720i | \(-0.754198\pi\) | ||||
−0.716371 | + | 0.697720i | \(0.754198\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 5.88163 | 0.306186 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −22.9417 | −1.19107 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 17.8518 | 0.924332 | 0.462166 | − | 0.886794i | \(-0.347072\pi\) | ||||
0.462166 | + | 0.886794i | \(0.347072\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −16.8032 | −0.867712 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 5.13946 | 0.264695 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −16.5018 | −0.847642 | −0.423821 | − | 0.905746i | \(-0.639311\pi\) | ||||
−0.423821 | + | 0.905746i | \(0.639311\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −3.81580 | −0.195489 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 17.1885 | 0.878291 | 0.439145 | − | 0.898416i | \(-0.355281\pi\) | ||||
0.439145 | + | 0.898416i | \(0.355281\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 20.8486 | 1.06254 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 10.9670 | 0.557482 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 2.66209 | 0.134973 | 0.0674866 | − | 0.997720i | \(-0.478502\pi\) | ||||
0.0674866 | + | 0.997720i | \(0.478502\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0.635767 | 0.0321521 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −1.08532 | −0.0547472 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 56.9976 | 2.86786 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −11.8959 | −0.597037 | −0.298519 | − | 0.954404i | \(-0.596493\pi\) | ||||
−0.298519 | + | 0.954404i | \(0.596493\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0.485281 | 0.0242945 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −1.12389 | −0.0561242 | −0.0280621 | − | 0.999606i | \(-0.508934\pi\) | ||||
−0.0280621 | + | 0.999606i | \(0.508934\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 3.60272 | 0.179464 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 3.79793 | 0.188721 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −13.1950 | −0.654051 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 13.7211 | 0.678464 | 0.339232 | − | 0.940703i | \(-0.389833\pi\) | ||||
0.339232 | + | 0.940703i | \(0.389833\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 5.31010 | 0.261928 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −12.2128 | −0.600953 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −54.3329 | −2.66710 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 12.3990 | 0.607183 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 13.1629 | 0.643048 | 0.321524 | − | 0.946901i | \(-0.395805\pi\) | ||||
0.321524 | + | 0.946901i | \(0.395805\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −11.9413 | −0.581984 | −0.290992 | − | 0.956726i | \(-0.593985\pi\) | ||||
−0.290992 | + | 0.956726i | \(0.593985\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −2.82843 | −0.137523 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 2.11837 | 0.102756 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −18.2807 | −0.884663 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −4.97567 | −0.240227 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −30.6054 | −1.47421 | −0.737105 | − | 0.675778i | \(-0.763808\pi\) | ||||
−0.737105 | + | 0.675778i | \(0.763808\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 15.3137 | 0.735930 | 0.367965 | − | 0.929840i | \(-0.380055\pi\) | ||||
0.367965 | + | 0.929840i | \(0.380055\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 9.97474 | 0.478252 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 0.635767 | 0.0304128 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −33.3676 | −1.59255 | −0.796274 | − | 0.604936i | \(-0.793199\pi\) | ||||
−0.796274 | + | 0.604936i | \(0.793199\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −2.33897 | −0.111380 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 3.23617 | 0.153755 | 0.0768776 | − | 0.997041i | \(-0.475505\pi\) | ||||
0.0768776 | + | 0.997041i | \(0.475505\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −5.42522 | −0.257180 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 1.45479 | 0.0688091 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −27.4165 | −1.29387 | −0.646933 | − | 0.762547i | \(-0.723948\pi\) | ||||
−0.646933 | + | 0.762547i | \(0.723948\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −14.9550 | −0.704203 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 2.03696 | 0.0957049 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 16.0454 | 0.752221 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −10.9147 | −0.510567 | −0.255284 | − | 0.966866i | \(-0.582169\pi\) | ||||
−0.255284 | + | 0.966866i | \(0.582169\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −0.224777 | −0.0104917 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −25.2181 | −1.17452 | −0.587261 | − | 0.809398i | \(-0.699794\pi\) | ||||
−0.587261 | + | 0.809398i | \(0.699794\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 22.4937 | 1.04537 | 0.522686 | − | 0.852525i | \(-0.324930\pi\) | ||||
0.522686 | + | 0.852525i | \(0.324930\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 6.99222 | 0.324256 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 34.2482 | 1.58482 | 0.792408 | − | 0.609991i | \(-0.208827\pi\) | ||||
0.792408 | + | 0.609991i | \(0.208827\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −31.8275 | −1.46966 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −8.61790 | −0.397092 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −27.8852 | −1.28216 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 2.11837 | 0.0971974 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 10.6264 | 0.486548 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 36.2362 | 1.65568 | 0.827838 | − | 0.560968i | \(-0.189571\pi\) | ||||
0.827838 | + | 0.560968i | \(0.189571\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −10.1551 | −0.463032 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 6.10641 | 0.277851 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −62.2824 | −2.82810 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −16.8200 | −0.762186 | −0.381093 | − | 0.924537i | \(-0.624452\pi\) | ||||
−0.381093 | + | 0.924537i | \(0.624452\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 4.86054 | 0.219801 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −8.63577 | −0.389727 | −0.194863 | − | 0.980830i | \(-0.562426\pi\) | ||||
−0.194863 | + | 0.980830i | \(0.562426\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −0.590346 | −0.0265879 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −9.65685 | −0.434043 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −9.32206 | −0.418151 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −27.8275 | −1.24573 | −0.622865 | − | 0.782329i | \(-0.714031\pi\) | ||||
−0.622865 | + | 0.782329i | \(0.714031\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −21.7023 | −0.969586 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 25.7308 | 1.14728 | 0.573639 | − | 0.819108i | \(-0.305531\pi\) | ||||
0.573639 | + | 0.819108i | \(0.305531\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −0.439861 | −0.0195736 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 9.17064 | 0.407283 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 2.45386 | 0.108765 | 0.0543826 | − | 0.998520i | \(-0.482681\pi\) | ||||
0.0543826 | + | 0.998520i | \(0.482681\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −12.8991 | −0.570623 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −0.224777 | −0.00992417 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −50.7050 | −2.23433 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 7.19173 | 0.316292 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −12.3695 | −0.542959 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −33.5944 | −1.47180 | −0.735898 | − | 0.677092i | \(-0.763240\pi\) | ||||
−0.735898 | + | 0.677092i | \(0.763240\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 30.8522 | 1.34907 | 0.674536 | − | 0.738242i | \(-0.264344\pi\) | ||||
0.674536 | + | 0.738242i | \(0.264344\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 20.3465 | 0.887994 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −0.413828 | −0.0180266 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −15.0000 | −0.652174 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 5.65685 | 0.245487 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −11.5096 | −0.498537 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 39.0907 | 1.69004 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −11.6413 | −0.502359 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 5.94721 | 0.256164 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 38.4825 | 1.65449 | 0.827245 | − | 0.561841i | \(-0.189907\pi\) | ||||
0.827245 | + | 0.561841i | \(0.189907\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −9.50732 | −0.407998 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 37.8155 | 1.61984 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 9.61829 | 0.411248 | 0.205624 | − | 0.978631i | \(-0.434078\pi\) | ||||
0.205624 | + | 0.978631i | \(0.434078\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 8.46742 | 0.361381 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −0.590346 | −0.0251496 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −32.4004 | −1.37780 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −19.7091 | −0.836606 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 6.07174 | 0.257268 | 0.128634 | − | 0.991692i | \(-0.458941\pi\) | ||||
0.128634 | + | 0.991692i | \(0.458941\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −21.4609 | −0.907701 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0.571533 | 0.0241301 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −14.2554 | −0.600793 | −0.300397 | − | 0.953814i | \(-0.597119\pi\) | ||||
−0.300397 | + | 0.953814i | \(0.597119\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −71.5857 | −3.01163 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −2.15894 | −0.0906670 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −32.5018 | −1.36255 | −0.681274 | − | 0.732029i | \(-0.738574\pi\) | ||||
−0.681274 | + | 0.732029i | \(0.738574\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −12.9706 | −0.542801 | −0.271401 | − | 0.962466i | \(-0.587487\pi\) | ||||
−0.271401 | + | 0.962466i | \(0.587487\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −20.8032 | −0.869065 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 26.6559 | 1.11163 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 11.7536 | 0.489308 | 0.244654 | − | 0.969611i | \(-0.421326\pi\) | ||||
0.244654 | + | 0.969611i | \(0.421326\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −14.1454 | −0.587862 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 30.8857 | 1.28135 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −27.0192 | −1.11902 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −7.43208 | −0.307279 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −9.13585 | −0.377077 | −0.188538 | − | 0.982066i | \(-0.560375\pi\) | ||||
−0.188538 | + | 0.982066i | \(0.560375\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −0.413828 | −0.0170515 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −3.43463 | −0.141282 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −5.49270 | −0.225558 | −0.112779 | − | 0.993620i | \(-0.535975\pi\) | ||||
−0.112779 | + | 0.993620i | \(0.535975\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −1.84307 | −0.0755583 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0.306182 | 0.0125312 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 36.4348 | 1.48868 | 0.744342 | − | 0.667799i | \(-0.232763\pi\) | ||||
0.744342 | + | 0.667799i | \(0.232763\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −9.97474 | −0.406878 | −0.203439 | − | 0.979088i | \(-0.565212\pi\) | ||||
−0.203439 | + | 0.979088i | \(0.565212\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 14.7422 | 0.600348 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −17.2232 | −0.700221 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −4.51900 | −0.183421 | −0.0917103 | − | 0.995786i | \(-0.529233\pi\) | ||||
−0.0917103 | + | 0.995786i | \(0.529233\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −5.67016 | −0.229766 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 5.53488 | 0.223917 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 11.9316 | 0.481913 | 0.240957 | − | 0.970536i | \(-0.422539\pi\) | ||||
0.240957 | + | 0.970536i | \(0.422539\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −22.3380 | −0.900757 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −32.1201 | −1.29311 | −0.646554 | − | 0.762869i | \(-0.723790\pi\) | ||||
−0.646554 | + | 0.762869i | \(0.723790\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −21.2715 | −0.854975 | −0.427488 | − | 0.904021i | \(-0.640601\pi\) | ||||
−0.427488 | + | 0.904021i | \(0.640601\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −2.82843 | −0.113501 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 3.08398 | 0.123557 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 16.6958 | 0.667833 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0.571533 | 0.0228248 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 1.16647 | 0.0465101 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −36.4685 | −1.45179 | −0.725894 | − | 0.687807i | \(-0.758574\pi\) | ||||
−0.725894 | + | 0.687807i | \(0.758574\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −10.2284 | −0.406542 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 14.4921 | 0.575103 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 4.57707 | 0.181350 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 4.31788 | 0.170813 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 14.0036 | 0.553109 | 0.276555 | − | 0.960998i | \(-0.410807\pi\) | ||||
0.276555 | + | 0.960998i | \(0.410807\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −23.4807 | −0.925990 | −0.462995 | − | 0.886361i | \(-0.653225\pi\) | ||||
−0.462995 | + | 0.886361i | \(0.653225\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −41.6517 | −1.64004 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 12.1908 | 0.479270 | 0.239635 | − | 0.970863i | \(-0.422972\pi\) | ||||
0.239635 | + | 0.970863i | \(0.422972\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −14.3835 | −0.564600 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −3.97474 | −0.155782 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −1.39055 | −0.0544165 | −0.0272083 | − | 0.999630i | \(-0.508662\pi\) | ||||
−0.0272083 | + | 0.999630i | \(0.508662\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 4.12198 | 0.161059 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 5.97474 | 0.233097 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −25.5349 | −0.994698 | −0.497349 | − | 0.867551i | \(-0.665693\pi\) | ||||
−0.497349 | + | 0.867551i | \(0.665693\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −6.44726 | −0.250769 | −0.125385 | − | 0.992108i | \(-0.540017\pi\) | ||||
−0.125385 | + | 0.992108i | \(0.540017\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0.439861 | 0.0170828 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −1.84307 | −0.0714710 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −7.42847 | −0.287631 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −1.71908 | −0.0664635 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −21.5298 | −0.831148 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −10.8569 | −0.418504 | −0.209252 | − | 0.977862i | \(-0.567103\pi\) | ||||
−0.209252 | + | 0.977862i | \(0.567103\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −9.42429 | −0.362741 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −33.5262 | −1.28852 | −0.644259 | − | 0.764807i | \(-0.722834\pi\) | ||||
−0.644259 | + | 0.764807i | \(0.722834\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 35.4045 | 1.35870 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 14.3059 | 0.548204 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 25.2206 | 0.965040 | 0.482520 | − | 0.875885i | \(-0.339722\pi\) | ||||
0.482520 | + | 0.875885i | \(0.339722\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −20.1674 | −0.770557 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −16.9981 | −0.648519 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −20.7945 | −0.792205 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 15.3523 | 0.584028 | 0.292014 | − | 0.956414i | \(-0.405675\pi\) | ||||
0.292014 | + | 0.956414i | \(0.405675\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 5.48946 | 0.208527 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −47.0907 | −1.78625 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1.32206 | 0.0500765 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −13.3779 | −0.506000 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −8.61079 | −0.325225 | −0.162613 | − | 0.986690i | \(-0.551992\pi\) | ||||
−0.162613 | + | 0.986690i | \(0.551992\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1.16647 | 0.0439942 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 10.7422 | 0.404574 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0.250040 | 0.00940372 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −32.3624 | −1.21539 | −0.607697 | − | 0.794169i | \(-0.707906\pi\) | ||||
−0.607697 | + | 0.794169i | \(0.707906\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 15.0075 | 0.562826 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −5.20730 | −0.195015 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 18.8972 | 0.706717 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −13.3675 | −0.499218 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −1.46744 | −0.0547262 | −0.0273631 | − | 0.999626i | \(-0.508711\pi\) | ||||
−0.0273631 | + | 0.999626i | \(0.508711\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 28.8233 | 1.07344 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0.211474 | 0.00786481 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −24.7516 | −0.919251 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 15.3928 | 0.570889 | 0.285445 | − | 0.958395i | \(-0.407859\pi\) | ||||
0.285445 | + | 0.958395i | \(0.407859\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 2.46512 | 0.0911759 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −17.5624 | −0.648683 | −0.324342 | − | 0.945940i | \(-0.605143\pi\) | ||||
−0.324342 | + | 0.945940i | \(0.605143\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 8.88325 | 0.327664 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −37.4844 | −1.38075 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 20.7266 | 0.762441 | 0.381220 | − | 0.924484i | \(-0.375504\pi\) | ||||
0.381220 | + | 0.924484i | \(0.375504\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0.439861 | 0.0161587 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 31.7821 | 1.16597 | 0.582986 | − | 0.812482i | \(-0.301884\pi\) | ||||
0.582986 | + | 0.812482i | \(0.301884\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −5.52518 | −0.202427 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −14.3059 | −0.523426 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −22.2212 | −0.811944 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 29.7594 | 1.08594 | 0.542968 | − | 0.839753i | \(-0.317301\pi\) | ||||
0.542968 | + | 0.839753i | \(0.317301\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −14.7555 | −0.537720 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −7.73625 | −0.281551 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 22.1119 | 0.803672 | 0.401836 | − | 0.915712i | \(-0.368372\pi\) | ||||
0.401836 | + | 0.915712i | \(0.368372\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 7.19173 | 0.261043 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −4.55957 | −0.165284 | −0.0826422 | − | 0.996579i | \(-0.526336\pi\) | ||||
−0.0826422 | + | 0.996579i | \(0.526336\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −21.4963 | −0.778219 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0.853690 | 0.0308652 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −11.0698 | −0.399706 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 36.5794 | 1.31909 | 0.659543 | − | 0.751667i | \(-0.270750\pi\) | ||||
0.659543 | + | 0.751667i | \(0.270750\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0.742176 | 0.0267288 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 26.4611 | 0.951739 | 0.475869 | − | 0.879516i | \(-0.342133\pi\) | ||||
0.475869 | + | 0.879516i | \(0.342133\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −17.3507 | −0.623255 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 11.2037 | 0.401930 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 1.32206 | 0.0473676 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −10.9789 | −0.392856 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 2.62636 | 0.0938584 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 32.7302 | 1.16819 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 18.9164 | 0.674298 | 0.337149 | − | 0.941451i | \(-0.390537\pi\) | ||||
0.337149 | + | 0.941451i | \(0.390537\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 5.48435 | 0.195248 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 40.6930 | 1.44688 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −16.5697 | −0.588406 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −40.3582 | −1.43136 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −47.8065 | −1.69339 | −0.846697 | − | 0.532075i | \(-0.821412\pi\) | ||||
−0.846697 | + | 0.532075i | \(0.821412\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −0.635767 | −0.0224918 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −1.42847 | −0.0504724 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −15.1917 | −0.536105 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −23.1917 | −0.817401 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 20.4694 | 0.720558 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 29.9862 | 1.05426 | 0.527129 | − | 0.849785i | \(-0.323268\pi\) | ||||
0.527129 | + | 0.849785i | \(0.323268\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 11.3899 | 0.399954 | 0.199977 | − | 0.979801i | \(-0.435913\pi\) | ||||
0.199977 | + | 0.979801i | \(0.435913\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 14.0370 | 0.492298 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −18.4600 | −0.646626 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 2.46512 | 0.0862438 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 4.22478 | 0.147626 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 19.6929 | 0.687286 | 0.343643 | − | 0.939100i | \(-0.388339\pi\) | ||||
0.343643 | + | 0.939100i | \(0.388339\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −22.4666 | −0.783137 | −0.391568 | − | 0.920149i | \(-0.628067\pi\) | ||||
−0.391568 | + | 0.920149i | \(0.628067\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 23.9628 | 0.834277 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 10.7927 | 0.375299 | 0.187649 | − | 0.982236i | \(-0.439913\pi\) | ||||
0.187649 | + | 0.982236i | \(0.439913\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −45.9421 | −1.59563 | −0.797817 | − | 0.602900i | \(-0.794012\pi\) | ||||
−0.797817 | + | 0.602900i | \(0.794012\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −13.4211 | −0.465572 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −0.525748 | −0.0182161 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 82.4238 | 2.85239 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 1.84106 | 0.0636363 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −22.9142 | −0.791085 | −0.395542 | − | 0.918448i | \(-0.629443\pi\) | ||||
−0.395542 | + | 0.918448i | \(0.629443\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −22.1022 | −0.762146 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −3.89359 | −0.134102 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −34.8295 | −1.19817 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 9.79053 | 0.336407 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 17.6569 | 0.605982 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 14.6779 | 0.503153 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 55.0728 | 1.88566 | 0.942829 | − | 0.333278i | \(-0.108155\pi\) | ||||
0.942829 | + | 0.333278i | \(0.108155\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0.853690 | 0.0291956 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −1.79079 | −0.0611723 | −0.0305861 | − | 0.999532i | \(-0.509737\pi\) | ||||
−0.0305861 | + | 0.999532i | \(0.509737\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 25.5468 | 0.871647 | 0.435823 | − | 0.900032i | \(-0.356457\pi\) | ||||
0.435823 | + | 0.900032i | \(0.356457\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 12.6981 | 0.432750 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −42.1150 | −1.43361 | −0.716806 | − | 0.697273i | \(-0.754397\pi\) | ||||
−0.716806 | + | 0.697273i | \(0.754397\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 46.9784 | 1.59731 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 16.9495 | 0.575634 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −38.1590 | −1.29446 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −28.8486 | −0.977497 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −16.3990 | −0.555023 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −36.2771 | −1.22639 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −1.01044 | −0.0341203 | −0.0170601 | − | 0.999854i | \(-0.505431\pi\) | ||||
−0.0170601 | + | 0.999854i | \(0.505431\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −15.7759 | −0.532108 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 44.3972 | 1.49578 | 0.747889 | − | 0.663823i | \(-0.231067\pi\) | ||||
0.747889 | + | 0.663823i | \(0.231067\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 1.82389 | 0.0613787 | 0.0306894 | − | 0.999529i | \(-0.490230\pi\) | ||||
0.0306894 | + | 0.999529i | \(0.490230\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −21.4844 | −0.722189 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −4.38532 | −0.147245 | −0.0736223 | − | 0.997286i | \(-0.523456\pi\) | ||||
−0.0736223 | + | 0.997286i | \(0.523456\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −8.23808 | −0.276296 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −2.54266 | −0.0851823 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −0.635767 | −0.0212751 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 44.2128 | 1.47787 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 5.53488 | 0.184804 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 4.83528 | 0.161266 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 2.38857 | 0.0795747 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 23.6770 | 0.787922 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 36.1082 | 1.20028 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 4.06248 | 0.134893 | 0.0674463 | − | 0.997723i | \(-0.478515\pi\) | ||||
0.0674463 | + | 0.997723i | \(0.478515\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −0.115816 | −0.00384137 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 42.3784 | 1.40406 | 0.702029 | − | 0.712149i | \(-0.252278\pi\) | ||||
0.702029 | + | 0.712149i | \(0.252278\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 36.3751 | 1.20384 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −32.1587 | −1.06313 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −2.34315 | −0.0773775 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −44.8603 | −1.47980 | −0.739902 | − | 0.672715i | \(-0.765128\pi\) | ||||
−0.739902 | + | 0.672715i | \(0.765128\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 7.64129 | 0.251789 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −8.44955 | −0.278120 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 48.9068 | 1.60804 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −13.3507 | −0.438494 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −2.96695 | −0.0973426 | −0.0486713 | − | 0.998815i | \(-0.515499\pi\) | ||||
−0.0486713 | + | 0.998815i | \(0.515499\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −0.525748 | −0.0172307 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 24.1623 | 0.791038 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −2.17064 | −0.0709876 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 54.7669 | 1.78916 | 0.894579 | − | 0.446910i | \(-0.147476\pi\) | ||||
0.894579 | + | 0.446910i | \(0.147476\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 16.6105 | 0.542063 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 8.89558 | 0.289988 | 0.144994 | − | 0.989433i | \(-0.453684\pi\) | ||||
0.144994 | + | 0.989433i | \(0.453684\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 16.6358 | 0.541735 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 8.19951 | 0.266730 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −15.8541 | −0.515189 | −0.257595 | − | 0.966253i | \(-0.582930\pi\) | ||||
−0.257595 | + | 0.966253i | \(0.582930\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −11.6918 | −0.379532 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −2.56213 | −0.0830826 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −30.2807 | −0.980887 | −0.490443 | − | 0.871473i | \(-0.663165\pi\) | ||||
−0.490443 | + | 0.871473i | \(0.663165\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 79.0090 | 2.55667 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −6.67794 | −0.215867 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 11.4642 | 0.370198 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −27.6105 | −0.890661 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 10.2926 | 0.331675 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 53.7232 | 1.72941 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 10.5273 | 0.338537 | 0.169268 | − | 0.985570i | \(-0.445860\pi\) | ||||
0.169268 | + | 0.985570i | \(0.445860\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −0.0505249 | −0.00162309 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −38.7050 | −1.24210 | −0.621051 | − | 0.783771i | \(-0.713294\pi\) | ||||
−0.621051 | + | 0.783771i | \(0.713294\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 26.7688 | 0.858168 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 18.4422 | 0.590622 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 16.9009 | 0.540706 | 0.270353 | − | 0.962761i | \(-0.412860\pi\) | ||||
0.270353 | + | 0.962761i | \(0.412860\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 3.63211 | 0.116083 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 9.95687 | 0.317899 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 10.0798 | 0.321496 | 0.160748 | − | 0.986995i | \(-0.448609\pi\) | ||||
0.160748 | + | 0.986995i | \(0.448609\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 13.0445 | 0.415632 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −6.10641 | −0.194369 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 31.0192 | 0.986354 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 42.3446 | 1.34512 | 0.672561 | − | 0.740042i | \(-0.265194\pi\) | ||||
0.672561 | + | 0.740042i | \(0.265194\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 19.1275 | 0.606993 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −1.16286 | −0.0368651 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 47.6132 | 1.50793 | 0.753963 | − | 0.656917i | \(-0.228140\pi\) | ||||
0.753963 | + | 0.656917i | \(0.228140\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −5.18944 | −0.164186 |
(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 | 3072.2.a.n.1.4 | 4 | ||
3.2 | odd | 2 | 9216.2.a.x.1.1 | 4 | |||
4.3 | odd | 2 | 3072.2.a.t.1.4 | 4 | |||
8.3 | odd | 2 | 3072.2.a.i.1.1 | 4 | |||
8.5 | even | 2 | 3072.2.a.o.1.1 | 4 | |||
12.11 | even | 2 | 9216.2.a.y.1.1 | 4 | |||
16.3 | odd | 4 | 3072.2.d.f.1537.5 | 8 | |||
16.5 | even | 4 | 3072.2.d.i.1537.8 | 8 | |||
16.11 | odd | 4 | 3072.2.d.f.1537.4 | 8 | |||
16.13 | even | 4 | 3072.2.d.i.1537.1 | 8 | |||
24.5 | odd | 2 | 9216.2.a.bn.1.4 | 4 | |||
24.11 | even | 2 | 9216.2.a.bo.1.4 | 4 | |||
32.3 | odd | 8 | 48.2.j.a.13.3 | ✓ | 8 | ||
32.5 | even | 8 | 384.2.j.a.97.4 | 8 | |||
32.11 | odd | 8 | 48.2.j.a.37.3 | yes | 8 | ||
32.13 | even | 8 | 384.2.j.a.289.4 | 8 | |||
32.19 | odd | 8 | 384.2.j.b.289.2 | 8 | |||
32.21 | even | 8 | 192.2.j.a.49.1 | 8 | |||
32.27 | odd | 8 | 384.2.j.b.97.2 | 8 | |||
32.29 | even | 8 | 192.2.j.a.145.1 | 8 | |||
96.5 | odd | 8 | 1152.2.k.f.865.1 | 8 | |||
96.11 | even | 8 | 144.2.k.b.37.2 | 8 | |||
96.29 | odd | 8 | 576.2.k.b.145.4 | 8 | |||
96.35 | even | 8 | 144.2.k.b.109.2 | 8 | |||
96.53 | odd | 8 | 576.2.k.b.433.4 | 8 | |||
96.59 | even | 8 | 1152.2.k.c.865.1 | 8 | |||
96.77 | odd | 8 | 1152.2.k.f.289.1 | 8 | |||
96.83 | even | 8 | 1152.2.k.c.289.1 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
48.2.j.a.13.3 | ✓ | 8 | 32.3 | odd | 8 | ||
48.2.j.a.37.3 | yes | 8 | 32.11 | odd | 8 | ||
144.2.k.b.37.2 | 8 | 96.11 | even | 8 | |||
144.2.k.b.109.2 | 8 | 96.35 | even | 8 | |||
192.2.j.a.49.1 | 8 | 32.21 | even | 8 | |||
192.2.j.a.145.1 | 8 | 32.29 | even | 8 | |||
384.2.j.a.97.4 | 8 | 32.5 | even | 8 | |||
384.2.j.a.289.4 | 8 | 32.13 | even | 8 | |||
384.2.j.b.97.2 | 8 | 32.27 | odd | 8 | |||
384.2.j.b.289.2 | 8 | 32.19 | odd | 8 | |||
576.2.k.b.145.4 | 8 | 96.29 | odd | 8 | |||
576.2.k.b.433.4 | 8 | 96.53 | odd | 8 | |||
1152.2.k.c.289.1 | 8 | 96.83 | even | 8 | |||
1152.2.k.c.865.1 | 8 | 96.59 | even | 8 | |||
1152.2.k.f.289.1 | 8 | 96.77 | odd | 8 | |||
1152.2.k.f.865.1 | 8 | 96.5 | odd | 8 | |||
3072.2.a.i.1.1 | 4 | 8.3 | odd | 2 | |||
3072.2.a.n.1.4 | 4 | 1.1 | even | 1 | trivial | ||
3072.2.a.o.1.1 | 4 | 8.5 | even | 2 | |||
3072.2.a.t.1.4 | 4 | 4.3 | odd | 2 | |||
3072.2.d.f.1537.4 | 8 | 16.11 | odd | 4 | |||
3072.2.d.f.1537.5 | 8 | 16.3 | odd | 4 | |||
3072.2.d.i.1537.1 | 8 | 16.13 | even | 4 | |||
3072.2.d.i.1537.8 | 8 | 16.5 | even | 4 | |||
9216.2.a.x.1.1 | 4 | 3.2 | odd | 2 | |||
9216.2.a.y.1.1 | 4 | 12.11 | even | 2 | |||
9216.2.a.bn.1.4 | 4 | 24.5 | odd | 2 | |||
9216.2.a.bo.1.4 | 4 | 24.11 | even | 2 |