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 | 1.4 | ||
Root | \(2.94749\) 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 | ||||||||
\(3\) | 2.94749 | 1.70173 | 0.850867 | − | 0.525381i | \(-0.176077\pi\) | ||||
0.850867 | + | 0.525381i | \(0.176077\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 2.36624 | 1.05821 | 0.529106 | − | 0.848556i | \(-0.322527\pi\) | ||||
0.529106 | + | 0.848556i | \(0.322527\pi\) | |||||||
\(6\) | −2.94749 | −1.20331 | ||||||||
\(7\) | 1.66073 | 0.627696 | 0.313848 | − | 0.949473i | \(-0.398382\pi\) | ||||
0.313848 | + | 0.949473i | \(0.398382\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 5.68769 | 1.89590 | ||||||||
\(10\) | −2.36624 | −0.748269 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | 2.94749 | 0.850867 | ||||||||
\(13\) | 0.633765 | 0.175775 | 0.0878874 | − | 0.996130i | \(-0.471988\pi\) | ||||
0.0878874 | + | 0.996130i | \(0.471988\pi\) | |||||||
\(14\) | −1.66073 | −0.443848 | ||||||||
\(15\) | 6.97445 | 1.80080 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −0.581254 | −0.140975 | −0.0704874 | − | 0.997513i | \(-0.522455\pi\) | ||||
−0.0704874 | + | 0.997513i | \(0.522455\pi\) | |||||||
\(18\) | −5.68769 | −1.34060 | ||||||||
\(19\) | 1.00000 | 0.229416 | ||||||||
\(20\) | 2.36624 | 0.529106 | ||||||||
\(21\) | 4.89498 | 1.06817 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 3.60822 | 0.752365 | 0.376183 | − | 0.926546i | \(-0.377237\pi\) | ||||
0.376183 | + | 0.926546i | \(0.377237\pi\) | |||||||
\(24\) | −2.94749 | −0.601654 | ||||||||
\(25\) | 0.599069 | 0.119814 | ||||||||
\(26\) | −0.633765 | −0.124291 | ||||||||
\(27\) | 7.92194 | 1.52458 | ||||||||
\(28\) | 1.66073 | 0.313848 | ||||||||
\(29\) | −9.13696 | −1.69669 | −0.848345 | − | 0.529443i | \(-0.822401\pi\) | ||||
−0.848345 | + | 0.529443i | \(0.822401\pi\) | |||||||
\(30\) | −6.97445 | −1.27335 | ||||||||
\(31\) | 1.02555 | 0.184194 | 0.0920969 | − | 0.995750i | \(-0.470643\pi\) | ||||
0.0920969 | + | 0.995750i | \(0.470643\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0.581254 | 0.0996842 | ||||||||
\(35\) | 3.92967 | 0.664236 | ||||||||
\(36\) | 5.68769 | 0.947949 | ||||||||
\(37\) | 2.15895 | 0.354929 | 0.177464 | − | 0.984127i | \(-0.443211\pi\) | ||||
0.177464 | + | 0.984127i | \(0.443211\pi\) | |||||||
\(38\) | −1.00000 | −0.162221 | ||||||||
\(39\) | 1.86801 | 0.299122 | ||||||||
\(40\) | −2.36624 | −0.374135 | ||||||||
\(41\) | 4.40093 | 0.687310 | 0.343655 | − | 0.939096i | \(-0.388335\pi\) | ||||
0.343655 | + | 0.939096i | \(0.388335\pi\) | |||||||
\(42\) | −4.89498 | −0.755312 | ||||||||
\(43\) | 9.58267 | 1.46134 | 0.730672 | − | 0.682729i | \(-0.239207\pi\) | ||||
0.730672 | + | 0.682729i | \(0.239207\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 13.4584 | 2.00626 | ||||||||
\(46\) | −3.60822 | −0.532003 | ||||||||
\(47\) | 8.73247 | 1.27376 | 0.636881 | − | 0.770962i | \(-0.280224\pi\) | ||||
0.636881 | + | 0.770962i | \(0.280224\pi\) | |||||||
\(48\) | 2.94749 | 0.425433 | ||||||||
\(49\) | −4.24198 | −0.605997 | ||||||||
\(50\) | −0.599069 | −0.0847212 | ||||||||
\(51\) | −1.71324 | −0.239901 | ||||||||
\(52\) | 0.633765 | 0.0878874 | ||||||||
\(53\) | −12.5302 | −1.72115 | −0.860575 | − | 0.509324i | \(-0.829895\pi\) | ||||
−0.860575 | + | 0.509324i | \(0.829895\pi\) | |||||||
\(54\) | −7.92194 | −1.07804 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −1.66073 | −0.221924 | ||||||||
\(57\) | 2.94749 | 0.390404 | ||||||||
\(58\) | 9.13696 | 1.19974 | ||||||||
\(59\) | 6.47623 | 0.843134 | 0.421567 | − | 0.906797i | \(-0.361480\pi\) | ||||
0.421567 | + | 0.906797i | \(0.361480\pi\) | |||||||
\(60\) | 6.97445 | 0.900398 | ||||||||
\(61\) | 1.32146 | 0.169195 | 0.0845976 | − | 0.996415i | \(-0.473040\pi\) | ||||
0.0845976 | + | 0.996415i | \(0.473040\pi\) | |||||||
\(62\) | −1.02555 | −0.130245 | ||||||||
\(63\) | 9.44571 | 1.19005 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 1.49964 | 0.186007 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −0.393199 | −0.0480369 | −0.0240184 | − | 0.999712i | \(-0.507646\pi\) | ||||
−0.0240184 | + | 0.999712i | \(0.507646\pi\) | |||||||
\(68\) | −0.581254 | −0.0704874 | ||||||||
\(69\) | 10.6352 | 1.28033 | ||||||||
\(70\) | −3.92967 | −0.469686 | ||||||||
\(71\) | −0.312308 | −0.0370642 | −0.0185321 | − | 0.999828i | \(-0.505899\pi\) | ||||
−0.0185321 | + | 0.999828i | \(0.505899\pi\) | |||||||
\(72\) | −5.68769 | −0.670301 | ||||||||
\(73\) | −9.31372 | −1.09009 | −0.545044 | − | 0.838407i | \(-0.683487\pi\) | ||||
−0.545044 | + | 0.838407i | \(0.683487\pi\) | |||||||
\(74\) | −2.15895 | −0.250973 | ||||||||
\(75\) | 1.76575 | 0.203891 | ||||||||
\(76\) | 1.00000 | 0.114708 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −1.86801 | −0.211511 | ||||||||
\(79\) | 11.2704 | 1.26801 | 0.634007 | − | 0.773327i | \(-0.281409\pi\) | ||||
0.634007 | + | 0.773327i | \(0.281409\pi\) | |||||||
\(80\) | 2.36624 | 0.264553 | ||||||||
\(81\) | 6.28676 | 0.698529 | ||||||||
\(82\) | −4.40093 | −0.486001 | ||||||||
\(83\) | −6.90413 | −0.757826 | −0.378913 | − | 0.925432i | \(-0.623702\pi\) | ||||
−0.378913 | + | 0.925432i | \(0.623702\pi\) | |||||||
\(84\) | 4.89498 | 0.534086 | ||||||||
\(85\) | −1.37538 | −0.149181 | ||||||||
\(86\) | −9.58267 | −1.03333 | ||||||||
\(87\) | −26.9311 | −2.88732 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 0.519595 | 0.0550769 | 0.0275385 | − | 0.999621i | \(-0.491233\pi\) | ||||
0.0275385 | + | 0.999621i | \(0.491233\pi\) | |||||||
\(90\) | −13.4584 | −1.41864 | ||||||||
\(91\) | 1.05251 | 0.110333 | ||||||||
\(92\) | 3.60822 | 0.376183 | ||||||||
\(93\) | 3.02279 | 0.313449 | ||||||||
\(94\) | −8.73247 | −0.900686 | ||||||||
\(95\) | 2.36624 | 0.242771 | ||||||||
\(96\) | −2.94749 | −0.300827 | ||||||||
\(97\) | −8.37894 | −0.850753 | −0.425376 | − | 0.905017i | \(-0.639858\pi\) | ||||
−0.425376 | + | 0.905017i | \(0.639858\pi\) | |||||||
\(98\) | 4.24198 | 0.428505 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0.599069 | 0.0599069 | ||||||||
\(101\) | −16.5379 | −1.64558 | −0.822791 | − | 0.568344i | \(-0.807584\pi\) | ||||
−0.822791 | + | 0.568344i | \(0.807584\pi\) | |||||||
\(102\) | 1.71324 | 0.169636 | ||||||||
\(103\) | 2.79627 | 0.275525 | 0.137762 | − | 0.990465i | \(-0.456009\pi\) | ||||
0.137762 | + | 0.990465i | \(0.456009\pi\) | |||||||
\(104\) | −0.633765 | −0.0621457 | ||||||||
\(105\) | 11.5827 | 1.13035 | ||||||||
\(106\) | 12.5302 | 1.21704 | ||||||||
\(107\) | 18.9681 | 1.83372 | 0.916859 | − | 0.399210i | \(-0.130716\pi\) | ||||
0.916859 | + | 0.399210i | \(0.130716\pi\) | |||||||
\(108\) | 7.92194 | 0.762289 | ||||||||
\(109\) | 17.0732 | 1.63531 | 0.817656 | − | 0.575707i | \(-0.195273\pi\) | ||||
0.817656 | + | 0.575707i | \(0.195273\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 6.36348 | 0.603995 | ||||||||
\(112\) | 1.66073 | 0.156924 | ||||||||
\(113\) | 21.1114 | 1.98599 | 0.992997 | − | 0.118137i | \(-0.0376922\pi\) | ||||
0.992997 | + | 0.118137i | \(0.0376922\pi\) | |||||||
\(114\) | −2.94749 | −0.276058 | ||||||||
\(115\) | 8.53789 | 0.796162 | ||||||||
\(116\) | −9.13696 | −0.848345 | ||||||||
\(117\) | 3.60466 | 0.333251 | ||||||||
\(118\) | −6.47623 | −0.596185 | ||||||||
\(119\) | −0.965305 | −0.0884893 | ||||||||
\(120\) | −6.97445 | −0.636677 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | −1.32146 | −0.119639 | ||||||||
\(123\) | 12.9717 | 1.16962 | ||||||||
\(124\) | 1.02555 | 0.0920969 | ||||||||
\(125\) | −10.4136 | −0.931424 | ||||||||
\(126\) | −9.44571 | −0.841491 | ||||||||
\(127\) | 4.62745 | 0.410620 | 0.205310 | − | 0.978697i | \(-0.434180\pi\) | ||||
0.205310 | + | 0.978697i | \(0.434180\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | 28.2448 | 2.48682 | ||||||||
\(130\) | −1.49964 | −0.131527 | ||||||||
\(131\) | −15.7763 | −1.37838 | −0.689191 | − | 0.724579i | \(-0.742034\pi\) | ||||
−0.689191 | + | 0.724579i | \(0.742034\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1.66073 | 0.144003 | ||||||||
\(134\) | 0.393199 | 0.0339672 | ||||||||
\(135\) | 18.7452 | 1.61333 | ||||||||
\(136\) | 0.581254 | 0.0498421 | ||||||||
\(137\) | −20.6366 | −1.76310 | −0.881552 | − | 0.472087i | \(-0.843501\pi\) | ||||
−0.881552 | + | 0.472087i | \(0.843501\pi\) | |||||||
\(138\) | −10.6352 | −0.905327 | ||||||||
\(139\) | −9.56721 | −0.811480 | −0.405740 | − | 0.913989i | \(-0.632986\pi\) | ||||
−0.405740 | + | 0.913989i | \(0.632986\pi\) | |||||||
\(140\) | 3.92967 | 0.332118 | ||||||||
\(141\) | 25.7389 | 2.16760 | ||||||||
\(142\) | 0.312308 | 0.0262083 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 5.68769 | 0.473974 | ||||||||
\(145\) | −21.6202 | −1.79546 | ||||||||
\(146\) | 9.31372 | 0.770809 | ||||||||
\(147\) | −12.5032 | −1.03125 | ||||||||
\(148\) | 2.15895 | 0.177464 | ||||||||
\(149\) | 18.3096 | 1.49998 | 0.749988 | − | 0.661451i | \(-0.230059\pi\) | ||||
0.749988 | + | 0.661451i | \(0.230059\pi\) | |||||||
\(150\) | −1.76575 | −0.144173 | ||||||||
\(151\) | 6.25562 | 0.509075 | 0.254538 | − | 0.967063i | \(-0.418077\pi\) | ||||
0.254538 | + | 0.967063i | \(0.418077\pi\) | |||||||
\(152\) | −1.00000 | −0.0811107 | ||||||||
\(153\) | −3.30599 | −0.267274 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 2.42669 | 0.194916 | ||||||||
\(156\) | 1.86801 | 0.149561 | ||||||||
\(157\) | −6.15619 | −0.491318 | −0.245659 | − | 0.969356i | \(-0.579004\pi\) | ||||
−0.245659 | + | 0.969356i | \(0.579004\pi\) | |||||||
\(158\) | −11.2704 | −0.896622 | ||||||||
\(159\) | −36.9325 | −2.92894 | ||||||||
\(160\) | −2.36624 | −0.187067 | ||||||||
\(161\) | 5.99227 | 0.472257 | ||||||||
\(162\) | −6.28676 | −0.493935 | ||||||||
\(163\) | −11.8439 | −0.927685 | −0.463842 | − | 0.885918i | \(-0.653530\pi\) | ||||
−0.463842 | + | 0.885918i | \(0.653530\pi\) | |||||||
\(164\) | 4.40093 | 0.343655 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 6.90413 | 0.535864 | ||||||||
\(167\) | −4.89142 | −0.378509 | −0.189255 | − | 0.981928i | \(-0.560607\pi\) | ||||
−0.189255 | + | 0.981928i | \(0.560607\pi\) | |||||||
\(168\) | −4.89498 | −0.377656 | ||||||||
\(169\) | −12.5983 | −0.969103 | ||||||||
\(170\) | 1.37538 | 0.105487 | ||||||||
\(171\) | 5.68769 | 0.434949 | ||||||||
\(172\) | 9.58267 | 0.730672 | ||||||||
\(173\) | −18.1206 | −1.37768 | −0.688840 | − | 0.724913i | \(-0.741880\pi\) | ||||
−0.688840 | + | 0.724913i | \(0.741880\pi\) | |||||||
\(174\) | 26.9311 | 2.04164 | ||||||||
\(175\) | 0.994891 | 0.0752067 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 19.0886 | 1.43479 | ||||||||
\(178\) | −0.519595 | −0.0389453 | ||||||||
\(179\) | 3.07947 | 0.230171 | 0.115085 | − | 0.993356i | \(-0.463286\pi\) | ||||
0.115085 | + | 0.993356i | \(0.463286\pi\) | |||||||
\(180\) | 13.4584 | 1.00313 | ||||||||
\(181\) | 0.0693910 | 0.00515779 | 0.00257889 | − | 0.999997i | \(-0.499179\pi\) | ||||
0.00257889 | + | 0.999997i | \(0.499179\pi\) | |||||||
\(182\) | −1.05251 | −0.0780173 | ||||||||
\(183\) | 3.89498 | 0.287925 | ||||||||
\(184\) | −3.60822 | −0.266001 | ||||||||
\(185\) | 5.10858 | 0.375590 | ||||||||
\(186\) | −3.02279 | −0.221642 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 8.73247 | 0.636881 | ||||||||
\(189\) | 13.1562 | 0.956972 | ||||||||
\(190\) | −2.36624 | −0.171665 | ||||||||
\(191\) | 13.6776 | 0.989677 | 0.494838 | − | 0.868985i | \(-0.335227\pi\) | ||||
0.494838 | + | 0.868985i | \(0.335227\pi\) | |||||||
\(192\) | 2.94749 | 0.212717 | ||||||||
\(193\) | 5.61830 | 0.404414 | 0.202207 | − | 0.979343i | \(-0.435189\pi\) | ||||
0.202207 | + | 0.979343i | \(0.435189\pi\) | |||||||
\(194\) | 8.37894 | 0.601573 | ||||||||
\(195\) | 4.42016 | 0.316534 | ||||||||
\(196\) | −4.24198 | −0.302999 | ||||||||
\(197\) | 5.46494 | 0.389361 | 0.194680 | − | 0.980867i | \(-0.437633\pi\) | ||||
0.194680 | + | 0.980867i | \(0.437633\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −13.5571 | −0.961039 | −0.480519 | − | 0.876984i | \(-0.659552\pi\) | ||||
−0.480519 | + | 0.876984i | \(0.659552\pi\) | |||||||
\(200\) | −0.599069 | −0.0423606 | ||||||||
\(201\) | −1.15895 | −0.0817459 | ||||||||
\(202\) | 16.5379 | 1.16360 | ||||||||
\(203\) | −15.1740 | −1.06501 | ||||||||
\(204\) | −1.71324 | −0.119951 | ||||||||
\(205\) | 10.4136 | 0.727320 | ||||||||
\(206\) | −2.79627 | −0.194826 | ||||||||
\(207\) | 20.5224 | 1.42641 | ||||||||
\(208\) | 0.633765 | 0.0439437 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | −11.5827 | −0.799280 | ||||||||
\(211\) | 14.3562 | 0.988318 | 0.494159 | − | 0.869371i | \(-0.335476\pi\) | ||||
0.494159 | + | 0.869371i | \(0.335476\pi\) | |||||||
\(212\) | −12.5302 | −0.860575 | ||||||||
\(213\) | −0.920526 | −0.0630734 | ||||||||
\(214\) | −18.9681 | −1.29664 | ||||||||
\(215\) | 22.6749 | 1.54641 | ||||||||
\(216\) | −7.92194 | −0.539020 | ||||||||
\(217\) | 1.70316 | 0.115618 | ||||||||
\(218\) | −17.0732 | −1.15634 | ||||||||
\(219\) | −27.4521 | −1.85504 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −0.368378 | −0.0247798 | ||||||||
\(222\) | −6.36348 | −0.427089 | ||||||||
\(223\) | −5.16251 | −0.345707 | −0.172854 | − | 0.984948i | \(-0.555299\pi\) | ||||
−0.172854 | + | 0.984948i | \(0.555299\pi\) | |||||||
\(224\) | −1.66073 | −0.110962 | ||||||||
\(225\) | 3.40732 | 0.227155 | ||||||||
\(226\) | −21.1114 | −1.40431 | ||||||||
\(227\) | −18.3435 | −1.21750 | −0.608751 | − | 0.793361i | \(-0.708329\pi\) | ||||
−0.608751 | + | 0.793361i | \(0.708329\pi\) | |||||||
\(228\) | 2.94749 | 0.195202 | ||||||||
\(229\) | 18.3344 | 1.21157 | 0.605785 | − | 0.795629i | \(-0.292859\pi\) | ||||
0.605785 | + | 0.795629i | \(0.292859\pi\) | |||||||
\(230\) | −8.53789 | −0.562972 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 9.13696 | 0.599871 | ||||||||
\(233\) | −14.6429 | −0.959289 | −0.479645 | − | 0.877463i | \(-0.659234\pi\) | ||||
−0.479645 | + | 0.877463i | \(0.659234\pi\) | |||||||
\(234\) | −3.60466 | −0.235644 | ||||||||
\(235\) | 20.6631 | 1.34791 | ||||||||
\(236\) | 6.47623 | 0.421567 | ||||||||
\(237\) | 33.2193 | 2.15782 | ||||||||
\(238\) | 0.965305 | 0.0625714 | ||||||||
\(239\) | −12.5868 | −0.814175 | −0.407088 | − | 0.913389i | \(-0.633456\pi\) | ||||
−0.407088 | + | 0.913389i | \(0.633456\pi\) | |||||||
\(240\) | 6.97445 | 0.450199 | ||||||||
\(241\) | −2.79627 | −0.180124 | −0.0900619 | − | 0.995936i | \(-0.528706\pi\) | ||||
−0.0900619 | + | 0.995936i | \(0.528706\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −5.23567 | −0.335868 | ||||||||
\(244\) | 1.32146 | 0.0845976 | ||||||||
\(245\) | −10.0375 | −0.641274 | ||||||||
\(246\) | −12.9717 | −0.827045 | ||||||||
\(247\) | 0.633765 | 0.0403255 | ||||||||
\(248\) | −1.02555 | −0.0651223 | ||||||||
\(249\) | −20.3498 | −1.28962 | ||||||||
\(250\) | 10.4136 | 0.658616 | ||||||||
\(251\) | −1.72891 | −0.109128 | −0.0545640 | − | 0.998510i | \(-0.517377\pi\) | ||||
−0.0545640 | + | 0.998510i | \(0.517377\pi\) | |||||||
\(252\) | 9.44571 | 0.595024 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | −4.62745 | −0.290352 | ||||||||
\(255\) | −4.05393 | −0.253867 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 21.5414 | 1.34372 | 0.671859 | − | 0.740679i | \(-0.265496\pi\) | ||||
0.671859 | + | 0.740679i | \(0.265496\pi\) | |||||||
\(258\) | −28.2448 | −1.75845 | ||||||||
\(259\) | 3.58543 | 0.222788 | ||||||||
\(260\) | 1.49964 | 0.0930035 | ||||||||
\(261\) | −51.9682 | −3.21675 | ||||||||
\(262\) | 15.7763 | 0.974664 | ||||||||
\(263\) | −22.7920 | −1.40541 | −0.702707 | − | 0.711479i | \(-0.748026\pi\) | ||||
−0.702707 | + | 0.711479i | \(0.748026\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −29.6493 | −1.82134 | ||||||||
\(266\) | −1.66073 | −0.101826 | ||||||||
\(267\) | 1.53150 | 0.0937263 | ||||||||
\(268\) | −0.393199 | −0.0240184 | ||||||||
\(269\) | −18.6429 | −1.13668 | −0.568339 | − | 0.822794i | \(-0.692414\pi\) | ||||
−0.568339 | + | 0.822794i | \(0.692414\pi\) | |||||||
\(270\) | −18.7452 | −1.14080 | ||||||||
\(271\) | −3.33571 | −0.202630 | −0.101315 | − | 0.994854i | \(-0.532305\pi\) | ||||
−0.101315 | + | 0.994854i | \(0.532305\pi\) | |||||||
\(272\) | −0.581254 | −0.0352437 | ||||||||
\(273\) | 3.10226 | 0.187758 | ||||||||
\(274\) | 20.6366 | 1.24670 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 10.6352 | 0.640163 | ||||||||
\(277\) | 23.5883 | 1.41728 | 0.708641 | − | 0.705570i | \(-0.249309\pi\) | ||||
0.708641 | + | 0.705570i | \(0.249309\pi\) | |||||||
\(278\) | 9.56721 | 0.573803 | ||||||||
\(279\) | 5.83300 | 0.349212 | ||||||||
\(280\) | −3.92967 | −0.234843 | ||||||||
\(281\) | 31.6366 | 1.88728 | 0.943641 | − | 0.330972i | \(-0.107377\pi\) | ||||
0.943641 | + | 0.330972i | \(0.107377\pi\) | |||||||
\(282\) | −25.7389 | −1.53273 | ||||||||
\(283\) | 6.06757 | 0.360680 | 0.180340 | − | 0.983604i | \(-0.442280\pi\) | ||||
0.180340 | + | 0.983604i | \(0.442280\pi\) | |||||||
\(284\) | −0.312308 | −0.0185321 | ||||||||
\(285\) | 6.97445 | 0.413131 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 7.30875 | 0.431422 | ||||||||
\(288\) | −5.68769 | −0.335150 | ||||||||
\(289\) | −16.6621 | −0.980126 | ||||||||
\(290\) | 21.6202 | 1.26958 | ||||||||
\(291\) | −24.6968 | −1.44775 | ||||||||
\(292\) | −9.31372 | −0.545044 | ||||||||
\(293\) | 16.8312 | 0.983288 | 0.491644 | − | 0.870796i | \(-0.336396\pi\) | ||||
0.491644 | + | 0.870796i | \(0.336396\pi\) | |||||||
\(294\) | 12.5032 | 0.729201 | ||||||||
\(295\) | 15.3243 | 0.892215 | ||||||||
\(296\) | −2.15895 | −0.125486 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −18.3096 | −1.06064 | ||||||||
\(299\) | 2.28676 | 0.132247 | ||||||||
\(300\) | 1.76575 | 0.101946 | ||||||||
\(301\) | 15.9142 | 0.917280 | ||||||||
\(302\) | −6.25562 | −0.359971 | ||||||||
\(303\) | −48.7453 | −2.80034 | ||||||||
\(304\) | 1.00000 | 0.0573539 | ||||||||
\(305\) | 3.12688 | 0.179044 | ||||||||
\(306\) | 3.30599 | 0.188991 | ||||||||
\(307\) | −5.10858 | −0.291562 | −0.145781 | − | 0.989317i | \(-0.546570\pi\) | ||||
−0.145781 | + | 0.989317i | \(0.546570\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 8.24198 | 0.468870 | ||||||||
\(310\) | −2.42669 | −0.137827 | ||||||||
\(311\) | −24.5635 | −1.39287 | −0.696435 | − | 0.717620i | \(-0.745231\pi\) | ||||
−0.696435 | + | 0.717620i | \(0.745231\pi\) | |||||||
\(312\) | −1.86801 | −0.105756 | ||||||||
\(313\) | −24.2868 | −1.37277 | −0.686387 | − | 0.727237i | \(-0.740804\pi\) | ||||
−0.686387 | + | 0.727237i | \(0.740804\pi\) | |||||||
\(314\) | 6.15619 | 0.347414 | ||||||||
\(315\) | 22.3508 | 1.25932 | ||||||||
\(316\) | 11.2704 | 0.634007 | ||||||||
\(317\) | −28.6225 | −1.60760 | −0.803801 | − | 0.594898i | \(-0.797192\pi\) | ||||
−0.803801 | + | 0.594898i | \(0.797192\pi\) | |||||||
\(318\) | 36.9325 | 2.07107 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 2.36624 | 0.132277 | ||||||||
\(321\) | 55.9084 | 3.12050 | ||||||||
\(322\) | −5.99227 | −0.333936 | ||||||||
\(323\) | −0.581254 | −0.0323418 | ||||||||
\(324\) | 6.28676 | 0.349264 | ||||||||
\(325\) | 0.379669 | 0.0210602 | ||||||||
\(326\) | 11.8439 | 0.655972 | ||||||||
\(327\) | 50.3229 | 2.78287 | ||||||||
\(328\) | −4.40093 | −0.243001 | ||||||||
\(329\) | 14.5023 | 0.799535 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −2.40960 | −0.132444 | −0.0662218 | − | 0.997805i | \(-0.521094\pi\) | ||||
−0.0662218 | + | 0.997805i | \(0.521094\pi\) | |||||||
\(332\) | −6.90413 | −0.378913 | ||||||||
\(333\) | 12.2794 | 0.672909 | ||||||||
\(334\) | 4.89142 | 0.267647 | ||||||||
\(335\) | −0.930401 | −0.0508332 | ||||||||
\(336\) | 4.89498 | 0.267043 | ||||||||
\(337\) | −17.5195 | −0.954346 | −0.477173 | − | 0.878809i | \(-0.658338\pi\) | ||||
−0.477173 | + | 0.878809i | \(0.658338\pi\) | |||||||
\(338\) | 12.5983 | 0.685259 | ||||||||
\(339\) | 62.2257 | 3.37963 | ||||||||
\(340\) | −1.37538 | −0.0745906 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | −5.68769 | −0.307555 | ||||||||
\(343\) | −18.6699 | −1.00808 | ||||||||
\(344\) | −9.58267 | −0.516663 | ||||||||
\(345\) | 25.1653 | 1.35486 | ||||||||
\(346\) | 18.1206 | 0.974167 | ||||||||
\(347\) | −32.1534 | −1.72609 | −0.863043 | − | 0.505130i | \(-0.831445\pi\) | ||||
−0.863043 | + | 0.505130i | \(0.831445\pi\) | |||||||
\(348\) | −26.9311 | −1.44366 | ||||||||
\(349\) | −0.407455 | −0.0218106 | −0.0109053 | − | 0.999941i | \(-0.503471\pi\) | ||||
−0.0109053 | + | 0.999941i | \(0.503471\pi\) | |||||||
\(350\) | −0.994891 | −0.0531792 | ||||||||
\(351\) | 5.02065 | 0.267982 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 3.94158 | 0.209789 | 0.104895 | − | 0.994483i | \(-0.466549\pi\) | ||||
0.104895 | + | 0.994483i | \(0.466549\pi\) | |||||||
\(354\) | −19.0886 | −1.01455 | ||||||||
\(355\) | −0.738995 | −0.0392218 | ||||||||
\(356\) | 0.519595 | 0.0275385 | ||||||||
\(357\) | −2.84522 | −0.150585 | ||||||||
\(358\) | −3.07947 | −0.162755 | ||||||||
\(359\) | 20.0781 | 1.05968 | 0.529842 | − | 0.848097i | \(-0.322251\pi\) | ||||
0.529842 | + | 0.848097i | \(0.322251\pi\) | |||||||
\(360\) | −13.4584 | −0.709321 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | −0.0693910 | −0.00364711 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 1.05251 | 0.0551666 | ||||||||
\(365\) | −22.0385 | −1.15355 | ||||||||
\(366\) | −3.89498 | −0.203594 | ||||||||
\(367\) | −20.5918 | −1.07488 | −0.537442 | − | 0.843301i | \(-0.680609\pi\) | ||||
−0.537442 | + | 0.843301i | \(0.680609\pi\) | |||||||
\(368\) | 3.60822 | 0.188091 | ||||||||
\(369\) | 25.0311 | 1.30307 | ||||||||
\(370\) | −5.10858 | −0.265582 | ||||||||
\(371\) | −20.8092 | −1.08036 | ||||||||
\(372\) | 3.02279 | 0.156724 | ||||||||
\(373\) | 20.8813 | 1.08119 | 0.540597 | − | 0.841282i | \(-0.318198\pi\) | ||||
0.540597 | + | 0.841282i | \(0.318198\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −30.6941 | −1.58504 | ||||||||
\(376\) | −8.73247 | −0.450343 | ||||||||
\(377\) | −5.79068 | −0.298235 | ||||||||
\(378\) | −13.1562 | −0.676681 | ||||||||
\(379\) | −0.753845 | −0.0387224 | −0.0193612 | − | 0.999813i | \(-0.506163\pi\) | ||||
−0.0193612 | + | 0.999813i | \(0.506163\pi\) | |||||||
\(380\) | 2.36624 | 0.121385 | ||||||||
\(381\) | 13.6394 | 0.698765 | ||||||||
\(382\) | −13.6776 | −0.699807 | ||||||||
\(383\) | −18.3142 | −0.935812 | −0.467906 | − | 0.883778i | \(-0.654991\pi\) | ||||
−0.467906 | + | 0.883778i | \(0.654991\pi\) | |||||||
\(384\) | −2.94749 | −0.150413 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −5.61830 | −0.285964 | ||||||||
\(387\) | 54.5033 | 2.77056 | ||||||||
\(388\) | −8.37894 | −0.425376 | ||||||||
\(389\) | −26.1206 | −1.32436 | −0.662182 | − | 0.749343i | \(-0.730370\pi\) | ||||
−0.662182 | + | 0.749343i | \(0.730370\pi\) | |||||||
\(390\) | −4.42016 | −0.223824 | ||||||||
\(391\) | −2.09729 | −0.106065 | ||||||||
\(392\) | 4.24198 | 0.214252 | ||||||||
\(393\) | −46.5005 | −2.34564 | ||||||||
\(394\) | −5.46494 | −0.275320 | ||||||||
\(395\) | 26.6683 | 1.34183 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −34.9079 | −1.75198 | −0.875988 | − | 0.482332i | \(-0.839790\pi\) | ||||
−0.875988 | + | 0.482332i | \(0.839790\pi\) | |||||||
\(398\) | 13.5571 | 0.679557 | ||||||||
\(399\) | 4.89498 | 0.245055 | ||||||||
\(400\) | 0.599069 | 0.0299535 | ||||||||
\(401\) | 6.35353 | 0.317280 | 0.158640 | − | 0.987336i | \(-0.449289\pi\) | ||||
0.158640 | + | 0.987336i | \(0.449289\pi\) | |||||||
\(402\) | 1.15895 | 0.0578031 | ||||||||
\(403\) | 0.649956 | 0.0323766 | ||||||||
\(404\) | −16.5379 | −0.822791 | ||||||||
\(405\) | 14.8760 | 0.739192 | ||||||||
\(406\) | 15.1740 | 0.753073 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 1.71324 | 0.0848180 | ||||||||
\(409\) | −26.1816 | −1.29460 | −0.647299 | − | 0.762237i | \(-0.724101\pi\) | ||||
−0.647299 | + | 0.762237i | \(0.724101\pi\) | |||||||
\(410\) | −10.4136 | −0.514293 | ||||||||
\(411\) | −60.8261 | −3.00033 | ||||||||
\(412\) | 2.79627 | 0.137762 | ||||||||
\(413\) | 10.7553 | 0.529232 | ||||||||
\(414\) | −20.5224 | −1.00862 | ||||||||
\(415\) | −16.3368 | −0.801941 | ||||||||
\(416\) | −0.633765 | −0.0310729 | ||||||||
\(417\) | −28.1992 | −1.38092 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 8.15060 | 0.398183 | 0.199091 | − | 0.979981i | \(-0.436201\pi\) | ||||
0.199091 | + | 0.979981i | \(0.436201\pi\) | |||||||
\(420\) | 11.5827 | 0.565176 | ||||||||
\(421\) | 10.9531 | 0.533820 | 0.266910 | − | 0.963721i | \(-0.413997\pi\) | ||||
0.266910 | + | 0.963721i | \(0.413997\pi\) | |||||||
\(422\) | −14.3562 | −0.698847 | ||||||||
\(423\) | 49.6676 | 2.41492 | ||||||||
\(424\) | 12.5302 | 0.608518 | ||||||||
\(425\) | −0.348211 | −0.0168907 | ||||||||
\(426\) | 0.920526 | 0.0445996 | ||||||||
\(427\) | 2.19458 | 0.106203 | ||||||||
\(428\) | 18.9681 | 0.916859 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −22.6749 | −1.09348 | ||||||||
\(431\) | −17.8510 | −0.859852 | −0.429926 | − | 0.902864i | \(-0.641460\pi\) | ||||
−0.429926 | + | 0.902864i | \(0.641460\pi\) | |||||||
\(432\) | 7.92194 | 0.381145 | ||||||||
\(433\) | 39.4138 | 1.89411 | 0.947054 | − | 0.321074i | \(-0.104044\pi\) | ||||
0.947054 | + | 0.321074i | \(0.104044\pi\) | |||||||
\(434\) | −1.70316 | −0.0817541 | ||||||||
\(435\) | −63.7253 | −3.05539 | ||||||||
\(436\) | 17.0732 | 0.817656 | ||||||||
\(437\) | 3.60822 | 0.172604 | ||||||||
\(438\) | 27.4521 | 1.31171 | ||||||||
\(439\) | −16.9993 | −0.811331 | −0.405666 | − | 0.914022i | \(-0.632960\pi\) | ||||
−0.405666 | + | 0.914022i | \(0.632960\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −24.1271 | −1.14891 | ||||||||
\(442\) | 0.368378 | 0.0175220 | ||||||||
\(443\) | 16.2668 | 0.772859 | 0.386430 | − | 0.922319i | \(-0.373708\pi\) | ||||
0.386430 | + | 0.922319i | \(0.373708\pi\) | |||||||
\(444\) | 6.36348 | 0.301997 | ||||||||
\(445\) | 1.22948 | 0.0582831 | ||||||||
\(446\) | 5.16251 | 0.244452 | ||||||||
\(447\) | 53.9672 | 2.55256 | ||||||||
\(448\) | 1.66073 | 0.0784620 | ||||||||
\(449\) | 16.5534 | 0.781201 | 0.390601 | − | 0.920560i | \(-0.372267\pi\) | ||||
0.390601 | + | 0.920560i | \(0.372267\pi\) | |||||||
\(450\) | −3.40732 | −0.160623 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 21.1114 | 0.992997 | ||||||||
\(453\) | 18.4384 | 0.866311 | ||||||||
\(454\) | 18.3435 | 0.860904 | ||||||||
\(455\) | 2.49049 | 0.116756 | ||||||||
\(456\) | −2.94749 | −0.138029 | ||||||||
\(457\) | 11.5805 | 0.541714 | 0.270857 | − | 0.962620i | \(-0.412693\pi\) | ||||
0.270857 | + | 0.962620i | \(0.412693\pi\) | |||||||
\(458\) | −18.3344 | −0.856709 | ||||||||
\(459\) | −4.60466 | −0.214927 | ||||||||
\(460\) | 8.53789 | 0.398081 | ||||||||
\(461\) | 5.42648 | 0.252736 | 0.126368 | − | 0.991983i | \(-0.459668\pi\) | ||||
0.126368 | + | 0.991983i | \(0.459668\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 26.9168 | 1.25093 | 0.625466 | − | 0.780252i | \(-0.284909\pi\) | ||||
0.625466 | + | 0.780252i | \(0.284909\pi\) | |||||||
\(464\) | −9.13696 | −0.424173 | ||||||||
\(465\) | 7.15263 | 0.331695 | ||||||||
\(466\) | 14.6429 | 0.678320 | ||||||||
\(467\) | 12.5581 | 0.581118 | 0.290559 | − | 0.956857i | \(-0.406159\pi\) | ||||
0.290559 | + | 0.956857i | \(0.406159\pi\) | |||||||
\(468\) | 3.60466 | 0.166625 | ||||||||
\(469\) | −0.652996 | −0.0301526 | ||||||||
\(470\) | −20.6631 | −0.953117 | ||||||||
\(471\) | −18.1453 | −0.836092 | ||||||||
\(472\) | −6.47623 | −0.298093 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | −33.2193 | −1.52581 | ||||||||
\(475\) | 0.599069 | 0.0274872 | ||||||||
\(476\) | −0.965305 | −0.0442447 | ||||||||
\(477\) | −71.2677 | −3.26312 | ||||||||
\(478\) | 12.5868 | 0.575709 | ||||||||
\(479\) | −40.2322 | −1.83826 | −0.919128 | − | 0.393960i | \(-0.871105\pi\) | ||||
−0.919128 | + | 0.393960i | \(0.871105\pi\) | |||||||
\(480\) | −6.97445 | −0.318339 | ||||||||
\(481\) | 1.36827 | 0.0623875 | ||||||||
\(482\) | 2.79627 | 0.127367 | ||||||||
\(483\) | 17.6621 | 0.803655 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −19.8265 | −0.900277 | ||||||||
\(486\) | 5.23567 | 0.237495 | ||||||||
\(487\) | −14.2795 | −0.647066 | −0.323533 | − | 0.946217i | \(-0.604871\pi\) | ||||
−0.323533 | + | 0.946217i | \(0.604871\pi\) | |||||||
\(488\) | −1.32146 | −0.0598195 | ||||||||
\(489\) | −34.9097 | −1.57867 | ||||||||
\(490\) | 10.0375 | 0.453449 | ||||||||
\(491\) | −14.0094 | −0.632233 | −0.316117 | − | 0.948720i | \(-0.602379\pi\) | ||||
−0.316117 | + | 0.948720i | \(0.602379\pi\) | |||||||
\(492\) | 12.9717 | 0.584809 | ||||||||
\(493\) | 5.31089 | 0.239191 | ||||||||
\(494\) | −0.633765 | −0.0285144 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 1.02555 | 0.0460484 | ||||||||
\(497\) | −0.518659 | −0.0232651 | ||||||||
\(498\) | 20.3498 | 0.911898 | ||||||||
\(499\) | 18.1506 | 0.812533 | 0.406266 | − | 0.913755i | \(-0.366831\pi\) | ||||
0.406266 | + | 0.913755i | \(0.366831\pi\) | |||||||
\(500\) | −10.4136 | −0.465712 | ||||||||
\(501\) | −14.4174 | −0.644122 | ||||||||
\(502\) | 1.72891 | 0.0771651 | ||||||||
\(503\) | 29.8672 | 1.33171 | 0.665855 | − | 0.746081i | \(-0.268067\pi\) | ||||
0.665855 | + | 0.746081i | \(0.268067\pi\) | |||||||
\(504\) | −9.44571 | −0.420745 | ||||||||
\(505\) | −39.1325 | −1.74138 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −37.1335 | −1.64916 | ||||||||
\(508\) | 4.62745 | 0.205310 | ||||||||
\(509\) | 24.2045 | 1.07285 | 0.536423 | − | 0.843949i | \(-0.319775\pi\) | ||||
0.536423 | + | 0.843949i | \(0.319775\pi\) | |||||||
\(510\) | 4.05393 | 0.179511 | ||||||||
\(511\) | −15.4676 | −0.684245 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 7.92194 | 0.349762 | ||||||||
\(514\) | −21.5414 | −0.950153 | ||||||||
\(515\) | 6.61664 | 0.291564 | ||||||||
\(516\) | 28.2448 | 1.24341 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | −3.58543 | −0.157535 | ||||||||
\(519\) | −53.4102 | −2.34445 | ||||||||
\(520\) | −1.49964 | −0.0657634 | ||||||||
\(521\) | −6.36899 | −0.279031 | −0.139515 | − | 0.990220i | \(-0.544554\pi\) | ||||
−0.139515 | + | 0.990220i | \(0.544554\pi\) | |||||||
\(522\) | 51.9682 | 2.27459 | ||||||||
\(523\) | 21.2749 | 0.930284 | 0.465142 | − | 0.885236i | \(-0.346003\pi\) | ||||
0.465142 | + | 0.885236i | \(0.346003\pi\) | |||||||
\(524\) | −15.7763 | −0.689191 | ||||||||
\(525\) | 2.93243 | 0.127982 | ||||||||
\(526\) | 22.7920 | 0.993778 | ||||||||
\(527\) | −0.596103 | −0.0259667 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −9.98077 | −0.433946 | ||||||||
\(530\) | 29.6493 | 1.28788 | ||||||||
\(531\) | 36.8348 | 1.59849 | ||||||||
\(532\) | 1.66073 | 0.0720017 | ||||||||
\(533\) | 2.78915 | 0.120812 | ||||||||
\(534\) | −1.53150 | −0.0662745 | ||||||||
\(535\) | 44.8831 | 1.94046 | ||||||||
\(536\) | 0.393199 | 0.0169836 | ||||||||
\(537\) | 9.07672 | 0.391689 | ||||||||
\(538\) | 18.6429 | 0.803753 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 18.7452 | 0.806664 | ||||||||
\(541\) | 34.2668 | 1.47324 | 0.736622 | − | 0.676304i | \(-0.236420\pi\) | ||||
0.736622 | + | 0.676304i | \(0.236420\pi\) | |||||||
\(542\) | 3.33571 | 0.143281 | ||||||||
\(543\) | 0.204529 | 0.00877718 | ||||||||
\(544\) | 0.581254 | 0.0249211 | ||||||||
\(545\) | 40.3991 | 1.73051 | ||||||||
\(546\) | −3.10226 | −0.132765 | ||||||||
\(547\) | 31.2732 | 1.33715 | 0.668573 | − | 0.743647i | \(-0.266906\pi\) | ||||
0.668573 | + | 0.743647i | \(0.266906\pi\) | |||||||
\(548\) | −20.6366 | −0.881552 | ||||||||
\(549\) | 7.51604 | 0.320777 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −9.13696 | −0.389248 | ||||||||
\(552\) | −10.6352 | −0.452663 | ||||||||
\(553\) | 18.7170 | 0.795928 | ||||||||
\(554\) | −23.5883 | −1.00217 | ||||||||
\(555\) | 15.0575 | 0.639155 | ||||||||
\(556\) | −9.56721 | −0.405740 | ||||||||
\(557\) | −24.7198 | −1.04741 | −0.523707 | − | 0.851899i | \(-0.675451\pi\) | ||||
−0.523707 | + | 0.851899i | \(0.675451\pi\) | |||||||
\(558\) | −5.83300 | −0.246931 | ||||||||
\(559\) | 6.07316 | 0.256867 | ||||||||
\(560\) | 3.92967 | 0.166059 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −31.6366 | −1.33451 | ||||||||
\(563\) | −8.94251 | −0.376882 | −0.188441 | − | 0.982085i | \(-0.560343\pi\) | ||||
−0.188441 | + | 0.982085i | \(0.560343\pi\) | |||||||
\(564\) | 25.7389 | 1.08380 | ||||||||
\(565\) | 49.9546 | 2.10160 | ||||||||
\(566\) | −6.06757 | −0.255039 | ||||||||
\(567\) | 10.4406 | 0.438464 | ||||||||
\(568\) | 0.312308 | 0.0131042 | ||||||||
\(569\) | 0.764409 | 0.0320457 | 0.0160228 | − | 0.999872i | \(-0.494900\pi\) | ||||
0.0160228 | + | 0.999872i | \(0.494900\pi\) | |||||||
\(570\) | −6.97445 | −0.292128 | ||||||||
\(571\) | −4.11866 | −0.172361 | −0.0861804 | − | 0.996280i | \(-0.527466\pi\) | ||||
−0.0861804 | + | 0.996280i | \(0.527466\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 40.3146 | 1.68417 | ||||||||
\(574\) | −7.30875 | −0.305061 | ||||||||
\(575\) | 2.16157 | 0.0901438 | ||||||||
\(576\) | 5.68769 | 0.236987 | ||||||||
\(577\) | 26.8538 | 1.11794 | 0.558968 | − | 0.829189i | \(-0.311197\pi\) | ||||
0.558968 | + | 0.829189i | \(0.311197\pi\) | |||||||
\(578\) | 16.6621 | 0.693054 | ||||||||
\(579\) | 16.5599 | 0.688205 | ||||||||
\(580\) | −21.6202 | −0.897730 | ||||||||
\(581\) | −11.4659 | −0.475685 | ||||||||
\(582\) | 24.6968 | 1.02372 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 9.31372 | 0.385405 | ||||||||
\(585\) | 8.52947 | 0.352650 | ||||||||
\(586\) | −16.8312 | −0.695289 | ||||||||
\(587\) | 11.4832 | 0.473964 | 0.236982 | − | 0.971514i | \(-0.423842\pi\) | ||||
0.236982 | + | 0.971514i | \(0.423842\pi\) | |||||||
\(588\) | −12.5032 | −0.515623 | ||||||||
\(589\) | 1.02555 | 0.0422570 | ||||||||
\(590\) | −15.3243 | −0.630891 | ||||||||
\(591\) | 16.1079 | 0.662589 | ||||||||
\(592\) | 2.15895 | 0.0887322 | ||||||||
\(593\) | −32.3508 | −1.32849 | −0.664245 | − | 0.747515i | \(-0.731247\pi\) | ||||
−0.664245 | + | 0.747515i | \(0.731247\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −2.28414 | −0.0936405 | ||||||||
\(596\) | 18.3096 | 0.749988 | ||||||||
\(597\) | −39.9595 | −1.63543 | ||||||||
\(598\) | −2.28676 | −0.0935126 | ||||||||
\(599\) | 6.06380 | 0.247760 | 0.123880 | − | 0.992297i | \(-0.460466\pi\) | ||||
0.123880 | + | 0.992297i | \(0.460466\pi\) | |||||||
\(600\) | −1.76575 | −0.0720864 | ||||||||
\(601\) | 23.0923 | 0.941953 | 0.470976 | − | 0.882146i | \(-0.343902\pi\) | ||||
0.470976 | + | 0.882146i | \(0.343902\pi\) | |||||||
\(602\) | −15.9142 | −0.648615 | ||||||||
\(603\) | −2.23639 | −0.0910730 | ||||||||
\(604\) | 6.25562 | 0.254538 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 48.7453 | 1.98014 | ||||||||
\(607\) | 11.1808 | 0.453815 | 0.226907 | − | 0.973916i | \(-0.427139\pi\) | ||||
0.226907 | + | 0.973916i | \(0.427139\pi\) | |||||||
\(608\) | −1.00000 | −0.0405554 | ||||||||
\(609\) | −44.7252 | −1.81236 | ||||||||
\(610\) | −3.12688 | −0.126604 | ||||||||
\(611\) | 5.53433 | 0.223895 | ||||||||
\(612\) | −3.30599 | −0.133637 | ||||||||
\(613\) | 33.8355 | 1.36660 | 0.683302 | − | 0.730136i | \(-0.260543\pi\) | ||||
0.683302 | + | 0.730136i | \(0.260543\pi\) | |||||||
\(614\) | 5.10858 | 0.206166 | ||||||||
\(615\) | 30.6941 | 1.23770 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 24.9927 | 1.00617 | 0.503085 | − | 0.864237i | \(-0.332198\pi\) | ||||
0.503085 | + | 0.864237i | \(0.332198\pi\) | |||||||
\(618\) | −8.24198 | −0.331541 | ||||||||
\(619\) | 7.68493 | 0.308884 | 0.154442 | − | 0.988002i | \(-0.450642\pi\) | ||||
0.154442 | + | 0.988002i | \(0.450642\pi\) | |||||||
\(620\) | 2.42669 | 0.0974581 | ||||||||
\(621\) | 28.5841 | 1.14704 | ||||||||
\(622\) | 24.5635 | 0.984907 | ||||||||
\(623\) | 0.862906 | 0.0345716 | ||||||||
\(624\) | 1.86801 | 0.0747804 | ||||||||
\(625\) | −27.6365 | −1.10546 | ||||||||
\(626\) | 24.2868 | 0.970697 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −6.15619 | −0.245659 | ||||||||
\(629\) | −1.25490 | −0.0500360 | ||||||||
\(630\) | −22.3508 | −0.890476 | ||||||||
\(631\) | 25.7004 | 1.02312 | 0.511558 | − | 0.859249i | \(-0.329068\pi\) | ||||
0.511558 | + | 0.859249i | \(0.329068\pi\) | |||||||
\(632\) | −11.2704 | −0.448311 | ||||||||
\(633\) | 42.3146 | 1.68185 | ||||||||
\(634\) | 28.6225 | 1.13675 | ||||||||
\(635\) | 10.9496 | 0.434523 | ||||||||
\(636\) | −36.9325 | −1.46447 | ||||||||
\(637\) | −2.68842 | −0.106519 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −1.77631 | −0.0702699 | ||||||||
\(640\) | −2.36624 | −0.0935337 | ||||||||
\(641\) | 4.03846 | 0.159510 | 0.0797548 | − | 0.996815i | \(-0.474586\pi\) | ||||
0.0797548 | + | 0.996815i | \(0.474586\pi\) | |||||||
\(642\) | −55.9084 | −2.20653 | ||||||||
\(643\) | 5.44194 | 0.214609 | 0.107305 | − | 0.994226i | \(-0.465778\pi\) | ||||
0.107305 | + | 0.994226i | \(0.465778\pi\) | |||||||
\(644\) | 5.99227 | 0.236128 | ||||||||
\(645\) | 66.8339 | 2.63158 | ||||||||
\(646\) | 0.581254 | 0.0228691 | ||||||||
\(647\) | −32.4046 | −1.27395 | −0.636977 | − | 0.770882i | \(-0.719816\pi\) | ||||
−0.636977 | + | 0.770882i | \(0.719816\pi\) | |||||||
\(648\) | −6.28676 | −0.246967 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | −0.379669 | −0.0148918 | ||||||||
\(651\) | 5.02003 | 0.196751 | ||||||||
\(652\) | −11.8439 | −0.463842 | ||||||||
\(653\) | 24.7672 | 0.969217 | 0.484609 | − | 0.874731i | \(-0.338962\pi\) | ||||
0.484609 | + | 0.874731i | \(0.338962\pi\) | |||||||
\(654\) | −50.3229 | −1.96778 | ||||||||
\(655\) | −37.3305 | −1.45862 | ||||||||
\(656\) | 4.40093 | 0.171827 | ||||||||
\(657\) | −52.9736 | −2.06670 | ||||||||
\(658\) | −14.5023 | −0.565357 | ||||||||
\(659\) | −27.5600 | −1.07358 | −0.536792 | − | 0.843715i | \(-0.680364\pi\) | ||||
−0.536792 | + | 0.843715i | \(0.680364\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −7.53372 | −0.293028 | −0.146514 | − | 0.989209i | \(-0.546805\pi\) | ||||
−0.146514 | + | 0.989209i | \(0.546805\pi\) | |||||||
\(662\) | 2.40960 | 0.0936517 | ||||||||
\(663\) | −1.08579 | −0.0421686 | ||||||||
\(664\) | 6.90413 | 0.267932 | ||||||||
\(665\) | 3.92967 | 0.152386 | ||||||||
\(666\) | −12.2794 | −0.475818 | ||||||||
\(667\) | −32.9681 | −1.27653 | ||||||||
\(668\) | −4.89142 | −0.189255 | ||||||||
\(669\) | −15.2164 | −0.588301 | ||||||||
\(670\) | 0.930401 | 0.0359445 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | −4.89498 | −0.188828 | ||||||||
\(673\) | −8.79534 | −0.339035 | −0.169518 | − | 0.985527i | \(-0.554221\pi\) | ||||
−0.169518 | + | 0.985527i | \(0.554221\pi\) | |||||||
\(674\) | 17.5195 | 0.674824 | ||||||||
\(675\) | 4.74579 | 0.182666 | ||||||||
\(676\) | −12.5983 | −0.484552 | ||||||||
\(677\) | 15.8310 | 0.608434 | 0.304217 | − | 0.952603i | \(-0.401605\pi\) | ||||
0.304217 | + | 0.952603i | \(0.401605\pi\) | |||||||
\(678\) | −62.2257 | −2.38976 | ||||||||
\(679\) | −13.9151 | −0.534014 | ||||||||
\(680\) | 1.37538 | 0.0527435 | ||||||||
\(681\) | −54.0673 | −2.07186 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 38.6640 | 1.47944 | 0.739719 | − | 0.672916i | \(-0.234958\pi\) | ||||
0.739719 | + | 0.672916i | \(0.234958\pi\) | |||||||
\(684\) | 5.68769 | 0.217474 | ||||||||
\(685\) | −48.8310 | −1.86574 | ||||||||
\(686\) | 18.6699 | 0.712819 | ||||||||
\(687\) | 54.0404 | 2.06177 | ||||||||
\(688\) | 9.58267 | 0.365336 | ||||||||
\(689\) | −7.94117 | −0.302535 | ||||||||
\(690\) | −25.1653 | −0.958028 | ||||||||
\(691\) | −27.4678 | −1.04492 | −0.522462 | − | 0.852663i | \(-0.674986\pi\) | ||||
−0.522462 | + | 0.852663i | \(0.674986\pi\) | |||||||
\(692\) | −18.1206 | −0.688840 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 32.1534 | 1.22053 | ||||||||
\(695\) | −22.6383 | −0.858718 | ||||||||
\(696\) | 26.9311 | 1.02082 | ||||||||
\(697\) | −2.55806 | −0.0968933 | ||||||||
\(698\) | 0.407455 | 0.0154224 | ||||||||
\(699\) | −43.1598 | −1.63245 | ||||||||
\(700\) | 0.994891 | 0.0376034 | ||||||||
\(701\) | −1.50892 | −0.0569911 | −0.0284955 | − | 0.999594i | \(-0.509072\pi\) | ||||
−0.0284955 | + | 0.999594i | \(0.509072\pi\) | |||||||
\(702\) | −5.02065 | −0.189492 | ||||||||
\(703\) | 2.15895 | 0.0814263 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 60.9042 | 2.29378 | ||||||||
\(706\) | −3.94158 | −0.148343 | ||||||||
\(707\) | −27.4649 | −1.03293 | ||||||||
\(708\) | 19.0886 | 0.717394 | ||||||||
\(709\) | 16.2959 | 0.612006 | 0.306003 | − | 0.952031i | \(-0.401008\pi\) | ||||
0.306003 | + | 0.952031i | \(0.401008\pi\) | |||||||
\(710\) | 0.738995 | 0.0277340 | ||||||||
\(711\) | 64.1023 | 2.40403 | ||||||||
\(712\) | −0.519595 | −0.0194726 | ||||||||
\(713\) | 3.70040 | 0.138581 | ||||||||
\(714\) | 2.84522 | 0.106480 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 3.07947 | 0.115085 | ||||||||
\(717\) | −37.0996 | −1.38551 | ||||||||
\(718\) | −20.0781 | −0.749309 | ||||||||
\(719\) | 40.6785 | 1.51705 | 0.758526 | − | 0.651643i | \(-0.225920\pi\) | ||||
0.758526 | + | 0.651643i | \(0.225920\pi\) | |||||||
\(720\) | 13.4584 | 0.501566 | ||||||||
\(721\) | 4.64385 | 0.172946 | ||||||||
\(722\) | −1.00000 | −0.0372161 | ||||||||
\(723\) | −8.24198 | −0.306523 | ||||||||
\(724\) | 0.0693910 | 0.00257889 | ||||||||
\(725\) | −5.47367 | −0.203287 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 27.7545 | 1.02936 | 0.514679 | − | 0.857383i | \(-0.327911\pi\) | ||||
0.514679 | + | 0.857383i | \(0.327911\pi\) | |||||||
\(728\) | −1.05251 | −0.0390087 | ||||||||
\(729\) | −34.2924 | −1.27009 | ||||||||
\(730\) | 22.0385 | 0.815680 | ||||||||
\(731\) | −5.56996 | −0.206013 | ||||||||
\(732\) | 3.89498 | 0.143963 | ||||||||
\(733\) | −6.89854 | −0.254803 | −0.127402 | − | 0.991851i | \(-0.540664\pi\) | ||||
−0.127402 | + | 0.991851i | \(0.540664\pi\) | |||||||
\(734\) | 20.5918 | 0.760058 | ||||||||
\(735\) | −29.5855 | −1.09128 | ||||||||
\(736\) | −3.60822 | −0.133001 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | −25.0311 | −0.921409 | ||||||||
\(739\) | 49.2039 | 1.80999 | 0.904997 | − | 0.425418i | \(-0.139873\pi\) | ||||
0.904997 | + | 0.425418i | \(0.139873\pi\) | |||||||
\(740\) | 5.10858 | 0.187795 | ||||||||
\(741\) | 1.86801 | 0.0686232 | ||||||||
\(742\) | 20.8092 | 0.763929 | ||||||||
\(743\) | 10.4046 | 0.381709 | 0.190854 | − | 0.981618i | \(-0.438874\pi\) | ||||
0.190854 | + | 0.981618i | \(0.438874\pi\) | |||||||
\(744\) | −3.02279 | −0.110821 | ||||||||
\(745\) | 43.3247 | 1.58729 | ||||||||
\(746\) | −20.8813 | −0.764520 | ||||||||
\(747\) | −39.2685 | −1.43676 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 31.5009 | 1.15102 | ||||||||
\(750\) | 30.6941 | 1.12079 | ||||||||
\(751\) | 37.7103 | 1.37607 | 0.688035 | − | 0.725677i | \(-0.258474\pi\) | ||||
0.688035 | + | 0.725677i | \(0.258474\pi\) | |||||||
\(752\) | 8.73247 | 0.318440 | ||||||||
\(753\) | −5.09595 | −0.185707 | ||||||||
\(754\) | 5.79068 | 0.210884 | ||||||||
\(755\) | 14.8023 | 0.538710 | ||||||||
\(756\) | 13.1562 | 0.478486 | ||||||||
\(757\) | 14.3972 | 0.523274 | 0.261637 | − | 0.965166i | \(-0.415738\pi\) | ||||
0.261637 | + | 0.965166i | \(0.415738\pi\) | |||||||
\(758\) | 0.753845 | 0.0273809 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −2.36624 | −0.0858324 | ||||||||
\(761\) | −39.7311 | −1.44025 | −0.720126 | − | 0.693843i | \(-0.755916\pi\) | ||||
−0.720126 | + | 0.693843i | \(0.755916\pi\) | |||||||
\(762\) | −13.6394 | −0.494102 | ||||||||
\(763\) | 28.3539 | 1.02648 | ||||||||
\(764\) | 13.6776 | 0.494838 | ||||||||
\(765\) | −7.82276 | −0.282832 | ||||||||
\(766\) | 18.3142 | 0.661719 | ||||||||
\(767\) | 4.10441 | 0.148202 | ||||||||
\(768\) | 2.94749 | 0.106358 | ||||||||
\(769\) | −2.27170 | −0.0819197 | −0.0409598 | − | 0.999161i | \(-0.513042\pi\) | ||||
−0.0409598 | + | 0.999161i | \(0.513042\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 63.4932 | 2.28665 | ||||||||
\(772\) | 5.61830 | 0.202207 | ||||||||
\(773\) | 3.64157 | 0.130978 | 0.0654891 | − | 0.997853i | \(-0.479139\pi\) | ||||
0.0654891 | + | 0.997853i | \(0.479139\pi\) | |||||||
\(774\) | −54.5033 | −1.95908 | ||||||||
\(775\) | 0.614374 | 0.0220690 | ||||||||
\(776\) | 8.37894 | 0.300786 | ||||||||
\(777\) | 10.5680 | 0.379125 | ||||||||
\(778\) | 26.1206 | 0.936467 | ||||||||
\(779\) | 4.40093 | 0.157680 | ||||||||
\(780\) | 4.42016 | 0.158267 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 2.09729 | 0.0749989 | ||||||||
\(783\) | −72.3825 | −2.58674 | ||||||||
\(784\) | −4.24198 | −0.151499 | ||||||||
\(785\) | −14.5670 | −0.519918 | ||||||||
\(786\) | 46.5005 | 1.65862 | ||||||||
\(787\) | 0.279643 | 0.00996821 | 0.00498410 | − | 0.999988i | \(-0.498414\pi\) | ||||
0.00498410 | + | 0.999988i | \(0.498414\pi\) | |||||||
\(788\) | 5.46494 | 0.194680 | ||||||||
\(789\) | −67.1791 | −2.39164 | ||||||||
\(790\) | −26.6683 | −0.948816 | ||||||||
\(791\) | 35.0603 | 1.24660 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0.837492 | 0.0297402 | ||||||||
\(794\) | 34.9079 | 1.23883 | ||||||||
\(795\) | −87.3910 | −3.09944 | ||||||||
\(796\) | −13.5571 | −0.480519 | ||||||||
\(797\) | −3.66014 | −0.129649 | −0.0648243 | − | 0.997897i | \(-0.520649\pi\) | ||||
−0.0648243 | + | 0.997897i | \(0.520649\pi\) | |||||||
\(798\) | −4.89498 | −0.173280 | ||||||||
\(799\) | −5.07578 | −0.179568 | ||||||||
\(800\) | −0.599069 | −0.0211803 | ||||||||
\(801\) | 2.95530 | 0.104420 | ||||||||
\(802\) | −6.35353 | −0.224351 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | −1.15895 | −0.0408730 | ||||||||
\(805\) | 14.1791 | 0.499748 | ||||||||
\(806\) | −0.649956 | −0.0228937 | ||||||||
\(807\) | −54.9498 | −1.93432 | ||||||||
\(808\) | 16.5379 | 0.581801 | ||||||||
\(809\) | −27.0990 | −0.952749 | −0.476375 | − | 0.879242i | \(-0.658049\pi\) | ||||
−0.476375 | + | 0.879242i | \(0.658049\pi\) | |||||||
\(810\) | −14.8760 | −0.522688 | ||||||||
\(811\) | −31.4212 | −1.10335 | −0.551673 | − | 0.834060i | \(-0.686010\pi\) | ||||
−0.551673 | + | 0.834060i | \(0.686010\pi\) | |||||||
\(812\) | −15.1740 | −0.532503 | ||||||||
\(813\) | −9.83198 | −0.344823 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −28.0254 | −0.981687 | ||||||||
\(816\) | −1.71324 | −0.0599754 | ||||||||
\(817\) | 9.58267 | 0.335255 | ||||||||
\(818\) | 26.1816 | 0.915418 | ||||||||
\(819\) | 5.98636 | 0.209180 | ||||||||
\(820\) | 10.4136 | 0.363660 | ||||||||
\(821\) | 20.1304 | 0.702557 | 0.351279 | − | 0.936271i | \(-0.385747\pi\) | ||||
0.351279 | + | 0.936271i | \(0.385747\pi\) | |||||||
\(822\) | 60.8261 | 2.12156 | ||||||||
\(823\) | −7.23922 | −0.252344 | −0.126172 | − | 0.992008i | \(-0.540269\pi\) | ||||
−0.126172 | + | 0.992008i | \(0.540269\pi\) | |||||||
\(824\) | −2.79627 | −0.0974128 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −10.7553 | −0.374223 | ||||||||
\(827\) | −23.1088 | −0.803571 | −0.401786 | − | 0.915734i | \(-0.631610\pi\) | ||||
−0.401786 | + | 0.915734i | \(0.631610\pi\) | |||||||
\(828\) | 20.5224 | 0.713204 | ||||||||
\(829\) | 21.7081 | 0.753955 | 0.376977 | − | 0.926223i | \(-0.376963\pi\) | ||||
0.376977 | + | 0.926223i | \(0.376963\pi\) | |||||||
\(830\) | 16.3368 | 0.567058 | ||||||||
\(831\) | 69.5261 | 2.41183 | ||||||||
\(832\) | 0.633765 | 0.0219718 | ||||||||
\(833\) | 2.46567 | 0.0854303 | ||||||||
\(834\) | 28.1992 | 0.976460 | ||||||||
\(835\) | −11.5742 | −0.400543 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 8.12433 | 0.280818 | ||||||||
\(838\) | −8.15060 | −0.281558 | ||||||||
\(839\) | −21.1935 | −0.731681 | −0.365841 | − | 0.930678i | \(-0.619218\pi\) | ||||
−0.365841 | + | 0.930678i | \(0.619218\pi\) | |||||||
\(840\) | −11.5827 | −0.399640 | ||||||||
\(841\) | 54.4840 | 1.87876 | ||||||||
\(842\) | −10.9531 | −0.377468 | ||||||||
\(843\) | 93.2485 | 3.21165 | ||||||||
\(844\) | 14.3562 | 0.494159 | ||||||||
\(845\) | −29.8106 | −1.02552 | ||||||||
\(846\) | −49.6676 | −1.70761 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −12.5302 | −0.430287 | ||||||||
\(849\) | 17.8841 | 0.613780 | ||||||||
\(850\) | 0.348211 | 0.0119435 | ||||||||
\(851\) | 7.78996 | 0.267036 | ||||||||
\(852\) | −0.920526 | −0.0315367 | ||||||||
\(853\) | −30.5835 | −1.04716 | −0.523579 | − | 0.851977i | \(-0.675404\pi\) | ||||
−0.523579 | + | 0.851977i | \(0.675404\pi\) | |||||||
\(854\) | −2.19458 | −0.0750970 | ||||||||
\(855\) | 13.4584 | 0.460268 | ||||||||
\(856\) | −18.9681 | −0.648318 | ||||||||
\(857\) | −48.3757 | −1.65248 | −0.826241 | − | 0.563317i | \(-0.809525\pi\) | ||||
−0.826241 | + | 0.563317i | \(0.809525\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −57.0941 | −1.94802 | −0.974012 | − | 0.226495i | \(-0.927273\pi\) | ||||
−0.974012 | + | 0.226495i | \(0.927273\pi\) | |||||||
\(860\) | 22.6749 | 0.773206 | ||||||||
\(861\) | 21.5425 | 0.734165 | ||||||||
\(862\) | 17.8510 | 0.608007 | ||||||||
\(863\) | 3.31963 | 0.113002 | 0.0565008 | − | 0.998403i | \(-0.482006\pi\) | ||||
0.0565008 | + | 0.998403i | \(0.482006\pi\) | |||||||
\(864\) | −7.92194 | −0.269510 | ||||||||
\(865\) | −42.8775 | −1.45788 | ||||||||
\(866\) | −39.4138 | −1.33934 | ||||||||
\(867\) | −49.1115 | −1.66791 | ||||||||
\(868\) | 1.70316 | 0.0578089 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 63.7253 | 2.16049 | ||||||||
\(871\) | −0.249195 | −0.00844367 | ||||||||
\(872\) | −17.0732 | −0.578170 | ||||||||
\(873\) | −47.6568 | −1.61294 | ||||||||
\(874\) | −3.60822 | −0.122050 | ||||||||
\(875\) | −17.2942 | −0.584651 | ||||||||
\(876\) | −27.4521 | −0.927521 | ||||||||
\(877\) | −4.46676 | −0.150832 | −0.0754159 | − | 0.997152i | \(-0.524028\pi\) | ||||
−0.0754159 | + | 0.997152i | \(0.524028\pi\) | |||||||
\(878\) | 16.9993 | 0.573698 | ||||||||
\(879\) | 49.6097 | 1.67329 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 6.10320 | 0.205622 | 0.102811 | − | 0.994701i | \(-0.467216\pi\) | ||||
0.102811 | + | 0.994701i | \(0.467216\pi\) | |||||||
\(882\) | 24.1271 | 0.812401 | ||||||||
\(883\) | 6.98526 | 0.235073 | 0.117536 | − | 0.993069i | \(-0.462500\pi\) | ||||
0.117536 | + | 0.993069i | \(0.462500\pi\) | |||||||
\(884\) | −0.368378 | −0.0123899 | ||||||||
\(885\) | 45.1682 | 1.51831 | ||||||||
\(886\) | −16.2668 | −0.546494 | ||||||||
\(887\) | −39.3670 | −1.32182 | −0.660908 | − | 0.750467i | \(-0.729829\pi\) | ||||
−0.660908 | + | 0.750467i | \(0.729829\pi\) | |||||||
\(888\) | −6.36348 | −0.213544 | ||||||||
\(889\) | 7.68493 | 0.257744 | ||||||||
\(890\) | −1.22948 | −0.0412124 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −5.16251 | −0.172854 | ||||||||
\(893\) | 8.73247 | 0.292221 | ||||||||
\(894\) | −53.9672 | −1.80493 | ||||||||
\(895\) | 7.28676 | 0.243570 | ||||||||
\(896\) | −1.66073 | −0.0554810 | ||||||||
\(897\) | 6.74020 | 0.225049 | ||||||||
\(898\) | −16.5534 | −0.552393 | ||||||||
\(899\) | −9.37039 | −0.312520 | ||||||||
\(900\) | 3.40732 | 0.113577 | ||||||||
\(901\) | 7.28320 | 0.242639 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 46.9070 | 1.56097 | ||||||||
\(904\) | −21.1114 | −0.702155 | ||||||||
\(905\) | 0.164195 | 0.00545804 | ||||||||
\(906\) | −18.4384 | −0.612574 | ||||||||
\(907\) | 56.7300 | 1.88369 | 0.941844 | − | 0.336050i | \(-0.109091\pi\) | ||||
0.941844 | + | 0.336050i | \(0.109091\pi\) | |||||||
\(908\) | −18.3435 | −0.608751 | ||||||||
\(909\) | −94.0624 | −3.11985 | ||||||||
\(910\) | −2.49049 | −0.0825589 | ||||||||
\(911\) | −47.8355 | −1.58486 | −0.792431 | − | 0.609962i | \(-0.791185\pi\) | ||||
−0.792431 | + | 0.609962i | \(0.791185\pi\) | |||||||
\(912\) | 2.94749 | 0.0976011 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | −11.5805 | −0.383050 | ||||||||
\(915\) | 9.21643 | 0.304686 | ||||||||
\(916\) | 18.3344 | 0.605785 | ||||||||
\(917\) | −26.2002 | −0.865206 | ||||||||
\(918\) | 4.60466 | 0.151976 | ||||||||
\(919\) | 0.295588 | 0.00975054 | 0.00487527 | − | 0.999988i | \(-0.498448\pi\) | ||||
0.00487527 | + | 0.999988i | \(0.498448\pi\) | |||||||
\(920\) | −8.53789 | −0.281486 | ||||||||
\(921\) | −15.0575 | −0.496161 | ||||||||
\(922\) | −5.42648 | −0.178712 | ||||||||
\(923\) | −0.197930 | −0.00651495 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1.29336 | 0.0425254 | ||||||||
\(926\) | −26.9168 | −0.884542 | ||||||||
\(927\) | 15.9043 | 0.522367 | ||||||||
\(928\) | 9.13696 | 0.299935 | ||||||||
\(929\) | −18.6254 | −0.611080 | −0.305540 | − | 0.952179i | \(-0.598837\pi\) | ||||
−0.305540 | + | 0.952179i | \(0.598837\pi\) | |||||||
\(930\) | −7.15263 | −0.234544 | ||||||||
\(931\) | −4.24198 | −0.139025 | ||||||||
\(932\) | −14.6429 | −0.479645 | ||||||||
\(933\) | −72.4007 | −2.37029 | ||||||||
\(934\) | −12.5581 | −0.410912 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −3.60466 | −0.117822 | ||||||||
\(937\) | −50.5786 | −1.65233 | −0.826165 | − | 0.563428i | \(-0.809482\pi\) | ||||
−0.826165 | + | 0.563428i | \(0.809482\pi\) | |||||||
\(938\) | 0.652996 | 0.0213211 | ||||||||
\(939\) | −71.5852 | −2.33609 | ||||||||
\(940\) | 20.6631 | 0.673955 | ||||||||
\(941\) | 47.1169 | 1.53597 | 0.767983 | − | 0.640470i | \(-0.221261\pi\) | ||||
0.767983 | + | 0.640470i | \(0.221261\pi\) | |||||||
\(942\) | 18.1453 | 0.591206 | ||||||||
\(943\) | 15.8795 | 0.517108 | ||||||||
\(944\) | 6.47623 | 0.210783 | ||||||||
\(945\) | 31.1306 | 1.01268 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 8.28227 | 0.269138 | 0.134569 | − | 0.990904i | \(-0.457035\pi\) | ||||
0.134569 | + | 0.990904i | \(0.457035\pi\) | |||||||
\(948\) | 33.2193 | 1.07891 | ||||||||
\(949\) | −5.90271 | −0.191610 | ||||||||
\(950\) | −0.599069 | −0.0194364 | ||||||||
\(951\) | −84.3646 | −2.73571 | ||||||||
\(952\) | 0.965305 | 0.0312857 | ||||||||
\(953\) | −10.0765 | −0.326410 | −0.163205 | − | 0.986592i | \(-0.552183\pi\) | ||||
−0.163205 | + | 0.986592i | \(0.552183\pi\) | |||||||
\(954\) | 71.2677 | 2.30738 | ||||||||
\(955\) | 32.3644 | 1.04729 | ||||||||
\(956\) | −12.5868 | −0.407088 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 40.2322 | 1.29984 | ||||||||
\(959\) | −34.2718 | −1.10669 | ||||||||
\(960\) | 6.97445 | 0.225099 | ||||||||
\(961\) | −29.9483 | −0.966073 | ||||||||
\(962\) | −1.36827 | −0.0441147 | ||||||||
\(963\) | 107.885 | 3.47654 | ||||||||
\(964\) | −2.79627 | −0.0900619 | ||||||||
\(965\) | 13.2942 | 0.427956 | ||||||||
\(966\) | −17.6621 | −0.568270 | ||||||||
\(967\) | 48.6402 | 1.56416 | 0.782082 | − | 0.623175i | \(-0.214158\pi\) | ||||
0.782082 | + | 0.623175i | \(0.214158\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −1.71324 | −0.0550372 | ||||||||
\(970\) | 19.8265 | 0.636592 | ||||||||
\(971\) | −4.89578 | −0.157113 | −0.0785565 | − | 0.996910i | \(-0.525031\pi\) | ||||
−0.0785565 | + | 0.996910i | \(0.525031\pi\) | |||||||
\(972\) | −5.23567 | −0.167934 | ||||||||
\(973\) | −15.8885 | −0.509363 | ||||||||
\(974\) | 14.2795 | 0.457545 | ||||||||
\(975\) | 1.11907 | 0.0358389 | ||||||||
\(976\) | 1.32146 | 0.0422988 | ||||||||
\(977\) | −36.1052 | −1.15511 | −0.577553 | − | 0.816353i | \(-0.695992\pi\) | ||||
−0.577553 | + | 0.816353i | \(0.695992\pi\) | |||||||
\(978\) | 34.9097 | 1.11629 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | −10.0375 | −0.320637 | ||||||||
\(981\) | 97.1069 | 3.10038 | ||||||||
\(982\) | 14.0094 | 0.447057 | ||||||||
\(983\) | −18.7371 | −0.597621 | −0.298811 | − | 0.954312i | \(-0.596590\pi\) | ||||
−0.298811 | + | 0.954312i | \(0.596590\pi\) | |||||||
\(984\) | −12.9717 | −0.413523 | ||||||||
\(985\) | 12.9313 | 0.412027 | ||||||||
\(986\) | −5.31089 | −0.169133 | ||||||||
\(987\) | 42.7453 | 1.36060 | ||||||||
\(988\) | 0.633765 | 0.0201627 | ||||||||
\(989\) | 34.5764 | 1.09946 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −8.60669 | −0.273400 | −0.136700 | − | 0.990612i | \(-0.543650\pi\) | ||||
−0.136700 | + | 0.990612i | \(0.543650\pi\) | |||||||
\(992\) | −1.02555 | −0.0325612 | ||||||||
\(993\) | −7.10226 | −0.225384 | ||||||||
\(994\) | 0.518659 | 0.0164509 | ||||||||
\(995\) | −32.0793 | −1.01698 | ||||||||
\(996\) | −20.3498 | −0.644809 | ||||||||
\(997\) | −13.3500 | −0.422798 | −0.211399 | − | 0.977400i | \(-0.567802\pi\) | ||||
−0.211399 | + | 0.977400i | \(0.567802\pi\) | |||||||
\(998\) | −18.1506 | −0.574547 | ||||||||
\(999\) | 17.1031 | 0.541117 |
(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.1.4 | ✓ | 4 | |
11.10 | odd | 2 | 4598.2.a.bu.1.4 | yes | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4598.2.a.br.1.4 | ✓ | 4 | 1.1 | even | 1 | trivial | |
4598.2.a.bu.1.4 | yes | 4 | 11.10 | odd | 2 |