Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4598,2,Mod(1,4598)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4598, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4598.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4598 = 2 \cdot 11^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4598.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: | \(36.7152148494\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | 4.4.33452.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} - 8x^{2} + 7x - 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(0.669883\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4598.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | 0.669883 | 0.386757 | 0.193379 | − | 0.981124i | \(-0.438055\pi\) | ||||
0.193379 | + | 0.981124i | \(0.438055\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −3.56566 | −1.59461 | −0.797306 | − | 0.603575i | \(-0.793742\pi\) | ||||
−0.797306 | + | 0.603575i | \(0.793742\pi\) | |||||||
\(6\) | −0.669883 | −0.273479 | ||||||||
\(7\) | 0.507202 | 0.191704 | 0.0958522 | − | 0.995396i | \(-0.469442\pi\) | ||||
0.0958522 | + | 0.995396i | \(0.469442\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | −2.55126 | −0.850419 | ||||||||
\(10\) | 3.56566 | 1.12756 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | 0.669883 | 0.193379 | ||||||||
\(13\) | 6.56566 | 1.82099 | 0.910493 | − | 0.413524i | \(-0.135702\pi\) | ||||
0.910493 | + | 0.413524i | \(0.135702\pi\) | |||||||
\(14\) | −0.507202 | −0.135555 | ||||||||
\(15\) | −2.38858 | −0.616728 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −4.23554 | −1.02727 | −0.513635 | − | 0.858009i | \(-0.671701\pi\) | ||||
−0.513635 | + | 0.858009i | \(0.671701\pi\) | |||||||
\(18\) | 2.55126 | 0.601337 | ||||||||
\(19\) | 1.00000 | 0.229416 | ||||||||
\(20\) | −3.56566 | −0.797306 | ||||||||
\(21\) | 0.339766 | 0.0741430 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0.177085 | 0.0369248 | 0.0184624 | − | 0.999830i | \(-0.494123\pi\) | ||||
0.0184624 | + | 0.999830i | \(0.494123\pi\) | |||||||
\(24\) | −0.669883 | −0.136739 | ||||||||
\(25\) | 7.71394 | 1.54279 | ||||||||
\(26\) | −6.56566 | −1.28763 | ||||||||
\(27\) | −3.71869 | −0.715663 | ||||||||
\(28\) | 0.507202 | 0.0958522 | ||||||||
\(29\) | −7.08251 | −1.31519 | −0.657595 | − | 0.753372i | \(-0.728426\pi\) | ||||
−0.657595 | + | 0.753372i | \(0.728426\pi\) | |||||||
\(30\) | 2.38858 | 0.436092 | ||||||||
\(31\) | 10.3886 | 1.86584 | 0.932922 | − | 0.360079i | \(-0.117250\pi\) | ||||
0.932922 | + | 0.360079i | \(0.117250\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 4.23554 | 0.726390 | ||||||||
\(35\) | −1.80851 | −0.305694 | ||||||||
\(36\) | −2.55126 | −0.425209 | ||||||||
\(37\) | −7.45668 | −1.22587 | −0.612936 | − | 0.790133i | \(-0.710012\pi\) | ||||
−0.612936 | + | 0.790133i | \(0.710012\pi\) | |||||||
\(38\) | −1.00000 | −0.162221 | ||||||||
\(39\) | 4.39822 | 0.704280 | ||||||||
\(40\) | 3.56566 | 0.563780 | ||||||||
\(41\) | −2.71394 | −0.423846 | −0.211923 | − | 0.977286i | \(-0.567973\pi\) | ||||
−0.211923 | + | 0.977286i | \(0.567973\pi\) | |||||||
\(42\) | −0.339766 | −0.0524270 | ||||||||
\(43\) | −3.21149 | −0.489748 | −0.244874 | − | 0.969555i | \(-0.578747\pi\) | ||||
−0.244874 | + | 0.969555i | \(0.578747\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 9.09692 | 1.35609 | ||||||||
\(46\) | −0.177085 | −0.0261098 | ||||||||
\(47\) | −3.13132 | −0.456750 | −0.228375 | − | 0.973573i | \(-0.573341\pi\) | ||||
−0.228375 | + | 0.973573i | \(0.573341\pi\) | |||||||
\(48\) | 0.669883 | 0.0966893 | ||||||||
\(49\) | −6.74275 | −0.963249 | ||||||||
\(50\) | −7.71394 | −1.09092 | ||||||||
\(51\) | −2.83732 | −0.397304 | ||||||||
\(52\) | 6.56566 | 0.910493 | ||||||||
\(53\) | 2.54161 | 0.349117 | 0.174558 | − | 0.984647i | \(-0.444150\pi\) | ||||
0.174558 | + | 0.984647i | \(0.444150\pi\) | |||||||
\(54\) | 3.71869 | 0.506050 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −0.507202 | −0.0677777 | ||||||||
\(57\) | 0.669883 | 0.0887282 | ||||||||
\(58\) | 7.08251 | 0.929979 | ||||||||
\(59\) | 5.57531 | 0.725844 | 0.362922 | − | 0.931820i | \(-0.381779\pi\) | ||||
0.362922 | + | 0.931820i | \(0.381779\pi\) | |||||||
\(60\) | −2.38858 | −0.308364 | ||||||||
\(61\) | −0.985596 | −0.126193 | −0.0630963 | − | 0.998007i | \(-0.520098\pi\) | ||||
−0.0630963 | + | 0.998007i | \(0.520098\pi\) | |||||||
\(62\) | −10.3886 | −1.31935 | ||||||||
\(63\) | −1.29400 | −0.163029 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −23.4109 | −2.90377 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 12.6241 | 1.54228 | 0.771141 | − | 0.636665i | \(-0.219686\pi\) | ||||
0.771141 | + | 0.636665i | \(0.219686\pi\) | |||||||
\(68\) | −4.23554 | −0.513635 | ||||||||
\(69\) | 0.118626 | 0.0142809 | ||||||||
\(70\) | 1.80851 | 0.216158 | ||||||||
\(71\) | −8.55126 | −1.01485 | −0.507424 | − | 0.861697i | \(-0.669402\pi\) | ||||
−0.507424 | + | 0.861697i | \(0.669402\pi\) | |||||||
\(72\) | 2.55126 | 0.300668 | ||||||||
\(73\) | −1.10422 | −0.129239 | −0.0646197 | − | 0.997910i | \(-0.520583\pi\) | ||||
−0.0646197 | + | 0.997910i | \(0.520583\pi\) | |||||||
\(74\) | 7.45668 | 0.866822 | ||||||||
\(75\) | 5.16744 | 0.596684 | ||||||||
\(76\) | 1.00000 | 0.114708 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −4.39822 | −0.498001 | ||||||||
\(79\) | −9.76275 | −1.09839 | −0.549197 | − | 0.835693i | \(-0.685067\pi\) | ||||
−0.549197 | + | 0.835693i | \(0.685067\pi\) | |||||||
\(80\) | −3.56566 | −0.398653 | ||||||||
\(81\) | 5.16268 | 0.573631 | ||||||||
\(82\) | 2.71394 | 0.299704 | ||||||||
\(83\) | 8.19709 | 0.899747 | 0.449874 | − | 0.893092i | \(-0.351469\pi\) | ||||
0.449874 | + | 0.893092i | \(0.351469\pi\) | |||||||
\(84\) | 0.339766 | 0.0370715 | ||||||||
\(85\) | 15.1025 | 1.63810 | ||||||||
\(86\) | 3.21149 | 0.346304 | ||||||||
\(87\) | −4.74445 | −0.508659 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 12.4423 | 1.31888 | 0.659439 | − | 0.751758i | \(-0.270794\pi\) | ||||
0.659439 | + | 0.751758i | \(0.270794\pi\) | |||||||
\(90\) | −9.09692 | −0.958899 | ||||||||
\(91\) | 3.33012 | 0.349091 | ||||||||
\(92\) | 0.177085 | 0.0184624 | ||||||||
\(93\) | 6.95913 | 0.721628 | ||||||||
\(94\) | 3.13132 | 0.322971 | ||||||||
\(95\) | −3.56566 | −0.365829 | ||||||||
\(96\) | −0.669883 | −0.0683697 | ||||||||
\(97\) | −8.82526 | −0.896069 | −0.448035 | − | 0.894016i | \(-0.647876\pi\) | ||||
−0.448035 | + | 0.894016i | \(0.647876\pi\) | |||||||
\(98\) | 6.74275 | 0.681120 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 7.71394 | 0.771394 | ||||||||
\(101\) | −7.36857 | −0.733201 | −0.366600 | − | 0.930379i | \(-0.619478\pi\) | ||||
−0.366600 | + | 0.930379i | \(0.619478\pi\) | |||||||
\(102\) | 2.83732 | 0.280936 | ||||||||
\(103\) | 16.0367 | 1.58015 | 0.790074 | − | 0.613012i | \(-0.210042\pi\) | ||||
0.790074 | + | 0.613012i | \(0.210042\pi\) | |||||||
\(104\) | −6.56566 | −0.643816 | ||||||||
\(105\) | −1.21149 | −0.118229 | ||||||||
\(106\) | −2.54161 | −0.246863 | ||||||||
\(107\) | −12.7458 | −1.23218 | −0.616091 | − | 0.787675i | \(-0.711285\pi\) | ||||
−0.616091 | + | 0.787675i | \(0.711285\pi\) | |||||||
\(108\) | −3.71869 | −0.357831 | ||||||||
\(109\) | −10.0856 | −0.966021 | −0.483011 | − | 0.875614i | \(-0.660457\pi\) | ||||
−0.483011 | + | 0.875614i | \(0.660457\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −4.99511 | −0.474114 | ||||||||
\(112\) | 0.507202 | 0.0479261 | ||||||||
\(113\) | 9.69394 | 0.911929 | 0.455964 | − | 0.889998i | \(-0.349294\pi\) | ||||
0.455964 | + | 0.889998i | \(0.349294\pi\) | |||||||
\(114\) | −0.669883 | −0.0627403 | ||||||||
\(115\) | −0.631426 | −0.0588807 | ||||||||
\(116\) | −7.08251 | −0.657595 | ||||||||
\(117\) | −16.7507 | −1.54860 | ||||||||
\(118\) | −5.57531 | −0.513249 | ||||||||
\(119\) | −2.14828 | −0.196932 | ||||||||
\(120\) | 2.38858 | 0.218046 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | 0.985596 | 0.0892317 | ||||||||
\(123\) | −1.81802 | −0.163925 | ||||||||
\(124\) | 10.3886 | 0.932922 | ||||||||
\(125\) | −9.67698 | −0.865536 | ||||||||
\(126\) | 1.29400 | 0.115279 | ||||||||
\(127\) | −11.7916 | −1.04633 | −0.523166 | − | 0.852231i | \(-0.675249\pi\) | ||||
−0.523166 | + | 0.852231i | \(0.675249\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | −2.15132 | −0.189413 | ||||||||
\(130\) | 23.4109 | 2.05327 | ||||||||
\(131\) | 7.81645 | 0.682927 | 0.341463 | − | 0.939895i | \(-0.389078\pi\) | ||||
0.341463 | + | 0.939895i | \(0.389078\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0.507202 | 0.0439800 | ||||||||
\(134\) | −12.6241 | −1.09056 | ||||||||
\(135\) | 13.2596 | 1.14120 | ||||||||
\(136\) | 4.23554 | 0.363195 | ||||||||
\(137\) | 6.32841 | 0.540672 | 0.270336 | − | 0.962766i | \(-0.412865\pi\) | ||||
0.270336 | + | 0.962766i | \(0.412865\pi\) | |||||||
\(138\) | −0.118626 | −0.0100981 | ||||||||
\(139\) | 15.0319 | 1.27499 | 0.637493 | − | 0.770456i | \(-0.279972\pi\) | ||||
0.637493 | + | 0.770456i | \(0.279972\pi\) | |||||||
\(140\) | −1.80851 | −0.152847 | ||||||||
\(141\) | −2.09762 | −0.176651 | ||||||||
\(142\) | 8.55126 | 0.717606 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −2.55126 | −0.212605 | ||||||||
\(145\) | 25.2538 | 2.09722 | ||||||||
\(146\) | 1.10422 | 0.0913861 | ||||||||
\(147\) | −4.51685 | −0.372544 | ||||||||
\(148\) | −7.45668 | −0.612936 | ||||||||
\(149\) | 21.1218 | 1.73037 | 0.865183 | − | 0.501456i | \(-0.167202\pi\) | ||||
0.865183 | + | 0.501456i | \(0.167202\pi\) | |||||||
\(150\) | −5.16744 | −0.421919 | ||||||||
\(151\) | 23.2387 | 1.89114 | 0.945570 | − | 0.325417i | \(-0.105505\pi\) | ||||
0.945570 | + | 0.325417i | \(0.105505\pi\) | |||||||
\(152\) | −1.00000 | −0.0811107 | ||||||||
\(153\) | 10.8060 | 0.873610 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −37.0421 | −2.97530 | ||||||||
\(156\) | 4.39822 | 0.352140 | ||||||||
\(157\) | 8.88613 | 0.709190 | 0.354595 | − | 0.935020i | \(-0.384619\pi\) | ||||
0.354595 | + | 0.935020i | \(0.384619\pi\) | |||||||
\(158\) | 9.76275 | 0.776682 | ||||||||
\(159\) | 1.70258 | 0.135023 | ||||||||
\(160\) | 3.56566 | 0.281890 | ||||||||
\(161\) | 0.0898180 | 0.00707865 | ||||||||
\(162\) | −5.16268 | −0.405619 | ||||||||
\(163\) | 11.4374 | 0.895845 | 0.447923 | − | 0.894072i | \(-0.352164\pi\) | ||||
0.447923 | + | 0.894072i | \(0.352164\pi\) | |||||||
\(164\) | −2.71394 | −0.211923 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −8.19709 | −0.636217 | ||||||||
\(167\) | 16.5880 | 1.28362 | 0.641809 | − | 0.766864i | \(-0.278184\pi\) | ||||
0.641809 | + | 0.766864i | \(0.278184\pi\) | |||||||
\(168\) | −0.339766 | −0.0262135 | ||||||||
\(169\) | 30.1079 | 2.31599 | ||||||||
\(170\) | −15.1025 | −1.15831 | ||||||||
\(171\) | −2.55126 | −0.195099 | ||||||||
\(172\) | −3.21149 | −0.244874 | ||||||||
\(173\) | 3.84292 | 0.292172 | 0.146086 | − | 0.989272i | \(-0.453332\pi\) | ||||
0.146086 | + | 0.989272i | \(0.453332\pi\) | |||||||
\(174\) | 4.74445 | 0.359676 | ||||||||
\(175\) | 3.91253 | 0.295759 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 3.73481 | 0.280725 | ||||||||
\(178\) | −12.4423 | −0.932588 | ||||||||
\(179\) | −1.72834 | −0.129182 | −0.0645912 | − | 0.997912i | \(-0.520574\pi\) | ||||
−0.0645912 | + | 0.997912i | \(0.520574\pi\) | |||||||
\(180\) | 9.09692 | 0.678044 | ||||||||
\(181\) | −2.29655 | −0.170701 | −0.0853507 | − | 0.996351i | \(-0.527201\pi\) | ||||
−0.0853507 | + | 0.996351i | \(0.527201\pi\) | |||||||
\(182\) | −3.33012 | −0.246845 | ||||||||
\(183\) | −0.660234 | −0.0488059 | ||||||||
\(184\) | −0.177085 | −0.0130549 | ||||||||
\(185\) | 26.5880 | 1.95479 | ||||||||
\(186\) | −6.95913 | −0.510268 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | −3.13132 | −0.228375 | ||||||||
\(189\) | −1.88613 | −0.137196 | ||||||||
\(190\) | 3.56566 | 0.258680 | ||||||||
\(191\) | 7.88053 | 0.570215 | 0.285108 | − | 0.958496i | \(-0.407971\pi\) | ||||
0.285108 | + | 0.958496i | \(0.407971\pi\) | |||||||
\(192\) | 0.669883 | 0.0483446 | ||||||||
\(193\) | −0.254703 | −0.0183339 | −0.00916697 | − | 0.999958i | \(-0.502918\pi\) | ||||
−0.00916697 | + | 0.999958i | \(0.502918\pi\) | |||||||
\(194\) | 8.82526 | 0.633617 | ||||||||
\(195\) | −15.6826 | −1.12305 | ||||||||
\(196\) | −6.74275 | −0.481625 | ||||||||
\(197\) | −18.2626 | −1.30116 | −0.650580 | − | 0.759438i | \(-0.725474\pi\) | ||||
−0.650580 | + | 0.759438i | \(0.725474\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 8.60007 | 0.609643 | 0.304821 | − | 0.952410i | \(-0.401403\pi\) | ||||
0.304821 | + | 0.952410i | \(0.401403\pi\) | |||||||
\(200\) | −7.71394 | −0.545458 | ||||||||
\(201\) | 8.45668 | 0.596488 | ||||||||
\(202\) | 7.36857 | 0.518451 | ||||||||
\(203\) | −3.59226 | −0.252128 | ||||||||
\(204\) | −2.83732 | −0.198652 | ||||||||
\(205\) | 9.67698 | 0.675870 | ||||||||
\(206\) | −16.0367 | −1.11733 | ||||||||
\(207\) | −0.451790 | −0.0314016 | ||||||||
\(208\) | 6.56566 | 0.455247 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 1.21149 | 0.0836008 | ||||||||
\(211\) | 10.8661 | 0.748055 | 0.374028 | − | 0.927418i | \(-0.377977\pi\) | ||||
0.374028 | + | 0.927418i | \(0.377977\pi\) | |||||||
\(212\) | 2.54161 | 0.174558 | ||||||||
\(213\) | −5.72834 | −0.392500 | ||||||||
\(214\) | 12.7458 | 0.871284 | ||||||||
\(215\) | 11.4511 | 0.780958 | ||||||||
\(216\) | 3.71869 | 0.253025 | ||||||||
\(217\) | 5.26911 | 0.357690 | ||||||||
\(218\) | 10.0856 | 0.683080 | ||||||||
\(219\) | −0.739700 | −0.0499843 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −27.8091 | −1.87065 | ||||||||
\(222\) | 4.99511 | 0.335250 | ||||||||
\(223\) | −12.4711 | −0.835126 | −0.417563 | − | 0.908648i | \(-0.637116\pi\) | ||||
−0.417563 | + | 0.908648i | \(0.637116\pi\) | |||||||
\(224\) | −0.507202 | −0.0338889 | ||||||||
\(225\) | −19.6802 | −1.31202 | ||||||||
\(226\) | −9.69394 | −0.644831 | ||||||||
\(227\) | 29.8483 | 1.98110 | 0.990551 | − | 0.137146i | \(-0.0437930\pi\) | ||||
0.990551 | + | 0.137146i | \(0.0437930\pi\) | |||||||
\(228\) | 0.669883 | 0.0443641 | ||||||||
\(229\) | −19.3115 | −1.27614 | −0.638068 | − | 0.769980i | \(-0.720266\pi\) | ||||
−0.638068 | + | 0.769980i | \(0.720266\pi\) | |||||||
\(230\) | 0.631426 | 0.0416350 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 7.08251 | 0.464990 | ||||||||
\(233\) | −10.0288 | −0.657009 | −0.328505 | − | 0.944502i | \(-0.606545\pi\) | ||||
−0.328505 | + | 0.944502i | \(0.606545\pi\) | |||||||
\(234\) | 16.7507 | 1.09503 | ||||||||
\(235\) | 11.1652 | 0.728339 | ||||||||
\(236\) | 5.57531 | 0.362922 | ||||||||
\(237\) | −6.53990 | −0.424812 | ||||||||
\(238\) | 2.14828 | 0.139252 | ||||||||
\(239\) | 11.2291 | 0.726349 | 0.363174 | − | 0.931721i | \(-0.381693\pi\) | ||||
0.363174 | + | 0.931721i | \(0.381693\pi\) | |||||||
\(240\) | −2.38858 | −0.154182 | ||||||||
\(241\) | −16.0367 | −1.03302 | −0.516509 | − | 0.856282i | \(-0.672769\pi\) | ||||
−0.516509 | + | 0.856282i | \(0.672769\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 14.6145 | 0.937519 | ||||||||
\(244\) | −0.985596 | −0.0630963 | ||||||||
\(245\) | 24.0423 | 1.53601 | ||||||||
\(246\) | 1.81802 | 0.115913 | ||||||||
\(247\) | 6.56566 | 0.417763 | ||||||||
\(248\) | −10.3886 | −0.659675 | ||||||||
\(249\) | 5.49109 | 0.347984 | ||||||||
\(250\) | 9.67698 | 0.612026 | ||||||||
\(251\) | 27.0591 | 1.70795 | 0.853977 | − | 0.520310i | \(-0.174184\pi\) | ||||
0.853977 | + | 0.520310i | \(0.174184\pi\) | |||||||
\(252\) | −1.29400 | −0.0815145 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 11.7916 | 0.739868 | ||||||||
\(255\) | 10.1169 | 0.633546 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 29.2963 | 1.82746 | 0.913728 | − | 0.406327i | \(-0.133190\pi\) | ||||
0.913728 | + | 0.406327i | \(0.133190\pi\) | |||||||
\(258\) | 2.15132 | 0.133936 | ||||||||
\(259\) | −3.78205 | −0.235005 | ||||||||
\(260\) | −23.4109 | −1.45188 | ||||||||
\(261\) | 18.0693 | 1.11846 | ||||||||
\(262\) | −7.81645 | −0.482902 | ||||||||
\(263\) | 30.7129 | 1.89384 | 0.946918 | − | 0.321475i | \(-0.104179\pi\) | ||||
0.946918 | + | 0.321475i | \(0.104179\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −9.06251 | −0.556706 | ||||||||
\(266\) | −0.507202 | −0.0310986 | ||||||||
\(267\) | 8.33487 | 0.510086 | ||||||||
\(268\) | 12.6241 | 0.771141 | ||||||||
\(269\) | −14.0288 | −0.855352 | −0.427676 | − | 0.903932i | \(-0.640667\pi\) | ||||
−0.427676 | + | 0.903932i | \(0.640667\pi\) | |||||||
\(270\) | −13.2596 | −0.806953 | ||||||||
\(271\) | 12.4350 | 0.755371 | 0.377685 | − | 0.925934i | \(-0.376720\pi\) | ||||
0.377685 | + | 0.925934i | \(0.376720\pi\) | |||||||
\(272\) | −4.23554 | −0.256818 | ||||||||
\(273\) | 2.23079 | 0.135013 | ||||||||
\(274\) | −6.32841 | −0.382313 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0.118626 | 0.00714047 | ||||||||
\(277\) | −16.6761 | −1.00197 | −0.500985 | − | 0.865456i | \(-0.667029\pi\) | ||||
−0.500985 | + | 0.865456i | \(0.667029\pi\) | |||||||
\(278\) | −15.0319 | −0.901551 | ||||||||
\(279\) | −26.5039 | −1.58675 | ||||||||
\(280\) | 1.80851 | 0.108079 | ||||||||
\(281\) | 4.67159 | 0.278684 | 0.139342 | − | 0.990244i | \(-0.455501\pi\) | ||||
0.139342 | + | 0.990244i | \(0.455501\pi\) | |||||||
\(282\) | 2.09762 | 0.124911 | ||||||||
\(283\) | 6.37907 | 0.379196 | 0.189598 | − | 0.981862i | \(-0.439282\pi\) | ||||
0.189598 | + | 0.981862i | \(0.439282\pi\) | |||||||
\(284\) | −8.55126 | −0.507424 | ||||||||
\(285\) | −2.38858 | −0.141487 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −1.37651 | −0.0812531 | ||||||||
\(288\) | 2.55126 | 0.150334 | ||||||||
\(289\) | 0.939832 | 0.0552843 | ||||||||
\(290\) | −25.2538 | −1.48296 | ||||||||
\(291\) | −5.91189 | −0.346561 | ||||||||
\(292\) | −1.10422 | −0.0646197 | ||||||||
\(293\) | −12.8283 | −0.749438 | −0.374719 | − | 0.927139i | \(-0.622261\pi\) | ||||
−0.374719 | + | 0.927139i | \(0.622261\pi\) | |||||||
\(294\) | 4.51685 | 0.263428 | ||||||||
\(295\) | −19.8797 | −1.15744 | ||||||||
\(296\) | 7.45668 | 0.433411 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −21.1218 | −1.22355 | ||||||||
\(299\) | 1.16268 | 0.0672396 | ||||||||
\(300\) | 5.16744 | 0.298342 | ||||||||
\(301\) | −1.62887 | −0.0938868 | ||||||||
\(302\) | −23.2387 | −1.33724 | ||||||||
\(303\) | −4.93608 | −0.283571 | ||||||||
\(304\) | 1.00000 | 0.0573539 | ||||||||
\(305\) | 3.51430 | 0.201228 | ||||||||
\(306\) | −10.8060 | −0.617736 | ||||||||
\(307\) | −26.5880 | −1.51746 | −0.758729 | − | 0.651407i | \(-0.774179\pi\) | ||||
−0.758729 | + | 0.651407i | \(0.774179\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 10.7427 | 0.611133 | ||||||||
\(310\) | 37.0421 | 2.10385 | ||||||||
\(311\) | 13.5664 | 0.769278 | 0.384639 | − | 0.923067i | \(-0.374326\pi\) | ||||
0.384639 | + | 0.923067i | \(0.374326\pi\) | |||||||
\(312\) | −4.39822 | −0.249000 | ||||||||
\(313\) | 15.1608 | 0.856941 | 0.428470 | − | 0.903556i | \(-0.359053\pi\) | ||||
0.428470 | + | 0.903556i | \(0.359053\pi\) | |||||||
\(314\) | −8.88613 | −0.501473 | ||||||||
\(315\) | 4.61398 | 0.259968 | ||||||||
\(316\) | −9.76275 | −0.549197 | ||||||||
\(317\) | 26.5958 | 1.49377 | 0.746885 | − | 0.664954i | \(-0.231549\pi\) | ||||
0.746885 | + | 0.664954i | \(0.231549\pi\) | |||||||
\(318\) | −1.70258 | −0.0954759 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | −3.56566 | −0.199327 | ||||||||
\(321\) | −8.53819 | −0.476555 | ||||||||
\(322\) | −0.0898180 | −0.00500536 | ||||||||
\(323\) | −4.23554 | −0.235672 | ||||||||
\(324\) | 5.16268 | 0.286816 | ||||||||
\(325\) | 50.6471 | 2.80940 | ||||||||
\(326\) | −11.4374 | −0.633458 | ||||||||
\(327\) | −6.75614 | −0.373616 | ||||||||
\(328\) | 2.71394 | 0.149852 | ||||||||
\(329\) | −1.58821 | −0.0875610 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −9.30131 | −0.511246 | −0.255623 | − | 0.966777i | \(-0.582281\pi\) | ||||
−0.255623 | + | 0.966777i | \(0.582281\pi\) | |||||||
\(332\) | 8.19709 | 0.449874 | ||||||||
\(333\) | 19.0239 | 1.04250 | ||||||||
\(334\) | −16.5880 | −0.907655 | ||||||||
\(335\) | −45.0133 | −2.45934 | ||||||||
\(336\) | 0.339766 | 0.0185358 | ||||||||
\(337\) | −32.8355 | −1.78867 | −0.894333 | − | 0.447402i | \(-0.852349\pi\) | ||||
−0.894333 | + | 0.447402i | \(0.852349\pi\) | |||||||
\(338\) | −30.1079 | −1.63765 | ||||||||
\(339\) | 6.49380 | 0.352695 | ||||||||
\(340\) | 15.1025 | 0.819049 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 2.55126 | 0.137956 | ||||||||
\(343\) | −6.97035 | −0.376364 | ||||||||
\(344\) | 3.21149 | 0.173152 | ||||||||
\(345\) | −0.422981 | −0.0227725 | ||||||||
\(346\) | −3.84292 | −0.206596 | ||||||||
\(347\) | −11.6844 | −0.627253 | −0.313626 | − | 0.949546i | \(-0.601544\pi\) | ||||
−0.313626 | + | 0.949546i | \(0.601544\pi\) | |||||||
\(348\) | −4.74445 | −0.254329 | ||||||||
\(349\) | 26.0735 | 1.39568 | 0.697841 | − | 0.716253i | \(-0.254144\pi\) | ||||
0.697841 | + | 0.716253i | \(0.254144\pi\) | |||||||
\(350\) | −3.91253 | −0.209133 | ||||||||
\(351\) | −24.4157 | −1.30321 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −6.91592 | −0.368097 | −0.184049 | − | 0.982917i | \(-0.558920\pi\) | ||||
−0.184049 | + | 0.982917i | \(0.558920\pi\) | |||||||
\(354\) | −3.73481 | −0.198503 | ||||||||
\(355\) | 30.4909 | 1.61829 | ||||||||
\(356\) | 12.4423 | 0.659439 | ||||||||
\(357\) | −1.43909 | −0.0761649 | ||||||||
\(358\) | 1.72834 | 0.0913457 | ||||||||
\(359\) | −6.60482 | −0.348589 | −0.174295 | − | 0.984694i | \(-0.555764\pi\) | ||||
−0.174295 | + | 0.984694i | \(0.555764\pi\) | |||||||
\(360\) | −9.09692 | −0.479450 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | 2.29655 | 0.120704 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 3.33012 | 0.174546 | ||||||||
\(365\) | 3.93728 | 0.206087 | ||||||||
\(366\) | 0.660234 | 0.0345110 | ||||||||
\(367\) | 2.74834 | 0.143462 | 0.0717312 | − | 0.997424i | \(-0.477148\pi\) | ||||
0.0717312 | + | 0.997424i | \(0.477148\pi\) | |||||||
\(368\) | 0.177085 | 0.00923120 | ||||||||
\(369\) | 6.92395 | 0.360447 | ||||||||
\(370\) | −26.5880 | −1.38224 | ||||||||
\(371\) | 1.28911 | 0.0669272 | ||||||||
\(372\) | 6.95913 | 0.360814 | ||||||||
\(373\) | 1.84378 | 0.0954675 | 0.0477337 | − | 0.998860i | \(-0.484800\pi\) | ||||
0.0477337 | + | 0.998860i | \(0.484800\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −6.48245 | −0.334752 | ||||||||
\(376\) | 3.13132 | 0.161486 | ||||||||
\(377\) | −46.5014 | −2.39494 | ||||||||
\(378\) | 1.88613 | 0.0970120 | ||||||||
\(379\) | −9.27484 | −0.476417 | −0.238208 | − | 0.971214i | \(-0.576560\pi\) | ||||
−0.238208 | + | 0.971214i | \(0.576560\pi\) | |||||||
\(380\) | −3.56566 | −0.182915 | ||||||||
\(381\) | −7.89896 | −0.404676 | ||||||||
\(382\) | −7.88053 | −0.403203 | ||||||||
\(383\) | 14.4479 | 0.738252 | 0.369126 | − | 0.929379i | \(-0.379657\pi\) | ||||
0.369126 | + | 0.929379i | \(0.379657\pi\) | |||||||
\(384\) | −0.669883 | −0.0341848 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0.254703 | 0.0129641 | ||||||||
\(387\) | 8.19334 | 0.416491 | ||||||||
\(388\) | −8.82526 | −0.448035 | ||||||||
\(389\) | −4.15708 | −0.210773 | −0.105386 | − | 0.994431i | \(-0.533608\pi\) | ||||
−0.105386 | + | 0.994431i | \(0.533608\pi\) | |||||||
\(390\) | 15.6826 | 0.794118 | ||||||||
\(391\) | −0.750052 | −0.0379318 | ||||||||
\(392\) | 6.74275 | 0.340560 | ||||||||
\(393\) | 5.23611 | 0.264127 | ||||||||
\(394\) | 18.2626 | 0.920059 | ||||||||
\(395\) | 34.8106 | 1.75151 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 4.98609 | 0.250245 | 0.125122 | − | 0.992141i | \(-0.460068\pi\) | ||||
0.125122 | + | 0.992141i | \(0.460068\pi\) | |||||||
\(398\) | −8.60007 | −0.431082 | ||||||||
\(399\) | 0.339766 | 0.0170096 | ||||||||
\(400\) | 7.71394 | 0.385697 | ||||||||
\(401\) | −5.95658 | −0.297457 | −0.148729 | − | 0.988878i | \(-0.547518\pi\) | ||||
−0.148729 | + | 0.988878i | \(0.547518\pi\) | |||||||
\(402\) | −8.45668 | −0.421781 | ||||||||
\(403\) | 68.2079 | 3.39768 | ||||||||
\(404\) | −7.36857 | −0.366600 | ||||||||
\(405\) | −18.4084 | −0.914719 | ||||||||
\(406\) | 3.59226 | 0.178281 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 2.83732 | 0.140468 | ||||||||
\(409\) | −23.8957 | −1.18157 | −0.590783 | − | 0.806830i | \(-0.701181\pi\) | ||||
−0.590783 | + | 0.806830i | \(0.701181\pi\) | |||||||
\(410\) | −9.67698 | −0.477912 | ||||||||
\(411\) | 4.23929 | 0.209109 | ||||||||
\(412\) | 16.0367 | 0.790074 | ||||||||
\(413\) | 2.82781 | 0.139147 | ||||||||
\(414\) | 0.451790 | 0.0222042 | ||||||||
\(415\) | −29.2280 | −1.43475 | ||||||||
\(416\) | −6.56566 | −0.321908 | ||||||||
\(417\) | 10.0696 | 0.493110 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 20.5785 | 1.00533 | 0.502663 | − | 0.864483i | \(-0.332354\pi\) | ||||
0.502663 | + | 0.864483i | \(0.332354\pi\) | |||||||
\(420\) | −1.21149 | −0.0591147 | ||||||||
\(421\) | −18.7947 | −0.916000 | −0.458000 | − | 0.888952i | \(-0.651434\pi\) | ||||
−0.458000 | + | 0.888952i | \(0.651434\pi\) | |||||||
\(422\) | −10.8661 | −0.528955 | ||||||||
\(423\) | 7.98881 | 0.388429 | ||||||||
\(424\) | −2.54161 | −0.123431 | ||||||||
\(425\) | −32.6727 | −1.58486 | ||||||||
\(426\) | 5.72834 | 0.277539 | ||||||||
\(427\) | −0.499896 | −0.0241917 | ||||||||
\(428\) | −12.7458 | −0.616091 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −11.4511 | −0.552220 | ||||||||
\(431\) | −28.4182 | −1.36885 | −0.684427 | − | 0.729081i | \(-0.739948\pi\) | ||||
−0.684427 | + | 0.729081i | \(0.739948\pi\) | |||||||
\(432\) | −3.71869 | −0.178916 | ||||||||
\(433\) | −3.03980 | −0.146083 | −0.0730416 | − | 0.997329i | \(-0.523271\pi\) | ||||
−0.0730416 | + | 0.997329i | \(0.523271\pi\) | |||||||
\(434\) | −5.26911 | −0.252925 | ||||||||
\(435\) | 16.9171 | 0.811114 | ||||||||
\(436\) | −10.0856 | −0.483011 | ||||||||
\(437\) | 0.177085 | 0.00847113 | ||||||||
\(438\) | 0.739700 | 0.0353442 | ||||||||
\(439\) | 32.8218 | 1.56650 | 0.783250 | − | 0.621706i | \(-0.213560\pi\) | ||||
0.783250 | + | 0.621706i | \(0.213560\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 17.2025 | 0.819166 | ||||||||
\(442\) | 27.8091 | 1.32275 | ||||||||
\(443\) | −21.6905 | −1.03055 | −0.515274 | − | 0.857026i | \(-0.672310\pi\) | ||||
−0.515274 | + | 0.857026i | \(0.672310\pi\) | |||||||
\(444\) | −4.99511 | −0.237057 | ||||||||
\(445\) | −44.3649 | −2.10310 | ||||||||
\(446\) | 12.4711 | 0.590523 | ||||||||
\(447\) | 14.1491 | 0.669232 | ||||||||
\(448\) | 0.507202 | 0.0239630 | ||||||||
\(449\) | 19.1889 | 0.905582 | 0.452791 | − | 0.891617i | \(-0.350428\pi\) | ||||
0.452791 | + | 0.891617i | \(0.350428\pi\) | |||||||
\(450\) | 19.6802 | 0.927735 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 9.69394 | 0.455964 | ||||||||
\(453\) | 15.5672 | 0.731412 | ||||||||
\(454\) | −29.8483 | −1.40085 | ||||||||
\(455\) | −11.8741 | −0.556665 | ||||||||
\(456\) | −0.669883 | −0.0313701 | ||||||||
\(457\) | −34.5863 | −1.61788 | −0.808939 | − | 0.587892i | \(-0.799958\pi\) | ||||
−0.808939 | + | 0.587892i | \(0.799958\pi\) | |||||||
\(458\) | 19.3115 | 0.902365 | ||||||||
\(459\) | 15.7507 | 0.735179 | ||||||||
\(460\) | −0.631426 | −0.0294404 | ||||||||
\(461\) | 7.67464 | 0.357444 | 0.178722 | − | 0.983900i | \(-0.442804\pi\) | ||||
0.178722 | + | 0.983900i | \(0.442804\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 18.1938 | 0.845539 | 0.422770 | − | 0.906237i | \(-0.361058\pi\) | ||||
0.422770 | + | 0.906237i | \(0.361058\pi\) | |||||||
\(464\) | −7.08251 | −0.328797 | ||||||||
\(465\) | −24.8139 | −1.15072 | ||||||||
\(466\) | 10.0288 | 0.464576 | ||||||||
\(467\) | −1.49500 | −0.0691805 | −0.0345902 | − | 0.999402i | \(-0.511013\pi\) | ||||
−0.0345902 | + | 0.999402i | \(0.511013\pi\) | |||||||
\(468\) | −16.7507 | −0.774301 | ||||||||
\(469\) | 6.40298 | 0.295662 | ||||||||
\(470\) | −11.1652 | −0.515014 | ||||||||
\(471\) | 5.95267 | 0.274284 | ||||||||
\(472\) | −5.57531 | −0.256624 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 6.53990 | 0.300388 | ||||||||
\(475\) | 7.71394 | 0.353940 | ||||||||
\(476\) | −2.14828 | −0.0984661 | ||||||||
\(477\) | −6.48429 | −0.296895 | ||||||||
\(478\) | −11.2291 | −0.513606 | ||||||||
\(479\) | 34.8658 | 1.59306 | 0.796529 | − | 0.604601i | \(-0.206667\pi\) | ||||
0.796529 | + | 0.604601i | \(0.206667\pi\) | |||||||
\(480\) | 2.38858 | 0.109023 | ||||||||
\(481\) | −48.9581 | −2.23230 | ||||||||
\(482\) | 16.0367 | 0.730454 | ||||||||
\(483\) | 0.0601675 | 0.00273772 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 31.4679 | 1.42888 | ||||||||
\(486\) | −14.6145 | −0.662926 | ||||||||
\(487\) | 17.2996 | 0.783920 | 0.391960 | − | 0.919982i | \(-0.371797\pi\) | ||||
0.391960 | + | 0.919982i | \(0.371797\pi\) | |||||||
\(488\) | 0.985596 | 0.0446158 | ||||||||
\(489\) | 7.66171 | 0.346475 | ||||||||
\(490\) | −24.0423 | −1.08612 | ||||||||
\(491\) | 38.2536 | 1.72636 | 0.863181 | − | 0.504895i | \(-0.168469\pi\) | ||||
0.863181 | + | 0.504895i | \(0.168469\pi\) | |||||||
\(492\) | −1.81802 | −0.0819627 | ||||||||
\(493\) | 29.9983 | 1.35106 | ||||||||
\(494\) | −6.56566 | −0.295403 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 10.3886 | 0.466461 | ||||||||
\(497\) | −4.33722 | −0.194551 | ||||||||
\(498\) | −5.49109 | −0.246062 | ||||||||
\(499\) | 30.5785 | 1.36888 | 0.684441 | − | 0.729069i | \(-0.260046\pi\) | ||||
0.684441 | + | 0.729069i | \(0.260046\pi\) | |||||||
\(500\) | −9.67698 | −0.432768 | ||||||||
\(501\) | 11.1120 | 0.496449 | ||||||||
\(502\) | −27.0591 | −1.20771 | ||||||||
\(503\) | −14.0304 | −0.625583 | −0.312791 | − | 0.949822i | \(-0.601264\pi\) | ||||
−0.312791 | + | 0.949822i | \(0.601264\pi\) | |||||||
\(504\) | 1.29400 | 0.0576395 | ||||||||
\(505\) | 26.2738 | 1.16917 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 20.1688 | 0.895727 | ||||||||
\(508\) | −11.7916 | −0.523166 | ||||||||
\(509\) | 22.4616 | 0.995592 | 0.497796 | − | 0.867294i | \(-0.334143\pi\) | ||||
0.497796 | + | 0.867294i | \(0.334143\pi\) | |||||||
\(510\) | −10.1169 | −0.447985 | ||||||||
\(511\) | −0.560064 | −0.0247758 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | −3.71869 | −0.164184 | ||||||||
\(514\) | −29.2963 | −1.29221 | ||||||||
\(515\) | −57.1816 | −2.51972 | ||||||||
\(516\) | −2.15132 | −0.0947067 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 3.78205 | 0.166174 | ||||||||
\(519\) | 2.57430 | 0.112999 | ||||||||
\(520\) | 23.4109 | 1.02664 | ||||||||
\(521\) | −5.86378 | −0.256897 | −0.128449 | − | 0.991716i | \(-0.541000\pi\) | ||||
−0.128449 | + | 0.991716i | \(0.541000\pi\) | |||||||
\(522\) | −18.0693 | −0.790872 | ||||||||
\(523\) | 25.2701 | 1.10498 | 0.552492 | − | 0.833518i | \(-0.313677\pi\) | ||||
0.552492 | + | 0.833518i | \(0.313677\pi\) | |||||||
\(524\) | 7.81645 | 0.341463 | ||||||||
\(525\) | 2.62093 | 0.114387 | ||||||||
\(526\) | −30.7129 | −1.33914 | ||||||||
\(527\) | −44.0013 | −1.91673 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −22.9686 | −0.998637 | ||||||||
\(530\) | 9.06251 | 0.393650 | ||||||||
\(531\) | −14.2240 | −0.617271 | ||||||||
\(532\) | 0.507202 | 0.0219900 | ||||||||
\(533\) | −17.8188 | −0.771818 | ||||||||
\(534\) | −8.33487 | −0.360685 | ||||||||
\(535\) | 45.4472 | 1.96485 | ||||||||
\(536\) | −12.6241 | −0.545279 | ||||||||
\(537\) | −1.15779 | −0.0499622 | ||||||||
\(538\) | 14.0288 | 0.604825 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 13.2596 | 0.570602 | ||||||||
\(541\) | −3.69052 | −0.158668 | −0.0793339 | − | 0.996848i | \(-0.525279\pi\) | ||||
−0.0793339 | + | 0.996848i | \(0.525279\pi\) | |||||||
\(542\) | −12.4350 | −0.534128 | ||||||||
\(543\) | −1.53842 | −0.0660200 | ||||||||
\(544\) | 4.23554 | 0.181597 | ||||||||
\(545\) | 35.9617 | 1.54043 | ||||||||
\(546\) | −2.23079 | −0.0954690 | ||||||||
\(547\) | −22.6568 | −0.968736 | −0.484368 | − | 0.874864i | \(-0.660950\pi\) | ||||
−0.484368 | + | 0.874864i | \(0.660950\pi\) | |||||||
\(548\) | 6.32841 | 0.270336 | ||||||||
\(549\) | 2.51451 | 0.107317 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −7.08251 | −0.301725 | ||||||||
\(552\) | −0.118626 | −0.00504907 | ||||||||
\(553\) | −4.95169 | −0.210567 | ||||||||
\(554\) | 16.6761 | 0.708500 | ||||||||
\(555\) | 17.8109 | 0.756029 | ||||||||
\(556\) | 15.0319 | 0.637493 | ||||||||
\(557\) | 31.8458 | 1.34935 | 0.674674 | − | 0.738116i | \(-0.264284\pi\) | ||||
0.674674 | + | 0.738116i | \(0.264284\pi\) | |||||||
\(558\) | 26.5039 | 1.12200 | ||||||||
\(559\) | −21.0856 | −0.891824 | ||||||||
\(560\) | −1.80851 | −0.0764235 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −4.67159 | −0.197059 | ||||||||
\(563\) | −6.18915 | −0.260841 | −0.130421 | − | 0.991459i | \(-0.541633\pi\) | ||||
−0.130421 | + | 0.991459i | \(0.541633\pi\) | |||||||
\(564\) | −2.09762 | −0.0883257 | ||||||||
\(565\) | −34.5653 | −1.45417 | ||||||||
\(566\) | −6.37907 | −0.268132 | ||||||||
\(567\) | 2.61852 | 0.109968 | ||||||||
\(568\) | 8.55126 | 0.358803 | ||||||||
\(569\) | −17.7090 | −0.742402 | −0.371201 | − | 0.928553i | \(-0.621054\pi\) | ||||
−0.371201 | + | 0.928553i | \(0.621054\pi\) | |||||||
\(570\) | 2.38858 | 0.100046 | ||||||||
\(571\) | −23.1562 | −0.969058 | −0.484529 | − | 0.874775i | \(-0.661009\pi\) | ||||
−0.484529 | + | 0.874775i | \(0.661009\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 5.27903 | 0.220535 | ||||||||
\(574\) | 1.37651 | 0.0574546 | ||||||||
\(575\) | 1.36602 | 0.0569671 | ||||||||
\(576\) | −2.55126 | −0.106302 | ||||||||
\(577\) | 42.8476 | 1.78377 | 0.891885 | − | 0.452263i | \(-0.149383\pi\) | ||||
0.891885 | + | 0.452263i | \(0.149383\pi\) | |||||||
\(578\) | −0.939832 | −0.0390919 | ||||||||
\(579\) | −0.170621 | −0.00709078 | ||||||||
\(580\) | 25.2538 | 1.04861 | ||||||||
\(581\) | 4.15758 | 0.172485 | ||||||||
\(582\) | 5.91189 | 0.245056 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 1.10422 | 0.0456930 | ||||||||
\(585\) | 59.7273 | 2.46942 | ||||||||
\(586\) | 12.8283 | 0.529932 | ||||||||
\(587\) | −33.3363 | −1.37594 | −0.687969 | − | 0.725740i | \(-0.741498\pi\) | ||||
−0.687969 | + | 0.725740i | \(0.741498\pi\) | |||||||
\(588\) | −4.51685 | −0.186272 | ||||||||
\(589\) | 10.3886 | 0.428054 | ||||||||
\(590\) | 19.8797 | 0.818433 | ||||||||
\(591\) | −12.2338 | −0.503233 | ||||||||
\(592\) | −7.45668 | −0.306468 | ||||||||
\(593\) | 23.7095 | 0.973634 | 0.486817 | − | 0.873504i | \(-0.338158\pi\) | ||||
0.486817 | + | 0.873504i | \(0.338158\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 7.66003 | 0.314030 | ||||||||
\(596\) | 21.1218 | 0.865183 | ||||||||
\(597\) | 5.76104 | 0.235784 | ||||||||
\(598\) | −1.16268 | −0.0475456 | ||||||||
\(599\) | 31.1681 | 1.27349 | 0.636746 | − | 0.771073i | \(-0.280280\pi\) | ||||
0.636746 | + | 0.771073i | \(0.280280\pi\) | |||||||
\(600\) | −5.16744 | −0.210960 | ||||||||
\(601\) | −13.6609 | −0.557241 | −0.278621 | − | 0.960401i | \(-0.589877\pi\) | ||||
−0.278621 | + | 0.960401i | \(0.589877\pi\) | |||||||
\(602\) | 1.62887 | 0.0663880 | ||||||||
\(603\) | −32.2074 | −1.31159 | ||||||||
\(604\) | 23.2387 | 0.945570 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 4.93608 | 0.200515 | ||||||||
\(607\) | −2.60262 | −0.105637 | −0.0528185 | − | 0.998604i | \(-0.516820\pi\) | ||||
−0.0528185 | + | 0.998604i | \(0.516820\pi\) | |||||||
\(608\) | −1.00000 | −0.0405554 | ||||||||
\(609\) | −2.40640 | −0.0975121 | ||||||||
\(610\) | −3.51430 | −0.142290 | ||||||||
\(611\) | −20.5592 | −0.831736 | ||||||||
\(612\) | 10.8060 | 0.436805 | ||||||||
\(613\) | 32.5978 | 1.31661 | 0.658306 | − | 0.752750i | \(-0.271273\pi\) | ||||
0.658306 | + | 0.752750i | \(0.271273\pi\) | |||||||
\(614\) | 26.5880 | 1.07300 | ||||||||
\(615\) | 6.48245 | 0.261397 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −5.46228 | −0.219903 | −0.109952 | − | 0.993937i | \(-0.535070\pi\) | ||||
−0.109952 | + | 0.993937i | \(0.535070\pi\) | |||||||
\(618\) | −10.7427 | −0.432137 | ||||||||
\(619\) | −5.98070 | −0.240385 | −0.120192 | − | 0.992751i | \(-0.538351\pi\) | ||||
−0.120192 | + | 0.992751i | \(0.538351\pi\) | |||||||
\(620\) | −37.0421 | −1.48765 | ||||||||
\(621\) | −0.658525 | −0.0264257 | ||||||||
\(622\) | −13.5664 | −0.543962 | ||||||||
\(623\) | 6.31075 | 0.252835 | ||||||||
\(624\) | 4.39822 | 0.176070 | ||||||||
\(625\) | −4.06485 | −0.162594 | ||||||||
\(626\) | −15.1608 | −0.605949 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 8.88613 | 0.354595 | ||||||||
\(629\) | 31.5831 | 1.25930 | ||||||||
\(630\) | −4.61398 | −0.183825 | ||||||||
\(631\) | 23.8397 | 0.949042 | 0.474521 | − | 0.880244i | \(-0.342621\pi\) | ||||
0.474521 | + | 0.880244i | \(0.342621\pi\) | |||||||
\(632\) | 9.76275 | 0.388341 | ||||||||
\(633\) | 7.27903 | 0.289316 | ||||||||
\(634\) | −26.5958 | −1.05625 | ||||||||
\(635\) | 42.0447 | 1.66849 | ||||||||
\(636\) | 1.70258 | 0.0675117 | ||||||||
\(637\) | −44.2706 | −1.75406 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 21.8165 | 0.863045 | ||||||||
\(640\) | 3.56566 | 0.140945 | ||||||||
\(641\) | −21.9373 | −0.866471 | −0.433235 | − | 0.901281i | \(-0.642628\pi\) | ||||
−0.433235 | + | 0.901281i | \(0.642628\pi\) | |||||||
\(642\) | 8.53819 | 0.336975 | ||||||||
\(643\) | 19.4950 | 0.768808 | 0.384404 | − | 0.923165i | \(-0.374407\pi\) | ||||
0.384404 | + | 0.923165i | \(0.374407\pi\) | |||||||
\(644\) | 0.0898180 | 0.00353932 | ||||||||
\(645\) | 7.67089 | 0.302041 | ||||||||
\(646\) | 4.23554 | 0.166645 | ||||||||
\(647\) | −3.89032 | −0.152944 | −0.0764721 | − | 0.997072i | \(-0.524366\pi\) | ||||
−0.0764721 | + | 0.997072i | \(0.524366\pi\) | |||||||
\(648\) | −5.16268 | −0.202809 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | −50.6471 | −1.98654 | ||||||||
\(651\) | 3.52969 | 0.138339 | ||||||||
\(652\) | 11.4374 | 0.447923 | ||||||||
\(653\) | −26.6031 | −1.04106 | −0.520530 | − | 0.853843i | \(-0.674266\pi\) | ||||
−0.520530 | + | 0.853843i | \(0.674266\pi\) | |||||||
\(654\) | 6.75614 | 0.264186 | ||||||||
\(655\) | −27.8708 | −1.08900 | ||||||||
\(656\) | −2.71394 | −0.105961 | ||||||||
\(657\) | 2.81715 | 0.109908 | ||||||||
\(658\) | 1.58821 | 0.0619150 | ||||||||
\(659\) | 27.4941 | 1.07102 | 0.535510 | − | 0.844529i | \(-0.320120\pi\) | ||||
0.535510 | + | 0.844529i | \(0.320120\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −9.38616 | −0.365079 | −0.182540 | − | 0.983198i | \(-0.558432\pi\) | ||||
−0.182540 | + | 0.983198i | \(0.558432\pi\) | |||||||
\(662\) | 9.30131 | 0.361506 | ||||||||
\(663\) | −18.6289 | −0.723486 | ||||||||
\(664\) | −8.19709 | −0.318109 | ||||||||
\(665\) | −1.80851 | −0.0701310 | ||||||||
\(666\) | −19.0239 | −0.737162 | ||||||||
\(667\) | −1.25421 | −0.0485631 | ||||||||
\(668\) | 16.5880 | 0.641809 | ||||||||
\(669\) | −8.35417 | −0.322991 | ||||||||
\(670\) | 45.0133 | 1.73902 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | −0.339766 | −0.0131068 | ||||||||
\(673\) | −13.9317 | −0.537027 | −0.268513 | − | 0.963276i | \(-0.586532\pi\) | ||||
−0.268513 | + | 0.963276i | \(0.586532\pi\) | |||||||
\(674\) | 32.8355 | 1.26478 | ||||||||
\(675\) | −28.6858 | −1.10412 | ||||||||
\(676\) | 30.1079 | 1.15800 | ||||||||
\(677\) | 27.8885 | 1.07184 | 0.535921 | − | 0.844268i | \(-0.319965\pi\) | ||||
0.535921 | + | 0.844268i | \(0.319965\pi\) | |||||||
\(678\) | −6.49380 | −0.249393 | ||||||||
\(679\) | −4.47619 | −0.171780 | ||||||||
\(680\) | −15.1025 | −0.579155 | ||||||||
\(681\) | 19.9949 | 0.766205 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −19.9390 | −0.762943 | −0.381472 | − | 0.924381i | \(-0.624583\pi\) | ||||
−0.381472 | + | 0.924381i | \(0.624583\pi\) | |||||||
\(684\) | −2.55126 | −0.0975497 | ||||||||
\(685\) | −22.5650 | −0.862163 | ||||||||
\(686\) | 6.97035 | 0.266129 | ||||||||
\(687\) | −12.9364 | −0.493555 | ||||||||
\(688\) | −3.21149 | −0.122437 | ||||||||
\(689\) | 16.6873 | 0.635737 | ||||||||
\(690\) | 0.422981 | 0.0161026 | ||||||||
\(691\) | 29.1567 | 1.10917 | 0.554587 | − | 0.832126i | \(-0.312876\pi\) | ||||
0.554587 | + | 0.832126i | \(0.312876\pi\) | |||||||
\(692\) | 3.84292 | 0.146086 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 11.6844 | 0.443535 | ||||||||
\(695\) | −53.5985 | −2.03311 | ||||||||
\(696\) | 4.74445 | 0.179838 | ||||||||
\(697\) | 11.4950 | 0.435404 | ||||||||
\(698\) | −26.0735 | −0.986896 | ||||||||
\(699\) | −6.71813 | −0.254103 | ||||||||
\(700\) | 3.91253 | 0.147880 | ||||||||
\(701\) | 37.3410 | 1.41035 | 0.705176 | − | 0.709033i | \(-0.250868\pi\) | ||||
0.705176 | + | 0.709033i | \(0.250868\pi\) | |||||||
\(702\) | 24.4157 | 0.921510 | ||||||||
\(703\) | −7.45668 | −0.281234 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 7.47940 | 0.281690 | ||||||||
\(706\) | 6.91592 | 0.260284 | ||||||||
\(707\) | −3.73736 | −0.140558 | ||||||||
\(708\) | 3.73481 | 0.140363 | ||||||||
\(709\) | 4.62583 | 0.173727 | 0.0868633 | − | 0.996220i | \(-0.472316\pi\) | ||||
0.0868633 | + | 0.996220i | \(0.472316\pi\) | |||||||
\(710\) | −30.4909 | −1.14430 | ||||||||
\(711\) | 24.9073 | 0.934096 | ||||||||
\(712\) | −12.4423 | −0.466294 | ||||||||
\(713\) | 1.83966 | 0.0688959 | ||||||||
\(714\) | 1.43909 | 0.0538567 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −1.72834 | −0.0645912 | ||||||||
\(717\) | 7.52217 | 0.280921 | ||||||||
\(718\) | 6.60482 | 0.246490 | ||||||||
\(719\) | 8.05534 | 0.300414 | 0.150207 | − | 0.988655i | \(-0.452006\pi\) | ||||
0.150207 | + | 0.988655i | \(0.452006\pi\) | |||||||
\(720\) | 9.09692 | 0.339022 | ||||||||
\(721\) | 8.13387 | 0.302921 | ||||||||
\(722\) | −1.00000 | −0.0372161 | ||||||||
\(723\) | −10.7427 | −0.399527 | ||||||||
\(724\) | −2.29655 | −0.0853507 | ||||||||
\(725\) | −54.6341 | −2.02906 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −29.9940 | −1.11242 | −0.556209 | − | 0.831043i | \(-0.687744\pi\) | ||||
−0.556209 | + | 0.831043i | \(0.687744\pi\) | |||||||
\(728\) | −3.33012 | −0.123422 | ||||||||
\(729\) | −5.69806 | −0.211039 | ||||||||
\(730\) | −3.93728 | −0.145725 | ||||||||
\(731\) | 13.6024 | 0.503103 | ||||||||
\(732\) | −0.660234 | −0.0244029 | ||||||||
\(733\) | −19.2675 | −0.711663 | −0.355831 | − | 0.934550i | \(-0.615802\pi\) | ||||
−0.355831 | + | 0.934550i | \(0.615802\pi\) | |||||||
\(734\) | −2.74834 | −0.101443 | ||||||||
\(735\) | 16.1056 | 0.594063 | ||||||||
\(736\) | −0.177085 | −0.00652744 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | −6.92395 | −0.254874 | ||||||||
\(739\) | −40.6838 | −1.49658 | −0.748288 | − | 0.663373i | \(-0.769124\pi\) | ||||
−0.748288 | + | 0.663373i | \(0.769124\pi\) | |||||||
\(740\) | 26.5880 | 0.977395 | ||||||||
\(741\) | 4.39822 | 0.161573 | ||||||||
\(742\) | −1.28911 | −0.0473247 | ||||||||
\(743\) | 16.8206 | 0.617087 | 0.308543 | − | 0.951210i | \(-0.400158\pi\) | ||||
0.308543 | + | 0.951210i | \(0.400158\pi\) | |||||||
\(744\) | −6.95913 | −0.255134 | ||||||||
\(745\) | −75.3132 | −2.75926 | ||||||||
\(746\) | −1.84378 | −0.0675057 | ||||||||
\(747\) | −20.9129 | −0.765162 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −6.46469 | −0.236215 | ||||||||
\(750\) | 6.48245 | 0.236705 | ||||||||
\(751\) | 36.8011 | 1.34289 | 0.671446 | − | 0.741053i | \(-0.265673\pi\) | ||||
0.671446 | + | 0.741053i | \(0.265673\pi\) | |||||||
\(752\) | −3.13132 | −0.114188 | ||||||||
\(753\) | 18.1264 | 0.660564 | ||||||||
\(754\) | 46.5014 | 1.69348 | ||||||||
\(755\) | −82.8614 | −3.01564 | ||||||||
\(756\) | −1.88613 | −0.0685978 | ||||||||
\(757\) | 32.0751 | 1.16579 | 0.582894 | − | 0.812548i | \(-0.301920\pi\) | ||||
0.582894 | + | 0.812548i | \(0.301920\pi\) | |||||||
\(758\) | 9.27484 | 0.336877 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 3.56566 | 0.129340 | ||||||||
\(761\) | −5.99220 | −0.217217 | −0.108609 | − | 0.994085i | \(-0.534639\pi\) | ||||
−0.108609 | + | 0.994085i | \(0.534639\pi\) | |||||||
\(762\) | 7.89896 | 0.286149 | ||||||||
\(763\) | −5.11542 | −0.185191 | ||||||||
\(764\) | 7.88053 | 0.285108 | ||||||||
\(765\) | −38.5304 | −1.39307 | ||||||||
\(766\) | −14.4479 | −0.522023 | ||||||||
\(767\) | 36.6056 | 1.32175 | ||||||||
\(768\) | 0.669883 | 0.0241723 | ||||||||
\(769\) | −3.11373 | −0.112284 | −0.0561420 | − | 0.998423i | \(-0.517880\pi\) | ||||
−0.0561420 | + | 0.998423i | \(0.517880\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 19.6251 | 0.706782 | ||||||||
\(772\) | −0.254703 | −0.00916697 | ||||||||
\(773\) | −22.8477 | −0.821774 | −0.410887 | − | 0.911686i | \(-0.634781\pi\) | ||||
−0.410887 | + | 0.911686i | \(0.634781\pi\) | |||||||
\(774\) | −8.19334 | −0.294503 | ||||||||
\(775\) | 80.1368 | 2.87860 | ||||||||
\(776\) | 8.82526 | 0.316808 | ||||||||
\(777\) | −2.53353 | −0.0908898 | ||||||||
\(778\) | 4.15708 | 0.149039 | ||||||||
\(779\) | −2.71394 | −0.0972369 | ||||||||
\(780\) | −15.6826 | −0.561526 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0.750052 | 0.0268218 | ||||||||
\(783\) | 26.3377 | 0.941232 | ||||||||
\(784\) | −6.74275 | −0.240812 | ||||||||
\(785\) | −31.6849 | −1.13088 | ||||||||
\(786\) | −5.23611 | −0.186766 | ||||||||
\(787\) | −34.6929 | −1.23667 | −0.618333 | − | 0.785916i | \(-0.712192\pi\) | ||||
−0.618333 | + | 0.785916i | \(0.712192\pi\) | |||||||
\(788\) | −18.2626 | −0.650580 | ||||||||
\(789\) | 20.5740 | 0.732455 | ||||||||
\(790\) | −34.8106 | −1.23851 | ||||||||
\(791\) | 4.91678 | 0.174821 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −6.47109 | −0.229795 | ||||||||
\(794\) | −4.98609 | −0.176950 | ||||||||
\(795\) | −6.07082 | −0.215310 | ||||||||
\(796\) | 8.60007 | 0.304821 | ||||||||
\(797\) | 50.7079 | 1.79617 | 0.898083 | − | 0.439826i | \(-0.144960\pi\) | ||||
0.898083 | + | 0.439826i | \(0.144960\pi\) | |||||||
\(798\) | −0.339766 | −0.0120276 | ||||||||
\(799\) | 13.2629 | 0.469206 | ||||||||
\(800\) | −7.71394 | −0.272729 | ||||||||
\(801\) | −31.7434 | −1.12160 | ||||||||
\(802\) | 5.95658 | 0.210334 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 8.45668 | 0.298244 | ||||||||
\(805\) | −0.320260 | −0.0112877 | ||||||||
\(806\) | −68.2079 | −2.40252 | ||||||||
\(807\) | −9.39766 | −0.330813 | ||||||||
\(808\) | 7.36857 | 0.259226 | ||||||||
\(809\) | −26.4677 | −0.930555 | −0.465277 | − | 0.885165i | \(-0.654045\pi\) | ||||
−0.465277 | + | 0.885165i | \(0.654045\pi\) | |||||||
\(810\) | 18.4084 | 0.646804 | ||||||||
\(811\) | 18.9010 | 0.663705 | 0.331852 | − | 0.943331i | \(-0.392326\pi\) | ||||
0.331852 | + | 0.943331i | \(0.392326\pi\) | |||||||
\(812\) | −3.59226 | −0.126064 | ||||||||
\(813\) | 8.32998 | 0.292145 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −40.7818 | −1.42853 | ||||||||
\(816\) | −2.83732 | −0.0993260 | ||||||||
\(817\) | −3.21149 | −0.112356 | ||||||||
\(818\) | 23.8957 | 0.835494 | ||||||||
\(819\) | −8.49598 | −0.296874 | ||||||||
\(820\) | 9.67698 | 0.337935 | ||||||||
\(821\) | 37.4421 | 1.30674 | 0.653369 | − | 0.757040i | \(-0.273355\pi\) | ||||
0.653369 | + | 0.757040i | \(0.273355\pi\) | |||||||
\(822\) | −4.23929 | −0.147862 | ||||||||
\(823\) | −4.31330 | −0.150352 | −0.0751761 | − | 0.997170i | \(-0.523952\pi\) | ||||
−0.0751761 | + | 0.997170i | \(0.523952\pi\) | |||||||
\(824\) | −16.0367 | −0.558667 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −2.82781 | −0.0983921 | ||||||||
\(827\) | −2.87123 | −0.0998424 | −0.0499212 | − | 0.998753i | \(-0.515897\pi\) | ||||
−0.0499212 | + | 0.998753i | \(0.515897\pi\) | |||||||
\(828\) | −0.451790 | −0.0157008 | ||||||||
\(829\) | 25.7498 | 0.894329 | 0.447165 | − | 0.894452i | \(-0.352434\pi\) | ||||
0.447165 | + | 0.894452i | \(0.352434\pi\) | |||||||
\(830\) | 29.2280 | 1.01452 | ||||||||
\(831\) | −11.1710 | −0.387519 | ||||||||
\(832\) | 6.56566 | 0.227623 | ||||||||
\(833\) | 28.5592 | 0.989518 | ||||||||
\(834\) | −10.0696 | −0.348681 | ||||||||
\(835\) | −59.1472 | −2.04687 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −38.6319 | −1.33531 | ||||||||
\(838\) | −20.5785 | −0.710872 | ||||||||
\(839\) | −13.7883 | −0.476025 | −0.238013 | − | 0.971262i | \(-0.576496\pi\) | ||||
−0.238013 | + | 0.971262i | \(0.576496\pi\) | |||||||
\(840\) | 1.21149 | 0.0418004 | ||||||||
\(841\) | 21.1620 | 0.729723 | ||||||||
\(842\) | 18.7947 | 0.647710 | ||||||||
\(843\) | 3.12942 | 0.107783 | ||||||||
\(844\) | 10.8661 | 0.374028 | ||||||||
\(845\) | −107.355 | −3.69311 | ||||||||
\(846\) | −7.98881 | −0.274661 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 2.54161 | 0.0872792 | ||||||||
\(849\) | 4.27323 | 0.146657 | ||||||||
\(850\) | 32.6727 | 1.12067 | ||||||||
\(851\) | −1.32047 | −0.0452651 | ||||||||
\(852\) | −5.72834 | −0.196250 | ||||||||
\(853\) | −29.2868 | −1.00276 | −0.501381 | − | 0.865227i | \(-0.667175\pi\) | ||||
−0.501381 | + | 0.865227i | \(0.667175\pi\) | |||||||
\(854\) | 0.499896 | 0.0171061 | ||||||||
\(855\) | 9.09692 | 0.311108 | ||||||||
\(856\) | 12.7458 | 0.435642 | ||||||||
\(857\) | 48.1428 | 1.64453 | 0.822263 | − | 0.569107i | \(-0.192711\pi\) | ||||
0.822263 | + | 0.569107i | \(0.192711\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −17.6634 | −0.602669 | −0.301334 | − | 0.953519i | \(-0.597432\pi\) | ||||
−0.301334 | + | 0.953519i | \(0.597432\pi\) | |||||||
\(860\) | 11.4511 | 0.390479 | ||||||||
\(861\) | −0.922104 | −0.0314252 | ||||||||
\(862\) | 28.4182 | 0.967926 | ||||||||
\(863\) | 3.69002 | 0.125610 | 0.0628049 | − | 0.998026i | \(-0.479995\pi\) | ||||
0.0628049 | + | 0.998026i | \(0.479995\pi\) | |||||||
\(864\) | 3.71869 | 0.126512 | ||||||||
\(865\) | −13.7025 | −0.465900 | ||||||||
\(866\) | 3.03980 | 0.103296 | ||||||||
\(867\) | 0.629578 | 0.0213816 | ||||||||
\(868\) | 5.26911 | 0.178845 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | −16.9171 | −0.573544 | ||||||||
\(871\) | 82.8857 | 2.80847 | ||||||||
\(872\) | 10.0856 | 0.341540 | ||||||||
\(873\) | 22.5155 | 0.762034 | ||||||||
\(874\) | −0.177085 | −0.00598999 | ||||||||
\(875\) | −4.90819 | −0.165927 | ||||||||
\(876\) | −0.739700 | −0.0249921 | ||||||||
\(877\) | 21.9383 | 0.740802 | 0.370401 | − | 0.928872i | \(-0.379220\pi\) | ||||
0.370401 | + | 0.928872i | \(0.379220\pi\) | |||||||
\(878\) | −32.8218 | −1.10768 | ||||||||
\(879\) | −8.59346 | −0.289850 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 13.3359 | 0.449296 | 0.224648 | − | 0.974440i | \(-0.427877\pi\) | ||||
0.224648 | + | 0.974440i | \(0.427877\pi\) | |||||||
\(882\) | −17.2025 | −0.579237 | ||||||||
\(883\) | 45.0015 | 1.51442 | 0.757210 | − | 0.653171i | \(-0.226562\pi\) | ||||
0.757210 | + | 0.653171i | \(0.226562\pi\) | |||||||
\(884\) | −27.8091 | −0.935323 | ||||||||
\(885\) | −13.3171 | −0.447648 | ||||||||
\(886\) | 21.6905 | 0.728707 | ||||||||
\(887\) | −44.9327 | −1.50869 | −0.754346 | − | 0.656477i | \(-0.772046\pi\) | ||||
−0.754346 | + | 0.656477i | \(0.772046\pi\) | |||||||
\(888\) | 4.99511 | 0.167625 | ||||||||
\(889\) | −5.98070 | −0.200586 | ||||||||
\(890\) | 44.3649 | 1.48712 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −12.4711 | −0.417563 | ||||||||
\(893\) | −3.13132 | −0.104786 | ||||||||
\(894\) | −14.1491 | −0.473218 | ||||||||
\(895\) | 6.16268 | 0.205996 | ||||||||
\(896\) | −0.507202 | −0.0169444 | ||||||||
\(897\) | 0.778860 | 0.0260054 | ||||||||
\(898\) | −19.1889 | −0.640343 | ||||||||
\(899\) | −73.5772 | −2.45394 | ||||||||
\(900\) | −19.6802 | −0.656008 | ||||||||
\(901\) | −10.7651 | −0.358637 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −1.09116 | −0.0363114 | ||||||||
\(904\) | −9.69394 | −0.322416 | ||||||||
\(905\) | 8.18873 | 0.272203 | ||||||||
\(906\) | −15.5672 | −0.517187 | ||||||||
\(907\) | 56.6039 | 1.87950 | 0.939751 | − | 0.341860i | \(-0.111057\pi\) | ||||
0.939751 | + | 0.341860i | \(0.111057\pi\) | |||||||
\(908\) | 29.8483 | 0.990551 | ||||||||
\(909\) | 18.7991 | 0.623528 | ||||||||
\(910\) | 11.8741 | 0.393622 | ||||||||
\(911\) | −46.5978 | −1.54385 | −0.771927 | − | 0.635711i | \(-0.780707\pi\) | ||||
−0.771927 | + | 0.635711i | \(0.780707\pi\) | |||||||
\(912\) | 0.669883 | 0.0221820 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 34.5863 | 1.14401 | ||||||||
\(915\) | 2.35417 | 0.0778265 | ||||||||
\(916\) | −19.3115 | −0.638068 | ||||||||
\(917\) | 3.96452 | 0.130920 | ||||||||
\(918\) | −15.7507 | −0.519850 | ||||||||
\(919\) | −47.4246 | −1.56439 | −0.782197 | − | 0.623032i | \(-0.785901\pi\) | ||||
−0.782197 | + | 0.623032i | \(0.785901\pi\) | |||||||
\(920\) | 0.631426 | 0.0208175 | ||||||||
\(921\) | −17.8109 | −0.586888 | ||||||||
\(922\) | −7.67464 | −0.252751 | ||||||||
\(923\) | −56.1447 | −1.84802 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −57.5204 | −1.89126 | ||||||||
\(926\) | −18.1938 | −0.597886 | ||||||||
\(927\) | −40.9139 | −1.34379 | ||||||||
\(928\) | 7.08251 | 0.232495 | ||||||||
\(929\) | −46.6008 | −1.52892 | −0.764462 | − | 0.644669i | \(-0.776995\pi\) | ||||
−0.764462 | + | 0.644669i | \(0.776995\pi\) | |||||||
\(930\) | 24.8139 | 0.813680 | ||||||||
\(931\) | −6.74275 | −0.220985 | ||||||||
\(932\) | −10.0288 | −0.328505 | ||||||||
\(933\) | 9.08788 | 0.297524 | ||||||||
\(934\) | 1.49500 | 0.0489180 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 16.7507 | 0.547513 | ||||||||
\(937\) | −10.4826 | −0.342451 | −0.171226 | − | 0.985232i | \(-0.554773\pi\) | ||||
−0.171226 | + | 0.985232i | \(0.554773\pi\) | |||||||
\(938\) | −6.40298 | −0.209065 | ||||||||
\(939\) | 10.1560 | 0.331428 | ||||||||
\(940\) | 11.1652 | 0.364170 | ||||||||
\(941\) | 11.6226 | 0.378885 | 0.189443 | − | 0.981892i | \(-0.439332\pi\) | ||||
0.189443 | + | 0.981892i | \(0.439332\pi\) | |||||||
\(942\) | −5.95267 | −0.193948 | ||||||||
\(943\) | −0.480598 | −0.0156504 | ||||||||
\(944\) | 5.57531 | 0.181461 | ||||||||
\(945\) | 6.72530 | 0.218774 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −17.8702 | −0.580702 | −0.290351 | − | 0.956920i | \(-0.593772\pi\) | ||||
−0.290351 | + | 0.956920i | \(0.593772\pi\) | |||||||
\(948\) | −6.53990 | −0.212406 | ||||||||
\(949\) | −7.24995 | −0.235343 | ||||||||
\(950\) | −7.71394 | −0.250273 | ||||||||
\(951\) | 17.8161 | 0.577726 | ||||||||
\(952\) | 2.14828 | 0.0696260 | ||||||||
\(953\) | −41.5590 | −1.34623 | −0.673114 | − | 0.739539i | \(-0.735044\pi\) | ||||
−0.673114 | + | 0.739539i | \(0.735044\pi\) | |||||||
\(954\) | 6.48429 | 0.209937 | ||||||||
\(955\) | −28.0993 | −0.909272 | ||||||||
\(956\) | 11.2291 | 0.363174 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −34.8658 | −1.12646 | ||||||||
\(959\) | 3.20978 | 0.103649 | ||||||||
\(960\) | −2.38858 | −0.0770910 | ||||||||
\(961\) | 76.9225 | 2.48137 | ||||||||
\(962\) | 48.9581 | 1.57847 | ||||||||
\(963\) | 32.5178 | 1.04787 | ||||||||
\(964\) | −16.0367 | −0.516509 | ||||||||
\(965\) | 0.908185 | 0.0292355 | ||||||||
\(966\) | −0.0601675 | −0.00193586 | ||||||||
\(967\) | 0.275849 | 0.00887071 | 0.00443536 | − | 0.999990i | \(-0.498588\pi\) | ||||
0.00443536 | + | 0.999990i | \(0.498588\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −2.83732 | −0.0911478 | ||||||||
\(970\) | −31.4679 | −1.01037 | ||||||||
\(971\) | −11.8381 | −0.379902 | −0.189951 | − | 0.981794i | \(-0.560833\pi\) | ||||
−0.189951 | + | 0.981794i | \(0.560833\pi\) | |||||||
\(972\) | 14.6145 | 0.468759 | ||||||||
\(973\) | 7.62419 | 0.244420 | ||||||||
\(974\) | −17.2996 | −0.554315 | ||||||||
\(975\) | 33.9276 | 1.08655 | ||||||||
\(976\) | −0.985596 | −0.0315482 | ||||||||
\(977\) | 35.9868 | 1.15132 | 0.575660 | − | 0.817689i | \(-0.304745\pi\) | ||||
0.575660 | + | 0.817689i | \(0.304745\pi\) | |||||||
\(978\) | −7.66171 | −0.244994 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 24.0423 | 0.768005 | ||||||||
\(981\) | 25.7308 | 0.821523 | ||||||||
\(982\) | −38.2536 | −1.22072 | ||||||||
\(983\) | 28.7010 | 0.915420 | 0.457710 | − | 0.889102i | \(-0.348670\pi\) | ||||
0.457710 | + | 0.889102i | \(0.348670\pi\) | |||||||
\(984\) | 1.81802 | 0.0579564 | ||||||||
\(985\) | 65.1184 | 2.07484 | ||||||||
\(986\) | −29.9983 | −0.955340 | ||||||||
\(987\) | −1.06392 | −0.0338648 | ||||||||
\(988\) | 6.56566 | 0.208881 | ||||||||
\(989\) | −0.568707 | −0.0180838 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 56.1431 | 1.78344 | 0.891722 | − | 0.452584i | \(-0.149498\pi\) | ||||
0.891722 | + | 0.452584i | \(0.149498\pi\) | |||||||
\(992\) | −10.3886 | −0.329838 | ||||||||
\(993\) | −6.23079 | −0.197728 | ||||||||
\(994\) | 4.33722 | 0.137568 | ||||||||
\(995\) | −30.6649 | −0.972143 | ||||||||
\(996\) | 5.49109 | 0.173992 | ||||||||
\(997\) | 15.8844 | 0.503062 | 0.251531 | − | 0.967849i | \(-0.419066\pi\) | ||||
0.251531 | + | 0.967849i | \(0.419066\pi\) | |||||||
\(998\) | −30.5785 | −0.967945 | ||||||||
\(999\) | 27.7291 | 0.877310 |
(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 | 4598.2.a.br.1.3 | ✓ | 4 | |
11.10 | odd | 2 | 4598.2.a.bu.1.3 | yes | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4598.2.a.br.1.3 | ✓ | 4 | 1.1 | even | 1 | trivial | |
4598.2.a.bu.1.3 | yes | 4 | 11.10 | odd | 2 |