Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2842,2,Mod(1,2842)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2842, 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("2842.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2842 = 2 \cdot 7^{2} \cdot 29 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2842.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: | \(22.6934842544\) |
Analytic rank: | \(0\) |
Dimension: | \(5\) |
Coefficient field: | 5.5.974241.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{5} - x^{4} - 9x^{3} - 2x^{2} + 11x + 3 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 406) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-1.76647\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2842.1 |
$q$-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 | ||||||||
\(3\) | −2.42629 | −1.40082 | −0.700409 | − | 0.713742i | \(-0.746999\pi\) | ||||
−0.700409 | + | 0.713742i | \(0.746999\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 0.260736 | 0.116605 | 0.0583023 | − | 0.998299i | \(-0.481431\pi\) | ||||
0.0583023 | + | 0.998299i | \(0.481431\pi\) | |||||||
\(6\) | 2.42629 | 0.990527 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 2.88687 | 0.962289 | ||||||||
\(10\) | −0.260736 | −0.0824519 | ||||||||
\(11\) | 2.14760 | 0.647527 | 0.323763 | − | 0.946138i | \(-0.395052\pi\) | ||||
0.323763 | + | 0.946138i | \(0.395052\pi\) | |||||||
\(12\) | −2.42629 | −0.700409 | ||||||||
\(13\) | 6.34036 | 1.75850 | 0.879249 | − | 0.476362i | \(-0.158045\pi\) | ||||
0.879249 | + | 0.476362i | \(0.158045\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −0.632619 | −0.163342 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 2.22705 | 0.540138 | 0.270069 | − | 0.962841i | \(-0.412953\pi\) | ||||
0.270069 | + | 0.962841i | \(0.412953\pi\) | |||||||
\(18\) | −2.88687 | −0.680441 | ||||||||
\(19\) | 8.43775 | 1.93575 | 0.967876 | − | 0.251428i | \(-0.0809002\pi\) | ||||
0.967876 | + | 0.251428i | \(0.0809002\pi\) | |||||||
\(20\) | 0.260736 | 0.0583023 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −2.14760 | −0.457870 | ||||||||
\(23\) | 4.38533 | 0.914404 | 0.457202 | − | 0.889363i | \(-0.348852\pi\) | ||||
0.457202 | + | 0.889363i | \(0.348852\pi\) | |||||||
\(24\) | 2.42629 | 0.495264 | ||||||||
\(25\) | −4.93202 | −0.986403 | ||||||||
\(26\) | −6.34036 | −1.24345 | ||||||||
\(27\) | 0.274492 | 0.0528261 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −1.00000 | −0.185695 | ||||||||
\(30\) | 0.632619 | 0.115500 | ||||||||
\(31\) | −3.04515 | −0.546925 | −0.273463 | − | 0.961883i | \(-0.588169\pi\) | ||||
−0.273463 | + | 0.961883i | \(0.588169\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | −5.21070 | −0.907067 | ||||||||
\(34\) | −2.22705 | −0.381935 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 2.88687 | 0.481145 | ||||||||
\(37\) | −7.24517 | −1.19110 | −0.595549 | − | 0.803319i | \(-0.703066\pi\) | ||||
−0.595549 | + | 0.803319i | \(0.703066\pi\) | |||||||
\(38\) | −8.43775 | −1.36878 | ||||||||
\(39\) | −15.3835 | −2.46333 | ||||||||
\(40\) | −0.260736 | −0.0412259 | ||||||||
\(41\) | 10.7302 | 1.67577 | 0.837887 | − | 0.545844i | \(-0.183791\pi\) | ||||
0.837887 | + | 0.545844i | \(0.183791\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0.195049 | 0.0297447 | 0.0148723 | − | 0.999889i | \(-0.495266\pi\) | ||||
0.0148723 | + | 0.999889i | \(0.495266\pi\) | |||||||
\(44\) | 2.14760 | 0.323763 | ||||||||
\(45\) | 0.752709 | 0.112207 | ||||||||
\(46\) | −4.38533 | −0.646581 | ||||||||
\(47\) | 12.2245 | 1.78312 | 0.891560 | − | 0.452902i | \(-0.149611\pi\) | ||||
0.891560 | + | 0.452902i | \(0.149611\pi\) | |||||||
\(48\) | −2.42629 | −0.350204 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 4.93202 | 0.697493 | ||||||||
\(51\) | −5.40345 | −0.756635 | ||||||||
\(52\) | 6.34036 | 0.879249 | ||||||||
\(53\) | −0.390391 | −0.0536243 | −0.0268121 | − | 0.999640i | \(-0.508536\pi\) | ||||
−0.0268121 | + | 0.999640i | \(0.508536\pi\) | |||||||
\(54\) | −0.274492 | −0.0373537 | ||||||||
\(55\) | 0.559957 | 0.0755045 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −20.4724 | −2.71163 | ||||||||
\(58\) | 1.00000 | 0.131306 | ||||||||
\(59\) | −14.7537 | −1.92076 | −0.960382 | − | 0.278687i | \(-0.910101\pi\) | ||||
−0.960382 | + | 0.278687i | \(0.910101\pi\) | |||||||
\(60\) | −0.632619 | −0.0816708 | ||||||||
\(61\) | −9.83960 | −1.25983 | −0.629916 | − | 0.776664i | \(-0.716911\pi\) | ||||
−0.629916 | + | 0.776664i | \(0.716911\pi\) | |||||||
\(62\) | 3.04515 | 0.386734 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 1.65316 | 0.205049 | ||||||||
\(66\) | 5.21070 | 0.641393 | ||||||||
\(67\) | 9.53790 | 1.16524 | 0.582620 | − | 0.812745i | \(-0.302028\pi\) | ||||
0.582620 | + | 0.812745i | \(0.302028\pi\) | |||||||
\(68\) | 2.22705 | 0.270069 | ||||||||
\(69\) | −10.6401 | −1.28091 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 2.18856 | 0.259734 | 0.129867 | − | 0.991531i | \(-0.458545\pi\) | ||||
0.129867 | + | 0.991531i | \(0.458545\pi\) | |||||||
\(72\) | −2.88687 | −0.340221 | ||||||||
\(73\) | 4.18350 | 0.489642 | 0.244821 | − | 0.969568i | \(-0.421271\pi\) | ||||
0.244821 | + | 0.969568i | \(0.421271\pi\) | |||||||
\(74\) | 7.24517 | 0.842234 | ||||||||
\(75\) | 11.9665 | 1.38177 | ||||||||
\(76\) | 8.43775 | 0.967876 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 15.3835 | 1.74184 | ||||||||
\(79\) | −4.48597 | −0.504712 | −0.252356 | − | 0.967635i | \(-0.581205\pi\) | ||||
−0.252356 | + | 0.967635i | \(0.581205\pi\) | |||||||
\(80\) | 0.260736 | 0.0291511 | ||||||||
\(81\) | −9.32660 | −1.03629 | ||||||||
\(82\) | −10.7302 | −1.18495 | ||||||||
\(83\) | 1.91389 | 0.210077 | 0.105038 | − | 0.994468i | \(-0.466503\pi\) | ||||
0.105038 | + | 0.994468i | \(0.466503\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0.580670 | 0.0629825 | ||||||||
\(86\) | −0.195049 | −0.0210327 | ||||||||
\(87\) | 2.42629 | 0.260125 | ||||||||
\(88\) | −2.14760 | −0.228935 | ||||||||
\(89\) | 11.8209 | 1.25301 | 0.626505 | − | 0.779418i | \(-0.284485\pi\) | ||||
0.626505 | + | 0.779418i | \(0.284485\pi\) | |||||||
\(90\) | −0.752709 | −0.0793425 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 4.38533 | 0.457202 | ||||||||
\(93\) | 7.38841 | 0.766142 | ||||||||
\(94\) | −12.2245 | −1.26086 | ||||||||
\(95\) | 2.20002 | 0.225717 | ||||||||
\(96\) | 2.42629 | 0.247632 | ||||||||
\(97\) | −0.283480 | −0.0287830 | −0.0143915 | − | 0.999896i | \(-0.504581\pi\) | ||||
−0.0143915 | + | 0.999896i | \(0.504581\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 6.19984 | 0.623108 | ||||||||
\(100\) | −4.93202 | −0.493202 | ||||||||
\(101\) | −10.9123 | −1.08581 | −0.542905 | − | 0.839794i | \(-0.682676\pi\) | ||||
−0.542905 | + | 0.839794i | \(0.682676\pi\) | |||||||
\(102\) | 5.40345 | 0.535022 | ||||||||
\(103\) | −11.5444 | −1.13750 | −0.568751 | − | 0.822509i | \(-0.692573\pi\) | ||||
−0.568751 | + | 0.822509i | \(0.692573\pi\) | |||||||
\(104\) | −6.34036 | −0.621723 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0.390391 | 0.0379181 | ||||||||
\(107\) | 9.96649 | 0.963497 | 0.481748 | − | 0.876310i | \(-0.340002\pi\) | ||||
0.481748 | + | 0.876310i | \(0.340002\pi\) | |||||||
\(108\) | 0.274492 | 0.0264130 | ||||||||
\(109\) | −9.82477 | −0.941042 | −0.470521 | − | 0.882389i | \(-0.655934\pi\) | ||||
−0.470521 | + | 0.882389i | \(0.655934\pi\) | |||||||
\(110\) | −0.559957 | −0.0533898 | ||||||||
\(111\) | 17.5789 | 1.66851 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −1.20430 | −0.113291 | −0.0566456 | − | 0.998394i | \(-0.518041\pi\) | ||||
−0.0566456 | + | 0.998394i | \(0.518041\pi\) | |||||||
\(114\) | 20.4724 | 1.91742 | ||||||||
\(115\) | 1.14341 | 0.106624 | ||||||||
\(116\) | −1.00000 | −0.0928477 | ||||||||
\(117\) | 18.3038 | 1.69218 | ||||||||
\(118\) | 14.7537 | 1.35819 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0.632619 | 0.0577500 | ||||||||
\(121\) | −6.38780 | −0.580709 | ||||||||
\(122\) | 9.83960 | 0.890835 | ||||||||
\(123\) | −26.0345 | −2.34745 | ||||||||
\(124\) | −3.04515 | −0.273463 | ||||||||
\(125\) | −2.58963 | −0.231624 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 4.82334 | 0.428002 | 0.214001 | − | 0.976833i | \(-0.431350\pi\) | ||||
0.214001 | + | 0.976833i | \(0.431350\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | −0.473244 | −0.0416668 | ||||||||
\(130\) | −1.65316 | −0.144991 | ||||||||
\(131\) | 14.0889 | 1.23095 | 0.615475 | − | 0.788156i | \(-0.288964\pi\) | ||||
0.615475 | + | 0.788156i | \(0.288964\pi\) | |||||||
\(132\) | −5.21070 | −0.453533 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −9.53790 | −0.823949 | ||||||||
\(135\) | 0.0715699 | 0.00615976 | ||||||||
\(136\) | −2.22705 | −0.190968 | ||||||||
\(137\) | −13.0249 | −1.11279 | −0.556396 | − | 0.830917i | \(-0.687816\pi\) | ||||
−0.556396 | + | 0.830917i | \(0.687816\pi\) | |||||||
\(138\) | 10.6401 | 0.905742 | ||||||||
\(139\) | −16.8987 | −1.43333 | −0.716664 | − | 0.697419i | \(-0.754332\pi\) | ||||
−0.716664 | + | 0.697419i | \(0.754332\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −29.6600 | −2.49783 | ||||||||
\(142\) | −2.18856 | −0.183660 | ||||||||
\(143\) | 13.6166 | 1.13867 | ||||||||
\(144\) | 2.88687 | 0.240572 | ||||||||
\(145\) | −0.260736 | −0.0216529 | ||||||||
\(146\) | −4.18350 | −0.346229 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −7.24517 | −0.595549 | ||||||||
\(149\) | −0.491974 | −0.0403040 | −0.0201520 | − | 0.999797i | \(-0.506415\pi\) | ||||
−0.0201520 | + | 0.999797i | \(0.506415\pi\) | |||||||
\(150\) | −11.9665 | −0.977060 | ||||||||
\(151\) | 2.10185 | 0.171046 | 0.0855230 | − | 0.996336i | \(-0.472744\pi\) | ||||
0.0855230 | + | 0.996336i | \(0.472744\pi\) | |||||||
\(152\) | −8.43775 | −0.684392 | ||||||||
\(153\) | 6.42919 | 0.519769 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −0.793979 | −0.0637739 | ||||||||
\(156\) | −15.3835 | −1.23167 | ||||||||
\(157\) | 9.92354 | 0.791985 | 0.395993 | − | 0.918254i | \(-0.370401\pi\) | ||||
0.395993 | + | 0.918254i | \(0.370401\pi\) | |||||||
\(158\) | 4.48597 | 0.356885 | ||||||||
\(159\) | 0.947199 | 0.0751178 | ||||||||
\(160\) | −0.260736 | −0.0206130 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 9.32660 | 0.732767 | ||||||||
\(163\) | 6.75259 | 0.528904 | 0.264452 | − | 0.964399i | \(-0.414809\pi\) | ||||
0.264452 | + | 0.964399i | \(0.414809\pi\) | |||||||
\(164\) | 10.7302 | 0.837887 | ||||||||
\(165\) | −1.35862 | −0.105768 | ||||||||
\(166\) | −1.91389 | −0.148547 | ||||||||
\(167\) | 7.22428 | 0.559032 | 0.279516 | − | 0.960141i | \(-0.409826\pi\) | ||||
0.279516 | + | 0.960141i | \(0.409826\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 27.2001 | 2.09232 | ||||||||
\(170\) | −0.580670 | −0.0445354 | ||||||||
\(171\) | 24.3587 | 1.86275 | ||||||||
\(172\) | 0.195049 | 0.0148723 | ||||||||
\(173\) | 8.60818 | 0.654468 | 0.327234 | − | 0.944943i | \(-0.393883\pi\) | ||||
0.327234 | + | 0.944943i | \(0.393883\pi\) | |||||||
\(174\) | −2.42629 | −0.183936 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 2.14760 | 0.161882 | ||||||||
\(177\) | 35.7966 | 2.69064 | ||||||||
\(178\) | −11.8209 | −0.886012 | ||||||||
\(179\) | 21.0797 | 1.57557 | 0.787786 | − | 0.615949i | \(-0.211227\pi\) | ||||
0.787786 | + | 0.615949i | \(0.211227\pi\) | |||||||
\(180\) | 0.752709 | 0.0561036 | ||||||||
\(181\) | −8.59244 | −0.638671 | −0.319336 | − | 0.947642i | \(-0.603460\pi\) | ||||
−0.319336 | + | 0.947642i | \(0.603460\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 23.8737 | 1.76479 | ||||||||
\(184\) | −4.38533 | −0.323291 | ||||||||
\(185\) | −1.88907 | −0.138888 | ||||||||
\(186\) | −7.38841 | −0.541744 | ||||||||
\(187\) | 4.78281 | 0.349754 | ||||||||
\(188\) | 12.2245 | 0.891560 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −2.20002 | −0.159606 | ||||||||
\(191\) | 8.52165 | 0.616605 | 0.308302 | − | 0.951288i | \(-0.400239\pi\) | ||||
0.308302 | + | 0.951288i | \(0.400239\pi\) | |||||||
\(192\) | −2.42629 | −0.175102 | ||||||||
\(193\) | 13.1790 | 0.948645 | 0.474322 | − | 0.880351i | \(-0.342693\pi\) | ||||
0.474322 | + | 0.880351i | \(0.342693\pi\) | |||||||
\(194\) | 0.283480 | 0.0203527 | ||||||||
\(195\) | −4.01103 | −0.287236 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −5.96908 | −0.425279 | −0.212640 | − | 0.977131i | \(-0.568206\pi\) | ||||
−0.212640 | + | 0.977131i | \(0.568206\pi\) | |||||||
\(198\) | −6.19984 | −0.440604 | ||||||||
\(199\) | 13.3315 | 0.945042 | 0.472521 | − | 0.881319i | \(-0.343344\pi\) | ||||
0.472521 | + | 0.881319i | \(0.343344\pi\) | |||||||
\(200\) | 4.93202 | 0.348746 | ||||||||
\(201\) | −23.1417 | −1.63229 | ||||||||
\(202\) | 10.9123 | 0.767784 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −5.40345 | −0.378317 | ||||||||
\(205\) | 2.79774 | 0.195403 | ||||||||
\(206\) | 11.5444 | 0.804336 | ||||||||
\(207\) | 12.6599 | 0.879921 | ||||||||
\(208\) | 6.34036 | 0.439625 | ||||||||
\(209\) | 18.1209 | 1.25345 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 9.91857 | 0.682823 | 0.341411 | − | 0.939914i | \(-0.389095\pi\) | ||||
0.341411 | + | 0.939914i | \(0.389095\pi\) | |||||||
\(212\) | −0.390391 | −0.0268121 | ||||||||
\(213\) | −5.31008 | −0.363840 | ||||||||
\(214\) | −9.96649 | −0.681295 | ||||||||
\(215\) | 0.0508562 | 0.00346836 | ||||||||
\(216\) | −0.274492 | −0.0186768 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 9.82477 | 0.665417 | ||||||||
\(219\) | −10.1504 | −0.685898 | ||||||||
\(220\) | 0.559957 | 0.0377523 | ||||||||
\(221\) | 14.1203 | 0.949832 | ||||||||
\(222\) | −17.5789 | −1.17982 | ||||||||
\(223\) | −19.5885 | −1.31174 | −0.655872 | − | 0.754872i | \(-0.727699\pi\) | ||||
−0.655872 | + | 0.754872i | \(0.727699\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −14.2381 | −0.949205 | ||||||||
\(226\) | 1.20430 | 0.0801090 | ||||||||
\(227\) | 15.6918 | 1.04150 | 0.520751 | − | 0.853708i | \(-0.325652\pi\) | ||||
0.520751 | + | 0.853708i | \(0.325652\pi\) | |||||||
\(228\) | −20.4724 | −1.35582 | ||||||||
\(229\) | −14.4197 | −0.952879 | −0.476440 | − | 0.879207i | \(-0.658073\pi\) | ||||
−0.476440 | + | 0.879207i | \(0.658073\pi\) | |||||||
\(230\) | −1.14341 | −0.0753943 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 1.00000 | 0.0656532 | ||||||||
\(233\) | −10.0291 | −0.657029 | −0.328515 | − | 0.944499i | \(-0.606548\pi\) | ||||
−0.328515 | + | 0.944499i | \(0.606548\pi\) | |||||||
\(234\) | −18.3038 | −1.19655 | ||||||||
\(235\) | 3.18735 | 0.207920 | ||||||||
\(236\) | −14.7537 | −0.960382 | ||||||||
\(237\) | 10.8843 | 0.707009 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −0.920380 | −0.0595344 | −0.0297672 | − | 0.999557i | \(-0.509477\pi\) | ||||
−0.0297672 | + | 0.999557i | \(0.509477\pi\) | |||||||
\(240\) | −0.632619 | −0.0408354 | ||||||||
\(241\) | −7.64883 | −0.492704 | −0.246352 | − | 0.969180i | \(-0.579232\pi\) | ||||
−0.246352 | + | 0.969180i | \(0.579232\pi\) | |||||||
\(242\) | 6.38780 | 0.410623 | ||||||||
\(243\) | 21.8055 | 1.39883 | ||||||||
\(244\) | −9.83960 | −0.629916 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 26.0345 | 1.65990 | ||||||||
\(247\) | 53.4983 | 3.40402 | ||||||||
\(248\) | 3.04515 | 0.193367 | ||||||||
\(249\) | −4.64365 | −0.294279 | ||||||||
\(250\) | 2.58963 | 0.163783 | ||||||||
\(251\) | 10.3042 | 0.650395 | 0.325197 | − | 0.945646i | \(-0.394569\pi\) | ||||
0.325197 | + | 0.945646i | \(0.394569\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 9.41794 | 0.592101 | ||||||||
\(254\) | −4.82334 | −0.302643 | ||||||||
\(255\) | −1.40887 | −0.0882270 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −4.43144 | −0.276425 | −0.138213 | − | 0.990403i | \(-0.544136\pi\) | ||||
−0.138213 | + | 0.990403i | \(0.544136\pi\) | |||||||
\(258\) | 0.473244 | 0.0294629 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 1.65316 | 0.102524 | ||||||||
\(261\) | −2.88687 | −0.178693 | ||||||||
\(262\) | −14.0889 | −0.870413 | ||||||||
\(263\) | 8.75489 | 0.539850 | 0.269925 | − | 0.962881i | \(-0.413001\pi\) | ||||
0.269925 | + | 0.962881i | \(0.413001\pi\) | |||||||
\(264\) | 5.21070 | 0.320696 | ||||||||
\(265\) | −0.101789 | −0.00625283 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −28.6808 | −1.75524 | ||||||||
\(268\) | 9.53790 | 0.582620 | ||||||||
\(269\) | 21.7855 | 1.32828 | 0.664141 | − | 0.747607i | \(-0.268797\pi\) | ||||
0.664141 | + | 0.747607i | \(0.268797\pi\) | |||||||
\(270\) | −0.0715699 | −0.00435561 | ||||||||
\(271\) | −16.9776 | −1.03132 | −0.515658 | − | 0.856794i | \(-0.672453\pi\) | ||||
−0.515658 | + | 0.856794i | \(0.672453\pi\) | |||||||
\(272\) | 2.22705 | 0.135035 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 13.0249 | 0.786863 | ||||||||
\(275\) | −10.5920 | −0.638722 | ||||||||
\(276\) | −10.6401 | −0.640457 | ||||||||
\(277\) | −0.608653 | −0.0365704 | −0.0182852 | − | 0.999833i | \(-0.505821\pi\) | ||||
−0.0182852 | + | 0.999833i | \(0.505821\pi\) | |||||||
\(278\) | 16.8987 | 1.01352 | ||||||||
\(279\) | −8.79094 | −0.526300 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −25.5555 | −1.52451 | −0.762256 | − | 0.647276i | \(-0.775908\pi\) | ||||
−0.762256 | + | 0.647276i | \(0.775908\pi\) | |||||||
\(282\) | 29.6600 | 1.76623 | ||||||||
\(283\) | 24.7141 | 1.46910 | 0.734551 | − | 0.678553i | \(-0.237393\pi\) | ||||
0.734551 | + | 0.678553i | \(0.237393\pi\) | |||||||
\(284\) | 2.18856 | 0.129867 | ||||||||
\(285\) | −5.33788 | −0.316189 | ||||||||
\(286\) | −13.6166 | −0.805164 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −2.88687 | −0.170110 | ||||||||
\(289\) | −12.0403 | −0.708251 | ||||||||
\(290\) | 0.260736 | 0.0153109 | ||||||||
\(291\) | 0.687804 | 0.0403198 | ||||||||
\(292\) | 4.18350 | 0.244821 | ||||||||
\(293\) | 20.9908 | 1.22630 | 0.613148 | − | 0.789968i | \(-0.289903\pi\) | ||||
0.613148 | + | 0.789968i | \(0.289903\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −3.84681 | −0.223970 | ||||||||
\(296\) | 7.24517 | 0.421117 | ||||||||
\(297\) | 0.589500 | 0.0342063 | ||||||||
\(298\) | 0.491974 | 0.0284993 | ||||||||
\(299\) | 27.8045 | 1.60798 | ||||||||
\(300\) | 11.9665 | 0.690885 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −2.10185 | −0.120948 | ||||||||
\(303\) | 26.4763 | 1.52102 | ||||||||
\(304\) | 8.43775 | 0.483938 | ||||||||
\(305\) | −2.56553 | −0.146902 | ||||||||
\(306\) | −6.42919 | −0.367532 | ||||||||
\(307\) | 24.9164 | 1.42205 | 0.711027 | − | 0.703164i | \(-0.248230\pi\) | ||||
0.711027 | + | 0.703164i | \(0.248230\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 28.0100 | 1.59343 | ||||||||
\(310\) | 0.793979 | 0.0450950 | ||||||||
\(311\) | 3.38252 | 0.191805 | 0.0959025 | − | 0.995391i | \(-0.469426\pi\) | ||||
0.0959025 | + | 0.995391i | \(0.469426\pi\) | |||||||
\(312\) | 15.3835 | 0.870920 | ||||||||
\(313\) | 27.7834 | 1.57041 | 0.785206 | − | 0.619235i | \(-0.212557\pi\) | ||||
0.785206 | + | 0.619235i | \(0.212557\pi\) | |||||||
\(314\) | −9.92354 | −0.560018 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −4.48597 | −0.252356 | ||||||||
\(317\) | −13.6437 | −0.766304 | −0.383152 | − | 0.923685i | \(-0.625161\pi\) | ||||
−0.383152 | + | 0.923685i | \(0.625161\pi\) | |||||||
\(318\) | −0.947199 | −0.0531163 | ||||||||
\(319\) | −2.14760 | −0.120243 | ||||||||
\(320\) | 0.260736 | 0.0145756 | ||||||||
\(321\) | −24.1816 | −1.34968 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 18.7913 | 1.04557 | ||||||||
\(324\) | −9.32660 | −0.518144 | ||||||||
\(325\) | −31.2707 | −1.73459 | ||||||||
\(326\) | −6.75259 | −0.373992 | ||||||||
\(327\) | 23.8377 | 1.31823 | ||||||||
\(328\) | −10.7302 | −0.592475 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 1.35862 | 0.0747893 | ||||||||
\(331\) | −12.1576 | −0.668244 | −0.334122 | − | 0.942530i | \(-0.608440\pi\) | ||||
−0.334122 | + | 0.942530i | \(0.608440\pi\) | |||||||
\(332\) | 1.91389 | 0.105038 | ||||||||
\(333\) | −20.9158 | −1.14618 | ||||||||
\(334\) | −7.22428 | −0.395295 | ||||||||
\(335\) | 2.48687 | 0.135872 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 12.7616 | 0.695168 | 0.347584 | − | 0.937649i | \(-0.387002\pi\) | ||||
0.347584 | + | 0.937649i | \(0.387002\pi\) | |||||||
\(338\) | −27.2001 | −1.47949 | ||||||||
\(339\) | 2.92198 | 0.158700 | ||||||||
\(340\) | 0.580670 | 0.0314913 | ||||||||
\(341\) | −6.53977 | −0.354149 | ||||||||
\(342\) | −24.3587 | −1.31717 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −0.195049 | −0.0105163 | ||||||||
\(345\) | −2.77424 | −0.149360 | ||||||||
\(346\) | −8.60818 | −0.462779 | ||||||||
\(347\) | −3.20642 | −0.172130 | −0.0860648 | − | 0.996290i | \(-0.527429\pi\) | ||||
−0.0860648 | + | 0.996290i | \(0.527429\pi\) | |||||||
\(348\) | 2.42629 | 0.130063 | ||||||||
\(349\) | 3.95168 | 0.211529 | 0.105764 | − | 0.994391i | \(-0.466271\pi\) | ||||
0.105764 | + | 0.994391i | \(0.466271\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1.74038 | 0.0928945 | ||||||||
\(352\) | −2.14760 | −0.114468 | ||||||||
\(353\) | −15.0305 | −0.799995 | −0.399998 | − | 0.916516i | \(-0.630989\pi\) | ||||
−0.399998 | + | 0.916516i | \(0.630989\pi\) | |||||||
\(354\) | −35.7966 | −1.90257 | ||||||||
\(355\) | 0.570636 | 0.0302862 | ||||||||
\(356\) | 11.8209 | 0.626505 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −21.0797 | −1.11410 | ||||||||
\(359\) | −12.5777 | −0.663823 | −0.331912 | − | 0.943310i | \(-0.607694\pi\) | ||||
−0.331912 | + | 0.943310i | \(0.607694\pi\) | |||||||
\(360\) | −0.752709 | −0.0396713 | ||||||||
\(361\) | 52.1956 | 2.74714 | ||||||||
\(362\) | 8.59244 | 0.451609 | ||||||||
\(363\) | 15.4986 | 0.813468 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 1.09079 | 0.0570944 | ||||||||
\(366\) | −23.8737 | −1.24790 | ||||||||
\(367\) | −15.2524 | −0.796166 | −0.398083 | − | 0.917349i | \(-0.630324\pi\) | ||||
−0.398083 | + | 0.917349i | \(0.630324\pi\) | |||||||
\(368\) | 4.38533 | 0.228601 | ||||||||
\(369\) | 30.9766 | 1.61258 | ||||||||
\(370\) | 1.88907 | 0.0982083 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 7.38841 | 0.383071 | ||||||||
\(373\) | −14.9777 | −0.775517 | −0.387759 | − | 0.921761i | \(-0.626751\pi\) | ||||
−0.387759 | + | 0.921761i | \(0.626751\pi\) | |||||||
\(374\) | −4.78281 | −0.247313 | ||||||||
\(375\) | 6.28319 | 0.324462 | ||||||||
\(376\) | −12.2245 | −0.630428 | ||||||||
\(377\) | −6.34036 | −0.326545 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 0.578081 | 0.0296940 | 0.0148470 | − | 0.999890i | \(-0.495274\pi\) | ||||
0.0148470 | + | 0.999890i | \(0.495274\pi\) | |||||||
\(380\) | 2.20002 | 0.112859 | ||||||||
\(381\) | −11.7028 | −0.599553 | ||||||||
\(382\) | −8.52165 | −0.436005 | ||||||||
\(383\) | −28.9218 | −1.47783 | −0.738917 | − | 0.673797i | \(-0.764662\pi\) | ||||
−0.738917 | + | 0.673797i | \(0.764662\pi\) | |||||||
\(384\) | 2.42629 | 0.123816 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −13.1790 | −0.670793 | ||||||||
\(387\) | 0.563080 | 0.0286230 | ||||||||
\(388\) | −0.283480 | −0.0143915 | ||||||||
\(389\) | −9.91719 | −0.502821 | −0.251411 | − | 0.967881i | \(-0.580894\pi\) | ||||
−0.251411 | + | 0.967881i | \(0.580894\pi\) | |||||||
\(390\) | 4.01103 | 0.203107 | ||||||||
\(391\) | 9.76633 | 0.493905 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −34.1836 | −1.72434 | ||||||||
\(394\) | 5.96908 | 0.300718 | ||||||||
\(395\) | −1.16965 | −0.0588516 | ||||||||
\(396\) | 6.19984 | 0.311554 | ||||||||
\(397\) | 10.3356 | 0.518729 | 0.259365 | − | 0.965779i | \(-0.416487\pi\) | ||||
0.259365 | + | 0.965779i | \(0.416487\pi\) | |||||||
\(398\) | −13.3315 | −0.668245 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −4.93202 | −0.246601 | ||||||||
\(401\) | −20.8127 | −1.03933 | −0.519667 | − | 0.854369i | \(-0.673944\pi\) | ||||
−0.519667 | + | 0.854369i | \(0.673944\pi\) | |||||||
\(402\) | 23.1417 | 1.15420 | ||||||||
\(403\) | −19.3073 | −0.961767 | ||||||||
\(404\) | −10.9123 | −0.542905 | ||||||||
\(405\) | −2.43178 | −0.120836 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −15.5598 | −0.771268 | ||||||||
\(408\) | 5.40345 | 0.267511 | ||||||||
\(409\) | 9.80067 | 0.484612 | 0.242306 | − | 0.970200i | \(-0.422096\pi\) | ||||
0.242306 | + | 0.970200i | \(0.422096\pi\) | |||||||
\(410\) | −2.79774 | −0.138171 | ||||||||
\(411\) | 31.6022 | 1.55882 | ||||||||
\(412\) | −11.5444 | −0.568751 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −12.6599 | −0.622198 | ||||||||
\(415\) | 0.499020 | 0.0244959 | ||||||||
\(416\) | −6.34036 | −0.310862 | ||||||||
\(417\) | 41.0010 | 2.00783 | ||||||||
\(418\) | −18.1209 | −0.886324 | ||||||||
\(419\) | 0.564842 | 0.0275943 | 0.0137972 | − | 0.999905i | \(-0.495608\pi\) | ||||
0.0137972 | + | 0.999905i | \(0.495608\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 28.1593 | 1.37240 | 0.686201 | − | 0.727412i | \(-0.259277\pi\) | ||||
0.686201 | + | 0.727412i | \(0.259277\pi\) | |||||||
\(422\) | −9.91857 | −0.482829 | ||||||||
\(423\) | 35.2904 | 1.71588 | ||||||||
\(424\) | 0.390391 | 0.0189590 | ||||||||
\(425\) | −10.9838 | −0.532794 | ||||||||
\(426\) | 5.31008 | 0.257274 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 9.96649 | 0.481748 | ||||||||
\(429\) | −33.0377 | −1.59507 | ||||||||
\(430\) | −0.0508562 | −0.00245250 | ||||||||
\(431\) | 28.1658 | 1.35670 | 0.678350 | − | 0.734739i | \(-0.262695\pi\) | ||||
0.678350 | + | 0.734739i | \(0.262695\pi\) | |||||||
\(432\) | 0.274492 | 0.0132065 | ||||||||
\(433\) | 17.6927 | 0.850259 | 0.425130 | − | 0.905132i | \(-0.360229\pi\) | ||||
0.425130 | + | 0.905132i | \(0.360229\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0.632619 | 0.0303318 | ||||||||
\(436\) | −9.82477 | −0.470521 | ||||||||
\(437\) | 37.0023 | 1.77006 | ||||||||
\(438\) | 10.1504 | 0.485003 | ||||||||
\(439\) | −28.1245 | −1.34231 | −0.671154 | − | 0.741318i | \(-0.734201\pi\) | ||||
−0.671154 | + | 0.741318i | \(0.734201\pi\) | |||||||
\(440\) | −0.559957 | −0.0266949 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −14.1203 | −0.671633 | ||||||||
\(443\) | −6.21048 | −0.295069 | −0.147534 | − | 0.989057i | \(-0.547134\pi\) | ||||
−0.147534 | + | 0.989057i | \(0.547134\pi\) | |||||||
\(444\) | 17.5789 | 0.834256 | ||||||||
\(445\) | 3.08212 | 0.146107 | ||||||||
\(446\) | 19.5885 | 0.927543 | ||||||||
\(447\) | 1.19367 | 0.0564586 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −5.87960 | −0.277475 | −0.138738 | − | 0.990329i | \(-0.544304\pi\) | ||||
−0.138738 | + | 0.990329i | \(0.544304\pi\) | |||||||
\(450\) | 14.2381 | 0.671189 | ||||||||
\(451\) | 23.0442 | 1.08511 | ||||||||
\(452\) | −1.20430 | −0.0566456 | ||||||||
\(453\) | −5.09969 | −0.239604 | ||||||||
\(454\) | −15.6918 | −0.736454 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 20.4724 | 0.958708 | ||||||||
\(457\) | −34.2340 | −1.60140 | −0.800700 | − | 0.599065i | \(-0.795539\pi\) | ||||
−0.800700 | + | 0.599065i | \(0.795539\pi\) | |||||||
\(458\) | 14.4197 | 0.673788 | ||||||||
\(459\) | 0.611307 | 0.0285334 | ||||||||
\(460\) | 1.14341 | 0.0533118 | ||||||||
\(461\) | −7.77623 | −0.362175 | −0.181088 | − | 0.983467i | \(-0.557962\pi\) | ||||
−0.181088 | + | 0.983467i | \(0.557962\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −6.50388 | −0.302261 | −0.151130 | − | 0.988514i | \(-0.548291\pi\) | ||||
−0.151130 | + | 0.988514i | \(0.548291\pi\) | |||||||
\(464\) | −1.00000 | −0.0464238 | ||||||||
\(465\) | 1.92642 | 0.0893356 | ||||||||
\(466\) | 10.0291 | 0.464590 | ||||||||
\(467\) | −5.00733 | −0.231712 | −0.115856 | − | 0.993266i | \(-0.536961\pi\) | ||||
−0.115856 | + | 0.993266i | \(0.536961\pi\) | |||||||
\(468\) | 18.3038 | 0.846092 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −3.18735 | −0.147022 | ||||||||
\(471\) | −24.0774 | −1.10943 | ||||||||
\(472\) | 14.7537 | 0.679093 | ||||||||
\(473\) | 0.418887 | 0.0192605 | ||||||||
\(474\) | −10.8843 | −0.499931 | ||||||||
\(475\) | −41.6151 | −1.90943 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −1.12701 | −0.0516020 | ||||||||
\(478\) | 0.920380 | 0.0420972 | ||||||||
\(479\) | −35.2838 | −1.61216 | −0.806080 | − | 0.591807i | \(-0.798415\pi\) | ||||
−0.806080 | + | 0.591807i | \(0.798415\pi\) | |||||||
\(480\) | 0.632619 | 0.0288750 | ||||||||
\(481\) | −45.9370 | −2.09455 | ||||||||
\(482\) | 7.64883 | 0.348395 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −6.38780 | −0.290355 | ||||||||
\(485\) | −0.0739133 | −0.00335623 | ||||||||
\(486\) | −21.8055 | −0.989119 | ||||||||
\(487\) | 4.73153 | 0.214406 | 0.107203 | − | 0.994237i | \(-0.465811\pi\) | ||||
0.107203 | + | 0.994237i | \(0.465811\pi\) | |||||||
\(488\) | 9.83960 | 0.445418 | ||||||||
\(489\) | −16.3837 | −0.740898 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −18.5337 | −0.836413 | −0.418206 | − | 0.908352i | \(-0.637341\pi\) | ||||
−0.418206 | + | 0.908352i | \(0.637341\pi\) | |||||||
\(492\) | −26.0345 | −1.17373 | ||||||||
\(493\) | −2.22705 | −0.100301 | ||||||||
\(494\) | −53.4983 | −2.40700 | ||||||||
\(495\) | 1.61652 | 0.0726572 | ||||||||
\(496\) | −3.04515 | −0.136731 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 4.64365 | 0.208087 | ||||||||
\(499\) | −8.49139 | −0.380127 | −0.190063 | − | 0.981772i | \(-0.560869\pi\) | ||||
−0.190063 | + | 0.981772i | \(0.560869\pi\) | |||||||
\(500\) | −2.58963 | −0.115812 | ||||||||
\(501\) | −17.5282 | −0.783101 | ||||||||
\(502\) | −10.3042 | −0.459899 | ||||||||
\(503\) | 25.6049 | 1.14167 | 0.570833 | − | 0.821066i | \(-0.306620\pi\) | ||||
0.570833 | + | 0.821066i | \(0.306620\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −2.84522 | −0.126610 | ||||||||
\(506\) | −9.41794 | −0.418679 | ||||||||
\(507\) | −65.9953 | −2.93095 | ||||||||
\(508\) | 4.82334 | 0.214001 | ||||||||
\(509\) | −2.16096 | −0.0957829 | −0.0478914 | − | 0.998853i | \(-0.515250\pi\) | ||||
−0.0478914 | + | 0.998853i | \(0.515250\pi\) | |||||||
\(510\) | 1.40887 | 0.0623859 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 2.31610 | 0.102258 | ||||||||
\(514\) | 4.43144 | 0.195462 | ||||||||
\(515\) | −3.01003 | −0.132638 | ||||||||
\(516\) | −0.473244 | −0.0208334 | ||||||||
\(517\) | 26.2533 | 1.15462 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −20.8859 | −0.916790 | ||||||||
\(520\) | −1.65316 | −0.0724957 | ||||||||
\(521\) | 38.3906 | 1.68192 | 0.840961 | − | 0.541096i | \(-0.181991\pi\) | ||||
0.840961 | + | 0.541096i | \(0.181991\pi\) | |||||||
\(522\) | 2.88687 | 0.126355 | ||||||||
\(523\) | −36.1101 | −1.57898 | −0.789492 | − | 0.613761i | \(-0.789656\pi\) | ||||
−0.789492 | + | 0.613761i | \(0.789656\pi\) | |||||||
\(524\) | 14.0889 | 0.615475 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −8.75489 | −0.381731 | ||||||||
\(527\) | −6.78169 | −0.295415 | ||||||||
\(528\) | −5.21070 | −0.226767 | ||||||||
\(529\) | −3.76889 | −0.163865 | ||||||||
\(530\) | 0.101789 | 0.00442142 | ||||||||
\(531\) | −42.5919 | −1.84833 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 68.0332 | 2.94685 | ||||||||
\(534\) | 28.6808 | 1.24114 | ||||||||
\(535\) | 2.59862 | 0.112348 | ||||||||
\(536\) | −9.53790 | −0.411975 | ||||||||
\(537\) | −51.1454 | −2.20709 | ||||||||
\(538\) | −21.7855 | −0.939238 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0.0715699 | 0.00307988 | ||||||||
\(541\) | −6.89449 | −0.296417 | −0.148209 | − | 0.988956i | \(-0.547351\pi\) | ||||
−0.148209 | + | 0.988956i | \(0.547351\pi\) | |||||||
\(542\) | 16.9776 | 0.729251 | ||||||||
\(543\) | 20.8477 | 0.894662 | ||||||||
\(544\) | −2.22705 | −0.0954838 | ||||||||
\(545\) | −2.56167 | −0.109730 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −39.4686 | −1.68756 | −0.843779 | − | 0.536691i | \(-0.819674\pi\) | ||||
−0.843779 | + | 0.536691i | \(0.819674\pi\) | |||||||
\(548\) | −13.0249 | −0.556396 | ||||||||
\(549\) | −28.4056 | −1.21232 | ||||||||
\(550\) | 10.5920 | 0.451645 | ||||||||
\(551\) | −8.43775 | −0.359460 | ||||||||
\(552\) | 10.6401 | 0.452871 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0.608653 | 0.0258592 | ||||||||
\(555\) | 4.58344 | 0.194556 | ||||||||
\(556\) | −16.8987 | −0.716664 | ||||||||
\(557\) | 21.9613 | 0.930530 | 0.465265 | − | 0.885171i | \(-0.345959\pi\) | ||||
0.465265 | + | 0.885171i | \(0.345959\pi\) | |||||||
\(558\) | 8.79094 | 0.372150 | ||||||||
\(559\) | 1.23668 | 0.0523059 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −11.6045 | −0.489941 | ||||||||
\(562\) | 25.5555 | 1.07799 | ||||||||
\(563\) | −17.4707 | −0.736303 | −0.368151 | − | 0.929766i | \(-0.620009\pi\) | ||||
−0.368151 | + | 0.929766i | \(0.620009\pi\) | |||||||
\(564\) | −29.6600 | −1.24891 | ||||||||
\(565\) | −0.314005 | −0.0132103 | ||||||||
\(566\) | −24.7141 | −1.03881 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −2.18856 | −0.0918300 | ||||||||
\(569\) | 11.0179 | 0.461896 | 0.230948 | − | 0.972966i | \(-0.425817\pi\) | ||||
0.230948 | + | 0.972966i | \(0.425817\pi\) | |||||||
\(570\) | 5.33788 | 0.223579 | ||||||||
\(571\) | 4.82287 | 0.201831 | 0.100915 | − | 0.994895i | \(-0.467823\pi\) | ||||
0.100915 | + | 0.994895i | \(0.467823\pi\) | |||||||
\(572\) | 13.6166 | 0.569337 | ||||||||
\(573\) | −20.6760 | −0.863751 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −21.6285 | −0.901971 | ||||||||
\(576\) | 2.88687 | 0.120286 | ||||||||
\(577\) | −11.9775 | −0.498629 | −0.249314 | − | 0.968423i | \(-0.580205\pi\) | ||||
−0.249314 | + | 0.968423i | \(0.580205\pi\) | |||||||
\(578\) | 12.0403 | 0.500809 | ||||||||
\(579\) | −31.9760 | −1.32888 | ||||||||
\(580\) | −0.260736 | −0.0108265 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −0.687804 | −0.0285104 | ||||||||
\(583\) | −0.838404 | −0.0347231 | ||||||||
\(584\) | −4.18350 | −0.173114 | ||||||||
\(585\) | 4.77244 | 0.197316 | ||||||||
\(586\) | −20.9908 | −0.867122 | ||||||||
\(587\) | 28.0949 | 1.15960 | 0.579800 | − | 0.814759i | \(-0.303131\pi\) | ||||
0.579800 | + | 0.814759i | \(0.303131\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −25.6942 | −1.05871 | ||||||||
\(590\) | 3.84681 | 0.158371 | ||||||||
\(591\) | 14.4827 | 0.595738 | ||||||||
\(592\) | −7.24517 | −0.297775 | ||||||||
\(593\) | 25.6900 | 1.05496 | 0.527481 | − | 0.849567i | \(-0.323137\pi\) | ||||
0.527481 | + | 0.849567i | \(0.323137\pi\) | |||||||
\(594\) | −0.589500 | −0.0241875 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −0.491974 | −0.0201520 | ||||||||
\(597\) | −32.3459 | −1.32383 | ||||||||
\(598\) | −27.8045 | −1.13701 | ||||||||
\(599\) | −8.23688 | −0.336550 | −0.168275 | − | 0.985740i | \(-0.553820\pi\) | ||||
−0.168275 | + | 0.985740i | \(0.553820\pi\) | |||||||
\(600\) | −11.9665 | −0.488530 | ||||||||
\(601\) | 12.0901 | 0.493166 | 0.246583 | − | 0.969122i | \(-0.420692\pi\) | ||||
0.246583 | + | 0.969122i | \(0.420692\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 27.5347 | 1.12130 | ||||||||
\(604\) | 2.10185 | 0.0855230 | ||||||||
\(605\) | −1.66553 | −0.0677133 | ||||||||
\(606\) | −26.4763 | −1.07553 | ||||||||
\(607\) | 25.0685 | 1.01750 | 0.508749 | − | 0.860915i | \(-0.330108\pi\) | ||||
0.508749 | + | 0.860915i | \(0.330108\pi\) | |||||||
\(608\) | −8.43775 | −0.342196 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 2.56553 | 0.103875 | ||||||||
\(611\) | 77.5074 | 3.13561 | ||||||||
\(612\) | 6.42919 | 0.259885 | ||||||||
\(613\) | −33.6592 | −1.35948 | −0.679741 | − | 0.733453i | \(-0.737908\pi\) | ||||
−0.679741 | + | 0.733453i | \(0.737908\pi\) | |||||||
\(614\) | −24.9164 | −1.00554 | ||||||||
\(615\) | −6.78813 | −0.273724 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −29.3861 | −1.18304 | −0.591519 | − | 0.806291i | \(-0.701472\pi\) | ||||
−0.591519 | + | 0.806291i | \(0.701472\pi\) | |||||||
\(618\) | −28.0100 | −1.12673 | ||||||||
\(619\) | 41.3752 | 1.66301 | 0.831504 | − | 0.555518i | \(-0.187480\pi\) | ||||
0.831504 | + | 0.555518i | \(0.187480\pi\) | |||||||
\(620\) | −0.793979 | −0.0318870 | ||||||||
\(621\) | 1.20374 | 0.0483044 | ||||||||
\(622\) | −3.38252 | −0.135627 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −15.3835 | −0.615834 | ||||||||
\(625\) | 23.9849 | 0.959395 | ||||||||
\(626\) | −27.7834 | −1.11045 | ||||||||
\(627\) | −43.9666 | −1.75586 | ||||||||
\(628\) | 9.92354 | 0.395993 | ||||||||
\(629\) | −16.1353 | −0.643358 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −3.03083 | −0.120656 | −0.0603278 | − | 0.998179i | \(-0.519215\pi\) | ||||
−0.0603278 | + | 0.998179i | \(0.519215\pi\) | |||||||
\(632\) | 4.48597 | 0.178442 | ||||||||
\(633\) | −24.0653 | −0.956510 | ||||||||
\(634\) | 13.6437 | 0.541859 | ||||||||
\(635\) | 1.25762 | 0.0499070 | ||||||||
\(636\) | 0.947199 | 0.0375589 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 2.14760 | 0.0850244 | ||||||||
\(639\) | 6.31809 | 0.249940 | ||||||||
\(640\) | −0.260736 | −0.0103065 | ||||||||
\(641\) | 25.6543 | 1.01328 | 0.506642 | − | 0.862157i | \(-0.330887\pi\) | ||||
0.506642 | + | 0.862157i | \(0.330887\pi\) | |||||||
\(642\) | 24.1816 | 0.954370 | ||||||||
\(643\) | −11.3614 | −0.448048 | −0.224024 | − | 0.974584i | \(-0.571919\pi\) | ||||
−0.224024 | + | 0.974584i | \(0.571919\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −0.123392 | −0.00485854 | ||||||||
\(646\) | −18.7913 | −0.739332 | ||||||||
\(647\) | −19.0817 | −0.750181 | −0.375090 | − | 0.926988i | \(-0.622388\pi\) | ||||
−0.375090 | + | 0.926988i | \(0.622388\pi\) | |||||||
\(648\) | 9.32660 | 0.366383 | ||||||||
\(649\) | −31.6850 | −1.24375 | ||||||||
\(650\) | 31.2707 | 1.22654 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 6.75259 | 0.264452 | ||||||||
\(653\) | 48.3668 | 1.89274 | 0.946370 | − | 0.323086i | \(-0.104720\pi\) | ||||
0.946370 | + | 0.323086i | \(0.104720\pi\) | |||||||
\(654\) | −23.8377 | −0.932128 | ||||||||
\(655\) | 3.67347 | 0.143534 | ||||||||
\(656\) | 10.7302 | 0.418943 | ||||||||
\(657\) | 12.0772 | 0.471177 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −7.57465 | −0.295067 | −0.147533 | − | 0.989057i | \(-0.547133\pi\) | ||||
−0.147533 | + | 0.989057i | \(0.547133\pi\) | |||||||
\(660\) | −1.35862 | −0.0528840 | ||||||||
\(661\) | −44.4433 | −1.72864 | −0.864322 | − | 0.502940i | \(-0.832252\pi\) | ||||
−0.864322 | + | 0.502940i | \(0.832252\pi\) | |||||||
\(662\) | 12.1576 | 0.472520 | ||||||||
\(663\) | −34.2598 | −1.33054 | ||||||||
\(664\) | −1.91389 | −0.0742734 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 20.9158 | 0.810473 | ||||||||
\(667\) | −4.38533 | −0.169801 | ||||||||
\(668\) | 7.22428 | 0.279516 | ||||||||
\(669\) | 47.5274 | 1.83751 | ||||||||
\(670\) | −2.48687 | −0.0960762 | ||||||||
\(671\) | −21.1316 | −0.815774 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −22.7141 | −0.875564 | −0.437782 | − | 0.899081i | \(-0.644236\pi\) | ||||
−0.437782 | + | 0.899081i | \(0.644236\pi\) | |||||||
\(674\) | −12.7616 | −0.491558 | ||||||||
\(675\) | −1.35380 | −0.0521078 | ||||||||
\(676\) | 27.2001 | 1.04616 | ||||||||
\(677\) | −1.67725 | −0.0644621 | −0.0322310 | − | 0.999480i | \(-0.510261\pi\) | ||||
−0.0322310 | + | 0.999480i | \(0.510261\pi\) | |||||||
\(678\) | −2.92198 | −0.112218 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −0.580670 | −0.0222677 | ||||||||
\(681\) | −38.0729 | −1.45895 | ||||||||
\(682\) | 6.53977 | 0.250421 | ||||||||
\(683\) | 49.9200 | 1.91014 | 0.955069 | − | 0.296385i | \(-0.0957811\pi\) | ||||
0.955069 | + | 0.296385i | \(0.0957811\pi\) | |||||||
\(684\) | 24.3587 | 0.931377 | ||||||||
\(685\) | −3.39606 | −0.129757 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 34.9863 | 1.33481 | ||||||||
\(688\) | 0.195049 | 0.00743617 | ||||||||
\(689\) | −2.47521 | −0.0942982 | ||||||||
\(690\) | 2.77424 | 0.105614 | ||||||||
\(691\) | 25.5835 | 0.973240 | 0.486620 | − | 0.873614i | \(-0.338230\pi\) | ||||
0.486620 | + | 0.873614i | \(0.338230\pi\) | |||||||
\(692\) | 8.60818 | 0.327234 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 3.20642 | 0.121714 | ||||||||
\(695\) | −4.40609 | −0.167132 | ||||||||
\(696\) | −2.42629 | −0.0919682 | ||||||||
\(697\) | 23.8966 | 0.905149 | ||||||||
\(698\) | −3.95168 | −0.149573 | ||||||||
\(699\) | 24.3335 | 0.920378 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 29.5973 | 1.11787 | 0.558936 | − | 0.829211i | \(-0.311210\pi\) | ||||
0.558936 | + | 0.829211i | \(0.311210\pi\) | |||||||
\(702\) | −1.74038 | −0.0656864 | ||||||||
\(703\) | −61.1329 | −2.30567 | ||||||||
\(704\) | 2.14760 | 0.0809408 | ||||||||
\(705\) | −7.73343 | −0.291258 | ||||||||
\(706\) | 15.0305 | 0.565682 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 35.7966 | 1.34532 | ||||||||
\(709\) | 0.307107 | 0.0115337 | 0.00576683 | − | 0.999983i | \(-0.498164\pi\) | ||||
0.00576683 | + | 0.999983i | \(0.498164\pi\) | |||||||
\(710\) | −0.570636 | −0.0214156 | ||||||||
\(711\) | −12.9504 | −0.485678 | ||||||||
\(712\) | −11.8209 | −0.443006 | ||||||||
\(713\) | −13.3540 | −0.500111 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 3.55032 | 0.132775 | ||||||||
\(716\) | 21.0797 | 0.787786 | ||||||||
\(717\) | 2.23311 | 0.0833969 | ||||||||
\(718\) | 12.5777 | 0.469394 | ||||||||
\(719\) | 22.2426 | 0.829511 | 0.414755 | − | 0.909933i | \(-0.363867\pi\) | ||||
0.414755 | + | 0.909933i | \(0.363867\pi\) | |||||||
\(720\) | 0.752709 | 0.0280518 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −52.1956 | −1.94252 | ||||||||
\(723\) | 18.5583 | 0.690189 | ||||||||
\(724\) | −8.59244 | −0.319336 | ||||||||
\(725\) | 4.93202 | 0.183171 | ||||||||
\(726\) | −15.4986 | −0.575208 | ||||||||
\(727\) | −23.8821 | −0.885739 | −0.442869 | − | 0.896586i | \(-0.646039\pi\) | ||||
−0.442869 | + | 0.896586i | \(0.646039\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −24.9267 | −0.923210 | ||||||||
\(730\) | −1.09079 | −0.0403719 | ||||||||
\(731\) | 0.434383 | 0.0160662 | ||||||||
\(732\) | 23.8737 | 0.882397 | ||||||||
\(733\) | −2.31726 | −0.0855899 | −0.0427949 | − | 0.999084i | \(-0.513626\pi\) | ||||
−0.0427949 | + | 0.999084i | \(0.513626\pi\) | |||||||
\(734\) | 15.2524 | 0.562975 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −4.38533 | −0.161645 | ||||||||
\(737\) | 20.4836 | 0.754524 | ||||||||
\(738\) | −30.9766 | −1.14027 | ||||||||
\(739\) | −20.4310 | −0.751566 | −0.375783 | − | 0.926708i | \(-0.622626\pi\) | ||||
−0.375783 | + | 0.926708i | \(0.622626\pi\) | |||||||
\(740\) | −1.88907 | −0.0694438 | ||||||||
\(741\) | −129.802 | −4.76841 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 16.7514 | 0.614550 | 0.307275 | − | 0.951621i | \(-0.400583\pi\) | ||||
0.307275 | + | 0.951621i | \(0.400583\pi\) | |||||||
\(744\) | −7.38841 | −0.270872 | ||||||||
\(745\) | −0.128275 | −0.00469963 | ||||||||
\(746\) | 14.9777 | 0.548373 | ||||||||
\(747\) | 5.52515 | 0.202155 | ||||||||
\(748\) | 4.78281 | 0.174877 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −6.28319 | −0.229430 | ||||||||
\(751\) | 27.2245 | 0.993438 | 0.496719 | − | 0.867911i | \(-0.334538\pi\) | ||||
0.496719 | + | 0.867911i | \(0.334538\pi\) | |||||||
\(752\) | 12.2245 | 0.445780 | ||||||||
\(753\) | −25.0009 | −0.911084 | ||||||||
\(754\) | 6.34036 | 0.230902 | ||||||||
\(755\) | 0.548027 | 0.0199447 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 7.31697 | 0.265940 | 0.132970 | − | 0.991120i | \(-0.457549\pi\) | ||||
0.132970 | + | 0.991120i | \(0.457549\pi\) | |||||||
\(758\) | −0.578081 | −0.0209969 | ||||||||
\(759\) | −22.8506 | −0.829426 | ||||||||
\(760\) | −2.20002 | −0.0798032 | ||||||||
\(761\) | −24.8920 | −0.902334 | −0.451167 | − | 0.892440i | \(-0.648992\pi\) | ||||
−0.451167 | + | 0.892440i | \(0.648992\pi\) | |||||||
\(762\) | 11.7028 | 0.423948 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 8.52165 | 0.308302 | ||||||||
\(765\) | 1.67632 | 0.0606074 | ||||||||
\(766\) | 28.9218 | 1.04499 | ||||||||
\(767\) | −93.5435 | −3.37766 | ||||||||
\(768\) | −2.42629 | −0.0875511 | ||||||||
\(769\) | −47.5147 | −1.71342 | −0.856712 | − | 0.515795i | \(-0.827497\pi\) | ||||
−0.856712 | + | 0.515795i | \(0.827497\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 10.7519 | 0.387221 | ||||||||
\(772\) | 13.1790 | 0.474322 | ||||||||
\(773\) | 35.8534 | 1.28956 | 0.644778 | − | 0.764370i | \(-0.276950\pi\) | ||||
0.644778 | + | 0.764370i | \(0.276950\pi\) | |||||||
\(774\) | −0.563080 | −0.0202395 | ||||||||
\(775\) | 15.0187 | 0.539489 | ||||||||
\(776\) | 0.283480 | 0.0101763 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 9.91719 | 0.355548 | ||||||||
\(779\) | 90.5386 | 3.24388 | ||||||||
\(780\) | −4.01103 | −0.143618 | ||||||||
\(781\) | 4.70016 | 0.168185 | ||||||||
\(782\) | −9.76633 | −0.349243 | ||||||||
\(783\) | −0.274492 | −0.00980955 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 2.58742 | 0.0923490 | ||||||||
\(786\) | 34.1836 | 1.21929 | ||||||||
\(787\) | −4.53121 | −0.161520 | −0.0807601 | − | 0.996734i | \(-0.525735\pi\) | ||||
−0.0807601 | + | 0.996734i | \(0.525735\pi\) | |||||||
\(788\) | −5.96908 | −0.212640 | ||||||||
\(789\) | −21.2419 | −0.756231 | ||||||||
\(790\) | 1.16965 | 0.0416144 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −6.19984 | −0.220302 | ||||||||
\(793\) | −62.3865 | −2.21541 | ||||||||
\(794\) | −10.3356 | −0.366797 | ||||||||
\(795\) | 0.246969 | 0.00875908 | ||||||||
\(796\) | 13.3315 | 0.472521 | ||||||||
\(797\) | −1.22332 | −0.0433324 | −0.0216662 | − | 0.999765i | \(-0.506897\pi\) | ||||
−0.0216662 | + | 0.999765i | \(0.506897\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 27.2244 | 0.963131 | ||||||||
\(800\) | 4.93202 | 0.174373 | ||||||||
\(801\) | 34.1253 | 1.20576 | ||||||||
\(802\) | 20.8127 | 0.734921 | ||||||||
\(803\) | 8.98450 | 0.317056 | ||||||||
\(804\) | −23.1417 | −0.816145 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 19.3073 | 0.680072 | ||||||||
\(807\) | −52.8578 | −1.86068 | ||||||||
\(808\) | 10.9123 | 0.383892 | ||||||||
\(809\) | −46.2305 | −1.62538 | −0.812689 | − | 0.582697i | \(-0.801997\pi\) | ||||
−0.812689 | + | 0.582697i | \(0.801997\pi\) | |||||||
\(810\) | 2.43178 | 0.0854439 | ||||||||
\(811\) | 20.0839 | 0.705241 | 0.352621 | − | 0.935766i | \(-0.385291\pi\) | ||||
0.352621 | + | 0.935766i | \(0.385291\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 41.1925 | 1.44469 | ||||||||
\(814\) | 15.5598 | 0.545369 | ||||||||
\(815\) | 1.76064 | 0.0616726 | ||||||||
\(816\) | −5.40345 | −0.189159 | ||||||||
\(817\) | 1.64577 | 0.0575783 | ||||||||
\(818\) | −9.80067 | −0.342672 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 2.79774 | 0.0977014 | ||||||||
\(821\) | 27.8598 | 0.972314 | 0.486157 | − | 0.873871i | \(-0.338398\pi\) | ||||
0.486157 | + | 0.873871i | \(0.338398\pi\) | |||||||
\(822\) | −31.6022 | −1.10225 | ||||||||
\(823\) | 54.1598 | 1.88789 | 0.943946 | − | 0.330099i | \(-0.107082\pi\) | ||||
0.943946 | + | 0.330099i | \(0.107082\pi\) | |||||||
\(824\) | 11.5444 | 0.402168 | ||||||||
\(825\) | 25.6993 | 0.894734 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −16.8852 | −0.587157 | −0.293579 | − | 0.955935i | \(-0.594846\pi\) | ||||
−0.293579 | + | 0.955935i | \(0.594846\pi\) | |||||||
\(828\) | 12.6599 | 0.439961 | ||||||||
\(829\) | −46.3467 | −1.60969 | −0.804844 | − | 0.593486i | \(-0.797751\pi\) | ||||
−0.804844 | + | 0.593486i | \(0.797751\pi\) | |||||||
\(830\) | −0.499020 | −0.0173212 | ||||||||
\(831\) | 1.47677 | 0.0512285 | ||||||||
\(832\) | 6.34036 | 0.219812 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −41.0010 | −1.41975 | ||||||||
\(835\) | 1.88363 | 0.0651856 | ||||||||
\(836\) | 18.1209 | 0.626726 | ||||||||
\(837\) | −0.835870 | −0.0288919 | ||||||||
\(838\) | −0.564842 | −0.0195121 | ||||||||
\(839\) | −24.9065 | −0.859866 | −0.429933 | − | 0.902861i | \(-0.641463\pi\) | ||||
−0.429933 | + | 0.902861i | \(0.641463\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1.00000 | 0.0344828 | ||||||||
\(842\) | −28.1593 | −0.970434 | ||||||||
\(843\) | 62.0049 | 2.13556 | ||||||||
\(844\) | 9.91857 | 0.341411 | ||||||||
\(845\) | 7.09204 | 0.243974 | ||||||||
\(846\) | −35.2904 | −1.21331 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −0.390391 | −0.0134061 | ||||||||
\(849\) | −59.9636 | −2.05794 | ||||||||
\(850\) | 10.9838 | 0.376742 | ||||||||
\(851\) | −31.7725 | −1.08915 | ||||||||
\(852\) | −5.31008 | −0.181920 | ||||||||
\(853\) | −13.4612 | −0.460903 | −0.230451 | − | 0.973084i | \(-0.574020\pi\) | ||||
−0.230451 | + | 0.973084i | \(0.574020\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 6.35117 | 0.217205 | ||||||||
\(856\) | −9.96649 | −0.340648 | ||||||||
\(857\) | 28.3203 | 0.967403 | 0.483702 | − | 0.875233i | \(-0.339292\pi\) | ||||
0.483702 | + | 0.875233i | \(0.339292\pi\) | |||||||
\(858\) | 33.0377 | 1.12789 | ||||||||
\(859\) | 21.8641 | 0.745995 | 0.372997 | − | 0.927832i | \(-0.378330\pi\) | ||||
0.372997 | + | 0.927832i | \(0.378330\pi\) | |||||||
\(860\) | 0.0508562 | 0.00173418 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −28.1658 | −0.959331 | ||||||||
\(863\) | 32.4502 | 1.10462 | 0.552308 | − | 0.833640i | \(-0.313747\pi\) | ||||
0.552308 | + | 0.833640i | \(0.313747\pi\) | |||||||
\(864\) | −0.274492 | −0.00933842 | ||||||||
\(865\) | 2.24446 | 0.0763139 | ||||||||
\(866\) | −17.6927 | −0.601224 | ||||||||
\(867\) | 29.2131 | 0.992130 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −9.63409 | −0.326814 | ||||||||
\(870\) | −0.632619 | −0.0214478 | ||||||||
\(871\) | 60.4737 | 2.04907 | ||||||||
\(872\) | 9.82477 | 0.332709 | ||||||||
\(873\) | −0.818369 | −0.0276976 | ||||||||
\(874\) | −37.0023 | −1.25162 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −10.1504 | −0.342949 | ||||||||
\(877\) | −4.92965 | −0.166462 | −0.0832312 | − | 0.996530i | \(-0.526524\pi\) | ||||
−0.0832312 | + | 0.996530i | \(0.526524\pi\) | |||||||
\(878\) | 28.1245 | 0.949155 | ||||||||
\(879\) | −50.9297 | −1.71782 | ||||||||
\(880\) | 0.559957 | 0.0188761 | ||||||||
\(881\) | −13.9409 | −0.469682 | −0.234841 | − | 0.972034i | \(-0.575457\pi\) | ||||
−0.234841 | + | 0.972034i | \(0.575457\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 44.4387 | 1.49548 | 0.747740 | − | 0.663992i | \(-0.231139\pi\) | ||||
0.747740 | + | 0.663992i | \(0.231139\pi\) | |||||||
\(884\) | 14.1203 | 0.474916 | ||||||||
\(885\) | 9.33346 | 0.313741 | ||||||||
\(886\) | 6.21048 | 0.208645 | ||||||||
\(887\) | −3.19391 | −0.107241 | −0.0536204 | − | 0.998561i | \(-0.517076\pi\) | ||||
−0.0536204 | + | 0.998561i | \(0.517076\pi\) | |||||||
\(888\) | −17.5789 | −0.589908 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −3.08212 | −0.103313 | ||||||||
\(891\) | −20.0298 | −0.671025 | ||||||||
\(892\) | −19.5885 | −0.655872 | ||||||||
\(893\) | 103.147 | 3.45168 | ||||||||
\(894\) | −1.19367 | −0.0399223 | ||||||||
\(895\) | 5.49623 | 0.183719 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −67.4618 | −2.25248 | ||||||||
\(898\) | 5.87960 | 0.196205 | ||||||||
\(899\) | 3.04515 | 0.101561 | ||||||||
\(900\) | −14.2381 | −0.474603 | ||||||||
\(901\) | −0.869418 | −0.0289645 | ||||||||
\(902\) | −23.0442 | −0.767287 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 1.20430 | 0.0400545 | ||||||||
\(905\) | −2.24036 | −0.0744720 | ||||||||
\(906\) | 5.09969 | 0.169426 | ||||||||
\(907\) | 20.0688 | 0.666372 | 0.333186 | − | 0.942861i | \(-0.391876\pi\) | ||||
0.333186 | + | 0.942861i | \(0.391876\pi\) | |||||||
\(908\) | 15.6918 | 0.520751 | ||||||||
\(909\) | −31.5022 | −1.04486 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −5.18802 | −0.171887 | −0.0859434 | − | 0.996300i | \(-0.527390\pi\) | ||||
−0.0859434 | + | 0.996300i | \(0.527390\pi\) | |||||||
\(912\) | −20.4724 | −0.677909 | ||||||||
\(913\) | 4.11028 | 0.136030 | ||||||||
\(914\) | 34.2340 | 1.13236 | ||||||||
\(915\) | 6.22472 | 0.205783 | ||||||||
\(916\) | −14.4197 | −0.476440 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −0.611307 | −0.0201761 | ||||||||
\(919\) | 10.2725 | 0.338859 | 0.169429 | − | 0.985542i | \(-0.445808\pi\) | ||||
0.169429 | + | 0.985542i | \(0.445808\pi\) | |||||||
\(920\) | −1.14341 | −0.0376972 | ||||||||
\(921\) | −60.4543 | −1.99204 | ||||||||
\(922\) | 7.77623 | 0.256097 | ||||||||
\(923\) | 13.8763 | 0.456743 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 35.7333 | 1.17490 | ||||||||
\(926\) | 6.50388 | 0.213731 | ||||||||
\(927\) | −33.3271 | −1.09461 | ||||||||
\(928\) | 1.00000 | 0.0328266 | ||||||||
\(929\) | −4.27777 | −0.140349 | −0.0701745 | − | 0.997535i | \(-0.522356\pi\) | ||||
−0.0701745 | + | 0.997535i | \(0.522356\pi\) | |||||||
\(930\) | −1.92642 | −0.0631698 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −10.0291 | −0.328515 | ||||||||
\(933\) | −8.20696 | −0.268684 | ||||||||
\(934\) | 5.00733 | 0.163845 | ||||||||
\(935\) | 1.24705 | 0.0407829 | ||||||||
\(936\) | −18.3038 | −0.598277 | ||||||||
\(937\) | −59.1093 | −1.93102 | −0.965508 | − | 0.260374i | \(-0.916154\pi\) | ||||
−0.965508 | + | 0.260374i | \(0.916154\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −67.4106 | −2.19986 | ||||||||
\(940\) | 3.18735 | 0.103960 | ||||||||
\(941\) | 35.6173 | 1.16109 | 0.580545 | − | 0.814228i | \(-0.302839\pi\) | ||||
0.580545 | + | 0.814228i | \(0.302839\pi\) | |||||||
\(942\) | 24.0774 | 0.784483 | ||||||||
\(943\) | 47.0554 | 1.53233 | ||||||||
\(944\) | −14.7537 | −0.480191 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −0.418887 | −0.0136192 | ||||||||
\(947\) | −56.0906 | −1.82270 | −0.911349 | − | 0.411634i | \(-0.864958\pi\) | ||||
−0.911349 | + | 0.411634i | \(0.864958\pi\) | |||||||
\(948\) | 10.8843 | 0.353504 | ||||||||
\(949\) | 26.5249 | 0.861034 | ||||||||
\(950\) | 41.6151 | 1.35017 | ||||||||
\(951\) | 33.1034 | 1.07345 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 30.7780 | 0.996998 | 0.498499 | − | 0.866890i | \(-0.333885\pi\) | ||||
0.498499 | + | 0.866890i | \(0.333885\pi\) | |||||||
\(954\) | 1.12701 | 0.0364882 | ||||||||
\(955\) | 2.22190 | 0.0718989 | ||||||||
\(956\) | −0.920380 | −0.0297672 | ||||||||
\(957\) | 5.21070 | 0.168438 | ||||||||
\(958\) | 35.2838 | 1.13997 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −0.632619 | −0.0204177 | ||||||||
\(961\) | −21.7271 | −0.700873 | ||||||||
\(962\) | 45.9370 | 1.48107 | ||||||||
\(963\) | 28.7719 | 0.927162 | ||||||||
\(964\) | −7.64883 | −0.246352 | ||||||||
\(965\) | 3.43623 | 0.110616 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 18.2916 | 0.588217 | 0.294108 | − | 0.955772i | \(-0.404977\pi\) | ||||
0.294108 | + | 0.955772i | \(0.404977\pi\) | |||||||
\(968\) | 6.38780 | 0.205312 | ||||||||
\(969\) | −45.5930 | −1.46466 | ||||||||
\(970\) | 0.0739133 | 0.00237321 | ||||||||
\(971\) | 19.2108 | 0.616503 | 0.308251 | − | 0.951305i | \(-0.400256\pi\) | ||||
0.308251 | + | 0.951305i | \(0.400256\pi\) | |||||||
\(972\) | 21.8055 | 0.699413 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −4.73153 | −0.151608 | ||||||||
\(975\) | 75.8718 | 2.42984 | ||||||||
\(976\) | −9.83960 | −0.314958 | ||||||||
\(977\) | 11.6484 | 0.372665 | 0.186332 | − | 0.982487i | \(-0.440340\pi\) | ||||
0.186332 | + | 0.982487i | \(0.440340\pi\) | |||||||
\(978\) | 16.3837 | 0.523894 | ||||||||
\(979\) | 25.3865 | 0.811357 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −28.3628 | −0.905555 | ||||||||
\(982\) | 18.5337 | 0.591433 | ||||||||
\(983\) | −1.00446 | −0.0320372 | −0.0160186 | − | 0.999872i | \(-0.505099\pi\) | ||||
−0.0160186 | + | 0.999872i | \(0.505099\pi\) | |||||||
\(984\) | 26.0345 | 0.829950 | ||||||||
\(985\) | −1.55635 | −0.0495895 | ||||||||
\(986\) | 2.22705 | 0.0709236 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 53.4983 | 1.70201 | ||||||||
\(989\) | 0.855353 | 0.0271986 | ||||||||
\(990\) | −1.61652 | −0.0513764 | ||||||||
\(991\) | −47.5781 | −1.51137 | −0.755684 | − | 0.654936i | \(-0.772695\pi\) | ||||
−0.755684 | + | 0.654936i | \(0.772695\pi\) | |||||||
\(992\) | 3.04515 | 0.0966836 | ||||||||
\(993\) | 29.4979 | 0.936088 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 3.47599 | 0.110196 | ||||||||
\(996\) | −4.64365 | −0.147140 | ||||||||
\(997\) | −13.6822 | −0.433320 | −0.216660 | − | 0.976247i | \(-0.569516\pi\) | ||||
−0.216660 | + | 0.976247i | \(0.569516\pi\) | |||||||
\(998\) | 8.49139 | 0.268790 | ||||||||
\(999\) | −1.98874 | −0.0629211 |
(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 | 2842.2.a.u.1.1 | 5 | ||
7.3 | odd | 6 | 406.2.e.d.233.1 | ✓ | 10 | ||
7.5 | odd | 6 | 406.2.e.d.291.1 | yes | 10 | ||
7.6 | odd | 2 | 2842.2.a.t.1.5 | 5 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
406.2.e.d.233.1 | ✓ | 10 | 7.3 | odd | 6 | ||
406.2.e.d.291.1 | yes | 10 | 7.5 | odd | 6 | ||
2842.2.a.t.1.5 | 5 | 7.6 | odd | 2 | |||
2842.2.a.u.1.1 | 5 | 1.1 | even | 1 | trivial |