Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6016,2,Mod(1,6016)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6016, 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("6016.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6016 = 2^{7} \cdot 47 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6016.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: | \(48.0380018560\) |
Analytic rank: | \(0\) |
Dimension: | \(13\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{13} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{13} - 4 x^{12} - 22 x^{11} + 96 x^{10} + 163 x^{9} - 840 x^{8} - 438 x^{7} + 3358 x^{6} + 5 x^{5} + \cdots - 832 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.8 | ||
Root | \(-0.319482\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6016.1 |
$q$-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 | ||||||||
\(3\) | 0.319482 | 0.184453 | 0.0922266 | − | 0.995738i | \(-0.470602\pi\) | ||||
0.0922266 | + | 0.995738i | \(0.470602\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −2.22340 | −0.994334 | −0.497167 | − | 0.867655i | \(-0.665626\pi\) | ||||
−0.497167 | + | 0.867655i | \(0.665626\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.484368 | 0.183074 | 0.0915369 | − | 0.995802i | \(-0.470822\pi\) | ||||
0.0915369 | + | 0.995802i | \(0.470822\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.89793 | −0.965977 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 3.07431 | 0.926938 | 0.463469 | − | 0.886113i | \(-0.346604\pi\) | ||||
0.463469 | + | 0.886113i | \(0.346604\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 5.65430 | 1.56822 | 0.784111 | − | 0.620621i | \(-0.213119\pi\) | ||||
0.784111 | + | 0.620621i | \(0.213119\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −0.710336 | −0.183408 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1.35477 | 0.328580 | 0.164290 | − | 0.986412i | \(-0.447467\pi\) | ||||
0.164290 | + | 0.986412i | \(0.447467\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.21910 | 0.509097 | 0.254548 | − | 0.967060i | \(-0.418073\pi\) | ||||
0.254548 | + | 0.967060i | \(0.418073\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.154747 | 0.0337686 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.53410 | 0.319883 | 0.159941 | − | 0.987127i | \(-0.448869\pi\) | ||||
0.159941 | + | 0.987127i | \(0.448869\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.0565035 | −0.0113007 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.88428 | −0.362631 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 3.86238 | 0.717226 | 0.358613 | − | 0.933486i | \(-0.383250\pi\) | ||||
0.358613 | + | 0.933486i | \(0.383250\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 5.33192 | 0.957641 | 0.478820 | − | 0.877913i | \(-0.341065\pi\) | ||||
0.478820 | + | 0.877913i | \(0.341065\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0.982186 | 0.170977 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −1.07694 | −0.182036 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −6.61936 | −1.08822 | −0.544108 | − | 0.839015i | \(-0.683132\pi\) | ||||
−0.544108 | + | 0.839015i | \(0.683132\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 1.80645 | 0.289264 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −0.811395 | −0.126719 | −0.0633593 | − | 0.997991i | \(-0.520181\pi\) | ||||
−0.0633593 | + | 0.997991i | \(0.520181\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −0.404417 | −0.0616731 | −0.0308365 | − | 0.999524i | \(-0.509817\pi\) | ||||
−0.0308365 | + | 0.999524i | \(0.509817\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 6.44325 | 0.960503 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −1.00000 | −0.145865 | ||||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.76539 | −0.966484 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0.432825 | 0.0606077 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −9.23122 | −1.26801 | −0.634003 | − | 0.773331i | \(-0.718589\pi\) | ||||
−0.634003 | + | 0.773331i | \(0.718589\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −6.83541 | −0.921686 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0.708963 | 0.0939045 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −1.47489 | −0.192014 | −0.0960069 | − | 0.995381i | \(-0.530607\pi\) | ||||
−0.0960069 | + | 0.995381i | \(0.530607\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −2.46683 | −0.315845 | −0.157923 | − | 0.987451i | \(-0.550480\pi\) | ||||
−0.157923 | + | 0.987451i | \(0.550480\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −1.40366 | −0.176845 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −12.5718 | −1.55934 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −13.7368 | −1.67822 | −0.839108 | − | 0.543965i | \(-0.816923\pi\) | ||||
−0.839108 | + | 0.543965i | \(0.816923\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0.490119 | 0.0590034 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 11.9263 | 1.41539 | 0.707694 | − | 0.706519i | \(-0.249736\pi\) | ||||
0.707694 | + | 0.706519i | \(0.249736\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −3.68046 | −0.430766 | −0.215383 | − | 0.976530i | \(-0.569100\pi\) | ||||
−0.215383 | + | 0.976530i | \(0.569100\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −0.0180519 | −0.00208445 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 1.48910 | 0.169698 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 15.1950 | 1.70957 | 0.854787 | − | 0.518980i | \(-0.173688\pi\) | ||||
0.854787 | + | 0.518980i | \(0.173688\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 8.09180 | 0.899089 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −5.17022 | −0.567505 | −0.283753 | − | 0.958898i | \(-0.591579\pi\) | ||||
−0.283753 | + | 0.958898i | \(0.591579\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −3.01219 | −0.326718 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 1.23396 | 0.132295 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 13.6589 | 1.44784 | 0.723922 | − | 0.689882i | \(-0.242337\pi\) | ||||
0.723922 | + | 0.689882i | \(0.242337\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 2.73876 | 0.287100 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 1.70345 | 0.176640 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −4.93394 | −0.506212 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 5.17590 | 0.525533 | 0.262766 | − | 0.964859i | \(-0.415365\pi\) | ||||
0.262766 | + | 0.964859i | \(0.415365\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −8.90913 | −0.895401 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 9.62759 | 0.957981 | 0.478990 | − | 0.877820i | \(-0.341003\pi\) | ||||
0.478990 | + | 0.877820i | \(0.341003\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 15.9258 | 1.56922 | 0.784608 | − | 0.619992i | \(-0.212864\pi\) | ||||
0.784608 | + | 0.619992i | \(0.212864\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −0.344064 | −0.0335772 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −14.9979 | −1.44990 | −0.724949 | − | 0.688803i | \(-0.758137\pi\) | ||||
−0.724949 | + | 0.688803i | \(0.758137\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −3.54676 | −0.339718 | −0.169859 | − | 0.985468i | \(-0.554331\pi\) | ||||
−0.169859 | + | 0.985468i | \(0.554331\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −2.11477 | −0.200725 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 20.4175 | 1.92072 | 0.960358 | − | 0.278769i | \(-0.0899264\pi\) | ||||
0.960358 | + | 0.278769i | \(0.0899264\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −3.41092 | −0.318070 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −16.3858 | −1.51487 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0.656208 | 0.0601545 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1.54864 | −0.140785 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −0.259226 | −0.0233736 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 11.2426 | 1.00557 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 3.36589 | 0.298674 | 0.149337 | − | 0.988786i | \(-0.452286\pi\) | ||||
0.149337 | + | 0.988786i | \(0.452286\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −0.129204 | −0.0113758 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 18.2049 | 1.59057 | 0.795285 | − | 0.606236i | \(-0.207321\pi\) | ||||
0.795285 | + | 0.606236i | \(0.207321\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1.07486 | 0.0932023 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 4.18951 | 0.360576 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 2.24716 | 0.191988 | 0.0959939 | − | 0.995382i | \(-0.469397\pi\) | ||||
0.0959939 | + | 0.995382i | \(0.469397\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −5.07267 | −0.430258 | −0.215129 | − | 0.976586i | \(-0.569017\pi\) | ||||
−0.215129 | + | 0.976586i | \(0.569017\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −0.319482 | −0.0269053 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 17.3831 | 1.45364 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −8.58761 | −0.713162 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −2.16142 | −0.178271 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 0.0464165 | 0.00380259 | 0.00190129 | − | 0.999998i | \(-0.499395\pi\) | ||||
0.00190129 | + | 0.999998i | \(0.499395\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −8.31165 | −0.676392 | −0.338196 | − | 0.941076i | \(-0.609817\pi\) | ||||
−0.338196 | + | 0.941076i | \(0.609817\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −3.92603 | −0.317401 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −11.8550 | −0.952214 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 17.4540 | 1.39298 | 0.696489 | − | 0.717568i | \(-0.254745\pi\) | ||||
0.696489 | + | 0.717568i | \(0.254745\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −2.94921 | −0.233888 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0.743071 | 0.0585622 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −23.1395 | −1.81243 | −0.906213 | − | 0.422821i | \(-0.861040\pi\) | ||||
−0.906213 | + | 0.422821i | \(0.861040\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −2.18379 | −0.170008 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −15.2533 | −1.18034 | −0.590168 | − | 0.807281i | \(-0.700938\pi\) | ||||
−0.590168 | + | 0.807281i | \(0.700938\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 18.9712 | 1.45932 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −6.43080 | −0.491776 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 22.7991 | 1.73339 | 0.866693 | − | 0.498843i | \(-0.166241\pi\) | ||||
0.866693 | + | 0.498843i | \(0.166241\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −0.0273685 | −0.00206886 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −0.471200 | −0.0354175 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 3.28783 | 0.245744 | 0.122872 | − | 0.992423i | \(-0.460790\pi\) | ||||
0.122872 | + | 0.992423i | \(0.460790\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 20.7882 | 1.54517 | 0.772586 | − | 0.634910i | \(-0.218963\pi\) | ||||
0.772586 | + | 0.634910i | \(0.218963\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −0.788108 | −0.0582587 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 14.7175 | 1.08205 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 4.16498 | 0.304574 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −0.912687 | −0.0663882 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 0.671922 | 0.0486186 | 0.0243093 | − | 0.999704i | \(-0.492261\pi\) | ||||
0.0243093 | + | 0.999704i | \(0.492261\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −4.70443 | −0.338632 | −0.169316 | − | 0.985562i | \(-0.554156\pi\) | ||||
−0.169316 | + | 0.985562i | \(0.554156\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −4.01646 | −0.287624 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 16.1862 | 1.15322 | 0.576610 | − | 0.817020i | \(-0.304375\pi\) | ||||
0.576610 | + | 0.817020i | \(0.304375\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 19.0137 | 1.34785 | 0.673923 | − | 0.738801i | \(-0.264608\pi\) | ||||
0.673923 | + | 0.738801i | \(0.264608\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −4.38866 | −0.309552 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 1.87081 | 0.131305 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1.80405 | 0.126001 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −4.44573 | −0.308999 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 6.82220 | 0.471901 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 17.2828 | 1.18980 | 0.594898 | − | 0.803801i | \(-0.297192\pi\) | ||||
0.594898 | + | 0.803801i | \(0.297192\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 3.81023 | 0.261073 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0.899181 | 0.0613236 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 2.58261 | 0.175319 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −1.17584 | −0.0794561 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 7.66029 | 0.515287 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 5.52092 | 0.369708 | 0.184854 | − | 0.982766i | \(-0.440819\pi\) | ||||
0.184854 | + | 0.982766i | \(0.440819\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0.163743 | 0.0109162 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 10.7768 | 0.715284 | 0.357642 | − | 0.933859i | \(-0.383581\pi\) | ||||
0.357642 | + | 0.933859i | \(0.383581\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 1.62920 | 0.107661 | 0.0538303 | − | 0.998550i | \(-0.482857\pi\) | ||||
0.0538303 | + | 0.998550i | \(0.482857\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0.475740 | 0.0313014 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 20.9418 | 1.37194 | 0.685970 | − | 0.727630i | \(-0.259378\pi\) | ||||
0.685970 | + | 0.727630i | \(0.259378\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 2.22340 | 0.145038 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 4.85454 | 0.315336 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 5.74445 | 0.371578 | 0.185789 | − | 0.982590i | \(-0.440516\pi\) | ||||
0.185789 | + | 0.982590i | \(0.440516\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 6.31475 | 0.406769 | 0.203384 | − | 0.979099i | \(-0.434806\pi\) | ||||
0.203384 | + | 0.979099i | \(0.434806\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 8.23804 | 0.528470 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 15.0421 | 0.961007 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 12.5475 | 0.798376 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −1.65179 | −0.104678 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −1.66570 | −0.105138 | −0.0525690 | − | 0.998617i | \(-0.516741\pi\) | ||||
−0.0525690 | + | 0.998617i | \(0.516741\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 4.71631 | 0.296512 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −0.962343 | −0.0602642 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 6.19750 | 0.386589 | 0.193295 | − | 0.981141i | \(-0.438083\pi\) | ||||
0.193295 | + | 0.981141i | \(0.438083\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −3.20620 | −0.199224 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −11.1929 | −0.692824 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −17.3028 | −1.06694 | −0.533469 | − | 0.845819i | \(-0.679112\pi\) | ||||
−0.533469 | + | 0.845819i | \(0.679112\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 20.5247 | 1.26082 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 4.36379 | 0.267060 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −6.30797 | −0.384604 | −0.192302 | − | 0.981336i | \(-0.561595\pi\) | ||||
−0.192302 | + | 0.981336i | \(0.561595\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −10.6993 | −0.649938 | −0.324969 | − | 0.945725i | \(-0.605354\pi\) | ||||
−0.324969 | + | 0.945725i | \(0.605354\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0.874986 | 0.0529566 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −0.173709 | −0.0104751 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 3.81187 | 0.229033 | 0.114517 | − | 0.993421i | \(-0.463468\pi\) | ||||
0.114517 | + | 0.993421i | \(0.463468\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −15.4515 | −0.925059 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 15.0178 | 0.895889 | 0.447944 | − | 0.894061i | \(-0.352156\pi\) | ||||
0.447944 | + | 0.894061i | \(0.352156\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −26.5823 | −1.58015 | −0.790076 | − | 0.613009i | \(-0.789959\pi\) | ||||
−0.790076 | + | 0.613009i | \(0.789959\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −1.57631 | −0.0933724 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −0.393014 | −0.0231989 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −15.1646 | −0.892035 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 1.65361 | 0.0969362 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 1.92391 | 0.112396 | 0.0561979 | − | 0.998420i | \(-0.482102\pi\) | ||||
0.0561979 | + | 0.998420i | \(0.482102\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 3.27926 | 0.190926 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −5.79287 | −0.336136 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 8.67429 | 0.501647 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −0.195887 | −0.0112907 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 3.07584 | 0.176703 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 5.48474 | 0.314056 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 5.02012 | 0.286513 | 0.143257 | − | 0.989686i | \(-0.454243\pi\) | ||||
0.143257 | + | 0.989686i | \(0.454243\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 5.08801 | 0.289447 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −20.4391 | −1.15900 | −0.579498 | − | 0.814974i | \(-0.696751\pi\) | ||||
−0.579498 | + | 0.814974i | \(0.696751\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 9.35860 | 0.528979 | 0.264490 | − | 0.964389i | \(-0.414797\pi\) | ||||
0.264490 | + | 0.964389i | \(0.414797\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 3.12090 | 0.175843 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −3.50828 | −0.197045 | −0.0985224 | − | 0.995135i | \(-0.531412\pi\) | ||||
−0.0985224 | + | 0.995135i | \(0.531412\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 11.8741 | 0.664824 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −4.79155 | −0.267438 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 3.00637 | 0.167279 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −0.319488 | −0.0177220 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −1.13313 | −0.0626620 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −0.484368 | −0.0267041 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 6.33727 | 0.348328 | 0.174164 | − | 0.984717i | \(-0.444278\pi\) | ||||
0.174164 | + | 0.984717i | \(0.444278\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 19.1824 | 1.05119 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 30.5423 | 1.66871 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −20.3821 | −1.11028 | −0.555142 | − | 0.831756i | \(-0.687336\pi\) | ||||
−0.555142 | + | 0.831756i | \(0.687336\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 6.52303 | 0.354282 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 16.3919 | 0.887674 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −6.66751 | −0.360012 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −1.08973 | −0.0586691 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 17.1246 | 0.919299 | 0.459649 | − | 0.888100i | \(-0.347975\pi\) | ||||
0.459649 | + | 0.888100i | \(0.347975\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 5.94264 | 0.318102 | 0.159051 | − | 0.987270i | \(-0.449157\pi\) | ||||
0.159051 | + | 0.987270i | \(0.449157\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −10.6543 | −0.568685 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 21.4991 | 1.14428 | 0.572141 | − | 0.820155i | \(-0.306113\pi\) | ||||
0.572141 | + | 0.820155i | \(0.306113\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −26.5168 | −1.40737 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0.209647 | 0.0110957 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 33.4888 | 1.76747 | 0.883735 | − | 0.467987i | \(-0.155021\pi\) | ||||
0.883735 | + | 0.467987i | \(0.155021\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −14.0756 | −0.740821 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −0.494763 | −0.0259683 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 8.18314 | 0.428325 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −15.5899 | −0.813786 | −0.406893 | − | 0.913476i | \(-0.633388\pi\) | ||||
−0.406893 | + | 0.913476i | \(0.633388\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 2.35137 | 0.122407 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −4.47131 | −0.232139 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −4.96106 | −0.256874 | −0.128437 | − | 0.991718i | \(-0.540996\pi\) | ||||
−0.128437 | + | 0.991718i | \(0.540996\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 3.59182 | 0.185481 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 21.8391 | 1.12477 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −6.00049 | −0.308224 | −0.154112 | − | 0.988053i | \(-0.549252\pi\) | ||||
−0.154112 | + | 0.988053i | \(0.549252\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 1.07534 | 0.0550914 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −0.332863 | −0.0170085 | −0.00850426 | − | 0.999964i | \(-0.502707\pi\) | ||||
−0.00850426 | + | 0.999964i | \(0.502707\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −3.31085 | −0.168737 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 1.17197 | 0.0595748 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −13.0435 | −0.661333 | −0.330666 | − | 0.943748i | \(-0.607273\pi\) | ||||
−0.330666 | + | 0.943748i | \(0.607273\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2.07836 | 0.105107 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 5.81614 | 0.293386 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −33.7846 | −1.69989 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −16.7275 | −0.839528 | −0.419764 | − | 0.907633i | \(-0.637887\pi\) | ||||
−0.419764 | + | 0.907633i | \(0.637887\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0.343399 | 0.0171915 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −9.79357 | −0.489068 | −0.244534 | − | 0.969641i | \(-0.578635\pi\) | ||||
−0.244534 | + | 0.969641i | \(0.578635\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 30.1483 | 1.50179 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −17.9913 | −0.893994 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −20.3499 | −1.00871 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −10.1041 | −0.499614 | −0.249807 | − | 0.968296i | \(-0.580367\pi\) | ||||
−0.249807 | + | 0.968296i | \(0.580367\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0.717927 | 0.0354127 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −0.714387 | −0.0351527 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 11.4954 | 0.564289 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −1.62063 | −0.0793625 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −11.5777 | −0.565607 | −0.282804 | − | 0.959178i | \(-0.591264\pi\) | ||||
−0.282804 | + | 0.959178i | \(0.591264\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −35.4182 | −1.72618 | −0.863088 | − | 0.505053i | \(-0.831473\pi\) | ||||
−0.863088 | + | 0.505053i | \(0.831473\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 2.89793 | 0.140902 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −0.0765494 | −0.00371319 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −1.19485 | −0.0578230 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 5.55358 | 0.268129 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −3.17684 | −0.153023 | −0.0765115 | − | 0.997069i | \(-0.524378\pi\) | ||||
−0.0765115 | + | 0.997069i | \(0.524378\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 12.8991 | 0.619891 | 0.309945 | − | 0.950754i | \(-0.399689\pi\) | ||||
0.309945 | + | 0.950754i | \(0.399689\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −2.74359 | −0.131545 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 3.40433 | 0.162851 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 21.3953 | 1.02114 | 0.510571 | − | 0.859836i | \(-0.329434\pi\) | ||||
0.510571 | + | 0.859836i | \(0.329434\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 19.6056 | 0.933601 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 22.6642 | 1.07681 | 0.538404 | − | 0.842687i | \(-0.319028\pi\) | ||||
0.538404 | + | 0.842687i | \(0.319028\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −30.3692 | −1.43964 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0.0148292 | 0.000701399 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −11.1457 | −0.525997 | −0.262999 | − | 0.964796i | \(-0.584711\pi\) | ||||
−0.262999 | + | 0.964796i | \(0.584711\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −2.49448 | −0.117460 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −2.65542 | −0.124763 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −6.08936 | −0.285474 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 9.75212 | 0.456185 | 0.228092 | − | 0.973639i | \(-0.426751\pi\) | ||||
0.228092 | + | 0.973639i | \(0.426751\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −2.55277 | −0.119153 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 24.1185 | 1.12331 | 0.561656 | − | 0.827371i | \(-0.310164\pi\) | ||||
0.561656 | + | 0.827371i | \(0.310164\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 14.8910 | 0.692042 | 0.346021 | − | 0.938227i | \(-0.387533\pi\) | ||||
0.346021 | + | 0.938227i | \(0.387533\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −3.78745 | −0.175639 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −31.2381 | −1.44552 | −0.722762 | − | 0.691097i | \(-0.757128\pi\) | ||||
−0.722762 | + | 0.691097i | \(0.757128\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −6.65366 | −0.307238 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 5.57623 | 0.256939 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −1.24330 | −0.0571671 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −0.125387 | −0.00575315 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 26.7514 | 1.22486 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −30.5583 | −1.39624 | −0.698122 | − | 0.715979i | \(-0.745980\pi\) | ||||
−0.698122 | + | 0.715979i | \(0.745980\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −37.4279 | −1.70656 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0.237398 | 0.0108020 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −11.5081 | −0.522555 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 32.0918 | 1.45422 | 0.727108 | − | 0.686523i | \(-0.240864\pi\) | ||||
0.727108 | + | 0.686523i | \(0.240864\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −7.39266 | −0.334308 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −24.3060 | −1.09692 | −0.548458 | − | 0.836178i | \(-0.684785\pi\) | ||||
−0.548458 | + | 0.836178i | \(0.684785\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 5.23264 | 0.235666 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 19.8085 | 0.890327 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 5.77670 | 0.259121 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −33.4247 | −1.49630 | −0.748148 | − | 0.663532i | \(-0.769057\pi\) | ||||
−0.748148 | + | 0.663532i | \(0.769057\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −4.87316 | −0.217717 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −2.00080 | −0.0892114 | −0.0446057 | − | 0.999005i | \(-0.514203\pi\) | ||||
−0.0446057 | + | 0.999005i | \(0.514203\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −21.4060 | −0.952553 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 6.06095 | 0.269176 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 18.4667 | 0.818524 | 0.409262 | − | 0.912417i | \(-0.365786\pi\) | ||||
0.409262 | + | 0.912417i | \(0.365786\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −1.78270 | −0.0788620 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −4.18142 | −0.184614 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −35.4094 | −1.56032 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −3.07431 | −0.135208 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 7.28392 | 0.319728 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 35.7052 | 1.56427 | 0.782136 | − | 0.623108i | \(-0.214130\pi\) | ||||
0.782136 | + | 0.623108i | \(0.214130\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −31.2754 | −1.36758 | −0.683788 | − | 0.729681i | \(-0.739669\pi\) | ||||
−0.683788 | + | 0.729681i | \(0.739669\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −0.00874375 | −0.000381609 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 7.22353 | 0.314662 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −20.6465 | −0.897675 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 4.27412 | 0.185481 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −4.58787 | −0.198723 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 33.3462 | 1.44168 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 1.05040 | 0.0453282 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −20.7989 | −0.895871 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 2.59469 | 0.111554 | 0.0557771 | − | 0.998443i | \(-0.482236\pi\) | ||||
0.0557771 | + | 0.998443i | \(0.482236\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 6.64145 | 0.285012 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 7.88585 | 0.337793 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −2.38576 | −0.102008 | −0.0510039 | − | 0.998698i | \(-0.516242\pi\) | ||||
−0.0510039 | + | 0.998698i | \(0.516242\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 7.14870 | 0.305099 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 8.57101 | 0.365137 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 7.35998 | 0.312978 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 4.70197 | 0.199587 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −15.6704 | −0.663975 | −0.331987 | − | 0.943284i | \(-0.607719\pi\) | ||||
−0.331987 | + | 0.943284i | \(0.607719\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −2.28670 | −0.0967171 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 1.33064 | 0.0561796 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −7.36541 | −0.310415 | −0.155208 | − | 0.987882i | \(-0.549605\pi\) | ||||
−0.155208 | + | 0.987882i | \(0.549605\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −45.3962 | −1.90983 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 3.91941 | 0.164600 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −10.3538 | −0.434055 | −0.217027 | − | 0.976166i | \(-0.569636\pi\) | ||||
−0.217027 | + | 0.976166i | \(0.569636\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 35.0150 | 1.46533 | 0.732667 | − | 0.680587i | \(-0.238275\pi\) | ||||
0.732667 | + | 0.680587i | \(0.238275\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0.214667 | 0.00896785 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −0.0866823 | −0.00361490 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −2.45390 | −0.102157 | −0.0510787 | − | 0.998695i | \(-0.516266\pi\) | ||||
−0.0510787 | + | 0.998695i | \(0.516266\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −1.50298 | −0.0624618 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −2.50429 | −0.103895 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −28.3796 | −1.17536 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 36.4321 | 1.50628 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −11.7076 | −0.483223 | −0.241612 | − | 0.970373i | \(-0.577676\pi\) | ||||
−0.241612 | + | 0.970373i | \(0.577676\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 11.8321 | 0.487532 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 5.17121 | 0.212715 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 11.3762 | 0.467164 | 0.233582 | − | 0.972337i | \(-0.424955\pi\) | ||||
0.233582 | + | 0.972337i | \(0.424955\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −1.45901 | −0.0598136 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 6.07455 | 0.248615 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 20.1049 | 0.821462 | 0.410731 | − | 0.911757i | \(-0.365273\pi\) | ||||
0.410731 | + | 0.911757i | \(0.365273\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 19.1573 | 0.781442 | 0.390721 | − | 0.920509i | \(-0.372226\pi\) | ||||
0.390721 | + | 0.920509i | \(0.372226\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 39.8083 | 1.62112 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 3.44324 | 0.139988 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −7.28066 | −0.295513 | −0.147756 | − | 0.989024i | \(-0.547205\pi\) | ||||
−0.147756 | + | 0.989024i | \(0.547205\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0.597692 | 0.0242197 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −5.65430 | −0.228749 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 46.2456 | 1.86784 | 0.933922 | − | 0.357478i | \(-0.116363\pi\) | ||||
0.933922 | + | 0.357478i | \(0.116363\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0.576363 | 0.0232412 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 27.3903 | 1.10269 | 0.551346 | − | 0.834276i | \(-0.314114\pi\) | ||||
0.551346 | + | 0.834276i | \(0.314114\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −6.45368 | −0.259395 | −0.129698 | − | 0.991554i | \(-0.541401\pi\) | ||||
−0.129698 | + | 0.991554i | \(0.541401\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −2.89069 | −0.115999 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 6.61595 | 0.265062 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −24.7143 | −0.988572 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 2.17957 | 0.0870437 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −8.96771 | −0.357566 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −3.54519 | −0.141132 | −0.0705658 | − | 0.997507i | \(-0.522480\pi\) | ||||
−0.0705658 | + | 0.997507i | \(0.522480\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 5.52154 | 0.219462 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −7.48371 | −0.296982 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −38.2536 | −1.51566 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −34.5615 | −1.36723 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −13.8851 | −0.548430 | −0.274215 | − | 0.961668i | \(-0.588418\pi\) | ||||
−0.274215 | + | 0.961668i | \(0.588418\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 26.5735 | 1.04796 | 0.523979 | − | 0.851731i | \(-0.324447\pi\) | ||||
0.523979 | + | 0.851731i | \(0.324447\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0.287272 | 0.0113113 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −25.2966 | −0.994513 | −0.497257 | − | 0.867604i | \(-0.665659\pi\) | ||||
−0.497257 | + | 0.867604i | \(0.665659\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −4.53425 | −0.177985 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0.825098 | 0.0323381 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 36.8365 | 1.44152 | 0.720762 | − | 0.693183i | \(-0.243792\pi\) | ||||
0.720762 | + | 0.693183i | \(0.243792\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −40.4767 | −1.58156 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 10.6657 | 0.416110 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 35.2527 | 1.37325 | 0.686625 | − | 0.727011i | \(-0.259091\pi\) | ||||
0.686625 | + | 0.727011i | \(0.259091\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 21.6035 | 0.840277 | 0.420139 | − | 0.907460i | \(-0.361981\pi\) | ||||
0.420139 | + | 0.907460i | \(0.361981\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 2.44733 | 0.0950463 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −2.38984 | −0.0926742 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 5.92529 | 0.229428 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 1.76384 | 0.0681938 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −7.58379 | −0.292769 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 50.6048 | 1.95067 | 0.975336 | − | 0.220725i | \(-0.0708422\pi\) | ||||
0.975336 | + | 0.220725i | \(0.0708422\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0.106469 | 0.00409798 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −19.4981 | −0.749372 | −0.374686 | − | 0.927152i | \(-0.622249\pi\) | ||||
−0.374686 | + | 0.927152i | \(0.622249\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 2.50704 | 0.0962113 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 3.44301 | 0.131936 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −15.7769 | −0.603687 | −0.301843 | − | 0.953358i | \(-0.597602\pi\) | ||||
−0.301843 | + | 0.953358i | \(0.597602\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −4.99633 | −0.190900 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0.520501 | 0.0198583 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −52.1961 | −1.98851 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −3.13237 | −0.119161 | −0.0595804 | − | 0.998224i | \(-0.518976\pi\) | ||||
−0.0595804 | + | 0.998224i | \(0.518976\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −4.31530 | −0.163925 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 11.2786 | 0.427820 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −1.09925 | −0.0416372 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 6.69052 | 0.253059 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 21.3411 | 0.806041 | 0.403020 | − | 0.915191i | \(-0.367960\pi\) | ||||
0.403020 | + | 0.915191i | \(0.367960\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −14.6890 | −0.554007 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0.710336 | 0.0267528 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 4.66330 | 0.175381 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −1.62825 | −0.0611504 | −0.0305752 | − | 0.999532i | \(-0.509734\pi\) | ||||
−0.0305752 | + | 0.999532i | \(0.509734\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −44.0341 | −1.65141 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 8.17972 | 0.306333 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −38.6495 | −1.44541 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 1.83525 | 0.0685387 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 27.7237 | 1.03392 | 0.516959 | − | 0.856010i | \(-0.327064\pi\) | ||||
0.516959 | + | 0.856010i | \(0.327064\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 7.71395 | 0.287283 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 2.01745 | 0.0750298 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −0.218238 | −0.00810516 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −1.03885 | −0.0385289 | −0.0192645 | − | 0.999814i | \(-0.506132\pi\) | ||||
−0.0192645 | + | 0.999814i | \(0.506132\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −21.6435 | −0.801611 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −0.547893 | −0.0202646 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 14.7895 | 0.546264 | 0.273132 | − | 0.961977i | \(-0.411940\pi\) | ||||
0.273132 | + | 0.961977i | \(0.411940\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 4.80570 | 0.177261 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −42.2311 | −1.55560 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −51.0700 | −1.87864 | −0.939320 | − | 0.343042i | \(-0.888543\pi\) | ||||
−0.939320 | + | 0.343042i | \(0.888543\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 4.00869 | 0.147263 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 50.3206 | 1.84609 | 0.923043 | − | 0.384698i | \(-0.125694\pi\) | ||||
0.923043 | + | 0.384698i | \(0.125694\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −0.103202 | −0.00378104 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 14.9829 | 0.548197 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −7.26448 | −0.265438 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 20.6518 | 0.753593 | 0.376797 | − | 0.926296i | \(-0.377026\pi\) | ||||
0.376797 | + | 0.926296i | \(0.377026\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −0.532161 | −0.0193930 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 18.4801 | 0.672559 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −15.2835 | −0.555490 | −0.277745 | − | 0.960655i | \(-0.589587\pi\) | ||||
−0.277745 | + | 0.960655i | \(0.589587\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 1.50678 | 0.0546925 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 17.4154 | 0.631307 | 0.315653 | − | 0.948875i | \(-0.397776\pi\) | ||||
0.315653 | + | 0.948875i | \(0.397776\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −1.71793 | −0.0621934 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 8.72913 | 0.315602 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −8.33945 | −0.301120 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 20.3812 | 0.734964 | 0.367482 | − | 0.930031i | \(-0.380220\pi\) | ||||
0.367482 | + | 0.930031i | \(0.380220\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 1.97999 | 0.0713076 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −27.7751 | −0.999001 | −0.499501 | − | 0.866314i | \(-0.666483\pi\) | ||||
−0.499501 | + | 0.866314i | \(0.666483\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −0.301272 | −0.0108220 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −1.02433 | −0.0367475 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −1.80057 | −0.0645120 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 36.6650 | 1.31198 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −7.27782 | −0.260088 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −38.8071 | −1.38508 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 21.2889 | 0.758869 | 0.379434 | − | 0.925219i | \(-0.376119\pi\) | ||||
0.379434 | + | 0.925219i | \(0.376119\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −5.52795 | −0.196800 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 9.88958 | 0.351633 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −13.9482 | −0.495315 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 6.55727 | 0.232562 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −4.85844 | −0.172095 | −0.0860474 | − | 0.996291i | \(-0.527424\pi\) | ||||
−0.0860474 | + | 0.996291i | \(0.527424\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −1.35477 | −0.0479284 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −39.5827 | −1.39858 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −11.3149 | −0.399293 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −1.65214 | −0.0582303 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −2.01528 | −0.0709414 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 29.1902 | 1.02627 | 0.513137 | − | 0.858307i | \(-0.328483\pi\) | ||||
0.513137 | + | 0.858307i | \(0.328483\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 27.0426 | 0.949593 | 0.474796 | − | 0.880096i | \(-0.342522\pi\) | ||||
0.474796 | + | 0.880096i | \(0.342522\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −3.41825 | −0.119883 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 51.4483 | 1.80216 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −0.897443 | −0.0313976 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −7.93675 | −0.277332 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −44.3932 | −1.54933 | −0.774667 | − | 0.632369i | \(-0.782083\pi\) | ||||
−0.774667 | + | 0.632369i | \(0.782083\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −41.1924 | −1.43588 | −0.717939 | − | 0.696106i | \(-0.754914\pi\) | ||||
−0.717939 | + | 0.696106i | \(0.754914\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −0.0554970 | −0.00193216 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 16.2906 | 0.566478 | 0.283239 | − | 0.959049i | \(-0.408591\pi\) | ||||
0.283239 | + | 0.959049i | \(0.408591\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −0.662232 | −0.0230003 | −0.0115001 | − | 0.999934i | \(-0.503661\pi\) | ||||
−0.0115001 | + | 0.999934i | \(0.503661\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 1.21783 | 0.0422459 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −9.16555 | −0.317568 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 33.9141 | 1.17365 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −10.0469 | −0.347270 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 17.7298 | 0.612100 | 0.306050 | − | 0.952015i | \(-0.400993\pi\) | ||||
0.306050 | + | 0.952015i | \(0.400993\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −14.0820 | −0.485587 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 4.79793 | 0.165250 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −42.1804 | −1.45105 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −0.750112 | −0.0257741 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −8.49256 | −0.291464 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −10.1548 | −0.348101 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 43.0506 | 1.47403 | 0.737013 | − | 0.675879i | \(-0.236236\pi\) | ||||
0.737013 | + | 0.675879i | \(0.236236\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 14.2982 | 0.488989 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 39.2426 | 1.34050 | 0.670250 | − | 0.742135i | \(-0.266187\pi\) | ||||
0.670250 | + | 0.742135i | \(0.266187\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 20.7175 | 0.706871 | 0.353436 | − | 0.935459i | \(-0.385013\pi\) | ||||
0.353436 | + | 0.935459i | \(0.385013\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −0.125561 | −0.00427910 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 6.56027 | 0.223314 | 0.111657 | − | 0.993747i | \(-0.464384\pi\) | ||||
0.111657 | + | 0.993747i | \(0.464384\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −50.6915 | −1.72356 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −4.84482 | −0.164539 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 46.7141 | 1.58467 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −77.6720 | −2.63182 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −14.9994 | −0.507653 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 5.44556 | 0.184094 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −31.7489 | −1.07208 | −0.536042 | − | 0.844191i | \(-0.680081\pi\) | ||||
−0.536042 | + | 0.844191i | \(0.680081\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0.614654 | 0.0207318 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −59.0699 | −1.99012 | −0.995058 | − | 0.0992929i | \(-0.968342\pi\) | ||||
−0.995058 | + | 0.0992929i | \(0.968342\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −35.7421 | −1.20282 | −0.601409 | − | 0.798941i | \(-0.705394\pi\) | ||||
−0.601409 | + | 0.798941i | \(0.705394\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 1.04766 | 0.0352168 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 6.45708 | 0.216808 | 0.108404 | − | 0.994107i | \(-0.465426\pi\) | ||||
0.108404 | + | 0.994107i | \(0.465426\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1.63033 | 0.0546795 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 24.8767 | 0.833400 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −2.21910 | −0.0742594 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −7.31015 | −0.244351 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 2.77128 | 0.0925304 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 20.5939 | 0.686845 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −12.5062 | −0.416641 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −0.0625824 | −0.00208261 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −46.2203 | −1.53642 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −8.85759 | −0.294111 | −0.147056 | − | 0.989128i | \(-0.546980\pi\) | ||||
−0.147056 | + | 0.989128i | \(0.546980\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −27.9001 | −0.925388 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 54.6382 | 1.81024 | 0.905122 | − | 0.425153i | \(-0.139780\pi\) | ||||
0.905122 | + | 0.425153i | \(0.139780\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −15.8948 | −0.526042 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 1.75228 | 0.0579285 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 8.81787 | 0.291192 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 10.8715 | 0.358617 | 0.179308 | − | 0.983793i | \(-0.442614\pi\) | ||||
0.179308 | + | 0.983793i | \(0.442614\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 1.60384 | 0.0528483 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 67.4348 | 2.21964 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0.374017 | 0.0122976 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −46.1519 | −1.51583 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 23.4837 | 0.770475 | 0.385238 | − | 0.922817i | \(-0.374120\pi\) | ||||
0.385238 | + | 0.922817i | \(0.374120\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −15.0131 | −0.492034 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −6.52993 | −0.213780 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −9.26041 | −0.302848 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 6.18294 | 0.201988 | 0.100994 | − | 0.994887i | \(-0.467798\pi\) | ||||
0.100994 | + | 0.994887i | \(0.467798\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 2.98991 | 0.0975719 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −8.11689 | −0.264603 | −0.132302 | − | 0.991210i | \(-0.542237\pi\) | ||||
−0.132302 | + | 0.991210i | \(0.542237\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −1.24476 | −0.0405351 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 2.02927 | 0.0660120 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 16.0127 | 0.520343 | 0.260172 | − | 0.965562i | \(-0.416221\pi\) | ||||
0.260172 | + | 0.965562i | \(0.416221\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −20.8105 | −0.675536 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −1.12083 | −0.0363455 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 8.03372 | 0.260238 | 0.130119 | − | 0.991498i | \(-0.458464\pi\) | ||||
0.130119 | + | 0.991498i | \(0.458464\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −1.49395 | −0.0483431 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 3.79358 | 0.122629 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 1.08845 | 0.0351479 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −2.57065 | −0.0829242 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 43.4628 | 1.40057 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 10.4598 | 0.336714 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −58.9584 | −1.89597 | −0.947986 | − | 0.318311i | \(-0.896885\pi\) | ||||
−0.947986 | + | 0.318311i | \(0.896885\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0.960483 | 0.0308552 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −53.8290 | −1.72745 | −0.863727 | − | 0.503961i | \(-0.831876\pi\) | ||||
−0.863727 | + | 0.503961i | \(0.831876\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −2.45704 | −0.0787690 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −0.102071 | −0.00326888 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 31.0563 | 0.993578 | 0.496789 | − | 0.867871i | \(-0.334512\pi\) | ||||
0.496789 | + | 0.867871i | \(0.334512\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 41.9918 | 1.34206 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 10.2783 | 0.328159 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 19.8434 | 0.632907 | 0.316454 | − | 0.948608i | \(-0.397508\pi\) | ||||
0.316454 | + | 0.948608i | \(0.397508\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −35.9884 | −1.14668 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −0.154747 | −0.00492565 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −0.620418 | −0.0197282 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −25.5528 | −0.811711 | −0.405856 | − | 0.913937i | \(-0.633026\pi\) | ||||
−0.405856 | + | 0.913937i | \(0.633026\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 2.02465 | 0.0642502 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −42.2751 | −1.34021 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −45.6882 | −1.44696 | −0.723481 | − | 0.690345i | \(-0.757459\pi\) | ||||
−0.723481 | + | 0.690345i | \(0.757459\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 12.4728 | 0.394620 |
(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 | 6016.2.a.n.1.8 | yes | 13 | |
4.3 | odd | 2 | 6016.2.a.p.1.6 | yes | 13 | ||
8.3 | odd | 2 | 6016.2.a.m.1.8 | ✓ | 13 | ||
8.5 | even | 2 | 6016.2.a.o.1.6 | yes | 13 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6016.2.a.m.1.8 | ✓ | 13 | 8.3 | odd | 2 | ||
6016.2.a.n.1.8 | yes | 13 | 1.1 | even | 1 | trivial | |
6016.2.a.o.1.6 | yes | 13 | 8.5 | even | 2 | ||
6016.2.a.p.1.6 | yes | 13 | 4.3 | odd | 2 |