Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [5625,2,Mod(1,5625)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(5625, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("5625.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 5625 = 3^{2} \cdot 5^{4} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 5625.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: | \(44.9158511370\) |
Analytic rank: | \(1\) |
Dimension: | \(8\) |
Coefficient field: | 8.8.6152203125.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 3x^{7} - 8x^{6} + 20x^{5} + 26x^{4} - 35x^{3} - 27x^{2} + 16x + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 625) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(-0.0573749\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 5625.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.05737 | −0.747677 | −0.373838 | − | 0.927494i | \(-0.621959\pi\) | ||||
−0.373838 | + | 0.927494i | \(0.621959\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −0.881958 | −0.440979 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.01199 | 0.382498 | 0.191249 | − | 0.981542i | \(-0.438746\pi\) | ||||
0.191249 | + | 0.981542i | \(0.438746\pi\) | |||||||
\(8\) | 3.04731 | 1.07739 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −5.12074 | −1.54396 | −0.771980 | − | 0.635647i | \(-0.780734\pi\) | ||||
−0.771980 | + | 0.635647i | \(0.780734\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 6.08528 | 1.68775 | 0.843876 | − | 0.536538i | \(-0.180268\pi\) | ||||
0.843876 | + | 0.536538i | \(0.180268\pi\) | |||||||
\(14\) | −1.07006 | −0.285985 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −1.45823 | −0.364558 | ||||||||
\(17\) | −3.19320 | −0.774464 | −0.387232 | − | 0.921982i | \(-0.626569\pi\) | ||||
−0.387232 | + | 0.921982i | \(0.626569\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 3.42871 | 0.786601 | 0.393300 | − | 0.919410i | \(-0.371333\pi\) | ||||
0.393300 | + | 0.919410i | \(0.371333\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 5.41454 | 1.15438 | ||||||||
\(23\) | −2.91916 | −0.608687 | −0.304343 | − | 0.952562i | \(-0.598437\pi\) | ||||
−0.304343 | + | 0.952562i | \(0.598437\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −6.43442 | −1.26189 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −0.892537 | −0.168674 | ||||||||
\(29\) | 1.55246 | 0.288285 | 0.144142 | − | 0.989557i | \(-0.453958\pi\) | ||||
0.144142 | + | 0.989557i | \(0.453958\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −7.99699 | −1.43630 | −0.718151 | − | 0.695887i | \(-0.755011\pi\) | ||||
−0.718151 | + | 0.695887i | \(0.755011\pi\) | |||||||
\(32\) | −4.55272 | −0.804815 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 3.37640 | 0.579049 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 8.40726 | 1.38214 | 0.691072 | − | 0.722786i | \(-0.257139\pi\) | ||||
0.691072 | + | 0.722786i | \(0.257139\pi\) | |||||||
\(38\) | −3.62544 | −0.588123 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1.86355 | 0.291037 | 0.145519 | − | 0.989356i | \(-0.453515\pi\) | ||||
0.145519 | + | 0.989356i | \(0.453515\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −5.22402 | −0.796655 | −0.398328 | − | 0.917243i | \(-0.630409\pi\) | ||||
−0.398328 | + | 0.917243i | \(0.630409\pi\) | |||||||
\(44\) | 4.51628 | 0.680854 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 3.08665 | 0.455101 | ||||||||
\(47\) | 4.80081 | 0.700269 | 0.350135 | − | 0.936699i | \(-0.386136\pi\) | ||||
0.350135 | + | 0.936699i | \(0.386136\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −5.97587 | −0.853695 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −5.36696 | −0.744264 | ||||||||
\(53\) | −10.0499 | −1.38046 | −0.690232 | − | 0.723588i | \(-0.742492\pi\) | ||||
−0.690232 | + | 0.723588i | \(0.742492\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 3.08386 | 0.412098 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −1.64153 | −0.215544 | ||||||||
\(59\) | −2.89450 | −0.376832 | −0.188416 | − | 0.982089i | \(-0.560335\pi\) | ||||
−0.188416 | + | 0.982089i | \(0.560335\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −2.30966 | −0.295722 | −0.147861 | − | 0.989008i | \(-0.547239\pi\) | ||||
−0.147861 | + | 0.989008i | \(0.547239\pi\) | |||||||
\(62\) | 8.45582 | 1.07389 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 7.73040 | 0.966300 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 4.64895 | 0.567960 | 0.283980 | − | 0.958830i | \(-0.408345\pi\) | ||||
0.283980 | + | 0.958830i | \(0.408345\pi\) | |||||||
\(68\) | 2.81626 | 0.341522 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 7.73711 | 0.918226 | 0.459113 | − | 0.888378i | \(-0.348167\pi\) | ||||
0.459113 | + | 0.888378i | \(0.348167\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −0.595540 | −0.0697027 | −0.0348513 | − | 0.999393i | \(-0.511096\pi\) | ||||
−0.0348513 | + | 0.999393i | \(0.511096\pi\) | |||||||
\(74\) | −8.88962 | −1.03340 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −3.02398 | −0.346875 | ||||||||
\(77\) | −5.18216 | −0.590562 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 11.0593 | 1.24427 | 0.622134 | − | 0.782910i | \(-0.286266\pi\) | ||||
0.622134 | + | 0.782910i | \(0.286266\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −1.97047 | −0.217602 | ||||||||
\(83\) | −14.2973 | −1.56933 | −0.784665 | − | 0.619920i | \(-0.787165\pi\) | ||||
−0.784665 | + | 0.619920i | \(0.787165\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 5.52374 | 0.595641 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −15.6045 | −1.66344 | ||||||||
\(89\) | 6.39323 | 0.677681 | 0.338841 | − | 0.940844i | \(-0.389965\pi\) | ||||
0.338841 | + | 0.940844i | \(0.389965\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 6.15827 | 0.645562 | ||||||||
\(92\) | 2.57458 | 0.268418 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −5.07625 | −0.523575 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −14.0833 | −1.42994 | −0.714970 | − | 0.699155i | \(-0.753560\pi\) | ||||
−0.714970 | + | 0.699155i | \(0.753560\pi\) | |||||||
\(98\) | 6.31873 | 0.638288 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 10.5130 | 1.04608 | 0.523040 | − | 0.852308i | \(-0.324798\pi\) | ||||
0.523040 | + | 0.852308i | \(0.324798\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −3.07770 | −0.303254 | −0.151627 | − | 0.988438i | \(-0.548451\pi\) | ||||
−0.151627 | + | 0.988438i | \(0.548451\pi\) | |||||||
\(104\) | 18.5437 | 1.81836 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 10.6265 | 1.03214 | ||||||||
\(107\) | 5.24731 | 0.507277 | 0.253638 | − | 0.967299i | \(-0.418373\pi\) | ||||
0.253638 | + | 0.967299i | \(0.418373\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −6.51906 | −0.624413 | −0.312206 | − | 0.950014i | \(-0.601068\pi\) | ||||
−0.312206 | + | 0.950014i | \(0.601068\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −1.47572 | −0.139443 | ||||||||
\(113\) | −0.385555 | −0.0362699 | −0.0181350 | − | 0.999836i | \(-0.505773\pi\) | ||||
−0.0181350 | + | 0.999836i | \(0.505773\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −1.36921 | −0.127128 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 3.06058 | 0.281749 | ||||||||
\(119\) | −3.23150 | −0.296231 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 15.2220 | 1.38381 | ||||||||
\(122\) | 2.44218 | 0.221104 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 7.05301 | 0.633379 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −4.64324 | −0.412021 | −0.206010 | − | 0.978550i | \(-0.566048\pi\) | ||||
−0.206010 | + | 0.978550i | \(0.566048\pi\) | |||||||
\(128\) | 0.931513 | 0.0823349 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −16.2213 | −1.41726 | −0.708630 | − | 0.705581i | \(-0.750686\pi\) | ||||
−0.708630 | + | 0.705581i | \(0.750686\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 3.46984 | 0.300873 | ||||||||
\(134\) | −4.91568 | −0.424650 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −9.73066 | −0.834397 | ||||||||
\(137\) | 19.1801 | 1.63867 | 0.819335 | − | 0.573315i | \(-0.194343\pi\) | ||||
0.819335 | + | 0.573315i | \(0.194343\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 3.58765 | 0.304300 | 0.152150 | − | 0.988357i | \(-0.451380\pi\) | ||||
0.152150 | + | 0.988357i | \(0.451380\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −8.18102 | −0.686536 | ||||||||
\(143\) | −31.1611 | −2.60582 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0.629709 | 0.0521151 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −7.41485 | −0.609497 | ||||||||
\(149\) | −1.60192 | −0.131234 | −0.0656170 | − | 0.997845i | \(-0.520902\pi\) | ||||
−0.0656170 | + | 0.997845i | \(0.520902\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 6.74218 | 0.548671 | 0.274336 | − | 0.961634i | \(-0.411542\pi\) | ||||
0.274336 | + | 0.961634i | \(0.411542\pi\) | |||||||
\(152\) | 10.4484 | 0.847474 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 5.47948 | 0.441549 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −14.2612 | −1.13817 | −0.569083 | − | 0.822280i | \(-0.692702\pi\) | ||||
−0.569083 | + | 0.822280i | \(0.692702\pi\) | |||||||
\(158\) | −11.6938 | −0.930311 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −2.95417 | −0.232822 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −10.1141 | −0.792194 | −0.396097 | − | 0.918209i | \(-0.629636\pi\) | ||||
−0.396097 | + | 0.918209i | \(0.629636\pi\) | |||||||
\(164\) | −1.64357 | −0.128341 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 15.1176 | 1.17335 | ||||||||
\(167\) | −16.7161 | −1.29353 | −0.646765 | − | 0.762689i | \(-0.723879\pi\) | ||||
−0.646765 | + | 0.762689i | \(0.723879\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 24.0306 | 1.84851 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 4.60736 | 0.351308 | ||||||||
\(173\) | −6.44267 | −0.489827 | −0.244914 | − | 0.969545i | \(-0.578760\pi\) | ||||
−0.244914 | + | 0.969545i | \(0.578760\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 7.46723 | 0.562864 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −6.76004 | −0.506687 | ||||||||
\(179\) | 15.4342 | 1.15361 | 0.576804 | − | 0.816882i | \(-0.304300\pi\) | ||||
0.576804 | + | 0.816882i | \(0.304300\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1.27794 | 0.0949885 | 0.0474943 | − | 0.998872i | \(-0.484876\pi\) | ||||
0.0474943 | + | 0.998872i | \(0.484876\pi\) | |||||||
\(182\) | −6.51160 | −0.482672 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −8.89559 | −0.655791 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 16.3515 | 1.19574 | ||||||||
\(188\) | −4.23411 | −0.308804 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −5.83613 | −0.422287 | −0.211144 | − | 0.977455i | \(-0.567719\pi\) | ||||
−0.211144 | + | 0.977455i | \(0.567719\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −4.17773 | −0.300719 | −0.150360 | − | 0.988631i | \(-0.548043\pi\) | ||||
−0.150360 | + | 0.988631i | \(0.548043\pi\) | |||||||
\(194\) | 14.8913 | 1.06913 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 5.27047 | 0.376462 | ||||||||
\(197\) | 17.4854 | 1.24579 | 0.622893 | − | 0.782307i | \(-0.285957\pi\) | ||||
0.622893 | + | 0.782307i | \(0.285957\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 5.89046 | 0.417564 | 0.208782 | − | 0.977962i | \(-0.433050\pi\) | ||||
0.208782 | + | 0.977962i | \(0.433050\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −11.1162 | −0.782130 | ||||||||
\(203\) | 1.57108 | 0.110268 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 3.25428 | 0.226736 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −8.87375 | −0.615284 | ||||||||
\(209\) | −17.5575 | −1.21448 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −11.9773 | −0.824549 | −0.412275 | − | 0.911060i | \(-0.635266\pi\) | ||||
−0.412275 | + | 0.911060i | \(0.635266\pi\) | |||||||
\(212\) | 8.86362 | 0.608756 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −5.54838 | −0.379279 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −8.09291 | −0.549383 | ||||||||
\(218\) | 6.89309 | 0.466859 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −19.4315 | −1.30710 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −1.27716 | −0.0855248 | −0.0427624 | − | 0.999085i | \(-0.513616\pi\) | ||||
−0.0427624 | + | 0.999085i | \(0.513616\pi\) | |||||||
\(224\) | −4.60733 | −0.307840 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0.407676 | 0.0271182 | ||||||||
\(227\) | −28.1382 | −1.86760 | −0.933798 | − | 0.357802i | \(-0.883526\pi\) | ||||
−0.933798 | + | 0.357802i | \(0.883526\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 11.2821 | 0.745544 | 0.372772 | − | 0.927923i | \(-0.378407\pi\) | ||||
0.372772 | + | 0.927923i | \(0.378407\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 4.73083 | 0.310594 | ||||||||
\(233\) | 13.4719 | 0.882576 | 0.441288 | − | 0.897365i | \(-0.354522\pi\) | ||||
0.441288 | + | 0.897365i | \(0.354522\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 2.55283 | 0.166175 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 3.41690 | 0.221485 | ||||||||
\(239\) | −1.90251 | −0.123063 | −0.0615315 | − | 0.998105i | \(-0.519598\pi\) | ||||
−0.0615315 | + | 0.998105i | \(0.519598\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −19.5685 | −1.26052 | −0.630258 | − | 0.776386i | \(-0.717051\pi\) | ||||
−0.630258 | + | 0.776386i | \(0.717051\pi\) | |||||||
\(242\) | −16.0953 | −1.03465 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 2.03702 | 0.130407 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 20.8647 | 1.32759 | ||||||||
\(248\) | −24.3693 | −1.54745 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −20.7096 | −1.30718 | −0.653590 | − | 0.756849i | \(-0.726738\pi\) | ||||
−0.653590 | + | 0.756849i | \(0.726738\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 14.9483 | 0.939789 | ||||||||
\(254\) | 4.90964 | 0.308058 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −16.4458 | −1.02786 | ||||||||
\(257\) | −15.0730 | −0.940225 | −0.470113 | − | 0.882606i | \(-0.655787\pi\) | ||||
−0.470113 | + | 0.882606i | \(0.655787\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 8.50810 | 0.528667 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 17.1520 | 1.05965 | ||||||||
\(263\) | −5.00327 | −0.308515 | −0.154257 | − | 0.988031i | \(-0.549298\pi\) | ||||
−0.154257 | + | 0.988031i | \(0.549298\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −3.66892 | −0.224956 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −4.10018 | −0.250458 | ||||||||
\(269\) | 27.6804 | 1.68770 | 0.843852 | − | 0.536576i | \(-0.180283\pi\) | ||||
0.843852 | + | 0.536576i | \(0.180283\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −26.3928 | −1.60325 | −0.801624 | − | 0.597829i | \(-0.796030\pi\) | ||||
−0.801624 | + | 0.597829i | \(0.796030\pi\) | |||||||
\(272\) | 4.65642 | 0.282337 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −20.2806 | −1.22520 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −7.12277 | −0.427966 | −0.213983 | − | 0.976837i | \(-0.568644\pi\) | ||||
−0.213983 | + | 0.976837i | \(0.568644\pi\) | |||||||
\(278\) | −3.79349 | −0.227518 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 10.3267 | 0.616037 | 0.308019 | − | 0.951380i | \(-0.400334\pi\) | ||||
0.308019 | + | 0.951380i | \(0.400334\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 4.55987 | 0.271056 | 0.135528 | − | 0.990773i | \(-0.456727\pi\) | ||||
0.135528 | + | 0.990773i | \(0.456727\pi\) | |||||||
\(284\) | −6.82381 | −0.404918 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 32.9490 | 1.94831 | ||||||||
\(287\) | 1.88590 | 0.111321 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −6.80350 | −0.400206 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0.525241 | 0.0307374 | ||||||||
\(293\) | 20.8237 | 1.21653 | 0.608267 | − | 0.793733i | \(-0.291865\pi\) | ||||
0.608267 | + | 0.793733i | \(0.291865\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 25.6195 | 1.48910 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 1.69383 | 0.0981207 | ||||||||
\(299\) | −17.7639 | −1.02731 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −5.28668 | −0.304719 | ||||||||
\(302\) | −7.12902 | −0.410229 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −4.99986 | −0.286762 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 9.44200 | 0.538884 | 0.269442 | − | 0.963017i | \(-0.413161\pi\) | ||||
0.269442 | + | 0.963017i | \(0.413161\pi\) | |||||||
\(308\) | 4.57045 | 0.260425 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −13.3804 | −0.758732 | −0.379366 | − | 0.925247i | \(-0.623858\pi\) | ||||
−0.379366 | + | 0.925247i | \(0.623858\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 23.9947 | 1.35626 | 0.678131 | − | 0.734941i | \(-0.262790\pi\) | ||||
0.678131 | + | 0.734941i | \(0.262790\pi\) | |||||||
\(314\) | 15.0794 | 0.850980 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −9.75384 | −0.548697 | ||||||||
\(317\) | −14.5616 | −0.817862 | −0.408931 | − | 0.912565i | \(-0.634098\pi\) | ||||
−0.408931 | + | 0.912565i | \(0.634098\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −7.94975 | −0.445100 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 3.12367 | 0.174075 | ||||||||
\(323\) | −10.9486 | −0.609194 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 10.6944 | 0.592305 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 5.67880 | 0.313560 | ||||||||
\(329\) | 4.85839 | 0.267852 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −24.4248 | −1.34251 | −0.671255 | − | 0.741226i | \(-0.734245\pi\) | ||||
−0.671255 | + | 0.741226i | \(0.734245\pi\) | |||||||
\(332\) | 12.6096 | 0.692042 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 17.6752 | 0.967143 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −8.57221 | −0.466958 | −0.233479 | − | 0.972362i | \(-0.575011\pi\) | ||||
−0.233479 | + | 0.972362i | \(0.575011\pi\) | |||||||
\(338\) | −25.4094 | −1.38209 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 40.9505 | 2.21759 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −13.1315 | −0.709035 | ||||||||
\(344\) | −15.9192 | −0.858306 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 6.81232 | 0.366233 | ||||||||
\(347\) | −10.8076 | −0.580182 | −0.290091 | − | 0.956999i | \(-0.593686\pi\) | ||||
−0.290091 | + | 0.956999i | \(0.593686\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −8.13956 | −0.435701 | −0.217850 | − | 0.975982i | \(-0.569904\pi\) | ||||
−0.217850 | + | 0.975982i | \(0.569904\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 23.3133 | 1.24260 | ||||||||
\(353\) | −21.1661 | −1.12656 | −0.563279 | − | 0.826267i | \(-0.690460\pi\) | ||||
−0.563279 | + | 0.826267i | \(0.690460\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −5.63856 | −0.298843 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −16.3198 | −0.862527 | ||||||||
\(359\) | 5.32585 | 0.281087 | 0.140544 | − | 0.990074i | \(-0.455115\pi\) | ||||
0.140544 | + | 0.990074i | \(0.455115\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −7.24392 | −0.381259 | ||||||||
\(362\) | −1.35126 | −0.0710207 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −5.43134 | −0.284679 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −17.0272 | −0.888812 | −0.444406 | − | 0.895826i | \(-0.646585\pi\) | ||||
−0.444406 | + | 0.895826i | \(0.646585\pi\) | |||||||
\(368\) | 4.25682 | 0.221902 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −10.1705 | −0.528025 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −6.85131 | −0.354748 | −0.177374 | − | 0.984144i | \(-0.556760\pi\) | ||||
−0.177374 | + | 0.984144i | \(0.556760\pi\) | |||||||
\(374\) | −17.2897 | −0.894028 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 14.6295 | 0.754461 | ||||||||
\(377\) | 9.44716 | 0.486554 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −7.38816 | −0.379504 | −0.189752 | − | 0.981832i | \(-0.560768\pi\) | ||||
−0.189752 | + | 0.981832i | \(0.560768\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 6.17097 | 0.315734 | ||||||||
\(383\) | −20.2032 | −1.03233 | −0.516167 | − | 0.856488i | \(-0.672641\pi\) | ||||
−0.516167 | + | 0.856488i | \(0.672641\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 4.41742 | 0.224841 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 12.4209 | 0.630574 | ||||||||
\(389\) | −8.80029 | −0.446192 | −0.223096 | − | 0.974796i | \(-0.571616\pi\) | ||||
−0.223096 | + | 0.974796i | \(0.571616\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 9.32145 | 0.471406 | ||||||||
\(392\) | −18.2103 | −0.919760 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −18.4887 | −0.931446 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 6.09306 | 0.305802 | 0.152901 | − | 0.988242i | \(-0.451138\pi\) | ||||
0.152901 | + | 0.988242i | \(0.451138\pi\) | |||||||
\(398\) | −6.22842 | −0.312203 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 1.71924 | 0.0858547 | 0.0429274 | − | 0.999078i | \(-0.486332\pi\) | ||||
0.0429274 | + | 0.999078i | \(0.486332\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −48.6639 | −2.42412 | ||||||||
\(404\) | −9.27201 | −0.461300 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −1.66122 | −0.0824451 | ||||||||
\(407\) | −43.0514 | −2.13398 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −27.7414 | −1.37173 | −0.685863 | − | 0.727731i | \(-0.740575\pi\) | ||||
−0.685863 | + | 0.727731i | \(0.740575\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 2.71440 | 0.133729 | ||||||||
\(413\) | −2.92922 | −0.144138 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −27.7046 | −1.35833 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 18.5649 | 0.908039 | ||||||||
\(419\) | −16.3540 | −0.798944 | −0.399472 | − | 0.916745i | \(-0.630807\pi\) | ||||
−0.399472 | + | 0.916745i | \(0.630807\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −9.94561 | −0.484719 | −0.242360 | − | 0.970186i | \(-0.577921\pi\) | ||||
−0.242360 | + | 0.970186i | \(0.577921\pi\) | |||||||
\(422\) | 12.6645 | 0.616496 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −30.6253 | −1.48729 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −2.33736 | −0.113113 | ||||||||
\(428\) | −4.62791 | −0.223699 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 20.5302 | 0.988903 | 0.494452 | − | 0.869205i | \(-0.335369\pi\) | ||||
0.494452 | + | 0.869205i | \(0.335369\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −25.9469 | −1.24693 | −0.623463 | − | 0.781853i | \(-0.714275\pi\) | ||||
−0.623463 | + | 0.781853i | \(0.714275\pi\) | |||||||
\(434\) | 8.55724 | 0.410761 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 5.74954 | 0.275353 | ||||||||
\(437\) | −10.0090 | −0.478794 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 25.1284 | 1.19931 | 0.599656 | − | 0.800258i | \(-0.295304\pi\) | ||||
0.599656 | + | 0.800258i | \(0.295304\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 20.5464 | 0.977291 | ||||||||
\(443\) | −27.0262 | −1.28405 | −0.642027 | − | 0.766682i | \(-0.721906\pi\) | ||||
−0.642027 | + | 0.766682i | \(0.721906\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 1.35043 | 0.0639449 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 7.82312 | 0.369608 | ||||||||
\(449\) | −37.9871 | −1.79272 | −0.896361 | − | 0.443325i | \(-0.853799\pi\) | ||||
−0.896361 | + | 0.443325i | \(0.853799\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −9.54273 | −0.449350 | ||||||||
\(452\) | 0.340043 | 0.0159943 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 29.7526 | 1.39636 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −29.9832 | −1.40256 | −0.701278 | − | 0.712888i | \(-0.747387\pi\) | ||||
−0.701278 | + | 0.712888i | \(0.747387\pi\) | |||||||
\(458\) | −11.9294 | −0.557426 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 2.13364 | 0.0993734 | 0.0496867 | − | 0.998765i | \(-0.484178\pi\) | ||||
0.0496867 | + | 0.998765i | \(0.484178\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −21.9804 | −1.02151 | −0.510757 | − | 0.859725i | \(-0.670635\pi\) | ||||
−0.510757 | + | 0.859725i | \(0.670635\pi\) | |||||||
\(464\) | −2.26385 | −0.105097 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −14.2449 | −0.659882 | ||||||||
\(467\) | −5.31093 | −0.245761 | −0.122880 | − | 0.992421i | \(-0.539213\pi\) | ||||
−0.122880 | + | 0.992421i | \(0.539213\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 4.70471 | 0.217243 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −8.82045 | −0.405994 | ||||||||
\(473\) | 26.7508 | 1.23000 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 2.85005 | 0.130632 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 2.01166 | 0.0920113 | ||||||||
\(479\) | 21.0877 | 0.963522 | 0.481761 | − | 0.876303i | \(-0.339997\pi\) | ||||
0.481761 | + | 0.876303i | \(0.339997\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 51.1605 | 2.33272 | ||||||||
\(482\) | 20.6912 | 0.942459 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −13.4251 | −0.610233 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −26.6121 | −1.20591 | −0.602954 | − | 0.797776i | \(-0.706010\pi\) | ||||
−0.602954 | + | 0.797776i | \(0.706010\pi\) | |||||||
\(488\) | −7.03825 | −0.318607 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −1.80069 | −0.0812638 | −0.0406319 | − | 0.999174i | \(-0.512937\pi\) | ||||
−0.0406319 | + | 0.999174i | \(0.512937\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −4.95731 | −0.223266 | ||||||||
\(494\) | −22.0618 | −0.992607 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 11.6615 | 0.523616 | ||||||||
\(497\) | 7.82991 | 0.351220 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 28.6962 | 1.28462 | 0.642309 | − | 0.766446i | \(-0.277977\pi\) | ||||
0.642309 | + | 0.766446i | \(0.277977\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 21.8978 | 0.977349 | ||||||||
\(503\) | 23.6827 | 1.05596 | 0.527980 | − | 0.849257i | \(-0.322949\pi\) | ||||
0.527980 | + | 0.849257i | \(0.322949\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −15.8059 | −0.702658 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 4.09514 | 0.181693 | ||||||||
\(509\) | −17.6957 | −0.784346 | −0.392173 | − | 0.919891i | \(-0.628277\pi\) | ||||
−0.392173 | + | 0.919891i | \(0.628277\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −0.602683 | −0.0266611 | ||||||||
\(512\) | 15.5263 | 0.686172 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 15.9378 | 0.702985 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −24.5837 | −1.08119 | ||||||||
\(518\) | −8.99625 | −0.395273 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −22.9756 | −1.00658 | −0.503289 | − | 0.864118i | \(-0.667877\pi\) | ||||
−0.503289 | + | 0.864118i | \(0.667877\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −28.9773 | −1.26709 | −0.633544 | − | 0.773707i | \(-0.718400\pi\) | ||||
−0.633544 | + | 0.773707i | \(0.718400\pi\) | |||||||
\(524\) | 14.3065 | 0.624982 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 5.29033 | 0.230669 | ||||||||
\(527\) | 25.5359 | 1.11236 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −14.4785 | −0.629500 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −3.06025 | −0.132679 | ||||||||
\(533\) | 11.3402 | 0.491199 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 14.1668 | 0.611912 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −29.2686 | −1.26186 | ||||||||
\(539\) | 30.6008 | 1.31807 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 24.4505 | 1.05121 | 0.525605 | − | 0.850729i | \(-0.323839\pi\) | ||||
0.525605 | + | 0.850729i | \(0.323839\pi\) | |||||||
\(542\) | 27.9071 | 1.19871 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 14.5377 | 0.623300 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −6.50334 | −0.278063 | −0.139031 | − | 0.990288i | \(-0.544399\pi\) | ||||
−0.139031 | + | 0.990288i | \(0.544399\pi\) | |||||||
\(548\) | −16.9161 | −0.722619 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 5.32295 | 0.226765 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 11.1920 | 0.475930 | ||||||||
\(554\) | 7.53144 | 0.319980 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −3.16416 | −0.134190 | ||||||||
\(557\) | −3.12305 | −0.132328 | −0.0661640 | − | 0.997809i | \(-0.521076\pi\) | ||||
−0.0661640 | + | 0.997809i | \(0.521076\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −31.7896 | −1.34456 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −10.9192 | −0.460597 | ||||||||
\(563\) | 36.5252 | 1.53935 | 0.769677 | − | 0.638433i | \(-0.220417\pi\) | ||||
0.769677 | + | 0.638433i | \(0.220417\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −4.82149 | −0.202663 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 23.5774 | 0.989285 | ||||||||
\(569\) | 37.7676 | 1.58330 | 0.791650 | − | 0.610975i | \(-0.209222\pi\) | ||||
0.791650 | + | 0.610975i | \(0.209222\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −41.2370 | −1.72571 | −0.862857 | − | 0.505448i | \(-0.831327\pi\) | ||||
−0.862857 | + | 0.505448i | \(0.831327\pi\) | |||||||
\(572\) | 27.4828 | 1.14911 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −1.99410 | −0.0832322 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −4.26929 | −0.177733 | −0.0888663 | − | 0.996044i | \(-0.528324\pi\) | ||||
−0.0888663 | + | 0.996044i | \(0.528324\pi\) | |||||||
\(578\) | 7.19385 | 0.299225 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −14.4688 | −0.600266 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 51.4631 | 2.13138 | ||||||||
\(584\) | −1.81480 | −0.0750968 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −22.0185 | −0.909574 | ||||||||
\(587\) | −11.4331 | −0.471893 | −0.235947 | − | 0.971766i | \(-0.575819\pi\) | ||||
−0.235947 | + | 0.971766i | \(0.575819\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −27.4194 | −1.12980 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −12.2597 | −0.503872 | ||||||||
\(593\) | −30.9375 | −1.27045 | −0.635225 | − | 0.772327i | \(-0.719092\pi\) | ||||
−0.635225 | + | 0.772327i | \(0.719092\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 1.41282 | 0.0578715 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 18.7831 | 0.768098 | ||||||||
\(599\) | 46.1912 | 1.88732 | 0.943660 | − | 0.330916i | \(-0.107358\pi\) | ||||
0.943660 | + | 0.330916i | \(0.107358\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −38.0963 | −1.55398 | −0.776990 | − | 0.629513i | \(-0.783254\pi\) | ||||
−0.776990 | + | 0.629513i | \(0.783254\pi\) | |||||||
\(602\) | 5.59000 | 0.227831 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −5.94632 | −0.241953 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 38.6361 | 1.56819 | 0.784095 | − | 0.620641i | \(-0.213127\pi\) | ||||
0.784095 | + | 0.620641i | \(0.213127\pi\) | |||||||
\(608\) | −15.6100 | −0.633068 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 29.2142 | 1.18188 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −10.7561 | −0.434434 | −0.217217 | − | 0.976123i | \(-0.569698\pi\) | ||||
−0.217217 | + | 0.976123i | \(0.569698\pi\) | |||||||
\(614\) | −9.98374 | −0.402911 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −15.7916 | −0.636264 | ||||||||
\(617\) | 10.8072 | 0.435082 | 0.217541 | − | 0.976051i | \(-0.430196\pi\) | ||||
0.217541 | + | 0.976051i | \(0.430196\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −36.8938 | −1.48289 | −0.741443 | − | 0.671016i | \(-0.765858\pi\) | ||||
−0.741443 | + | 0.671016i | \(0.765858\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 14.1481 | 0.567286 | ||||||||
\(623\) | 6.46992 | 0.259212 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −25.3714 | −1.01405 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 12.5778 | 0.501907 | ||||||||
\(629\) | −26.8460 | −1.07042 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 39.2593 | 1.56289 | 0.781445 | − | 0.623974i | \(-0.214483\pi\) | ||||
0.781445 | + | 0.623974i | \(0.214483\pi\) | |||||||
\(632\) | 33.7011 | 1.34056 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 15.3971 | 0.611497 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −36.3648 | −1.44083 | ||||||||
\(638\) | 8.40586 | 0.332791 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −8.34833 | −0.329739 | −0.164870 | − | 0.986315i | \(-0.552720\pi\) | ||||
−0.164870 | + | 0.986315i | \(0.552720\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −13.1408 | −0.518223 | −0.259112 | − | 0.965847i | \(-0.583430\pi\) | ||||
−0.259112 | + | 0.965847i | \(0.583430\pi\) | |||||||
\(644\) | 2.60546 | 0.102669 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 11.5767 | 0.455480 | ||||||||
\(647\) | −26.0801 | −1.02531 | −0.512656 | − | 0.858594i | \(-0.671339\pi\) | ||||
−0.512656 | + | 0.858594i | \(0.671339\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 14.8220 | 0.581814 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 8.92018 | 0.349341 | ||||||||
\(653\) | −23.0295 | −0.901213 | −0.450606 | − | 0.892723i | \(-0.648792\pi\) | ||||
−0.450606 | + | 0.892723i | \(0.648792\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −2.71749 | −0.106100 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −5.13714 | −0.200267 | ||||||||
\(659\) | −34.7580 | −1.35398 | −0.676990 | − | 0.735992i | \(-0.736716\pi\) | ||||
−0.676990 | + | 0.735992i | \(0.736716\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 18.0033 | 0.700249 | 0.350124 | − | 0.936703i | \(-0.386139\pi\) | ||||
0.350124 | + | 0.936703i | \(0.386139\pi\) | |||||||
\(662\) | 25.8262 | 1.00376 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −43.5682 | −1.69078 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −4.53188 | −0.175475 | ||||||||
\(668\) | 14.7429 | 0.570420 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 11.8272 | 0.456583 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 14.8622 | 0.572896 | 0.286448 | − | 0.958096i | \(-0.407526\pi\) | ||||
0.286448 | + | 0.958096i | \(0.407526\pi\) | |||||||
\(674\) | 9.06404 | 0.349134 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −21.1940 | −0.815153 | ||||||||
\(677\) | 23.1238 | 0.888720 | 0.444360 | − | 0.895848i | \(-0.353431\pi\) | ||||
0.444360 | + | 0.895848i | \(0.353431\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −14.2522 | −0.546949 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −43.3000 | −1.65804 | ||||||||
\(683\) | 19.6347 | 0.751302 | 0.375651 | − | 0.926761i | \(-0.377419\pi\) | ||||
0.375651 | + | 0.926761i | \(0.377419\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 13.8849 | 0.530129 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 7.61783 | 0.290427 | ||||||||
\(689\) | −61.1566 | −2.32988 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −5.87782 | −0.223603 | −0.111801 | − | 0.993731i | \(-0.535662\pi\) | ||||
−0.111801 | + | 0.993731i | \(0.535662\pi\) | |||||||
\(692\) | 5.68217 | 0.216004 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 11.4277 | 0.433788 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −5.95067 | −0.225398 | ||||||||
\(698\) | 8.60657 | 0.325763 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 50.0581 | 1.89067 | 0.945334 | − | 0.326103i | \(-0.105736\pi\) | ||||
0.945334 | + | 0.326103i | \(0.105736\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 28.8261 | 1.08720 | ||||||||
\(704\) | −39.5853 | −1.49193 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 22.3805 | 0.842301 | ||||||||
\(707\) | 10.6391 | 0.400124 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 13.7506 | 0.516414 | 0.258207 | − | 0.966090i | \(-0.416868\pi\) | ||||
0.258207 | + | 0.966090i | \(0.416868\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 19.4822 | 0.730125 | ||||||||
\(713\) | 23.3445 | 0.874258 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −13.6123 | −0.508717 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −5.63142 | −0.210163 | ||||||||
\(719\) | 10.5000 | 0.391582 | 0.195791 | − | 0.980646i | \(-0.437273\pi\) | ||||
0.195791 | + | 0.980646i | \(0.437273\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −3.11461 | −0.115994 | ||||||||
\(722\) | 7.65954 | 0.285059 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −1.12709 | −0.0418880 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −6.06366 | −0.224889 | −0.112444 | − | 0.993658i | \(-0.535868\pi\) | ||||
−0.112444 | + | 0.993658i | \(0.535868\pi\) | |||||||
\(728\) | 18.7662 | 0.695520 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 16.6813 | 0.616980 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 2.34070 | 0.0864558 | 0.0432279 | − | 0.999065i | \(-0.486236\pi\) | ||||
0.0432279 | + | 0.999065i | \(0.486236\pi\) | |||||||
\(734\) | 18.0041 | 0.664544 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 13.2901 | 0.489880 | ||||||||
\(737\) | −23.8061 | −0.876907 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −41.5352 | −1.52790 | −0.763949 | − | 0.645276i | \(-0.776742\pi\) | ||||
−0.763949 | + | 0.645276i | \(0.776742\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 10.7540 | 0.394792 | ||||||||
\(743\) | 0.813821 | 0.0298562 | 0.0149281 | − | 0.999889i | \(-0.495248\pi\) | ||||
0.0149281 | + | 0.999889i | \(0.495248\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 7.24441 | 0.265237 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −14.4214 | −0.527297 | ||||||||
\(749\) | 5.31025 | 0.194032 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 31.8919 | 1.16375 | 0.581877 | − | 0.813277i | \(-0.302319\pi\) | ||||
0.581877 | + | 0.813277i | \(0.302319\pi\) | |||||||
\(752\) | −7.00069 | −0.255289 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −9.98919 | −0.363785 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 26.7040 | 0.970572 | 0.485286 | − | 0.874355i | \(-0.338715\pi\) | ||||
0.485286 | + | 0.874355i | \(0.338715\pi\) | |||||||
\(758\) | 7.81205 | 0.283746 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −43.0644 | −1.56108 | −0.780542 | − | 0.625103i | \(-0.785057\pi\) | ||||
−0.780542 | + | 0.625103i | \(0.785057\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −6.59725 | −0.238837 | ||||||||
\(764\) | 5.14722 | 0.186220 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 21.3623 | 0.771852 | ||||||||
\(767\) | −17.6139 | −0.636000 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −1.05358 | −0.0379930 | −0.0189965 | − | 0.999820i | \(-0.506047\pi\) | ||||
−0.0189965 | + | 0.999820i | \(0.506047\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 3.68458 | 0.132611 | ||||||||
\(773\) | 13.2299 | 0.475845 | 0.237923 | − | 0.971284i | \(-0.423534\pi\) | ||||
0.237923 | + | 0.971284i | \(0.423534\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −42.9161 | −1.54060 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 9.30521 | 0.333608 | ||||||||
\(779\) | 6.38957 | 0.228930 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −39.6197 | −1.41770 | ||||||||
\(782\) | −9.85627 | −0.352459 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 8.71421 | 0.311222 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 33.6378 | 1.19906 | 0.599528 | − | 0.800354i | \(-0.295355\pi\) | ||||
0.599528 | + | 0.800354i | \(0.295355\pi\) | |||||||
\(788\) | −15.4214 | −0.549366 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −0.390179 | −0.0138732 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −14.0549 | −0.499105 | ||||||||
\(794\) | −6.44264 | −0.228641 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −5.19514 | −0.184137 | ||||||||
\(797\) | −6.89741 | −0.244319 | −0.122159 | − | 0.992511i | \(-0.538982\pi\) | ||||
−0.122159 | + | 0.992511i | \(0.538982\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −15.3299 | −0.542333 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −1.81788 | −0.0641916 | ||||||||
\(803\) | 3.04960 | 0.107618 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 51.4560 | 1.81246 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 32.0363 | 1.12703 | ||||||||
\(809\) | 35.3330 | 1.24224 | 0.621121 | − | 0.783715i | \(-0.286678\pi\) | ||||
0.621121 | + | 0.783715i | \(0.286678\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −3.97201 | −0.139476 | −0.0697380 | − | 0.997565i | \(-0.522216\pi\) | ||||
−0.0697380 | + | 0.997565i | \(0.522216\pi\) | |||||||
\(812\) | −1.38563 | −0.0486261 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 45.5214 | 1.59552 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −17.9117 | −0.626650 | ||||||||
\(818\) | 29.3331 | 1.02561 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −24.3758 | −0.850720 | −0.425360 | − | 0.905024i | \(-0.639853\pi\) | ||||
−0.425360 | + | 0.905024i | \(0.639853\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 22.2604 | 0.775947 | 0.387974 | − | 0.921670i | \(-0.373175\pi\) | ||||
0.387974 | + | 0.921670i | \(0.373175\pi\) | |||||||
\(824\) | −9.37870 | −0.326722 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 3.09729 | 0.107768 | ||||||||
\(827\) | −26.6196 | −0.925656 | −0.462828 | − | 0.886448i | \(-0.653165\pi\) | ||||
−0.462828 | + | 0.886448i | \(0.653165\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −7.83334 | −0.272063 | −0.136032 | − | 0.990704i | \(-0.543435\pi\) | ||||
−0.136032 | + | 0.990704i | \(0.543435\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 47.0416 | 1.63088 | ||||||||
\(833\) | 19.0821 | 0.661156 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 15.4850 | 0.535561 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 17.2923 | 0.597352 | ||||||||
\(839\) | −5.87401 | −0.202793 | −0.101397 | − | 0.994846i | \(-0.532331\pi\) | ||||
−0.101397 | + | 0.994846i | \(0.532331\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −26.5899 | −0.916892 | ||||||||
\(842\) | 10.5162 | 0.362413 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 10.5635 | 0.363609 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 15.4045 | 0.529306 | ||||||||
\(848\) | 14.6551 | 0.503260 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −24.5421 | −0.841293 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −28.1446 | −0.963654 | −0.481827 | − | 0.876266i | \(-0.660027\pi\) | ||||
−0.481827 | + | 0.876266i | \(0.660027\pi\) | |||||||
\(854\) | 2.47147 | 0.0845719 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 15.9902 | 0.546534 | ||||||||
\(857\) | 36.2976 | 1.23990 | 0.619951 | − | 0.784640i | \(-0.287152\pi\) | ||||
0.619951 | + | 0.784640i | \(0.287152\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 3.82400 | 0.130473 | 0.0652366 | − | 0.997870i | \(-0.479220\pi\) | ||||
0.0652366 | + | 0.997870i | \(0.479220\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −21.7081 | −0.739380 | ||||||||
\(863\) | −25.5955 | −0.871280 | −0.435640 | − | 0.900121i | \(-0.643478\pi\) | ||||
−0.435640 | + | 0.900121i | \(0.643478\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 27.4356 | 0.932298 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 7.13761 | 0.242266 | ||||||||
\(869\) | −56.6318 | −1.92110 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 28.2902 | 0.958575 | ||||||||
\(872\) | −19.8656 | −0.672734 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 10.5832 | 0.357983 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 14.8579 | 0.501715 | 0.250857 | − | 0.968024i | \(-0.419287\pi\) | ||||
0.250857 | + | 0.968024i | \(0.419287\pi\) | |||||||
\(878\) | −26.5701 | −0.896697 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −2.11362 | −0.0712096 | −0.0356048 | − | 0.999366i | \(-0.511336\pi\) | ||||
−0.0356048 | + | 0.999366i | \(0.511336\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −51.0828 | −1.71907 | −0.859537 | − | 0.511074i | \(-0.829248\pi\) | ||||
−0.859537 | + | 0.511074i | \(0.829248\pi\) | |||||||
\(884\) | 17.1378 | 0.576405 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 28.5768 | 0.960058 | ||||||||
\(887\) | −45.5799 | −1.53042 | −0.765212 | − | 0.643779i | \(-0.777366\pi\) | ||||
−0.765212 | + | 0.643779i | \(0.777366\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −4.69893 | −0.157597 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 1.12640 | 0.0377147 | ||||||||
\(893\) | 16.4606 | 0.550833 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0.942686 | 0.0314929 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 40.1666 | 1.34038 | ||||||||
\(899\) | −12.4150 | −0.414064 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 32.0914 | 1.06912 | ||||||||
\(902\) | 10.0902 | 0.335968 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −1.17490 | −0.0390767 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −27.5215 | −0.913837 | −0.456919 | − | 0.889508i | \(-0.651047\pi\) | ||||
−0.456919 | + | 0.889508i | \(0.651047\pi\) | |||||||
\(908\) | 24.8167 | 0.823570 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −50.4110 | −1.67019 | −0.835096 | − | 0.550104i | \(-0.814588\pi\) | ||||
−0.835096 | + | 0.550104i | \(0.814588\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 73.2126 | 2.42298 | ||||||||
\(914\) | 31.7035 | 1.04866 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −9.95037 | −0.328770 | ||||||||
\(917\) | −16.4158 | −0.542099 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 12.6543 | 0.417427 | 0.208714 | − | 0.977977i | \(-0.433072\pi\) | ||||
0.208714 | + | 0.977977i | \(0.433072\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −2.25606 | −0.0742992 | ||||||||
\(923\) | 47.0825 | 1.54974 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 23.2415 | 0.763763 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −7.06793 | −0.232016 | ||||||||
\(929\) | 3.03961 | 0.0997265 | 0.0498633 | − | 0.998756i | \(-0.484121\pi\) | ||||
0.0498633 | + | 0.998756i | \(0.484121\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −20.4895 | −0.671517 | ||||||||
\(932\) | −11.8817 | −0.389198 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 5.61565 | 0.183750 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 0.0480749 | 0.00157054 | 0.000785268 | − | 1.00000i | \(-0.499750\pi\) | ||||
0.000785268 | 1.00000i | \(0.499750\pi\) | ||||||||
\(938\) | −4.97465 | −0.162428 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 1.25393 | 0.0408769 | 0.0204384 | − | 0.999791i | \(-0.493494\pi\) | ||||
0.0204384 | + | 0.999791i | \(0.493494\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −5.43999 | −0.177150 | ||||||||
\(944\) | 4.22086 | 0.137377 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −28.2856 | −0.919646 | ||||||||
\(947\) | −44.5985 | −1.44926 | −0.724628 | − | 0.689140i | \(-0.757989\pi\) | ||||
−0.724628 | + | 0.689140i | \(0.757989\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −3.62403 | −0.117641 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −9.84737 | −0.319155 | ||||||||
\(953\) | 41.8227 | 1.35477 | 0.677385 | − | 0.735629i | \(-0.263113\pi\) | ||||
0.677385 | + | 0.735629i | \(0.263113\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 1.67793 | 0.0542682 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −22.2976 | −0.720404 | ||||||||
\(959\) | 19.4102 | 0.626788 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 32.9518 | 1.06296 | ||||||||
\(962\) | −54.0958 | −1.74412 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 17.2586 | 0.555861 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 44.4986 | 1.43098 | 0.715490 | − | 0.698623i | \(-0.246204\pi\) | ||||
0.715490 | + | 0.698623i | \(0.246204\pi\) | |||||||
\(968\) | 46.3860 | 1.49090 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −3.66499 | −0.117615 | −0.0588076 | − | 0.998269i | \(-0.518730\pi\) | ||||
−0.0588076 | + | 0.998269i | \(0.518730\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 3.63068 | 0.116394 | ||||||||
\(974\) | 28.1389 | 0.901629 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 3.36802 | 0.107808 | ||||||||
\(977\) | −15.7554 | −0.504060 | −0.252030 | − | 0.967719i | \(-0.581098\pi\) | ||||
−0.252030 | + | 0.967719i | \(0.581098\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −32.7381 | −1.04631 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 1.90400 | 0.0607591 | ||||||||
\(983\) | −26.9019 | −0.858036 | −0.429018 | − | 0.903296i | \(-0.641140\pi\) | ||||
−0.429018 | + | 0.903296i | \(0.641140\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 5.24174 | 0.166931 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −18.4018 | −0.585438 | ||||||||
\(989\) | 15.2497 | 0.484914 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 14.0680 | 0.446885 | 0.223442 | − | 0.974717i | \(-0.428271\pi\) | ||||
0.223442 | + | 0.974717i | \(0.428271\pi\) | |||||||
\(992\) | 36.4081 | 1.15596 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −8.27915 | −0.262599 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 0.618644 | 0.0195926 | 0.00979632 | − | 0.999952i | \(-0.496882\pi\) | ||||
0.00979632 | + | 0.999952i | \(0.496882\pi\) | |||||||
\(998\) | −30.3426 | −0.960479 | ||||||||
\(999\) | 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 | 5625.2.a.s.1.4 | 8 | ||
3.2 | odd | 2 | 625.2.a.g.1.5 | yes | 8 | ||
5.4 | even | 2 | 5625.2.a.be.1.5 | 8 | |||
12.11 | even | 2 | 10000.2.a.be.1.6 | 8 | |||
15.2 | even | 4 | 625.2.b.d.624.11 | 16 | |||
15.8 | even | 4 | 625.2.b.d.624.6 | 16 | |||
15.14 | odd | 2 | 625.2.a.e.1.4 | ✓ | 8 | ||
60.59 | even | 2 | 10000.2.a.bn.1.3 | 8 | |||
75.2 | even | 20 | 625.2.e.j.124.6 | 32 | |||
75.8 | even | 20 | 625.2.e.k.374.6 | 32 | |||
75.11 | odd | 10 | 625.2.d.m.501.3 | 16 | |||
75.14 | odd | 10 | 625.2.d.q.501.2 | 16 | |||
75.17 | even | 20 | 625.2.e.k.374.3 | 32 | |||
75.23 | even | 20 | 625.2.e.j.124.3 | 32 | |||
75.29 | odd | 10 | 625.2.d.p.376.3 | 16 | |||
75.38 | even | 20 | 625.2.e.j.499.6 | 32 | |||
75.41 | odd | 10 | 625.2.d.m.126.3 | 16 | |||
75.44 | odd | 10 | 625.2.d.p.251.3 | 16 | |||
75.47 | even | 20 | 625.2.e.k.249.6 | 32 | |||
75.53 | even | 20 | 625.2.e.k.249.3 | 32 | |||
75.56 | odd | 10 | 625.2.d.n.251.2 | 16 | |||
75.59 | odd | 10 | 625.2.d.q.126.2 | 16 | |||
75.62 | even | 20 | 625.2.e.j.499.3 | 32 | |||
75.71 | odd | 10 | 625.2.d.n.376.2 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
625.2.a.e.1.4 | ✓ | 8 | 15.14 | odd | 2 | ||
625.2.a.g.1.5 | yes | 8 | 3.2 | odd | 2 | ||
625.2.b.d.624.6 | 16 | 15.8 | even | 4 | |||
625.2.b.d.624.11 | 16 | 15.2 | even | 4 | |||
625.2.d.m.126.3 | 16 | 75.41 | odd | 10 | |||
625.2.d.m.501.3 | 16 | 75.11 | odd | 10 | |||
625.2.d.n.251.2 | 16 | 75.56 | odd | 10 | |||
625.2.d.n.376.2 | 16 | 75.71 | odd | 10 | |||
625.2.d.p.251.3 | 16 | 75.44 | odd | 10 | |||
625.2.d.p.376.3 | 16 | 75.29 | odd | 10 | |||
625.2.d.q.126.2 | 16 | 75.59 | odd | 10 | |||
625.2.d.q.501.2 | 16 | 75.14 | odd | 10 | |||
625.2.e.j.124.3 | 32 | 75.23 | even | 20 | |||
625.2.e.j.124.6 | 32 | 75.2 | even | 20 | |||
625.2.e.j.499.3 | 32 | 75.62 | even | 20 | |||
625.2.e.j.499.6 | 32 | 75.38 | even | 20 | |||
625.2.e.k.249.3 | 32 | 75.53 | even | 20 | |||
625.2.e.k.249.6 | 32 | 75.47 | even | 20 | |||
625.2.e.k.374.3 | 32 | 75.17 | even | 20 | |||
625.2.e.k.374.6 | 32 | 75.8 | even | 20 | |||
5625.2.a.s.1.4 | 8 | 1.1 | even | 1 | trivial | ||
5625.2.a.be.1.5 | 8 | 5.4 | even | 2 | |||
10000.2.a.be.1.6 | 8 | 12.11 | even | 2 | |||
10000.2.a.bn.1.3 | 8 | 60.59 | even | 2 |