Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3525,2,Mod(1,3525)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3525, 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("3525.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3525 = 3 \cdot 5^{2} \cdot 47 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3525.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: | \(28.1472667125\) |
Analytic rank: | \(1\) |
Dimension: | \(10\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{10} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{10} - 3x^{9} - 9x^{8} + 29x^{7} + 25x^{6} - 91x^{5} - 21x^{4} + 101x^{3} + 6x^{2} - 30x - 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 705) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.9 | ||
Root | \(2.38580\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3525.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.38580 | 1.68702 | 0.843508 | − | 0.537116i | \(-0.180486\pi\) | ||||
0.843508 | + | 0.537116i | \(0.180486\pi\) | |||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 3.69205 | 1.84603 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −2.38580 | −0.974000 | ||||||||
\(7\) | −1.19234 | −0.450662 | −0.225331 | − | 0.974282i | \(-0.572346\pi\) | ||||
−0.225331 | + | 0.974282i | \(0.572346\pi\) | |||||||
\(8\) | 4.03690 | 1.42726 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2.68688 | −0.810125 | −0.405063 | − | 0.914289i | \(-0.632750\pi\) | ||||
−0.405063 | + | 0.914289i | \(0.632750\pi\) | |||||||
\(12\) | −3.69205 | −1.06580 | ||||||||
\(13\) | −5.12547 | −1.42155 | −0.710775 | − | 0.703419i | \(-0.751656\pi\) | ||||
−0.710775 | + | 0.703419i | \(0.751656\pi\) | |||||||
\(14\) | −2.84469 | −0.760274 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 2.24714 | 0.561785 | ||||||||
\(17\) | −0.967149 | −0.234568 | −0.117284 | − | 0.993098i | \(-0.537419\pi\) | ||||
−0.117284 | + | 0.993098i | \(0.537419\pi\) | |||||||
\(18\) | 2.38580 | 0.562339 | ||||||||
\(19\) | 1.87461 | 0.430064 | 0.215032 | − | 0.976607i | \(-0.431014\pi\) | ||||
0.215032 | + | 0.976607i | \(0.431014\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.19234 | 0.260190 | ||||||||
\(22\) | −6.41037 | −1.36669 | ||||||||
\(23\) | 7.60212 | 1.58515 | 0.792575 | − | 0.609774i | \(-0.208740\pi\) | ||||
0.792575 | + | 0.609774i | \(0.208740\pi\) | |||||||
\(24\) | −4.03690 | −0.824029 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −12.2284 | −2.39818 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | −4.40218 | −0.831934 | ||||||||
\(29\) | −9.33467 | −1.73341 | −0.866703 | − | 0.498825i | \(-0.833765\pi\) | ||||
−0.866703 | + | 0.498825i | \(0.833765\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −7.48104 | −1.34363 | −0.671817 | − | 0.740717i | \(-0.734486\pi\) | ||||
−0.671817 | + | 0.740717i | \(0.734486\pi\) | |||||||
\(32\) | −2.71257 | −0.479519 | ||||||||
\(33\) | 2.68688 | 0.467726 | ||||||||
\(34\) | −2.30743 | −0.395720 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 3.69205 | 0.615342 | ||||||||
\(37\) | 8.35311 | 1.37324 | 0.686622 | − | 0.727015i | \(-0.259093\pi\) | ||||
0.686622 | + | 0.727015i | \(0.259093\pi\) | |||||||
\(38\) | 4.47244 | 0.725526 | ||||||||
\(39\) | 5.12547 | 0.820733 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0.858735 | 0.134112 | 0.0670559 | − | 0.997749i | \(-0.478639\pi\) | ||||
0.0670559 | + | 0.997749i | \(0.478639\pi\) | |||||||
\(42\) | 2.84469 | 0.438945 | ||||||||
\(43\) | −6.69665 | −1.02123 | −0.510615 | − | 0.859810i | \(-0.670582\pi\) | ||||
−0.510615 | + | 0.859810i | \(0.670582\pi\) | |||||||
\(44\) | −9.92010 | −1.49551 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 18.1371 | 2.67418 | ||||||||
\(47\) | 1.00000 | 0.145865 | ||||||||
\(48\) | −2.24714 | −0.324347 | ||||||||
\(49\) | −5.57833 | −0.796904 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0.967149 | 0.135428 | ||||||||
\(52\) | −18.9235 | −2.62422 | ||||||||
\(53\) | −8.42050 | −1.15664 | −0.578322 | − | 0.815809i | \(-0.696292\pi\) | ||||
−0.578322 | + | 0.815809i | \(0.696292\pi\) | |||||||
\(54\) | −2.38580 | −0.324667 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −4.81336 | −0.643212 | ||||||||
\(57\) | −1.87461 | −0.248298 | ||||||||
\(58\) | −22.2707 | −2.92428 | ||||||||
\(59\) | −11.2142 | −1.45996 | −0.729980 | − | 0.683469i | \(-0.760471\pi\) | ||||
−0.729980 | + | 0.683469i | \(0.760471\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −10.7671 | −1.37859 | −0.689295 | − | 0.724481i | \(-0.742080\pi\) | ||||
−0.689295 | + | 0.724481i | \(0.742080\pi\) | |||||||
\(62\) | −17.8483 | −2.26673 | ||||||||
\(63\) | −1.19234 | −0.150221 | ||||||||
\(64\) | −10.9659 | −1.37074 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 6.41037 | 0.789062 | ||||||||
\(67\) | 2.45600 | 0.300048 | 0.150024 | − | 0.988682i | \(-0.452065\pi\) | ||||
0.150024 | + | 0.988682i | \(0.452065\pi\) | |||||||
\(68\) | −3.57076 | −0.433019 | ||||||||
\(69\) | −7.60212 | −0.915187 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −7.42913 | −0.881675 | −0.440838 | − | 0.897587i | \(-0.645319\pi\) | ||||
−0.440838 | + | 0.897587i | \(0.645319\pi\) | |||||||
\(72\) | 4.03690 | 0.475753 | ||||||||
\(73\) | 5.18337 | 0.606667 | 0.303334 | − | 0.952884i | \(-0.401900\pi\) | ||||
0.303334 | + | 0.952884i | \(0.401900\pi\) | |||||||
\(74\) | 19.9289 | 2.31668 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 6.92114 | 0.793910 | ||||||||
\(77\) | 3.20368 | 0.365093 | ||||||||
\(78\) | 12.2284 | 1.38459 | ||||||||
\(79\) | 9.80667 | 1.10334 | 0.551669 | − | 0.834063i | \(-0.313991\pi\) | ||||
0.551669 | + | 0.834063i | \(0.313991\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 2.04877 | 0.226249 | ||||||||
\(83\) | −4.00659 | −0.439781 | −0.219890 | − | 0.975525i | \(-0.570570\pi\) | ||||
−0.219890 | + | 0.975525i | \(0.570570\pi\) | |||||||
\(84\) | 4.40218 | 0.480317 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −15.9769 | −1.72283 | ||||||||
\(87\) | 9.33467 | 1.00078 | ||||||||
\(88\) | −10.8467 | −1.15626 | ||||||||
\(89\) | 0.872329 | 0.0924667 | 0.0462333 | − | 0.998931i | \(-0.485278\pi\) | ||||
0.0462333 | + | 0.998931i | \(0.485278\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 6.11131 | 0.640639 | ||||||||
\(92\) | 28.0674 | 2.92623 | ||||||||
\(93\) | 7.48104 | 0.775747 | ||||||||
\(94\) | 2.38580 | 0.246077 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 2.71257 | 0.276850 | ||||||||
\(97\) | 6.63229 | 0.673407 | 0.336704 | − | 0.941611i | \(-0.390688\pi\) | ||||
0.336704 | + | 0.941611i | \(0.390688\pi\) | |||||||
\(98\) | −13.3088 | −1.34439 | ||||||||
\(99\) | −2.68688 | −0.270042 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 12.1860 | 1.21255 | 0.606274 | − | 0.795256i | \(-0.292663\pi\) | ||||
0.606274 | + | 0.795256i | \(0.292663\pi\) | |||||||
\(102\) | 2.30743 | 0.228469 | ||||||||
\(103\) | 3.37168 | 0.332222 | 0.166111 | − | 0.986107i | \(-0.446879\pi\) | ||||
0.166111 | + | 0.986107i | \(0.446879\pi\) | |||||||
\(104\) | −20.6910 | −2.02892 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −20.0896 | −1.95128 | ||||||||
\(107\) | 11.7874 | 1.13953 | 0.569765 | − | 0.821808i | \(-0.307034\pi\) | ||||
0.569765 | + | 0.821808i | \(0.307034\pi\) | |||||||
\(108\) | −3.69205 | −0.355268 | ||||||||
\(109\) | 3.50151 | 0.335384 | 0.167692 | − | 0.985839i | \(-0.446369\pi\) | ||||
0.167692 | + | 0.985839i | \(0.446369\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −8.35311 | −0.792842 | ||||||||
\(112\) | −2.67935 | −0.253175 | ||||||||
\(113\) | 4.70984 | 0.443064 | 0.221532 | − | 0.975153i | \(-0.428894\pi\) | ||||
0.221532 | + | 0.975153i | \(0.428894\pi\) | |||||||
\(114\) | −4.47244 | −0.418882 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −34.4641 | −3.19991 | ||||||||
\(117\) | −5.12547 | −0.473850 | ||||||||
\(118\) | −26.7548 | −2.46298 | ||||||||
\(119\) | 1.15317 | 0.105711 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −3.78067 | −0.343697 | ||||||||
\(122\) | −25.6882 | −2.32570 | ||||||||
\(123\) | −0.858735 | −0.0774295 | ||||||||
\(124\) | −27.6204 | −2.48038 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −2.84469 | −0.253425 | ||||||||
\(127\) | 1.51685 | 0.134599 | 0.0672994 | − | 0.997733i | \(-0.478562\pi\) | ||||
0.0672994 | + | 0.997733i | \(0.478562\pi\) | |||||||
\(128\) | −20.7374 | −1.83294 | ||||||||
\(129\) | 6.69665 | 0.589607 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −19.6769 | −1.71918 | −0.859591 | − | 0.510982i | \(-0.829282\pi\) | ||||
−0.859591 | + | 0.510982i | \(0.829282\pi\) | |||||||
\(132\) | 9.92010 | 0.863434 | ||||||||
\(133\) | −2.23517 | −0.193814 | ||||||||
\(134\) | 5.85954 | 0.506187 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −3.90428 | −0.334789 | ||||||||
\(137\) | 14.4732 | 1.23653 | 0.618264 | − | 0.785971i | \(-0.287836\pi\) | ||||
0.618264 | + | 0.785971i | \(0.287836\pi\) | |||||||
\(138\) | −18.1371 | −1.54394 | ||||||||
\(139\) | 0.397762 | 0.0337378 | 0.0168689 | − | 0.999858i | \(-0.494630\pi\) | ||||
0.0168689 | + | 0.999858i | \(0.494630\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −1.00000 | −0.0842152 | ||||||||
\(142\) | −17.7244 | −1.48740 | ||||||||
\(143\) | 13.7715 | 1.15163 | ||||||||
\(144\) | 2.24714 | 0.187262 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 12.3665 | 1.02346 | ||||||||
\(147\) | 5.57833 | 0.460093 | ||||||||
\(148\) | 30.8401 | 2.53504 | ||||||||
\(149\) | 10.5936 | 0.867864 | 0.433932 | − | 0.900946i | \(-0.357126\pi\) | ||||
0.433932 | + | 0.900946i | \(0.357126\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 16.7245 | 1.36102 | 0.680508 | − | 0.732740i | \(-0.261759\pi\) | ||||
0.680508 | + | 0.732740i | \(0.261759\pi\) | |||||||
\(152\) | 7.56760 | 0.613813 | ||||||||
\(153\) | −0.967149 | −0.0781893 | ||||||||
\(154\) | 7.64334 | 0.615918 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 18.9235 | 1.51509 | ||||||||
\(157\) | −15.7288 | −1.25529 | −0.627646 | − | 0.778499i | \(-0.715981\pi\) | ||||
−0.627646 | + | 0.778499i | \(0.715981\pi\) | |||||||
\(158\) | 23.3968 | 1.86135 | ||||||||
\(159\) | 8.42050 | 0.667789 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −9.06430 | −0.714367 | ||||||||
\(162\) | 2.38580 | 0.187446 | ||||||||
\(163\) | −11.3372 | −0.887995 | −0.443998 | − | 0.896028i | \(-0.646440\pi\) | ||||
−0.443998 | + | 0.896028i | \(0.646440\pi\) | |||||||
\(164\) | 3.17049 | 0.247574 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −9.55894 | −0.741917 | ||||||||
\(167\) | 1.61989 | 0.125351 | 0.0626753 | − | 0.998034i | \(-0.480037\pi\) | ||||
0.0626753 | + | 0.998034i | \(0.480037\pi\) | |||||||
\(168\) | 4.81336 | 0.371358 | ||||||||
\(169\) | 13.2705 | 1.02081 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1.87461 | 0.143355 | ||||||||
\(172\) | −24.7244 | −1.88522 | ||||||||
\(173\) | −24.6582 | −1.87473 | −0.937364 | − | 0.348351i | \(-0.886742\pi\) | ||||
−0.937364 | + | 0.348351i | \(0.886742\pi\) | |||||||
\(174\) | 22.2707 | 1.68834 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −6.03780 | −0.455116 | ||||||||
\(177\) | 11.2142 | 0.842908 | ||||||||
\(178\) | 2.08120 | 0.155993 | ||||||||
\(179\) | −2.12475 | −0.158811 | −0.0794056 | − | 0.996842i | \(-0.525302\pi\) | ||||
−0.0794056 | + | 0.996842i | \(0.525302\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 0.443183 | 0.0329415 | 0.0164708 | − | 0.999864i | \(-0.494757\pi\) | ||||
0.0164708 | + | 0.999864i | \(0.494757\pi\) | |||||||
\(182\) | 14.5804 | 1.08077 | ||||||||
\(183\) | 10.7671 | 0.795929 | ||||||||
\(184\) | 30.6890 | 2.26242 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 17.8483 | 1.30870 | ||||||||
\(187\) | 2.59861 | 0.190029 | ||||||||
\(188\) | 3.69205 | 0.269271 | ||||||||
\(189\) | 1.19234 | 0.0867300 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 6.10367 | 0.441646 | 0.220823 | − | 0.975314i | \(-0.429126\pi\) | ||||
0.220823 | + | 0.975314i | \(0.429126\pi\) | |||||||
\(192\) | 10.9659 | 0.791398 | ||||||||
\(193\) | −3.79802 | −0.273387 | −0.136694 | − | 0.990613i | \(-0.543648\pi\) | ||||
−0.136694 | + | 0.990613i | \(0.543648\pi\) | |||||||
\(194\) | 15.8233 | 1.13605 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −20.5955 | −1.47110 | ||||||||
\(197\) | 3.25900 | 0.232194 | 0.116097 | − | 0.993238i | \(-0.462962\pi\) | ||||
0.116097 | + | 0.993238i | \(0.462962\pi\) | |||||||
\(198\) | −6.41037 | −0.455565 | ||||||||
\(199\) | −0.0824884 | −0.00584745 | −0.00292372 | − | 0.999996i | \(-0.500931\pi\) | ||||
−0.00292372 | + | 0.999996i | \(0.500931\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −2.45600 | −0.173233 | ||||||||
\(202\) | 29.0733 | 2.04559 | ||||||||
\(203\) | 11.1301 | 0.781180 | ||||||||
\(204\) | 3.57076 | 0.250003 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 8.04417 | 0.560464 | ||||||||
\(207\) | 7.60212 | 0.528384 | ||||||||
\(208\) | −11.5177 | −0.798606 | ||||||||
\(209\) | −5.03685 | −0.348406 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −21.9720 | −1.51261 | −0.756307 | − | 0.654217i | \(-0.772998\pi\) | ||||
−0.756307 | + | 0.654217i | \(0.772998\pi\) | |||||||
\(212\) | −31.0889 | −2.13519 | ||||||||
\(213\) | 7.42913 | 0.509036 | ||||||||
\(214\) | 28.1224 | 1.92241 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −4.03690 | −0.274676 | ||||||||
\(217\) | 8.91994 | 0.605525 | ||||||||
\(218\) | 8.35390 | 0.565798 | ||||||||
\(219\) | −5.18337 | −0.350260 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 4.95710 | 0.333450 | ||||||||
\(222\) | −19.9289 | −1.33754 | ||||||||
\(223\) | 2.78392 | 0.186425 | 0.0932126 | − | 0.995646i | \(-0.470286\pi\) | ||||
0.0932126 | + | 0.995646i | \(0.470286\pi\) | |||||||
\(224\) | 3.23430 | 0.216101 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 11.2367 | 0.747457 | ||||||||
\(227\) | 7.69378 | 0.510654 | 0.255327 | − | 0.966855i | \(-0.417817\pi\) | ||||
0.255327 | + | 0.966855i | \(0.417817\pi\) | |||||||
\(228\) | −6.92114 | −0.458364 | ||||||||
\(229\) | 4.01668 | 0.265430 | 0.132715 | − | 0.991154i | \(-0.457631\pi\) | ||||
0.132715 | + | 0.991154i | \(0.457631\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −3.20368 | −0.210786 | ||||||||
\(232\) | −37.6831 | −2.47402 | ||||||||
\(233\) | 10.4924 | 0.687377 | 0.343688 | − | 0.939084i | \(-0.388324\pi\) | ||||
0.343688 | + | 0.939084i | \(0.388324\pi\) | |||||||
\(234\) | −12.2284 | −0.799393 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −41.4033 | −2.69512 | ||||||||
\(237\) | −9.80667 | −0.637012 | ||||||||
\(238\) | 2.75123 | 0.178336 | ||||||||
\(239\) | −27.4470 | −1.77540 | −0.887699 | − | 0.460425i | \(-0.847697\pi\) | ||||
−0.887699 | + | 0.460425i | \(0.847697\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 23.2503 | 1.49768 | 0.748841 | − | 0.662749i | \(-0.230611\pi\) | ||||
0.748841 | + | 0.662749i | \(0.230611\pi\) | |||||||
\(242\) | −9.01993 | −0.579823 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | −39.7528 | −2.54491 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −2.04877 | −0.130625 | ||||||||
\(247\) | −9.60825 | −0.611358 | ||||||||
\(248\) | −30.2002 | −1.91771 | ||||||||
\(249\) | 4.00659 | 0.253907 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 28.2831 | 1.78522 | 0.892608 | − | 0.450833i | \(-0.148873\pi\) | ||||
0.892608 | + | 0.450833i | \(0.148873\pi\) | |||||||
\(252\) | −4.40218 | −0.277311 | ||||||||
\(253\) | −20.4260 | −1.28417 | ||||||||
\(254\) | 3.61891 | 0.227070 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −27.5435 | −1.72147 | ||||||||
\(257\) | −5.57969 | −0.348051 | −0.174026 | − | 0.984741i | \(-0.555678\pi\) | ||||
−0.174026 | + | 0.984741i | \(0.555678\pi\) | |||||||
\(258\) | 15.9769 | 0.994677 | ||||||||
\(259\) | −9.95975 | −0.618869 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −9.33467 | −0.577802 | ||||||||
\(262\) | −46.9453 | −2.90029 | ||||||||
\(263\) | −12.8628 | −0.793156 | −0.396578 | − | 0.918001i | \(-0.629802\pi\) | ||||
−0.396578 | + | 0.918001i | \(0.629802\pi\) | |||||||
\(264\) | 10.8467 | 0.667566 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −5.33267 | −0.326967 | ||||||||
\(267\) | −0.872329 | −0.0533857 | ||||||||
\(268\) | 9.06769 | 0.553897 | ||||||||
\(269\) | −10.6101 | −0.646908 | −0.323454 | − | 0.946244i | \(-0.604844\pi\) | ||||
−0.323454 | + | 0.946244i | \(0.604844\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −20.2404 | −1.22951 | −0.614757 | − | 0.788716i | \(-0.710746\pi\) | ||||
−0.614757 | + | 0.788716i | \(0.710746\pi\) | |||||||
\(272\) | −2.17332 | −0.131777 | ||||||||
\(273\) | −6.11131 | −0.369873 | ||||||||
\(274\) | 34.5302 | 2.08604 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −28.0674 | −1.68946 | ||||||||
\(277\) | 23.2449 | 1.39665 | 0.698324 | − | 0.715782i | \(-0.253930\pi\) | ||||
0.698324 | + | 0.715782i | \(0.253930\pi\) | |||||||
\(278\) | 0.948982 | 0.0569162 | ||||||||
\(279\) | −7.48104 | −0.447878 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 31.5740 | 1.88355 | 0.941773 | − | 0.336249i | \(-0.109158\pi\) | ||||
0.941773 | + | 0.336249i | \(0.109158\pi\) | |||||||
\(282\) | −2.38580 | −0.142072 | ||||||||
\(283\) | 8.21270 | 0.488194 | 0.244097 | − | 0.969751i | \(-0.421508\pi\) | ||||
0.244097 | + | 0.969751i | \(0.421508\pi\) | |||||||
\(284\) | −27.4287 | −1.62760 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 32.8562 | 1.94283 | ||||||||
\(287\) | −1.02390 | −0.0604391 | ||||||||
\(288\) | −2.71257 | −0.159840 | ||||||||
\(289\) | −16.0646 | −0.944978 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −6.63229 | −0.388792 | ||||||||
\(292\) | 19.1373 | 1.11992 | ||||||||
\(293\) | 30.4424 | 1.77847 | 0.889233 | − | 0.457454i | \(-0.151239\pi\) | ||||
0.889233 | + | 0.457454i | \(0.151239\pi\) | |||||||
\(294\) | 13.3088 | 0.776184 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 33.7207 | 1.95997 | ||||||||
\(297\) | 2.68688 | 0.155909 | ||||||||
\(298\) | 25.2743 | 1.46410 | ||||||||
\(299\) | −38.9645 | −2.25337 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 7.98468 | 0.460229 | ||||||||
\(302\) | 39.9012 | 2.29606 | ||||||||
\(303\) | −12.1860 | −0.700065 | ||||||||
\(304\) | 4.21250 | 0.241604 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −2.30743 | −0.131907 | ||||||||
\(307\) | −9.63268 | −0.549766 | −0.274883 | − | 0.961478i | \(-0.588639\pi\) | ||||
−0.274883 | + | 0.961478i | \(0.588639\pi\) | |||||||
\(308\) | 11.8281 | 0.673970 | ||||||||
\(309\) | −3.37168 | −0.191808 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 9.90510 | 0.561667 | 0.280833 | − | 0.959757i | \(-0.409389\pi\) | ||||
0.280833 | + | 0.959757i | \(0.409389\pi\) | |||||||
\(312\) | 20.6910 | 1.17140 | ||||||||
\(313\) | −28.5259 | −1.61238 | −0.806190 | − | 0.591657i | \(-0.798474\pi\) | ||||
−0.806190 | + | 0.591657i | \(0.798474\pi\) | |||||||
\(314\) | −37.5257 | −2.11770 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 36.2067 | 2.03679 | ||||||||
\(317\) | 4.98153 | 0.279790 | 0.139895 | − | 0.990166i | \(-0.455323\pi\) | ||||
0.139895 | + | 0.990166i | \(0.455323\pi\) | |||||||
\(318\) | 20.0896 | 1.12657 | ||||||||
\(319\) | 25.0812 | 1.40428 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −11.7874 | −0.657908 | ||||||||
\(322\) | −21.6256 | −1.20515 | ||||||||
\(323\) | −1.81302 | −0.100879 | ||||||||
\(324\) | 3.69205 | 0.205114 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −27.0482 | −1.49806 | ||||||||
\(327\) | −3.50151 | −0.193634 | ||||||||
\(328\) | 3.46663 | 0.191412 | ||||||||
\(329\) | −1.19234 | −0.0657358 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 12.8791 | 0.707899 | 0.353949 | − | 0.935265i | \(-0.384839\pi\) | ||||
0.353949 | + | 0.935265i | \(0.384839\pi\) | |||||||
\(332\) | −14.7925 | −0.811846 | ||||||||
\(333\) | 8.35311 | 0.457748 | ||||||||
\(334\) | 3.86473 | 0.211469 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 2.67935 | 0.146171 | ||||||||
\(337\) | −22.6261 | −1.23252 | −0.616262 | − | 0.787541i | \(-0.711354\pi\) | ||||
−0.616262 | + | 0.787541i | \(0.711354\pi\) | |||||||
\(338\) | 31.6608 | 1.72212 | ||||||||
\(339\) | −4.70984 | −0.255803 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 20.1007 | 1.08851 | ||||||||
\(342\) | 4.47244 | 0.241842 | ||||||||
\(343\) | 14.9976 | 0.809796 | ||||||||
\(344\) | −27.0337 | −1.45756 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −58.8296 | −3.16270 | ||||||||
\(347\) | 6.32410 | 0.339495 | 0.169748 | − | 0.985488i | \(-0.445705\pi\) | ||||
0.169748 | + | 0.985488i | \(0.445705\pi\) | |||||||
\(348\) | 34.4641 | 1.84747 | ||||||||
\(349\) | 0.105596 | 0.00565243 | 0.00282621 | − | 0.999996i | \(-0.499100\pi\) | ||||
0.00282621 | + | 0.999996i | \(0.499100\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 5.12547 | 0.273578 | ||||||||
\(352\) | 7.28835 | 0.388470 | ||||||||
\(353\) | −6.54957 | −0.348598 | −0.174299 | − | 0.984693i | \(-0.555766\pi\) | ||||
−0.174299 | + | 0.984693i | \(0.555766\pi\) | |||||||
\(354\) | 26.7548 | 1.42200 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 3.22068 | 0.170696 | ||||||||
\(357\) | −1.15317 | −0.0610322 | ||||||||
\(358\) | −5.06923 | −0.267917 | ||||||||
\(359\) | −19.0004 | −1.00280 | −0.501402 | − | 0.865214i | \(-0.667182\pi\) | ||||
−0.501402 | + | 0.865214i | \(0.667182\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −15.4858 | −0.815045 | ||||||||
\(362\) | 1.05735 | 0.0555729 | ||||||||
\(363\) | 3.78067 | 0.198434 | ||||||||
\(364\) | 22.5633 | 1.18264 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 25.6882 | 1.34275 | ||||||||
\(367\) | 2.42929 | 0.126808 | 0.0634038 | − | 0.997988i | \(-0.479804\pi\) | ||||
0.0634038 | + | 0.997988i | \(0.479804\pi\) | |||||||
\(368\) | 17.0830 | 0.890514 | ||||||||
\(369\) | 0.858735 | 0.0447040 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 10.0401 | 0.521256 | ||||||||
\(372\) | 27.6204 | 1.43205 | ||||||||
\(373\) | −21.8107 | −1.12932 | −0.564659 | − | 0.825324i | \(-0.690992\pi\) | ||||
−0.564659 | + | 0.825324i | \(0.690992\pi\) | |||||||
\(374\) | 6.19978 | 0.320583 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 4.03690 | 0.208187 | ||||||||
\(377\) | 47.8446 | 2.46412 | ||||||||
\(378\) | 2.84469 | 0.146315 | ||||||||
\(379\) | −26.2597 | −1.34887 | −0.674434 | − | 0.738335i | \(-0.735612\pi\) | ||||
−0.674434 | + | 0.738335i | \(0.735612\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −1.51685 | −0.0777106 | ||||||||
\(382\) | 14.5622 | 0.745065 | ||||||||
\(383\) | 4.87094 | 0.248893 | 0.124447 | − | 0.992226i | \(-0.460284\pi\) | ||||
0.124447 | + | 0.992226i | \(0.460284\pi\) | |||||||
\(384\) | 20.7374 | 1.05825 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −9.06132 | −0.461209 | ||||||||
\(387\) | −6.69665 | −0.340410 | ||||||||
\(388\) | 24.4868 | 1.24313 | ||||||||
\(389\) | 35.6058 | 1.80529 | 0.902643 | − | 0.430389i | \(-0.141624\pi\) | ||||
0.902643 | + | 0.430389i | \(0.141624\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −7.35238 | −0.371826 | ||||||||
\(392\) | −22.5191 | −1.13739 | ||||||||
\(393\) | 19.6769 | 0.992570 | ||||||||
\(394\) | 7.77533 | 0.391715 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −9.92010 | −0.498504 | ||||||||
\(397\) | 19.4097 | 0.974146 | 0.487073 | − | 0.873361i | \(-0.338065\pi\) | ||||
0.487073 | + | 0.873361i | \(0.338065\pi\) | |||||||
\(398\) | −0.196801 | −0.00986474 | ||||||||
\(399\) | 2.23517 | 0.111898 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 2.51164 | 0.125425 | 0.0627126 | − | 0.998032i | \(-0.480025\pi\) | ||||
0.0627126 | + | 0.998032i | \(0.480025\pi\) | |||||||
\(402\) | −5.85954 | −0.292247 | ||||||||
\(403\) | 38.3439 | 1.91004 | ||||||||
\(404\) | 44.9912 | 2.23840 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 26.5542 | 1.31786 | ||||||||
\(407\) | −22.4438 | −1.11250 | ||||||||
\(408\) | 3.90428 | 0.193291 | ||||||||
\(409\) | −23.3785 | −1.15599 | −0.577996 | − | 0.816040i | \(-0.696165\pi\) | ||||
−0.577996 | + | 0.816040i | \(0.696165\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −14.4732 | −0.713910 | ||||||||
\(412\) | 12.4484 | 0.613290 | ||||||||
\(413\) | 13.3711 | 0.657949 | ||||||||
\(414\) | 18.1371 | 0.891392 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 13.9032 | 0.681660 | ||||||||
\(417\) | −0.397762 | −0.0194785 | ||||||||
\(418\) | −12.0169 | −0.587767 | ||||||||
\(419\) | −26.4200 | −1.29070 | −0.645352 | − | 0.763886i | \(-0.723289\pi\) | ||||
−0.645352 | + | 0.763886i | \(0.723289\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 7.81317 | 0.380791 | 0.190395 | − | 0.981708i | \(-0.439023\pi\) | ||||
0.190395 | + | 0.981708i | \(0.439023\pi\) | |||||||
\(422\) | −52.4208 | −2.55181 | ||||||||
\(423\) | 1.00000 | 0.0486217 | ||||||||
\(424\) | −33.9927 | −1.65083 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 17.7244 | 0.858751 | ||||||||
\(427\) | 12.8381 | 0.621278 | ||||||||
\(428\) | 43.5196 | 2.10360 | ||||||||
\(429\) | −13.7715 | −0.664896 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 14.5878 | 0.702670 | 0.351335 | − | 0.936250i | \(-0.385728\pi\) | ||||
0.351335 | + | 0.936250i | \(0.385728\pi\) | |||||||
\(432\) | −2.24714 | −0.108116 | ||||||||
\(433\) | 36.0701 | 1.73342 | 0.866708 | − | 0.498816i | \(-0.166232\pi\) | ||||
0.866708 | + | 0.498816i | \(0.166232\pi\) | |||||||
\(434\) | 21.2812 | 1.02153 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 12.9277 | 0.619127 | ||||||||
\(437\) | 14.2510 | 0.681717 | ||||||||
\(438\) | −12.3665 | −0.590894 | ||||||||
\(439\) | −30.7826 | −1.46918 | −0.734588 | − | 0.678514i | \(-0.762624\pi\) | ||||
−0.734588 | + | 0.678514i | \(0.762624\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −5.57833 | −0.265635 | ||||||||
\(442\) | 11.8266 | 0.562536 | ||||||||
\(443\) | 34.0184 | 1.61626 | 0.808132 | − | 0.589002i | \(-0.200479\pi\) | ||||
0.808132 | + | 0.589002i | \(0.200479\pi\) | |||||||
\(444\) | −30.8401 | −1.46361 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 6.64189 | 0.314502 | ||||||||
\(447\) | −10.5936 | −0.501062 | ||||||||
\(448\) | 13.0751 | 0.617741 | ||||||||
\(449\) | 0.223246 | 0.0105356 | 0.00526781 | − | 0.999986i | \(-0.498323\pi\) | ||||
0.00526781 | + | 0.999986i | \(0.498323\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −2.30732 | −0.108647 | ||||||||
\(452\) | 17.3890 | 0.817908 | ||||||||
\(453\) | −16.7245 | −0.785783 | ||||||||
\(454\) | 18.3558 | 0.861482 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −7.56760 | −0.354385 | ||||||||
\(457\) | 27.1629 | 1.27062 | 0.635312 | − | 0.772255i | \(-0.280871\pi\) | ||||
0.635312 | + | 0.772255i | \(0.280871\pi\) | |||||||
\(458\) | 9.58300 | 0.447784 | ||||||||
\(459\) | 0.967149 | 0.0451426 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −16.7028 | −0.777927 | −0.388963 | − | 0.921253i | \(-0.627167\pi\) | ||||
−0.388963 | + | 0.921253i | \(0.627167\pi\) | |||||||
\(462\) | −7.64334 | −0.355600 | ||||||||
\(463\) | 25.8498 | 1.20134 | 0.600672 | − | 0.799496i | \(-0.294900\pi\) | ||||
0.600672 | + | 0.799496i | \(0.294900\pi\) | |||||||
\(464\) | −20.9763 | −0.973801 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 25.0327 | 1.15962 | ||||||||
\(467\) | −14.8478 | −0.687074 | −0.343537 | − | 0.939139i | \(-0.611625\pi\) | ||||
−0.343537 | + | 0.939139i | \(0.611625\pi\) | |||||||
\(468\) | −18.9235 | −0.874740 | ||||||||
\(469\) | −2.92839 | −0.135220 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 15.7288 | 0.724743 | ||||||||
\(472\) | −45.2704 | −2.08374 | ||||||||
\(473\) | 17.9931 | 0.827324 | ||||||||
\(474\) | −23.3968 | −1.07465 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 4.25756 | 0.195145 | ||||||||
\(477\) | −8.42050 | −0.385548 | ||||||||
\(478\) | −65.4830 | −2.99512 | ||||||||
\(479\) | 30.8478 | 1.40947 | 0.704736 | − | 0.709469i | \(-0.251065\pi\) | ||||
0.704736 | + | 0.709469i | \(0.251065\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −42.8137 | −1.95214 | ||||||||
\(482\) | 55.4706 | 2.52662 | ||||||||
\(483\) | 9.06430 | 0.412440 | ||||||||
\(484\) | −13.9584 | −0.634474 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −2.38580 | −0.108222 | ||||||||
\(487\) | 36.9060 | 1.67237 | 0.836184 | − | 0.548449i | \(-0.184781\pi\) | ||||
0.836184 | + | 0.548449i | \(0.184781\pi\) | |||||||
\(488\) | −43.4658 | −1.96761 | ||||||||
\(489\) | 11.3372 | 0.512684 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −9.98900 | −0.450797 | −0.225399 | − | 0.974267i | \(-0.572368\pi\) | ||||
−0.225399 | + | 0.974267i | \(0.572368\pi\) | |||||||
\(492\) | −3.17049 | −0.142937 | ||||||||
\(493\) | 9.02802 | 0.406601 | ||||||||
\(494\) | −22.9234 | −1.03137 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −16.8109 | −0.754833 | ||||||||
\(497\) | 8.85805 | 0.397338 | ||||||||
\(498\) | 9.55894 | 0.428346 | ||||||||
\(499\) | −22.0497 | −0.987082 | −0.493541 | − | 0.869723i | \(-0.664298\pi\) | ||||
−0.493541 | + | 0.869723i | \(0.664298\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −1.61989 | −0.0723712 | ||||||||
\(502\) | 67.4780 | 3.01169 | ||||||||
\(503\) | −25.9351 | −1.15639 | −0.578195 | − | 0.815899i | \(-0.696243\pi\) | ||||
−0.578195 | + | 0.815899i | \(0.696243\pi\) | |||||||
\(504\) | −4.81336 | −0.214404 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −48.7324 | −2.16642 | ||||||||
\(507\) | −13.2705 | −0.589363 | ||||||||
\(508\) | 5.60029 | 0.248473 | ||||||||
\(509\) | −2.02078 | −0.0895693 | −0.0447847 | − | 0.998997i | \(-0.514260\pi\) | ||||
−0.0447847 | + | 0.998997i | \(0.514260\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −6.18034 | −0.273402 | ||||||||
\(512\) | −24.2385 | −1.07120 | ||||||||
\(513\) | −1.87461 | −0.0827659 | ||||||||
\(514\) | −13.3120 | −0.587169 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 24.7244 | 1.08843 | ||||||||
\(517\) | −2.68688 | −0.118169 | ||||||||
\(518\) | −23.7620 | −1.04404 | ||||||||
\(519\) | 24.6582 | 1.08237 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −34.5368 | −1.51308 | −0.756542 | − | 0.653945i | \(-0.773113\pi\) | ||||
−0.756542 | + | 0.653945i | \(0.773113\pi\) | |||||||
\(522\) | −22.2707 | −0.974761 | ||||||||
\(523\) | 10.4466 | 0.456796 | 0.228398 | − | 0.973568i | \(-0.426651\pi\) | ||||
0.228398 | + | 0.973568i | \(0.426651\pi\) | |||||||
\(524\) | −72.6483 | −3.17365 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −30.6881 | −1.33807 | ||||||||
\(527\) | 7.23527 | 0.315173 | ||||||||
\(528\) | 6.03780 | 0.262761 | ||||||||
\(529\) | 34.7922 | 1.51270 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −11.2142 | −0.486653 | ||||||||
\(532\) | −8.25236 | −0.357785 | ||||||||
\(533\) | −4.40143 | −0.190647 | ||||||||
\(534\) | −2.08120 | −0.0900625 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 9.91463 | 0.428247 | ||||||||
\(537\) | 2.12475 | 0.0916897 | ||||||||
\(538\) | −25.3135 | −1.09134 | ||||||||
\(539\) | 14.9883 | 0.645592 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 6.16979 | 0.265260 | 0.132630 | − | 0.991166i | \(-0.457658\pi\) | ||||
0.132630 | + | 0.991166i | \(0.457658\pi\) | |||||||
\(542\) | −48.2895 | −2.07421 | ||||||||
\(543\) | −0.443183 | −0.0190188 | ||||||||
\(544\) | 2.62346 | 0.112480 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −14.5804 | −0.623982 | ||||||||
\(547\) | 0.944715 | 0.0403931 | 0.0201965 | − | 0.999796i | \(-0.493571\pi\) | ||||
0.0201965 | + | 0.999796i | \(0.493571\pi\) | |||||||
\(548\) | 53.4357 | 2.28266 | ||||||||
\(549\) | −10.7671 | −0.459530 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −17.4988 | −0.745476 | ||||||||
\(552\) | −30.6890 | −1.30621 | ||||||||
\(553\) | −11.6929 | −0.497232 | ||||||||
\(554\) | 55.4576 | 2.35617 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 1.46856 | 0.0622808 | ||||||||
\(557\) | 11.0339 | 0.467520 | 0.233760 | − | 0.972294i | \(-0.424897\pi\) | ||||
0.233760 | + | 0.972294i | \(0.424897\pi\) | |||||||
\(558\) | −17.8483 | −0.755578 | ||||||||
\(559\) | 34.3235 | 1.45173 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −2.59861 | −0.109714 | ||||||||
\(562\) | 75.3293 | 3.17757 | ||||||||
\(563\) | 6.64368 | 0.279998 | 0.139999 | − | 0.990152i | \(-0.455290\pi\) | ||||
0.139999 | + | 0.990152i | \(0.455290\pi\) | |||||||
\(564\) | −3.69205 | −0.155463 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 19.5939 | 0.823592 | ||||||||
\(567\) | −1.19234 | −0.0500736 | ||||||||
\(568\) | −29.9906 | −1.25838 | ||||||||
\(569\) | 0.879548 | 0.0368726 | 0.0184363 | − | 0.999830i | \(-0.494131\pi\) | ||||
0.0184363 | + | 0.999830i | \(0.494131\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −7.30539 | −0.305721 | −0.152860 | − | 0.988248i | \(-0.548849\pi\) | ||||
−0.152860 | + | 0.988248i | \(0.548849\pi\) | |||||||
\(572\) | 50.8452 | 2.12595 | ||||||||
\(573\) | −6.10367 | −0.254985 | ||||||||
\(574\) | −2.44283 | −0.101962 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −10.9659 | −0.456914 | ||||||||
\(577\) | 12.0868 | 0.503179 | 0.251589 | − | 0.967834i | \(-0.419047\pi\) | ||||
0.251589 | + | 0.967834i | \(0.419047\pi\) | |||||||
\(578\) | −38.3270 | −1.59419 | ||||||||
\(579\) | 3.79802 | 0.157840 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 4.77722 | 0.198192 | ||||||||
\(582\) | −15.8233 | −0.655898 | ||||||||
\(583\) | 22.6249 | 0.937027 | ||||||||
\(584\) | 20.9247 | 0.865872 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 72.6296 | 3.00030 | ||||||||
\(587\) | −41.5536 | −1.71510 | −0.857551 | − | 0.514399i | \(-0.828015\pi\) | ||||
−0.857551 | + | 0.514399i | \(0.828015\pi\) | |||||||
\(588\) | 20.5955 | 0.849343 | ||||||||
\(589\) | −14.0240 | −0.577849 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −3.25900 | −0.134057 | ||||||||
\(592\) | 18.7706 | 0.771467 | ||||||||
\(593\) | 36.4434 | 1.49655 | 0.748276 | − | 0.663388i | \(-0.230882\pi\) | ||||
0.748276 | + | 0.663388i | \(0.230882\pi\) | |||||||
\(594\) | 6.41037 | 0.263021 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 39.1122 | 1.60210 | ||||||||
\(597\) | 0.0824884 | 0.00337602 | ||||||||
\(598\) | −92.9615 | −3.80148 | ||||||||
\(599\) | −43.0297 | −1.75815 | −0.879073 | − | 0.476688i | \(-0.841837\pi\) | ||||
−0.879073 | + | 0.476688i | \(0.841837\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 26.1555 | 1.06690 | 0.533452 | − | 0.845830i | \(-0.320894\pi\) | ||||
0.533452 | + | 0.845830i | \(0.320894\pi\) | |||||||
\(602\) | 19.0499 | 0.776415 | ||||||||
\(603\) | 2.45600 | 0.100016 | ||||||||
\(604\) | 61.7475 | 2.51247 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −29.0733 | −1.18102 | ||||||||
\(607\) | −14.2392 | −0.577953 | −0.288976 | − | 0.957336i | \(-0.593315\pi\) | ||||
−0.288976 | + | 0.957336i | \(0.593315\pi\) | |||||||
\(608\) | −5.08500 | −0.206224 | ||||||||
\(609\) | −11.1301 | −0.451014 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −5.12547 | −0.207355 | ||||||||
\(612\) | −3.57076 | −0.144340 | ||||||||
\(613\) | −9.75780 | −0.394114 | −0.197057 | − | 0.980392i | \(-0.563138\pi\) | ||||
−0.197057 | + | 0.980392i | \(0.563138\pi\) | |||||||
\(614\) | −22.9817 | −0.927465 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 12.9329 | 0.521082 | ||||||||
\(617\) | −36.3651 | −1.46400 | −0.732002 | − | 0.681303i | \(-0.761414\pi\) | ||||
−0.732002 | + | 0.681303i | \(0.761414\pi\) | |||||||
\(618\) | −8.04417 | −0.323584 | ||||||||
\(619\) | 0.982621 | 0.0394949 | 0.0197474 | − | 0.999805i | \(-0.493714\pi\) | ||||
0.0197474 | + | 0.999805i | \(0.493714\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −7.60212 | −0.305062 | ||||||||
\(622\) | 23.6316 | 0.947541 | ||||||||
\(623\) | −1.04011 | −0.0416712 | ||||||||
\(624\) | 11.5177 | 0.461075 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −68.0572 | −2.72011 | ||||||||
\(627\) | 5.03685 | 0.201152 | ||||||||
\(628\) | −58.0714 | −2.31730 | ||||||||
\(629\) | −8.07870 | −0.322119 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −20.4904 | −0.815709 | −0.407855 | − | 0.913047i | \(-0.633723\pi\) | ||||
−0.407855 | + | 0.913047i | \(0.633723\pi\) | |||||||
\(632\) | 39.5886 | 1.57475 | ||||||||
\(633\) | 21.9720 | 0.873308 | ||||||||
\(634\) | 11.8849 | 0.472011 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 31.0889 | 1.23276 | ||||||||
\(637\) | 28.5916 | 1.13284 | ||||||||
\(638\) | 59.8387 | 2.36904 | ||||||||
\(639\) | −7.42913 | −0.293892 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 19.9400 | 0.787585 | 0.393792 | − | 0.919199i | \(-0.371163\pi\) | ||||
0.393792 | + | 0.919199i | \(0.371163\pi\) | |||||||
\(642\) | −28.1224 | −1.10990 | ||||||||
\(643\) | −50.4839 | −1.99089 | −0.995446 | − | 0.0953270i | \(-0.969610\pi\) | ||||
−0.995446 | + | 0.0953270i | \(0.969610\pi\) | |||||||
\(644\) | −33.4659 | −1.31874 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −4.32552 | −0.170185 | ||||||||
\(647\) | −23.8703 | −0.938438 | −0.469219 | − | 0.883082i | \(-0.655464\pi\) | ||||
−0.469219 | + | 0.883082i | \(0.655464\pi\) | |||||||
\(648\) | 4.03690 | 0.158584 | ||||||||
\(649\) | 30.1311 | 1.18275 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −8.91994 | −0.349600 | ||||||||
\(652\) | −41.8574 | −1.63926 | ||||||||
\(653\) | 20.3088 | 0.794746 | 0.397373 | − | 0.917657i | \(-0.369922\pi\) | ||||
0.397373 | + | 0.917657i | \(0.369922\pi\) | |||||||
\(654\) | −8.35390 | −0.326663 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 1.92970 | 0.0753420 | ||||||||
\(657\) | 5.18337 | 0.202222 | ||||||||
\(658\) | −2.84469 | −0.110897 | ||||||||
\(659\) | 32.5448 | 1.26777 | 0.633883 | − | 0.773429i | \(-0.281460\pi\) | ||||
0.633883 | + | 0.773429i | \(0.281460\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 10.8368 | 0.421504 | 0.210752 | − | 0.977540i | \(-0.432409\pi\) | ||||
0.210752 | + | 0.977540i | \(0.432409\pi\) | |||||||
\(662\) | 30.7270 | 1.19424 | ||||||||
\(663\) | −4.95710 | −0.192518 | ||||||||
\(664\) | −16.1742 | −0.627681 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 19.9289 | 0.772228 | ||||||||
\(667\) | −70.9633 | −2.74771 | ||||||||
\(668\) | 5.98071 | 0.231401 | ||||||||
\(669\) | −2.78392 | −0.107633 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 28.9300 | 1.11683 | ||||||||
\(672\) | −3.23430 | −0.124766 | ||||||||
\(673\) | 21.4323 | 0.826156 | 0.413078 | − | 0.910696i | \(-0.364454\pi\) | ||||
0.413078 | + | 0.910696i | \(0.364454\pi\) | |||||||
\(674\) | −53.9815 | −2.07929 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 48.9953 | 1.88444 | ||||||||
\(677\) | −2.47078 | −0.0949597 | −0.0474799 | − | 0.998872i | \(-0.515119\pi\) | ||||
−0.0474799 | + | 0.998872i | \(0.515119\pi\) | |||||||
\(678\) | −11.2367 | −0.431544 | ||||||||
\(679\) | −7.90794 | −0.303479 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −7.69378 | −0.294826 | ||||||||
\(682\) | 47.9562 | 1.83634 | ||||||||
\(683\) | −35.0933 | −1.34281 | −0.671403 | − | 0.741092i | \(-0.734308\pi\) | ||||
−0.671403 | + | 0.741092i | \(0.734308\pi\) | |||||||
\(684\) | 6.92114 | 0.264637 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 35.7814 | 1.36614 | ||||||||
\(687\) | −4.01668 | −0.153246 | ||||||||
\(688\) | −15.0483 | −0.573711 | ||||||||
\(689\) | 43.1590 | 1.64423 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −30.0956 | −1.14489 | −0.572445 | − | 0.819943i | \(-0.694005\pi\) | ||||
−0.572445 | + | 0.819943i | \(0.694005\pi\) | |||||||
\(692\) | −91.0393 | −3.46080 | ||||||||
\(693\) | 3.20368 | 0.121698 | ||||||||
\(694\) | 15.0881 | 0.572735 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 37.6831 | 1.42838 | ||||||||
\(697\) | −0.830525 | −0.0314584 | ||||||||
\(698\) | 0.251931 | 0.00953574 | ||||||||
\(699\) | −10.4924 | −0.396857 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 42.6929 | 1.61249 | 0.806244 | − | 0.591583i | \(-0.201497\pi\) | ||||
0.806244 | + | 0.591583i | \(0.201497\pi\) | |||||||
\(702\) | 12.2284 | 0.461530 | ||||||||
\(703\) | 15.6588 | 0.590583 | ||||||||
\(704\) | 29.4642 | 1.11047 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −15.6260 | −0.588091 | ||||||||
\(707\) | −14.5298 | −0.546450 | ||||||||
\(708\) | 41.4033 | 1.55603 | ||||||||
\(709\) | 14.9760 | 0.562434 | 0.281217 | − | 0.959644i | \(-0.409262\pi\) | ||||
0.281217 | + | 0.959644i | \(0.409262\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 9.80667 | 0.367779 | ||||||||
\(712\) | 3.52150 | 0.131974 | ||||||||
\(713\) | −56.8717 | −2.12986 | ||||||||
\(714\) | −2.75123 | −0.102962 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −7.84468 | −0.293169 | ||||||||
\(717\) | 27.4470 | 1.02503 | ||||||||
\(718\) | −45.3313 | −1.69175 | ||||||||
\(719\) | −16.9803 | −0.633257 | −0.316629 | − | 0.948550i | \(-0.602551\pi\) | ||||
−0.316629 | + | 0.948550i | \(0.602551\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −4.02019 | −0.149720 | ||||||||
\(722\) | −36.9462 | −1.37499 | ||||||||
\(723\) | −23.2503 | −0.864687 | ||||||||
\(724\) | 1.63625 | 0.0608109 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 9.01993 | 0.334761 | ||||||||
\(727\) | −21.1613 | −0.784828 | −0.392414 | − | 0.919789i | \(-0.628360\pi\) | ||||
−0.392414 | + | 0.919789i | \(0.628360\pi\) | |||||||
\(728\) | 24.6707 | 0.914358 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 6.47665 | 0.239548 | ||||||||
\(732\) | 39.7528 | 1.46931 | ||||||||
\(733\) | −17.7710 | −0.656387 | −0.328194 | − | 0.944611i | \(-0.606440\pi\) | ||||
−0.328194 | + | 0.944611i | \(0.606440\pi\) | |||||||
\(734\) | 5.79579 | 0.213927 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −20.6213 | −0.760110 | ||||||||
\(737\) | −6.59899 | −0.243077 | ||||||||
\(738\) | 2.04877 | 0.0754163 | ||||||||
\(739\) | −7.02220 | −0.258316 | −0.129158 | − | 0.991624i | \(-0.541227\pi\) | ||||
−0.129158 | + | 0.991624i | \(0.541227\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 9.60825 | 0.352968 | ||||||||
\(742\) | 23.9537 | 0.879367 | ||||||||
\(743\) | 11.4581 | 0.420358 | 0.210179 | − | 0.977663i | \(-0.432595\pi\) | ||||
0.210179 | + | 0.977663i | \(0.432595\pi\) | |||||||
\(744\) | 30.2002 | 1.10719 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −52.0361 | −1.90518 | ||||||||
\(747\) | −4.00659 | −0.146594 | ||||||||
\(748\) | 9.59421 | 0.350799 | ||||||||
\(749\) | −14.0546 | −0.513543 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −20.7268 | −0.756332 | −0.378166 | − | 0.925738i | \(-0.623445\pi\) | ||||
−0.378166 | + | 0.925738i | \(0.623445\pi\) | |||||||
\(752\) | 2.24714 | 0.0819447 | ||||||||
\(753\) | −28.2831 | −1.03070 | ||||||||
\(754\) | 114.148 | 4.15702 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 4.40218 | 0.160106 | ||||||||
\(757\) | −10.9366 | −0.397498 | −0.198749 | − | 0.980050i | \(-0.563688\pi\) | ||||
−0.198749 | + | 0.980050i | \(0.563688\pi\) | |||||||
\(758\) | −62.6504 | −2.27556 | ||||||||
\(759\) | 20.4260 | 0.741416 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 6.68955 | 0.242496 | 0.121248 | − | 0.992622i | \(-0.461310\pi\) | ||||
0.121248 | + | 0.992622i | \(0.461310\pi\) | |||||||
\(762\) | −3.61891 | −0.131099 | ||||||||
\(763\) | −4.17499 | −0.151145 | ||||||||
\(764\) | 22.5351 | 0.815290 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 11.6211 | 0.419887 | ||||||||
\(767\) | 57.4779 | 2.07541 | ||||||||
\(768\) | 27.5435 | 0.993889 | ||||||||
\(769\) | −29.7060 | −1.07122 | −0.535612 | − | 0.844464i | \(-0.679919\pi\) | ||||
−0.535612 | + | 0.844464i | \(0.679919\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 5.57969 | 0.200948 | ||||||||
\(772\) | −14.0225 | −0.504680 | ||||||||
\(773\) | −50.0327 | −1.79955 | −0.899775 | − | 0.436354i | \(-0.856269\pi\) | ||||
−0.899775 | + | 0.436354i | \(0.856269\pi\) | |||||||
\(774\) | −15.9769 | −0.574277 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 26.7739 | 0.961127 | ||||||||
\(777\) | 9.95975 | 0.357304 | ||||||||
\(778\) | 84.9484 | 3.04555 | ||||||||
\(779\) | 1.60979 | 0.0576767 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 19.9612 | 0.714267 | ||||||||
\(782\) | −17.5413 | −0.627276 | ||||||||
\(783\) | 9.33467 | 0.333594 | ||||||||
\(784\) | −12.5353 | −0.447688 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 46.9453 | 1.67448 | ||||||||
\(787\) | −55.2085 | −1.96797 | −0.983985 | − | 0.178253i | \(-0.942956\pi\) | ||||
−0.983985 | + | 0.178253i | \(0.942956\pi\) | |||||||
\(788\) | 12.0324 | 0.428636 | ||||||||
\(789\) | 12.8628 | 0.457929 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −5.61573 | −0.199672 | ||||||||
\(792\) | −10.8467 | −0.385420 | ||||||||
\(793\) | 55.1867 | 1.95974 | ||||||||
\(794\) | 46.3078 | 1.64340 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −0.304551 | −0.0107945 | ||||||||
\(797\) | 9.23096 | 0.326977 | 0.163489 | − | 0.986545i | \(-0.447725\pi\) | ||||
0.163489 | + | 0.986545i | \(0.447725\pi\) | |||||||
\(798\) | 5.33267 | 0.188774 | ||||||||
\(799\) | −0.967149 | −0.0342153 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0.872329 | 0.0308222 | ||||||||
\(802\) | 5.99227 | 0.211594 | ||||||||
\(803\) | −13.9271 | −0.491477 | ||||||||
\(804\) | −9.06769 | −0.319793 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 91.4809 | 3.22228 | ||||||||
\(807\) | 10.6101 | 0.373492 | ||||||||
\(808\) | 49.1935 | 1.73062 | ||||||||
\(809\) | 21.2914 | 0.748566 | 0.374283 | − | 0.927314i | \(-0.377889\pi\) | ||||
0.374283 | + | 0.927314i | \(0.377889\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −44.5854 | −1.56560 | −0.782802 | − | 0.622270i | \(-0.786210\pi\) | ||||
−0.782802 | + | 0.622270i | \(0.786210\pi\) | |||||||
\(812\) | 41.0929 | 1.44208 | ||||||||
\(813\) | 20.2404 | 0.709861 | ||||||||
\(814\) | −53.5465 | −1.87680 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 2.17332 | 0.0760813 | ||||||||
\(817\) | −12.5536 | −0.439194 | ||||||||
\(818\) | −55.7764 | −1.95018 | ||||||||
\(819\) | 6.11131 | 0.213546 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −35.6050 | −1.24262 | −0.621312 | − | 0.783563i | \(-0.713400\pi\) | ||||
−0.621312 | + | 0.783563i | \(0.713400\pi\) | |||||||
\(822\) | −34.5302 | −1.20438 | ||||||||
\(823\) | −10.7836 | −0.375892 | −0.187946 | − | 0.982179i | \(-0.560183\pi\) | ||||
−0.187946 | + | 0.982179i | \(0.560183\pi\) | |||||||
\(824\) | 13.6111 | 0.474167 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 31.9008 | 1.10997 | ||||||||
\(827\) | 32.9146 | 1.14455 | 0.572277 | − | 0.820061i | \(-0.306060\pi\) | ||||
0.572277 | + | 0.820061i | \(0.306060\pi\) | |||||||
\(828\) | 28.0674 | 0.975410 | ||||||||
\(829\) | −25.8865 | −0.899074 | −0.449537 | − | 0.893262i | \(-0.648411\pi\) | ||||
−0.449537 | + | 0.893262i | \(0.648411\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −23.2449 | −0.806355 | ||||||||
\(832\) | 56.2056 | 1.94858 | ||||||||
\(833\) | 5.39507 | 0.186928 | ||||||||
\(834\) | −0.948982 | −0.0328606 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −18.5963 | −0.643166 | ||||||||
\(837\) | 7.48104 | 0.258582 | ||||||||
\(838\) | −63.0330 | −2.17744 | ||||||||
\(839\) | 28.2987 | 0.976980 | 0.488490 | − | 0.872569i | \(-0.337548\pi\) | ||||
0.488490 | + | 0.872569i | \(0.337548\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 58.1361 | 2.00469 | ||||||||
\(842\) | 18.6407 | 0.642400 | ||||||||
\(843\) | −31.5740 | −1.08747 | ||||||||
\(844\) | −81.1217 | −2.79232 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 2.38580 | 0.0820256 | ||||||||
\(847\) | 4.50784 | 0.154891 | ||||||||
\(848\) | −18.9220 | −0.649785 | ||||||||
\(849\) | −8.21270 | −0.281859 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 63.5013 | 2.17680 | ||||||||
\(852\) | 27.4287 | 0.939693 | ||||||||
\(853\) | −14.7962 | −0.506614 | −0.253307 | − | 0.967386i | \(-0.581518\pi\) | ||||
−0.253307 | + | 0.967386i | \(0.581518\pi\) | |||||||
\(854\) | 30.6291 | 1.04811 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 47.5845 | 1.62640 | ||||||||
\(857\) | 2.96468 | 0.101272 | 0.0506358 | − | 0.998717i | \(-0.483875\pi\) | ||||
0.0506358 | + | 0.998717i | \(0.483875\pi\) | |||||||
\(858\) | −32.8562 | −1.12169 | ||||||||
\(859\) | 31.3340 | 1.06910 | 0.534551 | − | 0.845136i | \(-0.320481\pi\) | ||||
0.534551 | + | 0.845136i | \(0.320481\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 1.02390 | 0.0348946 | ||||||||
\(862\) | 34.8036 | 1.18542 | ||||||||
\(863\) | −12.6764 | −0.431509 | −0.215755 | − | 0.976448i | \(-0.569221\pi\) | ||||
−0.215755 | + | 0.976448i | \(0.569221\pi\) | |||||||
\(864\) | 2.71257 | 0.0922834 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 86.0560 | 2.92430 | ||||||||
\(867\) | 16.0646 | 0.545583 | ||||||||
\(868\) | 32.9329 | 1.11781 | ||||||||
\(869\) | −26.3494 | −0.893841 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −12.5882 | −0.426534 | ||||||||
\(872\) | 14.1352 | 0.478679 | ||||||||
\(873\) | 6.63229 | 0.224469 | ||||||||
\(874\) | 34.0000 | 1.15007 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −19.1373 | −0.646588 | ||||||||
\(877\) | 27.3080 | 0.922125 | 0.461063 | − | 0.887368i | \(-0.347468\pi\) | ||||
0.461063 | + | 0.887368i | \(0.347468\pi\) | |||||||
\(878\) | −73.4413 | −2.47852 | ||||||||
\(879\) | −30.4424 | −1.02680 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −48.1526 | −1.62230 | −0.811151 | − | 0.584836i | \(-0.801159\pi\) | ||||
−0.811151 | + | 0.584836i | \(0.801159\pi\) | |||||||
\(882\) | −13.3088 | −0.448130 | ||||||||
\(883\) | −37.5633 | −1.26411 | −0.632053 | − | 0.774925i | \(-0.717787\pi\) | ||||
−0.632053 | + | 0.774925i | \(0.717787\pi\) | |||||||
\(884\) | 18.3019 | 0.615558 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 81.1612 | 2.72666 | ||||||||
\(887\) | −53.6172 | −1.80029 | −0.900144 | − | 0.435592i | \(-0.856539\pi\) | ||||
−0.900144 | + | 0.435592i | \(0.856539\pi\) | |||||||
\(888\) | −33.7207 | −1.13159 | ||||||||
\(889\) | −1.80860 | −0.0606585 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −2.68688 | −0.0900139 | ||||||||
\(892\) | 10.2784 | 0.344146 | ||||||||
\(893\) | 1.87461 | 0.0627313 | ||||||||
\(894\) | −25.2743 | −0.845299 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 24.7260 | 0.826039 | ||||||||
\(897\) | 38.9645 | 1.30099 | ||||||||
\(898\) | 0.532621 | 0.0177738 | ||||||||
\(899\) | 69.8330 | 2.32906 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 8.14387 | 0.271312 | ||||||||
\(902\) | −5.50481 | −0.183290 | ||||||||
\(903\) | −7.98468 | −0.265714 | ||||||||
\(904\) | 19.0131 | 0.632368 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −39.9012 | −1.32563 | ||||||||
\(907\) | −31.6933 | −1.05236 | −0.526180 | − | 0.850373i | \(-0.676376\pi\) | ||||
−0.526180 | + | 0.850373i | \(0.676376\pi\) | |||||||
\(908\) | 28.4058 | 0.942681 | ||||||||
\(909\) | 12.1860 | 0.404183 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 13.9704 | 0.462859 | 0.231429 | − | 0.972852i | \(-0.425660\pi\) | ||||
0.231429 | + | 0.972852i | \(0.425660\pi\) | |||||||
\(912\) | −4.21250 | −0.139490 | ||||||||
\(913\) | 10.7652 | 0.356277 | ||||||||
\(914\) | 64.8052 | 2.14357 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 14.8298 | 0.489990 | ||||||||
\(917\) | 23.4616 | 0.774770 | ||||||||
\(918\) | 2.30743 | 0.0761564 | ||||||||
\(919\) | −34.9368 | −1.15246 | −0.576229 | − | 0.817288i | \(-0.695477\pi\) | ||||
−0.576229 | + | 0.817288i | \(0.695477\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 9.63268 | 0.317408 | ||||||||
\(922\) | −39.8496 | −1.31238 | ||||||||
\(923\) | 38.0778 | 1.25335 | ||||||||
\(924\) | −11.8281 | −0.389117 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 61.6726 | 2.02669 | ||||||||
\(927\) | 3.37168 | 0.110741 | ||||||||
\(928\) | 25.3209 | 0.831201 | ||||||||
\(929\) | 25.4857 | 0.836157 | 0.418079 | − | 0.908411i | \(-0.362704\pi\) | ||||
0.418079 | + | 0.908411i | \(0.362704\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −10.4572 | −0.342720 | ||||||||
\(932\) | 38.7383 | 1.26892 | ||||||||
\(933\) | −9.90510 | −0.324278 | ||||||||
\(934\) | −35.4239 | −1.15911 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −20.6910 | −0.676307 | ||||||||
\(937\) | −12.1188 | −0.395904 | −0.197952 | − | 0.980212i | \(-0.563429\pi\) | ||||
−0.197952 | + | 0.980212i | \(0.563429\pi\) | |||||||
\(938\) | −6.98656 | −0.228119 | ||||||||
\(939\) | 28.5259 | 0.930908 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 14.9260 | 0.486573 | 0.243286 | − | 0.969955i | \(-0.421775\pi\) | ||||
0.243286 | + | 0.969955i | \(0.421775\pi\) | |||||||
\(942\) | 37.5257 | 1.22265 | ||||||||
\(943\) | 6.52820 | 0.212588 | ||||||||
\(944\) | −25.1998 | −0.820183 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 42.9280 | 1.39571 | ||||||||
\(947\) | 10.8787 | 0.353509 | 0.176755 | − | 0.984255i | \(-0.443440\pi\) | ||||
0.176755 | + | 0.984255i | \(0.443440\pi\) | |||||||
\(948\) | −36.2067 | −1.17594 | ||||||||
\(949\) | −26.5672 | −0.862409 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −4.98153 | −0.161537 | ||||||||
\(952\) | 4.65523 | 0.150877 | ||||||||
\(953\) | 40.6292 | 1.31611 | 0.658054 | − | 0.752970i | \(-0.271380\pi\) | ||||
0.658054 | + | 0.752970i | \(0.271380\pi\) | |||||||
\(954\) | −20.0896 | −0.650426 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −101.336 | −3.27743 | ||||||||
\(957\) | −25.0812 | −0.810759 | ||||||||
\(958\) | 73.5968 | 2.37780 | ||||||||
\(959\) | −17.2570 | −0.557256 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 24.9659 | 0.805352 | ||||||||
\(962\) | −102.145 | −3.29329 | ||||||||
\(963\) | 11.7874 | 0.379843 | ||||||||
\(964\) | 85.8412 | 2.76476 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 21.6256 | 0.695793 | ||||||||
\(967\) | 8.36117 | 0.268877 | 0.134438 | − | 0.990922i | \(-0.457077\pi\) | ||||
0.134438 | + | 0.990922i | \(0.457077\pi\) | |||||||
\(968\) | −15.2622 | −0.490545 | ||||||||
\(969\) | 1.81302 | 0.0582427 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −18.4198 | −0.591120 | −0.295560 | − | 0.955324i | \(-0.595506\pi\) | ||||
−0.295560 | + | 0.955324i | \(0.595506\pi\) | |||||||
\(972\) | −3.69205 | −0.118423 | ||||||||
\(973\) | −0.474268 | −0.0152043 | ||||||||
\(974\) | 88.0503 | 2.82131 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −24.1952 | −0.774471 | ||||||||
\(977\) | 0.448275 | 0.0143416 | 0.00717080 | − | 0.999974i | \(-0.497717\pi\) | ||||
0.00717080 | + | 0.999974i | \(0.497717\pi\) | |||||||
\(978\) | 27.0482 | 0.864907 | ||||||||
\(979\) | −2.34384 | −0.0749096 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 3.50151 | 0.111795 | ||||||||
\(982\) | −23.8318 | −0.760503 | ||||||||
\(983\) | −40.7150 | −1.29861 | −0.649303 | − | 0.760529i | \(-0.724939\pi\) | ||||
−0.649303 | + | 0.760529i | \(0.724939\pi\) | |||||||
\(984\) | −3.46663 | −0.110512 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 21.5391 | 0.685943 | ||||||||
\(987\) | 1.19234 | 0.0379526 | ||||||||
\(988\) | −35.4742 | −1.12858 | ||||||||
\(989\) | −50.9087 | −1.61880 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −7.49645 | −0.238133 | −0.119066 | − | 0.992886i | \(-0.537990\pi\) | ||||
−0.119066 | + | 0.992886i | \(0.537990\pi\) | |||||||
\(992\) | 20.2928 | 0.644298 | ||||||||
\(993\) | −12.8791 | −0.408705 | ||||||||
\(994\) | 21.1335 | 0.670315 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 14.7925 | 0.468720 | ||||||||
\(997\) | −33.1196 | −1.04891 | −0.524455 | − | 0.851438i | \(-0.675731\pi\) | ||||
−0.524455 | + | 0.851438i | \(0.675731\pi\) | |||||||
\(998\) | −52.6063 | −1.66522 | ||||||||
\(999\) | −8.35311 | −0.264281 |
(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 | 3525.2.a.bg.1.9 | 10 | ||
5.2 | odd | 4 | 705.2.c.b.424.19 | yes | 20 | ||
5.3 | odd | 4 | 705.2.c.b.424.2 | ✓ | 20 | ||
5.4 | even | 2 | 3525.2.a.bf.1.2 | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
705.2.c.b.424.2 | ✓ | 20 | 5.3 | odd | 4 | ||
705.2.c.b.424.19 | yes | 20 | 5.2 | odd | 4 | ||
3525.2.a.bf.1.2 | 10 | 5.4 | even | 2 | |||
3525.2.a.bg.1.9 | 10 | 1.1 | even | 1 | trivial |