Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [585,2,Mod(1,585)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(585, 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("585.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 585 = 3^{2} \cdot 5 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 585.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: | \(4.67124851824\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{17}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 4 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(2.56155\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 585.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.56155 | 1.81129 | 0.905646 | − | 0.424035i | \(-0.139387\pi\) | ||||
0.905646 | + | 0.424035i | \(0.139387\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 4.56155 | 2.28078 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.438447 | −0.165717 | −0.0828587 | − | 0.996561i | \(-0.526405\pi\) | ||||
−0.0828587 | + | 0.996561i | \(0.526405\pi\) | |||||||
\(8\) | 6.56155 | 2.31986 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 2.56155 | 0.810034 | ||||||||
\(11\) | −1.56155 | −0.470826 | −0.235413 | − | 0.971895i | \(-0.575644\pi\) | ||||
−0.235413 | + | 0.971895i | \(0.575644\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.00000 | −0.277350 | ||||||||
\(14\) | −1.12311 | −0.300163 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 7.68466 | 1.92116 | ||||||||
\(17\) | 1.56155 | 0.378732 | 0.189366 | − | 0.981907i | \(-0.439357\pi\) | ||||
0.189366 | + | 0.981907i | \(0.439357\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −5.12311 | −1.17532 | −0.587661 | − | 0.809108i | \(-0.699951\pi\) | ||||
−0.587661 | + | 0.809108i | \(0.699951\pi\) | |||||||
\(20\) | 4.56155 | 1.01999 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −4.00000 | −0.852803 | ||||||||
\(23\) | 2.43845 | 0.508451 | 0.254226 | − | 0.967145i | \(-0.418179\pi\) | ||||
0.254226 | + | 0.967145i | \(0.418179\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | −2.56155 | −0.502362 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −2.00000 | −0.377964 | ||||||||
\(29\) | −7.12311 | −1.32273 | −0.661364 | − | 0.750065i | \(-0.730022\pi\) | ||||
−0.661364 | + | 0.750065i | \(0.730022\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 6.00000 | 1.07763 | 0.538816 | − | 0.842424i | \(-0.318872\pi\) | ||||
0.538816 | + | 0.842424i | \(0.318872\pi\) | |||||||
\(32\) | 6.56155 | 1.15993 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 4.00000 | 0.685994 | ||||||||
\(35\) | −0.438447 | −0.0741111 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −10.6847 | −1.75655 | −0.878274 | − | 0.478159i | \(-0.841304\pi\) | ||||
−0.878274 | + | 0.478159i | \(0.841304\pi\) | |||||||
\(38\) | −13.1231 | −2.12885 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 6.56155 | 1.03747 | ||||||||
\(41\) | 3.56155 | 0.556221 | 0.278111 | − | 0.960549i | \(-0.410292\pi\) | ||||
0.278111 | + | 0.960549i | \(0.410292\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 3.12311 | 0.476269 | 0.238135 | − | 0.971232i | \(-0.423464\pi\) | ||||
0.238135 | + | 0.971232i | \(0.423464\pi\) | |||||||
\(44\) | −7.12311 | −1.07385 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 6.24621 | 0.920954 | ||||||||
\(47\) | 11.1231 | 1.62247 | 0.811236 | − | 0.584719i | \(-0.198795\pi\) | ||||
0.811236 | + | 0.584719i | \(0.198795\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.80776 | −0.972538 | ||||||||
\(50\) | 2.56155 | 0.362258 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −4.56155 | −0.632574 | ||||||||
\(53\) | −4.68466 | −0.643487 | −0.321744 | − | 0.946827i | \(-0.604269\pi\) | ||||
−0.321744 | + | 0.946827i | \(0.604269\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −1.56155 | −0.210560 | ||||||||
\(56\) | −2.87689 | −0.384441 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −18.2462 | −2.39584 | ||||||||
\(59\) | 12.0000 | 1.56227 | 0.781133 | − | 0.624364i | \(-0.214642\pi\) | ||||
0.781133 | + | 0.624364i | \(0.214642\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −6.68466 | −0.855883 | −0.427941 | − | 0.903806i | \(-0.640761\pi\) | ||||
−0.427941 | + | 0.903806i | \(0.640761\pi\) | |||||||
\(62\) | 15.3693 | 1.95191 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.43845 | 0.179806 | ||||||||
\(65\) | −1.00000 | −0.124035 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −11.3693 | −1.38898 | −0.694492 | − | 0.719501i | \(-0.744371\pi\) | ||||
−0.694492 | + | 0.719501i | \(0.744371\pi\) | |||||||
\(68\) | 7.12311 | 0.863803 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −1.12311 | −0.134237 | ||||||||
\(71\) | 10.4384 | 1.23882 | 0.619408 | − | 0.785069i | \(-0.287373\pi\) | ||||
0.619408 | + | 0.785069i | \(0.287373\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −6.00000 | −0.702247 | −0.351123 | − | 0.936329i | \(-0.614200\pi\) | ||||
−0.351123 | + | 0.936329i | \(0.614200\pi\) | |||||||
\(74\) | −27.3693 | −3.18162 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −23.3693 | −2.68064 | ||||||||
\(77\) | 0.684658 | 0.0780241 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 4.68466 | 0.527065 | 0.263533 | − | 0.964650i | \(-0.415112\pi\) | ||||
0.263533 | + | 0.964650i | \(0.415112\pi\) | |||||||
\(80\) | 7.68466 | 0.859171 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 9.12311 | 1.00748 | ||||||||
\(83\) | −16.4924 | −1.81028 | −0.905139 | − | 0.425115i | \(-0.860234\pi\) | ||||
−0.905139 | + | 0.425115i | \(0.860234\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.56155 | 0.169374 | ||||||||
\(86\) | 8.00000 | 0.862662 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −10.2462 | −1.09225 | ||||||||
\(89\) | 10.6847 | 1.13257 | 0.566286 | − | 0.824209i | \(-0.308380\pi\) | ||||
0.566286 | + | 0.824209i | \(0.308380\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0.438447 | 0.0459618 | ||||||||
\(92\) | 11.1231 | 1.15966 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 28.4924 | 2.93877 | ||||||||
\(95\) | −5.12311 | −0.525620 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 16.9309 | 1.71907 | 0.859535 | − | 0.511077i | \(-0.170753\pi\) | ||||
0.859535 | + | 0.511077i | \(0.170753\pi\) | |||||||
\(98\) | −17.4384 | −1.76155 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 4.56155 | 0.456155 | ||||||||
\(101\) | 10.2462 | 1.01954 | 0.509768 | − | 0.860312i | \(-0.329731\pi\) | ||||
0.509768 | + | 0.860312i | \(0.329731\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −15.1231 | −1.49012 | −0.745062 | − | 0.666995i | \(-0.767580\pi\) | ||||
−0.745062 | + | 0.666995i | \(0.767580\pi\) | |||||||
\(104\) | −6.56155 | −0.643413 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −12.0000 | −1.16554 | ||||||||
\(107\) | 10.9309 | 1.05673 | 0.528364 | − | 0.849018i | \(-0.322806\pi\) | ||||
0.528364 | + | 0.849018i | \(0.322806\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −2.00000 | −0.191565 | −0.0957826 | − | 0.995402i | \(-0.530535\pi\) | ||||
−0.0957826 | + | 0.995402i | \(0.530535\pi\) | |||||||
\(110\) | −4.00000 | −0.381385 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −3.36932 | −0.318371 | ||||||||
\(113\) | −4.87689 | −0.458780 | −0.229390 | − | 0.973335i | \(-0.573673\pi\) | ||||
−0.229390 | + | 0.973335i | \(0.573673\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 2.43845 | 0.227386 | ||||||||
\(116\) | −32.4924 | −3.01685 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 30.7386 | 2.82972 | ||||||||
\(119\) | −0.684658 | −0.0627625 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −8.56155 | −0.778323 | ||||||||
\(122\) | −17.1231 | −1.55025 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 27.3693 | 2.45784 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1.75379 | 0.155624 | 0.0778118 | − | 0.996968i | \(-0.475207\pi\) | ||||
0.0778118 | + | 0.996968i | \(0.475207\pi\) | |||||||
\(128\) | −9.43845 | −0.834249 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −2.56155 | −0.224663 | ||||||||
\(131\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 2.24621 | 0.194771 | ||||||||
\(134\) | −29.1231 | −2.51585 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 10.2462 | 0.878605 | ||||||||
\(137\) | 1.12311 | 0.0959534 | 0.0479767 | − | 0.998848i | \(-0.484723\pi\) | ||||
0.0479767 | + | 0.998848i | \(0.484723\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 3.31534 | 0.281204 | 0.140602 | − | 0.990066i | \(-0.455096\pi\) | ||||
0.140602 | + | 0.990066i | \(0.455096\pi\) | |||||||
\(140\) | −2.00000 | −0.169031 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 26.7386 | 2.24386 | ||||||||
\(143\) | 1.56155 | 0.130584 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −7.12311 | −0.591542 | ||||||||
\(146\) | −15.3693 | −1.27197 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −48.7386 | −4.00629 | ||||||||
\(149\) | −17.8078 | −1.45887 | −0.729434 | − | 0.684051i | \(-0.760217\pi\) | ||||
−0.729434 | + | 0.684051i | \(0.760217\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 11.3693 | 0.925222 | 0.462611 | − | 0.886561i | \(-0.346913\pi\) | ||||
0.462611 | + | 0.886561i | \(0.346913\pi\) | |||||||
\(152\) | −33.6155 | −2.72658 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 1.75379 | 0.141324 | ||||||||
\(155\) | 6.00000 | 0.481932 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 3.36932 | 0.268901 | 0.134450 | − | 0.990920i | \(-0.457073\pi\) | ||||
0.134450 | + | 0.990920i | \(0.457073\pi\) | |||||||
\(158\) | 12.0000 | 0.954669 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 6.56155 | 0.518736 | ||||||||
\(161\) | −1.06913 | −0.0842593 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 16.0540 | 1.25744 | 0.628722 | − | 0.777630i | \(-0.283578\pi\) | ||||
0.628722 | + | 0.777630i | \(0.283578\pi\) | |||||||
\(164\) | 16.2462 | 1.26862 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −42.2462 | −3.27894 | ||||||||
\(167\) | 4.87689 | 0.377385 | 0.188693 | − | 0.982036i | \(-0.439575\pi\) | ||||
0.188693 | + | 0.982036i | \(0.439575\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | 4.00000 | 0.306786 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 14.2462 | 1.08626 | ||||||||
\(173\) | 12.8769 | 0.979012 | 0.489506 | − | 0.872000i | \(-0.337177\pi\) | ||||
0.489506 | + | 0.872000i | \(0.337177\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −0.438447 | −0.0331435 | ||||||||
\(176\) | −12.0000 | −0.904534 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 27.3693 | 2.05142 | ||||||||
\(179\) | −4.87689 | −0.364516 | −0.182258 | − | 0.983251i | \(-0.558341\pi\) | ||||
−0.182258 | + | 0.983251i | \(0.558341\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 13.3153 | 0.989722 | 0.494861 | − | 0.868972i | \(-0.335219\pi\) | ||||
0.494861 | + | 0.868972i | \(0.335219\pi\) | |||||||
\(182\) | 1.12311 | 0.0832501 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 16.0000 | 1.17954 | ||||||||
\(185\) | −10.6847 | −0.785552 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −2.43845 | −0.178317 | ||||||||
\(188\) | 50.7386 | 3.70050 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −13.1231 | −0.952050 | ||||||||
\(191\) | 19.6155 | 1.41933 | 0.709665 | − | 0.704539i | \(-0.248846\pi\) | ||||
0.709665 | + | 0.704539i | \(0.248846\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 19.5616 | 1.40807 | 0.704036 | − | 0.710165i | \(-0.251379\pi\) | ||||
0.704036 | + | 0.710165i | \(0.251379\pi\) | |||||||
\(194\) | 43.3693 | 3.11374 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −31.0540 | −2.21814 | ||||||||
\(197\) | −3.36932 | −0.240054 | −0.120027 | − | 0.992771i | \(-0.538298\pi\) | ||||
−0.120027 | + | 0.992771i | \(0.538298\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −8.00000 | −0.567105 | −0.283552 | − | 0.958957i | \(-0.591513\pi\) | ||||
−0.283552 | + | 0.958957i | \(0.591513\pi\) | |||||||
\(200\) | 6.56155 | 0.463972 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 26.2462 | 1.84668 | ||||||||
\(203\) | 3.12311 | 0.219199 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 3.56155 | 0.248750 | ||||||||
\(206\) | −38.7386 | −2.69905 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −7.68466 | −0.532835 | ||||||||
\(209\) | 8.00000 | 0.553372 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 6.24621 | 0.430007 | 0.215003 | − | 0.976613i | \(-0.431024\pi\) | ||||
0.215003 | + | 0.976613i | \(0.431024\pi\) | |||||||
\(212\) | −21.3693 | −1.46765 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 28.0000 | 1.91404 | ||||||||
\(215\) | 3.12311 | 0.212994 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −2.63068 | −0.178582 | ||||||||
\(218\) | −5.12311 | −0.346980 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −7.12311 | −0.480240 | ||||||||
\(221\) | −1.56155 | −0.105041 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −15.3693 | −1.02921 | −0.514603 | − | 0.857429i | \(-0.672061\pi\) | ||||
−0.514603 | + | 0.857429i | \(0.672061\pi\) | |||||||
\(224\) | −2.87689 | −0.192221 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −12.4924 | −0.830984 | ||||||||
\(227\) | 5.75379 | 0.381892 | 0.190946 | − | 0.981601i | \(-0.438844\pi\) | ||||
0.190946 | + | 0.981601i | \(0.438844\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 17.1231 | 1.13153 | 0.565763 | − | 0.824568i | \(-0.308582\pi\) | ||||
0.565763 | + | 0.824568i | \(0.308582\pi\) | |||||||
\(230\) | 6.24621 | 0.411863 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −46.7386 | −3.06854 | ||||||||
\(233\) | −27.8078 | −1.82175 | −0.910874 | − | 0.412685i | \(-0.864591\pi\) | ||||
−0.910874 | + | 0.412685i | \(0.864591\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 11.1231 | 0.725591 | ||||||||
\(236\) | 54.7386 | 3.56318 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −1.75379 | −0.113681 | ||||||||
\(239\) | 22.9309 | 1.48327 | 0.741637 | − | 0.670801i | \(-0.234050\pi\) | ||||
0.741637 | + | 0.670801i | \(0.234050\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 24.7386 | 1.59356 | 0.796778 | − | 0.604272i | \(-0.206536\pi\) | ||||
0.796778 | + | 0.604272i | \(0.206536\pi\) | |||||||
\(242\) | −21.9309 | −1.40977 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −30.4924 | −1.95208 | ||||||||
\(245\) | −6.80776 | −0.434932 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 5.12311 | 0.325975 | ||||||||
\(248\) | 39.3693 | 2.49995 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 2.56155 | 0.162007 | ||||||||
\(251\) | 26.2462 | 1.65665 | 0.828323 | − | 0.560251i | \(-0.189295\pi\) | ||||
0.828323 | + | 0.560251i | \(0.189295\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −3.80776 | −0.239392 | ||||||||
\(254\) | 4.49242 | 0.281880 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −27.0540 | −1.69087 | ||||||||
\(257\) | −12.8769 | −0.803239 | −0.401619 | − | 0.915807i | \(-0.631552\pi\) | ||||
−0.401619 | + | 0.915807i | \(0.631552\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 4.68466 | 0.291091 | ||||||||
\(260\) | −4.56155 | −0.282895 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −2.24621 | −0.138507 | −0.0692537 | − | 0.997599i | \(-0.522062\pi\) | ||||
−0.0692537 | + | 0.997599i | \(0.522062\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −4.68466 | −0.287776 | ||||||||
\(266\) | 5.75379 | 0.352787 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −51.8617 | −3.16796 | ||||||||
\(269\) | −0.876894 | −0.0534652 | −0.0267326 | − | 0.999643i | \(-0.508510\pi\) | ||||
−0.0267326 | + | 0.999643i | \(0.508510\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −19.3693 | −1.17660 | −0.588301 | − | 0.808642i | \(-0.700203\pi\) | ||||
−0.588301 | + | 0.808642i | \(0.700203\pi\) | |||||||
\(272\) | 12.0000 | 0.727607 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 2.87689 | 0.173800 | ||||||||
\(275\) | −1.56155 | −0.0941652 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −12.2462 | −0.735804 | −0.367902 | − | 0.929865i | \(-0.619924\pi\) | ||||
−0.367902 | + | 0.929865i | \(0.619924\pi\) | |||||||
\(278\) | 8.49242 | 0.509342 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −2.87689 | −0.171927 | ||||||||
\(281\) | 4.24621 | 0.253308 | 0.126654 | − | 0.991947i | \(-0.459576\pi\) | ||||
0.126654 | + | 0.991947i | \(0.459576\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −4.00000 | −0.237775 | −0.118888 | − | 0.992908i | \(-0.537933\pi\) | ||||
−0.118888 | + | 0.992908i | \(0.537933\pi\) | |||||||
\(284\) | 47.6155 | 2.82546 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 4.00000 | 0.236525 | ||||||||
\(287\) | −1.56155 | −0.0921755 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −14.5616 | −0.856562 | ||||||||
\(290\) | −18.2462 | −1.07145 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −27.3693 | −1.60167 | ||||||||
\(293\) | −20.2462 | −1.18280 | −0.591398 | − | 0.806380i | \(-0.701424\pi\) | ||||
−0.591398 | + | 0.806380i | \(0.701424\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 12.0000 | 0.698667 | ||||||||
\(296\) | −70.1080 | −4.07494 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −45.6155 | −2.64244 | ||||||||
\(299\) | −2.43845 | −0.141019 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1.36932 | −0.0789261 | ||||||||
\(302\) | 29.1231 | 1.67585 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −39.3693 | −2.25799 | ||||||||
\(305\) | −6.68466 | −0.382762 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 7.56155 | 0.431561 | 0.215780 | − | 0.976442i | \(-0.430770\pi\) | ||||
0.215780 | + | 0.976442i | \(0.430770\pi\) | |||||||
\(308\) | 3.12311 | 0.177955 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 15.3693 | 0.872919 | ||||||||
\(311\) | 2.63068 | 0.149172 | 0.0745862 | − | 0.997215i | \(-0.476236\pi\) | ||||
0.0745862 | + | 0.997215i | \(0.476236\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 29.1231 | 1.64614 | 0.823068 | − | 0.567943i | \(-0.192261\pi\) | ||||
0.823068 | + | 0.567943i | \(0.192261\pi\) | |||||||
\(314\) | 8.63068 | 0.487058 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 21.3693 | 1.20212 | ||||||||
\(317\) | 1.50758 | 0.0846740 | 0.0423370 | − | 0.999103i | \(-0.486520\pi\) | ||||
0.0423370 | + | 0.999103i | \(0.486520\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 11.1231 | 0.622774 | ||||||||
\(320\) | 1.43845 | 0.0804116 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −2.73863 | −0.152618 | ||||||||
\(323\) | −8.00000 | −0.445132 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −1.00000 | −0.0554700 | ||||||||
\(326\) | 41.1231 | 2.27760 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 23.3693 | 1.29035 | ||||||||
\(329\) | −4.87689 | −0.268872 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 29.1231 | 1.60075 | 0.800375 | − | 0.599499i | \(-0.204634\pi\) | ||||
0.800375 | + | 0.599499i | \(0.204634\pi\) | |||||||
\(332\) | −75.2311 | −4.12884 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 12.4924 | 0.683555 | ||||||||
\(335\) | −11.3693 | −0.621172 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −30.4924 | −1.66103 | −0.830514 | − | 0.556998i | \(-0.811953\pi\) | ||||
−0.830514 | + | 0.556998i | \(0.811953\pi\) | |||||||
\(338\) | 2.56155 | 0.139330 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 7.12311 | 0.386305 | ||||||||
\(341\) | −9.36932 | −0.507377 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 6.05398 | 0.326884 | ||||||||
\(344\) | 20.4924 | 1.10488 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 32.9848 | 1.77328 | ||||||||
\(347\) | −26.0540 | −1.39865 | −0.699325 | − | 0.714804i | \(-0.746516\pi\) | ||||
−0.699325 | + | 0.714804i | \(0.746516\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −23.3693 | −1.25093 | −0.625465 | − | 0.780252i | \(-0.715091\pi\) | ||||
−0.625465 | + | 0.780252i | \(0.715091\pi\) | |||||||
\(350\) | −1.12311 | −0.0600325 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −10.2462 | −0.546125 | ||||||||
\(353\) | −22.4924 | −1.19715 | −0.598575 | − | 0.801066i | \(-0.704266\pi\) | ||||
−0.598575 | + | 0.801066i | \(0.704266\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 10.4384 | 0.554015 | ||||||||
\(356\) | 48.7386 | 2.58314 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −12.4924 | −0.660245 | ||||||||
\(359\) | −14.2462 | −0.751886 | −0.375943 | − | 0.926643i | \(-0.622681\pi\) | ||||
−0.375943 | + | 0.926643i | \(0.622681\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 7.24621 | 0.381380 | ||||||||
\(362\) | 34.1080 | 1.79267 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 2.00000 | 0.104828 | ||||||||
\(365\) | −6.00000 | −0.314054 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −1.75379 | −0.0915470 | −0.0457735 | − | 0.998952i | \(-0.514575\pi\) | ||||
−0.0457735 | + | 0.998952i | \(0.514575\pi\) | |||||||
\(368\) | 18.7386 | 0.976819 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −27.3693 | −1.42286 | ||||||||
\(371\) | 2.05398 | 0.106637 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 12.2462 | 0.634085 | 0.317042 | − | 0.948411i | \(-0.397310\pi\) | ||||
0.317042 | + | 0.948411i | \(0.397310\pi\) | |||||||
\(374\) | −6.24621 | −0.322984 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 72.9848 | 3.76391 | ||||||||
\(377\) | 7.12311 | 0.366859 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −30.4924 | −1.56629 | −0.783145 | − | 0.621839i | \(-0.786386\pi\) | ||||
−0.783145 | + | 0.621839i | \(0.786386\pi\) | |||||||
\(380\) | −23.3693 | −1.19882 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 50.2462 | 2.57082 | ||||||||
\(383\) | 3.50758 | 0.179229 | 0.0896144 | − | 0.995977i | \(-0.471437\pi\) | ||||
0.0896144 | + | 0.995977i | \(0.471437\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0.684658 | 0.0348934 | ||||||||
\(386\) | 50.1080 | 2.55043 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 77.2311 | 3.92081 | ||||||||
\(389\) | 37.8617 | 1.91967 | 0.959833 | − | 0.280571i | \(-0.0905239\pi\) | ||||
0.959833 | + | 0.280571i | \(0.0905239\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 3.80776 | 0.192567 | ||||||||
\(392\) | −44.6695 | −2.25615 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −8.63068 | −0.434808 | ||||||||
\(395\) | 4.68466 | 0.235711 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −4.43845 | −0.222759 | −0.111380 | − | 0.993778i | \(-0.535527\pi\) | ||||
−0.111380 | + | 0.993778i | \(0.535527\pi\) | |||||||
\(398\) | −20.4924 | −1.02719 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 7.68466 | 0.384233 | ||||||||
\(401\) | 3.75379 | 0.187455 | 0.0937276 | − | 0.995598i | \(-0.470122\pi\) | ||||
0.0937276 | + | 0.995598i | \(0.470122\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −6.00000 | −0.298881 | ||||||||
\(404\) | 46.7386 | 2.32533 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 8.00000 | 0.397033 | ||||||||
\(407\) | 16.6847 | 0.827028 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −6.87689 | −0.340041 | −0.170020 | − | 0.985441i | \(-0.554383\pi\) | ||||
−0.170020 | + | 0.985441i | \(0.554383\pi\) | |||||||
\(410\) | 9.12311 | 0.450558 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −68.9848 | −3.39864 | ||||||||
\(413\) | −5.26137 | −0.258895 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −16.4924 | −0.809581 | ||||||||
\(416\) | −6.56155 | −0.321707 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 20.4924 | 1.00232 | ||||||||
\(419\) | 7.61553 | 0.372043 | 0.186021 | − | 0.982546i | \(-0.440441\pi\) | ||||
0.186021 | + | 0.982546i | \(0.440441\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 39.3693 | 1.91874 | 0.959372 | − | 0.282146i | \(-0.0910462\pi\) | ||||
0.959372 | + | 0.282146i | \(0.0910462\pi\) | |||||||
\(422\) | 16.0000 | 0.778868 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −30.7386 | −1.49280 | ||||||||
\(425\) | 1.56155 | 0.0757464 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 2.93087 | 0.141835 | ||||||||
\(428\) | 49.8617 | 2.41016 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 8.00000 | 0.385794 | ||||||||
\(431\) | −3.50758 | −0.168954 | −0.0844770 | − | 0.996425i | \(-0.526922\pi\) | ||||
−0.0844770 | + | 0.996425i | \(0.526922\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −9.61553 | −0.462093 | −0.231046 | − | 0.972943i | \(-0.574215\pi\) | ||||
−0.231046 | + | 0.972943i | \(0.574215\pi\) | |||||||
\(434\) | −6.73863 | −0.323465 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −9.12311 | −0.436918 | ||||||||
\(437\) | −12.4924 | −0.597594 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 22.0540 | 1.05258 | 0.526289 | − | 0.850306i | \(-0.323583\pi\) | ||||
0.526289 | + | 0.850306i | \(0.323583\pi\) | |||||||
\(440\) | −10.2462 | −0.488469 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −4.00000 | −0.190261 | ||||||||
\(443\) | −7.80776 | −0.370958 | −0.185479 | − | 0.982648i | \(-0.559384\pi\) | ||||
−0.185479 | + | 0.982648i | \(0.559384\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 10.6847 | 0.506501 | ||||||||
\(446\) | −39.3693 | −1.86419 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −0.630683 | −0.0297970 | ||||||||
\(449\) | −35.1771 | −1.66011 | −0.830055 | − | 0.557682i | \(-0.811691\pi\) | ||||
−0.830055 | + | 0.557682i | \(0.811691\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −5.56155 | −0.261883 | ||||||||
\(452\) | −22.2462 | −1.04637 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 14.7386 | 0.691718 | ||||||||
\(455\) | 0.438447 | 0.0205547 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −13.3153 | −0.622865 | −0.311433 | − | 0.950268i | \(-0.600809\pi\) | ||||
−0.311433 | + | 0.950268i | \(0.600809\pi\) | |||||||
\(458\) | 43.8617 | 2.04952 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 11.1231 | 0.518617 | ||||||||
\(461\) | 8.05398 | 0.375111 | 0.187556 | − | 0.982254i | \(-0.439944\pi\) | ||||
0.187556 | + | 0.982254i | \(0.439944\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −28.9309 | −1.34453 | −0.672266 | − | 0.740310i | \(-0.734679\pi\) | ||||
−0.672266 | + | 0.740310i | \(0.734679\pi\) | |||||||
\(464\) | −54.7386 | −2.54118 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −71.2311 | −3.29971 | ||||||||
\(467\) | 6.93087 | 0.320722 | 0.160361 | − | 0.987058i | \(-0.448734\pi\) | ||||
0.160361 | + | 0.987058i | \(0.448734\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 4.98485 | 0.230179 | ||||||||
\(470\) | 28.4924 | 1.31426 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 78.7386 | 3.62424 | ||||||||
\(473\) | −4.87689 | −0.224240 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −5.12311 | −0.235064 | ||||||||
\(476\) | −3.12311 | −0.143147 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 58.7386 | 2.68664 | ||||||||
\(479\) | 26.0540 | 1.19044 | 0.595218 | − | 0.803564i | \(-0.297066\pi\) | ||||
0.595218 | + | 0.803564i | \(0.297066\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 10.6847 | 0.487178 | ||||||||
\(482\) | 63.3693 | 2.88639 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −39.0540 | −1.77518 | ||||||||
\(485\) | 16.9309 | 0.768791 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −32.0540 | −1.45250 | −0.726252 | − | 0.687428i | \(-0.758740\pi\) | ||||
−0.726252 | + | 0.687428i | \(0.758740\pi\) | |||||||
\(488\) | −43.8617 | −1.98553 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −17.4384 | −0.787789 | ||||||||
\(491\) | −27.6155 | −1.24627 | −0.623136 | − | 0.782114i | \(-0.714142\pi\) | ||||
−0.623136 | + | 0.782114i | \(0.714142\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −11.1231 | −0.500959 | ||||||||
\(494\) | 13.1231 | 0.590436 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 46.1080 | 2.07031 | ||||||||
\(497\) | −4.57671 | −0.205293 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 34.9848 | 1.56614 | 0.783068 | − | 0.621936i | \(-0.213653\pi\) | ||||
0.783068 | + | 0.621936i | \(0.213653\pi\) | |||||||
\(500\) | 4.56155 | 0.203999 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 67.2311 | 3.00067 | ||||||||
\(503\) | 13.7538 | 0.613251 | 0.306626 | − | 0.951830i | \(-0.400800\pi\) | ||||
0.306626 | + | 0.951830i | \(0.400800\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 10.2462 | 0.455950 | ||||||||
\(506\) | −9.75379 | −0.433609 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 8.00000 | 0.354943 | ||||||||
\(509\) | −23.5616 | −1.04435 | −0.522174 | − | 0.852839i | \(-0.674879\pi\) | ||||
−0.522174 | + | 0.852839i | \(0.674879\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 2.63068 | 0.116375 | ||||||||
\(512\) | −50.4233 | −2.22842 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −32.9848 | −1.45490 | ||||||||
\(515\) | −15.1231 | −0.666404 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −17.3693 | −0.763902 | ||||||||
\(518\) | 12.0000 | 0.527250 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −6.56155 | −0.287743 | ||||||||
\(521\) | −25.8617 | −1.13302 | −0.566512 | − | 0.824054i | \(-0.691707\pi\) | ||||
−0.566512 | + | 0.824054i | \(0.691707\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −30.7386 | −1.34411 | −0.672053 | − | 0.740503i | \(-0.734587\pi\) | ||||
−0.672053 | + | 0.740503i | \(0.734587\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −5.75379 | −0.250877 | ||||||||
\(527\) | 9.36932 | 0.408134 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −17.0540 | −0.741477 | ||||||||
\(530\) | −12.0000 | −0.521247 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 10.2462 | 0.444230 | ||||||||
\(533\) | −3.56155 | −0.154268 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 10.9309 | 0.472583 | ||||||||
\(536\) | −74.6004 | −3.22225 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −2.24621 | −0.0968410 | ||||||||
\(539\) | 10.6307 | 0.457896 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 18.8769 | 0.811581 | 0.405791 | − | 0.913966i | \(-0.366996\pi\) | ||||
0.405791 | + | 0.913966i | \(0.366996\pi\) | |||||||
\(542\) | −49.6155 | −2.13117 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 10.2462 | 0.439303 | ||||||||
\(545\) | −2.00000 | −0.0856706 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −5.36932 | −0.229575 | −0.114788 | − | 0.993390i | \(-0.536619\pi\) | ||||
−0.114788 | + | 0.993390i | \(0.536619\pi\) | |||||||
\(548\) | 5.12311 | 0.218848 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −4.00000 | −0.170561 | ||||||||
\(551\) | 36.4924 | 1.55463 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −2.05398 | −0.0873439 | ||||||||
\(554\) | −31.3693 | −1.33275 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 15.1231 | 0.641363 | ||||||||
\(557\) | 6.49242 | 0.275093 | 0.137546 | − | 0.990495i | \(-0.456078\pi\) | ||||
0.137546 | + | 0.990495i | \(0.456078\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −3.12311 | −0.132093 | ||||||||
\(560\) | −3.36932 | −0.142380 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 10.8769 | 0.458814 | ||||||||
\(563\) | −19.3153 | −0.814045 | −0.407022 | − | 0.913418i | \(-0.633433\pi\) | ||||
−0.407022 | + | 0.913418i | \(0.633433\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −4.87689 | −0.205172 | ||||||||
\(566\) | −10.2462 | −0.430680 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 68.4924 | 2.87388 | ||||||||
\(569\) | −32.8769 | −1.37827 | −0.689136 | − | 0.724632i | \(-0.742010\pi\) | ||||
−0.689136 | + | 0.724632i | \(0.742010\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −22.0540 | −0.922930 | −0.461465 | − | 0.887158i | \(-0.652676\pi\) | ||||
−0.461465 | + | 0.887158i | \(0.652676\pi\) | |||||||
\(572\) | 7.12311 | 0.297832 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −4.00000 | −0.166957 | ||||||||
\(575\) | 2.43845 | 0.101690 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 24.4384 | 1.01739 | 0.508693 | − | 0.860948i | \(-0.330129\pi\) | ||||
0.508693 | + | 0.860948i | \(0.330129\pi\) | |||||||
\(578\) | −37.3002 | −1.55148 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −32.4924 | −1.34917 | ||||||||
\(581\) | 7.23106 | 0.299995 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 7.31534 | 0.302970 | ||||||||
\(584\) | −39.3693 | −1.62911 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −51.8617 | −2.14239 | ||||||||
\(587\) | −32.4924 | −1.34111 | −0.670553 | − | 0.741862i | \(-0.733943\pi\) | ||||
−0.670553 | + | 0.741862i | \(0.733943\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −30.7386 | −1.26656 | ||||||||
\(590\) | 30.7386 | 1.26549 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −82.1080 | −3.37462 | ||||||||
\(593\) | 24.2462 | 0.995673 | 0.497836 | − | 0.867271i | \(-0.334128\pi\) | ||||
0.497836 | + | 0.867271i | \(0.334128\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −0.684658 | −0.0280683 | ||||||||
\(596\) | −81.2311 | −3.32735 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −6.24621 | −0.255427 | ||||||||
\(599\) | −9.36932 | −0.382820 | −0.191410 | − | 0.981510i | \(-0.561306\pi\) | ||||
−0.191410 | + | 0.981510i | \(0.561306\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −28.5464 | −1.16443 | −0.582216 | − | 0.813034i | \(-0.697814\pi\) | ||||
−0.582216 | + | 0.813034i | \(0.697814\pi\) | |||||||
\(602\) | −3.50758 | −0.142958 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 51.8617 | 2.11022 | ||||||||
\(605\) | −8.56155 | −0.348077 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −24.0000 | −0.974130 | −0.487065 | − | 0.873366i | \(-0.661933\pi\) | ||||
−0.487065 | + | 0.873366i | \(0.661933\pi\) | |||||||
\(608\) | −33.6155 | −1.36329 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −17.1231 | −0.693294 | ||||||||
\(611\) | −11.1231 | −0.449993 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −32.5464 | −1.31454 | −0.657268 | − | 0.753657i | \(-0.728288\pi\) | ||||
−0.657268 | + | 0.753657i | \(0.728288\pi\) | |||||||
\(614\) | 19.3693 | 0.781682 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 4.49242 | 0.181005 | ||||||||
\(617\) | 0.738634 | 0.0297363 | 0.0148681 | − | 0.999889i | \(-0.495267\pi\) | ||||
0.0148681 | + | 0.999889i | \(0.495267\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −8.63068 | −0.346896 | −0.173448 | − | 0.984843i | \(-0.555491\pi\) | ||||
−0.173448 | + | 0.984843i | \(0.555491\pi\) | |||||||
\(620\) | 27.3693 | 1.09918 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 6.73863 | 0.270195 | ||||||||
\(623\) | −4.68466 | −0.187687 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 74.6004 | 2.98163 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 15.3693 | 0.613303 | ||||||||
\(629\) | −16.6847 | −0.665261 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −32.7386 | −1.30330 | −0.651652 | − | 0.758518i | \(-0.725924\pi\) | ||||
−0.651652 | + | 0.758518i | \(0.725924\pi\) | |||||||
\(632\) | 30.7386 | 1.22272 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 3.86174 | 0.153369 | ||||||||
\(635\) | 1.75379 | 0.0695970 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 6.80776 | 0.269733 | ||||||||
\(638\) | 28.4924 | 1.12803 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −9.43845 | −0.373087 | ||||||||
\(641\) | −32.9848 | −1.30282 | −0.651412 | − | 0.758725i | \(-0.725823\pi\) | ||||
−0.651412 | + | 0.758725i | \(0.725823\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −10.6847 | −0.421362 | −0.210681 | − | 0.977555i | \(-0.567568\pi\) | ||||
−0.210681 | + | 0.977555i | \(0.567568\pi\) | |||||||
\(644\) | −4.87689 | −0.192177 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −20.4924 | −0.806264 | ||||||||
\(647\) | 31.8078 | 1.25049 | 0.625246 | − | 0.780428i | \(-0.284999\pi\) | ||||
0.625246 | + | 0.780428i | \(0.284999\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −18.7386 | −0.735556 | ||||||||
\(650\) | −2.56155 | −0.100472 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 73.2311 | 2.86795 | ||||||||
\(653\) | −33.3693 | −1.30584 | −0.652921 | − | 0.757426i | \(-0.726457\pi\) | ||||
−0.652921 | + | 0.757426i | \(0.726457\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 27.3693 | 1.06859 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −12.4924 | −0.487005 | ||||||||
\(659\) | 0.876894 | 0.0341590 | 0.0170795 | − | 0.999854i | \(-0.494563\pi\) | ||||
0.0170795 | + | 0.999854i | \(0.494563\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 6.49242 | 0.252526 | 0.126263 | − | 0.991997i | \(-0.459702\pi\) | ||||
0.126263 | + | 0.991997i | \(0.459702\pi\) | |||||||
\(662\) | 74.6004 | 2.89943 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −108.216 | −4.19959 | ||||||||
\(665\) | 2.24621 | 0.0871043 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −17.3693 | −0.672543 | ||||||||
\(668\) | 22.2462 | 0.860732 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −29.1231 | −1.12512 | ||||||||
\(671\) | 10.4384 | 0.402972 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 16.7386 | 0.645227 | 0.322613 | − | 0.946531i | \(-0.395439\pi\) | ||||
0.322613 | + | 0.946531i | \(0.395439\pi\) | |||||||
\(674\) | −78.1080 | −3.00861 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 4.56155 | 0.175444 | ||||||||
\(677\) | −14.4384 | −0.554915 | −0.277457 | − | 0.960738i | \(-0.589492\pi\) | ||||
−0.277457 | + | 0.960738i | \(0.589492\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −7.42329 | −0.284880 | ||||||||
\(680\) | 10.2462 | 0.392924 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −24.0000 | −0.919007 | ||||||||
\(683\) | 32.4924 | 1.24329 | 0.621644 | − | 0.783300i | \(-0.286465\pi\) | ||||
0.621644 | + | 0.783300i | \(0.286465\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 1.12311 | 0.0429117 | ||||||||
\(686\) | 15.5076 | 0.592082 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 24.0000 | 0.914991 | ||||||||
\(689\) | 4.68466 | 0.178471 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −21.6155 | −0.822293 | −0.411147 | − | 0.911569i | \(-0.634872\pi\) | ||||
−0.411147 | + | 0.911569i | \(0.634872\pi\) | |||||||
\(692\) | 58.7386 | 2.23291 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −66.7386 | −2.53336 | ||||||||
\(695\) | 3.31534 | 0.125758 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 5.56155 | 0.210659 | ||||||||
\(698\) | −59.8617 | −2.26580 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −2.00000 | −0.0755929 | ||||||||
\(701\) | −48.9848 | −1.85013 | −0.925066 | − | 0.379806i | \(-0.875991\pi\) | ||||
−0.925066 | + | 0.379806i | \(0.875991\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 54.7386 | 2.06451 | ||||||||
\(704\) | −2.24621 | −0.0846573 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −57.6155 | −2.16839 | ||||||||
\(707\) | −4.49242 | −0.168955 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 9.12311 | 0.342625 | 0.171313 | − | 0.985217i | \(-0.445199\pi\) | ||||
0.171313 | + | 0.985217i | \(0.445199\pi\) | |||||||
\(710\) | 26.7386 | 1.00348 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 70.1080 | 2.62741 | ||||||||
\(713\) | 14.6307 | 0.547923 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1.56155 | 0.0583988 | ||||||||
\(716\) | −22.2462 | −0.831380 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −36.4924 | −1.36189 | ||||||||
\(719\) | 36.0000 | 1.34257 | 0.671287 | − | 0.741198i | \(-0.265742\pi\) | ||||
0.671287 | + | 0.741198i | \(0.265742\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 6.63068 | 0.246940 | ||||||||
\(722\) | 18.5616 | 0.690789 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 60.7386 | 2.25733 | ||||||||
\(725\) | −7.12311 | −0.264546 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 12.8769 | 0.477578 | 0.238789 | − | 0.971072i | \(-0.423250\pi\) | ||||
0.238789 | + | 0.971072i | \(0.423250\pi\) | |||||||
\(728\) | 2.87689 | 0.106625 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −15.3693 | −0.568844 | ||||||||
\(731\) | 4.87689 | 0.180378 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −16.4384 | −0.607168 | −0.303584 | − | 0.952805i | \(-0.598183\pi\) | ||||
−0.303584 | + | 0.952805i | \(0.598183\pi\) | |||||||
\(734\) | −4.49242 | −0.165818 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 16.0000 | 0.589768 | ||||||||
\(737\) | 17.7538 | 0.653969 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 48.7386 | 1.79288 | 0.896440 | − | 0.443166i | \(-0.146145\pi\) | ||||
0.896440 | + | 0.443166i | \(0.146145\pi\) | |||||||
\(740\) | −48.7386 | −1.79167 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 5.26137 | 0.193151 | ||||||||
\(743\) | 18.7386 | 0.687454 | 0.343727 | − | 0.939070i | \(-0.388311\pi\) | ||||
0.343727 | + | 0.939070i | \(0.388311\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −17.8078 | −0.652426 | ||||||||
\(746\) | 31.3693 | 1.14851 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −11.1231 | −0.406701 | ||||||||
\(749\) | −4.79261 | −0.175118 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 14.0540 | 0.512837 | 0.256418 | − | 0.966566i | \(-0.417458\pi\) | ||||
0.256418 | + | 0.966566i | \(0.417458\pi\) | |||||||
\(752\) | 85.4773 | 3.11704 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 18.2462 | 0.664488 | ||||||||
\(755\) | 11.3693 | 0.413772 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −14.4924 | −0.526736 | −0.263368 | − | 0.964695i | \(-0.584833\pi\) | ||||
−0.263368 | + | 0.964695i | \(0.584833\pi\) | |||||||
\(758\) | −78.1080 | −2.83701 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −33.6155 | −1.21936 | ||||||||
\(761\) | 45.2311 | 1.63962 | 0.819812 | − | 0.572632i | \(-0.194078\pi\) | ||||
0.819812 | + | 0.572632i | \(0.194078\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0.876894 | 0.0317457 | ||||||||
\(764\) | 89.4773 | 3.23717 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 8.98485 | 0.324636 | ||||||||
\(767\) | −12.0000 | −0.433295 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −30.0000 | −1.08183 | −0.540914 | − | 0.841078i | \(-0.681921\pi\) | ||||
−0.540914 | + | 0.841078i | \(0.681921\pi\) | |||||||
\(770\) | 1.75379 | 0.0632022 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 89.2311 | 3.21150 | ||||||||
\(773\) | −9.12311 | −0.328135 | −0.164068 | − | 0.986449i | \(-0.552462\pi\) | ||||
−0.164068 | + | 0.986449i | \(0.552462\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 6.00000 | 0.215526 | ||||||||
\(776\) | 111.093 | 3.98800 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 96.9848 | 3.47708 | ||||||||
\(779\) | −18.2462 | −0.653738 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −16.3002 | −0.583267 | ||||||||
\(782\) | 9.75379 | 0.348795 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −52.3153 | −1.86841 | ||||||||
\(785\) | 3.36932 | 0.120256 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 11.3693 | 0.405272 | 0.202636 | − | 0.979254i | \(-0.435049\pi\) | ||||
0.202636 | + | 0.979254i | \(0.435049\pi\) | |||||||
\(788\) | −15.3693 | −0.547509 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 12.0000 | 0.426941 | ||||||||
\(791\) | 2.13826 | 0.0760278 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 6.68466 | 0.237379 | ||||||||
\(794\) | −11.3693 | −0.403482 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −36.4924 | −1.29344 | ||||||||
\(797\) | 4.68466 | 0.165939 | 0.0829696 | − | 0.996552i | \(-0.473560\pi\) | ||||
0.0829696 | + | 0.996552i | \(0.473560\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 17.3693 | 0.614482 | ||||||||
\(800\) | 6.56155 | 0.231986 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 9.61553 | 0.339536 | ||||||||
\(803\) | 9.36932 | 0.330636 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −1.06913 | −0.0376819 | ||||||||
\(806\) | −15.3693 | −0.541361 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 67.2311 | 2.36518 | ||||||||
\(809\) | 7.50758 | 0.263952 | 0.131976 | − | 0.991253i | \(-0.457868\pi\) | ||||
0.131976 | + | 0.991253i | \(0.457868\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 4.24621 | 0.149105 | 0.0745523 | − | 0.997217i | \(-0.476247\pi\) | ||||
0.0745523 | + | 0.997217i | \(0.476247\pi\) | |||||||
\(812\) | 14.2462 | 0.499944 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 42.7386 | 1.49799 | ||||||||
\(815\) | 16.0540 | 0.562346 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −16.0000 | −0.559769 | ||||||||
\(818\) | −17.6155 | −0.615912 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 16.2462 | 0.567342 | ||||||||
\(821\) | 48.5464 | 1.69428 | 0.847140 | − | 0.531369i | \(-0.178322\pi\) | ||||
0.847140 | + | 0.531369i | \(0.178322\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −29.7538 | −1.03715 | −0.518576 | − | 0.855032i | \(-0.673538\pi\) | ||||
−0.518576 | + | 0.855032i | \(0.673538\pi\) | |||||||
\(824\) | −99.2311 | −3.45688 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −13.4773 | −0.468934 | ||||||||
\(827\) | 7.12311 | 0.247695 | 0.123847 | − | 0.992301i | \(-0.460477\pi\) | ||||
0.123847 | + | 0.992301i | \(0.460477\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 0.738634 | 0.0256538 | 0.0128269 | − | 0.999918i | \(-0.495917\pi\) | ||||
0.0128269 | + | 0.999918i | \(0.495917\pi\) | |||||||
\(830\) | −42.2462 | −1.46639 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −1.43845 | −0.0498692 | ||||||||
\(833\) | −10.6307 | −0.368331 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 4.87689 | 0.168772 | ||||||||
\(836\) | 36.4924 | 1.26212 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 19.5076 | 0.673878 | ||||||||
\(839\) | −44.7926 | −1.54641 | −0.773206 | − | 0.634155i | \(-0.781348\pi\) | ||||
−0.773206 | + | 0.634155i | \(0.781348\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 21.7386 | 0.749608 | ||||||||
\(842\) | 100.847 | 3.47540 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 28.4924 | 0.980750 | ||||||||
\(845\) | 1.00000 | 0.0344010 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 3.75379 | 0.128982 | ||||||||
\(848\) | −36.0000 | −1.23625 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 4.00000 | 0.137199 | ||||||||
\(851\) | −26.0540 | −0.893119 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 41.4233 | 1.41831 | 0.709153 | − | 0.705054i | \(-0.249077\pi\) | ||||
0.709153 | + | 0.705054i | \(0.249077\pi\) | |||||||
\(854\) | 7.50758 | 0.256904 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 71.7235 | 2.45146 | ||||||||
\(857\) | 2.43845 | 0.0832958 | 0.0416479 | − | 0.999132i | \(-0.486739\pi\) | ||||
0.0416479 | + | 0.999132i | \(0.486739\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 3.80776 | 0.129919 | 0.0649596 | − | 0.997888i | \(-0.479308\pi\) | ||||
0.0649596 | + | 0.997888i | \(0.479308\pi\) | |||||||
\(860\) | 14.2462 | 0.485792 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −8.98485 | −0.306025 | ||||||||
\(863\) | −9.36932 | −0.318935 | −0.159468 | − | 0.987203i | \(-0.550978\pi\) | ||||
−0.159468 | + | 0.987203i | \(0.550978\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 12.8769 | 0.437828 | ||||||||
\(866\) | −24.6307 | −0.836985 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −12.0000 | −0.407307 | ||||||||
\(869\) | −7.31534 | −0.248156 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 11.3693 | 0.385235 | ||||||||
\(872\) | −13.1231 | −0.444404 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −32.0000 | −1.08242 | ||||||||
\(875\) | −0.438447 | −0.0148222 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 46.9848 | 1.58657 | 0.793283 | − | 0.608853i | \(-0.208370\pi\) | ||||
0.793283 | + | 0.608853i | \(0.208370\pi\) | |||||||
\(878\) | 56.4924 | 1.90653 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −12.0000 | −0.404520 | ||||||||
\(881\) | −21.3693 | −0.719951 | −0.359975 | − | 0.932962i | \(-0.617215\pi\) | ||||
−0.359975 | + | 0.932962i | \(0.617215\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −56.1080 | −1.88818 | −0.944091 | − | 0.329684i | \(-0.893058\pi\) | ||||
−0.944091 | + | 0.329684i | \(0.893058\pi\) | |||||||
\(884\) | −7.12311 | −0.239576 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −20.0000 | −0.671913 | ||||||||
\(887\) | 5.56155 | 0.186739 | 0.0933693 | − | 0.995632i | \(-0.470236\pi\) | ||||
0.0933693 | + | 0.995632i | \(0.470236\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −0.768944 | −0.0257895 | ||||||||
\(890\) | 27.3693 | 0.917422 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −70.1080 | −2.34739 | ||||||||
\(893\) | −56.9848 | −1.90693 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −4.87689 | −0.163017 | ||||||||
\(896\) | 4.13826 | 0.138250 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −90.1080 | −3.00694 | ||||||||
\(899\) | −42.7386 | −1.42541 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −7.31534 | −0.243709 | ||||||||
\(902\) | −14.2462 | −0.474347 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −32.0000 | −1.06430 | ||||||||
\(905\) | 13.3153 | 0.442617 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −2.63068 | −0.0873504 | −0.0436752 | − | 0.999046i | \(-0.513907\pi\) | ||||
−0.0436752 | + | 0.999046i | \(0.513907\pi\) | |||||||
\(908\) | 26.2462 | 0.871011 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 1.12311 | 0.0372306 | ||||||||
\(911\) | −12.0000 | −0.397578 | −0.198789 | − | 0.980042i | \(-0.563701\pi\) | ||||
−0.198789 | + | 0.980042i | \(0.563701\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 25.7538 | 0.852326 | ||||||||
\(914\) | −34.1080 | −1.12819 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 78.1080 | 2.58076 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 1.94602 | 0.0641934 | 0.0320967 | − | 0.999485i | \(-0.489782\pi\) | ||||
0.0320967 | + | 0.999485i | \(0.489782\pi\) | |||||||
\(920\) | 16.0000 | 0.527504 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 20.6307 | 0.679435 | ||||||||
\(923\) | −10.4384 | −0.343586 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −10.6847 | −0.351309 | ||||||||
\(926\) | −74.1080 | −2.43534 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −46.7386 | −1.53427 | ||||||||
\(929\) | 39.6695 | 1.30151 | 0.650757 | − | 0.759286i | \(-0.274452\pi\) | ||||
0.650757 | + | 0.759286i | \(0.274452\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 34.8769 | 1.14304 | ||||||||
\(932\) | −126.847 | −4.15500 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 17.7538 | 0.580922 | ||||||||
\(935\) | −2.43845 | −0.0797458 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −27.3693 | −0.894117 | −0.447058 | − | 0.894505i | \(-0.647528\pi\) | ||||
−0.447058 | + | 0.894505i | \(0.647528\pi\) | |||||||
\(938\) | 12.7689 | 0.416921 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 50.7386 | 1.65491 | ||||||||
\(941\) | −41.8078 | −1.36289 | −0.681447 | − | 0.731867i | \(-0.738649\pi\) | ||||
−0.681447 | + | 0.731867i | \(0.738649\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 8.68466 | 0.282811 | ||||||||
\(944\) | 92.2159 | 3.00137 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −12.4924 | −0.406164 | ||||||||
\(947\) | 60.6004 | 1.96925 | 0.984624 | − | 0.174688i | \(-0.0558918\pi\) | ||||
0.984624 | + | 0.174688i | \(0.0558918\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 6.00000 | 0.194768 | ||||||||
\(950\) | −13.1231 | −0.425770 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −4.49242 | −0.145600 | ||||||||
\(953\) | 29.5616 | 0.957593 | 0.478796 | − | 0.877926i | \(-0.341073\pi\) | ||||
0.478796 | + | 0.877926i | \(0.341073\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 19.6155 | 0.634744 | ||||||||
\(956\) | 104.600 | 3.38302 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 66.7386 | 2.15623 | ||||||||
\(959\) | −0.492423 | −0.0159012 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 5.00000 | 0.161290 | ||||||||
\(962\) | 27.3693 | 0.882422 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 112.847 | 3.63454 | ||||||||
\(965\) | 19.5616 | 0.629709 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −7.36932 | −0.236981 | −0.118491 | − | 0.992955i | \(-0.537806\pi\) | ||||
−0.118491 | + | 0.992955i | \(0.537806\pi\) | |||||||
\(968\) | −56.1771 | −1.80560 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 43.3693 | 1.39250 | ||||||||
\(971\) | −24.4924 | −0.785999 | −0.393000 | − | 0.919539i | \(-0.628563\pi\) | ||||
−0.393000 | + | 0.919539i | \(0.628563\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −1.45360 | −0.0466003 | ||||||||
\(974\) | −82.1080 | −2.63091 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −51.3693 | −1.64429 | ||||||||
\(977\) | −43.4773 | −1.39096 | −0.695481 | − | 0.718545i | \(-0.744808\pi\) | ||||
−0.695481 | + | 0.718545i | \(0.744808\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −16.6847 | −0.533244 | ||||||||
\(980\) | −31.0540 | −0.991983 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −70.7386 | −2.25736 | ||||||||
\(983\) | 42.7386 | 1.36315 | 0.681575 | − | 0.731748i | \(-0.261295\pi\) | ||||
0.681575 | + | 0.731748i | \(0.261295\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −3.36932 | −0.107355 | ||||||||
\(986\) | −28.4924 | −0.907384 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 23.3693 | 0.743477 | ||||||||
\(989\) | 7.61553 | 0.242160 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 10.0540 | 0.319375 | 0.159688 | − | 0.987168i | \(-0.448951\pi\) | ||||
0.159688 | + | 0.987168i | \(0.448951\pi\) | |||||||
\(992\) | 39.3693 | 1.24998 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −11.7235 | −0.371846 | ||||||||
\(995\) | −8.00000 | −0.253617 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 28.2462 | 0.894566 | 0.447283 | − | 0.894392i | \(-0.352392\pi\) | ||||
0.447283 | + | 0.894392i | \(0.352392\pi\) | |||||||
\(998\) | 89.6155 | 2.83673 | ||||||||
\(999\) | 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 | 585.2.a.l.1.2 | yes | 2 | |
3.2 | odd | 2 | 585.2.a.j.1.1 | ✓ | 2 | ||
4.3 | odd | 2 | 9360.2.a.cw.1.1 | 2 | |||
5.2 | odd | 4 | 2925.2.c.p.2224.4 | 4 | |||
5.3 | odd | 4 | 2925.2.c.p.2224.1 | 4 | |||
5.4 | even | 2 | 2925.2.a.x.1.1 | 2 | |||
12.11 | even | 2 | 9360.2.a.cl.1.1 | 2 | |||
13.12 | even | 2 | 7605.2.a.bd.1.1 | 2 | |||
15.2 | even | 4 | 2925.2.c.o.2224.1 | 4 | |||
15.8 | even | 4 | 2925.2.c.o.2224.4 | 4 | |||
15.14 | odd | 2 | 2925.2.a.bc.1.2 | 2 | |||
39.38 | odd | 2 | 7605.2.a.bi.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
585.2.a.j.1.1 | ✓ | 2 | 3.2 | odd | 2 | ||
585.2.a.l.1.2 | yes | 2 | 1.1 | even | 1 | trivial | |
2925.2.a.x.1.1 | 2 | 5.4 | even | 2 | |||
2925.2.a.bc.1.2 | 2 | 15.14 | odd | 2 | |||
2925.2.c.o.2224.1 | 4 | 15.2 | even | 4 | |||
2925.2.c.o.2224.4 | 4 | 15.8 | even | 4 | |||
2925.2.c.p.2224.1 | 4 | 5.3 | odd | 4 | |||
2925.2.c.p.2224.4 | 4 | 5.2 | odd | 4 | |||
7605.2.a.bd.1.1 | 2 | 13.12 | even | 2 | |||
7605.2.a.bi.1.2 | 2 | 39.38 | odd | 2 | |||
9360.2.a.cl.1.1 | 2 | 12.11 | even | 2 | |||
9360.2.a.cw.1.1 | 2 | 4.3 | odd | 2 |