Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8004,2,Mod(1,8004)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8004, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("8004.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8004 = 2^{2} \cdot 3 \cdot 23 \cdot 29 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8004.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: | \(63.9122617778\) |
Analytic rank: | \(1\) |
Dimension: | \(9\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{9} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{9} - 3x^{8} - 13x^{7} + 32x^{6} + 40x^{5} - 79x^{4} - 39x^{3} + 58x^{2} + 9x - 11 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{17}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-1.47135\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8004.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −3.48372 | −1.55797 | −0.778985 | − | 0.627043i | \(-0.784265\pi\) | ||||
−0.778985 | + | 0.627043i | \(0.784265\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.18462 | 0.825710 | 0.412855 | − | 0.910797i | \(-0.364532\pi\) | ||||
0.412855 | + | 0.910797i | \(0.364532\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −4.51219 | −1.36048 | −0.680239 | − | 0.732990i | \(-0.738124\pi\) | ||||
−0.680239 | + | 0.732990i | \(0.738124\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 4.71609 | 1.30801 | 0.654004 | − | 0.756491i | \(-0.273088\pi\) | ||||
0.654004 | + | 0.756491i | \(0.273088\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 3.48372 | 0.899494 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −4.53301 | −1.09942 | −0.549708 | − | 0.835357i | \(-0.685261\pi\) | ||||
−0.549708 | + | 0.835357i | \(0.685261\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.79821 | −0.412538 | −0.206269 | − | 0.978495i | \(-0.566132\pi\) | ||||
−0.206269 | + | 0.978495i | \(0.566132\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −2.18462 | −0.476724 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −1.00000 | −0.208514 | ||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 7.13634 | 1.42727 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1.00000 | 0.185695 | ||||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 5.46631 | 0.981778 | 0.490889 | − | 0.871222i | \(-0.336672\pi\) | ||||
0.490889 | + | 0.871222i | \(0.336672\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 4.51219 | 0.785472 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −7.61063 | −1.28643 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 2.75195 | 0.452418 | 0.226209 | − | 0.974079i | \(-0.427367\pi\) | ||||
0.226209 | + | 0.974079i | \(0.427367\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −4.71609 | −0.755179 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0.252352 | 0.0394108 | 0.0197054 | − | 0.999806i | \(-0.493727\pi\) | ||||
0.0197054 | + | 0.999806i | \(0.493727\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 5.62492 | 0.857792 | 0.428896 | − | 0.903354i | \(-0.358903\pi\) | ||||
0.428896 | + | 0.903354i | \(0.358903\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −3.48372 | −0.519323 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 2.83786 | 0.413945 | 0.206972 | − | 0.978347i | \(-0.433639\pi\) | ||||
0.206972 | + | 0.978347i | \(0.433639\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −2.22742 | −0.318203 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 4.53301 | 0.634748 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −4.43857 | −0.609685 | −0.304842 | − | 0.952403i | \(-0.598604\pi\) | ||||
−0.304842 | + | 0.952403i | \(0.598604\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 15.7192 | 2.11958 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 1.79821 | 0.238179 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 4.10392 | 0.534285 | 0.267142 | − | 0.963657i | \(-0.413921\pi\) | ||||
0.267142 | + | 0.963657i | \(0.413921\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −0.160730 | −0.0205793 | −0.0102897 | − | 0.999947i | \(-0.503275\pi\) | ||||
−0.0102897 | + | 0.999947i | \(0.503275\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 2.18462 | 0.275237 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −16.4296 | −2.03784 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −3.72772 | −0.455413 | −0.227706 | − | 0.973730i | \(-0.573123\pi\) | ||||
−0.227706 | + | 0.973730i | \(0.573123\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 1.00000 | 0.120386 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −0.134204 | −0.0159271 | −0.00796356 | − | 0.999968i | \(-0.502535\pi\) | ||||
−0.00796356 | + | 0.999968i | \(0.502535\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 8.61415 | 1.00821 | 0.504105 | − | 0.863642i | \(-0.331822\pi\) | ||||
0.504105 | + | 0.863642i | \(0.331822\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −7.13634 | −0.824033 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −9.85744 | −1.12336 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −2.48616 | −0.279715 | −0.139857 | − | 0.990172i | \(-0.544664\pi\) | ||||
−0.139857 | + | 0.990172i | \(0.544664\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −4.04290 | −0.443766 | −0.221883 | − | 0.975073i | \(-0.571220\pi\) | ||||
−0.221883 | + | 0.975073i | \(0.571220\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 15.7918 | 1.71286 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −1.00000 | −0.107211 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 14.3980 | 1.52618 | 0.763091 | − | 0.646291i | \(-0.223681\pi\) | ||||
0.763091 | + | 0.646291i | \(0.223681\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 10.3029 | 1.08004 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −5.46631 | −0.566830 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 6.26448 | 0.642722 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −11.5595 | −1.17369 | −0.586845 | − | 0.809699i | \(-0.699630\pi\) | ||||
−0.586845 | + | 0.809699i | \(0.699630\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −4.51219 | −0.453493 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −13.1324 | −1.30673 | −0.653363 | − | 0.757045i | \(-0.726642\pi\) | ||||
−0.653363 | + | 0.757045i | \(0.726642\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 5.32385 | 0.524574 | 0.262287 | − | 0.964990i | \(-0.415523\pi\) | ||||
0.262287 | + | 0.964990i | \(0.415523\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 7.61063 | 0.742721 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 0.141598 | 0.0136888 | 0.00684438 | − | 0.999977i | \(-0.497821\pi\) | ||||
0.00684438 | + | 0.999977i | \(0.497821\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −18.2960 | −1.75244 | −0.876220 | − | 0.481911i | \(-0.839943\pi\) | ||||
−0.876220 | + | 0.481911i | \(0.839943\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −2.75195 | −0.261203 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 16.8255 | 1.58281 | 0.791405 | − | 0.611292i | \(-0.209350\pi\) | ||||
0.791405 | + | 0.611292i | \(0.209350\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 3.48372 | 0.324859 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 4.71609 | 0.436003 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −9.90292 | −0.907799 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 9.35990 | 0.850900 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −0.252352 | −0.0227538 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −7.44242 | −0.665670 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −5.43208 | −0.482019 | −0.241010 | − | 0.970523i | \(-0.577479\pi\) | ||||
−0.241010 | + | 0.970523i | \(0.577479\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −5.62492 | −0.495246 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −1.54649 | −0.135118 | −0.0675589 | − | 0.997715i | \(-0.521521\pi\) | ||||
−0.0675589 | + | 0.997715i | \(0.521521\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −3.92842 | −0.340637 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 3.48372 | 0.299831 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 6.94494 | 0.593346 | 0.296673 | − | 0.954979i | \(-0.404123\pi\) | ||||
0.296673 | + | 0.954979i | \(0.404123\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 3.92270 | 0.332719 | 0.166360 | − | 0.986065i | \(-0.446799\pi\) | ||||
0.166360 | + | 0.986065i | \(0.446799\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −2.83786 | −0.238991 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −21.2799 | −1.77952 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −3.48372 | −0.289308 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 2.22742 | 0.183715 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 13.2396 | 1.08463 | 0.542313 | − | 0.840176i | \(-0.317549\pi\) | ||||
0.542313 | + | 0.840176i | \(0.317549\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 20.4856 | 1.66710 | 0.833548 | − | 0.552447i | \(-0.186306\pi\) | ||||
0.833548 | + | 0.552447i | \(0.186306\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −4.53301 | −0.366472 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −19.0431 | −1.52958 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −12.5555 | −1.00203 | −0.501017 | − | 0.865437i | \(-0.667041\pi\) | ||||
−0.501017 | + | 0.865437i | \(0.667041\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 4.43857 | 0.352002 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −2.18462 | −0.172172 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 14.2248 | 1.11417 | 0.557086 | − | 0.830455i | \(-0.311919\pi\) | ||||
0.557086 | + | 0.830455i | \(0.311919\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −15.7192 | −1.22374 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 2.36461 | 0.182979 | 0.0914896 | − | 0.995806i | \(-0.470837\pi\) | ||||
0.0914896 | + | 0.995806i | \(0.470837\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 9.24152 | 0.710886 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −1.79821 | −0.137513 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 4.08692 | 0.310722 | 0.155361 | − | 0.987858i | \(-0.450346\pi\) | ||||
0.155361 | + | 0.987858i | \(0.450346\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 15.5902 | 1.17851 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −4.10392 | −0.308469 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 4.27445 | 0.319487 | 0.159744 | − | 0.987159i | \(-0.448933\pi\) | ||||
0.159744 | + | 0.987159i | \(0.448933\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 4.85121 | 0.360588 | 0.180294 | − | 0.983613i | \(-0.442295\pi\) | ||||
0.180294 | + | 0.983613i | \(0.442295\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0.160730 | 0.0118815 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −9.58703 | −0.704853 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 20.4538 | 1.49573 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −2.18462 | −0.158908 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 9.30171 | 0.673048 | 0.336524 | − | 0.941675i | \(-0.390749\pi\) | ||||
0.336524 | + | 0.941675i | \(0.390749\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −6.40515 | −0.461053 | −0.230526 | − | 0.973066i | \(-0.574045\pi\) | ||||
−0.230526 | + | 0.973066i | \(0.574045\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 16.4296 | 1.17655 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −24.9249 | −1.77583 | −0.887913 | − | 0.460012i | \(-0.847845\pi\) | ||||
−0.887913 | + | 0.460012i | \(0.847845\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −22.7349 | −1.61164 | −0.805818 | − | 0.592163i | \(-0.798274\pi\) | ||||
−0.805818 | + | 0.592163i | \(0.798274\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 3.72772 | 0.262933 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 2.18462 | 0.153330 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −0.879125 | −0.0614008 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −1.00000 | −0.0695048 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 8.11388 | 0.561249 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −4.01682 | −0.276529 | −0.138265 | − | 0.990395i | \(-0.544152\pi\) | ||||
−0.138265 | + | 0.990395i | \(0.544152\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0.134204 | 0.00919552 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −19.5957 | −1.33641 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 11.9418 | 0.810664 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −8.61415 | −0.582090 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −21.3781 | −1.43805 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −21.3151 | −1.42737 | −0.713683 | − | 0.700469i | \(-0.752974\pi\) | ||||
−0.713683 | + | 0.700469i | \(0.752974\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 7.13634 | 0.475756 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −9.37961 | −0.622546 | −0.311273 | − | 0.950320i | \(-0.600755\pi\) | ||||
−0.311273 | + | 0.950320i | \(0.600755\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 0.756117 | 0.0499656 | 0.0249828 | − | 0.999688i | \(-0.492047\pi\) | ||||
0.0249828 | + | 0.999688i | \(0.492047\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 9.85744 | 0.648572 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 9.34510 | 0.612218 | 0.306109 | − | 0.951997i | \(-0.400973\pi\) | ||||
0.306109 | + | 0.951997i | \(0.400973\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −9.88633 | −0.644913 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 2.48616 | 0.161493 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −19.1832 | −1.24086 | −0.620429 | − | 0.784262i | \(-0.713042\pi\) | ||||
−0.620429 | + | 0.784262i | \(0.713042\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 8.64995 | 0.557192 | 0.278596 | − | 0.960408i | \(-0.410131\pi\) | ||||
0.278596 | + | 0.960408i | \(0.410131\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 7.75973 | 0.495751 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −8.48053 | −0.539603 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 4.04290 | 0.256208 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 1.74567 | 0.110186 | 0.0550928 | − | 0.998481i | \(-0.482455\pi\) | ||||
0.0550928 | + | 0.998481i | \(0.482455\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 4.51219 | 0.283679 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −15.7918 | −0.988918 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 14.6090 | 0.911286 | 0.455643 | − | 0.890163i | \(-0.349409\pi\) | ||||
0.455643 | + | 0.890163i | \(0.349409\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 6.01197 | 0.373566 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 1.00000 | 0.0618984 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −14.5588 | −0.897732 | −0.448866 | − | 0.893599i | \(-0.648172\pi\) | ||||
−0.448866 | + | 0.893599i | \(0.648172\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 15.4628 | 0.949870 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −14.3980 | −0.881142 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −5.12131 | −0.312252 | −0.156126 | − | 0.987737i | \(-0.549901\pi\) | ||||
−0.156126 | + | 0.987737i | \(0.549901\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 17.6495 | 1.07213 | 0.536067 | − | 0.844176i | \(-0.319910\pi\) | ||||
0.536067 | + | 0.844176i | \(0.319910\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −10.3029 | −0.623559 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −32.2006 | −1.94177 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −14.3682 | −0.863300 | −0.431650 | − | 0.902041i | \(-0.642068\pi\) | ||||
−0.431650 | + | 0.902041i | \(0.642068\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 5.46631 | 0.327259 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 11.2915 | 0.673592 | 0.336796 | − | 0.941578i | \(-0.390657\pi\) | ||||
0.336796 | + | 0.941578i | \(0.390657\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −22.8449 | −1.35799 | −0.678994 | − | 0.734144i | \(-0.737584\pi\) | ||||
−0.678994 | + | 0.734144i | \(0.737584\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −6.26448 | −0.371076 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0.551294 | 0.0325419 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 3.54818 | 0.208717 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 11.5595 | 0.677630 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 0.626712 | 0.0366129 | 0.0183065 | − | 0.999832i | \(-0.494173\pi\) | ||||
0.0183065 | + | 0.999832i | \(0.494173\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −14.2969 | −0.832399 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 4.51219 | 0.261824 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −4.71609 | −0.272739 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 12.2883 | 0.708287 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 13.1324 | 0.754438 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0.559938 | 0.0320620 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −13.0939 | −0.747308 | −0.373654 | − | 0.927568i | \(-0.621895\pi\) | ||||
−0.373654 | + | 0.927568i | \(0.621895\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −5.32385 | −0.302863 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 7.40225 | 0.419743 | 0.209872 | − | 0.977729i | \(-0.432695\pi\) | ||||
0.209872 | + | 0.977729i | \(0.432695\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −2.80091 | −0.158317 | −0.0791584 | − | 0.996862i | \(-0.525223\pi\) | ||||
−0.0791584 | + | 0.996862i | \(0.525223\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −7.61063 | −0.428810 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −0.140364 | −0.00788365 | −0.00394182 | − | 0.999992i | \(-0.501255\pi\) | ||||
−0.00394182 | + | 0.999992i | \(0.501255\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −4.51219 | −0.252634 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −0.141598 | −0.00790321 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 8.15132 | 0.453551 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 33.6556 | 1.86688 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 18.2960 | 1.01177 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 6.19966 | 0.341798 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −16.8838 | −0.928020 | −0.464010 | − | 0.885830i | \(-0.653590\pi\) | ||||
−0.464010 | + | 0.885830i | \(0.653590\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 2.75195 | 0.150806 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 12.9863 | 0.709519 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −29.7935 | −1.62296 | −0.811478 | − | 0.584383i | \(-0.801337\pi\) | ||||
−0.811478 | + | 0.584383i | \(0.801337\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −16.8255 | −0.913836 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −24.6651 | −1.33569 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −20.1584 | −1.08845 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −3.48372 | −0.187557 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 4.65350 | 0.249813 | 0.124906 | − | 0.992169i | \(-0.460137\pi\) | ||||
0.124906 | + | 0.992169i | \(0.460137\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −22.9746 | −1.22980 | −0.614901 | − | 0.788604i | \(-0.710804\pi\) | ||||
−0.614901 | + | 0.788604i | \(0.710804\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −4.71609 | −0.251726 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −19.0492 | −1.01389 | −0.506944 | − | 0.861979i | \(-0.669225\pi\) | ||||
−0.506944 | + | 0.861979i | \(0.669225\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0.467531 | 0.0248140 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 9.90292 | 0.524118 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 24.0776 | 1.27077 | 0.635384 | − | 0.772196i | \(-0.280842\pi\) | ||||
0.635384 | + | 0.772196i | \(0.280842\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −15.7664 | −0.829812 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −9.35990 | −0.491267 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −30.0093 | −1.57076 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −13.3992 | −0.699435 | −0.349717 | − | 0.936855i | \(-0.613722\pi\) | ||||
−0.349717 | + | 0.936855i | \(0.613722\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0.252352 | 0.0131369 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −9.69660 | −0.503423 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −3.38531 | −0.175285 | −0.0876424 | − | 0.996152i | \(-0.527933\pi\) | ||||
−0.0876424 | + | 0.996152i | \(0.527933\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 7.44242 | 0.384325 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 4.71609 | 0.242891 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −19.3622 | −0.994572 | −0.497286 | − | 0.867587i | \(-0.665670\pi\) | ||||
−0.497286 | + | 0.867587i | \(0.665670\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 5.43208 | 0.278294 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −12.9709 | −0.662780 | −0.331390 | − | 0.943494i | \(-0.607518\pi\) | ||||
−0.331390 | + | 0.943494i | \(0.607518\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 34.3406 | 1.75016 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 5.62492 | 0.285931 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 24.8051 | 1.25767 | 0.628833 | − | 0.777540i | \(-0.283533\pi\) | ||||
0.628833 | + | 0.777540i | \(0.283533\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 4.53301 | 0.229244 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 1.54649 | 0.0780103 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 8.66110 | 0.435787 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −21.0970 | −1.05883 | −0.529414 | − | 0.848364i | \(-0.677588\pi\) | ||||
−0.529414 | + | 0.848364i | \(0.677588\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 3.92842 | 0.196667 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −34.5825 | −1.72697 | −0.863484 | − | 0.504377i | \(-0.831722\pi\) | ||||
−0.863484 | + | 0.504377i | \(0.831722\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 25.7796 | 1.28417 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −3.48372 | −0.173108 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −12.4173 | −0.615504 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 5.30201 | 0.262168 | 0.131084 | − | 0.991371i | \(-0.458154\pi\) | ||||
0.131084 | + | 0.991371i | \(0.458154\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −6.94494 | −0.342569 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 8.96552 | 0.441164 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 14.0843 | 0.691373 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −3.92270 | −0.192096 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −31.1134 | −1.51999 | −0.759995 | − | 0.649929i | \(-0.774799\pi\) | ||||
−0.759995 | + | 0.649929i | \(0.774799\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −24.3469 | −1.18660 | −0.593298 | − | 0.804983i | \(-0.702175\pi\) | ||||
−0.593298 | + | 0.804983i | \(0.702175\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 2.83786 | 0.137982 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −32.3491 | −1.56916 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −0.351134 | −0.0169926 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 21.2799 | 1.02740 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −37.6740 | −1.81469 | −0.907346 | − | 0.420384i | \(-0.861895\pi\) | ||||
−0.907346 | + | 0.420384i | \(0.861895\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −33.5751 | −1.61352 | −0.806759 | − | 0.590881i | \(-0.798780\pi\) | ||||
−0.806759 | + | 0.590881i | \(0.798780\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 3.48372 | 0.167032 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 1.79821 | 0.0860202 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 2.70114 | 0.128919 | 0.0644593 | − | 0.997920i | \(-0.479468\pi\) | ||||
0.0644593 | + | 0.997920i | \(0.479468\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −2.22742 | −0.106068 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 13.6352 | 0.647830 | 0.323915 | − | 0.946086i | \(-0.395001\pi\) | ||||
0.323915 | + | 0.946086i | \(0.395001\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −50.1586 | −2.37775 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −13.2396 | −0.626209 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −28.6589 | −1.35250 | −0.676249 | − | 0.736673i | \(-0.736396\pi\) | ||||
−0.676249 | + | 0.736673i | \(0.736396\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1.13866 | −0.0536175 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −20.4856 | −0.962498 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −35.8924 | −1.68266 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −15.6633 | −0.732697 | −0.366348 | − | 0.930478i | \(-0.619392\pi\) | ||||
−0.366348 | + | 0.930478i | \(0.619392\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 4.53301 | 0.211583 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −35.8058 | −1.66764 | −0.833820 | − | 0.552036i | \(-0.813851\pi\) | ||||
−0.833820 | + | 0.552036i | \(0.813851\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −6.42392 | −0.298545 | −0.149273 | − | 0.988796i | \(-0.547693\pi\) | ||||
−0.149273 | + | 0.988796i | \(0.547693\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 19.0431 | 0.883104 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 13.6231 | 0.630401 | 0.315200 | − | 0.949025i | \(-0.397928\pi\) | ||||
0.315200 | + | 0.949025i | \(0.397928\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −8.14365 | −0.376039 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 12.5555 | 0.578525 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −25.3807 | −1.16701 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −12.8327 | −0.588803 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −4.43857 | −0.203228 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −28.5896 | −1.30629 | −0.653146 | − | 0.757232i | \(-0.726551\pi\) | ||||
−0.653146 | + | 0.757232i | \(0.726551\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 12.9784 | 0.591766 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 2.18462 | 0.0994038 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 40.2701 | 1.82857 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 17.1517 | 0.777216 | 0.388608 | − | 0.921403i | \(-0.372956\pi\) | ||||
0.388608 | + | 0.921403i | \(0.372956\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −14.2248 | −0.643268 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −2.67396 | −0.120674 | −0.0603372 | − | 0.998178i | \(-0.519218\pi\) | ||||
−0.0603372 | + | 0.998178i | \(0.519218\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −4.53301 | −0.204157 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 15.7192 | 0.706528 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −0.293186 | −0.0131512 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −0.493064 | −0.0220726 | −0.0110363 | − | 0.999939i | \(-0.503513\pi\) | ||||
−0.0110363 | + | 0.999939i | \(0.503513\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −2.36461 | −0.105643 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 19.3765 | 0.863955 | 0.431977 | − | 0.901884i | \(-0.357816\pi\) | ||||
0.431977 | + | 0.901884i | \(0.357816\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 45.7498 | 2.03584 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −9.24152 | −0.410430 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 3.02087 | 0.133898 | 0.0669488 | − | 0.997756i | \(-0.478674\pi\) | ||||
0.0669488 | + | 0.997756i | \(0.478674\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 18.8187 | 0.832489 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 1.79821 | 0.0793930 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −18.5468 | −0.817271 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −12.8050 | −0.563162 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −4.08692 | −0.179396 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 41.5227 | 1.81914 | 0.909571 | − | 0.415548i | \(-0.136410\pi\) | ||||
0.909571 | + | 0.415548i | \(0.136410\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −25.1615 | −1.10024 | −0.550118 | − | 0.835087i | \(-0.685417\pi\) | ||||
−0.550118 | + | 0.835087i | \(0.685417\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −15.5902 | −0.680413 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −24.7788 | −1.07938 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 4.10392 | 0.178095 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 1.19012 | 0.0515496 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −0.493287 | −0.0213267 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −4.27445 | −0.184456 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 10.0506 | 0.432908 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 25.1609 | 1.08175 | 0.540876 | − | 0.841102i | \(-0.318093\pi\) | ||||
0.540876 | + | 0.841102i | \(0.318093\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −4.85121 | −0.208185 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 63.7383 | 2.73025 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −8.28515 | −0.354247 | −0.177124 | − | 0.984189i | \(-0.556679\pi\) | ||||
−0.177124 | + | 0.984189i | \(0.556679\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −0.160730 | −0.00685978 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −1.79821 | −0.0766064 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −5.43132 | −0.230963 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 9.58703 | 0.406947 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −15.4270 | −0.653663 | −0.326832 | − | 0.945083i | \(-0.605981\pi\) | ||||
−0.326832 | + | 0.945083i | \(0.605981\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 26.5276 | 1.12200 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −20.4538 | −0.863561 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 21.7039 | 0.914711 | 0.457356 | − | 0.889284i | \(-0.348797\pi\) | ||||
0.457356 | + | 0.889284i | \(0.348797\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −58.6154 | −2.46597 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 2.18462 | 0.0917455 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 29.9165 | 1.25417 | 0.627083 | − | 0.778952i | \(-0.284249\pi\) | ||||
0.627083 | + | 0.778952i | \(0.284249\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 9.36487 | 0.391908 | 0.195954 | − | 0.980613i | \(-0.437220\pi\) | ||||
0.195954 | + | 0.980613i | \(0.437220\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −9.30171 | −0.388584 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −7.13634 | −0.297606 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 10.0273 | 0.417444 | 0.208722 | − | 0.977975i | \(-0.433070\pi\) | ||||
0.208722 | + | 0.977975i | \(0.433070\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 6.40515 | 0.266189 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −8.83221 | −0.366422 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 20.0277 | 0.829462 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −16.4296 | −0.679279 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −9.59203 | −0.395905 | −0.197953 | − | 0.980212i | \(-0.563429\pi\) | ||||
−0.197953 | + | 0.980212i | \(0.563429\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −9.82959 | −0.405021 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 24.9249 | 1.02527 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −18.0393 | −0.740784 | −0.370392 | − | 0.928876i | \(-0.620777\pi\) | ||||
−0.370392 | + | 0.928876i | \(0.620777\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 34.4990 | 1.41432 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 22.7349 | 0.930479 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 21.4214 | 0.875253 | 0.437627 | − | 0.899157i | \(-0.355819\pi\) | ||||
0.437627 | + | 0.899157i | \(0.355819\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −0.260657 | −0.0106324 | −0.00531620 | − | 0.999986i | \(-0.501692\pi\) | ||||
−0.00531620 | + | 0.999986i | \(0.501692\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −3.72772 | −0.151804 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −32.6073 | −1.32568 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 23.0460 | 0.935410 | 0.467705 | − | 0.883885i | \(-0.345081\pi\) | ||||
0.467705 | + | 0.883885i | \(0.345081\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −2.18462 | −0.0885254 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 13.3836 | 0.541443 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 27.8998 | 1.12686 | 0.563430 | − | 0.826164i | \(-0.309481\pi\) | ||||
0.563430 | + | 0.826164i | \(0.309481\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0.879125 | 0.0354497 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −5.37316 | −0.216315 | −0.108158 | − | 0.994134i | \(-0.534495\pi\) | ||||
−0.108158 | + | 0.994134i | \(0.534495\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −5.32142 | −0.213886 | −0.106943 | − | 0.994265i | \(-0.534106\pi\) | ||||
−0.106943 | + | 0.994265i | \(0.534106\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1.00000 | 0.0401286 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 31.4542 | 1.26018 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −9.75436 | −0.390174 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −8.11388 | −0.324037 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −12.4746 | −0.497395 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 5.48318 | 0.218282 | 0.109141 | − | 0.994026i | \(-0.465190\pi\) | ||||
0.109141 | + | 0.994026i | \(0.465190\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 4.01682 | 0.159654 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 18.9239 | 0.750971 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −10.5047 | −0.416212 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −0.134204 | −0.00530904 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 2.58562 | 0.102126 | 0.0510629 | − | 0.998695i | \(-0.483739\pi\) | ||||
0.0510629 | + | 0.998695i | \(0.483739\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −24.6027 | −0.970234 | −0.485117 | − | 0.874449i | \(-0.661223\pi\) | ||||
−0.485117 | + | 0.874449i | \(0.661223\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 19.5957 | 0.771578 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 28.1739 | 1.10763 | 0.553815 | − | 0.832640i | \(-0.313172\pi\) | ||||
0.553815 | + | 0.832640i | \(0.313172\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −18.5177 | −0.726883 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −11.9418 | −0.468037 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −29.3417 | −1.14823 | −0.574115 | − | 0.818774i | \(-0.694654\pi\) | ||||
−0.574115 | + | 0.818774i | \(0.694654\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 5.38756 | 0.210509 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 8.61415 | 0.336070 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 2.83816 | 0.110559 | 0.0552794 | − | 0.998471i | \(-0.482395\pi\) | ||||
0.0552794 | + | 0.998471i | \(0.482395\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −50.0625 | −1.94720 | −0.973602 | − | 0.228250i | \(-0.926700\pi\) | ||||
−0.973602 | + | 0.228250i | \(0.926700\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 21.3781 | 0.830256 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 13.6855 | 0.530702 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −1.00000 | −0.0387202 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 21.3151 | 0.824090 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0.725244 | 0.0279977 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −19.6293 | −0.756652 | −0.378326 | − | 0.925672i | \(-0.623500\pi\) | ||||
−0.378326 | + | 0.925672i | \(0.623500\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −7.13634 | −0.274678 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 26.6125 | 1.02280 | 0.511400 | − | 0.859343i | \(-0.329127\pi\) | ||||
0.511400 | + | 0.859343i | \(0.329127\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −25.2532 | −0.969128 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 9.37961 | 0.359427 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −25.4576 | −0.974109 | −0.487055 | − | 0.873372i | \(-0.661929\pi\) | ||||
−0.487055 | + | 0.873372i | \(0.661929\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −24.1943 | −0.924415 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −0.756117 | −0.0288477 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −20.9327 | −0.797473 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 37.4686 | 1.42537 | 0.712687 | − | 0.701482i | \(-0.247478\pi\) | ||||
0.712687 | + | 0.701482i | \(0.247478\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −9.85744 | −0.374453 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −13.6656 | −0.518366 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −1.14391 | −0.0433289 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −9.34510 | −0.353464 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −42.9212 | −1.62111 | −0.810556 | − | 0.585661i | \(-0.800835\pi\) | ||||
−0.810556 | + | 0.585661i | \(0.800835\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −4.94859 | −0.186640 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 9.88633 | 0.372341 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −28.6894 | −1.07898 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −45.7792 | −1.71927 | −0.859637 | − | 0.510905i | \(-0.829310\pi\) | ||||
−0.859637 | + | 0.510905i | \(0.829310\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −2.48616 | −0.0932383 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −5.46631 | −0.204715 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 74.1334 | 2.77243 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 19.1832 | 0.716410 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 34.2632 | 1.27780 | 0.638901 | − | 0.769289i | \(-0.279389\pi\) | ||||
0.638901 | + | 0.769289i | \(0.279389\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 11.6306 | 0.433146 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −8.64995 | −0.321695 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 7.13634 | 0.265037 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −12.9670 | −0.480918 | −0.240459 | − | 0.970659i | \(-0.577298\pi\) | ||||
−0.240459 | + | 0.970659i | \(0.577298\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −25.4978 | −0.943070 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 0.810299 | 0.0299291 | 0.0149645 | − | 0.999888i | \(-0.495236\pi\) | ||||
0.0149645 | + | 0.999888i | \(0.495236\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −7.75973 | −0.286222 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 16.8202 | 0.619579 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 15.4395 | 0.567951 | 0.283975 | − | 0.958832i | \(-0.408347\pi\) | ||||
0.283975 | + | 0.958832i | \(0.408347\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 8.48053 | 0.311540 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −1.62739 | −0.0597033 | −0.0298516 | − | 0.999554i | \(-0.509503\pi\) | ||||
−0.0298516 | + | 0.999554i | \(0.509503\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −46.1230 | −1.68981 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −4.04290 | −0.147922 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0.309337 | 0.0113029 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −3.93844 | −0.143716 | −0.0718579 | − | 0.997415i | \(-0.522893\pi\) | ||||
−0.0718579 | + | 0.997415i | \(0.522893\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −1.74567 | −0.0636157 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −71.3663 | −2.59728 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −17.9907 | −0.653884 | −0.326942 | − | 0.945044i | \(-0.606018\pi\) | ||||
−0.326942 | + | 0.945044i | \(0.606018\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −4.51219 | −0.163782 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 38.2900 | 1.38801 | 0.694006 | − | 0.719969i | \(-0.255844\pi\) | ||||
0.694006 | + | 0.719969i | \(0.255844\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −39.9699 | −1.44701 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 15.7918 | 0.570952 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 19.3545 | 0.698849 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −19.3218 | −0.696761 | −0.348381 | − | 0.937353i | \(-0.613268\pi\) | ||||
−0.348381 | + | 0.937353i | \(0.613268\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −14.6090 | −0.526131 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 10.8833 | 0.391443 | 0.195722 | − | 0.980659i | \(-0.437295\pi\) | ||||
0.195722 | + | 0.980659i | \(0.437295\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 39.0095 | 1.40126 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −6.01197 | −0.215678 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −0.453783 | −0.0162584 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0.605556 | 0.0216685 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −1.00000 | −0.0357371 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 43.7397 | 1.56114 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 41.9622 | 1.49579 | 0.747895 | − | 0.663817i | \(-0.231065\pi\) | ||||
0.747895 | + | 0.663817i | \(0.231065\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 14.5588 | 0.518306 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 36.7574 | 1.30694 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −0.758016 | −0.0269179 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −15.4628 | −0.548408 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 11.7595 | 0.416542 | 0.208271 | − | 0.978071i | \(-0.433216\pi\) | ||||
0.208271 | + | 0.978071i | \(0.433216\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −12.8641 | −0.455098 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 14.3980 | 0.508727 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −38.8687 | −1.37165 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 7.61063 | 0.268239 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 5.12131 | 0.180279 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −26.1473 | −0.919290 | −0.459645 | − | 0.888103i | \(-0.652023\pi\) | ||||
−0.459645 | + | 0.888103i | \(0.652023\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −15.6688 | −0.550207 | −0.275104 | − | 0.961415i | \(-0.588712\pi\) | ||||
−0.275104 | + | 0.961415i | \(0.588712\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −17.6495 | −0.618996 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −49.5553 | −1.73585 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −10.1148 | −0.353872 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 10.3029 | 0.360012 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 28.6999 | 1.00163 | 0.500816 | − | 0.865553i | \(-0.333033\pi\) | ||||
0.500816 | + | 0.865553i | \(0.333033\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −37.7360 | −1.31539 | −0.657697 | − | 0.753283i | \(-0.728469\pi\) | ||||
−0.657697 | + | 0.753283i | \(0.728469\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 32.2006 | 1.12108 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 15.3602 | 0.534125 | 0.267062 | − | 0.963679i | \(-0.413947\pi\) | ||||
0.267062 | + | 0.963679i | \(0.413947\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 50.3499 | 1.74872 | 0.874362 | − | 0.485274i | \(-0.161280\pi\) | ||||
0.874362 | + | 0.485274i | \(0.161280\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 14.3682 | 0.498427 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 10.0969 | 0.349838 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −8.23766 | −0.285076 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −5.46631 | −0.188943 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 4.23121 | 0.146078 | 0.0730388 | − | 0.997329i | \(-0.476730\pi\) | ||||
0.0730388 | + | 0.997329i | \(0.476730\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1.00000 | 0.0344828 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −11.2915 | −0.388899 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −32.1949 | −1.10754 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 20.4479 | 0.702597 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 22.8449 | 0.784035 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −2.75195 | −0.0943356 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 28.5417 | 0.977249 | 0.488625 | − | 0.872494i | \(-0.337499\pi\) | ||||
0.488625 | + | 0.872494i | \(0.337499\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 6.26448 | 0.214241 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −37.6372 | −1.28566 | −0.642831 | − | 0.766008i | \(-0.722240\pi\) | ||||
−0.642831 | + | 0.766008i | \(0.722240\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 27.4774 | 0.937518 | 0.468759 | − | 0.883326i | \(-0.344701\pi\) | ||||
0.468759 | + | 0.883326i | \(0.344701\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −0.551294 | −0.0187881 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 25.6281 | 0.872390 | 0.436195 | − | 0.899852i | \(-0.356326\pi\) | ||||
0.436195 | + | 0.899852i | \(0.356326\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −14.2377 | −0.484096 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −3.54818 | −0.120503 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 11.2180 | 0.380546 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −17.5802 | −0.595684 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −11.5595 | −0.391230 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −16.2589 | −0.549650 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −9.15603 | −0.309177 | −0.154589 | − | 0.987979i | \(-0.549405\pi\) | ||||
−0.154589 | + | 0.987979i | \(0.549405\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −0.626712 | −0.0211385 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 26.1589 | 0.881315 | 0.440657 | − | 0.897675i | \(-0.354745\pi\) | ||||
0.440657 | + | 0.897675i | \(0.354745\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 39.4335 | 1.32704 | 0.663522 | − | 0.748157i | \(-0.269061\pi\) | ||||
0.663522 | + | 0.748157i | \(0.269061\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 14.2969 | 0.480586 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −13.8289 | −0.464329 | −0.232164 | − | 0.972677i | \(-0.574581\pi\) | ||||
−0.232164 | + | 0.972677i | \(0.574581\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −11.8671 | −0.398008 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −4.51219 | −0.151164 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −5.10308 | −0.170768 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −14.8910 | −0.497752 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 4.71609 | 0.157466 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 5.46631 | 0.182312 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 20.1201 | 0.670297 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −12.2883 | −0.408930 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −16.9003 | −0.561785 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −11.8379 | −0.393070 | −0.196535 | − | 0.980497i | \(-0.562969\pi\) | ||||
−0.196535 | + | 0.980497i | \(0.562969\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −13.1324 | −0.435575 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 42.2595 | 1.40012 | 0.700060 | − | 0.714084i | \(-0.253157\pi\) | ||||
0.700060 | + | 0.714084i | \(0.253157\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 18.2423 | 0.603733 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −0.559938 | −0.0185110 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −3.37851 | −0.111568 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 34.9520 | 1.15296 | 0.576480 | − | 0.817111i | \(-0.304426\pi\) | ||||
0.576480 | + | 0.817111i | \(0.304426\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 13.0939 | 0.431458 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −0.632920 | −0.0208328 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 19.6388 | 0.645721 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 5.32385 | 0.174858 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −2.39407 | −0.0785470 | −0.0392735 | − | 0.999228i | \(-0.512504\pi\) | ||||
−0.0392735 | + | 0.999228i | \(0.512504\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 4.00538 | 0.131271 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −7.40225 | −0.242339 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −71.2555 | −2.33030 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −2.10672 | −0.0688235 | −0.0344118 | − | 0.999408i | \(-0.510956\pi\) | ||||
−0.0344118 | + | 0.999408i | \(0.510956\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 2.80091 | 0.0914042 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −24.4828 | −0.798116 | −0.399058 | − | 0.916926i | \(-0.630663\pi\) | ||||
−0.399058 | + | 0.916926i | \(0.630663\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −0.252352 | −0.00821771 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 7.61063 | 0.247574 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 23.8006 | 0.773416 | 0.386708 | − | 0.922202i | \(-0.373612\pi\) | ||||
0.386708 | + | 0.922202i | \(0.373612\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 40.6251 | 1.31875 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0.140364 | 0.00455162 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −8.22801 | −0.266531 | −0.133266 | − | 0.991080i | \(-0.542546\pi\) | ||||
−0.133266 | + | 0.991080i | \(0.542546\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −32.4046 | −1.04859 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 4.51219 | 0.145859 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 15.1721 | 0.489932 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −1.11944 | −0.0361110 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0.141598 | 0.00456292 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 22.3138 | 0.718306 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −35.1102 | −1.12907 | −0.564534 | − | 0.825410i | \(-0.690944\pi\) | ||||
−0.564534 | + | 0.825410i | \(0.690944\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −8.15132 | −0.261858 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −35.5969 | −1.14236 | −0.571179 | − | 0.820825i | \(-0.693514\pi\) | ||||
−0.571179 | + | 0.820825i | \(0.693514\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 8.56963 | 0.274730 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −33.6556 | −1.07784 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −1.67797 | −0.0536829 | −0.0268414 | − | 0.999640i | \(-0.508545\pi\) | ||||
−0.0268414 | + | 0.999640i | \(0.508545\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −64.9665 | −2.07634 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −18.2960 | −0.584147 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −4.78120 | −0.152497 | −0.0762484 | − | 0.997089i | \(-0.524294\pi\) | ||||
−0.0762484 | + | 0.997089i | \(0.524294\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 86.8315 | 2.76668 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −6.19966 | −0.197337 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −5.62492 | −0.178862 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −14.8296 | −0.471076 | −0.235538 | − | 0.971865i | \(-0.575685\pi\) | ||||
−0.235538 | + | 0.971865i | \(0.575685\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 16.8838 | 0.535793 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 79.2023 | 2.51088 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 23.0282 | 0.729309 | 0.364655 | − | 0.931143i | \(-0.381187\pi\) | ||||
0.364655 | + | 0.931143i | \(0.381187\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −2.75195 | −0.0870678 |
(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 | 8004.2.a.e.1.2 | ✓ | 9 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8004.2.a.e.1.2 | ✓ | 9 | 1.1 | even | 1 | trivial |