Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [10000,2,Mod(1,10000)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(10000, 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("10000.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 10000 = 2^{4} \cdot 5^{4} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 10000.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: | \(79.8504020213\) |
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 | 1.6 | ||
Root | \(3.01367\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 10000.1 |
$q$-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 | ||||||||
\(3\) | 0.687404 | 0.396873 | 0.198436 | − | 0.980114i | \(-0.436414\pi\) | ||||
0.198436 | + | 0.980114i | \(0.436414\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.01199 | −0.382498 | −0.191249 | − | 0.981542i | \(-0.561254\pi\) | ||||
−0.191249 | + | 0.981542i | \(0.561254\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.52748 | −0.842492 | ||||||||
\(10\) | 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 | \(0.180268\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 3.19320 | 0.774464 | 0.387232 | − | 0.921982i | \(-0.373431\pi\) | ||||
0.387232 | + | 0.921982i | \(0.373431\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −3.42871 | −0.786601 | −0.393300 | − | 0.919410i | \(-0.628667\pi\) | ||||
−0.393300 | + | 0.919410i | \(0.628667\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −0.695649 | −0.151803 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −2.91916 | −0.608687 | −0.304343 | − | 0.952562i | \(-0.598437\pi\) | ||||
−0.304343 | + | 0.952562i | \(0.598437\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −3.79961 | −0.731235 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −1.55246 | −0.288285 | −0.144142 | − | 0.989557i | \(-0.546042\pi\) | ||||
−0.144142 | + | 0.989557i | \(0.546042\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 7.99699 | 1.43630 | 0.718151 | − | 0.695887i | \(-0.244989\pi\) | ||||
0.718151 | + | 0.695887i | \(0.244989\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −3.52001 | −0.612756 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 8.40726 | 1.38214 | 0.691072 | − | 0.722786i | \(-0.257139\pi\) | ||||
0.691072 | + | 0.722786i | \(0.257139\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 4.18304 | 0.669823 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −1.86355 | −0.291037 | −0.145519 | − | 0.989356i | \(-0.546485\pi\) | ||||
−0.145519 | + | 0.989356i | \(0.546485\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 5.22402 | 0.796655 | 0.398328 | − | 0.917243i | \(-0.369591\pi\) | ||||
0.398328 | + | 0.917243i | \(0.369591\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 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 | ||||||||
\(51\) | 2.19501 | 0.307363 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 10.0499 | 1.38046 | 0.690232 | − | 0.723588i | \(-0.257508\pi\) | ||||
0.690232 | + | 0.723588i | \(0.257508\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −2.35691 | −0.312180 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −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 | \(0.547239\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 2.55779 | 0.322252 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −4.64895 | −0.567960 | −0.283980 | − | 0.958830i | \(-0.591655\pi\) | ||||
−0.283980 | + | 0.958830i | \(0.591655\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −2.00664 | −0.241571 | ||||||||
\(70\) | 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 | \(0.511096\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 5.18216 | 0.590562 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −11.0593 | −1.24427 | −0.622134 | − | 0.782910i | \(-0.713734\pi\) | ||||
−0.622134 | + | 0.782910i | \(0.713734\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 4.97057 | 0.552285 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −14.2973 | −1.56933 | −0.784665 | − | 0.619920i | \(-0.787165\pi\) | ||||
−0.784665 | + | 0.619920i | \(0.787165\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −1.06717 | −0.114412 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −6.39323 | −0.677681 | −0.338841 | − | 0.940844i | \(-0.610035\pi\) | ||||
−0.338841 | + | 0.940844i | \(0.610035\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −6.15827 | −0.645562 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 5.49716 | 0.570029 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −14.0833 | −1.42994 | −0.714970 | − | 0.699155i | \(-0.753560\pi\) | ||||
−0.714970 | + | 0.699155i | \(0.753560\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 12.9425 | 1.30077 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −10.5130 | −1.04608 | −0.523040 | − | 0.852308i | \(-0.675202\pi\) | ||||
−0.523040 | + | 0.852308i | \(0.675202\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 3.07770 | 0.303254 | 0.151627 | − | 0.988438i | \(-0.451549\pi\) | ||||
0.151627 | + | 0.988438i | \(0.451549\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 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 | ||||||||
\(111\) | 5.77918 | 0.548535 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 0.385555 | 0.0362699 | 0.0181350 | − | 0.999836i | \(-0.494227\pi\) | ||||
0.0181350 | + | 0.999836i | \(0.494227\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −15.3804 | −1.42192 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −3.23150 | −0.296231 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 15.2220 | 1.38381 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −1.28101 | −0.115505 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 4.64324 | 0.412021 | 0.206010 | − | 0.978550i | \(-0.433952\pi\) | ||||
0.206010 | + | 0.978550i | \(0.433952\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 3.59101 | 0.316171 | ||||||||
\(130\) | 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 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −19.1801 | −1.63867 | −0.819335 | − | 0.573315i | \(-0.805657\pi\) | ||||
−0.819335 | + | 0.573315i | \(0.805657\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −3.58765 | −0.304300 | −0.152150 | − | 0.988357i | \(-0.548620\pi\) | ||||
−0.152150 | + | 0.988357i | \(0.548620\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 3.30009 | 0.277918 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −31.1611 | −2.60582 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −4.10783 | −0.338808 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 1.60192 | 0.131234 | 0.0656170 | − | 0.997845i | \(-0.479098\pi\) | ||||
0.0656170 | + | 0.997845i | \(0.479098\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −6.74218 | −0.548671 | −0.274336 | − | 0.961634i | \(-0.588458\pi\) | ||||
−0.274336 | + | 0.961634i | \(0.588458\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −8.07073 | −0.652479 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −14.2612 | −1.13817 | −0.569083 | − | 0.822280i | \(-0.692702\pi\) | ||||
−0.569083 | + | 0.822280i | \(0.692702\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 6.90836 | 0.547869 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 2.95417 | 0.232822 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 10.1141 | 0.792194 | 0.396097 | − | 0.918209i | \(-0.370364\pi\) | ||||
0.396097 | + | 0.918209i | \(0.370364\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −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 | ||||||||
\(171\) | 8.66599 | 0.662705 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 6.44267 | 0.489827 | 0.244914 | − | 0.969545i | \(-0.421240\pi\) | ||||
0.244914 | + | 0.969545i | \(0.421240\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −1.98969 | −0.149554 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 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 | \(0.484876\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −1.58767 | −0.117364 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −16.3515 | −1.19574 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 3.84518 | 0.279696 | ||||||||
\(190\) | 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 | \(0.548043\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −17.4854 | −1.24579 | −0.622893 | − | 0.782307i | \(-0.714043\pi\) | ||||
−0.622893 | + | 0.782307i | \(0.714043\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −5.89046 | −0.417564 | −0.208782 | − | 0.977962i | \(-0.566950\pi\) | ||||
−0.208782 | + | 0.977962i | \(0.566950\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −3.19571 | −0.225408 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 1.57108 | 0.110268 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 7.37811 | 0.512814 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 17.5575 | 1.21448 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 11.9773 | 0.824549 | 0.412275 | − | 0.911060i | \(-0.364734\pi\) | ||||
0.412275 | + | 0.911060i | \(0.364734\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 5.31852 | 0.364419 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −8.09291 | −0.549383 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −0.409376 | −0.0276631 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 19.4315 | 1.30710 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 1.27716 | 0.0855248 | 0.0427624 | − | 0.999085i | \(-0.486384\pi\) | ||||
0.0427624 | + | 0.999085i | \(0.486384\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −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 | ||||||||
\(231\) | 3.56223 | 0.234378 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −13.4719 | −0.882576 | −0.441288 | − | 0.897365i | \(-0.645478\pi\) | ||||
−0.441288 | + | 0.897365i | \(0.645478\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −7.60220 | −0.493816 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −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 | \(0.717051\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 14.8156 | 0.950422 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −20.8647 | −1.32759 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −9.82800 | −0.622824 | ||||||||
\(250\) | 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 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 15.0730 | 0.940225 | 0.470113 | − | 0.882606i | \(-0.344213\pi\) | ||||
0.470113 | + | 0.882606i | \(0.344213\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −8.50810 | −0.528667 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 3.92381 | 0.242878 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −5.00327 | −0.308515 | −0.154257 | − | 0.988031i | \(-0.549298\pi\) | ||||
−0.154257 | + | 0.988031i | \(0.549298\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −4.39473 | −0.268953 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −27.6804 | −1.68770 | −0.843852 | − | 0.536576i | \(-0.819717\pi\) | ||||
−0.843852 | + | 0.536576i | \(0.819717\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 26.3928 | 1.60325 | 0.801624 | − | 0.597829i | \(-0.203970\pi\) | ||||
0.801624 | + | 0.597829i | \(0.203970\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −4.23322 | −0.256206 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −7.12277 | −0.427966 | −0.213983 | − | 0.976837i | \(-0.568644\pi\) | ||||
−0.213983 | + | 0.976837i | \(0.568644\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −20.2122 | −1.21007 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −10.3267 | −0.616037 | −0.308019 | − | 0.951380i | \(-0.599666\pi\) | ||||
−0.308019 | + | 0.951380i | \(0.599666\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −4.55987 | −0.271056 | −0.135528 | − | 0.990773i | \(-0.543273\pi\) | ||||
−0.135528 | + | 0.990773i | \(0.543273\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 1.88590 | 0.111321 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −6.80350 | −0.400206 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −9.68090 | −0.567504 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −20.8237 | −1.21653 | −0.608267 | − | 0.793733i | \(-0.708135\pi\) | ||||
−0.608267 | + | 0.793733i | \(0.708135\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 19.4568 | 1.12900 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −17.7639 | −1.02731 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −5.28668 | −0.304719 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −7.22666 | −0.415161 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −9.44200 | −0.538884 | −0.269442 | − | 0.963017i | \(-0.586839\pi\) | ||||
−0.269442 | + | 0.963017i | \(0.586839\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 2.11562 | 0.120353 | ||||||||
\(310\) | 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 | \(0.262790\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 14.5616 | 0.817862 | 0.408931 | − | 0.912565i | \(-0.365902\pi\) | ||||
0.408931 | + | 0.912565i | \(0.365902\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 7.94975 | 0.445100 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 3.60702 | 0.201324 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −10.9486 | −0.609194 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −4.48122 | −0.247812 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −4.85839 | −0.267852 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 24.4248 | 1.34251 | 0.671255 | − | 0.741226i | \(-0.265755\pi\) | ||||
0.671255 | + | 0.741226i | \(0.265755\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −21.2491 | −1.16445 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −8.57221 | −0.466958 | −0.233479 | − | 0.972362i | \(-0.575011\pi\) | ||||
−0.233479 | + | 0.972362i | \(0.575011\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0.265032 | 0.0143945 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −40.9505 | −2.21759 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 13.1315 | 0.709035 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −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 | ||||||||
\(351\) | −23.1217 | −1.23414 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 21.1661 | 1.12656 | 0.563279 | − | 0.826267i | \(-0.309540\pi\) | ||||
0.563279 | + | 0.826267i | \(0.309540\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −2.22134 | −0.117566 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 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 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 10.4636 | 0.549198 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 17.0272 | 0.888812 | 0.444406 | − | 0.895826i | \(-0.353415\pi\) | ||||
0.444406 | + | 0.895826i | \(0.353415\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 4.71007 | 0.245196 | ||||||||
\(370\) | 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 | \(0.556760\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −9.44716 | −0.486554 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 7.38816 | 0.379504 | 0.189752 | − | 0.981832i | \(-0.439232\pi\) | ||||
0.189752 | + | 0.981832i | \(0.439232\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 3.19178 | 0.163520 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −20.2032 | −1.03233 | −0.516167 | − | 0.856488i | \(-0.672641\pi\) | ||||
−0.516167 | + | 0.856488i | \(0.672641\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −13.2036 | −0.671176 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 8.80029 | 0.446192 | 0.223096 | − | 0.974796i | \(-0.428384\pi\) | ||||
0.223096 | + | 0.974796i | \(0.428384\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −9.32145 | −0.471406 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −11.1506 | −0.562471 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 6.09306 | 0.305802 | 0.152901 | − | 0.988242i | \(-0.451138\pi\) | ||||
0.152901 | + | 0.988242i | \(0.451138\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 2.38518 | 0.119408 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −1.71924 | −0.0858547 | −0.0429274 | − | 0.999078i | \(-0.513668\pi\) | ||||
−0.0429274 | + | 0.999078i | \(0.513668\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 48.6639 | 2.42412 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −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 | ||||||||
\(411\) | −13.1845 | −0.650343 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 2.92922 | 0.144138 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −2.46616 | −0.120768 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −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 | \(0.577921\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −12.1339 | −0.589972 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 2.33736 | 0.113113 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −21.4203 | −1.03418 | ||||||||
\(430\) | 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 | \(0.714275\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 10.0090 | 0.478794 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −25.1284 | −1.19931 | −0.599656 | − | 0.800258i | \(-0.704696\pi\) | ||||
−0.599656 | + | 0.800258i | \(0.704696\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 15.1039 | 0.719232 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −27.0262 | −1.28405 | −0.642027 | − | 0.766682i | \(-0.721906\pi\) | ||||
−0.642027 | + | 0.766682i | \(0.721906\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 1.10116 | 0.0520832 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 37.9871 | 1.79272 | 0.896361 | − | 0.443325i | \(-0.146201\pi\) | ||||
0.896361 | + | 0.443325i | \(0.146201\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 9.54273 | 0.449350 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −4.63460 | −0.217753 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −29.9832 | −1.40256 | −0.701278 | − | 0.712888i | \(-0.747387\pi\) | ||||
−0.701278 | + | 0.712888i | \(0.747387\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −12.1329 | −0.566315 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −2.13364 | −0.0993734 | −0.0496867 | − | 0.998765i | \(-0.515822\pi\) | ||||
−0.0496867 | + | 0.998765i | \(0.515822\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 21.9804 | 1.02151 | 0.510757 | − | 0.859725i | \(-0.329365\pi\) | ||||
0.510757 | + | 0.859725i | \(0.329365\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −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 | ||||||||
\(471\) | −9.80318 | −0.451707 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −26.7508 | −1.23000 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −25.4010 | −1.16303 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 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 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 2.03071 | 0.0924005 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 26.6121 | 1.20591 | 0.602954 | − | 0.797776i | \(-0.293990\pi\) | ||||
0.602954 | + | 0.797776i | \(0.293990\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 6.95244 | 0.314400 | ||||||||
\(490\) | 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 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −7.82991 | −0.351220 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −28.6962 | −1.28462 | −0.642309 | − | 0.766446i | \(-0.722023\pi\) | ||||
−0.642309 | + | 0.766446i | \(0.722023\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −11.4907 | −0.513367 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 23.6827 | 1.05596 | 0.527980 | − | 0.849257i | \(-0.322949\pi\) | ||||
0.527980 | + | 0.849257i | \(0.322949\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 16.5187 | 0.733622 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 17.6957 | 0.784346 | 0.392173 | − | 0.919891i | \(-0.371723\pi\) | ||||
0.392173 | + | 0.919891i | \(0.371723\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0.602683 | 0.0266611 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 13.0278 | 0.575190 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −24.5837 | −1.08119 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 4.42872 | 0.194399 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 22.9756 | 1.00658 | 0.503289 | − | 0.864118i | \(-0.332123\pi\) | ||||
0.503289 | + | 0.864118i | \(0.332123\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 28.9773 | 1.26709 | 0.633544 | − | 0.773707i | \(-0.281600\pi\) | ||||
0.633544 | + | 0.773707i | \(0.281600\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 25.5359 | 1.11236 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −14.4785 | −0.629500 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 7.31579 | 0.317478 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −11.3402 | −0.491199 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 10.6095 | 0.457836 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 30.6008 | 1.31807 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 24.4505 | 1.05121 | 0.525605 | − | 0.850729i | \(-0.323839\pi\) | ||||
0.525605 | + | 0.850729i | \(0.323839\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0.878460 | 0.0376983 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 6.50334 | 0.278063 | 0.139031 | − | 0.990288i | \(-0.455601\pi\) | ||||
0.139031 | + | 0.990288i | \(0.455601\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 5.83761 | 0.249143 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 5.32295 | 0.226765 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 11.1920 | 0.475930 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 3.12305 | 0.132328 | 0.0661640 | − | 0.997809i | \(-0.478924\pi\) | ||||
0.0661640 | + | 0.997809i | \(0.478924\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 31.7896 | 1.34456 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −11.2401 | −0.474557 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 36.5252 | 1.53935 | 0.769677 | − | 0.638433i | \(-0.220417\pi\) | ||||
0.769677 | + | 0.638433i | \(0.220417\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −5.03019 | −0.211248 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −37.7676 | −1.58330 | −0.791650 | − | 0.610975i | \(-0.790778\pi\) | ||||
−0.791650 | + | 0.610975i | \(0.790778\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 41.2370 | 1.72571 | 0.862857 | − | 0.505448i | \(-0.168673\pi\) | ||||
0.862857 | + | 0.505448i | \(0.168673\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −4.01177 | −0.167594 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −4.26929 | −0.177733 | −0.0888663 | − | 0.996044i | \(-0.528324\pi\) | ||||
−0.0888663 | + | 0.996044i | \(0.528324\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −2.87178 | −0.119347 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 14.4688 | 0.600266 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −51.4631 | −2.13138 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −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 | ||||||||
\(591\) | −12.0196 | −0.494418 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 30.9375 | 1.27045 | 0.635225 | − | 0.772327i | \(-0.280908\pi\) | ||||
0.635225 | + | 0.772327i | \(0.280908\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −4.04912 | −0.165720 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 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 | \(0.783254\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 11.7501 | 0.478502 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −38.6361 | −1.56819 | −0.784095 | − | 0.620641i | \(-0.786873\pi\) | ||||
−0.784095 | + | 0.620641i | \(0.786873\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 1.07997 | 0.0437625 | ||||||||
\(610\) | 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 | \(0.569698\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −10.8072 | −0.435082 | −0.217541 | − | 0.976051i | \(-0.569804\pi\) | ||||
−0.217541 | + | 0.976051i | \(0.569804\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 36.8938 | 1.48289 | 0.741443 | − | 0.671016i | \(-0.234142\pi\) | ||||
0.741443 | + | 0.671016i | \(0.234142\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 11.0917 | 0.445093 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 6.46992 | 0.259212 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 12.0691 | 0.481994 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 26.8460 | 1.07042 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −39.2593 | −1.56289 | −0.781445 | − | 0.623974i | \(-0.785517\pi\) | ||||
−0.781445 | + | 0.623974i | \(0.785517\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 8.23322 | 0.327241 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −36.3648 | −1.44083 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −19.5554 | −0.773598 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 8.34833 | 0.329739 | 0.164870 | − | 0.986315i | \(-0.447280\pi\) | ||||
0.164870 | + | 0.986315i | \(0.447280\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 13.1408 | 0.518223 | 0.259112 | − | 0.965847i | \(-0.416570\pi\) | ||||
0.259112 | + | 0.965847i | \(0.416570\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −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 | ||||||||
\(651\) | −5.56310 | −0.218035 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 23.0295 | 0.901213 | 0.450606 | − | 0.892723i | \(-0.351208\pi\) | ||||
0.450606 | + | 0.892723i | \(0.351208\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 1.50521 | 0.0587240 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −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 | \(0.386139\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 13.3573 | 0.518753 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 4.53188 | 0.175475 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0.877923 | 0.0339425 | ||||||||
\(670\) | 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 | \(0.407526\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −23.1238 | −0.888720 | −0.444360 | − | 0.895848i | \(-0.646569\pi\) | ||||
−0.444360 | + | 0.895848i | \(0.646569\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 14.2522 | 0.546949 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −19.3423 | −0.741197 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 19.6347 | 0.751302 | 0.375651 | − | 0.926761i | \(-0.377419\pi\) | ||||
0.375651 | + | 0.926761i | \(0.377419\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 7.75538 | 0.295886 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 61.1566 | 2.32988 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 5.87782 | 0.223603 | 0.111801 | − | 0.993731i | \(-0.464338\pi\) | ||||
0.111801 | + | 0.993731i | \(0.464338\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −13.0978 | −0.497544 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −5.95067 | −0.225398 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −9.26066 | −0.350270 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −50.0581 | −1.89067 | −0.945334 | − | 0.326103i | \(-0.894264\pi\) | ||||
−0.945334 | + | 0.326103i | \(0.894264\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −28.8261 | −1.08720 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 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 | ||||||||
\(711\) | 27.9521 | 1.04829 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −23.3445 | −0.874258 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −1.30779 | −0.0488403 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 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 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −13.4514 | −0.500264 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 6.06366 | 0.224889 | 0.112444 | − | 0.993658i | \(-0.464132\pi\) | ||||
0.112444 | + | 0.993658i | \(0.464132\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −4.72740 | −0.175089 | ||||||||
\(730\) | 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 | \(0.486236\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 23.8061 | 0.876907 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 41.5352 | 1.52790 | 0.763949 | − | 0.645276i | \(-0.223258\pi\) | ||||
0.763949 | + | 0.645276i | \(0.223258\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −14.3425 | −0.526883 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 0.813821 | 0.0298562 | 0.0149281 | − | 0.999889i | \(-0.495248\pi\) | ||||
0.0149281 | + | 0.999889i | \(0.495248\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 36.1360 | 1.32215 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −5.31025 | −0.194032 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −31.8919 | −1.16375 | −0.581877 | − | 0.813277i | \(-0.697681\pi\) | ||||
−0.581877 | + | 0.813277i | \(0.697681\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −14.2359 | −0.518784 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 26.7040 | 0.970572 | 0.485286 | − | 0.874355i | \(-0.338715\pi\) | ||||
0.485286 | + | 0.874355i | \(0.338715\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 10.2755 | 0.372976 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 43.0644 | 1.56108 | 0.780542 | − | 0.625103i | \(-0.214943\pi\) | ||||
0.780542 | + | 0.625103i | \(0.214943\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 6.59725 | 0.238837 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −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 | ||||||||
\(771\) | 10.3612 | 0.373150 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −13.2299 | −0.475845 | −0.237923 | − | 0.971284i | \(-0.576466\pi\) | ||||
−0.237923 | + | 0.971284i | \(0.576466\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −5.84850 | −0.209814 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 6.38957 | 0.228930 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −39.6197 | −1.41770 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 5.89874 | 0.210804 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −33.6378 | −1.19906 | −0.599528 | − | 0.800354i | \(-0.704645\pi\) | ||||
−0.599528 | + | 0.800354i | \(0.704645\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −3.43926 | −0.122441 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −0.390179 | −0.0138732 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −14.0549 | −0.499105 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 6.89741 | 0.244319 | 0.122159 | − | 0.992511i | \(-0.461018\pi\) | ||||
0.122159 | + | 0.992511i | \(0.461018\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 15.3299 | 0.542333 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 16.1587 | 0.570941 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 3.04960 | 0.107618 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −19.0276 | −0.669803 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −35.3330 | −1.24224 | −0.621121 | − | 0.783715i | \(-0.713322\pi\) | ||||
−0.621121 | + | 0.783715i | \(0.713322\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 3.97201 | 0.139476 | 0.0697380 | − | 0.997565i | \(-0.477784\pi\) | ||||
0.0697380 | + | 0.997565i | \(0.477784\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 18.1425 | 0.636285 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −17.9117 | −0.626650 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 15.5649 | 0.543881 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 24.3758 | 0.850720 | 0.425360 | − | 0.905024i | \(-0.360147\pi\) | ||||
0.425360 | + | 0.905024i | \(0.360147\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −22.2604 | −0.775947 | −0.387974 | − | 0.921670i | \(-0.626825\pi\) | ||||
−0.387974 | + | 0.921670i | \(0.626825\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −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 | ||||||||
\(831\) | −4.89622 | −0.169848 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −19.0821 | −0.661156 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −30.3854 | −1.05027 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −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 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −7.09859 | −0.244488 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −15.4045 | −0.529306 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −3.13447 | −0.107575 | ||||||||
\(850\) | 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 | \(0.660027\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −36.2976 | −1.23990 | −0.619951 | − | 0.784640i | \(-0.712848\pi\) | ||||
−0.619951 | + | 0.784640i | \(0.712848\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −3.82400 | −0.130473 | −0.0652366 | − | 0.997870i | \(-0.520780\pi\) | ||||
−0.0652366 | + | 0.997870i | \(0.520780\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 1.29637 | 0.0441803 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −25.5955 | −0.871280 | −0.435640 | − | 0.900121i | \(-0.643478\pi\) | ||||
−0.435640 | + | 0.900121i | \(0.643478\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −4.67675 | −0.158831 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 56.6318 | 1.92110 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −28.2902 | −0.958575 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 35.5952 | 1.20471 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 14.8579 | 0.501715 | 0.250857 | − | 0.968024i | \(-0.419287\pi\) | ||||
0.250857 | + | 0.968024i | \(0.419287\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −14.3143 | −0.482809 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 2.11362 | 0.0712096 | 0.0356048 | − | 0.999366i | \(-0.488664\pi\) | ||||
0.0356048 | + | 0.999366i | \(0.488664\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 51.0828 | 1.71907 | 0.859537 | − | 0.511074i | \(-0.170752\pi\) | ||||
0.859537 | + | 0.511074i | \(0.170752\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −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 | ||||||||
\(891\) | −25.4530 | −0.852706 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −16.4606 | −0.550833 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −12.2110 | −0.407712 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −12.4150 | −0.414064 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 32.0914 | 1.06912 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −3.63408 | −0.120935 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 27.5215 | 0.913837 | 0.456919 | − | 0.889508i | \(-0.348953\pi\) | ||||
0.456919 | + | 0.889508i | \(0.348953\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 26.5713 | 0.881315 | ||||||||
\(910\) | 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 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 16.4158 | 0.542099 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −12.6543 | −0.417427 | −0.208714 | − | 0.977977i | \(-0.566928\pi\) | ||||
−0.208714 | + | 0.977977i | \(0.566928\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −6.49047 | −0.213868 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 47.0825 | 1.54974 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −7.77881 | −0.255489 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −3.03961 | −0.0997265 | −0.0498633 | − | 0.998756i | \(-0.515879\pi\) | ||||
−0.0498633 | + | 0.998756i | \(0.515879\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 20.4895 | 0.671517 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −9.19772 | −0.301120 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 0.0480749 | 0.00157054 | 0.000785268 | − | 1.00000i | \(-0.499750\pi\) | ||||
0.000785268 | 1.00000i | \(0.499750\pi\) | ||||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 16.4941 | 0.538263 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −1.25393 | −0.0408769 | −0.0204384 | − | 0.999791i | \(-0.506506\pi\) | ||||
−0.0204384 | + | 0.999791i | \(0.506506\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 5.43999 | 0.177150 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −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 | ||||||||
\(951\) | 10.0097 | 0.324587 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −41.8227 | −1.35477 | −0.677385 | − | 0.735629i | \(-0.736887\pi\) | ||||
−0.677385 | + | 0.735629i | \(0.736887\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 5.46469 | 0.176648 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 19.4102 | 0.626788 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 32.9518 | 1.06296 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −13.2625 | −0.427377 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −44.4986 | −1.43098 | −0.715490 | − | 0.698623i | \(-0.753796\pi\) | ||||
−0.715490 | + | 0.698623i | \(0.753796\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −7.52607 | −0.241772 | ||||||||
\(970\) | 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 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 15.7554 | 0.504060 | 0.252030 | − | 0.967719i | \(-0.418902\pi\) | ||||
0.252030 | + | 0.967719i | \(0.418902\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 32.7381 | 1.04631 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 16.4768 | 0.526063 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −26.9019 | −0.858036 | −0.429018 | − | 0.903296i | \(-0.641140\pi\) | ||||
−0.429018 | + | 0.903296i | \(0.641140\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −3.33967 | −0.106303 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −15.2497 | −0.484914 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −14.0680 | −0.446885 | −0.223442 | − | 0.974717i | \(-0.571729\pi\) | ||||
−0.223442 | + | 0.974717i | \(0.571729\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 16.7897 | 0.532806 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 0.618644 | 0.0195926 | 0.00979632 | − | 0.999952i | \(-0.496882\pi\) | ||||
0.00979632 | + | 0.999952i | \(0.496882\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −31.9443 | −1.01067 |
(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 | 10000.2.a.be.1.6 | 8 | ||
4.3 | odd | 2 | 625.2.a.g.1.5 | yes | 8 | ||
5.4 | even | 2 | 10000.2.a.bn.1.3 | 8 | |||
12.11 | even | 2 | 5625.2.a.s.1.4 | 8 | |||
20.3 | even | 4 | 625.2.b.d.624.6 | 16 | |||
20.7 | even | 4 | 625.2.b.d.624.11 | 16 | |||
20.19 | odd | 2 | 625.2.a.e.1.4 | ✓ | 8 | ||
60.59 | even | 2 | 5625.2.a.be.1.5 | 8 | |||
100.3 | even | 20 | 625.2.e.k.249.3 | 32 | |||
100.11 | odd | 10 | 625.2.d.m.501.3 | 16 | |||
100.19 | odd | 10 | 625.2.d.p.251.3 | 16 | |||
100.23 | even | 20 | 625.2.e.j.124.3 | 32 | |||
100.27 | even | 20 | 625.2.e.j.124.6 | 32 | |||
100.31 | odd | 10 | 625.2.d.n.251.2 | 16 | |||
100.39 | odd | 10 | 625.2.d.q.501.2 | 16 | |||
100.47 | even | 20 | 625.2.e.k.249.6 | 32 | |||
100.59 | odd | 10 | 625.2.d.q.126.2 | 16 | |||
100.63 | even | 20 | 625.2.e.j.499.6 | 32 | |||
100.67 | even | 20 | 625.2.e.k.374.3 | 32 | |||
100.71 | odd | 10 | 625.2.d.n.376.2 | 16 | |||
100.79 | odd | 10 | 625.2.d.p.376.3 | 16 | |||
100.83 | even | 20 | 625.2.e.k.374.6 | 32 | |||
100.87 | even | 20 | 625.2.e.j.499.3 | 32 | |||
100.91 | odd | 10 | 625.2.d.m.126.3 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
625.2.a.e.1.4 | ✓ | 8 | 20.19 | odd | 2 | ||
625.2.a.g.1.5 | yes | 8 | 4.3 | odd | 2 | ||
625.2.b.d.624.6 | 16 | 20.3 | even | 4 | |||
625.2.b.d.624.11 | 16 | 20.7 | even | 4 | |||
625.2.d.m.126.3 | 16 | 100.91 | odd | 10 | |||
625.2.d.m.501.3 | 16 | 100.11 | odd | 10 | |||
625.2.d.n.251.2 | 16 | 100.31 | odd | 10 | |||
625.2.d.n.376.2 | 16 | 100.71 | odd | 10 | |||
625.2.d.p.251.3 | 16 | 100.19 | odd | 10 | |||
625.2.d.p.376.3 | 16 | 100.79 | odd | 10 | |||
625.2.d.q.126.2 | 16 | 100.59 | odd | 10 | |||
625.2.d.q.501.2 | 16 | 100.39 | odd | 10 | |||
625.2.e.j.124.3 | 32 | 100.23 | even | 20 | |||
625.2.e.j.124.6 | 32 | 100.27 | even | 20 | |||
625.2.e.j.499.3 | 32 | 100.87 | even | 20 | |||
625.2.e.j.499.6 | 32 | 100.63 | even | 20 | |||
625.2.e.k.249.3 | 32 | 100.3 | even | 20 | |||
625.2.e.k.249.6 | 32 | 100.47 | even | 20 | |||
625.2.e.k.374.3 | 32 | 100.67 | even | 20 | |||
625.2.e.k.374.6 | 32 | 100.83 | even | 20 | |||
5625.2.a.s.1.4 | 8 | 12.11 | even | 2 | |||
5625.2.a.be.1.5 | 8 | 60.59 | even | 2 | |||
10000.2.a.be.1.6 | 8 | 1.1 | even | 1 | trivial | ||
10000.2.a.bn.1.3 | 8 | 5.4 | even | 2 |