Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [9405,2,Mod(1,9405)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(9405, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("9405.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 9405 = 3^{2} \cdot 5 \cdot 11 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 9405.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: | \(75.0993031010\) |
Analytic rank: | \(0\) |
Dimension: | \(5\) |
Coefficient field: | \(\Q(\zeta_{22})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{5} - x^{4} - 4x^{3} + 3x^{2} + 3x - 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 1045) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.5 | ||
Root | \(1.91899\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 9405.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.39788 | 1.69556 | 0.847778 | − | 0.530352i | \(-0.177940\pi\) | ||||
0.847778 | + | 0.530352i | \(0.177940\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 3.74982 | 1.87491 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.89389 | −1.09379 | −0.546895 | − | 0.837201i | \(-0.684190\pi\) | ||||
−0.546895 | + | 0.837201i | \(0.684190\pi\) | |||||||
\(8\) | 4.19584 | 1.48345 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −2.39788 | −0.758275 | ||||||||
\(11\) | 1.00000 | 0.301511 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 4.73780 | 1.31403 | 0.657015 | − | 0.753878i | \(-0.271819\pi\) | ||||
0.657015 | + | 0.753878i | \(0.271819\pi\) | |||||||
\(14\) | −6.93920 | −1.85458 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 2.56149 | 0.640372 | ||||||||
\(17\) | 5.65389 | 1.37127 | 0.685635 | − | 0.727946i | \(-0.259525\pi\) | ||||
0.685635 | + | 0.727946i | \(0.259525\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.00000 | 0.229416 | ||||||||
\(20\) | −3.74982 | −0.838484 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 2.39788 | 0.511229 | ||||||||
\(23\) | 4.00714 | 0.835547 | 0.417773 | − | 0.908551i | \(-0.362811\pi\) | ||||
0.417773 | + | 0.908551i | \(0.362811\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 11.3607 | 2.22801 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −10.8516 | −2.05075 | ||||||||
\(29\) | −9.32825 | −1.73221 | −0.866106 | − | 0.499860i | \(-0.833385\pi\) | ||||
−0.866106 | + | 0.499860i | \(0.833385\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −6.60270 | −1.18588 | −0.592940 | − | 0.805247i | \(-0.702033\pi\) | ||||
−0.592940 | + | 0.805247i | \(0.702033\pi\) | |||||||
\(32\) | −2.24955 | −0.397669 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 13.5573 | 2.32506 | ||||||||
\(35\) | 2.89389 | 0.489157 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 6.07686 | 0.999029 | 0.499515 | − | 0.866305i | \(-0.333512\pi\) | ||||
0.499515 | + | 0.866305i | \(0.333512\pi\) | |||||||
\(38\) | 2.39788 | 0.388987 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −4.19584 | −0.663421 | ||||||||
\(41\) | −5.47333 | −0.854791 | −0.427395 | − | 0.904065i | \(-0.640569\pi\) | ||||
−0.427395 | + | 0.904065i | \(0.640569\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 10.9515 | 1.67009 | 0.835043 | − | 0.550185i | \(-0.185443\pi\) | ||||
0.835043 | + | 0.550185i | \(0.185443\pi\) | |||||||
\(44\) | 3.74982 | 0.565306 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 9.60863 | 1.41672 | ||||||||
\(47\) | 0.295438 | 0.0430940 | 0.0215470 | − | 0.999768i | \(-0.493141\pi\) | ||||
0.0215470 | + | 0.999768i | \(0.493141\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.37462 | 0.196375 | ||||||||
\(50\) | 2.39788 | 0.339111 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 17.7659 | 2.46368 | ||||||||
\(53\) | 3.81149 | 0.523549 | 0.261774 | − | 0.965129i | \(-0.415692\pi\) | ||||
0.261774 | + | 0.965129i | \(0.415692\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −1.00000 | −0.134840 | ||||||||
\(56\) | −12.1423 | −1.62259 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −22.3680 | −2.93706 | ||||||||
\(59\) | 5.54910 | 0.722431 | 0.361215 | − | 0.932482i | \(-0.382362\pi\) | ||||
0.361215 | + | 0.932482i | \(0.382362\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.01018 | −0.129340 | −0.0646700 | − | 0.997907i | \(-0.520599\pi\) | ||||
−0.0646700 | + | 0.997907i | \(0.520599\pi\) | |||||||
\(62\) | −15.8325 | −2.01073 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −10.5171 | −1.31464 | ||||||||
\(65\) | −4.73780 | −0.587652 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 6.98807 | 0.853729 | 0.426864 | − | 0.904316i | \(-0.359618\pi\) | ||||
0.426864 | + | 0.904316i | \(0.359618\pi\) | |||||||
\(68\) | 21.2010 | 2.57100 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 6.93920 | 0.829393 | ||||||||
\(71\) | 1.02085 | 0.121152 | 0.0605761 | − | 0.998164i | \(-0.480706\pi\) | ||||
0.0605761 | + | 0.998164i | \(0.480706\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −0.202033 | −0.0236462 | −0.0118231 | − | 0.999930i | \(-0.503763\pi\) | ||||
−0.0118231 | + | 0.999930i | \(0.503763\pi\) | |||||||
\(74\) | 14.5716 | 1.69391 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 3.74982 | 0.430133 | ||||||||
\(77\) | −2.89389 | −0.329790 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 7.28690 | 0.819840 | 0.409920 | − | 0.912121i | \(-0.365557\pi\) | ||||
0.409920 | + | 0.912121i | \(0.365557\pi\) | |||||||
\(80\) | −2.56149 | −0.286383 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −13.1244 | −1.44935 | ||||||||
\(83\) | 13.7041 | 1.50422 | 0.752109 | − | 0.659039i | \(-0.229037\pi\) | ||||
0.752109 | + | 0.659039i | \(0.229037\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −5.65389 | −0.613250 | ||||||||
\(86\) | 26.2603 | 2.83172 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 4.19584 | 0.447278 | ||||||||
\(89\) | 15.8152 | 1.67641 | 0.838203 | − | 0.545359i | \(-0.183606\pi\) | ||||
0.838203 | + | 0.545359i | \(0.183606\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −13.7107 | −1.43727 | ||||||||
\(92\) | 15.0260 | 1.56657 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0.708423 | 0.0730683 | ||||||||
\(95\) | −1.00000 | −0.102598 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 4.81308 | 0.488694 | 0.244347 | − | 0.969688i | \(-0.421426\pi\) | ||||
0.244347 | + | 0.969688i | \(0.421426\pi\) | |||||||
\(98\) | 3.29618 | 0.332964 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 3.74982 | 0.374982 | ||||||||
\(101\) | −1.76221 | −0.175346 | −0.0876730 | − | 0.996149i | \(-0.527943\pi\) | ||||
−0.0876730 | + | 0.996149i | \(0.527943\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −5.53571 | −0.545450 | −0.272725 | − | 0.962092i | \(-0.587925\pi\) | ||||
−0.272725 | + | 0.962092i | \(0.587925\pi\) | |||||||
\(104\) | 19.8791 | 1.94930 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 9.13949 | 0.887706 | ||||||||
\(107\) | 4.32073 | 0.417701 | 0.208851 | − | 0.977948i | \(-0.433028\pi\) | ||||
0.208851 | + | 0.977948i | \(0.433028\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −13.0039 | −1.24555 | −0.622776 | − | 0.782400i | \(-0.713995\pi\) | ||||
−0.622776 | + | 0.782400i | \(0.713995\pi\) | |||||||
\(110\) | −2.39788 | −0.228629 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −7.41267 | −0.700432 | ||||||||
\(113\) | 17.0047 | 1.59967 | 0.799833 | − | 0.600223i | \(-0.204922\pi\) | ||||
0.799833 | + | 0.600223i | \(0.204922\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −4.00714 | −0.373668 | ||||||||
\(116\) | −34.9792 | −3.24774 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 13.3061 | 1.22492 | ||||||||
\(119\) | −16.3618 | −1.49988 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | −2.42228 | −0.219303 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −24.7589 | −2.22342 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −9.80245 | −0.869826 | −0.434913 | − | 0.900472i | \(-0.643221\pi\) | ||||
−0.434913 | + | 0.900472i | \(0.643221\pi\) | |||||||
\(128\) | −20.7197 | −1.83138 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −11.3607 | −0.996396 | ||||||||
\(131\) | 13.4383 | 1.17411 | 0.587053 | − | 0.809549i | \(-0.300288\pi\) | ||||
0.587053 | + | 0.809549i | \(0.300288\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −2.89389 | −0.250932 | ||||||||
\(134\) | 16.7565 | 1.44754 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 23.7228 | 2.03422 | ||||||||
\(137\) | 16.2122 | 1.38510 | 0.692549 | − | 0.721371i | \(-0.256488\pi\) | ||||
0.692549 | + | 0.721371i | \(0.256488\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 19.0373 | 1.61472 | 0.807359 | − | 0.590060i | \(-0.200896\pi\) | ||||
0.807359 | + | 0.590060i | \(0.200896\pi\) | |||||||
\(140\) | 10.8516 | 0.917125 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 2.44787 | 0.205420 | ||||||||
\(143\) | 4.73780 | 0.396195 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 9.32825 | 0.774669 | ||||||||
\(146\) | −0.484451 | −0.0400934 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 22.7871 | 1.87309 | ||||||||
\(149\) | 15.3234 | 1.25534 | 0.627670 | − | 0.778480i | \(-0.284009\pi\) | ||||
0.627670 | + | 0.778480i | \(0.284009\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1.25936 | −0.102485 | −0.0512426 | − | 0.998686i | \(-0.516318\pi\) | ||||
−0.0512426 | + | 0.998686i | \(0.516318\pi\) | |||||||
\(152\) | 4.19584 | 0.340328 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −6.93920 | −0.559177 | ||||||||
\(155\) | 6.60270 | 0.530342 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 12.1861 | 0.972559 | 0.486279 | − | 0.873803i | \(-0.338354\pi\) | ||||
0.486279 | + | 0.873803i | \(0.338354\pi\) | |||||||
\(158\) | 17.4731 | 1.39008 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 2.24955 | 0.177843 | ||||||||
\(161\) | −11.5962 | −0.913912 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 6.09722 | 0.477571 | 0.238786 | − | 0.971072i | \(-0.423251\pi\) | ||||
0.238786 | + | 0.971072i | \(0.423251\pi\) | |||||||
\(164\) | −20.5240 | −1.60265 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 32.8607 | 2.55048 | ||||||||
\(167\) | −1.06720 | −0.0825826 | −0.0412913 | − | 0.999147i | \(-0.513147\pi\) | ||||
−0.0412913 | + | 0.999147i | \(0.513147\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 9.44675 | 0.726673 | ||||||||
\(170\) | −13.5573 | −1.03980 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 41.0661 | 3.13126 | ||||||||
\(173\) | 13.0289 | 0.990571 | 0.495286 | − | 0.868730i | \(-0.335063\pi\) | ||||
0.495286 | + | 0.868730i | \(0.335063\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −2.89389 | −0.218758 | ||||||||
\(176\) | 2.56149 | 0.193079 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 37.9229 | 2.84244 | ||||||||
\(179\) | −20.6273 | −1.54176 | −0.770878 | − | 0.636983i | \(-0.780182\pi\) | ||||
−0.770878 | + | 0.636983i | \(0.780182\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −20.5908 | −1.53050 | −0.765251 | − | 0.643732i | \(-0.777385\pi\) | ||||
−0.765251 | + | 0.643732i | \(0.777385\pi\) | |||||||
\(182\) | −32.8766 | −2.43697 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 16.8133 | 1.23950 | ||||||||
\(185\) | −6.07686 | −0.446779 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 5.65389 | 0.413453 | ||||||||
\(188\) | 1.10784 | 0.0807973 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −2.39788 | −0.173960 | ||||||||
\(191\) | −8.40047 | −0.607837 | −0.303918 | − | 0.952698i | \(-0.598295\pi\) | ||||
−0.303918 | + | 0.952698i | \(0.598295\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 11.4982 | 0.827661 | 0.413830 | − | 0.910354i | \(-0.364191\pi\) | ||||
0.413830 | + | 0.910354i | \(0.364191\pi\) | |||||||
\(194\) | 11.5412 | 0.828607 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 5.15458 | 0.368185 | ||||||||
\(197\) | −27.0376 | −1.92635 | −0.963173 | − | 0.268883i | \(-0.913345\pi\) | ||||
−0.963173 | + | 0.268883i | \(0.913345\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −5.18460 | −0.367526 | −0.183763 | − | 0.982971i | \(-0.558828\pi\) | ||||
−0.183763 | + | 0.982971i | \(0.558828\pi\) | |||||||
\(200\) | 4.19584 | 0.296691 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −4.22555 | −0.297309 | ||||||||
\(203\) | 26.9950 | 1.89468 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 5.47333 | 0.382274 | ||||||||
\(206\) | −13.2740 | −0.924840 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 12.1358 | 0.841467 | ||||||||
\(209\) | 1.00000 | 0.0691714 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −21.5427 | −1.48306 | −0.741529 | − | 0.670921i | \(-0.765899\pi\) | ||||
−0.741529 | + | 0.670921i | \(0.765899\pi\) | |||||||
\(212\) | 14.2924 | 0.981606 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 10.3606 | 0.708235 | ||||||||
\(215\) | −10.9515 | −0.746885 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 19.1075 | 1.29710 | ||||||||
\(218\) | −31.1818 | −2.11190 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −3.74982 | −0.252813 | ||||||||
\(221\) | 26.7870 | 1.80189 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −26.9600 | −1.80537 | −0.902687 | − | 0.430298i | \(-0.858408\pi\) | ||||
−0.902687 | + | 0.430298i | \(0.858408\pi\) | |||||||
\(224\) | 6.50997 | 0.434966 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 40.7751 | 2.71232 | ||||||||
\(227\) | −9.02570 | −0.599057 | −0.299528 | − | 0.954087i | \(-0.596829\pi\) | ||||
−0.299528 | + | 0.954087i | \(0.596829\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −13.7697 | −0.909926 | −0.454963 | − | 0.890510i | \(-0.650347\pi\) | ||||
−0.454963 | + | 0.890510i | \(0.650347\pi\) | |||||||
\(230\) | −9.60863 | −0.633575 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −39.1399 | −2.56966 | ||||||||
\(233\) | 2.45587 | 0.160890 | 0.0804448 | − | 0.996759i | \(-0.474366\pi\) | ||||
0.0804448 | + | 0.996759i | \(0.474366\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −0.295438 | −0.0192722 | ||||||||
\(236\) | 20.8081 | 1.35449 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −39.2335 | −2.54313 | ||||||||
\(239\) | 22.8439 | 1.47765 | 0.738825 | − | 0.673897i | \(-0.235381\pi\) | ||||
0.738825 | + | 0.673897i | \(0.235381\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 16.1181 | 1.03826 | 0.519129 | − | 0.854696i | \(-0.326256\pi\) | ||||
0.519129 | + | 0.854696i | \(0.326256\pi\) | |||||||
\(242\) | 2.39788 | 0.154141 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −3.78798 | −0.242501 | ||||||||
\(245\) | −1.37462 | −0.0878215 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 4.73780 | 0.301459 | ||||||||
\(248\) | −27.7039 | −1.75920 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −2.39788 | −0.151655 | ||||||||
\(251\) | 18.8758 | 1.19143 | 0.595716 | − | 0.803195i | \(-0.296868\pi\) | ||||
0.595716 | + | 0.803195i | \(0.296868\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 4.00714 | 0.251927 | ||||||||
\(254\) | −23.5051 | −1.47484 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −28.6490 | −1.79056 | ||||||||
\(257\) | −7.48029 | −0.466608 | −0.233304 | − | 0.972404i | \(-0.574954\pi\) | ||||
−0.233304 | + | 0.972404i | \(0.574954\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −17.5858 | −1.09273 | ||||||||
\(260\) | −17.7659 | −1.10179 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 32.2233 | 1.99076 | ||||||||
\(263\) | 17.7703 | 1.09577 | 0.547883 | − | 0.836555i | \(-0.315434\pi\) | ||||
0.547883 | + | 0.836555i | \(0.315434\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −3.81149 | −0.234138 | ||||||||
\(266\) | −6.93920 | −0.425470 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 26.2040 | 1.60066 | ||||||||
\(269\) | −25.9320 | −1.58110 | −0.790550 | − | 0.612398i | \(-0.790205\pi\) | ||||
−0.790550 | + | 0.612398i | \(0.790205\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −16.2686 | −0.988248 | −0.494124 | − | 0.869391i | \(-0.664511\pi\) | ||||
−0.494124 | + | 0.869391i | \(0.664511\pi\) | |||||||
\(272\) | 14.4824 | 0.878122 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 38.8748 | 2.34851 | ||||||||
\(275\) | 1.00000 | 0.0603023 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −17.9217 | −1.07681 | −0.538405 | − | 0.842686i | \(-0.680973\pi\) | ||||
−0.538405 | + | 0.842686i | \(0.680973\pi\) | |||||||
\(278\) | 45.6490 | 2.73784 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 12.1423 | 0.725643 | ||||||||
\(281\) | 28.8563 | 1.72142 | 0.860712 | − | 0.509093i | \(-0.170019\pi\) | ||||
0.860712 | + | 0.509093i | \(0.170019\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −10.7620 | −0.639736 | −0.319868 | − | 0.947462i | \(-0.603639\pi\) | ||||
−0.319868 | + | 0.947462i | \(0.603639\pi\) | |||||||
\(284\) | 3.82799 | 0.227149 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 11.3607 | 0.671770 | ||||||||
\(287\) | 15.8392 | 0.934961 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 14.9665 | 0.880380 | ||||||||
\(290\) | 22.3680 | 1.31349 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −0.757587 | −0.0443345 | ||||||||
\(293\) | −5.14307 | −0.300462 | −0.150231 | − | 0.988651i | \(-0.548002\pi\) | ||||
−0.150231 | + | 0.988651i | \(0.548002\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −5.54910 | −0.323081 | ||||||||
\(296\) | 25.4975 | 1.48201 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 36.7436 | 2.12850 | ||||||||
\(299\) | 18.9850 | 1.09793 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −31.6924 | −1.82672 | ||||||||
\(302\) | −3.01979 | −0.173769 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 2.56149 | 0.146911 | ||||||||
\(305\) | 1.01018 | 0.0578427 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 28.1017 | 1.60385 | 0.801925 | − | 0.597425i | \(-0.203809\pi\) | ||||
0.801925 | + | 0.597425i | \(0.203809\pi\) | |||||||
\(308\) | −10.8516 | −0.618326 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 15.8325 | 0.899224 | ||||||||
\(311\) | 14.1909 | 0.804692 | 0.402346 | − | 0.915488i | \(-0.368195\pi\) | ||||
0.402346 | + | 0.915488i | \(0.368195\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −9.46083 | −0.534758 | −0.267379 | − | 0.963591i | \(-0.586158\pi\) | ||||
−0.267379 | + | 0.963591i | \(0.586158\pi\) | |||||||
\(314\) | 29.2208 | 1.64903 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 27.3245 | 1.53712 | ||||||||
\(317\) | 23.8673 | 1.34052 | 0.670260 | − | 0.742126i | \(-0.266182\pi\) | ||||
0.670260 | + | 0.742126i | \(0.266182\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −9.32825 | −0.522282 | ||||||||
\(320\) | 10.5171 | 0.587926 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −27.8064 | −1.54959 | ||||||||
\(323\) | 5.65389 | 0.314591 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 4.73780 | 0.262806 | ||||||||
\(326\) | 14.6204 | 0.809748 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −22.9652 | −1.26804 | ||||||||
\(329\) | −0.854966 | −0.0471358 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −13.1843 | −0.724674 | −0.362337 | − | 0.932047i | \(-0.618021\pi\) | ||||
−0.362337 | + | 0.932047i | \(0.618021\pi\) | |||||||
\(332\) | 51.3877 | 2.82027 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −2.55902 | −0.140023 | ||||||||
\(335\) | −6.98807 | −0.381799 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 17.0148 | 0.926854 | 0.463427 | − | 0.886135i | \(-0.346620\pi\) | ||||
0.463427 | + | 0.886135i | \(0.346620\pi\) | |||||||
\(338\) | 22.6521 | 1.23211 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −21.2010 | −1.14979 | ||||||||
\(341\) | −6.60270 | −0.357556 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 16.2792 | 0.878997 | ||||||||
\(344\) | 45.9507 | 2.47750 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 31.2418 | 1.67957 | ||||||||
\(347\) | 30.2606 | 1.62447 | 0.812236 | − | 0.583329i | \(-0.198250\pi\) | ||||
0.812236 | + | 0.583329i | \(0.198250\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 5.13463 | 0.274851 | 0.137425 | − | 0.990512i | \(-0.456117\pi\) | ||||
0.137425 | + | 0.990512i | \(0.456117\pi\) | |||||||
\(350\) | −6.93920 | −0.370916 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −2.24955 | −0.119902 | ||||||||
\(353\) | 10.5661 | 0.562376 | 0.281188 | − | 0.959653i | \(-0.409272\pi\) | ||||
0.281188 | + | 0.959653i | \(0.409272\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −1.02085 | −0.0541809 | ||||||||
\(356\) | 59.3040 | 3.14311 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −49.4617 | −2.61413 | ||||||||
\(359\) | −16.5178 | −0.871778 | −0.435889 | − | 0.900000i | \(-0.643566\pi\) | ||||
−0.435889 | + | 0.900000i | \(0.643566\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | −49.3742 | −2.59505 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −51.4126 | −2.69475 | ||||||||
\(365\) | 0.202033 | 0.0105749 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 19.8761 | 1.03752 | 0.518762 | − | 0.854919i | \(-0.326393\pi\) | ||||
0.518762 | + | 0.854919i | \(0.326393\pi\) | |||||||
\(368\) | 10.2642 | 0.535061 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −14.5716 | −0.757539 | ||||||||
\(371\) | −11.0301 | −0.572652 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −11.4151 | −0.591052 | −0.295526 | − | 0.955335i | \(-0.595495\pi\) | ||||
−0.295526 | + | 0.955335i | \(0.595495\pi\) | |||||||
\(374\) | 13.5573 | 0.701033 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 1.23961 | 0.0639280 | ||||||||
\(377\) | −44.1954 | −2.27618 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 1.99925 | 0.102695 | 0.0513474 | − | 0.998681i | \(-0.483648\pi\) | ||||
0.0513474 | + | 0.998681i | \(0.483648\pi\) | |||||||
\(380\) | −3.74982 | −0.192362 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −20.1433 | −1.03062 | ||||||||
\(383\) | 7.07007 | 0.361264 | 0.180632 | − | 0.983551i | \(-0.442186\pi\) | ||||
0.180632 | + | 0.983551i | \(0.442186\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 2.89389 | 0.147487 | ||||||||
\(386\) | 27.5713 | 1.40334 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 18.0481 | 0.916256 | ||||||||
\(389\) | −17.0237 | −0.863135 | −0.431568 | − | 0.902081i | \(-0.642039\pi\) | ||||
−0.431568 | + | 0.902081i | \(0.642039\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 22.6559 | 1.14576 | ||||||||
\(392\) | 5.76771 | 0.291313 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −64.8327 | −3.26623 | ||||||||
\(395\) | −7.28690 | −0.366644 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −25.3590 | −1.27273 | −0.636366 | − | 0.771387i | \(-0.719563\pi\) | ||||
−0.636366 | + | 0.771387i | \(0.719563\pi\) | |||||||
\(398\) | −12.4320 | −0.623161 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 2.56149 | 0.128074 | ||||||||
\(401\) | −19.6449 | −0.981019 | −0.490509 | − | 0.871436i | \(-0.663189\pi\) | ||||
−0.490509 | + | 0.871436i | \(0.663189\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −31.2823 | −1.55828 | ||||||||
\(404\) | −6.60795 | −0.328758 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 64.7306 | 3.21253 | ||||||||
\(407\) | 6.07686 | 0.301219 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −28.6527 | −1.41678 | −0.708392 | − | 0.705819i | \(-0.750579\pi\) | ||||
−0.708392 | + | 0.705819i | \(0.750579\pi\) | |||||||
\(410\) | 13.1244 | 0.648167 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −20.7579 | −1.02267 | ||||||||
\(413\) | −16.0585 | −0.790187 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −13.7041 | −0.672706 | ||||||||
\(416\) | −10.6579 | −0.522548 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 2.39788 | 0.117284 | ||||||||
\(419\) | 2.80518 | 0.137042 | 0.0685211 | − | 0.997650i | \(-0.478172\pi\) | ||||
0.0685211 | + | 0.997650i | \(0.478172\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 3.26165 | 0.158963 | 0.0794815 | − | 0.996836i | \(-0.474674\pi\) | ||||
0.0794815 | + | 0.996836i | \(0.474674\pi\) | |||||||
\(422\) | −51.6566 | −2.51461 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 15.9924 | 0.776661 | ||||||||
\(425\) | 5.65389 | 0.274254 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 2.92335 | 0.141471 | ||||||||
\(428\) | 16.2020 | 0.783151 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −26.2603 | −1.26639 | ||||||||
\(431\) | −32.7606 | −1.57802 | −0.789012 | − | 0.614378i | \(-0.789407\pi\) | ||||
−0.789012 | + | 0.614378i | \(0.789407\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −21.8656 | −1.05079 | −0.525396 | − | 0.850858i | \(-0.676083\pi\) | ||||
−0.525396 | + | 0.850858i | \(0.676083\pi\) | |||||||
\(434\) | 45.8175 | 2.19931 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −48.7624 | −2.33529 | ||||||||
\(437\) | 4.00714 | 0.191688 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 30.6280 | 1.46180 | 0.730898 | − | 0.682486i | \(-0.239101\pi\) | ||||
0.730898 | + | 0.682486i | \(0.239101\pi\) | |||||||
\(440\) | −4.19584 | −0.200029 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 64.2319 | 3.05520 | ||||||||
\(443\) | −4.54914 | −0.216136 | −0.108068 | − | 0.994144i | \(-0.534466\pi\) | ||||
−0.108068 | + | 0.994144i | \(0.534466\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −15.8152 | −0.749711 | ||||||||
\(446\) | −64.6467 | −3.06111 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 30.4355 | 1.43794 | ||||||||
\(449\) | −11.5308 | −0.544172 | −0.272086 | − | 0.962273i | \(-0.587714\pi\) | ||||
−0.272086 | + | 0.962273i | \(0.587714\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −5.47333 | −0.257729 | ||||||||
\(452\) | 63.7644 | 2.99923 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −21.6425 | −1.01573 | ||||||||
\(455\) | 13.7107 | 0.642767 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 11.3778 | 0.532231 | 0.266115 | − | 0.963941i | \(-0.414260\pi\) | ||||
0.266115 | + | 0.963941i | \(0.414260\pi\) | |||||||
\(458\) | −33.0180 | −1.54283 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −15.0260 | −0.700593 | ||||||||
\(461\) | −4.37265 | −0.203655 | −0.101827 | − | 0.994802i | \(-0.532469\pi\) | ||||
−0.101827 | + | 0.994802i | \(0.532469\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −9.31982 | −0.433129 | −0.216564 | − | 0.976268i | \(-0.569485\pi\) | ||||
−0.216564 | + | 0.976268i | \(0.569485\pi\) | |||||||
\(464\) | −23.8942 | −1.10926 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 5.88888 | 0.272797 | ||||||||
\(467\) | 28.0711 | 1.29897 | 0.649487 | − | 0.760372i | \(-0.274984\pi\) | ||||
0.649487 | + | 0.760372i | \(0.274984\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −20.2227 | −0.933799 | ||||||||
\(470\) | −0.708423 | −0.0326771 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 23.2831 | 1.07169 | ||||||||
\(473\) | 10.9515 | 0.503550 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1.00000 | 0.0458831 | ||||||||
\(476\) | −61.3536 | −2.81214 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 54.7769 | 2.50544 | ||||||||
\(479\) | 5.65184 | 0.258239 | 0.129120 | − | 0.991629i | \(-0.458785\pi\) | ||||
0.129120 | + | 0.991629i | \(0.458785\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 28.7909 | 1.31275 | ||||||||
\(482\) | 38.6492 | 1.76042 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 3.74982 | 0.170446 | ||||||||
\(485\) | −4.81308 | −0.218550 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −6.09349 | −0.276122 | −0.138061 | − | 0.990424i | \(-0.544087\pi\) | ||||
−0.138061 | + | 0.990424i | \(0.544087\pi\) | |||||||
\(488\) | −4.23855 | −0.191870 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −3.29618 | −0.148906 | ||||||||
\(491\) | −8.56286 | −0.386436 | −0.193218 | − | 0.981156i | \(-0.561893\pi\) | ||||
−0.193218 | + | 0.981156i | \(0.561893\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −52.7409 | −2.37533 | ||||||||
\(494\) | 11.3607 | 0.511140 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −16.9127 | −0.759404 | ||||||||
\(497\) | −2.95422 | −0.132515 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −1.35537 | −0.0606749 | −0.0303374 | − | 0.999540i | \(-0.509658\pi\) | ||||
−0.0303374 | + | 0.999540i | \(0.509658\pi\) | |||||||
\(500\) | −3.74982 | −0.167697 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 45.2619 | 2.02014 | ||||||||
\(503\) | −13.9030 | −0.619903 | −0.309952 | − | 0.950752i | \(-0.600313\pi\) | ||||
−0.309952 | + | 0.950752i | \(0.600313\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 1.76221 | 0.0784172 | ||||||||
\(506\) | 9.60863 | 0.427156 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −36.7574 | −1.63084 | ||||||||
\(509\) | 3.21978 | 0.142714 | 0.0713572 | − | 0.997451i | \(-0.477267\pi\) | ||||
0.0713572 | + | 0.997451i | \(0.477267\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0.584663 | 0.0258640 | ||||||||
\(512\) | −27.2574 | −1.20462 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −17.9368 | −0.791160 | ||||||||
\(515\) | 5.53571 | 0.243933 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0.295438 | 0.0129933 | ||||||||
\(518\) | −42.1686 | −1.85278 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −19.8791 | −0.871755 | ||||||||
\(521\) | −3.09750 | −0.135704 | −0.0678520 | − | 0.997695i | \(-0.521615\pi\) | ||||
−0.0678520 | + | 0.997695i | \(0.521615\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 13.2007 | 0.577228 | 0.288614 | − | 0.957446i | \(-0.406806\pi\) | ||||
0.288614 | + | 0.957446i | \(0.406806\pi\) | |||||||
\(524\) | 50.3910 | 2.20134 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 42.6111 | 1.85793 | ||||||||
\(527\) | −37.3309 | −1.62616 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −6.94281 | −0.301861 | ||||||||
\(530\) | −9.13949 | −0.396994 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −10.8516 | −0.470475 | ||||||||
\(533\) | −25.9316 | −1.12322 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −4.32073 | −0.186802 | ||||||||
\(536\) | 29.3209 | 1.26647 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −62.1817 | −2.68084 | ||||||||
\(539\) | 1.37462 | 0.0592092 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −6.57608 | −0.282728 | −0.141364 | − | 0.989958i | \(-0.545149\pi\) | ||||
−0.141364 | + | 0.989958i | \(0.545149\pi\) | |||||||
\(542\) | −39.0102 | −1.67563 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −12.7187 | −0.545311 | ||||||||
\(545\) | 13.0039 | 0.557028 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −23.9559 | −1.02428 | −0.512139 | − | 0.858902i | \(-0.671147\pi\) | ||||
−0.512139 | + | 0.858902i | \(0.671147\pi\) | |||||||
\(548\) | 60.7926 | 2.59693 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 2.39788 | 0.102246 | ||||||||
\(551\) | −9.32825 | −0.397397 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −21.0875 | −0.896732 | ||||||||
\(554\) | −42.9740 | −1.82579 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 71.3862 | 3.02745 | ||||||||
\(557\) | 11.2404 | 0.476271 | 0.238135 | − | 0.971232i | \(-0.423464\pi\) | ||||
0.238135 | + | 0.971232i | \(0.423464\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 51.8860 | 2.19454 | ||||||||
\(560\) | 7.41267 | 0.313243 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 69.1939 | 2.91877 | ||||||||
\(563\) | −44.9880 | −1.89602 | −0.948009 | − | 0.318242i | \(-0.896907\pi\) | ||||
−0.948009 | + | 0.318242i | \(0.896907\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −17.0047 | −0.715392 | ||||||||
\(566\) | −25.8060 | −1.08471 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 4.28331 | 0.179724 | ||||||||
\(569\) | −33.2099 | −1.39223 | −0.696115 | − | 0.717930i | \(-0.745090\pi\) | ||||
−0.696115 | + | 0.717930i | \(0.745090\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −44.6440 | −1.86829 | −0.934146 | − | 0.356891i | \(-0.883837\pi\) | ||||
−0.934146 | + | 0.356891i | \(0.883837\pi\) | |||||||
\(572\) | 17.7659 | 0.742829 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 37.9806 | 1.58528 | ||||||||
\(575\) | 4.00714 | 0.167109 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −45.6776 | −1.90158 | −0.950792 | − | 0.309831i | \(-0.899728\pi\) | ||||
−0.950792 | + | 0.309831i | \(0.899728\pi\) | |||||||
\(578\) | 35.8877 | 1.49273 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 34.9792 | 1.45243 | ||||||||
\(581\) | −39.6581 | −1.64530 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 3.81149 | 0.157856 | ||||||||
\(584\) | −0.847700 | −0.0350781 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −12.3325 | −0.509449 | ||||||||
\(587\) | 17.5933 | 0.726155 | 0.363078 | − | 0.931759i | \(-0.381726\pi\) | ||||
0.363078 | + | 0.931759i | \(0.381726\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −6.60270 | −0.272060 | ||||||||
\(590\) | −13.3061 | −0.547802 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 15.5658 | 0.639750 | ||||||||
\(593\) | −32.4709 | −1.33342 | −0.666710 | − | 0.745317i | \(-0.732298\pi\) | ||||
−0.666710 | + | 0.745317i | \(0.732298\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 16.3618 | 0.670767 | ||||||||
\(596\) | 57.4598 | 2.35365 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 45.5238 | 1.86161 | ||||||||
\(599\) | −1.31594 | −0.0537679 | −0.0268839 | − | 0.999639i | \(-0.508558\pi\) | ||||
−0.0268839 | + | 0.999639i | \(0.508558\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −4.53331 | −0.184918 | −0.0924588 | − | 0.995717i | \(-0.529473\pi\) | ||||
−0.0924588 | + | 0.995717i | \(0.529473\pi\) | |||||||
\(602\) | −75.9946 | −3.09731 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −4.72236 | −0.192150 | ||||||||
\(605\) | −1.00000 | −0.0406558 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −14.2654 | −0.579016 | −0.289508 | − | 0.957176i | \(-0.593492\pi\) | ||||
−0.289508 | + | 0.957176i | \(0.593492\pi\) | |||||||
\(608\) | −2.24955 | −0.0912315 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 2.42228 | 0.0980754 | ||||||||
\(611\) | 1.39972 | 0.0566268 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 5.06662 | 0.204639 | 0.102319 | − | 0.994752i | \(-0.467374\pi\) | ||||
0.102319 | + | 0.994752i | \(0.467374\pi\) | |||||||
\(614\) | 67.3845 | 2.71942 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −12.1423 | −0.489228 | ||||||||
\(617\) | −19.5460 | −0.786893 | −0.393446 | − | 0.919348i | \(-0.628717\pi\) | ||||
−0.393446 | + | 0.919348i | \(0.628717\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 8.78654 | 0.353161 | 0.176580 | − | 0.984286i | \(-0.443496\pi\) | ||||
0.176580 | + | 0.984286i | \(0.443496\pi\) | |||||||
\(620\) | 24.7589 | 0.994342 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 34.0280 | 1.36440 | ||||||||
\(623\) | −45.7675 | −1.83363 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | −22.6859 | −0.906712 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 45.6957 | 1.82346 | ||||||||
\(629\) | 34.3579 | 1.36994 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −0.0559751 | −0.00222833 | −0.00111417 | − | 0.999999i | \(-0.500355\pi\) | ||||
−0.00111417 | + | 0.999999i | \(0.500355\pi\) | |||||||
\(632\) | 30.5747 | 1.21620 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 57.2308 | 2.27293 | ||||||||
\(635\) | 9.80245 | 0.388998 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 6.51269 | 0.258042 | ||||||||
\(638\) | −22.3680 | −0.885558 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 20.7197 | 0.819017 | ||||||||
\(641\) | −4.49262 | −0.177448 | −0.0887239 | − | 0.996056i | \(-0.528279\pi\) | ||||
−0.0887239 | + | 0.996056i | \(0.528279\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −5.48669 | −0.216374 | −0.108187 | − | 0.994131i | \(-0.534505\pi\) | ||||
−0.108187 | + | 0.994131i | \(0.534505\pi\) | |||||||
\(644\) | −43.4838 | −1.71350 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 13.5573 | 0.533406 | ||||||||
\(647\) | 34.5798 | 1.35947 | 0.679736 | − | 0.733456i | \(-0.262094\pi\) | ||||
0.679736 | + | 0.733456i | \(0.262094\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 5.54910 | 0.217821 | ||||||||
\(650\) | 11.3607 | 0.445602 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 22.8635 | 0.895402 | ||||||||
\(653\) | −11.3537 | −0.444304 | −0.222152 | − | 0.975012i | \(-0.571308\pi\) | ||||
−0.222152 | + | 0.975012i | \(0.571308\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −13.4383 | −0.525076 | ||||||||
\(656\) | −14.0199 | −0.547384 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −2.05010 | −0.0799213 | ||||||||
\(659\) | −27.1448 | −1.05741 | −0.528706 | − | 0.848805i | \(-0.677323\pi\) | ||||
−0.528706 | + | 0.848805i | \(0.677323\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 5.01901 | 0.195217 | 0.0976084 | − | 0.995225i | \(-0.468881\pi\) | ||||
0.0976084 | + | 0.995225i | \(0.468881\pi\) | |||||||
\(662\) | −31.6143 | −1.22873 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 57.5002 | 2.23144 | ||||||||
\(665\) | 2.89389 | 0.112220 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −37.3796 | −1.44734 | ||||||||
\(668\) | −4.00181 | −0.154835 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −16.7565 | −0.647362 | ||||||||
\(671\) | −1.01018 | −0.0389975 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −38.5035 | −1.48420 | −0.742100 | − | 0.670289i | \(-0.766170\pi\) | ||||
−0.742100 | + | 0.670289i | \(0.766170\pi\) | |||||||
\(674\) | 40.7994 | 1.57153 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 35.4236 | 1.36244 | ||||||||
\(677\) | −17.8660 | −0.686647 | −0.343324 | − | 0.939217i | \(-0.611553\pi\) | ||||
−0.343324 | + | 0.939217i | \(0.611553\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −13.9285 | −0.534528 | ||||||||
\(680\) | −23.7228 | −0.909729 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −15.8325 | −0.606257 | ||||||||
\(683\) | −44.9512 | −1.72001 | −0.860005 | − | 0.510286i | \(-0.829540\pi\) | ||||
−0.860005 | + | 0.510286i | \(0.829540\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −16.2122 | −0.619435 | ||||||||
\(686\) | 39.0356 | 1.49039 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 28.0521 | 1.06948 | ||||||||
\(689\) | 18.0581 | 0.687958 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 24.1309 | 0.917983 | 0.458991 | − | 0.888441i | \(-0.348211\pi\) | ||||
0.458991 | + | 0.888441i | \(0.348211\pi\) | |||||||
\(692\) | 48.8561 | 1.85723 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 72.5611 | 2.75438 | ||||||||
\(695\) | −19.0373 | −0.722124 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −30.9456 | −1.17215 | ||||||||
\(698\) | 12.3122 | 0.466024 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −10.8516 | −0.410151 | ||||||||
\(701\) | 1.53772 | 0.0580789 | 0.0290395 | − | 0.999578i | \(-0.490755\pi\) | ||||
0.0290395 | + | 0.999578i | \(0.490755\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 6.07686 | 0.229193 | ||||||||
\(704\) | −10.5171 | −0.396379 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 25.3362 | 0.953540 | ||||||||
\(707\) | 5.09964 | 0.191792 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 5.19348 | 0.195045 | 0.0975226 | − | 0.995233i | \(-0.468908\pi\) | ||||
0.0975226 | + | 0.995233i | \(0.468908\pi\) | |||||||
\(710\) | −2.44787 | −0.0918668 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 66.3580 | 2.48687 | ||||||||
\(713\) | −26.4580 | −0.990858 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −4.73780 | −0.177184 | ||||||||
\(716\) | −77.3485 | −2.89065 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −39.6077 | −1.47815 | ||||||||
\(719\) | 37.4841 | 1.39792 | 0.698960 | − | 0.715160i | \(-0.253646\pi\) | ||||
0.698960 | + | 0.715160i | \(0.253646\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 16.0198 | 0.596607 | ||||||||
\(722\) | 2.39788 | 0.0892398 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −77.2117 | −2.86955 | ||||||||
\(725\) | −9.32825 | −0.346443 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 28.1916 | 1.04557 | 0.522785 | − | 0.852464i | \(-0.324893\pi\) | ||||
0.522785 | + | 0.852464i | \(0.324893\pi\) | |||||||
\(728\) | −57.5279 | −2.13213 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0.484451 | 0.0179303 | ||||||||
\(731\) | 61.9185 | 2.29014 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −18.1906 | −0.671884 | −0.335942 | − | 0.941883i | \(-0.609055\pi\) | ||||
−0.335942 | + | 0.941883i | \(0.609055\pi\) | |||||||
\(734\) | 47.6604 | 1.75918 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −9.01428 | −0.332271 | ||||||||
\(737\) | 6.98807 | 0.257409 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 5.65484 | 0.208017 | 0.104008 | − | 0.994576i | \(-0.466833\pi\) | ||||
0.104008 | + | 0.994576i | \(0.466833\pi\) | |||||||
\(740\) | −22.7871 | −0.837670 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −26.4487 | −0.970963 | ||||||||
\(743\) | 44.5565 | 1.63462 | 0.817310 | − | 0.576198i | \(-0.195464\pi\) | ||||
0.817310 | + | 0.576198i | \(0.195464\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −15.3234 | −0.561405 | ||||||||
\(746\) | −27.3720 | −1.00216 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 21.2010 | 0.775187 | ||||||||
\(749\) | −12.5037 | −0.456877 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −18.8205 | −0.686769 | −0.343384 | − | 0.939195i | \(-0.611573\pi\) | ||||
−0.343384 | + | 0.939195i | \(0.611573\pi\) | |||||||
\(752\) | 0.756760 | 0.0275962 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −105.975 | −3.85939 | ||||||||
\(755\) | 1.25936 | 0.0458328 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 2.97780 | 0.108230 | 0.0541150 | − | 0.998535i | \(-0.482766\pi\) | ||||
0.0541150 | + | 0.998535i | \(0.482766\pi\) | |||||||
\(758\) | 4.79397 | 0.174125 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −4.19584 | −0.152199 | ||||||||
\(761\) | 41.9642 | 1.52120 | 0.760601 | − | 0.649219i | \(-0.224904\pi\) | ||||
0.760601 | + | 0.649219i | \(0.224904\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 37.6320 | 1.36237 | ||||||||
\(764\) | −31.5002 | −1.13964 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 16.9532 | 0.612542 | ||||||||
\(767\) | 26.2905 | 0.949295 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −2.33683 | −0.0842683 | −0.0421341 | − | 0.999112i | \(-0.513416\pi\) | ||||
−0.0421341 | + | 0.999112i | \(0.513416\pi\) | |||||||
\(770\) | 6.93920 | 0.250072 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 43.1162 | 1.55179 | ||||||||
\(773\) | −4.40125 | −0.158302 | −0.0791509 | − | 0.996863i | \(-0.525221\pi\) | ||||
−0.0791509 | + | 0.996863i | \(0.525221\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −6.60270 | −0.237176 | ||||||||
\(776\) | 20.1949 | 0.724955 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −40.8207 | −1.46349 | ||||||||
\(779\) | −5.47333 | −0.196102 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1.02085 | 0.0365288 | ||||||||
\(782\) | 54.3262 | 1.94270 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 3.52108 | 0.125753 | ||||||||
\(785\) | −12.1861 | −0.434942 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −13.1902 | −0.470180 | −0.235090 | − | 0.971974i | \(-0.575539\pi\) | ||||
−0.235090 | + | 0.971974i | \(0.575539\pi\) | |||||||
\(788\) | −101.386 | −3.61172 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −17.4731 | −0.621664 | ||||||||
\(791\) | −49.2097 | −1.74970 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −4.78602 | −0.169957 | ||||||||
\(794\) | −60.8078 | −2.15799 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −19.4413 | −0.689078 | ||||||||
\(797\) | 39.1687 | 1.38743 | 0.693713 | − | 0.720252i | \(-0.255974\pi\) | ||||
0.693713 | + | 0.720252i | \(0.255974\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1.67037 | 0.0590935 | ||||||||
\(800\) | −2.24955 | −0.0795338 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −47.1060 | −1.66337 | ||||||||
\(803\) | −0.202033 | −0.00712960 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 11.5962 | 0.408714 | ||||||||
\(806\) | −75.0111 | −2.64215 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −7.39394 | −0.260118 | ||||||||
\(809\) | −18.2003 | −0.639887 | −0.319944 | − | 0.947437i | \(-0.603664\pi\) | ||||
−0.319944 | + | 0.947437i | \(0.603664\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −54.6434 | −1.91879 | −0.959395 | − | 0.282065i | \(-0.908981\pi\) | ||||
−0.959395 | + | 0.282065i | \(0.908981\pi\) | |||||||
\(812\) | 101.226 | 3.55234 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 14.5716 | 0.510733 | ||||||||
\(815\) | −6.09722 | −0.213576 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 10.9515 | 0.383144 | ||||||||
\(818\) | −68.7056 | −2.40224 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 20.5240 | 0.716729 | ||||||||
\(821\) | −18.3540 | −0.640560 | −0.320280 | − | 0.947323i | \(-0.603777\pi\) | ||||
−0.320280 | + | 0.947323i | \(0.603777\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 9.63416 | 0.335826 | 0.167913 | − | 0.985802i | \(-0.446297\pi\) | ||||
0.167913 | + | 0.985802i | \(0.446297\pi\) | |||||||
\(824\) | −23.2270 | −0.809150 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −38.5063 | −1.33981 | ||||||||
\(827\) | −26.2829 | −0.913947 | −0.456973 | − | 0.889480i | \(-0.651067\pi\) | ||||
−0.456973 | + | 0.889480i | \(0.651067\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −45.2690 | −1.57226 | −0.786128 | − | 0.618064i | \(-0.787917\pi\) | ||||
−0.786128 | + | 0.618064i | \(0.787917\pi\) | |||||||
\(830\) | −32.8607 | −1.14061 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −49.8281 | −1.72748 | ||||||||
\(833\) | 7.77197 | 0.269283 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 1.06720 | 0.0369321 | ||||||||
\(836\) | 3.74982 | 0.129690 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 6.72648 | 0.232362 | ||||||||
\(839\) | −23.0656 | −0.796315 | −0.398157 | − | 0.917317i | \(-0.630350\pi\) | ||||
−0.398157 | + | 0.917317i | \(0.630350\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 58.0162 | 2.00056 | ||||||||
\(842\) | 7.82104 | 0.269531 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −80.7810 | −2.78060 | ||||||||
\(845\) | −9.44675 | −0.324978 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −2.89389 | −0.0994354 | ||||||||
\(848\) | 9.76309 | 0.335266 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 13.5573 | 0.465013 | ||||||||
\(851\) | 24.3508 | 0.834736 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −10.1175 | −0.346418 | −0.173209 | − | 0.984885i | \(-0.555414\pi\) | ||||
−0.173209 | + | 0.984885i | \(0.555414\pi\) | |||||||
\(854\) | 7.00983 | 0.239872 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 18.1291 | 0.619641 | ||||||||
\(857\) | −17.5975 | −0.601119 | −0.300559 | − | 0.953763i | \(-0.597173\pi\) | ||||
−0.300559 | + | 0.953763i | \(0.597173\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 51.9873 | 1.77378 | 0.886891 | − | 0.461978i | \(-0.152860\pi\) | ||||
0.886891 | + | 0.461978i | \(0.152860\pi\) | |||||||
\(860\) | −41.0661 | −1.40034 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −78.5560 | −2.67563 | ||||||||
\(863\) | 42.2968 | 1.43980 | 0.719900 | − | 0.694078i | \(-0.244188\pi\) | ||||
0.719900 | + | 0.694078i | \(0.244188\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −13.0289 | −0.442997 | ||||||||
\(866\) | −52.4310 | −1.78168 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 71.6497 | 2.43195 | ||||||||
\(869\) | 7.28690 | 0.247191 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 33.1081 | 1.12182 | ||||||||
\(872\) | −54.5625 | −1.84772 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 9.60863 | 0.325017 | ||||||||
\(875\) | 2.89389 | 0.0978315 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −4.60606 | −0.155535 | −0.0777677 | − | 0.996972i | \(-0.524779\pi\) | ||||
−0.0777677 | + | 0.996972i | \(0.524779\pi\) | |||||||
\(878\) | 73.4423 | 2.47856 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −2.56149 | −0.0863477 | ||||||||
\(881\) | −45.1124 | −1.51987 | −0.759937 | − | 0.649997i | \(-0.774770\pi\) | ||||
−0.759937 | + | 0.649997i | \(0.774770\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −40.3849 | −1.35906 | −0.679530 | − | 0.733648i | \(-0.737816\pi\) | ||||
−0.679530 | + | 0.733648i | \(0.737816\pi\) | |||||||
\(884\) | 100.446 | 3.37837 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −10.9083 | −0.366471 | ||||||||
\(887\) | −50.2462 | −1.68710 | −0.843551 | − | 0.537050i | \(-0.819539\pi\) | ||||
−0.843551 | + | 0.537050i | \(0.819539\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 28.3672 | 0.951407 | ||||||||
\(890\) | −37.9229 | −1.27118 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −101.095 | −3.38491 | ||||||||
\(893\) | 0.295438 | 0.00988645 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 20.6273 | 0.689494 | ||||||||
\(896\) | 59.9606 | 2.00314 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −27.6495 | −0.922674 | ||||||||
\(899\) | 61.5916 | 2.05420 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 21.5498 | 0.717926 | ||||||||
\(902\) | −13.1244 | −0.436994 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 71.3490 | 2.37303 | ||||||||
\(905\) | 20.5908 | 0.684462 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 58.4194 | 1.93979 | 0.969893 | − | 0.243532i | \(-0.0783062\pi\) | ||||
0.969893 | + | 0.243532i | \(0.0783062\pi\) | |||||||
\(908\) | −33.8447 | −1.12318 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 32.8766 | 1.08985 | ||||||||
\(911\) | 39.2409 | 1.30011 | 0.650054 | − | 0.759888i | \(-0.274746\pi\) | ||||
0.650054 | + | 0.759888i | \(0.274746\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 13.7041 | 0.453539 | ||||||||
\(914\) | 27.2826 | 0.902427 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −51.6337 | −1.70603 | ||||||||
\(917\) | −38.8889 | −1.28422 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 18.4113 | 0.607334 | 0.303667 | − | 0.952778i | \(-0.401789\pi\) | ||||
0.303667 | + | 0.952778i | \(0.401789\pi\) | |||||||
\(920\) | −16.8133 | −0.554319 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −10.4851 | −0.345308 | ||||||||
\(923\) | 4.83657 | 0.159198 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 6.07686 | 0.199806 | ||||||||
\(926\) | −22.3478 | −0.734393 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 20.9844 | 0.688847 | ||||||||
\(929\) | 32.8679 | 1.07836 | 0.539180 | − | 0.842191i | \(-0.318734\pi\) | ||||
0.539180 | + | 0.842191i | \(0.318734\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1.37462 | 0.0450515 | ||||||||
\(932\) | 9.20907 | 0.301653 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 67.3110 | 2.20248 | ||||||||
\(935\) | −5.65389 | −0.184902 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 4.34616 | 0.141983 | 0.0709914 | − | 0.997477i | \(-0.477384\pi\) | ||||
0.0709914 | + | 0.997477i | \(0.477384\pi\) | |||||||
\(938\) | −48.4917 | −1.58331 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −1.10784 | −0.0361337 | ||||||||
\(941\) | 55.1238 | 1.79699 | 0.898493 | − | 0.438989i | \(-0.144663\pi\) | ||||
0.898493 | + | 0.438989i | \(0.144663\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −21.9324 | −0.714218 | ||||||||
\(944\) | 14.2139 | 0.462625 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 26.2603 | 0.853797 | ||||||||
\(947\) | −16.6794 | −0.542007 | −0.271004 | − | 0.962578i | \(-0.587356\pi\) | ||||
−0.271004 | + | 0.962578i | \(0.587356\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −0.957193 | −0.0310718 | ||||||||
\(950\) | 2.39788 | 0.0777974 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −68.6514 | −2.22500 | ||||||||
\(953\) | −51.8274 | −1.67885 | −0.839427 | − | 0.543472i | \(-0.817109\pi\) | ||||
−0.839427 | + | 0.543472i | \(0.817109\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 8.40047 | 0.271833 | ||||||||
\(956\) | 85.6605 | 2.77046 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 13.5524 | 0.437859 | ||||||||
\(959\) | −46.9163 | −1.51501 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 12.5957 | 0.406312 | ||||||||
\(962\) | 69.0371 | 2.22585 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 60.4399 | 1.94664 | ||||||||
\(965\) | −11.4982 | −0.370141 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −28.7146 | −0.923398 | −0.461699 | − | 0.887037i | \(-0.652760\pi\) | ||||
−0.461699 | + | 0.887037i | \(0.652760\pi\) | |||||||
\(968\) | 4.19584 | 0.134860 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −11.5412 | −0.370564 | ||||||||
\(971\) | −43.9744 | −1.41121 | −0.705603 | − | 0.708607i | \(-0.749324\pi\) | ||||
−0.705603 | + | 0.708607i | \(0.749324\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −55.0918 | −1.76616 | ||||||||
\(974\) | −14.6114 | −0.468180 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −2.58756 | −0.0828258 | ||||||||
\(977\) | −19.2496 | −0.615848 | −0.307924 | − | 0.951411i | \(-0.599634\pi\) | ||||
−0.307924 | + | 0.951411i | \(0.599634\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 15.8152 | 0.505455 | ||||||||
\(980\) | −5.15458 | −0.164657 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −20.5327 | −0.655224 | ||||||||
\(983\) | 12.7410 | 0.406373 | 0.203187 | − | 0.979140i | \(-0.434870\pi\) | ||||
0.203187 | + | 0.979140i | \(0.434870\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 27.0376 | 0.861488 | ||||||||
\(986\) | −126.466 | −4.02750 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 17.7659 | 0.565208 | ||||||||
\(989\) | 43.8842 | 1.39544 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 27.9827 | 0.888900 | 0.444450 | − | 0.895804i | \(-0.353399\pi\) | ||||
0.444450 | + | 0.895804i | \(0.353399\pi\) | |||||||
\(992\) | 14.8531 | 0.471588 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −7.08387 | −0.224687 | ||||||||
\(995\) | 5.18460 | 0.164363 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −47.7121 | −1.51106 | −0.755528 | − | 0.655116i | \(-0.772620\pi\) | ||||
−0.755528 | + | 0.655116i | \(0.772620\pi\) | |||||||
\(998\) | −3.25002 | −0.102878 | ||||||||
\(999\) | 0 | 0 |
(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 | 9405.2.a.v.1.5 | 5 | ||
3.2 | odd | 2 | 1045.2.a.d.1.1 | ✓ | 5 | ||
15.14 | odd | 2 | 5225.2.a.j.1.5 | 5 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1045.2.a.d.1.1 | ✓ | 5 | 3.2 | odd | 2 | ||
5225.2.a.j.1.5 | 5 | 15.14 | odd | 2 | |||
9405.2.a.v.1.5 | 5 | 1.1 | even | 1 | trivial |